Finite Group Databasebeta

← C2×#13080072 #15626733

Subgroups — C2×#13080072 #15626733

Order 2816.

1882 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×#10623065C211yesmaximal, characteristic, complemented
2#13080072C2116yesmaximal, direct product factor
3C2×#10622634C211yesmaximal, characteristic, complemented
4C2×#10622704C211yesmaximal, characteristic, complemented
5C2×#10622620C211yesmaximal, characteristic, complemented
6C2×#10622700C211yesmaximal, characteristic, complemented
7C2×#10622662C211yesmaximal, characteristic, complemented
8C2×#10622655C211yesmaximal, characteristic, complemented
9C2×#10622664C211yesmaximal, characteristic, complemented
10C2×#10622651C211yesmaximal, characteristic
11C2×#10622641C211yesmaximal, characteristic, complemented
12C2×#10622667C211yesmaximal, characteristic, complemented
13C2×#10622629C211yesmaximal, characteristic, complemented
14C2×#10622670C211yesmaximal, characteristic, complemented
15C2×#10622612C211yesmaximal, characteristic, complemented
16C2×C11×#542C211yesmaximal, characteristic, complemented
17C11×#542—24no—
18C11×#542C2218yescomplemented
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C11×#126—21no—
21C2×C11×#124—21no—
22C2×C11×#124C2211yescharacteristic
23C2×C11×#123—21no—
24C2×C11×C22⋊Q8—21no—
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C2×C11×#117C2211yescharacteristic
30C22×#4326C2211yescharacteristic
31C22×#4325C2211yescharacteristic
32C22×#4324C2211yescharacteristic
33C22×#4323C2211yescharacteristic
34C2×#66983C2211yescharacteristic
35C2×#66977C2211yescharacteristic
36C22×#4318C2211yescharacteristic
37C23×C11⋊C8C2211yescharacteristic
38#10623065—24no—
39#10623065C2218yescomplemented
40C2×#66951—21no—
41C2×#66949—21no—
42C2×#66938—21no—
43C2×#66936—21no—
44C2×#66928C2211yescharacteristic
45C2×C4×D44C2211yescharacteristic
46C2×#66922C2211yescharacteristic
47C2×C4×Dic22C2211yescharacteristic
48C2×#66899C2211yescharacteristic
49C2×#66899C2211yescharacteristic
50C2×#66896C2211yescharacteristic
51C2×#66896C2211yescharacteristic
52#10622704C2218yescomplemented
53#10622700C2218yescomplemented
54#10622670C2218yescomplemented
55#10622667C2218yescomplemented
56#10622664C2218yescomplemented
57#10622662C2218yescomplemented
58#10622655C2218yescomplemented
59#10622651C2218yes—
60#10622641C2218yescomplemented
61#10622634C2218yescomplemented
62#10622629C2218yescomplemented
63#10622620C2218yescomplemented
64#10622612C2218yescomplemented
65C2×#66874C2211yescharacteristic
66C2×#66874C2211yescharacteristic
67C2×#66873C2211yescharacteristic
68C2×#66873C2211yescharacteristic
69C2×#66871C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71C2×#66871C2211yescharacteristic
72C2×#66871C2211yescharacteristic
73C2×C4⋊(C11⋊C8)C2211yescharacteristic
74C2×C4⋊(C11⋊C8)C2211yescharacteristic
75C2×C4⋊(C11⋊C8)C2211yescharacteristic
76C2×C4⋊(C11⋊C8)C2211yescharacteristic
77C22×Q8×C11—21no—
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11—21no—
80C22×D4×C11C2311yescharacteristic
81C23×C4×C11—21no—
82C23×C4×C11C2311yescharacteristic
83C22×C22⋊D11—21no—
84C22×D44C2311yescharacteristic
85C22×C4×D11—21no—
