Finite Group Databasebeta

← #15618572

Subgroups — #15618572

Order 2816.

2242 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C211yesmaximal, characteristic
2#13077676C214yesmaximal, complemented
3#13077670C214yesmaximal, complemented
4#13077666C214yesmaximal, complemented
5#13077661C214yesmaximal, complemented
6M16×C22⋊D11C214yesmaximal, complemented
7#13077348C214yesmaximal, complemented
8#13077251C212yesmaximal, complemented
9#13077059C212yesmaximal, complemented
10C2×#10622820C211yesmaximal, characteristic, complemented
11C2×C11×#407C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C22×#4339C2211yescharacteristic
14C22×C11×M16C2212yes—
15C2×#67006C412yes—
16#10623322C412yes—
17#10623322C412yes—
18#10623322C412yes—
19#10623322C412yes—
20#10623322C2212yes—
21#10623322C2212yes—
22#10623322C2212yes—
23#10623322C2212yes—
24C2×#66983C411yescharacteristic
25C2×#66983C411yescharacteristic
26C2×#66982C412yes—
27C2×C4×C22⋊D11C2212yes—
28C2×C4×C22⋊D11C2212yes—
29C2×#66979C2211yescharacteristic
30C2×#66977C411yescharacteristic
31C2×#66977C411yescharacteristic
32C22×#4318C2212yes—
33C2×M16×D11C2214yescomplemented
34C11×#407C2212yes—
35C11×#407C2212yes—
36C11×#407C2212yescomplemented
37C11×#407C2212yescomplemented
38C2×C11×C22⋊C8C2212yescomplemented
39C2×C11×C22⋊C8C2212yescomplemented
40#10622820C2212yes—
41#10622820C2212yes—
42#10622820C2212yescomplemented
43#10622820C2212yescomplemented
44C2×C22⋊(C11⋊C8)C2212yescomplemented
45C2×C22⋊(C11⋊C8)C2212yescomplemented
46#10622741C2218yescomplemented
47#10622740C2218yescomplemented
48#10622739C2214yescomplemented
49#10622731C2214yescomplemented
50M16×Dic11C2214yescomplemented
51#10622724C2218yescomplemented
52C8×C22⋊D11C2218yescomplemented
53#10622343C2218yescomplemented
54#10622342C2218yescomplemented
55#10622341C2218yescomplemented
56#10622340C2218yescomplemented
57#10622340C2218yescomplemented
58(C22⋊D11)⋊C8C2218yescomplemented
59#10622333C2218yescomplemented
60#10622333C2218yescomplemented
61C25×C11C2×C411yescharacteristic
62C23×C4×C11—44no—
63C23×C4×C11C2×C411yescharacteristic
64C23×C4×C11C2×C411yescharacteristic
65C23×C4×C11C2×C411yescharacteristic
66C23×C4×C11C2×C411yescharacteristic
67C23×C4×C11C2×C411yescharacteristic
68C23×C4×C11C2×C411yescharacteristic
69C23×C4×C11C2×C411yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C22×C22⋊D11C2×C412yes—
78C22×C22⋊D11C2×C412yes—
79C22×C22⋊D11C2×C412yes—
80C2×#4339—44no—
81C2×#4339C2×C412yes—
82C2×#4339C2×C412yes—
83C2×#4339C2312yes—
84C2×#4339C2312yes—
85C22×D44C2×C411yescharacteristic
86C22×C4×D11C2312yes—
87C22×Dic22C2×C411yescharacteristic
88C2×C11×M16—44no—
89C2×C11×M16C2314yes—
90C2×C11×M16C2314yes—
