Finite Group Databasebeta

← #11903538

Subgroups — #11903538

Order 1152.

2419 conjugacy classes of subgroups.

The subgroup lattice has 1258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595993C211yesmaximal, characteristic, complemented
2C3×#5528C212yesmaximal, complemented
3#10595076C212yesmaximal, complemented
4#10595033C211yesmaximal, characteristic, complemented
5C4×#3805C211yesmaximal, characteristic, complemented
6#10594655C212yesmaximal, complemented
7#10594616C211yesmaximal, characteristic, complemented
8#10594534C211yesmaximal, characteristic, complemented
9#10594476C211yesmaximal, characteristic, complemented
10#10594472C211yesmaximal, characteristic, complemented
11#10594430C212yesmaximal, complemented
12#10594305C212yesmaximal, complemented
13#10594276C211yesmaximal, characteristic, complemented
14#10594185C211yesmaximal, characteristic, complemented
15#10594155C211yesmaximal, characteristic, complemented
16#10594150C211yesmaximal, characteristic, complemented
17#10594124C212yesmaximal, complemented
18C4×#3802C211yesmaximal, characteristic, complemented
19D3×#872C212yesmaximal, complemented
20#10593980C211yesmaximal, characteristic, complemented
21C4×#3798C211yesmaximal, characteristic, complemented
22#10593911C212yesmaximal, complemented
23#10593882C211yesmaximal, characteristic, complemented
24#86150—32nomaximal
25C2×#3828C2211yescharacteristic
26C2×#3805C2211yescharacteristic
27C2×#3802C2211yescharacteristic
28C2×C4×D32C2212yes—
29C2×#3798C2211yescharacteristic
30C32×#117C2211yescharacteristic, complemented
31C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
32#64102C2211yescharacteristic
33#64102C2211yescharacteristic
34#64096C2211yescharacteristic, complemented
35#64096C2211yescharacteristic, complemented
36#64090C2211yescharacteristic
37#64090C2211yescharacteristic
38#64090C2211yescharacteristic, complemented
39#64090C2211yescharacteristic, complemented
40#64081C2211yescharacteristic
41#64081C2211yescharacteristic, complemented
42C42×C3⋊D3C2211yescharacteristic
43C42×C3⋊D3C2211yescharacteristic, complemented
44C3×C4×#67C2212yescomplemented
45C3×C4×#67C2212yescomplemented
46C3×#898C2212yescomplemented
47C3×#896C2212yescomplemented
48C3×#894C2212yes—
49C3×#889C2212yescomplemented
50C3×#885C2212yescomplemented
51C3×#884C2212yes—
52C3×#883C2212yescomplemented
53C3×#879C2212yescomplemented
54C3×C4×D12C2212yes—
55C3×#872C2212yescomplemented
56C3×C42×D3C2212yescomplemented
57C3×C4×Dic6C2212yescomplemented
58#63983C2212yes—
59#63982C2211yescharacteristic, complemented
60#63980C2211yescharacteristic
61#63975C2212yes—
62#67⋊Dic3C2212yescomplemented
63#63971C2212yescomplemented
64#63971C2212yescomplemented
65#63962C2212yescomplemented
66#63957C2211yescharacteristic, complemented
67#63923C2212yes—
68#63921C2212yes—
69D3×(C2×D3)⋊C4C2212yes—
70D3×(C2×D3)⋊C4C2212yes—
71#63919C2211yescharacteristic, complemented
72C4×#627C2211yescharacteristic, complemented
73C4×#627C2211yescharacteristic, complemented
74C4×#627C2211yescharacteristic, complemented
75#63915C2211yescharacteristic
76#63915C2211yescharacteristic
77#63912C2211yescharacteristic
78#63907C2212yescomplemented
79C4×#626C2212yescomplemented
80C4×#626C2212yescomplemented
81C4×#626C2212yescomplemented
82#63902C2211yescharacteristic
83#63902C2211yescharacteristic
84#63902C2211yescharacteristic
85C4×#625C2211yescharacteristic
86C4×#625C2211yescharacteristic
87C4×#625C2211yescharacteristic
88#63900C2211yescharacteristic
89#63898C2212yes—
90#63897C2212yes—
91#63896C2212yescomplemented
