Finite Group Databasebeta

← #20256275

Subgroups — #20256275

Order 6016.

324 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 133 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#15689851C211yesmaximal, characteristic
2#15689526C211yesmaximal, characteristic
3#15689522C212yesmaximal
4#15689430C212yesmaximal
5#15689427C212yesmaximal
6#15689408C211yesmaximal, characteristic
7#15689405C211yesmaximal, characteristic
8Q8×C47⋊C8C211yesmaximal, characteristic
9C4×#10625337C211yesmaximal, characteristic
10C4×#10625337C212yesmaximal
11C47×#557C211yesmaximal, characteristic
12C2×#10625337C2211yescharacteristic
13#13094024C2211yescharacteristic
14#13094022—21no—
15#13094016C2212yes—
16#13094014—22no—
17C4×Dic94C2211yescharacteristic
18C4×Dic94C2212yes—
19#13093989—21no—
20#13093957C2211yescharacteristic
21#13093957C2212yes—
22#13093957C2212yes—
23#13093955C2212yes—
24#13093955C2212yes—
25C4⋊(C47⋊C8)C2211yescharacteristic
26C4⋊(C47⋊C8)C2212yes—
27#13093948C2212yes—
28#13093948C2211yescharacteristic
29#13093947C2212yes—
30#13093947C2211yescharacteristic
31C4×C47⋊C8C2212yes—
32C4×C47⋊C8C2211yescharacteristic
33C4⋊Q8×C47—21no—
34C4⋊Q8×C47C2211yescharacteristic
35#125×C47—22no—
36#125×C47C2212yes—
37C4×Q8×C47—21no—
38C4×Q8×C47C2211yescharacteristic
39C4×Q8×C47C2212yes—
40C4×Q8×C47C2211yescharacteristic
41C2×Q8×C47—21no—
42C2×Q8×C47D411yescharacteristic
43C2×Q8×C47C2311yescharacteristic
44C2×Dic94—21no—
45C2×Dic94C2311yescharacteristic
46C4⋊C4×C47—22no—
47C4⋊C4×C47—21no—
48C4⋊C4×C47—22no—
49C4⋊C4×C47—21no—
50C4⋊C4×C47—22no—
51C4⋊C4×C47D411yescharacteristic
52C4⋊C4×C47D412yes—
53C4⋊C4×C47C2311yescharacteristic
54C4⋊C4×C47C2312yes—
55C42×C47—22no—
56C42×C47—21no—
57C42×C47C2312yes—
58C42×C47C2311yescharacteristic
59#10625337Q814yescomplemented
60C4⋊Dic47—21no—
61C4⋊Dic47C2311yescharacteristic
62C4⋊Dic47C2312yes—
63Dic47⋊C4—22no—
64Dic47⋊C4—21no—
65Dic47⋊C4—22no—
66Dic47⋊C4—22no—
67C4×Dic47—22no—
68C4×Dic47—21no—
69C2×C47⋊C8C2312yes—
70C2×C47⋊C8C2311yescharacteristic
71C2×C47⋊C8C2311yescharacteristic
72Q8×C47—22no—
73Q8×C47—21no—
74Q8×C47—42no—
75Q8×C47C2×Q812yes—
76C2×C4×C47—21no—
77C2×C4×C47—21no—
78C2×C4×C47—22no—
79C2×C4×C47C2×D412yes—
80C2×C4×C47C2×D412yes—
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47C2×D411yescharacteristic
83C2×C4×C47C2411yescharacteristic
84C2×Dic47—21no—
85C2×Dic47—21no—
86C2×Dic47—22no—
87Dic94—21no—
88Dic94—42no—
89Dic94C2×Q812yes—
90C47⋊C8—22no—
91C47⋊C8—21no—
92C47⋊C8C2×Q812yes—
93C22×C47C22×D411yescharacteristic
94C4×C47—22no—
95C4×C47—22no—
96C4×C47—22no—
97C4×C47—21no—
98C4×C47—42no—
99C4×C47—41no—
100C4×C47#13512yes—
