Finite Group Databasebeta

← C2×#13081097 #15632348

Subgroups — C2×#13081097 #15632348

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×#10623042C211yesmaximal, characteristic, complemented
2C2×#10623045C211yesmaximal, characteristic
3#13081097C2116yesmaximal, direct product factor
4C2×#10622489C211yesmaximal, characteristic, complemented
5C2×#10622583C211yesmaximal, characteristic, complemented
6C2×#10622581C211yesmaximal, characteristic, complemented
7C2×#10622501C211yesmaximal, characteristic, complemented
8C2×#10622495C211yesmaximal, characteristic, complemented
9C2×#10622490C211yesmaximal, characteristic, complemented
10C2×#10622503C211yesmaximal, characteristic, complemented
11C2×#10622499C211yesmaximal, characteristic, complemented
12C2×#10622727C211yesmaximal, characteristic, complemented
13C2×#10622502C211yesmaximal, characteristic, complemented
14C2×#10622724C211yesmaximal, characteristic, complemented
15C2×#10622494C211yesmaximal, characteristic, complemented
16C22×C11×#107C211yesmaximal, characteristic, complemented
17C23×C8×C11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C2×#66983—21no—
21C2×#66983C2211yescharacteristic
22C2×C4×C22⋊D11—21no—
23C2×C4×C22⋊D11—21no—
24C2×C4×C22⋊D11C2211yescharacteristic
25C2×#66977—21no—
26C2×#66977C2211yescharacteristic
27C22×#4314C2211yescharacteristic
28C22×#4313C2211yescharacteristic
29#10623045—24no—
30#10623045C2218yes—
31C2×#66951—21no—
32#10623042—24no—
33#10623042C2218yescomplemented
34C2×#66950C2211yescharacteristic
35C2×#66949—21no—
36C2×#66948C2211yescharacteristic
37C2×#66947—21no—
38C2×#66946C2211yescharacteristic
39C2×#66945C2211yescharacteristic
40C2×C4⋊C4×D11C2211yescharacteristic
41C2×#66943C2211yescharacteristic
42C2×#66942—21no—
43C2×#66941C2211yescharacteristic
44C2×#66940C2211yescharacteristic
45C2×C11×#107C2211yescharacteristic
46C2×C11×#107C2211yescharacteristic
47C2×C11×#107C2211yescharacteristic
48C2×C11×#107C2211yescharacteristic
49C2×C11×#107C2218yescomplemented
50C2×C22⋊(C11⋊C8)C2211yescharacteristic
51#10622727C2218yescomplemented
52C2×#66885C2211yescharacteristic
53#10622724C2218yescomplemented
54C2×(C2×D11)⋊C8C2211yescharacteristic
55C2×#66881C2211yescharacteristic
56C2×#66880C2211yescharacteristic
57C2×#66879C2211yescharacteristic
58C2×Dic11⋊C8C2211yescharacteristic
59#10622583C2218yescomplemented
60C2×#66874C2211yescharacteristic
61C2×#66874C2211yescharacteristic
62#10622581C2218yescomplemented
63C2×#66873C2211yescharacteristic
64C2×#66873C2211yescharacteristic
65C2×#66872C2211yescharacteristic
66C2×#66872C2211yescharacteristic
67C2×#66871C2211yescharacteristic
68C2×#66871C2211yescharacteristic
69#10622503C2218yescomplemented
70#10622502C2218yescomplemented
71#10622501C2218yescomplemented
72#10622499C2218yescomplemented
73#10622495C2218yescomplemented
74#10622494C2218yescomplemented
75#10622490C2218yescomplemented
76#10622489C2218yescomplemented
77C23×C4×C11—21no—
78C23×C4×C11—21no—
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11—21no—
81C22×C22⋊D11D411yescharacteristic
82C22×D44—21no—
83C22×D44C2311yescharacteristic
84C22×C4×D11—21no—
85C22×C4×D11—21no—
86C22×C4×D11C2311yescharacteristic
87C22×Dic22—21no—
