Finite Group Databasebeta

← #41×C22⋊D101 #27184617

Subgroups — #41×C22⋊D101 #27184617

Order 12928.

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×D101C211yesmaximal, characteristic, complemented
2#20265846C211yesmaximal, characteristic, complemented
3Q8×C22⋊D101C211yesmaximal, characteristic, complemented
4#20265838C211yesmaximal, characteristic, complemented
5#20265834C211yesmaximal, characteristic, complemented
6#20265826C213yesmaximal, complemented
7#20265821C213yesmaximal, complemented
8#20265815C213yesmaximal, complemented
9D4×C22⋊D101C213yesmaximal, complemented
10#20265723C213yesmaximal, complemented
11#20265688C213yesmaximal, complemented
12#20265684C213yesmaximal, complemented
13#41×Dic101C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊D101C213yesmaximal, complemented
15C22×#41×C101C211yesmaximal, characteristic, complemented
16C2×#13108075C2211yescharacteristic, complemented
17C2×#13108074C2213yescomplemented
18C2×#13108073C2213yescomplemented
19#41×D101—28no—
20C2×Q8×D101C2211yescharacteristic, complemented
21C22×C22⋊D101C2213yes—
22C2×D4×D101C2213yescomplemented
23C22×C4×D101C2213yescomplemented
24#15692253C2213yescomplemented
25#15692251C2213yescomplemented
26#15692244C2213yescomplemented
27#15692242C2213yescomplemented
28#15692238C2216yescomplemented
29#15692236C2216yescomplemented
30#15692234C2213yescomplemented
31#15692234C2213yescomplemented
32#15692231C2213yescomplemented
33#15692231C2213yescomplemented
34#15692229C2213yescomplemented
35#15692229C2213yescomplemented
36#15692227C2216yescomplemented
37#15692227C2216yescomplemented
38#15692226C2213yescomplemented
39#15692226C2213yescomplemented
40#15692224C2216yescomplemented
41#15692223C2216yescomplemented
42Q8×Dic101C2211yescharacteristic, complemented
43Q8×Dic101C2211yescharacteristic, complemented
44D4×Dic101C2213yescomplemented
45D4×Dic101C2213yescomplemented
46C4×C22⋊D101C2213yes—
47C4×C22⋊D101C2211yescharacteristic
48C4×C22⋊D101C2213yescomplemented
49C4×C22⋊D101C2213yescomplemented
50C4×C22⋊D101C2213yescomplemented
51C4×C22⋊D101C2213yescomplemented
52C4×C22⋊D101C2213yescomplemented
53C4×C22⋊D101C2213yescomplemented
54C4×C22⋊D101C2216yescomplemented
55#15692214C2213yescomplemented
56C2×#13108053C2213yescomplemented
57C2×C22⋊Dic101C2213yescomplemented
58C2×#13108051C2213yescomplemented
59C2×C4×Dic101C2213yescomplemented
60C2×#41×C101—28no—
61C2×#41×C101C2211yescharacteristic
62C2×#41×C101C2213yescomplemented
63C2×#41×C101C2211yescharacteristic, complemented
64C2×#41×C101C2213yescomplemented
65C22×Q8×C101C2211yescharacteristic, complemented
66C22×D4×C101C2213yescomplemented
67C23×C4×C101C2213yescomplemented
68C23×D101C2313yes—
69#13108075—24no—
70#13108074—212no—
71#13108073—212no—
72C2×Dic202C2313yes—
73Q8×D101—24no—
74C2×D404C2313yes—
75C2×C22⋊D101—212no—
76C2×C22⋊D101C2316yes—
77C2×C22⋊D101C2313yes—
78C2×C22⋊D101C2313yes—
79C2×C22⋊D101C2313yes—
80C2×C22⋊D101C2316yes—
81C2×C22⋊D101C2311yescharacteristic
82D4×D101—212no—
83C22×Dic101C2313yes—
84C22×Dic101C2313yes—
85C22×Dic101C2313yes—
86C2×C4×D101—212no—
87C2×C4×D101C2311yescharacteristic
88C2×C4×D101C2313yes—
89C2×C4×D101C2313yes—
90C2×C4×D101C2313yes—
91C4⋊Dic101C2313yes—
92C4⋊Dic101C2313yes—
93#13108053C2311yescharacteristic
