Finite Group Databasebeta

← #11904976

Subgroups — #11904976

Order 1152.

2273 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595957C211yesmaximal, characteristic, complemented
2C3×#5495C212yesmaximal, complemented
3#10595528C211yesmaximal, characteristic
4#10595509C212yesmaximal, complemented
5C2×#63975C211yesmaximal, characteristic, complemented
6#10595088C212yesmaximal, complemented
7#10594970C212yesmaximal, complemented
8#10594968C212yesmaximal, complemented
9#10594836C212yesmaximal, complemented
10#10594305C212yesmaximal, complemented
11#10594295C211yesmaximal, characteristic, complemented
12#10594256C211yesmaximal, characteristic, complemented
13#10594227C212yesmaximal, complemented
14#10594180C211yesmaximal, characteristic, complemented
15#10594155C212yesmaximal, complemented
16#10594137C212yesmaximal, complemented
17#10594135C212yesmaximal, complemented
18#10594052C211yesmaximal, characteristic, complemented
19#10594039C212yesmaximal, complemented
20#86816—32nomaximal
21C22×#638C2211yescharacteristic
22C2×#3811C2211yescharacteristic
23C22×#624C2211yescharacteristic
24C2×C32×C22⋊C4C2211yescharacteristic, complemented
25C2×#3757C2211yescharacteristic, complemented
26C4×#638C2212yes—
27C4×#638C2212yescomplemented
28#64090C2212yes—
29#64090C2212yescomplemented
30C22⋊C4×C3⋊D3C2211yescharacteristic
31C22⋊C4×C3⋊D3C2211yescharacteristic
32#64086C2211yescharacteristic, complemented
33#64086C2211yescharacteristic, complemented
34C3×#953C2212yes—
35C2×C3×#217C2212yescomplemented
36C3×#929C2212yescomplemented
37C3×C4×#67C2212yescomplemented
38C3×#926C2212yescomplemented
39C3×#924C2212yescomplemented
40C3×#886C2212yes—
41C3×#885C2212yescomplemented
42C3×#883C2212yescomplemented
43C3×#67⋊C4C2212yes—
44C3×#879C2212yescomplemented
45C3×#879C2212yescomplemented
46C3×#878C2212yescomplemented
47C3×#877C2212yescomplemented
48#63983C2211yescharacteristic
49#63983C2211yescharacteristic
50#63982C2212yescomplemented
51#63975C2212yes—
52#63975C2212yes—
53#63975C2211yescharacteristic
54#63975C2211yescharacteristic
55#63975C2211yescharacteristic, complemented
56#63975C2211yescharacteristic, complemented
57#63975C2211yescharacteristic, complemented
58#63975C2211yescharacteristic, complemented
59#63974C2211yescharacteristic
60#67⋊Dic3C2212yescomplemented
61Dic3×#67C2212yes—
62#63969C2212yescomplemented
63C2×Dic3⋊Dic3C2212yescomplemented
64#63964C2212yescomplemented
65C2×#3722C2211yescharacteristic
66#63962C2212yes—
67#63962C2212yescomplemented
68#63961C2212yes—
69#63959C2212yescomplemented
70#63958C2212yes—
71#63958C2212yes—
72#63957C2212yescomplemented
73#63956C2212yescomplemented
74#63956C2212yescomplemented
75#63955C2212yescomplemented
76#63921C2212yescomplemented
77D3×(C2×D3)⋊C4C2212yescomplemented
78C4×#627C2212yescomplemented
79C4×#626C2212yescomplemented
80#63900C2212yescomplemented
81#63895C2212yescomplemented
82#63888C2212yescomplemented
83#63887C2212yescomplemented
84#63883C2212yescomplemented
85C4×#624C2212yescomplemented
86#63881C2212yescomplemented
87#63878C2212yescomplemented
88#63872C2212yescomplemented
89#63871C2212yescomplemented
