Finite Group Databasebeta

← #28378264

Subgroups — #28378264

Order 13952.

264 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 76 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#20296043C212yesmaximal, complemented
2#20295872C212yesmaximal, complemented
3#20295869C212yesmaximal
4C2×#16812655C211yesmaximal, characteristic
5#16812766—22no—
6C22⋊#11724786C2214yes—
7C4×#11724786—22no—
8C23×Dic109C411yescharacteristic
9#16812655—22no—
10#16812655—22no—
11C2×#13182008C411yescharacteristic
12C2×#13182008C2211yescharacteristic
13C2×C22⋊Dic109C2211yescharacteristic
14C2×C4×Dic109C411yescharacteristic
15C2×C4×Dic109C2211yescharacteristic
16C2×C22⋊C4×C109C411yescharacteristic
17C2×#11724786—24no—
18C22×Dic109—21no—
19C22×Dic109—21no—
20C22×Dic109—22no—
21C22×Dic109C814yescomplemented
22C22×Dic109C2×C411yescharacteristic
23C22×Dic109C2×C411yescharacteristic
24C22×Dic109C2×C411yescharacteristic
25C22×Dic109C2311yescharacteristic
26#13182008—22no—
27#13182008—22no—
28C22⋊Dic109—22no—
29C4×Dic109—21no—
30C4×Dic109—21no—
31C4×Dic109D412yes—
32C4×Dic109D412yes—
33C24×C109C2×C411yescharacteristic
34C22×C4×C109C2×C411yescharacteristic
35C22×C4×C109C2×C411yescharacteristic
36C22⋊C4×C109—22no—
37C23×C109—21no—
38C23×C109—21no—
39C23×C109—41no—
40C23×C109—41no—
41C23×C109C2×C812yes—
42C23×C109C22×C411yescharacteristic
43C2×C4×C109—21no—
44C2×C4×C109—41no—
45C2×C4×C109—41no—
46C2×C4×C109C22⋊C412yes—
47C2×Dic109—21no—
48C2×Dic109—21no—
49C2×Dic109—24no—
50C2×Dic109—24no—
51C2×Dic109—21no—
52C2×Dic109—41no—
53C2×Dic109—41no—
54C2×Dic109C22⋊C411yescharacteristic
55C2×Dic109C22⋊C411yescharacteristic
56C2×Dic109C2×C812yes—
57C2×Dic109C2×C812yes—
58C2×Dic109M1612yes—
59C2×Dic109C2×D412yes—
60#11724786—44no—
61C22×C109—21no—
62C22×C109—21no—
63C22×C109—22no—
64C22×C109—42no—
65C22×C109—42no—
66C22×C109—41no—
67C22×C109—41no—
68C22×C109C2×C22⋊C411yescharacteristic
69C22×C109C22×C811yescharacteristic
70C22×C109C2×M1611yescharacteristic
71C4×C109—22no—
72C4×C109—41no—
73Dic109—22no—
74Dic109—22no—
75Dic109—41no—
76Dic109C22⋊C812yes—
77Dic109C22⋊C812yes—
78C2×C109—21no—
79C2×C109—21no—
80C2×C109—42no—
81C2×C109C2×C22⋊C811yescharacteristic
82C2×C109#41011yescharacteristic
83C2×C109#41311yescharacteristic
84#1458—1091nomaximal, Sylow
85C109#145811yescharacteristic, complemented, Sylow
86C2×#117—1091no—
87#431—1092no—
88#324—1092no—
89#323—1092no—
90C23×C4—1091no—
91#117—2182no—
92#117—2182no—
93C2×C4⋊C4—1091no—
94C2×C4⋊C4—1091no—
95C2×C22⋊C4—1091no—
96C2×C22⋊C4#8913711yescharacteristic
97C2×C42—1091no—
98C2×C42—1091no—
99C4⋊C8—2182no—
100C22⋊C8—1094no—
101C4×C8—2182no—
102C24C2×#8913711yescharacteristic
103C22×C4—1091no—
104C22×C4—1091no—
105C22×C4—1094no—
106C22×C4—1091no—
107C22×C4—1091no—
108C22×C4—2181no—
109C22×C4—2181no—
110C22×C4—2182no—
111C22×C4C2×#8913711yescharacteristic
112C22×C4C2×#8913711yescharacteristic
113C2×C8—2184no—
114C4⋊C4—2182no—
115C4⋊C4—2182no—
116C22⋊C4—22no—
117C22⋊C4—2182no—
118C42—1092no—
119C42—1092no—
120C42—2181no—
121C42—2181no—
122C23—21no—
123C23—21no—
124C23—41no—
125C23—41no—
126C23D109⋊C812yes—
127C23C22×#8913711yescharacteristic
128C2×C4—21no—
129C2×C4—41no—
130C2×C4—41no—
131C2×C4—1091no—
132C2×C4—1091no—
133C2×C4—1092no—
134C2×C4—1092no—
135C2×C4—1092no—
136C2×C4—1092no—
137C2×C4—4361no—
138C2×C4—4361no—
139C2×C4—2184no—
140C2×C4—2184no—
141C2×C4—2181no—
142C2×C4—2181no—
143C2×C4—2181no—
144C2×C4C22⋊#8913712yes—
145C8—4364no—
146C22—21no—
147C22—21no—
148C22—22no—
149C22—42no—
150C22—42no—
151C22—41no—
152C22—41no—
153C22C2×C22⋊#8913711yescharacteristic
154C22C2×D109⋊C811yescharacteristic
155C22D109⋊M1611yescharacteristic
156C4—22no—
157C4—41no—
158C4—1092no—
159C4—1092no—
160C4—4361no—
161C4—2182no—
162C4—2182no—
163C2—21no—
164C2—21no—
165C2—42no—
166C2D109⋊(C22⋊C8)11yescharacteristic
167C2#2029600611yescharacteristic
168C2#2029601311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC22×C109C22×C8
FrattiniC23C22×#89137
FittingC2×C22⋊C4×C109C4
socleC22×C109C2×C22⋊C4
prime radicalC24×C109C2×C4
cosocleC22×Dic109C23
hypercenterC2×C22⋊C4#89137
hypocenterC109#1458
LCSG ▷ C22×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #20296043C2semidirect
2. #20295872C2semidirect
21. C22×Dic109C8semidirect
85. C109#1458semidirect

Maximal subgroups

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

subgroupindex
#202960432
#202958722
#202958692
C2×#168126552
#1458109