Finite Group Databasebeta

← #11918521

Subgroups — #11918521

Order 1152.

2977 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596669C211yesmaximal, characteristic
2#10596216C211yesmaximal, characteristic, complemented
3C3×#5745C211yesmaximal, characteristic, complemented
4C2×C3×#907C211yesmaximal, characteristic, complemented
5C2×#63817C211yesmaximal, characteristic, complemented
6#10594776C211yesmaximal, characteristic, complemented
7C2×#63814C211yesmaximal, characteristic, complemented
8#10594708C214yesmaximal, complemented
9#10594707C214yesmaximal, complemented
10#10594706C214yesmaximal, complemented
11D3×#907C214yesmaximal, complemented
12#10594668C214yesmaximal, complemented
13D3×#901C214yesmaximal, complemented
14#87166—31nomaximal
15#87160—31nomaximal
16C2×#3828C2211yescharacteristic
17C2×C3×#235C2211yescharacteristic
18C2×C3×#235C2211yescharacteristic
19#64330C414yes—
20#64308C412yes—
21#64307C412yes—
22#64307C412yes—
23#64306C2214yes—
24D3×#235C2214yes—
25D3×#235C2214yes—
26#64298C412yes—
27#64297C412yes—
28#64297C412yes—
29C2×C32×M16C2211yescharacteristic, complemented
30C2×#3748C2211yescharacteristic, complemented
31#64116C2214yescomplemented
32M16×C3⋊D3C2214yescomplemented
33#64110C2214yescomplemented
34C2×C3×#208C2211yescharacteristic, complemented
35C22×C3×C3⋊C8C2211yescharacteristic, complemented
36C3×#907C2212yescomplemented
37C3×#907C2212yescomplemented
38C3×#907C2212yescomplemented
39C3×#907C2212yescomplemented
40C3×#907C2214yescomplemented
41C3×D3×M16C2214yescomplemented
42C3×#901C2214yescomplemented
43C2×C3×ΓL(1,𝔽25)C2212yescomplemented
44C2×C3×D3×C8C2212yescomplemented
45C2×#3712C2212yescomplemented
46C2×#3711C2212yescomplemented
47#63817C2212yescomplemented
48#63817C2212yescomplemented
49#63817C2212yescomplemented
50#63817C2212yescomplemented
51C2×#3710C2212yescomplemented
52#63815C2214yescomplemented
53#63814C2212yescomplemented
54#63814C2212yescomplemented
55#63814C2212yescomplemented
56#63814C2214yescomplemented
57#63814C2212yescomplemented
58D3×#208C2214yescomplemented
59C2×D3×C3⋊C8C2212yescomplemented
60#63805C2218yescomplemented
61#63804C2218yescomplemented
62#63804C2218yescomplemented
63#63803C2218yescomplemented
64#63791C2218yescomplemented
65D3×ΓL(1,𝔽25)C2218yescomplemented
66D3×ΓL(1,𝔽25)C2218yescomplemented
67D32×C8C2218yescomplemented
68#5964—31no—
69#5964—31no—
70C3×#568—31no—
71C2×C3×#131—31no—
72#5819—31no—
73C2×#948—31no—
74#5750—34no—
75#5750—34no—
76#5750—34no—
77#5750—34no—
78D3×#131—34no—
79D3×#131—34no—
80D3×#131—34no—
81D3×#131—34no—
82#5745—31no—
83#5745—31no—
84#5745—31no—
85#5745—34no—
86#5745—34no—
87#5745—61no—
88#5745D311yescharacteristic, complemented
89C2×#907—31no—
