Finite Group Databasebeta

← C2×#22581609 #31819867

Subgroups — C2×#22581609 #31819867

Order 17792.

1620 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14555784C211yesmaximal, characteristic, complemented
2C23×Dic278C211yesmaximal, characteristic, complemented
3#22581609C2116yesmaximal, direct product factor
4C2×#17984829C211yesmaximal, characteristic, complemented
5C2×#17984828C212yesmaximal, complemented
6C2×#17984822C211yesmaximal, characteristic, complemented
7C2×#17984819C212yesmaximal, complemented
8C2×#17984814C212yesmaximal, complemented
9C2×#17984807C211yesmaximal, characteristic, complemented
10C2×D4×Dic139C212yesmaximal, complemented
11C2×C4×C22⋊D139C211yesmaximal, characteristic, complemented
12C2×#121×C139C211yesmaximal, characteristic, complemented
13C2×#14555784—28no—
14C2×#14555784C2218yescomplemented
15C22×Dic278—28no—
16C22×Dic278C2212yes—
17C22×Dic278C2211yescharacteristic
18C22×Dic278C2211yescharacteristic
19C22×Dic278C2218yescomplemented
20C22×C22⋊D139C2212yes—
21C22×C22⋊D139C2211yescharacteristic
22C23×Dic139C2212yes—
23C23×Dic139C2212yes—
24C22×C4×D139C2211yescharacteristic
25#17984829C2218yescomplemented
26#17984828C22116yescomplemented
27#17984822C2218yescomplemented
28#17984819C22116yescomplemented
29#17984814C22116yescomplemented
30#17984807C2218yescomplemented
31D4×Dic139C22116yescomplemented
32C4×C22⋊D139C2218yescomplemented
33C2×C4⋊Dic139C2212yes—
34C2×Dic139⋊C4C2211yescharacteristic
35C2×Dic139⋊C4C2212yes—
36C2×C22⋊Dic139C2211yescharacteristic
37C2×C22⋊Dic139C2212yes—
38C2×C22⋊Dic139C2212yes—
39C2×(C2×D139)⋊C4C2211yescharacteristic
40C2×(C2×D139)⋊C4C2212yes—
41C2×C4×Dic139C2211yescharacteristic
42C2×C4×Dic139C2212yes—
43C22×D4×C139C2211yescharacteristic
44C22×D4×C139C2212yes—
45C23×C4×C139C2211yescharacteristic
46#121×C139C2218yescomplemented
47C2×C4⋊C4×C139C2211yescharacteristic
48C2×C22⋊C4×C139C2212yes—
49C23×D139C2311yescharacteristic
50#14555784—232no—
51C2×Dic278—232no—
52C2×Dic278—28no—
53C2×Dic278—24no—
54C2×Dic278D418yescomplemented
55C2×Dic278C2318yes—
56C2×Dic278C2314yes—
57C2×Dic278C2314yes—
58C2×C22⋊D139—28no—
59C2×C22⋊D139—24no—
60C2×C22⋊D139C2314yes—
61C2×C22⋊D139C2318yes—
62C22×Dic139—28no—
63C22×Dic139—28no—
64C22×Dic139C2311yescharacteristic
65C22×Dic139C2311yescharacteristic
66C22×Dic139C2312yes—
67C22×Dic139C2311yescharacteristic
68C22×Dic139C2318yes—
69C22×Dic139C2318yes—
70C22×Dic139C2312yes—
71C2×C4×D139—24no—
72C2×C4×D139C2314yes—
73C4⋊Dic139C2318yes—
74Dic139⋊C4C2314yes—
75Dic139⋊C4C2318yes—
76C22⋊Dic139C2314yes—
77C22⋊Dic139C2318yes—
78C22⋊Dic139C2318yes—
79(C2×D139)⋊C4C2314yes—
80(C2×D139)⋊C4C2318yes—
81C4×Dic139C2314yes—
82C4×Dic139C2318yes—
83C24×C139C2312yes—
84C24×C139C2311yescharacteristic
85C2×D4×C139—28no—
86C2×D4×C139—24no—
87C2×D4×C139C2318yes—
88C2×D4×C139C2314yes—
89C22×C4×C139—24no—
90C22×C4×C139C2312yes—
91C22×C4×C139C2311yescharacteristic
92C22×C4×C139C2314yes—
93C22×C4×C139C2311yescharacteristic
94C4⋊C4×C139C2314yes—
95C22⋊C4×C139C2318yes—
96C22×D139—22no—
97C22×D139—22no—
98C22×D139—22no—
99C22×D139C2412yes—
100Dic278—28no—
