Finite Group Databasebeta

← #102×C22⋊D11 #14769175

Subgroups — #102×C22⋊D11 #14769175

Order 2816.

2014 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C22⋊D11C211yesmaximal, characteristic
2C2×C8×C22⋊D11C211yesmaximal, characteristic, complemented
3C2×D11×#102C211yesmaximal, characteristic, complemented
4C4⋊C4×C22⋊D11C211yesmaximal, characteristic, complemented
5#13069541C211yesmaximal, characteristic, complemented
6#13069420C211yesmaximal, characteristic, complemented
7#13069044C211yesmaximal, characteristic, complemented
8#13069041C211yesmaximal, characteristic, complemented
9#13068933C211yesmaximal, characteristic, complemented
10#13068930C211yesmaximal, characteristic, complemented
11#13068614C211yesmaximal, characteristic, complemented
12#13068547C211yesmaximal, characteristic, complemented
13#13068545C211yesmaximal, characteristic, complemented
14#102×Dic11C211yesmaximal, characteristic, complemented
15C22×C11×#102C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C23×C22⋊D11—21no—
18C22×D4×D11C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic, complemented
20C22×C11×C4⋊C4C2211yescharacteristic, complemented
21C2×#67006—21no—
22C2×#66993C2211yescharacteristic
23C2×#66992—21no—
24D4×C22⋊D11—24no—
25D4×C22⋊D11C418yescomplemented
26C2×#66991C2211yescharacteristic
27C2×#66990—21no—
28C2×D4×Dic11C2211yescharacteristic
29C2×#66983C2211yescharacteristic
30C2×C4×C22⋊D11—21no—
31C2×C4×C22⋊D11C2211yescharacteristic
32C22×C8×D11C2211yescharacteristic, complemented
33C2×C4⋊C4×D11C2211yescharacteristic, complemented
34C2×C11×#102—24no—
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic, complemented
38C2×C11×#102C2211yescharacteristic, complemented
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic, complemented
42C2×#66896C2211yescharacteristic, complemented
43#10622825C2211yescharacteristic, complemented
44#10622823—21no—
45C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
46C2×#66885C2211yescharacteristic, complemented
47C2×#66885C2211yescharacteristic, complemented
48C8×C22⋊D11—24no—
49C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
50C2×Dic11⋊C8C2211yescharacteristic, complemented
51C2×C8×Dic11C2211yescharacteristic, complemented
52#10622602—21no—
53#10622600C2211yescharacteristic, complemented
54#10622589C2211yescharacteristic, complemented
55C4⋊C4×Dic11C2211yescharacteristic, complemented
56#10622585—21no—
57C2×#66873C2211yescharacteristic, complemented
58C2×#66873C2211yescharacteristic, complemented
59D11×#102—24no—
60#10622189C2211yescharacteristic, complemented
61#10622189C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622167C2211yescharacteristic, complemented
64C25×C11—21no—
65C24×D11—21no—
66C22×D4×C11—22no—
