Finite Group Databasebeta

← C2×#13079339 #15623721

Subgroups — C2×#13079339 #15623721

Order 2816.

2018 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623010C211yesmaximal, characteristic, complemented
2#13079339C2116yesmaximal, direct product factor
3C2×#10622677C211yesmaximal, characteristic, complemented
4C2×#10622672C211yesmaximal, characteristic, complemented
5C2×#10622681C211yesmaximal, characteristic, complemented
6C2×#10622669C211yesmaximal, characteristic, complemented
7C2×#10622665C211yesmaximal, characteristic, complemented
8C2×#10622652C211yesmaximal, characteristic
9C2×#10622662C211yesmaximal, characteristic, complemented
10C2×#10622655C211yesmaximal, characteristic, complemented
11C2×#10622627C211yesmaximal, characteristic, complemented
12C2×#10622643C211yesmaximal, characteristic, complemented
13C2×#10622631C211yesmaximal, characteristic, complemented
14C2×#10622639C211yesmaximal, characteristic, complemented
15C2×C4×#4318C211yesmaximal, characteristic, complemented
16C2×C11×#529C211yesmaximal, characteristic, complemented
17C11×#529—24no—
18C11×#529C2218yescomplemented
19C2×C11×#126—21no—
20C2×C11×#125C2211yescharacteristic
21C2×C11×#124C2211yescharacteristic
22C2×C11×#123—21no—
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×#121C2211yescharacteristic
25C2×C4×Q8×C11C2211yescharacteristic
26C2×C4×D4×C11—21no—
27C2×C4×D4×C11C2211yescharacteristic
28C2×C11×#117—21no—
29C22×C42×C11C2211yescharacteristic
30C22×#4326C2211yescharacteristic
31C22×#4325C2211yescharacteristic
32C22×#4324C2211yescharacteristic
33C22×#4323C2211yescharacteristic
34C2×#66983C2211yescharacteristic
35C2×#66982—21no—
36C2×C4×C22⋊D11—21no—
37C2×#66977C2211yescharacteristic
38C22×#4318C2211yescharacteristic
39C22×#4318C2211yescharacteristic
40#10623010—24no—
41#10623010C2218yescomplemented
42C2×#66929—21no—
43C2×#66928C2211yescharacteristic
44C2×C4×D44C2211yescharacteristic
45C2×#66925—21no—
46C2×#66923C2211yescharacteristic
47C2×C4×Dic22C2211yescharacteristic
48C2×#66899C2211yescharacteristic
49C2×#66899C2211yescharacteristic
50C2×#66896C2211yescharacteristic
51C2×#66896C2211yescharacteristic
52#10622681C2218yescomplemented
53#10622677C2218yescomplemented
54#10622672C2218yescomplemented
55#10622669C2218yescomplemented
56#10622665C2218yescomplemented
57#10622662C2218yescomplemented
58#10622655C2218yescomplemented
59#10622652C2218yes—
60#10622643C2218yescomplemented
61#10622639C2218yescomplemented
62#10622631C2218yescomplemented
63#10622627C2218yescomplemented
64C2×#66874C2211yescharacteristic
65C2×#66874C2211yescharacteristic
66C2×#66873C2211yescharacteristic
67C2×#66873C2211yescharacteristic
68C2×#66872C2211yescharacteristic
69C2×#66872C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71C2×#66871C2211yescharacteristic
72C4×#4318C2218yescomplemented
