Finite Group Databasebeta

← #14762867

Subgroups — #14762867

Order 2816.

1518 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623138C211yesmaximal, characteristic
2C2×#10622742C211yesmaximal, characteristic, complemented
3#13071205C211yesmaximal, characteristic, complemented
4#13069054C211yesmaximal, characteristic, complemented
5#13069045C211yesmaximal, characteristic, complemented
6#13069042C211yesmaximal, characteristic, complemented
7#13068937C211yesmaximal, characteristic, complemented
8#13068935C211yesmaximal, characteristic, complemented
9#13068932C211yesmaximal, characteristic, complemented
10#13068930C211yesmaximal, characteristic, complemented
11#13068710C211yesmaximal, characteristic, complemented
12#13068709C211yesmaximal, characteristic, complemented
13#13068545C211yesmaximal, characteristic, complemented
14#13068545C211yesmaximal, characteristic, complemented
15C11×#1895C211yesmaximal, characteristic, complemented
16C22×D4×D11C2211yescharacteristic
17C22×#4339C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic, complemented
19C2×C11×#121C2211yescharacteristic
20C2×#66993—21no—
21C2×#66991C2211yescharacteristic
22C2×#66990—21no—
23C2×#66983C2211yescharacteristic
24C23×C11⋊C8C2211yescharacteristic, complemented
25#10623138—24no—
26#10623138C418yescomplemented
27C2×#66948C2211yescharacteristic
28C2×#66945C2211yescharacteristic
29C2×#66945C2211yescharacteristic, complemented
30C2×C4⋊C4×D11C2211yescharacteristic, complemented
31C2×#66938—21no—
32C2×#66935—21no—
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C11×#380C2211yescharacteristic, complemented
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38#10622825C2211yescharacteristic, complemented
39#10622742—24no—
40C2×#66885C2211yescharacteristic
41C2×#66885C2211yescharacteristic
42C2×(C2×D11)⋊C8C2211yescharacteristic
43C2×(C2×D11)⋊C8C2211yescharacteristic
44C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
45C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
46#10622600C2211yescharacteristic
47#10622600C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49C2×#66873C2211yescharacteristic
50#10622570—21no—
51#10622569—21no—
52#10622278—21no—
53#10622259—21no—
54C11×#340C2211yescharacteristic, complemented
55C11×#340C2211yescharacteristic, complemented
56#10622189C2211yescharacteristic, complemented
57#10622189C2211yescharacteristic, complemented
58#10622167C2211yescharacteristic, complemented
59#10622167C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61#10622167C2211yescharacteristic, complemented
62C24×D11—21no—
63C22×D4×C11—21no—
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11—21no—
67C22×C22⋊D11—21no—
68C22×C22⋊D11—21no—
69C22×C22⋊D11D411yescharacteristic
70C22×C22⋊D11D411yescharacteristic
