Finite Group Databasebeta

← C22×#87207 #72271138

Subgroups — C22×#87207 #72271138

Order 1536.

115668 conjugacy classes of subgroups.

The subgroup lattice has 1728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#5968C211yesmaximal, characteristic, complemented
2C22×D3×H(5,𝔽2)C211yesmaximal, characteristic, complemented
3C2×#87207C2196yesmaximal, direct product factor
4C22×#5778C213yesmaximal, complemented
5C22×#5837C211yesmaximal, characteristic, complemented
6C22×#5762C213yesmaximal, complemented
7C22×#5752C211yesmaximal, characteristic, complemented
8C22×#5774C213yesmaximal, complemented
9C22×#5835C211yesmaximal, characteristic, complemented
10C22×#5769C213yesmaximal, complemented
11C22×#5777C213yesmaximal, complemented
12C22×#5768C213yesmaximal, complemented
13C23×#914C213yesmaximal, complemented
14C22×D3×AGL(1,ℤ/8)C213yesmaximal, complemented
15C22×#5750C211yesmaximal, characteristic, complemented
16C22×C3×#577C211yesmaximal, characteristic, complemented
17C22×#3585—31nomaximal, Sylow
18C22×C3×2−1+4C2211yescharacteristic, complemented
19C22×C3×H(5,𝔽2)C2211yescharacteristic, complemented
20C2×#5968—224no—
21C2×#5968C22148yescomplemented
22C2×D3×H(5,𝔽2)—224no—
23C2×D3×H(5,𝔽2)C22148yescomplemented
24C22×#1009—21no—
25C22×#1009—23no—
26C22×#1009C2213yescomplemented
27C22×#1009C2213yescomplemented
28C22×#1009C2211yescharacteristic, complemented
29C22×#1009C2211yescharacteristic, complemented
30C22×D3×#41—21no—
31C22×D3×#41—23no—
32C22×D3×#41C2211yescharacteristic
33C22×D3×#41C2213yescomplemented
34C22×D3×#41C2213yescomplemented
35C22×#1007—21no—
36C22×#1007C2213yescomplemented
37C23×#239—21no—
38C23×#239C2213yescomplemented
39C22×#1004—23no—
40C22×#1004C2213yescomplemented
41C23×D3×D4—23no—
42C23×D3×D4C2213yescomplemented
43C2×C3×#577C22148yescomplemented
44C22×C3×#137C2213yescomplemented
45C22×C3×AGL(1,ℤ/8)C2213yescomplemented
46C22×C3×#135C2213yescomplemented
47C23×C3×SD16C2213yescomplemented
48C22×C3×#131C2211yescharacteristic, complemented
49C2×#5837C22148yescomplemented
50C2×#5835C22148yescomplemented
51C22×#949C2213yescomplemented
52C22×#949C2213yescomplemented
53C22×#950C2213yescomplemented
54C22×#950C2213yescomplemented
55C22×#948C2211yescharacteristic, complemented
56C22×#942C2213yescomplemented
57C23×#215C2213yescomplemented
58C22×#932C2213yescomplemented
59C23×#213C2213yescomplemented
60#87207C2211024yesdirect product factor
61C2×#5778C221144yescomplemented
62C2×#5777C221144yescomplemented
63C2×#5774C221144yescomplemented
64C2×D3×AGL(1,ℤ/8)C221144yescomplemented
65C2×#5769C221144yescomplemented
66C2×#5768C221144yescomplemented
67C22×#918C2213yescomplemented
68C22×#918C2213yescomplemented
69C22×#919C2216yescomplemented
70C2×#5762C221144yescomplemented
71C22×#915C2211yescharacteristic, complemented
72C22×#915C2213yescomplemented
73C22×#914C2216yescomplemented
74C22×#914C2213yescomplemented
75C22×#914C2216yescomplemented
76C22×#914C2216yescomplemented
77C22×#914C2213yescomplemented
78C22×#914C221144yescomplemented
79C22×#916C2216yescomplemented
80C22×D3×SD16C2216yescomplemented
81C22×#911C2213yescomplemented
82C22×#911C2213yescomplemented
83C22×D3×D8C2216yescomplemented
84C2×#5752C22148yescomplemented
85C2×#5750C22148yescomplemented
86C22×#908C2213yescomplemented
87C22×#908C2213yescomplemented
88C22×#907C2213yescomplemented
89C22×D3×M16C2213yescomplemented
90C22×#904C2213yescomplemented
91C23×D24C2213yescomplemented
92C22×#901C2213yescomplemented
93C23×ΓL(1,𝔽25)C2213yescomplemented
94C22×#585—31no—
95C23×H(5,𝔽2)—31no—
96C2×#3585—396no—
97C22×#577—33no—
98C22×#577—33no—
99C22×#577—31no—
100C22×#577D311yescharacteristic, complemented
101C22×#576—33no—
102C22×#576—33no—
103C22×#576—31no—
104C22×#576—31no—
105C22×#575—33no—
106C22×#575—33no—
107C23×AGL(1,ℤ/8)—33no—
108C23×AGL(1,ℤ/8)—33no—
109C22×#568—31no—
110C25×D3—23no—
111C2×C3×2−1+4—212no—
112C2×C3×2−1+4C23124yescomplemented
113C2×C3×H(5,𝔽2)—212no—
114C2×C3×H(5,𝔽2)C23124yescomplemented
115C22×C3×#41—21no—
116C22×C3×#41—23no—
117C22×C3×#41C2313yes—
118C22×C3×#41C2311yescharacteristic
119C22×C3×#41C2313yescomplemented
120C23×C3×Q8—21no—
121C23×C3×Q8C2313yescomplemented
122C23×C3×D4—23no—
123C23×C3×D4C2313yes—
124C23×#67—26no—
125C23×#67—23no—
126#5968—2384no—
127#5968C231256yescomplemented
128D3×H(5,𝔽2)—2384no—
129D3×H(5,𝔽2)C231256yescomplemented
130C2×#1009—212no—
131C2×#1009—212no—
132C2×#1009—248no—
133C2×#1009—2144no—
134C2×#1009—236no—
135C2×#1009—236no—
136C2×#1009C23172yescomplemented
137C2×#1009C23172yescomplemented
138C2×#1009C23124yescomplemented
139C2×#1009C23124yescomplemented
140C2×D3×#41—248no—
141C2×D3×#41—2144no—
142C2×D3×#41—236no—
143C2×D3×#41—236no—
144C2×D3×#41D4124yes—
145C2×D3×#41C23124yes—
146C2×D3×#41C23172yescomplemented
147C2×D3×#41C23172yescomplemented
148C2×#1007—248no—
149C2×#1007—236no—
150C2×#1007C23172yescomplemented
151C22×#239—21no—
152C22×#239—21no—
153C22×#239—248no—
154C22×#239—23no—
155C22×#239—23no—
156C22×#239—23no—
157C22×#239—236no—
158C22×#239D411yescharacteristic
159C22×#239C2313yes—
160C22×#239C2313yes—
161C22×#239C2316yescomplemented
162C22×#239C23172yescomplemented
163C22×D3×Q8—23no—
164C22×D3×Q8D411yescharacteristic
165C22×D3×Q8C2311yescharacteristic
166C22×D3×Q8C2313yescomplemented
167C2×#1004—2144no—
168C2×#1004—236no—
169C2×#1004C23172yescomplemented
170C22×#237—23no—
171C22×#237—23no—
172C22×#237—23no—
173C22×#237D413yes—
174C22×#237C2313yes—
175C22×#237C2311yescharacteristic
176C22×D3×D4—23no—
177C22×D3×D4—23no—
178C22×D3×D4—23no—
179C22×D3×D4—23no—
180C22×D3×D4—26no—
181C22×D3×D4—26no—
182C22×D3×D4—2144no—
183C22×D3×D4—23no—
184C22×D3×D4—23no—
185C22×D3×D4—23no—
186C22×D3×D4—236no—
187C22×D3×D4D413yes—
188C22×D3×D4C2313yes—
189C22×D3×D4C2316yes—
190C22×D3×D4C23172yescomplemented
191C22×D3×D4C2313yescomplemented
192C22×#235—26no—
193C22×#235—23no—
194C22×#235—23no—
195C22×#235—23no—
196C22×#235—23no—
197C22×#235C2313yes—
198C22×#235C2313yes—
199C22×#235C2313yescomplemented
200C23×D12—23no—
201C23×D12—23no—
202C23×D12—23no—
