Finite Group Databasebeta

← C2×#13078880 #15622090

Subgroups — C2×#13078880 #15622090

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×#10623065C211yesmaximal, characteristic, complemented
2C2×#10623054C211yesmaximal, characteristic, complemented
3#13078880C2116yesmaximal, direct product factor
4C2×#10622335C211yesmaximal, characteristic, complemented
5C2×#10622349C211yesmaximal, characteristic, complemented
6C2×#10622463C211yesmaximal, characteristic, complemented
7C2×#10622459C211yesmaximal, characteristic, complemented
8C2×#10622458C211yesmaximal, characteristic, complemented
9C2×#10622457C211yesmaximal, characteristic, complemented
10C2×#10622346C211yesmaximal, characteristic, complemented
11C2×#10622347C211yesmaximal, characteristic
12C2×#10622323C211yesmaximal, characteristic, complemented
13C2×#10622323C211yesmaximal, characteristic, complemented
14C2×C4×Dic44C211yesmaximal, characteristic, complemented
15C2×C4×D88C211yesmaximal, characteristic, complemented
16C2×C11×#433C211yesmaximal, characteristic, complemented
17C22×#4339C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C2×#66983C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C2×#66977C2211yescharacteristic
22C22×Dic44C2211yescharacteristic
23C22×D88C2211yescharacteristic
24C22×#4314C2211yescharacteristic
25C22×#4314C2211yescharacteristic
26#10623065—24no—
27#10623065C2218yescomplemented
28#10623054—24no—
29#10623054C2218yescomplemented
30C2×#66951—21no—
31C2×#66949—21no—
32C2×#66945—21no—
33C2×C4⋊C4×D11—21no—
34C2×#66938—21no—
35C2×#66936—21no—
36C2×(C22⋊D11)⋊C4—21no—
37C2×(C22⋊D11)⋊C4—21no—
38C2×#66928C2211yescharacteristic
39C2×C4×D44C2211yescharacteristic
40C2×C4×D44C2211yescharacteristic
41C2×C4×D44C2211yescharacteristic
42C2×#66922C2211yescharacteristic
43C2×C4×Dic22C2211yescharacteristic
44C2×C4×Dic22C2211yescharacteristic
45C2×C4×Dic22C2211yescharacteristic
46C11×#433C2218yescomplemented
47C2×C11×C4⋊C8C2211yescharacteristic
48C2×C11×C4⋊C8C2211yescharacteristic
49C2×C11×C22⋊C8C2211yescharacteristic
50C2×C11×C22⋊C8C2211yescharacteristic
51C2×C11×#97C2211yescharacteristic
52C2×C4×C8×C11C2211yescharacteristic
53C2×#66885C2211yescharacteristic
54C2×#66885C2211yescharacteristic
55C2×#66885C2211yescharacteristic
56C2×#66885C2211yescharacteristic
57C2×#66882C2211yescharacteristic
58C2×#66882C2211yescharacteristic
59C2×#66882C2211yescharacteristic
60C2×#66882C2211yescharacteristic
61C2×#66880C2211yescharacteristic
62C2×#66880C2211yescharacteristic
63C2×#66880C2211yescharacteristic
64C2×#66880C2211yescharacteristic
65#10622463C2218yescomplemented
66#10622459C2218yescomplemented
67#10622458C2218yescomplemented
68#10622457C2218yescomplemented
69#10622349C2218yescomplemented
70#10622347C2218yes—
71#10622346C2218yescomplemented
72#10622335C2218yescomplemented
73#10622323C2218yescomplemented
74#10622323C2218yescomplemented
75C4×Dic44C2218yescomplemented
76C4×D88C2218yescomplemented
77C23×C4×C11C2311yescharacteristic
78C22×C22⋊D11—21no—
79C22×C22⋊D11—21no—
80C23×Dic11—21no—
81C2×#4339—22no—
