Finite Group Databasebeta

← #11870344

Subgroups — #11870344

Order 1152.

844 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595004C211yesmaximal, characteristic
2#10594986C211yesmaximal, characteristic, complemented
3#10592422C211yesmaximal, characteristic, complemented
4C3×#4735C211yesmaximal, characteristic, complemented
5C3×#4727C211yesmaximal, characteristic, complemented
6#10591124C211yesmaximal, characteristic, complemented
7#10591093C211yesmaximal, characteristic, complemented
8#10590954C211yesmaximal, characteristic, complemented
9#10590834C211yesmaximal, characteristic, complemented
10#10590709C211yesmaximal, characteristic, complemented
11#10590681C211yesmaximal, characteristic, complemented
12#10590676C211yesmaximal, characteristic, complemented
13#10590674C211yesmaximal, characteristic, complemented
14D3×#817C211yesmaximal, characteristic, complemented
15#10590670C211yesmaximal, characteristic, complemented
16#81328—31nomaximal
17#78654—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20#64135C2211yescharacteristic
21#64133C2211yescharacteristic
22C3×#930C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26Dic3×#67—21no—
27Dic3×#67—21no—
28#63970—21no—
29#63970—21no—
30#63908C2211yescharacteristic
31#63898—21no—
32D3×C4⋊Dic3C2211yescharacteristic
33D3×C4⋊Dic3C2211yescharacteristic
34D3×C4⋊Dic3C2211yescharacteristic
35#63887—21no—
36#63885—21no—
37#63857C2211yescharacteristic
38#63843—21no—
39#63841C2211yescharacteristic
40#63841C2211yescharacteristic
41C32×C22⋊C8C2211yescharacteristic
42#63645C2211yescharacteristic
43#63644C2211yescharacteristic
44#63643C2211yescharacteristic
45#63643C2211yescharacteristic
46C3×#830C2211yescharacteristic
47C3×#821C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#817C2211yescharacteristic
52C3×#817C2211yescharacteristic
53#63575C2211yescharacteristic
54#63573C2211yescharacteristic
55#63573C2211yescharacteristic
56#63573C2211yescharacteristic
57#63567C2211yescharacteristic
58#63567C2211yescharacteristic
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61#5833—31no—
62#5827—31no—
63#5608—31no—
64#5504—31no—
65C3×#481—31no—
66C3×#408—31no—
67#5133—31no—
68#5121—31no—
69#5113—31no—
70C2×#817—31no—
71#5035—31no—
72#4971—31no—
73#4868—31no—
74#4862—31no—
75#4861—31no—
76D3×#106—31no—
77#4784—31no—
78#4777—31no—
79#4772—31no—
80#4771—31no—
81#4737—31no—
82#4737—31no—
83#4735—31no—
84#4735D311yescharacteristic, complemented
85#4727D311yescharacteristic, complemented
86#4723—31no—
87#4723—31no—
88#4723—31no—
89#4723—61no—
90#4721—31no—
91#4721—31no—
92C22×C32×C4C2311yescharacteristic
93C2×#634C2311yescharacteristic
94C2×C3×#67—21no—
95C2×C3×#67D411yescharacteristic
96C2×C3×#67D411yescharacteristic
97C22×C3×Dic3—21no—
98C3×#235—22no—
99C3×#235—22no—
100C2×C3×D12D411yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6D411yescharacteristic
105C2×#625—21no—
106C2×#625—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111#3795—22no—
112#3795—22no—
113C2×C32×C8C2311yescharacteristic
114C2×C32×C8C2311yescharacteristic
115#3757—21no—
116#3757—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120#3750—21no—
121C4×C3⋊Dic3—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×ΓL(1,𝔽25)—22no—
130C3×D3×C8—22no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135(C2×D3)⋊Dic3—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×#237—31no—