90#63870C2212yescomplemented
91#63867C2212yescomplemented
92#63867C2212yescomplemented
93#63865C2212yescomplemented
94#63862C2212yescomplemented
95#63862C2212yescomplemented
96#63859C2212yescomplemented
97#63858C2212yescomplemented
98#63855C2212yescomplemented
99#63854C2212yescomplemented
100#63854C2212yescomplemented
101#63851C2212yescomplemented
102#63846C2212yescomplemented
103#63846C2212yescomplemented
104#63843C2212yescomplemented
105#63836C2212yescomplemented
106#63836C2212yescomplemented
107#63836C2212yescomplemented
108C3×#551—32no—
109#5708—32no—
110#5708—32no—
111#5707—32no—
112#5706—32no—
113#5680—32no—
114#5679—32no—
115#5660—32no—
116#5660—32no—
117#5659—32no—
118#5658—32no—
119D3×#123—32no—
120#5650—32no—
121#5642—32no—
122#5639—32no—
123#5638—32no—
124#5634—32no—
125#5589—32no—
126#5587—32no—
127#5557—32no—
128#5556—32no—
129#5545—32no—
130#5541—32no—
131#5531—32no—
132#5529—32no—
133#5528—32no—
134D3×#117—32no—
135#5495—32no—
136#5495D312yescomplemented
137C2×#883—32no—
138#5486—32no—
139#5486—61no—
140C24×C32C2311yescharacteristic
141C23×C3⋊D3C2311yescharacteristic
142C22×D32C2311yescharacteristic
143C22×C32×C4C2312yes—
144C2×#638—24no—
145C2×#638C2311yescharacteristic
146C2×#638C2311yescharacteristic
147C2×#638C2311yescharacteristic
148C2×#638C2311yescharacteristic
149C22×C3⋊Dic3C2311yescharacteristic
150C22×C3⋊Dic3C2312yes—
151C2×C4×C3⋊D3C2312yes—
152C2×C4×C3⋊D3C2312yes—
153C2×C3×#67C2312yes—
154C2×C3×#67C2312yes—
155C2×C3×#67C2312yes—
156C22×C3×Dic3C2312yes—
157C22×C3×Dic3C2312yes—
158C2×C3×C4×D3C2312yes—
159C2×C3×Dic6C2312yes—
160#3811—24no—
161C2×#627C2312yes—
162C2×#626C2312yes—
163C2×#624—24no—
164C2×#624C2312yes—
165C2×#624C2311yescharacteristic
166C2×#624C2311yescharacteristic
167C2×#624C2311yescharacteristic
168C2×#624C2312yes—
169C2×D3×Dic3C2312yes—
170C32×C22⋊C4C2311yescharacteristic
171C32×C22⋊C4C2311yescharacteristic
172C32×C22⋊C4C2312yes—
173#3757C2311yescharacteristic
174#3757C2311yescharacteristic
175#3757C2312yes—
176#3752C2312yes—
177#3752C2312yes—
178#3750C2312yes—
179#3750C2312yes—
180C4×C3⋊Dic3C2312yes—
181C4×C3⋊Dic3C2312yes—
182C3×#217C2312yes—
183C3×#217C2312yes—
184C3×#217C2312yes—
185C3×#217C2312yes—
186C3×#217C2312yes—
187C3×#217C2312yes—
188C3×#217C2312yes—
189C3×(C2×D3)⋊C4C2312yes—
190C3×(C2×D3)⋊C4C2312yes—
191C3×(C2×D3)⋊C4C2312yes—
192C3×C4⋊Dic3C2312yes—
193C3×C4⋊Dic3C2312yes—
194C3×C4⋊Dic3C2312yes—
195C3×Dic3⋊C4C2312yes—
196C3×Dic3⋊C4C2312yes—
197C3×Dic3⋊C4C2312yes—
198C3×Dic3⋊C4C2312yes—
199C3×Dic3⋊C4C2312yes—
200C3×C4×Dic3C2312yes—
201C3×C4×Dic3C2312yes—
202C3×C4×Dic3C2312yes—
203#3724C2312yes—
204#3724C2312yes—
205#3724C2312yes—
206Dic3⋊Dic3C2312yes—
207Dic3⋊Dic3C2312yes—
208Dic3⋊Dic3C2312yes—
209Dic3⋊Dic3C2312yes—
210Dic3⋊Dic3C2312yes—
211Dic3⋊Dic3C2312yes—
212Dic3⋊Dic3C2312yes—
213Dic3⋊Dic3C2312yes—
214Dic3⋊Dic3C2312yes—
215Dic3⋊Dic3C2312yes—
216Dic3⋊Dic3C2312yes—
217#3722C2311yescharacteristic
218#3722C2311yescharacteristic
219#3722C2312yes—
220#3722C2311yescharacteristic
221#3722C2311yescharacteristic
222(C2×D3)⋊Dic3C2312yes—
223(C2×D3)⋊Dic3C2312yes—
224(C2×D3)⋊Dic3C2312yes—
