Finite Group Databasebeta

← C2×#31771347 #46825005

Subgroups — C2×#31771347 #46825005

Order 34432.

1408 conjugacy classes of subgroups; only the 469 normal subgroups are shown.

normal subgroups only

This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 469 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#31771347C2116yesmaximal, direct product factor
2C2×#22575442C212yesmaximal, complemented
3C2×#22575441C212yesmaximal, complemented
4C2×#22575439C214yesmaximal, complemented
5C2×#22575423C214yesmaximal, complemented
6C2×#22575421C212yesmaximal, complemented
7C2×#124×C269C211yesmaximal, characteristic, complemented
8C24×D269C2212yescomplemented
9C22×Dic538C2212yescomplemented
10C22×D1076C2212yes—
11C22×D1076C2212yes—
12C22×C22⋊D269C2214yes—
13#22575442C22116yescomplemented
14#22575441C22116yescomplemented
15#22575439C22132yescomplemented
16#22575423C22132yescomplemented
17#22575421C22116yescomplemented
18C2×C22⋊Dic269C2212yescomplemented
19C2×#16864379C2214yescomplemented
20C2×#16864379C2214yescomplemented
21C2×#16864379C2214yescomplemented
22C2×C4×Dic269C2212yescomplemented
23C22×Q8×C269C2211yescharacteristic, complemented
24C22×D4×C269C2211yescharacteristic
25#124×C269C2218yescomplemented
26C2×C22⋊C4×C269C2214yescomplemented
27C2×C42×C269C2211yescharacteristic, complemented
28C23×D269—44no—
29C23×D269—48no—
30C23×D269C2314yes—
31C23×D269C2318yescomplemented
32C2×Dic538—44no—
33C2×Dic538C2318yescomplemented
34C2×D1076—44no—
35C2×D1076—44no—
36C2×D1076C2318yes—
37C2×D1076C2318yes—
38C2×C22⋊D269—48no—
39C2×C22⋊D269C23116yes—
40C22×Dic269C2314yes—
41C22⋊Dic269C2318yescomplemented
42#16864379C23116yescomplemented
43#16864379C23116yescomplemented
44#16864379C23116yescomplemented
45C4×Dic269C2318yescomplemented
46C24×C269C2312yes—
47C2×Q8×C269—42no—
48C2×Q8×C269C2314yescomplemented
49C2×D4×C269—42no—
50C2×D4×C269C2314yes—
51C22×C4×C269C2312yes—
52C22×C4×C269C2311yescharacteristic
53C22×C4×C269C2312yes—
54C22⋊C4×C269C23116yescomplemented
55C42×C269C2314yescomplemented
56C22×D269—28no—
57C22×D269—28no—
58C22×D269—28no—
59C22×D269—416no—
60C22×D269—48no—
61C22×D269—432no—
62C22×D269C2418yes—
63Dic538—48no—
64D1076—48no—
65D1076—48no—
66C22⋊D269—416no—
67C2×Dic269—28no—
68C2×Dic269C2418yes—
69C23×C269—24no—
70C23×C269—28no—
71C23×C269C2414yes—
72C23×C269C2411yescharacteristic
73Q8×C269—44no—
74D4×C269—44no—
75C2×C4×C269—22no—
76C2×C4×C269—24no—
77C2×C4×C269—24no—
78C2×C4×C269C2414yes—
79C2×C4×C269C2412yes—
80C2×C4×C269C2414yes—
81C22×C269—24no—
82C22×C269—28no—
83C22×C269—48no—
84C22×C269H(5,𝔽2)12yes—
85C22×C269H(5,𝔽2)14yes—
86C22×C269C2511yescharacteristic
87C2×D269—28no—
88C2×D269—28no—
89C2×D269—28no—
90C2×D269—432no—
91C2×D269—416no—
92C4×C269—22no—
93C4×C269—24no—
94C4×C269—24no—
95Dic269—28no—
96C2×C269—44no—
97C2×C269H(3,𝔽4)14yescomplemented
98C2×C269C2×H(5,𝔽2)11yescharacteristic
99C2×C269C2×H(5,𝔽2)12yes—
100D269—48no—
101C269C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
102C2×H(3,𝔽4)—2691nomaximal, Sylow
103H(3,𝔽4)—26916no—
104C2×#124—2692no—
105C2×#124—2694no—
106C2×#124—2692no—
107C2×#124D26911yescharacteristic, complemented
108C2×#120—2692no—
109C2×#120—2694no—
110C25—2692no—
111C22×Q8—2692no—
112C22×Q8C2×D26911yescharacteristic, complemented
113C22×D4—2694no—
114C22×D4—2692no—
115C22×D4—2692no—
116C22×D4C2×D26911yescharacteristic
117#124—26916no—