203C23×D12C2313yes—
204C23×D12C2313yescomplemented
205C23×C4×D3—23no—
206C23×C4×D3—23no—
207C23×C4×D3—23no—
208C23×C4×D3C2313yes—
209C3×#577C231256yescomplemented
210C2×C3×#137C23172yescomplemented
211C2×C3×AGL(1,ℤ/8)C23172yescomplemented
212C2×C3×#135C23172yescomplemented
213C22×C3×Q16C2313yescomplemented
214C22×C3×SD16C2316yescomplemented
215C22×C3×SD16C2313yescomplemented
216C22×C3×SD16C2311yescharacteristic, complemented
217C22×C3×SD16C23172yescomplemented
218C22×C3×D8C2313yescomplemented
219C2×C3×#131C23124yescomplemented
220C22×C3×M16C2313yescomplemented
221C23×C3×C8C2313yescomplemented
222#5837C231256yescomplemented
223#5835C231256yescomplemented
224C2×#950C23172yescomplemented
225C2×#950C23172yescomplemented
226C2×#949C23172yescomplemented
227C2×#949C23172yescomplemented
228C2×#948C23124yescomplemented
229C22×#216C2313yescomplemented
230C22×#216C2311yescharacteristic, complemented
231C2×#942C23172yescomplemented
232C22×#215C2316yescomplemented
233C22×#215C2313yescomplemented
234C22×#215C2313yescomplemented
235C22×#215C23172yescomplemented
236C22×#214C2311yescharacteristic, complemented
237C22×#214C2313yescomplemented
238C2×#932C23172yescomplemented
239C22×#213C2313yescomplemented
240C22×#213C2316yescomplemented
241C22×#213C2313yescomplemented
242C22×#213C23172yescomplemented
243C22×#208C2313yescomplemented
244C23×C3⋊C8C2313yescomplemented
245#5778C231768yescomplemented
246#5777C231768yescomplemented
247#5774C231768yescomplemented
248D3×AGL(1,ℤ/8)C231768yescomplemented
249#5769C231768yescomplemented
250#5768C231768yescomplemented
251C2×#919C231144yescomplemented
252C2×#918C23172yescomplemented
253C2×#918C23172yescomplemented
254#5762C231768yescomplemented
255C2×#916C231144yescomplemented
256C2×#915C23124yescomplemented
257C2×#915C23172yescomplemented
258C2×#914C23172yescomplemented
259C2×#914C231144yescomplemented
260C2×#914C231144yescomplemented
261C2×#914C231144yescomplemented
262C2×#914C23172yescomplemented
263C2×#914C231768yescomplemented
264C2×D3×SD16C231144yescomplemented
265C2×#911C23172yescomplemented
266C2×#911C23172yescomplemented
267C2×D3×D8C231144yescomplemented
268#5752C231256yescomplemented
269#5750C231256yescomplemented
270C2×#908C23172yescomplemented
271C2×#908C23172yescomplemented
272C2×#907C23172yescomplemented
273C2×D3×M16C23172yescomplemented
274C22×Dic12C2311yescharacteristic, complemented
275C2×#904C23172yescomplemented
276C22×D24C2313yescomplemented
277C22×D24C2316yescomplemented
278C22×D24C23172yescomplemented
279C22×#204C2313yescomplemented
280C22×#204C2313yescomplemented
281C2×#901C23172yescomplemented
282C22×ΓL(1,𝔽25)C2311yescharacteristic
283C22×ΓL(1,𝔽25)C2313yes—
284C22×ΓL(1,𝔽25)C23172yescomplemented
285C22×ΓL(1,𝔽25)C2313yescomplemented
286C22×ΓL(1,𝔽25)C2313yescomplemented
287C22×D3×C8C2316yescomplemented
288C2×#585—348no—
289C2×#585—624no—
290C22×2−1+4—33no—
291C22×2−1+4—61no—
292C22×2−1+4C2×D311yescharacteristic, complemented
293C22×H(5,𝔽2)—348no—
294C22×H(5,𝔽2)—33no—
295C22×H(5,𝔽2)—31no—
296C22×H(5,𝔽2)—31no—
297C22×H(5,𝔽2)—33no—
298C22×H(5,𝔽2)—33no—
299C22×H(5,𝔽2)—63no—
300C22×H(5,𝔽2)—63no—
301C22×H(5,𝔽2)—61no—
302C22×H(5,𝔽2)—624no—
303C22×H(5,𝔽2)C2×D311yescharacteristic, complemented
304C23×#41—31no—
305C23×#41—33no—
306C23×#41—33no—
307C23×#41—33no—
308C23×#41—61no—
309C23×#41—61no—
310C23×#41—63no—
311C24×D4—33no—
312C24×D4—63no—
313#3585—31024no—
314C2×#577—348no—
315C2×#577—3144no—
316C2×#577—3144no—
317C2×#577C2×D3148yescomplemented
318C2×#576—348no—
319C2×#576—3144no—
320C2×#576—3144no—
321C2×#576—348no—
322C2×#575—3144no—
323C2×#575—3144no—
324C22×#137—33no—
325C22×#137—33no—
326C22×#137—33no—
327C22×#137—31no—
328C22×#137—33no—
329C22×#137C2×D313yescomplemented
330C22×AGL(1,ℤ/8)—33no—
331C22×AGL(1,ℤ/8)—33no—
332C22×AGL(1,ℤ/8)—33no—
333C22×AGL(1,ℤ/8)—3144no—
334C22×AGL(1,ℤ/8)—36no—
335C22×AGL(1,ℤ/8)—33no—
336C22×AGL(1,ℤ/8)—36no—
337C22×AGL(1,ℤ/8)—36no—
338C22×AGL(1,ℤ/8)—3144no—
339C22×AGL(1,ℤ/8)—33no—
340C22×AGL(1,ℤ/8)—33no—
341C22×AGL(1,ℤ/8)—33no—
342C22×AGL(1,ℤ/8)—33no—
343C22×AGL(1,ℤ/8)—33no—
344C22×AGL(1,ℤ/8)C2×D313yescomplemented
345C22×#135—33no—
346C22×#135—33no—
347C22×#135—36no—
348C22×#135—36no—
349C22×#135—33no—
350C22×#135C2×D313yescomplemented
351C23×SD16—33no—
352C23×SD16—36no—
353C23×SD16C2×D313yescomplemented
354C23×D8—33no—
355C23×D8—36no—
356C23×D8—33no—
357C2×#568—348no—
358C22×#131—31no—
359C22×#131—33no—
360C22×#131—33no—
361C22×#131C2×D311yescharacteristic, complemented
362C23×M16—33no—
363C23×M16—33no—
364C25×C3—23no—
365C24×D3—23no—
366C24×D3—23no—
367C24×D3—23no—
368C24×D3—23no—
369C24×D3—26no—
370C24×D3—272no—
371C24×D3—824no—
372C24×D3C2×D413yes—
373C3×2−1+4—296no—
374C3×2−1+4C24164yescomplemented
375C3×H(5,𝔽2)—296no—
376C3×H(5,𝔽2)C24164yescomplemented
377C2×C3×#41—224no—
378C2×C3×#41—272no—
379C2×C3×#41—218no—
380C2×C3×#41—218no—
381C2×C3×#41C2×D4112yes—
382C2×C3×#41C24136yes—
383C2×C3×#41C24112yes—
384C2×C3×#41C24136yescomplemented
385C22×C3×Q8—224no—
386C22×C3×Q8—23no—
387C22×C3×Q8—218no—
388C22×C3×Q8C2×D411yescharacteristic
389C22×C3×Q8C2413yes—
390C22×C3×Q8C2411yescharacteristic
391C22×C3×Q8C24136yescomplemented
392C22×C3×D4—23no—
393C22×C3×D4—23no—
394C22×C3×D4—272no—
395C22×C3×D4—23no—
396C22×C3×D4—218no—
397C22×C3×D4C2×D413yes—
398C22×C3×D4C2411yescharacteristic
399C22×C3×D4C2413yes—
400C22×C3×D4C24136yes—
401C23×C3×C4—23no—
402C23×C3×C4—23no—
403C23×C3×C4—23no—
404C23×C3×C4C2413yes—
405C22×#67—23no—
406C22×#67—23no—
407C22×#67—21no—
408C22×#67—23no—
409C22×#67—2144no—
410C22×#67—23no—
411C22×#67—26no—
412C22×#67—23no—
413C22×#67—272no—
414C22×#67C2×D416yes—
415C23×Dic3—21no—
416C23×Dic3—23no—
417C23×Dic3C2×D413yes—
418#1009—296no—
419#1009—296no—
420#1009—2256no—
421#1009—2768no—
422#1009—2288no—
423#1009—2288no—
424#1009C241192yescomplemented
425#1009C241192yescomplemented
426#1009C24164yescomplemented
427#1009C24164yescomplemented
428D3×#41—2256no—
429D3×#41—2768no—
430D3×#41—2288no—
431D3×#41—2288no—
432D3×#41C2×D41192yes—
433D3×#41C24164yes—
434D3×#41C241192yescomplemented
