Finite Group Databasebeta

← #11864989

Subgroups — #11864989

Order 1152.

1579 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5964C211yesmaximal, characteristic, complemented
2#10596293C211yesmaximal, characteristic, complemented
3#10595029C211yesmaximal, characteristic, complemented
4#10594795C211yesmaximal, characteristic, complemented
5C2×C3×#837C211yesmaximal, characteristic, complemented
6#10591689C212yesmaximal, complemented
7#10591688C212yesmaximal, complemented
8#10591685C212yesmaximal, complemented
9#10591666C212yesmaximal, complemented
10C2×#63569C211yesmaximal, characteristic, complemented
11#10591076C211yesmaximal, characteristic, complemented
12#84121—31nomaximal
13#78986—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C2×#3828C2211yescharacteristic, complemented
16C3×#1010—21no—
17C3×#1010C2212yes—
18C3×#1009—21no—
19C3×#1009C2212yes—
20C3×D3×#41—22no—
21C3×D3×#41—22no—
22C3×#1007—21no—
23C3×#1004—21no—
24C3×#1004—22no—
25C2×C3×#235—22no—
26C2×C3×#235C2211yescharacteristic
27C2×C3×#235C2211yescharacteristic
28#64160C2212yescomplemented
29#64159—22no—
30#64158C2212yescomplemented
31#64151—21no—
32#64141—21no—
33C2×#3748C2211yescharacteristic, complemented
34C2×C3×C4×Dic3C2211yescharacteristic, complemented
35C2×C3×#208C2211yescharacteristic, complemented
36#63978—22no—
37#63911C2211yescharacteristic, complemented
38C4×#626—22no—
39#63866C2211yescharacteristic, complemented
40#63864C2211yescharacteristic, complemented
41#63860C2211yescharacteristic, complemented
42#63833—21no—
43#63831C2212yescomplemented
44#63830—21no—
45#63829—22no—
46#63825C2212yescomplemented
47C3×#837C2212yescomplemented
48C3×#837C2212yescomplemented
49#63569C2212yescomplemented
50#63569C2212yescomplemented
51#63560C2212yescomplemented
52#63558C2212yescomplemented
53C3×#585—31no—
54#5964D311yescharacteristic, complemented
55#5832—31no—
56#5822—31no—
57#5822—31no—
58#5822—31no—
59#5822—61no—
60#5748—31no—
61#5477—31no—
62C2×C3×#104—31no—
63#5246—32no—
64#5245—32no—
65#5242—32no—
66#5241—32no—
67#5237—31no—
68C2×#837—31no—
69C2×#837D311yescharacteristic, complemented
70#5132—31no—
71C2×#805—31no—
72#4827—32no—
73#4826—32no—
74#4825—32no—
75#4822—32no—
76C32×#41—21no—
77C32×#41—21no—
78C32×#41D412yescomplemented
79C32×#41C2312yes—
80C2×C32×Q8D411yescharacteristic, complemented
81C2×C32×D4—21no—
82C2×C32×D4D411yescharacteristic, complemented
83C22×C32×C4—21no—
84C22×C32×C4C2311yescharacteristic
85C2×#638—21no—
86#3828—21no—
87#3828—21no—
88#3828—21no—
89#3828—21no—
90C2×C4⋊(C3⋊D3)C2311yescharacteristic
91C2×C4×C3⋊D3—21no—
92C2×#634C2311yescharacteristic
93C2×C3×#67—24no—
94C2×C3×#67—21no—
95C2×C3×#67D412yes—
96C22×C3×Dic3—21no—
97C3×#239—22no—
98C3×#239—22no—
99C3×D3×Q8—22no—
100C3×D3×Q8—22no—
101C3×#237—24no—
102C3×#237—22no—
103C3×#237—22no—
104C3×#237—24no—
105C3×D3×D4—24no—
106C3×D3×D4—22no—
