Finite Group Databasebeta

← #72222785

Subgroups — #72222785

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#11899643C211yesmaximal, characteristic
2#11861222C211yesmaximal, characteristic, complemented
3C3×#79868C211yesmaximal, characteristic, complemented
4#11797980C211yesmaximal, characteristic, complemented
5#11797978C211yesmaximal, characteristic, complemented
6C3×#70918C211yesmaximal, characteristic, complemented
7#11797947C211yesmaximal, characteristic, complemented
8#11797928C211yesmaximal, characteristic, complemented
9#11797927C211yesmaximal, characteristic, complemented
10#11797922C211yesmaximal, characteristic, complemented
11#11797920C211yesmaximal, characteristic, complemented
12D3×#4487C211yesmaximal, characteristic, complemented
13#11796949C211yesmaximal, characteristic, complemented
14D3×#4488C211yesmaximal, characteristic, complemented
15#11795944C211yesmaximal, characteristic, complemented
16#10948644—31nomaximal
17#10948643—31nomaximal
18C2×C3×#912C2211yescharacteristic
19C3×#5546—21no—
20D3×#904C2211yescharacteristic
21#10594668—21no—
22C32×#442C2211yescharacteristic, complemented
23#10592846C2211yescharacteristic
24#10592416C2211yescharacteristic
25C3×#5152C2211yescharacteristic, complemented
26C3×#5147C2211yescharacteristic
27C3×C4×#214—21no—
28C3×D3×#106C2211yescharacteristic
29C3×#4853C2211yescharacteristic, complemented
30C3×#4771—21no—
31C3×#4758—21no—
32C3×#4717C2211yescharacteristic
33C3×#4716C2211yescharacteristic, complemented
34C3×#4708C2211yescharacteristic
35#10591034C412yescomplemented
36#10591032C412yescomplemented
37#10591028C412yescomplemented
38#10591024C412yescomplemented
39#10590923—21no—
40#10590918C2211yescharacteristic
41#10590916C2211yescharacteristic
42D3×#819C2211yescharacteristic
43#10590642C2211yescharacteristic
44#10590636C2211yescharacteristic
45D3×#812C2211yescharacteristic
46D3×#812C2211yescharacteristic
47#10590392—21no—
48#10590341—21no—
49#10589429C2211yescharacteristic, complemented
50#10589354C2211yescharacteristic
51#10589353C2211yescharacteristic, complemented
52#10589332C2211yescharacteristic, complemented
53C3×#4563C2211yescharacteristic, complemented
54C3×#4488C2211yescharacteristic
55C3×#4487C2211yescharacteristic, complemented
56C3×#4466C2211yescharacteristic, complemented
57#10589138C2211yescharacteristic, complemented
58#10589136C2211yescharacteristic, complemented
59#10589130C2211yescharacteristic, complemented
60#10589129C2211yescharacteristic, complemented
61#10589125C2211yescharacteristic
62#10589123C2211yescharacteristic
63#10589105C2211yescharacteristic, complemented
64#10589105C2211yescharacteristic, complemented
65C3×#2952—31no—
66#83894—31no—
67#82035—31no—
68#79899—31no—
69#79868D311yescharacteristic, complemented
70#78580—31no—
71C3×AGL(1,ℤ/16)—31no—
72#72081—31no—
73#71515—31no—
74#70928—31no—
75#70918—31no—
76#70918—31no—
77#70918—31no—
78#70918—31no—
79#70918—61no—
80#70918D311yescharacteristic, complemented
81#70917—31no—
82#70917—31no—
83#70917—31no—
84#70917—31no—
85C2×#4488—31no—
86C2×#4487—31no—
87#69884—31no—
88D3×#365—31no—
89#69309—31no—
90#69256—31no—
91#69254—31no—
92D3×#360—31no—
93#69248—31no—
94#69090—31no—
95#69087—31no—
96C2×C3×#237—21no—
97D3×#235—21no—
