Finite Group Databasebeta

← C2×#10595296 #11902447

Subgroups — C2×#10595296 #11902447

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
1C22×#3811C211yesmaximal, characteristic, complemented
2C22×#3804C211yesmaximal, characteristic, complemented
3C2×#64146C211yesmaximal, characteristic, complemented
4C2×C3×#939C211yesmaximal, characteristic, complemented
5C2×C3×#938C211yesmaximal, characteristic, complemented
6C2×#63983C211yesmaximal, characteristic, complemented
7C2×#63974C211yesmaximal, characteristic, complemented
8C2×#63969C211yesmaximal, characteristic, complemented
9C2×#63959C211yesmaximal, characteristic, complemented
10C2×#63958C211yesmaximal, characteristic, complemented
11C2×#63952C211yesmaximal, characteristic, complemented
12#10595296C2116yesmaximal, direct product factor
13C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
14C2×#63904C211yesmaximal, characteristic, complemented
15C2×#63895C211yesmaximal, characteristic, complemented
16C2×#63854C211yesmaximal, characteristic, complemented
17C2×#5612—31nomaximal
18C2×#5610—31nomaximal
19C24×C3⋊D3C2211yescharacteristic
20C23×D32C2211yescharacteristic
21C22×C32×D4C2211yescharacteristic, complemented
22C22×#638C2211yescharacteristic
23C22×#638C2211yescharacteristic, complemented
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic
26C22×C3×#67C2211yescharacteristic, complemented
27C22×C3×#67C2211yescharacteristic, complemented
28C23×C3×Dic3C2211yescharacteristic, complemented
29C22×C3×C4×D3C2211yescharacteristic, complemented
30C2×#3811—28no—
31C2×#3811C2218yescomplemented
32C22×#627C2211yescharacteristic, complemented
33C22×#626C2211yescharacteristic
34C22×#626C2211yescharacteristic
35C22×#624C2211yescharacteristic
36C22×#624C2211yescharacteristic, complemented
37C22×#624C2211yescharacteristic, complemented
38C2×#3804—28no—
39C2×#3804C2218yescomplemented
40C22×D3×Dic3C2211yescharacteristic, complemented
41C2×#3757C2211yescharacteristic, complemented
42#64146C2218yescomplemented
43C2×#3752C2211yescharacteristic
44C2×#3752C2211yescharacteristic, complemented
45C2×C3×#217C2211yescharacteristic, complemented
46C2×C3×#217C2211yescharacteristic, complemented
47C2×C3×#217C2211yescharacteristic, complemented
48C3×#939C2218yescomplemented
49C3×#938C2218yescomplemented
50C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
51C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
52C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
53#63983C2218yescomplemented
54#63974C2218yescomplemented
55#63969C2218yescomplemented
56C2×#3724C2211yescharacteristic, complemented
57C2×Dic3⋊Dic3C2211yescharacteristic, complemented
58C2×#3722C2211yescharacteristic
59C2×#3722C2211yescharacteristic
60C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
61C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
62C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
63#63959C2218yescomplemented
64#63958C2218yescomplemented
65C2×Dic32C2211yescharacteristic, complemented
66#63952C2218yescomplemented
67D3×(C2×D3)⋊C4C2218yescomplemented
68#63904C2218yescomplemented
69#63895C2218yescomplemented
70#63854C2218yescomplemented
71C22×#237—31no—
72C22×D3×D4—31no—
73C22×D3×D4—31no—
74C22×#235—31no—
75C2×C3×#121—31no—
