Finite Group Databasebeta

← #31816540

Subgroups — #31816540

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#22581485C211yesmaximal, characteristic, complemented
2C4×D4×D139C211yesmaximal, characteristic, complemented
3#22581285C211yesmaximal, characteristic, complemented
4#22581265C211yesmaximal, characteristic, complemented
5#22581252C211yesmaximal, characteristic, complemented
6#22581251C211yesmaximal, characteristic, complemented
7#22581167C211yesmaximal, characteristic, complemented
8#22581166C211yesmaximal, characteristic, complemented
9#22581105C211yesmaximal, characteristic, complemented
10#22581085C211yesmaximal, characteristic
11#22581063C211yesmaximal, characteristic, complemented
12#22581055C211yesmaximal, characteristic, complemented
13#22581053C211yesmaximal, characteristic, complemented
14#22581008C211yesmaximal, characteristic, complemented
15#442×C139C211yesmaximal, characteristic, complemented
16C2×D4×D139C2211yescharacteristic
17C22×C4×D139—21no—
18C2×#14555774C2211yescharacteristic
19C2×#14555773C2211yescharacteristic
20C2×#14555770C2211yescharacteristic
21#17984835—21no—
22#17984833C2211yescharacteristic, complemented
23#17984829C2211yescharacteristic, complemented
24#17984824—21no—
25#17984822C2211yescharacteristic
26#17984813C2211yescharacteristic
27C4×Dic278C2211yescharacteristic, complemented
28C4×D556C2211yescharacteristic
29D4×Dic139C2211yescharacteristic
30#17984804C2211yescharacteristic
31C4×C22⋊D139—21no—
32C4×C22⋊D139—21no—
33(C22⋊D139)⋊C4—21no—
34#17984801—21no—
35C4⋊C4×D139C2211yescharacteristic
36C22⋊C4×D139—21no—
37C42×D139C2211yescharacteristic
38#17984776C2211yescharacteristic, complemented
39#17984775C2211yescharacteristic, complemented
40#17984773C2211yescharacteristic, complemented
41Dic139⋊C8C2211yescharacteristic, complemented
42Dic139⋊C8C2211yescharacteristic, complemented
43#17984767C2211yescharacteristic, complemented
44#17984765C2211yescharacteristic, complemented
45#17984764C2211yescharacteristic
46#17984763C2211yescharacteristic
47#17984763C2211yescharacteristic, complemented
48#17984762C2211yescharacteristic
49(C2×D139)⋊C8C2211yescharacteristic
50(C2×D139)⋊C8C2211yescharacteristic
51#17984753C2211yescharacteristic, 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×Dic278C2311yescharacteristic
61C2×D556C2311yescharacteristic
62C2×C22⋊D139—21no—
63C2×C22⋊D139—21no—
64D4×D139—22no—
65D4×D139—22no—
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#14555774—22no—
75#14555773—22no—
76#14555770—22no—
77C2×C139⋊C8C2311yescharacteristic
78C2×C139⋊C8C2311yescharacteristic
79C4⋊Dic139—21no—
80C4⋊Dic139—21no—
81C4⋊Dic139C2311yescharacteristic
82C4⋊Dic139C2311yescharacteristic
83Dic139⋊C4—21no—
84Dic139⋊C4—21no—
85Dic139⋊C4—21no—
86C22⋊Dic139—21no—
87C22⋊Dic139—21no—
88C22⋊Dic139—21no—
89C22⋊Dic139—21no—
90(C2×D139)⋊C4—21no—
91(C2×D139)⋊C4—21no—
92(C2×D139)⋊C4—21no—
93C4×Dic139—21no—
94C4×Dic139D411yescharacteristic
95C4×Dic139D411yescharacteristic
96C4×Dic139C2311yescharacteristic
97C2×D4×C139C2311yescharacteristic
98C2×D4×C139C2311yescharacteristic
99C22×C4×C139—21no—
100C22×C4×C139—21no—
101D8×C139—22no—
102C2×C8×C139C2311yescharacteristic
103C2×C8×C139C2311yescharacteristic
104C4⋊C4×C139C2311yescharacteristic
105C4⋊C4×C139C2311yescharacteristic
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
114Dic278—21no—
115Dic278—21no—
116D556—21no—
117D556#4112yes—
118C22⋊D139—24no—
119C22⋊D139—42no—
120C2×Dic139—21no—
121C2×Dic139—21no—
122C2×Dic139—21no—
123C2×Dic139—42no—
124C2×Dic139C2×D411yescharacteristic
