Finite Group Databasebeta

← C2×#13081691 #15634789

Subgroups — C2×#13081691 #15634789

Order 2816.

1938 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×#10623115C211yesmaximal, characteristic, complemented
2#13081691C2116yesmaximal, direct product factor
3C2×#10622673C211yesmaximal, characteristic, complemented
4C2×#10622699C211yesmaximal, characteristic, complemented
5C2×#10622672C211yesmaximal, characteristic
6C2×#10622641C211yesmaximal, characteristic, complemented
7C2×#10622667C211yesmaximal, characteristic, complemented
8C2×#10622644C211yesmaximal, characteristic, complemented
9C2×#10622703C211yesmaximal, characteristic, complemented
10C2×#10622629C211yesmaximal, characteristic
11C2×#10622670C211yesmaximal, characteristic
12C2×#10622637C211yesmaximal, characteristic, complemented
13C2×#10622631C211yesmaximal, characteristic, complemented
14C2×#10622639C211yesmaximal, characteristic, complemented
15C2×C4×#4326C211yesmaximal, characteristic, complemented
16C2×C11×#556C211yesmaximal, characteristic, complemented
17C11×#556—24no—
18C11×#556C2218yescomplemented
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C11×#126—21no—
21C2×C11×#126—21no—
22C2×C11×#124C2211yescharacteristic
23C2×C11×#124C2211yescharacteristic
24C2×C11×C22⋊Q8—21no—
25C2×C4×Q8×C11C2211yescharacteristic
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C2×C11×#117—21no—
30C2×#66999—21no—
31C22×#4326C2211yescharacteristic
32C22×#4326C2211yescharacteristic
33C22×#4326C2211yescharacteristic
34C22×#4326C2211yescharacteristic
35C22×#4325C2211yescharacteristic
36C22×#4325C2211yescharacteristic
37C22×#4324C2211yescharacteristic
38C22×#4324C2211yescharacteristic
39C22×#4323C2211yescharacteristic
40#10623115—24no—
41#10623115C2218yescomplemented
42C2×#66951—21no—
43C2×#66951—21no—
44C2×#66945—21no—
45C2×#66928C2211yescharacteristic
46C2×#66928C2211yescharacteristic
47C2×C4×D44C2211yescharacteristic
48C2×#66922C2211yescharacteristic
49C2×C4×Dic22C2211yescharacteristic
50C2×C4×Dic22C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52C2×#66899C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54#10622703C2218yescomplemented
55#10622699C2218yescomplemented
56#10622673C2218yescomplemented
57#10622672C2218yes—
58#10622670C2218yes—
59#10622667C2218yescomplemented
60#10622644C2218yescomplemented
61C4×#4326C2218yescomplemented
62#10622641C2218yescomplemented
63#10622639C2218yescomplemented
64#10622637C2218yescomplemented
65#10622631C2218yescomplemented
66#10622629C2218yes—
67C2×#66874C2211yescharacteristic
68C2×#66874C2211yescharacteristic
69C2×#66873C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71C2×C4⋊(C11⋊C8)C2211yescharacteristic
72C2×C4⋊(C11⋊C8)C2211yescharacteristic
73C2×C4⋊(C11⋊C8)C2211yescharacteristic
74C2×#66867C2211yescharacteristic
75C2×#66867C2211yescharacteristic
76C2×C4×C11⋊C8C2211yescharacteristic
77C22×Q8×C11D411yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C23×C4×C11—21no—
82C22×D44C2311yescharacteristic
83C22×C4×D11—21no—
84C22×Dic22C2311yescharacteristic
85C22×Dic22C2311yescharacteristic
86C11×C4⋊Q8—22no—
87C11×C4⋊Q8C2314yes—
88C11×#126—28no—
89C11×#126—28no—
90C11×#124—22no—
91C11×#124—22no—
92C11×#124C2314yes—
93C11×#124C2314yes—