76C2×C3×#121—31no—
77C2×#939D311yescharacteristic, complemented
78C2×#938—31no—
79C2×#938D311yescharacteristic, complemented
80C2×#937—31no—
81C2×#937—31no—
82C2×#937—31no—
83C2×#937—31no—
84C2×#937—61no—
85C2×#936—31no—
86C2×#935—31no—
87C2×C4×#67—31no—
88C2×C4×#67—31no—
89C22×(C2×D3)⋊C4—31no—
90#5612—316no—
91#5610—316no—
92C2×#897—31no—
93C2×#896—31no—
94C2×#894—31no—
95C2×#893—31no—
96C2×#885—31no—
97C2×#884—31no—
98C2×#883—31no—
99C2×#883—31no—
100C2×#67⋊C4—31no—
101C2×D3×C22⋊C4—31no—
102C2×D3×C22⋊C4—31no—
103C2×D3×C22⋊C4—31no—
104C24×C32C2311yescharacteristic
105C24×C32C2311yescharacteristic
106C23×C3⋊D3—24no—
107C23×C3⋊D3—24no—
108C23×C3⋊D3—42no—
109C23×C3⋊D3C2314yes—
110C23×C3⋊D3C2311yescharacteristic
111C23×C3⋊D3C2311yescharacteristic
112C23×C3×D3C2311yescharacteristic
113C23×C3×D3C2311yescharacteristic
114C22×D32—24no—
115C22×D32—24no—
116C22×D32—42no—
117C22×D32C2314yes—
118C2×C32×D4—42no—
119C2×C32×D4C2314yescomplemented
120C22×C32×C4C2311yescharacteristic
121C2×#638—24no—
122C2×#638—24no—
123C2×#638C2314yes—
124C2×#638C2314yescomplemented
125C22×C3⋊Dic3C2311yescharacteristic
126C22×C3⋊Dic3C2311yescharacteristic
127C2×C3×#67—24no—
128C2×C3×#67—24no—
129C2×C3×#67—24no—
130C2×C3×#67—42no—
131C2×C3×#67C2314yes—
132C2×C3×#67C2314yes—
133C2×C3×#67C2314yescomplemented
134C2×C3×#67C2314yescomplemented
135C22×C3×Dic3—24no—
136C22×C3×Dic3C2311yescharacteristic
137C22×C3×Dic3C2311yescharacteristic
138C22×C3×Dic3C2311yescharacteristic
139C22×C3×Dic3C2311yescharacteristic
140C22×C3×Dic3C2311yescharacteristic
141C22×C3×Dic3C2311yescharacteristic
142C22×C3×Dic3C2314yescomplemented
143C2×C3×C4×D3—42no—
144C2×C3×C4×D3C2314yescomplemented
145#3811—232no—
146C2×#627—24no—
147C2×#627C2314yescomplemented
148C2×#626—24no—
149C2×#626D418yescomplemented
150C2×#626C2314yes—
151C2×#626C2314yes—
152C2×#624—24no—
153C2×#624—24no—
154C2×#624—42no—
155C2×#624C2314yes—
156C2×#624C2314yescomplemented
157C2×#624C2314yescomplemented
158#3804—232no—
159C2×D3×Dic3—24no—
160C2×D3×Dic3C2314yescomplemented
161#3757C2314yescomplemented
162#3752C2314yes—
163#3752C2314yescomplemented
164C3×#217C2314yescomplemented
165C3×#217C2314yescomplemented
166C3×#217C2314yescomplemented
167C3×(C2×D3)⋊C4C2314yescomplemented
168C3×C4⋊Dic3C2314yescomplemented
169C3×Dic3⋊C4C2314yescomplemented
170#3724C2314yescomplemented
171Dic3⋊Dic3C2314yescomplemented
172#3722C2314yes—
173#3722C2314yes—
174(C2×D3)⋊Dic3C2314yescomplemented
175(C2×D3)⋊Dic3C2314yescomplemented
176(C2×D3)⋊Dic3C2314yescomplemented
177Dic32C2314yescomplemented
178C2×#546—91noSylow
179C24×D3—31no—
180C24×D3—31no—
181C24×D3—31no—
182C24×D3—31no—
183C24×D3—61no—
184C22×C3×D4—21no—
185C22×C3×D4—31no—
186C22×C3×D4—31no—
187C22×C3×D4—31no—
188C22×C3×D4—31no—
189C22×C3×D4C2×D311yescharacteristic, complemented
190C22×C3×D4C2×D311yescharacteristic, complemented
191C23×C3×C4—31no—
192C23×C3×C4—31no—
193C22×#67—31no—
194C22×#67—31no—
195C22×#67—31no—
196C22×#67—31no—
197C22×#67—31no—
198C22×#67—31no—
199C22×#67—61no—
200C22×#67—61no—
201C22×#67C2×D311yescharacteristic
202C22×#67C2×D311yescharacteristic
203C22×#67C2×D311yescharacteristic, complemented
204C22×#67C2×D311yescharacteristic, complemented
205C23×Dic3—31no—
206C23×Dic3C2×D311yescharacteristic, complemented