225(C2×D3)⋊Dic3C2312yes—
226(C2×D3)⋊Dic3C2312yes—
227Dic32C2312yes—
228Dic32C2312yes—
229Dic32C2312yes—
230#3491—91noSylow
231C22×#67—32no—
232C22×#67—61no—
233C2×D3×D4—32no—
234C22×C4×D3—32no—
235C3×#126—32no—
236C3×#126—32no—
237C3×#124—32no—
238C3×#123—32no—
239C3×#123—32no—
240C3×#123—32no—
241C3×C22⋊Q8—32no—
242C3×C22⋊Q8—32no—
243C3×#120—32no—
244C3×C4×D4—32no—
245C3×C4×D4—32no—
246C3×#117—32no—
247C3×#117—32no—
248C2×C3×C22⋊C4—21no—
249C2×C3×C22⋊C4—32no—
250C2×C3×C22⋊C4C2×D312yescomplemented
251#953C2×D312yes—
252C2×#217—32no—
253C2×#217—61no—
254C2×#217C2×D312yescomplemented
255#946—32no—
256#946—32no—
257#946—32no—
258Q8×Dic3—32no—
259#938—32no—
260#938—32no—
261#937—32no—
262#937—32no—
263#936—32no—
264#935—32no—
265#935—32no—
266#935—32no—
267#935—32no—
268D4×Dic3—32no—
269D4×Dic3—32no—
270#929—32no—
271#929C2×D312yescomplemented
272C4×#67—32no—
273C4×#67—32no—
274C4×#67—32no—
275C4×#67—32no—
276C4×#67—32no—
277C4×#67—32no—
278C4×#67—62no—
279C4×#67—62no—
280C4×#67C2×D312yescomplemented
281C2×(C2×D3)⋊C4—32no—
282C2×(C2×D3)⋊C4—32no—
283#926—32no—
284#926—32no—
285#926C2×D312yescomplemented
286C2×C4⋊Dic3—32no—
287#924—32no—
288#924—32no—
289#924C2×D312yescomplemented
290C2×Dic3⋊C4—32no—
291#898—32no—
292#898—32no—
293#898—32no—
294#897—32no—
295#897—32no—
296#896—32no—
297#896—32no—
298#896—32no—
299#896—32no—
300#896—32no—
301#894—32no—
302#894—32no—
303#893—32no—
304#892—32no—
305#892—32no—
306#892—32no—
307#892—32no—
308D3×C4⋊C4—32no—
309D3×C4⋊C4—32no—
310D3×C4⋊C4—32no—
311D3×C4⋊C4—32no—
312#890—32no—
313#890—32no—
314#890—32no—
315#890—32no—
316#889—32no—
317#889—32no—
318#889—32no—
319#889—32no—
320#889—32no—
321#889—32no—
322#887—32no—
323#886—32no—
324#886—32no—
325#886C2×D312yes—
326#885—32no—
327#885C2×D312yescomplemented
328#884—32no—
329#884—32no—
330#883—32no—
331#883—32no—
332#883—32no—
333#883—32no—
334#883—32no—
335#883—32no—
336#883—32no—
337#883—32no—
338#883—32no—
339#883—32no—
340#883—32no—
341#883—32no—
342#883—32no—
343#883C2×D312yescomplemented
344#67⋊C4—32no—
345#67⋊C4—32no—
346#67⋊C4—32no—
347#67⋊C4—32no—
348#67⋊C4—32no—
349#67⋊C4—32no—
350#67⋊C4—62no—
351#67⋊C4—62no—
352#67⋊C4C2×D312yes—
353D3×C22⋊C4—32no—
354D3×C22⋊C4—32no—
355D3×C22⋊C4—32no—
356D3×C22⋊C4—32no—
357D3×C22⋊C4—32no—
358D3×C22⋊C4—32no—
359D3×C22⋊C4—61no—
360D3×C22⋊C4—61no—
361#879—32no—
362#879—32no—
363#879—32no—
364#879—32no—
365#879—32no—
366#879—32no—
367#879—32no—
368#879—32no—
369#879C2×D312yescomplemented
370#879C2×D312yescomplemented
371#878—32no—
372#878—32no—
373#878—32no—
374#878—32no—
375#878C2×D312yescomplemented
376#877—32no—
377#877—32no—
378#877—32no—
379#877—32no—
380#877—32no—
381#877—32no—
382#877—61no—
383#877—61no—
384#877C2×D312yescomplemented
385#876—32no—
386C4×D12—32no—
387#872—32no—
388#872—32no—
389#872—32no—
390#872—32no—
391C42×D3—32no—
392C42×D3—32no—
393#870—32no—
394#870—32no—
395C4×Dic6—32no—
396C4×Dic6—32no—
397C23×C32—22no—
398C23×C32—42no—
399C23×C32C2411yescharacteristic
400C23×C32C2411yescharacteristic
401C23×C32C2411yescharacteristic
402C22×C3⋊D3—42no—
403C22×C3⋊D3#4114yes—
