Finite Group Databasebeta

← #487×D113 #28400882

Subgroups — #487×D113 #28400882

Order 14464.

424 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C4⋊Q8×D113C211yesmaximal, characteristic
2C4⋊Q8×D113C211yesmaximal, characteristic
3#20298950C211yesmaximal, characteristic, complemented
4#20298949C211yesmaximal, characteristic, complemented
5#20298948C211yesmaximal, characteristic, complemented
6#20298947C214yesmaximal, complemented
7#103×D113C214yesmaximal
8C4×C8×D113C211yesmaximal, characteristic
9#487×C113C211yesmaximal, characteristic, complemented
10C2×Q8×D113—21no—
11C2×Q8×D113C2212yes—
12C2×C8×D113C2212yes—
13#16813622C2211yescharacteristic
14#16813622C2211yescharacteristic
15#16813621—21no—
16#16813621—21no—
17#16813621—21no—
18#16813621C2212yes—
19#16813620—21no—
20#16813620C2212yes—
21C4⋊C4×D113—21no—
22C4⋊C4×D113—21no—
23C4⋊C4×D113—21no—
24C4⋊C4×D113C2212yes—
25C42×D113C2211yescharacteristic
26#16813547C2214yes—
27#16813546C2214yes—
28#16813545C2214yes—
29C4×#11744751C2211yescharacteristic
30C8×Dic113C2212yes—
31C4⋊Q8×C113C2211yescharacteristic
32C4⋊Q8×C113C2211yescharacteristic
33#103×C113C2214yes—
34C4×C8×C113C2211yescharacteristic
35C2×Dic226—21no—
36C2×Dic226—22no—
37C2×Dic226—22no—
38C2×Dic226C2312yes—
39Q8×D113—28no—
40Q8×D113—44no—
41C2×C4×D113—22no—
42C2×C4×D113—22no—
43C2×C4×D113D411yescharacteristic
44C2×C4×D113D411yescharacteristic
45C2×C4×D113C2311yescharacteristic
46C2×#11744751C2312yes—
47C8×D113—24no—
48C4⋊Dic113—21no—
49C4⋊Dic113—21no—
50C4⋊Dic113—21no—
51C4⋊Dic113C2312yes—
52#14268626—22no—
53#14268626—22no—
54#14268626—22no—
55#14268626—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×D113C2×D411yescharacteristic
68Q8×C113—24no—
69Q8×C113—42no—
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—44no—
81C4×D113—44no—
82C4×D113SD1614yes—
83C4×D113Q1614yes—
84C4×D113#4114yes—
85Dic226—24no—
86Dic226—42no—
87Dic226—44no—
88Dic226—44no—
89C8×C113—22no—
90#11744751—22no—
91C22×C113C22×D411yescharacteristic
92C2×D113#12412yes—
93C2×D113C2×SD1612yes—
94C2×D113C2×Q1612yes—
95C4×C113—42no—
96C4×C113—42no—
97C4×C113C2×SD1612yes—
98C4×C113C2×Q1612yes—
99C4×C113C2×#4112yes—
100Dic113—42no—
101Dic113—42no—
102Dic113#12412yes—
103Dic113C2×SD1612yes—
104Dic113C2×Q1612yes—
105C2×C113C2×#12411yescharacteristic
106C2×C113C22×SD1611yescharacteristic
107C2×C113C22×Q1611yescharacteristic
108D113#48714yesdirect product factor
109C2×#487—1131nomaximal, Sylow
110C113C2×#48711yescharacteristic, complemented, Sylow
111C2×C4⋊Q8—1131no—
112C2×C4⋊Q8—1131no—
113#487—1131no—
114#487—1131no—
115#487—1134no—
116#487—1131no—
117#487D11311yescharacteristic, direct product factor
118C2×#103—1134no—
119C2×C4×C8—1131no—
120C22×Q8—1132no—
121C22×Q8—2261no—
122C22×C8—1132no—
123C4⋊Q8—1132no—
124C4⋊Q8—1132no—
125C4⋊Q8—1131no—
126C4⋊Q8—1131no—
127C4⋊Q8—2261no—
128C4⋊Q8—2261no—
129C4⋊Q8—2261no—
130C4⋊Q8—2261no—
131C4⋊Q8C2×D11311yescharacteristic
132C4⋊Q8C2×D11311yescharacteristic
133C2×C4⋊C4—1132no—
134C2×C4⋊C4—2261no—
135C2×C4⋊C4—2261no—
136C2×C4⋊C4—2261no—
137C2×C42—1131no—
138#103—1134no—
139#103—1134no—
140#103—1134no—
141#103C2×D11314yes—
142C4×C8—1132no—
143C4×C8—1131no—
144C4×C8C2×D11311yescharacteristic
145C2×Q8—21no—
146C2×Q8—1132no—
147C2×Q8—4524no—
148C2×Q8—2262no—
149C2×Q8—2262no—
150C2×Q8—2268no—
151C2×Q8—2261no—
152C2×Q8C22×D11312yes—
153C22×C4—1131no—
154C22×C4—1131no—
155C22×C4—1131no—
156C22×C4—2262no—
157C22×C4—2262no—
158C2×C8—1132no—
159C2×C8—2264no—
160C2×C8C22×D11312yes—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—1132no—
165C4⋊C4—2262no—
166C4⋊C4—2262no—
167C4⋊C4—2262no—
168C4⋊C4—2262no—
169C4⋊C4—2261no—
170C4⋊C4—2261no—
171C4⋊C4—2261no—
172C4⋊C4C22×D11312yes—
173C42—1131no—
174C42—1131no—
175C42—1131no—
176C42C22×D11311yescharacteristic
177C23—1131no—
178Q8—24no—
179Q8—42no—
180Q8—4524no—
181Q8—4524no—
182Q8—4522no—
183Q8—2264no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—1131no—
187C2×C4—1131no—
188C2×C4—1131no—
189C2×C4—1134no—
190C2×C4—1134no—
191C2×C4—1134no—
192C2×C4—4524no—
193C2×C4—4524no—
194C2×C4—2262no—
195C2×C4—2262no—
196C2×C4D4×D11311yescharacteristic
197C2×C4D4×D11311yescharacteristic
198C2×C4C23×D11311yescharacteristic
199C8—22no—
200C8—2262no—
201C22—1132no—
202C22—1132no—
203C22—1132no—
204C22C2×D4×D11311yescharacteristic
205C4—42no—
206C4—42no—
207C4—1132no—
208C4—1132no—
209C4—1132no—
210C4—4522no—
211C4—4522no—
212C4SD16×D11312yes—
213C4Q16×D11312yes—
214C4#41×D11312yes—
215C2—1134no—
216C2#124×D11311yescharacteristic
217C2C2×SD16×D11311yescharacteristic
218C2C2×Q16×D11311yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#487×C113C2
socleC22×C113C22×D4
prime radicalC22×D113C2×D4
hypercenter#487D113
hypocenterC113C2×#487
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
3. #20298950C2semidirect
4. #20298949C2semidirect
5. #20298948C2semidirect
6. #20298947C2semidirect
9. #487×C113C2semidirect
108. D113#487direct (N × H)
110. C113C2×#487semidirect
117. #487D113direct (N × H)

Maximal subgroups

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

subgroupindex
C4⋊Q8×D1132
#202989502
#202989492
#202989482
#202989472
#103×D1132
C4×C8×D1132
#487×C1132
C2×#487113