Finite Group Databasebeta

← C2×#10594187 #11902425

Subgroups — C2×#10594187 #11902425

Order 1152.

4131 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#626C211yesmaximal, characteristic, complemented
2C22×#3799C211yesmaximal, characteristic, complemented
3C2×#64091C211yesmaximal, characteristic, complemented
4C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
5C2×C3×#878C211yesmaximal, characteristic, complemented
6C2×#63977C211yesmaximal, characteristic, complemented
7C2×#63974C211yesmaximal, characteristic, complemented
8C2×#63952C211yesmaximal, characteristic, complemented
9C2×#63910C211yesmaximal, characteristic, complemented
10C2×#63910C211yesmaximal, characteristic, complemented
11C2×#63909C211yesmaximal, characteristic, complemented
12C2×#63907C211yesmaximal, characteristic, complemented
13C2×#63904C211yesmaximal, characteristic, complemented
14C2×#63854C211yesmaximal, characteristic, complemented
15C2×#63850C211yesmaximal, characteristic, complemented
16#10594187C2116yesmaximal, direct product factor
17C2×#5630—31nomaximal
18C2×#5490—31nomaximal
19C24×C3⋊D3C2211yescharacteristic
20C24×C3×D3C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
23C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
24C23×C3×Dic3C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic, complemented
26C22×C3×C4×D3C2211yescharacteristic, complemented
27C22×C3×Dic6C2211yescharacteristic, complemented
28C22×#626—28no—
29C22×#626C2211yescharacteristic
30C22×#626C2211yescharacteristic
31C22×#626C2211yescharacteristic
32C22×#626C2211yescharacteristic
33C22×#626C2218yescomplemented
34C22×#626C2211yescharacteristic, complemented
35C22×#626C2211yescharacteristic, complemented
36C22×#624C2211yescharacteristic, complemented
37C22×#624C2211yescharacteristic, complemented
38C22×#624C2211yescharacteristic, complemented
39C2×#3799—28no—
40C2×#3799C2218yescomplemented
41C2×C32×C22⋊C4C2211yescharacteristic
42C2×#3752C2211yescharacteristic, complemented
43C2×#3752C2211yescharacteristic, complemented
44#64091C2218yescomplemented
45C2×C3×#217C2211yescharacteristic
46C2×C3×#217C2211yescharacteristic
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
50C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
51C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
52C3×D3×C22⋊C4C2218yescomplemented
53C3×#878C2218yescomplemented
54#63977C2218yescomplemented
55#63974C2218yescomplemented
56C2×#3724C2211yescharacteristic, complemented
57C2×#3722C2211yescharacteristic, complemented
58C2×#3722C2211yescharacteristic, complemented
59C2×#3722C2211yescharacteristic, complemented
60C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
61C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
62C2×Dic32C2211yescharacteristic, complemented
63#63952C2218yescomplemented
64#63910C2218yescomplemented
65#63910C2218yescomplemented
66#63909C2218yescomplemented
67#63907C2218yescomplemented
68#63904C2218yescomplemented
69#63854C2218yescomplemented
70#63850C2218yescomplemented
71C23×#67—31no—
72C22×#239—31no—
73C22×#235—31no—
74C23×D12—31no—
75C2×C3×C22⋊Q8—31no—
76C22×C3×C22⋊C4—31no—
77C2×#953—31no—
78C2×#947—31no—
79C2×#930—31no—
80C2×#929—31no—
81C2×C4×#67—31no—
82C2×C4×#67—31no—
83#5630—316no—
84C2×#895—31no—
85C2×#895—31no—
86C2×#895—31no—
87C2×#894—31no—
88C2×#894—31no—
89C2×#893—31no—
90C2×#885—31no—
