Finite Group Databasebeta

← #13072903

Subgroups — #13072903

Order 1408.

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

normal subgroups only

This group has 512 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
1C22×C11×C4⋊C4C211yesmaximal, characteristic
2C2×#66979C211yesmaximal, characteristic
3#10622824C211yesmaximal, characteristic
4#10622824C212yesmaximal
5#10622823C212yesmaximal
6#10622599C212yesmaximal, complemented
7#10622596C212yesmaximal, complemented
8#10622591C214yesmaximal, complemented
9C23×C4×C11C2211yescharacteristic
10C23×C4×C11C2211yescharacteristic
11C23×C4×C11C2211yescharacteristic
12C2×C11×C4⋊C4—24no—
13C2×C11×C4⋊C4C2212yes—
14C2×C11×C4⋊C4C2212yes—
15C2×C22⋊Dic11C2212yes—
16C2×C22⋊Dic11C2212yes—
17#66979—24no—
18C2×C4⋊Dic11C2211yescharacteristic
19C2×C4⋊Dic11C2211yescharacteristic
20C2×Dic11⋊C4C2214yes—
21C2×C4×Dic11C2212yes—
22C11⋊#95C2214yes—
23C11⋊#95C2212yes—
24C11⋊#95C2214yes—
25C11⋊#95C2214yes—
26C11⋊#95C2212yes—
27C24×C11C2311yescharacteristic
28C22×C4×C11—22no—
29C22×C4×C11—24no—
30C22×C4×C11—24no—
31C22×C4×C11—22no—
32C22×C4×C11—24no—
33C22×C4×C11D414yes—
34C22×C4×C11C2312yes—
35C22×C4×C11C2311yescharacteristic
36C22×C4×C11C2311yescharacteristic
37C22×C4×C11C2312yes—
38C22×Dic11C2314yes—
39C22×Dic11C2312yes—
40C22×Dic11C2312yes—
41C11×C4⋊C4—24no—
42C11×C4⋊C4—24no—
43C22⋊Dic11—24no—
44C22⋊Dic11—24no—
45C4⋊Dic11—22no—
46C4⋊Dic11—22no—
47Dic11⋊C4—28no—
48C4×Dic11—24no—
49#2484—111nomaximal, Sylow
50C23×C11—22no—
51C23×C11—22no—
52C23×C11C2×D412yes—
53C23×C11#4114yes—
54C23×C11C2411yescharacteristic
55C2×C4×C11—28no—
56C2×C4×C11—28no—
57C2×C4×C11—22no—
58C2×C4×C11—22no—
59C2×C4×C11—22no—
60C2×C4×C11—22no—
61C2×C4×C11—22no—
62C2×C4×C11—24no—
63C2×C4×C11—44no—
64C2×C4×C11C2×D412yes—
65C2×C4×C11C2×D412yes—
66C2×C4×C11#4114yes—
67C2×Dic11—22no—
68C2×Dic11—22no—
69C2×Dic11—24no—
70C2×Dic11—24no—
71C2×Dic11—24no—
72C2×Dic11—24no—
73C2×Dic11—24no—
74C2×#117—111no—
75C22×C4⋊C4D1111yescharacteristic
76#400—112no—
77#398—112no—
78#387—114no—
79#385—112no—
80#381—111no—
81#381—112no—
82C22×C11—22no—
83C22×C11—22no—
84C22×C11—28no—
85C22×C11#12314yes—
86C22×C11C22×D411yescharacteristic
87C22×C11C2×#4112yes—
88C22×C11C2×#4112yes—
89C22×C112−1+412yes—
90C4×C11—22no—
91C4×C11—22no—
92C4×C11—24no—
93C4×C11—42no—
94Dic11—42no—
95Dic11—42no—
96Dic11—44no—
97C23×C4C2×D1111yescharacteristic
98C23×C4C2×D1111yescharacteristic
99C23×C4C2×D1111yescharacteristic
100#117—224no—
101C2×C4⋊C4—24no—
102C2×C4⋊C4—111no—
103C2×C4⋊C4—111no—
104C2×C4⋊C4—114no—
105C2×C4⋊C4C2×D1112yes—
106C2×C4⋊C4C2×D1112yes—
107C2×C22⋊C4—112no—
108C2×C22⋊C4—112no—
109C2×C42—112no—
110#95—112no—
111#95—114no—
112#95—114no—
113#95—112no—
114#95—114no—
115C2×C11—24no—
116C2×C11C2×#12311yescharacteristic
117C2×C11#52511yescharacteristic
118C2×C11#53611yescharacteristic
119C2×C11#55214yes—
120C24C22×D1111yescharacteristic
121C22×C4—24no—
122C22×C4—22no—
123C22×C4—24no—
124C22×C4—24no—
125C22×C4—22no—
126C22×C4—114no—
127C22×C4—112no—
128C22×C4—112no—
129C22×C4C22⋊D1114yes—
130C22×C4C22×D1112yes—
131C22×C4C22×D1112yes—
132C22×C4C22×D1111yescharacteristic
133C22×C4C22×D1111yescharacteristic
134C4⋊C4—24no—
135C4⋊C4—24no—
136C4⋊C4—228no—
137C4⋊C4—222no—
138C4⋊C4—222no—
139C22⋊C4—224no—
140C22⋊C4—224no—
141C42—224no—
142C11#248411yescharacteristic, complemented, Sylow
143C23—22no—
144C23—22no—
145C23#434114yes—
146C23C2×C22⋊D1112yes—
147C23C23×D1111yescharacteristic
148C2×C4—28no—
149C2×C4—28no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—24no—
155C2×C4—22no—
156C2×C4—44no—
157C2×C4—224no—
158C2×C4—224no—
159C2×C4—224no—
160C2×C4—224no—
161C2×C4—224no—
162C2×C4—222no—
163C2×C4—222no—
164C2×C4#433914yes—
165C2×C4C2×C22⋊D1112yes—
166C2×C4C2×C22⋊D1112yes—
167C22—28no—
168C22—22no—
169C22—22no—
170C22#6698814yes—
171C22C2×#433912yes—
172C22C2×#434112yes—
173C22#6704012yes—
174C22C22×C22⋊D1111yescharacteristic
175C4—24no—
176C4—22no—
177C4—22no—
178C4—42no—
179C4—444no—
180C4—442no—
181C4—442no—
182C2—24no—
183C2#1062304414yes—
184C2#1062332211yescharacteristic
185C2C2×#6698811yescharacteristic
186C2#1062334711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC22×C11×C4⋊C4C2
prime radicalC24×C11C23
hypercenterC22×C4⋊C4D11
hypocenterC11#2484
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
6. #10622599C2semidirect
7. #10622596C2semidirect
8. #10622591C2semidirect
142. C11#2484semidirect

Maximal subgroups

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

subgroupindex
C22×C11×C4⋊C42
C2×#669792
#106228242
#106228232
#106225992
#106225962
#106225912
#248411