Finite Group Databasebeta

← #11861210

Subgroups — #11861210

Order 1152.

957 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#950C211yesmaximal, characteristic
2#10595441C211yesmaximal, characteristic, complemented
3#10594706C211yesmaximal, characteristic, complemented
4#10592523C211yesmaximal, characteristic, complemented
5C3×#4823C211yesmaximal, characteristic, complemented
6C3×#4821C211yesmaximal, characteristic, complemented
7#10591676C211yesmaximal, characteristic, complemented
8#10591662C211yesmaximal, characteristic, complemented
9#10590978C211yesmaximal, characteristic, complemented
10#10590975C211yesmaximal, characteristic, complemented
11D3×#822C211yesmaximal, characteristic, complemented
12#10590392C211yesmaximal, characteristic, complemented
13#10590389C211yesmaximal, characteristic, complemented
14#10590342C211yesmaximal, characteristic, complemented
15#10590319C211yesmaximal, characteristic, complemented
16#79899—31nomaximal
17#78990—31nomaximal
18C3×D3×#41C2211yescharacteristic
19D3×#235C2211yescharacteristic
20#64159C2211yescharacteristic
21#64157C2211yescharacteristic, complemented
22#64116C2211yescharacteristic, complemented
23C3×#950C2211yescharacteristic
24C3×#948C2211yescharacteristic, complemented
25C3×#907C2211yescharacteristic, complemented
26C3×D3×M16C2211yescharacteristic
27C3×#872C2211yescharacteristic
28#63949C411yescharacteristic, complemented
29#63947C411yescharacteristic, complemented
30D3×#216C411yescharacteristic, complemented
31D3×#215C411yescharacteristic, complemented
32#63935C411yescharacteristic, complemented
33#63933C411yescharacteristic, complemented
34D3×#214C411yescharacteristic, complemented
35D3×#213C411yescharacteristic, complemented
36#63829C2211yescharacteristic
37#63822C2211yescharacteristic
38C2×#3711—21no—
39C2×#3711C2211yescharacteristic
40#63817C2211yescharacteristic, complemented
41#63815—21no—
42#63815C2211yescharacteristic, complemented
43#63815C2211yescharacteristic, complemented
44#63814—21no—
45#63814C2211yescharacteristic, complemented
46D3×#208—21no—
47D3×#208C2211yescharacteristic
48C2×D3×C3⋊C8C2211yescharacteristic
49#63804—21no—
50#63803—21no—
51#63791—21no—
52D3×ΓL(1,𝔽25)—21no—
53C32×#104C2211yescharacteristic, complemented
54#63649C2211yescharacteristic, complemented
55#63632C2211yescharacteristic, complemented
56C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
57C3×#837C2211yescharacteristic, complemented
58C3×#825C2211yescharacteristic, complemented
59C3×#822C2211yescharacteristic, complemented
60C3×#805C2211yescharacteristic, complemented
61C3×#805C2211yescharacteristic, complemented
62C3×#803C2211yescharacteristic, complemented
63#63578C2211yescharacteristic, complemented
64#63577C2211yescharacteristic, complemented
65#63570C2211yescharacteristic, complemented
66#63569C2211yescharacteristic, complemented
67#63554C2211yescharacteristic, complemented
68Dic3×C3⋊C8C2211yescharacteristic, complemented
69C2×#950—31no—
70#5819—31no—
71D3×#135—31no—
72#5750—31no—
