Finite Group Databasebeta

← #28393853

Subgroups — #28393853

Order 14464.

840 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 840 conjugacy classes of subgroups — too many to draw. Only its 177 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×C4×D452C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊D113C214yesmaximal, complemented
3#20298534C212yesmaximal, complemented
4#20298533C212yesmaximal, complemented
5#20298507C212yesmaximal, complemented
6#20298506C212yesmaximal, complemented
7#20298444C211yesmaximal, characteristic, complemented
8C2×C4×D4×C113C211yesmaximal, characteristic, complemented
9C22×D452C2211yescharacteristic
10C22×C22⋊D113C2214yes—
11C22×C4×D113C2212yes—
12C4×D452—24no—
13C4×C22⋊D113—216no—
14C2×C4⋊Dic113C2211yescharacteristic
15C2×#14268626C2214yes—
16C2×C22⋊Dic113C2214yes—
17C2×#14268624C2212yes—
18C2×#14268624C2214yes—
19C2×C4×Dic113C2212yes—
20#16813529C2212yes—
21#16813529C2212yes—
22C22×D4×C113C2211yescharacteristic
23C23×C4×C113C2212yes—
24C4×D4×C113—24no—
25C2×C4⋊C4×C113C2211yescharacteristic
26C2×C22⋊C4×C113C2212yes—
27C2×C42×C113C2211yescharacteristic
28C23×D113C2312yes—
29C2×D452—24no—
30C2×D452—22no—
31C2×C22⋊D113—28no—
32C2×C22⋊D113—28no—
33C2×C22⋊D113—28no—
34C22×Dic113C2312yes—
35C22×Dic113C2314yes—
36C2×C4×D113—28no—
37C2×C4×D113—24no—
38C4⋊Dic113—22no—
39#14268626—28no—
40C22⋊Dic113—28no—
41#14268624—24no—
42#14268624—28no—
43C4×Dic113D418yescomplemented
44C24×C113C2312yes—
45C2×D4×C113—24no—
46C2×D4×C113—22no—
47C22×C4×C113—28no—
48C22×C4×C113—24no—
49C22×C4×C113C2312yes—
50C22×C4×C113C2311yescharacteristic
51C22×C4×C113C2311yescharacteristic
52C22×C4×C113C2311yescharacteristic
53C4⋊C4×C113—22no—
54C22⋊C4×C113—24no—
55C42×C113D414yescomplemented
56C23×C113—22no—
57C23×C113—24no—
58C23×C113—22no—
59C23×C113—24no—
60C23×C113#4114yes—
61C23×C113C2411yescharacteristic
62C22×D113—24no—
63C22×D113—22no—
64C22×D113—24no—
65C22×D113—22no—
66C22×D113#4114yes—
67D4×C113—28no—
68C2×C4×C113—22no—
69C2×C4×C113—22no—
70C2×C4×C113—22no—
71C2×C4×C113—24no—
72C2×C4×C113—48no—
73C2×C4×C113C2×D414yes—
74C2×C4×C113C2×D412yes—
75C2×C4×C113C2×D412yes—
76C2×C4×C113C2×D412yes—
77C22⋊D113—232no—
78C2×Dic113—24no—
79C2×Dic113—24no—
80C2×Dic113—22no—
81C2×Dic113—24no—
82C2×Dic113C2×D418yes—
83D452—28no—
84C4×D113—48no—
85C22×C113—28no—
86C22×C113—24no—
87C22×C113—42no—
88C22×C113—44no—
89C22×C113—42no—
90C22×C113C22×D412yes—
91C22×C113C22×D411yescharacteristic
92C22×C113C2×#4112yes—
93C22×C113C2×#4112yes—
94C2×D113—24no—
95C2×D113—28no—
96C2×D113—44no—
97C2×D113—42no—
98C2×D113—42no—
99C4×C113—22no—
100C4×C113—22no—
101C4×C113—42no—
102C4×C113#12714yes—
103Dic113—28no—
104Dic113—42no—
105C2×C113—44no—
106C2×C113#52511yescharacteristic
107C2×C113#52514yes—
108C2×C113#52511yescharacteristic
109C2×C113C2×#12711yescharacteristic
110D113—44no—
111#2397—1131nomaximal, Sylow
