Finite Group Databasebeta

← #46821177

Subgroups — #46821177

Order 34432.

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

normal subgroups only

This group has 382 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#31771210C211yesmaximal, characteristic
2#31771082C211yesmaximal, characteristic, complemented
3#31770930C212yesmaximal, complemented
4#31770913C212yesmaximal, complemented
5#31770806C212yesmaximal, complemented
6#31770746C212yesmaximal, complemented
7#31770707C212yesmaximal, complemented
8C4×#16864391C212yesmaximal, complemented
9#433×C269C211yesmaximal, characteristic, complemented
10C22×Dic538C2211yescharacteristic
11C2×#16864391C2212yes—
12C2×#16864391C2212yes—
13#22575450C2211yescharacteristic
14#22575445C2211yescharacteristic
15#22575438—22no—
16#22575427C2212yes—
17#22575426—22no—
18C4×Dic538C2212yes—
19C4×Dic538C2212yes—
20#22575418—22no—
21C4×D1076C2212yes—
22#22575412C2211yescharacteristic
23#22575409—22no—
24#22575387C2212yes—
25#22575385C2212yes—
26#22575378C2212yes—
27#22575378C2212yes—
28#22575375C2212yes—
29#22575375C2212yes—
30#117×C269C2211yescharacteristic
31C4⋊C8×C269C2212yes—
32C22⋊C8×C269C2212yes—
33#97×C269C2211yescharacteristic
34C4×C8×C269C2211yescharacteristic
35C2×Dic538—24no—
36C2×Dic538—21no—
37C2×Dic538C2312yes—
38C2×D1076—22no—
39C2×D1076C2312yes—
40C2×C22⋊D269—22no—
41C22×Dic269—21no—
42C2×C4×D269—22no—
43#16864391—24no—
44#16864391—24no—
45C4⋊Dic269C2312yes—
46C4⋊Dic269C2312yes—
47#16864381—22no—
48#16864381—22no—
49#16864381—22no—
50C22⋊Dic269—21no—
51#16864379—22no—
52#16864379—22no—
53C4×Dic269—22no—
54C4×Dic269—22no—
55C4×Dic269—21no—
56C22×C4×C269C2311yescharacteristic
57C2×C8×C269C2312yes—
58C2×C8×C269C2312yes—
59C4⋊C4×C269D412yes—
60C22⋊C4×C269D412yes—
61C42×C269C2311yescharacteristic
62C42×C269C2311yescharacteristic
63C22×D269—22no—
64Dic538—24no—
65Dic538—22no—
66Dic538#4114yes—
67D1076—22no—
68D1076—22no—
69D1076—82no—
70C22⋊D269—82no—
71C2×Dic269—24no—
72C2×Dic269—22no—
73C2×Dic269—22no—
74C2×Dic269—22no—
75C4×D269—82no—
76C23×C269C2×D411yescharacteristic
77C2×C4×C269—22no—
78C2×C4×C269C2×D412yes—
79C2×C4×C269C2×D412yes—
80C2×C4×C269C2×D411yescharacteristic
81C2×C4×C269C2411yescharacteristic
82C8×C269—22no—
83C8×C269—22no—
84C22×C269—21no—
85C22×C269—22no—
86C22×C269C22×D411yescharacteristic
87C2×D269—42no—
88C2×D269—42no—
89C2×D269—42no—
90C4×C269—21no—
91C4×C269—22no—
92C4×C269—22no—
93C4×C269C2×#4112yes—
94Dic269—24no—
95Dic269—42no—
96Dic269—42no—
97C2×C269—41no—
98C2×C269#52511yescharacteristic
99C2×C269#57712yes—
100D269—82no—
101C269#312611yescharacteristic, complemented, Sylow
102#3126—2691nomaximal, Sylow
103#540—2691no—
104#519—2691no—
105#482—2692no—
106#479—2692no—
107#460—2692no—
108#448—2692no—
109#440—2692no—
110C4×SD16—2692no—
111#433D26911yescharacteristic, complemented
112C22×Q8—2691no—
113C2×SD16—2692no—
114C2×SD16—2692no—
115#127—2691no—
116#125—2691no—
117#123—5382no—
118#121—2692no—
119#121—5382no—
120C4×Q8—2692no—
121C4×Q8—2692no—
122C4×Q8—5382no—
123C4×D4—2692no—
124#117—2691no—
125#117—5382no—
126#117C2×D26911yescharacteristic
127#107—2692no—
128#106—2692no—
129C4⋊C8C2×D26912yes—
130#103—2692no—
131#103—2692no—
132#102—2692no—
133#102—2692no—
134C22⋊C8C2×D26912yes—
135#97C2×D26911yescharacteristic
136C4×C8C2×D26911yescharacteristic
137C2×Q8—2692no—
138C2×Q8—5384no—
139C2×Q8—5381no—
140C2×D4—2692no—
141C2×D4—5382no—
142C2×D4—5382no—
143C22×C4—5381no—
144C22×C4—5382no—
145C22×C4C22×D26911yescharacteristic
146SD16—5384no—
147SD16—5384no—
148C2×C8C22×D26912yes—
149C2×C8C22×D26912yes—
150C4⋊C4—2692no—
151C4⋊C4—2692no—
152C4⋊C4—5382no—
153C4⋊C4—5382no—
154C4⋊C4—5382no—
155C4⋊C4D107612yes—
156C22⋊C4—5381no—
157C22⋊C4—5382no—
158C22⋊C4—5382no—
159C22⋊C4D107612yes—
160C42—5381no—
161C42—5382no—
162C42—5382no—
163C42C22×D26911yescharacteristic
164C42C22×D26911yescharacteristic
165C23—5382no—
166C23C2×D107611yescharacteristic
167Q8—2694no—
168Q8—5384no—
169Q8—5382no—
170D4—5382no—
171D4—5382no—
172D4—21522no—
173D4—21522no—
174C2×C4—22no—
175C2×C4—5384no—
176C2×C4—5382no—
177C2×C4—5382no—
178C2×C4—5382no—
179C2×C4—21522no—
180C2×C4C2×D107612yes—
181C2×C4C2×D107612yes—
182C2×C4C2×D107611yescharacteristic
183C2×C4C23×D26911yescharacteristic
184C8—22no—
185C8—22no—
186C22—22no—
187C22—21no—
188C22—10762no—
189C22—10762no—
190C22—10762no—
191C22C22×D107611yescharacteristic
192C4—22no—
193C4—22no—
194C4—21no—
195C4—5384no—
196C4—10762no—
197C4—10762no—
198C4#41×D26912yes—
199C2—41no—
200C2—21522no—
201C2#3177111711yescharacteristic
202C2#3177141712yes—
subgroupG/H
centerC22C22×D1076
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#433×C269C2
socleC22×C269C22×D4
prime radical#31771210C2
hypercenter#433D269
hypocenterC269#3126
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #31771082C2semidirect
3. #31770930C2semidirect
4. #31770913C2semidirect
5. #31770806C2semidirect
6. #31770746C2semidirect
7. #31770707C2semidirect
8. C4×#16864391C2semidirect
9. #433×C269C2semidirect
101. C269#3126semidirect
111. #433D269semidirect

Maximal subgroups

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

subgroupindex
#317712102
#317710822
#317709302
#317709132
#317708062
#317707462
#317707072
C4×#168643912
#433×C2692
#3126269