435D3×#41C241192yescomplemented
436#1007—2256no—
437#1007—2288no—
438#1007C241192yescomplemented
439C2×#239—224no—
440C2×#239—224no—
441C2×#239—2256no—
442C2×#239—272no—
443C2×#239—218no—
444C2×#239—272no—
445C2×#239—272no—
446C2×#239—236no—
447C2×#239—2288no—
448C2×#239—218no—
449C2×#239C2×D4124yes—
450C2×#239C24136yes—
451C2×#239C24136yes—
452C2×#239C24172yescomplemented
453C2×#239C241192yescomplemented
454C2×D3×Q8—26no—
455C2×D3×Q8—218no—
456C2×D3×Q8—272no—
457C2×D3×Q8C2×D4124yes—
458C2×D3×Q8C24112yes—
459C2×D3×Q8C24136yescomplemented
460#1004—2768no—
461#1004—2288no—
462#1004C241192yescomplemented
463C2×#237—272no—
464C2×#237—272no—
465C2×#237—218no—
466C2×#237—26no—
467C2×#237—272no—
468C2×#237C2×D4172yes—
469C2×#237C24136yes—
470C2×#237C24112yes—
471C2×D3×D4—272no—
472C2×D3×D4—272no—
473C2×D3×D4—272no—
474C2×D3×D4—272no—
475C2×D3×D4—2144no—
476C2×D3×D4—2144no—
477C2×D3×D4—2768no—
478C2×D3×D4—272no—
479C2×D3×D4—218no—
480C2×D3×D4—272no—
481C2×D3×D4—236no—
482C2×D3×D4—272no—
483C2×D3×D4—2288no—
484C2×D3×D4—218no—
485C2×D3×D4C2×D4172yes—
486C2×D3×D4C24136yes—
487C2×D3×D4C24172yes—
488C2×D3×D4C241192yescomplemented
489C2×D3×D4C24136yescomplemented
490C2×#235—218no—
491C2×#235—218no—
492C2×#235—2144no—
493C2×#235—272no—
494C2×#235—272no—
495C2×#235—272no—
496C2×#235—272no—
497C2×#235C2×D4136yes—
498C2×#235C24136yes—
499C2×#235C24136yes—
500C2×#235C24136yescomplemented
501C22×D12—23no—
502C22×D12—23no—
503C22×D12—26no—
504C22×D12—272no—
505C22×D12—23no—
506C22×D12—23no—
507C22×D12—218no—
508C22×D12—218no—
509C22×D12—272no—
510C22×D12—272no—
511C22×D12C2×D413yes—
512C22×D12C2413yes—
513C22×D12C24136yes—
514C22×D12C2413yes—
515C22×D12C24136yescomplemented
516C22×C4×D3—21no—
517C22×C4×D3—23no—
518C22×C4×D3—23no—
519C22×C4×D3—23no—
520C22×C4×D3—23no—
521C22×C4×D3—23no—
522C22×C4×D3—26no—
523C22×C4×D3—272no—
524C22×C4×D3—272no—
525C22×C4×D3—272no—
526C22×C4×D3C2×D413yes—
527C22×C4×D3C2×D413yes—
528C22×C4×D3C2×D4136yes—
529C22×C4×D3C2411yescharacteristic
530C22×C4×D3C2413yes—
531C22×C4×D3C24136yes—
532C22×Dic6—21no—
533C22×Dic6—23no—
534C22×Dic6C2×D413yes—
535C22×Dic6C2411yescharacteristic
536C22×Dic6C2411yescharacteristic
537C3×#137C241192yescomplemented
538C3×AGL(1,ℤ/8)C241192yescomplemented
539C3×#135C241192yescomplemented
540C2×C3×Q16C24136yescomplemented
541C2×C3×SD16C24136yescomplemented
542C2×C3×SD16C24172yescomplemented
543C2×C3×SD16C24112yescomplemented
544C2×C3×SD16C241192yescomplemented
545C2×C3×D8C24136yescomplemented
546C3×#131C24164yescomplemented
547C2×C3×M16C24136yescomplemented
548C22×C3×C8C2411yescharacteristic
549C22×C3×C8C2413yes—
550C22×C3×C8C24136yescomplemented
551#950C241192yescomplemented
552#950C241192yescomplemented
553#949C241192yescomplemented
554#949C241192yescomplemented
555#948C24164yescomplemented
556C2×#216C24136yescomplemented
557C2×#216C24112yescomplemented
558#942C241192yescomplemented
559C2×#215C24172yescomplemented
560C2×#215C24136yescomplemented
561C2×#215C24136yescomplemented
562C2×#215C241192yescomplemented
563C2×#214C24112yescomplemented
564C2×#214C24136yescomplemented
565#932C241192yescomplemented
566C2×#213C24136yescomplemented
567C2×#213C24172yescomplemented
568C2×#213C24136yescomplemented
569C2×#213C241192yescomplemented
570C2×#208C24136yescomplemented
571C22×C3⋊C8C2413yes—
572C22×C3⋊C8C2411yescharacteristic
573C22×C3⋊C8C24136yescomplemented
574#919C241384yescomplemented
575#918C241192yescomplemented
576#918C241192yescomplemented
577#916C241384yescomplemented
578#915C24164yescomplemented
579#915C241192yescomplemented
580#914C241192yescomplemented
581#914C241384yescomplemented
582#914C241384yescomplemented
583#914C241384yescomplemented
584#914C241192yescomplemented
585D3×SD16C241384yescomplemented
586#911C241192yescomplemented
587#911C241192yescomplemented
588D3×D8C241384yescomplemented
589#908C241192yescomplemented
590#908C241192yescomplemented
591#907C241192yescomplemented
592D3×M16C241192yescomplemented
593C2×Dic12C24112yescomplemented
594#904C241192yescomplemented
595C2×D24C24136yescomplemented
596C2×D24C24172yescomplemented
597C2×D24C241192yescomplemented
598C2×#204C24136yescomplemented
599C2×#204C24136yescomplemented
600#901C241192yescomplemented
601C2×ΓL(1,𝔽25)C24112yes—
602C2×ΓL(1,𝔽25)C24136yes—
603C2×ΓL(1,𝔽25)C241192yescomplemented
604C2×ΓL(1,𝔽25)C24136yescomplemented
605C2×ΓL(1,𝔽25)C24136yescomplemented
606C2×D3×C8C24172yescomplemented
607C26—63no—
608#585—3256no—
609#585—6384no—
610C2×2−1+4—212no—
611C2×2−1+4—372no—
612C2×2−1+4—648no—
613C2×2−1+4—636no—
614C2×2−1+4C22×D3124yescomplemented
615C2×H(5,𝔽2)—212no—
616C2×H(5,𝔽2)—3256no—
617C2×H(5,𝔽2)—372no—
618C2×H(5,𝔽2)—324no—
619C2×H(5,𝔽2)—324no—
620C2×H(5,𝔽2)—372no—
621C2×H(5,𝔽2)—372no—
622C2×H(5,𝔽2)—6144no—
623C2×H(5,𝔽2)—636no—
624C2×H(5,𝔽2)—6144no—
625C2×H(5,𝔽2)—648no—
626C2×H(5,𝔽2)—636no—
627C2×H(5,𝔽2)—636no—
628C2×H(5,𝔽2)—6384no—
629C2×H(5,𝔽2)—612no—
630C2×H(5,𝔽2)—612no—
631C2×H(5,𝔽2)C22×D3124yescomplemented
632C22×#41—21no—
633C22×#41—23no—
634C22×#41—324no—
635C22×#41—324no—
636C22×#41—31no—
637C22×#41—33no—
638C22×#41—33no—
639C22×#41—372no—
640C22×#41—372no—
641C22×#41—33no—
642C22×#41—33no—
643C22×#41—36no—
644C22×#41—372no—
645C22×#41—31no—
646C22×#41—33no—
647C22×#41—33no—
648C22×#41—33no—
649C22×#41—63no—
650C22×#41—63no—
651C22×#41—66no—
652C22×#41—63no—
653C22×#41—63no—
654C22×#41—63no—
655C22×#41—63no—
656C22×#41—63no—
657C22×#41—63no—
658C22×#41—636no—
659C22×#41—636no—
660C22×#41—636no—
661C22×#41—63no—
662C22×#41—63no—
663C22×#41—648no—
664C22×#41—648no—
665C22×#41—6144no—
666C22×#41—61no—
667C22×#41—61no—
668C22×#41C22×D313yes—
669C22×#41C22×D311yescharacteristic
670C22×#41C22×D313yescomplemented
671C23×Q8—21no—
672C23×Q8—31no—
673C23×Q8—31no—
674C23×Q8—33no—
675C23×Q8—63no—
676C23×Q8C22×D313yescomplemented
677C23×D4—23no—
678C23×D4—33no—
679C23×D4—33no—
680C23×D4—36no—
681C23×D4—372no—
682C23×D4—33no—
683C23×D4—33no—
684C23×D4—33no—
685C23×D4—63no—
686C23×D4—63no—
687C23×D4—63no—
688C23×D4—63no—
689C23×D4—63no—
