Finite Group Databasebeta

← C2×#13081061 #15632309

Subgroups — C2×#13081061 #15632309

Order 2816.

2094 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×#10623112C211yesmaximal, characteristic, complemented
2C2×#10623082C211yesmaximal, characteristic
3#13081061C2116yesmaximal, direct product factor
4C2×#10622315C211yesmaximal, characteristic, complemented
5C2×#10622422C211yesmaximal, characteristic, complemented
6C2×#10622392C211yesmaximal, characteristic, complemented
7C2×#10622418C211yesmaximal, characteristic, complemented
8C2×#10622387C211yesmaximal, characteristic, complemented
9C2×#10622634C211yesmaximal, characteristic, complemented
10C2×#10622622C211yesmaximal, characteristic, complemented
11C2×#10622787C211yesmaximal, characteristic, complemented
12C2×#10622784C211yesmaximal, characteristic, complemented
13C2×#10622319C211yesmaximal, characteristic, complemented
14C2×#10622494C211yesmaximal, characteristic, complemented
15C2×D11×#107C211yesmaximal, characteristic, complemented
16C2×C11×#440C211yesmaximal, characteristic, complemented
17C22×#4339—21no—
18C22×C11×SD16C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×#66999C2211yescharacteristic
22C2×#66999C2211yescharacteristic
23C2×#66991C2211yescharacteristic
24C2×#66991C2211yescharacteristic
25C2×#66977—21no—
26C22×#4313C2211yescharacteristic
27C22×C8×D11C2211yescharacteristic
28#10623112—24no—
29#10623112C2218yescomplemented
30#10623082—24no—
31#10623082C2218yes—
32C2×#66947—21no—
33C2×#66945C2211yescharacteristic
34C2×C4⋊C4×D11C2211yescharacteristic
35C2×C4⋊C4×D11C2211yescharacteristic
36C2×C4⋊C4×D11C2211yescharacteristic
37C2×#66942—21no—
38C2×#66936—21no—
39C2×#66936—21no—
40C2×#66929—21no—
41C2×C4×D44C2211yescharacteristic
42C2×#66925—21no—
43C2×#66923C2211yescharacteristic
44C2×#66922C2211yescharacteristic
45C11×#440C2218yescomplemented
46C2×C11×#107C2211yescharacteristic
47C2×C11×#103C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×#97C2211yescharacteristic
50C2×#66899C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52C2×#66896C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54#10622787C2218yescomplemented
55#10622784C2218yescomplemented
56C2×(C2×D11)⋊C8C2211yescharacteristic
57C2×(C2×D11)⋊C8C2211yescharacteristic
58C2×#66882C2211yescharacteristic
59C2×#66882C2211yescharacteristic
60C2×#66881C2211yescharacteristic
61C2×#66881C2211yescharacteristic
62#10622634C2218yescomplemented
63#10622622C2218yescomplemented
64C2×#66872C2211yescharacteristic
65C2×#66871C2211yescharacteristic
66C2×#66871C2211yescharacteristic
67C2×#66871C2211yescharacteristic
68C2×C4⋊(C11⋊C8)C2211yescharacteristic
69#10622494C2218yescomplemented
70D11×#107C2218yescomplemented
71#10622422C2218yescomplemented
72#10622418C2218yescomplemented
73#10622392C2218yescomplemented
