Finite Group Databasebeta

← C2×#13078827 #15622033

Subgroups — C2×#13078827 #15622033

Order 2816.

2070 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×#10623262C211yesmaximal, characteristic, complemented
2C2×#10623077C211yesmaximal, characteristic
3#13078827C2116yesmaximal, direct product factor
4C2×#10622422C211yesmaximal, characteristic, complemented
5C2×#10622418C211yesmaximal, characteristic, complemented
6C2×#10622442C211yesmaximal, characteristic, complemented
7C2×#10622622C211yesmaximal, characteristic, complemented
8C2×#10622703C211yesmaximal, characteristic, complemented
9C2×#10622786C211yesmaximal, characteristic
10C2×#10622786C211yesmaximal, characteristic
11C2×#10622402C211yesmaximal, characteristic, complemented
12C2×#10622777C211yesmaximal, characteristic, complemented
13C2×#10622403C211yesmaximal, characteristic, complemented
14C2×SD16×Dic11C211yesmaximal, characteristic, complemented
15C2×#10622453C211yesmaximal, characteristic, complemented
16C2×C11×#461C211yesmaximal, characteristic, complemented
17C22×#4341C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C2×C11×C4⋊Q8C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×#66999C2211yescharacteristic
23C2×#66999C2211yescharacteristic
24C2×Q8×Dic11C2211yescharacteristic
25C2×Q8×Dic11C2211yescharacteristic
26C22×#4326C2211yescharacteristic
27C22×#4326C2211yescharacteristic
28C2×D4×Dic11C2211yescharacteristic
29C2×C4×C22⋊D11—21no—
30C22×Dic11⋊C4—21no—
31#10623262—24no—
32#10623262C2218yescomplemented
33#10623077—24no—
34#10623077C2218yes—
35C2×#66951—21no—
36C2×#66951—21no—
37C2×C4⋊C4×D11C2211yescharacteristic
38C2×#66942—21no—
39C2×#66942—21no—
40C2×#66940C2211yescharacteristic
41C2×(C22⋊D11)⋊C4—21no—
42C2×#66930—21no—
43C2×#66925C2211yescharacteristic
44C2×#66923C2211yescharacteristic
45C2×C4×Dic22C2211yescharacteristic
46C11×#461C2218yescomplemented
47C2×C11×C4⋊C8C2211yescharacteristic
48C2×C11×#103C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×#66899C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52C2×#66896C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54#10622786C2218yes—
55#10622786C2218yes—
56#10622777C2218yescomplemented
57SD16×Dic11C2218yescomplemented
58C2×(C2×D11)⋊C8C2211yescharacteristic
59C2×(C2×D11)⋊C8C2211yescharacteristic
60C2×#66882C2211yescharacteristic
61C2×#66881C2211yescharacteristic
62C2×#66880C2211yescharacteristic
63C2×#66880C2211yescharacteristic
64C2×#66879C2211yescharacteristic
65C2×C8×Dic11C2211yescharacteristic
66#10622703C2218yescomplemented
67#10622622C2218yescomplemented
68C2×#66872C2211yescharacteristic
69C2×#66871C2211yescharacteristic
70C2×C4⋊(C11⋊C8)C2211yescharacteristic
71#10622453C2218yescomplemented
72#10622442C2218yescomplemented
73#10622422C2218yescomplemented