98C2×C32×D8C2311yescharacteristic
99C32×C4×D4—21no—
100#64113C2311yescharacteristic
101#64110—21no—
102C3×D4×Dic3—21no—
103C2×C3×#214—21no—
104C3×C4×#67—41no—
105C2×C3×Dic3⋊C4—41no—
106C3×#912—21no—
107C3×#912—21no—
108C3×#912C2×C412yes—
109C3×#912C2×C412yes—
110C2×C3×Dic12C2311yescharacteristic
111C3×#904C2311yescharacteristic
112C3×#901—21no—
113C2×C3×ΓL(1,𝔽25)D411yescharacteristic
114C2×C3×D3×C8C2311yescharacteristic
115C3×D3×C4⋊C4—21no—
116C3×#887—21no—
117C3×#67⋊C4—41no—
118C3×#877—41no—
119C3×#872D411yescharacteristic
120C3×C4×Dic6—21no—
121#63829—21no—
122#63817—21no—
123#63814—21no—
124D3×#208—21no—
125#63808C2×C411yescharacteristic, complemented
126#63807C2×C411yescharacteristic, complemented
127#63806—21no—
128#63805—41no—
129#63804—41no—
130D3×Dic12C2×C411yescharacteristic, complemented
131D3×D24C2×C411yescharacteristic, complemented
132D3×#204—21no—
133#63791—41no—
134D3×ΓL(1,𝔽25)—41no—
135C32×#106C2311yescharacteristic
136C32×#102—21no—
137C32×#97C2311yescharacteristic
138#63654C2×C412yescomplemented
139#63653C2×C412yescomplemented
140#63646C2311yescharacteristic
141#63639C2311yescharacteristic
142#63639C2311yescharacteristic
143#63632—21no—
144C3×#832—21no—
145C3×#827C2×C412yescomplemented
146C3×#826C2×C412yescomplemented
147C3×#819C2311yescharacteristic
148C3×#817C2311yescharacteristic
149C3×#816—21no—
150C3×#815C2311yescharacteristic
151C3×C8×Dic3D411yescharacteristic
152C3×#812C2311yescharacteristic
153C3×#812C2311yescharacteristic
154C3×#810—21no—
155C3×#808—21no—
156C3×#805—21no—
157C3×C4×C3⋊C8D411yescharacteristic
158#63577—21no—
159#63570—21no—
160#63569—21no—
161#63551C2×C412yescomplemented
162#63550C2×C412yescomplemented
163#63549C2×C412yescomplemented
164#63547C2×C412yescomplemented
165#63543—21no—
166#63543C2×C412yescomplemented
167D3×C3⋊C16—21no—
168D3×C3⋊C16C2×C412yescomplemented
169#33469—91noSylow
170C2×C3×#135—31no—
171C3×#520—61no—
172D3×#135—31no—
173C2×#912C2×D311yescharacteristic
174#5750—61no—
175#5745—61no—
176C2×#904—31no—
177#5546—21no—
178C3×#509—31no—
179C3×#444—31no—
180C3×#442—21no—
181C3×#442—31no—
182C3×#442C2×D311yescharacteristic, complemented
183C3×#442C2×D311yescharacteristic, complemented
184C3×#441—31no—
185C3×#441—31no—
186C3×C4×SD16—61no—
187C3×C4×SD16—61no—
188C2×C3×#106—31no—
189C3×#417—61no—
190C3×#405—31no—
191#5197—31no—
192#5195—31no—
193#5195—32no—
194#5194—32no—
195#5194—32no—
196#5193—32no—
197#5179—31no—
198#5179—31no—
199#5152C2×D311yescharacteristic, complemented
200#5147—31no—
201#5147—31no—
202#5147—61no—
203#5147C2×D311yescharacteristic
204#5144—61no—
205C2×#819—31no—
206C2×#812—31no—
207C2×#812—31no—
208C4×#214—21no—
209#5005—61no—
210#4916—32no—
211#4915—32no—
212#4912—32no—
213#4911—32no—
214#4909—31no—
215D3×M32—31no—
216D3×M32—31no—
217#4894—31no—
218D3×#108—31no—
219D3×#106C2×D311yescharacteristic
220#4853C2×D311yescharacteristic, complemented
221#4824—61no—
222#4821—61no—
223#4771—21no—
224#4758—21no—
225#4717—31no—
226#4717—31no—
227#4717—31no—
228#4717—31no—
229#4717—61no—
230#4717C2×D311yescharacteristic
231#4716C2×D311yescharacteristic, complemented
232#4708C2×D311yescharacteristic
233#4700—61no—
234#4700—61no—
235C3×#365—31no—
236C3×#361—31no—
237C3×#360—31no—
238C3×#347—31no—
239#4566—31no—
