Finite Group Databasebeta

← #41×C22⋊D103 #27208629

Subgroups — #41×C22⋊D103 #27208629

Order 13184.

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×D103C211yesmaximal, characteristic, complemented
2#20268460C211yesmaximal, characteristic, complemented
3Q8×C22⋊D103C211yesmaximal, characteristic, complemented
4#20268452C211yesmaximal, characteristic, complemented
5#20268448C211yesmaximal, characteristic, complemented
6#20268440C213yesmaximal, complemented
7#20268435C213yesmaximal, complemented
8#20268429C213yesmaximal, complemented
9D4×C22⋊D103C213yesmaximal, complemented
10#20268337C213yesmaximal, complemented
11#20268302C213yesmaximal, complemented
12#20268298C213yesmaximal, complemented
13#41×Dic103C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊D103C213yesmaximal, complemented
15C22×#41×C103C211yesmaximal, characteristic, complemented
16C2×#13110106C2211yescharacteristic, complemented
17C2×#13110105C2213yescomplemented
18C2×#13110104C2213yescomplemented
19#41×D103—28no—
20C2×Q8×D103C2211yescharacteristic, complemented
21C22×C22⋊D103C2213yes—
22C2×D4×D103C2213yescomplemented
23C22×C4×D103C2213yescomplemented
24#15693019C2213yescomplemented
25#15693017C2213yescomplemented
26#15693010C2213yescomplemented
27#15693008C2213yescomplemented
28#15693004C2216yescomplemented
29#15693002C2216yescomplemented
30#15693000C2213yescomplemented
31#15693000C2213yescomplemented
32#15692997C2213yescomplemented
33#15692997C2213yescomplemented
34#15692995C2213yescomplemented
35#15692995C2213yescomplemented
36#15692993C2216yescomplemented
37#15692993C2216yescomplemented
38#15692992C2213yescomplemented
39#15692992C2213yescomplemented
40#15692990C2216yescomplemented
41#15692989C2216yescomplemented
42Q8×Dic103C2211yescharacteristic, complemented
43Q8×Dic103C2211yescharacteristic, complemented
44D4×Dic103C2213yescomplemented
45D4×Dic103C2213yescomplemented
46C4×C22⋊D103C2213yes—
47C4×C22⋊D103C2211yescharacteristic
48C4×C22⋊D103C2213yescomplemented
49C4×C22⋊D103C2216yescomplemented
50C4×C22⋊D103C2213yescomplemented
51C4×C22⋊D103C2213yescomplemented
52C4×C22⋊D103C2213yescomplemented
53C4×C22⋊D103C2213yescomplemented
54C4×C22⋊D103C2213yescomplemented
55#15692980C2213yescomplemented
56C2×Dic103⋊C4C2213yescomplemented
57C2×C22⋊Dic103C2213yescomplemented
58C2×(C2×D103)⋊C4C2213yescomplemented
59C2×C4×Dic103C2213yescomplemented
60C2×#41×C103—28no—
61C2×#41×C103C2211yescharacteristic
62C2×#41×C103C2213yescomplemented
63C2×#41×C103C2213yescomplemented
64C2×#41×C103C2211yescharacteristic, complemented
65C22×Q8×C103C2211yescharacteristic, complemented
66C22×D4×C103C2213yescomplemented
67C23×C4×C103C2213yescomplemented
68C23×D103C2313yes—
69#13110106—24no—
70#13110105—212no—
71#13110104—212no—
72C2×Dic206C2313yes—
73Q8×D103—24no—
74C2×D412C2313yes—
75C2×C22⋊D103—212no—
76C2×C22⋊D103C2316yes—
77C2×C22⋊D103C2313yes—
78C2×C22⋊D103C2313yes—
79C2×C22⋊D103C2313yes—
80C2×C22⋊D103C2316yes—
81C2×C22⋊D103C2311yescharacteristic
82D4×D103—212no—
83C22×Dic103C2313yes—
84C22×Dic103C2313yes—
85C22×Dic103C2313yes—
86C2×C4×D103—212no—
87C2×C4×D103C2313yes—
88C2×C4×D103C2313yes—
89C2×C4×D103C2313yes—
90C2×C4×D103C2311yescharacteristic
91C4⋊Dic103C2313yes—
92C4⋊Dic103C2313yes—
