Finite Group Databasebeta

← #11904619

Subgroups — #11904619

Order 1152.

3529 conjugacy classes of subgroups.

The subgroup lattice has 1430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64330C211yesmaximal, characteristic, complemented
2C22×#3805C211yesmaximal, characteristic, complemented
3C2×#64148C211yesmaximal, characteristic, complemented
4C3×D4×#67C212yesmaximal, complemented
5#10595526C212yesmaximal, complemented
6#10595502C211yesmaximal, characteristic, complemented
7#10595501C211yesmaximal, characteristic, complemented
8#10595494C212yesmaximal, complemented
9#10595290C212yesmaximal, complemented
10#10595287C212yesmaximal, complemented
11#10595286C212yesmaximal, complemented
12D3×#939C212yesmaximal, complemented
13#10595227C212yesmaximal, complemented
14#10595141C212yesmaximal, complemented
15#10595132C212yesmaximal, complemented
16#10595129C212yesmaximal, complemented
17#10595075C212yesmaximal, complemented
18#10594930C211yesmaximal, characteristic, complemented
19#10594876C211yesmaximal, characteristic, complemented
20#86607—32nomaximal
21C22×C32×D4C2211yescharacteristic, complemented
22C22×#638C2211yescharacteristic, complemented
23C22×#638C2211yescharacteristic, complemented
24C23×C3⋊Dic3C2211yescharacteristic, complemented
25C22×C3×#67C2212yescomplemented
26C22×C3×#67C2212yescomplemented
27C2×C3×D3×D4C2212yescomplemented
28#64330—28no—
29C2×#3811C2212yescomplemented
30C2×D3×#67C2212yescomplemented
31C2×D3×#67C2212yescomplemented
32C2×D3×#67C2212yescomplemented
33C22×#627C2211yescharacteristic, complemented
34C22×#625C2211yescharacteristic, complemented
35C2×#3805—28no—
36C2×#3805C2211yescharacteristic
37C2×#3805C2212yescomplemented
38C2×#3805C2212yescomplemented
39C2×#3805C2211yescharacteristic, complemented
40C2×#3805C2211yescharacteristic, complemented
41C2×#3805C2211yescharacteristic, complemented
42C2×#3805C2211yescharacteristic, complemented
43C2×#3804C2212yescomplemented
44C2×#3804C2212yescomplemented
45C22×D3×Dic3C2212yescomplemented
46C2×#3757C2211yescharacteristic, complemented
47#64148C2212yescomplemented
48#64148C2212yescomplemented
49#64148C2212yescomplemented
50#64148C2212yescomplemented
51C2×#3752C2211yescharacteristic, complemented
52C2×#3750C2211yescharacteristic, complemented
53C3×#953C2212yescomplemented
54C3×#953C2212yescomplemented
55C3×#940C2212yescomplemented
56C3×#939C2212yescomplemented
57C3×#939C2212yescomplemented
58C3×#938C2212yescomplemented
59C3×#937C2212yescomplemented
60C3×#937C2212yescomplemented
61C3×D4×Dic3C2212yescomplemented
62C3×#930C2212yescomplemented
63C3×C4×#67C2212yescomplemented
64#63983C2212yescomplemented
65#63982C2211yescharacteristic, complemented
66#63982C2211yescharacteristic, complemented
67#63981C2212yescomplemented
68#63980C2212yescomplemented
69#63980C2211yescharacteristic, complemented
70#63980C2211yescharacteristic, complemented
71#63979C2212yescomplemented
72#63979C2212yescomplemented
73#63978C2212yescomplemented
74#63977C2212yescomplemented
75#63976C2212yescomplemented
76#67⋊Dic3C2212yescomplemented
77#67⋊Dic3C2212yescomplemented
78#67⋊Dic3C2212yescomplemented
79Dic3×#67C2212yescomplemented
80#63971C2212yescomplemented
81#63971C2212yescomplemented
82#63971C2212yescomplemented
83#63970C2212yescomplemented
84#63970C2212yescomplemented
85#63969C2212yescomplemented
86D3×#217C2212yescomplemented
87#63964C2212yescomplemented
88#63962C2212yescomplemented
89#63959C2212yescomplemented
90#63958C2212yescomplemented
91#63957C2211yescharacteristic, complemented
92#63953C2212yescomplemented
93#63952C2212yescomplemented
94#63922C2212yescomplemented
95D3×(C2×D3)⋊C4C2212yescomplemented
96#63906C2212yescomplemented
97#63899C2212yescomplemented
98#63899C2212yescomplemented
99#63895C2212yescomplemented
100#63890C2212yescomplemented
101#63886C2212yescomplemented
102#63885C2212yescomplemented
103#63885C2212yescomplemented
104#63880C2212yescomplemented
