Finite Group Databasebeta

← #72222787

Subgroups — #72222787

Order 2304.

1369 conjugacy classes of subgroups.

The subgroup lattice has 1229 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11899640C211yesmaximal, characteristic
2C3×#79899C211yesmaximal, characteristic, complemented
3#11860954C211yesmaximal, characteristic, complemented
4#11797983C211yesmaximal, characteristic, complemented
5#11797972C211yesmaximal, characteristic, complemented
6#11797971C211yesmaximal, characteristic, complemented
7#11797953C211yesmaximal, characteristic, complemented
8#11797935C211yesmaximal, characteristic, complemented
9#11797928C211yesmaximal, characteristic, complemented
10#11797923C211yesmaximal, characteristic, complemented
11C3×#70928C211yesmaximal, characteristic, complemented
12D3×#4494C211yesmaximal, characteristic, complemented
13#11796946C211yesmaximal, characteristic, complemented
14D3×#4566C211yesmaximal, characteristic, complemented
15#11795944C211yesmaximal, characteristic, complemented
16#10948646—31nomaximal
17#10948641—31nomaximal
18C3×D3×#135C2211yescharacteristic
19C3×#5750—21no—
20C2×#63808C2211yescharacteristic
21#10593890—21no—
22C32×#444C2211yescharacteristic
23#10592892C2211yescharacteristic
24#10592410C2211yescharacteristic, complemented
25C3×#5197C2211yescharacteristic
26C3×#5195C2211yescharacteristic
27C3×#5144—21no—
28C3×#4894C2211yescharacteristic
29C3×D3×#108C2211yescharacteristic
30C3×#4824—21no—
31C3×#4821—21no—
32C3×#4717C2211yescharacteristic
33C3×#4716C2211yescharacteristic, complemented
34C3×#4708C2211yescharacteristic
35#10591048C412yescomplemented
36#10591047C412yescomplemented
37#10591034C412yescomplemented
38#10591033C412yescomplemented
39#10590812C2211yescharacteristic, complemented
40#10590792—21no—
41#10590768C2211yescharacteristic, complemented
42D3×#817C2211yescharacteristic
43#10590671—21no—
44#10590636C2211yescharacteristic
45#10590634C2211yescharacteristic
46D3×#812C2211yescharacteristic
47D3×#812C2211yescharacteristic
48C4×#3717—21no—
49#10589432C2211yescharacteristic
50#10589361C2211yescharacteristic, complemented
51#10589360C2211yescharacteristic, complemented
52#10589332C2211yescharacteristic, complemented
53C3×#4566C2211yescharacteristic
54C3×#4496C2211yescharacteristic, complemented
55C3×#4494C2211yescharacteristic, complemented
56C3×#4466C2211yescharacteristic, complemented
57#10589138C2211yescharacteristic, complemented
58#10589137C2211yescharacteristic, complemented
59#10589129C2211yescharacteristic, complemented
60#10589128C2211yescharacteristic, complemented
61#10589124C2211yescharacteristic
62#10589123C2211yescharacteristic
63#10589105C2211yescharacteristic, complemented
64#10589105C2211yescharacteristic, complemented
65C3×#2957—31no—
66#83894—31no—
67#82039—31no—
68#79899D311yescharacteristic, complemented
69#79832—31no—
70#78574—31no—
71C3×#2180—31no—
72C2×#4566—31no—
73#71521—31no—
74#70929—31no—
75#70929—31no—
76#70929—31no—
77#70929—31no—
78#70929—31no—
79#70929—61no—
80#70928—31no—
81#70928—31no—
82#70928—31no—
83#70928D311yescharacteristic, complemented
84#70917—31no—
85#70687—31no—
86C2×#4494—31no—
87#69884—31no—
88D3×#365—31no—
89#69310—31no—
90#69266—31no—
91#69264—31no—
92D3×#360—31no—
93#69249—31no—
94#69091—31no—
95#69087—31no—
96C3×D3×#41—21no—
97C2×#3799—21no—
98C32×#135C2311yescharacteristic
99C32×#131—21no—
100C2×#3745C2311yescharacteristic
101C4×C4⋊(C3⋊D3)—21no—
