Finite Group Databasebeta

← C2×#31827141 #49134758

Subgroups — C2×#31827141 #49134758

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#31827141C2116yesmaximal, direct product factor
2C2×#22583603C211yesmaximal, characteristic, complemented
3C2×#22583603C211yesmaximal, characteristic, complemented
4C2×#22583596C211yesmaximal, characteristic, complemented
5C2×#22583594C211yesmaximal, characteristic, complemented
6C2×#22583593C211yesmaximal, characteristic, complemented
7C2×#22583592C211yesmaximal, characteristic, complemented
8C2×#22583589C211yesmaximal, characteristic, complemented
9C2×#22583587C211yesmaximal, characteristic, complemented
10C2×#22583579C211yesmaximal, characteristic
11C2×C4×C22⋊D283C211yesmaximal, characteristic, complemented
12C2×(C22⋊D283)⋊C4C211yesmaximal, characteristic, complemented
13C2×#22583569C211yesmaximal, characteristic, complemented
14C2×#22583566C211yesmaximal, characteristic, complemented
15C22×C22⋊Dic283C211yesmaximal, characteristic, complemented
16C22×C22⋊C4×C283C211yesmaximal, characteristic, complemented
17C22×Dic566C2211yescharacteristic, complemented
18C22×C22⋊D283C2211yescharacteristic
19C22×C22⋊D283C2211yescharacteristic
20C22×C22⋊D283C2211yescharacteristic
21C23×Dic283C2211yescharacteristic
22C23×Dic283C2211yescharacteristic
23C22×C4×D283C2211yescharacteristic, complemented
24#22583603C2218yescomplemented
25#22583603C2218yescomplemented
26#22583596C2218yescomplemented
27#22583594C2218yescomplemented
28#22583593C2218yescomplemented
29#22583592C2218yescomplemented
30#22583589C2218yescomplemented
31#22583587C2218yescomplemented
32#22583579C2218yes—
33C4×C22⋊D283C2218yescomplemented
34(C22⋊D283)⋊C4C2218yescomplemented
35#22583569C2218yescomplemented
36#22583566C2218yescomplemented
37C2×C4⋊Dic283C2211yescharacteristic, complemented
38C2×C4⋊Dic283C2211yescharacteristic, complemented
39C2×C4⋊Dic283C2211yescharacteristic, complemented
40C2×Dic283⋊C4C2211yescharacteristic, complemented
41C2×Dic283⋊C4C2211yescharacteristic, complemented
42C2×Dic283⋊C4C2211yescharacteristic, complemented
43C2×Dic283⋊C4C2211yescharacteristic, complemented
44C2×Dic283⋊C4C2211yescharacteristic, complemented
45C2×C22⋊Dic283C2211yescharacteristic
46C2×C22⋊Dic283C2211yescharacteristic
47C2×C22⋊Dic283C2211yescharacteristic
48C2×C22⋊Dic283C2211yescharacteristic
49C2×C22⋊Dic283C2211yescharacteristic
50C2×C22⋊Dic283C2211yescharacteristic
51C2×C22⋊Dic283C2211yescharacteristic
52C2×C22⋊Dic283C2218yescomplemented
53C2×(C2×D283)⋊C4C2211yescharacteristic, complemented
54C2×(C2×D283)⋊C4C2211yescharacteristic, complemented
55C2×(C2×D283)⋊C4C2211yescharacteristic, complemented
56C2×C4×Dic283C2211yescharacteristic, complemented
57C2×C4×Dic283C2211yescharacteristic, complemented
58C2×C4×Dic283C2211yescharacteristic, complemented
59C25×C283C2211yescharacteristic
60C23×C4×C283C2211yescharacteristic
61C23×C4×C283C2211yescharacteristic
62C2×C22⋊C4×C283C2211yescharacteristic
63C2×C22⋊C4×C283C2211yescharacteristic
64C2×C22⋊C4×C283C2211yescharacteristic
65C2×C22⋊C4×C283C2211yescharacteristic
66C2×C22⋊C4×C283C2218yescomplemented
67C23×D283C2311yescharacteristic
68C2×Dic566—42no—
69C2×Dic566C2314yescomplemented
