Finite Group Databasebeta

← #421×D271 #46844903

Subgroups — #421×D271 #46844903

Order 34688.

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×D271C211yesmaximal, characteristic
2C2×M16×D271C211yesmaximal, characteristic, complemented
3#117×D271C211yesmaximal, characteristic, complemented
4#31773915C211yesmaximal, characteristic, complemented
5#31773914C211yesmaximal, characteristic, complemented
6#31773913C211yesmaximal, characteristic, complemented
7#31773912C214yesmaximal, complemented
8#104×D271C214yesmaximal, complemented
9#421×C271C211yesmaximal, characteristic, complemented
10C2×#16864655C411yescharacteristic, complemented
11C2×#16864654—21no—
12C2×#16864654C2211yescharacteristic
13C2×#16864653—21no—
14C2×#16864653C411yescharacteristic, complemented
15#41×D271—21no—
16#41×D271—21no—
17#41×D271—21no—
18#41×D271—21no—
19#41×D271C412yescomplemented
20#41×D271C412yescomplemented
21#41×D271C2212yes—
22#41×D271C2212yes—
23C2×Q8×D271C411yescharacteristic, complemented
24C2×D4×D271—21no—
25C2×D4×D271C411yescharacteristic, complemented
26C22×C4×D271—21no—
27C22×C4×D271C2211yescharacteristic
28C2×#16864638C2211yescharacteristic, complemented
29C2×#16864637—21no—
30M16×D271—21no—
31M16×D271—21no—
32M16×D271C2212yescomplemented
33M16×D271C2212yescomplemented
34C2×C8×D271—21no—
35#22576119C2211yescharacteristic, complemented
36#22576118—21no—
37#22576117C2212yescomplemented
38#22576116—21no—
39C4⋊C4×D271—21no—
40C22⋊C4×D271—21no—
41C42×D271C2212yescomplemented
42#22576088C2214yescomplemented
43#22576087C2214yescomplemented
44#22576086C2214yescomplemented
45C2×#41×C271C2211yescharacteristic
46C2×M16×C271C2211yescharacteristic, complemented
47#117×C271C2211yescharacteristic, complemented
48#104×C271C2214yescomplemented
49C23×D271—21no—
50C23×D271D411yescharacteristic
51#16864655—21no—
52#16864655—21no—
53#16864655C2×C412yes—
54#16864655C2×C412yescomplemented
55#16864654—22no—
56#16864654—22no—
57#16864654—22no—
58#16864654—22no—
59#16864654—21no—
60#16864654—21no—
61#16864654C2×C412yescomplemented
62#16864654C2312yes—
63#16864653—22no—
64#16864653—22no—
65#16864653—22no—
66#16864653—22no—
67#16864653—21no—
68#16864653—21no—
69#16864653C2×C412yes—
70#16864653C2×C412yescomplemented
71C2×Dic542—21no—
72C2×Dic542C2×C411yescharacteristic, complemented
73Q8×D271—21no—
74Q8×D271—21no—
75Q8×D271C2×C412yes—
76Q8×D271C2×C412yescomplemented
77C2×D1084—21no—
78C2×D1084C2×C411yescharacteristic, complemented
79C2×C22⋊D271—21no—
80C2×C22⋊D271—21no—
81C2×C22⋊D271—21no—
82D4×D271—22no—
83D4×D271—22no—
84D4×D271—22no—
85D4×D271—22no—
86D4×D271—21no—
87D4×D271—21no—
88D4×D271C2×C412yes—
89D4×D271C2×C412yescomplemented
90C22×Dic271—21no—
91C22×Dic271D411yescharacteristic
92C2×C4×D271—21no—
93C2×C4×D271—21no—
94C2×C4×D271—22no—
