Finite Group Databasebeta

← C2×#31827203 #49135376

Subgroups — C2×#31827203 #49135376

Order 36224.

1344 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827203C2116yesmaximal, direct product factor
2C2×#22583606C211yesmaximal, characteristic, complemented
3C2×#22583605C211yesmaximal, characteristic, complemented
4C2×#22583603C211yesmaximal, characteristic, complemented
5C2×#22583595C211yesmaximal, characteristic, complemented
6C2×#22583594C211yesmaximal, characteristic, complemented
7C2×#22583593C211yesmaximal, characteristic, complemented
8C2×#22583584C211yesmaximal, characteristic, complemented
9C2×#22583583C211yesmaximal, characteristic, complemented
10C2×#22583582C211yesmaximal, characteristic, complemented
11C2×#22583582C211yesmaximal, characteristic, complemented
12C2×#22583581C211yesmaximal, characteristic, complemented
13C2×#22583580C211yesmaximal, characteristic, complemented
14C2×#22583578C211yesmaximal, characteristic, complemented
15C2×#22583578C211yesmaximal, characteristic, complemented
16C2×#121×C283C211yesmaximal, characteristic, complemented
17C24×D283C2211yescharacteristic
18C22×D1132C2211yescharacteristic
19C22×D1132C2211yescharacteristic
20C22×C22⋊D283C2211yescharacteristic
21C22×C22⋊D283C2211yescharacteristic
22C22×C22⋊D283C2211yescharacteristic
23C22×C22⋊D283C2211yescharacteristic
24C22×C22⋊D283C2211yescharacteristic
25C22×C22⋊D283C2211yescharacteristic, complemented
26C22×C22⋊D283C2211yescharacteristic, complemented
27C23×Dic283C2211yescharacteristic, complemented
28C22×C4×D283C2211yescharacteristic, complemented
29#22583606C2218yescomplemented
30#22583605C2218yescomplemented
31#22583603C2218yescomplemented
32#22583595C2218yescomplemented
33#22583594C2218yescomplemented
34#22583593C2218yescomplemented
35#22583584C2218yescomplemented
36#22583583C2218yescomplemented
37#22583582C2218yescomplemented
38#22583582C2218yescomplemented
39#22583581C2218yescomplemented
40#22583580C2218yescomplemented
41#22583578C2218yescomplemented
42#22583578C2218yescomplemented
43C2×C4⋊Dic283C2211yescharacteristic, complemented
44C2×C4⋊Dic283C2211yescharacteristic, complemented
45C2×Dic283⋊C4C2211yescharacteristic, complemented
46C2×Dic283⋊C4C2211yescharacteristic, complemented
47C2×Dic283⋊C4C2211yescharacteristic, complemented
48C2×C22⋊Dic283C2211yescharacteristic
49C2×C22⋊Dic283C2211yescharacteristic
50C2×C22⋊Dic283C2211yescharacteristic, complemented
51C2×(C2×D283)⋊C4C2211yescharacteristic
52C2×(C2×D283)⋊C4C2211yescharacteristic
53C2×(C2×D283)⋊C4C2211yescharacteristic
54C2×(C2×D283)⋊C4C2211yescharacteristic
55C2×(C2×D283)⋊C4C2211yescharacteristic
56C2×(C2×D283)⋊C4C2211yescharacteristic
57C2×(C2×D283)⋊C4C2211yescharacteristic, complemented
58C2×C4×Dic283C2211yescharacteristic, complemented
59C22×D4×C283C2211yescharacteristic
60C22×D4×C283C2211yescharacteristic
61C22×D4×C283C2211yescharacteristic, complemented
