Finite Group Databasebeta

← #15625260

Subgroups — #15625260

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×#10623008C211yesmaximal, characteristic
2#13079623C214yesmaximal, complemented
3#13079615C214yesmaximal, complemented
4#13079568C214yesmaximal, complemented
5#13079561C212yesmaximal, complemented
6#13079554C212yesmaximal, complemented
7#13079073C212yesmaximal, complemented
8#13079012C212yesmaximal, complemented
9#13078088C214yesmaximal, complemented
10#13077874C214yesmaximal, complemented
11#13077249C211yesmaximal, characteristic, complemented
12C2×C11×#533C211yesmaximal, characteristic, complemented
13C22×#4339C2212yes—
14C11×#533—21no—
15C11×#533—21no—
16C11×#533—21no—
17C11×#533—21no—
18C11×#533C2212yes—
19C11×#533C2212yes—
20C11×#533C2212yescomplemented
21C11×#533C2212yescomplemented
22C2×C11×C4⋊Q8C2211yescharacteristic, complemented
23C2×C11×C4⋊Q8C2211yescharacteristic, complemented
24C2×C11×#125—21no—
25C2×C11×C22⋊Q8—21no—
26C2×C11×C22⋊Q8C2212yes—
27C2×C4×Q8×C11—21no—
28C2×C4×Q8×C11C2212yescomplemented
29C2×C11×#117—21no—
30C22×C42×C11C2211yescharacteristic
31C2×#66995C2218yescomplemented
32C2×#66983—21no—
33C2×#66983—21no—
34#10623008—21no—
35#10623008—21no—
36#10623008—21no—
37#10623008—21no—
38#10623008C2212yes—
39#10623008C2212yes—
40#10623008C2212yes—
41#10623008C2212yes—
42C2×#66928C2212yes—
43C2×#66927C2211yescharacteristic
44C2×C4×D44—21no—
45C2×C4×D44—21no—
46C2×#66922C2211yescharacteristic
47#10622820C2212yes—
48#10622706C2214yescomplemented
49#10622705C2214yescomplemented
50#10622702C2218yescomplemented
51#10622701C2214yescomplemented
52#10622699C2218yescomplemented
53#10622698C2214yescomplemented
54#10622663C2218yes—
55#10622660C22116yescomplemented
56#10622659C2218yes—
57#10622644C2218yescomplemented
58#10622641C22116yescomplemented
59#10622640C2218yescomplemented
60#10622579C2218yescomplemented
61#10622539C2212yes—
62#10622539C2212yescomplemented
63#10622538C2212yes—
64#10622538C2212yescomplemented
65#10622537C2212yescomplemented
66C4×#4318C2212yescomplemented
67C22×Q8×C11—21no—
68C22×Q8×C11C2312yes—
69C23×C4×C11D411yescharacteristic
70C23×C4×C11D411yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C22×C22⋊D11—22no—
73C2×#4339—22no—
74C2×#4339—22no—
75C2×#4339—48no—
76C2×#4339C2314yes—
77C2×#4339C2314yes—
78C22×D44—21no—
79C22×D44—21no—
80C22×D44C2312yes—
81C22×C4×D11—22no—
82C22×Dic22C2312yes—
83C11×C4⋊Q8—21no—
84C11×C4⋊Q8—21no—
85C11×C4⋊Q8—21no—
86C11×C4⋊Q8—21no—
87C11×C4⋊Q8C2312yes—
88C11×C4⋊Q8C2312yes—
89C11×C4⋊Q8C2312yes—
90C11×C4⋊Q8C2312yes—
91C11×#125—22no—
92C11×#125—22no—
93C11×#125—22no—
94C11×#125—22no—
95C11×C22⋊Q8—22no—
96C11×C22⋊Q8—22no—
97C11×C22⋊Q8—22no—
98C11×C22⋊Q8—22no—
99C11×C22⋊Q8—22no—
100C11×C22⋊Q8—22no—
101C11×C22⋊Q8C2314yes—
102C11×C22⋊Q8C2314yes—
103C4×Q8×C11—22no—
