Finite Group Databasebeta

← #13076667

Subgroups — #13076667

Order 1408.

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

normal subgroups only

This group has 464 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
1C2×C11×#124C211yesmaximal, characteristic
2C2×#66923C211yesmaximal, characteristic, complemented
3#10622842C212yesmaximal, complemented
4#10622835C212yesmaximal
5#10622566C212yesmaximal, complemented
6#10622562C212yesmaximal, complemented
7#10622561C214yesmaximal, complemented
8#10622549C211yesmaximal, characteristic, complemented
9C22×Q8×C11C2211yescharacteristic
10C22×D4×C11C2211yescharacteristic
11C11×#124—24no—
12C2×C11×C22⋊C4C2212yes—
13C2×C11×C22⋊C4C2212yes—
14C2×C42×C11C2211yescharacteristic
15C2×C22⋊Dic11C2214yes—
16C2×C22⋊Dic11C2214yes—
17C2×C4⋊Dic11C2211yescharacteristic
18C2×C4⋊Dic11C2211yescharacteristic
19C2×C4⋊Dic11C2212yes—
20C2×Dic11⋊C4C2212yes—
21C2×Dic11⋊C4C2212yes—
22C2×Dic11⋊C4C2214yes—
23#66923—24no—
24C11⋊#95C2212yes—
25C11⋊#95C2212yes—
26C11⋊#95C2214yes—
27C24×C11C2312yes—
28C2×Q8×C11—22no—
29C2×Q8×C11—42no—
30C2×D4×C11—22no—
31C2×D4×C11—42no—
32C22×C4×C11C2312yes—
33C22×C4×C11C2311yescharacteristic
34C22×C4×C11C2311yescharacteristic
35C22×C4×C11C2311yescharacteristic
36C22×Dic11C2314yes—
37C22×Dic11C2312yes—
38C22×Dic11C2312yes—
39C11×C22⋊C4—24no—
40C11×C22⋊C4—24no—
41C42×C11D414yes—
42C22⋊Dic11—44no—
43C22⋊Dic11—44no—
44C4⋊Dic11—22no—
45C4⋊Dic11—22no—
46C4⋊Dic11—42no—
47Dic11⋊C4—24no—
48Dic11⋊C4—24no—
49Dic11⋊C4—44no—
50#2820—111nomaximal, Sylow
51C23×C11—22no—
52C23×C11—22no—
53C23×C11—24no—
54C23×C11—24no—
55C23×C11—22no—
56C23×C11C2411yescharacteristic
57Q8×C11—44no—
58D4×C11—44no—
59C2×C4×C11—21no—
60C2×C4×C11—22no—
61C2×C4×C11—22no—
62C2×C4×C11—21no—
63C2×C4×C11—22no—
64C2×C4×C11—24no—
65C2×C4×C11C2×D412yes—
66C2×C4×C11C2×D412yes—
67C2×C4×C11C2×D412yes—
68C2×Dic11—22no—
69C2×Dic11—22no—
70C2×Dic11—24no—
71C2×Dic11—24no—
72C2×Dic11—24no—
73C2×Dic11—22no—
74C2×Dic11—22no—
75C2×Dic11—24no—
76C2×#125—111no—
77C2×#124D1111yescharacteristic
78#399—112no—
79#397—112no—
80#396—114no—
81#395—112no—
82#394—112no—
83#382—111no—
84C22×C11—42no—
85C22×C11—42no—
86C22×C11—42no—
87C22×C11—44no—
88C22×C11—44no—
89C22×C11C22×D411yescharacteristic
90C22×C11H(5,𝔽2)12yes—
91C22×C11H(5,𝔽2)11yescharacteristic
92C22×C112−1+412yes—
93C22×C112−1+411yescharacteristic
94C4×C11—22no—
95C4×C11—22no—
96C4×C11—22no—
97C4×C11—42no—
98Dic11—42no—
99Dic11—42no—
100Dic11—44no—
101C22×Q8C2×D1111yescharacteristic
102C22×D4C2×D1111yescharacteristic
103#125—224no—
104#124—24no—
105C2×C4⋊C4—112no—
106C2×C4⋊C4—112no—
107C2×C4⋊C4—111no—
108C2×C4⋊C4—111no—
109C2×C4⋊C4—112no—
110C2×C4⋊C4—114no—
111C2×C22⋊C4—114no—
112C2×C22⋊C4—114no—
113C2×C22⋊C4C2×D1112yes—
114C2×C22⋊C4C2×D1112yes—
115C2×C42C2×D1111yescharacteristic
116#95—112no—
117#95—112no—
118#95—114no—
119C2×C11—82no—
120C2×C11#53511yescharacteristic
121C2×C11#53611yescharacteristic
122C2×C11#53711yescharacteristic
123C2×C11#56212yes—
124C2×C11#56312yes—
125C24C22×D1112yes—
126C2×Q8—22no—
127C2×Q8—42no—
128C2×D4—22no—
129C2×D4—42no—
130C22×C4—114no—
131C22×C4—112no—
132C22×C4—112no—
133C22×C4C22×D1112yes—
134C22×C4C22×D1111yescharacteristic
135C22×C4C22×D1111yescharacteristic
136C22×C4C22×D1111yescharacteristic
137C4⋊C4—224no—
138C4⋊C4—224no—
139C4⋊C4—222no—
140C4⋊C4—222no—
141C4⋊C4—444no—
142C4⋊C4—442no—
143C22⋊C4—24no—
144C22⋊C4—24no—
145C22⋊C4—444no—
146C22⋊C4—444no—
147C42C22⋊D1114yes—
148C11#282011yescharacteristic, complemented, Sylow
149C23—24no—
150C23—22no—
151C23—24no—
152C23—22no—
153C23—22no—
154C23C23×D1111yescharacteristic
155Q8—44no—
156D4—44no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—22no—
163C2×C4—224no—
164C2×C4—224no—
165C2×C4—222no—
166C2×C4—224no—
167C2×C4—222no—
168C2×C4—224no—
169C2×C4—222no—
170C2×C4—222no—
171C2×C4C2×C22⋊D1112yes—
172C2×C4C2×C22⋊D1112yes—
173C2×C4C2×C22⋊D1112yes—
174C22—42no—
175C22—42no—
176C22—42no—
177C22—44no—
178C22—44no—
179C22#6703712yes—
180C22#6704211yescharacteristic
181C22#6704312yes—
182C22#6704311yescharacteristic
183C22C22×C22⋊D1111yescharacteristic
184C4—22no—
185C4—22no—
186C4—22no—
187C4—42no—
188C4—442no—
189C4—442no—
190C4—444no—
191C2—82no—
192C2#1062320312yes—
193C2#1062321512yes—
194C2#1062333611yescharacteristic
195C2#1062335611yescharacteristic
196C2#1062336411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#124C2
prime radicalC22×D4×C11C22
hypercenterC2×#124D11
hypocenterC11#2820
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
2. C2×#66923C2semidirect
3. #10622842C2semidirect
5. #10622566C2semidirect
6. #10622562C2semidirect
7. #10622561C2semidirect
8. #10622549C2semidirect
148. C11#2820semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1242
C2×#669232
#106228422
#106228352
#106225662
#106225622
#106225612
#106225492
#282011