Finite Group Databasebeta

← #31818221

Subgroups — #31818221

Order 17792.

462 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581661C211yesmaximal, characteristic, complemented
2D4×C22⋊D139C211yesmaximal, characteristic
3#22581298C211yesmaximal, characteristic, complemented
4#22581272C211yesmaximal, characteristic, complemented
5#22581270C211yesmaximal, characteristic, complemented
6#22581241C211yesmaximal, characteristic, complemented
7#22581184C211yesmaximal, characteristic, complemented
8#22581179C211yesmaximal, characteristic, complemented
9#22581151C211yesmaximal, characteristic, complemented
10#22581102C211yesmaximal, characteristic, complemented
11SD16×Dic139C211yesmaximal, characteristic, complemented
12(C22⋊D139)⋊C8C211yesmaximal, characteristic, complemented
13C2×#17984763C211yesmaximal, characteristic, complemented
14#102×D139C211yesmaximal, characteristic, complemented
15#450×C139C211yesmaximal, characteristic, complemented
16C22×C22⋊D139—21no—
17C2×D4×D139C2211yescharacteristic
18C2×#14555772C2211yescharacteristic, complemented
19C22×C139⋊C8C2211yescharacteristic, complemented
20C2×C8×D139C2211yescharacteristic, complemented
21#17984841C2211yescharacteristic, complemented
22#17984838C2211yescharacteristic
23#17984832—21no—
24#17984822—21no—
25#17984819—21no—
26#17984818C2211yescharacteristic, complemented
27#17984816C2211yescharacteristic
28#17984814—21no—
29#17984813C2211yescharacteristic
30#17984811—21no—
31#17984810—21no—
32Q8×Dic139C2211yescharacteristic, complemented
33D4×Dic139C2211yescharacteristic
34C4×C22⋊D139C2211yescharacteristic
35(C22⋊D139)⋊C4—21no—
36C2×C4⋊Dic139C2211yescharacteristic, complemented
37C4⋊C4×D139C2211yescharacteristic, complemented
38#17984774C2211yescharacteristic, complemented
39#17984774C2211yescharacteristic, complemented
40#17984773C2211yescharacteristic, complemented
41Dic139⋊C8C2211yescharacteristic, complemented
42#17984766C2211yescharacteristic, complemented
43#17984764C2211yescharacteristic, complemented
44#17984764C2211yescharacteristic, complemented
45#17984763C2211yescharacteristic
46#17984763C2211yescharacteristic
47#17984763C2211yescharacteristic, complemented
48#17984763C2211yescharacteristic, complemented
49#17984762C2211yescharacteristic, complemented
50(C2×D139)⋊C8C2211yescharacteristic, complemented
51C8×Dic139C2211yescharacteristic, complemented
52C22×D4×C139C2211yescharacteristic
53C2×SD16×C139C2211yescharacteristic
54C2×SD16×C139C2211yescharacteristic, complemented
55C22⋊Q8×C139C2211yescharacteristic, complemented
56#102×C139C2211yescharacteristic
57#102×C139C2211yescharacteristic, complemented
58C22⋊C8×C139C2211yescharacteristic, complemented
59C23×D139—21no—
60C2×Dic278—21no—
61C2×D556C2311yescharacteristic
62C2×C22⋊D139—21no—
63C2×C22⋊D139—21no—
64C2×C22⋊D139—21no—
65C2×C22⋊D139—21no—
66C2×C22⋊D139—21no—
67C2×C22⋊D139—44no—
68C2×C22⋊D139D411yescharacteristic
69D4×D139—22no—
70D4×D139—41no—
71C22×Dic139—21no—
72C22×Dic139—21no—
73C2×C4×D139—21no—
74C2×C4×D139C2311yescharacteristic
75#14555772—41no—
76C2×C139⋊C8—41no—
77C2×C139⋊C8C2311yescharacteristic
78C2×C139⋊C8C2311yescharacteristic
79C8×D139—41no—
80C4⋊Dic139—21no—
81C4⋊Dic139—21no—
82C4⋊Dic139C2311yescharacteristic
83C4⋊Dic139C2311yescharacteristic
84C4⋊Dic139C2311yescharacteristic
85Dic139⋊C4—21no—
86Dic139⋊C4—21no—
87Dic139⋊C4—21no—
88Dic139⋊C4D411yescharacteristic
89C22⋊Dic139—21no—
90C22⋊Dic139—21no—
91C22⋊Dic139D411yescharacteristic
92(C2×D139)⋊C4—21no—
93(C2×D139)⋊C4—21no—
94(C2×D139)⋊C4D411yescharacteristic
95C4×Dic139—21no—
96C4×Dic139C2311yescharacteristic
97C24×C139—21no—
98C2×Q8×C139C2311yescharacteristic
99C2×D4×C139—22no—
100C2×D4×C139—21no—
101C2×D4×C139—41no—
