Finite Group Databasebeta

← #28389196

Subgroups — #28389196

Order 14464.

248 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 59 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#124×D113C211yesmaximal, characteristic
2#20298653C212yesmaximal, complemented
3#20298338C211yesmaximal, characteristic, complemented
4#20298337C212yesmaximal, complemented
5#329×C113C211yesmaximal, characteristic, complemented
6C2×Q8×D113C411yescharacteristic
7C2×D4×D113C411yescharacteristic
8#16813611C411yescharacteristic
9#16813610C2211yescharacteristic
10#16813609C411yescharacteristic
11#16813608—22no—
12C22⋊C4×D113—22no—
13C42×D113C2211yescharacteristic
14#16813551—22no—
15#16813534—22no—
16#16813533C2212yescomplemented
17#124×C113C2211yescharacteristic
18#97×C113C2212yescomplemented
19C23×D113—21no—
20C2×Dic226—21no—
21C2×Dic226C2×C411yescharacteristic
22Q8×D113—42no—
23C2×D452C2×C411yescharacteristic
24C2×C22⋊D113—21no—
25D4×D113—42no—
26C2×C4×D113—21no—
27C2×C4×D113C2×C411yescharacteristic
28C2×C4×D113D412yes—
29C2×#11744751—22no—
30C22⋊Dic113—22no—
31#14268624—22no—
32#14268624—22no—
33C4×Dic113C2×C411yescharacteristic
34C4×Dic113D412yes—
35C2×Q8×C113C2×C411yescharacteristic
36C2×D4×C113C2×C411yescharacteristic
37C2×C8×C113—22no—
38C22⋊C4×C113—22no—
39C42×C113C2311yescharacteristic
40C23×C113—21no—
41C22×D113—21no—
42C22×D113—44no—
43C22×D113—42no—
44C22×D113C22⋊C411yescharacteristic
45Q8×C113—41no—
46D4×C113—41no—
47C2×C4×C113—21no—
48C2×C4×C113C22×C411yescharacteristic
49C2×C4×C113C2×D412yes—
50C22⋊D113—42no—
51C2×Dic113—21no—
52C2×Dic113C22⋊C412yes—
53C2×Dic113C22⋊C411yescharacteristic
54D452—41no—
55C4×D113—22no—
56C4×D113—42no—
57C4×D113—42no—
58Dic226—42no—
59Dic226—41no—
60C8×C113—42no—
61#11744751—42no—
62C22×C113—41no—
63C22×C113—42no—
64C22×C113C2×C22⋊C411yescharacteristic
65C2×D113—22no—
66C2×D113—41no—
67C2×D113—42no—
68C2×D113—84no—
69C2×D113#10012yes—
70C4×C113—21no—
71C4×C113—22no—
72C4×C113—41no—
73Dic113—21no—
74Dic113—22no—
75Dic113—41no—
76C2×C113—81no—
77C2×C113C2×#10011yescharacteristic
78C2×C113#42112yes—
79D113—22no—
80D113—81no—
81#1533—1131nomaximal, Sylow
82C113#153311yescharacteristic, complemented, Sylow
83C2×#124—1131no—
84#432—1132no—
85#329—1131no—
86#329—1132no—
87#329D11311yescharacteristic, complemented
88C22×Q8—1131no—
89C22×D4—1131no—
90#124—1131no—
91#124—1131no—
92#124—1131no—
93#124—2262no—
94#124C2×D11311yescharacteristic
95C2×C22⋊C4—2262no—
96C2×C42—1131no—
97C4⋊C8—2262no—
98C22⋊C8—2262no—
99#97—1132no—
100#97C2×D11312yescomplemented
101C24—2261no—
102C2×Q8—1131no—
103C2×Q8—4522no—
104C2×Q8—2261no—
105C2×Q8C4×D11311yescharacteristic
106C2×D4—1131no—
107C2×D4—4522no—
108C2×D4—2261no—
109C2×D4C4×D11311yescharacteristic
110C22×C4—1132no—
111C22×C4—1131no—
112C22×C4—2261no—
113C2×C8—22no—
114C2×C8—2262no—
115C22⋊C4—22no—
116C22⋊C4—2262no—
117C22⋊C4—2262no—
118C22⋊C4—2262no—
119C42—1131no—
120C42—1132no—
121C42C22×D11311yescharacteristic
122C23—21no—
123C23—1131no—
124C23—4522no—
125C23—4524no—
126C23—2261no—
127Q8—41no—
128Q8—4521no—
129Q8—4522no—
130D4—41no—
131D4—4521no—
132D4—4522no—
133C2×C4—21no—
134C2×C4—1132no—
135C2×C4—1131no—
136C2×C4—4522no—
137C2×C4—4522no—
138C2×C4—2262no—
139C2×C4—2261no—
140C2×C4C2×C4×D11311yescharacteristic
141C2×C4D4×D11312yes—
142C8—42no—
143C8—4522no—
144C22—41no—
145C22—42no—
146C22—1132no—
147C22—9044no—
148C22—4521no—
149C22—4522no—
150C22—2262no—
151C22C22⋊C4×D11311yescharacteristic
152C4—21no—
153C4—22no—
154C4—41no—
155C4—4521no—
156C4—2261no—
157C4—2262no—
158C2—81no—
159C2—9041no—
160C2—2262no—
161C2#100×D11311yescharacteristic
162C2#2029861312yes—
subgroupG/H
centerC22C22⋊C4×D113
commutatorC2×C4×C113C22×C4
FrattiniC42C22×D113
Fitting#329×C113C2
socleC22×C113C2×C22⋊C4
prime radicalC2×D4×D113C4
cosocleC42×C113C23
hypercenter#329D113
hypocenterC113#1533
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #20298653C2semidirect
3. #20298338C2semidirect
4. #20298337C2semidirect
5. #329×C113C2semidirect
16. #16813533C22semidirect
18. #97×C113C22semidirect
82. C113#1533semidirect
87. #329D113semidirect
100. #97C2×D113semidirect

Maximal subgroups

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

subgroupindex
#124×D1132
#202986532
#202983382
#202983372
#329×C1132
#1533113