Finite Group Databasebeta

← #13082287

Subgroups — #13082287

Order 1408.

1522 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#67043C211yesmaximal, characteristic, complemented
2C22×#4341C211yesmaximal, characteristic, complemented
3C11×#546C211yesmaximal, characteristic, complemented
4#10623355C211yesmaximal, characteristic, complemented
5#10623337C211yesmaximal, characteristic, complemented
6#10623208C211yesmaximal, characteristic, complemented
7#10623206C211yesmaximal, characteristic, complemented
8#10623186C212yesmaximal, complemented
9#10623179C212yesmaximal, complemented
10#10623163C211yesmaximal, characteristic, complemented
11D11×C22⋊Q8C211yesmaximal, characteristic, complemented
12#10623142C212yesmaximal, complemented
13#10623139C211yesmaximal, characteristic, complemented
14#10623129C211yesmaximal, characteristic, complemented
15#10623128C212yesmaximal, complemented
16#10623122C212yesmaximal, complemented
17#10623117C212yesmaximal, complemented
18#10623086C211yesmaximal, characteristic, complemented
19#10623078C211yesmaximal, characteristic, complemented
20#10623077C211yesmaximal, characteristic, complemented
21D4×Dic22C211yesmaximal, characteristic, complemented
22#10623021C212yesmaximal, complemented
23C2×#66931C212yesmaximal, complemented
24C2×C11×#41C2211yescharacteristic, complemented
25C22×D4×C11C2211yescharacteristic
26C22×C22⋊D11C2212yes—
27C23×Dic11C2212yes—
28#67043—28no—
29C2×Q8×D11C2211yescharacteristic, complemented
30C2×Q8×D11C2211yescharacteristic, complemented
31C2×#4341—28no—
32C2×#4341C2211yescharacteristic
33C2×#4341C2212yes—
34C2×#4341C2211yescharacteristic
35C2×#4341C2211yescharacteristic
36C2×#4341C2212yes—
37C2×#4341C2211yescharacteristic
38C2×#4341C2211yescharacteristic, complemented
39C2×#4341C2212yescomplemented
40C2×#4341C2212yescomplemented
41C2×#4339C2212yescomplemented
42C2×#4339C2211yescharacteristic, complemented
43C22×C4×D11C2211yescharacteristic
44C22×Dic22C2211yescharacteristic
45C22×Dic22C2212yescomplemented
46C22×Dic22C2211yescharacteristic, complemented
47C11×#124C2211yescharacteristic, complemented
48C11×#123C2212yescomplemented
49C11×C22⋊Q8C2211yescharacteristic
50C11×#121C2212yescomplemented
51C11×#121C2211yescharacteristic, complemented
52C11×#120C2212yes—
53C4×D4×C11C2211yescharacteristic
54C4×D4×C11C2211yescharacteristic, complemented
55C2×C11×C22⋊C4C2212yes—
56#67006C2212yes—
57C2×C22⋊Dic11C2212yes—
58#66999C2211yescharacteristic, complemented
59#66997C2211yescharacteristic, complemented
60#66992C2211yescharacteristic
61#66992C2212yescomplemented
62#66992C2212yescomplemented
63#66992C2212yescomplemented
64#66992C2212yescomplemented
65#66991C2211yescharacteristic, complemented
66#66991C2212yescomplemented
67#66990C2211yescharacteristic
68#66989C2211yescharacteristic, complemented
69#66988C2212yescomplemented
70#66988C2212yescomplemented
71D4×Dic11C2212yes—