91C22×C8×C11C2314yes—
92#67006C2×C414yes—
93#67006C2×C414yes—
94#67006C2×C414yes—
95#67006C2×C414yes—
96C2×C22⋊Dic11C2×C412yes—
97C2×C22⋊Dic11C2×C412yes—
98C2×C22⋊Dic11C2×C412yes—
99#66983C2×C412yes—
100#66983C2×C412yes—
101#66983C2×C412yes—
102#66983C2×C412yes—
103#66983C2×C412yes—
104#66983C2×C412yes—
105#66983C2×C412yes—
106#66983C2×C412yes—
107#66982C2×C414yes—
108#66982C2×C414yes—
109#66982C2×C414yes—
110#66982C2×C414yes—
111C4×C22⋊D11C2×C414yes—
112C4×C22⋊D11C2×C414yes—
113C4×C22⋊D11C2×C414yes—
114C4×C22⋊D11C2×C414yes—
115C4×C22⋊D11C2314yes—
116C4×C22⋊D11C2314yes—
117C4×C22⋊D11C2314yes—
118C4×C22⋊D11C2314yes—
119C2×(C2×D11)⋊C4C2×C412yes—
120C2×(C2×D11)⋊C4C2×C412yes—
121#66979C2×C412yes—
122#66979C2×C412yes—
123#66979C2312yes—
124#66979C2312yes—
125C2×C4⋊Dic11C2×C411yescharacteristic
126C2×C4⋊Dic11C2×C411yescharacteristic
127#66977C2×C412yes—
128#66977C2×C412yes—
129#66977C2×C412yes—
130#66977C2×C412yes—
131#66977C2×C412yes—
132#66977C2×C412yes—
133#66977C2×C412yes—
134#66977C2×C412yes—
135C2×Dic11⋊C4C2×C412yes—
136C2×Dic11⋊C4C2×C412yes—
137C2×C4×Dic11C2312yes—
138C2×#4318—44no—
139C2×#4318C2314yes—
140C2×#4318C2314yes—
141C22×C11⋊C8C2314yes—
142M16×D11—48no—
143C2×#4313C2318yescomplemented
144C2×C8×D11C2318yescomplemented
145C11×C22⋊C8C2314yes—
146C11×C22⋊C8C2314yes—
147C11×C22⋊C8C2314yes—
148C11×C22⋊C8C2314yes—
149C22⋊(C11⋊C8)C2314yes—
150C22⋊(C11⋊C8)C2314yes—
151C22⋊(C11⋊C8)C2314yes—
152C22⋊(C11⋊C8)C2314yes—
153(C2×D11)⋊C8C2318yescomplemented
154(C2×D11)⋊C8C2318yescomplemented
155#66879C2318yescomplemented
156Dic11⋊C8C2318yescomplemented
157Dic11⋊C8C2318yescomplemented
158C8×Dic11C2318yescomplemented
159#60231—111nomaximal, Sylow
160C24×C11—42no—
161C24×C11—42no—
162C24×C11—42no—
163C24×C11C22×C411yescharacteristic
164C24×C11C22×C411yescharacteristic
165C24×C11C22×C411yescharacteristic
166C24×C11C22×C411yescharacteristic
167C24×C11C22×C411yescharacteristic
168C24×C11C22×C411yescharacteristic
169C24×C11C22×C411yescharacteristic
170C23×D11C22×C412yes—
171C22×C4×C11—24no—
172C22×C4×C11—24no—
173C22×C4×C11—24no—
174C22×C4×C11—42no—
175C22×C4×C11—42no—
176C22×C4×C11—42no—
177C22×C4×C11—42no—
178C22×C4×C11—42no—
179C22×C4×C11—42no—
180C22×C4×C11—42no—
181C22×C4×C11—42no—
182C22×C4×C11—42no—
183C22×C4×C11—42no—
184C22×C4×C11—42no—
185C22×C4×C11C22×C411yescharacteristic
186C22×C4×C11C22×C411yescharacteristic
187C22×C4×C11C22×C411yescharacteristic
188C22×C4×C11C22×C411yescharacteristic
189C22×C4×C11C22×C411yescharacteristic
190C22×C4×C11C22×C411yescharacteristic
191C22×C4×C11C22×C411yescharacteristic
192C22×C4×C11C22×C411yescharacteristic
193C22×C4×C11C22×C411yescharacteristic
194C22×C4×C11C22×C411yescharacteristic
