Finite Group Databasebeta

← #28388501

Subgroups — #28388501

Order 14464.

294 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 37 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#20298453C211yesmaximal, characteristic
2#20298322C211yesmaximal, characteristic, complemented
3#323×C113C211yesmaximal, characteristic, complemented
4C24×D113C411yescharacteristic
5C2×C22⋊Dic113C411yescharacteristic
6C2×#14268624—21no—
7C2×#14268624—21no—
8C22⋊#11744751—21no—
9C2×C22⋊C4×C113C2211yescharacteristic
10C22⋊C8×C113—21no—
11C23×D113—21no—
12C23×D113—21no—
13C23×D113—42no—
14C23×D113—42no—
15C23×D113—41no—
16C23×D113—41no—
17C23×D113C812yescomplemented
18C22×Dic113—21no—
19C2×#11744751—41no—
20C22⋊Dic113—41no—
21#14268624—42no—
22#14268624—42no—
23C24×C113C2×C411yescharacteristic
24C22×C4×C113D411yescharacteristic
25C22×C4×C113D411yescharacteristic
26C2×C8×C113—41no—
27C22⋊C4×C113—41no—
28C23×C113—21no—
29C23×C113—21no—
30C23×C113—41no—
31C23×C113—41no—
32C23×C113C22⋊C411yescharacteristic
33C23×C113C2×C811yescharacteristic
34C23×C113M1611yescharacteristic
35C22×D113—22no—
36C22×D113—22no—
37C22×D113—22no—
38C22×D113—44no—
39C22×D113—44no—
40C22×D113—41no—
41C22×D113—41no—
42C22×D113—42no—
43C22×D113—48no—
44C22×D113—42no—
45C22×D113—42no—
46C22×D113—41no—
47C22×D113—41no—
48C22×D113—42no—
49C22×D113—42no—
50C22×D113—42no—
51C2×C4×C113—21no—
52C2×C4×C113—21no—
53C2×C4×C113—41no—
54C2×C4×C113—41no—
55C2×Dic113—41no—
56C2×Dic113—41no—
57C2×Dic113—41no—
58C8×C113—81no—
59#11744751—81no—
60C22×C113—21no—
61C22×C113—21no—
62C22×C113—21no—
63C22×C113—21no—
64C22×C113—41no—
65C22×C113—41no—
66C22×C113—42no—
67C22×C113—41no—
68C22×C113—41no—
69C22×C113C22⋊C811yescharacteristic
70C22×C113#9911yescharacteristic
71C22×C113#10011yescharacteristic
72C2×D113—24no—
73C2×D113—42no—
74C2×D113—42no—
75C2×D113—42no—
76C2×D113—44no—
77C2×D113—44no—
78C2×D113—44no—
79C2×D113—42no—
80C2×D113—42no—
81C2×D113—42no—
82C2×D113—44no—
83C4×C113—41no—
84C4×C113—41no—
85Dic113—81no—
86C2×C113—21no—
87C2×C113—21no—
88C2×C113—41no—
89C2×C113—41no—
90C2×C113#32311yescharacteristic
91C2×C113AΣL(1,𝔽16)11yescharacteristic
92C2×C113AΣL(1,𝔽16)11yescharacteristic
93D113—44no—
94#1316—1131nomaximal, Sylow
95C113#131611yescharacteristic, complemented, Sylow
96#379—1131no—
97#323—1131no—
98#323D11311yescharacteristic, complemented
99C25—1131no—
100C2×C22⋊C4—1131no—
101C2×C22⋊C4—2261no—
102C2×C22⋊C4—2261no—
103C2×C22⋊C4C2×D11311yescharacteristic
104C22⋊C8—21no—
105C22⋊C8—2261no—
106C24—1132no—
107C24—4521no—
108C24—4521no—
109C24—4522no—
110C24—4522no—
111C24—2261no—
112C24—2261no—
113C24C4×D11311yescharacteristic
114C22×C4—2261no—
115C22×C4D45211yescharacteristic
116C22×C4C22⋊D11311yescharacteristic
117C2×C8—41no—
118C2×C8—4521no—
119C22⋊C4—41no—
120C22⋊C4—4522no—
121C22⋊C4—4522no—
122C22⋊C4—4521no—
123C23—21no—
124C23—21no—
125C23—41no—
126C23—41no—
127C23—4522no—
128C23—4521no—
129C23—4521no—
130C23—4522no—
131C23—4522no—
132C23—4522no—
133C23—4528no—
134C23—4522no—
135C23—4522no—
136C23—4524no—
137C23—4524no—
138C23—4521no—
139C23—4521no—
140C23—2262no—
141C23—2262no—
142C23—2262no—
143C23#1426862411yescharacteristic
144C23C8×D11311yescharacteristic
145C23#1426863011yescharacteristic
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—4521no—
151C2×C4—4521no—
152C2×C4—4521no—
153C8—81no—
154C8—9041no—
155C22—21no—
156C22—21no—
157C22—21no—
158C22—21no—
159C22—41no—
160C22—41no—
161C22—42no—
162C22—41no—
163C22—41no—
164C22—4522no—
165C22—4522no—
166C22—4522no—
167C22—4524no—
168C22—4524no—
169C22—4524no—
170C22—4524no—
171C22—4522no—
172C22—4522no—
173C22—4522no—
174C22—2264no—
175C22#1681353411yescharacteristic
176C22#1681353611yescharacteristic
177C22#1681353811yescharacteristic
178C4—41no—
179C4—41no—
180C4—9041no—
181C2—21no—
182C2—21no—
183C2—41no—
184C2—41no—
185C2—4524no—
186C2#2029832111yescharacteristic
187C2#2029838411yescharacteristic
188C2#2029838611yescharacteristic
subgroupG/H
centerC22#16813536
commutatorC23×C113C2×C8
FrattiniC2×C22⋊C4C2×D113
Fitting#323×C113C2
socleC22×C113#99
prime radicalC24×D113C4
cosocleC2×C22⋊C4×C113C22
hypercenter#323D113
hypocenterC113#1316
LCSG ▷ C23×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #20298322C2semidirect
3. #323×C113C2semidirect
17. C23×D113C8semidirect
95. C113#1316semidirect
98. #323D113semidirect

Maximal subgroups

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

subgroupindex
#202984532
#202983222
#323×C1132
#1316113