Finite Group Databasebeta

← #46820361

Subgroups — #46820361

Order 34432.

584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C2×#22575479C212yesmaximal, complemented
2C4×#16864402C211yesmaximal, characteristic, complemented
3#31770802C214yesmaximal, complemented
4#31770797C214yesmaximal, complemented
5#31770629C211yesmaximal, characteristic, complemented
6#31770610C212yesmaximal, complemented
7C2×#127×C269C211yesmaximal, characteristic, complemented
8C2×#16864402C2211yescharacteristic
9#22575479—28no—
10C2×#16864390C2214yescomplemented
11C2×#16864387C2214yescomplemented
12C2×#16864386C2212yes—
13C4×Dic538C2212yescomplemented
14C4×D1076C2212yescomplemented
15C4×C22⋊D269—22no—
16#22575412C2211yescharacteristic
17#22575410—21no—
18C42×D269—21no—
19C4⋊#14524130C2214yescomplemented
20#22575374C2218yescomplemented
21C22×D4×C269—22no—
22C22×D4×C269C2212yes—
23#127×C269—21no—
24#127×C269—21no—
25#127×C269C2214yes—
26C2×C42×C269C2211yescharacteristic
27#16864402—22no—
28#16864402D414yescomplemented
29C2×Dic538C2311yescharacteristic
30C2×D1076C2311yescharacteristic
31C2×C22⋊D269—21no—
32C2×C4×D269—21no—
33C2×C4×D269—22no—
34#16864390—28no—
35#16864387—28no—
36#16864386—24no—
37C2×#14524130C2314yes—
38C4⋊Dic269C2312yes—
39#16864381—22no—
40C22⋊Dic269—21no—
41#16864379—22no—
42C4×Dic269—21no—
43C4×Dic269—22no—
44C24×C269—22no—
45C2×D4×C269—24no—
46C2×D4×C269—22no—
47C2×D4×C269—24no—
48C2×D4×C269—24no—
49C2×D4×C269—24no—
50C2×D4×C269—48no—
51C2×D4×C269C2314yes—
52C22×C4×C269D412yes—
53C22×C4×C269C2311yescharacteristic
54C42×C269D411yescharacteristic
55C42×C269D411yescharacteristic
56C42×C269C2312yes—
57C22×D269—21no—
58Dic538—21no—
59Dic538C2×D412yescomplemented
60D1076—21no—
61D1076C2×D412yescomplemented
62C22⋊D269—24no—
63C2×Dic269—21no—
64C2×Dic269—22no—
65C4×D269—24no—
66C4×D269—44no—
67#14524130—24no—
68C23×C269—24no—
69C23×C269—48no—
70C23×C269—44no—
71C23×C269C2×D411yescharacteristic
72D4×C269—24no—
73D4×C269—24no—
74D4×C269—48no—
75D4×C269—44no—
76D4×C269—48no—
77C2×C4×C269—24no—
78C2×C4×C269C2×D412yes—
79C2×C4×C269C2×D412yes—
80C2×C4×C269C2×D411yescharacteristic
81C2×C4×C269C2×D412yes—
82C2×C4×C269#4112yes—
83C2×C4×C269C2411yescharacteristic
84C22×C269—22no—
85C22×C269—44no—
86C22×C269—48no—
87C22×C269—88no—
88C22×C269#12112yes—
89C22×C269C22×D411yescharacteristic
90C2×D269—22no—
91C2×D269—42no—
92C4×C269—22no—
93C4×C269#12112yes—
94C4×C269AGL(1,ℤ/8)14yescomplemented
95C4×C269C22×D411yescharacteristic
96C4×C269C2×#4111yescharacteristic
97Dic269—22no—
98Dic269—42no—
99C2×C269—22no—
100C2×C269—84no—
101C2×C269C2×#12111yescharacteristic
102C2×C269C2×AGL(1,ℤ/8)12yes—
103D269—42no—
104C269#303811yescharacteristic, complemented, Sylow
105#3038—2691nomaximal, Sylow
106C2×AGL(1,ℤ/8)—2692no—
107C2×#127D26911yescharacteristic, complemented
108C4×#41—2691no—
