Finite Group Databasebeta

← #31818251

Subgroups — #31818251

Order 17792.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581656C211yesmaximal, characteristic, complemented
2#22581598C211yesmaximal, characteristic, complemented
3#22581310C211yesmaximal, characteristic, complemented
4#22581290C211yesmaximal, characteristic, complemented
5#22581279C211yesmaximal, characteristic, complemented
6#22581190C211yesmaximal, characteristic, complemented
7#22581183C211yesmaximal, characteristic, complemented
8#22581169C211yesmaximal, characteristic, complemented
9#22581099C211yesmaximal, characteristic, complemented
10#22581088C211yesmaximal, characteristic, complemented
11C4×#14555770C211yesmaximal, characteristic, complemented
12#22581018C211yesmaximal, characteristic, complemented
13#22580946C211yesmaximal, characteristic, complemented
14#102×D139C211yesmaximal, characteristic, complemented
15#478×C139C211yesmaximal, characteristic, complemented
16C2×#14555784C2211yescharacteristic
17C2×D4×D139C2211yescharacteristic
18C2×#14555774C2211yescharacteristic, complemented
19C2×D1112C2211yescharacteristic
20C2×#14555770C2211yescharacteristic
21C2×C8×D139C2211yescharacteristic
22C2×C8×D139C2211yescharacteristic, complemented
23#17984837—21no—
24#17984830C2211yescharacteristic
25#17984827—21no—
26#17984826—21no—
27#17984822C2211yescharacteristic
28#17984817—21no—
29#17984817C2211yescharacteristic
30#17984817C2211yescharacteristic
31#17984817C2211yescharacteristic, complemented
32#17984816—21no—
33#17984812—21no—
34C4×D556C2211yescharacteristic
35C4×D556C2211yescharacteristic, complemented
36#17984804—21no—
37#17984800C2211yescharacteristic, complemented
38C4⋊C4×D139C2211yescharacteristic
39C2×(C2×D139)⋊C4—21no—
40#17984775C2211yescharacteristic, complemented
41#17984767C2211yescharacteristic, complemented
42#17984765C2211yescharacteristic, complemented
43#17984765C2211yescharacteristic, complemented
44#17984764C2211yescharacteristic
45#17984763C2211yescharacteristic
46#17984762C2211yescharacteristic
47#17984762C2211yescharacteristic
48#17984762C2211yescharacteristic, complemented
49(C2×D139)⋊C8C2211yescharacteristic
50(C2×D139)⋊C8C2211yescharacteristic, complemented
51C4×C139⋊C8C2211yescharacteristic, complemented
52#125×C139C2211yescharacteristic, complemented
53C4×D4×C139C2211yescharacteristic
54#107×C139C2211yescharacteristic, complemented
55#106×C139C2211yescharacteristic, complemented
56C4⋊C8×C139C2211yescharacteristic, complemented
57#102×C139C2211yescharacteristic
58#102×C139C2211yescharacteristic
59C23×D139—21no—
60#14555784—22no—
61#14555784—41no—
62C2×Dic278C2311yescharacteristic
63C2×D556—21no—
64C2×D556—21no—
65C2×D556—21no—
66C2×D556D411yescharacteristic
67C2×D556C2311yescharacteristic
68C2×D556C2311yescharacteristic
69C2×C22⋊D139—21no—
70C2×C22⋊D139—21no—
71D4×D139—22no—
72D4×D139—41no—
73C22×Dic139—21no—
74C2×C4×D139—21no—
75C2×C4×D139—21no—
76C2×C4×D139C2311yescharacteristic
77C2×C4×D139C2311yescharacteristic
78#14555774—41no—
79D1112—41no—
80#14555770—22no—
81C2×C139⋊C8C2311yescharacteristic
82C2×C139⋊C8C2311yescharacteristic
83C8×D139—41no—
84C8×D139—41no—
85C4⋊Dic139—21no—
86C4⋊Dic139D411yescharacteristic
87C4⋊Dic139C2311yescharacteristic
88Dic139⋊C4—21no—
89(C2×D139)⋊C4—21no—
90(C2×D139)⋊C4—21no—
91(C2×D139)⋊C4—21no—
92(C2×D139)⋊C4—21no—
93(C2×D139)⋊C4—21no—
94(C2×D139)⋊C4—21no—
95(C2×D139)⋊C4—21no—
96(C2×D139)⋊C4—21no—
97(C2×D139)⋊C4D411yescharacteristic
98(C2×D139)⋊C4D411yescharacteristic
