Finite Group Databasebeta

← #46821008

Subgroups — #46821008

Order 34432.

424 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 129 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#31771155C211yesmaximal, characteristic
2C2×C4×Dic538C211yesmaximal, characteristic, complemented
3#31770919C212yesmaximal, complemented
4#31770901C212yesmaximal, complemented
5#31770806C212yesmaximal, complemented
6#31770746C212yesmaximal, complemented
7#31770707C214yesmaximal, complemented
8#432×C269C211yesmaximal, characteristic, complemented
9C2×#16864402—21no—
10C22×Dic538C2211yescharacteristic
11C2×#16864391C2214yes—
12#22575453C2211yescharacteristic
13#22575450C2211yescharacteristic
14#22575441—21no—
15#22575427—21no—
16#22575427C2212yes—
17C4×Dic538—21no—
18C4×Dic538—21no—
19C4×Dic538C2212yes—
20C4×Dic538C2212yes—
21C4×D1076—21no—
22C4×D1076C2212yes—
23C2×C4⋊Dic269C2211yescharacteristic
24C2×#16864381—21no—
25C2×C4×Dic269—21no—
26#22575387C2214yes—
27#22575378C2214yes—
28#22575375C2214yes—
29C2×C42×C269C2211yescharacteristic
30C4⋊C8×C269C2212yes—
31C22⋊C8×C269C2212yes—
32#97×C269C2212yes—
33#16864402—44no—
34C2×Dic538—24no—
35C2×Dic538—21no—
36C2×Dic538—21no—
37C2×Dic538C2312yes—
38C2×D1076—21no—
39C2×D1076—21no—
40C2×D1076C2312yes—
41C2×C22⋊D269—22no—
42C22×Dic269—21no—
43C22×Dic269—21no—
44C2×C4×D269—22no—
45#16864391—28no—
46C4⋊Dic269—21no—
47C4⋊Dic269—21no—
48C4⋊Dic269C2312yes—
49C4⋊Dic269C2312yes—
50#16864381—22no—
51#16864381—22no—
52#16864379—22no—
53#16864379—22no—
54C4×Dic269—22no—
55C4×Dic269—22no—
56C22×C4×C269D411yescharacteristic
57C22×C4×C269D411yescharacteristic
58C22×C4×C269C2311yescharacteristic
59C2×C8×C269C2314yes—
60C42×C269D411yescharacteristic
61C42×C269D411yescharacteristic
62C42×C269C2311yescharacteristic
63C42×C269C2311yescharacteristic
64C22×D269—22no—
65Dic538—24no—
66Dic538—22no—
67Dic538—42no—
68Dic538#4114yescomplemented
69D1076—24no—
70D1076—42no—
71D1076—42no—
72C22⋊D269—44no—
73C2×Dic269—24no—
74C2×Dic269—22no—
75C2×Dic269—22no—
76C2×Dic269—22no—
77C2×Dic269—42no—
78C4×D269—44no—
79C23×C269C2×D411yescharacteristic
80C2×C4×C269—22no—
81C2×C4×C269—22no—
82C2×C4×C269—22no—
83C2×C4×C269C2×D411yescharacteristic
84C2×C4×C269C2×D411yescharacteristic
85C2×C4×C269C2×D411yescharacteristic
86C2×C4×C269C2×D411yescharacteristic
87C2×C4×C269C2×D411yescharacteristic
88C2×C4×C269C2411yescharacteristic
89C8×C269—24no—
90C22×C269—21no—
91C22×C269—21no—
92C22×C269AGL(1,ℤ/8)12yes—
93C22×C269C22×D411yescharacteristic
94C2×D269—42no—
95C2×D269—42no—
96C2×D269—42no—
97C4×C269—21no—
98C4×C269—21no—
99C4×C269—21no—
100C4×C269—21no—
101C4×C269#13712yes—
102C4×C269C2×#4112yes—
103Dic269—24no—
104Dic269—42no—
105Dic269—42no—
106C2×C269—22no—
107C2×C269#52511yescharacteristic
108C2×C269C2×AGL(1,ℤ/8)11yescharacteristic
109C2×C269C2×#13711yescharacteristic
110D269—82no—
111C269#311211yescharacteristic, complemented, Sylow
