Finite Group Databasebeta

← #11911156

Subgroups — #11911156

Order 1152.

2497 conjugacy classes of subgroups.

The subgroup lattice has 1372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596098C211yesmaximal, characteristic, complemented
2C3×#5645C211yesmaximal, characteristic, complemented
3C3×#5644C211yesmaximal, characteristic, complemented
4#10595431C212yesmaximal, complemented
5#10595417C212yesmaximal, complemented
6#10595081C211yesmaximal, characteristic, complemented
7#10595072C211yesmaximal, characteristic, complemented
8#10594911C211yesmaximal, characteristic, complemented
9C2×#63853C211yesmaximal, characteristic, complemented
10#10594663C212yesmaximal, complemented
11#10594657C212yesmaximal, complemented
12#10594648C212yesmaximal, complemented
13#10594611C212yesmaximal, complemented
14#10594501C212yesmaximal, complemented
15#10594481C212yesmaximal, complemented
16#10594294C212yesmaximal, complemented
17#10594293C212yesmaximal, complemented
18#10594277C212yesmaximal, complemented
19#10594218C212yesmaximal, complemented
20#86459—31nomaximal
21#86420—31nomaximal
22C2×#3832C2211yescharacteristic, complemented
23C22×C4×C3⋊D3C2211yescharacteristic, complemented
24C2×#3811C2212yescomplemented
25C2×D3×#67C2212yescomplemented
26C22×#626C2211yescharacteristic
27C2×#3804C2212yescomplemented
28C2×#3802C2211yescharacteristic, complemented
29C2×D3×D12C2212yescomplemented
30C32×C22⋊Q8C2211yescharacteristic, complemented
31#64155C2211yescharacteristic, complemented
32#64139C2211yescharacteristic, complemented
33#64104C2211yescharacteristic, complemented
34#64103C2212yescomplemented
35#64102C2212yescomplemented
36#64101C2211yescharacteristic, complemented
37#64091C2212yescomplemented
38#64090C2212yescomplemented
39C3×#947C2212yescomplemented
40C3×#946C2212yescomplemented
41C3×#930C2211yescharacteristic
42C3×#930C2211yescharacteristic, complemented
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
45C3×#898C2212yescomplemented
46C3×#898C2212yescomplemented
47C3×#895C2212yescomplemented
48C3×#894C2212yescomplemented
49C3×#894C2212yescomplemented
50C3×#890C2212yescomplemented
51C3×#886C2212yescomplemented
52C3×#882C2212yescomplemented
53C3×#67⋊C4C2212yescomplemented
54C3×#67⋊C4C2212yescomplemented
55#63980C2212yescomplemented
56#63978C2212yescomplemented
57#63978C2212yescomplemented
58C2×Dic3⋊Dic3C2211yescharacteristic, complemented
59C2×#3722C2211yescharacteristic, complemented
60C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
61#63923C2212yescomplemented
62#63923C2212yescomplemented
63#63923C2212yescomplemented
64#63922C2212yes—
65#63922C2212yescomplemented
66#63922C2212yescomplemented
67#63921C2212yescomplemented
68#63921C2212yescomplemented
69D3×(C2×D3)⋊C4C2212yescomplemented
70#63916C2211yescharacteristic, complemented
71#63916C2211yescharacteristic, complemented
72#63916C2212yescomplemented
73#63915C2212yescomplemented
74#63912C2212yescomplemented
75#63911C2212yescomplemented
76#63910C2212yes—
77#63910C2212yescomplemented
78#63910C2212yescomplemented
79#63909C2212yescomplemented
80#63906C2212yescomplemented
81#63906C2212yescomplemented
82#63905C2212yescomplemented
83C4×#626C2212yescomplemented
84#63900C2211yescharacteristic, complemented
85#63899C2212yescomplemented
86#63898C2212yescomplemented
87#63895C2212yescomplemented
88#63895C2212yescomplemented
89#63894C2212yescomplemented
90#63893C2212yescomplemented
91#63891C2212yescomplemented
92#63890C2212yescomplemented
93#63890C2212yescomplemented
94#63886C2212yescomplemented
95#63886C2212yescomplemented
96#63885C2212yescomplemented
97#63880C2212yescomplemented
98#63868C2212yescomplemented
99#63867C2212yescomplemented
100#63862C2212yescomplemented
101#63855C2212yescomplemented
102#63854C2212yescomplemented
103#63853C2212yescomplemented
104#63853C2212yescomplemented
