Finite Group Databasebeta

← #11904650

Subgroups — #11904650

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#10595994C211yesmaximal, characteristic, complemented
4C3×#5525C211yesmaximal, characteristic, complemented
5C3×#5524C211yesmaximal, characteristic, complemented
6#10595044C211yesmaximal, characteristic, complemented
7C2×#63908C211yesmaximal, characteristic, complemented
8#10594634C212yesmaximal, complemented
9#10594632C212yesmaximal, complemented
10#10594612C212yesmaximal, complemented
11#10594528C212yesmaximal, complemented
12#10594294C214yesmaximal, complemented
13#10594271C214yesmaximal, complemented
14#10594007C212yesmaximal, complemented
15#10594004C212yesmaximal, complemented
16#10593906C212yesmaximal, complemented
17#10593905C212yesmaximal, complemented
18#86331—31nomaximal
19#86041—31nomaximal
20C2×#3828C2211yescharacteristic
21C2×C3×#235C2211yescharacteristic, complemented
22C2×C3×#235C2211yescharacteristic, complemented
23C22×C3×D12C2211yescharacteristic, complemented
24C22×C3×C4×D3C2211yescharacteristic, complemented
25C2×D3×#67C2212yescomplemented
26C2×D3×#67C2214yescomplemented
27C22×#625C2212yescomplemented
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
42C32×#117C2211yescharacteristic, complemented
43C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
44#64101C2212yescomplemented
45C4⋊C4×C3⋊D3C2212yescomplemented
46#64090C2214yescomplemented
47C4×C4⋊(C3⋊D3)C2212yescomplemented
48C4×#634C2212yescomplemented
49C3×#897C2211yescharacteristic, complemented
50C3×#897C2211yescharacteristic, complemented
51C3×#895C2211yescharacteristic, complemented
52C3×#895C2211yescharacteristic, complemented
53C3×#895C2212yescomplemented
54C3×#895C2212yescomplemented
55C3×#886C2212yescomplemented
56C3×#882C2212yescomplemented
57C3×#882C2214yescomplemented
58C3×#875C2212yescomplemented
59C3×#874C2212yescomplemented
60C3×C4×D12C2212yescomplemented
61C3×C4×D12C2212yescomplemented
62#63980C2214yescomplemented
63C2×(C2×D3)⋊Dic3C2212yescomplemented
64#63922C2214yescomplemented
65#63922C2214yescomplemented
66#63922C2214yescomplemented
67#63921C2214yescomplemented
68#63916C2214yescomplemented
69#63915C2214yescomplemented
70#63914C2214yescomplemented
71#63912C2214yescomplemented
72#63908C2212yescomplemented
73#63908C2212yescomplemented
74#63908C2212yescomplemented
75#63908C2212yescomplemented
76#63908C2212yescomplemented
77#63908C2212yescomplemented
78#63902C2214yescomplemented
79#63899C2214yescomplemented
80#63898C2214yescomplemented
81#63885C2214yescomplemented
82#63885C2214yescomplemented
83#63885C2214yescomplemented
84#63856C2212yescomplemented
85#63856C2212yescomplemented
86#63854C2214yescomplemented
87C2×#1009—31no—
88C2×D3×#41—31no—
89C2×#1004—31no—
90C22×#235—31no—
91C3×#535—31no—
92C3×#525—31no—
93#5833—31no—
94#5833—31no—
95C2×#938—31no—
96C2×#930—31no—
97#5718—32no—
98#5717—32no—
99#5677—32no—
100#5676—32no—
101#5654—34no—
102#5629—32no—