102C2×D4×C139C2311yescharacteristic
103C2×D4×C139C2311yescharacteristic
104C22×C4×C139C2311yescharacteristic
105SD16×C139—22no—
106SD16×C139—41no—
107C2×C8×C139C2311yescharacteristic
108C2×C8×C139C2311yescharacteristic
109C4⋊C4×C139—21no—
110C4⋊C4×C139C2311yescharacteristic
111C22⋊C4×C139—21no—
112C22×D139—21no—
113C22×D139—42no—
114C22×D139—42no—
115C22×D139—81no—
116C22×D139C2×D411yescharacteristic
117Dic278—81no—
118D556—21no—
119D556—21no—
120C22⋊D139—42no—
121C22⋊D139—42no—
122C22⋊D139—42no—
123C22⋊D139—42no—
124C22⋊D139—81no—
125C22⋊D139SD1614yescomplemented
126C2×Dic139—21no—
127C2×Dic139—21no—
128C2×Dic139—21no—
129C2×Dic139—42no—
130C2×Dic139—81no—
131C2×Dic139C2×D411yescharacteristic
132C2×Dic139C2×D411yescharacteristic
133C2×Dic139C2×D411yescharacteristic
134C4×D139—21no—
135C4×D139—21no—
136C4×D139—81no—
137C139⋊C8—21no—
138C139⋊C8—21no—
139C23×C139—21no—
140C23×C139—21no—
141C23×C139—42no—
142C23×C139—42no—
143C23×C139—81no—
144C23×C139C2×D411yescharacteristic
145Q8×C139—21no—
146Q8×C139—21no—
147D4×C139—21no—
148D4×C139—21no—
149D4×C139—21no—
150D4×C139—42no—
151D4×C139#4112yes—
152C2×C4×C139—21no—
153C2×C4×C139—21no—
154C2×C4×C139—21no—
155C2×C4×C139—21no—
156C2×C4×C139C2×D411yescharacteristic
157C2×C4×C139C2411yescharacteristic
158C8×C139—21no—
159C8×C139—21no—
160C22×C139—21no—
161C22×C139—21no—
162C22×C139—22no—
163C22×C139—41no—
164C22×C139—41no—
165C22×C139—41no—
166C22×C139—41no—
167C22×C139—41no—
168C22×C139—84no—
169C22×C139C2×SD1612yes—
170C22×C139C22×D411yescharacteristic
171C2×D139—21no—
172C2×D139—21no—
173C2×D139—41no—
174C2×D139—41no—
175C2×D139—41no—
176C2×D139—84no—
177C2×D139C2×SD1612yes—
178C4×C139—21no—
179C4×C139—41no—
180C4×C139—41no—
181C4×C139C2×#4111yescharacteristic
182C4×C139H(5,𝔽2)11yescharacteristic
183Dic139—21no—
184Dic139—21no—
185Dic139—41no—
186Dic139—41no—
187Dic139—41no—
188Dic139C2×SD1612yes—
189C2×C139—22no—
190C2×C139—42no—
191C2×C139—81no—
192C2×C139#54611yescharacteristic
193C2×C139C22×SD1611yescharacteristic
194C2×C139#57611yescharacteristic
195D139—22no—
196D139—81no—
197C139#329511yescharacteristic, complemented, Sylow
198#3295—1391nomaximal, Sylow
199#554—1391no—
200D42—1391no—
201#486—1391no—
202#481—1391no—
203#481—1391no—
204#476—1391no—
205#465—1391no—
206#465—1391no—
207#460—1391no—
208#450—1391no—
209#450D13911yescharacteristic, complemented
210C4×SD16—1391no—
211C8×D4—1391no—
212C2×#102—1391no—
213C2×#102—1391no—
214C22×D4—2781no—
215C22×D4—1391no—
216C22×D4C2×D13911yescharacteristic
217C2×SD16—1391no—
218C2×SD16C2×D13911yescharacteristic
219C2×SD16C2×D13911yescharacteristic, complemented
220C22×C8—1391no—
221C22×C8—1391no—
222C4⋊Q8—1391no—
223#127—1391no—
224#125—2781no—
225C22⋊Q8—2781no—
226C22⋊Q8—2781no—
227C22⋊Q8—1391no—
228C22⋊Q8C2×D13911yescharacteristic, complemented
229#121—2781no—
230#121—1391no—
231#121—1391no—
232#120—2781no—
233#120—2781no—
234C4×Q8—1391no—
235C4×D4—2781no—
236C4×D4—1391no—
237C4×D4—1391no—
238C2×C4⋊C4—1391no—
239C2×C4⋊C4—1391no—
240#106—1391no—
241#106—1391no—
242#106—1391no—
243C4⋊C8—1391no—
244#103—1391no—
245#102—1391no—
246#102—1391no—
247#102—1391no—
248#102—1391no—
249#102—1391no—
250#102—1391no—
251#102—1391no—
252#102C2×D13911yescharacteristic
253#102C2×D13911yescharacteristic, complemented
254C22⋊C8—1391no—
255C22⋊C8C2×D13911yescharacteristic, complemented
256C4×C8—1391no—
257C24—21no—
258C24—2781no—
259C2×Q8—2781no—
260C2×Q8C22×D13911yescharacteristic
261C2×D4—22no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—2782no—
265C2×D4—2781no—
266C2×D4—2781no—
267C2×D4—2781no—
268C2×D4—2781no—
269C2×D4—2781no—
270C2×D4—5561no—
271C2×D4—5564no—
272C2×D4—1391no—
273C2×D4—1391no—
274C2×D4C22×D13911yescharacteristic
275C2×D4C22×D13911yescharacteristic
