Finite Group Databasebeta

← #11887256

Subgroups — #11887256

Order 1152.

883 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5550C211yesmaximal, characteristic
2C3×#5541C211yesmaximal, characteristic, complemented
3D4×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
4#10591188C211yesmaximal, characteristic, complemented
5#10591179C211yesmaximal, characteristic, complemented
6#10591170C211yesmaximal, characteristic, complemented
7#10591169C211yesmaximal, characteristic, complemented
8#10591101C211yesmaximal, characteristic, complemented
9#10591090C211yesmaximal, characteristic, complemented
10#10591083C211yesmaximal, characteristic, complemented
11C2×#63562C211yesmaximal, characteristic, complemented
12C4×#3715C211yesmaximal, characteristic, complemented
13#10590278C211yesmaximal, characteristic, complemented
14#10590270C211yesmaximal, characteristic, complemented
15#10590267C211yesmaximal, characteristic, complemented
16#83598—31nomaximal
17#83494—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
23C3×#937—21no—
24C3×#935—21no—
25C3×#930C2211yescharacteristic
26C3×#926C2211yescharacteristic, complemented
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C3×#924C2211yescharacteristic
29C3×#924C2211yescharacteristic
30C3×#924C2211yescharacteristic, complemented
31C3×#894—21no—
32C3×#889—21no—
33C3×#884—21no—
34C3×D3×C22⋊C4—21no—
35C3×#879—21no—
36C3×#877—21no—
37C3×#875C2211yescharacteristic
38C3×C4×D12C2211yescharacteristic
39C3×#870C2211yescharacteristic, complemented
40C3×C4×Dic6C2211yescharacteristic, complemented
41C2×#3718C2211yescharacteristic, complemented
42C2×#3715C2211yescharacteristic
43C2×#3715C2211yescharacteristic
44#63657C2211yescharacteristic
45#63657C2211yescharacteristic, complemented
46C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
47C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
48#63576C2211yescharacteristic, complemented
49#63574C2211yescharacteristic, complemented
50#63574C2211yescharacteristic, complemented
51#63565C2211yescharacteristic, complemented
52#63565C2211yescharacteristic, complemented
53#63565C2211yescharacteristic, complemented
54#63565C2211yescharacteristic, complemented
55#63562C2211yescharacteristic
56#63562C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic
61C3×#552—31no—
62C3×#546—31no—
63#5550D311yescharacteristic
64#5541D311yescharacteristic, complemented
65#5239—31no—
66#5233—31no—
67#5218—31no—
68C2×#832—31no—
69#5068—31no—
70#5066—31no—
71#5056—31no—
72#5054—31no—
73#5051—31no—
74#5051—31no—
75#5048—31no—
76#5047—31no—
77#5046—31no—
78#5043—31no—
79#5041—31no—
80#5035—31no—
81#5028—31no—
82C4×#215—31no—
83C4×#214—31no—
84D4×C3⋊C8—31no—
85D4×C3⋊C8—31no—
86D4×C3⋊C8—61no—
87#5009—31no—
88#5003—31no—
89#5002—31no—
90#4971—31no—
91C2×#809—31no—
92C23×C3×D3—21no—
93C2×C32×D4D411yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C3×#235—22no—
100C3×#235—41no—
101C2×C3×D12—22no—
102C2×C3×D12—21no—
103C2×C3×D12—41no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×Dic6C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C32×C4⋊C4D411yescharacteristic
111C32×C22⋊C4D411yescharacteristic
