Finite Group Databasebeta

← #452×D107 #28345666

Subgroups — #452×D107 #28345666

Order 13696.

760 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D107C211yesmaximal, characteristic
2C2×Q16×D107C211yesmaximal, characteristic, complemented
3C2×SD16×D107C211yesmaximal, characteristic, complemented
4C22⋊Q8×D107C211yesmaximal, characteristic, complemented
5#20292792C211yesmaximal, characteristic, complemented
6#20292791C211yesmaximal, characteristic, complemented
7#20292790C211yesmaximal, characteristic, complemented
8#20292789C211yesmaximal, characteristic, complemented
9#20292788C211yesmaximal, characteristic, complemented
10#20292787C211yesmaximal, characteristic, complemented
11#20292786C211yesmaximal, characteristic, complemented
12#103×D107C211yesmaximal, characteristic, complemented
13#102×D107C211yesmaximal, characteristic, complemented
14C22⋊C8×D107C211yesmaximal, characteristic, complemented
15#452×C107C211yesmaximal, characteristic, complemented
16C2×#13133819C2211yescharacteristic
17C2×#13133818—21no—
18C2×#13133818C2211yescharacteristic
19C2×#13133817—21no—
20C2×#13133817C2211yescharacteristic
21#41×D107—24no—
22#41×D107—24no—
23C2×Q8×D107C2211yescharacteristic
24C2×Q8×D107C2211yescharacteristic
25C2×D4×D107—21no—
26C2×D4×D107C2211yescharacteristic
27C22×C4×D107—21no—
28C22×C4×D107C2211yescharacteristic
29C2×Dic428C2211yescharacteristic, complemented
30C2×#13133808C2211yescharacteristic, complemented
31C2×#13133808C2211yescharacteristic, complemented
32Q16×D107—24no—
33C2×#13133807C2211yescharacteristic, complemented
34C2×#13133806C2211yescharacteristic, complemented
35C2×#13133805C2211yescharacteristic, complemented
36SD16×D107—24no—
37C2×C8×D107C2211yescharacteristic
38C2×C8×D107C2211yescharacteristic
39#16812089C2211yescharacteristic, complemented
40#16812088C2211yescharacteristic, complemented
41#16812087—21no—
42#16812086—21no—
43#16812085C2211yescharacteristic, complemented
44C4⋊C4×D107—21no—
45C4⋊C4×D107C2211yescharacteristic
46C22⋊C4×D107—21no—
47#16812034C2211yescharacteristic, complemented
48#16812033C2211yescharacteristic, complemented
49#16812032C2211yescharacteristic, complemented
50#16812031C2211yescharacteristic, complemented
51#16812030C2211yescharacteristic, complemented
52#16812029C2211yescharacteristic, complemented
53C22⋊(C107⋊C8)C2211yescharacteristic, complemented
54(C2×D107)⋊C8C2211yescharacteristic, complemented
55(C2×D107)⋊C8C2211yescharacteristic, complemented
56C2×#41×C107C2211yescharacteristic
57C2×Q16×C107C2211yescharacteristic, complemented
58C2×SD16×C107C2211yescharacteristic, complemented
59C22⋊Q8×C107C2211yescharacteristic, complemented
60#103×C107C2211yescharacteristic, complemented
61#102×C107C2211yescharacteristic, complemented
62C22⋊C8×C107C2211yescharacteristic, complemented
63C23×D107—21no—
64C23×D107D411yescharacteristic
65#13133819—22no—
66#13133819—22no—
67#13133818—28no—
68#13133818—22no—
69#13133818—22no—
70#13133817—28no—
71#13133817—22no—
72#13133817—22no—
73C2×Dic214—21no—
74C2×Dic214—21no—
75C2×Dic214C2311yescharacteristic
76C2×Dic214C2311yescharacteristic
77Q8×D107—22no—
78Q8×D107—22no—
79Q8×D107—22no—
