Finite Group Databasebeta

← #31818367

Subgroups — #31818367

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#22581607C211yesmaximal, characteristic, complemented
2#22581599C211yesmaximal, characteristic, complemented
3#22581313C211yesmaximal, characteristic, complemented
4#22581284C211yesmaximal, characteristic, complemented
5#22581272C211yesmaximal, characteristic, complemented
6#22581244C211yesmaximal, characteristic, complemented
7#22581206C211yesmaximal, characteristic, complemented
8#22581182C211yesmaximal, characteristic, complemented
9#22581169C211yesmaximal, characteristic, complemented
10#22581100C211yesmaximal, characteristic, complemented
11#22581089C211yesmaximal, characteristic, complemented
12#22581066C211yesmaximal, characteristic, complemented
13#22580955C211yesmaximal, characteristic, complemented
14C2×#17984764C211yesmaximal, characteristic, complemented
15#435×C139C211yesmaximal, characteristic, complemented
16C2×#14555785C2211yescharacteristic
17C2×#14555784—21no—
18C22×D556C2211yescharacteristic
19C2×#14555774C2211yescharacteristic, complemented
20C2×D1112C2211yescharacteristic
21C2×D1112C2211yescharacteristic
22#17984842C2211yescharacteristic, complemented
23#17984830C2211yescharacteristic
24#17984827—21no—
25#17984826—21no—
26#17984826—21no—
27#17984822—21no—
28#17984821C2211yescharacteristic
29#17984816C2211yescharacteristic
30#17984816C2211yescharacteristic
31#17984816C2211yescharacteristic, complemented
32#17984815—21no—
33#17984810—21no—
34C4×D556C2211yescharacteristic
35C4×D556C2211yescharacteristic, complemented
36C2×C4⋊Dic139C2211yescharacteristic
37C2×C4⋊Dic139C2211yescharacteristic, complemented
38C22⋊C4×D139—21no—
39#17984774C2211yescharacteristic, complemented
40#17984774C2211yescharacteristic, complemented
41#17984774C2211yescharacteristic, complemented
42#17984767C2211yescharacteristic, complemented
43#17984767C2211yescharacteristic, complemented
44#17984767C2211yescharacteristic, complemented
45#17984764C2211yescharacteristic
46#17984764C2211yescharacteristic
47#17984764C2211yescharacteristic
48#17984764C2211yescharacteristic
49#17984764C2211yescharacteristic
50#17984764C2211yescharacteristic
51#17984764C2211yescharacteristic, complemented
52C2×M16×C139C2211yescharacteristic, complemented
53C22×C8×C139C2211yescharacteristic
54C4×D4×C139C2211yescharacteristic
55C4⋊C8×C139C2211yescharacteristic, complemented
56C22⋊C8×C139C2211yescharacteristic
57C22⋊C8×C139C2211yescharacteristic, complemented
58#97×C139C2211yescharacteristic, complemented
59C23×D139—21no—
60#14555785—22no—
61#14555785—41no—
62#14555784—44no—
63C2×Dic278—21no—
64C2×Dic278C2311yescharacteristic
65C2×D556—22no—
66C2×D556—21no—
67C2×D556—41no—
68C2×D556C2311yescharacteristic
69C2×D556C2311yescharacteristic
70C2×D556C2311yescharacteristic
71C2×C22⋊D139—21no—
72C2×C22⋊D139—21no—
73C2×C22⋊D139—21no—
74C2×C22⋊D139—21no—
75C22×Dic139—21no—
76C22×Dic139—21no—
77C2×C4×D139—21no—
78C2×C4×D139—21no—
79C2×C4×D139—21no—
80#14555774—41no—
81D1112—22no—
82D1112—41no—
83C4⋊Dic139—21no—
84C4⋊Dic139—21no—
85C4⋊Dic139—21no—
86C4⋊Dic139C2311yescharacteristic
87C4⋊Dic139C2311yescharacteristic
88C4⋊Dic139C2311yescharacteristic
89C4⋊Dic139C2311yescharacteristic
90Dic139⋊C4—21no—
91C22⋊Dic139—21no—
92(C2×D139)⋊C4—21no—
93(C2×D139)⋊C4—21no—
94(C2×D139)⋊C4—21no—
95(C2×D139)⋊C4—21no—
96(C2×D139)⋊C4—21no—
97(C2×D139)⋊C4—21no—