91#5490—316no—
92C2×#884—31no—
93C2×#884—31no—
94C2×#883—31no—
95C2×#882—31no—
96C2×#882—31no—
97C2×#882—31no—
98C2×#882—61no—
99C2×#67⋊C4—31no—
100C2×D3×C22⋊C4—31no—
101C2×D3×C22⋊C4—31no—
102C2×D3×C22⋊C4D311yescharacteristic, complemented
103C2×#878D311yescharacteristic, complemented
104C24×C32C2311yescharacteristic
105C23×C3⋊D3—24no—
106C23×C3⋊D3—24no—
107C23×C3⋊D3—42no—
108C23×C3⋊D3C2311yescharacteristic
109C23×C3⋊D3C2311yescharacteristic
110C23×C3⋊D3C2314yes—
111C23×C3⋊D3C2311yescharacteristic
112C23×C3×D3—24no—
113C23×C3×D3—24no—
114C23×C3×D3—42no—
115C23×C3×D3C2311yescharacteristic
116C23×C3×D3C2314yes—
117C23×C3×D3C2311yescharacteristic
118C22×C32×C4C2311yescharacteristic
119C22×C32×C4C2311yescharacteristic
120C2×#638—24no—
121C2×#638C2314yes—
122C22×C3⋊Dic3C2311yescharacteristic
123C2×C4⋊(C3⋊D3)—24no—
124C2×C4⋊(C3⋊D3)—42no—
125C2×C4⋊(C3⋊D3)C2314yescomplemented
126C2×C4⋊(C3⋊D3)C2314yescomplemented
127C22×C3×Dic3—24no—
128C22×C3×Dic3C2314yes—
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2311yescharacteristic
135C2×C3×C4×D3—24no—
136C2×C3×C4×D3—42no—
137C2×C3×C4×D3C2314yescomplemented
138C2×C3×C4×D3C2314yescomplemented
139C2×C3×Dic6—24no—
140C2×C3×Dic6C2314yescomplemented
141C2×#626—24no—
142C2×#626—24no—
143C2×#626—24no—
144C2×#626—24no—
145C2×#626—232no—
146C2×#626—42no—
147C2×#626D418yescomplemented
148C2×#626C2314yes—
149C2×#626C2314yes—
150C2×#626C2314yes—
151C2×#626C2314yes—
152C2×#626C2314yescomplemented
153C2×#626C2314yescomplemented
154C2×#624—24no—
155C2×#624—24no—
156C2×#624—42no—
157C2×#624C2314yescomplemented
158C2×#624C2314yescomplemented
159C2×#624C2314yescomplemented
160#3799—232no—
161C32×C22⋊C4C2314yes—
162#3752C2314yescomplemented
163#3752C2314yescomplemented
164C3×#217C2314yes—
165C3×#217C2314yes—
166C3×(C2×D3)⋊C4C2314yescomplemented
167C3×(C2×D3)⋊C4C2314yescomplemented
168C3×C4⋊Dic3C2314yescomplemented
169C3×Dic3⋊C4C2314yescomplemented
170C3×Dic3⋊C4C2314yescomplemented
171#3724C2314yescomplemented
172#3722C2314yescomplemented
173#3722C2314yescomplemented
174#3722C2314yescomplemented
175(C2×D3)⋊Dic3C2314yescomplemented
176(C2×D3)⋊Dic3C2314yescomplemented
177Dic32C2314yescomplemented
178C2×#546—91noSylow
179C25×C3—31no—
180C24×D3—31no—
181C24×D3—31no—
182C24×D3—61no—
183C24×D3C2×D311yescharacteristic
184C22×C3×Q8—31no—
185C23×C3×C4—31no—
186C23×C3×C4—31no—
187C23×C3×C4—31no—
188C22×#67—31no—
189C22×#67—31no—
190C22×#67—31no—
191C22×#67—31no—
192C22×#67—31no—
193C22×#67—31no—
194C22×#67—31no—
195C22×#67—38no—
196C22×#67—31no—
197C22×#67—61no—
198C22×#67—68no—
199C23×Dic3C2×D311yescharacteristic
200C2×#239—38no—
201C2×#239—68no—
202C2×#235—38no—
203C2×#235—68no—
204C22×D12—31no—
205C22×D12—31no—
206C22×D12—31no—
207C22×D12—31no—
208C22×D12—38no—
209C22×D12—31no—
210C22×D12—31no—
211C22×D12—31no—
212C22×D12—31no—
213C22×D12—31no—
214C22×D12—31no—
215C22×D12—61no—
216C22×D12—61no—
217C22×D12—68no—
218C22×C4×D3—31no—
219C22×C4×D3—31no—
220C22×C4×D3—31no—
221C22×C4×D3—31no—
222C22×C4×D3—31no—
223C22×C4×D3—31no—
224C22×C4×D3C2×D311yescharacteristic, complemented
225C22×C4×D3C2×D311yescharacteristic, complemented
226C22×Dic6C2×D311yescharacteristic, complemented
227C3×C22⋊Q8—38no—
228C2×C3×C4⋊C4—31no—
229C2×C3×C4⋊C4—31no—
230C2×C3×C4⋊C4—31no—
231C2×C3×C22⋊C4—21no—
232C2×C3×C22⋊C4—31no—
233C2×C3×C22⋊C4—31no—
234C2×C3×C22⋊C4—31no—