105#63853C2212yescomplemented
106#63853C2212yescomplemented
107#63853C2212yescomplemented
108#63852C2212yescomplemented
109C3×#539—31no—
110C3×#538—31no—
111#5711—32no—
112#5707—32no—
113#5705—32no—
114#5704—32no—
115#5697—32no—
116#5692—32no—
117#5684—32no—
118#5676—32no—
119#5666—32no—
120#5658—32no—
121#5657—32no—
122#5654—32no—
123#5654—32no—
124#5653—32no—
125#5647—32no—
126#5645D311yescharacteristic, complemented
127#5644D311yescharacteristic, complemented
128#5630—32no—
129#5627—31no—
130#5627—31no—
131#5627—61no—
132#5619—32no—
133#5605—31no—
134#5605—32no—
135D3×#121—31no—
136D3×#121—31no—
137#5597—31no—
138#5591—32no—
139#5590—32no—
140#5565—32no—
141#5554—32no—
142D4×D12—32no—
143#5540—32no—
144#5510—31no—
145C2×#894—31no—
146#5493—31no—
147C2×#883—31no—
148C23×C3⋊D3C2311yescharacteristic
149C23×C3×D3C2311yescharacteristic
150C22×D32C2312yes—
151C22×D32C2312yes—
152C2×C32×Q8C2311yescharacteristic
153C22×C32×C4C2311yescharacteristic
154C2×#638C2312yes—
155C22×C3⋊Dic3C2311yescharacteristic
156#3832—42no—
157C2×C4⋊(C3⋊D3)C2312yes—
158C2×C4⋊(C3⋊D3)C2312yes—
159C2×C4⋊(C3⋊D3)C2311yescharacteristic
160C2×C4×C3⋊D3—42no—
161C2×C4×C3⋊D3C2311yescharacteristic
162C2×C4×C3⋊D3C2311yescharacteristic
163C2×C4×C3⋊D3C2312yes—
164C2×C4×C3⋊D3C2311yescharacteristic
165C2×C4×C3⋊D3C2311yescharacteristic
166C2×C3×#67C2312yes—
167C2×C3×#67C2312yes—
168C22×C3×Dic3C2311yescharacteristic
169C22×C3×Dic3C2311yescharacteristic
170C22×C3×Dic3C2311yescharacteristic
171C2×C3×D12C2312yes—
172C2×C3×D12C2312yes—
173C2×C3×D12C2311yescharacteristic
174C2×C3×D12C2311yescharacteristic
175C2×C3×C4×D3C2312yes—
176C2×C3×C4×D3C2312yes—
177#3811—44no—
178D3×#67—44no—
179C2×#627C2312yes—
180C2×#626—42no—
181C2×#626C2312yes—
182C2×#626C2312yes—
183C2×#626C2312yes—
184C2×#626C2312yes—
185C2×#626C2312yes—
186C2×#626C2312yes—
187C2×#626C2312yes—
188C2×#626C2312yes—
189C2×#625C2312yes—
190C2×#625C2312yes—
191C2×#624C2312yes—
192C2×#624C2312yes—
193#3804—44no—
194C2×D3×Dic3C2312yes—
195C2×D3×Dic3C2312yes—
196#3802—42no—
197D3×D12—44no—
198C32×C4⋊C4C2312yes—
199C32×C4⋊C4C2311yescharacteristic
200C32×C22⋊C4C2312yes—
201#3752C2312yes—
202#3752C2312yes—
203#3752C2312yes—
204#3752C2312yes—
205C4⋊(C3⋊Dic3)C2311yescharacteristic
206#3750C2312yes—
207C4×C3⋊Dic3C2312yes—
208C3×(C2×D3)⋊C4C2312yes—
209C3×(C2×D3)⋊C4C2312yes—
210C3×(C2×D3)⋊C4C2312yes—
211C3×(C2×D3)⋊C4C2312yes—
212C3×(C2×D3)⋊C4C2312yes—
213C3×(C2×D3)⋊C4C2312yes—
214C3×(C2×D3)⋊C4C2312yes—
215C3×(C2×D3)⋊C4C2312yes—
216C3×(C2×D3)⋊C4C2312yes—
217C3×(C2×D3)⋊C4C2312yes—
218C3×C4⋊Dic3C2312yes—
219C3×C4⋊Dic3C2312yes—
220C3×C4⋊Dic3C2311yescharacteristic
221C3×C4⋊Dic3C2311yescharacteristic
222C3×Dic3⋊C4C2312yes—
223C3×Dic3⋊C4C2312yes—
224C3×Dic3⋊C4C2312yes—
225C3×Dic3⋊C4C2312yes—
226C3×C4×Dic3C2312yes—
227C3×C4×Dic3C2312yes—
228#3724C2312yes—
229Dic3⋊Dic3C2312yes—
230Dic3⋊Dic3C2312yes—
231Dic3⋊Dic3C2312yes—
232Dic3⋊Dic3C2312yes—
233#3722C2312yes—
234#3722C2312yes—
235#3722C2312yes—
236#3722C2312yes—
237(C2×D3)⋊Dic3C2312yes—
238(C2×D3)⋊Dic3C2312yes—
239(C2×D3)⋊Dic3C2312yes—
240(C2×D3)⋊Dic3C2312yes—
241(C2×D3)⋊Dic3C2312yes—
242(C2×D3)⋊Dic3C2312yes—
243#3534—91noSylow
244C22×#67—32no—
245C22×#67—31no—
246C2×#239—31no—
247C2×#239—31no—
248C2×#239—61no—
249C2×#237—32no—
250C2×D3×D4—32no—
251C2×D3×D4—32no—
252C2×D3×D4—32no—
253C2×D3×D4—31no—
254C2×D3×D4—31no—
255C2×D3×D4—32no—
256C2×#235—32no—
257C22×D12—31no—
258C22×D12—32no—
259C22×C4×D3—31no—
260C22×C4×D3—31no—
261C22×C4×D3—61no—
262C3×#126—32no—
263C3×#126—32no—
264C3×#125—32no—
265C3×#124—32no—
266C3×#123—32no—
267C3×#123—32no—
268C3×#123—32no—
269C3×C22⋊Q8—21no—
270C3×C22⋊Q8—32no—
271C3×C22⋊Q8C2×D311yescharacteristic, complemented
272C3×C22⋊Q8C2×D311yescharacteristic, complemented
273C3×#121—31no—
274C3×#121—31no—
275C3×#121—32no—
276C3×#120—32no—
277C3×C4×D4—32no—