74#10622418C2218yescomplemented
75#10622403C2218yescomplemented
76#10622402C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11C2311yescharacteristic
80C23×C4×C11—21no—
81C22×C22⋊D11—21no—
82C23×Dic11—21no—
83C23×Dic11—21no—
84C2×#4341—24no—
85C2×#4341—22no—
86C2×#4341—24no—
87C2×#4341C2314yes—
88C22×C4×D11—21no—
89C22×C4×D11C2311yescharacteristic
90C22×Dic22C2311yescharacteristic
91C2×C11×SD16—24no—
92C2×C11×SD16—24no—
93C2×C11×SD16C2314yes—
94C2×C11×SD16C2314yes—
95C22×C8×C11C2311yescharacteristic
96C22×C8×C11C2311yescharacteristic
97C11×C4⋊Q8—22no—
98C11×C4⋊Q8C2314yes—
99C4×D4×C11—22no—
100C4×D4×C11C2314yes—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C22⋊C4—21no—
105C2×C42×C11C2311yescharacteristic
106C2×C22⋊Dic11—21no—
107#66999—22no—
108#66999—22no—
109#66999C2314yes—
110#66999C2314yes—
111Q8×Dic11—22no—
112Q8×Dic11—22no—
113Q8×Dic11C2314yes—
114Q8×Dic11C2314yes—
115C2×#4326—24no—
116C2×#4326—24no—
117C2×#4326C2314yes—
118C2×#4326C2314yes—
119D4×Dic11—22no—
120D4×Dic11C2314yes—
121C4×C22⋊D11—28no—
122C2×(C2×D11)⋊C4—21no—
123C2×(C2×D11)⋊C4—21no—
124C2×(C2×D11)⋊C4D411yescharacteristic
125C2×(C2×D11)⋊C4D411yescharacteristic
126C2×C4⋊Dic11—21no—
127C2×C4⋊Dic11—21no—
128C2×C4⋊Dic11C2311yescharacteristic
129C2×C4⋊Dic11C2311yescharacteristic
130C2×C4⋊Dic11C2311yescharacteristic
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4—21no—
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4—21no—
135C2×Dic11⋊C4—21no—
136C2×Dic11⋊C4—21no—
137C2×Dic11⋊C4—21no—
138C2×Dic11⋊C4—28no—
139C2×Dic11⋊C4D411yescharacteristic
140C2×Dic11⋊C4D411yescharacteristic
141C2×C4×Dic11—21no—
142C2×C4×Dic11—21no—
143C2×C4×Dic11—21no—
144C2×C4×Dic11—21no—
145C2×C4×Dic11C2311yescharacteristic
146C22×C11⋊C8C2311yescharacteristic
147C22×C11⋊C8C2311yescharacteristic
148#66951—28no—
149#66951—28no—
150C4⋊C4×D11—22no—
151C4⋊C4×D11C2314yes—
152#66942—28no—
153#66942—28no—
154#66940—22no—
155#66940C2314yes—
156(C22⋊D11)⋊C4—28no—
157#66930—28no—
158#66925D414yes—
159#66925C2314yes—
160#66923—22no—
161#66923C2314yes—
162C4×Dic22—22no—
163C4×Dic22C2314yes—
164C11×C4⋊C8C2314yes—
165C11×#103C2314yes—
166C11×#103C2314yes—
167#66899C2314yes—
168#66899C2314yes—
169#66896C2314yes—
170#66896C2314yes—
171(C2×D11)⋊C8C2314yes—
172(C2×D11)⋊C8C2314yes—
173#66882C2314yes—
174#66881C2314yes—
175#66880C2314yes—
176#66880C2314yes—
177#66879C2314yes—
178C8×Dic11C2314yes—
179#66872C2314yes—
180#66871C2314yes—
181C4⋊(C11⋊C8)C2314yes—
182C2×#3120—111nomaximal, Sylow
183C24×C11—21no—
184C23×D11C2×D411yescharacteristic
185C2×Q8×C11—21no—
186C2×Q8×C11—21no—
187C2×Q8×C11—22no—
188C2×Q8×C11—22no—
189C2×Q8×C11—22no—
190C2×Q8×C11—22no—
191C2×Q8×C11C2412yes—
192C2×Q8×C11C2412yes—
193C2×D4×C11—21no—
194C2×D4×C11—22no—
195C2×D4×C11#4114yes—
