Finite Group Databasebeta

← C2×#22581387 #31819525

Subgroups — C2×#22581387 #31819525

Order 17792.

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×#17984861C211yesmaximal, characteristic, complemented
2C2×D8×D139C211yesmaximal, characteristic, complemented
3#22581387C218yesmaximal, direct product factor
4C2×#17984787C211yesmaximal, characteristic, complemented
5C2×#17984786C211yesmaximal, characteristic, complemented
6C2×#17984783C211yesmaximal, characteristic, complemented
7C2×#17984781C211yesmaximal, characteristic, complemented
8C2×D16×C139C211yesmaximal, characteristic, complemented
9C2×#14555784—21no—
10C2×D4×D139—21no—
11#17984861—22no—
12#17984861C2214yescomplemented
13C2×Dic556C2211yescharacteristic, complemented
14C2×#14555773—21no—
15C2×D1112C2211yescharacteristic
16C2×#14555770—21no—
17D8×D139—22no—
18D8×D139C2214yescomplemented
19C2×C8×D139C2211yescharacteristic
20#17984787C2214yescomplemented
21#17984786C2214yescomplemented
22#17984783C2214yescomplemented
23#17984781C2214yescomplemented
24C2×C139⋊C16C2211yescharacteristic, complemented
25C2×D8×C139C2211yescharacteristic
26C2×D8×C139C2211yescharacteristic, complemented
27D16×C139C2214yescomplemented
28C2×C16×C139C2211yescharacteristic, complemented
29C23×D139—41no—
30#14555784—24no—
31#14555784—42no—
32C2×Dic278—21no—
33C2×D556—21no—
34C2×C22⋊D139—41no—
35C2×C22⋊D139—41no—
36D4×D139—24no—
37D4×D139—42no—
38C22×Dic139—41no—
39C2×C4×D139D411yescharacteristic
40Dic556—21no—
41Dic556C2312yescomplemented
42#14555773—24no—
43D1112—21no—
44D1112C2312yes—
45#14555770—24no—
46C2×C139⋊C8D411yescharacteristic
47C8×D139D412yes—
48C8×D139C2312yes—
49C139⋊C16C2312yescomplemented
50C2×D4×C139—21no—
51C2×D4×C139—21no—
52D8×C139—21no—
53D8×C139—21no—
54D8×C139C2312yes—
55D8×C139C2312yescomplemented
56C2×C8×C139C2311yescharacteristic
57C16×C139C2312yescomplemented
58C22×D139—41no—
59C22×D139—44no—
60C22×D139—84no—
61C22×D139D811yescharacteristic
62Dic278—22no—
63Dic278—41no—
64D556—22no—
65D556—41no—
66C22⋊D139—44no—
67C22⋊D139—44no—
68C2×Dic139—41no—
69C2×Dic139—44no—
70C2×Dic139D811yescharacteristic
71C4×D139D812yes—
72C4×D139C2×D412yes—
73C139⋊C8C2×D412yes—
74C23×C139—41no—
75C23×C139—41no—
76D4×C139—22no—
77D4×C139—22no—
78D4×C139—41no—
79D4×C139—41no—
80C2×C4×C139C2×D411yescharacteristic
81C8×C139C2×D411yescharacteristic
82C8×C139C2411yescharacteristic
83C22×C139—42no—
84C22×C139—42no—
85C22×C139—82no—
86C22×C139—82no—
87C22×C139C2×D811yescharacteristic
88C2×D139—22no—
89C2×D139—42no—
90C2×D139—88no—
91C2×D139—82no—
92C2×D139C2×D812yes—
93C4×C139C2×D811yescharacteristic
94C4×C139C22×D411yescharacteristic
95Dic139—42no—
96Dic139C2×D812yes—
97C2×C139—82no—
98C2×C139—82no—
99C2×C139#50912yescomplemented
100C2×C139C22×D811yescharacteristic
101D139—22no—
102D139—82no—
103C139C2×#50911yescharacteristic, complemented, Sylow
104C2×#509—1391nomaximal, Sylow
105C2×#135—1391no—
106C22×D8—1391no—
107#509—1398no—
108C2×SD32—1391no—
109C2×SD32—1391no—
110C2×D16—1391no—
111C2×D16D13911yescharacteristic, complemented
112C2×M32—1391no—
