Finite Group Databasebeta

← #14769116

Subgroups — #14769116

Order 2816.

1474 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622853C212yesmaximal, complemented
2#13071485C212yesmaximal, complemented
3#13069453C212yesmaximal, complemented
4#13069075C214yesmaximal, complemented
5#13068604C211yesmaximal, characteristic, complemented
6#13068534C212yesmaximal, complemented
7C4×#66898C211yesmaximal, characteristic, complemented
8C2×C11×#547C211yesmaximal, characteristic
9C22×C11×#41C2212yes—
10C11×#547—22no—
11C11×#547—24no—
12C11×#547—22no—
13C2×C11×C4⋊Q8C411yescharacteristic, complemented
14C2×C11×#123C412yescomplemented
15C2×C11×#123C2212yes—
16C2×C11×C22⋊Q8C412yescomplemented
17C2×C11×#121C411yescharacteristic, complemented
18C2×C11×#121C2211yescharacteristic
19C2×C4×D4×C11C411yescharacteristic, complemented
20C2×C4×D4×C11C2211yescharacteristic
21C22×C11×C4⋊C4C411yescharacteristic, complemented
22C22×C11×C4⋊C4C2211yescharacteristic
23C2×#66979C2214yes—
24#10622853—28no—
25C2×#66898C2214yes—
26C2×#66898C2212yes—
27C2×#66898C2211yescharacteristic
28C2×#66898C2214yes—
29C2×#66898C2211yescharacteristic
30#10622825C2212yes—
31#10622824C2214yes—
32C4×C22⋊Dic11C2212yes—
33#10622598—22no—
34#10622594—24no—
35C4⋊C4×Dic11—22no—
36#10622164C2212yes—
37#10622164C2212yes—
38C2×C11×#41—24no—
39C2×C11×#41—24no—
40C2×C11×#41—24no—
41C2×C11×#41—24no—
42C2×C11×#41—44no—
43C22×Q8×C11C2×C412yes—
44C22×D4×C11C2×C412yes—
45C22×D4×C11C2×C411yescharacteristic
46C22×D4×C11C2312yes—
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11C2×C412yes—
49C23×C4×C11C2×C412yes—
50C23×C4×C11C2×C411yescharacteristic
51C23×C4×C11C2312yes—
52C23×C4×C11C2311yescharacteristic
53C11×C4⋊Q8—22no—
54C11×C4⋊Q8—22no—
55C11×#123—24no—
56C11×#123—24no—
57C11×#123—24no—
58C11×#123—24no—
59C11×C22⋊Q8—24no—
60C11×C22⋊Q8—24no—
61C11×#121—22no—
62C11×#121—22no—
63C11×#121—22no—
64C11×#121—22no—
65C4×D4×C11—22no—
66C4×D4×C11—22no—
67C4×D4×C11—22no—
68C4×D4×C11—21no—
69C4×D4×C11—21no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2×C411yescharacteristic
74C2×C11×C4⋊C4C2×C412yes—
75C2×C11×C4⋊C4C2×C411yescharacteristic
76C2×C11×C4⋊C4C2×C412yes—
77C2×C11×C4⋊C4C2×C411yescharacteristic
78C2×C11×C4⋊C4C2×C411yescharacteristic
79C2×C11×C4⋊C4C2×C412yes—
80C2×C11×C4⋊C4D412yes—
81C2×C11×C4⋊C4D414yes—
82C2×C11×C4⋊C4D412yes—
83C2×C11×C22⋊C4C2×C412yes—
84C2×C11×C22⋊C4C2×C411yescharacteristic
85C2×C11×C22⋊C4C2×C412yes—
86C2×C11×C22⋊C4C2×C412yes—
87C2×C11×C22⋊C4C2311yescharacteristic
88C2×C42×C11C2×C411yescharacteristic
89C2×C22⋊Dic11C2314yes—
90C2×C22⋊Dic11C2312yes—
91C2×C22⋊Dic11C2312yes—
92#66979—28no—
93#66979—44no—
94C2×C4⋊Dic11—24no—
95C2×C4⋊Dic11—22no—
96C2×C4×Dic11—24no—
97C2×C4×Dic11—22no—
98#66898—24no—
99#66898—22no—
100#66898—28no—
101#66898—44no—
102#66898D414yescomplemented
103C11⋊#95—22no—
104C11⋊#95—24no—
105C11⋊#95—24no—
106C11⋊#95—22no—
107#22406—111nomaximal, Sylow
108C24×C11C22×C412yes—
109C24×C11C22×C411yescharacteristic
110C24×C11C2411yescharacteristic
111C11×#41—48no—
112C11×#41—48no—
113C11×#41—48no—
114C11×#41—48no—
115C2×Q8×C11—24no—
116C2×Q8×C11—24no—
117C2×Q8×C11—42no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—24no—
121C2×D4×C11—22no—
122C2×D4×C11—24no—
123C2×D4×C11—22no—
124C2×D4×C11—24no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—24no—