240#4565—31no—
241#4565—31no—
242#4563—31no—
243#4563—31no—
244#4563—61no—
245#4563C2×D311yescharacteristic, complemented
246#4518—31no—
247#4517—31no—
248#4513—31no—
249#4512—31no—
250#4512—31no—
251#4496—31no—
252#4494—31no—
253#4488—31no—
254#4488—31no—
255#4488—31no—
256#4488—31no—
257#4488—61no—
258#4488C2×D311yescharacteristic
259#4487—31no—
260#4487—31no—
261#4487—31no—
262#4487—31no—
263#4487—61no—
264#4487C2×D311yescharacteristic, complemented
265#4466—31no—
266#4466—31no—
267#4466—31no—
268#4466—31no—
269#4466—61no—
270#4466C2×D311yescharacteristic, complemented
271C2×C32×D4—21no—
272C22×C32×C4—41no—
273#3828—21no—
274C2×C3×#67—41no—
275C22×C3×Dic3—41no—
276C22×C3×Dic3—41no—
277C3×#237—22no—
278C3×#237—22no—
279C3×#237—41no—
280C3×#237—41no—
281C3×#235—21no—
282C2×C3×C4×D3—41no—
283C2×C3×C4×D3C2×D411yescharacteristic
284C2×C3×Dic6—21no—
285D3×#67—41no—
286#3804—41no—
287D3×D12—21no—
288C4×D32—41no—
289#3799—21no—
290#3798—41no—
291#3795—21no—
292D3×Dic6—21no—
293C32×D8—21no—
294C32×D8C22×C412yes—
295C2×C32×C8C2×D411yescharacteristic
296C2×C32×C8C2411yescharacteristic
297C32×C4⋊C4—21no—
298C32×C22⋊C4—41no—
299C32×C42C2×D411yescharacteristic
300#3748—21no—
301#3746C22×C411yescharacteristic
302#3745C22×C411yescharacteristic
303#3744—21no—
304#3743—41no—
305C8×C3⋊D3—41no—
306C3×#217—41no—
307C3×#214—22no—
308C3×#214—22no—
309C3×(C2×D3)⋊C4—21no—
310C3×C4⋊Dic3—21no—
311C3×Dic3⋊C4—21no—
312C3×Dic3⋊C4—41no—
313C3×Dic3⋊C4—41no—
314C3×Dic3⋊C4—41no—
315C3×C4×Dic3—41no—
316C3×C4×Dic3—41no—
317C3×C4×Dic3C2×D411yescharacteristic
318C3×#208—21no—
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×D3×C8—41no—
330C3×D3×C8C22×C411yescharacteristic
331C3×D3×C8C22×C411yescharacteristic
332C3×D3×C8#4111yescharacteristic
333C3×D3×C8#4111yescharacteristic
334#3719—21no—
335#3717—21no—
336#3716—21no—
337#3714—21no—
338#3712—41no—
339#3711—41no—
340#3711—41no—
341#3710—41no—
342D3×C3⋊C8—41no—
343D3×C3⋊C8—41no—
344C3⋊(C3⋊C16)—21no—
345C3⋊(C3⋊C16)C22×C412yes—
346C3×C3⋊C16—21no—
347C3×C3⋊C16C22×C412yes—
348#3414—91no—
349#2957—91no—
350#2952—31no—
351AGL(1,ℤ/16)—31no—
352AGL(1,ℤ/16)—91no—
353AGL(1,ℤ/16)—91no—
354AGL(1,ℤ/16)—91no—
355#2180—91no—
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—61no—
365C2×#237—21no—
366C2×#235—61no—
367C3×#135—32no—
368C3×#135—32no—
369C3×#135—31no—
370C3×#135—61no—
371C3×#135—61no—
372C2×C3×Q16—31no—
373C2×C3×SD16—61no—
374C2×C3×D8—21no—
375C2×C3×D8C22×D311yescharacteristic
376C2×C3×D8C22×D311yescharacteristic
377C3×#131—61no—
378C2×C3×M16—31no—
379C22×C3×C8—31no—
380C3×C4×Q8—61no—
381C3×C4×Q8—61no—
382C3×C4×D4—21no—
383C3×C4×D4—21no—
384C3×C4×D4—41no—
385C3×C4×D4—61no—
386C3×C4×D4—121no—
387C3×C4×D4—121no—
388C3×#117—31no—
389C3×#117—121no—
390C2×C3×C4⋊C4—61no—
391C2×C3×C4⋊C4—121no—
392#950—61no—
393#948—61no—
394D4×Dic3—21no—
395C2×#214—21no—
396C4×#67—41no—
397C2×Dic3⋊C4—41no—
398C2×#208—61no—
399#919—31no—
400D3×Q16—31no—
401#916—61no—
402D3×SD16—61no—
403#912—21no—
404#912—21no—
405#912—31no—
406#912C4×D312yes—
407#912C4×D312yes—
408D3×D8—31no—
409#907—61no—
410#907—121no—
411#907—121no—
412#907—121no—
413D3×M16—61no—
414D3×M16—121no—
415D3×M16—121no—
416D3×M16—121no—
417C2×Dic12—31no—
418C2×Dic12C22×D311yescharacteristic
419#904—31no—