88C22×Dic22C2311yescharacteristic
89C22×C8×C11—24no—
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2314yes—
92C22×C8×C11C2311yescharacteristic
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4—22no—
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2314yes—
102C2×C11×C4⋊C4C2314yes—
103C2×C22⋊Dic11—21no—
104C2×C22⋊Dic11D411yescharacteristic
105#66983—22no—
106#66983—28no—
107#66983C2314yes—
108C4×C22⋊D11—28no—
109C4×C22⋊D11—28no—
110C4×C22⋊D11D414yes—
111C4×C22⋊D11C2314yes—
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)⋊C4D411yescharacteristic
118C2×C4⋊Dic11—21no—
119C2×C4⋊Dic11—21no—
120C2×C4⋊Dic11C2311yescharacteristic
121C2×C4⋊Dic11C2311yescharacteristic
122#66977—22no—
123#66977—28no—
124#66977C2314yes—
125C2×Dic11⋊C4—21no—
126C2×Dic11⋊C4—21no—
127C2×Dic11⋊C4—21no—
128C2×Dic11⋊C4—21no—
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4D411yescharacteristic
131C2×C4×Dic11—21no—
132C2×C4×Dic11—21no—
133C2×C4×Dic11C2311yescharacteristic
134C22×C11⋊C8C2311yescharacteristic
135C22×C11⋊C8C2311yescharacteristic
136C2×#4314—24no—
137C2×#4314C2314yes—
138C2×#4313—24no—
139C2×#4313C2314yes—
140#66951—28no—
141#66950—22no—
142#66950C2314yes—
143#66949—28no—
144#66948—22no—
145#66948C2314yes—
146#66947—28no—
147#66946—22no—
148#66946C2314yes—
149#66945—22no—
150#66945C2314yes—
151C4⋊C4×D11—22no—
152C4⋊C4×D11C2314yes—
153#66943—22no—
154#66943C2314yes—
155#66942—28no—
156#66941—22no—
157#66941C2314yes—
158#66940—22no—
159#66940C2314yes—
160C11×#107C2314yes—
161C11×#107C2314yes—
162C11×#107C2314yes—
163C11×#107C2314yes—
164C22⋊(C11⋊C8)C2314yes—
165#66885C2314yes—
166(C2×D11)⋊C8C2314yes—
167#66881C2314yes—
168#66880C2314yes—
169#66879C2314yes—
170Dic11⋊C8C2314yes—
171#66874C2314yes—
172#66874C2314yes—
173#66873C2314yes—
174#66873C2314yes—
175#66872C2314yes—
176#66872C2314yes—
177#66871C2314yes—
178#66871C2314yes—
179C2×#3346—111nomaximal, Sylow
180C24×C11C2×D411yescharacteristic
181C23×D11—21no—
182C23×D11C2×D411yescharacteristic
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—24no—
190C22×C4×C11—24no—
191C22×C4×C11—82no—
192C22×C4×C11—82no—
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D412yes—
195C22×C4×C11C2412yes—
196C22×C4×C11C2411yescharacteristic
197C2×C22⋊D11—24no—
198C2×C22⋊D11—24no—
199C2×C22⋊D11—44no—
200C2×C22⋊D11C2×D414yes—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11C2×D411yescharacteristic
205C22×Dic11C2×D411yescharacteristic
206C22×Dic11C2×D411yescharacteristic
207C2×D44—24no—
208C2×D44—21no—
209C2×D44—22no—
210C2×D44—22no—
211C2×D44—82no—
212C2×D44C2412yes—
213C2×C4×D11—24no—
214C2×C4×D11—24no—
215C2×C4×D11—22no—
216C2×C4×D11—22no—
217C2×C4×D11—82no—
218C2×C4×D11—82no—
219C2×C4×D11C2×D412yes—
220C2×C4×D11C2412yes—
221C2×Dic22—24no—
222C2×Dic22—21no—
223C2×Dic22—22no—
224C2×Dic22—22no—
225C2×Dic22—82no—
226C2×Dic22C2412yes—
227C2×C8×C11—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⋊C4—21no—
236C11×C4⋊C4—21no—
237C11×C4⋊C4—24no—
238C11×C4⋊C4C2412yes—
239C11×C4⋊C4C2412yes—
240C11×C4⋊C4C2412yes—
241C11×C4⋊C4C2412yes—
242C22⋊Dic11—24no—
243C22⋊Dic11C2×D414yes—
244(C2×D11)⋊C4—24no—
245(C2×D11)⋊C4—24no—
246(C2×D11)⋊C4—24no—
247(C2×D11)⋊C4—24no—
248(C2×D11)⋊C4—24no—