92#63896C2212yescomplemented
93#63890C2212yescomplemented
94#63887C2212yescomplemented
95#63886C2212yes—
96#63884C2212yes—
97#63878C2212yescomplemented
98#63877C2212yescomplemented
99#63877C2212yescomplemented
100D3×Dic3⋊C4C2212yescomplemented
101D3×Dic3⋊C4C2212yescomplemented
102C4×D3×Dic3C2212yescomplemented
103#63874C2212yes—
104#63874C2211yescharacteristic, complemented
105#63873C2211yescharacteristic, complemented
106#63871C2212yes—
107#63870C2212yescomplemented
108#63870C2211yescharacteristic, complemented
109#63870C2211yescharacteristic, complemented
110#63865C2211yescharacteristic
111#63865C2211yescharacteristic
112#63865C2211yescharacteristic, complemented
113#63862C2212yescomplemented
114#63862C2212yescomplemented
115#63858C2212yescomplemented
116#63855C2212yescomplemented
117#63855C2212yescomplemented
118#63853C2212yescomplemented
119#63848C2212yescomplemented
120#63846C2212yescomplemented
121#63838C2211yescharacteristic, complemented
122#63836C2212yes—
123#63836C2212yes—
124C3×#529—32no—
125#5709—32no—
126#5708—32no—
127#5705—32no—
128#5702—32no—
129#5693—32no—
130#5693—32no—
131#5679—32no—
132#5670—32no—
133#5658—32no—
134#5655—32no—
135#5654—32no—
136#5650—32no—
137#5637—32no—
138#5636—32no—
139#5610—32no—
140#5601—32no—
141#5580—32no—
142#5578—32no—
143#5547—32no—
144#5547—32no—
145C4×D3×D4—32no—
146#5538—32no—
147#5538—32no—
148C4×#237—32no—
149#5528—32no—
150#5528D312yescomplemented
151#5522—32no—
152#5522—61no—
153D3×#117—32no—
154C4×#235—32no—
155C2×#872—32no—
156C22×D32C2312yes—
157C22×C32×C4C2311yescharacteristic
158C2×#638C2311yescharacteristic
159C2×#638C2311yescharacteristic
160C22×C3⋊Dic3C2311yescharacteristic
161C22×C3⋊Dic3C2311yescharacteristic
162#3828—24no—
163C2×C4⋊(C3⋊D3)C2311yescharacteristic
164C2×C4×C3⋊D3C2311yescharacteristic
165C2×C4×C3⋊D3C2311yescharacteristic
166C2×C4×C3⋊D3C2311yescharacteristic
167C2×C4×C3⋊D3C2311yescharacteristic
168C2×C4×C3⋊D3C2311yescharacteristic
169C2×C4×C3⋊D3C2311yescharacteristic
170C2×#634C2311yescharacteristic
171C2×C3×#67C2312yes—
172C2×C3×#67C2312yes—
173C2×C3×D12C2312yes—
174C2×C3×C4×D3C2312yes—
175C2×C3×C4×D3C2312yes—
176C2×C3×C4×D3C2312yes—
177C2×C3×C4×D3C2312yes—
178C2×C3×Dic6C2312yes—
179C2×#627C2311yescharacteristic
180C2×#627C2311yescharacteristic
181C2×#626C2312yes—
182C2×#626C2312yes—
183C2×#625C2311yescharacteristic
184C2×#625C2311yescharacteristic
185C2×#624C2312yes—
186#3805—24no—
187C2×D3×Dic3C2312yes—
188C2×D3×Dic3C2312yes—
189C2×D3×Dic3C2312yes—
190C2×D3×Dic3C2312yes—
191#3802—24no—
192C4×D32—28no—
193#3798—24no—
194C32×C4⋊C4C2311yescharacteristic
195C32×C4⋊C4C2311yescharacteristic
196C32×C22⋊C4C2311yescharacteristic
197C32×C22⋊C4C2311yescharacteristic
198C32×C42C2311yescharacteristic
199C32×C42C2311yescharacteristic
200#3752C2311yescharacteristic
201#3752C2311yescharacteristic
202#3752C2311yescharacteristic
203#3752C2311yescharacteristic
204#3750C2311yescharacteristic
205#3750C2311yescharacteristic
206#3750C2311yescharacteristic
207#3750C2311yescharacteristic
208C4×C3⋊Dic3C2311yescharacteristic
209C4×C3⋊Dic3C2311yescharacteristic
210C4×C3⋊Dic3C2311yescharacteristic
211C4×C3⋊Dic3C2311yescharacteristic
212C4×C3⋊Dic3C2311yescharacteristic
213C4×C3⋊Dic3C2311yescharacteristic
214C4×C3⋊Dic3C2311yescharacteristic
215C4×C3⋊Dic3C2311yescharacteristic
216C3×#217C2312yes—
217C3×#217C2312yes—
218C3×(C2×D3)⋊C4C2312yes—
219C3×(C2×D3)⋊C4C2312yes—
220C3×(C2×D3)⋊C4C2312yes—
221C3×(C2×D3)⋊C4C2312yes—
222C3×(C2×D3)⋊C4C2312yes—
223C3×(C2×D3)⋊C4C2312yes—
224C3×C4⋊Dic3C2312yes—
225C3×C4⋊Dic3C2312yes—