404C22×C3⋊D3C2411yescharacteristic
405C22×C3⋊D3C2411yescharacteristic
406C22×C3×D3C2412yes—
407C2×D32—22no—
408C2×D32—42no—
409C2×C32×C4—42no—
410C2×C32×C4C2412yes—
411C2×C32×C4C2412yes—
412#638—22no—
413#638—22no—
414#638—22no—
415#638—22no—
416C2×C3⋊Dic3—22no—
417C2×C3⋊Dic3—42no—
418C2×C3⋊Dic3C2412yes—
419C2×C3⋊Dic3C2411yescharacteristic
420C2×C3⋊Dic3C2411yescharacteristic
421C2×C3⋊Dic3C2412yes—
422C4×C3⋊D3—42no—
423C4×C3⋊D3—42no—
424C3×#67—24no—
425C3×#67—42no—
426C3×#67—42no—
427C2×C3×Dic3—24no—
428C2×C3×Dic3—42no—
429C2×C3×Dic3C2412yes—
430C2×C3×Dic3C2412yes—
431C2×C3×Dic3C2412yes—
432C2×C3×Dic3C2412yes—
433C2×C3×Dic3C2412yes—
434C2×C3×Dic3C2412yes—
435C2×C3×Dic3C2412yes—
436C3×C4×D3—42no—
437C3×Dic6—42no—
438#627—42no—
439#626—24no—
440#624—24no—
441#624—22no—
442#624—22no—
443#624—22no—
444#624—42no—
445D3×Dic3—42no—
446#552—92no—
447#552—92no—
448#552—92no—
449#552—92no—
450#551—32no—
451#551—92no—
452#551—92no—
453#551—92no—
454#543—91no—
455#539—92no—
456#539—92no—
457#534—91no—
458#529—92no—
459#529—92no—
460C2×#123—91no—
461C2×#123—91no—
462#518—91no—
463#518—91no—
464C2×#117—91no—
465C24×C3—21no—
466C24×C3C22×D312yes—
467C23×D3—32no—
468C23×D3—32no—
469C23×D3—61no—
470C2×C3×Q8—32no—
471C2×C3×D4—32no—
472C2×C3×D4—32no—
473C2×C3×D4—32no—
474C22×C3×C4—22no—
475C22×C3×C4—32no—
476C22×C3×C4—32no—
477C22×C3×C4—32no—
478C22×C3×C4C22×D312yes—
479C22×C3×C4C22×D312yes—
480C2×#67—32no—
481C2×#67—32no—
482C2×#67—32no—
483C2×#67—32no—
484C2×#67—32no—
485C2×#67—61no—
486C2×#67—61no—
487C2×#67—61no—
488C2×#67—61no—
489C2×#67—68no—
490C2×#67—68no—
491C2×#67C22×D312yes—
492C2×#67C22×D312yes—
493C2×#67C22×D312yes—
494C22×Dic3—32no—
495C22×Dic3—32no—
496C22×Dic3—32no—
497C22×Dic3—32no—
498C22×Dic3—61no—
499C22×Dic3—62no—
500C22×Dic3C22×D312yes—
501C22×Dic3C22×D312yes—
502D3×D4—68no—
503C2×D12—32no—
504C2×C4×D3—32no—
505C2×C4×D3—32no—
506C2×C4×D3—32no—
507C2×C4×D3—32no—
508C2×C4×D3—32no—
509C2×C4×D3—32no—
510C2×C4×D3—32no—
511C2×C4×D3—32no—
512C2×C4×D3—32no—
513C2×C4×D3—32no—
514C2×C4×D3—32no—
515C2×C4×D3—32no—
516C2×C4×D3—62no—
517C2×C4×D3—62no—
518C2×C4×D3—68no—
519C2×C4×D3C22×D312yes—
520C2×Dic6—32no—
521C2×Dic6—32no—
522C2×Dic6C22×D312yes—
523C3×C4⋊C4—32no—
524C3×C4⋊C4—32no—
525C3×C4⋊C4—32no—
526C3×C4⋊C4—32no—
527C3×C4⋊C4—32no—
528C3×C4⋊C4—32no—
529C3×C4⋊C4—32no—
530C3×C4⋊C4—32no—
531C3×C22⋊C4—21no—
532C3×C22⋊C4—21no—
533C3×C22⋊C4—22no—
534C3×C22⋊C4—32no—
535C3×C22⋊C4—32no—
536C3×C22⋊C4—32no—
537C3×C22⋊C4—32no—
538C3×C22⋊C4—32no—
539C3×C22⋊C4—32no—
540C3×C22⋊C4—32no—
541C3×C22⋊C4—32no—
542C3×C22⋊C4—32no—
543C3×C22⋊C4—32no—
544C3×C22⋊C4C22×D312yes—
545C3×C22⋊C4C22×D312yes—
546C3×C22⋊C4C22×D312yes—
547C3×C22⋊C4C22×D312yes—
548C3×C42—32no—
549C3×C42—32no—
550C3×C42—32no—
551#217—32no—
552#217—32no—
553#217—32no—
554#217—32no—
555#217—32no—
556#217—32no—
557#217—32no—
558#217—32no—
559#217—32no—
560#217—61no—
561#217—61no—
562#217—62no—
563#217C22×D312yes—
564#217C22×D312yes—
565#217C22×D312yes—
566#217C22×D312yes—
567#217C22×D312yes—
568#217C22×D312yes—
569#217C22×D312yes—
570(C2×D3)⋊C4—32no—
571(C2×D3)⋊C4—32no—
572(C2×D3)⋊C4—32no—
573(C2×D3)⋊C4—32no—