67C22×D4×C11—22no—
68C22×D4×C11—21no—
69C22×D4×C11—22no—
70C22×D4×C11—41no—
71C22×D4×C11—41no—
72C22×D4×C11C2×C414yescomplemented
73C22×D4×C11C2311yescharacteristic
74C22×D4×C11C2311yescharacteristic
75C23×C4×C11—21no—
76C23×C4×C11C2311yescharacteristic
77C22×C22⋊D11—21no—
78C22×C22⋊D11—21no—
79C22×C22⋊D11—28no—
80C22×C22⋊D11—21no—
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C22×C22⋊D11—44no—
84C22×C22⋊D11—44no—
85C22×C22⋊D11D411yescharacteristic
86C23×Dic11—21no—
87C2×D4×D11—22no—
88C2×D4×D11—22no—
89C2×D4×D11—22no—
90C2×D4×D11—41no—
91C2×D4×D11—41no—
92C2×D4×D11C2×C414yescomplemented
93C22×D44C2311yescharacteristic
94C22×C4×D11—21no—
95C22×C4×D11C2311yescharacteristic
96C22×C8×C11—22no—
97C22×C8×C11—22no—
98C22×C8×C11—41no—
99C22×C8×C11C2311yescharacteristic
100C22×C8×C11C2311yescharacteristic
101C2×C11×C4⋊C4—22no—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—41no—
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106#67006—28no—
107C2×C22⋊Dic11—21no—
108C2×C22⋊Dic11—21no—
109C2×C22⋊Dic11—21no—
110C2×C22⋊Dic11D411yescharacteristic
111#66993—22no—
112#66993C2×C414yescomplemented
113#66992—28no—
114#66991—22no—
115#66991C2×C414yescomplemented
116#66990—28no—
117D4×Dic11—22no—
118D4×Dic11C2×C414yescomplemented
119#66983—22no—
120#66983C2×C414yescomplemented
121C4×C22⋊D11—44no—
122C4×C22⋊D11C2×C414yes—
123C4×C22⋊D11D414yes—
124C2×(C2×D11)⋊C4—21no—
125C2×(C2×D11)⋊C4—21no—
126C2×(C2×D11)⋊C4D411yescharacteristic
127C2×C4⋊Dic11C2311yescharacteristic
128C2×C4⋊Dic11C2311yescharacteristic
129C2×C4⋊Dic11C2311yescharacteristic
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4—21no—
133C2×Dic11⋊C4D411yescharacteristic
134C2×C4×Dic11—21no—
135C2×C4×Dic11C2311yescharacteristic
136C22×C11⋊C8C2311yescharacteristic
137C22×C11⋊C8C2311yescharacteristic
138C2×C8×D11—22no—
139C2×C8×D11—22no—
140C2×C8×D11—41no—
141C4⋊C4×D11—22no—
142C4⋊C4×D11—41no—
143C11×#102—22no—
144C11×#102—22no—
145C11×#102—22no—
146C11×#102D414yescomplemented
147#66896—22no—
148#66896—22no—
149#66896—41no—
150#66896—41no—
151C11⋊#95—21no—
152C11⋊#95—21no—
153C11⋊#95—21no—
154C22⋊(C11⋊C8)—22no—
155#66885—22no—
156#66885—41no—
157(C2×D11)⋊C8—22no—
158Dic11⋊C8—22no—
159C8×Dic11—22no—
160#66873—22no—
161#66873—41no—
162D4×#102—111nomaximal, Sylow
163C24×C11—21no—
164C24×C11—21no—
165C24×C11—24no—
166C24×C11—42no—
167C24×C11—42no—
168C24×C11—42no—
169C24×C11—42no—
170C24×C11—81no—
171C24×C11—81no—
172C24×C11C2×D411yescharacteristic
173C23×D11—21no—
174C23×D11—24no—
175C23×D11—42no—
176C23×D11—42no—
177C23×D11—42no—
178C23×D11—42no—
179C23×D11—81no—
180C23×D11—81no—
181C23×D11C2×D411yescharacteristic
182C2×D4×C11—28no—
183C2×D4×C11—24no—
184C2×D4×C11—21no—
185C2×D4×C11—21no—
186C2×D4×C11—21no—
