Finite Group Databasebeta

← #47985115

Subgroups — #47985115

Order 35456.

226 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 49 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#31800802C211yesmaximal, characteristic, complemented
2#31800440C212yesmaximal, complemented
3#31800255C211yesmaximal, characteristic, complemented
4#31799813C212yesmaximal, complemented
5#349×C277C211yesmaximal, characteristic, complemented
6C2×#17984563—21no—
7#22579913—22no—
8#22579908—22no—
9#22579902—21no—
10#22579902C2212yes—
11C2×D2216C2211yescharacteristic, complemented
12#22579854—21no—
13#22579825—22no—
14D4432—22no—
15#22579812C2211yescharacteristic, complemented
16#22579802—21no—
17C2×M16×C277C2211yescharacteristic
18M32×C277C2212yescomplemented
19#17984563—22no—
20#17984563—22no—
21#17984563—41no—
22#17984563—41no—
23C2×Dic554—21no—
24C2×D1108—21no—
25C2×D1108—21no—
26C2×C22⋊D277—41no—
27C2×C22⋊D277—41no—
28C2×C4×D277—41no—
29Dic1108—21no—
30Dic1108D412yescomplemented
31#17984552—22no—
32#17984552—22no—
33D2216—21no—
34D2216—22no—
35D2216D412yescomplemented
36C4⋊Dic277—21no—
37#17984540—41no—
38C22×C4×C277D411yescharacteristic
39M16×C277—22no—
40C2×C8×C277D411yescharacteristic
41C2×C8×C277C2311yescharacteristic
42C16×C277—22no—
43C22×D277—41no—
44C22×D277—41no—
45Dic554—22no—
46Dic554—41no—
47D1108—22no—
48D1108—41no—
49D1108—41no—
50D1108—41no—
51C22⋊D277—42no—
52C22⋊D277—42no—
53C22⋊D277—82no—
54C2×Dic277—41no—
55C2×Dic277—41no—
56C4×D277—42no—
57C4×D277—42no—
58C23×C277D811yescharacteristic
59C2×C4×C277—21no—
60C2×C4×C277—21no—
61C2×C4×C277D811yescharacteristic
62C2×C4×C277C2×D411yescharacteristic
63C8×C277—21no—
64C8×C277C2×D412yes—
65C22×C277—21no—
66C22×C277—41no—
67C22×C277C2×D811yescharacteristic
68C2×D277—42no—
69C2×D277—82no—
70C2×D277—81no—
71C2×D277—81no—
72C2×D277—81no—
73C4×C277—21no—
74C4×C277#12011yescharacteristic
75C4×C277AGL(1,ℤ/8)11yescharacteristic
76Dic277—42no—
77Dic277—81no—
78C2×C277—21no—
79C2×C277—41no—
80C2×C277#44711yescharacteristic
81D277—82no—
82D277—161no—
83C277#219011yescharacteristic, complemented, Sylow
84#2190—2771nomaximal, Sylow
85#575—2771no—
86#509—2772no—
87#469—2771no—
88#360—2772no—
89#349D27711yescharacteristic, complemented
90C2×#41—5541no—
91#137—5542no—
92AGL(1,ℤ/8)—5542no—
93#135—2772no—
94#135—5541no—
95C2×D8—2771no—
96C2×M16C2×D27711yescharacteristic
97#121—5541no—
98SD32—5542no—
99D16—5542no—
100M32C2×D27712yescomplemented
101#106—2771no—
102#102—5541no—
103#41—5542no—
104#41—5542no—
105#41—11081no—
106#41—11081no—
107C2×Q8—5541no—
108C2×D4—5541no—
109C2×D4—5541no—
110C2×D4—11081no—
111C2×D4—11081no—
112C22×C4—11081no—
113C22×C4D110811yescharacteristic
114Q16—2772no—
115Q16—5541no—
116SD16—5542no—
117SD16—5542no—
118D8—2772no—
119D8—5541no—
120D8—5542no—
121M16—22no—
122C2×C8D110811yescharacteristic
123C2×C8C22×D27711yescharacteristic
124C4⋊C4—5541no—
125C22⋊C4—11081no—
126C16—22no—
127C23—11081no—
128C23—11081no—
129C23D221611yescharacteristic
130Q8—5542no—
131Q8—11081no—
132D4—5542no—
133D4—11081no—
134D4—11082no—
135D4—11082no—
136D4—11081no—
137D4—11081no—
138D4—22162no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—11082no—
142C2×C4—11081no—
143C2×C4—11082no—
144C2×C4—11081no—
145C2×C4D221611yescharacteristic
146C2×C4C2×D110811yescharacteristic
147C8—21no—
148C8D4×D27712yes—
149C22—21no—
150C22—41no—
151C22—11082no—
152C22—22161no—
153C22—22161no—
154C22—22162no—
155C22—22161no—
156C22C2×D221611yescharacteristic
157C4—21no—
158C4—11082no—
159C4—22161no—
160C4#2257985011yescharacteristic
161C4#2257990811yescharacteristic
162C2—21no—
163C2—41no—
164C2—44321no—
165C2—22162no—
166C2#3180013811yescharacteristic
subgroupG/H
centerC2#31800138
commutator, cosocleC2×C8×C277C23
FrattiniC2×C8C22×D277
Fitting#349×C277C2
socleC2×C277#447
hypercenter#349D277
hypocenterC277#2190
LCSG ▷ C2×C8×C277 ▷ C4×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #349

Complements

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

NH ≅ G/Ntype
1. #31800802C2semidirect
2. #31800440C2semidirect
3. #31800255C2semidirect
4. #31799813C2semidirect
5. #349×C277C2semidirect
11. C2×D2216C22semidirect
15. #22579812C22semidirect
18. M32×C277C22semidirect
30. Dic1108D4semidirect
35. D2216D4semidirect
83. C277#2190semidirect
89. #349D277semidirect
100. M32C2×D277semidirect

Maximal subgroups

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

subgroupindex
#318008022
#318004402
#318002552
#317998132
#349×C2772
#2190277