107C3×D3×D4—24no—
108C3×D3×D4—22no—
109C3×#235—24no—
110C3×#235—24no—
111C3×#235—21no—
112C3×#235—21no—
113C3×#235—21no—
114C3×#235—21no—
115C3×#235—21no—
116C3×#235—21no—
117C3×#235—22no—
118C3×#235—22no—
119C3×#235D412yescomplemented
120C3×#235C2312yes—
121C2×C3×D12—22no—
122C2×C3×D12D411yescharacteristic, complemented
123C2×C3×D12C2311yescharacteristic
124C2×C3×C4×D3—24no—
125C2×C3×C4×D3—21no—
126C2×C3×C4×D3D412yes—
127C2×C3×Dic6—22no—
128C2×C3×Dic6D411yescharacteristic, complemented
129C2×C3×Dic6C2311yescharacteristic
130C2×#626—22no—
131#3756—22no—
132#3755—22no—
133#3754—22no—
134#3753—22no—
135#3748—21no—
136#3748C2312yes—
137C2×C3⋊(C3⋊C8)—21no—
138C3×C4×Dic3—21no—
139C3×C4×Dic3C2311yescharacteristic
140C3×C4×Dic3C2311yescharacteristic
141C3×#208—21no—
142C3×#208C2312yes—
143C2×C3×C3⋊C8—21no—
144Dic3⋊Dic3—22no—
145#3722—22no—
146(C2×D3)⋊Dic3—22no—
147#3719—22no—
148#3717—22no—
149#3716—22no—
150#3714—22no—
151#3018—91noSylow
152C3×2−1+4—32no—
153C3×2−1+4—61no—
154C3×2−1+4—61no—
155C3×H(5,𝔽2)—32no—
156C3×H(5,𝔽2)—62no—
157C3×H(5,𝔽2)—61no—
158C3×H(5,𝔽2)—61no—
159C2×C3×#41—21no—
160C2×C3×#41—31no—
161C2×C3×#41—31no—
162C2×C3×#41—62no—
163C2×C3×#41—62no—
164C2×C3×#41—62no—
165C2×C3×#41C2×D311yescharacteristic
166C2×C3×#41C2×D311yescharacteristic
167#1010—21no—
168#1010C2×D312yes—
169#1009—21no—
170#1009C2×D312yes—
171D3×#41—22no—
172D3×#41—22no—
173#1007—21no—
174#1004—21no—
175#1004—22no—
176C2×#235—22no—
177C2×#235—31no—
178C2×#235—31no—
179C2×#235—61no—
180C2×#235C2×D311yescharacteristic
181C2×#235C2×D311yescharacteristic
182C2×C3×M16—31no—
183C2×C3×C42—31no—
184#951—32no—
185#951—32no—
186#951—32no—
187#951—62no—
188#950—62no—
189#950—64no—
190#950—62no—
191#950—62no—
192#949—32no—
193#949—32no—
194#949—32no—
195#949—62no—
196#947—31no—
197#944—31no—
198#942—61no—
199#942—62no—
200#942—61no—
201#942—61no—
202#940—31no—
203#939—62no—
204#936—31no—
205#932—61no—
206#932—62no—
207#932—61no—
208#932—61no—
209#930—62no—
210C4×#67—62no—
211C2×C4×Dic3C2×D311yescharacteristic, complemented
212C2×#208—31no—
213C2×#208—31no—
214C2×#208—61no—
215C2×#208C2×D311yescharacteristic, complemented
216#909—32no—
217#909—61no—
218#908—32no—
219#908—61no—
220#904—62no—
221#875—31no—
222#875—31no—
223#874—31no—
224C4×D12—62no—
225#869—31no—
226C3×#104—32no—
227C3×#104—32no—
228#837—32no—
229#837—32no—
230#837C2×D312yescomplemented
231#837C2×D312yescomplemented
232#836—32no—
233#833—32no—
234#824—32no—
235#823—32no—
236#805—32no—
237#805—32no—
238C23×C32—21no—
239C23×C32C2×D411yescharacteristic
240C22×C3⋊D3—21no—
241C22×C3×D3—24no—
242C22×C3×D3—21no—
243C22×C3×D3C2×D412yes—
244C32×Q8—21no—
245C32×Q8C2×D412yes—
246C32×D4—22no—
247C32×D4—22no—
248C32×D4—21no—
249C32×D4C2×D412yes—
250C2×C32×C4—21no—
251C2×C32×C4—22no—
252C2×C32×C4—22no—
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2×D411yescharacteristic
