Finite Group Databasebeta

← #28405673

Subgroups — #28405673

Order 14464.

162 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 38 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#20299585C211yesmaximal, characteristic
2#20299572C211yesmaximal, characteristic
3#20298570C211yesmaximal, characteristic
4C2×#14268657C411yescharacteristic, complemented
5C2×#14268656—21no—
6C2×#14268655C411yescharacteristic, complemented
7#16813683C412yescomplemented
8#16813682—21no—
9C22⋊#11744753—21no—
10C22⋊#11744753—21no—
11C2×#14268646C2211yescharacteristic
12#16813578—21no—
13#16813537C411yescharacteristic
14#16813536—21no—
15#99×C113C411yescharacteristic
16#14268657—41no—
17#14268656—22no—
18#14268656—41no—
19#14268655—41no—
20C2×#11744753—21no—
21C2×#11744753—21no—
22C2×#11744753—41no—
23#14268646—41no—
24#14268646—41no—
25C2×Dic226C2×C411yescharacteristic
26C2×C22⋊D113D411yescharacteristic
27C2×C22⋊D113Q811yescharacteristic
28C22×Dic113D411yescharacteristic
29C22×Dic113D411yescharacteristic
30C2×C4×D113C2×C411yescharacteristic
31#14268626—41no—
32C22⋊Dic113—21no—
33C4×Dic113—41no—
34C2×D4×C113C2×C411yescharacteristic
35C22⋊C4×C113—21no—
36C23×C113C22⋊C411yescharacteristic
37C23×C113C4⋊C411yescharacteristic
38C22×D113C4⋊C411yescharacteristic
39D4×C113—41no—
40C2×C4×C113—41no—
41C2×C4×C113C4211yescharacteristic
42C22⋊D113—41no—
43C22⋊D113—41no—
44C2×Dic113—21no—
45C2×Dic113—21no—
46C2×Dic113—21no—
47C2×Dic113—21no—
48C2×Dic113—41no—
49C2×Dic113C22⋊C411yescharacteristic
50C2×Dic113C22⋊C411yescharacteristic
51C2×Dic113C4⋊C411yescharacteristic
52C4×D113—21no—
53C4×D113—21no—
54Dic226—41no—
55#11744753—42no—
56#11744753—41no—
57#11744753—41no—
58C22×C113—21no—
59C22×C113—21no—
60C22×C113—41no—
61C22×C113—41no—
62C22×C113#9511yescharacteristic
63C2×D113—21no—
64C2×D113—41no—
65C4×C113—21no—
66C4×C113—81no—
67Dic113—21no—
68Dic113—21no—
69Dic113—81no—
70Dic113#9911yescharacteristic
71Dic113#9911yescharacteristic
72C2×C113—21no—
73C2×C113—41no—
74C2×C113—41no—
75C2×C113#34211yescharacteristic
76D113—41no—
77#1395—1131nomaximal, Sylow
78C113#139511yescharacteristic, complemented, Sylow
79#413—1131no—
80#410—1131no—
81#408—1131no—
82C2×#41—1131no—
83C2×M16—1131no—
84C2×M16—2261no—
85C22×C8—1131no—
86#117—2261no—
87#101—1132no—
88#100—2261no—
89#99—1131no—
90#99—2261no—
91#99#9067311yescharacteristic
92C22⋊C8—2261no—
93C22⋊C8—2261no—
94#41—4521no—
95#41—4521no—
96C2×Q8—1131no—
97C2×D4—1131no—
98C2×D4—1131no—
99C2×D4C2×#9067311yescharacteristic
100C22×C4—1131no—
101C22×C4—1131no—
102C22×C4—1131no—
103M16—4521no—
104M16—4521no—
105M16—2262no—
106C2×C8—4521no—
107C2×C8—4521no—
108C2×C8—2261no—
109C2×C8—2261no—
110C4⋊C4—4521no—
111C22⋊C4—21no—
112C22⋊C4—2261no—
113C42—4521no—
114C23—1131no—
115C23C22⋊#9067311yescharacteristic
116C23C4⋊#9067311yescharacteristic
117Q8—4521no—
118D4—41no—
119D4—4521no—
120D4—4521no—
121C2×C4—41no—
122C2×C4—1131no—
123C2×C4—1131no—
124C2×C4—1131no—
125C2×C4—4521no—
126C2×C4—2261no—
127C2×C4—2261no—
128C2×C4—2261no—
129C2×C4—2261no—
130C2×C4—2261no—
131C2×C4—2261no—
132C2×C4C4×#9067311yescharacteristic
133C8—4521no—
134C8—4521no—
135C8—4522no—
136C22—21no—
137C22—21no—
138C22—41no—
139C22—41no—
140C22—4521no—
141C22—2261no—
142C22(C2×#90673)⋊C411yescharacteristic
143C4—21no—
144C4—81no—
145C4—1131no—
146C4—1131no—
147C4—9041no—
148C4—2261no—
149C4—2261no—
150C2—21no—
151C2—41no—
152C2—41no—
153C2—4521no—
154C2#2029947511yescharacteristic
subgroupG/H
centerC2#20299475
commutatorC2×C4×C113C42
FrattiniC2×D4C2×#90673
Fitting#99×C113C4
socleC2×C113#342
prime radical, cosocleC2×#14268646C22
hypercenter#99#90673
hypocenterC113#1395
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #99

Complements

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

NH ≅ G/Ntype
4. C2×#14268657C4semidirect
6. C2×#14268655C4semidirect
7. #16813683C4semidirect
78. C113#1395semidirect

Maximal subgroups

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

subgroupindex
#202995852
#202995722
#202985702
#1395113