Finite Group Databasebeta

← #31805697

Subgroups — #31805697

Order 17792.

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#22581343C212yesmaximal, complemented
2#22581319C211yesmaximal, characteristic, complemented
3#22580695C211yesmaximal, characteristic, complemented
4#22580693C212yesmaximal, complemented
5#562×C139C211yesmaximal, characteristic, complemented
6C2×#14555772—22no—
7C2×#14555770—22no—
8#17984839C2211yescharacteristic
9#17984762—22no—
10#17984753C2211yescharacteristic
11#17984753C2212yes—
12#125×C139C2211yescharacteristic
13#124×C139C2212yes—
14#123×C139—22no—
15C22⋊Q8×C139—22no—
16#121×C139—22no—
17C2×D556—22no—
18C2×D556—21no—
19#14555772—44no—
20#14555770—44no—
21C2×C139⋊C8—22no—
22C2×C139⋊C8—21no—
23C2×Q8×C139D412yes—
24C2×D4×C139—22no—
25C2×D4×C139D412yes—
26C22×C4×C139—22no—
27C4⋊C4×C139—22no—
28C4⋊C4×C139—22no—
29C4⋊C4×C139D412yes—
30C22⋊C4×C139—22no—
31C22⋊C4×C139—22no—
32C22⋊C4×C139—22no—
33C42×C139C2311yescharacteristic
34C22×D139—41no—
35D556—42no—
36D556—42no—
37D556—42no—
38C139⋊C8—24no—
39C139⋊C8—41no—
40C23×C139—22no—
41Q8×C139—42no—
42D4×C139—42no—
43D4×C139—82no—
44C2×C4×C139—22no—
45C2×C4×C139—22no—
46C2×C4×C139—82no—
47C2×C4×C139C2×D411yescharacteristic
48C2×C4×C139C2×D412yes—
49C22×C139—42no—
50C22×C139—42no—
51C22×C139—42no—
52C22×C139#12011yescharacteristic
53C2×D139—82no—
54C2×D139—81no—
55C4×C139—22no—
56C4×C139—21no—
57C4×C139—42no—
58C4×C139—42no—
59C2×C139—82no—
60C2×C139#45312yes—
61C2×C139#45411yescharacteristic
62D139—161no—
63C139#165611yescharacteristic, complemented, Sylow
64#1656—1391nomaximal, Sylow
65#562D13911yescharacteristic, complemented
66#496—1392no—
67#490—1391no—
68#330—1391no—
69#329—1392no—
70C2×SD16—2782no—
71C2×D8—2782no—
72#127—1391no—
73#125C2×D13911yescharacteristic
74#124C2×D13912yes—
75#123—22no—
76C22⋊Q8—22no—
77#121—22no—
78#102—2782no—
79#97—1391no—
80#97—1392no—
81C2×Q8C22⋊D13912yes—
82C2×D4—22no—
83C2×D4—2781no—
84C2×D4—2782no—
85C2×D4C22⋊D13912yes—
86C22×C4—22no—
87SD16—5564no—
88D8—5564no—
89C2×C8—2782no—
90C2×C8—2781no—
91C4⋊C4—22no—
92C4⋊C4—22no—
93C4⋊C4C22⋊D13912yes—
94C22⋊C4—22no—
95C22⋊C4—22no—
96C22⋊C4—22no—
97C42C22×D13911yescharacteristic
98C23—22no—
99C23—5561no—
100Q8—42no—
101D4—42no—
102D4—82no—
103D4—5562no—
104D4—5562no—
105D4—5562no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—82no—
109C2×C4C2×C22⋊D13911yescharacteristic
110C2×C4C2×C22⋊D13912yes—
111C8—2784no—
112C8—5561no—
113C22—42no—
114C22—42no—
115C22—42no—
116C22—11122no—
117C22—11121no—
118C22#1798481111yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—42no—
123C2—82no—
124C2—22241no—
125C2#2258112112yes—
126C2#2258112611yescharacteristic
subgroupG/H
centerC22#17984811
commutator, cosocleC42×C139C23
FrattiniC42C22×D139
Fitting#562×C139C2
socleC22×C139#120
hypercenter#562D139
hypocenterC139#1656
LCSG ▷ C42×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #22581343C2semidirect
2. #22581319C2semidirect
3. #22580695C2semidirect
4. #22580693C2semidirect
5. #562×C139C2semidirect
63. C139#1656semidirect
65. #562D139semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#225813432
#225813192
#225806952
#225806932
#562×C1392
#1656139