Finite Group Databasebeta

← C2×#13081106 #15632357

Subgroups — C2×#13081106 #15632357

Order 2816.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623110C211yesmaximal, characteristic, complemented
2C2×#10623089C211yesmaximal, characteristic
3#13081106C2116yesmaximal, direct product factor
4C2×#10622315C211yesmaximal, characteristic, complemented
5C2×#10622422C211yesmaximal, characteristic, complemented
6C2×#10622390C211yesmaximal, characteristic, complemented
7C2×#10622428C211yesmaximal, characteristic, complemented
8C2×#10622387C211yesmaximal, characteristic, complemented
9C2×#10622635C211yesmaximal, characteristic, complemented
10C2×#10622620C211yesmaximal, 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×C11×SD16C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×#66999C2211yescharacteristic
21C2×#66999C2211yescharacteristic
22C2×#66991C2211yescharacteristic
23C2×#66991C2211yescharacteristic
24C2×#66982—21no—
25C2×C4×C22⋊D11—21no—
26C22×#4313C2211yescharacteristic
27C22×C8×D11C2211yescharacteristic
28#10623110—24no—
29#10623110C2218yescomplemented
30#10623089—24no—
31#10623089C2218yes—
32C2×#66949—21no—
33C2×#66949—21no—
34C2×#66945C2211yescharacteristic
35C2×C4⋊C4×D11C2211yescharacteristic
36C2×C4⋊C4×D11C2211yescharacteristic
37C2×C4⋊C4×D11C2211yescharacteristic
38C2×#66937—21no—
39C2×#66932—21no—
40C2×C4×D44—21no—
41C2×C4×D44C2211yescharacteristic
42C2×#66923—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#10622635C2218yescomplemented
63#10622620C2218yescomplemented
64C2×#66872C2211yescharacteristic
65C2×#66871C2211yescharacteristic
66C2×#66871C2211yescharacteristic
67C2×#66871C2211yescharacteristic
68C2×C4⋊(C11⋊C8)C2211yescharacteristic
69#10622494C2218yescomplemented
70D11×#107C2218yescomplemented
71#10622428C2218yescomplemented
72#10622422C2218yescomplemented
73#10622390C2218yescomplemented
74#10622387C2218yescomplemented
75#10622319C2218yescomplemented
76#10622315C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11—21no—
80C22×C22⋊D11—21no—
81C22×C22⋊D11—21no—
82C22×D44D411yescharacteristic
83C22×C4×D11—21no—
84C22×C4×D11—21no—
85C22×C4×D11—21no—
86C22×C4×D11C2311yescharacteristic
87C22×C4×D11C2311yescharacteristic
88C22×Dic22—21no—
89C2×C11×SD16—24no—
90C2×C11×SD16C2314yes—
91C22×C8×C11C2311yescharacteristic
92C22×C8×C11C2311yescharacteristic
93C4×Q8×C11—22no—
94C4×Q8×C11C2314yes—
95C4×D4×C11—22no—
96C4×D4×C11C2314yes—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C22⋊C4—21no—
101C2×C42×C11—21no—
102C2×C42×C11C2311yescharacteristic
103C2×C22⋊Dic11—21no—
104C2×C22⋊Dic11—21no—
105#66999—22no—
106#66999—22no—
107#66999C2314yes—
108#66999C2314yes—
109#66991—22no—
110#66991—22no—
111#66991C2314yes—
112#66991C2314yes—
113#66982—28no—
114C4×C22⋊D11—28no—
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
126C2×Dic11⋊C4—21no—
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×C4×Dic11—21no—
134C22×C11⋊C8C2311yescharacteristic
135C22×C11⋊C8C2311yescharacteristic
136C2×#4313—24no—
137C2×#4313C2314yes—
138C2×C8×D11—24no—
139C2×C8×D11C2314yes—
140#66949—28no—
