Finite Group Databasebeta

← #28400969

Subgroups — #28400969

Order 14464.

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

normal subgroups only

This group has 424 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#20299149C211yesmaximal, characteristic
2C4⋊Q8×D113C211yesmaximal, characteristic, complemented
3#20298959C214yesmaximal, complemented
4#20298948C211yesmaximal, characteristic, complemented
5#20298946C211yesmaximal, characteristic, complemented
6#20298945C211yesmaximal, characteristic, complemented
7#20298598C214yesmaximal, complemented
8C4×#14268630C211yesmaximal, characteristic, complemented
9#487×C113C211yesmaximal, characteristic, complemented
10C2×#14268648C2212yes—
11C2×Q8×D113—21no—
12C2×#14268630C2212yes—
13#16813622C2211yescharacteristic
14#16813621—21no—
15#16813621C2212yes—
16#16813620—21no—
17#16813619C2211yescharacteristic
18#16813611C2212yes—
19#16813597—21no—
20#16813597—21no—
21#16813584—21no—
22#16813584—21no—
23C4⋊C4×D113—21no—
24C4⋊C4×D113C2212yes—
25C42×D113C2211yescharacteristic
26#16813546C2214yes—
27#16813544C2214yes—
28#16813542C2214yes—
29#16813532C2212yes—
30C4×#11744751C2211yescharacteristic
31C4⋊Q8×C113C2211yescharacteristic
32C4⋊Q8×C113C2211yescharacteristic
33#103×C113C2214yes—
34C4×C8×C113C2211yescharacteristic
35#14268648—28no—
36C2×Dic226—21no—
37C2×Dic226—22no—
38Q8×D113—44no—
39C2×D452—22no—
40C2×D452—21no—
41C2×D452—21no—
42C2×D452C2312yes—
43C2×C4×D113—22no—
44C2×C4×D113—22no—
45C2×C4×D113D411yescharacteristic
46C2×C4×D113D411yescharacteristic
47C2×C4×D113C2311yescharacteristic
48#14268630—24no—
49C2×#11744751C2312yes—
50C4⋊Dic113—21no—
51C4⋊Dic113C2312yes—
52#14268626—22no—
53#14268626—22no—
54#14268624—22no—
55#14268624—22no—
56C4×Dic113D411yescharacteristic
57C4×Dic113D411yescharacteristic
58C4×Dic113C2311yescharacteristic
59C2×Q8×C113—21no—
60C2×Q8×C113C2312yes—
61C2×C8×C113C2312yes—
62C4⋊C4×C113—21no—
63C4⋊C4×C113—21no—
64C4⋊C4×C113—21no—
65C4⋊C4×C113C2312yes—
66C42×C113C2311yescharacteristic
67C22×D113—22no—
68C22×D113C2×D411yescharacteristic
69Q8×C113—24no—
70Q8×C113—42no—
71C2×C4×C113—22no—
72C2×C4×C113—22no—
73C2×C4×C113C2×D411yescharacteristic
74C2×C4×C113C2×D411yescharacteristic
75C2×C4×C113C2411yescharacteristic
76C2×Dic113—22no—
77C2×Dic113C2×D411yescharacteristic
78C2×Dic113C2×D411yescharacteristic
79C2×Dic113C2×D411yescharacteristic
80D452—24no—
81D452—44no—
82D452—42no—
83D452—42no—
84C4×D113—22no—
85C4×D113—22no—
86C4×D113—44no—
87C4×D113—44no—
88C4×D113#4114yes—
89Dic226—44no—
90Dic226—42no—
91C8×C113—22no—
92#11744751—22no—
93C22×C113C22×D411yescharacteristic
94C2×D113—21no—
95C2×D113—21no—
96C2×D113—42no—
97C2×D113—42no—
98C2×D113—42no—
99C2×D113#12412yes—
100C4×C113—42no—
101C4×C113—42no—
102C4×C113AGL(1,ℤ/8)12yes—
103C4×C113#13712yes—
104C4×C113C2×#4112yes—
105Dic113—21no—
106Dic113—21no—
107Dic113—42no—
108Dic113#12412yes—
109C2×C113C2×#12411yescharacteristic
110C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