690C23×D4—636no—
691C23×D4—63no—
692C23×D4—66no—
693C23×D4—6144no—
694C23×D4—63no—
695C23×D4—66no—
696C23×D4—63no—
697C23×D4—63no—
698C23×D4—66no—
699C23×D4—63no—
700C23×D4—63no—
701C23×D4C22×D313yes—
702C24×C4—33no—
703C24×C4—63no—
704C24×C4—63no—
705C24×C4—63no—
706#577—3256no—
707#577—3768no—
708#577—3768no—
709#577C22×D31256yescomplemented
710#576—3256no—
711#576—3768no—
712#576—3768no—
713#576—3256no—
714#575—3768no—
715#575—3768no—
716C2×#137—372no—
717C2×#137—372no—
718C2×#137—372no—
719C2×#137—324no—
720C2×#137—372no—
721C2×#137C22×D3172yescomplemented
722C2×AGL(1,ℤ/8)—372no—
723C2×AGL(1,ℤ/8)—372no—
724C2×AGL(1,ℤ/8)—372no—
725C2×AGL(1,ℤ/8)—3768no—
726C2×AGL(1,ℤ/8)—3768no—
727C2×AGL(1,ℤ/8)—3144no—
728C2×AGL(1,ℤ/8)—372no—
729C2×AGL(1,ℤ/8)—3144no—
730C2×AGL(1,ℤ/8)—3144no—
731C2×AGL(1,ℤ/8)—372no—
732C2×AGL(1,ℤ/8)—372no—
733C2×AGL(1,ℤ/8)—372no—
734C2×AGL(1,ℤ/8)—372no—
735C2×AGL(1,ℤ/8)—372no—
736C2×AGL(1,ℤ/8)C22×D3172yescomplemented
737C2×#135—372no—
738C2×#135—372no—
739C2×#135—3144no—
740C2×#135—3144no—
741C2×#135—372no—
742C2×#135C22×D3172yescomplemented
743C22×Q16—31no—
744C22×Q16—33no—
745C22×Q16—31no—
746C22×Q16C22×D313yescomplemented
747C22×SD16—36no—
748C22×SD16—33no—
749C22×SD16—33no—
750C22×SD16—372no—
751C22×SD16—33no—
752C22×SD16—31no—
753C22×SD16—3144no—
754C22×SD16—33no—
755C22×SD16—33no—
756C22×SD16C22×D316yescomplemented
757C22×SD16C22×D313yescomplemented
758C22×SD16C22×D311yescharacteristic, complemented
759C22×SD16C22×D3172yescomplemented
760C22×D8—36no—
761C22×D8—33no—
762C22×D8—33no—
763C22×D8—372no—
764C22×D8—3144no—
765C22×D8—36no—
766C22×D8—33no—
767C22×D8—372no—
768C22×D8C22×D313yescomplemented
769#568—3256no—
770C2×#131—324no—
771C2×#131—372no—
772C2×#131—372no—
773C2×#131C22×D3124yescomplemented
774C22×M16—33no—
775C22×M16—372no—
776C22×M16—33no—
777C22×M16—31no—
778C22×M16—33no—
779C22×M16—33no—
780C22×M16—372no—
781C22×M16C22×D313yescomplemented
782C23×C8—33no—
783C23×C8—36no—
784C23×C8C22×D313yescomplemented
785C24×C3—23no—
786C24×C3—21no—
787C24×C3—236no—
788C24×C3—812no—
789C24×C3C22×D413yes—
790C23×D3—23no—
791C23×D3—23no—
792C23×D3—236no—
793C23×D3—236no—
794C23×D3—236no—
795C23×D3—236no—
796C23×D3—272no—
797C23×D3—2192no—
798C23×D3—412no—
799C23×D3—424no—
800C23×D3—812no—
801C23×D3—824no—
802C23×D3—8288no—
803C23×D3—812no—
804C23×D3—812no—
805C23×D3C22×D411yescharacteristic
806C23×D3C22×D413yes—
807C23×D3C22×D4136yes—
808C3×#41—264no—
809C3×#41—2192no—
810C3×#41—272no—
811C3×#41—272no—
812C3×#41C22×D4148yes—
813C3×#41C25148yes—
814C3×#41C25116yes—
815C3×#41C25148yescomplemented
816C2×C3×Q8—264no—
817C2×C3×Q8—29no—
818C2×C3×Q8—236no—
819C2×C3×Q8—23no—
820C2×C3×Q8—272no—
821C2×C3×Q8C22×D4112yes—
822C2×C3×Q8C25118yes—
823C2×C3×Q8C2516yes—
824C2×C3×Q8C25148yescomplemented
825C2×C3×D4—236no—
826C2×C3×D4—236no—
827C2×C3×D4—2192no—
828C2×C3×D4—29no—
829C2×C3×D4—236no—
830C2×C3×D4—23no—
831C2×C3×D4—272no—
832C2×C3×D4C22×D4136yes—
833C2×C3×D4C2516yes—
834C2×C3×D4C25118yes—
835C2×C3×D4C25148yes—
836C22×C3×C4—21no—
837C22×C3×C4—23no—
838C22×C3×C4—236no—
839C22×C3×C4—236no—
840C22×C3×C4—236no—
841C22×C3×C4C22×D413yes—
842C22×C3×C4C22×D4118yes—
843C22×C3×C4C2511yescharacteristic
844C22×C3×C4C25118yes—
845C2×#67—236no—
846C2×#67—236no—
847C2×#67—212no—
848C2×#67—236no—
849C2×#67—2384no—
850C2×#67—236no—
851C2×#67—272no—
852C2×#67—236no—
853C2×#67—2192no—
854C2×#67C22×D4172yes—
855C22×Dic3—21no—
856C22×Dic3—21no—
857C22×Dic3—212no—
858C22×Dic3—236no—
859C22×Dic3C22×D413yes—
860C22×Dic3C22×D411yescharacteristic
861C22×Dic3C22×D4136yes—
862#239—264no—
863#239—264no—
864#239—2192no—
865#239—272no—
866#239—2192no—
867#239—2192no—
868#239—2144no—
869#239—272no—
870#239C22×D4164yes—
871#239C25148yes—
872#239C25148yes—
873#239C25196yescomplemented
874D3×Q8—224no—
875D3×Q8—272no—
876D3×Q8—2192no—
877D3×Q8C22×D4164yes—
878D3×Q8C25116yes—
879D3×Q8C25148yescomplemented
880#237—2192no—
881#237—2192no—
882#237—272no—
883#237—224no—
884#237—2192no—
885#237C22×D41192yes—
886#237C25116yes—
887#237C25148yes—
888D3×D4—2192no—
889D3×D4—2192no—
890D3×D4—2192no—
891D3×D4—2192no—
892D3×D4—2384no—
893D3×D4—2384no—
894D3×D4—2192no—
895D3×D4—272no—
896D3×D4—2192no—
897D3×D4—2144no—
898D3×D4—2192no—
899D3×D4—272no—
900D3×D4C22×D41192yes—
901D3×D4C25196yes—
902D3×D4C25148yes—
903D3×D4C25148yescomplemented
904#235—272no—
905#235—272no—
906#235—2384no—
907#235—2192no—
908#235—2192no—
909#235—2192no—
910#235—2192no—
911#235C22×D41144yes—
912#235C25148yes—
913#235C25148yes—
914#235C25148yescomplemented
915C2×D12—236no—
916C2×D12—236no—
917C2×D12—272no—
918C2×D12—2192no—
919C2×D12—29no—
920C2×D12—236no—
921C2×D12—29no—
922C2×D12—236no—
923C2×D12—272no—
924C2×D12—272no—
925C2×D12—2192no—
926C2×D12—2192no—
927C2×D12C22×D4136yes—
928C2×D12C25118yes—
929C2×D12C25118yes—
930C2×D12C25148yes—
931C2×D12C25148yescomplemented
932C2×C4×D3—212no—
933C2×C4×D3—236no—
934C2×C4×D3—236no—
935C2×C4×D3—236no—
936C2×C4×D3—236no—
937C2×C4×D3—236no—
938C2×C4×D3—272no—
939C2×C4×D3—2192no—
940C2×C4×D3—2192no—
941C2×C4×D3—2192no—
942C2×C4×D3C22×D4136yes—
943C2×C4×D3C22×D4136yes—
944C2×C4×D3C22×D416yes—
945C2×C4×D3C22×D4118yes—
946C2×C4×D3C22×D41144yes—
947C2×C4×D3C25118yes—
948C2×C4×D3C2516yes—
949C2×C4×D3C25148yes—
950C2×Dic6—23no—
951C2×Dic6—23no—
952C2×Dic6—212no—
953C2×Dic6—236no—
954C2×Dic6C22×D4136yes—
955C2×Dic6C2516yes—
956C2×Dic6C2516yes—
957C3×Q16C25148yescomplemented
958C3×SD16C25196yescomplemented
959C3×SD16C25148yescomplemented
960C3×SD16C25116yescomplemented
961C3×D8C25148yescomplemented
962C3×M16C25148yescomplemented
963C2×C3×C8C25118yes—
964C2×C3×C8C2516yes—
965C2×C3×C8C25148yescomplemented
966#216C25148yescomplemented
967#216C25116yescomplemented
968#215C25196yescomplemented
969#215C25148yescomplemented
970#215C25148yescomplemented
971#214C25116yescomplemented
972#214C25148yescomplemented
973#213C25148yescomplemented
974#213C25196yescomplemented
975#213C25148yescomplemented
976#208C25148yescomplemented
977C2×C3⋊C8C25118yes—
978C2×C3⋊C8C2516yes—
979C2×C3⋊C8C25148yescomplemented