141#66949—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#66937—28no—
151#66932—28no—
152C4×D44—28no—
153C4×D44D414yes—
154C4×D44C2314yes—
155#66923—22no—
156#66923—28no—
157#66923C2314yes—
158#66922—22no—
159#66922C2314yes—
160C11×#107C2314yes—
161C11×#103C2314yes—
162C11×#102C2314yes—
163C11×#97C2314yes—
164#66899C2314yes—
165#66899C2314yes—
166#66896C2314yes—
167#66896C2314yes—
168(C2×D11)⋊C8C2314yes—
169(C2×D11)⋊C8C2314yes—
170#66882C2314yes—
171#66882C2314yes—
172#66881C2314yes—
173#66881C2314yes—
174#66872C2314yes—
175#66871C2314yes—
176#66871C2314yes—
177#66871C2314yes—
178C4⋊(C11⋊C8)C2314yes—
179C2×#3346—111nomaximal, Sylow
180C24×C11—21no—
181C23×D11C2×D411yescharacteristic
182C23×D11C2×D411yescharacteristic
183C2×Q8×C11—21no—
184C2×Q8×C11—22no—
185C2×Q8×C11—22no—
186C2×Q8×C11C2412yes—
187C2×D4×C11—21no—
188C2×D4×C11—22no—
189C2×D4×C11—22no—
190C2×D4×C11C2412yes—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—24no—
195C22×C4×C11—82no—
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2411yescharacteristic
199C2×C22⋊D11—24no—
200C2×C22⋊D11—24no—
201C2×C22⋊D11—44no—
202C2×C22⋊D11—82no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11C2×D411yescharacteristic
208C22×Dic11C2×D411yescharacteristic
209C2×D44—24no—
210C2×D44C2×D414yes—
211C2×C4×D11—24no—
212C2×C4×D11—24no—
213C2×C4×D11—24no—
214C2×C4×D11—22no—
215C2×C4×D11—22no—
216C2×C4×D11—22no—
217C2×C4×D11—22no—
218C2×C4×D11—82no—
219C2×C4×D11—82no—
220C2×C4×D11—82no—
221C2×C4×D11C2×D412yes—
222C2×C4×D11C2×D412yes—
223C2×C4×D11C2412yes—
224C2×C4×D11C2412yes—
225C2×Dic22—24no—
226C2×Dic22—82no—
227C11×SD16—28no—
228C2×C8×C11—22no—
229C2×C8×C11#4114yes—
230C2×C8×C11C2412yes—
231C2×C8×C11C2412yes—
232C11×C4⋊C4—21no—
233C11×C4⋊C4—21no—
234C11×C4⋊C4—24no—
235C11×C4⋊C4C2412yes—
236C11×C4⋊C4C2412yes—
237C11×C22⋊C4—24no—
238C42×C11—24no—
239C42×C11C2×D412yes—
240C42×C11C2412yes—
241C22⋊Dic11—24no—
242C22⋊Dic11—24no—
243(C2×D11)⋊C4—24no—
244(C2×D11)⋊C4—24no—
245(C2×D11)⋊C4—24no—
246(C2×D11)⋊C4C2×D414yes—
247(C2×D11)⋊C4C2×D414yes—
248C4⋊Dic11—21no—
249C4⋊Dic11—21no—
250C4⋊Dic11—24no—
251C4⋊Dic11—21no—
252C4⋊Dic11—21no—
253C4⋊Dic11C2×D414yes—
254C4⋊Dic11C2412yes—
255C4⋊Dic11C2412yes—
256C4⋊Dic11C2412yes—
257C4⋊Dic11C2412yes—
258Dic11⋊C4—24no—
259Dic11⋊C4—24no—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263Dic11⋊C4—24no—
264Dic11⋊C4—24no—
265C4×Dic11—24no—
266C2×C11⋊C8—22no—
267C2×C11⋊C8—22no—
268C2×C11⋊C8C2412yes—
269C2×C11⋊C8C2412yes—
270#4313—28no—
271C8×D11—28no—
272C2×#554—111no—
273C2×#553—111no—
274#3346—1116no—
275C2×#501—111no—
276C2×#484—111no—
277C2×#481—111no—
278C2×#485—111no—
279C2×#480—111no—
280C2×#479—111no—
281C2×#474—111no—
282C2×#468—111no—
283C2×#465—111no—
284C2×#440D1111yescharacteristic, complemented
285C2×#435—111no—
286C2×#428—111no—
287C22×#107—111no—
288C23×C11—22no—
289C23×C11—42no—
290C23×C11—42no—
291C23×C11—42no—
292C23×C11C22×D411yescharacteristic
293C22×D11—22no—
294C22×D11—22no—
295C22×D11—22no—
296C22×D11—22no—
297C22×D11—22no—
298C22×D11#13714yes—
299C22×D11C22×D412yes—
300C22×D11C22×D412yes—
301Q8×C11—22no—
302Q8×C11—22no—
303Q8×C11—42no—
304D4×C11—22no—
