Finite Group Databasebeta

← #11870342

Subgroups — #11870342

Order 1152.

853 conjugacy classes of subgroups.

The subgroup lattice has 781 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594992C211yesmaximal, characteristic, complemented
2#10594894C211yesmaximal, characteristic
3#10592434C211yesmaximal, characteristic, complemented
4C3×#4727C211yesmaximal, characteristic, complemented
5C3×#4723C211yesmaximal, characteristic, complemented
6#10591136C211yesmaximal, characteristic, complemented
7#10591126C211yesmaximal, characteristic, complemented
8#10590711C211yesmaximal, characteristic, complemented
9#10590705C211yesmaximal, characteristic, complemented
10#10590690C211yesmaximal, characteristic, complemented
11#10590683C211yesmaximal, characteristic, complemented
12#10590677C211yesmaximal, characteristic, complemented
13#10590675C211yesmaximal, characteristic, complemented
14D3×#817C211yesmaximal, characteristic, complemented
15#10590671C211yesmaximal, characteristic, complemented
16#81521—31nomaximal
17#78654—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20#64139C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C3×#926C2211yescharacteristic
23C3×#924C2211yescharacteristic
24C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26#67⋊Dic3—21no—
27#67⋊Dic3—21no—
28#63971—21no—
29#63958—21no—
30#63909C2211yescharacteristic
31Dic3×D12—21no—
32D3×C4⋊Dic3C2211yescharacteristic
33D3×C4⋊Dic3C2211yescharacteristic
34D3×C4⋊Dic3C2211yescharacteristic
35#63888—21no—
36#63886—21no—
37#63856C2211yescharacteristic
38Dic3×Dic6—21no—
39#63841C2211yescharacteristic
40#63841C2211yescharacteristic
41C32×C22⋊C8C2211yescharacteristic
42#63648C2211yescharacteristic
43#63648C2211yescharacteristic
44#63644C2211yescharacteristic
45#63644C2211yescharacteristic
46C3×#830C2211yescharacteristic
47C3×(C2×D3)⋊C8C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#818C2211yescharacteristic
50C3×#817C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#816C2211yescharacteristic
53#63575C2211yescharacteristic
54#63573C2211yescharacteristic
55#63573C2211yescharacteristic
56#63573C2211yescharacteristic
57#63566C2211yescharacteristic
58#63566C2211yescharacteristic
59#63564C2211yescharacteristic
60#63564C2211yescharacteristic
61#5833—31no—
62#5827—31no—
63#5629—31no—
64#5523—31no—
65C3×#485—31no—
66C3×#408—31no—
67#5133—31no—
68#5121—31no—
69#5113—31no—
70C2×#817—31no—
71#5043—31no—
72#5003—31no—
73#4885—31no—
74#4881—31no—
75#4863—31no—
76D3×#106—31no—
77#4815—31no—
78#4805—31no—
79#4804—31no—
80#4803—31no—
81#4737—31no—
82#4737—31no—
83#4735—31no—
84#4735—31no—
85#4735—31no—
86#4735—61no—
87#4727D311yescharacteristic, complemented
88#4723—31no—
89#4723D311yescharacteristic, complemented
90#4721—31no—
91#4721—31no—
92C22×C32×C4C2311yescharacteristic
93C2×#638—21no—
94C22×C3⋊Dic3—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C3×#67D411yescharacteristic
97C2×C3×#67D411yescharacteristic
98C3×#235—22no—
99C3×#235—22no—
100C2×C3×D12D411yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6D411yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#626—21no—
