Finite Group Databasebeta

← C2×#22581179 #31815961

Subgroups — C2×#22581179 #31815961

Order 17792.

564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C22×C8×D139C211yesmaximal, characteristic, complemented
2C2×#17984818C211yesmaximal, characteristic, complemented
3C2×#17984813C211yesmaximal, characteristic
4#22581179C218yesmaximal, direct product factor
5C2×#17984774C211yesmaximal, characteristic, complemented
6C2×#17984766C211yesmaximal, characteristic, complemented
7C2×#17984763C211yesmaximal, characteristic, complemented
8C22×SD16×C139C211yesmaximal, characteristic, complemented
9C22×C22⋊D139—21no—
10C22×C4×D139C2211yescharacteristic
11C22×C139⋊C8C2211yescharacteristic
12C2×C8×D139—24no—
13C2×C8×D139C2214yescomplemented
14#17984818—22no—
15#17984818C2214yescomplemented
16#17984813—22no—
17#17984813C2214yes—
18C2×C4⋊Dic139C2211yescharacteristic
19C2×C4⋊Dic139C2211yescharacteristic
20C2×Dic139⋊C4—21no—
21C2×C22⋊Dic139—21no—
22C2×(C2×D139)⋊C4—21no—
23#17984774C2214yescomplemented
24#17984766C2214yescomplemented
25#17984763C2214yescomplemented
26C22×Q8×C139C2211yescharacteristic
27C22×D4×C139C2211yescharacteristic
28C2×SD16×C139—24no—
29C2×SD16×C139C2214yescomplemented
30C22×C8×C139C2211yescharacteristic
31C23×D139D411yescharacteristic
32C2×C22⋊D139—24no—
33C2×C22⋊D139—44no—
34C22×Dic139—21no—
35C22×Dic139—21no—
36C22×Dic139D411yescharacteristic
37C2×C4×D139—22no—
38C2×C4×D139—22no—
39C2×C4×D139D412yes—
40C2×C4×D139C2312yes—
41C2×C139⋊C8—22no—
42C2×C139⋊C8C2312yes—
43C8×D139—28no—
44C4⋊Dic139—21no—
45C4⋊Dic139—21no—
46C4⋊Dic139C2312yes—
47C4⋊Dic139C2312yes—
48Dic139⋊C4—24no—
49C22⋊Dic139—24no—
50(C2×D139)⋊C4—24no—
51C24×C139—21no—
52C2×Q8×C139—21no—
53C2×Q8×C139—22no—
54C2×Q8×C139—22no—
55C2×Q8×C139C2312yes—
56C2×D4×C139—22no—
57C2×D4×C139—21no—
58C2×D4×C139—22no—
59C2×D4×C139C2312yes—
60C22×C4×C139—21no—
61C22×C4×C139C2311yescharacteristic
62SD16×C139—28no—
63C2×C8×C139D414yescomplemented
64C2×C8×C139C2312yes—
65C22×D139—22no—
66C22×D139—22no—
67C22×D139SD1614yescomplemented
68C22×D139C2×D412yes—
69C22⋊D139—48no—
70C2×Dic139—22no—
71C2×Dic139—22no—
72C2×Dic139—22no—
73C2×Dic139—42no—
74C2×Dic139—42no—
75C2×Dic139C2×D412yes—
76C4×D139—24no—
77C4×D139—22no—
78C4×D139—22no—
79C139⋊C8—22no—
80C23×C139—22no—
81C23×C139—42no—
82C23×C139—42no—
83C23×C139—42no—
84C23×C139C2×D411yescharacteristic
85Q8×C139—22no—
86Q8×C139—22no—
87Q8×C139—42no—
88D4×C139—22no—
89D4×C139—22no—
90D4×C139—42no—
91C2×C4×C139—22no—
92C2×C4×C139—42no—
93C2×C4×C139C2×D411yescharacteristic
94C2×C4×C139C2×D412yes—
95C2×C4×C139#4112yes—
96C2×C4×C139C2411yescharacteristic
97C8×C139C2×D414yescomplemented
98C22×C139—42no—
99C22×C139—42no—
100C22×C139—42no—
101C22×C139—84no—
102C22×C139#12112yes—
103C22×C139C2×SD1612yes—
104C22×C139#13512yes—
105C22×C139C22×D411yescharacteristic
106C2×D139—22no—
107C2×D139—22no—
108C2×D139—28no—
109C2×D139C2×SD1614yescomplemented
110C4×C139—42no—
111C4×C139#12112yes—
112C4×C139C22×D411yescharacteristic
113C4×C139C2×#4111yescharacteristic
114Dic139—22no—
115Dic139—42no—
116Dic139—42no—
117C2×C139—82no—
118C2×C139#46514yescomplemented
119C2×C139C2×#12111yescharacteristic
120C2×C139C22×SD1611yescharacteristic
121C2×C139C2×#13511yescharacteristic
122D139—24no—
123C139C2×#46511yescharacteristic, complemented, Sylow
124C2×#465—1391nomaximal, Sylow
125C22×SD16D13911yescharacteristic, complemented
126C23×C8—1391no—
127C2×C22⋊Q8—1391no—