249(C2×D11)⋊C4C2×D414yes—
250C4⋊Dic11—24no—
251C4⋊Dic11—24no—
252C4⋊Dic11—21no—
253C4⋊Dic11—21no—
254C4⋊Dic11C2412yes—
255C4⋊Dic11C2412yes—
256Dic11⋊C4—24no—
257Dic11⋊C4—24no—
258Dic11⋊C4—24no—
259Dic11⋊C4—24no—
260Dic11⋊C4—24no—
261Dic11⋊C4C2×D414yes—
262C4×Dic11—24no—
263C4×Dic11—24no—
264C4×Dic11C2×D412yes—
265C4×Dic11C2412yes—
266C2×C11⋊C8—22no—
267C2×C11⋊C8—22no—
268C2×C11⋊C8C2412yes—
269C2×C11⋊C8C2412yes—
270#4314—28no—
271#4313—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×#440—111no—
285C2×#435—111no—
286C2×#428—111no—
287C22×#107D1111yescharacteristic, complemented
288C23×C11—22no—
289C23×C11—22no—
290C23×C11#13714yes—
291C23×C11C22×D412yes—
292C23×C11C22×D411yescharacteristic
293C22×D11—22no—
294C22×D11—22no—
295C22×D11—22no—
296C22×D11—22no—
297C22×D11—42no—
298C22×D11—42no—
299C22×D11—42no—
300C22×D11C22×D412yes—
301C2×C4×C11—22no—
302C2×C4×C11—24no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—42no—
310C2×C4×C11—42no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
313C2×C4×C11—84no—
314C2×C4×C11—84no—
315C2×C4×C11C22×D412yes—
316C2×C4×C11C22×D411yescharacteristic
317C2×C4×C11C2×#4112yes—
318C2×C4×C112−1+412yes—
319C2×C4×C11C2511yescharacteristic
320C22⋊D11—28no—
321C22⋊D11—48no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—42no—
329C2×Dic11—42no—
330C2×Dic11—42no—
331C2×Dic11C22×D412yes—
332C2×Dic11C22×D412yes—
333C2×Dic11C22×D412yes—
334D44—22no—
335D44—22no—
336D44—42no—
337D44—84no—
338C4×D11—24no—
339C4×D11—22no—
340C4×D11—22no—
341C4×D11—84no—
342C4×D11—84no—
343Dic22—22no—
344Dic22—22no—
345Dic22—42no—
346Dic22—84no—
347C8×C11—22no—
348C8×C11C2×#4114yes—
349C11⋊C8—22no—
350C11⋊C8—22no—
351C22×SD16—111no—
352C22×M16—111no—
353C23×C8C2×D1111yescharacteristic
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×Q8—111no—
371C2×C4×D4—111no—
372C2×C4×D4—111no—
373C2×C4×D4—221no—
374C2×C4×D4—221no—
375C2×#117—111no—
376C22×C4⋊C4—111no—
377C22×C4⋊C4C2×D1111yescharacteristic
378C22×C4⋊C4C2×D1111yescharacteristic
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#440—118no—
389#435—118no—
390#428—118no—
391C2×#107—111no—
392C2×#107—111no—
393C2×#107C2×D1111yescharacteristic
394C2×#107C2×D1111yescharacteristic
395C2×#107C2×D1111yescharacteristic
396C2×#107C2×D1111yescharacteristic
397C2×#107C2×D1118yescomplemented
398C2×#106—111no—
399C2×#106—111no—
400C2×#106—111no—
401C2×C4⋊C8—111no—
402C2×#103—111no—
403C2×#103—111no—
404C2×#103—111no—
405C2×#102—111no—
406C2×#102—111no—
407C2×#102—111no—
408C2×C22⋊C8—111no—
409C2×C22⋊C8—111no—
410C2×#97—111no—
411C22×C11—28no—
412C22×C11—22no—
413C22×C11—22no—
414C22×C11#54712yes—
415C22×C11C2×#13714yes—
416C22×C11C2×#13712yes—
417C22×C11#57612yes—
418C22×C11C23×D411yescharacteristic
419C2×D11—22no—
420C2×D11—22no—
421C2×D11—22no—
422C2×D11—44no—
423C2×D11—42no—
424C2×D11—42no—
425C2×D11—42no—
426C2×D11—84no—
427C4×C11—22no—
428C4×C11—42no—
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—22no—
438Dic11—42no—
439Dic11—42no—
440Dic11—42no—
441C22×Q8—111no—
442C22×Q8—221no—
443C22×D4—111no—
444C22×D4—111no—
445C22×D4—221no—
446C22×D4—221no—
447C23×C4—21no—
448C23×C4—21no—
449C23×C4—111no—
450C23×C4—221no—
451C23×C4—221no—