196C2×D4×C11C2412yes—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—24no—
201C22×C4×C11—82no—
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11C2411yescharacteristic
205C2×C22⋊D11—28no—
206C2×C22⋊D11—24no—
207C22×Dic11—28no—
208C22×Dic11—24no—
209C22×Dic11—24no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—82no—
215C22×Dic11C2×D411yescharacteristic
216C22×Dic11C2×D411yescharacteristic
217C22×Dic11C2×D411yescharacteristic
218#4341—216no—
219#4341—28no—
220#4341—28no—
221C2×C4×D11—24no—
222C2×C4×D11—22no—
223C2×C4×D11—22no—
224C2×C4×D11—82no—
225C2×C4×D11C2×D412yes—
226C2×C4×D11C2412yes—
227C2×Dic22—21no—
228C2×Dic22—22no—
229C2×Dic22#4114yes—
230C2×Dic22C2412yes—
231C11×SD16—28no—
232C11×SD16—28no—
233C2×C8×C11—22no—
234C2×C8×C11—22no—
235C2×C8×C11C2412yes—
236C2×C8×C11C2412yes—
237C11×C4⋊C4—21no—
238C11×C4⋊C4—24no—
239C11×C4⋊C4—24no—
240C11×C4⋊C4C2412yes—
241C11×C22⋊C4—24no—
242C42×C11C2×D412yes—
243C42×C11C2412yes—
244C22⋊Dic11—24no—
245#4326—28no—
246#4326—28no—
247(C2×D11)⋊C4—24no—
248(C2×D11)⋊C4—24no—
249(C2×D11)⋊C4C2×D414yes—
250(C2×D11)⋊C4C2×D414yes—
251C4⋊Dic11—24no—
252C4⋊Dic11—24no—
253C4⋊Dic11—21no—
254C4⋊Dic11—21no—
255C4⋊Dic11—21no—
256C4⋊Dic11C2412yes—
257C4⋊Dic11C2412yes—
258C4⋊Dic11C2412yes—
259Dic11⋊C4—24no—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263Dic11⋊C4—24no—
264Dic11⋊C4—24no—
265Dic11⋊C4—24no—
266Dic11⋊C4C2×D414yes—
267Dic11⋊C4C2×D414yes—
268C4×Dic11—24no—
269C4×Dic11—24no—
270C4×Dic11—24no—
271C4×Dic11—24no—
272C4×Dic11C2×D412yes—
273C4×Dic11C2412yes—
274C2×C11⋊C8—22no—
275C2×C11⋊C8—22no—
276C2×C11⋊C8C2412yes—
277C2×C11⋊C8C2412yes—
278C2×#541—111no—
279C2×#520—111no—
280#3120—1116no—
281C2×#484—111no—
282C2×#483—111no—
283C2×#479—111no—
284C2×#478—111no—
285C2×#462—111no—
286C2×#461D1111yescharacteristic, complemented
287C2×#452—111no—
288C2×#452—111no—
289C2×#441—111no—
290C2×#440—111no—
291C2×C4×Q16—111no—
292C2×C4×SD16—111no—
293C2×#433—111no—
294C23×C11—24no—
295C23×C11—22no—
296C23×C11—42no—
297C23×C11—42no—
298C23×C11C22×D411yescharacteristic
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—22no—
302C22×D11C22×D412yes—
303Q8×C11—22no—
304Q8×C11—22no—
305Q8×C11—22no—
306Q8×C11—22no—
307Q8×C11—42no—
308Q8×C11—42no—
309D4×C11—24no—
310D4×C11—22no—
311D4×C11C2×#4114yes—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—42no—
318C2×C4×C11—42no—
319C2×C4×C11—42no—
320C2×C4×C11—84no—
321C2×C4×C11C22×D412yes—
322C2×C4×C11C22×D412yes—
323C2×C4×C11C22×D411yescharacteristic
324C2×C4×C11C2×#4112yes—
325C2×C4×C11C2×#4112yes—
326C2×C4×C11C2511yescharacteristic
327C22⋊D11—216no—
328C2×Dic11—216no—
329C2×Dic11—24no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—84no—
341C2×Dic11C22×D412yes—
342C2×Dic11C22×D412yes—
