Finite Group Databasebeta

← C2×#13081193 #15632470

Subgroups — C2×#13081193 #15632470

Order 2816.

2082 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623172C211yesmaximal, characteristic, complemented
2C2×#10623038C211yesmaximal, characteristic
3#13081193C2116yesmaximal, direct product factor
4C2×#10622487C211yesmaximal, characteristic, complemented
5C2×#10622422C211yesmaximal, characteristic, complemented
6C2×#10622498C211yesmaximal, characteristic, complemented
7C2×#10622350C211yesmaximal, characteristic, complemented
8C2×#10622404C211yesmaximal, characteristic, complemented
9C2×#10622503C211yesmaximal, characteristic, complemented
10C2×#10622425C211yesmaximal, characteristic, complemented
11C2×#10622662C211yesmaximal, characteristic, complemented
12C2×#10622401C211yesmaximal, characteristic, complemented
13C2×#10622342C211yesmaximal, characteristic, complemented
14C2×#10622494C211yesmaximal, characteristic, complemented
15C2×#10622577C211yesmaximal, characteristic, complemented
16C2×C11×#484C211yesmaximal, characteristic, complemented
17C22×#4339—21no—
18C2×C11×C22⋊Q8C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C2×#66999C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C22×#4325C2211yescharacteristic
23C2×#66983C2211yescharacteristic
24C2×#66982—21no—
25C2×C4×C22⋊D11C2211yescharacteristic
26C2×#66979C2211yescharacteristic
27C22×#4318C2211yescharacteristic
28C22×#4313C2211yescharacteristic
29#10623172—24no—
30#10623172C2218yescomplemented
31C2×#66951—21no—
32C2×#66949—21no—
33#10623038—24no—
34#10623038C2218yes—
35C2×#66948C2211yescharacteristic
36C2×#66947—21no—
37C2×#66946C2211yescharacteristic
38C2×#66945C2211yescharacteristic
39C2×C4⋊C4×D11C2211yescharacteristic
40C2×#66941C2211yescharacteristic
41C2×#66941C2211yescharacteristic
42C2×#66940—21no—
43C2×#66938—21no—
44C2×#66932—21no—
45C11×#484C2218yescomplemented
46C2×C11×#107C2211yescharacteristic
47C2×C11×#107C2211yescharacteristic
48C2×C11×#103C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×C22⋊C8C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52C2×#66885C2211yescharacteristic
53C2×#66885C2211yescharacteristic
54C2×(C2×D11)⋊C8C2211yescharacteristic
55C2×#66882C2211yescharacteristic
56C2×#66881C2211yescharacteristic
57C2×Dic11⋊C8C2211yescharacteristic
58C2×C8×Dic11C2211yescharacteristic
59#10622662C2218yescomplemented
60C2×#66873C2211yescharacteristic
61#10622577C2218yescomplemented
62C2×#66872C2211yescharacteristic
63C2×#66872C2211yescharacteristic
64C2×#66871C2211yescharacteristic
65C2×#66871C2211yescharacteristic
66C2×#66871C2211yescharacteristic
67#10622503C2218yescomplemented
68#10622498C2218yescomplemented
69#10622494C2218yescomplemented
70#10622487C2218yescomplemented
71#10622425C2218yescomplemented
72#10622422C2218yescomplemented