73#5750—31no—
74#5745—31no—
75C3×#444—31no—
76C3×#421—31no—
77#5197—31no—
78#5144—31no—
79#5144—31no—
80C2×#822—31no—
81#5005—31no—
82#4997—31no—
83#4894—31no—
84D3×#108—31no—
85#4824—31no—
86#4824—31no—
87#4824—31no—
88#4824—31no—
89#4824—31no—
90#4824—31no—
91#4824—61no—
92#4823—31no—
93#4823—31no—
94#4823—31no—
95#4823D311yescharacteristic, complemented
96#4821—31no—
97#4821D311yescharacteristic, complemented
98#4717—31no—
99#4708—31no—
100C32×#41C2311yescharacteristic
101#3828C2311yescharacteristic
102C3×#239C2×C411yescharacteristic
103C3×D3×Q8C2×C411yescharacteristic
104C3×#237—21no—
105C3×#237C2×C411yescharacteristic
106C3×D3×D4—21no—
107C3×D3×D4C2×C411yescharacteristic
108C3×#235—21no—
109C3×#235C2311yescharacteristic
110C3×#235C2311yescharacteristic
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3C2311yescharacteristic
113D3×#67—21no—
114#3804—21no—
115D3×D12C2×C411yescharacteristic
116C4×D32—21no—
117#3799C2×C411yescharacteristic
118#3798—21no—
119#3795C2×C411yescharacteristic
120D3×Dic6C2×C411yescharacteristic
121C32×M16C2311yescharacteristic
122C32×C42C2311yescharacteristic
123#3756C2×C411yescharacteristic
124#3755C2×C411yescharacteristic
125#3754C2×C411yescharacteristic
126#3753C2×C411yescharacteristic
127#3748—21no—
128#3748C2311yescharacteristic
129C2×C3⋊(C3⋊C8)—21no—
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132#3743—21no—
133C8×C3⋊D3—21no—
134C3×#216C2×C411yescharacteristic
135C3×#215C2×C411yescharacteristic
136C3×#214C2×C411yescharacteristic
137C3×#213C2×C411yescharacteristic
138C3×(C2×D3)⋊C4—21no—
139C3×Dic3⋊C4—21no—
140C3×C4×Dic3C2311yescharacteristic
141C3×#208—21no—
142C3×#208C2311yescharacteristic
143C3×#208C2311yescharacteristic
144C2×C3×C3⋊C8—21no—
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#3718C2×C411yescharacteristic
153#3717C2×C411yescharacteristic
154#3716C2×C411yescharacteristic
155#3715C2×C411yescharacteristic
156#3715C2×C411yescharacteristic
157#3714C2×C411yescharacteristic
158#3713C2×C411yescharacteristic
159#3712—21no—
160#3711—21no—
161#3711—21no—
162#3711—21no—
163#3711—21no—
164#3711D411yescharacteristic
165#3711D411yescharacteristic
166#3711D411yescharacteristic
167#3711D411yescharacteristic
168#3710—21no—
169D3×C3⋊C8—21no—
170D3×C3⋊C8—21no—
171D3×C3⋊C8—21no—
172D3×C3⋊C8—21no—
173D3×C3⋊C8C2×C411yescharacteristic
174D3×C3⋊C8C2×C411yescharacteristic
175D3×C3⋊C8C2×C411yescharacteristic
176D3×C3⋊C8C2×C411yescharacteristic
177#2957—91noSylow
178C2×C3×#41—31no—
179D3×#41—31no—
180D3×#41C2×D311yescharacteristic
181C2×#235—31no—
182C3×#135—31no—
183C3×#131—31no—
184C3×#131—31no—
185C2×C3×M16—31no—
186C3×#117—31no—
187#950—31no—
188#950—31no—
189#950—31no—
190#950—31no—
191#950—31no—
192#950—31no—
193#950—31no—
194#950—31no—
195#950—31no—
196#950—61no—
197#950C2×D311yescharacteristic
198#948—31no—
199#948—31no—
200#948—31no—
201#948—31no—
202#948—31no—
203#948—61no—
204#948—61no—
205#948—61no—
206#948C2×D311yescharacteristic, complemented
207C2×#216—31no—
208C2×#215—31no—
209C2×#214—31no—
