Finite Group Databasebeta

← #31816590

Subgroups — #31816590

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#22581574C211yesmaximal, characteristic, complemented
2#22581427C211yesmaximal, characteristic, complemented
3#22581295C211yesmaximal, characteristic, complemented
4#22581278C211yesmaximal, characteristic, complemented
5#22581244C211yesmaximal, characteristic, complemented
6#22581234C211yesmaximal, characteristic, complemented
7#22581169C211yesmaximal, characteristic, complemented
8#22581169C211yesmaximal, characteristic, complemented
9#22581106C211yesmaximal, characteristic, complemented
10#22581089C211yesmaximal, characteristic
11#22581066C211yesmaximal, characteristic, complemented
12#22581055C211yesmaximal, characteristic, complemented
13C4×#14555774C211yesmaximal, characteristic, complemented
14C4×D1112C211yesmaximal, characteristic, complemented
15#433×C139C211yesmaximal, characteristic, complemented
16C22×D556C2211yescharacteristic
17C2×#14555774C2211yescharacteristic
18C2×#14555774C2211yescharacteristic
19C2×D1112C2211yescharacteristic
20C2×D1112C2211yescharacteristic
21#17984842C2211yescharacteristic, complemented
22#17984837—21no—
23#17984830C2211yescharacteristic, complemented
24#17984828—21no—
25#17984824—21no—
26#17984821C2211yescharacteristic
27#17984820—21no—
28#17984816C2211yescharacteristic
29C4×Dic278C2211yescharacteristic, complemented
30C4×D556C2211yescharacteristic
31C4×D556C2211yescharacteristic
32C4×D556C2211yescharacteristic
33C4×D556C2211yescharacteristic
34C4×D556C2211yescharacteristic, complemented
35#17984804—21no—
36#17984804—21no—
37#17984801C2211yescharacteristic
38C22⋊C4×D139—21no—
39C22⋊C4×D139—21no—
40#17984776C2211yescharacteristic, complemented
41#17984776C2211yescharacteristic, complemented
42#17984774C2211yescharacteristic, complemented
43#17984774C2211yescharacteristic, complemented
44#17984767C2211yescharacteristic, complemented
45#17984767C2211yescharacteristic, complemented
46#17984764C2211yescharacteristic
47#17984764C2211yescharacteristic
48#17984764C2211yescharacteristic
49#17984764C2211yescharacteristic
50#17984764C2211yescharacteristic, complemented
51#17984764C2211yescharacteristic, complemented
52#117×C139C2211yescharacteristic
53C4⋊C8×C139C2211yescharacteristic, complemented
54C4⋊C8×C139C2211yescharacteristic, complemented
55C22⋊C8×C139C2211yescharacteristic
56C22⋊C8×C139C2211yescharacteristic
57#97×C139C2211yescharacteristic, complemented
58C4×C8×C139C2211yescharacteristic, complemented
59C23×D139—21no—
60C2×Dic278—21no—
61C2×Dic278C2311yescharacteristic
62C2×D556—22no—
63C2×D556—22no—
64C2×D556—21no—
65C2×D556C2311yescharacteristic
66C2×D556C2311yescharacteristic
67C2×D556C2311yescharacteristic
68C2×C22⋊D139—21no—
69C2×C4×D139—21no—
70C2×C4×D139—21no—
71C2×C4×D139—21no—
72C2×C4×D139—21no—
73C2×C4×D139—21no—
74#14555774—22no—
75#14555774—22no—
76D1112—22no—
77D1112—22no—
78C4⋊Dic139—21no—
79C4⋊Dic139C2311yescharacteristic
80C4⋊Dic139C2311yescharacteristic
81C4⋊Dic139C2311yescharacteristic
82C4⋊Dic139C2311yescharacteristic
83Dic139⋊C4—21no—
84Dic139⋊C4—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)⋊C4—21no—
92(C2×D139)⋊C4—21no—
