Finite Group Databasebeta

← #28401532

Subgroups — #28401532

Order 14464.

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

normal subgroups only

This group has 394 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#20299155C211yesmaximal, characteristic, complemented
2#20299148C211yesmaximal, characteristic
3#20298978C211yesmaximal, characteristic, complemented
4#20298971C211yesmaximal, characteristic, complemented
5#20298949C211yesmaximal, characteristic, complemented
6#20298945C211yesmaximal, characteristic, complemented
7#20298821C214yesmaximal, complemented
8#20298762C214yesmaximal, complemented
9#431×C113C211yesmaximal, characteristic, complemented
10C2×#14268647C2212yes—
11C2×Dic452C2214yes—
12C2×#14268636C2214yes—
13#16813622C2211yescharacteristic
14#16813622C2211yescharacteristic
15#16813622C2211yescharacteristic
16#16813619C2211yescharacteristic
17#16813614—21no—
18#16813610C2212yes—
19#16813601—21no—
20#16813601C2212yes—
21#16813596—21no—
22#16813596—21no—
23C4×Dic226—21no—
24C4×Dic226C2212yes—
25C4×D452—21no—
26C4×D452—21no—
27#16813581—21no—
28#16813547C2214yes—
29#16813544C2214yes—
30C2×C42×C113C2211yescharacteristic
31C4⋊C8×C113C2212yes—
32C22⋊C8×C113C2212yes—
33C4×C8×C113C2211yescharacteristic
34C4×C8×C113C2211yescharacteristic
35#14268647—44no—
36C2×Dic226—21no—
37C2×Dic226C2312yes—
38C2×Dic226C2312yes—
39C2×D452—21no—
40C2×D452—21no—
41C2×D452C2312yes—
42C2×C22⋊D113—22no—
43C2×C4×D113—22no—
44Dic452—44no—
45#14268636—44no—
46C4⋊Dic113—21no—
47C4⋊Dic113—21no—
48C4⋊Dic113—21no—
49C4⋊Dic113—21no—
50C4⋊Dic113—21no—
51C4⋊Dic113C2312yes—
52#14268626—22no—
53#14268626—22no—
54C22⋊Dic113—22no—
55#14268624—22no—
56#14268624—22no—
57C4×Dic113—22no—
58C22×C4×C113D411yescharacteristic
59C22×C4×C113D411yescharacteristic
60C22×C4×C113C2311yescharacteristic
61C2×C8×C113C2312yes—
62C2×C8×C113C2312yes—
63C42×C113D411yescharacteristic
64C42×C113D411yescharacteristic
65C42×C113C2311yescharacteristic
66C42×C113C2311yescharacteristic
67C23×C113C2×D411yescharacteristic
68C22×D113—22no—
69C2×C4×C113—22no—
70C2×C4×C113—22no—
71C2×C4×C113—22no—
72C2×C4×C113C2×D411yescharacteristic
73C2×C4×C113C2×D411yescharacteristic
74C2×C4×C113C2×D411yescharacteristic
75C2×C4×C113C2×D411yescharacteristic
76C2×C4×C113C2×D411yescharacteristic
77C2×C4×C113C2411yescharacteristic
78C22⋊D113—44no—
79C2×Dic113—22no—
80C2×Dic113—22no—
81C2×Dic113—22no—
82D452—24no—
83D452—42no—
84D452—42no—
85C4×D113—44no—
86Dic226—24no—
87Dic226—24no—
88Dic226—42no—
89C8×C113—22no—
90C8×C113—22no—
91C22×C113—21no—
92C22×C113—21no—
93C22×C113—21no—
94C22×C113C22×D411yescharacteristic
95C2×D113—42no—
96C2×D113—42no—
97C2×D113—42no—
98C4×C113—21no—
99C4×C113—21no—
100C4×C113—21no—
101C4×C113#13512yes—
102C4×C113#13712yes—
103C4×C113H(5,𝔽2)12yes—
104Dic113—42no—
105Dic113—42no—
106Dic113—42no—
107C2×C113—41no—
108C2×C113#53511yescharacteristic