210C2×#213—31no—
211C2×#208—31no—
212C2×#208—31no—
213C2×#208—61no—
214C2×#208—61no—
215C22×C3⋊C8—31no—
216#919—31no—
217D3×Q16—31no—
218#916—31no—
219#916—31no—
220D3×SD16—31no—
221D3×SD16—31no—
222#912—31no—
223D3×D8—31no—
224#907—31no—
225#907—31no—
226#907—31no—
227#907—31no—
228#907—31no—
229#907—61no—
230#907—61no—
231#907—61no—
232#907C2×D311yescharacteristic, complemented
233D3×M16—31no—
234D3×M16—61no—
235D3×M16—61no—
236D3×M16—61no—
237D3×M16—61no—
238D3×M16C2×D311yescharacteristic
239#904—31no—
240#901—31no—
241#901—31no—
242#901—61no—
243#901—61no—
244#901—61no—
245#901—61no—
246C2×ΓL(1,𝔽25)—31no—
247C2×ΓL(1,𝔽25)—61no—
248C2×ΓL(1,𝔽25)—61no—
249C2×D3×C8—31no—
250#872C2×D311yescharacteristic
251C3×#108—31no—
252C3×#104—21no—
253C3×#104—31no—
254C3×#104—31no—
255C3×#104—31no—
256C3×#104—31no—
257C3×#104C2×D311yescharacteristic, complemented
258C3×#104C2×D311yescharacteristic, complemented
259C3×#97—31no—
260#837—31no—
261#837C2×D311yescharacteristic, complemented
262#825—31no—
263#825C2×D311yescharacteristic, complemented
264#822—31no—
265#822—31no—
266#822—31no—
267#822—31no—
268#822—31no—
269#822—61no—
270#822C2×D311yescharacteristic, complemented
271#819—31no—
272#815—31no—
273C8×Dic3—31no—
274#805—31no—
275#805—31no—
276#805—31no—
277#805—31no—
278#805—61no—
279#805C2×D311yescharacteristic, complemented
280#805C2×D311yescharacteristic, complemented
281#803—31no—
282#803C2×D311yescharacteristic, complemented
283C4×C3⋊C8—31no—
284C4×C3⋊C8—31no—
285C4×C3⋊C8—31no—
286C4×C3⋊C8—61no—
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—
297C4⋊(C3⋊D3)C22×C411yescharacteristic
298C4×C3⋊D3—21no—
299#634C22×C411yescharacteristic
300C3×#67—21no—
301C3×#67—21no—
302C3×#67—21no—
303C3×#67—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3#4111yescharacteristic
307C3×D12—21no—
308C3×D12C22×C411yescharacteristic
309C3×D12C22×C411yescharacteristic
310C3×C4×D3—21no—
311C3×C4×D3—21no—
312C3×C4×D3—21no—
313C3×C4×D3—21no—
314C3×C4×D3C22×C411yescharacteristic
315C3×C4×D3C22×C411yescharacteristic
316C3×C4×D3C2×D411yescharacteristic
317C3×C4×D3C2×D411yescharacteristic
318C3×Dic6—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)C22×C411yescharacteristic
331C3⋊(C3⋊C8)C22×C411yescharacteristic
332C3⋊(C3⋊C8)C2×D411yescharacteristic
333C3⋊(C3⋊C8)C2×D411yescharacteristic
334C3×C3⋊C8—21no—
335C3×C3⋊C8—21no—
336C3×C3⋊C8C22×C411yescharacteristic
337C3×C3⋊C8C22×C411yescharacteristic
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—91no—
348#443—91no—
349#443—91no—
350#443—91no—
351C2×#108—91no—
352#421—31no—
353#421—91no—
354#405—91no—
355C3×#41—21no—
356C3×#41—31no—
357C3×#41—31no—
358C3×#41—31no—
359C3×#41—31no—
360C3×#41—61no—
361C3×#41—61no—
362C3×#41C22×D311yescharacteristic
363C3×#41C22×D311yescharacteristic
364C2×C3×Q8—31no—
365C2×C3×D4—31no—
366C2×C3×D4—61no—
367C22×C3×C4—31no—
368C22×C3×C4—61no—
369C2×#67—61no—
370#239—31no—
371#239C4×D311yescharacteristic
372D3×Q8—31no—
373D3×Q8C4×D311yescharacteristic
374#237—21no—
375#237—31no—