195C22×C4×C11C22×C411yescharacteristic
196C22×C4×C11C22×C411yescharacteristic
197C22×C4×C11C22×C411yescharacteristic
198C22×C4×C11C22×C411yescharacteristic
199C22×C4×C11C22×C411yescharacteristic
200C22×C4×C11C22×C411yescharacteristic
201C22×C4×C11C22×C411yescharacteristic
202C22×C4×C11C22×C411yescharacteristic
203C22×C4×C11C22×C411yescharacteristic
204C22×C4×C11C22×C411yescharacteristic
205C22×C4×C11C22×C411yescharacteristic
206C22×C4×C11C2411yescharacteristic
207C22×C4×C11C2411yescharacteristic
208C22×C4×C11C2411yescharacteristic
209C22×C4×C11C2411yescharacteristic
210C22×C4×C11C2411yescharacteristic
211C22×C4×C11C2411yescharacteristic
212C22×C4×C11C2411yescharacteristic
213C2×C22⋊D11—44no—
214C2×C22⋊D11—44no—
215C2×C22⋊D11—44no—
216C2×C22⋊D11C22×C414yes—
217C2×C22⋊D11C22×C414yes—
218C2×C22⋊D11C22×C414yes—
219C2×C22⋊D11C22×C414yes—
220C2×C22⋊D11C22×C414yes—
221C2×C22⋊D11C22×C414yes—
222C22×Dic11C22×C412yes—
223C22×Dic11C22×C412yes—
224C22×Dic11C22×C412yes—
225#4339—44no—
226#4339—44no—
227#4339—42no—
228#4339—44no—
229#4339—42no—
230C2×D44—42no—
231C2×D44C22×C412yes—
232C2×D44C22×C412yes—
233C2×C4×D11—28no—
234C2×C4×D11C22×C414yes—
235C2×C4×D11C2414yes—
236C2×Dic22—42no—
237C2×Dic22C22×C412yes—
238C2×Dic22C22×C412yes—
239C11×M16—28no—
240C11×M16—44no—
241C2×C8×C11—44no—
242C2×C8×C11C2418yes—
243C22⋊Dic11C22×C414yes—
244C22⋊Dic11C22×C414yes—
245C22⋊Dic11C22×C414yes—
246C22⋊Dic11C22×C414yes—
247C22⋊Dic11C22×C414yes—
248C22⋊Dic11C22×C414yes—
249(C2×D11)⋊C4C22×C414yes—
250(C2×D11)⋊C4C22×C414yes—
251(C2×D11)⋊C4C22×C414yes—
252(C2×D11)⋊C4C22×C414yes—
253C4⋊Dic11C22×C412yes—
254C4⋊Dic11C22×C412yes—
255C4⋊Dic11C22×C412yes—
256C4⋊Dic11C22×C412yes—
257Dic11⋊C4C22×C414yes—
258Dic11⋊C4C22×C414yes—
259Dic11⋊C4C22×C414yes—
260Dic11⋊C4C22×C414yes—
261C4×Dic11C22×C414yes—
262C4×Dic11C2414yes—
263#4318—28no—
264#4318—44no—
265C2×C11⋊C8—44no—
266C2×C11⋊C8C2418yes—
267#4313—48no—
268C8×D11—48no—
269C2×#525—111no—
270#2978—114no—
271#2977—114no—
272#2976—114no—
273#2976—114no—
274D4×M16—114no—
275D4×M16—114no—
276#2921—112no—
277#2879—112no—
278C2×#407—111no—
279C2×#407D1111yescharacteristic, complemented
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—22no—
289C23×C11—41no—
290C23×C11—41no—
291C23×C11—41no—
292C23×C11—41no—
293C23×C11—41no—
294C23×C11—41no—
295C23×C11—41no—
296C23×C11—41no—
297C23×C11—41no—
298C23×C11—41no—
299C23×C11—41no—
300C23×C11—41no—
301C23×C11—416no—
302C23×C11C23×C411yescharacteristic
303C23×C11C23×C411yescharacteristic
304C23×C11C23×C411yescharacteristic
305C23×C11C23×C411yescharacteristic
306C23×C11C23×C411yescharacteristic
307C23×C11C23×C411yescharacteristic
308C23×C11C23×C411yescharacteristic
