Finite Group Databasebeta

← C2×#31827054 #49134603

Subgroups — C2×#31827054 #49134603

Order 36224.

1336 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
1#31827054C2116yesmaximal, direct product factor
2C2×#22583605C211yesmaximal, characteristic, complemented
3C2×#22583598C211yesmaximal, characteristic, complemented
4C2×#22583596C211yesmaximal, characteristic, complemented
5C2×#22583595C211yesmaximal, characteristic, complemented
6C2×#22583592C211yesmaximal, characteristic, complemented
7C2×#22583588C211yesmaximal, characteristic, complemented
8C2×#22583585C211yesmaximal, characteristic, complemented
9C2×#22583585C211yesmaximal, characteristic, complemented
10C2×#22583583C211yesmaximal, characteristic, complemented
11C2×#22583580C211yesmaximal, characteristic, complemented
12C2×#22583580C211yesmaximal, characteristic, complemented
13C2×C4×D1132C211yesmaximal, characteristic, complemented
14C2×#22583572C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×D283C211yesmaximal, characteristic, complemented
16C2×#126×C283C211yesmaximal, characteristic, complemented
17C24×D283C2211yescharacteristic
18C22×Dic566C2211yescharacteristic, complemented
19C22×D1132C2211yescharacteristic
20C22×D1132C2211yescharacteristic
21C22×D1132C2211yescharacteristic
22C22×D1132C2211yescharacteristic
23C22×D1132C2211yescharacteristic, complemented
24C22×C22⋊D283C2211yescharacteristic
25C22×C22⋊D283C2211yescharacteristic
26C22×C4×D283C2211yescharacteristic
27C22×C4×D283C2211yescharacteristic
28C22×C4×D283C2211yescharacteristic, complemented
29C22×C4×D283C2211yescharacteristic, complemented
30#22583605C2218yescomplemented
31#22583598C2218yescomplemented
32#22583596C2218yescomplemented
33#22583595C2218yescomplemented
34#22583592C2218yescomplemented
35#22583588C2218yescomplemented
36#22583585C2218yescomplemented
37#22583585C2218yescomplemented
38#22583583C2218yescomplemented
39#22583580C2218yescomplemented
40#22583580C2218yescomplemented
41C4×D1132C2218yescomplemented
42#22583572C2218yescomplemented
43C2×C4⋊Dic283C2211yescharacteristic, complemented
44C2×Dic283⋊C4C2211yescharacteristic, complemented
45C2×Dic283⋊C4C2211yescharacteristic, complemented
46C2×C22⋊Dic283C2211yescharacteristic
47C2×(C2×D283)⋊C4C2211yescharacteristic
48C2×(C2×D283)⋊C4C2211yescharacteristic
49C2×(C2×D283)⋊C4C2211yescharacteristic
50C2×(C2×D283)⋊C4C2211yescharacteristic
51C2×(C2×D283)⋊C4C2211yescharacteristic
52C2×(C2×D283)⋊C4C2211yescharacteristic
53C2×(C2×D283)⋊C4C2211yescharacteristic, complemented
54C2×(C2×D283)⋊C4C2211yescharacteristic, complemented
55C2×(C2×D283)⋊C4C2211yescharacteristic, complemented
56C2×(C2×D283)⋊C4C2211yescharacteristic, complemented
57C22⋊C4×D283C2218yescomplemented
58C2×C4×Dic283C2211yescharacteristic, complemented
59#126×C283C2218yescomplemented
60C2×C4⋊C4×C283C2211yescharacteristic, complemented
