Finite Group Databasebeta

← #11904641

Subgroups — #11904641

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
2C2×#64306C211yesmaximal, characteristic, complemented
3C2×#64093C211yesmaximal, characteristic, complemented
4C3×#5490C212yesmaximal, complemented
5#10595526C212yesmaximal, complemented
6#10595502C211yesmaximal, characteristic, complemented
7#10595074C212yesmaximal, complemented
8#10595068C212yesmaximal, complemented
9#10594930C211yesmaximal, characteristic, complemented
10#10594920C211yesmaximal, characteristic, complemented
11#10594876C211yesmaximal, characteristic, complemented
12#10594275C212yesmaximal, complemented
13#10594272C212yesmaximal, complemented
14#10594270C212yesmaximal, complemented
15#10594266C212yesmaximal, complemented
16D3×#884C212yesmaximal, complemented
17#10594246C212yesmaximal, complemented
18#10594075C212yesmaximal, complemented
19#10594059C212yesmaximal, complemented
20#86629—32nomaximal
21C22×#638C2211yescharacteristic, complemented
22C22×#638C2211yescharacteristic, complemented
23C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
24C22×C4×C3⋊D3C2211yescharacteristic, complemented
25C22×C3×#67C2212yescomplemented
26C2×C3×#235C2212yescomplemented
27#64330—28no—
28C2×#3811C2212yescomplemented
29C2×#3811C2212yescomplemented
30C2×D3×#67C2212yescomplemented
31C2×D3×#67C2212yescomplemented
32C2×D3×#67C2212yescomplemented
33C2×#3805C2211yescharacteristic
34C2×#3805C2211yescharacteristic, complemented
35C2×#3805C2211yescharacteristic, complemented
36C2×#3804C2212yescomplemented
37C2×#3804C2212yescomplemented
38#64306—28no—
39C2×#3802C2211yescharacteristic, complemented
40C2×D3×D12C2212yescomplemented
41C2×C4×D32C2212yescomplemented
42C2×#3798C2211yescharacteristic, complemented
43C2×#3798C2211yescharacteristic, complemented
44C2×#3797C2211yescharacteristic, complemented
45C2×#3796C2212yescomplemented
46C2×C32×C22⋊C4C2211yescharacteristic, complemented
47C2×#3752C2211yescharacteristic, complemented
48C2×#3750C2211yescharacteristic, complemented
49#64093C2212yescomplemented
50#64093C2212yescomplemented
51#64093C2212yescomplemented
52#64093C2212yescomplemented
53C3×#953C2212yescomplemented
54C3×#930C2212yescomplemented
55C3×#929C2212yescomplemented
56C3×C4×#67C2212yescomplemented
57C3×#885C2212yescomplemented
58C3×#884C2212yescomplemented
59C3×#884C2212yescomplemented
60C3×#883C2212yescomplemented
61C3×#882C2212yescomplemented
62C3×#67⋊C4C2212yescomplemented
63C3×D3×C22⋊C4C2212yescomplemented
64C3×#878C2212yescomplemented
65#63983C2212yescomplemented
66#63981C2212yescomplemented
67#63981C2212yescomplemented
68#63980C2212yescomplemented
69#63979C2212yescomplemented
70#63979C2212yescomplemented
71#63978C2212yescomplemented
72#63977C2212yescomplemented
73#67⋊Dic3C2212yescomplemented
74#63971C2212yescomplemented
75#63971C2212yescomplemented
76#63971C2212yescomplemented
77#63958C2212yescomplemented
78#63957C2211yescharacteristic, complemented
79#63953C2212yescomplemented
80#63952C2212yescomplemented
81#63923C2212yescomplemented
82#63923C2212yescomplemented
83#63922C2212yescomplemented
84D3×(C2×D3)⋊C4C2212yescomplemented
85#63912C2211yescharacteristic, complemented
86#63912C2211yescharacteristic, complemented
87#63911C2212yescomplemented
88#63910C2212yescomplemented
89#63910C2212yescomplemented
90#63909C2212yescomplemented
91#63907C2212yescomplemented
92#63906C2212yescomplemented
93#63904C2212yescomplemented
94#63899C2212yescomplemented
95#63899C2212yescomplemented
96#63894C2212yescomplemented
97#63888C2212yescomplemented
