Finite Group Databasebeta

← #31818243

Subgroups — #31818243

Order 17792.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581645C211yesmaximal, characteristic, complemented
2#22581597C211yesmaximal, characteristic
3#22581306C211yesmaximal, characteristic, complemented
4#22581284C211yesmaximal, characteristic, complemented
5#22581276C211yesmaximal, characteristic, complemented
6#22581255C211yesmaximal, characteristic, complemented
7#22581192C211yesmaximal, characteristic, complemented
8#22581179C211yesmaximal, characteristic, complemented
9#22581173C211yesmaximal, characteristic, complemented
10#22581112C211yesmaximal, characteristic, complemented
11SD16×Dic139C211yesmaximal, characteristic, complemented
12(C22⋊D139)⋊C8C211yesmaximal, characteristic, complemented
13#22580946C211yesmaximal, characteristic, complemented
14C2×#17984763C211yesmaximal, characteristic, complemented
15#450×C139C211yesmaximal, characteristic, complemented
16C2×#14555784C2211yescharacteristic
17C2×#14555775C2211yescharacteristic, complemented
18C22×C139⋊C8C2211yescharacteristic
19C2×C8×D139C2211yescharacteristic, complemented
20#17984837—21no—
21#17984833—21no—
22#17984833C2211yescharacteristic, complemented
23#17984829C2211yescharacteristic
24#17984826—21no—
25#17984823—21no—
26#17984821C2211yescharacteristic
27#17984818C2211yescharacteristic, complemented
28#17984814—21no—
29#17984813C2211yescharacteristic
30#17984811—21no—
31Q8×Dic139C2211yescharacteristic, complemented
32D4×Dic139C2211yescharacteristic
33C4×C22⋊D139C2211yescharacteristic
34#17984800C2211yescharacteristic, complemented
35#17984798—21no—
36C2×C4⋊Dic139C2211yescharacteristic
37C2×C22⋊Dic139—21no—
38#17984775C2211yescharacteristic, complemented
39#17984774C2211yescharacteristic, complemented
40#17984774C2211yescharacteristic, complemented
41Dic139⋊C8C2211yescharacteristic, complemented
42#17984767C2211yescharacteristic, complemented
43#17984767C2211yescharacteristic, complemented
44#17984766C2211yescharacteristic, complemented
45#17984765C2211yescharacteristic, complemented
46#17984763C2211yescharacteristic
47#17984763C2211yescharacteristic
48#17984763C2211yescharacteristic
49#17984763C2211yescharacteristic
50(C2×D139)⋊C8C2211yescharacteristic, complemented
51C8×Dic139C2211yescharacteristic, complemented
52C22×D4×C139C2211yescharacteristic
53C2×SD16×C139C2211yescharacteristic
54C2×SD16×C139C2211yescharacteristic
55C22⋊Q8×C139C2211yescharacteristic
56#102×C139C2211yescharacteristic
57#102×C139C2211yescharacteristic
58C22⋊C8×C139C2211yescharacteristic
59#14555784—22no—
60#14555784—41no—
61C2×Dic278C2311yescharacteristic
62C2×C22⋊D139—21no—
63C2×C22⋊D139—21no—
64C2×C22⋊D139D411yescharacteristic
65C22×Dic139—21no—
66C22×Dic139—21no—
67C22×Dic139—21no—
68C2×C4×D139C2311yescharacteristic
69#14555775—41no—
70C2×C139⋊C8—41no—
71C2×C139⋊C8C2311yescharacteristic
72C2×C139⋊C8C2311yescharacteristic
73C8×D139—41no—
74C4⋊Dic139—21no—
75C4⋊Dic139—21no—
76C4⋊Dic139—21no—
77C4⋊Dic139C2311yescharacteristic
78C4⋊Dic139C2311yescharacteristic
79C4⋊Dic139C2311yescharacteristic
80Dic139⋊C4—21no—
81Dic139⋊C4—21no—
82Dic139⋊C4—21no—
83Dic139⋊C4D411yescharacteristic
84C22⋊Dic139—21no—
85C22⋊Dic139—21no—
86C22⋊Dic139—21no—
87C22⋊Dic139—21no—
88C22⋊Dic139—21no—
89C22⋊Dic139D411yescharacteristic
90(C2×D139)⋊C4—21no—
91(C2×D139)⋊C4—21no—
92(C2×D139)⋊C4D411yescharacteristic
93C4×Dic139—21no—
