Finite Group Databasebeta

← #47981192

Subgroups — #47981192

Order 35456.

154 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 35 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#31799938C211yesmaximal, characteristic
2#31799769C211yesmaximal, characteristic
3#323×C277C211yesmaximal, characteristic
4C2×C4⋊Dic277C411yescharacteristic, complemented
5C2×#17984542—21no—
6C2×C22⋊Dic277—21no—
7C2×C22⋊Dic277—21no—
8#22579787C411yescharacteristic, complemented
9C2×C22⋊C4×C277C2211yescharacteristic
10C22⋊C8×C277—21no—
11C22×Dic277—21no—
12C22×Dic277—21no—
13C22×Dic277—41no—
14C4⋊Dic277—41no—
15#17984542—42no—
16C22⋊Dic277—22no—
17C22⋊Dic277—42no—
18C22⋊Dic277—41no—
19C24×C277D411yescharacteristic
20C22×C4×C277C2×C411yescharacteristic
21C22×C4×C277D411yescharacteristic
22C2×C8×C277—41no—
23C22⋊C4×C277—41no—
24C2×Dic277—22no—
25C2×Dic277—41no—
26C2×Dic277—41no—
27C2×Dic277—42no—
28C2×Dic277—41no—
29C2×Dic277—41no—
30C2×Dic277—41no—
31C2×Dic277—81no—
32C2×Dic277—81no—
33C23×C277—21no—
34C23×C277—21no—
35C23×C277—41no—
36C23×C277—41no—
37C23×C277C22⋊C411yescharacteristic
38C23×C277SD1611yescharacteristic
39C23×C277Q1611yescharacteristic
40C2×C4×C277—21no—
41C2×C4×C277—21no—
42C2×C4×C277—41no—
43C2×C4×C277—41no—
44C8×C277—81no—
45C22×C277—21no—
46C22×C277—21no—
47C22×C277—21no—
48C22×C277—21no—
49C22×C277—41no—
50C22×C277—41no—
51C22×C277—41no—
52C22×C277—41no—
53C22×C277—81no—
54C22×C277#9911yescharacteristic
55C22×C277#10311yescharacteristic
56C22×C277#10411yescharacteristic
57C4×C277—41no—
58C4×C277—41no—
59Dic277—42no—
60Dic277—82no—
61Dic277—81no—
62C2×C277—21no—
63C2×C277—21no—
64C2×C277—41no—
65C2×C277—41no—
66C2×C277#32811yescharacteristic
67C2×C277#35211yescharacteristic
68C2×C277#35311yescharacteristic
69C277#135211yescharacteristic, complemented, Sylow
70#1352—2771nomaximal, Sylow
71#399—2771no—
72#342—2771no—
73#323D27711yescharacteristic
74C2×C4⋊C4—2771no—
75C2×C4⋊C4—5541no—
76C2×C22⋊C4—5541no—
77C2×C22⋊C4—5541no—
78C2×C22⋊C4C2×D27711yescharacteristic
79C22⋊C8—21no—
80#95—2771no—
81C24D110811yescharacteristic
82C22×C4—5541no—
83C22×C4—5541no—
84C22×C4—11081no—
85C22×C4C4×D27711yescharacteristic
86C22×C4C22⋊D27711yescharacteristic
87C2×C8—41no—
88C4⋊C4—11081no—
89C4⋊C4—11082no—
90C22⋊C4—41no—
91C22⋊C4—5542no—
92C22⋊C4—11082no—
93C22⋊C4—11081no—
94C23—21no—
95C23—21no—
96C23—41no—
97C23—41no—
98C23#1798454011yescharacteristic
99C23#1798455211yescharacteristic
100C23Dic110811yescharacteristic
101C2×C4—21no—
102C2×C4—21no—
103C2×C4—41no—
104C2×C4—41no—
105C2×C4—5542no—
106C2×C4—11081no—
107C2×C4—11081no—
108C2×C4—11082no—
109C2×C4—11081no—
110C2×C4—11081no—
111C2×C4—11081no—
112C2×C4—22161no—
113C2×C4—22161no—
114C8—81no—
115C22—21no—
116C22—21no—
117C22—21no—
118C22—21no—
119C22—41no—
120C22—41no—
121C22—41no—
122C22—41no—
123C22—81no—
124C22#2257979411yescharacteristic
125C22#2257980511yescharacteristic
126C22#2257980611yescharacteristic
127C4—41no—
128C4—41no—
129C4—11082no—
130C4—22162no—
131C4—22161no—
132C2—21no—
133C2—21no—
134C2—41no—
135C2—41no—
136C2#3179974011yescharacteristic
137C2#3179979311yescharacteristic
138C2#3179979411yescharacteristic
subgroupG/H
centerC22#22579794
commutatorC22×C4×C277C2×C4
FrattiniC2×C22⋊C4C2×D277
Fitting#323×C277C2
socleC22×C277#99
prime radicalC24×C277D4
cosocleC2×C22⋊C4×C277C22
hypercenter#323D277
hypocenterC277#1352
LCSG ▷ C22×C4×C277 ▷ C23×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #323

Complements

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

NH ≅ G/Ntype
4. C2×C4⋊Dic277C4semidirect
8. #22579787C4semidirect
69. C277#1352semidirect

Maximal subgroups

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

subgroupindex
#317999382
#317997692
#323×C2772
#1352277