Finite Group Databasebeta

← #15618593

Subgroups — #15618593

Order 2816.

2298 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C211yesmaximal, characteristic
2#13077670C214yesmaximal, complemented
3#13077666C214yesmaximal, complemented
4#13077652C214yesmaximal, complemented
5#13077642C212yesmaximal, complemented
6#13077638C212yesmaximal, complemented
7#13077341C214yesmaximal, complemented
8#13077306C214yesmaximal, complemented
9#13077276C212yesmaximal, complemented
10#13077066C212yesmaximal, complemented
11C22×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
12C2×C11×#407C211yesmaximal, characteristic, complemented
13C24×C4×C11C2211yescharacteristic
14C22×#4339C2211yescharacteristic
15C22×C11×M16C2212yescomplemented
16C2×#67006C412yes—
17#10623322C412yes—
18#10623322C412yes—
19#10623322C412yes—
20#10623322C412yes—
21#10623322C2212yes—
22#10623322C2212yes—
23#10623322C2212yes—
24#10623322C2212yes—
25C2×#66983C411yescharacteristic
26C2×#66983C411yescharacteristic
27C2×#66982C412yes—
28C2×C4×C22⋊D11C2212yes—
29C2×C4×C22⋊D11C2212yes—
30C2×#66979C2211yescharacteristic
31C2×#66977C411yescharacteristic
32C2×#66977C411yescharacteristic
33C23×C11⋊C8C2212yescomplemented
34C2×#66960C2214yescomplemented
35C11×#407C2212yes—
36C11×#407C2212yes—
37C11×#407C2212yescomplemented
38C11×#407C2212yescomplemented
39C2×C11×C22⋊C8C2212yes—
40C2×C11×C22⋊C8C2212yescomplemented
41C2×C22⋊(C11⋊C8)C2212yes—
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44C2×C22⋊(C11⋊C8)C2212yes—
45C2×C22⋊(C11⋊C8)C2212yescomplemented
46C2×C22⋊(C11⋊C8)C2212yescomplemented
47C2×C22⋊(C11⋊C8)C2212yescomplemented
48#10622742C2214yescomplemented
49#10622741C2218yescomplemented
50#10622740C2218yescomplemented
51#10622735C2214yescomplemented
52#10622732C2214yescomplemented
53#10622724C2218yescomplemented
54C8×C22⋊D11C2218yescomplemented
55#10622343C2218yescomplemented
56#10622343C2218yescomplemented
57#10622340C2218yescomplemented
58#10622339C2214yescomplemented
59(C22⋊D11)⋊C8C2218yescomplemented
60(C22⋊D11)⋊C8C2218yescomplemented
61D11×C22⋊C8C2214yescomplemented
62#10622333C2218yescomplemented
63#10622332C2214yescomplemented
64#10622331C2214yescomplemented
65C25×C11C2×C411yescharacteristic
66C23×C4×C11—44no—
67C23×C4×C11C2×C411yescharacteristic
68C23×C4×C11C2×C411yescharacteristic
69C23×C4×C11C2×C411yescharacteristic
70C23×C4×C11C2×C411yescharacteristic
71C23×C4×C11C2×C411yescharacteristic
72C23×C4×C11C2×C411yescharacteristic
73C23×C4×C11C2×C411yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C22×C22⋊D11C2×C412yes—
82C22×C22⋊D11C2×C412yes—
83C22×C22⋊D11C2×C412yes—
84C2×#4339—44no—
85C2×#4339C2×C412yes—