99C4×Dic139—21no—
100C2×D4×C139C2311yescharacteristic
101C22×C4×C139—21no—
102C2×C8×C139C2311yescharacteristic
103C2×C8×C139C2311yescharacteristic
104C4⋊C4×C139—21no—
105C4⋊C4×C139—21no—
106C4⋊C4×C139C2311yescharacteristic
107C4⋊C4×C139C2311yescharacteristic
108C4⋊C4×C139C2311yescharacteristic
109C22⋊C4×C139—21no—
110C42×C139C2311yescharacteristic
111C22×D139—21no—
112C22×D139—21no—
113C22×D139—42no—
114C22×D139—42no—
115C22×D139—81no—
116C22×D139C2×D411yescharacteristic
117C22×D139C2×D411yescharacteristic
118Dic278—21no—
119Dic278—21no—
120D556—22no—
121D556—21no—
122D556—21no—
123D556—21no—
124D556—21no—
125D556—42no—
126D556—81no—
127D556—81no—
128C22⋊D139—42no—
129C22⋊D139—42no—
130C2×Dic139—21no—
131C2×Dic139—21no—
132C2×Dic139—42no—
133C2×Dic139C2×D411yescharacteristic
134C2×Dic139C2×D411yescharacteristic
135C4×D139—21no—
136C4×D139—21no—
137C4×D139—21no—
138C4×D139—21no—
139C4×D139—81no—
140C4×D139—81no—
141C139⋊C8—21no—
142C139⋊C8—21no—
143C23×C139—21no—
144D4×C139—21no—
145D4×C139#4112yes—
146C2×C4×C139—21no—
147C2×C4×C139—21no—
148C2×C4×C139—21no—
149C2×C4×C139—81no—
150C2×C4×C139C2×D411yescharacteristic
151C2×C4×C139C2×D411yescharacteristic
152C2×C4×C139C2411yescharacteristic
153C8×C139—21no—
154C8×C139—21no—
155C22×C139—22no—
156C22×C139—41no—
157C22×C139—41no—
158C22×C139C22×D411yescharacteristic
159C2×D139—21no—
160C2×D139—21no—
161C2×D139—21no—
162C2×D139—21no—
163C2×D139—21no—
164C2×D139—41no—
165C2×D139—41no—
166C2×D139—41no—
167C2×D139—41no—
168C2×D139—41no—
169C2×D139—41no—
170C2×D139—84no—
171C2×D139#13512yes—
172C4×C139—21no—
173C4×C139—21no—
174C4×C139—41no—
175C4×C139—41no—
176C4×C139—41no—
177C4×C139C2×#4111yescharacteristic
178C4×C139H(5,𝔽2)11yescharacteristic
179Dic139—21no—
180Dic139—21no—
181Dic139—41no—
182Dic139—41no—
183C2×C139—42no—
184C2×C139#54611yescharacteristic
185C2×C139C2×#13511yescharacteristic
186C2×C139#57611yescharacteristic
187D139—22no—
188D139—41no—
189D139—81no—
190D139—81no—
191C139#329711yescharacteristic, complemented, Sylow
192#3297—1391nomaximal, Sylow
193#553—1391no—
194#546—1391no—
195#488—1391no—
196#484—1391no—
197#482—1391no—
198#478D13911yescharacteristic, complemented
199#466—1391no—
200#465—1391no—
201#463—1391no—
202#449—1391no—
203#447—1391no—
204C4×D8—1391no—
205C8×D4—1391no—
206#416—1391no—
207C2×#102—1391no—
208C2×#41—1391no—
209C22×D4—1391no—
210C2×SD16—1391no—
211C2×D8—1391no—
212C2×D8—1391no—
213C22×C8—1391no—
214C22×C8—1391no—
215#126—2781no—
216#125C2×D13911yescharacteristic, complemented
217#124—1391no—
218#123—2781no—
219#123—2781no—
220C22⋊Q8—1391no—
221#121—2781no—
222#121—2781no—
223#121—1391no—
224#121—1391no—
225#121—1391no—
226#120—2781no—
227C4×D4—2781no—
228C4×D4—1391no—
229C4×D4—1391no—
230C4×D4C2×D13911yescharacteristic
231#117—1391no—
232C2×C4⋊C4—1391no—
233C2×C22⋊C4—2781no—
234#107—1391no—
235#107C2×D13911yescharacteristic, complemented
236#106C2×D13911yescharacteristic, complemented
237C4⋊C8C2×D13911yescharacteristic, complemented
238#103—1391no—
239#103—1391no—
240#103—1391no—
241#102—1391no—
242#102—1391no—
243#102—1391no—
244#102—1391no—
245#102—1391no—
246#102C2×D13911yescharacteristic
247#102C2×D13911yescharacteristic
248C22⋊C8—1391no—
249C22⋊C8—1391no—
250C4×C8—1391no—
251C24—2781no—
252#41—2782no—
253#41—5561no—
254C2×Q8—1391no—
255C2×D4—2781no—
256C2×D4—2781no—
257C2×D4—2781no—
258C2×D4—2782no—
259C2×D4—2781no—
260C2×D4—2781no—
261C2×D4—5561no—
262C2×D4—1391no—
263C2×D4—1391no—
264C2×D4—1391no—
