Finite Group Databasebeta

← C2×#31827140 #49134757

Subgroups — C2×#31827140 #49134757

Order 36224.

1328 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827140C2116yesmaximal, direct product factor
2C2×#22583603C211yesmaximal, characteristic, complemented
3C2×#22583596C211yesmaximal, characteristic, complemented
4C2×#22583595C211yesmaximal, characteristic, complemented
5C2×#22583595C211yesmaximal, characteristic, complemented
6C2×#22583592C211yesmaximal, characteristic, complemented
7C2×#22583590C211yesmaximal, characteristic, complemented
8C2×#22583588C211yesmaximal, characteristic, complemented
9C2×#22583580C211yesmaximal, characteristic
10C2×C4×D1132C211yesmaximal, characteristic, complemented
11C2×#22583572C211yesmaximal, characteristic, complemented
12C2×#22583568C211yesmaximal, characteristic, complemented
13C2×#22583567C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×D283C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×D283C211yesmaximal, characteristic, complemented
16C2×#126×C283C211yesmaximal, characteristic, complemented
17C24×D283C2211yescharacteristic
18C22×Dic566C2211yescharacteristic, complemented
19C22×D1132C2211yescharacteristic
20C22×D1132C2211yescharacteristic
21C22×C22⋊D283C2211yescharacteristic
22C22×C4×D283C2211yescharacteristic
23C22×C4×D283C2211yescharacteristic
24C22×C4×D283C2211yescharacteristic
25C22×C4×D283C2211yescharacteristic
26C22×C4×D283C2211yescharacteristic, complemented
27#22583603C2218yescomplemented
28#22583596C2218yescomplemented
29#22583595C2218yescomplemented
30#22583595C2218yescomplemented
31#22583592C2218yescomplemented
32#22583590C2218yescomplemented
33#22583588C2218yescomplemented
34#22583580C2218yes—
35C4×D1132C2218yescomplemented
36#22583572C2218yescomplemented
37#22583568C2218yescomplemented
38#22583567C2218yescomplemented
39C2×C4⋊Dic283C2211yescharacteristic, complemented
40C2×C4⋊Dic283C2211yescharacteristic, complemented
41C2×Dic283⋊C4C2211yescharacteristic, complemented
42C2×Dic283⋊C4C2211yescharacteristic, complemented
43C2×Dic283⋊C4C2211yescharacteristic, complemented
44C2×C22⋊Dic283C2211yescharacteristic
45C2×C22⋊Dic283C2211yescharacteristic
46C2×(C2×D283)⋊C4C2211yescharacteristic
47C2×(C2×D283)⋊C4C2211yescharacteristic
48C2×(C2×D283)⋊C4C2211yescharacteristic
49C2×(C2×D283)⋊C4C2211yescharacteristic
50C2×(C2×D283)⋊C4C2211yescharacteristic
51C2×(C2×D283)⋊C4C2211yescharacteristic
52C2×(C2×D283)⋊C4C2211yescharacteristic, complemented
53C2×(C2×D283)⋊C4C2211yescharacteristic, complemented
54C2×(C2×D283)⋊C4C2211yescharacteristic, complemented
55C22⋊C4×D283C2218yescomplemented
56C22⋊C4×D283C2218yescomplemented
