Finite Group Databasebeta

← #28400957

Subgroups — #28400957

Order 14464.

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

normal subgroups only

This group has 400 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#20299154C211yesmaximal, characteristic, complemented
2#124×D113C211yesmaximal, characteristic
3#20298959C212yesmaximal, complemented
4#20298956C212yesmaximal, complemented
5#20298955C211yesmaximal, characteristic, complemented
6#20298953C211yesmaximal, characteristic, complemented
7#20298952C211yesmaximal, characteristic, complemented
8#20298605C212yesmaximal, complemented
9#20298601C212yesmaximal
10C4×#14268630C211yesmaximal, characteristic, complemented
11#488×C113C211yesmaximal, characteristic, complemented
12C2×Q8×D113C2211yescharacteristic
13C2×D4×D113C2211yescharacteristic
14C2×#14268630C2212yes—
15#16813621C2212yescomplemented
16#16813614C2211yescharacteristic, complemented
17#16813611C2211yescharacteristic
18#16813610C2211yescharacteristic
19#16813609C2211yescharacteristic
20#16813608—22no—
21#16813600—22no—
22#16813587—22no—
23#16813580C2212yes—
24C22⋊C4×D113—22no—
25C42×D113C2211yescharacteristic
26#16813547C2212yescomplemented
27#16813546C2212yescomplemented
28#16813545C2212yescomplemented
29#16813544C2212yes—
30#16813543C2212yes—
31#16813542C2212yes—
32#16813532C2212yescomplemented
33C4×#11744751C2211yescharacteristic, complemented
34#125×C113C2211yescharacteristic, complemented
35#124×C113C2211yescharacteristic
36#103×C113C2212yescomplemented
37#102×C113C2212yes—
38C4×C8×C113C2211yescharacteristic, complemented
39C23×D113—21no—
40C2×Dic226—22no—
41C2×Dic226—21no—
42C2×Dic226C2311yescharacteristic
43Q8×D113—24no—
44C2×D452C2311yescharacteristic
45C2×C22⋊D113—21no—
46D4×D113—24no—
47C2×C4×D113—21no—
48C2×C4×D113D412yes—
49C2×C4×D113C2311yescharacteristic
50#14268630—24no—
51C2×#11744751C2312yes—
52C4⋊Dic113C2312yes—
53#14268626—22no—
54#14268626—22no—
55C22⋊Dic113—22no—
56#14268624—22no—
57#14268624—22no—
58#14268624—22no—
59C4×Dic113—22no—
60C4×Dic113D412yes—
61C4×Dic113C2311yescharacteristic
62C2×Q8×C113C2311yescharacteristic
63C2×D4×C113C2311yescharacteristic
64C2×C8×C113C2312yes—
65C4⋊C4×C113—22no—
66C4⋊C4×C113C2312yes—
67C22⋊C4×C113—22no—
68C42×C113C2311yescharacteristic
69C23×C113—21no—
70C22×D113—21no—
71C22×D113—44no—
72C22×D113—42no—
73C22×D113C2×D411yescharacteristic
74Q8×C113—22no—
75D4×C113—22no—
76C2×C4×C113—21no—
77C2×C4×C113—22no—
78C2×C4×C113C2×D412yes—
79C2×C4×C113C2411yescharacteristic
80C22⋊D113—42no—
81C2×Dic113—22no—
82C2×Dic113—21no—
83C2×Dic113C2×D412yes—
84C2×Dic113C2×D411yescharacteristic
85D452—22no—
86C4×D113—42no—
87C4×D113—42no—
88C4×D113#4114yes—
89Dic226—22no—
90Dic226—44no—
91Dic226—42no—
92C8×C113—22no—
93#11744751—22no—
94C22×C113—41no—
95C22×C113—42no—
96C22×C113C22×D411yescharacteristic
97C2×D113—22no—
98C2×D113—41no—
99C2×D113—42no—
100C2×D113—84no—
101C2×D113#12412yes—
102C4×C113—22no—
103C4×C113—41no—
104C4×C113—42no—
105C4×C113C2×#4112yes—
106Dic113—22no—
107Dic113—41no—
108Dic113—42no—
109Dic113#12412yes—
110C2×C113—81no—
111C2×C113C2×#12411yescharacteristic
112C2×C113#57512yes—
113D113—22no—
114D113—81no—
115#3140—1131nomaximal, Sylow
