Finite Group Databasebeta

← #31817949

Subgroups — #31817949

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×#17984870C211yesmaximal, characteristic, complemented
2C2×#17984864C211yesmaximal, characteristic, complemented
3#22581624C211yesmaximal, characteristic, complemented
4#22581599C211yesmaximal, characteristic, complemented
5#22581342C211yesmaximal, characteristic, complemented
6#22581199C211yesmaximal, characteristic, complemented
7#22581189C211yesmaximal, characteristic, complemented
8#22581176C211yesmaximal, characteristic, complemented
9#22581149C211yesmaximal, characteristic, complemented
10#22581117C211yesmaximal, characteristic, complemented
11#22581100C211yesmaximal, characteristic, complemented
12#22581100C211yesmaximal, characteristic, complemented
13#22581089C211yesmaximal, characteristic, complemented
14#22581055C211yesmaximal, characteristic, complemented
15#435×C139C211yesmaximal, characteristic, complemented
16C2×#14555785C2211yescharacteristic
17C2×#14555785C2211yescharacteristic
18C2×#14555785C2211yescharacteristic, complemented
19C22×D556C2211yescharacteristic
20#17984870—24no—
21#17984864—24no—
22C2×Dic556C2211yescharacteristic, complemented
23C2×#14555774C2211yescharacteristic
24C2×#14555774C2211yescharacteristic
25C2×#14555774C2211yescharacteristic, complemented
26C2×#14555774C2211yescharacteristic, complemented
27C2×D1112C2211yescharacteristic
28C2×D1112C2211yescharacteristic
29C2×D1112C2211yescharacteristic
30C2×D1112C2211yescharacteristic
31#17984839C2211yescharacteristic, complemented
32#17984838—21no—
33#17984830C2211yescharacteristic
34#17984827—21no—
35#17984821C2211yescharacteristic
36#17984816C2211yescharacteristic
37#17984816C2211yescharacteristic
38#17984816C2211yescharacteristic, complemented
39#17984815—21no—
40#17984815—21no—
41#17984815—21no—
42#17984810—21no—
43C4×Dic278C2211yescharacteristic, complemented
44C4×D556C2211yescharacteristic
45#17984804—21no—
46C22⋊C4×D139—21no—
47#17984776C2211yescharacteristic, complemented
48#17984767C2211yescharacteristic, complemented
49#17984767C2211yescharacteristic, complemented
50#17984764C2211yescharacteristic
51#17984764C2211yescharacteristic
52#17984764C2211yescharacteristic, complemented
53#17984764C2211yescharacteristic, complemented
54C2×M16×C139C2211yescharacteristic
55C22×C8×C139C2211yescharacteristic, complemented
56C4×D4×C139C2211yescharacteristic
57C4⋊C8×C139C2211yescharacteristic, complemented
58C22⋊C8×C139C2211yescharacteristic
59C22⋊C8×C139C2211yescharacteristic, complemented
60#97×C139C2211yescharacteristic, complemented
61C23×D139—21no—
62#14555785—22no—
63#14555785—22no—
64#14555785—22no—
65#14555785—41no—
66#14555785—41no—
67#14555785—41no—
68C2×Dic278C2311yescharacteristic
69C2×Dic278C2311yescharacteristic
70C2×D556—22no—
71C2×D556—21no—
72C2×D556—21no—
73C2×D556—21no—
74C2×D556—41no—
75C2×D556C2311yescharacteristic
76C2×D556C2311yescharacteristic
77C2×D556C2311yescharacteristic
78C2×D556C2311yescharacteristic
79C2×C22⋊D139—21no—
80C2×C22⋊D139—21no—
81C2×C22⋊D139—21no—
82C2×C22⋊D139—21no—
83C2×C22⋊D139—21no—
84C2×C22⋊D139—21no—
85C2×C4×D139—21no—
86C2×C4×D139—21no—
87C2×C4×D139—21no—
88C2×C4×D139—21no—
89Dic556—22no—
90#14555774—22no—
91#14555774—22no—
92#14555774—41no—
93#14555774D414yescomplemented
94D1112—22no—
95D1112—22no—
96D1112—22no—
97D1112—41no—
98C4⋊Dic139C2311yescharacteristic
99C4⋊Dic139C2311yescharacteristic
100Dic139⋊C4—21no—
101Dic139⋊C4—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)⋊C4—21no—
