Finite Group Databasebeta

← #41×C22⋊D271 #46849849

Subgroups — #41×C22⋊D271 #46849849

Order 34688.

1648 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D271C211yesmaximal, characteristic, complemented
2#31774566C211yesmaximal, characteristic, complemented
3Q8×C22⋊D271C211yesmaximal, characteristic, complemented
4#31774558C211yesmaximal, characteristic, complemented
5#31774554C211yesmaximal, characteristic, complemented
6#31774546C213yesmaximal, complemented
7#31774541C213yesmaximal, complemented
8#31774535C213yesmaximal, complemented
9D4×C22⋊D271C213yesmaximal, complemented
10#31774443C213yesmaximal, complemented
11#31774408C213yesmaximal, complemented
12#31774404C213yesmaximal, complemented
13#41×Dic271C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊D271C213yesmaximal, complemented
15C22×#41×C271C211yesmaximal, characteristic, complemented
16C2×#16864655C2211yescharacteristic, complemented
17C2×#16864654C2213yescomplemented
18C2×#16864653C2213yescomplemented
19#41×D271—28no—
20C2×Q8×D271C2211yescharacteristic, complemented
21C22×C22⋊D271C2213yes—
22C2×D4×D271C2213yescomplemented
23C22×C4×D271C2213yescomplemented
24#22576158C2213yescomplemented
25#22576156C2213yescomplemented
26#22576149C2213yescomplemented
27#22576147C2213yescomplemented
28#22576143C2216yescomplemented
29#22576141C2216yescomplemented
30#22576139C2213yescomplemented
31#22576139C2213yescomplemented
32#22576136C2213yescomplemented
33#22576136C2213yescomplemented
34#22576134C2213yescomplemented
35#22576134C2213yescomplemented
36#22576132C2216yescomplemented
37#22576132C2216yescomplemented
38#22576131C2213yescomplemented
39#22576131C2213yescomplemented
40#22576129C2216yescomplemented
41#22576128C2216yescomplemented
42Q8×Dic271C2211yescharacteristic, complemented
43Q8×Dic271C2211yescharacteristic, complemented
44D4×Dic271C2213yescomplemented
45D4×Dic271C2213yescomplemented
46C4×C22⋊D271C2213yes—
47C4×C22⋊D271C2211yescharacteristic
48C4×C22⋊D271C2213yescomplemented
49C4×C22⋊D271C2213yescomplemented
50C4×C22⋊D271C2213yescomplemented
51C4×C22⋊D271C2213yescomplemented
52C4×C22⋊D271C2213yescomplemented
53C4×C22⋊D271C2213yescomplemented
54C4×C22⋊D271C2216yescomplemented
55#22576119C2213yescomplemented
56C2×Dic271⋊C4C2213yescomplemented
57C2×C22⋊Dic271C2213yescomplemented
58C2×(C2×D271)⋊C4C2213yescomplemented
59C2×C4×Dic271C2213yescomplemented
60C2×#41×C271—28no—
61C2×#41×C271C2211yescharacteristic
62C2×#41×C271C2213yescomplemented
63C2×#41×C271C2211yescharacteristic, complemented
64C2×#41×C271C2213yescomplemented
65C22×Q8×C271C2211yescharacteristic, complemented
