Finite Group Databasebeta

← #11904633

Subgroups — #11904633

Order 1152.

3761 conjugacy classes of subgroups.

The subgroup lattice has 1087 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3830C211yesmaximal, characteristic, complemented
2C2×#64313C211yesmaximal, characteristic, complemented
3C3×D4×#67C212yesmaximal, complemented
4#10595526C214yesmaximal, complemented
5C2×#63980C212yesmaximal, complemented
6#10595501C212yesmaximal, complemented
7#10595309C211yesmaximal, characteristic, complemented
8#10595307C214yesmaximal, complemented
9#10595246C212yesmaximal, complemented
10#10595240C211yesmaximal, characteristic, complemented
11#10595239C212yesmaximal, complemented
12#10595219C211yesmaximal, characteristic, complemented
13#10595166C212yesmaximal, complemented
14#10595164C212yesmaximal, complemented
15#10595081C211yesmaximal, characteristic, complemented
16#10595016C211yesmaximal, characteristic, complemented
17#10594918C212yesmaximal, complemented
18#86607—32nomaximal
19C22×C32×D4C2211yescharacteristic, complemented
20C22×#638C2212yescomplemented
21C23×C3⋊Dic3C2212yescomplemented
22C2×#3830—28no—
23C2×#3830C2211yescharacteristic
24C2×#3830C2211yescharacteristic, complemented
25C2×#3830C2212yescomplemented
26C2×#3830C2211yescharacteristic, complemented
27C2×#3830C2211yescharacteristic, complemented
28C2×#3830C2212yescomplemented
29C22×C4×C3⋊D3C2211yescharacteristic, complemented
30C22×#634C2211yescharacteristic, complemented
31C22×C3×#67C2214yescomplemented
32C2×C3×D3×D4C2212yescomplemented
33C2×#3811C2212yescomplemented
34C2×D3×#67C2214yescomplemented
35C22×#625C2212yescomplemented
36C2×#3805C2212yescomplemented
37#64313—28no—
38C2×#3802C2211yescharacteristic, complemented
39C2×#3798C2211yescharacteristic, complemented
40C2×#3795C2212yescomplemented
41C3×#953C2214yescomplemented
42C3×#940C2212yescomplemented
43C3×#939C2214yescomplemented
44C3×#938C2212yescomplemented
45C3×#937C2214yescomplemented
46C3×D4×Dic3C2212yescomplemented
47C3×#930C2212yescomplemented
48C3×C4×#67C2212yescomplemented
49#63983C2214yescomplemented
50#63982C2212yescomplemented
51#63982C2211yescharacteristic, complemented
52#63981C2212yescomplemented
53#63980C2212yescomplemented
54#63980C2214yescomplemented
55#63980C2212yescomplemented
56#63980C2214yescomplemented
57#63980C2212yescomplemented
58#63980C2212yescomplemented
59#63980C2211yescharacteristic, complemented
60#63979C2214yescomplemented
61#63978C2214yescomplemented
62#63977C2214yescomplemented
63#67⋊Dic3C2214yescomplemented
64#67⋊Dic3C2214yescomplemented
65#63971C2214yescomplemented
66C2×#3724C2212yescomplemented
67#63962C2214yescomplemented
68C2×(C2×D3)⋊Dic3C2214yescomplemented
69#63958C2214yescomplemented
70#63957C2212yescomplemented
71#63952C2214yescomplemented
72#63921C2212yescomplemented
73#63916C2212yescomplemented
74#63913C2214yescomplemented
75#63912C2212yescomplemented
76#63912C2211yescharacteristic, complemented
77C4×#626C2212yescomplemented
78#63900C2211yescharacteristic, complemented