86C2×#4339C2×C412yes—
87C2×#4339C2312yes—
88C2×#4339C2312yes—
89C22×D44C2×C411yescharacteristic
90C22×C4×D11C2312yes—
91C22×Dic22C2×C411yescharacteristic
92C2×C11×M16—44no—
93C2×C11×M16C2314yes—
94C2×C11×M16C2314yes—
95C22×C8×C11C2314yes—
96#67006C2×C414yes—
97#67006C2×C414yes—
98#67006C2×C414yes—
99#67006C2×C414yes—
100C2×C22⋊Dic11C2×C412yes—
101C2×C22⋊Dic11C2×C412yes—
102C2×C22⋊Dic11C2×C412yes—
103#66983C2×C412yes—
104#66983C2×C412yes—
105#66983C2×C412yes—
106#66983C2×C412yes—
107#66983C2×C412yes—
108#66983C2×C412yes—
109#66983C2×C412yes—
110#66983C2×C412yes—
111#66982C2×C414yes—
112#66982C2×C414yes—
113#66982C2×C414yes—
114#66982C2×C414yes—
115C4×C22⋊D11C2×C414yes—
116C4×C22⋊D11C2×C414yes—
117C4×C22⋊D11C2×C414yes—
118C4×C22⋊D11C2×C414yes—
119C4×C22⋊D11C2314yes—
120C4×C22⋊D11C2314yes—
121C4×C22⋊D11C2314yes—
122C4×C22⋊D11C2314yes—
123C2×(C2×D11)⋊C4C2×C412yes—
124C2×(C2×D11)⋊C4C2×C412yes—
125#66979C2×C412yes—
126#66979C2×C412yes—
127#66979C2312yes—
128#66979C2312yes—
129C2×C4⋊Dic11C2×C411yescharacteristic
130C2×C4⋊Dic11C2×C411yescharacteristic
131#66977C2×C412yes—
132#66977C2×C412yes—
133#66977C2×C412yes—
134#66977C2×C412yes—
135#66977C2×C412yes—
136#66977C2×C412yes—
137#66977C2×C412yes—
138#66977C2×C412yes—
139C2×Dic11⋊C4C2×C412yes—
140C2×Dic11⋊C4C2×C412yes—
141C2×C4×Dic11C2312yes—
142C22×C11⋊C8—44no—
143C22×C11⋊C8C2314yes—
144C22×C11⋊C8C2312yes—
145C22×C11⋊C8C2314yes—
146C22×C11⋊C8C2312yes—
147#66960—48no—
148C2×#4313C2318yescomplemented
149C2×C8×D11C2318yescomplemented
150C11×C22⋊C8C2314yes—
151C11×C22⋊C8C2314yes—
152C11×C22⋊C8C2314yes—
153C11×C22⋊C8C2314yes—
154C22⋊(C11⋊C8)C2312yes—
155C22⋊(C11⋊C8)C2312yes—
156C22⋊(C11⋊C8)C2314yes—
157C22⋊(C11⋊C8)C2312yes—
158C22⋊(C11⋊C8)C2312yes—
159C22⋊(C11⋊C8)C2314yes—
160(C2×D11)⋊C8C2318yescomplemented
161(C2×D11)⋊C8C2318yescomplemented
162#66879C2318yescomplemented
163Dic11⋊C8C2318yescomplemented
164Dic11⋊C8C2318yescomplemented
165C8×Dic11C2318yescomplemented
166#60233—111nomaximal, Sylow
167C24×C11—24no—
168C24×C11—42no—
169C24×C11—42no—
170C24×C11C22×C411yescharacteristic
171C24×C11C22×C411yescharacteristic
172C24×C11C22×C411yescharacteristic
173C24×C11C22×C411yescharacteristic
174C24×C11C22×C411yescharacteristic
175C24×C11C22×C411yescharacteristic
176C24×C11C22×C411yescharacteristic
177C23×D11C22×C412yes—
178C22×C4×C11—24no—
179C22×C4×C11—24no—
180C22×C4×C11—24no—
181C22×C4×C11—42no—
182C22×C4×C11—42no—
183C22×C4×C11—42no—
184C22×C4×C11—42no—
185C22×C4×C11—42no—
186C22×C4×C11—42no—
187C22×C4×C11—42no—
188C22×C4×C11—42no—
189C22×C4×C11—42no—
190C22×C4×C11—42no—
191C22×C4×C11—42no—
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×C11C22×C411yescharacteristic