57C2×C4×Dic283C2211yescharacteristic, complemented
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—24no—
69C23×D283—42no—
70C23×D283C2311yescharacteristic
71C23×D283C2314yes—
72C23×D283C2311yescharacteristic
73C23×D283C2311yescharacteristic
74C2×Dic566—42no—
75C2×Dic566C2314yescomplemented
76C2×D1132—24no—
77C2×D1132—24no—
78C2×D1132C2314yes—
79C2×D1132C2314yes—
80C2×C22⋊D283—42no—
81C2×C22⋊D283C2314yes—
82C22×Dic283C2311yescharacteristic
83C22×Dic283C2311yescharacteristic
84C22×Dic283C2311yescharacteristic
85C22×Dic283C2311yescharacteristic
86C22×Dic283C2311yescharacteristic
87C2×C4×D283—24no—
88C2×C4×D283—24no—
89C2×C4×D283—42no—
90C2×C4×D283—42no—
91C2×C4×D283—42no—
92C2×C4×D283C2314yes—
93C2×C4×D283C2314yes—
94C2×C4×D283C2314yes—
95C2×C4×D283C2314yes—
96C2×C4×D283C2314yescomplemented
97C4⋊Dic283C2314yescomplemented
98C4⋊Dic283C2314yescomplemented
99Dic283⋊C4C2314yescomplemented
100Dic283⋊C4C2314yescomplemented
101Dic283⋊C4C2314yescomplemented
102C22⋊Dic283C2314yes—
103C22⋊Dic283C2314yes—
104(C2×D283)⋊C4C2314yes—
105(C2×D283)⋊C4C2314yes—
106(C2×D283)⋊C4C2314yes—
107(C2×D283)⋊C4C2314yes—
108(C2×D283)⋊C4C2314yes—
109(C2×D283)⋊C4C2314yes—
110(C2×D283)⋊C4C2314yescomplemented
111(C2×D283)⋊C4C2314yescomplemented
112(C2×D283)⋊C4C2314yescomplemented
113C4×Dic283C2314yescomplemented
114C4×Dic283C2314yescomplemented
115C24×C283C2311yescharacteristic
116C22×C4×C283C2311yescharacteristic
117C22×C4×C283C2311yescharacteristic
118C22×C4×C283C2311yescharacteristic
119C22×C4×C283C2311yescharacteristic
120C22×C4×C283C2311yescharacteristic
121C22×C4×C283C2311yescharacteristic
122C4⋊C4×C283C2314yescomplemented
123C4⋊C4×C283C2314yescomplemented
124C4⋊C4×C283C2314yescomplemented
125C22⋊C4×C283C2314yes—
126C22⋊C4×C283C2314yes—
127C22⋊C4×C283C2314yes—
128C42×C283C2314yescomplemented
129C22×D283—22no—
130C22×D283—22no—
131C22×D283—22no—
132C22×D283—22no—
133C22×D283—22no—
134C22×D283—22no—
135C22×D283—22no—
136C22×D283—28no—
137C22×D283—28no—
138C22×D283—44no—
139C22×D283—416no—
140C22×D283#4114yes—
141C22×D283#4114yes—
142C22×D283C2412yes—
143C22×D283C2412yes—
144C22×D283C2412yes—
145Dic566—44no—
146D1132—28no—
147D1132—28no—
148C22⋊D283—44no—
149C2×Dic283—22no—
150C2×Dic283—22no—
151C2×Dic283—22no—
152C2×Dic283—22no—
153C2×Dic283—22no—
154C2×Dic283C2412yes—
155C2×Dic283C2412yes—
156C2×Dic283C2412yes—
157C2×Dic283C2412yes—
158C2×Dic283C2412yes—
159C4×D283—28no—
160C4×D283—28no—
161C4×D283—44no—
162C4×D283—44no—
163C4×D283—44no—
164C23×C283—22no—
165C23×C283—22no—
166C23×C283—22no—
167C23×C283C2412yes—
168C23×C283C2411yescharacteristic
169C2×C4×C283—22no—
170C2×C4×C283—22no—
171C2×C4×C283—22no—
172C2×C4×C283—22no—