452C23×C4C22×D1111yescharacteristic
453C2×SD16—114no—
454C2×SD16—224no—
455C2×M16—114no—
456C2×M16—224no—
457C22×C8—24no—
458C22×C8—111no—
459C22×C8—111no—
460C22×C8C22×D1111yescharacteristic
461C22×C8C22×D1114yes—
462C22×C8C22×D1111yescharacteristic
463C4⋊Q8—114no—
464C4⋊Q8—222no—
465#126—228no—
466#125—114no—
467#125—222no—
468#125—228no—
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—222no—
479#121—228no—
480#121—222no—
481C4×Q8—114no—
482C4×Q8—222no—
483C4×D4—114no—
484C4×D4—114no—
485C4×D4—114no—
486C4×D4—222no—
487C4×D4—228no—
488C4×D4—228no—
489#117—114no—
490#117—222no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—111no—
496C2×C4⋊C4—111no—
497C2×C4⋊C4—111no—
498C2×C4⋊C4—114no—
499C2×C4⋊C4—222no—
500C2×C4⋊C4—221no—
501C2×C4⋊C4—221no—
502C2×C4⋊C4—221no—
503C2×C4⋊C4—221no—
504C2×C4⋊C4—221no—
505C2×C4⋊C4—221no—
506C2×C4⋊C4—221no—
507C2×C4⋊C4C22×D1111yescharacteristic
508C2×C4⋊C4C22×D1111yescharacteristic
509C2×C4⋊C4C22×D1111yescharacteristic
510C2×C4⋊C4C22×D1111yescharacteristic
511C2×C4⋊C4C22×D1114yes—
512C2×C4⋊C4C22×D1114yes—
513C2×C22⋊C4—111no—
514C2×C22⋊C4—111no—
515C2×C22⋊C4—221no—
516C2×C22⋊C4—221no—
517C2×C22⋊C4—221no—
518C2×C22⋊C4—221no—
519C2×C22⋊C4—221no—
520C2×C22⋊C4—221no—
521C2×C42—111no—
522C2×C42—221no—
523C2×C42—221no—
524#107—114no—
525#107—114no—
526#107C22×D1114yes—
527#107C22×D1114yes—
528#107C22×D1114yes—
529#107C22×D1114yes—
530#106—114no—
531#106—114no—
532#106—114no—
533C4⋊C8—114no—
534#103—114no—
535#103—114no—
536#103—114no—
537#102—114no—
538#102—114no—
539#102—114no—
540C22⋊C8—114no—
541C22⋊C8—114no—
542#97—114no—
543C2×C11—24no—
544C2×C11#334614yescomplemented
545C2×C11C2×#54711yescharacteristic
546C2×C11C22×#13711yescharacteristic
547C2×C11C2×#57611yescharacteristic
548D11—42no—
549D11—82no—
550C24—111no—
551C24—221no—
552C24D4×D1111yescharacteristic
553C2×Q8—112no—
554C2×Q8—224no—
555C2×Q8—221no—
556C2×Q8—222no—
557C2×Q8—222no—
558C2×Q8—882no—
559C2×D4—114no—
560C2×D4—112no—
561C2×D4—224no—
562C2×D4—224no—
563C2×D4—224no—
564C2×D4—222no—
565C2×D4—221no—
566C2×D4—222no—
567C2×D4—444no—
568C2×D4—882no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—82no—
578C22×C4—82no—
579C22×C4—111no—
580C22×C4—111no—
581C22×C4—111no—
582C22×C4—112no—
583C22×C4—112no—
584C22×C4—224no—
585C22×C4—224no—
586C22×C4—222no—
587C22×C4—222no—
588C22×C4—221no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—882no—
592C22×C4—882no—
593C22×C4D4×D1112yes—
594C22×C4D4×D1111yescharacteristic
595C22×C4C23×D1112yes—
596C22×C4C23×D1111yescharacteristic
597SD16—228no—
598M16—228no—
599C2×C8—22no—
600C2×C8—28no—
601C2×C8—112no—
602C2×C8—112no—
603C2×C8—222no—
604C2×C8—222no—
605C2×C8#433914yes—
606C2×C8C23×D1112yes—
607C2×C8C23×D1112yes—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—24no—
612C4⋊C4—21no—
613C4⋊C4—24no—
614C4⋊C4—114no—
615C4⋊C4—112no—
616C4⋊C4—112no—
617C4⋊C4—224no—
618C4⋊C4—224no—
619C4⋊C4—224no—
620C4⋊C4—224no—
621C4⋊C4—224no—
622C4⋊C4—224no—
623C4⋊C4—221no—
624C4⋊C4—221no—
625C4⋊C4—224no—
626C4⋊C4C23×D1112yes—
627C4⋊C4C23×D1112yes—
628C4⋊C4C23×D1112yes—
629C4⋊C4C23×D1112yes—
630C22⋊C4—114no—
631C22⋊C4—114no—
632C22⋊C4—224no—
633C22⋊C4—224no—
634C22⋊C4—224no—
635C22⋊C4—224no—
