Finite Group Databasebeta

← #11884111

Subgroups — #11884111

Order 1152.

1128 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#634C211yesmaximal, characteristic, complemented
2C3×#5550C211yesmaximal, characteristic
3C2×#63831C211yesmaximal, characteristic, complemented
4C22×#3716C211yesmaximal, characteristic, complemented
5C3×#5011C211yesmaximal, characteristic, complemented
6#10591190C211yesmaximal, characteristic, complemented
7#10591187C211yesmaximal, characteristic, complemented
8#10591181C211yesmaximal, characteristic, complemented
9#10591176C211yesmaximal, characteristic, complemented
10#10591173C211yesmaximal, characteristic, complemented
11#10591172C211yesmaximal, characteristic, complemented
12#10590378C211yesmaximal, characteristic, complemented
13#10590372C211yesmaximal, characteristic, complemented
14#10590365C211yesmaximal, characteristic, complemented
15#10590360C211yesmaximal, characteristic, complemented
16#83506—31nomaximal
17#79495—31nomaximal
18C22×#634C2211yescharacteristic
19C22×#634C2211yescharacteristic, complemented
20C2×C3×#235C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic
22C32×C4×D4C2211yescharacteristic
23D4×C3⋊Dic3—21no—
24#64133C2211yescharacteristic
25#64133C2211yescharacteristic, complemented
26#64097—21no—
27#64087—21no—
28#64087—21no—
29#64078C2211yescharacteristic, complemented
30C4×#634C2211yescharacteristic, complemented
31C3×#937—21no—
32C3×#930C2211yescharacteristic
33C3×#924C2211yescharacteristic
34C2×C3×#208C2211yescharacteristic, complemented
35C22×C3×C3⋊C8C2211yescharacteristic
36C3×#894—21no—
37C3×#884—21no—
38C3×D3×C22⋊C4—21no—
39C3×#875C2211yescharacteristic
40C3×C4×D12C2211yescharacteristic
41C2×#3719C2211yescharacteristic, complemented
42C2×#3719C2211yescharacteristic, complemented
43C2×#3719C2211yescharacteristic, complemented
44#63831—24no—
45C2×#3716—24no—
46C2×#3716C2211yescharacteristic
47C2×#3716C2211yescharacteristic
48C2×#3716C2211yescharacteristic
49C2×#3716C2211yescharacteristic
50C2×#3716C2211yescharacteristic
51C2×#3716C2211yescharacteristic
52C3×#830C2211yescharacteristic
53C3×#830C2211yescharacteristic, complemented
54C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
55C3×#803C2211yescharacteristic, complemented
56#63575C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63567C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63566C2211yescharacteristic, complemented
61#63563C2211yescharacteristic
62#63563C2211yescharacteristic
63C3×#546—31no—
64C2×#951—31no—
65C22×#214—31no—
66C2×#909—31no—
67C22×#204—31no—
68#5550D311yescharacteristic
69D4×Dic6—31no—
70D4×Dic6—31no—
71D4×Dic6—61no—
72C3×#435—31no—
73#5239—31no—
74#5218—31no—
75#5134—31no—
76#5116—31no—
77#5060—31no—
78#5054—31no—
79#5051—31no—