74#10622387C2218yescomplemented
75#10622319C2218yescomplemented
76#10622315C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11—21no—
80C22×C22⋊D11—21no—
81C22×C22⋊D11—21no—
82C2×#4339—28no—
83C2×#4339—48no—
84C22×D44D411yescharacteristic
85C22×C4×D11—21no—
86C22×C4×D11—21no—
87C22×C4×D11—21no—
88C22×C4×D11C2311yescharacteristic
89C22×C4×D11C2311yescharacteristic
90C22×Dic22—21no—
91C2×C11×SD16—24no—
92C2×C11×SD16C2314yes—
93C22×C8×C11C2311yescharacteristic
94C22×C8×C11C2311yescharacteristic
95C4×Q8×C11—22no—
96C4×Q8×C11C2314yes—
97C4×D4×C11—22no—
98C4×D4×C11C2314yes—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C22⋊C4—21no—
103C2×C42×C11—21no—
104C2×C42×C11C2311yescharacteristic
105C2×C22⋊Dic11—21no—
106C2×C22⋊Dic11—21no—
107#66999—22no—
108#66999—22no—
109#66999C2314yes—
110#66999C2314yes—
111#66991—22no—
112#66991—22no—
113#66991C2314yes—
114#66991C2314yes—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4D411yescharacteristic
119C2×(C2×D11)⋊C4D411yescharacteristic
120C2×C4⋊Dic11—21no—
121C2×C4⋊Dic11D411yescharacteristic
122C2×C4⋊Dic11C2311yescharacteristic
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
126#66977—28no—
127C2×Dic11⋊C4—21no—
128C2×Dic11⋊C4—21no—
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4—21no—
133C2×Dic11⋊C4—21no—
134C2×C4×Dic11—21no—
135C22×C11⋊C8C2311yescharacteristic
136C22×C11⋊C8C2311yescharacteristic
137C2×#4313—24no—
138C2×#4313C2314yes—
139C2×C8×D11—24no—
140C2×C8×D11C2314yes—
141#66947—28no—
142#66945—22no—
143#66945C2314yes—
144C4⋊C4×D11—22no—
145C4⋊C4×D11—22no—
146C4⋊C4×D11—22no—
147C4⋊C4×D11C2314yes—
148C4⋊C4×D11C2314yes—
149C4⋊C4×D11C2314yes—
150#66942—28no—
151#66936—28no—
152#66936—28no—
153#66929—28no—
154C4×D44D414yes—
155C4×D44C2314yes—
156#66925—28no—
157#66923—22no—
158#66923C2314yes—
159#66922—22no—
160#66922C2314yes—
161C11×#107C2314yes—
162C11×#103C2314yes—
163C11×#102C2314yes—
164C11×#97C2314yes—
165#66899C2314yes—
166#66899C2314yes—
167#66896C2314yes—
168#66896C2314yes—
169(C2×D11)⋊C8C2314yes—
170(C2×D11)⋊C8C2314yes—
171#66882C2314yes—
172#66882C2314yes—
173#66881C2314yes—
174#66881C2314yes—
175#66872C2314yes—
176#66871C2314yes—
177#66871C2314yes—
178#66871C2314yes—
179C4⋊(C11⋊C8)C2314yes—
180C2×#3343—111nomaximal, Sylow
181C24×C11—21no—
182C23×D11C2×D411yescharacteristic
183C23×D11C2×D411yescharacteristic
184C2×Q8×C11—21no—
185C2×Q8×C11—22no—
186C2×Q8×C11—22no—
187C2×Q8×C11C2412yes—
188C2×D4×C11—21no—
189C2×D4×C11—22no—
190C2×D4×C11—22no—
191C2×D4×C11C2412yes—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—24no—
196C22×C4×C11—44no—
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2411yescharacteristic
200C2×C22⋊D11—24no—
201C2×C22⋊D11—24no—
202C2×C22⋊D11—44no—
203C2×C22⋊D11—44no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11C2×D411yescharacteristic
209C22×Dic11C2×D411yescharacteristic