66C22×D4×C271C2213yescomplemented
67C23×C4×C271C2213yescomplemented
68C23×D271C2313yes—
69#16864655—24no—
70#16864654—212no—
71#16864653—212no—
72C2×Dic542C2313yes—
73Q8×D271—24no—
74C2×D1084C2313yes—
75C2×C22⋊D271—212no—
76C2×C22⋊D271C2313yes—
77C2×C22⋊D271C2313yes—
78C2×C22⋊D271C2316yes—
79C2×C22⋊D271C2313yes—
80C2×C22⋊D271C2316yes—
81C2×C22⋊D271C2311yescharacteristic
82D4×D271—212no—
83C22×Dic271C2313yes—
84C22×Dic271C2313yes—
85C22×Dic271C2313yes—
86C2×C4×D271—212no—
87C2×C4×D271C2313yes—
88C2×C4×D271C2313yes—
89C2×C4×D271C2311yescharacteristic
90C2×C4×D271C2313yes—
91C4⋊Dic271C2313yes—
92C4⋊Dic271C2313yes—
93Dic271⋊C4C2313yes—
94Dic271⋊C4C2316yes—
95Dic271⋊C4C2313yes—
96Dic271⋊C4C2313yes—
97Dic271⋊C4C2311yescharacteristic
98C22⋊Dic271C2316yes—
99C22⋊Dic271C2313yes—
100C22⋊Dic271C2316yes—
101C22⋊Dic271C2313yes—
102C22⋊Dic271C2313yes—
103C22⋊Dic271C2311yescharacteristic
104(C2×D271)⋊C4C2313yes—
105(C2×D271)⋊C4C2316yes—
106(C2×D271)⋊C4C2313yes—
107(C2×D271)⋊C4C2313yes—
108(C2×D271)⋊C4C2311yescharacteristic
109C4×Dic271C2313yes—
110C4×Dic271C2313yes—
111C4×Dic271C2311yescharacteristic
112C4×Dic271C2313yes—
113C24×C271C2313yes—
114#41×C271—24no—
115#41×C271—212no—
116#41×C271—212no—
117#41×C271D418yescomplemented
118C2×Q8×C271—24no—
119C2×Q8×C271C2313yes—
120C2×Q8×C271C2311yescharacteristic
121C2×D4×C271—212no—
122C2×D4×C271C2316yes—
123C2×D4×C271C2313yes—
124C2×D4×C271C2313yes—
125C22×C4×C271—212no—
126C22×C4×C271C2313yes—
127C22×C4×C271C2313yes—
128C22×C4×C271C2313yes—
129C22×C4×C271C2311yescharacteristic
130C22×C4×C271C2313yes—
131C22×C4×C271C2313yes—
132C22×D271—26no—
133C22×D271—26no—
134C22×D271—43no—
135C22×D271C2413yes—
136C22×D271C2411yescharacteristic
137Dic542—26no—
138D1084—26no—
139C22⋊D271—212no—
140C22⋊D271—26no—
141C22⋊D271—26no—
142C22⋊D271—26no—
143C22⋊D271—46no—
144C22⋊D271#4114yesdirect product factor
145C2×Dic271—26no—
146C2×Dic271—26no—
147C2×Dic271—43no—
148C2×Dic271C2411yescharacteristic
149C2×Dic271C2413yes—
150C2×Dic271C2413yes—
151C2×Dic271C2411yescharacteristic
152C2×Dic271C2413yes—
153C2×Dic271C2411yescharacteristic
154C4×D271—22no—
155C4×D271—26no—
156C4×D271—26no—
157C4×D271—26no—
158C23×C271—26no—
159C23×C271—26no—
160C23×C271—43no—
161C23×C271C2413yes—
162C23×C271C2413yes—
163C23×C271C2411yescharacteristic
164Q8×C271—26no—
165Q8×C271C2×D414yescomplemented
166D4×C271—212no—
167D4×C271—26no—
168D4×C271C2×D4112yescomplemented
169C2×C4×C271—26no—
170C2×C4×C271—22no—
171C2×C4×C271—26no—
172C2×C4×C271—26no—
173C2×C4×C271—26no—
174C2×C4×C271C2×D4112yescomplemented
175C2×C4×C271C2411yescharacteristic