80#5050—31no—
81#5042—31no—
82#5040—31no—
83#5019—31no—
84#5018—31no—
85#5011D311yescharacteristic, complemented
86#4845—31no—
87#4841—31no—
88#4739—31no—
89#4738—31no—
90#4733—31no—
91#4731—31no—
92#4715—31no—
93#4710—31no—
94C23×C3×D3—21no—
95C2×C32×D4D411yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C22×C3⋊Dic3—21no—
99C22×C3⋊Dic3—21no—
100C2×#634—22no—
101C2×#634—22no—
102C2×#634—21no—
103C2×#634—21no—
104C2×#634—41no—
105C2×#634—41no—
106C2×#634C2311yescharacteristic
107C2×#634C2311yescharacteristic
108C2×#634C2311yescharacteristic
109C2×C3×#67—21no—
110C2×C3×#67—21no—
111C3×#235—22no—
112C3×#235—41no—
113C2×C3×D12—22no—
114C2×C3×D12—21no—
115C2×C3×D12—41no—
116C2×C3×D12C2311yescharacteristic
117C2×C3×D12C2311yescharacteristic
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3—21no—
120C2×C3×Dic6C2311yescharacteristic
121C32×C4⋊C4D411yescharacteristic
122C32×C22⋊C4D411yescharacteristic
123C32×C22⋊C4D411yescharacteristic
124C32×C42C2311yescharacteristic
125#3757—21no—
126#3757—21no—
127C4⋊(C3⋊Dic3)—21no—
128C4⋊(C3⋊Dic3)—21no—
129C4⋊(C3⋊Dic3)C2311yescharacteristic
130#3750—21no—
131#3750—21no—
132#3750—21no—
133C4×C3⋊Dic3—21no—
134C3×#217—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×C4⋊Dic3C2311yescharacteristic
140C3×Dic3⋊C4—21no—
141C3×#208—22no—
142C2×C3×C3⋊C8—22no—
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147#3719—22no—
148#3719—22no—
149#3719—41no—
150#3716—22no—
151#3716—22no—
152#3716—22no—
153#3716—22no—
154#3716—41no—
155#3716D414yescomplemented
156#3266—91noSylow
157C2×C3×#41—31no—
158C22×C3×D4—31no—
159C2×#235C2×D311yescharacteristic
160C22×D12C2×D311yescharacteristic
161C22×Dic6—31no—
162C22×Dic6—31no—
163C22×Dic6—31no—
164C22×Dic6—31no—
165C22×Dic6—61no—
166C22×Dic6—61no—
167C2×C3×M16—31no—
168C22×C3×C8—31no—
169C3×#124—31no—
170C3×#123—61no—
171C3×C22⋊Q8—31no—
172C3×#121—31no—
173C3×#121—61no—
174C3×#120—61no—
175C3×C4×D4—21no—
176C3×C4×D4—31no—
177C3×C4×D4C2×D311yescharacteristic
178C3×C4×D4C2×D311yescharacteristic
179C2×C3×C22⋊C4—61no—
180#951—64no—
181C2×#216—31no—
182C2×#216—31no—
183C2×#216—31no—
184#937—21no—
185D4×Dic3—62no—
186D4×Dic3—61no—
187D4×Dic3—61no—
188C2×#214—31no—
189C2×#214—31no—
190C2×#214—31no—
191C2×#214—31no—
192C2×#214—31no—
193C2×#214—31no—
194C2×#214—64no—
195#930C2×D311yescharacteristic
196#924—31no—
197#924—31no—
198#924—31no—
199#924—31no—
200#924—61no—
201#924—61no—
202#924C2×D311yescharacteristic
203C2×#208C2×D311yescharacteristic, complemented
204C22×C3⋊C8C2×D311yescharacteristic
205#909—64no—
206C2×Dic12—31no—
207C2×Dic12—31no—
208C2×Dic12—31no—
209C2×#204—31no—
210C2×#204—31no—
211C2×#204—31no—
212C2×#204—31no—
213C2×#204—31no—
214C2×#204—31no—
215C2×#204—64no—
216#894—21no—
217#888—62no—
218#888—61no—
219#888—61no—