73#10622404C2218yescomplemented
74#10622401C2218yescomplemented
75#10622350C2218yescomplemented
76#10622342C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C23×C4×C11—21no—
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11—21no—
81C22×C22⋊D11D411yescharacteristic
82C2×#4339—28no—
83C2×#4339—48no—
84C22×D44—21no—
85C22×D44C2311yescharacteristic
86C22×C4×D11—21no—
87C22×C4×D11—21no—
88C22×C4×D11C2311yescharacteristic
89C22×Dic22—21no—
90C22×Dic22—21no—
91C22×C8×C11C2311yescharacteristic
92C22×C8×C11C2311yescharacteristic
93C11×C22⋊Q8—22no—
94C11×C22⋊Q8C2314yes—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—22no—
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2314yes—
102C2×C11×C22⋊C4—21no—
103C2×C22⋊Dic11—21no—
104C2×C22⋊Dic11D411yescharacteristic
105#66999—22no—
106#66999C2314yes—
107Q8×Dic11—22no—
108Q8×Dic11C2314yes—
109C2×#4325—24no—
110C2×#4325C2314yes—
111#66983—22no—
112#66983C2314yes—
113#66982—28no—
114C4×C22⋊D11D414yes—
115C4×C22⋊D11C2314yes—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4D411yescharacteristic
122#66979—22no—
123#66979C2314yes—
124C2×C4⋊Dic11—21no—
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4⋊Dic11C2311yescharacteristic
127C2×C4⋊Dic11C2311yescharacteristic
128C2×Dic11⋊C4—21no—
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4D411yescharacteristic
133C2×C4×Dic11—21no—
134C2×C4×Dic11—21no—
135C2×C4×Dic11—21no—
136C2×C4×Dic11C2311yescharacteristic
137C2×#4318—24no—
138C2×#4318C2314yes—
139C22×C11⋊C8C2311yescharacteristic
140C22×C11⋊C8C2311yescharacteristic
141C2×#4313—24no—
142C2×#4313C2314yes—
143#66951—28no—
144#66949—28no—
145#66948—22no—
146#66948C2314yes—
147#66947—28no—
148#66946—22no—
149#66946C2314yes—
150#66945—22no—
151#66945C2314yes—
152C4⋊C4×D11—22no—
153C4⋊C4×D11C2314yes—
154#66941—22no—
155#66941—22no—
156#66941C2314yes—
157#66941C2314yes—
158#66940—28no—
159#66938—28no—
160#66932—28no—
161C11×#107C2314yes—
162C11×#107C2314yes—
163C11×#103C2314yes—
164C11×#103C2314yes—
165C11×C22⋊C8C2314yes—
166#66899C2314yes—
167#66885C2314yes—
168#66885C2314yes—
169(C2×D11)⋊C8C2314yes—
170#66882C2314yes—
171#66881C2314yes—
172Dic11⋊C8C2314yes—
173C8×Dic11C2314yes—
174#66873C2314yes—
175#66872C2314yes—
176#66872C2314yes—
177#66871C2314yes—
178#66871C2314yes—
179#66871C2314yes—
180C2×#3353—111nomaximal, Sylow
181C24×C11C2×D411yescharacteristic
182C23×D11—21no—
183C23×D11C2×D411yescharacteristic
184C2×Q8×C11—21no—
185C2×Q8×C11—22no—
186C2×Q8×C11—22no—
187C2×Q8×C11C2412yes—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—24no—
195C22×C4×C11—44no—
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D412yes—
198C22×C4×C11C2412yes—
199C22×C4×C11C2411yescharacteristic
200C2×C22⋊D11—24no—
201C2×C22⋊D11—24no—
202C2×C22⋊D11—44no—
203C2×C22⋊D11C2×D414yes—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11C2×D411yescharacteristic