73C2×#66867C2211yescharacteristic
74C2×#66867C2211yescharacteristic
75C2×C4×C11⋊C8C2211yescharacteristic
76C2×C4×C11⋊C8C2211yescharacteristic
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11—21no—
79C22×D4×C11C2311yescharacteristic
80C23×C4×C11—21no—
81C23×C4×C11D411yescharacteristic
82C23×C4×C11D411yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C22×C22⋊D11—21no—
85C22×D44C2311yescharacteristic
86C22×C4×D11—21no—
87C22×Dic22C2311yescharacteristic
88C11×#126—28no—
89C11×#125—22no—
90C11×#125C2314yes—
91C11×#124—22no—
92C11×#124C2314yes—
93C11×#123—28no—
94C11×C22⋊Q8—22no—
95C11×C22⋊Q8C2314yes—
96C11×#121—22no—
97C11×#121C2314yes—
98C4×Q8×C11—22no—
99C4×Q8×C11C2314yes—
100C4×D4×C11—28no—
101C4×D4×C11—22no—
102C4×D4×C11C2314yes—
103C11×#117—28no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C42×C11—21no—
116C2×C42×C11D411yescharacteristic
117C2×C42×C11D411yescharacteristic
118C2×C42×C11D414yes—
119C2×C42×C11C2311yescharacteristic
120C2×C42×C11C2311yescharacteristic
121C2×C42×C11C2314yes—
122C2×C22⋊Dic11—21no—
123C2×#4326—24no—
124C2×#4326C2314yes—
125C2×#4325—24no—
126C2×#4325C2314yes—
127C2×#4324—24no—
128C2×#4324C2314yes—
129C2×#4323—24no—
130C2×#4323C2314yes—
131#66983—22no—
132#66983C2314yes—
133#66982—28no—
134C4×C22⋊D11—28no—
135C2×(C2×D11)⋊C4—21no—
136C2×(C2×D11)⋊C4—21no—
137C2×(C2×D11)⋊C4—21no—
138C2×(C2×D11)⋊C4—21no—
139C2×C4⋊Dic11C2311yescharacteristic
140C2×C4⋊Dic11C2311yescharacteristic
141#66977—22no—
142#66977C2314yes—
143C2×Dic11⋊C4—21no—
144C2×Dic11⋊C4—21no—
145C2×Dic11⋊C4—21no—
146C2×Dic11⋊C4—21no—
147C2×C4×Dic11—21no—
148C2×#4318—24no—
149C2×#4318—24no—
150C2×#4318C2314yes—
151C2×#4318C2314yes—
152C22×C11⋊C8C2311yescharacteristic
153C22×C11⋊C8C2311yescharacteristic
154C22×C11⋊C8C2311yescharacteristic
155C22×C11⋊C8C2311yescharacteristic
156#66929—28no—
157#66928—22no—
158#66928C2314yes—
159C4×D44—22no—
160C4×D44C2314yes—
161#66925—28no—
162#66923—22no—
163#66923C2314yes—
164C4×Dic22—22no—
165C4×Dic22C2314yes—
166#66899C2314yes—
167#66899C2314yes—
168#66896C2314yes—
169#66896C2314yes—
170#66874C2314yes—
171#66874C2314yes—
172#66873C2314yes—
173#66873C2314yes—
174#66872C2314yes—
175#66872C2314yes—
176#66871C2314yes—
177#66871C2314yes—
178#66867C2314yes—
179#66867C2314yes—
180C4×C11⋊C8C2314yes—
181C4×C11⋊C8C2314yes—
182C2×#3183—111nomaximal, Sylow
183C24×C11—21no—
184C24×C11C2×D411yescharacteristic
185C23×D11—21no—
186C2×Q8×C11—21no—
187C2×Q8×C11—22no—
188C2×Q8×C11—22no—
189C2×Q8×C11C2412yes—
190C2×D4×C11—24no—
191C2×D4×C11—21no—
192C2×D4×C11—22no—
193C2×D4×C11—22no—
194C2×D4×C11—44no—
195C2×D4×C11C2412yes—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—24no—
202C22×C4×C11—42no—
203C22×C4×C11—42no—
204C22×C4×C11—44no—
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D412yes—
211C22×C4×C11C2×D414yes—
