Finite Group Databasebeta

← #28393195

Subgroups — #28393195

Order 14464.

600 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 229 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×#16813580C211yesmaximal, characteristic
2C2×#16813579C211yesmaximal, characteristic
3C2×C4⋊C4×D113C211yesmaximal, characteristic
4#20298493C214yesmaximal, complemented
5#20298469C214yesmaximal
6#20298467C211yesmaximal, characteristic, complemented
7#20298464C211yesmaximal, characteristic, complemented
8#20298463C211yesmaximal, characteristic, complemented
9#384×C113C211yesmaximal, characteristic, complemented
10C22×C4×D113C2212yes—
11C22×C4×D113C2211yescharacteristic
12#16813580—24no—
13#16813579C418yescomplemented
14C2×C4⋊Dic113C2211yescharacteristic
15C2×C4⋊Dic113C2211yescharacteristic
16C2×#14268626C2212yes—
17C2×#14268626C2214yes—
18C2×#14268626C2212yes—
19C4⋊C4×D113—24no—
20C2×#14268624C2212yes—
21C2×#14268624C2212yes—
22C2×C4×Dic113C2212yes—
23C2×C4×Dic113C2211yescharacteristic
24#16813529C2214yes—
25#16813529C2214yes—
26C2×C4⋊C4×C113C2211yescharacteristic
27C2×C4⋊C4×C113C2211yescharacteristic
28C2×C4⋊C4×C113C2214yes—
29C2×C42×C113C2211yescharacteristic
30C23×D113C2311yescharacteristic
31C22×Dic113C2312yes—
32C22×Dic113C2312yes—
33C22×Dic113C2312yes—
34C22×Dic113C2311yescharacteristic
35C2×C4×D113—24no—
36C2×C4×D113—44no—
37C2×C4×D113C2×C414yes—
38C2×C4×D113D414yes—
39C2×C4×D113Q814yes—
40C4⋊Dic113—22no—
41C4⋊Dic113—22no—
42#14268626—24no—
43#14268626—44no—
44#14268626C2×C418yescomplemented
45#14268624—24no—
46#14268624C2×C418yes—
47C4×Dic113—24no—
48C4×Dic113C2×C414yescomplemented
49C22×C4×C113C2312yes—
50C22×C4×C113C2312yes—
51C22×C4×C113C2312yes—
52C22×C4×C113C2311yescharacteristic
53C4⋊C4×C113—22no—
54C4⋊C4×C113—22no—
55C4⋊C4×C113—44no—
56C42×C113C2×C414yescomplemented
57C23×C113C2411yescharacteristic
58C22×D113—22no—
59C22×D113—22no—
60C22×D113C22×C412yes—
61C22×D113C2×D412yes—
62C22×D113C2×Q812yes—
63C2×C4×C113—22no—
64C2×C4×C113—22no—
65C2×C4×C113—22no—
66C2×C4×C113—22no—
67C2×C4×C113—24no—
68C2×C4×C113—24no—
69C2×C4×C113C22×C414yes—
70C2×C4×C113C22×C412yes—
71C2×C4×C113C2×D412yes—
72C2×C4×C113C2×Q812yes—
73C2×Dic113—22no—
74C2×Dic113—22no—
75C2×Dic113—22no—
76C2×Dic113—22no—
77C2×Dic113—24no—
78C2×Dic113—24no—
79C2×Dic113C22×C414yes—
80C2×Dic113C22×C412yes—
81C2×Dic113C2×D412yes—
82C2×Dic113C2×Q812yes—
83C4×D113—48no—
84C4×D113C4⋊C4116yescomplemented
85C22×C113C23×C411yescharacteristic
86C22×C113C22×D411yescharacteristic
87C22×C113C22×Q811yescharacteristic
88C22×C113H(5,𝔽2)12yes—
89C22×C1132−1+412yes—
90C2×D113—24no—
91C2×D113—22no—
92C2×D113—22no—
93C2×D113—24no—
94C2×D113C2×C4⋊C414yes—
95C4×C113—24no—
96C4×C113—42no—
97C4×C113—42no—
98C4×C113C2×C4⋊C414yes—
99Dic113—24no—
100Dic113—42no—
101Dic113—42no—
102Dic113C2×C4⋊C414yes—
103C2×C113C22×C4⋊C411yescharacteristic
104C2×C113#52012yes—
105C2×C113#53511yescharacteristic
106C2×C113#53611yescharacteristic
107C2×C113#54412yes—
108D113—24no—