376#237—61no—
377#237C4×D311yescharacteristic
378D3×D4—21no—
379D3×D4—31no—
380D3×D4—61no—
381D3×D4C4×D311yescharacteristic
382#235—21no—
383#235—31no—
384#235—31no—
385#235—31no—
386#235—31no—
387#235—61no—
388#235—61no—
389#235—61no—
390#235—61no—
391#235C22×D311yescharacteristic
392#235C22×D311yescharacteristic
393C2×D12—31no—
394C2×C4×D3—21no—
395C2×C4×D3—61no—
396C2×C4×D3—61no—
397C2×C4×D3C22×D311yescharacteristic
398C2×Dic6—31no—
399C3×Q16—31no—
400C3×SD16—31no—
401C3×SD16—31no—
402C3×D8—31no—
403C3×M16—21no—
404C3×M16—31no—
405C3×M16—31no—
406C3×M16—61no—
407C3×M16—61no—
408C3×M16—61no—
409C3×M16C22×D311yescharacteristic
410C3×M16C22×D311yescharacteristic
411C2×C3×C8—31no—
412C2×C3×C8—31no—
413C2×C3×C8—61no—
414C2×C3×C8—61no—
415C2×C3×C8—61no—
416C3×C4⋊C4—61no—
417C3×C22⋊C4—61no—
418C3×C42—21no—
419C3×C42—31no—
420C3×C42C22×D311yescharacteristic
421C3×C42C22×D311yescharacteristic
422#216—31no—
423#216—31no—
424#216—31no—
425#216—31no—
426#216—31no—
427#216—61no—
428#216C4×D311yescharacteristic
429#215—31no—
430#215—31no—
431#215—31no—
432#215—31no—
433#215—31no—
434#215—61no—
435#215C4×D311yescharacteristic
436#214—31no—
437#214—31no—
438#214—31no—
439#214—31no—
440#214—31no—
441#214—61no—
442#214C4×D311yescharacteristic
443#213—31no—
444#213—31no—
445#213—31no—
446#213—31no—
447#213—31no—
448#213—61no—
449#213C4×D311yescharacteristic
450(C2×D3)⋊C4—21no—
451Dic3⋊C4—21no—
452C4×Dic3C22×D311yescharacteristic
453#208—21no—
454#208—31no—
455#208—31no—
456#208—31no—
457#208—31no—
458#208—31no—
459#208—31no—
460#208—61no—
461#208—61no—
462#208—61no—
463#208—61no—
464#208—61no—
465#208—61no—
466#208—61no—
467#208—121no—
468#208C22×D311yescharacteristic
469#208C22×D311yescharacteristic
470C2×C3⋊C8—21no—
471C2×C3⋊C8—31no—
472C2×C3⋊C8—31no—
473C2×C3⋊C8—31no—
474C2×C3⋊C8—31no—
475C2×C3⋊C8—31no—
476C2×C3⋊C8—31no—
477C2×C3⋊C8—31no—
478C2×C3⋊C8—31no—
479C2×C3⋊C8—61no—
480C2×C3⋊C8—61no—
481C2×C3⋊C8—61no—
482C2×C3⋊C8—61no—
483C2×C3⋊C8—61no—
484C2×C3⋊C8—61no—
485C2×C3⋊C8—61no—
486C2×C3⋊C8—61no—
487C2×C3⋊C8—121no—
488C2×C3⋊C8C22×D311yescharacteristic
489C2×C3⋊C8C22×D311yescharacteristic
490Dic12—31no—
491D24—31no—
492#204—31no—
493#204—31no—
494ΓL(1,𝔽25)—21no—
495ΓL(1,𝔽25)—21no—
496ΓL(1,𝔽25)—31no—
497ΓL(1,𝔽25)—31no—
498ΓL(1,𝔽25)—31no—
499ΓL(1,𝔽25)—31no—
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)—61no—
507ΓL(1,𝔽25)—61no—
508ΓL(1,𝔽25)—121no—
509D3×C8—21no—
510D3×C8—21no—
511D3×C8—31no—
512D3×C8—31no—
513D3×C8—31no—
514D3×C8—31no—
515D3×C8—61no—
516D3×C8—61no—
517D3×C8—61no—
518D3×C8—61no—
519D3×C8—61no—
520D3×C8—61no—
521D3×C8—61no—
522D3×C8—61no—
523D3×C8—121no—
524C22×C32—21no—
525C22×C32C2×#4111yescharacteristic
526C2×C3⋊D3—21no—
527C2×C3×D3—21no—
528C2×C3×D3—21no—
529C2×C3×D3—41no—
530C2×C3×D3—81no—
531C2×C3×D3C4×D411yescharacteristic
532C2×C3×D3C4×D411yescharacteristic
533D32—81no—
534C32×C4—21no—
535C32×C4—41no—
536C32×C4C23×C411yescharacteristic
537C32×C4C22×D411yescharacteristic
538C3⋊Dic3—21no—
539C3×Dic3—21no—
540C3×Dic3—21no—