103#5627—32no—
104#5608—32no—
105#5607—32no—
106#5607—32no—
107#5606—32no—
108D3×#121—32no—
109D3×#121—32no—
110#5591—34no—
111#5590—34no—
112#5590—34no—
113#5553—32no—
114#5552—32no—
115#5550—32no—
116D4×D12—32no—
117#5525D311yescharacteristic, complemented
118#5524D311yescharacteristic, complemented
119#5523—31no—
120#5523—31no—
121#5523—61no—
122C23×C3×D3C2311yescharacteristic
123C23×C3×D3C2312yes—
124C22×D32C2312yes—
125C22×D32C2314yes—
126C22×C32×C4C2311yescharacteristic
127C2×#638C2312yes—
128C22×C3⋊Dic3C2312yes—
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×D12C2312yes—
141C2×C3×D12C2312yes—
142C2×C3×D12C2311yescharacteristic
143C2×C3×D12C2312yes—
144C2×C3×D12C2311yescharacteristic
145C2×C3×D12C2314yes—
146C2×C3×D12C2314yes—
147C2×C3×D12C2312yes—
148C2×C3×C4×D3—24no—
149C2×C3×C4×D3C2312yes—
150C2×C3×C4×D3C2311yescharacteristic
151C2×C3×C4×D3C2311yescharacteristic
152C2×C3×C4×D3C2311yescharacteristic
153C2×C3×C4×D3C2311yescharacteristic
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×#625—44no—
164C2×#625C2312yes—
165C2×#625C2314yes—
166C2×#625C2314yes—
167C2×#625C2314yes—
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⋊C4C2311yescharacteristic
186C32×C4⋊C4C2311yescharacteristic
187C32×C22⋊C4C2312yes—
188C32×C42C2312yes—
189#3752C2314yes—
190C4⋊(C3⋊Dic3)C2312yes—
191C4⋊(C3⋊Dic3)C2312yes—
192#3750C2314yes—
193C4×C3⋊Dic3C2314yes—
194C3×(C2×D3)⋊C4C2314yes—
195C3×(C2×D3)⋊C4C2314yes—
196C3×(C2×D3)⋊C4C2312yes—
197C3×(C2×D3)⋊C4C2312yes—
198C3×(C2×D3)⋊C4C2312yes—
199C3×(C2×D3)⋊C4C2312yes—
200C3×C4⋊Dic3C2312yes—
201C3×C4⋊Dic3C2312yes—
202#3724C2314yes—
203(C2×D3)⋊Dic3C2314yes—
204(C2×D3)⋊Dic3C2314yes—
205(C2×D3)⋊Dic3C2314yes—
206(C2×D3)⋊Dic3C2314yes—
207#3488—91noSylow
208C2×C3×#41—31no—
209C2×C3×#41—31no—
210C22×C3×D4—31no—
211C23×C3×C4—31no—
212C22×#67—32no—
213C22×#67—32no—
214C22×#67—32no—
215C22×#67—34no—
216#1009—68no—
217D3×#41—68no—
218C2×#239—32no—
219C2×#239—31no—
220C2×D3×Q8—31no—
221#1004—68no—
222C2×#237—32no—
223C2×#237—32no—
224C2×#237—31no—
225C2×#237—32no—
226C2×D3×D4—34no—
227C2×D3×D4—32no—
228C2×D3×D4—32no—
229C2×D3×D4—32no—
230C2×D3×D4—34no—
231C2×D3×D4—34no—
232C2×D3×D4—32no—
233C2×D3×D4—31no—
234C2×#235—31no—
235C2×#235—31no—
236C2×#235—32no—
237C2×#235—31no—
238C2×#235—32no—
239C2×#235—32no—
240C2×#235—32no—
241C2×#235—31no—
242C2×#235—61no—
243C2×#235—68no—
244C2×#235C2×D311yescharacteristic, complemented
245C2×#235C2×D311yescharacteristic, complemented
246C22×D12—31no—
247C22×D12—32no—
248C22×D12C2×D311yescharacteristic, complemented
249C22×C4×D3—32no—
250C22×C4×D3—32no—
251C22×C4×D3C2×D311yescharacteristic, complemented
252C22×Dic6—31no—
253C3×#127—32no—
254C3×#124—32no—
255C3×#123—32no—
256C3×C22⋊Q8—31no—
257C3×C22⋊Q8—31no—
258C3×#121—31no—
259C3×#121—31no—
260C3×#121—32no—
261C3×#121—32no—
262C3×#120—32no—
263C3×#120—34no—
264C3×C4×D4—32no—
265C3×C4×D4—32no—
266C3×#117—21no—
267C3×#117C2×D311yescharacteristic, complemented
