Finite Group Databasebeta

← #31818255

Subgroups — #31818255

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#22581647C211yesmaximal, characteristic, complemented
2#22581591C211yesmaximal, characteristic, complemented
3#22581309C211yesmaximal, characteristic, complemented
4#22581287C211yesmaximal, characteristic, complemented
5#22581277C211yesmaximal, characteristic, complemented
6#22581251C211yesmaximal, characteristic, complemented
7#22581189C211yesmaximal, characteristic, complemented
8#22581185C211yesmaximal, characteristic, complemented
9#22581171C211yesmaximal, characteristic, complemented
10#22581098C211yesmaximal, characteristic, complemented
11#22581088C211yesmaximal, characteristic, complemented
12#22581033C211yesmaximal, characteristic, complemented
13C8×C22⋊D139C211yesmaximal, characteristic, complemented
14#102×D139C211yesmaximal, characteristic, complemented
15#416×C139C211yesmaximal, characteristic, complemented
16C2×D4×D139C2211yescharacteristic
17C2×#14555772C2211yescharacteristic, complemented
18C2×D1112C2211yescharacteristic
19C2×#14555770C2211yescharacteristic
20C2×C8×D139C2211yescharacteristic
21#17984836—21no—
22#17984833C2211yescharacteristic, complemented
23#17984831C2211yescharacteristic
24#17984825—21no—
25#17984824—21no—
26#17984818C2211yescharacteristic
27#17984817C2211yescharacteristic
28#17984816C2211yescharacteristic
29#17984816C2211yescharacteristic, complemented
30#17984815—21no—
31#17984814—21no—
32#17984810—21no—
33C4×D556—21no—
34D4×Dic139C2211yescharacteristic
35#17984804C2211yescharacteristic, complemented
36C4×C22⋊D139C2211yescharacteristic
37C4⋊C4×D139C2211yescharacteristic
38C2×(C2×D139)⋊C4—21no—
39#17984776C2211yescharacteristic, complemented
40#17984775C2211yescharacteristic, complemented
41#17984773C2211yescharacteristic, complemented
42Dic139⋊C8C2211yescharacteristic, complemented
43#17984766C2211yescharacteristic, complemented
44#17984764C2211yescharacteristic
45#17984764C2211yescharacteristic, complemented
46#17984763C2211yescharacteristic
47#17984762C2211yescharacteristic
48#17984762C2211yescharacteristic
49C22⋊(C139⋊C8)C2211yescharacteristic, complemented
50(C2×D139)⋊C8C2211yescharacteristic
51C8×Dic139C2211yescharacteristic, complemented
52C2×#41×C139C2211yescharacteristic
53C22×C8×C139C2211yescharacteristic, complemented
54#117×C139C2211yescharacteristic, complemented
55#103×C139C2211yescharacteristic, complemented
56#103×C139C2211yescharacteristic, complemented
57#102×C139C2211yescharacteristic
58#102×C139C2211yescharacteristic
59C23×D139—21no—
60C2×D556—21no—
61C2×D556C2311yescharacteristic
62C2×D556C2311yescharacteristic
63C2×C22⋊D139—21no—
64C2×C22⋊D139—21no—
65C2×C22⋊D139—21no—
66C2×C22⋊D139D411yescharacteristic
67D4×D139—22no—
68D4×D139—41no—
69C22×Dic139—21no—
70C2×C4×D139—21no—
71C2×C4×D139—21no—
72C2×C4×D139C2311yescharacteristic
73#14555772—41no—
74D1112—41no—
75#14555770—22no—
76C2×C139⋊C8C2311yescharacteristic
77C2×C139⋊C8C2311yescharacteristic
78C8×D139—41no—
79C4⋊Dic139—21no—
80C4⋊Dic139C2311yescharacteristic