207C2×#237—38no—
208C2×#237—68no—
209C2×D3×D4—38no—
210C2×D3×D4—38no—
211C2×D3×D4—68no—
212C2×D3×D4—68no—
213C2×#235—38no—
214C2×#235—68no—
215C22×D12—31no—
216C22×D12—31no—
217C22×C4×D3—31no—
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×Dic6—31no—
226C22×Dic6—31no—
227C3×#121—38no—
228C3×#121—38no—
229C2×C3×C4⋊C4—31no—
230C2×C3×C4⋊C4—31no—
231C2×C3×C22⋊C4—31no—
232C2×C3×C22⋊C4—31no—
233C2×C3×C22⋊C4—31no—
234C2×C3×C22⋊C4—31no—
235C2×#217—31no—
236C2×#217—31no—
237C2×#217—31no—
238C2×#217—31no—
239C2×#217—31no—
240C2×#217—61no—
241C2×#217C2×D311yescharacteristic, complemented
242C2×#217C2×D311yescharacteristic, complemented
243C2×#217C2×D311yescharacteristic, complemented
244#939C2×D318yescomplemented
245#938—38no—
246#938C2×D318yescomplemented
247#937—38no—
248#937—38no—
249#937—38no—
250#937—38no—
251#937—68no—
252#936—38no—
253#935—38no—
254C4×#67—38no—
255C4×#67—38no—
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—31no—
262C2×(C2×D3)⋊C4—31no—
263C2×(C2×D3)⋊C4—31no—
264C2×(C2×D3)⋊C4—31no—
265C2×(C2×D3)⋊C4—31no—
266C2×(C2×D3)⋊C4—31no—
267C2×(C2×D3)⋊C4—38no—
268C2×(C2×D3)⋊C4—61no—
269C2×(C2×D3)⋊C4—61no—
270C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
271C2×C4⋊Dic3—31no—
272C2×C4⋊Dic3C2×D311yescharacteristic, complemented
273C2×Dic3⋊C4—31no—
274C2×Dic3⋊C4—31no—
275C2×Dic3⋊C4—31no—
276C2×Dic3⋊C4C2×D311yescharacteristic, complemented
277C2×C4×Dic3—31no—
278C2×C4×Dic3—31no—
279#897—38no—
280#896—38no—
281#894—38no—
282#893—38no—
283#885—38no—
284#884—38no—
285#883—38no—
286#883—38no—
287#67⋊C4—38no—
288D3×C22⋊C4—38no—
289D3×C22⋊C4—38no—
290D3×C22⋊C4—38no—
291C23×C32—22no—
292C23×C32—22no—
293C23×C32—22no—
294C23×C32—22no—
295C23×C32—22no—
296C23×C32—22no—
297C23×C32C2412yes—
298C23×C32C2412yes—
299C23×C32C2411yescharacteristic
300C22×C3⋊D3—22no—
301C22×C3⋊D3—22no—
302C22×C3⋊D3—22no—
303C22×C3⋊D3—22no—
304C22×C3⋊D3—28no—
305C22×C3⋊D3—28no—
306C22×C3⋊D3—44no—
307C22×C3⋊D3—416no—
308C22×C3⋊D3C2×D414yes—
309C22×C3⋊D3#4114yescomplemented
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—22no—
317C22×C3×D3C2×D414yes—
318C22×C3×D3C2412yes—
319C22×C3×D3C2412yes—
320C2×D32—28no—
321C2×D32—28no—
322C2×D32—44no—
323C2×D32—416no—
324C32×D4—44no—
325C2×C32×C4—22no—
326C2×C32×C4C2412yes—
327#638—28no—
328#638—28no—
329C2×C3⋊Dic3—22no—
330C2×C3⋊Dic3—22no—
331C2×C3⋊Dic3C2412yes—
332C2×C3⋊Dic3C2412yes—
333C3×#67—28no—
334C3×#67—28no—
335C3×#67—28no—
336C3×#67—44no—
337C2×C3×Dic3—22no—
338C2×C3×Dic3—22no—
339C2×C3×Dic3—22no—
340C2×C3×Dic3—22no—
341C2×C3×Dic3—22no—
342C2×C3×Dic3—28no—
343C2×C3×Dic3C2×D414yes—
344C2×C3×Dic3C2412yes—
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2412yes—
349C2×C3×Dic3C2412yes—
350C3×C4×D3—44no—
351#627—28no—
352#626—28no—
353#626C2×D4116yescomplemented
354#624—28no—
355#624—28no—
356#624—44no—
357D3×Dic3—28no—
358C22×#41—91no—
359C23×D4—91no—
360#546—916no—
361C2×#124—91no—
362C2×#123—91no—
363C2×#123—91no—
364C2×C22⋊Q8—91no—
365C2×#121—31no—
366C2×#121—31no—
367C2×#121—91no—
368C2×#120—91no—
369C2×#120—91no—
370C2×C4×D4—91no—
371C2×C4×D4—91no—
372C22×C22⋊C4—91no—
373C22×C22⋊C4—91no—
374C24×C3—21no—
375C24×C3—21no—
376C24×C3—31no—
377C24×C3—31no—
378C24×C3C22×D311yescharacteristic
379C24×C3C22×D311yescharacteristic