98#63886C2212yescomplemented
99#63885C2212yescomplemented
100#63885C2212yescomplemented
101#63881C2212yescomplemented
102#63881C2212yescomplemented
103#63879C2212yescomplemented
104#63877C2212yescomplemented
105D3×Dic3⋊C4C2212yescomplemented
106#63865C2211yescharacteristic, complemented
107#63865C2211yescharacteristic, complemented
108#63850C2212yescomplemented
109#63837C2212yescomplemented
110C2×D3×#41—32no—
111C2×#1004—32no—
112C3×#546—32no—
113#5829—32no—
114D4×#67—32no—
115#5677—32no—
116#5674—32no—
117#5656—32no—
118#5656—32no—
119#5654—32no—
120#5654—32no—
121#5633—32no—
122#5629—32no—
123#5609—32no—
124#5609—32no—
125D3×#121—32no—
126#5599—32no—
127#5597—32no—
128#5597—32no—
129#5592—32no—
130#5592—32no—
131#5590—32no—
132#5590—32no—
133#5553—32no—
134D4×D12—32no—
135#5547—32no—
136#5546—32no—
137#5490—32no—
138#5490D312yescomplemented
139C2×#884—32no—
140C2×#884—32no—
141C2×#884—61no—
142C24×C32C2311yescharacteristic
143C23×C3⋊D3C2311yescharacteristic
144C23×C3⋊D3C2311yescharacteristic
145C23×C3×D3C2312yes—
146C22×D32C2312yes—
147C22×D32C2312yes—
148C22×C32×C4C2311yescharacteristic
149C22×C32×C4C2311yescharacteristic
150C2×#638—24no—
151C2×#638—42no—
152C2×#638C2312yes—
153C2×#638C2312yes—
154C2×#638C2312yes—
155C2×#638C2312yes—
156C22×C3⋊Dic3C2311yescharacteristic
157C22×C3⋊Dic3C2311yescharacteristic
158C2×C4⋊(C3⋊D3)—42no—
159C2×C4⋊(C3⋊D3)C2312yes—
160C2×C4⋊(C3⋊D3)C2312yes—
161C2×C4×C3⋊D3—24no—
162C2×C4×C3⋊D3C2311yescharacteristic
163C2×C4×C3⋊D3C2311yescharacteristic
164C2×C4×C3⋊D3C2311yescharacteristic
165C2×C4×C3⋊D3C2311yescharacteristic
166C2×C3×#67—28no—
167C2×C3×#67C2312yes—
168C2×C3×#67C2312yes—
169C2×C3×#67C2312yes—
170C2×C3×#67C2312yes—
171C2×C3×#67C2312yes—
172C2×C3×#67C2312yes—
173C2×C3×#67C2312yes—
174C22×C3×Dic3C2312yes—
175C3×#235—28no—
176C2×C3×D12C2312yes—
177C2×C3×D12C2312yes—
178C2×C3×C4×D3C2312yes—
179C2×C3×C4×D3C2312yes—
180C2×C3×C4×D3C2312yes—
181C2×C3×Dic6C2312yes—
182#3811—28no—
183#3811—28no—
184D3×#67—28no—
185D3×#67—28no—
186D3×#67—44no—
187C2×#627C2311yescharacteristic
188C2×#627C2311yescharacteristic
189C2×#627C2311yescharacteristic
190C2×#626C2312yes—
191C2×#626C2312yes—
192C2×#626C2312yes—
193C2×#626C2312yes—
194C2×#626C2312yes—
195C2×#626C2312yes—
196C2×#626C2312yes—
197C2×#626C2312yes—
198C2×#625C2311yescharacteristic
199C2×#625C2311yescharacteristic
200C2×#625C2312yes—
201C2×#625C2311yescharacteristic
202C2×#624C2312yes—
203C2×#624C2312yes—
204#3805—24no—
205#3805—24no—
206#3805D418yescomplemented
207#3804—28no—
208#3804—28no—
209C2×D3×Dic3C2312yes—
210C2×D3×Dic3C2312yes—
211C2×D3×Dic3C2312yes—
212C2×D3×Dic3C2312yes—
213#3802—24no—
214D3×D12—44no—
215C4×D32—28no—
216#3798—24no—
217#3798—24no—
218#3797—24no—
219#3796—28no—
220C32×C22⋊C4C2312yes—
221C32×C22⋊C4C2312yes—
222#3752C2312yes—
223#3752C2312yes—
224#3750C2312yes—
225#3750C2312yes—
226C3×#217C2312yes—
227C3×#217C2312yes—
228C3×#217C2312yes—
229C3×(C2×D3)⋊C4C2312yes—
230C3×(C2×D3)⋊C4C2312yes—
231C3×(C2×D3)⋊C4C2312yes—
232C3×(C2×D3)⋊C4C2312yes—
233C3×(C2×D3)⋊C4C2312yes—
234C3×C4⋊Dic3C2312yes—
235C3×Dic3⋊C4C2312yes—
236C3×Dic3⋊C4C2312yes—
237C3×Dic3⋊C4C2312yes—
238C3×C4×Dic3C2312yes—
239#3724C2312yes—
240#3724C2311yescharacteristic
241#3724C2311yescharacteristic
242Dic3⋊Dic3C2312yes—
243#3722C2312yes—
244#3722C2312yes—
245#3722C2312yes—
246#3722C2312yes—
247(C2×D3)⋊Dic3C2312yes—
248(C2×D3)⋊Dic3C2312yes—
249(C2×D3)⋊Dic3C2312yes—
250Dic32C2312yes—
251Dic32C2312yes—
252#3488—91noSylow
253C2×C3×#41—32no—
254C22×C3×D4—32no—
255C22×#67—32no—
256C22×#67—32no—
257C22×#67—32no—
