Finite Group Databasebeta

← #31818244

Subgroups — #31818244

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#22581644C211yesmaximal, characteristic, complemented
2#22581598C211yesmaximal, characteristic
3#22581308C211yesmaximal, characteristic, complemented
4#22581285C211yesmaximal, characteristic, complemented
5#22581279C211yesmaximal, characteristic, complemented
6#22581253C211yesmaximal, characteristic, complemented
7#22581193C211yesmaximal, characteristic, complemented
8#22581185C211yesmaximal, characteristic, complemented
9#22581175C211yesmaximal, characteristic, complemented
10#22581112C211yesmaximal, characteristic, complemented
11#22581102C211yesmaximal, characteristic, complemented
12C8×D556C211yesmaximal, characteristic, complemented
13#22580946C211yesmaximal, characteristic, complemented
14#102×D139C211yesmaximal, characteristic, complemented
15C4×SD16×C139C211yesmaximal, characteristic, complemented
16C2×#14555784C2211yescharacteristic
17C2×D4×D139C2211yescharacteristic
18C2×#14555775C2211yescharacteristic, complemented
19C2×#14555772C2211yescharacteristic
20C2×C8×D139C2211yescharacteristic
21C2×C8×D139C2211yescharacteristic, complemented
22#17984836—21no—
23#17984834C2211yescharacteristic, complemented
24#17984832—21no—
25#17984830C2211yescharacteristic
26#17984827—21no—
27#17984826—21no—
28#17984822C2211yescharacteristic
29#17984818C2211yescharacteristic
30#17984818C2211yescharacteristic, complemented
31#17984817C2211yescharacteristic
32#17984816—21no—
33#17984812—21no—
34C4×D556C2211yescharacteristic
35#17984800C2211yescharacteristic, complemented
36#17984799—21no—
37C4⋊C4×D139C2211yescharacteristic
38C2×(C2×D139)⋊C4—21no—
39#17984775C2211yescharacteristic, complemented
40#17984773C2211yescharacteristic, complemented
41C4⋊(C139⋊C8)C2211yescharacteristic, complemented
42#17984767C2211yescharacteristic, complemented
43#17984767C2211yescharacteristic, complemented
44#17984765C2211yescharacteristic, complemented
45#17984764C2211yescharacteristic
46#17984764C2211yescharacteristic
47#17984763C2211yescharacteristic
48#17984763C2211yescharacteristic
49#17984762C2211yescharacteristic
50(C2×D139)⋊C8C2211yescharacteristic
51(C2×D139)⋊C8C2211yescharacteristic, complemented
52C2×SD16×C139C2211yescharacteristic
53C4×Q8×C139C2211yescharacteristic, complemented
54C4×D4×C139C2211yescharacteristic
55#106×C139C2211yescharacteristic, complemented
56#103×C139C2211yescharacteristic, complemented
57#102×C139C2211yescharacteristic
58C4×C8×C139C2211yescharacteristic, complemented
59C23×D139—21no—
60#14555784—22no—
61#14555784—41no—
62C2×Dic278C2311yescharacteristic
63C2×D556—21no—
64C2×D556D411yescharacteristic
65C2×D556C2311yescharacteristic
66C2×C22⋊D139—21no—
67C2×C22⋊D139—21no—
68D4×D139—22no—
69D4×D139—41no—
70C22×Dic139—21no—
71C2×C4×D139—21no—
72C2×C4×D139C2311yescharacteristic
73C2×C4×D139C2311yescharacteristic
74#14555775—41no—
75#14555772—41no—
76C2×C139⋊C8C2311yescharacteristic
77C2×C139⋊C8C2311yescharacteristic
78C8×D139—41no—
79C8×D139—41no—
80C4⋊Dic139—21no—
81C4⋊Dic139D411yescharacteristic
82C4⋊Dic139C2311yescharacteristic
