Finite Group Databasebeta

← #11884116

Subgroups — #11884116

Order 1152.

1050 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#204C211yesmaximal, characteristic, complemented
2#10594889C211yesmaximal, characteristic
3#10594803C211yesmaximal, characteristic, complemented
4C2×#63811C211yesmaximal, characteristic, complemented
5#10592810C211yesmaximal, characteristic, complemented
6C3×#5116C211yesmaximal, characteristic, complemented
7#10591185C211yesmaximal, characteristic, complemented
8#10591169C211yesmaximal, characteristic, complemented
9#10590961C211yesmaximal, characteristic, complemented
10#10590870C211yesmaximal, characteristic, complemented
11#10590845C211yesmaximal, characteristic, complemented
12#10590824C211yesmaximal, characteristic, complemented
13#10590796C211yesmaximal, characteristic, complemented
14#10590779C211yesmaximal, characteristic, complemented
15#10590748C211yesmaximal, characteristic, complemented
16#83866—31nomaximal
17#80771—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C2×#3797C2211yescharacteristic, complemented
21C2×#3796C2211yescharacteristic
22C22×C32×C8C2211yescharacteristic
23C4×#638C2211yescharacteristic
24C2×#3743C2211yescharacteristic, complemented
25C3×#924C2211yescharacteristic
26C3×#924C2211yescharacteristic
27C2×C3×Dic12C2211yescharacteristic, complemented
28C2×C3×#204—24no—
29C2×C3×#204C2211yescharacteristic
30C2×C3×#204C2211yescharacteristic
31C2×C3×#204C2211yescharacteristic
32C2×C3×#204C2211yescharacteristic
33#63977—21no—
34D3×#217—21no—
35#63964—21no—
36#63952—21no—
37#63916C2211yescharacteristic
38#63898C2211yescharacteristic
39#63888—21no—
40#63886—21no—
41#63884—21no—
42#63873C2211yescharacteristic, complemented
43#63871C2211yescharacteristic, complemented
44#63863C2211yescharacteristic
45#63843C2211yescharacteristic, complemented
46#63839—21no—
47C2×#3718C2211yescharacteristic, complemented
48C2×#3718C2211yescharacteristic, complemented
49C2×#3715C2211yescharacteristic
50C2×#3715C2211yescharacteristic
51#63811—24no—
52#63657C2211yescharacteristic
53#63647C2211yescharacteristic, complemented
54#63642C2211yescharacteristic, complemented
55#63641C2211yescharacteristic, complemented
56C3×#818C2211yescharacteristic, complemented
57C3×#816C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61#63562C2211yescharacteristic
62#63562C2211yescharacteristic
63C22×C3×SD16—31no—
64Q8×#67—31no—
65#5806—31no—
66C2×#918—31no—
67C2×#915—31no—
68C22×#204D311yescharacteristic, complemented
69#5632—31no—
70#5630—31no—
71C3×#467—31no—
72#5228—31no—
73#5218—31no—
74#5190—31no—
75#5174—31no—
76#5173—31no—
77#5170—31no—
78#5167—31no—
79#5166—31no—
80#5164—31no—
81#5162—31no—
82#5116D311yescharacteristic, complemented
83#5111—31no—
84#5111—31no—
85#5111—61no—
86#5050—31no—
87#5046—31no—
88#4889—31no—
89#4886—31no—
90#4818—31no—
91#4808—31no—
92#4806—31no—
93#4798—31no—
94C23×C3×D3—21no—
95C22×C32×C4C2311yescharacteristic
96C2×#638D411yescharacteristic
97C2×C4×C3⋊D3C2311yescharacteristic
98C22×C3×Dic3—21no—
99C2×C3×D12—22no—
100C2×C3×D12—21no—