187C2×D4×C11—21no—
188C2×D4×C11—21no—
189C2×D4×C11—21no—
190C2×D4×C11—21no—
191C2×D4×C11—21no—
192C2×D4×C11—44no—
193C2×D4×C11—44no—
194C2×D4×C11—44no—
195C2×D4×C11—42no—
196C2×D4×C11—42no—
197C2×D4×C11C22×C412yes—
198C2×D4×C11C22×C412yes—
199C2×D4×C11C2×D412yes—
200C2×D4×C11#4112yes—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—42no—
208C22×C4×C11—42no—
209C22×C4×C11—81no—
210C22×C4×C11C22×C412yes—
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D412yes—
213C22×C4×C11C2411yescharacteristic
214C2×C22⋊D11—24no—
215C2×C22⋊D11—24no—
216C2×C22⋊D11—24no—
217C2×C22⋊D11—24no—
218C2×C22⋊D11—24no—
219C2×C22⋊D11—42no—
220C2×C22⋊D11—42no—
221C2×C22⋊D11—432no—
222C2×C22⋊D11—42no—
223C2×C22⋊D11—42no—
224C2×C22⋊D11—42no—
225C2×C22⋊D11—42no—
226C2×C22⋊D11—42no—
227C2×C22⋊D11—42no—
228C2×C22⋊D11—81no—
229C2×C22⋊D11—81no—
230C2×C22⋊D11C22⋊C414yes—
231C2×C22⋊D11D814yes—
232C2×C22⋊D11SD1614yes—
233C22×Dic11—24no—
234C22×Dic11—21no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—42no—
238C22×Dic11—42no—
239C22×Dic11C2×D411yescharacteristic
240C22×Dic11C2×D411yescharacteristic
241C22×Dic11C2×D411yescharacteristic
242D4×D11—28no—
243D4×D11—44no—
244D4×D11—44no—
245D4×D11—44no—
246C2×D44—21no—
247C2×D44—21no—
248C2×D44—21no—
249C2×D44—21no—
250C2×D44—21no—
251C2×D44C22×C412yes—
252C2×C4×D11—21no—
253C2×C4×D11—21no—
254C2×C4×D11—21no—
255C2×C4×D11—21no—
256C2×C4×D11—42no—
257C2×C4×D11—42no—
258C2×C4×D11—81no—
259C2×C4×D11C22×C412yes—
260C2×C4×D11C2×D412yes—
261C2×C8×C11—21no—
262C2×C8×C11—21no—
263C2×C8×C11—21no—
264C2×C8×C11—21no—
265C2×C8×C11—21no—
266C2×C8×C11—44no—
267C2×C8×C11C2×D412yescomplemented
268C11×C4⋊C4—21no—
269C11×C4⋊C4—21no—
270C11×C4⋊C4—21no—
271C11×C4⋊C4—42no—
272C11×C4⋊C4C2×D412yescomplemented
273C22⋊Dic11—24no—
274C22⋊Dic11—24no—
275C22⋊Dic11—42no—
276C22⋊Dic11C22⋊C414yes—
277(C2×D11)⋊C4—24no—
278(C2×D11)⋊C4—42no—
279(C2×D11)⋊C4C22⋊C414yes—
280C4⋊Dic11—21no—
281C4⋊Dic11—21no—
282C4⋊Dic11—21no—
283C4⋊Dic11—21no—
284C4⋊Dic11—21no—
285C4⋊Dic11C22×C412yes—
286Dic11⋊C4—42no—
287Dic11⋊C4—42no—
288Dic11⋊C4—81no—
289Dic11⋊C4C22⋊C414yes—
290C4×Dic11—42no—
291C4×Dic11C22×C412yes—
292C4×Dic11C2×D412yes—
293C2×C11⋊C8—21no—
294C2×C11⋊C8—21no—
295C2×C11⋊C8—21no—
296C2×C11⋊C8—21no—
297C2×C11⋊C8—21no—
298C2×C11⋊C8—21no—
299C8×D11—44no—
300C2×D42—111no—
301C2×C8×D4—111no—
302C22×#102—111no—
303C22×#102D1111yescharacteristic, complemented
304D4×C4⋊C4—111no—
305#1982—111no—
306#1957—111no—
307#1893—111no—
308#1893—111no—
309#1874—111no—
310#1874—111no—
311#1802—111no—
312#1786—111no—
313#1786—111no—
314C4×#102—111no—
315C23×C11—21no—
316C23×C11—21no—
317C23×C11—21no—
318C23×C11—21no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—48no—
324C23×C11—41no—