101C4×C47C22×Q811yescharacteristic
102C4×C472−1+411yescharacteristic
103Dic47—22no—
104Dic47—42no—
105Dic47—41no—
106#3383—471nomaximal, Sylow
107C2×C47D4×Q811yescharacteristic
108C2×C47C2×#13511yescharacteristic
109C2×C47#57811yescharacteristic
110#557—471no—
111#557D4711yescharacteristic
112#500—471no—
113#499—472no—
114#479—472no—
115#479—472no—
116#475—471no—
117#475—471no—
118C8×Q8—471no—
119C4×Q16—472no—
120C4×Q16—471no—
121C47#338311yescharacteristic, complemented, Sylow
122C2×Q16—471no—
123C4⋊Q8—21no—
124C4⋊Q8—471no—
125C4⋊Q8—941no—
126C4⋊Q8C2×D4711yescharacteristic
127#125—22no—
128#125—472no—
129#125—942no—
130#125C2×D4712yes—
131C4×Q8—21no—
132C4×Q8—471no—
133C4×Q8—472no—
134C4×Q8—941no—
135C4×Q8C2×D4711yescharacteristic
136C4×Q8C2×D4712yes—
137C4×Q8C2×D4711yescharacteristic
138#107—471no—
139#107—472no—
140#107—472no—
141#106—472no—
142#106—472no—
143C4⋊C8—471no—
144C4⋊C8—472no—
145#103—472no—
146#103—471no—
147#103—472no—
148#103—471no—
149C4×C8—472no—
150C4×C8—471no—
151C2×Q8—21no—
152C2×Q8—471no—
153C2×Q8—941no—
154C2×Q8C22⋊D4711yescharacteristic
155C2×Q8C22×D4711yescharacteristic
156Q16—474no—
157C2×C8—471no—
158C2×C8—472no—
159C2×C8—471no—
160C4⋊C4—22no—
161C4⋊C4—21no—
162C4⋊C4—22no—
163C4⋊C4—21no—
164C4⋊C4—22no—
165C4⋊C4—471no—
166C4⋊C4—472no—
167C4⋊C4—941no—
168C4⋊C4—942no—
169C4⋊C4—942no—
170C4⋊C4—942no—
171C4⋊C4—941no—
172C4⋊C4C22⋊D4711yescharacteristic
173C4⋊C4C22⋊D4712yes—
174C4⋊C4C22×D4711yescharacteristic
175C4⋊C4C22×D4712yes—
176C42—22no—
177C42—21no—
178C42—942no—
179C42—941no—
180C42C22×D4712yes—
181C42C22×D4711yescharacteristic
182Q8—22no—
183Q8—21no—
184Q8—42no—
185Q8—472no—
186Q8—941no—
187Q8—1882no—
188Q8Q8×D4712yes—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—941no—
193C2×C4—941no—
194C2×C4—942no—
195C2×C4C2×C22⋊D4712yes—
196C2×C4C2×C22⋊D4711yescharacteristic
197C2×C4C2×C22⋊D4712yes—
198C2×C4C2×C22⋊D4711yescharacteristic
199C2×C4C23×D4711yescharacteristic
200C8—472no—
201C8—942no—
202C8—941no—
203C22C22×C22⋊D4711yescharacteristic
204C4—22no—
205C4—22no—
206C4—22no—
207C4—21no—
208C4—42no—
209C4—41no—
210C4—942no—
211C4—1882no—
212C4—1881no—
213C4#1309404412yes—
214C4C2×Q8×D4711yescharacteristic
215C4#1309407211yescharacteristic
216C2Q8×C22⋊D4711yescharacteristic
217C2C2×#1309404411yescharacteristic
218C2#1568993811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#557C2
socleC22×C47C22×D4
hypercenter#557D47
hypocenterC47#3383
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #557

Complements

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

NH ≅ G/Ntype
59. #10625337Q8semidirect
121. C47#3383semidirect