Finite Group Databasebeta

← #31816315

Subgroups — #31816315

Order 17792.

420 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581460C211yesmaximal, characteristic
2#117×D139C211yesmaximal, characteristic, complemented
3#22581293C211yesmaximal, characteristic, complemented
4#22581292C211yesmaximal, characteristic, complemented
5#22581287C211yesmaximal, characteristic, complemented
6#22581282C211yesmaximal, characteristic, complemented
7#22581276C211yesmaximal, characteristic, complemented
8#22581275C211yesmaximal, characteristic, complemented
9#22581270C211yesmaximal, characteristic, complemented
10#22581265C211yesmaximal, characteristic, complemented
11#22580991C211yesmaximal, characteristic, complemented
12#22580989C211yesmaximal, characteristic, complemented
13#22580949C211yesmaximal, characteristic, complemented
14C2×(C2×D139)⋊C8C211yesmaximal, characteristic, complemented
15#416×C139C211yesmaximal, characteristic, complemented
16C22×C4×D139C2211yescharacteristic
17C22×C139⋊C8C2211yescharacteristic
18#17984823—21no—
19#17984818C2211yescharacteristic
20#17984818C2211yescharacteristic
21#17984813C2211yescharacteristic
22#17984813C2211yescharacteristic
23#17984810—21no—
24C4×C22⋊D139—21no—
25C4×C22⋊D139—21no—
26#17984801C2211yescharacteristic
27#17984801C2211yescharacteristic
28#17984800C2211yescharacteristic
29#17984800C2211yescharacteristic
30#17984799—21no—
31#17984798—21no—
32C4⋊C4×D139C2211yescharacteristic
33C4⋊C4×D139C2211yescharacteristic
34C22⋊C4×D139—21no—
35C42×D139—21no—
36#17984776C2211yescharacteristic, complemented
37#17984776C2211yescharacteristic, complemented
38#17984775C2211yescharacteristic, complemented
39#17984775C2211yescharacteristic, complemented
40#17984774C2211yescharacteristic, complemented
41#17984774C2211yescharacteristic, complemented
42#17984773C2211yescharacteristic, complemented
43#17984773C2211yescharacteristic, complemented
44#17984766C2211yescharacteristic, complemented
45#17984766C2211yescharacteristic, complemented
46#17984763C2211yescharacteristic, complemented
47#17984763C2211yescharacteristic, complemented
48(C2×D139)⋊C8C2211yescharacteristic
49(C2×D139)⋊C8C2211yescharacteristic
50(C2×D139)⋊C8C2211yescharacteristic
51(C2×D139)⋊C8C2211yescharacteristic
52C2×#41×C139C2211yescharacteristic
53C22×C8×C139C2211yescharacteristic
54#117×C139C2211yescharacteristic
55#103×C139C2211yescharacteristic, complemented
56#103×C139C2211yescharacteristic, complemented
57#102×C139C2211yescharacteristic, complemented
58#102×C139C2211yescharacteristic, complemented
59C23×D139D411yescharacteristic
60C2×C22⋊D139—21no—
61C2×C22⋊D139—21no—
62C22×Dic139D411yescharacteristic
63C2×C4×D139—21no—
64C2×C4×D139—21no—
65C2×C4×D139—22no—
66C2×C4×D139—22no—
67C2×C4×D139D411yescharacteristic
68C2×C4×D139D411yescharacteristic
69C2×C4×D139C2311yescharacteristic
70C2×C4×D139C2311yescharacteristic
71C2×C139⋊C8—22no—
72C2×C139⋊C8C2311yescharacteristic
73C2×C139⋊C8C2311yescharacteristic
74C4⋊Dic139C2311yescharacteristic
75C4⋊Dic139C2311yescharacteristic
76C4⋊Dic139C2311yescharacteristic
77C4⋊Dic139C2311yescharacteristic
78Dic139⋊C4—21no—
79Dic139⋊C4—21no—
80Dic139⋊C4—21no—
81Dic139⋊C4—21no—
82C22⋊Dic139—21no—
83C22⋊Dic139—21no—
84C22⋊Dic139—21no—
85C22⋊Dic139—21no—
86(C2×D139)⋊C4—21no—
87(C2×D139)⋊C4—21no—
88(C2×D139)⋊C4—21no—
89(C2×D139)⋊C4—21no—
90C4×Dic139—21no—
91C4×Dic139—21no—
92C4×Dic139—21no—
93C4×Dic139—21no—
94#41×C139—22no—
