Finite Group Databasebeta

← #463×D271 #46845784

Subgroups — #463×D271 #46845784

Order 34688.

564 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×SD16×D271C211yesmaximal, characteristic, complemented
2C2×D8×D271C211yesmaximal, characteristic
3#124×D271C211yesmaximal, characteristic, complemented
4C4×D4×D271C211yesmaximal, characteristic, complemented
5#31774115C211yesmaximal, characteristic, complemented
6#31774114C211yesmaximal, characteristic, complemented
7#31774113C211yesmaximal, characteristic, complemented
8#31774112C211yesmaximal, characteristic, complemented
9#31774111C211yesmaximal, characteristic, complemented
10#31774110C211yesmaximal, characteristic, complemented
11#31774109C211yesmaximal, characteristic, complemented
12C4⋊C8×D271C211yesmaximal, characteristic, complemented
13#103×D271C211yesmaximal, characteristic, complemented
14#102×D271C211yesmaximal, characteristic, complemented
15#463×C271C211yesmaximal, characteristic, complemented
16C2×Q8×D271C2211yescharacteristic
17C2×D4×D271C2211yescharacteristic
18C2×D4×D271C2211yescharacteristic
19C22×C4×D271—21no—
20C2×#16864643C2211yescharacteristic, complemented
21C2×#16864642C2211yescharacteristic, complemented
22C2×#16864641C2211yescharacteristic, complemented
23SD16×D271—24no—
24C2×D2168C2211yescharacteristic
25C2×#16864639C2211yescharacteristic
26C2×#16864639C2211yescharacteristic
27D8×D271—24no—
28C2×C8×D271C2211yescharacteristic
29C2×C8×D271C2211yescharacteristic
30#22576149C2211yescharacteristic, complemented
31#22576148C2211yescharacteristic, complemented
32#22576147C2211yescharacteristic, complemented
33#22576146—21no—
34#22576146—21no—
35C4×D1084C2211yescharacteristic, complemented
36D4×Dic271C2211yescharacteristic, complemented
37#22576122C2211yescharacteristic, complemented
38C4×C22⋊D271—21no—
39(C22⋊D271)⋊C4—21no—
40C4⋊C4×D271C2211yescharacteristic
41C22⋊C4×D271—21no—
42C22⋊C4×D271—21no—
43C22⋊C4×D271—21no—
44C42×D271C2211yescharacteristic
45C4⋊(C271⋊C8)C2211yescharacteristic, complemented
46Dic271⋊C8C2211yescharacteristic, complemented
47Dic271⋊C8C2211yescharacteristic, complemented
48#22576085C2211yescharacteristic, complemented
49#22576084C2211yescharacteristic, complemented
50#22576083C2211yescharacteristic, complemented
51#22576082C2211yescharacteristic, complemented
52#22576081C2211yescharacteristic, complemented
53#22576080C2211yescharacteristic, complemented
54C2×SD16×C271C2211yescharacteristic, complemented
55C2×D8×C271C2211yescharacteristic
56#124×C271C2211yescharacteristic, complemented
57C4×D4×C271C2211yescharacteristic, complemented
58C4⋊C8×C271C2211yescharacteristic, complemented
59#103×C271C2211yescharacteristic, complemented
60#102×C271C2211yescharacteristic, complemented
61C23×D271—21no—
62C23×D271—21no—
63C2×Dic542—21no—
64C2×Dic542C2311yescharacteristic
65Q8×D271—22no—
66Q8×D271—22no—
67C2×D1084C2311yescharacteristic
68C2×D1084C2311yescharacteristic
