Finite Group Databasebeta

← #22587633

Subgroups — #22587633

Order 9088.

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

normal subgroups only

This group has 230 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#17986389C212yesmaximal, complemented
2#17986365C211yesmaximal, characteristic, complemented
3#17985741C211yesmaximal, characteristic, complemented
4#17985739C212yesmaximal, complemented
5#562×C71C211yesmaximal, characteristic, complemented
6C2×#11765852—22no—
7C2×#11765850—22no—
8#14556125C2211yescharacteristic
9#14556048—22no—
10#14556039C2211yescharacteristic
11#14556039C2212yes—
12#125×C71C2211yescharacteristic
13#124×C71C2212yes—
14#123×C71—22no—
15C22⋊Q8×C71—22no—
16#121×C71—22no—
17C2×D284—21no—
18C2×D284—22no—
19#11765852—44no—
20#11765850—44no—
21C2×C71⋊C8—22no—
22C2×C71⋊C8—21no—
23C2×Q8×C71D412yes—
24C2×D4×C71—22no—
25C2×D4×C71D412yes—
26C22×C4×C71—22no—
27C4⋊C4×C71—22no—
28C4⋊C4×C71—22no—
29C4⋊C4×C71D412yes—
30C22⋊C4×C71—22no—
31C22⋊C4×C71—22no—
32C22⋊C4×C71—22no—
33C42×C71C2311yescharacteristic
34C23×C71—22no—
35C22×D71—41no—
36Q8×C71—42no—
37D4×C71—42no—
38D4×C71—82no—
39C2×C4×C71—22no—
40C2×C4×C71—22no—
41C2×C4×C71—82no—
42C2×C4×C71C2×D411yescharacteristic
43C2×C4×C71C2×D412yes—
44D284—42no—
45D284—42no—
46D284—42no—
47C71⋊C8—24no—
48C71⋊C8—41no—
49C22×C71—42no—
50C22×C71—42no—
51C22×C71—42no—
52C22×C71#12011yescharacteristic
53C2×D71—82no—
54C2×D71—81no—
55C4×C71—22no—
56C4×C71—21no—
57C4×C71—42no—
58C4×C71—42no—
59C2×C71—82no—
60C2×C71#45312yes—
61C2×C71#45411yescharacteristic
62D71—161no—
63#1656—711nomaximal, Sylow
64C71#165611yescharacteristic, complemented, Sylow
65#562D7111yescharacteristic, complemented
66#496—712no—
67#490—711no—
68#330—711no—
69#329—712no—
70C2×SD16—1422no—
71C2×D8—1422no—
72#127—711no—
73#125C2×D7111yescharacteristic
74#124C2×D7112yes—
75#123—22no—
76C22⋊Q8—22no—
77#121—22no—
78#102—1422no—
79#97—711no—
80#97—712no—
81C2×Q8C22⋊D7112yes—
82C2×D4—22no—
83C2×D4—1421no—
84C2×D4—1422no—
85C2×D4C22⋊D7112yes—
86C22×C4—22no—
87SD16—2844no—
88D8—2844no—
89C2×C8—1421no—
90C2×C8—1422no—
91C4⋊C4—22no—
92C4⋊C4—22no—
93C4⋊C4C22⋊D7112yes—
94C22⋊C4—22no—
95C22⋊C4—22no—
96C22⋊C4—22no—
97C42C22×D7111yescharacteristic
98C23—22no—
99C23—2841no—
100Q8—42no—
101D4—42no—
102D4—82no—
103D4—2842no—
104D4—2842no—
105D4—2842no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—82no—
109C2×C4C2×C22⋊D7111yescharacteristic
110C2×C4C2×C22⋊D7112yes—
111C8—2841no—
112C8—1424no—
113C22—42no—
114C22—42no—
115C22—42no—
116C22—5682no—
117C22—5681no—
118C22#1455609711yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—42no—
123C2—82no—
124C2—11361no—
125C2#1798616712yes—
126C2#1798617211yescharacteristic
subgroupG/H
centerC22#14556097
commutatorC42×C71C23
FrattiniC42C22×D71
Fitting#562×C71C2
socleC22×C71#120
hypercenter#562D71
hypocenterC71#1656
LCSG ▷ C42×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ C42 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #17986389C2semidirect
2. #17986365C2semidirect
3. #17985741C2semidirect
4. #17985739C2semidirect
5. #562×C71C2semidirect
64. C71#1656semidirect
65. #562D71semidirect