Finite Group Databasebeta

← #15625266

Subgroups — #15625266

Order 2816.

2164 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623001C211yesmaximal, characteristic, complemented
2#13079627C214yesmaximal, complemented
3#13079619C214yesmaximal, complemented
4#13079572C214yesmaximal, complemented
5#13079564C212yesmaximal, complemented
6#13079557C212yesmaximal, complemented
7#13079076C212yesmaximal, complemented
8#13079009C212yesmaximal, complemented
9#13078084C214yesmaximal, complemented
10#13077876C214yesmaximal, complemented
11#13077249C211yesmaximal, characteristic, complemented
12C2×C11×#532C211yesmaximal, characteristic
13C22×C11×#41C2212yes—
14C11×#532—21no—
15C11×#532—21no—
16C11×#532—21no—
17C11×#532—21no—
18C11×#532C2212yes—
19C11×#532C2212yes—
20C11×#532C2212yes—
21C11×#532C2212yes—
22C2×C11×C4⋊Q8C2211yescharacteristic
23C2×C11×#127C2211yescharacteristic
24C2×C11×#124C2212yes—
25C2×C11×#121—21no—
26C2×C11×#121—21no—
27C2×C4×D4×C11—21no—
28C2×C4×D4×C11—21no—
29C22×C42×C11C2211yescharacteristic
30C2×#67004C2218yescomplemented
31C2×#66979—21no—
32C2×#66977—21no—
33C2×#66977C2212yes—
34#10623001—21no—
35#10623001—21no—
36#10623001—21no—
37#10623001—21no—
38#10623001C2212yes—
39#10623001C2212yes—
40#10623001C2212yescomplemented
41#10623001C2212yescomplemented
42C2×#66923—21no—
43C2×#66922C2211yescharacteristic, complemented
44C2×#66922C2211yescharacteristic, complemented
45C2×C4×Dic22—21no—
46C2×C4×Dic22C2212yescomplemented
47#10622852C22116yescomplemented
48#10622845C2218yescomplemented
49#10622841C2218yes—
50#10622831C2218yes—
51#10622820C2212yes—
52#10622705C2214yescomplemented
53#10622703C2218yescomplemented
54#10622694C2214yescomplemented
55#10622689C2214yescomplemented
56#10622688C2218yescomplemented
57#10622683C2214yescomplemented
58#10622673C2218yescomplemented
59#10622668C2218yescomplemented
60#10622667C22116yescomplemented
61#10622539C2212yes—
62#10622539C2212yescomplemented
63#10622538C2212yes—
64#10622538C2212yescomplemented
65#10622537C2212yescomplemented
66C4×#4318C2212yescomplemented
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—48no—
70C2×C11×#41C2314yes—
71C2×C11×#41C2314yes—
72C22×Q8×C11C2312yes—
73C22×D4×C11—22no—
74C22×D4×C11—21no—
75C22×D4×C11—21no—
76C22×D4×C11C2312yes—
77C23×C4×C11—22no—
78C23×C4×C11D411yescharacteristic
79C23×C4×C11D411yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C22×Dic22—21no—
82C22×Dic22C2312yes—
83C11×C4⋊Q8—21no—
84C11×C4⋊Q8—21no—
85C11×C4⋊Q8C2312yes—
86C11×C4⋊Q8C2312yes—
87C11×#127—21no—
88C11×#127—21no—
89C11×#127C2312yes—
90C11×#127C2312yes—
91C11×#124—22no—
92C11×#124—22no—
93C11×#124C2314yes—
94C11×#124C2314yes—
95C11×#121—22no—
96C11×#121—22no—
97C11×#121—22no—
98C11×#121—22no—
99C11×#121—22no—
100C11×#121—22no—
101C11×#121—22no—
102C11×#121—22no—
103C4×D4×C11—22no—
104C4×D4×C11—22no—
105C4×D4×C11—22no—
106C4×D4×C11—22no—