71C2×D4×D11—22no—
72C2×D4×D11—41no—
73C2×D4×D11—41no—
74C2×D4×D11—41no—
75C2×D4×D11—41no—
76C2×D4×D11C2×C414yescomplemented
77C2×#4339—41no—
78C2×#4339—41no—
79C2×#4339—41no—
80C2×#4339—41no—
81C2×#4339C2×C414yes—
82C2×#4339D414yes—
83C22×D44—21no—
84C22×D44D411yescharacteristic
85C22×D44C2311yescharacteristic
86C22×C4×D11—21no—
87C22×C4×D11C2311yescharacteristic
88C22×C4×D11C2311yescharacteristic
89C22×Dic22D411yescharacteristic
90C2×C11×M16—22no—
91C2×C11×M16—41no—
92C2×C11×M16—41no—
93C22×C8×C11C2311yescharacteristic
94C22×C8×C11C2311yescharacteristic
95C11×#121—22no—
96C11×#121C2×C414yescomplemented
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C22⋊Dic11—21no—
103C2×C22⋊Dic11—21no—
104#66993—28no—
105#66991—22no—
106#66991C2×C414yes—
107#66990—28no—
108#66983—22no—
109#66983C2×C414yescomplemented
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×(C2×D11)⋊C4—21no—
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2311yescharacteristic
119C2×Dic11⋊C4—21no—
120C2×C4×Dic11—21no—
121C2×C4×Dic11—21no—
122C22×C11⋊C8—22no—
123C22×C11⋊C8—41no—
124C22×C11⋊C8—41no—
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127#66948—22no—
128#66948C2×C414yes—
129#66945—22no—
130#66945—41no—
131#66945—41no—
132#66945C2×C414yescomplemented
133C4⋊C4×D11—41no—
134C4⋊C4×D11—41no—
135#66938—28no—
136#66935—28no—
137C11×#102—41no—
138C11×#102—41no—
139C11×#95—21no—
140#66896—41no—
141#66896—41no—
142C11⋊#95—21no—
143C11⋊#95—21no—
144C11⋊#95—21no—
145#66885—41no—
146#66885—41no—
147(C2×D11)⋊C8—22no—
148(C2×D11)⋊C8—22no—
149(C2×D11)⋊C8—22no—
150(C2×D11)⋊C8—22no—
151#66873—41no—
152#66873—41no—
153#21770—111nomaximal, Sylow
154C24×C11—21no—
155C24×C11C2×D411yescharacteristic
156C23×D11—21no—
157C23×D11—24no—
158C23×D11—42no—
159C23×D11—42no—
160C23×D11—81no—
161C23×D11—81no—
162C23×D11—81no—
163C23×D11—81no—
164C23×D11C2×D411yescharacteristic
165C23×D11C2×D411yescharacteristic
166C2×D4×C11—24no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11—21no—
172C2×D4×C11—81no—
173C2×D4×C11—81no—
174C2×D4×C11C22×C412yes—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11C22×C412yes—
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D412yes—
185C22×C4×C11C2411yescharacteristic
186C2×C22⋊D11—24no—
187C2×C22⋊D11—24no—
188C2×C22⋊D11—24no—
189C2×C22⋊D11—41no—
190C2×C22⋊D11—41no—
191C2×C22⋊D11—41no—
192C2×C22⋊D11—41no—
193C2×C22⋊D11—42no—
194C2×C22⋊D11—42no—
195C2×C22⋊D11—81no—
196C2×C22⋊D11—81no—
197C2×C22⋊D11—81no—
198C2×C22⋊D11—81no—
199C2×C22⋊D11C22⋊C414yes—
200C2×C22⋊D11C22⋊C414yes—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11C2×D411yescharacteristic
205C22×Dic11C2×D411yescharacteristic
206D4×D11—44no—
207D4×D11—44no—
208D4×D11—44no—
209D4×D11—44no—
210#4339—44no—
211#4339—44no—
212#4339—44no—
