Finite Group Databasebeta

← #28401294

Subgroups — #28401294

Order 14464.

402 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 125 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#20299153C211yesmaximal, characteristic, complemented
2#20299149C211yesmaximal, characteristic
3#20298971C211yesmaximal, characteristic, complemented
4#20298950C211yesmaximal, characteristic, complemented
5#20298946C211yesmaximal, characteristic, complemented
6#20298845C214yesmaximal, complemented
7#20298697C214yesmaximal, complemented
8C4×#14268630C211yesmaximal, characteristic, complemented
9#500×C113C211yesmaximal, characteristic, complemented
10C2×#14268648—21no—
11C2×#14268636C2214yes—
12C2×#14268630C2212yes—
13#16813622C2211yescharacteristic
14#16813619C2211yescharacteristic
15#16813613—21no—
16#16813611—21no—
17#16813602C2212yes—
18#16813598—21no—
19#16813597—21no—
20#16813597C2212yes—
21Q8×Dic113—21no—
22#16813587C2212yes—
23#16813584—21no—
24#16813584C2212yes—
25#16813580—21no—
26C42×D113C2211yescharacteristic
27#16813545C2214yes—
28#16813542C2214yes—
29#16813532C2212yes—
30C4×#11744751C2211yescharacteristic
31C4⋊Q8×C113C2211yescharacteristic
32C4⋊Q8×C113C2211yescharacteristic
33#107×C113C2214yes—
34C4×C8×C113C2211yescharacteristic
35#14268648—44no—
36C2×Dic226C2312yes—
37C2×D452—22no—
38C2×D452—21no—
39C2×D452—21no—
40C2×D452C2312yes—
41C2×C4×D113—22no—
42C2×C4×D113D411yescharacteristic
43C2×C4×D113D411yescharacteristic
44C2×C4×D113C2311yescharacteristic
45#14268636—28no—
46#14268630—24no—
47C2×#11744751C2312yes—
48C4⋊Dic113—21no—
49C4⋊Dic113—21no—
50C4⋊Dic113—22no—
51#14268626—22no—
52#14268624—22no—
53#14268624—22no—
54#14268624—22no—
55C4×Dic113—22no—
56C4×Dic113D411yescharacteristic
57C4×Dic113D411yescharacteristic
58C4×Dic113C2311yescharacteristic
59C2×Q8×C113—21no—
60C2×Q8×C113—21no—
61C2×C8×C113C2312yes—
62C4⋊C4×C113—21no—
63C4⋊C4×C113—21no—
64C4⋊C4×C113C2312yes—
65C4⋊C4×C113C2312yes—
66C42×C113C2311yescharacteristic
67C22×D113—22no—
68C22×D113C2×D411yescharacteristic
69Q8×C113—42no—
70Q8×C113—42no—
71C2×C4×C113—22no—
72C2×C4×C113—22no—
73C2×C4×C113C2×D411yescharacteristic
74C2×C4×C113C2×D411yescharacteristic
75C2×C4×C113C2411yescharacteristic
76C2×Dic113—22no—
77C2×Dic113C2×D411yescharacteristic
78C2×Dic113C2×D411yescharacteristic
79C2×Dic113C2×D411yescharacteristic
80D452—24no—
81D452—44no—
82D452—42no—
83D452—42no—
84C4×D113—22no—
85C4×D113—22no—
86C4×D113—22no—
87C4×D113—44no—
88Dic226—24no—
89C8×C113#4114yescomplemented
90#11744751—22no—
91C22×C113C22×D411yescharacteristic
92C2×D113—21no—
93C2×D113—21no—
94C2×D113—21no—
95C2×D113—42no—
96C2×D113—42no—
97C2×D113—42no—
98C4×C113—42no—
99C4×C113—42no—
100C4×C113AGL(1,ℤ/8)12yes—
101C4×C113#13712yes—
102C4×C113C2×#4112yes—
103Dic113—21no—
104Dic113—21no—
105Dic113—21no—
106Dic113—42no—
107C2×C113#53211yescharacteristic
108C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
109C2×C113C2×#13711yescharacteristic
