Finite Group Databasebeta

← #548×D103 #27208606

Subgroups — #548×D103 #27208606

Order 13184.

1620 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D103C211yesmaximal, characteristic, complemented
2C22×Q8×D103C211yesmaximal, characteristic, complemented
3#20268453C211yesmaximal, characteristic, complemented
4#20268452C211yesmaximal, characteristic, complemented
5#20268451C213yesmaximal, complemented
6#20268450C213yesmaximal, complemented
7#20268449C213yesmaximal, complemented
8#20268448C211yesmaximal, characteristic, complemented
9#20268447C213yesmaximal, complemented
10#124×D103C213yesmaximal, complemented
11C22⋊Q8×D103C213yesmaximal, complemented
12#121×D103C213yesmaximal, complemented
13C4×Q8×D103C211yesmaximal, characteristic, complemented
14C4×D4×D103C213yesmaximal, complemented
15#548×C103C211yesmaximal, characteristic, complemented
16C2×#13110106C2211yescharacteristic, complemented
17C2×#13110105C2213yescomplemented
18C2×#13110104C2213yescomplemented
19#41×D103—28no—
20C22×Dic206C2213yescomplemented
21C2×Q8×D103—28no—
22C2×Q8×D103C2213yes—
23C2×Q8×D103C2211yescharacteristic
24C2×Q8×D103C2211yescharacteristic, complemented
25C2×Q8×D103C2213yescomplemented
26C2×D4×D103C2213yes—
27C2×D4×D103C2213yes—
28C22×C4×D103C2213yes—
29C22×C4×D103C2213yes—
30#15693010C2213yescomplemented
31#15693009C2213yescomplemented
32#15693008C2213yescomplemented
33#15693007C2216yescomplemented
34#15693007C2216yescomplemented
35#15693001C2213yescomplemented
36#15693000C2213yescomplemented
37#15692999C2216yescomplemented
38#15692998C2216yescomplemented
39#15692997C2213yescomplemented
40#15692996C2213yescomplemented
41#15692995C2213yescomplemented
42#15692994C2216yescomplemented
43#15692993C2216yescomplemented
44#15692992C2213yescomplemented
45Q8×Dic103C2211yescharacteristic, complemented
46C4×Dic206C2213yescomplemented
47#15692986C2213yescomplemented
48C4×D412C2213yescomplemented
49D4×Dic103C2213yescomplemented
50#15692983C2213yescomplemented
51C4×C22⋊D103C2213yescomplemented
52C4×C22⋊D103C2213yescomplemented
53(C22⋊D103)⋊C4C2213yescomplemented
54(C22⋊D103)⋊C4C2213yescomplemented
55C4⋊C4×D103C2213yes—
56C4⋊C4×D103C2213yes—
57C22⋊C4×D103C2213yes—
58C22⋊C4×D103C2216yes—
59C22⋊C4×D103C2211yescharacteristic
60C42×D103C2213yes—
61C2×#41×C103C2211yescharacteristic, complemented
62C22×Q8×C103C2211yescharacteristic, complemented
63#124×C103C2213yescomplemented
64C22⋊Q8×C103C2213yescomplemented
65#121×C103C2213yescomplemented
66C4×Q8×C103C2211yescharacteristic, complemented
67C4×D4×C103C2213yescomplemented
68C23×D103C2313yes—
69C23×D103C2311yescharacteristic
70#13110106—24no—
71#13110105—212no—
72#13110104—212no—
73C2×Dic206—212no—
74C2×Dic206C2316yes—
75C2×Dic206C2313yes—
76C2×Dic206C2313yes—
77Q8×D103—24no—
78Q8×D103—212no—
79Q8×D103—212no—
80Q8×D103D418yescomplemented
81C2×D412C2313yes—
82C2×D412C2313yes—
83C2×C22⋊D103C2316yes—
84C2×C22⋊D103C2313yes—
85C2×C22⋊D103C2313yes—
86D4×D103—212no—
87D4×D103—212no—
88C22×Dic103C2313yes—
89C22×Dic103C2313yes—
90C2×C4×D103—212no—
91C2×C4×D103—212no—
92C2×C4×D103C2313yes—