106C2×#626—21no—
107C2×#624—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111#3799—22no—
112#3799—22no—
113C2×C32×C8C2311yescharacteristic
114C2×C32×C8C2311yescharacteristic
115#3752—21no—
116C4⋊(C3⋊Dic3)—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120C3×#217—21no—
121C3×#217—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3—21no—
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×ΓL(1,𝔽25)—22no—
130C3×D3×C8—22no—
131#3724—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135#3722—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139Dic32—21no—
140Dic32—21no—
141#3099—91noSylow
142C2×C3×#41—31no—
143C2×#239—31no—
144C2×#235—31no—
145C2×#235C2×D311yescharacteristic
146C2×C3×M16—31no—
147C22×C3×C8—31no—
148C3×C22⋊Q8—31no—
149C3×#117—31no—
150#946—31no—
151#946—61no—
152Q8×Dic3—61no—
153#939—61no—
154#939—61no—
155#938—61no—
156D4×Dic3—61no—
157D4×Dic3—61no—
158D4×Dic3—61no—
159#930—31no—
160#930—31no—
161#930—31no—
162#930—61no—
163#926—31no—
164#926—31no—
165#926C2×D311yescharacteristic
166C2×C4⋊Dic3—31no—
167C2×C4⋊Dic3—31no—
168C2×C4⋊Dic3—31no—
169C2×C4⋊Dic3—31no—
170C2×C4⋊Dic3—31no—
171C2×C4⋊Dic3—61no—
172#924—31no—
173#924C2×D311yescharacteristic
174C2×ΓL(1,𝔽25)C2×D311yescharacteristic
175C2×D3×C8C2×D311yescharacteristic
176#896—61no—
177#895—31no—
178#895—61no—
179#892—31no—
180#892—31no—
181D3×C4⋊C4—31no—
182D3×C4⋊C4—31no—
183D3×C4⋊C4—31no—
184#884—61no—
185#884—61no—
186#67⋊C4—61no—
187#67⋊C4—61no—
188C4×D12—61no—
189C4×Dic6—61no—
190C3×#107—31no—
191C3×#106—31no—
192C3×#103—31no—
193C3×#103—31no—
194C3×C22⋊C8—21no—
195C3×C22⋊C8—31no—
196C3×C22⋊C8—31no—
197C3×C22⋊C8—31no—
198C3×C22⋊C8C2×D311yescharacteristic
199C3×C22⋊C8C2×D311yescharacteristic
200#835—31no—
201#835—31no—
202#830C2×D311yescharacteristic
203#821—31no—
204#821—31no—
205#821—31no—
206#821—31no—
207#821—31no—
208#821—31no—
209#821—61no—
210#821—61no—
211(C2×D3)⋊C8C2×D311yescharacteristic
212(C2×D3)⋊C8C2×D311yescharacteristic
213#818—31no—
214#818C2×D311yescharacteristic
215#817—31no—
216#817—31no—
217#817—31no—
218#817—31no—
219#817—31no—
220#817—31no—
221#817—31no—
222#817—61no—
223#817—61no—
224#817C2×D311yescharacteristic
225#816—31no—
226#816—31no—
227#816C2×D311yescharacteristic
228#816C2×D311yescharacteristic
229#809—31no—
230#809—31no—
231#808—31no—
232#808—31no—
233#808—31no—
234#807—31no—
235C23×C32C2×D411yescharacteristic
236C22×C3⋊D3—21no—
237C22×C3×D3C2×D411yescharacteristic
238C22×C3×D3C2×D411yescharacteristic
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4C2×D411yescharacteristic
242C2×C32×C4C2411yescharacteristic
243#638—81no—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—81no—
248C4⋊(C3⋊D3)—21no—
249C4⋊(C3⋊D3)—21no—
250C3×#67—22no—
251C3×#67—22no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C3×D12—22no—
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261C3×C4×D3#4112yes—
262C3×C4×D3#4112yes—
263C3×Dic6—22no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266#626—42no—
267#626—81no—
