Finite Group Databasebeta

← #26125783

Subgroups — #26125783

Order 12032.

270 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 71 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#20252318C211yesmaximal, characteristic
2#20245201C212yesmaximal
3#20241340C212yesmaximal
4#20241339C211yesmaximal, characteristic
5C47×#1327C211yesmaximal, characteristic
6#15689680C411yescharacteristic
7#15689250—22no—
8#15689247—22no—
9#15689151C411yescharacteristic
10#15689151C2211yescharacteristic
11#15689081C411yescharacteristic
12#15689081C2211yescharacteristic
13C2×C4×C47⋊C8C411yescharacteristic
14#15688943—22no—
15#15688905C2212yes—
16#15688900—22no—
17C47×#423C2211yescharacteristic
18C47×#349C2212yes—
19C22×C47⋊C8C2×C411yescharacteristic
20C22×C47⋊C8C2×C411yescharacteristic
21#13094024—21no—
22#13094016—21no—
23#13094003—22no—
24C4×Dic94—22no—
25#13093983C2×C411yescharacteristic
26#13093983C2×C411yescharacteristic
27#13093964—22no—
28Dic47⋊C8—22no—
29Dic47⋊C8—22no—
30#13093934—21no—
31#13093934D412yes—
32C4×C47⋊C8—21no—
33C4×C47⋊C8—21no—
34C8×Dic47—21no—
35C8×Dic47D412yes—
36C2×M16×C47C2×C411yescharacteristic
37C2×M16×C47C2311yescharacteristic
38C2×C42×C47C2×C411yescharacteristic
39M32×C47—22no—
40C4⋊C8×C47—22no—
41C22×C4×C47—21no—
42C22×C4×C47C22×C411yescharacteristic
43C2×Dic94—22no—
44M16×C47—41no—
45M16×C47—41no—
46C2×C8×C47—21no—
47C2×C8×C47C2×D412yes—
48C42×C47—21no—
49C42×C47M1611yescharacteristic
50C42×C47M1611yescharacteristic
51C22⋊Dic47—21no—
52C22⋊Dic47M1612yes—
53C4⋊Dic47—22no—
54C4⋊Dic47—21no—
55C4⋊Dic47—21no—
56Dic47⋊C4—24no—
57C4×Dic47—21no—
58C4×Dic47C22⋊C412yes—
59C2×C47⋊C8—22no—
60C2×C47⋊C8—21no—
61C2×C47⋊C8—41no—
62C2×C47⋊C8C22⋊C411yescharacteristic
63C2×C47⋊C8C22⋊C411yescharacteristic
64C16×C47—42no—
65C47⋊C16—42no—
66C23×C47C2×M1611yescharacteristic
67C2×C4×C47—21no—
68C2×C4×C47—21no—
69C2×C4×C47—21no—
70C2×C4×C47—21no—
71C2×C4×C47—42no—
72C2×C4×C47C2×C22⋊C411yescharacteristic
73C2×C4×C47C2×M1611yescharacteristic
74C2×Dic47—22no—
75C2×Dic47—22no—
76Dic94—44no—
77C8×C47—22no—
78C8×C47—41no—
79C47⋊C8—21no—
80C47⋊C8—41no—
81C47⋊C8#10112yes—
82#11539—471nomaximal, Sylow
83C22×C47—21no—
84C22×C47—41no—
85C22×C47#40711yescharacteristic
86C4×C47—22no—
87C4×C47—21no—
88C4×C47—41no—
89C4×C47#41011yescharacteristic
90C4×C47C2×#10111yescharacteristic
91Dic47—42no—
92Dic47—42no—
93#2960—471no—
94#2166—472no—
95#1328—472no—
96#1327—471no—
97#1327D4711yescharacteristic
98C2×C47—21no—
99C2×C47—41no—
100C2×C47#146711yescharacteristic
101#533—471no—
102#446—942no—
103C8×Q8—942no—
104#424—471no—
105#424—471no—
106#423C2×D4711yescharacteristic
107#405—471no—
108#405—471no—
109C2×C4×C8—471no—
110#364—942no—
111#349—472no—
112#349C2×D4712yes—
113#347—942no—
114C47#1153911yescharacteristic, complemented, Sylow
115C2×M16C4×D4711yescharacteristic
116C2×M16C22×D4711yescharacteristic
117C22×C8—471no—
118C22×C8—471no—
119C4⋊Q8—941no—
120#125—941no—
121C22⋊Q8—942no—
122C4×Q8—942no—
123#117—471no—
124#117—471no—
125C2×C42C4×D4711yescharacteristic
126M32—22no—
127M32—942no—
128C4⋊C8—22no—
129C4⋊C8—942no—
130C4⋊C8—942no—
131#97—472no—
132#97—941no—
133C4×C8—472no—
134C4×C8—941no—
135C4×C8—941no—
136C4×C8—941no—
137C2×Q8—942no—
138C22×C4—21no—
139C22×C4C2×C4×D4711yescharacteristic
140M16—41no—
141M16—41no—
142C2×C8—21no—
143C2×C8—471no—
144C2×C8—471no—
145C2×C8—942no—
146C2×C8—941no—
147C2×C8—1881no—
148C2×C8D4×D4712yes—
149C4⋊C4—944no—
150C4⋊C4—942no—
151C4⋊C4—941no—
152C4⋊C4—941no—
153C22⋊C4—472no—
154C22⋊C4—941no—
155C42—21no—
156C42—472no—
157C42—941no—
158C42#1062532411yescharacteristic
159C42#1062532411yescharacteristic
160C16—42no—
161C16—1882no—
162C23M16×D4711yescharacteristic
163Q8—1884no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—42no—
169C2×C4—942no—
170C2×C4—942no—
171C2×C4C22⋊C4×D4711yescharacteristic
172C2×C4C2×#1062532411yescharacteristic
173C8—22no—
174C8—41no—
175C8—472no—
176C8—941no—
177C8—1881no—
178C22—21no—
179C22—41no—
180C22#1568908511yescharacteristic
181C4—22no—
182C4—21no—
183C4—41no—
184C4—1882no—
185C4—1882no—
186C4#1568909511yescharacteristic
187C4#101×D4711yescharacteristic
188C2—21no—
189C2—41no—
190C2#2024173011yescharacteristic
subgroupG/H
centerC4#15689095
commutatorC22×C4×C47C22×C4
FrattiniC2×M16C22×D47
FittingC47×#1327C2
socleC2×C47#1467
prime radicalC23×C47C2×M16
cosocleC2×M16×C47C23
hypercenter#1327D47
hypocenterC47#11539
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1327

Complements

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

NH ≅ G/Ntype
114. C47#11539semidirect

Maximal subgroups

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

subgroupindex
#202523182
#202452012
#202413402
#202413392
C47×#13272
#1153947