Finite Group Databasebeta

← C2×#22581119 #31815726

Subgroups — C2×#22581119 #31815726

Order 17792.

844 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 844 conjugacy classes of subgroups — too many to draw. Only its 149 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×#17984888C211yesmaximal, characteristic, complemented
2C2×#17984868C211yesmaximal, characteristic, complemented
3C2×#17984838C211yesmaximal, characteristic, complemented
4#22581119C218yesmaximal, direct product factor
5C2×#17984769C211yesmaximal, characteristic, complemented
6C2×#17984768C211yesmaximal, characteristic, complemented
7C2×#17984758C211yesmaximal, characteristic, complemented
8C2×AGL(1,ℤ/8)×C139C211yesmaximal, characteristic, complemented
9#17984888—22no—
10#17984888—22no—
11#17984888—22no—
12#17984888C2214yescomplemented
13C2×#14555786—21no—
14C2×#14555785—21no—
15C2×#14555785C2211yescharacteristic
16C22×D556—21no—
17C22×D556C2211yescharacteristic
18C22×C22⋊D139—22no—
19C2×D4×D139—22no—
20C2×D4×D139—21no—
21#17984868—22no—
22#17984868C2214yescomplemented
23C2×#14555773—21no—
24C2×#14555770—21no—
25C2×#14555769C2211yescharacteristic, complemented
26#17984838—22no—
27#17984838C2214yescomplemented
28C2×C4×Dic139C2211yescharacteristic, complemented
29#17984769C2214yescomplemented
30#17984768C2214yescomplemented
31#17984758C2214yescomplemented
32C2×#41×C139C2211yescharacteristic
33C22×D4×C139C2211yescharacteristic, complemented
34AGL(1,ℤ/8)×C139—22no—
35AGL(1,ℤ/8)×C139C2214yescomplemented
36C2×SD16×C139—21no—
37C2×D8×C139—21no—
38C2×M16×C139C2211yescharacteristic, complemented
39C23×D139—22no—
40C23×D139D412yes—
41#14555786—24no—
42#14555786—24no—
43#14555785—24no—
44#14555785—24no—
45#14555785—21no—
46#14555785—21no—
47#14555785D412yescomplemented
48#14555785C2312yes—
49C2×Dic278D411yescharacteristic, complemented
50C2×D556—22no—
51C2×D556—24no—
52C2×D556—24no—
53C2×D556—21no—
54C2×D556—21no—
55C2×D556—21no—
56C2×D556—21no—
57C2×D556D412yes—
58C2×D556D411yescharacteristic, complemented
59C2×D556C2312yes—
60C2×C22⋊D139—22no—
61C2×C22⋊D139—28no—
62C2×C22⋊D139—21no—
63C2×C22⋊D139—48no—
64D4×D139—28no—
65D4×D139—24no—
66D4×D139—28no—
67D4×D139—24no—
68C22×Dic139—21no—
69C2×C4×D139—22no—
70C2×C4×D139—21no—
71#14555773—24no—
72#14555770—24no—
73#14555769—21no—
74#14555769C2312yescomplemented
75C2×C139⋊C8—21no—
76C4×Dic139—21no—
77C4×Dic139C2312yescomplemented
78C24×C139—21no—
79#41×C139—21no—
80#41×C139—21no—
81#41×C139D412yescomplemented
82#41×C139C2312yes—
83C2×Q8×C139D411yescharacteristic, complemented
84C2×D4×C139—21no—
85C2×D4×C139—21no—
86C2×D4×C139—21no—
87C2×D4×C139—21no—
88C2×D4×C139—21no—
89C2×D4×C139—21no—
90C2×D4×C139D411yescharacteristic, complemented
91C2×D4×C139C2312yescomplemented
92C22×C4×C139—21no—
93C22×C4×C139C2311yescharacteristic
94SD16×C139—24no—
95D8×C139—24no—
96M16×C139—21no—
97M16×C139C2312yescomplemented
98C2×C8×C139—21no—
99C22×D139—22no—
100C22×D139—21no—
101C22×D139—28no—
102C22×D139—22no—
103C22×D139—44no—
104C22×D139—84no—
105C22×D139C2×D414yes—
106Dic278—21no—
107Dic278C2×D412yescomplemented
108D556—28no—
109D556—22no—
110D556—22no—
111D556—21no—
112D556—22no—
113D556—22no—
114D556C2×D412yescomplemented
115C22⋊D139—28no—
116C22⋊D139—22no—
117C22⋊D139—22no—
118C22⋊D139—416no—
119C2×Dic139—24no—
120C2×Dic139—21no—
121C2×Dic139—22no—
122C4×D139—28no—
