Finite Group Databasebeta

← #47981760

Subgroups — #47981760

Order 35456.

226 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 63 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#31800558C211yesmaximal, characteristic
2#31799954C212yesmaximal
3#31799744C211yesmaximal, characteristic, complemented
4#31799743C212yesmaximal, complemented
5#330×C277C211yesmaximal, characteristic, complemented
6C2×#17984546—22no—
7#22579879C412yes—
8#22579872C2211yescharacteristic
9#22579858—22no—
10#22579845—22no—
11#22579838C412yes—
12C42×D277C2211yescharacteristic
13#22579791C2212yes—
14C8×Dic277—22no—
15#125×C277C2211yescharacteristic
16#97×C277C2212yes—
17C2×Dic554—22no—
18C2×C4×D277C2×C411yescharacteristic
19C2×C4×D277D412yes—
20#17984546—28no—
21C2×#14555660—22no—
22C4⋊Dic277C2×C412yes—
23#17984542—22no—
24#17984542—22no—
25#17984540—22no—
26C4×Dic277—22no—
27C4×Dic277C2×C411yescharacteristic
28C4×Dic277D412yes—
29C2×C8×C277—22no—
30C4⋊C4×C277—22no—
31C4⋊C4×C277C2×C412yes—
32C42×C277C2311yescharacteristic
33C22×D277C22⋊C411yescharacteristic
34Dic554—44no—
35C2×Dic277—22no—
36C2×Dic277C22⋊C411yescharacteristic
37C2×Dic277C22⋊C412yes—
38C4×D277—22no—
39C4×D277—24no—
40#14555660—24no—
41C2×C4×C277—22no—
42C2×C4×C277C22×C411yescharacteristic
43C2×C4×C277C2×D412yes—
44C8×C277—24no—
45C22×C277C2×C22⋊C411yescharacteristic
46C2×D277—21no—
47C2×D277—22no—
48C4×C277—21no—
49C4×C277—22no—
50C4×C277—42no—
51Dic277—42no—
52Dic277#10112yes—
53Dic277#10414yes—
54C2×C277C2×#10111yescharacteristic
55C2×C277C2×#10412yes—
56D277—41no—
57C277#152611yescharacteristic, complemented, Sylow
58#1526—2771nomaximal, Sylow
59#533—2771no—
60C4×M16—2772no—
61#330—2771no—
62#330—2772no—
63#330D27711yescharacteristic, complemented
64C2×M16—5542no—
65C4⋊Q8—2772no—
66#125—2771no—
67#125C2×D27711yescharacteristic
68C22⋊Q8—5542no—
69C4×Q8—5542no—
70#117—2772no—
71C2×C42—2771no—
72#97—2772no—
73#97C2×D27712yes—
74C4×C8—5542no—
75C2×Q8—5542no—
76C22×C4—2771no—
77C22×C4—2772no—
78M16—5548no—
79C2×C8—22no—
80C2×C8—5542no—
81C4⋊C4—22no—
82C4⋊C4—2772no—
83C4⋊C4—5542no—
84C4⋊C4—5542no—
85C4⋊C4C4×D27712yes—
86C22⋊C4—5542no—
87C42—2771no—
88C42—2772no—
89C42—5542no—
90C42C22×D27711yescharacteristic
91C23—2771no—
92Q8—11084no—
93C2×C4—22no—
94C2×C4—2771no—
95C2×C4—2772no—
96C2×C4—5544no—
97C2×C4—5542no—
98C2×C4—5542no—
99C2×C4C2×C4×D27711yescharacteristic
100C2×C4D4×D27712yes—
101C8—24no—
102C8—5544no—
103C22—5541no—
104C22—5542no—
105C22C22⋊C4×D27711yescharacteristic
106C4—21no—
107C4—22no—
108C4—42no—
109C4—2772no—
110C4—2774no—
111C4—11082no—
112C2—11081no—
113C2#101×D27711yescharacteristic
114C2#104×D27712yes—
subgroupG/H
centerC22C22⋊C4×D277
commutatorC2×C4×C277C22×C4
FrattiniC42C22×D277
Fitting#330×C277C2
socleC22×C277C2×C22⋊C4
prime radicalC22×D277C22⋊C4
cosocleC42×C277C23
hypercenter#330D277
hypocenterC277#1526
LCSG ▷ C2×C4×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
3. #31799744C2semidirect
4. #31799743C2semidirect
5. #330×C277C2semidirect
57. C277#1526semidirect
63. #330D277semidirect

Maximal subgroups

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

subgroupindex
#318005582
#317999542
#317997442
#317997432
#330×C2772
#1526277