541C3×Dic3—41no—
542C3×Dic3C4×D411yescharacteristic
543C3×Dic3C4×D411yescharacteristic
544C2×#41—31no—
545C2×#41—91no—
546#135—31no—
547#135—91no—
548#135—91no—
549#135—91no—
550#135—91no—
551#135—91no—
552#135—91no—
553#135—91no—
554C2×Q16—91no—
555C2×SD16—91no—
556C2×SD16—91no—
557C2×D8—91no—
558#131—31no—
559#131—31no—
560#131—91no—
561#131—91no—
562#131—91no—
563#131—91no—
564#131—91no—
565#131—91no—
566#131—181no—
567#131—181no—
568#131—181no—
569#131—181no—
570C2×M16—31no—
571C2×M16—91no—
572C2×M16—91no—
573C2×M16—181no—
574C2×M16—181no—
575C2×M16—181no—
576C2×M16—181no—
577C22×C8—91no—
578#117—31no—
579#108—31no—
580#108—91no—
581#108—91no—
582#108—91no—
583#104—31no—
584#104—31no—
585#104—31no—
586#104—31no—
587#104—91no—
588#104—91no—
589#104—91no—
590#104D3211yescharacteristic, complemented
591#97—31no—
592#97—91no—
593C4×C8—91no—
594C4×C8—91no—
595C23×C3—31no—
596C23×C3—61no—
597C22×D3—21no—
598C22×D3—61no—
599C22×D3—61no—
600C22×D3#23711yescharacteristic
601C3×Q8—21no—
602C3×Q8—31no—
603C3×Q8—31no—
604C3×Q8—61no—
605C3×Q8C2×C4×D311yescharacteristic
606C3×Q8C2×C4×D311yescharacteristic
607C3×D4—21no—
608C3×D4—21no—
609C3×D4—21no—
610C3×D4—31no—
611C3×D4—31no—
612C3×D4—41no—
613C3×D4—61no—
614C3×D4—61no—
615C3×D4—61no—
616C3×D4—61no—
617C3×D4—61no—
618C3×D4C2×C4×D311yescharacteristic
619C3×D4C2×C4×D311yescharacteristic
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—31no—
626C2×C3×C4—31no—
627C2×C3×C4—31no—
628C2×C3×C4—31no—
629C2×C3×C4—31no—
630C2×C3×C4—41no—
631C2×C3×C4—41no—
632C2×C3×C4—61no—
633C2×C3×C4—61no—
634C2×C3×C4—61no—
635C2×C3×C4—61no—
636C2×C3×C4—61no—
637C2×C3×C4—61no—
638C2×C3×C4C23×D311yescharacteristic
639C2×C3×C4C23×D311yescharacteristic
640#67—21no—
641#67—21no—
642#67—21no—
643#67—21no—
644#67—61no—
645#67—61no—
646#67—61no—
647#67—61no—
648#67—61no—
649#67—61no—
650#67—121no—
651C2×Dic3—21no—
652C2×Dic3—21no—
653C2×Dic3—61no—
654C2×Dic3—61no—
655C2×Dic3#23711yescharacteristic
656D12—21no—
657D12—31no—
658D12—31no—
659D12—61no—
660D12—61no—
661D12—61no—
662D12C2×C4×D311yescharacteristic
663D12C2×C4×D311yescharacteristic
664C4×D3—21no—
665C4×D3—21no—
666C4×D3—21no—
667C4×D3—21no—
668C4×D3—61no—
669C4×D3—61no—
670C4×D3—61no—
671C4×D3—61no—
672C4×D3—61no—
673C4×D3—61no—
674C4×D3—121no—
675C4×D3C2×C4×D311yescharacteristic
676C4×D3C2×C4×D311yescharacteristic
677C4×D3D3×D411yescharacteristic
678C4×D3D3×D411yescharacteristic
679Dic6—21no—
680Dic6—31no—
681Dic6—31no—
682Dic6—61no—
683Dic6—61no—
684Dic6—61no—
685Dic6C2×C4×D311yescharacteristic
686Dic6C2×C4×D311yescharacteristic
687C3×C8—21no—
688C3×C8—21no—
689C3×C8—31no—
690C3×C8—31no—
691C3×C8—31no—
692C3×C8—31no—
693C3×C8—41no—
694C3×C8—61no—
695C3×C8—61no—
696C3⋊C8—21no—
697C3⋊C8—21no—
698C3⋊C8—31no—
699C3⋊C8—31no—
700C3⋊C8—31no—
701C3⋊C8—31no—
702C3⋊C8—31no—
703C3⋊C8—31no—
704C3⋊C8—31no—
705C3⋊C8—31no—
706C3⋊C8—61no—
707C3⋊C8—61no—
708C3⋊C8—61no—
709C3⋊C8—61no—
710C3⋊C8—61no—
711C3⋊C8—61no—
712C3⋊C8—121no—
713C3⋊C8C2×C4×D311yescharacteristic