93C2×C4×D103C2313yes—
94C2×C4×D103C2313yes—
95C2×C4×D103C2313yes—
96C2×C4×D103C2313yes—
97C2×C4×D103C2313yes—
98C2×C4×D103C2311yescharacteristic
99C2×C4×D103C2311yescharacteristic
100C2×C4×D103C2313yes—
101C4⋊Dic103C2313yes—
102C4⋊Dic103C2313yes—
103Dic103⋊C4C2313yes—
104Dic103⋊C4C2313yes—
105Dic103⋊C4C2316yes—
106C22⋊Dic103C2311yescharacteristic
107C22⋊Dic103C2313yes—
108C22⋊Dic103C2316yes—
109(C2×D103)⋊C4C2311yescharacteristic
110(C2×D103)⋊C4C2313yes—
111(C2×D103)⋊C4C2311yescharacteristic
112(C2×D103)⋊C4C2313yes—
113(C2×D103)⋊C4C2316yes—
114(C2×D103)⋊C4C2316yes—
115C4×Dic103C2313yes—
116C4×Dic103C2313yes—
117C4×Dic103C2313yes—
118#41×C103—24no—
119C2×Q8×C103—24no—
120C2×Q8×C103C2313yes—
121C2×Q8×C103C2311yescharacteristic
122C2×D4×C103C2313yes—
123C2×D4×C103C2313yes—
124C22×C4×C103C2313yes—
125C22×C4×C103C2313yes—
126C4⋊C4×C103C2313yes—
127C4⋊C4×C103C2313yes—
128C22⋊C4×C103C2311yescharacteristic
129C22⋊C4×C103C2313yes—
130C22⋊C4×C103C2316yes—
131C42×C103C2313yes—
132C23×C103C2413yes—
133C23×C103C2411yescharacteristic
134C22×D103—22no—
135C22×D103—22no—
136C22×D103—26no—
137C22×D103—26no—
138C22×D103—26no—
139C22×D103#4114yescomplemented
140C22×D103C2413yes—
141C22×D103C2411yescharacteristic
142C22×D103C2411yescharacteristic
143Q8×C103—26no—
144Q8×C103C2×D414yescomplemented
145D4×C103—26no—
146D4×C103—26no—
147C2×C4×C103—26no—
148C2×C4×C103—26no—
149C2×C4×C103C2411yescharacteristic
150C2×C4×C103C2413yes—
151C2×C4×C103C2413yes—
152C2×C4×C103C2411yescharacteristic
153C2×C4×C103C2413yes—
154C22⋊D103—26no—
155C22⋊D103—26no—
156C22⋊D103—212no—
157C2×Dic103—26no—
158C2×Dic103—26no—
159C2×Dic103C2411yescharacteristic
160C2×Dic103C2413yes—
161C2×Dic103C2413yes—
162C2×Dic103C2411yescharacteristic
163C2×Dic103C2413yes—
164D412—26no—
165D412—26no—
166C4×D103—22no—
167C4×D103—26no—
168C4×D103—26no—
169C4×D103—22no—
170C4×D103—26no—
171C4×D103—26no—
172C4×D103—26no—
173C4×D103—26no—
174C4×D103C2×D4112yes—
175Dic206—26no—
176Dic206—212no—
177Dic206C2×D4112yescomplemented
178C22×C103—21no—
179C22×C103—21no—
180C22×C103—23no—
181C22×C103—23no—
182C22×C103—23no—
183C22×C103C2×#4112yescomplemented
184C22×C103C2511yescharacteristic
185C2×D103—21no—
186C2×D103—21no—
187C2×D103—28no—
188C2×D103—23no—
189C2×D103—23no—
190C2×D103—23no—
191C2×D103—412no—
192C2×D103C22×D412yes—
193C2×D103C2×#4112yes—
194C2×D103C2×#4112yescomplemented
195C2×D1032−1+412yes—
196C4×C103—23no—
197C4×C103—21no—
198C4×C103—23no—
199C4×C103—21no—
200C4×C103C22×D416yes—
201Dic103—23no—
202Dic103—21no—
203Dic103—23no—
204Dic103—21no—
205Dic103C22×D416yes—
206C2×C103—22no—
207C2×C103—43no—
208C2×C103C23×D411yescharacteristic
209C2×C103C22×#4111yescharacteristic
210C2×C103C2×2−1+411yescharacteristic
211D103—22no—
212D103—43no—
213D103#54814yesdirect product factor
214C2×#548—1031nomaximal, Sylow
215C103C2×#54811yescharacteristic, complemented, Sylow
216C22×#41—1031no—
217C23×Q8—1031no—
218#548—1031no—
219#548—1031no—
220#548—1033no—
221#548—1033no—
222#548—1033no—
223#548—1031no—
224#548—1033no—
225#548D10311yescharacteristic, direct product factor
226C2×#124—1033no—