61C2×C4⋊C4×C283C2211yescharacteristic, complemented
62C2×C4⋊C4×C283C2211yescharacteristic, complemented
63C2×C22⋊C4×C283C2211yescharacteristic
64C2×C22⋊C4×C283C2211yescharacteristic
65C2×C22⋊C4×C283C2211yescharacteristic
66C2×C42×C283C2211yescharacteristic, complemented
67C23×D283—24no—
68C23×D283—42no—
69C23×D283—42no—
70C23×D283C2311yescharacteristic
71C23×D283C2311yescharacteristic
72C23×D283C2311yescharacteristic
73C23×D283C2311yescharacteristic
74C23×D283C2314yes—
75C2×Dic566—42no—
76C2×Dic566C2314yescomplemented
77C2×D1132—24no—
78C2×D1132—24no—
79C2×D1132—42no—
80C2×D1132—42no—
81C2×D1132—42no—
82C2×D1132C2314yes—
83C2×D1132C2314yes—
84C2×D1132C2314yes—
85C2×D1132C2314yes—
86C2×D1132C2314yescomplemented
87C2×C22⋊D283—42no—
88C2×C22⋊D283—42no—
89C2×C22⋊D283C2314yes—
90C2×C22⋊D283C2314yes—
91C22×Dic283C2311yescharacteristic
92C22×Dic283C2311yescharacteristic
93C22×Dic283C2311yescharacteristic
94C22×Dic283C2311yescharacteristic
95C2×C4×D283—42no—
96C2×C4×D283—42no—
97C2×C4×D283—42no—
98C2×C4×D283—42no—
99C2×C4×D283C2314yes—
100C2×C4×D283C2314yes—
101C2×C4×D283C2314yescomplemented
102C2×C4×D283C2314yescomplemented
103C4⋊Dic283C2314yescomplemented
104Dic283⋊C4C2314yescomplemented
105Dic283⋊C4C2314yescomplemented
106C22⋊Dic283C2314yes—
107(C2×D283)⋊C4C2314yes—
108(C2×D283)⋊C4C2314yes—
109(C2×D283)⋊C4C2314yes—
110(C2×D283)⋊C4C2314yes—
111(C2×D283)⋊C4C2314yes—
112(C2×D283)⋊C4C2314yes—
113(C2×D283)⋊C4C2314yescomplemented
114(C2×D283)⋊C4C2314yescomplemented
115(C2×D283)⋊C4C2314yescomplemented
116(C2×D283)⋊C4C2314yescomplemented
117C4×Dic283C2314yescomplemented
118C24×C283C2311yescharacteristic
119C22×C4×C283C2311yescharacteristic
120C22×C4×C283C2311yescharacteristic
121C22×C4×C283C2311yescharacteristic
122C22×C4×C283C2311yescharacteristic
123C22×C4×C283C2311yescharacteristic
124C22×C4×C283C2311yescharacteristic
125C4⋊C4×C283C2314yescomplemented
126C4⋊C4×C283C2314yescomplemented
127C4⋊C4×C283C2314yescomplemented
128C22⋊C4×C283C2314yes—
129C22⋊C4×C283C2314yes—
130C22⋊C4×C283C2314yes—
131C42×C283C2314yescomplemented
132C22×D283—22no—
133C22×D283—22no—
134C22×D283—22no—
135C22×D283—22no—
136C22×D283—22no—
137C22×D283—22no—
138C22×D283—22no—
139C22×D283—22no—
140C22×D283—22no—
141C22×D283—22no—
142C22×D283—22no—
143C22×D283—28no—
144C22×D283—44no—
145C22×D283—44no—
146C22×D283—416no—
147C22×D283#4114yes—
148C22×D283C2412yes—
149C22×D283C2412yes—
150C22×D283C2412yes—
151C22×D283C2412yes—
152Dic566—44no—
153D1132—28no—
154D1132—28no—
155D1132—44no—
156D1132—44no—
157D1132—44no—
158C22⋊D283—44no—
159C22⋊D283—44no—
160C2×Dic283—22no—
161C2×Dic283—22no—
162C2×Dic283—22no—
163C2×Dic283—22no—
164C2×Dic283C2412yes—
165C2×Dic283C2412yes—
166C2×Dic283C2412yes—
167C2×Dic283C2412yes—
168C4×D283—44no—
169C4×D283—44no—
170C4×D283—44no—
171C4×D283—44no—
172C23×C283—22no—
173C23×C283—22no—