235C2×C3×C22⋊C4—31no—
236C2×C3×C22⋊C4—38no—
237C2×C3×C22⋊C4C2×D311yescharacteristic
238C2×C3×C22⋊C4C2×D311yescharacteristic
239#953—38no—
240C2×#217—31no—
241C2×#217—31no—
242C2×#217C2×D311yescharacteristic
243C2×#217C2×D311yescharacteristic
244#947—38no—
245#930—38no—
246#929—38no—
247C4×#67—38no—
248C4×#67—38no—
249C2×(C2×D3)⋊C4—31no—
250C2×(C2×D3)⋊C4—31no—
251C2×(C2×D3)⋊C4—31no—
252C2×(C2×D3)⋊C4—31no—
253C2×(C2×D3)⋊C4—31no—
254C2×(C2×D3)⋊C4—31no—
255C2×(C2×D3)⋊C4—31no—
256C2×(C2×D3)⋊C4—31no—
257C2×(C2×D3)⋊C4—31no—
258C2×(C2×D3)⋊C4—31no—
259C2×(C2×D3)⋊C4—31no—
260C2×(C2×D3)⋊C4—31no—
261C2×(C2×D3)⋊C4—61no—
262C2×(C2×D3)⋊C4—61no—
263C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
264C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
265C2×C4⋊Dic3C2×D311yescharacteristic, complemented
266C2×Dic3⋊C4—31no—
267C2×Dic3⋊C4—31no—
268C2×Dic3⋊C4C2×D311yescharacteristic, complemented
269C2×Dic3⋊C4C2×D311yescharacteristic, complemented
270C2×C4×Dic3—31no—
271C2×C4×Dic3—31no—
272#895—38no—
273#895—38no—
274#895—38no—
275#894—38no—
276#894—38no—
277#893—38no—
278#885—38no—
279#884—38no—
280#884—38no—
281#883—38no—
282#882—38no—
283#882—38no—
284#882—38no—
285#882—68no—
286#67⋊C4—38no—
287D3×C22⋊C4—38no—
288D3×C22⋊C4—38no—
289D3×C22⋊C4C2×D318yescomplemented
290#878C2×D318yescomplemented
291C23×C32—22no—
292C23×C32—22no—
293C23×C32#4114yescomplemented
294C23×C32C2412yes—
295C23×C32C2411yescharacteristic
296C22×C3⋊D3—22no—
297C22×C3⋊D3—22no—
298C22×C3⋊D3—22no—
299C22×C3⋊D3—22no—
300C22×C3⋊D3—22no—
301C22×C3⋊D3—22no—
302C22×C3⋊D3—22no—
303C22×C3⋊D3—28no—
304C22×C3⋊D3—22no—
305C22×C3⋊D3—28no—
306C22×C3⋊D3—44no—
307C22×C3⋊D3—416no—
308C22×C3⋊D3C2×D414yes—
309C22×C3⋊D3C2412yes—
310C22×C3⋊D3C2412yes—
311C22×C3⋊D3C2412yes—
312C22×C3×D3—22no—
313C22×C3×D3—22no—
314C22×C3×D3—22no—
315C22×C3×D3—22no—
316C22×C3×D3—28no—
317C22×C3×D3—22no—
318C22×C3×D3—28no—
319C22×C3×D3—44no—
320C22×C3×D3—416no—
321C22×C3×D3C2×D414yes—
322C22×C3×D3C2412yes—
323C22×C3×D3C2412yes—
324C2×C32×C4—22no—
325C2×C32×C4—22no—
326C2×C32×C4C2412yes—
327C2×C32×C4C2412yes—
328#638—28no—
329C2×C3⋊Dic3—22no—
330C2×C3⋊Dic3C2412yes—
331C4⋊(C3⋊D3)—28no—
332C4⋊(C3⋊D3)—44no—
333C2×C3×Dic3—22no—
334C2×C3×Dic3—22no—
335C2×C3×Dic3—22no—
336C2×C3×Dic3—22no—
337C2×C3×Dic3—22no—
338C2×C3×Dic3—28no—
339C2×C3×Dic3C2×D414yes—
340C2×C3×Dic3C2412yes—
341C2×C3×Dic3C2412yes—
342C2×C3×Dic3C2412yes—
343C2×C3×Dic3C2412yes—
344C2×C3×Dic3C2412yes—
345C2×C3×Dic3C2412yes—
346C3×C4×D3—28no—
347C3×C4×D3—44no—
348C3×Dic6—28no—
349#626—28no—
350#626—28no—
351#626—28no—
352#626—28no—
353#626—44no—
354#626C2×D4116yescomplemented
355#624—28no—
356#624—28no—
357#624—44no—
358C22×#41—91no—
359C23×D4—91no—
360#546—916no—
361C2×#124—91no—
362C2×#123—91no—
363C2×#123—91no—
364C2×C22⋊Q8—31no—
365C2×#121—91no—
366C2×#121—91no—
367C2×#121—91no—
368C2×#120—91no—
369C2×#120—91no—
370C2×C4×D4—91no—
371C2×C4×D4—91no—
372C22×C22⋊C4—31no—
373C22×C22⋊C4—91no—
374C24×C3—21no—
375C24×C3—31no—
376C24×C3—31no—
377C24×C3—34no—
378C24×C3—64no—
379C24×C3—64no—
380C24×C3—122no—
381C24×C3C22×D311yescharacteristic
382C24×C3C22×D311yescharacteristic
383C23×D3—24no—
384C23×D3—24no—
385C23×D3—31no—
386C23×D3—31no—
387C23×D3—31no—
388C23×D3—31no—
389C23×D3—31no—
390C23×D3—31no—
391C23×D3—34no—
392C23×D3—34no—
393C23×D3—42no—
394C23×D3—61no—
395C23×D3—61no—
396C23×D3—64no—