62C23×C4×C283C2211yescharacteristic, complemented
63#121×C283C2218yescomplemented
64C2×C4⋊C4×C283C2211yescharacteristic, complemented
65C2×C22⋊C4×C283C2211yescharacteristic
66C2×C22⋊C4×C283C2211yescharacteristic, complemented
67C23×D283—42no—
68C23×D283—42no—
69C23×D283—42no—
70C23×D283C2311yescharacteristic
71C23×D283C2311yescharacteristic
72C23×D283C2311yescharacteristic
73C23×D283C2314yes—
74C2×D1132—42no—
75C2×D1132—42no—
76C2×D1132C2314yes—
77C2×D1132C2314yes—
78C2×C22⋊D283—42no—
79C2×C22⋊D283—42no—
80C2×C22⋊D283—42no—
81C2×C22⋊D283—42no—
82C2×C22⋊D283—42no—
83C2×C22⋊D283—42no—
84C2×C22⋊D283—42no—
85C2×C22⋊D283C2314yes—
86C2×C22⋊D283C2314yes—
87C2×C22⋊D283C2314yes—
88C2×C22⋊D283C2314yes—
89C2×C22⋊D283C2314yes—
90C2×C22⋊D283C2314yescomplemented
91C2×C22⋊D283C2314yescomplemented
92C22×Dic283—42no—
93C22×Dic283C2311yescharacteristic
94C22×Dic283C2311yescharacteristic
95C22×Dic283C2311yescharacteristic
96C22×Dic283C2311yescharacteristic
97C22×Dic283C2311yescharacteristic
98C22×Dic283C2314yescomplemented
99C2×C4×D283—42no—
100C2×C4×D283C2314yescomplemented
101C4⋊Dic283C2314yescomplemented
102C4⋊Dic283C2314yescomplemented
103Dic283⋊C4C2314yescomplemented
104Dic283⋊C4C2314yescomplemented
105Dic283⋊C4C2314yescomplemented
106C22⋊Dic283C2314yes—
107C22⋊Dic283C2314yes—
108C22⋊Dic283C2314yescomplemented
109(C2×D283)⋊C4C2314yes—
110(C2×D283)⋊C4C2314yes—
111(C2×D283)⋊C4C2314yes—
112(C2×D283)⋊C4C2314yes—
113(C2×D283)⋊C4C2314yes—
114(C2×D283)⋊C4C2314yes—
115(C2×D283)⋊C4C2314yescomplemented
116C4×Dic283C2314yescomplemented
117C24×C283C2311yescharacteristic
118C24×C283C2311yescharacteristic
119C24×C283C2311yescharacteristic
120C2×D4×C283—42no—
121C2×D4×C283—42no—
122C2×D4×C283—42no—
123C2×D4×C283C2314yes—
124C2×D4×C283C2314yes—
125C2×D4×C283C2314yescomplemented
126C22×C4×C283—42no—
127C22×C4×C283C2311yescharacteristic
128C22×C4×C283C2311yescharacteristic
129C22×C4×C283C2311yescharacteristic
130C22×C4×C283C2311yescharacteristic
131C22×C4×C283C2314yescomplemented
132C4⋊C4×C283C2314yescomplemented
133C22⋊C4×C283C2314yes—
134C22⋊C4×C283C2314yescomplemented
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—22no—
144C22×D283—44no—
145C22×D283—44no—
146C22×D283—44no—
147C22×D283—416no—
148C22×D283C2412yes—
149C22×D283C2412yes—
150C22×D283C2412yes—
151D1132—44no—
152D1132—44no—
153C22⋊D283—44no—
154C22⋊D283—44no—
155C22⋊D283—44no—
156C22⋊D283—44no—
157C22⋊D283—44no—
158C22⋊D283—44no—
159C22⋊D283—44no—
160C2×Dic283—22no—
161C2×Dic283—22no—
162C2×Dic283—22no—
163C2×Dic283—22no—
164C2×Dic283—22no—
165C2×Dic283—44no—
166C2×Dic283C2412yes—
167C2×Dic283C2412yes—
168C2×Dic283C2412yes—
169C2×Dic283C2412yes—
170C2×Dic283C2412yes—
171C4×D283—44no—
172C23×C283—22no—
173C23×C283—22no—
174C23×C283—22no—
175C23×C283—22no—
176C23×C283—22no—
177C23×C283—22no—
178C23×C283—22no—
179C23×C283—22no—
180C23×C283—22no—
181C23×C283C2412yes—