94C11×C22⋊Q8—28no—
95C4×Q8×C11—22no—
96C4×Q8×C11—22no—
97C4×Q8×C11D414yes—
98C4×Q8×C11C2314yes—
99C4×Q8×C11C2314yes—
100C4×Q8×C11C2314yes—
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⋊C4D411yescharacteristic
109C2×C11×C4⋊C4D411yescharacteristic
110C2×C11×C4⋊C4D411yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C42×C11—21no—
118C2×C42×C11—21no—
119C2×C42×C11C2311yescharacteristic
120C2×C42×C11C2311yescharacteristic
121C2×C42×C11C2311yescharacteristic
122#66999—28no—
123C2×#4326—24no—
124C2×#4326—42no—
125C2×#4326—42no—
126C2×#4326—42no—
127C2×#4326C2314yes—
128C2×#4326C2314yes—
129C2×#4326C2314yes—
130C2×#4326C2314yes—
131C2×#4325—24no—
132C2×#4325—42no—
133C2×#4325C2314yes—
134C2×#4325C2314yes—
135C2×#4324—24no—
136C2×#4324—42no—
137C2×#4324C2314yes—
138C2×#4324C2314yes—
139C2×#4323—42no—
140C2×#4323C2314yes—
141C2×(C2×D11)⋊C4—21no—
142C2×(C2×D11)⋊C4—21no—
143C2×(C2×D11)⋊C4—21no—
144C2×(C2×D11)⋊C4—21no—
145C2×(C2×D11)⋊C4—21no—
146C2×C4⋊Dic11—21no—
147C2×C4⋊Dic11—21no—
148C2×C4⋊Dic11C2311yescharacteristic
149C2×Dic11⋊C4—21no—
150C2×Dic11⋊C4—21no—
151C2×C4×Dic11—21no—
152C2×C4×Dic11—21no—
153C22×C11⋊C8C2311yescharacteristic
154C22×C11⋊C8C2311yescharacteristic
155C22×C11⋊C8C2311yescharacteristic
156C22×C11⋊C8C2311yescharacteristic
157#66951—28no—
158#66951—28no—
159#66945—28no—
160#66928—22no—
161#66928—22no—
162#66928C2314yes—
163#66928C2314yes—
164C4×D44—22no—
165C4×D44C2314yes—
166#66922—22no—
167#66922C2314yes—
168C4×Dic22—22no—
169C4×Dic22—22no—
170C4×Dic22C2314yes—
171C4×Dic22C2314yes—
172#66899C2314yes—
173#66899C2314yes—
174#66896C2314yes—
175#66874C2314yes—
176#66874C2314yes—
177#66873C2314yes—
178#66871C2314yes—
179C4⋊(C11⋊C8)C2314yes—
180C4⋊(C11⋊C8)C2314yes—
181C4⋊(C11⋊C8)C2314yes—
182#66867C2314yes—
183#66867C2314yes—
184C4×C11⋊C8C2314yes—
185C2×#3402—111nomaximal, Sylow
186C24×C11—21no—
187C23×D11—21no—
188C2×Q8×C11—21no—
189C2×Q8×C11—21no—
190C2×Q8×C11—22no—
191C2×Q8×C11—22no—
192C2×Q8×C11—22no—
193C2×Q8×C11—22no—
194C2×Q8×C11—42no—
195C2×Q8×C11C2×D414yes—
196C2×Q8×C11C2412yes—
197C2×Q8×C11C2412yes—
198C2×D4×C11—21no—
199C2×D4×C11—22no—
200C2×D4×C11—22no—
201C2×D4×C11C2412yes—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—24no—
206C22×C4×C11—44no—
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2411yescharacteristic
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C2×D44—21no—
218C2×D44—22no—
219C2×D44—22no—
220C2×D44C2412yes—
221C2×C4×D11—24no—
222C2×C4×D11—44no—
223C2×Dic22—21no—
224C2×Dic22—21no—
225C2×Dic22—22no—
226C2×Dic22—22no—
227C2×Dic22—22no—
228C2×Dic22—22no—
229C2×Dic22C2412yes—
230C2×Dic22C2412yes—
231C11×C4⋊C4—24no—
232C11×C4⋊C4—24no—
233C11×C4⋊C4—24no—
234C11×C4⋊C4—24no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4C2×D414yes—
237C11×C4⋊C4C2×D414yes—
238C11×C4⋊C4C2×D414yes—
239C11×C4⋊C4C2412yes—
240C11×C22⋊C4—24no—
241C11×C22⋊C4—24no—
242C11×C22⋊C4—24no—
243C11×C22⋊C4—24no—
244C11×C22⋊C4—24no—
245C42×C11—24no—
246C42×C11—24no—
247C42×C11C2×D412yes—
248C42×C11C2×D412yes—
249C42×C11C2×D412yes—
250C42×C11C2412yes—
251C42×C11C2412yes—
252C42×C11C2412yes—
253#4326—28no—
254#4326—44no—
255#4326—44no—
256#4326—44no—
257#4325—28no—
258#4325—44no—
259#4324—28no—
260#4324—44no—