980Dic12C25116yescomplemented
981D24C25148yescomplemented
982D24C25196yescomplemented
983#204C25148yescomplemented
984#204C25148yescomplemented
985ΓL(1,𝔽25)C25116yes—
986ΓL(1,𝔽25)C25148yes—
987ΓL(1,𝔽25)C25148yescomplemented
988ΓL(1,𝔽25)C25148yescomplemented
989D3×C8C25196yescomplemented
990C25—23no—
991C25—33no—
992C25—63no—
993C25—63no—
994C25—66no—
995C25—672no—
996C25—63no—
997C25—63no—
998C25—2424no—
9992−1+4—296no—
10002−1+4—3192no—
10012−1+4—6256no—
10022−1+4—6288no—
10032−1+4C23×D3164yescomplemented
1004H(5,𝔽2)—296no—
1005H(5,𝔽2)—364no—
1006H(5,𝔽2)—3192no—
1007H(5,𝔽2)—364no—
1008H(5,𝔽2)—3192no—
1009H(5,𝔽2)—3192no—
1010H(5,𝔽2)—6768no—
1011H(5,𝔽2)—6288no—
1012H(5,𝔽2)—6768no—
1013H(5,𝔽2)—6256no—
1014H(5,𝔽2)—6288no—
1015H(5,𝔽2)—6288no—
1016H(5,𝔽2)—696no—
1017H(5,𝔽2)—696no—
1018H(5,𝔽2)C23×D3164yescomplemented
1019C2×#41—224no—
1020C2×#41—272no—
1021C2×#41—218no—
1022C2×#41—218no—
1023C2×#41—3192no—
1024C2×#41—364no—
1025C2×#41—324no—
1026C2×#41—372no—
1027C2×#41—336no—
1028C2×#41—336no—
1029C2×#41—3192no—
1030C2×#41—3192no—
1031C2×#41—372no—
1032C2×#41—336no—
1033C2×#41—336no—
1034C2×#41—3192no—
1035C2×#41—336no—
1036C2×#41—312no—
1037C2×#41—336no—
1038C2×#41—336no—
1039C2×#41—672no—
1040C2×#41—672no—
1041C2×#41—6144no—
1042C2×#41—672no—
1043C2×#41—672no—
1044C2×#41—672no—
1045C2×#41—66no—
1046C2×#41—672no—
1047C2×#41—618no—
1048C2×#41—618no—
1049C2×#41—672no—
1050C2×#41—618no—
1051C2×#41—672no—
1052C2×#41—636no—
1053C2×#41—6288no—
1054C2×#41—6288no—
1055C2×#41—6288no—
1056C2×#41—672no—
1057C2×#41—672no—
1058C2×#41—6256no—
1059C2×#41—6256no—
1060C2×#41—6768no—
1061C2×#41—624no—
1062C2×#41—624no—
1063C2×#41—618no—
1064C2×#41—618no—
1065C2×#41D3×D4112yes—
1066C2×#41C23×D3136yes—
1067C2×#41C23×D3112yes—
1068C2×#41C23×D3136yescomplemented
1069C22×Q8—224no—
1070C22×Q8—23no—
1071C22×Q8—218no—
1072C22×Q8—324no—
1073C22×Q8—33no—
1074C22×Q8—336no—
1075C22×Q8—312no—
1076C22×Q8—31no—
1077C22×Q8—31no—
1078C22×Q8—63no—
1079C22×Q8—61no—
1080C22×Q8—66no—
1081C22×Q8—618no—
1082C22×Q8—672no—
1083C22×Q8D3×D411yescharacteristic
1084C22×Q8C23×D313yes—
1085C22×Q8C23×D311yescharacteristic
1086C22×Q8C23×D3136yescomplemented
1087C22×D4—23no—
1088C22×D4—23no—
1089C22×D4—272no—
1090C22×D4—23no—
1091C22×D4—218no—
1092C22×D4—36no—
1093C22×D4—372no—
1094C22×D4—336no—
1095C22×D4—372no—
1096C22×D4—336no—
1097C22×D4—3192no—
1098C22×D4—33no—
1099C22×D4—33no—
1100C22×D4—33no—
1101C22×D4—336no—
1102C22×D4—336no—
1103C22×D4—672no—
1104C22×D4—672no—
1105C22×D4—63no—
1106C22×D4—63no—
1107C22×D4—66no—
1108C22×D4—672no—
1109C22×D4—618no—
1110C22×D4—672no—
1111C22×D4—672no—
1112C22×D4—636no—
1113C22×D4—6288no—
1114C22×D4—618no—
1115C22×D4—63no—
1116C22×D4—66no—
1117C22×D4—63no—
1118C22×D4—672no—
1119C22×D4—6144no—
1120C22×D4—6768no—
1121C22×D4—672no—
1122C22×D4—6144no—
1123C22×D4—672no—
1124C22×D4—672no—
1125C22×D4—6144no—
1126C22×D4—63no—
1127C22×D4—61no—
1128C22×D4—63no—
1129C22×D4—63no—
1130C22×D4—672no—
1131C22×D4—672no—
1132C22×D4—63no—
1133C22×D4—63no—
1134C22×D4—618no—
1135C22×D4—618no—
1136C22×D4D3×D413yes—
1137C22×D4C23×D311yescharacteristic
1138C22×D4C23×D313yes—
1139C22×D4C23×D3136yes—
1140C23×C4—23no—
1141C23×C4—23no—
1142C23×C4—23no—
1143C23×C4—33no—
1144C23×C4—33no—
1145C23×C4—33no—
1146C23×C4—336no—
1147C23×C4—33no—
1148C23×C4—31no—
1149C23×C4—336no—
1150C23×C4—63no—
1151C23×C4—63no—
1152C23×C4—672no—
1153C23×C4—66no—
1154C23×C4—672no—
1155C23×C4—672no—
1156C23×C4—61no—
1157C23×C4—63no—
1158C23×C4—61no—
1159C23×C4—63no—
1160C23×C4—63no—
1161C23×C4—63no—
1162C23×C4C23×D313yes—
1163#137—3192no—
1164#137—3192no—
1165#137—3192no—
1166#137—364no—
1167#137—3192no—
1168#137C23×D31192yescomplemented
1169AGL(1,ℤ/8)—3192no—
1170AGL(1,ℤ/8)—3192no—
1171AGL(1,ℤ/8)—3192no—
1172AGL(1,ℤ/8)—3384no—
1173AGL(1,ℤ/8)—3192no—
1174AGL(1,ℤ/8)—3384no—
1175AGL(1,ℤ/8)—3384no—
1176AGL(1,ℤ/8)—3192no—
1177AGL(1,ℤ/8)—3192no—
1178AGL(1,ℤ/8)—3192no—
1179AGL(1,ℤ/8)—3192no—
1180AGL(1,ℤ/8)—3192no—
1181AGL(1,ℤ/8)C23×D31192yescomplemented
1182#135—3192no—
1183#135—3192no—
1184#135—3384no—
1185#135—3384no—
1186#135—3192no—
1187#135C23×D31192yescomplemented
1188C2×Q16—312no—
1189C2×Q16—336no—
1190C2×Q16—312no—
1191C2×Q16C23×D3136yescomplemented
1192C2×SD16—336no—
1193C2×SD16—372no—
1194C2×SD16—336no—
1195C2×SD16—3192no—
1196C2×SD16—336no—
1197C2×SD16—312no—
1198C2×SD16—3384no—
1199C2×SD16—336no—
1200C2×SD16—336no—
1201C2×SD16C23×D3172yescomplemented
1202C2×SD16C23×D3136yescomplemented
1203C2×SD16C23×D3112yescomplemented
1204C2×SD16C23×D31192yescomplemented
1205C2×D8—336no—
1206C2×D8—372no—
1207C2×D8—336no—
1208C2×D8—3192no—
1209C2×D8—3384no—
1210C2×D8—372no—
1211C2×D8—336no—
1212C2×D8—3192no—
1213C2×D8C23×D3136yescomplemented
1214#131—364no—
1215#131—3192no—
1216#131—3192no—
1217#131C23×D3164yescomplemented
1218C2×M16—336no—
1219C2×M16—3192no—
1220C2×M16—336no—
1221C2×M16—312no—
1222C2×M16—336no—
1223C2×M16—336no—
1224C2×M16—3192no—
1225C2×M16C23×D3136yescomplemented
1226C22×C8—31no—
1227C22×C8—33no—
1228C22×C8—336no—
1229C22×C8—372no—
1230C22×C8C23×D313yes—
1231C22×C8C23×D311yescharacteristic
1232C22×C8C23×D3136yescomplemented
1233C23×C3—212no—
1234C23×C3—26no—
1235C23×C3—218no—
1236C23×C3—248no—
1237C23×C3—412no—
1238C23×C3—44no—
1239C23×C3—872no—
1240C23×C3C23×D4118yes—
1241C23×C3C23×D411yescharacteristic
1242C22×D3—24no—
1243C22×D3—212no—
1244C22×D3—218no—
1245C22×D3—218no—
1246C22×D3—248no—
1247C22×D3—248no—
1248C22×D3—248no—
1249C22×D3—248no—
1250C22×D3—296no—
1251C22×D3—472no—
1252C22×D3—4144no—
1253C22×D3—412no—
1254C22×D3—412no—
1255C22×D3—872no—
1256C22×D3—8144no—
1257C22×D3—8384no—
1258C22×D3—872no—
1259C22×D3—872no—
1260C22×D3C23×D416yes—
1261C22×D3C23×D4118yes—
1262C22×D3C23×D4148yes—
1263C3×Q8—218no—
1264C3×Q8—248no—
1265C3×Q8—26no—
1266C3×Q8C23×D4116yes—
1267C3×Q8C26112yes—
1268C3×Q8C2614yes—
1269C3×D4—248no—
1270C3×D4—248no—
1271C3×D4—218no—
1272C3×D4—248no—
1273C3×D4—26no—
1274C3×D4C23×D4148yes—
1275C3×D4C2614yes—
1276C3×D4C26112yes—
1277C2×C3×C4—26no—
1278C2×C3×C4—218no—
1279C2×C3×C4—248no—