101C2×C3×D12—41no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×Dic6—22no—
105C2×C3×Dic6—21no—
106C2×C3×Dic6—41no—
107C2×C3×Dic6C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×#627—21no—
112C2×#626—21no—
113C2×#626—21no—
114C2×#624—21no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117#3797—22no—
118#3797—41no—
119#3796—22no—
120#3796—41no—
121C2×C32×C8—22no—
122C2×C32×C8C2311yescharacteristic
123C2×C32×C8C2311yescharacteristic
124#3757D411yescharacteristic
125#3752D411yescharacteristic
126#3750D411yescharacteristic
127C4×C3⋊Dic3C2311yescharacteristic
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130#3743—22no—
131C3×#217—21no—
132C3×#217—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×Dic12—22no—
138C3×#204—22no—
139C3×#204—22no—
140C3×#204—22no—
141C3×#204D414yescomplemented
142#3724—21no—
143#3724—21no—
144Dic3⋊Dic3—21no—
145Dic3⋊Dic3—21no—
146#3722—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151Dic32—21no—
152#3718—22no—
153#3718—41no—
154#3715—22no—
155#3715—41no—
156#3266—91noSylow
157C22×C3×Q8—31no—
158C22×C3×D4—31no—
159C2×#239—31no—
160C2×D3×Q8—31no—
161C2×D3×Q8—31no—
162C2×#237—31no—
163C22×D12C2×D311yescharacteristic
164C22×Dic6C2×D311yescharacteristic
165C2×C3×Q16—31no—
166C2×C3×SD16—31no—
167C2×C3×SD16—31no—
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C2×C3×SD16—64no—
171C22×C3×C8—21no—
172C22×C3×C8C2×D311yescharacteristic
173C22×C3×C8C2×D311yescharacteristic
174C3×C22⋊Q8—31no—
175C3×C22⋊Q8—31no—
176#953—61no—
177C2×#217—61no—
178#947—31no—
179#946—31no—
180#946—61no—
181Q8×Dic3—31no—
182#944—31no—
183#944—31no—
184#944—61no—
185C2×#216—31no—
186C2×#216—31no—
187C2×#216—31no—
188C2×#216—31no—
189C2×#215—31no—
190C2×#215—31no—
191#939—61no—
192#938—31no—
193#936—31no—
194#935—61no—
195D4×Dic3—31no—
196C2×#214—31no—
197C2×#214—31no—
198C4×#67—31no—
199C4×#67—31no—
200C4×#67—61no—
201C4×#67—61no—
202#924—61no—
203#924C2×D311yescharacteristic
204#924C2×D311yescharacteristic
205#918—64no—
206#915—64no—
207C2×Dic12C2×D311yescharacteristic, complemented
208C2×#204—24no—
209C2×#204C2×D311yescharacteristic
210C2×#204C2×D311yescharacteristic
211C2×#204C2×D311yescharacteristic
212C2×#204C2×D311yescharacteristic
213C2×ΓL(1,𝔽25)—31no—
214C2×ΓL(1,𝔽25)—31no—
215C2×ΓL(1,𝔽25)—61no—
216#897—31no—
217#896—61no—
218#895—31no—
219#895—61no—
220#894—61no—
221#893—31no—
222#888—61no—
223#887—31no—
224#882—61no—
225#67⋊C4—61no—
226D3×C22⋊C4—61no—
227#878—61no—
228C3×#107—31no—
229C3×#103—31no—
230C3×#103—31no—
231#835—31no—
232#835—31no—
233#832—31no—
234#832—31no—
235#830—31no—
236#830—31no—
237#830—61no—
238(C2×D3)⋊C8—31no—
239(C2×D3)⋊C8—31no—
240(C2×D3)⋊C8—61no—
241#818C2×D311yescharacteristic, complemented
242#816C2×D311yescharacteristic, complemented
243#816C2×D311yescharacteristic, complemented
244#815—31no—
245#815—31no—
246#815—61no—
247Dic3⋊C8—31no—
248Dic3⋊C8—31no—
249Dic3⋊C8—61no—
250#810—31no—
251#810—31no—
252#809—31no—
253#809—31no—
254C23×C32C2×D411yescharacteristic
255C22×C3⋊D3C2×D411yescharacteristic
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—42no—