207C22×C4×C11C22×C411yescharacteristic
208C22×C4×C11C22×C411yescharacteristic
209C22×C4×C11C22×C411yescharacteristic
210C22×C4×C11C22×C411yescharacteristic
211C22×C4×C11C22×C411yescharacteristic
212C22×C4×C11C22×C411yescharacteristic
213C22×C4×C11C2411yescharacteristic
214C22×C4×C11C2411yescharacteristic
215C22×C4×C11C2411yescharacteristic
216C22×C4×C11C2411yescharacteristic
217C22×C4×C11C2411yescharacteristic
218C22×C4×C11C2411yescharacteristic
219C22×C4×C11C2411yescharacteristic
220C2×C22⋊D11—28no—
221C2×C22⋊D11—44no—
222C2×C22⋊D11—44no—
223C2×C22⋊D11C22×C414yes—
224C2×C22⋊D11C22×C414yes—
225C2×C22⋊D11C22×C414yes—
226C2×C22⋊D11C22×C414yes—
227C2×C22⋊D11C22×C414yes—
228C2×C22⋊D11C22×C414yes—
229C22×Dic11C22×C412yes—
230C22×Dic11C22×C412yes—
231C22×Dic11C22×C412yes—
232#4339—28no—
233#4339—44no—
234#4339—44no—
235#4339—44no—
236C2×D44—42no—
237C2×D44C22×C412yes—
238C2×D44C22×C412yes—
239C2×C4×D11—44no—
240C2×C4×D11C22×C414yes—
241C2×C4×D11C2414yes—
242C2×Dic22—42no—
243C2×Dic22C22×C412yes—
244C2×Dic22C22×C412yes—
245C11×M16—28no—
246C11×M16—44no—
247C2×C8×C11—44no—
248C2×C8×C11C2418yes—
249C22⋊Dic11C22×C414yes—
250C22⋊Dic11C22×C414yes—
251C22⋊Dic11C22×C414yes—
252C22⋊Dic11C22×C414yes—
253C22⋊Dic11C22×C414yes—
254C22⋊Dic11C22×C414yes—
255(C2×D11)⋊C4C22×C414yes—
256(C2×D11)⋊C4C22×C414yes—
257(C2×D11)⋊C4C22×C414yes—
258(C2×D11)⋊C4C22×C414yes—
259C4⋊Dic11C22×C412yes—
260C4⋊Dic11C22×C412yes—
261C4⋊Dic11C22×C412yes—
262C4⋊Dic11C22×C412yes—
263Dic11⋊C4C22×C414yes—
264Dic11⋊C4C22×C414yes—
265Dic11⋊C4C22×C414yes—
266Dic11⋊C4C22×C414yes—
267C4×Dic11C22×C414yes—
268C4×Dic11C2414yes—
269C2×C11⋊C8—28no—
270C2×C11⋊C8—42no—
271C2×C11⋊C8—44no—
272C2×C11⋊C8—42no—
273C2×C11⋊C8C2414yes—
274C2×C11⋊C8C2414yes—
275#4313—48no—
276C8×D11—48no—
277C2×#525—111no—
278#2977—114no—
279#2976—114no—
280#2974—114no—
281#2973—112no—
282#2972—112no—
283#2933—114no—
284#2929—114no—
285#2924—112no—
286#2880—112no—
287C2×#407D1111yescharacteristic, complemented
288C22×C22⋊C8—111no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—41no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—416no—
310C23×C11#13114yescomplemented
311C23×C11C23×C411yescharacteristic
312C23×C11C23×C411yescharacteristic
313C23×C11C23×C411yescharacteristic
314C23×C11C23×C411yescharacteristic
315C23×C11C23×C411yescharacteristic
316C23×C11C23×C411yescharacteristic
317C23×C11C23×C411yescharacteristic
318C22×D11—24no—
319C22×D11—42no—
320C22×D11—42no—
321C22×D11C23×C414yes—
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—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11C23×C411yescharacteristic