102C3×#950—21no—
103C3×#948—21no—
104C3×#919C2×C411yescharacteristic, complemented
105C3×D3×Q16C2×C411yescharacteristic, complemented
106C3×#916—21no—
107C3×D3×SD16—21no—
108C3×#912C2×C411yescharacteristic, complemented
109C3×D3×D8C2×C411yescharacteristic, complemented
110C3×#907—21no—
111C3×#907—41no—
112C3×D3×M16—21no—
113C3×D3×M16—41no—
114C2×C3×Dic12C2311yescharacteristic
115C3×#904C2311yescharacteristic
116C3×#901—21no—
117C3×#901—41no—
118C2×C3×ΓL(1,𝔽25)—41no—
119C2×C3×ΓL(1,𝔽25)D411yescharacteristic
120C2×C3×D3×C8C2311yescharacteristic
121C3×#872D411yescharacteristic
122C3×C4×Dic6—21no—
123#63894—21no—
124D3×C4⋊Dic3—21no—
125#63883—41no—
126#63881—41no—
127#63880—41no—
128Dic3×Dic6—21no—
129#63836—41no—
130C2×#3717—21no—
131#63808—21no—
132#63808—21no—
133#63808C2×C412yes—
134#63808C2×C412yes—
135C32×#108C2311yescharacteristic
136C32×#104—21no—
137C32×#97C2311yescharacteristic
138#63655C2×C412yescomplemented
139#63653C2×C412yescomplemented
140#63648—21no—
141#63644C2311yescharacteristic
142#63639C2311yescharacteristic
143#63639C2311yescharacteristic
144C3×#837—21no—
145C3×#829C2×C412yescomplemented
146C3×#827C2×C412yescomplemented
147C3×#825—21no—
148C3×#822—21no—
149C3×#819C2311yescharacteristic
150C3×#817C2311yescharacteristic
151C3×#816—21no—
152C3×#815C2311yescharacteristic
153C3×C8×Dic3D411yescharacteristic
154C3×#812C2311yescharacteristic
155C3×#812C2311yescharacteristic
156C3×#805—21no—
157C3×C4×C3⋊C8D411yescharacteristic
158#63573—21no—
159#63566—21no—
160#63564—21no—
161#63550C2×C412yescomplemented
162#63549C2×C412yescomplemented
163#63547C2×C412yescomplemented
164#63546C2×C412yescomplemented
165#63543—21no—
166#63543C2×C412yescomplemented
167D3×C3⋊C16—21no—
168D3×C3⋊C16C2×C412yescomplemented
169#33469—91noSylow
170C2×C3×#135—31no—
171C3×#568—61no—
172D3×#135C2×D311yescharacteristic
173C2×#919—31no—
174#5750—21no—
175C2×#904—31no—
176#5574—61no—
177#5523—61no—
178C3×#510—31no—
179C3×#444—21no—
180C3×#444—31no—
181C3×#444—31no—
182C3×#444—31no—
183C3×#444C2×D311yescharacteristic
184C3×#444C2×D311yescharacteristic
185C3×#443—61no—
186C3×#443—61no—
187C3×#441—31no—
188C2×C3×#108—31no—
189C3×#421—61no—
190C3×#405—31no—
191#5197C2×D311yescharacteristic
192#5195—31no—
193#5195C2×D311yescharacteristic
194#5194—32no—
195#5194—32no—
196#5193—31no—
197#5193—31no—
198#5193—31no—
199#5193—61no—
200#5184—31no—
201#5179—31no—
202#5179—32no—
203#5147—32no—
204#5144—21no—
205#5133—61no—
206C2×#817—31no—
207C2×#812—31no—
208C2×#812—31no—
209C4×#215—61no—
210#4919—32no—
211#4918—32no—
212#4916—32no—
213#4914—32no—
214#4908—31no—
215D3×M32—31no—
216D3×M32—31no—
217#4894C2×D311yescharacteristic
218D3×#108C2×D311yescharacteristic
219#4869—31no—
220D3×#106—31no—
221#4824—21no—
222#4821—21no—
223#4803—61no—
224#4788—61no—
225#4717C2×D311yescharacteristic
226#4716—31no—
227#4716C2×D311yescharacteristic, complemented
228#4711—31no—
229#4711—31no—
230#4711—31no—
231#4711—61no—
232#4708C2×D311yescharacteristic
233C4×#204—61no—
234C4×#204—61no—
235C3×#365—31no—
236C3×#362—31no—
237C3×#360—31no—
238C3×#347—31no—
239#4566—31no—
240#4566—31no—
241#4566—31no—
242#4566—31no—
243#4566—61no—
244#4566C2×D311yescharacteristic
245#4565—31no—
246#4518—31no—
247#4516—31no—
248#4513—31no—
249#4512—31no—
250#4512—31no—
251#4496—31no—
252#4496C2×D311yescharacteristic, complemented
253#4495—31no—
254#4495—31no—
255#4495—31no—
256#4495—61no—
257#4494—31no—
258#4494—31no—