210#4339—432no—
211C2×D44—24no—
212C2×D44C2×D414yes—
213C2×C4×D11—24no—
214C2×C4×D11—24no—
215C2×C4×D11—24no—
216C2×C4×D11—22no—
217C2×C4×D11—22no—
218C2×C4×D11—22no—
219C2×C4×D11—22no—
220C2×C4×D11—44no—
221C2×C4×D11—44no—
222C2×C4×D11—44no—
223C2×C4×D11C2×D412yes—
224C2×C4×D11C2×D412yes—
225C2×C4×D11C2412yes—
226C2×C4×D11C2412yes—
227C2×Dic22—24no—
228C2×Dic22—44no—
229C11×SD16—28no—
230C2×C8×C11—22no—
231C2×C8×C11#4114yescomplemented
232C2×C8×C11C2412yes—
233C2×C8×C11C2412yes—
234C11×C4⋊C4—24no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—21no—
237C11×C4⋊C4C2412yes—
238C11×C4⋊C4C2412yes—
239C11×C22⋊C4—24no—
240C42×C11—24no—
241C42×C11C2×D412yes—
242C42×C11C2412yes—
243C22⋊Dic11—24no—
244C22⋊Dic11—24no—
245(C2×D11)⋊C4—24no—
246(C2×D11)⋊C4—24no—
247(C2×D11)⋊C4—24no—
248(C2×D11)⋊C4C2×D414yes—
249(C2×D11)⋊C4C2×D414yes—
250C4⋊Dic11—21no—
251C4⋊Dic11—21no—
252C4⋊Dic11—24no—
253C4⋊Dic11—21no—
254C4⋊Dic11—21no—
255C4⋊Dic11C2×D414yes—
256C4⋊Dic11C2412yes—
257C4⋊Dic11C2412yes—
258C4⋊Dic11C2412yes—
259C4⋊Dic11C2412yes—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263Dic11⋊C4—24no—
264Dic11⋊C4—24no—
265Dic11⋊C4—24no—
266Dic11⋊C4—24no—
267C4×Dic11—24no—
268C2×C11⋊C8—22no—
269C2×C11⋊C8—22no—
270C2×C11⋊C8C2412yes—
271C2×C11⋊C8C2412yes—
272#4313—28no—
273C8×D11—28no—
274C2×#552—111no—
275C2×#547—111no—
276#3343—1116no—
277C2×#501—111no—
278C2×#484—111no—
279C2×#482—111no—
280C2×#483—111no—
281C2×#480—111no—
282C2×#477—111no—
283C2×#478—111no—
284C2×#468—111no—
285C2×#465—111no—
286C2×#440D1111yescharacteristic, complemented
287C2×#435—111no—
288C2×#428—111no—
289C22×#107—111no—
290C23×C11—22no—
291C23×C11—42no—
292C23×C11—42no—
293C23×C11—42no—
294C23×C11C22×D411yescharacteristic
295C22×D11—22no—
296C22×D11—22no—
297C22×D11—22no—
298C22×D11—22no—
299C22×D11—22no—
300C22×D11AGL(1,ℤ/8)14yes—
301C22×D11C22×D412yes—
302C22×D11C22×D412yes—
303Q8×C11—22no—
304Q8×C11—22no—
305Q8×C11—42no—
306D4×C11—22no—
307D4×C11—22no—
308D4×C11—42no—
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×C11C22×D412yes—
319C2×C4×C11C22×D412yes—
320C2×C4×C11C22×D411yescharacteristic
321C2×C4×C11C2×#4112yes—
322C2×C4×C112−1+412yes—
323C2×C4×C11C2511yescharacteristic
324C22⋊D11—48no—
325C22⋊D11—48no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11C22×D412yes—
337C2×Dic11C22×D412yes—
338D44—28no—
339C4×D11—24no—
340C4×D11—24no—
341C4×D11—22no—
342C4×D11—22no—
343C4×D11—22no—
344C4×D11—22no—
345C4×D11—48no—
346C4×D11—48no—
347C4×D11—48no—
348Dic22—48no—
349C8×C11—22no—
350C8×C11C2×#4114yescomplemented
351C11⋊C8—22no—
352C11⋊C8—22no—
353C22×#41—221no—
354C22×SD16C2×D1111yescharacteristic
355C22×M16—111no—
356C23×C8—111no—
357#552—118no—
358#552—224no—
359#547—118no—
360#547—224no—
361C2×C4⋊Q8—111no—
362C2×#126—221no—
363C2×#125—111no—
364C2×#125—221no—