79#63896C2214yescomplemented
80#63874C2211yescharacteristic, complemented
81#63865C2211yescharacteristic, complemented
82#63860C2212yescomplemented
83#63857C2212yescomplemented
84#63853C2212yescomplemented
85#63844C2212yescomplemented
86C2×#1004—32no—
87C22×#237—32no—
88C22×#237—61no—
89C3×D42—32no—
90#5806—32no—
91C2×#939—34no—
92D4×#67—34no—
93D4×#67D312yescomplemented
94#5718—32no—
95#5715—32no—
96#5610—34no—
97#5608—32no—
98D3×#121—32no—
99#5599—32no—
100#5598—32no—
101#5597—34no—
102#5592—34no—
103#5591—34no—
104#5590—34no—
105#5586—34no—
106#5554—32no—
107#5552—32no—
108#5547—32no—
109#5546—32no—
110C24×C32C2312yes—
111C23×C3⋊D3C2311yescharacteristic
112C23×C3×D3C2314yes—
113C22×D32C2312yes—
114C2×C32×D4—24no—
115C2×C32×D4C2312yes—
116C2×C32×D4C2311yescharacteristic
117C2×C32×D4C2311yescharacteristic
118C22×C32×C4C2311yescharacteristic
119C2×#638—28no—
120C2×#638C2312yes—
121C2×#638C2312yes—
122C2×#638C2312yes—
123C2×#638C2312yes—
124C22×C3⋊Dic3—28no—
125C22×C3⋊Dic3C2312yes—
126C22×C3⋊Dic3C2311yescharacteristic
127C22×C3⋊Dic3C2312yes—
128C22×C3⋊Dic3C2312yes—
129C22×C3⋊Dic3C2312yes—
130C22×C3⋊Dic3C2312yes—
131#3830—24no—
132#3830—28no—
133#3830—28no—
134#3830—24no—
135#3830—24no—
136#3830D418yescomplemented
137C2×C4×C3⋊D3—24no—
138C2×C4×C3⋊D3C2311yescharacteristic
139C2×C4×C3⋊D3C2311yescharacteristic
140C2×C4×C3⋊D3C2311yescharacteristic
141C2×C4×C3⋊D3C2311yescharacteristic
142C2×#634—24no—
143C2×#634C2311yescharacteristic
144C2×#634C2312yes—
145C2×#634C2311yescharacteristic
146C2×C3×#67—48no—
147C2×C3×#67C2312yes—
148C2×C3×#67C2314yes—
149C2×C3×#67C2314yes—
150C2×C3×#67C2314yes—
151C2×C3×#67C2314yes—
152C2×C3×#67C2314yes—
153C22×C3×Dic3C2314yes—
154C3×D3×D4—28no—
155C2×C3×D12C2312yes—
156C2×C3×C4×D3C2312yes—
157#3811—44no—
158D3×#67—216no—
159C2×#627C2311yescharacteristic
160C2×#626C2312yes—
161C2×#626C2314yes—
162C2×#626C2312yes—
163C2×#625—28no—
164C2×#625C2314yes—
165C2×#625C2311yescharacteristic
166C2×#625C2312yes—
167C2×#624C2312yes—
168#3805—28no—
169C2×D3×Dic3C2314yes—
170#3802—24no—
171#3798—24no—
172#3795—28no—
173C3×#217C2312yes—
174C3×#217C2314yes—
175C3×#217C2314yes—
176C3×(C2×D3)⋊C4C2312yes—
177C3×(C2×D3)⋊C4C2314yes—
178C3×C4⋊Dic3C2312yes—
179C3×Dic3⋊C4C2312yes—
180C3×C4×Dic3C2312yes—
181#3724C2314yes—
182#3724C2311yescharacteristic
183#3724C2311yescharacteristic
184#3724C2312yes—
185Dic3⋊Dic3C2312yes—
186Dic3⋊Dic3C2314yes—
187#3722C2312yes—
188#3722C2312yes—
189(C2×D3)⋊Dic3C2312yes—
190(C2×D3)⋊Dic3C2314yes—
191(C2×D3)⋊Dic3C2314yes—
192(C2×D3)⋊Dic3C2314yes—
193(C2×D3)⋊Dic3C2314yes—
194Dic32C2314yes—
195#3488—91noSylow
196C22×C3×D4—21no—
197C22×C3×D4—34no—
198C22×C3×D4—32no—
199C22×C3×D4C2×D312yescomplemented
200C22×#67—34no—
201C22×#67—34no—
202C22×#67—34no—
203C22×#67—62no—
204C22×#67C2×D314yescomplemented
205C23×Dic3—34no—
206C23×Dic3—62no—
207#1004—616no—
208C2×#237—32no—
209C2×#237—32no—
210C2×#237—32no—
211C2×#237—32no—
212C2×#237—34no—
213C2×#237—34no—
214C2×#237—34no—
215C2×#237—32no—
216C2×#237—61no—