350C2×C4×C11C23×C411yescharacteristic
351C2×C4×C11C23×C411yescharacteristic
352C2×C4×C11C23×C411yescharacteristic
353C2×C4×C11C23×C411yescharacteristic
354C2×C4×C11C23×C411yescharacteristic
355C2×C4×C11C23×C411yescharacteristic
356C2×C4×C11H(5,𝔽2)14yes—
357C2×C4×C11C2511yescharacteristic
358C22⋊D11—28no—
359C22⋊D11—28no—
360C22⋊D11—28no—
361C22⋊D11—28no—
362C22⋊D11—44no—
363C22⋊D11—44no—
364C2×Dic11—24no—
365C2×Dic11—42no—
366C2×Dic11—42no—
367C2×Dic11C23×C414yes—
368C2×Dic11C23×C414yes—
369C2×Dic11C23×C414yes—
370D44—24no—
371D44—42no—
372C4×D11—28no—
373C4×D11—44no—
374Dic22—24no—
375Dic22—42no—
376C8×C11—28no—
377C11⋊C8—24no—
378C11⋊C8—24no—
379C22×#41—111no—
380C24×C4C2×D1111yescharacteristic
381C2×#131—114no—
382C22×M16C2×D1112yescomplemented
383C23×C8—112no—
384#525—112no—
385#525—112no—
386#525—112no—
387#525—112no—
388#525—112no—
389#525—112no—
390#525—112no—
391#525—112no—
392C2×#123—112no—
393C2×C22⋊Q8—111no—
394C2×C22⋊Q8—111no—
395C2×#121—111no—
396C2×#121—111no—
397C2×#120—112no—
398C2×C4×D4—112no—
399C2×C4×D4—112no—
400C2×#117—111no—
401#436—118no—
402#435—118no—
403#435—118no—
404#435—118no—
405#435—118no—
406C8×D4—118no—
407C8×D4—118no—
408C8×D4—118no—
409#433—118no—
410#432—114no—
411#431—114no—
412#424—114no—
413#408—114no—
414#408—118no—
415#407—114no—
416#407C2×D1112yes—
417#407C2×D1112yes—
418#407C2×D1112yescomplemented
419#407C2×D1112yescomplemented
420C2×C22⋊C8—112no—
421C2×C22⋊C8—111no—
422C2×C22⋊C8—111no—
423C2×C22⋊C8—112no—
424C2×C22⋊C8—112no—
425C2×C22⋊C8—112no—
426C2×C22⋊C8—112no—
427C2×C22⋊C8—114no—
428C2×C22⋊C8C2×D1112yes—
429C2×C22⋊C8C2×D1112yescomplemented
430#405—114no—
431C22×C11—28no—
432C22×C11—21no—
433C22×C11—21no—
434C22×C11—21no—
435C22×C11—21no—
436C22×C11—21no—
437C22×C11—21no—
438C22×C11—21no—
439C22×C11—21no—
440C22×C11—21no—
441C22×C11—21no—
442C22×C11—21no—
443C22×C11—21no—
444C22×C11—21no—
445C22×C11—21no—
446C22×C11—21no—
447C22×C11—21no—
448C22×C11—44no—
449C22×C11—44no—
450C22×C11—44no—
451C22×C11—44no—
452C22×C11—44no—
453C22×C11—44no—
454C22×C11#51812yes—
455C22×C11C2×#13112yes—
456C22×C11C2×#13112yes—
457C22×C11C2×#13112yes—
458C22×C11#56812yes—
459C22×C11C24×C411yescharacteristic
460C2×D11—24no—
461C2×D11—24no—
462C2×D11—24no—
463C2×D11—84no—
464C4×C11—21no—
465C4×C11—21no—
466C4×C11—21no—
467C4×C11—21no—
468C4×C11—21no—
469C4×C11—21no—
470C4×C11#51812yes—
471C4×C11C2×H(5,𝔽2)12yes—
472Dic11—24no—
473Dic11—24no—
474Dic11—24no—
475C25C4×D1111yescharacteristic
476C2×#41—112no—
477C2×#41—112no—
478C2×#41—112no—
479C2×#41—112no—
480C2×#41—444no—
481C22×Q8—111no—
482C22×D4—112no—
483C22×D4—112no—
484C22×D4—112no—
485C22×D4—111no—
