Finite Group Databasebeta

← #31817934

Subgroups — #31817934

Order 17792.

500 conjugacy classes of subgroups.

The subgroup lattice has 418 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#22581608C211yesmaximal, characteristic, complemented
4#22581599C211yesmaximal, characteristic, complemented
5#22581347C211yesmaximal, characteristic, complemented
6#22581211C211yesmaximal, characteristic, complemented
7#22581182C211yesmaximal, characteristic, complemented
8#22581169C211yesmaximal, characteristic, complemented
9#22581159C211yesmaximal, characteristic, complemented
10#22581117C211yesmaximal, characteristic, complemented
11#22581117C211yesmaximal, characteristic, complemented
12#22581106C211yesmaximal, characteristic, complemented
13#22581100C211yesmaximal, characteristic, complemented
14#22581066C211yesmaximal, 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×Dic556C2211yescharacteristic, complemented
24C2×#14555774C2211yescharacteristic
25C2×#14555774C2211yescharacteristic
26C2×#14555774C2211yescharacteristic
27C2×#14555774C2211yescharacteristic
28C2×#14555774C2211yescharacteristic, complemented
29C2×D1112C2211yescharacteristic
30C2×D1112C2211yescharacteristic
31#17984842C2211yescharacteristic, complemented
32#17984830C2211yescharacteristic
33#17984827—21no—
34#17984824—21no—
35#17984824—21no—
36#17984821C2211yescharacteristic
37#17984821C2211yescharacteristic
38#17984821C2211yescharacteristic, complemented
39#17984816C2211yescharacteristic
40#17984815—21no—
41#17984813—21no—
42#17984810—21no—
43C4×D556C2211yescharacteristic
44C4×D556C2211yescharacteristic, complemented
45C4⋊C4×D139—21no—
46C22⋊C4×D139—21no—
47#17984774C2211yescharacteristic, complemented
48#17984767C2211yescharacteristic, complemented
49#17984767C2211yescharacteristic, complemented
50#17984767C2211yescharacteristic, complemented
51#17984764C2211yescharacteristic
52#17984764C2211yescharacteristic
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×Dic278C2311yescharacteristic
71C2×D556—22no—
72C2×D556—21no—
73C2×D556—41no—
74C2×D556C2311yescharacteristic
75C2×D556C2311yescharacteristic
76C2×D556C2311yescharacteristic
77C2×C22⋊D139—21no—
78C2×C22⋊D139—21no—
79C2×C22⋊D139—21no—
80C2×C22⋊D139—21no—
81C2×C4×D139—21no—
82C2×C4×D139—21no—
83C2×C4×D139—21no—
84C2×C4×D139—21no—
85C2×C4×D139—21no—
86Dic556—22no—
87Dic556—41no—
88#14555774—22no—
89#14555774—22no—
90#14555774—22no—
91#14555774—22no—
92#14555774—41no—
93D1112—22no—
94D1112D414yescomplemented
95C4⋊Dic139—21no—
96C4⋊Dic139—21no—
97C4⋊Dic139C2311yescharacteristic
98C4⋊Dic139C2311yescharacteristic
99Dic139⋊C4—21no—
100Dic139⋊C4—21no—
101Dic139⋊C4—21no—
102C22⋊Dic139—21no—
103C22⋊Dic139—21no—
104C22⋊Dic139—21no—
105(C2×D139)⋊C4—21no—
106(C2×D139)⋊C4—21no—
107(C2×D139)⋊C4—21no—
108(C2×D139)⋊C4—21no—
109(C2×D139)⋊C4—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—42no—
127C22×D139—42no—
128C22×D139—81no—
129Dic278—21no—
130Dic278—21no—
131Dic278—21no—
132Dic278—21no—
133Dic278—21no—
134Dic278—21no—
135D556—21no—
136D556—21no—
137D556—21no—
138D556—21no—
139D556—42no—
140D556C2×D412yes—
141D556C2×D412yes—
142C22⋊D139—42no—
143C22⋊D139—42no—
144C22⋊D139—42no—
145C22⋊D139—81no—
146C2×Dic139—21no—
147C2×Dic139—21no—
148C2×Dic139—21no—
149C2×Dic139—21no—
150C2×Dic139—21no—