208C22×Dic11C2×D411yescharacteristic
209C22×Dic11C2×D411yescharacteristic
210#4339—432no—
211C2×D44—24no—
212C2×D44—21no—
213C2×D44—22no—
214C2×D44—22no—
215C2×D44—44no—
216C2×D44C2412yes—
217C2×C4×D11—24no—
218C2×C4×D11—24no—
219C2×C4×D11—22no—
220C2×C4×D11—22no—
221C2×C4×D11—44no—
222C2×C4×D11—44no—
223C2×C4×D11C2×D412yes—
224C2×C4×D11C2412yes—
225C2×Dic22—24no—
226C2×Dic22—24no—
227C2×Dic22—44no—
228C2×Dic22—44no—
229C2×C8×C11—22no—
230C2×C8×C11—22no—
231C2×C8×C11C2412yes—
232C2×C8×C11C2412yes—
233C11×C4⋊C4—24no—
234C11×C4⋊C4—21no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—21no—
237C11×C4⋊C4—24no—
238C11×C4⋊C4C2412yes—
239C11×C4⋊C4C2412yes—
240C11×C4⋊C4C2412yes—
241C11×C22⋊C4—24no—
242C22⋊Dic11—24no—
243C22⋊Dic11C2×D414yes—
244#4325—28no—
245(C2×D11)⋊C4—24no—
246(C2×D11)⋊C4—24no—
247(C2×D11)⋊C4—24no—
248(C2×D11)⋊C4—24no—
249(C2×D11)⋊C4—24no—
250(C2×D11)⋊C4C2×D414yes—
251C4⋊Dic11—24no—
252C4⋊Dic11—21no—
253C4⋊Dic11—21no—
254C4⋊Dic11—21no—
255C4⋊Dic11C2412yes—
256C4⋊Dic11C2412yes—
257C4⋊Dic11C2412yes—
258Dic11⋊C4—24no—
259Dic11⋊C4—24no—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262Dic11⋊C4C2×D414yes—
263C4×Dic11—24no—
264C4×Dic11—24no—
265C4×Dic11—24no—
266C4×Dic11C2×D412yes—
267C4×Dic11C2412yes—
268#4318—28no—
269C2×C11⋊C8—22no—
270C2×C11⋊C8#4114yescomplemented
271C2×C11⋊C8C2412yes—
272C2×C11⋊C8C2412yes—
273#4313—28no—
274C2×#556—111no—
275C2×#547—111no—
276#3353—1116no—
277C2×#500—111no—
278C2×#484—111no—
279C2×#484D1111yescharacteristic, complemented
280C2×#482—111no—
281C2×#482—111no—
282C2×#475—111no—
283C2×#474—111no—
284C2×#468—111no—
285C2×#468—111no—
286C2×C4×SD16—111no—
287C2×#436—111no—
288C2×#428—111no—
289C2×#428—111no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11C22×D412yes—
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×D11C22×D412yes—
303Q8×C11—22no—
304Q8×C11—22no—
305Q8×C11—42no—
306C2×C4×C11—22no—
307C2×C4×C11—24no—
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—48no—
315C2×C4×C11—42no—
316C2×C4×C11—42no—
317C2×C4×C11—42no—
318C2×C4×C11—42no—
319C2×C4×C11C22×D412yes—
320C2×C4×C11C22×D411yescharacteristic
321C2×C4×C11C2×#4112yes—
322C2×C4×C112−1+412yes—
323C2×C4×C11C2511yescharacteristic
324C22⋊D11—28no—
325C22⋊D11—48no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11AGL(1,ℤ/8)14yes—
335C2×Dic11C22×D412yes—
336C2×Dic11C22×D412yes—
337C2×Dic11C22×D412yes—
338D44—22no—
339D44—22no—
340D44—48no—
341D44—42no—
342C4×D11—24no—
343C4×D11—22no—
344C4×D11—22no—
345C4×D11—48no—
346C4×D11—48no—
347Dic22—48no—
348Dic22—48no—
349C8×C11—22no—
350C8×C11—22no—
351C11⋊C8—22no—
352C11⋊C8C2×#4114yescomplemented
353C22×#41—221no—
354C22×SD16—111no—
355C22×M16—111no—
356C22×M16—111no—
357#556—118no—
358#556—224no—
359#547—118no—
360#547—224no—
361C2×C4⋊Q8—111no—