259#4494—31no—
260#4494—31no—
261#4494—61no—
262#4494C2×D311yescharacteristic, complemented
263#4488—31no—
264#4487—31no—
265#4466—31no—
266#4466—31no—
267#4466—31no—
268#4466—31no—
269#4466—61no—
270#4466C2×D311yescharacteristic, complemented
271C32×#41—21no—
272C2×C4⋊(C3⋊D3)—21no—
273C2×C4×C3⋊D3—41no—
274C3×#239—21no—
275C3×D3×Q8—21no—
276C3×#237—21no—
277C3×#237—41no—
278C3×D3×D4—21no—
279C3×D3×D4—41no—
280C3×#235—21no—
281C3×#235—41no—
282C2×C3×C4×D3—41no—
283C2×C3×C4×D3C2×D411yescharacteristic
284C2×C3×Dic6—21no—
285C2×#626—41no—
286C2×#624—41no—
287C2×#624—41no—
288C2×D3×Dic3—41no—
289#3799—22no—
290#3799—22no—
291#3799—41no—
292#3799—41no—
293C32×Q16C22×C411yescharacteristic
294C32×SD16—21no—
295C32×D8C22×C411yescharacteristic
296C32×M16—21no—
297C32×M16—41no—
298C2×C32×C8—41no—
299C2×C32×C8C2×D411yescharacteristic
300C2×C32×C8C2411yescharacteristic
301C32×C42C2×D411yescharacteristic
302#3752—41no—
303C4⋊(C3⋊Dic3)—21no—
304#3745—21no—
305#3745C22×C412yes—
306C3×#216—21no—
307C3×#215—21no—
308C3×#214—21no—
309C3×#213—21no—
310C3×(C2×D3)⋊C4—21no—
311C3×C4⋊Dic3—21no—
312C3×Dic3⋊C4—21no—
313C3×Dic3⋊C4—41no—
314C3×C4×Dic3—41no—
315C3×C4×Dic3C2×D411yescharacteristic
316C3×#208—21no—
317C3×#208—41no—
318C2×C3×C3⋊C8—41no—
319C2×C3×C3⋊C8C2×D411yescharacteristic
320C2×C3×C3⋊C8C2×D411yescharacteristic
321C3×Dic12—21no—
322C3×Dic12C22×C411yescharacteristic
323C3×Dic12C22×C412yes—
324C3×D24C22×C411yescharacteristic
325C3×#204—21no—
326C3×ΓL(1,𝔽25)—21no—
327C3×ΓL(1,𝔽25)—21no—
328C3×ΓL(1,𝔽25)—41no—
329C3×ΓL(1,𝔽25)—41no—
330C3×ΓL(1,𝔽25)—41no—
331C3×D3×C8—41no—
332C3×D3×C8—41no—
333C3×D3×C8—41no—
334C3×D3×C8C22×C411yescharacteristic
335C3×D3×C8C22×C411yescharacteristic
336C3×D3×C8#4111yescharacteristic
337C3×D3×C8#4111yescharacteristic
338Dic3⋊Dic3—41no—
339Dic3⋊Dic3—41no—
340#3722—41no—
341Dic32—41no—
342#3717—22no—
343#3717—22no—
344C3⋊(C3⋊C16)—21no—
345C3⋊(C3⋊C16)C22×C412yes—
346C3×C3⋊C16—21no—
347C3×C3⋊C16C22×C412yes—
348#3414—91no—
349#2957—31no—
350#2952—91no—
351AGL(1,ℤ/16)—91no—
352AGL(1,ℤ/16)—91no—
353AGL(1,ℤ/16)—91no—
354AGL(1,ℤ/16)—91no—
355#2180—31no—
356#2180—91no—
357#2180—91no—
358#2180—91no—
359C2×#365—91no—
360#2148—91no—
361C2×#360—91no—
362#2110—91no—
363C2×C3×#41—61no—
364D3×#41—21no—
365C2×#239—61no—
366C2×#235—61no—
367C3×#135—21no—
368C3×#135—31no—
369C3×#135—31no—
370C3×#135—31no—
371C3×#135—61no—
372C3×#135—61no—
373C3×#135C22×D311yescharacteristic
374C3×#135C22×D311yescharacteristic
375C2×C3×Q16—31no—
376C2×C3×Q16—31no—
377C2×C3×SD16—61no—
378C2×C3×D8—31no—
379C3×#131—21no—
380C3×#131—21no—
381C3×#131—41no—
382C3×#131—61no—
383C3×#131—61no—
384C3×#131—61no—
385C3×#131—121no—
386C3×#131—121no—
387C2×C3×M16—31no—
388C2×C3×M16—61no—
389C2×C3×M16—121no—
390C2×C3×M16—121no—
391C22×C3×C8—31no—
392C3×C4×Q8—61no—
393C3×#117—31no—
394#950—21no—
395#948—21no—
396Q8×Dic3—61no—
397C2×#215—61no—
398C2×C4⋊Dic3—61no—
399#919—32no—
400#919—32no—
401#919—61no—
402#919—61no—
403#919C4×D311yescharacteristic, complemented
404D3×Q16C4×D311yescharacteristic, complemented
405#916—21no—
406D3×SD16—21no—
407#912C4×D311yescharacteristic, complemented
408D3×D8C4×D311yescharacteristic, complemented
409#907—21no—
410#907—41no—
411D3×M16—21no—
412D3×M16—41no—
413C2×Dic12C22×D311yescharacteristic
414#904—32no—
415#904—32no—
416#904—61no—
417#904—61no—
418#904C22×D311yescharacteristic
419C2×D24—31no—
420C2×D24—31no—
421C2×D24—61no—
422C2×#204—61no—
