Finite Group Databasebeta

← #11861211

Subgroups — #11861211

Order 1152.

981 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595459C211yesmaximal, characteristic
2#10595443C211yesmaximal, characteristic, complemented
3#10594708C211yesmaximal, characteristic, complemented
4#10592520C211yesmaximal, characteristic, complemented
5C3×#4824C211yesmaximal, characteristic, complemented
6C3×#4823C211yesmaximal, characteristic, complemented
7#10591674C211yesmaximal, characteristic, complemented
8#10591673C211yesmaximal, characteristic, complemented
9#10590995C211yesmaximal, characteristic, complemented
10#10590994C211yesmaximal, characteristic, complemented
11#10590972C211yesmaximal, characteristic, complemented
12#10590394C211yesmaximal, characteristic, complemented
13#10590342C211yesmaximal, characteristic, complemented
14#10590341C211yesmaximal, characteristic, complemented
15#10590321C211yesmaximal, characteristic, complemented
16#79899—31nomaximal
17#79890—31nomaximal
18#41×C3⋊D3C2211yescharacteristic
19#64306C2211yescharacteristic
20M16×C3⋊D3C2211yescharacteristic
21#64081C2211yescharacteristic
22C3×#950C2211yescharacteristic
23C3×#950C2211yescharacteristic
24C3×#948C2211yescharacteristic, complemented
25C3×#948C2211yescharacteristic, complemented
26C3×#907C2211yescharacteristic, complemented
27C3×#907C2211yescharacteristic, complemented
28#63950C411yescharacteristic, complemented
29#63950C411yescharacteristic, complemented
30#63944C411yescharacteristic, complemented
31#63940C411yescharacteristic, complemented
32#63936C411yescharacteristic, complemented
33#63936C411yescharacteristic, complemented
34#63930C411yescharacteristic, complemented
35#63926C411yescharacteristic, complemented
36#63829C2211yescharacteristic
37#63829C2211yescharacteristic
38C2×#3712—21no—
39C2×#3712C2211yescharacteristic
40#63818—21no—
41#63818C2211yescharacteristic
42#63817—21no—
43#63817—21no—
44#63817C2211yescharacteristic, complemented
45#63817C2211yescharacteristic, complemented
46C2×#3710C2211yescharacteristic
47#63814C2211yescharacteristic, complemented
48#63814C2211yescharacteristic, complemented
49#63805—21no—
50#63803—21no—
51D3×ΓL(1,𝔽25)—21no—
52D3×ΓL(1,𝔽25)—21no—
53C32×#104C2211yescharacteristic, complemented
54#63664C2211yescharacteristic, complemented
55#63652C2211yescharacteristic, complemented
56#63632C2211yescharacteristic, complemented
57C3×#822C2211yescharacteristic, complemented
58C3×#822C2211yescharacteristic, complemented
59C3×#805C2211yescharacteristic, complemented
60C3×#805C2211yescharacteristic, complemented
61C3×#803C2211yescharacteristic, complemented
62C3×C4×C3⋊C8C2211yescharacteristic, complemented