98(C2×D139)⋊C4—21no—
99C2×D4×C139D411yescharacteristic
100C22×C4×C139C2311yescharacteristic
101C22×C4×C139C2311yescharacteristic
102M16×C139—41no—
103C2×C8×C139—41no—
104C2×C8×C139C2311yescharacteristic
105C2×C8×C139C2311yescharacteristic
106C2×C8×C139C2311yescharacteristic
107C2×C8×C139C2311yescharacteristic
108C4⋊C4×C139D411yescharacteristic
109C22⋊C4×C139D411yescharacteristic
110C22⋊C4×C139D411yescharacteristic
111C42×C139C2311yescharacteristic
112C22×D139—21no—
113C22×D139—21no—
114C22×D139—21no—
115C22×D139—42no—
116C22×D139—42no—
117C22×D139—81no—
118Dic278—21no—
119Dic278—21no—
120Dic278—42no—
121D556—21no—
122D556—21no—
123D556—21no—
124D556—21no—
125D556—21no—
126D556—42no—
127D556#4112yescomplemented
128C22⋊D139—42no—
129C22⋊D139—42no—
130C22⋊D139—42no—
131C22⋊D139—81no—
132C2×Dic139—21no—
133C2×Dic139—21no—
134C2×Dic139—21no—
135C2×Dic139—21no—
136C2×Dic139—21no—
137C2×Dic139—42no—
138C2×Dic139—42no—
139C4×D139—42no—
140C4×D139—42no—
141C4×D139—81no—
142C23×C139C2×D411yescharacteristic
143C23×C139C2×D411yescharacteristic
144D4×C139—22no—
145C2×C4×C139—21no—
146C2×C4×C139—21no—
147C2×C4×C139—21no—
148C2×C4×C139—21no—
149C2×C4×C139C2×D411yescharacteristic
150C2×C4×C139C2×D411yescharacteristic
151C2×C4×C139C2×D411yescharacteristic
152C2×C4×C139C2×D411yescharacteristic
153C2×C4×C139C2411yescharacteristic
154C8×C139—21no—
155C8×C139—21no—
156C8×C139—21no—
157C8×C139—21no—
158C22×C139—21no—
159C22×C139—21no—
160C22×C139—21no—
161C22×C139—21no—
162C22×C139—21no—
163C22×C139AGL(1,ℤ/8)12yes—
164C22×C139C22×D411yescharacteristic
165C2×D139—22no—
166C2×D139—41no—
167C2×D139—41no—
168C2×D139—41no—
169C2×D139—41no—
170C2×D139—41no—
171C2×D139—41no—
172C2×D139—41no—
173C2×D139—41no—
174C2×D139—84no—
175C4×C139—21no—
176C4×C139—21no—
177C4×C139—21no—
178C4×C139—21no—
179C4×C139C2×#4111yescharacteristic
180C4×C139H(5,𝔽2)11yescharacteristic
181Dic139—41no—
182Dic139—41no—
183Dic139—41no—
184Dic139—41no—
185Dic139—41no—
186C2×C139—22no—
187C2×C139—41no—
188C2×C139#54611yescharacteristic
189C2×C139C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C139#57711yescharacteristic
191D139—42no—
192D139—81no—
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#442—1391no—
208#435D13911yescharacteristic, complemented
209#417—1391no—
210C2×#102—1391no—
211C2×#41—2781no—
212C2×#41—1391no—
213C22×D4—1391no—
214C2×SD16—1391no—
215C2×D8—1391no—
216C2×D8—1391no—
217C2×M16C2×D13911yescharacteristic, complemented
218C22×C8C2×D13911yescharacteristic
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×D4—1391no—
233C4×D4C2×D13911yescharacteristic
234C2×C4⋊C4—1391no—
235C2×C4⋊C4—1391no—
236C2×C22⋊C4—2781no—
237#106—1391no—
238#106—1391no—
239#106—1391no—
240C4⋊C8C2×D13911yescharacteristic, complemented
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#102—1391no—
250#102—1391no—
251C22⋊C8C2×D13911yescharacteristic
252C22⋊C8C2×D13911yescharacteristic, complemented
253#97C2×D13911yescharacteristic, complemented
254C24—2781no—
255#41—2782no—
256#41—5561no—
257#41—5564no—
258C2×Q8—2781no—
259C2×Q8—1391no—
260C2×D4—2782no—
261C2×D4—2781no—
262C2×D4—2781no—
263C2×D4—2781no—
264C2×D4—2781no—
265C2×D4—2781no—
266C2×D4—5561no—
267C2×D4—1391no—
268C2×D4—1391no—
269C2×D4—1391no—
270C2×D4D55611yescharacteristic
271C22×C4—2781no—
272C22×C4—2781no—
273C22×C4—2781no—
274C22×C4—2781no—
275C22×C4—2781no—