325C23×C11—41no—
326C23×C11—41no—
327C23×C11—41no—
328C23×C11—41no—
329C23×C11—41no—
330C23×C11—41no—
331C23×C11—41no—
332C23×C11—41no—
333C23×C11—41no—
334C23×C11—48no—
335C23×C11—84no—
336C23×C11—84no—
337C23×C11—84no—
338C23×C11—84no—
339C23×C11—84no—
340C23×C11C2×C22⋊C412yes—
341C23×C11C2×D812yes—
342C23×C11C2×SD1612yes—
343C23×C11C22×D411yescharacteristic
344C22×D11—21no—
345C22×D11—21no—
346C22×D11—21no—
347C22×D11—21no—
348C22×D11—22no—
349C22×D11—48no—
350C22×D11—41no—
351C22×D11—41no—
352C22×D11—41no—
353C22×D11—41no—
354C22×D11—41no—
355C22×D11—41no—
356C22×D11—48no—
357C22×D11—84no—
358C22×D11—84no—
359C22×D11—84no—
360C22×D11—84no—
361C22×D11—84no—
362C22×D11C2×C22⋊C412yes—
363C22×D11C2×D812yes—
364C22×D11C2×SD1612yes—
365D4×C11—22no—
366D4×C11—22no—
367D4×C11—22no—
368D4×C11—22no—
369D4×C11—22no—
370D4×C11—48no—
371D4×C11—41no—
372D4×C11—41no—
373D4×C11C4×D414yescomplemented
374C2×C4×C11—21no—
375C2×C4×C11—21no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—84no—
387C2×C4×C11C2×C22⋊C412yes—
388C2×C4×C11C23×C411yescharacteristic
389C2×C4×C11C22×D411yescharacteristic
390C2×C4×C11C22×D411yescharacteristic
391C2×C4×C11C2×#4111yescharacteristic
392C2×C4×C11H(5,𝔽2)11yescharacteristic
393C2×C4×C11H(5,𝔽2)11yescharacteristic
394C22⋊D11—48no—
395C22⋊D11—48no—
396C22⋊D11—48no—
397C22⋊D11—48no—
398C22⋊D11—84no—
399C22⋊D11#102116yesdirect product factor
400C2×Dic11—21no—
401C2×Dic11—21no—
402C2×Dic11—21no—
403C2×Dic11—21no—
404C2×Dic11—22no—
405C2×Dic11—41no—
406C2×Dic11—41no—
407C2×Dic11—48no—
408C2×Dic11—41no—
409C2×Dic11—41no—
410C2×Dic11—41no—
411C2×Dic11—41no—
412C2×Dic11—41no—
413C2×Dic11—41no—
414C2×Dic11C2×C22⋊C412yes—
415C2×Dic11C2×C22⋊C412yes—
416C2×Dic11C2×C22⋊C412yes—
417C2×Dic11C2×D812yes—
418C2×Dic11C2×SD1612yes—
419D44—22no—
420D44—22no—
421D44—41no—
422D44—41no—
423C4×D11—22no—
424C4×D11—22no—
425C4×D11—22no—
426C4×D11—22no—
427C4×D11—84no—
428C8×C11—22no—
429C8×C11—41no—
430C11⋊C8—41no—
431C11⋊C8—41no—
432C23×D4—111no—
433C23×D4—221no—
434C23×D4C2×D1111yescharacteristic
435C23×C8—111no—
436C23×C8C2×D1111yescharacteristic, complemented
437D42—118no—
438D42—224no—
439C2×#127—111no—
440C2×#121—111no—
441C2×#121—111no—
442C2×#121—221no—
443C2×#120—221no—
444C2×#120—221no—
445C2×C4×D4—111no—
446C2×C4×D4—111no—
447C2×C4×D4—221no—
448C22×C4⋊C4—111no—
449C22×C4⋊C4C2×D1111yescharacteristic, complemented
450C8×D4—224no—
451C2×C4⋊C8—111no—
452C2×#102—24no—
453C2×#102—111no—
454C2×#102—111no—
455C2×#102—111no—
456C2×#102—111no—
457C2×#102—111no—
458C2×#102—111no—
459C2×#102—111no—
460C2×#102—111no—
461C2×#102—224no—
462C2×#102C2×D1111yescharacteristic
463C2×#102C2×D1111yescharacteristic
464C2×#102C2×D1111yescharacteristic, complemented