63#63577C2211yescharacteristic, complemented
64#63577C2211yescharacteristic, complemented
65#63568C2211yescharacteristic, complemented
66#63568C2211yescharacteristic, complemented
67#63555C2211yescharacteristic, complemented
68#63553C2211yescharacteristic, complemented
69D3×#135—31no—
70D3×#135—31no—
71#5750—31no—
72#5750—31no—
73#5750—31no—
74#5750—31no—
75C3×#444—31no—
76C3×#443—31no—
77#5197—31no—
78#5196—31no—
79#5145—31no—
80#5145—31no—
81#5144—31no—
82#5144—31no—
83#4895—31no—
84#4894—31no—
85D3×#108—31no—
86D3×#108—31no—
87#4824—31no—
88#4824D311yescharacteristic, complemented
89#4823—31no—
90#4823D311yescharacteristic, complemented
91#4821—31no—
92#4821—31no—
93#4821—31no—
94#4821—31no—
95#4821—61no—
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×M16C2311yescharacteristic
122C32×C42C2311yescharacteristic
123#3752—21no—
124#3750—21no—
125C4×C3⋊Dic3C2311yescharacteristic
126#3748C2311yescharacteristic
127#3743—21no—
128C8×C3⋊D3—21no—
129C3×#216C2×C411yescharacteristic
130C3×#216C2×C411yescharacteristic
131C3×#215C2×C411yescharacteristic
132C3×#215C2×C411yescharacteristic
133C3×#214C2×C411yescharacteristic
134C3×#214C2×C411yescharacteristic
135C3×#213C2×C411yescharacteristic
136C3×#213C2×C411yescharacteristic
137C3×#208—21no—
138C3×#208—21no—
139C3×#208C2311yescharacteristic
140C3×#208C2311yescharacteristic
141C2×C3×C3⋊C8—21no—
142C2×C3×C3⋊C8—21no—
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147C3×ΓL(1,𝔽25)—21no—
148C3×ΓL(1,𝔽25)—21no—
149C3×D3×C8—21no—
150C3×D3×C8—21no—
151#3719C2×C411yescharacteristic
152#3719C2×C411yescharacteristic
153#3717C2×C411yescharacteristic
154#3717C2×C411yescharacteristic
155#3716C2×C411yescharacteristic
156#3716C2×C411yescharacteristic
157#3714C2×C411yescharacteristic
158#3714C2×C411yescharacteristic
159#3712—21no—
160#3712—21no—
161#3712—21no—
162#3712D411yescharacteristic
163#3712D411yescharacteristic
164#3712D411yescharacteristic
165#3712D411yescharacteristic
166#3711—21no—
167#3711—21no—
168#3710—21no—
169#3710—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—31no—
186C3×#131—31no—
187C3×#131—31no—
188C3×#131—31no—
189#950—31no—
190#950—31no—
191#950C2×D311yescharacteristic
192#950C2×D311yescharacteristic
193#948—31no—
194#948—31no—
195#948C2×D311yescharacteristic, complemented
196#948C2×D311yescharacteristic, complemented
197#919—31no—
198#919—31no—
199D3×Q16—31no—
200D3×Q16—31no—
201#916—31no—
202#916—31no—
203#916—31no—
204#916—31no—
205D3×SD16—31no—
206D3×SD16—31no—
207D3×SD16—31no—
208D3×SD16—31no—
209#912—31no—
210#912—31no—
211D3×D8—31no—
212D3×D8—31no—
213#907—31no—
214#907—31no—
215#907—61no—
