Finite Group Databasebeta

← #22590446

Subgroups — #22590446

Order 9088.

150 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 51 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×#14556074C211yesmaximal, characteristic, complemented
2C2×#14556068C211yesmaximal, characteristic
3#17986240C211yesmaximal, characteristic
4#17985826C211yesmaximal, characteristic, complemented
5#17985803C211yesmaximal, characteristic, complemented
6#17985802C211yesmaximal, characteristic, complemented
7#467×C71C211yesmaximal, characteristic
8C2×Dic284C2211yescharacteristic
9#14556107—21no—
10#14556074—22no—
11#14556068—22no—
12C2×C71⋊C16C2211yescharacteristic
13C2×C71⋊C16C2211yescharacteristic
14#14556062C2211yescharacteristic
15#14556053—21no—
16C2×Q16×C71C2211yescharacteristic
17C22×C8×C71C2211yescharacteristic
18C22⋊Q8×C71—21no—
19#107×C71C2211yescharacteristic
20#103×C71—21no—
21C2×Dic142—21no—
22Dic284—21no—
23Dic284—21no—
24C4⋊Dic71—21no—
25Dic71⋊C4—41no—
26C22⋊Dic71—41no—
27C71⋊C16—21no—
28C71⋊C16D412yes—
29C2×Q8×C71—21no—
30C22×C4×C71D411yescharacteristic
31Q16×C71—21no—
32Q16×C71—21no—
33C2×C8×C71—21no—
34C2×C8×C71—21no—
35C2×C8×C71D411yescharacteristic
36C2×C8×C71C2311yescharacteristic
37C4⋊C4×C71—21no—
38C4⋊C4×C71—41no—
39C22⋊C4×C71—41no—
40C23×C71D811yescharacteristic
41Q8×C71—41no—
42Q8×C71—41no—
43C2×C4×C71—21no—
44C2×C4×C71—21no—
45C2×C4×C71—41no—
46C2×C4×C71—41no—
47C2×C4×C71D811yescharacteristic
48C2×C4×C71C2×D411yescharacteristic
49C2×Dic71—41no—
50C2×Dic71—41no—
51Dic142—41no—
52Dic142—41no—
53C8×C71—21no—
54C8×C71C2×D411yescharacteristic
55C8×C71#4111yescharacteristic
56C22×C71—21no—
57C22×C71—21no—
58C22×C71—21no—
59C22×C71C2×D811yescharacteristic
60C4×C71—21no—
61C4×C71—81no—
62C4×C71—81no—
63C4×C71#12111yescharacteristic
64C4×C71#13511yescharacteristic
65Dic71—81no—
66Dic71—81no—
67C2×C71—41no—
68C2×C71#46611yescharacteristic
69C2×C71#51011yescharacteristic
70C2×C71#51011yescharacteristic
71#2219—711nomaximal, Sylow
72C71#221911yescharacteristic, complemented, Sylow
73C2×Q32—711no—
74C2×M32—711no—
75#467—711no—
76#467D7111yescharacteristic
77#367—711no—
78#358—711no—
79#358—711no—
80C2×Q16—711no—
81C2×Q16C2×D7111yescharacteristic
82C22×C8C2×D7111yescharacteristic
83C22⋊Q8—21no—
84C22⋊Q8—1421no—
85Q32—1422no—
86M32—1422no—
87C2×C16—711no—
88C2×C16—711no—
89#107—711no—
90#107C2×D7111yescharacteristic
91#103—21no—
92#103—1421no—
93C2×Q8—21no—
94C2×Q8—1421no—
95C22×C4C22⋊D7111yescharacteristic
96Q16—21no—
97Q16—21no—
98Q16—1421no—
99Q16—1421no—
100C2×C8—21no—
101C2×C8—21no—
102C2×C8C22⋊D7111yescharacteristic
103C2×C8C22×D7111yescharacteristic
104C4⋊C4—21no—
105C4⋊C4—41no—
106C4⋊C4—2841no—
107C4⋊C4—1421no—
108C22⋊C4—41no—
109C22⋊C4—2841no—
110C16—712no—
111C16—1421no—
112C23#1176585011yescharacteristic
113Q8—41no—
114Q8—41no—
115Q8—2841no—
116Q8—2841no—
117C2×C4—21no—
118C2×C4—21no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—2841no—
122C2×C4—2841no—
123C2×C4#1176585011yescharacteristic
124C2×C4C2×C22⋊D7111yescharacteristic
125C8—21no—
126C8D4×D7111yescharacteristic
127C8#1176586411yescharacteristic
128C22—21no—
129C22—21no—
130C22—21no—
131C22C2×#1176585011yescharacteristic
132C4—21no—
133C4—81no—
134C4—81no—
135C4—5681no—
136C4—5681no—
137C4#1455610011yescharacteristic
138C4#1455614811yescharacteristic
139C2—41no—
140C2#1798623311yescharacteristic
141C2#1798643911yescharacteristic
142C2#1798644011yescharacteristic
subgroupG/H
centerC22C2×#11765850
commutatorC2×C8×C71C23
FrattiniC2×C8C22×D71
Fitting#467×C71C2
socleC22×C71C2×D8
hypercenter#467D71
hypocenterC71#2219
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
1. C2×#14556074C2semidirect
4. #17985826C2semidirect
5. #17985803C2semidirect
6. #17985802C2semidirect
72. C71#2219semidirect