309C22×D11—24no—
310C22×D11—42no—
311C22×D11—42no—
312C22×D11C23×C414yes—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
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—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11C23×C411yescharacteristic
341C2×C4×C11C23×C411yescharacteristic
342C2×C4×C11C23×C411yescharacteristic
343C2×C4×C11C23×C411yescharacteristic
344C2×C4×C11C23×C411yescharacteristic
345C2×C4×C11C23×C411yescharacteristic
346C2×C4×C11C23×C411yescharacteristic
347C2×C4×C11H(5,𝔽2)14yes—
348C2×C4×C11C2511yescharacteristic
349C22⋊D11—28no—
350C22⋊D11—28no—
351C22⋊D11—44no—
352C22⋊D11—44no—
353C22⋊D11—44no—
354C22⋊D11—44no—
355C2×Dic11—24no—
356C2×Dic11—42no—
357C2×Dic11—42no—
358C2×Dic11C23×C414yes—
359C2×Dic11C23×C414yes—
360C2×Dic11C23×C414yes—
361D44—42no—
362D44—42no—
363C4×D11—28no—
364C4×D11—24no—
365C4×D11—24no—
366Dic22—42no—
367Dic22—42no—
368C8×C11—28no—
369C11⋊C8—28no—
370C22×#41—111no—
371C24×C4C2×D1111yescharacteristic
372C22×M16—112no—
373C22×M16—114no—
374C22×M16C2×D1112yes—
375#525—112no—
376#525—112no—
377#525—112no—
378#525—112no—
379#525—112no—
380#525—112no—
381#525—112no—
382#525—112no—
383C2×#123—112no—
384C2×C22⋊Q8—111no—
385C2×C22⋊Q8—111no—
386C2×#121—111no—
387C2×#121—111no—
388C2×#120—112no—
389C2×C4×D4—112no—
390C2×C4×D4—112no—
391C2×#117—111no—
392#436—118no—
393#436—118no—
394#435—118no—
395#435—118no—
396#435—118no—
397#435—118no—
398C8×D4—118no—
399C8×D4—118no—
400#433—118no—
401#433—118no—
402#423—114no—
403#408—118no—
404#408—118no—
405#407—112no—
406#407—112no—
407#407—112no—
408#407—112no—
409#407—114no—
410#407C2×D1112yes—
411#407C2×D1112yes—
412#407C2×D1112yescomplemented
413#407C2×D1112yescomplemented
414C2×C22⋊C8—112no—
415C2×C22⋊C8—112no—
416C2×C22⋊C8C2×D1112yescomplemented
417C2×C22⋊C8C2×D1112yescomplemented
418C4×M16—114no—
419C22×C11—21no—
420C22×C11—21no—
421C22×C11—21no—
422C22×C11—21no—
423C22×C11—21no—
424C22×C11—21no—
425C22×C11—21no—
426C22×C11—21no—
427C22×C11—21no—
428C22×C11—21no—
429C22×C11—21no—
430C22×C11—21no—
431C22×C11—21no—
432C22×C11—21no—
433C22×C11—21no—
434C22×C11—21no—
435C22×C11—21no—
436C22×C11—21no—
437C22×C11—44no—
438C22×C11—44no—
439C22×C11—44no—
440C22×C11—44no—
441C22×C11—44no—
442C22×C11—44no—
443C22×C11—44no—
444C22×C11#51812yes—
445C22×C11#56812yes—
446C22×C11#56812yes—
447C22×C11C24×C411yescharacteristic
448C2×D11—24no—
449C2×D11—24no—
450C2×D11—24no—
451C2×D11—84no—
452C4×C11—21no—
453C4×C11—21no—
454C4×C11—21no—
455C4×C11—21no—
456C4×C11—21no—
457C4×C11—21no—
458C4×C11#51812yes—
459C4×C11C2×H(5,𝔽2)12yes—
460Dic11—24no—
461Dic11—24no—
462Dic11—24no—
463C25C4×D1111yescharacteristic
464C2×#41—112no—