1280C2×C3×C4—248no—
1281C2×C3×C4—248no—
1282C2×C3×C4C23×D413yes—
1283C2×C3×C4C23×D4118yes—
1284C2×C3×C4C23×D4136yes—
1285C2×C3×C4C2613yes—
1286C2×C3×C4C26112yes—
1287#67—248no—
1288#67—248no—
1289#67—216no—
1290#67—248no—
1291#67—248no—
1292#67—296no—
1293#67—248no—
1294#67C23×D4196yes—
1295C2×Dic3—26no—
1296C2×Dic3—26no—
1297C2×Dic3—216no—
1298C2×Dic3—248no—
1299C2×Dic3C23×D4118yes—
1300C2×Dic3C23×D416yes—
1301C2×Dic3C23×D4148yes—
1302D12—248no—
1303D12—248no—
1304D12—296no—
1305D12—218no—
1306D12—248no—
1307D12—218no—
1308D12—248no—
1309D12C23×D4148yes—
1310D12C26112yes—
1311D12C26112yes—
1312C4×D3—216no—
1313C4×D3—248no—
1314C4×D3—248no—
1315C4×D3—248no—
1316C4×D3—248no—
1317C4×D3—248no—
1318C4×D3—296no—
1319C4×D3C23×D4148yes—
1320C4×D3C23×D4148yes—
1321C4×D3C23×D4112yes—
1322C4×D3C23×D4136yes—
1323C4×D3C26112yes—
1324C4×D3C2614yes—
1325Dic6—26no—
1326Dic6—26no—
1327Dic6—216no—
1328Dic6—248no—
1329Dic6C23×D4148yes—
1330Dic6C2614yes—
1331Dic6C2614yes—
1332C3×C8C26112yes—
1333C3×C8C2614yes—
1334C3⋊C8C26112yes—
1335C3⋊C8C2614yes—
1336C24—21no—
1337C24—23no—
1338C24—236no—
1339C24—31no—
1340C24—33no—
1341C24—336no—
1342C24—636no—
1343C24—636no—
1344C24—672no—
1345C24—6192no—
1346C24—63no—
1347C24—63no—
1348C24—636no—
1349C24—636no—
1350C24—812no—
1351C24—1212no—
1352C24—1224no—
1353C24—2412no—
1354C24—2412no—
1355C24—2424no—
1356C24—2412no—
1357C24—24288no—
1358C24C2×D3×D413yes—
1359#41—264no—
1360#41—2192no—
1361#41—272no—
1362#41—272no—
1363#41—364no—
1364#41—3192no—
1365#41—3144no—
1366#41—348no—
1367#41—396no—
1368#41—348no—
1369#41—348no—
1370#41—348no—
1371#41—316no—
1372#41—348no—
1373#41—348no—
1374#41—6192no—
1375#41—6192no—
1376#41—6384no—
1377#41—6192no—
1378#41—6192no—
1379#41—6192no—
1380#41—624no—
1381#41—6192no—
1382#41—672no—
1383#41—672no—
1384#41—6192no—
1385#41—672no—
1386#41—6192no—
1387#41—6144no—
1388#41—6192no—
1389#41—6192no—
1390#41—664no—
1391#41—664no—
1392#41—672no—
1393#41—672no—
1394#41C2×D3×D4148yes—
1395#41C24×D3148yes—
1396#41C24×D3116yes—
1397#41C24×D3148yescomplemented
1398C2×Q8—264no—
1399C2×Q8—29no—
1400C2×Q8—236no—
1401C2×Q8—272no—
1402C2×Q8—23no—
1403C2×Q8—364no—
1404C2×Q8—336no—
1405C2×Q8—348no—
1406C2×Q8—316no—
1407C2×Q8—36no—
1408C2×Q8—36no—
1409C2×Q8—636no—
1410C2×Q8—612no—
1411C2×Q8—624no—
1412C2×Q8—672no—
1413C2×Q8—6192no—
1414C2×Q8—63no—
1415C2×Q8—63no—
1416C2×Q8C2×D3×D4112yes—
1417C2×Q8C24×D3118yes—
1418C2×Q8C24×D316yes—
1419C2×Q8C24×D3148yescomplemented
1420C2×D4—236no—
1421C2×D4—236no—
1422C2×D4—2192no—
1423C2×D4—236no—
1424C2×D4—29no—
1425C2×D4—272no—
1426C2×D4—23no—
1427C2×D4—372no—
1428C2×D4—3192no—
1429C2×D4—348no—
1430C2×D4—396no—
1431C2×D4—348no—
1432C2×D4—336no—
1433C2×D4—318no—
1434C2×D4—318no—
1435C2×D4—348no—
1436C2×D4—348no—
1437C2×D4—6192no—
1438C2×D4—6192no—
1439C2×D4—636no—
1440C2×D4—636no—
1441C2×D4—672no—
1442C2×D4—6192no—
1443C2×D4—672no—
1444C2×D4—6192no—
1445C2×D4—6192no—
1446C2×D4—6144no—
1447C2×D4—672no—
1448C2×D4—636no—
1449C2×D4—672no—
1450C2×D4—636no—
1451C2×D4—6192no—
1452C2×D4—6384no—
1453C2×D4—6192no—
1454C2×D4—6384no—
1455C2×D4—6192no—
1456C2×D4—6192no—
1457C2×D4—6384no—
1458C2×D4—636no—
1459C2×D4—612no—
1460C2×D4—636no—
1461C2×D4—636no—
1462C2×D4—6192no—
1463C2×D4—6192no—
1464C2×D4—636no—
1465C2×D4—69no—
1466C2×D4—636no—
1467C2×D4—69no—
1468C2×D4—672no—
1469C2×D4—672no—
1470C2×D4C2×D3×D4136yes—
1471C2×D4C24×D316yes—
1472C2×D4C24×D3118yes—
1473C2×D4C24×D3148yes—
1474C22×C4—236no—
1475C22×C4—21no—
1476C22×C4—23no—
1477C22×C4—236no—
1478C22×C4—236no—
1479C22×C4—336no—
1480C22×C4—31no—
1481C22×C4—33no—
1482C22×C4—36no—
1483C22×C4—336no—
1484C22×C4—336no—
1485C22×C4—318no—
1486C22×C4—3144no—
1487C22×C4—318no—
1488C22×C4—36no—
1489C22×C4—348no—
1490C22×C4—636no—
1491C22×C4—636no—
1492C22×C4—6192no—
1493C22×C4—672no—
1494C22×C4—6192no—
1495C22×C4—6192no—
1496C22×C4—612no—
1497C22×C4—636no—
1498C22×C4—612no—
1499C22×C4—636no—
1500C22×C4—61no—
1501C22×C4—61no—
1502C22×C4—636no—
1503C22×C4—636no—
1504C22×C4C2×D3×D4118yes—
1505C22×C4C2×D3×D413yes—
1506C22×C4C24×D3118yes—
1507C22×C4C24×D311yescharacteristic
1508Q16—316no—
1509Q16—348no—
1510Q16—316no—
1511Q16C24×D3148yescomplemented
1512SD16—348no—
1513SD16—396no—
1514SD16—348no—
1515SD16—348no—
1516SD16—316no—
1517SD16—348no—
1518SD16—348no—
1519SD16C24×D3196yescomplemented
1520SD16C24×D3148yescomplemented
1521SD16C24×D3116yescomplemented
1522D8—348no—
1523D8—396no—
1524D8—348no—
1525D8—396no—
1526D8—348no—
1527D8C24×D3148yescomplemented
1528M16—348no—
1529M16—348no—
1530M16—316no—
1531M16—348no—
1532M16—348no—
1533M16C24×D3148yescomplemented
1534C2×C8—36no—
1535C2×C8—318no—
1536C2×C8—348no—
1537C2×C8—396no—
1538C2×C8C24×D3118yes—
1539C2×C8C24×D316yes—
1540C2×C8C24×D3148yescomplemented
1541C22×C3—236no—
1542C22×C3—24no—
1543C22×C3—212no—
1544C22×C3—436no—
1545C22×C3—412no—
1546C22×C3—848no—
1547C22×C3#358514yescomplemented
1548C22×C3C24×D4112yes—
1549C22×C3C24×D413yes—
1550C2×D3—212no—
1551C2×D3—236no—
1552C2×D3—212no—
1553C2×D3—212no—
1554C2×D3—448no—
1555C2×D3—496no—
1556C2×D3—436no—
1557C2×D3—436no—
1558C2×D3—848no—
1559C2×D3—896no—
1560C2×D3—848no—
1561C2×D3—848no—
1562C2×D3C24×D414yes—
1563C2×D3C24×D4112yes—
1564C3×C4—24no—
1565C3×C4—212no—
1566C3×C4C24×D413yes—
1567C3×C4C24×D4112yes—
1568C3×C4C2711yescharacteristic
1569Dic3—24no—
1570Dic3—24no—
1571Dic3C24×D4112yes—
1572Dic3C24×D414yes—
1573C23—212no—
1574C23—26no—
1575C23—218no—
1576C23—248no—
1577C23—36no—
1578C23—318no—
1579C23—348no—
1580C23—412no—
1581C23—44no—
1582C23—648no—
1583C23—648no—
1584C23—696no—
1585C23—64no—
1586C23—612no—
1587C23—618no—
1588C23—618no—
1589C23—648no—
1590C23—648no—
1591C23—872no—
1592C23—1272no—
1593C23—12144no—
1594C23—1212no—
1595C23—1212no—
1596C23—2472no—
1597C23—2472no—
1598C23—24144no—
1599C23—2472no—
1600C23—24384no—
1601C23C22×D3×D4118yes—
1602C23C22×D3×D411yescharacteristic
1603Q8—218no—
1604Q8—248no—
1605Q8—26no—
1606Q8—348no—
1607Q8—34no—
1608Q8—34no—
1609Q8—648no—
1610Q8—616no—
1611Q8—66no—
1612Q8—66no—
1613Q8C22×D3×D4116yes—
