Finite Group Databasebeta

← #11861218

Subgroups — #11861218

Order 1152.

1033 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596221C211yesmaximal, characteristic, complemented
2#10595459C211yesmaximal, characteristic
3#10594670C211yesmaximal, characteristic, complemented
4C3×#5145C211yesmaximal, characteristic, complemented
5C3×#5144C211yesmaximal, characteristic, complemented
6#10591676C211yesmaximal, characteristic, complemented
7#10591675C211yesmaximal, characteristic, complemented
8#10591672C211yesmaximal, characteristic, complemented
9#10591009C211yesmaximal, characteristic, complemented
10#10590978C211yesmaximal, characteristic, complemented
11#10590977C211yesmaximal, characteristic, complemented
12#10590972C211yesmaximal, characteristic, complemented
13#10590924C211yesmaximal, characteristic, complemented
14#10590923C211yesmaximal, characteristic, complemented
15#10590910C211yesmaximal, characteristic, complemented
16#79899—31nomaximal
17#79890—31nomaximal
18#41×C3⋊D3C2211yescharacteristic
19#64306C2211yescharacteristic
20C32×#131C2211yescharacteristic, complemented
21#64157C2211yescharacteristic, complemented
22#64116—21no—
23#64116C2211yescharacteristic, complemented
24M16×C3⋊D3—21no—
25M16×C3⋊D3C2211yescharacteristic
26#64110—21no—
27#64110C2211yescharacteristic, complemented
28C2×#3743—21no—
29C2×#3743C2211yescharacteristic
30C3×#950C2211yescharacteristic
31C3×#950C2211yescharacteristic
32C3×#901C2211yescharacteristic, complemented
33C3×#901C2211yescharacteristic, complemented
34#63950C411yescharacteristic, complemented
35#63950C411yescharacteristic, complemented
36#63944C411yescharacteristic, complemented
37#63940C411yescharacteristic, complemented
38#63936C411yescharacteristic, complemented
39#63936C411yescharacteristic, complemented
40#63930C411yescharacteristic, complemented
41#63926C411yescharacteristic, complemented
42#63874C2211yescharacteristic
43#63829C2211yescharacteristic
44#63829C2211yescharacteristic
45#63818C2211yescharacteristic
46C2×#3710C2211yescharacteristic
47#63815C2211yescharacteristic, complemented
48#63815C2211yescharacteristic, complemented
49#63804—21no—
50#63804—21no—
51D3×ΓL(1,𝔽25)—21no—
52D3×ΓL(1,𝔽25)—21no—
53C3×#837C2211yescharacteristic, complemented
54C3×#837C2211yescharacteristic, complemented
55C3×#825C2211yescharacteristic, complemented
56C3×#825C2211yescharacteristic, complemented
57C3×#822C2211yescharacteristic, complemented
58C3×#822C2211yescharacteristic, complemented
59C3×#815C2211yescharacteristic, complemented
60C3×C8×Dic3C2211yescharacteristic, complemented
61#63577C2211yescharacteristic, complemented
62#63577C2211yescharacteristic, complemented
63#63570C2211yescharacteristic, complemented
64#63570C2211yescharacteristic, complemented
65#63569C2211yescharacteristic, complemented