81C4⋊Dic139C2311yescharacteristic
82Dic139⋊C4—21no—
83Dic139⋊C4—21no—
84Dic139⋊C4—21no—
85Dic139⋊C4D411yescharacteristic
86C22⋊Dic139—21no—
87C22⋊Dic139D411yescharacteristic
88(C2×D139)⋊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)⋊C4D411yescharacteristic
96C4×Dic139C2311yescharacteristic
97#41×C139—22no—
98#41×C139—41no—
99C2×Q8×C139C2311yescharacteristic
100C2×D4×C139—21no—
101C2×D4×C139C2311yescharacteristic
102C22×C4×C139—21no—
103C22×C4×C139C2311yescharacteristic
104C2×C8×C139—41no—
105C2×C8×C139C2311yescharacteristic
106C2×C8×C139C2311yescharacteristic
107C4⋊C4×C139C2311yescharacteristic
108C4⋊C4×C139C2311yescharacteristic
109C22⋊C4×C139—21no—
110C42×C139—21no—
111C22×D139—21no—
112C22×D139—21no—
113C22×D139—42no—
114C22×D139—42no—
115C22×D139—81no—
116C22×D139C2×D411yescharacteristic
117D556—21no—
118D556—21no—
119D556—21no—
120D556—21no—
121D556—42no—
122C22⋊D139—22no—
123C22⋊D139—42no—
124C22⋊D139—81no—
125C22⋊D139—81no—
126C2×Dic139—21no—
127C2×Dic139—21no—
128C2×Dic139—81no—
129C2×Dic139C2×D411yescharacteristic
130C2×Dic139C2×D411yescharacteristic
131C2×Dic139C2×D411yescharacteristic
132C4×D139—21no—
133C4×D139—21no—
134C4×D139—81no—
135C4×D139—81no—
136C139⋊C8—21no—
137C139⋊C8—21no—
138C23×C139—21no—
139C23×C139C2×D411yescharacteristic
140Q8×C139—21no—
141Q8×C139—21no—
142D4×C139—21no—
143D4×C139—42no—
144D4×C139#4112yes—
145C2×C4×C139—21no—
146C2×C4×C139—21no—
147C2×C4×C139—21no—
148C2×C4×C139—21no—
149C2×C4×C139—21no—
150C2×C4×C139—42no—
151C2×C4×C139C2×D411yescharacteristic
152C2×C4×C139C2411yescharacteristic
153C8×C139—21no—
154C8×C139—21no—
155C22×C139—21no—
156C22×C139—22no—
157C22×C139—21no—
158C22×C139—21no—
159C22×C139—41no—
160C22×C139—41no—
161C22×C139C22×D411yescharacteristic
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—41no—
174C4×C139—41no—
175C4×C139—41no—
176C4×C139C2×#4111yescharacteristic
177C4×C139H(5,𝔽2)11yescharacteristic
178Dic139—21no—
179Dic139—21no—
180Dic139—21no—
181Dic139—41no—
182Dic139—41no—
183C2×C139—42no—
184C2×C139—41no—
185C2×C139#54611yescharacteristic
186C2×C139C2×#13511yescharacteristic
187C2×C139#57611yescharacteristic
188D139—22no—
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#478—1391no—
199#466—1391no—
200#465—1391no—
201#463—1391no—
202#449—1391no—
203#447—1391no—
204C4×D8—1391no—
205C8×D4—1391no—
206#416D13911yescharacteristic, complemented
207C2×#102—1391no—
208C2×#41C2×D13911yescharacteristic
209C22×D4—1391no—
210C2×SD16—1391no—
211C2×D8—1391no—
212C2×D8—1391no—
213C22×C8—1391no—
214C22×C8C2×D13911yescharacteristic, complemented
215#126—2781no—
216#125—1391no—
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×D4—1391no—
231#117C2×D13911yescharacteristic, complemented
232C2×C4⋊C4—1391no—
233C2×C22⋊C4—2781no—
234#107—1391no—
235#107—1391no—
236#106—1391no—
237C4⋊C8—1391no—
238#103—1391no—
239#103C2×D13911yescharacteristic, complemented
240#103C2×D13911yescharacteristic, complemented
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—22no—
253#41—41no—
254C2×Q8C22×D13911yescharacteristic