125C2×Dic139C2×D411yescharacteristic
126C2×Dic139C2×D411yescharacteristic
127C4×D139—22no—
128C4×D139—21no—
129C4×D139—21no—
130C4×D139—41no—
131C4×D139—42no—
132C4×D139—42no—
133C4×D139—42no—
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—42no—
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#463—1391no—
194#450—1391no—
195#447—1391no—
196#442—1391no—
197#442D13911yescharacteristic, complemented
198#440—1391no—
199#440—1391no—
200#432—1391no—
201C22×D4—1391no—
202C23×C4—2781no—
203C2×SD16—1391no—
204C2×SD16—1391no—
205C2×D8—1391no—
206C2×D8C2×D13911yescharacteristic
207#126—2781no—
208#125—1391no—
209#124—1391no—
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×D4C2×D13911yescharacteristic
221C4×D4C2×D13911yescharacteristic, complemented
222#117—2781no—
223C2×C4⋊C4—1391no—
224C2×C22⋊C4—2781no—
225C2×C42—1391no—
226#107—1391no—
227#107—1391no—
228#106—1391no—
229#106C2×D13911yescharacteristic, complemented
230C4⋊C8—1391no—
231C4⋊C8—1391no—
232#103—1391no—
233#103—1391no—
234#102—1391no—
235#102—1391no—
236#102—1391no—
237#102—1391no—
238#102C2×D13911yescharacteristic
239#102C2×D13911yescharacteristic, complemented
240C22⋊C8—1391no—
241C22⋊C8—1391no—
242#97—1391no—
243#97C2×D13911yescharacteristic, complemented
244C24—2781no—
245C2×Q8—1391no—
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—21no—
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—2782no—
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⋊C4C22×D13911yescharacteristic
279C4⋊C4C22×D13911yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—2781no—
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—2781no—
302Q8—2781no—
303D4—21no—
304D4—21no—
305D4—21no—
306D4—2784no—
307D4—2781no—
308D4—5562no—
309D4—1392no—
310D4#1455578512yes—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—2782no—
316C2×C4—2781no—
317C2×C4—2781no—
318C2×C4—2781no—
319C2×C4—2781no—
320C2×C4—2781no—
321C2×C4—5561no—
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×#1455578511yescharacteristic
362C2—42no—
363C2—81no—
364C2—2782no—
365C2—5562no—
366C2#2258146211yescharacteristic
367C2AGL(1,ℤ/8)×D13911yescharacteristic
368C2#2258174911yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#442×C139C2
socleC22×C139C22×D4
prime radical#22581085C2
hypercenter#442D139
hypocenterC139#3114
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. #22581485C2semidirect
2. C4×D4×D139C2semidirect
3. #22581285C2semidirect
4. #22581265C2semidirect
5. #22581252C2semidirect
6. #22581251C2semidirect
7. #22581167C2semidirect
8. #22581166C2semidirect
9. #22581105C2semidirect
11. #22581063C2semidirect
12. #22581055C2semidirect
13. #22581053C2semidirect
14. #22581008C2semidirect
15. #442×C139C2semidirect
22. #17984833C22semidirect
23. #17984829C22semidirect
27. C4×Dic278C22semidirect
38. #17984776C22semidirect
39. #17984775C22semidirect
40. #17984773C22semidirect
41. Dic139⋊C8C22semidirect
42. Dic139⋊C8C22semidirect
43. #17984767C22semidirect
44. #17984765C22semidirect
47. #17984763C22semidirect
51. #17984753C22semidirect
54. C4×D4×C139C22semidirect
55. #106×C139C22semidirect
57. #102×C139C22semidirect
58. #97×C139C22semidirect
184. C139#3114semidirect
197. #442D139semidirect
221. C4×D4C2×D139semidirect
229. #106C2×D139semidirect
239. #102C2×D139semidirect
243. #97C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225814852
C4×D4×D1392
#225812852
#225812652
#225812522
#225812512
#225811672
#225811662
#225811052
#225810852
#225810632
#225810552
#225810532
#225810082
#442×C1392
#3114139