144C2×#235—31no—
145C2×#235C2×D311yescharacteristic
146C2×C3×M16—31no—
147C22×C3×C8—31no—
148C3×#121—31no—
149C2×C3×C4⋊C4—31no—
150#946—61no—
151Q8×Dic3—61no—
152#939—61no—
153#939—61no—
154#939—61no—
155#938—31no—
156#938—61no—
157#938—61no—
158D4×Dic3—61no—
159D4×Dic3—61no—
160D4×Dic3—61no—
161#930—31no—
162#930C2×D311yescharacteristic
163C4×#67—61no—
164C4×#67—61no—
165#926—31no—
166#926—31no—
167#926—31no—
168#926—31no—
169#926—61no—
170C2×C4⋊Dic3—31no—
171C2×C4⋊Dic3—31no—
172C2×C4⋊Dic3—31no—
173C2×C4⋊Dic3C2×D311yescharacteristic
174#924—31no—
175#924—31no—
176#924—31no—
177#924—61no—
178C2×ΓL(1,𝔽25)C2×D311yescharacteristic
179C2×D3×C8C2×D311yescharacteristic
180#897—31no—
181#893—61no—
182#892—31no—
183#892—31no—
184D3×C4⋊C4—31no—
185D3×C4⋊C4—31no—
186D3×C4⋊C4—31no—
187#887—61no—
188#884—61no—
189#878—61no—
190C3×#106—31no—
191C3×#106—31no—
192C3×#102—31no—
193C3×#102—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#832—31no—
201#832—31no—
202#830C2×D311yescharacteristic
203#821—31no—
204#821—31no—
205#821C2×D311yescharacteristic
206#821C2×D311yescharacteristic
207(C2×D3)⋊C8C2×D311yescharacteristic
208(C2×D3)⋊C8C2×D311yescharacteristic
209#818—31no—
210#818—31no—
211#818—31no—
212#818—61no—
213#817—31no—
214#817—31no—
215#817—31no—
216#817—31no—
217#817—31no—
218#817—61no—
219#817C2×D311yescharacteristic
220#817C2×D311yescharacteristic
221#816—31no—
222#816—31no—
223#816—31no—
224#816—31no—
225#816—31no—
226#816—31no—
227#816—61no—
228#816—61no—
229#810—31no—
230#810—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
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247#634—21no—
248#634—21no—
249C3×#67—22no—
250C3×#67—22no—
251C3×#67—81no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—81no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C3×D12—22no—
259C3×D12—21no—
260C3×D12—21no—
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3#4112yes—
264C3×C4×D3#4112yes—
265C3×Dic6—22no—
266#625—42no—
267#625—81no—
268D3×Dic3—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—91no—
279#485—91no—
280#483—91no—
281#483—91no—
282#482—91no—
283#482—91no—
284#481—31no—
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×D4—31no—
295C2×C3×D4—31no—
296C2×C3×D4—31no—
297C2×C3×D4—31no—
298C2×C3×D4—61no—
299C22×C3×C4—21no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—61no—
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C2×#67—21no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67D1211yescharacteristic
311C2×#67D1211yescharacteristic
312C22×Dic3—21no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317#237—62no—
318#237—62no—
319#235—22no—
320#235—22no—
321#235—62no—
322#235—62no—
323C2×D12D1211yescharacteristic
324C2×D12C22×D311yescharacteristic
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3C22×D311yescharacteristic
330C2×C4×D3C22×D311yescharacteristic
331C2×Dic6—31no—
332C2×Dic6—31no—
333C2×Dic6—61no—
334C2×Dic6D1211yescharacteristic
335C3×M16—62no—
336C2×C3×C8—21no—
337C2×C3×C8—21no—
338C2×C3×C8—31no—
339C2×C3×C8—31no—
340C2×C3×C8—62no—
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C22×D311yescharacteristic
344C2×C3×C8C22×D311yescharacteristic
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—61no—
349C3×C22⋊C4—61no—
350#217—61no—
351#217—61no—
352#217—61no—
353#217—61no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—121no—
