Finite Group Databasebeta

← #13079752

Subgroups — #13079752

Order 1408.

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

normal subgroups only

This group has 370 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
1C11×#533C211yesmaximal, characteristic, complemented
2#10623008C211yesmaximal, characteristic
3#10622701C211yesmaximal, characteristic, complemented
4#10622701C211yesmaximal, characteristic, complemented
5#10622692C211yesmaximal, characteristic, complemented
6#10622691C211yesmaximal, characteristic, complemented
7#10622679C214yesmaximal, complemented
8#10622616C214yesmaximal, complemented
9#10622538C211yesmaximal, characteristic, complemented
10C2×#4339—21no—
11C11×C4⋊Q8C2211yescharacteristic
12C11×C4⋊Q8C2211yescharacteristic
13C11×#125C2212yes—
14C11×C22⋊Q8—21no—
15C11×C22⋊Q8—21no—
16C4×Q8×C11—21no—
17C4×Q8×C11—21no—
18C11×#117C2212yes—
19C2×C42×C11C2211yescharacteristic
20#66983—21no—
21#66983C2212yes—
22#66928—21no—
23#66927C2211yescharacteristic
24C4×D44—21no—
25C4×D44C2212yes—
26#66922C2211yescharacteristic
27C22⋊(C11⋊C8)C2212yes—
28#66873C2214yes—
29#66873C2214yes—
30#66872C2214yes—
31#66871C2214yes—
32C4⋊(C11⋊C8)C2212yes—
33C4×C11⋊C8C2211yescharacteristic
34C4×C11⋊C8C2211yescharacteristic
35C2×Q8×C11—21no—
36C2×Q8×C11—21no—
37C22×C4×C11D411yescharacteristic
38C22×C4×C11D411yescharacteristic
39C22×C4×C11C2311yescharacteristic
40C2×C22⋊D11—22no—
41#4339—44no—
42C2×D44—21no—
43C2×D44—21no—
44C2×D44C2312yes—
45C2×C4×D11—22no—
46C2×Dic22—21no—
47C11×C4⋊C4—22no—
48C11×C4⋊C4—22no—
49C11×C4⋊C4—21no—
50C11×C4⋊C4—21no—
51C11×C4⋊C4C2312yes—
52C11×C4⋊C4C2312yes—
53C11×C22⋊C4—22no—
54C42×C11—22no—
55C42×C11D411yescharacteristic
56C42×C11D411yescharacteristic
57C42×C11C2311yescharacteristic
58C42×C11C2311yescharacteristic
59(C2×D11)⋊C4—22no—
60(C2×D11)⋊C4—22no—
61C4⋊Dic11—21no—
62C4⋊Dic11C2312yes—
63C2×C11⋊C8C2312yes—
64C2×C11⋊C8C2312yes—
65#3228—111nomaximal, Sylow
66C23×C11C2×D411yescharacteristic
67C22×D11—22no—
68Q8×C11—42no—
69Q8×C11—42no—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11C2×D411yescharacteristic
76C2×C4×C11C2×D411yescharacteristic
77C2×C4×C11C2×D411yescharacteristic
78C2×C4×C11C2×D411yescharacteristic
79C2×C4×C11C2×D411yescharacteristic
80C2×C4×C11C2411yescharacteristic
81C22⋊D11—44no—
82C2×Dic11—22no—
83D44—24no—
84D44—42no—
85D44—42no—
86C4×D11—44no—
87Dic22—42no—
88C11⋊C8—22no—
89C11⋊C8—22no—
90#533D1111yescharacteristic, complemented
91#532—111no—
92#500—111no—
93#498—111no—
94#486—111no—
95#486—111no—
96#482—114no—
97#478—114no—
98#431—111no—
99C22×C11—21no—
100C22×C11—21no—
101C22×C11—21no—
102C22×C11C22×D411yescharacteristic
103C2×D11—42no—
104C2×D11—42no—
105C2×D11—42no—
106C4×C11—21no—
107C4×C11—21no—
108C4×C11—21no—
109C4×C11—42no—
110C4×C11—42no—
111C4×C11#13512yes—
112C4×C11AGL(1,ℤ/8)12yes—