213#4339—44no—
214C2×D44—24no—
215C2×D44—21no—
216C2×D44—21no—
217C2×D44—21no—
218C2×D44—21no—
219C2×D44—21no—
220C2×D44—41no—
221C2×D44—41no—
222C2×D44—81no—
223C2×D44—81no—
224C2×D44C22⋊C414yes—
225C2×D44C22×C412yes—
226C2×C4×D11—21no—
227C2×C4×D11—21no—
228C2×C4×D11—21no—
229C2×C4×D11—21no—
230C2×C4×D11—21no—
231C2×C4×D11—21no—
232C2×C4×D11—21no—
233C2×C4×D11—21no—
234C2×C4×D11—42no—
235C2×C4×D11—81no—
236C2×C4×D11—81no—
237C2×C4×D11C22×C412yes—
238C2×C4×D11C22×C412yes—
239C2×C4×D11C2×D412yes—
240C2×C4×D11C2×D412yes—
241C2×Dic22—41no—
242C2×Dic22—41no—
243C2×Dic22C22⋊C414yes—
244C11×M16—44no—
245C2×C8×C11—21no—
246C2×C8×C11—21no—
247C2×C8×C11—21no—
248C2×C8×C11—21no—
249C2×C8×C11—21no—
250C2×C8×C11—21no—
251C11×C4⋊C4—21no—
252C11×C4⋊C4—21no—
253C11×C4⋊C4—21no—
254C11×C4⋊C4—21no—
255C11×C4⋊C4—21no—
256C11×C4⋊C4C22×C412yes—
257C11×C22⋊C4—24no—
258C11×C22⋊C4—81no—
259C22⋊Dic11—24no—
260C22⋊Dic11—81no—
261(C2×D11)⋊C4—24no—
262(C2×D11)⋊C4—24no—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—42no—
265(C2×D11)⋊C4—81no—
266(C2×D11)⋊C4—81no—
267C4⋊Dic11—21no—
268C4⋊Dic11—21no—
269C4⋊Dic11—21no—
270C4⋊Dic11—21no—
271C4⋊Dic11—21no—
272C4⋊Dic11C22×C412yes—
273Dic11⋊C4—42no—
274C4×Dic11—24no—
275C4×Dic11—42no—
276C2×C11⋊C8—21no—
277C2×C11⋊C8—21no—
278C2×C11⋊C8—21no—
279C2×C11⋊C8—21no—
280C2×C11⋊C8—21no—
281C2×C11⋊C8—21no—
282C2×C11⋊C8—44no—
283C2×#535—111no—
284C2×#408—111no—
285#2311—111no—
286#1895—111no—
287#1895D1111yescharacteristic, complemented
288#1893—111no—
289#1893—111no—
290#1875—111no—
291#1875—111no—
292#1874—111no—
293#1874—111no—
294#1825—111no—
295#1825—111no—
296#1786—111no—
297#1786—111no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—22no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11C2×C22⋊C412yes—
312C23×C11C22×D411yescharacteristic
313C22×D11—21no—
314C22×D11—21no—
315C22×D11—21no—
316C22×D11—21no—
317C22×D11—21no—
318C22×D11—21no—
319C22×D11—21no—
320C22×D11—21no—
321C22×D11—21no—
322C22×D11—21no—
323C22×D11—21no—
324C22×D11—21no—
325C22×D11—22no—
326C22×D11—48no—
327C22×D11—41no—
328C22×D11—41no—
329C22×D11—41no—
330C22×D11—41no—
331C22×D11—41no—
332C22×D11—41no—
333C22×D11—84no—
334C22×D11—84no—
335C22×D11—84no—
336C22×D11—84no—
337C22×D11—84no—
338C22×D11—84no—
339C22×D11C2×C22⋊C412yes—
340C22×D11C2×C22⋊C412yes—
341D4×C11—22no—
342D4×C11—22no—
343D4×C11—41no—
344D4×C11—41no—
345D4×C11—84no—
346C2×C4×C11—21no—
347C2×C4×C11—21no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11C2×C22⋊C412yes—
362C2×C4×C11C23×C411yescharacteristic
363C2×C4×C11C22×D411yescharacteristic
364C2×C4×C11H(5,𝔽2)11yescharacteristic
365C2×C4×C11H(5,𝔽2)11yescharacteristic
366C2×C4×C11H(5,𝔽2)11yescharacteristic
367C2×C4×C11H(5,𝔽2)11yescharacteristic
368C22⋊D11—44no—
369C22⋊D11—44no—