226C3×Dic3⋊C4C2312yes—
227C3×Dic3⋊C4C2312yes—
228C3×Dic3⋊C4C2312yes—
229C3×Dic3⋊C4C2312yes—
230C3×Dic3⋊C4C2312yes—
231C3×Dic3⋊C4C2312yes—
232C3×C4×Dic3C2312yes—
233C3×C4×Dic3C2312yes—
234C3×C4×Dic3C2312yes—
235C3×C4×Dic3C2312yes—
236#3724C2311yescharacteristic
237#3724C2311yescharacteristic
238#3724C2311yescharacteristic
239#3724C2311yescharacteristic
240#3724C2312yes—
241#3724C2312yes—
242Dic3⋊Dic3C2312yes—
243Dic3⋊Dic3C2312yes—
244Dic3⋊Dic3C2312yes—
245Dic3⋊Dic3C2312yes—
246Dic3⋊Dic3C2312yes—
247Dic3⋊Dic3C2312yes—
248#3722C2312yes—
249#3722C2312yes—
250#3722C2312yes—
251#3722C2312yes—
252(C2×D3)⋊Dic3C2312yes—
253(C2×D3)⋊Dic3C2312yes—
254(C2×D3)⋊Dic3C2312yes—
255(C2×D3)⋊Dic3C2312yes—
256(C2×D3)⋊Dic3C2312yes—
257(C2×D3)⋊Dic3C2312yes—
258Dic32C2312yes—
259Dic32C2312yes—
260#3475—91noSylow
261C2×#237—32no—
262C2×D3×D4—32no—
263C2×#235—32no—
264C2×#235—32no—
265C2×#235—61no—
266C22×C4×D3—32no—
267C22×C4×D3—32no—
268C3×#126—32no—
269C3×#126—32no—
270C3×#125—32no—
271C3×#124—32no—
272C3×#123—32no—
273C3×#123—32no—
274C3×C22⋊Q8—32no—
275C3×#121—32no—
276C3×C4×Q8—32no—
277C3×C4×D4—32no—
278C3×C4×D4—32no—
279C3×C4×D4—32no—
280C3×#117—21no—
281C3×#117—32no—
282C3×#117C2×D312yescomplemented
283C2×C3×C42—32no—
284#947—32no—
285#946—32no—
286#946—32no—
287#944—32no—
288#939—32no—
289#939—32no—
290#939—32no—
291#939—32no—
292#937—32no—
293#937—32no—
294#935—32no—
295#935—32no—
296D4×Dic3—32no—
297D4×Dic3—32no—
298C4×#67—32no—
299C4×#67—32no—
300C4×#67—32no—
301C4×#67—32no—
302C4×#67—32no—
303C4×#67—32no—
304C4×#67C2×D312yescomplemented
305C4×#67C2×D312yescomplemented
306C2×(C2×D3)⋊C4—32no—
307C2×(C2×D3)⋊C4—32no—
308#926—32no—
309#926—32no—
310C2×Dic3⋊C4—32no—
311C2×Dic3⋊C4—32no—
312C2×C4×Dic3—32no—
313C2×C4×Dic3—32no—
314C2×C4×Dic3—61no—
315#898—32no—
316#898—32no—
317#898—32no—
318#898—32no—
319#898—32no—
320#898C2×D312yescomplemented
321#897—32no—
322#896—32no—
323#896—32no—
324#896—32no—
325#896—32no—
326#896—32no—
327#896C2×D312yescomplemented
328#895—32no—
329#894—32no—
330#894—32no—
331#894—32no—
332#894—32no—
333#894—32no—
334#894C2×D312yes—
335#893—32no—
336#893—32no—
337#893—32no—
338#893—61no—
339#893—61no—
340#892—32no—
341#892—32no—
342#892—32no—
343D3×C4⋊C4—32no—
344D3×C4⋊C4—32no—
345D3×C4⋊C4—32no—
346#890—32no—
347#889—32no—
348#889—32no—
349#889—32no—
350#889—32no—
351#889—32no—
352#889C2×D312yescomplemented
353#888—32no—
354#887—32no—
355#887—32no—
356#887—32no—
357#887—61no—
358#887—61no—
359#886—32no—
360#886—32no—
361#885—32no—
362#885—32no—
363#885—32no—
364#885C2×D312yescomplemented
365#884—32no—
366#884—32no—
367#884—32no—
368#884C2×D312yes—
369#883—32no—
370#883—32no—
371#883—32no—
372#883C2×D312yescomplemented
373#882—32no—
374#882—32no—
375#67⋊C4—32no—
376#67⋊C4—32no—
377#67⋊C4—32no—
378#67⋊C4—32no—
379#67⋊C4—32no—
380#67⋊C4—32no—
381#67⋊C4—32no—
382#67⋊C4—32no—
383#67⋊C4—61no—
384#67⋊C4—61no—
385#67⋊C4—61no—
386#67⋊C4—61no—
387D3×C22⋊C4—32no—
388D3×C22⋊C4—32no—
389D3×C22⋊C4—32no—
390D3×C22⋊C4—32no—
391#879—32no—
392#879—32no—
393#879—32no—
394#879C2×D312yescomplemented
395#878—32no—
396#878—32no—
397#878—32no—
398#878—32no—
399#877—32no—
400#877—32no—
401#877—32no—
402#877—32no—
403C4×D12—32no—
404C4×D12—32no—
405C4×D12—32no—
406C4×D12C2×D312yes—
407#872—32no—
408#872—32no—
409#872—32no—
410#872—32no—
411#872—32no—
412#872—32no—
413#872—32no—
414#872—32no—
415#872—32no—
416#872—32no—
417#872—32no—
418#872—61no—
419#872—61no—
420#872C2×D312yescomplemented
421C42×D3—32no—
422C42×D3—32no—
423C42×D3—32no—
424C42×D3—61no—
425C42×D3—61no—
426C42×D3C2×D312yescomplemented