86C22×Dic22—21no—
87C22×Dic22C2311yescharacteristic
88C11×C4⋊Q8—22no—
89C11×C4⋊Q8C2314yes—
90C11×#126—28no—
91C11×#124—28no—
92C11×#124—22no—
93C11×#124C2314yes—
94C11×#123—28no—
95C11×C22⋊Q8—22no—
96C11×C22⋊Q8—28no—
97C11×C22⋊Q8C2314yes—
98C11×#121—22no—
99C11×#121C2314yes—
100C4×Q8×C11—22no—
101C4×Q8×C11C2314yes—
102C4×D4×C11—22no—
103C4×D4×C11C2314yes—
104C11×#117D414yes—
105C11×#117C2314yes—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4D411yescharacteristic
110C2×C11×C4⋊C4D411yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4D411yescharacteristic
119C2×C11×C22⋊C4D411yescharacteristic
120C2×C42×C11—21no—
121C2×C42×C11C2311yescharacteristic
122C2×C42×C11C2311yescharacteristic
123C2×C22⋊Dic11—21no—
124C2×#4326—42no—
125C2×#4326C2314yes—
126C2×#4325—42no—
127C2×#4325C2314yes—
128C2×#4324—42no—
129C2×#4324C2314yes—
130C2×#4323—42no—
131C2×#4323C2314yes—
132#66983—22no—
133#66983C2314yes—
134C2×(C2×D11)⋊C4—21no—
135C2×(C2×D11)⋊C4—21no—
136C2×(C2×D11)⋊C4—21no—
137C2×(C2×D11)⋊C4—21no—
138C2×C4⋊Dic11—21no—
139C2×C4⋊Dic11C2311yescharacteristic
140C2×C4⋊Dic11C2311yescharacteristic
141#66977—22no—
142#66977C2314yes—
143C2×Dic11⋊C4—21no—
144C2×Dic11⋊C4—21no—
145C2×C4×Dic11—21no—
146C2×#4318—42no—
147C2×#4318C2314yes—
148C22×C11⋊C8—42no—
149C22×C11⋊C8C2311yescharacteristic
150C22×C11⋊C8C2311yescharacteristic
151C22×C11⋊C8C2311yescharacteristic
152C22×C11⋊C8C2311yescharacteristic
153C22×C11⋊C8C2314yes—
154#66951—28no—
155#66949—28no—
156#66938—28no—
157#66936—28no—
158#66928—22no—
159#66928C2314yes—
160C4×D44—22no—
161C4×D44C2314yes—
162#66922—22no—
163#66922C2314yes—
164C4×Dic22—22no—
165C4×Dic22C2314yes—
166#66899C2314yes—
167#66899C2314yes—
168#66896C2314yes—
169#66896C2314yes—
170#66874C2314yes—
171#66874C2314yes—
172#66873C2314yes—
173#66873C2314yes—
174#66871C2314yes—
175#66871C2314yes—
176#66871C2314yes—
177#66871C2314yes—
178C4⋊(C11⋊C8)C2314yes—
179C4⋊(C11⋊C8)C2314yes—
180C4⋊(C11⋊C8)C2314yes—
181C4⋊(C11⋊C8)C2314yes—
182C2×#3262—111nomaximal, Sylow
183C24×C11—21no—
184C24×C11C2×D411yescharacteristic
185C23×D11—21no—
186C2×Q8×C11—21no—
187C2×Q8×C11—24no—
188C2×Q8×C11—22no—
189C2×Q8×C11—22no—
190C2×Q8×C11—82no—
191C2×Q8×C11C2412yes—
192C2×D4×C11—24no—
193C2×D4×C11—21no—
194C2×D4×C11—22no—
195C2×D4×C11—22no—
196C2×D4×C11—82no—
197C2×D4×C11C2412yes—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—24no—
204C22×C4×C11—82no—
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D412yes—
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2412yes—
212C22×C4×C11C2411yescharacteristic
213C2×C22⋊D11—24no—
214C2×C22⋊D11—82no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C2×D44—21no—
219C2×D44—22no—
220C2×D44—22no—
221C2×D44C2412yes—
222C2×C4×D11—24no—
223C2×C4×D11—82no—
224C2×Dic22—21no—
225C2×Dic22—24no—
226C2×Dic22—22no—
227C2×Dic22—22no—
228C2×Dic22—82no—
229C2×Dic22C2412yes—
230C11×C4⋊C4—24no—
231C11×C4⋊C4—24no—
232C11×C4⋊C4—24no—
233C11×C4⋊C4—21no—
234C11×C4⋊C4—21no—
235C11×C4⋊C4C2×D414yes—
236C11×C4⋊C4C2×D414yes—
237C11×C4⋊C4C2412yes—
238C11×C4⋊C4C2412yes—
239C11×C22⋊C4—24no—
240C11×C22⋊C4—24no—
241C11×C22⋊C4—24no—
242C11×C22⋊C4—24no—