397C23×D3—61no—
398C23×D3—64no—
399C23×D3—64no—
400C23×D3—64no—
401C23×D3—64no—
402C23×D3—124no—
403C23×D3—124no—
404C23×D3—122no—
405C23×D3—122no—
406C23×D3—124no—
407C23×D3C22×D311yescharacteristic
408C23×D3C22×D314yes—
409C23×D3C22×D311yescharacteristic
410C2×C3×Q8—34no—
411C2×C3×Q8—64no—
412C22×C3×C4—21no—
413C22×C3×C4—21no—
414C22×C3×C4—31no—
415C22×C3×C4—31no—
416C22×C3×C4—31no—
417C22×C3×C4—31no—
418C22×C3×C4—31no—
419C22×C3×C4—31no—
420C22×C3×C4—34no—
421C22×C3×C4—34no—
422C22×C3×C4—34no—
423C22×C3×C4—64no—
424C22×C3×C4—64no—
425C22×C3×C4—122no—
426C22×C3×C4C22×D311yescharacteristic
427C22×C3×C4C22×D311yescharacteristic
428C22×C3×C4C22×D311yescharacteristic
429C22×C3×C4C22×D311yescharacteristic
430C2×#67—34no—
431C2×#67—34no—
432C2×#67—38no—
433C2×#67—34no—
434C2×#67—34no—
435C2×#67—34no—
436C2×#67—34no—
437C2×#67—34no—
438C2×#67—34no—
439C2×#67—64no—
440C2×#67—632no—
441C2×#67—64no—
442C2×#67—64no—
443C2×#67—64no—
444C2×#67—64no—
445C2×#67—64no—
446C2×#67—64no—
447C2×#67—124no—
448C2×#67—122no—
449C22×Dic3—24no—
450C22×Dic3—31no—
451C22×Dic3—31no—
452C22×Dic3—61no—
453C22×Dic3C22×D314yes—
454C22×Dic3C22×D311yescharacteristic
455C22×Dic3C22×D311yescharacteristic
456C22×Dic3C22×D311yescharacteristic
457C22×Dic3C22×D311yescharacteristic
458C22×Dic3C22×D311yescharacteristic
459C22×Dic3C22×D311yescharacteristic
460#239—632no—
461#235—632no—
462C2×D12—38no—
463C2×D12—34no—
464C2×D12—34no—
465C2×D12—34no—
466C2×D12—34no—
467C2×D12—34no—
468C2×D12—34no—
469C2×D12—34no—
470C2×D12—34no—
471C2×D12—34no—
472C2×D12—34no—
473C2×D12—64no—
474C2×D12—64no—
475C2×D12—632no—
476C2×D12—64no—
477C2×D12—64no—
478C2×D12—64no—
479C2×D12—64no—
480C2×D12—64no—
481C2×D12—64no—
482C2×D12—124no—
483C2×D12—122no—
484C2×D12—122no—
485C2×D12—124no—
486C2×D12—122no—
487C2×C4×D3—24no—
488C2×C4×D3—34no—
489C2×C4×D3—34no—
490C2×C4×D3—34no—
491C2×C4×D3—34no—
492C2×C4×D3—34no—
493C2×C4×D3—34no—
494C2×C4×D3—42no—
495C2×C4×D3—64no—
496C2×C4×D3—64no—
497C2×C4×D3—64no—
498C2×C4×D3—64no—
499C2×C4×D3—122no—
500C2×C4×D3—122no—
501C2×C4×D3C22×D314yescomplemented
502C2×C4×D3C22×D314yescomplemented
503C2×Dic6—24no—
504C2×Dic6C22×D314yescomplemented
505C3×C4⋊C4—34no—
506C3×C4⋊C4—34no—
507C3×C4⋊C4—34no—
508C3×C22⋊C4—24no—
509C3×C22⋊C4—34no—
510C3×C22⋊C4—34no—
511C3×C22⋊C4—34no—
512C3×C22⋊C4—34no—
513C3×C22⋊C4C22×D314yes—
514C3×C22⋊C4C22×D314yes—
515#217—34no—
516#217—34no—
517#217C22×D314yes—
518#217C22×D314yes—
519(C2×D3)⋊C4—34no—
520(C2×D3)⋊C4—34no—
521(C2×D3)⋊C4—34no—
522(C2×D3)⋊C4—34no—
523(C2×D3)⋊C4—34no—
524(C2×D3)⋊C4—34no—
525(C2×D3)⋊C4—34no—
526(C2×D3)⋊C4—34no—
527(C2×D3)⋊C4—34no—
528(C2×D3)⋊C4—34no—
529(C2×D3)⋊C4—34no—
530(C2×D3)⋊C4—34no—
531(C2×D3)⋊C4—64no—
532(C2×D3)⋊C4—64no—
533(C2×D3)⋊C4C22×D314yescomplemented
534(C2×D3)⋊C4C22×D314yescomplemented
535C4⋊Dic3C22×D314yescomplemented
536Dic3⋊C4—34no—
537Dic3⋊C4—34no—
538Dic3⋊C4C22×D314yescomplemented
539Dic3⋊C4C22×D314yescomplemented
540C4×Dic3—34no—
541C4×Dic3—34no—
542C22×C32—28no—
543C22×C32—22no—
544C22×C32—22no—
545C22×C32C22×D412yes—
546C22×C32C2×#4112yes—
547C22×C32C2×#4114yescomplemented
548C22×C32H(5,𝔽2)12yes—
549C22×C32C2511yescharacteristic
550C2×C3⋊D3—22no—
551C2×C3⋊D3—28no—
552C2×C3⋊D3—22no—
553C2×C3⋊D3—22no—
554C2×C3⋊D3—22no—
555C2×C3⋊D3—22no—
556C2×C3⋊D3—22no—
557C2×C3⋊D3—22no—
558C2×C3⋊D3—22no—
559C2×C3⋊D3—416no—
560C2×C3⋊D3—44no—