95C2×C4×D271—22no—
96C2×C4×D271—22no—
97C2×C4×D271—22no—
98C2×C4×D271—22no—
99C2×C4×D271—21no—
100C2×C4×D271C2×C411yescharacteristic
101C2×C4×D271C2×C411yescharacteristic
102C2×C4×D271C2×C411yescharacteristic
103C2×C4×D271C2×C411yescharacteristic
104C2×C4×D271D411yescharacteristic
105C2×C4×D271D411yescharacteristic
106C2×C4×D271D411yescharacteristic
107C2×C4×D271D411yescharacteristic
108C2×C4×D271D411yescharacteristic
109C2×C4×D271D411yescharacteristic
110C2×C4×D271C2311yescharacteristic
111C2×C4×D271C2311yescharacteristic
112#16864638—21no—
113#16864638C2312yescomplemented
114#16864637—22no—
115#16864637—22no—
116C2×C271⋊C8—21no—
117C8×D271—22no—
118C8×D271—22no—
119C4⋊Dic271—21no—
120Dic271⋊C4—22no—
121C22⋊Dic271—21no—
122(C2×D271)⋊C4—22no—
123C4×Dic271—22no—
124C4×Dic271C2312yescomplemented
125#41×C271—21no—
126#41×C271—21no—
127#41×C271C2×C412yescomplemented
128#41×C271C2312yes—
129C2×Q8×C271C2×C411yescharacteristic, complemented
130C2×D4×C271—21no—
131C2×D4×C271C2×C411yescharacteristic, complemented
132C22×C4×C271—21no—
133C22×C4×C271C2311yescharacteristic
134M16×C271—21no—
135M16×C271C2312yescomplemented
136C2×C8×C271—21no—
137C4⋊C4×C271—21no—
138C22⋊C4×C271—21no—
139C42×C271C2312yescomplemented
140C22×D271—21no—
141C22×D271—22no—
142C22×D271—22no—
143C22×D271—42no—
144C22×D271—44no—
145C22×D271C22⋊C411yescharacteristic
146C22×D271C22⋊C411yescharacteristic
147C22×D271C22⋊C411yescharacteristic
148C22×D271C22⋊C411yescharacteristic
149C22×D271C2×D411yescharacteristic
150C22×D271C2×D411yescharacteristic
151Dic542—21no—
152Dic542—22no—
153Dic542—22no—
154Dic542C22×C412yes—
155D1084—22no—
156D1084—22no—
157D1084—21no—
158D1084C22×C412yes—
159C22⋊D271—22no—
160C22⋊D271—22no—
161C22⋊D271—22no—
162C22⋊D271—22no—
163C22⋊D271—22no—
164C22⋊D271—22no—
165C2×Dic271—21no—
166C2×Dic271—22no—
167C2×Dic271—22no—
168C2×Dic271—22no—
169C2×Dic271C22⋊C411yescharacteristic
170C2×Dic271C22⋊C411yescharacteristic
171C2×Dic271C22⋊C411yescharacteristic
172C2×Dic271C22⋊C411yescharacteristic
173C2×Dic271C2×D411yescharacteristic
174C2×Dic271C2×D411yescharacteristic
175C4×D271—22no—
176C4×D271—22no—
177C4×D271—22no—
178C4×D271—22no—
179C4×D271—22no—
180C4×D271—22no—
181C4×D271—44no—
182C4×D271C22⋊C411yescharacteristic
183C4×D271C22⋊C411yescharacteristic
184C4×D271C22⋊C411yescharacteristic
185C4×D271C22⋊C411yescharacteristic
186C4×D271C22⋊C411yescharacteristic
187C4×D271C22⋊C411yescharacteristic
188C4×D271C22⋊C411yescharacteristic
189C4×D271C22⋊C411yescharacteristic
190C4×D271C22×C411yescharacteristic
191C4×D271C22×C411yescharacteristic
192C4×D271C22×C411yescharacteristic
193C4×D271C22×C411yescharacteristic
194C4×D271C2×D411yescharacteristic
195C4×D271C2×D411yescharacteristic
196C4×D271C2×D411yescharacteristic