365C2×#123—221no—
366C2×#123—221no—
367C2×#123—221no—
368C2×C22⋊Q8—111no—
369C2×C22⋊Q8—111no—
370C2×C22⋊Q8—221no—
371C2×#121—111no—
372C2×#121—111no—
373C2×C4×Q8C2×D1111yescharacteristic
374C2×C4×D4—111no—
375C2×C4×D4C2×D1111yescharacteristic
376C2×#117—111no—
377C2×#117—221no—
378C22×C4⋊C4—111no—
379C22×C4⋊C4—111no—
380C22×C4⋊C4—111no—
381#501—118no—
382#484—118no—
383#483—118no—
384#482—118no—
385#480—118no—
386#478—118no—
387#477—118no—
388#468—118no—
389#465—118no—
390#440C2×D1118yescomplemented
391#435—118no—
392#428—118no—
393C2×#107—111no—
394C2×#107—111no—
395C2×#107—111no—
396C2×#107—111no—
397C2×#107—111no—
398C2×#107—118no—
399C2×#107C2×D1111yescharacteristic
400C2×#106—111no—
401C2×#106—111no—
402C2×#106—111no—
403C2×C4⋊C8—111no—
404C2×#103—111no—
405C2×#103—111no—
406C2×#103C2×D1111yescharacteristic
407C2×#102—111no—
408C2×#102—111no—
409C2×#102C2×D1111yescharacteristic
410C2×C22⋊C8—111no—
411C2×C22⋊C8—111no—
412C2×#97C2×D1111yescharacteristic
413C22×C11—42no—
414C22×C11—42no—
415C22×C11—42no—
416C22×C11—84no—
417C22×C11#54712yes—
418C22×C11C2×AGL(1,ℤ/8)12yes—
419C22×C11#57812yes—
420C22×C11C23×D411yescharacteristic
421C2×D11—28no—
422C2×D11—22no—
423C2×D11—22no—
424C2×D11—22no—
425C2×D11—22no—
426C2×D11—22no—
427C2×D11—44no—
428C2×D11C2×AGL(1,ℤ/8)14yes—
429C4×C11—22no—
430C4×C11—22no—
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—
442Dic11—42no—
443C2×#41—228no—
444C2×#41—448no—
445C22×Q8—221no—
446C22×Q8C22×D1111yescharacteristic
447C22×D4—111no—
448C22×D4—221no—
449C22×D4—221no—
450C22×D4C22×D1111yescharacteristic
451C23×C4—21no—
452C23×C4—111no—
453C23×C4—111no—
454C23×C4—221no—
455C23×C4—221no—
456C23×C4—221no—
457C2×SD16—24no—
458C2×SD16C22×D1114yes—
459C2×M16—114no—
460C2×M16—224no—
461C22×C8—111no—
462C22×C8—111no—
463C22×C8—114no—
464C22×C8—224no—
465C22×C8C22×D1111yescharacteristic
466C22×C8C22×D1111yescharacteristic
467C4⋊Q8—114no—
468C4⋊Q8—222no—
469#126—228no—
470#125—114no—
471#125—228no—
472#125—222no—
473#123—228no—
474#123—228no—
475#123—228no—
476C22⋊Q8—114no—
477C22⋊Q8—114no—
478C22⋊Q8—228no—
479C22⋊Q8—222no—
480C22⋊Q8—222no—
481#121—114no—
482#121—114no—
483#121—222no—
484#121—222no—
485C4×Q8—22no—
486C4×Q8C22×D1114yes—
487C4×D4—22no—
488C4×D4—114no—
489C4×D4—114no—
490C4×D4C22×D1114yes—
491#117—114no—
492#117—228no—
493#117—222no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—111no—
496C2×C4⋊C4—111no—
497C2×C4⋊C4—111no—
498C2×C4⋊C4—111no—
499C2×C4⋊C4—111no—
500C2×C4⋊C4—114no—
501C2×C4⋊C4—114no—
502C2×C4⋊C4—114no—
503C2×C4⋊C4—222no—
504C2×C4⋊C4—222no—
505C2×C4⋊C4—222no—
506C2×C4⋊C4—221no—
507C2×C4⋊C4—221no—
508C2×C4⋊C4—221no—
509C2×C4⋊C4—221no—
510C2×C4⋊C4—221no—
511C2×C4⋊C4—221no—
512C2×C4⋊C4—221no—
513C2×C4⋊C4—221no—
514C2×C4⋊C4C22×D1111yescharacteristic
515C2×C4⋊C4C22×D1111yescharacteristic
