Finite Group Databasebeta

← #31818370

Subgroups — #31818370

Order 17792.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581608C211yesmaximal, characteristic, complemented
2#22581598C211yesmaximal, characteristic, complemented
3#22581313C211yesmaximal, characteristic, complemented
4#22581285C211yesmaximal, characteristic, complemented
5#22581273C211yesmaximal, characteristic, complemented
6#22581243C211yesmaximal, characteristic, complemented
7#22581205C211yesmaximal, characteristic, complemented
8#22581181C211yesmaximal, characteristic, complemented
9#22581168C211yesmaximal, characteristic, complemented
10#22581095C211yesmaximal, characteristic, complemented
11#22581085C211yesmaximal, characteristic, complemented
12#22581026C211yesmaximal, characteristic, complemented
13#22580951C211yesmaximal, characteristic, complemented
14#102×D139C211yesmaximal, characteristic, complemented
15#442×C139C211yesmaximal, characteristic, complemented
16C2×#14555785—21no—
17C2×#14555784C2211yescharacteristic
18C2×D4×D139C2211yescharacteristic
19C2×#14555773C2211yescharacteristic, complemented
20C2×#14555770C2211yescharacteristic
21C2×#14555768C2211yescharacteristic, complemented
22C2×C8×D139C2211yescharacteristic
23#17984842C2211yescharacteristic, complemented
24#17984830C2211yescharacteristic
25#17984826—21no—
26#17984824—21no—
27#17984824—21no—
28#17984822C2211yescharacteristic
29#17984821—21no—
30#17984817C2211yescharacteristic
31#17984816—21no—
32#17984813C2211yescharacteristic
33#17984813C2211yescharacteristic, complemented
34#17984812—21no—
35C4×D556C2211yescharacteristic
36C4⋊C4×D139C2211yescharacteristic
37C4⋊C4×D139C2211yescharacteristic, complemented
38C2×(C2×D139)⋊C4—21no—
39#17984773C2211yescharacteristic, complemented
40#17984773C2211yescharacteristic, complemented
41C4⋊(C139⋊C8)C2211yescharacteristic, complemented
42#17984767C2211yescharacteristic, complemented
43#17984767C2211yescharacteristic, complemented
44#17984765C2211yescharacteristic, complemented
45#17984764C2211yescharacteristic
46#17984764C2211yescharacteristic
47#17984763C2211yescharacteristic
48#17984763C2211yescharacteristic
49#17984762C2211yescharacteristic
50(C2×D139)⋊C8C2211yescharacteristic
51(C2×D139)⋊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—
60#14555785—44no—
61#14555784—22no—
62#14555784—41no—
63C2×Dic278—21no—
64C2×Dic278C2311yescharacteristic
65C2×D556—21no—
66C2×D556D411yescharacteristic
67C2×D556C2311yescharacteristic
68C2×C22⋊D139—21no—
69C2×C22⋊D139—21no—
70C2×C22⋊D139—21no—
71C2×C22⋊D139—21no—
72D4×D139—22no—
73D4×D139—41no—
74C22×Dic139—21no—
75C2×C4×D139—21no—
76C2×C4×D139—21no—
77C2×C4×D139C2311yescharacteristic
78C2×C4×D139C2311yescharacteristic
79#14555773—41no—
80#14555770—41no—
81#14555768—41no—
82C2×C139⋊C8C2311yescharacteristic
83C2×C139⋊C8C2311yescharacteristic
84C8×D139—41no—
85C4⋊Dic139—21no—
86C4⋊Dic139—21no—
87C4⋊Dic139D411yescharacteristic
88C4⋊Dic139C2311yescharacteristic
89C4⋊Dic139C2311yescharacteristic
90Dic139⋊C4—21no—
91Dic139⋊C4—21no—
92C22⋊Dic139—21no—
93C22⋊Dic139—21no—
94(C2×D139)⋊C4—21no—
95(C2×D139)⋊C4—21no—
96(C2×D139)⋊C4—21no—
97(C2×D139)⋊C4—21no—
98(C2×D139)⋊C4D411yescharacteristic
99(C2×D139)⋊C4D411yescharacteristic
100C2×D4×C139C2311yescharacteristic
101C2×D4×C139C2311yescharacteristic
102C22×C4×C139—21no—
103C22×C4×C139—21no—
104D8×C139—22no—
105C2×C8×C139C2311yescharacteristic
106C2×C8×C139C2311yescharacteristic
107C4⋊C4×C139C2311yescharacteristic