268C3×#117C2×D311yescharacteristic, complemented
269C2×#217—32no—
270#946—32no—
271#946—32no—
272#940—34no—
273#940—34no—
274#939—34no—
275#939—34no—
276#939—34no—
277#939—34no—
278#939—34no—
279#938—32no—
280#938—32no—
281#938—32no—
282#938—32no—
283#938—32no—
284#938—32no—
285#938—34no—
286#937—34no—
287#937—34no—
288#937—34no—
289D4×Dic3—34no—
290#930—32no—
291#930—32no—
292#930—32no—
293#930—32no—
294#930—32no—
295#930—32no—
296C2×(C2×D3)⋊C4—32no—
297C2×C4⋊Dic3—31no—
298C2×C4⋊Dic3—31no—
299C2×C4⋊Dic3—61no—
300#924—32no—
301#924—32no—
302#897C2×D311yescharacteristic, complemented
303#897C2×D311yescharacteristic, complemented
304#896—34no—
305#895—34no—
306#895C2×D311yescharacteristic, complemented
307#895C2×D311yescharacteristic, complemented
308#895C2×D312yescomplemented
309#895C2×D312yescomplemented
310#894—34no—
311#893—34no—
312#892—32no—
313#892—32no—
314#892—62no—
315D3×C4⋊C4—32no—
316D3×C4⋊C4—32no—
317D3×C4⋊C4—62no—
318#886C2×D312yescomplemented
319#885—34no—
320#885—34no—
321#884—34no—
322#884—34no—
323#884—34no—
324#884—34no—
325#884—34no—
326#883—34no—
327#882—34no—
328#882—34no—
329#882—34no—
330#882C2×D314yescomplemented
331#882C2×D312yescomplemented
332#67⋊C4—34no—
333#67⋊C4—34no—
334#67⋊C4—34no—
335#67⋊C4—34no—
336#67⋊C4—64no—
337D3×C22⋊C4—34no—
338D3×C22⋊C4—34no—
339#878—34no—
340#875C2×D312yescomplemented
341#874C2×D312yescomplemented
342C4×D12—32no—
343C4×D12—32no—
344C4×D12—62no—
345C4×D12C2×D312yescomplemented
346C4×D12C2×D312yescomplemented
347C4×Dic6—32no—
348C4×Dic6—32no—
349C4×Dic6—62no—
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×C4C2×D414yescomplemented
370C2×C32×C4C2412yes—
371C2×C32×C4C2412yes—
372C2×C32×C4C2411yescharacteristic
373C2×C32×C4C2411yescharacteristic
374#638C2×D418yescomplemented
375C2×C3⋊Dic3—42no—
376C2×C3⋊Dic3C2414yes—
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×Dic3C2411yescharacteristic
386C2×C3×Dic3C2411yescharacteristic
387C2×C3×Dic3C2412yes—
388C2×C3×Dic3C2412yes—
389C3×D12—24no—
390C3×D12—24no—
391C3×D12—22no—
392C3×D12—24no—
393C3×D12—22no—
394C3×D12—44no—
395C3×D12—44no—
396C3×D12—42no—
397C3×C4×D3—22no—
398C3×C4×D3—22no—
399C3×C4×D3—24no—
400C3×C4×D3—22no—
401C3×C4×D3—24no—
402C3×C4×D3—22no—
403C3×Dic6—22no—
404C3×Dic6—22no—
405#627—24no—
406#626—28no—
407#626—24no—
408#626—24no—
409#625—28no—
410#625—24no—
411#625—28no—
412#625—44no—
413#625—44no—
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—92no—
423#546—94no—
424D42—92no—
425D42—94no—
426#537—92no—
427#537—91no—
428#535—31no—
429#535—92no—
430#525—31no—
431#525—92no—
432C2×#121—92no—
433C2×#121—91no—
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—31no—
450C2×C3×D4—32no—
451C2×C3×D4—32no—
452C2×C3×D4—31no—
453C2×C3×D4—32no—
454C2×C3×D4—34no—
455C2×C3×D4—32no—
456C2×C3×D4—34no—
457C2×C3×D4—64no—
458C22×C3×C4—21no—
459C22×C3×C4—31no—
460C22×C3×C4—32no—
461C22×C3×C4—32no—
462C22×C3×C4—31no—
463C22×C3×C4—31no—
464C22×C3×C4—31no—
