Finite Group Databasebeta

← C2×#13079970 #15626597

Subgroups — C2×#13079970 #15626597

Order 2816.

1962 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×#10623111C211yesmaximal, characteristic, complemented
2C2×#10623222C211yesmaximal, characteristic, complemented
3#13079970C2116yesmaximal, direct product factor
4C2×#10622490C211yesmaximal, characteristic, complemented
5C2×#10622484C211yesmaximal, characteristic, complemented
6C2×#10622679C211yesmaximal, characteristic, complemented
7C2×#10622426C211yesmaximal, characteristic, complemented
8C2×#10622496C211yesmaximal, characteristic
9C2×#10622420C211yesmaximal, characteristic, complemented
10C2×#10622477C211yesmaximal, characteristic, complemented
11C2×#10622411C211yesmaximal, characteristic, complemented
12C2×#10622641C211yesmaximal, characteristic, complemented
13C2×#10622432C211yesmaximal, characteristic, complemented
14C2×#10622457C211yesmaximal, characteristic, complemented
15C2×D11×C4⋊C8C211yesmaximal, characteristic, complemented
16C2×C11×#479C211yesmaximal, characteristic, complemented
17C2×C11×#125C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×#67000C2211yescharacteristic
20C2×#66999C2211yescharacteristic
21C22×#4326C2211yescharacteristic
22C22×#4325C2211yescharacteristic
23C22×D88C2211yescharacteristic
24C22×#4314C2211yescharacteristic
25C22×C8×D11C2211yescharacteristic
26C22×C8×D11C2211yescharacteristic
27#10623222—24no—
28#10623222C2218yescomplemented
29#10623111—24no—
30#10623111C2218yescomplemented
31C2×#66951—21no—
32C2×#66951—21no—
33C2×#66950C2211yescharacteristic
34C2×#66948C2211yescharacteristic
35C2×#66948C2211yescharacteristic
36C2×#66947—21no—
37C2×#66947—21no—
38C2×#66946—21no—
39C2×#66946C2211yescharacteristic
40C2×#66945—21no—
41C2×#66943C2211yescharacteristic
42C2×#66940C2211yescharacteristic
43C2×#66928C2211yescharacteristic
44C2×C4×D44—21no—
45C2×C4×D44C2211yescharacteristic
46C2×#66925—21no—
47C2×C42×D11C2211yescharacteristic
48C11×#479C2218yescomplemented
49C2×C11×#107C2211yescharacteristic
50C2×C11×#106C2211yescharacteristic
51C2×C11×C4⋊C8C2211yescharacteristic
52C2×C11×#103C2211yescharacteristic
53C2×C11×#103C2211yescharacteristic
54C2×#66885C2211yescharacteristic
55C2×#66880C2211yescharacteristic
56C2×Dic11⋊C8C2211yescharacteristic
57C2×Dic11⋊C8C2211yescharacteristic
58#10622679C2218yescomplemented
59#10622641C2218yescomplemented
60C2×#66874C2211yescharacteristic
61C2×#66873C2211yescharacteristic
62C2×#66873C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66872C2211yescharacteristic
65C2×#66871C2211yescharacteristic
66C2×C4⋊(C11⋊C8)C2211yescharacteristic
67#10622496C2218yes—
68#10622490C2218yescomplemented
69#10622484C2218yescomplemented
70#10622477C2218yescomplemented