111C2×C113C2×#13711yescharacteristic
112D113—22no—
113D113—82no—
114#3141—1131nomaximal, Sylow
115C113#314111yescharacteristic, complemented, Sylow
116#532—1131no—
117C2×C4⋊Q8—1131no—
118#489—1134no—
119#487—1131no—
120#487D11311yescharacteristic, complemented
121#486—1131no—
122#486—1131no—
123#417—1134no—
124C4×M16—1131no—
125C2×#41—1132no—
126C22×Q8—2261no—
127C2×M16—1132no—
128C4⋊Q8—1132no—
129C4⋊Q8—1131no—
130C4⋊Q8—2261no—
131C4⋊Q8—2261no—
132C4⋊Q8C2×D11311yescharacteristic
133C4⋊Q8C2×D11311yescharacteristic
134#127—1131no—
135#124—1132no—
136#121—2261no—
137#121—2261no—
138C4×D4—2261no—
139C4×D4—2261no—
140C2×C4⋊C4—1132no—
141C2×C4⋊C4—2261no—
142C2×C42—1131no—
143#103—1134no—
144#103C2×D11314yes—
145#102—1134no—
146#102—1134no—
147#97—1132no—
148C4×C8—1131no—
149C4×C8C2×D11311yescharacteristic
150#41—2268no—
151C2×Q8—21no—
152C2×Q8—4524no—
153C2×Q8—2262no—
154C2×Q8—2261no—
155C2×Q8C22×D11312yes—
156C2×D4—1132no—
157C2×D4—2262no—
158C2×D4—2261no—
159C2×D4—2261no—
160C22×C4—1131no—
161C22×C4—1131no—
162C22×C4—1131no—
163C22×C4—2262no—
164C22×C4—2262no—
165M16—2264no—
166C2×C8—1132no—
167C2×C8C22×D11312yes—
168C4⋊C4—21no—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—1132no—
172C4⋊C4—2262no—
173C4⋊C4—2262no—
174C4⋊C4—2261no—
175C4⋊C4C22×D11312yes—
176C22⋊C4—2262no—
177C22⋊C4—2262no—
178C42—1131no—
179C42—1131no—
180C42—1131no—
181C42C22×D11311yescharacteristic
182C23—1131no—
183C23—2262no—
184Q8—24no—
185Q8—42no—
186Q8—4524no—
187Q8—4522no—
188D4—4524no—
189D4—4522no—
190D4—4522no—
191D4—2264no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—1131no—
195C2×C4—1134no—
196C2×C4—1131no—
197C2×C4—1131no—
198C2×C4—4524no—
199C2×C4—4524no—
200C2×C4—2262no—
201C2×C4—2262no—
202C2×C4—2262no—
203C2×C4D4×D11311yescharacteristic
204C2×C4D4×D11311yescharacteristic
205C2×C4C23×D11311yescharacteristic
206C8—22no—
207C8—2262no—
208C22—1132no—
209C22—4522no—
210C22—4522no—
211C22—4522no—
212C22—2261no—
213C22—2261no—
214C22C2×D4×D11311yescharacteristic
215C4—42no—
216C4—42no—
217C4—1132no—
218C4—4522no—
219C4—2261no—
220C4—2261no—
221C4#1681364912yes—
222C4#1681365412yes—
223C4#41×D11312yes—
224C2—9042no—
225C2—2262no—
226C2#124×D11311yescharacteristic
227C2C2×#1681364911yescharacteristic
228C2C2×#1681365411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#487×C113C2
socleC22×C113C22×D4
prime radical#20299149C2
hypercenter#487D113
hypocenterC113#3141
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. C4⋊Q8×D113C2semidirect
3. #20298959C2semidirect
4. #20298948C2semidirect
5. #20298946C2semidirect
6. #20298945C2semidirect
7. #20298598C2semidirect
8. C4×#14268630C2semidirect
9. #487×C113C2semidirect
115. C113#3141semidirect
120. #487D113semidirect

Maximal subgroups

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

subgroupindex
#202991492
C4⋊Q8×D1132
#202989592
#202989482
#202989462
#202989452
#202985982
C4×#142686302
#487×C1132
#3141113