72D4×Dic11C2211yescharacteristic, complemented
73D4×Dic11C2212yescomplemented
74#66983C2212yescomplemented
75#66982C2212yescomplemented
76C4×C22⋊D11C2211yescharacteristic
77C4×C22⋊D11C2212yescomplemented
78C4×C22⋊D11C2211yescharacteristic, complemented
79C2×C4⋊Dic11C2212yescomplemented
80#66977C2211yescharacteristic
81#66977C2211yescharacteristic, complemented
82C2×Dic11⋊C4C2212yescomplemented
83C2×Dic11⋊C4C2212yescomplemented
84#66950C2211yescharacteristic, complemented
85#66950C2211yescharacteristic, complemented
86#66949C2211yescharacteristic, complemented
87#66949C2212yescomplemented
88#66949C2212yescomplemented
89#66947C2211yescharacteristic, complemented
90C4⋊C4×D11C2211yescharacteristic, complemented
91C4⋊C4×D11C2212yescomplemented
92#66941C2212yescomplemented
93#66941C2212yescomplemented
94#66940C2211yescharacteristic, complemented
95#66939C2212yescomplemented
96#66939C2212yescomplemented
97#66938C2212yescomplemented
98#66938C2212yescomplemented
99#66937C2212yescomplemented
100#66937C2212yescomplemented
101#66937C2211yescharacteristic, complemented
102#66936C2212yescomplemented
103#66936C2211yescharacteristic, complemented
104#66936C2212yescomplemented
105#66935C2211yescharacteristic
106(C22⋊D11)⋊C4C2212yes—
107(C22⋊D11)⋊C4C2212yescomplemented
108(C22⋊D11)⋊C4C2212yescomplemented
109C22⋊C4×D11C2212yes—
110#66931C2211yescharacteristic
111#66931C2212yes—
112#66931C2212yes—
113#66931C2212yes—
114#66931C2212yescomplemented
115#66931C2212yescomplemented
116#66931C2212yescomplemented
117#66931C2212yescomplemented
118#66931C2212yescomplemented
119#66931C2212yescomplemented
120#66930C2212yescomplemented
121C4×D44C2211yescharacteristic, complemented
122#66925C2211yescharacteristic, complemented
123#66922C2211yescharacteristic, complemented
124C4×Dic22C2211yescharacteristic, complemented
125C24×C11C2312yes—
126C23×D11C2311yescharacteristic
127C11×#41—24no—
128C2×Q8×C11C2311yescharacteristic
129C2×D4×C11—24no—
130C2×D4×C11C2311yescharacteristic
131C2×D4×C11C2312yes—
132C2×D4×C11C2312yes—
133C2×D4×C11C2311yescharacteristic
134C2×D4×C11C2312yes—
135C2×D4×C11C2311yescharacteristic
136C22×C4×C11C2312yes—
137C22×C4×C11C2311yescharacteristic
138C22×C4×C11C2311yescharacteristic
139C22×C4×C11C2312yes—
140C2×C22⋊D11—28no—
141C2×C22⋊D11C2311yescharacteristic
142C2×C22⋊D11C2312yes—
143C2×C22⋊D11C2311yescharacteristic
144C2×C22⋊D11C2312yes—
145C2×C22⋊D11C2311yescharacteristic
146C2×C22⋊D11C2312yes—
147C2×C22⋊D11C2312yes—
148C2×C22⋊D11C2312yes—
149C2×C22⋊D11C2311yescharacteristic
150C2×C22⋊D11C2312yes—
151C22×Dic11—28no—
152C22×Dic11C2311yescharacteristic
153C22×Dic11C2312yes—
154C22×Dic11C2312yes—
155C22×Dic11C2312yes—
156C22×Dic11C2312yes—
157C22×Dic11C2312yes—
158C22×Dic11C2312yes—
159C22×Dic11C2312yes—
160C22×Dic11C2312yes—
161Q8×D11—24no—
162Q8×D11—24no—
163#4341—28no—
164#4341—28no—
165#4341—28no—
166#4341—28no—
167#4341—24no—