95#41×C139—22no—
96C2×Q8×C139C2311yescharacteristic
97C2×D4×C139—21no—
98C2×D4×C139C2311yescharacteristic
99C22×C4×C139—21no—
100C22×C4×C139C2311yescharacteristic
101C2×C8×C139—22no—
102C2×C8×C139C2311yescharacteristic
103C2×C8×C139C2311yescharacteristic
104C4⋊C4×C139C2311yescharacteristic
105C4⋊C4×C139C2311yescharacteristic
106C22⋊C4×C139—21no—
107C42×C139—21no—
108C22×D139—22no—
109C22×D139—22no—
110C22×D139—41no—
111C22×D139C2×D411yescharacteristic
112C22×D139C2×D411yescharacteristic
113C22⋊D139—42no—
114C22⋊D139—42no—
115C2×Dic139—22no—
116C2×Dic139—21no—
117C2×Dic139—21no—
118C2×Dic139—21no—
119C2×Dic139—21no—
120C2×Dic139C2×D411yescharacteristic
121C2×Dic139C2×D411yescharacteristic
122C4×D139—22no—
123C4×D139—22no—
124C4×D139—21no—
125C4×D139—21no—
126C4×D139—21no—
127C4×D139—21no—
128C4×D139—42no—
129C4×D139—42no—
130C139⋊C8—21no—
131C139⋊C8—21no—
132C23×C139—21no—
133C23×C139C2×D411yescharacteristic
134Q8×C139—21no—
135Q8×C139—21no—
136D4×C139—21no—
137D4×C139—21no—
138D4×C139—42no—
139C2×C4×C139—21no—
140C2×C4×C139—21no—
141C2×C4×C139—21no—
142C2×C4×C139—42no—
143C2×C4×C139C2×D411yescharacteristic
144C2×C4×C139#4112yes—
145C2×C4×C139#4112yes—
146C2×C4×C139C2411yescharacteristic
147C8×C139—21no—
148C8×C139—21no—
149C22×C139—21no—
150C22×C139—21no—
151C22×C139—41no—
152C22×C139—41no—
153C22×C139—41no—
154C22×C139#12312yes—
155C22×C139C22×D411yescharacteristic
156C2×D139—21no—
157C2×D139—21no—
158C2×D139—21no—
159C2×D139—21no—
160C2×D139—21no—
161C2×D139—44no—
162C2×D139#13512yes—
163C4×C139—41no—
164C4×C139—41no—
165C4×C139—41no—
166C4×C139#12312yes—
167C4×C139C2×#4111yescharacteristic
168C4×C139C2×#4111yescharacteristic
169Dic139—21no—
170Dic139—21no—
171Dic139—41no—
172Dic139—41no—
173Dic139—41no—
174Dic139—41no—
175C2×C139—22no—
176C2×C139—81no—
177C2×C139C2×#12311yescharacteristic
178C2×C139C2×#13511yescharacteristic
179C2×C139#57511yescharacteristic
180D139—22no—
181D139—41no—
182C139#309111yescharacteristic, complemented, Sylow
183#3091—1391nomaximal, Sylow
184#525—1391no—
185C2×#117—1391no—
186#485—1391no—
187#485—1391no—
188#484—1391no—
189#483—1391no—
190#482—1391no—
191#482—1391no—
192#481—1391no—
193#480—1391no—
194#427—1391no—
195#427—1391no—
196#416—1391no—
197#416D13911yescharacteristic, complemented
198C2×C22⋊C8—1391no—
199C2×#41C2×D13911yescharacteristic
200C23×C4—1391no—
201C22×C8—1391no—
202C22×C8C2×D13911yescharacteristic
203#123—2781no—
204C22⋊Q8—1391no—
205C22⋊Q8—1391no—
206#121—1391no—
207#121—1391no—
208#120—2781no—
209C4×D4—2781no—
210C4×D4—2781no—
211#117—2781no—
212#117—2781no—
213#117—1391no—
214#117—1391no—
215#117—1391no—
216#117—1391no—
217#117C2×D13911yescharacteristic
218C2×C4⋊C4—1391no—
219C2×C4⋊C4—1391no—
220C2×C22⋊C4—2781no—
221C2×C42—2781no—
222#107—1391no—
223#107—1391no—
224#107—1391no—
225#107—1391no—
226#106—1391no—
227#106—1391no—
228#106—1391no—
229#106—1391no—
230#103—1391no—
231#103—1391no—
232#103C2×D13911yescharacteristic, complemented
233#103C2×D13911yescharacteristic, complemented
234#102—1391no—
235#102—1391no—
236#102C2×D13911yescharacteristic, complemented
237#102C2×D13911yescharacteristic, complemented
238C22⋊C8—1391no—
239C22⋊C8—1391no—
240C22⋊C8—1391no—
241C22⋊C8—1391no—
242C24—1391no—
243#41—22no—
244#41—22no—
245C2×Q8C22×D13911yescharacteristic
246C2×D4—21no—
247C2×D4—2781no—
248C2×D4—2781no—
249C2×D4C22×D13911yescharacteristic
250C22×C4—21no—
251C22×C4—2781no—
252C22×C4—2781no—
