Finite Group Databasebeta

← #28378310

Subgroups — #28378310

Order 13952.

270 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 64 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#20295997C211yesmaximal, characteristic
2D109⋊(C22⋊C8)C211yesmaximal, characteristic
3#20295871C214yesmaximal, complemented
4C2×#16812679C211yesmaximal, characteristic
5C2×#13182039—21no—
6C2×D109⋊C8—21no—
7#16812756—21no—
8#16812756—21no—
9C22⋊#11724786C2212yes—
10C22⋊#11724786C2212yes—
11C22×Dic218C411yescharacteristic
12C22×C4×D109C2211yescharacteristic
13#16812679—21no—
14#16812679—21no—
15#16812679—21no—
16#16812679—21no—
17C2×C4⋊Dic109C2212yes—
18C2×#13182006C412yes—
19C2×C4⋊C4×C109C411yescharacteristic
20#13182039—42no—
21D109⋊C8—42no—
22C2×#11724786—22no—
23C2×#11724786—22no—
24C23×D109C2×C411yescharacteristic
25C2×Dic218—21no—
26C2×Dic218—21no—
27C2×Dic218—42no—
28C22×Dic109C2×C412yes—
29C22×Dic109C2311yescharacteristic
30C2×C4×D109—42no—
31C2×C4×D109D411yescharacteristic
32C2×C4×D109D411yescharacteristic
33C2×C4×D109D411yescharacteristic
34C2×C4×D109D411yescharacteristic
35C4⋊Dic109—22no—
36C4⋊Dic109—22no—
37#13182006—22no—
38#13182006—22no—
39C22×C4×C109C2×C412yes—
40C22×C4×C109C2×C411yescharacteristic
41C4⋊C4×C109—21no—
42C4⋊C4×C109—21no—
43C23×C109C22×C411yescharacteristic
44C22×D109—22no—
45C22×D109—22no—
46C22×D109—41no—
47C22×D109C22⋊C411yescharacteristic
48C22×D109C22⋊C411yescharacteristic
49C2×C4×C109—22no—
50C2×C4×C109—22no—
51C2×C4×C109—24no—
52C2×C4×C109C22⋊C411yescharacteristic
53C2×C4×C109C22⋊C411yescharacteristic
54C2×Dic109—22no—
55C2×Dic109—41no—
56C2×Dic109—42no—
57C2×Dic109C2×D411yescharacteristic
58C2×Dic109C2×D411yescharacteristic
59C4×D109—22no—
60C4×D109—22no—
61C4×D109—41no—
62C4×D109—41no—
63Dic218—42no—
64Dic218—42no—
65#11724786—42no—
66#11724786—42no—
67C22×C109—21no—
68C22×C109—21no—
69C22×C109C2×C22⋊C411yescharacteristic
70C22×C109#13112yes—
71C2×D109—21no—
72C2×D109—21no—
73C2×D109—21no—
74C2×D109—21no—
75C2×D109—21no—
76C2×D109—44no—
77C2×D109#10112yes—
78C4×C109—21no—
79C4×C109—42no—
80C4×C109#9912yes—
81Dic109—21no—
82Dic109—21no—
83Dic109—42no—
84C2×C109—22no—
85C2×C109#40811yescharacteristic
86C2×C109C2×#9911yescharacteristic
87C2×C109C2×#10111yescharacteristic
88D109—22no—
89D109—41no—
90#1472—1091nomaximal, Sylow
91C109#147211yescharacteristic, complemented, Sylow
92C2×C22⋊Q8—1091no—
93#407—1091no—
94C2×C22⋊C8—1091no—
95#324—1094no—
96C22×Q8—1091no—
97C23×C4—1091no—
98C2×M16—2181no—
99C22×C8—2181no—
100C22⋊Q8—2181no—
101C22⋊Q8—2181no—
102C22⋊Q8—2181no—
103C22⋊Q8—2181no—
104C2×C4⋊C4—1092no—
105C2×C4⋊C4#8913711yescharacteristic
106C2×C22⋊C4—1092no—
107C22⋊C8—1092no—
108C22⋊C8—1092no—
109C22⋊C8—2181no—
110C22⋊C8—2181no—
111C24—1091no—
112C2×Q8—4362no—
113C2×Q8—2181no—
114C2×Q8—2181no—
115C22×C4—1091no—
116C22×C4—1091no—
117C22×C4—1091no—
118C22×C4—1091no—
119C22×C4—1091no—
120C22×C4—1092no—
121C22×C4—4362no—
122C22×C4C2×#8913712yes—
123C22×C4C2×#8913711yescharacteristic
124M16—4362no—
125C2×C8—4362no—
126C2×C8—2182no—
127C2×C8—2182no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—2182no—
131C4⋊C4—2182no—
132C22⋊C4—2182no—
133C22⋊C4—2182no—
134C23—1091no—
135C23—1091no—
136C23—4361no—
137C23—2182no—
138C23—2182no—
139C23C22×#8913711yescharacteristic
140Q8—4362no—
141Q8—4362no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—24no—
145C2×C4—1091no—
146C2×C4—1091no—
147C2×C4—4361no—
148C2×C4—4361no—
149C2×C4—4362no—
150C2×C4—4361no—
151C2×C4—2182no—
152C2×C4—2182no—
153C2×C4—2182no—
154C2×C4C22⋊#8913711yescharacteristic
155C2×C4C22⋊#8913711yescharacteristic
156C8—4362no—
157C8—4362no—
158C22—21no—
159C22—21no—
160C22—1092no—
161C22—4364no—
162C22—2181no—
163C22—2181no—
164C22—2181no—
165C22—2181no—
166C22—2181no—
167C22C2×C22⋊#8913711yescharacteristic
168C22#1681278612yes—
169C4—21no—
170C4—42no—
171C4—4362no—
172C4—2181no—
173C4—2181no—
174C4#1681275812yes—
175C2—22no—
176C2—4361no—
177C2—2182no—
178C2#2029600011yescharacteristic
179C2C2×#1681275811yescharacteristic
180C2D109⋊#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC23×C109C22×C4
FrattiniC23C22×#89137
FittingC2×C4⋊C4×C109C4
socleC22×C109C2×C22⋊C4
prime radicalC23×D109C2×C4
cosocleC22×Dic109C23
hypercenterC2×C4⋊C4#89137
hypocenterC109#1472
LCSG ▷ C23×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #20295871C2semidirect
91. C109#1472semidirect

Maximal subgroups

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

subgroupindex
#202959972
D109⋊(C22⋊C8)2
#202958712
C2×#168126792
#1472109