66#63569C2211yescharacteristic, complemented
67#63554C2211yescharacteristic, complemented
68Dic3×C3⋊C8C2211yescharacteristic, complemented
69D3×#135—31no—
70D3×#135—31no—
71#5750—31no—
72#5750—31no—
73#5750—31no—
74#5750—31no—
75#5750—61no—
76C3×#444—31no—
77C3×#443—31no—
78#5197—31no—
79#5196—31no—
80#5145—31no—
81#5145D311yescharacteristic, complemented
82#5144—31no—
83#5144D311yescharacteristic, complemented
84#4895—31no—
85#4894—31no—
86D3×#108—31no—
87D3×#108—31no—
88#4824—31no—
89#4824—31no—
90#4823—31no—
91#4823—31no—
92#4821—31no—
93#4821—31no—
94#4821—31no—
95#4821—31no—
96#4717—31no—
97#4708—31no—
98#4700—31no—
99#4689—31no—
100C32×#41C2311yescharacteristic
101#3832C2×C411yescharacteristic
102Q8×C3⋊D3C2×C411yescharacteristic
103#3830—21no—
104#3830C2×C411yescharacteristic
105D4×C3⋊D3—21no—
106D4×C3⋊D3C2×C411yescharacteristic
107#3828—21no—
108#3828C2311yescharacteristic
109C2×C4×C3⋊D3—21no—
110C2×C4×C3⋊D3C2311yescharacteristic
111C3×#235C2311yescharacteristic
112C3×#235C2311yescharacteristic
113#3811—21no—
114#3805—21no—
115#3802C2×C411yescharacteristic
116C4×D32—21no—
117#3798—21no—
118#3797C2×C411yescharacteristic
119#3796C2×C411yescharacteristic
120#3796C2×C411yescharacteristic
121C32×M16—21no—
122C32×M16C2311yescharacteristic
123C2×C32×C8—21no—
124C2×C32×C8C2311yescharacteristic
125#3748—21no—
126#3748C2311yescharacteristic
127C2×C3⋊(C3⋊C8)—21no—
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129#3743—21no—
130#3743—21no—
131#3743—21no—
132#3743D411yescharacteristic
133#3743D411yescharacteristic
134#3743D411yescharacteristic
135#3743D411yescharacteristic
136C8×C3⋊D3—21no—
137C8×C3⋊D3—21no—
138C8×C3⋊D3—21no—
139C3×#216C2×C411yescharacteristic
140C3×#216C2×C411yescharacteristic
141C3×#215C2×C411yescharacteristic
142C3×#215C2×C411yescharacteristic
143C3×#214C2×C411yescharacteristic
144C3×#214C2×C411yescharacteristic
145C3×#213C2×C411yescharacteristic
146C3×#213C2×C411yescharacteristic
147C3×C4×Dic3C2311yescharacteristic
148C3×C4×Dic3C2311yescharacteristic
149C3×#208C2311yescharacteristic
150C3×#208C2311yescharacteristic
151C2×C3×C3⋊C8C2311yescharacteristic
152C2×C3×C3⋊C8C2311yescharacteristic
153C3×ΓL(1,𝔽25)—21no—
154C3×ΓL(1,𝔽25)—21no—
155C3×D3×C8—21no—
156C3×D3×C8—21no—
157#3724—21no—
158#3722—21no—
159#3719C2×C411yescharacteristic
160#3719C2×C411yescharacteristic
161#3717C2×C411yescharacteristic
162#3717C2×C411yescharacteristic
163#3716C2×C411yescharacteristic
164#3716C2×C411yescharacteristic
165#3714C2×C411yescharacteristic
166#3714C2×C411yescharacteristic
167#3712—21no—
168#3711—21no—
169#3711—21no—
170#3710—21no—
171#3710C2×C411yescharacteristic
172#3710C2×C411yescharacteristic
173#3710C2×C411yescharacteristic
174#3710C2×C411yescharacteristic
175D3×C3⋊C8—21no—
176D3×C3⋊C8—21no—
177#2957—91noSylow
178D3×#41—31no—
179D3×#41—31no—