108(C2×D139)⋊C4—21no—
109C4×Dic139—21no—
110C2×D4×C139D411yescharacteristic
111C22×C4×C139C2311yescharacteristic
112C22×C4×C139C2311yescharacteristic
113M16×C139—22no—
114C2×C8×C139—22no—
115C2×C8×C139C2311yescharacteristic
116C2×C8×C139C2311yescharacteristic
117C2×C8×C139C2311yescharacteristic
118C2×C8×C139C2311yescharacteristic
119C4⋊C4×C139D411yescharacteristic
120C22⋊C4×C139D411yescharacteristic
121C22⋊C4×C139D411yescharacteristic
122C42×C139C2311yescharacteristic
123C22×D139—21no—
124C22×D139—21no—
125C22×D139—21no—
126C22×D139—21no—
127C22×D139—42no—
128C22×D139—42no—
129C22×D139—81no—
130Dic278—21no—
131Dic278—21no—
132Dic278—21no—
133Dic278C2×D412yes—
134D556—21no—
135D556—21no—
136D556—21no—
137D556—21no—
138D556—21no—
139D556—21no—
140D556—21no—
141D556—42no—
142D556—42no—
143D556—81no—
144D556C2×D412yes—
145C22⋊D139—42no—
146C22⋊D139—42no—
147C22⋊D139—42no—
148C22⋊D139—81no—
149C22⋊D139—81no—
150C22⋊D139—81no—
151C2×Dic139—21no—
152C2×Dic139—21no—
153C2×Dic139—21no—
154C2×Dic139—21no—
155C4×D139—42no—
156C4×D139—42no—
157C4×D139—42no—
158C4×D139—81no—
159C23×C139C2×D411yescharacteristic
160C23×C139C2×D411yescharacteristic
161D4×C139—41no—
162C2×C4×C139—21no—
163C2×C4×C139—21no—
164C2×C4×C139—21no—
165C2×C4×C139—21no—
166C2×C4×C139C2×D411yescharacteristic
167C2×C4×C139C2×D411yescharacteristic
168C2×C4×C139C2×D411yescharacteristic
169C2×C4×C139C2×D411yescharacteristic
170C2×C4×C139C2411yescharacteristic
171C8×C139—21no—
172C8×C139—21no—
173C8×C139—21no—
174C8×C139C2×D412yes—
175C22×C139—21no—
176C22×C139—21no—
177C22×C139—21no—
178C22×C139—21no—
179C22×C139—21no—
180C22×C139—21no—
181C22×C139C22×D411yescharacteristic
182C2×D139—22no—
183C2×D139—41no—
184C2×D139—41no—
185C2×D139—41no—
186C2×D139—41no—
187C2×D139—41no—
188C2×D139—41no—
189C2×D139—41no—
190C2×D139—41no—
191C2×D139—41no—
192C2×D139—41no—
193C2×D139—41no—
194C2×D139—84no—
195C4×C139—21no—
196C4×C139—21no—
197C4×C139—21no—
198C4×C139—21no—
199C4×C139C22×D411yescharacteristic
200C4×C139H(5,𝔽2)11yescharacteristic
201Dic139—22no—
202Dic139—41no—
203Dic139—41no—
204Dic139—41no—
205C2×C139—41no—
206C2×C139—41no—
207C2×C139D4211yescharacteristic
208C2×C139#57511yescharacteristic
209C2×C139#57611yescharacteristic
210D139—42no—
211D139—81no—
212D139—81no—
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#459—1391no—
225#452—1391no—
226#449—1391no—
227#449—1391no—
228#447—1391no—
229#440—1391no—
230#435D13911yescharacteristic, complemented
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×D8—1391no—
245C2×D8—1391no—
246C2×M16C2×D13911yescharacteristic
247C22×C8C2×D13911yescharacteristic, complemented
248#127—2781no—
249#127—1391no—
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#102—1391no—
272#102—1391no—
273C22⋊C8C2×D13911yescharacteristic
274C22⋊C8C2×D13911yescharacteristic, complemented
275#97C2×D13911yescharacteristic, complemented
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—2782no—
286C2×D4—2781no—
287C2×D4—2781no—
288C2×D4—2781no—
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×D4—1391no—
299C2×D4—1391no—
300C2×D4D55611yescharacteristic
301C22×C4—2781no—
302C22×C4—2781no—
303C22×C4—2781no—
304C22×C4—2781no—
305C22×C4C22×D13911yescharacteristic
306C22×C4C22×D13911yescharacteristic
307Q16—2782no—
308SD16—2782no—
309SD16—2782no—
310SD16—5561no—
311SD16—1394no—
312D8—2782no—
313D8—2782no—
314D8—2782no—
315D8—5561no—
316M16—22no—
317C2×C8—22no—
318C2×C8C22×D13911yescharacteristic