305D4×C11—22no—
306D4×C11—42no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11—84no—
316C2×C4×C11C22×D412yes—
317C2×C4×C11C22×D412yes—
318C2×C4×C11C22×D411yescharacteristic
319C2×C4×C11C2×#4112yes—
320C2×C4×C112−1+412yes—
321C2×C4×C11C2511yescharacteristic
322C22⋊D11—48no—
323C22⋊D11—84no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—42no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11C22×D412yes—
335C2×Dic11C22×D412yes—
336D44—28no—
337C4×D11—24no—
338C4×D11—24no—
339C4×D11—22no—
340C4×D11—22no—
341C4×D11—22no—
342C4×D11—22no—
343C4×D11—84no—
344C4×D11—84no—
345C4×D11—84no—
346Dic22—84no—
347C8×C11—22no—
348C8×C11C2×#4114yes—
349C11⋊C8—22no—
350C11⋊C8—22no—
351C22×SD16C2×D1111yescharacteristic
352C22×M16—111no—
353C23×C8—111no—
354#554—118no—
355#554—224no—
356#553—118no—
357#553—224no—
358C2×C4⋊Q8—111no—
359C2×#126—221no—
360C2×#125—111no—
361C2×#125—221no—
362C2×#123—221no—
363C2×C22⋊Q8—111no—
364C2×C22⋊Q8—111no—
365C2×C22⋊Q8—221no—
366C2×C22⋊Q8—221no—
367C2×#121—111no—
368C2×#121—111no—
369C2×#121—221no—
370C2×C4×Q8C2×D1111yescharacteristic
371C2×C4×D4—111no—
372C2×C4×D4—221no—
373C2×C4×D4—221no—
374C2×C4×D4C2×D1111yescharacteristic
375C2×#117—111no—
376C22×C4⋊C4—111no—
377C22×C4⋊C4—111no—
378C22×C4⋊C4—111no—
379#501—118no—
380#485—118no—
381#484—118no—
382#481—118no—
383#480—118no—
384#479—118no—
385#474—118no—
386#468—118no—
387#465—118no—
388#440C2×D1118yescomplemented
389#435—118no—
390#428—118no—
391C2×#107—111no—
392C2×#107—111no—
393C2×#107—111no—
394C2×#107—111no—
395C2×#107—111no—
396C2×#107—118no—
397C2×#107C2×D1111yescharacteristic
398C2×#106—111no—
399C2×#106—111no—
400C2×#106—111no—
401C2×C4⋊C8—111no—
402C2×#103—111no—
403C2×#103—111no—
404C2×#103C2×D1111yescharacteristic
405C2×#102—111no—
406C2×#102—111no—
407C2×#102C2×D1111yescharacteristic
408C2×C22⋊C8—111no—
409C2×C22⋊C8—111no—
410C2×#97C2×D1111yescharacteristic
411C22×C11—42no—
412C22×C11—42no—
413C22×C11—42no—
414C22×C11—84no—
415C22×C11#54712yes—
416C22×C11C2×#13712yes—
417C22×C11#57612yes—
418C22×C11C23×D411yescharacteristic
419C2×D11—28no—
420C2×D11—22no—
421C2×D11—22no—
422C2×D11—22no—
423C2×D11—22no—
424C2×D11—22no—
425C2×D11—44no—
426C2×D11C2×#13714yes—
427C4×C11—22no—
428C4×C11—22no—
429C4×C11—42no—
430C4×C11—42no—
431C4×C11—42no—
432C4×C11#54712yes—
433C4×C11C22×#4111yescharacteristic
434C4×C11C2×2−1+411yescharacteristic
435Dic11—22no—
436Dic11—22no—
437Dic11—42no—
438Dic11—42no—
439Dic11—42no—
440Dic11—42no—
441C22×Q8—221no—
442C22×Q8C22×D1111yescharacteristic
443C22×D4—111no—
444C22×D4—221no—
445C22×D4—221no—
446C22×D4C22×D1111yescharacteristic
447C23×C4—21no—
448C23×C4—111no—
449C23×C4—111no—
450C23×C4—221no—
451C23×C4—221no—
452C23×C4—221no—
453C2×SD16—24no—
454C2×SD16C22×D1114yes—
455C2×M16—114no—
456C2×M16—224no—
457C22×C8—111no—
458C22×C8—111no—
459C22×C8—114no—
460C22×C8—224no—
461C22×C8C22×D1111yescharacteristic
462C22×C8C22×D1111yescharacteristic
463C4⋊Q8—114no—
464C4⋊Q8—222no—
465#126—228no—
466#125—114no—
467#125—228no—
468#125—222no—
469#123—228no—
470C22⋊Q8—114no—
471C22⋊Q8—114no—
472C22⋊Q8—228no—
473C22⋊Q8—228no—
