Finite Group Databasebeta

← #31817950

Subgroups — #31817950

Order 17792.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17984866C211yesmaximal, characteristic, complemented
2C2×#17984861C211yesmaximal, characteristic, complemented
3#22581623C211yesmaximal, characteristic, complemented
4#22581598C211yesmaximal, characteristic, complemented
5#22581340C211yesmaximal, characteristic, complemented
6#22581198C211yesmaximal, characteristic, complemented
7#22581188C211yesmaximal, characteristic, complemented
8#22581176C211yesmaximal, characteristic, complemented
9#22581116C211yesmaximal, characteristic, complemented
10#22581099C211yesmaximal, characteristic, complemented
11#22581095C211yesmaximal, characteristic, complemented
12#22581085C211yesmaximal, characteristic, complemented
13#22581053C211yesmaximal, characteristic, complemented
14#22581023C211yesmaximal, characteristic, complemented
15#459×C139C211yesmaximal, characteristic, complemented
16C2×#14555784C2211yescharacteristic
17C2×#14555784C2211yescharacteristic
18C2×#14555784C2211yescharacteristic, complemented
19C2×D4×D139C2211yescharacteristic
20#17984866—24no—
21#17984861—24no—
22C2×Dic556C2211yescharacteristic, complemented
23C2×#14555774C2211yescharacteristic
24C2×#14555773C2211yescharacteristic
25C2×#14555773C2211yescharacteristic, complemented
26C2×#14555773C2211yescharacteristic, complemented
27C2×#14555770C2211yescharacteristic
28C2×#14555770C2211yescharacteristic
29C2×#14555768C2211yescharacteristic
30C2×C8×D139C2211yescharacteristic, complemented
31#17984838—21no—
32#17984830C2211yescharacteristic
33#17984826—21no—
34#17984822C2211yescharacteristic
35#17984817C2211yescharacteristic
36#17984816—21no—
37#17984814—21no—
38#17984814—21no—
39#17984813C2211yescharacteristic
40#17984813C2211yescharacteristic, complemented
41#17984812—21no—
42C4×Dic278C2211yescharacteristic, complemented
43C4×D556C2211yescharacteristic
44D4×Dic139—21no—
45C2×(C2×D139)⋊C4—21no—
46#17984775C2211yescharacteristic, complemented
47#17984767C2211yescharacteristic, complemented
48#17984765C2211yescharacteristic, complemented
49#17984764C2211yescharacteristic
50#17984763C2211yescharacteristic
51(C2×D139)⋊C8C2211yescharacteristic
52(C2×D139)⋊C8C2211yescharacteristic, complemented
53#17984753C2211yescharacteristic, complemented
54C2×D8×C139C2211yescharacteristic
55C2×D8×C139C2211yescharacteristic
56#127×C139C2211yescharacteristic, complemented
57C4×D4×C139C2211yescharacteristic
58C4⋊C8×C139C2211yescharacteristic, complemented
59#102×C139C2211yescharacteristic, complemented
60#102×C139C2211yescharacteristic, complemented
61C23×D139—21no—
62#14555784—22no—
63#14555784—22no—
64#14555784—22no—
65#14555784—41no—
66#14555784—41no—
67#14555784—41no—
68C2×Dic278C2311yescharacteristic
69C2×Dic278C2311yescharacteristic
70C2×D556—21no—