258C22×#67—32no—
259C22×#67—32no—
260C22×#67—61no—
261C22×#67—61no—
262C22×#67C2×D312yescomplemented
263D3×#41—616no—
264C2×#239—32no—
265C2×D3×Q8—32no—
266#1004—616no—
267C2×#237—32no—
268C2×#237—32no—
269C2×#237—32no—
270C2×#237—32no—
271C2×#237—32no—
272C2×#237—32no—
273C2×D3×D4—32no—
274C2×D3×D4—32no—
275C2×D3×D4—32no—
276C2×D3×D4—32no—
277C2×D3×D4—32no—
278C2×D3×D4—32no—
279C2×D3×D4—32no—
280C2×D3×D4—32no—
281C2×D3×D4—32no—
282C2×#235—32no—
283C2×#235—32no—
284C2×#235—32no—
285C2×#235—32no—
286C2×#235C2×D312yescomplemented
287C22×D12—32no—
288C22×D12—32no—
289C22×D12—61no—
290C22×C4×D3—32no—
291C22×C4×D3—32no—
292C22×C4×D3—32no—
293C22×C4×D3—61no—
294C3×#124—32no—
295C3×#123—32no—
296C3×#123—32no—
297C3×C22⋊Q8—32no—
298C3×#121—32no—
299C3×#121—32no—
300C3×#121—32no—
301C3×#120—32no—
302C3×#120—32no—
303C3×C4×D4—32no—
304C3×C4×D4—32no—
305C2×C3×C22⋊C4—21no—
306C2×C3×C22⋊C4—32no—
307C2×C3×C22⋊C4C2×D312yescomplemented
308#953—32no—
309#953C2×D312yescomplemented
310#947—32no—
311#946—32no—
312#940—32no—
313#940—32no—
314#940—32no—
315#940—32no—
316#940—32no—
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#938—32no—
327#937—32no—
328#937—32no—
329#937—32no—
330#937—32no—
331#937—32no—
332D4×Dic3—32no—
333#930—32no—
334#930—32no—
335#930—32no—
336#930C2×D312yescomplemented
337#929—32no—
338#929C2×D312yescomplemented
339C4×#67—32no—
340C4×#67—32no—
341C4×#67—32no—
342C4×#67C2×D312yescomplemented
343C2×(C2×D3)⋊C4—32no—
344C2×(C2×D3)⋊C4—32no—
345C2×(C2×D3)⋊C4—61no—
346C2×Dic3⋊C4—32no—
347C2×Dic3⋊C4—32no—
348C2×Dic3⋊C4—61no—
349#896—32no—
350#896—32no—
351#896—32no—
352#896—32no—
353#896—32no—
354#895—32no—
355#895—32no—
356#895—32no—
357#895—32no—
358#894—32no—
359#893—32no—
360#893—32no—
361#893—32no—
362#893—32no—
363D3×C4⋊C4—32no—
364#887—32no—
365#885—32no—
366#885—32no—
367#885—32no—
368#885C2×D312yescomplemented
369#884—32no—
370#884—32no—
371#884—32no—
372#884—32no—
373#884—32no—
374#884—32no—
375#884—32no—
376#884—32no—
377#884—32no—
378#884—32no—
379#884—32no—
380#884—32no—
381#884—32no—
382#884—32no—
383#884—32no—
384#884—32no—
385#884—32no—
386#884—32no—
387#884—32no—
388#884—62no—
389#884—62no—
390#884—62no—
391#884—62no—
392#884C2×D312yescomplemented
393#884C2×D312yescomplemented
394#883C2×D312yescomplemented
395#882—32no—
396#882—32no—
397#882—32no—
398#882—32no—
399#882—32no—
400#882—32no—
401#882—32no—
402#882—32no—
403#882C2×D312yescomplemented
404#67⋊C4—32no—
405#67⋊C4—32no—
406#67⋊C4—32no—
407#67⋊C4—32no—
408#67⋊C4—32no—
409#67⋊C4C2×D312yescomplemented
410D3×C22⋊C4—32no—
411D3×C22⋊C4C2×D312yescomplemented
412#878—32no—
413#878—32no—
414#878C2×D312yescomplemented
415#877—32no—
416#877—32no—
417#874—32no—
418C4×D12—32no—
419#872—32no—
420C4×Dic6—32no—
421C23×C32—22no—
422C23×C32—41no—
423C23×C32—41no—
424C23×C32C2412yes—
425C23×C32C2411yescharacteristic
426C22×C3⋊D3—22no—
427C22×C3⋊D3—22no—
428C22×C3⋊D3—22no—
429C22×C3⋊D3—41no—
430C22×C3⋊D3—41no—
431C22×C3⋊D3—41no—
432C22×C3⋊D3C2412yes—
433C22×C3⋊D3C2411yescharacteristic
434C22×C3⋊D3C2411yescharacteristic
435C22×C3×D3—24no—
436C22×C3×D3—42no—
437C22×C3×D3—42no—
438C22×C3×D3C2412yes—
439C22×C3×D3C2412yes—
440C22×C3×D3C2412yes—
441C2×D32—24no—
442C2×D32—24no—
443C2×D32—24no—
444C2×D32—42no—
445C2×D32—42no—
446C2×D32—42no—
447C2×C32×C4—22no—
448C2×C32×C4—41no—
449C2×C32×C4C2412yes—
450C2×C32×C4C2411yescharacteristic
451C2×C32×C4C2411yescharacteristic
452#638—24no—
453#638—24no—
454#638—24no—
455#638—42no—
456C2×C3⋊Dic3—41no—
457C2×C3⋊Dic3C2×D414yescomplemented
458C2×C3⋊Dic3C2412yes—
