Finite Group Databasebeta

← C2×#22581102 #31815584

Subgroups — C2×#22581102 #31815584

Order 17792.

996 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 996 conjugacy classes of subgroups — too many to draw. Only its 173 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×D4×D139C211yesmaximal, characteristic
2C22×#14555772C211yesmaximal, characteristic, complemented
3C2×#17984818C211yesmaximal, characteristic, complemented
4#22581102C218yesmaximal, direct product factor
5C2×#17984764C211yesmaximal, characteristic, complemented
6C2×#17984763C211yesmaximal, characteristic, complemented
7C2×(C2×D139)⋊C8C211yesmaximal, characteristic, complemented
8C22×SD16×C139C211yesmaximal, characteristic, complemented
9C24×D139—21no—
10C22×D556C2211yescharacteristic
11C22×C22⋊D139—21no—
12C2×D4×D139—24no—
13C2×D4×D139—22no—
14C2×D4×D139—24no—
15C2×D4×D139C2214yes—
16C22×C4×D139C2211yescharacteristic
17C2×#14555772—24no—
18C2×#14555772C2214yescomplemented
19C22×C139⋊C8C2211yescharacteristic, complemented
20#17984818—22no—
21#17984818C2214yescomplemented
22C2×C4⋊Dic139C2211yescharacteristic, complemented
23C2×Dic139⋊C4—21no—
24C2×(C2×D139)⋊C4—21no—
25#17984764C2214yescomplemented
26#17984763C2214yescomplemented
27(C2×D139)⋊C8C2214yescomplemented
28C22×Q8×C139C2211yescharacteristic, complemented
29C22×D4×C139C2211yescharacteristic
30C2×SD16×C139—24no—
31C2×SD16×C139C2214yescomplemented
32C22×C8×C139C2211yescharacteristic, complemented
33C23×D139—28no—
34C23×D139—24no—
35C23×D139—21no—
36C23×D139—44no—
37C23×D139—44no—
38C23×D139D411yescharacteristic
39C2×D556—21no—
40C2×D556—22no—
41C2×D556D414yes—
42C2×D556C2312yes—
43C2×C22⋊D139—28no—
44C2×C22⋊D139—24no—
45D4×D139—216no—
46D4×D139—28no—
47D4×D139—28no—
48C22×Dic139—21no—
49C22×Dic139D411yescharacteristic
50C2×C4×D139—22no—
51C2×C4×D139—22no—
52C2×C4×D139D412yes—
53C2×C4×D139C2312yes—
54#14555772—28no—
55C2×C139⋊C8—22no—
56C2×C139⋊C8C2312yescomplemented
57C4⋊Dic139—21no—
58C4⋊Dic139C2312yescomplemented
59Dic139⋊C4—24no—
60(C2×D139)⋊C4—24no—
61C24×C139—21no—
62C2×Q8×C139—21no—
63C2×Q8×C139—22no—
64C2×Q8×C139—22no—
65C2×Q8×C139C2312yescomplemented
66C2×D4×C139—21no—
67C2×D4×C139—22no—
68C2×D4×C139D414yes—
69C2×D4×C139C2312yes—
70C22×C4×C139—21no—
71C22×C4×C139C2311yescharacteristic
72SD16×C139—28no—
73C2×C8×C139—22no—
74C2×C8×C139C2312yescomplemented
75C22×D139—22no—
76C22×D139—22no—
77C22×D139—216no—
78C22×D139—24no—
79C22×D139—22no—
80C22×D139—48no—
81C22×D139—432no—
82C22×D139—42no—
83C22×D139—42no—
84C22×D139—48no—
85C22×D139SD1614yescomplemented
86C22×D139C2×D412yes—
87D556—24no—
88D556—22no—
89D556C2×D414yes—
90C22⋊D139—216no—
91C2×Dic139—22no—
92C2×Dic139—22no—
93C2×Dic139—42no—
