Finite Group Databasebeta

← #26102923

Subgroups — #26102923

Order 12032.

210 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 47 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#20243570C211yesmaximal, characteristic
2#20241312C211yesmaximal, characteristic
3C47×#1314C211yesmaximal, characteristic
4C22×#10625329C411yescharacteristic
5C2×Dic47⋊C8—21no—
6C4×C22⋊Dic47C411yescharacteristic
7C22⋊(C47⋊C16)—21no—
8#15688877—21no—
9C2×C22⋊C8×C47C2211yescharacteristic
10C47×C22⋊C16—21no—
11C2×#10625329—42no—
12C2×#10625329—41no—
13C22×C47⋊C8—21no—
14C2×C22⋊Dic47—21no—
15C2×C4×Dic47—21no—
16C2×C47⋊C16—41no—
17Dic47⋊C8—42no—
18C47⋊#95C811yescharacteristic
19C47⋊#95C811yescharacteristic
20C23×C4×C47C2×C411yescharacteristic
21C22×C8×C47D411yescharacteristic
22C22×C8×C47D411yescharacteristic
23C2×C16×C47—41no—
24C22⋊C8×C47—41no—
25C24×C47M1611yescharacteristic
26C22×C4×C47—21no—
27C22×C4×C47—21no—
28C22×C4×C47—41no—
29C22×C4×C47—41no—
30C22×C4×C47C22⋊C411yescharacteristic
31C22×C4×C47C2×C811yescharacteristic
32C22×Dic47—21no—
33C22×Dic47—21no—
34C2×C8×C47—21no—
35C2×C8×C47—21no—
36C2×C8×C47—41no—
37C2×C8×C47—41no—
38C22⋊Dic47—42no—
39C4×Dic47—41no—
40C4×Dic47—41no—
41#10625329—42no—
42#10625329—42no—
43C2×C47⋊C8—22no—
44C2×C47⋊C8—41no—
45C2×C47⋊C8—41no—
46C16×C47—81no—
47C47⋊C16—81no—
48C23×C47—21no—
49C23×C47—21no—
50C23×C47—21no—
51C23×C47—41no—
52C23×C47—41no—
53C23×C47C22⋊C811yescharacteristic
54C2×C4×C47—21no—
55C2×C4×C47—21no—
56C2×C4×C47—21no—
57C2×C4×C47—42no—
58C2×C4×C47—41no—
59C2×C4×C47—41no—
60C2×C4×C47—41no—
61C2×C4×C47#9911yescharacteristic
62C2×C4×C47#10111yescharacteristic
63C2×Dic47—22no—
64C2×Dic47—41no—
65C2×Dic47—41no—
66C2×Dic47—41no—
67C2×Dic47—41no—
68C2×Dic47—41no—
69C8×C47—41no—
70C8×C47—41no—
71C47⋊C8—42no—
72#7067—471nomaximal, Sylow
73C22×C47—21no—
74C22×C47—21no—
75C22×C47—41no—
76C22×C47—41no—
77C22×C47—41no—
78C22×C47—81no—
79C22×C47—81no—
80C22×C47#32411yescharacteristic
81C22×C47#35011yescharacteristic
82C22×C47#35011yescharacteristic
83C4×C47—21no—
84C4×C47—41no—
85C4×C47AΣL(1,𝔽16)11yescharacteristic
86C4×C47#35211yescharacteristic
87Dic47—42no—
88Dic47—81no—
89#1851—471no—
90#1314—471no—
91#1314D4711yescharacteristic
92C2×C47—21no—
93C2×C47—21no—
94C2×C47—81no—
95C2×C47#132311yescharacteristic
96C2×C47#132611yescharacteristic
97C2×C47#132711yescharacteristic
98C22×M16—471no—
99C2×C4⋊C8—941no—
100C2×C22⋊C8C2×D4711yescharacteristic
101C4×C22⋊C4—471no—
102C22⋊C16—21no—
103C22⋊C16—941no—
104#336—941no—
105C47#706711yescharacteristic, complemented, Sylow
106C23×C4C4×D4711yescharacteristic
107C2×M16—1882no—
108C2×M16—1881no—
109C22×C8—941no—
110C22×C8D18811yescharacteristic
111C22×C8C22⋊D4711yescharacteristic
112C2×C22⋊C4—941no—
113C2×C42—941no—
114C2×C16—41no—
115C2×C16—1881no—
116C4⋊C8—1882no—
117C22⋊C8—41no—
118#95—471no—
119#95—471no—
120C24#1062532411yescharacteristic
121C22×C4—21no—
122C22×C4—21no—
123C22×C4—41no—
124C22×C4—41no—
125C22×C4—941no—
126C22×C4—941no—
127C22×C4C8×D4711yescharacteristic
128C22×C4(C2×D47)⋊C411yescharacteristic
129M16—1882no—
130M16—1882no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—41no—
134C2×C8—41no—
135C2×C8—942no—
136C2×C8—1881no—
137C2×C8—1881no—
138C22⋊C4—1882no—
139C42—1881no—
140C42—1881no—
141C16—81no—
142C16—3761no—
143C23—21no—
144C23—21no—
145C23—21no—
146C23—41no—
147C23—41no—
148C23(C2×D47)⋊C811yescharacteristic
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—42no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—942no—
157C2×C4—1881no—
158C2×C4—1881no—
159C2×C4—1881no—
160C2×C4—1881no—
161C2×C4—1881no—
162C2×C4#1309393811yescharacteristic
163C2×C4#1309394211yescharacteristic
164C8—41no—
165C8—41no—
166C8—1882no—
167C22—21no—
168C22—21no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22—81no—
173C22—81no—
174C22#1568884811yescharacteristic
175C22#1568890611yescharacteristic
176C22#1568890811yescharacteristic
177C4—21no—
178C4—41no—
179C4—3761no—
180C4—1882no—
181C4#1568890911yescharacteristic
182C4#1568891411yescharacteristic
183C2—21no—
184C2—21no—
185C2—81no—
186C2#2024132911yescharacteristic
187C2#2024133511yescharacteristic
188C2#2024133811yescharacteristic
subgroupG/H
centerC2×C4#13093938
commutatorC22×C4×C47C2×C8
FrattiniC2×C22⋊C8C2×D47
FittingC47×#1314C2
socleC22×C47#324
prime radicalC24×C47M16
cosocleC2×C22⋊C8×C47C22
hypercenter#1314D47
hypocenterC47#7067
LCSG ▷ C22×C4×C47 ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #1314

Complements

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

NH ≅ G/Ntype
105. C47#7067semidirect

Maximal subgroups

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

subgroupindex
#202435702
#202413122
C47×#13142
#706747