278C3×C4×D4—32no—
279C2×C3×C4⋊C4—31no—
280C2×C3×C22⋊C4—31no—
281C2×#217—31no—
282#947C2×D312yescomplemented
283#946—31no—
284#946—31no—
285#946—61no—
286#946C2×D312yescomplemented
287#940—32no—
288#939—32no—
289#939—32no—
290#939—32no—
291#939—32no—
292#939—32no—
293#939—32no—
294#939—32no—
295#938—31no—
296#938—32no—
297#938—31no—
298#937—32no—
299#937—32no—
300#937—32no—
301D4×Dic3—32no—
302#930—31no—
303#930—31no—
304#930—32no—
305#930—32no—
306#930—32no—
307#930—32no—
308#930—32no—
309#930—61no—
310#930C2×D311yescharacteristic
311#930C2×D311yescharacteristic, complemented
312#929—32no—
313C4×#67—32no—
314C2×(C2×D3)⋊C4—31no—
315C2×(C2×D3)⋊C4—31no—
316C2×(C2×D3)⋊C4—31no—
317C2×(C2×D3)⋊C4—32no—
318C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
319#926—32no—
320C2×C4⋊Dic3—31no—
321C2×Dic3⋊C4—31no—
322C2×Dic3⋊C4C2×D311yescharacteristic, complemented
323#898—32no—
324#898—32no—
325#898C2×D312yescomplemented
326#898C2×D312yescomplemented
327#897—32no—
328#897—32no—
329#897—32no—
330#896—32no—
331#896—32no—
332#896—32no—
333#895—32no—
334#895—32no—
335#895—32no—
336#895—31no—
337#895—31no—
338#895—32no—
339#895—31no—
340#895—31no—
341#895—32no—
342#895—32no—
343#895—32no—
344#895—61no—
345#895C2×D312yescomplemented
346#894—32no—
347#894—32no—
348#894—32no—
349#894—32no—
350#894—32no—
351#894—32no—
352#894—32no—
353#894—32no—
354#894—32no—
355#894—32no—
356#894—62no—
357#894C2×D312yescomplemented
358#894C2×D312yescomplemented
359#893—32no—
360#893—32no—
361#893—32no—
362#893—32no—
363#893—62no—
364#892—31no—
365#892—31no—
366#892—61no—
367D3×C4⋊C4—31no—
368D3×C4⋊C4—31no—
369#890C2×D312yescomplemented
370#889—32no—
371#886—32no—
372#886—32no—
373#886—32no—
374#886C2×D312yescomplemented
375#885—32no—
376#885—32no—
377#885—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#883—32no—
387#883—32no—
388#883—32no—
389#883—32no—
390#883—32no—
391#883—32no—
392#883—32no—
393#883—32no—
394#882—32no—
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#882—32no—
404#882—32no—
405#882—62no—
406#882C2×D312yescomplemented
407#67⋊C4—32no—
408#67⋊C4—32no—
409#67⋊C4—32no—
410#67⋊C4—62no—
411#67⋊C4C2×D312yescomplemented
412#67⋊C4C2×D312yescomplemented
413D3×C22⋊C4—32no—
414D3×C22⋊C4—32no—
415D3×C22⋊C4—32no—
416D3×C22⋊C4—32no—
417D3×C22⋊C4—32no—
418#879—32no—
419#878—32no—
420#878—32no—
421#876—32no—
422#875—32no—
423#874—32no—
424C4×D12—32no—
425C4×D12—32no—
426C4×D12—32no—
427#872—32no—
428#870—32no—
429C23×C32C2411yescharacteristic
430C22×C3⋊D3—22no—
431C22×C3⋊D3—22no—
432C22×C3⋊D3—41no—
433C22×C3⋊D3C2412yes—
434C22×C3⋊D3C2411yescharacteristic
435C22×C3⋊D3C2411yescharacteristic
436C22×C3×D3—22no—
437C22×C3×D3—41no—
438C22×C3×D3—41no—
439C22×C3×D3C2412yes—
440C22×C3×D3C2412yes—
441C22×C3×D3C2412yes—
442C2×D32—24no—
443C2×D32—42no—
444C2×D32—42no—
445C2×D32—42no—
446C2×D32—42no—
447C2×D32—42no—
448C32×Q8—41no—
449C2×C32×C4—41no—
450C2×C32×C4C2412yes—
451C2×C32×C4C2412yes—
452C2×C32×C4C2411yescharacteristic
453C2×C32×C4C2411yescharacteristic
454#638—24no—
455C2×C3⋊Dic3—41no—
456C2×C3⋊Dic3C2411yescharacteristic
457C2×C3⋊Dic3C2411yescharacteristic
458C2×C3⋊Dic3C2412yes—
459C4⋊(C3⋊D3)—24no—
460C4⋊(C3⋊D3)—42no—
461C4⋊(C3⋊D3)—41no—
462C4×C3⋊D3—22no—
463C4×C3⋊D3—22no—
464C4×C3⋊D3—41no—
465C4×C3⋊D3—41no—
466C4×C3⋊D3—42no—
467C3×#67—24no—
468C3×#67—24no—
469C2×C3×Dic3—22no—
470C2×C3×Dic3—41no—
471C2×C3×Dic3—41no—
472C2×C3×Dic3C2412yes—
473C2×C3×Dic3C2412yes—
474C2×C3×Dic3C2412yes—
475C2×C3×Dic3C2412yes—
476C2×C3×Dic3C2412yes—
477C3×D12—42no—
478C3×D12—41no—
479C3×D12—41no—
480C3×D12—42no—
481C3×C4×D3—42no—
482C3×C4×D3—42no—
483#627—42no—
484#626—24no—
485#626—42no—
486#626—42no—
487#626—42no—
488#626—42no—
489#626—42no—
490#626—42no—
491#626—42no—
492#625—42no—
493#625—42no—
494#624—42no—
495#624—42no—
496D3×Dic3—42no—
497D3×Dic3—42no—
498#562—92no—