94#13108053C2313yes—
95#13108053C2313yes—
96#13108053C2313yes—
97#13108053C2316yes—
98C22⋊Dic101C2311yescharacteristic
99C22⋊Dic101C2313yes—
100C22⋊Dic101C2313yes—
101C22⋊Dic101C2313yes—
102C22⋊Dic101C2316yes—
103C22⋊Dic101C2316yes—
104#13108051C2311yescharacteristic
105#13108051C2313yes—
106#13108051C2313yes—
107#13108051C2313yes—
108#13108051C2316yes—
109C4×Dic101C2311yescharacteristic
110C4×Dic101C2313yes—
111C4×Dic101C2313yes—
112C4×Dic101C2313yes—
113C24×C101C2313yes—
114#41×C101—24no—
115#41×C101—212no—
116#41×C101—212no—
117#41×C101D418yescomplemented
118C2×Q8×C101—24no—
119C2×Q8×C101C2313yes—
120C2×Q8×C101C2311yescharacteristic
121C2×D4×C101—212no—
122C2×D4×C101C2316yes—
123C2×D4×C101C2313yes—
124C2×D4×C101C2313yes—
125C22×C4×C101—212no—
126C22×C4×C101C2311yescharacteristic
127C22×C4×C101C2313yes—
128C22×C4×C101C2313yes—
129C22×C4×C101C2313yes—
130C22×C4×C101C2313yes—
131C22×C4×C101C2313yes—
132C23×C101—26no—
133C23×C101—26no—
134C23×C101—43no—
135C23×C101C2413yes—
136C23×C101C2413yes—
137C23×C101C2411yescharacteristic
138C22×D101—26no—
139C22×D101—26no—
140C22×D101—43no—
141C22×D101C2413yes—
142C22×D101C2411yescharacteristic
143Q8×C101—26no—
144Q8×C101C2×D414yescomplemented
145D4×C101—212no—
146D4×C101—26no—
147D4×C101C2×D4112yescomplemented
148C2×C4×C101—26no—
149C2×C4×C101—22no—
150C2×C4×C101—26no—
151C2×C4×C101—26no—
152C2×C4×C101—26no—
153C2×C4×C101C2×D4112yescomplemented
154C2×C4×C101C2411yescharacteristic
155C2×C4×C101C2413yes—
156C2×C4×C101C2413yes—
157C2×C4×C101C2411yescharacteristic
158C22⋊D101—212no—
159C22⋊D101—26no—
160C22⋊D101—26no—
161C22⋊D101—26no—
162C22⋊D101—46no—
163C22⋊D101#4114yesdirect product factor
164C2×Dic101—26no—
165C2×Dic101—26no—
166C2×Dic101—43no—
167C2×Dic101C2411yescharacteristic
168C2×Dic101C2413yes—
169C2×Dic101C2413yes—
170C2×Dic101C2411yescharacteristic
171C2×Dic101C2413yes—
172C2×Dic101C2411yescharacteristic
173D404—26no—
174C4×D101—22no—
175C4×D101—26no—
176C4×D101—26no—
177C4×D101—26no—
178Dic202—26no—
179C22×C101—21no—
180C22×C101—23no—
181C22×C101—23no—
182C22×C101—21no—
183C22×C101—23no—
184C22×C101—23no—
185C22×C101—23no—
186C22×C101—412no—
187C22×C101C22×D416yes—
188C22×C101C2×#4112yescomplemented
189C22×C101C2511yescharacteristic
190C2×D101—21no—
191C2×D101—21no—
192C2×D101—23no—
193C2×D101—23no—
194C2×D101—23no—
195C2×D101—412no—
196C2×D101C2×#4112yescomplemented
197C4×C101—21no—
198C4×C101—23no—
199C4×C101C22×D416yes—
200C4×C101C22×D412yes—
201Dic101—23no—
202Dic101—21no—
203Dic101—23no—
204Dic101—21no—
205Dic101—23no—
206Dic101C2×#4112yescomplemented
207C2×C101—26no—
208C2×C101—22no—
209C2×C101—43no—
210C2×C101C23×D411yescharacteristic
211C2×C101C22×#4111yescharacteristic
212C2×C101#58511yescharacteristic
213D101—22no—
214D101—43no—
215D4×#41—1011nomaximal, Sylow
216C101D4×#4111yescharacteristic, complemented, Sylow
217C22×#41—1011no—
218C22×#41D10111yescharacteristic, complemented
219#550—1011no—
220D4×Q8—1011no—
221#548—1011no—
222#548—1011no—
223#547—1013no—
224#546—1013no—
225#546—1013no—
226D42—1013no—
227#532—1013no—
228#525—1013no—
229#525—1013no—
230C4×#41—1011no—
231C2×C4×D4—1013no—
232C2×#41—28no—
233C2×#41—1011no—
234C2×#41—1013no—
235C2×#41—1013no—
236C2×#41—2028no—
