Finite Group Databasebeta

← C2×#31827105 #49134706

Subgroups — C2×#31827105 #49134706

Order 36224.

1900 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#17985392C211yesmaximal, characteristic, complemented
2C23×C22⋊D283C211yesmaximal, characteristic, complemented
3#31827105C2116yesmaximal, direct product factor
4C2×#22583596C211yesmaximal, characteristic, complemented
5C2×#22583593C211yesmaximal, characteristic, complemented
6C2×#22583592C211yesmaximal, characteristic, complemented
7C2×#22583587C211yesmaximal, characteristic, complemented
8C2×#22583584C211yesmaximal, characteristic, complemented
9C2×#22583583C211yesmaximal, characteristic, complemented
10C2×#22583583C211yesmaximal, characteristic, complemented
11C2×#22583580C211yesmaximal, characteristic, complemented
12C2×#22583579C211yesmaximal, characteristic, complemented
13C2×C4×C22⋊D283C211yesmaximal, characteristic, complemented
14C2×(C22⋊D283)⋊C4C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×D283C211yesmaximal, characteristic, complemented
16C22×C22⋊C4×C283C211yesmaximal, characteristic, complemented
17C24×D283C2211yescharacteristic
18C2×#17985392—28no—
19C2×#17985392C2218yescomplemented
20C22×Dic566C2211yescharacteristic, complemented
21C22×D1132C2211yescharacteristic, complemented
22C22×D1132C2211yescharacteristic, complemented
23C22×C22⋊D283—28no—
24C22×C22⋊D283C2211yescharacteristic
25C22×C22⋊D283C2211yescharacteristic
26C22×C22⋊D283C2211yescharacteristic
27C22×C22⋊D283C2211yescharacteristic
28C22×C22⋊D283C2211yescharacteristic
29C22×C22⋊D283C2218yescomplemented
30C22×C22⋊D283C2211yescharacteristic, complemented
31C22×C22⋊D283C2211yescharacteristic, complemented
32C23×Dic283C2211yescharacteristic
33C22×C4×D283C2211yescharacteristic, complemented
34C22×C4×D283C2211yescharacteristic, complemented
35C22×C4×D283C2211yescharacteristic, complemented
36#22583596C2218yescomplemented
37#22583593C2218yescomplemented
38#22583592C2218yescomplemented
39#22583587C2218yescomplemented
40#22583584C2218yescomplemented
41#22583583C2218yescomplemented
42#22583583C2218yescomplemented
43#22583580C2218yescomplemented
44#22583579C2218yescomplemented
45C4×C22⋊D283C2218yescomplemented
46(C22⋊D283)⋊C4C2218yescomplemented
47C2×C4⋊Dic283C2211yescharacteristic, complemented
48C2×Dic283⋊C4C2211yescharacteristic, complemented
49C2×Dic283⋊C4C2211yescharacteristic, complemented
50C2×Dic283⋊C4C2211yescharacteristic, complemented
51C2×C22⋊Dic283C2211yescharacteristic
52C2×C22⋊Dic283C2211yescharacteristic, complemented
53C2×C22⋊Dic283C2211yescharacteristic, complemented
54C2×(C2×D283)⋊C4C2211yescharacteristic, complemented
55C2×(C2×D283)⋊C4C2211yescharacteristic, complemented
