Finite Group Databasebeta

← #27208633

Subgroups — #27208633

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
1C22×#13110106C211yesmaximal, characteristic, complemented
2C2×#41×D103C211yesmaximal, characteristic, complemented
3#20268460C211yesmaximal, characteristic, complemented
4Q8×C22⋊D103C211yesmaximal, characteristic, complemented
5#20268453C211yesmaximal, characteristic, complemented
6#20268443C213yesmaximal, complemented
7#20268437C213yesmaximal, complemented
8#20268434C213yesmaximal, complemented
9#20268425C213yesmaximal, complemented
10#20268340C213yesmaximal, complemented
11#20268304C213yesmaximal, complemented
12#20268301C213yesmaximal, complemented
13C4×#13110106C211yesmaximal, characteristic, complemented
14C4×D4×D103C213yesmaximal, complemented
15#548×C103C211yesmaximal, characteristic, complemented
16C2×#13110106—28no—
17C2×#13110106C2211yescharacteristic
18C2×#13110106C2213yescomplemented
19C2×#13110106C2213yescomplemented
20C2×#13110106C2211yescharacteristic, complemented
21C2×#13110105C2213yescomplemented
22C2×#13110104C2213yescomplemented
23#41×D103—28no—
24C2×Q8×D103C2211yescharacteristic, complemented
25C22×D412C2213yescomplemented
26C2×D4×D103C2213yes—
27C2×D4×D103C2213yescomplemented
28C22×C4×D103C2213yescomplemented
29C22×C4×D103C2213yescomplemented
30#15693019C2213yescomplemented
31#15693017C2213yescomplemented
32#15693009C2213yescomplemented
33#15693006C2216yescomplemented
34#15693003C2216yescomplemented
35#15693001C2213yescomplemented
36#15693000C2213yescomplemented
37#15692997C2213yescomplemented
38#15692996C2213yescomplemented
39#15692995C2213yescomplemented
40#15692994C2216yescomplemented
41#15692994C2216yescomplemented
42#15692992C2213yescomplemented
43#15692991C2216yescomplemented
44#15692989C2216yescomplemented
45Q8×Dic103C2211yescharacteristic, complemented
46C4×D412C2213yescomplemented
47C4×D412C2213yescomplemented
48D4×Dic103C2213yescomplemented
49#15692983C2213yescomplemented
50#15692983C2213yescomplemented
51C4×C22⋊D103C2213yes—
52C4×C22⋊D103C2213yescomplemented
53(C22⋊D103)⋊C4C2211yescharacteristic
54(C22⋊D103)⋊C4C2216yescomplemented
55(C22⋊D103)⋊C4C2213yescomplemented
56#15692979C2213yescomplemented
57C4⋊C4×D103C2213yescomplemented
58C22⋊C4×D103C2213yescomplemented
59C22⋊C4×D103C2213yescomplemented
60C42×D103C2213yescomplemented
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×D103C2313yes—
70#13110106—24no—
71#13110106—212no—
72#13110106—212no—
73#13110106D418yescomplemented
74#13110105—212no—
75#13110104—212no—
76C2×Dic206C2313yes—
77Q8×D103—24no—
78C2×D412—212no—
79C2×D412C2313yes—
80C2×D412C2316yes—
81C2×D412C2313yes—
82C2×D412C2313yes—
83C2×C22⋊D103C2313yes—
84C2×C22⋊D103C2316yes—
85C2×C22⋊D103C2316yes—
86C2×C22⋊D103C2311yescharacteristic
87D4×D103—212no—
88D4×D103—212no—
89C22×Dic103C2313yes—
90C22×Dic103C2311yescharacteristic
