Finite Group Databasebeta

← #47982284

Subgroups — #47982284

Order 35456.

314 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 57 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#31800637C211yesmaximal, characteristic
2#31800374C211yesmaximal, characteristic, complemented
3#31800293C212yesmaximal, complemented
4#31799729C212yesmaximal, complemented
5#331×C277C211yesmaximal, characteristic, complemented
6C2×D4×D277—22no—
7C2×#17984551—22no—
8#22579880C2211yescharacteristic, complemented
9#22579851—22no—
10#22579848—22no—
11C4×D1108C2212yes—
12#22579812—22no—
13#22579802—22no—
14C4×#14555660C2211yescharacteristic, complemented
15#127×C277C2211yescharacteristic
16C4⋊C8×C277C2212yescomplemented
17C23×D277—22no—
18C2×Dic554—21no—
19C2×D1108D412yes—
20C2×C22⋊D277—24no—
21D4×D277—44no—
22D4×D277—44no—
23C2×C4×D277—22no—
24#17984551—44no—
25C2×#14555660—21no—
26C4⋊Dic277—22no—
27C4⋊Dic277D412yes—
28C22⋊Dic277—22no—
29#17984540—22no—
30C2×D4×C277—22no—
31C2×D4×C277D412yes—
32C2×C8×C277—22no—
33C42×C277C2311yescharacteristic
34C22×D277—22no—
35C22×D277—48no—
36C22×D277—82no—
37Dic554—42no—
38D1108—22no—
39D1108SD1614yescomplemented
40C22⋊D277—48no—
41C2×Dic277—22no—
42C2×Dic277—41no—
43C4×D277—42no—
44C4×D277—42no—
45#14555660—22no—
46C23×C277—22no—
47D4×C277—42no—
48D4×C277—42no—
49D4×C277—42no—
50C2×C4×C277C2×D412yes—
51C2×C4×C277C2×D411yescharacteristic
52C8×C277—42no—
53C22×C277—44no—
54C22×C277—42no—
55C22×C277#12011yescharacteristic
56C2×D277—24no—
57C2×D277—42no—
58C2×D277—42no—
59C2×D277—88no—
60C4×C277—21no—
61C4×C277C2×SD1612yes—
62C4×C277AGL(1,ℤ/8)12yes—
63Dic277—42no—
64Dic277—81no—
65C2×C277—82no—
66C2×C277#45012yes—
67C2×C277#45311yescharacteristic
68D277—44no—
69C277#162911yescharacteristic, complemented, Sylow
70#1629—2771nomaximal, Sylow
71D42—2771no—
72#492—2771no—
73#476—2772no—
74#331D27711yescharacteristic, complemented
75D4⋊C8—2772no—
76C22×D4—5542no—
77C2×SD16—5542no—
78C4⋊Q8—2771no—
79#127C2×D27711yescharacteristic
80#121—5542no—
81#120—5542no—
82C4×D4—2772no—
83#106—5542no—
84C4⋊C8C2×D27712yescomplemented
85#102—5542no—
86C4×C8—2771no—
87C24—5542no—
88C2×Q8—5541no—
89C2×D4—22no—
90C2×D4—2772no—
91C2×D4—5544no—
92C2×D4—11084no—
93C2×D4—11084no—
94C2×D4D110812yes—
95C22×C4—5542no—
96SD16—11084no—
97C2×C8—22no—
98C2×C8—5541no—
99C4⋊C4—2772no—
100C4⋊C4—5542no—
101C22⋊C4—5542no—
102C22⋊C4—5542no—
103C42C22×D27711yescharacteristic
104C23—22no—
105C23—5542no—
106C23—11088no—
107C23—22162no—
108Q8—11082no—
109D4—42no—
110D4—42no—
111D4—42no—
112D4—2774no—
113D4—5542no—
114D4—11088no—
115C2×C4—5542no—
116C2×C4—11082no—
117C2×C4—11082no—
118C2×C4—11081no—
119C2×C4D4×D27712yes—
120C2×C4C2×D110811yescharacteristic
121C8—42no—
122C8—5542no—
123C22—44no—
124C22—42no—
125C22—5544no—
126C22—11082no—
127C22—11082no—
128C22—22168no—
129C22#2257985011yescharacteristic
130C4—21no—
131C4—11082no—
132C4—22161no—
133C4SD16×D27712yes—
134C4#2257990412yes—
135C2—82no—
136C2—11084no—
137C2#3180015412yes—
138C2#3180017211yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#331×C277C2
socleC22×C277#120
prime radical#31800637C2
hypercenter#331D277
hypocenterC277#1629
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #31800374C2semidirect
3. #31800293C2semidirect
4. #31799729C2semidirect
5. #331×C277C2semidirect
8. #22579880C22semidirect
14. C4×#14555660C22semidirect
16. C4⋊C8×C277C22semidirect
39. D1108SD16semidirect
69. C277#1629semidirect
74. #331D277semidirect
84. C4⋊C8C2×D277semidirect

Maximal subgroups

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

subgroupindex
#318006372
#318003742
#318002932
#317997292
#331×C2772
#1629277