Finite Group Databasebeta

← #14754778

Subgroups — #14754778

Order 2816.

1458 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623077C211yesmaximal, characteristic
2C2×#10622474C211yesmaximal, characteristic, complemented
3C2×#10622384C211yesmaximal, characteristic
4C2×#10622385C211yesmaximal, characteristic
5#13071231C211yesmaximal, characteristic, complemented
6#13068883C211yesmaximal, characteristic, complemented
7#13068881C211yesmaximal, characteristic, complemented
8#13068875C211yesmaximal, characteristic, complemented
9#13068873C211yesmaximal, characteristic, complemented
10#13068871C211yesmaximal, characteristic, complemented
11#13068865C211yesmaximal, characteristic, complemented
12#13068863C211yesmaximal, characteristic, complemented
13D11×#340C211yesmaximal, characteristic, complemented
14#13068311C211yesmaximal, characteristic, complemented
15C11×#1864C211yesmaximal, characteristic, complemented
16C22×#4341C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C2×C4×C22⋊D11—21no—
20C22×Dic11⋊C4—21no—
21C22×#4313C2211yescharacteristic
22C22×C8×D11C2211yescharacteristic
23#10623077—24no—
24#10623077—24no—
25C2×#66945C2211yescharacteristic
26C2×C4⋊C4×D11C2211yescharacteristic
27C2×C4⋊C4×D11C2211yescharacteristic
28C2×#66940C2211yescharacteristic
29C2×(C22⋊D11)⋊C4—21no—
30C2×#66930—21no—
31C2×#66925C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C2×C11×#106C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C11×#389C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×#66882C2211yescharacteristic
40C2×#66880C2211yescharacteristic
41C2×#66880C2211yescharacteristic
42#10622600—21no—
43#10622598C2211yescharacteristic
44#10622586C2211yescharacteristic
45#10622585—21no—
46C2×#66874C2211yescharacteristic
47C2×#66874C2211yescharacteristic
48C2×#66872C2211yescharacteristic
49C2×#66871C2211yescharacteristic
50#10622541C2211yescharacteristic
51#10622474—24no—
52#10622385—24no—
53#10622384C418yescomplemented
54#10622280—21no—
55#10622260—21no—
56C11×#340C2211yescharacteristic
57C11×#336C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622188C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63#10622162C2211yescharacteristic
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11—21no—
66C22×C22⋊D11—21no—
67C23×Dic11—21no—
68C23×Dic11—21no—
69C2×#4341—22no—
70C2×#4341—22no—
71C2×#4341—22no—
72C2×#4341C2×C414yes—
73C2×#4341D414yes—
74C2×#4341Q814yes—
75C22×C4×D11—21no—
76C22×C4×D11—21no—
77C22×C4×D11C2311yescharacteristic
78C22×Dic22C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C4×D4×C11—22no—
82C4×D4×C11—22no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C22⋊C4—21no—
88C2×C42×C11C2311yescharacteristic
89C2×C22⋊Dic11—21no—
90D4×Dic11—22no—
91D4×Dic11—22no—
92C4×C22⋊D11—28no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4D411yescharacteristic
95C2×(C2×D11)⋊C4D411yescharacteristic
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×Dic11⋊C4—28no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×Dic11⋊C4—21no—
106C2×Dic11⋊C4—21no—
107C2×Dic11⋊C4D411yescharacteristic
108C2×Dic11⋊C4D411yescharacteristic
109C2×C4×Dic11—21no—
110C2×C4×Dic11—21no—
111C2×C4×Dic11—21no—
112C2×C4×Dic11C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C2×#4313—22no—
116C2×#4313—22no—