243C11×C22⋊C4—24no—
244C11×C22⋊C4C2×D414yes—
245C11×C22⋊C4C2×D414yes—
246C42×C11—24no—
247C42×C11C2×D412yes—
248C42×C11C2×D412yes—
249C42×C11C2412yes—
250C42×C11C2412yes—
251C22⋊Dic11—24no—
252#4326—44no—
253#4325—44no—
254#4324—44no—
255#4323—44no—
256(C2×D11)⋊C4—24no—
257(C2×D11)⋊C4—24no—
258(C2×D11)⋊C4—24no—
259(C2×D11)⋊C4—24no—
260C4⋊Dic11—21no—
261C4⋊Dic11—21no—
262C4⋊Dic11—24no—
263C4⋊Dic11C2412yes—
264C4⋊Dic11C2412yes—
265Dic11⋊C4—24no—
266Dic11⋊C4—24no—
267C4×Dic11—24no—
268#4318—44no—
269C2×C11⋊C8—22no—
270C2×C11⋊C8—22no—
271C2×C11⋊C8—22no—
272C2×C11⋊C8—22no—
273C2×C11⋊C8—44no—
274C2×C11⋊C8C2412yes—
275C2×C11⋊C8C2412yes—
276C2×C11⋊C8C2412yes—
277C2×C11⋊C8C2412yes—
278C2×#542—111no—
279C2×#542D1111yescharacteristic, complemented
280#3262—1116no—
281C2×#477—111no—
282C2×#477—111no—
283C2×#474—111no—
284C2×#474—111no—
285C2×#468—111no—
286C2×#468—111no—
287C2×#467—111no—
288C2×#466—111no—
289C2×#464—111no—
290C2×#464—111no—
291C2×#463—111no—
292C2×#463—111no—
293C2×#424—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—
310Q8×C11—84no—
311D4×C11—22no—
312D4×C11—22no—
313D4×C11—42no—
314D4×C11—84no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—24no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—42no—
327C2×C4×C11—42no—
328C2×C4×C11—42no—
329C2×C4×C11—84no—
330C2×C4×C11C22×D412yes—
331C2×C4×C11C22×D412yes—
332C2×C4×C11C22×D412yes—
333C2×C4×C11C22×D412yes—
334C2×C4×C11C22×D412yes—
335C2×C4×C11C22×D411yescharacteristic
336C2×C4×C11H(5,𝔽2)12yes—
337C2×C4×C112−1+412yes—
338C2×C4×C11C2511yescharacteristic
339C22⋊D11—84no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—42no—
344C2×Dic11—42no—
345C2×Dic11—42no—
346D44—22no—
347D44—22no—
348D44—42no—
349C4×D11—84no—
350Dic22—22no—
351Dic22—22no—
352Dic22—42no—
353Dic22—84no—
354C11⋊C8—22no—
355C11⋊C8—22no—
356C11⋊C8—22no—
357C11⋊C8—22no—
358C22×Q16—111no—
359C22×SD16—111no—
360C22×SD16—111no—
361C22×D8—111no—
362C22×M16—111no—
363C23×C8—111no—
364#542—24no—
365#542—118no—
366#542—224no—
367#542C2×D1118yescomplemented
368C2×C4⋊Q8—111no—
369C2×C4⋊Q8C2×D1111yescharacteristic
370C2×#126—21no—
371C2×#126—221no—
372C2×#124—21no—
373C2×#124—111no—
374C2×#124—221no—
375C2×#124C2×D1111yescharacteristic
376C2×#123—21no—
377C2×#123—221no—
378C2×C22⋊Q8—21no—
379C2×C22⋊Q8—111no—
380C2×C22⋊Q8—221no—
381C2×C22⋊Q8C2×D1111yescharacteristic
382C2×#121—111no—
383C2×#121C2×D1111yescharacteristic
384C2×C4×Q8—111no—
385C2×C4×Q8C2×D1111yescharacteristic
386C2×C4×D4—111no—
387C2×C4×D4C2×D1111yescharacteristic
388C2×#117C2×D1111yescharacteristic
389#477—118no—
390#477—118no—
391#474—118no—
392#474—118no—
393#468—118no—
394#468—118no—
395#467—118no—
396#466—118no—
397#464—118no—
398#464—118no—
399#463—118no—
400#463—118no—
401C2×#107—111no—
402C2×#107—111no—
403C2×#107—111no—
404C2×#107—111no—
405#424—118no—
406C2×C4⋊C8—111no—
407C2×C4⋊C8—111no—
408C2×C4⋊C8—111no—
409C2×C4⋊C8—111no—
410C2×#103—111no—
411C2×#103—111no—
412C2×#103—111no—
413C2×#103—111no—
414C2×#102—111no—
415C2×#102—111no—
416C2×#102—111no—
417C2×#102—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#53712yes—
427C22×C11#57612yes—