420#904—31no—
421#904—31no—
422#904—31no—
423#904—61no—
424#904—61no—
425#904—61no—
426#904C22×D311yescharacteristic
427C2×D24—31no—
428C2×#204—61no—
429#901—21no—
430#901—61no—
431#901—61no—
432#901—61no—
433#901—61no—
434#901—121no—
435#901—121no—
436C2×ΓL(1,𝔽25)—121no—
437C2×ΓL(1,𝔽25)#6711yescharacteristic
438C2×D3×C8C22×D311yescharacteristic
439D3×C4⋊C4—21no—
440#887—21no—
441#67⋊C4—41no—
442#877—41no—
443#872#6711yescharacteristic
444C4×Dic6—21no—
445C3×SD32—32no—
446C3×D16—32no—
447C3×M32—31no—
448C3×M32—31no—
449C3×#108—31no—
450C3×#106—21no—
451C3×#106—31no—
452C3×#106—61no—
453C3×#106C22×D311yescharacteristic
454C3×#106C22×D311yescharacteristic
455C3×#104—61no—
456C3×#103—61no—
457C3×#103—61no—
458C3×#102—21no—
459C3×#102—21no—
460C3×#102—41no—
461C3×#102—61no—
462C3×#97—21no—
463C3×#97—31no—
464C3×#97C22×D311yescharacteristic
465C3×#97C22×D311yescharacteristic
466C3×C4×C8—31no—
467C3×C4×C8—31no—
468#837—61no—
469#832—21no—
470#829—32no—
471#829—32no—
472#829—32no—
473#828—32no—
474#828—32no—
475#827—32no—
476#827—32no—
477#827—32no—
478#827—62no—
479#827C4×D312yescomplemented
480#826—32no—
481#826—32no—
482#826—62no—
483#826C4×D312yescomplemented
484#825—61no—
485#822—61no—
486#819—31no—
487#819—31no—
488#819—61no—
489#819—61no—
490#819C22×D311yescharacteristic
491#817C22×D311yescharacteristic
492#816—21no—
493#815C22×D311yescharacteristic
494C8×Dic3#6711yescharacteristic
495#812—31no—
496#812—31no—
497#812—32no—
498#812—31no—
499#812—31no—
500#812—61no—
501#812—61no—
502#812—61no—
503#812C22×D311yescharacteristic
504#812C22×D311yescharacteristic
505C2×C3⋊C16—32no—
506C2×C3⋊C16—61no—
507#810—21no—
508#808—21no—
509#805—21no—
510#805—61no—
511#805—61no—
512#805—61no—
513#805—61no—
514#805—121no—
515C4×C3⋊C8#6711yescharacteristic
516Dic24—32no—
517#800—32no—
518#798—32no—
519#798—61no—
520D3×C16—32no—
521D3×C16—61no—
522C23×C32—41no—
523C22×C3×D3AGL(1,ℤ/8)11yescharacteristic
524C2×D32—41no—
525C32×D4—22no—
526C32×D4—41no—
527C2×C32×C4—21no—
528C2×C32×C4—41no—
529C2×C32×C4—161no—
530C2×C32×C4C22×D411yescharacteristic
531#638—41no—
532C4⋊(C3⋊D3)—21no—
533C4×C3⋊D3—41no—
534#634—21no—
535C3×#67—41no—
536C3×#67—42no—
537C3×#67—42no—
538C2×C3×Dic3—21no—
539C2×C3×Dic3—41no—
540C2×C3×Dic3—42no—
541C2×C3×Dic3—42no—
542C2×C3×Dic3—41no—
543C2×C3×Dic3—161no—
544C2×C3×Dic3AGL(1,ℤ/8)11yescharacteristic
545C3×D12—21no—
546C3×C4×D3—41no—
547C3×C4×D3—161no—
548C3×C4×D3C4×D411yescharacteristic
549C3×C4×D3C4×D411yescharacteristic
550C3×C4×D3AGL(1,ℤ/8)11yescharacteristic
551C3×C4×D3AGL(1,ℤ/8)11yescharacteristic
552C3×Dic6—21no—
553C3×Dic6—22no—
554C3×Dic6—41no—
555#627—41no—
556#626—41no—
557#626—41no—
558#625—41no—
559#624—41no—
560D3×Dic3—41no—
561D3×Dic3—41no—
562C32×C8—21no—
563C32×C8C23×C411yescharacteristic
564C32×C8C2×#4111yescharacteristic
565C3⋊(C3⋊C8)—41no—
566C3×C3⋊C8—21no—
567C3×C3⋊C8—41no—
568C3×C3⋊C8C4×D411yescharacteristic
569C3×C3⋊C8C4×D411yescharacteristic
570C2×#135—31no—
571C2×#135—91no—
572#568—181no—
573#520—61no—
574#510—91no—
575#510—92no—
576#510—91no—
577#509—31no—
578#509—92no—
579#509—91no—
580#508—92no—
581#508—92no—
582C2×M32—91no—
583C2×M32—91no—
584#444—31no—
585#444—91no—
586#444—91no—
587#444—91no—
588#443—181no—
589#443—181no—
590#442—31no—
