Finite Group Databasebeta

← #13079806

Subgroups — #13079806

Order 1408.

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

normal subgroups only

This group has 368 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
1C2×C11×#125C211yesmaximal, characteristic, complemented
2#10623008C211yesmaximal, characteristic
3#10622680C212yesmaximal, complemented
4#10622679C214yesmaximal, complemented
5#10622678C212yesmaximal, complemented
6#10622581C212yesmaximal, complemented
7#10622580C212yesmaximal, complemented
8#10622539C211yesmaximal, characteristic, complemented
9C2×#4339—21no—
10C11×#125—21no—
11C11×#125—21no—
12C11×#125C2212yes—
13C11×#125C2212yes—
14C2×C11×C4⋊C4—21no—
15C2×C11×C4⋊C4—21no—
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C42×C11C2211yescharacteristic
19#66983—21no—
20#66983C2212yes—
21#66928—21no—
22#66927C2211yescharacteristic
23C4×D44—21no—
24C4×D44C2212yes—
25#66922C2211yescharacteristic
26C22⋊(C11⋊C8)C2212yes—
27#66873C2214yes—
28#66873C2214yes—
29#66872C2214yes—
30#66871C2214yes—
31C4⋊(C11⋊C8)C2212yes—
32#66867C2212yes—
33C22×C4×C11—21no—
34C22×C4×C11—21no—
35C22×C4×C11D411yescharacteristic
36C22×C4×C11D411yescharacteristic
37C22×C4×C11C2311yescharacteristic
38C2×C22⋊D11—22no—
39#4339—44no—
40C2×D44—21no—
41C2×D44—21no—
42C2×D44C2312yes—
43C2×C4×D11—22no—
44C2×Dic22—21no—
45C11×C4⋊C4—22no—
46C11×C4⋊C4—22no—
47C11×C4⋊C4—22no—
48C11×C4⋊C4—22no—
49C11×C4⋊C4—21no—
50C11×C4⋊C4—21no—
51C11×C4⋊C4C2312yes—
52C11×C4⋊C4C2312yes—
53C42×C11D411yescharacteristic
54C42×C11D411yescharacteristic
55C42×C11C2311yescharacteristic
56C42×C11C2311yescharacteristic
57(C2×D11)⋊C4—22no—
58(C2×D11)⋊C4—22no—
59C4⋊Dic11—21no—
60C4⋊Dic11C2312yes—
61C2×C11⋊C8C2314yes—
62#3234—111nomaximal, Sylow
63C23×C11C2×D411yescharacteristic
64C22×D11—22no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—22no—
68C2×C4×C11—22no—
69C2×C4×C11—41no—
70C2×C4×C11—42no—
71C2×C4×C11—42no—
72C2×C4×C11C2×D411yescharacteristic
73C2×C4×C11C2×D411yescharacteristic
74C2×C4×C11C2×D411yescharacteristic
75C2×C4×C11C2×D411yescharacteristic
76C2×C4×C11C2×D411yescharacteristic
77C2×C4×C11C2411yescharacteristic
78C22⋊D11—44no—
79C2×Dic11—22no—
80D44—24no—
81D44—42no—
82D44—42no—
83C4×D11—44no—
84Dic22—42no—
85C11⋊C8—24no—
86#532—111no—
87C2×#125D1111yescharacteristic, complemented
88#501—112no—
89#490—112no—
90#481—112no—
91#480—112no—
92#478—114no—
93#432—111no—
94C22×C11—21no—
95C22×C11—21no—
96C22×C11AGL(1,ℤ/8)12yes—
97C22×C11C22×D411yescharacteristic
98C2×D11—42no—
99C2×D11—42no—
100C2×D11—42no—
101C4×C11—21no—
102C4×C11—21no—
103C4×C11—21no—
104C4×C11—21no—
105C4×C11—21no—
106C4×C11—42no—
107C4×C11—42no—
108C4×C112−1+412yes—
109Dic11—42no—
110C2×#41—221no—
111C4⋊Q8—111no—
112#127—111no—
113#125—21no—
114#125—21no—
115#125C2×D1112yes—
116#125C2×D1112yes—
117#124—221no—
118#121—112no—
119#121—221no—
120C4×D4—112no—
121C4×D4—221no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4C2×D1111yescharacteristic
125C2×C4⋊C4C2×D1111yescharacteristic
126C2×C42C2×D1111yescharacteristic
127#107—114no—
128#106—114no—
129C4⋊C8—112no—
130#102—114no—
131#102—114no—
132C22⋊C8—112no—
133#97—112no—
134C2×C11—22no—
135C2×C11#53611yescharacteristic
136C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
137C2×C11#57511yescharacteristic
138D11—82no—
139#41—444no—
140C2×Q8—221no—
141C2×D4—112no—
142C2×D4—222no—
143C2×D4—221no—
144C2×D4—221no—
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—222no—
148C22×C4C22⋊D1111yescharacteristic
149C22×C4C22⋊D1111yescharacteristic
150C22×C4C22×D1111yescharacteristic
151C2×C8—114no—
152C4⋊C4—22no—
153C4⋊C4—22no—
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—112no—
159C4⋊C4—221no—
160C4⋊C4C22×D1112yes—
161C4⋊C4C22×D1112yes—
162C22⋊C4—222no—
163C22⋊C4—222no—
164C42C22⋊D1111yescharacteristic
165C42C22⋊D1111yescharacteristic
166C42C22×D1111yescharacteristic
167C42C22×D1111yescharacteristic
168C11#323411yescharacteristic, complemented, Sylow
169C23—222no—
170C23C2×C22⋊D1111yescharacteristic
171Q8—442no—
172D4—224no—
173D4—442no—
174D4—442no—
175D4—444no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—41no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—222no—
184C2×C4—444no—
185C2×C4C2×C22⋊D1111yescharacteristic
186C2×C4C2×C22⋊D1111yescharacteristic
187C2×C4C2×C22⋊D1111yescharacteristic
188C2×C4C2×C22⋊D1111yescharacteristic
189C2×C4C2×C22⋊D1111yescharacteristic
190C2×C4C23×D1111yescharacteristic
191C8—224no—
192C22—21no—
193C22—21no—
194C22—442no—
195C22—442no—
196C22—442no—
197C22#6700212yes—
198C22C22×C22⋊D1111yescharacteristic
199C4—21no—
200C4—21no—
201C4—21no—
202C4—21no—
203C4—21no—
204C4—42no—
205C4—42no—
206C4—442no—
207C4#6704012yes—
208C2—22no—
209C2—882no—
210C2#1062334711yescharacteristic
211C2C2×#6700211yescharacteristic
212C2#1062335311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×#125C2
socleC22×C11C22×D4
prime radical#10623008C2
hypercenterC2×#125D11
hypocenterC11#3234
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. C2×C11×#125C2semidirect
3. #10622680C2semidirect
4. #10622679C2semidirect
5. #10622678C2semidirect
6. #10622581C2semidirect
7. #10622580C2semidirect
8. #10622539C2semidirect
87. C2×#125D11semidirect
168. C11#3234semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1252
#106230082
#106226802
#106226792
#106226782
#106225812
#106225802
#106225392
#323411