113C4×C112−1+412yes—
114Dic11—42no—
115C2×#41—221no—
116C4⋊Q8—111no—
117C4⋊Q8C2×D1111yescharacteristic
118C4⋊Q8C2×D1111yescharacteristic
119#127—111no—
120#125C2×D1112yes—
121#124—221no—
122C22⋊Q8—21no—
123C22⋊Q8—21no—
124#121—112no—
125#121—221no—
126C4×Q8—21no—
127C4×Q8—21no—
128C4×D4—112no—
129C4×D4—221no—
130#117C2×D1112yes—
131C2×C42C2×D1111yescharacteristic
132#107—114no—
133#106—114no—
134C4⋊C8—112no—
135#102—114no—
136#102—114no—
137C22⋊C8—112no—
138C4×C8—111no—
139C4×C8—111no—
140C2×C11—41no—
141C2×C11#53611yescharacteristic
142C2×C11C2×#13511yescharacteristic
143C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
144D11—82no—
145#41—444no—
146C2×Q8—21no—
147C2×Q8—21no—
148C2×Q8—221no—
149C2×D4—112no—
150C2×D4—222no—
151C2×D4—221no—
152C2×D4—221no—
153C22×C4—222no—
154C22×C4C22⋊D1111yescharacteristic
155C22×C4C22⋊D1111yescharacteristic
156C22×C4C22×D1111yescharacteristic
157C2×C8—112no—
158C2×C8—112no—
159C4⋊C4—22no—
160C4⋊C4—22no—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—112no—
164C4⋊C4—221no—
165C4⋊C4C22×D1112yes—
166C4⋊C4C22×D1112yes—
167C22⋊C4—22no—
168C22⋊C4—222no—
169C22⋊C4—222no—
170C42—22no—
171C42C22⋊D1111yescharacteristic
172C42C22⋊D1111yescharacteristic
173C42C22×D1111yescharacteristic
174C42C22×D1111yescharacteristic
175C11#322811yescharacteristic, complemented, Sylow
176C23—222no—
177C23C2×C22⋊D1111yescharacteristic
178Q8—42no—
179Q8—42no—
180Q8—442no—
181D4—224no—
182D4—444no—
183D4—442no—
184D4—442no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—222no—
191C2×C4—444no—
192C2×C4C2×C22⋊D1111yescharacteristic
193C2×C4C2×C22⋊D1111yescharacteristic
194C2×C4C2×C22⋊D1111yescharacteristic
195C2×C4C2×C22⋊D1111yescharacteristic
196C2×C4C2×C22⋊D1111yescharacteristic
197C2×C4C23×D1111yescharacteristic
198C8—222no—
199C8—222no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—442no—
204C22—442no—
205C22—442no—
206C22C22×C22⋊D1111yescharacteristic
207C4—21no—
208C4—21no—
209C4—21no—
210C4—42no—
211C4—42no—
212C4—442no—
213C4#6700212yes—
214C4#6700312yes—
215C4#6704012yes—
216C2—41no—
217C2—882no—
218C2#1062334711yescharacteristic
219C2C2×#6700211yescharacteristic
220C2C2×#6700311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#533C2
socleC22×C11C22×D4
prime radical#10623008C2
hypercenter#533D11
hypocenterC11#3228
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
1. C11×#533C2semidirect
3. #10622701C2semidirect
4. #10622701C2semidirect
5. #10622692C2semidirect
6. #10622691C2semidirect
7. #10622679C2semidirect
8. #10622616C2semidirect
9. #10622538C2semidirect
90. #533D11semidirect
175. C11#3228semidirect

Maximal subgroups

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

subgroupindex
C11×#5332
#106230082
#106227012
#106226922
#106226912
#106226792
#106226162
#106225382
#322811