105#63879C2212yescomplemented
106#63877C2212yescomplemented
107D3×Dic3⋊C4C2212yescomplemented
108#63852C2212yescomplemented
109#63837C2212yescomplemented
110C2×#1004—32no—
111C22×#237—32no—
112C3×D42—32no—
113#5806—32no—
114C2×#939—32no—
115C2×#939—32no—
116C2×#939—61no—
117D4×#67—32no—
118D4×#67—32no—
119D4×#67D312yescomplemented
120#5718—32no—
121#5715—32no—
122#5610—32no—
123#5610—32no—
124#5608—32no—
125D3×#121—32no—
126#5599—32no—
127#5598—32no—
128#5597—32no—
129#5597—32no—
130#5592—32no—
131#5592—32no—
132#5591—32no—
133#5591—32no—
134#5590—32no—
135#5590—32no—
136#5586—32no—
137#5586—32no—
138#5554—32no—
139#5552—32no—
140#5547—32no—
141#5546—32no—
142C24×C32C2311yescharacteristic
143C24×C32C2311yescharacteristic
144C23×C3⋊D3C2311yescharacteristic
145C23×C3×D3C2312yes—
146C23×C3×D3C2312yes—
147C22×D32C2312yes—
148C2×C32×D4—42no—
149C2×C32×D4C2312yes—
150C2×C32×D4C2312yes—
151C22×C32×C4C2311yescharacteristic
152C2×#638—24no—
153C2×#638—42no—
154C2×#638C2312yes—
155C2×#638C2312yes—
156C2×#638C2312yes—
157C2×#638C2312yes—
158C22×C3⋊Dic3—24no—
159C22×C3⋊Dic3C2311yescharacteristic
160C22×C3⋊Dic3C2311yescharacteristic
161C22×C3⋊Dic3C2311yescharacteristic
162C22×C3⋊Dic3C2311yescharacteristic
163C22×C3⋊Dic3C2311yescharacteristic
164C22×C3⋊Dic3C2311yescharacteristic
165C22×C3⋊Dic3C2311yescharacteristic
166C2×C3×#67—28no—
167C2×C3×#67—28no—
168C2×C3×#67C2312yes—
169C2×C3×#67C2312yes—
170C2×C3×#67C2312yes—
171C2×C3×#67C2312yes—
172C2×C3×#67C2312yes—
173C2×C3×#67C2312yes—
174C2×C3×#67C2312yes—
175C2×C3×#67C2312yes—
176C2×C3×#67C2312yes—
177C2×C3×#67C2312yes—
178C2×C3×#67C2312yes—
179C22×C3×Dic3C2312yes—
180C22×C3×Dic3C2312yes—
181C3×D3×D4—44no—
182C2×C3×D12C2312yes—
183C2×C3×C4×D3C2312yes—
184#3811—28no—
185D3×#67—28no—
186D3×#67—28no—
187D3×#67—44no—
188C2×#627—24no—
189C2×#627C2311yescharacteristic
190C2×#627C2312yes—
191C2×#627C2311yescharacteristic
192C2×#627C2311yescharacteristic
193C2×#626C2312yes—
194C2×#626C2312yes—
195C2×#626C2312yes—
196C2×#626C2312yes—
197C2×#625—24no—
198C2×#625C2311yescharacteristic
199C2×#625C2312yes—
200C2×#625C2311yescharacteristic
201C2×#625C2312yes—
202C2×#625C2311yescharacteristic
203C2×#624C2312yes—
204#3805—24no—
205#3805—24no—
206#3805—28no—
207#3805—24no—
208#3805—24no—
209#3805—28no—
210#3805D418yescomplemented
211#3804—28no—
212#3804—28no—
213C2×D3×Dic3—28no—
214C2×D3×Dic3C2312yes—
215C2×D3×Dic3C2312yes—
216C2×D3×Dic3C2312yes—
217C2×D3×Dic3C2312yes—
218C2×D3×Dic3C2312yes—
219C2×D3×Dic3C2312yes—
220#3757C2312yes—
221#3757C2312yes—
222#3752C2312yes—
223#3752C2312yes—
224#3750C2312yes—
225#3750C2312yes—
226C3×#217C2312yes—
227C3×#217C2312yes—
228C3×#217C2312yes—
229C3×#217C2312yes—
230C3×#217C2312yes—
231C3×(C2×D3)⋊C4C2312yes—
232C3×(C2×D3)⋊C4C2312yes—
233C3×(C2×D3)⋊C4C2312yes—
234C3×C4⋊Dic3C2312yes—
235C3×Dic3⋊C4C2312yes—
236C3×C4×Dic3C2312yes—
237#3724C2311yescharacteristic
238#3724C2311yescharacteristic
239#3724C2312yes—
240Dic3⋊Dic3C2312yes—
241Dic3⋊Dic3C2312yes—
242Dic3⋊Dic3C2312yes—
243#3722C2312yes—
244#3722C2312yes—
245(C2×D3)⋊Dic3C2312yes—
246(C2×D3)⋊Dic3C2312yes—
247(C2×D3)⋊Dic3C2312yes—
248(C2×D3)⋊Dic3C2312yes—
249(C2×D3)⋊Dic3C2312yes—
250Dic32C2312yes—
251Dic32C2312yes—
252#3488—91noSylow
253C22×C3×D4—21no—
254C22×C3×D4—32no—
255C22×C3×D4—32no—
256C22×C3×D4—32no—
257C22×C3×D4C2×D312yescomplemented
258C22×#67—32no—
259C22×#67—32no—
260C22×#67—32no—
261C22×#67—32no—
262C22×#67—32no—
263C22×#67—32no—
264C22×#67—61no—
265C22×#67—61no—
266C22×#67C2×D312yescomplemented
267C22×#67C2×D312yescomplemented
268C23×Dic3—32no—
269C23×Dic3—32no—
270C23×Dic3—61no—
271#1004—616no—
272C2×#237—32no—
273C2×#237—32no—
274C2×#237—32no—
275C2×#237—32no—
276C2×#237—32no—
277C2×#237—32no—
278C2×#237—32no—
279C2×#237—32no—
280C2×#237—32no—
281C2×#237—32no—
282C2×#237—32no—
283C2×#237—616no—
284C2×D3×D4—32no—
285C2×D3×D4—32no—
286C2×D3×D4—32no—
287C2×D3×D4—32no—
288C2×D3×D4—32no—