217C2×#237—62no—
218C2×#237—61no—
219C2×#237—61no—
220C2×#237—62no—
221C2×#237—61no—
222C2×#237—616no—
223C2×#237—616no—
224C2×D3×D4—34no—
225C2×D3×D4—34no—
226C2×D3×D4—32no—
227C2×D3×D4C2×D312yescomplemented
228C2×#235—32no—
229C2×#235—32no—
230C22×C4×D3—32no—
231C22×C4×D3—61no—
232C22×Dic6—32no—
233C22×Dic6—61no—
234C3×#127—32no—
235C3×#121—32no—
236C3×#121—34no—
237C3×#121—32no—
238C3×#120—34no—
239C3×#120—34no—
240C3×C4×D4—32no—
241C3×C4×D4—32no—
242#953—34no—
243#953C2×D314yescomplemented
244C2×#217—34no—
245#940—34no—
246#940—34no—
247#940C2×D312yescomplemented
248#939—34no—
249#939—34no—
250#939—34no—
251#939—34no—
252#939—32no—
253#939—34no—
254#939—34no—
255#939—34no—
256#939—34no—
257#939—34no—
258#939—34no—
259#939C2×D314yescomplemented
260#938—34no—
261#938—32no—
262#938C2×D312yescomplemented
263#937—34no—
264#937—34no—
265#937—32no—
266#937C2×D314yescomplemented
267#936—32no—
268#935—34no—
269D4×Dic3—34no—
270D4×Dic3—34no—
271D4×Dic3C2×D312yescomplemented
272#930—34no—
273#930C2×D312yescomplemented
274C4×#67—34no—
275C4×#67—32no—
276C4×#67C2×D312yescomplemented
277C2×(C2×D3)⋊C4—34no—
278#924—32no—
279C2×Dic3⋊C4—34no—
280#897—32no—
281#896—34no—
282#896—32no—
283#895—32no—
284#894—32no—
285D3×C4⋊C4—32no—
286#887—32no—
287#886—34no—
288#885—34no—
289#885—34no—
290#884—34no—
291#884—34no—
292#884—32no—
293#884—34no—
294#883—32no—
295#882—34no—
296#882—32no—
297#67⋊C4—34no—
298#67⋊C4—34no—
299#67⋊C4—34no—
300D3×C22⋊C4—34no—
301#878—32no—
302#878—34no—
303#878—34no—
304#877—34no—
305#875—32no—
306C4×D12—32no—
307#872—32no—
308C4×Dic6—32no—
309C23×C32—24no—
310C23×C32—24no—
311C23×C32—42no—
312C23×C32C2412yes—
313C23×C32C2412yes—
314C23×C32C2411yescharacteristic
315C22×C3⋊D3—22no—
316C22×C3⋊D3—22no—
317C22×C3⋊D3—41no—
318C22×C3⋊D3C2411yescharacteristic
319C22×C3⋊D3C2411yescharacteristic
320C22×C3×D3—28no—
321C22×C3×D3—44no—
322C22×C3×D3—44no—
323C22×C3×D3C2414yes—
324C22×C3×D3C2412yes—
325C2×D32—24no—
326C2×D32—42no—
327C2×D32—42no—
328C32×D4—24no—
329C32×D4—22no—
330C32×D4C2×D414yescomplemented
331C2×C32×C4—22no—
332C2×C32×C4C2411yescharacteristic
333C2×C32×C4C2411yescharacteristic
334#638—24no—
335#638—24no—
336#638—24no—
337#638C2×D418yescomplemented
338C2×C3⋊Dic3—24no—
339C2×C3⋊Dic3—24no—
340C2×C3⋊Dic3—22no—
341C2×C3⋊Dic3—24no—
342C2×C3⋊Dic3—24no—
343C2×C3⋊Dic3C2×D418yescomplemented
344C2×C3⋊Dic3C2412yes—
345C2×C3⋊Dic3C2411yescharacteristic
346C2×C3⋊Dic3C2412yes—
347C2×C3⋊Dic3C2411yescharacteristic
348C4×C3⋊D3—22no—
349C4×C3⋊D3—22no—
350C4×C3⋊D3—22no—
351C4×C3⋊D3C2×D414yescomplemented
352#634—22no—
353#634—24no—
354#634C2×D414yescomplemented
355C3×#67—28no—
356C3×#67—28no—
357C3×#67—24no—
358C3×#67—44no—
359C3×#67—44no—
360C3×#67—44no—
361C2×C3×Dic3—44no—
362C2×C3×Dic3C2412yes—
363C2×C3×Dic3C2414yes—
364C2×C3×Dic3C2412yes—
365C2×C3×Dic3C2412yes—
366C3×D12—24no—
367C3×C4×D3—24no—
368#627—22no—
369#626—24no—
370#626—42no—
371#626—44no—
372#625—28no—
373#625—22no—
374#625—24no—
375#624—42no—
376D3×Dic3—28no—
377C2×H(5,𝔽2)—91no—