499#560—92no—
500#553—92no—
501#551—92no—
502#546—92no—
503#546—92no—
504#546—92no—
505D42—92no—
506#540—92no—
507#539—31no—
508#539—92no—
509#538—31no—
510#538—92no—
511#537—91no—
512#534—91no—
513#534—92no—
514#525—91no—
515C2×#123—91no—
516C2×#121—91no—
517C24×C3—31no—
518C23×D3—31no—
519C23×D3—31no—
520C23×D3—32no—
521C23×D3—32no—
522C23×D3—32no—
523C23×D3—32no—
524C23×D3—61no—
525C23×D3C22×D311yescharacteristic
526C2×C3×Q8—21no—
527C2×C3×Q8C22×D311yescharacteristic
528C2×C3×Q8C22×D311yescharacteristic
529C2×C3×D4—32no—
530C2×C3×D4—32no—
531C2×C3×D4—32no—
532C2×C3×D4—31no—
533C2×C3×D4—32no—
534C2×C3×D4—31no—
535C22×C3×C4—21no—
536C22×C3×C4—31no—
537C22×C3×C4—31no—
538C22×C3×C4—31no—
539C22×C3×C4—32no—
540C22×C3×C4—32no—
541C22×C3×C4C22×D311yescharacteristic
542C22×C3×C4C22×D311yescharacteristic
543C2×#67—32no—
544C2×#67—32no—
545C2×#67—32no—
546C2×#67—32no—
547C2×#67—32no—
548C2×#67—32no—
549C2×#67—32no—
550C2×#67—32no—
551C2×#67—32no—
552C2×#67—32no—
553C2×#67—32no—
554C2×#67—32no—
555C2×#67—32no—
556C2×#67—32no—
557C2×#67—62no—
558C2×#67—122no—
559C2×#67—124no—
560C2×#67C22×D312yes—
561C2×#67C22×D312yes—
562C22×Dic3—31no—
563C22×Dic3—31no—
564C22×Dic3—32no—
565C22×Dic3—32no—
566C22×Dic3—61no—
567C22×Dic3C22×D311yescharacteristic
568C22×Dic3C22×D311yescharacteristic
569C22×Dic3C22×D311yescharacteristic
570#239—122no—
571#239—122no—
572#239—124no—
573#237—124no—
574D3×D4—124no—
575D3×D4—122no—
576D3×D4—122no—
577D3×D4—124no—
578D3×D4—124no—
579D3×D4—124no—
580#235—124no—
581C2×D12—32no—
582C2×D12—32no—
583C2×D12—32no—
584C2×D12—32no—
585C2×D12—32no—
586C2×D12—32no—
587C2×D12—32no—
588C2×D12—32no—
589C2×D12—32no—
590C2×D12—32no—
591C2×D12—32no—
592C2×D12—31no—
593C2×D12—32no—
594C2×D12—31no—
595C2×D12—62no—
596C2×D12—62no—
597C2×D12—61no—
598C2×D12—124no—
599C2×D12—122no—
600C2×D12C22×D312yes—
601C2×D12C22×D311yescharacteristic
602C2×D12C22×D312yes—
603C2×D12C22×D311yescharacteristic
604C2×C4×D3—31no—
605C2×C4×D3—31no—
606C2×C4×D3—31no—
607C2×C4×D3—31no—
608C2×C4×D3—32no—
609C2×C4×D3—32no—
610C2×C4×D3—32no—
611C2×C4×D3—32no—
612C2×C4×D3—31no—
613C2×C4×D3—31no—
614C2×C4×D3—31no—
615C2×C4×D3—31no—
616C2×C4×D3—32no—
617C2×C4×D3—32no—
618C2×C4×D3—32no—
619C2×C4×D3—32no—
620C2×C4×D3—61no—
621C2×C4×D3—62no—
622C2×C4×D3—61no—
623C2×C4×D3—61no—
624C2×C4×D3—61no—
625C2×C4×D3—122no—
626C2×C4×D3—122no—
627C2×C4×D3—124no—
628C2×C4×D3C22×D312yes—
629C2×C4×D3C22×D312yes—
630C2×Dic6—32no—
631C2×Dic6—32no—
632C3×C4⋊C4—21no—
633C3×C4⋊C4—22no—
634C3×C4⋊C4—32no—
635C3×C4⋊C4—31no—
636C3×C4⋊C4—31no—
637C3×C4⋊C4—32no—
638C3×C4⋊C4—32no—
639C3×C4⋊C4—32no—
640C3×C4⋊C4—32no—
641C3×C4⋊C4—32no—
642C3×C4⋊C4C22×D312yes—
643C3×C4⋊C4C22×D311yescharacteristic
644C3×C4⋊C4C22×D311yescharacteristic
645C3×C4⋊C4C22×D312yes—
646C3×C22⋊C4—22no—
647C3×C22⋊C4—32no—
648C3×C22⋊C4—32no—
649C3×C22⋊C4—32no—
650C3×C22⋊C4—32no—
651C3×C22⋊C4—32no—
652C3×C22⋊C4—32no—
653C3×C22⋊C4—32no—
654C3×C22⋊C4—32no—
655C3×C22⋊C4—32no—
656C3×C22⋊C4—32no—
657C3×C22⋊C4C22×D312yes—
658C3×C22⋊C4C22×D312yes—
659C3×C42—32no—
660C3×C42—32no—
661#217—32no—
662#217—32no—
663#217—32no—
664#217—32no—
665#217—32no—
666#217—32no—
667(C2×D3)⋊C4—32no—
668(C2×D3)⋊C4—32no—
669(C2×D3)⋊C4—32no—
670(C2×D3)⋊C4—32no—
671(C2×D3)⋊C4—32no—
672(C2×D3)⋊C4—32no—
673(C2×D3)⋊C4—32no—
674(C2×D3)⋊C4—32no—
675(C2×D3)⋊C4—32no—
676(C2×D3)⋊C4—32no—
677(C2×D3)⋊C4—32no—
678(C2×D3)⋊C4—32no—
679(C2×D3)⋊C4—32no—
680(C2×D3)⋊C4—32no—
681(C2×D3)⋊C4—32no—
682(C2×D3)⋊C4—32no—
683(C2×D3)⋊C4—32no—
684(C2×D3)⋊C4—32no—
685(C2×D3)⋊C4—32no—
686(C2×D3)⋊C4—32no—
687(C2×D3)⋊C4—32no—
688(C2×D3)⋊C4—32no—
689(C2×D3)⋊C4—62no—
690(C2×D3)⋊C4—62no—
691(C2×D3)⋊C4—62no—
692(C2×D3)⋊C4—62no—
693(C2×D3)⋊C4C22×D312yes—
694(C2×D3)⋊C4C22×D312yes—
695(C2×D3)⋊C4C22×D312yes—
696(C2×D3)⋊C4C22×D312yes—
697(C2×D3)⋊C4C22×D312yes—
698(C2×D3)⋊C4C22×D312yes—