180D3×#41—31no—
181D3×#41—31no—
182D3×#41—61no—
183C3×#135—31no—
184C3×#135—31no—
185C3×#131—21no—
186C3×#131—31no—
187C3×#131—31no—
188C3×#131C2×D311yescharacteristic, complemented
189C3×#131C2×D311yescharacteristic, complemented
190#950—31no—
191#950—31no—
192#950C2×D311yescharacteristic
193#950C2×D311yescharacteristic
194#948—31no—
195#948—31no—
196#948—31no—
197#948—31no—
198#948—61no—
199#919—31no—
200#919—31no—
201D3×Q16—31no—
202D3×Q16—31no—
203#916—31no—
204#916—31no—
205#916—31no—
206#916—31no—
207D3×SD16—31no—
208D3×SD16—31no—
209D3×SD16—31no—
210D3×SD16—31no—
211#912—31no—
212#912—31no—
213D3×D8—31no—
214D3×D8—31no—
215#907—31no—
216#907—31no—
217#907—31no—
218#907—31no—
219#907—61no—
220#907—61no—
221#907—61no—
222#907—61no—
223#907—61no—
224#907—62no—
225D3×M16—31no—
226D3×M16—31no—
227D3×M16—31no—
228D3×M16—31no—
229D3×M16—61no—
230D3×M16—61no—
231D3×M16—61no—
232D3×M16—61no—
233D3×M16—61no—
234D3×M16—62no—
235#904—31no—
236#904—31no—
237#901—31no—
238#901—31no—
239#901—61no—
240#901—61no—
241#901—61no—
242#901—61no—
243#901—61no—
244#901—62no—
245#901C2×D311yescharacteristic, complemented
246#901C2×D311yescharacteristic, complemented
247C2×ΓL(1,𝔽25)—31no—
248C2×ΓL(1,𝔽25)—31no—
249C2×ΓL(1,𝔽25)—61no—
250C2×ΓL(1,𝔽25)—61no—
251C2×ΓL(1,𝔽25)—61no—
252C2×ΓL(1,𝔽25)—61no—
253C2×ΓL(1,𝔽25)—61no—
254C2×ΓL(1,𝔽25)—62no—
255C2×D3×C8—31no—
256C2×D3×C8—31no—
257#872—31no—
258#872—31no—
259C3×#108—31no—
260C3×#108—31no—
261C3×#104—31no—
262C3×#104—31no—
263C3×#104—31no—
264C3×#104—31no—
265C3×#97—31no—
266C3×C4×C8—31no—
267#837—31no—
268#837—31no—
269#837C2×D311yescharacteristic, complemented
270#837C2×D311yescharacteristic, complemented
271#825—31no—
272#825—31no—
273#825C2×D311yescharacteristic, complemented
274#825C2×D311yescharacteristic, complemented
275#822—31no—
276#822—31no—
277#822C2×D311yescharacteristic, complemented
278#822C2×D311yescharacteristic, complemented
279#819—31no—
280#819—31no—
281#815—31no—
282#815C2×D311yescharacteristic, complemented
283C8×Dic3—31no—
284C8×Dic3C2×D311yescharacteristic, complemented
285#805—31no—
286#805—31no—
287#805—31no—
288#805—31no—
289#803—31no—
290C4×C3⋊C8—31no—
291C22×C3⋊D3—21no—
292C22×C3⋊D3#4111yescharacteristic
293C2×D32—21no—
294C32×Q8C22×C411yescharacteristic
295C32×D4—21no—
296C32×D4C22×C411yescharacteristic
297C2×C32×C4—21no—
298C2×C32×C4C2411yescharacteristic
299#638—21no—
300#638—21no—
301#638—21no—
302C2×C3⋊Dic3—21no—
303C2×C3⋊Dic3#4111yescharacteristic
304C4⋊(C3⋊D3)—21no—
305C4⋊(C3⋊D3)C22×C411yescharacteristic
306C4×C3⋊D3—21no—
307C4×C3⋊D3—21no—
308C4×C3⋊D3—21no—
309C4×C3⋊D3C22×C411yescharacteristic
310C4×C3⋊D3C22×C411yescharacteristic
311C4×C3⋊D3C2×D411yescharacteristic
312C4×C3⋊D3C2×D411yescharacteristic
313#634—21no—
314#634C22×C411yescharacteristic
315C3×#67—21no—
316C3×#67—21no—
317C2×C3×Dic3—21no—