168#4341—24no—
169#4341—24no—
170#4341—24no—
171#4341D418yescomplemented
172#4339—28no—
173#4339—24no—
174C2×D44C2311yescharacteristic
175C2×D44C2311yescharacteristic
176C2×C4×D11—24no—
177C2×C4×D11C2311yescharacteristic
178C2×C4×D11C2311yescharacteristic
179C2×C4×D11C2312yes—
180C2×C4×D11C2312yes—
181C2×C4×D11C2311yescharacteristic
182C2×C4×D11C2311yescharacteristic
183C2×C4×D11C2312yes—
184C2×C4×D11C2311yescharacteristic
185C2×Dic22—28no—
186C2×Dic22—24no—
187C2×Dic22—24no—
188C2×Dic22C2311yescharacteristic
189C2×Dic22C2311yescharacteristic
190C2×Dic22C2311yescharacteristic
191C2×Dic22C2312yes—
192C2×Dic22C2312yes—
193C2×Dic22C2312yes—
194C2×Dic22C2312yes—
195C2×Dic22C2311yescharacteristic
196C11×C4⋊C4C2311yescharacteristic
197C11×C4⋊C4C2311yescharacteristic
198C11×C4⋊C4C2312yes—
199C11×C22⋊C4C2312yes—
200C11×C22⋊C4C2311yescharacteristic
201C11×C22⋊C4C2312yes—
202C11×C22⋊C4C2312yes—
203C11×C22⋊C4C2311yescharacteristic
204C11×C22⋊C4C2312yes—
205C11×C22⋊C4C2312yes—
206C42×C11C2311yescharacteristic
207C22⋊Dic11C2312yes—
208C22⋊Dic11C2311yescharacteristic
209C22⋊Dic11C2312yes—
210C22⋊Dic11C2312yes—
211C22⋊Dic11C2312yes—
212C22⋊Dic11C2312yes—
213C22⋊Dic11C2312yes—
214C22⋊Dic11C2311yescharacteristic
215(C2×D11)⋊C4C2311yescharacteristic
216(C2×D11)⋊C4C2311yescharacteristic
217(C2×D11)⋊C4C2311yescharacteristic
218(C2×D11)⋊C4C2311yescharacteristic
219(C2×D11)⋊C4C2312yes—
220(C2×D11)⋊C4C2312yes—
221(C2×D11)⋊C4C2312yes—
222(C2×D11)⋊C4C2311yescharacteristic
223(C2×D11)⋊C4C2311yescharacteristic
224C4⋊Dic11C2311yescharacteristic
225C4⋊Dic11C2312yes—
226C4⋊Dic11C2312yes—
227C4⋊Dic11C2311yescharacteristic
228C4⋊Dic11C2312yes—
229C4⋊Dic11C2312yes—
230Dic11⋊C4C2312yes—
231Dic11⋊C4C2311yescharacteristic
232Dic11⋊C4C2311yescharacteristic
233Dic11⋊C4C2312yes—
234Dic11⋊C4C2311yescharacteristic
235Dic11⋊C4C2312yes—
236Dic11⋊C4C2312yes—
237Dic11⋊C4C2312yes—
238Dic11⋊C4C2312yes—
239Dic11⋊C4C2312yes—
240Dic11⋊C4C2312yes—
241Dic11⋊C4C2311yescharacteristic
242C4×Dic11C2312yes—
243C4×Dic11C2311yescharacteristic
244C4×Dic11C2312yes—
245#3489—111nomaximal, Sylow
246C23×C11—24no—
247C23×C11—24no—
248C23×C11—42no—
249C23×C11C2412yes—
250C23×C11C2411yescharacteristic
251C23×C11C2412yes—
252C23×C11C2411yescharacteristic
253C22×D11—22no—
254C22×D11—22no—
255C22×D11—41no—
256C22×D11C2411yescharacteristic
257C22×D11C2411yescharacteristic
258C22×D11C2411yescharacteristic
259Q8×C11—22no—
260D4×C11—24no—
261D4×C11—24no—
262D4×C11—22no—
263D4×C11—22no—
264D4×C11—42no—
265D4×C11C2×D414yes—
266C2×C4×C11—24no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—42no—
270C2×C4×C11C2411yescharacteristic
271C2×C4×C11C2412yes—
272C2×C4×C11C2411yescharacteristic
273C2×C4×C11C2411yescharacteristic
274C2×C4×C11C2412yes—
275C2×C4×C11C2411yescharacteristic
276C2×C4×C11C2411yescharacteristic
277C22⋊D11—24no—
278C22⋊D11—24no—
279C22⋊D11—22no—
280C22⋊D11—22no—
281C22⋊D11—24no—