117C2×#4313C2×C414yescomplemented
118C2×C8×D11—22no—
119C2×C8×D11—22no—
120C2×C8×D11—22no—
121#66945—22no—
122#66945—22no—
123C4⋊C4×D11—22no—
124C4⋊C4×D11—22no—
125C4⋊C4×D11C2×C414yescomplemented
126C4⋊C4×D11D414yes—
127#66940—22no—
128#66940—22no—
129(C22⋊D11)⋊C4—28no—
130#66930—28no—
131#66925—22no—
132#66925—22no—
133C4×Dic22—22no—
134C4×Dic22—22no—
135C11×#106—22no—
136C11×#102—22no—
137C11×#102C2×C414yescomplemented
138C11×#95—21no—
139#66896—22no—
140#66896C2×C414yescomplemented
141C11⋊#95—21no—
142C11⋊#95—21no—
143C11⋊#95—21no—
144#66882—22no—
145#66880—22no—
146#66880C2×C414yescomplemented
147#66874—22no—
148#66874C2×C414yescomplemented
149#66872—22no—
150#66871—22no—
151#20878—111nomaximal, Sylow
152C24×C11—21no—
153C23×D11C2×D411yescharacteristic
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11C22×C412yes—
158C2×D4×C11C2×D412yes—
159C2×D4×C11C2×Q812yes—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—24no—
163C22×C4×C11—21no—
164C22×C4×C11—81no—
165C22×C4×C11—81no—
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2411yescharacteristic
169C2×C22⋊D11—24no—
170C2×C22⋊D11—24no—
171C2×C22⋊D11—24no—
172C22×Dic11—24no—
173C22×Dic11—24no—
174C22×Dic11—24no—
175C22×Dic11—24no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—81no—
181C22×Dic11—81no—
182C22×Dic11C2×D411yescharacteristic
183C22×Dic11C2×D411yescharacteristic
184C22×Dic11C2×D411yescharacteristic
185#4341—28no—
186#4341—28no—
187#4341—28no—
188#4341C4⋊C4116yescomplemented
189C2×C4×D11—24no—
190C2×C4×D11—24no—
191C2×C4×D11—81no—
192C2×C4×D11—81no—
193C2×C4×D11—81no—
194C2×C4×D11—81no—
195C2×C4×D11C22×C412yes—
196C2×C4×D11C2×D412yes—
197C2×C4×D11C2×D412yes—
198C2×C4×D11C2×Q812yes—
199C2×C4×D11#4112yes—
200C2×C4×D11#4112yes—
201C2×Dic22—21no—
202C2×Dic22—21no—
203C2×Dic22—21no—
204C2×Dic22C22×C412yes—
205C2×Dic22C2×D412yes—
206C2×Dic22C2×Q812yes—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
209C2×C8×C11—21no—
210C2×C8×C11—21no—
211C2×C8×C11—21no—
212C2×C8×C11C22×C412yes—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—81no—
218C11×C4⋊C4C22×C412yes—
219C11×C4⋊C4C2×D412yes—
220C11×C22⋊C4—24no—
221C42×C11—21no—
222C42×C11—21no—
223C22⋊Dic11—24no—
224(C2×D11)⋊C4—22no—
225(C2×D11)⋊C4—22no—
226(C2×D11)⋊C4—42no—
227C4⋊Dic11—21no—
228C4⋊Dic11—21no—
229C4⋊Dic11—21no—
230C4⋊Dic11—21no—
231C4⋊Dic11—81no—
232C4⋊Dic11C22×C412yes—
233C4⋊Dic11C2×D412yes—
234Dic11⋊C4—24no—
235Dic11⋊C4—24no—
236Dic11⋊C4—24no—
237Dic11⋊C4—22no—
238Dic11⋊C4—22no—
239Dic11⋊C4—24no—
240Dic11⋊C4—81no—
241Dic11⋊C4—81no—
242C4×Dic11—24no—
243C4×Dic11—24no—
244C4×Dic11—21no—
245C4×Dic11—21no—
246C4×Dic11—42no—
247C2×C11⋊C8—21no—
248C2×C11⋊C8—21no—
249C2×C11⋊C8—21no—
250C2×C11⋊C8—21no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8C22×C412yes—
253#4313—28no—
254C8×D11—44no—
255C2×#520—111no—
256C2×#428—111no—
257C2×#417—111no—
258C2×#416—111no—
259#2316—111no—
260#1865—111no—
261#1865—111no—
262#1864—111no—
263#1864D1111yescharacteristic, complemented
264#1863—111no—
265#1863—111no—
266#1862—111no—
267#1862—111no—
268C2×#340—111no—
269#1729—111no—
270C23×C11—22no—
271C23×C11—22no—
272C23×C11—22no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11C22×D411yescharacteristic
278C22×D11—21no—
279C22×D11—21no—
280C22×D11—21no—
281C22×D11—21no—
282C22×D11C4×D412yes—
