Finite Group Databasebeta

← #324×D113 #28388882

Subgroups — #324×D113 #28388882

Order 14464.

328 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 87 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×C4⋊C4×D113C211yesmaximal, characteristic
2C22⋊C8×D113C212yesmaximal
3#20298324C211yesmaximal, characteristic, complemented
4#20298323C212yesmaximal, complemented
5#324×C113C211yesmaximal, characteristic, complemented
6C22×C4×D113C411yescharacteristic
7C22×C4×D113C411yescharacteristic
8C22×C4×D113C2211yescharacteristic
9C2×C8×D113—22no—
10C2×C4⋊Dic113C411yescharacteristic
11C2×#14268626C411yescharacteristic
12C2×#14268626C2211yescharacteristic
13C4⋊C4×D113—22no—
14C4⋊C4×D113—22no—
15C22⋊#11744751C2212yes—
16#16813534—22no—
17C2×C4⋊C4×C113C2211yescharacteristic
18C22⋊C8×C113C2212yes—
19C23×D113C2×C411yescharacteristic
20C22×Dic113C2×C411yescharacteristic
21C22×Dic113C2×C411yescharacteristic
22C22×Dic113C2×C411yescharacteristic
23C2×C4×D113—21no—
24C2×C4×D113—21no—
25C2×C4×D113—22no—
26C2×C4×D113—21no—
27C2×C4×D113—21no—
28C2×C4×D113—42no—
29C2×C4×D113—42no—
30C2×C4×D113C814yescomplemented
31C2×C4×D113D412yes—
32C2×C4×D113D412yes—
33C2×#11744751—22no—
34C8×D113—44no—
35C4⋊Dic113—22no—
36#14268626—22no—
37#14268626—22no—
38C22×C4×C113C2×C411yescharacteristic
39C22×C4×C113C2×C411yescharacteristic
40C22×C4×C113C2311yescharacteristic
41C2×C8×C113—22no—
42C4⋊C4×C113—22no—
43C23×C113C22×C411yescharacteristic
44C22×D113—22no—
45C22×D113—22no—
46C22×D113C22⋊C411yescharacteristic
47C22×D113C22⋊C411yescharacteristic
48C22×D113C2×C812yes—
49C22×D113M1612yes—
50C2×C4×C113—21no—
51C2×C4×C113—21no—
52C2×C4×C113—21no—
53C2×C4×C113—41no—
54C2×C4×C113—41no—
55C2×C4×C113C2×C812yescomplemented
56C2×C4×C113C2×D412yes—
57C2×Dic113—21no—
58C2×Dic113—21no—
59C2×Dic113—21no—
60C2×Dic113—41no—
61C2×Dic113—41no—
62C2×Dic113C22⋊C412yes—
63C2×Dic113C2×C812yescomplemented
64C4×D113—24no—
65C4×D113—24no—
66C4×D113—24no—
67C4×D113—42no—
68C4×D113—42no—
69C4×D113—42no—
70C8×C113—42no—
71#11744751—42no—
72C22×C113—21no—
73C22×C113—21no—
74C22×C113C2×C22⋊C411yescharacteristic
75C22×C113C22×C811yescharacteristic
76C22×C113C2×M1611yescharacteristic
77C2×D113—21no—
78C2×D113—21no—
79C2×D113—24no—
80C2×D113—24no—
81C2×D113C22⋊C812yes—
82C2×D113C22⋊C812yes—
83C2×D113#9912yes—
84C2×D113#10112yes—
85C4×C113—22no—
86C4×C113—22no—
87C4×C113—41no—
88Dic113—22no—
89Dic113—22no—
90Dic113—41no—
91C2×C113—21no—
92C2×C113—21no—
93C2×C113C2×C22⋊C811yescharacteristic
94C2×C113C2×#9911yescharacteristic
95C2×C113C2×#10111yescharacteristic
96D113—22no—
97D113#32414yesdirect product factor
98C2×#324—1131nomaximal, Sylow
99C113C2×#32411yescharacteristic, complemented, Sylow
100C22×C4⋊C4—1131no—
101C2×C22⋊C8—1132no—
102#324—1131no—
103#324—1132no—
104#324D11311yescharacteristic, direct product factor
105C23×C4—1131no—
106C23×C4—1131no—
107C23×C4—1131no—
108C22×C8—2262no—
109C2×C4⋊C4—1131no—
110C2×C4⋊C4—1131no—
111C2×C4⋊C4—1131no—
112C2×C4⋊C4—2262no—
113C2×C4⋊C4—2262no—
114C2×C4⋊C4C2×D11311yescharacteristic
115C22⋊C8—1132no—
116C22⋊C8—2262no—
117C22⋊C8C2×D11312yes—
118C24—1131no—
119C22×C4—1131no—
120C22×C4—1131no—
121C22×C4—1132no—
122C22×C4—1134no—
123C22×C4—1132no—
124C22×C4—1131no—
125C22×C4—4522no—
126C22×C4—4522no—
127C22×C4—2261no—
128C22×C4—2261no—
129C22×C4—2261no—
130C22×C4—2261no—
131C22×C4—2262no—
132C22×C4C4×D11311yescharacteristic
133C22×C4C4×D11311yescharacteristic
134C22×C4C22×D11311yescharacteristic
135C2×C8—22no—
136C2×C8—4524no—
137C2×C8—2262no—
138C4⋊C4—22no—
139C4⋊C4—2262no—
140C4⋊C4—2262no—
141C4⋊C4—2262no—
142C23—1131no—
143C23—1131no—
144C23—1132no—
145C23—1132no—
146C23—2262no—
147C23—2262no—
148C23C2×C4×D11311yescharacteristic
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—1132no—
155C2×C4—1132no—
156C2×C4—4522no—
157C2×C4—4522no—
158C2×C4—4522no—
159C2×C4—4521no—
160C2×C4—4521no—
161C2×C4—2264no—
162C2×C4—2264no—
163C2×C4—2264no—
164C2×C4—2261no—
165C2×C4—2261no—
166C2×C4—2261no—
167C2×C4C8×D11312yescomplemented
168C2×C4D4×D11312yes—
169C8—42no—
170C8—4522no—
171C22—21no—
172C22—21no—
173C22—1132no—
174C22—1132no—
175C22—1132no—
176C22—1132no—
177C22—2264no—
178C22—2264no—
179C22—2261no—
180C22—2261no—
181C22C22⋊C4×D11311yescharacteristic
182C22C2×C8×D11311yescharacteristic
183C22M16×D11311yescharacteristic
184C4—22no—
185C4—22no—
186C4—41no—
187C4—4521no—
188C4—2262no—
189C4—2262no—
190C2—21no—
191C2—21no—
192C2—1134no—
193C2—2262no—
194C2C22⋊C8×D11311yescharacteristic
195C2#99×D11311yescharacteristic
196C2#101×D11311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D113
commutatorC22×C113C22×C8
FrattiniC22×C4C22×D113
Fitting#324×C113C2
socleC22×C113C2×C22⋊C4
prime radicalC23×D113C2×C4
cosocleC22×C4×C113C23
hypercenter#324D113
hypocenterC113C2×#324
LCSG ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
3. #20298324C2semidirect
4. #20298323C2semidirect
5. #324×C113C2semidirect
30. C2×C4×D113C8semidirect
55. C2×C4×C113C2×C8semidirect
63. C2×Dic113C2×C8semidirect
97. D113#324direct (N × H)
99. C113C2×#324semidirect
104. #324D113direct (N × H)
167. C2×C4C8×D113semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D1132
C22⋊C8×D1132
#202983242
#202983232
#324×C1132
C2×#324113