Finite Group Databasebeta

← #28400505

Subgroups — #28400505

Order 14464.

414 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 133 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#20299109C211yesmaximal, characteristic
2#20298939C214yesmaximal, complemented
3#20298922C214yesmaximal, complemented
4#20298638C212yesmaximal, complemented
5#20298597C212yesmaximal, complemented
6#20298562C211yesmaximal, characteristic, complemented
7C2×#117×C113C211yesmaximal, characteristic, complemented
8C2×#14268647C2211yescharacteristic
9C2×#14268631C2212yes—
10#16813605—21no—
11#16813601C2212yes—
12#16813596C2212yes—
13#16813591—21no—
14C4×C22⋊D113—22no—
15#16813581C2211yescharacteristic
16#16813555C2214yescomplemented
17#16813553C2214yescomplemented
18#16813545C2214yescomplemented
19#16813542C2214yescomplemented
20C22⋊#11744751C2214yes—
21C23×C4×C113C2211yescharacteristic
22#117×C113—22no—
23#117×C113C2214yes—
24C2×C4⋊C4×C113C2212yes—
25C2×C22⋊C4×C113—21no—
26C2×C42×C113—21no—
27#14268647—24no—
28C2×Dic226C2311yescharacteristic
29C2×D452C2311yescharacteristic
30C2×C22⋊D113—22no—
31C2×C22⋊D113—21no—
32C2×C4×D113—21no—
33#14268631—24no—
34C2×#11744751C2314yes—
35C4⋊Dic113C2312yes—
36#14268626—22no—
37C22⋊Dic113—21no—
38C22⋊Dic113—22no—
39#14268624—22no—
40C4×Dic113—21no—
41C24×C113D411yescharacteristic
42C22×C4×C113—24no—
43C22×C4×C113—22no—
44C22×C4×C113D412yes—
45C22×C4×C113D411yescharacteristic
46C22×C4×C113C2312yes—
47C22×C4×C113C2311yescharacteristic
48C4⋊C4×C113—22no—
49C4⋊C4×C113C2314yes—
50C22⋊C4×C113—24no—
51C42×C113—24no—
52C23×C113—22no—
53C23×C113—42no—
54C23×C113C2×D412yes—
55C23×C113C2×D411yescharacteristic
56C22×D113—21no—
57C2×C4×C113—22no—
58C2×C4×C113—24no—
59C2×C4×C113—24no—
60C2×C4×C113—24no—
61C2×C4×C113—44no—
62C2×C4×C113C2×D412yes—
63C2×C4×C113C2×D411yescharacteristic
64C2×C4×C113#4114yes—
65C2×C4×C113C2411yescharacteristic
66C22⋊D113—44no—
67C22⋊D113—42no—
68C2×Dic113—22no—
69C2×Dic113—21no—
70D452—22no—
71C4×D113—42no—
72Dic226—22no—
73#11744751—24no—
74C22×C113—22no—
75C22×C113—22no—
76C22×C113—22no—
77C22×C113—22no—
78C22×C113—44no—
79C22×C113#12312yes—
80C22×C113C22×D411yescharacteristic
81C2×D113—41no—
82C2×D113—42no—
83C4×C113—22no—
84C4×C113—44no—
85C4×C113#12312yes—
86C4×C113C2×#4112yes—
87Dic113—41no—
88Dic113—42no—
89C2×C113—22no—
90C2×C113—42no—
91C2×C113C2×#12311yescharacteristic
92C2×C113#57512yes—
93D113—81no—
94#3093—1131nomaximal, Sylow
95C113#309311yescharacteristic, complemented, Sylow
96#525—1131no—
97C2×#117D11311yescharacteristic, complemented
98#485—1134no—
99#482—1134no—
100#428—1132no—
101#417—1132no—
102#407—1131no—
103C2×#41—1131no—
104C23×C4C2×D11311yescharacteristic
105C2×M16—1132no—
106#123—2261no—
107C22⋊Q8—1132no—
108#121—1132no—
109#120—2261no—
110C4×D4—2262no—
111#117—22no—
112#117—1131no—
113#117C2×D11314yes—
114C2×C4⋊C4C2×D11312yes—
115C2×C22⋊C4—21no—
116C2×C42—21no—
117#107—1134no—
118#106—1134no—
119#103—1134no—
120#102—1134no—
121C22⋊C8—1134no—
122C24C22⋊D11311yescharacteristic
123#41—2264no—
124C2×Q8—1131no—
125C2×D4—1131no—
126C2×D4—2262no—
127C2×D4—2261no—
128C22×C4—24no—
129C22×C4—22no—
130C22×C4—2261no—
131C22×C4C22⋊D11311yescharacteristic
132C22×C4C22⋊D11312yes—
133C22×C4C22×D11312yes—
134C22×C4C22×D11311yescharacteristic
135M16—2264no—
136C2×C8—1134no—
137C4⋊C4—22no—
138C4⋊C4—1132no—
139C4⋊C4—2262no—
140C4⋊C4C22×D11314yes—
141C22⋊C4—24no—
142C22⋊C4—2261no—
143C22⋊C4—2262no—
144C22⋊C4—2262no—
145C42—24no—
146C42—2261no—
147C23—22no—
148C23—42no—
149C23—2261no—
150C23C2×C22⋊D11312yes—
151C23C2×C22⋊D11311yescharacteristic
152Q8—2262no—
153D4—4524no—
154D4—4522no—
155D4—2262no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—24no—
160C2×C4—44no—
161C2×C4—4522no—
162C2×C4—2262no—
163C2×C4—2261no—
164C2×C4C2×C22⋊D11312yes—
165C2×C4C2×C22⋊D11311yescharacteristic
166C2×C4#1426864714yes—
167C2×C4C23×D11311yescharacteristic
168C8—2264no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—4521no—
175C22—4522no—
176C22#1681360512yes—
177C22C22×C22⋊D11311yescharacteristic
178C4—22no—
179C4—44no—
180C4—4521no—
181C4—4522no—
182C4#1681360512yes—
183C4C2×#1426864712yes—
184C2—22no—
185C2—42no—
186C2—9041no—
187C2C2×#1681360511yescharacteristic
188C2#2029939612yes—
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#117×C113C2
socleC22×C113C22×D4
prime radical#20299109C2
hypercenterC2×#117D113
hypocenterC113#3093
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #20298939C2semidirect
3. #20298922C2semidirect
4. #20298638C2semidirect
5. #20298597C2semidirect
6. #20298562C2semidirect
7. C2×#117×C113C2semidirect
16. #16813555C22semidirect
17. #16813553C22semidirect
18. #16813545C22semidirect
19. #16813542C22semidirect
95. C113#3093semidirect
97. C2×#117D113semidirect

Maximal subgroups

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

subgroupindex
#202991092
#202989392
#202989222
#202986382
#202985972
#202985622
C2×#117×C1132
#3093113