Finite Group Databasebeta

← #14909498

Subgroups — #14909498

Order 2816.

694 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 694 conjugacy classes of subgroups — too many to draw. Only its 139 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
1D11×#466C212yesmaximal, complemented
2#13070798C212yesmaximal, complemented
3#13070795C212yesmaximal, complemented
4#13070702C211yesmaximal, characteristic, complemented
5#13070700C212yesmaximal, complemented
6#13070529C212yesmaximal, complemented
7#13070526C212yesmaximal, complemented
8C2×(C2×D11)⋊C16C211yesmaximal, characteristic, complemented
9C11×#2215C211yesmaximal, characteristic, complemented
10C2×D8×D11C2212yescomplemented
11C22×C8×D11C2211yescharacteristic
12D11×#121—22no—
13C2×C11×D16C2211yescharacteristic, complemented
14C22×C11×C16C2211yescharacteristic, complemented
15C11×#466C2212yescomplemented
16#10622770C2212yes—
17C2×#66890C2212yescomplemented
18#10622728C2212yescomplemented
19C22×C11⋊C16C2211yescharacteristic, complemented
20#10622651—22no—
21C2×D176C2211yescharacteristic, complemented
22#10622496C2212yes—
23D11×#107C2212yescomplemented
24#10622388—22no—
25D11×#102—22no—
26C11×#366C2211yescharacteristic, complemented
27C11×#357C2212yescomplemented
28#10622200C2212yescomplemented
29#10622147C2212yescomplemented
30(C2×D11)⋊C16C2212yescomplemented
31(C2×D11)⋊C16C2212yescomplemented
32#10622142C2211yescharacteristic, complemented
33#10622129C2212yescomplemented
34#10622127C2212yescomplemented
35C2×D4×D11—22no—
36C2×D4×D11—42no—
37C22×C4×D11D411yescharacteristic
38C2×C11×D8C2312yes—
39C22×C8×C11C2311yescharacteristic
40C11×#121—22no—
41#66992—42no—
42#66991—22no—
43C2×#4323—22no—
44#66983—22no—
45C22×C11⋊C8D411yescharacteristic
46D8×D11—42no—
47D8×D11—42no—
48C2×D88C2312yes—
49C2×C8×D11—41no—
50C2×C8×D11—41no—
51C2×C8×D11D412yes—
52C2×C8×D11C2312yes—
53#66948—22no—
54C4⋊C4×D11—22no—
55#66937—42no—
56C22⋊C4×D11—42no—
57C11×D16—41no—
58C2×C11×C16—41no—
59C2×C11×C16C2311yescharacteristic
60C2×C11×C16C2311yescharacteristic
61C11×#107C2312yes—
62C11×#102—22no—
63#66896—22no—
64#66890—42no—
65#66885—22no—
66#66882C2312yes—
67C2×C11⋊C16—41no—
68C2×C11⋊C16C2312yes—
69#66873—22no—
70#66871—22no—
71D176—41no—
72#33752—111nomaximal, Sylow
73C23×D11—42no—
74C23×D11D811yescharacteristic
75C2×D4×C11—22no—
76C2×D4×C11—42no—
77C22×C4×C11C2×D411yescharacteristic
78C2×C22⋊D11—42no—
79C2×C22⋊D11—42no—
80C2×C22⋊D11—42no—
81C22×Dic11D811yescharacteristic
82D4×D11—44no—
83D4×D11—44no—
84D4×D11—88no—
85C2×D44—22no—
86C2×D44—42no—
87C2×C4×D11—41no—
88C2×C4×D11—41no—
89C2×C4×D11—42no—
90C2×C4×D11D812yes—
91C2×C4×D11C2×D412yes—
92C11×D8—22no—
93C11×D8—22no—
94C2×C8×C11—21no—
95C2×C8×C11—21no—
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2411yescharacteristic
98C11×C4⋊C4—22no—
99C11×C22⋊C4—42no—
100C22⋊Dic11—42no—
101#4323—44no—
102(C2×D11)⋊C4—42no—
103(C2×D11)⋊C4—42no—
104C4⋊Dic11—22no—
105Dic11⋊C4—42no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8C2×D412yes—
108D88—22no—
109D88—22no—
110C8×D11—22no—
111C8×D11—22no—
112C8×D11—42no—
113C11×C16—21no—
114C11×C16—21no—
115C11⋊C16—22no—
116C2×#466—112no—
117#2232—112no—
118#2232—112no—
119#2215—111no—
120#2215—112no—
121#2215D1111yescharacteristic, complemented
122#2184—112no—
123#2184—112no—
124C2×C22⋊C16—111no—
125C23×C11—42no—
126C23×C11C2×D811yescharacteristic
127C22×D11—41no—
128C22×D11—41no—
129C22×D11—42no—
130C22×D11—84no—
131C22×D11—84no—
132C22×D11—84no—
133C22×D11D1614yescomplemented
134C22×D11C2×D812yes—
135D4×C11—42no—
136D4×C11—42no—
137D4×C11—84no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—42no—
141C2×C4×C11C2×D811yescharacteristic
142C2×C4×C11C22×D411yescharacteristic
143C22⋊D11—84no—
144C22⋊D11—84no—
145C22⋊D11—84no—
146C2×Dic11—41no—
147C2×Dic11—42no—
148C2×Dic11C2×D812yes—
149D44—42no—
150D44—42no—
151D44—84no—
152C4×D11—22no—
153C4×D11—22no—
154C4×D11—42no—
155C4×D11—84no—
156C8×C11—21no—