257C2×C32×C4C2×D411yescharacteristic
258C2×C32×C4C2411yescharacteristic
259#638—41no—
260#638—41no—
261C2×C3⋊Dic3—21no—
262C4⋊(C3⋊D3)—21no—
263C4⋊(C3⋊D3)—21no—
264C4×C3⋊D3—41no—
265C4×C3⋊D3—41no—
266#634—21no—
267#634—21no—
268C3×#67—24no—
269C3×#67—24no—
270C3×#67—22no—
271C3×#67—22no—
272C3×#67—22no—
273C3×#67—22no—
274C2×C3×Dic3—24no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—42no—
279C2×C3×Dic3C2×D412yes—
280C3×D12—24no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—21no—
284C3×D12C2×D412yes—
285C3×C4×D3—24no—
286C3×C4×D3—24no—
287C3×C4×D3—22no—
288C3×C4×D3—22no—
289C3×C4×D3—22no—
290C3×C4×D3—22no—
291C3×Dic6—24no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295C3×Dic6C2×D412yes—
296#626—44no—
297C3⋊(C3⋊C8)—22no—
298C3×C3⋊C8—22no—
299#585—31no—
300#575—91no—
301#575—91no—
302#532—91no—
303#456—92no—
304#455—92no—
305#454—92no—
306#453—92no—
307C2×#104—31no—
308C2×#104—91no—
309#413—91no—
310C3×#41—21no—
311C3×#41—21no—
312C3×#41—21no—
313C3×#41—21no—
314C3×#41—22no—
315C3×#41—22no—
316C3×#41—32no—
317C3×#41—32no—
318C3×#41—41no—
319C3×#41—41no—
320C3×#41—62no—
321C3×#41—62no—
322C3×#41—64no—
323C3×#41—64no—
324C3×#41—64no—
325C3×#41—64no—
326C3×#41—62no—
327C3×#41—62no—
328C3×#41—62no—
329C3×#41—62no—
330C3×#41—61no—
331C3×#41—61no—
332C3×#41—61no—
333C3×#41—61no—
334C3×#41—61no—
335C3×#41—61no—
336C3×#41D1212yescomplemented
337C3×#41#6712yescomplemented
338C3×#41C22×D312yes—
339C3×#41C22×D312yes—
340C2×C3×Q8—21no—
341C2×C3×Q8—31no—
342C2×C3×Q8—31no—
343C2×C3×Q8—62no—
344C2×C3×Q8—62no—
345C2×C3×Q8—62no—
346C2×C3×Q8D1211yescharacteristic, complemented
347C2×C3×Q8#6711yescharacteristic, complemented
348C2×C3×D4—21no—
349C2×C3×D4—21no—
350C2×C3×D4—21no—
351C2×C3×D4—32no—
352C2×C3×D4—31no—
353C2×C3×D4—31no—
354C2×C3×D4—41no—
355C2×C3×D4—62no—
356C2×C3×D4—64no—
357C2×C3×D4—64no—
358C2×C3×D4—62no—
359C2×C3×D4—64no—
360C2×C3×D4—61no—
361C2×C3×D4—62no—
362C2×C3×D4D1211yescharacteristic, complemented
363C2×C3×D4#6711yescharacteristic, complemented
364C22×C3×C4—21no—
365C22×C3×C4—21no—
366C22×C3×C4—21no—
367C22×C3×C4—32no—
368C22×C3×C4—41no—
369C22×C3×C4—64no—
370C22×C3×C4—61no—
371C22×C3×C4—61no—
372C22×C3×C4C22×D311yescharacteristic
373C22×C3×C4C22×D311yescharacteristic
374C2×#67—24no—
375C2×#67—21no—
376C2×#67—62no—
377C2×#67—61no—
378C2×#67—61no—
379C2×#67—121no—
380C2×#67#6712yes—
381C22×Dic3—21no—
382#239—22no—
383#239—22no—
384D3×Q8—22no—
385D3×Q8—22no—
386#237—24no—
387#237—22no—
388#237—22no—
389#237—24no—
390D3×D4—24no—
391D3×D4—22no—
392D3×D4—24no—
393D3×D4—22no—
394#235—24no—
395#235—24no—
396#235—21no—
397#235—21no—
398#235—21no—
399#235—21no—
400#235—21no—
401#235—21no—
402#235—22no—
403#235—22no—
404#235—62no—
405#235—62no—
406#235—61no—
407#235—61no—
408#235—61no—
409#235—61no—
410#235—61no—
411#235—61no—
412#235—61no—
413#235—61no—
414#235—121no—
