Finite Group Databasebeta

← #468×D103 #27204728

Subgroups — #468×D103 #27204728

Order 13184.

544 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D103C211yesmaximal, characteristic, complemented
2C2×M16×D103C211yesmaximal, characteristic, complemented
3C22⋊Q8×D103C211yesmaximal, characteristic, complemented
4#121×D103C211yesmaximal, characteristic
5#20268040C211yesmaximal, characteristic, complemented
6#20268039C211yesmaximal, characteristic, complemented
7#20268038C211yesmaximal, characteristic, complemented
8#20268037C211yesmaximal, characteristic, complemented
9#20268036C211yesmaximal, characteristic, complemented
10#20268035C211yesmaximal, characteristic, complemented
11#20268034C211yesmaximal, characteristic, complemented
12#107×D103C211yesmaximal, characteristic, complemented
13#103×D103C211yesmaximal, characteristic, complemented
14#102×D103C211yesmaximal, characteristic, complemented
15#468×C103C211yesmaximal, characteristic, complemented
16C2×Q8×D103C2211yescharacteristic
17C2×D4×D103—21no—
18C2×D4×D103C2211yescharacteristic
19C22×C4×D103C2211yescharacteristic
20C2×#13110094C2211yescharacteristic, complemented
21C2×#13110093C2211yescharacteristic, complemented
22C2×#13110092C2211yescharacteristic, complemented
23SD16×D103—24no—
24C2×#13110089C2211yescharacteristic, complemented
25C2×#13110088C2211yescharacteristic, complemented
26C2×#13110088C2211yescharacteristic, complemented
27M16×D103—24no—
28C2×C8×D103C2211yescharacteristic
29C2×C8×D103C2211yescharacteristic
30#15693001C2211yescharacteristic, complemented
31#15693000C2211yescharacteristic, complemented
32#15692999—21no—
33#15692998—21no—
34#15692997C2211yescharacteristic, complemented
35#15692996C2211yescharacteristic
36#15692995C2211yescharacteristic
37#15692994—21no—
38#15692993—21no—
39#15692992C2211yescharacteristic
40C4⋊C4×D103—21no—
41C4⋊C4×D103C2211yescharacteristic
42C4⋊C4×D103C2211yescharacteristic
43C22⋊C4×D103—21no—
44C22⋊C4×D103—21no—
45#15692955C2211yescharacteristic, complemented
46#15692954C2211yescharacteristic, complemented
47#15692954C2211yescharacteristic, complemented
48#15692946C2211yescharacteristic, complemented
49#15692945C2211yescharacteristic, complemented
50#15692944C2211yescharacteristic, complemented
51#15692943C2211yescharacteristic, complemented
52#15692942C2211yescharacteristic, complemented
53#15692941C2211yescharacteristic, complemented
54C2×SD16×C103C2211yescharacteristic, complemented
55C2×M16×C103C2211yescharacteristic, complemented
56C22⋊Q8×C103C2211yescharacteristic, complemented
57#121×C103C2211yescharacteristic
58#107×C103C2211yescharacteristic, complemented
59#103×C103C2211yescharacteristic, complemented
60#102×C103C2211yescharacteristic, complemented
61C23×D103—21no—
62C23×D103D411yescharacteristic
63C2×Dic206—21no—
64C2×Dic206C2311yescharacteristic
65Q8×D103—22no—
66Q8×D103—22no—
67C2×D412—21no—
68C2×D412C2311yescharacteristic
69C2×C22⋊D103—21no—
70C2×C22⋊D103—21no—
71C2×C22⋊D103—21no—