1614Q8C25×D3112yes—
1615Q8C25×D314yes—
1616D4—248no—
1617D4—248no—
1618D4—248no—
1619D4—218no—
1620D4—26no—
1621D4—396no—
1622D4—348no—
1623D4—312no—
1624D4—312no—
1625D4—648no—
1626D4—648no—
1627D4—696no—
1628D4—648no—
1629D4—696no—
1630D4—648no—
1631D4—648no—
1632D4—616no—
1633D4—648no—
1634D4—648no—
1635D4—648no—
1636D4—618no—
1637D4—648no—
1638D4—618no—
1639D4C22×D3×D4148yes—
1640D4C25×D314yes—
1641D4C25×D3112yes—
1642C2×C4—26no—
1643C2×C4—218no—
1644C2×C4—248no—
1645C2×C4—248no—
1646C2×C4—248no—
1647C2×C4—36no—
1648C2×C4—318no—
1649C2×C4—348no—
1650C2×C4—312no—
1651C2×C4—348no—
1652C2×C4—348no—
1653C2×C4—336no—
1654C2×C4—312no—
1655C2×C4—34no—
1656C2×C4—648no—
1657C2×C4—648no—
1658C2×C4—696no—
1659C2×C4—616no—
1660C2×C4—648no—
1661C2×C4—616no—
1662C2×C4—648no—
1663C2×C4—66no—
1664C2×C4—66no—
1665C2×C4—648no—
1666C2×C4—648no—
1667C2×C4C22×D3×D4118yes—
1668C2×C4C22×D3×D413yes—
1669C2×C4C22×D3×D4136yes—
1670C2×C4C25×D313yes—
1671C2×C4C25×D3112yes—
1672C8—34no—
1673C8—312no—
1674C8C25×D3112yes—
1675C8C25×D314yes—
1676C2×C3—212no—
1677C2×C3—412no—
1678C2×C3—44no—
1679C2×C3C2×#358516yescomplemented
1680C2×C3C25×D411yescharacteristic
1681D3—24no—
1682D3—212no—
1683D3—412no—
1684D3—412no—
1685C22—236no—
1686C22—24no—
1687C22—212no—
1688C22—34no—
1689C22—312no—
1690C22—436no—
1691C22—412no—
1692C22—612no—
1693C22—636no—
1694C22—612no—
1695C22—612no—
1696C22—848no—
1697C22—1248no—
1698C22—1296no—
1699C22—1236no—
1700C22—1236no—
1701C22—2448no—
1702C22—2448no—
1703C22—2496no—
1704C22—2448no—
1705C22#8720714yesdirect product factor
1706C22C23×D3×D4112yes—
1707C22C23×D3×D413yes—
1708C4—24no—
1709C4—212no—
1710C4—34no—
1711C4—312no—
1712C4—64no—
1713C4—64no—
1714C4C23×D3×D4112yes—
1715C4C23×D3×D413yes—
1716C4C26×D311yescharacteristic
1717C3C22×#358511yescharacteristic, complemented, Sylow
1718C2—212no—
1719C2—412no—
1720C2—44no—
1721C2—64no—
1722C2—612no—
1723C2—1212no—
1724C2—1212no—
1725C2C2×#8720716yesdirect product factor
1726C2C24×D3×D411yescharacteristic
subgroupG/H
centerC23C22×D3×D4
commutator, cosocleC3×C4C27
FrattiniC4C26×D3
FittingC22×C3×#577C2
socleC23×C3C23×D4
hypercenterC22×#577D3
hypocenterC3C22×#3585
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C22×#41 ◁ C22×#577

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#5968C2semidirect
2. C22×D3×H(5,𝔽2)C2semidirect
3. C2×#87207C2direct (N × H)
4. C22×#5778C2semidirect
5. C22×#5837C2semidirect
6. C22×#5762C2semidirect
7. C22×#5752C2semidirect
8. C22×#5774C2semidirect
9. C22×#5835C2semidirect
10. C22×#5769C2semidirect
11. C22×#5777C2semidirect
12. C22×#5768C2semidirect
13. C23×#914C2semidirect
14. C22×D3×AGL(1,ℤ/8)C2semidirect
15. C22×#5750C2semidirect
16. C22×C3×#577C2semidirect
18. C22×C3×2−1+4C22semidirect
19. C22×C3×H(5,𝔽2)C22semidirect
21. C2×#5968C22semidirect
23. C2×D3×H(5,𝔽2)C22semidirect
26. C22×#1009C22semidirect
27. C22×#1009C22semidirect
28. C22×#1009C22semidirect
29. C22×#1009C22semidirect
33. C22×D3×#41C22semidirect
34. C22×D3×#41C22semidirect
36. C22×#1007C22semidirect
38. C23×#239C22semidirect
40. C22×#1004C22semidirect
42. C23×D3×D4C22semidirect
43. C2×C3×#577C22semidirect
44. C22×C3×#137C22semidirect
45. C22×C3×AGL(1,ℤ/8)C22semidirect
46. C22×C3×#135C22semidirect
47. C23×C3×SD16C22semidirect
48. C22×C3×#131C22semidirect
49. C2×#5837C22semidirect
50. C2×#5835C22semidirect
51. C22×#949C22semidirect
52. C22×#949C22semidirect
53. C22×#950C22semidirect
54. C22×#950C22semidirect
55. C22×#948C22semidirect
56. C22×#942C22semidirect
57. C23×#215C22semidirect
58. C22×#932C22semidirect
59. C23×#213C22semidirect
60. #87207C22direct (N × H)
61. C2×#5778C22semidirect
62. C2×#5777C22semidirect
63. C2×#5774C22semidirect
64. C2×D3×AGL(1,ℤ/8)C22semidirect
65. C2×#5769C22semidirect
66. C2×#5768C22semidirect
67. C22×#918C22semidirect
68. C22×#918C22semidirect
69. C22×#919C22semidirect
70. C2×#5762C22semidirect
71. C22×#915C22semidirect
72. C22×#915C22semidirect
73. C22×#914C22semidirect
74. C22×#914C22semidirect
75. C22×#914C22semidirect
76. C22×#914C22semidirect
77. C22×#914C22semidirect
78. C22×#914C22semidirect
79. C22×#916C22semidirect
80. C22×D3×SD16C22semidirect
81. C22×#911C22semidirect
82. C22×#911C22semidirect
83. C22×D3×D8C22semidirect
84. C2×#5752C22semidirect
85. C2×#5750C22semidirect
86. C22×#908C22semidirect
87. C22×#908C22semidirect
88. C22×#907C22semidirect
89. C22×D3×M16C22semidirect
90. C22×#904C22semidirect
91. C23×D24C22semidirect
92. C22×#901C22semidirect
93. C23×ΓL(1,𝔽25)C22semidirect
100. C22×#577D3semidirect
112. C2×C3×2−1+4C23semidirect
114. C2×C3×H(5,𝔽2)C23semidirect
119. C22×C3×#41C23semidirect
121. C23×C3×Q8C23semidirect
127. #5968C23semidirect
129. D3×H(5,𝔽2)C23semidirect
136. C2×#1009C23semidirect
137. C2×#1009C23semidirect
138. C2×#1009C23semidirect
139. C2×#1009C23semidirect
146. C2×D3×#41C23semidirect
147. C2×D3×#41C23semidirect
150. C2×#1007C23semidirect
161. C22×#239C23semidirect
162. C22×#239C23semidirect
166. C22×D3×Q8C23semidirect
169. C2×#1004C23semidirect
190. C22×D3×D4C23semidirect
191. C22×D3×D4C23semidirect
199. C22×#235C23semidirect
204. C23×D12C23semidirect
209. C3×#577C23semidirect
210. C2×C3×#137C23semidirect
211. C2×C3×AGL(1,ℤ/8)C23semidirect
212. C2×C3×#135C23semidirect
213. C22×C3×Q16C23semidirect
214. C22×C3×SD16C23semidirect
215. C22×C3×SD16C23semidirect
216. C22×C3×SD16C23semidirect
217. C22×C3×SD16C23semidirect
218. C22×C3×D8C23semidirect
219. C2×C3×#131C23semidirect
220. C22×C3×M16C23semidirect
221. C23×C3×C8C23semidirect
222. #5837C23semidirect
223. #5835C23semidirect
224. C2×#950C23semidirect
225. C2×#950C23semidirect
226. C2×#949C23semidirect
227. C2×#949C23semidirect
228. C2×#948C23semidirect
229. C22×#216C23semidirect
230. C22×#216C23semidirect
231. C2×#942C23semidirect
232. C22×#215C23semidirect
233. C22×#215C23semidirect
234. C22×#215C23semidirect
235. C22×#215C23semidirect
236. C22×#214C23semidirect
237. C22×#214C23semidirect
238. C2×#932C23semidirect
239. C22×#213C23semidirect
240. C22×#213C23semidirect
241. C22×#213C23semidirect