94C4×Dic139—21no—
95C4×Dic139C2311yescharacteristic
96C24×C139—21no—
97C2×Q8×C139C2311yescharacteristic
98C2×D4×C139—22no—
99C2×D4×C139—21no—
100C2×D4×C139—41no—
101C2×D4×C139C2311yescharacteristic
102C2×D4×C139C2311yescharacteristic
103C22×C4×C139C2311yescharacteristic
104SD16×C139—22no—
105SD16×C139—41no—
106C2×C8×C139C2311yescharacteristic
107C2×C8×C139C2311yescharacteristic
108C4⋊C4×C139—21no—
109C4⋊C4×C139C2311yescharacteristic
110C22⋊C4×C139—21no—
111C22×D139C2×D411yescharacteristic
112Dic278—21no—
113Dic278—21no—
114C22⋊D139—22no—
115C22⋊D139—42no—
116C22⋊D139—81no—
117C2×Dic139—21no—
118C2×Dic139—21no—
119C2×Dic139—21no—
120C2×Dic139—21no—
121C2×Dic139—42no—
122C2×Dic139—42no—
123C2×Dic139—81no—
124C2×Dic139C2×D411yescharacteristic
125C2×Dic139C2×D411yescharacteristic
126C2×Dic139C2×D411yescharacteristic
127C4×D139—21no—
128C4×D139—21no—
129C139⋊C8—21no—
130C139⋊C8—21no—
131C23×C139—21no—
132C23×C139—21no—
133C23×C139—42no—
134C23×C139—42no—
135C23×C139—81no—
136C23×C139C2×D411yescharacteristic
137Q8×C139—21no—
138Q8×C139—21no—
139D4×C139—21no—
140D4×C139—21no—
141D4×C139—21no—
142D4×C139—42no—
143D4×C139#4112yes—
144C2×C4×C139—21no—
145C2×C4×C139—21no—
146C2×C4×C139—21no—
147C2×C4×C139—21no—
148C2×C4×C139C2×D411yescharacteristic
149C2×C4×C139C2411yescharacteristic
150C8×C139—21no—
151C8×C139—21no—
152C22×C139—21no—
153C22×C139—21no—
154C22×C139—22no—
155C22×C139—41no—
156C22×C139—41no—
157C22×C139—41no—
158C22×C139—41no—
159C22×C139—41no—
160C22×C139—84no—
161C22×C139#13512yes—
162C22×C139C22×D411yescharacteristic
163C2×D139—21no—
164C2×D139—21no—
165C2×D139—21no—
166C4×C139—21no—
167C4×C139—41no—
168C4×C139—41no—
169C4×C139C2×#4111yescharacteristic
170C4×C139H(5,𝔽2)11yescharacteristic
171Dic139—21no—
172Dic139—21no—
173Dic139—21no—
174Dic139—41no—
175Dic139—41no—
176Dic139—41no—
177Dic139—41no—
178C2×C139—22no—
179C2×C139—42no—
180C2×C139—81no—
181C2×C139#54611yescharacteristic
182C2×C139C2×#13511yescharacteristic
183C2×C139#57711yescharacteristic
184D139—41no—
185C139#329611yescharacteristic, complemented, Sylow
186#3296—1391nomaximal, Sylow
187#552—1391no—
188#546—1391no—
189#488—1391no—
190#483—1391no—
191#482—1391no—
192#478—1391no—
193#467—1391no—
194#465—1391no—
195#464—1391no—
196#452—1391no—
197#450D13911yescharacteristic, complemented
198C4×SD16—1391no—
199C8×D4—1391no—
200#416—1391no—
201C2×#102—1391no—
202C2×#41—1391no—
203C22×D4C2×D13911yescharacteristic
204C2×Q16—1391no—
205C2×SD16C2×D13911yescharacteristic
206C2×SD16C2×D13911yescharacteristic
207C22×C8—1391no—
208C22×C8—1391no—
209#126—2781no—
210#125—2781no—
211#125—1391no—
212#124—1391no—
213#123—2781no—
214#123—2781no—
215C22⋊Q8—1391no—
216C22⋊Q8—1391no—
217C22⋊Q8C2×D13911yescharacteristic
218#121—2781no—
219#121—1391no—
220#120—2781no—
221C4×Q8—1391no—
222C4×D4—1391no—
223C4×D4—1391no—
224#117—2781no—
225#117—1391no—
226C2×C4⋊C4—1391no—
227C2×C22⋊C4—2781no—
228#107—1391no—
229#106—1391no—
230#106—1391no—
231C4⋊C8—1391no—
232#103—1391no—
233#103—1391no—
234#103—1391no—
235#103—1391no—
236#102—1391no—
237#102—1391no—
238#102—1391no—
239#102—1391no—
240#102C2×D13911yescharacteristic
241#102C2×D13911yescharacteristic
242C22⋊C8—1391no—
243C22⋊C8C2×D13911yescharacteristic
244C4×C8—1391no—
245C24—21no—
246#41—2782no—
247#41—5561no—
248C2×Q8—1391no—
249C2×Q8C22×D13911yescharacteristic
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—41no—