101Dic278—216no—
102Dic278C2×D4116yescomplemented
103C22⋊D139—28no—
104C22⋊D139—216no—
105C2×Dic139—22no—
106C2×Dic139—24no—
107C2×Dic139—22no—
108C2×Dic139—22no—
109C2×Dic139—216no—
110C2×Dic139—216no—
111C2×Dic139C2×D418yes—
112C2×Dic139C2412yes—
113C2×Dic139C2412yes—
114C2×Dic139C2414yes—
115C2×Dic139C2412yes—
116C2×Dic139C2414yes—
117C4×D139—28no—
118C23×C139—22no—
119C23×C139—22no—
120C23×C139—24no—
121C23×C139—24no—
122C23×C139—24no—
123C23×C139#4114yescomplemented
124C23×C139C2414yes—
125C23×C139C2412yes—
126C23×C139C2411yescharacteristic
127D4×C139—216no—
128D4×C139—28no—
129C2×C4×C139—22no—
130C2×C4×C139—24no—
131C2×C4×C139—28no—
132C2×C4×C139C2×D414yes—
133C2×C4×C139C2412yes—
134C2×C4×C139C2414yes—
135C2×C4×C139C2412yes—
136C22×C139—28no—
137C22×C139—22no—
138C22×C139—22no—
139C22×C139—24no—
140C22×C139—24no—
141C22×C139—24no—
142C22×C139—48no—
143C22×C139C22×D412yes—
144C22×C139C2×#4112yes—
145C22×C139C2×#4114yescomplemented
146C22×C1392−1+412yes—
147C22×C139C2511yescharacteristic
148C2×D139—22no—
149C2×D139—22no—
150C2×D139—22no—
151C2×D139—44no—
152C4×C139—22no—
153C4×C139—24no—
154C4×C139C22×D414yes—
155Dic139—22no—
156Dic139—24no—
157Dic139—22no—
158Dic139—22no—
159Dic139C22×D418yes—
160C2×C139—24no—
161C2×C139—44no—
162C2×C139#54814yescomplemented
163C2×C139C23×D411yescharacteristic
164C2×C139C22×#4111yescharacteristic
165C2×C139C2×2−1+411yescharacteristic
166D139—42no—
167C139C2×#54811yescharacteristic, complemented, Sylow
168C2×#548—1391nomaximal, Sylow
169C22×#41—1391no—
170C23×Q8—1391no—
171#548—13916no—
172C2×#124—1391no—
173C2×#124—1392no—
174C2×C22⋊Q8—1391no—
175C2×C22⋊Q8—1392no—
176C2×#121—1392no—
177C2×#121D13911yescharacteristic, complemented
178C2×C4×Q8—1391no—
179C2×C4×D4—1392no—
180C2×C4×D4—1391no—
181C2×#41—2788no—
182C2×#41—1398no—
183C22×Q8—2788no—
184C22×Q8—1391no—
185C22×Q8—1392no—
186C22×Q8—1398no—
187C22×Q8—1391no—
188C22×D4—1391no—
189C22×D4—1392no—
190C22×D4C2×D13912yes—
191C22×D4C2×D13911yescharacteristic
192C23×C4—1392no—
193C23×C4—1392no—
194C23×C4—1391no—
195C23×C4C2×D13911yescharacteristic
196#124—1398no—
197#124—13916no—
198C22⋊Q8—1398no—
199C22⋊Q8—13916no—
200#121—13916no—
201#121C2×D13918yescomplemented
202C4×Q8—1398no—
203C4×D4—13916no—
204C4×D4—1398no—
205C2×C4⋊C4—1391no—
206C2×C4⋊C4—1392no—
207C2×C4⋊C4—1392no—
208C2×C4⋊C4C2×D13911yescharacteristic
209C2×C22⋊C4—1391no—
210C2×C22⋊C4—1392no—
211C2×C22⋊C4—1392no—
212C2×C22⋊C4—1391no—
213C2×C22⋊C4—1392no—
214C2×C22⋊C4C2×D13912yes—
215C2×C42—1391no—
216C2×C42—1392no—
217C24—1391no—
218C24C22×D13912yes—
219C24C22×D13911yescharacteristic
220#41—27832no—
221C2×Q8—27832no—
222C2×Q8—2788no—
223C2×Q8—2784no—
224C2×Q8—1398no—
225C2×Q8—1394no—
226C2×Q8—1398no—
227C2×Q8—1394no—
228C2×D4—28no—
229C2×D4—24no—
230C2×D4—2784no—
231C2×D4—2788no—
232C2×D4—1394no—
233C2×D4—1398no—
234C2×D4C22×D13918yes—
235C2×D4C22×D13914yes—
236C22×C4—24no—
237C22×C4—2788no—
238C22×C4—2788no—
239C22×C4—2784no—
240C22×C4—1398no—
241C22×C4—1398no—
242C22×C4—1391no—
243C22×C4—1391no—
244C22×C4—1392no—
245C22×C4—1391no—
246C22×C4—1394no—
