Finite Group Databasebeta

← #31816541

Subgroups — #31816541

Order 17792.

450 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581482C211yesmaximal, characteristic, complemented
2C4×D4×D139C211yesmaximal, characteristic, complemented
3#22581282C211yesmaximal, characteristic, complemented
4#22581265C211yesmaximal, characteristic, complemented
5#22581254C211yesmaximal, characteristic, complemented
6#22581253C211yesmaximal, characteristic, complemented
7#22581165C211yesmaximal, characteristic, complemented
8#22581102C211yesmaximal, characteristic, complemented
9#22581085C211yesmaximal, characteristic
10#22581065C211yesmaximal, characteristic, complemented
11#22581062C211yesmaximal, characteristic, complemented
12#22581056C211yesmaximal, characteristic, complemented
13#22581054C211yesmaximal, characteristic, complemented
14#22581009C211yesmaximal, characteristic, complemented
15#463×C139C211yesmaximal, characteristic, complemented
16C2×D4×D139C2211yescharacteristic
17C22×C4×D139—21no—
18C2×#14555772C2211yescharacteristic
19C2×#14555770C2211yescharacteristic
20#17984835—21no—
21#17984834C2211yescharacteristic, complemented
22#17984824—21no—
23#17984818C2211yescharacteristic
24#17984813C2211yescharacteristic
25Q8×Dic139C2211yescharacteristic, complemented
26C4×D556C2211yescharacteristic
27D4×Dic139C2211yescharacteristic
28D4×Dic139C2211yescharacteristic, complemented
29#17984804C2211yescharacteristic
30C4×C22⋊D139—21no—
31(C22⋊D139)⋊C4—21no—
32(C22⋊D139)⋊C4—21no—
33#17984798—21no—
34C4⋊C4×D139C2211yescharacteristic
35C22⋊C4×D139—21no—
36C42×D139C2211yescharacteristic
37#17984776C2211yescharacteristic, complemented
38#17984775C2211yescharacteristic, complemented
39#17984774C2211yescharacteristic, complemented
40#17984773C2211yescharacteristic, complemented
41C4⋊(C139⋊C8)C2211yescharacteristic, complemented
42#17984766C2211yescharacteristic, complemented
43#17984764C2211yescharacteristic
44#17984764C2211yescharacteristic
45#17984763C2211yescharacteristic
46#17984763C2211yescharacteristic
47#17984763C2211yescharacteristic, complemented
48(C2×D139)⋊C8C2211yescharacteristic
49(C2×D139)⋊C8C2211yescharacteristic
50#17984752C2211yescharacteristic, complemented
51#17984752C2211yescharacteristic, complemented
52C2×SD16×C139C2211yescharacteristic
53C2×D8×C139C2211yescharacteristic
54#124×C139C2211yescharacteristic, complemented
55C4×D4×C139C2211yescharacteristic
56C4⋊C8×C139C2211yescharacteristic, complemented
57#103×C139C2211yescharacteristic, complemented
58#102×C139C2211yescharacteristic, complemented
59C23×D139—21no—
60C2×D556C2311yescharacteristic
61C2×C22⋊D139—21no—
62C2×C22⋊D139—21no—
63D4×D139—22no—
64D4×D139—22no—
65C22×Dic139—21no—
66C22×Dic139—21no—
67C2×C4×D139—21no—
68C2×C4×D139—21no—
69C2×C4×D139—21no—
70C2×C4×D139—44no—
71C2×C4×D139D411yescharacteristic
72C2×C4×D139D411yescharacteristic
73C2×C4×D139C2311yescharacteristic
74#14555772—22no—
75#14555770—22no—
76C2×C139⋊C8C2311yescharacteristic
77C2×C139⋊C8C2311yescharacteristic
78C4⋊Dic139—21no—
79C4⋊Dic139C2311yescharacteristic
80C4⋊Dic139C2311yescharacteristic
81C4⋊Dic139C2311yescharacteristic
82Dic139⋊C4—21no—
83Dic139⋊C4—21no—
84Dic139⋊C4—21no—
85Dic139⋊C4—21no—
86C22⋊Dic139—21no—
87C22⋊Dic139—21no—
88C22⋊Dic139—21no—
89(C2×D139)⋊C4—21no—
90(C2×D139)⋊C4—21no—
91(C2×D139)⋊C4—21no—