268#624—42no—
269D3×Dic3—81no—
270D3×Dic3—81no—
271D3×Dic3—81no—
272C32×C8—21no—
273C32×C8—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#537—91no—
277#520—91no—
278#485—31no—
279#485—91no—
280#483—91no—
281#483—91no—
282#482—91no—
283#482—91no—
284#481—91no—
285#481—91no—
286#428—91no—
287C2×#106—91no—
288#417—91no—
289#416—91no—
290#408—31no—
291C3×#41—62no—
292C3×#41—62no—
293C2×C3×Q8—31no—
294C2×C3×Q8—31no—
295C2×C3×D4—31no—
296C2×C3×D4—31no—
297C2×C3×D4—31no—
298C22×C3×C4—21no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4C22×D311yescharacteristic
302C22×C3×C4C22×D311yescharacteristic
303C2×#67—61no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—121no—
308C2×#67D1211yescharacteristic
309C2×#67D1211yescharacteristic
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315C22×Dic3—121no—
316#239—62no—
317#239—62no—
318#235—22no—
319#235—22no—
320#235—62no—
321#235—62no—
322C2×D12—31no—
323C2×D12—31no—
324C2×D12—61no—
325C2×D12—61no—
326C2×D12—61no—
327C2×D12D1211yescharacteristic
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3C22×D311yescharacteristic
334C2×C4×D3C22×D311yescharacteristic
335C2×Dic6D1211yescharacteristic
336C2×Dic6C22×D311yescharacteristic
337C3×M16—62no—
338C2×C3×C8—21no—
339C2×C3×C8—21no—
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C2×C3×C8—62no—
343C2×C3×C8C22×D311yescharacteristic
344C2×C3×C8C22×D311yescharacteristic
345C2×C3×C8C22×D311yescharacteristic
346C2×C3×C8C22×D311yescharacteristic
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C42—61no—
354#217—21no—
355#217—21no—
356#217—61no—
357#217—61no—
358#217—61no—
359(C2×D3)⋊C4—61no—
360(C2×D3)⋊C4—61no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—121no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—121no—
382C4⋊Dic3C22×D311yescharacteristic
383C4⋊Dic3C22×D311yescharacteristic
384C4⋊Dic3C22×D311yescharacteristic
385Dic3⋊C4—21no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391C4×Dic3—21no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C2×C3⋊C8C22×D311yescharacteristic
397C2×C3⋊C8C22×D311yescharacteristic
398ΓL(1,𝔽25)—22no—
399D3×C8—22no—
400C22×C32—21no—
401C22×C32—21no—
402C22×C32—21no—
403C22×C32C22×D411yescharacteristic
404C2×C3⋊D3—41no—
405C2×C3⋊D3—41no—
406C2×C3⋊D3—41no—
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3#12312yes—
413C32×C4—21no—
414C32×C4C2×#4111yescharacteristic
415C32×C4C2×#4111yescharacteristic
416C3⋊Dic3—41no—
417C3⋊Dic3—41no—
418C3⋊Dic3—41no—
419C3×Dic3—21no—
420C3×Dic3—41no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3#12312yes—
425C2×#41—31no—
426C2×#41—91no—
427C2×M16—31no—
428C22×C8—31no—
429C22⋊Q8—31no—
430C22⋊Q8—91no—
431C22⋊Q8—181no—
432#121—91no—
433#121—91no—
434#121—181no—
435#121—181no—
436#121—181no—
437C4×Q8—181no—
438C4×D4—181no—
439C4×D4—181no—
440C4×D4—181no—
441#117—31no—
442#117—91no—
443#117—91no—
444C2×C4⋊C4—91no—
445C2×C4⋊C4—91no—
446C2×C4⋊C4—91no—
447C2×C4⋊C4—91no—
448#107—31no—
449#107—91no—
450#106—31no—
451#106—91no—
452#106—91no—
453#106—91no—
454#106—91no—
455#106—91no—
