Finite Group Databasebeta

← #20245487

Subgroups — #20245487

Order 6016.

164 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 49 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×#13093967C211yesmaximal, characteristic, complemented
2C2×C16×D47C211yesmaximal, characteristic, complemented
3#15689361C211yesmaximal, characteristic, complemented
4#15689360C211yesmaximal, characteristic
5#15688950C211yesmaximal, characteristic, complemented
6#15688925C211yesmaximal, characteristic, complemented
7C47×#358C211yesmaximal, characteristic, complemented
8C2×D376C2211yescharacteristic
9C2×C8×D47C2211yescharacteristic
10#13094000—21no—
11#13093999—21no—
12#13093967—22no—
13C2×C47⋊C16C2211yescharacteristic
14C16×D47—22no—
15#13093958C2211yescharacteristic
16#13093948—21no—
17#13093944—21no—
18C2×Q16×C47C2211yescharacteristic
19C2×C16×C47C2211yescharacteristic
20#107×C47C2211yescharacteristic
21C2×Q8×C47—21no—
22C2×D188—21no—
23C2×D188—41no—
24C2×C4×D47D411yescharacteristic
25Q16×C47—21no—
26Q16×C47—21no—
27C2×C8×C47C2311yescharacteristic
28C4⋊C4×C47—21no—
29(C2×D47)⋊C4—41no—
30(C2×D47)⋊C4—41no—
31C4⋊Dic47—21no—
32Dic47⋊C4—41no—
33C2×C47⋊C8D411yescharacteristic
34D376—21no—
35D376—21no—
36C8×D47—21no—
37C8×D47—21no—
38C16×C47—21no—
39C47⋊C16D412yescomplemented
40C22×D47—41no—
41C22×D47D811yescharacteristic
42Q8×C47—41no—
43Q8×C47—41no—
44C2×C4×C47—41no—
45C2×C4×C47—41no—
46C2×C4×C47C2×D411yescharacteristic
47C2×Dic47—41no—
48C2×Dic47D811yescharacteristic
49D188—41no—
50D188—41no—
51D188—82no—
52C4×D47—21no—
53C4×D47—21no—
54C8×C47C2×D411yescharacteristic
55C8×C47#4111yescharacteristic
56C47⋊C8—21no—
57C22×C47C2×D811yescharacteristic
58C2×D47—21no—
59C2×D47—21no—
60C2×D47—81no—
61C2×D47—81no—
62C2×D47—81no—
63C2×D47SD3212yescomplemented
64C4×C47—81no—
65C4×C47—81no—
66C4×C47#12111yescharacteristic
67C4×C47#13511yescharacteristic
68Dic47—21no—
69Dic47—81no—
70#2217—471nomaximal, Sylow
71C2×C47#46611yescharacteristic
72C2×C47C2×SD3211yescharacteristic
73C2×C47#50811yescharacteristic
74D47—22no—
75D47—161no—
76C2×SD32—471no—
77C22×C16—471no—
78#467—471no—
79#466—471no—
80#367—471no—
81#358D4711yescharacteristic, complemented
82#357—471no—
83C47#221711yescharacteristic, complemented, Sylow
84C2×Q16C2×D4711yescharacteristic
85C2×D8—471no—
86C22×C8—471no—
87C22⋊Q8—941no—
88#121—941no—
89SD32—942no—
90C2×C16—471no—
91C2×C16—942no—
92C2×C16C2×D4711yescharacteristic
93#107—471no—
94#107C2×D4711yescharacteristic
95#103—941no—
96#102—941no—
97C2×Q8—21no—
98C2×D4—941no—
99C2×D4—1881no—
100C22×C4—471no—
101Q16—21no—
102Q16—21no—
103D8—941no—
104D8—941no—
105C2×C8—471no—
106C2×C8—941no—
107C2×C8—941no—
108C2×C8C22×D4711yescharacteristic
109C4⋊C4—21no—
110C4⋊C4—941no—
111C4⋊C4—1881no—
112C22⋊C4—1881no—
113C22⋊C4—1881no—
114C16—21no—
115C16—472no—
116C23—471no—
117C23—1881no—
118Q8—41no—
119Q8—41no—
120D4—3762no—
121D4—1881no—
122D4—1881no—
123C2×C4—41no—
124C2×C4—41no—
125C2×C4—471no—
126C2×C4—941no—
127C2×C4—941no—
128C2×C4—1881no—
129C2×C4D4×D4711yescharacteristic
130C8—941no—
131C8#1062535011yescharacteristic
132C8D4×D4711yescharacteristic
133C22—472no—
134C22—941no—
135C22—941no—
136C22—3761no—
137C22—3761no—
138C22—3761no—
139C22D8×D4711yescharacteristic
140C4—81no—
141C4—81no—
142C4—941no—
143C4—3761no—
144C4#1309399711yescharacteristic
145C4#1309404511yescharacteristic
146C2—942no—
147C2—7521no—
148C2#1568935811yescharacteristic
149C2SD32×D4711yescharacteristic
150C2#1568955611yescharacteristic
subgroupG/H
centerC22D8×D47
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×#358C2
socleC22×C47C2×D8
hypercenter#358D47
hypocenterC47#2217
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
1. C2×#13093967C2semidirect
2. C2×C16×D47C2semidirect
3. #15689361C2semidirect
5. #15688950C2semidirect
6. #15688925C2semidirect
7. C47×#358C2semidirect
39. C47⋊C16D4semidirect
63. C2×D47SD32semidirect
81. #358D47semidirect
83. C47#2217semidirect