699(C2×D3)⋊C4C22×D312yes—
700(C2×D3)⋊C4C22×D312yes—
701(C2×D3)⋊C4C22×D312yes—
702(C2×D3)⋊C4C22×D312yes—
703C4⋊Dic3—31no—
704C4⋊Dic3—31no—
705C4⋊Dic3—32no—
706C4⋊Dic3—32no—
707C4⋊Dic3—32no—
708C4⋊Dic3—32no—
709C4⋊Dic3—61no—
710C4⋊Dic3C22×D312yes—
711C4⋊Dic3C22×D312yes—
712C4⋊Dic3C22×D311yescharacteristic
713C4⋊Dic3C22×D311yescharacteristic
714Dic3⋊C4—32no—
715Dic3⋊C4—32no—
716Dic3⋊C4—32no—
717Dic3⋊C4—32no—
718Dic3⋊C4—32no—
719Dic3⋊C4—32no—
720Dic3⋊C4—32no—
721Dic3⋊C4—32no—
722Dic3⋊C4—62no—
723Dic3⋊C4C22×D312yes—
724Dic3⋊C4C22×D312yes—
725Dic3⋊C4C22×D312yes—
726Dic3⋊C4C22×D312yes—
727C4×Dic3—32no—
728C4×Dic3—32no—
729C4×Dic3—62no—
730C4×Dic3C22×D312yes—
731C4×Dic3C22×D312yes—
732C22×C32—21no—
733C22×C32—21no—
734C22×C32H(5,𝔽2)12yes—
735C22×C32C2511yescharacteristic
736C2×C3⋊D3—21no—
737C2×C3⋊D3—21no—
738C2×C3⋊D3—21no—
739C2×C3⋊D3—22no—
740C2×C3⋊D3—21no—
741C2×C3⋊D3—21no—
742C2×C3⋊D3—22no—
743C2×C3⋊D3—22no—
744C2×C3⋊D3—44no—
745C2×C3⋊D3H(5,𝔽2)12yes—
746C2×C3×D3—22no—
747C2×C3×D3—22no—
748C2×C3×D3—22no—
749C2×C3×D3—22no—
750C2×C3×D3—22no—
751C2×C3×D3—22no—
752C2×C3×D3—22no—
753C2×C3×D3—22no—
754C2×C3×D3—22no—
755C2×C3×D3—82no—
756D32—84no—
757D32—84no—
758C32×C4—21no—
759C32×C4—22no—
760C32×C4—21no—
761C32×C4—22no—
762C3⋊Dic3—21no—
763C3⋊Dic3—22no—
764C3⋊Dic3—21no—
765C3×Dic3—22no—
766C3×Dic3—22no—
767C3×Dic3—22no—
768C3×Dic3—22no—
769C3×Dic3—22no—
770C2×#41—92no—
771C2×#41—91no—
772C22×D4—92no—
773C22×D4—91no—
774C22×D4—91no—
775C22×D4—92no—
776C22×D4—92no—
777C23×C4—91no—
778#127—92no—
779#126—32no—
780#126—32no—
781#126—92no—
782#126—92no—
783#125—32no—
784#125—92no—
785#124—32no—
786#124—92no—
787#124—92no—
788#123—32no—
789#123—32no—
790#123—32no—
791#123—92no—
792#123—92no—
793#123—92no—
794#123—92no—
795#123—92no—
796#123—92no—
797#123—92no—
798#123—92no—
799#123—92no—
800#123—92no—
801#123—92no—
802C22⋊Q8—32no—
803C22⋊Q8—92no—
804C22⋊Q8—92no—
805C22⋊Q8—92no—
806C22⋊Q8—92no—
807C22⋊Q8—91no—
808C22⋊Q8D3211yescharacteristic, complemented
809#121—31no—
810#121—31no—
811#121—32no—
812#121—92no—
813#121—92no—
814#121—92no—
815#121—92no—
816#121—92no—
817#121—92no—
818#121—92no—
819#121—92no—
820#121—91no—
821#121—91no—
822#121—92no—
823#121—92no—
824#121—92no—
825#121—92no—
826#121—92no—
827#121—92no—
828#121—91no—
829#121—91no—
830#120—32no—
831#120—92no—
832#120—92no—
833#120—92no—
834#120—92no—
835#120—92no—
836#120—92no—
837#120—92no—
838C4×D4—32no—
839C4×D4—32no—
840C4×D4—92no—
841C4×D4—92no—
842C4×D4—92no—
843C4×D4—92no—
844C4×D4—92no—
845C4×D4—92no—
846#117—92no—
847#117—91no—
848C2×C4⋊C4—31no—
849C2×C4⋊C4—91no—
850C2×C4⋊C4—91no—
851C2×C22⋊C4—31no—
852C2×C22⋊C4—92no—
853C2×C22⋊C4—92no—
854C2×C22⋊C4—92no—
855C2×C22⋊C4—91no—
856C2×C22⋊C4—91no—
857C23×C3—21no—
858C23×C3—32no—
859C23×C3—32no—
860C23×C3—32no—
861C23×C3—62no—
862C23×C3—121no—
863C23×C3—121no—
864C23×C3C23×D311yescharacteristic
865C23×C3C23×D311yescharacteristic
866C22×D3—22no—
867C22×D3—31no—
868C22×D3—31no—
869C22×D3—32no—
870C22×D3—31no—
871C22×D3—32no—
872C22×D3—31no—
873C22×D3—41no—
874C22×D3—41no—
875C22×D3—61no—
876C22×D3—61no—
877C22×D3—62no—
878C22×D3—64no—
879C22×D3—64no—
880C22×D3—62no—
881C22×D3—62no—
882C22×D3—62no—
883C22×D3—62no—
884C22×D3—122no—
885C22×D3—122no—
886C22×D3—122no—
887C22×D3—122no—
888C22×D3—122no—
889C22×D3—122no—
890C22×D3—122no—
891C22×D3—122no—
892C22×D3—122no—
893C22×D3—122no—
894C22×D3—122no—
895C22×D3—122no—
896C22×D3—121no—
897C22×D3—121no—
898C22×D3—122no—
899C22×D3C23×D312yes—
900C22×D3C23×D312yes—
901C22×D3C23×D312yes—
902C3×Q8—41no—
903C3×Q8—41no—
904C3×Q8—42no—
905C3×D4—64no—
906C3×D4—64no—
907C3×D4—122no—
908C3×D4—121no—
909C3×D4—121no—
910C3×D4—122no—
911C2×C3×C4—21no—
912C2×C3×C4—22no—
913C2×C3×C4—22no—
914C2×C3×C4—21no—
915C2×C3×C4—32no—
916C2×C3×C4—32no—
917C2×C3×C4—32no—
918C2×C3×C4—32no—
919C2×C3×C4—32no—