107C4×D4×C11—22no—
108C4×D4×C11—22no—
109C4×D4×C11—22no—
110C4×D4×C11—22no—
111C2×C11×C4⋊C4—21no—
112C2×C11×C4⋊C4—21no—
113C2×C11×C22⋊C4—22no—
114C2×C11×C22⋊C4—22no—
115C2×C42×C11D411yescharacteristic
116C2×C42×C11D411yescharacteristic
117C2×C42×C11D411yescharacteristic
118C2×C42×C11D411yescharacteristic
119C2×C42×C11D411yescharacteristic
120C2×C42×C11D411yescharacteristic
121C2×C42×C11C2311yescharacteristic
122C2×C42×C11C2311yescharacteristic
123C2×C42×C11C2311yescharacteristic
124C2×C42×C11C2311yescharacteristic
125C2×C42×C11C2311yescharacteristic
126C2×C42×C11C2311yescharacteristic
127C2×C22⋊Dic11—22no—
128#67004—416no—
129C2×#4326C23116yes—
130C2×#4324C23116yes—
131#66979—22no—
132#66979—22no—
133#66979—22no—
134#66979—22no—
135C2×C4⋊Dic11—21no—
136C2×C4⋊Dic11—21no—
137C2×C4⋊Dic11—21no—
138C2×C4⋊Dic11C2312yes—
139#66977—22no—
140#66977—22no—
141#66977—22no—
142#66977—22no—
143#66977—22no—
144#66977—22no—
145#66977C2314yes—
146#66977C2314yes—
147C2×Dic11⋊C4—22no—
148C2×Dic11⋊C4—22no—
149C2×C4×Dic11—22no—
150C2×#4318C2314yes—
151#66923—22no—
152#66923—22no—
153#66923—22no—
154#66923—22no—
155#66922—21no—
156#66922—21no—
157#66922—21no—
158#66922—21no—
159#66922C2312yes—
160#66922C2312yes—
161#66922C2312yes—
162#66922C2312yes—
163C4×Dic22—22no—
164C4×Dic22—22no—
165C4×Dic22—22no—
166C4×Dic22—22no—
167C4×Dic22—22no—
168C4×Dic22—22no—
169C4×Dic22C2314yes—
170C4×Dic22C2314yes—
171#66899C23116yes—
172#66896C23116yes—
173C22⋊(C11⋊C8)C2314yes—
174C22⋊(C11⋊C8)C2314yes—
175C4⋊(C11⋊C8)C2314yes—
176C4⋊(C11⋊C8)C2314yes—
177#66867C2314yes—
178C4×C11⋊C8C2314yes—
179#60804—111nomaximal, Sylow
180C24×C11—22no—
181C24×C11C2×D411yescharacteristic
182C11×#41—216no—
183C11×#41—48no—
184C11×#41—48no—
185C11×#41—48no—
186C2×Q8×C11—22no—
187C2×Q8×C11—44no—
188C2×Q8×C11C2414yes—
189C2×D4×C11—24no—
190C2×D4×C11—24no—
191C2×D4×C11—22no—
192C2×D4×C11—22no—
193C2×D4×C11—22no—
194C2×D4×C11—22no—
195C2×D4×C11—22no—
196C2×D4×C11—44no—
197C2×D4×C11—44no—
198C2×D4×C11—48no—
199C2×D4×C11—44no—
200C2×D4×C11C2414yes—
201C22×C4×C11—24no—
202C22×C4×C11—24no—
203C22×C4×C11—22no—
204C22×C4×C11—24no—
205C22×C4×C11—24no—
206C22×C4×C11—42no—
207C22×C4×C11—48no—
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2×D411yescharacteristic
214C22×C4×C11C2×D411yescharacteristic
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D411yescharacteristic
220C22×C4×C11C2×D411yescharacteristic
221C22×C4×C11C2×D411yescharacteristic
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2411yescharacteristic
224C22×C4×C11C2411yescharacteristic
225C22×C4×C11C2411yescharacteristic
226C22×Dic11—22no—
227C22×Dic11—22no—
228C2×Dic22—22no—
229C2×Dic22—22no—
230C2×Dic22—22no—
231C2×Dic22—28no—
232C2×Dic22—44no—
233C2×Dic22C2414yes—
234C11×C4⋊C4—22no—
235C11×C4⋊C4—22no—
236C11×C4⋊C4—22no—
237C11×C4⋊C4—22no—
238C11×C22⋊C4—24no—
239C11×C22⋊C4—24no—
240C11×C22⋊C4—24no—
