Finite Group Databasebeta

← #31805728

Subgroups — #31805728

Order 17792.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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#22581701C211yesmaximal, characteristic
2#22581323C211yesmaximal, characteristic, complemented
3#22581313C212yesmaximal, complemented
4#22580692C212yesmaximal, complemented
5#330×C139C211yesmaximal, characteristic, complemented
6#17984842C2211yescharacteristic
7#17984830C2212yes—
8#17984827—22no—
9#17984820—22no—
10#17984817—22no—
11#17984767—22no—
12#17984765—22no—
13#17984764—22no—
14#17984753C2211yescharacteristic
15#125×C139C2211yescharacteristic
16#97×C139C2212yes—
17C2×Dic278—21no—
18C2×Dic278D412yes—
19C2×D556—22no—
20C2×D556D412yes—
21C2×C4×D139—22no—
22C2×C139⋊C8—21no—
23C4⋊Dic139—22no—
24Dic139⋊C4—22no—
25(C2×D139)⋊C4—22no—
26(C2×D139)⋊C4—22no—
27(C2×D139)⋊C4—22no—
28C2×C8×C139—22no—
29C4⋊C4×C139—22no—
30C4⋊C4×C139D412yes—
31C42×C139C2311yescharacteristic
32C22×D139—22no—
33Dic278—42no—
34Dic278—42no—
35D556—42no—
36D556—82no—
37C2×Dic139—22no—
38C2×Dic139—41no—
39C4×D139—82no—
40C139⋊C8—41no—
41C2×C4×C139—22no—
42C2×C4×C139C2×D412yes—
43C2×C4×C139C2×D411yescharacteristic
44C8×C139—42no—
45C22×C139#12011yescharacteristic
46C2×D139—42no—
47C2×D139—42no—
48C2×D139—42no—
49C4×C139—21no—
50C4×C139—22no—
51C4×C139—42no—
52Dic139—42no—
53Dic139—81no—
54C2×C139#45411yescharacteristic
55C2×C139#45512yes—
56D139—82no—
57C139#166211yescharacteristic, complemented, Sylow
58#1662—1391nomaximal, Sylow
59#562—1391no—
60#491—1391no—
61#489—1392no—
62#330D13911yescharacteristic, complemented
63#329—1392no—
64C4⋊Q8—1391no—
65#125C2×D13911yescharacteristic
66#124—1392no—
67#123—2782no—
68C22⋊Q8—2782no—
69#121—2782no—
70#103—2782no—
71#103—2782no—
72#102—2782no—
73#97—1391no—
74#97C2×D13912yes—
75C2×Q8—2781no—
76C2×Q8—1392no—
77C2×D4—2782no—
78C2×D4—1392no—
79C22×C4—2782no—
80C2×C8—22no—
81C2×C8—2781no—
82C4⋊C4—22no—
83C4⋊C4—2782no—
84C4⋊C4—2782no—
85C4⋊C4D55612yes—
86C22⋊C4—2782no—
87C22⋊C4—2782no—
88C22⋊C4—2782no—
89C42C22×D13911yescharacteristic
90C23—2782no—
91Q8—5562no—
92Q8—5562no—
93D4—5562no—
94D4—11122no—
95C2×C4—22no—
96C2×C4—2782no—
97C2×C4—5561no—
98C2×C4—11122no—
99C2×C4D4×D13912yes—
100C2×C4C2×D55611yescharacteristic
101C8—42no—
102C8—5561no—
103C22—5562no—
104C22—5562no—
105C22—5562no—
106C22#1798481211yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—5562no—
111C4—11121no—
112C2—11122no—
113C2#2258112811yescharacteristic
114C2#2258113212yes—
subgroupG/H
centerC22#17984812
commutator, cosocleC42×C139C23
FrattiniC42C22×D139
Fitting#330×C139C2
socleC22×C139#120
prime radical#22581701C2
hypercenter#330D139
hypocenterC139#1662
LCSG ▷ C42×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #22581323C2semidirect
3. #22581313C2semidirect
4. #22580692C2semidirect
5. #330×C139C2semidirect
57. C139#1662semidirect
62. #330D139semidirect

Maximal subgroups

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

subgroupindex
#225817012
#225813232
#225813132
#225806922
#330×C1392
#1662139