Finite Group Databasebeta

← #488×D113 #28400887

Subgroups — #488×D113 #28400887

Order 14464.

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

normal subgroups only

This group has 412 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#125×D113C211yesmaximal, characteristic, complemented
2#124×D113C211yesmaximal, characteristic
3#20298955C211yesmaximal, characteristic, complemented
4#20298954C212yesmaximal, complemented
5#20298953C211yesmaximal, characteristic, complemented
6#20298952C211yesmaximal, characteristic, complemented
7#20298951C212yesmaximal, complemented
8#103×D113C212yesmaximal, complemented
9#102×D113C212yesmaximal
10C4×C8×D113C211yesmaximal, characteristic, complemented
11#488×C113C211yesmaximal, characteristic, complemented
12C2×Q8×D113C2211yescharacteristic
13C2×D4×D113C2211yescharacteristic
14C2×C8×D113C2212yes—
15#16813614C2211yescharacteristic, complemented
16#16813613C2212yescomplemented
17#16813612—22no—
18#16813611C2211yescharacteristic
19#16813610C2211yescharacteristic
20#16813609C2211yescharacteristic
21#16813608—22no—
22C4⋊C4×D113—22no—
23C4⋊C4×D113C2212yes—
24C22⋊C4×D113—22no—
25C42×D113C2211yescharacteristic
26#16813547C2212yescomplemented
27#16813546C2212yescomplemented
28#16813545C2212yescomplemented
29#16813544C2212yes—
30#16813543C2212yes—
31#16813542C2212yes—
32C4×#11744751C2211yescharacteristic, complemented
33C8×Dic113C2212yescomplemented
34#125×C113C2211yescharacteristic, complemented
35#124×C113C2211yescharacteristic
36#103×C113C2212yescomplemented
37#102×C113C2212yes—
38C4×C8×C113C2211yescharacteristic, complemented
39C23×D113—21no—
40C2×Dic226—21no—
41C2×Dic226C2311yescharacteristic
42Q8×D113—24no—
43C2×D452C2311yescharacteristic
44C2×C22⋊D113—21no—
45D4×D113—24no—
46C2×C4×D113—21no—
47C2×C4×D113—22no—
48C2×C4×D113D412yes—
49C2×C4×D113C2311yescharacteristic
50C2×#11744751C2312yes—
51C8×D113—24no—
52C4⋊Dic113—22no—
53C4⋊Dic113C2312yes—
54#14268626—22no—
55#14268626—22no—
56#14268626—22no—
57C22⋊Dic113—22no—
58#14268624—22no—
59#14268624—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—42no—
72C22×D113—44no—
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—21no—
82C2×Dic113—22no—
83C2×Dic113C2×D412yes—
84C2×Dic113C2×D411yescharacteristic
85D452—22no—
86C4×D113—24no—
87C4×D113—42no—
88C4×D113—44no—
89C4×D113#4114yes—
90Dic226—22no—
91Dic226—42no—
92C8×C113—22no—
93#11744751—22no—
94C22×C113—41no—
95C22×C113—42no—
96C22×C113C22×D411yescharacteristic
97C2×D113—41no—
98C2×D113—42no—
99C2×D113—84no—
100C2×D113#12412yes—
101C2×D113#13514yes—
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×C113C2×#13512yes—
113D113—81no—
114D113#48814yesdirect product factor
115C2×#488—1131nomaximal, Sylow
116C113C2×#48811yescharacteristic, complemented, Sylow
117C2×#125—1131no—
118C2×#124—1131no—
119#488—1131no—
120#488—1131no—
121#488—1132no—
122#488—1132no—
123#488—1131no—
124#488D11311yescharacteristic, direct product factor
125C2×#103—1132no—
126C2×#102—1132no—
127C2×C4×C8—1131no—
128C22×Q8—1131no—
129C22×D4—1131no—
130C22×C8—1132no—
131#125—1132no—
132#125—1131no—
133#125—2262no—
134#125C2×D11311yescharacteristic, complemented
135#124—1131no—
136#124—1131no—
137#124—1131no—
138#124—2262no—
139#124C2×D11311yescharacteristic
140C2×C4⋊C4—1132no—
141C2×C4⋊C4—2262no—
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—
152C4×C8—1132no—
153C4×C8—1131no—
154C4×C8C2×D11311yescharacteristic, complemented
155C24—2261no—
156C2×Q8—1131no—
157C2×Q8—2261no—
158C2×Q8—2264no—
159C2×Q8C22×D11311yescharacteristic
160C2×D4—1131no—
161C2×D4—2264no—
162C2×D4—2261no—
163C2×D4C22×D11311yescharacteristic
164C22×C4—1131no—
165C22×C4—1132no—
166C22×C4—2261no—
167C22×C4—2262no—
168C2×C8—1132no—
169C2×C8—2264no—
170C2×C8C22×D11312yes—
171C4⋊C4—22no—
172C4⋊C4—1132no—
173C4⋊C4—2262no—
174C4⋊C4—2262no—
175C4⋊C4—2262no—
176C4⋊C4—2262no—
177C4⋊C4C22×D11312yes—
178C22⋊C4—22no—
179C22⋊C4—2262no—
180C22⋊C4—2262no—
181C22⋊C4—2262no—
182C42—1132no—
183C42—1131no—
184C42C22×D11311yescharacteristic
185C23—21no—
186C23—1131no—
187C23—4522no—
188C23—4524no—
189C23—2261no—
190Q8—22no—
191Q8—4522no—
192Q8—2262no—
193D4—22no—
194D4—4522no—
195D4—2262no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—1131no—
199C2×C4—1134no—
200C2×C4—1132no—
201C2×C4—4522no—
202C2×C4—4524no—
203C2×C4—2264no—
204C2×C4—2261no—
205C2×C4—2262no—
206C2×C4D4×D11312yes—
207C2×C4C23×D11311yescharacteristic
208C8—22no—
209C8—2262no—
210C22—41no—
211C22—42no—
212C22—1132no—
213C22—1134no—
214C22—9044no—
215C22—4521no—
216C22—4522no—
217C22C2×D4×D11311yescharacteristic
218C4—22no—
219C4—41no—
220C4—42no—
221C4—1132no—
222C4—4521no—
223C4—4522no—
224C4—2262no—
225C4#41×D11312yes—
226C2—81no—
227C2—1134no—
228C2—9041no—
229C2#124×D11311yescharacteristic
230C2#135×D11312yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#488×C113C2
socleC22×C113C22×D4
prime radicalC2×D4×D113C22
hypercenter#488D113
hypocenterC113C2×#488
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. #125×D113C2semidirect
3. #20298955C2semidirect
4. #20298954C2semidirect
5. #20298953C2semidirect
6. #20298952C2semidirect
7. #20298951C2semidirect
8. #103×D113C2semidirect
10. C4×C8×D113C2semidirect
11. #488×C113C2semidirect
15. #16813614C22semidirect
16. #16813613C22semidirect
26. #16813547C22semidirect
27. #16813546C22semidirect
28. #16813545C22semidirect
32. C4×#11744751C22semidirect
33. C8×Dic113C22semidirect
34. #125×C113C22semidirect
36. #103×C113C22semidirect
38. C4×C8×C113C22semidirect
114. D113#488direct (N × H)
116. C113C2×#488semidirect
124. #488D113direct (N × H)
134. #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
#125×D1132
#124×D1132
#202989552
#202989542
#202989532
#202989522
#202989512
#103×D1132
#102×D1132
C4×C8×D1132
#488×C1132
C2×#488113