71#10622457C2218yescomplemented
72D11×C4⋊C8C2218yescomplemented
73#10622432C2218yescomplemented
74#10622426C2218yescomplemented
75#10622420C2218yescomplemented
76#10622411C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D44—21no—
79C22×D44—21no—
80C22×D44C2311yescharacteristic
81C22×D44C2311yescharacteristic
82C22×C4×D11—21no—
83C22×C4×D11—21no—
84C22×C4×D11D411yescharacteristic
85C22×C4×D11D411yescharacteristic
86C22×C4×D11C2311yescharacteristic
87C22×Dic22C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C11×#125—22no—
91C11×#125C2314yes—
92C4×Q8×C11—22no—
93C4×Q8×C11C2314yes—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C42×C11—21no—
101C2×C42×C11C2311yescharacteristic
102#67000—22no—
103#67000C2314yes—
104#66999—22no—
105#66999C2314yes—
106C2×#4326—42no—
107C2×#4326C2314yes—
108C2×#4325—42no—
109C2×#4325C2314yes—
110C2×(C2×D11)⋊C4—21no—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×C4⋊Dic11—21no—
121C2×C4⋊Dic11—21no—
122C2×C4⋊Dic11C2311yescharacteristic
123C2×Dic11⋊C4—21no—
124C2×Dic11⋊C4—21no—
125C2×Dic11⋊C4—21no—
126C2×C4×Dic11—21no—
127C2×C4×Dic11D411yescharacteristic
128C2×C4×Dic11D411yescharacteristic
129C2×C4×Dic11C2311yescharacteristic
130C22×C11⋊C8C2311yescharacteristic
131C22×C11⋊C8C2311yescharacteristic
132C2×D88—42no—
133C2×D88C2314yes—
134C2×#4314—42no—
135C2×#4314C2314yes—
136C2×C8×D11—42no—
137C2×C8×D11—42no—
138C2×C8×D11C2314yes—
139C2×C8×D11C2314yes—
140#66951—28no—
141#66951—28no—
142#66950—22no—
143#66950C2314yes—
144#66948—22no—
145#66948—22no—
146#66948C2314yes—
147#66948C2314yes—
148#66947—28no—
149#66947—28no—
150#66946—28no—
151#66946—22no—
152#66946C2314yes—
153#66945—28no—
154#66943—22no—
155#66943C2314yes—
156#66940—22no—
157#66940C2314yes—
158#66928—22no—
159#66928C2314yes—
160C4×D44—28no—
161C4×D44—22no—
162C4×D44C2314yes—
163#66925—28no—
164C42×D11D414yes—
165C42×D11C2314yes—
166C11×#107C2314yes—
167C11×#106C2314yes—
168C11×C4⋊C8C2314yes—
169C11×#103C2314yes—
170C11×#103C2314yes—
171#66885C2314yes—
172#66880C2314yes—
173Dic11⋊C8C2314yes—
174Dic11⋊C8C2314yes—
175#66874C2314yes—
176#66873C2314yes—
177#66873C2314yes—
178#66873C2314yes—
179#66872C2314yes—
180#66871C2314yes—
181C4⋊(C11⋊C8)C2314yes—
182C2×#3250—111nomaximal, Sylow
183C23×D11—21no—
184C23×D11—21no—
185C23×D11C2×D411yescharacteristic
186C2×Q8×C11—21no—
187C2×Q8×C11—22no—
188C2×Q8×C11—22no—
189C2×Q8×C11C2412yes—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2411yescharacteristic
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11C2×D411yescharacteristic
200C22×Dic11C2×D411yescharacteristic
201C22×Dic11C2×D411yescharacteristic
202C2×D44—24no—
203C2×D44—24no—
204C2×D44—21no—
205C2×D44—21no—
206C2×D44—22no—
207C2×D44—22no—
208C2×D44—22no—
209C2×D44—22no—
210C2×D44—44no—
