Finite Group Databasebeta

← #463×D107 #28345881

Subgroups — #463×D107 #28345881

Order 13696.

564 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D107C211yesmaximal, characteristic, complemented
2C2×D8×D107C211yesmaximal, characteristic
3#124×D107C211yesmaximal, characteristic, complemented
4C4×D4×D107C211yesmaximal, characteristic, complemented
5#20292845C211yesmaximal, characteristic, complemented
6#20292844C211yesmaximal, characteristic, complemented
7#20292843C211yesmaximal, characteristic, complemented
8#20292842C211yesmaximal, characteristic, complemented
9#20292841C211yesmaximal, characteristic, complemented
10#20292840C211yesmaximal, characteristic, complemented
11#20292839C211yesmaximal, characteristic, complemented
12C4⋊C8×D107C211yesmaximal, characteristic, complemented
13#103×D107C211yesmaximal, characteristic, complemented
14#102×D107C211yesmaximal, characteristic, complemented
15#463×C107C211yesmaximal, characteristic, complemented
16C2×Q8×D107C2211yescharacteristic
17C2×D4×D107C2211yescharacteristic
18C2×D4×D107C2211yescharacteristic
19C22×C4×D107—21no—
20C2×#13133807C2211yescharacteristic, complemented
21C2×#13133806C2211yescharacteristic, complemented
22C2×#13133805C2211yescharacteristic, complemented
23SD16×D107—24no—
24C2×D856C2211yescharacteristic
25C2×#13133803C2211yescharacteristic
26C2×#13133803C2211yescharacteristic
27D8×D107—24no—
28C2×C8×D107C2211yescharacteristic
29C2×C8×D107C2211yescharacteristic
30#16812098C2211yescharacteristic, complemented
31#16812097C2211yescharacteristic, complemented
32#16812096C2211yescharacteristic, complemented
33#16812095—21no—
34#16812095—21no—
35C4×D428C2211yescharacteristic, complemented
36D4×Dic107C2211yescharacteristic, complemented
37#16812071C2211yescharacteristic, complemented
38C4×C22⋊D107—21no—
39(C22⋊D107)⋊C4—21no—
40C4⋊C4×D107C2211yescharacteristic
41C22⋊C4×D107—21no—
42C22⋊C4×D107—21no—
43C22⋊C4×D107—21no—
44C42×D107C2211yescharacteristic
45C4⋊(C107⋊C8)C2211yescharacteristic, complemented
46Dic107⋊C8C2211yescharacteristic, complemented
47Dic107⋊C8C2211yescharacteristic, complemented
48#16812034C2211yescharacteristic, complemented
49#16812033C2211yescharacteristic, complemented
50#16812032C2211yescharacteristic, complemented
51#16812031C2211yescharacteristic, complemented
52#16812030C2211yescharacteristic, complemented
53#16812029C2211yescharacteristic, complemented
54C2×SD16×C107C2211yescharacteristic, complemented
55C2×D8×C107C2211yescharacteristic
56#124×C107C2211yescharacteristic, complemented
57C4×D4×C107C2211yescharacteristic, complemented
58C4⋊C8×C107C2211yescharacteristic, complemented
59#103×C107C2211yescharacteristic, complemented
60#102×C107C2211yescharacteristic, complemented
61C23×D107—21no—
62C23×D107—21no—
63C2×Dic214—21no—
64C2×Dic214C2311yescharacteristic
65Q8×D107—22no—
66Q8×D107—22no—
67C2×D428C2311yescharacteristic
68C2×D428C2311yescharacteristic