82C2×#4339—24no—
83C2×#4339—24no—
84C2×#4339C2314yes—
85C22×D44C2311yescharacteristic
86C22×D44C2311yescharacteristic
87C22×C4×D11—21no—
88C22×C4×D11—21no—
89C22×C4×D11—21no—
90C22×C4×D11—21no—
91C22×Dic22—21no—
92C22×Dic22C2311yescharacteristic
93C22×Dic22C2311yescharacteristic
94C22×C8×C11C2311yescharacteristic
95C22×C8×C11C2311yescharacteristic
96C22×C8×C11C2311yescharacteristic
97C22×C8×C11C2311yescharacteristic
98C11×#117D414yes—
99C11×#117C2314yes—
100C2×C11×C4⋊C4D411yescharacteristic
101C2×C11×C4⋊C4D411yescharacteristic
102C2×C11×C22⋊C4D411yescharacteristic
103C2×C11×C22⋊C4D411yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C2×C42×C11C2311yescharacteristic
106C2×C22⋊Dic11—21no—
107#66983—22no—
108#66983C2314yes—
109C2×(C2×D11)⋊C4—21no—
110C2×(C2×D11)⋊C4—21no—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×C4⋊Dic11—21no—
116C2×C4⋊Dic11—21no—
117C2×C4⋊Dic11—22no—
118C2×C4⋊Dic11C2311yescharacteristic
119C2×C4⋊Dic11C2311yescharacteristic
120C2×C4⋊Dic11C2311yescharacteristic
121C2×C4⋊Dic11C2311yescharacteristic
122C2×C4⋊Dic11C2314yes—
123#66977—22no—
124#66977C2314yes—
125C2×Dic11⋊C4—21no—
126C2×Dic11⋊C4—21no—
127C2×Dic11⋊C4—21no—
128C2×Dic11⋊C4—21no—
129C2×C4×Dic11—21no—
130C2×C4×Dic11—21no—
131C2×C4×Dic11—21no—
132C2×Dic44—24no—
133C2×Dic44C2314yes—
134C2×D88—24no—
135C2×D88C2314yes—
136C2×#4314—24no—
137C2×#4314—24no—
138C2×#4314C2314yes—
139C2×#4314C2314yes—
140#66951—28no—
141#66949—28no—
142#66945—28no—
143C4⋊C4×D11—28no—
144#66938—28no—
145#66936—28no—
146(C22⋊D11)⋊C4—28no—
147(C22⋊D11)⋊C4—28no—
148#66928—22no—
149#66928C2314yes—
150C4×D44—22no—
151C4×D44—22no—
152C4×D44—22no—
153C4×D44C2314yes—
154C4×D44C2314yes—
155C4×D44C2314yes—
156#66922—22no—
157#66922C2314yes—
158C4×Dic22—22no—
159C4×Dic22—22no—
160C4×Dic22—22no—
161C4×Dic22C2314yes—
162C4×Dic22C2314yes—
163C4×Dic22C2314yes—
164C11×C4⋊C8C2314yes—
165C11×C4⋊C8C2314yes—
166C11×C22⋊C8C2314yes—
167C11×C22⋊C8C2314yes—
168C11×#97C2314yes—
169C4×C8×C11C2314yes—
170#66885C2314yes—
171#66885C2314yes—
172#66885C2314yes—
173#66885C2314yes—
174#66882C2314yes—
175#66882C2314yes—
176#66882C2314yes—
177#66882C2314yes—
178#66880C2314yes—
179#66880C2314yes—
180#66880C2314yes—
181#66880C2314yes—
182C2×#3124—111nomaximal, Sylow
183C24×C11C2×D411yescharacteristic
184C23×D11—21no—
185C23×D11—21no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D412yes—
194C22×C4×C11C2412yes—
195C22×C4×C11C2411yescharacteristic
196C2×C22⋊D11—28no—
197C2×C22⋊D11—24no—
198C2×C22⋊D11—24no—
199C2×C22⋊D11—82no—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—24no—
207C22×Dic11—82no—
208#4339—216no—
209#4339—28no—
210#4339—28no—
211C2×D44—21no—
212C2×D44—21no—
213C2×D44—22no—
214C2×D44—22no—
215C2×D44—22no—
216C2×D44#4114yes—
217C2×D44C2412yes—
218C2×D44C2412yes—
219C2×C4×D11—28no—
220C2×C4×D11—24no—
221C2×C4×D11—24no—
222C2×C4×D11—24no—
223C2×C4×D11—24no—
224C2×C4×D11—82no—
225C2×C4×D11—82no—
226C2×C4×D11—82no—
227C2×Dic22—21no—
228C2×Dic22—21no—
229C2×Dic22—24no—
230C2×Dic22—22no—
231C2×Dic22—22no—
232C2×Dic22—22no—
