Finite Group Databasebeta

← #31816586

Subgroups — #31816586

Order 17792.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581568C211yesmaximal, characteristic, complemented
2#22581425C211yesmaximal, characteristic, complemented
3#22581297C211yesmaximal, characteristic, complemented
4#22581275C211yesmaximal, characteristic, complemented
5#22581242C211yesmaximal, characteristic, complemented
6#22581231C211yesmaximal, characteristic, complemented
7#22581167C211yesmaximal, characteristic, complemented
8#22581166C211yesmaximal, characteristic, complemented
9#22581105C211yesmaximal, characteristic, complemented
10#22581085C211yesmaximal, characteristic
11#22581055C211yesmaximal, characteristic, complemented
12C4×#14555773C211yesmaximal, characteristic, complemented
13C4×#14555770C211yesmaximal, characteristic, complemented
14#22581015C211yesmaximal, characteristic, complemented
15#442×C139C211yesmaximal, characteristic, complemented
16C2×D4×D139C2211yescharacteristic
17C2×#14555774C2211yescharacteristic
18C2×#14555773C2211yescharacteristic
19C2×#14555770C2211yescharacteristic
20#17984841C2211yescharacteristic, complemented
21#17984835—21no—
22#17984829C2211yescharacteristic, complemented
23#17984828—21no—
24#17984825—21no—
25#17984822C2211yescharacteristic
26#17984821—21no—
27#17984813C2211yescharacteristic
28C4×Dic278C2211yescharacteristic, complemented
29C4×D556C2211yescharacteristic
30D4×Dic139C2211yescharacteristic
31#17984804C2211yescharacteristic
32C4×C22⋊D139—21no—
33(C22⋊D139)⋊C4—21no—
34#17984800C2211yescharacteristic
35#17984799C2211yescharacteristic
36C2×(C2×D139)⋊C4—21no—
37C22⋊C4×D139—21no—
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
51C4×C139⋊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—
60C2×Dic278—21no—
61C2×Dic278C2311yescharacteristic
62C2×D556C2311yescharacteristic
63C2×C22⋊D139—21no—
64C2×C22⋊D139—21no—
65D4×D139—22no—
66D4×D139—22no—
67C22×Dic139—21no—
68C2×C4×D139—21no—
69C2×C4×D139—21no—
70C2×C4×D139C2311yescharacteristic
71#14555774—22no—
72#14555773—22no—
73#14555770—22no—
74C2×C139⋊C8C2311yescharacteristic
75C2×C139⋊C8C2311yescharacteristic
76C4⋊Dic139—21no—
77C4⋊Dic139C2311yescharacteristic
78C4⋊Dic139C2311yescharacteristic
79Dic139⋊C4—21no—
80Dic139⋊C4—21no—
81Dic139⋊C4D411yescharacteristic
82Dic139⋊C4D411yescharacteristic
83C22⋊Dic139—21no—
84C22⋊Dic139—21no—
85C22⋊Dic139—21no—
86C22⋊Dic139—21no—
87(C2×D139)⋊C4—21no—
88(C2×D139)⋊C4—21no—
89(C2×D139)⋊C4—21no—
90(C2×D139)⋊C4—21no—
91(C2×D139)⋊C4D411yescharacteristic
92(C2×D139)⋊C4D411yescharacteristic
93C4×Dic139—21no—
94C4×Dic139—21no—
95C4×Dic139C2311yescharacteristic
96C2×D4×C139C2311yescharacteristic
97C2×D4×C139C2311yescharacteristic
98C22×C4×C139—21no—
99C22×C4×C139—21no—
100D8×C139—22no—
101C2×C8×C139C2311yescharacteristic
102C2×C8×C139C2311yescharacteristic
103C4⋊C4×C139C2311yescharacteristic
104C4⋊C4×C139C2311yescharacteristic
105C22⋊C4×C139—21no—
106C22⋊C4×C139—21no—
107C42×C139C2311yescharacteristic
108C22×D139—21no—
109C22×D139—24no—
110C22×D139—81no—
111C22×D139—81no—
112C22×D139C2×D411yescharacteristic
113Dic278—21no—