112C32×C22⋊C4D411yescharacteristic
113C32×C42C2311yescharacteristic
114C2×C3⋊(C3⋊C8)—41no—
115C2×C3⋊(C3⋊C8)—41no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#217—21no—
121C3×#217—21no—
122C3×#217—21no—
123C3×#217—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C3×C4×Dic3—21no—
140C3×C4×Dic3—21no—
141#3718—41no—
142#3715—22no—
143#3715—41no—
144#3296—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×#235C2×D311yescharacteristic
148C22×D12C2×D311yescharacteristic
149C3×#126—61no—
150C3×#125—31no—
151C3×#125—61no—
152C3×#124—31no—
153C3×#123—61no—
154C3×#123—61no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—31no—
158C3×#121—31no—
159C3×#121—61no—
160C3×#120—61no—
161C3×C4×Q8—31no—
162C3×C4×D4—21no—
163C3×C4×D4—31no—
164C3×C4×D4C2×D311yescharacteristic
165C3×C4×D4C2×D311yescharacteristic
166C3×#117—31no—
167C3×#117—61no—
168C2×C3×C4⋊C4—31no—
169C2×C3×C22⋊C4—61no—
170C2×#216—31no—
171C2×#216—31no—
172C2×#215—31no—
173C2×#215—31no—
174#937—21no—
175#935—21no—
176C2×#214—31no—
177C2×#214—31no—
178#930C2×D311yescharacteristic
179#926C2×D311yescharacteristic, complemented
180C2×C4⋊Dic3C2×D311yescharacteristic
181#924C2×D311yescharacteristic
182#924C2×D311yescharacteristic
183#924C2×D311yescharacteristic, complemented
184C22×C3⋊C8—31no—
185C22×C3⋊C8—31no—
186C22×C3⋊C8—31no—
187C22×C3⋊C8—31no—
188C22×C3⋊C8—61no—
189C22×C3⋊C8—61no—
190#894—21no—
191#889—21no—
192#884—21no—
193D3×C22⋊C4—21no—
194#879—21no—
195#877—21no—
196#875C2×D311yescharacteristic
197C4×D12C2×D311yescharacteristic
198#870C2×D311yescharacteristic, complemented
199C4×Dic6C2×D311yescharacteristic, complemented
200#835—31no—
201#835—31no—
202#835—31no—
203#835—31no—
204#832—31no—
205#832—31no—
206#832—31no—
207#832—31no—
208#832—31no—
209#832—31no—
210#830—31no—
211#830—31no—
212#830—31no—
213#830—31no—
214#830—61no—
215#830—61no—
216#810—31no—
217#810—31no—
218#810—31no—
219#810—31no—
220#809—31no—
221#809—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#808—31no—
227#808—31no—
228#808—31no—
229#808—31no—
230#807—31no—
231#807—31no—
232C4⋊(C3⋊C8)—31no—
233C4⋊(C3⋊C8)—31no—
234C4⋊(C3⋊C8)—61no—
235C4×C3⋊C8—31no—
236C4×C3⋊C8—31no—
237C4×C3⋊C8—61no—
238C23×C32C2×D411yescharacteristic
239C23×C32C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—42no—
243C22×C3×D3—42no—
244C22×C3×D3—81no—
245C32×D4—22no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2411yescharacteristic
255C3×#67—42no—
256C3×#67—81no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—42no—
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—42no—
268C3×D12#4112yes—
269C3×C4×D3—42no—
270C3×C4×D3—81no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275C3⋊(C3⋊C8)—21no—
276C3⋊(C3⋊C8)—21no—
277C3⋊(C3⋊C8)—21no—
278C3⋊(C3⋊C8)—21no—
279#552—31no—
280#546—31no—
281#488—91no—
282#483—91no—
283#482—91no—
284#478—91no—
285#467—91no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—91no—
290C4×SD16—91no—
291C8×D4—91no—
292#416—91no—
293C2×#102—91no—
294C24×C3—61no—
295C23×D3—21no—
296C3×#41—62no—
297C3×#41—121no—
298C2×C3×Q8—31no—
299C2×C3×Q8—31no—
300C2×C3×D4—21no—
301C2×C3×D4—31no—
302C2×C3×D4—31no—
303C2×C3×D4—62no—