259C22×C3×D3—42no—
260C22×C3×D3—81no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4C2×D411yescharacteristic
264C2×C32×C4C2411yescharacteristic
265#638—22no—
266C2×C3⋊Dic3C2×D411yescharacteristic
267C2×C3⋊Dic3C2×D411yescharacteristic
268C2×C3⋊Dic3C2×D411yescharacteristic
269C4×C3⋊D3—21no—
270C4×C3⋊D3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—42no—
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—21no—
281C3×D12—42no—
282C3×D12C2×D412yes—
283C3×Dic6—21no—
284C3×Dic6—21no—
285C3×Dic6—21no—
286C3×Dic6—21no—
287C3×Dic6—21no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—42no—
291C3×Dic6C2×D412yes—
292#627—42no—
293#626—42no—
294#626—81no—
295#624—42no—
296D3×Dic3—42no—
297D3×Dic3—81no—
298C32×C8—21no—
299C32×C8C2×D412yes—
300C3⋊(C3⋊C8)—21no—
301C3⋊(C3⋊C8)—21no—
302C2×#137—91no—
303C22×SD16—31no—
304D4×Q8—91no—
305#546—91no—
306#497—91no—
307#468—91no—
308#467—31no—
309#464—91no—
310#461—91no—
311#452—91no—
312#451—91no—
313#450—91no—
314#448—91no—
315#440—91no—
316#435—91no—
317C24×C3—61no—
318C23×D3—21no—
319C2×C3×Q8—31no—
320C2×C3×Q8—31no—
321C2×C3×Q8—31no—
322C2×C3×Q8—31no—
323C2×C3×Q8—62no—
324C2×C3×Q8—61no—
325C2×C3×Q8—121no—
326C2×C3×D4—31no—
327C2×C3×D4—31no—
328C2×C3×D4—62no—
329C2×C3×D4—61no—
330C2×C3×D4—121no—
331C22×C3×C4—21no—
332C22×C3×C4—61no—
333C22×C3×C4C22×D311yescharacteristic
334C22×C3×C4C22×D311yescharacteristic
335C2×#67—31no—
336C2×#67—31no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C22×Dic3—21no—
341C22×Dic3—61no—
342C22×Dic3—61no—
343#239—62no—
344#239—121no—
345D3×Q8—62no—
346D3×Q8—62no—
347D3×Q8—121no—
348D3×Q8—121no—
349#237—62no—
350#237—121no—
351C2×D12—22no—
352C2×D12—21no—
353C2×D12—41no—
354C2×D12—61no—
355C2×D12—61no—
356C2×D12C22×D311yescharacteristic
357C2×D12C22×D311yescharacteristic
358C2×C4×D3—31no—
359C2×C4×D3—31no—
360C2×C4×D3—61no—
361C2×C4×D3—61no—
362C2×C4×D3—61no—
363C2×C4×D3—61no—
364C2×C4×D3—61no—
365C2×Dic6—22no—
366C2×Dic6—21no—
367C2×Dic6—41no—
368C2×Dic6—61no—
369C2×Dic6—61no—
370C2×Dic6C22×D311yescharacteristic
371C2×Dic6C22×D311yescharacteristic
372C2×Dic6C22×D311yescharacteristic
373C2×Dic6C22×D311yescharacteristic
374C3×Q16—62no—
375C3×SD16—34no—
376C3×SD16—62no—
377C3×SD16—62no—
378C3×SD16—62no—
379C2×C3×C8—22no—
380C2×C3×C8—22no—
381C2×C3×C8—21no—
382C2×C3×C8—21no—
383C2×C3×C8—42no—
384C2×C3×C8C22×D311yescharacteristic
385C2×C3×C8C22×D311yescharacteristic
386C2×C3×C8C22×D311yescharacteristic
387C2×C3×C8C22×D311yescharacteristic
388C3×C4⋊C4—31no—
389C3×C4⋊C4—31no—
390C3×C4⋊C4—61no—
391C3×C4⋊C4—61no—
392C3×C22⋊C4—61no—
393C3×C22⋊C4—61no—
394#217—21no—
395#217—21no—
396#217—31no—
397#217—31no—
398#217—61no—
399#217—61no—
400#217—61no—
401#217—61no—
402#217—61no—
403#216—62no—
404#216—62no—
405#216—121no—
406#216—121no—
407#215—62no—
408#215—121no—
409#214—62no—
410#214—121no—
411(C2×D3)⋊C4—31no—
412(C2×D3)⋊C4—31no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—61no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420C4⋊Dic3—61no—
421C4⋊Dic3—61no—
422C4⋊Dic3C22×D311yescharacteristic