380C24×C3C22×D311yescharacteristic
381C24×C3C22×D311yescharacteristic
382C23×D3—31no—
383C23×D3—31no—
384C23×D3—31no—
385C23×D3—31no—
386C23×D3—34no—
387C23×D3—34no—
388C23×D3—34no—
389C23×D3—34no—
390C23×D3—61no—
391C23×D3—61no—
392C23×D3—64no—
393C23×D3—64no—
394C23×D3—64no—
395C23×D3—64no—
396C23×D3—64no—
397C23×D3—64no—
398C23×D3—64no—
399C23×D3—64no—
400C23×D3—64no—
401C23×D3—124no—
402C23×D3—124no—
403C23×D3—122no—
404C23×D3—122no—
405C23×D3—122no—
406C23×D3—122no—
407C23×D3—124no—
408C23×D3C22×D311yescharacteristic
409C23×D3C22×D311yescharacteristic
410C2×C3×D4—24no—
411C2×C3×D4—34no—
412C2×C3×D4—34no—
413C2×C3×D4—34no—
414C2×C3×D4—34no—
415C2×C3×D4—42no—
416C2×C3×D4—42no—
417C2×C3×D4—44no—
418C2×C3×D4—64no—
419C2×C3×D4—64no—
420C2×C3×D4—64no—
421C2×C3×D4—122no—
422C2×C3×D4C22×D314yescomplemented
423C2×C3×D4C22×D314yescomplemented
424C22×C3×C4—21no—
425C22×C3×C4—31no—
426C22×C3×C4—31no—
427C22×C3×C4—31no—
428C22×C3×C4—31no—
429C22×C3×C4—31no—
430C22×C3×C4—31no—
431C22×C3×C4—34no—
432C22×C3×C4—34no—
433C22×C3×C4—64no—
434C22×C3×C4—122no—
435C22×C3×C4C22×D311yescharacteristic
436C22×C3×C4C22×D311yescharacteristic
437C2×#67—24no—
438C2×#67—24no—
439C2×#67—24no—
440C2×#67—34no—
441C2×#67—34no—
442C2×#67—34no—
443C2×#67—34no—
444C2×#67—38no—
445C2×#67—34no—
446C2×#67—34no—
447C2×#67—42no—
448C2×#67—64no—
449C2×#67—64no—
450C2×#67—64no—
451C2×#67—64no—
452C2×#67—64no—
453C2×#67—64no—
454C2×#67—64no—
455C2×#67—124no—
456C2×#67—124no—
457C2×#67C22×D314yes—
458C2×#67C22×D314yes—
459C2×#67C22×D314yescomplemented
460C2×#67C22×D314yescomplemented
461C22×Dic3—24no—
462C22×Dic3—31no—
463C22×Dic3—31no—
464C22×Dic3—31no—
465C22×Dic3—31no—
466C22×Dic3—34no—
467C22×Dic3—61no—
468C22×Dic3—61no—
469C22×Dic3—64no—
470C22×Dic3C22×D311yescharacteristic
471C22×Dic3C22×D311yescharacteristic
472C22×Dic3C22×D311yescharacteristic
473C22×Dic3C22×D311yescharacteristic
474C22×Dic3C22×D311yescharacteristic
475C22×Dic3C22×D311yescharacteristic
476C22×Dic3C22×D314yescomplemented
477#237—632no—
478D3×D4—632no—
479D3×D4—632no—
480#235—632no—
481C2×D12—38no—
482C2×D12—34no—
483C2×D12—34no—
484C2×D12—64no—
485C2×C4×D3—34no—
486C2×C4×D3—34no—
487C2×C4×D3—34no—
488C2×C4×D3—34no—
489C2×C4×D3—34no—
490C2×C4×D3—34no—
491C2×C4×D3—34no—
492C2×C4×D3—42no—
493C2×C4×D3—64no—
494C2×C4×D3—64no—
495C2×C4×D3—64no—
496C2×C4×D3—64no—
497C2×C4×D3—64no—
498C2×C4×D3—122no—
499C2×C4×D3—122no—
500C2×C4×D3C22×D314yescomplemented
501C2×Dic6—34no—
502C2×Dic6—34no—
503C2×Dic6—64no—
504C2×Dic6—64no—
505C3×C4⋊C4—34no—
506C3×C4⋊C4—34no—
507C3×C22⋊C4—34no—
508C3×C22⋊C4—34no—
509C3×C22⋊C4—34no—
510C3×C22⋊C4—34no—
511#217—34no—
512#217—34no—
513#217—34no—
514#217—34no—
515#217—34no—
516#217—64no—
517#217C22×D314yescomplemented
518#217C22×D314yescomplemented
519#217C22×D314yescomplemented
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
534C4⋊Dic3—34no—
535C4⋊Dic3C22×D314yescomplemented
536Dic3⋊C4—34no—
537Dic3⋊C4—34no—
538Dic3⋊C4—34no—
539Dic3⋊C4C22×D314yescomplemented
540C4×Dic3—34no—
541C4×Dic3—34no—
542C22×C32—22no—
543C22×C32—22no—
544C22×C32—22no—
545C22×C32—22no—
546C22×C32—22no—
547C22×C32—22no—
548C22×C32—44no—
549C22×C32—44no—
550C22×C32C22×D412yes—
551C22×C32C2×#4112yes—
552C22×C32H(5,𝔽2)12yes—
