Finite Group Databasebeta

← #28400673

Subgroups — #28400673

Order 14464.

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

normal subgroups only

This group has 444 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#20299155C211yesmaximal, characteristic, complemented
2#20298933C212yesmaximal, complemented
3#20298878C212yesmaximal, complemented
4#20298803C212yesmaximal, complemented
5#20298749C212yesmaximal
6#20298698C214yesmaximal, complemented
7#20298655C211yesmaximal, characteristic, complemented
8C2×C4×D4×C113C211yesmaximal, characteristic
9C2×#14268635C2214yes—
10#16813622C2211yescharacteristic, complemented
11#16813622C2211yescharacteristic, complemented
12#16813614—21no—
13#16813601—21no—
14#16813601C2212yes—
15C4×Dic226—21no—
16C4×Dic226C2212yescomplemented
17#16813581—21no—
18#16813555C2214yescomplemented
19C4⋊#11744751C2212yescomplemented
20#16813545C2214yescomplemented
21#16813543C2214yes—
22C22⋊#11744751C2212yes—
23#16813533C2212yescomplemented
24C22×D4×C113C2211yescharacteristic
25C23×C4×C113—21no—
26C4×D4×C113—21no—
27C4×D4×C113—21no—
28C4×D4×C113C2212yes—
29C4×D4×C113C2212yes—
30C2×C4⋊C4×C113C2211yescharacteristic
31C2×C22⋊C4×C113—21no—
32C2×C42×C113C2211yescharacteristic
33C2×Dic226—21no—
34C2×Dic226C2312yes—
35#14268635—28no—
36C2×#11744751C2314yes—
37C4⋊Dic113—21no—
38C4⋊Dic113—21no—
39C4⋊Dic113—21no—
40C4⋊Dic113C2312yes—
41#14268626—22no—
42#14268626—22no—
43C22⋊Dic113—22no—
44C4×Dic113—22no—
45C24×C113—21no—
46C2×D4×C113—24no—
47C2×D4×C113—21no—
48C2×D4×C113C2312yes—
49C22×C4×C113—21no—
50C22×C4×C113—22no—
51C22×C4×C113—22no—
52C22×C4×C113—44no—
53C22×C4×C113D411yescharacteristic
54C22×C4×C113D411yescharacteristic
55C22×C4×C113C2311yescharacteristic
56C4⋊C4×C113—21no—
57C4⋊C4×C113C2312yes—
58C22⋊C4×C113—22no—
59C22⋊C4×C113—22no—
60C42×C113D411yescharacteristic
61C42×C113D411yescharacteristic
62C42×C113C2311yescharacteristic
63C42×C113C2311yescharacteristic
64C23×C113—24no—
65C23×C113—22no—
66C23×C113—42no—
67C23×C113—42no—
68C23×C113C2×D411yescharacteristic
69D4×C113—24no—
70D4×C113—22no—
71D4×C113#4114yes—
72C2×C4×C113—22no—
73C2×C4×C113—22no—
74C2×C4×C113—22no—
75C2×C4×C113—22no—
76C2×C4×C113—44no—
77C2×C4×C113—42no—
78C2×C4×C113—44no—
79C2×C4×C113C2×D411yescharacteristic
80C2×C4×C113C2×D411yescharacteristic
81C2×C4×C113C2×D411yescharacteristic
82C2×C4×C113C2×D411yescharacteristic
83C2×C4×C113C2×D411yescharacteristic
84C2×C4×C113C2411yescharacteristic
85C2×Dic113—22no—
86C2×Dic113—22no—
87Dic226—24no—
88Dic226—42no—
89#11744751—24no—
90C22×C113—21no—
91C22×C113—21no—
92C22×C113—24no—
93C22×C113—48no—
94C22×C113—42no—
95C22×C113—42no—
96C22×C113#13712yes—
97C22×C113C22×D411yescharacteristic
98C4×C113—21no—
99C4×C113—21no—
100C4×C113—21no—
101C4×C113—21no—
102C4×C113—42no—
103C4×C113AGL(1,ℤ/8)12yes—
104C4×C113C2×#4112yes—
105Dic113—42no—
106Dic113—42no—
107C2×C113—22no—
108C2×C113—44no—
109C2×C113#52511yescharacteristic
110C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
111C2×C113C2×#13711yescharacteristic
112#3110—1131nomaximal, Sylow