415#235—121no—
416#235#6712yescomplemented
417#235C22×D312yes—
418C2×D12—22no—
419C2×D12—31no—
420C2×D12—31no—
421C2×D12—61no—
422C2×D12—62no—
423C2×D12#6711yescharacteristic, complemented
424C2×D12C22×D311yescharacteristic
425C2×C4×D3—24no—
426C2×C4×D3—21no—
427C2×C4×D3—61no—
428C2×C4×D3—61no—
429C2×C4×D3—121no—
430C2×C4×D3#6712yes—
431C2×Dic6—22no—
432C2×Dic6—31no—
433C2×Dic6—31no—
434C2×Dic6—61no—
435C2×Dic6#6711yescharacteristic, complemented
436C2×Dic6C22×D311yescharacteristic
437C3×M16—32no—
438C3×M16—61no—
439C2×C3×C8—61no—
440C3×C42—31no—
441C3×C42—31no—
442C3×C42—61no—
443#217—62no—
444#216—62no—
445#216—64no—
446#216—62no—
447#216—62no—
448#215—62no—
449#215—64no—
450#215—62no—
451#215—62no—
452#214—62no—
453#214—64no—
454#214—62no—
455#214—62no—
456#213—62no—
457#213—64no—
458#213—62no—
459#213—62no—
460(C2×D3)⋊C4—62no—
461(C2×D3)⋊C4—62no—
462(C2×D3)⋊C4—62no—
463C4⋊Dic3—62no—
464Dic3⋊C4—62no—
465C4×Dic3—21no—
466C4×Dic3C22×D311yescharacteristic
467C4×Dic3C22×D311yescharacteristic
468#208—21no—
469#208—32no—
470#208—32no—
471#208—62no—
472#208—62no—
473#208—61no—
474#208—61no—
475#208C22×D312yes—
476C2×C3⋊C8—21no—
477C2×C3⋊C8—62no—
478C2×C3⋊C8—61no—
479C2×C3⋊C8—61no—
480Dic12—62no—
481D24—62no—
482#204—62no—
483#204—62no—
484C22×C32—22no—
485C22×C32—41no—
486C22×C32—81no—
487C22×C32#12011yescharacteristic
488C22×C32#12011yescharacteristic
489C22×C32C22×D411yescharacteristic
490C2×C3⋊D3—41no—
491C2×C3⋊D3—42no—
492C2×C3×D3—22no—
493C2×C3×D3—22no—
494C2×C3×D3—42no—
495C2×C3×D3—81no—
496C2×C3×D3—84no—
497C32×C4—22no—
498C32×C4#12011yescharacteristic
499C32×C4#12011yescharacteristic
500C32×C4C22×D411yescharacteristic
501C32×C4C22×D411yescharacteristic
502C3⋊Dic3—41no—
503C3×Dic3—22no—
504C3×Dic3—22no—
505C3×Dic3—22no—
506C3×Dic3—41no—
5072−1+4—32no—
5082−1+4—61no—
5092−1+4—61no—
510H(5,𝔽2)—32no—
511H(5,𝔽2)—62no—
512H(5,𝔽2)—61no—
513H(5,𝔽2)—61no—
514C2×#41—31no—
515C2×#41—31no—
516C2×#41—62no—
517C2×#41—62no—
518C2×#41—62no—
519C2×#41—91no—
520C2×#41D3211yescharacteristic
521#137—92no—
522#137—92no—
523#137—181no—
524#137—181no—
525AGL(1,ℤ/8)—92no—
526AGL(1,ℤ/8)—92no—
527AGL(1,ℤ/8)—181no—
528AGL(1,ℤ/8)—181no—
529#135—182no—
530#135—182no—
531C2×M16—31no—
532C2×M16—91no—
533C4⋊Q8—91no—
534#127—91no—
535#124—91no—
536#124—91no—
537#121—182no—
538C4×D4—182no—
539C2×C42—31no—
540#104—32no—
541#104—32no—
542#104—92no—
543#104—92no—
544#101—92no—
545#100—92no—
546C23×C3—21no—
547C23×C3—21no—
548C23×C3—21no—
549C23×C3—32no—
550C23×C3—41no—
551C23×C3—64no—
552C23×C3—61no—
553C23×C3D3×D411yescharacteristic
554C23×C3C2×#6711yescharacteristic
555C22×D3—24no—
556C22×D3—21no—
557C22×D3—61no—
558C22×D3—61no—
559C22×D3—121no—
560C22×D3C2×#6712yes—
561C3×Q8—21no—
562C3×Q8—21no—
563C3×Q8—22no—
564C3×Q8—32no—
565C3×Q8—41no—
566C3×Q8—64no—
567C3×Q8—61no—
568C3×Q8—61no—
569C3×Q8—61no—
570C3×Q8C2×D1212yes—