108C4⋊C4×C139C2311yescharacteristic
109C22⋊C4×C139—21no—
110C22⋊C4×C139—21no—
111C42×C139C2311yescharacteristic
112C22×D139—21no—
113C22×D139—42no—
114C22×D139—42no—
115C22×D139—81no—
116C22×D139C2×D411yescharacteristic
117C22×D139C2×D411yescharacteristic
118Dic278—21no—
119Dic278—21no—
120Dic278—42no—
121D556—22no—
122D556—21no—
123D556—21no—
124D556—81no—
125C22⋊D139—42no—
126C22⋊D139—42no—
127C22⋊D139—42no—
128C22⋊D139—42no—
129C2×Dic139—21no—
130C2×Dic139—21no—
131C2×Dic139—21no—
132C2×Dic139—42no—
133C2×Dic139C2×D411yescharacteristic
134C2×Dic139C2×D411yescharacteristic
135C4×D139—21no—
136C4×D139—21no—
137C4×D139—21no—
138C4×D139—21no—
139C4×D139—42no—
140C4×D139—42no—
141C139⋊C8—21no—
142C139⋊C8—21no—
143C23×C139—21no—
144C23×C139—21no—
145D4×C139—21no—
146D4×C139—21no—
147D4×C139—21no—
148D4×C139#4112yescomplemented
149C2×C4×C139—21no—
150C2×C4×C139—21no—
151C2×C4×C139—42no—
152C2×C4×C139—81no—
153C2×C4×C139C2×D411yescharacteristic
154C2×C4×C139C2×D411yescharacteristic
155C2×C4×C139C2411yescharacteristic
156C8×C139—21no—
157C8×C139—21no—
158C22×C139—22no—
159C22×C139—41no—
160C22×C139—41no—
161C22×C139—41no—
162C22×C139—41no—
163C22×C139—41no—
164C22×C139C22×D411yescharacteristic
165C2×D139—21no—
166C2×D139—21no—
167C2×D139—21no—
168C2×D139—21no—
169C2×D139—21no—
170C2×D139—41no—
171C2×D139—41no—
172C2×D139—41no—
173C2×D139—84no—
174C2×D139AGL(1,ℤ/8)12yes—
175C4×C139—21no—
176C4×C139—21no—
177C4×C139—41no—
178C4×C139—41no—
179C4×C139C2×#4111yescharacteristic
180C4×C139H(5,𝔽2)11yescharacteristic
181Dic139—21no—
182Dic139—21no—
183Dic139—41no—
184Dic139—41no—
185Dic139—41no—
186C2×C139—42no—
187C2×C139—81no—
188C2×C139#54611yescharacteristic
189C2×C139C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C139#57711yescharacteristic
191D139—22no—
192D139—41no—
193D139—81no—
194C139#330611yescharacteristic, complemented, Sylow
195#3306—1391nomaximal, Sylow
196#547—1391no—
197#546—1391no—
198#489—1391no—
199#483—1391no—
200#481—1391no—
201#476—1391no—
202#469—1391no—
203#465—1391no—
204#463—1391no—
205#449—1391no—
206#447—1391no—
207#442D13911yescharacteristic, complemented
208#435—1391no—
209#417—1391no—
210C2×#102—1391no—
211C2×#41—2781no—
212C2×#41—1391no—
213C22×D4—1391no—
214C2×SD16—1391no—
215C2×D8—1391no—
216C2×D8C2×D13911yescharacteristic
217C2×M16—1391no—
218C22×C8—1391no—
219C4⋊Q8—1391no—
220#124—1391no—
221#123—2781no—
222#123—2781no—
223#123—2781no—
224C22⋊Q8—2781no—
225C22⋊Q8—1391no—
226#121—2781no—
227#121—1391no—
228#121—1391no—
229#121—1391no—
230#120—2781no—
231C4×D4—1391no—
232C4×D4C2×D13911yescharacteristic
233C4×D4C2×D13911yescharacteristic, complemented
234C2×C4⋊C4—1391no—
235C2×C4⋊C4—1391no—
236C2×C22⋊C4—2781no—
237#106—1391no—
238#106—1391no—
239#106C2×D13911yescharacteristic, complemented
240C4⋊C8—1391no—
241#103—1391no—
242#103—1391no—
243#103—1391no—
244#102—1391no—
245#102—1391no—
246#102—1391no—
247#102—1391no—
248#102—1391no—
249#102C2×D13911yescharacteristic
250#102C2×D13911yescharacteristic, complemented
251C22⋊C8—1391no—
252C22⋊C8—1391no—
253#97C2×D13911yescharacteristic, complemented
254C24—2781no—
255#41—2782no—
256#41—5564no—
257#41—5561no—
258C2×Q8—2781no—
259C2×Q8—1391no—
260C2×D4—2781no—
261C2×D4—2782no—
262C2×D4—2781no—
263C2×D4—2781no—
264C2×D4—2781no—
265C2×D4—2781no—
266C2×D4—5561no—
267C2×D4—1391no—
268C2×D4—1391no—
269C2×D4C22×D13911yescharacteristic
270C2×D4C22×D13911yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—2781no—
274C22×C4—2781no—
275C22×C4—2781no—