319C2×C8C22×D13911yescharacteristic
320C2×C8C22×D13911yescharacteristic
321C2×C8C22×D13911yescharacteristic
322C4⋊C4—2781no—
323C4⋊C4—2781no—
324C4⋊C4—1391no—
325C4⋊C4—1391no—
326C4⋊C4D55611yescharacteristic
327C22⋊C4—2781no—
328C22⋊C4—2781no—
329C22⋊C4—2781no—
330C22⋊C4—2781no—
331C22⋊C4—2781no—
332C22⋊C4—2781no—
333C22⋊C4—2781no—
334C22⋊C4D55611yescharacteristic
335C22⋊C4D55611yescharacteristic
336C42—2781no—
337C42C22×D13911yescharacteristic
338C23—2781no—
339C23—2781no—
340C23—2781no—
341C23—2781no—
342C23—5562no—
343C23—5562no—
344C23—11121no—
345C23C2×D55611yescharacteristic
346C23C2×D55611yescharacteristic
347Q8—2781no—
348Q8—2781no—
349Q8—2781no—
350Q8—1392no—
351D4—41no—
352D4—2781no—
353D4—2781no—
354D4—2781no—
355D4—2781no—
356D4—2781no—
357D4—2781no—
358D4—2781no—
359D4—5562no—
360D4—5562no—
361D4—5562no—
362D4—5562no—
363D4—5562no—
364D4—11121no—
365D4—11121no—
366D4—11121no—
367D4—11121no—
368D4—1392no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—2781no—
374C2×C4—2781no—
375C2×C4—2781no—
376C2×C4—2781no—
377C2×C4—5562no—
378C2×C4—5562no—
379C2×C4—5562no—
380C2×C4—11121no—
381C2×C4C2×D55611yescharacteristic
382C2×C4C2×D55611yescharacteristic
383C2×C4C2×D55611yescharacteristic
384C2×C4C2×D55611yescharacteristic
385C2×C4C23×D13911yescharacteristic
386C8—21no—
387C8—21no—
388C8—21no—
389C8D4×D13912yes—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—2782no—
397C22—5561no—
398C22—5561no—
399C22—5561no—
400C22—5561no—
401C22—5561no—
402C22—5561no—
403C22—5561no—
404C22—5561no—
405C22—5561no—
406C22—5561no—
407C22—5561no—
408C22—11124no—
409C22C22×D55611yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—2782no—
415C4—5561no—
416C4—5561no—
417C4—5561no—
418C4C2×D4×D13911yescharacteristic
419C4#1798488811yescharacteristic
420C2—41no—
421C2—41no—
422C2—5562no—
423C2—11121no—
424C2—11121no—
425C2—11121no—
426C2D4×D55611yescharacteristic
427C2#2258175311yescharacteristic
428C2#2258175811yescharacteristic
subgroupG/H
centerC22C22×D556
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#435×C139C2
socleC22×C139C22×D4
hypercenter#435D139
hypocenterC139#3268
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#17984870C2semidirect
2. C2×#17984864C2semidirect
3. #22581624C2semidirect
4. #22581599C2semidirect
5. #22581342C2semidirect
6. #22581199C2semidirect
7. #22581189C2semidirect
8. #22581176C2semidirect
9. #22581149C2semidirect
10. #22581117C2semidirect
11. #22581100C2semidirect
12. #22581100C2semidirect
13. #22581089C2semidirect
14. #22581055C2semidirect
15. #435×C139C2semidirect
18. C2×#14555785C22semidirect
22. C2×Dic556C22semidirect
25. C2×#14555774C22semidirect
26. C2×#14555774C22semidirect
31. #17984839C22semidirect
38. #17984816C22semidirect
43. C4×Dic278C22semidirect
47. #17984776C22semidirect
48. #17984767C22semidirect
49. #17984767C22semidirect
52. #17984764C22semidirect
53. #17984764C22semidirect
55. C22×C8×C139C22semidirect
57. C4⋊C8×C139C22semidirect
59. C22⋊C8×C139C22semidirect
60. #97×C139C22semidirect
93. #14555774D4semidirect
214. C139#3268semidirect
230. #435D139semidirect
247. C22×C8C2×D139semidirect
266. C4⋊C8C2×D139semidirect
274. C22⋊C8C2×D139semidirect
275. #97C2×D139semidirect

Maximal subgroups

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

subgroupindex
C2×#179848702
C2×#179848642
#225816242
#225815992
#225813422
#225811992
#225811892
#225811762
#225811492
#225811172
#225811002
#225810892
#225810552
#435×C1392
#3268139