Finite Group Databasebeta

← #11904656

Subgroups — #11904656

Order 1152.

3463 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64307C211yesmaximal, characteristic, complemented
2C2×D3×#235C211yesmaximal, characteristic, complemented
3#10595975C211yesmaximal, characteristic, complemented
4C3×#5510C211yesmaximal, characteristic, complemented
5C2×C3×#895C211yesmaximal, characteristic, complemented
6#10595083C214yesmaximal, complemented
7#10595069C214yesmaximal, complemented
8#10595040C211yesmaximal, characteristic, complemented
9#10595022C211yesmaximal, characteristic, complemented
10#10594634C212yesmaximal, complemented
11#10594633C212yesmaximal, complemented
12#10594632C212yesmaximal, complemented
13#10594618C212yesmaximal, complemented
14#10594612C212yesmaximal, complemented
15#10594528C212yesmaximal, complemented
16#10594527C212yesmaximal, complemented
17#10594525C212yesmaximal, complemented
18#86379—31nomaximal
19#85949—31nomaximal
20C2×#3828C2211yescharacteristic
21C2×C3×#235C2211yescharacteristic, complemented
22C2×C3×#235C2211yescharacteristic, complemented
23C22×C3×D12C2211yescharacteristic, complemented
24C22×C3×D12C2212yescomplemented
25C22×C3×C4×D3C2211yescharacteristic, complemented
26C2×D3×#67C2214yescomplemented
27C2×D3×#67C2212yescomplemented
28C2×#3804C2212yescomplemented
29#64307—28no—
30D3×#235—28no—
31C2×#3802C2212yescomplemented
32C2×#3802C2214yescomplemented
33C2×D3×D12C2211yescharacteristic, complemented
34C2×D3×D12C2212yescomplemented
35C2×C4×D32C2212yescomplemented
36C2×#3799C2211yescharacteristic, complemented
37C2×#3798C2212yescomplemented
38C2×#3796C2212yescomplemented
39C2×#3795C2211yescharacteristic, complemented
40C2×#3795C2212yescomplemented
41C2×D3×Dic6C2211yescharacteristic, complemented
42C2×C32×C4⋊C4C2211yescharacteristic, complemented
43C4×#638C2214yescomplemented
44#64135C2211yescharacteristic, complemented
45#64102C2212yescomplemented
46#64101C2212yescomplemented
47C4⋊C4×C3⋊D3C2212yescomplemented
48#64096C2212yescomplemented
49C3×#930C2214yescomplemented
50C2×C3×(C2×D3)⋊C4C2212yescomplemented
51C3×#897C2212yescomplemented
52C3×#897C2212yescomplemented
53C3×#895C2212yescomplemented
54C3×#895C2212yescomplemented
55C3×#895C2212yescomplemented
56C3×#895C2212yescomplemented
57C3×#895C2212yescomplemented
58C3×#895C2212yescomplemented
59#63976C2214yescomplemented
60#63976C2212yescomplemented
61#63961C2212yescomplemented
62#63922C2214yescomplemented
63#63922C2214yescomplemented
64#63922C2214yescomplemented
65#63921C2214yescomplemented
66#63916C2214yescomplemented
67#63915C2214yescomplemented
68#63914C2212yescomplemented
69#63914C2214yescomplemented
70#63912C2214yescomplemented
71#63908C2211yescharacteristic, complemented
72#63908C2212yescomplemented
73#63908C2212yescomplemented
74#63908C2211yescharacteristic, complemented
75#63902C2214yescomplemented
76C4×#625C2212yescomplemented
77C4×#625C2212yescomplemented
78#63899C2214yescomplemented
79#63898C2214yescomplemented
80#63885C2214yescomplemented
81#63885C2214yescomplemented
82#63885C2214yescomplemented
83#63863C2212yescomplemented
84#63856C2211yescharacteristic, complemented
85#63856C2211yescharacteristic, complemented
86#63854C2214yescomplemented
87C2×#1009—31no—
88C2×D3×#41—31no—
89C2×#1004—31no—
90C22×#235—31no—
91C3×#537—31no—
92C2×C3×#121—31no—
93#5830—31no—
94#5828—31no—
95#5805—31no—
96D4×#67—34no—