104C4×Q8×C11—22no—
105C4×Q8×C11—22no—
106C4×Q8×C11—22no—
107C4×Q8×C11—22no—
108C4×Q8×C11—22no—
109C4×Q8×C11C2314yes—
110C4×Q8×C11C2314yes—
111C11×#117—22no—
112C11×#117—22no—
113C11×#117—22no—
114C11×#117—22no—
115C2×C11×C4⋊C4—21no—
116C2×C11×C4⋊C4—21no—
117C2×C11×C4⋊C4—21no—
118C2×C11×C4⋊C4—22no—
119C2×C11×C4⋊C4—22no—
120C2×C11×C4⋊C4C2312yes—
121C2×C11×C22⋊C4—22no—
122C2×C42×C11—22no—
123C2×C42×C11D411yescharacteristic
124C2×C42×C11D411yescharacteristic
125C2×C42×C11D411yescharacteristic
126C2×C42×C11D411yescharacteristic
127C2×C42×C11D411yescharacteristic
128C2×C42×C11D411yescharacteristic
129C2×C42×C11C2311yescharacteristic
130C2×C42×C11C2311yescharacteristic
131C2×C42×C11C2311yescharacteristic
132C2×C42×C11C2311yescharacteristic
133C2×C42×C11C2311yescharacteristic
134C2×C42×C11C2311yescharacteristic
135C2×#4326C23116yes—
136#66995—416no—
137C2×#4325C23116yes—
138#66983—22no—
139#66983—22no—
140#66983—22no—
141#66983—22no—
142#66983—22no—
143#66983—22no—
144#66983—22no—
145#66983—22no—
146C2×(C2×D11)⋊C4—22no—
147C2×(C2×D11)⋊C4—22no—
148C2×C4⋊Dic11—21no—
149C2×C4⋊Dic11—21no—
150C2×#4318C2314yes—
151#66928—22no—
152#66928—22no—
153#66928C2314yes—
154#66928C2314yes—
155#66927—21no—
156#66927—21no—
157#66927C2312yes—
158#66927C2312yes—
159C4×D44—22no—
160C4×D44—22no—
161C4×D44—22no—
162C4×D44—22no—
163C4×D44—22no—
164C4×D44—22no—
165C4×D44—22no—
166C4×D44—22no—
167#66922—21no—
168#66922—21no—
169#66922C2312yes—
170#66922C2312yes—
171C22⋊(C11⋊C8)C2314yes—
172C22⋊(C11⋊C8)C2314yes—
173#66874C23116yes—
174#66873C23116yes—
175C4⋊(C11⋊C8)C2314yes—
176C4⋊(C11⋊C8)C2314yes—
177#66867C2314yes—
178C4×C11⋊C8C2314yes—
179#60804—111nomaximal, Sylow
180C24×C11C2×D411yescharacteristic
181C23×D11—22no—
182C2×Q8×C11—22no—
183C2×Q8×C11—22no—
184C2×Q8×C11—22no—
185C2×Q8×C11—28no—
186C2×Q8×C11—44no—
187C2×Q8×C11C2414yes—
188C22×C4×C11—24no—
189C22×C4×C11—24no—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—42no—
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2411yescharacteristic
209C22×C4×C11C2411yescharacteristic
210C22×C4×C11C2411yescharacteristic
211C2×C22⋊D11—24no—
212C2×C22⋊D11—24no—
213C2×C22⋊D11—48no—
214C22×Dic11—22no—
215#4339—216no—
216#4339—48no—
217#4339—48no—
218#4339—48no—
219C2×D44—22no—
220C2×D44—22no—
221C2×D44—22no—
222C2×D44—22no—
223C2×D44—22no—
224C2×D44—44no—
225C2×D44—44no—
226C2×D44—44no—
227C2×D44C2414yes—
228C2×C4×D11—24no—
229C2×C4×D11—24no—
230C2×C4×D11—48no—
231C2×Dic22—22no—
232C2×Dic22—44no—
233C2×Dic22C2414yes—
234C11×C4⋊C4—22no—
235C11×C4⋊C4—22no—
236C11×C4⋊C4—22no—
237C11×C4⋊C4—22no—
238C11×C4⋊C4—22no—
239C11×C4⋊C4—22no—
240C11×C4⋊C4—24no—
241C11×C4⋊C4—24no—
242C11×C4⋊C4—24no—
243C11×C4⋊C4—24no—
244C11×C4⋊C4—22no—
245C11×C4⋊C4C2414yes—
246C11×C22⋊C4—24no—
247C11×C22⋊C4—24no—
248C42×C11—24no—
249C42×C11—24no—
