Finite Group Databasebeta

← #14735644

Subgroups — #14735644

Order 2816.

898 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 898 conjugacy classes of subgroups — too many to draw. Only its 171 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079631C212yesmaximal, complemented
2C2×#10622680C211yesmaximal, characteristic, complemented
3#13067918C212yesmaximal, complemented
4#13067914C214yesmaximal, complemented
5#13067909C212yesmaximal, complemented
6#13067243C211yesmaximal, characteristic, complemented
7#13067236C212yesmaximal, complemented
8C11×#3553C211yesmaximal, characteristic, complemented
9C11×#564C2211yescharacteristic, complemented
10C11×#563C2212yescomplemented
11C11×#562C2211yescharacteristic, complemented
12C11×#554—22no—
13C11×#553—22no—
14C11×#552—22no—
15C11×#541—22no—
16C11×#539—22no—
17C11×#539—22no—
18C11×#529C2212yes—
19C2×C11×#125C2211yescharacteristic
20C2×#66927C2211yescharacteristic
21#10622680—22no—
22#10622680C2214yes—
23#10622680C2212yes—
24#10622680C2212yes—
25#10622671C2214yes—
26#10622659—22no—
27#10622649—22no—
28#10622640—22no—
29#10622628—22no—
30C2×#66873—22no—
31#10622539C2212yes—
32C2×#66867C2211yescharacteristic
33#10622181C2212yescomplemented
34#10622181C2212yescomplemented
35#10622181C2214yescomplemented
36#10622178C2214yescomplemented
37C22×D44—21no—
38C22×D44—22no—
39C11×C4⋊Q8—22no—
40C11×#126—22no—
41C11×#126—22no—
42C11×#126—22no—
43C11×#126—22no—
44C11×#126—22no—
45C11×#125—22no—
46C11×#125—22no—
47C11×#125—22no—
48C11×#125—22no—
49C11×#125—22no—
50C11×#125—22no—
51C11×#125D412yes—
52C11×#125C2311yescharacteristic
53C11×#125C2311yescharacteristic
54C11×#125C2312yes—
55C11×#124C2312yes—
56C11×#123—22no—
57C11×#123—22no—
58C11×#123—22no—
59C11×#123—22no—
60C11×#123—22no—
61C11×C22⋊Q8—22no—
62C11×C22⋊Q8—22no—
63C11×C22⋊Q8—22no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—22no—
66C11×C22⋊Q8—22no—
67C11×C22⋊Q8D412yes—
68C11×#121—22no—
69C11×#121—22no—
70C11×#121D412yes—
71C4×Q8×C11—22no—
72C4×Q8×C11D412yes—
73C4×D4×C11—22no—
74C4×D4×C11—22no—
75C4×D4×C11—22no—
76C4×D4×C11—22no—
77C4×D4×C11D412yes—
78C11×#117—22no—
79C11×#117—22no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4D412yes—
83C2×C42×C11C2311yescharacteristic
84C2×#4325—24no—
85C2×#4323—24no—
86C22×C11⋊C8—21no—
87#66927—22no—
88#66927—21no—
89#66927C2312yes—
90C22⋊(C11⋊C8)—22no—
91#66873—24no—
92#66873—24no—
93#66873—24no—
94#66873—24no—
95C4⋊(C11⋊C8)—22no—
96#66867—21no—
97#66867C2312yes—
98#66867C2314yes—
99#19059—111nomaximal, Sylow
100C23×D11—41no—
101C2×Q8×C11—22no—
102C2×Q8×C11C2×D412yes—
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11C2×D412yes—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D412yes—
112C2×D44—22no—
113C2×D44—24no—
114C2×D44—44no—
115C2×D44—42no—
116C2×D44—41no—
117C2×D44—84no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4C2×D412yes—
134C11×C4⋊C4C2×D412yes—
135C11×C4⋊C4C2×D412yes—
136C11×C4⋊C4C2×D412yes—
