Finite Group Databasebeta

← #26103658

Subgroups — #26103658

Order 12032.

204 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 43 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#20244207C211yesmaximal, characteristic
2#20241332C211yesmaximal, characteristic
3C47×#1324C211yesmaximal, characteristic
4C2×#13094024C411yescharacteristic
5C2×#13093947—21no—
6C2×#13093947—21no—
7C2×#13093935C411yescharacteristic
8#15688849—21no—
9C47×#382C2211yescharacteristic
10C47×#324—21no—
11C22×Dic94—21no—
12C22×C47⋊C8—21no—
13#13094024—21no—
14#13094024—41no—
15#13094024C812yescomplemented
16C2×C4⋊Dic47—41no—
17#13093947—42no—
18#13093947—42no—
19C22⋊(C47⋊C8)—41no—
20#13093935—41no—
21C2×C4⋊C4×C47D411yescharacteristic
22C2×C4⋊C4×C47D411yescharacteristic
23C2×C42×C47C2×C411yescharacteristic
24C22⋊C8×C47—41no—
25#95×C47—41no—
26C22×C4×C47—21no—
27C22×C4×C47—21no—
28C22×C4×C47—21no—
29C22×C4×C47C22⋊C411yescharacteristic
30C22×Dic47—41no—
31C2×Dic94—22no—
32C2×Dic94—41no—
33C2×Dic94—41no—
34C2×Dic94—41no—
35C2×Dic94—41no—
36C2×Dic94—41no—
37C2×C8×C47—81no—
38C4⋊C4×C47—41no—
39C4⋊C4×C47—41no—
40C42×C47—21no—
41C42×C47C2×C811yescharacteristic
42C42×C47M1611yescharacteristic
43C4⋊Dic47—42no—
44C4⋊Dic47—42no—
45C2×C47⋊C8—22no—
46C2×C47⋊C8—41no—
47C2×C47⋊C8—41no—
48C2×C47⋊C8—81no—
49C23×C47#9911yescharacteristic
50C2×C4×C47—21no—
51C2×C4×C47—21no—
52C2×C4×C47—21no—
53C2×C4×C47—21no—
54C2×C4×C47—41no—
55C2×C4×C47—41no—
56C2×C4×C47—41no—
57C2×C4×C47—41no—
58C2×C4×C47—81no—
59C2×C4×C47—81no—
60C2×C4×C47C22⋊C811yescharacteristic
61C2×C4×C47#10011yescharacteristic
62C2×Dic47—42no—
63C2×Dic47—81no—
64C2×Dic47—81no—
65Dic94—42no—
66Dic94—42no—
67Dic94—81no—
68Dic94—81no—
69C8×C47—161no—
70C47⋊C8—42no—
71C47⋊C8—161no—
72#7353—471nomaximal, Sylow
73C22×C47—21no—
74C22×C47—21no—
75C22×C47#32311yescharacteristic
76C22×C47#35311yescharacteristic
77C22×C47#35511yescharacteristic
78C4×C47—21no—
79C4×C47—21no—
80C4×C47—41no—
81C4×C47—41no—
82C4×C47—81no—
83C4×C47—81no—
84Dic47—82no—
85#1960—471no—
86#1324—471no—
87#1324D4711yescharacteristic
88C2×C47—21no—
89C2×C47—21no—
90C2×C47#131811yescharacteristic
91C2×C47#140711yescharacteristic
92C2×C47#140711yescharacteristic
93C2×C4⋊Q8—471no—
94C2×#103—941no—
95C2×#103—941no—
96C2×#97—471no—
97#382C2×D4711yescharacteristic
98#324—21no—
99#324—941no—
100C47#735311yescharacteristic, complemented, Sylow
101C22×Q8—941no—
102C22×C8—941no—
103C4⋊Q8—472no—
104C4⋊Q8—941no—
105C4⋊Q8—1881no—
106C2×C4⋊C4—1881no—
107C2×C4⋊C4D18811yescharacteristic
108C2×C4⋊C4C22⋊D4711yescharacteristic
109C2×C42C4×D4711yescharacteristic
110#103—1882no—
111#103—1882no—
112C22⋊C8—41no—
113C22⋊C8—1881no—
114#97—1881no—
115#95—41no—
116C2×Q8—942no—
117C2×Q8—1881no—
118C2×Q8—1881no—
119C2×Q8—1881no—
120C2×Q8—1881no—
121C2×Q8—1881no—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—1881no—
126C22×C4(C2×D47)⋊C411yescharacteristic
127C2×C8—81no—
128C2×C8—942no—
129C2×C8—3761no—
130C2×C8—1881no—
131C2×C8—1881no—
132C4⋊C4—41no—
133C4⋊C4—41no—
134C4⋊C4—1882no—
135C4⋊C4—1882no—
136C42—21no—
137C42C8×D4711yescharacteristic
138C42#1062532411yescharacteristic
139C23#1309393811yescharacteristic
140Q8—3761no—
141Q8—3761no—
142Q8—1882no—
143Q8—1882no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—81no—
153C2×C4—81no—
154C2×C4—3761no—
155C2×C4—3761no—
156C2×C4—1882no—
157C2×C4(C2×D47)⋊C811yescharacteristic
158C2×C4#1309394011yescharacteristic
159C8—161no—
160C8—1882no—
161C8—7521no—
162C22—21no—
163C22—21no—
164C22#1568884611yescharacteristic
165C22#1568891511yescharacteristic
166C22#1568891911yescharacteristic
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—81no—
172C4—81no—
173C4—3762no—
174C2—21no—
175C2—21no—
176C2#2024131911yescharacteristic
177C2#2024154711yescharacteristic
178C2#2024154911yescharacteristic
subgroupG/H
centerC22#15688915
commutatorC42×C47C2×C8
Frattini#382C2×D47
FittingC47×#1324C2
socleC22×C47#353
prime radicalC23×C47#99
cosocleC47×#382C22
hypercenter#1324D47
hypocenterC47#7353
LCSG ▷ C42×C47 ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #382 ◁ #1324

Complements

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

NH ≅ G/Ntype
15. #13094024C8semidirect
100. C47#7353semidirect

Maximal subgroups

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

subgroupindex
#202442072
#202413322
C47×#13242
#735347