109#460—2694no—
110#459—2694no—
111#423—2691no—
112#418—2692no—
113C2×#41—2691no—
114C22×D4—22no—
115C22×D4C2×D26912yes—
116AGL(1,ℤ/8)—5388no—
117C2×SD16—2694no—
118C2×D8—2694no—
119C2×M16—2692no—
120#127—21no—
121#127—21no—
122#127C2×D26914yes—
123C4×Q8—2692no—
124C4×D4—2692no—
125C4×D4—5382no—
126#117—2691no—
127#117—5381no—
128C2×C42—5381no—
129C2×C42C2×D26911yescharacteristic
130C4⋊C8—2694no—
131#102—2698no—
132C24—22no—
133#41—2694no—
134#41—5382no—
135C2×Q8—2691no—
136C2×D4—24no—
137C2×D4—22no—
138C2×D4—24no—
139C2×D4—24no—
140C2×D4—24no—
141C2×D4—48no—
142C2×D4—2691no—
143C2×D4—5381no—
144C2×D4C22×D26914yes—
145C22×C4—5381no—
146C22×C4—5382no—
147C22×C4C22⋊D26912yes—
148C22×C4C22×D26911yescharacteristic
149SD16—5388no—
150D8—5388no—
151M16—5384no—
152C2×C8—2694no—
153C4⋊C4—2692no—
154C4⋊C4—5382no—
155C22⋊C4—5381no—
156C22⋊C4—5382no—
157C42—5381no—
158C42—5382no—
159C42C22⋊D26911yescharacteristic
160C42C22⋊D26911yescharacteristic
161C42C22×D26912yes—
162C23—24no—
163C23—48no—
164C23—44no—
165C23—5381no—
166C23C2×C22⋊D26911yescharacteristic
167Q8—2692no—
168Q8—5381no—
169D4—24no—
170D4—24no—
171D4—48no—
172D4—44no—
173D4—48no—
174D4—2692no—
175D4—5384no—
176D4—5381no—
177C2×C4—24no—
178C2×C4—5381no—
179C2×C4—5384no—
180C2×C4—5382no—
181C2×C4—10764no—
182C2×C4D4×D26912yes—
183C2×C4C2×C22⋊D26912yes—
184C2×C4C2×C22⋊D26911yescharacteristic
185C2×C4C2×C22⋊D26912yes—
186C2×C4#1686440112yes—
187C2×C4C23×D26911yescharacteristic
188C8—5384no—
189C22—22no—
190C22—48no—
191C22—44no—
192C22—88no—
193C22—5382no—
194C22—10762no—
195C22#2257542412yes—
196C22C22×C22⋊D26911yescharacteristic
197C4—22no—
198C4—5382no—
199C4—10762no—
200C4#2257542412yes—
201C4#2257547914yescomplemented
202C4C2×D4×D26911yescharacteristic
203C4C2×#1686440111yescharacteristic
204C2—22no—
205C2—84no—
206C2—10762no—
207C2C2×#2257542411yescharacteristic
208C2C2×#2257547912yes—
subgroupG/H
centerC22C22×C22⋊D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
FittingC2×#127×C269C2
socleC22×C269C22×D4
hypercenterC2×#127D269
hypocenterC269#3038
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C2×#22575479C2semidirect
2. C4×#16864402C2semidirect
3. #31770802C2semidirect
4. #31770797C2semidirect
5. #31770629C2semidirect
6. #31770610C2semidirect
7. C2×#127×C269C2semidirect
10. C2×#16864390C22semidirect
11. C2×#16864387C22semidirect
13. C4×Dic538C22semidirect
14. C4×D1076C22semidirect
19. C4⋊#14524130C22semidirect
20. #22575374C22semidirect
28. #16864402D4semidirect
59. Dic538C2×D4semidirect
61. D1076C2×D4semidirect
94. C4×C269AGL(1,ℤ/8)semidirect
104. C269#3038semidirect
107. C2×#127D269semidirect
201. C4#22575479semidirect

Maximal subgroups

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

subgroupindex
C2×#225754792
C4×#168644022
#317708022
#317707972
#317706292
#317706102
C2×#127×C2692
#3038269