90C2×#907—34no—
91C2×#907D311yescharacteristic, complemented
92C2×#901—31no—
93C2×#901—31no—
94C2×#901—34no—
95C22×C32×C4C2311yescharacteristic
96C2×#638C2×C412yes—
97#3828C2×C412yes—
98#3828C2×C412yes—
99#3828C2312yes—
100#3828C2312yes—
101C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
102C2×C4×C3⋊D3C2312yes—
103C2×#634C2×C411yescharacteristic
104C2×C3×#67C2×C412yes—
105C2×C3×#67C2×C412yes—
106C3×#235C2×C412yes—
107C3×#235C2×C412yes—
108C3×#235C2×C412yes—
109C3×#235C2×C412yes—
110C3×#235C2312yes—
111C3×#235C2312yes—
112C3×#235C2312yes—
113C3×#235C2312yes—
114C2×C3×D12C2×C411yescharacteristic
115C2×C3×D12C2×C411yescharacteristic
116C2×C3×C4×D3C2312yes—
117C2×C3×C4×D3C2312yes—
118C2×C3×Dic6C2×C411yescharacteristic
119C2×C3×Dic6C2×C411yescharacteristic
120#3811C2×C418yes—
121D3×#67C2×C418yes—
122D3×#67C2×C418yes—
123#3805C2×C418yes—
124#3804C2×C418yes—
125#3804C2×C418yes—
126#3802C2×C414yes—
127D3×D12C2×C414yes—
128D3×D12C2×C414yes—
129C4×D32C2318yes—
130#3799C2×C414yes—
131#3799C2×C414yes—
132#3798C2318yes—
133#3797C2×C414yes—
134#3796C2×C414yes—
135#3796C2×C414yes—
136#3795C2×C414yes—
137#3795C2×C414yes—
138D3×Dic6C2×C414yes—
139D3×Dic6C2×C414yes—
140C32×M16C2312yes—
141C32×M16C2312yes—
142C2×C32×C8C2312yes—
143#3748C2312yes—
144#3748C2312yes—
145C2×C3⋊(C3⋊C8)C2312yes—
146#3743C2318yes—
147C8×C3⋊D3C2318yes—
148C3×#208C2312yes—
149C3×#208C2312yes—
150C2×C3×C3⋊C8C2311yescharacteristic
151C2×C3×C3⋊C8C2311yescharacteristic
152C2×C3×C3⋊C8C2311yescharacteristic
153C2×C3×C3⋊C8C2311yescharacteristic
154C2×C3×C3⋊C8C2311yescharacteristic
155C2×C3×C3⋊C8C2311yescharacteristic
156C2×C3×C3⋊C8C2312yes—
157C3×ΓL(1,𝔽25)C2314yes—
158C3×ΓL(1,𝔽25)C2314yes—
159C3×ΓL(1,𝔽25)C2318yes—
160C3×D3×C8C2314yes—
161C3×D3×C8C2314yes—
162C3×D3×C8C2318yes—
163#3712C2314yes—
164#3712C2314yes—
165#3711C2314yes—
166#3711C2318yes—
167#3711C2314yes—
168#3710C2314yes—
169#3710C2314yes—
170D3×C3⋊C8C2314yes—
171D3×C3⋊C8C2318yes—
172D3×C3⋊C8C2314yes—
173#3573—91noSylow
174C2×C3×#41—31no—
175C2×C3×#41—31no—
176#1010—32no—
177#1010—32no—
178#1010—32no—
179#1010—32no—
180#1009—32no—
181#1009—32no—
182#1009—32no—
183#1009—32no—
184D3×#41—34no—
185D3×#41—34no—
186D3×#41—34no—
187D3×#41—34no—
188#1007—32no—
189#1007—32no—
190#1004—34no—
191#1004—34no—
192#1004—32no—
193#1004—32no—
194C2×#235—31no—
195C2×#235—31no—
196C2×#235—34no—
197C2×#235—34no—
198C2×#235—61no—
199C2×#235C2×D311yescharacteristic
200C2×#235C2×D311yescharacteristic
201C3×#131—32no—
202C3×#131—32no—
203C3×#131—32no—
204C3×#131—32no—
205C3×#131—34no—
206C3×#131—34no—
207C2×C3×M16—21no—
208C2×C3×M16—31no—
209C2×C3×M16—34no—
210C2×C3×M16—32no—
211C2×C3×M16C2×D311yescharacteristic, complemented