69C2×C22⋊D271—21no—
70C2×C22⋊D271—21no—
71D4×D271—22no—
72D4×D271—22no—
73D4×D271—22no—
74D4×D271D414yes—
75C22×Dic271—21no—
76C2×C4×D271—21no—
77C2×C4×D271—21no—
78C2×C4×D271—21no—
79C2×C4×D271—21no—
80C2×C4×D271—44no—
81C2×C4×D271D411yescharacteristic
82C2×C4×D271D411yescharacteristic
83C2×C4×D271C2311yescharacteristic
84#16864643—22no—
85#16864642—22no—
86#16864641—22no—
87D2168—22no—
88#16864639—22no—
89#16864639—22no—
90C2×C271⋊C8C2311yescharacteristic
91C2×C271⋊C8C2311yescharacteristic
92C8×D271—22no—
93C8×D271—22no—
94C4⋊Dic271C2311yescharacteristic
95Dic271⋊C4—21no—
96C22⋊Dic271—21no—
97C22⋊Dic271—21no—
98C22⋊Dic271—21no—
99(C2×D271)⋊C4—21no—
100(C2×D271)⋊C4—21no—
101(C2×D271)⋊C4—21no—
102(C2×D271)⋊C4—21no—
103(C2×D271)⋊C4—21no—
104(C2×D271)⋊C4—21no—
105C4×Dic271D411yescharacteristic
106C4×Dic271D411yescharacteristic
107C4×Dic271C2311yescharacteristic
108C2×Q8×C271C2311yescharacteristic
109C2×D4×C271C2311yescharacteristic
110C2×D4×C271C2311yescharacteristic
111C22×C4×C271—21no—
112SD16×C271—22no—
113D8×C271—22no—
114C2×C8×C271C2311yescharacteristic
115C2×C8×C271C2311yescharacteristic
116C4⋊C4×C271C2311yescharacteristic
117C22⋊C4×C271—21no—
118C22⋊C4×C271—21no—
119C22⋊C4×C271—21no—
120C42×C271C2311yescharacteristic
121C22×D271—21no—
122C22×D271—24no—
123C22×D271—21no—
124C22×D271—42no—
125C22×D271—42no—
126C22×D271—42no—
127C22×D271—42no—
128C22×D271—42no—
129C22×D271C2×D411yescharacteristic
130Dic542—21no—
131Dic542—21no—
132Dic542—42no—
133D1084—21no—
134D1084—21no—
135D1084—21no—
136D1084C2×D412yes—
137C22⋊D271—24no—
138C22⋊D271—42no—
139C2×Dic271—21no—
140C2×Dic271—21no—
141C2×Dic271—42no—
142C2×Dic271C2×D411yescharacteristic
143C2×Dic271C2×D411yescharacteristic
144C2×Dic271C2×D411yescharacteristic
145C4×D271—22no—
146C4×D271—22no—
147C4×D271—42no—
148C4×D271—42no—
149C4×D271—42no—
150C4×D271—42no—
151C4×D271C2×D412yes—
152C4×D271#4112yes—
153C271⋊C8—21no—
154C271⋊C8—21no—
155C23×C271—21no—
156C23×C271—21no—
157Q8×C271—21no—
158Q8×C271—21no—
159D4×C271—21no—
160D4×C271—21no—
161D4×C271—21no—
162D4×C271C2×D412yes—
163C2×C4×C271—21no—
164C2×C4×C271—21no—
165C2×C4×C271—42no—
166C2×C4×C271C2×D411yescharacteristic
167C2×C4×C271C2×D411yescharacteristic
168C2×C4×C271C2411yescharacteristic
169C8×C271—21no—
170C8×C271—21no—
171C22×C271—22no—
172C22×C271—41no—
173C22×C271—41no—
174C22×C271—41no—
175C22×C271—41no—
176C22×C271—41no—
177C22×C271C22×D411yescharacteristic
178C2×D271—22no—
179C2×D271—41no—
180C2×D271—41no—
181C2×D271—48no—
182C2×D271—41no—
183C2×D271—41no—
184C2×D271—41no—
185C2×D271—84no—
186C2×D271#12112yes—
187C2×D271#13512yes—
188C2×D271AGL(1,ℤ/8)12yes—
189C4×C271—21no—
190C4×C271—21no—
191C4×C271—41no—
192C4×C271—41no—
193C4×C271C22×D411yescharacteristic
194C4×C271C2×#4111yescharacteristic
195Dic271—21no—
196Dic271—21no—
197Dic271—41no—
198Dic271—41no—
199Dic271#12112yes—
200C2×C271—42no—
201C2×C271—81no—
202C2×C271C2×#12111yescharacteristic