137C11×C22⋊C4—22no—
138C11×C22⋊C4—22no—
139C11×C22⋊C4—22no—
140C11×C22⋊C4—22no—
141C11×C22⋊C4—22no—
142C11×C22⋊C4—22no—
143C11×C22⋊C4—22no—
144C11×C22⋊C4—22no—
145C11×C22⋊C4—22no—
146C42×C11—22no—
147C42×C11—22no—
148C42×C11—22no—
149C42×C11C2×D411yescharacteristic
150C42×C11C2×D412yes—
151C42×C11C2411yescharacteristic
152#4325—84no—
153#4323—84no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—24no—
156C2×C11⋊C8—42no—
157#3553D1111yescharacteristic, complemented
158#3217—112no—
159C2×#490—111no—
160#1658—112no—
161#1657—114no—
162#1656—112no—
163#1534—111no—
164#1532—112no—
165C23×C11—22no—
166C23×C11#12011yescharacteristic
167C22×D11—42no—
168C22×D11—84no—
169C22×D11—82no—
170Q8×C11—42no—
171Q8×C11—82no—
172D4×C11—42no—
173D4×C11—44no—
174D4×C11—82no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—42no—
182C2×C4×C11—82no—
183C2×C4×C11—82no—
184C2×C4×C11—82no—
185C2×C4×C11—82no—
186C2×C4×C11#12012yes—
187C2×C4×C11#12011yescharacteristic
188C2×C4×C11C22×D411yescharacteristic
189C2×C4×C11C22×D412yes—
190D44—44no—
191D44—44no—
192D44—44no—
193D44—82no—
194D44—84no—
195C11⋊C8—42no—
196C11⋊C8—44no—
197#564C2×D1111yescharacteristic, complemented
198#563C2×D1112yescomplemented
199#562C2×D1111yescharacteristic, complemented
200#554—22no—
201#553—22no—
202#552—22no—
203#541—22no—
204#539—22no—
205#539—22no—
206C2×#127—111no—
207#529C2×D1112yes—
208C2×#125C2×D1111yescharacteristic
209#496—114no—
210#490—112no—
211#490—112no—
212#490—114no—
213#490—222no—
214#460—222no—
215#459—222no—
216#450—222no—
217#447—222no—
218#432—112no—
219C2×#102—222no—
220C2×#97—111no—
221#330—112no—
222#330—112no—
223#330—114no—
224#329—114no—
225C22×C11—22no—
226C22×C11—42no—
227C22×C11—42no—
228C22×C11—42no—
229C22×C11#45412yes—
230C22×C11C2×#12011yescharacteristic
231C2×D11—82no—
232C2×D11—84no—
233C2×D11—164no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—22no—
237C4×C11—22no—
238C4×C11—42no—
239C4×C11—42no—
240C4×C11—42no—
241C4×C11—42no—
242C4×C11—42no—
243C22×D4—221no—
244C22×D4—222no—
245C2×SD16—224no—
246C2×D8—224no—
247C22×C8—221no—
248C4⋊Q8—22no—
249#127—112no—
250#127—222no—
251#127—221no—
252#126—22no—
253#126—22no—
254#126—22no—
255#126—22no—
256#126—22no—
257#125—22no—
258#125—22no—
259#125—22no—
260#125—22no—
261#125—22no—
262#125—22no—
263#125C22⋊D1112yes—
264#125C22×D1111yescharacteristic
265#125C22×D1111yescharacteristic
266#125C22×D1112yes—
267#124C22×D1112yes—
268#123—22no—
269#123—22no—
270#123—22no—
271#123—22no—
272#123—22no—
273C22⋊Q8—22no—
274C22⋊Q8—22no—
275C22⋊Q8—22no—
276C22⋊Q8—22no—
277C22⋊Q8—22no—
278C22⋊Q8—22no—
279C22⋊Q8C22⋊D1112yes—
280#121—22no—
281#121—22no—
282#121C22⋊D1112yes—
283C4×Q8—22no—
284C4×Q8C22⋊D1112yes—
285C4×D4—22no—
286C4×D4—22no—
287C4×D4—22no—
288C4×D4—22no—
289C4×D4C22⋊D1112yes—
290#117—22no—
291#117—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4C22⋊D1112yes—
295C2×C42C22×D1111yescharacteristic
296C4⋊C8—222no—
297#102—224no—