318C2×C3×Dic3—21no—
319C3×D12C22×C411yescharacteristic
320C3×D12C22×C411yescharacteristic
321C3×C4×D3—21no—
322C3×C4×D3—21no—
323C3×Dic6C22×C411yescharacteristic
324C3×Dic6C22×C411yescharacteristic
325#627—21no—
326#626—21no—
327#626—21no—
328#625—21no—
329#624—21no—
330D3×Dic3—21no—
331D3×Dic3—21no—
332C32×C8—21no—
333C32×C8C2×D411yescharacteristic
334C32×C8C2×D411yescharacteristic
335C3⋊(C3⋊C8)—21no—
336C3⋊(C3⋊C8)C2×D411yescharacteristic
337C3⋊(C3⋊C8)C2×D411yescharacteristic
338C3×C3⋊C8—21no—
339C3×C3⋊C8—21no—
340C3×C3⋊C8C22×C411yescharacteristic
341C3×C3⋊C8C22×C411yescharacteristic
342C3×C3⋊C8C22×C411yescharacteristic
343C3×C3⋊C8C22×C411yescharacteristic
344C2×#135—91no—
345#568—91no—
346#568—91no—
347#444—31no—
348#444—91no—
349#444—91no—
350#444—91no—
351#443—31no—
352#443—91no—
353#443—91no—
354#443—91no—
355C2×#108—91no—
356#421—91no—
357#421—91no—
358#405—91no—
359C3×#41—21no—
360C3×#41—31no—
361C3×#41—31no—
362C3×#41C22×D311yescharacteristic
363C3×#41C22×D311yescharacteristic
364#239—31no—
365#239—31no—
366#239—31no—
367#239—31no—
368#239—61no—
369D3×Q8—31no—
370D3×Q8—31no—
371D3×Q8—31no—
372D3×Q8—31no—
373D3×Q8—61no—
374#237—31no—
375#237—31no—
376#237—31no—
377#237—31no—
378#237—61no—
379#237—61no—
380#237—61no—
381#237—61no—
382#237—61no—
383#237—62no—
384D3×D4—31no—
385D3×D4—31no—
386D3×D4—31no—
387D3×D4—31no—
388D3×D4—61no—
389D3×D4—61no—
390D3×D4—61no—
391D3×D4—61no—
392D3×D4—61no—
393D3×D4—62no—
394#235—31no—
395#235—31no—
396#235—61no—
397#235—61no—
398#235—61no—
399#235—61no—
400#235—61no—
401#235—62no—
402#235C22×D311yescharacteristic
403#235C22×D311yescharacteristic
404C2×C4×D3—31no—
405C2×C4×D3—31no—
406C2×C4×D3—61no—
407C2×C4×D3—61no—
408C2×C4×D3—61no—
409C2×C4×D3—61no—
410C2×C4×D3—61no—
411C2×C4×D3—62no—
412C3×Q16—31no—
413C3×Q16—31no—
414C3×SD16—31no—
415C3×SD16—31no—
416C3×SD16—31no—
417C3×SD16—31no—
418C3×D8—31no—
419C3×D8—31no—
420C3×M16—22no—
421C3×M16—21no—
422C3×M16—21no—
423C3×M16—21no—
424C3×M16—31no—
425C3×M16—31no—
426C3×M16—61no—
427C3×M16—61no—
428C3×M16C22×D311yescharacteristic
429C3×M16C22×D311yescharacteristic
430C2×C3×C8—22no—
431C2×C3×C8—21no—
432C2×C3×C8—21no—
433C2×C3×C8—21no—
434C2×C3×C8—31no—
435C2×C3×C8—31no—
436C2×C3×C8—61no—
437C2×C3×C8—61no—
438C2×C3×C8C22×D311yescharacteristic
439C2×C3×C8C22×D311yescharacteristic
440C3×C42—31no—
441C3×C42—31no—
442#216—31no—
443#216—31no—
444#216C4×D311yescharacteristic
445#216C4×D311yescharacteristic
446#215—31no—
447#215—31no—
448#215C4×D311yescharacteristic
449#215C4×D311yescharacteristic
450#214—31no—
451#214—31no—
452#214C4×D311yescharacteristic
453#214C4×D311yescharacteristic
454#213—31no—
455#213—31no—
456#213C4×D311yescharacteristic
457#213C4×D311yescharacteristic
458(C2×D3)⋊C4—61no—
459(C2×D3)⋊C4—61no—
460Dic3⋊C4—61no—
461Dic3⋊C4—61no—