283C22×D11#12012yes—
284C22×D11C22⋊Q812yes—
285D4×C11—22no—
286D4×C11—22no—
287D4×C11—22no—
288D4×C11C2×C4⋊C414yes—
289C2×C4×C11—22no—
290C2×C4×C11—21no—
291C2×C4×C11—22no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—84no—
305C2×C4×C11C23×C411yescharacteristic
306C2×C4×C11C22×D411yescharacteristic
307C2×C4×C11C22×D411yescharacteristic
308C2×C4×C11C22×Q811yescharacteristic
309C2×C4×C11C2×#4111yescharacteristic
310C2×C4×C11C2×#4111yescharacteristic
311C22⋊D11—216no—
312C2×Dic11—22no—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—216no—
316C2×Dic11—22no—
317C2×Dic11—21no—
318C2×Dic11—21no—
319C2×Dic11—22no—
320C2×Dic11—21no—
321C2×Dic11—21no—
322C2×Dic11—21no—
323C2×Dic11—21no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—84no—
332C2×Dic11C4×D412yes—
333C2×Dic11#12012yes—
334C2×Dic11C22⋊Q812yes—
335C4×D11—84no—
336C4×D11—84no—
337C4×D11C2×C4⋊C414yes—
338C4×D11C4×D414yes—
339C4×D11C22⋊Q814yes—
340C4×D11#12314yes—
341Dic22—22no—
342Dic22—22no—
343Dic22—22no—
344Dic22C2×C4⋊C414yes—
345C8×C11—22no—
346C8×C11—41no—
347C11⋊C8—22no—
348C11⋊C8—41no—
349C22×#41—111no—
350C22×M16—111no—
351C23×C8—111no—
352#520—224no—
353#520—224no—
354C2×C4×Q8—111no—
355C2×C4×Q8—111no—
356C2×C4×D4—111no—
357C2×C4×D4—221no—
358C2×C4×D4—221no—
359C2×C4×D4C2×D1111yescharacteristic
360C2×#117—111no—
361C2×#117—111no—
362C2×#117—221no—
363C22×C4⋊C4—111no—
364C22×C4⋊C4—111no—
365C22×C4⋊C4—221no—
366#428—224no—
367C2×#107—111no—
368C2×#107—111no—
369C2×#106—111no—
370C2×#106C2×D1111yescharacteristic
371#417—118no—
372#416—224no—
373C2×#103—111no—
374C2×#103—111no—
375C2×#103—111no—
376C2×#103—111no—
377C2×#102—111no—
378C2×#102—111no—
379C2×#102C2×D1111yescharacteristic
380C2×#102C2×D1111yescharacteristic
381#389—111no—
382#389—111no—
383#389—111no—
384#389—221no—
385#389—221no—
386#389C2×D1111yescharacteristic
387#380—221no—
388#380—221no—
389#340—111no—
390#340—111no—
391#340—111no—
392#340C2×D1111yescharacteristic
393#336—111no—
394#336—111no—
395#336—111no—
396#336C2×D1111yescharacteristic
397C22×C11—24no—
398C22×C11—42no—
399C22×C11—42no—
400C22×C11—42no—
401C22×C11—42no—
402C22×C11—42no—
403C22×C11—42no—
404C22×C11C2×C4×D411yescharacteristic
405C22×C11C2×#12011yescharacteristic
406C22×C11C2×C22⋊Q811yescharacteristic
407C22×C11#57611yescharacteristic
408C22×C11#57711yescharacteristic
409C22×C11#57711yescharacteristic
410C22×C11#57811yescharacteristic
411C2×D11—22no—
412C2×D11—22no—
413C2×D11—22no—
414C2×D11—22no—
415C2×D11—22no—
416C2×D11—22no—
417C2×D11#38514yes—
418C4×C11—42no—
419C4×C11—41no—
420C4×C11—42no—
421C4×C11—41no—
422C4×C11—81no—
423C4×C11C22×C4⋊C411yescharacteristic
424C4×C11C2×C4×D411yescharacteristic
425C4×C11C2×C22⋊Q811yescharacteristic
426C4×C11C2×#12311yescharacteristic
427Dic11—24no—
428Dic11—42no—
429Dic11—42no—
430Dic11—41no—
431Dic11—41no—
432Dic11—81no—
433Dic11#38514yes—
434C2×#41—114no—
435C2×#41—114no—
436C2×#41—114no—
437C2×#41—222no—
438C2×#41—222no—
439C2×#41—222no—
440C22×Q8—111no—
441C22×D4—221no—
442C22×D4C22×D1111yescharacteristic
443C23×C4—21no—
444C23×C4—111no—
445C23×C4—221no—
446C23×C4—221no—
447C23×C4—221no—
448C23×C4—221no—
449C2×M16—114no—
450C2×M16—222no—
451C2×M16—222no—
452C22×C8—111no—
453C22×C8—111no—
454C22×C8—222no—
455C22×C8—222no—
456C22×C8—222no—
457C22×C8C22×D1111yescharacteristic