298#102—224no—
299#102—224no—
300#102—224no—
301C22⋊C8—222no—
302#97—112no—
303#97—114no—
304#97—221no—
305C2×C11—22no—
306C2×C11—82no—
307C2×C11C2×#45411yescharacteristic
308C2×C11#302112yes—
309D11—162no—
310C24—441no—
311C2×Q8—22no—
312C2×Q8C2×C22⋊D1112yes—
313C2×D4—22no—
314C2×D4—22no—
315C2×D4—222no—
316C2×D4—224no—
317C2×D4—444no—
318C2×D4—442no—
319C2×D4—441no—
320C2×D4—884no—
321C2×D4C2×C22⋊D1112yes—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4C2×C22⋊D1111yescharacteristic
327C22×C4C2×C22⋊D1112yes—
328SD16—884no—
329D8—884no—
330C2×C8—222no—
331C2×C8—224no—
332C2×C8—442no—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—22no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4C2×C22⋊D1112yes—
349C4⋊C4C2×C22⋊D1112yes—
350C4⋊C4C2×C22⋊D1112yes—
351C4⋊C4C2×C22⋊D1112yes—
352C22⋊C4—22no—
353C22⋊C4—22no—
354C22⋊C4—22no—
355C22⋊C4—22no—
356C22⋊C4—22no—
357C22⋊C4—22no—
358C22⋊C4—22no—
359C22⋊C4—22no—
360C22⋊C4—22no—
361C42—22no—
362C42—22no—
363C42—22no—
364C42C2×C22⋊D1111yescharacteristic
365C42C2×C22⋊D1112yes—
366C42C23×D1111yescharacteristic
367C11#1905911yescharacteristic, complemented, Sylow
368C23—22no—
369C23—442no—
370C23—884no—
371C23—882no—
372C23#6700611yescharacteristic
373Q8—42no—
374Q8—82no—
375D4—42no—
376D4—44no—
377D4—82no—
378D4—444no—
379D4—444no—
380D4—444no—
381D4—882no—
382D4—884no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—42no—
390C2×C4—82no—
391C2×C4—82no—
392C2×C4—82no—
393C2×C4—82no—
394C2×C4#6700612yes—
395C2×C4#6700611yescharacteristic
396C2×C4C22×C22⋊D1111yescharacteristic
397C2×C4C22×C22⋊D1112yes—
398C8—442no—
399C8—444no—
400C22—22no—
401C22—42no—
402C22—42no—
403C22—42no—
404C22—882no—
405C22—884no—
406C22—1764no—
407C22#1062285812yes—
408C22C2×#6700611yescharacteristic
409C4—21no—
410C4—21no—
411C4—22no—
412C4—22no—
413C4—42no—
414C4—42no—
415C4—42no—
416C4—42no—
417C4—42no—
418C2—22no—
419C2—82no—
420C2—1762no—
421C2C2×#1062285811yescharacteristic
422C2#1307798812yes—
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3553C2
socleC22×C11C2×#120
hypercenter#3553D11
hypocenterC11#19059
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3553

Complements

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

NH ≅ G/Ntype
1. #13079631C2semidirect
2. C2×#10622680C2semidirect
3. #13067918C2semidirect
4. #13067914C2semidirect
5. #13067909C2semidirect
6. #13067243C2semidirect
7. #13067236C2semidirect
8. C11×#3553C2semidirect
9. C11×#564C22semidirect
10. C11×#563C22semidirect
11. C11×#562C22semidirect
33. #10622181C22semidirect
34. #10622181C22semidirect
35. #10622181C22semidirect
36. #10622178C22semidirect
157. #3553D11semidirect
197. #564C2×D11semidirect
198. #563C2×D11semidirect
199. #562C2×D11semidirect
367. C11#19059semidirect

Maximal subgroups

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

subgroupindex
#130796312
C2×#106226802
#130679182
#130679142
#130679092
#130672432
#130672362
C11×#35532
#1905911