94C2×Dic139C2×D412yes—
95C4×D139—24no—
96C4×D139—22no—
97C4×D139—22no—
98C139⋊C8—22no—
99C23×C139—24no—
100C23×C139—22no—
101C23×C139—42no—
102C23×C139—42no—
103C23×C139C2×D411yescharacteristic
104Q8×C139—22no—
105Q8×C139—22no—
106Q8×C139—42no—
107D4×C139—24no—
108D4×C139—22no—
109D4×C139C2×D414yes—
110C2×C4×C139—22no—
111C2×C4×C139—42no—
112C2×C4×C139C2×D411yescharacteristic
113C2×C4×C139C2×D412yes—
114C2×C4×C139C2×D412yes—
115C2×C4×C139C2411yescharacteristic
116C8×C139—22no—
117C22×C139—24no—
118C22×C139—42no—
119C22×C139—42no—
120C22×C139—48no—
121C22×C139#12012yes—
122C22×C139C2×SD1612yes—
123C22×C139AGL(1,ℤ/8)12yes—
124C22×C139C22×D411yescharacteristic
125C2×D139—22no—
126C2×D139—22no—
127C2×D139—28no—
128C2×D139—24no—
129C2×D139—432no—
130C2×D139—42no—
131C2×D139—42no—
132C2×D139—48no—
133C2×D139C2×SD1614yescomplemented
134C4×C139—42no—
135C4×C139#12012yes—
136C4×C139C22×D411yescharacteristic
137C4×C139C22×D411yescharacteristic
138Dic139—22no—
139Dic139—42no—
140C2×C139—44no—
141C2×C139#45014yescomplemented
142C2×C139C2×#12011yescharacteristic
143C2×C139C22×SD1611yescharacteristic
144C2×C139C2×AGL(1,ℤ/8)11yescharacteristic
145D139—24no—
146D139—44no—
147C139C2×#45011yescharacteristic, complemented, Sylow
148C2×#450—1391nomaximal, Sylow
149C23×D4—1391no—
150C22×SD16—1391no—
151C22×SD16D13911yescharacteristic, complemented
152C2×C22⋊Q8—1391no—
153#450—1398no—
154C2×#102—1391no—
155C2×#102—1391no—
156C2×C22⋊C8—1391no—
157C25—2781no—
158C22×Q8C2×D13911yescharacteristic, complemented
159C22×D4—2784no—
160C22×D4—2784no—
161C22×D4—2782no—
162C22×D4—2781no—
163C22×D4—1394no—
164C22×D4—1391no—
165C22×D4C2×D13911yescharacteristic
166C23×C4—1391no—
167C2×SD16—24no—
168C2×SD16—2784no—
169C2×SD16—1394no—
170C2×SD16C2×D13914yescomplemented
171C22×C8—1391no—
172C22×C8C2×D13911yescharacteristic, complemented
173C22⋊Q8—2782no—
174C22⋊Q8—1394no—
175C2×C4⋊C4—2781no—
176C2×C4⋊C4—1391no—
177C2×C22⋊C4—2781no—
178#102—1394no—
179#102—1394no—
180C22⋊C8—1394no—
181C24—21no—
182C24—2788no—
183C24—2784no—
184C24—2781no—
185C24—5564no—
186C24—5564no—
187C24—1391no—
188C2×Q8—21no—
189C2×Q8—22no—
190C2×Q8—22no—
191C2×Q8C22×D13912yescomplemented
192C2×D4—21no—
193C2×D4—22no—
194C2×D4—27816no—
195C2×D4—2788no—
196C2×D4—2788no—
197C2×D4—2788no—
198C2×D4—2784no—
199C2×D4—2781no—
200C2×D4—2782no—
201C2×D4—1394no—
202C2×D4—1392no—
203C2×D4C22⋊D13914yes—
204C2×D4C22×D13912yes—
205C22×C4—21no—
206C22×C4—2782no—
207C22×C4—2782no—
208C22×C4—2781no—
209C22×C4—1391no—
210C22×C4—1392no—
211C22×C4—1392no—
212C22×C4C22×D13911yescharacteristic
213SD16—28no—
214SD16—2788no—
215C2×C8—22no—
216C2×C8—2782no—
217C2×C8—1392no—
218C2×C8C22×D13912yescomplemented
219C4⋊C4—2784no—