128C2×D4×C11—42no—
129C2×D4×C11—42no—
130C2×D4×C11C2×D412yes—
131C2×D4×C11#4112yes—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—24no—
135C22×C4×C11—24no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—24no—
143C22×C4×C11—42no—
144C22×C4×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11—42no—
147C22×C4×C11C22×C412yes—
148C22×C4×C11C22×C411yescharacteristic
149C22×C4×C11C22×C412yes—
150C22×C4×C11C22×C412yes—
151C22×C4×C11C22×C411yescharacteristic
152C22×C4×C11C22×C411yescharacteristic
153C22×C4×C11C22×C411yescharacteristic
154C22×C4×C11C22×C411yescharacteristic
155C22×C4×C11C2×D414yes—
156C22×C4×C11C2×D414yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D412yes—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—24no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—24no—
168C11×C4⋊C4C22⋊C412yes—
169C11×C4⋊C4C22⋊C411yescharacteristic
170C11×C4⋊C4C22⋊C411yescharacteristic
171C11×C4⋊C4C22⋊C412yes—
172C11×C4⋊C4C22⋊C412yes—
173C11×C4⋊C4C22⋊C414yes—
174C11×C4⋊C4C22⋊C414yes—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—24no—
180C11×C22⋊C4—24no—
181C42×C11—21no—
182C42×C11—21no—
183C22⋊Dic11—24no—
184C22⋊Dic11—22no—
185C22⋊Dic11—22no—
186C22⋊Dic11—22no—
187C22⋊Dic11—24no—
188C22⋊Dic11C2×D414yes—
189C4⋊Dic11—48no—
190C4⋊Dic11—44no—
191C4×Dic11—48no—
192C4×Dic11—44no—
193C2×#547D1111yescharacteristic
194C2×#410—112no—
195#2344—112no—
196#1964—112no—
197#1899—114no—
198#1799—111no—
199#1782—112no—
200C4×#99—111no—
201C23×C11—21no—
202C23×C11—21no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11C4×D412yes—
213C23×C11C23×C411yescharacteristic
214C23×C11C22×D411yescharacteristic
215C23×C11C22×D412yes—
216C23×C11C2×#4111yescharacteristic
217C23×C11H(5,𝔽2)12yes—
218Q8×C11—48no—
219D4×C11—24no—
220D4×C11—24no—
221D4×C11—48no—
222D4×C11—42no—
223D4×C11—44no—
224D4×C11—44no—
225D4×C11—42no—
226C2×C4×C11—21no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—21no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—22no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—41no—
244C2×C4×C11—42no—
245C2×C4×C11—44no—
246C2×C4×C11—44no—
247C2×C4×C11—44no—
248C2×C4×C11—44no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11C2×C22⋊C411yescharacteristic
254C2×C4×C11C2×C22⋊C412yes—
255C2×C4×C11C2×C22⋊C412yes—
256C2×C4×C11C2×C22⋊C412yes—
257C2×C4×C11C2×C22⋊C414yes—
258C2×C4×C11C2×C22⋊C411yescharacteristic
259C2×C4×C11C4×D412yes—
260C2×Dic11—24no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263C2×Dic11—42no—
264C2×Dic11—44no—
265C2×Dic11—42no—
266C2×Dic11—44no—
267C2×Dic11—44no—
268C2×Dic11—42no—
269C22×#41C2×D1112yes—
270#547—22no—
271#547—24no—
272#547—22no—
273C2×C4⋊Q8Dic1111yescharacteristic, complemented
274C2×#123Dic1112yescomplemented
275C2×#123C2×D1112yes—
276C2×C22⋊Q8Dic1112yescomplemented
277C2×#121Dic1111yescharacteristic, complemented
278C2×#121C2×D1111yescharacteristic
279C2×C4×D4Dic1111yescharacteristic, complemented
280C2×C4×D4C2×D1111yescharacteristic
281C2×#117—114no—
282C22×C4⋊C4Dic1111yescharacteristic, complemented
283C22×C4⋊C4C2×D1111yescharacteristic
284#410—228no—
285C2×#99—111no—
286C2×#99—112no—
287C2×#99—114no—
288C2×#99—111no—
289C2×#99—114no—
290#389—222no—
291#387—224no—
292#381—114no—
293#380—112no—
294C4×C4⋊C4—222no—
295C4×C22⋊C4—112no—
296#342—112no—
297#342—112no—
298C22×C11—21no—