465C2×#102C2×D1111yescharacteristic, complemented
466C2×C22⋊C8—111no—
467C2×C22⋊C8—111no—
468C2×C4×C8—111no—
469#389—221no—
470#385—221no—
471#385—221no—
472#384—111no—
473#380—111no—
474#380—111no—
475C4×C4⋊C4—111no—
476#340—111no—
477#340—111no—
478#340—111no—
479#340—111no—
480C22×C11—22no—
481C22×C11—22no—
482C22×C11—22no—
483C22×C11—22no—
484C22×C11—22no—
485C22×C11—22no—
486C22×C11—24no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11—42no—
492C22×C11—42no—
493C22×C11—42no—
494C22×C11—42no—
495C22×C11—42no—
496C22×C11—816no—
497C22×C11—81no—
498C22×C11—81no—
499C22×C11—81no—
500C22×C11—81no—
501C22×C11C2×#10214yescomplemented
502C22×C11C22×C22⋊C411yescharacteristic
503C22×C11D4211yescharacteristic
504C22×C11#54611yescharacteristic
505C22×C11C22×D811yescharacteristic
506C22×C11C22×SD1611yescharacteristic
507C22×C11#57611yescharacteristic
508C22×C11#57711yescharacteristic
509C2×D11—22no—
510C2×D11—22no—
511C2×D11—22no—
512C2×D11—22no—
513C2×D11—22no—
514C2×D11—22no—
515C2×D11—42no—
516C2×D11—42no—
517C2×D11—42no—
518C2×D11—816no—
519C2×D11—81no—
520C2×D11—81no—
521C2×D11—81no—
522C2×D11—81no—
523C2×D11C2×#10214yescomplemented
524C4×C11—22no—
525C4×C11—42no—
526C4×C11—81no—
527C4×C11C2×C4×D411yescharacteristic
528C4×C11#51811yescharacteristic
529C4×C11D4211yescharacteristic
530C4×C11#54611yescharacteristic
531Dic11—22no—
532Dic11—22no—
533Dic11—42no—
534Dic11—81no—
535Dic11—81no—
536Dic11C2×#10214yescomplemented
537C25—21no—
538C25—221no—
539C22×D4—22no—
540C22×D4—22no—
541C22×D4—21no—
542C22×D4—22no—
543C22×D4—41no—
544C22×D4—41no—
545C22×D4—111no—
546C22×D4—114no—
547C22×D4—111no—
548C22×D4—222no—
549C22×D4—221no—
550C22×D4—221no—
551C22×D4—221no—
552C22×D4—228no—
553C22×D4—222no—
554C22×D4—222no—
555C22×D4—221no—
556C22×D4—221no—
557C22×D4—441no—
558C22×D4—441no—
559C22×D4—444no—
560C22×D4—444no—
561C22×D4C4×D1114yescomplemented
562C22×D4C22×D1111yescharacteristic
563C22×D4C22×D1111yescharacteristic
564C23×C4—21no—
565C23×C4—111no—
566C23×C4—221no—
567C23×C4—221no—
568C23×C4C22×D1111yescharacteristic
569C22×C8—22no—
570C22×C8—22no—
571C22×C8—41no—
572C22×C8—111no—
573C22×C8—111no—
574C22×C8—222no—
575C22×C8—222no—
576C22×C8—441no—
577C22×C8C22×D1111yescharacteristic
578C22×C8C22×D1111yescharacteristic
579#127—114no—
580#127—222no—
581#121—114no—
582#121—114no—
583#121—228no—
584#121—222no—
585#121—222no—
586#120—228no—
587#120—228no—
588C4×D4—114no—
589C4×D4—114no—
590C4×D4—114no—
591C4×D4—222no—
592C4×D4—444no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—41no—
596C2×C4⋊C4—111no—
597C2×C4⋊C4—111no—
598C2×C4⋊C4—111no—
599C2×C4⋊C4—111no—
600C2×C4⋊C4—222no—
601C2×C4⋊C4—221no—
602C2×C4⋊C4—221no—
603C2×C4⋊C4—221no—
604C2×C4⋊C4—441no—
605C2×C4⋊C4C22×D1111yescharacteristic