465C2×#41—112no—
466C2×#41—112no—
467C2×#41—112no—
468C2×#41—444no—
469C22×Q8—111no—
470C22×D4—112no—
471C22×D4—112no—
472C22×D4—112no—
473C22×D4—111no—
474C23×C4—44no—
475C23×C4—112no—
476C23×C4C4×D1111yescharacteristic
477C23×C4C4×D1111yescharacteristic
478C23×C4C4×D1111yescharacteristic
479C23×C4C4×D1111yescharacteristic
480C23×C4C4×D1111yescharacteristic
481C23×C4C4×D1111yescharacteristic
482C23×C4C4×D1111yescharacteristic
483C23×C4C22×D1111yescharacteristic
484C23×C4C22×D1111yescharacteristic
485C23×C4C22×D1111yescharacteristic
486C23×C4C22×D1111yescharacteristic
487C23×C4C22×D1111yescharacteristic
488C23×C4C22×D1111yescharacteristic
489C23×C4C22×D1111yescharacteristic
490C2×M16—44no—
491C2×M16—114no—
492C2×M16—114no—
493C2×M16—118no—
494C2×M16—448no—
495C2×M16—444no—
496C2×M16C22×D1114yes—
497C2×M16C22×D1114yes—
498C22×C8—114no—
499C22×C8—118no—
500C22×C8C22×D1114yes—
501#123—114no—
502#123—114no—
503#123—114no—
504#123—114no—
505C22⋊Q8—112no—
506C22⋊Q8—112no—
507C22⋊Q8—112no—
508C22⋊Q8—112no—
509C22⋊Q8—112no—
510C22⋊Q8—112no—
511C22⋊Q8—112no—
512C22⋊Q8—112no—
513#121—112no—
514#121—112no—
515#121—112no—
516#121—112no—
517#121—112no—
518#121—112no—
519#121—112no—
520#121—112no—
521#120—114no—
522#120—114no—
523#120—114no—
524#120—114no—
525C4×D4—114no—
526C4×D4—114no—
527C4×D4—114no—
528C4×D4—114no—
529C4×D4—114no—
530C4×D4—114no—
531C4×D4—114no—
532C4×D4—114no—
533#117—112no—
534#117—112no—
535#117—112no—
536#117—112no—
537C2×C4⋊C4—111no—
538C2×C4⋊C4—111no—
539C2×C4⋊C4—112no—
540C2×C4⋊C4—112no—
541C2×C22⋊C4—112no—
542C2×C22⋊C4—112no—
543C2×C22⋊C4—112no—
544C2×C22⋊C4—112no—
545C2×C22⋊C4—112no—
546C2×C42—112no—
547C4⋊C8—118no—
548C4⋊C8—118no—
549C22⋊C8—114no—
550C22⋊C8—114no—
551C22⋊C8—114no—
552C22⋊C8—114no—
553C22⋊C8—118no—
554C22⋊C8—118no—
555C22⋊C8C22×D1114yes—
556C22⋊C8C22×D1114yes—
557C22⋊C8C22×D1114yes—
558C22⋊C8C22×D1114yes—
559#97—118no—
560C4×C8—118no—
561C2×C11—22no—
562C2×C11—22no—
563C2×C11—22no—
564C2×C11—41no—
565C2×C11—41no—
566C2×C11—41no—
567C2×C11—41no—
568C2×C11C2×#51811yescharacteristic
569C2×C11C2×#56811yescharacteristic
570C2×C11C2×#56811yescharacteristic
571D11—44no—
572C24—42no—
573C24—42no—
574C24—42no—
575C24—112no—
576C24C2×C4×D1111yescharacteristic
577C24C2×C4×D1111yescharacteristic
578C24C2×C4×D1111yescharacteristic
579C24C2×C4×D1111yescharacteristic
580C24C2×C4×D1111yescharacteristic
581C24C2×C4×D1111yescharacteristic
582C24C2×C4×D1111yescharacteristic
583#41—444no—
584#41—444no—
585#41—442no—
586#41—444no—
587#41—442no—
588C2×Q8—112no—
589C2×Q8—112no—
590C2×Q8—442no—
591C2×D4—114no—
592C2×D4—114no—
593C2×D4—114no—
594C2×D4—114no—
595C2×D4—114no—
596C2×D4—114no—