261#4323—44no—
262(C2×D11)⋊C4—24no—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—24no—
265(C2×D11)⋊C4—24no—
266(C2×D11)⋊C4—24no—
267C4⋊Dic11—21no—
268C4⋊Dic11—24no—
269C4⋊Dic11—24no—
270C4⋊Dic11C2412yes—
271Dic11⋊C4—24no—
272Dic11⋊C4—24no—
273C4×Dic11—24no—
274C4×Dic11—24no—
275C2×C11⋊C8—22no—
276C2×C11⋊C8—22no—
277C2×C11⋊C8—22no—
278C2×C11⋊C8#4114yes—
279C2×C11⋊C8C2412yes—
280C2×C11⋊C8C2412yes—
281C2×C11⋊C8C2412yes—
282C2×C11⋊C8C2412yes—
283C2×#556—111no—
284C2×#556D1111yescharacteristic, complemented
285#3402—1116no—
286C2×#497—111no—
287C2×#497—111no—
288C2×#495—111no—
289C2×#464—111no—
290C2×#464—111no—
291C2×#462—111no—
292C2×#462—111no—
293C2×#463—111no—
294C2×#463—111no—
295C2×#446—111no—
296C2×#440—111no—
297C2×#440—111no—
298C2×C4×Q16—111no—
299C23×C11—22no—
300C23×C11—42no—
301C23×C11—42no—
302C23×C11—42no—
303C23×C11C22×D411yescharacteristic
304C22×D11—22no—
305C22×D11—42no—
306C22×D11—42no—
307C22×D11—42no—
308Q8×C11—22no—
309Q8×C11—22no—
310Q8×C11—22no—
311Q8×C11—22no—
312Q8×C11—44no—
313Q8×C11—42no—
314Q8×C11—42no—
315D4×C11—22no—
316D4×C11—22no—
317D4×C11—42no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
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×D412yes—
337C2×C4×C11C22×D411yescharacteristic
338C2×C4×C11C2×#4112yes—
339C2×C4×C11H(5,𝔽2)12yes—
340C2×C4×C11C2511yescharacteristic
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—22no—
354Dic22—22no—
355Dic22—42no—
356Dic22—42no—
357C11⋊C8—22no—
358C11⋊C8—22no—
359C11⋊C8—22no—
360C11⋊C8C2×#4114yes—
361C22×Q16—111no—
362C22×Q16—111no—
363C22×Q16—111no—
364C22×Q16—111no—
365C22×SD16—111no—
366C22×SD16—111no—
367C22×SD16—111no—
368C22×SD16—111no—
369C22×D8—111no—
370#556—24no—
371#556—118no—
372#556—224no—
373#556C2×D1118yescomplemented
374C2×C4⋊Q8—111no—
375C2×C4⋊Q8C2×D1111yescharacteristic
376C2×#126—21no—
377C2×#126—21no—
378C2×#126—221no—
379C2×#126—221no—
380C2×#124—111no—
381C2×#124—111no—
382C2×#124C2×D1111yescharacteristic
383C2×#124C2×D1111yescharacteristic
384C2×C22⋊Q8—21no—
385C2×C22⋊Q8—221no—
386C2×C4×Q8—111no—
387C2×C4×Q8—111no—
388C2×C4×Q8C2×D1111yescharacteristic
389C2×C4×Q8C2×D1111yescharacteristic
390C2×C4×Q8C2×D1111yescharacteristic
391C2×C4×D4—111no—
392C2×C4×D4C2×D1111yescharacteristic
393C2×#117—21no—
394C2×#117—221no—
395#497—118no—
396#497—118no—
397#495—118no—
398#464—118no—
399#464—118no—
400#463—118no—
401#463—118no—
402#462—118no—
403#462—118no—
404#446—118no—
405#440—118no—
406#440—118no—
407C4×Q16—118no—
408C2×#107—111no—
409C2×C4⋊C8—111no—
410C2×C4⋊C8—111no—
411C2×C4⋊C8—111no—
412C2×#103—111no—
413C2×#103—111no—
414C2×#103—111no—
415C2×#103—111no—
416C2×#102—111no—
417C2×#102—111no—
418C2×#97—111no—
419C2×#97—111no—
420C2×C4×C8—111no—
421C22×C11—42no—
422C22×C11—42no—
423C22×C11—42no—
424C22×C11—84no—
425C22×C11#55012yes—
426C22×C11#57512yes—
427C22×C11#57812yes—
428C22×C11C23×D411yescharacteristic
429C2×D11—42no—
430C2×D11—42no—
431C2×D11—42no—
432C2×D11—84no—
433C4×C11—22no—
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#55012yes—
443C4×C11C22×#4111yescharacteristic
444C4×C11C2×H(5,𝔽2)11yescharacteristic
445Dic11—42no—
446Dic11—42no—
447Dic11—42no—
448C22×Q8—111no—
449C22×Q8—111no—
450C22×Q8C22⋊D1111yescharacteristic