606C2×C4⋊C4C22×D1111yescharacteristic
607C2×C22⋊C4—111no—
608C2×C22⋊C4—111no—
609C2×C22⋊C4—221no—
610C2×C22⋊C4—221no—
611C2×C22⋊C4—221no—
612C2×C22⋊C4—221no—
613C2×C22⋊C4—221no—
614C2×C42—111no—
615C2×C42—221no—
616C4⋊C8—222no—
617#102—22no—
618#102—22no—
619#102—22no—
620#102—222no—
621#102—222no—
622#102—222no—
623#102—222no—
624#102—441no—
625#102—441no—
626#102—441no—
627#102—441no—
628#102C22⋊D1114yesdirect product factor
629C22⋊C8—222no—
630C22⋊C8—222no—
631C4×C8—222no—
632#95—221no—
633#95—221no—
634#95—221no—
635C2×C11—24no—
636C2×C11—44no—
637C2×C11—82no—
638C2×C11D4×C22⋊C411yescharacteristic
639C2×C11C22×#10211yescharacteristic
640C2×C11#289711yescharacteristic
641C2×C11D4×D811yescharacteristic
642C2×C11D4×SD1611yescharacteristic
643C2×C11#329411yescharacteristic
644C2×C11#329511yescharacteristic
645D11—24no—
646D11—82no—
647C24—21no—
648C24—21no—
649C24—24no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—42no—
654C24—81no—
655C24—81no—
656C24—111no—
657C24—224no—
658C24—221no—
659C24—442no—
660C24—442no—
661C24—442no—
662C24—442no—
663C24—881no—
664C24—881no—
665C24D4×D1111yescharacteristic
666C2×D4—28no—
667C2×D4—24no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—44no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—42no—
680C2×D4—42no—
681C2×D4—114no—
682C2×D4—114no—
683C2×D4—114no—
684C2×D4—112no—
685C2×D4—224no—
686C2×D4—224no—
687C2×D4—224no—
688C2×D4—228no—
689C2×D4—224no—
690C2×D4—224no—
691C2×D4—221no—
692C2×D4—221no—
693C2×D4—221no—
694C2×D4—221no—
695C2×D4—221no—
696C2×D4—442no—
697C2×D4—442no—
698C2×D4—444no—
699C2×D4—444no—
700C2×D4—444no—
701C2×D4—442no—
702C2×D4—442no—
703C2×D4—4432no—
704C2×D4—442no—
705C2×D4—442no—
706C2×D4—442no—
707C2×D4—442no—
708C2×D4—881no—
709C2×D4—881no—
710C2×D4C2×C4×D1112yes—
711C2×D4C2×C4×D1112yes—
712C2×D4#433912yes—
713C2×D4C2×C22⋊D1112yes—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—42no—
721C22×C4—42no—
722C22×C4—81no—
723C22×C4—111no—
724C22×C4—111no—
725C22×C4—111no—
726C22×C4—112no—
727C22×C4—112no—
728C22×C4—224no—
729C22×C4—221no—
730C22×C4—221no—
731C22×C4—221no—
732C22×C4—221no—
733C22×C4—221no—
734C22×C4—221no—
735C22×C4—221no—
736C22×C4—442no—
737C22×C4—442no—
738C22×C4—442no—
739C22×C4—442no—
740C22×C4—881no—
741C22×C4C2×C4×D1112yes—
742C22×C4D4×D1111yescharacteristic
743C22×C4D4×D1112yes—
744C22×C4C23×D1111yescharacteristic
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—44no—
751C2×C8—221no—
752C2×C8—221no—
753C2×C8—221no—
754C2×C8—221no—
755C2×C8—221no—
756C2×C8—221no—
757C2×C8—444no—
758C2×C8C2×C22⋊D1112yescomplemented
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—42no—
763C4⋊C4—114no—
764C4⋊C4—112no—
765C4⋊C4—221no—
766C4⋊C4—221no—