173C2×C4×C283—22no—
174C2×C4×C283—22no—
175C2×C4×C283C2412yes—
176C2×C4×C283C2412yes—
177C2×C4×C283C2412yes—
178C2×C4×C283C2412yes—
179C2×C4×C283C2412yes—
180C2×C4×C283C2412yes—
181C22×C283—22no—
182C22×C283—22no—
183C22×C283—22no—
184C22×C283—44no—
185C22×C283C2×#4112yes—
186C22×C283C2×#4112yes—
187C22×C283H(5,𝔽2)12yes—
188C22×C283C2511yescharacteristic
189C2×D283—28no—
190C2×D283—28no—
191C2×D283—22no—
192C2×D283—22no—
193C2×D283—22no—
194C2×D283—22no—
195C2×D283—22no—
196C2×D283—22no—
197C2×D283—22no—
198C2×D283—416no—
199C2×D283—44no—
200C2×D283C2×#4114yes—
201C2×D283C2×#4114yes—
202C4×C283—22no—
203C4×C283—22no—
204C4×C283—22no—
205C4×C283—22no—
206C4×C283—22no—
207C4×C283—22no—
208Dic283—22no—
209Dic283—22no—
210Dic283—22no—
211Dic283—22no—
212Dic283—22no—
213C2×C283—42no—
214C2×C283#55114yescomplemented
215C2×C283C22×#4111yescharacteristic
216C2×C283C22×#4111yescharacteristic
217C2×C283C2×H(5,𝔽2)11yescharacteristic
218D283—24no—
219D283—24no—
220D283—42no—
221C283C2×#55111yescharacteristic, complemented, Sylow
222C2×#551—2831nomaximal, Sylow
223#551—28316no—
224C2×#126—2831no—
225C2×#126D28311yescharacteristic, complemented
226C2×#124—2831no—
227C2×#123—2831no—
228C2×#123—2831no—
229C2×#123—2831no—
230C2×C22⋊Q8—2831no—
231C2×C22⋊Q8—2831no—
232C2×#120—2831no—
233C2×C4×D4—2831no—
234C2×C4×D4—2831no—
235C2×#117—2831no—
236C2×#117—2831no—
237C22×C22⋊C4—2831no—
238C22×C22⋊C4—2831no—
239C25—2831no—
240C22×Q8—2831no—
241C22×D4—2831no—
242C22×D4—2831no—
243C22×D4—2831no—
244C23×C4—2831no—
245C23×C4—2831no—
246C23×C4—2831no—
247C23×C4—2831no—
248C23×C4—2831no—
249#126—2838no—
250#126C2×D28318yescomplemented
251#124—2838no—
252#123—2838no—
253#123—2838no—
254#123—2838no—
255C22⋊Q8—2838no—
256C22⋊Q8—2838no—
257#120—2838no—
258C4×D4—2838no—
259C4×D4—2838no—
260#117—2838no—
261#117—2838no—
262C2×C4⋊C4—2831no—
263C2×C4⋊C4—2831no—
264C2×C4⋊C4—2831no—
265C2×C4⋊C4—2831no—
266C2×C4⋊C4—2831no—
267C2×C4⋊C4C2×D28311yescharacteristic, complemented
268C2×C4⋊C4C2×D28311yescharacteristic, complemented
269C2×C4⋊C4C2×D28311yescharacteristic, complemented
270C2×C22⋊C4—2831no—
271C2×C22⋊C4—2831no—
272C2×C22⋊C4—2831no—
273C2×C22⋊C4—2831no—
274C2×C22⋊C4—2831no—
275C2×C22⋊C4—2831no—
276C2×C22⋊C4—2831no—
277C2×C22⋊C4—2831no—
278C2×C22⋊C4—2831no—
279C2×C22⋊C4—2831no—
280C2×C22⋊C4—2831no—
281C2×C22⋊C4—2838no—
282C2×C22⋊C4—2838no—
283C2×C22⋊C4C2×D28311yescharacteristic
284C2×C22⋊C4C2×D28311yescharacteristic
285C2×C22⋊C4C2×D28311yescharacteristic
286C2×C42—2831no—
287C2×C42—2831no—
288C2×C42C2×D28311yescharacteristic, complemented
289C24—2831no—
290C24—2831no—
291C24—2831no—
292C24—2834no—
293C24—5664no—
294C24—5664no—