242. C22×#213C23semidirect
243. C22×#208C23semidirect
244. C23×C3⋊C8C23semidirect
245. #5778C23semidirect
246. #5777C23semidirect
247. #5774C23semidirect
248. D3×AGL(1,ℤ/8)C23semidirect
249. #5769C23semidirect
250. #5768C23semidirect
251. C2×#919C23semidirect
252. C2×#918C23semidirect
253. C2×#918C23semidirect
254. #5762C23semidirect
255. C2×#916C23semidirect
256. C2×#915C23semidirect
257. C2×#915C23semidirect
258. C2×#914C23semidirect
259. C2×#914C23semidirect
260. C2×#914C23semidirect
261. C2×#914C23semidirect
262. C2×#914C23semidirect
263. C2×#914C23semidirect
264. C2×D3×SD16C23semidirect
265. C2×#911C23semidirect
266. C2×#911C23semidirect
267. C2×D3×D8C23semidirect
268. #5752C23semidirect
269. #5750C23semidirect
270. C2×#908C23semidirect
271. C2×#908C23semidirect
272. C2×#907C23semidirect
273. C2×D3×M16C23semidirect
274. C22×Dic12C23semidirect
275. C2×#904C23semidirect
276. C22×D24C23semidirect
277. C22×D24C23semidirect
278. C22×D24C23semidirect
279. C22×#204C23semidirect
280. C22×#204C23semidirect
281. C2×#901C23semidirect
284. C22×ΓL(1,𝔽25)C23semidirect
285. C22×ΓL(1,𝔽25)C23semidirect
286. C22×ΓL(1,𝔽25)C23semidirect
287. C22×D3×C8C23semidirect
292. C22×2−1+4C2×D3semidirect
303. C22×H(5,𝔽2)C2×D3semidirect
317. C2×#577C2×D3semidirect
329. C22×#137C2×D3semidirect
344. C22×AGL(1,ℤ/8)C2×D3semidirect
350. C22×#135C2×D3semidirect
353. C23×SD16C2×D3semidirect
361. C22×#131C2×D3semidirect
374. C3×2−1+4C24semidirect
376. C3×H(5,𝔽2)C24semidirect
384. C2×C3×#41C24semidirect
391. C22×C3×Q8C24semidirect
424. #1009C24semidirect
425. #1009C24semidirect
426. #1009C24semidirect
427. #1009C24semidirect
434. D3×#41C24semidirect
435. D3×#41C24semidirect
438. #1007C24semidirect
452. C2×#239C24semidirect
453. C2×#239C24semidirect
459. C2×D3×Q8C24semidirect
462. #1004C24semidirect
488. C2×D3×D4C24semidirect
489. C2×D3×D4C24semidirect
500. C2×#235C24semidirect
515. C22×D12C24semidirect
537. C3×#137C24semidirect
538. C3×AGL(1,ℤ/8)C24semidirect
539. C3×#135C24semidirect
540. C2×C3×Q16C24semidirect
541. C2×C3×SD16C24semidirect
542. C2×C3×SD16C24semidirect
543. C2×C3×SD16C24semidirect
544. C2×C3×SD16C24semidirect
545. C2×C3×D8C24semidirect
546. C3×#131C24semidirect
547. C2×C3×M16C24semidirect
550. C22×C3×C8C24semidirect
551. #950C24semidirect
552. #950C24semidirect
553. #949C24semidirect
554. #949C24semidirect
555. #948C24semidirect
556. C2×#216C24semidirect
557. C2×#216C24semidirect
558. #942C24semidirect
559. C2×#215C24semidirect
560. C2×#215C24semidirect
561. C2×#215C24semidirect
562. C2×#215C24semidirect
563. C2×#214C24semidirect
564. C2×#214C24semidirect
565. #932C24semidirect
566. C2×#213C24semidirect
567. C2×#213C24semidirect
568. C2×#213C24semidirect
569. C2×#213C24semidirect
570. C2×#208C24semidirect
573. C22×C3⋊C8C24semidirect
574. #919C24semidirect
575. #918C24semidirect
576. #918C24semidirect
577. #916C24semidirect
578. #915C24semidirect
579. #915C24semidirect
580. #914C24semidirect
581. #914C24semidirect
582. #914C24semidirect
583. #914C24semidirect
584. #914C24semidirect
585. D3×SD16C24semidirect
586. #911C24semidirect
587. #911C24semidirect
588. D3×D8C24semidirect
589. #908C24semidirect
590. #908C24semidirect
591. #907C24semidirect
592. D3×M16C24semidirect
593. C2×Dic12C24semidirect
594. #904C24semidirect
595. C2×D24C24semidirect
596. C2×D24C24semidirect
597. C2×D24C24semidirect
598. C2×#204C24semidirect
599. C2×#204C24semidirect
600. #901C24semidirect
603. C2×ΓL(1,𝔽25)C24semidirect
604. C2×ΓL(1,𝔽25)C24semidirect
605. C2×ΓL(1,𝔽25)C24semidirect
606. C2×D3×C8C24semidirect
614. C2×2−1+4C22×D3semidirect
631. C2×H(5,𝔽2)C22×D3semidirect
670. C22×#41C22×D3semidirect
676. C23×Q8C22×D3semidirect
709. #577C22×D3semidirect
721. C2×#137C22×D3semidirect
736. C2×AGL(1,ℤ/8)C22×D3semidirect
742. C2×#135C22×D3semidirect
746. C22×Q16C22×D3semidirect
756. C22×SD16C22×D3semidirect
757. C22×SD16C22×D3semidirect
758. C22×SD16C22×D3semidirect
759. C22×SD16C22×D3semidirect
768. C22×D8C22×D3semidirect
773. C2×#131C22×D3semidirect
781. C22×M16C22×D3semidirect
784. C23×C8C22×D3semidirect
815. C3×#41C25semidirect
824. C2×C3×Q8C25semidirect
873. #239C25semidirect
879. D3×Q8C25semidirect
903. D3×D4C25semidirect
914. #235C25semidirect
931. C2×D12C25semidirect
957. C3×Q16C25semidirect
958. C3×SD16C25semidirect
959. C3×SD16C25semidirect
960. C3×SD16C25semidirect
961. C3×D8C25semidirect
962. C3×M16C25semidirect
965. C2×C3×C8C25semidirect
966. #216C25semidirect
967. #216C25semidirect
968. #215C25semidirect
969. #215C25semidirect
970. #215C25semidirect
971. #214C25semidirect
972. #214C25semidirect
973. #213C25semidirect
974. #213C25semidirect
975. #213C25semidirect
976. #208C25semidirect
979. C2×C3⋊C8C25semidirect
980. Dic12C25semidirect
981. D24C25semidirect
982. D24C25semidirect
983. #204C25semidirect
984. #204C25semidirect
987. ΓL(1,𝔽25)C25semidirect
988. ΓL(1,𝔽25)C25semidirect
989. D3×C8C25semidirect
1003. 2−1+4C23×D3semidirect
1018. H(5,𝔽2)C23×D3semidirect
1068. C2×#41C23×D3semidirect
1086. C22×Q8C23×D3semidirect
1168. #137C23×D3semidirect
1181. AGL(1,ℤ/8)C23×D3semidirect
1187. #135C23×D3semidirect
1191. C2×Q16C23×D3semidirect
1201. C2×SD16C23×D3semidirect
1202. C2×SD16C23×D3semidirect
1203. C2×SD16C23×D3semidirect
1204. C2×SD16C23×D3semidirect
1213. C2×D8C23×D3semidirect
1217. #131C23×D3semidirect
1225. C2×M16C23×D3semidirect
1232. C22×C8C23×D3semidirect
1397. #41C24×D3semidirect
1419. C2×Q8C24×D3semidirect
1511. Q16C24×D3semidirect
1519. SD16C24×D3semidirect
1520. SD16C24×D3semidirect
1521. SD16C24×D3semidirect
1527. D8C24×D3semidirect
1533. M16C24×D3semidirect
1540. C2×C8C24×D3semidirect
1547. C22×C3#3585semidirect
1679. C2×C3C2×#3585semidirect
1705. C22#87207direct (N × H)
1717. C3C22×#3585semidirect
1725. C2C2×#87207direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#59682
C22×D3×H(5,𝔽2)2
C2×#872072
C22×#57782
C22×#58372
C22×#57622
C22×#57522
C22×#57742
C22×#58352
C22×#57692
C22×#57772
C22×#57682
C23×#9142
C22×D3×AGL(1,ℤ/8)2
C22×#57502
C22×C3×#5772
C22×#35853