220#884—21no—
221D3×C22⋊C4—21no—
222#878—62no—
223#878—62no—
224#878—61no—
225#878—61no—
226#878—61no—
227#878—61no—
228#875C2×D311yescharacteristic
229C4×D12C2×D311yescharacteristic
230#869—31no—
231#869—31no—
232#869—61no—
233C4×Dic6—31no—
234C4×Dic6—31no—
235C4×Dic6—61no—
236C3×C4⋊C8—31no—
237C3×C22⋊C8—31no—
238C3×C22⋊C8—31no—
239C3×#97—31no—
240#835—31no—
241#832—31no—
242#832—31no—
243#830C2×D311yescharacteristic
244#830C2×D311yescharacteristic, complemented
245#821—31no—
246#821—31no—
247#818—31no—
248#816—31no—
249#816—31no—
250#816—31no—
251#816—31no—
252#810—31no—
253#810—31no—
254#810—31no—
255#807—31no—
256C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
257#803C2×D311yescharacteristic, complemented
258C23×C32C2×D411yescharacteristic
259C23×C32C2×D411yescharacteristic
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3—42no—
263C22×C3×D3—42no—
264C22×C3×D3—81no—
265C32×D4—22no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4C2×D411yescharacteristic
271C2×C32×C4C2×D411yescharacteristic
272C2×C32×C4C2×D411yescharacteristic
273C2×C32×C4C2×D411yescharacteristic
274C2×C32×C4C2411yescharacteristic
275C2×C3⋊Dic3—21no—
276C2×C3⋊Dic3—21no—
277C2×C3⋊Dic3—21no—
278C2×C3⋊Dic3—21no—
279C2×C3⋊Dic3—42no—
280C2×C3⋊Dic3—42no—
281#634—21no—
282#634—21no—
283#634—21no—
284#634—21no—
285#634—21no—
286#634—42no—
287#634—42no—
288#634C2×D412yes—
289C3×#67—42no—
290C3×#67—81no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C3×D12—21no—
294C3×D12—21no—
295C3×D12—21no—
296C3×D12—42no—
297C3×D12C2×D412yes—
298C3×C4×D3—42no—
299C3×C4×D3—81no—
300C3×Dic6—21no—
301C3×Dic6—21no—
302C3×C3⋊C8—21no—
303C3×C3⋊C8—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8C2×D412yes—
306C2×#137—91no—
307C22×SD16—91no—
308D4×Q8—91no—
309#546—31no—
310#497—91no—
311#468—91no—
312#467—91no—
313#464—91no—
314#461—91no—
315#452—91no—
316#451—91no—
317#450—91no—
318#448—91no—
319#440—91no—
320#435—31no—
321C24×C3—61no—
322C23×D3—21no—
323C3×#41—62no—
324C3×#41—121no—
325C2×C3×Q8—31no—
326C2×C3×D4—21no—
327C2×C3×D4—31no—
328C2×C3×D4—31no—
329C2×C3×D4—62no—
330C2×C3×D4—61no—
331C2×C3×D4—61no—
332C2×C3×D4—61no—
333C2×C3×D4—121no—
334C2×C3×D4D1211yescharacteristic
335C2×C3×D4#6711yescharacteristic
336C22×C3×C4—21no—
337C22×C3×C4—21no—
338C22×C3×C4—61no—
339C22×C3×C4—61no—
340C22×C3×C4C22×D311yescharacteristic
341C22×C3×C4C22×D311yescharacteristic
342C22×C3×C4C22×D311yescharacteristic
343C22×C3×C4C22×D311yescharacteristic
344C2×#67—21no—
345C2×#67—21no—
346C22×Dic3—62no—
347C22×Dic3—62no—
348C22×Dic3—61no—
349C22×Dic3—61no—
350C22×Dic3—61no—
351C22×Dic3—61no—
352#235—22no—
353#235—41no—
354C2×D12—22no—
355C2×D12—21no—
356C2×D12—41no—
357C2×D12C22×D311yescharacteristic
358C2×D12C22×D311yescharacteristic
359C2×C4×D3—21no—