553C22×C32C2511yescharacteristic
554C2×C3⋊D3—28no—
555C2×C3⋊D3—28no—
556C2×C3⋊D3—22no—
557C2×C3⋊D3—22no—
558C2×C3⋊D3—22no—
559C2×C3⋊D3—22no—
560C2×C3⋊D3—416no—
561C2×C3⋊D3C22×D414yes—
562C2×C3⋊D3C2×#4114yescomplemented
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—44no—
570C2×C3×D3C22×D414yes—
571D32—416no—
572C32×C4—22no—
573C3⋊Dic3—22no—
574C3⋊Dic3—22no—
575C3×Dic3—22no—
576C3×Dic3—22no—
577C3×Dic3—22no—
578C3×Dic3—22no—
579C3×Dic3—22no—
580C3×Dic3C22×D414yes—
581C25—91no—
582C25—91no—
583C2×#41—98no—
584C2×#41—188no—
585C22×Q8—91no—
586C22×D4—31no—
587C22×D4—31no—
588C22×D4—31no—
589C22×D4—31no—
590C22×D4—91no—
591C22×D4—91no—
592C22×D4—98no—
593C22×D4—91no—
594C22×D4—91no—
595C22×D4—188no—
596C22×D4D3211yescharacteristic, complemented
597C23×C4—31no—
598C23×C4—31no—
599C23×C4—91no—
600C23×C4—91no—
601C23×C4—91no—
602C23×C4—91no—
603#124—98no—
604#123—98no—
605#123—98no—
606C22⋊Q8—98no—
607#121—38no—
608#121—38no—
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—91no—
617C2×C4⋊C4—91no—
618C2×C22⋊C4—31no—
619C2×C22⋊C4—31no—
620C2×C22⋊C4—31no—
621C2×C22⋊C4—31no—
622C2×C22⋊C4—98no—
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⋊C4—91no—
632C2×C42—91no—
633C23×C3—24no—
634C23×C3—22no—
635C23×C3—22no—
636C23×C3—22no—
637C23×C3—22no—
638C23×C3—22no—
639C23×C3—22no—
640C23×C3—22no—
641C23×C3—22no—
642C23×C3—22no—
643C23×C3—22no—
644C23×C3—22no—
645C23×C3—22no—
646C23×C3—22no—
647C23×C3—22no—
648C23×C3—21no—
649C23×C3—34no—
650C23×C3—32no—
651C23×C3—32no—
652C23×C3—42no—
653C23×C3—42no—
654C23×C3—42no—
655C23×C3—42no—
656C23×C3—42no—
657C23×C3—62no—
658C23×C3—62no—
659C23×C3—62no—
660C23×C3—62no—
661C23×C3—62no—
662C23×C3C23×D312yes—
663C23×C3C23×D312yes—
664C23×C3C23×D312yes—
665C23×C3C23×D312yes—
666C23×C3C23×D311yescharacteristic
667C23×C3C23×D311yescharacteristic
668C22×D3—22no—
669C22×D3—22no—
670C22×D3—22no—
671C22×D3—22no—
672C22×D3—22no—
673C22×D3—34no—
674C22×D3—34no—
675C22×D3—34no—
676C22×D3—34no—
677C22×D3—32no—
678C22×D3—32no—
679C22×D3—32no—
680C22×D3—32no—
681C22×D3—64no—
682C22×D3—64no—
683C22×D3—62no—
684C22×D3—62no—
685C22×D3—68no—
686C22×D3—68no—
687C22×D3—68no—
688C22×D3—68no—
689C22×D3—68no—
690C22×D3—68no—
691C22×D3—68no—
692C22×D3—62no—
693C22×D3—62no—
694C22×D3—62no—
695C22×D3—62no—
696C22×D3—62no—
697C22×D3—62no—
698C22×D3—62no—
699C22×D3—62no—
700C22×D3—68no—
701C22×D3—128no—
702C22×D3—128no—
703C22×D3—122no—
704C22×D3—122no—
705C22×D3—122no—
706C22×D3—122no—
707C22×D3—124no—
708C22×D3—124no—
709C22×D3—1216no—
710C22×D3—1216no—
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×D4—44no—
721C3×D4—44no—
722C3×D4—48no—
723C3×D4—68no—
724C3×D4—68no—
725C3×D4—68no—
726C3×D4—124no—
727C2×C3×C4—22no—
728C2×C3×C4—22no—
729C2×C3×C4—22no—
730C2×C3×C4—34no—
731C2×C3×C4—32no—
732C2×C3×C4—32no—
733C2×C3×C4—32no—
734C2×C3×C4—32no—
735C2×C3×C4—32no—
736C2×C3×C4—32no—
737C2×C3×C4—42no—
738C2×C3×C4—68no—
739C2×C3×C4—62no—
740C2×C3×C4—62no—
741C2×C3×C4—62no—
742C2×C3×C4—62no—
743C2×C3×C4—62no—
744C2×C3×C4—124no—
745C2×C3×C4C23×D312yes—
746C2×C3×C4C23×D312yes—
747#67—28no—
748#67—28no—
749#67—28no—
750#67—316no—
751#67—44no—
752#67—68no—
753#67—68no—
754#67—68no—
755#67—68no—
756#67—68no—
757#67—128no—
758#67—128no—
759C2×Dic3—22no—