282C22⋊D11—22no—
283C22⋊D11—24no—
284C22⋊D11—42no—
285C22⋊D11—41no—
286C22⋊D11C2×D418yes—
287C2×Dic11—24no—
288C2×Dic11—24no—
289C2×Dic11—24no—
290C2×Dic11—24no—
291C2×Dic11—22no—
292C2×Dic11—24no—
293C2×Dic11—24no—
294C2×Dic11—42no—
295C2×Dic11C2×D418yes—
296C2×Dic11C2411yescharacteristic
297C2×Dic11C2411yescharacteristic
298C2×Dic11C2412yes—
299C2×Dic11C2412yes—
300C2×Dic11C2411yescharacteristic
301C2×Dic11C2412yes—
302C2×Dic11C2411yescharacteristic
303C2×Dic11C2412yes—
304C2×Dic11C2411yescharacteristic
305D44—22no—
306D44—41no—
307C4×D11—22no—
308C4×D11—24no—
309C4×D11—22no—
310C4×D11—22no—
311C4×D11—22no—
312C4×D11—24no—
313C4×D11—42no—
314C4×D11C2×D414yes—
315Dic22—22no—
316Dic22—22no—
317Dic22—24no—
318Dic22—22no—
319Dic22—24no—
320Dic22—24no—
321Dic22—24no—
322Dic22C2×D414yes—
323C2×2−1+4—111no—
324C22×#41—111no—
325D4×Q8—111no—
326D4×Q8—111no—
327#548—111no—
328#548—111no—
329#547—111no—
330#547—112no—
331#547—112no—
332#547—111no—
333#546—111no—
334#546—112no—
335#546—112no—
336#546D1111yescharacteristic, complemented
337#537—112no—
338#537—111no—
339#536—111no—
340#536—112no—
341#525—112no—
342#525—111no—
343C2×C22⋊Q8—111no—
344C2×C22⋊Q8—112no—
345#520—111no—
346C22×C11—21no—
347C22×C11—22no—
348C22×C11—22no—
349C22×C11—21no—
350C22×C11—21no—
351C22×C11—22no—
352C22×C11—21no—
353C22×C11—22no—
354C22×C11—21no—
355C22×C11—22no—
356C22×C11—48no—
357C22×C11C22×D414yes—
358C22×C112−1+412yescomplemented
359C22×C11C2511yescharacteristic
360C2×D11—21no—
361C2×D11—21no—
362C2×D11—21no—
363C2×D11—21no—
364C2×D11—21no—
365C2×D11—21no—
366C2×D11—21no—
367C2×D11—21no—
368C2×D11—44no—
369C2×D11C22×D412yes—
370C4×C11—21no—
371C4×C11—21no—
372C4×C11—22no—
373C4×C11—21no—
374C4×C11—21no—
375C4×C11—22no—
376C4×C11C22×D412yes—
377Dic11—22no—
378Dic11—21no—
379Dic11—22no—
380Dic11—21no—
381Dic11—21no—
382Dic11—22no—
383Dic11—21no—
384Dic11C22×D414yes—
385Dic11C22×D412yes—
3862−1+4—228no—
387C2×#41—111no—
388C2×#41—112no—
389C2×#41—112no—
390C2×#41—111no—
391C2×#41—111no—
392C2×#41—112no—
393C2×#41—111no—
394C2×#41—112no—
395C2×#41—111no—
396C2×#41—111no—
397C2×#41—112no—
398C2×#41—228no—
399C2×#41C2×D1111yescharacteristic, complemented
400C22×Q8—111no—
401C22×Q8—111no—
402C22×Q8—112no—
403C22×Q8—111no—
404C22×Q8—111no—
405C22×D4—112no—
406C22×D4C2×D1111yescharacteristic
407C23×C4—112no—
408C23×C4—111no—
409C4⋊Q8—111no—
410C4⋊Q8—112no—
411C4⋊Q8—112no—
412C4⋊Q8—111no—
413#124—111no—
414#124—112no—
415#124—112no—
416#124C2×D1111yescharacteristic, complemented
417#123—112no—
418#123—112no—
419#123—112no—
420#123—111no—
421#123—111no—
422#123—112no—
423#123—112no—
424#123—112no—
425#123—112no—
426#123C2×D1112yescomplemented
427C22⋊Q8—111no—
428C22⋊Q8—111no—
429C22⋊Q8—111no—
430C22⋊Q8—112no—
431C22⋊Q8—111no—
432C22⋊Q8—111no—
433C22⋊Q8—112no—
434C22⋊Q8—111no—
435C22⋊Q8—112no—
436C22⋊Q8—111no—
437C22⋊Q8—112no—
438C22⋊Q8—112no—