360C2×C4×D3—21no—
361C2×Dic6—31no—
362C2×Dic6—31no—
363C2×Dic6—31no—
364C2×Dic6—31no—
365C2×Dic6—31no—
366C2×Dic6—31no—
367C2×Dic6—61no—
368C2×Dic6—61no—
369C2×Dic6—61no—
370C2×Dic6—62no—
371C2×Dic6—62no—
372C2×Dic6—62no—
373C2×Dic6—62no—
374C2×Dic6—62no—
375C2×Dic6—62no—
376C2×Dic6—61no—
377C2×Dic6—61no—
378C2×Dic6—61no—
379C2×Dic6—61no—
380C2×Dic6—122no—
381C2×Dic6—122no—
382C2×Dic6—121no—
383C2×Dic6—121no—
384C2×Dic6—121no—
385C2×Dic6—121no—
386C2×Dic6—122no—
387C2×Dic6—122no—
388C2×Dic6C22×D311yescharacteristic
389C3×M16—62no—
390C2×C3×C8—31no—
391C2×C3×C8—31no—
392C2×C3×C8—31no—
393C2×C3×C8—31no—
394C2×C3×C8—62no—
395C3×C4⋊C4—21no—
396C3×C4⋊C4—31no—
397C3×C4⋊C4—61no—
398C3×C4⋊C4D1211yescharacteristic
399C3×C4⋊C4#6711yescharacteristic
400C3×C22⋊C4—21no—
401C3×C22⋊C4—21no—
402C3×C22⋊C4—61no—
403C3×C22⋊C4—61no—
404C3×C22⋊C4—61no—
405C3×C22⋊C4—61no—
406C3×C22⋊C4—61no—
407C3×C22⋊C4D1211yescharacteristic
408C3×C22⋊C4D1211yescharacteristic
409C3×C22⋊C4#6711yescharacteristic
410C3×C22⋊C4#6711yescharacteristic
411C3×C42—21no—
412C3×C42C22×D311yescharacteristic
413C3×C42C22×D311yescharacteristic
414#217—21no—
415#217—62no—
416#217—62no—
417#217—61no—
418#217—61no—
419#217—61no—
420#217—61no—
421#216—62no—
422#216—62no—
423#216—121no—
424#214—34no—
425#214—62no—
426#214—62no—
427#214—62no—
428#214—62no—
429#214—121no—
430(C2×D3)⋊C4—21no—
431(C2×D3)⋊C4—21no—
432(C2×D3)⋊C4—21no—
433(C2×D3)⋊C4—21no—
434C4⋊Dic3—31no—
435C4⋊Dic3—31no—
436C4⋊Dic3—61no—
437C4⋊Dic3—62no—
438C4⋊Dic3—62no—
439C4⋊Dic3—61no—
440C4⋊Dic3—61no—
441C4⋊Dic3—61no—
442C4⋊Dic3—61no—
443C4⋊Dic3C22×D311yescharacteristic
444Dic3⋊C4—21no—
445Dic3⋊C4—62no—
446Dic3⋊C4—62no—
447Dic3⋊C4—62no—
448Dic3⋊C4—61no—
449Dic3⋊C4—61no—
450Dic3⋊C4—61no—
451Dic3⋊C4—61no—
452Dic3⋊C4—61no—
453Dic3⋊C4—61no—
454C4×Dic3—62no—
455C4×Dic3—61no—
456C4×Dic3—61no—
457#208—22no—
458C2×C3⋊C8—22no—
459C2×C3⋊C8C22×D311yescharacteristic
460C2×C3⋊C8C22×D311yescharacteristic
461C2×C3⋊C8C22×D311yescharacteristic
462C2×C3⋊C8C22×D311yescharacteristic
463Dic12—62no—
464Dic12—62no—
465Dic12—121no—
466#204—34no—
467#204—62no—
468#204—62no—
469#204—62no—
470#204—62no—
471#204—121no—
472C22×C32—21no—
473C22×C32—21no—
474C22×C32—21no—
475C22×C32—21no—
476C22×C32—21no—
477C22×C32#13712yescomplemented
478C22×C32C22×D411yescharacteristic
479C2×C3×D3—22no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3—41no—
484C2×C3×D3—41no—
485C2×C3×D3—84no—
486C32×C4—21no—
487C32×C4—21no—
488C32×C4—21no—
489C32×C4—21no—
490C32×C4C22×D411yescharacteristic
491C32×C4H(5,𝔽2)11yescharacteristic
492C3⋊Dic3—22no—
493C3⋊Dic3—41no—
494C3⋊Dic3—41no—
495C3⋊Dic3—41no—
496C3×Dic3—41no—
497C3×Dic3—41no—
498C2×#41—31no—
499C22×Q8—91no—
500C22×Q8—91no—
501C22×D4—31no—
502#137—184no—
503C2×Q16—91no—
