Finite Group Databasebeta

← #31816646

Subgroups — #31816646

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#22581554C211yesmaximal, characteristic, complemented
2#22581425C211yesmaximal, characteristic, complemented
3#22581279C211yesmaximal, characteristic, complemented
4#22581276C211yesmaximal, characteristic, complemented
5#22581255C211yesmaximal, characteristic, complemented
6#22581252C211yesmaximal, characteristic, complemented
7#22581147C211yesmaximal, characteristic, complemented
8#22581146C211yesmaximal, characteristic, complemented
9#22581088C211yesmaximal, characteristic, complemented
10#22581085C211yesmaximal, characteristic, complemented
11#22581066C211yesmaximal, characteristic, complemented
12C4×#14555770C211yesmaximal, characteristic, complemented
13C4×#14555770C211yesmaximal, characteristic, complemented
14#22581015C211yesmaximal, characteristic, complemented
15#442×C139C211yesmaximal, characteristic, complemented
16C2×D4×D139C2211yescharacteristic
17C2×D1112C2211yescharacteristic
18C2×#14555770C2211yescharacteristic
19C2×#14555770C2211yescharacteristic
20#17984838C2211yescharacteristic, complemented
21#17984833C2211yescharacteristic, complemented
22#17984825—21no—
23#17984824—21no—
24#17984817C2211yescharacteristic
25#17984816—21no—
26#17984815—21no—
27#17984813C2211yescharacteristic
28C4×D556C2211yescharacteristic
29C4×D556C2211yescharacteristic, complemented
30D4×Dic139C2211yescharacteristic
31#17984804C2211yescharacteristic
32C4×C22⋊D139—21no—
33(C22⋊D139)⋊C4—21no—
34#17984800C2211yescharacteristic
35#17984799C2211yescharacteristic
36C2×(C2×D139)⋊C4—21no—
37C22⋊C4×D139—21no—
38#17984775C2211yescharacteristic, complemented
39#17984775C2211yescharacteristic, complemented
40#17984774C2211yescharacteristic, complemented
41Dic139⋊C8C2211yescharacteristic, complemented
42Dic139⋊C8C2211yescharacteristic, complemented
43#17984764C2211yescharacteristic
44#17984764C2211yescharacteristic, complemented
45#17984763C2211yescharacteristic
46#17984763C2211yescharacteristic, complemented
47#17984762C2211yescharacteristic
48#17984762C2211yescharacteristic, complemented
49(C2×D139)⋊C8C2211yescharacteristic
50(C2×D139)⋊C8C2211yescharacteristic
51C4×C139⋊C8C2211yescharacteristic, complemented
52C2×D8×C139C2211yescharacteristic
53C4×D4×C139C2211yescharacteristic
54C4×D4×C139C2211yescharacteristic, complemented
55#106×C139C2211yescharacteristic, complemented
56#102×C139C2211yescharacteristic
57#102×C139C2211yescharacteristic, complemented
58#97×C139C2211yescharacteristic, complemented
59C23×D139—21no—
60C2×D556—21no—
61C2×D556C2311yescharacteristic
62C2×D556C2311yescharacteristic
63C2×C22⋊D139—21no—
64C2×C22⋊D139—21no—
65C2×C22⋊D139—21no—
66C2×C22⋊D139—21no—
67D4×D139—22no—
68D4×D139—22no—
69C22×Dic139—21no—
70C2×C4×D139—21no—
71C2×C4×D139—21no—
72C2×C4×D139—21no—
73C2×C4×D139C2311yescharacteristic
74D1112—22no—
75#14555770—22no—
76#14555770—22no—
77C2×C139⋊C8C2311yescharacteristic
78C2×C139⋊C8C2311yescharacteristic
79C4⋊Dic139—21no—
80C4⋊Dic139C2311yescharacteristic
81C4⋊Dic139C2311yescharacteristic
82Dic139⋊C4—21no—
83Dic139⋊C4D411yescharacteristic
84Dic139⋊C4D411yescharacteristic
85C22⋊Dic139—21no—
86C22⋊Dic139—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)⋊C4D411yescharacteristic
93(C2×D139)⋊C4D411yescharacteristic
94C4×Dic139—21no—
95C4×Dic139C2311yescharacteristic
96C2×D4×C139C2311yescharacteristic
97C2×D4×C139C2311yescharacteristic
98C22×C4×C139—21no—
99C22×C4×C139—21no—
100D8×C139—22no—
101C2×C8×C139C2311yescharacteristic
102C2×C8×C139C2311yescharacteristic
103C4⋊C4×C139C2311yescharacteristic
104C4⋊C4×C139C2311yescharacteristic
105C22⋊C4×C139—21no—
106C22⋊C4×C139—21no—
107C42×C139C2311yescharacteristic
108C22×D139—21no—
109C22×D139—24no—
110C22×D139—21no—
111C22×D139—81no—
112C22×D139—81no—
113C22×D139C2×D411yescharacteristic
114D556—21no—
115D556—21no—
116D556—21no—
117D556—81no—
118D556#4112yes—
119C22⋊D139—24no—
120C22⋊D139—81no—
121C22⋊D139—81no—
122C22⋊D139—81no—
123C2×Dic139—21no—
124C2×Dic139—21no—
125C2×Dic139—81no—
126C2×Dic139C2×D411yescharacteristic
127C2×Dic139C2×D411yescharacteristic
128C2×Dic139C2×D411yescharacteristic
129C4×D139—21no—
130C4×D139—21no—
131C4×D139—81no—
132C4×D139—81no—
133C4×D139—81no—
134C139⋊C8—21no—
135C139⋊C8—21no—
136C23×C139—21no—
137C23×C139—21no—
138D4×C139—21no—
139D4×C139—21no—
140D4×C139—21no—
