Finite Group Databasebeta

← #13080426

Subgroups — #13080426

Order 1408.

494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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#10623257C211yesmaximal, characteristic, complemented
2D4×D44C211yesmaximal, characteristic, complemented
3C11×#474C211yesmaximal, characteristic, complemented
4#10622701C211yesmaximal, characteristic, complemented
5C4×#4323C211yesmaximal, characteristic, complemented
6#10622496C212yesmaximal, complemented
7#10622495C212yesmaximal, complemented
8#10622456C211yesmaximal, characteristic, complemented
9#10622447C211yesmaximal, characteristic, complemented
10#10622386C212yesmaximal, complemented
11D11×#102C212yesmaximal, complemented
12C2×#4343—21no—
13C2×D4×D11C2212yes—
14C22×D44—21no—
15C11×C4⋊Q8C2211yescharacteristic, complemented
16C4×D4×C11C2211yescharacteristic
17#66999—21no—
18C2×#4323C2211yescharacteristic
19#66983—21no—
20C2×D88C2212yescomplemented
21C2×C8×D11C2212yescomplemented
22#66948C2212yes—
23#66948C2212yescomplemented
24#66947—22no—
25C4⋊C4×D11C2212yescomplemented
26#66935—22no—
27#66927C2211yescharacteristic
28C4×D44C2211yescharacteristic
29C4×D44C2211yescharacteristic, complemented
30C11×#107C2212yescomplemented
31C11×C4⋊C8C2211yescharacteristic, complemented
32C11×#102C2212yes—
33#66896C2211yescharacteristic
34#66885C2212yescomplemented
35(C2×D11)⋊C8C2212yescomplemented
36#66873C2212yescomplemented
37#66873C2211yescharacteristic, complemented
38#66873C2212yescomplemented
39#66871C2211yescharacteristic, complemented
40C4×C11⋊C8C2211yescharacteristic, complemented
41C23×D11—22no—
42C2×Q8×C11—21no—
43C2×D4×C11C2311yescharacteristic
44C22×C4×C11—21no—
45C2×C22⋊D11—22no—
46#4343—44no—
47D4×D11—24no—
48D4×D11—42no—
49C2×D44—22no—
50C2×D44—22no—
51C2×D44—21no—
52C2×D44—21no—
53C2×D44—44no—
54C2×D44D411yescharacteristic
55C2×D44C2312yes—
56C2×D44C2311yescharacteristic
57C2×C4×D11—22no—
58C2×C4×D11—21no—
59C2×C4×D11C2312yes—
60C2×C8×C11C2312yes—
61C11×C4⋊C4—21no—
62C11×C4⋊C4C2311yescharacteristic
63C11×C4⋊C4C2312yes—
64C11×C22⋊C4—21no—
65C42×C11C2311yescharacteristic
66#4323—22no—
67(C2×D11)⋊C4—22no—
68(C2×D11)⋊C4—22no—
69(C2×D11)⋊C4—21no—
70(C2×D11)⋊C4D412yes—
71C4⋊Dic11D411yescharacteristic
72C4⋊Dic11C2311yescharacteristic
73Dic11⋊C4—22no—
74C2×C11⋊C8C2311yescharacteristic
75C2×C11⋊C8C2311yescharacteristic
76D88—42no—
77C8×D11—42no—
78#3294—111nomaximal, Sylow
79C23×C11—21no—
80C22×D11—21no—
81C22×D11—22no—
82C22×D11—44no—
83C22×D11—44no—
84C22×D11—82no—
85C22×D11C2×D412yes—
86Q8×C11—42no—
87D4×C11—21no—
88D4×C11#4112yescomplemented
89C2×C4×C11—22no—
90C2×C4×C11—21no—
91C2×C4×C11—42no—
92C2×C4×C11C2×D411yescharacteristic
93C2×C4×C11C2×D411yescharacteristic
94C2×C4×C11C2411yescharacteristic
95C22⋊D11—44no—
96C2×Dic11—21no—
97C2×Dic11C2×D412yes—
98D44—21no—
99D44—22no—
100D44—21no—
101D44—22no—
102D44—44no—
103D44—44no—
104D44—42no—
105D44—81no—
106D44D814yescomplemented
107C4×D11—22no—
108C4×D11—22no—
109C4×D11—44no—
110C4×D11—42no—
111C8×C11—22no—
112C11⋊C8—21no—
113C11⋊C8—21no—
114#547—111no—
115D42—111no—
116#486—111no—
117#480—112no—
118#474D1111yescharacteristic, complemented
119#466—112no—
120#459—111no—
121#447—112no—
122C4×D8—111no—
123C8×D4—111no—
124C2×#102—112no—
125C22×C11—22no—
126C22×C11—41no—
127C22×C11—41no—
128C22×C11C22×D411yescharacteristic
129C2×D11—22no—
130C2×D11—22no—
131C2×D11—42no—
132C2×D11—41no—
133C2×D11—42no—
134C2×D11—41no—
135C2×D11—41no—
136C2×D11—42no—
137C2×D11—88no—
138C2×D11C2×D814yes—
139C4×C11—21no—
140C4×C11—41no—
141C4×C11—42no—
142C4×C11C2×D812yes—
143C4×C11C2×#4111yescharacteristic
144C4×C11H(5,𝔽2)11yescharacteristic
145Dic11—22no—
146Dic11—41no—
147C2×#41—221no—
148C22×D4—112no—