458C22×C8C22×D1111yescharacteristic
459C4×Q8—222no—
460C4×Q8—222no—
461C4×Q8—222no—
462C4×Q8—222no—
463C4×D4—22no—
464C4×D4—22no—
465C4×D4—228no—
466C4×D4—222no—
467C4×D4—228no—
468C4×D4—222no—
469#117—222no—
470#117—222no—
471#117—228no—
472#117—222no—
473#117—222no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—111no—
476C2×C4⋊C4—111no—
477C2×C4⋊C4—114no—
478C2×C4⋊C4—114no—
479C2×C4⋊C4—111no—
480C2×C4⋊C4—111no—
481C2×C4⋊C4—111no—
482C2×C4⋊C4—222no—
483C2×C4⋊C4—222no—
484C2×C4⋊C4—221no—
485C2×C4⋊C4—221no—
486C2×C4⋊C4—221no—
487C2×C4⋊C4—228no—
488C2×C4⋊C4—221no—
489C2×C4⋊C4—221no—
490C2×C4⋊C4—221no—
491C2×C4⋊C4—221no—
492C2×C4⋊C4C22×D1111yescharacteristic
493C2×C4⋊C4C22×D1111yescharacteristic
494C2×C4⋊C4C22×D1111yescharacteristic
495C2×C22⋊C4—21no—
496C2×C22⋊C4—111no—
497C2×C22⋊C4—111no—
498C2×C22⋊C4—221no—
499C2×C22⋊C4—221no—
500C2×C42—111no—
501C2×C42—221no—
502C2×C42—221no—
503C2×C42—221no—
504C2×C42C22×D1111yescharacteristic
505#107—222no—
506#107—222no—
507#106—22no—
508#106—222no—
509#103—114no—
510#103—114no—
511#103—222no—
512#103—222no—
513#102—22no—
514#102—114no—
515#102—222no—
516#102C4×D1114yescomplemented
517#95—21no—
518#95—221no—
519#95—221no—
520#95—221no—
521C2×C11—44no—
522C2×C11C2×#38511yescharacteristic
523C2×C11#294611yescharacteristic
524C2×C11#294711yescharacteristic
525C2×C11#301211yescharacteristic
526C2×C11#301311yescharacteristic
527C2×C11#308311yescharacteristic
528C2×C11#308411yescharacteristic
529D11—24no—
530C24—21no—
531C24—111no—
532#41—1116no—
533#41—228no—
534#41—228no—
535#41—228no—
536C2×Q8—112no—
537C2×Q8—112no—
538C2×Q8—112no—
539C2×Q8—221no—
540C2×Q8—221no—
541C2×Q8—221no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—224no—
546C2×D4—224no—
547C2×D4—224no—
548C2×D4C2×C4×D1112yes—
549C2×D4D4×D1112yes—
550C2×D4Q8×D1112yes—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—24no—
554C22×C4—21no—
555C22×C4—81no—
556C22×C4—81no—
557C22×C4—111no—
558C22×C4—112no—
559C22×C4—112no—
560C22×C4—112no—
561C22×C4—112no—
562C22×C4—112no—
563C22×C4—112no—
564C22×C4—111no—
565C22×C4—111no—
566C22×C4—224no—
567C22×C4—224no—
568C22×C4—224no—
569C22×C4—224no—
570C22×C4—224no—
571C22×C4—221no—
572C22×C4—221no—
573C22×C4—221no—
574C22×C4—224no—
575C22×C4—221no—
576C22×C4—881no—
577C22×C4—881no—
578C22×C4—881no—
579C22×C4—881no—
580C22×C4—881no—
581C22×C4—881no—
582C22×C4D4×D1111yescharacteristic
583C22×C4D4×D1111yescharacteristic
584C22×C4C23×D1111yescharacteristic
585M16—228no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—112no—
592C2×C8—221no—
593C2×C8—221no—
594C2×C8—221no—
595C2×C8—221no—
596C2×C8—221no—
597C2×C8—444no—
598C2×C8C2×C4×D1112yes—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—81no—
604C4⋊C4—112no—
605C4⋊C4—112no—
606C4⋊C4—222no—
607C4⋊C4—224no—
608C4⋊C4—224no—
609C4⋊C4—222no—
610C4⋊C4—224no—
611C4⋊C4—224no—
612C4⋊C4—221no—
613C4⋊C4—221no—
614C4⋊C4—221no—
615C4⋊C4—221no—
616C4⋊C4—881no—
617C4⋊C4—881no—
618C4⋊C4—881no—
619C4⋊C4C2×C4×D1112yes—
620C4⋊C4D4×D1112yes—
621C22⋊C4—24no—
622C22⋊C4—222no—
623C22⋊C4—222no—
624C22⋊C4—224no—
625C22⋊C4—442no—
626C42—21no—
627C42—21no—
628C42—224no—
629C42—224no—
630C42—221no—
631C42—221no—
632C42—442no—
633C11#2087811yescharacteristic, complemented, Sylow
634C23—22no—
635C23—22no—