241C11×C22⋊C4—24no—
242C42×C11C2×D411yescharacteristic
243C42×C11C2×D411yescharacteristic
244C42×C11C2×D411yescharacteristic
245C42×C11C2×D411yescharacteristic
246C42×C11C2×D411yescharacteristic
247C42×C11C2×D411yescharacteristic
248C42×C11C2×D411yescharacteristic
249C42×C11C2×D411yescharacteristic
250C42×C11C2×D411yescharacteristic
251C42×C11C2×D411yescharacteristic
252C42×C11C2×D411yescharacteristic
253C42×C11C2×D411yescharacteristic
254C42×C11C2411yescharacteristic
255C42×C11C2411yescharacteristic
256C42×C11C2411yescharacteristic
257C42×C11C2411yescharacteristic
258C22⋊Dic11—24no—
259C22⋊Dic11—24no—
260#4326—416no—
261#4324—416no—
262C4⋊Dic11—22no—
263C4⋊Dic11—22no—
264C4⋊Dic11—22no—
265C4⋊Dic11—22no—
266C4⋊Dic11—22no—
267C4⋊Dic11—22no—
268C4⋊Dic11—22no—
269C4⋊Dic11C2414yes—
270Dic11⋊C4—24no—
271Dic11⋊C4—24no—
272Dic11⋊C4—24no—
273Dic11⋊C4—24no—
274C4×Dic11—24no—
275C4×Dic11—24no—
276#4318—28no—
277C2×C11⋊C8C2418yes—
278C2×#533—111no—
279C2×#532D1111yescharacteristic
280#3216—114no—
281#3215—114no—
282#3210—114no—
283#3209—112no—
284#3208—112no—
285#3152—112no—
286#3141—112no—
287#3037—114no—
288#3007—114no—
289#2920—111no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—24no—
293C23×C11—41no—
294C23×C11—44no—
295C23×C11—44no—
296C23×C11—44no—
297C23×C11C22×D411yescharacteristic
298C23×C11C22×D411yescharacteristic
299C23×C11C22×D411yescharacteristic
300Q8×C11—28no—
301Q8×C11—44no—
302D4×C11—28no—
303D4×C11—44no—
304D4×C11—44no—
305D4×C11—48no—
306D4×C11—48no—
307D4×C11—44no—
308D4×C11—44no—
309D4×C11—44no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—24no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—48no—
328C2×C4×C11—44no—
329C2×C4×C11—48no—
330C2×C4×C11#13714yescomplemented
331C2×C4×C11C22×D411yescharacteristic
332C2×C4×C11C22×D411yescharacteristic
333C2×C4×C11C22×D411yescharacteristic
334C2×C4×C11C22×D411yescharacteristic
335C2×C4×C11C22×D411yescharacteristic
336C2×C4×C11C22×D411yescharacteristic
337C2×C4×C11C22×D411yescharacteristic
338C2×C4×C11C22×D411yescharacteristic
339C2×C4×C11C22×D411yescharacteristic
340C2×C4×C11C22×D411yescharacteristic
341C2×C4×C11C22×D411yescharacteristic
342C2×C4×C11H(5,𝔽2)14yes—
343C2×C4×C11C2511yescharacteristic
344C2×Dic11—24no—
345C2×Dic11—24no—
346C2×Dic11—44no—
347C2×Dic11—44no—
348Dic22—28no—
349Dic22—44no—
350Dic22—44no—
351Dic22—44no—
352C11⋊C8—28no—
353C22×#41C2×D1112yes—
354C2×#137—118no—
355#533—112no—
356#533—112no—
357#533—112no—
358#533—112no—
359#533—221no—
360#533—221no—
361#533—221no—
362#533—221no—
363#532—21no—
364#532—21no—
365#532—21no—
366#532—21no—
367#532C2×D1112yes—
368#532C2×D1112yes—
369#532C2×D1112yes—
370#532C2×D1112yes—
371C2×C4⋊Q8—111no—
372C2×C4⋊Q8—111no—
373C2×C4⋊Q8C2×D1111yescharacteristic
374C2×#127C2×D1111yescharacteristic
375C2×#125—221no—
376C2×#124C2×D1112yes—
377C2×C22⋊Q8—112no—
378C2×C22⋊Q8—221no—
379C2×#121—21no—