72D4×D103—22no—
73D4×D103—22no—
74D4×D103—44no—
75C22×Dic103D411yescharacteristic
76C2×C4×D103—22no—
77C2×C4×D103—22no—
78C2×C4×D103—21no—
79C2×C4×D103—21no—
80C2×C4×D103—21no—
81C2×C4×D103D411yescharacteristic
82C2×C4×D103D411yescharacteristic
83C2×C4×D103C2311yescharacteristic
84C2×C4×D103C2311yescharacteristic
85#13110094—22no—
86#13110093—22no—
87#13110092—22no—
88#13110089—22no—
89#13110088—22no—
90#13110088—22no—
91C2×C103⋊C8C2311yescharacteristic
92C2×C103⋊C8C2311yescharacteristic
93C8×D103—22no—
94C8×D103D414yescomplemented
95C4⋊Dic103—21no—
96C4⋊Dic103C2311yescharacteristic
97C4⋊Dic103C2311yescharacteristic
98Dic103⋊C4—21no—
99Dic103⋊C4—21no—
100Dic103⋊C4—21no—
101Dic103⋊C4—21no—
102C22⋊Dic103—21no—
103C22⋊Dic103—21no—
104(C2×D103)⋊C4—21no—
105(C2×D103)⋊C4—21no—
106(C2×D103)⋊C4—21no—
107(C2×D103)⋊C4—21no—
108C2×Q8×C103C2311yescharacteristic
109C2×D4×C103—21no—
110C2×D4×C103C2311yescharacteristic
111C22×C4×C103C2311yescharacteristic
112SD16×C103—22no—
113M16×C103—22no—
114C2×C8×C103C2311yescharacteristic
115C2×C8×C103C2311yescharacteristic
116C4⋊C4×C103—21no—
117C4⋊C4×C103C2311yescharacteristic
118C4⋊C4×C103C2311yescharacteristic
119C22⋊C4×C103—21no—
120C22⋊C4×C103—21no—
121C23×C103—21no—
122C23×C103C2×D411yescharacteristic
123C22×D103—22no—
124C22×D103—22no—
125C22×D103—22no—
126C22×D103—21no—
127C22×D103—42no—
128C22×D103—42no—
129C22×D103—42no—
130C22×D103C2×D411yescharacteristic
131C22×D103C2×D411yescharacteristic
132Q8×C103—21no—
133Q8×C103—21no—
134D4×C103—21no—
135D4×C103—21no—
136D4×C103—42no—
137C2×C4×C103—21no—
138C2×C4×C103—21no—
139C2×C4×C103—21no—
140C2×C4×C103—21no—
141C2×C4×C103—21no—
142C2×C4×C103C2×D411yescharacteristic
143C2×C4×C103C2411yescharacteristic
144C22⋊D103—42no—
145C22⋊D103—42no—
146C22⋊D103—42no—
147C2×Dic103—22no—
148C2×Dic103—21no—
149C2×Dic103—21no—
150C2×Dic103—21no—
151C2×Dic103C2×D411yescharacteristic
152C2×Dic103C2×D411yescharacteristic
153D412—21no—
154D412—21no—
155D412—42no—
156C4×D103—22no—
157C4×D103—21no—
158C4×D103—21no—
159C4×D103—22no—
160C4×D103—42no—
161C4×D103—42no—
162C4×D103—42no—
163C4×D103C2×D412yes—
164C4×D103#4112yes—
165Dic206—21no—
166Dic206—21no—
167Dic206—42no—
168C8×C103—21no—
169C8×C103C2×D412yescomplemented
170C103⋊C8—21no—
171C103⋊C8C2×D412yescomplemented
172C22×C103—21no—
173C22×C103—21no—
174C22×C103—21no—
175C22×C103—41no—
176C22×C103—41no—
177C22×C103—41no—
178C22×C103C22×D411yescharacteristic
179C2×D103—21no—
180C2×D103—21no—
181C2×D103—21no—
182C2×D103—44no—
183C2×D103—41no—
184C2×D103—41no—
185C2×D103—41no—
186C2×D103—84no—
187C2×D103#12112yes—
188C2×D103AGL(1,ℤ/8)12yes—
189C2×D103#13712yes—
190C4×C103—21no—
191C4×C103—41no—
192C4×C103—41no—
193C4×C103—41no—
194C4×C103C22×D411yescharacteristic
195C4×C103C2×#4111yescharacteristic
196Dic103—21no—
197Dic103—41no—
198Dic103—41no—
199Dic103—41no—
200Dic103#12112yes—
201C2×C103—41no—
202C2×C103—81no—
203C2×C103C2×#12111yescharacteristic
204C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