56C2×(C2×D283)⋊C4C2211yescharacteristic, complemented
57C2×(C2×D283)⋊C4C2211yescharacteristic, complemented
58C2×(C2×D283)⋊C4C2211yescharacteristic, complemented
59C22⋊C4×D283C2218yescomplemented
60C2×C4×Dic283C2211yescharacteristic, complemented
61C25×C283C2211yescharacteristic
62C23×C4×C283C2211yescharacteristic, complemented
63C23×C4×C283C2211yescharacteristic, complemented
64C2×C22⋊C4×C283C2211yescharacteristic
65C2×C22⋊C4×C283C2211yescharacteristic
66C2×C22⋊C4×C283C2218yescomplemented
67C2×C22⋊C4×C283C2211yescharacteristic, complemented
68C2×C22⋊C4×C283C2211yescharacteristic, complemented
69C23×D283—24no—
70C23×D283—24no—
71C23×D283—42no—
72C23×D283C2311yescharacteristic
73C23×D283C2311yescharacteristic
74C23×D283C2314yes—
75C23×D283C2311yescharacteristic
76#17985392—232no—
77C2×Dic566—24no—
78C2×Dic566C2314yescomplemented
79C2×D1132—24no—
80C2×D1132—42no—
81C2×D1132C2314yescomplemented
82C2×D1132C2314yescomplemented
83C2×C22⋊D283—24no—
84C2×C22⋊D283—232no—
85C2×C22⋊D283—24no—
86C2×C22⋊D283—24no—
87C2×C22⋊D283—24no—
88C2×C22⋊D283—24no—
89C2×C22⋊D283—42no—
90C2×C22⋊D283D418yescomplemented
91C2×C22⋊D283C2314yes—
92C2×C22⋊D283C2314yes—
93C2×C22⋊D283C2314yes—
94C2×C22⋊D283C2314yes—
95C2×C22⋊D283C2314yes—
96C2×C22⋊D283C2314yescomplemented
97C2×C22⋊D283C2314yescomplemented
98C22×Dic283—24no—
99C22×Dic283C2311yescharacteristic
100C22×Dic283C2311yescharacteristic
101C22×Dic283C2311yescharacteristic
102C22×Dic283C2311yescharacteristic
103C22×Dic283C2314yes—
104C22×Dic283C2311yescharacteristic
105C2×C4×D283—24no—
106C2×C4×D283—24no—
107C2×C4×D283—42no—
108C2×C4×D283C2314yescomplemented
109C2×C4×D283C2314yescomplemented
110C2×C4×D283C2314yescomplemented
111C4⋊Dic283C2314yescomplemented
112Dic283⋊C4C2314yescomplemented
113Dic283⋊C4C2314yescomplemented
114Dic283⋊C4C2314yescomplemented
115C22⋊Dic283C2314yes—
116C22⋊Dic283C2314yescomplemented
117C22⋊Dic283C2314yescomplemented
118(C2×D283)⋊C4C2314yescomplemented
119(C2×D283)⋊C4C2314yescomplemented
120(C2×D283)⋊C4C2314yescomplemented
121(C2×D283)⋊C4C2314yescomplemented
122(C2×D283)⋊C4C2314yescomplemented
123C4×Dic283C2314yescomplemented
124C24×C283—24no—
125C24×C283—24no—
126C24×C283—42no—
127C24×C283C2311yescharacteristic
128C24×C283C2314yes—
129C24×C283C2311yescharacteristic
130C24×C283C2311yescharacteristic
131C22×C4×C283—24no—
132C22×C4×C283—42no—
133C22×C4×C283C2311yescharacteristic
134C22×C4×C283C2311yescharacteristic
135C22×C4×C283C2311yescharacteristic
136C22×C4×C283C2311yescharacteristic
137C22×C4×C283C2314yescomplemented
138C22×C4×C283C2314yescomplemented
139C22⋊C4×C283C2314yes—
140C22⋊C4×C283C2314yes—
141C22⋊C4×C283C2314yescomplemented
142C22⋊C4×C283C2314yescomplemented
143C22×D283—22no—