182C23×C283C2412yes—
183C23×C283C2412yes—
184C23×C283C2411yescharacteristic
185D4×C283—44no—
186D4×C283—44no—
187D4×C283—44no—
188C2×C4×C283—22no—
189C2×C4×C283—22no—
190C2×C4×C283—22no—
191C2×C4×C283—22no—
192C2×C4×C283—44no—
193C2×C4×C283C2412yes—
194C2×C4×C283C2412yes—
195C2×C4×C283C2412yes—
196C2×C4×C283C2412yes—
197C22×C283—22no—
198C22×C283—22no—
199C22×C283—22no—
200C22×C283—22no—
201C22×C283—22no—
202C22×C283—22no—
203C22×C283—22no—
204C22×C283—22no—
205C22×C283—22no—
206C22×C283—44no—
207C22×C283—44no—
208C22×C283—44no—
209C22×C283H(5,𝔽2)12yes—
210C22×C283H(5,𝔽2)12yes—
211C22×C283H(5,𝔽2)12yes—
212C22×C283C2511yescharacteristic
213C2×D283—22no—
214C2×D283—22no—
215C2×D283—22no—
216C2×D283—22no—
217C2×D283—22no—
218C2×D283—22no—
219C2×D283—22no—
220C2×D283—22no—
221C2×D283—22no—
222C2×D283—416no—
223C2×D283—44no—
224C2×D283—44no—
225C2×D283—44no—
226C4×C283—22no—
227C4×C283—22no—
228C4×C283—22no—
229C4×C283—22no—
230Dic283—22no—
231Dic283—22no—
232Dic283—22no—
233Dic283—22no—
234Dic283—22no—
235C2×C283—42no—
236C2×C283—42no—
237C2×C283—42no—
238C2×C283#56014yescomplemented
239C2×C283C2×H(5,𝔽2)11yescharacteristic
240C2×C283C2×H(5,𝔽2)11yescharacteristic
241C2×C283C2×H(5,𝔽2)11yescharacteristic
242D283—42no—
243D283—42no—
244D283—42no—
245C283C2×#56011yescharacteristic, complemented, Sylow
246C2×#560—2831nomaximal, Sylow
247#560—28316no—
248C2×#127—2831no—
249C2×#126—2831no—
250C2×#126—2831no—
251C2×#123—2831no—
252C2×#123—2831no—
253C2×#123—2831no—
254C2×#121—2831no—
255C2×#121—2831no—
256C2×#121—2831no—
257C2×#121—2831no—
258C2×#121—2831no—
259C2×#121D28311yescharacteristic, complemented
260C2×#120—2831no—
261C2×#120—2831no—
262C2×#120—2831no—
263C25—2831no—
264C22×D4—2831no—
265C22×D4—2831no—
266C22×D4—2831no—
267C22×D4—2831no—
268C22×D4—2831no—
269C22×D4—2831no—
270C22×D4—2831no—
271C22×D4—2831no—
272C22×D4—2831no—
273C22×D4C2×D28311yescharacteristic
274C22×D4C2×D28311yescharacteristic
275C22×D4C2×D28311yescharacteristic, complemented
276C23×C4—2831no—
277C23×C4—2831no—
278C23×C4C2×D28311yescharacteristic, complemented
279#127—2838no—
280#126—2838no—
281#126—2838no—
282#123—2838no—
283#123—2838no—
284#123—2838no—
285#121—2838no—
286#121—2838no—
287#121—2838no—
288#121—2838no—
289#121—2838no—
290#121C2×D28318yescomplemented
291#120—2838no—
292#120—2838no—
293#120—2838no—
294C2×C4⋊C4—2831no—
295C2×C4⋊C4—2831no—
296C2×C4⋊C4—2831no—
297C2×C4⋊C4—2831no—
298C2×C4⋊C4—2831no—
299C2×C4⋊C4C2×D28311yescharacteristic, complemented
300C2×C22⋊C4—2831no—
301C2×C22⋊C4—2831no—
302C2×C22⋊C4—2831no—
303C2×C22⋊C4—2831no—
304C2×C22⋊C4—2831no—
305C2×C22⋊C4—2831no—
306C2×C22⋊C4—2831no—
307C2×C22⋊C4—2831no—
308C2×C22⋊C4—2831no—
309C2×C22⋊C4—2831no—
310C2×C22⋊C4C2×D28311yescharacteristic
311C2×C22⋊C4C2×D28311yescharacteristic, complemented
312C2×C42—2831no—
313C24—2831no—
314C24—2831no—
315C24—2831no—
316C24—2834no—
317C24—11322no—