456#103—31no—
457#103—31no—
458#103—91no—
459#103—91no—
460#102—91no—
461#102—91no—
462#102—91no—
463#102—91no—
464C22⋊C8—31no—
465C22⋊C8—31no—
466C22⋊C8—31no—
467C22⋊C8D3211yescharacteristic
468C23×C3—21no—
469C23×C3—31no—
470C23×C3—31no—
471C23×C3C2×D1211yescharacteristic
472C23×C3D3×D411yescharacteristic
473C22×D3—61no—
474C22×D3—61no—
475C22×D3—121no—
476C22×D3C2×D1211yescharacteristic
477C22×D3C2×D1211yescharacteristic
478C3×Q8—62no—
479C3×Q8—61no—
480C3×Q8—61no—
481C3×D4—62no—
482C3×D4—62no—
483C3×D4—62no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—31no—
491C2×C3×C4—32no—
492C2×C3×C4—32no—
493C2×C3×C4—31no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4C2×D1211yescharacteristic
503C2×C3×C4D3×D411yescharacteristic
504C2×C3×C4C23×D311yescharacteristic
505C2×C3×C4C23×D311yescharacteristic
506#67—22no—
507#67—22no—
508#67—122no—
509#67—241no—
510#67—241no—
511#67—241no—
512#67—242no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—121no—
524C2×Dic3—121no—
525C2×Dic3—121no—
526C2×Dic3—241no—
527C2×Dic3—241no—
528C2×Dic3—241no—
529C2×Dic3—241no—
530C2×Dic3—241no—
531C2×Dic3—242no—
532C2×Dic3C2×D1211yescharacteristic
533C2×Dic3C2×D1211yescharacteristic
534D12—22no—
535D12—61no—
536D12—61no—
537D12—61no—
538D12—61no—
539D12—121no—
540D12—121no—
541D12—122no—
542D12—241no—
543C4×D3—21no—
544C4×D3—21no—
545C4×D3—122no—
546C4×D3—122no—
547C4×D3—241no—
548C4×D3—241no—
549C4×D3—241no—
550C4×D3#23712yes—
551C4×D3#23712yes—
552Dic6—22no—
553Dic6—21no—
554Dic6—21no—
555C3×C8—21no—
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—21no—
559C3×C8—41no—
560C3×C8—41no—
561C3×C8—61no—
562C3×C8—61no—
563C3⋊C8—21no—
564C3⋊C8—21no—
565C2×C32—41no—
566C2×C32C2×#12311yescharacteristic
567C2×C32#57711yescharacteristic
568C2×C32#57711yescharacteristic
569C3⋊D3—81no—
570C3×D3—22no—
571C3×D3—41no—
572#41—62no—
573#41—62no—
574#41—182no—
575#41—182no—
576C2×Q8—31no—
577C2×Q8—31no—
578C2×D4—31no—
579C2×D4—31no—
580C2×D4—31no—
581C2×D4—91no—
582C2×D4—181no—
583C2×D4—181no—
584C2×D4—181no—
585C22×C4—31no—
586C22×C4—31no—
587C22×C4—181no—
588C22×C4—181no—
589C22×C4—181no—
590C22×C4—181no—
591C22×C4—181no—
592C22×C4C2×D3211yescharacteristic
593M16—62no—
594C2×C8—31no—
595C2×C8—31no—
596C2×C8—62no—
597C2×C8C2×D3211yescharacteristic
598C2×C8C2×D3211yescharacteristic
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—61no—
603C4⋊C4—91no—
604C4⋊C4—91no—
605C4⋊C4—91no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C22⋊C4—181no—
618C42—61no—
619C42—181no—
620C42—181no—
621C22×C3—22no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—32no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—61no—
633C22×C3—61no—
634C22×C3—61no—
635C22×C3—61no—
636C22×C3—61no—
637C22×C3C22×D1211yescharacteristic
638C22×C3C2×D3×D411yescharacteristic
639C2×D3—21no—
640C2×D3—21no—
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—121no—
645C2×D3—121no—
646C2×D3—121no—
647C2×D3—121no—
648C2×D3—121no—
649C2×D3—121no—
650C2×D3—241no—
651C2×D3—241no—
652C2×D3—241no—
653C2×D3#88612yes—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—32no—