459C2×C3⋊Dic3C2411yescharacteristic
460C2×C3⋊Dic3C2411yescharacteristic
461C4⋊(C3⋊D3)—24no—
462C4⋊(C3⋊D3)—42no—
463C4×C3⋊D3—22no—
464C4×C3⋊D3—22no—
465C4×C3⋊D3—22no—
466C4×C3⋊D3—22no—
467C3×#67—24no—
468C3×#67—24no—
469C3×#67—24no—
470C3×#67—24no—
471C3×#67—42no—
472C3×#67—42no—
473C3×#67C2×D418yescomplemented
474C2×C3×Dic3—24no—
475C2×C3×Dic3C2412yes—
476C2×C3×Dic3C2412yes—
477C2×C3×Dic3C2412yes—
478C2×C3×Dic3C2412yes—
479C2×C3×Dic3C2412yes—
480C3×D12—24no—
481C3×D12—42no—
482C3×C4×D3—24no—
483C3×C4×D3—24no—
484C3×C4×D3—42no—
485C3×Dic6—24no—
486#627—22no—
487#627—22no—
488#627C2×D414yescomplemented
489#626—24no—
490#626—24no—
491#626—24no—
492#626—24no—
493#626—24no—
494#626—42no—
495#626—42no—
496#626—42no—
497#625—22no—
498#625—22no—
499#625—42no—
500#625C2×D414yescomplemented
501#624—24no—
502#624—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—32no—
512#546—92no—
513#546—92no—
514D42—92no—
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—32no—
528C24×C3C22×D312yes—
529C23×D3—32no—
530C23×D3—32no—
531C23×D3—32no—
532C23×D3—32no—
533C23×D3—32no—
534C23×D3—32no—
535C23×D3—61no—
536C23×D3—61no—
537C23×D3C22×D312yes—
538C3×#41—68no—
539C2×C3×Q8—32no—
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—68no—
550C22×C3×C4—21no—
551C22×C3×C4—21no—
552C22×C3×C4—32no—
553C22×C3×C4—32no—
554C22×C3×C4—32no—
555C22×C3×C4—32no—
556C22×C3×C4C22×D312yes—
557C22×C3×C4C22×D312yes—
558C2×#67—28no—
559C2×#67—32no—
560C2×#67—32no—
561C2×#67—32no—
562C2×#67—32no—
563C2×#67—32no—
564C2×#67—32no—
565C2×#67—32no—
566C2×#67—32no—
567C2×#67—32no—
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—62no—
581C2×#67—62no—
582C2×#67—62no—
583C2×#67—62no—
584C2×#67—68no—
585C2×#67—68no—
586C2×#67—68no—
587C2×#67—124no—
588C2×#67—124no—
589C2×#67—124no—
590C2×#67—124no—
591C2×#67C22×D312yes—
592C2×#67C22×D312yes—
593C2×#67C22×D312yes—
594C2×#67C22×D312yes—
595C2×#67C22×D312yes—
596C2×#67C22×D312yes—
597C2×#67C22×D312yes—
598C22×Dic3—32no—
599C22×Dic3—32no—
600C22×Dic3—32no—
601C22×Dic3—32no—
602C22×Dic3—32no—
603C22×Dic3—32no—
604C22×Dic3—61no—
605C22×Dic3—61no—
606C22×Dic3C22×D312yes—
607#239—68no—
608D3×Q8—68no—
609#237—316no—
610#237—68no—
611#237—68no—
612#237—68no—
613#237—68no—
614#237—68no—
615D3×D4—68no—
616D3×D4—68no—
617D3×D4—68no—
618D3×D4—68no—
619D3×D4—68no—
620D3×D4—68no—
621D3×D4—68no—
622D3×D4—124no—
623D3×D4—124no—
624#235—28no—
625#235—68no—
626#235—68no—
627#235—68no—
628#235—68no—
629C2×D12—32no—
630C2×D12—32no—
631C2×D12—32no—
632C2×D12—32no—
633C2×D12—32no—
634C2×D12—32no—
635C2×D12—32no—
636C2×D12—32no—
637C2×D12—32no—
638C2×D12—32no—
639C2×D12—32no—
640C2×D12—32no—
641C2×D12—62no—
642C2×D12—62no—
643C2×D12—124no—
644C2×D12—124no—
645C2×D12—124no—
646C2×D12C22×D312yes—
647C2×D12C22×D312yes—
648C2×C4×D3—32no—
649C2×C4×D3—32no—
650C2×C4×D3—32no—
651C2×C4×D3—32no—
652C2×C4×D3—32no—
653C2×C4×D3—32no—
654C2×C4×D3—32no—
655C2×C4×D3—32no—
656C2×C4×D3—32no—
657C2×C4×D3—32no—
658C2×C4×D3—32no—
659C2×C4×D3—32no—
660C2×C4×D3—61no—
661C2×C4×D3—61no—
662C2×C4×D3—61no—
663C2×C4×D3—61no—
664C2×C4×D3—68no—
665C2×C4×D3—68no—
666C2×C4×D3—68no—
667C2×C4×D3—124no—
668C2×C4×D3C22×D312yes—
669C2×C4×D3C22×D312yes—
670C2×C4×D3C22×D312yes—
671C2×Dic6—32no—
672C2×Dic6—32no—
673C2×Dic6—32no—
674C2×Dic6C22×D312yes—
675C3×C4⋊C4—32no—
676C3×C4⋊C4—32no—
677C3×C4⋊C4—32no—
678C3×C4⋊C4—32no—
679C3×C22⋊C4—22no—
680C3×C22⋊C4—22no—
681C3×C22⋊C4—32no—
682C3×C22⋊C4—32no—
683C3×C22⋊C4—32no—
684C3×C22⋊C4—32no—
685C3×C22⋊C4—32no—
686C3×C22⋊C4—32no—
687C3×C22⋊C4—32no—
688C3×C22⋊C4—32no—