423#901—21no—
424#901—41no—
425C2×ΓL(1,𝔽25)—41no—
426C2×ΓL(1,𝔽25)#6711yescharacteristic
427C2×D3×C8C22×D311yescharacteristic
428#893—61no—
429#893—121no—
430#892—121no—
431D3×C4⋊C4—61no—
432D3×C4⋊C4—121no—
433D3×C4⋊C4—121no—
434#67⋊C4—121no—
435#67⋊C4—121no—
436C4×D12—61no—
437C4×D12—61no—
438C4×D12—61no—
439C4×D12—121no—
440C4×D12—121no—
441#872—121no—
442#872#6711yescharacteristic
443C4×Dic6—21no—
444C4×Dic6—61no—
445C3×Q32—32no—
446C3×SD32—32no—
447C3×M32—31no—
448C3×M32—31no—
449C3×#108—21no—
450C3×#108—31no—
451C3×#108—61no—
452C3×#108C22×D311yescharacteristic
453C3×#108C22×D311yescharacteristic
454C3×#106—31no—
455C3×#104—21no—
456C3×#104—21no—
457C3×#104—41no—
458C3×#104—61no—
459C3×#104—61no—
460C3×#104—61no—
461C3×#103—61no—
462C3×#97—21no—
463C3×#97—31no—
464C3×#97C22×D311yescharacteristic
465C3×#97C22×D311yescharacteristic
466C3×C4×C8—31no—
467C3×C4×C8—31no—
468#837—21no—
469#835—61no—
470#829—32no—
471#829—32no—
472#829C4×D312yescomplemented
473#828—32no—
474#828—32no—
475#828—32no—
476#828—32no—
477#828—62no—
478#827—32no—
479#827C4×D312yescomplemented
480#826—32no—
481#826—32no—
482#826—32no—
483#826—62no—
484#825—21no—
485#822—21no—
486#821—61no—
487#821—61no—
488#821—61no—
489#821—121no—
490#819C22×D311yescharacteristic
491#817—31no—
492#817—31no—
493#817—61no—
494#817—61no—
495#817C22×D311yescharacteristic
496#816—21no—
497#816—61no—
498#815C22×D311yescharacteristic
499C8×Dic3#6711yescharacteristic
500#812—31no—
501#812—31no—
502#812—32no—
503#812—31no—
504#812—31no—
505#812—61no—
506#812—61no—
507#812—61no—
508#812C22×D311yescharacteristic
509#812C22×D311yescharacteristic
510C2×C3⋊C16—32no—
511C2×C3⋊C16—61no—
512#809—61no—
513#808—61no—
514#805—21no—
515C4×C3⋊C8#6711yescharacteristic
516#800—32no—
517D48—32no—
518#798—32no—
519#798—61no—
520D3×C16—32no—
521D3×C16—61no—
522C22×C3⋊D3—41no—
523C22×C3×D3—41no—
524C22×C3×D3AGL(1,ℤ/8)11yescharacteristic
525C32×Q8—21no—
526C32×D4—21no—
527C32×D4—41no—
528C2×C32×C4—21no—
529C2×C32×C4—41no—
530C2×C32×C4C22×D411yescharacteristic
531C2×C3⋊Dic3—41no—
532C4⋊(C3⋊D3)—22no—
533C4⋊(C3⋊D3)—41no—
534C4×C3⋊D3—161no—
535C3×#67—41no—
536C3×#67—41no—
537C3×#67—41no—
538C2×C3×Dic3—21no—
539C2×C3×Dic3—41no—
540C2×C3×Dic3—41no—
541C2×C3×Dic3—41no—
542C2×C3×Dic3AGL(1,ℤ/8)11yescharacteristic
543C3×D12—21no—
544C3×D12—41no—
545C3×C4×D3—41no—
546C3×C4×D3—41no—
547C3×C4×D3—41no—
548C3×C4×D3C4×D411yescharacteristic
549C3×C4×D3C4×D411yescharacteristic
550C3×C4×D3AGL(1,ℤ/8)11yescharacteristic
551C3×C4×D3AGL(1,ℤ/8)11yescharacteristic
552C3×Dic6—22no—
553C3×Dic6—21no—
554C3×Dic6—41no—
555C3×Dic6—41no—
556#626—42no—
557#626—42no—
558#624—42no—
559#624—42no—
560#624—161no—
561D3×Dic3—161no—
562C32×C8—21no—
563C32×C8—41no—
564C32×C8C23×C411yescharacteristic
565C32×C8C2×#4111yescharacteristic
566C3×C3⋊C8—21no—
567C3×C3⋊C8—41no—
568C3×C3⋊C8C4×D411yescharacteristic
569C3×C3⋊C8C4×D411yescharacteristic
570C2×#135—31no—
571C2×#135—91no—
572#568—61no—
573#520—181no—
574#510—31no—
575#510—92no—
576#510—91no—
577#509—91no—
578#509—92no—
579#509—91no—
580#508—92no—
581#508—92no—
582C2×M32—91no—
583C2×M32—91no—
584#444—31no—
585#444—31no—
586#444—31no—
587#444D3211yescharacteristic
588#443—61no—
589#443—61no—
590#442—91no—
591#442—91no—
592#441—31no—
593#441—91no—
594C4×SD16—181no—
595C4×SD16—181no—
596C2×#108—31no—
597C2×#106—91no—
598#421—61no—
599#417—181no—
600#405—31no—
601#365—31no—
602#365—91no—
603#365—91no—
