Finite Group Databasebeta

← #28401518

Subgroups — #28401518

Order 14464.

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

normal subgroups only

This group has 384 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
2C4⋊Q8×D113C211yesmaximal, characteristic
3#20298977C211yesmaximal, characteristic, complemented
4#20298949C211yesmaximal, characteristic, complemented
5#20298948C211yesmaximal, characteristic, complemented
6#20298806C214yesmaximal, complemented
7#20298752C214yesmaximal
8#20298649C211yesmaximal, characteristic
9#494×C113C211yesmaximal, characteristic, complemented
10C2×Q8×D113C2212yes—
11C2×#14268637C2214yes—
12#16813622C2211yescharacteristic
13#16813622C2211yescharacteristic
14#16813621—21no—
15#16813621—21no—
16#16813620C2212yes—
17#16813613—21no—
18#16813602—21no—
19#16813598C2212yes—
20Q8×Dic113C2212yes—
21#16813587—21no—
22#16813580—21no—
23C4⋊C4×D113—21no—
24C4⋊C4×D113—21no—
25C42×D113C2211yescharacteristic
26#16813551C2212yes—
27#16813547C2214yes—
28#16813546C2214yes—
29#16813534C2212yes—
30C4×#11744751C2211yescharacteristic
31C2×Q16×C113C2214yes—
32C4⋊Q8×C113C2211yescharacteristic
33C4⋊Q8×C113C2211yescharacteristic
34C4×C8×C113C2211yescharacteristic
35C2×Dic226—21no—
36C2×Dic226—22no—
37C2×Dic226C2312yes—
38Q8×D113—44no—
39C2×C4×D113—22no—
40C2×C4×D113D411yescharacteristic
41C2×C4×D113D411yescharacteristic
42C2×C4×D113C2311yescharacteristic
43#14268637—44no—
44C2×#11744751C2312yes—
45C4⋊Dic113—21no—
46C4⋊Dic113—21no—
47C4⋊Dic113—21no—
48C4⋊Dic113—22no—
49C4⋊Dic113C2312yes—
50#14268626—22no—
51#14268626—22no—
52#14268626—22no—
53#14268624—22no—
54C4×Dic113—22no—
55C4×Dic113D411yescharacteristic
56C4×Dic113D411yescharacteristic
57C4×Dic113C2311yescharacteristic
58C2×Q8×C113C2312yes—
59C2×Q8×C113C2312yes—
60Q16×C113—44no—
61C2×C8×C113C2312yes—
62C4⋊C4×C113—21no—
63C4⋊C4×C113—21no—
64C4⋊C4×C113—21no—
65C4⋊C4×C113—21no—
66C42×C113C2311yescharacteristic
67C22×D113C2×D411yescharacteristic
68Q8×C113—24no—
69Q8×C113—24no—
70C2×C4×C113—22no—
71C2×C4×C113—22no—
72C2×C4×C113C2×D411yescharacteristic
73C2×C4×C113C2×D411yescharacteristic
74C2×C4×C113C2411yescharacteristic
75C2×Dic113—22no—
76C2×Dic113—22no—
77C2×Dic113C2×D411yescharacteristic
78C2×Dic113C2×D411yescharacteristic
79C2×Dic113C2×D411yescharacteristic
80C4×D113—22no—
81C4×D113—22no—
82C4×D113—44no—
83C4×D113Q1614yescomplemented
84Dic226—24no—
85Dic226—44no—
86Dic226—42no—
87C8×C113—22no—
88#11744751—22no—
89C22×C113C22×D411yescharacteristic
90C2×D113—21no—
91C2×D113—21no—
92C2×D113C2×Q1612yes—
93C4×C113—42no—
94C4×C113—42no—
95C4×C113C2×Q1612yes—
96C4×C113#13712yes—
97C4×C113H(5,𝔽2)12yes—
98Dic113—21no—
99Dic113—21no—
100Dic113—42no—
101Dic113—42no—
102Dic113C2×Q1612yes—
103C2×C113#53511yescharacteristic
