Finite Group Databasebeta

← #28399051

Subgroups — #28399051

Order 14464.

756 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 756 conjugacy classes of subgroups — too many to draw. Only its 209 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
1C2×#16813668C211yesmaximal, characteristic
2#20299364C212yesmaximal, complemented
3#20298582C211yesmaximal, characteristic, complemented
4#20298581C214yesmaximal, complemented
5C2×#16813538C212yesmaximal, complemented
6#100×D113C214yesmaximal, complemented
7#413×C113C211yesmaximal, characteristic, complemented
8#16813668—24no—
9#16813668—24no—
10C2×#14268648C2212yes—
11C2×#14268647C412yes—
12C2×#14268647C2211yescharacteristic
13C22×D452C412yes—
14C22×D452C2211yescharacteristic
15C2×D4×D113C414yes—
16C2×D4×D113C2212yes—
17#16813630—24no—
18#16813628—24no—
19C2×#14268631C2212yescomplemented
20M16×D113C2218yescomplemented
21#16813541C2212yescomplemented
22#16813539C2212yescomplemented
23#16813538C2218yescomplemented
24C2×#41×C113C2211yescharacteristic
25C2×M16×C113C2212yescomplemented
26#101×C113C2212yescomplemented
27#100×C113C2212yescomplemented
28C23×D113C2×C412yes—
29C23×D113C2×C414yes—
30#14268648—28no—
31#14268647—24no—
32#14268647—24no—
33#14268647D414yes—
34#14268647D414yes—
35C2×Dic226C2×C411yescharacteristic
36C2×D452—22no—
37C2×D452—22no—
38C2×D452—24no—
39C2×D452—24no—
40C2×D452C2×C414yes—
41C2×D452C2×C412yes—
42C2×D452C2×C411yescharacteristic
43C2×D452C2312yes—
44C2×C22⋊D113C2×C414yes—
45C2×C22⋊D113C2×C412yes—
46D4×D113—216no—
47D4×D113—28no—
48C2×C4×D113C2×C414yes—
49C2×C4×D113C2312yes—
50#14268631—22no—
51#14268631C2314yes—
52#14268630—28no—
53C2×#11744751—22no—
54C8×D113—28no—
55#41×C113—22no—
56#41×C113—22no—
57C2×Q8×C113C2311yescharacteristic
58C2×D4×C113C2×C412yes—
59C2×D4×C113C2311yescharacteristic
60C22×C4×C113C2×C412yes—
61C22×C4×C113C2311yescharacteristic
62M16×C113—22no—
63M16×C113C2314yes—
64C2×C8×C113—22no—
65C23×C113C22×C412yes—
66C23×C113C22×C411yescharacteristic
67C22×D113—24no—
68C22×D113—28no—
69C22×D113—84no—
70C22×D113—82no—
71C22×D113C22×C414yes—
72C22×D113C22×C412yes—
73Q8×C113—22no—
74D4×C113—24no—
75D4×C113—22no—
76C2×C4×C113—22no—
77C2×C4×C113—22no—
78C2×C4×C113C22×C412yes—
79C2×C4×C113C22×C411yescharacteristic
80C2×C4×C113C2×D412yes—
81C2×C4×C113C2×D412yes—
82C2×C4×C113C2411yescharacteristic
83C22⋊D113—28no—
84C22⋊D113C22⋊C418yes—
85C2×Dic113C22×C412yes—
86D452—28no—
87D452—22no—
88D452—22no—
89D452—24no—
90D452C22⋊C412yes—
91D452C22⋊C412yes—
92C4×D113—28no—
93C4×D113C2×D418yes—
94Dic226C22⋊C412yes—
95Dic226C22⋊C412yes—
96C8×C113—24no—
97#11744751—24no—
98C22×C113—22no—
99C22×C113—41no—
100C22×C113—42no—
101C22×C113C2×C22⋊C412yes—
102C22×C113C23×C411yescharacteristic
103C2×D113—24no—
104C2×D113—42no—
105C2×D113—44no—
106C2×D113—88no—
107C2×D113—84no—
108C2×D113C2×C22⋊C414yes—
109C4×C113—22no—
110C4×C113C2×C22⋊C411yescharacteristic
111C4×C113C2×C22⋊C411yescharacteristic
112C4×C113C22×D412yes—
113Dic113C2×C22⋊C414yes—
114C2×C113—21no—
115C2×C113—22no—
116C2×C113—42no—
117C2×C113C22×C22⋊C411yescharacteristic
118D113—24no—
119D113—44no—
120#2888—1131nomaximal, Sylow
121C113#288811yescharacteristic, complemented, Sylow