370C22⋊D11—48no—
371C22⋊D11—84no—
372C22⋊D11—84no—
373C2×Dic11—21no—
374C2×Dic11—21no—
375C2×Dic11—21no—
376C2×Dic11—21no—
377C2×Dic11—22no—
378C2×Dic11—41no—
379C2×Dic11—41no—
380C2×Dic11—41no—
381C2×Dic11—41no—
382C2×Dic11—41no—
383C2×Dic11—41no—
384C2×Dic11—41no—
385C2×Dic11—41no—
386C2×Dic11C2×C22⋊C412yes—
387C2×Dic11C2×C22⋊C412yes—
388D44—22no—
389D44—22no—
390D44—44no—
391D44—41no—
392D44—41no—
393D44—84no—
394C4×D11—22no—
395C4×D11—22no—
396C4×D11—22no—
397C4×D11—22no—
398C4×D11—22no—
399C4×D11—22no—
400C4×D11—22no—
401C4×D11—22no—
402C4×D11—84no—
403Dic22—44no—
404C8×C11—41no—
405C8×C11—41no—
406C11⋊C8—41no—
407C11⋊C8—41no—
408C22×#41—111no—
409C23×D4—111no—
410C22×M16C2×D1111yescharacteristic, complemented
411C23×C8—111no—
412#535—118no—
413#535—224no—
414C2×#127—221no—
415C2×#124—221no—
416C2×#121—111no—
417C2×#121—111no—
418C2×#121—111no—
419C2×#121C2×D1111yescharacteristic
420C2×#120—221no—
421C2×#120—221no—
422C2×#117—111no—
423C2×#117—111no—
424C22×C4⋊C4—111no—
425C2×#102—111no—
426C2×#102—111no—
427C2×#102—111no—
428C2×#102—111no—
429C2×#102—111no—
430C2×#102—111no—
431C2×#102C2×D1111yescharacteristic
432C2×#102C2×D1111yescharacteristic
433#408—224no—
434C2×C22⋊C8—111no—
435C2×C22⋊C8—111no—
436C2×C22⋊C8—111no—
437C2×C22⋊C8—111no—
438#391—221no—
439#390—221no—
440#386—221no—
441#386—221no—
442#380—111no—
443#380—111no—
444#380—111no—
445#380C2×D1111yescharacteristic, complemented
446#340—111no—
447#340—111no—
448#340—111no—
449#340—111no—
450#340—111no—
451#340—111no—
452#340C2×D1111yescharacteristic, complemented
453#340C2×D1111yescharacteristic, complemented
454C22×C11—22no—
455C22×C11—22no—
456C22×C11—22no—
457C22×C11—41no—
458C22×C11—41no—
459C22×C11—41no—
460C22×C11—41no—
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11—81no—
465C22×C11—81no—
466C22×C11—81no—
467C22×C11—81no—
468C22×C11C22×C22⋊C411yescharacteristic
469C22×C11#53411yescharacteristic
470C22×C11#53411yescharacteristic
471C22×C11#57611yescharacteristic
472C22×C11#57611yescharacteristic
473C22×C11#57711yescharacteristic
474C22×C11#57711yescharacteristic
475C2×D11—22no—
476C2×D11—22no—
477C2×D11—22no—
478C2×D11—22no—
479C2×D11—22no—
480C2×D11—22no—
481C2×D11—41no—
482C2×D11—41no—
483C2×D11—41no—
484C2×D11—41no—
485C2×D11—41no—
486C2×D11—41no—
487C2×D11—41no—
488C2×D11—41no—
489C2×D11—42no—
490C2×D11—42no—
491C2×D11—42no—
492C2×D11—816no—
493C2×D11—81no—
494C2×D11—81no—
495C2×D11—81no—
496C2×D11—81no—
497C4×C11—22no—
498C4×C11—42no—
499C4×C11—81no—
500C4×C11—81no—
501C4×C11#51811yescharacteristic
502C4×C11#51811yescharacteristic
503C4×C11#53411yescharacteristic
504C4×C11#53411yescharacteristic
505Dic11—22no—
506Dic11—22no—
507Dic11—42no—
508Dic11—81no—
509Dic11—81no—
510C25—221no—
511C2×#41—114no—
512C2×#41—114no—
