Finite Group Databasebeta

← #28389549

Subgroups — #28389549

Order 14464.

238 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 51 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#20299227C211yesmaximal, characteristic
2#20298756C211yesmaximal, characteristic
3#20298753C211yesmaximal, characteristic
4#20298519C211yesmaximal, characteristic
5#20298334C211yesmaximal, characteristic
6#20298323C211yesmaximal, characteristic
7#328×C113C211yesmaximal, characteristic
8C22×Dic226C2211yescharacteristic
9C2×Dic452—21no—
10C2×#14268637—21no—
11#16813621—21no—
12#16813620—21no—
13#16813612—21no—
14#16813612—21no—
15#16813601C2211yescharacteristic
16#16813599—21no—
17#16813578—21no—
18C2×C4⋊Dic113—21no—
19C2×#14268626C2211yescharacteristic
20#16813547—21no—
21#16813545—21no—
22C22⋊#11744751C2211yescharacteristic
23#16813529—21no—
24C22⋊Q8×C113C2211yescharacteristic
25C22⋊C8×C113C2211yescharacteristic
26#95×C113C2211yescharacteristic
27C2×Dic226—21no—
28C2×Dic226—21no—
29C2×Dic226—21no—
30C2×Dic226—42no—
31C2×Dic226D411yescharacteristic
32C22×Dic113—21no—
33C22×Dic113D411yescharacteristic
34C22×Dic113D411yescharacteristic
35Dic452—42no—
36#14268637—42no—
37C2×#11744751—21no—
38C4⋊Dic113—21no—
39C4⋊Dic113—42no—
40C4⋊Dic113D411yescharacteristic
41#14268626—21no—
42#14268626—21no—
43#14268626—21no—
44#14268626—21no—
45#14268626—21no—
46#14268626—21no—
47#14268626—21no—
48C22⋊Dic113—21no—
49C4×Dic113—21no—
50C4×Dic113—21no—
51C2×Q8×C113D411yescharacteristic
52C22×C4×C113—21no—
53C22×C4×C113C2311yescharacteristic
54C2×C8×C113—21no—
55C4⋊C4×C113—21no—
56C4⋊C4×C113D411yescharacteristic
57C22⋊C4×C113—21no—
58C23×C113C2×D411yescharacteristic
59Q8×C113—41no—
60C2×C4×C113—22no—
61C2×C4×C113—21no—
62C2×C4×C113—21no—
63C2×C4×C113—41no—
64C2×C4×C113—41no—
65C2×C4×C113—41no—
66C2×C4×C113C2×D411yescharacteristic
67C2×C4×C113C2×D411yescharacteristic
68C2×Dic113—21no—
69C2×Dic113—21no—
70C2×Dic113—22no—
71C2×Dic113—21no—
72C2×Dic113—21no—
73C2×Dic113—21no—
74C2×Dic113—41no—
75C2×Dic113—41no—
76C2×Dic113—41no—
77C2×Dic113Q1612yescomplemented
78Dic226—22no—
79Dic226—22no—
80Dic226—41no—
81Dic226—41no—
82Dic226—41no—
83Dic226—81no—
84C8×C113—41no—
85#11744751—41no—
86C22×C113—21no—
87C22×C113—21no—
88C22×C113#12011yescharacteristic
89C22×C113C2×Q1611yescharacteristic
90C22×C113#13711yescharacteristic
91C4×C113—21no—
92C4×C113—21no—
93C4×C113—42no—
94C4×C113—41no—
95C4×C113—41no—
96Dic113—22no—
97Dic113—41no—
98Dic113—42no—
99Dic113—41no—
100Dic113—41no—
101C2×C113—21no—
102C2×C113—21no—
103C2×C113#45111yescharacteristic
104C2×C113#45611yescharacteristic
105C2×C113B(4,𝔽2)11yescharacteristic
106#1605—1131nomaximal, Sylow
107C113#160511yescharacteristic, complemented, Sylow
108#544—1131no—
109#451—1131no—
110#451—1131no—
111#395—1131no—
112#328—1131no—
113#328D11311yescharacteristic
114#324—1131no—
115C22×Q8—1131no—
116C2×Q16—2261no—
117C2×Q16—2261no—
118C4⋊Q8—2261no—
119C4⋊Q8—2261no—
120#125—2261no—
121#125—2261no—
122C22⋊Q8—1131no—
123C22⋊Q8—2261no—
124C22⋊Q8C2×D11311yescharacteristic
125#117—2261no—
126C2×C4⋊C4—1131no—
127C2×C4⋊C4—2261no—
128#103—2261no—
129#103—2261no—
130C22⋊C8—1131no—
131C22⋊C8C2×D11311yescharacteristic
132#95—2261no—
133#95C2×D11311yescharacteristic
134C2×Q8—1131no—
135C2×Q8—4522no—
136C2×Q8—2261no—
137C2×Q8—2261no—
138C2×Q8—2261no—
139C2×Q8D45211yescharacteristic
140C22×C4—21no—
141C22×C4—1131no—
142C22×C4—1131no—
143C22×C4—2261no—
144C22×C4C22×D11311yescharacteristic
145Q16—4522no—
146Q16—4522no—
147C2×C8—21no—
148C2×C8—2261no—
149C4⋊C4—21no—
150C4⋊C4—1131no—
151C4⋊C4—4522no—
152C4⋊C4—2261no—
153C4⋊C4—2261no—
154C4⋊C4—2261no—
155C4⋊C4—2261no—
156C4⋊C4—2261no—
157C4⋊C4—2261no—
158C4⋊C4—2261no—
159C4⋊C4—2261no—
160C4⋊C4D45211yescharacteristic
161C22⋊C4—21no—
162C22⋊C4—2261no—
163C42—2261no—
164C42—2261no—
165C23D4×D11311yescharacteristic
166Q8—41no—
167Q8—9041no—
168Q8—4521no—
169Q8—4521no—
170Q8—4521no—
171Q8—2262no—
172Q8—2262no—
173C2×C4—22no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—1132no—
180C2×C4—4521no—
181C2×C4—4521no—
182C2×C4—4521no—
183C2×C4—2262no—
184C2×C4—2261no—
185C2×C4—2261no—
186C2×C4—2261no—
187C2×C4—2261no—
188C2×C4—2261no—
189C2×C4D4×D11311yescharacteristic
190C2×C4C2×D45211yescharacteristic
191C8—41no—
192C8—4521no—
193C22—21no—
194C22—21no—
195C22#1681359211yescharacteristic
196C22Q16×D11311yescharacteristic
197C22#1681365111yescharacteristic
198C4—21no—
199C4—21no—
200C4—42no—
201C4—41no—
202C4—41no—
203C4—4521no—
204C4—4522no—
205C4—4521no—
206C4—4521no—
207C4—2262no—
208C2—21no—
209C2—21no—
210C2#2029875511yescharacteristic
211C2#2029878211yescharacteristic
212C2#2029878611yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#328×C113C2
socleC22×C113#120
prime radicalC23×C113C2×D4
hypercenter#328D113
hypocenterC113#1605
LCSG ▷ C22×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
77. C2×Dic113Q16semidirect
107. C113#1605semidirect

Maximal subgroups

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

subgroupindex
#202992272
#202987562
#202987532
#202985192
#202983342
#202983232
#328×C1132
#1605113