Finite Group Databasebeta

← #28400893

Subgroups — #28400893

Order 14464.

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

normal subgroups only

This group has 400 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#20299153C211yesmaximal, characteristic, complemented
2#20299146C211yesmaximal, characteristic
3#20298951C214yesmaximal, complemented
4#20298950C211yesmaximal, characteristic, complemented
5#20298949C211yesmaximal, characteristic, complemented
6#20298944C211yesmaximal, characteristic, complemented
7#20298591C214yesmaximal, complemented
8C4×C8×D113C211yesmaximal, characteristic, complemented
9#486×C113C211yesmaximal, characteristic, complemented
10C2×#14268646C2212yes—
11C2×C8×D113C2212yes—
12#16813622C2211yescharacteristic
13#16813622C2211yescharacteristic
14#16813613C2212yes—
15#16813609C2212yes—
16#16813602—21no—
17#16813598—21no—
18#16813593—21no—
19#16813593—21no—
20Q8×Dic113—21no—
21#16813587—21no—
22D4×Dic113—21no—
23D4×Dic113—21no—
24#16813580C2212yes—
25C42×D113C2211yescharacteristic
26#16813547C2214yes—
27#16813545C2214yes—
28#16813543C2214yes—
29C4×#11744751C2211yescharacteristic
30C8×Dic113C2212yes—
31C4⋊Q8×C113C2211yescharacteristic
32#127×C113C2211yescharacteristic
33#102×C113C2214yes—
34C4×C8×C113C2211yescharacteristic
35#14268646—28no—
36C2×Dic226—21no—
37C2×Dic226C2312yes—
38C2×C22⋊D113—22no—
39C22×Dic113—22no—
40C2×C4×D113D411yescharacteristic
41C2×C4×D113D411yescharacteristic
42C2×C4×D113C2311yescharacteristic
43C2×#11744751C2312yes—
44C8×D113—24no—
45C4⋊Dic113—21no—
46C4⋊Dic113—21no—
47C4⋊Dic113—21no—
48C4⋊Dic113—22no—
49C4⋊Dic113C2312yes—
50#14268626—22no—
51C22⋊Dic113—22no—
52C22⋊Dic113—22no—
53#14268624—22no—
54C4×Dic113—22no—
55C4×Dic113D411yescharacteristic
56C4×Dic113D411yescharacteristic
57C4×Dic113C2311yescharacteristic
58C2×Q8×C113—21no—
59C2×D4×C113—21no—
60C2×D4×C113—21no—
61C2×D4×C113C2312yes—
62C2×C8×C113C2312yes—
63C4⋊C4×C113—21no—
64C4⋊C4×C113C2312yes—
65C42×C113C2311yescharacteristic
66C23×C113—22no—
67C22×D113C2×D411yescharacteristic
68Q8×C113—42no—
69D4×C113—24no—
70D4×C113—42no—
71D4×C113—42no—
72C2×C4×C113—22no—
73C2×C4×C113C2×D411yescharacteristic
74C2×C4×C113C2×D411yescharacteristic
75C2×C4×C113C2411yescharacteristic
76C22⋊D113—44no—
77C2×Dic113—22no—
78C2×Dic113—22no—
79C2×Dic113—44no—
80C2×Dic113C2×D411yescharacteristic
81C2×Dic113C2×D411yescharacteristic
82C2×Dic113C2×D411yescharacteristic
83C4×D113—22no—
84C4×D113—22no—
85C4×D113#4114yes—
86Dic226—24no—
87Dic226—42no—
88C8×C113—22no—
89#11744751—22no—
90C22×C113—42no—
91C22×C113—42no—
92C22×C113—42no—
93C22×C113C22×D411yescharacteristic
94C2×D113—21no—
95C2×D113—21no—
96C2×D113#12412yes—
97C4×C113—42no—
98C4×C113#13512yes—
99C4×C113#13512yes—
100C4×C113C2×#4112yes—
101Dic113—21no—
102Dic113—21no—
103Dic113—42no—
104Dic113—42no—
105Dic113#12412yes—
106C2×C113—82no—
