Finite Group Databasebeta

← #28400392

Subgroups — #28400392

Order 14464.

384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C4×#14268647C211yesmaximal, characteristic
2#20298902C214yesmaximal, complemented
3#20298895C214yesmaximal, complemented
4#20298638C212yesmaximal, complemented
5#20298622C211yesmaximal, characteristic, complemented
6#20298597C212yesmaximal
7C2×#125×C113C211yesmaximal, characteristic, complemented
8C2×#14268647C2211yescharacteristic
9C2×#14268631C2212yes—
10C4×Dic226C2212yes—
11C4×D452C2212yes—
12C4×C22⋊D113—22no—
13#16813581C2211yescharacteristic
14#16813579—21no—
15C42×D113—21no—
16#16813555C2214yes—
17#16813553C2214yes—
18C4⋊#11744751C2214yes—
19#16813545C2214yes—
20#16813542C2214yes—
21#125×C113—21no—
22#125×C113—21no—
23#125×C113C2214yes—
24C2×C4⋊C4×C113—22no—
25C2×C4⋊C4×C113C2212yes—
26C2×C42×C113C2211yescharacteristic
27#14268647—22no—
28#14268647Q814yes—
29C2×Dic226C2311yescharacteristic
30C2×D452C2311yescharacteristic
31C2×C22⋊D113—21no—
32C2×C4×D113—21no—
33C2×C4×D113—22no—
34#14268631—24no—
35C2×#11744751C2314yes—
36C4⋊Dic113C2312yes—
37#14268626—22no—
38C22⋊Dic113—21no—
39#14268624—22no—
40C4×Dic113—21no—
41C4×Dic113—22no—
42C22×C4×C113—22no—
43C22×C4×C113D412yes—
44C22×C4×C113C2311yescharacteristic
45C4⋊C4×C113—24no—
46C4⋊C4×C113—24no—
47C4⋊C4×C113—22no—
48C4⋊C4×C113C2314yes—
49C42×C113D411yescharacteristic
50C42×C113D411yescharacteristic
51C42×C113C2312yes—
52C23×C113C2×D411yescharacteristic
53C22×D113—21no—
54C2×C4×C113—24no—
55C2×C4×C113—42no—
56C2×C4×C113—44no—
57C2×C4×C113C2×D412yes—
58C2×C4×C113C2×D412yes—
59C2×C4×C113C2×D411yescharacteristic
60C2×C4×C113C2×Q812yes—
61C2×C4×C113#4112yes—
62C2×C4×C113C2411yescharacteristic
63C22⋊D113—24no—
64C2×Dic113—21no—
65C2×Dic113—22no—
66D452—21no—
67D452C2×Q812yes—
68C4×D113—24no—
69C4×D113—44no—
70Dic226—21no—
71Dic226C2×Q812yes—
72#11744751—24no—
73C22×C113—22no—
74C22×C113C22⋊Q812yes—
75C22×C113C22×D411yescharacteristic
76C2×D113—22no—
77C2×D113—42no—
78C4×C113—22no—
79C4×C113—22no—
80C4×C113—44no—
81C4×C113C22⋊Q812yes—
82C4×C113C22×Q811yescharacteristic
83C4×C113C2×#4111yescharacteristic
84Dic113—22no—
85Dic113—42no—
86C2×C113—22no—
87C2×C113C2×C22⋊Q811yescharacteristic
88C2×C113#57512yes—
89D113—42no—
90#3080—1131nomaximal, Sylow
91C113#308011yescharacteristic, complemented, Sylow
92C2×#125D11311yescharacteristic, complemented
93C4×#41—1131no—
94#479—1134no—
95#478—1134no—
96#428—1132no—
97#423—1131no—
98#417—1132no—
99C2×#41—1131no—
100C2×M16—1132no—
101#125—21no—
102#125—21no—
103#125C2×D11314yes—
104C4×Q8—1132no—
105C4×D4—1132no—
106C4×D4—2262no—
107#117—1131no—
108#117—2261no—
109C2×C4⋊C4—22no—
110C2×C4⋊C4C2×D11312yes—
111C2×C42—2261no—
112C2×C42C2×D11311yescharacteristic
113#107—1134no—
114#106—1134no—
115C4⋊C8—1134no—
116#103—1134no—
117#102—1134no—
118#41—1134no—
119#41—2262no—
120C2×Q8—1131no—
121C2×D4—1131no—
122C2×D4—2261no—
123C22×C4—22no—
124C22×C4—2262no—
125C22×C4—2261no—
126C22×C4C22⋊D11312yes—
127C22×C4C22×D11311yescharacteristic
128M16—2264no—
129C2×C8—1134no—
130C4⋊C4—24no—
131C4⋊C4—24no—
132C4⋊C4—22no—
133C4⋊C4—1132no—
134C4⋊C4—2262no—
135C4⋊C4C22×D11314yes—
136C22⋊C4—2261no—
137C22⋊C4—2262no—
138C42—2261no—
139C42—2262no—
140C42C22⋊D11311yescharacteristic
141C42C22⋊D11311yescharacteristic
142C42C22×D11312yes—
143C23—2261no—
144C23C2×C22⋊D11311yescharacteristic
145Q8—1132no—
146Q8—2261no—
147D4—1132no—
148D4—2264no—
149D4—2261no—
150C2×C4—24no—
151C2×C4—42no—
152C2×C4—44no—
153C2×C4—4524no—
154C2×C4—2262no—
155C2×C4—2261no—
156C2×C4—2264no—
157C2×C4C2×C22⋊D11312yes—
158C2×C4C2×C22⋊D11312yes—
159C2×C4C2×C22⋊D11311yescharacteristic
160C2×C4Q8×D11312yes—
161C2×C4#1426864812yes—
162C2×C4C23×D11311yescharacteristic
163C8—2264no—
164C22—22no—
165C22—4522no—
166C22—2262no—
167C22#1681359812yes—
168C22C22×C22⋊D11311yescharacteristic
169C4—22no—
170C4—22no—
171C4—44no—
172C4—4522no—
173C4—2262no—
174C4#1681359812yes—
175C4C2×Q8×D11311yescharacteristic
176C4C2×#1426864811yescharacteristic
177C2—22no—
178C2—4522no—
179C2C2×#1681359811yescharacteristic
180C2#2029939612yes—
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#125×C113C2
socleC22×C113C22×D4
prime radicalC2×#14268647C22
hypercenterC2×#125D113
hypocenterC113#3080
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #20298902C2semidirect
3. #20298895C2semidirect
4. #20298638C2semidirect
5. #20298622C2semidirect
7. C2×#125×C113C2semidirect
91. C113#3080semidirect
92. C2×#125D113semidirect

Maximal subgroups

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

subgroupindex
C4×#142686472
#202989022
#202988952
#202986382
#202986222
#202985972
C2×#125×C1132
#3080113