Finite Group Databasebeta

← #27204760

Subgroups — #27204760

Order 13184.

548 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15693045C211yesmaximal, characteristic, complemented
2C22×#13110088C211yesmaximal, characteristic, complemented
3#20268301C211yesmaximal, characteristic, complemented
4#121×D103C211yesmaximal, characteristic, complemented
5#20268043C211yesmaximal, characteristic, complemented
6#20268041C211yesmaximal, characteristic, complemented
7#20268038C211yesmaximal, characteristic, complemented
8#20268036C211yesmaximal, characteristic, complemented
9#20268025C211yesmaximal, characteristic, complemented
10#20268020C211yesmaximal, characteristic, complemented
11#20268018C211yesmaximal, characteristic, complemented
12#20267832C211yesmaximal, characteristic, complemented
13#20267794C211yesmaximal, characteristic, complemented
14#20267789C211yesmaximal, characteristic, complemented
15#466×C103C211yesmaximal, characteristic, complemented
16C2×#13110104C2211yescharacteristic
17C2×D4×D103—21no—
18C2×D4×D103C2211yescharacteristic
19C22×C4×D103C2211yescharacteristic
20#15693045—24no—
21C2×#13110094C2211yescharacteristic, complemented
22C2×#13110093C2211yescharacteristic, complemented
23C2×#13110090C2211yescharacteristic, complemented
24C2×#13110088—24no—
25C2×#13110088C2211yescharacteristic
26C2×#13110088C2211yescharacteristic
27C2×#13110088C2211yescharacteristic, complemented
28C2×#13110088C2211yescharacteristic, complemented
29C22×C103⋊C8C2211yescharacteristic, complemented
30#15693003—21no—
31#15693001C2211yescharacteristic, complemented
32#15693000C2211yescharacteristic, complemented
33#15692996C2211yescharacteristic
34#15692995C2211yescharacteristic
35#15692994—21no—
36#15692993—21no—
37#15692992C2211yescharacteristic
38#15692992C2211yescharacteristic, complemented
39#15692989—21no—
40D4×Dic103—21no—
41(C22⋊D103)⋊C4—21no—
42#15692979C2211yescharacteristic
43C4⋊C4×D103C2211yescharacteristic
44C22⋊C4×D103—21no—
45#15692954C2211yescharacteristic, complemented
46#15692953C2211yescharacteristic, complemented
47#15692952C2211yescharacteristic, complemented
48#15692946C2211yescharacteristic, complemented
49#15692944C2211yescharacteristic, complemented
50#15692943C2211yescharacteristic, complemented
51#15692942C2211yescharacteristic, complemented
52#15692942C2211yescharacteristic, complemented
53#15692941C2211yescharacteristic, complemented
54C2×D8×C103C2211yescharacteristic, complemented
55C22×C8×C103C2211yescharacteristic, complemented
56#121×C103C2211yescharacteristic
57#121×C103C2211yescharacteristic, complemented
58#107×C103C2211yescharacteristic, complemented
59#102×C103C2211yescharacteristic, complemented
60#102×C103C2211yescharacteristic, complemented
61C23×D103—21no—
62C23×D103D411yescharacteristic
63#13110104—22no—
64#13110104—22no—
65C2×Dic206C2311yescharacteristic
66C2×D412—21no—
67C2×D412C2311yescharacteristic
68C2×C22⋊D103—21no—
69C2×C22⋊D103—21no—
70C2×C22⋊D103—21no—
71C2×C22⋊D103—21no—
72C2×C22⋊D103—21no—