233C2×Dic22—82no—
234C2×Dic22#4114yes—
235C2×Dic22C2412yes—
236C2×Dic22C2412yes—
237C2×C8×C11—22no—
238C2×C8×C11—22no—
239C2×C8×C11—22no—
240C2×C8×C11—22no—
241C2×C8×C11C2412yes—
242C2×C8×C11C2412yes—
243C2×C8×C11C2412yes—
244C2×C8×C11C2412yes—
245C11×C4⋊C4C2×D414yes—
246C11×C4⋊C4C2×D414yes—
247C11×C22⋊C4C2×D414yes—
248C11×C22⋊C4C2×D414yes—
249C42×C11C2×D412yes—
250C42×C11C2×D412yes—
251C42×C11C2412yes—
252C42×C11C2412yes—
253C22⋊Dic11—24no—
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—21no—
261C4⋊Dic11—21no—
262C4⋊Dic11—21no—
263C4⋊Dic11—21no—
264C4⋊Dic11—24no—
265C4⋊Dic11—24no—
266C4⋊Dic11C2412yes—
267C4⋊Dic11C2412yes—
268C4⋊Dic11C2412yes—
269C4⋊Dic11C2412yes—
270Dic11⋊C4—24no—
271Dic11⋊C4—24no—
272Dic11⋊C4—24no—
273Dic11⋊C4—24no—
274C4×Dic11—24no—
275C4×Dic11—24no—
276C4×Dic11—24no—
277Dic44—28no—
278D88—28no—
279#4314—28no—
280#4314—28no—
281C2×#542—111no—
282C2×#520—111no—
283#3124—1116no—
284C2×#484—111no—
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×#433D1111yescharacteristic, complemented
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—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—24no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11C22×D412yes—
319C2×C4×C11C22×D412yes—
320C2×C4×C11C22×D412yes—
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—
328C22⋊D11—84no—
329C2×Dic11—24no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—42no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11—84no—
342D44—24no—
343D44—22no—
344D44—22no—
345D44—22no—
346D44—42no—
347D44C2×#4114yes—
348C4×D11—216no—
349C4×D11—84no—
350C4×D11—84no—
351C4×D11—84no—
352Dic22—24no—
353Dic22—22no—
354Dic22—22no—
355Dic22—22no—
356Dic22—42no—
357Dic22—84no—
358Dic22C2×#4114yes—
359C8×C11—22no—
360C8×C11—22no—
361C8×C11—22no—
362C8×C11—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—111no—
376C2×C22⋊Q8—221no—
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—221no—
389C2×#117C2×D1111yescharacteristic
390C22×C4⋊C4—111no—
391C22×C4⋊C4—221no—
392#484—118no—
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#433C2×D1118yescomplemented
405C2×#107—111no—
406C2×#107—111no—
407C2×#107—111no—
408C2×#107—111no—
409C2×C4⋊C8C2×D1111yescharacteristic
410C2×C4⋊C8C2×D1111yescharacteristic
411C2×#103—111no—
412C2×#103—111no—
413C2×#103—111no—
414C2×#103—111no—
415C2×#102—111no—
416C2×#102—111no—
417C2×#102—111no—
418C2×#102—111no—
419C2×C22⋊C8C2×D1111yescharacteristic
420C2×C22⋊C8C2×D1111yescharacteristic
421C2×#97C2×D1111yescharacteristic
422C2×C4×C8C2×D1111yescharacteristic
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—22no—
441C4×C11—22no—
442C4×C11—22no—
443C4×C11—22no—
444C4×C11#52512yes—
445C4×C11C22×#4111yescharacteristic
446C4×C11C22×#4111yescharacteristic
447Dic11—24no—
448Dic11—42no—
449Dic11—42no—
450Dic11—42no—
451Dic11—42no—
452Dic11—42no—
453C2×#41—114no—
454C2×#41—224no—
455C2×#41—224no—
456C2×#41—222no—
457C22×Q8—111no—
458C22×Q8—111no—
459C22×Q8—221no—
460C22×D4—111no—
461C22×D4—111no—
462C22×D4—221no—
463C22×D4—221no—
464C23×C4—221no—