80Q8×D107D414yes—
81C2×D428—21no—
82C2×D428C2311yescharacteristic
83C2×C22⋊D107—21no—
84C2×C22⋊D107—21no—
85C2×C22⋊D107—21no—
86D4×D107—28no—
87D4×D107—22no—
88D4×D107D414yes—
89C22×Dic107—21no—
90C22×Dic107D411yescharacteristic
91C2×C4×D107—28no—
92C2×C4×D107—21no—
93C2×C4×D107—21no—
94C2×C4×D107—21no—
95C2×C4×D107—22no—
96C2×C4×D107—22no—
97C2×C4×D107—21no—
98C2×C4×D107—21no—
99C2×C4×D107D411yescharacteristic
100C2×C4×D107D411yescharacteristic
101C2×C4×D107C2311yescharacteristic
102C2×C4×D107C2311yescharacteristic
103Dic428—22no—
104#13133808—22no—
105#13133808—22no—
106#13133807—22no—
107#13133806—22no—
108#13133805—22no—
109C2×C107⋊C8C2311yescharacteristic
110C2×C107⋊C8C2311yescharacteristic
111C8×D107—22no—
112C8×D107—22no—
113C4⋊Dic107—21no—
114C4⋊Dic107C2311yescharacteristic
115Dic107⋊C4—21no—
116Dic107⋊C4—21no—
117Dic107⋊C4—21no—
118C22⋊Dic107—21no—
119(C2×D107)⋊C4—21no—
120(C2×D107)⋊C4—21no—
121#41×C107—22no—
122#41×C107—22no—
123C2×Q8×C107C2311yescharacteristic
124C2×Q8×C107C2311yescharacteristic
125C2×D4×C107—21no—
126C2×D4×C107C2311yescharacteristic
127C22×C4×C107—21no—
128C22×C4×C107C2311yescharacteristic
129Q16×C107—22no—
130SD16×C107—22no—
131C2×C8×C107C2311yescharacteristic
132C2×C8×C107C2311yescharacteristic
133C4⋊C4×C107—21no—
134C4⋊C4×C107C2311yescharacteristic
135C22⋊C4×C107—21no—
136C23×C107—21no—
137C23×C107C2×D411yescharacteristic
138C22×D107—21no—
139C22×D107—22no—
140C22×D107—24no—
141C22×D107—22no—
142C22×D107—22no—
143C22×D107—42no—
144C22×D107—42no—
145C22×D107C2×D411yescharacteristic
146C22×D107C2×D411yescharacteristic
147Q8×C107—21no—
148Q8×C107—21no—
149Q8×C107—21no—
150Q8×C107C2×D412yes—
151D4×C107—24no—
152D4×C107—21no—
153D4×C107C2×D412yes—
154C2×C4×C107—24no—
155C2×C4×C107—21no—
156C2×C4×C107—21no—
157C2×C4×C107—21no—
158C2×C4×C107—21no—
159C2×C4×C107—21no—
160C2×C4×C107C2×D411yescharacteristic
161C2×C4×C107C2411yescharacteristic
162C22⋊D107—24no—
163C22⋊D107—24no—
164C22⋊D107—24no—
165C2×Dic107—24no—
166C2×Dic107—21no—
167C2×Dic107—22no—
168C2×Dic107—21no—
169C2×Dic107—21no—
170C2×Dic107C2×D411yescharacteristic
171C2×Dic107C2×D411yescharacteristic
172D428—24no—
173D428—21no—
174D428C2×D412yes—
175C4×D107—24no—
176C4×D107—24no—
177C4×D107—22no—
178C4×D107—24no—
179C4×D107—21no—
180C4×D107—21no—
181C4×D107—22no—
182C4×D107—42no—
183C4×D107—42no—
184C4×D107C2×D412yes—
185C4×D107C2×D412yes—
186Dic214—21no—
187Dic214—24no—
188Dic214—21no—
189Dic214—21no—
190Dic214—42no—
191Dic214C2×D412yes—
192C8×C107—21no—
193C8×C107—21no—
194C107⋊C8—21no—
195C107⋊C8—21no—
196C22×C107—21no—
197C22×C107—22no—
198C22×C107—21no—
199C22×C107—21no—
200C22×C107—41no—
201C22×C107—41no—
202C22×C107C22×D411yescharacteristic
203C2×D107—21no—
204C2×D107—22no—
205C2×D107—21no—
206C2×D107—21no—
207C2×D107—41no—
208C2×D107—41no—
209C2×D107—44no—
210C2×D107—48no—
211C2×D107#12012yes—
212C2×D107#13512yes—
213C2×D107#13712yes—
214C4×C107—22no—
215C4×C107—21no—
216C4×C107—41no—
217C4×C107—41no—
218C4×C107C22×D411yescharacteristic
219C4×C107C22×D411yescharacteristic
220Dic107—22no—
221Dic107—21no—
222Dic107—41no—
223Dic107—41no—
224Dic107#12012yes—
225C2×C107—41no—
226C2×C107—42no—
