Finite Group Databasebeta

← #11870382

Subgroups — #11870382

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#10595232C211yesmaximal, characteristic
2#10594510C211yesmaximal, characteristic, complemented
3#10592476C211yesmaximal, characteristic, complemented
4C3×#4784C211yesmaximal, characteristic, complemented
5C3×#4771C211yesmaximal, characteristic, complemented
6#10591425C211yesmaximal, characteristic, complemented
7#10591420C211yesmaximal, characteristic, complemented
8#10591415C211yesmaximal, characteristic, complemented
9#10590955C211yesmaximal, characteristic, complemented
10#10590715C211yesmaximal, characteristic, complemented
11#10590683C211yesmaximal, characteristic, complemented
12#10590675C211yesmaximal, characteristic, complemented
13D3×#808C211yesmaximal, characteristic, complemented
14#10590529C211yesmaximal, characteristic, complemented
15#10590519C211yesmaximal, characteristic, complemented
16#81377—31nomaximal
17#78875—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×#3798C2211yescharacteristic
20#64147C2211yescharacteristic
21C4⋊C4×C3⋊D3C2211yescharacteristic
22C3×#938C2211yescharacteristic
23C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
24C3×#892C2211yescharacteristic
25C3×D3×C4⋊C4C2211yescharacteristic
26#63978—21no—
27#63971—21no—
28#63970—21no—
29#63964—21no—
30C4×#626—21no—
31D3×C4⋊Dic3C2211yescharacteristic
32D3×C4⋊Dic3C2211yescharacteristic
33#63881—21no—
34#63879—21no—
35#63871C2211yescharacteristic
36#63856C2211yescharacteristic
37#63849C2211yescharacteristic
38#63841C2211yescharacteristic
39#63837—21no—
40C2×D3×C3⋊C8C2211yescharacteristic
41C32×#102C2211yescharacteristic
42#63659C2211yescharacteristic
43#63647C2211yescharacteristic
44#63644C2211yescharacteristic
45#63635C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#818C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#808C2211yescharacteristic
53#63575C2211yescharacteristic
54#63574C2211yescharacteristic
55#63573C2211yescharacteristic
56#63573C2211yescharacteristic
57#63566C2211yescharacteristic
58#63565C2211yescharacteristic
59#63557C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61#5833—31no—
62#5608—31no—
63#5523—31no—
64#5504—31no—
65C3×#482—31no—
66C3×#417—31no—
67#5233—31no—
68#5129—31no—
69#5121—31no—
70#5034—31no—
71#4996—31no—
72C2×#808—31no—
73#4888—31no—
74#4881—31no—
75#4862—31no—
76D3×#106—31no—
77#4814—31no—
78#4814—31no—
79#4805—31no—
80#4805—31no—
81#4784—31no—
82#4784D311yescharacteristic, complemented
83#4779—31no—
84#4777—31no—
85#4777—31no—
86#4777—31no—
87#4777—61no—
88#4772—31no—
89#4771D311yescharacteristic, complemented
90#4727—31no—
91#4721—31no—
92C2×C32×D4C2311yescharacteristic
93C2×#638—21no—
94C2×C4×C3⋊D3—21no—
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C3×#237—22no—
100C3×#237—22no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#627D411yescharacteristic
106C2×#626D411yescharacteristic
107C2×#626D411yescharacteristic
108C2×#625D411yescharacteristic
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111#3798—22no—
112#3798—22no—
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115#3757—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#217—21no—
121C3×(C2×D3)⋊C4—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—
130#3724—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134#3722—21no—
135#3722—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139Dic32—21no—
140D3×C3⋊C8—22no—
141#3099—91noSylow
142C2×C3×#41—31no—
143C2×#237C2×D311yescharacteristic
144C2×#235—31no—
145C2×#235—31no—