97#5791—31no—
98#5633—32no—
99#5630—32no—
100#5629—32no—
101#5627—32no—
102#5612—32no—
103#5610—34no—
104#5609—34no—
105#5609—32no—
106#5609—32no—
107#5608—32no—
108#5607—32no—
109#5607—32no—
110#5606—32no—
111D3×#121—32no—
112D3×#121—32no—
113#5599—32no—
114#5599—32no—
115#5598—32no—
116#5510D311yescharacteristic, complemented
117C2×#895D311yescharacteristic, complemented
118#5504—31no—
119#5504—31no—
120#5504—61no—
121#5490—34no—
122C23×C3×D3C2311yescharacteristic
123C23×C3×D3C2312yes—
124C22×D32C2312yes—
125C22×D32C2314yes—
126C22×C32×C4C2312yes—
127C22×C32×C4C2311yescharacteristic
128C2×#638C2312yes—
129#3828D418yescomplemented
130C2×C4⋊(C3⋊D3)C2311yescharacteristic
131C2×C4×C3⋊D3C2314yes—
132C2×C4×C3⋊D3C2312yes—
133C2×#634C2311yescharacteristic
134C2×C3×#67C2312yes—
135C2×C3×#67C2312yes—
136C22×C3×Dic3C2311yescharacteristic
137C3×#235—24no—
138C3×#235—24no—
139C2×C3×D12—24no—
140C2×C3×D12—44no—
141C2×C3×D12C2312yes—
142C2×C3×D12C2311yescharacteristic
143C2×C3×D12C2312yes—
144C2×C3×D12C2311yescharacteristic
145C2×C3×D12C2314yes—
146C2×C3×D12C2314yes—
147C2×C3×D12C2314yes—
148C2×C3×C4×D3—24no—
149C2×C3×C4×D3C2311yescharacteristic
150C2×C3×C4×D3C2311yescharacteristic
151C2×C3×C4×D3C2311yescharacteristic
152C2×C3×C4×D3C2311yescharacteristic
153C2×C3×C4×D3C2312yes—
154C2×C3×C4×D3C2312yes—
155C2×C3×Dic6C2311yescharacteristic
156C2×C3×Dic6C2311yescharacteristic
157D3×#67—28no—
158D3×#67—216no—
159C2×#627C2312yes—
160C2×#626C2314yes—
161C2×#626C2312yes—
162C2×#626C2312yes—
163C2×#625C2312yes—
164C2×#625C2314yes—
165C2×#625C2312yes—
166C2×#625C2314yes—
167C2×#625C2312yes—
168C2×#625C2314yes—
169C2×#624C2312yes—
170#3804—28no—
171C2×D3×Dic3C2312yes—
172C2×D3×Dic3C2314yes—
173C2×D3×Dic3C2312yes—
174#3802—28no—
175#3802—48no—
176D3×D12—24no—
177D3×D12—28no—
178C4×D32—28no—
179#3799—24no—
180#3798—28no—
181#3796—28no—
182#3795—24no—
183#3795—28no—
184D3×Dic6—24no—
185C32×C4⋊C4C2312yes—
186C32×C4⋊C4C2312yes—
187#3757C2312yes—
188#3752C2314yes—
189C4⋊(C3⋊Dic3)C2311yescharacteristic
190C4⋊(C3⋊Dic3)C2311yescharacteristic
191#3750C2314yes—
192C4×C3⋊Dic3C2314yes—
193C4×C3⋊Dic3C2312yes—
194C3×(C2×D3)⋊C4C2314yes—
195C3×(C2×D3)⋊C4C2314yes—
196C3×(C2×D3)⋊C4C2314yes—
197C3×(C2×D3)⋊C4C2314yes—
198C3×C4⋊Dic3C2314yes—
199#3724C2312yes—
200#3724C2312yes—
201(C2×D3)⋊Dic3C2314yes—
202(C2×D3)⋊Dic3C2312yes—
203(C2×D3)⋊Dic3C2312yes—
204(C2×D3)⋊Dic3C2314yes—
205(C2×D3)⋊Dic3C2312yes—
206(C2×D3)⋊Dic3C2312yes—
207#3488—91noSylow
208C2×C3×#41—31no—
209C2×C3×#41—31no—
210C22×C3×D4—31no—
211C22×C3×D4—32no—
212C23×C3×C4—31no—
213C22×#67—32no—
214C22×#67—34no—
215#1009—68no—
216D3×#41—68no—
217C2×#239—32no—
218C2×#239—31no—
219C2×D3×Q8—31no—
220#1004—68no—
221C2×#237—32no—
222C2×#237—32no—
223C2×#237—31no—
224C2×#237—32no—
225C2×D3×D4—32no—
226C2×D3×D4—34no—
227C2×D3×D4—32no—
228C2×D3×D4—32no—
229C2×D3×D4—34no—
230C2×D3×D4—34no—
231C2×D3×D4—32no—
232C2×D3×D4—31no—
233C2×#235—31no—
234C2×#235—31no—
235C2×#235—32no—
236C2×#235—32no—
237C2×#235—31no—
238C2×#235—32no—
239C2×#235—32no—
240C2×#235—31no—
241C2×#235—61no—
242C2×#235—68no—
243C2×#235C2×D311yescharacteristic, complemented
244C2×#235C2×D311yescharacteristic, complemented
245C22×D12—31no—
246C22×D12—32no—
247C22×D12C2×D311yescharacteristic, complemented
248C22×D12C2×D312yescomplemented
249C22×C4×D3—32no—
250C22×C4×D3—32no—
251C22×C4×D3C2×D311yescharacteristic, complemented
