Finite Group Databasebeta

← #14763774

Subgroups — #14763774

Order 2816.

1242 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081912C211yesmaximal, characteristic
2C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
3#13069560C212yesmaximal, complemented
4#13069535C212yesmaximal, complemented
5#13069057C214yesmaximal, complemented
6#13068633C214yesmaximal, complemented
7C11×#2920C211yesmaximal, characteristic, complemented
8C22×C42×C11C2211yescharacteristic
9#10623322—21no—
10#10623322—21no—
11#10623322C2212yes—
12C22×C4⋊Dic11—21no—
13C22×C4×Dic11C2212yes—
14#10623010—21no—
15#10623010—21no—
16#10623010—21no—
17#10623010—21no—
18#10623010C412yescomplemented
19#10623010C412yescomplemented
20#10623008C411yescharacteristic, complemented
21#10623008C411yescharacteristic, complemented
22#10623008C2211yescharacteristic
23C4×#4339—21no—
24C4×#4339—21no—
25C4×#4339C2212yes—
26#10623001C411yescharacteristic, complemented
27#10623001C411yescharacteristic, complemented
28#10623001C2211yescharacteristic
29C11×#432—21no—
30C11×#432—21no—
31C11×#431—21no—
32C11×#431—21no—
33C11×#423C2212yes—
34C11×#407C2212yes—
35C4×C11×M16C2212yes—
36C2×C11⋊#95—21no—
37C2×#66889C2218yes—
38C4×C4⋊Dic11—21no—
39C4×C4⋊Dic11—21no—
40C4×C4⋊Dic11C2212yes—
41C4×C4⋊Dic11C2212yes—
42#10622193C2218yes—
43C23×C4×C11D411yescharacteristic
44C23×C4×C11D411yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×Dic11—22no—
47C2×#4339—21no—
48C2×#4339—21no—
49C2×#4339C2312yes—
50C2×C11×M16C2314yes—
51C2×C42×C11C2×C411yescharacteristic
52C2×C42×C11C2×C411yescharacteristic
53C2×C42×C11C2×C411yescharacteristic
54C2×C42×C11C2×C411yescharacteristic
55C2×C42×C11D411yescharacteristic
56C2×C42×C11D411yescharacteristic
57C2×C42×C11D411yescharacteristic
58C2×C42×C11D411yescharacteristic
59C2×C42×C11D411yescharacteristic
60C2×C42×C11D411yescharacteristic
61C2×C42×C11C2311yescharacteristic
62C2×C42×C11C2311yescharacteristic
63#67006—22no—
64#66983—21no—
65#66983—21no—
66#66983—21no—
67#66983—21no—
68#66983C2×C412yes—
69#66983C2×C412yes—
70#66982—22no—
71#66982—22no—
72#66982—22no—
73C4×C22⋊D11—22no—
74C4×C22⋊D11—22no—
75C4×C22⋊D11—22no—
76C4×C22⋊D11—22no—
77C4×C22⋊D11—22no—
78C4×C22⋊D11—22no—
79#66979—21no—
80#66979—21no—
81#66979C2312yes—
82C2×C4⋊Dic11—28no—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11—22no—
85#66977—21no—
86#66977—21no—
87#66977—21no—
88#66977—21no—
89#66977C2×C412yes—
90#66977C2×C412yes—
91C2×C4×Dic11—22no—
92C2×C4×Dic11—44no—
93C2×C4×Dic11C2314yes—
94#66929—22no—
95#66929—22no—
96#66928—21no—
97#66928—21no—
98#66928C2×C412yescomplemented
99#66927C2×C411yescharacteristic, complemented
100C4×D44—21no—
101C4×D44—21no—
102C4×D44—21no—
103C4×D44—21no—
104C4×D44C2×C412yescomplemented
105C4×D44C2×C412yescomplemented
106#66925—22no—
107#66925—22no—
108#66925—22no—
109C42×D11—22no—
110#66923—21no—
111#66923—21no—
112#66923C2×C412yescomplemented
113#66922C2×C411yescharacteristic, complemented
114#66922C2×C411yescharacteristic, complemented