144C22×D283—22no—
145C22×D283—22no—
146C22×D283—22no—
147C22×D283—22no—
148C22×D283—22no—
149C22×D283—28no—
150C22×D283—22no—
151C22×D283—22no—
152C22×D283—28no—
153C22×D283—44no—
154C22×D283—416no—
155C22×D283C2×D414yes—
156C22×D283C2412yes—
157C22×D283C2412yes—
158C22×D283C2412yes—
159Dic566—28no—
160D1132—28no—
161D1132—44no—
162C22⋊D283—28no—
163C22⋊D283—28no—
164C22⋊D283—28no—
165C22⋊D283—28no—
166C22⋊D283—28no—
167C22⋊D283—44no—
168C22⋊D283C2×D4116yescomplemented
169C2×Dic283—22no—
170C2×Dic283—22no—
171C2×Dic283—22no—
172C2×Dic283—22no—
173C2×Dic283—28no—
174C2×Dic283C2×D414yes—
175C2×Dic283C2412yes—
176C2×Dic283C2412yes—
177C2×Dic283C2412yes—
178C2×Dic283C2412yes—
179C2×Dic283C2412yes—
180C4×D283—28no—
181C4×D283—28no—
182C4×D283—44no—
183C23×C283—22no—
184C23×C283—22no—
185C23×C283—22no—
186C23×C283—22no—
187C23×C283—28no—
188C23×C283—22no—
189C23×C283—22no—
190C23×C283—28no—
191C23×C283—22no—
192C23×C283—44no—
193C23×C283—416no—
194C23×C283C2×D414yes—
195C23×C283#4114yescomplemented
196C23×C283C2412yes—
197C23×C283C2412yes—
198C23×C283C2412yes—
199C23×C283C2411yescharacteristic
200C2×C4×C283—22no—
201C2×C4×C283—22no—
202C2×C4×C283—28no—
203C2×C4×C283—22no—
204C2×C4×C283—22no—
205C2×C4×C283—44no—
206C2×C4×C283C2412yes—
207C2×C4×C283C2412yes—
208C2×C4×C283C2412yes—
209C2×C4×C283C2412yes—
210C22×C283—28no—
211C22×C283—28no—
212C22×C283—22no—
213C22×C283—22no—
214C22×C283—22no—
215C22×C283—22no—
216C22×C283—22no—
217C22×C283—22no—
218C22×C283—22no—
219C22×C283—416no—
220C22×C283—44no—
221C22×C283C22×D414yes—
222C22×C283C22×D412yes—
223C22×C283C2×#4112yes—
224C22×C283C2×#4114yescomplemented
225C22×C283H(5,𝔽2)12yes—
226C22×C283C2511yescharacteristic
227C2×D283—28no—
228C2×D283—22no—
229C2×D283—22no—
230C2×D283—22no—
231C2×D283—22no—
232C2×D283—22no—
233C2×D283—22no—
234C2×D283—22no—
235C2×D283—22no—
236C2×D283—416no—
237C2×D283—44no—
238C2×D283—44no—
239C2×D283C22×D414yes—
240C4×C283—22no—
241C4×C283—22no—
242C4×C283—22no—
243C4×C283—22no—
244Dic283—22no—
245Dic283—22no—
246Dic283—22no—
247Dic283—22no—
248Dic283C22×D414yes—
249C2×C283—24no—
250C2×C283—24no—
251C2×C283—42no—
252C2×C283#54614yescomplemented
253C2×C283C23×D411yescharacteristic
254C2×C283C22×#4111yescharacteristic
255C2×C283C2×H(5,𝔽2)11yescharacteristic
256D283—24no—
257D283—42no—
258D283—42no—
259C283C2×#54611yescharacteristic, complemented, Sylow
260C2×#546—2831nomaximal, Sylow
261C22×#41—2831no—
262C23×D4—2831no—
263#546—28316no—
264C2×#124—2831no—
265C2×#123—2831no—
266C2×#123—2831no—
267C2×C22⋊Q8—2831no—
268C2×#121—2831no—
269C2×#121—2831no—
270C2×#121—2831no—
271C2×#120—2831no—
272C2×#120—2831no—
273C2×C4×D4—2831no—
274C2×C4×D4—2831no—
275C22×C22⋊C4—2831no—