591#442D3211yescharacteristic, complemented
592#441—31no—
593#441—31no—
594C4×SD16—61no—
595C4×SD16—61no—
596C2×#108—91no—
597C2×#106—31no—
598#421—181no—
599#417—61no—
600#405—31no—
601#365—31no—
602#365—91no—
603#365—91no—
604#365—91no—
605#362—91no—
606#362—91no—
607#361—31no—
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—62no—
618C3×#41—62no—
619C3×#41—61no—
620C3×#41—121no—
621C3×#41—121no—
622C2×C3×Q8—61no—
623C2×C3×D4—21no—
624C2×C3×D4—21no—
625C2×C3×D4—41no—
626C2×C3×D4—121no—
627C22×C3×C4—31no—
628C22×C3×C4—41no—
629C22×C3×C4—41no—
630C22×C3×C4—81no—
631C22×C3×C4—121no—
632C22×C3×C4—121no—
633C22×C3×C4—121no—
634C2×#67—41no—
635C2×#67—121no—
636C22×Dic3—41no—
637C22×Dic3—41no—
638#239—61no—
639D3×Q8—61no—
640#237—22no—
641#237—22no—
642#237—41no—
643#237—41no—
644#237—61no—
645#237—121no—
646D3×D4—61no—
647D3×D4—121no—
648#235—21no—
649#235—61no—
650#235—61no—
651#235—61no—
652#235—61no—
653#235—121no—
654#235—121no—
655#235—121no—
656#235—121no—
657C2×D12—61no—
658C2×C4×D3—41no—
659C2×C4×D3—121no—
660C2×C4×D3—121no—
661C2×C4×D3C2×#6711yescharacteristic
662C2×Dic6—21no—
663C2×Dic6—61no—
664C3×Q16—32no—
665C3×Q16—31no—
666C3×Q16—61no—
667C3×SD16—62no—
668C3×SD16—62no—
669C3×SD16—61no—
670C3×D8—21no—
671C3×D8—21no—
672C3×D8—22no—
673C3×D8—31no—
674C3×D8—41no—
675C3×D8C2×C4×D312yes—
676C3×D8C2×C4×D312yes—
677C3×M16—61no—
678C3×M16—61no—
679C3×M16—61no—
680C3×M16—121no—
681C2×C3×C8—21no—
682C2×C3×C8—21no—
683C2×C3×C8—31no—
684C2×C3×C8—31no—
685C2×C3×C8—31no—
686C2×C3×C8—31no—
687C2×C3×C8—31no—
688C2×C3×C8—31no—
689C2×C3×C8—121no—
690C2×C3×C8D3×D411yescharacteristic
691C2×C3×C8C2×#6711yescharacteristic
692C2×C3×C8C23×D311yescharacteristic
693C2×C3×C8C23×D311yescharacteristic
694C3×C4⋊C4—21no—
695C3×C4⋊C4—21no—
696C3×C4⋊C4—41no—
697C3×C4⋊C4—61no—
698C3×C4⋊C4—61no—
699C3×C4⋊C4—121no—
700C3×C4⋊C4—121no—
701C3×C4⋊C4—121no—
702C3×C22⋊C4—41no—
703C3×C22⋊C4—41no—
704C3×C22⋊C4—61no—
705C3×C22⋊C4—81no—
706C3×C22⋊C4—121no—
707C3×C42—21no—
708C3×C42—31no—
709C3×C42—121no—
710C3×C42—121no—
711C3×C42D3×D411yescharacteristic
712C3×C42C2×#6711yescharacteristic
713#217—41no—
714#216—61no—
715#215—61no—
716#214—22no—
717#214—22no—
718#214—61no—
719#213—61no—
720(C2×D3)⋊C4—21no—
721C4⋊Dic3—21no—
722Dic3⋊C4—21no—
723Dic3⋊C4—41no—
724Dic3⋊C4—41no—
725Dic3⋊C4—41no—
726C4×Dic3—41no—
727C4×Dic3—41no—
728C4×Dic3C2×#6711yescharacteristic
729#208—21no—
730#208—61no—
731#208—61no—
732#208—121no—
733#208—121no—
734#208—121no—
735C2×C3⋊C8—121no—
736C2×C3⋊C8—121no—
737C2×C3⋊C8C2×#6711yescharacteristic
738C2×C3⋊C8C2×#6711yescharacteristic
739Dic12—21no—
740Dic12—31no—
741Dic12—31no—
742Dic12—61no—
743Dic12—61no—
744Dic12C2×C4×D312yes—
745Dic12C2×C4×D311yescharacteristic
746D24—31no—
747D24—31no—
748D24—61no—
749D24—61no—
750D24C2×C4×D311yescharacteristic
751#204—21no—
752#204—61no—
753#204—61no—
754#204—61no—
755#204—61no—
756#204—121no—
757ΓL(1,𝔽25)—21no—
758ΓL(1,𝔽25)—21no—
759ΓL(1,𝔽25)—41no—
760ΓL(1,𝔽25)—121no—
761ΓL(1,𝔽25)—121no—
762ΓL(1,𝔽25)—121no—
763ΓL(1,𝔽25)—121no—
764ΓL(1,𝔽25)—121no—
765ΓL(1,𝔽25)—121no—
766ΓL(1,𝔽25)—241no—
767D3×C8—41no—
768D3×C8—121no—
769D3×C8—121no—
770D3×C8—121no—
771D3×C8—121no—
772D3×C8—121no—
773D3×C8—121no—
774D3×C8—241no—
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—42no—