378C22×#41—91no—
379#550—92no—
380#548—92no—
381#546—92no—
382#546—94no—
383D42—32no—
384D42—94no—
385#537—92no—
386#537—91no—
387#535—92no—
388#535—91no—
389#525—91no—
390#525—92no—
391C2×#121—91no—
392C2×#121—92no—
393#520—91no—
394C24×C3—22no—
395C24×C3—34no—
396C24×C3C22×D314yes—
397C23×D3—32no—
398C23×D3—34no—
399C23×D3—61no—
400C23×D3C22×D314yes—
401C2×C3×D4—28no—
402C2×C3×D4—28no—
403C2×C3×D4—22no—
404C2×C3×D4—21no—
405C2×C3×D4—21no—
406C2×C3×D4—34no—
407C2×C3×D4—34no—
408C2×C3×D4—32no—
409C2×C3×D4—34no—
410C2×C3×D4—34no—
411C2×C3×D4—34no—
412C2×C3×D4—32no—
413C2×C3×D4—68no—
414C2×C3×D4—128no—
415C2×C3×D4C22×D314yes—
416C2×C3×D4C22×D312yes—
417C2×C3×D4C22×D312yes—
418C22×C3×C4—21no—
419C22×C3×C4—34no—
420C22×C3×C4—32no—
421C22×C3×C4C22×D312yes—
422C2×#67—34no—
423C2×#67—34no—
424C2×#67—34no—
425C2×#67—34no—
426C2×#67—32no—
427C2×#67—34no—
428C2×#67—34no—
429C2×#67—34no—
430C2×#67—32no—
431C2×#67—32no—
432C2×#67—34no—
433C2×#67—48no—
434C2×#67—62no—
435C2×#67—62no—
436C2×#67—62no—
437C2×#67—62no—
438C2×#67—616no—
439C2×#67—616no—
440C2×#67—616no—
441C2×#67—616no—
442C2×#67C22×D314yes—
443C2×#67C22×D312yes—
444C2×#67C22×D314yes—
445C2×#67C22×D314yes—
446C2×#67C22×D314yes—
447C2×#67C22×D314yes—
448C22×Dic3—34no—
449C22×Dic3—32no—
450C22×Dic3—34no—
451C22×Dic3—34no—
452C22×Dic3—34no—
453C22×Dic3—34no—
454C22×Dic3—34no—
455C22×Dic3—62no—
456C22×Dic3—61no—
457C22×Dic3—62no—
458C22×Dic3—62no—
459C22×Dic3—62no—
460C22×Dic3—62no—
461C22×Dic3—616no—
462C22×Dic3—616no—
463C22×Dic3C22×D314yes—
464#237—316no—
465#237—68no—
466#237—68no—
467#237—68no—
468#237—68no—
469#237—616no—
470#237—616no—
471#237—616no—
472#237—68no—
473#237—616no—
474#237—616no—
475#237—68no—
476#237—68no—
477#237—68no—
478D3×D4—28no—
479D3×D4—68no—
480D3×D4—616no—
481D3×D4—128no—
482#235—68no—
483#235—68no—
484C2×D12—32no—
485C2×D12—32no—
486C2×D12—34no—
487C2×D12C22×D312yes—
488C2×C4×D3—32no—
489C2×C4×D3—34no—
490C2×C4×D3—32no—
491C2×C4×D3—32no—
492C2×C4×D3—32no—
493C2×C4×D3—34no—
494C2×C4×D3—61no—
495C2×C4×D3—61no—
496C2×C4×D3—61no—
497C2×C4×D3—61no—
498C2×C4×D3—68no—
499C2×C4×D3—68no—
500C2×C4×D3C22×D312yes—
501C2×Dic6—32no—
502C2×Dic6—32no—
503C2×Dic6—34no—
504C2×Dic6—32no—
505C2×Dic6—61no—
506C2×Dic6—61no—
507C2×Dic6—62no—
508C2×Dic6—68no—
509C2×Dic6—68no—
510C3×C4⋊C4—32no—
511C3×C4⋊C4—32no—
512C3×C22⋊C4—34no—
513C3×C22⋊C4—32no—
514C3×C22⋊C4—34no—
515C3×C22⋊C4—34no—
516C3×C22⋊C4—32no—
517C3×C42—32no—
518#217—34no—
519#217—34no—
520#217—32no—
521#217—34no—
522#217—34no—
523#217C22×D314yes—
524#217C22×D312yes—
525#217C22×D314yes—
526(C2×D3)⋊C4—32no—
527(C2×D3)⋊C4—34no—
528(C2×D3)⋊C4—34no—
529(C2×D3)⋊C4—34no—
530(C2×D3)⋊C4—34no—
531(C2×D3)⋊C4—32no—
532(C2×D3)⋊C4—32no—
533(C2×D3)⋊C4—32no—
534(C2×D3)⋊C4—32no—
535(C2×D3)⋊C4C22×D314yes—
536(C2×D3)⋊C4C22×D312yes—
537C4⋊Dic3—32no—
538C4⋊Dic3—34no—
539C4⋊Dic3C22×D312yes—
540Dic3⋊C4—34no—
541Dic3⋊C4—32no—
542Dic3⋊C4—32no—
543Dic3⋊C4—34no—
544Dic3⋊C4—32no—
545Dic3⋊C4—34no—
546Dic3⋊C4—34no—
547Dic3⋊C4C22×D312yes—
548C4×Dic3—34no—
