Finite Group Databasebeta

← #47982206

Subgroups — #47982206

Order 35456.

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

normal subgroups only

This group has 246 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#31800321C212yesmaximal, complemented
3#31799941C211yesmaximal, 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
12#22579812—22no—
13#22579802—22no—
14#22579787—21no—
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#17984540—22no—
33#17984540—22no—
34C22×C4×C277D411yescharacteristic
35C22×C4×C277D411yescharacteristic
36C22×C4×C277C2311yescharacteristic
37C2×C8×C277—22no—
38C4⋊C4×C277—22no—
39C22×D277—22no—
40Dic554—42no—
41D1108—42no—
42D1108—42no—
43D1108—81no—
44C22⋊D277—42no—
45C22⋊D277—42no—
46C2×Dic277—22no—
47C2×Dic277—41no—
48C2×Dic277—41no—
49C2×Dic277—42no—
50C2×Dic277—41no—
51C2×Dic277—41no—
52C4×D277—44no—
53C23×C277C2×D411yescharacteristic
54C2×C4×C277—21no—
55C2×C4×C277—21no—
56C2×C4×C277—21no—
57C2×C4×C277—41no—
58C2×C4×C277—41no—
59C2×C4×C277SD1612yes—
60C2×C4×C277C2×D412yes—
61C8×C277—42no—
62C22×C277—21no—
63C22×C277—21no—
64C22×C277#12011yescharacteristic
65C22×C277C2×SD1611yescharacteristic
66C22×C277AGL(1,ℤ/8)11yescharacteristic
67C2×D277—42no—
68C2×D277—42no—
69C2×D277—42no—
70C4×C277—22no—
71C4×C277—22no—
72C4×C277—41no—
73Dic277—42no—
74Dic277—81no—
75Dic277—81no—
76C2×C277—21no—
77C2×C277—21no—
78C2×C277#45011yescharacteristic
79C2×C277#45411yescharacteristic
80C2×C277#45811yescharacteristic
81D277—82no—
82C277#161611yescharacteristic, complemented, Sylow
83#1616—2771nomaximal, Sylow
84#537—2771no—
85#481—2772no—
86#400—2771no—
87#327—2772no—
88#324D27711yescharacteristic, complemented
89C2×#41—5541no—
90C22⋊Q8—5542no—
91#121—2772no—
92#121—5542no—
93#121—5541no—
94C2×C4⋊C4—2771no—
95C2×C4⋊C4C2×D27711yescharacteristic
96#106—5542no—
97#102—5542no—
98C22⋊C8C2×D27712yes—
99#95—2771no—
100#95—5541no—
101#95—5541no—
102#41—11082no—
103#41—11082no—
104C2×Q8—5541no—
105C2×D4—2772no—
106C2×D4—5541no—
107C2×D4—5541no—
108C2×D4—5542no—
109C22×C4—5542no—
110C22×C4—5541no—
111C22×C4—5541no—
112C22×C4D110811yescharacteristic
113C22×C4D110811yescharacteristic
114C22×C4C22×D27711yescharacteristic
115C2×C8—22no—
116C4⋊C4—22no—
117C4⋊C4—2772no—
118C4⋊C4—5541no—
119C4⋊C4—5542no—
120C22⋊C4—5542no—
121C22⋊C4—5542no—
122C23—5542no—
123C23C2×D110811yescharacteristic
124Q8—11082no—
125D4—11082no—
126D4—11082no—
127D4—11082no—
128D4—11082no—
129D4—22161no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—5542no—
136C2×C4—11084no—
137C2×C4—11081no—
138C2×C4—11081no—
139C2×C4—11082no—
140C2×C4—11081no—
141C2×C4—11081no—
142C2×C4#1798455212yes—
143C2×C4D4×D27712yes—
144C8—42no—
145C22—21no—
146C22—21no—
147C22—11082no—
148C22—11082no—
149C22—11082no—
150C22#2257985011yescharacteristic
151C22C2×#1798455211yescharacteristic
152C22#2257990811yescharacteristic
153C4—22no—
154C4—22no—
155C4—41no—
156C4—11082no—
157C4—22161no—
158C4—22161no—
159C2—21no—
160C2—21no—
161C2—22162no—
162C2#3180015511yescharacteristic
163C2#3180017711yescharacteristic
164C2#3180019311yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC22×C4×C277C23
FrattiniC22×C4C22×D277
Fitting#324×C277C2
socleC22×C277#120
prime radical#31800583C2
hypercenter#324D277
hypocenterC277#1616
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. #31800321C2semidirect
3. #31799941C2semidirect
4. #31799737C2semidirect
5. #324×C277C2semidirect
82. C277#1616semidirect
88. #324D277semidirect

Maximal subgroups

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

subgroupindex
#318005832
#318003212
#317999412
#317997372
#324×C2772
#1616277