109#2317—1131nomaximal, Sylow
110C113#231711yescharacteristic, complemented, Sylow
111C2×#117—1131no—
112C2×#117—1131no—
113C22×C4⋊C4—1131no—
114#389—1134no—
115#385—1134no—
116#384—1131no—
117#384D11311yescharacteristic, complemented
118#382—1131no—
119#382—1131no—
120C23×C4—1131no—
121C23×C4—1132no—
122#117—1138no—
123#117—2264no—
124C2×C4⋊C4—1132no—
125C2×C4⋊C4—1134no—
126C2×C4⋊C4—1132no—
127C2×C4⋊C4—1131no—
128C2×C4⋊C4—1131no—
129C2×C4⋊C4—2264no—
130C2×C4⋊C4C2×D11311yescharacteristic
131C2×C4⋊C4C2×D11311yescharacteristic
132C2×C4⋊C4C2×D11314yes—
133C2×C22⋊C4—1132no—
134C2×C22⋊C4—1132no—
135C2×C42—1131no—
136C2×C42—1132no—
137C2×C42C2×D11311yescharacteristic
138#95—1134no—
139#95—1134no—
140C24—1131no—
141C22×C4—1131no—
142C22×C4—1134no—
143C22×C4—1134no—
144C22×C4—1134no—
145C22×C4—1132no—
146C22×C4—1132no—
147C22×C4—1132no—
148C22×C4—4524no—
149C22×C4—2264no—
150C22×C4C22×D11312yes—
151C22×C4C22×D11312yes—
152C22×C4C22×D11312yes—
153C22×C4C22×D11311yescharacteristic
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4—44no—
157C4⋊C4—1138no—
158C4⋊C4—4524no—
159C4⋊C4—2264no—
160C4⋊C4—2262no—
161C4⋊C4—2262no—
162C22⋊C4—1138no—
163C22⋊C4—2264no—
164C42—1134no—
165C42—2264no—
166C42C4×D11314yescomplemented
167C23—1132no—
168C23—1132no—
169C23—1132no—
170C23—2262no—
171C23—2262no—
172C23C23×D11311yescharacteristic
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—24no—
178C2×C4—24no—
179C2×C4—1132no—
180C2×C4—1132no—
181C2×C4—1132no—
182C2×C4—11316no—
183C2×C4—1134no—
184C2×C4—4528no—
185C2×C4—2262no—
186C2×C4—2262no—
187C2×C4—2264no—
188C2×C4—2264no—
189C2×C4—2262no—
190C2×C4—2262no—
191C2×C4C2×C4×D11314yes—
192C2×C4C2×C4×D11312yes—
193C2×C4D4×D11312yes—
194C2×C4Q8×D11312yes—
195C22—1134no—
196C22—2264no—
197C22—2262no—
198C22—2262no—
199C22—2264no—
200C22C22×C4×D11311yescharacteristic
201C22C2×D4×D11311yescharacteristic
202C22C2×Q8×D11311yescharacteristic
203C22#1681366712yes—
204C22#1681367012yes—
205C4—24no—
206C4—42no—
207C4—42no—
208C4—1134no—
209C4—4522no—
210C4—4522no—
211C4—2264no—
212C4C4⋊C4×D11314yes—
213C2—2264no—
214C2C2×C4⋊C4×D11311yescharacteristic
215C2#2029907912yes—
216C2#2029916111yescharacteristic
217C2#2029917311yescharacteristic
218C2#2029922512yes—
subgroupG/H
center, FrattiniC23C23×D113
commutatorC22×C113C23×C4
Fitting#384×C113C2
socle, cosocleC23×C113C24
prime radicalC23×D113C23
hypercenter#384D113
hypocenterC113#2317
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
4. #20298493C2semidirect
6. #20298467C2semidirect
7. #20298464C2semidirect
8. #20298463C2semidirect
9. #384×C113C2semidirect
13. #16813579C4semidirect
44. #14268626C2×C4semidirect
48. C4×Dic113C2×C4semidirect
56. C42×C113C2×C4semidirect
84. C4×D113C4⋊C4semidirect
110. C113#2317semidirect
117. #384D113semidirect
166. C42C4×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168135802
C2×#168135792
C2×C4⋊C4×D1132
#202984932
#202984692
#202984672
#202984642
#202984632
#384×C1132
#2317113