427C4×Dic6—32no—
428C4×Dic6—32no—
429C4×Dic6—32no—
430C4×Dic6C2×D312yescomplemented
431C23×C32C2411yescharacteristic
432C22×C3⋊D3C2411yescharacteristic
433C22×C3⋊D3C2411yescharacteristic
434C22×C3×D3C2412yes—
435C22×C3×D3C2412yes—
436C2×D32—24no—
437C2×D32—24no—
438C2×D32—42no—
439C2×C32×C4—22no—
440C2×C32×C4C2411yescharacteristic
441C2×C32×C4C2411yescharacteristic
442C2×C32×C4C2411yescharacteristic
443C2×C32×C4C2411yescharacteristic
444C2×C32×C4C2411yescharacteristic
445C2×C32×C4C2411yescharacteristic
446#638—22no—
447#638—22no—
448C2×C3⋊Dic3—22no—
449C2×C3⋊Dic3—41no—
450C2×C3⋊Dic3C2411yescharacteristic
451C2×C3⋊Dic3C2411yescharacteristic
452C2×C3⋊Dic3C2411yescharacteristic
453C2×C3⋊Dic3C2411yescharacteristic
454C2×C3⋊Dic3C2411yescharacteristic
455C2×C3⋊Dic3C2411yescharacteristic
456C4⋊(C3⋊D3)—22no—
457C4×C3⋊D3—22no—
458C4×C3⋊D3—22no—
459C4×C3⋊D3—22no—
460C4×C3⋊D3—41no—
461C4×C3⋊D3—41no—
462C4×C3⋊D3#4114yescomplemented
463#634—22no—
464C3×#67—24no—
465C3×#67—42no—
466C2×C3×Dic3C2412yes—
467C2×C3×Dic3C2412yes—
468C2×C3×Dic3C2412yes—
469C2×C3×Dic3C2412yes—
470C2×C3×Dic3C2412yes—
471C2×C3×Dic3C2412yes—
472C3×D12—24no—
473C3×C4×D3—24no—
474C3×C4×D3—24no—
475C3×C4×D3—24no—
476C3×C4×D3—42no—
477C3×Dic6—42no—
478#627—22no—
479#627—22no—
480#626—24no—
481#626—42no—
482#625—22no—
483#625#4114yescomplemented
484#624—24no—
485D3×Dic3—24no—
486D3×Dic3—24no—
487D3×Dic3—24no—
488D3×Dic3—42no—
489#556—91no—
490#555—91no—
491#554—91no—
492#553—92no—
493#552—92no—
494#552—91no—
495#552—91no—
496#551—92no—
497#551—92no—
498#547—91no—
499#546—91no—
500#546—91no—
501#533—91no—
502#529—32no—
503#529—91no—
504#529—91no—
505#529—92no—
506#525—92no—
507C4×#41—91no—
508C4×#41—91no—
509C4×#41—91no—
510C2×C4×D4—91no—
511C2×#117—92no—
512C23×D3—32no—
513C23×D3—32no—
514C2×C3×Q8—32no—
515C2×C3×D4—32no—
516C2×C3×D4—32no—
517C2×C3×D4—32no—
518C22×C3×C4—21no—
519C22×C3×C4—32no—
520C22×C3×C4—32no—
521C22×C3×C4—32no—
522C22×C3×C4—32no—
523C22×C3×C4C22×D312yes—
524C2×#67—32no—
525C2×#67—32no—
526C2×#67—32no—
527C2×#67—32no—
528C2×#67—32no—
529C2×#67—32no—
530C2×#67—61no—
531C2×#67—61no—
532C2×#67C22×D312yes—
533C2×#67C22×D312yes—
534C22×Dic3—32no—
535C22×Dic3—32no—
536C22×Dic3—32no—
537C22×Dic3—32no—
538C22×Dic3—32no—
539C22×Dic3—32no—
540C22×Dic3—61no—
541C22×Dic3—61no—
542#237—68no—
543D3×D4—68no—
544#235—68no—
545#235—68no—
546#235—68no—
547C2×D12—32no—
548C2×D12—32no—
549C2×D12—32no—
550C2×D12—61no—
551C2×D12C22×D312yes—
552C2×C4×D3—32no—
553C2×C4×D3—32no—
554C2×C4×D3—32no—
555C2×C4×D3—32no—
556C2×C4×D3—32no—
557C2×C4×D3—32no—
558C2×C4×D3—32no—
559C2×C4×D3—32no—
560C2×C4×D3—32no—
561C2×C4×D3—32no—
562C2×C4×D3—32no—
563C2×C4×D3—32no—
564C2×C4×D3—61no—
565C2×C4×D3—61no—
566C2×C4×D3—61no—
567C2×C4×D3—61no—
568C2×C4×D3—61no—
569C2×C4×D3—61no—
570C2×C4×D3—68no—
571C2×C4×D3—68no—
572C2×C4×D3C22×D312yes—
573C2×C4×D3C22×D312yes—
574C2×C4×D3C22×D312yes—
575C2×C4×D3C22×D312yes—
576C2×Dic6—32no—
577C2×Dic6—32no—
578C2×Dic6—32no—
579C2×Dic6—61no—
580C2×Dic6C22×D312yes—
581C3×C4⋊C4—21no—
582C3×C4⋊C4—21no—
583C3×C4⋊C4—32no—
584C3×C4⋊C4—32no—
585C3×C4⋊C4—32no—
586C3×C4⋊C4—32no—
587C3×C4⋊C4—32no—
588C3×C4⋊C4—32no—
589C3×C4⋊C4—32no—
590C3×C4⋊C4—32no—
591C3×C4⋊C4C22×D312yes—
592C3×C4⋊C4C22×D312yes—
593C3×C22⋊C4—21no—
594C3×C22⋊C4—21no—
595C3×C22⋊C4—32no—
596C3×C22⋊C4—32no—
597C3×C22⋊C4—32no—
598C3×C22⋊C4—32no—
599C3×C22⋊C4—32no—
600C3×C22⋊C4—32no—
601C3×C22⋊C4—32no—
602C3×C22⋊C4—32no—
603C3×C22⋊C4C22×D312yes—
604C3×C22⋊C4C22×D312yes—
605C3×C42—21no—
606C3×C42—21no—
607C3×C42—32no—
608C3×C42—32no—