250C42×C11C2×D411yescharacteristic
251C42×C11C2×D411yescharacteristic
252C42×C11C2×D411yescharacteristic
253C42×C11C2×D411yescharacteristic
254C42×C11C2×D411yescharacteristic
255C42×C11C2×D411yescharacteristic
256C42×C11C2×D411yescharacteristic
257C42×C11C2×D411yescharacteristic
258C42×C11C2×D411yescharacteristic
259C42×C11C2×D411yescharacteristic
260C42×C11C2×D411yescharacteristic
261C42×C11C2×D411yescharacteristic
262C42×C11C2411yescharacteristic
263C42×C11C2411yescharacteristic
264C42×C11C2411yescharacteristic
265C42×C11C2411yescharacteristic
266#4326—416no—
267#4325—416no—
268(C2×D11)⋊C4—24no—
269(C2×D11)⋊C4—24no—
270(C2×D11)⋊C4—24no—
271(C2×D11)⋊C4—24no—
272C4⋊Dic11—22no—
273C4⋊Dic11—22no—
274C4⋊Dic11—22no—
275C4⋊Dic11—22no—
276#4318—28no—
277C2×C11⋊C8C2418yes—
278C2×#533D1111yescharacteristic, complemented
279C2×#532—111no—
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—41no—
293C23×C11C22×D411yescharacteristic
294C23×C11C22×D411yescharacteristic
295C23×C11C22×D411yescharacteristic
296C22×D11—24no—
297C22×D11—44no—
298C22×D11—44no—
299C22×D11—44no—
300Q8×C11—28no—
301Q8×C11—44no—
302Q8×C11—44no—
303Q8×C11—44no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
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—24no—
318C2×C4×C11—24no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—44no—
323C2×C4×C11—44no—
324C2×C4×C11#13714yescomplemented
325C2×C4×C11C22×D411yescharacteristic
326C2×C4×C11C22×D411yescharacteristic
327C2×C4×C11C22×D411yescharacteristic
328C2×C4×C11C22×D411yescharacteristic
329C2×C4×C11C22×D411yescharacteristic
330C2×C4×C11C22×D411yescharacteristic
331C2×C4×C11C22×D411yescharacteristic
332C2×C4×C11C22×D411yescharacteristic
333C2×C4×C11C22×D411yescharacteristic
334C2×C4×C11C22×D411yescharacteristic
335C2×C4×C11C22×D411yescharacteristic
336C2×C4×C11H(5,𝔽2)14yes—
337C2×C4×C11C2511yescharacteristic
338C22⋊D11—48no—
339C22⋊D11—48no—
340C2×Dic11—24no—
341C2×Dic11—44no—
342D44—28no—
343D44—44no—
344D44—44no—
345D44—44no—
346D44—44no—
347D44—44no—
348C4×D11—48no—
349C4×D11—48no—
350Dic22—28no—
351Dic22—44no—
352C11⋊C8—28no—
353C22×#41—112no—
354C2×#137—118no—
355#533—21no—
356#533—21no—
357#533—21no—
358#533—21no—
359#533C2×D1112yes—
360#533C2×D1112yes—
361#533C2×D1112yescomplemented
362#533C2×D1112yescomplemented
363#532—112no—
364#532—112no—
365#532—112no—
366#532—112no—
367#532—221no—
368#532—221no—
369#532—221no—
370#532—221no—
371C2×C4⋊Q8—111no—
372C2×C4⋊Q8C2×D1111yescharacteristic, complemented
373C2×C4⋊Q8C2×D1111yescharacteristic, complemented
374C2×#127—111no—
375C2×#125—21no—
376C2×#124—112no—
377C2×C22⋊Q8—21no—
378C2×C22⋊Q8C2×D1112yes—
379C2×#121—221no—
380C2×#121—221no—
381C2×C4×Q8—21no—
382C2×C4×Q8C2×D1112yescomplemented
383C2×C4×D4—221no—
384C2×C4×D4—221no—
385C2×#117—21no—