212C2×C3×M16C2×D311yescharacteristic, complemented
213C22×C3×C8—31no—
214C22×C3×C8—32no—
215#948—34no—
216#948—32no—
217#948—32no—
218#948—34no—
219#948—32no—
220#948—32no—
221C2×#208—31no—
222C2×#208—31no—
223C2×#208—34no—
224C2×#208—32no—
225C2×#208—61no—
226C2×#208C2×D311yescharacteristic, complemented
227C22×C3⋊C8—32no—
228C22×C3⋊C8C2×D311yescharacteristic, complemented
229#907—34no—
230#907—34no—
231#907—34no—
232#907—32no—
233#907—32no—
234#907—32no—
235#907—32no—
236#907—38no—
237#907—38no—
238#907—38no—
239#907—38no—
240#907—64no—
241#907C2×D312yescomplemented
242#907C2×D312yescomplemented
243#907C2×D312yescomplemented
244#907C2×D312yescomplemented
245#907C2×D314yescomplemented
246D3×M16—34no—
247D3×M16—34no—
248D3×M16—34no—
249D3×M16—38no—
250D3×M16—38no—
251D3×M16—38no—
252D3×M16—38no—
253D3×M16—64no—
254D3×M16C2×D314yescomplemented
255#901—32no—
256#901—32no—
257#901—32no—
258#901—32no—
259#901—34no—
260#901—34no—
261#901—34no—
262#901—32no—
263#901—32no—
264#901—32no—
265#901—32no—
266#901—38no—
267#901—38no—
268#901—38no—
269#901—38no—
270#901—64no—
271#901C2×D314yescomplemented
272C2×ΓL(1,𝔽25)—32no—
273C2×ΓL(1,𝔽25)—32no—
274C2×ΓL(1,𝔽25)—32no—
275C2×ΓL(1,𝔽25)—38no—
276C2×ΓL(1,𝔽25)—38no—
277C2×ΓL(1,𝔽25)C2×D312yescomplemented
278C2×D3×C8—32no—
279C2×D3×C8—32no—
280C2×D3×C8—32no—
281C2×D3×C8—38no—
282C2×D3×C8—38no—
283C2×D3×C8C2×D312yescomplemented
284C23×C32C22×C411yescharacteristic
285C22×C3⋊D3C22×C412yes—
286C22×C3×D3C22×C412yes—
287C22×C3×D3C22×C412yes—
288C2×D32C22×C418yes—
289C2×C32×C4C22×C411yescharacteristic
290C2×C32×C4C22×C411yescharacteristic
291C2×C32×C4C22×C411yescharacteristic
292C2×C32×C4C2411yescharacteristic
293C2×C32×C4C2411yescharacteristic
294C2×C32×C4C2411yescharacteristic
295#638C22×C414yes—
296#638C22×C414yes—
297C2×C3⋊Dic3C22×C412yes—
298C4⋊(C3⋊D3)C22×C412yes—
299C4⋊(C3⋊D3)C22×C412yes—
300C4×C3⋊D3C22×C414yes—
301C4×C3⋊D3C2414yes—
302#634C22×C412yes—
303#634C22×C412yes—
304C3×#67C22×C414yes—
305C3×#67C22×C414yes—
306C3×#67C22×C414yes—
307C3×#67C22×C414yes—
308C2×C3×Dic3C22×C412yes—
309C2×C3×Dic3C22×C412yes—
310C3×D12C22×C412yes—
311C3×D12C22×C412yes—
312C3×D12C22×C412yes—
313C3×D12C22×C412yes—
314C3×C4×D3C22×C414yes—
315C3×C4×D3C22×C414yes—
316C3×C4×D3C2414yes—
317C3×C4×D3C2414yes—
318C3×Dic6C22×C412yes—
319C3×Dic6C22×C412yes—
320C3×Dic6C22×C412yes—
321C3×Dic6C22×C412yes—
322#627C22×C418yes—
323#626C22×C418yes—
324#626C22×C418yes—
325#625C22×C418yes—
326#624C22×C418yes—
327D3×Dic3C22×C418yes—
328D3×Dic3C22×C418yes—
329C32×C8C2414yes—
330C3⋊(C3⋊C8)C2414yes—
331C3×C3⋊C8C2411yescharacteristic
332C3×C3⋊C8C2411yescharacteristic
333C3×C3⋊C8C2414yes—
334C3×C3⋊C8C2411yescharacteristic
335C3×C3⋊C8C2411yescharacteristic
