Finite Group Databasebeta

← #46821258

Subgroups — #46821258

Order 34432.

484 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 121 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#31771161C211yesmaximal, characteristic, complemented
2#127×D269C211yesmaximal, characteristic
3#31770971C211yesmaximal, characteristic, complemented
4#31770970C211yesmaximal, characteristic, complemented
5#31770969C211yesmaximal, characteristic, complemented
6#31770950C214yesmaximal, complemented
7#31770608C214yesmaximal, complemented
8#31770557C211yesmaximal, characteristic, complemented
9#490×C269C211yesmaximal, characteristic, complemented
10C2×D4×D269—22no—
11C2×D4×D269C2212yes—
12C2×#16864385C2212yes—
13#22575452C2212yescomplemented
14#22575450C2211yescharacteristic
15#22575449—22no—
16#22575449C2212yes—
17#22575445C2211yescharacteristic, complemented
18#22575431—22no—
19#22575418—22no—
20#22575411C2212yes—
21C42×D269C2211yescharacteristic
22#22575375C2214yescomplemented
23#22575374C2214yescomplemented
24#22575373C2214yescomplemented
25#22575364C2211yescharacteristic, complemented
26C8×Dic269C2212yescomplemented
27#127×C269C2211yescharacteristic
28#125×C269C2211yescharacteristic, complemented
29#102×C269C2214yescomplemented
30#97×C269C2211yescharacteristic, complemented
31C23×D269—22no—
32C2×Dic538—22no—
33C2×D1076—22no—
34C2×D1076C2312yes—
35C2×C22⋊D269—22no—
36C2×C22⋊D269—24no—
37D4×D269—28no—
38D4×D269—48no—
39C2×C4×D269D412yes—
40C2×C4×D269C2311yescharacteristic
41#16864385—24no—
42C2×#14524130C2312yes—
43C4⋊Dic269C2312yes—
44#16864381—22no—
45#16864381—22no—
46#16864379—22no—
47C4×Dic269—22no—
48C4×Dic269D412yes—
49C4×Dic269C2311yescharacteristic
50C2×D4×C269—22no—
51C2×D4×C269C2312yes—
52C2×C8×C269C2312yes—
53C4⋊C4×C269—22no—
54C4⋊C4×C269C2312yes—
55C42×C269C2311yescharacteristic
56C22×D269—22no—
57C22×D269—48no—
58C22×D269—44no—
59C22×D269C2×D411yescharacteristic
60Dic538—44no—
61D1076—24no—
62D1076—44no—
63C22⋊D269—44no—
64C22⋊D269—48no—
65C2×Dic269—22no—
66C2×Dic269C2×D411yescharacteristic
67C2×Dic269C2×D412yes—
68C4×D269—24no—
69C4×D269#4114yes—
70#14524130—22no—
71C23×C269—22no—
72D4×C269—24no—
73D4×C269—44no—
74C2×C4×C269—22no—
75C2×C4×C269C2×D412yes—
76C2×C4×C269C2411yescharacteristic
77C8×C269—22no—
78C22×C269—42no—
79C22×C269—44no—
80C22×C269C22×D411yescharacteristic
81C2×D269—22no—
82C2×D269—42no—
83C2×D269—44no—
84C2×D269—88no—
85C2×D269#12412yes—
86C4×C269—22no—
87C4×C269—42no—
88C4×C269C2×#4112yes—
89Dic269—42no—
90Dic269#12412yes—
91Dic269AGL(1,ℤ/8)14yes—
92C2×C269—82no—
93C2×C269C2×#12411yescharacteristic
94C2×C269C2×AGL(1,ℤ/8)12yes—
95D269—22no—
96D269—82no—
97C269#313811yescharacteristic, complemented, Sylow
98#3138—2691nomaximal, Sylow
99#533—2691no—
100C2×#127—2691no—
101#490—2691no—
102#490—2691no—
103#490—2691no—
104#490D26911yescharacteristic, complemented
105#486—2694no—
106#418—2694no—
107C4×M16—2691no—
108C22×D4—2692no—
109C22×D4—5382no—
110C2×M16—2692no—
111C4⋊Q8—2692no—
112#127—2692no—
113#127—2691no—
114#127—5382no—
115#127C2×D26911yescharacteristic
116#125—2691no—
117#125C2×D26911yescharacteristic, complemented
118C22⋊Q8—5382no—
119C4×Q8—5382no—
120#117—2692no—
121C2×C42—2691no—
122#102—2694no—
123#102—2694no—
124#102—2694no—
125#102C2×D26914yescomplemented
126#97—2691no—
127#97C2×D26911yescharacteristic, complemented
128C4×C8—2692no—
129C24—5382no—
130C2×Q8—5382no—
131C2×D4—22no—
132C2×D4—2692no—
133C2×D4—5388no—
134C2×D4—5384no—
135C2×D4—5382no—
136C2×D4—5382no—
137C2×D4—10768no—
138C2×D4C22×D26912yes—
139C22×C4—2691no—
140C22×C4—2692no—
141M16—5384no—
142C2×C8—2692no—
143C2×C8C22×D26912yes—
144C4⋊C4—22no—
145C4⋊C4—2692no—
146C4⋊C4—5382no—
147C4⋊C4—5382no—
148C4⋊C4C22×D26912yes—
149C22⋊C4—5382no—
150C42—2692no—
151C42—2691no—
152C42—5382no—
153C42C22×D26911yescharacteristic
154C23—22no—
155C23—2691no—
156C23—5382no—
157C23—10764no—
158C23—10768no—
159Q8—10764no—
160D4—24no—
161D4—44no—
162D4—5384no—
163D4—10764no—
164D4—10764no—
165D4—10768no—
166C2×C4—22no—
167C2×C4—2691no—
168C2×C4—2692no—
169C2×C4—2694no—
170C2×C4—5384no—
171C2×C4—5382no—
172C2×C4D4×D26912yes—
173C2×C4C23×D26911yescharacteristic
174C8—22no—
175C8—5382no—
176C22—42no—
177C22—44no—
178C22—2692no—
179C22—5382no—
180C22—10762no—
181C22—10764no—
182C22—21528no—
183C22C2×D4×D26911yescharacteristic
184C4—22no—
185C4—42no—
186C4—2692no—
187C4—2694no—
188C4—10762no—
189C4#41×D26912yes—
190C2—82no—
191C2—5382no—
192C2—21522no—
193C2#124×D26911yescharacteristic
194C2AGL(1,ℤ/8)×D26912yes—
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#490×C269C2
socleC22×C269C22×D4
prime radical#127×D269C2
hypercenter#490D269
hypocenterC269#3138
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #31771161C2semidirect
3. #31770971C2semidirect
4. #31770970C2semidirect
5. #31770969C2semidirect
6. #31770950C2semidirect
7. #31770608C2semidirect
8. #31770557C2semidirect
9. #490×C269C2semidirect
13. #22575452C22semidirect
17. #22575445C22semidirect
22. #22575375C22semidirect
23. #22575374C22semidirect
24. #22575373C22semidirect
25. #22575364C22semidirect
26. C8×Dic269C22semidirect
28. #125×C269C22semidirect
29. #102×C269C22semidirect
30. #97×C269C22semidirect
97. C269#3138semidirect
104. #490D269semidirect
117. #125C2×D269semidirect
125. #102C2×D269semidirect
127. #97C2×D269semidirect

Maximal subgroups

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

subgroupindex
#317711612
#127×D2692
#317709712
#317709702
#317709692
#317709502
#317706082
#317705572
#490×C2692
#3138269