486C23×C4—44no—
487C23×C4—112no—
488C23×C4C4×D1111yescharacteristic
489C23×C4C4×D1111yescharacteristic
490C23×C4C4×D1111yescharacteristic
491C23×C4C4×D1111yescharacteristic
492C23×C4C4×D1111yescharacteristic
493C23×C4C4×D1111yescharacteristic
494C23×C4C4×D1111yescharacteristic
495C23×C4C22×D1111yescharacteristic
496C23×C4C22×D1111yescharacteristic
497C23×C4C22×D1111yescharacteristic
498C23×C4C22×D1111yescharacteristic
499C23×C4C22×D1111yescharacteristic
500C23×C4C22×D1111yescharacteristic
501C23×C4C22×D1111yescharacteristic
502#131—448no—
503C2×M16—44no—
504C2×M16—118no—
505C2×M16C22×D1114yes—
506C2×M16C22×D1114yes—
507C22×C8—114no—
508C22×C8—112no—
509C22×C8—114no—
510C22×C8—112no—
511C22×C8—118no—
512C22×C8—444no—
513C22×C8C22×D1114yes—
514#123—114no—
515#123—114no—
516#123—114no—
517#123—114no—
518C22⋊Q8—112no—
519C22⋊Q8—112no—
520C22⋊Q8—112no—
521C22⋊Q8—112no—
522C22⋊Q8—112no—
523C22⋊Q8—112no—
524C22⋊Q8—112no—
525C22⋊Q8—112no—
526#121—112no—
527#121—112no—
528#121—112no—
529#121—112no—
530#121—112no—
531#121—112no—
532#121—112no—
533#121—112no—
534#120—114no—
535#120—114no—
536#120—114no—
537#120—114no—
538C4×D4—114no—
539C4×D4—114no—
540C4×D4—114no—
541C4×D4—114no—
542C4×D4—114no—
543C4×D4—114no—
544C4×D4—114no—
545C4×D4—114no—
546#117—112no—
547#117—112no—
548#117—112no—
549#117—112no—
550C2×C4⋊C4—111no—
551C2×C4⋊C4—111no—
552C2×C4⋊C4—112no—
553C2×C4⋊C4—112no—
554C2×C22⋊C4—112no—
555C2×C22⋊C4—112no—
556C2×C22⋊C4—112no—
557C2×C22⋊C4—112no—
558C2×C22⋊C4—112no—
559C2×C42—112no—
560C4⋊C8—118no—
561C4⋊C8—118no—
562C22⋊C8—112no—
563C22⋊C8—112no—
564C22⋊C8—114no—
565C22⋊C8—112no—
566C22⋊C8—112no—
567C22⋊C8—114no—
568C22⋊C8—118no—
569C22⋊C8—118no—
570C22⋊C8C22×D1114yes—
571C22⋊C8C22×D1114yes—
572C22⋊C8C22×D1114yes—
573C22⋊C8C22×D1114yes—
574#97—118no—
575C4×C8—118no—
576C2×C11—22no—
577C2×C11—22no—
578C2×C11—22no—
579C2×C11—22no—
580C2×C11—22no—
581C2×C11—41no—
582C2×C11—41no—
583C2×C11C2×#51811yescharacteristic
584C2×C11C22×#13111yescharacteristic
585C2×C11C2×#56811yescharacteristic
586D11—44no—
587C24—24no—
588C24—42no—
589C24—42no—
590C24—112no—
591C24C2×C4×D1111yescharacteristic
592C24C2×C4×D1111yescharacteristic
593C24C2×C4×D1111yescharacteristic
594C24C2×C4×D1111yescharacteristic
595C24C2×C4×D1111yescharacteristic
596C24C2×C4×D1111yescharacteristic
597C24C2×C4×D1111yescharacteristic
598#41—228no—
599#41—444no—
600#41—444no—
601#41—444no—
602C2×Q8—112no—
603C2×Q8—112no—
604C2×Q8—442no—
605C2×D4—114no—
606C2×D4—114no—
607C2×D4—114no—
608C2×D4—114no—
609C2×D4—114no—
610C2×D4—114no—
611C2×D4—112no—
612C2×D4—112no—
613C2×D4—228no—
614C2×D4—442no—
615C2×D4—444no—
616C2×D4—444no—