146C2×C3×M16—31no—
147C3×#121—31no—
148C3×#117—31no—
149C2×C3×C4⋊C4—31no—
150#946—31no—
151#946—31no—
152#939—61no—
153#939—61no—
154#939—61no—
155#938—31no—
156#938—31no—
157#938—61no—
158#938—61no—
159#938C2×D311yescharacteristic
160#930—61no—
161C4×#67—61no—
162C4×#67—61no—
163#926—31no—
164C2×C4⋊Dic3—31no—
165C2×C4⋊Dic3—31no—
166#924—31no—
167#924—61no—
168C22×C3⋊C8—31no—
169C2×ΓL(1,𝔽25)C2×D311yescharacteristic
170C2×D3×C8—31no—
171#897—31no—
172#893—61no—
173#892—31no—
174#892—31no—
175#892—31no—
176#892C2×D311yescharacteristic
177D3×C4⋊C4—31no—
178D3×C4⋊C4—31no—
179D3×C4⋊C4—31no—
180D3×C4⋊C4—31no—
181D3×C4⋊C4—61no—
182D3×C4⋊C4C2×D311yescharacteristic
183#887—61no—
184#884—61no—
185#67⋊C4—61no—
186#67⋊C4—61no—
187#878—61no—
188C4×D12—61no—
189C4×Dic6—61no—
190C3×#107—31no—
191C3×#106—31no—
192C3×#103—31no—
193C3×#103—31no—
194C3×#102—21no—
195C3×#102—31no—
196C3×#102—31no—
197C3×#102C2×D311yescharacteristic
198C3×#102C2×D311yescharacteristic
199C3×C22⋊C8—31no—
200#835—31no—
201#835—31no—
202#832—31no—
203#832—31no—
204#832—61no—
205#832C2×D311yescharacteristic
206#832C2×D311yescharacteristic
207#830—31no—
208(C2×D3)⋊C8—31no—
209(C2×D3)⋊C8—31no—
210(C2×D3)⋊C8—31no—
211(C2×D3)⋊C8—31no—
212(C2×D3)⋊C8—31no—
213(C2×D3)⋊C8—61no—
214(C2×D3)⋊C8C2×D311yescharacteristic
215#818—31no—
216#818C2×D311yescharacteristic
217#817—31no—
218#817—31no—
219#817—31no—
220#817—31no—
221#817—61no—
222#816—31no—
223#816C2×D311yescharacteristic
224#810—31no—
225#810C2×D311yescharacteristic
226#808—31no—
227#808—31no—
228#808—31no—
229#808—31no—
230#808—31no—
231#808—31no—
232#808—61no—
233#808C2×D311yescharacteristic
234#807—31no—
235C23×C32—21no—
236C22×C3⋊D3C2×D411yescharacteristic
237C22×C3×D3C2×D411yescharacteristic
238C22×C3×D3C2×D411yescharacteristic
239C32×D4—21no—
240C32×D4—21no—
241C2×C32×C4—21no—
242C2×C32×C4C2411yescharacteristic
243#638—81no—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3C2×D411yescharacteristic
247C4×C3⋊D3—21no—
248C4×C3⋊D3—21no—
249C4×C3⋊D3—81no—
250C3×#67—42no—
251C3×#67—81no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—42no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261C3×C4×D3—81no—
262C3×C4×D3#4112yes—
263C3×C4×D3#4112yes—
264C3×Dic6—21no—
265C3×Dic6—21no—
266#627—22no—
267#626—22no—
268#626—22no—
269#625—22no—
270D3×Dic3—81no—
271D3×Dic3—81no—
272C32×C8—21no—
273C3⋊(C3⋊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—31no—
283#482—91no—
284#481—91no—
285#481—91no—
286#428—91no—
287C2×#106—91no—
288#417—31no—
289#416—91no—
290#408—91no—
291C3×#41—62no—
292C3×#41—62no—
293C2×C3×Q8—31no—
294C2×C3×D4—21no—
295C2×C3×D4—61no—
296C2×C3×D4—61no—
297C2×C3×D4C22×D311yescharacteristic
298C2×C3×D4C22×D311yescharacteristic
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C2×#67—21no—
304C2×#67—21no—
305C2×#67—31no—
306C2×#67—31no—
307C2×#67—31no—
308C2×#67—31no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—121no—
312C22×Dic3—21no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315#237—22no—
316#237—22no—
317#235—62no—
318#235—62no—
319#235—62no—
320#235—62no—
321C2×D12—31no—
322C2×D12—31no—
323C2×C4×D3—21no—
324C2×C4×D3—31no—
325C2×C4×D3—31no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—121no—
332C2×C4×D3C22×D311yescharacteristic
333C2×C4×D3C22×D311yescharacteristic
334C2×Dic6—31no—
335C2×Dic6—31no—
336C2×Dic6C22×D311yescharacteristic
337C3×M16—62no—
338C2×C3×C8—21no—
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C3×C4⋊C4—21no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C42—61no—