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×C8C22×D1111yescharacteristic
479C22×C8C22×D1111yescharacteristic
480C22×C8C22×D1111yescharacteristic
481C22×C8C22×D1111yescharacteristic
482C4⋊Q8—114no—
483C4⋊Q8—222no—
484#126—228no—
485#124—114no—
486#124—228no—
487#124—222no—
488#123—228no—
489C22⋊Q8—114no—
490C22⋊Q8—222no—
491C22⋊Q8—228no—
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—228no—
504C4×D4—228no—
505C4×D4—222no—
506C4×D4—222no—
507C4×D4—222no—
508#117—228no—
509#117D4414yes—
510#117C22×D1114yes—
511C2×C4⋊C4—111no—
512C2×C4⋊C4—111no—
513C2×C4⋊C4—114no—
514C2×C4⋊C4—111no—
515C2×C4⋊C4—111no—
516C2×C4⋊C4—221no—
517C2×C4⋊C4—222no—
518C2×C4⋊C4—221no—
519C2×C4⋊C4—221no—
520C2×C4⋊C4—221no—
521C2×C4⋊C4—221no—
522C2×C4⋊C4—221no—
523C2×C4⋊C4—228no—
524C2×C4⋊C4D4411yescharacteristic
525C2×C4⋊C4D4411yescharacteristic
526C2×C22⋊C4—221no—
527C2×C22⋊C4—221no—
528C2×C22⋊C4—221no—
529C2×C22⋊C4—221no—
530C2×C22⋊C4—221no—
531C2×C22⋊C4—221no—
532C2×C22⋊C4—221no—
533C2×C22⋊C4D4411yescharacteristic
534C2×C22⋊C4D4411yescharacteristic
535C2×C42—221no—
536C2×C42—221no—
537C2×C42—221no—
538C2×C42C22×D1111yescharacteristic
539C2×C42C22×D1111yescharacteristic
540#107—114no—
541#107—114no—
542#107—114no—
543#107—114no—
544C4⋊C8C22×D1114yes—
545C4⋊C8C22×D1114yes—
546#103—114no—
547#103—114no—
548#103—114no—
549#103—114no—
550#102—114no—
551#102—114no—
552#102—114no—
553#102—114no—
554C22⋊C8C22×D1114yes—
555C22⋊C8C22×D1114yes—
556#97C22×D1114yes—
557C4×C8C22×D1114yes—
558C2×C11—42no—
559C2×C11#312414yescomplemented
560C2×C11C2×#52511yescharacteristic
561C2×C11C2×#57611yescharacteristic
562C2×C11C2×#57811yescharacteristic
563D11—44no—
564D11—82no—
565C24—221no—
566C24—221no—
567C24C2×D4411yescharacteristic
568#41—228no—
569#41—228no—
570#41—2216no—
571C2×Q8—114no—
572C2×Q8—112no—
573C2×Q8—112no—
574C2×Q8—221no—
575C2×Q8—221no—
576C2×Q8—224no—
577C2×Q8—222no—
578C2×Q8—222no—
579C2×Q8—222no—
580C2×Q8—882no—
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—228no—
596C22×C4—221no—
597C22×C4—224no—
598C22×C4—221no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—221no—
602C22×C4—221no—
603C22×C4—224no—
604C22×C4—224no—
605C22×C4—224no—
606C22×C4—224no—
607C22×C4—882no—
608C22×C4—882no—
609C22×C4—882no—
610C22×C4—882no—
611C22×C4C2×D4412yes—
612C22×C4C2×D4411yescharacteristic
613C22×C4C2×D4411yescharacteristic
614C22×C4C2×D4411yescharacteristic
615C22×C4C2×D4411yescharacteristic
616C22×C4C2×D4411yescharacteristic
617C22×C4C23×D1112yes—
618C22×C4C23×D1111yescharacteristic
619Q16—228no—
620SD16—228no—
621SD16—228no—
622D8—228no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8C23×D1112yes—
628C2×C8C23×D1112yes—
629C2×C8C23×D1112yes—
630C2×C8C23×D1112yes—
631C4⋊C4—112no—
632C4⋊C4—112no—
633C4⋊C4—112no—
634C4⋊C4—112no—
635C4⋊C4—224no—
636C4⋊C4—221no—
637C4⋊C4—221no—
638C4⋊C4—221no—
639C4⋊C4—221no—
640C4⋊C4—224no—
641C4⋊C4—224no—
642C4⋊C4—224no—
643C4⋊C4—224no—
644C4⋊C4—224no—
645C4⋊C4C2×D4414yes—
646C4⋊C4C2×D4414yes—
647C22⋊C4—224no—
648C22⋊C4—224no—
649C22⋊C4—224no—
