Finite Group Databasebeta

← #26127474

Subgroups — #26127474

Order 12032.

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

normal subgroups only

This group has 274 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#20253769C211yesmaximal, characteristic
2#20245200C211yesmaximal, characteristic
3#20241422C214yesmaximal, complemented
4C47×#2165C211yesmaximal, characteristic
5#15689680C411yescharacteristic
6C2×#13094024C411yescharacteristic
7#15689492C412yes—
8#15689492C2212yes—
9#15689474—21no—
10#15689474—21no—
11#15689133—21no—
12#15689133—21no—
13#15688944—21no—
14#15688905—21no—
15#15688901C2212yes—
16C4×M16×C47C2211yescharacteristic
17C47×#364—21no—
18C47×#349—21no—
19C47×#347C2212yes—
20C22×Dic94—21no—
21#13094024—21no—
22#13094024—21no—
23#13094024—41no—
24#13094024C2×C412yes—
25#13094016C2×C412yes—
26#13094003—41no—
27C4×Dic94—41no—
28#13093983—21no—
29C2×C4⋊Dic47—41no—
30#13093964—22no—
31#13093949—22no—
32#13093949—22no—
33#13093949—22no—
34#13093949—22no—
35C2×M16×C47D411yescharacteristic
36C2×M16×C47D411yescharacteristic
37C2×C42×C47C2×C411yescharacteristic
38M32×C47—22no—
39#97×C47C2×C411yescharacteristic
40#97×C47C2311yescharacteristic
41C4×C8×C47D411yescharacteristic
42C4×C8×C47D411yescharacteristic
43C22×C4×C47—21no—
44C22×C4×C47C22⋊C411yescharacteristic
45C22×Dic47—41no—
46C2×Dic94—22no—
47C2×Dic94—42no—
48C2×Dic94—42no—
49C2×Dic94—41no—
50C2×Dic94—41no—
51M16×C47—41no—
52M16×C47—41no—
53C2×C8×C47C22⋊C411yescharacteristic
54C2×C8×C47C22⋊C411yescharacteristic
55C2×C8×C47C2×D411yescharacteristic
56C2×C8×C47C2×D411yescharacteristic
57C42×C47—21no—
58C42×C47C22⋊C411yescharacteristic
59C42×C47C22×C411yescharacteristic
60C22⋊Dic47—41no—
61C4⋊Dic47—22no—
62C4⋊Dic47—42no—
63C4⋊Dic47—41no—
64C4⋊Dic47—42no—
65Dic47⋊C4—42no—
66C4×Dic47—41no—
67C16×C47—42no—
68C47⋊C16—42no—
69C23×C47#10011yescharacteristic
70C2×C4×C47—21no—
71C2×C4×C47—21no—
72C2×C4×C47—21no—
73C2×C4×C47—21no—
74C2×C4×C47—42no—
75C2×C4×C47#10011yescharacteristic
76C2×C4×C47C2×C22⋊C411yescharacteristic
77C2×Dic47—42no—
78C2×Dic47—42no—
79C2×Dic47—82no—
80Dic94—42no—
81Dic94—42no—
82Dic94—82no—
83Dic94—82no—
84C8×C47—21no—
85C8×C47—21no—
86C8×C47—21no—
87C8×C47—21no—
88#11916—471nomaximal, Sylow
89C22×C47—21no—
90C22×C47—41no—
91C22×C47C2×#10011yescharacteristic
92C4×C47—22no—
93C4×C47—21no—
94C4×C47—41no—
95C4×C47#42111yescharacteristic
96C4×C47#42111yescharacteristic
97Dic47—82no—
98Dic47—82no—
99#3139—471no—
100#2165—471no—
101#2165D4711yescharacteristic
102#1356—474no—
103C2×C47—21no—
104C2×C47—41no—
105C2×C47#153311yescharacteristic
106#533—471no—
107C2×C4⋊Q8—471no—
108#491—472no—
109#491—472no—
110#487—941no—
111#487—941no—
112#419—941no—
113#419—941no—
114C4×M16C2×D4711yescharacteristic
115#364—21no—
116#364—941no—
117#349—21no—
118#349—941no—
119#347—472no—
120#347C2×D4712yes—
121C47#1191611yescharacteristic, complemented, Sylow
122C22×Q8—941no—
123C2×M16D18811yescharacteristic
124C2×M16C22⋊D4711yescharacteristic
125C4⋊Q8—472no—
126C4⋊Q8—941no—
127C4⋊Q8—941no—
128C4⋊Q8—1881no—
129#125—472no—
130C22⋊Q8—1881no—
131C4×Q8—1881no—
132#117—941no—
133C2×C4⋊C4—1881no—
134C2×C42C4×D4711yescharacteristic
135M32—22no—
136M32—942no—
137#103—942no—
138#103—942no—
139#103—942no—
140#103—942no—
141#97C4×D4711yescharacteristic
142#97C22×D4711yescharacteristic
143C4×C8D18811yescharacteristic
144C4×C8C22⋊D4711yescharacteristic
145C2×Q8—942no—
146C2×Q8—1882no—
147C2×Q8—1882no—
148C2×Q8—1881no—
149C2×Q8—1881no—
150C22×C4—21no—
151C22×C4—1881no—
152C22×C4(C2×D47)⋊C411yescharacteristic
153M16—41no—
154M16—41no—
155C2×C8(C2×D47)⋊C411yescharacteristic
156C2×C8(C2×D47)⋊C411yescharacteristic
157C2×C8C2×D18811yescharacteristic
158C2×C8C2×C22⋊D4711yescharacteristic
159C4⋊C4—942no—
160C4⋊C4—1882no—
161C4⋊C4—1882no—
162C4⋊C4—1882no—
163C4⋊C4—1881no—
164C22⋊C4—1881no—
165C42—21no—
166C42—1881no—
167C42(C2×D47)⋊C411yescharacteristic
168C42C2×C4×D4711yescharacteristic
169C16—42no—
170C16—1882no—
171C23#1309394011yescharacteristic
172Q8—3762no—
173Q8—3762no—
174Q8—1882no—
175Q8—1882no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—42no—
181C2×C4—3762no—
182C2×C4—1882no—
183C2×C4—1882no—
184C2×C4#1309394011yescharacteristic
185C2×C4C2×(C2×D47)⋊C411yescharacteristic
186C8—21no—
187C8—21no—
188C8—21no—
189C8—21no—
190C22—21no—
191C22—41no—
192C22C2×#1309394011yescharacteristic
193C4—22no—
194C4—21no—
195C4—41no—
196C4—3762no—
197C4—3762no—
198C4#1568913911yescharacteristic
199C4#1568914111yescharacteristic
200C2—21no—
201C2—41no—
202C2#2024201111yescharacteristic
subgroupG/H
centerC2#20242011
commutatorC42×C47C22×C4
Frattini#97C22×D47
FittingC47×#2165C2
socleC2×C47#1533
prime radicalC23×C47#100
cosocle#97×C47C23
hypercenter#2165D47
hypocenterC47#11916
LCSG ▷ C42×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #2165

Complements

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

NH ≅ G/Ntype
3. #20241422C2semidirect
121. C47#11916semidirect

Maximal subgroups

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

subgroupindex
#202537692
#202452002
#202414222
C47×#21652
#1191647