462C4×Dic3C22×D311yescharacteristic
463C4×Dic3C22×D311yescharacteristic
464#208—31no—
465#208—31no—
466#208—61no—
467#208—61no—
468#208—61no—
469#208—61no—
470#208—61no—
471#208—62no—
472#208C22×D311yescharacteristic
473#208C22×D311yescharacteristic
474C2×C3⋊C8—31no—
475C2×C3⋊C8—31no—
476C2×C3⋊C8—61no—
477C2×C3⋊C8—61no—
478C2×C3⋊C8—61no—
479C2×C3⋊C8—61no—
480C2×C3⋊C8—61no—
481C2×C3⋊C8—62no—
482C2×C3⋊C8C22×D311yescharacteristic
483C2×C3⋊C8C22×D311yescharacteristic
484Dic12—31no—
485Dic12—31no—
486D24—31no—
487D24—31no—
488#204—31no—
489#204—31no—
490#204—31no—
491#204—31no—
492ΓL(1,𝔽25)—21no—
493ΓL(1,𝔽25)—21no—
494ΓL(1,𝔽25)—31no—
495ΓL(1,𝔽25)—31no—
496ΓL(1,𝔽25)—31no—
497ΓL(1,𝔽25)—31no—
498ΓL(1,𝔽25)—31no—
499ΓL(1,𝔽25)—31no—
500ΓL(1,𝔽25)—31no—
501ΓL(1,𝔽25)—31no—
502ΓL(1,𝔽25)—61no—
503ΓL(1,𝔽25)—61no—
504ΓL(1,𝔽25)—61no—
505ΓL(1,𝔽25)—61no—
506ΓL(1,𝔽25)—61no—
507ΓL(1,𝔽25)—61no—
508ΓL(1,𝔽25)—61no—
509ΓL(1,𝔽25)—61no—
510ΓL(1,𝔽25)—61no—
511ΓL(1,𝔽25)—61no—
512ΓL(1,𝔽25)—61no—
513ΓL(1,𝔽25)—61no—
514ΓL(1,𝔽25)—62no—
515ΓL(1,𝔽25)—62no—
516ΓL(1,𝔽25)—62no—
517ΓL(1,𝔽25)—61no—
518ΓL(1,𝔽25)—61no—
519D3×C8—21no—
520D3×C8—21no—
521D3×C8—31no—
522D3×C8—31no—
523D3×C8—31no—
524D3×C8—31no—
525D3×C8—31no—
526D3×C8—31no—
527D3×C8—31no—
528D3×C8—31no—
529D3×C8—61no—
530D3×C8—61no—
531D3×C8—61no—
532D3×C8—61no—
533D3×C8—61no—
534D3×C8—61no—
535D3×C8—61no—
536D3×C8—61no—
537D3×C8—62no—
538D3×C8—62no—
539D3×C8—62no—
540D3×C8—61no—
541D3×C8—61no—
542C22×C32—21no—
543C22×C32C2×#4111yescharacteristic
544C2×C3⋊D3—21no—
545C2×C3⋊D3—41no—
546C2×C3⋊D3—81no—
547C2×C3⋊D3C4×D411yescharacteristic
548C2×C3⋊D3C4×D411yescharacteristic
549C2×C3×D3—21no—
550C2×C3×D3—21no—
551D32—81no—
552C32×C4—21no—
553C32×C4C23×C411yescharacteristic
554C32×C4C22×D411yescharacteristic
555C3⋊Dic3—21no—
556C3⋊Dic3C4×D411yescharacteristic
557C3⋊Dic3C4×D411yescharacteristic
558C3×Dic3—21no—
559C3×Dic3—21no—
560C3×Dic3—41no—
561C3×Dic3—41no—
562C2×#41—91no—
563C2×#41—91no—
564#135—31no—
565#135—31no—
566#135—91no—
567#135—91no—
568#135—91no—
569#135—91no—
570#135—91no—
571#135—91no—
572C2×Q16—91no—
573C2×SD16—91no—
574C2×SD16—91no—
575C2×D8—91no—
576#131—31no—
577#131—31no—
578#131—91no—
579#131—91no—
580#131—91no—
581#131—91no—
582#131—91no—
583#131—181no—
584#131—181no—
585#131—181no—
586#131—181no—
587#131D3211yescharacteristic, complemented
588C2×M16—91no—
589C2×M16—91no—
590C2×M16—91no—
591C2×M16—181no—
592C2×M16—181no—
593C2×M16—181no—
594C2×M16—181no—
595C22×C8—91no—
596#117—91no—
597#108—31no—
598#108—31no—
599#108—91no—
600#108—91no—
601#104—31no—
602#104—31no—
603#104—31no—
604#104—31no—
605#104—91no—
606#104—91no—
607#104—91no—
608#104—91no—
609#97—31no—
610#97—91no—
611C4×C8—31no—
612C4×C8—91no—
613C22×D3—31no—
614C22×D3—31no—
615C22×D3—61no—
616C22×D3—61no—
617C22×D3—61no—
618C22×D3—61no—
619C22×D3—61no—
620C22×D3—62no—