359#217—121no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365C4⋊Dic3—21no—
366C4⋊Dic3—31no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—121no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—121no—
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—21no—
405C2×C3×D3—21no—
406C2×C3×D3—21no—
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3#12312yes—
413C32×C4—21no—
414C32×C4C2×#4111yescharacteristic
415C32×C4C2×#4111yescharacteristic
416C3⋊Dic3—41no—
417C3⋊Dic3—41no—
418C3⋊Dic3—41no—
419C3⋊Dic3—41no—
420C3×Dic3—21no—
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—91no—
430C22⋊Q8—91no—
431C22⋊Q8—181no—
432#121—31no—
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—91no—
442#117—91no—
443#117—91no—
444C2×C4⋊C4—31no—
445C2×C4⋊C4—91no—
446C2×C4⋊C4—91no—
447C2×C4⋊C4—91no—
448#107—91no—
449#107—91no—
450#106—31no—
451#106—31no—
452#106—91no—
453#106—91no—
454#106—91no—
455#106—91no—
456#103—91no—
457#103—91no—
458#103—91no—
459#103—91no—
460#102—31no—
461#102—31no—
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×C3—61no—
472C23×C3C2×D1211yescharacteristic
473C23×C3D3×D411yescharacteristic
474C22×D3—21no—
475C22×D3C2×D1211yescharacteristic
476C22×D3C2×D1211yescharacteristic
477C3×Q8—62no—
478C3×D4—62no—
479C3×D4—62no—
480C3×D4—62no—
481C3×D4—61no—
482C3×D4—61no—
483C3×D4—241no—
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—241no—
502C2×C3×C4C2×D1211yescharacteristic
503C2×C3×C4D3×D411yescharacteristic
504C2×C3×C4C23×D311yescharacteristic
505C2×C3×C4C23×D311yescharacteristic
506#67—22no—
507#67—22no—
508#67—81no—
509#67—122no—
510#67—122no—
511#67—241no—
512#67—241no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—81no—
525C2×Dic3—121no—
526C2×Dic3—121no—
527C2×Dic3—121no—
528C2×Dic3—121no—
529C2×Dic3—122no—
530C2×Dic3—241no—
531C2×Dic3—241no—
532C2×Dic3—241no—
533C2×Dic3C2×D1211yescharacteristic
534C2×Dic3C2×D1211yescharacteristic
535D12—22no—
536D12—21no—
537D12—21no—
538C4×D3—21no—
539C4×D3—21no—
540C4×D3—122no—
541C4×D3—241no—
542C4×D3—241no—
543C4×D3—241no—
544C4×D3#23712yes—
545C4×D3#23712yes—
546Dic6—22no—
547Dic6—61no—
548Dic6—61no—
549Dic6—61no—
550Dic6—61no—
551Dic6—121no—
552Dic6—121no—
553C3×C8—21no—
554C3×C8—21no—
555C3×C8—21no—
556C3×C8—21no—
557C3×C8—41no—
558C3×C8—41no—
559C3×C8—61no—
560C3×C8—61no—
561C3⋊C8—21no—
562C3⋊C8—21no—
563C2×C32—41no—
564C2×C32C2×#12311yescharacteristic
565C2×C32#57711yescharacteristic
566C2×C32#57711yescharacteristic
567C3×D3—22no—
568C3×D3—41no—
569C3×D3—81no—
570#41—62no—
571#41—62no—
572#41—182no—
573#41—182no—
574C2×Q8—31no—
575C2×Q8—91no—
576C2×D4—31no—
577C2×D4—31no—
578C2×D4—31no—
579C2×D4—31no—
580C2×D4—61no—
581C2×D4—181no—
582C2×D4—181no—
583C22×C4—31no—
584C22×C4—31no—
585C22×C4—61no—
586C22×C4—181no—
587C22×C4—181no—
588C22×C4—181no—
589C22×C4—181no—
590C22×C4C2×D3211yescharacteristic
591M16—62no—
592C2×C8—31no—
593C2×C8—31no—
594C2×C8—62no—
595C2×C8C2×D3211yescharacteristic
596C2×C8C2×D3211yescharacteristic
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—61no—
601C4⋊C4—91no—
602C4⋊C4—91no—
603C4⋊C4—91no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C22⋊C4—61no—
610C22⋊C4—181no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C42—181no—
617C42—181no—
618C42—181no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—32no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—61no—
631C22×C3—61no—
