Finite Group Databasebeta

← #22590546

Subgroups — #22590546

Order 9088.

132 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 45 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#17986237C211yesmaximal, characteristic
2#17986036C211yesmaximal, characteristic
3#17985827C211yesmaximal, characteristic, complemented
4#17985824C211yesmaximal, characteristic, complemented
5#17985803C211yesmaximal, characteristic, complemented
6(C2×D71)⋊C16C211yesmaximal, characteristic
7#358×C71C211yesmaximal, characteristic, complemented
8C2×C8×D71C2211yescharacteristic
9#14556104—21no—
10#14556086—21no—
11C2×C71⋊C16C2211yescharacteristic
12#14556062C2211yescharacteristic
13#14556062C2211yescharacteristic
14#14556059—21no—
15#14556052—21no—
16C2×Q16×C71C2211yescharacteristic
17C2×C16×C71C2211yescharacteristic
18#107×C71C2211yescharacteristic
19C2×C4×D71D411yescharacteristic
20C2×C71⋊C8D411yescharacteristic
21C8×D71—21no—
22C8×D71—21no—
23C4⋊Dic71—21no—
24C4⋊Dic71—21no—
25Dic71⋊C4—41no—
26(C2×D71)⋊C4—41no—
27(C2×D71)⋊C4—41no—
28C4×Dic71—41no—
29C71⋊C16—21no—
30C2×Q8×C71—21no—
31Q16×C71—21no—
32Q16×C71—21no—
33C2×C8×C71C2311yescharacteristic
34C4⋊C4×C71—21no—
35C16×C71—21no—
36C22×D71D811yescharacteristic
37Q8×C71—41no—
38Q8×C71—41no—
39C2×C4×C71—41no—
40C2×C4×C71—41no—
41C2×C4×C71C2×D411yescharacteristic
42C2×Dic71—41no—
43C2×Dic71—41no—
44C2×Dic71D811yescharacteristic
45C4×D71—21no—
46C4×D71—21no—
47C8×C71#4111yescharacteristic
48C8×C71#4111yescharacteristic
49C71⋊C8—21no—
50C22×C71C2×D811yescharacteristic
51C2×D71—21no—
52C2×D71—21no—
53C2×D71—21no—
54C4×C71—81no—
55C4×C71—81no—
56C4×C71#12311yescharacteristic
57C4×C71#13711yescharacteristic
58Dic71—21no—
59Dic71—81no—
60Dic71—81no—
61C2×C71#48011yescharacteristic
62C2×C71#50811yescharacteristic
63C2×C71#51011yescharacteristic
64D71—41no—
65#2237—711nomaximal, Sylow
66C71#223711yescharacteristic, complemented, Sylow
67#467—711no—
68#427—711no—
69#367—711no—
70#366—711no—
71#358—711no—
72#358D7111yescharacteristic, complemented
73C22⋊C16—711no—
74C2×Q16C2×D7111yescharacteristic
75C22×C8—711no—
76C22⋊Q8—1421no—
77#117—1421no—
78C2×C16—711no—
79C2×C16C2×D7111yescharacteristic
80#107—711no—
81#107—711no—
82#107C2×D7111yescharacteristic
83#106—1421no—
84#103—1421no—
85C2×Q8—21no—
86C22×C4—711no—
87Q16—21no—
88Q16—21no—
89C2×C8—711no—
90C2×C8—1421no—
91C2×C8—1421no—
92C2×C8C22×D7111yescharacteristic
93C4⋊C4—21no—
94C4⋊C4—2841no—
95C4⋊C4—1421no—
96C4⋊C4—1421no—
97C22⋊C4—2841no—
98C22⋊C4—2841no—
99C42—2841no—
100C16—21no—
101C16—1421no—
102C23—711no—
103Q8—41no—
104Q8—41no—
105C2×C4—41no—
106C2×C4—41no—
107C2×C4—2841no—
108C2×C4—2841no—
109C2×C4—711no—
110C2×C4—1421no—
111C2×C4—1421no—
112C2×C4D4×D7111yescharacteristic
113C8—1421no—
114C8#1176586411yescharacteristic
115C8#1176586511yescharacteristic
116C22—1421no—
117C22—1421no—
118C22—1421no—
119C22D8×D7111yescharacteristic
120C4—81no—
121C4—81no—
122C4—5681no—
123C4—5681no—
124C4—1421no—
125C4#1455611011yescharacteristic
126C4#1455615711yescharacteristic
127C2—2841no—
128C2#1798631111yescharacteristic
129C2#1798643011yescharacteristic
130C2#1798644111yescharacteristic
subgroupG/H
centerC22D8×D71
commutatorC2×C8×C71C23
FrattiniC2×C8C22×D71
Fitting#358×C71C2
socleC22×C71C2×D8
hypercenter#358D71
hypocenterC71#2237
LCSG ▷ C2×C8×C71 ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
3. #17985827C2semidirect
4. #17985824C2semidirect
5. #17985803C2semidirect
7. #358×C71C2semidirect
66. C71#2237semidirect
72. #358D71semidirect