439C22⋊Q8—112no—
440C22⋊Q8—112no—
441C22⋊Q8—112no—
442C22⋊Q8—112no—
443C22⋊Q8—112no—
444C22⋊Q8—112no—
445C22⋊Q8C2×D1111yescharacteristic
446#121—111no—
447#121—112no—
448#121—112no—
449#121—112no—
450#121—112no—
451#121—111no—
452#121—112no—
453#121—112no—
454#121—111no—
455#121—112no—
456#121—112no—
457#121C2×D1112yescomplemented
458#121C2×D1111yescharacteristic, complemented
459#120—112no—
460#120—111no—
461#120—111no—
462#120C2×D1112yes—
463C4×Q8—111no—
464C4×Q8—111no—
465C4×D4—111no—
466C4×D4—112no—
467C4×D4—112no—
468C4×D4—112no—
469C4×D4—111no—
470C4×D4—111no—
471C4×D4—112no—
472C4×D4—112no—
473C4×D4—112no—
474C4×D4—111no—
475C4×D4C2×D1111yescharacteristic
476C4×D4C2×D1111yescharacteristic, complemented
477#117—112no—
478#117—111no—
479C2×C4⋊C4—112no—
480C2×C4⋊C4—112no—
481C2×C4⋊C4—112no—
482C2×C4⋊C4—111no—
483C2×C4⋊C4—112no—
484C2×C22⋊C4—112no—
485C2×C22⋊C4—112no—
486C2×C22⋊C4C2×D1112yes—
487C2×C11—22no—
488C2×C11—24no—
489C2×C11—41no—
490C2×C11—42no—
491C2×C11C23×D411yescharacteristic
492C2×C11C2×2−1+411yescharacteristic
493C2×C11#58511yescharacteristic
494D11—22no—
495D11—41no—
496D11—41no—
497C24—111no—
498C24C22×D1112yes—
499#41—24no—
500#41—118no—
501#41—224no—
502#41—228no—
503#41—228no—
504#41—224no—
505#41—228no—
506#41—228no—
507#41—228no—
508#41—224no—
509#41—224no—
510#41—224no—
511C2×Q8—111no—
512C2×Q8—112no—
513C2×Q8—111no—
514C2×Q8—112no—
515C2×Q8—112no—
516C2×Q8—111no—
517C2×Q8—112no—
518C2×Q8—111no—
519C2×Q8—228no—
520C2×Q8—224no—
521C2×Q8—224no—
522C2×Q8—224no—
523C2×Q8—224no—
524C2×Q8C22×D1111yescharacteristic
525C2×D4—24no—
526C2×D4—112no—
527C2×D4—111no—
528C2×D4—111no—
529C2×D4—112no—
530C2×D4—111no—
531C2×D4—112no—
532C2×D4—112no—
533C2×D4—112no—
534C2×D4—111no—
535C2×D4—112no—
536C2×D4—111no—
537C2×D4—111no—
538C2×D4—228no—
539C2×D4C22×D1111yescharacteristic
540C2×D4C22×D1112yes—
541C2×D4C22×D1112yes—
542C2×D4C22×D1111yescharacteristic
543C2×D4C22×D1112yes—
544C2×D4C22×D1111yescharacteristic
545C22×C4—112no—
546C22×C4—111no—
547C22×C4—112no—
548C22×C4—112no—
549C22×C4—112no—
550C22×C4—112no—
551C22×C4—112no—
552C22×C4—111no—
553C22×C4—112no—
554C22×C4—112no—
555C22×C4—112no—
556C22×C4—111no—
557C22×C4—112no—
558C22×C4—111no—
559C22×C4—111no—
560C22×C4—111no—
561C22×C4—112no—
562C22×C4—224no—
563C22×C4—228no—
564C22×C4C22×D1112yes—
565C22×C4C22×D1111yescharacteristic
566C22×C4C22×D1111yescharacteristic
567C22×C4C22×D1112yes—
568C4⋊C4—112no—
569C4⋊C4—111no—
570C4⋊C4—112no—
571C4⋊C4—111no—
572C4⋊C4—112no—
573C4⋊C4—111no—
574C4⋊C4—112no—
575C4⋊C4—112no—
576C4⋊C4—111no—
577C4⋊C4—112no—
578C4⋊C4—112no—
579C4⋊C4—112no—
580C4⋊C4—112no—
581C4⋊C4—112no—
582C4⋊C4—111no—
583C4⋊C4—111no—
584C4⋊C4—112no—
585C4⋊C4—112no—
586C4⋊C4C22×D1111yescharacteristic
587C4⋊C4C22×D1112yes—
588C4⋊C4C22×D1111yescharacteristic
589C22⋊C4—111no—
590C22⋊C4—112no—
591C22⋊C4—112no—
592C22⋊C4—112no—
593C22⋊C4—112no—
594C22⋊C4—111no—