318C24—11322no—
319C24—11322no—
320C24C22×D28311yescharacteristic
321C24C22×D28311yescharacteristic
322C24C22×D28311yescharacteristic
323C2×D4—42no—
324C2×D4—42no—
325C2×D4—42no—
326C2×D4—2834no—
327C2×D4—2834no—
328C2×D4—2834no—
329C2×D4—2834no—
330C2×D4—2834no—
331C2×D4—2834no—
332C2×D4—2834no—
333C2×D4—2834no—
334C2×D4—2834no—
335C2×D4—11322no—
336C2×D4—11322no—
337C2×D4—11322no—
338C2×D4—11322no—
339C2×D4—11322no—
340C2×D4—11322no—
341C2×D4—11322no—
342C2×D4—11322no—
343C2×D4—11322no—
344C2×D4C22×D28314yes—
345C2×D4C22×D28314yes—
346C2×D4C22×D28314yescomplemented
347C22×C4—42no—
348C22×C4—2831no—
349C22×C4—2831no—
350C22×C4—2831no—
351C22×C4—2831no—
352C22×C4—2831no—
353C22×C4—2834no—
354C22×C4—2834no—
355C22×C4—11322no—
356C22×C4—11322no—
357C22×C4C22×D28311yescharacteristic
358C22×C4C22×D28311yescharacteristic
359C22×C4C22×D28311yescharacteristic
360C22×C4C22×D28311yescharacteristic
361C22×C4C22×D28314yescomplemented
362C4⋊C4—2834no—
363C4⋊C4—2834no—
364C4⋊C4—2834no—
365C4⋊C4—2834no—
366C4⋊C4—2834no—
367C4⋊C4C22×D28314yescomplemented
368C22⋊C4—2834no—
369C22⋊C4—2834no—
370C22⋊C4—2834no—
371C22⋊C4—2834no—
372C22⋊C4—2834no—
373C22⋊C4—2834no—
374C22⋊C4—2834no—
375C22⋊C4—2834no—
376C22⋊C4—2834no—
377C22⋊C4—2834no—
378C22⋊C4C22×D28314yes—
379C22⋊C4C22×D28314yescomplemented
380C42—2834no—
381C23—22no—
382C23—22no—
383C23—22no—
384C23—22no—
385C23—22no—
386C23—22no—
387C23—22no—
388C23—22no—
389C23—22no—
390C23—2832no—
391C23—2832no—
392C23—2832no—
393C23—5662no—
394C23—5662no—
395C23—5662no—
396C23—5662no—
397C23—5662no—
398C23—5662no—
399C23—5662no—
400C23—5662no—
401C23—5662no—
402C23—11324no—
403C23—11324no—
404C23—11324no—
405C23—113216no—
406C23C23×D28312yes—
407C23C23×D28312yes—
408C23C23×D28312yes—
409C23C23×D28311yescharacteristic
410D4—44no—
411D4—44no—
412D4—44no—
413D4—11324no—
414D4—11324no—
415D4—11324no—
416D4—11324no—
417D4—11324no—
418D4—11324no—
419D4—11324no—
420D4—11324no—
421D4—11324no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—44no—
427C2×C4—2832no—
428C2×C4—2832no—
429C2×C4—2832no—
430C2×C4—2832no—
431C2×C4—2832no—
432C2×C4—5662no—
433C2×C4—5662no—
434C2×C4—5662no—
435C2×C4—5662no—
436C2×C4—5662no—
437C2×C4—11324no—
438C2×C4—11324no—
439C2×C4C23×D28312yes—
440C2×C4C23×D28312yes—
441C2×C4C23×D28312yes—
442C2×C4C23×D28312yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—44no—
453C22—44no—
454C22—44no—
455C22—5662no—
456C22—5662no—
457C22—5662no—
458C22—5662no—
459C22—5662no—
460C22—5662no—
461C22—5662no—
462C22—5662no—
463C22—5662no—
464C22—113216no—
465C22—11324no—
466C22—11324no—
467C22—11324no—
468C22#2258365512yes—
469C22#2258365512yes—
470C22#2258365612yes—
471C22C24×D28311yescharacteristic
472C4—22no—
473C4—22no—
474C4—22no—
475C4—22no—
476C4—5662no—
477C4—5662no—
478C4—5662no—
479C4—5662no—
480C4—5662no—
481C2—42no—
482C2—42no—
483C2—42no—
484C2—11322no—
485C2—11322no—
