Finite Group Databasebeta

← #46810138

Subgroups — #46810138

Order 34432.

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

normal subgroups only

This group has 200 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#31771329C211yesmaximal, characteristic
2#31770887C211yesmaximal, characteristic, complemented
3#31770807C211yesmaximal, characteristic
4#31770351C211yesmaximal, characteristic, complemented
5#31770337C211yesmaximal, characteristic, complemented
6#31770334C211yesmaximal, characteristic
7#500×C269C211yesmaximal, characteristic, complemented
8C2×#16864389—21no—
9#22575448—22no—
10#22575442—21no—
11#22575433—21no—
12Q8×Dic269—21no—
13C4×Dic538C2211yescharacteristic
14C4×D1076C2211yescharacteristic
15#22575411—21no—
16#22575384—21no—
17C4⋊#14524130C2211yescharacteristic
18C4⋊#14524130C2211yescharacteristic
19#22575377—21no—
20#22575376—21no—
21C4⋊Q8×C269C2211yescharacteristic
22C4⋊Q8×C269C2211yescharacteristic
23#107×C269—22no—
24C4×C8×C269C2211yescharacteristic
25C2×Dic538D411yescharacteristic
26C2×D1076D411yescharacteristic
27C2×C4×D269—21no—
28#16864389—42no—
29C2×#14524130—21no—
30C2×#14524130—21no—
31C4⋊Dic269—22no—
32C4⋊Dic269D411yescharacteristic
33C4⋊Dic269D411yescharacteristic
34#16864381—21no—
35#16864379—22no—
36#16864379—22no—
37#16864379—21no—
38C4×Dic269—22no—
39C4×Dic269—21no—
40C2×Q8×C269—21no—
41C2×Q8×C269—21no—
42C2×C8×C269—21no—
43C4⋊C4×C269—21no—
44C4⋊C4×C269—21no—
45C4⋊C4×C269—21no—
46C4⋊C4×C269D412yes—
47C42×C269C2311yescharacteristic
48C22×D269—21no—
49Dic538—21no—
50Dic538—21no—
51D1076—21no—
52D1076—21no—
53C2×Dic269—21no—
54C2×Dic269—21no—
55C2×Dic269—21no—
56C4×D269—41no—
57C4×D269—41no—
58#14524130—41no—
59#14524130—41no—
60Q8×C269—41no—
61Q8×C269—41no—
62Q8×C269—41no—
63Q8×C269—41no—
64C2×C4×C269—22no—
65C2×C4×C269—41no—
66C2×C4×C269C2×D411yescharacteristic
67C2×C4×C269C2×D411yescharacteristic
68C2×C4×C269C2×D411yescharacteristic
69C8×C269—22no—
70C22×C269#12011yescharacteristic
71C2×D269—41no—
72C2×D269—41no—
73C2×D269—41no—
74C4×C269—21no—
75C4×C269—42no—
76C4×C269—81no—
77C4×C269#13511yescharacteristic
78C4×C269#13511yescharacteristic
79C4×C269AGL(1,ℤ/8)11yescharacteristic
80C4×C269#13711yescharacteristic
81Dic269—41no—
82Dic269—41no—
83Dic269—41no—
84C2×C269#44911yescharacteristic
85C2×C269#45211yescharacteristic
86C2×C269#45611yescharacteristic
87D269—81no—
88C269#165011yescharacteristic, complemented, Sylow
89#1650—2691nomaximal, Sylow
90#556—2691no—
91#500D26911yescharacteristic, complemented
92#475—2691no—
93#461—2691no—
94#332—2691no—
95Q8⋊C8—2691no—
96D4⋊C8—2691no—
97C2×SD16—5381no—
98C4⋊Q8C2×D26911yescharacteristic
99C4⋊Q8C2×D26911yescharacteristic
100#126—5382no—
101#124—5381no—
102C22⋊Q8—5381no—
103C4×Q8—2691no—
104C4×Q8—5381no—
105C4×D4—2691no—
106#117—5381no—
107#107—22no—
108#106—5381no—
109C4⋊C8—2691no—
110C4⋊C8—2691no—
111#103—5381no—
112#103—5381no—
113C4×C8C2×D26911yescharacteristic
114C2×Q8—21no—
115C2×Q8—21no—
116C2×Q8—2691no—
117C2×D4—2691no—
118C22×C4—5381no—
119SD16—10762no—
120C2×C8—21no—
121C2×C8—5381no—
122C2×C8—5381no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—2691no—
127C4⋊C4—2691no—
128C4⋊C4—5382no—
129C4⋊C4—5381no—
130C4⋊C4C22⋊D26912yes—
131C22⋊C4—5382no—
132C22⋊C4—5382no—
133C22⋊C4—5381no—
134C42—5382no—
135C42—5381no—
136C42C22×D26911yescharacteristic
137C23—5381no—
138Q8—41no—
139Q8—41no—
140Q8—41no—
141Q8—41no—
142Q8—5381no—
143Q8—5381no—
144D4—5381no—
145D4—5381no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—5381no—
149C2×C4—5381no—
150C2×C4—5381no—
151C2×C4—10761no—
152C2×C4—10761no—
153C2×C4D4×D26911yescharacteristic
154C2×C4D4×D26911yescharacteristic
155C2×C4C2×C22⋊D26911yescharacteristic
156C8—22no—
157C8—10761no—
158C8—10761no—
159C22—10761no—
160C22—10761no—
161C22—10761no—
162C22#2257542111yescharacteristic
163C4—21no—
164C4—42no—
165C4—81no—
166C4—10761no—
167C4—10761no—
168C4—10761no—
169C4#2257547211yescharacteristic
170C4#2257547611yescharacteristic
171C4#2257547711yescharacteristic
172C4#2257548511yescharacteristic
173C2—21521no—
174C2#3177074711yescharacteristic
175C2#3177076611yescharacteristic
176C2#3177078711yescharacteristic
subgroupG/H
centerC22#22575421
commutator, cosocleC42×C269C23
FrattiniC42C22×D269
Fitting#500×C269C2
socleC22×C269#120
prime radicalC2×D1076D4
hypercenter#500D269
hypocenterC269#1650
LCSG ▷ C42×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
2. #31770887C2semidirect
4. #31770351C2semidirect
5. #31770337C2semidirect
7. #500×C269C2semidirect
88. C269#1650semidirect
91. #500D269semidirect

Maximal subgroups

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

subgroupindex
#317713292
#317708872
#317708072
#317703512
#317703372
#317703342
#500×C2692
#1650269