Finite Group Databasebeta

← #26103662

Subgroups — #26103662

Order 12032.

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

normal subgroups only

This group has 216 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#20244189C211yesmaximal, characteristic
2#20241334C211yesmaximal, characteristic
3C47×#1325C211yesmaximal, characteristic
4C2×#13094024C411yescharacteristic
5C2×#13093947—21no—
6C2×#13093947—21no—
7C2×C4×C47⋊C8C411yescharacteristic
8#15688849—21no—
9C47×#384C2211yescharacteristic
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—
20C4×C47⋊C8—41no—
21C2×C4⋊C4×C47—41no—
22C2×C4⋊C4×C47D411yescharacteristic
23C2×C4⋊C4×C47D411yescharacteristic
24C2×C42×C47C2×C411yescharacteristic
25C22⋊C8×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—
40C4⋊C4×C47—82no—
41C42×C47—21no—
42C42×C47C2×C811yescharacteristic
43C42×C47M1611yescharacteristic
44C4⋊Dic47—42no—
45C4⋊Dic47—42no—
46C2×C47⋊C8—22no—
47C2×C47⋊C8—41no—
48C2×C47⋊C8—41no—
49C2×C47⋊C8—81no—
50C23×C47#9911yescharacteristic
51C2×C4×C47—22no—
52C2×C4×C47—22no—
53C2×C4×C47—21no—
54C2×C4×C47—21no—
55C2×C4×C47—21no—
56C2×C4×C47—21no—
57C2×C4×C47—41no—
58C2×C4×C47—41no—
59C2×C4×C47—81no—
60C2×C4×C47—81no—
61C2×C4×C47C22⋊C811yescharacteristic
62C2×C4×C47#10011yescharacteristic
63C2×Dic47—42no—
64C2×Dic47—81no—
65C2×Dic47—81no—
66Dic94—42no—
67Dic94—42no—
68Dic94—81no—
69Dic94—81no—
70C8×C47—161no—
71C47⋊C8—42no—
72C47⋊C8—161no—
73#7355—471nomaximal, Sylow
74C22×C47—21no—
75C22×C47—21no—
76C22×C47#32311yescharacteristic
77C22×C47#35311yescharacteristic
78C22×C47#35511yescharacteristic
79C4×C47—22no—
80C4×C47—22no—
81C4×C47—21no—
82C4×C47—21no—
83C4×C47—81no—
84C4×C47—81no—
85Dic47—82no—
86#1956—471no—
87#1325—471no—
88#1325D4711yescharacteristic
89C2×C47—21no—
90C2×C47—21no—
91C2×C47#131811yescharacteristic
92C2×C47#140911yescharacteristic
93C2×C47#141111yescharacteristic
94C2×C4⋊Q8—471no—
95C2×#103—941no—
96C2×#103—941no—
97C2×C4×C8—471no—
98#384C2×D4711yescharacteristic
99#324—21no—
100#324—941no—
101C47#735511yescharacteristic, complemented, Sylow
102C22×Q8—941no—
103C22×C8—941no—
104C4⋊Q8—472no—
105C4⋊Q8—941no—
106C4⋊Q8—1881no—
107C2×C4⋊C4—41no—
108C2×C4⋊C4—1881no—
109C2×C4⋊C4D18811yescharacteristic
110C2×C4⋊C4C22⋊D4711yescharacteristic
111C2×C42C4×D4711yescharacteristic
112#103—1882no—
113#103—1882no—
114C22⋊C8—41no—
115C22⋊C8—1881no—
116C4×C8—1881no—
117C2×Q8—942no—
118C2×Q8—1881no—
119C2×Q8—1881no—
120C2×Q8—1881no—
121C2×Q8—1881no—
122C2×Q8—1881no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—21no—
126C22×C4—1881no—
127C22×C4(C2×D47)⋊C411yescharacteristic
128C2×C8—81no—
129C2×C8—942no—
130C2×C8—3761no—
131C2×C8—1881no—
132C2×C8—1881no—
133C4⋊C4—41no—
134C4⋊C4—41no—
135C4⋊C4—82no—
136C4⋊C4—1882no—
137C4⋊C4—1882no—
138C42—21no—
139C42C8×D4711yescharacteristic
140C42#1062532411yescharacteristic
141C23#1309393811yescharacteristic
142Q8—3761no—
143Q8—3761no—
144Q8—1882no—
145Q8—1882no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—81no—
155C2×C4—81no—
156C2×C4—3761no—
157C2×C4—3761no—
158C2×C4—1882no—
159C2×C4(C2×D47)⋊C811yescharacteristic
160C2×C4#1309394011yescharacteristic
161C8—161no—
162C8—1882no—
163C8—7521no—
164C22—21no—
165C22—21no—
166C22#1568884611yescharacteristic
167C22#1568891511yescharacteristic
168C22#1568891911yescharacteristic
169C4—22no—
170C4—22no—
171C4—21no—
172C4—21no—
173C4—81no—
174C4—81no—
175C4—3762no—
176C2—21no—
177C2—21no—
178C2#2024131911yescharacteristic
179C2#2024155211yescharacteristic
180C2#2024155611yescharacteristic
subgroupG/H
centerC22#15688915
commutatorC42×C47C2×C8
Frattini#384C2×D47
FittingC47×#1325C2
socleC22×C47#353
prime radicalC23×C47#99
cosocleC47×#384C22
hypercenter#1325D47
hypocenterC47#7355
LCSG ▷ C42×C47 ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #384 ◁ #1325

Complements

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

NH ≅ G/Ntype
15. #13094024C8semidirect
101. C47#7355semidirect

Maximal subgroups

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

subgroupindex
#202441892
#202413342
C47×#13252
#735547