Finite Group Databasebeta

← #47982264

Subgroups — #47982264

Order 35456.

210 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 55 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#31800727C211yesmaximal, characteristic, complemented
2#31800350C211yesmaximal, characteristic
3#31800203C211yesmaximal, characteristic
4#31800203C211yesmaximal, characteristic
5#31799732C211yesmaximal, characteristic, complemented
6#31799732C211yesmaximal, characteristic, complemented
7#332×C277C211yesmaximal, characteristic, complemented
8C2×#17984552—21no—
9C2×#17984552—21no—
10#22579878—21no—
11#22579877C2211yescharacteristic
12#22579871—21no—
13#22579870—22no—
14Q8×Dic277—21no—
15C4×Dic554C2211yescharacteristic
16C4×Dic554C2211yescharacteristic
17#22579845—21no—
18#22579802—21no—
19#22579802—21no—
20#22579800—22no—
21C4×#14555660C2211yescharacteristic
22C4⋊Q8×C277C2211yescharacteristic
23C4⋊C8×C277C2211yescharacteristic
24C4⋊C8×C277C2211yescharacteristic
25C2×Dic554D411yescharacteristic
26C2×Dic554D411yescharacteristic
27C2×D1108—21no—
28C2×D1108—21no—
29C2×D1108—21no—
30#17984552—42no—
31#17984552—42no—
32C2×#14555660—21no—
33C4⋊Dic277—22no—
34C4⋊Dic277D411yescharacteristic
35C4⋊Dic277D411yescharacteristic
36#17984542—22no—
37#17984542—22no—
38#17984542—21no—
39#17984542—21no—
40C4×Dic277—22no—
41C4×Dic277—21no—
42C4×Dic277—21no—
43C2×Q8×C277—21no—
44C2×C8×C277—21no—
45C2×C8×C277—21no—
46C4⋊C4×C277—21no—
47C4⋊C4×C277D412yes—
48C42×C277C2311yescharacteristic
49C22×D277—41no—
50Dic554—21no—
51Dic554—21no—
52Dic554—21no—
53Dic554SD1612yescomplemented
54D1108—42no—
55D1108—41no—
56D1108—41no—
57D1108—41no—
58D1108—41no—
59C2×Dic277—21no—
60C2×Dic277—21no—
61C2×Dic277—21no—
62C2×Dic277—21no—
63#14555660—41no—
64Q8×C277—41no—
65Q8×C277—41no—
66C2×C4×C277—22no—
67C2×C4×C277C2×D411yescharacteristic
68C2×C4×C277C2×D411yescharacteristic
69C2×C4×C277C2×D411yescharacteristic
70C8×C277—41no—
71C8×C277—41no—
72C22×C277#12011yescharacteristic
73C2×D277—81no—
74C2×D277—81no—
75C2×D277—81no—
76C4×C277—21no—
77C4×C277—42no—
78C4×C277C2×SD1611yescharacteristic
79C4×C277#13511yescharacteristic
80C4×C277AGL(1,ℤ/8)11yescharacteristic
81C4×C277#13711yescharacteristic
82Dic277—22no—
83Dic277—41no—
84Dic277—41no—
85Dic277—41no—
86C2×C277#44811yescharacteristic
87C2×C277#44911yescharacteristic
88C2×C277#45411yescharacteristic
89D277—161no—
90C277#162611yescharacteristic, complemented, Sylow
91#1626—2771nomaximal, Sylow
92#557—2771no—
93#486—2771no—
94#460—2771no—
95#460—2771no—
96#332D27711yescharacteristic, complemented
97Q8⋊C8—2771no—
98Q8⋊C8—2771no—
99C2×SD16—5541no—
100C2×SD16—5541no—
101C4⋊Q8—5541no—
102C4⋊Q8C2×D27711yescharacteristic
103#127—2771no—
104#125—5541no—
105#125—5542no—
106C4×Q8—2771no—
107C4×Q8—2771no—
108C4×Q8—5541no—
109C4×Q8—5541no—
110C4⋊C8C2×D27711yescharacteristic
111C4⋊C8C2×D27711yescharacteristic
112#102—5541no—
113#102—5541no—
114#102—5542no—
115C4×C8—2771no—
116C2×Q8—21no—
117C2×Q8—2771no—
118C2×Q8—2771no—
119C2×D4—5541no—
120C2×D4—5541no—
121C2×D4—5541no—
122SD16—11082no—
123SD16—11082no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—5541no—
127C4⋊C4—21no—
128C4⋊C4—2771no—
129C4⋊C4—2771no—
130C4⋊C4—5542no—
131C4⋊C4—5542no—
132C4⋊C4—5542no—
133C4⋊C4—5541no—
134C4⋊C4—5541no—
135C4⋊C4D110812yes—
136C42—5542no—
137C42—5541no—
138C42—5541no—
139C42C22×D27711yescharacteristic
140C23—11081no—
141Q8—41no—
142Q8—41no—
143Q8—2772no—
144Q8—5541no—
145Q8—5541no—
146Q8—5541no—
147D4—11082no—
148D4—11081no—
149D4—11081no—
150D4—11081no—
151D4—11081no—
152C2×C4—22no—
153C2×C4—5541no—
154C2×C4—5541no—
155C2×C4—5541no—
156C2×C4—5541no—
157C2×C4D4×D27711yescharacteristic
158C2×C4D4×D27711yescharacteristic
159C2×C4C2×D110811yescharacteristic
160C8—41no—
161C8—41no—
162C8—11081no—
163C22—22161no—
164C22—22161no—
165C22—22161no—
166C22#2257985011yescharacteristic
167C4—21no—
168C4—42no—
169C4—5542no—
170C4—11081no—
171C4—11081no—
172C4—11081no—
173C4SD16×D27711yescharacteristic
174C4#2257990111yescharacteristic
175C4#2257990411yescharacteristic
176C4#2257991211yescharacteristic
177C2—44321no—
178C2#3180014211yescharacteristic
179C2#3180014811yescharacteristic
180C2#3180017711yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
Fitting#332×C277C2
socleC22×C277#120
prime radical#22579877C22
hypercenter#332D277
hypocenterC277#1626
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #31800727C2semidirect
5. #31799732C2semidirect
6. #31799732C2semidirect
7. #332×C277C2semidirect
53. Dic554SD16semidirect
90. C277#1626semidirect
96. #332D277semidirect

Maximal subgroups

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

subgroupindex
#318007272
#318003502
#318002032
#317997322
#332×C2772
#1626277