151C4×D139—42no—
152C4×D139—42no—
153C4×D139—42no—
154C4×D139—42no—
155C4×D139—81no—
156C23×C139C2×D411yescharacteristic
157C23×C139C2×D411yescharacteristic
158D4×C139—41no—
159C2×C4×C139—21no—
160C2×C4×C139—21no—
161C2×C4×C139—21no—
162C2×C4×C139—21no—
163C2×C4×C139C2×D411yescharacteristic
164C2×C4×C139C2×D411yescharacteristic
165C2×C4×C139C2×D411yescharacteristic
166C2×C4×C139C2×D411yescharacteristic
167C2×C4×C139C2411yescharacteristic
168C8×C139—21no—
169C8×C139—21no—
170C8×C139—21no—
171C8×C139C2×D412yes—
172C22×C139—21no—
173C22×C139—21no—
174C22×C139—21no—
175C22×C139—21no—
176C22×C139—21no—
177C22×C139—21no—
178C22×C139C22×D411yescharacteristic
179C2×D139—22no—
180C2×D139—22no—
181C2×D139—41no—
182C2×D139—41no—
183C2×D139—41no—
184C2×D139—41no—
185C2×D139—41no—
186C2×D139—41no—
187C2×D139—41no—
188C2×D139—84no—
189C4×C139—21no—
190C4×C139—21no—
191C4×C139—21no—
192C4×C139—21no—
193C4×C139C22×D411yescharacteristic
194C4×C139H(5,𝔽2)11yescharacteristic
195Dic139—41no—
196Dic139—41no—
197Dic139—41no—
198Dic139—41no—
199Dic139—41no—
200C2×C139—41no—
201C2×C139—41no—
202C2×C139D4211yescharacteristic
203C2×C139#57511yescharacteristic
204C2×C139#57711yescharacteristic
205D139—42no—
206D139—42no—
207D139—81no—
208C139#326711yescharacteristic, complemented, Sylow
209#3267—1391nomaximal, Sylow
210C2×AGL(1,ℤ/8)—1391no—
211C2×#135—1391no—
212#547—1391no—
213#546—1391no—
214#497—1391no—
215#470—1391no—
216#465—1391no—
217#463—1391no—
218#461—1391no—
219#452—1391no—
220#452—1391no—
221#450—1391no—
222#449—1391no—
223#442—1391no—
224#435D13911yescharacteristic, complemented
225C2×#41—1391no—
226C2×#41—1391no—
227C2×#41—1391no—
228C22×D4—1391no—
229AGL(1,ℤ/8)—2784no—
230#135—2784no—
231C2×Q16—1391no—
232C2×Q16—1391no—
233C2×SD16—1391no—
234C2×SD16—1391no—
235C2×SD16—1391no—
236C2×SD16—1391no—
237C2×SD16—1391no—
238C2×D8—1391no—
239C2×D8—1391no—
240C2×M16C2×D13911yescharacteristic
241C22×C8C2×D13911yescharacteristic, complemented
242C4⋊Q8—1391no—
243#124—1391no—
244#123—2781no—
245#123—2781no—
246#123—2781no—
247C22⋊Q8—1391no—
248C22⋊Q8—1391no—
249C22⋊Q8—1391no—
250#121—2781no—
251#121—2781no—
252#121—1391no—
253#120—2781no—
254C4×D4—1391no—
255C4×D4—1391no—
256C4×D4C2×D13911yescharacteristic
257C2×C4⋊C4—2781no—
258C2×C22⋊C4—2781no—
259#106—1391no—
260C4⋊C8C2×D13911yescharacteristic, complemented
261#103—1391no—
262#103—1391no—
263#103—1391no—
264#102—1391no—
265#102—1391no—
266#102—1391no—
267C22⋊C8C2×D13911yescharacteristic
268C22⋊C8C2×D13911yescharacteristic, complemented
269#97C2×D13911yescharacteristic, complemented
270C24—2781no—
271#41—2782no—
272#41—2782no—
273#41—2782no—
274#41—5561no—
275#41—5561no—
276#41—5561no—
277C2×Q8—1391no—
278C2×Q8—1391no—
279C2×Q8—1391no—
280C2×D4—2782no—
281C2×D4—2781no—
282C2×D4—2781no—
283C2×D4—2781no—
284C2×D4—2781no—
285C2×D4—2781no—
286C2×D4—5561no—
287C2×D4—1391no—
288C2×D4—1391no—
289C2×D4—1391no—
290C2×D4D55611yescharacteristic
291C22×C4—2781no—
292C22×C4—2781no—
293C22×C4—2781no—
294C22×C4—2781no—
295C22×C4—2781no—
296C22×C4C22×D13911yescharacteristic
297C22×C4C22×D13911yescharacteristic
298Q16—2782no—
299Q16—5561no—
300SD16—2782no—
301SD16—2782no—
302SD16—2782no—
303SD16—2782no—
304SD16—5561no—
305D8—2782no—
306D8—1394no—
307M16—22no—
308C2×C8—22no—
309C2×C8C22×D13911yescharacteristic