216#907—61no—
217#907—61no—
218#907—61no—
219#907C2×D311yescharacteristic, complemented
220#907C2×D311yescharacteristic, complemented
221D3×M16—31no—
222D3×M16—31no—
223D3×M16—31no—
224D3×M16—31no—
225D3×M16—61no—
226D3×M16—61no—
227D3×M16—61no—
228D3×M16—61no—
229D3×M16—61no—
230#904—31no—
231#904—31no—
232#901—31no—
233#901—31no—
234#901—31no—
235#901—31no—
236#901—61no—
237#901—61no—
238#901—61no—
239#901—61no—
240C2×ΓL(1,𝔽25)—31no—
241C2×ΓL(1,𝔽25)—31no—
242C2×ΓL(1,𝔽25)—61no—
243C2×ΓL(1,𝔽25)—61no—
244C2×ΓL(1,𝔽25)—61no—
245C2×ΓL(1,𝔽25)—61no—
246C2×D3×C8—31no—
247C2×D3×C8—31no—
248#872—31no—
249#872—31no—
250#872—61no—
251C3×#108—31no—
252C3×#108—31no—
253C3×#104—21no—
254C3×#104—31no—
255C3×#104—31no—
256C3×#104C2×D311yescharacteristic, complemented
257C3×#104C2×D311yescharacteristic, complemented
258C3×#97—31no—
259C3×C4×C8—31no—
260#837—31no—
261#837—31no—
262#837—31no—
263#837—31no—
264#837—61no—
265#825—31no—
266#825—31no—
267#825—31no—
268#825—31no—
269#825—61no—
270#822—31no—
271#822—31no—
272#822C2×D311yescharacteristic, complemented
273#822C2×D311yescharacteristic, complemented
274#819—31no—
275#819—31no—
276#815—31no—
277#815—31no—
278C8×Dic3—31no—
279C8×Dic3—31no—
280#805—31no—
281#805—31no—
282#805—61no—
283#805C2×D311yescharacteristic, complemented
284#805C2×D311yescharacteristic, complemented
285#803C2×D311yescharacteristic, complemented
286C4×C3⋊C8C2×D311yescharacteristic, complemented
287C22×C3⋊D3—21no—
288C22×C3⋊D3#4111yescharacteristic
289C2×D32—21no—
290C32×Q8C22×C411yescharacteristic
291C32×D4—21no—
292C32×D4C22×C411yescharacteristic
293C2×C32×C4—21no—
294C2×C32×C4—21no—
295C2×C32×C4C2411yescharacteristic
296#638—21no—
297#638—21no—
298#638—21no—
299C2×C3⋊Dic3—21no—
300C2×C3⋊Dic3—21no—
301C2×C3⋊Dic3#4111yescharacteristic
302C4⋊(C3⋊D3)—21no—
303C4⋊(C3⋊D3)C22×C411yescharacteristic
304C4×C3⋊D3—21no—
305C4×C3⋊D3—21no—
306C4×C3⋊D3—21no—
307C4×C3⋊D3C22×C411yescharacteristic
308C4×C3⋊D3C22×C411yescharacteristic
309C4×C3⋊D3C2×D411yescharacteristic
310C4×C3⋊D3C2×D411yescharacteristic
311#634—21no—
312#634C22×C411yescharacteristic
313C3×#67—21no—
314C3×#67—21no—
315C3×D12C22×C411yescharacteristic
316C3×D12C22×C411yescharacteristic
317C3×C4×D3—21no—
318C3×C4×D3—21no—
319C3×Dic6C22×C411yescharacteristic
320C3×Dic6C22×C411yescharacteristic
321#627—21no—
322#626—21no—
323#626—21no—
324#625—21no—
325#624—21no—
326D3×Dic3—21no—
327D3×Dic3—21no—
328C32×C8—21no—
329C3⋊(C3⋊C8)—21no—
330C3×C3⋊C8—21no—
331C3×C3⋊C8—21no—
332C3×C3⋊C8C22×C411yescharacteristic
333C3×C3⋊C8C22×C411yescharacteristic
334C3×C3⋊C8C22×C411yescharacteristic
335C3×C3⋊C8C22×C411yescharacteristic
