Finite Group Databasebeta

← #47982172

Subgroups — #47982172

Order 35456.

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

normal subgroups only

This group has 254 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#31800583C211yesmaximal, characteristic
2#31800316C212yesmaximal, complemented
3#31799932C211yesmaximal, characteristic, complemented
4#31799737C212yesmaximal, complemented
5#324×C277C211yesmaximal, characteristic, complemented
6C2×#17984563—21no—
7#22579860—22no—
8#22579855—22no—
9#22579854—21no—
10#22579854C2212yes—
11C2×C4⋊Dic277C2211yescharacteristic
12C2×#17984542—21no—
13#22579814—22no—
14#22579802—22no—
15#22579787—21no—
16#22579787C2211yescharacteristic
17C2×C4⋊C4×C277C2211yescharacteristic
18C22⋊C8×C277C2212yes—
19#17984563—42no—
20#17984563—42no—
21C2×Dic554—21no—
22C2×D1108—21no—
23C2×D1108—21no—
24C2×D1108D412yes—
25C2×C22⋊D277—22no—
26C22×Dic277—21no—
27C22×Dic277—21no—
28C2×C4×D277—22no—
29C4⋊Dic277—21no—
30C4⋊Dic277—22no—
31C4⋊Dic277D412yes—
32#17984542—42no—
33#17984540—22no—
34#17984540—22no—
35C22×C4×C277D411yescharacteristic
36C22×C4×C277D411yescharacteristic
37C22×C4×C277C2311yescharacteristic
38C2×C8×C277—22no—
39C4⋊C4×C277—22no—
40C22×D277—22no—
41Dic554—42no—
42D1108—42no—
43D1108—42no—
44D1108—81no—
45C22⋊D277—42no—
46C22⋊D277—42no—
47C2×Dic277—22no—
48C2×Dic277—22no—
49C2×Dic277—41no—
50C2×Dic277—41no—
51C2×Dic277—41no—
52C2×Dic277—41no—
53C2×Dic277—41no—
54C4×D277—44no—
55C23×C277C2×D411yescharacteristic
56C2×C4×C277—21no—
57C2×C4×C277—21no—
58C2×C4×C277—21no—
59C2×C4×C277—41no—
60C2×C4×C277—41no—
61C2×C4×C277D812yes—
62C2×C4×C277C2×D412yes—
63C8×C277—42no—
64C22×C277—21no—
65C22×C277—21no—
66C22×C277#12011yescharacteristic
67C22×C277C2×D811yescharacteristic
68C22×C277AGL(1,ℤ/8)11yescharacteristic
69C2×D277—42no—
70C2×D277—42no—
71C2×D277—42no—
72C4×C277—22no—
73C4×C277—22no—
74C4×C277—41no—
75Dic277—42no—
76Dic277—42no—
77Dic277—81no—
78C2×C277—21no—
79C2×C277—21no—
80C2×C277#44711yescharacteristic
81C2×C277#45611yescharacteristic
82C2×C277#45811yescharacteristic
83D277—82no—
84C277#161011yescharacteristic, complemented, Sylow
85#1610—2771nomaximal, Sylow
86#537—2771no—
87#480—2772no—
88#398—2771no—
89#327—2772no—
90#324D27711yescharacteristic, complemented
91C2×#41—5541no—
92C22⋊Q8—5542no—
93#121—2772no—
94#121—5542no—
95#121—5541no—
96C2×C4⋊C4—2771no—
97C2×C4⋊C4—5541no—
98C2×C4⋊C4C2×D27711yescharacteristic
99#107—5542no—
100#102—5542no—
101C22⋊C8C2×D27712yes—
102#95—2771no—
103#95—5541no—
104#41—11082no—
105#41—11082no—
106C2×Q8—5541no—
107C2×D4—2772no—
108C2×D4—5541no—
109C2×D4—5541no—
110C2×D4—5542no—
111C22×C4—5542no—
112C22×C4—5541no—
113C22×C4—5541no—
114C22×C4D110811yescharacteristic
115C22×C4D110811yescharacteristic
116C22×C4C22×D27711yescharacteristic
117C2×C8—22no—
118C4⋊C4—22no—
119C4⋊C4—2772no—
120C4⋊C4—5541no—
121C4⋊C4—5542no—
122C4⋊C4—11082no—
123C22⋊C4—5542no—
124C22⋊C4—5542no—
125C23—5542no—
126C23C2×D110811yescharacteristic
127Q8—11082no—
128D4—11082no—
129D4—11082no—
130D4—11082no—
131D4—11082no—
132D4—22161no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—5542no—
139C2×C4—5542no—
140C2×C4—11084no—
141C2×C4—11081no—
142C2×C4—11081no—
143C2×C4—11081no—
144C2×C4—11081no—
145C2×C4—11081no—
146C2×C4D221612yes—
147C2×C4D4×D27712yes—
148C8—42no—
149C22—21no—
150C22—21no—
151C22—11082no—
152C22—11082no—
153C22—11082no—
154C22#2257985011yescharacteristic
155C22C2×D221611yescharacteristic
156C22#2257990811yescharacteristic
157C4—22no—
158C4—22no—
159C4—41no—
160C4—11082no—
161C4—11082no—
162C4—22161no—
163C2—21no—
164C2—21no—
165C2—22162no—
166C2#3180013811yescharacteristic
167C2#3180018711yescharacteristic
168C2#3180019311yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC22×C4×C277C23
FrattiniC22×C4C22×D277
Fitting#324×C277C2
socleC22×C277#120
prime radical#31800583C2
hypercenter#324D277
hypocenterC277#1610
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
2. #31800316C2semidirect
3. #31799932C2semidirect
4. #31799737C2semidirect
5. #324×C277C2semidirect
84. C277#1610semidirect
90. #324D277semidirect

Maximal subgroups

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

subgroupindex
#318005832
#318003162
#317999322
#317997372
#324×C2772
#1610277