561C2×C3⋊D3—44no—
562C2×C3⋊D3C22×D414yes—
563C2×C3×D3—28no—
564C2×C3×D3—22no—
565C2×C3×D3—22no—
566C2×C3×D3—22no—
567C2×C3×D3—22no—
568C2×C3×D3—22no—
569C2×C3×D3—416no—
570C2×C3×D3—44no—
571C2×C3×D3C22×D414yes—
572C32×C4—22no—
573C32×C4—22no—
574C3⋊Dic3—22no—
575C3×Dic3—22no—
576C3×Dic3—22no—
577C3×Dic3—22no—
578C3×Dic3—22no—
579C3×Dic3—22no—
580C3×Dic3C22×D414yes—
581C25—31no—
582C25—91no—
583C2×#41—98no—
584C2×#41—188no—
585C22×Q8—31no—
586C22×D4—91no—
587C22×D4—91no—
588C22×D4—91no—
589C22×D4—91no—
590C22×D4—91no—
591C22×D4—98no—
592C22×D4—91no—
593C22×D4—91no—
594C22×D4—91no—
595C22×D4—91no—
596C22×D4—188no—
597C23×C4—31no—
598C23×C4—31no—
599C23×C4—31no—
600C23×C4—91no—
601C23×C4—91no—
602C23×C4—91no—
603#124—98no—
604#123—98no—
605#123—98no—
606C22⋊Q8—38no—
607#121—98no—
608#121—98no—
609#121—98no—
610#120—98no—
611#120—98no—
612C4×D4—98no—
613C4×D4—98no—
614C2×C4⋊C4—31no—
615C2×C4⋊C4—31no—
616C2×C4⋊C4—31no—
617C2×C4⋊C4—91no—
618C2×C22⋊C4—31no—
619C2×C22⋊C4—31no—
620C2×C22⋊C4—31no—
621C2×C22⋊C4—31no—
622C2×C22⋊C4—38no—
623C2×C22⋊C4—98no—
624C2×C22⋊C4—91no—
625C2×C22⋊C4—91no—
626C2×C22⋊C4—91no—
627C2×C22⋊C4—91no—
628C2×C22⋊C4—91no—
629C2×C22⋊C4—91no—
630C2×C22⋊C4—91no—
631C2×C22⋊C4D3211yescharacteristic
632C2×C42—91no—
633C23×C3—22no—
634C23×C3—22no—
635C23×C3—22no—
636C23×C3—22no—
637C23×C3—22no—
638C23×C3—21no—
639C23×C3—24no—
640C23×C3—34no—
641C23×C3—32no—
642C23×C3—32no—
643C23×C3—42no—
644C23×C3—42no—
645C23×C3—68no—
646C23×C3—62no—
647C23×C3—62no—
648C23×C3—62no—
649C23×C3—62no—
650C23×C3—68no—
651C23×C3—62no—
652C23×C3—124no—
653C23×C3—1216no—
654C23×C3#23514yescomplemented
655C23×C3#23914yescomplemented
656C23×C3C23×D312yes—
657C23×C3C23×D312yes—
658C23×C3C23×D311yescharacteristic
659C23×C3C23×D311yescharacteristic
660C22×D3—22no—
661C22×D3—22no—
662C22×D3—22no—
663C22×D3—28no—
664C22×D3—22no—
665C22×D3—22no—
666C22×D3—28no—
667C22×D3—34no—
668C22×D3—34no—
669C22×D3—32no—
670C22×D3—32no—
671C22×D3—32no—
672C22×D3—32no—
673C22×D3—32no—
674C22×D3—32no—
675C22×D3—44no—
676C22×D3—416no—
677C22×D3—64no—
678C22×D3—62no—
679C22×D3—62no—
680C22×D3—62no—
681C22×D3—68no—
682C22×D3—68no—
683C22×D3—62no—
684C22×D3—62no—
685C22×D3—62no—
686C22×D3—62no—
687C22×D3—64no—
688C22×D3—62no—
689C22×D3—62no—
690C22×D3—68no—
691C22×D3—62no—
692C22×D3—62no—
693C22×D3—62no—
694C22×D3—62no—
695C22×D3—62no—
696C22×D3—62no—
697C22×D3—62no—
698C22×D3—62no—
699C22×D3—68no—
700C22×D3—62no—
701C22×D3—62no—
702C22×D3—128no—
703C22×D3—122no—
704C22×D3—122no—
705C22×D3—122no—
706C22×D3—128no—
707C22×D3—122no—
708C22×D3—122no—
709C22×D3—122no—
710C22×D3—122no—
711C22×D3—124no—
712C22×D3—124no—
713C22×D3—1216no—
714C22×D3—1216no—
715C22×D3—128no—
716C22×D3—1232no—
717C22×D3D3×D414yes—
718C22×D3C23×D312yes—
719C22×D3C23×D312yes—
720C3×Q8—68no—
721C2×C3×C4—22no—
722C2×C3×C4—22no—
723C2×C3×C4—22no—
724C2×C3×C4—22no—
725C2×C3×C4—22no—
726C2×C3×C4—22no—
727C2×C3×C4—34no—
728C2×C3×C4—32no—
729C2×C3×C4—32no—
730C2×C3×C4—32no—
731C2×C3×C4—32no—
732C2×C3×C4—32no—
733C2×C3×C4—32no—
734C2×C3×C4—42no—
735C2×C3×C4—42no—
736C2×C3×C4—68no—
737C2×C3×C4—68no—
738C2×C3×C4—62no—
739C2×C3×C4—62no—
740C2×C3×C4—62no—
741C2×C3×C4—62no—
742C2×C3×C4—62no—
743C2×C3×C4—124no—
744C2×C3×C4C23×D312yes—
745C2×C3×C4C23×D312yes—
746C2×C3×C4C23×D312yes—
747C2×C3×C4C23×D312yes—
748#67—316no—
749#67—68no—
750#67—68no—
751#67—68no—