451C22×Q8C22×D1111yescharacteristic
452C22×Q8C22×D1111yescharacteristic
453C22×D4—111no—
454C22×D4C22×D1111yescharacteristic
455C23×C4—21no—
456C23×C4—221no—
457C2×Q16—114no—
458C2×Q16—114no—
459C2×Q16—114no—
460C2×Q16—114no—
461C2×Q16—224no—
462C2×Q16—442no—
463C2×Q16—442no—
464C2×Q16—442no—
465C2×SD16—114no—
466C2×SD16—114no—
467C2×SD16—114no—
468C2×SD16—114no—
469C2×SD16—224no—
470C2×SD16—224no—
471C2×SD16—442no—
472C2×SD16—442no—
473C2×D8—114no—
474C2×D8—442no—
475C22×C8—111no—
476C22×C8—111no—
477C22×C8—111no—
478C22×C8—111no—
479C4⋊Q8—22no—
480C4⋊Q8—114no—
481C4⋊Q8—222no—
482C4⋊Q8C22×D1114yes—
483#126—28no—
484#126—28no—
485#126—228no—
486#126—228no—
487#124—22no—
488#124—22no—
489#124—114no—
490#124—114no—
491#124—222no—
492#124—222no—
493#124C22×D1114yes—
494#124C22×D1114yes—
495C22⋊Q8—28no—
496C22⋊Q8—228no—
497C4×Q8—22no—
498C4×Q8—22no—
499C4×Q8—114no—
500C4×Q8—114no—
501C4×Q8—222no—
502C4×Q8—222no—
503C4×Q8C22⋊D1114yes—
504C4×Q8C22×D1114yes—
505C4×Q8C22×D1114yes—
506C4×Q8C22×D1114yes—
507C4×D4—22no—
508C4×D4—114no—
509C4×D4—222no—
510C4×D4C22×D1114yes—
511#117—28no—
512#117—228no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—111no—
518C2×C4⋊C4—221no—
519C2×C4⋊C4—221no—
520C2×C4⋊C4—221no—
521C2×C4⋊C4—221no—
522C2×C4⋊C4C22⋊D1111yescharacteristic
523C2×C4⋊C4C22⋊D1111yescharacteristic
524C2×C4⋊C4C22⋊D1111yescharacteristic
525C2×C4⋊C4C22×D1111yescharacteristic
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—221no—
532C2×C22⋊C4—221no—
533C2×C22⋊C4—221no—
534C2×C22⋊C4—221no—
535C2×C22⋊C4—221no—
536C2×C42—21no—
537C2×C42—21no—
538C2×C42—221no—
539C2×C42—221no—
540C2×C42C22×D1111yescharacteristic
541C2×C42C22×D1111yescharacteristic
542C2×C42C22×D1111yescharacteristic
543#107—114no—
544C4⋊C8—114no—
545C4⋊C8—114no—
546C4⋊C8—114no—
547#103—114no—
548#103—114no—
549#103—114no—
550#103—114no—
551#102—114no—
552#102—114no—
553#97—114no—
554#97—114no—
555C4×C8—114no—
556C2×C11—82no—
557C2×C11#340214yescomplemented
558C2×C11C2×#55011yescharacteristic
559C2×C11C2×#57511yescharacteristic
560C2×C11C2×#57811yescharacteristic
561D11—82no—
562C24—21no—
563C24—221no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—42no—
571C2×Q8—112no—
572C2×Q8—112no—
573C2×Q8—221no—
574C2×Q8—221no—
575C2×Q8—222no—
576C2×Q8—222no—
577C2×Q8—222no—
578C2×Q8—222no—
579C2×Q8C2×C22⋊D1114yes—
580C2×Q8C23×D1112yes—
581C2×Q8C23×D1112yes—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—21no—
585C2×D4—112no—
586C2×D4—222no—
587C2×D4—222no—
588C2×D4—221no—
589C2×D4C23×D1112yes—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—24no—
594C22×C4—44no—
595C22×C4—221no—
596C22×C4—221no—
597C22×C4—221no—
598C22×C4—224no—
599C22×C4—444no—
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×C4C23×D1111yescharacteristic
607Q16—228no—
608Q16—444no—
609Q16—444no—
610Q16—444no—
611SD16—228no—
612SD16—228no—
613SD16—444no—
614SD16—444no—
615D8—444no—
616C2×C8—114no—
617C2×C8—112no—
618C2×C8—112no—
619C2×C8—112no—
620C2×C8—112no—
621C2×C8—222no—
622C2×C8—222no—
623C2×C8—222no—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—24no—
628C4⋊C4—21no—
629C4⋊C4—112no—
630C4⋊C4—221no—
631C4⋊C4—224no—
632C4⋊C4—224no—
633C4⋊C4—224no—
634C4⋊C4—224no—
