Finite Group Databasebeta

← #28406098

Subgroups — #28406098

Order 14464.

242 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 58 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#20299618C211yesmaximal, characteristic, complemented
2#20299615C211yesmaximal, characteristic, complemented
3#20299457C212yesmaximal, complemented
4#20299456C212yesmaximal, complemented
5#20299143C211yesmaximal, characteristic
6#16813689C2212yes—
7#16813689C2212yes—
8C22⋊#11744753—21no—
9C22⋊#11744753—21no—
10#16813677—21no—
11C4×#11744753—21no—
12C2×#14268646—21no—
13#16813621C2211yescharacteristic
14#16813618C2211yescharacteristic
15#16813608—21no—
16#16813596C411yescharacteristic
17#16813594—21no—
18D4×Dic113C411yescharacteristic
19#16813584C411yescharacteristic
20#16813582—21no—
21C2×C4×Dic113C2211yescharacteristic
22#121×C113C411yescharacteristic
23C2×#11744753—22no—
24C2×#11744753—22no—
25#14268646—44no—
26C2×Dic226—21no—
27C2×D452C2×C411yescharacteristic
28C2×C22⋊D113—21no—
29C2×C22⋊D113—21no—
30C2×C22⋊D113—21no—
31C22×Dic113—21no—
32C22×Dic113D411yescharacteristic
33C22×Dic113D411yescharacteristic
34C2×C4×D113—21no—
35C4⋊Dic113C2×C411yescharacteristic
36#14268626—21no—
37C22⋊Dic113—21no—
38#14268624—21no—
39#14268624—21no—
40C4×Dic113C2×C411yescharacteristic
41C4×Dic113D411yescharacteristic
42C4×Dic113D411yescharacteristic
43C4×Dic113C2311yescharacteristic
44C2×D4×C113—21no—
45C2×D4×C113C2×C411yescharacteristic
46C22×C4×C113C2×C411yescharacteristic
47C4⋊C4×C113C2×C411yescharacteristic
48C22⋊C4×C113—21no—
49C23×C113—21no—
50C23×C113C22⋊C411yescharacteristic
51C22×D113—21no—
52D4×C113—41no—
53D4×C113—42no—
54C2×C4×C113—21no—
55C2×C4×C113—41no—
56C2×C4×C113C22⋊C411yescharacteristic
57C2×C4×C113C22×C411yescharacteristic
58C22⋊D113—42no—
59C22⋊D113—42no—
60C22⋊D113—42no—
61C2×Dic113—22no—
62C2×Dic113—22no—
63C2×Dic113—21no—
64C2×Dic113—42no—
65C2×Dic113C22⋊C411yescharacteristic
66C2×Dic113C22⋊C411yescharacteristic
67C2×Dic113C2×D411yescharacteristic
68C2×Dic113C2×D411yescharacteristic
69D452—41no—
70C4×D113—42no—
71Dic226—42no—
72#11744753—42no—
73#11744753—42no—
74C22×C113—21no—
75C22×C113—21no—
76C22×C113—21no—
77C22×C113—41no—
78C22×C113—41no—
79C22×C113—41no—
80C22×C113C2×C22⋊C411yescharacteristic
81C2×D113—41no—
82C2×D113—41no—
83C2×D113—41no—
84C4×C113—21no—
85C4×C113—21no—
86C4×C113—41no—
87Dic113—21no—
88Dic113—21no—
89Dic113—41no—
90Dic113#13512yes—
91Dic113AGL(1,ℤ/8)12yes—
92C2×C113—41no—
93C2×C113—81no—
94C2×C113#41311yescharacteristic
95C2×C113#41611yescharacteristic
96C2×C113#41811yescharacteristic
97D113—81no—
98#1553—1131nomaximal, Sylow
99C113#155311yescharacteristic, complemented, Sylow
100#532—1131no—
101#432—1131no—
102#431—1131no—
103#332—1132no—
104#331—1132no—
105C2×#41—2261no—
106C4⋊Q8—1131no—
107#127—1131no—
108#124—2261no—
109#121—1131no—
110#121—2261no—
111#121#9067311yescharacteristic
112C4×D4—1131no—
113C4×D4—1131no—
114C4×D4—2261no—
115C2×C42—1131no—
116C4⋊C8—1132no—
117C4⋊C8—1132no—
118C22⋊C8—2261no—
119C22⋊C8—2261no—
120#97—2261no—
121C4×C8—2261no—
122#41—4524no—
123C2×Q8—2261no—
124C2×D4—21no—
125C2×D4—1131no—
126C2×D4—2261no—
127C2×D4—2261no—
128C2×D4—2261no—
129C2×D4C2×#9067311yescharacteristic
130C22×C4—1131no—
131C22×C4—1131no—
132C22×C4—2261no—
133C22×C4—2261no—
134C22×C4C2×#9067311yescharacteristic
135C2×C8—2262no—
136C2×C8—2262no—
137C4⋊C4—1131no—
138C4⋊C4—2261no—
139C4⋊C4C2×#9067311yescharacteristic
140C22⋊C4—21no—
141C22⋊C4—2261no—
142C22⋊C4—2261no—
143C22⋊C4—2261no—
144C42—1131no—
145C42—1131no—
146C42—1131no—
147C42—1131no—
148C23—21no—
149C23—2261no—
150C23C22⋊#9067311yescharacteristic
151Q8—4522no—
152D4—41no—
153D4—42no—
154D4—4521no—
155D4—4522no—
156D4—4522no—
157D4—4522no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—1131no—
161C2×C4—1131no—
162C2×C4—1131no—
163C2×C4—1131no—
164C2×C4—4522no—
165C2×C4—4522no—
166C2×C4—2262no—
167C2×C4—2262no—
168C2×C4—2261no—
169C2×C4C22⋊#9067311yescharacteristic
170C2×C4C22×#9067311yescharacteristic
171C8—4522no—
172C8—4522no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—41no—
177C22—41no—
178C22—41no—
179C22—4521no—
180C22—4521no—
181C22—4521no—
182C22C2×C22⋊#9067311yescharacteristic
183C4—21no—
184C4—21no—
185C4—41no—
186C4—1132no—
187C4—1132no—
188C4—4521no—
189C4—2261no—
190C4—2261no—
191C2—41no—
192C2—81no—
193C2—9041no—
194C2#2029958511yescharacteristic
195C2#2029958811yescharacteristic
196C2#2029959011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
Fitting#121×C113C4
socleC22×C113C2×C22⋊C4
prime radical#20299143C2
cosocleC4×Dic113C23
hypercenter#121#90673
hypocenterC113#1553
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #20299618C2semidirect
2. #20299615C2semidirect
3. #20299457C2semidirect
4. #20299456C2semidirect
99. C113#1553semidirect

Maximal subgroups

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

subgroupindex
#202996182
#202996152
#202994572
#202994562
#202991432
#1553113