247C22×C4—1392no—
248C22×C4C22×D13914yes—
249C22×C4C22×D13912yes—
250C22×C4C22×D13911yescharacteristic
251C22×C4C22×D13911yescharacteristic
252C4⋊C4—1394no—
253C4⋊C4—1398no—
254C4⋊C4—1398no—
255C4⋊C4C22×D13914yes—
256C22⋊C4—1394no—
257C22⋊C4—1398no—
258C22⋊C4—1398no—
259C22⋊C4—1394no—
260C22⋊C4—1398no—
261C22⋊C4C22×D13918yes—
262C42—1394no—
263C42—1398no—
264C23—22no—
265C23—22no—
266C23—24no—
267C23—24no—
268C23—24no—
269C23—2782no—
270C23—2782no—
271C23—2782no—
272C23—1392no—
273C23#1455578414yescomplemented
274C23C23×D13914yes—
275C23C23×D13912yes—
276C23C23×D13911yescharacteristic
277Q8—27816no—
278Q8—2788no—
279Q8—13916no—
280D4—216no—
281D4—28no—
282D4—2788no—
283D4—27816no—
284C2×C4—22no—
285C2×C4—24no—
286C2×C4—28no—
287C2×C4—2782no—
288C2×C4—2784no—
289C2×C4—2782no—
290C2×C4—2782no—
291C2×C4—27816no—
292C2×C4—27816no—
293C2×C4—2788no—
294C2×C4—1392no—
295C2×C4—1392no—
296C2×C4—1394no—
297C2×C4—1392no—
298C2×C4—1398no—
299C2×C4—1394no—
300C2×C4D4×D13914yes—
301C2×C4C23×D13914yes—
302C2×C4C23×D13912yes—
303C2×C4C23×D13912yes—
304C22—22no—
305C22—22no—
306C22—28no—
307C22—24no—
308C22—24no—
309C22—24no—
310C22—48no—
311C22—2782no—
312C22—2782no—
313C22—2782no—
314C22—5564no—
315C22C2×D4×D13912yes—
316C22C2×#1455578412yes—
317C22C2×#1455578414yescomplemented
318C22#1798488912yes—
319C22C24×D13911yescharacteristic
320C4—22no—
321C4—24no—
322C4—2782no—
323C4—2784no—
324C4—2782no—
325C4—2782no—
326C4—1398no—
327C4C2×D4×D13914yes—
328C2—24no—
329C2—44no—
330C2—5562no—
331C2#2258160914yesdirect product factor
332C2C22×D4×D13911yescharacteristic
333C2C22×#1455578411yescharacteristic
334C2C2×#1798488911yescharacteristic
subgroupG/H
centerC23C23×D139
commutator, cosocleC22×C139C25
FrattiniC22C24×D139
FittingC2×#121×C139C2
socleC23×C139C24
hypercenterC2×#121D139
hypocenterC139C2×#548
LCSG ▷ C22×C139 ▷ C139
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C22×#14555784C2semidirect
2. C23×Dic278C2semidirect
3. #22581609C2direct (N × H)
4. C2×#17984829C2semidirect
5. C2×#17984828C2semidirect
6. C2×#17984822C2semidirect
7. C2×#17984819C2semidirect
8. C2×#17984814C2semidirect
9. C2×#17984807C2semidirect
10. C2×D4×Dic139C2semidirect
11. C2×C4×C22⋊D139C2semidirect
12. C2×#121×C139C2semidirect
14. C2×#14555784C22semidirect
19. C22×Dic278C22semidirect
25. #17984829C22semidirect
26. #17984828C22semidirect
27. #17984822C22semidirect
28. #17984819C22semidirect
29. #17984814C22semidirect
30. #17984807C22semidirect
31. D4×Dic139C22semidirect
32. C4×C22⋊D139C22semidirect
46. #121×C139C22semidirect
54. C2×Dic278D4semidirect
102. Dic278C2×D4semidirect
123. C23×C139#41semidirect
145. C22×C139C2×#41semidirect
162. C2×C139#548semidirect
167. C139C2×#548semidirect
177. C2×#121D139semidirect
201. #121C2×D139semidirect
273. C23#14555784semidirect
317. C22C2×#14555784semidirect
331. C2#22581609direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145557842
C23×Dic2782
#225816092
C2×#179848292
C2×#179848282
C2×#179848222
C2×#179848192
C2×#179848142
C2×#179848072
C2×D4×Dic1392
C2×C4×C22⋊D1392
C2×#121×C1392
C2×#548139