203C2×C271C2×#13511yescharacteristic
204C2×C271C2×AGL(1,ℤ/8)11yescharacteristic
205D271—42no—
206D271—81no—
207D271#46314yesdirect product factor
208C271C2×#46311yescharacteristic, complemented, Sylow
209C2×#463—2711nomaximal, Sylow
210C22×SD16—2711no—
211C22×D8—2711no—
212C2×#124—2711no—
213C2×C4×D4—2711no—
214#463—2711no—
215#463—2711no—
216#463—2711no—
217#463—2711no—
218#463—2711no—
219#463—2711no—
220#463—2711no—
221#463D27111yescharacteristic, direct product factor
222C2×C4⋊C8—2711no—
223C2×#103—2711no—
224C2×#102—2711no—
225C22×Q8—2711no—
226C22×D4—2711no—
227C22×D4—2711no—
228C23×C4—5421no—
229C2×SD16—2711no—
230C2×SD16—2711no—
231C2×SD16—2711no—
232C2×SD16—5424no—
233C2×SD16C2×D27111yescharacteristic, complemented
234C2×D8—2711no—
235C2×D8—2711no—
236C2×D8—2711no—
237C2×D8—5424no—
238C2×D8C2×D27111yescharacteristic
239C22×C8—2711no—
240C22×C8—2711no—
241#124—2711no—
242#124—2711no—
243#124—2711no—
244#124—5421no—
245#124—5421no—
246#124C2×D27111yescharacteristic, complemented
247C4×D4—2711no—
248C4×D4—2711no—
249C4×D4—2711no—
250C4×D4—5421no—
251C4×D4—5421no—
252C4×D4C2×D27111yescharacteristic, complemented
253C2×C4⋊C4—2711no—
254C2×C22⋊C4—5421no—
255C2×C22⋊C4—5421no—
256C2×C22⋊C4—5421no—
257C2×C42—2711no—
258C4⋊C8—2711no—
259C4⋊C8—2711no—
260C4⋊C8—2711no—
261C4⋊C8C2×D27111yescharacteristic, complemented
262#103—2711no—
263#103—2711no—
264#103—2711no—
265#103C2×D27111yescharacteristic, complemented
266#102—2711no—
267#102—2711no—
268#102—2711no—
269#102C2×D27111yescharacteristic, complemented
270C24—5421no—
271C24—5421no—
272C2×Q8—2711no—
273C2×Q8—5421no—
274C2×Q8—5422no—
275C2×Q8—5422no—
276C2×Q8C22×D27111yescharacteristic
277C2×D4—2714no—
278C2×D4—2711no—
279C2×D4—2711no—
280C2×D4—5422no—
281C2×D4—5422no—
282C2×D4—5422no—
283C2×D4—5421no—
284C2×D4—5421no—
285C2×D4C22×D27111yescharacteristic
286C2×D4C22×D27111yescharacteristic
287C22×C4—21no—
288C22×C4—2711no—
289C22×C4—2711no—
290C22×C4—2711no—
291C22×C4—5421no—
292C22×C4—5421no—
293C22×C4—5421no—
294C22×C4—5421no—
295C22×C4—5421no—
296C22×C4—10844no—
297SD16—22no—
298SD16—5422no—
299SD16—5422no—
300SD16—5422no—
301D8—22no—
302D8—5422no—
303D8—5422no—
304D8—5422no—
305C2×C8—2711no—
306C2×C8—2711no—
307C2×C8—5422no—
308C2×C8—5422no—
309C2×C8C22×D27111yescharacteristic
310C2×C8C22×D27111yescharacteristic
311C4⋊C4—2711no—
312C4⋊C4—5421no—
313C4⋊C4C22×D27111yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—5421no—
318C22⋊C4—5421no—
319C22⋊C4—5421no—
320C22⋊C4—5421no—
321C22⋊C4—5421no—
322C22⋊C4—5421no—
323C22⋊C4—5421no—
324C22⋊C4—5421no—
325C22⋊C4—5421no—
326C42—2711no—
327C42—2711no—
328C42—2711no—
329C42C22×D27111yescharacteristic
330C23—21no—
331C23—21no—
332C23—2711no—
333C23—5424no—
334C23—5421no—
335C23—5421no—
336C23—10842no—
337C23—10842no—
338C23—10842no—
339C23—10842no—
340C23—10842no—
341Q8—21no—
342Q8—21no—
343Q8—5421no—
344Q8—5421no—
345Q8—10842no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—2712no—
