Finite Group Databasebeta

← #421×D107 #28345000

Subgroups — #421×D107 #28345000

Order 13696.

772 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D107C211yesmaximal, characteristic
2C2×M16×D107C211yesmaximal, characteristic, complemented
3#117×D107C211yesmaximal, characteristic, complemented
4#20292645C211yesmaximal, characteristic, complemented
5#20292644C211yesmaximal, characteristic, complemented
6#20292643C211yesmaximal, characteristic, complemented
7#20292642C214yesmaximal, complemented
8#104×D107C214yesmaximal, complemented
9#421×C107C211yesmaximal, characteristic, complemented
10C2×#13133819C411yescharacteristic, complemented
11C2×#13133818—21no—
12C2×#13133818C2211yescharacteristic
13C2×#13133817—21no—
14C2×#13133817C411yescharacteristic, complemented
15#41×D107—21no—
16#41×D107—21no—
17#41×D107—21no—
18#41×D107—21no—
19#41×D107C412yescomplemented
20#41×D107C412yescomplemented
21#41×D107C2212yes—
22#41×D107C2212yes—
23C2×Q8×D107C411yescharacteristic, complemented
24C2×D4×D107—21no—
25C2×D4×D107C411yescharacteristic, complemented
26C22×C4×D107—21no—
27C22×C4×D107C2211yescharacteristic
28C2×#13133802C2211yescharacteristic, complemented
29C2×#13133801—21no—
30M16×D107—21no—
31M16×D107—21no—
32M16×D107C2212yescomplemented
33M16×D107C2212yescomplemented
34C2×C8×D107—21no—
35#16812068C2211yescharacteristic, complemented
36#16812067—21no—
37#16812066C2212yescomplemented
38#16812065—21no—
39C4⋊C4×D107—21no—
40C22⋊C4×D107—21no—
41C42×D107C2212yescomplemented
42#16812037C2214yescomplemented
43#16812036C2214yescomplemented
44#16812035C2214yescomplemented
45C2×#41×C107C2211yescharacteristic
46C2×M16×C107C2211yescharacteristic, complemented
47#117×C107C2211yescharacteristic, complemented
48#104×C107C2214yescomplemented
49C23×D107—21no—
50C23×D107D411yescharacteristic
51#13133819—21no—
52#13133819—21no—
53#13133819C2×C412yes—
54#13133819C2×C412yescomplemented
55#13133818—21no—
56#13133818—21no—
57#13133818—22no—
58#13133818—22no—
59#13133818—22no—
60#13133818—22no—
61#13133818C2×C412yescomplemented
62#13133818C2312yes—
63#13133817—22no—
64#13133817—22no—
65#13133817—22no—
66#13133817—22no—
67#13133817—21no—
68#13133817—21no—
69#13133817C2×C412yes—
70#13133817C2×C412yescomplemented
71C2×Dic214—21no—
72C2×Dic214C2×C411yescharacteristic, complemented
73Q8×D107—21no—
74Q8×D107—21no—
75Q8×D107C2×C412yes—
76Q8×D107C2×C412yescomplemented
77C2×D428—21no—
78C2×D428C2×C411yescharacteristic, complemented
79C2×C22⋊D107—21no—
80C2×C22⋊D107—21no—
81C2×C22⋊D107—21no—
82D4×D107—22no—
83D4×D107—22no—
84D4×D107—22no—
85D4×D107—22no—
86D4×D107—21no—
87D4×D107—21no—
88D4×D107C2×C412yes—
89D4×D107C2×C412yescomplemented
90C22×Dic107—21no—
91C22×Dic107D411yescharacteristic
92C2×C4×D107—21no—
93C2×C4×D107—21no—