174C23×C283—22no—
175C23×C283C2412yes—
176C23×C283C2411yescharacteristic
177C2×C4×C283—22no—
178C2×C4×C283—22no—
179C2×C4×C283—22no—
180C2×C4×C283—22no—
181C2×C4×C283—22no—
182C2×C4×C283—22no—
183C2×C4×C283C2412yes—
184C2×C4×C283C2412yes—
185C2×C4×C283C2412yes—
186C2×C4×C283C2412yes—
187C2×C4×C283C2412yes—
188C2×C4×C283C2412yes—
189C22×C283—22no—
190C22×C283—22no—
191C22×C283—22no—
192C22×C283—44no—
193C22×C283C2×#4112yes—
194C22×C283H(5,𝔽2)12yes—
195C22×C283H(5,𝔽2)12yes—
196C22×C283C2511yescharacteristic
197C2×D283—28no—
198C2×D283—22no—
199C2×D283—22no—
200C2×D283—22no—
201C2×D283—22no—
202C2×D283—22no—
203C2×D283—22no—
204C2×D283—22no—
205C2×D283—22no—
206C2×D283—22no—
207C2×D283—22no—
208C2×D283—22no—
209C2×D283—416no—
210C2×D283—44no—
211C2×D283—44no—
212C2×D283—44no—
213C2×D283C2×#4114yes—
214C4×C283—22no—
215C4×C283—22no—
216C4×C283—22no—
217C4×C283—22no—
218C4×C283—22no—
219C4×C283—22no—
220Dic283—22no—
221Dic283—22no—
222Dic283—22no—
223Dic283—22no—
224C2×C283—42no—
225C2×C283#53814yescomplemented
226C2×C283C22×#4111yescharacteristic
227C2×C283C2×H(5,𝔽2)11yescharacteristic
228C2×C283C2×H(5,𝔽2)11yescharacteristic
229D283—24no—
230D283—42no—
231D283—42no—
232D283—42no—
233C283C2×#53811yescharacteristic, complemented, Sylow
234C2×#538—2831nomaximal, Sylow
235#538—28316no—
236C2×#126—2831no—
237C2×#126D28311yescharacteristic, complemented
238C2×#124—2831no—
239C2×#124—2831no—
240C2×#123—2831no—
241C2×#123—2831no—
242C2×C22⋊Q8—2831no—
243C2×#121—2831no—
244C2×#121—2831no—
245C2×#121—2831no—
246C2×#120—2831no—
247C2×#120—2831no—
248C2×C4×D4—2831no—
249C2×C4×D4—2831no—
250C22×C22⋊C4—2831no—
251C25—2831no—
252C22×Q8—2831no—
253C22×D4—2831no—
254C22×D4—2831no—
255C22×D4—2831no—
256C22×D4—2831no—
257C22×D4—2831no—
258C22×D4—2831no—
259C22×D4—2831no—
260C23×C4—2831no—
261C23×C4—2831no—
262C23×C4—2831no—
263C23×C4—2831no—
264#126—2838no—
265#126C2×D28318yescomplemented
266#124—2838no—
267#124—2838no—
268#123—2838no—
269#123—2838no—
270C22⋊Q8—2838no—
271#121—2838no—
272#121—2838no—
273#121—2838no—
274#120—2838no—
275#120—2838no—
276C4×D4—2838no—
277C4×D4—2838no—
278C2×C4⋊C4—2831no—
279C2×C4⋊C4—2831no—
280C2×C4⋊C4—2831no—
281C2×C4⋊C4C2×D28311yescharacteristic, complemented
282C2×C4⋊C4C2×D28311yescharacteristic, complemented
283C2×C4⋊C4C2×D28311yescharacteristic, complemented
284C2×C22⋊C4—2831no—
285C2×C22⋊C4—2831no—
286C2×C22⋊C4—2831no—
287C2×C22⋊C4—2831no—
288C2×C22⋊C4—2831no—
289C2×C22⋊C4—2831no—
290C2×C22⋊C4—2831no—
291C2×C22⋊C4—2831no—
292C2×C22⋊C4—2831no—
293C2×C22⋊C4—2831no—
294C2×C22⋊C4—2831no—
295C2×C22⋊C4—2838no—
296C2×C22⋊C4C2×D28311yescharacteristic
297C2×C22⋊C4C2×D28311yescharacteristic
298C2×C22⋊C4C2×D28311yescharacteristic
299C2×C42—2831no—
300C2×C42C2×D28311yescharacteristic, complemented
301C24—2831no—
302C24—2831no—
303C24—2831no—
304C24—2831no—
