Finite Group Databasebeta

← C2×#14271905 #16833612

Subgroups — C2×#14271905 #16833612

Order 3712.

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#14271905C2116yesmaximal, direct product factor
2C2×#11745309C212yesmaximal, complemented
3C2×#11745237C212yesmaximal, complemented
4C2×#11745247C214yesmaximal, complemented
5C2×#11745244C214yesmaximal, complemented
6C2×#11745299C212yesmaximal, complemented
7C2×C29×#124C211yesmaximal, characteristic, complemented
8C24×D29C2212yescomplemented
9C22×Q8×C29C2211yescharacteristic, complemented
10C22×D4×C29C2211yescharacteristic
11C22×C22⋊D29C2214yes—
12C22×D116C2212yes—
13C22×D116C2212yes—
14C22×Dic58C2212yescomplemented
15C29×#124C2218yescomplemented
16C2×C22⋊C4×C29C2214yescomplemented
17C2×C42×C29C2211yescharacteristic, complemented
18C2×C22⋊Dic29C2212yescomplemented
19#11745309C22116yescomplemented
20#11745299C22116yescomplemented
21C2×#90781C2214yescomplemented
22C2×#90781C2214yescomplemented
23C2×#90781C2214yescomplemented
24C2×C4×Dic29C2212yescomplemented
25#11745247C22132yescomplemented
26#11745244C22132yescomplemented
27#11745237C22116yescomplemented
28C24×C29C2312yes—
29C23×D29—44no—
30C23×D29—48no—
31C23×D29C2314yes—
32C23×D29C2318yescomplemented
33C2×Q8×C29—42no—
34C2×Q8×C29C2314yescomplemented
35C2×D4×C29—42no—
36C2×D4×C29C2314yes—
37C22×C4×C29C2312yes—
38C22×C4×C29C2311yescharacteristic
39C22×C4×C29C2312yes—
40C2×C22⋊D29—48no—
41C2×C22⋊D29C23116yes—
42C22×Dic29C2314yes—
43C2×D116—44no—
44C2×D116—44no—
45C2×D116C2318yes—
46C2×D116C2318yes—
47C2×Dic58—44no—
48C2×Dic58C2318yescomplemented
49C22⋊C4×C29C23116yescomplemented
50C42×C29C2314yescomplemented
51C22⋊Dic29C2318yescomplemented
52#90781C23116yescomplemented
53#90781C23116yescomplemented
54#90781C23116yescomplemented
55C4×Dic29C2318yescomplemented
56C23×C29—28no—
57C23×C29—24no—
58C23×C29C2414yes—
59C23×C29C2411yescharacteristic
60C22×D29—28no—
61C22×D29—28no—
62C22×D29—28no—
63C22×D29—48no—
64C22×D29—416no—
65C22×D29—432no—
66C22×D29C2418yes—
67Q8×C29—44no—
68D4×C29—44no—
69C2×C4×C29—24no—
70C2×C4×C29—24no—
71C2×C4×C29—22no—
72C2×C4×C29C2414yes—
73C2×C4×C29C2412yes—
74C2×C4×C29C2414yes—
75C22⋊D29—416no—
76C2×Dic29—28no—
77C2×Dic29C2418yes—
78D116—48no—
79D116—48no—
80Dic58—48no—
81C2×H(3,𝔽4)—291nomaximal, Sylow
82C22×C29—28no—
83C22×C29—24no—
84C22×C29—48no—
85C22×C29H(5,𝔽2)12yes—
86C22×C29H(5,𝔽2)14yes—
87C22×C29C2511yescharacteristic
88C2×D29—28no—
89C2×D29—28no—
90C2×D29—28no—
91C2×D29—432no—
92C2×D29—416no—
93C4×C29—24no—
94C4×C29—24no—
95C4×C29—22no—
96Dic29—28no—
97H(3,𝔽4)—2916no—
98C2×#124—292no—
99C2×#124—294no—
100C2×#124—292no—
101C2×#124D2911yescharacteristic, complemented
102C2×#120—292no—
103C2×#120—294no—
104C2×C29—44no—
105C2×C29H(3,𝔽4)14yescomplemented
106C2×C29C2×H(5,𝔽2)11yescharacteristic
107C2×C29C2×H(5,𝔽2)12yes—
108D29—48no—
109C25—292no—
110C22×Q8—292no—
111C22×Q8C2×D2911yescharacteristic, complemented
112C22×D4—294no—
113C22×D4—292no—
114C22×D4—292no—
115C22×D4C2×D2911yescharacteristic
116#124—2916no—
117#124—2932no—
118#124—2916no—
119#124C2×D2918yescomplemented
120#120—2916no—
121#120—2932no—
122C2×C22⋊C4—292no—
123C2×C22⋊C4—294no—
