Finite Group Databasebeta

← #20246554

Subgroups — #20246554

Order 6016.

464 conjugacy classes of subgroups; only the 213 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 213 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#15689030C212yesmaximal, complemented
2#15689022C212yesmaximal, complemented
3#15689016C212yesmaximal
4#15689016C212yesmaximal
5#15689009C212yesmaximal, complemented
6#15689009C212yesmaximal, complemented
7#15688986C211yesmaximal, characteristic
8#15688983C211yesmaximal, characteristic
9C2×C22⋊Q8×C47C211yesmaximal, characteristic
10C2×C4⋊Dic47C2212yes—
11C2×C4⋊Dic47C2212yes—
12C2×C4⋊Dic47C2212yes—
13C2×C22⋊Dic47C2211yescharacteristic
14C2×C22⋊Dic47C2211yescharacteristic
15C2×C22⋊Dic47C2212yes—
16C2×C4×Dic47C2212yes—
17C2×C4×Dic47C2212yes—
18C47⋊#95C2212yes—
19C47⋊#95C2211yescharacteristic
20C47⋊#95C2212yes—
21C47⋊#95C2211yescharacteristic
22C47⋊#95C2212yes—
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2212yes—
26C22×Q8×C47C2211yescharacteristic
27C23×C4×C47C2211yescharacteristic
28C22⋊Q8×C47C418yescomplemented
29C2×C4⋊C4×C47C2211yescharacteristic
30C2×C4⋊C4×C47C2212yes—
31C2×C22⋊C4×C47C2212yes—
32C24×C47C2311yescharacteristic
33C2×Q8×C47—42no—
34C2×Q8×C47C2×C414yes—
35C22×C4×C47—42no—
36C22×C4×C47C2×C414yes—
37C22×C4×C47C2312yes—
38C22×C4×C47C2312yes—
39C22×C4×C47C2311yescharacteristic
40C22×C4×C47C2311yescharacteristic
41C22×Dic47C2312yes—
42C22×Dic47C2312yes—
43C22×Dic47C2312yes—
44C22×Dic47C2312yes—
45C4⋊C4×C47C2×C414yes—
46C4⋊C4×C47C2×C418yes—
47C22⋊C4×C47C2×C418yes—
48C22⋊Dic47—41no—
49C22⋊Dic47—42no—
50C22⋊Dic47—41no—
51C4⋊Dic47—42no—
52C4⋊Dic47—42no—
53C4⋊Dic47—42no—
54C4×Dic47—42no—
55C4×Dic47—42no—
56C23×C47—21no—
57C23×C47—22no—
58C23×C47—21no—
59C23×C47—22no—
60C23×C47C22×C412yes—
61C23×C47C2411yescharacteristic
62Q8×C47—44no—
63C2×C4×C47—22no—
64C2×C4×C47—22no—
65C2×C4×C47—22no—
66C2×C4×C47—22no—
67C2×C4×C47—22no—
68C2×C4×C47—22no—
69C2×C4×C47—44no—
70C2×C4×C47C22×C414yes—
71C2×C4×C47C22×C414yes—
72C2×C4×C47C22×C412yes—
73C2×C4×C47C22×C412yes—
74C2×Dic47—22no—
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47—22no—
78C2×Dic47—22no—
79C2×Dic47—22no—
80C2×Dic47—22no—
81C2×Dic47—22no—
82C2×Dic47—22no—
83C2×Dic47—22no—
84C2×Dic47—22no—
85C2×Dic47—22no—
86C22×C47—22no—
87C22×C47—22no—
88C22×C47—22no—
89C22×C47—42no—
90C22×C47—42no—
91C22×C47C23×C411yescharacteristic
92C22×C47H(5,𝔽2)12yes—
93C22×C47H(5,𝔽2)11yescharacteristic
94C22×C472−1+411yescharacteristic
95C22×C472−1+412yes—
96C4×C47—22no—
97C4×C47—22no—
98C4×C47—24no—
99C4×C47—24no—
100Dic47—42no—
101Dic47—42no—
102Dic47—42no—
103Dic47—42no—
104#2378—471nomaximal, Sylow