91C2×C4×D103—212no—
92C2×C4×D103—212no—
93C2×C4×D103C2313yes—
94C2×C4×D103C2313yes—
95C2×C4×D103C2313yes—
96C2×C4×D103C2313yes—
97C2×C4×D103C2313yes—
98C2×C4×D103C2313yes—
99C2×C4×D103C2311yescharacteristic
100C2×C4×D103C2313yes—
101C2×C4×D103C2313yes—
102C4⋊Dic103C2313yes—
103C4⋊Dic103C2313yes—
104Dic103⋊C4C2311yescharacteristic
105Dic103⋊C4C2313yes—
106Dic103⋊C4C2316yes—
107C22⋊Dic103C2313yes—
108C22⋊Dic103C2313yes—
109(C2×D103)⋊C4C2311yescharacteristic
110(C2×D103)⋊C4C2313yes—
111(C2×D103)⋊C4C2313yes—
112(C2×D103)⋊C4C2313yes—
113(C2×D103)⋊C4C2316yes—
114(C2×D103)⋊C4C2316yes—
115C4×Dic103C2311yescharacteristic
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—26no—
135C22×D103—26no—
136C22×D103—26no—
137C22×D103—26no—
138C22×D103—43no—
139C22×D103—43no—
140C22×D103C2413yes—
141C22×D103C2413yes—
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—212no—
155C22⋊D103—26no—
156C22⋊D103—46no—
157C22⋊D103#4114yescomplemented
158C2×Dic103—22no—
159C2×Dic103—26no—
160C2×Dic103C2413yes—
161C2×Dic103C2413yes—
162C2×Dic103C2411yescharacteristic
163C2×Dic103C2411yescharacteristic
164C2×Dic103C2411yescharacteristic
165D412—212no—
166D412—26no—
167D412—26no—
168D412C2×D4112yescomplemented
169C4×D103—26no—
170C4×D103—26no—
171C4×D103—26no—
172C4×D103—26no—
173C4×D103—22no—
174C4×D103—26no—
175C4×D103—26no—
176C4×D103—43no—
177C4×D103C2×D4112yescomplemented
178Dic206—26no—
179C22×C103—21no—
180C22×C103—21no—
181C22×C103—23no—
182C22×C103—23no—
183C22×C103—23no—
184C22×C103C2×#4112yescomplemented
185C22×C103C2511yescharacteristic
186C2×D103—21no—
187C2×D103—23no—
188C2×D103—23no—
189C2×D103—21no—
190C2×D103—23no—
191C2×D103—23no—
192C2×D103—23no—
193C2×D103—412no—
194C2×D103—412no—
195C2×D103C22×D416yes—
196C2×D103C2×#4112yescomplemented
197C4×C103—21no—
198C4×C103—23no—
199C4×C103—23no—
200C4×C103—21no—
201C4×C103C22×D416yes—
202Dic103—23no—
203Dic103—21no—
204Dic103—23no—
205Dic103C22×D412yes—
206Dic103C2×#4112yescomplemented
207C2×C103—22no—
208C2×C103—43no—
209C2×C103C23×D411yescharacteristic
210C2×C103C22×#4111yescharacteristic
211C2×C103#58511yescharacteristic
212D103—22no—
213D103—26no—
214D103—43no—
215D4×#41—1031nomaximal, Sylow
216C103D4×#4111yescharacteristic, complemented, Sylow
217C22×#41—1031no—
218C22×#41—1031no—
219#550—1031no—
220D4×Q8—1031no—
221#548—1031no—
222#548D10311yescharacteristic, complemented
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—1031no—
233C2×#41—1033no—
234C2×#41—1033no—
235C2×#41—1031no—
236C2×#41—1033no—
237C2×#41—1033no—
238C2×#41—2068no—
239C2×#41—2068no—
240C2×#41C2×D10311yescharacteristic, complemented
241C22×Q8—1031no—
242C22×Q8C2×D10311yescharacteristic, complemented
243C22×D4—1033no—
244C22×D4—1033no—
245C22×D4—1033no—
246C23×C4—1033no—
247C23×C4—1033no—
248C4⋊Q8—1033no—
249#127—1033no—
250#124—1033no—
251#124C2×D10313yescomplemented
252#123—1036no—