336#585—91no—
337#568—31no—
338#568—94no—
339#568—94no—
340#568—91no—
341#568—94no—
342#568—91no—
343C2×#131—31no—
344C2×#131—91no—
345C2×#131—94no—
346C2×#131—91no—
347C2×#131—94no—
348C2×#131—94no—
349C3×#41—32no—
350C3×#41—32no—
351C3×#41—32no—
352C3×#41—32no—
353C3×#41—32no—
354C3×#41—32no—
355C3×#41—32no—
356C3×#41—32no—
357C2×C3×Q8—31no—
358C2×C3×Q8—31no—
359C2×C3×D4—32no—
360C2×C3×D4—32no—
361C2×C3×D4—31no—
362C2×C3×D4—31no—
363C22×C3×C4—21no—
364C22×C3×C4—32no—
365C22×C3×C4—32no—
366C22×C3×C4C22×D311yescharacteristic
367C22×C3×C4C22×D311yescharacteristic
368C2×#67—32no—
369C2×#67—32no—
370C2×#67—38no—
371C2×#67—38no—
372C2×#67—62no—
373C2×#67C4×D312yes—
374C2×#67C4×D312yes—
375#239—34no—
376#239—34no—
377#239—34no—
378#239—34no—
379D3×Q8—34no—
380D3×Q8—34no—
381D3×Q8—34no—
382D3×Q8—34no—
383#237—38no—
384#237—38no—
385#237—38no—
386#237—38no—
387#237—34no—
388#237—34no—
389#237—34no—
390#237—34no—
391D3×D4—38no—
392D3×D4—38no—
393D3×D4—38no—
394D3×D4—38no—
395D3×D4—34no—
396D3×D4—34no—
397D3×D4—34no—
398D3×D4—34no—
399#235—32no—
400#235—32no—
401#235—32no—
402#235—32no—
403#235—32no—
404#235—32no—
405#235—32no—
406#235—32no—
407#235—38no—
408#235—38no—
409#235—34no—
410#235—34no—
411#235—38no—
412#235—38no—
413#235—34no—
414#235—34no—
415#235—62no—
416#235—62no—
417#235—62no—
418#235—62no—
419#235C4×D312yes—
420#235C4×D312yes—
421#235C4×D312yes—
422#235C4×D312yes—
423#235C22×D312yes—
424#235C22×D312yes—
425#235C22×D312yes—
426#235C22×D312yes—
427C2×D12—31no—
428C2×D12—31no—
429C2×D12—34no—
430C2×D12—34no—
431C2×D12—61no—
432C2×D12C4×D311yescharacteristic
433C2×D12C4×D311yescharacteristic
434C2×C4×D3—32no—
435C2×C4×D3—32no—
436C2×C4×D3—38no—
437C2×C4×D3—38no—
438C2×C4×D3—62no—
439C2×C4×D3C22×D312yes—
440C2×C4×D3C22×D312yes—
441C2×Dic6—31no—
442C2×Dic6—31no—
443C2×Dic6—34no—
444C2×Dic6—34no—
445C2×Dic6—61no—
446C2×Dic6C4×D311yescharacteristic
447C2×Dic6C4×D311yescharacteristic
448C3×M16—22no—
449C3×M16—22no—
450C3×M16—32no—
451C3×M16—32no—
452C3×M16—34no—
453C3×M16—38no—
454C3×M16—34no—
455C3×M16C22×D312yes—
456C3×M16C22×D312yes—
457C3×M16C22×D312yes—
458C3×M16C22×D312yes—
459C2×C3×C8—22no—
460C2×C3×C8—31no—
461C2×C3×C8—31no—
462C2×C3×C8—32no—
463C2×C3×C8—31no—
464C2×C3×C8—31no—
465C2×C3×C8—31no—
466C2×C3×C8—31no—
467C2×C3×C8—34no—
468C2×C3×C8—38no—
469C2×C3×C8—34no—
470C2×C3×C8C22×D312yes—
471C2×C3×C8C22×D312yes—
472#208—32no—
473#208—32no—
474#208—32no—
475#208—32no—
476#208—34no—
477#208—38no—
478#208—34no—
479#208—62no—
480#208—62no—
481#208C22×D312yes—
482#208C22×D312yes—
483C2×C3⋊C8—32no—
484C2×C3⋊C8—32no—
485C2×C3⋊C8—34no—
486C2×C3⋊C8—38no—
487C2×C3⋊C8—34no—
488C2×C3⋊C8—62no—
489C2×C3⋊C8C22×D311yescharacteristic