105C2×C47—42no—
106C2×C47#51811yescharacteristic
107C2×C47#51911yescharacteristic
108C2×C47#52011yescharacteristic
109C2×C47#56212yes—
110C2×C47#56312yes—
111C2×C22⋊Q8D4711yescharacteristic
112#391—472no—
113#389—472no—
114#388—472no—
115#388—472no—
116#387—472no—
117#387—472no—
118#381—471no—
119#380—471no—
120C47#237811yescharacteristic, complemented, Sylow
121C22×Q8C2×D4711yescharacteristic
122C23×C4C2×D4711yescharacteristic
123C22⋊Q8Dic4718yescomplemented
124C2×C4⋊C4—472no—
125C2×C4⋊C4—472no—
126C2×C4⋊C4—472no—
127C2×C4⋊C4C2×D4711yescharacteristic
128C2×C4⋊C4C2×D4712yes—
129C2×C22⋊C4—471no—
130C2×C22⋊C4—471no—
131C2×C22⋊C4—472no—
132C2×C22⋊C4C2×D4712yes—
133C2×C42—472no—
134C2×C42—472no—
135#95—472no—
136#95—471no—
137#95—472no—
138#95—471no—
139#95—472no—
140#95—472no—
141#95—472no—
142#95—472no—
143C24C22×D4711yescharacteristic
144C2×Q8—42no—
145C2×Q8C2×Dic4714yes—
146C22×C4—42no—
147C22×C4—472no—
148C22×C4—472no—
149C22×C4—472no—
150C22×C4—472no—
151C22×C4C2×Dic4714yes—
152C22×C4C22×D4711yescharacteristic
153C22×C4C22×D4712yes—
154C22×C4C22×D4712yes—
155C22×C4C22×D4711yescharacteristic
156C4⋊C4—1882no—
157C4⋊C4—1882no—
158C4⋊C4—1882no—
159C4⋊C4C2×Dic4714yes—
160C4⋊C4C2×Dic4718yes—
161C22⋊C4—1882no—
162C22⋊C4—1881no—
163C22⋊C4—1881no—
164C22⋊C4C2×Dic4718yes—
165C42—1882no—
166C42—1882no—
167C23—22no—
168C23—21no—
169C23—21no—
170C23—22no—
171C23C22×Dic4712yes—
172C23C23×D4711yescharacteristic
173Q8—44no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—44no—
181C2×C4—942no—
182C2×C4—942no—
183C2×C4—942no—
184C2×C4—942no—
185C2×C4—942no—
186C2×C4—942no—
187C2×C4—942no—
188C2×C4—942no—
189C2×C4—942no—
190C2×C4—942no—
191C2×C4—942no—
192C2×C4—942no—
193C2×C4C22×Dic4714yes—
194C2×C4C22×Dic4714yes—
195C2×C4C22×Dic4712yes—
196C2×C4C22×Dic4712yes—
197C22—22no—
198C22—22no—
199C22—22no—
200C22—42no—
201C22—42no—
202C22C23×Dic4711yescharacteristic
203C22#1309406912yes—
204C22#1309407011yescharacteristic
205C22#1309407111yescharacteristic
206C22#1309407212yes—
207C4—22no—
208C4—22no—
209C4—24no—
210C4—24no—
211C4—1882no—
212C4—1882no—
213C4—1882no—
214C4—1882no—
215C2—42no—
216C2#1568959811yescharacteristic
217C2#1568960111yescharacteristic
218C2#1568960611yescharacteristic
219C2#1568986912yes—
220C2#1568987412yes—
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC2×C22⋊Q8×C47C2
socleC23×C47C24
hypercenterC2×C22⋊Q8D47
hypocenterC47#2378
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #15689030C2semidirect
2. #15689022C2semidirect
5. #15689009C2semidirect
6. #15689009C2semidirect
28. C22⋊Q8×C47C4semidirect
120. C47#2378semidirect
123. C22⋊Q8Dic47semidirect