621C3×Q8—21no—
622C3×Q8—31no—
623C3×Q8—31no—
624C3×Q8C2×C4×D311yescharacteristic
625C3×Q8C2×C4×D311yescharacteristic
626C3×D4—22no—
627C3×D4—21no—
628C3×D4—21no—
629C3×D4—21no—
630C3×D4—31no—
631C3×D4—31no—
632C3×D4—61no—
633C3×D4—61no—
634C3×D4C2×C4×D311yescharacteristic
635C3×D4C2×C4×D311yescharacteristic
636C2×C3×C4—22no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—61no—
641C2×C3×C4—61no—
642C2×C3×C4—61no—
643C2×C3×C4—61no—
644C2×C3×C4C23×D311yescharacteristic
645C2×C3×C4C23×D311yescharacteristic
646#67—21no—
647#67—21no—
648#67—61no—
649#67—61no—
650#67—61no—
651#67—61no—
652#67—61no—
653#67—61no—
654#67—61no—
655#67—61no—
656#67—62no—
657#67—62no—
658#67—62no—
659#67—61no—
660#67—61no—
661C2×Dic3—21no—
662C2×Dic3—21no—
663C2×Dic3—31no—
664C2×Dic3—31no—
665C2×Dic3—61no—
666C2×Dic3—61no—
667C2×Dic3—61no—
668C2×Dic3—61no—
669C2×Dic3—61no—
670C2×Dic3—62no—
671D12—31no—
672D12—31no—
673D12—61no—
674D12—61no—
675D12—61no—
676D12—62no—
677D12—61no—
678D12—61no—
679D12C2×C4×D311yescharacteristic
680D12C2×C4×D311yescharacteristic
681C4×D3—21no—
682C4×D3—21no—
683C4×D3—31no—
684C4×D3—31no—
685C4×D3—31no—
686C4×D3—31no—
687C4×D3—31no—
688C4×D3—31no—
689C4×D3—31no—
690C4×D3—31no—
691C4×D3—61no—
692C4×D3—61no—
693C4×D3—61no—
694C4×D3—61no—
695C4×D3—61no—
696C4×D3—61no—
697C4×D3—61no—
698C4×D3—61no—
699C4×D3—61no—
700C4×D3—61no—
701C4×D3—61no—
702C4×D3—61no—
703C4×D3—62no—
704C4×D3—62no—
705C4×D3—62no—
706C4×D3—61no—
707C4×D3—61no—
708Dic6—31no—
709Dic6—31no—
710Dic6—61no—
711Dic6—61no—
712Dic6—61no—
713Dic6—61no—
714Dic6—61no—
715Dic6—62no—
716Dic6C2×C4×D311yescharacteristic
717Dic6C2×C4×D311yescharacteristic
718C3×C8—22no—
719C3×C8—21no—
720C3×C8—21no—
721C3×C8—21no—
722C3×C8—21no—
723C3×C8—31no—
724C3×C8—31no—
725C3×C8—31no—
726C3×C8—31no—
727C3×C8—61no—
728C3×C8—61no—
729C3×C8D3×D411yescharacteristic
730C3×C8D3×D411yescharacteristic
731C3×C8D3×D411yescharacteristic
732C3×C8D3×D411yescharacteristic
733C3⋊C8—21no—
734C3⋊C8—21no—
735C3⋊C8—31no—
736C3⋊C8—31no—
737C3⋊C8—31no—
738C3⋊C8—31no—
739C3⋊C8—61no—
740C3⋊C8—61no—
741C3⋊C8—62no—
742C3⋊C8—61no—
743C3⋊C8—61no—
744C3⋊C8C2×C4×D311yescharacteristic
745C3⋊C8C2×C4×D311yescharacteristic
746C3⋊C8C2×C4×D311yescharacteristic
747C3⋊C8C2×C4×D311yescharacteristic
748C2×C32—21no—
749C2×C32—41no—
750C2×C32C2×C4×D411yescharacteristic
751C3⋊D3—21no—
752C3⋊D3—21no—
753C3⋊D3—41no—
754C3×D3—41no—
755C3×D3—41no—
756#41—31no—
757#41—31no—
758#41—91no—
759#41—91no—
760#41—91no—
761#41—91no—
762#41—91no—
763#41—181no—
764#41—181no—
765#41—181no—
766#41—181no—
767#41C2×D3211yescharacteristic
768C2×Q8—91no—
769C2×Q8—91no—
770C2×D4—91no—
771C2×D4—91no—
772C2×D4—181no—
773C2×D4—181no—
774C22×C4—91no—
775C22×C4—181no—
776C22×C4—181no—
777Q16—31no—
778Q16—31no—
779Q16—91no—
780Q16—91no—
781SD16—31no—
782SD16—31no—