336C3×C3⋊C8C2×D411yescharacteristic
337C3×C3⋊C8C2×D411yescharacteristic
338C3×C3⋊C8C2×D411yescharacteristic
339C3×C3⋊C8C2×D411yescharacteristic
340C2×#135—91no—
341#568—91no—
342#568—91no—
343#444—31no—
344#444—91no—
345#444—91no—
346#444—91no—
347#443—31no—
348#443—91no—
349#443—91no—
350#443—91no—
351C2×#108—91no—
352#421—91no—
353#421—91no—
354#405—91no—
355C3×#41—21no—
356C3×#41—31no—
357C3×#41—31no—
358C3×#41C22×D311yescharacteristic
359C3×#41C22×D311yescharacteristic
360#239—31no—
361#239—31no—
362#239—31no—
363#239—31no—
364#239—61no—
365D3×Q8—31no—
366D3×Q8—31no—
367D3×Q8—31no—
368D3×Q8—31no—
369D3×Q8—61no—
370#237—31no—
371#237—31no—
372#237—31no—
373#237—31no—
374#237—61no—
375#237—61no—
376#237—61no—
377#237—61no—
378#237—61no—
379#237—121no—
380D3×D4—31no—
381D3×D4—31no—
382D3×D4—31no—
383D3×D4—31no—
384D3×D4—61no—
385D3×D4—61no—
386D3×D4—61no—
387D3×D4—61no—
388D3×D4—61no—
389D3×D4—121no—
390#235—31no—
391#235—31no—
392#235—61no—
393#235—61no—
394#235—61no—
395#235—61no—
396#235—61no—
397#235—121no—
398#235C22×D311yescharacteristic
399#235C22×D311yescharacteristic
400C2×C4×D3—31no—
401C2×C4×D3—31no—
402C2×C4×D3—61no—
403C2×C4×D3—61no—
404C2×C4×D3—61no—
405C2×C4×D3—61no—
406C2×C4×D3—61no—
407C2×C4×D3—121no—
408C3×Q16—31no—
409C3×Q16—31no—
410C3×SD16—31no—
411C3×SD16—31no—
412C3×SD16—31no—
413C3×SD16—31no—
414C3×D8—31no—
415C3×D8—31no—
416C3×M16—21no—
417C3×M16—31no—
418C3×M16—31no—
419C3×M16—61no—
420C3×M16—61no—
421C3×M16—61no—
422C3×M16—61no—
423C3×M16C22×D311yescharacteristic
424C3×M16C22×D311yescharacteristic
425C2×C3×C8—31no—
426C2×C3×C8—31no—
427C2×C3×C8—31no—
428C2×C3×C8—31no—
429C2×C3×C8—61no—
430C2×C3×C8—61no—
431C2×C3×C8—61no—
432C2×C3×C8—61no—
433C3×C42—21no—
434C3×C42C22×D311yescharacteristic
435C3×C42C22×D311yescharacteristic
436#216—31no—
437#216—31no—
438#216C4×D311yescharacteristic
439#216C4×D311yescharacteristic
440#215—31no—
441#215—31no—
442#215C4×D311yescharacteristic
443#215C4×D311yescharacteristic
444#214—31no—
445#214—31no—
446#214C4×D311yescharacteristic
447#214C4×D311yescharacteristic
448#213—31no—
449#213—31no—
450#213C4×D311yescharacteristic
451#213C4×D311yescharacteristic
452(C2×D3)⋊C4—61no—
453(C2×D3)⋊C4—61no—
454(C2×D3)⋊C4—121no—
455Dic3⋊C4—61no—
456Dic3⋊C4—61no—
457Dic3⋊C4—121no—
458C4×Dic3—31no—
459C4×Dic3—31no—
460C4×Dic3—61no—
461#208—21no—
462#208—21no—
463#208—31no—
464#208—31no—
465#208—61no—
466#208—61no—
467#208—61no—
468#208C22×D311yescharacteristic
469#208C22×D311yescharacteristic
470C2×C3⋊C8—21no—
471C2×C3⋊C8—21no—
472C2×C3⋊C8—61no—
473C2×C3⋊C8—61no—
474C2×C3⋊C8C22×D311yescharacteristic
475C2×C3⋊C8C22×D311yescharacteristic