83C4⋊Dic139C2311yescharacteristic
84Dic139⋊C4—21no—
85Dic139⋊C4—21no—
86Dic139⋊C4—21no—
87Dic139⋊C4—21no—
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)⋊C4D411yescharacteristic
97(C2×D139)⋊C4D411yescharacteristic
98C4×Dic139—21no—
99C2×Q8×C139C2311yescharacteristic
100C2×D4×C139C2311yescharacteristic
101C22×C4×C139—21no—
102SD16×C139—22no—
103C2×C8×C139C2311yescharacteristic
104C2×C8×C139C2311yescharacteristic
105C4⋊C4×C139—21no—
106C4⋊C4×C139C2311yescharacteristic
107C4⋊C4×C139C2311yescharacteristic
108C22⋊C4×C139—21no—
109C42×C139—21no—
110C42×C139C2311yescharacteristic
111C22×D139—21no—
112C22×D139—42no—
113C22×D139—42no—
114C22×D139—81no—
115C22×D139C2×D411yescharacteristic
116C22×D139C2×D411yescharacteristic
117Dic278—21no—
118Dic278—21no—
119D556—22no—
120D556—21no—
121D556—21no—
122D556—81no—
123C22⋊D139—42no—
124C22⋊D139—42no—
125C2×Dic139—21no—
126C2×Dic139—21no—
127C2×Dic139—21no—
128C2×Dic139—42no—
129C2×Dic139C2×D411yescharacteristic
130C2×Dic139C2×D411yescharacteristic
131C4×D139—21no—
132C4×D139—21no—
133C4×D139—21no—
134C4×D139—21no—
135C4×D139—42no—
136C139⋊C8—21no—
137C139⋊C8—21no—
138C23×C139—21no—
139Q8×C139—21no—
140Q8×C139—21no—
141D4×C139—21no—
142D4×C139#4112yes—
143C2×C4×C139—21no—
144C2×C4×C139—21no—
145C2×C4×C139—21no—
146C2×C4×C139—81no—
147C2×C4×C139C2×D411yescharacteristic
148C2×C4×C139C2×D411yescharacteristic
149C2×C4×C139C2411yescharacteristic
150C8×C139—21no—
151C8×C139—21no—
152C22×C139—22no—
153C22×C139—41no—
154C22×C139—41no—
155C22×C139C22×D411yescharacteristic
156C2×D139—21no—
157C2×D139—21no—
158C2×D139—21no—
159C2×D139—21no—
160C2×D139—21no—
161C2×D139—41no—
162C2×D139—41no—
163C2×D139—41no—
164C2×D139—84no—
165C2×D139#13512yes—
166C4×C139—21no—
167C4×C139—21no—
168C4×C139—41no—
169C4×C139—41no—
170C4×C139—41no—
171C4×C139C2×#4111yescharacteristic
172C4×C139H(5,𝔽2)11yescharacteristic
173Dic139—21no—
174Dic139—21no—
175Dic139—41no—
176Dic139—41no—
177Dic139—41no—
178C2×C139—42no—
179C2×C139#54611yescharacteristic
180C2×C139C2×#13511yescharacteristic
181C2×C139#57711yescharacteristic
182D139—22no—
183D139—41no—
184D139—81no—
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#450—1391no—
198C4×SD16D13911yescharacteristic, complemented
199C8×D4—1391no—
200#416—1391no—
201C2×#102—1391no—
202C2×#41—1391no—
203C22×D4—1391no—
204C2×Q16—1391no—
205C2×SD16—1391no—
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⋊Q8—1391no—
218#121—2781no—
219#121—1391no—
220#120—2781no—
221C4×Q8C2×D13911yescharacteristic, complemented
222C4×D4—1391no—
223C4×D4C2×D13911yescharacteristic
224#117—2781no—
225#117—1391no—
226C2×C4⋊C4—1391no—
227C2×C22⋊C4—2781no—
228#107—1391no—
229#106—1391no—
230#106C2×D13911yescharacteristic, complemented
231C4⋊C8—1391no—
232#103—1391no—
233#103—1391no—
234#103—1391no—
235#103C2×D13911yescharacteristic, complemented
236#102—1391no—
237#102—1391no—
238#102—1391no—
239#102—1391no—
240#102—1391no—
241#102C2×D13911yescharacteristic
242C22⋊C8—1391no—
243C22⋊C8—1391no—
244C4×C8C2×D13911yescharacteristic, complemented
245C24—2781no—
246#41—2782no—
247#41—5561no—
248C2×Q8—1391no—
249C2×Q8C22×D13911yescharacteristic