490C2×C3⋊C8C22×D312yes—
491C2×C3⋊C8C22×D311yescharacteristic
492C2×C3⋊C8C22×D311yescharacteristic
493C2×C3⋊C8C22×D311yescharacteristic
494C2×C3⋊C8C22×D311yescharacteristic
495C2×C3⋊C8C22×D311yescharacteristic
496ΓL(1,𝔽25)—34no—
497ΓL(1,𝔽25)—38no—
498ΓL(1,𝔽25)—34no—
499ΓL(1,𝔽25)—38no—
500ΓL(1,𝔽25)—38no—
501ΓL(1,𝔽25)—34no—
502ΓL(1,𝔽25)—34no—
503ΓL(1,𝔽25)—34no—
504ΓL(1,𝔽25)—34no—
505ΓL(1,𝔽25)—68no—
506ΓL(1,𝔽25)C22×D314yes—
507ΓL(1,𝔽25)C22×D318yes—
508ΓL(1,𝔽25)C22×D314yes—
509D3×C8—34no—
510D3×C8—38no—
511D3×C8—34no—
512D3×C8—38no—
513D3×C8—38no—
514D3×C8—34no—
515D3×C8—34no—
516D3×C8—34no—
517D3×C8—34no—
518D3×C8—68no—
519D3×C8C22×D314yes—
520D3×C8C22×D318yes—
521D3×C8C22×D314yes—
522C22×C32—41no—
523C22×C32C23×C411yescharacteristic
524C22×C32C23×C411yescharacteristic
525C22×C32C23×C411yescharacteristic
526C2×C3⋊D3—42no—
527C2×C3⋊D3C23×C414yes—
528C2×C3×D3—42no—
529C2×C3×D3—42no—
530C2×C3×D3C23×C414yes—
531C2×C3×D3C23×C414yes—
532D32—48no—
533C32×C4C23×C411yescharacteristic
534C32×C4C23×C411yescharacteristic
535C32×C4C23×C411yescharacteristic
536C32×C4C2511yescharacteristic
537C3⋊Dic3C23×C414yes—
538C3×Dic3C23×C414yes—
539C3×Dic3C23×C414yes—
5402−1+4—92no—
5412−1+4—92no—
5422−1+4—92no—
543H(5,𝔽2)—94no—
544H(5,𝔽2)—92no—
545H(5,𝔽2)—92no—
546H(5,𝔽2)—92no—
547C2×#41—31no—
548C2×#41—31no—
549C2×#41—94no—
550C2×#41—94no—
551C2×#41—94no—
552C2×#41—91no—
553#131—32no—
554#131—32no—
555#131—32no—
556#131—32no—
557#131—34no—
558#131—34no—
559#131—98no—
560#131—92no—
561#131—92no—
562#131—98no—
563#131—92no—
564#131—92no—
565#131—98no—
566#131—92no—
567#131—92no—
568#131—92no—
569#131—92no—
570#131—94no—
571#131—98no—
572#131—94no—
573#131—94no—
574#131—94no—
575C2×M16—31no—
576C2×M16—34no—
577C2×M16—32no—
578C2×M16—92no—
579C2×M16—98no—
580C2×M16—98no—
581C2×M16—92no—
582C2×M16—98no—
583C2×M16—94no—
584C2×M16—91no—
585C2×M16—94no—
586C2×M16D3211yescharacteristic, complemented
587C22×C8—31no—
588C22×C8—32no—
589C22×C8—92no—
590C22×C8—98no—
591C22×C8—92no—
592C23×C3—21no—
593C23×C3—32no—
594C23×C3—32no—
595C23×C3C2×C4×D311yescharacteristic
596C23×C3C2×C4×D311yescharacteristic
597C22×D3—32no—
598C22×D3—32no—
599C22×D3—38no—
600C22×D3—38no—
601C22×D3—62no—
602C22×D3C2×C4×D312yes—
603C22×D3C2×C4×D312yes—
604C3×Q8—32no—
605C3×Q8—32no—
606C3×Q8—32no—
607C3×Q8—32no—
608C3×D4—34no—
609C3×D4—34no—
610C3×D4—34no—
611C3×D4—34no—
612C3×D4—32no—
613C3×D4—32no—
614C3×D4—32no—
615C3×D4—32no—
616C2×C3×C4—21no—
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—32no—
623C2×C3×C4—32no—
624C2×C3×C4—34no—
625C2×C3×C4—34no—
626C2×C3×C4—34no—
627C2×C3×C4—34no—
628C2×C3×C4C2×C4×D311yescharacteristic
629C2×C3×C4C2×C4×D311yescharacteristic
630C2×C3×C4C2×C4×D311yescharacteristic