305C24—2834no—
306C24—5664no—
307C24—11322no—
308C24—11322no—
309C24C22×D28311yescharacteristic
310C2×Q8—2834no—
311C2×Q8—11322no—
312C2×D4—2834no—
313C2×D4—2834no—
314C2×D4—2834no—
315C2×D4—2834no—
316C2×D4—2834no—
317C2×D4—2834no—
318C2×D4—2834no—
319C2×D4—5664no—
320C2×D4—5664no—
321C2×D4—11322no—
322C2×D4—11322no—
323C2×D4—11322no—
324C2×D4—11322no—
325C2×D4—11322no—
326C22×C4—2831no—
327C22×C4—2831no—
328C22×C4—2831no—
329C22×C4—2831no—
330C22×C4—2834no—
331C22×C4—2834no—
332C22×C4—2834no—
333C22×C4—2834no—
334C22×C4—11322no—
335C22×C4—11322no—
336C22×C4—11322no—
337C22×C4—11322no—
338C22×C4C22×D28311yescharacteristic
339C22×C4C22×D28311yescharacteristic
340C22×C4C22×D28311yescharacteristic
341C22×C4C22×D28311yescharacteristic
342C22×C4C22×D28311yescharacteristic
343C22×C4C22×D28311yescharacteristic
344C4⋊C4—2834no—
345C4⋊C4—2834no—
346C4⋊C4—2834no—
347C4⋊C4C22×D28314yescomplemented
348C4⋊C4C22×D28314yescomplemented
349C4⋊C4C22×D28314yescomplemented
350C22⋊C4—2834no—
351C22⋊C4—2834no—
352C22⋊C4—2834no—
353C22⋊C4—2834no—
354C22⋊C4—2834no—
355C22⋊C4—2834no—
356C22⋊C4—2834no—
357C22⋊C4—2834no—
358C22⋊C4—2834no—
359C22⋊C4—2834no—
360C22⋊C4—2834no—
361C22⋊C4C22×D28314yes—
362C22⋊C4C22×D28314yes—
363C22⋊C4C22×D28314yes—
364C42—2834no—
365C42C22×D28314yescomplemented
366C23—22no—
367C23—22no—
368C23—22no—
369C23—2834no—
370C23—2832no—
371C23—2832no—
372C23—2832no—
373C23—2832no—
374C23—5668no—
375C23—5662no—
376C23—5662no—
377C23—5662no—
378C23—5662no—
379C23—5662no—
380C23—5662no—
381C23—5662no—
382C23—5662no—
383C23—5662no—
384C23—5662no—
385C23—5662no—
386C23—11324no—
387C23—11324no—
388C23—113216no—
389C23C23×D28312yes—
390C23C23×D28311yescharacteristic
391Q8—11324no—
392D4—5668no—
393D4—5668no—
394D4—11324no—
395D4—11324no—
396D4—11324no—
397D4—11324no—
398D4—11324no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—2832no—
406C2×C4—2832no—
407C2×C4—2832no—
408C2×C4—2832no—
409C2×C4—5662no—
410C2×C4—5662no—
411C2×C4—5662no—
412C2×C4—5662no—
413C2×C4—11324no—
414C2×C4—11324no—
415C2×C4—11324no—
416C2×C4—11324no—
417C2×C4C23×D28312yes—
418C2×C4C23×D28312yes—
419C2×C4C23×D28312yes—
420C2×C4C23×D28312yes—
421C2×C4C23×D28312yes—
422C2×C4C23×D28312yes—
423C22—22no—
424C22—22no—
425C22—22no—
426C22—44no—
427C22—2834no—
428C22—5662no—
429C22—5662no—
430C22—5668no—
431C22—5662no—
432C22—5662no—
433C22—5662no—
434C22—5662no—
435C22—5662no—
436C22—5662no—
437C22—5662no—
438C22—5662no—
439C22—5662no—
440C22—113216no—
441C22—11324no—
442C22—11324no—
443C22—11324no—
444C22#41×D28312yes—
445C22#2258365612yes—
446C22#2258365612yes—
447C22C24×D28311yescharacteristic
448C4—22no—
449C4—22no—
450C4—22no—
451C4—22no—
452C4—22no—
453C4—22no—
454C4—5662no—
455C4—5662no—
456C4—5662no—
457C4—5662no—
458C2—42no—
459C2—5664no—
460C2—11322no—
461C2—11322no—
462C2—11322no—
463C2#3182705414yesdirect product factor