128C2×#121—1391no—
129#465—1398no—
130C2×#106—1391no—
131C2×#103—1391no—
132C2×#102—1391no—
133C22×Q8C2×D13911yescharacteristic
134C22×D4—2781no—
135C22×D4C2×D13911yescharacteristic
136C23×C4—1391no—
137C2×SD16—24no—
138C2×SD16C2×D13914yescomplemented
139C22×C8—2784no—
140C22×C8—1391no—
141C22×C8—1394no—
142C22×C8C2×D13911yescharacteristic
143C22⋊Q8—2782no—
144C22⋊Q8—1394no—
145#121—2782no—
146#121—1394no—
147C2×C4⋊C4—2781no—
148C2×C4⋊C4—1391no—
149C2×C4⋊C4—1391no—
150C2×C22⋊C4—2781no—
151C2×C22⋊C4—2781no—
152#106—1394no—
153#103—1394no—
154#102—1394no—
155C24—21no—
156C24—1391no—
157C2×Q8—21no—
158C2×Q8—22no—
159C2×Q8—22no—
160C2×Q8C22×D13912yes—
161C2×D4—21no—
162C2×D4—22no—
163C2×D4—22no—
164C2×D4—2784no—
165C2×D4—5564no—
166C2×D4C22×D13912yes—
167C22×C4—21no—
168C22×C4—2782no—
169C22×C4—2782no—
170C22×C4—2781no—
171C22×C4—2781no—
172C22×C4—1391no—
173C22×C4—1392no—
174C22×C4—1392no—
175C22×C4C22×D13911yescharacteristic
176SD16—28no—
177C2×C8—2782no—
178C2×C8—2788no—
179C2×C8—1392no—
180C2×C8C22⋊D13914yescomplemented
181C2×C8C22×D13912yes—
182C4⋊C4—2784no—
183C4⋊C4—2781no—
184C4⋊C4—2781no—
185C4⋊C4—1392no—
186C4⋊C4—1392no—
187C22⋊C4—2784no—
188C22⋊C4—2784no—
189C23—22no—
190C23—42no—
191C23—42no—
192C23—42no—
193C23—2782no—
194C23—2782no—
195C23—1394no—
196C23—1392no—
197C23D4×D13911yescharacteristic
198Q8—22no—
199Q8—22no—
200Q8—42no—
201D4—22no—
202D4—22no—
203D4—42no—
204D4—5568no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—2782no—
208C2×C4—2784no—
209C2×C4—2782no—
210C2×C4—2782no—
211C2×C4—2782no—
212C2×C4—2782no—
213C2×C4—5562no—
214C2×C4—5562no—
215C2×C4—1392no—
216C2×C4D4×D13911yescharacteristic
217C2×C4C2×C22⋊D13912yes—
218C2×C4#1455578412yes—
219C2×C4C23×D13911yescharacteristic
220C8—2782no—
221C8C2×C22⋊D13914yescomplemented
222C22—42no—
223C22—42no—
224C22—42no—
225C22—84no—
226C22—2788no—
227C22—2782no—
228C22—2782no—
229C22—1394no—
230C22#1798481312yes—
231C22SD16×D13912yes—
232C22#1798486312yes—
233C22C2×D4×D13911yescharacteristic
234C4—42no—
235C4—2782no—
236C4—5562no—
237C4—5562no—
238C4#1798481312yes—
239C4C22×C22⋊D13911yescharacteristic
240C4C2×#1455578411yescharacteristic
241C2—82no—
242C2—2784no—
243C2#2258117914yesdirect product factor
244C2C2×#1798481311yescharacteristic
245C2C2×SD16×D13911yescharacteristic
246C2C2×#1798486311yescharacteristic
subgroupG/H
centerC23D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
FittingC22×SD16×C139C2
socleC23×C139C2×D4
prime radicalC2×#17984813C2
hypercenterC22×SD16D139
hypocenterC139C2×#465
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×C8×D139C2semidirect
2. C2×#17984818C2semidirect
4. #22581179C2direct (N × H)
5. C2×#17984774C2semidirect
6. C2×#17984766C2semidirect
7. C2×#17984763C2semidirect
8. C22×SD16×C139C2semidirect
13. C2×C8×D139C22semidirect
15. #17984818C22semidirect
23. #17984774C22semidirect
24. #17984766C22semidirect
25. #17984763C22semidirect
29. C2×SD16×C139C22semidirect
63. C2×C8×C139D4semidirect
67. C22×D139SD16semidirect
97. C8×C139C2×D4semidirect
109. C2×D139C2×SD16semidirect
118. C2×C139#465semidirect
123. C139C2×#465semidirect
125. C22×SD16D139semidirect
138. C2×SD16C2×D139semidirect
180. C2×C8C22⋊D139semidirect
221. C8C2×C22⋊D139semidirect
243. C2#22581179direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C8×D1392
C2×#179848182
C2×#179848132
#225811792
C2×#179847742
C2×#179847662
C2×#179847632
C22×SD16×C1392
C2×#465139