265C2×D4C22×D13911yescharacteristic
266C22×C4—21no—
267C22×C4—2781no—
268C22×C4—2781no—
269C22×C4—2781no—
270C22×C4—1391no—
271C22×C4—1391no—
272SD16—5561no—
273D8—2782no—
274D8—5561no—
275C2×C8—5561no—
276C2×C8—5561no—
277C2×C8—1391no—
278C2×C8—1391no—
279C2×C8C22×D13911yescharacteristic
280C2×C8C22×D13911yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—2781no—
284C4⋊C4—2781no—
285C4⋊C4—1391no—
286C4⋊C4—1391no—
287C4⋊C4C22×D13911yescharacteristic
288C4⋊C4C22×D13911yescharacteristic
289C4⋊C4C22×D13911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—2781no—
292C22⋊C4—2781no—
293C22⋊C4—2781no—
294C22⋊C4—2781no—
295C22⋊C4—2781no—
296C22⋊C4—2781no—
297C22⋊C4—2781no—
298C22⋊C4—2781no—
299C22⋊C4—1391no—
300C22⋊C4—1391no—
301C42—2781no—
302C42C22×D13911yescharacteristic
303C23—21no—
304C23—2781no—
305C23—2781no—
306C23—5562no—
307C23—5562no—
308C23—11121no—
309C23—1391no—
310C23—1391no—
311Q8—2781no—
312Q8—2781no—
313D4—21no—
314D4—2782no—
315D4—2781no—
316D4—2781no—
317D4—2781no—
318D4—2781no—
319D4—5562no—
320D4—5562no—
321D4—5562no—
322D4—11121no—
323D4—11121no—
324D4#1455578612yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—81no—
329C2×C4—2781no—
330C2×C4—2781no—
331C2×C4—2781no—
332C2×C4—2781no—
333C2×C4—2781no—
334C2×C4—2781no—
335C2×C4—5562no—
336C2×C4—11121no—
337C2×C4—11121no—
338C2×C4—1391no—
339C2×C4—1391no—
340C2×C4D4×D13911yescharacteristic
341C2×C4D4×D13911yescharacteristic
342C2×C4C23×D13911yescharacteristic
343C8—21no—
344C8—21no—
345C8—2781no—
346C8—2781no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—2781no—
351C22—2781no—
352C22—2781no—
353C22—2781no—
354C22—2781no—
355C22—5561no—
356C22—5561no—
357C22—5561no—
358C22—5561no—
359C22—5561no—
360C22—5561no—
361C22—11124no—
362C22—1392no—
363C22C2×D4×D13911yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—2781no—
370C4—2781no—
371C4—5561no—
372C4—5561no—
373C4C2×#1455578611yescharacteristic
374C4#1798488811yescharacteristic
375C2—42no—
376C2—2782no—
377C2—5561no—
378C2—11121no—
379C2—11121no—
380C2#2258159411yescharacteristic
381C2#135×D13911yescharacteristic
382C2#2258175711yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#478×C139C2
socleC22×C139C22×D4
hypercenter#478D139
hypocenterC139#3297
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #22581656C2semidirect
2. #22581598C2semidirect
3. #22581310C2semidirect
4. #22581290C2semidirect
5. #22581279C2semidirect
6. #22581190C2semidirect
7. #22581183C2semidirect
8. #22581169C2semidirect
9. #22581099C2semidirect
10. #22581088C2semidirect
11. C4×#14555770C2semidirect
12. #22581018C2semidirect
13. #22580946C2semidirect
14. #102×D139C2semidirect
15. #478×C139C2semidirect
18. C2×#14555774C22semidirect
22. C2×C8×D139C22semidirect
31. #17984817C22semidirect
35. C4×D556C22semidirect
37. #17984800C22semidirect
40. #17984775C22semidirect
41. #17984767C22semidirect
42. #17984765C22semidirect
43. #17984765C22semidirect
48. #17984762C22semidirect
50. (C2×D139)⋊C8C22semidirect
51. C4×C139⋊C8C22semidirect
52. #125×C139C22semidirect
54. #107×C139C22semidirect
55. #106×C139C22semidirect
56. C4⋊C8×C139C22semidirect
191. C139#3297semidirect
198. #478D139semidirect
216. #125C2×D139semidirect
235. #107C2×D139semidirect
236. #106C2×D139semidirect
237. C4⋊C8C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225816562
#225815982
#225813102
#225812902
#225812792
#225811902
#225811832
#225811692
#225810992
#225810882
C4×#145557702
#225810182
#225809462
#102×D1392
#478×C1392
#3297139