Finite Group Databasebeta

← #13074097

Subgroups — #13074097

Order 1408.

596 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 153 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×#121C211yesmaximal, characteristic
2C22×Dic11⋊C4C211yesmaximal, characteristic, complemented
3#10622835C212yesmaximal, complemented
4#10622833C212yesmaximal, complemented
5#10622833C212yesmaximal, complemented
6C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
7#10622595C212yesmaximal, complemented
8#10622558C214yesmaximal, complemented
9C22×D4×C11C2212yes—
10C22×D4×C11C2211yescharacteristic
11C23×C4×C11C2211yescharacteristic
12C23×Dic11C2211yescharacteristic
13C23×Dic11C2211yescharacteristic
14C11×#121—24no—
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×C11×C22⋊C4C2212yes—
17C2×C22⋊Dic11C2214yes—
18C2×C22⋊Dic11C2212yes—
19C2×C22⋊Dic11C2214yes—
20C2×Dic11⋊C4—24no—
21C2×Dic11⋊C4C2212yes—
22C2×Dic11⋊C4C2212yes—
23C2×C4×Dic11C2212yes—
24C11⋊#95C2214yes—
25C11⋊#95C2214yes—
26C11⋊#95C2212yes—
27C24×C11C2312yes—
28C24×C11C2311yescharacteristic
29C2×D4×C11—24no—
30C2×D4×C11—28no—
31C2×D4×C11—22no—
32C2×D4×C11—42no—
33C22×C4×C11—42no—
34C22×C4×C11D414yes—
35C22×C4×C11C2312yes—
36C22×C4×C11C2311yescharacteristic
37C22×C4×C11C2311yescharacteristic
38C22×Dic11—24no—
39C22×Dic11—22no—
40C22×Dic11—22no—
41C22×Dic11—42no—
42C22×Dic11C2314yes—
43C22×Dic11C2312yes—
44C22×Dic11C2312yes—
45C11×C4⋊C4—22no—
46C11×C22⋊C4—24no—
47C22⋊Dic11—28no—
48C22⋊Dic11—24no—
49C22⋊Dic11—44no—
50Dic11⋊C4—24no—
51Dic11⋊C4—24no—
52C4×Dic11—42no—
53#2591—111nomaximal, Sylow
54C23×C11—22no—
55C23×C11—22no—
56C23×C11—22no—
57C23×C11—24no—
58C23×C11—24no—
59C23×C11—24no—
60C23×C11C2×D412yes—
61C23×C11#4114yes—
62C23×C11C2411yescharacteristic
63D4×C11—44no—
64D4×C11—48no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—22no—
68C2×C4×C11—24no—
69C2×C4×C11—44no—
70C2×C4×C11C2×D412yes—
71C2×C4×C11C2×D412yes—
72C2×Dic11—28no—
73C2×Dic11—22no—
74C2×Dic11—22no—
75C2×Dic11—22no—
76C2×Dic11—24no—
77C2×Dic11—24no—
78C2×Dic11—24no—
79C2×Dic11—24no—
80C2×Dic11—44no—
81C2×Dic11#4114yes—
82C2×#121D1111yescharacteristic
83C22×C4⋊C4—111no—
84#400—112no—
85#394—112no—
86#388—114no—
87#386—112no—
88#386—112no—
89C4×C22⋊C4—111no—
90C22×C11—22no—
91C22×C11—22no—
92C22×C11—28no—
93C22×C11—42no—
94C22×C11—42no—
95C22×C11—42no—
96C22×C11—48no—
97C22×C11#12414yes—
98C22×C11C22×D411yescharacteristic
99C22×C11C2×#4112yes—
100C22×C11C2×#4112yes—
101C22×C11H(5,𝔽2)12yes—
102C4×C11—22no—
103C4×C11—22no—
104C4×C11—42no—
105Dic11—24no—
106Dic11—42no—
107Dic11—44no—
108C22×D4C2×D1112yes—
109C22×D4C2×D1111yescharacteristic
110C23×C4—111no—
111C23×C4—111no—
112C23×C4C2×D1111yescharacteristic
113#121—24no—
114C2×C4⋊C4—112no—
115C2×C4⋊C4—112no—
116C2×C4⋊C4—224no—
117C2×C4⋊C4C2×D1111yescharacteristic
118C2×C22⋊C4—112no—
119C2×C22⋊C4—114no—
120C2×C22⋊C4—114no—
121C2×C22⋊C4C2×D1112yes—
122C2×C42—112no—
123#95—112no—
124#95—114no—
125#95—114no—
126C2×C11—24no—
127C2×C11—82no—
128C2×C11#52511yescharacteristic
129C2×C11C2×#12411yescharacteristic
130C2×C11#53411yescharacteristic
131C2×C11#55314yes—
132C24C22×D1112yes—
133C24C22×D1111yescharacteristic
134C2×D4—28no—
135C2×D4—24no—
136C2×D4—22no—
137C2×D4—42no—
138C22×C4—42no—
139C22×C4—112no—
140C22×C4—114no—
141C22×C4—112no—
142C22×C4—224no—
143C22×C4—222no—
144C22×C4—222no—
145C22×C4—442no—
146C22×C4C22⋊D1114yes—
147C22×C4C22×D1112yes—
148C22×C4C22×D1111yescharacteristic
149C22×C4C22×D1111yescharacteristic
150C4⋊C4—22no—
151C4⋊C4—224no—
152C4⋊C4—224no—
153C22⋊C4—24no—
154C22⋊C4—228no—
155C22⋊C4—224no—
156C22⋊C4—444no—
157C42—442no—
158C11#259111yescharacteristic, complemented, Sylow
159C23—22no—
160C23—22no—
161C23—24no—
162C23—24no—
163C23—24no—
164C23—22no—
165C23#434114yes—
166C23C2×C22⋊D1112yes—
167C23C23×D1111yescharacteristic
168D4—44no—
169D4—48no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—24no—
173C2×C4—22no—
174C2×C4—44no—
175C2×C4—114no—
176C2×C4—228no—
177C2×C4—222no—
178C2×C4—222no—
179C2×C4—224no—
180C2×C4—224no—
181C2×C4—224no—
182C2×C4—224no—
183C2×C4—222no—
184C2×C4—444no—
185C2×C4C2×C22⋊D1112yes—
186C2×C4C2×C22⋊D1112yes—
187C22—22no—
188C22—22no—
189C22—28no—
190C22—42no—
191C22—42no—
192C22—42no—
193C22—48no—
194C22#6698914yes—
195C22C2×#434112yes—
196C22#6703712yes—
197C22#41×D1112yes—
198C22C22×C22⋊D1111yescharacteristic
199C4—22no—
200C4—22no—
201C4—42no—
202C4—224no—
203C4—442no—
204C4—444no—
205C2—24no—
206C2—82no—
207C2#1062313214yes—
208C2C2×#6698911yescharacteristic
209C2#1062333511yescharacteristic
210C2#1062335911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
Fitting, prime radicalC2×C11×#121C2
hypercenterC2×#121D11
hypocenterC11#2591
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
2. C22×Dic11⋊C4C2semidirect
3. #10622835C2semidirect
4. #10622833C2semidirect
5. #10622833C2semidirect
6. C4×C22⋊Dic11C2semidirect
7. #10622595C2semidirect
8. #10622558C2semidirect
158. C11#2591semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1212
C22×Dic11⋊C42
#106228352
#106228332
C4×C22⋊Dic112
#106225952
#106225582
#259111