Finite Group Databasebeta

← #26125626

Subgroups — #26125626

Order 12032.

288 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 87 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#20252321C211yesmaximal, characteristic
2#20245188C212yesmaximal
3#20241330C211yesmaximal, characteristic
4#20241329C212yesmaximal
5C47×#1323C211yesmaximal, characteristic
6#15689676C411yescharacteristic
7#15689252—22no—
8#15689247—22no—
9#15689149C2211yescharacteristic
10#15689146C411yescharacteristic
11#15689081C411yescharacteristic
12#15689079C411yescharacteristic
13C2×C8×Dic47C2211yescharacteristic
14Dic47⋊C16—22no—
15C22⋊(C47⋊C16)C2212yes—
16#15688898—22no—
17C47×#424C2211yescharacteristic
18C47×C22⋊C16C2212yes—
19C2×#10625329C2×C411yescharacteristic
20C22×C47⋊C8C2×C411yescharacteristic
21#13094023C812yes—
22#13094015C812yes—
23#13094001—22no—
24C4×Dic94—22no—
25#13093983C2×C411yescharacteristic
26C2×C4×Dic47C2×C411yescharacteristic
27C2×C47⋊C16—22no—
28Dic47⋊C8—22no—
29Dic47⋊C8—22no—
30#13093935—21no—
31#13093934—21no—
32C4×C47⋊C8—21no—
33C8×Dic47—21no—
34C8×Dic47D412yes—
35C8×Dic47D412yes—
36C2×M16×C47C2×C411yescharacteristic
37C22×C8×C47C2311yescharacteristic
38#117×C47C2×C411yescharacteristic
39C2×C16×C47—22no—
40C4⋊C8×C47—22no—
41C22×C4×C47C22×C411yescharacteristic
42C22×Dic47M1612yes—
43C2×Dic94—22no—
44M16×C47—41no—
45C2×C8×C47—21no—
46C2×C8×C47—41no—
47C2×C8×C47C2×D412yes—
48C4⋊C4×C47C2×C812yes—
49C22⋊C4×C47—21no—
50C42×C47—21no—
51C22⋊Dic47—21no—
52C4⋊Dic47—22no—
53C4⋊Dic47C2×C812yes—
54Dic47⋊C4—22no—
55Dic47⋊C4—22no—
56C4×Dic47—21no—
57C4×Dic47C22⋊C412yes—
58C4×Dic47C2×C811yescharacteristic
59C4×Dic47C2×C811yescharacteristic
60#10625329—41no—
61C2×C47⋊C8—22no—
62C2×C47⋊C8—21no—
63C2×C47⋊C8C22⋊C411yescharacteristic
64C2×C47⋊C8C22⋊C411yescharacteristic
65C16×C47—42no—
66C47⋊C16—42no—
67C23×C47C2×M1611yescharacteristic
68C2×C4×C47—21no—
69C2×C4×C47—21no—
70C2×C4×C47—22no—
71C2×C4×C47C2×C22⋊C411yescharacteristic
72C2×C4×C47C22×C811yescharacteristic
73C2×Dic47—22no—
74C2×Dic47—42no—
75C2×Dic47C22⋊C812yes—
76C2×Dic47C22⋊C812yes—
77Dic94—44no—
78C8×C47—22no—
79C8×C47—41no—
80C47⋊C8—21no—
81C47⋊C8—41no—
82C47⋊C8#10112yes—
83#11497—471nomaximal, Sylow
84C22×C47—22no—
85C22×C47—21no—
86C22×C47C2×C22⋊C811yescharacteristic
87C4×C47—21no—
88C4×C47—42no—
89C4×C47#41011yescharacteristic
90C4×C47C2×#10111yescharacteristic
91Dic47—22no—
92Dic47—22no—
93Dic47—42no—
94#2960—471no—
95#2163—472no—
96#1323—471no—
97#1323—472no—
98#1323D4711yescharacteristic
99C2×C47—41no—
100C2×C47#146111yescharacteristic
101C2×C47#211712yes—
102#533—471no—
103#446—942no—
104C8×Q8—942no—
105#424—471no—
106#424C2×D4711yescharacteristic
107#423—471no—
108#405—471no—
109#405—471no—
110C2×C4×C8—471no—
111C4⋊C16—942no—
112C22⋊C16—472no—
113C22⋊C16C2×D4712yes—
114#346—942no—
115C47#1149711yescharacteristic, complemented, Sylow
116C2×M16—471no—
117C2×M16C4×D4711yescharacteristic
118C22×C8—471no—
119C22×C8C22×D4711yescharacteristic
120C4⋊Q8—472no—
121#125—472no—
122C22⋊Q8—942no—
123C4×Q8—942no—
124#117—471no—
125#117C4×D4711yescharacteristic
126C2×C42—471no—
127C2×C16—22no—
128C2×C16—942no—
129C4⋊C8—22no—
130C4⋊C8—942no—
131C4⋊C8—942no—
132#97—941no—
133#97—941no—
134C4×C8—472no—
135C4×C8—472no—
136C4×C8—941no—
137C4×C8—941no—
138C2×Q8—942no—
139C22×C4—472no—
140C22×C4C2×C4×D4711yescharacteristic
141M16—41no—
142M16—1881no—
143C2×C8—21no—
144C2×C8—41no—
145C2×C8—471no—
146C2×C8—471no—
147C2×C8—942no—
148C2×C8—941no—
149C2×C8D4×D4712yes—
150C4⋊C4—472no—
151C4⋊C4—942no—
152C4⋊C4—942no—
153C4⋊C4—942no—
154C4⋊C4C8×D4712yes—
155C22⋊C4—21no—
156C22⋊C4—941no—
157C42—21no—
158C42—472no—
159C42—471no—
160C42—471no—
161C42—941no—
162C16—42no—
163C16—1882no—
164C23M16×D4711yescharacteristic
165Q8—1884no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—472no—
170C2×C4—472no—
171C2×C4—942no—
172C2×C4—1882no—
173C2×C4C22⋊C4×D4711yescharacteristic
174C2×C4C2×C8×D4711yescharacteristic
175C8—22no—
176C8—41no—
177C8—472no—
178C8—941no—
179C8—1881no—
180C22—22no—
181C22—21no—
182C22C22⋊C8×D4711yescharacteristic
183C4—21no—
184C4—42no—
185C4—942no—
186C4—942no—
187C4—1882no—
188C4#1568909511yescharacteristic
189C4#101×D4711yescharacteristic
190C2—41no—
191C2#2024171011yescharacteristic
192C2#2024501412yes—
subgroupG/H
centerC2×C4C22⋊C4×D47
commutatorC2×C4×C47C22×C8
FrattiniC22×C8C22×D47
FittingC47×#1323C2
socleC22×C47C2×C22⋊C8
prime radicalC23×C47C2×M16
cosocleC22×C8×C47C23
hypercenter#1323D47
hypocenterC47#11497
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1323

Complements

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

NH ≅ G/Ntype
115. C47#11497semidirect

Maximal subgroups

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

subgroupindex
#202523212
#202451882
#202413302
#202413292
C47×#13232
#1149747