304C2×C3×D4—61no—
305C2×C3×D4—61no—
306C2×C3×D4—61no—
307C2×C3×D4—121no—
308C2×C3×D4#6711yescharacteristic
309C2×C3×D4#6711yescharacteristic
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C22×C3×C4C22×D311yescharacteristic
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C22×D311yescharacteristic
319C2×#67—21no—
320C2×#67—21no—
321C22×Dic3—21no—
322#235—22no—
323#235—41no—
324C2×D12—22no—
325C2×D12—21no—
326C2×D12—41no—
327C2×D12C22×D311yescharacteristic
328C2×D12C22×D311yescharacteristic
329C2×C4×D3—21no—
330C2×C4×D3—21no—
331C2×Dic6C22×D311yescharacteristic
332C2×Dic6C22×D311yescharacteristic
333C3×C4⋊C4—21no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4#6711yescharacteristic
346C3×C4⋊C4#6711yescharacteristic
347C3×C22⋊C4—21no—
348C3×C22⋊C4—21no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4#6711yescharacteristic
358C3×C22⋊C4#6711yescharacteristic
359C3×C22⋊C4#6711yescharacteristic
360C3×C22⋊C4#6711yescharacteristic
361C3×C42—21no—
362C3×C42—61no—
363C3×C42—61no—
364C3×C42C22×D311yescharacteristic
365C3×C42C22×D311yescharacteristic
366#217—21no—
367#217—21no—
368#217—21no—
369#217—21no—
370#216—121no—
371#216—121no—
372#215—62no—
373#215—121no—
374#214—62no—
375#214—121no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—21no—
380C4⋊Dic3—21no—
381C4⋊Dic3C22×D311yescharacteristic
382C4⋊Dic3C22×D311yescharacteristic
383C4⋊Dic3C22×D311yescharacteristic
384C4⋊Dic3C22×D311yescharacteristic
385Dic3⋊C4—21no—
386Dic3⋊C4—21no—
387Dic3⋊C4—21no—
388Dic3⋊C4—21no—
389Dic3⋊C4—21no—
390Dic3⋊C4—21no—
391C4×Dic3—21no—
392C4×Dic3—21no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—61no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—121no—
406C2×C3⋊C8—121no—
407C2×C3⋊C8—121no—
408C2×C3⋊C8—121no—
409C2×C3⋊C8—122no—
410C2×C3⋊C8—122no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32#13512yes—
417C22×C32C22×D411yescharacteristic
418C2×C3×D3—22no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—84no—
425C32×C4—21no—
426C32×C4—21no—
427C32×C4—21no—
428C32×C4—21no—
429C32×C4C2×#4111yescharacteristic
430C32×C4H(5,𝔽2)11yescharacteristic
431C3×Dic3—41no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—31no—
438C22×D4—31no—
439C2×Q16—91no—
440C2×SD16—91no—
441C2×SD16—91no—
442C22×C8—91no—
443C22×C8—91no—
444#126—61no—
445#125—31no—
446#125—61no—
447#124—31no—
448#123—61no—
449#123—61no—
450C22⋊Q8—31no—
451C22⋊Q8—31no—
452C22⋊Q8—31no—
453#121—31no—
454#121—61no—
455#120—61no—
456C4×Q8—31no—
457C4×D4—31no—
458C4×D4D3211yescharacteristic
459#117—31no—
460#117—61no—
461C2×C4⋊C4—31no—
462C2×C22⋊C4—61no—
463#107—91no—
464#106—91no—
465#106—91no—
466C4⋊C8—91no—
467#103—91no—
468#103—91no—
469#103—91no—
470#103—91no—
471#102—91no—
472#102—91no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477C22⋊C8—91no—
478C22⋊C8—91no—
479C4×C8—91no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—61no—
483C23×C3—61no—
484C23×C3—122no—
485C23×C3—122no—
486C23×C3—241no—
487C23×C3C2×#6711yescharacteristic
488C23×C3C2×#6711yescharacteristic
489C23×C3C2×#6711yescharacteristic
490C23×C3C2×#6711yescharacteristic
491C22×D3—21no—
492C22×D3—21no—
493C22×D3—42no—
494C22×D3—42no—