513C2×#41—441no—
514C2×#41—441no—
515C2×#41—441no—
516C2×#41—441no—
517C22×Q8—111no—
518C22×D4—21no—
519C22×D4—111no—
520C22×D4—111no—
521C22×D4—114no—
522C22×D4—111no—
523C22×D4—111no—
524C22×D4—221no—
525C22×D4—222no—
526C22×D4—221no—
527C22×D4—221no—
528C22×D4—221no—
529C22×D4—441no—
530C22×D4—441no—
531C22×D4—441no—
532C22×D4—441no—
533C22×D4C22×D1111yescharacteristic
534C23×C4—111no—
535C23×C4—111no—
536C23×C4—221no—
537C23×C4C22×D1111yescharacteristic
538C2×M16—22no—
539C2×M16—41no—
540C2×M16—41no—
541C22×C8—111no—
542C22×C8—111no—
543C22×C8—222no—
544C22×C8—441no—
545C22×C8—441no—
546C22×C8C22×D1111yescharacteristic
547C22×C8C22×D1111yescharacteristic
548#127—228no—
549#124—228no—
550#121—22no—
551#121—114no—
552#121—114no—
553#121—114no—
554#121—222no—
555#121—222no—
556#121—222no—
557#121C4×D1114yescomplemented
558#120—228no—
559#120—228no—
560#117—114no—
561#117—222no—
562#117—441no—
563#117—441no—
564C2×C4⋊C4—111no—
565C2×C4⋊C4—111no—
566C2×C4⋊C4—111no—
567C2×C4⋊C4—221no—
568C2×C4⋊C4—441no—
569C2×C4⋊C4—441no—
570C2×C4⋊C4C22×D1111yescharacteristic
571C2×C4⋊C4C22×D1111yescharacteristic
572C2×C4⋊C4C22×D1111yescharacteristic
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—221no—
576C2×C22⋊C4—221no—
577C2×C22⋊C4—221no—
578C2×C22⋊C4—221no—
579C2×C22⋊C4—221no—
580C2×C22⋊C4—221no—
581C2×C22⋊C4—221no—
582C2×C22⋊C4—221no—
583C2×C42—221no—
584C2×C42—221no—
585#102—41no—
586#102—41no—
587#102—441no—
588#102—441no—
589#102—441no—
590#102—441no—
591#102—441no—
592#102—441no—
593C22⋊C8—222no—
594C22⋊C8—222no—
595C22⋊C8—222no—
596C22⋊C8—222no—
597#95—21no—
598#95—221no—
599#95—221no—
600#95—221no—
601C2×C11—42no—
602C2×C11—82no—
603C2×C11#230811yescharacteristic
604C2×C11#289711yescharacteristic
605C2×C11#289711yescharacteristic
606C2×C11#319811yescharacteristic
607C2×C11#319811yescharacteristic
608C2×C11#319911yescharacteristic
609C2×C11#320011yescharacteristic
610D11—42no—
611D11—42no—
612D11—82no—
613C24—21no—
614C24—111no—
615C24—111no—
616C24—224no—
617C24—221no—
618C24—442no—
619C24—442no—
620C24—881no—
621C24—881no—
622C24—881no—
623C24—881no—
624C24D4×D1111yescharacteristic
625#41—444no—
626#41—444no—
627#41—444no—
628#41—444no—
629C2×Q8—114no—
630C2×Q8—441no—
631C2×Q8—441no—
632C2×D4—24no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—81no—
639C2×D4—81no—
640C2×D4—114no—
641C2×D4—114no—
642C2×D4—114no—
643C2×D4—112no—
644C2×D4—224no—
645C2×D4—224no—
646C2×D4—224no—
647C2×D4—224no—
648C2×D4—221no—
649C2×D4—221no—
650C2×D4—221no—
651C2×D4—221no—
652C2×D4—221no—
653C2×D4—441no—
654C2×D4—441no—
655C2×D4—444no—
656C2×D4—444no—
657C2×D4—444no—
658C2×D4—444no—
659C2×D4—441no—
660C2×D4—441no—
661C2×D4—441no—
662C2×D4—441no—
663C2×D4—442no—
664C2×D4—442no—
665C2×D4—881no—
666C2×D4—881no—