504C2×Q16—91no—
505C2×Q16—91no—
506C2×SD16—91no—
507C2×SD16—91no—
508C2×SD16—91no—
509C2×SD16—91no—
510C2×SD16—91no—
511C2×SD16—91no—
512C2×SD16—184no—
513C2×M16—31no—
514C22×C8—31no—
515C4⋊Q8—91no—
516C4⋊Q8—181no—
517#124—31no—
518#123—61no—
519C22⋊Q8—31no—
520C22⋊Q8—91no—
521C22⋊Q8—91no—
522C22⋊Q8—181no—
523C22⋊Q8—181no—
524#121—31no—
525#121—61no—
526#120—61no—
527C4×Q8—91no—
528C4×D4—31no—
529C4×D4—181no—
530C4×D4D3211yescharacteristic
531C2×C22⋊C4—61no—
532#107—91no—
533C4⋊C8—31no—
534#103—91no—
535#103—91no—
536#103—91no—
537#103—91no—
538#102—91no—
539#102—91no—
540C22⋊C8—31no—
541C22⋊C8—31no—
542#97—31no—
543C23×C3—21no—
544C23×C3—21no—
545C23×C3—61no—
546C23×C3—61no—
547C23×C3—122no—
548C23×C3—122no—
549C23×C3—241no—
550C23×C3C2×D1211yescharacteristic
551C23×C3C2×D1211yescharacteristic
552C23×C3C2×#6711yescharacteristic
553C23×C3C2×#6711yescharacteristic
554C22×D3—21no—
555C22×D3—21no—
556C22×D3—42no—
557C22×D3—42no—
558C22×D3—81no—
559C3×Q8—61no—
560C3×Q8—61no—
561C3×D4—24no—
562C3×D4—22no—
563C3×D4—22no—
564C3×D4—32no—
565C3×D4—61no—
566C3×D4—61no—
567C3×D4—61no—
568C3×D4—122no—
569C3×D4—122no—
570C3×D4—241no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—122no—
591C2×C3×C4—241no—
592C2×C3×C4C2×D1211yescharacteristic
593C2×C3×C4C2×D1211yescharacteristic
594C2×C3×C4C2×D1211yescharacteristic
595C2×C3×C4C2×D1211yescharacteristic
596C2×C3×C4C2×#6711yescharacteristic
597C2×C3×C4C2×#6711yescharacteristic
598C2×C3×C4C2×#6711yescharacteristic
599C2×C3×C4C2×#6711yescharacteristic
600C2×C3×C4C23×D311yescharacteristic
601C2×C3×C4C23×D311yescharacteristic
602#67—42no—
603#67—81no—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—62no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3—62no—
610C2×Dic3—62no—
611C2×Dic3—62no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—61no—
617C2×Dic3—61no—
618C2×Dic3—122no—
619C2×Dic3—122no—
620C2×Dic3—122no—
621C2×Dic3—122no—
622C2×Dic3—124no—
623C2×Dic3—124no—
624D12—21no—
625D12—21no—
626D12—21no—
627D12—42no—
628D12D3×D412yes—
629C4×D3—42no—
630C4×D3—81no—
631Dic6—21no—
632Dic6—21no—
633Dic6—32no—
634Dic6—32no—
635Dic6—62no—
636Dic6—62no—
637Dic6—61no—
638Dic6—61no—
639Dic6—61no—
640Dic6—61no—
641Dic6—61no—
642Dic6—61no—
643Dic6—61no—
644Dic6—61no—
645Dic6—61no—
646Dic6—61no—
647Dic6—121no—
648Dic6—121no—
649Dic6—121no—
650Dic6—121no—
651Dic6—122no—
652Dic6—122no—
653Dic6—122no—
654Dic6—122no—
655Dic6—124no—
656Dic6—124no—
657C3×C8—32no—
658C3×C8—61no—
659C3×C8—61no—
660C3×C8—61no—
661C3⋊C8—21no—
662C3⋊C8—21no—
663C3⋊C8—21no—
664C3⋊C8D3×D412yes—
665C2×C32—22no—
666C2×C32—41no—
667C2×C32D4211yescharacteristic
668C2×C32C2×#13711yescharacteristic
669C2×C32#57711yescharacteristic
670C3×D3—42no—
671C3×D3—81no—
672C24—61no—
673#41—62no—