609C3×C42—32no—
610C3×C42—32no—
611C3×C42C22×D312yes—
612C3×C42C22×D312yes—
613#217—32no—
614#217—32no—
615#217—32no—
616#217—32no—
617#217—32no—
618#217—32no—
619#217C22×D312yes—
620#217C22×D312yes—
621(C2×D3)⋊C4—32no—
622(C2×D3)⋊C4—32no—
623(C2×D3)⋊C4—32no—
624(C2×D3)⋊C4—32no—
625(C2×D3)⋊C4—32no—
626(C2×D3)⋊C4—32no—
627(C2×D3)⋊C4—32no—
628(C2×D3)⋊C4—32no—
629(C2×D3)⋊C4—32no—
630(C2×D3)⋊C4—32no—
631(C2×D3)⋊C4—32no—
632(C2×D3)⋊C4—32no—
633(C2×D3)⋊C4—32no—
634(C2×D3)⋊C4—32no—
635(C2×D3)⋊C4—32no—
636(C2×D3)⋊C4—32no—
637(C2×D3)⋊C4—32no—
638(C2×D3)⋊C4—32no—
639(C2×D3)⋊C4—61no—
640(C2×D3)⋊C4—61no—
641(C2×D3)⋊C4—61no—
642(C2×D3)⋊C4—61no—
643(C2×D3)⋊C4C22×D312yes—
644(C2×D3)⋊C4C22×D312yes—
645(C2×D3)⋊C4C22×D312yes—
646(C2×D3)⋊C4C22×D312yes—
647(C2×D3)⋊C4C22×D312yes—
648(C2×D3)⋊C4C22×D312yes—
649C4⋊Dic3—32no—
650C4⋊Dic3—32no—
651C4⋊Dic3—32no—
652C4⋊Dic3—32no—
653C4⋊Dic3—32no—
654C4⋊Dic3—32no—
655C4⋊Dic3C22×D312yes—
656C4⋊Dic3C22×D312yes—
657Dic3⋊C4—32no—
658Dic3⋊C4—32no—
659Dic3⋊C4—32no—
660Dic3⋊C4—32no—
661Dic3⋊C4—32no—
662Dic3⋊C4—32no—
663Dic3⋊C4—32no—
664Dic3⋊C4—32no—
665Dic3⋊C4—32no—
666Dic3⋊C4—32no—
667Dic3⋊C4—32no—
668Dic3⋊C4—32no—
669Dic3⋊C4—32no—
670Dic3⋊C4—32no—
671Dic3⋊C4—32no—
672Dic3⋊C4—32no—
673Dic3⋊C4—32no—
674Dic3⋊C4—32no—
675Dic3⋊C4—61no—
676Dic3⋊C4—61no—
677Dic3⋊C4—61no—
678Dic3⋊C4—61no—
679Dic3⋊C4C22×D312yes—
680Dic3⋊C4C22×D312yes—
681Dic3⋊C4C22×D312yes—
682Dic3⋊C4C22×D312yes—
683Dic3⋊C4C22×D312yes—
684Dic3⋊C4C22×D312yes—
685C4×Dic3—32no—
686C4×Dic3—32no—
687C4×Dic3—32no—
688C4×Dic3—32no—
689C4×Dic3—32no—
690C4×Dic3—32no—
691C4×Dic3—32no—
692C4×Dic3—32no—
693C4×Dic3—32no—
694C4×Dic3—32no—
695C4×Dic3—32no—
696C4×Dic3—32no—
697C4×Dic3—61no—
698C4×Dic3—61no—
699C4×Dic3—61no—
700C4×Dic3—61no—
701C4×Dic3—61no—
702C4×Dic3—61no—
703C4×Dic3—61no—
704C4×Dic3—61no—
705C4×Dic3C22×D312yes—
706C4×Dic3C22×D312yes—
707C4×Dic3C22×D312yes—
708C4×Dic3C22×D312yes—
709C22×C32—21no—
710C22×C32—21no—
711C22×C32—21no—
712C22×C32C2511yescharacteristic
713C2×C3⋊D3—21no—
714C2×C3⋊D3—21no—
715C2×C3⋊D3—21no—
716C2×C3⋊D3—21no—
717C2×C3⋊D3—21no—
718C2×C3⋊D3C2×#4112yes—
719C2×C3×D3—22no—
720C2×C3×D3—22no—
721C2×C3×D3—22no—
722C2×C3×D3—22no—
723C2×C3×D3—22no—
724C2×C3×D3C2×#4114yes—
725D32—48no—
726C32×C4—21no—
727C32×C4—21no—
728C32×C4—21no—
729C32×C4—21no—
730C32×C4—21no—
731C32×C4C2×#4112yes—
732C3⋊Dic3—21no—
733C3⋊Dic3—21no—
734C3⋊Dic3—21no—
735C3⋊Dic3—21no—
736C3⋊Dic3C2×#4112yes—
737C3⋊Dic3C2×#4112yes—
738C3×Dic3—22no—
739C3×Dic3—22no—
740C3×Dic3—22no—
741C3×Dic3—22no—
742C3×Dic3—22no—
743C3×Dic3—22no—
744C2×#41—91no—
745C2×#41—91no—
746C2×#41—91no—
747C22×D4—91no—
748C23×C4—92no—
749C4⋊Q8—91no—
750C4⋊Q8—91no—
751#126—32no—
752#126—32no—
753#126—92no—
754#126—92no—
755#126—92no—
756#126—92no—
757#125—32no—
758#125—92no—
759#125—91no—
760#125—91no—
761#125—92no—
762#124—32no—
763#124—91no—
764#124—91no—
765#124—92no—
766#123—32no—
767#123—32no—
768#123—92no—
769#123—92no—
770#123—92no—
771#123—92no—
772#123—92no—
773#123—92no—
774C22⋊Q8—32no—
775C22⋊Q8—91no—
776C22⋊Q8—92no—
777C22⋊Q8—92no—
778C22⋊Q8—92no—
779C22⋊Q8—91no—
780C22⋊Q8—91no—
781C22⋊Q8—91no—
782C22⋊Q8—92no—
783#121—32no—
784#121—91no—
785#121—92no—
786#121—92no—
787#121—92no—
788#121—91no—
789#120—92no—
790#120—92no—
791C4×Q8—32no—
792C4×Q8—91no—
793C4×Q8—91no—
794C4×Q8—91no—
795C4×Q8—91no—
796C4×Q8—91no—
797C4×Q8—91no—
798C4×D4—32no—
799C4×D4—32no—
800C4×D4—32no—
801C4×D4—92no—
802C4×D4—92no—
803C4×D4—92no—
804C4×D4—91no—
805C4×D4—91no—
806C4×D4—91no—
807C4×D4—92no—
808C4×D4—92no—
809C4×D4—91no—
810C4×D4—91no—