595C22⋊C4—112no—
596C22⋊C4—112no—
597C22⋊C4—112no—
598C22⋊C4—112no—
599C22⋊C4—111no—
600C22⋊C4—111no—
601C22⋊C4—111no—
602C22⋊C4—111no—
603C22⋊C4—111no—
604C22⋊C4—111no—
605C22⋊C4—112no—
606C22⋊C4C22×D1112yes—
607C22⋊C4C22×D1111yescharacteristic
608C22⋊C4C22×D1112yes—
609C22⋊C4C22×D1112yes—
610C22⋊C4C22×D1112yes—
611C22⋊C4C22×D1112yes—
612C22⋊C4C22×D1111yescharacteristic
613C42—112no—
614C42—112no—
615C42—111no—
616C42C22×D1111yescharacteristic
617C11#348911yescharacteristic, complemented, Sylow
618C23—24no—
619C23—24no—
620C23—42no—
621C23—111no—
622C23—111no—
623C23—111no—
624C23—222no—
625C23—222no—
626C23—441no—
627C23C23×D1112yes—
628C23C23×D1111yescharacteristic
629C23C23×D1112yes—
630C23C23×D1111yescharacteristic
631Q8—22no—
632Q8—114no—
633Q8—222no—
634Q8—224no—
635Q8—224no—
636Q8—224no—
637Q8—224no—
638Q8—222no—
639Q8—222no—
640D4—24no—
641D4—24no—
642D4—22no—
643D4—22no—
644D4—42no—
645D4—118no—
646D4—222no—
647D4—224no—
648D4—222no—
649D4—224no—
650D4—222no—
651D4—224no—
652D4—224no—
653D4—222no—
654D4—441no—
655D4—441no—
656D4—442no—
657D4D4×D1114yes—
658C2×C4—24no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—42no—
662C2×C4—118no—
663C2×C4—112no—
664C2×C4—111no—
665C2×C4—114no—
666C2×C4—111no—
667C2×C4—111no—
668C2×C4—112no—
669C2×C4—111no—
670C2×C4—112no—
671C2×C4—111no—
672C2×C4—112no—
673C2×C4—222no—
674C2×C4—224no—
675C2×C4—222no—
676C2×C4—224no—
677C2×C4—222no—
678C2×C4—224no—
679C2×C4—224no—
680C2×C4—224no—
681C2×C4—224no—
682C2×C4—224no—
683C2×C4—224no—
684C2×C4—222no—
685C2×C4—222no—
686C2×C4—442no—
687C2×C4—442no—
688C2×C4C23×D1111yescharacteristic
689C2×C4C23×D1112yes—
690C2×C4C23×D1111yescharacteristic
691C2×C4C23×D1112yes—
692C2×C4C23×D1111yescharacteristic
693C2×C4C23×D1111yescharacteristic
694C2×C4C23×D1111yescharacteristic
695C22—21no—
696C22—22no—
697C22—22no—
698C22—21no—
699C22—21no—
700C22—22no—
701C22—21no—
702C22—22no—
703C22—21no—
704C22—22no—
705C22—48no—
706C22—112no—
707C22—221no—
708C22—221no—
709C22—221no—
710C22—221no—
711C22—221no—
712C22—221no—
713C22—221no—
714C22—221no—
715C22—444no—
716C22C2×D4×D1114yes—
717C22#6704312yescomplemented
718C22C24×D1111yescharacteristic
719C4—21no—
720C4—21no—
721C4—22no—
722C4—21no—
723C4—21no—
724C4—22no—
725C4—112no—
726C4—114no—
727C4—221no—
728C4—222no—
729C4—222no—
730C4—221no—
731C4—221no—
732C4—222no—
733C4—221no—
734C4C2×D4×D1112yes—
735C2—22no—
736C2—24no—
737C2—42no—
738C2—41no—
739C2—222no—
740C2—441no—
741C2—441no—
742C2C22×D4×D1111yescharacteristic
743C2C2×#6704311yescharacteristic
744C2#1062345511yescharacteristic
subgroupG/H
center, FrattiniC22C24×D11
commutator, socle, cosocleC22×C11C25
FittingC11×#546C2
hypercenter#546D11
hypocenterC11#3489
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C2×#67043C2semidirect
2. C22×#4341C2semidirect
3. C11×#546C2semidirect
4. #10623355C2semidirect
5. #10623337C2semidirect