276C22×C4—2781no—
277C22×C4—2781no—
278C22×C4—2781no—
279C22×C4—1391no—
280C22×C4C22×D13911yescharacteristic
281SD16—22no—
282SD16—41no—
283SD16—5561no—
284C2×C8—5561no—
285C2×C8—5561no—
286C2×C8—1391no—
287C2×C8—1391no—
288C2×C8C22×D13911yescharacteristic
289C2×C8C22×D13911yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—2781no—
292C4⋊C4—2781no—
293C4⋊C4—2781no—
294C4⋊C4—2781no—
295C4⋊C4—2781no—
296C4⋊C4—1391no—
297C4⋊C4—1391no—
298C4⋊C4—1391no—
299C4⋊C4—1391no—
300C4⋊C4C22×D13911yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—2781no—
303C22⋊C4—2781no—
304C22⋊C4—2781no—
305C22⋊C4—2781no—
306C22⋊C4—1391no—
307C22⋊C4—1391no—
308C42—2781no—
309C42—1391no—
310C23—21no—
311C23—21no—
312C23—42no—
313C23—42no—
314C23—81no—
315C23—2781no—
316C23—5562no—
317C23—5562no—
318C23—11121no—
319C23—1391no—
320C23D4×D13911yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—11121no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—42no—
328D4—2781no—
329D4—2781no—
330D4—5562no—
331D4—5562no—
332D4—5562no—
333D4—5562no—
334D4—11121no—
335D4—1394no—
336D4#1455578412yes—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—2781no—
342C2×C4—2781no—
343C2×C4—2781no—
344C2×C4—2781no—
345C2×C4—2781no—
346C2×C4—5562no—
347C2×C4—11121no—
348C2×C4—11121no—
349C2×C4—1391no—
350C2×C4—1391no—
351C2×C4—1391no—
352C2×C4D4×D13911yescharacteristic
353C2×C4C23×D13911yescharacteristic
354C8—21no—
355C8—21no—
356C8—2781no—
357C8—2781no—
358C22—21no—
359C22—21no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—84no—
367C22—2781no—
368C22—2781no—
369C22—5561no—
370C22—5561no—
371C22—5561no—
372C22—11124no—
373C22—1392no—
374C22SD16×D13912yes—
375C22C2×D4×D13911yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—2781no—
380C4—2781no—
381C4—5561no—
382C4—5561no—
383C4—5561no—
384C4—1392no—
385C4C2×#1455578411yescharacteristic
386C4#1798488711yescharacteristic
387C2—22no—
388C2—42no—
389C2—81no—
390C2—2782no—
391C2—11121no—
392C2#2258159011yescharacteristic
393C2C2×SD16×D13911yescharacteristic
394C2#2258175711yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#450×C139C2
socleC22×C139C22×D4
prime radicalD4×C22⋊D139C2
hypercenter#450D139
hypocenterC139#3295
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #22581661C2semidirect
3. #22581298C2semidirect
4. #22581272C2semidirect
5. #22581270C2semidirect
6. #22581241C2semidirect
7. #22581184C2semidirect
8. #22581179C2semidirect
9. #22581151C2semidirect
10. #22581102C2semidirect
11. SD16×Dic139C2semidirect
12. (C22⋊D139)⋊C8C2semidirect
13. C2×#17984763C2semidirect
14. #102×D139C2semidirect
15. #450×C139C2semidirect
18. C2×#14555772C22semidirect
19. C22×C139⋊C8C22semidirect
20. C2×C8×D139C22semidirect
21. #17984841C22semidirect
26. #17984818C22semidirect
32. Q8×Dic139C22semidirect
36. C2×C4⋊Dic139C22semidirect
37. C4⋊C4×D139C22semidirect
38. #17984774C22semidirect
39. #17984774C22semidirect
40. #17984773C22semidirect
41. Dic139⋊C8C22semidirect
42. #17984766C22semidirect
43. #17984764C22semidirect
44. #17984764C22semidirect
47. #17984763C22semidirect
48. #17984763C22semidirect
49. #17984762C22semidirect
50. (C2×D139)⋊C8C22semidirect
51. C8×Dic139C22semidirect
54. C2×SD16×C139C22semidirect
55. C22⋊Q8×C139C22semidirect
57. #102×C139C22semidirect
58. C22⋊C8×C139C22semidirect
125. C22⋊D139SD16semidirect
197. C139#3295semidirect
209. #450D139semidirect
219. C2×SD16C2×D139semidirect
228. C22⋊Q8C2×D139semidirect
253. #102C2×D139semidirect
255. C22⋊C8C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225816612
D4×C22⋊D1392
#225812982
#225812722
#225812702
#225812412
#225811842
#225811792
#225811512
#225811022
SD16×Dic1392
(C22⋊D139)⋊C82
C2×#179847632
#102×D1392
#450×C1392
#3295139