Finite Group Databasebeta

← #31817919

Subgroups — #31817919

Order 17792.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17984875C211yesmaximal, characteristic, complemented
2C22×#14555774C211yesmaximal, characteristic, complemented
3D4×Dic278C211yesmaximal, characteristic, complemented
4#22581599C211yesmaximal, characteristic
5#22581347C211yesmaximal, characteristic, complemented
6#22581199C211yesmaximal, characteristic, complemented
7#22581194C211yesmaximal, characteristic, complemented
8#22581176C211yesmaximal, characteristic, complemented
9#22581159C211yesmaximal, characteristic, complemented
10#22581117C211yesmaximal, characteristic, complemented
11#22581111C211yesmaximal, characteristic, complemented
12#22581106C211yesmaximal, characteristic, complemented
13#22581094C211yesmaximal, characteristic, complemented
14#22581055C211yesmaximal, characteristic, complemented
15#435×C139C211yesmaximal, characteristic, complemented
16C2×#14555785C2211yescharacteristic
17C22×Dic278C2211yescharacteristic
18C22×Dic278C2211yescharacteristic, complemented
19C22×D556C2211yescharacteristic
20#17984875—24no—
21C2×Dic556C2211yescharacteristic, complemented
22C2×Dic556C2211yescharacteristic, complemented
23C2×Dic556C2211yescharacteristic, complemented
24C2×#14555774—24no—
25C2×#14555774C2211yescharacteristic
26C2×#14555774C2211yescharacteristic
27C2×#14555774C2211yescharacteristic
28C2×#14555774C2211yescharacteristic
29C2×#14555774C2211yescharacteristic
30C2×#14555774C2211yescharacteristic
31#17984842C2211yescharacteristic, complemented
32#17984841—21no—
33#17984830C2211yescharacteristic
34#17984827—21no—
35#17984821C2211yescharacteristic
36#17984821C2211yescharacteristic
37#17984821C2211yescharacteristic, complemented
38#17984819—21no—
39#17984819—21no—
40#17984816C2211yescharacteristic
41#17984815—21no—
42#17984810—21no—
43C4×Dic278C2211yescharacteristic, complemented
44C4×D556C2211yescharacteristic
45D4×Dic139—21no—
46C22⋊C4×D139—21no—
47#17984776C2211yescharacteristic, complemented
48#17984767C2211yescharacteristic, complemented
49#17984767C2211yescharacteristic, complemented
50#17984767C2211yescharacteristic, complemented
51#17984767C2211yescharacteristic, complemented
52#17984764C2211yescharacteristic
53#17984764C2211yescharacteristic
54C2×M16×C139C2211yescharacteristic, complemented
55C22×C8×C139C2211yescharacteristic
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—41no—
64C2×Dic278—22no—
65C2×Dic278—22no—
66C2×Dic278—21no—
67C2×Dic278—21no—
68C2×Dic278—41no—
69C2×Dic278—41no—
70C2×Dic278C2311yescharacteristic
71C2×Dic278C2311yescharacteristic
72C2×Dic278C2311yescharacteristic
73C2×Dic278C2311yescharacteristic
74C2×D556—22no—
75C2×D556—21no—
76C2×D556—41no—
77C2×D556C2311yescharacteristic
78C2×D556C2311yescharacteristic
79C2×C22⋊D139—21no—
80C2×C22⋊D139—21no—
81C22×Dic139—21no—
82C22×Dic139—21no—
83C2×C4×D139—21no—
84C2×C4×D139—21no—
85Dic556—22no—
86Dic556—22no—
87Dic556—41no—
88#14555774—22no—
89#14555774—22no—
90#14555774—22no—
91#14555774—22no—
92#14555774—41no—
93#14555774D414yescomplemented
94C4⋊Dic139—21no—
95C4⋊Dic139—21no—
96C4⋊Dic139C2311yescharacteristic
97C4⋊Dic139C2311yescharacteristic
98Dic139⋊C4—21no—
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—
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—42no—
126C22×D139—42no—
127C22×D139—81no—
128Dic278—21no—
129Dic278—21no—
130Dic278—21no—
131Dic278—21no—
132Dic278—21no—
133Dic278—21no—
134Dic278—21no—
135Dic278—42no—
136Dic278—42no—