495C22×D3—81no—
496C3×Q8—61no—
497C3×Q8—61no—
498C3×Q8—61no—
499C3×Q8—61no—
500C3×D4—24no—
501C3×D4—22no—
502C3×D4—22no—
503C3×D4—32no—
504C3×D4—61no—
505C3×D4—61no—
506C3×D4—61no—
507C3×D4—122no—
508C3×D4—122no—
509C3×D4—241no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—122no—
534C2×C3×C4—122no—
535C2×C3×C4—241no—
536C2×C3×C4C2×#6711yescharacteristic
537C2×C3×C4C2×#6711yescharacteristic
538C2×C3×C4C2×#6711yescharacteristic
539C2×C3×C4C2×#6711yescharacteristic
540C2×C3×C4C2×#6711yescharacteristic
541C2×C3×C4C2×#6711yescharacteristic
542C2×C3×C4C2×#6711yescharacteristic
543C2×C3×C4C2×#6711yescharacteristic
544C2×C3×C4C23×D311yescharacteristic
545C2×C3×C4C23×D311yescharacteristic
546#67—42no—
547#67—81no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—42no—
555D12—21no—
556D12—21no—
557D12—21no—
558D12—42no—
559D12#23712yes—
560C4×D3—42no—
561C4×D3—81no—
562Dic6—21no—
563Dic6—21no—
564Dic6—21no—
565Dic6—21no—
566C3⋊C8—62no—
567C3⋊C8—61no—
568C3⋊C8—61no—
569C3⋊C8—61no—
570C3⋊C8—61no—
571C3⋊C8—61no—
572C3⋊C8—61no—
573C3⋊C8—61no—
574C3⋊C8—61no—
575C3⋊C8—121no—
576C3⋊C8—121no—
577C3⋊C8—121no—
578C2×C32—22no—
579C2×C32—41no—
580C2×C32#54611yescharacteristic
581C2×C32C2×#13511yescharacteristic
582C2×C32#57711yescharacteristic
583C3×D3—42no—
584C3×D3—81no—
585C24—61no—
586#41—62no—
587#41—121no—
588C2×Q8—31no—
589C2×Q8—31no—
590C2×D4—31no—
591C2×D4—31no—
592C2×D4—62no—
593C2×D4—61no—
594C2×D4—61no—
595C2×D4—61no—
596C2×D4—121no—
597C2×D4#62511yescharacteristic
598C22×C4—61no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4C2×D3211yescharacteristic
602C22×C4C2×D3211yescharacteristic
603Q16—361no—
604SD16—182no—
605SD16—361no—
606C2×C8—91no—
607C2×C8—91no—
608C2×C8—91no—
609C2×C8—91no—
610C2×C8—361no—
611C2×C8—361no—
612C4⋊C4—31no—
613C4⋊C4—31no—
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—61no—
617C4⋊C4—61no—
618C4⋊C4—61no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4#62511yescharacteristic
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—61no—
627C22⋊C4—61no—
628C22⋊C4—61no—
629C22⋊C4—61no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4#62511yescharacteristic
633C22⋊C4#62511yescharacteristic
634C42—61no—
635C42—61no—
636C42C2×D3211yescharacteristic
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—22no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—22no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—62no—
655C22×C3—121no—
656C22×C3—121no—
657C22×C3—121no—
658C22×C3—121no—
659C22×C3—121no—
660C22×C3—244no—
661C22×C3#95012yes—
662C22×C3#95012yes—
663C22×C3C22×#6711yescharacteristic
664C22×C3C22×#6711yescharacteristic
665C2×D3—22no—
666C2×D3—41no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—41no—
671C2×D3—84no—
672C3×C4—22no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—21no—
682C3×C4—21no—
683C3×C4—41no—
684C3×C4—41no—
685C3×C4—41no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4—121no—
689C3×C4—121no—
690C3×C4—121no—
691C3×C4—121no—
692C3×C4C2×#23711yescharacteristic
693C3×C4#100411yescharacteristic
694C3×C4D3×#4111yescharacteristic
695C3×C4#100911yescharacteristic
696Dic3—41no—
697Dic3—41no—
