Finite Group Databasebeta

← #26127473

Subgroups — #26127473

Order 12032.

274 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 61 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#20253767C211yesmaximal, characteristic
2#20245198C212yesmaximal
3#20241423C211yesmaximal, characteristic, complemented
4#20241422C212yesmaximal, complemented
5C47×#1356C211yesmaximal, characteristic, complemented
6#15689679C411yescharacteristic
7C4⋊Q8×D47C411yescharacteristic
8#15689493C411yescharacteristic
9#15689492C2211yescharacteristic
10#15689491C411yescharacteristic
11#15689472—22no—
12#15689130—22no—
13#15689075C2211yescharacteristic
14#15688943—22no—
15#15688904—22no—
16#15688901C2212yes—
17C47×#491C2211yescharacteristic
18C47×#347C2212yes—
19C2×Q8×D47—21no—
20C2×#10625324D412yes—
21#13094024C2×C411yescharacteristic
22#13094023—21no—
23#13094023—41no—
24#13094022—21no—
25#13094016C2×C411yescharacteristic
26#13094002—41no—
27#13093989—41no—
28#13093982—21no—
29C4⋊C4×D47—41no—
30C42×D47C2×C411yescharacteristic
31#13093964—22no—
32#13093949—22no—
33#13093948—22no—
34#13093947—22no—
35#13093935C2×C411yescharacteristic
36C8×Dic47D412yes—
37C4⋊Q8×C47C2×C411yescharacteristic
38#125×C47C2×C411yescharacteristic
39M32×C47—22no—
40#103×C47—22no—
41#97×C47C2311yescharacteristic
42C2×Q8×C47—21no—
43Q8×D47—44no—
44C2×C4×D47—21no—
45C2×C4×D47—41no—
46C2×C4×D47C22⋊C411yescharacteristic
47C2×Dic94—21no—
48C2×Dic94—41no—
49C2×Dic94—41no—
50C2×C8×C47C2×D412yes—
51C4⋊C4×C47—21no—
52C4⋊C4×C47—41no—
53C4⋊C4×C47—41no—
54C42×C47C22×C411yescharacteristic
55(C2×D47)⋊C4—41no—
56C4⋊Dic47—21no—
57C4⋊Dic47—41no—
58Dic47⋊C4—42no—
59Dic47⋊C4—41no—
60Dic47⋊C4—41no—
61C4×Dic47—21no—
62C4×Dic47—41no—
63C4×Dic47C22⋊C411yescharacteristic
64C2×C47⋊C8C22⋊C412yes—
65#10625324—42no—
66C16×C47—42no—
67C47⋊C16—42no—
68C22×D47#10011yescharacteristic
69Q8×C47—42no—
70C2×C4×C47—21no—
71C2×C4×C47—41no—
72C2×C4×C47—41no—
73C2×C4×C47C2×C22⋊C411yescharacteristic
74C2×Dic47—21no—
75C2×Dic47—41no—
76C2×Dic47—41no—
77C2×Dic47#10011yescharacteristic
78C4×D47—22no—
79C4×D47—42no—
80C4×D47—82no—
81Dic94—42no—
82Dic94—82no—
83Dic94—82no—
84C8×C47—22no—
85C47⋊C8—22no—
86#11916—471nomaximal, Sylow
87C22×C47C2×#10011yescharacteristic
88C2×D47—21no—
89C2×D47—41no—
90C4×C47—41no—
91C4×C47—81no—
92C4×C47—81no—
93C4×C47#42112yes—
94Dic47—22no—
95Dic47—21no—
96Dic47—81no—
97Dic47—81no—
98#3139—471no—
99#2165—472no—
100#1356—471no—
101#1356—472no—
102#1356D4711yescharacteristic, complemented
103C2×C47—21no—
104C2×C47#153311yescharacteristic
105D47—41no—
106#533—471no—
107C2×C4⋊Q8—471no—
108#491—471no—
109#491—471no—
110#491—471no—
111#491C2×D4711yescharacteristic
112#487—942no—
113#419—942no—
114C4×M16—471no—
115#364—942no—
116#349—942no—
117#347—472no—
118#347C2×D4712yes—
119C47#1191611yescharacteristic, complemented, Sylow
120C22×Q8—941no—
121C2×M16—472no—
122C4⋊Q8—471no—
123C4⋊Q8—941no—
124C4⋊Q8—941no—
125C4⋊Q8—1881no—
126C4⋊Q8C4×D4711yescharacteristic
127#125—471no—
128#125C4×D4711yescharacteristic
129C22⋊Q8—1881no—
130C4×Q8—1881no—
131#117—941no—
132C2×C4⋊C4—1881no—
133C2×C42—471no—
134M32—22no—
135M32—942no—
136#103—22no—
137#103—942no—
138#103—942no—
139#103—942no—
140#97—471no—
141#97C22×D4711yescharacteristic
142C4×C8—472no—
143C2×Q8—21no—
144C2×Q8—941no—
145C2×Q8—1881no—
146C2×Q8—1881no—
147C2×Q8—1884no—
148C22×C4—471no—
149C22×C4—941no—
150C22×C4—1881no—
151M16—1882no—
152C2×C8—472no—
153C2×C8D4×D4712yes—
154C4⋊C4—21no—
155C4⋊C4—41no—
156C4⋊C4—41no—
157C4⋊C4—941no—
158C4⋊C4—1881no—
159C4⋊C4—1881no—
160C4⋊C4—1882no—
161C4⋊C4—1881no—
162C22⋊C4—1881no—
163C42—471no—
164C42—941no—
165C42—1881no—
166C42C2×C4×D4711yescharacteristic
167C16—42no—
168C16—1882no—
169C23—471no—
170Q8—42no—
171Q8—3762no—
172Q8—3762no—
173Q8—1882no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—471no—
178C2×C4—941no—
179C2×C4—942no—
180C2×C4—3762no—
181C2×C4—1882no—
182C2×C4—1881no—
183C2×C4—1881no—
184C2×C4C22⋊C4×D4711yescharacteristic
185C8—22no—
186C8—942no—
187C22—941no—
188C22—1881no—
189C22#100×D4711yescharacteristic
190C4—41no—
191C4—81no—
192C4—81no—
193C4—942no—
194C4—941no—
195C4—3761no—
196C4—3761no—
197C4#1568913812yes—
198C2—21no—
199C2—1881no—
200C2#2024201011yescharacteristic
subgroupG/H
centerC2#20242010
commutatorC42×C47C22×C4
Frattini#97C22×D47
FittingC47×#1356C2
socleC2×C47#1533
prime radicalC22×D47#100
cosocle#97×C47C23
hypercenter#1356D47
hypocenterC47#11916
LCSG ▷ C42×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #1356

Complements

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

NH ≅ G/Ntype
3. #20241423C2semidirect
4. #20241422C2semidirect
5. C47×#1356C2semidirect
102. #1356D47semidirect
119. C47#11916semidirect

Maximal subgroups

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

subgroupindex
#202537672
#202451982
#202414232
#202414222
C47×#13562
#1191647