617C22×C4—24no—
618C22×C4—24no—
619C22×C4—24no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—112no—
632C22×C4—112no—
633C22×C4—112no—
634C22×C4—114no—
635C22×C4—114no—
636C22×C4—444no—
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×C4C2×C4×D1111yescharacteristic
645C22×C4C2×C4×D1111yescharacteristic
646C22×C4C2×C4×D1111yescharacteristic
647C22×C4C2×C4×D1111yescharacteristic
648C22×C4C2×C4×D1111yescharacteristic
649C22×C4C2×C4×D1111yescharacteristic
650C22×C4C2×C4×D1111yescharacteristic
651C22×C4C2×C4×D1111yescharacteristic
652C22×C4C2×C4×D1111yescharacteristic
653C22×C4C2×C4×D1111yescharacteristic
654C22×C4C2×C4×D1111yescharacteristic
655C22×C4C2×C4×D1111yescharacteristic
656C22×C4C2×C4×D1111yescharacteristic
657C22×C4C2×C4×D1111yescharacteristic
658C22×C4C23×D1111yescharacteristic
659C22×C4C23×D1111yescharacteristic
660C22×C4C23×D1111yescharacteristic
661C22×C4C23×D1111yescharacteristic
662C22×C4C23×D1111yescharacteristic
663C22×C4C23×D1111yescharacteristic
664C22×C4C23×D1111yescharacteristic
665M16—28no—
666M16—44no—
667M16—448no—
668C2×C8—44no—
669C2×C8—114no—
670C2×C8—114no—
671C2×C8—228no—
672C2×C8—448no—
673C2×C8—442no—
674C2×C8—444no—
675C2×C8—442no—
676C2×C8C23×D1118yes—
677C4⋊C4—112no—
678C4⋊C4—112no—
679C4⋊C4—112no—
680C4⋊C4—112no—
681C4⋊C4—114no—
682C4⋊C4—114no—
683C4⋊C4—114no—
684C4⋊C4—114no—
685C22⋊C4—114no—
686C22⋊C4—114no—
687C22⋊C4—114no—
688C22⋊C4—114no—
689C22⋊C4—114no—
690C22⋊C4—114no—
691C22⋊C4—114no—
692C22⋊C4—114no—
693C22⋊C4—114no—
694C22⋊C4—114no—
695C42—114no—
696C42—114no—
697C11#6023311yescharacteristic, complemented, Sylow
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—416no—
719C23—114no—
720C23—224no—
721C23—442no—
722C23—442no—
723C23#6696014yescomplemented
724C23C22×C4×D1111yescharacteristic
725C23C22×C4×D1111yescharacteristic
726C23C22×C4×D1111yescharacteristic
727C23C22×C4×D1111yescharacteristic
728C23C22×C4×D1111yescharacteristic
729C23C22×C4×D1111yescharacteristic
730C23C22×C4×D1111yescharacteristic
731Q8—224no—
732Q8—442no—
733D4—228no—
734D4—228no—
735D4—228no—
736D4—228no—
737D4—224no—
738D4—442no—
739D4—444no—
740D4—444no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—114no—
769C2×C4—114no—
770C2×C4—114no—
771C2×C4—224no—
772C2×C4—228no—
773C2×C4—444no—
774C2×C4—442no—
775C2×C4—442no—
776C2×C4C22×C4×D1111yescharacteristic
777C2×C4C22×C4×D1111yescharacteristic
778C2×C4C22×C4×D1111yescharacteristic
779C2×C4C22×C4×D1111yescharacteristic
780C2×C4C22×C4×D1111yescharacteristic
781C2×C4C22×C4×D1111yescharacteristic
782C2×C4C22×C4×D1111yescharacteristic
783C2×C4#6703714yes—
784C2×C4C24×D1111yescharacteristic
785C8—28no—
