Finite Group Databasebeta

← #31815231

Subgroups — #31815231

Order 17792.

506 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17984869C211yesmaximal, characteristic
2#22581435C211yesmaximal, characteristic, complemented
3#22581425C211yesmaximal, characteristic, complemented
4#22581064C211yesmaximal, characteristic, complemented
5#22581063C211yesmaximal, characteristic, complemented
6#22581054C211yesmaximal, characteristic, complemented
7#22581051C211yesmaximal, characteristic, complemented
8#22581038C211yesmaximal, characteristic, complemented
9C4×D1112C211yesmaximal, characteristic, complemented
10#22581033C211yesmaximal, characteristic, complemented
11#22580992C211yesmaximal, characteristic, complemented
12#22580948C211yesmaximal, characteristic, complemented
13#102×D139C211yesmaximal, characteristic, complemented
14#22580907C211yesmaximal, characteristic, complemented
15C4×SD16×C139C211yesmaximal, characteristic, complemented
16C2×#14555786C2211yescharacteristic
17C2×D4×D139C2211yescharacteristic
18#17984869C418yescomplemented
19C2×#14555772C2211yescharacteristic
20C2×D1112C2211yescharacteristic
21C2×#14555770C2211yescharacteristic
22C2×#14555768C2211yescharacteristic
23C2×C8×D139C2211yescharacteristic
24Q8×Dic139C2211yescharacteristic, complemented
25C4×D556—21no—
26C4×D556C2211yescharacteristic
27C4×D556C2211yescharacteristic, complemented
28D4×Dic139C2211yescharacteristic
29#17984804—21no—
30#17984804C2211yescharacteristic
31#17984804C2211yescharacteristic, complemented
32C4×C22⋊D139—21no—
33(C22⋊D139)⋊C4—21no—
34#17984800C2211yescharacteristic
35#17984799—21no—
36#17984799C2211yescharacteristic
37C4⋊C4×D139—21no—
38C4⋊C4×D139C2211yescharacteristic
39C2×(C2×D139)⋊C4—21no—
40C22⋊C4×D139—21no—
41#17984776C2211yescharacteristic, complemented
42#17984775C2211yescharacteristic, complemented
43#17984773C2211yescharacteristic, complemented
44#17984766C2211yescharacteristic, complemented
45#17984764C2211yescharacteristic
46#17984764C2211yescharacteristic, complemented
47#17984763C2211yescharacteristic
48#17984762C2211yescharacteristic
49#17984762C2211yescharacteristic, complemented
50#17984753C2211yescharacteristic, complemented
51#17984752C2211yescharacteristic, complemented
52C8×Dic139C2211yescharacteristic, complemented
53C2×SD16×C139C2211yescharacteristic
54C4×Q8×C139C2211yescharacteristic, complemented
55C4×D4×C139C2211yescharacteristic
56#106×C139C2211yescharacteristic, complemented
57#103×C139C2211yescharacteristic, complemented
58#102×C139C2211yescharacteristic
59C4×C8×C139C2211yescharacteristic, complemented
60C23×D139—21no—
61#14555786—22no—
62#14555786C2×C414yescomplemented
63C2×D556—21no—
64C2×D556C2311yescharacteristic
65C2×D556C2311yescharacteristic
66C2×C22⋊D139—21no—
67D4×D139—22no—
68D4×D139C2×C414yescomplemented
69C22×Dic139—21no—
70C2×C4×D139—21no—
71C2×C4×D139—21no—
72C2×C4×D139—21no—
73C2×C4×D139—21no—
74C2×C4×D139—21no—
75C2×C4×D139—21no—
76C2×C4×D139C2311yescharacteristic
77#14555772C2×C414yescomplemented
78D1112C2×C414yescomplemented
79#14555770C2×C414yescomplemented
80#14555768C2×C414yescomplemented
81C2×C139⋊C8C2311yescharacteristic
82C2×C139⋊C8C2311yescharacteristic
83C8×D139—22no—
84C4⋊Dic139—21no—
85C4⋊Dic139C2311yescharacteristic
86C4⋊Dic139C2311yescharacteristic
87Dic139⋊C4—21no—
88Dic139⋊C4D411yescharacteristic
89Dic139⋊C4D411yescharacteristic
90C22⋊Dic139—21no—
91(C2×D139)⋊C4—21no—
92(C2×D139)⋊C4—21no—
93(C2×D139)⋊C4—21no—
94(C2×D139)⋊C4—21no—
95(C2×D139)⋊C4—21no—
96(C2×D139)⋊C4D411yescharacteristic
97(C2×D139)⋊C4D411yescharacteristic
98C4×Dic139—21no—
99C4×Dic139—21no—
100C4×Dic139C2311yescharacteristic
101C2×Q8×C139C2311yescharacteristic