714C3⋊C8C2×C4×D311yescharacteristic
715C3⋊C8D3×D411yescharacteristic
716C3⋊C8D3×D411yescharacteristic
717C2×C32—21no—
718C2×C32—41no—
719C2×C32C2×C4×D411yescharacteristic
720C3⋊D3—41no—
721C3×D3—21no—
722C3×D3—21no—
723C3×D3—41no—
724C3×D3—41no—
725#41—31no—
726#41—31no—
727#41—31no—
728#41—31no—
729#41—61no—
730#41—61no—
731#41—91no—
732#41—91no—
733#41—91no—
734#41—181no—
735#41—181no—
736#41C2×D3211yescharacteristic
737C2×Q8—31no—
738C2×Q8—91no—
739C2×D4—31no—
740C2×D4—61no—
741C2×D4—91no—
742C2×D4—181no—
743C22×C4—31no—
744C22×C4—61no—
745C22×C4—181no—
746Q16—31no—
747Q16—91no—
748Q16—91no—
749Q16—91no—
750SD16—31no—
751SD16—31no—
752SD16—91no—
753SD16—91no—
754SD16—91no—
755SD16—91no—
756SD16—91no—
757SD16—91no—
758D8—31no—
759D8—91no—
760D8—91no—
761D8—91no—
762M16—31no—
763M16—31no—
764M16—61no—
765M16—61no—
766M16—61no—
767M16—91no—
768M16—91no—
769M16—91no—
770M16—91no—
771M16—91no—
772M16—181no—
773M16—181no—
774M16—181no—
775M16—181no—
776M16—181no—
777M16—181no—
778M16—181no—
779M16C2×D3211yescharacteristic
780C2×C8—31no—
781C2×C8—31no—
782C2×C8—61no—
783C2×C8—61no—
784C2×C8—61no—
785C2×C8—91no—
786C2×C8—91no—
787C2×C8—91no—
788C2×C8—91no—
789C2×C8—91no—
790C2×C8—91no—
791C2×C8—181no—
792C2×C8—181no—
793C2×C8—181no—
794C2×C8—181no—
795C2×C8—181no—
796C2×C8—181no—
797C2×C8—181no—
798C4⋊C4—61no—
799C22⋊C4—61no—
800C42—31no—
801C42C2×D3211yescharacteristic
802C22×C3—21no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—31no—
806C22×C3—31no—
807C22×C3—41no—
808C22×C3—61no—
809C22×C3—61no—
810C22×C3—121no—
811C22×C3—241no—
812C22×C3C2×#23711yescharacteristic
813C22×C3D3×#4111yescharacteristic
814C2×D3—21no—
815C2×D3—21no—
816C2×D3—41no—
817C2×D3—61no—
818C2×D3—61no—
819C2×D3—81no—
820C2×D3—121no—
821C2×D3—241no—
822C2×D3—241no—
823C2×D3#67⋊C411yescharacteristic
824C2×D3#67⋊C411yescharacteristic
825C3×C4—21no—
826C3×C4—21no—
827C3×C4—21no—
828C3×C4—21no—
829C3×C4—31no—
830C3×C4—31no—
831C3×C4—41no—
832C3×C4—41no—
833C3×C4—41no—
834C3×C4—42no—
835C3×C4—61no—
836C3×C4—61no—
837C3×C4—121no—
838C3×C4C22×C4×D311yescharacteristic
839C3×C4C22×C4×D311yescharacteristic
840C3×C4C2×D3×D411yescharacteristic
841C3×C4C2×D3×D411yescharacteristic
842Dic3—21no—
843Dic3—21no—
844Dic3—41no—
845Dic3—61no—
846Dic3—61no—
847Dic3—121no—
848Dic3#67⋊C411yescharacteristic
849Dic3#67⋊C411yescharacteristic
850C32#295711yescharacteristic, complemented, Sylow
851C23—31no—
852C23—61no—
853C23—181no—
854Q8—31no—
855Q8—31no—
856Q8—61no—
857Q8—91no—
858Q8—181no—
859Q8C4×D3211yescharacteristic
860D4—21no—
861D4—31no—
862D4—31no—
863D4—61no—
864D4—61no—
865D4—61no—
866D4—61no—
867D4—61no—
868D4—91no—
869D4—181no—
870D4—181no—
871D4—181no—
872D4—181no—
873D4C4×D3211yescharacteristic
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—31no—
877C2×C4—31no—
878C2×C4—31no—
879C2×C4—31no—
880C2×C4—31no—
881C2×C4—61no—
882C2×C4—61no—
883C2×C4—61no—
884C2×C4—61no—
885C2×C4—61no—
886C2×C4—61no—
887C2×C4—181no—
888C2×C4—181no—
889C2×C4—181no—
890C2×C4—181no—
891C2×C4C22×D3211yescharacteristic