465C22×C3×C4—31no—
466C22×C3×C4—64no—
467C22×C3×C4C22×D311yescharacteristic
468C22×C3×C4C22×D311yescharacteristic
469C2×#67—32no—
470C2×#67—32no—
471C2×#67—34no—
472C2×#67—34no—
473C2×#67—32no—
474C2×#67—34no—
475C2×#67—34no—
476C2×#67—32no—
477C2×#67—34no—
478C2×#67—34no—
479C2×#67—34no—
480C2×#67—34no—
481C2×#67—34no—
482C2×#67—32no—
483C2×#67—32no—
484C2×#67—62no—
485C2×#67—68no—
486C2×#67—616no—
487C2×#67—124no—
488C2×#67—124no—
489C2×#67C22×D312yes—
490C2×#67C22×D312yes—
491C22×Dic3—32no—
492C22×Dic3—32no—
493C22×Dic3—34no—
494C22×Dic3—32no—
495C22×Dic3—32no—
496C22×Dic3—62no—
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—61no—
531C2×D12—64no—
532C2×D12—68no—
533C2×D12C22×D312yes—
534C2×D12C22×D311yescharacteristic
535C2×D12C22×D312yes—
536C2×D12C22×D312yes—
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×D312yes—
558C2×C4×D3C22×D312yes—
559C2×C4×D3C22×D311yescharacteristic
560C2×C4×D3C22×D311yescharacteristic
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—21no—
570C3×C4⋊C4—21no—
571C3×C4⋊C4—32no—
572C3×C4⋊C4—32no—
573C3×C4⋊C4C22×D311yescharacteristic
574C3×C4⋊C4C22×D311yescharacteristic
575C3×C4⋊C4C22×D311yescharacteristic
576C3×C4⋊C4C22×D311yescharacteristic
577C3×C22⋊C4—22no—
578C3×C22⋊C4—34no—
579C3×C22⋊C4—32no—
580C3×C22⋊C4—32no—
581C3×C22⋊C4—34no—
582C3×C22⋊C4—32no—
583C3×C22⋊C4—32no—
584C3×C22⋊C4C22×D312yes—
585C3×C22⋊C4C22×D312yes—
586C3×C42—22no—
587C3×C42C22×D312yes—
588C3×C42C22×D312yes—
589#217—34no—
590#217—34no—
591#217—34no—
592#217—34no—
593(C2×D3)⋊C4—34no—
594(C2×D3)⋊C4—34no—
595(C2×D3)⋊C4—34no—
596(C2×D3)⋊C4—34no—
597(C2×D3)⋊C4—34no—
598(C2×D3)⋊C4—34no—
599(C2×D3)⋊C4—64no—
600(C2×D3)⋊C4C22×D312yes—
601(C2×D3)⋊C4C22×D312yes—
602(C2×D3)⋊C4C22×D312yes—
603(C2×D3)⋊C4C22×D312yes—
604(C2×D3)⋊C4C22×D314yes—
605(C2×D3)⋊C4C22×D314yes—
606C4⋊Dic3—32no—
607C4⋊Dic3—32no—
608C4⋊Dic3—32no—
609C4⋊Dic3—32no—
610C4⋊Dic3—62no—
611C4⋊Dic3—62no—
612C4⋊Dic3C22×D312yes—
613C4⋊Dic3C22×D312yes—
614Dic3⋊C4—34no—
615Dic3⋊C4—34no—
616Dic3⋊C4—34no—
617Dic3⋊C4—34no—
618Dic3⋊C4—64no—
619C4×Dic3—34no—
620C4×Dic3—34no—
621C4×Dic3—64no—
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—24no—
636C2×C3×D3—21no—
637C2×C3×D3—22no—
638C2×C3×D3—22no—
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—22no—
649C32×C4—22no—
650C32×C4C22×D412yes—
651C32×C4C22×D412yes—
652C3⋊Dic3—24no—
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—91no—
672C22×D4—92no—
673C22×D4—92no—
674C22×D4—94no—
675C22×D4—92no—
676C22×D4—94no—
677C22×D4—92no—
678C23×C4—31no—
679C23×C4—92no—
680#127—32no—
681#127—94no—
682#124—32no—
683#124—94no—
684#123—32no—
685#123—94no—
686C22⋊Q8—31no—
687C22⋊Q8—31no—
688C22⋊Q8—94no—
689C22⋊Q8—92no—
690C22⋊Q8—92no—
691#121—31no—
692#121—32no—
693#121—31no—
694#121—32no—
695#121—94no—
696#121—94no—
697#121—94no—
698#121—94no—
699#121—94no—
700#121—92no—
701#121—92no—
702#121—92no—
703#121—92no—
704#121—92no—
705#121—92no—
706#121—94no—