93(C2×D139)⋊C4—21no—
94(C2×D139)⋊C4—21no—
95C4×Dic139—21no—
96C4×Dic139—21no—
97C22×C4×C139C2311yescharacteristic
98C2×C8×C139C2311yescharacteristic
99C2×C8×C139C2311yescharacteristic
100C2×C8×C139C2311yescharacteristic
101C2×C8×C139C2311yescharacteristic
102C4⋊C4×C139D411yescharacteristic
103C4⋊C4×C139D411yescharacteristic
104C22⋊C4×C139D411yescharacteristic
105C22⋊C4×C139D411yescharacteristic
106C42×C139C2311yescharacteristic
107C42×C139C2311yescharacteristic
108C22×D139—21no—
109C22×D139—21no—
110C22×D139—24no—
111C22×D139—21no—
112C22×D139—81no—
113C22×D139—81no—
114Dic278—21no—
115Dic278—21no—
116Dic278—81no—
117D556—24no—
118D556—21no—
119D556—21no—
120D556—21no—
121D556—21no—
122D556#4112yes—
123D556#4112yes—
124C22⋊D139—81no—
125C2×Dic139—21no—
126C2×Dic139—21no—
127C2×Dic139—21no—
128C2×Dic139—21no—
129C2×Dic139—21no—
130C4×D139—81no—
131C4×D139—81no—
132C4×D139—81no—
133C4×D139—81no—
134C4×D139—81no—
135C23×C139C2×D411yescharacteristic
136C2×C4×C139—21no—
137C2×C4×C139—21no—
138C2×C4×C139C2×D411yescharacteristic
139C2×C4×C139C2×D411yescharacteristic
140C2×C4×C139C2×D411yescharacteristic
141C2×C4×C139C2×D411yescharacteristic
142C2×C4×C139C2×D411yescharacteristic
143C2×C4×C139C2411yescharacteristic
144C8×C139—21no—
145C8×C139—21no—
146C8×C139—21no—
147C8×C139—21no—
148C22×C139—21no—
149C22×C139—21no—
150C22×C139—21no—
151C22×C139C22×D411yescharacteristic
152C2×D139—22no—
153C2×D139—22no—
154C2×D139—41no—
155C2×D139—41no—
156C2×D139—41no—
157C2×D139—41no—
158C2×D139—41no—
159C2×D139—41no—
160C2×D139—41no—
161C2×D139—84no—
162C4×C139—21no—
163C4×C139—21no—
164C4×C139—21no—
165C4×C139—21no—
166C4×C139—21no—
167C4×C139C2×#4111yescharacteristic
168C4×C139C2×#4111yescharacteristic
169Dic139—41no—
170Dic139—41no—
171Dic139—41no—
172Dic139—41no—
173Dic139—41no—
174C2×C139—41no—
175C2×C139#52511yescharacteristic
176C2×C139#57611yescharacteristic
177C2×C139#57711yescharacteristic
178D139—42no—
179D139—42no—
180D139—81no—
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#442—1391no—
194#440—1391no—
195C4×SD16—1391no—
196C4×D8—1391no—
197#433D13911yescharacteristic, complemented
198C22×D4—1391no—
199C2×SD16—1391no—
200C2×SD16—1391no—
201C2×D8—1391no—
202C2×D8—1391no—
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×D4—1391no—
218C4×D4—1391no—
219#117—1391no—
220#117C2×D13911yescharacteristic
221C2×C22⋊C4—2781no—
222C2×C22⋊C4—2781no—
223#107—1391no—
224#107—1391no—
225#106—1391no—
226#106—1391no—
227C4⋊C8C2×D13911yescharacteristic, complemented
228C4⋊C8C2×D13911yescharacteristic, complemented
229#103—1391no—
230#103—1391no—
231#102—1391no—
232#102—1391no—
233#102—1391no—
234#102—1391no—
235#102—1391no—
236#102—1391no—
237C22⋊C8C2×D13911yescharacteristic
238C22⋊C8C2×D13911yescharacteristic
239#97C2×D13911yescharacteristic, complemented
240C4×C8C2×D13911yescharacteristic, complemented
241C24—2781no—
242C2×Q8—2781no—
243C2×Q8—1391no—
244C2×D4—2782no—
245C2×D4—2782no—
246C2×D4—2781no—
247C2×D4—2781no—
248C2×D4—1391no—
249C2×D4—1391no—
250C2×D4—1391no—
251C22×C4—2781no—
252C22×C4—2781no—
253C22×C4—2781no—
254C22×C4—2781no—
255C22×C4—2781no—
256C22×C4C22×D13911yescharacteristic
257SD16—2782no—
