Finite Group Databasebeta

← #22590545

Subgroups — #22590545

Order 9088.

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

normal subgroups only

This group has 132 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
1#17986037C211yesmaximal, characteristic
2#17985826C211yesmaximal, characteristic, complemented
3#17985824C211yesmaximal, characteristic, complemented
4#17985803C211yesmaximal, characteristic, complemented
5#17985803C211yesmaximal, characteristic, complemented
6C22⋊(C71⋊C16)C211yesmaximal, characteristic
7#467×C71C211yesmaximal, characteristic
8#14556087—21no—
9C2×C71⋊C16C2211yescharacteristic
10C2×C71⋊C16C2211yescharacteristic
11#14556062C2211yescharacteristic
12#14556062C2211yescharacteristic
13#14556060—21no—
14C2×Q16×C71C2211yescharacteristic
15C22×C8×C71C2211yescharacteristic
16C22⋊Q8×C71—21no—
17#107×C71C2211yescharacteristic
18#103×C71—21no—
19C4⋊Dic71—21no—
20C4⋊Dic71—21no—
21C22⋊Dic71—41no—
22C4×Dic71—41no—
23C71⋊C16—21no—
24C71⋊C16—21no—
25C2×Q8×C71—21no—
26C22×C4×C71D411yescharacteristic
27Q16×C71—21no—
28Q16×C71—21no—
29C2×C8×C71—21no—
30C2×C8×C71—21no—
31C2×C8×C71D411yescharacteristic
32C2×C8×C71C2311yescharacteristic
33C4⋊C4×C71—21no—
34C4⋊C4×C71—41no—
35C22⋊C4×C71—41no—
36C23×C71D811yescharacteristic
37Q8×C71—41no—
38Q8×C71—41no—
39C2×C4×C71—21no—
40C2×C4×C71—21no—
41C2×C4×C71—41no—
42C2×C4×C71—41no—
43C2×C4×C71D811yescharacteristic
44C2×C4×C71C2×D411yescharacteristic
45C2×Dic71—41no—
46C2×Dic71—41no—
47C8×C71—21no—
48C8×C71#4111yescharacteristic
49C8×C71#4111yescharacteristic
50C22×C71—21no—
51C22×C71—21no—
52C22×C71—21no—
53C22×C71C2×D811yescharacteristic
54C4×C71—21no—
55C4×C71—81no—
56C4×C71—81no—
57C4×C71#12311yescharacteristic
58C4×C71#13711yescharacteristic
59Dic71—81no—
60Dic71—81no—
61C2×C71—41no—
62C2×C71#48011yescharacteristic
63C2×C71#50811yescharacteristic
64C2×C71#51011yescharacteristic
65#2237—711nomaximal, Sylow
66C71#223711yescharacteristic, complemented, Sylow
67#467D7111yescharacteristic
68#427—711no—
69#367—711no—
70#366—711no—
71#358—711no—
72#358—711no—
73C22⋊C16—711no—
74C2×Q16C2×D7111yescharacteristic
75C22×C8C2×D7111yescharacteristic
76C22⋊Q8—21no—
77#117—1421no—
78C2×C16—711no—
79C2×C16—711no—
80#107—711no—
81#107—711no—
82#107C2×D7111yescharacteristic
83#106—1421no—
84#103—21no—
85C2×Q8—21no—
86C22×C4C22⋊D7111yescharacteristic
87Q16—21no—
88Q16—21no—
89C2×C8—21no—
90C2×C8—21no—
91C2×C8C22⋊D7111yescharacteristic
92C2×C8C22×D7111yescharacteristic
93C4⋊C4—21no—
94C4⋊C4—41no—
95C4⋊C4—1421no—
96C4⋊C4—1421no—
97C22⋊C4—41no—
98C22⋊C4—2841no—
99C42—2841no—
100C16—1421no—
101C16—1421no—
102C23#1176585011yescharacteristic
103Q8—41no—
104Q8—41no—
105C2×C4—21no—
106C2×C4—21no—
107C2×C4—41no—
108C2×C4—41no—
109C2×C4—2841no—
110C2×C4—2841no—
111C2×C4#1176585011yescharacteristic
112C2×C4C2×C22⋊D7111yescharacteristic
113C8—21no—
114C8#1176586411yescharacteristic
115C8#1176586411yescharacteristic
116C22—21no—
117C22—21no—
118C22—21no—
119C22C2×#1176585011yescharacteristic
120C4—21no—
121C4—81no—
122C4—81no—
123C4—5681no—
124C4—5681no—
125C4#1455610911yescharacteristic
126C4#1455615811yescharacteristic
127C2—41no—
128C2#1798631011yescharacteristic
129C2#1798642911yescharacteristic
130C2#1798644011yescharacteristic
subgroupG/H
centerC22C2×#11765850
commutatorC2×C8×C71C23
FrattiniC2×C8C22×D71
Fitting#467×C71C2
socleC22×C71C2×D8
hypercenter#467D71
hypocenterC71#2237
LCSG ▷ C2×C8×C71 ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #467

Complements

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

NH ≅ G/Ntype
2. #17985826C2semidirect
3. #17985824C2semidirect
4. #17985803C2semidirect
5. #17985803C2semidirect
66. C71#2237semidirect