Finite Group Databasebeta

← #31818258

Subgroups — #31818258

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#22581655C211yesmaximal, characteristic, complemented
2#22581597C211yesmaximal, characteristic, complemented
3#22581306C211yesmaximal, characteristic, complemented
4#22581289C211yesmaximal, characteristic, complemented
5#22581275C211yesmaximal, characteristic, complemented
6#22581251C211yesmaximal, characteristic, complemented
7#22581186C211yesmaximal, characteristic, complemented
8#22581180C211yesmaximal, characteristic, complemented
9#22581166C211yesmaximal, characteristic, complemented
10#22581095C211yesmaximal, characteristic, complemented
11D8×Dic139C211yesmaximal, characteristic, complemented
12(C22⋊D139)⋊C8C211yesmaximal, characteristic, complemented
13#22580946C211yesmaximal, characteristic, complemented
14C2×#17984763C211yesmaximal, characteristic, complemented
15#447×C139C211yesmaximal, characteristic, complemented
16C2×#14555784C2211yescharacteristic
17C2×#14555773C2211yescharacteristic, complemented
18C22×C139⋊C8C2211yescharacteristic
19C2×C8×D139C2211yescharacteristic, complemented
20#17984835—21no—
21#17984833C2211yescharacteristic, complemented
22#17984829C2211yescharacteristic
23#17984826—21no—
24#17984823—21no—
25#17984821C2211yescharacteristic
26#17984814—21no—
27#17984814—21no—
28#17984813C2211yescharacteristic
29#17984813C2211yescharacteristic, complemented
30#17984811—21no—
31D4×Dic139—21no—
32D4×Dic139C2211yescharacteristic
33D4×Dic139C2211yescharacteristic, complemented
34C4×C22⋊D139C2211yescharacteristic
35#17984800C2211yescharacteristic, complemented
36C2×C4⋊Dic139C2211yescharacteristic
37C2×C22⋊Dic139—21no—
38#17984776C2211yescharacteristic, complemented
39#17984776C2211yescharacteristic, complemented
40#17984773C2211yescharacteristic, complemented
41Dic139⋊C8C2211yescharacteristic, complemented
42#17984767C2211yescharacteristic, complemented
43#17984767C2211yescharacteristic, complemented
44#17984765C2211yescharacteristic, complemented
45#17984763C2211yescharacteristic
46#17984763C2211yescharacteristic
47#17984763C2211yescharacteristic
48#17984763C2211yescharacteristic
49#17984763C2211yescharacteristic, complemented
50(C2×D139)⋊C8C2211yescharacteristic, complemented
51C8×Dic139C2211yescharacteristic, complemented
52C22×D4×C139C2211yescharacteristic
53C2×D8×C139C2211yescharacteristic
54C2×D8×C139C2211yescharacteristic
55#121×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⋊D139—21no—
65C2×C22⋊D139D411yescharacteristic
66C22×Dic139—21no—
67C22×Dic139—21no—
68C22×Dic139—21no—
69C22×Dic139—21no—
70C2×C4×D139C2311yescharacteristic
71#14555773—41no—
72C2×C139⋊C8—41no—
73C2×C139⋊C8C2311yescharacteristic
74C2×C139⋊C8C2311yescharacteristic
75C8×D139—41no—
76C4⋊Dic139—21no—
77C4⋊Dic139—21no—
78C4⋊Dic139C2311yescharacteristic
79C4⋊Dic139C2311yescharacteristic
80C4⋊Dic139C2311yescharacteristic
81Dic139⋊C4—21no—
82Dic139⋊C4—21no—
83Dic139⋊C4D411yescharacteristic
84C22⋊Dic139—21no—
85C22⋊Dic139—21no—
86C22⋊Dic139—21no—