428C22×C11#57812yes—
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#53712yes—
443C4×C11C2×H(5,𝔽2)11yescharacteristic
444C4×C11C2×2−1+411yescharacteristic
445Dic11—42no—
446Dic11—42no—
447Dic11—42no—
448C22×Q8—21no—
449C22×Q8—111no—
450C22×Q8—221no—
451C22×Q8C22×D1111yescharacteristic
452C22×D4—21no—
453C22×D4—111no—
454C22×D4—221no—
455C22×D4C22×D1111yescharacteristic
456C23×C4—21no—
457C23×C4—221no—
458C23×C4C22×D1111yescharacteristic
459C2×Q16—114no—
460C2×Q16—442no—
461C2×SD16—114no—
462C2×SD16—114no—
463C2×SD16—442no—
464C2×SD16—442no—
465C2×D8—114no—
466C2×D8—442no—
467C2×M16—114no—
468C2×M16—442no—
469C22×C8—111no—
470C22×C8—111no—
471C22×C8—111no—
472C22×C8—111no—
473C22×C8—114no—
474C22×C8—442no—
475C4⋊Q8—22no—
476C4⋊Q8—114no—
477C4⋊Q8—222no—
478C4⋊Q8C22×D1114yes—
479#126—28no—
480#126—228no—
481#124—28no—
482#124—22no—
483#124—114no—
484#124—228no—
485#124—222no—
486#124C22×D1114yes—
487#123—28no—
488#123—228no—
489C22⋊Q8—22no—
490C22⋊Q8—28no—
491C22⋊Q8—114no—
492C22⋊Q8—222no—
493C22⋊Q8—228no—
494C22⋊Q8C22×D1114yes—
495#121—22no—
496#121—114no—
497#121—222no—
498#121C22×D1114yes—
499C4×Q8—22no—
500C4×Q8—114no—
501C4×Q8—222no—
502C4×Q8C22×D1114yes—
503C4×D4—22no—
504C4×D4—114no—
505C4×D4—222no—
506C4×D4C22×D1114yes—
507#117C22⋊D1114yes—
508#117C22×D1114yes—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—111no—
513C2×C4⋊C4—111no—
514C2×C4⋊C4—221no—
515C2×C4⋊C4—221no—
516C2×C4⋊C4—221no—
517C2×C4⋊C4C22⋊D1111yescharacteristic
518C2×C4⋊C4C22⋊D1111yescharacteristic
519C2×C4⋊C4C22×D1111yescharacteristic
520C2×C4⋊C4C22×D1111yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—221no—
527C2×C22⋊C4—221no—
528C2×C22⋊C4—221no—
529C2×C22⋊C4—221no—
530C2×C22⋊C4—221no—
531C2×C22⋊C4C22⋊D1111yescharacteristic
532C2×C22⋊C4C22⋊D1111yescharacteristic
533C2×C42—21no—
534C2×C42—221no—
535C2×C42C22×D1111yescharacteristic
536C2×C42C22×D1111yescharacteristic
537#107—114no—
538#107—114no—
539#107—114no—
540#107—114no—
541C4⋊C8—114no—
542C4⋊C8—114no—
543C4⋊C8—114no—
544C4⋊C8—114no—
545#103—114no—
546#103—114no—
547#103—114no—
548#103—114no—
549#102—114no—
550#102—114no—
551#102—114no—
552#102—114no—
553C2×C11—42no—
554C2×C11—82no—
555C2×C11#326214yescomplemented
556C2×C11C2×#53711yescharacteristic
557C2×C11C2×#57611yescharacteristic
558C2×C11C2×#57811yescharacteristic
559D11—82no—
560C24—21no—
561C24—221no—
562C24C2×C22⋊D1111yescharacteristic
563C2×Q8—21no—
564C2×Q8—24no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—82no—
568C2×Q8—112no—
569C2×Q8—221no—
570C2×Q8—224no—
571C2×Q8—222no—
572C2×Q8—222no—
573C2×Q8—882no—
574C2×Q8C23×D1112yes—
575C2×D4—24no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—21no—
579C2×D4—82no—
580C2×D4—112no—
581C2×D4—224no—
582C2×D4—222no—
583C2×D4—222no—
584C2×D4—221no—
585C2×D4—882no—
586C2×D4C23×D1112yes—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—24no—
593C22×C4—82no—
594C22×C4—221no—
595C22×C4—221no—
596C22×C4—221no—
597C22×C4—224no—
598C22×C4—882no—
599C22×C4C2×C22⋊D1112yes—
600C22×C4C2×C22⋊D1111yescharacteristic
601C22×C4C2×C22⋊D1111yescharacteristic
602C22×C4C2×C22⋊D1111yescharacteristic
