Finite Group Databasebeta

← #28389617

Subgroups — #28389617

Order 14464.

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

normal subgroups only

This group has 202 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#20298934C211yesmaximal, characteristic
3#20298931C211yesmaximal, characteristic
4#20298538C211yesmaximal, 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⋊Dic113C2211yescharacteristic
16C2×#14268626C2211yescharacteristic
17#16813556—21no—
18#16813555—21no—
19#16813547—21no—
20#16813546—21no—
21C22⋊#11744751C2211yescharacteristic
22#16813529—21no—
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⋊Dic113D411yescharacteristic
37#14268626—21no—
38#14268626—21no—
39#14268626—21no—
40#14268626—21no—
41#14268626—21no—
42#14268626—21no—
43#14268626—21no—
44C22⋊Dic113—21no—
45C4×Dic113—21no—
46C4×Dic113—21no—
47C2×Q8×C113D411yescharacteristic
48C22×C4×C113—21no—
49C22×C4×C113C2311yescharacteristic
50C2×C8×C113—21no—
51C4⋊C4×C113—21no—
52C4⋊C4×C113D411yescharacteristic
53C22⋊C4×C113—21no—
54C23×C113C2×D411yescharacteristic
55Q8×C113—41no—
56C2×C4×C113—21no—
57C2×C4×C113—21no—
58C2×C4×C113—41no—
59C2×C4×C113—41no—
60C2×C4×C113—41no—
61C2×C4×C113—41no—
62C2×C4×C113C2×D411yescharacteristic
63C2×C4×C113C2×D411yescharacteristic
64C2×Dic113—21no—
65C2×Dic113—21no—
66C2×Dic113—21no—
67C2×Dic113—21no—
68C2×Dic113—21no—
69C2×Dic113—41no—
70C2×Dic113—42no—
71C2×Dic113—41no—
72C2×Dic113Q1612yes—
73Dic226—41no—
74Dic226—81no—
75C8×C113—41no—
76#11744751—41no—
77C22×C113—21no—
78C22×C113—21no—
79C22×C113#12011yescharacteristic
80C22×C113C2×Q1611yescharacteristic
81C22×C113#13711yescharacteristic
82C4×C113—21no—
83C4×C113—21no—
84C4×C113—41no—
85C4×C113—41no—
86C4×C113—81no—
87Dic113—22no—
88Dic113—41no—
89Dic113—41no—
90Dic113—41no—
91Dic113—81no—
92C2×C113—21no—
93C2×C113—21no—
94C2×C113#45111yescharacteristic
95C2×C113#45411yescharacteristic
96C2×C113#45811yescharacteristic
97#1617—1131nomaximal, Sylow
98C113#161711yescharacteristic, complemented, Sylow
99#544—1131no—
100#484—1131no—
101#484—1131no—
102#400—1131no—
103#328—1131no—
104#328D11311yescharacteristic
105#324—1131no—
106C4⋊Q8—2261no—
107C4⋊Q8—2261no—
108#125—2261no—
109#125—2261no—
110C22⋊Q8—1131no—
111C22⋊Q8—2261no—
112C22⋊Q8C2×D11311yescharacteristic
113#117—2261no—
114C2×C4⋊C4—1131no—
115C2×C4⋊C4—1131no—
116#107—2261no—
117#107—2261no—
118#103—2261no—
119#103—2261no—
120C22⋊C8—1131no—
121C22⋊C8C2×D11311yescharacteristic
122#95—2261no—
123#95—2261no—
124#95C2×D11311yescharacteristic
125C2×Q8—1131no—
126C2×Q8—2261no—
127C2×Q8D45211yescharacteristic
128C22×C4—21no—
129C22×C4—1131no—
130C22×C4—1131no—
131C22×C4—2261no—
132C22×C4C22×D11311yescharacteristic
133C2×C8—21no—
134C2×C8—2261no—
135C4⋊C4—21no—
136C4⋊C4—1131no—
137C4⋊C4—2261no—
138C4⋊C4—2261no—
139C4⋊C4—2261no—
140C4⋊C4—2261no—
141C4⋊C4—2261no—
142C4⋊C4—2261no—
143C4⋊C4—2261no—
144C4⋊C4—2261no—
145C4⋊C4—2261no—
146C4⋊C4—2261no—
147C4⋊C4D45211yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—2261no—
150C42—2261no—
151C42—2261no—
152C23D4×D11311yescharacteristic
153Q8—41no—
154Q8—9041no—
155Q8—4521no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—1132no—
163C2×C4—4522no—
164C2×C4—4521no—
165C2×C4—4521no—
166C2×C4—2261no—
167C2×C4—2261no—
168C2×C4—2261no—
169C2×C4—2261no—
170C2×C4—2261no—
171C2×C4D4×D11311yescharacteristic
172C2×C4C2×D45211yescharacteristic
173C8—41no—
174C8—4521no—
175C22—21no—
176C22—21no—
177C22#1681359211yescharacteristic
178C22Q16×D11311yescharacteristic
179C22#1681365111yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—9041no—
186C4—4521no—
187C4—4521no—
188C4—4521no—
189C4—2262no—
190C2—21no—
191C2—21no—
192C2#2029875511yescharacteristic
193C2#2029877211yescharacteristic
194C2#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#1617
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
98. C113#1617semidirect

Maximal subgroups

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

subgroupindex
#202992272
#202989342
#202989312
#202985382
#202983342
#202983232
#328×C1132
#1617113