486C2—11322no—
487C2#3182720314yesdirect product factor
488C2C2×#2258365511yescharacteristic
489C2C2×#2258365511yescharacteristic
490C2C2×#2258365611yescharacteristic
subgroupG/H
centerC23C23×D283
commutator, cosocleC22×C283C25
FrattiniC22C24×D283
FittingC2×#121×C283C2
socleC23×C283C24
hypercenterC2×#121D283
hypocenterC283C2×#560
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. #31827203C2direct (N × H)
2. C2×#22583606C2semidirect
3. C2×#22583605C2semidirect
4. C2×#22583603C2semidirect
5. C2×#22583595C2semidirect
6. C2×#22583594C2semidirect
7. C2×#22583593C2semidirect
8. C2×#22583584C2semidirect
9. C2×#22583583C2semidirect
10. C2×#22583582C2semidirect
11. C2×#22583582C2semidirect
12. C2×#22583581C2semidirect
13. C2×#22583580C2semidirect
14. C2×#22583578C2semidirect
15. C2×#22583578C2semidirect
16. C2×#121×C283C2semidirect
25. C22×C22⋊D283C22semidirect
26. C22×C22⋊D283C22semidirect
27. C23×Dic283C22semidirect
28. C22×C4×D283C22semidirect
29. #22583606C22semidirect
30. #22583605C22semidirect
31. #22583603C22semidirect
32. #22583595C22semidirect
33. #22583594C22semidirect
34. #22583593C22semidirect
35. #22583584C22semidirect
36. #22583583C22semidirect
37. #22583582C22semidirect
38. #22583582C22semidirect
39. #22583581C22semidirect
40. #22583580C22semidirect
41. #22583578C22semidirect
42. #22583578C22semidirect
43. C2×C4⋊Dic283C22semidirect
44. C2×C4⋊Dic283C22semidirect
45. C2×Dic283⋊C4C22semidirect
46. C2×Dic283⋊C4C22semidirect
47. C2×Dic283⋊C4C22semidirect
50. C2×C22⋊Dic283C22semidirect
57. C2×(C2×D283)⋊C4C22semidirect
58. C2×C4×Dic283C22semidirect
61. C22×D4×C283C22semidirect
62. C23×C4×C283C22semidirect
63. #121×C283C22semidirect
64. C2×C4⋊C4×C283C22semidirect
66. C2×C22⋊C4×C283C22semidirect
90. C2×C22⋊D283C23semidirect
91. C2×C22⋊D283C23semidirect
98. C22×Dic283C23semidirect
100. C2×C4×D283C23semidirect
101. C4⋊Dic283C23semidirect
102. C4⋊Dic283C23semidirect
103. Dic283⋊C4C23semidirect
104. Dic283⋊C4C23semidirect
105. Dic283⋊C4C23semidirect
108. C22⋊Dic283C23semidirect
115. (C2×D283)⋊C4C23semidirect
116. C4×Dic283C23semidirect
125. C2×D4×C283C23semidirect
131. C22×C4×C283C23semidirect
132. C4⋊C4×C283C23semidirect
134. C22⋊C4×C283C23semidirect
238. C2×C283#560semidirect
245. C283C2×#560semidirect
259. C2×#121D283semidirect
275. C22×D4C2×D283semidirect
278. C23×C4C2×D283semidirect
290. #121C2×D283semidirect
299. C2×C4⋊C4C2×D283semidirect
311. C2×C22⋊C4C2×D283semidirect
346. C2×D4C22×D283semidirect
361. C22×C4C22×D283semidirect
367. C4⋊C4C22×D283semidirect
379. C22⋊C4C22×D283semidirect
487. C2#31827203direct (N × H)

Maximal subgroups

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

subgroupindex
#318272032
C2×#225836062
C2×#225836052
C2×#225836032
C2×#225835952
C2×#225835942
C2×#225835932
C2×#225835842
C2×#225835832
C2×#225835822
C2×#225835812
C2×#225835802
C2×#225835782
C2×#121×C2832
C2×#560283