Finite Group Databasebeta

← C2×#13078881 #15622091

Subgroups — C2×#13078881 #15622091

Order 2816.

2134 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623174C211yesmaximal, characteristic, complemented
2C2×#10623035C211yesmaximal, characteristic, complemented
3#13078881C2116yesmaximal, direct product factor
4C2×#10622580C211yesmaximal, characteristic, complemented
5C2×#10622488C211yesmaximal, characteristic, complemented
6C2×#10622503C211yesmaximal, characteristic, complemented
7C2×#10622411C211yesmaximal, characteristic, complemented
8C2×#10622432C211yesmaximal, characteristic, complemented
9C2×#10622660C211yesmaximal, characteristic, complemented
10C2×#10622347C211yesmaximal, characteristic
11C2×#10622430C211yesmaximal, characteristic, complemented
12C2×#10622502C211yesmaximal, characteristic, complemented
13C2×#10622403C211yesmaximal, characteristic, complemented
14C2×#10622485C211yesmaximal, characteristic, complemented
15C2×#10622333C211yesmaximal, characteristic, complemented
16C2×C11×#484C211yesmaximal, characteristic, complemented
17C22×#4339C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C2×#67000C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C22×#4326C2211yescharacteristic
23C22×#4325C2211yescharacteristic
24C2×#66983C2211yescharacteristic
25C2×C4×C22⋊D11—21no—
26C2×C4×C22⋊D11—21no—
27C2×#66979C2211yescharacteristic
28C22×D88C2211yescharacteristic
29C22×#4314C2211yescharacteristic
30#10623174—24no—
31#10623174C2218yescomplemented
32C2×#66951—21no—
33C2×#66950—21no—
34#10623035—24no—
35#10623035C2218yescomplemented
36C2×#66946C2211yescharacteristic
37C2×#66946C2211yescharacteristic
38C2×#66946C2211yescharacteristic
39C2×#66945—21no—
40C2×C4⋊C4×D11—21no—
41C2×#66941C2211yescharacteristic
42C2×#66940C2211yescharacteristic
43C2×#66940C2211yescharacteristic
44C2×#66938—21no—
45C2×#66936—21no—
46C11×#484C2218yescomplemented
47C2×C11×#107C2211yescharacteristic
48C2×C11×#107C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×#103C2211yescharacteristic
51C2×C11×C22⋊C8C2211yescharacteristic
52C2×C22⋊(C11⋊C8)C2211yescharacteristic
53C2×#66885C2211yescharacteristic
54C2×#66880C2211yescharacteristic
55C2×#66879C2211yescharacteristic
56C2×Dic11⋊C8C2211yescharacteristic
57C2×Dic11⋊C8C2211yescharacteristic
58C2×C8×Dic11C2211yescharacteristic
59#10622660C2218yescomplemented
60C2×#66874C2211yescharacteristic
61#10622580C2218yescomplemented
62C2×#66873C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66873C2211yescharacteristic
65C2×#66871C2211yescharacteristic
66C2×#66871C2211yescharacteristic
67#10622503C2218yescomplemented
68#10622502C2218yescomplemented
69#10622488C2218yescomplemented
70#10622485C2218yescomplemented
71#10622432C2218yescomplemented
72#10622430C2218yescomplemented
73#10622411C2218yescomplemented
74#10622403C2218yescomplemented
75#10622347C2218yes—
