Finite Group Databasebeta

← C2×#31771167 #46824188

Subgroups — C2×#31771167 #46824188

Order 34432.

1984 conjugacy classes of subgroups; only the 565 normal subgroups are shown.

normal subgroups only

This group has 1984 conjugacy classes of subgroups — too many to draw. Only its 565 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
1C23×C22⋊D269C212yesmaximal, complemented
2#31771167C2116yesmaximal, direct product factor
3C2×#22575437C214yesmaximal, complemented
4C2×#22575427C214yesmaximal, complemented
5C2×#22575423C214yesmaximal, complemented
6C22×C22⋊C4×C269C211yesmaximal, characteristic, complemented
7C24×D269C2212yescomplemented
8C22×D1076C2214yescomplemented
9C22×C22⋊D269—216no—
10C22×C22⋊D269C2214yes—
11C22×C22⋊D269C2214yescomplemented
12C22×C22⋊D269C22116yescomplemented
13C23×Dic269C2212yescomplemented
14#22575437C22132yescomplemented
15#22575427C22132yescomplemented
16#22575423C22132yescomplemented
17C2×C4⋊Dic269C2214yescomplemented
18C2×#16864379C2218yescomplemented
19C25×C269C2211yescharacteristic
20C23×C4×C269C2212yescomplemented
21C2×C22⋊C4×C269C2214yescomplemented
22C2×C22⋊C4×C269C2218yescomplemented
23C23×D269—28no—
24C23×D269—48no—
25C23×D269C2314yes—
26C23×D269C2318yescomplemented
27C2×D1076—48no—
28C2×D1076C23116yescomplemented
29C2×C22⋊D269—216no—
30C2×C22⋊D269—216no—
31C2×C22⋊D269—264no—
32C2×C22⋊D269C23116yes—
33C2×C22⋊D269C23116yescomplemented
34C22×Dic269—28no—
35C22×Dic269C2314yes—
36C22×Dic269C2318yescomplemented
37C4⋊Dic269C23116yescomplemented
38#16864379C23132yescomplemented
39C24×C269—44no—
40C24×C269D418yescomplemented
41C24×C269C2312yes—
42C24×C269C2311yescharacteristic
43C24×C269C2314yes—
44C22×C4×C269—44no—
45C22×C4×C269C2314yes—
46C22×C4×C269C2318yescomplemented
47C22⋊C4×C269C23116yescomplemented
48C22×D269—28no—
49C22×D269—216no—
50C22×D269—216no—
51C22×D269—416no—
52C22×D269—432no—
53C22×D269C2418yes—
54D1076—416no—
55C22⋊D269—232no—
56C22⋊D269—232no—
57C2×Dic269—28no—
58C2×Dic269—216no—
59C2×Dic269C2418yes—
60C23×C269—24no—
61C23×C269—28no—
62C23×C269—416no—
63C23×C269—48no—
64C23×C269C2×D418yes—
65C23×C269C2×D414yes—
66C23×C269C2×D4116yescomplemented
67C23×C269C2414yes—
68C23×C269C2412yes—
69C23×C269C2411yescharacteristic
70C2×C4×C269—28no—
71C2×C4×C269—48no—
72C2×C4×C269C2418yes—
73C22×C269—28no—
74C22×C269—216no—
75C22×C269—24no—
76C22×C269—28no—
77C22×C269—416no—
78C22×C269C22×D418yes—
79C22×C269C22×D414yes—
80C22×C269C22×D412yes—
81C22×C269H(5,𝔽2)14yes—
82C22×C269C2511yescharacteristic
83C2×D269—28no—
84C2×D269—216no—
85C2×D269—432no—
86C2×D269—416no—
87C4×C269—28no—
88Dic269—28no—
89C2×C269—28no—
90C2×C269—24no—
91C2×C269#53414yescomplemented
92C2×C269C23×D411yescharacteristic
93C2×C269C2×H(5,𝔽2)12yes—
94D269—48no—
95C269C2×#53411yescharacteristic, complemented, Sylow
96C2×#534—2691nomaximal, Sylow
97C23×D4—2692no—
98#534—26916no—
99C2×#123—2694no—
100C2×#121—2694no—
101C2×#120—2694no—
102C22×C22⋊C4D26911yescharacteristic, complemented
103C25—2692no—
104C25C2×D26911yescharacteristic
105C22×D4—2694no—
106C22×D4—2694no—
107C22×D4—26916no—
108C22×D4—2694no—
109C22×D4—53816no—