197C4×D271C2×D411yescharacteristic
198C271⋊C8—22no—
199C23×C271—21no—
200C23×C271C2×D411yescharacteristic
201Q8×C271—21no—
202Q8×C271C22×C412yes—
203D4×C271—22no—
204D4×C271—22no—
205D4×C271—21no—
206D4×C271C22×C412yes—
207C2×C4×C271—21no—
208C2×C4×C271—22no—
209C2×C4×C271—22no—
210C2×C4×C271—22no—
211C2×C4×C271C22×C411yescharacteristic
212C2×C4×C271C22×C411yescharacteristic
213C2×C4×C271C2×D411yescharacteristic
214C2×C4×C271C2×D411yescharacteristic
215C2×C4×C271C2×D411yescharacteristic
216C2×C4×C271C2411yescharacteristic
217C8×C271—22no—
218C22×C271—22no—
219C22×C271—41no—
220C22×C271—42no—
221C22×C271C2×C22⋊C411yescharacteristic
222C22×C271C2×C22⋊C411yescharacteristic
223C22×C271C22×D411yescharacteristic
224C2×D271—22no—
225C2×D271—22no—
226C2×D271—22no—
227C2×D271—22no—
228C2×D271—41no—
229C2×D271—41no—
230C2×D271—41no—
231C2×D271—44no—
232C2×D271—42no—
233C2×D271—44no—
234C2×D271C2×C22⋊C411yescharacteristic
235C2×D271C2×C22⋊C411yescharacteristic
236C2×D271C2×C22⋊C411yescharacteristic
237C2×D271C2×C22⋊C411yescharacteristic
238C4×C271—22no—
239C4×C271—42no—
240C4×C271C2×C22⋊C411yescharacteristic
241C4×C271C2×C22⋊C411yescharacteristic
242C4×C271C23×C411yescharacteristic
243C4×C271C22×D411yescharacteristic
244Dic271—22no—
245Dic271—42no—
246Dic271C2×C22⋊C411yescharacteristic
247Dic271C2×C22⋊C411yescharacteristic
248Dic271C2×C22⋊C411yescharacteristic
249Dic271C2×C22⋊C411yescharacteristic
250C2×C271—21no—
251C2×C271—21no—
252C2×C271—21no—
253C2×C271—42no—
254C2×C271C22×C22⋊C411yescharacteristic
255D271—21no—
256D271—21no—
257D271—21no—
258D271—42no—
259D271#42112yesdirect product factor
260C271C2×#42111yescharacteristic, complemented, Sylow
261C2×#421—2711nomaximal, Sylow
262C22×#41—2711no—
263C22×M16—2711no—
264C2×#117—2711no—
265#421—2711no—
266#421—2711no—
267#421—2711no—
268#421—2714no—
269#421D27111yescharacteristic, direct product factor
270C2×#104—2714no—
271C2×#41—2712no—
272C2×#41—2712no—
273C2×#41—2712no—
274C2×#41—2712no—
275C2×#41—2711no—
276C2×#41—2711no—
277C2×#41—2711no—
278C2×#41—5421no—
279C2×#41—5421no—
280C2×#41—5421no—
281C2×#41—5421no—
282C2×#41—5421no—
283C2×#41—5421no—
284C2×#41C2×D27111yescharacteristic
285C22×Q8—2711no—
286C22×D4—2711no—
287C22×D4—5421no—
288C23×C4—2711no—
289C23×C4—5421no—
290C2×M16—2711no—
291C2×M16—2712no—
292C2×M16—2712no—
293C2×M16—5421no—
294C2×M16—5421no—
295C2×M16—5421no—
296C2×M16C2×D27111yescharacteristic, complemented
297C22×C8—5421no—
298#117—2711no—
299#117—2712no—
300#117—5421no—
301#117—5421no—
302#117C2×D27111yescharacteristic, complemented
303C2×C4⋊C4—5421no—
304C2×C22⋊C4—5421no—
305C2×C42—2712no—
306#104—2714no—
307#104—2714no—
308#104—2714no—
309#104C2×D27114yescomplemented
310C24—2711no—
311C24—5421no—
312#41—21no—
313#41—21no—
314#41—2712no—