707#120—32no—
708#120—34no—
709#120—94no—
710#120—94no—
711#120—94no—
712C4×Q8—92no—
713C4×D4—32no—
714C4×D4—32no—
715C4×D4—94no—
716C4×D4—94no—
717C4×D4—94no—
718C4×D4—92no—
719#117—92no—
720#117D3211yescharacteristic, complemented
721C2×C4⋊C4—91no—
722C2×C4⋊C4—92no—
723C2×C22⋊C4—94no—
724C2×C22⋊C4—92no—
725C23×C3—21no—
726C23×C3—31no—
727C23×C3—34no—
728C23×C3—32no—
729C23×C3—32no—
730C23×C3—31no—
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×D312yes—
763C22×D3C23×D311yescharacteristic
764C22×D3C23×D311yescharacteristic
765C3×Q8—62no—
766C3×Q8—62no—
767C3×D4—64no—
768C3×D4—64no—
769C3×D4—64no—
770C3×D4—62no—
771C3×D4—64no—
772C3×D4—64no—
773C3×D4—62no—
774C3×D4—124no—
775C3×D4—124no—
776C3×D4—122no—
777C2×C3×C4—21no—
778C2×C3×C4—21no—
779C2×C3×C4—22no—
780C2×C3×C4—22no—
781C2×C3×C4—24no—
782C2×C3×C4—32no—
783C2×C3×C4—32no—
784C2×C3×C4—31no—
785C2×C3×C4—31no—
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×C4D3×D414yescomplemented
794C2×C3×C4D3×D414yescomplemented
795C2×C3×C4C23×D312yes—
796C2×C3×C4C23×D312yes—
797C2×C3×C4C23×D312yes—
798C2×C3×C4C23×D312yes—
799C2×C3×C4C23×D311yescharacteristic
800C2×C3×C4C23×D311yescharacteristic
801C2×C3×C4C23×D311yescharacteristic
802C2×C3×C4C23×D311yescharacteristic
803#67—24no—
804#67—24no—
805#67—38no—
806#67—38no—
807#67—68no—
808#67—64no—
809#67—64no—
810#67—68no—
811#67—64no—
812#67—68no—
813#67—64no—
814#67—68no—
815#67—68no—
816#67—68no—
817#67—124no—
818#67—124no—
819#67—124no—
820#67—124no—
821C2×Dic3—22no—
822C2×Dic3—32no—
823C2×Dic3—32no—
824C2×Dic3—34no—
825C2×Dic3—34no—
826C2×Dic3—62no—
827C2×Dic3—64no—
828C2×Dic3—64no—
829C2×Dic3—64no—
830C2×Dic3—68no—
831C2×Dic3—122no—
832C2×Dic3—122no—
833C2×Dic3—242no—
834C2×Dic3C23×D312yes—
835C2×Dic3C23×D312yes—
836C2×Dic3C23×D311yescharacteristic
837C2×Dic3C23×D311yescharacteristic
838D12—24no—
839D12—24no—
840D12—24no—
841D12—22no—
842D12—22no—
843D12—34no—
844D12—34no—
845D12—42no—
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—32no—
907C2×D4—32no—
908C2×D4—31no—
909C2×D4—32no—
910C2×D4—31no—
911C2×D4—32no—
912C2×D4—34no—
913C2×D4—34no—
914C2×D4—64no—
915C2×D4—92no—
916C2×D4—92no—
917C2×D4—94no—
918C2×D4—92no—
919C2×D4—94no—
920C2×D4—94no—
921C2×D4—92no—
922C2×D4—94no—
923C2×D4—94no—
924C2×D4—91no—
925C2×D4—184no—
926C2×D4—188no—
927C2×D4—188no—
928C2×D4—188no—
929C2×D4—1816no—
930C2×D4—368no—
931C2×D4—364no—
932C22×C4—31no—
933C22×C4—31no—
934C22×C4—31no—
935C22×C4—32no—
936C22×C4—32no—
937C22×C4—31no—
938C22×C4—31no—
939C22×C4—64no—
940C22×C4—92no—
941C22×C4—92no—
942C22×C4—92no—
943C22×C4—94no—
944C22×C4—92no—
945C22×C4—92no—
946C22×C4—94no—
947C22×C4—188no—
948C22×C4C2×D3211yescharacteristic
949C4⋊C4—32no—
950C4⋊C4—32no—
951C4⋊C4—94no—
952C4⋊C4—92no—
953C4⋊C4—94no—
954C4⋊C4—92no—
955C4⋊C4C2×D3211yescharacteristic
956C4⋊C4C2×D3211yescharacteristic
957C22⋊C4—32no—
958C22⋊C4—34no—
959C22⋊C4—32no—
960C22⋊C4—32no—
961C22⋊C4—32no—
962C22⋊C4—34no—
