Finite Group Databasebeta

← C2×#14271725 #16832795

Subgroups — C2×#14271725 #16832795

Order 3712.

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⋊D29C212yesmaximal, complemented
2#14271725C2116yesmaximal, direct product factor
3C2×#11745248C214yesmaximal, complemented
4C2×#11745292C214yesmaximal, complemented
5C2×#11745244C214yesmaximal, complemented
6C22×C22⋊C4×C29C211yesmaximal, characteristic, complemented
7C25×C29C2211yescharacteristic
8C24×D29C2212yescomplemented
9C23×C4×C29C2212yescomplemented
10C22×C22⋊D29—216no—
11C22×C22⋊D29C2214yes—
12C22×C22⋊D29C2214yescomplemented
13C22×C22⋊D29C22116yescomplemented
14C23×Dic29C2212yescomplemented
15C22×D116C2214yescomplemented
16C2×C22⋊C4×C29C2214yescomplemented
17C2×C22⋊C4×C29C2218yescomplemented
18#11745292C22132yescomplemented
19C2×#90781C2218yescomplemented
20C2×C4⋊Dic29C2214yescomplemented
21#11745248C22132yescomplemented
22#11745244C22132yescomplemented
23C24×C29—44no—
24C24×C29D418yescomplemented
25C24×C29C2312yes—
26C24×C29C2311yescharacteristic
27C24×C29C2314yes—
28C23×D29—28no—
29C23×D29—48no—
30C23×D29C2314yes—
31C23×D29C2318yescomplemented
32C22×C4×C29—44no—
33C22×C4×C29C2314yes—
34C22×C4×C29C2318yescomplemented
35C2×C22⋊D29—216no—
36C2×C22⋊D29—216no—
37C2×C22⋊D29—264no—
38C2×C22⋊D29C23116yes—
39C2×C22⋊D29C23116yescomplemented
40C22×Dic29—28no—
41C22×Dic29C2314yes—
42C22×Dic29C2318yescomplemented
43C2×D116—48no—
44C2×D116C23116yescomplemented
45C22⋊C4×C29C23116yescomplemented
46#90781C23132yescomplemented
47C4⋊Dic29C23116yescomplemented
48C23×C29—24no—
49C23×C29—28no—
50C23×C29—416no—
51C23×C29—48no—
52C23×C29C2×D418yes—
53C23×C29C2×D414yes—
54C23×C29C2×D4116yescomplemented
55C23×C29C2414yes—
56C23×C29C2412yes—
57C23×C29C2411yescharacteristic
58C22×D29—28no—
59C22×D29—216no—
60C22×D29—216no—
61C22×D29—416no—
62C22×D29—432no—
63C22×D29C2418yes—
64C2×C4×C29—28no—
65C2×C4×C29—48no—
66C2×C4×C29C2418yes—
67C22⋊D29—232no—
68C22⋊D29—232no—
69C2×Dic29—28no—
70C2×Dic29—216no—
71C2×Dic29C2418yes—
72D116—416no—
73C2×#534—291nomaximal, Sylow
74C22×C29—216no—
75C22×C29—28no—
76C22×C29—24no—
77C22×C29—28no—
78C22×C29—416no—
79C22×C29C22×D418yes—
80C22×C29C22×D414yes—
81C22×C29C22×D412yes—
82C22×C29H(5,𝔽2)14yes—
83C22×C29C2511yescharacteristic
84C2×D29—28no—
85C2×D29—216no—
86C2×D29—432no—
87C2×D29—416no—
88C4×C29—28no—
89Dic29—28no—
90C23×D4—292no—
91#534—2916no—
92C2×#123—294no—
93C2×#121—294no—
94C2×#120—294no—
95C22×C22⋊C4D2911yescharacteristic, complemented
96C2×C29—28no—
97C2×C29—24no—
98C2×C29#53414yescomplemented
99C2×C29C23×D411yescharacteristic
100C2×C29C2×H(5,𝔽2)12yes—
101D29—48no—
102C25—292no—
103C25C2×D2911yescharacteristic
104C22×D4—294no—
105C22×D4—294no—
106C22×D4—2916no—
107C22×D4—294no—
108C22×D4—5816no—
109C23×C4—292no—
110C23×C4C2×D2912yescomplemented
111#123—2932no—
112#121—2932no—
113#120—2932no—
114C2×C4⋊C4—294no—
115C2×C22⋊C4—298no—