211C2×D44—44no—
212C2×D44C2412yes—
213C2×D44C2412yes—
214C2×C4×D11—24no—
215C2×C4×D11—24no—
216C2×C4×D11—24no—
217C2×C4×D11—22no—
218C2×C4×D11—22no—
219C2×C4×D11—42no—
220C2×C4×D11—44no—
221C2×C4×D11—44no—
222C2×C4×D11C2×D412yes—
223C2×C4×D11C2×D414yes—
224C2×C4×D11C2×D414yes—
225C2×C4×D11C2412yes—
226C2×Dic22—21no—
227C2×Dic22—22no—
228C2×Dic22—22no—
229C2×Dic22C2412yes—
230C2×C8×C11—22no—
231C2×C8×C11—22no—
232C2×C8×C11C2412yes—
233C2×C8×C11C2412yes—
234C11×C4⋊C4—21no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—24no—
237C11×C4⋊C4—21no—
238C11×C4⋊C4—24no—
239C11×C4⋊C4—24no—
240C11×C4⋊C4C2412yes—
241C11×C4⋊C4C2412yes—
242C11×C4⋊C4C2412yes—
243C42×C11—24no—
244C42×C11C2×D412yes—
245C42×C11C2412yes—
246#4326—44no—
247#4325—44no—
248(C2×D11)⋊C4—24no—
249(C2×D11)⋊C4—24no—
250(C2×D11)⋊C4—24no—
251(C2×D11)⋊C4—24no—
252(C2×D11)⋊C4—24no—
253(C2×D11)⋊C4—24no—
254(C2×D11)⋊C4—24no—
255(C2×D11)⋊C4—24no—
256(C2×D11)⋊C4—24no—
257(C2×D11)⋊C4—24no—
258C4⋊Dic11—24no—
259C4⋊Dic11—24no—
260C4⋊Dic11—21no—
261C4⋊Dic11C2412yes—
262Dic11⋊C4—24no—
263Dic11⋊C4—24no—
264Dic11⋊C4—24no—
265C4×Dic11—24no—
266C4×Dic11C2×D412yes—
267C4×Dic11C2×D414yes—
268C4×Dic11C2×D414yes—
269C4×Dic11C2412yes—
270C2×C11⋊C8—22no—
271C2×C11⋊C8—22no—
272C2×C11⋊C8C2412yes—
273C2×C11⋊C8C2412yes—
274D88—44no—
275#4314—44no—
276C8×D11—44no—
277C8×D11—44no—
278C2×#529—111no—
279C2×#529—111no—
280#3250—1116no—
281C2×#479—111no—
282C2×#479D1111yescharacteristic, complemented
283C2×#478—111no—
284C2×#478—111no—
285C2×#467—111no—
286C2×#466—111no—
287C2×#465—111no—
288C2×#465—111no—
289C2×#464—111no—
290C2×#464—111no—
291C2×#463—111no—
292C2×#463—111no—
293C22×C4⋊C8—111no—
294C23×C11C22×D411yescharacteristic
295C22×D11—22no—
296C22×D11—22no—
297C22×D11—22no—
298C22×D11—22no—
299C22×D11—42no—
300C22×D11—42no—
301C22×D11—42no—
302C22×D11—42no—
303C22×D11—42no—
304C22×D11—42no—
305C22×D11#13514yes—
306C22×D11C22×D412yes—
307Q8×C11—22no—
308Q8×C11—22no—
309Q8×C11—42no—
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—42no—
317C2×C4×C11—42no—
318C2×C4×C11—42no—
319C2×C4×C11—42no—
320C2×C4×C11C22×D412yes—
321C2×C4×C11C22×D412yes—
322C2×C4×C11C22×D411yescharacteristic
323C2×C4×C11H(5,𝔽2)12yes—
324C2×C4×C112−1+412yes—
325C2×C4×C11C2511yescharacteristic
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11C22×D412yes—
334C2×Dic11C22×D412yes—
335C2×Dic11C22×D412yes—
336D44—22no—
337D44—22no—
338D44—22no—
339D44—22no—
340D44—48no—
341D44—48no—
342D44—42no—
343D44—42no—
344C4×D11—28no—
345C4×D11—24no—
346C4×D11—22no—
347C4×D11—22no—
348C4×D11—44no—
349C4×D11—48no—
350C4×D11—48no—
351Dic22—22no—
352Dic22—22no—
353Dic22—42no—
354C8×C11—22no—
355C8×C11—22no—
356C11⋊C8—22no—
357C11⋊C8—22no—
358C22×Q16—111no—
359C22×SD16—111no—
360C22×SD16—111no—
