Finite Group Databasebeta

← C2×#22581097 #31815604

Subgroups — C2×#22581097 #31815604

Order 17792.

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

normal subgroups only

This group has 812 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×#14555786C211yesmaximal, characteristic, complemented
2C22×#14555770C211yesmaximal, characteristic, complemented
3C2×#17984813C211yesmaximal, characteristic, complemented
4#22581097C218yesmaximal, direct product factor
5C2×#17984766C211yesmaximal, characteristic, complemented
6C2×#17984764C211yesmaximal, characteristic, complemented
7C2×(C2×D139)⋊C8C211yesmaximal, characteristic, complemented
8C22×SD16×C139C211yesmaximal, characteristic, complemented
9C2×#14555786—24no—
10C2×#14555786—22no—
11C2×#14555786—24no—
12C2×#14555786C2214yescomplemented
13C22×D556—21no—
14C22×D556C2211yescharacteristic
15C22×C22⋊D139—21no—
16C22×C4×D139—21no—
17C22×C4×D139C2211yescharacteristic
18C2×#14555770—24no—
19C2×#14555770C2214yescomplemented
20C22×C139⋊C8C2211yescharacteristic
21#17984813—22no—
22#17984813C2214yescomplemented
23C2×C4⋊Dic139C2211yescharacteristic
24C2×C22⋊Dic139—21no—
25#17984766C2214yescomplemented
26#17984764C2214yescomplemented
27(C2×D139)⋊C8C2214yescomplemented
28C22×Q8×C139C2211yescharacteristic
29C22×D4×C139C2211yescharacteristic
30C2×SD16×C139—24no—
31C2×SD16×C139C2214yescomplemented
32C22×C8×C139C2211yescharacteristic
33C23×D139—21no—
34C23×D139D411yescharacteristic
35#14555786—216no—
36#14555786—28no—
37#14555786—28no—
38C2×D556—28no—
39C2×D556—24no—
40C2×D556—21no—
41C2×D556—22no—
42C2×D556D414yescomplemented
43C2×D556C2312yes—
44C2×C22⋊D139—24no—
45C2×C22⋊D139—44no—
46C22×Dic139—21no—
47C22×Dic139D411yescharacteristic
48C2×C4×D139—28no—
49C2×C4×D139—24no—
50C2×C4×D139—22no—
51C2×C4×D139—22no—
52C2×C4×D139D412yes—
53C2×C4×D139C2312yes—
54#14555770—28no—
55C2×C139⋊C8—22no—
56C2×C139⋊C8C2312yes—
57C4⋊Dic139—21no—
58C4⋊Dic139C2312yes—
59C22⋊Dic139—24no—
60C24×C139—21no—
61C2×Q8×C139—22no—
62C2×Q8×C139—21no—
63C2×Q8×C139D414yescomplemented
64C2×Q8×C139C2312yes—
65C2×D4×C139—22no—
66C2×D4×C139—22no—
67C2×D4×C139—21no—
68C2×D4×C139C2312yes—
69C22×C4×C139—21no—
70C22×C4×C139C2311yescharacteristic
71SD16×C139—28no—
72C2×C8×C139—22no—
73C2×C8×C139C2312yes—
74C22×D139—22no—
75C22×D139—24no—
76C22×D139—22no—
77C22×D139—22no—
78C22×D139—22no—
79C22×D139—42no—
80C22×D139—42no—
81C22×D139C2×D412yes—
82D556—216no—
83D556—24no—
84D556—22no—
85D556C2×D414yescomplemented
86C22⋊D139—48no—
87C2×Dic139—22no—
88C2×Dic139—22no—
89C2×Dic139—42no—
90C2×Dic139C2×D412yes—
91C4×D139—216no—
92C4×D139—24no—
93C4×D139—22no—
94C4×D139—22no—
95C139⋊C8—22no—
96C23×C139—22no—
97C23×C139—42no—
98C23×C139—42no—
99C23×C139—42no—
100C23×C139C2×D411yescharacteristic
101Q8×C139—24no—
102Q8×C139—22no—
103Q8×C139C2×D414yescomplemented
104D4×C139—22no—
105D4×C139—22no—
106D4×C139—42no—
107C2×C4×C139—24no—
108C2×C4×C139—22no—
109C2×C4×C139C2×D411yescharacteristic
110C2×C4×C139C2×D412yes—
111C2×C4×C139C2×D412yes—
112C2×C4×C139C2411yescharacteristic
113C8×C139—22no—
114C22×C139—42no—
115C22×C139—42no—
116C22×C139—42no—
117C22×C139—84no—
118C22×C139#12012yes—
119C22×C139#13512yes—
120C22×C139AGL(1,ℤ/8)12yes—
121C22×C139C22×D411yescharacteristic
122C2×D139—22no—
123C2×D139—24no—
124C2×D139—22no—
125C2×D139—22no—
126C2×D139—42no—
127C2×D139—42no—
128C2×D139—44no—
129C2×D139—48no—
130C4×C139—24no—
131C4×C139#12012yes—
132C4×C139C22×D411yescharacteristic
133C4×C139C22×D411yescharacteristic
134Dic139—22no—
135Dic139—42no—
136C2×C139—82no—
137C2×C139#44914yescomplemented
138C2×C139C2×#12011yescharacteristic
139C2×C139C2×#13511yescharacteristic
140C2×C139C2×AGL(1,ℤ/8)11yescharacteristic
141D139—42no—
142D139—44no—
143C139C2×#44911yescharacteristic, complemented, Sylow
144C2×#449—1391nomaximal, Sylow
145C22×#41—1391no—