255C2×D4—21no—
256C2×D4—2781no—
257C2×D4—2782no—
258C2×D4—2781no—
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×C4C22×D13911yescharacteristic
272SD16—5561no—
273D8—2782no—
274D8—5561no—
275C2×C8—41no—
276C2×C8—5561no—
277C2×C8—1391no—
278C2×C8—1391no—
279C2×C8C22×D13911yescharacteristic
280C2×C8C22×D13911yescharacteristic
281C4⋊C4—2781no—
282C4⋊C4—2781no—
283C4⋊C4—2781no—
284C4⋊C4—2781no—
285C4⋊C4—1391no—
286C4⋊C4—1391no—
287C4⋊C4—1391no—
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—21no—
302C42—1391no—
303C23—21no—
304C23—2781no—
305C23—2781no—
306C23—5562no—
307C23—5562no—
308C23—11121no—
309C23—1391no—
310C23D4×D13911yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—42no—
315D4—2782no—
316D4—2781no—
317D4—2781no—
318D4—2781no—
319D4—2781no—
320D4—5562no—
321D4—5562no—
322D4—11121no—
323D4—11121no—
324D4#1455578512yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—2781no—
332C2×C4—2781no—
333C2×C4—2781no—
334C2×C4—2781no—
335C2×C4—11121no—
336C2×C4—11121no—
337C2×C4—11121no—
338C2×C4—1391no—
339C2×C4—1391no—
340C2×C4—1391no—
341C2×C4D4×D13911yescharacteristic
342C2×C4C23×D13911yescharacteristic
343C8—21no—
344C8—21no—
345C8—2781no—
346C8—2781no—
347C22—21no—
348C22—22no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
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—41no—
366C4—41no—
367C4—41no—
368C4—2781no—
369C4—2781no—
370C4—2781no—
371C4—5561no—
372C4—5561no—
373C4C2×#1455578511yescharacteristic
374C4#1798488711yescharacteristic
375C2—41no—
376C2—42no—
377C2—2782no—
378C2—11121no—
379C2—11121no—
380C2#2258159311yescharacteristic
381C2#135×D13911yescharacteristic
382C2#2258175511yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#416×C139C2
socleC22×C139C22×D4
hypercenter#416D139
hypocenterC139#3297
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #22581647C2semidirect
2. #22581591C2semidirect
3. #22581309C2semidirect
4. #22581287C2semidirect
5. #22581277C2semidirect
6. #22581251C2semidirect
7. #22581189C2semidirect
8. #22581185C2semidirect
9. #22581171C2semidirect
10. #22581098C2semidirect
11. #22581088C2semidirect
12. #22581033C2semidirect
13. C8×C22⋊D139C2semidirect
14. #102×D139C2semidirect
15. #416×C139C2semidirect
17. C2×#14555772C22semidirect
22. #17984833C22semidirect
29. #17984816C22semidirect
35. #17984804C22semidirect
39. #17984776C22semidirect
40. #17984775C22semidirect
41. #17984773C22semidirect
42. Dic139⋊C8C22semidirect
43. #17984766C22semidirect
45. #17984764C22semidirect
49. C22⋊(C139⋊C8)C22semidirect
51. C8×Dic139C22semidirect
53. C22×C8×C139C22semidirect
54. #117×C139C22semidirect
55. #103×C139C22semidirect
56. #103×C139C22semidirect
191. C139#3297semidirect
206. #416D139semidirect
214. C22×C8C2×D139semidirect
231. #117C2×D139semidirect
239. #103C2×D139semidirect
240. #103C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225816472
#225815912
#225813092
#225812872
#225812772
#225812512
#225811892
#225811852
#225811712
#225810982
#225810882
#225810332
C8×C22⋊D1392
#102×D1392
#416×C1392
#3297139