604#365—91no—
605#362—31no—
606#362—91no—
607#361—91no—
608#361—91no—
609#360—31no—
610#360—91no—
611#360—91no—
612#360—91no—
613#347—31no—
614#347—91no—
615#347—91no—
616#347—91no—
617C3×#41—21no—
618C3×#41—21no—
619C3×#41—41no—
620C3×#41—61no—
621C3×#41—61no—
622C3×#41—61no—
623C3×#41—121no—
624C3×#41—121no—
625C2×C3×Q8—61no—
626C2×C3×Q8—61no—
627C2×C3×D4—61no—
628C2×C3×D4—121no—
629C22×C3×C4—31no—
630C22×C3×C4—121no—
631C2×#67—121no—
632C22×Dic3—121no—
633#239—21no—
634#239—62no—
635#239—62no—
636#239—121no—
637#239—121no—
638D3×Q8—21no—
639#237—21no—
640#237—41no—
641D3×D4—21no—
642D3×D4—41no—
643#235—21no—
644#235—41no—
645#235—62no—
646#235—62no—
647#235—121no—
648#235—121no—
649C2×D12—61no—
650C2×D12—61no—
651C2×D12—121no—
652C2×D12—121no—
653C2×C4×D3—41no—
654C2×C4×D3—121no—
655C2×C4×D3—121no—
656C2×C4×D3—121no—
657C2×C4×D3—121no—
658C2×C4×D3—121no—
659C2×C4×D3—121no—
660C2×C4×D3—121no—
661C2×C4×D3—241no—
662C2×C4×D3C2×#6711yescharacteristic
663C2×Dic6—21no—
664C3×Q16—21no—
665C3×Q16—31no—
666C3×Q16—32no—
667C3×Q16—61no—
668C3×Q16—61no—
669C3×Q16C2×C4×D311yescharacteristic
670C3×Q16C2×C4×D311yescharacteristic
671C3×SD16—21no—
672C3×SD16—21no—
673C3×SD16—41no—
674C3×SD16—61no—
675C3×SD16—61no—
676C3×SD16—61no—
677C3×D8—21no—
678C3×D8—31no—
679C3×D8—61no—
680C3×D8C2×C4×D311yescharacteristic
681C3×D8C2×C4×D311yescharacteristic
682C3×M16—21no—
683C3×M16—21no—
684C3×M16—41no—
685C3×M16—41no—
686C3×M16—41no—
687C3×M16—61no—
688C3×M16—61no—
689C3×M16—61no—
690C3×M16—81no—
691C3×M16—121no—
692C3×M16—121no—
693C3×M16—121no—
694C3×M16—121no—
695C2×C3×C8—21no—
696C2×C3×C8—21no—
697C2×C3×C8—31no—
698C2×C3×C8—31no—
699C2×C3×C8—31no—
700C2×C3×C8—31no—
701C2×C3×C8—31no—
702C2×C3×C8—31no—
703C2×C3×C8—41no—
704C2×C3×C8—41no—
705C2×C3×C8—81no—
706C2×C3×C8—121no—
707C2×C3×C8—121no—
708C2×C3×C8—121no—
709C2×C3×C8—121no—
710C2×C3×C8D3×D411yescharacteristic
711C2×C3×C8C2×#6711yescharacteristic
712C2×C3×C8C23×D311yescharacteristic
713C2×C3×C8C23×D311yescharacteristic
714C3×C4⋊C4—61no—
715C3×C4⋊C4—61no—
716C3×C4⋊C4—121no—
717C3×C22⋊C4—61no—
718C3×C42—21no—
719C3×C42—31no—
720C3×C42—121no—
721C3×C42D3×D411yescharacteristic
722C3×C42C2×#6711yescharacteristic
723#216—21no—
724#215—21no—
725#215—62no—
726#215—62no—
727#214—21no—
728#213—21no—
729(C2×D3)⋊C4—21no—
730(C2×D3)⋊C4—121no—
731(C2×D3)⋊C4—121no—
732(C2×D3)⋊C4—121no—
733(C2×D3)⋊C4—121no—
734(C2×D3)⋊C4—241no—
735C4⋊Dic3—21no—
736C4⋊Dic3—61no—
737C4⋊Dic3—61no—
738C4⋊Dic3—121no—
739C4⋊Dic3—121no—
740C4⋊Dic3—121no—
741Dic3⋊C4—21no—
742Dic3⋊C4—41no—
743Dic3⋊C4—121no—
744Dic3⋊C4—121no—
745C4×Dic3—41no—
746C4×Dic3—121no—
747C4×Dic3—121no—
748C4×Dic3C2×#6711yescharacteristic
749#208—21no—
750#208—41no—
751C2×C3⋊C8—41no—
752C2×C3⋊C8C2×#6711yescharacteristic
753C2×C3⋊C8C2×#6711yescharacteristic
754Dic12—21no—
755Dic12C2×C4×D311yescharacteristic
756Dic12C2×C4×D312yes—
757D24—32no—
758D24—32no—
759D24—62no—
760D24—61no—
761D24—61no—
762D24—121no—
763D24C2×C4×D311yescharacteristic
764#204—21no—
765#204—62no—
766#204—62no—
767ΓL(1,𝔽25)—21no—
768ΓL(1,𝔽25)—21no—
769ΓL(1,𝔽25)—41no—
770ΓL(1,𝔽25)—41no—
771ΓL(1,𝔽25)—41no—
772D3×C8—41no—
773D3×C8—41no—
774D3×C8—41no—
775D3×C8C2×C4×D311yescharacteristic
776D3×C8C2×C4×D311yescharacteristic
777D3×C8#23511yescharacteristic
778D3×C8#23511yescharacteristic
779C3×C16—32no—
780C3×C16—61no—
781C3⋊C16—21no—
782C3⋊C16—32no—
783C3⋊C16—32no—
784C3⋊C16—62no—
785C3⋊C16—61no—
