Finite Group Databasebeta

← #31816649

Subgroups — #31816649

Order 17792.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581559C211yesmaximal, characteristic, complemented
2#22581425C211yesmaximal, characteristic, complemented
3#22581280C211yesmaximal, characteristic, complemented
4#22581279C211yesmaximal, characteristic, complemented
5#22581250C211yesmaximal, characteristic, complemented
6#22581149C211yesmaximal, characteristic, complemented
7#22581148C211yesmaximal, characteristic, complemented
8#22581088C211yesmaximal, characteristic, complemented
9#22581088C211yesmaximal, characteristic, complemented
10#22581064C211yesmaximal, characteristic, complemented
11#22581062C211yesmaximal, characteristic, complemented
12#22581035C211yesmaximal, characteristic, complemented
13#22581033C211yesmaximal, characteristic, complemented
14#22581013C211yesmaximal, characteristic, complemented
15#478×C139C211yesmaximal, characteristic, complemented
16C2×D4×D139C2211yescharacteristic
17C2×D1112C2211yescharacteristic
18C2×D1112C2211yescharacteristic
19C2×#14555770C2211yescharacteristic
20C2×#14555770C2211yescharacteristic
21#17984839C2211yescharacteristic, complemented
22#17984827—21no—
23#17984827—21no—
24#17984817—21no—
25#17984817—21no—
26#17984817C2211yescharacteristic
27#17984817C2211yescharacteristic
28C4×D556C2211yescharacteristic
29D4×Dic139C2211yescharacteristic
30#17984804C2211yescharacteristic
31#17984804C2211yescharacteristic, complemented
32#17984804C2211yescharacteristic, complemented
33C4×C22⋊D139—21no—
34(C22⋊D139)⋊C4—21no—
35#17984800C2211yescharacteristic
36#17984799C2211yescharacteristic
37C2×(C2×D139)⋊C4—21no—
38C22⋊C4×D139—21no—
39#17984775C2211yescharacteristic, complemented
40#17984773C2211yescharacteristic, complemented
41C4⋊(C139⋊C8)C2211yescharacteristic, complemented
42#17984764C2211yescharacteristic, complemented
43#17984764C2211yescharacteristic, complemented
44#17984762C2211yescharacteristic
45#17984762C2211yescharacteristic
46#17984762C2211yescharacteristic, complemented
47#17984762C2211yescharacteristic, complemented
48(C2×D139)⋊C8C2211yescharacteristic
49(C2×D139)⋊C8C2211yescharacteristic
50#17984752C2211yescharacteristic, complemented
51C8×Dic139C2211yescharacteristic, 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—
60C2×D556—21no—
61C2×D556—21no—
62C2×D556—21no—
63C2×D556—21no—
64C2×D556C2311yescharacteristic
65C2×D556C2311yescharacteristic
66C2×D556C2311yescharacteristic
67C2×C22⋊D139—21no—
68D4×D139—22no—
69D4×D139—22no—
70C22×Dic139—21no—
71C2×C4×D139—21no—
72C2×C4×D139—21no—
73C2×C4×D139—21no—
74C2×C4×D139—21no—
75C2×C4×D139C2311yescharacteristic
76D1112—22no—
77D1112—22no—
78#14555770—22no—
79#14555770—22no—
80C2×C139⋊C8C2311yescharacteristic
81C2×C139⋊C8C2311yescharacteristic
82C4⋊Dic139C2311yescharacteristic
83Dic139⋊C4D411yescharacteristic
84Dic139⋊C4D411yescharacteristic
85C22⋊Dic139—21no—
86(C2×D139)⋊C4—21no—
87(C2×D139)⋊C4—21no—
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)⋊C4D411yescharacteristic
94(C2×D139)⋊C4D411yescharacteristic
95C4×Dic139—21no—
96C4×Dic139C2311yescharacteristic
97C2×D4×C139C2311yescharacteristic
98C22×C4×C139—21no—
99C2×C8×C139C2311yescharacteristic
100C2×C8×C139C2311yescharacteristic
101C4⋊C4×C139—21no—
102C4⋊C4×C139—21no—
103C4⋊C4×C139C2311yescharacteristic
