Finite Group Databasebeta

← #13079366

Subgroups — #13079366

Order 1408.

520 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 121 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×#121C211yesmaximal, characteristic, complemented
2C2×#66948C211yesmaximal, characteristic, complemented
3C11×#480C211yesmaximal, characteristic, complemented
4#10622649C211yesmaximal, characteristic, complemented
5#10622580C211yesmaximal, characteristic, complemented
6#10622496C212yesmaximal, complemented
7#10622495C212yesmaximal, complemented
8#10622388C212yesmaximal, complemented
9#10622386C212yesmaximal, complemented
10#10622345C211yesmaximal, characteristic, complemented
11D11×C22⋊C8C211yesmaximal, characteristic, complemented
12C2×D4×D11—21no—
13C2×D4×D11C2211yescharacteristic, complemented
14C22×D44—21no—
15C22×D44C2211yescharacteristic, complemented
16C22×C4×D11C2211yescharacteristic
17C11×#121C2211yescharacteristic
18C2×C11×C4⋊C4C2211yescharacteristic, complemented
19#66992—21no—
20#66991C2211yescharacteristic, complemented
21C2×#4323C2212yescomplemented
22#66983C2211yescharacteristic
23C2×(C2×D11)⋊C4—21no—
24C2×D88C2212yescomplemented
25C2×C8×D11C2212yescomplemented
26#66948—21no—
27#66948—21no—
28#66948C2212yes—
29#66948C2211yescharacteristic, complemented
30#66948C2212yescomplemented
31C4⋊C4×D11C2211yescharacteristic, complemented
32#66937—21no—
33C22⋊C4×D11—21no—
34C11×#107C2212yescomplemented
35C11×#102C2212yescomplemented
36C11×C22⋊C8C2211yescharacteristic, complemented
37C22⋊(C11⋊C8)C2211yescharacteristic, complemented
38#66885C2212yescomplemented
39(C2×D11)⋊C8C2212yescomplemented
40#66873C2212yescomplemented
41#66873C2212yescomplemented
42#66871C2212yescomplemented
43C23×D11—21no—
44C23×D11—21no—
45C23×D11D411yescharacteristic
46C2×D4×C11—21no—
47C2×D4×C11C2311yescharacteristic
48C22×C4×C11—21no—
49C22×C4×C11C2311yescharacteristic
50C2×C22⋊D11—21no—
51C2×C22⋊D11—21no—
52C2×C22⋊D11—21no—
53C22×Dic11D411yescharacteristic
54D4×D11—42no—
55D4×D11—44no—
56C2×D44—21no—
57C2×D44—22no—
58C2×D44—22no—
59C2×D44—21no—
60C2×D44—42no—
61C2×D44—44no—
62C2×D44C2311yescharacteristic
63C2×D44C2312yes—
64C2×C4×D11—21no—
65C2×C4×D11—42no—
66C2×C4×D11D411yescharacteristic
67C2×C4×D11D411yescharacteristic
68C2×C4×D11C2311yescharacteristic
69C2×C4×D11C2311yescharacteristic
70C2×C8×C11C2312yes—
71C11×C4⋊C4—21no—
72C11×C4⋊C4C2312yes—
73C11×C4⋊C4C2311yescharacteristic
74C11×C22⋊C4—21no—
75C22⋊Dic11—21no—
76#4323—42no—
77(C2×D11)⋊C4—21no—
78(C2×D11)⋊C4—22no—
79(C2×D11)⋊C4—22no—
80(C2×D11)⋊C4—21no—
81C4⋊Dic11C2311yescharacteristic
82Dic11⋊C4—21no—
83C2×C11⋊C8C2312yes—
84D88—42no—
85C8×D11—42no—
86#3186—111nomaximal, Sylow
87C23×C11—21no—
88C23×C11C2×D411yescharacteristic
89C22×D11—22no—
90C22×D11—21no—
91C22×D11—41no—
92C22×D11—41no—
93C22×D11—42no—
94C22×D11—42no—
95C22×D11—42no—