76#10622333C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C23×C4×C11—21no—
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11—21no—
81C22×C22⋊D11—21no—
82C2×#4339—22no—
83C2×#4339—24no—
84C2×#4339—24no—
85C2×#4339C2314yes—
86C22×D44C2311yescharacteristic
87C22×D44C2311yescharacteristic
88C22×C4×D11—21no—
89C22×C4×D11—21no—
90C22×C4×D11—21no—
91C22×C4×D11—21no—
92C22×Dic22—21no—
93C22×Dic22C2311yescharacteristic
94C22×C8×C11C2311yescharacteristic
95C22×C8×C11C2311yescharacteristic
96C11×C22⋊Q8—22no—
97C11×C22⋊Q8C2314yes—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4—22no—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2314yes—
105C2×C11×C22⋊C4—21no—
106C2×C22⋊Dic11D411yescharacteristic
107C2×C22⋊Dic11D411yescharacteristic
108#67000—22no—
109#67000C2314yes—
110Q8×Dic11—22no—
111Q8×Dic11C2314yes—
112C2×#4326—24no—
113C2×#4326C2314yes—
114C2×#4325—24no—
115C2×#4325C2314yes—
116#66983—22no—
117#66983C2314yes—
118C4×C22⋊D11—28no—
119C4×C22⋊D11—28no—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4—21no—
122C2×(C2×D11)⋊C4—21no—
123C2×(C2×D11)⋊C4—21no—
124C2×(C2×D11)⋊C4—21no—
125C2×(C2×D11)⋊C4—21no—
126#66979D414yes—
127#66979C2314yes—
128C2×C4⋊Dic11—21no—
129C2×C4⋊Dic11D411yescharacteristic
130C2×C4⋊Dic11D411yescharacteristic
131C2×C4⋊Dic11C2311yescharacteristic
132C2×Dic11⋊C4—21no—
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4—21no—
135C2×C4×Dic11—21no—
136C2×C4×Dic11—21no—
137C2×C4×Dic11—21no—
138C2×C4×Dic11C2311yescharacteristic
139C2×C4×Dic11C2311yescharacteristic
140C22×C11⋊C8C2311yescharacteristic
141C22×C11⋊C8C2311yescharacteristic
142C2×D88—24no—
143C2×D88C2314yes—
144C2×#4314—24no—
145C2×#4314C2314yes—
146#66951—28no—
147#66950—28no—
148#66946—22no—
149#66946—22no—
150#66946—22no—
151#66946C2314yes—
152#66946C2314yes—
153#66946C2314yes—
154#66945—28no—
155C4⋊C4×D11—28no—
156#66941—22no—
157#66941C2314yes—
158#66940—22no—
159#66940—22no—
160#66940C2314yes—
161#66940C2314yes—
162#66938—28no—
163#66936—28no—
164C11×#107C2314yes—
165C11×#107C2314yes—
166C11×#103C2314yes—
167C11×#103C2314yes—
168C11×C22⋊C8C2314yes—
169C22⋊(C11⋊C8)C2314yes—
170#66885C2314yes—
171#66880C2314yes—
172#66879C2314yes—
173Dic11⋊C8C2314yes—
174Dic11⋊C8C2314yes—
175C8×Dic11C2314yes—
176#66874C2314yes—
177#66873C2314yes—
178#66873C2314yes—
179#66873C2314yes—
180#66871C2314yes—
181#66871C2314yes—
182C2×#3124—111nomaximal, Sylow
183C24×C11C2×D411yescharacteristic
184C23×D11—21no—
185C23×D11—21no—
186C2×Q8×C11—21no—
187C2×Q8×C11—22no—
188C2×Q8×C11—22no—
189C2×Q8×C11C2412yes—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—24no—
197C22×C4×C11—82no—
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D412yes—
200C22×C4×C11C2412yes—
201C22×C4×C11C2411yescharacteristic
202C2×C22⋊D11—28no—
203C2×C22⋊D11—24no—
204C2×C22⋊D11—24no—
205C2×C22⋊D11—82no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11C2×D411yescharacteristic
