Finite Group Databasebeta

← #28401307

Subgroups — #28401307

Order 14464.

446 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 119 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#20299143C212yesmaximal, complemented
2#20298995C211yesmaximal, characteristic, complemented
3#20298973C211yesmaximal, characteristic, complemented
4#20298943C212yesmaximal, complemented
5#20298851C211yesmaximal, characteristic, complemented
6#20298849C212yesmaximal, complemented
7#20298710C211yesmaximal, characteristic, complemented
8#20298709C211yesmaximal, characteristic, complemented
9#20298707C212yesmaximal, complemented
10M16×Dic113C211yesmaximal, characteristic, complemented
11#469×C113C211yesmaximal, characteristic, complemented
12C2×#14268646—22no—
13C2×D904C2211yescharacteristic
14C2×#14268632C2212yes—
15C2×#14268631C2211yescharacteristic
16#16813621C2212yes—
17#16813618C2212yes—
18#16813608—22no—
19#16813596C2212yes—
20#16813594—22no—
21D4×Dic113C2212yes—
22#16813584C2212yes—
23#16813582—22no—
24C2×C4×Dic113C2211yescharacteristic
25#16813554C2211yescharacteristic
26#16813553C2212yes—
27#16813544C2212yes—
28#16813543C2212yes—
29#16813542C2212yes—
30#16813532C2211yescharacteristic
31#16813532C2211yescharacteristic
32C8×Dic113C2211yescharacteristic
33C8×Dic113C2211yescharacteristic
34C2×D8×C113C2211yescharacteristic
35C2×M16×C113C2211yescharacteristic
36#121×C113C2212yes—
37#106×C113C2211yescharacteristic
38#102×C113C2212yes—
39#14268646—48no—
40C2×Dic226—22no—
41C2×D452C2312yes—
42C2×C22⋊D113—22no—
43C2×C22⋊D113—22no—
44C2×C22⋊D113—22no—
45C22×Dic113—22no—
46C22×Dic113D412yes—
47C2×C4×D113—22no—
48D904—22no—
49#14268632—24no—
50#14268631—22no—
51C2×#11744751C2311yescharacteristic
52C2×#11744751C2311yescharacteristic
53C4⋊Dic113C2312yes—
54#14268626—22no—
55C22⋊Dic113—22no—
56#14268624—22no—
57#14268624—22no—
58C4×Dic113D412yes—
59C4×Dic113C2311yescharacteristic
60C4×Dic113C2311yescharacteristic
61C2×D4×C113—22no—
62C2×D4×C113C2312yes—
63C22×C4×C113C2311yescharacteristic
64D8×C113—22no—
65M16×C113—22no—
66C2×C8×C113C2311yescharacteristic
67C2×C8×C113C2311yescharacteristic
68C4⋊C4×C113C2312yes—
69C22⋊C4×C113—22no—
70C23×C113—22no—
71C23×C113C2×D411yescharacteristic
72C22×D113—22no—
73D4×C113—22no—
74D4×C113—22no—
75D4×C113—44no—
76C2×C4×C113—21no—
77C2×C4×C113—21no—
78C2×C4×C113—22no—
79C2×C4×C113C2×D411yescharacteristic
80C2×C4×C113C2411yescharacteristic
81C22⋊D113—44no—
82C22⋊D113—44no—
83C22⋊D113—44no—
84C2×Dic113—24no—
85C2×Dic113—22no—
86C2×Dic113—44no—
87C2×Dic113C2×D412yes—
88C2×Dic113C2×D412yes—
89D452—22no—
90D452—22no—
91C4×D113—44no—
92Dic226—44no—
93C8×C113—21no—
94C8×C113#4112yescomplemented
95#11744751—21no—
96#11744751#4112yescomplemented
97C22×C113—21no—
98C22×C113—22no—
99C22×C113—42no—
100C22×C113—42no—
101C22×C113—42no—
102C22×C113C22×D411yescharacteristic
103C2×D113—42no—
104C2×D113—42no—
105C2×D113—42no—
106C4×C113—21no—
107C4×C113—42no—
108C4×C113C2×#4111yescharacteristic
109C4×C113C2×#4111yescharacteristic
110Dic113—22no—
111Dic113—42no—
112Dic113AGL(1,ℤ/8)14yes—
113C2×C113—41no—
114C2×C113—82no—