667C2×D4—881no—
668C2×D4—881no—
669C2×D4—881no—
670C2×D4—881no—
671C2×D4C2×C4×D1112yes—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—111no—
680C22×C4—111no—
681C22×C4—112no—
682C22×C4—112no—
683C22×C4—112no—
684C22×C4—112no—
685C22×C4—221no—
686C22×C4—221no—
687C22×C4—221no—
688C22×C4—221no—
689C22×C4—221no—
690C22×C4—221no—
691C22×C4—221no—
692C22×C4—221no—
693C22×C4—221no—
694C22×C4—221no—
695C22×C4—221no—
696C22×C4—442no—
697C22×C4—881no—
698C22×C4—881no—
699C22×C4C2×C4×D1112yes—
700C22×C4D4×D1111yescharacteristic
701C22×C4D4×D1112yes—
702C22×C4C23×D1111yescharacteristic
703M16—44no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—221no—
711C2×C8—221no—
712C2×C8—221no—
713C2×C8—221no—
714C2×C8—221no—
715C2×C8—221no—
716C2×C8—444no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—112no—
723C4⋊C4—221no—
724C4⋊C4—221no—
725C4⋊C4—221no—
726C4⋊C4—221no—
727C4⋊C4—221no—
728C4⋊C4—442no—
729C4⋊C4C2×C4×D1112yes—
730C22⋊C4—24no—
731C22⋊C4—81no—
732C22⋊C4—224no—
733C22⋊C4—224no—
734C22⋊C4—224no—
735C22⋊C4—224no—
736C22⋊C4—442no—
737C22⋊C4—881no—
738C22⋊C4—881no—
739C22⋊C4—881no—
740C42—224no—
741C42—442no—
742C11#2177011yescharacteristic, complemented, Sylow
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—22no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—112no—
757C23—112no—
758C23—221no—
759C23—221no—
760C23—221no—
761C23—221no—
762C23—221no—
763C23—221no—
764C23—221no—
765C23—221no—
766C23—221no—
767C23—221no—
768C23—221no—
769C23—221no—
770C23—222no—
771C23—448no—
772C23—441no—
773C23—441no—
774C23—441no—
775C23—441no—
776C23—441no—
777C23—441no—
778C23—884no—
779C23—884no—
780C23—884no—
781C23—884no—
782C23—884no—
783C23—884no—
784C23C22⋊C4×D1112yes—
785C23C2×D4×D1111yescharacteristic
786Q8—444no—
787D4—22no—
788D4—22no—
789D4—41no—
790D4—41no—
791D4—84no—
792D4—222no—
793D4—222no—
794D4—444no—
795D4—444no—
796D4—444no—
797D4—448no—
798D4—441no—
799D4—441no—
800D4—884no—
801D4—884no—
802D4—884no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—112no—
819C2×C4—112no—
820C2×C4—221no—
821C2×C4—221no—
822C2×C4—221no—
823C2×C4—221no—
824C2×C4—222no—
825C2×C4—222no—
826C2×C4—222no—
827C2×C4—222no—
828C2×C4—222no—
829C2×C4—222no—
830C2×C4—222no—
831C2×C4—222no—
832C2×C4—222no—
833C2×C4—441no—
834C2×C4—441no—
835C2×C4—441no—
836C2×C4—441no—
837C2×C4—441no—
838C2×C4—441no—
839C2×C4—441no—
840C2×C4—441no—
841C2×C4—884no—
842C2×C4C22⋊C4×D1112yes—
843C2×C4C22×C4×D1111yescharacteristic
844C2×C4C2×D4×D1111yescharacteristic
845C2×C4#6703711yescharacteristic
846C2×C4#6703711yescharacteristic
847C2×C4#6704211yescharacteristic
848C2×C4#6704211yescharacteristic
849C8—41no—
850C8—41no—
851C8—441no—
852C8—441no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—222no—
868C22—222no—