209C22×Dic11C2×D411yescharacteristic
210C22×Dic11C2×D411yescharacteristic
211C22×Dic11C2×D411yescharacteristic
212#4339—216no—
213#4339—28no—
214#4339—28no—
215C2×D44—21no—
216C2×D44—21no—
217C2×D44—22no—
218C2×D44—22no—
219C2×D44—22no—
220C2×D44#4114yes—
221C2×D44C2412yes—
222C2×D44C2412yes—
223C2×C4×D11—28no—
224C2×C4×D11—24no—
225C2×C4×D11—24no—
226C2×C4×D11—24no—
227C2×C4×D11—24no—
228C2×C4×D11—82no—
229C2×C4×D11—82no—
230C2×C4×D11—82no—
231C2×Dic22—24no—
232C2×Dic22—21no—
233C2×Dic22—22no—
234C2×Dic22—82no—
235C2×Dic22#4114yes—
236C2×Dic22C2412yes—
237C2×C8×C11—22no—
238C2×C8×C11—22no—
239C2×C8×C11C2412yes—
240C2×C8×C11C2412yes—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—21no—
243C11×C4⋊C4—21no—
244C11×C4⋊C4—24no—
245C11×C4⋊C4—24no—
246C11×C4⋊C4C2412yes—
247C11×C4⋊C4C2412yes—
248C11×C4⋊C4C2412yes—
249C11×C22⋊C4—24no—
250C22⋊Dic11C2×D414yes—
251C22⋊Dic11C2×D414yes—
252#4326—28no—
253#4325—28no—
254(C2×D11)⋊C4—24no—
255(C2×D11)⋊C4—24no—
256(C2×D11)⋊C4—24no—
257(C2×D11)⋊C4—24no—
258(C2×D11)⋊C4—24no—
259(C2×D11)⋊C4—24no—
260C4⋊Dic11—24no—
261C4⋊Dic11—21no—
262C4⋊Dic11C2×D414yes—
263C4⋊Dic11C2×D414yes—
264C4⋊Dic11C2412yes—
265Dic11⋊C4—24no—
266Dic11⋊C4—24no—
267Dic11⋊C4—24no—
268C4×Dic11—24no—
269C4×Dic11—24no—
270C4×Dic11—24no—
271C4×Dic11C2×D412yes—
272C4×Dic11C2×D412yes—
273C4×Dic11C2412yes—
274C4×Dic11C2412yes—
275C2×C11⋊C8—22no—
276C2×C11⋊C8—22no—
277C2×C11⋊C8C2412yes—
278C2×C11⋊C8C2412yes—
279D88—28no—
280#4314—28no—
281C2×#542—111no—
282C2×#520—111no—
283#3124—1116no—
284C2×#484D1111yescharacteristic, complemented
285C2×#480—111no—
286C2×#477—111no—
287C2×#474—111no—
288C2×#464—111no—
289C2×#463—111no—
290C2×#452—111no—
291C2×#449—111no—
292C2×#440—111no—
293C2×#440—111no—
294C2×C4×Q16—111no—
295C2×C4×D8—111no—
296C2×#433—111no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11C22×D412yes—
301C23×C11C22×D411yescharacteristic
302C22×D11—24no—
303C22×D11—22no—
304C22×D11—22no—
305C22×D11—42no—
306C22×D11—42no—
307C22×D11—42no—
308C22×D11—42no—
309C22×D11—42no—
310Q8×C11—22no—
311Q8×C11—22no—
312Q8×C11—42no—
313C2×C4×C11—22no—
314C2×C4×C11—24no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—42no—
322C2×C4×C11—42no—
323C2×C4×C11—42no—
324C2×C4×C11—42no—
325C2×C4×C11—84no—
326C2×C4×C11C22×D412yes—
327C2×C4×C11C22×D411yescharacteristic
328C2×C4×C11C2×#4112yes—
329C2×C4×C11C2×#4112yes—
330C2×C4×C11C2511yescharacteristic
331C22⋊D11—216no—
332C22⋊D11—84no—
333C2×Dic11—24no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—42no—
341C2×Dic11C22×D412yes—
342C2×Dic11C22×D412yes—
343C2×Dic11C22×D412yes—
344C2×Dic11C22×D412yes—
345D44—24no—
346D44—22no—
347D44—22no—
348D44—22no—
349D44—42no—
350D44C2×#4114yes—
351C4×D11—216no—
352C4×D11—84no—
353C4×D11—84no—
354C4×D11—84no—
355Dic22—24no—
356Dic22—22no—
357Dic22—84no—
358Dic22C2×#4114yes—
359C8×C11—22no—
360C8×C11—22no—
361C11⋊C8—22no—