87C22⋊Dic139—21no—
88C22⋊Dic139—21no—
89C22⋊Dic139—21no—
90C22⋊Dic139—21no—
91C22⋊Dic139D411yescharacteristic
92(C2×D139)⋊C4—21no—
93(C2×D139)⋊C4D411yescharacteristic
94C4×Dic139—21no—
95C4×Dic139C2311yescharacteristic
96C24×C139—21no—
97C2×D4×C139—22no—
98C2×D4×C139—21no—
99C2×D4×C139—21no—
100C2×D4×C139—41no—
101C2×D4×C139C2311yescharacteristic
102C2×D4×C139C2311yescharacteristic
103C2×D4×C139C2311yescharacteristic
104C22×C4×C139C2311yescharacteristic
105D8×C139—22no—
106D8×C139—41no—
107C2×C8×C139C2311yescharacteristic
108C2×C8×C139C2311yescharacteristic
109C4⋊C4×C139C2311yescharacteristic
110C22⋊C4×C139—21no—
111C22×D139C2×D411yescharacteristic
112Dic278—21no—
113Dic278—21no—
114C22⋊D139—22no—
115C22⋊D139—42no—
116C22⋊D139—81no—
117C22⋊D139—81no—
118C2×Dic139—21no—
119C2×Dic139—21no—
120C2×Dic139—21no—
121C2×Dic139—21no—
122C2×Dic139—42no—
123C2×Dic139—81no—
124C2×Dic139—81no—
125C2×Dic139—81no—
126C2×Dic139C2×D411yescharacteristic
127C2×Dic139C2×D411yescharacteristic
128C2×Dic139C2×D411yescharacteristic
129C4×D139—21no—
130C4×D139—21no—
131C139⋊C8—21no—
132C139⋊C8—21no—
133C23×C139—21no—
134C23×C139—21no—
135C23×C139—21no—
136C23×C139—42no—
137C23×C139—42no—
138C23×C139—81no—
139C23×C139C2×D411yescharacteristic
140D4×C139—21no—
141D4×C139—21no—
142D4×C139—21no—
143D4×C139—21no—
144D4×C139—21no—
145D4×C139—42no—
146D4×C139—42no—
147D4×C139#4112yes—
148C2×C4×C139—21no—
149C2×C4×C139—21no—
150C2×C4×C139—21no—
151C2×C4×C139C2×D411yescharacteristic
152C2×C4×C139C2411yescharacteristic
153C8×C139—21no—
154C8×C139—21no—
155C22×C139—21no—
156C22×C139—21no—
157C22×C139—22no—
158C22×C139—41no—
159C22×C139—41no—
160C22×C139—41no—
161C22×C139—41no—
162C22×C139—41no—
163C22×C139—41no—
164C22×C139—41no—
165C22×C139—41no—
166C22×C139—84no—
167C22×C139#13512yes—
168C22×C139C22×D411yescharacteristic
169C2×D139—21no—
170C2×D139—21no—
171C2×D139—21no—
172C4×C139—21no—
173C4×C139—41no—
174C4×C139C2×#4111yescharacteristic
175C4×C139H(5,𝔽2)11yescharacteristic
176Dic139—21no—
177Dic139—21no—
178Dic139—21no—
179Dic139—41no—
180Dic139—41no—
181Dic139—41no—
182Dic139—41no—
183C2×C139—22no—
184C2×C139—42no—
185C2×C139—81no—
186C2×C139—81no—
187C2×C139#54611yescharacteristic
188C2×C139C2×#13511yescharacteristic
189C2×C139#57611yescharacteristic
190D139—41no—
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#447D13911yescharacteristic, complemented
204C4×D8—1391no—
205C8×D4—1391no—
206#416—1391no—
207C2×#102—1391no—
208C2×#41—1391no—
209C22×D4C2×D13911yescharacteristic
210C2×SD16—1391no—
211C2×D8C2×D13911yescharacteristic
212C2×D8C2×D13911yescharacteristic
213C22×C8—1391no—
214C22×C8—1391no—
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#121C2×D13911yescharacteristic
226#120—2781no—
227C4×D4—2781no—
228C4×D4—1391no—
229C4×D4—1391no—
230C4×D4—1391no—
231#117—1391no—
232C2×C4⋊C4—1391no—
233C2×C22⋊C4—2781no—
234#107—1391no—
235#107—1391no—
236#106—1391no—
237C4⋊C8—1391no—
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⋊C8C2×D13911yescharacteristic
250C4×C8—1391no—