752#67—68no—
753#67—68no—
754#67—68no—
755#67—128no—
756#67—124no—
757C2×Dic3—22no—
758C2×Dic3—22no—
759C2×Dic3—22no—
760C2×Dic3—22no—
761C2×Dic3—22no—
762C2×Dic3—28no—
763C2×Dic3—32no—
764C2×Dic3—32no—
765C2×Dic3—62no—
766C2×Dic3—62no—
767C2×Dic3—62no—
768C2×Dic3—122no—
769C2×Dic3D3×D414yes—
770C2×Dic3C23×D312yes—
771C2×Dic3C23×D312yes—
772C2×Dic3C23×D312yes—
773C2×Dic3C23×D312yes—
774C2×Dic3C23×D312yes—
775C2×Dic3C23×D312yes—
776D12—316no—
777D12—68no—
778D12—68no—
779D12—68no—
780D12—68no—
781D12—68no—
782D12—68no—
783D12—128no—
784D12—124no—
785D12—124no—
786D12—128no—
787D12—124no—
788C4×D3—28no—
789C4×D3—44no—
790C4×D3—68no—
791C4×D3—68no—
792C4×D3—68no—
793C4×D3—68no—
794C4×D3—124no—
795C4×D3—124no—
796Dic6—28no—
797C2×C32—24no—
798C2×C32#54614yescomplemented
799C2×C32C23×D411yescharacteristic
800C2×C32C22×#4111yescharacteristic
801C2×C32C2×H(5,𝔽2)11yescharacteristic
802C3⋊D3—24no—
803C3⋊D3—42no—
804C3⋊D3—42no—
805C3×D3—24no—
806C3×D3—42no—
807C24—31no—
808C24—31no—
809C24—34no—
810C24—64no—
811C24—64no—
812C24—91no—
813C24—91no—
814C24—91no—
815C24—94no—
816C24—122no—
817C24—184no—
818C24—184no—
819C24—362no—
820C24C2×D3211yescharacteristic
821#41—1832no—
822C2×Q8—34no—
823C2×Q8—64no—
824C2×D4—94no—
825C2×D4—98no—
826C2×D4—94no—
827C2×D4—94no—
828C2×D4—94no—
829C2×D4—94no—
830C2×D4—94no—
831C2×D4—94no—
832C2×D4—94no—
833C2×D4—94no—
834C2×D4—184no—
835C2×D4—184no—
836C2×D4—1832no—
837C2×D4—184no—
838C2×D4—184no—
839C2×D4—184no—
840C2×D4—184no—
841C2×D4—362no—
842C2×D4—362no—
843C22×C4—31no—
844C22×C4—34no—
845C22×C4—31no—
846C22×C4—31no—
847C22×C4—31no—
848C22×C4—31no—
849C22×C4—31no—
850C22×C4—34no—
851C22×C4—34no—
852C22×C4—64no—
853C22×C4—64no—
854C22×C4—94no—
855C22×C4—94no—
856C22×C4—94no—
857C22×C4—91no—
858C22×C4—122no—
859C22×C4—184no—
860C22×C4—184no—
861C22×C4—362no—
862C22×C4C2×D3211yescharacteristic
863C22×C4C2×D3211yescharacteristic
864C4⋊C4—34no—
865C4⋊C4—34no—
866C4⋊C4—34no—
867C4⋊C4—94no—
868C22⋊C4—34no—
869C22⋊C4—34no—
870C22⋊C4—34no—
871C22⋊C4—34no—
872C22⋊C4—94no—
873C22⋊C4—94no—
874C22⋊C4—94no—
875C22⋊C4—94no—
876C22⋊C4—94no—
877C22⋊C4—94no—
878C22⋊C4—94no—
879C22⋊C4C2×D3214yes—
880C42—94no—
881C22×C3—22no—
882C22×C3—22no—
883C22×C3—22no—
884C22×C3—22no—
885C22×C3—28no—
886C22×C3—28no—
887C22×C3—22no—
888C22×C3—24no—
889C22×C3—22no—
890C22×C3—22no—
891C22×C3—21no—
892C22×C3—34no—
893C22×C3—42no—
894C22×C3—42no—
895C22×C3—48no—
896C22×C3—62no—
897C22×C3—62no—
898C22×C3—68no—
899C22×C3—62no—
900C22×C3—62no—
901C22×C3—62no—
902C22×C3—1216no—
903C22×C3—124no—
904C22×C3C2×#23512yes—
905C22×C3C2×#23514yescomplemented
906C22×C3C2×D3×D412yes—
907C22×C3C2×D3×D412yes—
908C22×C3#100412yes—
909C22×C3C2×#23912yes—
910C22×C3C2×#23914yescomplemented
911C22×C3#100912yes—
912C22×C3C24×D311yescharacteristic
913C22×C3C24×D311yescharacteristic
914C2×D3—22no—
915C2×D3—22no—
916C2×D3—28no—
917C2×D3—22no—
918C2×D3—22no—
919C2×D3—22no—
920C2×D3—34no—
921C2×D3—34no—
922C2×D3—416no—
923C2×D3—44no—
924C2×D3—64no—
925C2×D3—62no—
926C2×D3—62no—
927C2×D3—62no—
928C2×D3—62no—
929C2×D3—68no—
930C2×D3—68no—
931C2×D3—64no—
932C2×D3—62no—
933C2×D3—62no—
934C2×D3—62no—
935C2×D3—62no—
936C2×D3—62no—
937C2×D3—62no—
938C2×D3—62no—
939C2×D3—62no—
940C2×D3—62no—
941C2×D3—62no—
942C2×D3—62no—
943C2×D3—62no—
944C2×D3—122no—
945C2×D3—122no—
946C2×D3—128no—
947C2×D3—122no—