137Dic278C2×D412yes—
138D556—21no—
139D556—21no—
140D556—21no—
141D556—42no—
142D556C2×D412yes—
143C22⋊D139—42no—
144C22⋊D139—81no—
145C2×Dic139—21no—
146C2×Dic139—21no—
147C2×Dic139—21no—
148C2×Dic139—21no—
149C2×Dic139—21no—
150C2×Dic139—21no—
151C2×Dic139—42no—
152C2×Dic139—42no—
153C4×D139—42no—
154C4×D139—81no—
155C23×C139C2×D411yescharacteristic
156C23×C139C2×D411yescharacteristic
157D4×C139—22no—
158C2×C4×C139—21no—
159C2×C4×C139—21no—
160C2×C4×C139—21no—
161C2×C4×C139—21no—
162C2×C4×C139C2×D411yescharacteristic
163C2×C4×C139C2×D411yescharacteristic
164C2×C4×C139C2×D411yescharacteristic
165C2×C4×C139C2×D411yescharacteristic
166C2×C4×C139C2411yescharacteristic
167C8×C139—21no—
168C8×C139—21no—
169C8×C139—21no—
170C8×C139C2×D412yes—
171C22×C139—21no—
172C22×C139—21no—
173C22×C139—21no—
174C22×C139—21no—
175C22×C139—21no—
176C22×C139#13712yescomplemented
177C22×C139C22×D411yescharacteristic
178C2×D139—22no—
179C2×D139—41no—
180C2×D139—41no—
181C2×D139—41no—
182C2×D139—41no—
183C2×D139—41no—
184C2×D139—84no—
185C4×C139—21no—
186C4×C139—21no—
187C4×C139—21no—
188C4×C139—21no—
189C4×C139C22×D411yescharacteristic
190C4×C139H(5,𝔽2)11yescharacteristic
191Dic139—22no—
192Dic139—41no—
193Dic139—41no—
194Dic139—41no—
195Dic139—41no—
196Dic139—41no—
197C2×C139—22no—
198C2×C139—41no—
199C2×C139D4211yescharacteristic
200C2×C139C2×#13711yescharacteristic
201C2×C139#57711yescharacteristic
202D139—42no—
203D139—81no—
204C139#326611yescharacteristic, complemented, Sylow
205#3266—1391nomaximal, Sylow
206C2×#137—1391no—
207C22×SD16—1391no—
208D4×Q8—1391no—
209#546—1391no—
210#497—1391no—
211#468—1391no—
212#467—1391no—
213#464—1391no—
214#461—1391no—
215#452—1391no—
216#451—1391no—
217#450—1391no—
218#448—1391no—
219#440—1391no—
220#435D13911yescharacteristic, complemented
221C2×#41—1391no—
222C22×Q8—1391no—
223C22×Q8—1391no—
224C22×D4—1391no—
225#137—2784no—
226C2×Q16—1391no—
227C2×Q16—1391no—
228C2×Q16—1391no—
229C2×SD16—2784no—
230C2×SD16—1391no—
231C2×SD16—1391no—
232C2×SD16—1391no—
233C2×SD16—1391no—
234C2×SD16—1391no—
235C2×SD16—1391no—
236C2×M16C2×D13911yescharacteristic, complemented
237C22×C8C2×D13911yescharacteristic
238C4⋊Q8—2781no—
239C4⋊Q8—1391no—
240#124—1391no—
241#123—2781no—
242C22⋊Q8—2781no—
243C22⋊Q8—2781no—
244C22⋊Q8—1391no—
245C22⋊Q8—1391no—
246C22⋊Q8—1391no—
247#121—2781no—
248#121—1391no—
249#120—2781no—
250C4×Q8—1391no—
251C4×D4—2781no—
252C4×D4—1391no—
253C4×D4C2×D13911yescharacteristic
254C2×C22⋊C4—2781no—
255#107—1391no—
256C4⋊C8C2×D13911yescharacteristic, complemented
257#103—1391no—
258#103—1391no—
259#103—1391no—
260#103—1391no—
261#102—1391no—
262#102—1391no—
263C22⋊C8C2×D13911yescharacteristic
264C22⋊C8C2×D13911yescharacteristic, complemented
265#97C2×D13911yescharacteristic, complemented
266C24—2781no—
267#41—2782no—
268#41—5561no—
269C2×Q8—2782no—
270C2×Q8—2782no—
271C2×Q8—2781no—
272C2×Q8—2781no—
273C2×Q8—5561no—
274C2×Q8—5561no—
275C2×Q8—1391no—
276C2×Q8—1391no—
277C2×Q8—1391no—
278C2×Q8—1391no—
279C2×D4—2782no—
280C2×D4—2781no—
281C2×D4—2781no—
282C2×D4—2781no—
283C2×D4—5561no—
284C2×D4—1391no—
285C2×D4—1391no—
286C2×D4D55611yescharacteristic
287C22×C4—2781no—
288C22×C4—2781no—
289C22×C4—2781no—
290C22×C4—2781no—
291C22×C4C22×D13911yescharacteristic
292C22×C4C22×D13911yescharacteristic
293Q16—2782no—
294Q16—2782no—
295Q16—5561no—
296SD16—2782no—
297SD16—2782no—
298SD16—2782no—
299SD16—2782no—
300SD16—5561no—
301SD16—1394no—
302M16—22no—
303C2×C8—22no—
304C2×C8C22×D13911yescharacteristic