110D113—41no—
111D113—82no—
112#3182—1131nomaximal, Sylow
113C113#318211yescharacteristic, complemented, Sylow
114#533—1131no—
115#532—1131no—
116#500D11311yescharacteristic, complemented
117#492—1131no—
118#487—1131no—
119#486—1131no—
120#468—1134no—
121#440—1134no—
122C4×M16—1131no—
123C2×#41—2261no—
124C2×SD16—1134no—
125C2×M16—1132no—
126C4⋊Q8—1131no—
127C4⋊Q8C2×D11311yescharacteristic
128C4⋊Q8C2×D11311yescharacteristic
129#127—1131no—
130#125—2261no—
131#124—2261no—
132C22⋊Q8—1132no—
133C22⋊Q8—2261no—
134#121—1132no—
135#121—2261no—
136C4×Q8—1132no—
137C4×Q8—2261no—
138C4×D4—1132no—
139C4×D4—2261no—
140#117—2261no—
141C2×C42—1131no—
142#107C2×D11314yes—
143#103—1134no—
144#102—1134no—
145#97—1132no—
146C4×C8—1131no—
147C4×C8C2×D11311yescharacteristic
148#41—4524no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—1132no—
152C2×D4—1132no—
153C2×D4—2262no—
154C2×D4—2261no—
155C2×D4—2261no—
156C22×C4—1131no—
157C22×C4—1131no—
158C22×C4—1131no—
159C22×C4—2262no—
160SD16—2268no—
161M16—2264no—
162C2×C8—1132no—
163C2×C8C22×D11312yes—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—2262no—
167C4⋊C4—2262no—
168C4⋊C4—2261no—
169C4⋊C4—2261no—
170C4⋊C4C22×D11312yes—
171C4⋊C4C22×D11312yes—
172C22⋊C4—2262no—
173C22⋊C4—2262no—
174C22⋊C4—2262no—
175C42—1131no—
176C42—1131no—
177C42—1131no—
178C42—2262no—
179C42C22×D11311yescharacteristic
180C23—1131no—
181C23—2262no—
182Q8—42no—
183Q8—42no—
184Q8—2264no—
185D4—4524no—
186D4—4522no—
187D4—4522no—
188D4—2264no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—1131no—
192C2×C4—1131no—
193C2×C4—1131no—
194C2×C4—4524no—
195C2×C4—2262no—
196C2×C4—2262no—
197C2×C4—2262no—
198C2×C4—2262no—
199C2×C4D4×D11311yescharacteristic
200C2×C4D4×D11311yescharacteristic
201C2×C4C23×D11311yescharacteristic
202C8—2262no—
203C8#1426864814yescomplemented
204C22—4522no—
205C22—4522no—
206C22—4522no—
207C22—2261no—
208C22—2261no—
209C22—2261no—
210C22C2×D4×D11311yescharacteristic
211C4—42no—
212C4—42no—
213C4—4522no—
214C4—2261no—
215C4—2261no—
216C4—2261no—
217C4#1681364612yes—
218C4#1681365412yes—
219C4C2×#1426864812yes—
220C2—9042no—
221C2—4521no—
222C2#2029914911yescharacteristic
223C2C2×#1681364611yescharacteristic
224C2C2×#1681365411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#500×C113C2
socleC22×C113C22×D4
prime radical#20299149C2
hypercenter#500D113
hypocenterC113#3182
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
1. #20299153C2semidirect
3. #20298971C2semidirect
4. #20298950C2semidirect
5. #20298946C2semidirect
6. #20298845C2semidirect
7. #20298697C2semidirect
8. C4×#14268630C2semidirect
9. #500×C113C2semidirect
89. C8×C113#41semidirect
113. C113#3182semidirect
116. #500D113semidirect
203. C8#14268648semidirect

Maximal subgroups

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

subgroupindex
#202991532
#202991492
#202989712
#202989502
#202989462
#202988452
#202986972
C4×#142686302
#500×C1132
#3182113