920C2×C3×C4—41no—
921C2×C3×C4—41no—
922C2×C3×C4—42no—
923C2×C3×C4—62no—
924C2×C3×C4—122no—
925C2×C3×C4—122no—
926C2×C3×C4—121no—
927C2×C3×C4—121no—
928C2×C3×C4C23×D312yes—
929C2×C3×C4C23×D312yes—
930C2×C3×C4C23×D312yes—
931C2×C3×C4C23×D312yes—
932C2×C3×C4C23×D311yescharacteristic
933C2×C3×C4C23×D311yescharacteristic
934C2×C3×C4C23×D311yescharacteristic
935C2×C3×C4C23×D311yescharacteristic
936#67—24no—
937#67—24no—
938#67—64no—
939#67—64no—
940#67—64no—
941#67—124no—
942#67—122no—
943#67—122no—
944#67—122no—
945#67—122no—
946#67—122no—
947#67—122no—
948#67—122no—
949#67—122no—
950#67—122no—
951#67—122no—
952#67—122no—
953C2×Dic3—22no—
954C2×Dic3—31no—
955C2×Dic3—31no—
956C2×Dic3—32no—
957C2×Dic3—32no—
958C2×Dic3—31no—
959C2×Dic3—31no—
960C2×Dic3—41no—
961C2×Dic3—41no—
962C2×Dic3—61no—
963C2×Dic3—62no—
964C2×Dic3—61no—
965C2×Dic3—122no—
966C2×Dic3—122no—
967C2×Dic3—121no—
968C2×Dic3—121no—
969C2×Dic3—122no—
970C2×Dic3C23×D312yes—
971C2×Dic3C23×D312yes—
972C2×Dic3C23×D312yes—
973C2×Dic3C23×D312yes—
974C2×Dic3C23×D312yes—
975D12—42no—
976D12—42no—
977D12—41no—
978D12—41no—
979D12—64no—
980D12—64no—
981D12—64no—
982D12—124no—
983D12—122no—
984D12—122no—
985D12—121no—
986D12—121no—
987D12—122no—
988D12—124no—
989D12—122no—
990D12—122no—
991D12—122no—
992D12—122no—
993D12—122no—
994D12—122no—
995D12—122no—
996C4×D3—42no—
997C4×D3—42no—
998C4×D3—62no—
999C4×D3—62no—
1000C4×D3—62no—
1001C4×D3—62no—
1002C4×D3—64no—
1003C4×D3—122no—
1004C4×D3—122no—
1005C4×D3—122no—
1006C4×D3—122no—
1007C4×D3—122no—
1008C4×D3—121no—
1009C4×D3—121no—
1010C4×D3—121no—
1011C4×D3—121no—
1012C4×D3—122no—
1013C4×D3—122no—
1014C4×D3—122no—
1015C4×D3—124no—
1016C4×D3—122no—
1017C4×D3—122no—
1018C4×D3—122no—
1019Dic6—122no—
1020Dic6—122no—
1021C2×C32—22no—
1022C2×C32C2×H(5,𝔽2)11yescharacteristic
1023C2×C32C2×H(5,𝔽2)11yescharacteristic
1024C2×C32#58511yescharacteristic
1025C3⋊D3—22no—
1026C3⋊D3—41no—
1027C3⋊D3—42no—
1028C3×D3—42no—
1029C3×D3—42no—
1030C3×D3—42no—
1031C24—31no—
1032C24—92no—
1033C24—92no—
1034C24—91no—
1035#41—364no—
1036#41—362no—
1037C2×Q8—92no—
1038C2×Q8C2×D3211yescharacteristic
1039C2×D4—32no—
1040C2×D4—32no—
1041C2×D4—32no—
1042C2×D4—32no—
1043C2×D4—31no—
1044C2×D4—31no—
1045C2×D4—92no—
1046C2×D4—92no—
1047C2×D4—92no—
1048C2×D4—92no—
1049C2×D4—92no—
1050C2×D4—92no—
1051C2×D4—92no—
1052C2×D4—92no—
1053C2×D4—92no—
1054C2×D4—92no—
1055C2×D4—92no—
1056C2×D4—92no—
1057C2×D4—92no—
1058C2×D4—91no—
1059C2×D4—364no—
1060C2×D4—362no—
1061C2×D4—362no—
1062C2×D4—364no—
1063C2×D4—364no—
1064C22×C4—31no—
1065C22×C4—31no—
1066C22×C4—31no—
1067C22×C4—32no—
1068C22×C4—32no—
1069C22×C4—92no—
1070C22×C4—92no—
1071C22×C4—92no—
1072C22×C4—92no—
1073C22×C4—91no—
1074C22×C4—91no—
1075C22×C4—91no—
1076C22×C4—92no—
1077C22×C4—91no—
1078C22×C4—91no—
1079C22×C4—362no—
1080C22×C4C2×D3211yescharacteristic
1081C4⋊C4—32no—
1082C4⋊C4—32no—
1083C4⋊C4—31no—
1084C4⋊C4—31no—
1085C4⋊C4—32no—
1086C4⋊C4—32no—
1087C4⋊C4—32no—
1088C4⋊C4—32no—
1089C4⋊C4—92no—
1090C4⋊C4—92no—
1091C4⋊C4—92no—
1092C4⋊C4—92no—
1093C4⋊C4—92no—
1094C4⋊C4—91no—
1095C4⋊C4—92no—
1096C4⋊C4C2×D3211yescharacteristic
1097C4⋊C4C2×D3212yes—
1098C22⋊C4—32no—
1099C22⋊C4—32no—
1100C22⋊C4—32no—
1101C22⋊C4—32no—
1102C22⋊C4—32no—
1103C22⋊C4—32no—
1104C22⋊C4—32no—
1105C22⋊C4—32no—
1106C22⋊C4—32no—
1107C22⋊C4—32no—
1108C22⋊C4—92no—
1109C22⋊C4—92no—
1110C22⋊C4—92no—
1111C22⋊C4—92no—
1112C22⋊C4—92no—
1113C22⋊C4—92no—
1114C22⋊C4—92no—
1115C22⋊C4—92no—
1116C22⋊C4—92no—
1117C22⋊C4—92no—
1118C22⋊C4—92no—
1119C22⋊C4—92no—
1120C22⋊C4—92no—
1121C22⋊C4—92no—
1122C22⋊C4C2×D3212yes—
1123C42—32no—
1124C42—32no—
1125C42—92no—
1126C22×C3—21no—
1127C22×C3—21no—
1128C22×C3—21no—
1129C22×C3—21no—
1130C22×C3—22no—
1131C22×C3—21no—
1132C22×C3—41no—
1133C22×C3—41no—
1134C22×C3—62no—
1135C22×C3—62no—
1136C22×C3—62no—
1137C22×C3—62no—
1138C22×C3—62no—