70C2×C22⋊D283—24no—
71C2×C22⋊D283—24no—
72C2×C22⋊D283—42no—
73C2×C22⋊D283C2314yes—
74C2×C22⋊D283C2314yes—
75C2×C22⋊D283C2314yes—
76C22×Dic283—24no—
77C22×Dic283—42no—
78C22×Dic283C2311yescharacteristic
79C22×Dic283C2311yescharacteristic
80C22×Dic283C2311yescharacteristic
81C22×Dic283C2311yescharacteristic
82C22×Dic283C2311yescharacteristic
83C22×Dic283C2311yescharacteristic
84C22×Dic283C2311yescharacteristic
85C22×Dic283C2314yes—
86C22×Dic283C2314yes—
87C2×C4×D283—42no—
88C2×C4×D283C2314yescomplemented
89C4⋊Dic283C2314yescomplemented
90C4⋊Dic283C2314yescomplemented
91C4⋊Dic283C2314yescomplemented
92Dic283⋊C4C2314yescomplemented
93Dic283⋊C4C2314yescomplemented
94Dic283⋊C4C2314yescomplemented
95Dic283⋊C4C2314yescomplemented
96Dic283⋊C4C2314yescomplemented
97C22⋊Dic283C2314yes—
98C22⋊Dic283C2314yes—
99C22⋊Dic283C2314yes—
100C22⋊Dic283C2314yes—
101C22⋊Dic283C2314yes—
102C22⋊Dic283C2314yes—
103C22⋊Dic283C2314yes—
104(C2×D283)⋊C4C2314yescomplemented
105(C2×D283)⋊C4C2314yescomplemented
106(C2×D283)⋊C4C2314yescomplemented
107C4×Dic283C2314yescomplemented
108C4×Dic283C2314yescomplemented
109C4×Dic283C2314yescomplemented
110C24×C283—24no—
111C24×C283—24no—
112C24×C283—42no—
113C24×C283C2311yescharacteristic
114C24×C283C2314yes—
115C24×C283C2311yescharacteristic
116C24×C283C2311yescharacteristic
117C22×C4×C283—24no—
118C22×C4×C283—42no—
119C22×C4×C283C2311yescharacteristic
120C22×C4×C283C2311yescharacteristic
121C22×C4×C283C2311yescharacteristic
122C22×C4×C283C2311yescharacteristic
123C22×C4×C283C2314yes—
124C22×C4×C283C2314yes—
125C22⋊C4×C283C2314yes—
126C22⋊C4×C283C2314yes—
127C22⋊C4×C283C2314yes—
128C22⋊C4×C283C2314yes—
129C22×D283—22no—
130C22×D283—22no—
131C22×D283—22no—
132C22×D283C2412yes—
133Dic566—44no—
134C22⋊D283—28no—
135C22⋊D283—28no—
136C22⋊D283—44no—
137C2×Dic283—28no—
138C2×Dic283—22no—
139C2×Dic283—22no—
140C2×Dic283—22no—
141C2×Dic283—22no—
142C2×Dic283—22no—
143C2×Dic283—22no—
144C2×Dic283—22no—
145C2×Dic283—44no—
146C2×Dic283C2412yes—
147C2×Dic283C2412yes—
148C2×Dic283C2412yes—
149C2×Dic283C2412yes—
150C2×Dic283C2412yes—
151C2×Dic283C2412yes—
152C2×Dic283C2412yes—
153C4×D283—44no—
154C23×C283—22no—
155C23×C283—22no—
156C23×C283—22no—
157C23×C283—22no—
158C23×C283—28no—
159C23×C283—22no—
160C23×C283—28no—
161C23×C283—22no—
162C23×C283—22no—
163C23×C283—44no—
164C23×C283—416no—
165C23×C283#4114yes—
166C23×C283#4114yes—
167C23×C283C2412yes—
168C23×C283C2412yes—
169C23×C283C2412yes—
170C23×C283C2411yescharacteristic
171C2×C4×C283—28no—
172C2×C4×C283—22no—
173C2×C4×C283—22no—
174C2×C4×C283—22no—
175C2×C4×C283—22no—
176C2×C4×C283—44no—
177C2×C4×C283C2412yes—
178C2×C4×C283C2412yes—
179C2×C4×C283C2412yes—
180C2×C4×C283C2412yes—
181C22×C283—28no—
182C22×C283—28no—
183C22×C283—22no—
184C22×C283—22no—
185C22×C283—22no—
186C22×C283—22no—
187C22×C283—22no—
188C22×C283—22no—
189C22×C283—22no—
190C22×C283—416no—
191C22×C283—44no—
192C22×C283C2×#4114yes—
193C22×C283C2×#4112yes—
194C22×C283C2×#4114yes—
195C22×C283C2×#4112yes—
196C22×C283H(5,𝔽2)12yes—
197C22×C283C2511yescharacteristic
198C2×D283—22no—
199C2×D283—22no—
200C2×D283—22no—
201C2×D283—44no—
202C4×C283—22no—
203C4×C283—22no—
204C4×C283—22no—
205C4×C283—22no—