790C22×C32—81no—
791C22×C32—81no—
792C22×C32C2×AGL(1,ℤ/8)11yescharacteristic
793C2×C3⋊D3—41no—
794C2×C3×D3—41no—
795C2×C3×D3—41no—
796C2×C3×D3#44211yescharacteristic
797C2×C3×D3#44211yescharacteristic
798D32—161no—
799C32×C4—41no—
800C32×C4—81no—
801C32×C4C2×C4×D411yescharacteristic
802C32×C4C2×AGL(1,ℤ/8)11yescharacteristic
803C3⋊Dic3—41no—
804C3×Dic3—41no—
805C3×Dic3—41no—
806C3×Dic3—42no—
807C3×Dic3—81no—
808C3×Dic3#44211yescharacteristic
809C3×Dic3#44211yescharacteristic
810C2×#41—61no—
811C2×#41—181no—
812#135—32no—
813#135—32no—
814#135—31no—
815#135—61no—
816#135—61no—
817#135—91no—
818#135—91no—
819#135—91no—
820#135—181no—
821#135—181no—
822C2×Q16—31no—
823C2×Q16—91no—
824C2×SD16—61no—
825C2×SD16—181no—
826C2×D8—91no—
827C2×D8C2×D3211yescharacteristic
828#131—61no—
829#131—181no—
830#131—181no—
831#131—181no—
832#131—361no—
833#131—361no—
834C2×M16—31no—
835C2×M16—181no—
836C2×M16—361no—
837C2×M16—361no—
838C22×C8—31no—
839C4×Q8—61no—
840C4×Q8—61no—
841C4×D4—21no—
842C4×D4—61no—
843C4×D4—121no—
844C4×D4—121no—
845#117—31no—
846#117—121no—
847C2×C4⋊C4—61no—
848C2×C4⋊C4—121no—
849Q32—92no—
850Q32—92no—
851SD32—32no—
852SD32—92no—
853SD32—92no—
854SD32—92no—
855D16—32no—
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—91no—
867#108—181no—
868#106—31no—
869#106—61no—
870#106C2×D3211yescharacteristic
871#104—61no—
872#104—181no—
873#104—181no—
874#104—181no—
875#103—61no—
876#103—61no—
877#102—21no—
878#102—61no—
879#97—31no—
880#97C2×D3211yescharacteristic
881C4×C8—31no—
882C4×C8—31no—
883C23×C3—31no—
884C23×C3—41no—
885C23×C3—41no—
886C23×C3—81no—
887C22×D3—121no—
888C22×D3—121no—
889C22×D3#93211yescharacteristic
890C3×Q8—61no—
891C3×Q8—62no—
892C3×Q8—121no—
893C3×D4—22no—
894C3×D4—22no—
895C3×D4—42no—
896C3×D4—41no—
897C3×D4—41no—
898C3×D4—61no—
899C3×D4—81no—
900C3×D4—122no—
901C3×D4—122no—
902C3×D4—121no—
903C2×C3×C4—21no—
904C2×C3×C4—21no—
905C2×C3×C4—21no—
906C2×C3×C4—31no—
907C2×C3×C4—31no—
908C2×C3×C4—31no—
909C2×C3×C4—31no—
910C2×C3×C4—31no—
911C2×C3×C4—41no—
912C2×C3×C4—41no—
913C2×C3×C4—41no—
914C2×C3×C4—61no—
915C2×C3×C4—81no—
916C2×C3×C4—122no—
917C2×C3×C4—122no—
918C2×C3×C4—121no—
919C2×C3×C4—121no—
920C2×C3×C4—121no—
921C2×C3×C4—161no—
922C2×C3×C4—161no—
923C2×C3×C4—162no—
924C2×C3×C4—481no—
925C2×C3×C4—481no—
926C2×C3×C4C2×D3×D411yescharacteristic
927C2×C3×C4C22×#6711yescharacteristic
928#67—41no—
929#67—42no—
930#67—42no—
931#67—121no—
932#67—121no—
933#67—121no—
934#67—121no—
935#67—121no—
936#67—121no—
937#67—241no—
938C2×Dic3—21no—
939C2×Dic3—41no—
940C2×Dic3—42no—
941C2×Dic3—42no—
942C2×Dic3—41no—
943C2×Dic3—121no—
944C2×Dic3—121no—
945C2×Dic3—161no—
946C2×Dic3#93211yescharacteristic
947D12—21no—
948D12—61no—
949D12—61no—
950D12—121no—
951D12—121no—
952D12—121no—
953C4×D3—41no—
954C4×D3—121no—
955C4×D3—121no—
956C4×D3—121no—
957C4×D3—121no—
958C4×D3—121no—
959C4×D3—121no—
960C4×D3—161no—
961C4×D3—241no—
962C4×D3C4×#6711yescharacteristic
963C4×D3C4×#6711yescharacteristic
964C4×D3#94911yescharacteristic
965C4×D3#94911yescharacteristic
966Dic6—22no—
967Dic6—21no—
968Dic6—41no—
969Dic6—61no—
970Dic6—61no—
971Dic6—121no—
972Dic6—121no—
973Dic6—121no—
974C3×C8—21no—
975C3×C8—21no—
976C3×C8—21no—
977C3×C8—21no—