786C3⋊C16—61no—
787C3⋊C16—121no—
788C3⋊C16C2×C4×D312yes—
789C22×C32—41no—
790C22×C32C2×AGL(1,ℤ/8)11yescharacteristic
791C2×C3⋊D3—42no—
792C2×C3⋊D3—81no—
793C2×C3⋊D3—81no—
794C2×C3×D3—41no—
795C2×C3×D3—41no—
796C2×C3×D3—161no—
797C2×C3×D3#44211yescharacteristic
798C2×C3×D3#44211yescharacteristic
799C32×C4—41no—
800C32×C4—41no—
801C32×C4C2×C4×D411yescharacteristic
802C32×C4C2×AGL(1,ℤ/8)11yescharacteristic
803C3⋊Dic3—81no—
804C3×Dic3—41no—
805C3×Dic3—42no—
806C3×Dic3—41no—
807C3×Dic3—81no—
808C3×Dic3#44211yescharacteristic
809C3×Dic3#44211yescharacteristic
810C2×#41—61no—
811C2×#41—181no—
812#135—31no—
813#135—31no—
814#135—31no—
815#135—61no—
816#135—61no—
817#135—92no—
818#135—92no—
819#135—181no—
820#135—181no—
821#135C2×D3211yescharacteristic
822C2×Q16—31no—
823C2×Q16—31no—
824C2×SD16—61no—
825C2×SD16—181no—
826C2×D8—31no—
827C2×D8—91no—
828#131—21no—
829#131—61no—
830#131—61no—
831#131—61no—
832#131—121no—
833#131—121no—
834C2×M16—31no—
835C2×M16—61no—
836C2×M16—121no—
837C2×M16—121no—
838C22×C8—31no—
839C4×Q8—61no—
840C4×Q8—181no—
841C4×D4—181no—
842C4×D4—181no—
843C4×D4—361no—
844C4×D4—361no—
845#117—31no—
846#117—361no—
847C2×C4⋊C4—181no—
848C2×C4⋊C4—361no—
849Q32—32no—
850Q32—92no—
851SD32—32no—
852SD32—92no—
853SD32—92no—
854SD32—92no—
855D16—92no—
856D16—92no—
857M32—31no—
858M32—31no—
859M32—92no—
860M32—91no—
861M32—91no—
862M32—181no—
863C2×C16—92no—
864C2×C16—181no—
865#108—31no—
866#108—61no—
867#108C2×D3211yescharacteristic
868#106—31no—
869#106—91no—
870#106—181no—
871#104—21no—
872#104—61no—
873#104—61no—
874#104—61no—
875#103—61no—
876#103—181no—
877#102—181no—
878#102—181no—
879#97—31no—
880#97C2×D3211yescharacteristic
881C4×C8—31no—
882C4×C8—31no—
883C23×C3—31no—
884C23×C3—121no—
885C22×D3—41no—
886C22×D3—121no—
887C22×D3—121no—
888C22×D3—241no—
889C22×D3#94911yescharacteristic
890C3×Q8—21no—
891C3×Q8—21no—
892C3×Q8—41no—
893C3×Q8—62no—
894C3×Q8—61no—
895C3×Q8—121no—
896C3×Q8—121no—
897C3×D4—21no—
898C3×D4—21no—
899C3×D4—41no—
900C3×D4—41no—
901C3×D4—41no—
902C3×D4—61no—
903C3×D4—81no—
904C3×D4—121no—
905C3×D4—121no—
906C3×D4—121no—
907C3×D4—121no—
908C2×C3×C4—21no—
909C2×C3×C4—21no—
910C2×C3×C4—21no—
911C2×C3×C4—31no—
912C2×C3×C4—31no—
913C2×C3×C4—31no—
914C2×C3×C4—31no—
915C2×C3×C4—31no—
916C2×C3×C4—41no—
917C2×C3×C4—41no—
918C2×C3×C4—41no—
919C2×C3×C4—61no—
920C2×C3×C4—81no—
921C2×C3×C4—121no—
922C2×C3×C4—121no—
923C2×C3×C4—121no—
924C2×C3×C4—121no—
925C2×C3×C4—121no—
926C2×C3×C4—121no—
927C2×C3×C4C2×D3×D411yescharacteristic
928C2×C3×C4C22×#6711yescharacteristic
929#67—41no—
930#67—41no—
931#67—41no—
932#67—122no—
933#67—122no—
934C2×Dic3—21no—
935C2×Dic3—41no—
936C2×Dic3—41no—
937C2×Dic3—41no—
938C2×Dic3—121no—
939C2×Dic3—121no—
940C2×Dic3—241no—
941C2×Dic3—481no—
942C2×Dic3#94911yescharacteristic
943D12—21no—
944D12—41no—
945D12—62no—
946D12—62no—
947D12—122no—
948D12—122no—
949D12—122no—
950D12—121no—
951D12—121no—
952D12—241no—
953C4×D3—41no—
954C4×D3—41no—
955C4×D3—41no—
956C4×D3—122no—
957C4×D3—122no—
958C4×D3—122no—
959C4×D3—122no—
960C4×D3—481no—
961C4×D3—481no—
962C4×D3—481no—
963C4×D3—481no—
964C4×D3—481no—
965C4×D3—482no—
966C4×D3C4×#6711yescharacteristic
967C4×D3C4×#6711yescharacteristic
968C4×D3#93211yescharacteristic
969C4×D3#93211yescharacteristic
970Dic6—21no—
971Dic6—22no—
972Dic6—41no—
973Dic6—41no—
974C3×C8—21no—
975C3×C8—21no—
976C3×C8—21no—
977C3×C8—21no—
978C3×C8—31no—
979C3×C8—31no—
980C3×C8—41no—