380C2×#121—21no—
381C2×C4×Q8—112no—
382C2×C4×Q8—221no—
383C2×C4×D4—21no—
384C2×C4×D4—21no—
385C2×#117—221no—
386C22×C42C2×D1111yescharacteristic
387#497—118no—
388#494—114no—
389#492—114no—
390#489—118no—
391#487—114no—
392#486—114no—
393#464—1116no—
394#462—118no—
395#460—118no—
396#452—1116no—
397#451—118no—
398#450—118no—
399#432—112no—
400#432—112no—
401#431—112no—
402#431—112no—
403#423—112no—
404#417—118no—
405#407—112no—
406C4×M16—112no—
407C22×C11—21no—
408C22×C11—21no—
409C22×C11—21no—
410C22×C11—21no—
411C22×C11—21no—
412C22×C11—21no—
413C22×C11—21no—
414C22×C11—44no—
415C22×C11—44no—
416C22×C11—44no—
417C22×C11—44no—
418C22×C11—88no—
419C22×C11#53512yes—
420C22×C11C2×#13712yes—
421C22×C11C23×D411yescharacteristic
422C4×C11—21no—
423C4×C11—21no—
424C4×C11—21no—
425C4×C11—21no—
426C4×C11—21no—
427C4×C11—21no—
428C4×C11—21no—
429C4×C11—44no—
430C4×C11#53512yes—
431C4×C11C2×#13712yes—
432C4×C11C2×#13712yes—
433C4×C11#57512yes—
434C4×C11C2×H(5,𝔽2)12yes—
435Dic11—44no—
436Dic11—44no—
437C2×#41—22no—
438C2×#41—22no—
439C2×#41—48no—
440C2×#41C22×D1114yes—
441C2×#41C22×D1114yes—
442C22×Q8—112no—
443C22×Q8—221no—
444C22×Q8C22×D1112yes—
445C22×D4—22no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4C22×D1112yes—
449C23×C4—22no—
450C23×C4C22⋊D1111yescharacteristic
451C23×C4C22⋊D1111yescharacteristic
452C23×C4C22×D1111yescharacteristic
453#137—4416no—
454C2×Q16—1116no—
455C2×SD16—1116no—
456C2×M16—114no—
457C4⋊Q8—21no—
458C4⋊Q8—21no—
459C4⋊Q8—112no—
460C4⋊Q8—112no—
461C4⋊Q8—112no—
462C4⋊Q8—112no—
463C4⋊Q8—221no—
464C4⋊Q8—221no—
465C4⋊Q8—221no—
466C4⋊Q8—221no—
467C4⋊Q8C22×D1112yes—
468C4⋊Q8C22×D1112yes—
469#127—21no—
470#127—21no—
471#127C22×D1112yes—
472#127C22×D1112yes—
473#125—222no—
474#125—222no—
475#125—222no—
476#125—222no—
477#124—22no—
478#124—22no—
479#124C22×D1114yes—
480#124C22×D1114yes—
481C22⋊Q8—114no—
482C22⋊Q8—114no—
483C22⋊Q8—222no—
484C22⋊Q8—222no—
485C22⋊Q8—222no—
486C22⋊Q8—222no—
487C22⋊Q8—222no—
488C22⋊Q8—222no—
489#121—22no—
490#121—22no—
491#121—22no—
492#121—22no—
493#121—22no—
494#121—22no—
495#121—22no—
496#121—22no—
497C4×Q8—114no—
498C4×Q8—114no—
499C4×Q8—222no—
500C4×Q8—222no—
501C4×Q8—222no—
502C4×Q8—222no—
503C4×Q8—222no—
504C4×Q8—222no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513#117—222no—
514#117—222no—
515#117—222no—
516#117—222no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—112no—
520C2×C4⋊C4—221no—
521C2×C4⋊C4—221no—
522C2×C4⋊C4—222no—
523C2×C4⋊C4—222no—
524C2×C4⋊C4—221no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—222no—
528C2×C42—222no—
529C2×C42C22⋊D1111yescharacteristic
530C2×C42C22⋊D1111yescharacteristic
531C2×C42C22⋊D1111yescharacteristic
532C2×C42C22⋊D1111yescharacteristic
533C2×C42C22⋊D1111yescharacteristic
534C2×C42C22⋊D1111yescharacteristic
535C2×C42C22×D1111yescharacteristic
536C2×C42C22×D1111yescharacteristic
537C2×C42C22×D1111yescharacteristic