104C4⋊C4×C139C2311yescharacteristic
105C4⋊C4×C139C2311yescharacteristic
106C22⋊C4×C139—21no—
107C42×C139C2311yescharacteristic
108C22×D139—21no—
109C22×D139—24no—
110C22×D139—21no—
111C22×D139—21no—
112C22×D139—81no—
113C22×D139—81no—
114C22×D139C2×D411yescharacteristic
115D556—21no—
116D556—21no—
117D556—21no—
118D556—21no—
119D556—21no—
120D556—81no—
121D556—81no—
122D556—81no—
123D556—81no—
124D556#4112yes—
125C22⋊D139—24no—
126C2×Dic139—21no—
127C2×Dic139—81no—
128C2×Dic139C2×D411yescharacteristic
129C2×Dic139C2×D411yescharacteristic
130C2×Dic139C2×D411yescharacteristic
131C4×D139—21no—
132C4×D139—21no—
133C4×D139—81no—
134C4×D139—81no—
135C4×D139—81no—
136C4×D139—81no—
137C139⋊C8—21no—
138C139⋊C8—21no—
139C23×C139—21no—
140D4×C139—21no—
141D4×C139#4112yes—
142C2×C4×C139—21no—
143C2×C4×C139—21no—
144C2×C4×C139—21no—
145C2×C4×C139—81no—
146C2×C4×C139C2×D411yescharacteristic
147C2×C4×C139C2×D411yescharacteristic
148C2×C4×C139C2411yescharacteristic
149C8×C139—21no—
150C8×C139—21no—
151C22×C139—22no—
152C22×C139—41no—
153C22×C139—41no—
154C22×C139C22×D411yescharacteristic
155C2×D139—21no—
156C2×D139—22no—
157C2×D139—21no—
158C2×D139—21no—
159C2×D139—41no—
160C2×D139—41no—
161C2×D139—41no—
162C2×D139—41no—
163C2×D139—41no—
164C2×D139—41no—
165C2×D139—41no—
166C2×D139—41no—
167C2×D139—84no—
168C4×C139—21no—
169C4×C139—21no—
170C4×C139—41no—
171C4×C139—41no—
172C4×C139—41no—
173C4×C139C2×#4111yescharacteristic
174C4×C139C2×#4111yescharacteristic
175Dic139—21no—
176Dic139—21no—
177Dic139—21no—
178Dic139—41no—
179C2×C139—42no—
180C2×C139#52511yescharacteristic
181C2×C139#57611yescharacteristic
182C2×C139#57611yescharacteristic
183D139—41no—
184D139—42no—
185D139—81no—
186D139—81no—
187C139#312211yescharacteristic, complemented, Sylow
188#3122—1391nomaximal, Sylow
189#540—1391no—
190#518—1391no—
191#482—1391no—
192#482—1391no—
193#478—1391no—
194#478D13911yescharacteristic, complemented
195#459—1391no—
196#459—1391no—
197#447—1391no—
198#447—1391no—
199#442—1391no—
200#442—1391no—
201C4×D8—1391no—
202C4×D8—1391no—
203#433—1391no—
204C22×D4—1391no—
205C2×D8—1391no—
206C2×D8—1391no—
207C2×D8—1391no—
208C2×D8—1391no—
209#127—1391no—
210#125C2×D13911yescharacteristic, complemented
211#123—2781no—
212#123—2781no—
213#121—2781no—
214#121—2781no—
215#121—1391no—
216#121—1391no—
217C4×D4—2781no—
218C4×D4—2781no—
219C4×D4—1391no—
220C4×D4—1391no—
221C4×D4—1391no—
222C4×D4—1391no—
223C4×D4—1391no—
224C4×D4C2×D13911yescharacteristic
225#117—1391no—
226#117—1391no—
227C2×C22⋊C4—2781no—
228C2×C22⋊C4—2781no—
229#107—1391no—
230#107C2×D13911yescharacteristic, complemented
231#106—1391no—
232#106C2×D13911yescharacteristic, complemented
233C4⋊C8—1391no—
234C4⋊C8C2×D13911yescharacteristic, complemented
235#102—1391no—
236#102—1391no—
237#102—1391no—
238#102—1391no—
239#102—1391no—
240#102—1391no—
241#102C2×D13911yescharacteristic
242#102C2×D13911yescharacteristic
243C22⋊C8—1391no—
244C22⋊C8—1391no—
245#97—1391no—
246C4×C8—1391no—
247C24—2781no—
248C2×D4—2781no—
249C2×D4—2781no—
250C2×D4—2782no—
251C2×D4—2782no—
252C2×D4—2781no—
253C2×D4—2781no—
254C2×D4—2781no—
255C2×D4—1391no—
256C2×D4—1391no—
257C2×D4—1391no—
258C2×D4C22×D13911yescharacteristic
259C22×C4—21no—
260C22×C4—2781no—
261C22×C4—2781no—
262C22×C4—2781no—
263C22×C4—2781no—
264C22×C4—2781no—