362C11⋊C8—22no—
363C22×#41—111no—
364C22×Q16—111no—
365C22×SD16—111no—
366C22×SD16—111no—
367C22×D8—111no—
368#542—118no—
369#542—224no—
370C2×C4⋊Q8—111no—
371C2×#126—221no—
372C2×#124—111no—
373C2×#124—221no—
374C2×#123—221no—
375C2×C22⋊Q8—221no—
376C2×C22⋊Q8C2×D1111yescharacteristic
377C2×#121—111no—
378#520—118no—
379#520—224no—
380C2×C4×Q8—111no—
381C2×C4×Q8—111no—
382C2×C4×Q8—111no—
383C2×C4×D4—111no—
384C2×C4×D4—111no—
385C2×C4×D4—111no—
386C2×C4×D4—221no—
387C2×C4×D4—221no—
388C2×#117—111no—
389C2×#117—221no—
390C22×C4⋊C4—221no—
391C22×C4⋊C4C2×D1111yescharacteristic
392#484C2×D1118yescomplemented
393#480—118no—
394#477—118no—
395#474—118no—
396#464—118no—
397#463—118no—
398#452—118no—
399#449—118no—
400#440—118no—
401#440—118no—
402C4×Q16—118no—
403C4×D8—118no—
404#433—118no—
405C2×#107—111no—
406C2×#107—111no—
407C2×#107C2×D1111yescharacteristic
408C2×#107C2×D1111yescharacteristic
409C2×C4⋊C8—111no—
410C2×C4⋊C8—111no—
411C2×#103—111no—
412C2×#103—111no—
413C2×#103C2×D1111yescharacteristic
414C2×#103C2×D1111yescharacteristic
415C2×#102—111no—
416C2×#102—111no—
417C2×#102—111no—
418C2×#102—111no—
419C2×C22⋊C8—111no—
420C2×C22⋊C8C2×D1111yescharacteristic
421C2×#97—111no—
422C2×C4×C8—111no—
423C22×C11—22no—
424C22×C11—22no—
425C22×C11—22no—
426C22×C11—44no—
427C22×C11#52512yes—
428C22×C11#57612yes—
429C22×C11#57812yes—
430C22×C11C23×D411yescharacteristic
431C2×D11—24no—
432C2×D11—48no—
433C2×D11—42no—
434C2×D11—42no—
435C2×D11—42no—
436C2×D11—42no—
437C2×D11—42no—
438C2×D11—84no—
439C4×C11—22no—
440C4×C11—42no—
441C4×C11—42no—
442C4×C11—42no—
443C4×C11—42no—
444C4×C11#52512yes—
445C4×C11C22×#4111yescharacteristic
446C4×C11C22×#4111yescharacteristic
447Dic11—24no—
448Dic11—22no—
449Dic11—22no—
450Dic11—22no—
451Dic11—22no—
452Dic11—42no—
453C2×#41—114no—
454C2×#41—224no—
455C2×#41—224no—
456C2×#41—222no—
457C22×Q8—111no—
458C22×Q8—221no—
459C22×Q8C22×D1111yescharacteristic
460C22×D4—111no—
461C22×D4—111no—
462C22×D4—221no—
463C22×D4—221no—
464C23×C4—21no—
465C23×C4—221no—
466C23×C4—221no—
467C23×C4—221no—
468C23×C4—221no—
469C23×C4C22×D1111yescharacteristic
470C2×Q16—114no—
471C2×Q16—224no—
472C2×SD16—114no—
473C2×SD16—114no—
474C2×SD16—224no—
475C2×SD16—224no—
476C2×D8—114no—
477C2×D8—224no—
478C22×C8—111no—
479C22×C8—111no—
480C22×C8C22×D1111yescharacteristic
481C22×C8C22×D1111yescharacteristic
482C4⋊Q8—114no—
483C4⋊Q8—222no—
484#126—228no—
485#124—114no—
486#124—222no—
487#124—228no—
488#123—228no—
489C22⋊Q8—22no—
490C22⋊Q8—228no—
491C22⋊Q8C22×D1114yes—
492#121—114no—
493#121—222no—
494C4×Q8—114no—
495C4×Q8—114no—
496C4×Q8—114no—
497C4×Q8—222no—
498C4×Q8—222no—
499C4×Q8—222no—
500C4×D4—114no—
501C4×D4—114no—
502C4×D4—114no—
503C4×D4—222no—
504C4×D4—222no—
505C4×D4—222no—
506C4×D4—228no—
507C4×D4—228no—
508#117—114no—
509#117—114no—
510#117—228no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—22no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—111no—