295C24—11322no—
296C24C22×D28311yescharacteristic
297C2×Q8—2834no—
298C2×Q8—11322no—
299C2×D4—2834no—
300C2×D4—2834no—
301C2×D4—2834no—
302C2×D4—5664no—
303C2×D4—5664no—
304C2×D4—11322no—
305C22×C4—2831no—
306C22×C4—2831no—
307C22×C4—2831no—
308C22×C4—2831no—
309C22×C4—2831no—
310C22×C4—2834no—
311C22×C4—2834no—
312C22×C4—2834no—
313C22×C4—2834no—
314C22×C4—2834no—
315C22×C4—5664no—
316C22×C4—5664no—
317C22×C4—11322no—
318C22×C4—11322no—
319C22×C4—11322no—
320C22×C4C22×D28311yescharacteristic
321C22×C4C22×D28311yescharacteristic
322C22×C4C22×D28311yescharacteristic
323C22×C4C22×D28311yescharacteristic
324C22×C4C22×D28311yescharacteristic
325C22×C4C22×D28311yescharacteristic
326C4⋊C4—2834no—
327C4⋊C4—2834no—
328C4⋊C4—2834no—
329C4⋊C4—2834no—
330C4⋊C4—2834no—
331C4⋊C4C22×D28314yescomplemented
332C4⋊C4C22×D28314yescomplemented
333C4⋊C4C22×D28314yescomplemented
334C22⋊C4—2834no—
335C22⋊C4—2834no—
336C22⋊C4—2834no—
337C22⋊C4—2834no—
338C22⋊C4—2834no—
339C22⋊C4—2834no—
340C22⋊C4—2834no—
341C22⋊C4—2834no—
342C22⋊C4—2834no—
343C22⋊C4—2834no—
344C22⋊C4—2834no—
345C22⋊C4C22×D28314yes—
346C22⋊C4C22×D28314yes—
347C22⋊C4C22×D28314yes—
348C42—2834no—
349C42—2834no—
350C42C22×D28314yescomplemented
351C23—22no—
352C23—22no—
353C23—22no—
354C23—2834no—
355C23—2834no—
356C23—2832no—
357C23—2832no—
358C23—2832no—
359C23—5668no—
360C23—5668no—
361C23—5662no—
362C23—5662no—
363C23—5662no—
364C23—5662no—
365C23—5662no—
366C23—5662no—
367C23—5662no—
368C23—11324no—
369C23—113216no—
370C23C23×D28312yes—
371C23C23×D28311yescharacteristic
372Q8—11324no—
373D4—5668no—
374D4—5668no—
375D4—11324no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—2832no—
383C2×C4—2832no—
384C2×C4—2832no—
385C2×C4—2832no—
386C2×C4—2832no—
387C2×C4—5668no—
388C2×C4—5668no—
389C2×C4—5662no—
390C2×C4—5662no—
391C2×C4—5662no—
392C2×C4—5662no—
393C2×C4—5662no—
394C2×C4—11324no—
395C2×C4—11324no—
396C2×C4—11324no—
397C2×C4C23×D28312yes—
398C2×C4C23×D28312yes—
399C2×C4C23×D28312yes—
400C2×C4C23×D28312yes—
401C2×C4C23×D28312yes—
402C2×C4C23×D28312yes—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—44no—
407C22—2834no—
408C22—2834no—
409C22—5662no—
410C22—5662no—
411C22—5662no—
412C22—5662no—
413C22—5668no—
414C22—5668no—
415C22—5662no—
416C22—5662no—
417C22—5662no—
418C22—113216no—
419C22—11324no—
420C22#41×D28312yes—
421C22#41×D28312yes—
422C22#2258365612yes—
423C22C24×D28311yescharacteristic
424C4—22no—
425C4—22no—
426C4—22no—
427C4—22no—
428C4—22no—
429C4—22no—
430C4—5662no—
431C4—5662no—
432C4—5662no—
433C4—5662no—
434C4—5662no—
435C2—42no—
436C2—5664no—
437C2—5664no—
438C2—11322no—
439C2#3182714014yesdirect product factor