892C8—21no—
893C8—31no—
894C8—31no—
895C8—31no—
896C8—31no—
897C8—61no—
898C8—61no—
899C8—91no—
900C8—91no—
901C8—91no—
902C8—91no—
903C8—181no—
904C2×C3—21no—
905C2×C3—21no—
906C2×C3—21no—
907C2×C3—41no—
908C2×C3—41no—
909C2×C3—41no—
910C2×C3—61no—
911C2×C3—61no—
912C2×C3—81no—
913C2×C3—121no—
914C2×C3—121no—
915C2×C3C2×#67⋊C411yescharacteristic
916C2×C3C4×D3×D411yescharacteristic
917D3—21no—
918D3—21no—
919D3—41no—
920D3—41no—
921D3—121no—
922D3—121no—
923D3—241no—
924C22—21no—
925C22—31no—
926C22—31no—
927C22—61no—
928C22—61no—
929C22—121no—
930C22—181no—
931C22—241no—
932C22—721no—
933C22D3×#23711yescharacteristic
934C4—21no—
935C4—31no—
936C4—31no—
937C4—41no—
938C4—61no—
939C4—61no—
940C4—121no—
941C4—181no—
942C4C2×C4×D3211yescharacteristic
943C4D32×D411yescharacteristic
944C3—21no—
945C3#7899011yescharacteristic, complemented
946C3#7989911yescharacteristic, complemented
947C2—21no—
948C2—41no—
949C2—61no—
950C2—61no—
951C2—121no—
952C2—121no—
953C2—361no—
954C2D3×#67⋊C411yescharacteristic
subgroupG/H
centerC4D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#104C22
socleC2×C32C2×C4×D4
prime radicalD3×#950C2
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. #10595441C2semidirect
3. #10594706C2semidirect
4. #10592523C2semidirect
5. C3×#4823C2semidirect
6. C3×#4821C2semidirect
7. #10591676C2semidirect
8. #10591662C2semidirect
9. #10590978C2semidirect
10. #10590975C2semidirect
11. D3×#822C2semidirect
12. #10590392C2semidirect
13. #10590389C2semidirect
14. #10590342C2semidirect
15. #10590319C2semidirect
21. #64157C22semidirect
22. #64116C22semidirect
24. C3×#948C22semidirect
25. C3×#907C22semidirect
28. #63949C4semidirect
29. #63947C4semidirect
30. D3×#216C4semidirect
31. D3×#215C4semidirect
32. #63935C4semidirect
33. #63933C4semidirect
34. D3×#214C4semidirect
35. D3×#213C4semidirect
40. #63817C22semidirect
42. #63815C22semidirect
43. #63815C22semidirect
45. #63814C22semidirect
53. C32×#104C22semidirect
54. #63649C22semidirect
55. #63632C22semidirect
56. C4×C3⋊(C3⋊C8)C22semidirect
57. C3×#837C22semidirect
58. C3×#825C22semidirect
59. C3×#822C22semidirect
60. C3×#805C22semidirect
61. C3×#805C22semidirect
62. C3×#803C22semidirect
63. #63578C22semidirect
64. #63577C22semidirect
65. #63570C22semidirect
66. #63569C22semidirect
67. #63554C22semidirect
68. Dic3×C3⋊C8C22semidirect
95. #4823D3semidirect
97. #4821D3semidirect
206. #948C2×D3semidirect
232. #907C2×D3semidirect
257. C3×#104C2×D3semidirect
258. C3×#104C2×D3semidirect
261. #837C2×D3semidirect
263. #825C2×D3semidirect
270. #822C2×D3semidirect
279. #805C2×D3semidirect
280. #805C2×D3semidirect
282. #803C2×D3semidirect
590. #104D32semidirect
850. C32#2957semidirect
945. C3#78990semidirect
946. C3#79899semidirect

Maximal subgroups

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

subgroupindex
D3×#9502
#105954412
#105947062
#105925232
C3×#48232
C3×#48212
#105916762
#105916622
#105909782
#105909752
D3×#8222
#105903922
#105903892
#105903422
#105903192
#798993
#789903