289C2×D3×D4C2×D312yescomplemented
290C2×#235—32no—
291C2×#235—32no—
292C22×C4×D3—32no—
293C22×Dic6—32no—
294C3×#127—32no—
295C3×#121—32no—
296C3×#121—32no—
297C3×#121—32no—
298C3×#121—32no—
299C3×#120—32no—
300C3×#120—32no—
301C3×#120—32no—
302C3×#120—32no—
303C3×C4×D4—32no—
304C3×C4×D4—32no—
305#953—32no—
306#953—32no—
307#953C2×D312yescomplemented
308#953C2×D312yescomplemented
309C2×#217—32no—
310C2×#217—32no—
311C2×#217—61no—
312#940—32no—
313#940—32no—
314#940—32no—
315#940—32no—
316#940C2×D312yescomplemented
317#939—32no—
318#939—32no—
319#939—32no—
320#939—32no—
321#939—32no—
322#939—32no—
323#939—32no—
324#939—32no—
325#939—32no—
326#939—32no—
327#939—32no—
328#939—32no—
329#939—32no—
330#939—32no—
331#939—32no—
332#939—32no—
333#939—32no—
334#939—32no—
335#939—32no—
336#939—32no—
337#939—32no—
338#939—62no—
339#939—62no—
340#939—62no—
341#939—62no—
342#939C2×D312yescomplemented
343#939C2×D312yescomplemented
344#938—32no—
345#938—32no—
346#938—32no—
347#938C2×D312yescomplemented
348#937—32no—
349#937—32no—
350#937—32no—
351#937—32no—
352#937—32no—
353#937C2×D312yescomplemented
354#937C2×D312yescomplemented
355#936—32no—
356#935—32no—
357#935—32no—
358D4×Dic3—32no—
359D4×Dic3—32no—
360D4×Dic3—32no—
361D4×Dic3—32no—
362D4×Dic3C2×D312yescomplemented
363#930—32no—
364#930—32no—
365#930C2×D312yescomplemented
366C4×#67—32no—
367C4×#67—32no—
368C4×#67—32no—
369C4×#67C2×D312yescomplemented
370C2×(C2×D3)⋊C4—32no—
371C2×(C2×D3)⋊C4—32no—
372C2×(C2×D3)⋊C4—61no—
373#924—32no—
374C2×Dic3⋊C4—32no—
375C2×Dic3⋊C4—32no—
376C2×Dic3⋊C4—61no—
377#897—32no—
378#896—32no—
379#896—32no—
380#896—32no—
381#895—32no—
382#894—32no—
383D3×C4⋊C4—32no—
384#887—32no—
385#886—32no—
386#886—32no—
387#885—32no—
388#885—32no—
389#885—32no—
390#885—32no—
391#884—32no—
392#884—32no—
393#884—32no—
394#884—32no—
395#884—32no—
396#884—32no—
397#884—32no—
398#883—32no—
399#882—32no—
400#882—32no—
401#882—32no—
402#67⋊C4—32no—
403#67⋊C4—32no—
404#67⋊C4—32no—
405#67⋊C4—32no—
406#67⋊C4—32no—
407#67⋊C4—32no—
408D3×C22⋊C4—32no—
409D3×C22⋊C4—32no—
410#878—32no—
411#878—32no—
412#878—32no—
413#878—32no—
414#878—32no—
415#877—32no—
416#877—32no—
417#875—32no—
418C4×D12—32no—
419#872—32no—
420C4×Dic6—32no—
421C23×C32—22no—
422C23×C32—22no—
423C23×C32—22no—
424C23×C32—41no—
425C23×C32—41no—
426C23×C32—41no—
427C23×C32C2412yes—
428C23×C32C2411yescharacteristic
429C23×C32C2411yescharacteristic
430C23×C32C2411yescharacteristic
431C22×C3⋊D3—22no—
432C22×C3⋊D3—41no—
433C22×C3⋊D3—41no—
434C22×C3⋊D3C2412yes—
435C22×C3×D3—24no—
436C22×C3×D3—24no—
437C22×C3×D3—24no—
438C22×C3×D3—42no—
439C22×C3×D3—42no—
440C22×C3×D3—42no—
441C22×C3×D3C2412yes—
442C22×C3×D3C2412yes—
443C22×C3×D3C2412yes—
444C2×D32—24no—
445C2×D32—42no—
446C2×D32—42no—
447C32×D4—24no—
448C32×D4—42no—
449C2×C32×C4—41no—
450C2×C32×C4C2412yes—
451#638—24no—
452#638—24no—
453#638—24no—
454#638—42no—
455C2×C3⋊Dic3—22no—
456C2×C3⋊Dic3—22no—
457C2×C3⋊Dic3—22no—
458C2×C3⋊Dic3—22no—
459C2×C3⋊Dic3—22no—
460C2×C3⋊Dic3—41no—
461C2×C3⋊Dic3C2×D414yescomplemented
462C2×C3⋊Dic3C2412yes—
463C2×C3⋊Dic3C2411yescharacteristic
464C2×C3⋊Dic3C2411yescharacteristic
465C2×C3⋊Dic3C2411yescharacteristic
466C2×C3⋊Dic3C2411yescharacteristic
467C3×#67—24no—
468C3×#67—24no—
469C3×#67—24no—
470C3×#67—24no—
471C3×#67—24no—
472C3×#67—24no—
473C3×#67—24no—
474C3×#67—42no—
475C3×#67—42no—
476C3×#67—42no—
477C3×#67C2×D418yescomplemented
478C2×C3×Dic3—24no—
479C2×C3×Dic3—24no—
480C2×C3×Dic3C2412yes—
481C2×C3×Dic3C2412yes—
482C2×C3×Dic3C2412yes—
483C2×C3×Dic3C2412yes—
484C2×C3×Dic3C2412yes—
485C3×D12—42no—
486C3×C4×D3—42no—
487#627—22no—
488#627—22no—
489#627—24no—
490#627C2×D414yescomplemented
491#626—24no—
492#626—24no—
493#626—42no—
494#626—42no—
495#625—24no—
496#625—22no—
497#625—22no—
498#625—42no—
499#625C2×D414yescomplemented
500#624—24no—
501D3×Dic3—24no—
502D3×Dic3—24no—
503D3×Dic3—24no—
504D3×Dic3—24no—
505D3×Dic3—42no—