92C4×Dic139—21no—
93C4×Dic139D411yescharacteristic
94C4×Dic139D411yescharacteristic
95C4×Dic139C2311yescharacteristic
96C2×Q8×C139C2311yescharacteristic
97C2×D4×C139C2311yescharacteristic
98C2×D4×C139C2311yescharacteristic
99C22×C4×C139—21no—
100SD16×C139—22no—
101D8×C139—22no—
102C2×C8×C139C2311yescharacteristic
103C2×C8×C139C2311yescharacteristic
104C4⋊C4×C139C2311yescharacteristic
105C22⋊C4×C139—21no—
106C22⋊C4×C139—21no—
107C22⋊C4×C139—21no—
108C42×C139C2311yescharacteristic
109C22×D139—24no—
110C22×D139—21no—
111C22×D139—42no—
112C22×D139—42no—
113C22×D139C2×D411yescharacteristic
114D556—21no—
115D556#4112yes—
116C22⋊D139—24no—
117C22⋊D139—42no—
118C2×Dic139—21no—
119C2×Dic139—21no—
120C2×Dic139—21no—
121C2×Dic139—42no—
122C2×Dic139—42no—
123C2×Dic139C2×D411yescharacteristic
124C2×Dic139C2×D411yescharacteristic
125C2×Dic139C2×D411yescharacteristic
126C4×D139—22no—
127C4×D139—21no—
128C4×D139—21no—
129C4×D139—41no—
130C4×D139—42no—
131C4×D139—42no—
132C4×D139—42no—
133C139⋊C8—21no—
134C139⋊C8—21no—
135C23×C139—21no—
136C23×C139—21no—
137Q8×C139—21no—
138Q8×C139—21no—
139D4×C139—21no—
140D4×C139—21no—
141D4×C139—21no—
142D4×C139#4112yes—
143C2×C4×C139—21no—
144C2×C4×C139—21no—
145C2×C4×C139—42no—
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—21no—
160C2×D139—22no—
161C2×D139—48no—
162C2×D139—41no—
163C2×D139—41no—
164C2×D139AGL(1,ℤ/8)12yes—
165C4×C139—21no—
166C4×C139—21no—
167C4×C139—41no—
168C4×C139—41no—
169C4×C139C2×#4111yescharacteristic
170C4×C139C2×#4111yescharacteristic
171Dic139—21no—
172Dic139—21no—
173Dic139—21no—
174Dic139—41no—
175Dic139—41no—
176Dic139—41no—
177C2×C139—42no—
178C2×C139—81no—
179C2×C139#52511yescharacteristic
180C2×C139C2×AGL(1,ℤ/8)11yescharacteristic
181C2×C139#57511yescharacteristic
182D139—22no—
183D139—42no—
184C139#311411yescharacteristic, complemented, Sylow
185#3114—1391nomaximal, Sylow
186#529—1391no—
187C2×C4×D4—1391no—
188#483—1391no—
189#480—1391no—
190#478—1391no—
191#478—1391no—
192#463—1391no—
193#463D13911yescharacteristic, complemented
194#450—1391no—
195#447—1391no—
196#442—1391no—
197#442—1391no—
198#440—1391no—
199#440—1391no—
200#432—1391no—
201C22×D4—1391no—
202C23×C4—2781no—
203C2×SD16—1391no—
204C2×SD16C2×D13911yescharacteristic
205C2×D8—1391no—
206C2×D8C2×D13911yescharacteristic
207#126—2781no—
208#125—1391no—
209#124C2×D13911yescharacteristic, complemented
210#123—2781no—
211C22⋊Q8—1391no—
212#121—1391no—
213C4×Q8—1391no—
214C4×D4—2781no—
215C4×D4—2781no—
216C4×D4—2781no—
217C4×D4—1391no—
218C4×D4—1391no—
219C4×D4—1391no—
220C4×D4—1391no—
221C4×D4C2×D13911yescharacteristic
222#117—2781no—
223C2×C4⋊C4—1391no—
224C2×C22⋊C4—2781no—
225C2×C42—1391no—
226#107—1391no—
227#107—1391no—
228#106—1391no—
229#106—1391no—
230C4⋊C8—1391no—
231C4⋊C8C2×D13911yescharacteristic, complemented
232#103—1391no—
233#103C2×D13911yescharacteristic, complemented
234#102—1391no—
235#102—1391no—
236#102—1391no—
237#102—1391no—
238#102—1391no—
239#102C2×D13911yescharacteristic, complemented
240C22⋊C8—1391no—
241C22⋊C8—1391no—
242#97—1391no—
243#97—1391no—
244C24—2781no—
245C2×Q8C22×D13911yescharacteristic
246C2×D4—2782no—
247C2×D4—2782no—
248C2×D4—2781no—
249C2×D4—2781no—
250C2×D4—1391no—
251C2×D4C22×D13911yescharacteristic
252C2×D4C22×D13911yescharacteristic
253C22×C4—21no—
254C22×C4—2781no—