423C4⋊Dic3C22×D311yescharacteristic
424Dic3⋊C4—21no—
425Dic3⋊C4—21no—
426Dic3⋊C4—31no—
427Dic3⋊C4—31no—
428Dic3⋊C4—61no—
429Dic3⋊C4—61no—
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433Dic3⋊C4—61no—
434Dic3⋊C4—61no—
435C4×Dic3—31no—
436C4×Dic3—31no—
437C4×Dic3—61no—
438C4×Dic3—61no—
439C4×Dic3—61no—
440C2×C3⋊C8—31no—
441C2×C3⋊C8—31no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—31no—
444C2×C3⋊C8—61no—
445C2×C3⋊C8—61no—
446Dic12—22no—
447#204—22no—
448#204—22no—
449#204—22no—
450#204#6714yescomplemented
451ΓL(1,𝔽25)—62no—
452ΓL(1,𝔽25)—62no—
453ΓL(1,𝔽25)—122no—
454C22×C32—21no—
455C22×C32—21no—
456C22×C32#13712yescomplemented
457C22×C32C22×D411yescharacteristic
458C2×C3⋊D3—21no—
459C2×C3⋊D3—21no—
460C2×C3⋊D3—21no—
461C2×C3×D3—22no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—84no—
468C32×C4—21no—
469C32×C4C22×D411yescharacteristic
470C32×C4H(5,𝔽2)11yescharacteristic
471C3⋊Dic3—21no—
472C3⋊Dic3—21no—
473C3⋊Dic3—21no—
474C3×Dic3—22no—
475C3×Dic3—41no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3—41no—
479C3×Dic3—41no—
480C2×#41—91no—
481C22×Q8—31no—
482C22×Q8—91no—
483C22×D4—31no—
484#137—184no—
485C2×Q16—31no—
486C2×Q16—91no—
487C2×Q16—91no—
488C2×SD16—31no—
489C2×SD16—31no—
490C2×SD16—31no—
491C2×SD16—31no—
492C2×SD16—64no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×M16—91no—
496C22×C8D3211yescharacteristic
497C4⋊Q8—91no—
498C4⋊Q8—181no—
499#124—91no—
500#123—181no—
501C22⋊Q8—31no—
502C22⋊Q8—31no—
503C22⋊Q8—91no—
504C22⋊Q8—181no—
505C22⋊Q8—181no—
506#121—91no—
507#121—181no—
508#120—181no—
509C4×Q8—91no—
510C4×D4—91no—
511C4×D4—91no—
512C4×D4—181no—
513C2×C22⋊C4—181no—
514#107—31no—
515C4⋊C8—91no—
516#103—31no—
517#103—31no—
518#103—91no—
519#103—91no—
520#102—91no—
521#102—91no—
522C22⋊C8—91no—
523C22⋊C8—91no—
524#97—91no—
525C23×C3—21no—
526C23×C3—61no—
527C23×C3—61no—
528C23×C3—122no—
529C23×C3—122no—
530C23×C3—241no—
531C23×C3D3×D411yescharacteristic
532C23×C3D3×D411yescharacteristic
533C22×D3—21no—
534C22×D3—21no—
535C22×D3—31no—
536C22×D3—31no—
537C22×D3—42no—
538C22×D3—42no—
539C22×D3—61no—
540C22×D3—81no—
541C3×Q8—32no—
542C3×Q8—61no—
543C3×Q8—61no—
544C3×Q8—61no—
545C3×Q8—61no—
546C3×Q8—61no—
547C3×Q8—61no—
548C3×Q8—61no—
549C3×Q8—122no—
550C3×D4—32no—
551C3×D4—61no—
552C3×D4—61no—
553C3×D4—61no—
554C3×D4—122no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—41no—
562C2×C3×C4—41no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—122no—
570C2×C3×C4D3×D411yescharacteristic
571C2×C3×C4D3×D411yescharacteristic
572C2×C3×C4C23×D311yescharacteristic
573C2×C3×C4C23×D311yescharacteristic
574#67—62no—
575#67—62no—
576#67—122no—
577#67—122no—
578#67—241no—
579C2×Dic3—21no—
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—31no—
586C2×Dic3—31no—
587C2×Dic3—31no—
588C2×Dic3—31no—
589C2×Dic3—31no—
590C2×Dic3—31no—
591C2×Dic3—42no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594C2×Dic3—61no—
595C2×Dic3—122no—
596C2×Dic3—241no—
597D12—21no—
598D12—21no—
599D12—21no—
600D12—42no—
601D12—122no—
602D12—241no—
603D12C2×#6712yes—