71C2×D556D411yescharacteristic
72C2×D556C2311yescharacteristic
73C2×C22⋊D139—21no—
74C2×C22⋊D139—21no—
75C2×C22⋊D139—21no—
76C2×C22⋊D139—21no—
77C2×C22⋊D139—21no—
78C2×C22⋊D139—21no—
79D4×D139—22no—
80D4×D139—41no—
81C22×Dic139—21no—
82C22×Dic139—21no—
83C22×Dic139—21no—
84C2×C4×D139C2311yescharacteristic
85C2×C4×D139C2311yescharacteristic
86Dic556—22no—
87#14555774—22no—
88#14555773—22no—
89#14555773—41no—
90#14555773D414yescomplemented
91#14555770—22no—
92#14555770—41no—
93#14555768—22no—
94C2×C139⋊C8C2311yescharacteristic
95C2×C139⋊C8C2311yescharacteristic
96C8×D139—22no—
97C4⋊Dic139—21no—
98C4⋊Dic139D411yescharacteristic
99C4⋊Dic139C2311yescharacteristic
100Dic139⋊C4—21no—
101C22⋊Dic139—21no—
102C22⋊Dic139—21no—
103(C2×D139)⋊C4—21no—
104(C2×D139)⋊C4—21no—
105(C2×D139)⋊C4—21no—
106(C2×D139)⋊C4—21no—
107(C2×D139)⋊C4D411yescharacteristic
108(C2×D139)⋊C4D411yescharacteristic
109C4×Dic139—21no—
110C2×D4×C139—21no—
111C2×D4×C139—21no—
112C2×D4×C139C2311yescharacteristic
113C2×D4×C139C2311yescharacteristic
114C2×D4×C139C2311yescharacteristic
115C22×C4×C139—21no—
116D8×C139—22no—
117D8×C139—22no—
118C2×C8×C139C2311yescharacteristic
119C2×C8×C139C2311yescharacteristic
120C4⋊C4×C139C2311yescharacteristic
121C22⋊C4×C139—21no—
122C42×C139C2311yescharacteristic
123C22×D139—21no—
124C22×D139—42no—
125C22×D139—42no—
126C22×D139—81no—
127C22×D139C2×D411yescharacteristic
128C22×D139C2×D411yescharacteristic
129Dic278—21no—
130Dic278—21no—
131Dic278—21no—
132Dic278C2×D412yes—
133D556—21no—
134D556—21no—
135D556—41no—
136D556—81no—
137C22⋊D139—42no—
138C22⋊D139—42no—
139C22⋊D139—42no—
140C22⋊D139—42no—
141C22⋊D139—81no—
142C22⋊D139—81no—
143C2×Dic139—21no—
144C2×Dic139—21no—
145C2×Dic139—21no—
146C2×Dic139—42no—
147C2×Dic139—42no—
148C2×Dic139—42no—
149C2×Dic139C2×D411yescharacteristic
150C2×Dic139C2×D411yescharacteristic
151C4×D139—21no—
152C4×D139—21no—
153C4×D139—21no—
154C4×D139—21no—
155C139⋊C8—21no—
156C139⋊C8C2×D412yes—
157C23×C139—21no—
158C23×C139—21no—
159C23×C139—21no—
160D4×C139—21no—
161D4×C139—21no—
162D4×C139—21no—
163D4×C139—21no—
164D4×C139—21no—
165D4×C139—42no—
166D4×C139—81no—
167D4×C139C2×D412yes—
168C2×C4×C139—21no—
169C2×C4×C139—81no—
170C2×C4×C139C2×D411yescharacteristic
171C2×C4×C139C2×D411yescharacteristic
172C2×C4×C139C2411yescharacteristic
173C8×C139—21no—
174C8×C139—21no—
175C22×C139—22no—
176C22×C139—41no—
177C22×C139—41no—
178C22×C139—41no—
179C22×C139—41no—
180C22×C139—41no—
181C22×C139—41no—
182C22×C139—41no—
183C22×C139—41no—
184C22×C139C22×D411yescharacteristic
185C2×D139—21no—
186C2×D139—21no—
187C2×D139—21no—
188C2×D139—21no—
189C2×D139—21no—
190C2×D139—21no—
191C2×D139—41no—
192C2×D139—41no—
193C2×D139—41no—
194C2×D139—84no—
195C4×C139—21no—
196C4×C139—21no—
197C4×C139—41no—
198C4×C139C22×D411yescharacteristic
199C4×C139H(5,𝔽2)11yescharacteristic