141D4×C139#4112yes—
142C2×C4×C139—21no—
143C2×C4×C139—21no—
144C2×C4×C139—81no—
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×C139C22×D411yescharacteristic
158C2×D139—21no—
159C2×D139—22no—
160C2×D139—21no—
161C2×D139—21no—
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×C139C2×#4111yescharacteristic
173C4×C139C2×#4111yescharacteristic
174Dic139—21no—
175Dic139—21no—
176Dic139—21no—
177Dic139—41no—
178Dic139—41no—
179C2×C139—42no—
180C2×C139—81no—
181C2×C139#52511yescharacteristic
182C2×C139#57611yescharacteristic
183C2×C139#57611yescharacteristic
184D139—41no—
185D139—42no—
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#447—1391no—
199#442—1391no—
200#442D13911yescharacteristic, complemented
201C4×D8—1391no—
202C4×D8—1391no—
203#433—1391no—
204C22×D4—1391no—
205C2×D8—1391no—
206C2×D8—1391no—
207C2×D8—1391no—
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#121—1391no—
217C4×D4—2781no—
218C4×D4—2781no—
219C4×D4—1391no—
220C4×D4—1391no—
221C4×D4—1391no—
222C4×D4—1391no—
223C4×D4C2×D13911yescharacteristic
224C4×D4C2×D13911yescharacteristic, complemented
225#117—1391no—
226#117—1391no—
227C2×C22⋊C4—2781no—
228C2×C22⋊C4—2781no—
229#107—1391no—
230#107—1391no—
231#106—1391no—
232#106C2×D13911yescharacteristic, complemented
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, complemented
243C22⋊C8—1391no—
244C22⋊C8—1391no—
245#97C2×D13911yescharacteristic, complemented
246C4×C8—1391no—
247C24—2781no—
248C2×D4—2781no—
249C2×D4—2782no—
250C2×D4—2782no—
251C2×D4—2781no—
252C2×D4—2781no—
253C2×D4—2781no—
254C2×D4—2781no—
255C2×D4—1391no—
256C2×D4—1391no—
257C2×D4C22×D13911yescharacteristic
258C2×D4C22×D13911yescharacteristic
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—2781no—
262C22×C4—2781no—
263C22×C4—2781no—
264C22×C4—2781no—
265C22×C4—1391no—
266D8—22no—
267D8—2782no—
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⋊C4C22×D13911yescharacteristic
281C4⋊C4C22×D13911yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
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—2784no—
299C23—2781no—
300C23—2781no—
301C23—11121no—
302C23—11121no—
303C23—1391no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—2784no—
308D4—2781no—
309D4—2781no—
310D4—2781no—
311D4—11121no—
312D4—11121no—
313D4—11121no—
314D4—11121no—
315D4—1392no—
316D4#1455578512yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—2781no—
322C2×C4—2781no—
323C2×C4—2781no—
324C2×C4—2781no—
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—2781no—
346C22—2782no—
347C22—2781no—
348C22—2781no—
349C22—5561no—
350C22—5561no—
351C22—5561no—
352C22—5561no—
353C22—5561no—
354C22—11124no—
355C22C2×D4×D13911yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—2781no—
361C4—2781no—
362C4—2781no—
363C4—5561no—
364C4—5561no—
365C4#41×D13911yescharacteristic
366C4C2×#1455578511yescharacteristic
367C2—42no—
368C2—81no—
369C2—5561no—
370C2—5562no—
371C2—11121no—
372C2#2258146211yescharacteristic
373C2#2258175711yescharacteristic
374C2#2258175711yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#442×C139C2
socleC22×C139C22×D4
hypercenter#442D139
hypocenterC139#3122
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #22581554C2semidirect
2. #22581425C2semidirect
3. #22581279C2semidirect
4. #22581276C2semidirect
5. #22581255C2semidirect
6. #22581252C2semidirect
7. #22581147C2semidirect
8. #22581146C2semidirect
9. #22581088C2semidirect
10. #22581085C2semidirect
11. #22581066C2semidirect
12. C4×#14555770C2semidirect
13. C4×#14555770C2semidirect
14. #22581015C2semidirect
15. #442×C139C2semidirect
20. #17984838C22semidirect
21. #17984833C22semidirect
29. C4×D556C22semidirect
38. #17984775C22semidirect
39. #17984775C22semidirect
40. #17984774C22semidirect
41. Dic139⋊C8C22semidirect
42. Dic139⋊C8C22semidirect
44. #17984764C22semidirect
46. #17984763C22semidirect
48. #17984762C22semidirect
51. C4×C139⋊C8C22semidirect
54. C4×D4×C139C22semidirect
55. #106×C139C22semidirect
57. #102×C139C22semidirect
58. #97×C139C22semidirect
187. C139#3122semidirect
200. #442D139semidirect
224. C4×D4C2×D139semidirect
232. #106C2×D139semidirect
242. #102C2×D139semidirect
245. #97C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225815542
#225814252
#225812792
#225812762
#225812552
#225812522
#225811472
#225811462
#225810882
#225810852
#225810662
C4×#145557702
#225810152
#442×C1392
#3122139