112C113#239711yescharacteristic, complemented, Sylow
113C2×C4×D4—1134no—
114C2×C4×D4—1131no—
115C2×C4×D4D11311yescharacteristic, complemented
116#399—1132no—
117#399—1132no—
118#392—1132no—
119#392—1132no—
120#376—1131no—
121C22×D4—1134no—
122C22×D4—1131no—
123C22×D4C2×D11311yescharacteristic
124C23×C4—1132no—
125C23×C4C2×D11312yes—
126C4×D4—24no—
127C4×D4—22616no—
128C4×D4—2264no—
129C2×C4⋊C4—1134no—
130C2×C4⋊C4—1131no—
131C2×C4⋊C4C2×D11311yescharacteristic
132C2×C22⋊C4—1134no—
133C2×C22⋊C4—1134no—
134C2×C22⋊C4—1132no—
135C2×C22⋊C4C2×D11312yes—
136C2×C42—1132no—
137C2×C42C2×D11311yescharacteristic
138#95—1132no—
139#95—1132no—
140C24—1132no—
141C24C22×D11312yes—
142C2×D4—24no—
143C2×D4—22no—
144C2×D4—2264no—
145C2×D4—2268no—
146C2×D4—2268no—
147C2×D4—2268no—
148C2×D4—2262no—
149C22×C4—28no—
150C22×C4—24no—
151C22×C4—1134no—
152C22×C4—1132no—
153C22×C4—2268no—
154C22×C4—2264no—
155C22×C4C22×D11312yes—
156C22×C4C22×D11311yescharacteristic
157C22×C4C22×D11311yescharacteristic
158C22×C4C22×D11311yescharacteristic
159C4⋊C4—22no—
160C4⋊C4—2268no—
161C4⋊C4—2262no—
162C22⋊C4—24no—
163C22⋊C4—2268no—
164C22⋊C4—2268no—
165C22⋊C4—2264no—
166C42—1138no—
167C42C22⋊D11314yescomplemented
168C23—24no—
169C23—22no—
170C23—24no—
171C23—22no—
172C23—1134no—
173C23—2264no—
174C23—2262no—
175C23—2262no—
176C23—2264no—
177C23#1426864714yes—
178C23C23×D11311yescharacteristic
179D4—28no—
180D4—2268no—
181D4—22632no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—24no—
185C2×C4—22no—
186C2×C4—48no—
187C2×C4—1138no—
188C2×C4—4528no—
189C2×C4—2264no—
190C2×C4—2262no—
191C2×C4—2264no—
192C2×C4—2264no—
193C2×C4D4×D11314yes—
194C2×C4C2×C22⋊D11312yes—
195C2×C4C2×C22⋊D11312yes—
196C2×C4C2×C22⋊D11312yes—
197C22—28no—
198C22—24no—
199C22—42no—
200C22—44no—
201C22—42no—
202C22—4524no—
203C22—4522no—
204C22—4522no—
205C22—2264no—
206C22—2268no—
207C22C2×D4×D11312yes—
208C22C22×C22⋊D11311yescharacteristic
209C22#41×D11312yes—
210C22C2×#1426864712yes—
211C4—22no—
212C4—22no—
213C4—42no—
214C4—4522no—
215C4—2268no—
216C4#1681361814yes—
217C2—44no—
218C2—4524no—
219C2#2029910511yescharacteristic
220C2#2029910714yes—
221C2#2029910911yescharacteristic
222C2C2×#1681361811yescharacteristic
subgroupG/H
centerC22×C4C22×D113
commutator, socle, cosocleC23×C113C24
FrattiniC23C23×D113
FittingC2×C4×D4×C113C2
hypercenterC2×C4×D4D113
hypocenterC113#2397
LCSG ▷ C23×C113 ▷ C113
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C4×D452C2semidirect
2. C2×C4×C22⋊D113C2semidirect
3. #20298534C2semidirect
4. #20298533C2semidirect
5. #20298507C2semidirect
6. #20298506C2semidirect
7. #20298444C2semidirect
8. C2×C4×D4×C113C2semidirect
43. C4×Dic113D4semidirect
55. C42×C113D4semidirect
112. C113#2397semidirect
115. C2×C4×D4D113semidirect
167. C42C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4522
C2×C4×C22⋊D1132
#202985342
#202985332
#202985072
#202985062
#202984442
C2×C4×D4×C1132
#2397113