571C3×Q8C2×#6712yes—
572C3×D4—22no—
573C3×D4—22no—
574C3×D4—22no—
575C3×D4—22no—
576C3×D4—21no—
577C3×D4—21no—
578C3×D4—22no—
579C3×D4—32no—
580C3×D4—41no—
581C3×D4—42no—
582C3×D4—42no—
583C3×D4—64no—
584C3×D4—64no—
585C3×D4—64no—
586C3×D4—62no—
587C3×D4—62no—
588C3×D4—62no—
589C3×D4—62no—
590C3×D4—61no—
591C3×D4—61no—
592C3×D4—61no—
593C3×D4C2×D1212yes—
594C3×D4C2×#6712yes—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—22no—
598C2×C3×C4—22no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—32no—
608C2×C3×C4—42no—
609C2×C3×C4—42no—
610C2×C3×C4—41no—
611C2×C3×C4—64no—
612C2×C3×C4—64no—
613C2×C3×C4—64no—
614C2×C3×C4—61no—
615C2×C3×C4—61no—
616C2×C3×C4—62no—
617C2×C3×C4—62no—
618C2×C3×C4—62no—
619C2×C3×C4—62no—
620C2×C3×C4—61no—
621C2×C3×C4—122no—
622C2×C3×C4C2×D1211yescharacteristic
623C2×C3×C4C2×D1211yescharacteristic
624C2×C3×C4D3×D411yescharacteristic
625C2×C3×C4D3×D411yescharacteristic
626C2×C3×C4D3×D411yescharacteristic
627C2×C3×C4C2×#6711yescharacteristic
628C2×C3×C4C2×#6711yescharacteristic
629C2×C3×C4C2×#6711yescharacteristic
630C2×C3×C4C2×#6711yescharacteristic
631C2×C3×C4C2×#6711yescharacteristic
632C2×C3×C4C23×D311yescharacteristic
633C2×C3×C4C23×D311yescharacteristic
634#67—24no—
635#67—24no—
636#67—22no—
637#67—22no—
638#67—22no—
639#67—22no—
640#67—124no—
641#67—122no—
642#67—122no—
643#67—121no—
644#67—121no—
645#67—121no—
646#67—121no—
647C2×Dic3—24no—
648C2×Dic3—21no—
649C2×Dic3—21no—
650C2×Dic3—21no—
651C2×Dic3—42no—
652C2×Dic3—61no—
653C2×Dic3—61no—
654C2×Dic3—121no—
655C2×Dic3C2×#6712yes—
656D12—24no—
657D12—21no—
658D12—21no—
659D12—21no—
660D12—62no—
661D12—61no—
662D12—61no—
663D12—61no—
664D12—61no—
665D12—121no—
666D12—124no—
667D12C2×#6712yes—
668C4×D3—24no—
669C4×D3—24no—
670C4×D3—22no—
671C4×D3—22no—
672C4×D3—22no—
673C4×D3—22no—
674C4×D3—122no—
675C4×D3—122no—
676C4×D3—121no—
677C4×D3—121no—
678C4×D3—121no—
679C4×D3—121no—
680Dic6—24no—
681Dic6—21no—
682Dic6—21no—
683Dic6—21no—
684Dic6—62no—
685Dic6—61no—
686Dic6—61no—
687Dic6—61no—
688Dic6—61no—
689Dic6—121no—
690Dic6C2×#6712yes—
691C3×C8—62no—
692C3⋊C8—22no—
693C3⋊C8—64no—
694C3⋊C8—62no—
695C3⋊C8—62no—
696C2×C32—21no—
697C2×C32—21no—
698C2×C32—21no—
699C2×C32—42no—
700C2×C32C2×#12011yescharacteristic
701C3⋊D3—81no—
702C3×D3—42no—
703C3×D3—42no—
704#41—21no—
705#41—21no—
706#41—32no—
707#41—32no—
708#41—62no—
709#41—62no—
710#41—64no—
711#41—64no—
712#41—64no—
713#41—64no—
714#41—62no—
715#41—62no—
716#41—62no—
717#41—62no—
718#41—61no—
719#41—61no—
720#41—61no—
721#41—61no—
722#41—61no—
723#41—61no—
724#41—181no—
725#41—181no—
726#41—181no—
727#41—181no—
728#41#62612yescomplemented
729#41C2×D3212yes—
730C2×Q8—31no—
731C2×Q8—31no—
732C2×Q8—62no—
733C2×Q8—62no—
734C2×Q8—62no—
735C2×Q8—91no—
736C2×Q8#62611yescharacteristic, complemented
737C2×D4—21no—
738C2×D4—32no—
739C2×D4—31no—
740C2×D4—31no—