276C22×C22⋊C4D28311yescharacteristic, complemented
277C25—2831no—
278C25C2×D28311yescharacteristic
279C2×#41—2838no—
280C2×#41—5668no—
281C22×Q8—2831no—
282C22×D4—2831no—
283C22×D4—2831no—
284C22×D4—2831no—
285C22×D4—2831no—
286C22×D4—2831no—
287C22×D4—2831no—
288C22×D4—2838no—
289C22×D4—2831no—
290C22×D4—2831no—
291C22×D4—2831no—
292C22×D4—5668no—
293C23×C4—2831no—
294C23×C4—2831no—
295C23×C4—2831no—
296C23×C4—2831no—
297C23×C4C2×D28311yescharacteristic, complemented
298C23×C4C2×D28311yescharacteristic, complemented
299#124—2838no—
300#123—2838no—
301#123—2838no—
302C22⋊Q8—2838no—
303#121—2838no—
304#121—2838no—
305#121—2838no—
306#120—2838no—
307#120—2838no—
308C4×D4—2838no—
309C4×D4—2838no—
310C2×C4⋊C4—2831no—
311C2×C4⋊C4—2831no—
312C2×C4⋊C4—2831no—
313C2×C4⋊C4—2831no—
314C2×C22⋊C4—2831no—
315C2×C22⋊C4—2831no—
316C2×C22⋊C4—2831no—
317C2×C22⋊C4—2831no—
318C2×C22⋊C4—2831no—
319C2×C22⋊C4—2831no—
320C2×C22⋊C4—2831no—
321C2×C22⋊C4—2831no—
322C2×C22⋊C4—2838no—
323C2×C22⋊C4C2×D28311yescharacteristic
324C2×C22⋊C4C2×D28311yescharacteristic
325C2×C22⋊C4C2×D28318yescomplemented
326C2×C22⋊C4C2×D28311yescharacteristic, complemented
327C2×C22⋊C4C2×D28311yescharacteristic, complemented
328C2×C42—2831no—
329C24—24no—
330C24—24no—
331C24—42no—
332C24—2831no—
333C24—2831no—
334C24—2831no—
335C24—2834no—
336C24—5664no—
337C24—5664no—
338C24—11322no—
339C24C22×D28311yescharacteristic
340C24C22×D28314yes—
341C24C22×D28311yescharacteristic
342C24C22×D28311yescharacteristic
343#41—56632no—
344C2×Q8—2834no—
345C2×Q8—5664no—
346C2×D4—2838no—
347C2×D4—2834no—
348C2×D4—2834no—
349C2×D4—2834no—
350C2×D4—2834no—
351C2×D4—2834no—
352C2×D4—2834no—
353C2×D4—2834no—
354C2×D4—2834no—
355C2×D4—2834no—
356C2×D4—5664no—
357C2×D4—5664no—
358C2×D4—56632no—
359C2×D4—5664no—
360C2×D4—5664no—
361C2×D4—5664no—
362C2×D4—5664no—
363C2×D4—11322no—
364C2×D4—11322no—
365C22×C4—24no—
366C22×C4—42no—
367C22×C4—2831no—
368C22×C4—2834no—
369C22×C4—2831no—
370C22×C4—2831no—
371C22×C4—2831no—
372C22×C4—2831no—
373C22×C4—2834no—
374C22×C4—2834no—
375C22×C4—2834no—
376C22×C4—5664no—
377C22×C4—5664no—
378C22×C4—5664no—
379C22×C4—11322no—
380C22×C4C22×D28311yescharacteristic
381C22×C4C22×D28311yescharacteristic
382C22×C4C22×D28311yescharacteristic
383C22×C4C22×D28311yescharacteristic
384C22×C4C22×D28314yescomplemented
385C22×C4C22×D28314yescomplemented
386C4⋊C4—2834no—
387C4⋊C4—2834no—
388C4⋊C4—2834no—
389C4⋊C4—2834no—
390C22⋊C4—2834no—
391C22⋊C4—2834no—
392C22⋊C4—2834no—
393C22⋊C4—2834no—
394C22⋊C4—2834no—
395C22⋊C4—2834no—
396C22⋊C4—2834no—
397C22⋊C4—2834no—
398C22⋊C4C22×D28314yes—
399C22⋊C4C22×D28314yes—
400C22⋊C4C22×D28314yescomplemented
401C22⋊C4C22×D28314yescomplemented
402C42—2834no—