252C22×Dic6—31no—
253C3×C22⋊Q8—32no—
254C3×C22⋊Q8—32no—
255C3×#121—34no—
256C3×#121—32no—
257C3×#121—32no—
258C3×#121—32no—
259C3×#121—32no—
260C3×#121—32no—
261C3×#121—32no—
262C2×C3×C4⋊C4—21no—
263C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
264C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
265C2×C3×C22⋊C4—32no—
266#953—34no—
267#953—32no—
268#947—32no—
269#946—31no—
270#946—31no—
271#940—34no—
272#940—32no—
273#940—32no—
274#940—34no—
275#939—34no—
276#939—34no—
277#939—34no—
278#938—32no—
279#938—32no—
280#938—31no—
281#938—31no—
282#938—34no—
283#937—32no—
284#937—34no—
285#937—34no—
286#937—34no—
287#937—34no—
288#936—32no—
289#935—32no—
290D4×Dic3—34no—
291#930—31no—
292#930—31no—
293#930—32no—
294#930—32no—
295#930C2×D314yescomplemented
296#929—32no—
297C4×#67—34no—
298C4×#67—34no—
299C4×#67—32no—
300C4×#67—32no—
301C4×#67—32no—
302C4×#67—32no—
303C4×#67—64no—
304C2×(C2×D3)⋊C4C2×D312yescomplemented
305#926—31no—
306#926—31no—
307#926—61no—
308#924—31no—
309#924—31no—
310#897C2×D312yescomplemented
311#897C2×D312yescomplemented
312#896—34no—
313#895—34no—
314#895C2×D312yescomplemented
315#895C2×D312yescomplemented
316#895C2×D312yescomplemented
317#895C2×D312yescomplemented
318#895C2×D312yescomplemented
319#895C2×D312yescomplemented
320#894—34no—
321#893—34no—
322#893—32no—
323#893—32no—
324#893—62no—
325#892—32no—
326#892—32no—
327#892—62no—
328D3×C4⋊C4—32no—
329D3×C4⋊C4—32no—
330D3×C4⋊C4—62no—
331#887—32no—
332#887—32no—
333#887—62no—
334#885—34no—
335#885—34no—
336#884—34no—
337#884—34no—
338#884—34no—
339#884—34no—
340#884—34no—
341#883—34no—
342#882—34no—
343#882—34no—
344#882—34no—
345#67⋊C4—34no—
346#67⋊C4—34no—
347D3×C22⋊C4—34no—
348D3×C22⋊C4—34no—
349#878—34no—
350C23×C32C2411yescharacteristic
351C22×C3⋊D3C2412yes—
352C22×C3×D3—22no—
353C22×C3×D3—24no—
354C22×C3×D3—22no—
355C22×C3×D3—41no—
356C22×C3×D3—42no—
357C22×C3×D3—42no—
358C22×C3×D3C2412yes—
359C22×C3×D3C2414yes—
360C22×C3×D3C2412yes—
361C22×C3×D3C2411yescharacteristic
362C22×C3×D3C2411yescharacteristic
363C2×D32—24no—
364C2×D32—24no—
365C2×D32—28no—
366C2×D32—42no—
367C2×D32—44no—
368C2×D32—44no—
369C2×C32×C4—42no—
370C2×C32×C4C2×D414yescomplemented
371C2×C32×C4C2414yes—
372C2×C32×C4C2411yescharacteristic
373C2×C32×C4C2411yescharacteristic
374#638C2×D418yescomplemented
375C2×C3⋊Dic3C2412yes—
376C2×C3⋊Dic3C2412yes—
377C2×C3⋊Dic3C2412yes—
378C4⋊(C3⋊D3)C2×D414yescomplemented
379C4×C3⋊D3—44no—
380C4×C3⋊D3C2×D418yescomplemented
381#634C2×D414yescomplemented
382C3×#67—24no—
383C3×#67—24no—
384C2×C3×Dic3—22no—
385C2×C3×Dic3C2412yes—
386C2×C3×Dic3C2412yes—
387C2×C3×Dic3C2411yescharacteristic
388C2×C3×Dic3C2411yescharacteristic
389C3×D12—28no—
390C3×D12—24no—
391C3×D12—22no—
392C3×D12—24no—
393C3×D12—22no—
394C3×D12—44no—
395C3×D12—44no—
396C3×C4×D3—22no—
397C3×C4×D3—22no—
398C3×C4×D3—24no—
399C3×C4×D3—22no—
400C3×C4×D3—24no—
401C3×C4×D3—22no—
402C3×Dic6—22no—
403C3×Dic6—22no—
404#627—24no—
405#626—28no—
406#626—24no—
407#626—24no—
408#625—24no—
409#625—24no—
410#625—28no—
411#625—44no—
412#625—44no—
413#625—42no—
414#624—24no—
415D3×Dic3—24no—
416D3×Dic3—28no—
417D3×Dic3—24no—
418C2×H(5,𝔽2)—91no—
419C22×#41—91no—
420#550—92no—
421#548—92no—
422#546—94no—
423#546—92no—
424D42—92no—
425D42—94no—
426#537—31no—
427#537—92no—
428#535—92no—
429#535—91no—
430#525—92no—
431#525—91no—
432C2×#121—31no—
433C2×#121—92no—
434#520—91no—