689C3×C22⋊C4C22×D312yes—
690C3×C22⋊C4C22×D312yes—
691C3×C22⋊C4C22×D312yes—
692C3×C22⋊C4C22×D312yes—
693C3×C42—32no—
694#217—32no—
695#217—32no—
696#217—32no—
697#217C22×D312yes—
698#217C22×D312yes—
699#217C22×D312yes—
700(C2×D3)⋊C4—32no—
701(C2×D3)⋊C4—32no—
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—
720(C2×D3)⋊C4C22×D312yes—
721(C2×D3)⋊C4C22×D312yes—
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—62no—
734Dic3⋊C4—62no—
735Dic3⋊C4C22×D312yes—
736Dic3⋊C4C22×D312yes—
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—22no—
746C22×C32—22no—
747C22×C32—22no—
748C22×C32—82no—
749C22×C32C22×D412yes—
750C22×C32C2511yescharacteristic
751C2×C3⋊D3—21no—
752C2×C3⋊D3—21no—
753C2×C3⋊D3—21no—
754C2×C3⋊D3—22no—
755C2×C3⋊D3—21no—
756C2×C3⋊D3—22no—
757C2×C3⋊D3—21no—
758C2×C3⋊D3—22no—
759C2×C3⋊D3—44no—
760C2×C3⋊D3—82no—
761C2×C3⋊D3H(5,𝔽2)12yescomplemented
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—84no—
771C2×C3×D3C22×D414yes—
772D32—48no—
773D32—84no—
774C32×C4—21no—
775C32×C4—21no—
776C32×C4—22no—
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—32no—
787C2×#41—91no—
788C2×#41—91no—
789C2×#41—92no—
790C2×#41—92no—
791C2×#41—91no—
792C2×#41—91no—
793C2×#41—91no—
794C2×#41—92no—
795C2×#41—188no—
796C22×Q8—91no—
797C22×D4—32no—
798C22×D4—92no—
799C22×D4—92no—
800C22×D4—91no—
801C22×D4—92no—
802C22×D4—92no—
803C22×D4—92no—
804C22×D4—92no—
805C22×D4—91no—
806C22×D4—91no—
807C22×D4—91no—
808C23×C4—92no—
809C23×C4—91no—
810#127—92no—
811#127—92no—
812#127—92no—
813#124—32no—
814#124—92no—
815#124—92no—
816#123—32no—
817#123—32no—
818#123—92no—
819C22⋊Q8—32no—
820C22⋊Q8—92no—
821C22⋊Q8—92no—
822C22⋊Q8—91no—
823C22⋊Q8—91no—
824C22⋊Q8—92no—
825#121—32no—
826#121—32no—
827#121—32no—
828#121—91no—
829#121—91no—
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—92no—
839#121—92no—
840#121—92no—
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—92no—
850#120—92no—
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—32no—
871C2×C22⋊C4—92no—
872C2×C22⋊C4—91no—
873C2×C22⋊C4D3211yescharacteristic, complemented
874C23×C3—24no—
875C23×C3—21no—
876C23×C3—22no—
877C23×C3—32no—
878C23×C3—32no—
879C23×C3—32no—
880C23×C3—42no—
881C23×C3—42no—
882C23×C3—42no—
883C23×C3—42no—
884C23×C3—42no—
885C23×C3—64no—
886C23×C3—122no—
887C23×C3—122no—
888C23×C3C23×D312yes—
889C23×C3C23×D312yes—
890C23×C3C23×D312yes—
891C22×D3—24no—
892C22×D3—32no—
893C22×D3—32no—
894C22×D3—32no—
895C22×D3—32no—
896C22×D3—42no—
897C22×D3—42no—
898C22×D3—61no—
899C22×D3—61no—
900C22×D3—62no—
901C22×D3—64no—
902C22×D3—64no—
903C22×D3—64no—
904C22×D3—64no—
905C22×D3—64no—
906C22×D3—64no—
907C22×D3—64no—
908C22×D3—64no—
909C22×D3—64no—
910C22×D3—64no—
911C22×D3—122no—
912C22×D3—122no—
913C22×D3—122no—
914C22×D3—122no—
915C22×D3—122no—
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×Q8—64no—
929C3×D4—38no—
930C3×D4—64no—
931C3×D4—64no—
932C3×D4—64no—
933C3×D4—64no—
934C3×D4—64no—
935C3×D4—122no—
936C3×D4—122no—
937C3×D4—122no—
938C2×C3×C4—24no—
939C2×C3×C4—22no—
940C2×C3×C4—21no—
941C2×C3×C4—21no—
942C2×C3×C4—32no—
943C2×C3×C4—32no—
944C2×C3×C4—32no—
945C2×C3×C4—32no—
946C2×C3×C4—32no—
947C2×C3×C4—42no—
948C2×C3×C4—42no—
949C2×C3×C4—42no—
950C2×C3×C4—64no—
951C2×C3×C4—64no—
952C2×C3×C4—64no—
953C2×C3×C4—122no—
954C2×C3×C4C23×D312yes—
955C2×C3×C4C23×D312yes—
956C2×C3×C4C23×D312yes—
957C2×C3×C4C23×D312yes—
958#67—24no—
959#67—24no—
960#67—24no—
961#67—24no—
962#67—38no—
963#67—42no—
964#67—42no—
965#67—64no—
966#67—64no—
967#67—64no—
968#67—64no—
969#67—64no—