93Dic103⋊C4C2311yescharacteristic
94Dic103⋊C4C2313yes—
95Dic103⋊C4C2313yes—
96Dic103⋊C4C2313yes—
97Dic103⋊C4C2316yes—
98C22⋊Dic103C2311yescharacteristic
99C22⋊Dic103C2313yes—
100C22⋊Dic103C2313yes—
101C22⋊Dic103C2313yes—
102C22⋊Dic103C2316yes—
103C22⋊Dic103C2316yes—
104(C2×D103)⋊C4C2311yescharacteristic
105(C2×D103)⋊C4C2313yes—
106(C2×D103)⋊C4C2313yes—
107(C2×D103)⋊C4C2313yes—
108(C2×D103)⋊C4C2316yes—
109C4×Dic103C2311yescharacteristic
110C4×Dic103C2313yes—
111C4×Dic103C2313yes—
112C4×Dic103C2313yes—
113C24×C103C2313yes—
114#41×C103—24no—
115#41×C103—212no—
116#41×C103—212no—
117#41×C103D418yescomplemented
118C2×Q8×C103—24no—
119C2×Q8×C103C2313yes—
120C2×Q8×C103C2311yescharacteristic
121C2×D4×C103—212no—
122C2×D4×C103C2316yes—
123C2×D4×C103C2313yes—
124C2×D4×C103C2313yes—
125C22×C4×C103—212no—
126C22×C4×C103C2311yescharacteristic
127C22×C4×C103C2313yes—
128C22×C4×C103C2313yes—
129C22×C4×C103C2313yes—
130C22×C4×C103C2313yes—
131C22×C4×C103C2313yes—
132C23×C103—26no—
133C23×C103—26no—
134C23×C103—43no—
135C23×C103C2413yes—
136C23×C103C2413yes—
137C23×C103C2411yescharacteristic
138C22×D103—26no—
139C22×D103—26no—
140C22×D103—43no—
141C22×D103C2413yes—
142C22×D103C2411yescharacteristic
143Q8×C103—26no—
144Q8×C103C2×D414yescomplemented
145D4×C103—212no—
146D4×C103—26no—
147D4×C103C2×D4112yescomplemented
148C2×C4×C103—26no—
149C2×C4×C103—22no—
150C2×C4×C103—26no—
151C2×C4×C103—26no—
152C2×C4×C103—26no—
153C2×C4×C103C2×D4112yescomplemented
154C2×C4×C103C2411yescharacteristic
155C2×C4×C103C2413yes—
156C2×C4×C103C2413yes—
157C2×C4×C103C2411yescharacteristic
158C22⋊D103—212no—
159C22⋊D103—26no—
160C22⋊D103—26no—
161C22⋊D103—26no—
162C22⋊D103—46no—
163C22⋊D103#4114yesdirect product factor
164C2×Dic103—26no—
165C2×Dic103—26no—
166C2×Dic103—43no—
167C2×Dic103C2411yescharacteristic
168C2×Dic103C2413yes—
169C2×Dic103C2413yes—
170C2×Dic103C2411yescharacteristic
171C2×Dic103C2413yes—
172C2×Dic103C2411yescharacteristic
173D412—26no—
174C4×D103—22no—
175C4×D103—26no—
176C4×D103—26no—
177C4×D103—26no—
178Dic206—26no—
179C22×C103—21no—
180C22×C103—23no—
181C22×C103—23no—
182C22×C103—21no—
183C22×C103—23no—
184C22×C103—23no—
185C22×C103—23no—
186C22×C103—412no—
187C22×C103C22×D416yes—
188C22×C103C2×#4112yescomplemented
189C22×C103C2511yescharacteristic
190C2×D103—21no—
191C2×D103—21no—
192C2×D103—23no—
193C2×D103—23no—
194C2×D103—23no—
195C2×D103—412no—
196C2×D103C2×#4112yescomplemented
197C4×C103—21no—
198C4×C103—23no—
199C4×C103C22×D416yes—
200C4×C103C22×D412yes—
201Dic103—23no—
202Dic103—21no—
203Dic103—23no—
204Dic103—21no—
205Dic103—23no—
206Dic103C2×#4112yescomplemented
207C2×C103—26no—
208C2×C103—22no—
209C2×C103—43no—
210C2×C103C23×D411yescharacteristic
211C2×C103C22×#4111yescharacteristic
212C2×C103#58511yescharacteristic
213D103—22no—
214D103—43no—
215D4×#41—1031nomaximal, Sylow
216C103D4×#4111yescharacteristic, complemented, Sylow
217C22×#41—1031no—
218C22×#41D10311yescharacteristic, complemented
219#550—1031no—
220D4×Q8—1031no—
221#548—1031no—
222#548—1031no—
223#547—1033no—
224#546—1033no—
225#546—1033no—
226D42—1033no—
227#532—1033no—
228#525—1033no—
229#525—1033no—
230C4×#41—1031no—
231C2×C4×D4—1033no—
232C2×#41—28no—
233C2×#41—1031no—
234C2×#41—1033no—
235C2×#41—1033no—