315#41—2712no—
316#41—2712no—
317#41—2712no—
318#41—2712no—
319#41—2712no—
320#41—5422no—
321#41—5422no—
322#41—5422no—
323#41—5422no—
324#41—5422no—
325#41—5422no—
326#41—5422no—
327#41—5422no—
328#41—5421no—
329#41—5421no—
330#41—5421no—
331#41—5421no—
332#41—5421no—
333#41—5421no—
334#41C4×D27112yescomplemented
335#41C22×D27112yes—
336C2×Q8—2712no—
337C2×Q8—2712no—
338C2×Q8—2711no—
339C2×Q8—5421no—
340C2×Q8—5421no—
341C2×Q8—5421no—
342C2×Q8C4×D27111yescharacteristic, complemented
343C2×D4—21no—
344C2×D4—2712no—
345C2×D4—2712no—
346C2×D4—2711no—
347C2×D4—5421no—
348C2×D4—5421no—
349C2×D4—5421no—
350C2×D4—5421no—
351C2×D4—5422no—
352C2×D4—5422no—
353C2×D4—5422no—
354C2×D4—5422no—
355C2×D4—5421no—
356C2×D4—5421no—
357C2×D4C4×D27111yescharacteristic, complemented
358C22×C4—21no—
359C22×C4—2711no—
360C22×C4—2711no—
361C22×C4—2711no—
362C22×C4—2711no—
363C22×C4—2711no—
364C22×C4—2711no—
365C22×C4—2711no—
366C22×C4—2711no—
367C22×C4—2711no—
368C22×C4—2711no—
369C22×C4—2711no—
370C22×C4—2711no—
371C22×C4—2711no—
372C22×C4—5421no—
373C22×C4—5422no—
374C22×C4—5422no—
375C22×C4—5422no—
376C22×C4—5422no—
377C22×C4—5421no—
378C22×C4—5422no—
379C22×C4—5421no—
380C22×C4—5421no—
381C22×C4C22×D27111yescharacteristic
382M16—21no—
383M16—2712no—
384M16—5422no—
385M16—5422no—
386M16—5421no—
387M16C22×D27112yescomplemented
388C2×C8—21no—
389C2×C8—5422no—
390C2×C8—5422no—
391C2×C8—5421no—
392C4⋊C4—21no—
393C4⋊C4—5422no—
394C4⋊C4—5421no—
395C22⋊C4—21no—
396C22⋊C4—5422no—
397C22⋊C4—5421no—
398C42—2712no—
399C42—5422no—
400C42C22×D27112yescomplemented
401C23—21no—
402C23—2711no—
403C23—2711no—
404C23—2711no—
405C23—2711no—
406C23—2711no—
407C23—2711no—
408C23—5422no—
409C23—5422no—
410C23—5421no—
411C23—10842no—
412C23—10844no—
413C23D4×D27111yescharacteristic
414Q8—21no—
415Q8—2712no—
416Q8—5422no—
417Q8—5422no—
418Q8—5421no—
419Q8C2×C4×D27112yes—
420D4—22no—
421D4—22no—
422D4—21no—
423D4—2712no—
424D4—5422no—
425D4—5422no—
426D4—5422no—
427D4—5422no—
428D4—5422no—
429D4—5422no—
430D4—5422no—
431D4—5422no—
432D4—5421no—
433D4C2×C4×D27112yes—
434C2×C4—21no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—2711no—
439C2×C4—2711no—
440C2×C4—2711no—
441C2×C4—2711no—
442C2×C4—2711no—
443C2×C4—2711no—
444C2×C4—2711no—
445C2×C4—2711no—
446C2×C4—2711no—
447C2×C4—2711no—
448C2×C4—2711no—
449C2×C4—2711no—
450C2×C4—2711no—
451C2×C4—2711no—
452C2×C4—2711no—
453C2×C4—2711no—
454C2×C4—2711no—
455C2×C4—2711no—
456C2×C4—2711no—
457C2×C4—2711no—
458C2×C4—2711no—
459C2×C4—2711no—
460C2×C4—5422no—
461C2×C4—5422no—
462C2×C4—5422no—
463C2×C4—5422no—
464C2×C4—5422no—
465C2×C4—5422no—
466C2×C4—5421no—
467C2×C4—5422no—
468C2×C4—5422no—
469C2×C4—5422no—
470C2×C4—10844no—
471C2×C4C2×C4×D27111yescharacteristic
472C2×C4C2×C4×D27111yescharacteristic