515C2×C4⋊C4—111no—
516C2×C4⋊C4—111no—
517C2×C4⋊C4—228no—
518C2×C4⋊C4—221no—
519C2×C4⋊C4—221no—
520C2×C4⋊C4—221no—
521C2×C4⋊C4—221no—
522C2×C4⋊C4C22×D1111yescharacteristic
523C2×C4⋊C4C22×D1111yescharacteristic
524C2×C4⋊C4C22×D1114yes—
525C2×C4⋊C4C22×D1111yescharacteristic
526C2×C22⋊C4—21no—
527C2×C22⋊C4—111no—
528C2×C22⋊C4—111no—
529C2×C22⋊C4—221no—
530C2×C22⋊C4—221no—
531C2×C22⋊C4—221no—
532C2×C22⋊C4—221no—
533C2×C22⋊C4—221no—
534C2×C22⋊C4—221no—
535C2×C42—111no—
536C2×C42—111no—
537C2×C42—221no—
538C2×C42—221no—
539C2×C42—221no—
540#107—114no—
541#107—114no—
542#107C22×D1114yes—
543#107C22×D1114yes—
544C4⋊C8—114no—
545C4⋊C8—114no—
546#103—114no—
547#103—114no—
548#103C22×D1114yes—
549#103C22×D1114yes—
550#102—114no—
551#102—114no—
552#102—114no—
553#102—114no—
554C22⋊C8—114no—
555C22⋊C8C22×D1114yes—
556#97—114no—
557C4×C8—114no—
558C2×C11—42no—
559C2×C11#312414yescomplemented
560C2×C11C2×#52511yescharacteristic
561C2×C11C2×#57611yescharacteristic
562C2×C11C2×#57811yescharacteristic
563D11—44no—
564D11—82no—
565C24—221no—
566C24—221no—
567C24D4×D1111yescharacteristic
568#41—228no—
569#41—228no—
570#41—2216no—
571C2×Q8—21no—
572C2×Q8—22no—
573C2×Q8—22no—
574C2×Q8—114no—
575C2×Q8—112no—
576C2×Q8—224no—
577C2×Q8—221no—
578C2×Q8—222no—
579C2×Q8—882no—
580C2×Q8C23×D1112yes—
581C2×D4—114no—
582C2×D4—112no—
583C2×D4—112no—
584C2×D4—228no—
585C2×D4—224no—
586C2×D4—224no—
587C2×D4—221no—
588C2×D4—221no—
589C2×D4—222no—
590C2×D4—222no—
591C2×D4—222no—
592C2×D4—882no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—82no—
601C22×C4—111no—
602C22×C4—111no—
603C22×C4—111no—
604C22×C4—111no—
605C22×C4—224no—
606C22×C4—224no—
607C22×C4—224no—
608C22×C4—228no—
609C22×C4—221no—
610C22×C4—224no—
611C22×C4—221no—
612C22×C4—882no—
613C22×C4—882no—
614C22×C4—882no—
615C22×C4D4×D1112yes—
616C22×C4D4×D1111yescharacteristic
617C22×C4C23×D1112yes—
618C22×C4C23×D1111yescharacteristic
619Q16—228no—
620SD16—228no—
621SD16—228no—
622D8—228no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—112no—
626C2×C8—112no—
627C2×C8—222no—
628C2×C8—222no—
629C2×C8C23×D1112yes—
630C2×C8C23×D1112yes—
631C4⋊C4—24no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—24no—
635C4⋊C4—21no—
636C4⋊C4—114no—
637C4⋊C4—114no—
638C4⋊C4—112no—
639C4⋊C4—224no—
640C4⋊C4—224no—
641C4⋊C4—224no—
642C4⋊C4—224no—
643C4⋊C4—221no—
644C4⋊C4C23×D1112yes—
645C4⋊C4C23×D1112yes—
646C4⋊C4C23×D1112yes—
647C22⋊C4—24no—
648C22⋊C4—114no—
649C22⋊C4—114no—
650C22⋊C4—224no—
651C22⋊C4—224no—
652C22⋊C4—224no—
653C22⋊C4—224no—
654C22⋊C4—224no—
655C22⋊C4—224no—
656C42—112no—
657C42—112no—
658C42—112no—
659C42—112no—
660C42—224no—
661C42—224no—
662C42—224no—
663C11C2×#312411yescharacteristic, complemented, Sylow
664C23—22no—
665C23—22no—
666C23—22no—
667C23—224no—
668C23—222no—
669C23—222no—
670C23—442no—
671C23—442no—
672C23—442no—