276C22×C4C22×D13911yescharacteristic
277C22×C4C22×D13911yescharacteristic
278SD16—5561no—
279D8—2782no—
280D8—5561no—
281M16—41no—
282C2×C8—41no—
283C2×C8C22×D13911yescharacteristic
284C2×C8C22×D13911yescharacteristic
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⋊C4—1391no—
295C4⋊C4D55611yescharacteristic
296C22⋊C4—2781no—
297C22⋊C4—2781no—
298C22⋊C4—2781no—
299C22⋊C4—2781no—
300C22⋊C4—2781no—
301C22⋊C4—2781no—
302C22⋊C4—2781no—
303C22⋊C4—2781no—
304C22⋊C4D55611yescharacteristic
305C22⋊C4D55611yescharacteristic
306C42C22×D13911yescharacteristic
307C23—2781no—
308C23—2781no—
309C23—2781no—
310C23—5562no—
311C23—5562no—
312C23—11121no—
313C23C2×D55611yescharacteristic
314C23C2×D55611yescharacteristic
315Q8—2781no—
316Q8—2781no—
317Q8—5562no—
318D4—22no—
319D4—2781no—
320D4—2781no—
321D4—2781no—
322D4—2781no—
323D4—2781no—
324D4—5562no—
325D4—5562no—
326D4—5562no—
327D4—5562no—
328D4—11121no—
329D4—1392no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—2781no—
335C2×C4—2781no—
336C2×C4—2781no—
337C2×C4—2781no—
338C2×C4—2781no—
339C2×C4—5562no—
340C2×C4—5562no—
341C2×C4—5562no—
342C2×C4—5562no—
343C2×C4—11121no—
344C2×C4C2×D55611yescharacteristic
345C2×C4C2×D55611yescharacteristic
346C2×C4C2×D55611yescharacteristic
347C2×C4C2×D55611yescharacteristic
348C2×C4C23×D13911yescharacteristic
349C8—21no—
350C8—21no—
351C8—21no—
352C8—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—2782no—
359C22—5561no—
360C22—5561no—
361C22—5561no—
362C22—5561no—
363C22—5561no—
364C22—5561no—
365C22—5561no—
366C22—5561no—
367C22—11124no—
368C22#1798487012yes—
369C22C22×D55611yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—5561no—
375C4—5561no—
376C4—5561no—
377C4—5561no—
378C4—5561no—
379C4#41×D13911yescharacteristic
380C4#1798488711yescharacteristic
381C2—22no—
382C2—41no—
383C2—5562no—
384C2—11121no—
385C2—11121no—
386C2#2258159811yescharacteristic
387C2C2×#1798487011yescharacteristic
388C2#2258176511yescharacteristic
subgroupG/H
centerC22C22×D556
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#435×C139C2
socleC22×C139C22×D4
hypercenter#435D139
hypocenterC139#3306
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #22581607C2semidirect
2. #22581599C2semidirect
3. #22581313C2semidirect
4. #22581284C2semidirect
5. #22581272C2semidirect
6. #22581244C2semidirect
7. #22581206C2semidirect
8. #22581182C2semidirect
9. #22581169C2semidirect
10. #22581100C2semidirect
11. #22581089C2semidirect
12. #22581066C2semidirect
13. #22580955C2semidirect
14. C2×#17984764C2semidirect
15. #435×C139C2semidirect
19. C2×#14555774C22semidirect
22. #17984842C22semidirect
31. #17984816C22semidirect
35. C4×D556C22semidirect
37. C2×C4⋊Dic139C22semidirect
39. #17984774C22semidirect
40. #17984774C22semidirect
41. #17984774C22semidirect
42. #17984767C22semidirect
43. #17984767C22semidirect
44. #17984767C22semidirect
51. #17984764C22semidirect
52. C2×M16×C139C22semidirect
55. C4⋊C8×C139C22semidirect
57. C22⋊C8×C139C22semidirect
58. #97×C139C22semidirect
127. D556#41semidirect
194. C139#3306semidirect
208. #435D139semidirect
217. C2×M16C2×D139semidirect
240. C4⋊C8C2×D139semidirect
252. C22⋊C8C2×D139semidirect
253. #97C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225816072
#225815992
#225813132
#225812842
#225812722
#225812442
#225812062
#225811822
#225811692
#225811002
#225810892
#225810662
#225809552
C2×#179847642
#435×C1392
#3306139