94C2×C4×D107—21no—
95C2×C4×D107—22no—
96C2×C4×D107—22no—
97C2×C4×D107—22no—
98C2×C4×D107—22no—
99C2×C4×D107—22no—
100C2×C4×D107C2×C411yescharacteristic
101C2×C4×D107C2×C411yescharacteristic
102C2×C4×D107C2×C411yescharacteristic
103C2×C4×D107C2×C411yescharacteristic
104C2×C4×D107D411yescharacteristic
105C2×C4×D107D411yescharacteristic
106C2×C4×D107D411yescharacteristic
107C2×C4×D107D411yescharacteristic
108C2×C4×D107D411yescharacteristic
109C2×C4×D107D411yescharacteristic
110C2×C4×D107C2311yescharacteristic
111C2×C4×D107C2311yescharacteristic
112#13133802—21no—
113#13133802C2312yescomplemented
114#13133801—22no—
115#13133801—22no—
116C2×C107⋊C8—21no—
117C8×D107—22no—
118C8×D107—22no—
119C4⋊Dic107—21no—
120Dic107⋊C4—22no—
121C22⋊Dic107—21no—
122(C2×D107)⋊C4—22no—
123C4×Dic107—22no—
124C4×Dic107C2312yescomplemented
125#41×C107—21no—
126#41×C107—21no—
127#41×C107C2×C412yescomplemented
128#41×C107C2312yes—
129C2×Q8×C107C2×C411yescharacteristic, complemented
130C2×D4×C107—21no—
131C2×D4×C107C2×C411yescharacteristic, complemented
132C22×C4×C107—21no—
133C22×C4×C107C2311yescharacteristic
134M16×C107—21no—
135M16×C107C2312yescomplemented
136C2×C8×C107—21no—
137C4⋊C4×C107—21no—
138C22⋊C4×C107—21no—
139C42×C107C2312yescomplemented
140C23×C107—21no—
141C23×C107C2×D411yescharacteristic
142C22×D107—21no—
143C22×D107—22no—
144C22×D107—22no—
145C22×D107—42no—
146C22×D107—44no—
147C22×D107C22⋊C411yescharacteristic
148C22×D107C22⋊C411yescharacteristic
149C22×D107C22⋊C411yescharacteristic
150C22×D107C22⋊C411yescharacteristic
151C22×D107C2×D411yescharacteristic
152C22×D107C2×D411yescharacteristic
153Q8×C107—21no—
154Q8×C107C22×C412yes—
155D4×C107—22no—
156D4×C107—22no—
157D4×C107—21no—
158D4×C107C22×C412yes—
159C2×C4×C107—21no—
160C2×C4×C107—22no—
161C2×C4×C107—22no—
162C2×C4×C107—22no—
163C2×C4×C107C22×C411yescharacteristic
164C2×C4×C107C22×C411yescharacteristic
165C2×C4×C107C2×D411yescharacteristic
166C2×C4×C107C2×D411yescharacteristic
167C2×C4×C107C2×D411yescharacteristic
168C2×C4×C107C2411yescharacteristic
169C22⋊D107—22no—
170C22⋊D107—22no—
171C22⋊D107—22no—
172C22⋊D107—22no—
173C22⋊D107—22no—
174C22⋊D107—22no—
175C2×Dic107—21no—
176C2×Dic107—22no—
177C2×Dic107—22no—
178C2×Dic107—22no—
179C2×Dic107C22⋊C411yescharacteristic
180C2×Dic107C22⋊C411yescharacteristic
181C2×Dic107C22⋊C411yescharacteristic
182C2×Dic107C22⋊C411yescharacteristic
183C2×Dic107C2×D411yescharacteristic
184C2×Dic107C2×D411yescharacteristic
185D428—22no—
186D428—22no—
187D428—21no—
188D428C22×C412yes—
189C4×D107—22no—
190C4×D107—22no—
191C4×D107—22no—
192C4×D107—22no—
193C4×D107—22no—
194C4×D107—22no—
195C4×D107—44no—
196C4×D107C22⋊C411yescharacteristic
197C4×D107C22⋊C411yescharacteristic
198C4×D107C22⋊C411yescharacteristic
199C4×D107C22⋊C411yescharacteristic