516C2×C22⋊C4—21no—
517C2×C22⋊C4—111no—
518C2×C22⋊C4—111no—
519C2×C22⋊C4—221no—
520C2×C22⋊C4—221no—
521C2×C22⋊C4—221no—
522C2×C22⋊C4—221no—
523C2×C22⋊C4—221no—
524C2×C42—21no—
525C2×C42—221no—
526C2×C42C22×D1111yescharacteristic
527#107—114no—
528#107—114no—
529#107—114no—
530#107—114no—
531#107—114no—
532#107C22×D1114yes—
533#106—114no—
534#106—114no—
535#106—114no—
536C4⋊C8—114no—
537#103—114no—
538#103—114no—
539#103C22×D1114yes—
540#102—114no—
541#102—114no—
542#102C22×D1114yes—
543C22⋊C8—114no—
544C22⋊C8—114no—
545#97C22×D1114yes—
546C2×C11—82no—
547C2×C11#334314yescomplemented
548C2×C11C2×#54711yescharacteristic
549C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
550C2×C11C2×#57811yescharacteristic
551D11—24no—
552D11—42no—
553C24—21no—
554C24—111no—
555C24—111no—
556#41—4432no—
557C2×Q8—21no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—224no—
561C2×Q8—444no—
562C2×Q8C23×D1112yes—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—22no—
566C2×D4—114no—
567C2×D4—224no—
568C2×D4—224no—
569C2×D4—224no—
570C2×D4—444no—
571C2×D4—444no—
572C2×D4C23×D1112yes—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—24no—
577C22×C4—44no—
578C22×C4—111no—
579C22×C4—111no—
580C22×C4—112no—
581C22×C4—112no—
582C22×C4—112no—
583C22×C4—112no—
584C22×C4—224no—
585C22×C4—224no—
586C22×C4—224no—
587C22×C4—222no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—222no—
591C22×C4—221no—
592C22×C4—221no—
593C22×C4—221no—
594C22×C4—221no—
595C22×C4—444no—
596C22×C4—444no—
597C22×C4—444no—
598C22×C4D4×D1111yescharacteristic
599C22×C4D4×D1111yescharacteristic
600C22×C4C23×D1111yescharacteristic
601SD16—28no—
602M16—228no—
603C2×C8—22no—
604C2×C8—112no—
605C2×C8—112no—
606C2×C8—222no—
607C2×C8—222no—
608C2×C8—228no—
609C2×C8#433914yescomplemented
610C2×C8C23×D1112yes—
611C2×C8C23×D1112yes—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—114no—
616C4⋊C4—112no—
617C4⋊C4—112no—
618C4⋊C4—112no—
619C4⋊C4—112no—
620C4⋊C4—224no—
621C4⋊C4—224no—
622C4⋊C4—224no—
623C4⋊C4—224no—
624C4⋊C4—224no—
625C4⋊C4—221no—
626C4⋊C4—221no—
627C4⋊C4—221no—
628C4⋊C4—221no—
629C4⋊C4—224no—
630C4⋊C4—224no—
631C4⋊C4—224no—
632C4⋊C4C23×D1112yes—
633C4⋊C4C23×D1112yes—
634C22⋊C4—24no—
635C22⋊C4—114no—
636C22⋊C4—114no—
637C22⋊C4—224no—
638C22⋊C4—224no—
639C22⋊C4—224no—
640C22⋊C4—224no—
641C22⋊C4—224no—
642C42—24no—
643C42—224no—
644C42D4×D1112yes—
645C42C23×D1112yes—
646C11C2×#334311yescharacteristic, complemented, Sylow
647C23—22no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—114no—
652C23—112no—
653C23—112no—
654C23—222no—
655C23—222no—
656C23—222no—
657C23—222no—
658C23—222no—
659C23C2×D4×D1111yescharacteristic
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—448no—
664D4—22no—
665D4—22no—
666D4—42no—
667D4—228no—
668D4—448no—
