Finite Group Databasebeta

← #46812960

Subgroups — #46812960

Order 34432.

170 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 43 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#31771043C211yesmaximal, characteristic, complemented
2#31771041C211yesmaximal, characteristic, complemented
3#31770980C211yesmaximal, characteristic, complemented
4#31770721C211yesmaximal, characteristic, complemented
5#31770425C211yesmaximal, characteristic, complemented
6#31770417C211yesmaximal, characteristic, complemented
7#361×C269C211yesmaximal, characteristic, complemented
8#22575475C2211yescharacteristic
9C2×D2152C2211yescharacteristic
10C2×#16864387—21no—
11#22575461—21no—
12#22575449—21no—
13#22575398—21no—
14#22575397—21no—
15D4304—21no—
16#22575394—21no—
17#22575393C2211yescharacteristic
18#22575379—21no—
19C8×Dic269C2211yescharacteristic
20C2×D8×C269C2211yescharacteristic
21M32×C269C2211yescharacteristic
22#108×C269C2211yescharacteristic
23#16864402—21no—
24C2×D1076—21no—
25C2×C22⋊D269—42no—
26Dic1076D411yescharacteristic, complemented
27#16864391—21no—
28D2152—21no—
29D2152—21no—
30D2152D411yescharacteristic, complemented
31#16864387—41no—
32#16864387—41no—
33#16864385—41no—
34C2×#14524130D411yescharacteristic
35C8×D269—41no—
36C4×Dic269D411yescharacteristic
37#16864377—21no—
38C2×D4×C269—21no—
39D8×C269—21no—
40D8×C269—21no—
41M16×C269—21no—
42C2×C8×C269C2311yescharacteristic
43C16×C269—21no—
44C22×D269—41no—
45Dic538—21no—
46D1076—21no—
47D1076—41no—
48D1076—41no—
49C22⋊D269—41no—
50C22⋊D269—84no—
51C2×Dic269—21no—
52C4×D269—41no—
53#14524130D811yescharacteristic
54#14524130D811yescharacteristic
55C23×C269—41no—
56D4×C269—41no—
57D4×C269—41no—
58C2×C4×C269C2×D411yescharacteristic
59C8×C269—41no—
60C8×C269C2×D411yescharacteristic
61C8×C269#4111yescharacteristic
62C22×C269—82no—
63C22×C269—81no—
64C22×C269AGL(1,ℤ/8)11yescharacteristic
65C2×D269—41no—
66C2×D269—82no—
67C2×D269—81no—
68C4×C269#12111yescharacteristic
69C4×C269C2×D811yescharacteristic
70Dic269—22no—
71Dic269—41no—
72C2×C269—21no—
73C2×C269—161no—
74C2×C269#45911yescharacteristic
75D269—81no—
76D269—161no—
77C269#221311yescharacteristic, complemented, Sylow
78#2213—2691nomaximal, Sylow
79#509—2691no—
80#509—2691no—
81#493—2691no—
82#443—2691no—
83#364—2691no—
84#361—2691no—
85#361D26911yescharacteristic, complemented
86#135—2691no—
87C2×D8—2691no—
88C2×D8—5381no—
89C2×D8C2×D26911yescharacteristic
90#131—5381no—
91#127—5381no—
92SD32—5381no—
93SD32—5381no—
94D16—5381no—
95D16—5381no—
96M32—2691no—
97M32C2×D26911yescharacteristic
98#108C2×D26911yescharacteristic
99#104—5381no—
100C4×C8—2691no—
101#41—5381no—
102C2×D4—21no—
103C2×D4—5381no—
104C2×D4—10762no—
105Q16—2691no—
106SD16—5381no—
107D8—21no—
108D8—21no—
109D8—2691no—
110D8—5381no—
111D8—5381no—
112D8—10761no—
113D8—10761no—
114M16—21no—
115M16—10761no—
116C2×C8—2691no—
117C2×C8—10761no—
118C2×C8C22×D26911yescharacteristic
119C42—2691no—
120C16—21no—
121C16—5381no—
122C23—41no—
123C23—10761no—
124Q8—5381no—
125D4—41no—
126D4—41no—
127D4—5381no—
128D4—10761no—
129D4—10761no—
130D4—10761no—
131D4—21524no—
132C2×C4—5381no—
133C2×C4—10761no—
134C2×C4D4×D26911yescharacteristic
135C8—41no—
136C8—2691no—
137C8—2691no—
138C8D4×D26911yescharacteristic
139C8#1686440211yescharacteristic
140C22—82no—
141C22—81no—
142C22—10761no—
143C22—21522no—
144C22—21521no—
145C22#2257548011yescharacteristic
146C4—5382no—
147C4—10761no—
148C4#2257542611yescharacteristic
149C4D8×D26911yescharacteristic
150C2—21no—
151C2—161no—
152C2—21521no—
153C2—43041no—
154C2#3177079911yescharacteristic
subgroupG/H
centerC2#31770799
commutator, cosocleC2×C8×C269C23
FrattiniC2×C8C22×D269
Fitting#361×C269C2
socleC2×C269#459
hypercenter#361D269
hypocenterC269#2213
LCSG ▷ C2×C8×C269 ▷ C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #361

Complements

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

NH ≅ G/Ntype
1. #31771043C2semidirect
2. #31771041C2semidirect
3. #31770980C2semidirect
4. #31770721C2semidirect
5. #31770425C2semidirect
6. #31770417C2semidirect
7. #361×C269C2semidirect
26. Dic1076D4semidirect
30. D2152D4semidirect
77. C269#2213semidirect
85. #361D269semidirect

Maximal subgroups

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

subgroupindex
#317710432
#317710412
#317709802
#317707212
#317704252
#317704172
#361×C2692
#2213269