474C22⋊Q8—222no—
475C22⋊Q8—222no—
476#121—114no—
477#121—114no—
478#121—228no—
479#121—222no—
480#121—222no—
481C4×Q8—22no—
482C4×Q8C22×D1114yes—
483C4×D4—22no—
484C4×D4—114no—
485C4×D4—114no—
486C4×D4—228no—
487C4×D4—228no—
488C4×D4C22×D1114yes—
489#117—114no—
490#117—222no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—111no—
493C2×C4⋊C4—111no—
494C2×C4⋊C4—111no—
495C2×C4⋊C4—111no—
496C2×C4⋊C4—111no—
497C2×C4⋊C4—114no—
498C2×C4⋊C4—114no—
499C2×C4⋊C4—114no—
500C2×C4⋊C4—222no—
501C2×C4⋊C4—222no—
502C2×C4⋊C4—222no—
503C2×C4⋊C4—221no—
504C2×C4⋊C4—221no—
505C2×C4⋊C4—221no—
506C2×C4⋊C4—221no—
507C2×C4⋊C4—221no—
508C2×C4⋊C4—221no—
509C2×C4⋊C4—221no—
510C2×C4⋊C4—221no—
511C2×C4⋊C4C22×D1111yescharacteristic
512C2×C4⋊C4C22×D1111yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—111no—
515C2×C22⋊C4—111no—
516C2×C22⋊C4—221no—
517C2×C22⋊C4—221no—
518C2×C22⋊C4—221no—
519C2×C22⋊C4—221no—
520C2×C22⋊C4—221no—
521C2×C42—21no—
522C2×C42—221no—
523C2×C42C22×D1111yescharacteristic
524#107—114no—
525#107—114no—
526#107—114no—
527#107—114no—
528#107—114no—
529#107C22×D1114yes—
530#106—114no—
531#106—114no—
532#106—114no—
533C4⋊C8—114no—
534#103—114no—
535#103—114no—
536#103C22×D1114yes—
537#102—114no—
538#102—114no—
539#102C22×D1114yes—
540C22⋊C8—114no—
541C22⋊C8—114no—
542#97C22×D1114yes—
543C2×C11—82no—
544C2×C11#334614yescomplemented
545C2×C11C2×#54711yescharacteristic
546C2×C11C22×#13711yescharacteristic
547C2×C11C2×#57611yescharacteristic
548D11—24no—
549D11—42no—
550C24—21no—
551C24—111no—
552C24—111no—
553C2×Q8—21no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—224no—
557C2×Q8—882no—
558C2×Q8C23×D1112yes—
559C2×D4—22no—
560C2×D4—21no—
561C2×D4—22no—
562C2×D4—114no—
563C2×D4—224no—
564C2×D4—224no—
565C2×D4—224no—
566C2×D4—444no—
567C2×D4—882no—
568C2×D4C23×D1112yes—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—24no—
573C22×C4—82no—
574C22×C4—111no—
575C22×C4—111no—
576C22×C4—112no—
577C22×C4—112no—
578C22×C4—112no—
579C22×C4—112no—
580C22×C4—224no—
581C22×C4—224no—
582C22×C4—224no—
583C22×C4—222no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—222no—
587C22×C4—221no—
588C22×C4—221no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—882no—
592C22×C4—882no—
593C22×C4—882no—
594C22×C4D4×D1111yescharacteristic
595C22×C4D4×D1111yescharacteristic
596C22×C4C23×D1111yescharacteristic
597SD16—28no—
598M16—228no—
599C2×C8—22no—
600C2×C8—112no—
601C2×C8—112no—
602C2×C8—222no—
603C2×C8—222no—
604C2×C8—228no—
605C2×C8#433914yes—
606C2×C8C23×D1112yes—
607C2×C8C23×D1112yes—
608C4⋊C4—24no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—114no—
612C4⋊C4—112no—
613C4⋊C4—112no—
614C4⋊C4—112no—
615C4⋊C4—112no—
616C4⋊C4—224no—
617C4⋊C4—224no—
618C4⋊C4—224no—
619C4⋊C4—224no—
620C4⋊C4—224no—
621C4⋊C4—221no—
622C4⋊C4—221no—
623C4⋊C4—221no—
624C4⋊C4—221no—
625C4⋊C4—224no—
626C4⋊C4—224no—
627C4⋊C4—224no—
628C4⋊C4C23×D1112yes—
629C4⋊C4C23×D1112yes—
630C22⋊C4—24no—
631C22⋊C4—114no—
632C22⋊C4—114no—
633C22⋊C4—224no—
634C22⋊C4—224no—
635C22⋊C4—224no—
636C22⋊C4—224no—
637C22⋊C4—224no—
638C42—24no—
639C42—224no—
640C42D4×D1112yes—