118#124—26932no—
119#124—26916no—
120#124C2×D26918yescomplemented
121#120—26916no—
122#120—26932no—
123C2×C22⋊C4—2692no—
124C2×C22⋊C4—2694no—
125C2×C22⋊C4—2694no—
126C2×C22⋊C4—2694no—
127C2×C22⋊C4C2×D26914yescomplemented
128C2×C42—2692no—
129C2×C42C2×D26911yescharacteristic, complemented
130C24—2694no—
131C24—2698no—
132C24—10764no—
133C24—10768no—
134C24C22×D26912yes—
135C2×Q8—42no—
136C2×Q8—2698no—
137C2×Q8—10764no—
138C2×Q8C22×D26914yescomplemented
139C2×D4—42no—
140C2×D4—26916no—
141C2×D4—2698no—
142C2×D4—2698no—
143C2×D4—10764no—
144C2×D4—10764no—
145C2×D4—10768no—
146C2×D4C22×D26914yes—
147C22×C4—2694no—
148C22×C4C22×D26912yes—
149C22×C4C22×D26911yescharacteristic
150C22×C4C22×D26912yes—
151C22⋊C4—2698no—
152C22⋊C4—26916no—
153C22⋊C4—26916no—
154C22⋊C4—26916no—
155C22⋊C4C22×D269116yescomplemented
156C42—2698no—
157C42C22×D26914yescomplemented
158C23—24no—
159C23—28no—
160C23—2698no—
161C23—5388no—
162C23—5388no—
163C23—5388no—
164C23—10768no—
165C23—107616no—
166C23—107632no—
167C23C23×D26914yes—
168C23C23×D26911yescharacteristic
169Q8—44no—
170Q8—10768no—
171D4—44no—
172D4—10768no—
173D4—10768no—
174D4—107616no—
175C2×C4—22no—
176C2×C4—24no—
177C2×C4—24no—
178C2×C4—2698no—
179C2×C4—5388no—
180C2×C4C23×D26914yes—
181C2×C4C23×D26912yes—
182C2×C4C23×D26914yes—
183C22—24no—
184C22—28no—
185C22—48no—
186C22—5388no—
187C22—5388no—
188C22—5388no—
189C22—107632no—
190C22—107616no—
191C22#2257549812yes—
192C22#2257549914yes—
193C22C24×D26911yescharacteristic
194C4—22no—
195C4—24no—
196C4—24no—
197C4—5388no—
198C2—44no—
199C2—10768no—
200C2#3177134714yesdirect product factor
201C2C2×#2257549811yescharacteristic
202C2C2×#2257549912yes—
subgroupG/H
centerC23C23×D269
commutator, cosocleC22×C269C25
FrattiniC22C24×D269
FittingC2×#124×C269C2
socleC23×C269C24
hypercenterC2×#124D269
hypocenterC269C2×H(3,𝔽4)
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #31771347C2direct (N × H)
2. C2×#22575442C2semidirect
3. C2×#22575441C2semidirect
4. C2×#22575439C2semidirect
5. C2×#22575423C2semidirect
6. C2×#22575421C2semidirect
7. C2×#124×C269C2semidirect
8. C24×D269C22semidirect
9. C22×Dic538C22semidirect
13. #22575442C22semidirect
14. #22575441C22semidirect
15. #22575439C22semidirect
16. #22575423C22semidirect
17. #22575421C22semidirect
18. C2×C22⋊Dic269C22semidirect
19. C2×#16864379C22semidirect
20. C2×#16864379C22semidirect
21. C2×#16864379C22semidirect
22. C2×C4×Dic269C22semidirect
23. C22×Q8×C269C22semidirect
25. #124×C269C22semidirect
26. C2×C22⋊C4×C269C22semidirect
27. C2×C42×C269C22semidirect
31. C23×D269C23semidirect
33. C2×Dic538C23semidirect
41. C22⋊Dic269C23semidirect
42. #16864379C23semidirect
43. #16864379C23semidirect
44. #16864379C23semidirect
45. C4×Dic269C23semidirect
48. C2×Q8×C269C23semidirect
54. C22⋊C4×C269C23semidirect
55. C42×C269C23semidirect
97. C2×C269H(3,𝔽4)semidirect
101. C269C2×H(3,𝔽4)semidirect
107. C2×#124D269semidirect
112. C22×Q8C2×D269semidirect
120. #124C2×D269semidirect
127. C2×C22⋊C4C2×D269semidirect
129. C2×C42C2×D269semidirect
138. C2×Q8C22×D269semidirect
155. C22⋊C4C22×D269semidirect
157. C42C22×D269semidirect
200. C2#31771347direct (N × H)

Maximal subgroups

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

subgroupindex
#317713472
C2×#225754422
C2×#225754412
C2×#225754392
C2×#225754232
C2×#225754212
C2×#124×C2692
C2×H(3,𝔽4)269