698Dic3—41no—
699Dic3—41no—
700Dic3—41no—
701Dic3—41no—
702C32#329611yescharacteristic, complemented, Sylow
703C23—61no—
704C23—61no—
705C23—122no—
706C23—122no—
707C23—241no—
708C23C2×#62511yescharacteristic
709C23C2×#62511yescharacteristic
710Q8—61no—
711Q8—61no—
712Q8—61no—
713Q8—61no—
714D4—22no—
715D4—32no—
716D4—61no—
717D4—61no—
718D4—61no—
719D4—122no—
720D4—122no—
721D4—241no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—122no—
733C2×C4—122no—
734C2×C4—241no—
735C2×C4C2×#62511yescharacteristic
736C2×C4C2×#62511yescharacteristic
737C2×C4C2×#62511yescharacteristic
738C2×C4C2×#62511yescharacteristic
739C2×C4C22×D3211yescharacteristic
740C8—181no—
741C8—181no—
742C8—181no—
743C8—181no—
744C2×C3—22no—
745C2×C3—22no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—42no—
750C2×C3—42no—
751C2×C3—41no—
752C2×C3—41no—
753C2×C3—122no—
754C2×C3—241no—
755C2×C3#580611yescharacteristic
756C2×C3C2×#95011yescharacteristic
757C2×C3C2×#95011yescharacteristic
758C2×C3#582911yescharacteristic
759C2×C3#583611yescharacteristic
760C2×C3#583711yescharacteristic
761D3—42no—
762D3—81no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—62no—
769C22—121no—
770C22—121no—
771C22—121no—
772C22—121no—
773C22—121no—
774C22—244no—
775C22#6382212yes—
776C22C22×#62511yescharacteristic
777C4—21no—
778C4—21no—
779C4—21no—
780C4—21no—
781C4—121no—
782C4—121no—
783C4—121no—
784C4—121no—
785C4—121no—
786C4—121no—
787C4D3×#23711yescharacteristic
788C4#6431411yescharacteristic
789C3—21no—
790C3#8349411yescharacteristic, complemented
791C3#8359811yescharacteristic, complemented
792C2—22no—
793C2—41no—
794C2—122no—
795C2—241no—
796C2C2×#6382211yescharacteristic
797C2#1059524411yescharacteristic
798C2#1059544611yescharacteristic
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC3×#5550C2
hypercenterC4×D4D32
hypocenterC32#3296
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
2. C3×#5541C2semidirect
3. D4×C3⋊(C3⋊C8)C2semidirect
4. #10591188C2semidirect
5. #10591179C2semidirect
6. #10591170C2semidirect
7. #10591169C2semidirect
8. #10591101C2semidirect
9. #10591090C2semidirect
10. #10591083C2semidirect
11. C2×#63562C2semidirect
12. C4×#3715C2semidirect
13. #10590278C2semidirect
14. #10590270C2semidirect
15. #10590267C2semidirect
22. C22×C3⋊(C3⋊C8)C22semidirect
26. C3×#926C22semidirect
30. C3×#924C22semidirect
39. C3×#870C22semidirect
40. C3×C4×Dic6C22semidirect
41. C2×#3718C22semidirect
45. #63657C22semidirect
46. C4⋊(C3⋊(C3⋊C8))C22semidirect
47. C4×C3⋊(C3⋊C8)C22semidirect
48. #63576C22semidirect
49. #63574C22semidirect
50. #63574C22semidirect
51. #63565C22semidirect
52. #63565C22semidirect
53. #63565C22semidirect
54. #63565C22semidirect
64. #5541D3semidirect
179. #926C2×D3semidirect
183. #924C2×D3semidirect
198. #870C2×D3semidirect
199. C4×Dic6C2×D3semidirect
702. C32#3296semidirect
790. C3#83494semidirect
791. C3#83598semidirect

Maximal subgroups

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

subgroupindex
C3×#55502
C3×#55412
D4×C3⋊(C3⋊C8)2
#105911882
#105911792
#105911702
#105911692
#105911012
#105910902
#105910832
C2×#635622
C4×#37152
#105902782
#105902702
#105902672
#835983
#834943