109C2×C113C2×#13511yescharacteristic
110C2×C113C2×#13711yescharacteristic
111D113—82no—
112#3210—1131nomaximal, Sylow
113C113#321011yescharacteristic, complemented, Sylow
114#533—1131no—
115#532—1131no—
116#494—1131no—
117#492—1131no—
118#487—1131no—
119#486—1131no—
120#464—1134no—
121#452—1134no—
122#431D11311yescharacteristic, complemented
123C2×#41—1132no—
124C2×Q16—1134no—
125C2×SD16—1134no—
126C4⋊Q8—1131no—
127C4⋊Q8—1131no—
128C4⋊Q8—1131no—
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×C42C2×D11311yescharacteristic
142C4⋊C8C2×D11312yes—
143#103—1134no—
144#102—1134no—
145C22⋊C8C2×D11312yes—
146C4×C8C2×D11311yescharacteristic
147C4×C8C2×D11311yescharacteristic
148#41—4524no—
149C2×Q8—1132no—
150C2×Q8—1132no—
151C2×Q8—2261no—
152C2×D4—1132no—
153C2×D4—2262no—
154C2×D4—2261no—
155C2×D4—2261no—
156C22×C4—2262no—
157C22×C4D45211yescharacteristic
158C22×C4D45211yescharacteristic
159C22×C4C22×D11311yescharacteristic
160Q16—4524no—
161SD16—4524no—
162C2×C8C22×D11312yes—
163C2×C8C22×D11312yes—
164C4⋊C4—1132no—
165C4⋊C4—2261no—
166C4⋊C4—2261no—
167C4⋊C4—2261no—
168C4⋊C4—2261no—
169C4⋊C4—2262no—
170C4⋊C4—2262no—
171C4⋊C4—2261no—
172C22⋊C4—2262no—
173C22⋊C4—2262no—
174C22⋊C4—2262no—
175C42—2262no—
176C42D45211yescharacteristic
177C42D45211yescharacteristic
178C42C22×D11311yescharacteristic
179C42C22×D11311yescharacteristic
180C23—2262no—
181C23C2×D45211yescharacteristic
182Q8—4522no—
183Q8—2264no—
184Q8—2264no—
185D4—4524no—
186D4—4522no—
187D4—4522no—
188D4—2264no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—4524no—
193C2×C4—2262no—
194C2×C4—2262no—
195C2×C4—2262no—
196C2×C4C2×D45211yescharacteristic
197C2×C4C2×D45211yescharacteristic
198C2×C4C2×D45211yescharacteristic
199C2×C4C2×D45211yescharacteristic
200C2×C4C2×D45211yescharacteristic
201C2×C4C23×D11311yescharacteristic
202C8—22no—
203C8—22no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—4522no—
208C22—4522no—
209C22—4522no—
210C22C22×D45211yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—4522no—
215C4—4522no—
216C4—4522no—
217C4#1681364412yes—
218C4#1681365512yes—
219C4#1681366812yes—
220C2—41no—
221C2—9042no—
222C2#2029916711yescharacteristic
223C2C2×#1681364411yescharacteristic
224C2C2×#1681365511yescharacteristic
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#431×C113C2
socleC22×C113C22×D4
prime radical#20299148C2
hypercenter#431D113
hypocenterC113#3210
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
1. #20299155C2semidirect
3. #20298978C2semidirect
4. #20298971C2semidirect
5. #20298949C2semidirect
6. #20298945C2semidirect
7. #20298821C2semidirect
8. #20298762C2semidirect
9. #431×C113C2semidirect
113. C113#3210semidirect
122. #431D113semidirect

Maximal subgroups

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

subgroupindex
#202991552
#202991482
#202989782
#202989712
#202989492
#202989452
#202988212
#202987622
#431×C1132
#3210113