Finite Group Databasebeta

← #28388911

Subgroups — #28388911

Order 14464.

316 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 69 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
1C2×#16813584C211yesmaximal, characteristic
2#20298560C212yesmaximal, complemented
3#20298324C211yesmaximal, characteristic, complemented
4#20298321C212yesmaximal, complemented
5#324×C113C211yesmaximal, characteristic, complemented
6C22×D452C411yescharacteristic
7C22×C4×D113C411yescharacteristic
8C22×C4×D113C2211yescharacteristic
9C2×#14268630—22no—
10#16813584—22no—
11#16813584—22no—
12C2×#14268624C411yescharacteristic
13C2×#14268624C2211yescharacteristic
14C2×C4×Dic113C411yescharacteristic
15C22⋊#11744751C2212yes—
16#16813534—22no—
17C2×C4⋊C4×C113C2211yescharacteristic
18C22⋊C8×C113C2212yes—
19C23×D113C2×C411yescharacteristic
20C23×D113C2×C411yescharacteristic
21C2×D452—22no—
22C2×D452—22no—
23C2×D452—22no—
24C22×Dic113C2×C411yescharacteristic
25C22×Dic113C2×C411yescharacteristic
26C2×C4×D113—21no—
27C2×C4×D113—21no—
28C2×C4×D113—42no—
29C2×C4×D113—42no—
30C2×C4×D113D412yes—
31C2×C4×D113D412yes—
32#14268630—44no—
33C2×#11744751—22no—
34#14268624—22no—
35#14268624—22no—
36C4×Dic113—21no—
37C4×Dic113—21no—
38C22×C4×C113C2×C411yescharacteristic
39C22×C4×C113C2×C411yescharacteristic
40C22×C4×C113C2311yescharacteristic
41C2×C8×C113—22no—
42C4⋊C4×C113—22no—
43C23×C113C22×C411yescharacteristic
44C22×D113—21no—
45C22×D113—21no—
46C22×D113—21no—
47C22×D113—21no—
48C22×D113—41no—
49C22×D113—41no—
50C22×D113—41no—
51C22×D113—41no—
52C22×D113C22⋊C412yes—
53C22×D113M1612yescomplemented
54C2×C4×C113—21no—
55C2×C4×C113—21no—
56C2×C4×C113—21no—
57C2×C4×C113—41no—
58C2×C4×C113—41no—
59C2×C4×C113M1612yescomplemented
60C2×C4×C113C2×D412yes—
61C2×Dic113—22no—
62C2×Dic113—21no—
63C2×Dic113—41no—
64C2×Dic113C22⋊C411yescharacteristic
65C2×Dic113C22⋊C411yescharacteristic
66D452—28no—
67C4×D113—24no—
68C4×D113—42no—
69C4×D113—42no—
70C4×D113—42no—
71C8×C113—42no—
72#11744751—42no—
73C22×C113—21no—
74C22×C113—21no—
75C22×C113C2×C22⋊C411yescharacteristic
76C22×C113C2×M1611yescharacteristic
77C22×C113C2×M1611yescharacteristic
78C2×D113—22no—
79C2×D113—22no—
80C2×D113—22no—
81C2×D113—22no—
82C2×D113—42no—
83C2×D113—42no—
84C2×D113—42no—
85C2×D113—41no—
86C2×D113—41no—
87C2×D113—42no—
88C4×C113—22no—
89C4×C113—22no—
90C4×C113—41no—
91Dic113—21no—
92Dic113—41no—
93Dic113#9912yes—
94C2×C113—21no—
95C2×C113—21no—
96C2×C113#40711yescharacteristic
97C2×C113C2×#9911yescharacteristic
98C2×C113#41311yescharacteristic
99D113—42no—
100D113—42no—
101#1465—1131nomaximal, Sylow
102C113#146511yescharacteristic, complemented, Sylow
103C2×C4×D4—1131no—
104#407—1132no—
105#324—1131no—
106#324D11311yescharacteristic, complemented
107#323—1132no—
108C22×D4—1131no—
109C23×C4—1131no—
110C23×C4—1131no—
111C2×M16—2262no—
112C4×D4—2262no—
113C4×D4—2262no—
114C2×C4⋊C4C2×D11311yescharacteristic
115C2×C22⋊C4—1131no—
116C2×C22⋊C4—1131no—
117C2×C42—1131no—
118C22⋊C8—1132no—
119C22⋊C8—2262no—
120C22⋊C8C2×D11312yes—
121C24—1131no—
122C24—1131no—
123C2×D4—2262no—
124C2×D4—2262no—
125C2×D4—2262no—
126C22×C4—1131no—
127C22×C4—1132no—
128C22×C4—1132no—
129C22×C4—1131no—
130C22×C4—4522no—
131C22×C4—4522no—
132C22×C4—2261no—
133C22×C4—2261no—
134C22×C4C4×D11311yescharacteristic
135C22×C4C4×D11311yescharacteristic
136C22×C4C22×D11311yescharacteristic
137M16—4524no—
138C2×C8—22no—
139C2×C8—2262no—
140C4⋊C4—22no—
141C22⋊C4—2262no—
142C22⋊C4—2262no—
143C42—2261no—
144C42—2261no—
145C23—1132no—
146C23—1132no—
147C23—4521no—
148C23—4521no—
149C23—4521no—
150C23—4521no—
151C23—2261no—
152C23—2261no—
153C23—2261no—
154C23—2261no—
155C23C2×C4×D11311yescharacteristic
156D4—2268no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—1131no—
163C2×C4—1131no—
164C2×C4—4522no—
165C2×C4—4522no—
166C2×C4—4522no—
167C2×C4—4521no—
168C2×C4—2264no—
169C2×C4—2262no—
170C2×C4—2261no—
171C2×C4#1426863012yescomplemented
172C2×C4D4×D11312yes—
173C8—42no—
174C8—4522no—
175C22—21no—
176C22—21no—
177C22—4522no—
178C22—4522no—
179C22—4522no—
180C22—4522no—
181C22—4521no—
182C22—4521no—
183C22—2262no—
184C22—2262no—
185C22—2262no—
186C22—2262no—
187C22C22⋊C4×D11311yescharacteristic
188C22M16×D11311yescharacteristic
189C22C2×#1426863011yescharacteristic
190C4—22no—
191C4—22no—
192C4—41no—
193C4—1132no—
194C4—4521no—
195C4—2261no—
196C2—21no—
197C2—21no—
198C2—4522no—
199C2—4522no—
200C2#2029856011yescharacteristic
201C2#99×D11311yescharacteristic
202C2#2029858111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D113
commutatorC23×C113C22×C4
FrattiniC22×C4C22×D113
Fitting#324×C113C2
socleC22×C113C2×C22⋊C4
prime radicalC22×D452C4
cosocleC22×C4×C113C23
hypercenter#324D113
hypocenterC113#1465
LCSG ▷ C23×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #20298560C2semidirect
3. #20298324C2semidirect
4. #20298321C2semidirect
5. #324×C113C2semidirect
53. C22×D113M16semidirect
59. C2×C4×C113M16semidirect
102. C113#1465semidirect
106. #324D113semidirect
171. C2×C4#14268630semidirect

Maximal subgroups

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

subgroupindex
C2×#168135842
#202985602
#202983242
#202983212
#324×C1132
#1465113