Finite Group Databasebeta

← #46821287

Subgroups — #46821287

Order 34432.

392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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#31771156C211yesmaximal, characteristic
2#125×D269C211yesmaximal, characteristic, complemented
3#31770973C211yesmaximal, characteristic, complemented
4#31770971C211yesmaximal, characteristic, complemented
5#31770970C211yesmaximal, characteristic, complemented
6#31770961C214yesmaximal, complemented
7#31770605C214yesmaximal, complemented
8#31770557C211yesmaximal, characteristic, complemented
9#491×C269C211yesmaximal, characteristic, complemented
10C2×#16864403C2212yes—
11C2×#16864385C2212yes—
12#22575450C2211yescharacteristic
13#22575445C2211yescharacteristic
14#22575444C2212yes—
15#22575443—22no—
16#22575442C2212yes—
17#22575428—22no—
18#22575415—22no—
19C4⋊C4×D269—22no—
20C4⋊C4×D269C2212yes—
21C42×D269C2211yescharacteristic
22#22575377C2214yes—
23#22575375C2214yes—
24#22575373C2214yes—
25#22575364C2211yescharacteristic
26C8×Dic269C2212yes—
27C4⋊Q8×C269C2211yescharacteristic
28#125×C269C2211yescharacteristic
29#103×C269C2214yes—
30#97×C269C2211yescharacteristic
31#16864403—28no—
32C2×D1076—22no—
33C2×D1076—22no—
34C2×D1076C2312yes—
35C2×C4×D269—22no—
36C2×C4×D269—22no—
37C2×C4×D269D412yes—
38C2×C4×D269C2311yescharacteristic
39#16864385—24no—
40C2×#14524130C2312yes—
41C4⋊Dic269—22no—
42C4⋊Dic269C2312yes—
43#16864381—22no—
44#16864381—22no—
45#16864381—22no—
46#16864379—24no—
47C4×Dic269D412yes—
48C4×Dic269C2311yescharacteristic
49C2×Q8×C269C2312yes—
50C2×C8×C269C2312yes—
51C4⋊C4×C269—22no—
52C4⋊C4×C269—22no—
53C4⋊C4×C269C2312yes—
54C42×C269C2311yescharacteristic
55C22×D269—22no—
56C22×D269C2×D411yescharacteristic
57D1076—24no—
58D1076—44no—
59D1076—44no—
60C2×Dic269—22no—
61C2×Dic269C2×D412yes—
62C2×Dic269C2×D411yescharacteristic
63C4×D269—42no—
64C4×D269—44no—
65C4×D269—44no—
66C4×D269#4114yes—
67#14524130—22no—
68Q8×C269—24no—
69C2×C4×C269—22no—
70C2×C4×C269—22no—
71C2×C4×C269C2×D412yes—
72C2×C4×C269C2411yescharacteristic
73C8×C269—22no—
74C22×C269C22×D411yescharacteristic
75C2×D269—22no—
76C2×D269—42no—
77C2×D269—44no—
78C2×D269#12412yes—
79C4×C269—22no—
80C4×C269—42no—
81C4×C269—42no—
82C4×C269C2×#4112yes—
83Dic269—22no—
84Dic269—42no—
85Dic269#12412yes—
86C2×C269C2×#12411yescharacteristic
87C2×C269#57512yes—
88D269—22no—
89D269—82no—
90C269#314211yescharacteristic, complemented, Sylow
91#3142—2691nomaximal, Sylow
92#532—2691no—
93C2×#125—2691no—
94#491—2691no—
95#491D26911yescharacteristic, complemented
96#490—2691no—
97#490—2691no—
98#488—2694no—
99#417—2694no—
100C4×M16—2691no—
101C2×#41—2692no—
102C2×M16—2692no—
103C4⋊Q8C2×D26911yescharacteristic
104#127—2691no—
105#125—2692no—
106#125—2691no—
107#125—5382no—
108#125C2×D26911yescharacteristic
109#124—2692no—
110#121—5382no—
111C4×D4—5382no—
112C2×C4⋊C4—2692no—
113C2×C4⋊C4—5382no—
114C2×C42—2691no—
115#103—2694no—
116#103C2×D26914yes—
117#102—2694no—
118#102—2694no—
119#97—2691no—
120#97C2×D26911yescharacteristic
121C4×C8—2692no—
122#41—5388no—
123C2×Q8C22×D26912yes—
124C2×D4—2692no—
125C2×D4—5382no—
126C2×D4—5382no—
127C22×C4—2691no—
128C22×C4—2692no—
129C22×C4—5382no—
130C22×C4—5382no—
131M16—5384no—
132C2×C8—2692no—
133C2×C8C22×D26912yes—
134C4⋊C4—22no—
135C4⋊C4—22no—
136C4⋊C4—2692no—
137C4⋊C4—5382no—
138C4⋊C4—5382no—
139C4⋊C4—5382no—
140C4⋊C4—5382no—
141C4⋊C4C22×D26912yes—
142C22⋊C4—5384no—
143C42—2692no—
144C42—2691no—
145C42C22×D26911yescharacteristic
146C23—2691no—
147C23—5382no—
148Q8—24no—
149D4—5384no—
150D4—10764no—
151D4—10764no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—2691no—
155C2×C4—2694no—
156C2×C4—2692no—
157C2×C4—5382no—
158C2×C4—10762no—
159C2×C4—10764no—
160C2×C4—10764no—
161C2×C4D4×D26912yes—
162C2×C4C23×D26911yescharacteristic
163C8—22no—
164C8—5382no—
165C22—2692no—
166C22—5382no—
167C22—10764no—
168C22—10762no—
169C22C2×D4×D26911yescharacteristic
170C4—22no—
171C4—42no—
172C4—42no—
173C4—2692no—
174C4—5382no—
175C4—10762no—
176C4#41×D26912yes—
177C2—5382no—
178C2—21522no—
179C2#124×D26911yescharacteristic
180C2#3177140412yes—
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#491×C269C2
socleC22×C269C22×D4
prime radical#31771156C2
hypercenter#491D269
hypocenterC269#3142
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #125×D269C2semidirect
3. #31770973C2semidirect
4. #31770971C2semidirect
5. #31770970C2semidirect
6. #31770961C2semidirect
7. #31770605C2semidirect
8. #31770557C2semidirect
9. #491×C269C2semidirect
90. C269#3142semidirect
95. #491D269semidirect

Maximal subgroups

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

subgroupindex
#317711562
#125×D2692
#317709732
#317709712
#317709702
#317709612
#317706052
#317705572
#491×C2692
#3142269