115#66922C2×C411yescharacteristic, complemented
116C4×Dic22—21no—
117C4×Dic22—21no—
118C4×Dic22—21no—
119C4×Dic22—21no—
120C4×Dic22C2×C412yescomplemented
121C4×Dic22C2×C412yescomplemented
122C11×C4⋊C8—22no—
123C11×C4⋊C8—22no—
124C11×C22⋊C8—22no—
125C11×C22⋊C8—22no—
126C11×#97—22no—
127C4×C8×C11—22no—
128C11⋊#95—22no—
129C11⋊#95—22no—
130#66889—48no—
131#21899—111nomaximal, Sylow
132C24×C11C2×D411yescharacteristic
133C22×C4×C11—24no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—42no—
137C22×C4×C11C22⋊C411yescharacteristic
138C22×C4×C11C22⋊C411yescharacteristic
139C22×C4×C11C22⋊C411yescharacteristic
140C22×C4×C11C22⋊C411yescharacteristic
141C22×C4×C11C22⋊C411yescharacteristic
142C22×C4×C11C22⋊C411yescharacteristic
143C22×C4×C11C22⋊C411yescharacteristic
144C22×C4×C11C22⋊C411yescharacteristic
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2411yescharacteristic
155C2×C22⋊D11—22no—
156C2×C22⋊D11—22no—
157C2×C22⋊D11—22no—
158C22×Dic11—28no—
159C22×Dic11—24no—
160C22×Dic11—44no—
161C22×Dic11—44no—
162#4339—24no—
163#4339—24no—
164#4339—44no—
165#4339—44no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44C22×C412yes—
169C2×C4×D11—22no—
170C2×C4×D11—22no—
171C2×C4×D11—22no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22C22×C412yes—
175C11×M16—24no—
176C11×M16—24no—
177C2×C8×C11—24no—
178C42×C11C22⋊C411yescharacteristic
179C42×C11C22⋊C411yescharacteristic
180C42×C11C22⋊C411yescharacteristic
181C42×C11C22⋊C411yescharacteristic
182C42×C11C22⋊C411yescharacteristic
183C42×C11C22⋊C411yescharacteristic
184C42×C11C22⋊C411yescharacteristic
185C42×C11C22⋊C411yescharacteristic
186C42×C11C22×C411yescharacteristic
187C42×C11C22×C411yescharacteristic
188C42×C11C22×C411yescharacteristic
189C42×C11C22×C411yescharacteristic
190C42×C11C2×D411yescharacteristic
191C42×C11C2×D411yescharacteristic
192C42×C11C2×D411yescharacteristic
193C42×C11C2×D411yescharacteristic
194C22⋊Dic11—22no—
195C22⋊Dic11—22no—
196C22⋊Dic11—22no—
197(C2×D11)⋊C4—22no—
198(C2×D11)⋊C4—22no—
199(C2×D11)⋊C4—22no—
200(C2×D11)⋊C4—22no—
201(C2×D11)⋊C4—22no—
202(C2×D11)⋊C4—22no—
203C4⋊Dic11—28no—
204C4⋊Dic11—28no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11C22×C412yes—
210C4⋊Dic11C22×C412yes—
211Dic11⋊C4—22no—
212Dic11⋊C4—22no—
213Dic11⋊C4—22no—
214Dic11⋊C4—22no—
215Dic11⋊C4—22no—
216Dic11⋊C4—22no—
217C4×Dic11—22no—
218C4×Dic11—22no—
219C4×Dic11—22no—
220C4×Dic11—28no—
221C4×Dic11—44no—
222#3444—111no—
223#2920D1111yescharacteristic, complemented
224C2×C4×C4⋊C4—111no—
225#1986—112no—
226#1980—112no—
227#1896—114no—
228#1806—114no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—22no—
232C23×C11—22no—
233C23×C11C2×C22⋊C411yescharacteristic
234C23×C11C2×C22⋊C411yescharacteristic
235C23×C11C22×D411yescharacteristic
236C22×D11—22no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11#10414yescomplemented
255C2×C4×C11C2×C22⋊C411yescharacteristic
256C2×C4×C11C2×C22⋊C411yescharacteristic
257C2×C4×C11C2×C22⋊C411yescharacteristic