113C113#311011yescharacteristic, complemented, Sylow
114#533—1131no—
115C2×C4×D4D11311yescharacteristic
116#484—1132no—
117#474—1132no—
118#461—1132no—
119#450—1132no—
120#440—1134no—
121#432—1131no—
122C22×D4C2×D11311yescharacteristic
123C23×C4—21no—
124C2×SD16—1134no—
125C4⋊Q8—1131no—
126C4⋊Q8—1131no—
127#125—2261no—
128C22⋊Q8—1132no—
129C22⋊Q8—2261no—
130C4×Q8—1132no—
131C4×Q8—2261no—
132C4×D4—21no—
133C4×D4—21no—
134C4×D4C2×D11312yes—
135C4×D4C2×D11312yes—
136#117—2261no—
137C2×C4⋊C4C2×D11311yescharacteristic
138C2×C22⋊C4—21no—
139C2×C42C2×D11311yescharacteristic
140#107—1134no—
141C4⋊C8—1132no—
142#103—1134no—
143#102—1134no—
144C22⋊C8—1132no—
145#97—1132no—
146C24—21no—
147C2×Q8—1132no—
148C2×Q8—2261no—
149C2×D4—24no—
150C2×D4—21no—
151C2×D4C22×D11312yes—
152C22×C4—21no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—44no—
156C22×C4C22⋊D11311yescharacteristic
157C22×C4C22⋊D11311yescharacteristic
158C22×C4C22×D11311yescharacteristic
159SD16—2268no—
160C2×C8—1134no—
161C4⋊C4—21no—
162C4⋊C4—1132no—
163C4⋊C4—2261no—
164C4⋊C4—2261no—
165C4⋊C4—2262no—
166C4⋊C4—2262no—
167C4⋊C4—2261no—
168C4⋊C4C22×D11312yes—
169C22⋊C4—22no—
170C22⋊C4—22no—
171C22⋊C4—2262no—
172C42—2262no—
173C42C22⋊D11311yescharacteristic
174C42C22⋊D11311yescharacteristic
175C42C22×D11311yescharacteristic
176C42C22×D11311yescharacteristic
177C23—24no—
178C23—22no—
179C23—42no—
180C23—42no—
181C23C2×C22⋊D11311yescharacteristic
182Q8—4522no—
183Q8—2264no—
184D4—24no—
185D4—22no—
186D4#1426864714yes—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—44no—
192C2×C4—42no—
193C2×C4—44no—
194C2×C4—2262no—
195C2×C4—2262no—
196C2×C4C2×C22⋊D11311yescharacteristic
197C2×C4C2×C22⋊D11311yescharacteristic
198C2×C4C2×C22⋊D11311yescharacteristic
199C2×C4C2×C22⋊D11311yescharacteristic
200C2×C4C2×C22⋊D11311yescharacteristic
201C2×C4C23×D11311yescharacteristic
202C8—2264no—
203C22—21no—
204C22—21no—
205C22—24no—
206C22—48no—
207C22—42no—
208C22—42no—
209C22#1681365212yes—
210C22C22×C22⋊D11311yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—21no—
215C4—42no—
216C4—4522no—
217C4—4522no—
218C4#1681364812yes—
219C4C2×#1426864712yes—
220C2—22no—
221C2—44no—
222C2#2029910911yescharacteristic
223C2C2×#1681364811yescharacteristic
224C2C2×#1681365211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×C4×D4×C113C2
socleC22×C113C22×D4
prime radicalC22×D4×C113C22
hypercenterC2×C4×D4D113
hypocenterC113#3110
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #20299155C2semidirect
2. #20298933C2semidirect
3. #20298878C2semidirect
4. #20298803C2semidirect
6. #20298698C2semidirect
7. #20298655C2semidirect
10. #16813622C22semidirect
11. #16813622C22semidirect
16. C4×Dic226C22semidirect
18. #16813555C22semidirect
19. C4⋊#11744751C22semidirect
20. #16813545C22semidirect
23. #16813533C22semidirect
113. C113#3110semidirect

Maximal subgroups

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

subgroupindex
#202991552
#202989332
#202988782
#202988032
#202987492
#202986982
#202986552
C2×C4×D4×C1132
#3110113