981C3×C8—41no—
982C3×C8—41no—
983C3×C8—61no—
984C3×C8—81no—
985C3×C8—121no—
986C3×C8C22×C4×D311yescharacteristic
987C3×C8C22×C4×D311yescharacteristic
988C3×C8C2×#23511yescharacteristic
989C3×C8D3×#4111yescharacteristic
990C3⋊C8—21no—
991C3⋊C8—41no—
992C3⋊C8C4×#6711yescharacteristic
993C3⋊C8C4×#6711yescharacteristic
994C2×C32—21no—
995C2×C32—81no—
996C2×C32C2×#44211yescharacteristic
997C3⋊D3—82no—
998C3×D3—21no—
999C3×D3—21no—
1000C3×D3—81no—
1001#41—21no—
1002#41—61no—
1003#41—61no—
1004#41—61no—
1005#41—121no—
1006#41—121no—
1007#41—182no—
1008#41—182no—
1009#41—361no—
1010#41—361no—
1011C2×Q8—61no—
1012C2×Q8—61no—
1013C2×D4—61no—
1014C2×D4—121no—
1015C2×D4—181no—
1016C2×D4—361no—
1017C22×C4—31no—
1018C22×C4—121no—
1019C22×C4—361no—
1020C22×C4—361no—
1021C22×C4—361no—
1022C22×C4—361no—
1023Q16—32no—
1024Q16—31no—
1025Q16—61no—
1026Q16—61no—
1027Q16C4×D3211yescharacteristic
1028SD16—21no—
1029SD16—61no—
1030SD16—61no—
1031SD16—61no—
1032SD16—182no—
1033SD16—182no—
1034D8—31no—
1035D8—61no—
1036D8—92no—
1037D8—181no—
1038D8C4×D3211yescharacteristic
1039M16—21no—
1040M16—41no—
1041M16—61no—
1042M16—61no—
1043M16—61no—
1044M16—121no—
1045M16—121no—
1046M16—121no—
1047M16—121no—
1048C2×C8—31no—
1049C2×C8—31no—
1050C2×C8—31no—
1051C2×C8—31no—
1052C2×C8—31no—
1053C2×C8—31no—
1054C2×C8—41no—
1055C2×C8—121no—
1056C2×C8—121no—
1057C2×C8—121no—
1058C2×C8—121no—
1059C2×C8D3×#6711yescharacteristic
1060C2×C8C22×D3211yescharacteristic
1061C4⋊C4—61no—
1062C4⋊C4—61no—
1063C4⋊C4—121no—
1064C4⋊C4—181no—
1065C4⋊C4—361no—
1066C4⋊C4—361no—
1067C22⋊C4—61no—
1068C22⋊C4—361no—
1069C22⋊C4—361no—
1070C42—31no—
1071C42—121no—
1072C42—361no—
1073C42D3×#6711yescharacteristic
1074C16—32no—
1075C16—61no—
1076C16—92no—
1077C16—181no—
1078C22×C3—21no—
1079C22×C3—31no—
1080C22×C3—31no—
1081C22×C3—41no—
1082C22×C3—41no—
1083C22×C3—81no—
1084C22×C3—121no—
1085C22×C3—121no—
1086C22×C3—481no—
1087C22×C3D3×AGL(1,ℤ/8)11yescharacteristic
1088C22×C3C2×#94911yescharacteristic
1089C2×D3—41no—
1090C2×D3—41no—
1091C2×D3—122no—
1092C2×D3—122no—
1093C2×D3—161no—
1094C2×D3—242no—
1095C2×D3—241no—
1096C2×D3—241no—
1097C2×D3—241no—
1098C2×D3—241no—
1099C2×D3—481no—
1100C2×D3—481no—
1101C2×D3#501411yescharacteristic
1102C2×D3#501411yescharacteristic
1103C3×C4—21no—
1104C3×C4—21no—
1105C3×C4—31no—
1106C3×C4—31no—
1107C3×C4—41no—
1108C3×C4—41no—
1109C3×C4—41no—
1110C3×C4—41no—
1111C3×C4—81no—
1112C3×C4—81no—
1113C3×C4—121no—
1114C3×C4—122no—
1115C3×C4—121no—
1116C3×C4—241no—
1117C3×C4C4×D3×D411yescharacteristic
1118C3×C4D3×AGL(1,ℤ/8)11yescharacteristic
1119C3×C4C2×C4×#6711yescharacteristic
1120C3×C4C2×#93211yescharacteristic
1121Dic3—41no—
1122Dic3—41no—
1123Dic3—42no—
1124Dic3—81no—
1125Dic3—241no—
1126Dic3—241no—
1127Dic3—481no—
1128Dic3#501411yescharacteristic
1129Dic3#501411yescharacteristic
1130C32#3346911yescharacteristic, complemented, Sylow
1131C23—31no—
1132C23—121no—
1133C23—361no—
1134Q8—21no—
1135Q8—61no—
1136Q8—62no—
1137Q8—121no—
1138Q8—121no—
1139D4—21no—
1140D4—41no—
1141D4—61no—
1142D4—121no—
1143D4—121no—
1144D4—121no—
1145D4—121no—
1146D4—182no—
1147D4—362no—
1148D4—362no—
1149D4—361no—
1150C2×C4—21no—
1151C2×C4—31no—
1152C2×C4—31no—
1153C2×C4—31no—
1154C2×C4—31no—
1155C2×C4—31no—
1156C2×C4—41no—
1157C2×C4—61no—
1158C2×C4—121no—
1159C2×C4—121no—
1160C2×C4—121no—
1161C2×C4—121no—
1162C2×C4—121no—
1163C2×C4—121no—
1164C2×C4—362no—
1165C2×C4—362no—
1166C2×C4—361no—