206Dic283—22no—
207Dic283—22no—
208Dic283—22no—
209Dic283—22no—
210Dic283—22no—
211Dic283—22no—
212Dic283—22no—
213C2×C283—24no—
214C2×C283—24no—
215C2×C283—42no—
216C2×C283#55114yescomplemented
217C2×C283C22×#4111yescharacteristic
218C2×C283C22×#4111yescharacteristic
219C2×C283C2×H(5,𝔽2)11yescharacteristic
220D283—42no—
221C283C2×#55111yescharacteristic, complemented, Sylow
222C2×#551—2831nomaximal, Sylow
223#551—28316no—
224C2×#126—2831no—
225C2×#126—2831no—
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⋊C4D28311yescharacteristic, complemented
239C25C2×D28311yescharacteristic
240C22×Q8—2831no—
241C22×D4—2831no—
242C22×D4—2831no—
243C22×D4—2831no—
244C23×C4—2831no—
245C23×C4—2831no—
246C23×C4—2831no—
247C23×C4C2×D28311yescharacteristic
248C23×C4C2×D28311yescharacteristic
249#126—2838no—
250#126—2838no—
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⋊C4—2831no—
268C2×C4⋊C4—2831no—
269C2×C4⋊C4—2831no—
270C2×C22⋊C4—2831no—
271C2×C22⋊C4—2831no—
272C2×C22⋊C4—2831no—
273C2×C22⋊C4—2831no—
274C2×C22⋊C4—2838no—
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⋊C4C2×D28311yescharacteristic
282C2×C22⋊C4C2×D28311yescharacteristic
283C2×C22⋊C4C2×D28311yescharacteristic
284C2×C22⋊C4C2×D28311yescharacteristic
285C2×C22⋊C4C2×D28318yescomplemented
286C2×C42—2831no—
287C2×C42—2831no—
288C2×C42—2831no—
289C24—24no—
290C24—24no—
291C24—42no—
292C24—2831no—
293C24C22×D28311yescharacteristic
294C24C22×D28314yes—
295C24C22×D28311yescharacteristic
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—24no—
306C22×C4—42no—
307C22×C4—2834no—
308C22×C4—2831no—
309C22×C4—2831no—
310C22×C4—2831no—
311C22×C4—2831no—
312C22×C4—2831no—
313C22×C4—2831no—
314C22×C4—2831no—
315C22×C4—2834no—
316C22×C4—2834no—
317C22×C4—5664no—
318C22×C4—11322no—
319C22×C4—11322no—
320C22×C4C22×D28314yes—
321C22×C4C22×D28311yescharacteristic
322C22×C4C22×D28311yescharacteristic
323C22×C4C22×D28311yescharacteristic
324C22×C4C22×D28311yescharacteristic
325C22×C4C22×D28314yes—
326C4⋊C4—2834no—
327C4⋊C4—2834no—
328C4⋊C4—2834no—
329C4⋊C4—2834no—
330C4⋊C4—2834no—
331C4⋊C4—2834no—
332C4⋊C4—2834no—
333C4⋊C4—2834no—
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⋊C4C22×D28314yes—
345C22⋊C4C22×D28314yes—
346C22⋊C4C22×D28314yes—
347C22⋊C4C22×D28314yes—
348C42—2834no—
349C42—2834no—
350C42—2834no—
351C23—22no—
352C23—22no—
353C23—22no—
354C23—22no—
355C23—28no—
356C23—22no—
357C23—28no—
358C23—22no—
359C23—22no—
360C23—44no—
361C23—416no—
362C23—2832no—
363C23—5662no—
364C23—5662no—
365C23—5662no—
366C23#1798539114yes—
367C23#1798539214yes—
368C23C23×D28312yes—
369C23C23×D28312yes—
370C23C23×D28312yes—
371C23C23×D28311yescharacteristic
372Q8—11324no—
373D4—5668no—
374D4—5668no—
375D4—11324no—
376C2×C4—28no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—44no—
382C2×C4—2832no—
383C2×C4—2832no—
384C2×C4—2832no—
385C2×C4—2832no—
386C2×C4—2832no—
387C2×C4—2832no—
388C2×C4—2832no—
389C2×C4—5662no—
390C2×C4—5668no—
391C2×C4—5662no—
392C2×C4—5662no—
393C2×C4—5662no—
394C2×C4—5662no—
395C2×C4—5662no—
396C2×C4—5662no—
397C2×C4—11324no—
398C2×C4—11324no—
399C2×C4C23×D28312yes—
400C2×C4C23×D28312yes—
401C2×C4C23×D28312yes—
