Finite Group Databasebeta

← #20242428

Subgroups — #20242428

Order 6016.

202 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 51 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#15689752C211yesmaximal, characteristic
2#15689458C211yesmaximal, characteristic
3#15689061C211yesmaximal, characteristic
4#15688861C211yesmaximal, characteristic
5#15688860C211yesmaximal, characteristic
6#15688848C211yesmaximal, characteristic
7C47×#484C211yesmaximal, characteristic
8#13094023—21no—
9#13094022—21no—
10#13094014—21no—
11#13094014—21no—
12#13094003C2211yescharacteristic
13#13094001—21no—
14#13093980—21no—
15C2×Dic47⋊C4C2211yescharacteristic
16#13093957—21no—
17#13093947—21no—
18C22⋊(C47⋊C8)C2211yescharacteristic
19C47⋊#95—21no—
20C47⋊#95—21no—
21C47⋊#95C2211yescharacteristic
22C22⋊Q8×C47C2211yescharacteristic
23C2×C4⋊C4×C47C2211yescharacteristic
24#107×C47—21no—
25#103×C47—21no—
26C22⋊C8×C47C2211yescharacteristic
27C2×Q8×C47D411yescharacteristic
28C22×C4×C47—21no—
29C22×C4×C47C2311yescharacteristic
30C22×Dic47—21no—
31C22×Dic47D411yescharacteristic
32C22×Dic47D411yescharacteristic
33C2×Dic94—21no—
34C2×Dic94D411yescharacteristic
35C2×C8×C47—21no—
36C4⋊C4×C47—21no—
37C4⋊C4×C47—21no—
38C4⋊C4×C47—21no—
39C4⋊C4×C47D411yescharacteristic
40C22⋊C4×C47—21no—
41C22⋊Dic47—21no—
42C4⋊Dic47—21no—
43C4⋊Dic47D411yescharacteristic
44Dic47⋊C4—21no—
45Dic47⋊C4—21no—
46Dic47⋊C4—21no—
47Dic47⋊C4—21no—
48Dic47⋊C4—21no—
49Dic47⋊C4—21no—
50Dic47⋊C4—21no—
51C4×Dic47—21no—
52C4×Dic47—21no—
53C2×C47⋊C8—21no—
54C23×C47C2×D411yescharacteristic
55Q8×C47—41no—
56C2×C4×C47—21no—
57C2×C4×C47—21no—
58C2×C4×C47—41no—
59C2×C4×C47—42no—
60C2×C4×C47—41no—
61C2×C4×C47C2×D411yescharacteristic
62C2×C4×C47C2×D411yescharacteristic
63C2×Dic47—21no—
64C2×Dic47—21no—
65C2×Dic47—21no—
66C2×Dic47—21no—
67C2×Dic47—21no—
68C2×Dic47—41no—
69C2×Dic47—41no—
70C2×Dic47—41no—
71C2×Dic47—41no—
72C2×Dic47Q1612yes—
73Dic94—41no—
74Dic94—81no—
75C8×C47—41no—
76C47⋊C8—41no—
77C22×C47—21no—
78C22×C47—21no—
79C22×C47#12011yescharacteristic
80C22×C47C2×Q1611yescharacteristic
81C22×C47#13711yescharacteristic
82C4×C47—21no—
83C4×C47—21no—
84C4×C47—41no—
85C4×C47—41no—
86C4×C47—81no—
87Dic47—22no—
88Dic47—41no—
89Dic47—41no—
90Dic47—41no—
91Dic47—81no—
92#1617—471nomaximal, Sylow
93C2×C47—21no—
94C2×C47—21no—
95C2×C47#45111yescharacteristic
96C2×C47#45411yescharacteristic
97C2×C47#45811yescharacteristic
98#544—471no—
99#484—471no—
100#484D4711yescharacteristic
101#400—471no—
102#328—471no—
103#328—471no—
104#324—471no—
105C47#161711yescharacteristic, complemented, Sylow
106C4⋊Q8—941no—
107C4⋊Q8—941no—
108#125—941no—
109#125—941no—
110C22⋊Q8—471no—
111C22⋊Q8—941no—
112C22⋊Q8C2×D4711yescharacteristic
113#117—941no—
114C2×C4⋊C4—471no—
115C2×C4⋊C4C2×D4711yescharacteristic
116#107—21no—
117#107—941no—
118#103—21no—
119#103—941no—
120C22⋊C8—471no—
121C22⋊C8C2×D4711yescharacteristic
122#95—471no—
123#95—941no—
124#95—941no—
125C2×Q8—471no—
126C2×Q8—941no—
127C2×Q8C22⋊D4711yescharacteristic
128C22×C4—21no—
129C22×C4—471no—
130C22×C4—471no—
131C22×C4—941no—
132C22×C4C22×D4711yescharacteristic
133C2×C8—21no—
134C2×C8—941no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—471no—
139C4⋊C4—941no—
140C4⋊C4—941no—
141C4⋊C4—941no—
142C4⋊C4—941no—
143C4⋊C4—941no—
144C4⋊C4—941no—
145C4⋊C4—941no—
146C4⋊C4—941no—
147C4⋊C4C22⋊D4711yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—941no—
150C42—941no—
151C42—941no—
152C23D4×D4711yescharacteristic
153Q8—41no—
154Q8—3761no—
155Q8—1881no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—42no—
160C2×C4—41no—
161C2×C4—472no—
162C2×C4—941no—
163C2×C4—941no—
164C2×C4—941no—
165C2×C4—941no—
166C2×C4—941no—
167C2×C4—1881no—
168C2×C4—1881no—
169C2×C4—1881no—
170C2×C4—1881no—
171C2×C4D4×D4711yescharacteristic
172C2×C4C2×C22⋊D4711yescharacteristic
173C8—41no—
174C8—1881no—
175C22—21no—
176C22—21no—
177C22#1309399211yescharacteristic
178C22Q16×D4711yescharacteristic
179C22#1309405611yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—942no—
186C4—3761no—
187C4—1881no—
188C4—1881no—
189C4—1881no—
190C2—21no—
191C2—21no—
192C2#1568927711yescharacteristic
193C2#1568929411yescharacteristic
194C2#1568931211yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#484C2
socleC22×C47#120
hypercenter#484D47
hypocenterC47#1617
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
105. C47#1617semidirect