122C2×H(5,𝔽2)—1131no—
123#568—1132no—
124#413—1131no—
125#413—1134no—
126#413D11311yescharacteristic, complemented
127C2×#100—1132no—
128C2×#100—1134no—
129H(5,𝔽2)—2264no—
130H(5,𝔽2)—2264no—
131C2×#41—1132no—
132C2×#41—1132no—
133C2×#41—1131no—
134C2×#41C2×D11311yescharacteristic
135C22×D4—1134no—
136C22×D4—1132no—
137C22×D4—1132no—
138C22×D4—1131no—
139#131—2264no—
140#131—2264no—
141C2×M16—1132no—
142C2×M16—1138no—
143C2×M16C2×D11312yescomplemented
144#101—1132no—
145#101C2×D11312yescomplemented
146#100—1132no—
147#100—1138no—
148#100C2×D11312yescomplemented
149C24—1134no—
150C24—1132no—
151#41—22no—
152#41—22no—
153#41—1134no—
154#41—1134no—
155#41—2264no—
156#41—2264no—
157#41—2268no—
158C2×Q8—1131no—
159C2×Q8C22×D11311yescharacteristic
160C2×D4—1132no—
161C2×D4—1134no—
162C2×D4—1131no—
163C2×D4—1134no—
164C2×D4—1132no—
165C2×D4—1132no—
166C2×D4—2264no—
167C2×D4—2264no—
168C2×D4—2268no—
169C2×D4—22616no—
170C2×D4—2262no—
171C2×D4—2262no—
172C2×D4C4×D11312yes—
173C2×D4C22×D11311yescharacteristic
174C22×C4—1132no—
175C22×C4—1134no—
176C22×C4C4×D11312yes—
177C22×C4C22×D11311yescharacteristic
178M16—22no—
179M16—1134no—
180M16—2268no—
181M16—2262no—
182M16C22×D11314yes—
183C2×C8—22no—
184C2×C8—2268no—
185C2×C8—2262no—
186C23—1132no—
187C23—1134no—
188C23—9042no—
189C23—9044no—
190C23—2268no—
191C23—2264no—
192C23C2×C4×D11312yes—
193C23C2×C4×D11311yescharacteristic
194Q8—22no—
195Q8—1132no—
196Q8—1132no—
197D4—24no—
198D4—22no—
199D4—1138no—
200D4—1132no—
201D4—1132no—
202D4—2268no—
203D4—2268no—
204D4—2262no—
205D4—2262no—
206D4—2264no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—1132no—
210C2×C4—1138no—
211C2×C4—2268no—
212C2×C4C2×C4×D11312yes—
213C2×C4C2×C4×D11311yescharacteristic
214C2×C4D4×D11312yes—
215C2×C4D4×D11312yes—
216C2×C4C23×D11311yescharacteristic
217C8—24no—
218C8—2264no—
219C22—22no—
220C22—41no—
221C22—42no—
222C22—1134no—
223C22—9044no—
224C22—9048no—
225C22—4524no—
226C22—4522no—
227C22—2264no—
228C22C22⋊C4×D11312yes—
229C22C22×C4×D11311yescharacteristic
230C4—22no—
231C4—1134no—
232C4C22⋊C4×D11311yescharacteristic
233C4C22⋊C4×D11311yescharacteristic
234C4C2×D4×D11312yes—
235C2—21no—
236C2—22no—
237C2—42no—
238C2—4524no—
239C2—2264no—
240C2C2×C22⋊C4×D11311yescharacteristic
subgroupG/H
centerC2C2×C22⋊C4×D113
commutatorC22×C113C23×C4
FrattiniC2×C4C23×D113
Fitting#413×C113C2
socleC2×C113C22×C22⋊C4
prime radicalC2×#16813668C2
cosocleC2×C4×C113C24
hypercenter#413D113
hypocenterC113#2888
LCSG ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #20299364C2semidirect
3. #20298582C2semidirect
4. #20298581C2semidirect
5. C2×#16813538C2semidirect
6. #100×D113C2semidirect
7. #413×C113C2semidirect
19. C2×#14268631C22semidirect
20. M16×D113C22semidirect
21. #16813541C22semidirect
22. #16813539C22semidirect
23. #16813538C22semidirect
25. C2×M16×C113C22semidirect
26. #101×C113C22semidirect
27. #100×C113C22semidirect
121. C113#2888semidirect
126. #413D113semidirect
143. C2×M16C2×D113semidirect
145. #101C2×D113semidirect
148. #100C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136682
#202993642
#202985822
#202985812
C2×#168135382
#100×D1132
#413×C1132
#2888113