149C22×D4—221no—
150C2×D8—111no—
151C2×D8—112no—
152C22×C8—112no—
153C4⋊Q8C2×D1111yescharacteristic, complemented
154#127—111no—
155#123—222no—
156C22⋊Q8—221no—
157#121—112no—
158#121—112no—
159#121—221no—
160#120—222no—
161C4×D4—111no—
162C4×D4—111no—
163C4×D4C2×D1111yescharacteristic
164C2×C4⋊C4—112no—
165#107—111no—
166#107C2×D1112yescomplemented
167C4⋊C8C2×D1111yescharacteristic, complemented
168#102—111no—
169#102—112no—
170#102—112no—
171#102—111no—
172#102—112no—
173#102C2×D1112yes—
174C22⋊C8—112no—
175C4×C8—111no—
176C2×C11—42no—
177C2×C11#54611yescharacteristic
178C2×C11C22×D811yescharacteristic
179C2×C11#57711yescharacteristic
180D11—24no—
181D11—81no—
182D11—82no—
183C24—222no—
184#41—444no—
185C2×Q8—21no—
186C2×D4—111no—
187C2×D4—112no—
188C2×D4—111no—
189C2×D4—222no—
190C2×D4—222no—
191C2×D4—222no—
192C2×D4—224no—
193C2×D4—221no—
194C2×D4—221no—
195C2×D4—444no—
196C2×D4—442no—
197C2×D4C22×D1111yescharacteristic
198C22×C4—21no—
199C22×C4—112no—
200C22×C4—222no—
201C22×C4—221no—
202D8—222no—
203D8—442no—
204C2×C8—111no—
205C2×C8—111no—
206C2×C8—442no—
207C2×C8C22×D1112yes—
208C4⋊C4—21no—
209C4⋊C4—111no—
210C4⋊C4—111no—
211C4⋊C4—222no—
212C4⋊C4C22×D1112yes—
213C4⋊C4C22×D1111yescharacteristic
214C22⋊C4—21no—
215C22⋊C4—112no—
216C22⋊C4—222no—
217C22⋊C4—222no—
218C22⋊C4—221no—
219C42C22×D1111yescharacteristic
220C11#329411yescharacteristic, complemented, Sylow
221C23—21no—
222C23—112no—
223C23—221no—
224C23—222no—
225C23—444no—
226C23—444no—
227C23—882no—
228Q8—42no—
229D4—21no—
230D4—114no—
231D4—221no—
232D4—222no—
233D4—221no—
234D4—222no—
235D4—444no—
236D4—444no—
237D4—444no—
238D4—442no—
239D4—881no—
240D4#434312yescomplemented
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—42no—
244C2×C4—112no—
245C2×C4—222no—
246C2×C4—222no—
247C2×C4—221no—
248C2×C4—444no—
249C2×C4—442no—
250C2×C4D4×D1111yescharacteristic
251C2×C4D4×D1111yescharacteristic
252C2×C4C23×D1111yescharacteristic
253C8—22no—
254C8—221no—
255C8—221no—
256C22—22no—
257C22—41no—
258C22—41no—
259C22—114no—
260C22—222no—
261C22—222no—
262C22—441no—
263C22—442no—
264C22—442no—
265C22—441no—
266C22—442no—
267C22—441no—
268C22—888no—
269C22C2×D4×D1111yescharacteristic
270C4—21no—
271C4—41no—
272C4—42no—
273C4—222no—
274C4—441no—
275C4D8×D1112yes—
276C4C2×#434311yescharacteristic
277C4#6704211yescharacteristic
278C2—42no—
279C2—224no—
280C2—882no—
281C2—881no—
282C2#1062316111yescharacteristic
283C2C2×D8×D1111yescharacteristic
284C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#474C2
socleC22×C11C22×D4
hypercenter#474D11
hypocenterC11#3294
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #10623257C2semidirect
2. D4×D44C2semidirect
3. C11×#474C2semidirect
4. #10622701C2semidirect
5. C4×#4323C2semidirect
6. #10622496C2semidirect
7. #10622495C2semidirect
8. #10622456C2semidirect
9. #10622447C2semidirect
10. #10622386C2semidirect
11. D11×#102C2semidirect
15. C11×C4⋊Q8C22semidirect
20. C2×D88C22semidirect
21. C2×C8×D11C22semidirect
23. #66948C22semidirect
25. C4⋊C4×D11C22semidirect
29. C4×D44C22semidirect
30. C11×#107C22semidirect
31. C11×C4⋊C8C22semidirect
34. #66885C22semidirect
35. (C2×D11)⋊C8C22semidirect
36. #66873C22semidirect
37. #66873C22semidirect
38. #66873C22semidirect
39. #66871C22semidirect
40. C4×C11⋊C8C22semidirect
88. D4×C11#41semidirect
106. D44D8semidirect
118. #474D11semidirect
153. C4⋊Q8C2×D11semidirect
166. #107C2×D11semidirect
167. C4⋊C8C2×D11semidirect
220. C11#3294semidirect
240. D4#4343semidirect

Maximal subgroups

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

subgroupindex
#106232572
D4×D442
C11×#4742
#106227012
C4×#43232
#106224962
#106224952
#106224562
#106224472
#106223862
D11×#1022
#329411