361C22×D8—111no—
362C23×C8—111no—
363C23×C8—111no—
364#529—118no—
365#529—118no—
366#529—224no—
367#529—224no—
368C2×#126—221no—
369C2×#126—221no—
370C2×#125—111no—
371C2×#125C2×D1111yescharacteristic
372C2×#124—111no—
373C2×#124—111no—
374C2×#123—221no—
375C2×#123—221no—
376C2×C22⋊Q8—111no—
377C2×C22⋊Q8—111no—
378C2×#121—111no—
379C2×#121—111no—
380C2×C4×Q8—111no—
381C2×C4×Q8C2×D1111yescharacteristic
382C2×C4×D4—111no—
383C2×C4×D4—111no—
384C2×C4×D4—221no—
385C2×C4×D4—221no—
386C2×#117—221no—
387C2×#117—221no—
388C22×C42—111no—
389#479—118no—
390#479C2×D1118yescomplemented
391#478—118no—
392#478—118no—
393#467—118no—
394#466—118no—
395#465—118no—
396#465—118no—
397#464—118no—
398#464—118no—
399#463—118no—
400#463—118no—
401C2×#107—111no—
402C2×#107C2×D1111yescharacteristic
403C2×#106—111no—
404C2×#106C2×D1111yescharacteristic
405C2×C4⋊C8—111no—
406C2×C4⋊C8—111no—
407C2×C4⋊C8—111no—
408C2×C4⋊C8—118no—
409C2×C4⋊C8C2×D1111yescharacteristic
410C2×#103—111no—
411C2×#103—111no—
412C2×#103C2×D1111yescharacteristic
413C2×#103C2×D1111yescharacteristic
414C2×#102—111no—
415C2×#102—111no—
416C2×#102—111no—
417C2×#102—111no—
418C22×C11#53712yes—
419C22×C11C2×#13512yes—
420C22×C11#57512yes—
421C22×C11C23×D411yescharacteristic
422C2×D11—22no—
423C2×D11—28no—
424C2×D11—22no—
425C2×D11—42no—
426C2×D11—42no—
427C2×D11—42no—
428C2×D11—42no—
429C2×D11—42no—
430C2×D11—42no—
431C2×D11—84no—
432C2×D11—84no—
433C2×D11C2×#13514yes—
434C4×C11—22no—
435C4×C11—22no—
436C4×C11—42no—
437C4×C11—42no—
438C4×C11—42no—
439C4×C11—42no—
440C4×C11#53712yes—
441C4×C11C2×H(5,𝔽2)11yescharacteristic
442C4×C11C2×2−1+411yescharacteristic
443Dic11—22no—
444Dic11—22no—
445Dic11—22no—
446Dic11—42no—
447Dic11—42no—
448C22×Q8—111no—
449C22×Q8C22×D1111yescharacteristic
450C22×D4—111no—
451C22×D4—111no—
452C22×D4—221no—
453C22×D4—221no—
454C23×C4—111no—
455C23×C4—111no—
456C23×C4—111no—
457C23×C4—221no—
458C23×C4—221no—
459C2×Q16—114no—
460C2×Q16—442no—
461C2×SD16—114no—
462C2×SD16—114no—
463C2×SD16—442no—
464C2×SD16—442no—
465C2×D8—114no—
466C2×D8—442no—
467C22×C8—111no—
468C22×C8—111no—
469C22×C8—114no—
470C22×C8—114no—
471C22×C8—442no—
472C22×C8—442no—
473C22×C8C22×D1111yescharacteristic
474C22×C8C22×D1111yescharacteristic
475#126—228no—
476#126—228no—
477#125—22no—
478#125—114no—
479#125—222no—
480#125C22×D1114yes—
481#124—114no—
482#124—114no—
483#124—222no—
484#124—222no—
485#123—228no—
486#123—228no—
487C22⋊Q8—114no—
488C22⋊Q8—114no—
489C22⋊Q8—222no—
490C22⋊Q8—222no—
491#121—114no—
492#121—114no—
493#121—222no—
494#121—222no—
495C4×Q8—22no—
496C4×Q8—114no—
497C4×Q8—222no—
498C4×Q8C22×D1114yes—
499C4×D4—114no—
500C4×D4—114no—
501C4×D4—228no—
502C4×D4—222no—
503C4×D4—228no—
504C4×D4—222no—
505#117—228no—
