Finite Group Databasebeta

← #28405809

Subgroups — #28405809

Order 14464.

332 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 80 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#20299566C212yesmaximal, complemented
2#20299444C212yesmaximal, complemented
3#20299441C212yesmaximal, complemented
4C2×C4×C22⋊D113C211yesmaximal, characteristic
5C2×#14268655—22no—
6#16813679—22no—
7C22⋊#11744753C2214yes—
8C22×C22⋊D113C411yescharacteristic
9C22×C4×D113C2211yescharacteristic
10C4×C22⋊D113—22no—
11C4×C22⋊D113—22no—
12C2×#14268626C2211yescharacteristic
13C2×C22⋊Dic113C2211yescharacteristic
14C2×#14268624C411yescharacteristic
15C2×C4×Dic113C411yescharacteristic
16C23×C4×C113C411yescharacteristic
17#14268655—44no—
18C2×#11744753—24no—
19C23×D113C2×C411yescharacteristic
20C2×C22⋊D113—22no—
21C2×C22⋊D113—22no—
22C2×C22⋊D113C814yescomplemented
23C22×Dic113C2×C411yescharacteristic
24C22×Dic113C2×C411yescharacteristic
25C22×Dic113C2311yescharacteristic
26C2×C4×D113—42no—
27C2×C4×D113D412yes—
28C2×C4×D113D412yes—
29#14268626—22no—
30C22⋊Dic113—22no—
31#14268624—22no—
32C4×Dic113—21no—
33C4×Dic113—21no—
34C24×C113C2×C411yescharacteristic
35C22×C4×C113—21no—
36C22×C4×C113—21no—
37C22×C4×C113—42no—
38C22×C4×C113C2×C411yescharacteristic
39C22×C4×C113C2×C411yescharacteristic
40C23×C113—21no—
41C23×C113—21no—
42C23×C113—41no—
43C23×C113—41no—
44C23×C113C2×C812yescomplemented
45C23×C113C22×C411yescharacteristic
46C22×D113—41no—
47C22×D113—41no—
48C22×D113C22⋊C412yes—
49C22×D113C2×C812yes—
50C22×D113M1612yes—
51C2×C4×C113—22no—
52C2×C4×C113—21no—
53C2×C4×C113—42no—
54C2×C4×C113—42no—
55C2×C4×C113—41no—
56C2×C4×C113C22⋊C411yescharacteristic
57C2×C4×C113C22⋊C411yescharacteristic
58C22⋊D113—28no—
59C2×Dic113—21no—
60C2×Dic113—21no—
61C2×Dic113—21no—
62C2×Dic113—41no—
63C2×Dic113—41no—
64C2×Dic113C2×C812yescomplemented
65C2×Dic113C2×D412yes—
66C4×D113—24no—
67C4×D113—42no—
68#11744753—44no—
69C22×C113—21no—
70C22×C113—21no—
71C22×C113—22no—
72C22×C113—42no—
73C22×C113—42no—
74C22×C113—41no—
75C22×C113—41no—
76C22×C113C2×C22⋊C411yescharacteristic
77C22×C113C22×C811yescharacteristic
78C22×C113C2×M1611yescharacteristic
79C2×D113—22no—
80C2×D113—22no—
81C2×D113—42no—
82C2×D113—42no—
83C2×D113C22⋊C814yes—
84C4×C113—21no—
85C4×C113—41no—
86C4×C113#9912yes—
87Dic113—22no—
88Dic113—22no—
89Dic113—41no—
90C2×C113—21no—
91C2×C113—21no—
92C2×C113—42no—
93C2×C113C2×C22⋊C811yescharacteristic
94C2×C113C2×#9911yescharacteristic
95C2×C113#41311yescharacteristic
96D113—24no—
97#1459—1131nomaximal, Sylow
98C113#145911yescharacteristic, complemented, Sylow
99C2×C4×D4—1131no—
100C2×C22⋊C8—1132no—
101#324—1132no—
102#323—1132no—
103C22×D4—1131no—
104C23×C4—1131no—
105C23×C4#9067311yescharacteristic
106C22×C8—2262no—
107C4×D4—2262no—
108C4×D4—2262no—
109C2×C4⋊C4—1131no—
110C2×C22⋊C4—1131no—
111C2×C22⋊C4—1131no—
112C2×C42—1131no—
113C22⋊C8—1134no—
114C22⋊C8—2262no—
115C24—1131no—
116C24C2×#9067311yescharacteristic
117C2×D4—1134no—
118C2×D4—2262no—
119C2×D4—2262no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—42no—
123C22×C4—1131no—
124C22×C4—1131no—
125C22×C4—1132no—
126C22×C4—1132no—
127C22×C4—1131no—
128C22×C4—4522no—
129C22×C4C2×#9067311yescharacteristic
130C22×C4C2×#9067311yescharacteristic
131C2×C8—4524no—
132C2×C8—2264no—
133C4⋊C4—2262no—
134C22⋊C4—2262no—
135C22⋊C4—2262no—
136C42—2261no—
137C42—2261no—
138C23—21no—
139C23—21no—
140C23—41no—
141C23—41no—
142C23—1132no—
143C23—1132no—
144C23—1132no—
145C23—4521no—
146C23—4521no—
147C23#1426865512yescomplemented
148C23C22×#9067311yescharacteristic
149D4—2268no—
150C2×C4—22no—
151C2×C4—21no—
152C2×C4—42no—
153C2×C4—42no—
154C2×C4—41no—
155C2×C4—1132no—
156C2×C4—1132no—
157C2×C4—4522no—
158C2×C4—4521no—
159C2×C4—4521no—
160C2×C4—2261no—
161C2×C4—2261no—
162C2×C4—2261no—
163C2×C4—2264no—
164C2×C4C22⋊#9067311yescharacteristic
165C2×C4C22⋊#9067311yescharacteristic
166C8—4524no—
167C22—21no—
168C22—21no—
169C22—22no—
170C22—42no—
171C22—42no—
172C22—41no—
173C22—41no—
174C22—1134no—
175C22—4522no—
176C22—4522no—
177C22—2262no—
178C22—2262no—
179C22C2×C22⋊#9067311yescharacteristic
180C22C2×#1426865511yescharacteristic
181C22D113⋊M1611yescharacteristic
182C4—21no—
183C4—41no—
184C4—4521no—
185C4—2262no—
186C4—2262no—
187C4#1681368012yes—
188C2—21no—
189C2—21no—
190C2—42no—
191C2—2264no—
192C2#2029956611yescharacteristic
193C2C2×#1681368011yescharacteristic
194C2#2029958411yescharacteristic
subgroupG/H
centerC2×C4C22⋊#90673
commutatorC22×C113C22×C8
FrattiniC23C22×#90673
FittingC23×C4×C113C4
socleC22×C113C2×C22⋊C4
prime radicalC22×C22⋊D113C4
cosocleC22×Dic113C23
hypercenterC23×C4#90673
hypocenterC113#1459
LCSG ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. #20299566C2semidirect
2. #20299444C2semidirect
3. #20299441C2semidirect
22. C2×C22⋊D113C8semidirect
44. C23×C113C2×C8semidirect
64. C2×Dic113C2×C8semidirect
98. C113#1459semidirect
147. C23#14268655semidirect

Maximal subgroups

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

subgroupindex
#202995662
#202994442
#202994412
C2×C4×C22⋊D1132
#1459113