276C22×C4—1391no—
277C22×C4—1391no—
278SD16—5561no—
279D8—22no—
280D8—5561no—
281M16—5561no—
282C2×C8—5561no—
283C2×C8—1391no—
284C2×C8—1391no—
285C2×C8C22×D13911yescharacteristic
286C2×C8C22×D13911yescharacteristic
287C4⋊C4—2781no—
288C4⋊C4—2781no—
289C4⋊C4—2781no—
290C4⋊C4—2781no—
291C4⋊C4—1391no—
292C4⋊C4—1391no—
293C4⋊C4—1391no—
294C4⋊C4C22×D13911yescharacteristic
295C4⋊C4C22×D13911yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—2781no—
299C22⋊C4—2781no—
300C22⋊C4—2781no—
301C22⋊C4—2781no—
302C22⋊C4—2781no—
303C22⋊C4—2781no—
304C22⋊C4—1391no—
305C22⋊C4—1391no—
306C42C22×D13911yescharacteristic
307C23—21no—
308C23—21no—
309C23—2781no—
310C23—5562no—
311C23—5562no—
312C23—11121no—
313C23—1391no—
314C23—1391no—
315Q8—2781no—
316Q8—2781no—
317Q8—5562no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—2782no—
322D4—2781no—
323D4—2781no—
324D4—5562no—
325D4—5562no—
326D4—5562no—
327D4—5562no—
328D4—11121no—
329D4#1455578512yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—42no—
333C2×C4—81no—
334C2×C4—2781no—
335C2×C4—2781no—
336C2×C4—2781no—
337C2×C4—2781no—
338C2×C4—2781no—
339C2×C4—2781no—
340C2×C4—2781no—
341C2×C4—5562no—
342C2×C4—5562no—
343C2×C4—5562no—
344C2×C4—1391no—
345C2×C4—1391no—
346C2×C4D4×D13911yescharacteristic
347C2×C4D4×D13911yescharacteristic
348C2×C4C23×D13911yescharacteristic
349C8—21no—
350C8—21no—
351C8—2781no—
352C8—2781no—
353C22—22no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—2781no—
360C22—2781no—
361C22—2781no—
362C22—2781no—
363C22—2781no—
364C22—5561no—
365C22—5561no—
366C22—5561no—
367C22—11124no—
368C22—1392no—
369C22C2×D4×D13911yescharacteristic
370C4—21no—
371C4—21no—
372C4—41no—
373C4—41no—
374C4—2781no—
375C4—2781no—
376C4—5561no—
377C4—5561no—
378C4—5561no—
379C4C2×#1455578511yescharacteristic
380C4#1798488811yescharacteristic
381C2—42no—
382C2—81no—
383C2—2782no—
384C2—5561no—
385C2—11121no—
386C2#2258159911yescharacteristic
387C2AGL(1,ℤ/8)×D13911yescharacteristic
388C2#2258176311yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#442×C139C2
socleC22×C139C22×D4
hypercenter#442D139
hypocenterC139#3306
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. #22581608C2semidirect
2. #22581598C2semidirect
3. #22581313C2semidirect
4. #22581285C2semidirect
5. #22581273C2semidirect
6. #22581243C2semidirect
7. #22581205C2semidirect
8. #22581181C2semidirect
9. #22581168C2semidirect
10. #22581095C2semidirect
11. #22581085C2semidirect
12. #22581026C2semidirect
13. #22580951C2semidirect
14. #102×D139C2semidirect
15. #442×C139C2semidirect
19. C2×#14555773C22semidirect
21. C2×#14555768C22semidirect
23. #17984842C22semidirect
33. #17984813C22semidirect
37. C4⋊C4×D139C22semidirect
39. #17984773C22semidirect
40. #17984773C22semidirect
41. C4⋊(C139⋊C8)C22semidirect
42. #17984767C22semidirect
43. #17984767C22semidirect
44. #17984765C22semidirect
51. (C2×D139)⋊C8C22semidirect
54. C4×D4×C139C22semidirect
55. #106×C139C22semidirect
57. #102×C139C22semidirect
58. #97×C139C22semidirect
148. D4×C139#41semidirect
194. C139#3306semidirect
207. #442D139semidirect
233. C4×D4C2×D139semidirect
239. #106C2×D139semidirect
250. #102C2×D139semidirect
253. #97C2×D139semidirect
329. D4#14555785semidirect

Maximal subgroups

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

subgroupindex
#225816082
#225815982
#225813132
#225812852
#225812732
#225812432
#225812052
#225811812
#225811682
#225810952
#225810852
#225810262
#225809512
#102×D1392
#442×C1392
#3306139