948C2×D3—122no—
949C2×D3—122no—
950C2×D3—122no—
951C2×D3—122no—
952C2×D3—1216no—
953C2×D3—1216no—
954C2×D3—128no—
955C2×D3—1232no—
956C2×D3—124no—
957C2×D3—124no—
958C2×D3—124no—
959C2×D3—124no—
960C2×D3—244no—
961C2×D3C2×D3×D414yes—
962C3×C4—22no—
963C3×C4—22no—
964C3×C4—22no—
965C3×C4—22no—
966C3×C4—34no—
967C3×C4—42no—
968C3×C4—42no—
969C3×C4—62no—
970C3×C4—62no—
971C3×C4—62no—
972C3×C4—62no—
973C3×C4—62no—
974Dic3—22no—
975Dic3—22no—
976Dic3—22no—
977Dic3—22no—
978Dic3—22no—
979Dic3—62no—
980Dic3—62no—
981Dic3—122no—
982Dic3C2×D3×D414yes—
983C32C2×#54611yescharacteristic, complemented, Sylow
984C23—22no—
985C23—22no—
986C23—34no—
987C23—32no—
988C23—32no—
989C23—68no—
990C23—62no—
991C23—62no—
992C23—62no—
993C23—68no—
994C23—62no—
995C23—62no—
996C23—94no—
997C23—92no—
998C23—92no—
999C23—92no—
1000C23—124no—
1001C23—1216no—
1002C23—188no—
1003C23—182no—
1004C23—182no—
1005C23—182no—
1006C23—182no—
1007C23—188no—
1008C23—182no—
1009C23—182no—
1010C23—182no—
1011C23—182no—
1012C23—364no—
1013C23—3616no—
1014C23#379914yescomplemented
1015C23C22×D3212yes—
1016C23C22×D3211yescharacteristic
1017Q8—68no—
1018D4—916no—
1019D4—188no—
1020D4—188no—
1021D4—188no—
1022D4—188no—
1023D4—188no—
1024D4—188no—
1025D4—364no—
1026D4—364no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—34no—
1030C2×C4—32no—
1031C2×C4—32no—
1032C2×C4—32no—
1033C2×C4—32no—
1034C2×C4—32no—
1035C2×C4—32no—
1036C2×C4—68no—
1037C2×C4—68no—
1038C2×C4—62no—
1039C2×C4—62no—
1040C2×C4—62no—
1041C2×C4—62no—
1042C2×C4—62no—
1043C2×C4—92no—
1044C2×C4—124no—
1045C2×C4—188no—
1046C2×C4—188no—
1047C2×C4—182no—
1048C2×C4—364no—
1049C2×C4C22×D3212yes—
1050C2×C4C22×D3212yes—
1051C2×C3—24no—
1052C2×C3—24no—
1053C2×C3—21no—
1054C2×C3—21no—
1055C2×C3—21no—
1056C2×C3—24no—
1057C2×C3—44no—
1058C2×C3—64no—
1059C2×C3—122no—
1060C2×C3#549014yescomplemented
1061C2×C3#563014yescomplemented
1062C2×C3C22×#23511yescharacteristic
1063C2×C3C22×D3×D411yescharacteristic
1064C2×C3C22×D3×D411yescharacteristic
1065C2×C3C2×#100411yescharacteristic
1066C2×C3C22×#23911yescharacteristic
1067C2×C3C2×#100911yescharacteristic
1068D3—24no—
1069D3—42no—
1070D3—64no—
1071D3—64no—
1072D3—124no—
1073D3—124no—
1074D3—122no—
1075D3—122no—
1076D3—122no—
1077D3—122no—
1078D3—242no—
1079C22—22no—
1080C22—22no—
1081C22—28no—
1082C22—34no—
1083C22—62no—
1084C22—62no—
1085C22—68no—
1086C22—62no—
1087C22—62no—
1088C22—62no—
1089C22—94no—
1090C22—1216no—
1091C22—124no—
1092C22—182no—
1093C22—182no—
1094C22—188no—
1095C22—182no—
1096C22—182no—
1097C22—182no—
1098C22—182no—
1099C22—182no—
1100C22—182no—
1101C22—3616no—
1102C22—364no—
1103C22—364no—
1104C22C2×#379912yes—
1105C22C2×#379914yescomplemented
1106C22D32×D412yes—
1107C22#6431412yes—
1108C22C23×D3211yescharacteristic
1109C4—22no—
1110C4—22no—
1111C4—34no—
1112C4—62no—
1113C4—62no—
1114C4—62no—
1115C4—62no—
1116C4—62no—
1117C4—182no—
1118C3—21no—
1119C3C2×#549011yescharacteristic, complemented
1120C3C2×#563011yescharacteristic, complemented
1121C2—24no—
1122C2—64no—
1123C2—122no—
1124C2—184no—
1125C2—362no—
1126C2—362no—
1127C2#1059418714yesdirect product factor
1128C2C22×#379911yescharacteristic
1129C2C2×D32×D411yescharacteristic
1130C2C2×#6431411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×#626C2semidirect
2. C22×#3799C2semidirect
3. C2×#64091C2semidirect
4. C2×C3×D3×C22⋊C4C2semidirect