476C2×C3⋊C8C22×D311yescharacteristic
477C2×C3⋊C8C22×D311yescharacteristic
478Dic12—31no—
479Dic12—31no—
480D24—31no—
481D24—31no—
482#204—31no—
483#204—31no—
484#204—31no—
485#204—31no—
486ΓL(1,𝔽25)—21no—
487ΓL(1,𝔽25)—21no—
488ΓL(1,𝔽25)—31no—
489ΓL(1,𝔽25)—31no—
490ΓL(1,𝔽25)—31no—
491ΓL(1,𝔽25)—31no—
492ΓL(1,𝔽25)—31no—
493ΓL(1,𝔽25)—31no—
494ΓL(1,𝔽25)—31no—
495ΓL(1,𝔽25)—31no—
496ΓL(1,𝔽25)—61no—
497ΓL(1,𝔽25)—61no—
498ΓL(1,𝔽25)—61no—
499ΓL(1,𝔽25)—61no—
500ΓL(1,𝔽25)—61no—
501ΓL(1,𝔽25)—61no—
502ΓL(1,𝔽25)—61no—
503ΓL(1,𝔽25)—61no—
504ΓL(1,𝔽25)—61no—
505ΓL(1,𝔽25)—61no—
506ΓL(1,𝔽25)—121no—
507D3×C8—21no—
508D3×C8—21no—
509D3×C8—31no—
510D3×C8—31no—
511D3×C8—31no—
512D3×C8—31no—
513D3×C8—31no—
514D3×C8—31no—
515D3×C8—31no—
516D3×C8—31no—
517D3×C8—61no—
518D3×C8—61no—
519D3×C8—61no—
520D3×C8—61no—
521D3×C8—61no—
522D3×C8—61no—
523D3×C8—61no—
524D3×C8—61no—
525D3×C8—61no—
526D3×C8—61no—
527D3×C8—121no—
528C22×C32—21no—
529C22×C32C2×#4111yescharacteristic
530C2×C3⋊D3—21no—
531C2×C3⋊D3—41no—
532C2×C3⋊D3—81no—
533C2×C3⋊D3C4×D411yescharacteristic
534C2×C3⋊D3C4×D411yescharacteristic
535C2×C3×D3—21no—
536C2×C3×D3—21no—
537D32—81no—
538C32×C4—21no—
539C32×C4—41no—
540C32×C4C23×C411yescharacteristic
541C32×C4C22×D411yescharacteristic
542C3⋊Dic3—21no—
543C3⋊Dic3—41no—
544C3⋊Dic3C4×D411yescharacteristic
545C3⋊Dic3C4×D411yescharacteristic
546C3×Dic3—21no—
547C3×Dic3—21no—
548C2×#41—91no—
549C2×#41—91no—
550#135—31no—
551#135—31no—
552#135—91no—
553#135—91no—
554#135—91no—
555#135—91no—
556#135—91no—
557#135—91no—
558C2×Q16—91no—
559C2×SD16—91no—
560C2×SD16—91no—
561C2×D8—91no—
562#131—31no—
563#131—31no—
564#131—31no—
565#131—31no—
566#131—91no—
567#131—91no—
568#131—91no—
569#131—91no—
570#131—181no—
571#131—181no—
572#131—181no—
573#131—181no—
574C2×M16—91no—
575C2×M16—91no—
576C2×M16—91no—
577C2×M16—181no—
578C2×M16—181no—
579C2×M16—181no—
580C2×M16—181no—
581C22×C8—91no—
582#117—91no—
583#108—31no—
584#108—31no—
585#108—91no—
586#108—91no—
587#104—31no—
588#104—31no—
589#104—91no—
590#104—91no—
591#104—91no—
592#104—91no—
593#104—91no—
594#104D3211yescharacteristic, complemented
595#97—31no—
596#97—91no—
597C4×C8—31no—
598C4×C8—91no—
599C22×D3—31no—
600C22×D3—31no—
601C22×D3—61no—
602C22×D3—61no—
603C22×D3—61no—
604C22×D3—61no—
605C22×D3—61no—
606C22×D3—121no—
607C3×Q8—21no—
608C3×Q8—31no—
609C3×Q8—31no—
610C3×Q8C2×C4×D311yescharacteristic
611C3×Q8C2×C4×D311yescharacteristic
612C3×D4—21no—
613C3×D4—21no—
614C3×D4—21no—
615C3×D4—31no—
616C3×D4—31no—
617C3×D4—41no—
618C3×D4—61no—
619C3×D4—61no—
620C3×D4C2×C4×D311yescharacteristic
621C3×D4C2×C4×D311yescharacteristic
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—41no—