549C4×Dic3—34no—
550C4×Dic3C22×D312yes—
551C22×C32—21no—
552C22×C32—21no—
553C22×C32—22no—
554C22×C32—22no—
555C22×C32—22no—
556C22×C32—22no—
557C22×C32—22no—
558C22×C32—48no—
559C22×C32C22×D414yes—
560C22×C32H(5,𝔽2)12yescomplemented
561C22×C32C2511yescharacteristic
562C2×C3⋊D3—21no—
563C2×C3⋊D3—21no—
564C2×C3⋊D3—21no—
565C2×C3⋊D3—21no—
566C2×C3⋊D3—21no—
567C2×C3⋊D3—44no—
568C2×C3⋊D3C22×D412yes—
569C2×C3×D3—24no—
570C2×C3×D3—22no—
571C2×C3×D3—24no—
572C2×C3×D3—22no—
573C2×C3×D3—22no—
574C2×C3×D3—24no—
575C2×C3×D3—88no—
576D32—84no—
577C32×C4—21no—
578C32×C4C22×D412yes—
579C3⋊Dic3—22no—
580C3⋊Dic3—21no—
581C3⋊Dic3C22×D414yes—
582C3⋊Dic3C22×D412yes—
583C3×Dic3—22no—
584C3×Dic3—24no—
585C3×Dic3—22no—
586C3×Dic3—22no—
587H(5,𝔽2)—188no—
588C2×#41—91no—
589C2×#41—92no—
590C2×#41—92no—
591C2×#41—91no—
592C2×#41—92no—
593C2×#41—91no—
594C2×#41—91no—
595C2×#41—92no—
596C2×#41—91no—
597C2×#41—188no—
598C22×Q8—91no—
599C22×D4—34no—
600C22×D4—32no—
601C22×D4—91no—
602C22×D4—92no—
603C22×D4—94no—
604C22×D4—92no—
605C22×D4—92no—
606C22×D4D3211yescharacteristic, complemented
607C23×C4—92no—
608C23×C4—91no—
609#127—32no—
610#127—94no—
611#124—92no—
612#124—94no—
613#123—92no—
614#123—94no—
615C22⋊Q8—91no—
616C22⋊Q8—92no—
617C22⋊Q8—94no—
618C22⋊Q8—91no—
619C22⋊Q8—92no—
620#121—34no—
621#121—32no—
622#121—32no—
623#121—92no—
624#121—91no—
625#121—94no—
626#121—94no—
627#121—92no—
628#121—94no—
629#121—91no—
630#121—92no—
631#121—92no—
632#121—92no—
633#121—94no—
634#121—94no—
635#121—92no—
636#120—34no—
637#120—34no—
638#120—92no—
639#120—94no—
640#120—94no—
641C4×Q8—92no—
642C4×D4—32no—
643C4×D4—32no—
644C4×D4—92no—
645C4×D4—94no—
646C4×D4—94no—
647C4×D4—94no—
648#117—91no—
649#117—92no—
650C2×C4⋊C4—91no—
651C2×C4⋊C4—92no—
652C2×C22⋊C4—92no—
653C2×C22⋊C4—94no—
654C23×C3—28no—
655C23×C3—28no—
656C23×C3—28no—
657C23×C3—21no—
658C23×C3—22no—
659C23×C3—22no—
660C23×C3—34no—
661C23×C3—32no—
662C23×C3—44no—
663C23×C3—44no—
664C23×C3—44no—
665C23×C3—68no—
666C23×C3—124no—
667C23×C3—124no—
668C23×C3C23×D314yes—
669C23×C3C23×D314yes—
670C23×C3C23×D312yes—
671C22×D3—28no—
672C22×D3—32no—
673C22×D3—32no—
674C22×D3—44no—
675C22×D3—44no—
676C22×D3—61no—
677C22×D3—61no—
678C22×D3—68no—
679C22×D3—64no—
680C22×D3—64no—
681C22×D3—64no—
682C22×D3—122no—
683C22×D3—124no—
684C22×D3—124no—
685C22×D3—122no—
686C22×D3—122no—
687C22×D3C23×D314yes—
688C22×D3C23×D312yes—
689C3×D4—28no—
690C3×D4—24no—
691C3×D4—28no—
692C3×D4—24no—
693C3×D4—24no—
694C3×D4—68no—
695C3×D4—68no—
696C3×D4—64no—
697C3×D4—64no—
698C3×D4—124no—
699C3×D4—124no—
700C3×D4—124no—
701C3×D4D3×D418yescomplemented
702C2×C3×C4—24no—
703C2×C3×C4—24no—
704C2×C3×C4—21no—
705C2×C3×C4—21no—
706C2×C3×C4—32no—
707C2×C3×C4—34no—
708C2×C3×C4—32no—
709C2×C3×C4—32no—
710C2×C3×C4—64no—
711C2×C3×C4—124no—
712C2×C3×C4C23×D312yes—
713C2×C3×C4C23×D312yes—
714#67—28no—
715#67—28no—
716#67—24no—
717#67—316no—
718#67—44no—
719#67—44no—
720#67—44no—
721#67—68no—
722#67—64no—
723#67—68no—
724#67—64no—
725#67—68no—
726#67—68no—