116C113#314011yescharacteristic, complemented, Sylow
117#533—1131no—
118C2×#124—1131no—
119#489—1132no—
120#489—1132no—
121#488—1131no—
122#488—1131no—
123#488—1131no—
124#488D11311yescharacteristic, complemented
125#419—1132no—
126#418—1132no—
127C4×M16—1131no—
128C22×Q8—1131no—
129C22×D4—1131no—
130C2×M16—1132no—
131C4⋊Q8—1132no—
132#125—1131no—
133#125C2×D11311yescharacteristic, complemented
134#124—1131no—
135#124—1131no—
136#124—1131no—
137#124—2262no—
138#124C2×D11311yescharacteristic
139C22⋊Q8—2262no—
140C4×Q8—2262no—
141#117—1132no—
142C2×C22⋊C4—2262no—
143C2×C42—1131no—
144#103—1132no—
145#103—1132no—
146#103—1132no—
147#103C2×D11312yescomplemented
148#102—1132no—
149#102—1132no—
150#102—1132no—
151#102C2×D11312yes—
152#97—1132no—
153C4×C8—1131no—
154C4×C8C2×D11311yescharacteristic, complemented
155C24—2261no—
156C2×Q8—1131no—
157C2×Q8—2262no—
158C2×Q8—2261no—
159C2×Q8—2264no—
160C2×Q8C22×D11311yescharacteristic
161C2×D4—1131no—
162C2×D4—2264no—
163C2×D4—2261no—
164C2×D4C22×D11311yescharacteristic
165C22×C4—1131no—
166C22×C4—1132no—
167C22×C4—2261no—
168M16—2264no—
169C2×C8—1132no—
170C2×C8C22×D11312yes—
171C4⋊C4—22no—
172C4⋊C4—1132no—
173C4⋊C4—2262no—
174C4⋊C4—2262no—
175C4⋊C4C22×D11312yes—
176C22⋊C4—22no—
177C22⋊C4—2262no—
178C22⋊C4—2262no—
179C22⋊C4—2262no—
180C22⋊C4—2262no—
181C42—1132no—
182C42—1131no—
183C42—2262no—
184C42C22×D11311yescharacteristic
185C23—21no—
186C23—1131no—
187C23—4522no—
188C23—4524no—
189C23—2261no—
190Q8—22no—
191Q8—4522no—
192Q8—4524no—
193Q8—2262no—
194D4—22no—
195D4—4522no—
196D4—2262no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—1131no—
200C2×C4—1134no—
201C2×C4—1132no—
202C2×C4—4522no—
203C2×C4—4522no—
204C2×C4—2262no—
205C2×C4—2261no—
206C2×C4D4×D11312yes—
207C2×C4C23×D11311yescharacteristic
208C8—22no—
209C8—2262no—
210C22—41no—
211C22—42no—
212C22—1132no—
213C22—9044no—
214C22—4521no—
215C22—4522no—
216C22—2262no—
217C22C2×D4×D11311yescharacteristic
218C4—22no—
219C4—41no—
220C4—42no—
221C4—1132no—
222C4—4521no—
223C4—4522no—
224C4—2262no—
225C4#41×D11312yes—
226C2—81no—
227C2—9041no—
228C2—2262no—
229C2#124×D11311yescharacteristic
230C2#2029939512yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#488×C113C2
socleC22×C113C22×D4
prime radicalC2×D4×D113C22
hypercenter#488D113
hypocenterC113#3140
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #20299154C2semidirect
3. #20298959C2semidirect
4. #20298956C2semidirect
5. #20298955C2semidirect
6. #20298953C2semidirect
7. #20298952C2semidirect
8. #20298605C2semidirect
10. C4×#14268630C2semidirect
11. #488×C113C2semidirect
15. #16813621C22semidirect
16. #16813614C22semidirect
26. #16813547C22semidirect
27. #16813546C22semidirect
28. #16813545C22semidirect
32. #16813532C22semidirect
33. C4×#11744751C22semidirect
34. #125×C113C22semidirect
36. #103×C113C22semidirect
38. C4×C8×C113C22semidirect
116. C113#3140semidirect
124. #488D113semidirect
133. #125C2×D113semidirect
147. #103C2×D113semidirect
154. C4×C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991542
#124×D1132
#202989592
#202989562
#202989552
#202989532
#202989522
#202986052
#202986012
C4×#142686302
#488×C1132
#3140113