Finite Group Databasebeta

← #13076682

Subgroups — #13076682

Order 1408.

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

normal subgroups only

This group has 380 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
1C2×#66942C212yesmaximal
2C11×#398C211yesmaximal, characteristic
3#10622597C212yesmaximal
4#10622597C212yesmaximal
5#10622596C211yesmaximal, characteristic
6#10622590C211yesmaximal, characteristic
7#10622273C212yesmaximal
8#10622271C212yesmaximal
9#10622270C212yesmaximal
10C2×C11×C4⋊C4C2212yes—
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×C4⋊Dic11C2212yes—
14C2×C4⋊Dic11C2211yescharacteristic
15C2×C4⋊Dic11C2211yescharacteristic
16C2×Dic11⋊C4C2212yes—
17C2×Dic11⋊C4C2212yes—
18C2×Dic11⋊C4C2212yes—
19C2×Dic11⋊C4C2212yes—
20C2×Dic11⋊C4C2212yes—
21C2×C4×Dic11C2211yescharacteristic
22#66942—28no—
23C11×#95C2212yes—
24C11×#95C2211yescharacteristic
25C11⋊#95C2212yes—
26C11⋊#95C2212yes—
27C11⋊#95C2212yes—
28C11⋊#95C2212yes—
29C11⋊#95C2212yes—
30C11⋊#95C2211yescharacteristic
31C11⋊#95C2212yes—
32C22×C4×C11C2311yescharacteristic
33C22×C4×C11C2311yescharacteristic
34C22×C4×C11C2312yes—
35C22×C4×C11C2312yes—
36C22×C4×C11C2311yescharacteristic
37C22×Dic11C2312yes—
38C22×Dic11C2312yes—
39C22×Dic11C2312yes—
40C22×Dic11C2312yes—
41C11×C4⋊C4—24no—
42C11×C4⋊C4—41no—
43C11×C4⋊C4—41no—
44C4⋊Dic11—24no—
45C4⋊Dic11—41no—
46C4⋊Dic11—41no—
47Dic11⋊C4—24no—
48Dic11⋊C4—24no—
49Dic11⋊C4—24no—
50Dic11⋊C4—24no—
51Dic11⋊C4—42no—
52C4×Dic11D414yes—
53#2822—111nomaximal, Sylow
54C23×C11C2411yescharacteristic
55C2×C4×C11—21no—
56C2×C4×C11—21no—
57C2×C4×C11—22no—
58C2×C4×C11—22no—
59C2×C4×C11—22no—
60C2×C4×C11—21no—
61C2×C4×C11—21no—
62C2×C4×C11—22no—
63C2×C4×C11—22no—
64C2×C4×C11—22no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11C2×D412yes—
68C2×Dic11—22no—
69C2×Dic11—22no—
70C2×Dic11—22no—
71C2×Dic11—22no—
72C2×Dic11—22no—
73C2×Dic11—22no—
74C2×Dic11—22no—
75C2×Dic11—24no—
76C2×Dic11—22no—
77C2×Dic11—22no—
78C2×Dic11C2×D414yes—
79C2×#125—112no—
80#400—112no—
81#400—112no—
82#398—111no—
83#398—112no—
84#398—112no—
85#398—112no—
86#398D1111yescharacteristic
87#382—111no—
88C22×C11C22×D411yescharacteristic
89C22×C11H(5,𝔽2)11yescharacteristic
90C22×C112−1+412yes—
91C22×C112−1+412yes—
92C22×C112−1+411yescharacteristic
93C4×C11—22no—
94C4×C11—42no—
95C4×C11—42no—
96C4×C11—41no—
97C4×C11—41no—
98Dic11—24no—
99Dic11—42no—
100Dic11—42no—
101Dic11—42no—
102#125—228no—
103C2×C4⋊C4—112no—
104C2×C4⋊C4—112no—
105C2×C4⋊C4—112no—
106C2×C4⋊C4—112no—
107C2×C4⋊C4—112no—
108C2×C4⋊C4—111no—
109C2×C4⋊C4—112no—
110C2×C4⋊C4—111no—
111C2×C4⋊C4C2×D1112yes—
112C2×C4⋊C4C2×D1111yescharacteristic
113C2×C4⋊C4C2×D1111yescharacteristic
114C2×C42—111no—
115#95—112no—
116#95—112no—
117#95—112no—
118#95—112no—
119#95—112no—
120#95—112no—
121#95—111no—
122#95C2×D1112yes—
123#95C2×D1111yescharacteristic
124C2×C11#53612yes—
125C2×C11#53711yescharacteristic
126C2×C11#56311yescharacteristic
127C2×C11#56311yescharacteristic
128C2×C11#56412yes—
129C22×C4—112no—
130C22×C4—112no—
131C22×C4—112no—
132C22×C4—112no—
133C22×C4C22×D1111yescharacteristic
134C22×C4C22×D1111yescharacteristic
135C22×C4C22×D1112yes—
136C22×C4C22×D1112yes—
137C22×C4C22×D1111yescharacteristic
138C4⋊C4—24no—
139C4⋊C4—41no—
140C4⋊C4—41no—
141C4⋊C4—224no—
142C4⋊C4—224no—
143C4⋊C4—224no—
144C4⋊C4—224no—
145C4⋊C4—224no—
146C4⋊C4—442no—
147C4⋊C4—441no—
148C4⋊C4—441no—
149C42—114no—
150C11#282211yescharacteristic, complemented, Sylow
151C23C23×D1111yescharacteristic
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—114no—
165C2×C4—222no—
166C2×C4—222no—
167C2×C4—222no—
168C2×C4—222no—
169C2×C4—222no—
170C2×C4—222no—
171C2×C4—224no—
172C2×C4—222no—
173C2×C4—222no—
174C2×C4—222no—
175C2×C4D4×D1112yes—
176C22C2×D4×D1111yescharacteristic
177C22#6703711yescharacteristic
178C22#6704012yes—
179C22#6704311yescharacteristic
180C22#6704312yes—
181C4—22no—
182C4—42no—
183C4—42no—
184C4—41no—
185C4—41no—
186C4—224no—
187C4—442no—
188C4—442no—
189C4—442no—
190C2#1062312811yescharacteristic
191C2#1062315912yes—
192C2#1062318211yescharacteristic
193C2C11⋊#56412yes—
194C2#1062326611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#398C2
hypercenter#398D11
hypocenterC11#2822
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
150. C11#2822semidirect

Maximal subgroups

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

subgroupindex
C2×#669422
C11×#3982
#106225972
#106225962
#106225902
#106222732
#106222712
#106222702
#282211