811C4×D4—91no—
812C4×D4—91no—
813C4×D4—91no—
814C4×D4—91no—
815C4×D4—91no—
816C4×D4—91no—
817C4×D4—91no—
818#117—32no—
819#117—92no—
820#117—91no—
821#117—92no—
822#117—92no—
823#117—92no—
824#117—92no—
825#117—92no—
826#117—92no—
827#117—91no—
828#117—92no—
829#117—91no—
830#117—91no—
831#117D3211yescharacteristic, complemented
832C2×C4⋊C4—91no—
833C2×C4⋊C4—92no—
834C2×C4⋊C4—92no—
835C2×C22⋊C4—92no—
836C2×C22⋊C4—92no—
837C2×C22⋊C4—92no—
838C2×C42—32no—
839C2×C42—92no—
840C2×C42—91no—
841C2×C42—91no—
842C2×C42—91no—
843C23×C3—21no—
844C23×C3—32no—
845C23×C3—32no—
846C23×C3C23×D312yes—
847C22×D3—32no—
848C22×D3—32no—
849C22×D3—61no—
850C22×D3—61no—
851C22×D3—64no—
852C22×D3—64no—
853C22×D3—64no—
854C22×D3—64no—
855C22×D3—122no—
856C22×D3—122no—
857C22×D3C23×D312yes—
858C22×D3C23×D312yes—
859C3×Q8—122no—
860C3×D4—64no—
861C3×D4—64no—
862C3×D4—122no—
863C2×C3×C4—24no—
864C2×C3×C4—24no—
865C2×C3×C4—21no—
866C2×C3×C4—21no—
867C2×C3×C4—21no—
868C2×C3×C4—21no—
869C2×C3×C4—21no—
870C2×C3×C4—21no—
871C2×C3×C4—32no—
872C2×C3×C4—32no—
873C2×C3×C4—32no—
874C2×C3×C4—32no—
875C2×C3×C4—32no—
876C2×C3×C4—32no—
877C2×C3×C4—64no—
878C2×C3×C4—64no—
879C2×C3×C4—64no—
880C2×C3×C4—122no—
881C2×C3×C4C23×D312yes—
882C2×C3×C4C23×D312yes—
883C2×C3×C4C23×D312yes—
884C2×C3×C4C23×D312yes—
885C2×C3×C4C23×D312yes—
886C2×C3×C4C23×D312yes—
887#67—24no—
888#67—38no—
889#67—42no—
890#67—64no—
891#67—64no—
892#67—64no—
893#67—64no—
894#67—64no—
895#67—64no—
896#67—122no—
897C2×Dic3—32no—
898C2×Dic3—32no—
899C2×Dic3—32no—
900C2×Dic3—32no—
901C2×Dic3—32no—
902C2×Dic3—32no—
903C2×Dic3—61no—
904C2×Dic3—61no—
905C2×Dic3—61no—
906C2×Dic3—61no—
907C2×Dic3—61no—
908C2×Dic3—61no—
909C2×Dic3—64no—
910C2×Dic3—64no—
911C2×Dic3—64no—
912C2×Dic3—64no—
913C2×Dic3—122no—
914C2×Dic3—122no—
915C2×Dic3—122no—
916C2×Dic3—122no—
917C2×Dic3C23×D312yes—
918C2×Dic3C23×D312yes—
919C2×Dic3C23×D312yes—
920C2×Dic3C23×D312yes—
921C2×Dic3C23×D312yes—
922C2×Dic3C23×D312yes—
923D12—24no—
924D12—64no—
925D12—64no—
926D12—64no—
927D12—122no—
928C4×D3—24no—
929C4×D3—24no—
930C4×D3—24no—
931C4×D3—38no—
932C4×D3—42no—
933C4×D3—64no—
934C4×D3—64no—
935C4×D3—64no—
936C4×D3—64no—
937C4×D3—64no—
938C4×D3—64no—
939C4×D3—64no—
940C4×D3—64no—
941C4×D3—64no—
942C4×D3—64no—
943C4×D3—122no—
944C4×D3—122no—
945C4×D3—122no—
946C4×D3—122no—
947C4×D3—122no—
948C4×D3—122no—
949C4×D3—122no—
950Dic6—42no—
951Dic6—64no—
952Dic6—64no—
953Dic6—64no—
954Dic6—64no—
955C2×C32—41no—
956C2×C32C22×#4111yescharacteristic
957C2×C32C22×#4111yescharacteristic
958C2×C32#58511yescharacteristic
959C3⋊D3—22no—
960C3⋊D3—41no—
961C3×D3—24no—
962C3×D3—42no—
963C24—92no—
964#41—184no—
965#41—184no—
966#41—184no—
967C2×Q8—32no—
968C2×Q8—91no—
969C2×Q8—91no—
970C2×Q8—91no—
971C2×D4—32no—
972C2×D4—32no—
973C2×D4—32no—
974C2×D4—92no—
975C2×D4—92no—
976C2×D4—91no—
977C2×D4—91no—
978C2×D4—91no—
979C2×D4—91no—
980C2×D4—91no—
981C2×D4—184no—
982C22×C4—32no—
983C22×C4—32no—
984C22×C4—32no—
985C22×C4—32no—
986C22×C4—92no—
987C22×C4—92no—
988C22×C4—92no—
989C22×C4—92no—
990C22×C4—92no—
991C22×C4—91no—
992C22×C4—91no—
993C22×C4—91no—
994C22×C4—91no—
995C22×C4—91no—
996C22×C4—91no—
997C22×C4—91no—
998C22×C4—91no—
999C22×C4—188no—
1000C22×C4C2×D3211yescharacteristic
1001C4⋊C4—32no—
1002C4⋊C4—32no—
1003C4⋊C4—32no—
1004C4⋊C4—32no—
1005C4⋊C4—32no—
1006C4⋊C4—32no—
1007C4⋊C4—32no—
1008C4⋊C4—32no—
1009C4⋊C4—91no—
1010C4⋊C4—92no—
1011C4⋊C4—92no—
1012C4⋊C4—92no—
1013C4⋊C4—92no—
1014C4⋊C4—91no—
1015C4⋊C4—91no—
1016C4⋊C4—91no—
1017C4⋊C4—92no—
1018C4⋊C4—92no—
1019C4⋊C4—92no—
1020C4⋊C4—92no—
1021C4⋊C4—91no—