783SD16—31no—
784SD16—31no—
785SD16—91no—
786SD16—91no—
787SD16—91no—
788SD16—91no—
789D8—31no—
790D8—31no—
791D8—91no—
792D8—91no—
793M16—21no—
794M16—31no—
795M16—31no—
796M16—61no—
797M16—61no—
798M16—91no—
799M16—91no—
800M16—91no—
801M16—91no—
802M16—91no—
803M16—181no—
804M16—181no—
805M16—181no—
806M16—181no—
807M16—181no—
808M16—181no—
809M16—181no—
810M16C2×D3211yescharacteristic
811C2×C8—21no—
812C2×C8—31no—
813C2×C8—31no—
814C2×C8—61no—
815C2×C8—61no—
816C2×C8—91no—
817C2×C8—91no—
818C2×C8—91no—
819C2×C8—91no—
820C2×C8—91no—
821C2×C8—181no—
822C2×C8—181no—
823C2×C8—181no—
824C2×C8—181no—
825C2×C8—181no—
826C2×C8—181no—
827C2×C8—181no—
828C2×C8C2×D3211yescharacteristic
829C4⋊C4—181no—
830C22⋊C4—181no—
831C42—31no—
832C42—31no—
833C22×C3—22no—
834C22×C3—21no—
835C22×C3—21no—
836C22×C3—21no—
837C22×C3—61no—
838C22×C3—61no—
839C22×C3D3×#4111yescharacteristic
840C22×C3D3×#4111yescharacteristic
841C2×D3—21no—
842C2×D3—21no—
843C2×D3—31no—
844C2×D3—31no—
845C2×D3—31no—
846C2×D3—31no—
847C2×D3—61no—
848C2×D3—61no—
849C2×D3—62no—
850C2×D3—61no—
851C2×D3—61no—
852C2×D3—121no—
853C2×D3—121no—
854C2×D3—241no—
855C2×D3—241no—
856C2×D3—241no—
857C2×D3—241no—
858C2×D3—241no—
859C2×D3—242no—
860C3×C4—22no—
861C3×C4—21no—
862C3×C4—21no—
863C3×C4—21no—
864C3×C4—21no—
865C3×C4—61no—
866C3×C4—61no—
867C3×C4—121no—
868C3×C4—121no—
869C3×C4C22×C4×D311yescharacteristic
870C3×C4C22×C4×D311yescharacteristic
871C3×C4C2×D3×D411yescharacteristic
872C3×C4C2×D3×D411yescharacteristic
873Dic3—21no—
874Dic3—21no—
875Dic3—31no—
876Dic3—31no—
877Dic3—31no—
878Dic3—31no—
879Dic3—41no—
880Dic3—41no—
881Dic3—61no—
882Dic3—61no—
883Dic3—62no—
884Dic3—61no—
885Dic3—61no—
886C32#295711yescharacteristic, complemented, Sylow
887C23—91no—
888C23—181no—
889C23—181no—
890Q8—31no—
891Q8—31no—
892Q8—91no—
893Q8—181no—
894Q8—181no—
895Q8C4×D3211yescharacteristic
896D4—21no—
897D4—31no—
898D4—31no—
899D4—61no—
900D4—61no—
901D4—91no—
902D4—181no—
903D4—181no—
904D4—181no—
905D4—181no—
906D4—181no—
907D4—181no—
908D4—181no—
909D4C4×D3211yescharacteristic
910C2×C4—21no—
911C2×C4—61no—
912C2×C4—61no—
913C2×C4—61no—
914C2×C4—61no—
915C2×C4—91no—
916C2×C4—91no—
917C2×C4—91no—
918C2×C4—91no—
919C2×C4—91no—
920C2×C4—181no—
921C2×C4—181no—
922C2×C4—181no—
923C2×C4—181no—
924C2×C4—181no—
925C2×C4—181no—
926C2×C4—181no—
927C2×C4C22×D3211yescharacteristic
928C8—21no—
929C8—31no—
930C8—31no—
931C8—31no—
932C8—31no—
933C8—61no—
934C8—61no—
935C8—91no—
936C8—91no—
937C8—181no—
938C8#381111yescharacteristic
939C8#381111yescharacteristic
940C2×C3—21no—
941C2×C3—21no—
942C2×C3—21no—
943C2×C3—41no—
944C2×C3—42no—
945C2×C3—41no—
946C2×C3—41no—
947C2×C3—121no—
948C2×C3—121no—
949C2×C3C4×D3×D411yescharacteristic
950C2×C3C4×D3×D411yescharacteristic
951D3—41no—
952D3—41no—
953D3—61no—
954D3—61no—
955D3—61no—