220C4⋊C4—2781no—
221C4⋊C4—1392no—
222C22⋊C4—2784no—
223C23—24no—
224C23—22no—
225C23—42no—
226C23—42no—
227C23—27816no—
228C23—2782no—
229C23—2782no—
230C23—2784no—
231C23—2782no—
232C23—55632no—
233C23—5568no—
234C23—5568no—
235C23—5562no—
236C23—5562no—
237C23—1394no—
238C23—1392no—
239C23D4×D13911yescharacteristic
240Q8—22no—
241Q8—22no—
242Q8—42no—
243D4—24no—
244D4—22no—
245D4—27816no—
246D4—2784no—
247D4—2782no—
248D4—1394no—
249D4C2×C22⋊D13914yes—
250C2×C4—22no—
251C2×C4—42no—
252C2×C4—2782no—
253C2×C4—2784no—
254C2×C4—2782no—
255C2×C4—2782no—
256C2×C4—2782no—
257C2×C4—5562no—
258C2×C4—1392no—
259C2×C4D4×D13911yescharacteristic
260C2×C4D4×D13912yes—
261C2×C4C2×C22⋊D13912yes—
262C2×C4C23×D13911yescharacteristic
263C8—22no—
264C8—2782no—
265C22—24no—
266C22—48no—
267C22—42no—
268C22—42no—
269C22—2788no—
270C22—2782no—
271C22—2782no—
272C22—2784no—
273C22—55632no—
274C22—5568no—
275C22—5562no—
276C22—5562no—
277C22—1394no—
278C22#1798481012yes—
279C22SD16×D13912yes—
280C22#1798486912yes—
281C22C2×D4×D13911yescharacteristic
282C4—42no—
283C4—2782no—
284C4—5562no—
285C4#1798481012yes—
286C4C2×D4×D13911yescharacteristic
287C4C22×C22⋊D13911yescharacteristic
288C2—44no—
289C2—2784no—
290C2—5564no—
291C2#2258110214yesdirect product factor
292C2C2×#1798481011yescharacteristic
293C2C2×SD16×D13911yescharacteristic
294C2C2×#1798486911yescharacteristic
subgroupG/H
centerC23D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
FittingC22×SD16×C139C2
socleC23×C139C2×D4
prime radicalC22×D4×D139C2
hypercenterC22×SD16D139
hypocenterC139C2×#450
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
2. C22×#14555772C2semidirect
3. C2×#17984818C2semidirect
4. #22581102C2direct (N × H)
5. C2×#17984764C2semidirect
6. C2×#17984763C2semidirect
7. C2×(C2×D139)⋊C8C2semidirect
8. C22×SD16×C139C2semidirect
18. C2×#14555772C22semidirect
19. C22×C139⋊C8C22semidirect
21. #17984818C22semidirect
22. C2×C4⋊Dic139C22semidirect
25. #17984764C22semidirect
26. #17984763C22semidirect
27. (C2×D139)⋊C8C22semidirect
28. C22×Q8×C139C22semidirect
31. C2×SD16×C139C22semidirect
32. C22×C8×C139C22semidirect
56. C2×C139⋊C8C23semidirect
58. C4⋊Dic139C23semidirect
65. C2×Q8×C139C23semidirect
74. C2×C8×C139C23semidirect
85. C22×D139SD16semidirect
133. C2×D139C2×SD16semidirect
141. C2×C139#450semidirect
147. C139C2×#450semidirect
151. C22×SD16D139semidirect
158. C22×Q8C2×D139semidirect
170. C2×SD16C2×D139semidirect
172. C22×C8C2×D139semidirect
191. C2×Q8C22×D139semidirect
218. C2×C8C22×D139semidirect
291. C2#22581102direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D1392
C22×#145557722
C2×#179848182
#225811022
C2×#179847642
C2×#179847632
C2×(C2×D139)⋊C82
C22×SD16×C1392
C2×#450139