506D3×Dic3C2×D418yescomplemented
507C2×H(5,𝔽2)—91no—
508C22×#41—91no—
509#550—92no—
510#548—92no—
511#546—92no—
512#546—92no—
513#546—92no—
514D42—32no—
515D42—92no—
516D42—92no—
517#537—91no—
518#537—92no—
519#535—91no—
520#535—92no—
521#525—92no—
522#525—91no—
523C2×#121—92no—
524C2×#121—91no—
525#520—91no—
526C24×C3—21no—
527C24×C3—21no—
528C24×C3—32no—
529C24×C3—32no—
530C24×C3C22×D312yes—
531C24×C3C22×D312yes—
532C23×D3—32no—
533C23×D3—32no—
534C23×D3—32no—
535C23×D3—61no—
536C23×D3C22×D312yes—
537C23×D3C22×D312yes—
538C2×C3×D4—22no—
539C2×C3×D4—22no—
540C2×C3×D4—32no—
541C2×C3×D4—32no—
542C2×C3×D4—32no—
543C2×C3×D4—32no—
544C2×C3×D4—32no—
545C2×C3×D4—32no—
546C2×C3×D4—32no—
547C2×C3×D4—32no—
548C2×C3×D4—32no—
549C2×C3×D4—32no—
550C2×C3×D4—32no—
551C2×C3×D4—32no—
552C2×C3×D4—44no—
553C2×C3×D4—44no—
554C2×C3×D4—68no—
555C2×C3×D4—68no—
556C2×C3×D4—124no—
557C2×C3×D4C22×D312yes—
558C2×C3×D4C22×D312yes—
559C2×C3×D4C22×D312yes—
560C2×C3×D4C22×D312yes—
561C22×C3×C4—21no—
562C22×C3×C4—32no—
563C22×C3×C4—32no—
564C22×C3×C4—32no—
565C22×C3×C4C22×D312yes—
566C2×#67—28no—
567C2×#67—28no—
568C2×#67—32no—
569C2×#67—32no—
570C2×#67—32no—
571C2×#67—32no—
572C2×#67—32no—
573C2×#67—32no—
574C2×#67—32no—
575C2×#67—32no—
576C2×#67—32no—
577C2×#67—32no—
578C2×#67—32no—
579C2×#67—32no—
580C2×#67—32no—
581C2×#67—32no—
582C2×#67—32no—
583C2×#67—32no—
584C2×#67—32no—
585C2×#67—32no—
586C2×#67—32no—
587C2×#67—62no—
588C2×#67—62no—
589C2×#67—62no—
590C2×#67—62no—
591C2×#67—68no—
592C2×#67—68no—
593C2×#67—68no—
594C2×#67—68no—
595C2×#67—124no—
596C2×#67—124no—
597C2×#67—124no—
598C2×#67—124no—
599C2×#67C22×D312yes—
600C2×#67C22×D312yes—
601C2×#67C22×D312yes—
602C2×#67C22×D312yes—
603C2×#67C22×D312yes—
604C2×#67C22×D312yes—
605C2×#67C22×D312yes—
606C2×#67C22×D312yes—
607C2×#67C22×D312yes—
608C2×#67C22×D312yes—
609C2×#67C22×D312yes—
610C22×Dic3—32no—
611C22×Dic3—32no—
612C22×Dic3—32no—
613C22×Dic3—32no—
614C22×Dic3—32no—
615C22×Dic3—32no—
616C22×Dic3—32no—
617C22×Dic3—32no—
618C22×Dic3—32no—
619C22×Dic3—32no—
620C22×Dic3—32no—
621C22×Dic3—32no—
622C22×Dic3—32no—
623C22×Dic3—61no—
624C22×Dic3—61no—
625C22×Dic3—61no—
626C22×Dic3—61no—
627C22×Dic3—61no—
628C22×Dic3—61no—
629C22×Dic3—61no—
630C22×Dic3—68no—
631C22×Dic3—68no—
632C22×Dic3—124no—
633C22×Dic3C22×D312yes—
634C22×Dic3C22×D312yes—
635#237—316no—
636#237—68no—
637#237—68no—
638#237—68no—
639#237—68no—
640#237—68no—
641#237—68no—
642#237—68no—
643#237—68no—
644#237—68no—
645#237—68no—
646D3×D4—44no—
647D3×D4—68no—
648D3×D4—68no—
649D3×D4—68no—
650D3×D4—68no—
651D3×D4—124no—
652#235—68no—
653#235—68no—
654C2×D12—32no—
655C2×D12—32no—
656C2×D12—32no—
657C2×D12—32no—
658C2×D12C22×D312yes—
659C2×C4×D3—32no—
660C2×C4×D3—32no—
661C2×C4×D3—32no—
662C2×C4×D3—32no—
663C2×C4×D3—32no—
664C2×C4×D3—32no—
665C2×C4×D3—32no—
666C2×C4×D3—32no—
667C2×C4×D3—68no—
668C2×C4×D3C22×D312yes—
669C2×Dic6—32no—
670C2×Dic6—32no—
671C2×Dic6—32no—
672C2×Dic6—32no—
673C2×Dic6—32no—
674C2×Dic6—68no—
675C3×C4⋊C4—32no—
676C3×C4⋊C4—32no—
677C3×C22⋊C4—32no—
678C3×C22⋊C4—32no—
679C3×C22⋊C4—32no—
680C3×C22⋊C4—32no—
681C3×C22⋊C4—32no—
682C3×C22⋊C4—32no—
683C3×C22⋊C4—32no—
684C3×C22⋊C4—32no—
685C3×C42—32no—
686#217—32no—
687#217—32no—
688#217—32no—
689#217—32no—
690#217—32no—
691#217—32no—
692#217—32no—
693#217—32no—
694#217—32no—
695#217—62no—
696#217—62no—
697#217C22×D312yes—
698#217C22×D312yes—
699#217C22×D312yes—
700#217C22×D312yes—
701#217C22×D312yes—
702(C2×D3)⋊C4—32no—
703(C2×D3)⋊C4—32no—
704(C2×D3)⋊C4—32no—
705(C2×D3)⋊C4—32no—
706(C2×D3)⋊C4—32no—
707(C2×D3)⋊C4—32no—
708(C2×D3)⋊C4—32no—
709(C2×D3)⋊C4—32no—
710(C2×D3)⋊C4—32no—
711(C2×D3)⋊C4—32no—
712(C2×D3)⋊C4—32no—
713(C2×D3)⋊C4—32no—
714(C2×D3)⋊C4—32no—
715(C2×D3)⋊C4—62no—
716(C2×D3)⋊C4—62no—
717(C2×D3)⋊C4C22×D312yes—
718(C2×D3)⋊C4C22×D312yes—
719(C2×D3)⋊C4C22×D312yes—
720C4⋊Dic3—32no—
721C4⋊Dic3—32no—
722C4⋊Dic3—32no—
723C4⋊Dic3C22×D312yes—
724Dic3⋊C4—32no—
