Finite Group Databasebeta

← #13073782

Subgroups — #13073782

Order 1408.

532 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 157 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×C4×D4×C11C211yesmaximal, characteristic
2C2×#66923C211yesmaximal, characteristic, complemented
3#10622835C212yesmaximal
4#10622825C212yesmaximal, complemented
5#10622825C212yesmaximal, complemented
6#10622595C212yesmaximal, complemented
7#10622558C214yesmaximal, complemented
8C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
9C22×D4×C11C2211yescharacteristic
10C23×C4×C11C2212yes—
11C4×D4×C11—24no—
12C2×C11×C4⋊C4C2211yescharacteristic
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×C4×Dic11C2212yes—
23#66923—24no—
24C11⋊#95C2212yes—
25C11⋊#95C2214yes—
26C11⋊#95C2214yes—
27C24×C11C2312yes—
28C2×D4×C11—24no—
29C2×D4×C11—22no—
30C22×C4×C11—24no—
31C22×C4×C11—24no—
32C22×C4×C11—24no—
33C22×C4×C11C2312yes—
34C22×C4×C11C2311yescharacteristic
35C22×C4×C11C2311yescharacteristic
36C22×C4×C11C2311yescharacteristic
37C22×Dic11C2314yes—
38C22×Dic11C2312yes—
39C22×Dic11C2312yes—
40C11×C4⋊C4—22no—
41C11×C22⋊C4—24no—
42C42×C11D414yes—
43C22⋊Dic11—28no—
44C22⋊Dic11—44no—
45C4⋊Dic11—22no—
46C4⋊Dic11—22no—
47C4⋊Dic11—24no—
48Dic11⋊C4—24no—
49Dic11⋊C4—24no—
50C4×Dic11—42no—
51#2562—111nomaximal, Sylow
52C23×C11—22no—
53C23×C11—22no—
54C23×C11—22no—
55C23×C11—22no—
56C23×C11—22no—
57C23×C11—22no—
58C23×C11#4114yes—
59C23×C11C2411yescharacteristic
60D4×C11—28no—
61C2×C4×C11—22no—
62C2×C4×C11—21no—
63C2×C4×C11—21no—
64C2×C4×C11—22no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—48no—
68C2×C4×C11C2×D412yes—
69C2×C4×C11C2×D412yes—
70C2×C4×C11C2×D412yes—
71C2×C4×C11#4114yes—
72C2×Dic11—22no—
73C2×Dic11—22no—
74C2×Dic11—24no—
75C2×Dic11—24no—
76C2×Dic11—24no—
77C2×Dic11—24no—
78C2×Dic11—22no—
79C2×Dic11—22no—
80C2×#125—111no—
81C2×C4×D4D1111yescharacteristic
82#400—112no—
83#394—112no—
84#388—114no—
85#380—112no—
86#380—112no—
87C4×C4⋊C4—111no—
88C22×C11—24no—
89C22×C11—24no—
90C22×C11—24no—
91C22×C11—42no—
92C22×C11—42no—
93C22×C11—42no—
94C22×C11—42no—
95C22×C11C22×D411yescharacteristic
96C22×C11C2×#4112yes—
97C22×C11C2×#4112yes—
98C22×C11H(5,𝔽2)11yescharacteristic
99C22×C112−1+411yescharacteristic
100C4×C11—22no—
101C4×C11—22no—
102C4×C11—42no—
103C4×C11#12414yes—
104Dic11—42no—
105Dic11—42no—
106Dic11—44no—
107C22×D4C2×D1111yescharacteristic
108C23×C4C2×D1112yes—
109#125—224no—
110C4×D4—24no—
111C2×C4⋊C4—111no—
112C2×C4⋊C4—111no—
113C2×C4⋊C4—112no—
114C2×C4⋊C4—112no—
115C2×C4⋊C4—112no—
116C2×C4⋊C4C2×D1111yescharacteristic
117C2×C22⋊C4—114no—
118C2×C22⋊C4—114no—
119C2×C22⋊C4C2×D1112yes—
120C2×C42—112no—
121C2×C42C2×D1111yescharacteristic
122#95—112no—
123#95—114no—
124#95—114no—
125C2×C11—44no—
126C2×C11#52511yescharacteristic
127C2×C11C2×#12411yescharacteristic
128C2×C11#53711yescharacteristic
129C2×C11#55212yes—
130C2×C11#55312yes—
131C24C22×D1112yes—
132C2×D4—24no—
133C2×D4—22no—
134C22×C4—24no—
135C22×C4—24no—
136C22×C4—24no—
137C22×C4—114no—
138C22×C4—112no—
139C22×C4—112no—
140C22×C4C22×D1112yes—
141C22×C4C22×D1111yescharacteristic
142C22×C4C22×D1111yescharacteristic
143C22×C4C22×D1111yescharacteristic
144C4⋊C4—22no—
145C4⋊C4—224no—
146C4⋊C4—224no—
147C4⋊C4—224no—
148C4⋊C4—222no—
149C4⋊C4—222no—
150C22⋊C4—24no—
151C22⋊C4—228no—
152C22⋊C4—444no—
153C42—442no—
154C42C22⋊D1114yes—
155C11#256211yescharacteristic, complemented, Sylow
156C23—22no—
157C23—22no—
158C23—22no—
159C23—22no—
160C23—22no—
161C23—22no—
162C23#433914yes—
163C23C23×D1111yescharacteristic
164D4—28no—
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—48no—
172C2×C4—224no—
173C2×C4—224no—
174C2×C4—224no—
175C2×C4—224no—
176C2×C4—222no—
177C2×C4—222no—
178C2×C4—222no—
179C2×C4—222no—
180C2×C4#434114yes—
181C2×C4C2×C22⋊D1112yes—
182C2×C4C2×C22⋊D1112yes—
183C2×C4C2×C22⋊D1112yes—
184C22—24no—
185C22—24no—
186C22—24no—
187C22—42no—
188C22—42no—
189C22—42no—
190C22—42no—
191C22C2×#433912yes—
192C22C2×#434112yes—
193C22#6704211yescharacteristic
194C22#6704311yescharacteristic
195C22C22×C22⋊D1111yescharacteristic
196C4—22no—
197C4—22no—
198C4—42no—
199C4—442no—
200C4—444no—
201C4—442no—
202C4#6698914yes—
203C2—44no—
204C2#1062307212yes—
205C2#1062309612yes—
206C2#1062332211yescharacteristic
207C2C2×#6698911yescharacteristic
208C2#1062336411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C4×D4×C11C2
prime radicalC22×D4×C11C22
hypercenterC2×C4×D4D11
hypocenterC11#2562
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#66923C2semidirect
4. #10622825C2semidirect
5. #10622825C2semidirect
6. #10622595C2semidirect
7. #10622558C2semidirect
8. C4×C4⋊Dic11C2semidirect
155. C11#2562semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×C112
C2×#669232
#106228352
#106228252
#106225952
#106225582
C4×C4⋊Dic112
#256211