659C3×C4—41no—
660C3×C4—61no—
661C3×C4—121no—
662C3×C4—121no—
663C3×C4—121no—
664C3×C4—121no—
665C3×C4C2×#23711yescharacteristic
666C3×C4C2×#23711yescharacteristic
667C3×C4D3×#4111yescharacteristic
668C3×C4D3×#4111yescharacteristic
669Dic3—21no—
670Dic3—41no—
671Dic3—41no—
672Dic3—41no—
673Dic3—41no—
674Dic3—121no—
675Dic3—121no—
676Dic3—121no—
677Dic3—121no—
678Dic3—121no—
679Dic3—121no—
680Dic3—241no—
681Dic3—241no—
682Dic3—241no—
683Dic3#88612yes—
684C32#309911yescharacteristic, complemented, Sylow
685C23—31no—
686C23—31no—
687C23—181no—
688C23D3×D1211yescharacteristic
689Q8—62no—
690Q8—61no—
691Q8—61no—
692D4—62no—
693D4—62no—
694D4—62no—
695D4—181no—
696D4—181no—
697D4—362no—
698D4—721no—
699D4—721no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—31no—
703C2×C4—32no—
704C2×C4—32no—
705C2×C4—31no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—181no—
713C2×C4—181no—
714C2×C4—181no—
715C2×C4—362no—
716C2×C4—721no—
717C2×C4—721no—
718C2×C4—721no—
719C2×C4—721no—
720C2×C4D3×D1211yescharacteristic
721C2×C4C22×D3211yescharacteristic
722C8—21no—
723C8—21no—
724C8—61no—
725C8—61no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—42no—
730C2×C3—41no—
731C2×C3—41no—
732C2×C3—62no—
733C2×C3—121no—
734C2×C3C2×#88611yescharacteristic
735C2×C3D3×#12311yescharacteristic
736C2×C3#575111yescharacteristic
737C2×C3#575111yescharacteristic
738C2×C3#577011yescharacteristic
739C2×C3#577811yescharacteristic
740D3—22no—
741D3—41no—
742D3—241no—
743D3—241no—
744D3—481no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—32no—
749C22—61no—
750C22—61no—
751C22—61no—
752C22—61no—
753C22—61no—
754C22—361no—
755C22—361no—
756C22—361no—
757C22C2×D3×D1211yescharacteristic
758C4—21no—
759C4—32no—
760C4—61no—
761C4—121no—
762C4—121no—
763C4—121no—
764C4—121no—
765C4—361no—
766C4—361no—
767C4—361no—
768C4D3×#23711yescharacteristic
769C4D3×#23711yescharacteristic
770C3—21no—
771C3#7865411yescharacteristic, complemented
772C3#8152111yescharacteristic, complemented
773C2—41no—
774C2—62no—
775C2—121no—
776C2—721no—
777C2D3×#88611yescharacteristic
778C2#1059467911yescharacteristic
779C2#1059471511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10594894C2
hypercenterC22⋊C8D32
hypocenterC32#3099
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. #10594992C2semidirect
3. #10592434C2semidirect
4. C3×#4727C2semidirect
5. C3×#4723C2semidirect
6. #10591136C2semidirect
7. #10591126C2semidirect
8. #10590711C2semidirect
9. #10590705C2semidirect
10. #10590690C2semidirect
11. #10590683C2semidirect
12. #10590677C2semidirect
13. #10590675C2semidirect
14. D3×#817C2semidirect
15. #10590671C2semidirect
87. #4727D3semidirect
89. #4723D3semidirect
684. C32#3099semidirect
771. C3#78654semidirect
772. C3#81521semidirect

Maximal subgroups

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

subgroupindex
#105949922
#105948942
#105924342
C3×#47272
C3×#47232
#105911362
#105911262
#105907112
#105907052
#105906902
#105906832
#105906772
#105906752
D3×#8172
#105906712
#815213
#786543