869C22—222no—
870C22—222no—
871C22—222no—
872C22—222no—
873C22—441no—
874C22—441no—
875C22—441no—
876C22—441no—
877C22—441no—
878C22—441no—
879C22—441no—
880C22—441no—
881C22—442no—
882C22—442no—
883C22—442no—
884C22—8816no—
885C22—881no—
886C22—881no—
887C22—881no—
888C22—881no—
889C22C2×C22⋊C4×D1111yescharacteristic
890C22#1062313611yescharacteristic
891C22#1062313611yescharacteristic
892C22#1062330511yescharacteristic
893C22#1062330511yescharacteristic
894C22#1062330611yescharacteristic
895C22#1062330911yescharacteristic
896C4—22no—
897C4—42no—
898C4—81no—
899C4—81no—
900C4—222no—
901C4—222no—
902C4—442no—
903C4—881no—
904C4—881no—
905C4#1062307611yescharacteristic
906C4#1062307611yescharacteristic
907C4#1062312011yescharacteristic
908C4#1062318411yescharacteristic
909C2—42no—
910C2—82no—
911C2—442no—
912C2—442no—
913C2—882no—
914C2#1307119011yescharacteristic
915C2#1307714011yescharacteristic
916C2#1307714111yescharacteristic
917C2#1307946311yescharacteristic
918C2#1307946911yescharacteristic
919C2#1307947811yescharacteristic
920C2#1307948411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1895C2
socleC23×C11C22×D4
prime radicalC2×#10623138C2
cosocleC22×C4×C11C24
hypercenter#1895D11
hypocenterC11#21770
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1895

Complements

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

NH ≅ G/Ntype
2. C2×#10622742C2semidirect
3. #13071205C2semidirect
4. #13069054C2semidirect
5. #13069045C2semidirect
6. #13069042C2semidirect
7. #13068937C2semidirect
8. #13068935C2semidirect
9. #13068932C2semidirect
10. #13068930C2semidirect
11. #13068710C2semidirect
12. #13068709C2semidirect
13. #13068545C2semidirect
14. #13068545C2semidirect
15. C11×#1895C2semidirect
18. C22×C11×M16C22semidirect
24. C23×C11⋊C8C22semidirect
26. #10623138C4semidirect
29. C2×#66945C22semidirect
30. C2×C4⋊C4×D11C22semidirect
35. C11×#380C22semidirect
38. #10622825C22semidirect
44. C2×(C2×D11)⋊C8C22semidirect
45. C2×(C2×D11)⋊C8C22semidirect
54. C11×#340C22semidirect
55. C11×#340C22semidirect
56. #10622189C22semidirect
57. #10622189C22semidirect
58. #10622167C22semidirect
59. #10622167C22semidirect
60. #10622167C22semidirect
61. #10622167C22semidirect
76. C2×D4×D11C2×C4semidirect
96. C11×#121C2×C4semidirect
109. #66983C2×C4semidirect
132. #66945C2×C4semidirect
287. #1895D11semidirect
410. C22×M16C2×D11semidirect
445. #380C2×D11semidirect
452. #340C2×D11semidirect
453. #340C2×D11semidirect
557. #121C4×D11semidirect
742. C11#21770semidirect

Maximal subgroups

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

subgroupindex
C2×#106231382
C2×#106227422
#130712052
#130690542
#130690452
#130690422
#130689372
#130689352
#130689322
#130689302
#130687102
#130687092
#130685452
C11×#18952
#2177011