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#53512yes—
416C22×C11C2×#13712yes—
417C22×C11C23×D411yescharacteristic
418C2×D11—44no—
419C2×D11—44no—
420C2×D11—44no—
421C2×D11—88no—
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—44no—
431C4×C11#53512yes—
432C4×C11C2×#13712yes—
433C4×C11C2×#13712yes—
434C4×C11#57512yes—
435C4×C11C2×H(5,𝔽2)12yes—
436Dic11—44no—
437C2×#41—114no—
438C2×#41—114no—
439C2×#41—222no—
440C2×#41—222no—
441C2×#41—448no—
442C22×Q8—21no—
443C22×Q8—112no—
444C22×Q8C22×D1112yes—
445C22×D4—112no—
446C22×D4—222no—
447C22×D4—221no—
448C22×D4—221no—
449C23×C4—222no—
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—21no—
460C4⋊Q8—21no—
461C4⋊Q8—112no—
462C4⋊Q8—112no—
463C4⋊Q8—221no—
464C4⋊Q8—221no—
465C4⋊Q8C22×D1112yes—
466C4⋊Q8C22×D1112yes—
467C4⋊Q8C22×D1112yes—
468C4⋊Q8C22×D1112yes—
469#127—112no—
470#127—112no—
471#127—221no—
472#127—221no—
473#125—22no—
474#125—22no—
475#125—22no—
476#125—22no—
477#124—114no—
478#124—114no—
479#124—222no—
480#124—222no—
481C22⋊Q8—22no—
482C22⋊Q8—22no—
483C22⋊Q8—22no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8C22×D1114yes—
488C22⋊Q8C22×D1114yes—
489#121—222no—
490#121—222no—
491#121—222no—
492#121—222no—
493#121—222no—
494#121—222no—
495#121—222no—
496#121—222no—
497C4×Q8—22no—
498C4×Q8—22no—
499C4×Q8—22no—
500C4×Q8—22no—
501C4×Q8—22no—
502C4×Q8—22no—
503C4×Q8C22×D1114yes—
504C4×Q8C22×D1114yes—
505C4×D4—222no—
506C4×D4—222no—
507C4×D4—222no—
508C4×D4—222no—
509C4×D4—222no—
510C4×D4—222no—
511C4×D4—222no—
512C4×D4—222no—
513#117—22no—
514#117—22no—
515#117—22no—
516#117—22no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—221no—
523C2×C4⋊C4—221no—
524C2×C4⋊C4C22×D1112yes—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—222no—
527C2×C22⋊C4—222no—
528C2×C42—22no—
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×C11C2×#53511yescharacteristic
553C2×C11C22×#13711yescharacteristic
554C2×C11C2×#57511yescharacteristic
555D11—84no—
556C24—222no—
557C24C2×C22⋊D1111yescharacteristic
558#41—2216no—
559#41—448no—
560#41—448no—
561#41—448no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—28no—
566C2×Q8—44no—
567C2×Q8—114no—
568C2×Q8—222no—
569C2×Q8—444no—
570C2×Q8C23×D1114yes—
571C2×D4—114no—
572C2×D4—224no—
573C2×D4—224no—
574C2×D4—222no—
575C2×D4—222no—
576C2×D4—222no—
577C2×D4—222no—
578C2×D4—222no—
579C2×D4—444no—
580C2×D4—444no—
581C2×D4—448no—
582C2×D4—444no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—42no—
588C22×C4—222no—
589C22×C4—224no—
590C22×C4—224no—
591C22×C4—448no—
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—22no—
619C4⋊C4—22no—
620C4⋊C4—24no—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—22no—
625C4⋊C4—222no—
626C4⋊C4—222no—
627C4⋊C4—222no—
628C4⋊C4—222no—
629C4⋊C4C23×D1114yes—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—224no—