114Dic278—21no—
115Dic278—81no—
116D556—21no—
117D556#4112yes—
118C22⋊D139—24no—
119C22⋊D139—81no—
120C2×Dic139—21no—
121C2×Dic139—21no—
122C2×Dic139—21no—
123C2×Dic139—81no—
124C2×Dic139C2×D411yescharacteristic
125C2×Dic139C2×D411yescharacteristic
126C2×Dic139C2×D411yescharacteristic
127C4×D139—21no—
128C4×D139—21no—
129C4×D139—81no—
130C4×D139—81no—
131C139⋊C8—21no—
132C139⋊C8—21no—
133C23×C139—21no—
134C23×C139—21no—
135D4×C139—21no—
136D4×C139—21no—
137D4×C139—21no—
138D4×C139#4112yes—
139C2×C4×C139—21no—
140C2×C4×C139—21no—
141C2×C4×C139—81no—
142C2×C4×C139—81no—
143C2×C4×C139C2×D411yescharacteristic
144C2×C4×C139C2×D411yescharacteristic
145C2×C4×C139C2411yescharacteristic
146C8×C139—21no—
147C8×C139—21no—
148C22×C139—22no—
149C22×C139—41no—
150C22×C139—41no—
151C22×C139—41no—
152C22×C139—41no—
153C22×C139—41no—
154C22×C139C22×D411yescharacteristic
155C2×D139—21no—
156C2×D139—22no—
157C2×D139—21no—
158C2×D139—21no—
159C2×D139—41no—
160C2×D139—41no—
161C2×D139—84no—
162C4×C139—21no—
163C4×C139—21no—
164C4×C139—41no—
165C4×C139—41no—
166C4×C139C2×#4111yescharacteristic
167C4×C139C2×#4111yescharacteristic
168Dic139—21no—
169Dic139—21no—
170Dic139—21no—
171Dic139—41no—
172Dic139—41no—
173Dic139—41no—
174C2×C139—42no—
175C2×C139—81no—
176C2×C139#52511yescharacteristic
177C2×C139#57611yescharacteristic
178C2×C139#57711yescharacteristic
179D139—41no—
180D139—42no—
181C139#311811yescharacteristic, complemented, Sylow
182#3118—1391nomaximal, Sylow
183#542—1391no—
184#518—1391no—
185#485—1391no—
186#482—1391no—
187#476—1391no—
188#474—1391no—
189#463—1391no—
190#463—1391no—
191#450—1391no—
192#447—1391no—
193#442D13911yescharacteristic, complemented
194#440—1391no—
195C4×SD16—1391no—
196C4×D8—1391no—
197#433—1391no—
198C22×D4—1391no—
199C2×SD16—1391no—
200C2×SD16—1391no—
201C2×D8—1391no—
202C2×D8C2×D13911yescharacteristic
203C4⋊Q8—1391no—
204#126—2781no—
205#124—2781no—
206#124—1391no—
207#123—2781no—
208C22⋊Q8—2781no—
209C22⋊Q8—1391no—
210#121—1391no—
211C4×Q8—1391no—
212C4×D4—2781no—
213C4×D4—2781no—
214C4×D4—1391no—
215C4×D4—1391no—
216C4×D4—1391no—
217C4×D4C2×D13911yescharacteristic
218C4×D4C2×D13911yescharacteristic, complemented
219#117—1391no—
220#117—1391no—
221C2×C22⋊C4—2781no—
222C2×C22⋊C4—2781no—
223#107—1391no—
224#107—1391no—
225#106—1391no—
226#106C2×D13911yescharacteristic, complemented
227C4⋊C8—1391no—
228C4⋊C8—1391no—
229#103—1391no—
230#103—1391no—
231#102—1391no—
232#102—1391no—
233#102—1391no—
234#102—1391no—
235#102C2×D13911yescharacteristic
236#102C2×D13911yescharacteristic, complemented
237C22⋊C8—1391no—
238C22⋊C8—1391no—
239#97C2×D13911yescharacteristic, complemented
240C4×C8—1391no—
241C24—2781no—
242C2×Q8—2781no—
243C2×Q8—1391no—
244C2×D4—2782no—
245C2×D4—2782no—
246C2×D4—2781no—
247C2×D4—2781no—
248C2×D4—1391no—
249C2×D4C22×D13911yescharacteristic
250C2×D4C22×D13911yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—2781no—
254C22×C4—2781no—
255C22×C4—2781no—
256C22×C4—1391no—
257SD16—2782no—
258SD16—2782no—
259D8—22no—
260D8—2782no—
261C2×C8—1391no—
262C2×C8—1391no—
263C2×C8C22×D13911yescharacteristic