265C22×C4—1391no—
266D8—2782no—
267D8—2782no—
268D8—2782no—
269D8—2782no—
270C2×C8—1391no—
271C2×C8—1391no—
272C2×C8C22×D13911yescharacteristic
273C2×C8C22×D13911yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—1391no—
277C4⋊C4—1391no—
278C4⋊C4—1391no—
279C4⋊C4C22×D13911yescharacteristic
280C4⋊C4C22×D13911yescharacteristic
281C4⋊C4C22×D13911yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—2781no—
284C22⋊C4—2781no—
285C22⋊C4—2781no—
286C22⋊C4—2781no—
287C22⋊C4—2781no—
288C22⋊C4—2781no—
289C22⋊C4—2781no—
290C22⋊C4—2781no—
291C22⋊C4—1391no—
292C22⋊C4—1391no—
293C42—2781no—
294C42—1391no—
295C42C22×D13911yescharacteristic
296C23—21no—
297C23—2784no—
298C23—2781no—
299C23—2781no—
300C23—2781no—
301C23—11121no—
302C23—11121no—
303C23—1391no—
304D4—21no—
305D4—2784no—
306D4—2781no—
307D4—2781no—
308D4—2781no—
309D4—2781no—
310D4—2781no—
311D4—11121no—
312D4—11121no—
313D4—11121no—
314D4—11121no—
315D4—1392no—
316D4#1455578612yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—81no—
321C2×C4—2781no—
322C2×C4—2781no—
323C2×C4—2781no—
324C2×C4—11121no—
325C2×C4—11121no—
326C2×C4—11121no—
327C2×C4—11121no—
328C2×C4—11121no—
329C2×C4—1391no—
330C2×C4—1391no—
331C2×C4—1391no—
332C2×C4D4×D13911yescharacteristic
333C2×C4D4×D13911yescharacteristic
334C2×C4C23×D13911yescharacteristic
335C8—21no—
336C8—21no—
337C8—2781no—
338C8—2781no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—2781no—
343C22—2782no—
344C22—2781no—
345C22—2781no—
346C22—5561no—
347C22—5561no—
348C22—5561no—
349C22—5561no—
350C22—5561no—
351C22—5561no—
352C22—5561no—
353C22—5561no—
354C22—11124no—
355C22C2×D4×D13911yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—2781no—
362C4—2781no—
363C4—2781no—
364C4—5561no—
365C4#41×D13911yescharacteristic
366C4C2×#1455578611yescharacteristic
367C2—42no—
368C2—5561no—
369C2—5562no—
370C2—11121no—
371C2—11121no—
372C2#2258146611yescharacteristic
373C2#2258175511yescharacteristic
374C2#2258175711yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#478×C139C2
socleC22×C139C22×D4
hypercenter#478D139
hypocenterC139#3122
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. #22581559C2semidirect
2. #22581425C2semidirect
3. #22581280C2semidirect
4. #22581279C2semidirect
5. #22581250C2semidirect
6. #22581149C2semidirect
7. #22581148C2semidirect
8. #22581088C2semidirect
9. #22581088C2semidirect
10. #22581064C2semidirect
11. #22581062C2semidirect
12. #22581035C2semidirect
13. #22581033C2semidirect
14. #22581013C2semidirect
15. #478×C139C2semidirect
21. #17984839C22semidirect
31. #17984804C22semidirect
32. #17984804C22semidirect
39. #17984775C22semidirect
40. #17984773C22semidirect
41. C4⋊(C139⋊C8)C22semidirect
42. #17984764C22semidirect
43. #17984764C22semidirect
46. #17984762C22semidirect
47. #17984762C22semidirect
50. #17984752C22semidirect
51. C8×Dic139C22semidirect
52. #125×C139C22semidirect
54. #107×C139C22semidirect
55. #106×C139C22semidirect
56. C4⋊C8×C139C22semidirect
187. C139#3122semidirect
194. #478D139semidirect
210. #125C2×D139semidirect
230. #107C2×D139semidirect
232. #106C2×D139semidirect
234. C4⋊C8C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225815592
#225814252
#225812802
#225812792
#225812502
#225811492
#225811482
#225810882
#225810642
#225810622
#225810352
#225810332
#225810132
#478×C1392
#3122139