200C4×D107C22⋊C411yescharacteristic
201C4×D107C22⋊C411yescharacteristic
202C4×D107C22⋊C411yescharacteristic
203C4×D107C22⋊C411yescharacteristic
204C4×D107C22×C411yescharacteristic
205C4×D107C22×C411yescharacteristic
206C4×D107C22×C411yescharacteristic
207C4×D107C22×C411yescharacteristic
208C4×D107C2×D411yescharacteristic
209C4×D107C2×D411yescharacteristic
210C4×D107C2×D411yescharacteristic
211C4×D107C2×D411yescharacteristic
212Dic214—21no—
213Dic214—22no—
214Dic214—22no—
215Dic214C22×C412yes—
216C8×C107—22no—
217C107⋊C8—22no—
218C22×C107—22no—
219C22×C107—41no—
220C22×C107—42no—
221C22×C107C2×C22⋊C411yescharacteristic
222C22×C107C2×C22⋊C411yescharacteristic
223C22×C107C22×D411yescharacteristic
224C2×D107—22no—
225C2×D107—22no—
226C2×D107—22no—
227C2×D107—22no—
228C2×D107—41no—
229C2×D107—41no—
230C2×D107—41no—
231C2×D107—44no—
232C2×D107—42no—
233C2×D107—44no—
234C2×D107C2×C22⋊C411yescharacteristic
235C2×D107C2×C22⋊C411yescharacteristic
236C2×D107C2×C22⋊C411yescharacteristic
237C2×D107C2×C22⋊C411yescharacteristic
238C4×C107—22no—
239C4×C107—42no—
240C4×C107C2×C22⋊C411yescharacteristic
241C4×C107C2×C22⋊C411yescharacteristic
242C4×C107C23×C411yescharacteristic
243C4×C107C22×D411yescharacteristic
244Dic107—22no—
245Dic107—42no—
246Dic107C2×C22⋊C411yescharacteristic
247Dic107C2×C22⋊C411yescharacteristic
248Dic107C2×C22⋊C411yescharacteristic
249Dic107C2×C22⋊C411yescharacteristic
250C2×C107—21no—
251C2×C107—21no—
252C2×C107—21no—
253C2×C107—42no—
254C2×C107C22×C22⋊C411yescharacteristic
255D107—21no—
256D107—21no—
257D107—21no—
258D107—42no—
259D107#42112yesdirect product factor
260C2×#421—1071nomaximal, Sylow
261C107C2×#42111yescharacteristic, complemented, Sylow
262C22×#41—1071no—
263C22×M16—1071no—
264C2×#117—1071no—
265#421—1071no—
266#421—1071no—
267#421—1071no—
268#421—1074no—
269#421D10711yescharacteristic, direct product factor
270C2×#104—1074no—
271C2×#41—1072no—
272C2×#41—1072no—
273C2×#41—1072no—
274C2×#41—1072no—
275C2×#41—1071no—
276C2×#41—1071no—
277C2×#41—1071no—
278C2×#41—2141no—
279C2×#41—2141no—
280C2×#41—2141no—
281C2×#41—2141no—
282C2×#41—2141no—
283C2×#41—2141no—
284C2×#41C2×D10711yescharacteristic
285C22×Q8—1071no—
286C22×D4—1071no—
287C22×D4—2141no—
288C23×C4—1071no—
289C23×C4—2141no—
290C2×M16—1071no—
291C2×M16—1072no—
292C2×M16—1072no—
293C2×M16—2141no—
294C2×M16—2141no—
295C2×M16—2141no—
296C2×M16C2×D10711yescharacteristic, complemented
297C22×C8—2141no—
298#117—1071no—
299#117—1072no—
300#117—2141no—
301#117—2141no—
302#117C2×D10711yescharacteristic, complemented
303C2×C4⋊C4—2141no—
304C2×C22⋊C4—2141no—
305C2×C42—1072no—
306#104—1074no—
307#104—1074no—
308#104—1074no—
309#104C2×D10714yescomplemented
310C24—1071no—
311C24—2141no—
312#41—21no—
313#41—21no—
