Finite Group Databasebeta

← #20256278

Subgroups — #20256278

Order 6016.

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

normal subgroups only

This group has 324 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#15689852C211yesmaximal, characteristic
2#15689848C211yesmaximal, characteristic
3#15689526C211yesmaximal, characteristic
4#15689523C212yesmaximal
5#15689433C212yesmaximal
6#15689428C212yesmaximal
7#15689409C211yesmaximal, characteristic
8#15689247C211yesmaximal, characteristic
9C4×#10625337C211yesmaximal, characteristic
10#15689215C212yesmaximal
11C47×#475C211yesmaximal, characteristic
12C2×#10625337C2211yescharacteristic
13#13094024—21no—
14#13094024C2211yescharacteristic
15#13094022—21no—
16#13094015—22no—
17#13094015C2212yes—
18#13094015C2212yes—
19#13094014—22no—
20Q8×Dic47—21no—
21Q8×Dic47C2212yes—
22C4×Dic94—21no—
23C4×Dic94C2211yescharacteristic
24C4×Dic94C2211yescharacteristic
25#13093989C2212yes—
26#13093957C2211yescharacteristic
27#13093957C2212yes—
28#13093957C2212yes—
29#13093956C2212yes—
30Dic47⋊C8C2212yes—
31#13093949C2212yes—
32#13093948C2211yescharacteristic
33#13093947C2211yescharacteristic
34C4×C47⋊C8C2211yescharacteristic
35C8×Dic47C2212yes—
36C4⋊Q8×C47C2211yescharacteristic
37C4×Q8×C47C2211yescharacteristic
38#106×C47C2212yes—
39C4⋊C8×C47C2211yescharacteristic
40#103×C47C2212yes—
41C2×Q8×C47—21no—
42C2×Q8×C47C2311yescharacteristic
43C2×Dic94—21no—
44C2×Dic94D411yescharacteristic
45C2×Dic94C2311yescharacteristic
46C2×C8×C47C2312yes—
47C4⋊C4×C47—21no—
48C4⋊C4×C47—21no—
49C4⋊C4×C47C2312yes—
50C4⋊C4×C47C2311yescharacteristic
51C42×C47—21no—
52C42×C47C2311yescharacteristic
53#10625337Q814yescomplemented
54C4⋊Dic47—21no—
55C4⋊Dic47—22no—
56C4⋊Dic47—22no—
57C4⋊Dic47—22no—
58C4⋊Dic47D411yescharacteristic
59C4⋊Dic47C2311yescharacteristic
60C4⋊Dic47C2312yes—
61Dic47⋊C4—21no—
62Dic47⋊C4—22no—
63Dic47⋊C4—22no—
64Dic47⋊C4—22no—
65Dic47⋊C4D412yes—
66C4×Dic47—21no—
67C4×Dic47—22no—
68C4×Dic47—22no—
69C4×Dic47C2312yes—
70C2×C47⋊C8C2311yescharacteristic
71C2×C47⋊C8C2311yescharacteristic
72Q8×C47—21no—
73Q8×C47—42no—
74Q8×C47C2×Q812yes—
75C2×C4×C47—21no—
76C2×C4×C47—22no—
77C2×C4×C47—21no—
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47C2411yescharacteristic
81C2×Dic47—21no—
82C2×Dic47—21no—
83C2×Dic47—22no—
84C2×Dic47C2×D412yes—
85C2×Dic47C2×D412yes—
86Dic94—22no—
87Dic94—21no—
88Dic94—42no—
89Dic94C2×Q812yes—
90C8×C47—22no—
91C47⋊C8—21no—
92C47⋊C8C2×Q812yes—
93C22×C47C22×D411yescharacteristic
94C4×C47—22no—
95C4×C47—21no—
96C4×C47—42no—
97C4×C47—41no—
98C4×C47#13512yes—
99C4×C47C22×Q811yescharacteristic
100C4×C472−1+411yescharacteristic
101Dic47—22no—
102Dic47—22no—
103Dic47—22no—
104Dic47—42no—
105Dic47—41no—
106#3383—471nomaximal, Sylow
107C2×C47D4×Q811yescharacteristic
108C2×C47C2×#13511yescharacteristic
109C2×C47#57811yescharacteristic
110#557—471no—
111#557—471no—
112#500—471no—
113#499—472no—
114#479—472no—
115#479—472no—
116#475—471no—
117#475D4711yescharacteristic
118C8×Q8—471no—
119C4×Q16—471no—
120C4×Q16—472no—
121C47#338311yescharacteristic, complemented, Sylow
122C2×Q16—471no—
123C4⋊Q8—471no—
124C4⋊Q8—941no—
125C4⋊Q8—941no—
126C4⋊Q8C2×D4711yescharacteristic
127#125—472no—
128#125—472no—
129#125—942no—
130#125—942no—
131C4×Q8—471no—
132C4×Q8—472no—
133C4×Q8—472no—
134C4×Q8—471no—
135C4×Q8—941no—
136C4×Q8—941no—
137C4×Q8C2×D4711yescharacteristic
138#107—471no—
139#107—472no—
140#107—472no—
141#106—472no—
142#106C2×D4712yes—
143C4⋊C8—472no—
144C4⋊C8C2×D4711yescharacteristic
145#103—471no—
146#103—472no—
147#103—471no—
148#103C2×D4712yes—
149C4×C8—472no—
150C4×C8—471no—
151C2×Q8—21no—
152C2×Q8—471no—
153C2×Q8—471no—
154C2×Q8—941no—
155C2×Q8C22×D4711yescharacteristic
156Q16—474no—
157C2×C8—471no—
158C2×C8—471no—
159C2×C8C22×D4712yes—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—472no—
163C4⋊C4—471no—
164C4⋊C4—471no—
165C4⋊C4—472no—
166C4⋊C4—942no—
167C4⋊C4—942no—
168C4⋊C4—942no—
169C4⋊C4—942no—
170C4⋊C4—942no—
171C4⋊C4—942no—
172C4⋊C4—941no—
173C4⋊C4—941no—
174C4⋊C4C22×D4711yescharacteristic
175C4⋊C4C22×D4712yes—
176C42—21no—
177C42—472no—
178C42—942no—
179C42—942no—
180C42—941no—
181C42C22×D4711yescharacteristic
182Q8—21no—
183Q8—42no—
184Q8—472no—
185Q8—942no—
186Q8—941no—
187Q8—1882no—
188Q8Q8×D4712yes—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—472no—
193C2×C4—472no—
194C2×C4—941no—
195C2×C4—941no—
196C2×C4—942no—
197C2×C4D4×D4711yescharacteristic
198C2×C4D4×D4711yescharacteristic
199C2×C4C23×D4711yescharacteristic
200C8—22no—
201C8—472no—
202C8—941no—
203C22C2×D4×D4711yescharacteristic
204C4—22no—
205C4—21no—
206C4—42no—
207C4—41no—
208C4—942no—
209C4—942no—
210C4—942no—
211C4—1882no—
212C4—1881no—
213C4#1309404512yes—
214C4C2×Q8×D4711yescharacteristic
215C4#1309407111yescharacteristic
216C2#1568978611yescharacteristic
217C2C2×#1309404511yescharacteristic
218C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#475C2
socleC22×C47C22×D4
hypercenter#475D47
hypocenterC47#3383
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
53. #10625337Q8semidirect
121. C47#3383semidirect