264C2×C8C22×D13911yescharacteristic
265C4⋊C4—2781no—
266C4⋊C4—2781no—
267C4⋊C4—2781no—
268C4⋊C4—1391no—
269C4⋊C4—1391no—
270C4⋊C4—1391no—
271C4⋊C4—1391no—
272C4⋊C4C22×D13911yescharacteristic
273C4⋊C4C22×D13911yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—2781no—
277C22⋊C4—2781no—
278C22⋊C4—2781no—
279C22⋊C4—2781no—
280C22⋊C4—2781no—
281C22⋊C4—2781no—
282C22⋊C4—2781no—
283C22⋊C4—2781no—
284C22⋊C4—1391no—
285C22⋊C4—1391no—
286C42—2781no—
287C42—2781no—
288C42—1391no—
289C42C22×D13911yescharacteristic
290C23—21no—
291C23—21no—
292C23—2784no—
293C23—2781no—
294C23—11121no—
295C23—11121no—
296C23—1391no—
297Q8—2781no—
298Q8—2781no—
299Q8—11121no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—2784no—
304D4—2781no—
305D4—11121no—
306D4—1392no—
307D4#1455578512yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—2781no—
313C2×C4—2781no—
314C2×C4—2781no—
315C2×C4—2781no—
316C2×C4—2781no—
317C2×C4—11121no—
318C2×C4—11121no—
319C2×C4—11121no—
320C2×C4—1391no—
321C2×C4—1391no—
322C2×C4—1391no—
323C2×C4D4×D13911yescharacteristic
324C2×C4D4×D13911yescharacteristic
325C2×C4C23×D13911yescharacteristic
326C8—21no—
327C8—21no—
328C8—2781no—
329C8—2781no—
330C22—22no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—2781no—
337C22—2781no—
338C22—2782no—
339C22—2781no—
340C22—5561no—
341C22—5561no—
342C22—11124no—
343C22C2×D4×D13911yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—2781no—
349C4—2781no—
350C4—2781no—
351C4—5561no—
352C4—5561no—
353C4—5561no—
354C4#41×D13911yescharacteristic
355C4C2×#1455578511yescharacteristic
356C2—42no—
357C2—81no—
358C2—5561no—
359C2—5562no—
360C2#2258146211yescharacteristic
361C2#2258175711yescharacteristic
362C2#2258176311yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#442×C139C2
socleC22×C139C22×D4
prime radical#22581085C2
hypercenter#442D139
hypocenterC139#3118
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. #22581568C2semidirect
2. #22581425C2semidirect
3. #22581297C2semidirect
4. #22581275C2semidirect
5. #22581242C2semidirect
6. #22581231C2semidirect
7. #22581167C2semidirect
8. #22581166C2semidirect
9. #22581105C2semidirect
11. #22581055C2semidirect
12. C4×#14555773C2semidirect
13. C4×#14555770C2semidirect
14. #22581015C2semidirect
15. #442×C139C2semidirect
20. #17984841C22semidirect
22. #17984829C22semidirect
28. C4×Dic278C22semidirect
38. #17984776C22semidirect
39. #17984775C22semidirect
40. #17984773C22semidirect
41. Dic139⋊C8C22semidirect
42. Dic139⋊C8C22semidirect
43. #17984767C22semidirect
44. #17984765C22semidirect
47. #17984763C22semidirect
51. C4×C139⋊C8C22semidirect
54. C4×D4×C139C22semidirect
55. #106×C139C22semidirect
57. #102×C139C22semidirect
58. #97×C139C22semidirect
181. C139#3118semidirect
193. #442D139semidirect
218. C4×D4C2×D139semidirect
226. #106C2×D139semidirect
236. #102C2×D139semidirect
239. #97C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225815682
#225814252
#225812972
#225812752
#225812422
#225812312
#225811672
#225811662
#225811052
#225810852
#225810552
C4×#145557732
C4×#145557702
#225810152
#442×C1392
#3118139