104C2×C113C22×Q1611yescharacteristic
105C2×C113C2×#13711yescharacteristic
106D113—22no—
107#3209—1131nomaximal, Sylow
108C113#320911yescharacteristic, complemented, Sylow
109#533—1131no—
110C2×C4⋊Q8—1131no—
111#494—1131no—
112#494D11311yescharacteristic, complemented
113#487—1131no—
114#487—1131no—
115#462—1134no—
116#451—1134no—
117#431—1131no—
118C22×Q8—1132no—
119C2×Q16—1134no—
120C2×Q16C2×D11314yes—
121C4⋊Q8—1132no—
122C4⋊Q8—1131no—
123C4⋊Q8—1131no—
124C4⋊Q8—2261no—
125C4⋊Q8—2261no—
126C4⋊Q8C2×D11311yescharacteristic
127C4⋊Q8C2×D11311yescharacteristic
128#125—2261no—
129C22⋊Q8—1132no—
130C22⋊Q8—2261no—
131C4×Q8—1132no—
132C4×Q8—2261no—
133#117—2261no—
134C2×C4⋊C4—2261no—
135C2×C4⋊C4—2261no—
136C2×C42—1131no—
137C4⋊C8—1132no—
138#103—1134no—
139#103—1134no—
140C22⋊C8—1132no—
141C4×C8—1131no—
142C4×C8C2×D11311yescharacteristic
143C2×Q8—1132no—
144C2×Q8—4524no—
145C2×Q8—2262no—
146C2×Q8—2261no—
147C2×Q8C22×D11312yes—
148C2×Q8C22×D11312yes—
149C22×C4—1131no—
150C22×C4—1131no—
151C22×C4—1131no—
152C22×C4—2262no—
153Q16—44no—
154Q16—4524no—
155C2×C8—1132no—
156C2×C8C22×D11312yes—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—1132no—
162C4⋊C4—2262no—
163C4⋊C4—2262no—
164C4⋊C4—2262no—
165C4⋊C4—2262no—
166C4⋊C4—2261no—
167C4⋊C4—2261no—
168C4⋊C4—2261no—
169C22⋊C4—2262no—
170C42—1131no—
171C42—1131no—
172C42—1131no—
173C42—2262no—
174C42C22×D11311yescharacteristic
175C23—1131no—
176Q8—24no—
177Q8—24no—
178Q8—4524no—
179Q8—4522no—
180Q8—2264no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—1131no—
184C2×C4—1134no—
185C2×C4—1131no—
186C2×C4—1131no—
187C2×C4—4524no—
188C2×C4—2262no—
189C2×C4—2262no—
190C2×C4—2262no—
191C2×C4—2262no—
192C2×C4D4×D11311yescharacteristic
193C2×C4D4×D11311yescharacteristic
194C2×C4C23×D11311yescharacteristic
195C8—22no—
196C8—2262no—
197C22—1132no—
198C22—2261no—
199C22—2261no—
200C22C2×D4×D11311yescharacteristic
201C4—42no—
202C4—42no—
203C4—1132no—
204C4—4522no—
205C4—4522no—
206C4—2261no—
207C4—2261no—
208C4Q16×D11312yes—
209C4#1681365412yes—
210C4#1681366712yes—
211C2—2262no—
212C2#2029916111yescharacteristic
213C2C2×Q16×D11311yescharacteristic
214C2C2×#1681365411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#494×C113C2
socleC22×C113C22×D4
prime radicalC22×D113C2×D4
hypercenter#494D113
hypocenterC113#3209
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
3. #20298977C2semidirect
4. #20298949C2semidirect
5. #20298948C2semidirect
6. #20298806C2semidirect
9. #494×C113C2semidirect
83. C4×D113Q16semidirect
108. C113#3209semidirect
112. #494D113semidirect

Maximal subgroups

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

subgroupindex
#202991532
C4⋊Q8×D1132
#202989772
#202989492
#202989482
#202988062
#202987522
#202986492
#494×C1132
#3209113