1139C22×C3—62no—
1140C22×C3—62no—
1141C22×C3—62no—
1142C22×C3—62no—
1143C22×C3—242no—
1144C22×C3#100912yes—
1145C22×C3#100912yes—
1146C22×C3C24×D311yescharacteristic
1147C22×C3C24×D311yescharacteristic
1148C2×D3—22no—
1149C2×D3—22no—
1150C2×D3—22no—
1151C2×D3—22no—
1152C2×D3—22no—
1153C2×D3—22no—
1154C2×D3—22no—
1155C2×D3—22no—
1156C2×D3—22no—
1157C2×D3—32no—
1158C2×D3—32no—
1159C2×D3—62no—
1160C2×D3—61no—
1161C2×D3—61no—
1162C2×D3—61no—
1163C2×D3—61no—
1164C2×D3—62no—
1165C2×D3—62no—
1166C2×D3—62no—
1167C2×D3—61no—
1168C2×D3—61no—
1169C2×D3—61no—
1170C2×D3—61no—
1171C2×D3—62no—
1172C2×D3—62no—
1173C2×D3—61no—
1174C2×D3—62no—
1175C2×D3—61no—
1176C2×D3—62no—
1177C2×D3—82no—
1178C2×D3—121no—
1179C2×D3—121no—
1180C2×D3—121no—
1181C2×D3—121no—
1182C2×D3—122no—
1183C2×D3—122no—
1184C2×D3—122no—
1185C2×D3—124no—
1186C2×D3—124no—
1187C2×D3—128no—
1188C2×D3—244no—
1189C2×D3—244no—
1190C2×D3—244no—
1191C2×D3—244no—
1192C3×C4—22no—
1193C3×C4—22no—
1194C3×C4—21no—
1195C3×C4—21no—
1196C3×C4—21no—
1197C3×C4—21no—
1198C3×C4—22no—
1199C3×C4—22no—
1200C3×C4—22no—
1201C3×C4—41no—
1202C3×C4—42no—
1203C3×C4—42no—
1204C3×C4—62no—
1205C3×C4—62no—
1206C3×C4—62no—
1207C3×C4—62no—
1208C3×C4—62no—
1209Dic3—22no—
1210Dic3—22no—
1211Dic3—22no—
1212Dic3—22no—
1213Dic3—22no—
1214Dic3—62no—
1215Dic3—62no—
1216Dic3—62no—
1217Dic3—61no—
1218Dic3—61no—
1219Dic3—61no—
1220Dic3—61no—
1221Dic3—121no—
1222Dic3—122no—
1223C32#353411yescharacteristic, complemented, Sylow
1224C23—32no—
1225C23—32no—
1226C23—32no—
1227C23—62no—
1228C23—91no—
1229C23—91no—
1230C23—92no—
1231C23—121no—
1232C23—121no—
1233C23—182no—
1234C23—184no—
1235C23—182no—
1236C23—361no—
1237C23—362no—
1238C23—362no—
1239C23—362no—
1240C23—362no—
1241C23—362no—
1242C23C22×D3211yescharacteristic
1243Q8—41no—
1244Q8—362no—
1245D4—64no—
1246D4—64no—
1247D4—121no—
1248D4—121no—
1249D4—122no—
1250D4—122no—
1251D4—184no—
1252D4—184no—
1253D4—184no—
1254D4—361no—
1255D4—362no—
1256D4—362no—
1257D4—362no—
1258D4—362no—
1259D4—362no—
1260D4—362no—
1261D4—362no—
1262D4—362no—
1263D4—362no—
1264D4—362no—
1265C2×C4—32no—
1266C2×C4—32no—
1267C2×C4—32no—
1268C2×C4—32no—
1269C2×C4—32no—
1270C2×C4—41no—
1271C2×C4—62no—
1272C2×C4—91no—
1273C2×C4—92no—
1274C2×C4—91no—
1275C2×C4—122no—
1276C2×C4—122no—
1277C2×C4—121no—
1278C2×C4—121no—
1279C2×C4—182no—
1280C2×C4—182no—
1281C2×C4—361no—
1282C2×C4—361no—
1283C2×C4—362no—
1284C2×C4—362no—
1285C2×C4—362no—
1286C2×C4—362no—
1287C2×C4—362no—
1288C2×C4—361no—
1289C2×C4C22×D3212yes—
1290C2×C4C22×D3212yes—
1291C2×C4C22×D3211yescharacteristic
1292C2×C4C22×D3211yescharacteristic
1293C2×C3—22no—
1294C2×C3—22no—
1295C2×C3—21no—
1296C2×C3—21no—
1297C2×C3—21no—
1298C2×C3—42no—
1299C2×C3—122no—
1300C2×C3—122no—
1301C2×C3—122no—
1302C2×C3C2×#100911yescharacteristic
1303C2×C3C2×#100911yescharacteristic
1304C2×C3D3×H(5,𝔽2)11yescharacteristic
1305C2×C3D3×H(5,𝔽2)11yescharacteristic
1306C2×C3#596611yescharacteristic
1307C2×C3#596811yescharacteristic
1308D3—42no—
1309D3—42no—
1310D3—42no—
1311D3—62no—
1312D3—62no—
1313D3—122no—
1314D3—122no—
1315D3—121no—
1316D3—122no—
1317D3—121no—
1318D3—122no—
1319D3—242no—
1320C22—21no—
1321C22—21no—
1322C22—62no—
1323C22—62no—
1324C22—62no—
1325C22—62no—
1326C22—62no—
1327C22—62no—
1328C22—62no—
1329C22—62no—
1330C22—62no—
1331C22—92no—
1332C22—181no—
1333C22—181no—
1334C22—181no—
1335C22—182no—
1336C22—182no—
1337C22—181no—
1338C22—181no—
1339C22—182no—
1340C22—242no—
1341C22—364no—
1342C22—724no—
1343C22—724no—
1344C22#6432012yes—
1345C22C23×D3211yescharacteristic
1346C4—21no—
1347C4—21no—
1348C4—22no—
1349C4—22no—
1350C4—62no—
1351C4—62no—
1352C4—62no—
1353C4—62no—
1354C4—62no—
1355C4—181no—
1356C4—181no—
1357C4—182no—
1358C3—21no—
1359C3#8642011yescharacteristic, complemented
1360C3#8645911yescharacteristic, complemented
1361C2—22no—