299C22×C11—22no—
300C22×C11—21no—
301C22×C11—22no—
302C22×C11—22no—
303C22×C11—41no—
304C22×C11—41no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11—41no—
309C22×C11—41no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11—42no—
313C22×C11—82no—
314C22×C11—82no—
315C22×C11C22×C22⋊C411yescharacteristic
316C22×C11C2×C4×D411yescharacteristic
317C22×C11#51811yescharacteristic
318C22×C11D4212yes—
319C22×C11#54612yes—
320C4×C11—22no—
321C4×C11—22no—
322C4×C11—24no—
323C4×C11—22no—
324C4×C11—21no—
325C4×C11—22no—
326C4×C11—42no—
327C4×C11—41no—
328C4×C11—41no—
329C4×C11#41012yescomplemented
330Dic11—44no—
331Dic11—84no—
332Dic11—82no—
333C2×#41—24no—
334C2×#41—24no—
335C2×#41—24no—
336C2×#41—24no—
337C2×#41—44no—
338C22×Q8C2×Dic1112yes—
339C22×D4C2×Dic1112yes—
340C22×D4C2×Dic1111yescharacteristic
341C22×D4C22×D1112yes—
342C22×D4C22×D1111yescharacteristic
343C23×C4C2×Dic1112yes—
344C23×C4C2×Dic1112yes—
345C23×C4C2×Dic1111yescharacteristic
346C23×C4C22×D1112yes—
347C23×C4C22×D1111yescharacteristic
348C4⋊Q8—22no—
349C4⋊Q8—22no—
350#123—24no—
351#123—24no—
352#123—24no—
353#123—24no—
354C22⋊Q8—24no—
355C22⋊Q8—24no—
356#121—22no—
357#121—22no—
358#121—22no—
359#121—22no—
360C4×D4—22no—
361C4×D4—22no—
362C4×D4—22no—
363C4×D4—21no—
364C4×D4—21no—
365#117—228no—
366#117—444no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—224no—
371C2×C4⋊C4—222no—
372C2×C4⋊C4C2×Dic1111yescharacteristic
373C2×C4⋊C4C2×Dic1112yes—
374C2×C4⋊C4C2×Dic1111yescharacteristic
375C2×C4⋊C4C2×Dic1112yes—
376C2×C4⋊C4C2×Dic1111yescharacteristic
377C2×C4⋊C4C2×Dic1111yescharacteristic
378C2×C4⋊C4C2×Dic1112yes—
379C2×C4⋊C4C22⋊D1112yes—
380C2×C4⋊C4C22⋊D1114yes—
381C2×C4⋊C4C22⋊D1112yes—
382C2×C22⋊C4—112no—
383C2×C22⋊C4—114no—
384C2×C22⋊C4—112no—
385C2×C22⋊C4C2×Dic1112yes—
386C2×C22⋊C4C2×Dic1111yescharacteristic
387C2×C22⋊C4C2×Dic1112yes—
388C2×C22⋊C4C2×Dic1112yes—
389C2×C22⋊C4C22×D1111yescharacteristic
390C2×C42—224no—
391C2×C42—222no—
392C2×C42C2×Dic1111yescharacteristic
393#99—114no—
394#99—228no—
395#99—224no—
396#99—222no—
397#99—444no—
398#95—222no—
399#95—224no—
400#95—222no—
401#95—224no—
402C2×C11—22no—
403C2×C11—22no—
404C2×C11—21no—
405C2×C11—21no—
406C2×C11—42no—
407C2×C11—82no—
408C2×C11D4×C22⋊C411yescharacteristic
409C2×C11C2×#41011yescharacteristic
410C2×C11#288411yescharacteristic
411C24C22×Dic1112yes—
412C24C22×Dic1111yescharacteristic
413C24C23×D1111yescharacteristic
414#41—48no—
415#41—48no—
416#41—48no—
417#41—48no—
418C2×Q8—24no—
419C2×Q8—24no—
420C2×Q8—42no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—24no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—24no—
427C2×D4—24no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—24no—
431C2×D4—42no—
432C2×D4—42no—
433C2×D4D4×D1112yes—
434C2×D4#434112yes—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—24no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4—224no—
453C22×C4C22×Dic1112yes—
454C22×C4C22×Dic1111yescharacteristic
455C22×C4C22×Dic1111yescharacteristic
456C22×C4C22×Dic1112yes—
457C22×C4C22×Dic1112yes—
458C22×C4C22×Dic1111yescharacteristic
459C22×C4C22×Dic1111yescharacteristic
460C22×C4C22×Dic1111yescharacteristic
461C22×C4C2×C22⋊D1114yes—
462C22×C4C2×C22⋊D1114yes—
463C22×C4C2×C22⋊D1112yes—
464C22×C4C2×C22⋊D1112yes—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—24no—