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—124no—
979#67—124no—
980#67—124no—
981#67—122no—
982#67—122no—
983#67—122no—
984#67—122no—
985#67—122no—
986#67—122no—
987#67—122no—
988#67—124no—
989#67D3×D418yescomplemented
990C2×Dic3—24no—
991C2×Dic3—38no—
992C2×Dic3—32no—
993C2×Dic3—32no—
994C2×Dic3—38no—
995C2×Dic3—32no—
996C2×Dic3—32no—
997C2×Dic3—64no—
998C2×Dic3—61no—
999C2×Dic3—61no—
1000C2×Dic3—62no—
1001C2×Dic3—64no—
1002C2×Dic3—64no—
1003C2×Dic3—122no—
1004C2×Dic3—122no—
1005C2×Dic3—122no—
1006C2×Dic3C23×D312yes—
1007C2×Dic3C23×D312yes—
1008C2×Dic3C23×D312yes—
1009C2×Dic3C23×D312yes—
1010C2×Dic3C23×D312yes—
1011D12—24no—
1012D12—42no—
1013D12—64no—
1014D12—64no—
1015D12—64no—
1016D12—64no—
1017D12—64no—
1018D12—64no—
1019D12—64no—
1020D12—124no—
1021D12—122no—
1022D12—122no—
1023D12—124no—
1024D12—122no—
1025D12—122no—
1026D12—122no—
1027C4×D3—24no—
1028C4×D3—24no—
1029C4×D3—38no—
1030C4×D3—42no—
1031C4×D3—64no—
1032C4×D3—64no—
1033C4×D3—64no—
1034C4×D3—64no—
1035C4×D3—64no—
1036C4×D3—64no—
1037C4×D3—64no—
1038C4×D3—64no—
1039C4×D3—64no—
1040C4×D3—64no—
1041C4×D3—122no—
1042C4×D3—122no—
1043C4×D3—122no—
1044C4×D3—122no—
1045C4×D3—122no—
1046Dic6—24no—
1047Dic6—38no—
1048Dic6—64no—
1049Dic6—64no—
1050C2×C32—22no—
1051C2×C32—42no—
1052C2×C32C23×D411yescharacteristic
1053C2×C32C2×H(5,𝔽2)11yescharacteristic
1054C2×C32#58511yescharacteristic
1055C3⋊D3—22no—
1056C3⋊D3—41no—
1057C3⋊D3—42no—
1058C3×D3—24no—
1059C3×D3—42no—
1060C3×D3—42no—
1061C24—32no—
1062C24—92no—
1063C24—92no—
1064C24—91no—
1065C24—91no—
1066C24C2×D3211yescharacteristic
1067#41—68no—
1068#41—98no—
1069#41—184no—
1070#41—184no—
1071#41—188no—
1072#41—188no—
1073#41—184no—
1074#41—184no—
1075#41—188no—
1076C2×Q8—32no—
1077C2×Q8—91no—
1078C2×Q8—91no—
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—68no—
1091C2×D4—92no—
1092C2×D4—92no—
1093C2×D4—92no—
1094C2×D4—92no—
1095C2×D4—92no—
1096C2×D4—92no—
1097C2×D4—92no—
1098C2×D4—92no—
1099C2×D4—91no—
1100C2×D4—91no—
1101C2×D4—91no—
1102C2×D4—92no—
1103C2×D4—92no—
1104C2×D4—92no—
1105C2×D4—92no—
1106C2×D4—92no—
1107C2×D4—92no—
1108C2×D4—92no—
1109C2×D4—188no—
1110C2×D4—184no—
1111C2×D4—188no—
1112C2×D4—188no—
1113C2×D4—184no—
1114C2×D4—188no—
1115C2×D4—362no—
1116C2×D4—364no—
1117C2×D4—364no—
1118C2×D4—362no—
1119C22×C4—32no—
1120C22×C4—32no—
1121C22×C4—32no—
1122C22×C4—32no—
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—184no—
1136C22×C4—188no—
1137C22×C4C2×D3211yescharacteristic
1138C22×C4C2×D3211yescharacteristic
1139C4⋊C4—32no—
1140C4⋊C4—32no—
1141C4⋊C4—32no—
1142C4⋊C4—32no—
1143C4⋊C4—91no—
1144C4⋊C4—92no—
1145C4⋊C4—91no—
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⋊C4C2×D3212yes—
1167C22⋊C4C2×D3212yes—
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—21no—
1183C22×C3—34no—
1184C22×C3—42no—
1185C22×C3—42no—
1186C22×C3—42no—
1187C22×C3—62no—
1188C22×C3—62no—
1189C22×C3—62no—
1190C22×C3—62no—
1191C22×C3—62no—
1192C22×C3—62no—
1193C22×C3—62no—
1194C22×C3—62no—
1195C22×C3—84no—
1196C22×C3—84no—
1197C22×C3—244no—
1198C22×C3C2×D3×D414yes—
1199C22×C3C24×D312yes—
1200C2×D3—22no—
1201C2×D3—22no—
1202C2×D3—22no—
1203C2×D3—22no—
1204C2×D3—22no—
1205C2×D3—22no—
1206C2×D3—22no—
1207C2×D3—22no—
1208C2×D3—34no—
1209C2×D3—62no—
1210C2×D3—62no—
1211C2×D3—62no—
1212C2×D3—62no—
1213C2×D3—62no—
1214C2×D3—62no—
1215C2×D3—62no—
1216C2×D3—62no—
1217C2×D3—62no—
1218C2×D3—62no—
1219C2×D3—62no—
1220C2×D3—62no—
1221C2×D3—62no—
1222C2×D3—84no—
1223C2×D3—121no—
1224C2×D3—121no—
1225C2×D3—121no—
1226C2×D3—121no—
1227C2×D3—122no—
1228C2×D3—122no—