205C2×C103C2×#13711yescharacteristic
206D103—41no—
207D103—81no—
208D103#46814yesdirect product factor
209C2×#468—1031nomaximal, Sylow
210C103C2×#46811yescharacteristic, complemented, Sylow
211C22×SD16—1031no—
212C22×M16—1031no—
213C2×C22⋊Q8—1031no—
214C2×#121—1031no—
215#468—1031no—
216#468—1031no—
217#468—1031no—
218#468—1031no—
219#468—1031no—
220#468—1031no—
221#468—1031no—
222#468D10311yescharacteristic, direct product factor
223C2×#107—1031no—
224C2×#103—1031no—
225C2×#102—1031no—
226C22×Q8—1031no—
227C22×D4—1031no—
228C22×D4—2061no—
229C23×C4—1031no—
230C2×SD16—1031no—
231C2×SD16—1031no—
232C2×SD16—1031no—
233C2×SD16—2064no—
234C2×SD16C2×D10311yescharacteristic, complemented
235C2×M16—1031no—
236C2×M16—1031no—
237C2×M16—1031no—
238C2×M16—2064no—
239C2×M16C2×D10311yescharacteristic, complemented
240C22×C8—1031no—
241C22×C8—1031no—
242C22⋊Q8—1031no—
243C22⋊Q8—1031no—
244C22⋊Q8—1031no—
245C22⋊Q8—2061no—
246C22⋊Q8—2061no—
247C22⋊Q8C2×D10311yescharacteristic, complemented
248#121—1031no—
249#121—1031no—
250#121—1031no—
251#121—2061no—
252#121—2061no—
253#121C2×D10311yescharacteristic
254C2×C4⋊C4—1031no—
255C2×C4⋊C4—1031no—
256C2×C4⋊C4—2061no—
257C2×C22⋊C4—2061no—
258C2×C22⋊C4—2061no—
259#107—1031no—
260#107—1031no—
261#107—1031no—
262#107C2×D10311yescharacteristic, complemented
263#103—1031no—
264#103—1031no—
265#103—1031no—
266#103C2×D10311yescharacteristic, complemented
267#102—1031no—
268#102—1031no—
269#102—1031no—
270#102C2×D10311yescharacteristic, complemented
271C24—1031no—
272C24—2061no—
273C2×Q8—1031no—
274C2×Q8—2061no—
275C2×Q8—2062no—
276C2×Q8—2062no—
277C2×Q8C22×D10311yescharacteristic
278C2×D4—21no—
279C2×D4—1031no—
280C2×D4—4124no—
281C2×D4—2061no—
282C2×D4—2062no—
283C2×D4—2062no—
284C2×D4—2061no—
285C2×D4—2061no—
286C2×D4—2061no—
287C2×D4C22×D10311yescharacteristic
288C22×C4—1031no—
289C22×C4—1031no—
290C22×C4—1031no—
291C22×C4—1031no—
292C22×C4—1031no—
293C22×C4—2062no—
294C22×C4—2062no—
295C22×C4—2061no—
296C22×C4—2061no—
297C22×C4—2061no—
298C22×C4C22×D10311yescharacteristic
299SD16—22no—
300SD16—2062no—
301SD16—2062no—
302SD16—2062no—
303M16—22no—
304M16—2062no—
305M16—2062no—
306M16—2062no—
307C2×C8—1031no—
308C2×C8—1034no—
309C2×C8—1031no—
310C2×C8—2062no—
311C2×C8C22×D10311yescharacteristic
312C2×C8C22×D10311yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—1031no—
315C4⋊C4—1031no—
316C4⋊C4—2061no—
317C4⋊C4—2061no—
318C4⋊C4—2061no—
319C4⋊C4—2061no—
320C4⋊C4—2061no—
321C4⋊C4C22×D10311yescharacteristic
322C4⋊C4C22×D10311yescharacteristic
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—2061no—
326C22⋊C4—2061no—
327C22⋊C4—2061no—
328C22⋊C4—2061no—
329C22⋊C4—2061no—
330C22⋊C4—2061no—
331C23—21no—
332C23—1031no—
333C23—1031no—
334C23—4122no—
335C23—4122no—
336C23—4122no—
337C23—2062no—
338C23—2062no—
339C23—2062no—
340C23—2061no—
341C23D4×D10311yescharacteristic
342Q8—21no—
343Q8—21no—
344Q8—4122no—
345Q8—2061no—
346Q8—2061no—
347D4—21no—
348D4—21no—
349D4—42no—