258C2×C4×C11C2×C22⋊C411yescharacteristic
259C2×C4×C11C2×C22⋊C411yescharacteristic
260C2×C4×C11C2×C22⋊C411yescharacteristic
261C2×C4×C11C2×C22⋊C411yescharacteristic
262C2×C4×C11C2×C22⋊C411yescharacteristic
263C2×C4×C11C2×C22⋊C411yescharacteristic
264C2×C4×C11C2×C22⋊C411yescharacteristic
265C2×C4×C11C23×C411yescharacteristic
266C2×C4×C11C22×D411yescharacteristic
267C2×C4×C11H(5,𝔽2)12yes—
268C2×C4×C112−1+412yes—
269C22⋊D11—42no—
270C22⋊D11—42no—
271C22⋊D11—44no—
272C22⋊D11—44no—
273C2×Dic11—28no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—416no—
278C2×Dic11—44no—
279C2×Dic11—44no—
280D44—24no—
281D44—42no—
282D44—42no—
283C4×D11—44no—
284C4×D11—44no—
285C4×D11—44no—
286Dic22—24no—
287Dic22—42no—
288Dic22—42no—
289C8×C11—44no—
290#533—111no—
291#533—111no—
292#533—111no—
293#532—111no—
294#532—111no—
295#532—111no—
296#529—112no—
297#529—112no—
298#529—221no—
299#529—221no—
300#529—221no—
301#529—221no—
302#525—112no—
303#525—221no—
304#525—221no—
305C4×#41—112no—
306C4×#41—221no—
307C4×#41—221no—
308C22×C4⋊C4—221no—
309C22×C42—112no—
310C22×C42C2×D1111yescharacteristic
311#432—21no—
312#432—21no—
313#431—21no—
314#431—21no—
315#423C2×D1112yes—
316C2×#104—118no—
317#407C2×D1112yes—
318C4×M16C2×D1112yes—
319C4×C4⋊C4—112no—
320C4×C4⋊C4—112no—
321C4×C4⋊C4—221no—
322C4×C4⋊C4—221no—
323C2×#95—221no—
324#339—118no—
325C22×C11—24no—
326C22×C11—24no—
327C22×C11—21no—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11C2×#10412yes—
334C22×C11#42112yes—
335C22×C11C22×C22⋊C411yescharacteristic
336C22×C11#53511yescharacteristic
337C22×C11#53611yescharacteristic
338C2×D11—42no—
339C2×D11—42no—
340C2×D11—42no—
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—21no—
344C4×C11—21no—
345C4×C11—21no—
346C4×C11—21no—
347C4×C11—21no—
348C4×C11—21no—
349C4×C11C2×#10412yes—
350C4×C11C2×#10412yes—
351C4×C11#52012yes—
352C4×C11#53712yes—
353Dic11—48no—
354Dic11—42no—
355Dic11—42no—
356Dic11—42no—
357C2×#41—112no—
358C2×#41—221no—
359C2×#41—221no—
360C23×C4—222no—
361C23×C4D4411yescharacteristic
362C23×C4D4411yescharacteristic
363C23×C4C22×D1111yescharacteristic
364C2×M16C22×D1114yes—
365C4⋊Q8—111no—
366C4⋊Q8—111no—
367C4⋊Q8—111no—
368#127—111no—
369#126—222no—
370#126—222no—
371#125—112no—
372#125—221no—
373#125—221no—
374#124—112no—
375#124—221no—
376#124—221no—
377#123—222no—
378#123—222no—
379#123—222no—
380C22⋊Q8—112no—
381C22⋊Q8—112no—
382C22⋊Q8—221no—
383C22⋊Q8—221no—
384C22⋊Q8—221no—
385C22⋊Q8—221no—
386#121—112no—
387#121—112no—
388#121—221no—
389#121—221no—
390#121—221no—
391#121—221no—
392#120—222no—
393C4×Q8—112no—
394C4×Q8—112no—
395C4×Q8—221no—
396C4×Q8—221no—
397C4×Q8—221no—
398C4×Q8—221no—
399C4×D4—112no—
400C4×D4—112no—
401C4×D4—222no—
402C4×D4—222no—
403C4×D4—222no—
404C4×D4—222no—
405C4×D4—222no—
406C4×D4—222no—
407C4×D4—221no—
408C4×D4—221no—
409C4×D4—221no—
410C4×D4—221no—
411#117—112no—
412#117—221no—
413#117—221no—
414#117—222no—
415#117—222no—
416#117—222no—
417C2×C4⋊C4—228no—
418C2×C4⋊C4—222no—
419C2×C4⋊C4—222no—
420C2×C42—114no—