674#41—121no—
675C2×Q8—31no—
676C2×Q8—91no—
677C2×Q8—91no—
678C2×Q8—91no—
679C2×Q8—182no—
680C2×Q8—182no—
681C2×Q8—181no—
682C2×Q8—181no—
683C2×Q8—361no—
684C2×Q8—361no—
685C2×D4—31no—
686C2×D4—31no—
687C2×D4—62no—
688C2×D4—61no—
689C2×D4—61no—
690C2×D4—61no—
691C2×D4—121no—
692C2×D4#62611yescharacteristic
693C22×C4—61no—
694C22×C4—61no—
695C22×C4—181no—
696C22×C4—181no—
697C22×C4C2×D3211yescharacteristic
698C22×C4C2×D3211yescharacteristic
699Q16—182no—
700Q16—182no—
701Q16—361no—
702SD16—94no—
703SD16—182no—
704SD16—182no—
705SD16—182no—
706SD16—182no—
707SD16—361no—
708M16—62no—
709C2×C8—31no—
710C2×C8—31no—
711C2×C8—31no—
712C2×C8—31no—
713C2×C8—62no—
714C4⋊C4—31no—
715C4⋊C4—61no—
716C4⋊C4—91no—
717C4⋊C4—181no—
718C4⋊C4—181no—
719C4⋊C4—181no—
720C4⋊C4—181no—
721C4⋊C4—181no—
722C4⋊C4#62611yescharacteristic
723C22⋊C4—61no—
724C22⋊C4—61no—
725C22⋊C4—61no—
726C22⋊C4—61no—
727C22⋊C4—61no—
728C22⋊C4—181no—
729C22⋊C4—181no—
730C22⋊C4#62611yescharacteristic
731C22⋊C4#62611yescharacteristic
732C42—181no—
733C42C2×D3211yescharacteristic
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—22no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—22no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—62no—
752C22×C3—121no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3—244no—
758C22×C3#90912yescomplemented
759C22×C3#95112yescomplemented
760C22×C3C22×D1211yescharacteristic
761C22×C3C22×#6711yescharacteristic
762C2×D3—22no—
763C2×D3—41no—
764C2×D3—41no—
765C2×D3—41no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—84no—
769C3×C4—22no—
770C3×C4—21no—
771C3×C4—21no—
772C3×C4—21no—
773C3×C4—21no—
774C3×C4—21no—
775C3×C4—21no—
776C3×C4—21no—
777C3×C4—21no—
778C3×C4—21no—
779C3×C4—21no—
780C3×C4—41no—
781C3×C4—41no—
782C3×C4—41no—
783C3×C4—121no—
784C3×C4—121no—
785C3×C4C2×D3×D411yescharacteristic
786C3×C4C2×D3×D411yescharacteristic
787C3×C4#100411yescharacteristic
788C3×C4#100911yescharacteristic
789Dic3—41no—
790Dic3—41no—
791Dic3—64no—
792Dic3—62no—
793Dic3—62no—
794Dic3—122no—
795Dic3—122no—
796Dic3—122no—
797Dic3—121no—
798Dic3—121no—
799Dic3—121no—
800Dic3—121no—
801Dic3—121no—
802Dic3—121no—
803C32#326611yescharacteristic, complemented, Sylow
804C23—61no—
805C23—61no—
806C23—122no—
807C23—122no—
808C23—241no—
809C23C2×#62611yescharacteristic
810C23C2×#62611yescharacteristic
811Q8—61no—
812Q8—61no—
813Q8—92no—
814Q8—181no—
815Q8—181no—
816Q8—181no—
817Q8—181no—
818Q8—181no—
819Q8—362no—
820Q8—362no—
821D4—22no—
822D4—32no—
823D4—61no—
824D4—61no—
825D4—61no—
826D4—122no—
827D4—122no—
828D4—241no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—122no—
836C2×C4—181no—
837C2×C4—181no—
838C2×C4—181no—
839C2×C4—181no—
840C2×C4—241no—
841C2×C4—362no—
842C2×C4—362no—
843C2×C4C2×#62611yescharacteristic