786C8—224no—
787C8—224no—
788C22—28no—
789C22—21no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—44no—
806C22—44no—
807C22—44no—
808C22—44no—
809C22—44no—
810C22—44no—
811C22—224no—
812C22—224no—
813C22—224no—
814C22—884no—
815C22#1062301712yes—
816C22C2×#6696012yes—
817C22C2×#6696012yes—
818C22C2×#6696012yes—
819C22#1062327612yes—
820C22C23×C4×D1111yescharacteristic
821C4—21no—
822C4—21no—
823C4—21no—
824C4—21no—
825C4—21no—
826C4—21no—
827C4—224no—
828C4—224no—
829C4—224no—
830C4#1062301712yes—
831C4C2×#6703712yes—
832C2—22no—
833C2—22no—
834C2—22no—
835C2—22no—
836C2—22no—
837C2—41no—
838C2—41no—
839C2—444no—
840C2C2×#1062301711yescharacteristic
841C2C22×#6696011yescharacteristic
842C2C2×#1062327611yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC2×C11×#407C2
prime radicalC2×#10623322C2
cosocleC2×C4×C11C25
hypercenterC2×#407D11
hypocenterC11#60233
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. #13077670C2semidirect
3. #13077666C2semidirect
4. #13077652C2semidirect
5. #13077642C2semidirect
6. #13077638C2semidirect
7. #13077341C2semidirect
8. #13077306C2semidirect
9. #13077276C2semidirect
10. #13077066C2semidirect
11. C22×C22⋊(C11⋊C8)C2semidirect
12. C2×C11×#407C2semidirect
15. C22×C11×M16C22semidirect
33. C23×C11⋊C8C22semidirect
34. C2×#66960C22semidirect
37. C11×#407C22semidirect
38. C11×#407C22semidirect
40. C2×C11×C22⋊C8C22semidirect
45. C2×C22⋊(C11⋊C8)C22semidirect
46. C2×C22⋊(C11⋊C8)C22semidirect
47. C2×C22⋊(C11⋊C8)C22semidirect
48. #10622742C22semidirect
49. #10622741C22semidirect
50. #10622740C22semidirect
51. #10622735C22semidirect
52. #10622732C22semidirect
53. #10622724C22semidirect
54. C8×C22⋊D11C22semidirect
55. #10622343C22semidirect
56. #10622343C22semidirect
57. #10622340C22semidirect
58. #10622339C22semidirect
59. (C22⋊D11)⋊C8C22semidirect
60. (C22⋊D11)⋊C8C22semidirect
61. D11×C22⋊C8C22semidirect
62. #10622333C22semidirect
63. #10622332C22semidirect
64. #10622331C22semidirect
148. C2×#4313C23semidirect
149. C2×C8×D11C23semidirect
160. (C2×D11)⋊C8C23semidirect
161. (C2×D11)⋊C8C23semidirect
162. #66879C23semidirect
163. Dic11⋊C8C23semidirect
164. Dic11⋊C8C23semidirect
165. C8×Dic11C23semidirect
287. C2×#407D11semidirect
310. C23×C11#131semidirect
382. C22×M16C2×D11semidirect
418. #407C2×D11semidirect
419. #407C2×D11semidirect
429. C2×C22⋊C8C2×D11semidirect
697. C11#60233semidirect
723. C23#66960semidirect

Maximal subgroups

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

subgroupindex
C2×#106233222
#130776702
#130776662
#130776522
#130776422
#130776382
#130773412
#130773062
#130772762
#130770662
C22×C22⋊(C11⋊C8)2
C2×C11×#4072
#6023311