963C22⋊C4—94no—
964C22⋊C4—94no—
965C22⋊C4—94no—
966C22⋊C4—94no—
967C22⋊C4—94no—
968C22⋊C4C2×D3212yes—
969C42—94no—
970C42C2×D3212yes—
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—64no—
987C22×C3—62no—
988C22×C3—62no—
989C22×C3—64no—
990C22×C3—61no—
991C22×C3—62no—
992C22×C3—61no—
993C22×C3—62no—
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—22no—
1007C2×D3—21no—
1008C2×D3—21no—
1009C2×D3—22no—
1010C2×D3—22no—
1011C2×D3—24no—
1012C2×D3—22no—
1013C2×D3—24no—
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#100912yescomplemented
1030C3×C4—22no—
1031C3×C4—22no—
1032C3×C4—22no—
1033C3×C4—22no—
1034C3×C4—22no—
1035C3×C4—22no—
1036C3×C4—42no—
1037C3×C4—42no—
1038C3×C4—61no—
1039C3×C4—62no—
1040C3×C4—61no—
1041C3×C4—62no—
1042C3×C4C2×D3×D412yes—
1043C3×C4C2×D3×D412yes—
1044C3×C4C2×D3×D412yes—
1045C3×C4C2×D3×D412yes—
1046Dic3—22no—
1047Dic3—22no—
1048Dic3—21no—
1049Dic3—21no—
1050Dic3—34no—
1051Dic3—34no—
1052Dic3—64no—
1053Dic3—64no—
1054Dic3—64no—
1055Dic3—124no—
1056C32#348811yescharacteristic, complemented, Sylow
1057C23—31no—
1058C23—32no—
1059C23—34no—
1060C23—31no—
1061C23—32no—
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—64no—
1081D4—64no—
1082D4—64no—
1083D4—64no—
1084D4—64no—
1085D4—62no—
1086D4—62no—
1087D4—98no—
1088D4—94no—
1089D4—124no—
1090D4—122no—
1091D4—124no—
1092D4—188no—
1093D4—184no—
1094D4—184no—
1095D4—188no—
1096D4—184no—
1097D4—188no—
1098D4—364no—
1099D4—364no—
1100C2×C4—32no—
1101C2×C4—31no—
1102C2×C4—31no—
1103C2×C4—32no—
1104C2×C4—62no—
1105C2×C4—62no—
1106C2×C4—62no—
1107C2×C4—62no—
1108C2×C4—62no—
1109C2×C4—64no—
1110C2×C4—64no—
1111C2×C4—92no—
1112C2×C4—98no—
1113C2×C4—94no—
1114C2×C4—184no—
1115C2×C4—184no—
1116C2×C4—184no—
1117C2×C4—188no—
1118C2×C4—364no—
1119C2×C4—362no—
1120C2×C4#380214yescomplemented
1121C2×C4C22×D3212yes—
1122C2×C4C22×D3212yes—
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—122no—
1133C2×C3—124no—
1134C2×C3—122no—
1135C2×C3—121no—
1136C2×C3C22×D3×D411yescharacteristic
1137C2×C3C22×D3×D411yescharacteristic
1138C2×C3C2×#100911yescharacteristic
1139C2×C3#596411yescharacteristic
1140C2×C3D3×H(5,𝔽2)11yescharacteristic
1141C2×C3#596611yescharacteristic
1142D3—22no—
1143D3—41no—
1144D3—42no—
1145D3—44no—
1146D3—42no—
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—62no—
1160C22—62no—
1161C22—64no—
1162C22—61no—
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—22no—
1177C4—22no—
1178C4—61no—
1179C4—61no—
1180C4—62no—
1181C4—62no—
1182C4—94no—
1183C4—184no—
1184C4C2×#380212yes—
1185C4C2×#380212yes—
1186C3—21no—
1187C3#8604111yescharacteristic, complemented
1188C3#8633111yescharacteristic, complemented
1189C2—22no—
1190C2—62no—
1191C2—121no—
1192C2—124no—
1193C2—122no—
1194C2—122no—
1195C2—184no—
1196C2C22×#380211yescharacteristic
1197C2D3×#100911yescharacteristic
1198C2#1059669611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
hypercenter#117D32
hypocenterC32#3488