1229C2×D3—122no—
1230C2×D3—128no—
1231C2×D3—128no—
1232C2×D3—128no—
1233C2×D3—128no—
1234C2×D3—244no—
1235C2×D3—244no—
1236C2×D3—244no—
1237C2×D3—244no—
1238C2×D3C2×D3×D414yes—
1239C3×C4—22no—
1240C3×C4—22no—
1241C3×C4—22no—
1242C3×C4—22no—
1243C3×C4—34no—
1244C3×C4—41no—
1245C3×C4—41no—
1246C3×C4—42no—
1247C3×C4—62no—
1248C3×C4—62no—
1249C3×C4—62no—
1250C3×C4—62no—
1251Dic3—22no—
1252Dic3—22no—
1253Dic3—22no—
1254Dic3—22no—
1255Dic3—34no—
1256Dic3—34no—
1257Dic3—62no—
1258Dic3—62no—
1259Dic3—62no—
1260Dic3—62no—
1261Dic3—122no—
1262Dic3C2×D3×D414yes—
1263C32#348811yescharacteristic, complemented, Sylow
1264C23—22no—
1265C23—32no—
1266C23—32no—
1267C23—32no—
1268C23—41no—
1269C23—41no—
1270C23—64no—
1271C23—91no—
1272C23—92no—
1273C23—91no—
1274C23—122no—
1275C23—122no—
1276C23—182no—
1277C23—184no—
1278C23—184no—
1279C23—184no—
1280C23—182no—
1281C23—182no—
1282C23—361no—
1283C23—361no—
1284C23—361no—
1285C23—362no—
1286C23—362no—
1287C23—362no—
1288C23C22×D3212yes—
1289C23C22×D3211yescharacteristic
1290Q8—64no—
1291Q8—94no—
1292Q8—182no—
1293Q8—182no—
1294D4—38no—
1295D4—64no—
1296D4—64no—
1297D4—64no—
1298D4—64no—
1299D4—64no—
1300D4—94no—
1301D4—122no—
1302D4—122no—
1303D4—122no—
1304D4—184no—
1305D4—184no—
1306D4—184no—
1307D4—184no—
1308D4—184no—
1309D4—184no—
1310D4—184no—
1311D4—184no—
1312D4—182no—
1313D4—182no—
1314D4—184no—
1315D4—362no—
1316D4—362no—
1317D4—362no—
1318D4—362no—
1319D4—362no—
1320D4—362no—
1321C2×C4—22no—
1322C2×C4—32no—
1323C2×C4—32no—
1324C2×C4—32no—
1325C2×C4—32no—
1326C2×C4—32no—
1327C2×C4—41no—
1328C2×C4—64no—
1329C2×C4—64no—
1330C2×C4—64no—
1331C2×C4—98no—
1332C2×C4—94no—
1333C2×C4—91no—
1334C2×C4—91no—
1335C2×C4—92no—
1336C2×C4—122no—
1337C2×C4—182no—
1338C2×C4—182no—
1339C2×C4—182no—
1340C2×C4—182no—
1341C2×C4—184no—
1342C2×C4—184no—
1343C2×C4—184no—
1344C2×C4—184no—
1345C2×C4—362no—
1346C2×C4—361no—
1347C2×C4C22×D3212yes—
1348C2×C4C22×D3211yescharacteristic
1349C2×C4C22×D3211yescharacteristic
1350C2×C3—24no—
1351C2×C3—24no—
1352C2×C3—21no—
1353C2×C3—21no—
1354C2×C3—21no—
1355C2×C3—42no—
1356C2×C3—42no—
1357C2×C3—64no—
1358C2×C3—82no—
1359C2×C3—122no—
1360C2×C3—122no—
1361C2×C3C22×D3×D412yes—
1362C2×C3#596412yes—
1363C2×C3D3×H(5,𝔽2)12yes—
1364D3—24no—
1365D3—42no—
1366D3—42no—
1367D3—64no—
1368D3—122no—
1369D3—122no—
1370D3—122no—
1371D3—122no—
1372D3—122no—
1373D3—242no—
1374C22—21no—
1375C22—21no—
1376C22—22no—
1377C22—22no—
1378C22—22no—
1379C22—34no—
1380C22—62no—
1381C22—62no—
1382C22—62no—
1383C22—62no—
1384C22—62no—
1385C22—62no—
1386C22—62no—
1387C22—62no—
1388C22—82no—
1389C22—92no—
1390C22—181no—
1391C22—181no—
1392C22—181no—
1393C22—182no—
1394C22—181no—
1395C22—182no—
1396C22—182no—
1397C22—181no—
1398C22—244no—
1399C22—364no—
1400C22—368no—
1401C22—722no—
1402C22—724no—
1403C22D32×D412yes—
1404C22C23×D3211yescharacteristic
1405C4—21no—
1406C4—21no—
1407C4—22no—
1408C4—34no—
1409C4—62no—
1410C4—62no—
1411C4—62no—
1412C4—62no—
1413C4—92no—
1414C4—92no—
1415C4—182no—
1416C3—21no—
1417C3#8662912yescomplemented
1418C2—22no—
1419C2—42no—
1420C2—64no—
1421C2—122no—
1422C2—122no—
1423C2—182no—
1424C2—361no—
1425C2—362no—
1426C2#1059666911yescharacteristic
1427C2C2×D32×D411yescharacteristic
1428C2#1059667511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C22⋊C4C22
hypercenterC2×C22⋊C4D32
hypocenterC32#3488
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64330C2semidirect
2. C2×#64306C2semidirect
3. C2×#64093C2semidirect
4. C3×#5490C2semidirect
5. #10595526C2semidirect
6. #10595502C2semidirect
