Finite Group Databasebeta

← #26136893

Subgroups — #26136893

Order 12032.

182 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 59 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#20245705C211yesmaximal, characteristic
2#20245274C211yesmaximal, characteristic
3#20245258C211yesmaximal, characteristic, complemented
4#20241593C211yesmaximal, characteristic, complemented
5#20241582C211yesmaximal, characteristic, complemented
6#20241523C211yesmaximal, characteristic, complemented
7C47×#1418C211yesmaximal, characteristic
8C2×Dic376C2211yescharacteristic
9#15689240—21no—
10#15689217—21no—
11#15688963C412yescomplemented
12#15688961C412yescomplemented
13#15688957C2211yescharacteristic
14#15688953C2211yescharacteristic
15#15688930—21no—
16#15688926—21no—
17#15688898C2211yescharacteristic
18C47×#508C2211yescharacteristic
19C47×M64C2211yescharacteristic
20C47×#367C2211yescharacteristic
21C2×Dic188—21no—
22#13094031—41no—
23#13093989—41no—
24Dic376—21no—
25Dic376C2×C412yes—
26C2×C47⋊C16D411yescharacteristic
27#13093960—21no—
28#13093951—41no—
29#13093947—41no—
30C8×Dic47D411yescharacteristic
31C47⋊C32C2×C412yes—
32#135×C47—21no—
33Q32×C47C2×C411yescharacteristic
34SD32×C47—21no—
35D16×C47C2×C411yescharacteristic
36C2×C16×C47C2311yescharacteristic
37#107×C47—21no—
38C32×C47—21no—
39#41×C47—41no—
40C2×Dic94—41no—
41Q16×C47—21no—
42SD16×C47—41no—
43D8×C47—21no—
44C2×C8×C47C2×D411yescharacteristic
45C4⋊C4×C47—41no—
46Dic47⋊C4—81no—
47C4×Dic47—81no—
48C4×Dic47D811yescharacteristic
49#10625329—41no—
50#10625329—81no—
51C2×C47⋊C8—81no—
52C2×C47⋊C8D811yescharacteristic
53Dic188—22no—
54Dic188—41no—
55C16×C47C22×C411yescharacteristic
56C16×C47#4111yescharacteristic
57C47⋊C16—21no—
58Q8×C47—41no—
59D4×C47—41no—
60D4×C47—81no—
61C2×C4×C47—81no—
62C2×C4×C47—81no—
63C2×C4×C47C2×D811yescharacteristic
64C2×Dic47—21no—
65C2×Dic47—81no—
66Dic94—42no—
67Dic94—81no—
68C8×C47C4×D411yescharacteristic
69C8×C47#13511yescharacteristic
70C47⋊C8—21no—
71C47⋊C8—81no—
72#13657—471nomaximal, Sylow
73C22×C47—81no—
74C22×C47#50911yescharacteristic
75C4×C47—81no—
76C4×C47—161no—
77C4×C47C4×D811yescharacteristic
78C4×C47#50911yescharacteristic
79Dic47—41no—
80Dic47—82no—
81#2264—471no—
82#2179—471no—
83#2176—471no—
84#1426—471no—
85#1420—471no—
86#1418D4711yescharacteristic
87#1398—471no—
88C2×C47—21no—
89C2×C47—161no—
90C2×C47#217711yescharacteristic
91#508C2×D4711yescharacteristic
92C2×Q32—471no—
93#443—941no—
94C4×Q16—941no—
95Q64—472no—
96SD64—472no—
97M64—471no—
98M64C2×D4711yescharacteristic
99#368—471no—
100#367C2×D4711yescharacteristic
101#359—941no—
102#358—941no—
103#346—471no—
104C47#1365711yescharacteristic, complemented, Sylow
105#135—21no—
106C2×Q16—941no—
107#131—1881no—
108C4×Q8—1881no—
109Q32—472no—
110Q32—941no—
111Q32C4×D4711yescharacteristic
112SD32—21no—
113D16C4×D4711yescharacteristic
114C2×C16—471no—
115C2×C16C22×D4711yescharacteristic
116#108—941no—
117#107—21no—
118#104—1881no—
119#103—1881no—
120C4×C8—471no—
121C32—21no—
122C32—472no—
123#41—41no—
124C2×Q8—1881no—
125Q16—21no—
126Q16—942no—
127Q16—1881no—
128SD16—41no—
129D8—21no—
130M16—3761no—
131M16—1881no—
132C2×C8—471no—
133C2×C8—3761no—
134C2×C8D4×D4711yescharacteristic
135C4⋊C4—41no—
136C4⋊C4—3761no—
137C42—471no—
138C42—3761no—
139C16—941no—
140C16C2×C4×D4711yescharacteristic
141C16#1062535211yescharacteristic
142Q8—41no—
143Q8—3761no—
144Q8—1882no—
145D4—41no—
146D4—81no—
147C2×C4—81no—
148C2×C4—81no—
149C2×C4—941no—
150C2×C4—3761no—
151C2×C4D8×D4711yescharacteristic
152C8—941no—
153C8—3761no—
154C8(C22⋊D47)⋊C411yescharacteristic
155C8#1309404511yescharacteristic
156C22—81no—
157C22#1568955711yescharacteristic
158C4—81no—
159C4—161no—
160C4—3762no—
161C4—1881no—
162C4#1568920311yescharacteristic
163C4#1568956011yescharacteristic
164C2—21no—
165C2—161no—
166C2#2024526111yescharacteristic
subgroupG/H
centerC2#20245261
commutatorC16×C47C22×C4
FrattiniC2×C16C22×D47
FittingC47×#1418C2
socleC2×C47#2177
prime radicalC47×#508C22
cosocleC2×C16×C47C23
hypercenter#1418D47
hypocenterC47#13657
LCSG ▷ C16×C47 ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1418

Complements

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

NH ≅ G/Ntype
3. #20245258C2semidirect
4. #20241593C2semidirect
5. #20241582C2semidirect
6. #20241523C2semidirect
11. #15688963C4semidirect
12. #15688961C4semidirect
104. C47#13657semidirect

Maximal subgroups

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

subgroupindex
#202457052
#202452742
#202452582
#202415932
#202415822
#202415232
C47×#14182
#1365747