Finite Group Databasebeta

← #31816645

Subgroups — #31816645

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#22581557C211yesmaximal, characteristic, complemented
2#22581425C211yesmaximal, characteristic, complemented
3#22581276C211yesmaximal, characteristic, complemented
4#22581275C211yesmaximal, characteristic, complemented
5#22581254C211yesmaximal, characteristic, complemented
6#22581253C211yesmaximal, characteristic, complemented
7#22581145C211yesmaximal, characteristic, complemented
8#22581085C211yesmaximal, characteristic, complemented
9#22581085C211yesmaximal, characteristic, complemented
10#22581065C211yesmaximal, characteristic, complemented
11#22581062C211yesmaximal, characteristic, complemented
12D8×Dic139C211yesmaximal, characteristic, complemented
13#22581033C211yesmaximal, characteristic, complemented
14#22581013C211yesmaximal, characteristic, complemented
15#459×C139C211yesmaximal, characteristic, complemented
16C2×D4×D139C2211yescharacteristic
17C2×#14555770C2211yescharacteristic
18C2×#14555770C2211yescharacteristic
19#17984834C2211yescharacteristic, complemented
20#17984823—21no—
21#17984823—21no—
22#17984814—21no—
23#17984814—21no—
24#17984813C2211yescharacteristic
25#17984813C2211yescharacteristic
26C4×D556C2211yescharacteristic
27D4×Dic139C2211yescharacteristic
28D4×Dic139C2211yescharacteristic, complemented
29D4×Dic139C2211yescharacteristic, complemented
30#17984804C2211yescharacteristic
31C4×C22⋊D139—21no—
32(C22⋊D139)⋊C4—21no—
33#17984800C2211yescharacteristic
34#17984799C2211yescharacteristic
35C2×(C2×D139)⋊C4—21no—
36C22⋊C4×D139—21no—
37#17984776C2211yescharacteristic, complemented
38#17984775C2211yescharacteristic, complemented
39#17984774C2211yescharacteristic, complemented
40#17984773C2211yescharacteristic, complemented
41C4⋊(C139⋊C8)C2211yescharacteristic, complemented
42#17984764C2211yescharacteristic
43#17984764C2211yescharacteristic
44#17984763C2211yescharacteristic
45#17984763C2211yescharacteristic
46#17984763C2211yescharacteristic, complemented
47#17984763C2211yescharacteristic, complemented
48(C2×D139)⋊C8C2211yescharacteristic
49(C2×D139)⋊C8C2211yescharacteristic
50#17984752C2211yescharacteristic, complemented
51C8×Dic139C2211yescharacteristic, complemented
52C2×D8×C139C2211yescharacteristic
53C2×D8×C139C2211yescharacteristic
54#127×C139C2211yescharacteristic, complemented
55C4×D4×C139C2211yescharacteristic
56C4⋊C8×C139C2211yescharacteristic, complemented
57#102×C139C2211yescharacteristic, complemented
58#102×C139C2211yescharacteristic, complemented
59C23×D139—21no—
60C2×D556C2311yescharacteristic
61C2×C22⋊D139—21no—
62C2×C22⋊D139—21no—
63C2×C22⋊D139—21no—
64D4×D139—22no—
65D4×D139—22no—
66C22×Dic139—21no—
67C22×Dic139—21no—
68C22×Dic139—21no—
69C2×C4×D139—21no—
70C2×C4×D139—21no—
71C2×C4×D139C2311yescharacteristic
72#14555770—22no—
73#14555770—22no—
74C2×C139⋊C8C2311yescharacteristic
75C2×C139⋊C8C2311yescharacteristic
76C4⋊Dic139C2311yescharacteristic
77C4⋊Dic139C2311yescharacteristic
78C4⋊Dic139C2311yescharacteristic
79Dic139⋊C4—21no—
80Dic139⋊C4—21no—
81Dic139⋊C4D411yescharacteristic
82Dic139⋊C4D411yescharacteristic
83C22⋊Dic139—21no—
84C22⋊Dic139—21no—
85C22⋊Dic139—21no—
86C22⋊Dic139—21no—
87C22⋊Dic139—21no—
88(C2×D139)⋊C4—21no—
89(C2×D139)⋊C4—21no—
90(C2×D139)⋊C4—21no—
91(C2×D139)⋊C4D411yescharacteristic
92(C2×D139)⋊C4D411yescharacteristic
93C4×Dic139—21no—
94C4×Dic139C2311yescharacteristic
95C2×D4×C139—21no—
96C2×D4×C139—21no—
97C2×D4×C139C2311yescharacteristic
98C2×D4×C139C2311yescharacteristic
99C2×D4×C139C2311yescharacteristic
100C22×C4×C139—21no—
101D8×C139—22no—
102D8×C139—22no—
103C2×C8×C139C2311yescharacteristic
104C2×C8×C139C2311yescharacteristic
105C4⋊C4×C139C2311yescharacteristic
106C22⋊C4×C139—21no—
107C42×C139C2311yescharacteristic
108C22×D139—21no—
109C22×D139—24no—
110C22×D139—81no—
111C22×D139—81no—
112C22×D139C2×D411yescharacteristic
113D556—21no—
114D556#4112yes—
115C22⋊D139—24no—
116C22⋊D139—81no—
117C22⋊D139—81no—
118C2×Dic139—21no—
119C2×Dic139—21no—
120C2×Dic139—21no—
121C2×Dic139—81no—
122C2×Dic139—81no—
123C2×Dic139—81no—
124C2×Dic139C2×D411yescharacteristic
125C2×Dic139C2×D411yescharacteristic
126C2×Dic139C2×D411yescharacteristic
127C4×D139—21no—
128C4×D139—21no—
129C4×D139—81no—
130C4×D139—81no—
131C139⋊C8—21no—
132C139⋊C8—21no—
133C23×C139—21no—
134C23×C139—21no—
135C23×C139—21no—
136D4×C139—21no—
137D4×C139—21no—