176C2×C4×C271C2413yes—
177C2×C4×C271C2413yes—
178C2×C4×C271C2411yescharacteristic
179C22×C271—21no—
180C22×C271—23no—
181C22×C271—21no—
182C22×C271—23no—
183C22×C271—23no—
184C22×C271—23no—
185C22×C271—23no—
186C22×C271—412no—
187C22×C271C22×D416yes—
188C22×C271C2×#4112yescomplemented
189C22×C271C2511yescharacteristic
190C2×D271—21no—
191C2×D271—21no—
192C2×D271—23no—
193C2×D271—23no—
194C2×D271—23no—
195C2×D271—412no—
196C2×D271C2×#4112yescomplemented
197C4×C271—21no—
198C4×C271—23no—
199C4×C271C22×D412yes—
200C4×C271C22×D416yes—
201Dic271—21no—
202Dic271—23no—
203Dic271—23no—
204Dic271—21no—
205Dic271—23no—
206Dic271C2×#4112yescomplemented
207C2×C271—26no—
208C2×C271—22no—
209C2×C271—43no—
210C2×C271C23×D411yescharacteristic
211C2×C271C22×#4111yescharacteristic
212C2×C271#58511yescharacteristic
213D271—22no—
214D271—43no—
215C271D4×#4111yescharacteristic, complemented, Sylow
216D4×#41—2711nomaximal, Sylow
217C22×#41—2711no—
218C22×#41D27111yescharacteristic, complemented
219#550—2711no—
220D4×Q8—2711no—
221#548—2711no—
222#548—2711no—
223#547—2713no—
224#546—2713no—
225#546—2713no—
226D42—2713no—
227#532—2713no—
228#525—2713no—
229#525—2713no—
230C4×#41—2711no—
231C2×C4×D4—2713no—
232C2×#41—28no—
233C2×#41—2711no—
234C2×#41—2713no—
235C2×#41—2713no—
236C2×#41—5428no—
237C2×#41C2×D27111yescharacteristic
238C2×#41C2×D27113yescomplemented
239C2×#41C2×D27113yescomplemented
240C2×#41C2×D27111yescharacteristic, complemented
241C22×Q8—2711no—
242C22×Q8C2×D27111yescharacteristic, complemented
243C22×D4—2713no—
244C22×D4—2713no—
245C22×D4C2×D27113yescomplemented
246C23×C4—2713no—
247C23×C4C2×D27113yescomplemented
248C4⋊Q8—2713no—
249#127—2713no—
250#124—2713no—
251#124—2713no—
252#123—2716no—
253#123—2716no—
254C22⋊Q8—2713no—
255C22⋊Q8—2713no—
256C22⋊Q8—2713no—
257C22⋊Q8—2713no—
258#121—2713no—
259#121—2713no—
260#121—2716no—
261#121—2716no—
262#121—2713no—
263#121—2713no—
264#120—2716no—
265#120—2716no—
266C4×Q8—2711no—
267C4×Q8—2711no—
268C4×D4—2713no—
269C4×D4—2713no—
270C4×D4—2711no—
271C4×D4—2713no—
272C4×D4—2713no—
273C4×D4—2713no—
274C4×D4—2713no—
275C4×D4—2713no—
276C4×D4—2713no—
277C4×D4—2713no—
278C4×D4—2716no—
279#117—2713no—
280C2×C4⋊C4—2713no—
281C2×C22⋊C4—2713no—
282C2×C22⋊C4—2713no—
283C2×C42—2713no—
284C24—2713no—
285C24C22×D27113yes—
286#41—24no—
287#41—212no—
288#41—212no—
289#41—5424no—
290#41—54212no—
291#41—54212no—
292#41C22⋊D27118yesdirect product factor
293C2×Q8—24no—
294C2×Q8—2713no—
295C2×Q8—5424no—
296C2×Q8C22×D27113yes—
297C2×Q8C22×D27111yescharacteristic
298C2×D4—212no—
299C2×D4—2711no—
300C2×D4—2713no—