353#217—21no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—121no—
359(C2×D3)⋊C4—21no—
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—
366C4⋊Dic3—31no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3C22×D311yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378Dic3⋊C4—21no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—121no—
387C4×Dic3—21no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—61no—
395C2×C3⋊C8—62no—
396C2×C3⋊C8C22×D311yescharacteristic
397C2×C3⋊C8C22×D311yescharacteristic
398ΓL(1,𝔽25)—22no—
399D3×C8—62no—
400C22×C32—41no—
401C22×C32—41no—
402C22×C32—41no—
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—21no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3#12312yes—
413C32×C4—41no—
414C32×C4C2×#4111yescharacteristic
415C32×C4C2×#4111yescharacteristic
416C3⋊Dic3—21no—
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—91no—
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—31no—
442#117—91no—
443#117—91no—
444C2×C4⋊C4—31no—
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—31no—
461#102—31no—
462#102—91no—
463#102D3211yescharacteristic
464C22⋊C8—31no—
465C22⋊C8—91no—
466C22⋊C8—91no—
467C22⋊C8—91no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—31no—
471C23×C3—31no—
472C23×C3—41no—
473C22×D3—31no—
474C22×D3—31no—
475C22×D3—61no—
476C22×D3D3×D411yescharacteristic
477C22×D3D3×D411yescharacteristic
478C3×Q8—61no—
479C3×Q8—61no—
480C3×D4—21no—
481C3×D4—21no—
482C3×D4—21no—
483C3×D4—21no—
484C3×D4—41no—
485C3×D4—41no—
486C3×D4—122no—
487C3×D4—241no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—31no—
492C2×C3×C4—32no—
493C2×C3×C4—32no—
494C2×C3×C4—31no—
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×C4—122no—
503C2×C3×C4—241no—
504C2×C3×C4C23×D311yescharacteristic
505C2×C3×C4C23×D311yescharacteristic
506#67—42no—
507#67—62no—
508#67—62no—
509#67—62no—
510#67—62no—
511#67—81no—
512#67—241no—
513#67—241no—
514#67—242no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—31no—
520C2×Dic3—31no—
521C2×Dic3—42no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—121no—
528C2×Dic3—121no—
529C2×Dic3—241no—
530C2×Dic3—241no—
531C2×Dic3D3×D411yescharacteristic
532C2×Dic3D3×D411yescharacteristic
533D12—62no—
534D12—62no—
535C4×D3—21no—
536C4×D3—21no—
537C4×D3—61no—
538C4×D3—61no—
539C4×D3—61no—
540C4×D3—61no—
541C4×D3—81no—
542C4×D3—121no—
543C4×D3—121no—
544C4×D3—241no—
545C4×D3—241no—
546C4×D3—241no—
547C4×D3—241no—
548C4×D3—242no—
549C4×D3#23512yes—
550C4×D3#23712yes—
551Dic6—21no—
552Dic6—21no—
553Dic6—62no—
554Dic6—62no—
555C3×C8—21no—
556C3×C8—21no—
557C3×C8—41no—
558C3×C8—61no—
559C3×C8—61no—
560C3⋊C8—21no—
561C3⋊C8—21no—
562C3⋊C8—61no—
563C3⋊C8—61no—
564C3⋊C8—121no—
565C2×C32—81no—
566C2×C32C2×#12311yescharacteristic
567C2×C32#57711yescharacteristic
568C2×C32#57711yescharacteristic
569C3⋊D3—41no—
570C3×D3—22no—
571C3×D3—41no—
572#41—62no—
573#41—62no—
574#41—182no—
575#41—182no—
576C2×Q8—31no—
577C2×Q8—91no—
578C2×D4—61no—
579C2×D4—61no—
580C2×D4—91no—
581C2×D4—91no—
582C2×D4—91no—
583C2×D4—181no—
584C2×D4C2×D3211yescharacteristic
585C22×C4—31no—
586C22×C4—31no—
587C22×C4—61no—
588C22×C4—61no—
589C22×C4—91no—
590C22×C4—181no—
591C22×C4—181no—
592C22×C4—181no—
593M16—62no—
594C2×C8—31no—
595C2×C8—31no—
596C2×C8—91no—
597C2×C8—182no—
598C2×C8C2×D3211yescharacteristic
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—61no—
603C4⋊C4—91no—
604C4⋊C4—91no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4C2×D3211yescharacteristic
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—21no—