978C3×C8—31no—
979C3×C8—31no—
980C3×C8—41no—
981C3×C8—61no—
982C3×C8—121no—
983C3×C8C22×C4×D311yescharacteristic
984C3×C8C22×C4×D311yescharacteristic
985C3×C8C2×#23511yescharacteristic
986C3×C8D3×#4111yescharacteristic
987C3⋊C8—21no—
988C3⋊C8—41no—
989C3⋊C8—121no—
990C3⋊C8—121no—
991C3⋊C8—241no—
992C3⋊C8C4×#6711yescharacteristic
993C3⋊C8C4×#6711yescharacteristic
994C2×C32—21no—
995C2×C32—82no—
996C2×C32C2×#44211yescharacteristic
997C3⋊D3—81no—
998C3×D3—21no—
999C3×D3—21no—
1000C3×D3—81no—
1001#41—62no—
1002#41—62no—
1003#41—61no—
1004#41—121no—
1005#41—121no—
1006#41—181no—
1007#41—181no—
1008#41—181no—
1009#41—361no—
1010#41—361no—
1011C2×Q8—61no—
1012C2×Q8—181no—
1013C2×D4—21no—
1014C2×D4—121no—
1015C2×D4—181no—
1016C2×D4—361no—
1017C22×C4—31no—
1018C22×C4—41no—
1019C22×C4—121no—
1020C22×C4—121no—
1021C22×C4—121no—
1022C22×C4—361no—
1023Q16—31no—
1024Q16—32no—
1025Q16—61no—
1026Q16—91no—
1027Q16—181no—
1028SD16—62no—
1029SD16—62no—
1030SD16—61no—
1031SD16—181no—
1032SD16—181no—
1033SD16—181no—
1034D8—21no—
1035D8—31no—
1036D8—91no—
1037D8—181no—
1038D8C4×D3212yes—
1039M16—61no—
1040M16—61no—
1041M16—61no—
1042M16—121no—
1043M16—181no—
1044M16—361no—
1045M16—361no—
1046M16—361no—
1047M16—361no—
1048C2×C8—31no—
1049C2×C8—31no—
1050C2×C8—31no—
1051C2×C8—31no—
1052C2×C8—31no—
1053C2×C8—31no—
1054C2×C8—121no—
1055C2×C8—361no—
1056C2×C8—361no—
1057C2×C8—361no—
1058C2×C8—361no—
1059C2×C8D3×#6711yescharacteristic
1060C2×C8C22×D3211yescharacteristic
1061C4⋊C4—21no—
1062C4⋊C4—61no—
1063C4⋊C4—61no—
1064C4⋊C4—121no—
1065C4⋊C4—121no—
1066C4⋊C4—121no—
1067C22⋊C4—41no—
1068C22⋊C4—61no—
1069C22⋊C4—121no—
1070C42—31no—
1071C42—121no—
1072C42—121no—
1073C42D3×#6711yescharacteristic
1074C16—32no—
1075C16—61no—
1076C16—92no—
1077C16—181no—
1078C22×C3—21no—
1079C22×C3—31no—
1080C22×C3—31no—
1081C22×C3—42no—
1082C22×C3—42no—
1083C22×C3—82no—
1084C22×C3—81no—
1085C22×C3—81no—
1086C22×C3—81no—
1087C22×C3—81no—
1088C22×C3—121no—
1089C22×C3—121no—
1090C22×C3—161no—
1091C22×C3—161no—
1092C22×C3D3×AGL(1,ℤ/8)11yescharacteristic
1093C22×C3C2×#93211yescharacteristic
1094C2×D3—41no—
1095C2×D3—41no—
1096C2×D3—121no—
1097C2×D3—121no—
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—81no—
1110C3×C4—81no—
1111C3×C4—81no—
1112C3×C4—121no—
1113C3×C4—121no—
1114C3×C4—122no—
1115C3×C4—161no—
1116C3×C4—241no—
1117C3×C4C4×D3×D411yescharacteristic
1118C3×C4D3×AGL(1,ℤ/8)11yescharacteristic
1119C3×C4C2×C4×#6711yescharacteristic
1120C3×C4C2×#94911yescharacteristic
1121Dic3—41no—
1122Dic3—42no—
1123Dic3—41no—
1124Dic3—81no—
1125Dic3—121no—
1126Dic3—121no—
1127Dic3—241no—
1128Dic3#501411yescharacteristic
1129Dic3#501411yescharacteristic
1130C32#3346911yescharacteristic, complemented, Sylow
1131C23—31no—
1132C23—41no—
1133C23—361no—
1134Q8—62no—
1135Q8—61no—
1136Q8—121no—
1137Q8—181no—
1138Q8—361no—
1139D4—22no—
1140D4—41no—
1141D4—61no—
1142D4—122no—
1143D4—122no—
1144D4—121no—
1145D4—181no—
1146D4—361no—
1147D4—361no—
1148D4—361no—
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—122no—
1159C2×C4—122no—
1160C2×C4—121no—
1161C2×C4—121no—
1162C2×C4—121no—
1163C2×C4—161no—
1164C2×C4—361no—
1165C2×C4—361no—
1166C2×C4—361no—
1167C2×C4—361no—
1168C2×C4—481no—
1169C2×C4—481no—
1170C2×C4C2×D3×#6711yescharacteristic