538C2×C42C22×D1111yescharacteristic
539C2×C42C22×D1111yescharacteristic
540C2×C42C22×D1111yescharacteristic
541C4⋊C8—114no—
542C4⋊C8—114no—
543#103—1116no—
544#102—1116no—
545C22⋊C8—114no—
546C22⋊C8—114no—
547#97—114no—
548C4×C8—114no—
549C2×C11—22no—
550C2×C11—22no—
551C2×C11—41no—
552C2×C11—84no—
553C2×C11C2×#53511yescharacteristic
554C2×C11C22×#13711yescharacteristic
555C2×C11C2×#57511yescharacteristic
556C24—22no—
557C24C2×C22⋊D1111yescharacteristic
558#41—216no—
559#41—48no—
560#41—48no—
561#41—48no—
562C2×Q8—22no—
563C2×Q8—44no—
564C2×Q8—114no—
565C2×Q8—222no—
566C2×Q8—222no—
567C2×Q8—222no—
568C2×Q8—228no—
569C2×Q8—444no—
570C2×Q8C23×D1114yes—
571C2×D4—24no—
572C2×D4—24no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—44no—
579C2×D4—44no—
580C2×D4—48no—
581C2×D4—44no—
582C2×D4C23×D1114yes—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—22no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—42no—
589C22×C4—48no—
590C22×C4—222no—
591C22×C4—222no—
592C22×C4C2×C22⋊D1111yescharacteristic
593C22×C4C2×C22⋊D1111yescharacteristic
594C22×C4C2×C22⋊D1111yescharacteristic
595C22×C4C2×C22⋊D1111yescharacteristic
596C22×C4C2×C22⋊D1111yescharacteristic
597C22×C4C2×C22⋊D1111yescharacteristic
598C22×C4C2×C22⋊D1111yescharacteristic
599C22×C4C2×C22⋊D1111yescharacteristic
600C22×C4C2×C22⋊D1111yescharacteristic
601C22×C4C2×C22⋊D1111yescharacteristic
602C22×C4C2×C22⋊D1111yescharacteristic
603C22×C4C2×C22⋊D1111yescharacteristic
604C22×C4C2×C22⋊D1111yescharacteristic
605C22×C4C2×C22⋊D1111yescharacteristic
606C22×C4C2×C22⋊D1111yescharacteristic
607C22×C4C23×D1111yescharacteristic
608C22×C4C23×D1111yescharacteristic
609C22×C4C23×D1111yescharacteristic
610Q16—4416no—
611SD16—4416no—
612M16—228no—
613C2×C8—118no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—114no—
619C4⋊C4—222no—
620C4⋊C4—222no—
621C4⋊C4—222no—
622C4⋊C4—222no—
623C4⋊C4—222no—
624C4⋊C4—224no—
625C4⋊C4—224no—
626C4⋊C4—224no—
627C4⋊C4—224no—
628C4⋊C4—222no—
629C4⋊C4—222no—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—224no—
635C22⋊C4—224no—
636C42—224no—
637C42—224no—
638C42C2×C22⋊D1111yescharacteristic
639C42C2×C22⋊D1111yescharacteristic
640C42C2×C22⋊D1111yescharacteristic
641C42C2×C22⋊D1111yescharacteristic
642C42C2×C22⋊D1111yescharacteristic
643C42C2×C22⋊D1111yescharacteristic
644C42C2×C22⋊D1111yescharacteristic
645C42C2×C22⋊D1111yescharacteristic
646C42C2×C22⋊D1111yescharacteristic
647C42C2×C22⋊D1111yescharacteristic
648C42C2×C22⋊D1111yescharacteristic
649C42C2×C22⋊D1111yescharacteristic
650C42C23×D1111yescharacteristic
651C42C23×D1111yescharacteristic
652C42C23×D1111yescharacteristic
653C42C23×D1111yescharacteristic
654C11#6080411yescharacteristic, complemented, Sylow
655C23—22no—
656C23—22no—
657C23—24no—
658C23—41no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23C22×C22⋊D1111yescharacteristic
663C23C22×C22⋊D1111yescharacteristic