73D4×D103—22no—
74D4×D103—22no—
75D4×D103—44no—
76C22×Dic103—21no—
77C22×Dic103D411yescharacteristic
78C2×C4×D103—22no—
79C2×C4×D103—22no—
80C2×C4×D103—21no—
81C2×C4×D103D411yescharacteristic
82C2×C4×D103D411yescharacteristic
83C2×C4×D103C2311yescharacteristic
84C2×C4×D103C2311yescharacteristic
85#13110094—22no—
86#13110093—22no—
87#13110090—22no—
88#13110088—22no—
89#13110088—22no—
90#13110088—22no—
91#13110088D414yescomplemented
92C2×C103⋊C8—22no—
93C2×C103⋊C8C2311yescharacteristic
94C2×C103⋊C8C2311yescharacteristic
95C4⋊Dic103—21no—
96C4⋊Dic103C2311yescharacteristic
97C4⋊Dic103C2311yescharacteristic
98Dic103⋊C4—21no—
99Dic103⋊C4—21no—
100C22⋊Dic103—21no—
101C22⋊Dic103—21no—
102C22⋊Dic103—21no—
103(C2×D103)⋊C4—21no—
104(C2×D103)⋊C4—21no—
105(C2×D103)⋊C4—21no—
106(C2×D103)⋊C4—21no—
107C4×Dic103—21no—
108C2×D4×C103—21no—
109C2×D4×C103—21no—
110C2×D4×C103C2311yescharacteristic
111C2×D4×C103C2311yescharacteristic
112C22×C4×C103C2311yescharacteristic
113D8×C103—22no—
114C2×C8×C103—22no—
115C2×C8×C103C2311yescharacteristic
116C2×C8×C103C2311yescharacteristic
117C4⋊C4×C103C2311yescharacteristic
118C4⋊C4×C103C2311yescharacteristic
119C22⋊C4×C103—21no—
120C22⋊C4×C103—21no—
121C23×C103—21no—
122C23×C103—21no—
123C23×C103C2×D411yescharacteristic
124C22×D103—22no—
125C22×D103—22no—
126C22×D103—21no—
127C22×D103—41no—
128C22×D103—42no—
129C22×D103—42no—
130C22×D103—42no—
131C22×D103C2×D411yescharacteristic
132C22×D103C2×D411yescharacteristic
133D4×C103—21no—
134D4×C103—21no—
135D4×C103—21no—
136D4×C103—21no—
137D4×C103—42no—
138D4×C103—42no—
139C2×C4×C103—21no—
140C2×C4×C103—21no—
141C2×C4×C103—21no—
142C2×C4×C103—21no—
143C2×C4×C103C2×D411yescharacteristic
144C2×C4×C103C2411yescharacteristic
145C22⋊D103—42no—
146C22⋊D103—42no—
147C22⋊D103—42no—
148C22⋊D103—42no—
149C22⋊D103—42no—
150C2×Dic103—22no—
151C2×Dic103—21no—
152C2×Dic103—21no—
153C2×Dic103—21no—
154C2×Dic103—42no—
155C2×Dic103C2×D411yescharacteristic
156C2×Dic103C2×D411yescharacteristic
157D412—21no—
158D412—21no—
159D412—42no—
160C4×D103—22no—
161C4×D103—21no—
162C4×D103—21no—
163C4×D103—22no—
164C4×D103—42no—
165C4×D103C2×D412yes—
166C4×D103#4112yes—
167Dic206—21no—
168Dic206—21no—
169C8×C103—21no—
170C8×C103C2×D412yescomplemented
171C103⋊C8—21no—
172C103⋊C8C2×D412yescomplemented
173C22×C103—21no—
174C22×C103—21no—
175C22×C103—41no—
176C22×C103—41no—
177C22×C103—41no—
178C22×C103—41no—
179C22×C103—41no—
180C22×C103—41no—
181C22×C103AGL(1,ℤ/8)12yescomplemented
182C22×C103C22×D411yescharacteristic
183C2×D103—21no—
184C2×D103—21no—
185C2×D103—21no—
186C2×D103—21no—
187C2×D103—21no—
188C2×D103—44no—
189C2×D103—41no—
190C2×D103—41no—
191C2×D103—41no—
192C2×D103—84no—
193C2×D103#12112yes—
194C4×C103—21no—
195C4×C103—41no—
196C4×C103—41no—
197C4×C103C22×D411yescharacteristic
198C4×C103C2×#4111yescharacteristic
199Dic103—21no—
200Dic103—41no—
201Dic103—41no—
202Dic103—41no—
203Dic103#12112yes—
204C2×C103—22no—
205C2×C103—81no—
206C2×C103—81no—
207C2×C103C2×#12111yescharacteristic