123C4×D139—22no—
124C4×D139—22no—
125C139⋊C8—22no—
126C23×C139—21no—
127C23×C139—22no—
128C23×C139—44no—
129C23×C139—41no—
130C23×C139—41no—
131C23×C139C2×D411yescharacteristic
132Q8×C139—21no—
133Q8×C139C2×D412yescomplemented
134D4×C139—22no—
135D4×C139—22no—
136D4×C139—21no—
137D4×C139—22no—
138D4×C139—22no—
139D4×C139—41no—
140D4×C139—41no—
141D4×C139C2×D412yescomplemented
142C2×C4×C139—21no—
143C2×C4×C139—22no—
144C2×C4×C139—22no—
145C2×C4×C139C2×D411yescharacteristic
146C2×C4×C139C2×D411yescharacteristic
147C2×C4×C139C2×D411yescharacteristic
148C2×C4×C139C2×D411yescharacteristic
149C2×C4×C139C2×D411yescharacteristic
150C2×C4×C139C2411yescharacteristic
151C8×C139—22no—
152C22×C139—22no—
153C22×C139—22no—
154C22×C139—44no—
155C22×C139—42no—
156C22×C139—42no—
157C22×C139—82no—
158C22×C139—82no—
159C22×C139#12011yescharacteristic
160C22×C139#12011yescharacteristic
161C22×C139C22×D411yescharacteristic
162C2×D139—24no—
163C2×D139—22no—
164C2×D139—44no—
165C2×D139—42no—
166C2×D139—44no—
167C2×D139—82no—
168C2×D139—88no—
169C4×C139—22no—
170C4×C139#12011yescharacteristic
171C4×C139#12011yescharacteristic
172C4×C139C22×D411yescharacteristic
173C4×C139C22×D411yescharacteristic
174Dic139—24no—
175Dic139—22no—
176C2×C139—21no—
177C2×C139—21no—
178C2×C139—42no—
179C2×C139—82no—
180C2×C139#45312yescomplemented
181C2×C139C2×#12011yescharacteristic
182D139—44no—
183D139—42no—
184C139C2×#45311yescharacteristic, complemented, Sylow
185C2×#453—1391nomaximal, Sylow
186C2×H(5,𝔽2)—1391no—
187C2×AGL(1,ℤ/8)—1391no—
188C2×AGL(1,ℤ/8)D13911yescharacteristic, complemented
189C2×#127—1391no—
190#453—1398no—
191C2×#104—1391no—
192C2×#104—1391no—
193C2×#100—1391no—
194H(5,𝔽2)—2782no—
195H(5,𝔽2)—2782no—
196H(5,𝔽2)—2782no—
197H(5,𝔽2)—1394no—
198C2×#41—2781no—
199C2×#41—2781no—
200C2×#41—1391no—
201C2×#41C2×D13911yescharacteristic
202C22×D4—2781no—
203C22×D4—2782no—
204C22×D4—2781no—
205C22×D4—2782no—
206C22×D4—1391no—
207C22×D4C2×D13911yescharacteristic, complemented
208AGL(1,ℤ/8)—22no—
209AGL(1,ℤ/8)—2782no—
210AGL(1,ℤ/8)—1394no—
211AGL(1,ℤ/8)C2×D13914yescomplemented
212C2×SD16—21no—
213C2×SD16—2781no—
214C2×D8—21no—
215C2×D8—2781no—
216C2×M16—1391no—
217C2×M16C2×D13911yescharacteristic, complemented
218#127—2782no—
219#127—1394no—
220C2×C42—1391no—
221#104—1394no—
222#104—1394no—
223#100—1394no—
224C24—21no—
225C24—2782no—
226C24—1392no—
227#41—21no—
228#41—21no—
229#41—2784no—
230#41—2784no—
231#41—2784no—
232#41—2784no—
233#41—2781no—
234#41—2781no—
235#41—1392no—
236#41—1392no—
237#41C22⋊D13912yescomplemented
238#41C22×D13912yes—
239C2×Q8—1391no—
240C2×Q8C22⋊D13911yescharacteristic, complemented
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—2782no—
248C2×D4—2784no—
249C2×D4—2784no—
250C2×D4—2788no—
251C2×D4—2784no—
252C2×D4—2788no—
253C2×D4—2782no—
254C2×D4—2781no—
255C2×D4—2784no—
256C2×D4—2788no—
257C2×D4—2781no—
258C2×D4—2781no—
259C2×D4—2781no—
260C2×D4—2781no—
261C2×D4—5568no—
262C2×D4—1392no—
263C2×D4—1391no—
264C2×D4—1392no—
265C2×D4C22⋊D13911yescharacteristic, complemented
266C2×D4C22×D13912yescomplemented
267C22×C4—21no—
268C22×C4—2782no—
269C22×C4—2781no—
270C22×C4—2781no—
271C22×C4C22×D13911yescharacteristic
272SD16—24no—
273SD16—2784no—
274D8—24no—
275D8—2784no—
276M16—21no—
277M16—2781no—
278M16—1392no—
279M16C22×D13912yescomplemented
280C2×C8—21no—
281C2×C8—2781no—