115C2×C113#53211yescharacteristic
116C2×C113C2×AGL(1,ℤ/8)12yes—
117D113—82no—
118#3184—1131nomaximal, Sylow
119C113#318411yescharacteristic, complemented, Sylow
120#532—1132no—
121#498—1131no—
122#493—1131no—
123#486—1132no—
124#469—1131no—
125#469—1132no—
126#469D11311yescharacteristic, complemented
127#442—1131no—
128#442—1131no—
129#442—1132no—
130C4×M16—1131no—
131C2×#41—2262no—
132C2×D8—1132no—
133C2×D8—1131no—
134C2×D8C2×D11311yescharacteristic
135C2×M16—1131no—
136C2×M16C2×D11311yescharacteristic
137C4⋊Q8—1132no—
138#127—1132no—
139#124—2262no—
140#121—1132no—
141#121—2262no—
142#121C2×D11312yes—
143C4×D4—1132no—
144C4×D4—1132no—
145C4×D4—2262no—
146C2×C42—1131no—
147#106—1131no—
148#106—1132no—
149#106C2×D11311yescharacteristic
150#102—1132no—
151#102—1132no—
152#102—1132no—
153#102C2×D11312yes—
154#97—1131no—
155#97—1131no—
156C4×C8—1131no—
157C4×C8—1131no—
158#41—4528no—
159C2×Q8—2262no—
160C2×D4—22no—
161C2×D4—1132no—
162C2×D4—2262no—
163C2×D4—2262no—
164C2×D4—2262no—
165C2×D4C22×D11312yes—
166C22×C4—1132no—
167C22×C4—2262no—
168C22×C4—2262no—
169C22×C4C22×D11311yescharacteristic
170D8—22no—
171D8—2264no—
172D8—2262no—
173M16—22no—
174M16—2262no—
175C2×C8—1131no—
176C2×C8—1131no—
177C2×C8C22×D11311yescharacteristic
178C2×C8C22×D11311yescharacteristic
179C4⋊C4—1132no—
180C4⋊C4—2262no—
181C4⋊C4C22×D11312yes—
182C22⋊C4—22no—
183C22⋊C4—2262no—
184C22⋊C4—2262no—
185C22⋊C4—2262no—
186C42—1132no—
187C42—1131no—
188C42—1131no—
189C23—22no—
190C23—2262no—
191C23D4×D11311yescharacteristic
192Q8—4524no—
193D4—22no—
194D4—22no—
195D4—44no—
196D4—4524no—
197D4—4524no—
198D4—4524no—
199D4—2262no—
200D4—2262no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—1132no—
205C2×C4—1132no—
206C2×C4—4524no—
207C2×C4—4524no—
208C2×C4—2264no—
209C2×C4—2262no—
210C2×C4D4×D11311yescharacteristic
211C2×C4C23×D11311yescharacteristic
212C8—21no—
213C8—1132no—
214C8—2261no—
215C8#1426864612yescomplemented
216C22—22no—
217C22—21no—
218C22—42no—
219C22—42no—
220C22—42no—
221C22—4522no—
222C22—4522no—
223C22—4522no—
224C22C2×D4×D11311yescharacteristic
225C4—21no—
226C4—42no—
227C4—1134no—
228C4—4522no—
229C4—2262no—
230C4#41×D11311yescharacteristic
231C4C2×#1426864611yescharacteristic
232C2—41no—
233C2—82no—
234C2—9042no—
235C2#2029914311yescharacteristic
236C2AGL(1,ℤ/8)×D11312yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#469×C113C2
socleC22×C113C22×D4
hypercenter#469D113
hypocenterC113#3184
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #20299143C2semidirect
2. #20298995C2semidirect
3. #20298973C2semidirect
4. #20298943C2semidirect
5. #20298851C2semidirect
6. #20298849C2semidirect
7. #20298710C2semidirect
8. #20298709C2semidirect
9. #20298707C2semidirect
10. M16×Dic113C2semidirect
11. #469×C113C2semidirect
94. C8×C113#41semidirect
96. #11744751#41semidirect
119. C113#3184semidirect
126. #469D113semidirect
215. C8#14268646semidirect

Maximal subgroups

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

subgroupindex
#202991432
#202989952
#202989732
#202989432
#202988512
#202988492
#202987102
#202987092
#202987072
M16×Dic1132
#469×C1132
#3184113