227C2×C22⋊Q8—1033no—
228C2×#121—1033no—
229C2×C4×Q8—1031no—
230C2×C4×D4—1033no—
231C2×#41—1031no—
232C2×#41—1033no—
233C2×#41—1033no—
234C2×#41—2068no—
235C2×#41C2×D10311yescharacteristic, complemented
236C22×Q8—1031no—
237C22×Q8—1033no—
238C22×Q8—1033no—
239C22×Q8—1031no—
240C22×Q8—1033no—
241C22×Q8—2068no—
242C22×Q8C2×D10311yescharacteristic, complemented
243C22×D4—1033no—
244C22×D4—1033no—
245C23×C4—1033no—
246C23×C4—1033no—
247#124—1033no—
248#124—1033no—
249#124—1036no—
250#124—1036no—
251#124—1033no—
252#124C2×D10313yescomplemented
253C22⋊Q8—1033no—
254C22⋊Q8—1033no—
255C22⋊Q8—1036no—
256C22⋊Q8—1033no—
257C22⋊Q8—1036no—
258C22⋊Q8C2×D10313yescomplemented
259#121—1033no—
260#121—1036no—
261#121—1033no—
262#121—1033no—
263#121—1036no—
264#121C2×D10313yescomplemented
265C4×Q8—1031no—
266C4×Q8—1033no—
267C4×Q8—1033no—
268C4×Q8C2×D10311yescharacteristic, complemented
269C4×D4—1033no—
270C4×D4—1033no—
271C4×D4—1033no—
272C4×D4—1033no—
273C4×D4—1033no—
274C4×D4—1033no—
275C4×D4—1033no—
276C4×D4C2×D10313yescomplemented
277C2×C4⋊C4—1033no—
278C2×C4⋊C4—1033no—
279C2×C22⋊C4—1031no—
280C2×C22⋊C4—1033no—
281C2×C22⋊C4—1036no—
282C2×C42—1033no—
283C24—1031no—
284C24—1033no—
285#41—24no—
286#41—20612no—
287#41—20612no—
288#41—2064no—
289C2×Q8—24no—
290C2×Q8—1038no—
291C2×Q8—1033no—
292C2×Q8—1036no—
293C2×Q8—1033no—
294C2×Q8—20612no—
295C2×Q8—20612no—
296C2×Q8—20612no—
297C2×Q8—2064no—
298C2×Q8C22×D10313yes—
299C2×Q8C22×D10311yescharacteristic
300C2×D4—1033no—
301C2×D4—1033no—
302C2×D4—1036no—
303C2×D4—1033no—
304C2×D4—1033no—
305C2×D4—20612no—
306C2×D4—20612no—
307C2×D4C22×D10313yes—
308C2×D4C22×D10313yes—
309C22×C4—1033no—
310C22×C4—1033no—
311C22×C4—1033no—
312C22×C4—1031no—
313C22×C4—1033no—
314C22×C4—1033no—
315C22×C4—1031no—
316C22×C4—1033no—
317C22×C4—1033no—
318C22×C4—1033no—
319C22×C4—1033no—
320C22×C4—20612no—
321C22×C4—20612no—
322C22×C4C22×D10313yes—
323C22×C4C22×D10313yes—
324C4⋊C4—1033no—
325C4⋊C4—1033no—
326C4⋊C4—1036no—
327C4⋊C4—1033no—
328C4⋊C4—1033no—
329C4⋊C4C22×D10313yes—
330C4⋊C4C22×D10313yes—
331C22⋊C4—1031no—
332C22⋊C4—1033no—
333C22⋊C4—1036no—
334C22⋊C4—1031no—
335C22⋊C4—1031no—
336C22⋊C4—1033no—
337C22⋊C4—1033no—
338C22⋊C4—1036no—
339C22⋊C4—1036no—
340C22⋊C4C22×D10311yescharacteristic
341C22⋊C4C22×D10313yes—
342C22⋊C4C22×D10316yes—
343C42—1033no—
344C42—1033no—
345C42—1033no—
346C42C22×D10313yes—
347C23—1031no—
348C23—1034no—
349C23—1031no—
350C23—1033no—
351C23—2066no—
352C23—2066no—
353C23—2066no—
354C23—2062no—
355C23—2062no—
356C23C23×D10313yes—
357C23C23×D10311yescharacteristic
358Q8—26no—
359Q8—10312no—
360Q8—20612no—
361Q8—2066no—
362Q8D4×D10314yescomplemented
363D4—26no—
364D4—26no—
365D4—2066no—
366D4—20612no—
367D4—2066no—
368D4—2066no—
369D4—2066no—
370C2×C4—26no—
371C2×C4—26no—
372C2×C4—1033no—
373C2×C4—10312no—
374C2×C4—1031no—
375C2×C4—1033no—
376C2×C4—1033no—
377C2×C4—1031no—
378C2×C4—2066no—
379C2×C4—2066no—
380C2×C4—2062no—
381C2×C4—2066no—
382C2×C4—2066no—
383C2×C4—2062no—
384C2×C4—2066no—
385C2×C4—2066no—
386C2×C4—2066no—
387C2×C4—2066no—
388C2×C4C23×D10311yescharacteristic