641C42C23×D1112yes—
642C11C2×#334611yescharacteristic, complemented, Sylow
643C23—22no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—114no—
648C23—112no—
649C23—112no—
650C23—222no—
651C23—222no—
652C23—222no—
653C23—222no—
654C23—222no—
655C23C2×D4×D1111yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—884no—
660D4—22no—
661D4—22no—
662D4—42no—
663D4—228no—
664D4—448no—
665D4—884no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—84no—
675C2×C4—112no—
676C2×C4—112no—
677C2×C4—222no—
678C2×C4—222no—
679C2×C4—224no—
680C2×C4—224no—
681C2×C4—222no—
682C2×C4—222no—
683C2×C4—222no—
684C2×C4—222no—
685C2×C4—222no—
686C2×C4—222no—
687C2×C4—222no—
688C2×C4—222no—
689C2×C4—442no—
690C2×C4—442no—
691C2×C4—442no—
692C2×C4—442no—
693C2×C4—884no—
694C2×C4—884no—
695C2×C4—884no—
696C2×C4C2×#433912yes—
697C2×C4C2×D4×D1112yes—
698C2×C4C2×D4×D1112yes—
699C2×C4C2×D4×D1111yescharacteristic
700C2×C4#6704312yes—
701C2×C4C24×D1111yescharacteristic
702C8—22no—
703C8—222no—
704C8—222no—
705C8C2×#433914yes—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—84no—
710C22—114no—
711C22—228no—
712C22—222no—
713C22—222no—
714C22—222no—
715C22—222no—
716C22—222no—
717C22—444no—
718C22#1062308212yes—
719C22#1062330512yes—
720C22D11×#13712yes—
721C22C22×D4×D1111yescharacteristic
722C4—22no—
723C4—22no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—222no—
728C4—222no—
729C4—442no—
730C4—442no—
731C4—442no—
732C4—442no—
733C4#1062308212yes—
734C4C22×#433911yescharacteristic
735C4C2×#6704311yescharacteristic
736C2—82no—
737C2—224no—
738C2—442no—
739C2#1308110614yesdirect product factor
740C2C2×#1062308211yescharacteristic
741C2C2×D11×#13711yescharacteristic
742C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#440C2
socleC23×C11C22×D4
prime radicalC2×#10623089C2
hypercenterC2×#440D11
hypocenterC11C2×#3346
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×#10623110C2semidirect
3. #13081106C2direct (N × H)
4. C2×#10622315C2semidirect
5. C2×#10622422C2semidirect
6. C2×#10622390C2semidirect
7. C2×#10622428C2semidirect
8. C2×#10622387C2semidirect
9. C2×#10622635C2semidirect
10. C2×#10622620C2semidirect
11. C2×#10622787C2semidirect
12. C2×#10622784C2semidirect
13. C2×#10622319C2semidirect
14. C2×#10622494C2semidirect
15. C2×D11×#107C2semidirect
16. C2×C11×#440C2semidirect
29. #10623110C22semidirect
45. C11×#440C22semidirect
54. #10622787C22semidirect
55. #10622784C22semidirect
62. #10622635C22semidirect
63. #10622620C22semidirect
69. #10622494C22semidirect
70. D11×#107C22semidirect
71. #10622428C22semidirect
72. #10622422C22semidirect
73. #10622390C22semidirect
74. #10622387C22semidirect
75. #10622319C22semidirect
76. #10622315C22semidirect
284. C2×#440D11semidirect
388. #440C2×D11semidirect
544. C2×C11#3346semidirect
642. C11C2×#3346semidirect
739. C2#13081106direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231102
C2×#106230892
#130811062
C2×#106223152
C2×#106224222
C2×#106223902
C2×#106224282
C2×#106223872
C2×#106226352
C2×#106226202
C2×#106227872
C2×#106227842
C2×#106223192
C2×#106224942
C2×D11×#1072
C2×C11×#4402
C2×#334611