1171C8—21no—
1172C8—31no—
1173C8—31no—
1174C8—61no—
1175C8—121no—
1176C8—361no—
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—82no—
1186C2×C3—82no—
1187C2×C3—162no—
1188C2×C3—241no—
1189C2×C3D3×#44211yescharacteristic
1190C2×C3C2×#501411yescharacteristic
1191D3—21no—
1192D3—21no—
1193D3—81no—
1194D3—241no—
1195D3—241no—
1196D3—481no—
1197C22—31no—
1198C22—31no—
1199C22—42no—
1200C22—81no—
1201C22—81no—
1202C22—121no—
1203C22—121no—
1204C22—361no—
1205C22—1441no—
1206C22D3×#93211yescharacteristic
1207C4—31no—
1208C4—31no—
1209C4—41no—
1210C4—81no—
1211C4—121no—
1212C4—122no—
1213C4—121no—
1214C4—241no—
1215C4—361no—
1216C4C4×D3×#6711yescharacteristic
1217C4D3×#94911yescharacteristic
1218C3—21no—
1219C3#1094864311yescharacteristic, complemented
1220C3#1094864411yescharacteristic, complemented
1221C2—21no—
1222C2—61no—
1223C2—61no—
1224C2—82no—
1225C2—241no—
1226C2—721no—
1227C2D3×#501411yescharacteristic
subgroupG/H
centerC2D3×#5014
commutatorC32×C8C23×C4
FrattiniC2×C8C22×D32
FittingC32×#442C22
socleC2×C32C2×#442
prime radical#11899643C2
cosocleC2×C32×C8C24
hypercenter#442D32
hypocenterC32#33469
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #442

Complements

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

NH ≅ G/Ntype
2. #11861222C2semidirect
3. C3×#79868C2semidirect
4. #11797980C2semidirect
5. #11797978C2semidirect
6. C3×#70918C2semidirect
7. #11797947C2semidirect
8. #11797928C2semidirect
9. #11797927C2semidirect
10. #11797922C2semidirect
11. #11797920C2semidirect
12. D3×#4487C2semidirect
13. #11796949C2semidirect
14. D3×#4488C2semidirect
15. #11795944C2semidirect
22. C32×#442C22semidirect
25. C3×#5152C22semidirect
29. C3×#4853C22semidirect
33. C3×#4716C22semidirect
35. #10591034C4semidirect
36. #10591032C4semidirect
37. #10591028C4semidirect
38. #10591024C4semidirect
49. #10589429C22semidirect
51. #10589353C22semidirect
52. #10589332C22semidirect
53. C3×#4563C22semidirect
55. C3×#4487C22semidirect
56. C3×#4466C22semidirect
57. #10589138C22semidirect
58. #10589136C22semidirect
59. #10589130C22semidirect
60. #10589129C22semidirect
63. #10589105C22semidirect
64. #10589105C22semidirect
69. #79868D3semidirect
80. #70918D3semidirect
125. #63808C2×C4semidirect
126. #63807C2×C4semidirect
130. D3×Dic12C2×C4semidirect
131. D3×D24C2×C4semidirect
138. #63654C2×C4semidirect
139. #63653C2×C4semidirect
145. C3×#827C2×C4semidirect
146. C3×#826C2×C4semidirect
161. #63551C2×C4semidirect
162. #63550C2×C4semidirect
163. #63549C2×C4semidirect
164. #63547C2×C4semidirect
166. #63543C2×C4semidirect
168. D3×C3⋊C16C2×C4semidirect
182. C3×#442C2×D3semidirect
183. C3×#442C2×D3semidirect
199. #5152C2×D3semidirect
220. #4853C2×D3semidirect
231. #4716C2×D3semidirect
245. #4563C2×D3semidirect
264. #4487C2×D3semidirect
270. #4466C2×D3semidirect
479. #827C4×D3semidirect
483. #826C4×D3semidirect
591. #442D32semidirect
1130. C32#33469semidirect
1219. C3#10948643semidirect
1220. C3#10948644semidirect

Maximal subgroups

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

subgroupindex
#118996432
#118612222
C3×#798682
#117979802
#117979782
C3×#709182
#117979472
#117979282
#117979272
#117979222
#117979202
D3×#44872
#117969492
D3×#44882
#117959442
#109486443
#109486433