Finite Group Databasebeta

← #28389583

Subgroups — #28389583

Order 14464.

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

normal subgroups only

This group has 210 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#20298929C211yesmaximal, characteristic
3#20298926C211yesmaximal, characteristic
4#20298530C211yesmaximal, characteristic
5#20298334C211yesmaximal, characteristic
6#20298323C211yesmaximal, characteristic
7#328×C113C211yesmaximal, characteristic
8#16813621—21no—
9#16813620—21no—
10#16813612—21no—
11#16813612—21no—
12#16813601C2211yescharacteristic
13#16813599—21no—
14#16813578—21no—
15C2×C4⋊Dic113—21no—
16C2×C4⋊Dic113C2211yescharacteristic
17C2×#14268626C2211yescharacteristic
18#16813554—21no—
19#16813553—21no—
20#16813547—21no—
21#16813546—21no—
22C22⋊#11744751C2211yescharacteristic
23#16813529—21no—
24C22⋊Q8×C113C2211yescharacteristic
25C22⋊C8×C113C2211yescharacteristic
26#95×C113C2211yescharacteristic
27C2×Dic226—21no—
28C2×Dic226D411yescharacteristic
29C22×Dic113—21no—
30C22×Dic113D411yescharacteristic
31C22×Dic113D411yescharacteristic
32C2×#11744751—21no—
33C4⋊Dic113—21no—
34C4⋊Dic113—21no—
35C4⋊Dic113—21no—
36C4⋊Dic113—42no—
37C4⋊Dic113D411yescharacteristic
38#14268626—21no—
39#14268626—21no—
40#14268626—21no—
41#14268626—21no—
42#14268626—21no—
43#14268626—21no—
44#14268626—21no—
45C22⋊Dic113—21no—
46C4×Dic113—21no—
47C4×Dic113—21no—
48C2×Q8×C113D411yescharacteristic
49C22×C4×C113—21no—
50C22×C4×C113C2311yescharacteristic
51C2×C8×C113—21no—
52C4⋊C4×C113—21no—
53C4⋊C4×C113D411yescharacteristic
54C22⋊C4×C113—21no—
55C23×C113C2×D411yescharacteristic
56Q8×C113—41no—
57C2×C4×C113—22no—
58C2×C4×C113—21no—
59C2×C4×C113—21no—
60C2×C4×C113—41no—
61C2×C4×C113—41no—
62C2×C4×C113—41no—
63C2×C4×C113C2×D411yescharacteristic
64C2×C4×C113C2×D411yescharacteristic
65C2×Dic113—21no—
66C2×Dic113—21no—
67C2×Dic113—21no—
68C2×Dic113—21no—
69C2×Dic113—21no—
70C2×Dic113—41no—
71C2×Dic113—41no—
72C2×Dic113—41no—
73C2×Dic113—41no—
74C2×Dic113SD1612yes—
75Dic226—41no—
76Dic226—81no—
77C8×C113—41no—
78#11744751—41no—
79C22×C113—21no—
80C22×C113—21no—
81C22×C113#12011yescharacteristic
82C22×C113C2×SD1611yescharacteristic
83C22×C113#13711yescharacteristic
84C4×C113—21no—
85C4×C113—21no—
86C4×C113—42no—
87C4×C113—41no—
88C4×C113—41no—
89Dic113—22no—
90Dic113—41no—
91Dic113—41no—
92Dic113—41no—
93Dic113—81no—
94C2×C113—21no—
95C2×C113—21no—
96C2×C113#44811yescharacteristic
97C2×C113#45611yescharacteristic
98C2×C113#45811yescharacteristic
99#1611—1131nomaximal, Sylow
100C113#161111yescharacteristic, complemented, Sylow
101#544—1131no—
102#483—1131no—
103#483—1131no—
104#398—1131no—
105#328—1131no—
106#328D11311yescharacteristic
107#324—1131no—
108C4⋊Q8—2261no—
109C4⋊Q8—2261no—
110#125—2261no—
111#125—2261no—
112C22⋊Q8—1131no—
113C22⋊Q8—2261no—
114C22⋊Q8C2×D11311yescharacteristic
115#117—2261no—
116C2×C4⋊C4—1131no—
117C2×C4⋊C4—1131no—
118C2×C4⋊C4—2261no—
119#106—2261no—
120#106—2261no—
121#103—2261no—
122#103—2261no—
123C22⋊C8—1131no—
124C22⋊C8C2×D11311yescharacteristic
125#95—2261no—
126#95C2×D11311yescharacteristic
127C2×Q8—1131no—
128C2×Q8—2261no—
129C2×Q8D45211yescharacteristic
130C22×C4—21no—
131C22×C4—1131no—
132C22×C4—1131no—
133C22×C4—2261no—
134C22×C4C22×D11311yescharacteristic
135C2×C8—21no—
136C2×C8—2261no—
137C4⋊C4—21no—
138C4⋊C4—1131no—
139C4⋊C4—4522no—
140C4⋊C4—2261no—
141C4⋊C4—2261no—
142C4⋊C4—2261no—
143C4⋊C4—2261no—
144C4⋊C4—2261no—
145C4⋊C4—2261no—
146C4⋊C4—2261no—
147C4⋊C4—2261no—
148C4⋊C4—2261no—
149C4⋊C4—2261no—
150C4⋊C4D45211yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—2261no—
153C42—2261no—
154C42—2261no—
155C23D4×D11311yescharacteristic
156Q8—41no—
157Q8—9041no—
158Q8—4521no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—1132no—
166C2×C4—4521no—
167C2×C4—4521no—
168C2×C4—4521no—
169C2×C4—4521no—
170C2×C4—2261no—
171C2×C4—2261no—
172C2×C4—2261no—
173C2×C4—2261no—
174C2×C4—2261no—
175C2×C4D4×D11311yescharacteristic
176C2×C4C2×D45211yescharacteristic
177C8—41no—
178C8—4521no—
179C22—21no—
180C22—21no—
181C22#1681359211yescharacteristic
182C22SD16×D11311yescharacteristic
183C22#1681365411yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—41no—
188C4—41no—
189C4—9041no—
190C4—4521no—
191C4—4521no—
192C4—4521no—
193C4—2262no—
194C2—21no—
195C2—21no—
196C2#2029873811yescharacteristic
197C2#2029878211yescharacteristic
198C2#2029878911yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#328×C113C2
socleC22×C113#120
prime radicalC23×C113C2×D4
hypercenter#328D113
hypocenterC113#1611
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
100. C113#1611semidirect

Maximal subgroups

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

subgroupindex
#202992272
#202989292
#202989262
#202985302
#202983342
#202983232
#328×C1132
#1611113