343C2×Dic11C22×D412yes—
344C4×D11—24no—
345C4×D11—22no—
346C4×D11—22no—
347C4×D11—84no—
348Dic22—24no—
349Dic22—22no—
350Dic22C2×#4114yes—
351C8×C11—22no—
352C8×C11—22no—
353C11⋊C8—22no—
354C11⋊C8—22no—
355C22×#41—111no—
356C22×Q16—111no—
357C22×Q16—111no—
358C22×SD16C2×D1111yescharacteristic
359C22×SD16C2×D1111yescharacteristic
360#541—118no—
361#541—224no—
362C2×C4⋊Q8C2×D1111yescharacteristic
363C2×#126—221no—
364C2×#126—221no—
365C2×#125—111no—
366C2×#125—221no—
367C2×#125—221no—
368C2×C22⋊Q8—111no—
369C2×C22⋊Q8—111no—
370#520—118no—
371#520—224no—
372C2×C4×Q8—111no—
373C2×C4×Q8—111no—
374C2×C4×Q8—111no—
375C2×C4×Q8—111no—
376C2×C4×D4—111no—
377C2×C4×D4—221no—
378C2×C4×D4—221no—
379C2×C4×D4C2×D1111yescharacteristic
380C2×#117—111no—
381C2×#117—221no—
382C22×C4⋊C4—111no—
383C22×C4⋊C4—221no—
384#484—118no—
385#483—118no—
386#479—118no—
387#478—118no—
388#462—118no—
389#461C2×D1118yescomplemented
390#452—118no—
391#452—118no—
392#441—118no—
393#440—118no—
394C4×Q16—118no—
395C4×SD16—118no—
396#433—118no—
397C2×#107—111no—
398C2×#107—111no—
399C2×#106—111no—
400C2×#106—111no—
401C2×C4⋊C8—111no—
402C2×C4⋊C8C2×D1111yescharacteristic
403C2×#103—111no—
404C2×#103—111no—
405C2×#103—111no—
406C2×#103—111no—
407C2×#103C2×D1111yescharacteristic
408C2×#103C2×D1111yescharacteristic
409C2×#102—111no—
410C2×#102—111no—
411C2×C22⋊C8—111no—
412C2×C22⋊C8—111no—
413C2×#97—111no—
414C2×C4×C8—111no—
415C22×C11—24no—
416C22×C11—48no—
417C22×C11—42no—
418C22×C11—42no—
419C22×C11#52512yes—
420C22×C11#57712yes—
421C22×C11#57812yes—
422C22×C11C23×D411yescharacteristic
423C2×D11—22no—
424C2×D11—22no—
425C2×D11—22no—
426C2×D11—44no—
427C4×C11—22no—
428C4×C11—22no—
429C4×C11—42no—
430C4×C11—42no—
431C4×C11—42no—
432C4×C11#52512yes—
433C4×C11C22×#4111yescharacteristic
434C4×C11C22×#4111yescharacteristic
435Dic11—24no—
436Dic11—22no—
437Dic11—22no—
438Dic11—22no—
439Dic11—42no—
440Dic11—42no—
441Dic11—42no—
442C2×#41—114no—
443C2×#41—222no—
444C2×#41—224no—
445C2×#41—224no—
446C22×Q8—111no—
447C22×Q8C22×D1111yescharacteristic
448C22×Q8C22×D1111yescharacteristic
449C22×D4—221no—
450C22×D4C22×D1111yescharacteristic
451C23×C4—21no—
452C23×C4—111no—
453C23×C4—221no—
454C23×C4—221no—
455C23×C4—221no—
456C2×Q16—114no—
457C2×Q16—114no—
458C2×Q16—224no—
459C2×Q16—224no—
460C2×SD16—24no—
461C2×SD16—24no—
462C2×SD16C22×D1114yes—
463C2×SD16C22×D1114yes—
464C22×C8—111no—
465C22×C8—111no—
466C22×C8C22×D1111yescharacteristic
467C22×C8C22×D1111yescharacteristic
468C4⋊Q8—22no—
469C4⋊Q8C22×D1114yes—
470#126—228no—
471#126—228no—
472#125—114no—
473#125—228no—
474#125—228no—
475#125—222no—
476C22⋊Q8—114no—
477C22⋊Q8—114no—
478C22⋊Q8—222no—
479C22⋊Q8—222no—
480C4×Q8—114no—
481C4×Q8—114no—
482C4×Q8—114no—
483C4×Q8—114no—
484C4×Q8—222no—
485C4×Q8—222no—