650C22⋊C4—224no—
651C22⋊C4—224no—
652C22⋊C4—224no—
653C22⋊C4—224no—
654C22⋊C4C2×D4414yes—
655C22⋊C4C2×D4414yes—
656C42—224no—
657C42—224no—
658C42—224no—
659C42C2×D4412yes—
660C42C2×D4412yes—
661C42C23×D1112yes—
662C42C23×D1112yes—
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—
675C23C22×D4412yes—
676C23C22×D4411yescharacteristic
677Q8—114no—
678Q8—224no—
679Q8—222no—
680Q8—222no—
681Q8—222no—
682Q8—442no—
683Q8—884no—
684D4—114no—
685D4—2216no—
686D4—224no—
687D4—222no—
688D4—222no—
689D4—222no—
690D4—442no—
691D4—884no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—2216no—
701C2×C4—224no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—222no—
706C2×C4—222no—
707C2×C4—222no—
708C2×C4—442no—
709C2×C4—442no—
710C2×C4—442no—
711C2×C4—442no—
712C2×C4—442no—
713C2×C4—884no—
714C2×C4—884no—
715C2×C4—884no—
716C2×C4—884no—
717C2×C4C22×D4412yes—
718C2×C4C22×D4412yes—
719C2×C4C22×D4412yes—
720C2×C4C22×D4412yes—
721C2×C4C22×D4412yes—
722C2×C4C22×D4411yescharacteristic
723C2×C4#41×D1112yes—
724C2×C4#41×D1112yes—
725C2×C4C24×D1111yescharacteristic
726C8—22no—
727C8—22no—
728C8—22no—
729C8—22no—
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#1062305512yes—
743C22#1062328312yes—
744C22#1062328412yes—
745C22C23×D4411yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—224no—
752C4—442no—
753C4—442no—
754C4—442no—
755C4—442no—
756C4—442no—
757C4#1062305512yes—
758C4C2×#41×D1111yescharacteristic
759C4C2×#41×D1111yescharacteristic
760C2—42no—
761C2—444no—
762C2—882no—
763C2#1307888014yesdirect product factor
764C2C2×#1062305511yescharacteristic
765C2C2×#1062328311yescharacteristic
766C2C2×#1062328411yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#433C2
socleC23×C11C22×D4
prime radicalC2×#10622347C2
hypercenterC2×#433D11
hypocenterC11C2×#3124
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#10623065C2semidirect
2. C2×#10623054C2semidirect
3. #13078880C2direct (N × H)
4. C2×#10622335C2semidirect
5. C2×#10622349C2semidirect
6. C2×#10622463C2semidirect
7. C2×#10622459C2semidirect
8. C2×#10622458C2semidirect
9. C2×#10622457C2semidirect
10. C2×#10622346C2semidirect
12. C2×#10622323C2semidirect
13. C2×#10622323C2semidirect
14. C2×C4×Dic44C2semidirect
15. C2×C4×D88C2semidirect
16. C2×C11×#433C2semidirect
27. #10623065C22semidirect
29. #10623054C22semidirect
46. C11×#433C22semidirect
65. #10622463C22semidirect
66. #10622459C22semidirect
67. #10622458C22semidirect
68. #10622457C22semidirect
69. #10622349C22semidirect
71. #10622346C22semidirect
72. #10622335C22semidirect
73. #10622323C22semidirect
74. #10622323C22semidirect
75. C4×Dic44C22semidirect
76. C4×D88C22semidirect
296. C2×#433D11semidirect
404. #433C2×D11semidirect
559. C2×C11#3124semidirect
663. C11C2×#3124semidirect
763. C2#13078880direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230652
C2×#106230542
#130788802
C2×#106223352
C2×#106223492
C2×#106224632
C2×#106224592
C2×#106224582
C2×#106224572
C2×#106223462
C2×#106223472
C2×#106223232
C2×C4×Dic442
C2×C4×D882
C2×C11×#4332
C2×#312411