258SD16—2782no—
259D8—2782no—
260D8—2782no—
261C2×C8C22×D13911yescharacteristic
262C2×C8C22×D13911yescharacteristic
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⋊C4D55611yescharacteristic
273C4⋊C4D55611yescharacteristic
274C22⋊C4—2781no—
275C22⋊C4—2781no—
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⋊C4D55611yescharacteristic
285C22⋊C4D55611yescharacteristic
286C42—2781no—
287C42—2781no—
288C42C22×D13911yescharacteristic
289C42C22×D13911yescharacteristic
290C23—2784no—
291C23—2781no—
292C23—2781no—
293C23—2781no—
294C23—11121no—
295C23—11121no—
296C23C2×D55611yescharacteristic
297Q8—2781no—
298Q8—2781no—
299Q8—11121no—
300D4—2784no—
301D4—2781no—
302D4—2781no—
303D4—2781no—
304D4—2781no—
305D4—11121no—
306D4—1392no—
307D4—1392no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—2781no—
311C2×C4—2781no—
312C2×C4—2781no—
313C2×C4—2781no—
314C2×C4—2781no—
315C2×C4—11121no—
316C2×C4—11121no—
317C2×C4—11121no—
318C2×C4—11121no—
319C2×C4—11121no—
320C2×C4C2×D55611yescharacteristic
321C2×C4C2×D55611yescharacteristic
322C2×C4C2×D55611yescharacteristic
323C2×C4C2×D55611yescharacteristic
324C2×C4C2×D55611yescharacteristic
325C2×C4C23×D13911yescharacteristic
326C8—21no—
327C8—21no—
328C8—21no—
329C8—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—2782no—
334C22—2782no—
335C22—5561no—
336C22—5561no—
337C22—5561no—
338C22—5561no—
339C22—5561no—
340C22—5561no—
341C22—5561no—
342C22—11124no—
343C22C22×D55611yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—5561no—
350C4—5561no—
351C4—5561no—
352C4—5561no—
353C4—5561no—
354C4#41×D13911yescharacteristic
355C4#41×D13911yescharacteristic
356C2—41no—
357C2—5562no—
358C2—5562no—
359C2—11121no—
360C2#2258146511yescharacteristic
361C2#2258175811yescharacteristic
362C2#2258176511yescharacteristic
subgroupG/H
centerC22C22×D556
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#433×C139C2
socleC22×C139C22×D4
prime radical#22581089C2
hypercenter#433D139
hypocenterC139#3118
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #22581574C2semidirect
2. #22581427C2semidirect
3. #22581295C2semidirect
4. #22581278C2semidirect
5. #22581244C2semidirect
6. #22581234C2semidirect
7. #22581169C2semidirect
8. #22581169C2semidirect
9. #22581106C2semidirect
11. #22581066C2semidirect
12. #22581055C2semidirect
13. C4×#14555774C2semidirect
14. C4×D1112C2semidirect
15. #433×C139C2semidirect
21. #17984842C22semidirect
23. #17984830C22semidirect
29. C4×Dic278C22semidirect
34. C4×D556C22semidirect
40. #17984776C22semidirect
41. #17984776C22semidirect
42. #17984774C22semidirect
43. #17984774C22semidirect
44. #17984767C22semidirect
45. #17984767C22semidirect
50. #17984764C22semidirect
51. #17984764C22semidirect
53. C4⋊C8×C139C22semidirect
54. C4⋊C8×C139C22semidirect
57. #97×C139C22semidirect
58. C4×C8×C139C22semidirect
181. C139#3118semidirect
197. #433D139semidirect
227. C4⋊C8C2×D139semidirect
228. C4⋊C8C2×D139semidirect
239. #97C2×D139semidirect
240. C4×C8C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225815742
#225814272
#225812952
#225812782
#225812442
#225812342
#225811692
#225811062
#225810892
#225810662
#225810552
C4×#145557742
C4×D11122
#433×C1392
#3118139