421C2×C42—222no—
422C2×C42—222no—
423C2×C42—444no—
424C2×C42C4×D1111yescharacteristic
425C2×C42C4×D1111yescharacteristic
426C2×C42C4×D1111yescharacteristic
427C2×C42C4×D1111yescharacteristic
428C2×C42D4411yescharacteristic
429C2×C42D4411yescharacteristic
430C2×C42C22⋊D1111yescharacteristic
431C2×C42C22⋊D1111yescharacteristic
432C2×C42C22⋊D1111yescharacteristic
433C2×C42C22⋊D1111yescharacteristic
434C2×C42C22×D1111yescharacteristic
435C2×C42C22×D1111yescharacteristic
436C4⋊C8—22no—
437C4⋊C8—22no—
438#104—448no—
439C22⋊C8—22no—
440C22⋊C8—22no—
441#97—22no—
442C4×C8—22no—
443#95—222no—
444#95—222no—
445C2×C11—21no—
446C2×C11—21no—
447C2×C11—22no—
448C2×C11—22no—
449C2×C11#231111yescharacteristic
450C2×C11C22×#10411yescharacteristic
451C2×C11C2×#42111yescharacteristic
452D11—82no—
453C24C2×D4411yescharacteristic
454#41—224no—
455#41—224no—
456#41—444no—
457#41—444no—
458C2×Q8—112no—
459C2×Q8—221no—
460C2×Q8—221no—
461C2×D4—112no—
462C2×D4—222no—
463C2×D4—222no—
464C2×D4—222no—
465C2×D4—221no—
466C2×D4—221no—
467C22×C4—24no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—42no—
471C22×C4—228no—
472C22×C4—224no—
473C22×C4—222no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—444no—
477C22×C4—444no—
478C22×C4(C2×D11)⋊C411yescharacteristic
479C22×C4(C2×D11)⋊C411yescharacteristic
480C22×C4(C2×D11)⋊C411yescharacteristic
481C22×C4(C2×D11)⋊C411yescharacteristic
482C22×C4(C2×D11)⋊C411yescharacteristic
483C22×C4(C2×D11)⋊C411yescharacteristic
484C22×C4(C2×D11)⋊C411yescharacteristic
485C22×C4(C2×D11)⋊C411yescharacteristic
486C22×C4C2×C4×D1111yescharacteristic
487C22×C4C2×C4×D1111yescharacteristic
488C22×C4C2×D4411yescharacteristic
489C22×C4C2×D4411yescharacteristic
490C22×C4C2×D4411yescharacteristic
491C22×C4C2×D4411yescharacteristic
492C22×C4C2×D4411yescharacteristic
493C22×C4C2×C22⋊D1111yescharacteristic
494C22×C4C2×C22⋊D1111yescharacteristic
495C22×C4C23×D1111yescharacteristic
496M16—24no—
497M16—24no—
498C2×C8—24no—
499C4⋊C4—112no—
500C4⋊C4—112no—
501C4⋊C4—228no—
502C4⋊C4—228no—
503C4⋊C4—222no—
504C4⋊C4—222no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—222no—
510C4⋊C4—222no—
511C4⋊C4—222no—
512C4⋊C4—222no—
513C22⋊C4—222no—
514C22⋊C4—222no—
515C22⋊C4—222no—
516C22⋊C4—222no—
517C22⋊C4—222no—
518C22⋊C4—222no—
519C22⋊C4—222no—
520C22⋊C4—222no—
521C22⋊C4—222no—
522C42—222no—
523C42—222no—
524C42—222no—
525C42—228no—
526C42—444no—
527C42(C2×D11)⋊C411yescharacteristic
528C42(C2×D11)⋊C411yescharacteristic
529C42(C2×D11)⋊C411yescharacteristic
530C42(C2×D11)⋊C411yescharacteristic
531C42(C2×D11)⋊C411yescharacteristic
532C42(C2×D11)⋊C411yescharacteristic
533C42(C2×D11)⋊C411yescharacteristic
534C42(C2×D11)⋊C411yescharacteristic
535C42C2×C4×D1111yescharacteristic
536C42C2×C4×D1111yescharacteristic
537C42C2×C4×D1111yescharacteristic
538C42C2×C4×D1111yescharacteristic
539C42C2×C22⋊D1111yescharacteristic
540C42C2×C22⋊D1111yescharacteristic
541C42C2×C22⋊D1111yescharacteristic
542C42C2×C22⋊D1111yescharacteristic