435C24×C3—31no—
436C24×C3—32no—
437C23×D3—32no—
438C23×D3—32no—
439C23×D3—34no—
440C23×D3—34no—
441C23×D3C22×D311yescharacteristic
442C23×D3C22×D312yes—
443C3×#41—64no—
444C3×#41—64no—
445C2×C3×Q8—31no—
446C2×C3×Q8—31no—
447C2×C3×D4—32no—
448C2×C3×D4—32no—
449C2×C3×D4—34no—
450C2×C3×D4—32no—
451C2×C3×D4—31no—
452C2×C3×D4—32no—
453C2×C3×D4—31no—
454C2×C3×D4—34no—
455C2×C3×D4—34no—
456C2×C3×D4—64no—
457C2×C3×D4—124no—
458C22×C3×C4—21no—
459C22×C3×C4—22no—
460C22×C3×C4—31no—
461C22×C3×C4—31no—
462C22×C3×C4—31no—
463C22×C3×C4—31no—
464C22×C3×C4—31no—
465C22×C3×C4—32no—
466C22×C3×C4—32no—
467C22×C3×C4—64no—
468C22×C3×C4C22×D312yes—
469C22×C3×C4C22×D312yes—
470C22×C3×C4C22×D311yescharacteristic
471C22×C3×C4C22×D311yescharacteristic
472C2×#67—32no—
473C2×#67—32no—
474C2×#67—32no—
475C2×#67—32no—
476C2×#67—34no—
477C2×#67—34no—
478C2×#67—32no—
479C2×#67—32no—
480C2×#67—34no—
481C2×#67—34no—
482C2×#67—32no—
483C2×#67—34no—
484C2×#67—34no—
485C2×#67—32no—
486C2×#67—34no—
487C2×#67—32no—
488C2×#67—32no—
489C2×#67—62no—
490C2×#67—68no—
491C2×#67—616no—
492C2×#67C22×D312yes—
493C2×#67C22×D312yes—
494C22×Dic3—34no—
495C22×Dic3—32no—
496C22×Dic3—32no—
497C22×Dic3C22×D311yescharacteristic
498#239—64no—
499#239—68no—
500D3×Q8—64no—
501#237—68no—
502#237—68no—
503#237—64no—
504#237—68no—
505D3×D4—68no—
506D3×D4—64no—
507D3×D4—68no—
508D3×D4—68no—
509D3×D4—68no—
510D3×D4—616no—
511D3×D4—128no—
512D3×D4—128no—
513#235—24no—
514#235—24no—
515#235—38no—
516#235—38no—
517#235—68no—
518#235—64no—
519#235—64no—
520#235—68no—
521#235—68no—
522#235—68no—
523#235—68no—
524C2×D12—24no—
525C2×D12—31no—
526C2×D12—31no—
527C2×D12—32no—
528C2×D12—32no—
529C2×D12—34no—
530C2×D12—44no—
531C2×D12—61no—
532C2×D12—64no—
533C2×D12—68no—
534C2×D12C22×D314yes—
535C2×D12C22×D312yes—
536C2×D12C22×D311yescharacteristic
537C2×D12C22×D311yescharacteristic
538C2×D12C22×D312yes—
539C2×D12C22×D314yes—
540C2×D12C22×D314yes—
541C2×C4×D3—24no—
542C2×C4×D3—32no—
543C2×C4×D3—32no—
544C2×C4×D3—32no—
545C2×C4×D3—34no—
546C2×C4×D3—32no—
547C2×C4×D3—32no—
548C2×C4×D3—32no—
549C2×C4×D3—34no—
550C2×C4×D3—34no—
551C2×C4×D3—62no—
552C2×C4×D3—64no—
553C2×C4×D3—68no—
554C2×C4×D3—68no—
555C2×C4×D3C22×D311yescharacteristic
556C2×C4×D3C22×D311yescharacteristic
557C2×C4×D3C22×D311yescharacteristic
558C2×C4×D3C22×D311yescharacteristic
559C2×C4×D3C22×D312yes—
560C2×C4×D3C22×D312yes—
561C2×Dic6—31no—
562C2×Dic6—31no—
563C2×Dic6—32no—
564C2×Dic6—32no—
565C2×Dic6—61no—
566C2×Dic6—64no—
567C2×Dic6C22×D311yescharacteristic
568C2×Dic6C22×D311yescharacteristic
569C3×C4⋊C4—22no—
570C3×C4⋊C4—22no—
571C3×C4⋊C4—34no—
572C3×C4⋊C4C22×D312yes—
573C3×C4⋊C4C22×D312yes—
574C3×C4⋊C4C22×D312yes—
575C3×C4⋊C4C22×D312yes—
576C3×C22⋊C4—34no—
577C3×C22⋊C4—34no—
578C3×C22⋊C4—34no—
579C3×C22⋊C4—34no—
580#217—32no—
581#217—32no—
582#217—34no—
583#217—32no—
584#217—34no—
585#217—32no—
586#217—32no—
587#217—32no—
588#217—62no—
589(C2×D3)⋊C4—32no—
590(C2×D3)⋊C4—34no—
591(C2×D3)⋊C4—32no—
592(C2×D3)⋊C4—32no—
593(C2×D3)⋊C4—34no—
594(C2×D3)⋊C4—32no—
595(C2×D3)⋊C4—34no—
596(C2×D3)⋊C4—34no—
597(C2×D3)⋊C4—64no—
598(C2×D3)⋊C4C22×D314yes—
599(C2×D3)⋊C4C22×D314yes—
600(C2×D3)⋊C4C22×D314yes—
601(C2×D3)⋊C4C22×D314yes—
602C4⋊Dic3—31no—
603C4⋊Dic3—31no—
604C4⋊Dic3—31no—
605C4⋊Dic3—31no—
606C4⋊Dic3—61no—
607C4⋊Dic3—61no—
608C4⋊Dic3C22×D314yes—
609Dic3⋊C4—34no—
610Dic3⋊C4—34no—
611Dic3⋊C4—32no—
612Dic3⋊C4—32no—