633C22⋊C4—224no—
634C22⋊C4—224no—
635C22⋊C4—224no—
636C42—24no—
637C42—24no—
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—41no—
658C23—224no—
659C23—444no—
660C23—444no—
661C23—444no—
662C23C22×C22⋊D1111yescharacteristic
663C23C22×C22⋊D1111yescharacteristic
664C23C22×C22⋊D1111yescharacteristic
665Q8—28no—
666Q8—44no—
667Q8—44no—
668Q8—44no—
669Q8—228no—
670Q8—444no—
671D4—228no—
672D4—444no—
673D4—444no—
674D4—448no—
675D4—448no—
676D4—444no—
677D4—444no—
678D4—444no—
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—24no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—224no—
700C2×C4—448no—
701C2×C4—444no—
702C2×C4—448no—
703C2×C4#6699514yescomplemented
704C2×C4#6704214yes—
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—444no—
727C22—444no—
728C22—444no—
729C22—888no—
730C22C2×#6699512yes—
731C22#1062336112yes—
732C22C23×C22⋊D1111yescharacteristic
733C4—21no—
734C4—21no—
735C4—21no—
736C4—21no—
737C4—21no—
738C4—21no—
739C4—21no—
740C4—44no—
741C4—44no—
742C4—444no—
743C4C2×#6699512yes—
744C4C2×#6699512yes—
745C4#1062335312yes—
746C4#1062336112yes—
747C4C2×#6704212yes—
748C2—22no—
749C2—22no—
750C2—41no—
751C2—884no—
752C2C2×#1062336111yescharacteristic
753C2C22×#6699511yescharacteristic
754C2C2×#1062335311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#533C2
socleC22×C11C23×D4
prime radicalC2×#10623008C2
hypercenterC2×#533D11
hypocenterC11#60804
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
2. #13079623C2semidirect
3. #13079615C2semidirect
4. #13079568C2semidirect
5. #13079561C2semidirect
6. #13079554C2semidirect
7. #13079073C2semidirect
8. #13079012C2semidirect
9. #13078088C2semidirect
10. #13077874C2semidirect
11. #13077249C2semidirect
12. C2×C11×#533C2semidirect
20. C11×#533C22semidirect
21. C11×#533C22semidirect
22. C2×C11×C4⋊Q8C22semidirect
23. C2×C11×C4⋊Q8C22semidirect
28. C2×C4×Q8×C11C22semidirect
31. C2×#66995C22semidirect
48. #10622706C22semidirect
49. #10622705C22semidirect
50. #10622702C22semidirect
51. #10622701C22semidirect
52. #10622699C22semidirect
53. #10622698C22semidirect
55. #10622660C22semidirect
57. #10622644C22semidirect
58. #10622641C22semidirect
59. #10622640C22semidirect
60. #10622579C22semidirect
62. #10622539C22semidirect
64. #10622538C22semidirect
65. #10622537C22semidirect
66. C4×#4318C22semidirect
278. C2×#533D11semidirect
324. C2×C4×C11#137semidirect
361. #533C2×D11semidirect
362. #533C2×D11semidirect
372. C2×C4⋊Q8C2×D11semidirect
373. C2×C4⋊Q8C2×D11semidirect
382. C2×C4×Q8C2×D11semidirect
654. C11#60804semidirect
703. C2×C4#66995semidirect

Maximal subgroups

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

subgroupindex
C2×#106230082
#130796232
#130796152
#130795682
#130795612
#130795542
#130790732
#130790122
#130780882
#130778742
#130772492
C2×C11×#5332
#6080411