506#117—228no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—111no—
511C2×C4⋊C4—221no—
512C2×C4⋊C4—221no—
513C2×C4⋊C4—221no—
514C2×C4⋊C4—221no—
515C2×C4⋊C4—221no—
516C2×C4⋊C4C22×D1111yescharacteristic
517C2×C4⋊C4C22×D1111yescharacteristic
518C2×C4⋊C4C22×D1111yescharacteristic
519C2×C22⋊C4—221no—
520C2×C22⋊C4—221no—
521C2×C22⋊C4—221no—
522C2×C22⋊C4—221no—
523C2×C22⋊C4—221no—
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—111no—
531C2×C42—111no—
532C2×C42—111no—
533C2×C42—114no—
534C2×C42—114no—
535C2×C42—221no—
536C2×C42C22×D1111yescharacteristic
537#107—114no—
538#107C22×D1114yes—
539#106—114no—
540#106C22×D1114yes—
541C4⋊C8—114no—
542C4⋊C8—114no—
543C4⋊C8—114no—
544C4⋊C8C22×D1114yes—
545#103—114no—
546#103—114no—
547#103C22×D1114yes—
548#103C22×D1114yes—
549#102—114no—
550#102—114no—
551#102—114no—
552#102—114no—
553C2×C11#325014yescomplemented
554C2×C11C2×#53711yescharacteristic
555C2×C11C22×#13511yescharacteristic
556C2×C11C2×#57511yescharacteristic
557D11—24no—
558D11—82no—
559D11—82no—
560C24—111no—
561C24—221no—
562C24—221no—
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—112no—
572C2×D4—112no—
573C2×D4—224no—
574C2×D4—224no—
575C2×D4—221no—
576C2×D4—221no—
577C2×D4—222no—
578C2×D4—222no—
579C2×D4—222no—
580C2×D4—222no—
581C2×D4—444no—
582C2×D4—444no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—111no—
588C22×C4—111no—
589C22×C4—111no—
590C22×C4—112no—
591C22×C4—114no—
592C22×C4—112no—
593C22×C4—114no—
594C22×C4—224no—
595C22×C4—224no—
596C22×C4—222no—
597C22×C4—222no—
598C22×C4—221no—
599C22×C4—221no—
600C22×C4—224no—
601C22×C4—442no—
602C22×C4—444no—
603C22×C4—444no—
604C22×C4D4×D1111yescharacteristic
605C22×C4D4×D1111yescharacteristic
606C22×C4C23×D1111yescharacteristic
607Q16—444no—
608SD16—444no—
609SD16—444no—
610D8—444no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—112no—
614C2×C8—112no—
615C2×C8—222no—
616C2×C8—222no—
617C2×C8—444no—
618C2×C8—444no—
619C2×C8C23×D1112yes—
620C2×C8C23×D1112yes—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—112no—
628C4⋊C4—224no—
629C4⋊C4—224no—
630C4⋊C4—224no—
631C4⋊C4—224no—
632C4⋊C4—224no—
633C4⋊C4—221no—
634C4⋊C4C23×D1112yes—
635C4⋊C4C23×D1112yes—
636C4⋊C4C23×D1112yes—
637C22⋊C4—224no—
638C22⋊C4—224no—
639C22⋊C4—224no—
640C22⋊C4—224no—
641C22⋊C4—224no—
642C22⋊C4—224no—
643C22⋊C4—224no—
644C22⋊C4—224no—
645C22⋊C4—224no—
646C22⋊C4—224no—
647C42—24no—
648C42—114no—
649C42—114no—
650C42—112no—
651C42—112no—
652C42—224no—
653C42D4×D1112yes—
654C42C23×D1112yes—
655C11C2×#325011yescharacteristic, complemented, Sylow
656C23—114no—
657C23—112no—
658C23—222no—
659C23—222no—
660C23—222no—
661C23—222no—
662C23—442no—
663C23—442no—
664C23—442no—
665C23—442no—
666C23—442no—
667C23—442no—
668C23C2×D4×D1111yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—222no—
