Finite Group Databasebeta

← C2×#14271600 #16832616

Subgroups — C2×#14271600 #16832616

Order 3712.

400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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×#11745281C211yesmaximal, characteristic, complemented
2C2×D8×D29C211yesmaximal, characteristic, complemented
3#14271600C218yesmaximal, direct product factor
4C2×#11745176C211yesmaximal, characteristic, complemented
5C2×D464C211yesmaximal, characteristic, complemented
6C2×#11745174C211yesmaximal, characteristic, complemented
7C2×#11745146C211yesmaximal, characteristic, complemented
8C2×C29×SD32C211yesmaximal, characteristic, complemented
9C2×#90809—21no—
10C2×D4×D29—21no—
11C2×Q16×C29C2211yescharacteristic, complemented
12C2×D8×C29C2211yescharacteristic
13C2×#90784—21no—
14C2×#90782—21no—
15#11745281—22no—
16#11745281C2214yescomplemented
17D8×D29—22no—
18D8×D29C2214yescomplemented
19C2×D232C2211yescharacteristic
20C2×D232C2211yescharacteristic, complemented
21C2×C8×D29C2211yescharacteristic
22C29×SD32C2214yescomplemented
23C2×C16×C29C2211yescharacteristic, complemented
24#11745176C2214yescomplemented
25#11745174C2214yescomplemented
26C2×#90768C2211yescharacteristic, complemented
27D464C2214yescomplemented
28#11745146C2214yescomplemented
29C23×D29—41no—
30C2×Q8×C29—21no—
31C2×D4×C29—21no—
32C2×C22⋊D29—41no—
33#90809—24no—
34#90809—42no—
35D4×D29—24no—
36D4×D29—42no—
37C2×D116—21no—
38C2×D116—21no—
39C2×D116—41no—
40C2×C4×D29—41no—
41C2×C4×D29D411yescharacteristic
42Q16×C29—21no—
43Q16×C29C2312yescomplemented
44D8×C29—21no—
45D8×C29C2312yes—
46C2×C8×C29C2311yescharacteristic
47#90784—24no—
48#90782—24no—
49C2×#6597D411yescharacteristic
50D232—21no—
51D232—21no—
52D232C2312yes—
53D232C2312yescomplemented
54C8×D29D412yes—
55C8×D29C2312yes—
56C16×C29C2312yescomplemented
57#90768C2312yescomplemented
58C23×C29—41no—
59C22×D29—41no—
60C22×D29—41no—
61C22×D29—44no—
62C22×D29—84no—
63C22×D29D811yescharacteristic
64Q8×C29—22no—
65Q8×C29—41no—
66D4×C29—22no—
67D4×C29—41no—
68C2×C4×C29—41no—
69C2×C4×C29C2×D411yescharacteristic
70C22⋊D29—44no—
71C2×Dic29D811yescharacteristic
72D116—22no—
73D116—22no—
74D116—44no—
75D116—41no—
76D116—41no—
77C4×D29—44no—
78C4×D29D812yes—
79C4×D29C2×D412yes—
80C8×C29C2×D411yescharacteristic
81C8×C29C2411yescharacteristic
82#6597C2×D412yes—
83C2×#509—291nomaximal, Sylow
84C22×C29—42no—
85C22×C29—82no—
86C22×C29C2×D811yescharacteristic
87C2×D29—22no—
88C2×D29—42no—
89C2×D29—42no—
90C2×D29—88no—
91C2×D29—82no—
92C2×D29—82no—
93C2×D29C2×D812yes—
94C4×C29—42no—
95C4×C29C2×D811yescharacteristic
96C4×C29C22×D411yescharacteristic
97Dic29C2×D812yes—
98C2×#135—291no—
99C22×D8—291no—
100#509—298no—
101C2×SD32—291no—
102C2×SD32D2911yescharacteristic, complemented
103C2×D16—291no—
104C2×D16—291no—
105C2×M32—291no—
106C2×C29—82no—
107C2×C29#50912yescomplemented
108C2×C29C22×D811yescharacteristic
109D29—22no—
110D29—82no—
111D29—82no—
112C2×#41—581no—
113C22×D4—581no—