636C23—22no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—112no—
642C23—112no—
643C23—112no—
644C23—221no—
645C23—221no—
646C23—221no—
647C23—221no—
648C23C2×D4×D1111yescharacteristic
649Q8—114no—
650Q8—222no—
651Q8—222no—
652Q8—222no—
653D4—22no—
654D4—22no—
655D4—22no—
656D4—2216no—
657D4C4⋊C4×D1114yes—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—22no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—84no—
674C2×C4—112no—
675C2×C4—112no—
676C2×C4—112no—
677C2×C4—114no—
678C2×C4—114no—
679C2×C4—114no—
680C2×C4—114no—
681C2×C4—2216no—
682C2×C4—222no—
683C2×C4—222no—
684C2×C4—222no—
685C2×C4—221no—
686C2×C4—221no—
687C2×C4—221no—
688C2×C4—221no—
689C2×C4—222no—
690C2×C4—221no—
691C2×C4—222no—
692C2×C4—221no—
693C2×C4—441no—
694C2×C4—441no—
695C2×C4—441no—
696C2×C4—441no—
697C2×C4—441no—
698C2×C4—441no—
699C2×C4—441no—
700C2×C4—884no—
701C2×C4—884no—
702C2×C4—884no—
703C2×C4C22×C4×D1111yescharacteristic
704C2×C4C2×D4×D1111yescharacteristic
705C2×C4C2×D4×D1111yescharacteristic
706C2×C4C2×Q8×D1111yescharacteristic
707C2×C4#41×D1111yescharacteristic
708C2×C4#41×D1111yescharacteristic
709C8—22no—
710C8—41no—
711C8—222no—
712C8—441no—
713C22—24no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—114no—
721C22—222no—
722C22—222no—
723C22—222no—
724C22—222no—
725C22—222no—
726C22—222no—
727C22C4×D4×D1111yescharacteristic
728C22D11×#12011yescharacteristic
729C22D11×C22⋊Q811yescharacteristic
730C22#1062329311yescharacteristic
731C22#1062330211yescharacteristic
732C22#1062330511yescharacteristic
733C22#1062330611yescharacteristic
734C4—41no—
735C4—42no—
736C4—41no—
737C4—42no—
738C4—81no—
739C4—114no—
740C4—224no—
741C4—441no—
742C4—442no—
743C4—441no—
744C4—442no—
745C4—881no—
746C4C2×C4⋊C4×D1111yescharacteristic
747C4C4×D4×D1111yescharacteristic
748C4D11×C22⋊Q811yescharacteristic
749C4D11×#12311yescharacteristic
750C2—44no—
751C2—224no—
752C2D11×#38511yescharacteristic
753C2#1307744511yescharacteristic
754C2#1307745211yescharacteristic
755C2#1307792111yescharacteristic
756C2#1307792911yescharacteristic
757C2#1307846811yescharacteristic
758C2#1307847311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1864C2
socleC23×C11C22×D4
prime radicalC22×#4341C22
cosocleC22×C4×C11C24
hypercenter#1864D11
hypocenterC11#20878
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1864

Complements

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

NH ≅ G/Ntype
2. C2×#10622474C2semidirect
5. #13071231C2semidirect
6. #13068883C2semidirect
7. #13068881C2semidirect
8. #13068875C2semidirect
9. #13068873C2semidirect
10. #13068871C2semidirect
11. #13068865C2semidirect
12. #13068863C2semidirect
13. D11×#340C2semidirect
14. #13068311C2semidirect
15. C11×#1864C2semidirect
53. #10622384C4semidirect
117. C2×#4313C2×C4semidirect
125. C4⋊C4×D11C2×C4semidirect
137. C11×#102C2×C4semidirect
140. #66896C2×C4semidirect
146. #66880C2×C4semidirect
148. #66874C2×C4semidirect
188. #4341C4⋊C4semidirect
263. #1864D11semidirect
516. #102C4×D11semidirect
633. C11#20878semidirect

Maximal subgroups

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

subgroupindex
C2×#106230772
C2×#106224742
C2×#106223842
C2×#106223852
#130712312
#130688832
#130688812
#130688752
#130688732
#130688712
#130688652
#130688632
D11×#3402
#130683112
C11×#18642
#2087811