Finite Group Databasebeta

← #28400952

Subgroups — #28400952

Order 14464.

380 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 129 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#20299151C211yesmaximal, characteristic
2C2×#16813620C211yesmaximal, characteristic
3#20298965C214yesmaximal, complemented
4#20298947C214yesmaximal, complemented
5#20298608C211yesmaximal, characteristic
6#20298607C211yesmaximal, characteristic
7#20298606C211yesmaximal, characteristic
8M16×Dic113C211yesmaximal, characteristic
9#419×C113C211yesmaximal, characteristic
10C22×Dic226C2211yescharacteristic
11C2×#14268631C2211yescharacteristic
12#16813621C2212yes—
13#16813620—22no—
14#16813620C2212yes—
15#16813620C2212yes—
16#16813613C2212yes—
17#16813599—22no—
18C4×Dic226—22no—
19#16813581C2211yescharacteristic
20C2×#14268626—22no—
21C2×C4×Dic113C2211yescharacteristic
22#16813547C2214yes—
23#16813546C2214yes—
24#16813545C2214yes—
25#16813532C2212yes—
26C8×Dic113C2212yes—
27C22×Q8×C113C2211yescharacteristic
28C2×M16×C113C2211yescharacteristic
29#117×C113C2211yescharacteristic
30#103×C113C2214yes—
31C2×Dic226—22no—
32C2×Dic226—22no—
33C2×Dic226—21no—
34C2×Dic226—22no—
35C2×Dic226C2312yes—
36C22×Dic113—21no—
37C22×Dic113D412yes—
38#14268631—22no—
39C2×#11744751C2312yes—
40C4⋊Dic113—22no—
41C4⋊Dic113C2312yes—
42#14268626—24no—
43#14268626—24no—
44#14268626—22no—
45#14268626—22no—
46C22⋊Dic113—21no—
47C4×Dic113—21no—
48C4×Dic113D412yes—
49C4×Dic113C2311yescharacteristic
50C4×Dic113C2311yescharacteristic
51C2×Q8×C113—21no—
52C2×Q8×C113—22no—
53C2×Q8×C113—22no—
54C2×Q8×C113C2312yes—
55C22×C4×C113—21no—
56C22×C4×C113C2311yescharacteristic
57M16×C113—22no—
58C2×C8×C113C2312yes—
59C4⋊C4×C113C2312yes—
60C22⋊C4×C113—21no—
61C42×C113—21no—
62C23×C113C2×D411yescharacteristic
63Q8×C113—22no—
64Q8×C113—22no—
65Q8×C113—42no—
66C2×C4×C113—22no—
67C2×C4×C113—22no—
68C2×C4×C113—42no—
69C2×C4×C113C2×D411yescharacteristic
70C2×C4×C113#4112yes—
71C2×C4×C113#4112yes—
72C2×C4×C113C2411yescharacteristic
73C2×Dic113—24no—
74C2×Dic113—22no—
75C2×Dic113—22no—
76C2×Dic113—42no—
77C2×Dic113C2×D412yes—
78C2×Dic113C2×D412yes—
79Dic226—22no—
80Dic226—22no—
81Dic226—42no—
82Dic226—44no—
83C8×C113—22no—
84#11744751—22no—
85C22×C113—22no—
86C22×C113#12412yes—
87C22×C113C22×D411yescharacteristic
88C4×C113—42no—
89C4×C113—42no—
90C4×C113#12412yes—
91C4×C113C2×#4111yescharacteristic
92C4×C113C2×#4111yescharacteristic
93Dic113—22no—
94Dic113—42no—
95Dic113—42no—
96Dic113#13714yes—
97C2×C113—22no—
98C2×C113C2×#12411yescharacteristic
99C2×C113C2×#13712yes—
100#3139—1131nomaximal, Sylow
101C113#313911yescharacteristic, complemented, Sylow
102#533—1131no—
103C2×C4⋊Q8—1131no—
104#491—1134no—
105#487—1134no—
106#419—1131no—
107#419—1131no—
108#419—1131no—
109#419D11311yescharacteristic
110C4×M16—1131no—
111C22×Q8—1131no—
112C22×Q8C2×D11311yescharacteristic
113C2×M16—1131no—
114C2×M16C2×D11311yescharacteristic
115C4⋊Q8—1132no—
116C4⋊Q8—1132no—
117C4⋊Q8—1132no—
118C4⋊Q8—2262no—
119#125—1132no—
120C22⋊Q8—2262no—
121C4×Q8—2262no—
122#117—1131no—
123#117C2×D11311yescharacteristic
124C2×C4⋊C4—2262no—
125C2×C42—1131no—
126#103—1134no—
127#103—1134no—
128#103—1134no—
129#103C2×D11314yes—
130#97—1132no—
131C4×C8—1132no—
132C2×Q8—21no—
133C2×Q8—22no—
134C2×Q8—22no—
135C2×Q8—1132no—
136C2×Q8—2262no—
137C2×Q8—2262no—
138C2×Q8—2262no—
139C2×Q8—2261no—
140C2×Q8C22×D11312yes—
141C22×C4—21no—
142C22×C4—1132no—
143C22×C4—2261no—
144C22×C4C22×D11311yescharacteristic
145M16—22no—
146M16—2262no—
147C2×C8—1132no—
148C2×C8C22×D11312yes—
149C4⋊C4—1132no—
150C4⋊C4—2264no—
151C4⋊C4—2264no—
152C4⋊C4—2262no—
153C4⋊C4—2262no—
154C4⋊C4—2262no—
155C4⋊C4C22×D11312yes—
156C22⋊C4—21no—
157C22⋊C4—2261no—
158C42—21no—
159C42—1132no—
160C42—1131no—
161C42—1131no—
162C42—2261no—
163C23D4×D11311yescharacteristic
164Q8—22no—
165Q8—22no—
166Q8—42no—
167Q8—4524no—
168Q8—4522no—
169Q8—2262no—
170Q8—2262no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—42no—
174C2×C4—1132no—
175C2×C4—1132no—
176C2×C4—4522no—
177C2×C4—2264no—
178C2×C4—2262no—
179C2×C4—2262no—
180C2×C4D4×D11311yescharacteristic
181C2×C4#1426864612yes—
182C2×C4#1426864712yes—
183C2×C4C23×D11311yescharacteristic
184C8—22no—
185C8—2262no—
186C22—22no—
187C22#1681360812yes—
188C22C2×D4×D11311yescharacteristic
189C4—42no—
190C4—42no—
191C4—1134no—
192C4—4522no—
193C4—4522no—
194C4—2262no—
195C4#1681360812yes—
196C4C2×#1426864611yescharacteristic
197C4C2×#1426864711yescharacteristic
198C2—22no—
199C2C2×#1681360811yescharacteristic
200C2#137×D11312yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#419×C113C2
socleC22×C113C22×D4
prime radicalC23×C113C2×D4
hypercenter#419D113
hypocenterC113#3139
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. #20298965C2semidirect
4. #20298947C2semidirect
101. C113#3139semidirect

Maximal subgroups

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

subgroupindex
#202991512
C2×#168136202
#202989652
#202989472
#202986082
#202986072
#202986062
M16×Dic1132
#419×C1132
#3139113