597C2×D4—112no—
598C2×D4—112no—
599C2×D4—442no—
600C2×D4—444no—
601C2×D4—444no—
602C2×D4—444no—
603C22×C4—24no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—112no—
618C22×C4—112no—
619C22×C4—112no—
620C22×C4—114no—
621C22×C4—114no—
622C22×C4—228no—
623C22×C4C2×C4×D1111yescharacteristic
624C22×C4C2×C4×D1111yescharacteristic
625C22×C4C2×C4×D1111yescharacteristic
626C22×C4C2×C4×D1111yescharacteristic
627C22×C4C2×C4×D1111yescharacteristic
628C22×C4C2×C4×D1111yescharacteristic
629C22×C4C2×C4×D1111yescharacteristic
630C22×C4C2×C4×D1111yescharacteristic
631C22×C4C2×C4×D1111yescharacteristic
632C22×C4C2×C4×D1111yescharacteristic
633C22×C4C2×C4×D1111yescharacteristic
634C22×C4C2×C4×D1111yescharacteristic
635C22×C4C2×C4×D1111yescharacteristic
636C22×C4C2×C4×D1111yescharacteristic
637C22×C4C2×C4×D1111yescharacteristic
638C22×C4C2×C4×D1111yescharacteristic
639C22×C4C2×C4×D1111yescharacteristic
640C22×C4C2×C4×D1111yescharacteristic
641C22×C4C2×C4×D1111yescharacteristic
642C22×C4C2×C4×D1111yescharacteristic
643C22×C4C2×C4×D1111yescharacteristic
644C22×C4C23×D1111yescharacteristic
645C22×C4C23×D1111yescharacteristic
646C22×C4C23×D1111yescharacteristic
647C22×C4C23×D1111yescharacteristic
648C22×C4C23×D1111yescharacteristic
649C22×C4C23×D1111yescharacteristic
650C22×C4C23×D1111yescharacteristic
651M16—28no—
652M16—44no—
653M16—228no—
654M16—448no—
655M16—444no—
656C2×C8—44no—
657C2×C8—118no—
658C2×C8—448no—
659C2×C8—444no—
660C2×C8C23×D1118yes—
661C4⋊C4—112no—
662C4⋊C4—112no—
663C4⋊C4—112no—
664C4⋊C4—112no—
665C4⋊C4—114no—
666C4⋊C4—114no—
667C4⋊C4—114no—
668C4⋊C4—114no—
669C22⋊C4—114no—
670C22⋊C4—114no—
671C22⋊C4—114no—
672C22⋊C4—114no—
673C22⋊C4—114no—
674C22⋊C4—114no—
675C22⋊C4—114no—
676C22⋊C4—114no—
677C22⋊C4—114no—
678C22⋊C4—114no—
679C42—114no—
680C42—114no—
681C11#6023111yescharacteristic, complemented, Sylow
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—416no—
704C23—114no—
705C23—224no—
706C23—442no—
707C23—442no—
708C23C22×C4×D1111yescharacteristic
709C23C22×C4×D1111yescharacteristic
710C23C22×C4×D1111yescharacteristic
711C23C22×C4×D1111yescharacteristic
712C23C22×C4×D1111yescharacteristic
713C23C22×C4×D1111yescharacteristic
714C23C22×C4×D1111yescharacteristic
715Q8—442no—
716Q8—442no—
717D4—228no—
718D4—228no—
719D4—442no—
720D4—442no—
721D4—444no—
722D4—444no—
723D4—444no—
724D4—444no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—114no—
753C2×C4—114no—
754C2×C4—114no—
755C2×C4—224no—
756C2×C4—228no—
757C2×C4—224no—
758C2×C4—224no—
759C2×C4—442no—
760C2×C4—442no—
761C2×C4C22×C4×D1111yescharacteristic
762C2×C4C22×C4×D1111yescharacteristic
763C2×C4C22×C4×D1111yescharacteristic
764C2×C4C22×C4×D1111yescharacteristic