113C2×#41—2781no—
114C22×D4—2781no—
115#135—2782no—
116#135—1394no—
117C2×Q16—1391no—
118C2×SD16—2781no—
119C2×D8—2782no—
120C2×D8—2781no—
121C2×D8—1394no—
122C2×D8—1391no—
123C2×D8C2×D13911yescharacteristic
124C2×D8C2×D13911yescharacteristic, complemented
125C22×C8—1391no—
126SD32—1394no—
127SD32—1394no—
128D16—1394no—
129D16C2×D13914yescomplemented
130M32—1394no—
131C2×C16—1391no—
132C2×C16C2×D13911yescharacteristic, complemented
133C24—5561no—
134#41—2784no—
135#41—5562no—
136C2×Q8—2781no—
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—2784no—
140C2×D4—2781no—
141C2×D4—5561no—
142C2×D4—5562no—
143C2×D4—5561no—
144C22×C4—5561no—
145C22×C4—1391no—
146Q16—2781no—
147Q16—1392no—
148SD16—2784no—
149D8—21no—
150D8—21no—
151D8—2784no—
152D8—2781no—
153D8—1392no—
154D8C22×D13912yes—
155D8C22×D13912yescomplemented
156C2×C8—1391no—
157C2×C8—1392no—
158C2×C8—1392no—
159C2×C8C22×D13911yescharacteristic
160C16—1392no—
161C16C22×D13912yescomplemented
162C23—41no—
163C23—41no—
164C23—5564no—
165C23—5561no—
166C23—11124no—
167C23—1391no—
168Q8—2782no—
169Q8—5561no—
170D4—22no—
171D4—22no—
172D4—41no—
173D4—41no—
174D4—2782no—
175D4—5564no—
176D4—5564no—
177D4—5561no—
178C2×C4—5561no—
179C2×C4—5564no—
180C2×C4—1391no—
181C2×C4—1392no—
182C2×C4—1392no—
183C2×C4D4×D13911yescharacteristic
184C8—1392no—
185C8D4×D13911yescharacteristic
186C8C23×D13911yescharacteristic
187C22—42no—
188C22—42no—
189C22—82no—
190C22—82no—
191C22—2782no—
192C22—5562no—
193C22—11128no—
194C22—11122no—
195C22—1392no—
196C22D8×D13911yescharacteristic
197C4—5562no—
198C4—1392no—
199C4D8×D13911yescharacteristic
200C4C2×D4×D13911yescharacteristic
201C2—82no—
202C2—82no—
203C2—2782no—
204C2—11122no—
205C2#2258138712yesdirect product factor
206C2C2×D8×D13911yescharacteristic
subgroupG/H
centerC22D8×D139
commutator, cosocleC8×C139C24
FrattiniC8C23×D139
FittingC2×D16×C139C2
socleC22×C139C2×D8
hypercenterC2×D16D139
hypocenterC139C2×#509
LCSG ▷ C8×C139 ▷ C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. C2×#17984861C2semidirect
2. C2×D8×D139C2semidirect
3. #22581387C2direct (N × H)
4. C2×#17984787C2semidirect
5. C2×#17984786C2semidirect
6. C2×#17984783C2semidirect
7. C2×#17984781C2semidirect
8. C2×D16×C139C2semidirect
12. #17984861C22semidirect
13. C2×Dic556C22semidirect
18. D8×D139C22semidirect
20. #17984787C22semidirect
21. #17984786C22semidirect
22. #17984783C22semidirect
23. #17984781C22semidirect
24. C2×C139⋊C16C22semidirect
26. C2×D8×C139C22semidirect
27. D16×C139C22semidirect
28. C2×C16×C139C22semidirect
41. Dic556C23semidirect
49. C139⋊C16C23semidirect
55. D8×C139C23semidirect
57. C16×C139C23semidirect
99. C2×C139#509semidirect
103. C139C2×#509semidirect
111. C2×D16D139semidirect
124. C2×D8C2×D139semidirect
129. D16C2×D139semidirect
132. C2×C16C2×D139semidirect
155. D8C22×D139semidirect
161. C16C22×D139semidirect
205. C2#22581387direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179848612
C2×D8×D1392
#225813872
C2×#179847872
C2×#179847862
C2×#179847832
C2×#179847812
C2×D16×C1392
C2×#509139