Finite Group Databasebeta

← #31816641

Subgroups — #31816641

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#22581556C211yesmaximal, characteristic, complemented
2#22581428C211yesmaximal, characteristic, complemented
3#22581278C211yesmaximal, characteristic, complemented
4#22581274C211yesmaximal, characteristic, complemented
5#22581255C211yesmaximal, characteristic, complemented
6#22581251C211yesmaximal, characteristic, complemented
7#22581146C211yesmaximal, characteristic, complemented
8#22581146C211yesmaximal, characteristic, complemented
9#22581087C211yesmaximal, characteristic, complemented
10#22581065C211yesmaximal, characteristic, complemented
11#22581062C211yesmaximal, characteristic, complemented
12D8×Dic139C211yesmaximal, characteristic, complemented
13#22581033C211yesmaximal, characteristic, complemented
14#22581011C211yesmaximal, characteristic, complemented
15#447×C139C211yesmaximal, characteristic, complemented
16C2×#14555770C2211yescharacteristic
17C2×#14555770C2211yescharacteristic
18#17984838C2211yescharacteristic, complemented
19#17984833C2211yescharacteristic, complemented
20#17984826—21no—
21#17984824—21no—
22#17984816C2211yescharacteristic
23#17984814—21no—
24#17984813—21no—
25D4×Dic139—21no—
26D4×Dic139—21no—
27D4×Dic139C2211yescharacteristic
28D4×Dic139C2211yescharacteristic
29D4×Dic139C2211yescharacteristic
30D4×Dic139C2211yescharacteristic
31D4×Dic139C2211yescharacteristic, complemented
32#17984804C2211yescharacteristic, complemented
33#17984801C2211yescharacteristic
34#17984801C2211yescharacteristic
35C2×C22⋊Dic139—21no—
36C2×C22⋊Dic139—21no—
37#17984776C2211yescharacteristic, complemented
38#17984775C2211yescharacteristic, complemented
39#17984774C2211yescharacteristic, complemented
40#17984773C2211yescharacteristic, complemented
41Dic139⋊C8C2211yescharacteristic, complemented
42Dic139⋊C8C2211yescharacteristic, complemented
43#17984764C2211yescharacteristic, complemented
44#17984764C2211yescharacteristic, complemented
45#17984763C2211yescharacteristic
46#17984763C2211yescharacteristic
47#17984763C2211yescharacteristic, complemented
48#17984763C2211yescharacteristic, complemented
49C22⋊(C139⋊C8)C2211yescharacteristic
50#17984752C2211yescharacteristic, 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
59C2×D556C2311yescharacteristic
60C2×C22⋊D139—21no—
61C2×C22⋊D139—21no—
62C2×C22⋊D139—21no—
63C22×Dic139—21no—
64C22×Dic139—21no—
65C22×Dic139—21no—
66C22×Dic139—21no—
67C22×Dic139—21no—
68C2×C4×D139—21no—
69#14555770—22no—
70#14555770—22no—
71C2×C139⋊C8C2311yescharacteristic
72C2×C139⋊C8C2311yescharacteristic
73C4⋊Dic139—21no—
74C4⋊Dic139D411yescharacteristic
75C4⋊Dic139D411yescharacteristic
76C4⋊Dic139C2311yescharacteristic
77C4⋊Dic139C2311yescharacteristic
78C4⋊Dic139C2311yescharacteristic
79Dic139⋊C4—21no—
80C22⋊Dic139—21no—
81C22⋊Dic139—21no—
82C22⋊Dic139—21no—
83C22⋊Dic139—21no—
84C22⋊Dic139—21no—
85C22⋊Dic139—21no—
86C22⋊Dic139D411yescharacteristic
87C22⋊Dic139D411yescharacteristic
88(C2×D139)⋊C4—21no—
89(C2×D139)⋊C4—21no—
90C4×Dic139—21no—
91C4×Dic139C2311yescharacteristic
92C4×Dic139C2311yescharacteristic
93C24×C139—21no—
94C2×D4×C139—22no—
95C2×D4×C139—22no—
96C2×D4×C139—21no—
97C2×D4×C139—21no—
98C2×D4×C139C2311yescharacteristic
99C2×D4×C139C2311yescharacteristic
100C2×D4×C139C2311yescharacteristic
101C22×C4×C139C2311yescharacteristic
102D8×C139—22no—
103D8×C139—22no—
104C2×C8×C139C2311yescharacteristic
105C2×C8×C139C2311yescharacteristic
106C4⋊C4×C139C2311yescharacteristic
107C22⋊C4×C139—21no—
108C22×D139—21no—
109D556—21no—
110D556—21no—
111C22⋊D139—81no—
112C22⋊D139—81no—
113C22⋊D139—81no—
114C2×Dic139—21no—
115C2×Dic139—21no—
116C2×Dic139—21no—
117C2×Dic139—81no—
118C2×Dic139—81no—
119C2×Dic139—81no—
120C2×Dic139—81no—
121C2×Dic139—81no—
122C2×Dic139C2×D411yescharacteristic
123C2×Dic139C2×D411yescharacteristic
124C2×Dic139C2×D411yescharacteristic
125C2×Dic139C2×D411yescharacteristic
126C4×D139—81no—
127C139⋊C8—21no—
128C139⋊C8—21no—
129C23×C139—24no—
130C23×C139—21no—
131C23×C139—21no—
132C23×C139—21no—
133C23×C139—81no—
134C23×C139—81no—
135C23×C139C2×D411yescharacteristic
136D4×C139—24no—
137D4×C139—21no—
138D4×C139—21no—
139D4×C139—21no—
140D4×C139—21no—
141D4×C139—81no—
142D4×C139#4112yes—
143D4×C139#4112yes—
144C2×C4×C139—21no—
145C2×C4×C139—21no—
146C2×C4×C139—21no—
147C2×C4×C139C2×D411yescharacteristic
148C2×C4×C139C2411yescharacteristic
149C8×C139—21no—
150C8×C139—21no—
151C22×C139—21no—