362C2×C4⋊Q8—111no—
363C2×#126—221no—
364C2×#126—221no—
365C2×#124—221no—
366C2×#123—221no—
367C2×#123—221no—
368C2×C22⋊Q8—111no—
369C2×C22⋊Q8—221no—
370C2×C22⋊Q8C2×D1111yescharacteristic
371C2×#121—111no—
372C2×#121—111no—
373C2×C4×Q8—111no—
374C2×C4×Q8—221no—
375C2×C4×D4—111no—
376C2×C4×D4—111no—
377C2×#117—111no—
378C2×#117—111no—
379C22×C4⋊C4—111no—
380C22×C4⋊C4C2×D1111yescharacteristic
381#500—118no—
382#484—118no—
383#484C2×D1118yescomplemented
384#482—118no—
385#482—118no—
386#475—118no—
387#474—118no—
388#468—118no—
389#468—118no—
390C4×SD16—118no—
391#436—118no—
392#428—118no—
393#428—118no—
394C2×#107—111no—
395C2×#107—111no—
396C2×#107—111no—
397C2×#107—111no—
398C2×#107C2×D1111yescharacteristic
399C2×#107C2×D1111yescharacteristic
400C2×#106—111no—
401C2×#106—111no—
402C2×#106—111no—
403C2×C4⋊C8—111no—
404C2×#103—111no—
405C2×#103C2×D1111yescharacteristic
406C2×#103C2×D1111yescharacteristic
407C2×#102—111no—
408C2×#102—111no—
409C2×#102—111no—
410C2×C22⋊C8—111no—
411C2×C22⋊C8C2×D1111yescharacteristic
412C2×C4×C8—111no—
413C22×C11—22no—
414C22×C11—22no—
415C22×C11—22no—
416C22×C11—44no—
417C22×C11#54712yes—
418C22×C11C2×AGL(1,ℤ/8)12yes—
419C22×C11#57812yes—
420C22×C11C23×D411yescharacteristic
421C2×D11—22no—
422C2×D11—22no—
423C2×D11—22no—
424C2×D11—44no—
425C2×D11—42no—
426C2×D11—42no—
427C2×D11—42no—
428C2×D11—84no—
429C4×C11—22no—
430C4×C11—42no—
431C4×C11—42no—
432C4×C11—42no—
433C4×C11—42no—
434C4×C11#54712yes—
435C4×C11C22×#4111yescharacteristic
436C4×C11C2×2−1+411yescharacteristic
437Dic11—22no—
438Dic11—22no—
439Dic11—42no—
440Dic11—42no—
441Dic11—42no—
442Dic11C2×AGL(1,ℤ/8)14yes—
443C2×#41—228no—
444C2×#41—448no—
445C22×Q8—221no—
446C22×Q8—221no—
447C22×Q8C22×D1111yescharacteristic
448C22×D4—111no—
449C22×D4—111no—
450C22×D4—221no—
451C22×D4—221no—
452C23×C4—21no—
453C23×C4—111no—
454C23×C4—221no—
455C23×C4—221no—
456C23×C4C22×D1111yescharacteristic
457C2×SD16—114no—
458C2×SD16—224no—
459C2×M16—114no—
460C2×M16—114no—
461C2×M16—224no—
462C2×M16—224no—
463C22×C8—111no—
464C22×C8—111no—
465C22×C8C22×D1111yescharacteristic
466C22×C8C22×D1111yescharacteristic
467C4⋊Q8—114no—
468C4⋊Q8—114no—
469C4⋊Q8—222no—
470C4⋊Q8—222no—
471#126—228no—
472#126—228no—
473#124—228no—
474#123—228no—
475#123—228no—
476C22⋊Q8—22no—
477C22⋊Q8—114no—
478C22⋊Q8—228no—
479C22⋊Q8—222no—
480C22⋊Q8C22×D1114yes—
481#121—114no—
482#121—114no—
483#121—222no—
484#121—222no—
485C4×Q8—114no—
486C4×Q8—222no—
487C4×Q8—228no—
488C4×D4—114no—
489C4×D4—114no—
490C4×D4—114no—
491C4×D4—222no—
492#117—114no—
493#117—114no—
494#117—222no—
495#117—222no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—111no—
500C2×C4⋊C4—111no—
501C2×C4⋊C4—111no—
502C2×C4⋊C4—111no—
503C2×C4⋊C4—114no—
504C2×C4⋊C4—222no—
505C2×C4⋊C4—221no—
506C2×C4⋊C4—221no—
507C2×C4⋊C4—221no—
508C2×C4⋊C4—221no—