212C22×C4×C11C2×D414yes—
213C22×C4×C11C2412yes—
214C22×C4×C11C2411yescharacteristic
215C2×C22⋊D11—24no—
216C2×C22⋊D11—44no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C2×D44—21no—
221C2×D44—22no—
222C2×D44—22no—
223C2×D44C2412yes—
224C2×C4×D11—24no—
225C2×C4×D11—44no—
226C2×Dic22—21no—
227C2×Dic22—22no—
228C2×Dic22—22no—
229C2×Dic22C2412yes—
230C11×C4⋊C4—24no—
231C11×C4⋊C4—24no—
232C11×C4⋊C4—24no—
233C11×C4⋊C4—24no—
234C11×C4⋊C4—21no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4C2412yes—
237C11×C4⋊C4C2412yes—
238C11×C22⋊C4—24no—
239C11×C22⋊C4—24no—
240C11×C22⋊C4—24no—
241C11×C22⋊C4—24no—
242C11×C22⋊C4—24no—
243C42×C11—24no—
244C42×C11C2×D412yes—
245C42×C11C2×D412yes—
246C42×C11C2×D414yes—
247C42×C11C2×D414yes—
248C42×C11C2412yes—
249C42×C11C2412yes—
250C22⋊Dic11—24no—
251#4326—28no—
252#4325—28no—
253#4324—28no—
254#4323—28no—
255(C2×D11)⋊C4—24no—
256(C2×D11)⋊C4—24no—
257(C2×D11)⋊C4—24no—
258(C2×D11)⋊C4—24no—
259C4⋊Dic11—21no—
260C4⋊Dic11—21no—
261C4⋊Dic11C2412yes—
262C4⋊Dic11C2412yes—
263Dic11⋊C4—24no—
264Dic11⋊C4—24no—
265Dic11⋊C4—24no—
266Dic11⋊C4—24no—
267C4×Dic11—24no—
268#4318—28no—
269#4318—28no—
270C2×C11⋊C8—22no—
271C2×C11⋊C8—22no—
272C2×C11⋊C8#4114yes—
273C2×C11⋊C8#4114yes—
274C2×C11⋊C8C2412yes—
275C2×C11⋊C8C2412yes—
276C2×C11⋊C8C2412yes—
277C2×C11⋊C8C2412yes—
278C2×#529—111no—
279C2×#529D1111yescharacteristic, complemented
280#3183—1116no—
281C2×#499—111no—
282C2×#495—111no—
283C2×#488—111no—
284C2×#488—111no—
285C2×#470—111no—
286C2×#469—111no—
287C2×#468—111no—
288C2×#468—111no—
289C2×#442—111no—
290C2×#441—111no—
291C2×#440—111no—
292C2×#440—111no—
293C2×C4×M16—111no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—42no—
299C23×C11—42no—
300C23×C11—42no—
301C23×C11C22×D412yes—
302C23×C11C22×D411yescharacteristic
303C22×D11—22no—
304C22×D11—42no—
305C22×D11—42no—
306C22×D11—42no—
307Q8×C11—22no—
308Q8×C11—22no—
309Q8×C11—42no—
310D4×C11—22no—
311D4×C11—22no—
312D4×C11—48no—
313D4×C11—42no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—24no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—44no—
326C2×C4×C11—44no—
327C2×C4×C11—48no—
328C2×C4×C11—42no—
329C2×C4×C11—42no—
330C2×C4×C11—42no—
331C2×C4×C11C22×D412yes—
332C2×C4×C11C22×D412yes—
333C2×C4×C11C22×D412yes—
334C2×C4×C11C22×D412yes—
335C2×C4×C11C22×D412yes—
336C2×C4×C11C22×D411yescharacteristic
337C2×C4×C11C2×#4112yes—
338C2×C4×C11C2×#4112yes—
339C2×C4×C11C2511yescharacteristic
340C22⋊D11—48no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—42no—
345C2×Dic11—42no—
346C2×Dic11—42no—
347D44—22no—
348D44—22no—
349D44—42no—
350C4×D11—48no—
351Dic22—22no—
352Dic22—22no—
353Dic22—42no—
354C11⋊C8—22no—
355C11⋊C8—22no—
356C11⋊C8C2×#4114yes—
357C11⋊C8C2×#4114yes—
358C22×Q16—111no—
359C22×SD16—111no—
360C22×SD16—111no—
361C22×D8—111no—
362C22×M16—111no—