727#67—68no—
728#67—68no—
729#67—68no—
730#67—68no—
731#67—68no—
732#67—68no—
733#67—124no—
734#67—122no—
735C2×Dic3—316no—
736C2×Dic3—34no—
737C2×Dic3—32no—
738C2×Dic3—34no—
739C2×Dic3—32no—
740C2×Dic3—44no—
741C2×Dic3—68no—
742C2×Dic3—62no—
743C2×Dic3—62no—
744C2×Dic3—61no—
745C2×Dic3—61no—
746C2×Dic3—68no—
747C2×Dic3—68no—
748C2×Dic3—64no—
749C2×Dic3—68no—
750C2×Dic3—68no—
751C2×Dic3—68no—
752C2×Dic3—64no—
753C2×Dic3—68no—
754C2×Dic3—68no—
755C2×Dic3—68no—
756C2×Dic3—68no—
757C2×Dic3C23×D312yes—
758C2×Dic3C23×D314yes—
759C2×Dic3C23×D312yes—
760C2×Dic3C23×D312yes—
761D12—24no—
762D12—64no—
763D12—122no—
764D12—124no—
765C4×D3—24no—
766C4×D3—38no—
767C4×D3—64no—
768C4×D3—64no—
769C4×D3—68no—
770C4×D3—64no—
771C4×D3—64no—
772C4×D3—64no—
773C4×D3—64no—
774C4×D3—64no—
775C4×D3—124no—
776Dic6—38no—
777Dic6—64no—
778Dic6—64no—
779Dic6—68no—
780Dic6—68no—
781Dic6—64no—
782Dic6—64no—
783C2×C32—22no—
784C2×C32—24no—
785C2×C32—42no—
786C2×C32C23×D411yescharacteristic
787C2×C32C2×H(5,𝔽2)11yescharacteristic
788C2×C32#58511yescharacteristic
789C3⋊D3—22no—
790C3⋊D3—41no—
791C3×D3—44no—
792C3×D3—42no—
793C24—34no—
794C24—92no—
795C24—91no—
796C24C2×D3212yes—
797#41—98no—
798#41—184no—
799#41—188no—
800#41—188no—
801#41—184no—
802#41—188no—
803#41—188no—
804#41—184no—
805#41—184no—
806C2×Q8—91no—
807C2×Q8—91no—
808C2×Q8—92no—
809C2×Q8—91no—
810C2×Q8—184no—
811C2×D4—24no—
812C2×D4—32no—
813C2×D4—34no—
814C2×D4—34no—
815C2×D4—34no—
816C2×D4—34no—
817C2×D4—34no—
818C2×D4—32no—
819C2×D4—68no—
820C2×D4—92no—
821C2×D4—92no—
822C2×D4—94no—
823C2×D4—92no—
824C2×D4—91no—
825C2×D4—92no—
826C2×D4—94no—
827C2×D4—92no—
828C2×D4—92no—
829C2×D4—92no—
830C2×D4—128no—
831C2×D4—184no—
832C2×D4—188no—
833C2×D4—1816no—
834C2×D4—188no—
835C2×D4—364no—
836C2×D4C2×D3212yes—
837C2×D4C2×D3211yescharacteristic
838C2×D4C2×D3211yescharacteristic
839C22×C4—34no—
840C22×C4—32no—
841C22×C4—92no—
842C22×C4—94no—
843C22×C4—92no—
844C22×C4—91no—
845C22×C4—92no—
846C22×C4—92no—
847C22×C4—92no—
848C22×C4—91no—
849C22×C4—92no—
850C22×C4—91no—
851C22×C4—91no—
852C22×C4—91no—
853C22×C4—184no—
854C22×C4—188no—
855C22×C4C2×D3211yescharacteristic
856C4⋊C4—32no—
857C4⋊C4—32no—
858C4⋊C4—91no—
859C4⋊C4—92no—
860C4⋊C4—94no—
861C4⋊C4—91no—
862C4⋊C4—92no—
863C4⋊C4—94no—
864C22⋊C4—34no—
865C22⋊C4—32no—
866C22⋊C4—34no—
867C22⋊C4—34no—
868C22⋊C4—32no—
869C22⋊C4—92no—
870C22⋊C4—92no—
871C22⋊C4—92no—
872C22⋊C4—94no—
873C22⋊C4—94no—
874C22⋊C4—94no—
875C22⋊C4—94no—
876C42—32no—
877C42—94no—
878C22×C3—22no—
879C22×C3—22no—
880C22×C3—22no—
881C22×C3—24no—
882C22×C3—24no—
883C22×C3—22no—
884C22×C3—24no—
885C22×C3—24no—
886C22×C3—24no—
887C22×C3—24no—
888C22×C3—22no—
889C22×C3—24no—
890C22×C3—21no—
891C22×C3—42no—
892C22×C3—42no—
893C22×C3—42no—
894C22×C3—42no—
895C22×C3—416no—
896C22×C3—416no—
897C22×C3—64no—
898C22×C3—62no—
899C22×C3—64no—
900C22×C3—62no—
901C22×C3—62no—
902C22×C3—64no—
903C22×C3—248no—
904C22×C3C2×D3×D418yes—
905C22×C3#100414yescomplemented
906C22×C3C24×D312yes—
907C2×D3—22no—
908C2×D3—24no—