208C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
209C2×C103#57511yescharacteristic
210D103—22no—
211D103—41no—
212D103—81no—
213#3055—1031nomaximal, Sylow
214C103#305511yescharacteristic, complemented, Sylow
215C2×AGL(1,ℤ/8)—1031no—
216C22×M16—1031no—
217#525—1031no—
218C2×#121—1031no—
219#469—1031no—
220#469—1031no—
221#468—1031no—
222#468—1031no—
223#466—1031no—
224#466D10311yescharacteristic, complemented
225#465—1031no—
226#465—1031no—
227#428—1031no—
228#418—1031no—
229#417—1031no—
230C2×#41—1031no—
231C22×D4—1031no—
232C22×D4—2061no—
233C23×C4—1031no—
234AGL(1,ℤ/8)—2064no—
235C2×SD16—1031no—
236C2×SD16—1031no—
237C2×D8—1031no—
238C2×D8C2×D10311yescharacteristic, complemented
239C2×M16—1031no—
240C2×M16—1031no—
241C2×M16—1031no—
242C2×M16—1031no—
243C2×M16—2064no—
244C22×C8—1031no—
245C22×C8C2×D10311yescharacteristic, complemented
246#123—2061no—
247C22⋊Q8—1031no—
248C22⋊Q8—1031no—
249#121—1031no—
250#121—1031no—
251#121—1031no—
252#121—1031no—
253#121—2061no—
254#121—2061no—
255#121C2×D10311yescharacteristic
256#121C2×D10311yescharacteristic, complemented
257#120—2061no—
258C4×D4—2061no—
259C4×D4—2061no—
260#117—1031no—
261C2×C4⋊C4—1031no—
262C2×C22⋊C4—2061no—
263#107—1031no—
264#107C2×D10311yescharacteristic, complemented
265#106—1031no—
266#106—1031no—
267#103—1031no—
268#103—1031no—
269#102—1031no—
270#102—1031no—
271#102—1031no—
272#102—1031no—
273#102C2×D10311yescharacteristic, complemented
274#102C2×D10311yescharacteristic, complemented
275C24—1031no—
276C24—2061no—
277#41—2062no—
278#41—2062no—
279C2×Q8—1031no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—1031no—
283C2×D4—4124no—
284C2×D4—2061no—
285C2×D4—2062no—
286C2×D4—2062no—
287C2×D4—2061no—
288C2×D4—2061no—
289C2×D4—2061no—
290C2×D4—2061no—
291C2×D4—2061no—
292C2×D4C22×D10311yescharacteristic
293C2×D4C22×D10311yescharacteristic
294C22×C4—1031no—
295C22×C4—1031no—
296C22×C4—1031no—
297C22×C4—1031no—
298C22×C4—1031no—
299C22×C4—2062no—
300C22×C4—2062no—
301C22×C4—2061no—
302C22×C4—2061no—
303C22×C4C22×D10311yescharacteristic
304SD16—2062no—
305SD16—2062no—
306D8—22no—
307D8—2062no—
308M16—1034no—
309M16—2062no—
310M16—2062no—
311M16—2062no—
312C2×C8—22no—
313C2×C8—1031no—
314C2×C8—1031no—
315C2×C8—2062no—
316C2×C8C22×D10311yescharacteristic
317C2×C8C22×D10311yescharacteristic
318C4⋊C4—1031no—
319C4⋊C4—1031no—
320C4⋊C4—2061no—
321C4⋊C4—2061no—
322C4⋊C4—2061no—
323C4⋊C4C22×D10311yescharacteristic
324C4⋊C4C22×D10311yescharacteristic
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—2061no—
328C22⋊C4—2061no—
329C22⋊C4—2061no—
330C22⋊C4—2061no—
331C22⋊C4—2061no—
332C22⋊C4—2061no—
333C22⋊C4—2061no—
334C42—2061no—
335C23—21no—
336C23—21no—
337C23—1031no—
338C23—1031no—
339C23—4121no—
340C23—4122no—
341C23—4122no—
342C23—4122no—
343C23—2062no—
344C23—2061no—
345C23—2062no—
346C23D4×D10311yescharacteristic
347Q8—2061no—
348Q8—2061no—
349D4—21no—
350D4—21no—
351D4—21no—
352D4—21no—
353D4—42no—
354D4—42no—
355D4—4122no—
356D4—4122no—
357D4—4122no—
358D4—4122no—
359D4—4122no—