603C22×C4C2×C22⋊D1111yescharacteristic
604C22×C4C2×C22⋊D1111yescharacteristic
605C22×C4C23×D1112yes—
606C22×C4C23×D1111yescharacteristic
607Q16—444no—
608SD16—444no—
609SD16—444no—
610D8—444no—
611M16—444no—
612C2×C8—112no—
613C2×C8—112no—
614C2×C8—112no—
615C2×C8—112no—
616C2×C8—222no—
617C2×C8—222no—
618C2×C8—222no—
619C2×C8—222no—
620C2×C8—444no—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—112no—
627C4⋊C4—112no—
628C4⋊C4—221no—
629C4⋊C4—221no—
630C4⋊C4—224no—
631C4⋊C4—224no—
632C4⋊C4—224no—
633C4⋊C4C2×C22⋊D1114yes—
634C4⋊C4C2×C22⋊D1114yes—
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—
647C22⋊C4C2×C22⋊D1114yes—
648C22⋊C4C2×C22⋊D1114yes—
649C42—24no—
650C42—224no—
651C42C2×C22⋊D1112yes—
652C42C2×C22⋊D1112yes—
653C42C23×D1112yes—
654C42C23×D1112yes—
655C11C2×#326211yescharacteristic, 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—84no—
673Q8—222no—
674Q8—222no—
675Q8—442no—
676Q8—884no—
677D4—22no—
678D4—22no—
679D4—42no—
680D4—84no—
681D4—222no—
682D4—222no—
683D4—442no—
684D4—884no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—84no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—442no—
704C2×C4—442no—
705C2×C4—442no—
706C2×C4—884no—
707C2×C4#6704212yes—
708C2×C4#6704312yes—
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—222no—
717C8—222no—
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#1062336412yes—
733C22#1062336612yes—
734C22#1062336912yes—
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#1062336412yes—
748C4C2×#6704211yescharacteristic
749C4C2×#6704311yescharacteristic
750C2—42no—
751C2—82no—
752C2—882no—
753C2#1308007214yesdirect product factor
754C2C2×#1062336411yescharacteristic
755C2C2×#1062336611yescharacteristic
756C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#542C2
socleC23×C11C22×D4
prime radicalC2×#10622651C2
hypercenterC2×#542D11
hypocenterC11C2×#3262
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#10623065C2semidirect
2. #13080072C2direct (N × H)
3. C2×#10622634C2semidirect
4. C2×#10622704C2semidirect
5. C2×#10622620C2semidirect
6. C2×#10622700C2semidirect
7. C2×#10622662C2semidirect
8. C2×#10622655C2semidirect
9. C2×#10622664C2semidirect
11. C2×#10622641C2semidirect
12. C2×#10622667C2semidirect
13. C2×#10622629C2semidirect
14. C2×#10622670C2semidirect
15. C2×#10622612C2semidirect
16. C2×C11×#542C2semidirect
18. C11×#542C22semidirect
39. #10623065C22semidirect
52. #10622704C22semidirect
53. #10622700C22semidirect
54. #10622670C22semidirect
55. #10622667C22semidirect
56. #10622664C22semidirect
57. #10622662C22semidirect
58. #10622655C22semidirect
60. #10622641C22semidirect
61. #10622634C22semidirect
62. #10622629C22semidirect
63. #10622620C22semidirect
64. #10622612C22semidirect
279. C2×#542D11semidirect
367. #542C2×D11semidirect
555. C2×C11#3262semidirect
655. C11C2×#3262semidirect
753. C2#13080072direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230652
#130800722
C2×#106226342
C2×#106227042
C2×#106226202
C2×#106227002
C2×#106226622
C2×#106226552
C2×#106226642
C2×#106226512
C2×#106226412
C2×#106226672
C2×#106226292
C2×#106226702
C2×#106226122
C2×C11×#5422
C2×#326211