741C2×D4—62no—
742C2×D4—64no—
743C2×D4—64no—
744C2×D4—62no—
745C2×D4—64no—
746C2×D4—61no—
747C2×D4—62no—
748C2×D4—91no—
749C2×D4—182no—
750C2×D4—181no—
751C2×D4#62611yescharacteristic, complemented
752C22×C4—21no—
753C22×C4—32no—
754C22×C4—64no—
755C22×C4—61no—
756C22×C4—61no—
757C22×C4—181no—
758C22×C4C2×D3211yescharacteristic
759Q16—182no—
760Q16—182no—
761SD16—182no—
762SD16—182no—
763SD16—182no—
764SD16—182no—
765D8—182no—
766D8—182no—
767M16—32no—
768M16—61no—
769M16—92no—
770M16—181no—
771C2×C8—61no—
772C2×C8—181no—
773C4⋊C4—182no—
774C22⋊C4—182no—
775C22⋊C4—182no—
776C42—31no—
777C42—31no—
778C42—61no—
779C22×C3—22no—
780C22×C3—22no—
781C22×C3—21no—
782C22×C3—21no—
783C22×C3—21no—
784C22×C3—42no—
785C22×C3—41no—
786C22×C3—41no—
787C22×C3—62no—
788C22×C3—62no—
789C22×C3—81no—
790C22×C3—81no—
791C22×C3—81no—
792C22×C3—82no—
793C22×C3—122no—
794C22×C3—241no—
795C22×C3—244no—
796C22×C3#88211yescharacteristic
797C22×C3#88211yescharacteristic
798C22×C3#95311yescharacteristic
799C22×C3#95311yescharacteristic
800C22×C3C2×D3×D411yescharacteristic
801C22×C3C22×#6711yescharacteristic
802C2×D3—22no—
803C2×D3—22no—
804C2×D3—42no—
805C2×D3—81no—
806C2×D3—84no—
807C2×D3—122no—
808C2×D3—122no—
809C2×D3—122no—
810C2×D3—121no—
811C2×D3—121no—
812C2×D3—242no—
813C3×C4—22no—
814C3×C4—22no—
815C3×C4—21no—
816C3×C4—21no—
817C3×C4—21no—
818C3×C4—21no—
819C3×C4—42no—
820C3×C4—62no—
821C3×C4—62no—
822C3×C4—62no—
823C3×C4—121no—
824C3×C4#88211yescharacteristic
825C3×C4#88211yescharacteristic
826C3×C4#95311yescharacteristic
827C3×C4#95311yescharacteristic
828C3×C4C22×D1211yescharacteristic
829C3×C4C2×D3×D411yescharacteristic
830C3×C4C22×#6711yescharacteristic
831C3×C4C22×#6711yescharacteristic
832Dic3—22no—
833Dic3—22no—
834Dic3—22no—
835Dic3—41no—
836Dic3—122no—
837Dic3—121no—
838Dic3—121no—
839C32#301811yescharacteristic, complemented, Sylow
840C23—21no—
841C23—32no—
842C23—64no—
843C23—61no—
844C23—181no—
845C23D3×#6711yescharacteristic
846Q8—21no—
847Q8—32no—
848Q8—64no—
849Q8—61no—
850Q8—61no—
851Q8—61no—
852Q8—181no—
853Q8—181no—
854Q8C2×#62612yes—
855D4—22no—
856D4—22no—
857D4—21no—
858D4—32no—
859D4—64no—
860D4—64no—
861D4—64no—
862D4—62no—
863D4—62no—
864D4—62no—
865D4—62no—
866D4—61no—
867D4—61no—
868D4—61no—
869D4—181no—
870D4—181no—
871D4—364no—
872D4—361no—
873D4—361no—
874D4C2×#62612yes—
875C2×C4—21no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—32no—
879C2×C4—64no—
880C2×C4—64no—
881C2×C4—64no—
882C2×C4—61no—
883C2×C4—61no—
884C2×C4—62no—
885C2×C4—62no—
886C2×C4—62no—
887C2×C4—62no—
888C2×C4—61no—
889C2×C4—122no—
890C2×C4—181no—
891C2×C4—361no—
892C2×C4—361no—
893C2×C4C2×#62611yescharacteristic
894C2×C4C2×#62611yescharacteristic
895C2×C4D3×#6711yescharacteristic
896C2×C4D3×#6711yescharacteristic
897C2×C4D3×#6711yescharacteristic
898C2×C4C22×D3211yescharacteristic
899C8—62no—
900C8—182no—