760C2×Dic3—22no—
761C2×Dic3—22no—
762C2×Dic3—22no—
763C2×Dic3—22no—
764C2×Dic3—28no—
765C2×Dic3—32no—
766C2×Dic3—32no—
767C2×Dic3—32no—
768C2×Dic3—32no—
769C2×Dic3—62no—
770C2×Dic3—62no—
771C2×Dic3—68no—
772C2×Dic3—62no—
773C2×Dic3—62no—
774C2×Dic3—62no—
775C2×Dic3—62no—
776C2×Dic3—122no—
777C2×Dic3—122no—
778C2×Dic3D3×D414yes—
779C2×Dic3C23×D312yes—
780C2×Dic3C23×D312yes—
781C2×Dic3C23×D312yes—
782C2×Dic3C23×D312yes—
783C2×Dic3C23×D312yes—
784C2×Dic3C23×D312yes—
785D12—316no—
786D12—68no—
787C4×D3—44no—
788C4×D3—68no—
789C4×D3—68no—
790C4×D3—68no—
791C4×D3—68no—
792C4×D3—68no—
793C4×D3—124no—
794C4×D3—124no—
795Dic6—68no—
796Dic6—68no—
797C2×C32—42no—
798C2×C32—42no—
799C2×C32#54614yescomplemented
800C2×C32C23×D411yescharacteristic
801C2×C32C22×#4111yescharacteristic
802C2×C32C2×H(5,𝔽2)11yescharacteristic
803C3⋊D3—24no—
804C3⋊D3—24no—
805C3×D3—24no—
806C3×D3—42no—
807C24—31no—
808C24—31no—
809C24—94no—
810C24—91no—
811C24—91no—
812C24—94no—
813C24—184no—
814C24—184no—
815C24—184no—
816C24—184no—
817C24—362no—
818C24—362no—
819C24C2×D3211yescharacteristic
820C24C2×D3211yescharacteristic
821#41—1832no—
822C2×Q8—94no—
823C2×Q8—184no—
824C2×D4—34no—
825C2×D4—34no—
826C2×D4—34no—
827C2×D4—34no—
828C2×D4—42no—
829C2×D4—64no—
830C2×D4—64no—
831C2×D4—64no—
832C2×D4—94no—
833C2×D4—98no—
834C2×D4—94no—
835C2×D4—94no—
836C2×D4—94no—
837C2×D4—122no—
838C2×D4—184no—
839C2×D4—1832no—
840C2×D4—184no—
841C2×D4—184no—
842C2×D4C2×D3214yescomplemented
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—64no—
852C22×C4—94no—
853C22×C4—94no—
854C22×C4—94no—
855C22×C4—94no—
856C22×C4—91no—
857C22×C4—91no—
858C22×C4—122no—
859C22×C4—184no—
860C22×C4—184no—
861C22×C4—184no—
862C22×C4—362no—
863C22×C4C2×D3211yescharacteristic
864C4⋊C4—34no—
865C4⋊C4—34no—
866C4⋊C4—94no—
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⋊C4—94no—
880C42—94no—
881C22×C3—24no—
882C22×C3—22no—
883C22×C3—22no—
884C22×C3—22no—
885C22×C3—22no—
886C22×C3—22no—
887C22×C3—22no—
888C22×C3—22no—
889C22×C3—22no—
890C22×C3—22no—
891C22×C3—22no—
892C22×C3—22no—
893C22×C3—22no—
894C22×C3—22no—
895C22×C3—22no—
896C22×C3—22no—
897C22×C3—21no—
898C22×C3—34no—
899C22×C3—42no—
900C22×C3—42no—
901C22×C3—42no—
902C22×C3—42no—
903C22×C3—42no—
904C22×C3—48no—
905C22×C3—44no—
906C22×C3—44no—
907C22×C3—44no—
908C22×C3—44no—
909C22×C3—62no—
910C22×C3—62no—
911C22×C3—68no—
912C22×C3—62no—
913C22×C3—62no—
914C22×C3—62no—
915C22×C3—84no—
916C22×C3—124no—
917C22×C3C2×D3×D412yes—
918C22×C3C2×D3×D412yes—
919C22×C3#100412yes—
920C22×C3#100412yes—
921C22×C3D3×#4112yes—
922C22×C3D3×#4112yes—
923C22×C3C24×D311yescharacteristic
924C22×C3C24×D311yescharacteristic
925C2×D3—22no—
926C2×D3—22no—
927C2×D3—28no—
928C2×D3—22no—
929C2×D3—22no—
930C2×D3—22no—
931C2×D3—34no—
932C2×D3—34no—
933C2×D3—34no—
934C2×D3—34no—
935C2×D3—44no—
936C2×D3—64no—
937C2×D3—64no—
938C2×D3—62no—
939C2×D3—62no—
940C2×D3—62no—
941C2×D3—62no—
942C2×D3—62no—
943C2×D3—62no—
944C2×D3—62no—
945C2×D3—62no—
946C2×D3—68no—
947C2×D3—68no—
948C2×D3—68no—
949C2×D3—68no—
950C2×D3—122no—
951C2×D3—122no—
952C2×D3—122no—
953C2×D3—122no—
954C2×D3—128no—
955C2×D3—128no—
956C2×D3—1216no—
957C2×D3—1216no—
958C2×D3—1216no—
959C2×D3—1216no—
960C2×D3—1232no—
961C2×D3C2×D3×D414yes—