604C4×D3—61no—
605C4×D3—61no—
606C4×D3—61no—
607C4×D3—61no—
608C4×D3—121no—
609C4×D3—121no—
610C4×D3—122no—
611C4×D3—122no—
612C4×D3—122no—
613C4×D3—241no—
614Dic6—21no—
615Dic6—21no—
616Dic6—21no—
617Dic6—21no—
618Dic6—21no—
619Dic6—21no—
620Dic6—21no—
621Dic6—42no—
622Dic6—122no—
623Dic6—122no—
624Dic6C2×#6712yes—
625C3×C8—21no—
626C3×C8—21no—
627C3×C8—22no—
628C3×C8—41no—
629C3×C8D3×D412yes—
630C3×C8C2×#6712yes—
631C3⋊C8—61no—
632C3⋊C8—61no—
633C3⋊C8—61no—
634C3⋊C8—61no—
635C3⋊C8—121no—
636C3⋊C8—121no—
637C2×C32—22no—
638C2×C32D4211yescharacteristic
639C2×C32C2×#13711yescharacteristic
640C2×C32#57711yescharacteristic
641C3⋊D3—41no—
642C3×D3—42no—
643C3×D3—81no—
644C24—61no—
645#41—182no—
646#41—361no—
647C2×Q8—31no—
648C2×Q8—31no—
649C2×Q8—31no—
650C2×Q8—31no—
651C2×Q8—62no—
652C2×Q8—61no—
653C2×Q8—121no—
654C2×Q8—181no—
655C2×Q8—182no—
656C2×Q8—361no—
657C2×D4—31no—
658C2×D4—31no—
659C2×D4—62no—
660C2×D4—61no—
661C2×D4—91no—
662C2×D4—121no—
663C2×D4—181no—
664C2×D4—181no—
665C22×C4—61no—
666C22×C4—91no—
667C22×C4—181no—
668C22×C4—181no—
669C22×C4—181no—
670C22×C4C2×D3211yescharacteristic
671Q16—62no—
672Q16—182no—
673Q16—361no—
674SD16—34no—
675SD16—62no—
676SD16—62no—
677SD16—62no—
678SD16—182no—
679SD16—361no—
680M16—182no—
681C2×C8—22no—
682C2×C8—91no—
683C2×C8—91no—
684C2×C8C2×D3211yescharacteristic
685C2×C8C2×D3211yescharacteristic
686C4⋊C4—31no—
687C4⋊C4—31no—
688C4⋊C4—61no—
689C4⋊C4—61no—
690C4⋊C4—91no—
691C4⋊C4—181no—
692C4⋊C4—181no—
693C4⋊C4—181no—
694C4⋊C4—181no—
695C22⋊C4—61no—
696C22⋊C4—61no—
697C22⋊C4—91no—
698C22⋊C4—91no—
699C22⋊C4—181no—
700C22⋊C4—181no—
701C22⋊C4—181no—
702C22⋊C4—181no—
703C22⋊C4—181no—
704C42—91no—
705C42—181no—
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—21no—
710C22×C3—21no—
711C22×C3—22no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—62no—
715C22×C3—121no—
716C22×C3—121no—
717C22×C3—121no—
718C22×C3—121no—
719C22×C3—121no—
720C22×C3—244no—
721C22×C3#91512yescomplemented
722C22×C3#91812yescomplemented
723C22×C3C2×D3×D411yescharacteristic
724C22×C3C2×D3×D411yescharacteristic
725C2×D3—22no—
726C2×D3—41no—
727C2×D3—41no—
728C2×D3—41no—
729C2×D3—41no—
730C2×D3—41no—
731C2×D3—61no—
732C2×D3—61no—
733C2×D3—61no—
734C2×D3—61no—
735C2×D3—61no—
736C2×D3—61no—
737C2×D3—84no—
738C2×D3—121no—
739C2×D3—121no—
740C2×D3—121no—
741C3×C4—21no—
742C3×C4—21no—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—41no—
746C3×C4—62no—
747C3×C4—121no—
748C3×C4—121no—
749C3×C4—121no—
750C3×C4—121no—
751C3×C4—121no—
752C3×C4C2×D3×D411yescharacteristic
753C3×C4#100411yescharacteristic
754C3×C4#100911yescharacteristic
755C3×C4C22×#6711yescharacteristic
756Dic3—22no—
757Dic3—41no—
758Dic3—41no—
759Dic3—41no—
760Dic3—41no—
761Dic3—41no—
762Dic3—61no—
763Dic3—61no—
764Dic3—61no—
765Dic3—61no—
766Dic3—61no—
767Dic3—61no—
768Dic3—121no—
769Dic3—121no—
770Dic3—121no—
771C32#326611yescharacteristic, complemented, Sylow
772C23—61no—
773C23—61no—
774C23—91no—
775C23—122no—
776C23—122no—
777C23—241no—
778C23#380211yescharacteristic
779Q8—32no—
780Q8—61no—
781Q8—61no—
782Q8—61no—
