Finite Group Databasebeta

← #47982462

Subgroups — #47982462

Order 35456.

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

normal subgroups only

This group has 230 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#31800750C211yesmaximal, characteristic, complemented
2#31800391C212yesmaximal, complemented
3#31800368C211yesmaximal, characteristic, complemented
4#31799741C212yesmaximal, complemented
5#330×C277C211yesmaximal, characteristic, complemented
6C2×#17984552—22no—
7C2×D2216—22no—
8#22579877C2211yescharacteristic
9#22579868C2212yes—
10#22579865—22no—
11#22579858—22no—
12#22579855—22no—
13#22579800—22no—
14#22579791C2211yescharacteristic
15#125×C277C2211yescharacteristic
16#97×C277C2212yes—
17C2×Dic554D412yes—
18C2×D1108—22no—
19C2×D1108—21no—
20C2×D1108—22no—
21C2×D1108D412yes—
22C2×C4×D277—22no—
23#17984552—44no—
24D2216—44no—
25C2×#14555660—21no—
26#17984542—22no—
27#17984540—22no—
28#17984540—22no—
29#17984540—22no—
30C2×C8×C277—22no—
31C4⋊C4×C277—22no—
32C4⋊C4×C277D412yes—
33C42×C277C2311yescharacteristic
34C22×D277—22no—
35C22×D277—41no—
36Dic554—42no—
37D1108—42no—
38D1108—42no—
39D1108—42no—
40D1108—42no—
41D1108—82no—
42C2×Dic277—22no—
43C4×D277—82no—
44#14555660—41no—
45C2×C4×C277—22no—
46C2×C4×C277C2×D412yes—
47C2×C4×C277C2×D411yescharacteristic
48C8×C277—24no—
49C22×C277#12011yescharacteristic
50C2×D277—42no—
51C2×D277—42no—
52C2×D277—42no—
53C2×D277—82no—
54C2×D277—81no—
55C4×C277—22no—
56C4×C277—21no—
57C4×C277—42no—
58Dic277—42no—
59C2×C277#45312yes—
60C2×C277#45411yescharacteristic
61D277—82no—
62D277—161no—
63C277#165611yescharacteristic, complemented, Sylow
64#1656—2771nomaximal, Sylow
65#562—2771no—
66#496—2772no—
67#490—2771no—
68#330D27711yescharacteristic, complemented
69#329—2772no—
70C2×SD16—5542no—
71C2×D8—5542no—
72#127—2771no—
73#125C2×D27711yescharacteristic
74#124—2772no—
75#123—5542no—
76C22⋊Q8—5542no—
77#121—5542no—
78#102—5542no—
79#97—2771no—
80#97C2×D27712yes—
81C2×Q8—2772no—
82C2×D4—2772no—
83C2×D4—5542no—
84C2×D4—5542no—
85C2×D4—5541no—
86C22×C4—5542no—
87SD16—11084no—
88D8—11084no—
89C2×C8—22no—
90C2×C8—5541no—
91C4⋊C4—22no—
92C4⋊C4—5542no—
93C4⋊C4D110812yes—
94C22⋊C4—5542no—
95C22⋊C4—5542no—
96C22⋊C4—5542no—
97C42C22×D27711yescharacteristic
98C23—5542no—
99C23—11081no—
100Q8—11082no—
101D4—11082no—
102D4—11082no—
103D4—11082no—
104D4—11082no—
105D4—22162no—
106C2×C4—22no—
107C2×C4—5542no—
108C2×C4—22162no—
109C2×C4D4×D27712yes—
110C2×C4C2×D110811yescharacteristic
111C8—24no—
112C8—11081no—
113C22—11082no—
114C22—11082no—
115C22—11082no—
116C22—22162no—
117C22—22161no—
118C22#2257985011yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—11082no—
123C2—44321no—
124C2—22162no—
125C2#3180017112yes—
126C2#3180017711yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#330×C277C2
socleC22×C277#120
hypercenter#330D277
hypocenterC277#1656
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
1. #31800750C2semidirect
2. #31800391C2semidirect
3. #31800368C2semidirect
4. #31799741C2semidirect
5. #330×C277C2semidirect
63. C277#1656semidirect
68. #330D277semidirect

Maximal subgroups

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

subgroupindex
#318007502
#318003912
#318003682
#317997412
#330×C2772
#1656277