574(C2×D3)⋊C4—32no—
575(C2×D3)⋊C4—32no—
576(C2×D3)⋊C4—32no—
577(C2×D3)⋊C4—32no—
578(C2×D3)⋊C4—32no—
579(C2×D3)⋊C4—32no—
580(C2×D3)⋊C4—32no—
581(C2×D3)⋊C4—32no—
582(C2×D3)⋊C4—32no—
583(C2×D3)⋊C4—32no—
584(C2×D3)⋊C4—32no—
585(C2×D3)⋊C4—62no—
586(C2×D3)⋊C4—62no—
587(C2×D3)⋊C4C22×D312yes—
588(C2×D3)⋊C4C22×D312yes—
589(C2×D3)⋊C4C22×D312yes—
590C4⋊Dic3—32no—
591C4⋊Dic3—32no—
592C4⋊Dic3—32no—
593C4⋊Dic3—32no—
594C4⋊Dic3—32no—
595C4⋊Dic3—32no—
596C4⋊Dic3—32no—
597C4⋊Dic3—32no—
598C4⋊Dic3—32no—
599C4⋊Dic3—32no—
600C4⋊Dic3—32no—
601C4⋊Dic3C22×D312yes—
602C4⋊Dic3C22×D312yes—
603C4⋊Dic3C22×D312yes—
604Dic3⋊C4—32no—
605Dic3⋊C4—32no—
606Dic3⋊C4—32no—
607Dic3⋊C4—32no—
608Dic3⋊C4—32no—
609Dic3⋊C4—32no—
610Dic3⋊C4—32no—
611Dic3⋊C4—32no—
612Dic3⋊C4—32no—
613Dic3⋊C4—32no—
614Dic3⋊C4—32no—
615Dic3⋊C4—32no—
616Dic3⋊C4—32no—
617Dic3⋊C4—32no—
618Dic3⋊C4—32no—
619Dic3⋊C4—32no—
620Dic3⋊C4—32no—
621Dic3⋊C4—32no—
622Dic3⋊C4—32no—
623Dic3⋊C4—32no—
624Dic3⋊C4—32no—
625Dic3⋊C4—62no—
626Dic3⋊C4—62no—
627Dic3⋊C4C22×D312yes—
628Dic3⋊C4C22×D312yes—
629Dic3⋊C4C22×D312yes—
630Dic3⋊C4C22×D312yes—
631Dic3⋊C4C22×D312yes—
632C4×Dic3—32no—
633C4×Dic3—32no—
634C4×Dic3—32no—
635C4×Dic3—32no—
636C4×Dic3—32no—
637C4×Dic3—32no—
638C4×Dic3—32no—
639C4×Dic3—32no—
640C4×Dic3—32no—
641C4×Dic3—32no—
642C4×Dic3—62no—
643C4×Dic3—62no—
644C4×Dic3C22×D312yes—
645C4×Dic3C22×D312yes—
646C4×Dic3C22×D312yes—
647C22×C32—21no—
648C22×C32—21no—
649C22×C32—22no—
650C22×C32—22no—
651C22×C32—22no—
652C22×C32—82no—
653C22×C32C2×#4112yes—
654C22×C32C2511yescharacteristic
655C2×C3⋊D3—22no—
656C2×C3⋊D3—22no—
657C2×C3⋊D3—44no—
658C2×C3⋊D3C2×#4112yes—
659C2×C3⋊D3C2×#4112yes—
660C2×C3×D3—22no—
661C2×C3×D3—22no—
662C2×C3×D3—22no—
663D32—82no—
664C32×C4—22no—
665C32×C4—22no—
666C3⋊Dic3—21no—
667C3⋊Dic3—21no—
668C3⋊Dic3—22no—
669C3⋊Dic3—22no—
670C3×Dic3—22no—
671C3×Dic3—22no—
672C3×Dic3—22no—
673C3×Dic3—22no—
674C3×Dic3—22no—
675C3×Dic3—22no—
676C3×Dic3—22no—
677C22×D4—91no—
678C22×D4—91no—
679C23×C4—91no—
680#126—32no—
681#126—32no—
682#126—92no—
683#126—92no—
684#126—92no—
685#126—92no—
686#126—92no—
687#126—92no—
688#125—92no—
689#125—92no—
690#125—92no—
691#125—92no—
692#125—92no—
693#125—92no—
694#124—32no—
695#124—92no—
696#123—32no—
697#123—32no—
698#123—32no—
699#123—91no—
700#123—91no—
701#123—91no—
702#123—91no—
703#123—92no—
704#123—92no—
705#123—91no—
706#123—91no—
707#123—92no—
708#123—92no—
709#123—92no—
710#123—92no—
711#123—92no—
712#123—92no—
713C22⋊Q8—32no—
714C22⋊Q8—32no—
715C22⋊Q8—92no—
716C22⋊Q8—92no—
717C22⋊Q8—92no—
718C22⋊Q8—92no—
719C22⋊Q8—92no—
720C22⋊Q8—92no—
721C22⋊Q8—92no—
722C22⋊Q8—92no—
723#121—92no—
724#121—92no—
725#120—32no—
726#120—91no—
727#120—91no—
728C4×Q8—92no—
729C4×Q8—92no—
730C4×D4—32no—
731C4×D4—32no—
732C4×D4—92no—
733C4×D4—92no—
734C4×D4—92no—
735C4×D4—92no—
736C4×D4—92no—
737C4×D4—92no—
738C4×D4—92no—
739C4×D4—92no—
740#117—32no—
741#117—32no—
742#117—92no—
743#117—92no—
744#117—92no—
745#117—92no—
746#117—92no—
747#117—92no—
748#117—92no—
749#117—91no—
750#117—91no—
751C2×C4⋊C4—92no—
752C2×C4⋊C4—92no—
753C2×C4⋊C4—92no—
754C2×C22⋊C4—32no—
755C2×C22⋊C4—91no—