783Q8—61no—
784Q8—61no—
785Q8—61no—
786Q8—61no—
787Q8—122no—
788Q8—362no—
789D4—32no—
790D4—61no—
791D4—61no—
792D4—61no—
793D4—122no—
794D4—182no—
795D4—362no—
796D4—721no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—91no—
806C2×C4—91no—
807C2×C4—91no—
808C2×C4—122no—
809C2×C4—181no—
810C2×C4—181no—
811C2×C4—362no—
812C2×C4—362no—
813C2×C4—721no—
814C2×C4#380211yescharacteristic
815C2×C4C22×D3211yescharacteristic
816C8—21no—
817C8—181no—
818C8—181no—
819C8D3×#6712yes—
820C2×C3—22no—
821C2×C3—22no—
822C2×C3—21no—
823C2×C3—21no—
824C2×C3—21no—
825C2×C3—42no—
826C2×C3—122no—
827C2×C3—241no—
828C2×C3#560911yescharacteristic
829C2×C3C2×#91511yescharacteristic
830C2×C3#576211yescharacteristic
831C2×C3C2×#91811yescharacteristic
832C2×C3#577011yescharacteristic
833C2×C3D4×#6711yescharacteristic
834D3—42no—
835D3—81no—
836D3—121no—
837D3—121no—
838D3—241no—
839C22—21no—
840C22—21no—
841C22—62no—
842C22—121no—
843C22—121no—
844C22—121no—
845C22—121no—
846C22—121no—
847C22—181no—
848C22—181no—
849C22—181no—
850C22—244no—
851C22#6381112yescomplemented
852C22C2×#380211yescharacteristic
853C4—21no—
854C4—62no—
855C4—121no—
856C4—121no—
857C4—121no—
858C4—121no—
859C4—121no—
860C4—181no—
861C4—181no—
862C4—181no—
863C4#6430711yescharacteristic
864C4C2×D3×#6711yescharacteristic
865C3—21no—
866C3#8077111yescharacteristic, complemented
867C3#8386611yescharacteristic, complemented
868C2—22no—
869C2—122no—
870C2—241no—
871C2—361no—
872C2#1059468611yescharacteristic
873C2C2×#6381111yescharacteristic
874C2#1059506911yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radical#10594889C2
hypercenterC22×C8D32
hypocenterC32#3266
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×C3×#204C2semidirect
3. #10594803C2semidirect
4. C2×#63811C2semidirect
5. #10592810C2semidirect
6. C3×#5116C2semidirect
7. #10591185C2semidirect
8. #10591169C2semidirect
9. #10590961C2semidirect
10. #10590870C2semidirect
11. #10590845C2semidirect
12. #10590824C2semidirect
13. #10590796C2semidirect
14. #10590779C2semidirect
15. #10590748C2semidirect
20. C2×#3797C22semidirect
24. C2×#3743C22semidirect
27. C2×C3×Dic12C22semidirect
42. #63873C22semidirect
43. #63871C22semidirect
45. #63843C22semidirect
47. C2×#3718C22semidirect
48. C2×#3718C22semidirect
53. #63647C22semidirect
54. #63642C22semidirect
55. #63641C22semidirect
56. C3×#818C22semidirect
57. C3×#816C22semidirect
58. C3×#816C22semidirect
59. #63565C22semidirect
60. #63565C22semidirect
68. C22×#204D3semidirect
82. #5116D3semidirect
141. C3×#204D4semidirect
207. C2×Dic12C2×D3semidirect
241. #818C2×D3semidirect
242. #816C2×D3semidirect
243. #816C2×D3semidirect
450. #204#67semidirect
456. C22×C32#137semidirect
721. C22×C3#915semidirect
722. C22×C3#918semidirect
771. C32#3266semidirect
851. C22#63811semidirect
866. C3#80771semidirect
867. C3#83866semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2042
#105948892
#105948032
C2×#638112
#105928102
C3×#51162
#105911852
#105911692
#105909612
#105908702
#105908452
#105908242
#105907962
#105907792
#105907482
#838663
#807713