486C4×Q8—222no—
487C4×Q8—222no—
488C4×D4—22no—
489C4×D4—114no—
490C4×D4—222no—
491C4×D4—228no—
492C4×D4—228no—
493C4×D4C22×D1114yes—
494#117—114no—
495#117—114no—
496#117—228no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—111no—
500C2×C4⋊C4—111no—
501C2×C4⋊C4—111no—
502C2×C4⋊C4—111no—
503C2×C4⋊C4—111no—
504C2×C4⋊C4—114no—
505C2×C4⋊C4—222no—
506C2×C4⋊C4—228no—
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⋊C4—221no—
515C2×C4⋊C4—221no—
516C2×C4⋊C4C22×D1111yescharacteristic
517C2×C22⋊C4—21no—
518C2×C22⋊C4—111no—
519C2×C22⋊C4—111no—
520C2×C22⋊C4—221no—
521C2×C22⋊C4—221no—
522C2×C22⋊C4—221no—
523C2×C42—111no—
524C2×C42—221no—
525C2×C42—221no—
526C2×C42—221no—
527C2×C42—221no—
528C2×C42C22×D1111yescharacteristic
529#107—114no—
530#107—114no—
531#106—114no—
532#106—114no—
533C4⋊C8—114no—
534C4⋊C8C22×D1114yes—
535#103—114no—
536#103—114no—
537#103—114no—
538#103—114no—
539#103C22×D1114yes—
540#103C22×D1114yes—
541#102—114no—
542#102—114no—
543C22⋊C8—114no—
544C22⋊C8—114no—
545#97—114no—
546C4×C8—114no—
547C2×C11—44no—
548C2×C11#312014yescomplemented
549C2×C11C2×#52511yescharacteristic
550C2×C11C2×#57711yescharacteristic
551C2×C11C2×#57811yescharacteristic
552D11—42no—
553C24—21no—
554C24—111no—
555#41—228no—
556#41—2216no—
557#41—228no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—114no—
565C2×Q8—112no—
566C2×Q8—221no—
567C2×Q8—222no—
568C2×Q8C23×D1112yes—
569C2×Q8C23×D1112yes—
570C2×D4—21no—
571C2×D4—22no—
572C2×D4—224no—
573C2×D4—228no—
574C2×D4#434114yes—
575C2×D4C23×D1112yes—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—24no—
580C22×C4—82no—
581C22×C4—111no—
582C22×C4—111no—
583C22×C4—111no—
584C22×C4—112no—
585C22×C4—112no—
586C22×C4—224no—
587C22×C4—224no—
588C22×C4—224no—
589C22×C4—228no—
590C22×C4—221no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4—221no—
594C22×C4—221no—
595C22×C4—221no—
596C22×C4—882no—
597C22×C4—882no—
598C22×C4D4×D1111yescharacteristic
599C22×C4D4×D1111yescharacteristic
600C22×C4C23×D1111yescharacteristic
601Q16—228no—
602Q16—228no—
603SD16—28no—
604SD16—28no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—112no—
608C2×C8—112no—
609C2×C8—222no—
610C2×C8—222no—
611C2×C8C23×D1112yes—
612C2×C8C23×D1112yes—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—114no—
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—224no—
627C4⋊C4—221no—
628C4⋊C4—221no—
629C4⋊C4—221no—
630C4⋊C4—224no—
631C4⋊C4—224no—
632C4⋊C4—224no—
633C4⋊C4C23×D1112yes—
634C22⋊C4—24no—
635C22⋊C4—114no—
636C22⋊C4—114no—
637C22⋊C4—224no—
638C22⋊C4—224no—
639C22⋊C4—224no—
640C42—112no—
641C42—112no—
642C42—224no—
643C42—224no—
644C42—224no—
645C42—224no—
646C42D4×D1112yes—
647C42C23×D1112yes—
648C11C2×#312011yescharacteristic, complemented, Sylow
649C23—24no—