116C2×C22⋊C4C2×D2914yescomplemented
117C2×C22⋊C4C2×D2918yescomplemented
118C29C2×#53411yescharacteristic, complemented, Sylow
119C24—44no—
120C24—294no—
121C24—298no—
122C24—588no—
123C24—1168no—
124C24D11618yescomplemented
125C24C22×D2912yes—
126C24C22×D2911yescharacteristic
127C24C22×D2914yes—
128C2×D4—2916no—
129C2×D4—2916no—
130C2×D4—2916no—
131C2×D4—5816no—
132C2×D4—5816no—
133C2×D4—5864no—
134C2×D4—1168no—
135C22×C4—44no—
136C22×C4—298no—
137C22×C4—294no—
138C22×C4—588no—
139C22×C4C22×D2914yes—
140C22×C4C22×D2918yescomplemented
141C4⋊C4—2916no—
142C22⋊C4—2932no—
143C22⋊C4C22×D29116yescomplemented
144C23—24no—
145C23—28no—
146C23—416no—
147C23—48no—
148C23—298no—
149C23—5816no—
150C23—588no—
151C23—5816no—
152C23—11616no—
153C23—11632no—
154C23C2×D11618yes—
155C23C2×D11614yes—
156C23C2×D116116yescomplemented
157C23C23×D2914yes—
158C23C23×D2912yes—
159C23C23×D2911yescharacteristic
160D4—5832no—
161D4—5832no—
162D4—11616no—
163C2×C4—28no—
164C2×C4—48no—
165C2×C4—298no—
166C2×C4—5816no—
167C2×C4—588no—
168C2×C4C23×D2918yes—
169C22—216no—
170C22—28no—
171C22—24no—
172C22—28no—
173C22—416no—
174C22—588no—
175C22—5816no—
176C22—11632no—
177C22—11616no—
178C22C22×D11618yes—
179C22C22×D11614yes—
180C22C22×D11612yes—
181C22#1174535914yes—
182C22C24×D2911yescharacteristic
183C4—28no—
184C4—588no—
185C2—28no—
186C2—24no—
187C2—1168no—
188C2#1427172514yesdirect product factor
189C2C23×D11611yescharacteristic
190C2C2×#1174535912yes—
subgroupG/H
centerC23C23×D29
commutator, cosocleC22×C29C25
FrattiniC22C24×D29
FittingC22×C22⋊C4×C29C2
socleC23×C29C24
hypercenterC22×C22⋊C4D29
hypocenterC29C2×#534
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊D29C2semidirect
2. #14271725C2direct (N × H)
3. C2×#11745248C2semidirect
4. C2×#11745292C2semidirect
5. C2×#11745244C2semidirect
6. C22×C22⋊C4×C29C2semidirect
8. C24×D29C22semidirect
9. C23×C4×C29C22semidirect
12. C22×C22⋊D29C22semidirect
13. C22×C22⋊D29C22semidirect
14. C23×Dic29C22semidirect
15. C22×D116C22semidirect
16. C2×C22⋊C4×C29C22semidirect
17. C2×C22⋊C4×C29C22semidirect
18. #11745292C22semidirect
19. C2×#90781C22semidirect
20. C2×C4⋊Dic29C22semidirect
21. #11745248C22semidirect
22. #11745244C22semidirect
24. C24×C29D4semidirect
31. C23×D29C23semidirect
34. C22×C4×C29C23semidirect
39. C2×C22⋊D29C23semidirect
42. C22×Dic29C23semidirect
44. C2×D116C23semidirect
45. C22⋊C4×C29C23semidirect
46. #90781C23semidirect
47. C4⋊Dic29C23semidirect
54. C23×C29C2×D4semidirect
95. C22×C22⋊C4D29semidirect
98. C2×C29#534semidirect
110. C23×C4C2×D29semidirect
116. C2×C22⋊C4C2×D29semidirect
117. C2×C22⋊C4C2×D29semidirect
118. C29C2×#534semidirect
124. C24D116semidirect
140. C22×C4C22×D29semidirect
143. C22⋊C4C22×D29semidirect
156. C23C2×D116semidirect
188. C2#14271725direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊D292
#142717252
C2×#117452482
C2×#117452922
C2×#117452442
C22×C22⋊C4×C292
C2×#53429