314#41—1072no—
315#41—1072no—
316#41—1072no—
317#41—1072no—
318#41—1072no—
319#41—1072no—
320#41—2142no—
321#41—2142no—
322#41—2142no—
323#41—2142no—
324#41—2142no—
325#41—2142no—
326#41—2142no—
327#41—2142no—
328#41—2141no—
329#41—2141no—
330#41—2141no—
331#41—2141no—
332#41—2141no—
333#41—2141no—
334#41C4×D10712yescomplemented
335#41C22×D10712yes—
336C2×Q8—1072no—
337C2×Q8—1072no—
338C2×Q8—1071no—
339C2×Q8—2141no—
340C2×Q8—2141no—
341C2×Q8—2141no—
342C2×Q8C4×D10711yescharacteristic, complemented
343C2×D4—21no—
344C2×D4—1072no—
345C2×D4—1072no—
346C2×D4—1071no—
347C2×D4—2141no—
348C2×D4—2141no—
349C2×D4—2141no—
350C2×D4—2141no—
351C2×D4—2142no—
352C2×D4—2142no—
353C2×D4—2142no—
354C2×D4—2142no—
355C2×D4—2141no—
356C2×D4—2141no—
357C2×D4C4×D10711yescharacteristic, complemented
358C22×C4—21no—
359C22×C4—1071no—
360C22×C4—1071no—
361C22×C4—1071no—
362C22×C4—1071no—
363C22×C4—1071no—
364C22×C4—1071no—
365C22×C4—1071no—
366C22×C4—1071no—
367C22×C4—1071no—
368C22×C4—1071no—
369C22×C4—1071no—
370C22×C4—1071no—
371C22×C4—1071no—
372C22×C4—2141no—
373C22×C4—2142no—
374C22×C4—2142no—
375C22×C4—2142no—
376C22×C4—2142no—
377C22×C4—2142no—
378C22×C4—2141no—
379C22×C4—2141no—
380C22×C4—2141no—
381C22×C4C22×D10711yescharacteristic
382M16—21no—
383M16—1072no—
384M16—2142no—
385M16—2142no—
386M16—2141no—
387M16C22×D10712yescomplemented
388C2×C8—21no—
389C2×C8—2142no—
390C2×C8—2142no—
391C2×C8—2141no—
392C4⋊C4—21no—
393C4⋊C4—2142no—
394C4⋊C4—2141no—
395C22⋊C4—21no—
396C22⋊C4—2142no—
397C22⋊C4—2141no—
398C42—1072no—
399C42—2142no—
400C42C22×D10712yescomplemented
401C23—21no—
402C23—1071no—
403C23—1071no—
404C23—1071no—
405C23—1071no—
406C23—1071no—
407C23—1071no—
408C23—4284no—
409C23—4282no—
410C23—2142no—
411C23—2142no—
412C23—2141no—
413C23D4×D10711yescharacteristic
414Q8—21no—
415Q8—1072no—
416Q8—2142no—
417Q8—2142no—
418Q8—2141no—
419Q8C2×C4×D10712yes—
420D4—22no—
421D4—22no—
422D4—21no—
423D4—1072no—
424D4—2142no—
425D4—2142no—
426D4—2142no—
427D4—2142no—
428D4—2142no—
429D4—2142no—
430D4—2142no—
431D4—2142no—
432D4—2141no—
433D4C2×C4×D10712yes—
434C2×C4—21no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—1071no—
439C2×C4—1071no—
440C2×C4—1071no—
441C2×C4—1071no—
442C2×C4—1071no—
443C2×C4—1071no—
444C2×C4—1071no—
445C2×C4—1071no—
446C2×C4—1071no—
447C2×C4—1071no—
448C2×C4—1071no—
449C2×C4—1071no—
450C2×C4—1071no—
451C2×C4—1071no—
452C2×C4—1071no—
453C2×C4—1071no—
454C2×C4—1071no—
455C2×C4—1071no—
456C2×C4—1071no—
457C2×C4—1071no—
458C2×C4—1071no—
459C2×C4—1071no—
460C2×C4—4284no—
461C2×C4—2142no—
462C2×C4—2142no—
463C2×C4—2142no—
464C2×C4—2142no—
465C2×C4—2142no—
466C2×C4—2142no—
467C2×C4—2142no—
468C2×C4—2141no—
469C2×C4—2142no—
470C2×C4—2142no—
471C2×C4C2×C4×D10711yescharacteristic
472C2×C4C2×C4×D10711yescharacteristic