725Dic3⋊C4—32no—
726Dic3⋊C4—32no—
727Dic3⋊C4—32no—
728Dic3⋊C4—32no—
729Dic3⋊C4—32no—
730Dic3⋊C4—32no—
731Dic3⋊C4—32no—
732Dic3⋊C4—32no—
733Dic3⋊C4—32no—
734Dic3⋊C4—32no—
735Dic3⋊C4—62no—
736Dic3⋊C4—62no—
737Dic3⋊C4C22×D312yes—
738C4×Dic3—32no—
739C4×Dic3—32no—
740C4×Dic3—32no—
741C4×Dic3—32no—
742C4×Dic3C22×D312yes—
743C22×C32—21no—
744C22×C32—21no—
745C22×C32—21no—
746C22×C32—21no—
747C22×C32—21no—
748C22×C32—22no—
749C22×C32—21no—
750C22×C32—22no—
751C22×C32—21no—
752C22×C32—22no—
753C22×C32—44no—
754C22×C32—82no—
755C22×C32C22×D412yes—
756C22×C32H(5,𝔽2)12yescomplemented
757C22×C32C2511yescharacteristic
758C2×C3⋊D3—22no—
759C2×C3⋊D3—22no—
760C2×C3⋊D3—22no—
761C2×C3⋊D3—82no—
762C2×C3×D3—22no—
763C2×C3×D3—22no—
764C2×C3×D3—22no—
765C2×C3×D3—22no—
766C2×C3×D3—22no—
767C2×C3×D3—22no—
768C2×C3×D3—22no—
769C2×C3×D3—22no—
770C2×C3×D3—48no—
771C2×C3×D3—84no—
772C2×C3×D3C22×D414yes—
773D32—84no—
774C32×C4—22no—
775C3⋊Dic3—21no—
776C3⋊Dic3—21no—
777C3⋊Dic3—22no—
778C3⋊Dic3C22×D412yes—
779C3⋊Dic3C22×D412yes—
780C3×Dic3—22no—
781C3×Dic3—22no—
782C3×Dic3—22no—
783C3×Dic3—22no—
784C3×Dic3C22×D414yes—
785H(5,𝔽2)—188no—
786C2×#41—92no—
787C2×#41—92no—
788C2×#41—91no—
789C2×#41—91no—
790C2×#41—92no—
791C2×#41—91no—
792C2×#41—91no—
793C2×#41—92no—
794C2×#41—91no—
795C2×#41—188no—
796C22×Q8—91no—
797C22×D4—32no—
798C22×D4—32no—
799C22×D4—32no—
800C22×D4—92no—
801C22×D4—92no—
802C22×D4—92no—
803C22×D4—92no—
804C22×D4—91no—
805C22×D4—91no—
806C22×D4—91no—
807C22×D4D3211yescharacteristic, complemented
808C23×C4—92no—
809C23×C4—91no—
810#127—32no—
811#127—92no—
812#127—92no—
813#124—92no—
814#124—92no—
815#124—92no—
816#123—92no—
817#123—92no—
818#123—92no—
819C22⋊Q8—91no—
820C22⋊Q8—91no—
821C22⋊Q8—92no—
822C22⋊Q8—92no—
823C22⋊Q8—92no—
824C22⋊Q8—92no—
825#121—32no—
826#121—32no—
827#121—32no—
828#121—32no—
829#121—92no—
830#121—92no—
831#121—92no—
832#121—92no—
833#121—92no—
834#121—92no—
835#121—92no—
836#121—92no—
837#121—92no—
838#121—91no—
839#121—92no—
840#121—91no—
841#121—92no—
842#121—92no—
843#121—92no—
844#121—92no—
845#121—92no—
846#121—92no—
847#120—32no—
848#120—32no—
849#120—32no—
850#120—32no—
851#120—92no—
852#120—92no—
853#120—92no—
854#120—92no—
855#120—92no—
856C4×Q8—92no—
857C4×D4—32no—
858C4×D4—32no—
859C4×D4—92no—
860C4×D4—92no—
861C4×D4—92no—
862C4×D4—92no—
863C4×D4—92no—
864C4×D4—92no—
865C4×D4—92no—
866#117—92no—
867#117—91no—
868C2×C4⋊C4—92no—
869C2×C4⋊C4—91no—
870C2×C22⋊C4—92no—
871C2×C22⋊C4—92no—
872C2×C22⋊C4—91no—
873C2×C22⋊C4—91no—
874C23×C3—24no—
875C23×C3—24no—
876C23×C3—24no—
877C23×C3—24no—
878C23×C3—21no—
879C23×C3—21no—
880C23×C3—21no—
881C23×C3—22no—
882C23×C3—32no—
883C23×C3—32no—
884C23×C3—32no—
885C23×C3—42no—
886C23×C3—42no—
887C23×C3—42no—
888C23×C3—42no—
889C23×C3—42no—
890C23×C3—42no—
891C23×C3—42no—
892C23×C3—42no—
893C23×C3—64no—
894C23×C3—64no—
895C23×C3—64no—
896C23×C3—122no—
897C23×C3—122no—
898C23×C3—122no—
899C23×C3C23×D312yes—
900C23×C3C23×D312yes—
901C23×C3C23×D312yes—
902C23×C3C23×D312yes—
903C23×C3C23×D312yes—
904C22×D3—24no—
905C22×D3—24no—
906C22×D3—24no—
907C22×D3—32no—
908C22×D3—32no—
909C22×D3—42no—
910C22×D3—42no—
911C22×D3—42no—
912C22×D3—62no—
913C22×D3—64no—
914C22×D3—64no—
915C22×D3—64no—
916C22×D3—122no—
917C22×D3—122no—
918C22×D3—122no—
919C22×D3—122no—
920C22×D3—122no—
921C22×D3—122no—
922C22×D3—122no—
923C22×D3—122no—
924C22×D3—122no—
925C22×D3C23×D312yes—
926C22×D3C23×D312yes—
927C22×D3C23×D312yes—
928C3×D4—24no—
929C3×D4—24no—
930C3×D4—38no—
931C3×D4—44no—
932C3×D4—42no—
933C3×D4—42no—
934C3×D4—44no—
935C3×D4—64no—
936C3×D4—64no—
937C3×D4—64no—
938C3×D4—64no—
939C3×D4—64no—
940C3×D4—64no—
941C3×D4—64no—
942C3×D4—122no—
943C3×D4—122no—
944C3×D4—122no—
945C3×D4—122no—
946C2×C3×C4—22no—
947C2×C3×C4—32no—
948C2×C3×C4—32no—
949C2×C3×C4—32no—
950C2×C3×C4—32no—
951C2×C3×C4—32no—
952C2×C3×C4—42no—
953C2×C3×C4—42no—
954C2×C3×C4—64no—
955C2×C3×C4—64no—
956C2×C3×C4—122no—