301C2×D4—2713no—
302C2×D4—2713no—
303C2×D4—2716no—
304C2×D4—2716no—
305C2×D4—2713no—
306C2×D4—54212no—
307C2×D4—54212no—
308C2×D4C22×D27116yes—
309C2×D4C22×D27113yes—
310C2×D4C22×D27113yes—
311C22×C4—212no—
312C22×C4—2713no—
313C22×C4—2713no—
314C22×C4—2713no—
315C22×C4—2713no—
316C22×C4—2713no—
317C22×C4—2711no—
318C22×C4—2713no—
319C22×C4—54212no—
320C22×C4C22×D27113yes—
321C22×C4C22×D27113yes—
322C22×C4C22×D27113yes—
323C22×C4C22×D27111yescharacteristic
324C22×C4C22×D27113yes—
325C22×C4C22×D27113yes—
326C4⋊C4—2711no—
327C4⋊C4—2713no—
328C4⋊C4—2713no—
329C4⋊C4—2713no—
330C4⋊C4—2713no—
331C4⋊C4—2713no—
332C4⋊C4—2716no—
333C22⋊C4—2711no—
334C22⋊C4—2713no—
335C22⋊C4—2713no—
336C22⋊C4—2713no—
337C22⋊C4—2716no—
338C22⋊C4—2716no—
339C22⋊C4—2711no—
340C22⋊C4—2713no—
341C22⋊C4—2713no—
342C22⋊C4—2713no—
343C22⋊C4—2716no—
344C42—2713no—
345C42—2713no—
346C42—2711no—
347C42—2713no—
348C23—26no—
349C23—26no—
350C23—43no—
351C23—2711no—
352C23—2713no—
353C23—5426no—
354C23—5426no—
355C23—10843no—
356C23C23×D27113yes—
357C23C23×D27113yes—
358C23C23×D27111yescharacteristic
359Q8—26no—
360Q8—5426no—
361Q8C2×C22⋊D27114yescomplemented
362D4—212no—
363D4—26no—
364D4—2714no—
365D4—5426no—
366D4—5426no—
367D4—54212no—
368D4—5426no—
369D4—5426no—
370D4—10846no—
371D4C2×C22⋊D271112yescomplemented
372C2×C4—26no—
373C2×C4—22no—
374C2×C4—26no—
375C2×C4—26no—
376C2×C4—26no—
377C2×C4—2711no—
378C2×C4—2711no—
379C2×C4—2713no—
380C2×C4—2713no—
381C2×C4—2711no—
382C2×C4—2713no—
383C2×C4—5426no—
384C2×C4—5426no—
385C2×C4—5422no—
386C2×C4—5426no—
387C2×C4—5426no—
388C2×C4—5426no—
389C2×C4—10843no—
390C2×C4C2×C22⋊D271112yescomplemented
391C2×C4C23×D27111yescharacteristic
392C2×C4C23×D27113yes—
393C2×C4C23×D27113yes—
394C2×C4C23×D27111yescharacteristic
395C22—23no—
396C22—23no—
397C22—21no—
398C22—21no—
399C22—23no—
400C22—23no—
401C22—23no—
402C22—412no—
403C22—2712no—
404C22—5421no—
405C22—5421no—
406C22—5423no—
407C22—5423no—
408C22—5423no—
409C22—108412no—
410C22C22×C22⋊D27116yes—
411C22#41×D27112yescomplemented
412C22C24×D27111yescharacteristic
413C4—21no—
414C4—23no—
415C4—2712no—
416C4—5423no—
417C4—5421no—
418C4—5423no—
419C4—5421no—
420C4—5423no—
421C4C22×C22⋊D27112yes—
422C4C22×C22⋊D27116yes—
423C2—22no—
424C2—26no—
425C2—43no—
426C2—5422no—
427C2—10843no—
428C2C23×C22⋊D27111yescharacteristic
429C2C2×#41×D27111yescharacteristic
430C2#3177473311yescharacteristic
subgroupG/H
centerC2×C4C23×D271
commutator, socle, cosocleC22×C271C25
FrattiniC22C24×D271
FittingC22×#41×C271C2
hypercenterC22×#41D271
hypocenterC271D4×#41
LCSG ▷ C22×C271 ▷ C271