628C2×C3×C4—41no—
629C2×C3×C4—61no—
630C2×C3×C4—61no—
631C2×C3×C4C23×D311yescharacteristic
632C2×C3×C4C23×D311yescharacteristic
633#67—21no—
634#67—21no—
635#67—61no—
636#67—61no—
637#67—61no—
638#67—61no—
639#67—61no—
640#67—61no—
641#67—61no—
642#67—61no—
643#67—61no—
644#67—61no—
645#67—121no—
646#67—121no—
647#67—121no—
648C2×Dic3—31no—
649C2×Dic3—31no—
650C2×Dic3—61no—
651C2×Dic3—61no—
652C2×Dic3—61no—
653C2×Dic3—61no—
654C2×Dic3—61no—
655C2×Dic3—61no—
656C2×Dic3—61no—
657C2×Dic3—121no—
658C2×Dic3—121no—
659D12—31no—
660D12—31no—
661D12—61no—
662D12—61no—
663D12—61no—
664D12—61no—
665D12—61no—
666D12—121no—
667D12C2×C4×D311yescharacteristic
668D12C2×C4×D311yescharacteristic
669C4×D3—21no—
670C4×D3—21no—
671C4×D3—31no—
672C4×D3—31no—
673C4×D3—31no—
674C4×D3—31no—
675C4×D3—31no—
676C4×D3—31no—
677C4×D3—31no—
678C4×D3—31no—
679C4×D3—61no—
680C4×D3—61no—
681C4×D3—61no—
682C4×D3—61no—
683C4×D3—61no—
684C4×D3—61no—
685C4×D3—61no—
686C4×D3—61no—
687C4×D3—61no—
688C4×D3—61no—
689C4×D3—61no—
690C4×D3—61no—
691C4×D3—61no—
692C4×D3—61no—
693C4×D3—121no—
694C4×D3—121no—
695C4×D3—121no—
696Dic6—31no—
697Dic6—31no—
698Dic6—61no—
699Dic6—61no—
700Dic6—61no—
701Dic6—61no—
702Dic6—61no—
703Dic6—121no—
704Dic6C2×C4×D311yescharacteristic
705Dic6C2×C4×D311yescharacteristic
706C3×C8—21no—
707C3×C8—21no—
708C3×C8—31no—
709C3×C8—31no—
710C3×C8—31no—
711C3×C8—31no—
712C3×C8—31no—
713C3×C8—31no—
714C3×C8—31no—
715C3×C8—31no—
716C3×C8—41no—
717C3×C8—61no—
718C3×C8—61no—
719C3⋊C8—21no—
720C3⋊C8—21no—
721C3⋊C8—61no—
722C3⋊C8—61no—
723C3⋊C8—121no—
724C3⋊C8C2×C4×D311yescharacteristic
725C3⋊C8C2×C4×D311yescharacteristic
726C3⋊C8C2×C4×D311yescharacteristic
727C3⋊C8C2×C4×D311yescharacteristic
728C3⋊C8D3×D411yescharacteristic
729C3⋊C8D3×D411yescharacteristic
730C3⋊C8D3×D411yescharacteristic
731C3⋊C8D3×D411yescharacteristic
732C2×C32—21no—
733C2×C32—41no—
734C2×C32C2×C4×D411yescharacteristic
735C3⋊D3—21no—
736C3⋊D3—21no—
737C3⋊D3—41no—
738C3×D3—41no—
739C3×D3—41no—
740#41—31no—
741#41—31no—
742#41—91no—
743#41—91no—
744#41—91no—
745#41—91no—
746#41—91no—
747#41—181no—
748#41—181no—
749#41—181no—
750#41—181no—
751#41C2×D3211yescharacteristic
752C2×Q8—91no—
753C2×Q8—91no—
754C2×D4—91no—
755C2×D4—91no—
756C2×D4—181no—
757C2×D4—181no—
758C22×C4—91no—
759C22×C4—181no—
760C22×C4—181no—
761Q16—31no—
762Q16—31no—
763Q16—91no—
764Q16—91no—
765SD16—31no—
766SD16—31no—
767SD16—31no—
768SD16—31no—
769SD16—91no—
770SD16—91no—
771SD16—91no—
772SD16—91no—
773D8—31no—
774D8—31no—
775D8—91no—
776D8—91no—
777M16—31no—
778M16—31no—
779M16—61no—
780M16—61no—
781M16—61no—
782M16—61no—
783M16—91no—
784M16—91no—
785M16—91no—