363C22×M16—111no—
364#529—24no—
365#529—118no—
366#529—224no—
367#529C2×D1118yescomplemented
368C2×#126—21no—
369C2×#126—221no—
370C2×#125—111no—
371C2×#125C2×D1111yescharacteristic
372C2×#124—111no—
373C2×#124C2×D1111yescharacteristic
374C2×#123—21no—
375C2×#123—221no—
376C2×C22⋊Q8—111no—
377C2×C22⋊Q8C2×D1111yescharacteristic
378C2×#121—111no—
379C2×#121C2×D1111yescharacteristic
380C2×C4×Q8—111no—
381C2×C4×Q8C2×D1111yescharacteristic
382C2×C4×D4—21no—
383C2×C4×D4—111no—
384C2×C4×D4—221no—
385C2×C4×D4C2×D1111yescharacteristic
386C2×#117—21no—
387C2×#117—221no—
388C22×C42C2×D1111yescharacteristic
389#499—118no—
390#495—118no—
391#488—118no—
392#488—118no—
393#470—118no—
394#469—118no—
395#468—118no—
396#468—118no—
397#442—118no—
398#441—118no—
399#440—118no—
400#440—118no—
401C2×#107—111no—
402C2×#107—111no—
403C2×#106—111no—
404C2×#106—111no—
405C2×#103—111no—
406C2×#103—111no—
407C2×#103—111no—
408C2×#103—111no—
409C2×#102—111no—
410C2×#102—111no—
411C2×#102—111no—
412C2×#102—111no—
413C4×M16—118no—
414C2×#97—111no—
415C2×#97—111no—
416C2×C4×C8—111no—
417C2×C4×C8—111no—
418C22×C11—22no—
419C22×C11—22no—
420C22×C11—22no—
421C22×C11—44no—
422C22×C11—42no—
423C22×C11—42no—
424C22×C11—42no—
425C22×C11—84no—
426C22×C11#53212yes—
427C22×C11#57512yes—
428C22×C11#57512yes—
429C22×C11C23×D411yescharacteristic
430C2×D11—42no—
431C2×D11—42no—
432C2×D11—42no—
433C2×D11—84no—
434C4×C11—22no—
435C4×C11—22no—
436C4×C11—22no—
437C4×C11—22no—
438C4×C11—22no—
439C4×C11—42no—
440C4×C11—42no—
441C4×C11—42no—
442C4×C11#53212yes—
443C4×C11C22×#4111yescharacteristic
444C4×C11C22×#4111yescharacteristic
445Dic11—42no—
446Dic11—42no—
447Dic11—42no—
448C22×Q8—111no—
449C22×Q8C22×D1111yescharacteristic
450C22×D4—21no—
451C22×D4—111no—
452C22×D4—221no—
453C22×D4C22×D1111yescharacteristic
454C23×C4—21no—
455C23×C4—221no—
456C23×C4C22⋊D1111yescharacteristic
457C23×C4C22⋊D1111yescharacteristic
458C23×C4C22×D1111yescharacteristic
459C2×Q16—114no—
460C2×Q16—224no—
461C2×SD16—114no—
462C2×SD16—114no—
463C2×SD16—224no—
464C2×SD16—224no—
465C2×D8—114no—
466C2×D8—224no—
467C2×M16—114no—
468C2×M16—114no—
469C2×M16—224no—
470C2×M16—224no—
471C22×C8—111no—
472C22×C8—111no—
473C22×C8—111no—
474C22×C8—111no—
475#126—28no—
476#126—228no—
477#125—22no—
478#125—114no—
479#125—222no—
480#125C22×D1114yes—
481#124—22no—
482#124—114no—
483#124—222no—
484#124C22×D1114yes—
485#123—28no—
486#123—228no—
487C22⋊Q8—22no—
488C22⋊Q8—114no—
489C22⋊Q8—222no—
490C22⋊Q8C22×D1114yes—
491#121—22no—
492#121—114no—
493#121—222no—
494#121C22×D1114yes—
495C4×Q8—22no—
496C4×Q8—114no—
497C4×Q8—222no—
498C4×Q8C22×D1114yes—
499C4×D4—28no—
500C4×D4—22no—
501C4×D4—114no—
502C4×D4—228no—
503C4×D4—222no—
504C4×D4C22×D1114yes—
505#117—28no—
506#117—228no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—111no—
512C2×C4⋊C4—111no—