5. C2×C3×#878C2semidirect
6. C2×#63977C2semidirect
7. C2×#63974C2semidirect
8. C2×#63952C2semidirect
9. C2×#63910C2semidirect
10. C2×#63910C2semidirect
11. C2×#63909C2semidirect
12. C2×#63907C2semidirect
13. C2×#63904C2semidirect
14. C2×#63854C2semidirect
15. C2×#63850C2semidirect
16. #10594187C2direct (N × H)
22. C22×C4⋊(C3⋊D3)C22semidirect
23. C22×C4⋊(C3⋊D3)C22semidirect
25. C22×C3×C4×D3C22semidirect
26. C22×C3×C4×D3C22semidirect
27. C22×C3×Dic6C22semidirect
33. C22×#626C22semidirect
34. C22×#626C22semidirect
35. C22×#626C22semidirect
36. C22×#624C22semidirect
37. C22×#624C22semidirect
38. C22×#624C22semidirect
40. C2×#3799C22semidirect
42. C2×#3752C22semidirect
43. C2×#3752C22semidirect
44. #64091C22semidirect
47. C2×C3×(C2×D3)⋊C4C22semidirect
48. C2×C3×(C2×D3)⋊C4C22semidirect
49. C2×C3×C4⋊Dic3C22semidirect
50. C2×C3×Dic3⋊C4C22semidirect
51. C2×C3×Dic3⋊C4C22semidirect
52. C3×D3×C22⋊C4C22semidirect
53. C3×#878C22semidirect
54. #63977C22semidirect
55. #63974C22semidirect
56. C2×#3724C22semidirect
57. C2×#3722C22semidirect
58. C2×#3722C22semidirect
59. C2×#3722C22semidirect
60. C2×(C2×D3)⋊Dic3C22semidirect
61. C2×(C2×D3)⋊Dic3C22semidirect
62. C2×Dic32C22semidirect
63. #63952C22semidirect
64. #63910C22semidirect
65. #63910C22semidirect
66. #63909C22semidirect
67. #63907C22semidirect
68. #63904C22semidirect
69. #63854C22semidirect
70. #63850C22semidirect
102. C2×D3×C22⋊C4D3semidirect
103. C2×#878D3semidirect
125. C2×C4⋊(C3⋊D3)C23semidirect
126. C2×C4⋊(C3⋊D3)C23semidirect
137. C2×C3×C4×D3C23semidirect
138. C2×C3×C4×D3C23semidirect
140. C2×C3×Dic6C23semidirect
147. C2×#626D4semidirect
152. C2×#626C23semidirect
153. C2×#626C23semidirect
157. C2×#624C23semidirect
158. C2×#624C23semidirect
159. C2×#624C23semidirect
162. #3752C23semidirect
163. #3752C23semidirect
166. C3×(C2×D3)⋊C4C23semidirect
167. C3×(C2×D3)⋊C4C23semidirect
168. C3×C4⋊Dic3C23semidirect
169. C3×Dic3⋊C4C23semidirect
170. C3×Dic3⋊C4C23semidirect
171. #3724C23semidirect
172. #3722C23semidirect
173. #3722C23semidirect
174. #3722C23semidirect
175. (C2×D3)⋊Dic3C23semidirect
176. (C2×D3)⋊Dic3C23semidirect
177. Dic32C23semidirect
224. C22×C4×D3C2×D3semidirect
225. C22×C4×D3C2×D3semidirect
226. C22×Dic6C2×D3semidirect
263. C2×(C2×D3)⋊C4C2×D3semidirect
264. C2×(C2×D3)⋊C4C2×D3semidirect
265. C2×C4⋊Dic3C2×D3semidirect
268. C2×Dic3⋊C4C2×D3semidirect
269. C2×Dic3⋊C4C2×D3semidirect
289. D3×C22⋊C4C2×D3semidirect
290. #878C2×D3semidirect
293. C23×C32#41semidirect
354. #626C2×D4semidirect
501. C2×C4×D3C22×D3semidirect
502. C2×C4×D3C22×D3semidirect
504. C2×Dic6C22×D3semidirect
533. (C2×D3)⋊C4C22×D3semidirect
534. (C2×D3)⋊C4C22×D3semidirect
535. C4⋊Dic3C22×D3semidirect
538. Dic3⋊C4C22×D3semidirect
539. Dic3⋊C4C22×D3semidirect
547. C22×C32C2×#41semidirect
654. C23×C3#235semidirect
655. C23×C3#239semidirect
798. C2×C32#546semidirect
905. C22×C3C2×#235semidirect
910. C22×C3C2×#239semidirect
983. C32C2×#546semidirect
1014. C23#3799semidirect
1060. C2×C3#5490semidirect
1061. C2×C3#5630semidirect
1105. C22C2×#3799semidirect
1119. C3C2×#5490semidirect
1120. C3C2×#5630semidirect
1127. C2#10594187direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#6262
C22×#37992
C2×#640912
C2×C3×D3×C22⋊C42
C2×C3×#8782
C2×#639772
C2×#639742
C2×#639522
C2×#639102
C2×#639092
C2×#639072
C2×#639042
C2×#638542
C2×#638502
#105941872
C2×#56303
C2×#54903