440C2C2×#41×D28311yescharacteristic
441C2C2×#41×D28311yescharacteristic
442C2C2×#2258365611yescharacteristic
subgroupG/H
centerC23C23×D283
commutator, cosocleC22×C283C25
FrattiniC22C24×D283
FittingC2×#126×C283C2
socleC23×C283C24
prime radicalC2×#22583580C2
hypercenterC2×#126D283
hypocenterC283C2×#551
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #31827140C2direct (N × H)
2. C2×#22583603C2semidirect
3. C2×#22583596C2semidirect
4. C2×#22583595C2semidirect
5. C2×#22583595C2semidirect
6. C2×#22583592C2semidirect
7. C2×#22583590C2semidirect
8. C2×#22583588C2semidirect
10. C2×C4×D1132C2semidirect
11. C2×#22583572C2semidirect
12. C2×#22583568C2semidirect
13. C2×#22583567C2semidirect
14. C2×C22⋊C4×D283C2semidirect
15. C2×C22⋊C4×D283C2semidirect
16. C2×#126×C283C2semidirect
18. C22×Dic566C22semidirect
26. C22×C4×D283C22semidirect
27. #22583603C22semidirect
28. #22583596C22semidirect
29. #22583595C22semidirect
30. #22583595C22semidirect
31. #22583592C22semidirect
32. #22583590C22semidirect
33. #22583588C22semidirect
35. C4×D1132C22semidirect
36. #22583572C22semidirect
37. #22583568C22semidirect
38. #22583567C22semidirect
39. C2×C4⋊Dic283C22semidirect
40. C2×C4⋊Dic283C22semidirect
41. C2×Dic283⋊C4C22semidirect
42. C2×Dic283⋊C4C22semidirect
43. C2×Dic283⋊C4C22semidirect
52. C2×(C2×D283)⋊C4C22semidirect
53. C2×(C2×D283)⋊C4C22semidirect
54. C2×(C2×D283)⋊C4C22semidirect
55. C22⋊C4×D283C22semidirect
56. C22⋊C4×D283C22semidirect
57. C2×C4×Dic283C22semidirect
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
75. C2×Dic566C23semidirect
96. C2×C4×D283C23semidirect
97. C4⋊Dic283C23semidirect
98. C4⋊Dic283C23semidirect
99. Dic283⋊C4C23semidirect
100. Dic283⋊C4C23semidirect
101. Dic283⋊C4C23semidirect
110. (C2×D283)⋊C4C23semidirect
111. (C2×D283)⋊C4C23semidirect
112. (C2×D283)⋊C4C23semidirect
113. C4×Dic283C23semidirect
114. C4×Dic283C23semidirect
122. C4⋊C4×C283C23semidirect
123. C4⋊C4×C283C23semidirect
124. C4⋊C4×C283C23semidirect
128. C42×C283C23semidirect
214. C2×C283#551semidirect
221. C283C2×#551semidirect
225. C2×#126D283semidirect
250. #126C2×D283semidirect
267. C2×C4⋊C4C2×D283semidirect
268. C2×C4⋊C4C2×D283semidirect
269. C2×C4⋊C4C2×D283semidirect
288. C2×C42C2×D283semidirect
331. C4⋊C4C22×D283semidirect
332. C4⋊C4C22×D283semidirect
333. C4⋊C4C22×D283semidirect
350. C42C22×D283semidirect
439. C2#31827140direct (N × H)

Maximal subgroups

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

subgroupindex
#318271402
C2×#225836032
C2×#225835962
C2×#225835952
C2×#225835922
C2×#225835902
C2×#225835882
C2×#225835802
C2×C4×D11322
C2×#225835722
C2×#225835682
C2×#225835672
C2×C22⋊C4×D2832
C2×#126×C2832
C2×#551283