Finite Group Databasebeta

← #13081513

Subgroups — #13081513

Order 1408.

374 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 133 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#10623074C211yesmaximal, characteristic, complemented
2D4×Dic22C211yesmaximal, characteristic, complemented
3C4×C11×D8C211yesmaximal, characteristic
4#10622765C212yesmaximal
5#10622621C211yesmaximal, characteristic, complemented
6#10622620C211yesmaximal, characteristic, complemented
7#10622489C212yesmaximal, complemented
8#10622376C212yesmaximal, complemented
9#10622374C212yesmaximal, complemented
10#10622293C211yesmaximal, characteristic, complemented
11#10622292C211yesmaximal, characteristic, complemented
12C22×Dic22—21no—
13C2×C11×D8C2211yescharacteristic
14C4×D4×C11C2211yescharacteristic
15C4×D4×C11C2211yescharacteristic
16D4×Dic11C2212yes—
17D4×Dic11C2212yes—
18C2×C4⋊Dic11—21no—
19#66977—21no—
20#66977—21no—
21#66943C2212yes—
22#66941C2212yes—
23#66931—22no—
24#66931—22no—
25#66922C2211yescharacteristic
26#66922C2211yescharacteristic
27C4×Dic22C2211yescharacteristic
28C11×#107C2211yescharacteristic
29C11×#102C2211yescharacteristic
30C11×#102C2211yescharacteristic
31C4×C8×C11C2211yescharacteristic
32#66896C2212yes—
33#66896C2212yes—
34#66881C2212yes—
35#66881C2212yes—
36#66879C2212yes—
37Dic11⋊C8C2212yes—
38#66872C2212yes—
39#66871C2212yes—
40C4⋊(C11⋊C8)C2211yescharacteristic
41C2×D4×C11C2311yescharacteristic
42C2×D4×C11C2311yescharacteristic
43C22×C4×C11—21no—
44C22×C4×C11—21no—
45C22×Dic11—22no—
46C22×Dic11—22no—
47C2×Dic22—22no—
48C2×Dic22—21no—
49C2×Dic22—21no—
50C2×Dic22—44no—
51C2×Dic22D411yescharacteristic
52C11×D8Q814yescomplemented
53C2×C8×C11C2311yescharacteristic
54C2×C8×C11C2311yescharacteristic
55C11×C4⋊C4C2311yescharacteristic
56C11×C4⋊C4C2311yescharacteristic
57C11×C22⋊C4—21no—
58C11×C22⋊C4—21no—
59C42×C11C2311yescharacteristic
60C22⋊Dic11—22no—
61C22⋊Dic11—22no—
62C4⋊Dic11—22no—
63C4⋊Dic11—21no—
64C4⋊Dic11—21no—
65C4⋊Dic11D411yescharacteristic
66C4⋊Dic11C2312yes—
67C4⋊Dic11C2312yes—
68Dic11⋊C4—22no—
69Dic11⋊C4—22no—
70Dic11⋊C4D412yes—
71C4×Dic11C2312yes—
72C2×C11⋊C8C2312yes—
73#3384—111nomaximal, Sylow
74C23×C11—21no—
75C23×C11—21no—
76D4×C11—21no—
77D4×C11—21no—
78D4×C11C2×Q812yes—
79D4×C11C2×Q812yescomplemented
80C2×C4×C11—21no—
81C2×C4×C11—21no—
82C2×C4×C11—42no—
83C2×C4×C11—42no—
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11C2×D411yescharacteristic
86C2×C4×C11C2411yescharacteristic
87C2×Dic11—22no—
88C2×Dic11—22no—
89C2×Dic11—44no—
90C2×Dic11—82no—
91C2×Dic11C2×D412yes—
92C2×Dic11C2×D412yes—
93Dic22—22no—
94Dic22—44no—
95Dic22—42no—
96Dic22—81no—
97C8×C11—21no—
98C8×C11C2×Q812yescomplemented
99C11⋊C8—22no—
100#554—111no—
101D4×Q8—111no—
102#501—112no—
103#498—111no—
104#478—112no—
105#476—111no—
106#476—112no—
107#474—111no—
108#446—111no—
109#442—112no—
110C4×D8D1111yescharacteristic
111C22×C11—22no—
112C22×C11—22no—
113C22×C11—41no—
114C22×C11—41no—
115C22×C11—41no—
116C22×C11—41no—
117C22×C11C22×D411yescharacteristic
118C4×C11—21no—
119C4×C11—41no—
120C4×C11—41no—
121C4×C11AGL(1,ℤ/8)12yes—
122C4×C11C22×Q811yescharacteristic
123C4×C112−1+411yescharacteristic
124Dic11—22no—
125Dic11—22no—