102C2×D4×C139C2311yescharacteristic
103C22×C4×C139—21no—
104SD16×C139C2×C414yescomplemented
105C2×C8×C139C2311yescharacteristic
106C2×C8×C139C2311yescharacteristic
107C4⋊C4×C139—21no—
108C4⋊C4×C139C2311yescharacteristic
109C4⋊C4×C139C2311yescharacteristic
110C22⋊C4×C139—21no—
111C42×C139—21no—
112C42×C139C2311yescharacteristic
113C22×D139—21no—
114C22×D139—21no—
115C22×D139—24no—
116C22×D139—81no—
117C22×D139—81no—
118C22×D139C2×D411yescharacteristic
119D556—24no—
120D556—21no—
121D556—21no—
122D556C22×C412yes—
123D556C22×C412yes—
124C22⋊D139—24no—
125C2×Dic139—21no—
126C2×Dic139—21no—
127C2×Dic139—81no—
128C2×Dic139C2×D411yescharacteristic
129C2×Dic139C2×D411yescharacteristic
130C2×Dic139C2×D411yescharacteristic
131C4×D139—24no—
132C4×D139—81no—
133C4×D139—81no—
134C4×D139—81no—
135C4×D139—81no—
136C4×D139—81no—
137C4×D139C22×C412yes—
138C4×D139#4112yes—
139C139⋊C8—21no—
140C139⋊C8C22×C412yes—
141C23×C139—21no—
142Q8×C139—21no—
143Q8×C139C22×C412yes—
144D4×C139—21no—
145D4×C139C22×C412yes—
146C2×C4×C139—21no—
147C2×C4×C139—21no—
148C2×C4×C139—21no—
149C2×C4×C139—81no—
150C2×C4×C139C2×D411yescharacteristic
151C2×C4×C139C2×D411yescharacteristic
152C2×C4×C139C2411yescharacteristic
153C8×C139—21no—
154C8×C139C22×C412yes—
155C22×C139—22no—
156C22×C139—41no—
157C22×C139—41no—
158C22×C139C22×D411yescharacteristic
159C2×D139—21no—
160C2×D139—21no—
161C2×D139—22no—
162C2×D139—22no—
163C2×D139—41no—
164C2×D139—41no—
165C2×D139—41no—
166C2×D139—41no—
167C2×D139—84no—
168C2×D139C4×D412yes—
169C4×C139—22no—
170C4×C139—21no—
171C4×C139—21no—
172C4×C139—41no—
173C4×C139—41no—
174C4×C139C23×C411yescharacteristic
175C4×C139C2×#4111yescharacteristic
176Dic139—21no—
177Dic139—21no—
178Dic139—41no—
179Dic139—41no—
180Dic139C4×D412yes—
181C2×C139—42no—
182C2×C139C2×C4×D411yescharacteristic
183C2×C139#57611yescharacteristic
184C2×C139#57711yescharacteristic
185D139—22no—
186D139—42no—
187D139—42no—
188C139#294611yescharacteristic, complemented, Sylow
189#2946—1391nomaximal, Sylow
190C2×AGL(1,ℤ/8)—1391no—
191#520—1391no—
192#518—1391no—
193#442—1391no—
194#442—1391no—
195#440—1391no—
196#440—1391no—
197C4×SD16—1391no—
198C4×SD16D13911yescharacteristic, complemented
199C4×D8—1391no—
200C4×D8—1391no—
201#428—1391no—
202#416—1391no—
203C2×#102—1391no—
204#405—1391no—
205C2×#41—1391no—
206C22×D4—1391no—
207AGL(1,ℤ/8)—1398no—
208C2×SD16—1391no—
209C2×SD16C2×D13911yescharacteristic
210C2×D8—1391no—
211C2×D8—1391no—
212C2×M16—1391no—
213C22×C8—1391no—
214C4×Q8—1391no—
215C4×Q8C2×D13911yescharacteristic, complemented
216C4×D4—2781no—
217C4×D4—2781no—
218C4×D4—2781no—
219C4×D4—2781no—
220C4×D4—1391no—
221C4×D4—1391no—
222C4×D4—1391no—
223C4×D4—1391no—
224C4×D4—1391no—
225C4×D4C2×D13911yescharacteristic
226#117—2781no—
227#117—1391no—
228#117—1391no—
229C2×C4⋊C4—2781no—
230C2×C4⋊C4—1391no—
231C2×C22⋊C4—2781no—
232C2×C22⋊C4—2781no—
233#107—1391no—
234#107—1391no—
235#106—1391no—
236#106C2×D13911yescharacteristic, complemented
237#103—1391no—
238#103C2×D13911yescharacteristic, complemented
239#102—1391no—
240#102—1391no—
241#102—1391no—
242#102—1391no—
243#102—1391no—
244#102C2×D13911yescharacteristic
245#97—1391no—
246#97—1391no—
247C4×C8—1391no—
248C4×C8C2×D13911yescharacteristic, complemented
249C24—2781no—
250#41—2782no—
251#41—1394no—
252C2×Q8C22×D13911yescharacteristic
253C2×D4—2781no—
254C2×D4—2782no—
255C2×D4—2781no—
256C2×D4—1394no—
257C2×D4—1391no—
258C2×D4—1391no—
259C2×D4C22×D13911yescharacteristic
260C22×C4—21no—
261C22×C4—2781no—
262C22×C4—2781no—
263C22×C4—2781no—
264C22×C4—2781no—
265C22×C4—2781no—
266C22×C4—2781no—
267C22×C4—2781no—
268C22×C4—1391no—
269SD16—1394no—
270SD16C4×D13914yescomplemented
271D8—1394no—
272D8—1394no—