509C2×C4⋊C4—221no—
510C2×C4⋊C4C22×D1111yescharacteristic
511C2×C4⋊C4C22×D1111yescharacteristic
512C2×C4⋊C4C22×D1114yes—
513C2×C4⋊C4C22×D1111yescharacteristic
514C2×C22⋊C4—21no—
515C2×C22⋊C4—111no—
516C2×C22⋊C4—111no—
517C2×C22⋊C4—221no—
518C2×C22⋊C4—221no—
519C2×C22⋊C4—221no—
520C2×C22⋊C4—221no—
521C2×C22⋊C4—221no—
522C2×C22⋊C4—221no—
523C2×C42—111no—
524C2×C42—221no—
525C2×C42—221no—
526C2×C42—221no—
527#107—114no—
528#107—114no—
529#107—114no—
530#107—114no—
531#107C22×D1114yes—
532#107C22×D1114yes—
533#106—114no—
534#106—114no—
535#106—114no—
536C4⋊C8—114no—
537#103—114no—
538#103C22×D1114yes—
539#103C22×D1114yes—
540#102—114no—
541#102—114no—
542#102—114no—
543C22⋊C8—114no—
544C22⋊C8C22×D1114yes—
545C4×C8—114no—
546C2×C11—42no—
547C2×C11#335314yescomplemented
548C2×C11C2×#54711yescharacteristic
549C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
550C2×C11C2×#57811yescharacteristic
551D11—42no—
552D11—82no—
553C24—111no—
554C24—221no—
555C24D4×D1111yescharacteristic
556#41—4432no—
557C2×Q8—21no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—224no—
561C2×Q8—224no—
562C2×Q8—444no—
563C2×Q8—444no—
564C2×Q8C23×D1112yes—
565C2×D4—114no—
566C2×D4—112no—
567C2×D4—224no—
568C2×D4—224no—
569C2×D4—224no—
570C2×D4—221no—
571C2×D4—222no—
572C2×D4—222no—
573C2×D4—444no—
574C2×D4—444no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—44no—
583C22×C4—111no—
584C22×C4—111no—
585C22×C4—111no—
586C22×C4—112no—
587C22×C4—112no—
588C22×C4—224no—
589C22×C4—224no—
590C22×C4—222no—
591C22×C4—222no—
592C22×C4—221no—
593C22×C4—221no—
594C22×C4—221no—
595C22×C4—444no—
596C22×C4—444no—
597C22×C4D4×D1112yes—
598C22×C4D4×D1111yescharacteristic
599C22×C4C23×D1112yes—
600C22×C4C23×D1111yescharacteristic
601SD16—228no—
602M16—228no—
603M16—228no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—114no—
607C2×C8—112no—
608C2×C8—112no—
609C2×C8—222no—
610C2×C8C23×D1112yes—
611C2×C8C23×D1112yes—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—21no—
617C4⋊C4—114no—
618C4⋊C4—112no—
619C4⋊C4—112no—
620C4⋊C4—112no—
621C4⋊C4—224no—
622C4⋊C4—224no—
623C4⋊C4—224no—
624C4⋊C4—224no—
625C4⋊C4—224no—
626C4⋊C4—221no—
627C4⋊C4—221no—
628C4⋊C4—221no—
629C4⋊C4C23×D1112yes—
630C4⋊C4C23×D1112yes—
631C4⋊C4C23×D1112yes—
632C22⋊C4—24no—
633C22⋊C4—114no—
634C22⋊C4—114no—
635C22⋊C4—224no—
636C22⋊C4—224no—
637C22⋊C4—224no—
638C22⋊C4—224no—
639C22⋊C4—224no—
640C22⋊C4—224no—
641C42—112no—
642C42—112no—
643C42—224no—
644C42—224no—
645C42—224no—
646C11C2×#335311yescharacteristic, complemented, Sylow
647C23—22no—
648C23—22no—
649C23—22no—
650C23—112no—
651C23—222no—
652C23—222no—
653C23—222no—
654C23—222no—
655C23—442no—
656C23—442no—
657C23—442no—
658C23C2×D4×D1112yes—
659C23C2×D4×D1111yescharacteristic
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—448no—
664Q8—448no—