126Dic11—42no—
127Dic11—42no—
128C22×Q8—221no—
129C2×D8C2×D1111yescharacteristic
130C4⋊Q8—112no—
131C4⋊Q8—111no—
132C4⋊Q8—111no—
133#125—112no—
134C22⋊Q8—222no—
135C22⋊Q8—222no—
136C22⋊Q8—221no—
137C22⋊Q8—221no—
138C4×Q8—111no—
139C4×D4—112no—
140C4×D4—112no—
141C4×D4C2×D1111yescharacteristic
142C4×D4C2×D1111yescharacteristic
143C2×C4⋊C4—221no—
144#107—112no—
145#107C2×D1111yescharacteristic
146#106—112no—
147#106—112no—
148#106—112no—
149C4⋊C8—112no—
150C4⋊C8—111no—
151#102—112no—
152#102—112no—
153#102C2×D1111yescharacteristic
154#102C2×D1111yescharacteristic
155#97—112no—
156C4×C8C2×D1111yescharacteristic
157C2×C11—42no—
158C2×C11—42no—
159C2×C11D4×Q811yescharacteristic
160C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
161C2×C11#57711yescharacteristic
162C2×Q8—111no—
163C2×Q8—222no—
164C2×Q8—221no—
165C2×Q8—221no—
166C2×Q8—444no—
167C2×D4C22×D1111yescharacteristic
168C2×D4C22×D1111yescharacteristic
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—222no—
172C22×C4—222no—
173D8Dic2214yescomplemented
174C2×C8—112no—
175C2×C8C22×D1111yescharacteristic
176C2×C8C22×D1111yescharacteristic
177C4⋊C4—111no—
178C4⋊C4—112no—
179C4⋊C4—112no—
180C4⋊C4—112no—
181C4⋊C4—222no—
182C4⋊C4—222no—
183C4⋊C4—222no—
184C4⋊C4—221no—
185C4⋊C4—221no—
186C4⋊C4C22×D1111yescharacteristic
187C4⋊C4C22×D1111yescharacteristic
188C22⋊C4—21no—
189C22⋊C4—21no—
190C22⋊C4—222no—
191C22⋊C4—222no—
192C42—112no—
193C42C22×D1111yescharacteristic
194C11#338411yescharacteristic, complemented, Sylow
195C23—21no—
196C23—21no—
197Q8—222no—
198Q8—444no—
199Q8—442no—
200Q8—881no—
201D4—21no—
202D4—21no—
203D4C2×Dic2212yes—
204D4C2×Dic2212yescomplemented
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—112no—
210C2×C4—112no—
211C2×C4—222no—
212C2×C4—222no—
213C2×C4—444no—
214C2×C4—882no—
215C2×C4D4×D1111yescharacteristic
216C2×C4D4×D1111yescharacteristic
217C2×C4C23×D1111yescharacteristic
218C8—21no—
219C8—222no—
220C8C2×Dic2212yescomplemented
221C22—22no—
222C22—22no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—41no—
227C22C2×D4×D1111yescharacteristic
228C4—21no—
229C4—41no—
230C4—41no—
231C4—222no—
232C4—222no—
233C4—442no—
234C4—442no—
235C4#6696412yes—
236C4C22×Dic2211yescharacteristic
237C4#6704311yescharacteristic
238C2—42no—
239C2—42no—
240C2D4×Dic2211yescharacteristic
241C2C2×#6696411yescharacteristic
242C2#1062330111yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC4×C11×D8C2
socleC22×C11C22×D4
prime radicalC2×C11×D8C22
hypercenterC4×D8D11
hypocenterC11#3384
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #10623074C2semidirect
2. D4×Dic22C2semidirect
5. #10622621C2semidirect
6. #10622620C2semidirect
7. #10622489C2semidirect
8. #10622376C2semidirect
9. #10622374C2semidirect
10. #10622293C2semidirect
11. #10622292C2semidirect
52. C11×D8Q8semidirect
79. D4×C11C2×Q8semidirect
98. C8×C11C2×Q8semidirect
173. D8Dic22semidirect
194. C11#3384semidirect
204. D4C2×Dic22semidirect
220. C8C2×Dic22semidirect

Maximal subgroups

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

subgroupindex
#106230742
D4×Dic222
C4×C11×D82
#106227652
#106226212
#106226202
#106224892
#106223762
#106223742
#106222932
#106222922
#338411