305C2×C8C22×D13911yescharacteristic
306C2×C8C22×D13911yescharacteristic
307C2×C8C22×D13911yescharacteristic
308C4⋊C4—2781no—
309C4⋊C4—2781no—
310C4⋊C4—2781no—
311C4⋊C4—2781no—
312C4⋊C4—2781no—
313C4⋊C4—2781no—
314C4⋊C4—1391no—
315C4⋊C4—1391no—
316C4⋊C4D55611yescharacteristic
317C22⋊C4—2781no—
318C22⋊C4—2781no—
319C22⋊C4—2781no—
320C22⋊C4—2781no—
321C22⋊C4—2781no—
322C22⋊C4—2781no—
323C22⋊C4—2781no—
324C22⋊C4D55611yescharacteristic
325C22⋊C4D55611yescharacteristic
326C42—2781no—
327C42C22×D13911yescharacteristic
328C23—2781no—
329C23—2781no—
330C23—5562no—
331C23—5562no—
332C23—11121no—
333C23C2×D55611yescharacteristic
334C23C2×D55611yescharacteristic
335Q8—2781no—
336Q8—2781no—
337Q8—2781no—
338Q8—2781no—
339Q8—2781no—
340Q8—2781no—
341Q8—2781no—
342Q8—5562no—
343Q8—5562no—
344Q8—1392no—
345D4—22no—
346D4—2781no—
347D4—2781no—
348D4—2781no—
349D4—5562no—
350D4—5562no—
351D4—11121no—
352D4—1392no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—2781no—
358C2×C4—2781no—
359C2×C4—2781no—
360C2×C4—2781no—
361C2×C4—2781no—
362C2×C4—2781no—
363C2×C4—5562no—
364C2×C4—5562no—
365C2×C4—5562no—
366C2×C4—11121no—
367C2×C4C2×D55611yescharacteristic
368C2×C4C2×D55611yescharacteristic
369C2×C4C2×D55611yescharacteristic
370C2×C4C2×D55611yescharacteristic
371C2×C4C23×D13911yescharacteristic
372C8—21no—
373C8—21no—
374C8—21no—
375C8D4×D13912yes—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—2782no—
382C22—5561no—
383C22—5561no—
384C22—5561no—
385C22—5561no—
386C22—5561no—
387C22—11124no—
388C22#1798487512yescomplemented
389C22C22×D55611yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—2782no—
395C4—5561no—
396C4—5561no—
397C4—5561no—
398C4—5561no—
399C4—5561no—
400C4C2×D4×D13911yescharacteristic
401C4#1798488811yescharacteristic
402C2—22no—
403C2—41no—
404C2—5562no—
405C2—11121no—
406C2D4×D55611yescharacteristic
407C2C2×#1798487511yescharacteristic
408C2#2258176511yescharacteristic
subgroupG/H
centerC22C22×D556
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#435×C139C2
socleC22×C139C22×D4
prime radical#22581599C2
hypercenter#435D139
hypocenterC139#3266
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×#17984875C2semidirect
2. C22×#14555774C2semidirect
3. D4×Dic278C2semidirect
5. #22581347C2semidirect
6. #22581199C2semidirect
7. #22581194C2semidirect
8. #22581176C2semidirect
9. #22581159C2semidirect
10. #22581117C2semidirect
11. #22581111C2semidirect
12. #22581106C2semidirect
13. #22581094C2semidirect
14. #22581055C2semidirect
15. #435×C139C2semidirect
18. C22×Dic278C22semidirect
21. C2×Dic556C22semidirect
22. C2×Dic556C22semidirect
23. C2×Dic556C22semidirect
31. #17984842C22semidirect
37. #17984821C22semidirect
43. C4×Dic278C22semidirect
47. #17984776C22semidirect
48. #17984767C22semidirect
49. #17984767C22semidirect
50. #17984767C22semidirect
51. #17984767C22semidirect
54. C2×M16×C139C22semidirect
57. C4⋊C8×C139C22semidirect
59. C22⋊C8×C139C22semidirect
60. #97×C139C22semidirect
93. #14555774D4semidirect
176. C22×C139#137semidirect
204. C139#3266semidirect
220. #435D139semidirect
236. C2×M16C2×D139semidirect
256. C4⋊C8C2×D139semidirect
264. C22⋊C8C2×D139semidirect
265. #97C2×D139semidirect
388. C22#17984875semidirect

Maximal subgroups

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

subgroupindex
C2×#179848752
C22×#145557742
D4×Dic2782
#225815992
#225813472
#225811992
#225811942
#225811762
#225811592
#225811172
#225811112
#225811062
#225810942
#225810552
#435×C1392
#3266139