157C8×C11H(5,𝔽2)11yescharacteristic
158C8×C11H(5,𝔽2)11yescharacteristic
159C11⋊C8—22no—
160C22×D8—112no—
161C23×C8—111no—
162C2×#121—222no—
163C2×D16—112no—
164C2×D16—111no—
165C2×D16C2×D1111yescharacteristic, complemented
166C22×C16—111no—
167C22×C16C2×D1111yescharacteristic, complemented
168#466—112no—
169#466—112no—
170#466—112no—
171#466—222no—
172#466—222no—
173#466C2×D1112yescomplemented
174C2×#107—112no—
175C2×#102—222no—
176#366—111no—
177#366—112no—
178#366C2×D1111yescharacteristic, complemented
179#357—112no—
180#357—112no—
181#357—112no—
182#357C2×D1112yescomplemented
183C22⋊C16—112no—
184C22⋊C16—112no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—82no—
188C22×C11—82no—
189C22×C11—82no—
190C22×C11C2×D1612yes—
191C22×C11C22×D811yescharacteristic
192C2×D11—22no—
193C2×D11—22no—
194C2×D11—44no—
195C2×D11—82no—
196C2×D11—82no—
197C2×D11—82no—
198C2×D11—168no—
199C2×D11C2×D1614yes—
200C4×C11—21no—
201C4×C11—82no—
202C4×C11#53411yescharacteristic
203C4×C11#57511yescharacteristic
204Dic11—22no—
205Dic11—82no—
206C22×D4—222no—
207C22×D4—442no—
208C23×C4—111no—
209C2×D8—112no—
210C2×D8—222no—
211C2×D8—442no—
212C2×D8—442no—
213C2×D8C22×D1112yes—
214C22×C8—111no—
215C22×C8—112no—
216C22×C8—112no—
217C22×C8—441no—
218C22×C8—441no—
219C22×C8C22×D1111yescharacteristic
220#121—22no—
221#121—222no—
222#121—222no—
223#121—222no—
224#121—442no—
225#121—442no—
226C2×C4⋊C4—222no—
227C2×C22⋊C4—442no—
228D16—41no—
229D16—441no—
230D16—442no—
231C2×C16—41no—
232C2×C16—112no—
233C2×C16—441no—
234C2×C16C22×D1111yescharacteristic
235C2×C16C22×D1111yescharacteristic
236#107—112no—
237#107—222no—
238#107C22×D1112yes—
239#102—22no—
240#102—222no—
241#102—222no—
242#102—222no—
243C2×C11—22no—
244C2×C11—162no—
245C2×C11#318611yescharacteristic
246C2×C11C22×D1611yescharacteristic
247C2×C11#341411yescharacteristic
248D11—24no—
249D11—162no—
250C24—111no—
251C24—442no—
252C2×D4—22no—
253C2×D4—42no—
254C2×D4—222no—
255C2×D4—442no—
256C2×D4—442no—
257C2×D4—444no—
258C2×D4—444no—
259C2×D4—442no—
260C2×D4—442no—
261C2×D4—888no—
262C22×C4—111no—
263C22×C4—112no—
264C22×C4—112no—
265C22×C4—441no—
266C22×C4—441no—
267C22×C4—442no—
268C22×C4D4×D1111yescharacteristic
269D8—22no—
270D8—22no—
271D8—222no—
272D8—222no—
273D8—444no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—112no—
277C2×C8—222no—
278C2×C8—222no—
279C2×C8—442no—
280C2×C8—441no—
281C2×C8D4×D1111yescharacteristic
282C2×C8C23×D1111yescharacteristic
283C4⋊C4—22no—
284C4⋊C4—222no—
285C4⋊C4—442no—
286C22⋊C4—42no—
287C22⋊C4—442no—
288C22⋊C4—442no—
289C22⋊C4—442no—
290C16—21no—
291C16—21no—
292C16—222no—
293C11#3375211yescharacteristic, complemented, Sylow
294C23—42no—
295C23—112no—
296C23—114no—
297C23—441no—
298C23—441no—
299C23—442no—
300C23—884no—
301C23—884no—
302C23—884no—
303C23D8×D1111yescharacteristic
304D4—42no—
305D4—42no—
306D4—84no—
307D4—442no—
308D4—442no—
309D4—884no—
310D4—884no—
311D4—884no—
312D4—884no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—42no—
316C2×C4—112no—
317C2×C4—222no—
318C2×C4—222no—
319C2×C4—442no—
320C2×C4—441no—
321C2×C4—442no—
322C2×C4—884no—
323C2×C4D8×D1111yescharacteristic
324C2×C4C2×D4×D1111yescharacteristic
325C8—21no—
326C8—222no—
327C8#6703711yescharacteristic
328C8#6704211yescharacteristic
329C22—21no—
330C22—21no—
331C22—82no—
332C22—82no—
333C22—82no—
334C22—114no—
335C22—222no—
336C22—222no—
337C22—444no—
338C22—882no—
339C22—882no—
340C22—882no—
341C22—1768no—
342C22D11×D1612yes—
343C22C2×D8×D1111yescharacteristic
344C4—21no—
345C4—82no—
346C4—222no—
347C4—882no—
348C4#1062313611yescharacteristic
349C4#1062329911yescharacteristic
350C2—22no—
351C2—162no—
352C2—224no—
353C2—1762no—
354C2#1307936311yescharacteristic
355C2C2×D11×D1611yescharacteristic
356C2#1308174911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2215C2
socleC22×C11C22×D8
hypercenter#2215D11
hypocenterC11#33752
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2215