543C11#2189911yescharacteristic, complemented, Sylow
544C23—22no—
545C23—22no—
546C23—21no—
547C23—21no—
548C23—222no—
549C23C2×(C2×D11)⋊C411yescharacteristic
550C23C2×(C2×D11)⋊C411yescharacteristic
551C23C22×D4411yescharacteristic
552Q8—224no—
553Q8—442no—
554Q8—442no—
555D4—224no—
556D4—442no—
557D4—444no—
558D4—444no—
559D4—442no—
560D4—442no—
561D4—442no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—228no—
580C2×C4—222no—
581C2×C4—222no—
582C2×C4—222no—
583C2×C4—444no—
584C2×C4—4416no—
585C2×C4—444no—
586C2×C4—444no—
587C2×C4—444no—
588C2×C4—444no—
589C2×C4#6688914yescomplemented
590C2×C4C2×(C2×D11)⋊C411yescharacteristic
591C2×C4C2×(C2×D11)⋊C411yescharacteristic
592C2×C4C2×(C2×D11)⋊C411yescharacteristic
593C2×C4C2×(C2×D11)⋊C411yescharacteristic
594C2×C4C2×(C2×D11)⋊C411yescharacteristic
595C2×C4C2×(C2×D11)⋊C411yescharacteristic
596C2×C4C2×(C2×D11)⋊C411yescharacteristic
597C2×C4C2×(C2×D11)⋊C411yescharacteristic
598C2×C4C2×(C2×D11)⋊C411yescharacteristic
599C2×C4C2×(C2×D11)⋊C411yescharacteristic
600C2×C4C22×C4×D1111yescharacteristic
601C2×C4#6704212yes—
602C2×C4#6704312yes—
603C2×C4C22×C22⋊D1111yescharacteristic
604C8—44no—
605C22—24no—
606C22—24no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—442no—
614C22—442no—
615C22—442no—
616C22C2×#6688912yes—
617C22#1062275212yes—
618C22#1062305611yescharacteristic
619C22#1062305711yescharacteristic
620C22C22×(C2×D11)⋊C411yescharacteristic
621C4—21no—
622C4—21no—
623C4—21no—
624C4—21no—
625C4—21no—
626C4—21no—
627C4—21no—
628C4—21no—
629C4—448no—
630C4—442no—
631C4—442no—
632C4—442no—
633C4C2×#6688912yes—
634C4C2×#6688912yes—
635C4#1062305412yes—
636C4#1062336412yes—
637C2—21no—
638C2—22no—
639C2—22no—
640C2—21no—
641C2—882no—
642C2#1307120411yescharacteristic
643C2C22×#6688911yescharacteristic
644C2C2×#1062275211yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2920C2
socleC22×C11C22×C22⋊C4
prime radical#13081912C2
cosocleC22×C4×C11C24
hypercenter#2920D11
hypocenterC11#21899
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ #2920

Complements

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

NH ≅ G/Ntype
2. C2×C4×C4⋊Dic11C2semidirect
3. #13069560C2semidirect
4. #13069535C2semidirect
5. #13069057C2semidirect
6. #13068633C2semidirect
7. C11×#2920C2semidirect
18. #10623010C4semidirect
19. #10623010C4semidirect
20. #10623008C4semidirect
21. #10623008C4semidirect
26. #10623001C4semidirect
27. #10623001C4semidirect
98. #66928C2×C4semidirect
99. #66927C2×C4semidirect
104. C4×D44C2×C4semidirect
105. C4×D44C2×C4semidirect
112. #66923C2×C4semidirect
113. #66922C2×C4semidirect
114. #66922C2×C4semidirect
115. #66922C2×C4semidirect
120. C4×Dic22C2×C4semidirect
121. C4×Dic22C2×C4semidirect
223. #2920D11semidirect
254. C2×C4×C11#104semidirect
543. C11#21899semidirect
589. C2×C4#66889semidirect

Maximal subgroups

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

subgroupindex
#130819122
C2×C4×C4⋊Dic112
#130695602
#130695352
#130690572
#130686332
C11×#29202
#2189911