Finite Group Databasebeta

← #22590536

Subgroups — #22590536

Order 9088.

140 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 47 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#107×D71C211yesmaximal, characteristic
3#17985827C211yesmaximal, characteristic, complemented
4#17985826C211yesmaximal, characteristic, complemented
5#17985803C211yesmaximal, characteristic, complemented
6(C2×D71)⋊C16C211yesmaximal, characteristic
7#358×C71C211yesmaximal, characteristic, complemented
8C2×C8×D71C2211yescharacteristic
9#14556104—21no—
10C4⋊C4×D71—21no—
11C2×C71⋊C16C2211yescharacteristic
12#14556062C2211yescharacteristic
13#14556062C2211yescharacteristic
14#14556061—21no—
15#14556052—21no—
16C2×Q16×C71C2211yescharacteristic
17C2×C16×C71C2211yescharacteristic
18#107×C71C2211yescharacteristic
19C2×C4×D71—41no—
20C2×C4×D71D411yescharacteristic
21C2×C71⋊C8D411yescharacteristic
22C8×D71—21no—
23C8×D71—21no—
24C4⋊Dic71—21no—
25C4⋊Dic71—21no—
26Dic71⋊C4—41no—
27Dic71⋊C4—41no—
28(C2×D71)⋊C4—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—
47C4×D71—82no—
48C8×C71#4111yescharacteristic
49C8×C71#4111yescharacteristic
50C71⋊C8—21no—
51C22×C71C2×D811yescharacteristic
52C2×D71—21no—
53C2×D71—21no—
54C2×D71SD3212yes—
55C4×C71—81no—
56C4×C71—81no—
57C4×C71#12311yescharacteristic
58C4×C71#13711yescharacteristic
59Dic71—21no—
60Dic71—81no—
61Dic71—81no—
62C2×C71#48011yescharacteristic
63C2×C71C2×SD3211yescharacteristic
64C2×C71#51011yescharacteristic
65D71—22no—
66#2235—711nomaximal, Sylow
67C71#223511yescharacteristic, complemented, Sylow
68#467—711no—
69C2×#107—711no—
70#367—711no—
71#367—711no—
72#358—711no—
73#358D7111yescharacteristic, complemented
74C22⋊C16—711no—
75C2×Q16C2×D7111yescharacteristic
76C22×C8—711no—
77C22⋊Q8—1421no—
78C2×C4⋊C4—1421no—
79C2×C16—711no—
80C2×C16C2×D7111yescharacteristic
81#107—711no—
82#107—711no—
83#107—1421no—
84#107C2×D7111yescharacteristic
85#103—1421no—
86C2×Q8—21no—
87C22×C4—2841no—
88C22×C4—711no—
89Q16—21no—
90Q16—21no—
91C2×C8—711no—
92C2×C8—1421no—
93C2×C8—1421no—
94C2×C8C22×D7111yescharacteristic
95C4⋊C4—21no—
96C4⋊C4—2841no—
97C4⋊C4—2841no—
98C4⋊C4—1421no—
99C4⋊C4—1421no—
100C22⋊C4—2841no—
101C16—21no—
102C16—1421no—
103C23—711no—
104Q8—41no—
105Q8—41no—
106C2×C4—41no—
107C2×C4—41no—
108C2×C4—2841no—
109C2×C4—2841no—
110C2×C4—5682no—
111C2×C4—711no—
112C2×C4—1421no—
113C2×C4—1421no—
114C2×C4D4×D7111yescharacteristic
115C8—1421no—
116C8#1176586411yescharacteristic
117C8#1176586511yescharacteristic
118C22—712no—
119C22—1421no—
120C22—1421no—
121C22D8×D7111yescharacteristic
122C4—81no—
123C4—81no—
124C4—5681no—
125C4—5681no—
126C4—1421no—
127C4#1455611011yescharacteristic
128C4#1455615711yescharacteristic
129C2—1422no—
130C2#1798631111yescharacteristic
131C2SD32×D7111yescharacteristic
132C2#1798644111yescharacteristic
subgroupG/H
centerC22D8×D71
commutatorC2×C8×C71C23
FrattiniC2×C8C22×D71
Fitting#358×C71C2
socleC22×C71C2×D8
hypercenter#358D71
hypocenterC71#2235
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. #17985826C2semidirect
5. #17985803C2semidirect
7. #358×C71C2semidirect
67. C71#2235semidirect
73. #358D71semidirect