962C3×C4—22no—
963C3×C4—22no—
964C3×C4—34no—
965C3×C4—42no—
966C3×C4—62no—
967C3×C4—62no—
968C3×C4—62no—
969C3×C4—62no—
970C3×C4—62no—
971Dic3—22no—
972Dic3—22no—
973Dic3—22no—
974Dic3—22no—
975Dic3—22no—
976Dic3—62no—
977Dic3—62no—
978Dic3—62no—
979Dic3—62no—
980Dic3—122no—
981Dic3—122no—
982Dic3C2×D3×D414yes—
983C32C2×#54611yescharacteristic, complemented, Sylow
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—34no—
991C23—32no—
992C23—32no—
993C23—62no—
994C23—62no—
995C23—62no—
996C23—62no—
997C23—62no—
998C23—94no—
999C23—94no—
1000C23—92no—
1001C23—92no—
1002C23—188no—
1003C23—188no—
1004C23—188no—
1005C23—188no—
1006C23—182no—
1007C23—182no—
1008C23—182no—
1009C23—182no—
1010C23—364no—
1011C23—3616no—
1012C23—364no—
1013C23—3616no—
1014C23C22×D3212yes—
1015C23C22×D3212yes—
1016C23C22×D3211yescharacteristic
1017Q8—188no—
1018D4—44no—
1019D4—68no—
1020D4—68no—
1021D4—68no—
1022D4—916no—
1023D4—124no—
1024D4—188no—
1025D4—188no—
1026D4—188no—
1027C2×C4—22no—
1028C2×C4—34no—
1029C2×C4—32no—
1030C2×C4—32no—
1031C2×C4—32no—
1032C2×C4—32no—
1033C2×C4—32no—
1034C2×C4—32no—
1035C2×C4—68no—
1036C2×C4—62no—
1037C2×C4—62no—
1038C2×C4—62no—
1039C2×C4—62no—
1040C2×C4—62no—
1041C2×C4—92no—
1042C2×C4—92no—
1043C2×C4—124no—
1044C2×C4—188no—
1045C2×C4—188no—
1046C2×C4—188no—
1047C2×C4—182no—
1048C2×C4—182no—
1049C2×C4—364no—
1050C2×C4C22×D3212yes—
1051C2×C3—21no—
1052C2×C3—21no—
1053C2×C3—21no—
1054C2×C3—24no—
1055C2×C3—44no—
1056C2×C3—42no—
1057C2×C3—42no—
1058C2×C3—42no—
1059C2×C3—42no—
1060C2×C3—64no—
1061C2×C3—82no—
1062C2×C3—122no—
1063C2×C3#561014yescomplemented
1064C2×C3#561214yescomplemented
1065C2×C3C22×D3×D411yescharacteristic
1066C2×C3C22×D3×D411yescharacteristic
1067C2×C3C2×#100411yescharacteristic
1068C2×C3C2×#100411yescharacteristic
1069C2×C3C2×D3×#4111yescharacteristic
1070C2×C3C2×D3×#4111yescharacteristic
1071D3—24no—
1072D3—42no—
1073D3—64no—
1074D3—64no—
1075D3—64no—
1076D3—64no—
1077D3—124no—
1078D3—124no—
1079C22—22no—
1080C22—22no—
1081C22—22no—
1082C22—22no—
1083C22—22no—
1084C22—22no—
1085C22—34no—
1086C22—44no—
1087C22—44no—
1088C22—62no—
1089C22—62no—
1090C22—68no—
1091C22—62no—
1092C22—62no—
1093C22—62no—
1094C22—94no—
1095C22—94no—
1096C22—124no—
1097C22—182no—
1098C22—182no—
1099C22—182no—
1100C22—182no—
1101C22—188no—
1102C22—188no—
1103C22—3616no—
1104C22—3616no—
1105C22D32×D412yes—
1106C22#6431212yes—
1107C22#6433012yes—
1108C22C23×D3211yescharacteristic
1109C4—22no—
1110C4—34no—
1111C4—62no—
1112C4—62no—
1113C4—62no—
1114C4—62no—
1115C4—62no—
1116C4—182no—
1117C4—182no—
1118C3—21no—
1119C3C2×#561011yescharacteristic, complemented
1120C3C2×#561211yescharacteristic, complemented
1121C2—42no—
1122C2—42no—
1123C2—64no—
1124C2—122no—
1125C2—184no—
1126C2—184no—
1127C2#1059529614yesdirect product factor
1128C2C2×D32×D411yescharacteristic
1129C2C2×#6431211yescharacteristic
1130C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#3811C2semidirect
2. C22×#3804C2semidirect
3. C2×#64146C2semidirect
4. C2×C3×#939C2semidirect
5. C2×C3×#938C2semidirect
6. C2×#63983C2semidirect
7. C2×#63974C2semidirect
8. C2×#63969C2semidirect
9. C2×#63959C2semidirect
10. C2×#63958C2semidirect
11. C2×#63952C2semidirect
12. #10595296C2direct (N × H)
