Finite Group Databasebeta

← #46809992

Subgroups — #46809992

Order 34432.

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

normal subgroups only

This group has 216 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, complemented
2#31770802C211yesmaximal, characteristic, complemented
3#31770797C211yesmaximal, characteristic
4#31770351C211yesmaximal, characteristic, complemented
5#31770337C211yesmaximal, characteristic, complemented
6#31770334C211yesmaximal, characteristic, complemented
7#486×C269C211yesmaximal, characteristic, complemented
8C2×#16864390—21no—
9C2×#16864387—21no—
10#22575448—22no—
11#22575442—21no—
12#22575433—21no—
13Q8×Dic269—21no—
14C4×Dic538C2211yescharacteristic
15C4×D1076C2211yescharacteristic
16#22575411—21no—
17C4⋊#14524130C2211yescharacteristic
18C4⋊#14524130C2211yescharacteristic
19#22575374—21no—
20#22575374—21no—
21C4⋊Q8×C269C2211yescharacteristic
22#127×C269C2211yescharacteristic
23#102×C269—22no—
24C4×C8×C269C2211yescharacteristic
25C2×Dic538D411yescharacteristic
26C2×D1076D411yescharacteristic
27C2×C4×D269—21no—
28#16864390—42no—
29#16864387—42no—
30C2×#14524130—21no—
31C2×#14524130—21no—
32C4⋊Dic269—22no—
33C4⋊Dic269D411yescharacteristic
34C4⋊Dic269D411yescharacteristic
35#16864381—21no—
36#16864379—22no—
37#16864379—22no—
38#16864379—21no—
39C4×Dic269—22no—
40C4×Dic269—21no—
41C2×Q8×C269—21no—
42C2×D4×C269—21no—
43C2×D4×C269—21no—
44C2×D4×C269—21no—
45C2×C8×C269—21no—
46C4⋊C4×C269—21no—
47C4⋊C4×C269D412yes—
48C42×C269C2311yescharacteristic
49C22×D269—21no—
50Dic538—21no—
51Dic538—21no—
52D1076—21no—
53D1076—21no—
54C2×Dic269—21no—
55C2×Dic269—21no—
56C2×Dic269—21no—
57C4×D269—41no—
58C4×D269—41no—
59#14524130—41no—
60#14524130—41no—
61C23×C269—41no—
62Q8×C269—41no—
63Q8×C269—41no—
64D4×C269—42no—
65D4×C269—41no—
66D4×C269—41no—
67D4×C269—41no—
68D4×C269—41no—
69C2×C4×C269—22no—
70C2×C4×C269C2×D411yescharacteristic
71C2×C4×C269C2×D411yescharacteristic
72C2×C4×C269C2×D411yescharacteristic
73C8×C269—41no—
74C22×C269—81no—
75C22×C269—81no—
76C22×C269—81no—
77C22×C269#12011yescharacteristic
78C2×D269—41no—
79C2×D269—41no—
80C2×D269—41no—
81C4×C269—21no—
82C4×C269—42no—
83C4×C269#13511yescharacteristic
84C4×C269#13511yescharacteristic
85C4×C269AGL(1,ℤ/8)11yescharacteristic
86C4×C269AGL(1,ℤ/8)11yescharacteristic
87Dic269—41no—
88Dic269—41no—
89Dic269—41no—
90C2×C269—161no—
91C2×C269#44911yescharacteristic
92C2×C269#44911yescharacteristic
93C2×C269#45411yescharacteristic
94D269—81no—
95C269#162811yescharacteristic, complemented, Sylow
96#1628—2691nomaximal, Sylow
97#556—2691no—
98#486D26911yescharacteristic, complemented
99#460—2691no—
100#459—2691no—
101#332—2691no—
102Q8⋊C8—2691no—
103D4⋊C8—2691no—
104C2×SD16—5381no—
105C2×D8—5381no—
106C4⋊Q8C2×D26911yescharacteristic
107#127C2×D26911yescharacteristic
108#126—5382no—
109#124—5381no—
110C22⋊Q8—5381no—
111C4×Q8—2691no—
112C4×Q8—5381no—
113C4×D4—2691no—
114#117—5381no—
115C4⋊C8—2691no—
116C4⋊C8—2691no—
117#102—22no—
118#102—5381no—
119#102—5381no—
120C4×C8C2×D26911yescharacteristic
121C2×Q8—21no—
122C2×Q8—2691no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—2691no—
127C22×C4—5381no—
128SD16—10762no—
129D8—10762no—
130C2×C8—21no—
131C2×C8—5381no—
132C2×C8—5381no—
133C4⋊C4—21no—
134C4⋊C4—2691no—
135C4⋊C4—2691no—
136C4⋊C4—5382no—
137C4⋊C4—5381no—
138C4⋊C4C22⋊D26912yes—
139C22⋊C4—5382no—
140C22⋊C4—5382no—
141C22⋊C4—5381no—
142C42—5382no—
143C42—5381no—
144C42C22×D26911yescharacteristic
145C23—41no—
146C23—5381no—
147Q8—41no—
148Q8—41no—
149Q8—5381no—
150Q8—5381no—
151D4—42no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—5381no—
157D4—5381no—
158C2×C4—22no—
159C2×C4—5381no—
160C2×C4—5381no—
161C2×C4—5381no—
162C2×C4—10761no—
163C2×C4—10761no—
164C2×C4D4×D26911yescharacteristic
165C2×C4D4×D26911yescharacteristic
166C2×C4C2×C22⋊D26911yescharacteristic
167C8—41no—
168C8—10761no—
169C8—10761no—
170C22—81no—
171C22—81no—
172C22—81no—
173C22—10761no—
174C22—10761no—
175C22—10761no—
176C22#2257542111yescharacteristic
177C4—21no—
178C4—42no—
179C4—10761no—
180C4—10761no—
181C4—10761no—
182C4#2257547211yescharacteristic
183C4#2257547411yescharacteristic
184C4#2257547711yescharacteristic
185C4#2257548011yescharacteristic
186C2—161no—
187C2—21521no—
188C2#3177074711yescharacteristic
189C2#3177074911yescharacteristic
190C2#3177077711yescharacteristic
subgroupG/H
centerC22#22575421
commutator, cosocleC42×C269C23
FrattiniC42C22×D269
Fitting#486×C269C2
socleC22×C269#120
prime radical#31770797C2
hypercenter#486D269
hypocenterC269#1628
LCSG ▷ C42×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #31771329C2semidirect
2. #31770802C2semidirect
4. #31770351C2semidirect
5. #31770337C2semidirect
6. #31770334C2semidirect
7. #486×C269C2semidirect
95. C269#1628semidirect
98. #486D269semidirect

Maximal subgroups

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

subgroupindex
#317713292
#317708022
#317707972
#317703512
#317703372
#317703342
#486×C2692
#1628269