756C2×C22⋊C4—92no—
757C2×C22⋊C4—92no—
758C2×C22⋊C4—91no—
759C2×C22⋊C4—91no—
760C2×C22⋊C4—91no—
761C2×C22⋊C4—91no—
762C2×C22⋊C4D3211yescharacteristic, complemented
763C2×C42—92no—
764C23×C3—24no—
765C23×C3—24no—
766C23×C3—21no—
767C23×C3—21no—
768C23×C3—21no—
769C23×C3—32no—
770C23×C3—42no—
771C23×C3—42no—
772C23×C3—82no—
773C23×C3C23×D312yes—
774C23×C3C23×D312yes—
775C23×C3C23×D312yes—
776C22×D3—32no—
777C22×D3—32no—
778C22×D3—38no—
779C22×D3—61no—
780C22×D3—61no—
781C22×D3—64no—
782C22×D3—64no—
783C22×D3—122no—
784C22×D3—122no—
785C22×D3—122no—
786C22×D3—122no—
787C22×D3—242no—
788C22×D3C23×D312yes—
789C3×Q8—122no—
790C3×D4—64no—
791C3×D4—122no—
792C3×D4—122no—
793C2×C3×C4—22no—
794C2×C3×C4—22no—
795C2×C3×C4—32no—
796C2×C3×C4—32no—
797C2×C3×C4—32no—
798C2×C3×C4—32no—
799C2×C3×C4—32no—
800C2×C3×C4—32no—
801C2×C3×C4—32no—
802C2×C3×C4—42no—
803C2×C3×C4—42no—
804C2×C3×C4—64no—
805C2×C3×C4—82no—
806C2×C3×C4—122no—
807C2×C3×C4—122no—
808C2×C3×C4C23×D312yes—
809C2×C3×C4C23×D312yes—
810C2×C3×C4C23×D312yes—
811C2×C3×C4C23×D312yes—
812#67—24no—
813#67—42no—
814#67—42no—
815#67—64no—
816#67—64no—
817#67—64no—
818#67—64no—
819#67—64no—
820#67—64no—
821#67—64no—
822#67—64no—
823#67—64no—
824C2×Dic3—24no—
825C2×Dic3—32no—
826C2×Dic3—32no—
827C2×Dic3—32no—
828C2×Dic3—32no—
829C2×Dic3—32no—
830C2×Dic3—32no—
831C2×Dic3—42no—
832C2×Dic3—61no—
833C2×Dic3—61no—
834C2×Dic3—62no—
835C2×Dic3—62no—
836C2×Dic3—64no—
837C2×Dic3—64no—
838C2×Dic3—122no—
839C2×Dic3—122no—
840C2×Dic3—122no—
841C2×Dic3—242no—
842C2×Dic3C23×D312yes—
843C2×Dic3C23×D312yes—
844C2×Dic3C23×D312yes—
845C2×Dic3C23×D312yes—
846C2×Dic3C23×D312yes—
847C2×Dic3C23×D312yes—
848C2×Dic3C23×D312yes—
849D12—64no—
850C4×D3—42no—
851C4×D3—64no—
852C4×D3—64no—
853C4×D3—64no—
854C4×D3—64no—
855C4×D3—64no—
856C4×D3—122no—
857C4×D3—122no—
858C4×D3—122no—
859C4×D3—122no—
860C4×D3—122no—
861C4×D3—122no—
862C4×D3—122no—
863C4×D3—242no—
864C4×D3—242no—
865Dic6—42no—
866Dic6—122no—
867Dic6—122no—
868C2×C32—22no—
869C2×C32—41no—
870C2×C32—41no—
871C2×C32C22×#4111yescharacteristic
872C2×C32#58512yes—
873C3⋊D3—22no—
874C3⋊D3—22no—
875C3×D3—42no—
876C24—91no—
877C24—91no—
878C24C2×D3211yescharacteristic
879C2×Q8—32no—
880C2×Q8—92no—
881C2×D4—32no—
882C2×D4—32no—
883C2×D4—32no—
884C2×D4—92no—
885C2×D4—91no—
886C2×D4—91no—
887C2×D4—91no—
888C2×D4—91no—
889C2×D4—184no—
890C2×D4—184no—
891C22×C4—32no—
892C22×C4—32no—
893C22×C4—32no—
894C22×C4—91no—
895C22×C4—92no—
896C22×C4—91no—
897C22×C4—91no—
898C22×C4—92no—
899C22×C4—92no—
900C22×C4—91no—
901C22×C4—92no—
902C22×C4—92no—
903C22×C4—92no—
904C22×C4—184no—
905C22×C4C2×D3212yes—
906C4⋊C4—32no—
907C4⋊C4—32no—
908C4⋊C4—32no—
909C4⋊C4—32no—
910C4⋊C4—32no—
911C4⋊C4—32no—
912C4⋊C4—32no—
913C4⋊C4—32no—
914C4⋊C4—92no—
915C4⋊C4—92no—
916C4⋊C4—92no—
917C4⋊C4—92no—
918C4⋊C4—92no—
919C4⋊C4—92no—
920C4⋊C4—92no—
921C4⋊C4—92no—
922C4⋊C4—92no—
923C4⋊C4—92no—
924C4⋊C4—92no—
925C4⋊C4—92no—
926C4⋊C4—92no—
927C4⋊C4—92no—
928C4⋊C4—92no—
929C4⋊C4—92no—
930C22⋊C4—32no—
931C22⋊C4—32no—
932C22⋊C4—32no—
933C22⋊C4—32no—
934C22⋊C4—32no—
935C22⋊C4—32no—
936C22⋊C4—32no—
937C22⋊C4—32no—