282C42—2781no—
283C42—1392no—
284C23—21no—
285C23—22no—
286C23—44no—
287C23—41no—
288C23—41no—
289C23—2788no—
290C23—2782no—
291C23—2781no—
292C23—2782no—
293C23—5564no—
294C23—11124no—
295C23—1394no—
296C23D4×D13911yescharacteristic
297Q8—21no—
298Q8—2781no—
299Q8—1392no—
300Q8C2×C22⋊D13912yescomplemented
301D4—22no—
302D4—22no—
303D4—21no—
304D4—22no—
305D4—22no—
306D4—41no—
307D4—41no—
308D4—2788no—
309D4—2788no—
310D4—2782no—
311D4—2782no—
312D4—2782no—
313D4—2781no—
314D4—2782no—
315D4—2782no—
316D4—2782no—
317D4—55616no—
318D4—1392no—
319D4C2×C22⋊D13912yescomplemented
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—2788no—
324C2×C4—2784no—
325C2×C4—2781no—
326C2×C4—2782no—
327C2×C4—2782no—
328C2×C4—2782no—
329C2×C4D4×D13911yescharacteristic
330C2×C4D4×D13911yescharacteristic
331C2×C4D4×D13911yescharacteristic
332C2×C4C2×C22⋊D13911yescharacteristic
333C2×C4C2×C22⋊D13911yescharacteristic
334C2×C4C23×D13911yescharacteristic
335C8—22no—
336C8—2782no—
337C22—22no—
338C22—22no—
339C22—44no—
340C22—42no—
341C22—42no—
342C22—82no—
343C22—82no—
344C22—2784no—
345C22—2782no—
346C22—5564no—
347C22—5564no—
348C22—5562no—
349C22—11122no—
350C22—11128no—
351C22#1798481011yescharacteristic
352C22#1798481011yescharacteristic
353C22C2×D4×D13911yescharacteristic
354C4—22no—
355C4—2784no—
356C4—2782no—
357C4#1798481011yescharacteristic
358C4#1798481011yescharacteristic
359C4C2×D4×D13911yescharacteristic
360C4C22×C22⋊D13911yescharacteristic
361C2—21no—
362C2—21no—
363C2—42no—
364C2—82no—
365C2—5564no—
366C2—5562no—
367C2#2258111912yesdirect product factor
368C2C2×#1798481011yescharacteristic
subgroupG/H
centerC22#17984810
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
FittingC2×AGL(1,ℤ/8)×C139C2
socleC22×C139#120
hypercenterC2×AGL(1,ℤ/8)D139
hypocenterC139C2×#453
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#17984888C2semidirect
2. C2×#17984868C2semidirect
3. C2×#17984838C2semidirect
4. #22581119C2direct (N × H)
5. C2×#17984769C2semidirect
6. C2×#17984768C2semidirect
7. C2×#17984758C2semidirect
8. C2×AGL(1,ℤ/8)×C139C2semidirect
12. #17984888C22semidirect
22. #17984868C22semidirect
25. C2×#14555769C22semidirect
27. #17984838C22semidirect
28. C2×C4×Dic139C22semidirect
29. #17984769C22semidirect
30. #17984768C22semidirect
31. #17984758C22semidirect
33. C22×D4×C139C22semidirect
35. AGL(1,ℤ/8)×C139C22semidirect
38. C2×M16×C139C22semidirect
47. #14555785D4semidirect
49. C2×Dic278D4semidirect
58. C2×D556D4semidirect
74. #14555769C23semidirect
77. C4×Dic139C23semidirect
81. #41×C139D4semidirect
83. C2×Q8×C139D4semidirect
90. C2×D4×C139D4semidirect
91. C2×D4×C139C23semidirect
97. M16×C139C23semidirect
107. Dic278C2×D4semidirect
114. D556C2×D4semidirect
133. Q8×C139C2×D4semidirect
141. D4×C139C2×D4semidirect
180. C2×C139#453semidirect
184. C139C2×#453semidirect
188. C2×AGL(1,ℤ/8)D139semidirect
207. C22×D4C2×D139semidirect
211. AGL(1,ℤ/8)C2×D139semidirect
217. C2×M16C2×D139semidirect
237. #41C22⋊D139semidirect
240. C2×Q8C22⋊D139semidirect
265. C2×D4C22⋊D139semidirect
266. C2×D4C22×D139semidirect
279. M16C22×D139semidirect
300. Q8C2×C22⋊D139semidirect
319. D4C2×C22⋊D139semidirect
367. C2#22581119direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179848882
C2×#179848682
C2×#179848382
#225811192
C2×#179847692
C2×#179847682
C2×#179847582
C2×AGL(1,ℤ/8)×C1392
C2×#453139