UCSC1 ◁ C2×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#41×D271C2semidirect
2. #31774566C2semidirect
3. Q8×C22⋊D271C2semidirect
4. #31774558C2semidirect
5. #31774554C2semidirect
6. #31774546C2semidirect
7. #31774541C2semidirect
8. #31774535C2semidirect
9. D4×C22⋊D271C2semidirect
10. #31774443C2semidirect
11. #31774408C2semidirect
12. #31774404C2semidirect
13. #41×Dic271C2semidirect
14. C2×C4×C22⋊D271C2semidirect
15. C22×#41×C271C2semidirect
16. C2×#16864655C22semidirect
17. C2×#16864654C22semidirect
18. C2×#16864653C22semidirect
20. C2×Q8×D271C22semidirect
22. C2×D4×D271C22semidirect
23. C22×C4×D271C22semidirect
24. #22576158C22semidirect
25. #22576156C22semidirect
26. #22576149C22semidirect
27. #22576147C22semidirect
28. #22576143C22semidirect
29. #22576141C22semidirect
30. #22576139C22semidirect
31. #22576139C22semidirect
32. #22576136C22semidirect
33. #22576136C22semidirect
34. #22576134C22semidirect
35. #22576134C22semidirect
36. #22576132C22semidirect
37. #22576132C22semidirect
38. #22576131C22semidirect
39. #22576131C22semidirect
40. #22576129C22semidirect
41. #22576128C22semidirect
42. Q8×Dic271C22semidirect
43. Q8×Dic271C22semidirect
44. D4×Dic271C22semidirect
45. D4×Dic271C22semidirect
48. C4×C22⋊D271C22semidirect
49. C4×C22⋊D271C22semidirect
50. C4×C22⋊D271C22semidirect
51. C4×C22⋊D271C22semidirect
52. C4×C22⋊D271C22semidirect
53. C4×C22⋊D271C22semidirect
54. C4×C22⋊D271C22semidirect
55. #22576119C22semidirect
56. C2×Dic271⋊C4C22semidirect
57. C2×C22⋊Dic271C22semidirect
58. C2×(C2×D271)⋊C4C22semidirect
59. C2×C4×Dic271C22semidirect
62. C2×#41×C271C22semidirect
63. C2×#41×C271C22semidirect
64. C2×#41×C271C22semidirect
65. C22×Q8×C271C22semidirect
66. C22×D4×C271C22semidirect
67. C23×C4×C271C22semidirect
117. #41×C271D4semidirect
144. C22⋊D271#41direct (N × H)
165. Q8×C271C2×D4semidirect
168. D4×C271C2×D4semidirect
174. C2×C4×C271C2×D4semidirect
188. C22×C271C2×#41semidirect
196. C2×D271C2×#41semidirect
206. Dic271C2×#41semidirect
215. C271D4×#41semidirect
218. C22×#41D271semidirect
238. C2×#41C2×D271semidirect
239. C2×#41C2×D271semidirect
240. C2×#41C2×D271semidirect
242. C22×Q8C2×D271semidirect
245. C22×D4C2×D271semidirect
247. C23×C4C2×D271semidirect
292. #41C22⋊D271direct (N × H)
361. Q8C2×C22⋊D271semidirect
371. D4C2×C22⋊D271semidirect
390. C2×C4C2×C22⋊D271semidirect
411. C22#41×D271semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D2712
#317745662
Q8×C22⋊D2712
#317745582
#317745542
#317745462
#317745412
#317745352
D4×C22⋊D2712
#317744432
#317744082
#317744042
#41×Dic2712
C2×C4×C22⋊D2712
C22×#41×C2712
D4×#41271