Finite Group Databasebeta

← #13079802

Subgroups — #13079802

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
1C11×#532C211yesmaximal, characteristic
2C2×#66923C211yesmaximal, characteristic, complemented
3#10622693C212yesmaximal, complemented
4#10622684C212yesmaximal, complemented
5#10622647C212yesmaximal, complemented
6#10622646C212yesmaximal, complemented
7#10622622C214yesmaximal, complemented
8#10622539C211yesmaximal, characteristic, complemented
9C2×C11×#41—21no—
10C11×C4⋊Q8C2211yescharacteristic
11C11×#127C2211yescharacteristic
12C11×#124—21no—
13C11×#121—21no—
14C11×#121C2212yes—
15C4×D4×C11—21no—
16C4×D4×C11C2212yes—
17C2×C42×C11C2211yescharacteristic
18C2×C4⋊Dic11C2211yescharacteristic
19C2×C4⋊Dic11C2211yescharacteristic
20C2×Dic11⋊C4—21no—
21C2×Dic11⋊C4—21no—
22#66923—21no—
23#66923—21no—
24#66923C2212yes—
25#66923C2212yes—
26#66896C2214yes—
27#66896C2214yes—
28C22⋊(C11⋊C8)C2212yes—
29#66872C2214yes—
30#66871C2214yes—
31C4⋊(C11⋊C8)C2212yes—
32#66867C2212yes—
33C11×#41—44no—
34C2×Q8×C11—21no—
35C2×D4×C11—22no—
36C2×D4×C11—21no—
37C2×D4×C11—21no—
38C2×D4×C11C2312yes—
39C22×C4×C11—22no—
40C22×C4×C11D411yescharacteristic
41C22×C4×C11D411yescharacteristic
42C22×C4×C11C2311yescharacteristic
43C22×Dic11—21no—
44C22×Dic11—21no—
45C11×C4⋊C4—21no—
46C11×C4⋊C4C2312yes—
47C11×C22⋊C4—22no—
48C11×C22⋊C4—22no—
49C42×C11D411yescharacteristic
50C42×C11D411yescharacteristic
51C42×C11C2311yescharacteristic
52C42×C11C2311yescharacteristic
53C4⋊Dic11—21no—
54C4⋊Dic11—21no—
55C4⋊Dic11C2312yes—
56C4⋊Dic11C2312yes—
57Dic11⋊C4—22no—
58Dic11⋊C4—22no—
59Dic11⋊C4—22no—
60Dic11⋊C4—22no—
61C2×C11⋊C8C2314yes—
62#3234—111nomaximal, Sylow
63C23×C11—22no—
64C23×C11C2×D411yescharacteristic
65Q8×C11—42no—
66D4×C11—24no—
67D4×C11—42no—
68D4×C11—42no—
69D4×C11—44no—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—41no—
74C2×C4×C11—44no—
75C2×C4×C11C2×D411yescharacteristic
76C2×C4×C11C2×D411yescharacteristic
77C2×C4×C11C2×D411yescharacteristic
78C2×C4×C11C2×D411yescharacteristic
79C2×C4×C11C2×D411yescharacteristic
80C2×C4×C11C2411yescharacteristic
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11—42no—
84C2×Dic11—42no—
85C11⋊C8—24no—
86#532D1111yescharacteristic
87C2×#125—111no—
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×C11—42no—
97C22×C11—42no—
98C22×C11—42no—
99C22×C11AGL(1,ℤ/8)12yes—
100C22×C11C22×D411yescharacteristic
101C4×C11—21no—
102C4×C11—21no—
103C4×C11—21no—
104C4×C11—21no—
105C4×C11—21no—
106C4×C11—42no—
107C4×C112−1+412yes—
108Dic11—42no—
109Dic11—42no—
110C2×#41—21no—
111C4⋊Q8C2×D1111yescharacteristic
112#127C2×D1111yescharacteristic
113#125—112no—
114#125—112no—
115#125—221no—
116#125—221no—
117#124—21no—
118#121—21no—
119#121C2×D1112yes—
120C4×D4—21no—
121C4×D4C2×D1112yes—
122C2×C4⋊C4—111no—
123C2×C4⋊C4—111no—
124C2×C4⋊C4—221no—
125C2×C4⋊C4—221no—
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—82no—
136C2×C11#53611yescharacteristic
137C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C11#57511yescharacteristic
139#41—44no—
140C2×Q8—21no—
141C2×D4—22no—
142C2×D4—21no—
143C2×D4—21no—
144C2×D4C22×D1112yes—
145C22×C4—22no—
146C22×C4—221no—
147C22×C4—221no—
148C22×C4C22⋊D1111yescharacteristic
149C22×C4C22⋊D1111yescharacteristic
150C22×C4C22×D1111yescharacteristic
151C2×C8—114no—
152C4⋊C4—21no—
153C4⋊C4—112no—
154C4⋊C4—112no—
155C4⋊C4—221no—
156C4⋊C4—221no—
157C4⋊C4—222no—
158C4⋊C4—222no—
159C4⋊C4—222no—
160C4⋊C4—222no—
161C4⋊C4C22×D1112yes—
162C22⋊C4—22no—
163C22⋊C4—22no—
164C42C22⋊D1111yescharacteristic
165C42C22⋊D1111yescharacteristic
166C42C22×D1111yescharacteristic
167C42C22×D1111yescharacteristic
168C11#323411yescharacteristic, complemented, Sylow
169C23—22no—
170C23C2×C22⋊D1111yescharacteristic
171Q8—42no—
172D4—24no—
173D4—42no—
174D4—42no—
175D4—44no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—41no—
180C2×C4—44no—
181C2×C4—222no—
182C2×C4—222no—
183C2×C4—442no—
184C2×C4—442no—
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—42no—
195C22—42no—
196C22—42no—
197C22#6698512yes—
198C22C22×C22⋊D1111yescharacteristic
199C4—21no—
200C4—21no—
201C4—21no—
202C4—21no—
203C4—21no—
204C4—42no—
205C4—442no—
206C4—442no—
207C4#6704312yes—
208C2—22no—
209C2—82no—
210C2C2×#6698511yescharacteristic
211C2#1062335311yescharacteristic
212C2#1062335611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
Fitting, prime radicalC11×#532C2
socleC22×C11C22×D4
hypercenter#532D11
hypocenterC11#3234
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
2. C2×#66923C2semidirect
3. #10622693C2semidirect
4. #10622684C2semidirect
5. #10622647C2semidirect
6. #10622646C2semidirect
7. #10622622C2semidirect
8. #10622539C2semidirect
168. C11#3234semidirect

Maximal subgroups

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

subgroupindex
C11×#5322
C2×#669232
#106226932
#106226842
#106226472
#106226462
#106226222
#106225392
#323411