255C22×C4—2781no—
256C22×C4—2781no—
257C22×C4—2781no—
258C22×C4—2781no—
259C22×C4—5564no—
260C22×C4—1391no—
261C22×C4—1391no—
262C22×C4—1391no—
263SD16—22no—
264SD16—2782no—
265D8—22no—
266D8—2782no—
267C2×C8—1391no—
268C2×C8—1391no—
269C2×C8C22×D13911yescharacteristic
270C2×C8C22×D13911yescharacteristic
271C4⋊C4—2781no—
272C4⋊C4—2781no—
273C4⋊C4—2781no—
274C4⋊C4—2781no—
275C4⋊C4—2781no—
276C4⋊C4—1391no—
277C4⋊C4—1391no—
278C4⋊C4—1391no—
279C4⋊C4C22×D13911yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—2781no—
284C22⋊C4—2781no—
285C22⋊C4—2781no—
286C22⋊C4—2781no—
287C22⋊C4—2781no—
288C22⋊C4—2781no—
289C42—2781no—
290C42—1391no—
291C42—1391no—
292C42—1391no—
293C42C22×D13911yescharacteristic
294C23—21no—
295C23—21no—
296C23—2784no—
297C23—2781no—
298C23—5562no—
299C23—5562no—
300C23—1391no—
301Q8—21no—
302Q8—21no—
303D4—21no—
304D4—21no—
305D4—21no—
306D4—2784no—
307D4—2781no—
308D4—5562no—
309D4—1392no—
310D4#1455578412yes—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—2782no—
315C2×C4—2781no—
316C2×C4—2781no—
317C2×C4—2781no—
318C2×C4—2781no—
319C2×C4—2781no—
320C2×C4—5561no—
321C2×C4—5562no—
322C2×C4—5562no—
323C2×C4—5562no—
324C2×C4—5562no—
325C2×C4—5562no—
326C2×C4—1391no—
327C2×C4—1391no—
328C2×C4—1391no—
329C2×C4D4×D13911yescharacteristic
330C2×C4D4×D13911yescharacteristic
331C2×C4C23×D13911yescharacteristic
332C8—21no—
333C8—21no—
334C8—2781no—
335C8—2781no—
336C22—22no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—2781no—
343C22—2781no—
344C22—2782no—
345C22—5568no—
346C22—5561no—
347C22—5561no—
348C22—1392no—
349C22C2×D4×D13911yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—2781no—
355C4—2781no—
356C4—2781no—
357C4—5561no—
358C4—5561no—
359C4—5561no—
360C4#41×D13911yescharacteristic
361C4C2×#1455578411yescharacteristic
362C2—42no—
363C2—81no—
364C2—2782no—
365C2—5562no—
366C2#2258146311yescharacteristic
367C2AGL(1,ℤ/8)×D13911yescharacteristic
368C2#2258175011yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#463×C139C2
socleC22×C139C22×D4
prime radical#22581085C2
hypercenter#463D139
hypocenterC139#3114
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #22581482C2semidirect
2. C4×D4×D139C2semidirect
3. #22581282C2semidirect
4. #22581265C2semidirect
5. #22581254C2semidirect
6. #22581253C2semidirect
7. #22581165C2semidirect
8. #22581102C2semidirect
10. #22581065C2semidirect
11. #22581062C2semidirect
12. #22581056C2semidirect
13. #22581054C2semidirect
14. #22581009C2semidirect
15. #463×C139C2semidirect
21. #17984834C22semidirect
25. Q8×Dic139C22semidirect
28. D4×Dic139C22semidirect
37. #17984776C22semidirect
38. #17984775C22semidirect
39. #17984774C22semidirect
40. #17984773C22semidirect
41. C4⋊(C139⋊C8)C22semidirect
42. #17984766C22semidirect
47. #17984763C22semidirect
50. #17984752C22semidirect
51. #17984752C22semidirect
54. #124×C139C22semidirect
56. C4⋊C8×C139C22semidirect
57. #103×C139C22semidirect
58. #102×C139C22semidirect
184. C139#3114semidirect
193. #463D139semidirect
209. #124C2×D139semidirect
231. C4⋊C8C2×D139semidirect
233. #103C2×D139semidirect
239. #102C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225814822
C4×D4×D1392
#225812822
#225812652
#225812542
#225812532
#225811652
#225811022
#225810852
#225810652
#225810622
#225810562
#225810542
#225810092
#463×C1392
#3114139