957C2×C3×C4C23×D312yes—
958C2×C3×C4C23×D312yes—
959#67—24no—
960#67—24no—
961#67—24no—
962#67—24no—
963#67—24no—
964#67—24no—
965#67—24no—
966#67—38no—
967#67—42no—
968#67—42no—
969#67—42no—
970#67—64no—
971#67—64no—
972#67—64no—
973#67—64no—
974#67—64no—
975#67—64no—
976#67—64no—
977#67—64no—
978#67—64no—
979#67—64no—
980#67—64no—
981#67—64no—
982#67—124no—
983#67—124no—
984#67—124no—
985#67—122no—
986#67—122no—
987#67—122no—
988#67—122no—
989#67—122no—
990#67—122no—
991#67—124no—
992#67D3×D418yescomplemented
993C2×Dic3—24no—
994C2×Dic3—24no—
995C2×Dic3—38no—
996C2×Dic3—32no—
997C2×Dic3—32no—
998C2×Dic3—38no—
999C2×Dic3—32no—
1000C2×Dic3—32no—
1001C2×Dic3—32no—
1002C2×Dic3—32no—
1003C2×Dic3—64no—
1004C2×Dic3—61no—
1005C2×Dic3—61no—
1006C2×Dic3—62no—
1007C2×Dic3—61no—
1008C2×Dic3—61no—
1009C2×Dic3—64no—
1010C2×Dic3—64no—
1011C2×Dic3—64no—
1012C2×Dic3—64no—
1013C2×Dic3—64no—
1014C2×Dic3—64no—
1015C2×Dic3—64no—
1016C2×Dic3—64no—
1017C2×Dic3—64no—
1018C2×Dic3—122no—
1019C2×Dic3—122no—
1020C2×Dic3—122no—
1021C2×Dic3—122no—
1022C2×Dic3—122no—
1023C2×Dic3—122no—
1024C2×Dic3—122no—
1025C2×Dic3—122no—
1026C2×Dic3C23×D312yes—
1027C2×Dic3C23×D312yes—
1028C2×Dic3C23×D312yes—
1029C2×Dic3C23×D312yes—
1030C2×Dic3C23×D312yes—
1031D12—42no—
1032D12—64no—
1033D12—64no—
1034D12—122no—
1035D12—122no—
1036C4×D3—38no—
1037C4×D3—42no—
1038C4×D3—64no—
1039C4×D3—64no—
1040C4×D3—64no—
1041C4×D3—64no—
1042C4×D3—64no—
1043C4×D3—64no—
1044C4×D3—122no—
1045Dic6—38no—
1046Dic6—64no—
1047Dic6—64no—
1048Dic6—64no—
1049Dic6—64no—
1050C2×C32—22no—
1051C2×C32—22no—
1052C2×C32—41no—
1053C2×C32—42no—
1054C2×C32C23×D411yescharacteristic
1055C2×C32C2×H(5,𝔽2)11yescharacteristic
1056C2×C32#58511yescharacteristic
1057C3⋊D3—42no—
1058C3×D3—24no—
1059C3×D3—42no—
1060C3×D3—42no—
1061C24—32no—
1062C24—32no—
1063C24—92no—
1064C24—91no—
1065C24C2×D3211yescharacteristic
1066C24C2×D3211yescharacteristic
1067#41—98no—
1068#41—188no—
1069#41—188no—
1070#41—188no—
1071#41—184no—
1072#41—184no—
1073#41—188no—
1074#41—184no—
1075#41—184no—
1076C2×Q8—91no—
1077C2×Q8—91no—
1078C2×Q8—92no—
1079C2×Q8—91no—
1080C2×Q8—184no—
1081C2×D4—32no—
1082C2×D4—32no—
1083C2×D4—32no—
1084C2×D4—32no—
1085C2×D4—32no—
1086C2×D4—32no—
1087C2×D4—32no—
1088C2×D4—32no—
1089C2×D4—32no—
1090C2×D4—32no—
1091C2×D4—32no—
1092C2×D4—32no—
1093C2×D4—42no—
1094C2×D4—68no—
1095C2×D4—68no—
1096C2×D4—92no—
1097C2×D4—92no—
1098C2×D4—92no—
1099C2×D4—92no—
1100C2×D4—91no—
1101C2×D4—92no—
1102C2×D4—91no—
1103C2×D4—91no—
1104C2×D4—92no—
1105C2×D4—92no—
1106C2×D4—92no—
1107C2×D4—92no—
1108C2×D4—92no—
1109C2×D4—124no—
1110C2×D4—188no—
1111C2×D4—184no—
1112C2×D4—188no—
1113C2×D4—188no—
1114C2×D4—184no—
1115C2×D4—364no—
1116C2×D4—362no—
1117C2×D4C2×D3212yes—
1118C2×D4C2×D3212yes—
1119C22×C4—32no—
1120C22×C4—32no—
1121C22×C4—32no—
1122C22×C4—92no—
1123C22×C4—92no—
1124C22×C4—92no—
1125C22×C4—92no—
1126C22×C4—92no—
1127C22×C4—92no—
1128C22×C4—92no—
1129C22×C4—91no—
1130C22×C4—91no—
1131C22×C4—91no—
1132C22×C4—91no—
1133C22×C4—91no—
1134C22×C4—91no—
1135C22×C4—91no—
1136C22×C4—188no—
1137C22×C4—184no—
1138C22×C4C2×D3211yescharacteristic
1139C4⋊C4—32no—
1140C4⋊C4—32no—
1141C4⋊C4—91no—
1142C4⋊C4—92no—
1143C4⋊C4—91no—
1144C4⋊C4—92no—
1145C4⋊C4—92no—
1146C4⋊C4—92no—
1147C4⋊C4—92no—
1148C4⋊C4—92no—
1149C22⋊C4—32no—
1150C22⋊C4—32no—
1151C22⋊C4—32no—
1152C22⋊C4—32no—
1153C22⋊C4—32no—
1154C22⋊C4—32no—
1155C22⋊C4—32no—
1156C22⋊C4—32no—
1157C22⋊C4—92no—
1158C22⋊C4—92no—
1159C22⋊C4—92no—
1160C22⋊C4—92no—
1161C22⋊C4—92no—
1162C22⋊C4—92no—
1163C22⋊C4—92no—
1164C22⋊C4—92no—
1165C22⋊C4—92no—
1166C22⋊C4—92no—
1167C22⋊C4—92no—
1168C42—32no—
1169C42—92no—
1170C42—92no—
1171C22×C3—22no—
1172C22×C3—22no—
1173C22×C3—22no—
1174C22×C3—22no—
1175C22×C3—22no—
1176C22×C3—22no—
1177C22×C3—22no—
1178C22×C3—22no—
1179C22×C3—22no—
1180C22×C3—22no—
1181C22×C3—22no—
1182C22×C3—22no—
1183C22×C3—22no—
1184C22×C3—22no—
1185C22×C3—22no—