138D4×C139—21no—
139D4×C139—21no—
140D4×C139—21no—
141D4×C139—81no—
142D4×C139—81no—
143D4×C139#4112yes—
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×C139—41no—
155C22×C139—41no—
156C22×C139—41no—
157C22×C139—41no—
158C22×C139—41no—
159C22×C139—41no—
160C22×C139C22×D411yescharacteristic
161C2×D139—21no—
162C2×D139—22no—
163C2×D139—21no—
164C2×D139—21no—
165C2×D139—41no—
166C2×D139—41no—
167C2×D139—84no—
168C4×C139—21no—
169C4×C139—21no—
170C4×C139—41no—
171C4×C139C2×#4111yescharacteristic
172C4×C139C2×#4111yescharacteristic
173Dic139—21no—
174Dic139—21no—
175Dic139—21no—
176Dic139—41no—
177Dic139—41no—
178Dic139—41no—
179C2×C139—42no—
180C2×C139—81no—
181C2×C139—81no—
182C2×C139#52511yescharacteristic
183C2×C139#57611yescharacteristic
184C2×C139#57611yescharacteristic
185D139—41no—
186D139—42no—
187C139#312211yescharacteristic, complemented, Sylow
188#3122—1391nomaximal, Sylow
189#540—1391no—
190#518—1391no—
191#482—1391no—
192#482—1391no—
193#478—1391no—
194#478—1391no—
195#459—1391no—
196#459D13911yescharacteristic, complemented
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×D8C2×D13911yescharacteristic
208C2×D8C2×D13911yescharacteristic
209#127C2×D13911yescharacteristic, complemented
210#125—1391no—
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#107—1391no—
231#106—1391no—
232#106—1391no—
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, complemented
242#102C2×D13911yescharacteristic, complemented
243C22⋊C8—1391no—
244C22⋊C8—1391no—
245#97—1391no—
246C4×C8—1391no—
247C24—2781no—
248C2×D4—21no—
249C2×D4—21no—
250C2×D4—2782no—
251C2×D4—2782no—
252C2×D4—2781no—
253C2×D4—2781no—
254C2×D4—2781no—
255C2×D4—1391no—
256C2×D4C22×D13911yescharacteristic
257C2×D4C22×D13911yescharacteristic
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—22no—
267D8—22no—
268D8—2782no—
269D8—2782no—
270C2×C8—1391no—
271C2×C8—1391no—
272C2×C8C22×D13911yescharacteristic
273C2×C8C22×D13911yescharacteristic
274C4⋊C4—2781no—
275C4⋊C4—2781no—
276C4⋊C4—1391no—
277C4⋊C4—1391no—
278C4⋊C4—1391no—
279C4⋊C4—1391no—
280C4⋊C4—1391no—
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—21no—
298C23—21no—
299C23—2784no—
300C23—2781no—
301C23—11121no—
302C23—11121no—
303C23—1391no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—81no—
310D4—81no—
311D4—2784no—
312D4—2781no—
313D4—11121no—
314D4—11121no—
315D4—1392no—
316D4#1455578412yes—
317C2×C4—21no—
318C2×C4—81no—
319C2×C4—2781no—
320C2×C4—2781no—
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—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—2781no—
349C22—2782no—
350C22—2781no—
351C22—2781no—
352C22—5561no—
353C22—5561no—
354C22—11124no—
355C22C2×D4×D13911yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—2781no—
360C4—2781no—
361C4—2781no—
362C4—5561no—
363C4—5561no—
364C4—5561no—
365C4#41×D13911yescharacteristic
366C4C2×#1455578411yescharacteristic
367C2—42no—
368C2—81no—
369C2—81no—
370C2—5561no—
371C2—5562no—
372C2#2258146311yescharacteristic
373C2#2258175411yescharacteristic
374C2#2258175711yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#459×C139C2
socleC22×C139C22×D4
hypercenter#459D139
hypocenterC139#3122
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #22581557C2semidirect
2. #22581425C2semidirect
3. #22581276C2semidirect
4. #22581275C2semidirect
5. #22581254C2semidirect
6. #22581253C2semidirect
7. #22581145C2semidirect
8. #22581085C2semidirect
9. #22581085C2semidirect
10. #22581065C2semidirect
11. #22581062C2semidirect
12. D8×Dic139C2semidirect
13. #22581033C2semidirect
14. #22581013C2semidirect
15. #459×C139C2semidirect
19. #17984834C22semidirect
28. D4×Dic139C22semidirect
29. D4×Dic139C22semidirect
37. #17984776C22semidirect
38. #17984775C22semidirect
39. #17984774C22semidirect
40. #17984773C22semidirect
41. C4⋊(C139⋊C8)C22semidirect
46. #17984763C22semidirect
47. #17984763C22semidirect
50. #17984752C22semidirect
51. C8×Dic139C22semidirect
54. #127×C139C22semidirect
56. C4⋊C8×C139C22semidirect
57. #102×C139C22semidirect
58. #102×C139C22semidirect
187. C139#3122semidirect
196. #459D139semidirect
209. #127C2×D139semidirect
234. C4⋊C8C2×D139semidirect
241. #102C2×D139semidirect
242. #102C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225815572
#225814252
#225812762
#225812752
#225812542
#225812532
#225811452
#225810852
#225810652
#225810622
D8×Dic1392
#225810332
#225810132
#459×C1392
#3122139