69C2×C22⋊D107—21no—
70C2×C22⋊D107—21no—
71D4×D107—22no—
72D4×D107—22no—
73D4×D107—22no—
74D4×D107D414yes—
75C22×Dic107—21no—
76C2×C4×D107—21no—
77C2×C4×D107—21no—
78C2×C4×D107—21no—
79C2×C4×D107—21no—
80C2×C4×D107—44no—
81C2×C4×D107D411yescharacteristic
82C2×C4×D107D411yescharacteristic
83C2×C4×D107C2311yescharacteristic
84#13133807—22no—
85#13133806—22no—
86#13133805—22no—
87D856—22no—
88#13133803—22no—
89#13133803—22no—
90C2×C107⋊C8C2311yescharacteristic
91C2×C107⋊C8C2311yescharacteristic
92C8×D107—22no—
93C8×D107—22no—
94C4⋊Dic107C2311yescharacteristic
95Dic107⋊C4—21no—
96C22⋊Dic107—21no—
97C22⋊Dic107—21no—
98C22⋊Dic107—21no—
99(C2×D107)⋊C4—21no—
100(C2×D107)⋊C4—21no—
101(C2×D107)⋊C4—21no—
102(C2×D107)⋊C4—21no—
103(C2×D107)⋊C4—21no—
104(C2×D107)⋊C4—21no—
105C4×Dic107D411yescharacteristic
106C4×Dic107D411yescharacteristic
107C4×Dic107C2311yescharacteristic
108C2×Q8×C107C2311yescharacteristic
109C2×D4×C107C2311yescharacteristic
110C2×D4×C107C2311yescharacteristic
111C22×C4×C107—21no—
112SD16×C107—22no—
113D8×C107—22no—
114C2×C8×C107C2311yescharacteristic
115C2×C8×C107C2311yescharacteristic
116C4⋊C4×C107C2311yescharacteristic
117C22⋊C4×C107—21no—
118C22⋊C4×C107—21no—
119C22⋊C4×C107—21no—
120C42×C107C2311yescharacteristic
121C23×C107—21no—
122C23×C107—21no—
123C22×D107—21no—
124C22×D107—24no—
125C22×D107—21no—
126C22×D107—42no—
127C22×D107—42no—
128C22×D107—42no—
129C22×D107—42no—
130C22×D107—42no—
131C22×D107C2×D411yescharacteristic
132Q8×C107—21no—
133Q8×C107—21no—
134D4×C107—21no—
135D4×C107—21no—
136D4×C107—21no—
137D4×C107C2×D412yes—
138C2×C4×C107—21no—
139C2×C4×C107—21no—
140C2×C4×C107—42no—
141C2×C4×C107C2×D411yescharacteristic
142C2×C4×C107C2×D411yescharacteristic
143C2×C4×C107C2411yescharacteristic
144C22⋊D107—24no—
145C22⋊D107—42no—
146C2×Dic107—21no—
147C2×Dic107—21no—
148C2×Dic107—42no—
149C2×Dic107C2×D411yescharacteristic
150C2×Dic107C2×D411yescharacteristic
151C2×Dic107C2×D411yescharacteristic
152D428—21no—
153D428—21no—
154D428—21no—
155D428C2×D412yes—
156C4×D107—22no—
157C4×D107—22no—
158C4×D107—42no—
159C4×D107—42no—
160C4×D107—42no—
161C4×D107—42no—
162C4×D107C2×D412yes—
163C4×D107#4112yes—
164Dic214—21no—
165Dic214—21no—
166Dic214—42no—
167C8×C107—21no—
168C8×C107—21no—
169C107⋊C8—21no—
170C107⋊C8—21no—
171C22×C107—22no—
172C22×C107—41no—
173C22×C107—41no—
174C22×C107—41no—
175C22×C107—41no—
176C22×C107—41no—
177C22×C107C22×D411yescharacteristic
178C2×D107—22no—
179C2×D107—41no—
180C2×D107—41no—
181C2×D107—48no—
182C2×D107—41no—
183C2×D107—41no—
184C2×D107—41no—
185C2×D107—84no—
186C2×D107#12112yes—
187C2×D107#13512yes—
188C2×D107AGL(1,ℤ/8)12yes—
189C4×C107—21no—
190C4×C107—21no—
191C4×C107—41no—
192C4×C107—41no—
193C4×C107C22×D411yescharacteristic
194C4×C107C2×#4111yescharacteristic
195Dic107—21no—
196Dic107—21no—
197Dic107—41no—
198Dic107—41no—
199Dic107#12112yes—
200C2×C107—42no—
201C2×C107—81no—