1186C22×C3—22no—
1187C22×C3—22no—
1188C22×C3—22no—
1189C22×C3—21no—
1190C22×C3—34no—
1191C22×C3—41no—
1192C22×C3—41no—
1193C22×C3—41no—
1194C22×C3—41no—
1195C22×C3—42no—
1196C22×C3—42no—
1197C22×C3—42no—
1198C22×C3—48no—
1199C22×C3—48no—
1200C22×C3—62no—
1201C22×C3—62no—
1202C22×C3—62no—
1203C22×C3—62no—
1204C22×C3—62no—
1205C22×C3—62no—
1206C22×C3—62no—
1207C22×C3—62no—
1208C22×C3—84no—
1209C22×C3—84no—
1210C22×C3—128no—
1211C22×C3—244no—
1212C22×C3C2×D3×D414yes—
1213C22×C3#100414yescomplemented
1214C22×C3C24×D312yes—
1215C2×D3—22no—
1216C2×D3—22no—
1217C2×D3—22no—
1218C2×D3—22no—
1219C2×D3—22no—
1220C2×D3—22no—
1221C2×D3—22no—
1222C2×D3—22no—
1223C2×D3—48no—
1224C2×D3—62no—
1225C2×D3—62no—
1226C2×D3—62no—
1227C2×D3—62no—
1228C2×D3—62no—
1229C2×D3—62no—
1230C2×D3—84no—
1231C2×D3—122no—
1232C2×D3—122no—
1233C2×D3—122no—
1234C2×D3—244no—
1235C2×D3—244no—
1236C2×D3—244no—
1237C2×D3—244no—
1238C2×D3C2×D3×D414yes—
1239C3×C4—22no—
1240C3×C4—22no—
1241C3×C4—34no—
1242C3×C4—42no—
1243C3×C4—62no—
1244C3×C4—62no—
1245C3×C4—62no—
1246C3×C4—62no—
1247Dic3—22no—
1248Dic3—22no—
1249Dic3—22no—
1250Dic3—22no—
1251Dic3—34no—
1252Dic3—34no—
1253Dic3—62no—
1254Dic3—62no—
1255Dic3—62no—
1256Dic3—62no—
1257Dic3—62no—
1258Dic3—62no—
1259Dic3—121no—
1260Dic3—121no—
1261Dic3—122no—
1262Dic3C2×D3×D414yes—
1263C32#348811yescharacteristic, complemented, Sylow
1264C23—22no—
1265C23—22no—
1266C23—22no—
1267C23—32no—
1268C23—32no—
1269C23—32no—
1270C23—41no—
1271C23—41no—
1272C23—41no—
1273C23—64no—
1274C23—64no—
1275C23—64no—
1276C23—92no—
1277C23—122no—
1278C23—122no—
1279C23—122no—
1280C23—184no—
1281C23—182no—
1282C23—361no—
1283C23—361no—
1284C23—362no—
1285C23—362no—
1286C23C22×D3212yes—
1287C23C22×D3211yescharacteristic
1288C23C22×D3211yescharacteristic
1289C23C22×D3211yescharacteristic
1290Q8—94no—
1291Q8—184no—
1292Q8—182no—
1293Q8—182no—
1294D4—24no—
1295D4—38no—
1296D4—42no—
1297D4—64no—
1298D4—64no—
1299D4—64no—
1300D4—64no—
1301D4—64no—
1302D4—64no—
1303D4—64no—
1304D4—94no—
1305D4—122no—
1306D4—122no—
1307D4—122no—
1308D4—122no—
1309D4—184no—
1310D4—184no—
1311D4—184no—
1312D4—184no—
1313D4—182no—
1314D4—182no—
1315D4—184no—
1316D4—184no—
1317D4—362no—
1318D4—362no—
1319D4—362no—
1320D4—362no—
1321C2×C4—32no—
1322C2×C4—32no—
1323C2×C4—32no—
1324C2×C4—32no—
1325C2×C4—32no—
1326C2×C4—41no—
1327C2×C4—64no—
1328C2×C4—64no—
1329C2×C4—98no—
1330C2×C4—94no—
1331C2×C4—91no—
1332C2×C4—91no—
1333C2×C4—92no—
1334C2×C4—91no—
1335C2×C4—91no—
1336C2×C4—122no—
1337C2×C4—184no—
1338C2×C4—184no—
1339C2×C4—184no—
1340C2×C4—184no—
1341C2×C4—184no—
1342C2×C4—182no—
1343C2×C4—182no—
1344C2×C4—182no—
1345C2×C4—182no—
1346C2×C4—182no—
1347C2×C4—362no—
1348C2×C4—361no—
1349C2×C4C22×D3212yes—
1350C2×C3—24no—
1351C2×C3—24no—
1352C2×C3—24no—
1353C2×C3—21no—
1354C2×C3—21no—
1355C2×C3—21no—
1356C2×C3—42no—
1357C2×C3—42no—
1358C2×C3—42no—
1359C2×C3—42no—
1360C2×C3—42no—
1361C2×C3—64no—
1362C2×C3—82no—
1363C2×C3—122no—
1364C2×C3—122no—
1365C2×C3C22×D3×D412yes—
1366C2×C3C2×#100412yes—
1367C2×C3#596612yes—
1368D3—24no—
1369D3—42no—
1370D3—42no—
1371D3—122no—
1372D3—122no—
1373D3—242no—
1374C22—21no—
1375C22—21no—
1376C22—21no—
1377C22—21no—
1378C22—22no—
1379C22—21no—
1380C22—21no—
1381C22—22no—
1382C22—22no—
1383C22—21no—
1384C22—34no—
1385C22—44no—
1386C22—62no—
1387C22—62no—
1388C22—62no—
1389C22—62no—
1390C22—62no—
1391C22—62no—
1392C22—62no—
1393C22—62no—
1394C22—82no—
1395C22—128no—
1396C22—182no—
1397C22—182no—
1398C22—182no—
1399C22—244no—
1400C22—722no—
1401C22—724no—
1402C22D32×D412yes—
1403C22#6433012yescomplemented
1404C22C23×D3211yescharacteristic
1405C4—22no—
1406C4—34no—
1407C4—62no—
1408C4—62no—
1409C4—62no—
1410C4—62no—
1411C4—92no—
1412C4—92no—
1413C4—181no—
1414C4—181no—
1415C4—182no—
1416C3—21no—
1417C3#8660712yescomplemented
1418C2—22no—
1419C2—22no—
1420C2—41no—
1421C2—42no—
1422C2—64no—
1423C2—122no—
1424C2—122no—
1425C2—362no—