200Dic139—21no—
201Dic139—21no—
202Dic139—22no—
203Dic139—41no—
204Dic139—41no—
205C2×C139—42no—
206C2×C139—81no—
207C2×C139—81no—
208C2×C139D4211yescharacteristic
209C2×C139#57511yescharacteristic
210C2×C139#57611yescharacteristic
211D139—41no—
212D139—41no—
213D139—81no—
214C139#326811yescharacteristic, complemented, Sylow
215#3268—1391nomaximal, Sylow
216C2×AGL(1,ℤ/8)—1391no—
217C2×#135—1391no—
218#550—1391no—
219#546—1391no—
220#496—1391no—
221#468—1391no—
222#466—1391no—
223#464—1391no—
224#459D13911yescharacteristic, complemented
225#452—1391no—
226#449—1391no—
227#449—1391no—
228#447—1391no—
229#440—1391no—
230#435—1391no—
231C2×#41—1391no—
232C2×#41—1391no—
233C2×#41—1391no—
234C22×D4—1391no—
235AGL(1,ℤ/8)—2784no—
236#135—2784no—
237C2×Q16—1391no—
238C2×SD16—1391no—
239C2×SD16—1391no—
240C2×SD16—1391no—
241C2×SD16—1391no—
242C2×D8—1391no—
243C2×D8—1391no—
244C2×D8C2×D13911yescharacteristic
245C2×D8C2×D13911yescharacteristic
246C2×M16—1391no—
247C22×C8—1391no—
248#127—2781no—
249#127C2×D13911yescharacteristic, complemented
250#124—1391no—
251#123—2781no—
252C22⋊Q8—1391no—
253#121—2781no—
254#121—2781no—
255#121—2781no—
256#121—1391no—
257#121—1391no—
258#121—1391no—
259#120—2781no—
260C4×Q8—1391no—
261C4×D4—2781no—
262C4×D4—1391no—
263C4×D4C2×D13911yescharacteristic
264C2×C22⋊C4—2781no—
265#107—1391no—
266C4⋊C8C2×D13911yescharacteristic, complemented
267#103—1391no—
268#103—1391no—
269#102—1391no—
270#102—1391no—
271#102C2×D13911yescharacteristic, complemented
272#102C2×D13911yescharacteristic, complemented
273C22⋊C8—1391no—
274C22⋊C8—1391no—
275#97—1391no—
276C24—2781no—
277#41—2782no—
278#41—2782no—
279#41—2782no—
280#41—5561no—
281#41—5561no—
282#41—5561no—
283C2×Q8—1391no—
284C2×Q8—1391no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—2781no—
288C2×D4—2782no—
289C2×D4—2781no—
290C2×D4—2781no—
291C2×D4—2781no—
292C2×D4—2781no—
293C2×D4—2781no—
294C2×D4—2781no—
295C2×D4—5561no—
296C2×D4—1391no—
297C2×D4—1391no—
298C2×D4C22×D13911yescharacteristic
299C2×D4C22×D13911yescharacteristic
300C2×D4C22×D13911yescharacteristic
301C22×C4—21no—
302C22×C4—2781no—
303C22×C4—2781no—
304C22×C4—2781no—
305C22×C4—1391no—
306C22×C4—1391no—
307Q16—2782no—
308SD16—2782no—
309SD16—2782no—
310SD16—5561no—
311SD16—1394no—
312D8—22no—
313D8—22no—
314D8—2782no—
315D8—5561no—
316M16—2782no—
317C2×C8—2782no—
318C2×C8—1391no—
319C2×C8—1391no—
320C2×C8C22×D13911yescharacteristic
321C2×C8C22×D13911yescharacteristic
322C4⋊C4—2781no—
323C4⋊C4—2781no—
324C4⋊C4—1391no—
325C4⋊C4—1391no—
326C4⋊C4C22×D13911yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—2781no—
329C22⋊C4—2781no—
330C22⋊C4—2781no—
331C22⋊C4—2781no—
332C22⋊C4—2781no—
333C22⋊C4—2781no—
334C22⋊C4—1391no—
335C22⋊C4—1391no—
336C42—2781no—
337C42C22×D13911yescharacteristic
338C23—21no—
339C23—21no—
340C23—21no—
341C23—2781no—