236C2×#41—2068no—
237C2×#41C2×D10311yescharacteristic
238C2×#41C2×D10313yescomplemented
239C2×#41C2×D10313yescomplemented
240C2×#41C2×D10311yescharacteristic, complemented
241C22×Q8—1031no—
242C22×Q8C2×D10311yescharacteristic, complemented
243C22×D4—1033no—
244C22×D4—1033no—
245C22×D4C2×D10313yescomplemented
246C23×C4—1033no—
247C23×C4C2×D10313yescomplemented
248C4⋊Q8—1033no—
249#127—1033no—
250#124—1033no—
251#124—1033no—
252#123—1036no—
253#123—1036no—
254C22⋊Q8—1033no—
255C22⋊Q8—1033no—
256C22⋊Q8—1033no—
257C22⋊Q8—1033no—
258#121—1033no—
259#121—1033no—
260#121—1036no—
261#121—1036no—
262#121—1033no—
263#121—1033no—
264#120—1036no—
265#120—1036no—
266C4×Q8—1031no—
267C4×Q8—1031no—
268C4×D4—1033no—
269C4×D4—1033no—
270C4×D4—1031no—
271C4×D4—1033no—
272C4×D4—1033no—
273C4×D4—1033no—
274C4×D4—1033no—
275C4×D4—1033no—
276C4×D4—1033no—
277C4×D4—1033no—
278C4×D4—1036no—
279#117—1033no—
280C2×C4⋊C4—1033no—
281C2×C22⋊C4—1033no—
282C2×C22⋊C4—1033no—
283C2×C42—1033no—
284C24—1033no—
285C24C22×D10313yes—
286#41—24no—
287#41—212no—
288#41—212no—
289#41—2064no—
290#41—20612no—
291#41—20612no—
292#41C22⋊D10318yesdirect product factor
293C2×Q8—24no—
294C2×Q8—1033no—
295C2×Q8—2064no—
296C2×Q8C22×D10313yes—
297C2×Q8C22×D10311yescharacteristic
298C2×D4—212no—
299C2×D4—1031no—
300C2×D4—1036no—
301C2×D4—1033no—
302C2×D4—1033no—
303C2×D4—1033no—
304C2×D4—1036no—
305C2×D4—1033no—
306C2×D4—20612no—
307C2×D4—20612no—
308C2×D4C22×D10316yes—
309C2×D4C22×D10313yes—
310C2×D4C22×D10313yes—
311C22×C4—212no—
312C22×C4—1033no—
313C22×C4—1033no—
314C22×C4—1033no—
315C22×C4—1033no—
316C22×C4—1033no—
317C22×C4—1031no—
318C22×C4—1033no—
319C22×C4—20612no—
320C22×C4C22×D10313yes—
321C22×C4C22×D10313yes—
322C22×C4C22×D10313yes—
323C22×C4C22×D10311yescharacteristic
324C22×C4C22×D10313yes—
325C22×C4C22×D10313yes—
326C4⋊C4—1031no—
327C4⋊C4—1033no—
328C4⋊C4—1033no—
329C4⋊C4—1033no—
330C4⋊C4—1036no—
331C4⋊C4—1033no—
332C4⋊C4—1033no—
333C22⋊C4—1031no—
334C22⋊C4—1033no—
335C22⋊C4—1033no—
336C22⋊C4—1033no—
337C22⋊C4—1036no—
338C22⋊C4—1036no—
339C22⋊C4—1031no—
340C22⋊C4—1033no—
341C22⋊C4—1033no—
342C22⋊C4—1033no—
343C22⋊C4—1036no—
344C42—1033no—
345C42—1033no—
346C42—1031no—
347C42—1033no—
348C23—26no—
349C23—26no—
350C23—43no—
351C23—1031no—
352C23—1033no—
353C23—4123no—
354C23—2066no—
355C23—2066no—
356C23C23×D10313yes—
357C23C23×D10313yes—
358C23C23×D10311yescharacteristic
359Q8—26no—
360Q8—2066no—
361Q8C2×C22⋊D10314yescomplemented
362D4—212no—
363D4—26no—
364D4—1034no—
365D4—4126no—
366D4—2066no—
367D4—2066no—
368D4—20612no—
369D4—2066no—
370D4—2066no—
371D4C2×C22⋊D103112yescomplemented
372C2×C4—26no—
373C2×C4—22no—
374C2×C4—26no—
375C2×C4—26no—
376C2×C4—26no—
377C2×C4—1031no—
378C2×C4—1031no—
379C2×C4—1033no—
380C2×C4—1033no—
381C2×C4—1031no—
382C2×C4—1033no—
383C2×C4—4123no—
384C2×C4—2066no—
385C2×C4—2066no—
386C2×C4—2062no—
387C2×C4—2066no—
388C2×C4—2066no—
389C2×C4—2066no—
390C2×C4C2×C22⋊D103112yescomplemented
391C2×C4C23×D10311yescharacteristic
392C2×C4C23×D10313yes—
393C2×C4C23×D10313yes—
394C2×C4C23×D10311yescharacteristic
395C22—21no—
396C22—23no—
397C22—23no—
398C22—21no—
399C22—23no—
400C22—23no—
401C22—23no—
402C22—412no—
403C22—1032no—
404C22—41212no—
405C22—2063no—