114#135—294no—
115#135—582no—
116C2×Q16C2×D2911yescharacteristic, complemented
117C2×SD16—581no—
118C2×D8—294no—
119C2×D8—291no—
120C2×D8—291no—
121C2×D8—582no—
122C2×D8—581no—
123C2×D8C2×D2911yescharacteristic
124C22×C8—291no—
125SD32—294no—
126SD32C2×D2914yescomplemented
127D16—294no—
128D16—294no—
129M32—294no—
130C2×C16—291no—
131C2×C16C2×D2911yescharacteristic, complemented
132C29C2×#50911yescharacteristic, complemented, Sylow
133C24—1161no—
134#41—584no—
135#41—1162no—
136C2×Q8—21no—
137C2×D4—21no—
138C2×D4—584no—
139C2×D4—581no—
140C2×D4—581no—
141C2×D4—1161no—
142C2×D4—1162no—
143C2×D4—1161no—
144C22×C4—291no—
145C22×C4—1161no—
146Q16—21no—
147Q16C22×D2912yescomplemented
148SD16—584no—
149D8—21no—
150D8—292no—
151D8—292no—
152D8—584no—
153D8—581no—
154D8—581no—
155D8C22×D2912yes—
156C2×C8—291no—
157C2×C8—292no—
158C2×C8—292no—
159C2×C8C22×D2911yescharacteristic
160C16—292no—
161C16C22×D2912yescomplemented
162C23—41no—
163C23—291no—
164C23—1164no—
165C23—1161no—
166C23—1161no—
167C23—2324no—
168Q8—22no—
169Q8—41no—
170D4—22no—
171D4—41no—
172D4—582no—
173D4—582no—
174D4—1164no—
175D4—1164no—
176D4—1161no—
177D4—1161no—
178C2×C4—41no—
179C2×C4—291no—
180C2×C4—292no—
181C2×C4—292no—
182C2×C4—1164no—
183C2×C4D4×D2911yescharacteristic
184C8—292no—
185C8D4×D2911yescharacteristic
186C8C23×D2911yescharacteristic
187C22—42no—
188C22—82no—
189C22—292no—
190C22—582no—
191C22—1162no—
192C22—1162no—
193C22—2328no—
194C22—2322no—
195C22—2322no—
196C22D8×D2911yescharacteristic
197C4—42no—
198C4—292no—
199C4D8×D2911yescharacteristic
200C4C2×D4×D2911yescharacteristic
201C2—82no—
202C2—582no—
203C2—2322no—
204C2—2322no—
205C2#1427160012yesdirect product factor
206C2C2×D8×D2911yescharacteristic
subgroupG/H
centerC22D8×D29
commutator, cosocleC8×C29C24
FrattiniC8C23×D29
FittingC2×C29×SD32C2
socleC22×C29C2×D8
hypercenterC2×SD32D29
hypocenterC29C2×#509
LCSG ▷ C8×C29 ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. C2×#11745281C2semidirect
2. C2×D8×D29C2semidirect
3. #14271600C2direct (N × H)
4. C2×#11745176C2semidirect
5. C2×D464C2semidirect
6. C2×#11745174C2semidirect
7. C2×#11745146C2semidirect
8. C2×C29×SD32C2semidirect
11. C2×Q16×C29C22semidirect
16. #11745281C22semidirect
18. D8×D29C22semidirect
20. C2×D232C22semidirect
22. C29×SD32C22semidirect
23. C2×C16×C29C22semidirect
24. #11745176C22semidirect
25. #11745174C22semidirect
26. C2×#90768C22semidirect
27. D464C22semidirect
28. #11745146C22semidirect
43. Q16×C29C23semidirect
53. D232C23semidirect
56. C16×C29C23semidirect
57. #90768C23semidirect
102. C2×SD32D29semidirect
107. C2×C29#509semidirect
116. C2×Q16C2×D29semidirect
126. SD32C2×D29semidirect
131. C2×C16C2×D29semidirect
132. C29C2×#509semidirect
147. Q16C22×D29semidirect
161. C16C22×D29semidirect
205. C2#14271600direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117452812
C2×D8×D292
#142716002
C2×#117451762
C2×D4642
C2×#117451742
C2×#117451462
C2×C29×SD322
C2×#50929