1022C4⋊C4—91no—
1023C4⋊C4—91no—
1024C4⋊C4—91no—
1025C4⋊C4C2×D3211yescharacteristic
1026C4⋊C4C2×D3211yescharacteristic
1027C22⋊C4—32no—
1028C22⋊C4—32no—
1029C22⋊C4—32no—
1030C22⋊C4—32no—
1031C22⋊C4—32no—
1032C22⋊C4—32no—
1033C22⋊C4—32no—
1034C22⋊C4—32no—
1035C22⋊C4—92no—
1036C22⋊C4—92no—
1037C22⋊C4—92no—
1038C22⋊C4—92no—
1039C22⋊C4—92no—
1040C22⋊C4—92no—
1041C22⋊C4—92no—
1042C22⋊C4—92no—
1043C22⋊C4—92no—
1044C22⋊C4—92no—
1045C22⋊C4—91no—
1046C22⋊C4—91no—
1047C22⋊C4—91no—
1048C22⋊C4—91no—
1049C22⋊C4C2×D3211yescharacteristic
1050C22⋊C4C2×D3211yescharacteristic
1051C42—32no—
1052C42—32no—
1053C42—32no—
1054C42—32no—
1055C42—92no—
1056C42—92no—
1057C42—91no—
1058C42—91no—
1059C42—91no—
1060C42—91no—
1061C42—91no—
1062C42—91no—
1063C42—91no—
1064C42—91no—
1065C42C2×D3211yescharacteristic
1066C42C2×D3211yescharacteristic
1067C22×C3—22no—
1068C22×C3—22no—
1069C22×C3—22no—
1070C22×C3—22no—
1071C22×C3—21no—
1072C22×C3—34no—
1073C22×C3—41no—
1074C22×C3—41no—
1075C22×C3—62no—
1076C22×C3—62no—
1077C22×C3—62no—
1078C22×C3—62no—
1079C22×C3—62no—
1080C22×C3C24×D312yes—
1081C2×D3—22no—
1082C2×D3—22no—
1083C2×D3—22no—
1084C2×D3—22no—
1085C2×D3—22no—
1086C2×D3—34no—
1087C2×D3—62no—
1088C2×D3—62no—
1089C2×D3—62no—
1090C2×D3—62no—
1091C2×D3—62no—
1092C2×D3—62no—
1093C2×D3—62no—
1094C2×D3—121no—
1095C2×D3—121no—
1096C2×D3—121no—
1097C2×D3—121no—
1098C2×D3—128no—
1099C2×D3—128no—
1100C2×D3D3×#4114yes—
1101C3×C4—22no—
1102C3×C4—22no—
1103C3×C4—22no—
1104C3×C4—22no—
1105C3×C4—22no—
1106C3×C4—22no—
1107C3×C4—22no—
1108C3×C4—41no—
1109C3×C4—41no—
1110C3×C4—41no—
1111C3×C4—41no—
1112C3×C4—62no—
1113C3×C4—62no—
1114C3×C4—62no—
1115C3×C4—62no—
1116C3×C4—62no—
1117C3×C4—62no—
1118C3×C4D3×#4114yes—
1119Dic3—22no—
1120Dic3—22no—
1121Dic3—22no—
1122Dic3—22no—
1123Dic3—22no—
1124Dic3—22no—
1125Dic3—34no—
1126Dic3—34no—
1127Dic3—62no—
1128Dic3—62no—
1129Dic3—62no—
1130Dic3—62no—
1131Dic3—62no—
1132Dic3—62no—
1133Dic3—62no—
1134Dic3—62no—
1135Dic3—121no—
1136Dic3—121no—
1137C32#347511yescharacteristic, complemented, Sylow
1138C23—32no—
1139C23—32no—
1140C23—91no—
1141C23—91no—
1142C23—184no—
1143C23—184no—
1144C23—362no—
1145C23C22×D3211yescharacteristic
1146Q8—122no—
1147Q8—182no—
1148Q8—182no—
1149Q8—182no—
1150D4—64no—
1151D4—64no—
1152D4—94no—
1153D4—122no—
1154D4—182no—
1155D4—184no—
1156D4—182no—
1157D4—182no—
1158D4—182no—
1159D4—362no—
1160C2×C4—22no—
1161C2×C4—32no—
1162C2×C4—32no—
1163C2×C4—32no—
1164C2×C4—32no—
1165C2×C4—32no—
1166C2×C4—32no—
1167C2×C4—64no—
1168C2×C4—64no—
1169C2×C4—64no—
1170C2×C4—91no—
1171C2×C4—91no—
1172C2×C4—94no—
1173C2×C4—91no—
1174C2×C4—91no—
1175C2×C4—91no—
1176C2×C4—91no—
1177C2×C4—122no—
1178C2×C4—182no—
1179C2×C4—182no—
1180C2×C4—184no—
1181C2×C4—184no—
1182C2×C4—184no—
1183C2×C4—184no—
1184C2×C4—182no—
1185C2×C4—182no—
1186C2×C4—361no—
1187C2×C4—361no—
1188C2×C4—362no—
1189C2×C4—361no—
1190C2×C4C22×D3211yescharacteristic
1191C2×C4C22×D3211yescharacteristic
1192C2×C4C22×D3211yescharacteristic
1193C2×C4C22×D3211yescharacteristic
1194C2×C4C22×D3211yescharacteristic
1195C2×C4C22×D3211yescharacteristic
1196C2×C3—21no—
1197C2×C3—21no—
1198C2×C3—21no—
1199C2×C3—42no—
1200C2×C3—42no—
1201C2×C3—64no—
1202C2×C3—122no—
1203C2×C3C2×D3×#4112yes—
1204C2×C3C2×D3×#4112yes—
1205C2×C3#596412yes—
1206D3—24no—
1207D3—42no—
1208D3—64no—
1209D3—122no—
1210D3—122no—
1211D3—122no—
1212C22—21no—
1213C22—21no—
1214C22—21no—
1215C22—34no—
1216C22—62no—
1217C22—62no—
1218C22—62no—
1219C22—62no—
1220C22—62no—
1221C22—92no—
1222C22—181no—
1223C22—181no—
1224C22—181no—
1225C22—181no—