96C22×D11—42no—
97C22×D11—42no—
98C22×D11—42no—
99C22×D11D814yescomplemented
100C22×D11C2×D411yescharacteristic
101C22×D11C2×D411yescharacteristic
102D4×C11—22no—
103D4×C11—42no—
104C2×C4×C11—22no—
105C2×C4×C11—21no—
106C2×C4×C11—22no—
107C2×C4×C11—42no—
108C2×C4×C11C2×D411yescharacteristic
109C2×C4×C11C2411yescharacteristic
110C22⋊D11—42no—
111C22⋊D11—42no—
112C22⋊D11—42no—
113C2×Dic11—21no—
114C2×Dic11—41no—
115C2×Dic11C2×D411yescharacteristic
116C2×Dic11C2×D411yescharacteristic
117D44—22no—
118D44—22no—
119D44—22no—
120D44—42no—
121D44—44no—
122D44—44no—
123D44—42no—
124C4×D11—22no—
125C4×D11—22no—
126C4×D11—41no—
127C4×D11—41no—
128C4×D11—42no—
129C8×C11—22no—
130C11⋊C8—22no—
131C2×#121—111no—
132C2×#121—111no—
133#480—111no—
134#480—112no—
135#480D1111yescharacteristic, complemented
136#466—112no—
137#466—112no—
138#447—111no—
139#447—112no—
140#447—111no—
141C2×C22⋊C8—111no—
142C22×C11—21no—
143C22×C11—21no—
144C22×C11—41no—
145C22×C11—41no—
146C22×C11—41no—
147C22×C11C2×D812yes—
148C22×C11C22×D411yescharacteristic
149C2×D11—21no—
150C2×D11—21no—
151C2×D11—21no—
152C2×D11—21no—
153C2×D11—44no—
154C2×D11—42no—
155C2×D11—41no—
156C2×D11—42no—
157C2×D11—41no—
158C2×D11—42no—
159C2×D11—41no—
160C2×D11—84no—
161C2×D11—84no—
162C2×D11C2×D812yes—
163C2×D11C2×D812yes—
164C4×C11—21no—
165C4×C11—42no—
166C4×C11—41no—
167C4×C11H(5,𝔽2)12yes—
168Dic11—21no—
169Dic11—21no—
170Dic11—41no—
171C22×D4—111no—
172C22×D4—111no—
173C22×D4—221no—
174C22×D4—221no—
175C23×C4—111no—
176C2×D8—112no—
177C2×D8—112no—
178C22×C8—112no—
179#121—111no—
180#121—111no—
181#121—112no—
182#121—111no—
183#121—112no—
184#121—221no—
185#121—221no—
186#121—221no—
187#121—221no—
188#121C2×D1111yescharacteristic
189C2×C4⋊C4—111no—
190C2×C4⋊C4C2×D1111yescharacteristic, complemented
191C2×C22⋊C4—221no—
192C2×C22⋊C4—221no—
193#107—112no—
194#107C2×D1112yescomplemented
195#102—112no—
196#102—112no—
197#102—112no—
198#102C2×D1112yescomplemented
199C22⋊C8—111no—
200C22⋊C8—112no—
201C22⋊C8C2×D1111yescharacteristic, complemented
202C2×C11—22no—
203C2×C11—81no—
204C2×C11#53411yescharacteristic
205C2×C11C22×D811yescharacteristic
206C2×C11#57511yescharacteristic
207D11—22no—
208D11—22no—
209D11—82no—
210D11—81no—
211C24—111no—
212C24—221no—
213C24—221no—
214C2×D4—21no—
215C2×D4—112no—
216C2×D4—111no—
217C2×D4—221no—
218C2×D4—222no—
219C2×D4—222no—
220C2×D4—221no—
221C2×D4—221no—
222C2×D4—221no—
223C2×D4—221no—
224C2×D4—442no—
225C2×D4—444no—
226C2×D4—442no—
227C2×D4—444no—
228C2×D4C22×D1111yescharacteristic
229C22×C4—21no—
230C22×C4—111no—
231C22×C4—111no—
232C22×C4—111no—
233C22×C4—111no—
234C22×C4—111no—
235C22×C4—221no—
236C22×C4—442no—
237C22×C4C22×D1111yescharacteristic
238D8—442no—
239D8—442no—
240C2×C8—112no—
241C2×C8—442no—
242C2×C8C22×D1112yes—
243C4⋊C4—21no—
244C4⋊C4—111no—
245C4⋊C4—221no—