253C2×D4—2781no—
254C2×D4—2781no—
255C2×D4—1391no—
256C2×D4C22×D13911yescharacteristic
257C2×D4C22×D13911yescharacteristic
258C22×C4—2781no—
259C22×C4—2781no—
260C22×C4—2781no—
261C22×C4—1391no—
262C22×C4C22×D13911yescharacteristic
263Q16—5561no—
264SD16—22no—
265SD16—41no—
266C2×C8—5561no—
267C2×C8—5561no—
268C2×C8—1391no—
269C2×C8—1391no—
270C2×C8C22×D13911yescharacteristic
271C2×C8C22×D13911yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—2781no—
274C4⋊C4—2781no—
275C4⋊C4—2781no—
276C4⋊C4—2781no—
277C4⋊C4—2781no—
278C4⋊C4—2781no—
279C4⋊C4—1391no—
280C4⋊C4—1391no—
281C4⋊C4—1391no—
282C4⋊C4—1391no—
283C4⋊C4C22×D13911yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—2781no—
286C22⋊C4—2781no—
287C22⋊C4—2781no—
288C22⋊C4—2781no—
289C22⋊C4—2781no—
290C22⋊C4—2781no—
291C22⋊C4—2781no—
292C22⋊C4—1391no—
293C22⋊C4—1391no—
294C42—2781no—
295C42—2781no—
296C42—1391no—
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23—1391no—
303C23D4×D13911yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—2781no—
307Q8—2781no—
308D4—21no—
309D4—21no—
310D4—21no—
311D4—42no—
312D4—2782no—
313D4—5562no—
314D4—11121no—
315D4#1455578412yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—2781no—
321C2×C4—2781no—
322C2×C4—2781no—
323C2×C4—2781no—
324C2×C4—2781no—
325C2×C4—2781no—
326C2×C4—5562no—
327C2×C4—5562no—
328C2×C4—11121no—
329C2×C4—1391no—
330C2×C4—1391no—
331C2×C4—1391no—
332C2×C4D4×D13911yescharacteristic
333C2×C4C23×D13911yescharacteristic
334C8—21no—
335C8—21no—
336C8—2781no—
337C8—2781no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—84no—
347C22—2781no—
348C22—2781no—
349C22—2781no—
350C22#1798486312yes—
351C22C2×D4×D13911yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—2781no—
356C4—2781no—
357C4—2781no—
358C4—5561no—
359C4—5561no—
360C4—5561no—
361C4—5561no—
362C4C2×#1455578411yescharacteristic
363C4#1798488711yescharacteristic
364C2—22no—
365C2—42no—
366C2—81no—
367C2—5561no—
368C2#2258159011yescharacteristic
369C2C2×#1798486311yescharacteristic
370C2#2258176311yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#450×C139C2
socleC22×C139C22×D4
prime radical#22581597C2
hypercenter#450D139
hypocenterC139#3296
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #22581645C2semidirect
3. #22581306C2semidirect
4. #22581284C2semidirect
5. #22581276C2semidirect
6. #22581255C2semidirect
7. #22581192C2semidirect
8. #22581179C2semidirect
9. #22581173C2semidirect
10. #22581112C2semidirect
11. SD16×Dic139C2semidirect
12. (C22⋊D139)⋊C8C2semidirect
13. #22580946C2semidirect
14. C2×#17984763C2semidirect
15. #450×C139C2semidirect
17. C2×#14555775C22semidirect
19. C2×C8×D139C22semidirect
22. #17984833C22semidirect
27. #17984818C22semidirect
31. Q8×Dic139C22semidirect
34. #17984800C22semidirect
38. #17984775C22semidirect
39. #17984774C22semidirect
40. #17984774C22semidirect
41. Dic139⋊C8C22semidirect
42. #17984767C22semidirect
43. #17984767C22semidirect
44. #17984766C22semidirect
45. #17984765C22semidirect
50. (C2×D139)⋊C8C22semidirect
51. C8×Dic139C22semidirect
185. C139#3296semidirect
197. #450D139semidirect

Maximal subgroups

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

subgroupindex
#225816452
#225815972
#225813062
#225812842
#225812762
#225812552
#225811922
#225811792
#225811732
#225811122
SD16×Dic1392
(C22⋊D139)⋊C82
#225809462
C2×#179847632
#450×C1392
#3296139