273M16—1394no—
274C2×C8—2782no—
275C2×C8—1391no—
276C2×C8—1391no—
277C2×C8C22×D13911yescharacteristic
278C2×C8C22×D13911yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—2781no—
281C4⋊C4—2781no—
282C4⋊C4—1391no—
283C4⋊C4—1391no—
284C4⋊C4—1391no—
285C4⋊C4—1391no—
286C4⋊C4C22×D13911yescharacteristic
287C4⋊C4C22×D13911yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—2781no—
290C22⋊C4—2781no—
291C22⋊C4—2781no—
292C22⋊C4—2781no—
293C22⋊C4—2781no—
294C22⋊C4—2781no—
295C22⋊C4—1391no—
296C22⋊C4—1391no—
297C42—21no—
298C42—2781no—
299C42—2781no—
300C42—1391no—
301C42C22×D13911yescharacteristic
302C23—21no—
303C23—2784no—
304C23—2781no—
305C23—2781no—
306C23—11121no—
307C23—11121no—
308C23—1391no—
309Q8—21no—
310Q8C2×C4×D13912yes—
311D4—21no—
312D4—2784no—
313D4—2784no—
314D4—2781no—
315D4—2781no—
316D4—1392no—
317D4—1392no—
318D4C2×C4×D13912yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—81no—
323C2×C4—2784no—
324C2×C4—2781no—
325C2×C4—2781no—
326C2×C4—11121no—
327C2×C4—11121no—
328C2×C4—11121no—
329C2×C4—11121no—
330C2×C4—11121no—
331C2×C4—11121no—
332C2×C4—1391no—
333C2×C4—1391no—
334C2×C4—1391no—
335C2×C4—1392no—
336C2×C4—1392no—
337C2×C4D4×D13911yescharacteristic
338C2×C4D4×D13911yescharacteristic
339C2×C4C23×D13911yescharacteristic
340C8—21no—
341C8—2781no—
342C8—1392no—
343C8C2×C4×D13912yes—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—2781no—
348C22—2781no—
349C22—2782no—
350C22—2782no—
351C22—5561no—
352C22—5561no—
353C22—5561no—
354C22—5561no—
355C22—11124no—
356C22—1392no—
357C22C2×D4×D13911yescharacteristic
358C4—22no—
359C4—21no—
360C4—21no—
361C4—41no—
362C4—41no—
363C4—2781no—
364C4—2781no—
365C4—5561no—
366C4—5561no—
367C4—1392no—
368C4C22×C4×D13911yescharacteristic
369C4#41×D13911yescharacteristic
370C2—42no—
371C2—2782no—
372C2—5562no—
373C2—5562no—
374C2C4×D4×D13911yescharacteristic
375C2#2258175511yescharacteristic
376C2#2258175911yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutatorC4×C139C23×C4
FrattiniC2×C4C23×D139
FittingC4×SD16×C139C2
socleC22×C139C22×D4
prime radicalC2×#17984869C2
cosocleC2×C4×C139C24
hypercenterC4×SD16D139
hypocenterC139#2946
LCSG ▷ C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #22581435C2semidirect
3. #22581425C2semidirect
4. #22581064C2semidirect
5. #22581063C2semidirect
6. #22581054C2semidirect
7. #22581051C2semidirect
8. #22581038C2semidirect
9. C4×D1112C2semidirect
10. #22581033C2semidirect
11. #22580992C2semidirect
12. #22580948C2semidirect
13. #102×D139C2semidirect
14. #22580907C2semidirect
15. C4×SD16×C139C2semidirect
18. #17984869C4semidirect
24. Q8×Dic139C22semidirect
27. C4×D556C22semidirect
31. #17984804C22semidirect
41. #17984776C22semidirect
42. #17984775C22semidirect
43. #17984773C22semidirect
44. #17984766C22semidirect
46. #17984764C22semidirect
49. #17984762C22semidirect
50. #17984753C22semidirect
51. #17984752C22semidirect
52. C8×Dic139C22semidirect
54. C4×Q8×C139C22semidirect
56. #106×C139C22semidirect
57. #103×C139C22semidirect
59. C4×C8×C139C22semidirect
62. #14555786C2×C4semidirect
68. D4×D139C2×C4semidirect
77. #14555772C2×C4semidirect
78. D1112C2×C4semidirect
79. #14555770C2×C4semidirect
80. #14555768C2×C4semidirect
104. SD16×C139C2×C4semidirect
188. C139#2946semidirect
198. C4×SD16D139semidirect
215. C4×Q8C2×D139semidirect
236. #106C2×D139semidirect
238. #103C2×D139semidirect
248. C4×C8C2×D139semidirect
270. SD16C4×D139semidirect

Maximal subgroups

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

subgroupindex
C2×#179848692
#225814352
#225814252
#225810642
#225810632
#225810542
#225810512
#225810382
C4×D11122
#225810332
#225809922
#225809482
#102×D1392
#225809072
C4×SD16×C1392
#2946139