Complements

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

NH ≅ G/Ntype
1. D11×#466C2semidirect
2. #13070798C2semidirect
3. #13070795C2semidirect
4. #13070702C2semidirect
5. #13070700C2semidirect
6. #13070529C2semidirect
7. #13070526C2semidirect
8. C2×(C2×D11)⋊C16C2semidirect
9. C11×#2215C2semidirect
10. C2×D8×D11C22semidirect
13. C2×C11×D16C22semidirect
14. C22×C11×C16C22semidirect
15. C11×#466C22semidirect
17. C2×#66890C22semidirect
18. #10622728C22semidirect
19. C22×C11⋊C16C22semidirect
21. C2×D176C22semidirect
23. D11×#107C22semidirect
26. C11×#366C22semidirect
27. C11×#357C22semidirect
28. #10622200C22semidirect
29. #10622147C22semidirect
30. (C2×D11)⋊C16C22semidirect
31. (C2×D11)⋊C16C22semidirect
32. #10622142C22semidirect
33. #10622129C22semidirect
34. #10622127C22semidirect
121. #2215D11semidirect
133. C22×D11D16semidirect
165. C2×D16C2×D11semidirect
167. C22×C16C2×D11semidirect
173. #466C2×D11semidirect
178. #366C2×D11semidirect
182. #357C2×D11semidirect
293. C11#33752semidirect

Maximal subgroups

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

subgroupindex
D11×#4662
#130707982
#130707952
#130707022
#130707002
#130705292
#130705262
C2×(C2×D11)⋊C162
C11×#22152
#3375211