909C2×D3—24no—
910C2×D3—22no—
911C2×D3—22no—
912C2×D3—24no—
913C2×D3—34no—
914C2×D3—62no—
915C2×D3—62no—
916C2×D3—62no—
917C2×D3—62no—
918C2×D3—62no—
919C2×D3—62no—
920C2×D3—62no—
921C2×D3—88no—
922C2×D3—121no—
923C2×D3—121no—
924C2×D3—121no—
925C2×D3—121no—
926C2×D3—128no—
927C2×D3—128no—
928C2×D3—248no—
929C3×C4—22no—
930C3×C4—22no—
931C3×C4—22no—
932C3×C4—62no—
933C3×C4—64no—
934C3×C4—62no—
935C3×C4—62no—
936C3×C4C2×D3×D414yes—
937Dic3—22no—
938Dic3—24no—
939Dic3—22no—
940Dic3—22no—
941Dic3—38no—
942Dic3—34no—
943Dic3—64no—
944Dic3—62no—
945Dic3—64no—
946Dic3—62no—
947Dic3—64no—
948Dic3—62no—
949C32#348811yescharacteristic, complemented, Sylow
950C23—24no—
951C23—24no—
952C23—32no—
953C23—34no—
954C23—42no—
955C23—68no—
956C23—91no—
957C23—91no—
958C23—124no—
959C23—124no—
960C23—182no—
961C23—184no—
962C23—182no—
963C23—361no—
964C23—362no—
965C23—362no—
966C23C22×D3212yes—
967C23C22×D3211yescharacteristic
968C23C22×D3212yes—
969Q8—94no—
970Q8—184no—
971Q8—182no—
972Q8—182no—
973D4—24no—
974D4—22no—
975D4—64no—
976D4—68no—
977D4—68no—
978D4—64no—
979D4—98no—
980D4—124no—
981D4—124no—
982D4—124no—
983D4—184no—
984D4—184no—
985D4—182no—
986D4—184no—
987D4—188no—
988D4—184no—
989D4—184no—
990D4—364no—
991D4—362no—
992D4#381114yescomplemented
993C2×C4—22no—
994C2×C4—32no—
995C2×C4—32no—
996C2×C4—34no—
997C2×C4—32no—
998C2×C4—64no—
999C2×C4—98no—
1000C2×C4—92no—
1001C2×C4—91no—
1002C2×C4—94no—
1003C2×C4—91no—
1004C2×C4—92no—
1005C2×C4—124no—
1006C2×C4—182no—
1007C2×C4—182no—
1008C2×C4—188no—
1009C2×C4—182no—
1010C2×C4—184no—
1011C2×C4—184no—
1012C2×C4—184no—
1013C2×C4—184no—
1014C2×C4—182no—
1015C2×C4—362no—
1016C2×C4C22×D3211yescharacteristic
1017C2×C4C22×D3211yescharacteristic
1018C2×C3—24no—
1019C2×C3—28no—
1020C2×C3—24no—
1021C2×C3—21no—
1022C2×C3—21no—
1023C2×C3—21no—
1024C2×C3—44no—
1025C2×C3—44no—
1026C2×C3—44no—
1027C2×C3—124no—
1028C2×C3—122no—
1029C2×C3C22×D3×D412yes—
1030C2×C3C2×#100412yes—
1031C2×C3#596612yes—
1032D3—42no—
1033D3—44no—
1034D3—64no—
1035D3—122no—
1036D3—122no—
1037D3—122no—
1038C22—22no—
1039C22—21no—
1040C22—22no—
1041C22—21no—
1042C22—22no—
1043C22—22no—
1044C22—22no—
1045C22—48no—
1046C22—62no—
1047C22—64no—
1048C22—64no—
1049C22—62no—
1050C22—62no—
1051C22—64no—
1052C22—92no—
1053C22—181no—
1054C22—181no—
1055C22—181no—
1056C22—181no—
1057C22—181no—
1058C22—248no—
1059C22—364no—
1060C22—724no—
1061C22#6431312yescomplemented
1062C22C2×#381114yes—
1063C22C23×D3211yescharacteristic
1064C4—21no—
1065C4—62no—
1066C4—64no—
1067C4—62no—
1068C4—62no—
1069C4—92no—
1070C4—94no—
1071C4—181no—
1072C4—182no—
1073C4C2×#381112yes—
1074C3—21no—
1075C3#8660712yescomplemented
1076C2—22no—
1077C2—24no—
1078C2—42no—
1079C2—122no—
1080C2—124no—
1081C2—182no—
1082C2—361no—
1083C2C2×#6431311yescharacteristic
1084C2#1059667911yescharacteristic
1085C2C22×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×D4C22
hypercenterC22×D4D32
hypocenterC32#3488
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#3830C2semidirect