1362C2—122no—
1363C2—122no—
1364C2—122no—
1365C2—182no—
1366C2—361no—
1367C2—362no—
1368C2#1059667511yescharacteristic
1369C2C2×#6432011yescharacteristic
1370C2#1059669811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C22⋊Q8C22
hypercenterC22⋊Q8D32
hypocenterC32#3534
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596098C2semidirect
2. C3×#5645C2semidirect
3. C3×#5644C2semidirect
4. #10595431C2semidirect
5. #10595417C2semidirect
6. #10595081C2semidirect
7. #10595072C2semidirect
8. #10594911C2semidirect
9. C2×#63853C2semidirect
10. #10594663C2semidirect
11. #10594657C2semidirect
12. #10594648C2semidirect
13. #10594611C2semidirect
14. #10594501C2semidirect
15. #10594481C2semidirect
16. #10594294C2semidirect
17. #10594293C2semidirect
18. #10594277C2semidirect
19. #10594218C2semidirect
22. C2×#3832C22semidirect
23. C22×C4×C3⋊D3C22semidirect
24. C2×#3811C22semidirect
25. C2×D3×#67C22semidirect
27. C2×#3804C22semidirect
28. C2×#3802C22semidirect
29. C2×D3×D12C22semidirect
30. C32×C22⋊Q8C22semidirect
31. #64155C22semidirect
32. #64139C22semidirect
33. #64104C22semidirect
34. #64103C22semidirect
35. #64102C22semidirect
36. #64101C22semidirect
37. #64091C22semidirect
38. #64090C22semidirect
39. C3×#947C22semidirect
40. C3×#946C22semidirect
42. C3×#930C22semidirect
43. C2×C3×(C2×D3)⋊C4C22semidirect
44. C2×C3×Dic3⋊C4C22semidirect
45. C3×#898C22semidirect
46. C3×#898C22semidirect
47. C3×#895C22semidirect
48. C3×#894C22semidirect
49. C3×#894C22semidirect
50. C3×#890C22semidirect
51. C3×#886C22semidirect
52. C3×#882C22semidirect
53. C3×#67⋊C4C22semidirect
54. C3×#67⋊C4C22semidirect
55. #63980C22semidirect
56. #63978C22semidirect
57. #63978C22semidirect
58. C2×Dic3⋊Dic3C22semidirect
59. C2×#3722C22semidirect
60. C2×(C2×D3)⋊Dic3C22semidirect
61. #63923C22semidirect
62. #63923C22semidirect
63. #63923C22semidirect
65. #63922C22semidirect
66. #63922C22semidirect
67. #63921C22semidirect
68. #63921C22semidirect
69. D3×(C2×D3)⋊C4C22semidirect
70. #63916C22semidirect
71. #63916C22semidirect
72. #63916C22semidirect
73. #63915C22semidirect
74. #63912C22semidirect
75. #63911C22semidirect
77. #63910C22semidirect
78. #63910C22semidirect
79. #63909C22semidirect
80. #63906C22semidirect
81. #63906C22semidirect
82. #63905C22semidirect
83. C4×#626C22semidirect
84. #63900C22semidirect
85. #63899C22semidirect
86. #63898C22semidirect
87. #63895C22semidirect
88. #63895C22semidirect
89. #63894C22semidirect
90. #63893C22semidirect
91. #63891C22semidirect
92. #63890C22semidirect
93. #63890C22semidirect
94. #63886C22semidirect
95. #63886C22semidirect
96. #63885C22semidirect
97. #63880C22semidirect
98. #63868C22semidirect
99. #63867C22semidirect
100. #63862C22semidirect
101. #63855C22semidirect
102. #63854C22semidirect
103. #63853C22semidirect
104. #63853C22semidirect
105. #63853C22semidirect
106. #63853C22semidirect
107. #63853C22semidirect
108. #63852C22semidirect
126. #5645D3semidirect
127. #5644D3semidirect
271. C3×C22⋊Q8C2×D3semidirect
272. C3×C22⋊Q8C2×D3semidirect
282. #947C2×D3semidirect
286. #946C2×D3semidirect
311. #930C2×D3semidirect
318. C2×(C2×D3)⋊C4C2×D3semidirect
322. C2×Dic3⋊C4C2×D3semidirect
325. #898C2×D3semidirect
326. #898C2×D3semidirect
345. #895C2×D3semidirect
357. #894C2×D3semidirect
358. #894C2×D3semidirect
369. #890C2×D3semidirect
374. #886C2×D3semidirect
406. #882C2×D3semidirect
411. #67⋊C4C2×D3semidirect
412. #67⋊C4C2×D3semidirect
808. C22⋊Q8D32semidirect
1223. C32#3534semidirect
1359. C3#86420semidirect
1360. C3#86459semidirect

Maximal subgroups

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

subgroupindex
#105960982
C3×#56452
C3×#56442
#105954312
#105954172
#105950812
#105950722
#105949112
C2×#638532
#105946632
#105946572
#105946482
#105946112
#105945012
#105944812
#105942942
#105942932
#105942772
#105942182
#864593
#864203