124C2×C22⋊C4—294no—
125C2×C22⋊C4—294no—
126C2×C22⋊C4C2×D2914yescomplemented
127C2×C42—292no—
128C2×C42C2×D2911yescharacteristic, complemented
129C29C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
130C24—294no—
131C24—298no—
132C24—1164no—
133C24—1168no—
134C24C22×D2912yes—
135C2×Q8—42no—
136C2×Q8—298no—
137C2×Q8—1164no—
138C2×Q8C22×D2914yescomplemented
139C2×D4—42no—
140C2×D4—2916no—
141C2×D4—298no—
142C2×D4—298no—
143C2×D4—1164no—
144C2×D4—1164no—
145C2×D4—1168no—
146C2×D4C22×D2914yes—
147C22×C4—294no—
148C22×C4C22×D2912yes—
149C22×C4C22×D2911yescharacteristic
150C22×C4C22×D2912yes—
151C22⋊C4—298no—
152C22⋊C4—2916no—
153C22⋊C4—2916no—
154C22⋊C4—2916no—
155C22⋊C4C22×D29116yescomplemented
156C42—298no—
157C42C22×D2914yescomplemented
158C23—24no—
159C23—28no—
160C23—298no—
161C23—588no—
162C23—588no—
163C23—588no—
164C23—1168no—
165C23—11616no—
166C23—11632no—
167C23C23×D2914yes—
168C23C23×D2911yescharacteristic
169Q8—44no—
170Q8—1168no—
171D4—44no—
172D4—1168no—
173D4—1168no—
174D4—11616no—
175C2×C4—22no—
176C2×C4—24no—
177C2×C4—24no—
178C2×C4—298no—
179C2×C4—588no—
180C2×C4C23×D2914yes—
181C2×C4C23×D2912yes—
182C2×C4C23×D2914yes—
183C22—24no—
184C22—28no—
185C22—48no—
186C22—588no—
187C22—588no—
188C22—588no—
189C22—11632no—
190C22—11616no—
191C22#1174535912yes—
192C22#1174536414yes—
193C22C24×D2911yescharacteristic
194C4—22no—
195C4—24no—
196C4—24no—
197C4—588no—
198C2—44no—
199C2—1168no—
200C2#1427190514yesdirect product factor
201C2C2×#1174535911yescharacteristic
202C2C2×#1174536412yes—
subgroupG/H
centerC23C23×D29
commutator, cosocleC22×C29C25
FrattiniC22C24×D29
FittingC2×C29×#124C2
socleC23×C29C24
hypercenterC2×#124D29
hypocenterC29C2×H(3,𝔽4)
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #14271905C2direct (N × H)
2. C2×#11745309C2semidirect
3. C2×#11745237C2semidirect
4. C2×#11745247C2semidirect
5. C2×#11745244C2semidirect
6. C2×#11745299C2semidirect
7. C2×C29×#124C2semidirect
8. C24×D29C22semidirect
9. C22×Q8×C29C22semidirect
14. C22×Dic58C22semidirect
15. C29×#124C22semidirect
16. C2×C22⋊C4×C29C22semidirect
17. C2×C42×C29C22semidirect
18. C2×C22⋊Dic29C22semidirect
19. #11745309C22semidirect
20. #11745299C22semidirect
21. C2×#90781C22semidirect
22. C2×#90781C22semidirect
23. C2×#90781C22semidirect
24. C2×C4×Dic29C22semidirect
25. #11745247C22semidirect
26. #11745244C22semidirect
27. #11745237C22semidirect
32. C23×D29C23semidirect
34. C2×Q8×C29C23semidirect
48. C2×Dic58C23semidirect
49. C22⋊C4×C29C23semidirect
50. C42×C29C23semidirect
51. C22⋊Dic29C23semidirect
52. #90781C23semidirect
53. #90781C23semidirect
54. #90781C23semidirect
55. C4×Dic29C23semidirect
101. C2×#124D29semidirect
105. C2×C29H(3,𝔽4)semidirect
111. C22×Q8C2×D29semidirect
119. #124C2×D29semidirect
126. C2×C22⋊C4C2×D29semidirect
128. C2×C42C2×D29semidirect
129. C29C2×H(3,𝔽4)semidirect
138. C2×Q8C22×D29semidirect
155. C22⋊C4C22×D29semidirect
157. C42C22×D29semidirect
200. C2#14271905direct (N × H)

Maximal subgroups

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

subgroupindex
#142719052
C2×#117453092
C2×#117452372
C2×#117452472
C2×#117452442
C2×#117452992
C2×C29×#1242
C2×H(3,𝔽4)29