938C22⋊C4—32no—
939C22⋊C4—32no—
940C22⋊C4—92no—
941C22⋊C4—91no—
942C22⋊C4—91no—
943C22⋊C4—91no—
944C22⋊C4—91no—
945C22⋊C4—92no—
946C22⋊C4—92no—
947C22⋊C4—92no—
948C22⋊C4—92no—
949C22⋊C4—92no—
950C22⋊C4—91no—
951C22⋊C4—91no—
952C22⋊C4—92no—
953C22⋊C4—92no—
954C22⋊C4—92no—
955C22⋊C4C2×D3211yescharacteristic
956C22⋊C4C2×D3211yescharacteristic
957C22⋊C4C2×D3212yes—
958C42—32no—
959C42—32no—
960C42—32no—
961C42—92no—
962C42—92no—
963C42—92no—
964C42—92no—
965C42—92no—
966C22×C3—22no—
967C22×C3—22no—
968C22×C3—22no—
969C22×C3—22no—
970C22×C3—22no—
971C22×C3—22no—
972C22×C3—22no—
973C22×C3—22no—
974C22×C3—22no—
975C22×C3—22no—
976C22×C3—22no—
977C22×C3—21no—
978C22×C3—42no—
979C22×C3—42no—
980C22×C3—42no—
981C22×C3—62no—
982C22×C3—62no—
983C22×C3—62no—
984C22×C3—84no—
985C22×C3—84no—
986C22×C3D3×#4114yes—
987C22×C3C24×D312yes—
988C2×D3—22no—
989C2×D3—22no—
990C2×D3—22no—
991C2×D3—34no—
992C2×D3—34no—
993C2×D3—62no—
994C2×D3—62no—
995C2×D3—62no—
996C2×D3—62no—
997C2×D3—62no—
998C2×D3—62no—
999C2×D3—122no—
1000C2×D3—122no—
1001C2×D3—128no—
1002C2×D3—244no—
1003C2×D3—244no—
1004C3×C4—22no—
1005C3×C4—22no—
1006C3×C4—22no—
1007C3×C4—22no—
1008C3×C4—42no—
1009C3×C4—42no—
1010C3×C4—62no—
1011C3×C4—62no—
1012C3×C4—62no—
1013C3×C4—62no—
1014C3×C4—62no—
1015C3×C4—62no—
1016C3×C4—62no—
1017Dic3—22no—
1018Dic3—22no—
1019Dic3—22no—
1020Dic3—22no—
1021Dic3—22no—
1022Dic3—22no—
1023Dic3—22no—
1024Dic3—62no—
1025Dic3—62no—
1026Dic3—62no—
1027Dic3—62no—
1028Dic3—62no—
1029Dic3—62no—
1030Dic3—62no—
1031Dic3—62no—
1032Dic3—122no—
1033Dic3—122no—
1034C32#349111yescharacteristic, complemented, Sylow
1035C23—22no—
1036C23—32no—
1037C23—42no—
1038C23—91no—
1039C23—91no—
1040C23—94no—
1041C23—182no—
1042C23—362no—
1043C23—362no—
1044C23C22×D3211yescharacteristic
1045C23C22×D3211yescharacteristic
1046C23C22×D3211yescharacteristic
1047Q8—122no—
1048Q8—362no—
1049D4—64no—
1050D4—122no—
1051D4—122no—
1052D4—184no—
1053D4—182no—
1054D4—182no—
1055D4—182no—
1056D4—182no—
1057C2×C4—32no—
1058C2×C4—32no—
1059C2×C4—32no—
1060C2×C4—32no—
1061C2×C4—32no—
1062C2×C4—32no—
1063C2×C4—32no—
1064C2×C4—42no—
1065C2×C4—64no—
1066C2×C4—92no—
1067C2×C4—91no—
1068C2×C4—91no—
1069C2×C4—92no—
1070C2×C4—122no—
1071C2×C4—122no—
1072C2×C4—184no—
1073C2×C4—182no—
1074C2×C4—182no—
1075C2×C4—182no—
1076C2×C4—182no—
1077C2×C4—362no—
1078C2×C4—362no—
1079C2×C4—362no—
1080C2×C4—362no—
1081C2×C4—362no—
1082C2×C4C22×D3212yes—
1083C2×C4C22×D3212yes—
1084C2×C3—24no—
1085C2×C3—21no—
1086C2×C3—22no—
1087C2×C3—42no—
1088C2×C3—42no—
1089C2×C3—42no—
1090C2×C3—42no—
1091C2×C3—42no—
1092C2×C3—122no—
1093C2×C3C2×D3×#4112yes—
1094C2×C3#596412yes—
1095C2×C3#596612yes—
1096D3—42no—
1097D3—64no—
1098D3—64no—
1099D3—122no—
1100D3—122no—
1101C22—22no—
1102C22—21no—
1103C22—21no—
1104C22—22no—
1105C22—22no—
1106C22—62no—
1107C22—62no—
1108C22—62no—
1109C22—82no—
1110C22—92no—
1111C22—92no—
1112C22—182no—
1113C22—182no—
1114C22—364no—
1115C22—722no—
1116C22#6430612yes—
1117C22C23×D3211yescharacteristic
1118C4—22no—
1119C4—22no—
1120C4—62no—
1121C4—62no—
1122C4—62no—
1123C4—62no—
1124C4—62no—
1125C4—62no—