464C2C2×#41×D28311yescharacteristic
465C2C2×#2258365611yescharacteristic
466C2C2×#2258365611yescharacteristic
subgroupG/H
centerC23C23×D283
commutator, cosocleC22×C283C25
FrattiniC22C24×D283
FittingC2×#126×C283C2
socleC23×C283C24
hypercenterC2×#126D283
hypocenterC283C2×#538
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #31827054C2direct (N × H)
2. C2×#22583605C2semidirect
3. C2×#22583598C2semidirect
4. C2×#22583596C2semidirect
5. C2×#22583595C2semidirect
6. C2×#22583592C2semidirect
7. C2×#22583588C2semidirect
8. C2×#22583585C2semidirect
9. C2×#22583585C2semidirect
10. C2×#22583583C2semidirect
11. C2×#22583580C2semidirect
12. C2×#22583580C2semidirect
13. C2×C4×D1132C2semidirect
14. C2×#22583572C2semidirect
15. C2×C22⋊C4×D283C2semidirect
16. C2×#126×C283C2semidirect
18. C22×Dic566C22semidirect
23. C22×D1132C22semidirect
28. C22×C4×D283C22semidirect
29. C22×C4×D283C22semidirect
30. #22583605C22semidirect
31. #22583598C22semidirect
32. #22583596C22semidirect
33. #22583595C22semidirect
34. #22583592C22semidirect
35. #22583588C22semidirect
36. #22583585C22semidirect
37. #22583585C22semidirect
38. #22583583C22semidirect
39. #22583580C22semidirect
40. #22583580C22semidirect
41. C4×D1132C22semidirect
42. #22583572C22semidirect
43. C2×C4⋊Dic283C22semidirect
44. C2×Dic283⋊C4C22semidirect
45. C2×Dic283⋊C4C22semidirect
53. C2×(C2×D283)⋊C4C22semidirect
54. C2×(C2×D283)⋊C4C22semidirect
55. C2×(C2×D283)⋊C4C22semidirect
56. C2×(C2×D283)⋊C4C22semidirect
57. C22⋊C4×D283C22semidirect
58. C2×C4×Dic283C22semidirect
59. #126×C283C22semidirect
60. C2×C4⋊C4×C283C22semidirect
61. C2×C4⋊C4×C283C22semidirect
62. C2×C4⋊C4×C283C22semidirect
66. C2×C42×C283C22semidirect
76. C2×Dic566C23semidirect
86. C2×D1132C23semidirect
101. C2×C4×D283C23semidirect
102. C2×C4×D283C23semidirect
103. C4⋊Dic283C23semidirect
104. Dic283⋊C4C23semidirect
105. Dic283⋊C4C23semidirect
113. (C2×D283)⋊C4C23semidirect
114. (C2×D283)⋊C4C23semidirect
115. (C2×D283)⋊C4C23semidirect
116. (C2×D283)⋊C4C23semidirect
117. C4×Dic283C23semidirect
125. C4⋊C4×C283C23semidirect
126. C4⋊C4×C283C23semidirect
127. C4⋊C4×C283C23semidirect
131. C42×C283C23semidirect
225. C2×C283#538semidirect
233. C283C2×#538semidirect
237. C2×#126D283semidirect
265. #126C2×D283semidirect
281. C2×C4⋊C4C2×D283semidirect
282. C2×C4⋊C4C2×D283semidirect
283. C2×C4⋊C4C2×D283semidirect
300. C2×C42C2×D283semidirect
347. C4⋊C4C22×D283semidirect
348. C4⋊C4C22×D283semidirect
349. C4⋊C4C22×D283semidirect
365. C42C22×D283semidirect
463. C2#31827054direct (N × H)

Maximal subgroups

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

subgroupindex
#318270542
C2×#225836052
C2×#225835982
C2×#225835962
C2×#225835952
C2×#225835922
C2×#225835882
C2×#225835852
C2×#225835832
C2×#225835802
C2×C4×D11322
C2×#225835722
C2×C22⋊C4×D2832
C2×#126×C2832
C2×#538283