Finite Group Databasebeta

← #28378290

Subgroups — #28378290

Order 13952.

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

normal subgroups only

This group has 316 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#20295996C212yesmaximal, complemented
2#20295872C212yesmaximal, complemented
3#20295870C212yesmaximal, complemented
4C2×#16812659C211yesmaximal, characteristic
5C2×#13182038—22no—
6C22⋊#11724786—22no—
7C22⋊#11724786C2214yes—
8C22×C22⋊D109C411yescharacteristic
9C23×Dic109C2211yescharacteristic
10C22×C4×D109C411yescharacteristic
11#16812659—22no—
12#16812659—22no—
13C2×#13182008C2211yescharacteristic
14C2×#13182006C2211yescharacteristic
15C2×C4×Dic109C411yescharacteristic
16C2×C22⋊C4×C109C411yescharacteristic
17#13182038—44no—
18C2×#11724786—24no—
19C23×D109C2×C411yescharacteristic
20C2×C22⋊D109—22no—
21C2×C22⋊D109—22no—
22C2×C22⋊D109—22no—
23C22×Dic109—42no—
24C22×Dic109C2×C411yescharacteristic
25C22×Dic109C2×C411yescharacteristic
26C22×Dic109D412yes—
27C22×Dic109D412yes—
28C22×Dic109C2311yescharacteristic
29C2×C4×D109—21no—
30C2×C4×D109—21no—
31C2×C4×D109—42no—
32#13182008—22no—
33#13182006—22no—
34C4×Dic109—21no—
35C4×Dic109—21no—
36C24×C109C2×C411yescharacteristic
37C22×C4×C109C2×C411yescharacteristic
38C22×C4×C109C2×C411yescharacteristic
39C22⋊C4×C109—22no—
40C23×C109—21no—
41C23×C109—21no—
42C23×C109—41no—
43C23×C109—41no—
44C23×C109C22⋊C412yes—
45C23×C109C22×C411yescharacteristic
46C22×D109—21no—
47C22×D109—21no—
48C22×D109—41no—
49C22×D109—41no—
50C22×D109M1612yescomplemented
51C2×C4×C109—21no—
52C2×C4×C109—21no—
53C2×C4×C109—41no—
54C2×C4×C109—41no—
55C22⋊D109—28no—
56C2×Dic109—21no—
57C2×Dic109—21no—
58C2×Dic109—22no—
59C2×Dic109—24no—
60C2×Dic109—42no—
61C2×Dic109—41no—
62C2×Dic109C22⋊C411yescharacteristic
63C2×Dic109C22⋊C411yescharacteristic
64C2×Dic109M1612yescomplemented
65C2×Dic109C2×D412yes—
66C4×D109—42no—
67C4×D109—42no—
68#11724786—44no—
69C22×C109—21no—
70C22×C109—21no—
71C22×C109—22no—
72C22×C109—22no—
73C22×C109—22no—
74C22×C109—42no—
75C22×C109—42no—
76C22×C109C2×C22⋊C411yescharacteristic
77C22×C109C2×M1611yescharacteristic
78C22×C109C2×M1611yescharacteristic
79C2×D109—22no—
80C2×D109—42no—
81C2×D109—41no—
82C2×D109—41no—
83C2×D109—42no—
84C4×C109—41no—
85C4×C109—41no—
86Dic109—22no—
87Dic109—22no—
88Dic109—21no—
89Dic109#9912yes—
90C2×C109—21no—
91C2×C109—21no—
92C2×C109—42no—
93C2×C109#40711yescharacteristic
94C2×C109C2×#9911yescharacteristic
95C2×C109#41311yescharacteristic
96D109—42no—
97#1465—1091nomaximal, Sylow
98C109#146511yescharacteristic, complemented, Sylow
99C2×C4×D4—1091no—
100#407—1092no—
101#324—1092no—
102#323—1092no—
103C22×D4—1091no—
104C23×C4—1091no—
105C23×C4—1091no—
106C2×M16—2182no—
107C4×D4—2182no—
108C4×D4—2182no—
109C2×C4⋊C4—1091no—
110C2×C22⋊C4—1091no—
111C2×C22⋊C4#8913711yescharacteristic
112C2×C42—1091no—
113C22⋊C8—1094no—
114C22⋊C8—2182no—
115C24—1091no—
116C24C2×#8913711yescharacteristic
117C2×D4—2182no—
118C2×D4—2182no—
119C2×D4—2182no—
120C22×C4—1092no—
121C22×C4—1091no—
122C22×C4—1092no—
123C22×C4—1091no—
124C22×C4—1091no—
125C22×C4—4362no—
126C22×C4—4362no—
127C22×C4—2181no—
128C22×C4—2181no—
129C22×C4C2×#8913711yescharacteristic
130C22×C4C2×#8913711yescharacteristic
131M16—4364no—
132C2×C8—2184no—
133C4⋊C4—2182no—
134C22⋊C4—22no—
135C22⋊C4—2182no—
136C42—2181no—
137C42—2181no—
138C23—21no—
139C23—21no—
140C23—41no—
141C23—41no—
142C23—1092no—
143C23—4361no—
144C23—4361no—
145C23—2181no—
146C23—2181no—
147C23C22⋊#8913712yes—
148C23C22×#8913711yescharacteristic
149D4—2188no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—1091no—
155C2×C4—1091no—
156C2×C4—1092no—
157C2×C4—1092no—
158C2×C4—4362no—
159C2×C4—4362no—
160C2×C4—4361no—
161C2×C4—4362no—
162C2×C4—2184no—
163C2×C4—2182no—
164C2×C4—2181no—
165C2×C4—2181no—
166C8—4364no—
167C22—21no—
168C22—21no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—42no—
173C22—42no—
174C22—4362no—
175C22—4362no—
176C22—4361no—
177C22—4361no—
178C22—2182no—
179C22C2×C22⋊#8913711yescharacteristic
180C22D109⋊M1611yescharacteristic
181C22D109⋊M1611yescharacteristic
182C4—41no—
183C4—41no—
184C4—1092no—
185C4—2182no—
186C4—2182no—
187C4—2181no—
188C2—21no—
189C2—21no—
190C2—42no—
191C2—4362no—
192C2#2029599811yescharacteristic
193C2D109⋊#9911yescharacteristic
194C2#2029601311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC23×C109C22×C4
FrattiniC23C22×#89137
FittingC2×C22⋊C4×C109C4
socleC22×C109C2×C22⋊C4
prime radicalC22×C22⋊D109C4
cosocleC22×Dic109C23
hypercenterC2×C22⋊C4#89137
hypocenterC109#1465
LCSG ▷ C23×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #20295996C2semidirect
2. #20295872C2semidirect
3. #20295870C2semidirect
50. C22×D109M16semidirect
64. C2×Dic109M16semidirect
98. C109#1465semidirect

Maximal subgroups

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

subgroupindex
#202959962
#202958722
#202958702
C2×#168126592
#1465109