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C2×#64307C2semidirect
2. C2×D3×#235C2semidirect
3. #10595994C2semidirect
4. C3×#5525C2semidirect
5. C3×#5524C2semidirect
6. #10595044C2semidirect
7. C2×#63908C2semidirect
8. #10594634C2semidirect
9. #10594632C2semidirect
10. #10594612C2semidirect
11. #10594528C2semidirect
12. #10594294C2semidirect
13. #10594271C2semidirect
14. #10594007C2semidirect
15. #10594004C2semidirect
16. #10593906C2semidirect
17. #10593905C2semidirect
21. C2×C3×#235C22semidirect
22. C2×C3×#235C22semidirect
23. C22×C3×D12C22semidirect
24. C22×C3×C4×D3C22semidirect
25. C2×D3×#67C22semidirect
26. C2×D3×#67C22semidirect
27. C22×#625C22semidirect
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. C32×#117C22semidirect
43. C2×C4⋊(C3⋊Dic3)C22semidirect
44. #64101C22semidirect
45. C4⋊C4×C3⋊D3C22semidirect
46. #64090C22semidirect
47. C4×C4⋊(C3⋊D3)C22semidirect
48. C4×#634C22semidirect
49. C3×#897C22semidirect
50. C3×#897C22semidirect
51. C3×#895C22semidirect
52. C3×#895C22semidirect
53. C3×#895C22semidirect
54. C3×#895C22semidirect
55. C3×#886C22semidirect
56. C3×#882C22semidirect
57. C3×#882C22semidirect
58. C3×#875C22semidirect
59. C3×#874C22semidirect
60. C3×C4×D12C22semidirect
61. C3×C4×D12C22semidirect
62. #63980C22semidirect
63. C2×(C2×D3)⋊Dic3C22semidirect
64. #63922C22semidirect
65. #63922C22semidirect
66. #63922C22semidirect
67. #63921C22semidirect
68. #63916C22semidirect
69. #63915C22semidirect
70. #63914C22semidirect
71. #63912C22semidirect
72. #63908C22semidirect
73. #63908C22semidirect
74. #63908C22semidirect
75. #63908C22semidirect
76. #63908C22semidirect
77. #63908C22semidirect
78. #63902C22semidirect
79. #63899C22semidirect
80. #63898C22semidirect
81. #63885C22semidirect
82. #63885C22semidirect
83. #63885C22semidirect
84. #63856C22semidirect
85. #63856C22semidirect
86. #63854C22semidirect
117. #5525D3semidirect
118. #5524D3semidirect
129. #3828D4semidirect
244. C2×#235C2×D3semidirect
245. C2×#235C2×D3semidirect
248. C22×D12C2×D3semidirect
251. C22×C4×D3C2×D3semidirect
267. C3×#117C2×D3semidirect
268. C3×#117C2×D3semidirect
302. #897C2×D3semidirect
303. #897C2×D3semidirect
306. #895C2×D3semidirect
307. #895C2×D3semidirect
308. #895C2×D3semidirect
309. #895C2×D3semidirect
318. #886C2×D3semidirect
330. #882C2×D3semidirect
331. #882C2×D3semidirect
340. #875C2×D3semidirect
341. #874C2×D3semidirect
345. C4×D12C2×D3semidirect
346. C4×D12C2×D3semidirect
369. 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
720. #117D32semidirect
793. C2×C3×C4D3×D4semidirect
794. C2×C3×C4D3×D4semidirect
1029. C2×D3#1009semidirect
1056. C32#3488semidirect
1120. C2×C4#3802semidirect
1187. C3#86041semidirect
1188. C3#86331semidirect

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
#105959942
C3×#55252
C3×#55242
#105950442
C2×#639082
#105946342
#105946322
#105946122
#105945282
#105942942
#105942712
#105940072
#105940042
#105939062
#105939052
#863313
#860413