350D4—4122no—
351D4—4122no—
352D4—4122no—
353D4—4122no—
354D4—2061no—
355D4—2061no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—1031no—
362C2×C4—1032no—
363C2×C4—1032no—
364C2×C4—1031no—
365C2×C4—4122no—
366C2×C4—4122no—
367C2×C4—4122no—
368C2×C4—2062no—
369C2×C4—2062no—
370C2×C4—2062no—
371C2×C4—2061no—
372C2×C4—2061no—
373C2×C4—2061no—
374C2×C4—2061no—
375C2×C4—2061no—
376C2×C4D4×D10311yescharacteristic
377C2×C4C23×D10311yescharacteristic
378C8—21no—
379C8—1032no—
380C8—2061no—
381C8D4×D10312yescomplemented
382C22—21no—
383C22—21no—
384C22—21no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—8244no—
389C22—1032no—
390C22—1032no—
391C22—1032no—
392C22—4124no—
393C22—4121no—
394C22—4121no—
395C22—4121no—
396C22—2061no—
397C22—2061no—
398C22—2061no—
399C22C2×D4×D10311yescharacteristic
400C4—21no—
401C4—41no—
402C4—41no—
403C4—41no—
404C4—1032no—
405C4—4121no—
406C4—4121no—
407C4—4121no—
408C4—2061no—
409C4C2×D4×D10311yescharacteristic
410C4#41×D10311yescharacteristic
411C2—41no—
412C2—81no—
413C2—8241no—
414C2—1034no—
415C2—4121no—
416C2#121×D10311yescharacteristic
417C2AGL(1,ℤ/8)×D10311yescharacteristic
418C2#137×D10311yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#468×C103C2
socleC22×C103C22×D4
prime radical#121×D103C2
hypercenter#468D103
hypocenterC103C2×#468
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D103C2semidirect
2. C2×M16×D103C2semidirect
3. C22⋊Q8×D103C2semidirect
5. #20268040C2semidirect
6. #20268039C2semidirect
7. #20268038C2semidirect
8. #20268037C2semidirect
9. #20268036C2semidirect
10. #20268035C2semidirect
11. #20268034C2semidirect
12. #107×D103C2semidirect
13. #103×D103C2semidirect
14. #102×D103C2semidirect
15. #468×C103C2semidirect
20. C2×#13110094C22semidirect
21. C2×#13110093C22semidirect
22. C2×#13110092C22semidirect
24. C2×#13110089C22semidirect
25. C2×#13110088C22semidirect
26. C2×#13110088C22semidirect
30. #15693001C22semidirect
31. #15693000C22semidirect
34. #15692997C22semidirect
45. #15692955C22semidirect
46. #15692954C22semidirect
47. #15692954C22semidirect
48. #15692946C22semidirect
49. #15692945C22semidirect
50. #15692944C22semidirect
51. #15692943C22semidirect
52. #15692942C22semidirect
53. #15692941C22semidirect
54. C2×SD16×C103C22semidirect
55. C2×M16×C103C22semidirect
56. C22⋊Q8×C103C22semidirect
58. #107×C103C22semidirect
59. #103×C103C22semidirect
60. #102×C103C22semidirect
94. C8×D103D4semidirect
169. C8×C103C2×D4semidirect
171. C103⋊C8C2×D4semidirect
208. D103#468direct (N × H)
210. C103C2×#468semidirect
222. #468D103direct (N × H)
234. C2×SD16C2×D103semidirect
239. C2×M16C2×D103semidirect
247. C22⋊Q8C2×D103semidirect
262. #107C2×D103semidirect
266. #103C2×D103semidirect
270. #102C2×D103semidirect
381. C8D4×D103semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1032
C2×M16×D1032
C22⋊Q8×D1032
#121×D1032
#202680402
#202680392
#202680382
#202680372
#202680362
#202680352
#202680342
#107×D1032
#103×D1032
#102×D1032
#468×C1032
C2×#468103