Finite Group Databasebeta

← #47982203

Subgroups — #47982203

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#31800320C212yesmaximal, complemented
3#31799735C212yesmaximal, complemented
4#31799728C211yesmaximal, characteristic, complemented
5#400×C277C211yesmaximal, characteristic, complemented
6C2×#17984563—21no—
7#22579860—22no—
8#22579855—22no—
9#22579854—21no—
10#22579854C2212yes—
11#22579811—22no—
12#22579800—22no—
13C22⋊#14555660C2212yes—
14C2×C4⋊C4×C277C2211yescharacteristic
15C2×C4⋊C4×C277C2211yescharacteristic
16#95×C277—21no—
17#95×C277—21no—
18#95×C277C2211yescharacteristic
19#17984563—42no—
20#17984563—42no—
21C2×Dic554—21no—
22C2×D1108—21no—
23C2×D1108—21no—
24C2×D1108D412yes—
25C2×C22⋊D277—22no—
26C2×C4×D277—22no—
27C2×#14555660—22no—
28C4⋊Dic277—21no—
29C4⋊Dic277D412yes—
30#17984540—22no—
31#17984540—22no—
32C22×C4×C277—21no—
33C22×C4×C277—21no—
34C22×C4×C277D411yescharacteristic
35C22×C4×C277D411yescharacteristic
36C22×C4×C277C2311yescharacteristic
37C4⋊C4×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—
47C4×D277—44no—
48#14555660—42no—
49C23×C277C2×D411yescharacteristic
50C2×C4×C277—21no—
51C2×C4×C277—21no—
52C2×C4×C277—21no—
53C2×C4×C277—41no—
54C2×C4×C277—41no—
55C2×C4×C277—41no—
56C2×C4×C277—41no—
57C2×C4×C277—42no—
58C2×C4×C277—41no—
59C2×C4×C277—41no—
60C2×C4×C277SD1612yes—
61C2×C4×C277C2×D412yes—
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—
73C4×C277—81no—
74C4×C277—81no—
75Dic277—42no—
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#400D27711yescharacteristic, complemented
87#327—2772no—
88#324—2771no—
89C2×#41—5541no—
90C22⋊Q8—5542no—
91#121—2772no—
92#121—5542no—
93#121—5541no—
94C2×C4⋊C4C2×D27711yescharacteristic
95C2×C4⋊C4C2×D27711yescharacteristic
96#106—5542no—
97#102—5542no—
98C22⋊C8—2772no—
99#95—21no—
100#95—21no—
101#95C2×D27711yescharacteristic
102#41—11082no—
103#41—11082no—
104C2×Q8—5541no—
105C2×D4—2772no—
106C2×D4—5541no—
107C2×D4—5541no—
108C2×D4—5542no—
109C22×C4—21no—
110C22×C4—21no—
111C22×C4—5542no—
112C22×C4C22⋊D27711yescharacteristic
113C22×C4C22⋊D27711yescharacteristic
114C22×C4C22×D27711yescharacteristic
115C2×C8—5542no—
116C4⋊C4—22no—
117C4⋊C4—22no—
118C4⋊C4—2772no—
119C4⋊C4—5541no—
120C22⋊C4—5542no—
121C22⋊C4—5542no—
122C23—5542no—
123C23C2×C22⋊D27711yescharacteristic
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—41no—
136C2×C4—41no—
137C2×C4—42no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—5542no—
141C2×C4—11084no—
142C2×C4#1798455012yes—
143C2×C4D4×D27712yes—
144C8—11082no—
145C22—21no—
146C22—21no—
147C22—11082no—
148C22—11082no—
149C22—11082no—
150C22#2257984811yescharacteristic
151C22C2×#1798455011yescharacteristic
152C22#2257990511yescharacteristic
153C4—22no—
154C4—22no—
155C4—41no—
156C4—81no—
157C4—81no—
158C4—11082no—
159C2—21no—
160C2—21no—
161C2—22162no—
162C2#3180015211yescharacteristic
163C2#3180017411yescharacteristic
164C2#3180019111yescharacteristic
subgroupG/H
centerC22#22579848
commutator, cosocleC22×C4×C277C23
FrattiniC22×C4C22×D277
Fitting#400×C277C2
socleC22×C277#120
prime radical#31800583C2
hypercenter#400D277
hypocenterC277#1616
LCSG ▷ C22×C4×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C22×C4 ◁ #400

Complements

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

NH ≅ G/Ntype
2. #31800320C2semidirect
3. #31799735C2semidirect
4. #31799728C2semidirect
5. #400×C277C2semidirect
82. C277#1616semidirect
86. #400D277semidirect

Maximal subgroups

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

subgroupindex
#318005832
#318003202
#317997352
#317997282
#400×C2772
#1616277