669D4—448no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—48no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—112no—
680C2×C4—112no—
681C2×C4—222no—
682C2×C4—222no—
683C2×C4—224no—
684C2×C4—224no—
685C2×C4—222no—
686C2×C4—222no—
687C2×C4—222no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—448no—
694C2×C4—448no—
695C2×C4—448no—
696C2×C4—442no—
697C2×C4—442no—
698C2×C4—442no—
699C2×C4—442no—
700C2×C4C2×#433912yes—
701C2×C4C2×D4×D1112yes—
702C2×C4C2×D4×D1112yes—
703C2×C4C2×D4×D1111yescharacteristic
704C2×C4#6704312yes—
705C2×C4C24×D1111yescharacteristic
706C8—22no—
707C8—222no—
708C8—222no—
709C8C2×#433914yescomplemented
710C22—42no—
711C22—42no—
712C22—42no—
713C22—84no—
714C22—114no—
715C22—222no—
716C22—228no—
717C22—222no—
718C22—222no—
719C22—222no—
720C22—222no—
721C22—444no—
722C22#1062308212yes—
723C22D11×AGL(1,ℤ/8)12yes—
724C22#1062331012yes—
725C22C22×D4×D1111yescharacteristic
726C4—22no—
727C4—22no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—222no—
732C4—222no—
733C4—442no—
734C4—442no—
735C4—442no—
736C4—442no—
737C4#1062308212yes—
738C4C22×#433911yescharacteristic
739C4C2×#6704311yescharacteristic
740C2—82no—
741C2—224no—
742C2—442no—
743C2#1308106114yesdirect product factor
744C2C2×#1062308211yescharacteristic
745C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
746C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#440C2
socleC23×C11C22×D4
prime radicalC2×#10623082C2
hypercenterC2×#440D11
hypocenterC11C2×#3343
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#10623112C2semidirect
3. #13081061C2direct (N × H)
4. C2×#10622315C2semidirect
5. C2×#10622422C2semidirect
6. C2×#10622392C2semidirect
7. C2×#10622418C2semidirect
8. C2×#10622387C2semidirect
9. C2×#10622634C2semidirect
10. C2×#10622622C2semidirect
11. C2×#10622787C2semidirect
12. C2×#10622784C2semidirect
13. C2×#10622319C2semidirect
14. C2×#10622494C2semidirect
15. C2×D11×#107C2semidirect
16. C2×C11×#440C2semidirect
29. #10623112C22semidirect
45. C11×#440C22semidirect
54. #10622787C22semidirect
55. #10622784C22semidirect
62. #10622634C22semidirect
63. #10622622C22semidirect
69. #10622494C22semidirect
70. D11×#107C22semidirect
71. #10622422C22semidirect
72. #10622418C22semidirect
73. #10622392C22semidirect
74. #10622387C22semidirect
75. #10622319C22semidirect
76. #10622315C22semidirect
231. C2×C8×C11#41semidirect
286. C2×#440D11semidirect
350. C8×C11C2×#41semidirect
390. #440C2×D11semidirect
547. C2×C11#3343semidirect
609. C2×C8#4339semidirect
646. C11C2×#3343semidirect
709. C8C2×#4339semidirect
743. C2#13081061direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231122
C2×#106230822
#130810612
C2×#106223152
C2×#106224222
C2×#106223922
C2×#106224182
C2×#106223872
C2×#106226342
C2×#106226222
C2×#106227872
C2×#106227842
C2×#106223192
C2×#106224942
C2×D11×#1072
C2×C11×#4402
C2×#334311