613Dic3⋊C4—32no—
614Dic3⋊C4—32no—
615Dic3⋊C4—64no—
616C4×Dic3—34no—
617C4×Dic3—34no—
618C4×Dic3—32no—
619C4×Dic3—32no—
620C4×Dic3—64no—
621C4×Dic3—62no—
622C22×C32—21no—
623C22×C32—21no—
624C22×C32C22×D412yes—
625C22×C32C2511yescharacteristic
626C2×C3⋊D3—22no—
627C2×C3⋊D3—22no—
628C2×C3⋊D3C22×D414yes—
629C2×C3×D3—21no—
630C2×C3×D3—21no—
631C2×C3×D3—22no—
632C2×C3×D3—24no—
633C2×C3×D3—21no—
634C2×C3×D3—22no—
635C2×C3×D3—22no—
636C2×C3×D3—22no—
637C2×C3×D3—24no—
638C2×C3×D3—21no—
639C2×C3×D3—22no—
640C2×C3×D3—21no—
641C2×C3×D3—22no—
642C2×C3×D3—24no—
643C2×C3×D3—44no—
644C2×C3×D3—84no—
645C2×C3×D3H(5,𝔽2)12yescomplemented
646D32—48no—
647D32—88no—
648C32×C4—24no—
649C32×C4C22×D412yes—
650C32×C4C22×D412yes—
651C3⋊Dic3—22no—
652C3⋊Dic3—22no—
653C3⋊Dic3C22×D414yes—
654C3×Dic3—21no—
655C3×Dic3—22no—
656C3×Dic3—22no—
657C3×Dic3—21no—
658H(5,𝔽2)—188no—
659C2×#41—31no—
660C2×#41—31no—
661C2×#41—92no—
662C2×#41—92no—
663C2×#41—92no—
664C2×#41—91no—
665C2×#41—91no—
666C2×#41—92no—
667C2×#41—91no—
668C2×#41—188no—
669C22×Q8—91no—
670C22×D4—31no—
671C22×D4—32no—
672C22×D4—91no—
673C22×D4—92no—
674C22×D4—92no—
675C22×D4—94no—
676C22×D4—92no—
677C22×D4—94no—
678C23×C4—31no—
679C23×C4—92no—
680#127—92no—
681#127—94no—
682#124—94no—
683#124—92no—
684#123—94no—
685#123—92no—
686C22⋊Q8—32no—
687C22⋊Q8—32no—
688C22⋊Q8—94no—
689C22⋊Q8—91no—
690C22⋊Q8—91no—
691#121—34no—
692#121—32no—
693#121—32no—
694#121—32no—
695#121—32no—
696#121—32no—
697#121—32no—
698#121—94no—
699#121—94no—
700#121—94no—
701#121—94no—
702#121—94no—
703#121—91no—
704#121—92no—
705#121—91no—
706#121—92no—
707#120—94no—
708#120—94no—
709#120—94no—
710#120—92no—
711#120—94no—
712C4×Q8—92no—
713C4×D4—94no—
714C4×D4—94no—
715C4×D4—92no—
716C4×D4—92no—
717C4×D4—94no—
718C4×D4—92no—
719#117—91no—
720#117—92no—
721C2×C4⋊C4—92no—
722C2×C4⋊C4D3211yescharacteristic, complemented
723C2×C22⋊C4—32no—
724C2×C22⋊C4—94no—
725C23×C3—21no—
726C23×C3—31no—
727C23×C3—34no—
728C23×C3—32no—
729C23×C3—31no—
730C23×C3—32no—
731C23×C3—62no—
732C23×C3—62no—
733C23×C3—64no—
734C23×C3—121no—
735C23×C3—122no—
736C23×C3—122no—
737C23×C3C23×D311yescharacteristic
738C23×C3C23×D311yescharacteristic
739C22×D3—22no—
740C22×D3—24no—
741C22×D3—22no—
742C22×D3—32no—
743C22×D3—32no—
744C22×D3—41no—
745C22×D3—42no—
746C22×D3—42no—
747C22×D3—62no—
748C22×D3—64no—
749C22×D3—64no—
750C22×D3—68no—
751C22×D3—68no—
752C22×D3—64no—
753C22×D3—64no—
754C22×D3—122no—
755C22×D3—122no—
756C22×D3—124no—
757C22×D3—124no—
758C22×D3—124no—
759C22×D3—124no—
760C22×D3C23×D314yes—
761C22×D3C23×D312yes—
762C22×D3C23×D311yescharacteristic
763C22×D3C23×D312yes—
764C22×D3C23×D311yescharacteristic
765C3×Q8—62no—
766C3×Q8—62no—
767C3×D4—68no—
768C3×D4—64no—
769C3×D4—64no—
770C3×D4—62no—
771C3×D4—64no—
772C3×D4—64no—
773C3×D4—62no—
774C3×D4—124no—
775C3×D4—124no—
776C2×C3×C4—21no—
777C2×C3×C4—21no—
778C2×C3×C4—24no—
779C2×C3×C4—24no—
780C2×C3×C4—31no—
781C2×C3×C4—31no—
782C2×C3×C4—32no—
783C2×C3×C4—32no—
784C2×C3×C4—42no—
785C2×C3×C4—42no—
786C2×C3×C4—62no—
787C2×C3×C4—62no—
788C2×C3×C4—62no—
789C2×C3×C4—64no—
790C2×C3×C4—64no—
791C2×C3×C4—62no—
792C2×C3×C4—62no—
793C2×C3×C4—82no—
794C2×C3×C4D3×D414yescomplemented
795C2×C3×C4D3×D414yescomplemented
796C2×C3×C4C23×D314yes—
797C2×C3×C4C23×D314yes—
798C2×C3×C4C23×D311yescharacteristic
799C2×C3×C4C23×D311yescharacteristic
800C2×C3×C4C23×D311yescharacteristic