844C2×C4C2×#62611yescharacteristic
845C2×C4C2×#62611yescharacteristic
846C2×C4C2×#62611yescharacteristic
847C2×C4C22×D3211yescharacteristic
848C8—32no—
849C8—61no—
850C8—61no—
851C8—61no—
852C2×C3—22no—
853C2×C3—22no—
854C2×C3—21no—
855C2×C3—21no—
856C2×C3—21no—
857C2×C3—42no—
858C2×C3—42no—
859C2×C3—41no—
860C2×C3—41no—
861C2×C3—122no—
862C2×C3—241no—
863C2×C3D4×D1211yescharacteristic
864C2×C3C2×#90911yescharacteristic
865C2×C3#575111yescharacteristic
866C2×C3D4×#6711yescharacteristic
867C2×C3C2×#95111yescharacteristic
868C2×C3#583611yescharacteristic
869D3—42no—
870D3—81no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—21no—
876C22—62no—
877C22—121no—
878C22—121no—
879C22—121no—
880C22—121no—
881C22—121no—
882C22—244no—
883C22#6383112yescomplemented
884C22C22×#62611yescharacteristic
885C4—21no—
886C4—21no—
887C4—21no—
888C4—21no—
889C4—121no—
890C4—121no—
891C4—182no—
892C4—361no—
893C4—361no—
894C4—361no—
895C4D32×D411yescharacteristic
896C4#6431411yescharacteristic
897C3—21no—
898C3#7949511yescharacteristic, complemented
899C3#8350611yescharacteristic, complemented
900C2—22no—
901C2—41no—
902C2—122no—
903C2—241no—
904C2C2×#6383111yescharacteristic
905C2D4×#62611yescharacteristic
906C2#1059544711yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC3×#5550C2
hypercenterC4×D4D32
hypocenterC32#3266
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. D4×#634C2semidirect
3. C2×#63831C2semidirect
4. C22×#3716C2semidirect
5. C3×#5011C2semidirect
6. #10591190C2semidirect
7. #10591187C2semidirect
8. #10591181C2semidirect
9. #10591176C2semidirect
10. #10591173C2semidirect
11. #10591172C2semidirect
12. #10590378C2semidirect
13. #10590372C2semidirect
14. #10590365C2semidirect
15. #10590360C2semidirect
19. C22×#634C22semidirect
25. #64133C22semidirect
29. #64078C22semidirect
30. C4×#634C22semidirect
34. C2×C3×#208C22semidirect
41. C2×#3719C22semidirect
42. C2×#3719C22semidirect
43. C2×#3719C22semidirect
53. C3×#830C22semidirect
54. C3×C4⋊(C3⋊C8)C22semidirect
55. C3×#803C22semidirect
56. #63575C22semidirect
57. #63567C22semidirect
58. #63567C22semidirect
59. #63567C22semidirect
60. #63566C22semidirect
85. #5011D3semidirect
155. #3716D4semidirect
203. C2×#208C2×D3semidirect
244. #830C2×D3semidirect
256. C4⋊(C3⋊C8)C2×D3semidirect
257. #803C2×D3semidirect
477. C22×C32#137semidirect
758. C22×C3#909semidirect
759. C22×C3#951semidirect
803. C32#3266semidirect
883. C22#63831semidirect
898. C3#79495semidirect
899. C3#83506semidirect

Maximal subgroups

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

subgroupindex
D4×#6342
C3×#55502
C2×#638312
C22×#37162
C3×#50112
#105911902
#105911872
#105911812
#105911762
#105911732
#105911722
#105903782
#105903722
#105903652
#105903602
#835063
#794953