7. #10595074C2semidirect
8. #10595068C2semidirect
9. #10594930C2semidirect
10. #10594920C2semidirect
11. #10594876C2semidirect
12. #10594275C2semidirect
13. #10594272C2semidirect
14. #10594270C2semidirect
15. #10594266C2semidirect
16. D3×#884C2semidirect
17. #10594246C2semidirect
18. #10594075C2semidirect
19. #10594059C2semidirect
21. C22×#638C22semidirect
22. C22×#638C22semidirect
23. C22×C4⋊(C3⋊D3)C22semidirect
24. C22×C4×C3⋊D3C22semidirect
25. C22×C3×#67C22semidirect
26. C2×C3×#235C22semidirect
28. C2×#3811C22semidirect
29. C2×#3811C22semidirect
30. C2×D3×#67C22semidirect
31. C2×D3×#67C22semidirect
32. C2×D3×#67C22semidirect
34. C2×#3805C22semidirect
35. C2×#3805C22semidirect
36. C2×#3804C22semidirect
37. C2×#3804C22semidirect
39. C2×#3802C22semidirect
40. C2×D3×D12C22semidirect
41. C2×C4×D32C22semidirect
42. C2×#3798C22semidirect
43. C2×#3798C22semidirect
44. C2×#3797C22semidirect
45. C2×#3796C22semidirect
46. C2×C32×C22⋊C4C22semidirect
47. C2×#3752C22semidirect
48. C2×#3750C22semidirect
49. #64093C22semidirect
50. #64093C22semidirect
51. #64093C22semidirect
52. #64093C22semidirect
53. C3×#953C22semidirect
54. C3×#930C22semidirect
55. C3×#929C22semidirect
56. C3×C4×#67C22semidirect
57. C3×#885C22semidirect
58. C3×#884C22semidirect
59. C3×#884C22semidirect
60. C3×#883C22semidirect
61. C3×#882C22semidirect
62. C3×#67⋊C4C22semidirect
63. C3×D3×C22⋊C4C22semidirect
64. C3×#878C22semidirect
65. #63983C22semidirect
66. #63981C22semidirect
67. #63981C22semidirect
68. #63980C22semidirect
69. #63979C22semidirect
70. #63979C22semidirect
71. #63978C22semidirect
72. #63977C22semidirect
73. #67⋊Dic3C22semidirect
74. #63971C22semidirect
75. #63971C22semidirect
76. #63971C22semidirect
77. #63958C22semidirect
78. #63957C22semidirect
79. #63953C22semidirect
80. #63952C22semidirect
81. #63923C22semidirect
82. #63923C22semidirect
83. #63922C22semidirect
84. D3×(C2×D3)⋊C4C22semidirect
85. #63912C22semidirect
86. #63912C22semidirect
87. #63911C22semidirect
88. #63910C22semidirect
89. #63910C22semidirect
90. #63909C22semidirect
91. #63907C22semidirect
92. #63906C22semidirect
93. #63904C22semidirect
94. #63899C22semidirect
95. #63899C22semidirect
96. #63894C22semidirect
97. #63888C22semidirect
98. #63886C22semidirect
99. #63885C22semidirect
100. #63885C22semidirect
101. #63881C22semidirect
102. #63881C22semidirect
103. #63879C22semidirect
104. #63877C22semidirect
105. D3×Dic3⋊C4C22semidirect
106. #63865C22semidirect
107. #63865C22semidirect
108. #63850C22semidirect
109. #63837C22semidirect
138. #5490D3semidirect
206. #3805D4semidirect
262. C22×#67C2×D3semidirect
286. C2×#235C2×D3semidirect
307. C2×C3×C22⋊C4C2×D3semidirect
309. #953C2×D3semidirect
336. #930C2×D3semidirect
338. #929C2×D3semidirect
342. C4×#67C2×D3semidirect
368. #885C2×D3semidirect
392. #884C2×D3semidirect
393. #884C2×D3semidirect
394. #883C2×D3semidirect
403. #882C2×D3semidirect
409. #67⋊C4C2×D3semidirect
411. D3×C22⋊C4C2×D3semidirect
414. #878C2×D3semidirect
457. C2×C3⋊Dic3C2×D4semidirect
473. C3×#67C2×D4semidirect
488. #627C2×D4semidirect
500. #625C2×D4semidirect
506. D3×Dic3C2×D4semidirect
761. C2×C3⋊D3H(5,𝔽2)semidirect
873. C2×C22⋊C4D32semidirect
989. #67D3×D4semidirect
1263. C32#3488semidirect
1417. C3#86629semidirect

Maximal subgroups

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

subgroupindex
C2×#643302
C2×#643062
C2×#640932
C3×#54902
#105955262
#105955022
#105950742
#105950682
#105949302
#105949202
#105948762
#105942752
#105942722
#105942702
#105942662
D3×#8842
#105942462
#105940752
#105940592
#866293