Finite Group Databasebeta

← #47982491

Subgroups — #47982491

Order 35456.

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#31800750C211yesmaximal, characteristic
2#31800372C211yesmaximal, characteristic, complemented
3#31800362C212yesmaximal, complemented
4#31799741C212yesmaximal, complemented
5#330×C277C211yesmaximal, characteristic, complemented
6#22579880C2211yescharacteristic
7#22579868C2212yes—
8#22579865—22no—
9#22579858—22no—
10#22579855—22no—
11#22579805—22no—
12#22579803—22no—
13#22579802—22no—
14#22579791C2211yescharacteristic
15#125×C277C2211yescharacteristic
16#97×C277C2212yes—
17C2×Dic554—21no—
18C2×Dic554D412yes—
19C2×D1108—22no—
20C2×D1108D412yes—
21C2×C4×D277—22no—
22C2×#14555660—21no—
23C4⋊Dic277—22no—
24#17984542—22no—
25#17984540—22no—
26#17984540—22no—
27#17984540—22no—
28C2×C8×C277—22no—
29C4⋊C4×C277—22no—
30C4⋊C4×C277D412yes—
31C42×C277C2311yescharacteristic
32C22×D277—22no—
33Dic554—42no—
34Dic554—42no—
35D1108—42no—
36D1108—82no—
37C2×Dic277—22no—
38C2×Dic277—41no—
39C4×D277—82no—
40#14555660—41no—
41C2×C4×C277—22no—
42C2×C4×C277C2×D412yes—
43C2×C4×C277C2×D411yescharacteristic
44C8×C277—42no—
45C22×C277#12011yescharacteristic
46C2×D277—42no—
47C2×D277—42no—
48C2×D277—42no—
49C4×C277—21no—
50C4×C277—22no—
51C4×C277—42no—
52Dic277—42no—
53Dic277—81no—
54C2×C277#45411yescharacteristic
55C2×C277#45512yes—
56D277—82no—
57C277#166211yescharacteristic, complemented, Sylow
58#1662—2771nomaximal, Sylow
59#562—2771no—
60#491—2771no—
61#489—2772no—
62#330D27711yescharacteristic, complemented
63#329—2772no—
64C4⋊Q8—2771no—
65#125C2×D27711yescharacteristic
66#124—2772no—
67#123—5542no—
68C22⋊Q8—5542no—
69#121—5542no—
70#103—5542no—
71#103—5542no—
72#102—5542no—
73#97—2771no—
74#97C2×D27712yes—
75C2×Q8—2772no—
76C2×Q8—5541no—
77C2×D4—2772no—
78C2×D4—5542no—
79C22×C4—5542no—
80C2×C8—22no—
81C2×C8—5541no—
82C4⋊C4—22no—
83C4⋊C4—5542no—
84C4⋊C4—5542no—
85C4⋊C4D110812yes—
86C22⋊C4—5542no—
87C22⋊C4—5542no—
88C22⋊C4—5542no—
89C42C22×D27711yescharacteristic
90C23—5542no—
91Q8—11082no—
92Q8—11082no—
93D4—11082no—
94D4—22162no—
95C2×C4—22no—
96C2×C4—5542no—
97C2×C4—11081no—
98C2×C4—22162no—
99C2×C4D4×D27712yes—
100C2×C4C2×D110811yescharacteristic
101C8—42no—
102C8—11081no—
103C22—11082no—
104C22—11082no—
105C22—11082no—
106C22#2257985011yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—11082no—
111C4—22161no—
112C2—22162no—
113C2#3180017711yescharacteristic
114C2#3180018112yes—
subgroupG/H
centerC22#22579850
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#330×C277C2
socleC22×C277#120
prime radical#31800750C2
hypercenter#330D277
hypocenterC277#1662
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #31800372C2semidirect
3. #31800362C2semidirect
4. #31799741C2semidirect
5. #330×C277C2semidirect
57. C277#1662semidirect
62. #330D277semidirect

Maximal subgroups

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

subgroupindex
#318007502
#318003722
#318003622
#317997412
#330×C2772
#1662277