360D4—4122no—
361D4—2061no—
362D4—2061no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—1031no—
368C2×C4—1032no—
369C2×C4—1032no—
370C2×C4—1031no—
371C2×C4—4122no—
372C2×C4—4122no—
373C2×C4—2062no—
374C2×C4—2062no—
375C2×C4—2062no—
376C2×C4—2061no—
377C2×C4—2061no—
378C2×C4—2061no—
379C2×C4—2061no—
380C2×C4—2061no—
381C2×C4D4×D10311yescharacteristic
382C2×C4C23×D10311yescharacteristic
383C8—21no—
384C8—1032no—
385C8—2061no—
386C8D4×D10312yescomplemented
387C22—21no—
388C22—21no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—8244no—
396C22—1032no—
397C22—4124no—
398C22—4121no—
399C22—4121no—
400C22—4121no—
401C22—2061no—
402C22—2061no—
403C22—2061no—
404C22—2061no—
405C22—2061no—
406C22#1569304512yescomplemented
407C22C2×D4×D10311yescharacteristic
408C4—21no—
409C4—41no—
410C4—41no—
411C4—1032no—
412C4—4121no—
413C4—4121no—
414C4—4121no—
415C4—2061no—
416C4C2×D4×D10311yescharacteristic
417C4#41×D10311yescharacteristic
418C2—22no—
419C2—81no—
420C2—81no—
421C2—8241no—
422C2—4121no—
423C2—2062no—
424C2#121×D10311yescharacteristic
425C2C2×#1569304511yescharacteristic
426C2#2026858811yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#466×C103C2
socleC22×C103C22×D4
hypercenter#466D103
hypocenterC103#3055
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C2×#15693045C2semidirect
2. C22×#13110088C2semidirect
3. #20268301C2semidirect
4. #121×D103C2semidirect
5. #20268043C2semidirect
6. #20268041C2semidirect
7. #20268038C2semidirect
8. #20268036C2semidirect
9. #20268025C2semidirect
10. #20268020C2semidirect
11. #20268018C2semidirect
12. #20267832C2semidirect
13. #20267794C2semidirect
14. #20267789C2semidirect
15. #466×C103C2semidirect
21. C2×#13110094C22semidirect
22. C2×#13110093C22semidirect
23. C2×#13110090C22semidirect
27. C2×#13110088C22semidirect
28. C2×#13110088C22semidirect
29. C22×C103⋊C8C22semidirect
31. #15693001C22semidirect
32. #15693000C22semidirect
38. #15692992C22semidirect
45. #15692954C22semidirect
46. #15692953C22semidirect
47. #15692952C22semidirect
48. #15692946C22semidirect
49. #15692944C22semidirect
50. #15692943C22semidirect
51. #15692942C22semidirect
52. #15692942C22semidirect
53. #15692941C22semidirect
54. C2×D8×C103C22semidirect
55. C22×C8×C103C22semidirect
57. #121×C103C22semidirect
58. #107×C103C22semidirect
59. #102×C103C22semidirect
60. #102×C103C22semidirect
91. #13110088D4semidirect
170. C8×C103C2×D4semidirect
172. C103⋊C8C2×D4semidirect
181. C22×C103AGL(1,ℤ/8)semidirect
214. C103#3055semidirect
224. #466D103semidirect
238. C2×D8C2×D103semidirect
245. C22×C8C2×D103semidirect
256. #121C2×D103semidirect
264. #107C2×D103semidirect
273. #102C2×D103semidirect
274. #102C2×D103semidirect
386. C8D4×D103semidirect
406. C22#15693045semidirect

Maximal subgroups

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

subgroupindex
C2×#156930452
C22×#131100882
#202683012
#121×D1032
#202680432
#202680412
#202680382
#202680362
#202680252
#202680202
#202680182
#202678322
#202677942
#202677892
#466×C1032
#3055103