956D3—61no—
957D3—121no—
958D3—121no—
959D3—122no—
960D3—121no—
961D3—121no—
962C22—21no—
963C22—61no—
964C22—61no—
965C22—91no—
966C22—91no—
967C22—181no—
968C22—361no—
969C22—721no—
970C22—721no—
971C22#6430611yescharacteristic
972C4—21no—
973C4—61no—
974C4—61no—
975C4—91no—
976C4—91no—
977C4—121no—
978C4—121no—
979C4—181no—
980C4C2×C4×D3211yescharacteristic
981C4C2×#381111yescharacteristic
982C3—21no—
983C3#7989011yescharacteristic, complemented
984C3#7989911yescharacteristic, complemented
985C2—21no—
986C2—41no—
987C2—121no—
988C2—121no—
989C2—181no—
990C2—181no—
991C2—361no—
992C2C4×#381111yescharacteristic
subgroupG/H
centerC4C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#131C22
socleC2×C32C2×C4×D4
prime radical#10595459C2
cosocleC2×C32×C4C24
hypercenter#131D32
hypocenterC32#2957
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C8 ◁ #131

Complements

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

NH ≅ G/Ntype
1. #10596221C2semidirect
3. #10594670C2semidirect
4. C3×#5145C2semidirect
5. C3×#5144C2semidirect
6. #10591676C2semidirect
7. #10591675C2semidirect
8. #10591672C2semidirect
9. #10591009C2semidirect
10. #10590978C2semidirect
11. #10590977C2semidirect
12. #10590972C2semidirect
13. #10590924C2semidirect
14. #10590923C2semidirect
15. #10590910C2semidirect
20. C32×#131C22semidirect
21. #64157C22semidirect
23. #64116C22semidirect
27. #64110C22semidirect
32. C3×#901C22semidirect
33. C3×#901C22semidirect
34. #63950C4semidirect
35. #63950C4semidirect
36. #63944C4semidirect
37. #63940C4semidirect
38. #63936C4semidirect
39. #63936C4semidirect
40. #63930C4semidirect
41. #63926C4semidirect
47. #63815C22semidirect
48. #63815C22semidirect
53. C3×#837C22semidirect
54. C3×#837C22semidirect
55. C3×#825C22semidirect
56. C3×#825C22semidirect
57. C3×#822C22semidirect
58. C3×#822C22semidirect
59. C3×#815C22semidirect
60. C3×C8×Dic3C22semidirect
61. #63577C22semidirect
62. #63577C22semidirect
63. #63570C22semidirect
64. #63570C22semidirect
65. #63569C22semidirect
66. #63569C22semidirect
67. #63554C22semidirect
68. Dic3×C3⋊C8C22semidirect
81. #5145D3semidirect
83. #5144D3semidirect
188. C3×#131C2×D3semidirect
189. C3×#131C2×D3semidirect
245. #901C2×D3semidirect
246. #901C2×D3semidirect
269. #837C2×D3semidirect
270. #837C2×D3semidirect
273. #825C2×D3semidirect
274. #825C2×D3semidirect
277. #822C2×D3semidirect
278. #822C2×D3semidirect
282. #815C2×D3semidirect
284. C8×Dic3C2×D3semidirect
587. #131D32semidirect
886. C32#2957semidirect
983. C3#79890semidirect
984. C3#79899semidirect

Maximal subgroups

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

subgroupindex
#105962212
#105954592
#105946702
C3×#51452
C3×#51442
#105916762
#105916752
#105916722
#105910092
#105909782
#105909772
#105909722
#105909242
#105909232
#105909102
#798993
#798903