146C22×SD16D13911yescharacteristic, complemented
147C22×D8—1391no—
148C2×#121—1391no—
149#449—1398no—
150C2×#103—1391no—
151C2×#102—1391no—
152C2×C22⋊C8—1391no—
153C2×#41—2784no—
154C2×#41—2784no—
155C2×#41—2782no—
156C2×#41—1394no—
157C22×Q8C2×D13911yescharacteristic
158C22×D4—2781no—
159C22×D4—2781no—
160C22×D4—1391no—
161C22×D4C2×D13911yescharacteristic
162C23×C4—2781no—
163C23×C4—1391no—
164C2×SD16—24no—
165C2×SD16C2×D13914yescomplemented
166C2×D8—2784no—
167C2×D8—1394no—
168C22×C8—1391no—
169C22×C8C2×D13911yescharacteristic
170#121—2782no—
171#121—1394no—
172C2×C4⋊C4—1391no—
173C2×C22⋊C4—2781no—
174#103—1394no—
175#102—1394no—
176C22⋊C8—1394no—
177C24—21no—
178C24—2781no—
179C24—1391no—
180#41—27816no—
181#41—2788no—
182#41—2788no—
183C2×Q8—22no—
184C2×Q8—21no—
185C2×Q8C22⋊D13914yescomplemented
186C2×Q8C22×D13912yes—
187C2×D4—22no—
188C2×D4—21no—
189C2×D4—22no—
190C2×D4—2788no—
191C2×D4—2784no—
192C2×D4—2784no—
193C2×D4—2781no—
194C2×D4—2782no—
195C2×D4—5564no—
196C2×D4—1394no—
197C2×D4—1392no—
198C2×D4C22×D13912yes—
199C22×C4—21no—
200C22×C4—2788no—
201C22×C4—2784no—
202C22×C4—2782no—
203C22×C4—2782no—
204C22×C4—2781no—
205C22×C4—1391no—
206C22×C4—1392no—
207C22×C4—1392no—
208C22×C4C22×D13911yescharacteristic
209SD16—28no—
210D8—2788no—
211C2×C8—22no—
212C2×C8—2782no—
213C2×C8—1392no—
214C2×C8C22×D13912yes—
215C4⋊C4—2781no—
216C4⋊C4—1392no—
217C22⋊C4—2784no—
218C23—22no—
219C23—42no—
220C23—42no—
221C23—42no—
222C23—2782no—
223C23—2784no—
224C23—2782no—
225C23—2782no—
226C23—2782no—
227C23—5562no—
228C23—5562no—
229C23—1392no—
230C23D4×D13911yescharacteristic
231Q8—24no—
232Q8—22no—
233Q8C2×C22⋊D13914yescomplemented
234D4—22no—
235D4—22no—
236D4—42no—
237D4—27816no—
238D4—2784no—
239D4—2782no—
240D4—5568no—
241D4—1394no—
242C2×C4—24no—
243C2×C4—22no—
244C2×C4—27816no—
245C2×C4—2782no—
246C2×C4—2784no—
247C2×C4—2782no—
248C2×C4—2782no—
249C2×C4—2782no—
250C2×C4—5562no—
251C2×C4—1392no—
252C2×C4D4×D13911yescharacteristic
253C2×C4D4×D13912yes—
254C2×C4C2×C22⋊D13912yes—
255C2×C4C23×D13911yescharacteristic
256C8—22no—
257C8—2782no—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—84no—
262C22—2782no—
263C22—2784no—
264C22—2782no—
265C22—2782no—
266C22—5564no—
267C22—5568no—
268C22—5562no—
269C22—5562no—
270C22#1798481012yes—
271C22#1798486312yes—
272C22#1798486912yes—
273C22C2×D4×D13911yescharacteristic
274C4—24no—
275C4—2782no—
276C4—5562no—
277C4#1798481012yes—
278C4C2×D4×D13911yescharacteristic
279C4C22×C22⋊D13911yescharacteristic
280C2—82no—
281C2—5562no—
282C2—5564no—
283C2#2258109714yesdirect product factor
284C2C2×#1798481011yescharacteristic
285C2C2×#1798486311yescharacteristic
286C2C2×#1798486911yescharacteristic
subgroupG/H
centerC23D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
FittingC22×SD16×C139C2
socleC23×C139C2×D4
hypercenterC22×SD16D139
hypocenterC139C2×#449
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×#14555786C2semidirect
2. C22×#14555770C2semidirect
3. C2×#17984813C2semidirect
4. #22581097C2direct (N × H)
5. C2×#17984766C2semidirect
6. C2×#17984764C2semidirect
7. C2×(C2×D139)⋊C8C2semidirect
8. C22×SD16×C139C2semidirect
12. C2×#14555786C22semidirect
19. C2×#14555770C22semidirect
22. #17984813C22semidirect
25. #17984766C22semidirect
26. #17984764C22semidirect
27. (C2×D139)⋊C8C22semidirect
31. C2×SD16×C139C22semidirect
42. C2×D556D4semidirect
63. C2×Q8×C139D4semidirect
85. D556C2×D4semidirect
103. Q8×C139C2×D4semidirect
137. C2×C139#449semidirect
143. C139C2×#449semidirect
146. C22×SD16D139semidirect
165. C2×SD16C2×D139semidirect
185. C2×Q8C22⋊D139semidirect
233. Q8C2×C22⋊D139semidirect
283. C2#22581097direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145557862
C22×#145557702
C2×#179848132
#225810972
C2×#179847662
C2×#179847642
C2×(C2×D139)⋊C82
C22×SD16×C1392
C2×#449139