251C24—21no—
252#41—2782no—
253#41—5561no—
254C2×Q8—1391no—
255C2×D4—22no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—41no—
259C2×D4—2781no—
260C2×D4—2781no—
261C2×D4—2781no—
262C2×D4—1391no—
263C2×D4C22×D13911yescharacteristic
264C2×D4C22×D13911yescharacteristic
265C2×D4C22×D13911yescharacteristic
266C22×C4—2781no—
267C22×C4—2781no—
268C22×C4—2781no—
269C22×C4—2781no—
270C22×C4—1391no—
271C22×C4C22×D13911yescharacteristic
272SD16—5561no—
273D8—22no—
274D8—41no—
275C2×C8—5561no—
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⋊C4—1391no—
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—
302C42—1391no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—42no—
307C23—42no—
308C23—81no—
309C23—1391no—
310C23D4×D13911yescharacteristic
311Q8—2781no—
312Q8—2781no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—21no—
318D4—42no—
319D4—42no—
320D4—2782no—
321D4—5562no—
322D4—11121no—
323D4—11121no—
324D4#1455578412yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—2781no—
329C2×C4—2781no—
330C2×C4—2781no—
331C2×C4—2781no—
332C2×C4—2781no—
333C2×C4—2781no—
334C2×C4—5562no—
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—21no—
349C22—22no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—84no—
359C22—2781no—
360C22—2781no—
361C22—2781no—
362C22#1798486112yes—
363C22C2×D4×D13911yescharacteristic
364C4—21no—
365C4—41no—
366C4—2781no—
367C4—2781no—
368C4—2781no—
369C4—5561no—
370C4—5561no—
371C4—5561no—
372C4—5561no—
373C4C2×#1455578411yescharacteristic
374C4#1798488711yescharacteristic
375C2—22no—
376C2—42no—
377C2—81no—
378C2—81no—
379C2—5561no—
380C2#2258159011yescharacteristic
381C2C2×#1798486111yescharacteristic
382C2#2258175711yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#447×C139C2
socleC22×C139C22×D4
hypercenter#447D139
hypocenterC139#3297
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #22581655C2semidirect
2. #22581597C2semidirect
3. #22581306C2semidirect
4. #22581289C2semidirect
5. #22581275C2semidirect
6. #22581251C2semidirect
7. #22581186C2semidirect
8. #22581180C2semidirect
9. #22581166C2semidirect
10. #22581095C2semidirect
11. D8×Dic139C2semidirect
12. (C22⋊D139)⋊C8C2semidirect
13. #22580946C2semidirect
14. C2×#17984763C2semidirect
15. #447×C139C2semidirect
17. C2×#14555773C22semidirect
19. C2×C8×D139C22semidirect
21. #17984833C22semidirect
29. #17984813C22semidirect
33. D4×Dic139C22semidirect
35. #17984800C22semidirect
38. #17984776C22semidirect
39. #17984776C22semidirect
40. #17984773C22semidirect
41. Dic139⋊C8C22semidirect
42. #17984767C22semidirect
43. #17984767C22semidirect
44. #17984765C22semidirect
49. #17984763C22semidirect
50. (C2×D139)⋊C8C22semidirect
51. C8×Dic139C22semidirect
191. C139#3297semidirect
203. #447D139semidirect

Maximal subgroups

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

subgroupindex
#225816552
#225815972
#225813062
#225812892
#225812752
#225812512
#225811862
#225811802
#225811662
#225810952
D8×Dic1392
(C22⋊D139)⋊C82
#225809462
C2×#179847632
#447×C1392
#3297139