152C22×C139—22no—
153C22×C139—22no—
154C22×C139—21no—
155C22×C139—21no—
156C22×C139—41no—
157C22×C139—41no—
158C22×C139—41no—
159C22×C139—41no—
160C22×C139—41no—
161C22×C139—41no—
162C22×C139—41no—
163C22×C139—84no—
164C22×C139C22×D411yescharacteristic
165C2×D139—41no—
166C2×D139—41no—
167C2×D139—41no—
168C4×C139—21no—
169C4×C139—41no—
170C4×C139C2×#4111yescharacteristic
171C4×C139C2×#4111yescharacteristic
172Dic139—21no—
173Dic139—21no—
174Dic139—21no—
175Dic139—21no—
176Dic139—41no—
177Dic139—41no—
178Dic139—41no—
179C2×C139—41no—
180C2×C139—42no—
181C2×C139—42no—
182C2×C139—81no—
183C2×C139#52511yescharacteristic
184C2×C139#57611yescharacteristic
185C2×C139#57611yescharacteristic
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#478—1391no—
195#459—1391no—
196#459—1391no—
197#447—1391no—
198#447D13911yescharacteristic, complemented
199#442—1391no—
200#442—1391no—
201C4×D8—1391no—
202C4×D8—1391no—
203#433—1391no—
204C22×D4C2×D13911yescharacteristic
205C2×D8—1391no—
206C2×D8—1391no—
207C2×D8C2×D13911yescharacteristic
208C2×D8C2×D13911yescharacteristic
209#127—1391no—
210#125—1391no—
211#123—2781no—
212#123—2781no—
213#121—2781no—
214#121—2781no—
215#121—1391no—
216#121C2×D13911yescharacteristic
217C4×D4—2781no—
218C4×D4—2781no—
219C4×D4—1391no—
220C4×D4—1391no—
221C4×D4—1391no—
222C4×D4—1391no—
223C4×D4—1391no—
224C4×D4—1391no—
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⋊C8—1391no—
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⋊C8C2×D13911yescharacteristic
245#97—1391no—
246C4×C8—1391no—
247C24—21no—
248C2×D4—22no—
249C2×D4—22no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—2781no—
253C2×D4—2781no—
254C2×D4—2781no—
255C2×D4—1391no—
256C2×D4C22×D13911yescharacteristic
257C2×D4C22×D13911yescharacteristic
258C2×D4C22×D13911yescharacteristic
259C22×C4—2781no—
260C22×C4—2781no—
261C22×C4—2781no—
262C22×C4—2781no—
263C22×C4—2781no—
264C22×C4—2781no—
265C22×C4C22×D13911yescharacteristic
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—
295C42—1391no—
296C23—24no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—81no—
301C23—81no—
302C23—2781no—
303C23D4×D13911yescharacteristic
304D4—24no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—81no—
310D4—2781no—
311D4—2781no—
312D4—11121no—
313D4—11121no—
314D4—11121no—
315D4#1455578412yes—
316D4#1455578412yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—2781no—
321C2×C4—2781no—
322C2×C4—2781no—
323C2×C4—11121no—
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×C4—1391no—
333C2×C4D4×D13911yescharacteristic
334C2×C4C23×D13911yescharacteristic
335C8—21no—
336C8—21no—
337C8—2781no—
338C8—2781no—
339C22—21no—
340C22—22no—
341C22—22no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—84no—
352C22—5561no—
353C22—5561no—
354C22—5561no—
355C22C2×D4×D13911yescharacteristic
356C4—21no—
357C4—41no—
358C4—2781no—
359C4—2781no—
360C4—2781no—
361C4—2781no—
362C4—5561no—
363C4—5561no—
364C4—5561no—
365C4C2×#1455578411yescharacteristic
366C4C2×#1455578411yescharacteristic
367C2—41no—
368C2—42no—
369C2—42no—
370C2—81no—
371C2—11121no—
372C2#2258145911yescharacteristic
373C2#2258175411yescharacteristic
374C2#2258175711yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#447×C139C2
socleC22×C139C22×D4
hypercenter#447D139
hypocenterC139#3122
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. #22581556C2semidirect
2. #22581428C2semidirect
3. #22581278C2semidirect
4. #22581274C2semidirect
5. #22581255C2semidirect
6. #22581251C2semidirect
7. #22581146C2semidirect
8. #22581146C2semidirect
9. #22581087C2semidirect
10. #22581065C2semidirect
11. #22581062C2semidirect
12. D8×Dic139C2semidirect
13. #22581033C2semidirect
14. #22581011C2semidirect
15. #447×C139C2semidirect
18. #17984838C22semidirect
19. #17984833C22semidirect
31. D4×Dic139C22semidirect
32. #17984804C22semidirect
37. #17984776C22semidirect
38. #17984775C22semidirect
39. #17984774C22semidirect
40. #17984773C22semidirect
41. Dic139⋊C8C22semidirect
42. Dic139⋊C8C22semidirect
43. #17984764C22semidirect
44. #17984764C22semidirect
47. #17984763C22semidirect
48. #17984763C22semidirect
50. #17984752C22semidirect
51. C8×Dic139C22semidirect
187. C139#3122semidirect
198. #447D139semidirect

Maximal subgroups

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

subgroupindex
#225815562
#225814282
#225812782
#225812742
#225812552
#225812512
#225811462
#225810872
#225810652
#225810622
D8×Dic1392
#225810332
#225810112
#447×C1392
#3122139