342C23—5562no—
343C23—5562no—
344C23—11121no—
345C23—1391no—
346C23—1391no—
347Q8—2781no—
348Q8—2781no—
349Q8—2781no—
350Q8—1392no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—21no—
356D4—42no—
357D4—81no—
358D4—2781no—
359D4—2781no—
360D4—5561no—
361D4—5562no—
362D4—5562no—
363D4—5562no—
364D4—5562no—
365D4—11121no—
366D4—11121no—
367D4—11121no—
368D4D4×D13912yes—
369C2×C4—21no—
370C2×C4—81no—
371C2×C4—2781no—
372C2×C4—2781no—
373C2×C4—2781no—
374C2×C4—2781no—
375C2×C4—2781no—
376C2×C4—2781no—
377C2×C4—2781no—
378C2×C4—5562no—
379C2×C4—5562no—
380C2×C4—5562no—
381C2×C4—1391no—
382C2×C4—1391no—
383C2×C4D4×D13911yescharacteristic
384C2×C4D4×D13911yescharacteristic
385C2×C4C23×D13911yescharacteristic
386C8—21no—
387C8—21no—
388C8—2781no—
389C8—1392no—
390C22—22no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—2781no—
400C22—2781no—
401C22—2781no—
402C22—2781no—
403C22—2781no—
404C22—2781no—
405C22—5561no—
406C22—5561no—
407C22—5561no—
408C22—11124no—
409C22C2×D4×D13911yescharacteristic
410C4—21no—
411C4—21no—
412C4—41no—
413C4—2781no—
414C4—2781no—
415C4—2782no—
416C4—5561no—
417C4—5561no—
418C4C2×D4×D13911yescharacteristic
419C4#1798488811yescharacteristic
420C2—42no—
421C2—81no—
422C2—81no—
423C2—5561no—
424C2—5561no—
425C2—11121no—
426C2#2258158711yescharacteristic
427C2#2258174911yescharacteristic
428C2#2258175411yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#459×C139C2
socleC22×C139C22×D4
hypercenter#459D139
hypocenterC139#3268
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#17984866C2semidirect
2. C2×#17984861C2semidirect
3. #22581623C2semidirect
4. #22581598C2semidirect
5. #22581340C2semidirect
6. #22581198C2semidirect
7. #22581188C2semidirect
8. #22581176C2semidirect
9. #22581116C2semidirect
10. #22581099C2semidirect
11. #22581095C2semidirect
12. #22581085C2semidirect
13. #22581053C2semidirect
14. #22581023C2semidirect
15. #459×C139C2semidirect
18. C2×#14555784C22semidirect
22. C2×Dic556C22semidirect
25. C2×#14555773C22semidirect
26. C2×#14555773C22semidirect
30. C2×C8×D139C22semidirect
40. #17984813C22semidirect
42. C4×Dic278C22semidirect
46. #17984775C22semidirect
47. #17984767C22semidirect
48. #17984765C22semidirect
52. (C2×D139)⋊C8C22semidirect
53. #17984753C22semidirect
56. #127×C139C22semidirect
58. C4⋊C8×C139C22semidirect
59. #102×C139C22semidirect
60. #102×C139C22semidirect
90. #14555773D4semidirect
214. C139#3268semidirect
224. #459D139semidirect
249. #127C2×D139semidirect
266. C4⋊C8C2×D139semidirect
271. #102C2×D139semidirect
272. #102C2×D139semidirect

Maximal subgroups

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

subgroupindex
C2×#179848662
C2×#179848612
#225816232
#225815982
#225813402
#225811982
#225811882
#225811762
#225811162
#225810992
#225810952
#225810852
#225810532
#225810232
#459×C1392
#3268139