1126C4—62no—
1127C4—181no—
1128C4—181no—
1129C4—182no—
1130C4—182no—
1131C3—21no—
1132C3#8681612yescomplemented
1133C2—22no—
1134C2—41no—
1135C2—41no—
1136C2—122no—
1137C2—182no—
1138C2—182no—
1139C2C2×#6430611yescharacteristic
1140C2#1059667812yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C22⋊C4C22
prime radical#10595528C2
hypercenterC2×C22⋊C4D32
hypocenterC32#3491
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #10595957C2semidirect
2. C3×#5495C2semidirect
4. #10595509C2semidirect
5. C2×#63975C2semidirect
6. #10595088C2semidirect
7. #10594970C2semidirect
8. #10594968C2semidirect
9. #10594836C2semidirect
10. #10594305C2semidirect
11. #10594295C2semidirect
12. #10594256C2semidirect
13. #10594227C2semidirect
14. #10594180C2semidirect
15. #10594155C2semidirect
16. #10594137C2semidirect
17. #10594135C2semidirect
18. #10594052C2semidirect
19. #10594039C2semidirect
24. C2×C32×C22⋊C4C22semidirect
25. C2×#3757C22semidirect
27. C4×#638C22semidirect
29. #64090C22semidirect
32. #64086C22semidirect
33. #64086C22semidirect
35. C2×C3×#217C22semidirect
36. C3×#929C22semidirect
37. C3×C4×#67C22semidirect
38. C3×#926C22semidirect
39. C3×#924C22semidirect
41. C3×#885C22semidirect
42. C3×#883C22semidirect
44. C3×#879C22semidirect
45. C3×#879C22semidirect
46. C3×#878C22semidirect
47. C3×#877C22semidirect
50. #63982C22semidirect
55. #63975C22semidirect
56. #63975C22semidirect
57. #63975C22semidirect
58. #63975C22semidirect
60. #67⋊Dic3C22semidirect
62. #63969C22semidirect
63. C2×Dic3⋊Dic3C22semidirect
64. #63964C22semidirect
67. #63962C22semidirect
69. #63959C22semidirect
72. #63957C22semidirect
73. #63956C22semidirect
74. #63956C22semidirect
75. #63955C22semidirect
76. #63921C22semidirect
77. D3×(C2×D3)⋊C4C22semidirect
78. C4×#627C22semidirect
79. C4×#626C22semidirect
80. #63900C22semidirect
81. #63895C22semidirect
82. #63888C22semidirect
83. #63887C22semidirect
84. #63883C22semidirect
85. C4×#624C22semidirect
86. #63881C22semidirect
87. #63878C22semidirect
88. #63872C22semidirect
89. #63871C22semidirect
90. #63870C22semidirect
91. #63867C22semidirect
92. #63867C22semidirect
93. #63865C22semidirect
94. #63862C22semidirect
95. #63862C22semidirect
96. #63859C22semidirect
97. #63858C22semidirect
98. #63855C22semidirect
99. #63854C22semidirect
100. #63854C22semidirect
101. #63851C22semidirect
102. #63846C22semidirect
103. #63846C22semidirect
104. #63843C22semidirect
105. #63836C22semidirect
106. #63836C22semidirect
107. #63836C22semidirect
136. #5495D3semidirect
250. C2×C3×C22⋊C4C2×D3semidirect
254. C2×#217C2×D3semidirect
271. #929C2×D3semidirect
280. C4×#67C2×D3semidirect
285. #926C2×D3semidirect
289. #924C2×D3semidirect
327. #885C2×D3semidirect
343. #883C2×D3semidirect
369. #879C2×D3semidirect
370. #879C2×D3semidirect
375. #878C2×D3semidirect
384. #877C2×D3semidirect
762. C2×C22⋊C4D32semidirect
1034. C32#3491semidirect
1132. C3#86816semidirect

Maximal subgroups

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

subgroupindex
#105959572
C3×#54952
#105955282
#105955092
C2×#639752
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