786M16—91no—
787M16—91no—
788M16—181no—
789M16—181no—
790M16—181no—
791M16—181no—
792M16—181no—
793M16—181no—
794M16C2×D3211yescharacteristic
795C2×C8—31no—
796C2×C8—31no—
797C2×C8—31no—
798C2×C8—31no—
799C2×C8—61no—
800C2×C8—61no—
801C2×C8—61no—
802C2×C8—61no—
803C2×C8—91no—
804C2×C8—91no—
805C2×C8—91no—
806C2×C8—91no—
807C2×C8—181no—
808C2×C8—181no—
809C2×C8—181no—
810C2×C8—181no—
811C2×C8—181no—
812C2×C8—181no—
813C4⋊C4—181no—
814C22⋊C4—181no—
815C42—91no—
816C42C2×D3211yescharacteristic
817C22×C3—21no—
818C22×C3—21no—
819C22×C3—21no—
820C22×C3—41no—
821C22×C3—61no—
822C22×C3—61no—
823C22×C3D3×#4111yescharacteristic
824C22×C3D3×#4111yescharacteristic
825C2×D3—21no—
826C2×D3—21no—
827C2×D3—31no—
828C2×D3—31no—
829C2×D3—31no—
830C2×D3—31no—
831C2×D3—61no—
832C2×D3—61no—
833C2×D3—61no—
834C2×D3—61no—
835C2×D3—121no—
836C2×D3—121no—
837C2×D3—121no—
838C2×D3—241no—
839C2×D3—241no—
840C2×D3—241no—
841C2×D3—241no—
842C2×D3—241no—
843C2×D3—242no—
844C3×C4—21no—
845C3×C4—21no—
846C3×C4—21no—
847C3×C4—21no—
848C3×C4—41no—
849C3×C4—41no—
850C3×C4—41no—
851C3×C4—61no—
852C3×C4—61no—
853C3×C4—81no—
854C3×C4C22×C4×D311yescharacteristic
855C3×C4C22×C4×D311yescharacteristic
856C3×C4C2×D3×D411yescharacteristic
857C3×C4C2×D3×D411yescharacteristic
858Dic3—21no—
859Dic3—21no—
860Dic3—31no—
861Dic3—31no—
862Dic3—31no—
863Dic3—31no—
864Dic3—61no—
865Dic3—61no—
866Dic3—61no—
867Dic3—61no—
868Dic3—121no—
869Dic3—121no—
870Dic3—121no—
871Dic3—241no—
872C32#295711yescharacteristic, complemented, Sylow
873C23—91no—
874C23—181no—
875C23—181no—
876Q8—31no—
877Q8—31no—
878Q8—91no—
879Q8—181no—
880Q8—181no—
881Q8C4×D3211yescharacteristic
882D4—21no—
883D4—31no—
884D4—31no—
885D4—61no—
886D4—61no—
887D4—91no—
888D4—181no—
889D4—181no—
890D4—181no—
891D4—181no—
892D4—181no—
893D4—181no—
894D4—181no—
895D4C4×D3211yescharacteristic
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—61no—
899C2×C4—61no—
900C2×C4—91no—
901C2×C4—91no—
902C2×C4—91no—
903C2×C4—91no—
904C2×C4—91no—
905C2×C4—181no—
906C2×C4—181no—
907C2×C4—181no—
908C2×C4—181no—
909C2×C4—181no—
910C2×C4—181no—
911C2×C4—181no—
912C2×C4—181no—
913C2×C4C22×D3211yescharacteristic
914C8—21no—
915C8—31no—
916C8—31no—
917C8—31no—
918C8—31no—
919C8—31no—
920C8—31no—
921C8—31no—
922C8—31no—
923C8—61no—
924C8—61no—
925C8—181no—
926C2×C3—21no—
927C2×C3—21no—
928C2×C3—21no—
929C2×C3—41no—
930C2×C3—41no—
931C2×C3—41no—
932C2×C3—81no—
933C2×C3—121no—
934C2×C3—121no—
935C2×C3C4×D3×D411yescharacteristic
936C2×C3C4×D3×D411yescharacteristic
937D3—41no—
938D3—41no—
939D3—61no—
940D3—61no—
941D3—61no—
942D3—61no—
943D3—121no—
944D3—121no—
945D3—121no—
946D3—121no—
947D3—241no—
