Finite Group Databasebeta

← #28389148

Subgroups — #28389148

Order 14464.

218 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 61 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#20299129C211yesmaximal, characteristic
2#20298648C211yesmaximal, characteristic, complemented
3#20298465C211yesmaximal, characteristic, complemented
4#20298336C211yesmaximal, characteristic, complemented
5#20298334C211yesmaximal, characteristic, complemented
6#20298332C211yesmaximal, characteristic
7#327×C113C211yesmaximal, characteristic
8#16813615—21no—
9#16813613C411yescharacteristic, complemented
10#16813609C411yescharacteristic, complemented
11#16813603—21no—
12#16813601C2211yescharacteristic
13#16813587C411yescharacteristic, complemented
14D4×Dic113—21no—
15D4×Dic113C411yescharacteristic, complemented
16#16813578—21no—
17C2×C4×Dic113C2211yescharacteristic
18#16813551—21no—
19C22⋊#11744751C2211yescharacteristic
20C8×Dic113—21no—
21#16813529—21no—
22#16813529—21no—
23#16813529C2211yescharacteristic
24#121×C113C2211yescharacteristic
25C22⋊C8×C113C2211yescharacteristic
26#95×C113C2211yescharacteristic
27C2×Dic226C2×C411yescharacteristic
28C22×Dic113—21no—
29C22×Dic113—21no—
30C22×Dic113D411yescharacteristic
31C22×Dic113D411yescharacteristic
32C2×#11744751—21no—
33C4⋊Dic113—21no—
34C4⋊Dic113C2×C411yescharacteristic
35#14268626—21no—
36#14268626—21no—
37#14268626—21no—
38C22⋊Dic113—21no—
39C22⋊Dic113—21no—
40C22⋊Dic113—21no—
41C22⋊Dic113—21no—
42C4×Dic113—21no—
43C4×Dic113C2×C411yescharacteristic
44C4×Dic113C2×C411yescharacteristic
45C4×Dic113D411yescharacteristic
46C4×Dic113D411yescharacteristic
47C2×D4×C113—21no—
48C2×D4×C113C2×C411yescharacteristic
49C22×C4×C113—21no—
50C22×C4×C113C2311yescharacteristic
51C2×C8×C113—21no—
52C4⋊C4×C113C2×C411yescharacteristic
53C22⋊C4×C113—21no—
54C23×C113—21no—
55C23×C113C2×D411yescharacteristic
56D4×C113—41no—
57D4×C113—41no—
58D4×C113—41no—
59C2×C4×C113—21no—
60C2×C4×C113—41no—
61C2×C4×C113—41no—
62C2×C4×C113—41no—
63C2×C4×C113—41no—
64C2×C4×C113C22×C411yescharacteristic
65C2×C4×C113C2×D411yescharacteristic
66C2×Dic113—21no—
67C2×Dic113—21no—
68C2×Dic113—21no—
69C2×Dic113—21no—
70C2×Dic113—41no—
71C2×Dic113—42no—
72C2×Dic113—41no—
73C2×Dic113—41no—
74C2×Dic113—41no—
75C2×Dic113C22⋊C411yescharacteristic
76C2×Dic113C22⋊C411yescharacteristic
77C2×Dic113C22⋊C411yescharacteristic
78C2×Dic113C22⋊C411yescharacteristic
79Dic226—41no—
80C8×C113—41no—
81#11744751—41no—
82C22×C113—21no—
83C22×C113—21no—
84C22×C113—41no—
85C22×C113—41no—
86C22×C113—41no—
87C22×C113C2×C22⋊C411yescharacteristic
88C22×C113#13511yescharacteristic
89C22×C113#13511yescharacteristic
90C4×C113—21no—
91C4×C113—21no—
92C4×C113—41no—
93C4×C113—81no—
94Dic113—21no—
95Dic113—21no—
96Dic113—21no—
97Dic113—21no—
98Dic113—41no—
99Dic113—41no—
100Dic113—81no—
101C2×C113—21no—
102C2×C113—21no—
103C2×C113—81no—
104C2×C113#41011yescharacteristic
105C2×C113#41611yescharacteristic
106C2×C113#42111yescharacteristic
107#1521—1131nomaximal, Sylow
108C113#152111yescharacteristic, complemented, Sylow
109#529—1131no—
110#431—1131no—
111#383—1131no—
112#328—1131no—
113#328—1131no—
114#327—1131no—
115#327D11311yescharacteristic
116#126—2261no—
117#125—1131no—
118#124—1131no—
119#123—2261no—
120C22⋊Q8—1131no—
121#121C2×D11311yescharacteristic
122C4×Q8—1131no—
123C4×D4—1131no—
124C4×D4—2261no—
125#117—2261no—
126C2×C42—1131no—
127C4⋊C8—2261no—
128C22⋊C8—1131no—
129C22⋊C8C2×D11311yescharacteristic
130C4×C8—2261no—
131#95—1131no—
132#95—2261no—
133#95—2261no—
134#95C2×D11311yescharacteristic
135C2×Q8—1131no—
136C2×D4—21no—
137C2×D4C4×D11311yescharacteristic
138C22×C4—21no—
139C22×C4—1131no—
140C22×C4—1131no—
141C22×C4—2261no—
142C22×C4—2261no—
143C22×C4C22×D11311yescharacteristic
144C2×C8—21no—
145C2×C8—2261no—
146C4⋊C4—1131no—
147C4⋊C4—2261no—
148C4⋊C4—2261no—
149C4⋊C4—2261no—
150C4⋊C4—2261no—
151C4⋊C4C4×D11311yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—2261no—
154C22⋊C4—2261no—
155C22⋊C4—2261no—
156C22⋊C4—2261no—
157C42—1131no—
158C42—1131no—
159C42—1131no—
160C42—1131no—
161C42—2261no—
162C23—21no—
163C23D4×D11311yescharacteristic
164Q8—4521no—
165D4—41no—
166D4—41no—
167D4—41no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—1131no—
174C2×C4—1131no—
175C2×C4—1131no—
176C2×C4—1131no—
177C2×C4—4521no—
178C2×C4—4521no—
179C2×C4—4521no—
180C2×C4—4522no—
181C2×C4—4521no—
182C2×C4—2261no—
183C2×C4—2261no—
184C2×C4—2261no—
185C2×C4—2261no—
186C2×C4C2×C4×D11311yescharacteristic
187C2×C4D4×D11311yescharacteristic
188C8—41no—
189C8—4521no—
190C22—21no—
191C22—21no—
192C22—41no—
193C22—41no—
194C22—41no—
195C22C22⋊C4×D11311yescharacteristic
196C22#1681364111yescharacteristic
197C22#1681364311yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—81no—
202C4—9041no—
203C4—4521no—
204C4—4521no—
205C4—2261no—
206C4—2261no—
207C4—2261no—
208C4—2261no—
209C2—21no—
210C2—21no—
211C2—81no—
212C2#2029857011yescharacteristic
213C2#2029859111yescharacteristic
214C2#2029861311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D113
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
Fitting#327×C113C2
socleC22×C113C2×C22⋊C4
prime radical#121×C113C22
cosocleC22×C4×C113C23
hypercenter#327D113
hypocenterC113#1521
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #20298648C2semidirect
3. #20298465C2semidirect
4. #20298336C2semidirect
5. #20298334C2semidirect
9. #16813613C4semidirect
10. #16813609C4semidirect
13. #16813587C4semidirect
15. D4×Dic113C4semidirect
108. C113#1521semidirect

Maximal subgroups

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

subgroupindex
#202991292
#202986482
#202984652
#202983362
#202983342
#202983322
#327×C1132
#1521113