350D4—5424no—
351D4—5421no—
352D4—5421no—
353D4—5421no—
354D4—10842no—
355D4D4×D27112yes—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—2711no—
360C2×C4—2712no—
361C2×C4—2712no—
362C2×C4—2711no—
363C2×C4—2711no—
364C2×C4—5422no—
365C2×C4—5422no—
366C2×C4—5421no—
367C2×C4—5421no—
368C2×C4—10842no—
369C2×C4—10842no—
370C2×C4—10842no—
371C2×C4—10842no—
372C2×C4—10842no—
373C2×C4D4×D27111yescharacteristic
374C2×C4D4×D27111yescharacteristic
375C2×C4C23×D27111yescharacteristic
376C8—21no—
377C8—21no—
378C8—5421no—
379C8—5421no—
380C22—22no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—2712no—
387C22—2712no—
388C22—2712no—
389C22—5422no—
390C22—10848no—
391C22—10841no—
392C22—10841no—
393C22—10841no—
394C22—10841no—
395C22—10841no—
396C22—21684no—
397C22C2×D4×D27111yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—2712no—
403C4—5421no—
404C4—5421no—
405C4—10841no—
406C4—10841no—
407C4C2×D4×D27111yescharacteristic
408C4#41×D27111yescharacteristic
409C2—42no—
410C2—81no—
411C2—2714no—
412C2—10842no—
413C2—21681no—
414C2#121×D27111yescharacteristic
415C2#135×D27111yescharacteristic
416C2AGL(1,ℤ/8)×D27111yescharacteristic
subgroupG/H
centerC22C2×D4×D271
commutator, cosocleC2×C4×C271C24
FrattiniC2×C4C23×D271
Fitting#463×C271C2
socleC22×C271C22×D4
prime radicalC2×D8×D271C2
hypercenter#463D271
hypocenterC271C2×#463
LCSG ▷ C2×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D271C2semidirect
3. #124×D271C2semidirect
4. C4×D4×D271C2semidirect
5. #31774115C2semidirect
6. #31774114C2semidirect
7. #31774113C2semidirect
8. #31774112C2semidirect
9. #31774111C2semidirect
10. #31774110C2semidirect
11. #31774109C2semidirect
12. C4⋊C8×D271C2semidirect
13. #103×D271C2semidirect
14. #102×D271C2semidirect
15. #463×C271C2semidirect
20. C2×#16864643C22semidirect
21. C2×#16864642C22semidirect
22. C2×#16864641C22semidirect
30. #22576149C22semidirect
31. #22576148C22semidirect
32. #22576147C22semidirect
35. C4×D1084C22semidirect
36. D4×Dic271C22semidirect
37. #22576122C22semidirect
45. C4⋊(C271⋊C8)C22semidirect
46. Dic271⋊C8C22semidirect
47. Dic271⋊C8C22semidirect
48. #22576085C22semidirect
49. #22576084C22semidirect
50. #22576083C22semidirect
51. #22576082C22semidirect
52. #22576081C22semidirect
53. #22576080C22semidirect
54. C2×SD16×C271C22semidirect
56. #124×C271C22semidirect
57. C4×D4×C271C22semidirect
58. C4⋊C8×C271C22semidirect
59. #103×C271C22semidirect
60. #102×C271C22semidirect
207. D271#463direct (N × H)
208. C271C2×#463semidirect
221. #463D271direct (N × H)
233. C2×SD16C2×D271semidirect
246. #124C2×D271semidirect
252. C4×D4C2×D271semidirect
261. C4⋊C8C2×D271semidirect
265. #103C2×D271semidirect
269. #102C2×D271semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D2712
C2×D8×D2712
#124×D2712
C4×D4×D2712
#317741152
#317741142
#317741132
#317741122
#317741112
#317741102
#317741092
C4⋊C8×D2712
#103×D2712
#102×D2712
#463×C2712
C2×#463271