631C2×C3×C4C2×C4×D311yescharacteristic
632C2×C3×C4C2×C4×D311yescharacteristic
633C2×C3×C4C2×C4×D311yescharacteristic
634C2×C3×C4C23×D311yescharacteristic
635C2×C3×C4C23×D311yescharacteristic
636C2×C3×C4C23×D311yescharacteristic
637C2×C3×C4C23×D311yescharacteristic
638C2×C3×C4C23×D311yescharacteristic
639C2×C3×C4C23×D311yescharacteristic
640#67—34no—
641#67—34no—
642#67—34no—
643#67—34no—
644#67—38no—
645#67—38no—
646#67—38no—
647#67—38no—
648#67—64no—
649#67—64no—
650#67C2×C4×D314yes—
651#67C2×C4×D314yes—
652#67C2×C4×D314yes—
653#67C2×C4×D314yes—
654C2×Dic3—32no—
655C2×Dic3—32no—
656C2×Dic3—38no—
657C2×Dic3—38no—
658C2×Dic3—62no—
659C2×Dic3C2×C4×D312yes—
660C2×Dic3C2×C4×D312yes—
661D12—38no—
662D12—38no—
663D12—32no—
664D12—32no—
665D12—32no—
666D12—32no—
667D12—62no—
668D12—62no—
669D12C2×C4×D312yes—
670D12C2×C4×D312yes—
671D12C2×C4×D312yes—
672D12C2×C4×D312yes—
673C4×D3—38no—
674C4×D3—38no—
675C4×D3—34no—
676C4×D3—34no—
677C4×D3—34no—
678C4×D3—34no—
679C4×D3—38no—
680C4×D3—38no—
681C4×D3—64no—
682C4×D3—64no—
683C4×D3C2×C4×D314yes—
684C4×D3C2×C4×D314yes—
685C4×D3C23×D314yes—
686C4×D3C23×D314yes—
687Dic6—32no—
688Dic6—32no—
689Dic6—32no—
690Dic6—32no—
691Dic6—38no—
692Dic6—38no—
693Dic6—62no—
694Dic6—62no—
695Dic6C2×C4×D312yes—
696Dic6C2×C4×D312yes—
697Dic6C2×C4×D312yes—
698Dic6C2×C4×D312yes—
699C3×C8—24no—
700C3×C8—31no—
701C3×C8—31no—
702C3×C8—34no—
703C3×C8—31no—
704C3×C8—31no—
705C3×C8C23×D314yes—
706C3×C8C23×D314yes—
707C3⋊C8—34no—
708C3⋊C8—34no—
709C3⋊C8—64no—
710C3⋊C8C23×D311yescharacteristic
711C3⋊C8C23×D311yescharacteristic
712C3⋊C8C23×D314yes—
713C3⋊C8C23×D311yescharacteristic
714C3⋊C8C23×D311yescharacteristic
715C2×C32—21no—
716C2×C32—21no—
717C2×C32—21no—
718C2×C32C24×C411yescharacteristic
719C3⋊D3—24no—
720C3×D3—24no—
721C3×D3—24no—
722#41—32no—
723#41—32no—
724#41—32no—
725#41—32no—
726#41—32no—
727#41—32no—
728#41—32no—
729#41—32no—
730#41—98no—
731#41—98no—
732#41—98no—
733#41—94no—
734#41—94no—
735#41—94no—
736#41—94no—
737#41—98no—
738#41—94no—
739#41—94no—
740#41—92no—
741#41—92no—
742#41—92no—
743#41—92no—
744C2×Q8—31no—
745C2×Q8—31no—
746C2×Q8—94no—
747C2×Q8—94no—
748C2×Q8—94no—
749C2×Q8—91no—
750C2×D4—32no—
751C2×D4—32no—
752C2×D4—31no—
753C2×D4—31no—
754C2×D4—94no—
755C2×D4—94no—
756C2×D4—98no—
757C2×D4—94no—
758C2×D4—98no—
759C2×D4—98no—
760C2×D4—92no—
761C2×D4—91no—
762C22×C4—32no—
763C22×C4—32no—
764C22×C4—98no—
765C22×C4—92no—
766C22×C4C2×D3211yescharacteristic
767M16—32no—
768M16—32no—
769M16—38no—
770M16—34no—
771M16—34no—
772M16—94no—
773M16—94no—
774M16—94no—
775M16—98no—
776M16—94no—
777M16—92no—
778M16—92no—
779M16—98no—
780M16C2×D3212yes—
781M16C2×D3212yes—
782C2×C8—31no—
783C2×C8—31no—