110C23×C4—2692no—
111C23×C4C2×D26912yescomplemented
112#123—26932no—
113#121—26932no—
114#120—26932no—
115C2×C4⋊C4—2694no—
116C2×C22⋊C4—2698no—
117C2×C22⋊C4C2×D26914yescomplemented
118C2×C22⋊C4C2×D26918yescomplemented
119C24—44no—
120C24—2694no—
121C24—2698no—
122C24—5388no—
123C24—10768no—
124C24D107618yescomplemented
125C24C22×D26912yes—
126C24C22×D26911yescharacteristic
127C24C22×D26914yes—
128C2×D4—26916no—
129C2×D4—26916no—
130C2×D4—26916no—
131C2×D4—53816no—
132C2×D4—53816no—
133C2×D4—53864no—
134C2×D4—10768no—
135C22×C4—44no—
136C22×C4—2698no—
137C22×C4—2694no—
138C22×C4—5388no—
139C22×C4C22×D26914yes—
140C22×C4C22×D26918yescomplemented
141C4⋊C4—26916no—
142C22⋊C4—26932no—
143C22⋊C4C22×D269116yescomplemented
144C23—24no—
145C23—28no—
146C23—416no—
147C23—48no—
148C23—2698no—
149C23—53816no—
150C23—5388no—
151C23—53816no—
152C23—107616no—
153C23—107632no—
154C23C2×D107618yes—
155C23C2×D107614yes—
156C23C2×D1076116yescomplemented
157C23C23×D26914yes—
158C23C23×D26912yes—
159C23C23×D26911yescharacteristic
160D4—53832no—
161D4—53832no—
162D4—107616no—
163C2×C4—28no—
164C2×C4—48no—
165C2×C4—2698no—
166C2×C4—53816no—
167C2×C4—5388no—
168C2×C4C23×D26918yes—
169C22—216no—
170C22—28no—
171C22—24no—
172C22—28no—
173C22—416no—
174C22—5388no—
175C22—53816no—
176C22—107632no—
177C22—107616no—
178C22C22×D107618yes—
179C22C22×D107614yes—
180C22C22×D107612yes—
181C22#2257549814yes—
182C22C24×D26911yescharacteristic
183C4—28no—
184C4—5388no—
185C2—28no—
186C2—24no—
187C2—10768no—
188C2#3177116714yesdirect product factor
189C2C23×D107611yescharacteristic
190C2C2×#2257549812yes—
subgroupG/H
centerC23C23×D269
commutator, cosocleC22×C269C25
FrattiniC22C24×D269
FittingC22×C22⋊C4×C269C2
socleC23×C269C24
hypercenterC22×C22⋊C4D269
hypocenterC269C2×#534
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊D269C2semidirect
2. #31771167C2direct (N × H)
3. C2×#22575437C2semidirect
4. C2×#22575427C2semidirect
5. C2×#22575423C2semidirect
6. C22×C22⋊C4×C269C2semidirect
7. C24×D269C22semidirect
8. C22×D1076C22semidirect
11. C22×C22⋊D269C22semidirect
12. C22×C22⋊D269C22semidirect
13. C23×Dic269C22semidirect
14. #22575437C22semidirect
15. #22575427C22semidirect
16. #22575423C22semidirect
17. C2×C4⋊Dic269C22semidirect
18. C2×#16864379C22semidirect
20. C23×C4×C269C22semidirect
21. C2×C22⋊C4×C269C22semidirect
22. C2×C22⋊C4×C269C22semidirect
26. C23×D269C23semidirect
28. C2×D1076C23semidirect
33. C2×C22⋊D269C23semidirect
36. C22×Dic269C23semidirect
37. C4⋊Dic269C23semidirect
38. #16864379C23semidirect
40. C24×C269D4semidirect
46. C22×C4×C269C23semidirect
47. C22⋊C4×C269C23semidirect
66. C23×C269C2×D4semidirect
91. C2×C269#534semidirect
95. C269C2×#534semidirect
102. C22×C22⋊C4D269semidirect
111. C23×C4C2×D269semidirect
117. C2×C22⋊C4C2×D269semidirect
118. C2×C22⋊C4C2×D269semidirect
124. C24D1076semidirect
140. C22×C4C22×D269semidirect
143. C22⋊C4C22×D269semidirect
156. C23C2×D1076semidirect
188. C2#31771167direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊D2692
#317711672
C2×#225754372
C2×#225754272
C2×#225754232
C22×C22⋊C4×C2692
C2×#534269