253#123—1036no—
254C22⋊Q8—1033no—
255C22⋊Q8—1033no—
256C22⋊Q8—1033no—
257C22⋊Q8C2×D10313yescomplemented
258#121—1033no—
259#121—1033no—
260#121—1033no—
261#121—1036no—
262#121—1036no—
263#121C2×D10313yescomplemented
264#120—1036no—
265#120—1036no—
266C4×Q8—1031no—
267C4×Q8C2×D10311yescharacteristic, complemented
268C4×D4—1033no—
269C4×D4—1033no—
270C4×D4—1033no—
271C4×D4—1033no—
272C4×D4—1033no—
273C4×D4—1031no—
274C4×D4—1033no—
275C4×D4—1036no—
276C4×D4—1033no—
277C4×D4—1033no—
278C4×D4C2×D10313yescomplemented
279#117—1033no—
280C2×C4⋊C4—1033no—
281C2×C22⋊C4—1033no—
282C2×C22⋊C4—1033no—
283C2×C42—1033no—
284C24—1033no—
285C24—1033no—
286#41—24no—
287#41—1038no—
288#41—20612no—
289#41—20612no—
290#41—20612no—
291#41—20612no—
292#41—2064no—
293C2×Q8—24no—
294C2×Q8—1033no—
295C2×Q8—2064no—
296C2×Q8C22×D10313yes—
297C2×Q8C22×D10311yescharacteristic
298C2×D4—1031no—
299C2×D4—1036no—
300C2×D4—1033no—
301C2×D4—1036no—
302C2×D4—1033no—
303C2×D4—1033no—
304C2×D4—1036no—
305C2×D4—1033no—
306C2×D4—20612no—
307C2×D4—20612no—
308C2×D4—20612no—
309C2×D4C22×D10313yes—
310C2×D4C22×D10313yes—
311C22×C4—1033no—
312C22×C4—1031no—
313C22×C4—1033no—
314C22×C4—1033no—
315C22×C4—1033no—
316C22×C4—1033no—
317C22×C4—1033no—
318C22×C4—1031no—
319C22×C4—1033no—
320C22×C4—1033no—
321C22×C4—1033no—
322C22×C4—20612no—
323C22×C4—20612no—
324C22×C4C22×D10313yes—
325C22×C4C22×D10313yes—
326C4⋊C4—1031no—
327C4⋊C4—1033no—
328C4⋊C4—1036no—
329C4⋊C4—1033no—
330C4⋊C4—1033no—
331C4⋊C4C22×D10313yes—
332C4⋊C4C22×D10313yes—
333C22⋊C4—1033no—
334C22⋊C4—1033no—
335C22⋊C4—1031no—
336C22⋊C4—1033no—
337C22⋊C4—1033no—
338C22⋊C4—1033no—
339C22⋊C4—1036no—
340C22⋊C4—1036no—
341C22⋊C4C22×D10311yescharacteristic
342C22⋊C4C22×D10313yes—
343C22⋊C4C22×D10316yes—
344C42—1031no—
345C42—1033no—
346C42—1033no—
347C42C22×D10313yes—
348C23—1031no—
349C23—1033no—
350C23—1033no—
351C23—4123no—
352C23—4123no—
353C23—2066no—
354C23—2066no—
355C23—2066no—
356C23—2066no—
357C23C23×D10313yes—
358C23C23×D10311yescharacteristic
359Q8—26no—
360Q8—2066no—
361Q8D4×D10314yescomplemented
362D4—26no—
363D4—26no—
364D4—1034no—
365D4—10312no—
366D4—4126no—
367D4—20612no—
368D4—2066no—
369D4—2066no—
370D4—20612no—
371D4—2066no—
372C2×C4—26no—
373C2×C4—26no—
374C2×C4—1031no—
375C2×C4—1031no—
376C2×C4—10312no—
377C2×C4—1033no—
378C2×C4—1031no—
379C2×C4—1033no—
380C2×C4—4123no—
381C2×C4—2062no—
382C2×C4—2066no—
383C2×C4—2066no—
384C2×C4—2066no—
385C2×C4—2066no—
386C2×C4—2062no—
387C2×C4—2066no—
388C2×C4—2066no—
389C2×C4—2066no—
390C2×C4C23×D10311yescharacteristic
391C2×C4C23×D10313yes—
392C2×C4C23×D10311yescharacteristic
393C2×C4C23×D10313yes—
394C2×C4C23×D10313yes—
395C22—21no—
396C22—21no—
397C22—23no—
398C22—23no—
399C22—23no—
400C22—1036no—
401C22—1032no—
402C22—41212no—
403C22—41212no—
404C22—2063no—
405C22—2063no—
406C22—2063no—
407C22—2061no—
408C22—2063no—