471C4⋊C4—448no—
472C4⋊C4—444no—
473C4⋊C4C22⋊Dic1112yes—
474C4⋊C4C22⋊Dic1111yescharacteristic
475C4⋊C4C22⋊Dic1111yescharacteristic
476C4⋊C4C22⋊Dic1112yes—
477C4⋊C4C22⋊Dic1112yes—
478C4⋊C4C22⋊Dic1114yes—
479C4⋊C4C22⋊Dic1114yes—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—24no—
485C22⋊C4—24no—
486C22⋊C4—114no—
487C22⋊C4—222no—
488C22⋊C4—224no—
489C22⋊C4—222no—
490C22⋊C4—222no—
491C22⋊C4—224no—
492C42—21no—
493C42—21no—
494C42—448no—
495C42—444no—
496C11#2240611yescharacteristic, complemented, Sylow
497C23—21no—
498C23—21no—
499C23—22no—
500C23—22no—
501C23—22no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—42no—
507C23—42no—
508C23D4×Dic1112yes—
509C23C2×D4×D1111yescharacteristic
510C23C2×#434111yescharacteristic
511C23#6703712yes—
512C23C23×Dic1111yescharacteristic
513C23C22×C22⋊D1112yes—
514Q8—48no—
515D4—24no—
516D4—24no—
517D4—48no—
518D4—42no—
519D4—44no—
520D4—44no—
521D4—42no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—21no—
532C2×C4—24no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—44no—
542C2×C4—44no—
543C2×C4—44no—
544C2×C4—44no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—224no—
550C2×C4—442no—
551C2×C4—442no—
552C2×C4—442no—
553C2×C4—444no—
554C2×C4—442no—
555C2×C4—444no—
556C2×C4—444no—
557C2×C4—442no—
558C2×C4D4×Dic1112yes—
559C2×C4C2×C22⋊Dic1111yescharacteristic
560C2×C4C2×C22⋊Dic1112yes—
561C2×C4C2×C22⋊Dic1112yes—
562C2×C4C2×C22⋊Dic1112yes—
563C2×C4C2×C22⋊Dic1114yes—
564C2×C4C2×C22⋊Dic1111yescharacteristic
565C22—21no—
566C22—22no—
567C22—21no—
568C22—22no—
569C22—22no—
570C22—41no—
571C22—41no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—41no—
576C22—41no—
577C22—42no—
578C22—42no—
579C22—42no—
580C22—82no—
581C22—82no—
582C22C2×D4×Dic1111yescharacteristic
583C22#1062332911yescharacteristic
584C22D4×C22⋊D1112yes—
585C22#1062333712yes—
586C22C22×C22⋊Dic1111yescharacteristic
587C4—22no—
588C4—22no—
589C4—24no—
590C4—22no—
591C4—21no—
592C4—22no—
593C4—42no—
594C4—41no—
595C4—41no—
596C4—444no—
597C4—884no—
598C4—882no—
599C4#1062285312yescomplemented
600C2—22no—
601C2—22no—
602C2—21no—
603C2—21no—
604C2—42no—
605C2—82no—
606C2D4×C22⋊Dic1111yescharacteristic
607C2C2×#1062285311yescharacteristic
608C2#1307708011yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
Fitting, prime radicalC2×C11×#547C2
socleC22×C11C22×C22⋊C4
cosocleC24×C11C24
hypercenterC2×#547D11
hypocenterC11#22406
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4⋊C4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#10622853C2semidirect
2. #13071485C2semidirect
3. #13069453C2semidirect
4. #13069075C2semidirect
5. #13068604C2semidirect
6. #13068534C2semidirect
7. C4×#66898C2semidirect
13. C2×C11×C4⋊Q8C4semidirect
14. C2×C11×#123C4semidirect
16. C2×C11×C22⋊Q8C4semidirect
17. C2×C11×#121C4semidirect
19. C2×C4×D4×C11C4semidirect
21. C22×C11×C4⋊C4C4semidirect
102. #66898D4semidirect
273. C2×C4⋊Q8Dic11semidirect
274. C2×#123Dic11semidirect
276. C2×C22⋊Q8Dic11semidirect
277. C2×#121Dic11semidirect
279. C2×C4×D4Dic11semidirect
282. C22×C4⋊C4Dic11semidirect
329. C4×C11#410semidirect
496. C11#22406semidirect
599. C4#10622853semidirect

Maximal subgroups

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

subgroupindex
C2×#106228532
#130714852
#130694532
#130690752
#130686042
#130685342
C4×#668982
C2×C11×#5472
#2240611