765C2×C4C22×C4×D1111yescharacteristic
766C2×C4C22×C4×D1111yescharacteristic
767C2×C4C22×C4×D1111yescharacteristic
768C2×C4#6703714yes—
769C2×C4C24×D1111yescharacteristic
770C8—28no—
771C8—228no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—21no—
778C22—21no—
779C22—21no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—21no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—224no—
798C22—224no—
799C22—224no—
800C22—884no—
801C22#1062301712yes—
802C22#1062327612yes—
803C22#1062327612yes—
804C22C23×C4×D1111yescharacteristic
805C4—21no—
806C4—21no—
807C4—21no—
808C4—21no—
809C4—21no—
810C4—21no—
811C4—224no—
812C4—224no—
813C4—224no—
814C4#1062301712yes—
815C4C2×#6703712yes—
816C2—22no—
817C2—22no—
818C2—22no—
819C2—41no—
820C2—41no—
821C2—41no—
822C2—41no—
823C2—444no—
824C2C2×#1062301711yescharacteristic
825C2C2×#1062327611yescharacteristic
826C2C2×#1062327611yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC2×C11×#407C2
prime radicalC2×#10623322C2
cosocleC2×C4×C11C25
hypercenterC2×#407D11
hypocenterC11#60231
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. #13077676C2semidirect
3. #13077670C2semidirect
4. #13077666C2semidirect
5. #13077661C2semidirect
6. M16×C22⋊D11C2semidirect
7. #13077348C2semidirect
8. #13077251C2semidirect
9. #13077059C2semidirect
10. C2×#10622820C2semidirect
11. C2×C11×#407C2semidirect
33. C2×M16×D11C22semidirect
36. C11×#407C22semidirect
37. C11×#407C22semidirect
38. C2×C11×C22⋊C8C22semidirect
39. C2×C11×C22⋊C8C22semidirect
42. #10622820C22semidirect
43. #10622820C22semidirect
44. C2×C22⋊(C11⋊C8)C22semidirect
45. C2×C22⋊(C11⋊C8)C22semidirect
46. #10622741C22semidirect
47. #10622740C22semidirect
48. #10622739C22semidirect
49. #10622731C22semidirect
50. M16×Dic11C22semidirect
51. #10622724C22semidirect
52. C8×C22⋊D11C22semidirect
53. #10622343C22semidirect
54. #10622342C22semidirect
55. #10622341C22semidirect
56. #10622340C22semidirect
57. #10622340C22semidirect
58. (C22⋊D11)⋊C8C22semidirect
59. #10622333C22semidirect
60. #10622333C22semidirect
143. C2×#4313C23semidirect
144. C2×C8×D11C23semidirect
153. (C2×D11)⋊C8C23semidirect
154. (C2×D11)⋊C8C23semidirect
155. #66879C23semidirect
156. Dic11⋊C8C23semidirect
157. Dic11⋊C8C23semidirect
158. C8×Dic11C23semidirect
279. C2×#407D11semidirect
412. #407C2×D11semidirect
413. #407C2×D11semidirect
416. C2×C22⋊C8C2×D11semidirect
417. C2×C22⋊C8C2×D11semidirect
681. C11#60231semidirect

Maximal subgroups

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

subgroupindex
C2×#106233222
#130776762
#130776702
#130776662
#130776612
M16×C22⋊D112
#130773482
#130772512
#130770592
C2×#106228202
C2×C11×#4072
#6023111