403C23—22no—
404C23—22no—
405C23—22no—
406C23—22no—
407C23—28no—
408C23—22no—
409C23—22no—
410C23—28no—
411C23—22no—
412C23—44no—
413C23—416no—
414C23—2834no—
415C23—2832no—
416C23—2832no—
417C23—2832no—
418C23—5668no—
419C23—5662no—
420C23—5662no—
421C23—5662no—
422C23—5662no—
423C23—5662no—
424C23—5662no—
425C23—5668no—
426C23—5662no—
427C23—5662no—
428C23—11324no—
429C23—113216no—
430C23D4×D28314yes—
431C23#1798539214yescomplemented
432C23C23×D28312yes—
433C23C23×D28312yes—
434C23C23×D28312yes—
435C23C23×D28311yescharacteristic
436Q8—5668no—
437D4—28316no—
438D4—5668no—
439D4—5668no—
440D4—5668no—
441D4—5668no—
442D4—5668no—
443D4—5668no—
444D4—11324no—
445D4—11324no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—28no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—44no—
452C2×C4—2834no—
453C2×C4—2832no—
454C2×C4—2832no—
455C2×C4—2832no—
456C2×C4—2832no—
457C2×C4—2832no—
458C2×C4—5668no—
459C2×C4—5668no—
460C2×C4—5668no—
461C2×C4—5662no—
462C2×C4—5662no—
463C2×C4—5662no—
464C2×C4—5662no—
465C2×C4—11324no—
466C2×C4C23×D28312yes—
467C2×C4C23×D28312yes—
468C2×C4C23×D28312yes—
469C2×C4C23×D28312yes—
470C22—22no—
471C22—22no—
472C22—22no—
473C22—22no—
474C22—28no—
475C22—28no—
476C22—22no—
477C22—22no—
478C22—22no—
479C22—416no—
480C22—44no—
481C22—2834no—
482C22—5662no—
483C22—5662no—
484C22—5668no—
485C22—5662no—
486C22—5662no—
487C22—5662no—
488C22—5662no—
489C22—5662no—
490C22—5662no—
491C22—113216no—
492C22—11324no—
493C22—11324no—
494C22C2×D4×D28314yes—
495C22C2×D4×D28312yes—
496C22C2×#1798539212yes—
497C22C2×#1798539214yescomplemented
498C22#2258365512yes—
499C22C24×D28311yescharacteristic
500C4—22no—
501C4—22no—
502C4—22no—
503C4—22no—
504C4—2834no—
505C4—5662no—
506C4—5662no—
507C4—5662no—
508C4—5662no—
509C2—24no—
510C2—24no—
511C2—42no—
512C2—5664no—
513C2—11322no—
514C2—11322no—
515C2#3182710514yesdirect product factor
516C2C22×D4×D28311yescharacteristic
517C2C22×#1798539211yescharacteristic
518C2C2×#2258365511yescharacteristic
subgroupG/H
centerC23C23×D283
commutator, cosocleC22×C283C25
FrattiniC22C24×D283
FittingC22×C22⋊C4×C283C2
socleC23×C283C24
hypercenterC22×C22⋊C4D283
hypocenterC283C2×#546
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#17985392C2semidirect
2. C23×C22⋊D283C2semidirect
3. #31827105C2direct (N × H)
4. C2×#22583596C2semidirect
5. C2×#22583593C2semidirect
6. C2×#22583592C2semidirect
7. C2×#22583587C2semidirect
8. C2×#22583584C2semidirect
9. C2×#22583583C2semidirect
10. C2×#22583583C2semidirect
11. C2×#22583580C2semidirect
12. C2×#22583579C2semidirect
13. C2×C4×C22⋊D283C2semidirect
14. C2×(C22⋊D283)⋊C4C2semidirect
15. C2×C22⋊C4×D283C2semidirect
16. C22×C22⋊C4×C283C2semidirect