665D4—228no—
666D4—222no—
667D4—222no—
668D4—448no—
669D4—448no—
670D4—442no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—48no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—114no—
685C2×C4—112no—
686C2×C4—112no—
687C2×C4—112no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—224no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—222no—
694C2×C4—222no—
695C2×C4—222no—
696C2×C4—448no—
697C2×C4—448no—
698C2×C4—442no—
699C2×C4—442no—
700C2×C4—442no—
701C2×C4C2×D4×D1112yes—
702C2×C4C2×D4×D1111yescharacteristic
703C2×C4#41×D1112yes—
704C2×C4#6704312yes—
705C2×C4C24×D1111yescharacteristic
706C8—22no—
707C8—22no—
708C8—114no—
709C8—222no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—222no—
715C22—222no—
716C22—222no—
717C22—444no—
718C22—442no—
719C22—442no—
720C22—442no—
721C22—884no—
722C22#1062318612yes—
723C22#1062329712yes—
724C22D11×AGL(1,ℤ/8)12yes—
725C22C22×D4×D1111yescharacteristic
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—114no—
732C4—222no—
733C4—222no—
734C4—442no—
735C4—442no—
736C4—442no—
737C4#1062318612yes—
738C4C2×#41×D1111yescharacteristic
739C4C2×#6704311yescharacteristic
740C2—42no—
741C2—442no—
742C2—882no—
743C2#1308119314yesdirect product factor
744C2C2×#1062318611yescharacteristic
745C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
746C2C2×#1062329711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#484C2
socleC23×C11C22×D4
prime radicalC2×#10623038C2
hypercenterC2×#484D11
hypocenterC11C2×#3353
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
1. C2×#10623172C2semidirect
3. #13081193C2direct (N × H)
4. C2×#10622487C2semidirect
5. C2×#10622422C2semidirect
6. C2×#10622498C2semidirect
7. C2×#10622350C2semidirect
8. C2×#10622404C2semidirect
9. C2×#10622503C2semidirect
10. C2×#10622425C2semidirect
11. C2×#10622662C2semidirect
12. C2×#10622401C2semidirect
13. C2×#10622342C2semidirect
14. C2×#10622494C2semidirect
15. C2×#10622577C2semidirect
16. C2×C11×#484C2semidirect
30. #10623172C22semidirect
45. C11×#484C22semidirect
59. #10622662C22semidirect
61. #10622577C22semidirect
67. #10622503C22semidirect
68. #10622498C22semidirect
69. #10622494C22semidirect
70. #10622487C22semidirect
71. #10622425C22semidirect
72. #10622422C22semidirect
73. #10622404C22semidirect
74. #10622401C22semidirect
75. #10622350C22semidirect
76. #10622342C22semidirect
270. C2×C11⋊C8#41semidirect
279. C2×#484D11semidirect
352. C11⋊C8C2×#41semidirect
383. #484C2×D11semidirect
547. C2×C11#3353semidirect
646. C11C2×#3353semidirect
743. C2#13081193direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231722
C2×#106230382
#130811932
C2×#106224872
C2×#106224222
C2×#106224982
C2×#106223502
C2×#106224042
C2×#106225032
C2×#106224252
C2×#106226622
C2×#106224012
C2×#106223422
C2×#106224942
C2×#106225772
C2×C11×#4842
C2×#335311