1167C2×C4—1441no—
1168C2×C4—1441no—
1169C2×C4—1441no—
1170C2×C4C2×D3×#6711yescharacteristic
1171C8—21no—
1172C8—31no—
1173C8—31no—
1174C8—41no—
1175C8—61no—
1176C8—121no—
1177C8C2×C4×D3211yescharacteristic
1178C8D3×#23511yescharacteristic
1179C2×C3—21no—
1180C2×C3—21no—
1181C2×C3—21no—
1182C2×C3—41no—
1183C2×C3—61no—
1184C2×C3—61no—
1185C2×C3—81no—
1186C2×C3—81no—
1187C2×C3—161no—
1188C2×C3—241no—
1189C2×C3D3×#44211yescharacteristic
1190C2×C3C2×#501411yescharacteristic
1191D3—21no—
1192D3—21no—
1193D3—81no—
1194D3—242no—
1195D3—242no—
1196D3—482no—
1197C22—31no—
1198C22—31no—
1199C22—41no—
1200C22—121no—
1201C22—121no—
1202C22—362no—
1203C22—481no—
1204C22—721no—
1205C22—721no—
1206C22D3×#94911yescharacteristic
1207C4—31no—
1208C4—31no—
1209C4—41no—
1210C4—41no—
1211C4—121no—
1212C4—121no—
1213C4—122no—
1214C4—241no—
1215C4—721no—
1216C4C4×D3×#6711yescharacteristic
1217C4D3×#93211yescharacteristic
1218C3—21no—
1219C3#1094864111yescharacteristic, complemented
1220C3#1094864611yescharacteristic, complemented
1221C2—21no—
1222C2—61no—
1223C2—61no—
1224C2—81no—
1225C2—241no—
1226C2—722no—
1227C2D3×#501411yescharacteristic
subgroupG/H
centerC2D3×#5014
commutatorC32×C8C23×C4
FrattiniC2×C8C22×D32
FittingC32×#444C22
socleC2×C32C2×#442
prime radical#11899640C2
cosocleC2×C32×C8C24
hypercenter#444D32
hypocenterC32#33469
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #444

Complements

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

NH ≅ G/Ntype
2. C3×#79899C2semidirect
3. #11860954C2semidirect
4. #11797983C2semidirect
5. #11797972C2semidirect
6. #11797971C2semidirect
7. #11797953C2semidirect
8. #11797935C2semidirect
9. #11797928C2semidirect
10. #11797923C2semidirect
11. C3×#70928C2semidirect
12. D3×#4494C2semidirect
13. #11796946C2semidirect
14. D3×#4566C2semidirect
15. #11795944C2semidirect
24. #10592410C22semidirect
33. C3×#4716C22semidirect
35. #10591048C4semidirect
36. #10591047C4semidirect
37. #10591034C4semidirect
38. #10591033C4semidirect
39. #10590812C22semidirect
41. #10590768C22semidirect
50. #10589361C22semidirect
51. #10589360C22semidirect
52. #10589332C22semidirect
54. C3×#4496C22semidirect
55. C3×#4494C22semidirect
56. C3×#4466C22semidirect
57. #10589138C22semidirect
58. #10589137C22semidirect
59. #10589129C22semidirect
60. #10589128C22semidirect
63. #10589105C22semidirect
64. #10589105C22semidirect
68. #79899D3semidirect
83. #70928D3semidirect
104. C3×#919C2×C4semidirect
105. C3×D3×Q16C2×C4semidirect
108. C3×#912C2×C4semidirect
109. C3×D3×D8C2×C4semidirect
138. #63655C2×C4semidirect
139. #63653C2×C4semidirect
145. C3×#829C2×C4semidirect
146. C3×#827C2×C4semidirect
161. #63550C2×C4semidirect
162. #63549C2×C4semidirect
163. #63547C2×C4semidirect
164. #63546C2×C4semidirect
166. #63543C2×C4semidirect
168. D3×C3⋊C16C2×C4semidirect
227. #4716C2×D3semidirect
252. #4496C2×D3semidirect
262. #4494C2×D3semidirect
270. #4466C2×D3semidirect
403. #919C4×D3semidirect
404. D3×Q16C4×D3semidirect
407. #912C4×D3semidirect
408. D3×D8C4×D3semidirect
472. #829C4×D3semidirect
479. #827C4×D3semidirect
1130. C32#33469semidirect
1219. C3#10948641semidirect
1220. C3#10948646semidirect

Maximal subgroups

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

subgroupindex
#118996402
C3×#798992
#118609542
#117979832
#117979722
#117979712
#117979532
#117979352
#117979282
#117979232
C3×#709282
D3×#44942
#117969462
D3×#45662
#117959442
#109486463
#109486413