513C2×C4⋊C4—221no—
514C2×C4⋊C4—221no—
515C2×C4⋊C4—221no—
516C2×C4⋊C4—221no—
517C2×C4⋊C4C22×D1111yescharacteristic
518C2×C4⋊C4C22×D1111yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—221no—
525C2×C22⋊C4—221no—
526C2×C22⋊C4—221no—
527C2×C22⋊C4—221no—
528C2×C22⋊C4—221no—
529C2×C42—21no—
530C2×C42—221no—
531C2×C42C22⋊D1111yescharacteristic
532C2×C42C22⋊D1111yescharacteristic
533C2×C42C22⋊D1114yes—
534C2×C42C22×D1111yescharacteristic
535C2×C42C22×D1111yescharacteristic
536C2×C42C22×D1114yes—
537#107—114no—
538#107—114no—
539#106—114no—
540#106—114no—
541#103—114no—
542#103—114no—
543#103—114no—
544#103—114no—
545#102—114no—
546#102—114no—
547#102—114no—
548#102—114no—
549#97—114no—
550#97—114no—
551C4×C8—114no—
552C4×C8—114no—
553C2×C11—42no—
554C2×C11—82no—
555C2×C11#318314yescomplemented
556C2×C11C2×#53211yescharacteristic
557C2×C11C2×#57511yescharacteristic
558C2×C11C2×#57511yescharacteristic
559D11—82no—
560C24—21no—
561C24—221no—
562C24C2×C22⋊D1111yescharacteristic
563C2×Q8—21no—
564C2×Q8—22no—
565C2×Q8—22no—
566C2×Q8—112no—
567C2×Q8—221no—
568C2×Q8—222no—
569C2×Q8—222no—
570C2×Q8C23×D1112yes—
571C2×D4—24no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—21no—
575C2×D4—44no—
576C2×D4—112no—
577C2×D4—224no—
578C2×D4—222no—
579C2×D4—222no—
580C2×D4—221no—
581C2×D4—444no—
582C2×D4C23×D1112yes—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—24no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—44no—
592C22×C4—221no—
593C22×C4—221no—
594C22×C4—221no—
595C22×C4—224no—
596C22×C4—444no—
597C22×C4C2×C22⋊D1112yes—
598C22×C4C2×C22⋊D1111yescharacteristic
599C22×C4C2×C22⋊D1111yescharacteristic
600C22×C4C2×C22⋊D1111yescharacteristic
601C22×C4C2×C22⋊D1111yescharacteristic
602C22×C4C2×C22⋊D1111yescharacteristic
603C22×C4C2×C22⋊D1114yes—
604C22×C4C2×C22⋊D1114yes—
605C22×C4C23×D1112yes—
606C22×C4C23×D1111yescharacteristic
607Q16—228no—
608SD16—228no—
609SD16—228no—
610D8—228no—
611M16—228no—
612M16—228no—
613C2×C8—114no—
614C2×C8—114no—
615C2×C8—112no—
616C2×C8—112no—
617C2×C8—112no—
618C2×C8—112no—
619C2×C8—222no—
620C2×C8—222no—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—24no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—112no—
628C4⋊C4—112no—
629C4⋊C4—221no—
630C4⋊C4—221no—
631C4⋊C4—224no—
632C4⋊C4—224no—
633C4⋊C4—224no—
634C4⋊C4—224no—
635C4⋊C4C23×D1112yes—
636C4⋊C4C23×D1112yes—
637C22⋊C4—24no—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—224no—
643C22⋊C4—224no—
644C22⋊C4—224no—
645C22⋊C4—224no—
646C22⋊C4—224no—
647C42—24no—
648C42—224no—
649C42C2×C22⋊D1114yes—
650C42C2×C22⋊D1114yes—
651C42C2×C22⋊D1112yes—
652C42C2×C22⋊D1112yes—
653C42C23×D1112yes—
654C42C23×D1112yes—
655C11C2×#318311yescharacteristic, complemented, Sylow
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—222no—
664C23—442no—
665C23—442no—