253C22×C4—2782no—
254C22×C4—2782no—
255C22×C4—1391no—
256C22×C4—1391no—
257C22×C4—1391no—
258C22×C4—1391no—
259C22×C4—1391no—
260C22×C4C22×D13911yescharacteristic
261C2×C8—22no—
262C2×C8—2782no—
263C2×C8—1391no—
264C2×C8—1391no—
265C2×C8C22×D13911yescharacteristic
266C2×C8C22×D13911yescharacteristic
267C4⋊C4—2781no—
268C4⋊C4—2781no—
269C4⋊C4—2781no—
270C4⋊C4—2781no—
271C4⋊C4—1391no—
272C4⋊C4—1391no—
273C4⋊C4—1391no—
274C4⋊C4—1391no—
275C4⋊C4C22×D13911yescharacteristic
276C4⋊C4C22×D13911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—2781no—
279C22⋊C4—2781no—
280C22⋊C4—2781no—
281C22⋊C4—2781no—
282C22⋊C4—2781no—
283C22⋊C4—2781no—
284C22⋊C4—2781no—
285C22⋊C4—2781no—
286C42—21no—
287C42—2781no—
288C42—2781no—
289C42—2781no—
290C42—2781no—
291C23—21no—
292C23—2782no—
293C23—2782no—
294C23—5561no—
295C23—1391no—
296C23—1391no—
297C23D4×D13911yescharacteristic
298Q8—21no—
299Q8—21no—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—5562no—
304D4—5562no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—2782no—
310C2×C4—2782no—
311C2×C4—2782no—
312C2×C4—2781no—
313C2×C4—2781no—
314C2×C4—2781no—
315C2×C4—2781no—
316C2×C4—2781no—
317C2×C4—2781no—
318C2×C4—2781no—
319C2×C4—2781no—
320C2×C4—5562no—
321C2×C4—5562no—
322C2×C4—1391no—
323C2×C4—1391no—
324C2×C4D4×D13911yescharacteristic
325C2×C4#1455578412yes—
326C2×C4#1455578512yes—
327C2×C4C23×D13911yescharacteristic
328C8—21no—
329C8—21no—
330C8—2781no—
331C8—2781no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—2781no—
338C22—2781no—
339C22—2781no—
340C22—2781no—
341C22—2781no—
342C22—5564no—
343C22—1392no—
344C22#1798482412yes—
345C22C2×D4×D13911yescharacteristic
346C4—41no—
347C4—41no—
348C4—41no—
349C4—2781no—
350C4—2781no—
351C4—5561no—
352C4—5561no—
353C4—5561no—
354C4—5561no—
355C4#1798482412yes—
356C4C2×#1455578411yescharacteristic
357C4C2×#1455578511yescharacteristic
358C2—22no—
359C2—81no—
360C2—2782no—
361C2—5561no—
362C2C2×#1798482411yescharacteristic
363C2#135×D13911yescharacteristic
364C2#2258175011yescharacteristic
subgroupG/H
centerC2×C4D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#416×C139C2
socleC22×C139C22×D4
prime radical#22581460C2
hypercenter#416D139
hypocenterC139#3091
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. #117×D139C2semidirect
3. #22581293C2semidirect
4. #22581292C2semidirect
5. #22581287C2semidirect
6. #22581282C2semidirect
7. #22581276C2semidirect
8. #22581275C2semidirect
9. #22581270C2semidirect
10. #22581265C2semidirect
11. #22580991C2semidirect
12. #22580989C2semidirect
13. #22580949C2semidirect
14. C2×(C2×D139)⋊C8C2semidirect
15. #416×C139C2semidirect
36. #17984776C22semidirect
37. #17984776C22semidirect
38. #17984775C22semidirect
39. #17984775C22semidirect
40. #17984774C22semidirect
41. #17984774C22semidirect
42. #17984773C22semidirect
43. #17984773C22semidirect
44. #17984766C22semidirect
45. #17984766C22semidirect
46. #17984763C22semidirect
47. #17984763C22semidirect
55. #103×C139C22semidirect
56. #103×C139C22semidirect
57. #102×C139C22semidirect
58. #102×C139C22semidirect
182. C139#3091semidirect
197. #416D139semidirect
232. #103C2×D139semidirect
233. #103C2×D139semidirect
236. #102C2×D139semidirect
237. #102C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225814602
#117×D1392
#225812932
#225812922
#225812872
#225812822
#225812762
#225812752
#225812702
#225812652
#225809912
#225809892
#225809492
C2×(C2×D139)⋊C82
#416×C1392
#3091139