Finite Group Databasebeta

← #47982211

Subgroups — #47982211

Order 35456.

202 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 53 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#31800633C211yesmaximal, characteristic
2#31800338C212yesmaximal
3#31799941C211yesmaximal, characteristic
4#31799740C212yesmaximal
5#324×C277C211yesmaximal, characteristic
6#22579879—22no—
7#22579871—22no—
8#22579859—21no—
9#22579859C2212yes—
10#22579839—21no—
11C2×C4⋊Dic277C2211yescharacteristic
12#22579814—22no—
13#22579805—22no—
14#22579787—21no—
15#22579787—21no—
16#22579787C2211yescharacteristic
17C2×C4⋊C4×C277C2211yescharacteristic
18C22⋊C8×C277C2212yes—
19C2×Dic554—21no—
20C2×Dic554D412yes—
21C22×Dic277—21no—
22C22×Dic277—21no—
23C4⋊Dic277—21no—
24C4⋊Dic277—21no—
25C4⋊Dic277—21no—
26C4⋊Dic277—22no—
27C4⋊Dic277D412yes—
28#17984542—22no—
29#17984542—22no—
30C22⋊Dic277—22no—
31C4×Dic277—22no—
32C22×C4×C277D411yescharacteristic
33C22×C4×C277D411yescharacteristic
34C22×C4×C277C2311yescharacteristic
35C2×C8×C277—22no—
36C4⋊C4×C277—22no—
37Dic554—42no—
38Dic554—81no—
39C2×Dic277—22no—
40C2×Dic277—22no—
41C2×Dic277—41no—
42C2×Dic277—41no—
43C2×Dic277—42no—
44C2×Dic277—41no—
45C2×Dic277—41no—
46C23×C277C2×D411yescharacteristic
47C2×C4×C277—21no—
48C2×C4×C277—21no—
49C2×C4×C277—21no—
50C2×C4×C277—41no—
51C2×C4×C277—41no—
52C2×C4×C277Q1612yes—
53C2×C4×C277C2×D412yes—
54C8×C277—42no—
55C22×C277—21no—
56C22×C277—21no—
57C22×C277#12011yescharacteristic
58C22×C277C2×Q1611yescharacteristic
59C22×C277#13711yescharacteristic
60C4×C277—22no—
61C4×C277—22no—
62C4×C277—41no—
63Dic277—42no—
64Dic277—42no—
65Dic277—81no—
66Dic277—81no—
67C2×C277—21no—
68C2×C277—21no—
69C2×C277#45111yescharacteristic
70C2×C277#45411yescharacteristic
71C2×C277#45811yescharacteristic
72C277#161711yescharacteristic, complemented, Sylow
73#1617—2771nomaximal, Sylow
74#544—2771no—
75#484—2772no—
76#400—2771no—
77#328—2772no—
78#324D27711yescharacteristic
79C4⋊Q8—5542no—
80#125—5542no—
81C22⋊Q8—2772no—
82C22⋊Q8—5541no—
83#117—5541no—
84C2×C4⋊C4—2771no—
85C2×C4⋊C4C2×D27711yescharacteristic
86#107—5542no—
87#103—5542no—
88C22⋊C8C2×D27712yes—
89#95—2771no—
90#95—5541no—
91#95—5541no—
92C2×Q8—2772no—
93C2×Q8—5541no—
94C22×C4—5541no—
95C22×C4—5541no—
96C22×C4D110811yescharacteristic
97C22×C4D110811yescharacteristic
98C22×C4C22×D27711yescharacteristic
99C2×C8—22no—
100C4⋊C4—22no—
101C4⋊C4—2772no—
102C4⋊C4—5542no—
103C4⋊C4—5541no—
104C4⋊C4—5541no—
105C4⋊C4—5541no—
106C4⋊C4—5542no—
107C4⋊C4—5542no—
108C22⋊C4—5542no—
109C42—5542no—
110C23C2×D110811yescharacteristic
111Q8—11082no—
112Q8—22161no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—5542no—
119C2×C4—5542no—
120C2×C4—11081no—
121C2×C4—11081no—
122C2×C4—11082no—
123C2×C4—11081no—
124C2×C4—11081no—
125C2×C4Dic110812yes—
126C2×C4D4×D27712yes—
127C8—42no—
128C22—21no—
129C22—21no—
130C22#2257985011yescharacteristic
131C22C2×Dic110811yescharacteristic
132C22#2257991311yescharacteristic
133C4—22no—
134C4—22no—
135C4—41no—
136C4—11082no—
137C4—11082no—
138C4—22161no—
139C4—22161no—
140C2—21no—
141C2—21no—
142C2#3180016011yescharacteristic
143C2#3180017711yescharacteristic
144C2#3180019311yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC22×C4×C277C23
FrattiniC22×C4C22×D277
Fitting#324×C277C2
socleC22×C277#120
prime radicalC23×C277C2×D4
hypercenter#324D277
hypocenterC277#1617
LCSG ▷ C22×C4×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
72. C277#1617semidirect

Maximal subgroups

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

subgroupindex
#318006332
#318003382
#317999412
#317997402
#324×C2772
#1617277