801C2×C3×C4C23×D311yescharacteristic
802#67—24no—
803#67—24no—
804#67—38no—
805#67—38no—
806#67—68no—
807#67—64no—
808#67—64no—
809#67—68no—
810#67—64no—
811#67—68no—
812#67—64no—
813#67—68no—
814#67—64no—
815#67—64no—
816#67—124no—
817#67—124no—
818#67—122no—
819#67—124no—
820#67—124no—
821#67—122no—
822C2×Dic3—22no—
823C2×Dic3—32no—
824C2×Dic3—32no—
825C2×Dic3—32no—
826C2×Dic3—32no—
827C2×Dic3—32no—
828C2×Dic3—32no—
829C2×Dic3—62no—
830C2×Dic3—62no—
831C2×Dic3—62no—
832C2×Dic3—64no—
833C2×Dic3—64no—
834C2×Dic3—68no—
835C2×Dic3C23×D312yes—
836C2×Dic3C23×D311yescharacteristic
837C2×Dic3C23×D311yescharacteristic
838C2×Dic3C23×D312yes—
839D12—28no—
840D12—24no—
841D12—24no—
842D12—22no—
843D12—22no—
844D12—34no—
845D12—34no—
846D12—44no—
847D12—44no—
848D12—64no—
849D12—64no—
850D12—68no—
851D12—64no—
852C4×D3—22no—
853C4×D3—22no—
854C4×D3—22no—
855C4×D3—22no—
856C4×D3—24no—
857C4×D3—24no—
858C4×D3—38no—
859C4×D3—38no—
860C4×D3—68no—
861C4×D3—64no—
862C4×D3—64no—
863C4×D3—64no—
864C4×D3—64no—
865C4×D3—68no—
866C4×D3—124no—
867C4×D3—124no—
868C4×D3—244no—
869Dic6—22no—
870Dic6—22no—
871Dic6—34no—
872Dic6—34no—
873Dic6—64no—
874Dic6—64no—
875Dic6—64no—
876C2×C32—22no—
877C2×C32C23×D411yescharacteristic
878C2×C32C2×H(5,𝔽2)11yescharacteristic
879C2×C32#58511yescharacteristic
880C3⋊D3—24no—
881C3×D3—22no—
882C3×D3—42no—
883C3×D3—42no—
884C3×D3—44no—
885C3×D3—41no—
886C24—31no—
887C24—32no—
888C24—92no—
889C24—94no—
890#41—64no—
891#41—64no—
892#41—98no—
893#41—188no—
894#41—188no—
895#41—184no—
896#41—188no—
897#41—184no—
898#41—188no—
899C2×Q8—31no—
900C2×Q8—31no—
901C2×Q8—92no—
902C2×Q8—91no—
903C2×Q8—184no—
904C2×D4—32no—
905C2×D4—32no—
906C2×D4—34no—
907C2×D4—32no—
908C2×D4—31no—
909C2×D4—32no—
910C2×D4—31no—
911C2×D4—34no—
912C2×D4—34no—
913C2×D4—64no—
914C2×D4—92no—
915C2×D4—92no—
916C2×D4—94no—
917C2×D4—92no—
918C2×D4—92no—
919C2×D4—94no—
920C2×D4—92no—
921C2×D4—92no—
922C2×D4—94no—
923C2×D4—94no—
924C2×D4—91no—
925C2×D4—124no—
926C2×D4—184no—
927C2×D4—188no—
928C2×D4—188no—
929C2×D4—188no—
930C2×D4—1816no—
931C2×D4—368no—
932C22×C4—31no—
933C22×C4—31no—
934C22×C4—31no—
935C22×C4—32no—
936C22×C4—31no—
937C22×C4—31no—
938C22×C4—32no—
939C22×C4—64no—
940C22×C4—92no—
941C22×C4—92no—
942C22×C4—92no—
943C22×C4—94no—
944C22×C4—92no—
945C22×C4—94no—
946C22×C4—188no—
947C22×C4C2×D3212yes—
948C22×C4C2×D3211yescharacteristic
949C4⋊C4—34no—
950C4⋊C4—92no—
951C4⋊C4—92no—
952C4⋊C4—91no—
953C4⋊C4—94no—
954C4⋊C4—91no—
955C4⋊C4C2×D3212yes—
956C4⋊C4C2×D3212yes—
957C22⋊C4—34no—
958C22⋊C4—34no—
959C22⋊C4—34no—
960C22⋊C4—34no—
961C22⋊C4—92no—
962C22⋊C4—94no—
963C22⋊C4—92no—
964C22⋊C4—92no—
965C22⋊C4—94no—
966C22⋊C4—92no—
967C22⋊C4—92no—
968C22⋊C4—94no—
969C42—94no—
970C42—92no—
971C22×C3—21no—
972C22×C3—21no—
973C22×C3—21no—
974C22×C3—21no—
975C22×C3—22no—
976C22×C3—21no—
977C22×C3—32no—
978C22×C3—41no—
979C22×C3—41no—
980C22×C3—61no—
981C22×C3—61no—
982C22×C3—62no—
983C22×C3—64no—
984C22×C3—61no—
985C22×C3—62no—
986C22×C3—62no—
987C22×C3—62no—
988C22×C3—62no—
989C22×C3—62no—
990C22×C3—64no—
991C22×C3—61no—
992C22×C3—61no—
993C22×C3—64no—
994C22×C3—124no—
995C22×C3—244no—
996C22×C3C2×D3×D412yes—
997C22×C3C2×D3×D412yes—
998C22×C3C24×D311yescharacteristic
999C22×C3C24×D311yescharacteristic
1000C2×D3—21no—
1001C2×D3—21no—
1002C2×D3—21no—
1003C2×D3—22no—
1004C2×D3—22no—
1005C2×D3—24no—
1006C2×D3—24no—
1007C2×D3—21no—
