Finite Group Databasebeta

← #13079015

Subgroups — #13079015

Order 1408.

392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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
1#10623247C211yesmaximal, characteristic
2D11×#125C211yesmaximal, characteristic, complemented
3C11×#490C211yesmaximal, characteristic, complemented
4#10622684C211yesmaximal, characteristic, complemented
5#10622682C211yesmaximal, characteristic, complemented
6#10622384C214yesmaximal, complemented
7#10622381C214yesmaximal, complemented
8#10622320C211yesmaximal, characteristic, complemented
9#10622316C211yesmaximal, characteristic, complemented
10C2×#4341C2212yes—
11C11×#127C2211yescharacteristic
12C11×#125C2211yescharacteristic
13#66991—22no—
14#66989C2212yes—
15D4×Dic11—22no—
16C2×#4313C2212yes—
17C4⋊C4×D11—22no—
18C4⋊C4×D11C2212yes—
19#66943C2212yes—
20#66942—22no—
21C42×D11C2211yescharacteristic
22#66923C2211yescharacteristic
23#66922C2211yescharacteristic
24C11×#102C2214yes—
25C11×#97C2211yescharacteristic
26#66896C2214yes—
27#66880C2214yes—
28C8×Dic11C2212yes—
29#66874C2214yes—
30#66867C2211yescharacteristic
31C2×D4×C11—22no—
32C2×D4×C11C2312yes—
33C2×C22⋊D11—22no—
34C22×Dic11—22no—
35#4341—28no—
36C2×C4×D11—22no—
37C2×C4×D11D412yes—
38C2×C4×D11C2311yescharacteristic
39C2×Dic22C2312yes—
40C2×C8×C11C2312yes—
41C11×C4⋊C4—22no—
42C11×C4⋊C4C2312yes—
43C42×C11C2311yescharacteristic
44C22⋊Dic11—24no—
45C4⋊Dic11—22no—
46C4⋊Dic11—22no—
47C4⋊Dic11C2312yes—
48Dic11⋊C4—22no—
49Dic11⋊C4—22no—
50Dic11⋊C4—22no—
51C4×Dic11D412yes—
52C4×Dic11C2311yescharacteristic
53C2×C11⋊C8C2312yes—
54#4313—24no—
55#3142—111nomaximal, Sylow
56C23×C11—22no—
57C22×D11C2×D411yescharacteristic
58D4×C11—24no—
59D4×C11—44no—
60C2×C4×C11—22no—
61C2×C4×C11C2×D412yes—
62C2×C4×C11C2411yescharacteristic
63C22⋊D11—44no—
64C2×Dic11—22no—
65C2×Dic11—22no—
66C2×Dic11—44no—
67C2×Dic11C2×D412yes—
68C2×Dic11C2×D411yescharacteristic
69C4×D11—42no—
70C4×D11—44no—
71C4×D11#4114yes—
72Dic22—24no—
73C8×C11—22no—
74C11⋊C8—22no—
75#532—111no—
76C2×#125—111no—
77#491—111no—
78#491—111no—
79#490—111no—
80#490D1111yescharacteristic, complemented
81#488—114no—
82#417—114no—
83C4×M16—111no—
84C22×C11—42no—
85C22×C11—44no—
86C22×C11C22×D411yescharacteristic
87C2×D11—22no—
88C2×D11#12412yes—
89C4×C11—22no—
90C4×C11—42no—
91C4×C11C2×#4112yes—
92Dic11—22no—
93Dic11—42no—
94Dic11—42no—
95Dic11#12412yes—
96C2×#41—112no—
97C2×M16—112no—
98C4⋊Q8—111no—
99#127C2×D1111yescharacteristic
100#125—112no—
101#125—111no—
102#125—222no—
103#125C2×D1111yescharacteristic
104#124—112no—
105#121—222no—
106C4×D4—222no—
107C2×C4⋊C4—112no—
108C2×C4⋊C4—222no—
109C2×C42—111no—
110#103—114no—
111#103—114no—
112#102—114no—
113#102C2×D1114yes—
114#97—111no—
115#97C2×D1111yescharacteristic
116C4×C8—112no—
117C2×C11—82no—
118C2×C11C2×#12411yescharacteristic
119C2×C11#57512yes—
120D11—22no—
121#41—228no—
122C2×Q8—112no—
123C2×D4—22no—
124C2×D4—222no—
125C2×D4C22×D1112yes—
126C22×C4—111no—
127C22×C4—112no—
128C22×C4—222no—
129C22×C4—222no—
130M16—224no—
131C2×C8—112no—
132C2×C8C22×D1112yes—
133C4⋊C4—22no—
134C4⋊C4—112no—
135C4⋊C4—222no—
136C4⋊C4—222no—
137C4⋊C4—222no—
138C4⋊C4—222no—
139C4⋊C4—222no—
140C4⋊C4C22×D1112yes—
141C22⋊C4—224no—
142C42—112no—
143C42—111no—
144C42C22×D1111yescharacteristic
145C11#314211yescharacteristic, complemented, Sylow
146C23—22no—
147C23—111no—
148Q8—224no—
149D4—24no—
150D4—44no—
151D4—444no—
152C2×C4—22no—
153C2×C4—111no—
154C2×C4—114no—
155C2×C4—112no—
156C2×C4—222no—
157C2×C4—222no—
158C2×C4—442no—
159C2×C4—444no—
160C2×C4—444no—
161C2×C4D4×D1112yes—
162C2×C4C23×D1111yescharacteristic
163C8—22no—
164C8—222no—
165C22—44no—
166C22—42no—
167C22—112no—
168C22—222no—
169C22C2×D4×D1111yescharacteristic
170C4—22no—
171C4—42no—
172C4—112no—
173C4—222no—
174C4—442no—
175C4—442no—
176C4#41×D1112yes—
177C2—82no—
178C2—222no—
179C2D11×#12411yescharacteristic
180C2#1062330412yes—
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#490C2
socleC22×C11C22×D4
prime radical#10623247C2
hypercenter#490D11
hypocenterC11#3142
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
2. D11×#125C2semidirect
3. C11×#490C2semidirect
4. #10622684C2semidirect
5. #10622682C2semidirect
6. #10622384C2semidirect
7. #10622381C2semidirect
8. #10622320C2semidirect
9. #10622316C2semidirect
80. #490D11semidirect
145. C11#3142semidirect

Maximal subgroups

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

subgroupindex
#106232472
D11×#1252
C11×#4902
#106226842
#106226822
#106223842
#106223812
#106223202
#106223162
#314211