666C23—442no—
667C23C22×C22⋊D1112yes—
668C23C22×C22⋊D1111yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—222no—
673Q8—222no—
674Q8—442no—
675D4—22no—
676D4—22no—
677D4—48no—
678D4—42no—
679D4—222no—
680D4—222no—
681D4—448no—
682D4—442no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—48no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—448no—
704C2×C4—442no—
705C2×C4—442no—
706C2×C4—442no—
707C2×C4#41×D1112yes—
708C2×C4#41×D1112yes—
709C2×C4C22×C22⋊D1112yes—
710C2×C4C22×C22⋊D1112yes—
711C2×C4C22×C22⋊D1112yes—
712C2×C4C22×C22⋊D1112yes—
713C2×C4C22×C22⋊D1112yes—
714C2×C4C22×C22⋊D1111yescharacteristic
715C2×C4C24×D1111yescharacteristic
716C8—114no—
717C8—114no—
718C8—222no—
719C8—222no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—44no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—84no—
728C22—442no—
729C22—442no—
730C22—442no—
731C22—884no—
732C22#1062335312yes—
733C22#1062335312yes—
734C22#1062336312yes—
735C22C23×C22⋊D1111yescharacteristic
736C4—22no—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—22no—
741C4—42no—
742C4—42no—
743C4—42no—
744C4—442no—
745C4—442no—
746C4—442no—
747C4#1062336312yes—
748C4C2×#41×D1111yescharacteristic
749C4C2×#41×D1111yescharacteristic
750C2—42no—
751C2—82no—
752C2—882no—
753C2#1307933914yesdirect product factor
754C2C2×#1062336311yescharacteristic
755C2C2×#1062335311yescharacteristic
756C2C2×#1062335311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#529C2
socleC23×C11C22×D4
prime radicalC2×#10622652C2
hypercenterC2×#529D11
hypocenterC11C2×#3183
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×#10623010C2semidirect
2. #13079339C2direct (N × H)
3. C2×#10622677C2semidirect
4. C2×#10622672C2semidirect
5. C2×#10622681C2semidirect
6. C2×#10622669C2semidirect
7. C2×#10622665C2semidirect
9. C2×#10622662C2semidirect
10. C2×#10622655C2semidirect
11. C2×#10622627C2semidirect
12. C2×#10622643C2semidirect
13. C2×#10622631C2semidirect
14. C2×#10622639C2semidirect
15. C2×C4×#4318C2semidirect
16. C2×C11×#529C2semidirect
18. C11×#529C22semidirect
41. #10623010C22semidirect
52. #10622681C22semidirect
53. #10622677C22semidirect
54. #10622672C22semidirect
55. #10622669C22semidirect
56. #10622665C22semidirect
57. #10622662C22semidirect
58. #10622655C22semidirect
60. #10622643C22semidirect
61. #10622639C22semidirect
62. #10622631C22semidirect
63. #10622627C22semidirect
72. C4×#4318C22semidirect
279. C2×#529D11semidirect
367. #529C2×D11semidirect
555. C2×C11#3183semidirect
655. C11C2×#3183semidirect
753. C2#13079339direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230102
#130793392
C2×#106226772
C2×#106226722
C2×#106226812
C2×#106226692
C2×#106226652
C2×#106226522
C2×#106226622
C2×#106226552
C2×#106226272
C2×#106226432
C2×#106226312
C2×#106226392
C2×C4×#43182
C2×C11×#5292
C2×#318311