Finite Group Databasebeta

← #26125789

Subgroups — #26125789

Order 12032.

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

normal subgroups only

This group has 262 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#20252327C211yesmaximal, characteristic
2#20245201C212yesmaximal
3#20241341C211yesmaximal, characteristic
4#20241338C212yesmaximal
5C47×#1328C211yesmaximal, characteristic
6#15689676C411yescharacteristic
7#15689252—22no—
8#15689250—22no—
9#15689149C411yescharacteristic
10#15689146C2211yescharacteristic
11#15689081C2211yescharacteristic
12#15689079C411yescharacteristic
13C2×#13093934C411yescharacteristic
14#15688943—22no—
15#15688905C2212yes—
16#15688900—22no—
17C47×#424C2211yescharacteristic
18C47×#349C2212yes—
19C2×#10625329C2×C411yescharacteristic
20C22×C47⋊C8C2×C411yescharacteristic
21#13094023—21no—
22#13094015—21no—
23#13094001—22no—
24C4×Dic94—22no—
25#13093983C2×C411yescharacteristic
26C2×C4×Dic47C2×C411yescharacteristic
27#13093964—22no—
28Dic47⋊C8—22no—
29Dic47⋊C8—22no—
30#13093935—21no—
31#13093934—21no—
32#13093934—21no—
33#13093934D412yes—
34C4×C47⋊C8—21no—
35C8×Dic47D412yes—
36C2×M16×C47C2311yescharacteristic
37C22×C8×C47C2×C411yescharacteristic
38#117×C47C2×C411yescharacteristic
39M32×C47—22no—
40C4⋊C8×C47—22no—
41C22×C4×C47C22×C411yescharacteristic
42C22×Dic47—21no—
43C2×Dic94—22no—
44M16×C47—41no—
45C2×C8×C47—21no—
46C2×C8×C47—41no—
47C2×C8×C47C2×D412yes—
48C4⋊C4×C47—21no—
49C22⋊C4×C47M1612yes—
50C42×C47—21no—
51C22⋊Dic47—21no—
52C4⋊Dic47—22no—
53C4⋊Dic47—21no—
54Dic47⋊C4—22no—
55Dic47⋊C4—22no—
56C4×Dic47—21no—
57C4×Dic47C22⋊C412yes—
58C4×Dic47M1611yescharacteristic
59C4×Dic47M1611yescharacteristic
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×C47C2×M1611yescharacteristic
73C2×Dic47—21no—
74C2×Dic47—21no—
75C2×Dic47—22no—
76C2×Dic47—81no—
77Dic94—82no—
78C8×C47—22no—
79C8×C47—41no—
80C47⋊C8—21no—
81C47⋊C8—41no—
82C47⋊C8#10112yes—
83#11540—471nomaximal, Sylow
84C22×C47—21no—
85C22×C47—41no—
86C22×C47#40711yescharacteristic
87C4×C47—21no—
88C4×C47—42no—
89C4×C47#41011yescharacteristic
90C4×C47C2×#10111yescharacteristic
91Dic47—41no—
92Dic47—42no—
93Dic47—41no—
94#2961—471no—
95#2166—472no—
96#1328—471no—
97#1328D4711yescharacteristic
98#1327—472no—
99C2×C47—21no—
100C2×C47—41no—
101C2×C47#146711yescharacteristic
102#533—471no—
103#446—942no—
104#446—942no—
105#424—471no—
106#424C2×D4711yescharacteristic
107#423—471no—
108#405—471no—
109#405—471no—
110C2×#97—471no—
111#364—942no—
112#349—472no—
113#349C2×D4712yes—
114#347—942no—
115C47#1154011yescharacteristic, complemented, Sylow
116C2×M16—471no—
117C2×M16C22×D4711yescharacteristic
118C22×C8—471no—
119C22×C8C4×D4711yescharacteristic
120C4⋊Q8—941no—
121#125—941no—
122C22⋊Q8—942no—
123C4×Q8—942no—
124#117—471no—
125#117C4×D4711yescharacteristic
126C2×C42—471no—
127M32—22no—
128M32—942no—
129C4⋊C8—22no—
130C4⋊C8—942no—
131C4⋊C8—942no—
132#97—472no—
133#97—941no—
134#97—941no—
135#97—941no—
136C4×C8—472no—
137C4×C8—941no—
138C2×Q8—942no—
139C22×C4—941no—
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—21no—
151C4⋊C4—942no—
152C4⋊C4—942no—
153C4⋊C4—942no—
154C4⋊C4—941no—
155C22⋊C4—941no—
156C22⋊C4#1062532412yes—
157C42—21no—
158C42—472no—
159C42—471no—
160C42—471no—
161C42—941no—
162C16—42no—
163C16—1882no—
164C23C2×#1062532411yescharacteristic
165Q8—3762no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—941no—
170C2×C4—941no—
171C2×C4—942no—
172C2×C4—3761no—
173C2×C4C22⋊C4×D4711yescharacteristic
174C2×C4M16×D4711yescharacteristic
175C8—22no—
176C8—41no—
177C8—472no—
178C8—941no—
179C8—1881no—
180C22—21no—
181C22—41no—
182C22#1568908511yescharacteristic
183C4—21no—
184C4—42no—
185C4—1881no—
186C4—1881no—
187C4—1882no—
188C4#1568909511yescharacteristic
189C4#101×D4711yescharacteristic
190C2—21no—
191C2—41no—
192C2#2024173011yescharacteristic
subgroupG/H
centerC4#15689095
commutatorC22×C4×C47C22×C4
FrattiniC2×M16C22×D47
FittingC47×#1328C2
socleC2×C47#1467
prime radicalC23×C47C2×M16
cosocleC2×M16×C47C23
hypercenter#1328D47
hypocenterC47#11540
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1328

Complements

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

NH ≅ G/Ntype
115. C47#11540semidirect

Maximal subgroups

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

subgroupindex
#202523272
#202452012
#202413412
#202413382
C47×#13282
#1154047