473C2×C4D4×D27111yescharacteristic
474C2×C4D4×D27111yescharacteristic
475C2×C4D4×D27111yescharacteristic
476C2×C4C23×D27111yescharacteristic
477C8—22no—
478C8—5422no—
479C22—22no—
480C22—41no—
481C22—42no—
482C22—2711no—
483C22—2711no—
484C22—2711no—
485C22—2711no—
486C22—5422no—
487C22—5422no—
488C22—5422no—
489C22—5422no—
490C22—10841no—
491C22—10841no—
492C22—10841no—
493C22—10842no—
494C22—10844no—
495C22—10844no—
496C22C22⋊C4×D27111yescharacteristic
497C22C22⋊C4×D27111yescharacteristic
498C22C2×D4×D27111yescharacteristic
499C4—22no—
500C4—42no—
501C4—2711no—
502C4—2711no—
503C4—2711no—
504C4—2711no—
505C4—5422no—
506C4—10842no—
507C4C22⋊C4×D27111yescharacteristic
508C4C22⋊C4×D27111yescharacteristic
509C4C22×C4×D27111yescharacteristic
510C4C2×D4×D27111yescharacteristic
511C2—21no—
512C2—21no—
513C2—21no—
514C2—42no—
515C2—2712no—
516C2—5421no—
517C2—5421no—
518C2—5421no—
519C2—10842no—
520C2C2×C22⋊C4×D27111yescharacteristic
subgroupG/H
centerC4C2×D4×D271
commutatorC4×C271C23×C4
FrattiniC2×C4C23×D271
Fitting#421×C271C2
socleC2×C271C22×C22⋊C4
prime radicalC2×#41×D271C2
cosocleC2×C4×C271C24
hypercenter#421D271
hypocenterC271C2×#421
LCSG ▷ C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. C2×M16×D271C2semidirect
3. #117×D271C2semidirect
4. #31773915C2semidirect
5. #31773914C2semidirect
6. #31773913C2semidirect
7. #31773912C2semidirect
8. #104×D271C2semidirect
9. #421×C271C2semidirect
10. C2×#16864655C4semidirect
14. C2×#16864653C4semidirect
19. #41×D271C4semidirect
20. #41×D271C4semidirect
23. C2×Q8×D271C4semidirect
25. C2×D4×D271C4semidirect
28. C2×#16864638C22semidirect
32. M16×D271C22semidirect
33. M16×D271C22semidirect
35. #22576119C22semidirect
37. #22576117C22semidirect
41. C42×D271C22semidirect
42. #22576088C22semidirect
43. #22576087C22semidirect
44. #22576086C22semidirect
46. C2×M16×C271C22semidirect
47. #117×C271C22semidirect
48. #104×C271C22semidirect
54. #16864655C2×C4semidirect
61. #16864654C2×C4semidirect
70. #16864653C2×C4semidirect
72. C2×Dic542C2×C4semidirect
76. Q8×D271C2×C4semidirect
78. C2×D1084C2×C4semidirect
89. D4×D271C2×C4semidirect
113. #16864638C23semidirect
124. C4×Dic271C23semidirect
127. #41×C271C2×C4semidirect
129. C2×Q8×C271C2×C4semidirect
131. C2×D4×C271C2×C4semidirect
135. M16×C271C23semidirect
139. C42×C271C23semidirect
259. D271#421direct (N × H)
260. C271C2×#421semidirect
269. #421D271direct (N × H)
296. C2×M16C2×D271semidirect
302. #117C2×D271semidirect
309. #104C2×D271semidirect
334. #41C4×D271semidirect
342. C2×Q8C4×D271semidirect
357. C2×D4C4×D271semidirect
387. M16C22×D271semidirect
400. C42C22×D271semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D2712
C2×M16×D2712
#117×D2712
#317739152
#317739142
#317739132
#317739122
#104×D2712
#421×C2712
C2×#421271