673C23—442no—
674C23—442no—
675C23C2×D4×D1112yes—
676C23C2×D4×D1111yescharacteristic
677Q8—22no—
678Q8—22no—
679Q8—42no—
680Q8—114no—
681Q8—224no—
682Q8—222no—
683Q8—884no—
684D4—114no—
685D4—2216no—
686D4—224no—
687D4—222no—
688D4—222no—
689D4—222no—
690D4—442no—
691D4—884no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—84no—
705C2×C4—112no—
706C2×C4—112no—
707C2×C4—112no—
708C2×C4—112no—
709C2×C4—2216no—
710C2×C4—222no—
711C2×C4—222no—
712C2×C4—222no—
713C2×C4—222no—
714C2×C4—224no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—442no—
718C2×C4—884no—
719C2×C4—884no—
720C2×C4—884no—
721C2×C4C2×D4×D1112yes—
722C2×C4C2×D4×D1111yescharacteristic
723C2×C4#41×D1112yes—
724C2×C4#41×D1112yes—
725C2×C4C24×D1111yescharacteristic
726C8—22no—
727C8—22no—
728C8—222no—
729C8—222no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—224no—
735C22—448no—
736C22—442no—
737C22—442no—
738C22—442no—
739C22—442no—
740C22—442no—
741C22—884no—
742C22#1062318712yes—
743C22#1062329712yes—
744C22#1062330512yes—
745C22C22×D4×D1111yescharacteristic
746C4—22no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—222no—
752C4—222no—
753C4—222no—
754C4—222no—
755C4—224no—
756C4—442no—
757C4#1062318712yes—
758C4C2×#41×D1111yescharacteristic
759C4C2×#41×D1111yescharacteristic
760C2—42no—
761C2—444no—
762C2—882no—
763C2#1307888114yesdirect product factor
764C2C2×#1062318711yescharacteristic
765C2C2×#1062330511yescharacteristic
766C2C2×#1062329711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#484C2
socleC23×C11C22×D4
prime radicalC2×#10622347C2
hypercenterC2×#484D11
hypocenterC11C2×#3124
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×#10623174C2semidirect
2. C2×#10623035C2semidirect
3. #13078881C2direct (N × H)
4. C2×#10622580C2semidirect
5. C2×#10622488C2semidirect
6. C2×#10622503C2semidirect
7. C2×#10622411C2semidirect
8. C2×#10622432C2semidirect
9. C2×#10622660C2semidirect
11. C2×#10622430C2semidirect
12. C2×#10622502C2semidirect
13. C2×#10622403C2semidirect
14. C2×#10622485C2semidirect
15. C2×#10622333C2semidirect
16. C2×C11×#484C2semidirect
31. #10623174C22semidirect
35. #10623035C22semidirect
46. C11×#484C22semidirect
59. #10622660C22semidirect
61. #10622580C22semidirect
67. #10622503C22semidirect
68. #10622502C22semidirect
69. #10622488C22semidirect
70. #10622485C22semidirect
71. #10622432C22semidirect
72. #10622430C22semidirect
73. #10622411C22semidirect
74. #10622403C22semidirect
76. #10622333C22semidirect
284. C2×#484D11semidirect
392. #484C2×D11semidirect
559. C2×C11#3124semidirect
663. C11C2×#3124semidirect
763. C2#13078881direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231742
C2×#106230352
#130788812
C2×#106225802
C2×#106224882
C2×#106225032
C2×#106224112
C2×#106224322
C2×#106226602
C2×#106223472
C2×#106224302
C2×#106225022
C2×#106224032
C2×#106224852
C2×#106223332
C2×C11×#4842
C2×#312411