2. C2×#64313C2semidirect
3. C3×D4×#67C2semidirect
4. #10595526C2semidirect
5. C2×#63980C2semidirect
6. #10595501C2semidirect
7. #10595309C2semidirect
8. #10595307C2semidirect
9. #10595246C2semidirect
10. #10595240C2semidirect
11. #10595239C2semidirect
12. #10595219C2semidirect
13. #10595166C2semidirect
14. #10595164C2semidirect
15. #10595081C2semidirect
16. #10595016C2semidirect
17. #10594918C2semidirect
19. C22×C32×D4C22semidirect
20. C22×#638C22semidirect
21. C23×C3⋊Dic3C22semidirect
24. C2×#3830C22semidirect
25. C2×#3830C22semidirect
26. C2×#3830C22semidirect
27. C2×#3830C22semidirect
28. C2×#3830C22semidirect
29. C22×C4×C3⋊D3C22semidirect
30. C22×#634C22semidirect
31. C22×C3×#67C22semidirect
32. C2×C3×D3×D4C22semidirect
33. C2×#3811C22semidirect
34. C2×D3×#67C22semidirect
35. C22×#625C22semidirect
36. C2×#3805C22semidirect
38. C2×#3802C22semidirect
39. C2×#3798C22semidirect
40. C2×#3795C22semidirect
41. C3×#953C22semidirect
42. C3×#940C22semidirect
43. C3×#939C22semidirect
44. C3×#938C22semidirect
45. C3×#937C22semidirect
46. C3×D4×Dic3C22semidirect
47. C3×#930C22semidirect
48. C3×C4×#67C22semidirect
49. #63983C22semidirect
50. #63982C22semidirect
51. #63982C22semidirect
52. #63981C22semidirect
53. #63980C22semidirect
54. #63980C22semidirect
55. #63980C22semidirect
56. #63980C22semidirect
57. #63980C22semidirect
58. #63980C22semidirect
59. #63980C22semidirect
60. #63979C22semidirect
61. #63978C22semidirect
62. #63977C22semidirect
63. #67⋊Dic3C22semidirect
64. #67⋊Dic3C22semidirect
65. #63971C22semidirect
66. C2×#3724C22semidirect
67. #63962C22semidirect
68. C2×(C2×D3)⋊Dic3C22semidirect
69. #63958C22semidirect
70. #63957C22semidirect
71. #63952C22semidirect
72. #63921C22semidirect
73. #63916C22semidirect
74. #63913C22semidirect
75. #63912C22semidirect
76. #63912C22semidirect
77. C4×#626C22semidirect
78. #63900C22semidirect
79. #63896C22semidirect
80. #63874C22semidirect
81. #63865C22semidirect
82. #63860C22semidirect
83. #63857C22semidirect
84. #63853C22semidirect
85. #63844C22semidirect
93. D4×#67D3semidirect
136. #3830D4semidirect
199. C22×C3×D4C2×D3semidirect
204. C22×#67C2×D3semidirect
227. C2×D3×D4C2×D3semidirect
243. #953C2×D3semidirect
247. #940C2×D3semidirect
259. #939C2×D3semidirect
262. #938C2×D3semidirect
266. #937C2×D3semidirect
271. D4×Dic3C2×D3semidirect
273. #930C2×D3semidirect
276. C4×#67C2×D3semidirect
330. C32×D4C2×D4semidirect
337. #638C2×D4semidirect
343. C2×C3⋊Dic3C2×D4semidirect
351. C4×C3⋊D3C2×D4semidirect
354. #634C2×D4semidirect
560. C22×C32H(5,𝔽2)semidirect
606. C22×D4D32semidirect
701. C3×D4D3×D4semidirect
905. C22×C3#1004semidirect
949. C32#3488semidirect
992. D4#3811semidirect
1061. C22#64313semidirect
1075. C3#86607semidirect

Maximal subgroups

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

subgroupindex
C22×#38302
C2×#643132
C3×D4×#672
#105955262
C2×#639802
#105955012
#105953092
#105953072
#105952462
#105952402
#105952392
#105952192
#105951662
#105951642
#105950812
#105950162
#105949182
#866073