6. #10623208C2semidirect
7. #10623206C2semidirect
8. #10623186C2semidirect
9. #10623179C2semidirect
10. #10623163C2semidirect
11. D11×C22⋊Q8C2semidirect
12. #10623142C2semidirect
13. #10623139C2semidirect
14. #10623129C2semidirect
15. #10623128C2semidirect
16. #10623122C2semidirect
17. #10623117C2semidirect
18. #10623086C2semidirect
19. #10623078C2semidirect
20. #10623077C2semidirect
21. D4×Dic22C2semidirect
22. #10623021C2semidirect
23. C2×#66931C2semidirect
24. C2×C11×#41C22semidirect
29. C2×Q8×D11C22semidirect
30. C2×Q8×D11C22semidirect
38. C2×#4341C22semidirect
39. C2×#4341C22semidirect
40. C2×#4341C22semidirect
41. C2×#4339C22semidirect
42. C2×#4339C22semidirect
45. C22×Dic22C22semidirect
46. C22×Dic22C22semidirect
47. C11×#124C22semidirect
48. C11×#123C22semidirect
50. C11×#121C22semidirect
51. C11×#121C22semidirect
54. C4×D4×C11C22semidirect
58. #66999C22semidirect
59. #66997C22semidirect
61. #66992C22semidirect
62. #66992C22semidirect
63. #66992C22semidirect
64. #66992C22semidirect
65. #66991C22semidirect
66. #66991C22semidirect
68. #66989C22semidirect
69. #66988C22semidirect
70. #66988C22semidirect
72. D4×Dic11C22semidirect
73. D4×Dic11C22semidirect
74. #66983C22semidirect
75. #66982C22semidirect
77. C4×C22⋊D11C22semidirect
78. C4×C22⋊D11C22semidirect
79. C2×C4⋊Dic11C22semidirect
81. #66977C22semidirect
82. C2×Dic11⋊C4C22semidirect
83. C2×Dic11⋊C4C22semidirect
84. #66950C22semidirect
85. #66950C22semidirect
86. #66949C22semidirect
87. #66949C22semidirect
88. #66949C22semidirect
89. #66947C22semidirect
90. C4⋊C4×D11C22semidirect
91. C4⋊C4×D11C22semidirect
92. #66941C22semidirect
93. #66941C22semidirect
94. #66940C22semidirect
95. #66939C22semidirect
96. #66939C22semidirect
97. #66938C22semidirect
98. #66938C22semidirect
99. #66937C22semidirect
100. #66937C22semidirect
101. #66937C22semidirect
102. #66936C22semidirect
103. #66936C22semidirect
104. #66936C22semidirect
107. (C22⋊D11)⋊C4C22semidirect
108. (C22⋊D11)⋊C4C22semidirect
114. #66931C22semidirect
115. #66931C22semidirect
116. #66931C22semidirect
117. #66931C22semidirect
118. #66931C22semidirect
119. #66931C22semidirect
120. #66930C22semidirect
121. C4×D44C22semidirect
122. #66925C22semidirect
123. #66922C22semidirect
124. C4×Dic22C22semidirect
171. #4341D4semidirect
336. #546D11semidirect
358. C22×C112−1+4semidirect
399. C2×#41C2×D11semidirect
416. #124C2×D11semidirect
426. #123C2×D11semidirect
457. #121C2×D11semidirect
458. #121C2×D11semidirect
476. C4×D4C2×D11semidirect
617. C11#3489semidirect
717. C22#67043semidirect

Maximal subgroups

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

subgroupindex
C2×#670432
C22×#43412
C11×#5462
#106233552
#106233372
#106232082
#106232062
#106231862
#106231792
#106231632
D11×C22⋊Q82
#106231422
#106231392
#106231292
#106231282
#106231222
#106231172
#106230862
#106230782
#106230772
D4×Dic222
#106230212
C2×#669312
#348911