202C2×C107C2×#12111yescharacteristic
203C2×C107C2×#13511yescharacteristic
204C2×C107C2×AGL(1,ℤ/8)11yescharacteristic
205D107—42no—
206D107—81no—
207D107#46314yesdirect product factor
208C2×#463—1071nomaximal, Sylow
209C107C2×#46311yescharacteristic, complemented, Sylow
210C22×SD16—1071no—
211C22×D8—1071no—
212C2×#124—1071no—
213C2×C4×D4—1071no—
214#463—1071no—
215#463—1071no—
216#463—1071no—
217#463—1071no—
218#463—1071no—
219#463—1071no—
220#463—1071no—
221#463D10711yescharacteristic, direct product factor
222C2×C4⋊C8—1071no—
223C2×#103—1071no—
224C2×#102—1071no—
225C22×Q8—1071no—
226C22×D4—1071no—
227C22×D4—1071no—
228C23×C4—2141no—
229C2×SD16—1071no—
230C2×SD16—1071no—
231C2×SD16—1071no—
232C2×SD16—2144no—
233C2×SD16C2×D10711yescharacteristic, complemented
234C2×D8—1071no—
235C2×D8—1071no—
236C2×D8—1071no—
237C2×D8—2144no—
238C2×D8C2×D10711yescharacteristic
239C22×C8—1071no—
240C22×C8—1071no—
241#124—1071no—
242#124—1071no—
243#124—1071no—
244#124—2141no—
245#124—2141no—
246#124C2×D10711yescharacteristic, complemented
247C4×D4—1071no—
248C4×D4—1071no—
249C4×D4—1071no—
250C4×D4—2141no—
251C4×D4—2141no—
252C4×D4C2×D10711yescharacteristic, complemented
253C2×C4⋊C4—1071no—
254C2×C22⋊C4—2141no—
255C2×C22⋊C4—2141no—
256C2×C22⋊C4—2141no—
257C2×C42—1071no—
258C4⋊C8—1071no—
259C4⋊C8—1071no—
260C4⋊C8—1071no—
261C4⋊C8C2×D10711yescharacteristic, complemented
262#103—1071no—
263#103—1071no—
264#103—1071no—
265#103C2×D10711yescharacteristic, complemented
266#102—1071no—
267#102—1071no—
268#102—1071no—
269#102C2×D10711yescharacteristic, complemented
270C24—2141no—
271C24—2141no—
272C2×Q8—1071no—
273C2×Q8—2141no—
274C2×Q8—2142no—
275C2×Q8—2142no—
276C2×Q8C22×D10711yescharacteristic
277C2×D4—1074no—
278C2×D4—1071no—
279C2×D4—1071no—
280C2×D4—2142no—
281C2×D4—2142no—
282C2×D4—2142no—
283C2×D4—2141no—
284C2×D4—2141no—
285C2×D4C22×D10711yescharacteristic
286C2×D4C22×D10711yescharacteristic
287C22×C4—21no—
288C22×C4—1071no—
289C22×C4—1071no—
290C22×C4—1071no—
291C22×C4—4284no—
292C22×C4—2141no—
293C22×C4—2141no—
294C22×C4—2141no—
295C22×C4—2141no—
296C22×C4—2141no—
297SD16—22no—
298SD16—2142no—
299SD16—2142no—
300SD16—2142no—
301D8—22no—
302D8—2142no—
303D8—2142no—
304D8—2142no—
305C2×C8—1071no—
306C2×C8—1071no—
307C2×C8—2142no—
308C2×C8—2142no—
309C2×C8C22×D10711yescharacteristic
310C2×C8C22×D10711yescharacteristic
311C4⋊C4—1071no—
312C4⋊C4—2141no—
313C4⋊C4C22×D10711yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—2141no—
318C22⋊C4—2141no—
319C22⋊C4—2141no—
320C22⋊C4—2141no—
321C22⋊C4—2141no—
322C22⋊C4—2141no—
323C22⋊C4—2141no—
324C22⋊C4—2141no—
325C22⋊C4—2141no—
326C42—1071no—
327C42—1071no—
328C42—1071no—
329C42C22×D10711yescharacteristic
330C23—21no—
331C23—21no—
332C23—1071no—
333C23—4282no—
334C23—4282no—
335C23—4282no—
336C23—4282no—
337C23—4282no—
338C23—2144no—
339C23—2141no—
340C23—2141no—
341Q8—21no—
342Q8—21no—
343Q8—4282no—