635C4⋊C4C2×C22⋊D1114yes—
636C4⋊C4C2×C22⋊D1114yes—
637C4⋊C4C2×C22⋊D1114yes—
638C4⋊C4C23×D1112yes—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—24no—
644C22⋊C4—224no—
645C22⋊C4—224no—
646C22⋊C4—224no—
647C22⋊C4—224no—
648C22⋊C4—224no—
649C42—24no—
650C42—24no—
651C42—224no—
652C42—224no—
653C42C2×C22⋊D1112yes—
654C42C2×C22⋊D1112yes—
655C42C2×C22⋊D1112yes—
656C42C23×D1112yes—
657C42C23×D1112yes—
658C42C23×D1112yes—
659C11C2×#340211yescharacteristic, complemented, Sylow
660C23—22no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—222no—
665C23—442no—
666C23—442no—
667C23—442no—
668C23C22×C22⋊D1111yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8—22no—
673Q8—44no—
674Q8—42no—
675Q8—42no—
676Q8—222no—
677Q8—222no—
678Q8—222no—
679Q8—222no—
680Q8—442no—
681Q8—442no—
682D4—22no—
683D4—22no—
684D4—42no—
685D4—222no—
686D4—222no—
687D4—442no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—48no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—448no—
705C2×C4—442no—
706C2×C4—442no—
707C2×C4—442no—
708C2×C4#41×D1112yes—
709C2×C4#6704212yes—
710C2×C4C22×C22⋊D1112yes—
711C2×C4C22×C22⋊D1112yes—
712C2×C4C22×C22⋊D1112yes—
713C2×C4C22×C22⋊D1112yes—
714C2×C4C22×C22⋊D1112yes—
715C2×C4C22×C22⋊D1112yes—
716C2×C4C22×C22⋊D1111yescharacteristic
717C2×C4C24×D1111yescharacteristic
718C8—114no—
719C8—222no—
720C8—222no—
721C8—222no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—442no—
727C22—442no—
728C22—442no—
729C22—884no—
730C22#1062335312yes—
731C22#1062336512yes—
732C22#1062336912yes—
733C22C23×C22⋊D1111yescharacteristic
734C4—22no—
735C4—22no—
736C4—22no—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—442no—
744C4—442no—
745C4—442no—
746C4#1062336512yes—
747C4C2×#41×D1111yescharacteristic
748C4C2×#6704211yescharacteristic
749C2—82no—
750C2—882no—
751C2#1308169114yesdirect product factor
752C2C2×#1062336511yescharacteristic
753C2C2×#1062335311yescharacteristic
754C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#556C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenterC2×#556D11
hypocenterC11C2×#3402
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×#10623115C2semidirect
2. #13081691C2direct (N × H)
3. C2×#10622673C2semidirect
4. C2×#10622699C2semidirect
6. C2×#10622641C2semidirect
7. C2×#10622667C2semidirect
8. C2×#10622644C2semidirect
9. C2×#10622703C2semidirect
12. C2×#10622637C2semidirect
13. C2×#10622631C2semidirect
14. C2×#10622639C2semidirect
15. C2×C4×#4326C2semidirect
16. C2×C11×#556C2semidirect
18. C11×#556C22semidirect
41. #10623115C22semidirect
54. #10622703C22semidirect
55. #10622699C22semidirect
56. #10622673C22semidirect
59. #10622667C22semidirect
60. #10622644C22semidirect
61. C4×#4326C22semidirect
62. #10622641C22semidirect
63. #10622639C22semidirect
64. #10622637C22semidirect
65. #10622631C22semidirect
284. C2×#556D11semidirect
373. #556C2×D11semidirect
557. C2×C11#3402semidirect
659. C11C2×#3402semidirect
751. C2#13081691direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231152
#130816912
C2×#106226732
C2×#106226992
C2×#106226722
C2×#106226412
C2×#106226672
C2×#106226442
C2×#106227032
C2×#106226292
C2×#106226702
C2×#106226372
C2×#106226312
C2×#106226392
C2×C4×#43262
C2×C11×#5562
C2×#340211