1426C2C2×D32×D411yescharacteristic
1427C2#1059667911yescharacteristic
1428C2C2×#6433011yescharacteristic
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. C2×#64330C2semidirect
2. C22×#3805C2semidirect
3. C2×#64148C2semidirect
4. C3×D4×#67C2semidirect
5. #10595526C2semidirect
6. #10595502C2semidirect
7. #10595501C2semidirect
8. #10595494C2semidirect
9. #10595290C2semidirect
10. #10595287C2semidirect
11. #10595286C2semidirect
12. D3×#939C2semidirect
13. #10595227C2semidirect
14. #10595141C2semidirect
15. #10595132C2semidirect
16. #10595129C2semidirect
17. #10595075C2semidirect
18. #10594930C2semidirect
19. #10594876C2semidirect
21. C22×C32×D4C22semidirect
22. C22×#638C22semidirect
23. C22×#638C22semidirect
24. C23×C3⋊Dic3C22semidirect
25. C22×C3×#67C22semidirect
26. C22×C3×#67C22semidirect
27. C2×C3×D3×D4C22semidirect
29. C2×#3811C22semidirect
30. C2×D3×#67C22semidirect
31. C2×D3×#67C22semidirect
32. C2×D3×#67C22semidirect
33. C22×#627C22semidirect
34. C22×#625C22semidirect
37. C2×#3805C22semidirect
38. C2×#3805C22semidirect
39. C2×#3805C22semidirect
40. C2×#3805C22semidirect
41. C2×#3805C22semidirect
42. C2×#3805C22semidirect
43. C2×#3804C22semidirect
44. C2×#3804C22semidirect
45. C22×D3×Dic3C22semidirect
46. C2×#3757C22semidirect
47. #64148C22semidirect
48. #64148C22semidirect
49. #64148C22semidirect
50. #64148C22semidirect
51. C2×#3752C22semidirect
52. C2×#3750C22semidirect
53. C3×#953C22semidirect
54. C3×#953C22semidirect
55. C3×#940C22semidirect
56. C3×#939C22semidirect
57. C3×#939C22semidirect
58. C3×#938C22semidirect
59. C3×#937C22semidirect
60. C3×#937C22semidirect
61. C3×D4×Dic3C22semidirect
62. C3×#930C22semidirect
63. C3×C4×#67C22semidirect
64. #63983C22semidirect
65. #63982C22semidirect
66. #63982C22semidirect
67. #63981C22semidirect
68. #63980C22semidirect
69. #63980C22semidirect
70. #63980C22semidirect
71. #63979C22semidirect
72. #63979C22semidirect
73. #63978C22semidirect
74. #63977C22semidirect
75. #63976C22semidirect
76. #67⋊Dic3C22semidirect
77. #67⋊Dic3C22semidirect
78. #67⋊Dic3C22semidirect
79. Dic3×#67C22semidirect
80. #63971C22semidirect
81. #63971C22semidirect
82. #63971C22semidirect
83. #63970C22semidirect
84. #63970C22semidirect
85. #63969C22semidirect
86. D3×#217C22semidirect
87. #63964C22semidirect
88. #63962C22semidirect
89. #63959C22semidirect
90. #63958C22semidirect
91. #63957C22semidirect
92. #63953C22semidirect
93. #63952C22semidirect
94. #63922C22semidirect
95. D3×(C2×D3)⋊C4C22semidirect
96. #63906C22semidirect
97. #63899C22semidirect
98. #63899C22semidirect
99. #63895C22semidirect
100. #63890C22semidirect
101. #63886C22semidirect
102. #63885C22semidirect
103. #63885C22semidirect
104. #63880C22semidirect
105. #63879C22semidirect
106. #63877C22semidirect
107. D3×Dic3⋊C4C22semidirect
108. #63852C22semidirect
109. #63837C22semidirect
119. D4×#67D3semidirect
210. #3805D4semidirect
257. C22×C3×D4C2×D3semidirect
266. C22×#67C2×D3semidirect
267. C22×#67C2×D3semidirect
289. C2×D3×D4C2×D3semidirect
307. #953C2×D3semidirect
308. #953C2×D3semidirect
316. #940C2×D3semidirect
342. #939C2×D3semidirect
343. #939C2×D3semidirect
347. #938C2×D3semidirect
353. #937C2×D3semidirect
354. #937C2×D3semidirect
362. D4×Dic3C2×D3semidirect
365. #930C2×D3semidirect
369. C4×#67C2×D3semidirect
461. C2×C3⋊Dic3C2×D4semidirect
477. C3×#67C2×D4semidirect
490. #627C2×D4semidirect
499. #625C2×D4semidirect
506. D3×Dic3C2×D4semidirect
756. C22×C32H(5,𝔽2)semidirect
807. C22×D4D32semidirect
992. #67D3×D4semidirect
1213. C22×C3#1004semidirect
1263. C32#3488semidirect
1403. C22#64330semidirect
1417. C3#86607semidirect

Maximal subgroups

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

subgroupindex
C2×#643302
C22×#38052
C2×#641482
C3×D4×#672
#105955262
#105955022
#105955012
#105954942
#105952902
#105952872
#105952862
D3×#9392
#105952272
#105951412
#105951322
#105951292
#105950752
#105949302
#105948762
#866073