310C2×C8C22×D13911yescharacteristic
311C2×C8C22×D13911yescharacteristic
312C2×C8C22×D13911yescharacteristic
313C4⋊C4—2781no—
314C4⋊C4—2781no—
315C4⋊C4—2781no—
316C4⋊C4—2781no—
317C4⋊C4—2781no—
318C4⋊C4—1391no—
319C4⋊C4—1391no—
320C4⋊C4D55611yescharacteristic
321C22⋊C4—2781no—
322C22⋊C4—2781no—
323C22⋊C4—2781no—
324C22⋊C4—2781no—
325C22⋊C4—2781no—
326C22⋊C4—2781no—
327C22⋊C4—2781no—
328C22⋊C4—2781no—
329C22⋊C4D55611yescharacteristic
330C22⋊C4D55611yescharacteristic
331C42C22×D13911yescharacteristic
332C23—2781no—
333C23—2781no—
334C23—2781no—
335C23—5562no—
336C23—5562no—
337C23—11121no—
338C23C2×D55611yescharacteristic
339C23C2×D55611yescharacteristic
340Q8—2781no—
341Q8—2781no—
342Q8—2781no—
343Q8—2781no—
344Q8—2781no—
345Q8—2781no—
346D4—41no—
347D4—2781no—
348D4—2781no—
349D4—2781no—
350D4—2781no—
351D4—5562no—
352D4—5562no—
353D4—5562no—
354D4—5562no—
355D4—11121no—
356D4—1392no—
357D4—1392no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—2781no—
363C2×C4—2781no—
364C2×C4—2781no—
365C2×C4—2781no—
366C2×C4—2781no—
367C2×C4—5562no—
368C2×C4—5562no—
369C2×C4—5562no—
370C2×C4—5562no—
371C2×C4—11121no—
372C2×C4C2×D55611yescharacteristic
373C2×C4C2×D55611yescharacteristic
374C2×C4C2×D55611yescharacteristic
375C2×C4C2×D55611yescharacteristic
376C2×C4C23×D13911yescharacteristic
377C8—21no—
378C8—21no—
379C8—21no—
380C8D4×D13912yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—2782no—
388C22—2782no—
389C22—5561no—
390C22—5561no—
391C22—5561no—
392C22—5561no—
393C22—5561no—
394C22—5561no—
395C22—5561no—
396C22—11124no—
397C22C22×D55611yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—5561no—
403C4—5561no—
404C4—5561no—
405C4—5561no—
406C4—5561no—
407C4C2×D4×D13911yescharacteristic
408C4#1798488811yescharacteristic
409C2—41no—
410C2—41no—
411C2—5562no—
412C2—5562no—
413C2—11121no—
414C2D4×D55611yescharacteristic
415C2#2258175311yescharacteristic
416C2#2258176511yescharacteristic
subgroupG/H
centerC22C22×D556
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#435×C139C2
socleC22×C139C22×D4
hypercenter#435D139
hypocenterC139#3267
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. #22581608C2semidirect
4. #22581599C2semidirect
5. #22581347C2semidirect
6. #22581211C2semidirect
7. #22581182C2semidirect
8. #22581169C2semidirect
9. #22581159C2semidirect
10. #22581117C2semidirect
11. #22581117C2semidirect
12. #22581106C2semidirect
13. #22581100C2semidirect
14. #22581066C2semidirect
15. #435×C139C2semidirect
18. C2×#14555785C22semidirect
22. C2×Dic556C22semidirect
23. C2×Dic556C22semidirect
28. C2×#14555774C22semidirect
31. #17984842C22semidirect
38. #17984821C22semidirect
44. C4×D556C22semidirect
47. #17984774C22semidirect
48. #17984767C22semidirect
49. #17984767C22semidirect
50. #17984767C22semidirect
53. #17984764C22semidirect
55. C22×C8×C139C22semidirect
57. C4⋊C8×C139C22semidirect
59. C22⋊C8×C139C22semidirect
60. #97×C139C22semidirect
94. D1112D4semidirect
208. C139#3267semidirect
224. #435D139semidirect
241. C22×C8C2×D139semidirect
260. C4⋊C8C2×D139semidirect
268. C22⋊C8C2×D139semidirect
269. #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
#225816082
#225815992
#225813472
#225812112
#225811822
#225811692
#225811592
#225811172
#225811062
#225811002
#225810662
#435×C1392
#3267139