650C23—22no—
651C23—42no—
652C23—42no—
653C23—112no—
654C23—222no—
655C23—222no—
656C23—222no—
657C23C2×D4×D1111yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—42no—
664Q8—114no—
665Q8—224no—
666Q8—222no—
667D4—24no—
668D4—22no—
669D4—2216no—
670D4C2×#434114yes—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—84no—
680C2×C4—112no—
681C2×C4—112no—
682C2×C4—112no—
683C2×C4—2216no—
684C2×C4—222no—
685C2×C4—222no—
686C2×C4—222no—
687C2×C4—224no—
688C2×C4—222no—
689C2×C4—224no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—222no—
694C2×C4—222no—
695C2×C4—442no—
696C2×C4—442no—
697C2×C4—442no—
698C2×C4—884no—
699C2×C4—884no—
700C2×C4C2×D4×D1112yes—
701C2×C4C2×D4×D1112yes—
702C2×C4C2×D4×D1111yescharacteristic
703C2×C4C2×#434112yes—
704C2×C4#41×D1112yes—
705C2×C4C24×D1111yescharacteristic
706C8—22no—
707C8—22no—
708C8—222no—
709C8—222no—
710C22—24no—
711C22—48no—
712C22—42no—
713C22—42no—
714C22—222no—
715C22—222no—
716C22—222no—
717C22—444no—
718C22#1062313712yes—
719C22#1062329312yes—
720C22#1062331012yes—
721C22C22×D4×D1111yescharacteristic
722C4—22no—
723C4—22no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—222no—
728C4—224no—
729C4—222no—
730C4—222no—
731C4—442no—
732C4—442no—
733C4—442no—
734C4#1062313712yes—
735C4C22×#434111yescharacteristic
736C4C2×#41×D1111yescharacteristic
737C2—44no—
738C2—442no—
739C2#1307882714yesdirect product factor
740C2C2×#1062313711yescharacteristic
741C2C2×#1062329311yescharacteristic
742C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#461C2
socleC23×C11C22×D4
prime radicalC22×#4341C22
hypercenterC2×#461D11
hypocenterC11C2×#3120
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#10623262C2semidirect
3. #13078827C2direct (N × H)
4. C2×#10622422C2semidirect
5. C2×#10622418C2semidirect
6. C2×#10622442C2semidirect
7. C2×#10622622C2semidirect
8. C2×#10622703C2semidirect
11. C2×#10622402C2semidirect
12. C2×#10622777C2semidirect
13. C2×#10622403C2semidirect
14. C2×SD16×Dic11C2semidirect
15. C2×#10622453C2semidirect
16. C2×C11×#461C2semidirect
32. #10623262C22semidirect
46. C11×#461C22semidirect
56. #10622777C22semidirect
57. SD16×Dic11C22semidirect
66. #10622703C22semidirect
67. #10622622C22semidirect
71. #10622453C22semidirect
72. #10622442C22semidirect
73. #10622422C22semidirect
74. #10622418C22semidirect
75. #10622403C22semidirect
76. #10622402C22semidirect
286. C2×#461D11semidirect
389. #461C2×D11semidirect
548. C2×C11#3120semidirect
648. C11C2×#3120semidirect
739. C2#13078827direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232622
C2×#106230772
#130788272
C2×#106224222
C2×#106224182
C2×#106224422
C2×#106226222
C2×#106227032
C2×#106227862
C2×#106224022
C2×#106227772
C2×#106224032
C2×SD16×Dic112
C2×#106224532
C2×C11×#4612
C2×#312011