901C2×C3—21no—
902C2×C3—21no—
903C2×C3—21no—
904C2×C3—21no—
905C2×C3—21no—
906C2×C3—21no—
907C2×C3—21no—
908C2×C3—41no—
909C2×C3—41no—
910C2×C3—41no—
911C2×C3—42no—
912C2×C3—42no—
913C2×C3—82no—
914C2×C3—122no—
915C2×C3—122no—
916C2×C3C2×#88211yescharacteristic
917C2×C3C2×#95311yescharacteristic
918D3—42no—
919D3—42no—
920D3—242no—
921D3—241no—
922D3—241no—
923C22—22no—
924C22—41no—
925C22—62no—
926C22—62no—
927C22—81no—
928C22—122no—
929C22—241no—
930C22—244no—
931C22—362no—
932C22—361no—
933C22#6397711yescharacteristic
934C22#6397711yescharacteristic
935C22C2×D3×#6711yescharacteristic
936C4—22no—
937C4—62no—
938C4—62no—
939C4—62no—
940C4—121no—
941C4—361no—
942C4#6397711yescharacteristic
943C4#6397711yescharacteristic
944C4C22×#62611yescharacteristic
945C4C2×D3×#6711yescharacteristic
946C3—21no—
947C3#7898611yescharacteristic, complemented
948C3#8412111yescharacteristic, complemented
949C2—21no—
950C2—21no—
951C2—21no—
952C2—42no—
953C2—122no—
954C2—122no—
955C2—721no—
956C2C2×#6397711yescharacteristic
subgroupG/H
centerC4#63977
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC2×C32C2×#120
hypercenterC2×#41D32
hypocenterC32#3018
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C3×#5964C2semidirect
2. #10596293C2semidirect
3. #10595029C2semidirect
4. #10594795C2semidirect
5. C2×C3×#837C2semidirect
6. #10591689C2semidirect
7. #10591688C2semidirect
8. #10591685C2semidirect
9. #10591666C2semidirect
10. C2×#63569C2semidirect
11. #10591076C2semidirect
15. C2×#3828C22semidirect
28. #64160C22semidirect
30. #64158C22semidirect
33. C2×#3748C22semidirect
34. C2×C3×C4×Dic3C22semidirect
35. C2×C3×#208C22semidirect
37. #63911C22semidirect
39. #63866C22semidirect
40. #63864C22semidirect
41. #63860C22semidirect
43. #63831C22semidirect
46. #63825C22semidirect
47. C3×#837C22semidirect
48. C3×#837C22semidirect
49. #63569C22semidirect
50. #63569C22semidirect
51. #63560C22semidirect
52. #63558C22semidirect
54. #5964D3semidirect
69. C2×#837D3semidirect
78. C32×#41D4semidirect
80. C2×C32×Q8D4semidirect
82. C2×C32×D4D4semidirect
119. C3×#235D4semidirect
122. C2×C3×D12D4semidirect
128. C2×C3×Dic6D4semidirect
211. C2×C4×Dic3C2×D3semidirect
215. C2×#208C2×D3semidirect
230. #837C2×D3semidirect
231. #837C2×D3semidirect
336. C3×#41D12semidirect
337. C3×#41#67semidirect
346. C2×C3×Q8D12semidirect
347. C2×C3×Q8#67semidirect
362. C2×C3×D4D12semidirect
363. C2×C3×D4#67semidirect
416. #235#67semidirect
423. C2×D12#67semidirect
435. C2×Dic6#67semidirect
728. #41#626semidirect
736. C2×Q8#626semidirect
751. C2×D4#626semidirect
839. C32#3018semidirect
947. C3#78986semidirect
948. C3#84121semidirect

Maximal subgroups

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

subgroupindex
C3×#59642
#105962932
#105950292
#105947952
C2×C3×#8372
#105916892
#105916882
#105916852
#105916662
C2×#635692
#105910762
#841213
#789863