344Q8—2141no—
345Q8—2141no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—1072no—
350D4—4282no—
351D4—2144no—
352D4—2141no—
353D4—2141no—
354D4—2141no—
355D4D4×D10712yes—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—1071no—
360C2×C4—1072no—
361C2×C4—1072no—
362C2×C4—1071no—
363C2×C4—1071no—
364C2×C4—4282no—
365C2×C4—4282no—
366C2×C4—4282no—
367C2×C4—4282no—
368C2×C4—4282no—
369C2×C4—2142no—
370C2×C4—2142no—
371C2×C4—2141no—
372C2×C4—2141no—
373C2×C4D4×D10711yescharacteristic
374C2×C4D4×D10711yescharacteristic
375C2×C4C23×D10711yescharacteristic
376C8—21no—
377C8—21no—
378C8—2141no—
379C8—2141no—
380C22—22no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—8564no—
387C22—1072no—
388C22—1072no—
389C22—1072no—
390C22—4288no—
391C22—4281no—
392C22—4281no—
393C22—4281no—
394C22—4281no—
395C22—4281no—
396C22—2142no—
397C22C2×D4×D10711yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—1072no—
403C4—4281no—
404C4—4281no—
405C4—2141no—
406C4—2141no—
407C4C2×D4×D10711yescharacteristic
408C4#41×D10711yescharacteristic
409C2—42no—
410C2—81no—
411C2—8561no—
412C2—1074no—
413C2—4282no—
414C2#121×D10711yescharacteristic
415C2#135×D10711yescharacteristic
416C2AGL(1,ℤ/8)×D10711yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#463×C107C2
socleC22×C107C22×D4
prime radicalC2×D8×D107C2
hypercenter#463D107
hypocenterC107C2×#463
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D107C2semidirect
3. #124×D107C2semidirect
4. C4×D4×D107C2semidirect
5. #20292845C2semidirect
6. #20292844C2semidirect
7. #20292843C2semidirect
8. #20292842C2semidirect
9. #20292841C2semidirect
10. #20292840C2semidirect
11. #20292839C2semidirect
12. C4⋊C8×D107C2semidirect
13. #103×D107C2semidirect
14. #102×D107C2semidirect
15. #463×C107C2semidirect
20. C2×#13133807C22semidirect
21. C2×#13133806C22semidirect
22. C2×#13133805C22semidirect
30. #16812098C22semidirect
31. #16812097C22semidirect
32. #16812096C22semidirect
35. C4×D428C22semidirect
36. D4×Dic107C22semidirect
37. #16812071C22semidirect
45. C4⋊(C107⋊C8)C22semidirect
46. Dic107⋊C8C22semidirect
47. Dic107⋊C8C22semidirect
48. #16812034C22semidirect
49. #16812033C22semidirect
50. #16812032C22semidirect
51. #16812031C22semidirect
52. #16812030C22semidirect
53. #16812029C22semidirect
54. C2×SD16×C107C22semidirect
56. #124×C107C22semidirect
57. C4×D4×C107C22semidirect
58. C4⋊C8×C107C22semidirect
59. #103×C107C22semidirect
60. #102×C107C22semidirect
207. D107#463direct (N × H)
209. C107C2×#463semidirect
221. #463D107direct (N × H)
233. C2×SD16C2×D107semidirect
246. #124C2×D107semidirect
252. C4×D4C2×D107semidirect
261. C4⋊C8C2×D107semidirect
265. #103C2×D107semidirect
269. #102C2×D107semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1072
C2×D8×D1072
#124×D1072
C4×D4×D1072
#202928452
#202928442
#202928432
#202928422
#202928412
#202928402
#202928392
C4⋊C8×D1072
#103×D1072
#102×D1072
#463×C1072
C2×#463107