Finite Group Databasebeta

← #20245312

Subgroups — #20245312

Order 6016.

230 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 51 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
1C2×#13094043C211yesmaximal, characteristic, complemented
2C2×#13093969C211yesmaximal, characteristic, complemented
3C2×#13093965C211yesmaximal, characteristic, complemented
4#15689360C211yesmaximal, characteristic, complemented
5#15688926C211yesmaximal, characteristic, complemented
6(C2×D47)⋊C16C211yesmaximal, characteristic, complemented
7C47×#357C211yesmaximal, characteristic, complemented
8C2×#10625352—21no—
9#13094043—22no—
10#13094043—22no—
11C2×Dic188C2211yescharacteristic
12C2×#10625335—21no—
13C2×D376C2211yescharacteristic
14C2×C8×D47C2211yescharacteristic
15#13093999—21no—
16#13093969—22no—
17#13093965—22no—
18C2×C47⋊C16C2211yescharacteristic
19#13093944—21no—
20C2×D8×C47C2211yescharacteristic
21C2×C16×C47C2211yescharacteristic
22#107×C47C2211yescharacteristic
23C2×D4×C47—21no—
24C2×C22⋊D47—41no—
25C22×Dic47—41no—
26#10625352—24no—
27#10625352—42no—
28C2×D188—21no—
29C2×D188—41no—
30C2×C4×D47D411yescharacteristic
31C2×Dic94—21no—
32D8×C47—21no—
33D8×C47D412yescomplemented
34C2×C8×C47C2311yescharacteristic
35C4⋊C4×C47—21no—
36#10625335—24no—
37(C2×D47)⋊C4—41no—
38C2×C47⋊C8D411yescharacteristic
39Dic188—21no—
40Dic188D412yescomplemented
41D376—21no—
42D376—21no—
43C8×D47—21no—
44C8×D47—21no—
45C16×C47—21no—
46C47⋊C16—21no—
47C23×C47—41no—
48C22×D47—41no—
49C22×D47D811yescharacteristic
50D4×C47—22no—
51D4×C47—41no—
52C2×C4×C47—41no—
53C2×C4×C47C2×D411yescharacteristic
54C22⋊D47—44no—
55C2×Dic47—44no—
56C2×Dic47—41no—
57C2×Dic47D811yescharacteristic
58D188—41no—
59D188—41no—
60D188—82no—
61C4×D47—21no—
62C4×D47—21no—
63Dic94—22no—
64Dic94—41no—
65C8×C47C2×D411yescharacteristic
66C8×C47C2×D411yescharacteristic
67C47⋊C8—21no—
68C22×C47—42no—
69C22×C47—81no—
70C22×C47—81no—
71C22×C47C2×D811yescharacteristic
72C2×D47—21no—
73C2×D47—21no—
74C2×D47—21no—
75C2×D47—81no—
76C2×D47—81no—
77C2×D47—81no—
78C4×C47—81no—
79C4×C47#12011yescharacteristic
80C4×C47AGL(1,ℤ/8)11yescharacteristic
81Dic47—21no—
82Dic47—42no—
83#2186—471nomaximal, Sylow
84C2×C47—82no—
85C2×C47#44711yescharacteristic
86C2×C47#50811yescharacteristic
87C2×C47#50911yescharacteristic
88D47—41no—
89D47—161no—
90C2×#135—471no—
91C2×SD32—471no—
92C2×D16—471no—
93#466—471no—
94#358—471no—
95#357D4711yescharacteristic, complemented
96C22⋊C16—471no—
97C47#218611yescharacteristic, complemented, Sylow
98C2×#41—941no—
99#135—942no—
100#135—942no—
101C2×Q16—471no—
102C2×SD16—941no—
103C2×D8—471no—
104C2×D8C2×D4711yescharacteristic
105C22×C8—471no—
106#121—941no—
107SD32—942no—
108D16—942no—
109C2×C16—471no—
110C2×C16C2×D4711yescharacteristic
111#107C2×D4711yescharacteristic
112#102—941no—
113#41—944no—
114#41—1882no—
115C2×Q8—941no—
116C2×D4—21no—
117C2×D4—941no—
118C2×D4—1881no—
119C2×D4—1881no—
120C22×C4—471no—
121C22×C4—1881no—
122Q16—472no—
123Q16—941no—
124SD16—944no—
125D8—21no—
126D8—941no—
127D8—941no—
128D8D18812yescomplemented
129C2×C8—471no—
130C2×C8—941no—
131C2×C8—941no—
132C2×C8C22×D4711yescharacteristic
133C4⋊C4—21no—
134C22⋊C4—1881no—
135C16—21no—
136C16—941no—
137C23—41no—
138C23—471no—
139C23—1881no—
140Q8—942no—
141Q8—1881no—
142D4—22no—
143D4—41no—
144D4—3762no—
145D4—1884no—
146D4—1881no—
147D4—1881no—
148C2×C4—41no—
149C2×C4—471no—
150C2×C4—941no—
151C2×C4—941no—
152C2×C4—1884no—
153C2×C4—1881no—
154C2×C4D4×D4711yescharacteristic
155C8—941no—
156C8C2×D18811yescharacteristic
157C8D4×D4711yescharacteristic
158C22—42no—
159C22—81no—
160C22—81no—
161C22—941no—
162C22—941no—
163C22—941no—
164C22—3761no—
165C22—3761no—
166C22—3761no—
167C22D8×D4711yescharacteristic
168C4—81no—
169C4—941no—
170C4—1882no—
171C4#1309399411yescharacteristic
172C4#1309405111yescharacteristic
173C2—82no—
174C2—1881no—
175C2—7521no—
176C2#1568925811yescharacteristic
177C2#1568955411yescharacteristic
178C2#1568955711yescharacteristic
subgroupG/H
centerC22D8×D47
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×#357C2
socleC22×C47C2×D8
hypercenter#357D47
hypocenterC47#2186
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #357

Complements

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

NH ≅ G/Ntype
1. C2×#13094043C2semidirect
2. C2×#13093969C2semidirect
3. C2×#13093965C2semidirect
4. #15689360C2semidirect
5. #15688926C2semidirect
6. (C2×D47)⋊C16C2semidirect
7. C47×#357C2semidirect
33. D8×C47D4semidirect
40. Dic188D4semidirect
95. #357D47semidirect
97. C47#2186semidirect
128. D8D188semidirect