1008C2×D3—21no—
1009C2×D3—24no—
1010C2×D3—22no—
1011C2×D3—22no—
1012C2×D3—22no—
1013C2×D3—22no—
1014C2×D3—34no—
1015C2×D3—34no—
1016C2×D3—44no—
1017C2×D3—64no—
1018C2×D3—62no—
1019C2×D3—62no—
1020C2×D3—62no—
1021C2×D3—62no—
1022C2×D3—84no—
1023C2×D3—122no—
1024C2×D3—122no—
1025C2×D3—128no—
1026C2×D3—128no—
1027C2×D3—248no—
1028C2×D3—248no—
1029C2×D3#100412yescomplemented
1030C3×C4—24no—
1031C3×C4—24no—
1032C3×C4—22no—
1033C3×C4—22no—
1034C3×C4—44no—
1035C3×C4—61no—
1036C3×C4—62no—
1037C3×C4—61no—
1038C3×C4—62no—
1039C3×C4C2×D3×D412yes—
1040C3×C4C2×D3×D412yes—
1041C3×C4C2×D3×D412yes—
1042C3×C4C2×D3×D412yes—
1043Dic3—22no—
1044Dic3—22no—
1045Dic3—21no—
1046Dic3—21no—
1047Dic3—34no—
1048Dic3—34no—
1049Dic3—64no—
1050Dic3—62no—
1051Dic3—62no—
1052Dic3—62no—
1053Dic3—62no—
1054Dic3—122no—
1055Dic3—122no—
1056C32#348811yescharacteristic, complemented, Sylow
1057C23—31no—
1058C23—32no—
1059C23—34no—
1060C23—32no—
1061C23—31no—
1062C23—62no—
1063C23—62no—
1064C23—64no—
1065C23—92no—
1066C23—121no—
1067C23—122no—
1068C23—122no—
1069C23—184no—
1070C23—184no—
1071C23—188no—
1072C23—362no—
1073C23—364no—
1074C23—364no—
1075C23C22×D3211yescharacteristic
1076Q8—62no—
1077Q8—62no—
1078Q8—94no—
1079Q8—184no—
1080D4—68no—
1081D4—64no—
1082D4—64no—
1083D4—64no—
1084D4—64no—
1085D4—62no—
1086D4—62no—
1087D4—98no—
1088D4—94no—
1089D4—124no—
1090D4—124no—
1091D4—188no—
1092D4—184no—
1093D4—184no—
1094D4—188no—
1095D4—184no—
1096D4—184no—
1097D4—364no—
1098D4—362no—
1099D4—364no—
1100C2×C4—31no—
1101C2×C4—31no—
1102C2×C4—32no—
1103C2×C4—32no—
1104C2×C4—42no—
1105C2×C4—62no—
1106C2×C4—62no—
1107C2×C4—62no—
1108C2×C4—62no—
1109C2×C4—62no—
1110C2×C4—64no—
1111C2×C4—64no—
1112C2×C4—92no—
1113C2×C4—98no—
1114C2×C4—92no—
1115C2×C4—92no—
1116C2×C4—184no—
1117C2×C4—184no—
1118C2×C4—184no—
1119C2×C4—188no—
1120C2×C4—364no—
1121C2×C4#380214yescomplemented
1122C2×C4C22×D3214yes—
1123C2×C4C22×D3211yescharacteristic
1124C2×C4C22×D3211yescharacteristic
1125C2×C3—22no—
1126C2×C3—22no—
1127C2×C3—21no—
1128C2×C3—21no—
1129C2×C3—21no—
1130C2×C3—42no—
1131C2×C3—62no—
1132C2×C3—124no—
1133C2×C3—121no—
1134C2×C3—122no—
1135C2×C3—122no—
1136C2×C3C22×D3×D411yescharacteristic
1137C2×C3C22×D3×D411yescharacteristic
1138C2×C3C2×#100411yescharacteristic
1139C2×C3#596411yescharacteristic
1140C2×C3D3×H(5,𝔽2)11yescharacteristic
1141C2×C3#596811yescharacteristic
1142D3—22no—
1143D3—42no—
1144D3—42no—
1145D3—41no—
1146D3—44no—
1147D3—64no—
1148D3—64no—
1149D3—124no—
1150C22—21no—
1151C22—21no—
1152C22—32no—
1153C22—61no—
1154C22—61no—
1155C22—61no—
1156C22—62no—
1157C22—62no—
1158C22—64no—
1159C22—64no—
1160C22—61no—
1161C22—62no—
1162C22—62no—
1163C22—61no—
1164C22—62no—
1165C22—64no—
1166C22—62no—
1167C22—94no—
1168C22—124no—
1169C22—182no—
1170C22—182no—
1171C22—244no—
1172C22—368no—
1173C22—728no—
1174C22C2×#380212yes—
1175C22C23×D3211yescharacteristic
1176C4—24no—
1177C4—61no—
1178C4—61no—
1179C4—62no—
1180C4—62no—
1181C4—94no—
1182C4—182no—
1183C4—182no—
1184C4C2×#380212yes—
1185C4C2×#380212yes—
1186C3—21no—
1187C3#8594911yescharacteristic, complemented
1188C3#8637911yescharacteristic, complemented
1189C2—22no—
1190C2—62no—
1191C2—121no—
1192C2—124no—
1193C2—122no—
1194C2—122no—
1195C2—184no—
1196C2C22×#380211yescharacteristic
1197C2D3×#100411yescharacteristic
1198C2#1059668811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C4⋊C4C22