250C2×D4—2781no—
251C2×D4—2782no—
252C2×D4—2781no—
253C2×D4—2781no—
254C2×D4—5561no—
255C2×D4—1391no—
256C2×D4—1391no—
257C2×D4C22×D13911yescharacteristic
258C22×C4—21no—
259C22×C4—2781no—
260C22×C4—2781no—
261C22×C4—1391no—
262C22×C4—1391no—
263Q16—5561no—
264SD16—22no—
265SD16—5561no—
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⋊C4C22×D13911yescharacteristic
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—21no—
295C42—2781no—
296C42C22×D13911yescharacteristic
297C23—21no—
298C23—2781no—
299C23—5562no—
300C23—5562no—
301C23—11121no—
302C23—1391no—
303C23—1391no—
304Q8—21no—
305Q8—21no—
306Q8—2781no—
307Q8—2781no—
308D4—21no—
309D4—2782no—
310D4—2781no—
311D4—2781no—
312D4—5562no—
313D4—5562no—
314D4—11121no—
315D4#1455578512yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—2781no—
321C2×C4—2781no—
322C2×C4—2781no—
323C2×C4—2781no—
324C2×C4—2781no—
325C2×C4—2781no—
326C2×C4—2781no—
327C2×C4—5562no—
328C2×C4—5562no—
329C2×C4—1391no—
330C2×C4—1391no—
331C2×C4D4×D13911yescharacteristic
332C2×C4D4×D13911yescharacteristic
333C2×C4C23×D13911yescharacteristic
334C8—21no—
335C8—21no—
336C8—2781no—
337C8—2781no—
338C22—22no—
339C22—41no—
340C22—41no—
341C22—2781no—
342C22—2781no—
343C22—2781no—
344C22—2781no—
345C22—2781no—
346C22—5561no—
347C22—5561no—
348C22—5561no—
349C22—11124no—
350C22—1392no—
351C22C2×D4×D13911yescharacteristic
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—2781no—
358C4—2781no—
359C4—5561no—
360C4—5561no—
361C4—5561no—
362C4C2×#1455578511yescharacteristic
363C4#1798488811yescharacteristic
364C2—42no—
365C2—2782no—
366C2—5561no—
367C2—11121no—
368C2#2258159911yescharacteristic
369C2#135×D13911yescharacteristic
370C2#2258175911yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
FittingC4×SD16×C139C2
socleC22×C139C22×D4
prime radical#22581598C2
hypercenterC4×SD16D139
hypocenterC139#3296
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #22581644C2semidirect
3. #22581308C2semidirect
4. #22581285C2semidirect
5. #22581279C2semidirect
6. #22581253C2semidirect
7. #22581193C2semidirect
8. #22581185C2semidirect
9. #22581175C2semidirect
10. #22581112C2semidirect
11. #22581102C2semidirect
12. C8×D556C2semidirect
13. #22580946C2semidirect
14. #102×D139C2semidirect
15. C4×SD16×C139C2semidirect
18. C2×#14555775C22semidirect
21. C2×C8×D139C22semidirect
23. #17984834C22semidirect
30. #17984818C22semidirect
35. #17984800C22semidirect
39. #17984775C22semidirect
40. #17984773C22semidirect
41. C4⋊(C139⋊C8)C22semidirect
42. #17984767C22semidirect
43. #17984767C22semidirect
44. #17984765C22semidirect
51. (C2×D139)⋊C8C22semidirect
53. C4×Q8×C139C22semidirect
55. #106×C139C22semidirect
56. #103×C139C22semidirect
58. C4×C8×C139C22semidirect
185. C139#3296semidirect
198. C4×SD16D139semidirect
221. C4×Q8C2×D139semidirect
230. #106C2×D139semidirect
235. #103C2×D139semidirect
244. C4×C8C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225816442
#225815982
#225813082
#225812852
#225812792
#225812532
#225811932
#225811852
#225811752
#225811122
#225811022
C8×D5562
#225809462
#102×D1392
C4×SD16×C1392
#3296139