632C22×C3—61no—
633C22×C3—61no—
634C22×C3—61no—
635C22×C3—121no—
636C22×C3—121no—
637C22×C3—121no—
638C22×C3C22×D1211yescharacteristic
639C22×C3C2×D3×D411yescharacteristic
640C2×D3—21no—
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—21no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3#88612yes—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—32no—
654C3×C4—41no—
655C3×C4—61no—
656C3×C4—121no—
657C3×C4—121no—
658C3×C4—121no—
659C3×C4C2×#23711yescharacteristic
660C3×C4C2×#23711yescharacteristic
661C3×C4D3×#4111yescharacteristic
662C3×C4D3×#4111yescharacteristic
663Dic3—21no—
664Dic3—41no—
665Dic3—41no—
666Dic3—41no—
667Dic3—121no—
668Dic3—121no—
669Dic3—121no—
670Dic3—121no—
671Dic3—121no—
672Dic3—121no—
673Dic3—121no—
674Dic3—121no—
675Dic3—241no—
676Dic3—241no—
677Dic3—241no—
678Dic3—241no—
679Dic3#88612yes—
680C32#309911yescharacteristic, complemented, Sylow
681C23—31no—
682C23—31no—
683C23—61no—
684C23D3×D1211yescharacteristic
685Q8—62no—
686Q8—181no—
687Q8—181no—
688D4—62no—
689D4—62no—
690D4—62no—
691D4—61no—
692D4—61no—
693D4—241no—
694D4—362no—
695D4—721no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—31no—
699C2×C4—32no—
700C2×C4—32no—
701C2×C4—31no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—181no—
708C2×C4—181no—
709C2×C4—181no—
710C2×C4—181no—
711C2×C4—241no—
712C2×C4—362no—
713C2×C4—721no—
714C2×C4—721no—
715C2×C4—721no—
716C2×C4D3×D1211yescharacteristic
717C2×C4C22×D3211yescharacteristic
718C8—21no—
719C8—21no—
720C8—61no—
721C8—61no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—41no—
726C2×C3—41no—
727C2×C3—62no—
728C2×C3—81no—
729C2×C3—121no—
730C2×C3—241no—
731C2×C3C2×#88611yescharacteristic
732C2×C3D3×#12311yescharacteristic
733C2×C3#575111yescharacteristic
734C2×C3#575111yescharacteristic
735C2×C3#576211yescharacteristic
736C2×C3#577511yescharacteristic
737D3—22no—
738D3—41no—
739D3—81no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—32no—
744C22—61no—
745C22—61no—
746C22—61no—
747C22—61no—
748C22—61no—
749C22—121no—
750C22—121no—
751C22—121no—
752C22C2×D3×D1211yescharacteristic
753C4—21no—
754C4—32no—
755C4—61no—
756C4—121no—
757C4—121no—
758C4—121no—
759C4—361no—
760C4—361no—
761C4—361no—
762C4—361no—
763C4D3×#23711yescharacteristic
764C4D3×#23711yescharacteristic
765C3—21no—
766C3#7865411yescharacteristic, complemented
767C3#8132811yescharacteristic, complemented
768C2—41no—
769C2—62no—
770C2—121no—
771C2—241no—
772C2D3×#88611yescharacteristic
773C2#1059467711yescharacteristic
774C2#1059471311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10595004C2
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
2. #10594986C2semidirect
3. #10592422C2semidirect
4. C3×#4735C2semidirect
5. C3×#4727C2semidirect
6. #10591124C2semidirect
7. #10591093C2semidirect
8. #10590954C2semidirect
9. #10590834C2semidirect
10. #10590709C2semidirect
11. #10590681C2semidirect
12. #10590676C2semidirect
13. #10590674C2semidirect
14. D3×#817C2semidirect
15. #10590670C2semidirect
84. #4735D3semidirect
85. #4727D3semidirect
680. C32#3099semidirect
766. C3#78654semidirect
767. C3#81328semidirect

Maximal subgroups

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

subgroupindex
#105950042
#105949862
#105924222
C3×#47352
C3×#47272
#105911242
#105910932
#105909542
#105908342
#105907092
#105906812
#105906762
#105906742
D3×#8172
#105906702
#813283
#786543