112#3112—2691nomaximal, Sylow
113#532—2691no—
114C2×C4×Q8—2691no—
115#480—2692no—
116#477—2692no—
117#460—2692no—
118#448—2692no—
119#440—2694no—
120#432D26911yescharacteristic, complemented
121C2×#41—5381no—
122C22×Q8—2691no—
123C2×SD16—2694no—
124C4⋊Q8—2691no—
125#127—2691no—
126#124—5381no—
127#121—2692no—
128#121—5381no—
129C4×Q8—2692no—
130C4×Q8—2692no—
131C4×Q8—5381no—
132C4×Q8—5381no—
133C4×D4—2692no—
134C4×D4—5381no—
135C2×C4⋊C4—2691no—
136C2×C4⋊C4—5381no—
137C2×C42—5381no—
138C2×C42C2×D26911yescharacteristic
139#107—2694no—
140C4⋊C8C2×D26912yes—
141#103—2694no—
142#102—2694no—
143C22⋊C8C2×D26912yes—
144#97C2×D26912yes—
145#41—10764no—
146C2×Q8—2692no—
147C2×Q8—5384no—
148C2×Q8—5381no—
149C2×Q8—5381no—
150C2×D4—2692no—
151C2×D4—5382no—
152C2×D4—5381no—
153C2×D4—5381no—
154C22×C4—5381no—
155C22×C4—5381no—
156C22×C4—5382no—
157C22×C4D107611yescharacteristic
158C22×C4D107611yescharacteristic
159C22×C4C22×D26911yescharacteristic
160SD16—5388no—
161C2×C8C22×D26914yes—
162C4⋊C4—2692no—
163C4⋊C4—2692no—
164C4⋊C4—5381no—
165C4⋊C4—5382no—
166C4⋊C4—5382no—
167C4⋊C4—5381no—
168C22⋊C4—5382no—
169C22⋊C4—5382no—
170C42—5382no—
171C42—5382no—
172C42D107611yescharacteristic
173C42D107611yescharacteristic
174C42C22×D26911yescharacteristic
175C42C22×D26911yescharacteristic
176C23—5382no—
177C23C2×D107611yescharacteristic
178Q8—2694no—
179Q8—5384no—
180Q8—5382no—
181Q8—10762no—
182D4—5384no—
183D4—10762no—
184D4—10764no—
185D4—10762no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—5384no—
190C2×C4—5382no—
191C2×C4—5382no—
192C2×C4—5382no—
193C2×C4—10764no—
194C2×C4—10762no—
195C2×C4C2×D107611yescharacteristic
196C2×C4C2×D107611yescharacteristic
197C2×C4C2×D107611yescharacteristic
198C2×C4C2×D107611yescharacteristic
199C2×C4C2×D107611yescharacteristic
200C2×C4C23×D26911yescharacteristic
201C8—24no—
202C22—21no—
203C22—21no—
204C22—10762no—
205C22—10762no—
206C22—10762no—
207C22#2257548112yes—
208C22C22×D107611yescharacteristic
209C4—21no—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—5384no—
214C4—10762no—
215C4—10762no—
216C4#2257548612yes—
217C4#41×D26912yes—
218C2—22no—
219C2—21522no—
220C2#3177111711yescharacteristic
221C2C2×#2257548111yescharacteristic
222C2C2×#2257548611yescharacteristic
subgroupG/H
centerC22C22×D1076
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#432×C269C2
socleC22×C269C22×D4
prime radical#31771155C2
hypercenter#432D269
hypocenterC269#3112
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic538C2semidirect
3. #31770919C2semidirect
4. #31770901C2semidirect
5. #31770806C2semidirect
6. #31770746C2semidirect
7. #31770707C2semidirect
8. #432×C269C2semidirect
68. Dic538#41semidirect
111. C269#3112semidirect
120. #432D269semidirect

Maximal subgroups

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

subgroupindex
#317711552
C2×C4×Dic5382
#317709192
#317709012
#317708062
#317707462
#317707072
#432×C2692
#3112269