hypercenterC2×C4⋊C4D32
hypocenterC32#3488
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64307C2semidirect
2. C2×D3×#235C2semidirect
3. #10595975C2semidirect
4. C3×#5510C2semidirect
5. C2×C3×#895C2semidirect
6. #10595083C2semidirect
7. #10595069C2semidirect
8. #10595040C2semidirect
9. #10595022C2semidirect
10. #10594634C2semidirect
11. #10594633C2semidirect
12. #10594632C2semidirect
13. #10594618C2semidirect
14. #10594612C2semidirect
15. #10594528C2semidirect
16. #10594527C2semidirect
17. #10594525C2semidirect
21. C2×C3×#235C22semidirect
22. C2×C3×#235C22semidirect
23. C22×C3×D12C22semidirect
24. C22×C3×D12C22semidirect
25. C22×C3×C4×D3C22semidirect
26. C2×D3×#67C22semidirect
27. C2×D3×#67C22semidirect
28. C2×#3804C22semidirect
31. C2×#3802C22semidirect
32. C2×#3802C22semidirect
33. C2×D3×D12C22semidirect
34. C2×D3×D12C22semidirect
35. C2×C4×D32C22semidirect
36. C2×#3799C22semidirect
37. C2×#3798C22semidirect
38. C2×#3796C22semidirect
39. C2×#3795C22semidirect
40. C2×#3795C22semidirect
41. C2×D3×Dic6C22semidirect
42. C2×C32×C4⋊C4C22semidirect
43. C4×#638C22semidirect
44. #64135C22semidirect
45. #64102C22semidirect
46. #64101C22semidirect
47. C4⋊C4×C3⋊D3C22semidirect
48. #64096C22semidirect
49. C3×#930C22semidirect
50. C2×C3×(C2×D3)⋊C4C22semidirect
51. C3×#897C22semidirect
52. C3×#897C22semidirect
53. C3×#895C22semidirect
54. C3×#895C22semidirect
55. C3×#895C22semidirect
56. C3×#895C22semidirect
57. C3×#895C22semidirect
58. C3×#895C22semidirect
59. #63976C22semidirect
60. #63976C22semidirect
61. #63961C22semidirect
62. #63922C22semidirect
63. #63922C22semidirect
64. #63922C22semidirect
65. #63921C22semidirect
66. #63916C22semidirect
67. #63915C22semidirect
68. #63914C22semidirect
69. #63914C22semidirect
70. #63912C22semidirect
71. #63908C22semidirect
72. #63908C22semidirect
73. #63908C22semidirect
74. #63908C22semidirect
75. #63902C22semidirect
76. C4×#625C22semidirect
77. C4×#625C22semidirect
78. #63899C22semidirect
79. #63898C22semidirect
80. #63885C22semidirect
81. #63885C22semidirect
82. #63885C22semidirect
83. #63863C22semidirect
84. #63856C22semidirect
85. #63856C22semidirect
86. #63854C22semidirect
116. #5510D3semidirect
117. C2×#895D3semidirect
129. #3828D4semidirect
243. C2×#235C2×D3semidirect
244. C2×#235C2×D3semidirect
247. C22×D12C2×D3semidirect
248. C22×D12C2×D3semidirect
251. C22×C4×D3C2×D3semidirect
263. C2×C3×C4⋊C4C2×D3semidirect
264. C2×C3×C4⋊C4C2×D3semidirect
295. #930C2×D3semidirect
304. C2×(C2×D3)⋊C4C2×D3semidirect
310. #897C2×D3semidirect
311. #897C2×D3semidirect
314. #895C2×D3semidirect
315. #895C2×D3semidirect
316. #895C2×D3semidirect
317. #895C2×D3semidirect
318. #895C2×D3semidirect
319. #895C2×D3semidirect
370. C2×C32×C4C2×D4semidirect
374. #638C2×D4semidirect
378. C4⋊(C3⋊D3)C2×D4semidirect
380. C4×C3⋊D3C2×D4semidirect
381. #634C2×D4semidirect
645. C2×C3×D3H(5,𝔽2)semidirect
722. C2×C4⋊C4D32semidirect
794. C2×C3×C4D3×D4semidirect
795. C2×C3×C4D3×D4semidirect
1029. C2×D3#1004semidirect
1056. C32#3488semidirect
1121. C2×C4#3802semidirect
1187. C3#85949semidirect
1188. C3#86379semidirect

Maximal subgroups

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

subgroupindex
C2×#643072
C2×D3×#2352
#105959752
C3×#55102
C2×C3×#8952
#105950832
#105950692
#105950402
#105950222
#105946342
#105946332
#105946322
#105946182
#105946122
#105945282
#105945272
#105945252
#863793
#859493