636C22⋊C4—224no—
637C22⋊C4—224no—
638C42—112no—
639C42—112no—
640C42—224no—
641C42—224no—
642C11C2×#334611yescharacteristic, complemented, Sylow
643C23—22no—
644C23—22no—
645C23—112no—
646C23—222no—
647C23—222no—
648C23—222no—
649C23—222no—
650C23—442no—
651C23—442no—
652C23—442no—
653C23#6697114yes—
654C23C2×D4×D1112yes—
655C23C2×D4×D1111yescharacteristic
656Q8—222no—
657Q8—222no—
658Q8—442no—
659Q8—884no—
660D4—228no—
661D4—222no—
662D4—222no—
663D4—448no—
664D4—442no—
665D4—884no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—84no—
679C2×C4—84no—
680C2×C4—112no—
681C2×C4—112no—
682C2×C4—112no—
683C2×C4—222no—
684C2×C4—222no—
685C2×C4—222no—
686C2×C4—224no—
687C2×C4—222no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—442no—
693C2×C4—442no—
694C2×C4—442no—
695C2×C4—884no—
696C2×C4—884no—
697C2×C4C2×#433912yes—
698C2×C4C2×D4×D1112yes—
699C2×C4C2×D4×D1111yescharacteristic
700C2×C4#6704012yes—
701C2×C4C24×D1111yescharacteristic
702C8—22no—
703C8—222no—
704C8—222no—
705C8C2×#433914yes—
706C22—28no—
707C22—22no—
708C22—22no—
709C22—222no—
710C22—222no—
711C22—222no—
712C22—444no—
713C22—442no—
714C22—442no—
715C22—442no—
716C22—884no—
717C22#1062303812yes—
718C22#1062328812yes—
719C22C2×#6697114yes—
720C22C2×#6697112yes—
721C22C22×D4×D1111yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—222no—
728C4—222no—
729C4—222no—
730C4—442no—
731C4—442no—
732C4—442no—
733C4#1062303812yes—
734C4C22×#433911yescharacteristic
735C4C2×#6704011yescharacteristic
736C2—24no—
737C2—442no—
738C2—882no—
739C2#1308109714yesdirect product factor
740C2C2×#1062303811yescharacteristic
741C2C22×#6697111yescharacteristic
742C2C2×#1062328811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×#107C2
socleC23×C11C22×D4
prime radicalC2×#10623045C2
hypercenterC22×#107D11
hypocenterC11C2×#3346
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#107

Complements

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

NH ≅ G/Ntype
1. C2×#10623042C2semidirect
3. #13081097C2direct (N × H)
4. C2×#10622489C2semidirect
5. C2×#10622583C2semidirect
6. C2×#10622581C2semidirect
7. C2×#10622501C2semidirect
8. C2×#10622495C2semidirect
9. C2×#10622490C2semidirect
10. C2×#10622503C2semidirect
11. C2×#10622499C2semidirect
12. C2×#10622727C2semidirect
13. C2×#10622502C2semidirect
14. C2×#10622724C2semidirect
15. C2×#10622494C2semidirect
16. C22×C11×#107C2semidirect
33. #10623042C22semidirect
49. C2×C11×#107C22semidirect
51. #10622727C22semidirect
53. #10622724C22semidirect
59. #10622583C22semidirect
62. #10622581C22semidirect
69. #10622503C22semidirect
70. #10622502C22semidirect
71. #10622501C22semidirect
72. #10622499C22semidirect
73. #10622495C22semidirect
74. #10622494C22semidirect
75. #10622490C22semidirect
76. #10622489C22semidirect
287. C22×#107D11semidirect
397. C2×#107C2×D11semidirect
544. C2×C11#3346semidirect
642. C11C2×#3346semidirect
739. C2#13081097direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230422
C2×#106230452
#130810972
C2×#106224892
C2×#106225832
C2×#106225812
C2×#106225012
C2×#106224952
C2×#106224902
C2×#106225032
C2×#106224992
C2×#106227272
C2×#106225022
C2×#106227242
C2×#106224942
C22×C11×#1072
C2×#334611