784C2×C8—31no—
785C2×C8—31no—
786C2×C8—31no—
787C2×C8—31no—
788C2×C8—32no—
789C2×C8—34no—
790C2×C8—34no—
791C2×C8—38no—
792C2×C8—94no—
793C2×C8—94no—
794C2×C8—94no—
795C2×C8—98no—
796C2×C8—94no—
797C2×C8—92no—
798C2×C8—98no—
799C2×C8C2×D3212yes—
800C22×C3—21no—
801C22×C3—21no—
802C22×C3—21no—
803C22×C3—34no—
804C22×C3—34no—
805C22×C3—41no—
806C22×C3—41no—
807C22×C3—81no—
808C22×C3—122no—
809C22×C3—122no—
810C22×C3C22×C4×D311yescharacteristic
811C22×C3C22×C4×D311yescharacteristic
812C22×C3C22×C4×D311yescharacteristic
813C22×C3C22×C4×D311yescharacteristic
814C22×C3C22×C4×D311yescharacteristic
815C22×C3C22×C4×D311yescharacteristic
816C2×D3—34no—
817C2×D3—34no—
818C2×D3—42no—
819C2×D3—42no—
820C2×D3—64no—
821C2×D3—128no—
822C2×D3—128no—
823C2×D3—122no—
824C2×D3—122no—
825C2×D3—242no—
826C2×D3C22×C4×D314yes—
827C2×D3C22×C4×D314yes—
828C3×C4—21no—
829C3×C4—21no—
830C3×C4—21no—
831C3×C4—21no—
832C3×C4—34no—
833C3×C4—34no—
834C3×C4C22×C4×D311yescharacteristic
835C3×C4C22×C4×D311yescharacteristic
836C3×C4C22×C4×D311yescharacteristic
837C3×C4C22×C4×D311yescharacteristic
838C3×C4C22×C4×D311yescharacteristic
839C3×C4C22×C4×D311yescharacteristic
840C3×C4C24×D311yescharacteristic
841C3×C4C24×D311yescharacteristic
842Dic3—34no—
843Dic3—34no—
844Dic3—64no—
845Dic3C22×C4×D314yes—
846Dic3C22×C4×D314yes—
847C32#357311yescharacteristic, complemented, Sylow
848C23—32no—
849C23—32no—
850C23—98no—
851C23—92no—
852C23C4×D3211yescharacteristic
853Q8—32no—
854Q8—32no—
855Q8—32no—
856Q8—32no—
857Q8—98no—
858Q8—92no—
859Q8—92no—
860D4—34no—
861D4—34no—
862D4—34no—
863D4—34no—
864D4—32no—
865D4—32no—
866D4—32no—
867D4—32no—
868D4—98no—
869D4—98no—
870D4—98no—
871D4—94no—
872D4—94no—
873D4—92no—
874D4—92no—
875C2×C4—32no—
876C2×C4—32no—
877C2×C4—34no—
878C2×C4—34no—
879C2×C4—34no—
880C2×C4—34no—
881C2×C4—98no—
882C2×C4—98no—
883C2×C4—98no—
884C2×C4—92no—
885C2×C4—94no—
886C2×C4—94no—
887C2×C4C4×D3211yescharacteristic
888C2×C4C4×D3211yescharacteristic
889C2×C4C4×D3211yescharacteristic
890C2×C4C22×D3211yescharacteristic
891C2×C4C22×D3211yescharacteristic
892C2×C4C22×D3211yescharacteristic
893C8—31no—
894C8—31no—
895C8—31no—
896C8—31no—
897C8—34no—
898C8—94no—
899C8C22×D3214yes—
900C2×C3—21no—
901C2×C3—21no—
902C2×C3—21no—
903C2×C3—21no—
904C2×C3—21no—
905C2×C3—21no—
906C2×C3—21no—
907C2×C3—41no—
908C2×C3—41no—
909C2×C3—41no—
910C2×C3—64no—
911C2×C3—64no—
912C2×C3C23×C4×D311yescharacteristic
913C2×C3C23×C4×D311yescharacteristic
914D3—24no—
915D3—24no—
916D3—64no—
917D3—64no—
918D3—124no—
919C22—34no—
920C22—34no—
921C22—41no—
922C22—94no—
923C22—122no—
924C22—122no—
925C22—362no—
926C22—368no—
927C22C2×C4×D3211yescharacteristic
928C22C2×C4×D3211yescharacteristic