767C4⋊C4—221no—
768C4⋊C4—221no—
769C4⋊C4—221no—
770C4⋊C4—442no—
771C4⋊C4—442no—
772C4⋊C4—881no—
773C4⋊C4C2×C22⋊D1112yescomplemented
774C22⋊C4—114no—
775C22⋊C4—114no—
776C22⋊C4—224no—
777C22⋊C4—224no—
778C22⋊C4—224no—
779C22⋊C4—442no—
780C22⋊C4—442no—
781C42—112no—
782C42—112no—
783C42—442no—
784C11D4×#10211yescharacteristic, complemented, Sylow
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—48no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—48no—
805C23—84no—
806C23—84no—
807C23—84no—
808C23—84no—
809C23—84no—
810C23—112no—
811C23—112no—
812C23—112no—
813C23—221no—
814C23—221no—
815C23—221no—
816C23—221no—
817C23—222no—
818C23—448no—
819C23—448no—
820C23—441no—
821C23—441no—
822C23—441no—
823C23—441no—
824C23—441no—
825C23—441no—
826C23—884no—
827C23—884no—
828C23—884no—
829C23—884no—
830C23—884no—
831C23C22⋊C4×D1112yes—
832C23D8×D1112yes—
833C23SD16×D1112yes—
834C23C2×D4×D1111yescharacteristic
835D4—22no—
836D4—22no—
837D4—22no—
838D4—22no—
839D4—22no—
840D4—48no—
841D4—41no—
842D4—41no—
843D4—1116no—
844D4—222no—
845D4—222no—
846D4—448no—
847D4—448no—
848D4—448no—
849D4—448no—
850D4—441no—
851D4—441no—
852D4—884no—
853D4C4×C22⋊D1114yescomplemented
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—84no—
867C2×C4—112no—
868C2×C4—112no—
869C2×C4—112no—
870C2×C4—112no—
871C2×C4—112no—
872C2×C4—221no—
873C2×C4—221no—
874C2×C4—221no—
875C2×C4—221no—
876C2×C4—222no—
877C2×C4—222no—
878C2×C4—222no—
879C2×C4—222no—
880C2×C4—222no—
881C2×C4—448no—
882C2×C4—441no—
883C2×C4—441no—
884C2×C4—441no—
885C2×C4—441no—
886C2×C4—441no—
887C2×C4—441no—
888C2×C4—441no—
889C2×C4—441no—
890C2×C4—884no—
891C2×C4C22⋊C4×D1112yes—
892C2×C4C22×C4×D1111yescharacteristic
893C2×C4C2×#433911yescharacteristic
894C2×C4C2×D4×D1111yescharacteristic
895C2×C4#6703711yescharacteristic
896C2×C4#6703711yescharacteristic
897C2×C4C22×C22⋊D1111yescharacteristic
898C8—22no—
899C8—41no—
900C8—441no—
901C8—441no—
902C22—22no—
903C22—22no—
904C22—22no—
905C22—22no—
906C22—22no—
907C22—22no—
908C22—24no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—816no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—114no—
924C22—222no—
925C22—222no—
926C22—222no—
927C22—222no—
928C22—222no—
929C22—222no—
930C22—442no—
931C22—442no—
932C22—442no—
933C22—8816no—
934C22—881no—
935C22—881no—
936C22—881no—
937C22—881no—
938C22D11×#10214yescomplemented
939C22C2×C22⋊C4×D1111yescharacteristic
940C22#1062302111yescharacteristic
941C22C2×D8×D1111yescharacteristic
942C22#1062328811yescharacteristic
943C22C2×SD16×D1111yescharacteristic
944C22#1062329311yescharacteristic
945C22D4×C22⋊D1111yescharacteristic
946C4—22no—
947C4—42no—
948C4—81no—
949C4—114no—
950C4—222no—
951C4—222no—
952C4—442no—
953C4—881no—