19. C2×#17985392C22semidirect
20. C22×Dic566C22semidirect
21. C22×D1132C22semidirect
22. C22×D1132C22semidirect
29. C22×C22⋊D283C22semidirect
30. C22×C22⋊D283C22semidirect
31. C22×C22⋊D283C22semidirect
33. C22×C4×D283C22semidirect
34. C22×C4×D283C22semidirect
35. C22×C4×D283C22semidirect
36. #22583596C22semidirect
37. #22583593C22semidirect
38. #22583592C22semidirect
39. #22583587C22semidirect
40. #22583584C22semidirect
41. #22583583C22semidirect
42. #22583583C22semidirect
43. #22583580C22semidirect
44. #22583579C22semidirect
45. C4×C22⋊D283C22semidirect
46. (C22⋊D283)⋊C4C22semidirect
47. C2×C4⋊Dic283C22semidirect
48. C2×Dic283⋊C4C22semidirect
49. C2×Dic283⋊C4C22semidirect
50. C2×Dic283⋊C4C22semidirect
52. C2×C22⋊Dic283C22semidirect
53. C2×C22⋊Dic283C22semidirect
54. C2×(C2×D283)⋊C4C22semidirect
55. C2×(C2×D283)⋊C4C22semidirect
56. C2×(C2×D283)⋊C4C22semidirect
57. C2×(C2×D283)⋊C4C22semidirect
58. C2×(C2×D283)⋊C4C22semidirect
59. C22⋊C4×D283C22semidirect
60. C2×C4×Dic283C22semidirect
62. C23×C4×C283C22semidirect
63. C23×C4×C283C22semidirect
66. C2×C22⋊C4×C283C22semidirect
67. C2×C22⋊C4×C283C22semidirect
68. C2×C22⋊C4×C283C22semidirect
78. C2×Dic566C23semidirect
81. C2×D1132C23semidirect
82. C2×D1132C23semidirect
90. C2×C22⋊D283D4semidirect
96. C2×C22⋊D283C23semidirect
97. C2×C22⋊D283C23semidirect
108. C2×C4×D283C23semidirect
109. C2×C4×D283C23semidirect
110. C2×C4×D283C23semidirect
111. C4⋊Dic283C23semidirect
112. Dic283⋊C4C23semidirect
113. Dic283⋊C4C23semidirect
114. Dic283⋊C4C23semidirect
116. C22⋊Dic283C23semidirect
117. C22⋊Dic283C23semidirect
118. (C2×D283)⋊C4C23semidirect
119. (C2×D283)⋊C4C23semidirect
120. (C2×D283)⋊C4C23semidirect
121. (C2×D283)⋊C4C23semidirect
122. (C2×D283)⋊C4C23semidirect
123. C4×Dic283C23semidirect
137. C22×C4×C283C23semidirect
138. C22×C4×C283C23semidirect
141. C22⋊C4×C283C23semidirect
142. C22⋊C4×C283C23semidirect
168. C22⋊D283C2×D4semidirect
195. C23×C283#41semidirect
224. C22×C283C2×#41semidirect
252. C2×C283#546semidirect
259. C283C2×#546semidirect
276. C22×C22⋊C4D283semidirect
297. C23×C4C2×D283semidirect
298. C23×C4C2×D283semidirect
325. C2×C22⋊C4C2×D283semidirect
326. C2×C22⋊C4C2×D283semidirect
327. C2×C22⋊C4C2×D283semidirect
384. C22×C4C22×D283semidirect
385. C22×C4C22×D283semidirect
400. C22⋊C4C22×D283semidirect
401. C22⋊C4C22×D283semidirect
431. C23#17985392semidirect
497. C22C2×#17985392semidirect
515. C2#31827105direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#179853922
C23×C22⋊D2832
#318271052
C2×#225835962
C2×#225835932
C2×#225835922
C2×#225835872
C2×#225835842
C2×#225835832
C2×#225835802
C2×#225835792
C2×C4×C22⋊D2832
C2×(C22⋊D283)⋊C42
C2×C22⋊C4×D2832
C22×C22⋊C4×C2832
C2×#546283