Finite Group Databasebeta

← #28401527

Subgroups — #28401527

Order 14464.

394 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 117 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#20298972C211yesmaximal, characteristic, complemented
4#20298948C211yesmaximal, characteristic, complemented
5#20298945C211yesmaximal, characteristic, complemented
6#20298822C214yesmaximal, complemented
7#20298759C214yesmaximal, complemented
8#20298649C211yesmaximal, characteristic, complemented
9#494×C113C211yesmaximal, characteristic, complemented
10C2×#14268648C2212yes—
11C2×#14268634C2214yes—
12#16813622C2211yescharacteristic
13#16813619C2211yescharacteristic
14#16813613—21no—
15#16813611C2212yes—
16#16813602—21no—
17#16813598C2212yes—
18#16813597—21no—
19#16813597—21no—
20Q8×Dic113C2212yes—
21#16813587—21no—
22#16813584—21no—
23#16813584—21no—
24#16813580—21no—
25C42×D113C2211yescharacteristic
26#16813551C2212yes—
27#16813546C2214yes—
28#16813544C2214yes—
29#16813534C2212yes—
30C4×#11744751C2211yescharacteristic
31C2×Q16×C113C2214yes—
32C4⋊Q8×C113C2211yescharacteristic
33C4⋊Q8×C113C2211yescharacteristic
34C4×C8×C113C2211yescharacteristic
35#14268648—44no—
36C2×Dic226—21no—
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#14268634—44no—
46C2×#11744751C2312yes—
47C4⋊Dic113—21no—
48C4⋊Dic113—22no—
49C4⋊Dic113C2312yes—
50#14268626—22no—
51#14268624—22no—
52#14268624—22no—
53#14268624—22no—
54C4×Dic113—22no—
55C4×Dic113D411yescharacteristic
56C4×Dic113D411yescharacteristic
57C4×Dic113C2311yescharacteristic
58C2×Q8×C113C2312yes—
59C2×Q8×C113C2312yes—
60Q16×C113—44no—
61C2×C8×C113C2312yes—
62C4⋊C4×C113—21no—
63C4⋊C4×C113—21no—
64C4⋊C4×C113—21no—
65C4⋊C4×C113—21no—
66C42×C113C2311yescharacteristic
67C22×D113—22no—
68C22×D113C2×D411yescharacteristic
69Q8×C113—24no—
70Q8×C113—24no—
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—42no—
89C8×C113—22no—
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×C113#13512yes—
101C4×C113#13712yes—
102C4×C113H(5,𝔽2)12yes—
103Dic113—21no—
104Dic113—21no—
105Dic113—21no—
106Dic113—42no—
107C2×C113#53511yescharacteristic
108C2×C113C2×#13511yescharacteristic
109C2×C113C2×#13711yescharacteristic
110D113—41no—
111D113—82no—
112#3210—1131nomaximal, Sylow
113C113#321011yescharacteristic, complemented, Sylow
114#533—1131no—
115#532—1131no—
116#494D11311yescharacteristic, complemented
117#492—1131no—
118#487—1131no—
119#486—1131no—
120#464—1134no—
121#452—1134no—
122#431—1131no—
123C2×#41—1132no—
124C2×Q16C2×D11314yes—
125C2×SD16—1134no—
126C4⋊Q8—1131no—
127C4⋊Q8C2×D11311yescharacteristic
128C4⋊Q8C2×D11311yescharacteristic
129#127—1131no—
130#125—2261no—
131#124—1132no—
132C22⋊Q8—1132no—
133C22⋊Q8—2261no—
134#121—2261no—
135#121—2261no—
136C4×Q8—1132no—
137C4×Q8—2261no—
138C4×D4—2261no—
139C4×D4—2261no—
140#117—2261no—
141C2×C42—1131no—
142C4⋊C8—1132no—
143#103—1134no—
144#102—1134no—
145C22⋊C8—1132no—
146C4×C8—1131no—
147C4×C8C2×D11311yescharacteristic
148#41—4524no—
149C2×Q8—2261no—
150C2×Q8C22×D11312yes—
151C2×Q8C22×D11312yes—
152C2×D4—1132no—
153C2×D4—2262no—
154C2×D4—2261no—
155C2×D4—2261no—
156C22×C4—1131no—
157C22×C4—1131no—
158C22×C4—1131no—
159C22×C4—2262no—
160Q16—44no—
161SD16—4524no—
162C2×C8—1132no—
163C2×C8C22×D11312yes—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—1132no—
169C4⋊C4—2262no—
170C4⋊C4—2262no—
171C4⋊C4—2261no—
172C22⋊C4—2262no—
173C22⋊C4—2262no—
174C22⋊C4—2262no—
175C42—1131no—
176C42—1131no—
177C42—1131no—
178C42—2262no—
179C42C22×D11311yescharacteristic
180C23—1131no—
181C23—2262no—
182Q8—24no—
183Q8—24no—
184Q8—4522no—
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—22no—
203C8—2262no—
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#1681364512yes—
218C4#1681365412yes—
219C4#1681366712yes—
220C2—9042no—
221C2—4521no—
222C2#2029916111yescharacteristic
223C2C2×#1681364511yescharacteristic
224C2C2×#1681365411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#494×C113C2
socleC22×C113C22×D4
prime radical#20299149C2
hypercenter#494D113
hypocenterC113#3210
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
1. #20299153C2semidirect
3. #20298972C2semidirect
4. #20298948C2semidirect
5. #20298945C2semidirect
6. #20298822C2semidirect
7. #20298759C2semidirect
8. #20298649C2semidirect
9. #494×C113C2semidirect
113. C113#3210semidirect
116. #494D113semidirect

Maximal subgroups

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

subgroupindex
#202991532
#202991492
#202989722
#202989482
#202989452
#202988222
#202987592
#202986492
#494×C1132
#3210113