1226C22—181no—
1227C22—368no—
1228C22C23×D3211yescharacteristic
1229C4—21no—
1230C4—21no—
1231C4—21no—
1232C4—21no—
1233C4—21no—
1234C4—62no—
1235C4—62no—
1236C4—62no—
1237C4—62no—
1238C4—62no—
1239C4—62no—
1240C4—92no—
1241C4—92no—
1242C4—181no—
1243C4—181no—
1244C4—181no—
1245C4—181no—
1246C4#6430612yes—
1247C3—21no—
1248C3#8615012yescomplemented
1249C2—41no—
1250C2—64no—
1251C2—122no—
1252C2—182no—
1253C2—361no—
1254C2C2×#6430611yescharacteristic
1255C2D32×#4111yescharacteristic
1256C2#1059669511yescharacteristic
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC32×#117C22
hypercenter#117D32
hypocenterC32#3475
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595993C2semidirect
2. C3×#5528C2semidirect
3. #10595076C2semidirect
4. #10595033C2semidirect
5. C4×#3805C2semidirect
6. #10594655C2semidirect
7. #10594616C2semidirect
8. #10594534C2semidirect
9. #10594476C2semidirect
10. #10594472C2semidirect
11. #10594430C2semidirect
12. #10594305C2semidirect
13. #10594276C2semidirect
14. #10594185C2semidirect
15. #10594155C2semidirect
16. #10594150C2semidirect
17. #10594124C2semidirect
18. C4×#3802C2semidirect
19. D3×#872C2semidirect
20. #10593980C2semidirect
21. C4×#3798C2semidirect
22. #10593911C2semidirect
23. #10593882C2semidirect
30. C32×#117C22semidirect
31. C2×C4×C3⋊Dic3C22semidirect
34. #64096C22semidirect
35. #64096C22semidirect
38. #64090C22semidirect
39. #64090C22semidirect
41. #64081C22semidirect
43. C42×C3⋊D3C22semidirect
44. C3×C4×#67C22semidirect
45. C3×C4×#67C22semidirect
46. C3×#898C22semidirect
47. C3×#896C22semidirect
49. C3×#889C22semidirect
50. C3×#885C22semidirect
52. C3×#883C22semidirect
53. C3×#879C22semidirect
55. C3×#872C22semidirect
56. C3×C42×D3C22semidirect
57. C3×C4×Dic6C22semidirect
59. #63982C22semidirect
62. #67⋊Dic3C22semidirect
63. #63971C22semidirect
64. #63971C22semidirect
65. #63962C22semidirect
66. #63957C22semidirect
71. #63919C22semidirect
72. C4×#627C22semidirect
73. C4×#627C22semidirect
74. C4×#627C22semidirect
78. #63907C22semidirect
79. C4×#626C22semidirect
80. C4×#626C22semidirect
81. C4×#626C22semidirect
91. #63896C22semidirect
92. #63896C22semidirect
93. #63890C22semidirect
94. #63887C22semidirect
97. #63878C22semidirect
98. #63877C22semidirect
99. #63877C22semidirect
100. D3×Dic3⋊C4C22semidirect
101. D3×Dic3⋊C4C22semidirect
102. C4×D3×Dic3C22semidirect
104. #63874C22semidirect
105. #63873C22semidirect
107. #63870C22semidirect
108. #63870C22semidirect
109. #63870C22semidirect
112. #63865C22semidirect
113. #63862C22semidirect
114. #63862C22semidirect
115. #63858C22semidirect
116. #63855C22semidirect
117. #63855C22semidirect
118. #63853C22semidirect
119. #63848C22semidirect
120. #63846C22semidirect
121. #63838C22semidirect
150. #5528D3semidirect
282. C3×#117C2×D3semidirect
304. C4×#67C2×D3semidirect
305. C4×#67C2×D3semidirect
320. #898C2×D3semidirect
327. #896C2×D3semidirect
352. #889C2×D3semidirect
364. #885C2×D3semidirect
372. #883C2×D3semidirect
394. #879C2×D3semidirect
420. #872C2×D3semidirect
426. C42×D3C2×D3semidirect
430. C4×Dic6C2×D3semidirect
462. C4×C3⋊D3#41semidirect
483. #625#41semidirect
831. #117D32semidirect
1137. C32#3475semidirect
1248. C3#86150semidirect

Maximal subgroups

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

subgroupindex
#105959932
C3×#55282
#105950762
#105950332
C4×#38052
#105946552
#105946162
#105945342
#105944762
#105944722
#105944302
#105943052
#105942762
#105941852
#105941552
#105941502
#105941242
C4×#38022
D3×#8722
#105939802
C4×#37982
#105939112
#105938822
#861503