402C2×C4C23×D28312yes—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—28no—
408C22—28no—
409C22—22no—
410C22—22no—
411C22—22no—
412C22—416no—
413C22—44no—
414C22—5662no—
415C22—5662no—
416C22—5662no—
417C22—11324no—
418C22C2×#1798539114yes—
419C22C2×#1798539112yes—
420C22C2×#1798539214yes—
421C22C2×#1798539212yes—
422C22#2258365512yes—
423C22C24×D28311yescharacteristic
424C4—22no—
425C4—22no—
426C4—22no—
427C4—22no—
428C4—5662no—
429C4—5662no—
430C4—5662no—
431C4—5662no—
432C4—5662no—
433C4—5662no—
434C4—5662no—
435C2—24no—
436C2—24no—
437C2—42no—
438C2—11322no—
439C2#3182714114yesdirect product factor
440C2C22×#1798539111yescharacteristic
441C2C22×#1798539211yescharacteristic
442C2C2×#2258365511yescharacteristic
subgroupG/H
centerC23C23×D283
commutator, cosocleC22×C283C25
FrattiniC22C24×D283
FittingC22×C22⋊C4×C283C2
socleC23×C283C24
prime radicalC2×#22583579C2
hypercenterC22×C22⋊C4D283
hypocenterC283C2×#551
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #31827141C2direct (N × H)
2. C2×#22583603C2semidirect
3. C2×#22583603C2semidirect
4. C2×#22583596C2semidirect
5. C2×#22583594C2semidirect
6. C2×#22583593C2semidirect
7. C2×#22583592C2semidirect
8. C2×#22583589C2semidirect
9. C2×#22583587C2semidirect
11. C2×C4×C22⋊D283C2semidirect
12. C2×(C22⋊D283)⋊C4C2semidirect
13. C2×#22583569C2semidirect
14. C2×#22583566C2semidirect
15. C22×C22⋊Dic283C2semidirect
16. C22×C22⋊C4×C283C2semidirect
17. C22×Dic566C22semidirect
23. C22×C4×D283C22semidirect
24. #22583603C22semidirect
25. #22583603C22semidirect
26. #22583596C22semidirect
27. #22583594C22semidirect
28. #22583593C22semidirect
29. #22583592C22semidirect
30. #22583589C22semidirect
31. #22583587C22semidirect
33. C4×C22⋊D283C22semidirect
34. (C22⋊D283)⋊C4C22semidirect
35. #22583569C22semidirect
36. #22583566C22semidirect
37. C2×C4⋊Dic283C22semidirect
38. C2×C4⋊Dic283C22semidirect
39. C2×C4⋊Dic283C22semidirect
40. C2×Dic283⋊C4C22semidirect
41. C2×Dic283⋊C4C22semidirect
42. C2×Dic283⋊C4C22semidirect
43. C2×Dic283⋊C4C22semidirect
44. C2×Dic283⋊C4C22semidirect
52. C2×C22⋊Dic283C22semidirect
53. C2×(C2×D283)⋊C4C22semidirect
54. C2×(C2×D283)⋊C4C22semidirect
55. C2×(C2×D283)⋊C4C22semidirect
56. C2×C4×Dic283C22semidirect
57. C2×C4×Dic283C22semidirect
58. C2×C4×Dic283C22semidirect
66. C2×C22⋊C4×C283C22semidirect
69. C2×Dic566C23semidirect
88. C2×C4×D283C23semidirect
89. C4⋊Dic283C23semidirect
90. C4⋊Dic283C23semidirect
91. C4⋊Dic283C23semidirect
92. Dic283⋊C4C23semidirect
93. Dic283⋊C4C23semidirect
94. Dic283⋊C4C23semidirect
95. Dic283⋊C4C23semidirect
96. Dic283⋊C4C23semidirect
104. (C2×D283)⋊C4C23semidirect
105. (C2×D283)⋊C4C23semidirect
106. (C2×D283)⋊C4C23semidirect
107. C4×Dic283C23semidirect
108. C4×Dic283C23semidirect
109. C4×Dic283C23semidirect
216. C2×C283#551semidirect
221. C283C2×#551semidirect
238. C22×C22⋊C4D283semidirect
285. C2×C22⋊C4C2×D283semidirect
439. C2#31827141direct (N × H)

Maximal subgroups

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

subgroupindex
#318271412
C2×#225836032
C2×#225835962
C2×#225835942
C2×#225835932
C2×#225835922
C2×#225835892
C2×#225835872
C2×#225835792
C2×C4×C22⋊D2832
C2×(C22⋊D283)⋊C42
C2×#225835692
C2×#225835662
C22×C22⋊Dic2832
C22×C22⋊C4×C2832
C2×#551283