473C2×C4D4×D10711yescharacteristic
474C2×C4D4×D10711yescharacteristic
475C2×C4D4×D10711yescharacteristic
476C2×C4C23×D10711yescharacteristic
477C8—22no—
478C8—2142no—
479C22—22no—
480C22—41no—
481C22—42no—
482C22—1071no—
483C22—1071no—
484C22—1071no—
485C22—1071no—
486C22—4282no—
487C22—4281no—
488C22—4281no—
489C22—4281no—
490C22—4284no—
491C22—4284no—
492C22—2142no—
493C22—2142no—
494C22—2142no—
495C22—2142no—
496C22C22⋊C4×D10711yescharacteristic
497C22C22⋊C4×D10711yescharacteristic
498C22C2×D4×D10711yescharacteristic
499C4—22no—
500C4—42no—
501C4—1071no—
502C4—1071no—
503C4—1071no—
504C4—1071no—
505C4—4282no—
506C4—2142no—
507C4C22⋊C4×D10711yescharacteristic
508C4C22⋊C4×D10711yescharacteristic
509C4C22×C4×D10711yescharacteristic
510C4C2×D4×D10711yescharacteristic
511C2—21no—
512C2—21no—
513C2—21no—
514C2—42no—
515C2—1072no—
516C2—4282no—
517C2—2141no—
518C2—2141no—
519C2—2141no—
520C2C2×C22⋊C4×D10711yescharacteristic
subgroupG/H
centerC4C2×D4×D107
commutatorC4×C107C23×C4
FrattiniC2×C4C23×D107
Fitting#421×C107C2
socleC2×C107C22×C22⋊C4
prime radicalC2×#41×D107C2
cosocleC2×C4×C107C24
hypercenter#421D107
hypocenterC107C2×#421
LCSG ▷ C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. C2×M16×D107C2semidirect
3. #117×D107C2semidirect
4. #20292645C2semidirect
5. #20292644C2semidirect
6. #20292643C2semidirect
7. #20292642C2semidirect
8. #104×D107C2semidirect
9. #421×C107C2semidirect
10. C2×#13133819C4semidirect
14. C2×#13133817C4semidirect
19. #41×D107C4semidirect
20. #41×D107C4semidirect
23. C2×Q8×D107C4semidirect
25. C2×D4×D107C4semidirect
28. C2×#13133802C22semidirect
32. M16×D107C22semidirect
33. M16×D107C22semidirect
35. #16812068C22semidirect
37. #16812066C22semidirect
41. C42×D107C22semidirect
42. #16812037C22semidirect
43. #16812036C22semidirect
44. #16812035C22semidirect
46. C2×M16×C107C22semidirect
47. #117×C107C22semidirect
48. #104×C107C22semidirect
54. #13133819C2×C4semidirect
61. #13133818C2×C4semidirect
70. #13133817C2×C4semidirect
72. C2×Dic214C2×C4semidirect
76. Q8×D107C2×C4semidirect
78. C2×D428C2×C4semidirect
89. D4×D107C2×C4semidirect
113. #13133802C23semidirect
124. C4×Dic107C23semidirect
127. #41×C107C2×C4semidirect
129. C2×Q8×C107C2×C4semidirect
131. C2×D4×C107C2×C4semidirect
135. M16×C107C23semidirect
139. C42×C107C23semidirect
259. D107#421direct (N × H)
261. C107C2×#421semidirect
269. #421D107direct (N × H)
296. C2×M16C2×D107semidirect
302. #117C2×D107semidirect
309. #104C2×D107semidirect
334. #41C4×D107semidirect
342. C2×Q8C4×D107semidirect
357. C2×D4C4×D107semidirect
387. M16C22×D107semidirect
400. C42C22×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×M16×D1072
#117×D1072
#202926452
#202926442
#202926432
#202926422
#104×D1072
#421×C1072
C2×#421107