406C22—2063no—
407C22—2063no—
408C22—2061no—
409C22—2061no—
410C22C22×C22⋊D10316yes—
411C22#41×D10312yescomplemented
412C22C24×D10311yescharacteristic
413C4—21no—
414C4—23no—
415C4—1032no—
416C4—2061no—
417C4—2063no—
418C4—2063no—
419C4—2061no—
420C4—2063no—
421C4C22×C22⋊D10312yes—
422C4C22×C22⋊D10316yes—
423C2—22no—
424C2—26no—
425C2—43no—
426C2—4123no—
427C2—2062no—
428C2C23×C22⋊D10311yescharacteristic
429C2C2×#41×D10311yescharacteristic
430C2#2026862711yescharacteristic
subgroupG/H
centerC2×C4C23×D103
commutator, socle, cosocleC22×C103C25
FrattiniC22C24×D103
FittingC22×#41×C103C2
hypercenterC22×#41D103
hypocenterC103D4×#41
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#41×D103C2semidirect
2. #20268460C2semidirect
3. Q8×C22⋊D103C2semidirect
4. #20268452C2semidirect
5. #20268448C2semidirect
6. #20268440C2semidirect
7. #20268435C2semidirect
8. #20268429C2semidirect
9. D4×C22⋊D103C2semidirect
10. #20268337C2semidirect
11. #20268302C2semidirect
12. #20268298C2semidirect
13. #41×Dic103C2semidirect
14. C2×C4×C22⋊D103C2semidirect
15. C22×#41×C103C2semidirect
16. C2×#13110106C22semidirect
17. C2×#13110105C22semidirect
18. C2×#13110104C22semidirect
20. C2×Q8×D103C22semidirect
22. C2×D4×D103C22semidirect
23. C22×C4×D103C22semidirect
24. #15693019C22semidirect
25. #15693017C22semidirect
26. #15693010C22semidirect
27. #15693008C22semidirect
28. #15693004C22semidirect
29. #15693002C22semidirect
30. #15693000C22semidirect
31. #15693000C22semidirect
32. #15692997C22semidirect
33. #15692997C22semidirect
34. #15692995C22semidirect
35. #15692995C22semidirect
36. #15692993C22semidirect
37. #15692993C22semidirect
38. #15692992C22semidirect
39. #15692992C22semidirect
40. #15692990C22semidirect
41. #15692989C22semidirect
42. Q8×Dic103C22semidirect
43. Q8×Dic103C22semidirect
44. D4×Dic103C22semidirect
45. D4×Dic103C22semidirect
48. C4×C22⋊D103C22semidirect
49. C4×C22⋊D103C22semidirect
50. C4×C22⋊D103C22semidirect
51. C4×C22⋊D103C22semidirect
52. C4×C22⋊D103C22semidirect
53. C4×C22⋊D103C22semidirect
54. C4×C22⋊D103C22semidirect
55. #15692980C22semidirect
56. C2×Dic103⋊C4C22semidirect
57. C2×C22⋊Dic103C22semidirect
58. C2×(C2×D103)⋊C4C22semidirect
59. C2×C4×Dic103C22semidirect
62. C2×#41×C103C22semidirect
63. C2×#41×C103C22semidirect
64. C2×#41×C103C22semidirect
65. C22×Q8×C103C22semidirect
66. C22×D4×C103C22semidirect
67. C23×C4×C103C22semidirect
117. #41×C103D4semidirect
144. Q8×C103C2×D4semidirect
147. D4×C103C2×D4semidirect
153. C2×C4×C103C2×D4semidirect
163. C22⋊D103#41direct (N × H)
188. C22×C103C2×#41semidirect
196. C2×D103C2×#41semidirect
206. Dic103C2×#41semidirect
216. C103D4×#41semidirect
218. C22×#41D103semidirect
238. C2×#41C2×D103semidirect
239. C2×#41C2×D103semidirect
240. C2×#41C2×D103semidirect
242. C22×Q8C2×D103semidirect
245. C22×D4C2×D103semidirect
247. C23×C4C2×D103semidirect
292. #41C22⋊D103direct (N × H)
361. Q8C2×C22⋊D103semidirect
371. D4C2×C22⋊D103semidirect
390. C2×C4C2×C22⋊D103semidirect
411. C22#41×D103semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D1032
#202684602
Q8×C22⋊D1032
#202684522
#202684482
#202684402
#202684352
#202684292
D4×C22⋊D1032
#202683372
#202683022
#202682982
#41×Dic1032
C2×C4×C22⋊D1032
C22×#41×C1032
D4×#41103