954C4—881no—
955C4#1062301711yescharacteristic
956C4#1062302111yescharacteristic
957C4C2×C4×C22⋊D1111yescharacteristic
958C4D4×C22⋊D1111yescharacteristic
959C2—24no—
960C2—44no—
961C2—82no—
962C2—224no—
963C2—882no—
964C2C22⋊C4×C22⋊D1111yescharacteristic
965C2C2×D11×#10211yescharacteristic
966C2#1307713711yescharacteristic
967C2D8×C22⋊D1111yescharacteristic
968C2SD16×C22⋊D1111yescharacteristic
969C2#1308042511yescharacteristic
970C2#1308043611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#102C2
socleC23×C11C22×D4
prime radicalC2×D4×C22⋊D11C2
cosocleC22×C4×C11C24
hypercenterC22×#102D11
hypocenterC11D4×#102
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C2×C8×C22⋊D11C2semidirect
3. C2×D11×#102C2semidirect
4. C4⋊C4×C22⋊D11C2semidirect
5. #13069541C2semidirect
6. #13069420C2semidirect
7. #13069044C2semidirect
8. #13069041C2semidirect
9. #13068933C2semidirect
10. #13068930C2semidirect
11. #13068614C2semidirect
12. #13068547C2semidirect
13. #13068545C2semidirect
14. #102×Dic11C2semidirect
15. C22×C11×#102C2semidirect
19. C23×C8×C11C22semidirect
20. C22×C11×C4⋊C4C22semidirect
25. D4×C22⋊D11C4semidirect
32. C22×C8×D11C22semidirect
33. C2×C4⋊C4×D11C22semidirect
37. C2×C11×#102C22semidirect
38. C2×C11×#102C22semidirect
41. C2×#66896C22semidirect
42. C2×#66896C22semidirect
43. #10622825C22semidirect
45. C2×C22⋊(C11⋊C8)C22semidirect
46. C2×#66885C22semidirect
47. C2×#66885C22semidirect
49. C2×(C2×D11)⋊C8C22semidirect
50. C2×Dic11⋊C8C22semidirect
51. C2×C8×Dic11C22semidirect
53. #10622600C22semidirect
54. #10622589C22semidirect
55. C4⋊C4×Dic11C22semidirect
57. C2×#66873C22semidirect
58. C2×#66873C22semidirect
60. #10622189C22semidirect
61. #10622189C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
72. C22×D4×C11C2×C4semidirect
92. C2×D4×D11C2×C4semidirect
112. #66993C2×C4semidirect
115. #66991C2×C4semidirect
118. D4×Dic11C2×C4semidirect
120. #66983C2×C4semidirect
146. C11×#102D4semidirect
267. C2×C8×C11C2×D4semidirect
272. C11×C4⋊C4C2×D4semidirect
303. C22×#102D11semidirect
373. D4×C11C4×D4semidirect
399. C22⋊D11#102direct (N × H)
436. C23×C8C2×D11semidirect
449. C22×C4⋊C4C2×D11semidirect
464. C2×#102C2×D11semidirect
465. C2×#102C2×D11semidirect
501. C22×C11C2×#102semidirect
523. C2×D11C2×#102semidirect
536. Dic11C2×#102semidirect
561. C22×D4C4×D11semidirect
628. #102C22⋊D11direct (N × H)
758. C2×C8C2×C22⋊D11semidirect
773. C4⋊C4C2×C22⋊D11semidirect
784. C11D4×#102semidirect
853. D4C4×C22⋊D11semidirect
938. C22D11×#102semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C22⋊D112
C2×C8×C22⋊D112
C2×D11×#1022
C4⋊C4×C22⋊D112
#130695412
#130694202
#130690442
#130690412
#130689332
#130689302
#130686142
#130685472
#130685452
#102×Dic112
C22×C11×#1022
D4×#10211