Finite Group Databasebeta

← #22586363

Subgroups — #22586363

Order 9088.

154 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 35 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#17985935C211yesmaximal, characteristic
2#17985723C211yesmaximal, characteristic
3#342×C71C211yesmaximal, characteristic
4C2×C4⋊Dic71C411yescharacteristic, complemented
5C2×Dic71⋊C4—21no—
6C2×C22⋊Dic71—21no—
7C22⋊(C71⋊C8)—21no—
8C71⋊#95C411yescharacteristic, complemented
9C2×C22⋊C4×C71—21no—
10C2×C22⋊C4×C71C2211yescharacteristic
11C22×Dic71—21no—
12C22×Dic71—21no—
13C2×C71⋊C8—41no—
14C4⋊Dic71—41no—
15Dic71⋊C4—42no—
16C22⋊Dic71—42no—
17C24×C71D411yescharacteristic
18C22×C4×C71—41no—
19C22×C4×C71C2×C411yescharacteristic
20C22×C4×C71D411yescharacteristic
21C22⋊C4×C71—22no—
22C22⋊C4×C71—41no—
23C22⋊C4×C71—41no—
24C23×C71—21no—
25C23×C71—21no—
26C23×C71—41no—
27C23×C71—41no—
28C23×C71C22⋊C411yescharacteristic
29C23×C71SD1611yescharacteristic
30C23×C71Q1611yescharacteristic
31C2×C4×C71—21no—
32C2×C4×C71—21no—
33C2×C4×C71—41no—
34C2×C4×C71—41no—
35C2×C4×C71—42no—
36C2×C4×C71—81no—
37C2×C4×C71—81no—
38C2×Dic71—22no—
39C2×Dic71—41no—
40C2×Dic71—41no—
41C2×Dic71—41no—
42C2×Dic71—41no—
43C2×Dic71—41no—
44C71⋊C8—81no—
45C22×C71—21no—
46C22×C71—21no—
47C22×C71—21no—
48C22×C71—21no—
49C22×C71—41no—
50C22×C71—41no—
51C22×C71—41no—
52C22×C71—41no—
53C22×C71—81no—
54C22×C71#9911yescharacteristic
55C22×C71#10311yescharacteristic
56C22×C71#10411yescharacteristic
57C4×C71—41no—
58C4×C71—41no—
59C4×C71—82no—
60Dic71—42no—
61Dic71—81no—
62C2×C71—21no—
63C2×C71—21no—
64C2×C71—41no—
65C2×C71—41no—
66C2×C71#32811yescharacteristic
67C2×C71#35211yescharacteristic
68C2×C71#35311yescharacteristic
69#1352—711nomaximal, Sylow
70C71#135211yescharacteristic, complemented, Sylow
71#399—711no—
72#342D7111yescharacteristic
73#323—711no—
74C2×C4⋊C4—711no—
75C2×C4⋊C4—1421no—
76C2×C22⋊C4—21no—
77C2×C22⋊C4—1421no—
78C2×C22⋊C4C2×D7111yescharacteristic
79C22⋊C8—1421no—
80#95—711no—
81C24C22⋊D7111yescharacteristic
82C22×C4—41no—
83C22×C4—1421no—
84C22×C4—1421no—
85C22×C4C4×D7111yescharacteristic
86C22×C4D28411yescharacteristic
87C2×C8—2841no—
88C4⋊C4—2841no—
89C4⋊C4—2842no—
90C22⋊C4—22no—
91C22⋊C4—41no—
92C22⋊C4—41no—
93C22⋊C4—2842no—
94C23—21no—
95C23—21no—
96C23—41no—
97C23—41no—
98C23(C2×D71)⋊C411yescharacteristic
99C23#1176585311yescharacteristic
100C23#1176585511yescharacteristic
101C2×C4—21no—
102C2×C4—21no—
103C2×C4—41no—
104C2×C4—41no—
105C2×C4—42no—
106C2×C4—81no—
107C2×C4—81no—
108C2×C4—2841no—
109C2×C4—2841no—
110C2×C4—2841no—
111C2×C4—2841no—
112C2×C4—2841no—
113C2×C4—1422no—
114C8—5681no—
115C22—21no—
116C22—21no—
117C22—21no—
118C22—21no—
119C22—41no—
120C22—41no—
121C22—41no—
122C22—41no—
123C22—81no—
124C22#1455604211yescharacteristic
125C22#1455605111yescharacteristic
126C22#1455605611yescharacteristic
127C4—41no—
128C4—41no—
129C4—82no—
130C4—2842no—
131C4—5681no—
132C2—21no—
133C2—21no—
134C2—41no—
135C2—41no—
136C2#1798573511yescharacteristic
137C2#1798578811yescharacteristic
138C2#1798579111yescharacteristic
subgroupG/H
centerC22#14556042
commutatorC22×C4×C71C2×C4
FrattiniC2×C22⋊C4C2×D71
Fitting#342×C71C2
socleC22×C71#99
hypercenter#342D71
hypocenterC71#1352
LCSG ▷ C22×C4×C71 ▷ C23×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #342

Complements

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

NH ≅ G/Ntype
4. C2×C4⋊Dic71C4semidirect
8. C71⋊#95C4semidirect
70. C71#1352semidirect