664C23C22×C22⋊D1111yescharacteristic
665Q8—28no—
666Q8—44no—
667Q8—228no—
668Q8—444no—
669Q8—444no—
670Q8—444no—
671D4—28no—
672D4—44no—
673D4—44no—
674D4—48no—
675D4—48no—
676D4—44no—
677D4—44no—
678D4—44no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—48no—
697C2×C4—44no—
698C2×C4—48no—
699C2×C4—224no—
700C2×C4—224no—
701C2×C4—444no—
702C2×C4—444no—
703C2×C4#6700414yescomplemented
704C2×C4#6703714yes—
705C2×C4C22×C22⋊D1111yescharacteristic
706C2×C4C22×C22⋊D1111yescharacteristic
707C2×C4C22×C22⋊D1111yescharacteristic
708C2×C4C22×C22⋊D1111yescharacteristic
709C2×C4C22×C22⋊D1111yescharacteristic
710C2×C4C22×C22⋊D1111yescharacteristic
711C2×C4C22×C22⋊D1111yescharacteristic
712C2×C4C22×C22⋊D1111yescharacteristic
713C2×C4C22×C22⋊D1111yescharacteristic
714C2×C4C22×C22⋊D1111yescharacteristic
715C2×C4C22×C22⋊D1111yescharacteristic
716C2×C4C24×D1111yescharacteristic
717C8—228no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—44no—
726C22—44no—
727C22—44no—
728C22—44no—
729C22—88no—
730C22#1062333612yes—
731C22C2×#6700412yes—
732C22C23×C22⋊D1111yescharacteristic
733C4—21no—
734C4—21no—
735C4—21no—
736C4—21no—
737C4—21no—
738C4—21no—
739C4—21no—
740C4—44no—
741C4—444no—
742C4—444no—
743C4#1062333612yes—
744C4#1062335312yes—
745C4C2×#6700412yes—
746C4C2×#6700412yes—
747C4C2×#6703712yes—
748C2—22no—
749C2—22no—
750C2—41no—
751C2—84no—
752C2C2×#1062333611yescharacteristic
753C2C22×#6700411yescharacteristic
754C2C2×#1062335311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#532C2
socleC22×C11C23×D4
hypercenterC2×#532D11
hypocenterC11#60804
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C42 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. C2×#10623001C2semidirect
2. #13079627C2semidirect
3. #13079619C2semidirect
4. #13079572C2semidirect
5. #13079564C2semidirect
6. #13079557C2semidirect
7. #13079076C2semidirect
8. #13079009C2semidirect
9. #13078084C2semidirect
10. #13077876C2semidirect
11. #13077249C2semidirect
30. C2×#67004C22semidirect
40. #10623001C22semidirect
41. #10623001C22semidirect
43. C2×#66922C22semidirect
44. C2×#66922C22semidirect
46. C2×C4×Dic22C22semidirect
47. #10622852C22semidirect
48. #10622845C22semidirect
52. #10622705C22semidirect
53. #10622703C22semidirect
54. #10622694C22semidirect
55. #10622689C22semidirect
56. #10622688C22semidirect
57. #10622683C22semidirect
58. #10622673C22semidirect
59. #10622668C22semidirect
60. #10622667C22semidirect
62. #10622539C22semidirect
64. #10622538C22semidirect
65. #10622537C22semidirect
66. C4×#4318C22semidirect
330. C2×C4×C11#137semidirect
654. C11#60804semidirect
703. C2×C4#67004semidirect

Maximal subgroups

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

subgroupindex
C2×#106230012
#130796272
#130796192
#130795722
#130795642
#130795572
#130790762
#130790092
#130780842
#130778762
#130772492
C2×C11×#5322
#6080411