673Q8—222no—
674Q8—442no—
675D4—222no—
676D4—222no—
677D4—222no—
678D4—222no—
679D4—448no—
680D4—448no—
681D4—442no—
682D4—442no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—112no—
694C2×C4—112no—
695C2×C4—112no—
696C2×C4—228no—
697C2×C4—222no—
698C2×C4—222no—
699C2×C4—222no—
700C2×C4—224no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—444no—
706C2×C4—448no—
707C2×C4—448no—
708C2×C4—442no—
709C2×C4—442no—
710C2×C4C2×D4×D1112yes—
711C2×C4C2×D4×D1112yes—
712C2×C4C2×D4×D1111yescharacteristic
713C2×C4#6704012yes—
714C2×C4#6704212yes—
715C2×C4C24×D1111yescharacteristic
716C8—22no—
717C8—22no—
718C8—222no—
719C8—222no—
720C22—114no—
721C22—222no—
722C22—228no—
723C22—222no—
724C22—442no—
725C22—442no—
726C22—442no—
727C22—442no—
728C22—442no—
729C22—442no—
730C22—884no—
731C22—884no—
732C22#1062316012yes—
733C22D11×#13512yes—
734C22#1062330812yes—
735C22C22×D4×D1111yescharacteristic
736C4—22no—
737C4—22no—
738C4—42no—
739C4—42no—
740C4—42no—
741C4—42no—
742C4—222no—
743C4—222no—
744C4—222no—
745C4—442no—
746C4—442no—
747C4#1062316012yes—
748C4C2×#6704011yescharacteristic
749C4C2×#6704211yescharacteristic
750C2—224no—
751C2—882no—
752C2—882no—
753C2#1307997014yesdirect product factor
754C2C2×#1062316011yescharacteristic
755C2C2×D11×#13511yescharacteristic
756C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#479C2
socleC23×C11C22×D4
prime radicalC2×#10622496C2
hypercenterC2×#479D11
hypocenterC11C2×#3250
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
1. C2×#10623111C2semidirect
2. C2×#10623222C2semidirect
3. #13079970C2direct (N × H)
4. C2×#10622490C2semidirect
5. C2×#10622484C2semidirect
6. C2×#10622679C2semidirect
7. C2×#10622426C2semidirect
9. C2×#10622420C2semidirect
10. C2×#10622477C2semidirect
11. C2×#10622411C2semidirect
12. C2×#10622641C2semidirect
13. C2×#10622432C2semidirect
14. C2×#10622457C2semidirect
15. C2×D11×C4⋊C8C2semidirect
16. C2×C11×#479C2semidirect
28. #10623222C22semidirect
30. #10623111C22semidirect
48. C11×#479C22semidirect
58. #10622679C22semidirect
59. #10622641C22semidirect
68. #10622490C22semidirect
69. #10622484C22semidirect
70. #10622477C22semidirect
71. #10622457C22semidirect
72. D11×C4⋊C8C22semidirect
73. #10622432C22semidirect
74. #10622426C22semidirect
75. #10622420C22semidirect
76. #10622411C22semidirect
282. C2×#479D11semidirect
390. #479C2×D11semidirect
553. C2×C11#3250semidirect
655. C11C2×#3250semidirect
753. C2#13079970direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231112
C2×#106232222
#130799702
C2×#106224902
C2×#106224842
C2×#106226792
C2×#106224262
C2×#106224962
C2×#106224202
C2×#106224772
C2×#106224112
C2×#106226412
C2×#106224322
C2×#106224572
C2×D11×C4⋊C82
C2×C11×#4792
C2×#325011