929C22C2×C4×D3211yescharacteristic
930C4—34no—
931C4—34no—
932C4—94no—
933C4C2×C4×D3211yescharacteristic
934C4C2×C4×D3211yescharacteristic
935C4C2×C4×D3211yescharacteristic
936C4C23×D3211yescharacteristic
937C3—21no—
938C3#8716011yescharacteristic, complemented
939C3#8716611yescharacteristic, complemented
940C2—21no—
941C2—21no—
942C2—21no—
943C2—64no—
944C2—64no—
945C2—184no—
946C2C22×C4×D3211yescharacteristic
subgroupG/H
center, FrattiniC4C23×D32
commutator, socleC2×C32C24×C4
FittingC2×C32×M16C22
prime radical#10596669C2
cosocleC32×C4C25
hypercenterC2×M16D32
hypocenterC32#3573
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #10596216C2semidirect
3. C3×#5745C2semidirect
4. C2×C3×#907C2semidirect
5. C2×#63817C2semidirect
6. #10594776C2semidirect
7. C2×#63814C2semidirect
8. #10594708C2semidirect
9. #10594707C2semidirect
10. #10594706C2semidirect
11. D3×#907C2semidirect
12. #10594668C2semidirect
13. D3×#901C2semidirect
29. C2×C32×M16C22semidirect
30. C2×#3748C22semidirect
31. #64116C22semidirect
32. M16×C3⋊D3C22semidirect
33. #64110C22semidirect
34. C2×C3×#208C22semidirect
35. C22×C3×C3⋊C8C22semidirect
36. C3×#907C22semidirect
37. C3×#907C22semidirect
38. C3×#907C22semidirect
39. C3×#907C22semidirect
40. C3×#907C22semidirect
41. C3×D3×M16C22semidirect
42. C3×#901C22semidirect
43. C2×C3×ΓL(1,𝔽25)C22semidirect
44. C2×C3×D3×C8C22semidirect
45. C2×#3712C22semidirect
46. C2×#3711C22semidirect
47. #63817C22semidirect
48. #63817C22semidirect
49. #63817C22semidirect
50. #63817C22semidirect
51. C2×#3710C22semidirect
52. #63815C22semidirect
53. #63814C22semidirect
54. #63814C22semidirect
55. #63814C22semidirect
56. #63814C22semidirect
57. #63814C22semidirect
58. D3×#208C22semidirect
59. C2×D3×C3⋊C8C22semidirect
60. #63805C22semidirect
61. #63804C22semidirect
62. #63804C22semidirect
63. #63803C22semidirect
64. #63791C22semidirect
65. D3×ΓL(1,𝔽25)C22semidirect
66. D3×ΓL(1,𝔽25)C22semidirect
67. D32×C8C22semidirect
88. #5745D3semidirect
91. C2×#907D3semidirect
211. C2×C3×M16C2×D3semidirect
212. C2×C3×M16C2×D3semidirect
226. C2×#208C2×D3semidirect
228. C22×C3⋊C8C2×D3semidirect
241. #907C2×D3semidirect
242. #907C2×D3semidirect
243. #907C2×D3semidirect
244. #907C2×D3semidirect
245. #907C2×D3semidirect
254. D3×M16C2×D3semidirect
271. #901C2×D3semidirect
277. C2×ΓL(1,𝔽25)C2×D3semidirect
283. C2×D3×C8C2×D3semidirect
586. C2×M16D32semidirect
847. C32#3573semidirect
938. C3#87160semidirect
939. C3#87166semidirect

Maximal subgroups

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

subgroupindex
#105966692
#105962162
C3×#57452
C2×C3×#9072
C2×#638172
#105947762
C2×#638142
#105947082
#105947072
#105947062
D3×#9072
#105946682
D3×#9012
#871663
#871603