237C2×#41C2×D10111yescharacteristic
238C2×#41C2×D10113yescomplemented
239C2×#41C2×D10113yescomplemented
240C2×#41C2×D10111yescharacteristic, complemented
241C22×Q8—1011no—
242C22×Q8C2×D10111yescharacteristic, complemented
243C22×D4—1013no—
244C22×D4—1013no—
245C22×D4C2×D10113yescomplemented
246C23×C4—1013no—
247C23×C4C2×D10113yescomplemented
248C4⋊Q8—1013no—
249#127—1013no—
250#124—1013no—
251#124—1013no—
252#123—1016no—
253#123—1016no—
254C22⋊Q8—1013no—
255C22⋊Q8—1013no—
256C22⋊Q8—1013no—
257C22⋊Q8—1013no—
258#121—1013no—
259#121—1013no—
260#121—1016no—
261#121—1016no—
262#121—1013no—
263#121—1013no—
264#120—1016no—
265#120—1016no—
266C4×Q8—1011no—
267C4×Q8—1011no—
268C4×D4—1013no—
269C4×D4—1013no—
270C4×D4—1011no—
271C4×D4—1013no—
272C4×D4—1013no—
273C4×D4—1013no—
274C4×D4—1013no—
275C4×D4—1013no—
276C4×D4—1013no—
277C4×D4—1013no—
278C4×D4—1016no—
279#117—1013no—
280C2×C4⋊C4—1013no—
281C2×C22⋊C4—1013no—
282C2×C22⋊C4—1013no—
283C2×C42—1013no—
284C24—1013no—
285C24C22×D10113yes—
286#41—24no—
287#41—212no—
288#41—212no—
289#41—2024no—
290#41—20212no—
291#41—20212no—
292#41C22⋊D10118yesdirect product factor
293C2×Q8—24no—
294C2×Q8—1013no—
295C2×Q8—2024no—
296C2×Q8C22×D10113yes—
297C2×Q8C22×D10111yescharacteristic
298C2×D4—212no—
299C2×D4—1011no—
300C2×D4—1016no—
301C2×D4—1013no—
302C2×D4—1013no—
303C2×D4—1013no—
304C2×D4—1016no—
305C2×D4—1013no—
306C2×D4—20212no—
307C2×D4—20212no—
308C2×D4C22×D10116yes—
309C2×D4C22×D10113yes—
310C2×D4C22×D10113yes—
311C22×C4—212no—
312C22×C4—1013no—
313C22×C4—1013no—
314C22×C4—1013no—
315C22×C4—1013no—
316C22×C4—1013no—
317C22×C4—1011no—
318C22×C4—1013no—
319C22×C4—20212no—
320C22×C4C22×D10113yes—
321C22×C4C22×D10113yes—
322C22×C4C22×D10113yes—
323C22×C4C22×D10111yescharacteristic
324C22×C4C22×D10113yes—
325C22×C4C22×D10113yes—
326C4⋊C4—1011no—
327C4⋊C4—1013no—
328C4⋊C4—1013no—
329C4⋊C4—1013no—
330C4⋊C4—1016no—
331C4⋊C4—1013no—
332C4⋊C4—1013no—
333C22⋊C4—1011no—
334C22⋊C4—1013no—
335C22⋊C4—1013no—
336C22⋊C4—1013no—
337C22⋊C4—1016no—
338C22⋊C4—1016no—
339C22⋊C4—1011no—
340C22⋊C4—1013no—
341C22⋊C4—1013no—
342C22⋊C4—1013no—
343C22⋊C4—1016no—
344C42—1013no—
345C42—1013no—
346C42—1011no—
347C42—1013no—
348C23—26no—
349C23—26no—
350C23—43no—
351C23—1011no—
352C23—1013no—
353C23—4043no—
354C23—2026no—
355C23—2026no—
356C23C23×D10113yes—
357C23C23×D10113yes—
358C23C23×D10111yescharacteristic
359Q8—26no—
360Q8—2026no—
361Q8C2×C22⋊D10114yescomplemented
362D4—212no—
363D4—26no—
364D4—1014no—
365D4—4046no—
366D4—2026no—
367D4—2026no—
368D4—20212no—
369D4—2026no—
370D4—2026no—
371D4C2×C22⋊D101112yescomplemented
372C2×C4—26no—
373C2×C4—22no—
374C2×C4—26no—
375C2×C4—26no—
376C2×C4—26no—
377C2×C4—1011no—
378C2×C4—1011no—
379C2×C4—1013no—
380C2×C4—1013no—
381C2×C4—1011no—
382C2×C4—1013no—
383C2×C4—4043no—
384C2×C4—2026no—
385C2×C4—2026no—
386C2×C4—2022no—
387C2×C4—2026no—
388C2×C4—2026no—
389C2×C4—2026no—
390C2×C4C2×C22⋊D101112yescomplemented
391C2×C4C23×D10111yescharacteristic
392C2×C4C23×D10113yes—
393C2×C4C23×D10113yes—
394C2×C4C23×D10111yescharacteristic
395C22—21no—
396C22—23no—
397C22—23no—
398C22—21no—
399C22—23no—
400C22—23no—
401C22—23no—
402C22—412no—
403C22—1012no—
404C22—40412no—
405C22—2023no—
406C22—2023no—
407C22—2023no—
408C22—2021no—