409C22—2063no—
410C22—2061no—
411C22#41×D10312yescomplemented
412C22C24×D10311yescharacteristic
413C4—21no—
414C4—23no—
415C4—23no—
416C4—21no—
417C4—1032no—
418C4—1032no—
419C4—2061no—
420C4—2063no—
421C4—2063no—
422C4C2×D4×D10316yes—
423C2—22no—
424C2—43no—
425C2—4123no—
426C2—2062no—
427C2—2066no—
428C2C22×D4×D10311yescharacteristic
429C2C2×#41×D10311yescharacteristic
430C2#2026862811yescharacteristic
subgroupG/H
center, FrattiniC22C24×D103
commutator, socle, cosocleC22×C103C25
Fitting#548×C103C2
hypercenter#548D103
hypocenterC103D4×#41
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C22×#13110106C2semidirect
2. C2×#41×D103C2semidirect
3. #20268460C2semidirect
4. Q8×C22⋊D103C2semidirect
5. #20268453C2semidirect
6. #20268443C2semidirect
7. #20268437C2semidirect
8. #20268434C2semidirect
9. #20268425C2semidirect
10. #20268340C2semidirect
11. #20268304C2semidirect
12. #20268301C2semidirect
13. C4×#13110106C2semidirect
14. C4×D4×D103C2semidirect
15. #548×C103C2semidirect
18. C2×#13110106C22semidirect
19. C2×#13110106C22semidirect
20. C2×#13110106C22semidirect
21. C2×#13110105C22semidirect
22. C2×#13110104C22semidirect
24. C2×Q8×D103C22semidirect
25. C22×D412C22semidirect
27. C2×D4×D103C22semidirect
28. C22×C4×D103C22semidirect
29. C22×C4×D103C22semidirect
30. #15693019C22semidirect
31. #15693017C22semidirect
32. #15693009C22semidirect
33. #15693006C22semidirect
34. #15693003C22semidirect
35. #15693001C22semidirect
36. #15693000C22semidirect
37. #15692997C22semidirect
38. #15692996C22semidirect
39. #15692995C22semidirect
40. #15692994C22semidirect
41. #15692994C22semidirect
42. #15692992C22semidirect
43. #15692991C22semidirect
44. #15692989C22semidirect
45. Q8×Dic103C22semidirect
46. C4×D412C22semidirect
47. C4×D412C22semidirect
48. D4×Dic103C22semidirect
49. #15692983C22semidirect
50. #15692983C22semidirect
52. C4×C22⋊D103C22semidirect
54. (C22⋊D103)⋊C4C22semidirect
55. (C22⋊D103)⋊C4C22semidirect
56. #15692979C22semidirect
57. C4⋊C4×D103C22semidirect
58. C22⋊C4×D103C22semidirect
59. C22⋊C4×D103C22semidirect
60. C42×D103C22semidirect
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
73. #13110106D4semidirect
144. Q8×C103C2×D4semidirect
157. C22⋊D103#41semidirect
168. D412C2×D4semidirect
177. C4×D103C2×D4semidirect
184. C22×C103C2×#41semidirect
196. C2×D103C2×#41semidirect
206. Dic103C2×#41semidirect
216. C103D4×#41semidirect
222. #548D103semidirect
240. C2×#41C2×D103semidirect
242. C22×Q8C2×D103semidirect
251. #124C2×D103semidirect
257. C22⋊Q8C2×D103semidirect
263. #121C2×D103semidirect
267. C4×Q8C2×D103semidirect
278. C4×D4C2×D103semidirect
361. Q8D4×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
C22×#131101062
C2×#41×D1032
#202684602
Q8×C22⋊D1032
#202684532
#202684432
#202684372
#202684342
#202684252
#202683402
#202683042
#202683012
C4×#131101062
C4×D4×D1032
#548×C1032
D4×#41103