13. C2×D3×(C2×D3)⋊C4C2semidirect
14. C2×#63904C2semidirect
15. C2×#63895C2semidirect
16. C2×#63854C2semidirect
21. C22×C32×D4C22semidirect
23. C22×#638C22semidirect
26. C22×C3×#67C22semidirect
27. C22×C3×#67C22semidirect
28. C23×C3×Dic3C22semidirect
29. C22×C3×C4×D3C22semidirect
31. C2×#3811C22semidirect
32. C22×#627C22semidirect
36. C22×#624C22semidirect
37. C22×#624C22semidirect
39. C2×#3804C22semidirect
40. C22×D3×Dic3C22semidirect
41. C2×#3757C22semidirect
42. #64146C22semidirect
44. C2×#3752C22semidirect
45. C2×C3×#217C22semidirect
46. C2×C3×#217C22semidirect
47. C2×C3×#217C22semidirect
48. C3×#939C22semidirect
49. C3×#938C22semidirect
50. C2×C3×(C2×D3)⋊C4C22semidirect
51. C2×C3×C4⋊Dic3C22semidirect
52. C2×C3×Dic3⋊C4C22semidirect
53. #63983C22semidirect
54. #63974C22semidirect
55. #63969C22semidirect
56. C2×#3724C22semidirect
57. C2×Dic3⋊Dic3C22semidirect
60. C2×(C2×D3)⋊Dic3C22semidirect
61. C2×(C2×D3)⋊Dic3C22semidirect
62. C2×(C2×D3)⋊Dic3C22semidirect
63. #63959C22semidirect
64. #63958C22semidirect
65. C2×Dic32C22semidirect
66. #63952C22semidirect
67. D3×(C2×D3)⋊C4C22semidirect
68. #63904C22semidirect
69. #63895C22semidirect
70. #63854C22semidirect
77. C2×#939D3semidirect
79. C2×#938D3semidirect
119. C2×C32×D4C23semidirect
124. C2×#638C23semidirect
133. C2×C3×#67C23semidirect
134. C2×C3×#67C23semidirect
142. C22×C3×Dic3C23semidirect
144. C2×C3×C4×D3C23semidirect
147. C2×#627C23semidirect
149. C2×#626D4semidirect
156. C2×#624C23semidirect
157. C2×#624C23semidirect
160. C2×D3×Dic3C23semidirect
161. #3757C23semidirect
163. #3752C23semidirect
164. C3×#217C23semidirect
165. C3×#217C23semidirect
166. C3×#217C23semidirect
167. C3×(C2×D3)⋊C4C23semidirect
168. C3×C4⋊Dic3C23semidirect
169. C3×Dic3⋊C4C23semidirect
170. #3724C23semidirect
171. Dic3⋊Dic3C23semidirect
174. (C2×D3)⋊Dic3C23semidirect
175. (C2×D3)⋊Dic3C23semidirect
176. (C2×D3)⋊Dic3C23semidirect
177. Dic32C23semidirect
189. C22×C3×D4C2×D3semidirect
190. C22×C3×D4C2×D3semidirect
203. C22×#67C2×D3semidirect
204. C22×#67C2×D3semidirect
206. C23×Dic3C2×D3semidirect
224. C22×C4×D3C2×D3semidirect
241. C2×#217C2×D3semidirect
242. C2×#217C2×D3semidirect
243. C2×#217C2×D3semidirect
244. #939C2×D3semidirect
246. #938C2×D3semidirect
270. C2×(C2×D3)⋊C4C2×D3semidirect
272. C2×C4⋊Dic3C2×D3semidirect
276. C2×Dic3⋊C4C2×D3semidirect
309. C22×C3⋊D3#41semidirect
353. #626C2×D4semidirect
422. C2×C3×D4C22×D3semidirect
423. C2×C3×D4C22×D3semidirect
459. C2×#67C22×D3semidirect
460. C2×#67C22×D3semidirect
476. C22×Dic3C22×D3semidirect
500. C2×C4×D3C22×D3semidirect
517. #217C22×D3semidirect
518. #217C22×D3semidirect
519. #217C22×D3semidirect
533. (C2×D3)⋊C4C22×D3semidirect
535. C4⋊Dic3C22×D3semidirect
539. Dic3⋊C4C22×D3semidirect
562. C2×C3⋊D3C2×#41semidirect
596. C22×D4D32semidirect
799. C2×C32#546semidirect
842. C2×D4C2×D32semidirect
983. C32C2×#546semidirect
1063. C2×C3#5610semidirect
1064. C2×C3#5612semidirect
1119. C3C2×#5610semidirect
1120. C3C2×#5612semidirect
1127. C2#10595296direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38112
C22×#38042
C2×#641462
C2×C3×#9392
C2×C3×#9382
C2×#639832
C2×#639742
C2×#639692
C2×#639592
C2×#639582
C2×#639522
#105952962
C2×D3×(C2×D3)⋊C42
C2×#639042
C2×#638952
C2×#638542
C2×#56123
C2×#56103