409C22—2021no—
410C22C22×C22⋊D10116yes—
411C22#41×D10112yescomplemented
412C22C24×D10111yescharacteristic
413C4—21no—
414C4—23no—
415C4—1012no—
416C4—2021no—
417C4—2023no—
418C4—2023no—
419C4—2021no—
420C4—2023no—
421C4C22×C22⋊D10112yes—
422C4C22×C22⋊D10116yes—
423C2—22no—
424C2—26no—
425C2—43no—
426C2—4043no—
427C2—2022no—
428C2C23×C22⋊D10111yescharacteristic
429C2C2×#41×D10111yescharacteristic
430C2#2026601311yescharacteristic
subgroupG/H
centerC2×C4C23×D101
commutator, socle, cosocleC22×C101C25
FrattiniC22C24×D101
FittingC22×#41×C101C2
hypercenterC22×#41D101
hypocenterC101D4×#41
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C2×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#41×D101C2semidirect
2. #20265846C2semidirect
3. Q8×C22⋊D101C2semidirect
4. #20265838C2semidirect
5. #20265834C2semidirect
6. #20265826C2semidirect
7. #20265821C2semidirect
8. #20265815C2semidirect
9. D4×C22⋊D101C2semidirect
10. #20265723C2semidirect
11. #20265688C2semidirect
12. #20265684C2semidirect
13. #41×Dic101C2semidirect
14. C2×C4×C22⋊D101C2semidirect
15. C22×#41×C101C2semidirect
16. C2×#13108075C22semidirect
17. C2×#13108074C22semidirect
18. C2×#13108073C22semidirect
20. C2×Q8×D101C22semidirect
22. C2×D4×D101C22semidirect
23. C22×C4×D101C22semidirect
24. #15692253C22semidirect
25. #15692251C22semidirect
26. #15692244C22semidirect
27. #15692242C22semidirect
28. #15692238C22semidirect
29. #15692236C22semidirect
30. #15692234C22semidirect
31. #15692234C22semidirect
32. #15692231C22semidirect
33. #15692231C22semidirect
34. #15692229C22semidirect
35. #15692229C22semidirect
36. #15692227C22semidirect
37. #15692227C22semidirect
38. #15692226C22semidirect
39. #15692226C22semidirect
40. #15692224C22semidirect
41. #15692223C22semidirect
42. Q8×Dic101C22semidirect
43. Q8×Dic101C22semidirect
44. D4×Dic101C22semidirect
45. D4×Dic101C22semidirect
48. C4×C22⋊D101C22semidirect
49. C4×C22⋊D101C22semidirect
50. C4×C22⋊D101C22semidirect
51. C4×C22⋊D101C22semidirect
52. C4×C22⋊D101C22semidirect
53. C4×C22⋊D101C22semidirect
54. C4×C22⋊D101C22semidirect
55. #15692214C22semidirect
56. C2×#13108053C22semidirect
57. C2×C22⋊Dic101C22semidirect
58. C2×#13108051C22semidirect
59. C2×C4×Dic101C22semidirect
62. C2×#41×C101C22semidirect
63. C2×#41×C101C22semidirect
64. C2×#41×C101C22semidirect
65. C22×Q8×C101C22semidirect
66. C22×D4×C101C22semidirect
67. C23×C4×C101C22semidirect
117. #41×C101D4semidirect
144. Q8×C101C2×D4semidirect
147. D4×C101C2×D4semidirect
153. C2×C4×C101C2×D4semidirect
163. C22⋊D101#41direct (N × H)
188. C22×C101C2×#41semidirect
196. C2×D101C2×#41semidirect
206. Dic101C2×#41semidirect
216. C101D4×#41semidirect
218. C22×#41D101semidirect
238. C2×#41C2×D101semidirect
239. C2×#41C2×D101semidirect
240. C2×#41C2×D101semidirect
242. C22×Q8C2×D101semidirect
245. C22×D4C2×D101semidirect
247. C23×C4C2×D101semidirect
292. #41C22⋊D101direct (N × H)
361. Q8C2×C22⋊D101semidirect
371. D4C2×C22⋊D101semidirect
390. C2×C4C2×C22⋊D101semidirect
411. C22#41×D101semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D1012
#202658462
Q8×C22⋊D1012
#202658382
#202658342
#202658262
#202658212
#202658152
D4×C22⋊D1012
#202657232
#202656882
#202656842
#41×Dic1012
C2×C4×C22⋊D1012
C22×#41×C1012
D4×#41101