389C2×C4C23×D10313yes—
390C2×C4C23×D10313yes—
391C2×C4C23×D10311yescharacteristic
392C2×C4C23×D10313yes—
393C22—21no—
394C22—21no—
395C22—23no—
396C22—23no—
397C22—23no—
398C22—1032no—
399C22—1032no—
400C22—1032no—
401C22—1032no—
402C22—41212no—
403C22—2068no—
404C22—2063no—
405C22—2063no—
406C22—2063no—
407C22—2061no—
408C22—2061no—
409C22#41×D10312yescomplemented
410C22C24×D10311yescharacteristic
411C4—21no—
412C4—23no—
413C4—23no—
414C4—21no—
415C4—1036no—
416C4—2061no—
417C4—2063no—
418C4—2063no—
419C4—2061no—
420C4C2×D4×D10316yes—
421C2—22no—
422C2—43no—
423C2—1034no—
424C2—4123no—
425C2—2062no—
426C2C22×D4×D10311yescharacteristic
427C2C2×#41×D10311yescharacteristic
428C22−1+4×D10311yescharacteristic
subgroupG/H
center, FrattiniC22C24×D103
commutator, socle, cosocleC22×C103C25
Fitting#548×C103C2
hypercenter#548D103
hypocenterC103C2×#548
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#41×D103C2semidirect
2. C22×Q8×D103C2semidirect
3. #20268453C2semidirect
4. #20268452C2semidirect
5. #20268451C2semidirect
6. #20268450C2semidirect
7. #20268449C2semidirect
8. #20268448C2semidirect
9. #20268447C2semidirect
10. #124×D103C2semidirect
11. C22⋊Q8×D103C2semidirect
12. #121×D103C2semidirect
13. C4×Q8×D103C2semidirect
14. C4×D4×D103C2semidirect
15. #548×C103C2semidirect
16. C2×#13110106C22semidirect
17. C2×#13110105C22semidirect
18. C2×#13110104C22semidirect
20. C22×Dic206C22semidirect
24. C2×Q8×D103C22semidirect
25. C2×Q8×D103C22semidirect
30. #15693010C22semidirect
31. #15693009C22semidirect
32. #15693008C22semidirect
33. #15693007C22semidirect
34. #15693007C22semidirect
35. #15693001C22semidirect
36. #15693000C22semidirect
37. #15692999C22semidirect
38. #15692998C22semidirect
39. #15692997C22semidirect
40. #15692996C22semidirect
41. #15692995C22semidirect
42. #15692994C22semidirect
43. #15692993C22semidirect
44. #15692992C22semidirect
45. Q8×Dic103C22semidirect
46. C4×Dic206C22semidirect
47. #15692986C22semidirect
48. C4×D412C22semidirect
49. D4×Dic103C22semidirect
50. #15692983C22semidirect
51. C4×C22⋊D103C22semidirect
52. C4×C22⋊D103C22semidirect
53. (C22⋊D103)⋊C4C22semidirect
54. (C22⋊D103)⋊C4C22semidirect
61. C2×#41×C103C22semidirect
62. C22×Q8×C103C22semidirect
63. #124×C103C22semidirect
64. C22⋊Q8×C103C22semidirect
65. #121×C103C22semidirect
66. C4×Q8×C103C22semidirect
67. C4×D4×C103C22semidirect
80. Q8×D103D4semidirect
139. C22×D103#41semidirect
144. Q8×C103C2×D4semidirect
177. Dic206C2×D4semidirect
183. C22×C103C2×#41semidirect
194. C2×D103C2×#41semidirect
213. D103#548direct (N × H)
215. C103C2×#548semidirect
225. #548D103direct (N × H)
235. C2×#41C2×D103semidirect
242. C22×Q8C2×D103semidirect
252. #124C2×D103semidirect
258. C22⋊Q8C2×D103semidirect
264. #121C2×D103semidirect
268. C4×Q8C2×D103semidirect
276. C4×D4C2×D103semidirect
362. Q8D4×D103semidirect
409. 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
C22×Q8×D1032
#202684532
#202684522
#202684512
#202684502
#202684492
#202684482
#202684472
#124×D1032
C22⋊Q8×D1032
#121×D1032
C4×Q8×D1032
C4×D4×D1032
#548×C1032
C2×#548103