227C2×C107C2×#12011yescharacteristic
228C2×C107C2×#13511yescharacteristic
229C2×C107C2×#13711yescharacteristic
230D107—41no—
231D107—42no—
232D107#45214yesdirect product factor
233C2×#452—1071nomaximal, Sylow
234C107C2×#45211yescharacteristic, complemented, Sylow
235C22×#41—1071no—
236C22×Q16—1071no—
237C22×SD16—1071no—
238C2×C22⋊Q8—1071no—
239#452—1071no—
240#452—1071no—
241#452—1071no—
242#452—1071no—
243#452—1071no—
244#452—1071no—
245#452—1071no—
246#452D10711yescharacteristic, direct product factor
247C2×#103—1071no—
248C2×#102—1071no—
249C2×C22⋊C8—1071no—
250C2×#41—1071no—
251C2×#41—1071no—
252C2×#41—1071no—
253C2×#41—2141no—
254C2×#41—2141no—
255C2×#41—2144no—
256C2×#41—2144no—
257C2×#41C2×D10711yescharacteristic
258C22×Q8—1071no—
259C22×Q8—1071no—
260C22×D4—1071no—
261C22×D4—2141no—
262C23×C4—1071no—
263C23×C4—2141no—
264C2×Q16—1071no—
265C2×Q16—1071no—
266C2×Q16—1071no—
267C2×Q16—2144no—
268C2×Q16C2×D10711yescharacteristic, complemented
269C2×SD16—1071no—
270C2×SD16—1071no—
271C2×SD16—1071no—
272C2×SD16—2144no—
273C2×SD16C2×D10711yescharacteristic, complemented
274C22×C8—1071no—
275C22×C8—1071no—
276C22⋊Q8—1071no—
277C22⋊Q8—1071no—
278C22⋊Q8—1071no—
279C22⋊Q8—2141no—
280C22⋊Q8—2141no—
281C22⋊Q8C2×D10711yescharacteristic, complemented
282C2×C4⋊C4—1071no—
283C2×C4⋊C4—2141no—
284C2×C22⋊C4—2141no—
285#103—1071no—
286#103—1071no—
287#103—1071no—
288#103C2×D10711yescharacteristic, complemented
289#102—1071no—
290#102—1071no—
291#102—1071no—
292#102C2×D10711yescharacteristic, complemented
293C22⋊C8—1071no—
294C22⋊C8—1071no—
295C22⋊C8—1071no—
296C22⋊C8C2×D10711yescharacteristic, complemented
297C24—1071no—
298C24—2141no—
299#41—22no—
300#41—22no—
301#41—2142no—
302#41—2142no—
303#41—2148no—
304#41—2142no—
305#41—2148no—
306#41—2142no—
307#41—2142no—
308#41—2142no—
309C2×Q8—1074no—
310C2×Q8—1071no—
311C2×Q8—1071no—
312C2×Q8—2141no—
313C2×Q8—2141no—
314C2×Q8—2142no—
315C2×Q8—2142no—
316C2×Q8—2142no—
317C2×Q8C22×D10711yescharacteristic
318C2×Q8C22×D10711yescharacteristic
319C2×D4—21no—
320C2×D4—1074no—
321C2×D4—1071no—
322C2×D4—2141no—
323C2×D4—2142no—
324C2×D4—2141no—
325C2×D4—2148no—
326C2×D4—2141no—
327C2×D4—2141no—
328C2×D4C22×D10711yescharacteristic
329C22×C4—21no—
330C22×C4—1071no—
331C22×C4—1071no—
332C22×C4—1071no—
333C22×C4—1071no—
334C22×C4—1071no—
335C22×C4—2142no—
336C22×C4—2142no—
337C22×C4—2141no—
338C22×C4—2141no—
339C22×C4—2141no—
340C22×C4—2141no—
341C22×C4—2148no—
342C22×C4—2141no—
343C22×C4—2141no—
344C22×C4C22×D10711yescharacteristic
345Q16—22no—
346Q16—2142no—
347Q16—2142no—
348Q16—2142no—
349SD16—22no—
350SD16—2142no—
351SD16—2142no—
352SD16—2142no—
353C2×C8—1071no—
354C2×C8—1071no—
355C2×C8—2142no—
356C2×C8—2142no—
357C2×C8C22×D10711yescharacteristic
358C2×C8C22×D10711yescharacteristic
359C4⋊C4—21no—
360C4⋊C4—1071no—
361C4⋊C4—2141no—
362C4⋊C4—2141no—
363C4⋊C4—2141no—
364C4⋊C4—2141no—
365C4⋊C4C22×D10711yescharacteristic
366C22⋊C4—21no—
367C22⋊C4—2141no—
368C22⋊C4—2141no—
369C22⋊C4—2141no—
370C23—21no—
371C23—1071no—
372C23—1071no—
373C23—4282no—
374C23—4282no—
375C23—2144no—
376C23—2142no—
377C23—2142no—
378C23—2142no—
379C23—2141no—