246C4⋊C4C22×D1111yescharacteristic
247C4⋊C4C22×D1112yes—
248C22⋊C4—21no—
249C22⋊C4—221no—
250C22⋊C4—222no—
251C22⋊C4—222no—
252C22⋊C4—221no—
253C22⋊C4—221no—
254C11#318611yescharacteristic, complemented, Sylow
255C23—21no—
256C23—111no—
257C23—111no—
258C23—114no—
259C23—222no—
260C23—221no—
261C23—441no—
262C23—441no—
263C23—442no—
264C23—442no—
265C23—442no—
266C23—442no—
267C23—442no—
268C23—442no—
269C23D4×D1111yescharacteristic
270D4—22no—
271D4—42no—
272D4—222no—
273D4—222no—
274D4—222no—
275D4—442no—
276D4—444no—
277D4—444no—
278D4—442no—
279D4—442no—
280D4—442no—
281D4—442no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—22no—
285C2×C4—42no—
286C2×C4—111no—
287C2×C4—111no—
288C2×C4—222no—
289C2×C4—222no—
290C2×C4—221no—
291C2×C4—441no—
292C2×C4—441no—
293C2×C4—442no—
294C2×C4—441no—
295C2×C4D4×D1111yescharacteristic
296C2×C4C23×D1111yescharacteristic
297C8—22no—
298C8—222no—
299C22—21no—
300C22—21no—
301C22—41no—
302C22—41no—
303C22—41no—
304C22—112no—
305C22—112no—
306C22—221no—
307C22—221no—
308C22—221no—
309C22—221no—
310C22—444no—
311C22—442no—
312C22—441no—
313C22—442no—
314C22—441no—
315C22—442no—
316C22—441no—
317C22—884no—
318C22—884no—
319C22D8×D1112yes—
320C22C2×D4×D1111yescharacteristic
321C4—21no—
322C4—42no—
323C4—41no—
324C4—221no—
325C4—221no—
326C4—441no—
327C4#6704212yes—
328C2—22no—
329C2—81no—
330C2—222no—
331C2—222no—
332C2—882no—
333C2—881no—
334C2#1062318411yescharacteristic
335C2C2×D8×D1111yescharacteristic
336C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#480C2
socleC22×C11C22×D4
hypercenter#480D11
hypocenterC11#3186
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. D11×#121C2semidirect
2. C2×#66948C2semidirect
3. C11×#480C2semidirect
4. #10622649C2semidirect
5. #10622580C2semidirect
6. #10622496C2semidirect
7. #10622495C2semidirect
8. #10622388C2semidirect
9. #10622386C2semidirect
10. #10622345C2semidirect
11. D11×C22⋊C8C2semidirect
13. C2×D4×D11C22semidirect
15. C22×D44C22semidirect
18. C2×C11×C4⋊C4C22semidirect
20. #66991C22semidirect
21. C2×#4323C22semidirect
24. C2×D88C22semidirect
25. C2×C8×D11C22semidirect
29. #66948C22semidirect
30. #66948C22semidirect
31. C4⋊C4×D11C22semidirect
34. C11×#107C22semidirect
35. C11×#102C22semidirect
36. C11×C22⋊C8C22semidirect
37. C22⋊(C11⋊C8)C22semidirect
38. #66885C22semidirect
39. (C2×D11)⋊C8C22semidirect
40. #66873C22semidirect
41. #66873C22semidirect
42. #66871C22semidirect
99. C22×D11D8semidirect
135. #480D11semidirect
190. C2×C4⋊C4C2×D11semidirect
194. #107C2×D11semidirect
198. #102C2×D11semidirect
201. C22⋊C8C2×D11semidirect
254. C11#3186semidirect

Maximal subgroups

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

subgroupindex
D11×#1212
C2×#669482
C11×#4802
#106226492
#106225802
#106224962
#106224952
#106223882
#106223862
#106223452
D11×C22⋊C82
#318611