107C2×C113C2×#12411yescharacteristic
108C2×C113C2×#13511yescharacteristic
109C2×C113C2×#13511yescharacteristic
110D113—22no—
111#3131—1131nomaximal, Sylow
112C113#313111yescharacteristic, complemented, Sylow
113#533—1131no—
114#532—1131no—
115#488—1134no—
116#487—1131no—
117#487—1131no—
118#486—1131no—
119#486D11311yescharacteristic, complemented
120#416—1134no—
121C2×C4×C8—1131no—
122C2×#41—1132no—
123C22×C8—1132no—
124C4⋊Q8—1131no—
125C4⋊Q8—1131no—
126C4⋊Q8C2×D11311yescharacteristic
127#127C2×D11311yescharacteristic
128#125—1132no—
129#124—1132no—
130C22⋊Q8—2261no—
131C22⋊Q8—2261no—
132#121—2261no—
133#121—2261no—
134C4×Q8—2261no—
135C4×Q8—2261no—
136C4×D4—2261no—
137C4×D4—2261no—
138#117—1132no—
139C2×C42—1131no—
140#103—1134no—
141#103—1134no—
142#102—1134no—
143#102C2×D11314yes—
144C4×C8—1132no—
145C4×C8—1131no—
146C4×C8C2×D11311yescharacteristic
147#41—2268no—
148C2×Q8—21no—
149C2×Q8—1132no—
150C2×Q8—2261no—
151C2×D4—21no—
152C2×D4—21no—
153C2×D4—2262no—
154C2×D4C22×D11312yes—
155C22×C4—1131no—
156C22×C4—1131no—
157C22×C4—1131no—
158C22×C4—2262no—
159C2×C8—1132no—
160C2×C8—2264no—
161C2×C8C22×D11312yes—
162C4⋊C4—21no—
163C4⋊C4—1132no—
164C4⋊C4—2262no—
165C4⋊C4—2262no—
166C4⋊C4—2261no—
167C4⋊C4—2261no—
168C4⋊C4—2261no—
169C4⋊C4C22×D11312yes—
170C22⋊C4—2262no—
171C22⋊C4—2262no—
172C22⋊C4—2262no—
173C42—1131no—
174C42—1131no—
175C42—1131no—
176C42—2262no—
177C42C22×D11311yescharacteristic
178C23—22no—
179C23—1131no—
180Q8—42no—
181Q8—4522no—
182Q8—2264no—
183D4—24no—
184D4—42no—
185D4—42no—
186D4—4524no—
187C2×C4—22no—
188C2×C4—1131no—
189C2×C4—1134no—
190C2×C4—1131no—
191C2×C4—1131no—
192C2×C4—4524no—
193C2×C4—2262no—
194C2×C4—2262no—
195C2×C4—2262no—
196C2×C4—2262no—
197C2×C4D4×D11311yescharacteristic
198C2×C4D4×D11311yescharacteristic
199C2×C4C23×D11311yescharacteristic
200C8—22no—
201C8—2262no—
202C22—42no—
203C22—42no—
204C22—42no—
205C22—1132no—
206C22—2261no—
207C22—2261no—
208C22C2×D4×D11311yescharacteristic
209C4—42no—
210C4—1132no—
211C4—4522no—
212C4—4522no—
213C4—2261no—
214C4—2261no—
215C4#1681364112yes—
216C4#1681364312yes—
217C4#41×D11312yes—
218C2—82no—
219C2—2262no—
220C2#124×D11311yescharacteristic
221C2C2×#1681364111yescharacteristic
222C2C2×#1681364311yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#486×C113C2
socleC22×C113C22×D4
prime radical#20299146C2
hypercenter#486D113
hypocenterC113#3131
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #20299153C2semidirect
3. #20298951C2semidirect
4. #20298950C2semidirect
5. #20298949C2semidirect
6. #20298944C2semidirect
7. #20298591C2semidirect
8. C4×C8×D113C2semidirect
9. #486×C113C2semidirect
112. C113#3131semidirect
119. #486D113semidirect

Maximal subgroups

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

subgroupindex
#202991532
#202991462
#202989512
#202989502
#202989492
#202989442
#202985912
C4×C8×D1132
#486×C1132
#3131113