948C22—21no—
949C22—61no—
950C22—61no—
951C22—91no—
952C22—91no—
953C22—181no—
954C22—361no—
955C22—721no—
956C22—721no—
957C22#6431211yescharacteristic
958C4—21no—
959C4—41no—
960C4—61no—
961C4—61no—
962C4—91no—
963C4—91no—
964C4—181no—
965C4—361no—
966C4C2×C4×D3211yescharacteristic
967C4D32×D411yescharacteristic
968C3—21no—
969C3#7989011yescharacteristic, complemented
970C3#7989911yescharacteristic, complemented
971C2—21no—
972C2—41no—
973C2—121no—
974C2—121no—
975C2—181no—
976C2—181no—
977C2—361no—
978C2#1059425511yescharacteristic
subgroupG/H
centerC4D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#104C22
socleC2×C32C2×C4×D4
prime radical#10595459C2
cosocleC2×C32×C4C24
hypercenter#104D32
hypocenterC32#2957
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #10595443C2semidirect
3. #10594708C2semidirect
4. #10592520C2semidirect
5. C3×#4824C2semidirect
6. C3×#4823C2semidirect
7. #10591674C2semidirect
8. #10591673C2semidirect
9. #10590995C2semidirect
10. #10590994C2semidirect
11. #10590972C2semidirect
12. #10590394C2semidirect
13. #10590342C2semidirect
14. #10590341C2semidirect
15. #10590321C2semidirect
24. C3×#948C22semidirect
25. C3×#948C22semidirect
26. C3×#907C22semidirect
27. C3×#907C22semidirect
28. #63950C4semidirect
29. #63950C4semidirect
30. #63944C4semidirect
31. #63940C4semidirect
32. #63936C4semidirect
33. #63936C4semidirect
34. #63930C4semidirect
35. #63926C4semidirect
44. #63817C22semidirect
45. #63817C22semidirect
47. #63814C22semidirect
48. #63814C22semidirect
53. C32×#104C22semidirect
54. #63664C22semidirect
55. #63652C22semidirect
56. #63632C22semidirect
57. C3×#822C22semidirect
58. C3×#822C22semidirect
59. C3×#805C22semidirect
60. C3×#805C22semidirect
61. C3×#803C22semidirect
62. C3×C4×C3⋊C8C22semidirect
63. #63577C22semidirect
64. #63577C22semidirect
65. #63568C22semidirect
66. #63568C22semidirect
67. #63555C22semidirect
68. #63553C22semidirect
88. #4824D3semidirect
90. #4823D3semidirect
195. #948C2×D3semidirect
196. #948C2×D3semidirect
219. #907C2×D3semidirect
220. #907C2×D3semidirect
256. C3×#104C2×D3semidirect
257. C3×#104C2×D3semidirect
272. #822C2×D3semidirect
273. #822C2×D3semidirect
283. #805C2×D3semidirect
284. #805C2×D3semidirect
285. #803C2×D3semidirect
286. C4×C3⋊C8C2×D3semidirect
594. #104D32semidirect
872. C32#2957semidirect
969. C3#79890semidirect
970. C3#79899semidirect

Maximal subgroups

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

subgroupindex
#105954592
#105954432
#105947082
#105925202
C3×#48242
C3×#48232
#105916742
#105916732
#105909952
#105909942
#105909722
#105903942
#105903422
#105903412
#105903212
#798993
#798903