380C23D4×D10711yescharacteristic
381Q8—21no—
382Q8—21no—
383Q8—21no—
384Q8—1072no—
385Q8—4282no—
386Q8—2144no—
387Q8—2141no—
388Q8—2141no—
389Q8—2141no—
390Q8D4×D10712yes—
391D4—24no—
392D4—21no—
393D4—1072no—
394D4—2144no—
395D4—2144no—
396D4—2144no—
397D4—2144no—
398D4—2141no—
399D4D4×D10712yes—
400C2×C4—24no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—1071no—
407C2×C4—1072no—
408C2×C4—1072no—
409C2×C4—1071no—
410C2×C4—4282no—
411C2×C4—4282no—
412C2×C4—2142no—
413C2×C4—2142no—
414C2×C4—2144no—
415C2×C4—2144no—
416C2×C4—2144no—
417C2×C4—2142no—
418C2×C4—2141no—
419C2×C4—2141no—
420C2×C4—2144no—
421C2×C4—2141no—
422C2×C4—2141no—
423C2×C4—2141no—
424C2×C4D4×D10711yescharacteristic
425C2×C4C23×D10711yescharacteristic
426C8—21no—
427C8—21no—
428C8—2141no—
429C8—2141no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—22no—
434C22—41no—
435C22—41no—
436C22—1072no—
437C22—1072no—
438C22—1072no—
439C22—4288no—
440C22—4284no—
441C22—4281no—
442C22—4281no—
443C22—2141no—
444C22—2141no—
445C22—2142no—
446C22—2141no—
447C22C2×D4×D10711yescharacteristic
448C4—21no—
449C4—22no—
450C4—41no—
451C4—41no—
452C4—1072no—
453C4—4281no—
454C4—4281no—
455C4—2141no—
456C4—2142no—
457C4C2×D4×D10711yescharacteristic
458C4C2×D4×D10711yescharacteristic
459C2—41no—
460C2—42no—
461C2—1074no—
462C2—4282no—
463C2—4281no—
464C2#120×D10711yescharacteristic
465C2#135×D10711yescharacteristic
466C2#137×D10711yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#452×C107C2
socleC22×C107C22×D4
prime radicalC2×#41×D107C2
hypercenter#452D107
hypocenterC107C2×#452
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
2. C2×Q16×D107C2semidirect
3. C2×SD16×D107C2semidirect
4. C22⋊Q8×D107C2semidirect
5. #20292792C2semidirect
6. #20292791C2semidirect
7. #20292790C2semidirect
8. #20292789C2semidirect
9. #20292788C2semidirect
10. #20292787C2semidirect
11. #20292786C2semidirect
12. #103×D107C2semidirect
13. #102×D107C2semidirect
14. C22⋊C8×D107C2semidirect
15. #452×C107C2semidirect
29. C2×Dic428C22semidirect
30. C2×#13133808C22semidirect
31. C2×#13133808C22semidirect
33. C2×#13133807C22semidirect
34. C2×#13133806C22semidirect
35. C2×#13133805C22semidirect
39. #16812089C22semidirect
40. #16812088C22semidirect
43. #16812085C22semidirect
47. #16812034C22semidirect
48. #16812033C22semidirect
49. #16812032C22semidirect
50. #16812031C22semidirect
51. #16812030C22semidirect
52. #16812029C22semidirect
53. C22⋊(C107⋊C8)C22semidirect
54. (C2×D107)⋊C8C22semidirect
55. (C2×D107)⋊C8C22semidirect
57. C2×Q16×C107C22semidirect
58. C2×SD16×C107C22semidirect
59. C22⋊Q8×C107C22semidirect
60. #103×C107C22semidirect
61. #102×C107C22semidirect
62. C22⋊C8×C107C22semidirect
232. D107#452direct (N × H)
234. C107C2×#452semidirect
246. #452D107direct (N × H)
268. C2×Q16C2×D107semidirect
273. C2×SD16C2×D107semidirect
281. C22⋊Q8C2×D107semidirect
288. #103C2×D107semidirect
292. #102C2×D107semidirect
296. C22⋊C8C2×D107semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D1072
C2×Q16×D1072
C2×SD16×D1072
C22⋊Q8×D1072
#202927922
#202927912
#202927902
#202927892
#202927882
#202927872
#202927862
#103×D1072
#102×D1072
C22⋊C8×D1072
#452×C1072
C2×#452107