622C22×C3—32no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—61no—
630C22×C3—61no—
631C22×C3—61no—
632C22×C3—61no—
633C22×C3—61no—
634C22×C3—81no—
635C22×C3—81no—
636C22×C3—81no—
637C22×C3C2×D3×D411yescharacteristic
638C22×C3C2×D3×D411yescharacteristic
639C2×D3—21no—
640C2×D3—21no—
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—62no—
645C2×D3—61no—
646C2×D3—61no—
647C2×D3—61no—
648C2×D3—61no—
649C2×D3—61no—
650C2×D3—61no—
651C2×D3—121no—
652C2×D3—121no—
653C2×D3#88312yes—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—32no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—61no—
660C3×C4—81no—
661C3×C4—121no—
662C3×C4—121no—
663C3×C4—121no—
664C3×C4—121no—
665C3×C4C2×#23511yescharacteristic
666C3×C4C2×#23711yescharacteristic
667C3×C4D3×#4111yescharacteristic
668C3×C4D3×#4111yescharacteristic
669Dic3—21no—
670Dic3—41no—
671Dic3—41no—
672Dic3—41no—
673Dic3—41no—
674Dic3—61no—
675Dic3—61no—
676Dic3—121no—
677Dic3—121no—
678Dic3—121no—
679Dic3—121no—
680Dic3—121no—
681Dic3—241no—
682Dic3—241no—
683Dic3#88312yes—
684C32#309911yescharacteristic, complemented, Sylow
685C23—21no—
686C23—31no—
687C23—31no—
688C23—91no—
689Q8—61no—
690Q8—61no—
691Q8—182no—
692D4—21no—
693D4—21no—
694D4—122no—
695D4—182no—
696D4—182no—
697D4—182no—
698D4—241no—
699D4—721no—
700C2×C4—21no—
701C2×C4—31no—
702C2×C4—32no—
703C2×C4—32no—
704C2×C4—31no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—91no—
712C2×C4—122no—
713C2×C4—181no—
714C2×C4—181no—
715C2×C4—181no—
716C2×C4—181no—
717C2×C4—241no—
718C2×C4—721no—
719C2×C4—721no—
720C2×C4—721no—
721C2×C4C22×D3211yescharacteristic
722C8—21no—
723C8—61no—
724C8—61no—
725C8—181no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—62no—
730C2×C3—81no—
731C2×C3—81no—
732C2×C3—121no—
733C2×C3—161no—
734C2×C3C2×#88311yescharacteristic
735C2×C3D3×#12311yescharacteristic
736C2×C3#577011yescharacteristic
737C2×C3#577511yescharacteristic
738C2×C3#577511yescharacteristic
739C2×C3#577811yescharacteristic
740D3—22no—
741D3—41no—
742D3—122no—
743D3—121no—
744D3—121no—
745C22—32no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—61no—
750C22—61no—
751C22—61no—
752C22—61no—
753C22—61no—
754C22—181no—
755C22—181no—
756C22—181no—
757C22D32×D411yescharacteristic
758C4—32no—
759C4—41no—
760C4—61no—
761C4—121no—
762C4—121no—
763C4—121no—
764C4—121no—
765C4—181no—
766C4—361no—
767C4—361no—
768C4D3×#23511yescharacteristic
769C4D3×#23711yescharacteristic
770C3—21no—
771C3#7887511yescharacteristic, complemented
772C3#8137711yescharacteristic, complemented
773C2—62no—
774C2—81no—
775C2—121no—
776C2—361no—
777C2D3×#88311yescharacteristic
778C2#1059473611yescharacteristic
779C2#1059475411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595232C2
hypercenter#102D32
hypocenterC32#3099
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. #10594510C2semidirect
3. #10592476C2semidirect
4. C3×#4784C2semidirect
5. C3×#4771C2semidirect
6. #10591425C2semidirect
7. #10591420C2semidirect
8. #10591415C2semidirect
9. #10590955C2semidirect
10. #10590715C2semidirect
11. #10590683C2semidirect
12. #10590675C2semidirect
13. D3×#808C2semidirect
14. #10590529C2semidirect
15. #10590519C2semidirect
82. #4784D3semidirect
89. #4771D3semidirect
684. C32#3099semidirect
771. C3#78875semidirect
772. C3#81377semidirect

Maximal subgroups

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

subgroupindex
#105952322
#105945102
#105924762
C3×#47842
C3×#47712
#105914252
#105914202
#105914152
#105909552
#105907152
#105906832
#105906752
D3×#8082
#105905292
#105905192
#813773
#788753