Finite Group Databasebeta

← C2×#3532 #62718

Subgroups — C2×#3532 #62718

Order 256.

4771 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3532C2132yesmaximal, direct product factor
2C2×H(3,𝔽4)C211yesmaximal, characteristic, complemented
3C2×#560C213yesmaximal, complemented
4C2×#551C213yesmaximal, complemented
5C2×#546C216yesmaximal, complemented
6C2×D42C213yesmaximal, complemented
7C2×#538C216yesmaximal, complemented
8C2×#535C213yesmaximal, complemented
9C2×#534C213yesmaximal, complemented
10C22×#120C213yesmaximal, complemented
11C26C2211yescharacteristic, complemented
12C22×#41C2213yescomplemented
13C23×D4C2213yescomplemented
14C23×D4C2216yescomplemented
15C23×D4C2213yescomplemented
16H(3,𝔽4)C22116yescomplemented
17#560C22148yescomplemented
18#551C22148yescomplemented
19#546C22196yescomplemented
20D42C22148yescomplemented
21#538C22196yescomplemented
22#535C22148yescomplemented
23#534C22148yescomplemented
24C2×#127C2211yescharacteristic, complemented
25C2×#127C2213yescomplemented
26C2×#126C2212yescomplemented
27C2×#126C2216yescomplemented
28C2×#124C2213yescomplemented
29C2×#124C2213yescomplemented
30C2×#124C2216yescomplemented
31C2×#123C2213yescomplemented
32C2×#123C2213yescomplemented
33C2×#123C2216yescomplemented
34C2×#123C2216yescomplemented
35C2×C22⋊Q8C2216yescomplemented
36C2×#121C2216yescomplemented
37C2×#121C2216yescomplemented
38C2×#121C2216yescomplemented
39C2×#121C2216yescomplemented
40C2×#121C2216yescomplemented
41C2×#120C2213yes—
42C2×#120C2216yescomplemented
43C2×#120C2216yescomplemented
44C2×#120C2213yescomplemented
45C2×#120C2213yescomplemented
46C2×#120C2213yescomplemented
47C2×#120C2216yescomplemented
48C2×#120C22148yescomplemented
49C2×#120C2211yescharacteristic, complemented
50C2×#120C2213yescomplemented
51C2×C4×D4C2216yescomplemented
52C2×C4×D4C2216yescomplemented
53C2×#117C2213yescomplemented
54C22×C22⋊C4C2213yescomplemented
55C22×C22⋊C4C2216yescomplemented
56C22×C22⋊C4C2213yescomplemented
57C25—412no—
58C25C2313yes—
59C25C2313yes—
60C25C2313yes—
61C25C2311yescharacteristic
62C25C2318yescomplemented
63C25C2311yescharacteristic, complemented
64C2×#41—412no—
65C2×#41C23124yescomplemented
66C22×Q8C2313yescomplemented
67C22×D4—412no—
68C22×D4—424no—
69C22×D4—412no—
70C22×D4C2316yes—
71C22×D4C2316yes—
72C22×D4C2313yes—
73C22×D4C2313yes—
74C22×D4C2316yes—
75C22×D4C2313yes—
76C22×D4C2316yes—
77C22×D4C2313yes—
78C22×D4C23124yescomplemented
79C22×D4C23148yescomplemented
80C22×D4C2313yescomplemented
81C22×D4C2316yescomplemented
82C22×D4C23124yescomplemented
83C23×C4C2313yes—
84C23×C4C2316yes—
85C23×C4C2316yescomplemented
86C23×C4C2313yescomplemented
87#127C2318yescomplemented
88#127C23124yescomplemented
89#126C23116yescomplemented
90#126C23148yescomplemented
91#124C23124yescomplemented
92#124C23124yescomplemented
93#124C23148yescomplemented
94#123C23124yescomplemented
95#123C23124yescomplemented
96#123C23148yescomplemented
97#123C23148yescomplemented
98C22⋊Q8C23148yescomplemented
99#121C23148yescomplemented
100#121C23148yescomplemented
101#121C23148yescomplemented
102#121C23148yescomplemented
103#121C23148yescomplemented
104#120C23124yes—
105#120C23148yescomplemented
106#120C23148yescomplemented
107#120C23124yescomplemented
108#120C23124yescomplemented
109#120C23124yescomplemented
110#120C23148yescomplemented
111#120C2318yescomplemented
112#120C23124yescomplemented
113C4×D4C23148yescomplemented
114C4×D4C23148yescomplemented
115#117C23124yescomplemented
116C2×C4⋊C4C2316yescomplemented
117C2×C4⋊C4C2316yescomplemented
118C2×C4⋊C4C2316yescomplemented
119C2×C22⋊C4C2316yes—
120C2×C22⋊C4C2316yes—
121C2×C22⋊C4C2313yes—
122C2×C22⋊C4C2316yes—
123C2×C22⋊C4C2316yes—
124C2×C22⋊C4C2316yes—
125C2×C22⋊C4C2313yes—
126C2×C22⋊C4C23124yescomplemented
127C2×C22⋊C4C23148yescomplemented
128C2×C22⋊C4C23124yescomplemented
129C2×C22⋊C4C2313yescomplemented
130C2×C22⋊C4C2313yescomplemented
131C2×C22⋊C4C2316yescomplemented
132C2×C22⋊C4C2316yescomplemented
133C2×C42C2311yescharacteristic, complemented
134C2×C42C2313yescomplemented
135C2×C42C2312yescomplemented
136C24—224no—
137C24—212no—
138C24—212no—
139C24—46no—
140C24—412no—
141C24—46no—
142C24—448no—
143C24—412no—
144C24—46no—
145C24—464no—
146C24C2413yes—
147C24C2411yescharacteristic
148C24C2413yes—
149C24C2413yes—
150C24C24112yes—
151C24C2413yes—
152C24C24112yes—
153C24C24112yes—
154C24C2414yes—
155C24C2414yescomplemented
156#41—448no—
157C2×Q8—46no—
158C2×Q8C24112yescomplemented
159C2×D4—224no—
160C2×D4—224no—
161C2×D4—46no—
162C2×D4—46no—
163C2×D4—46no—
164C2×D4—46no—
165C2×D4—412no—
166C2×D4—412no—
167C2×D4—448no—
168C2×D4—412no—
169C2×D4—46no—
170C2×D4—496no—
171C2×D4—448no—
172C2×D4C24124yes—
173C2×D4C24124yes—
174C2×D4C24112yes—
175C2×D4C24112yes—
176C2×D4C24124yes—
177C2×D4C24112yes—
178C2×D4C24124yes—
179C2×D4C24112yes—
180C2×D4C24112yescomplemented
181C2×D4C24124yescomplemented
182C22×C4—212no—
183C22×C4—412no—
184C22×C4—46no—
185C22×C4—412no—
186C22×C4C24112yes—
187C22×C4C2413yes—
188C22×C4C2416yes—
189C22×C4C2416yes—
190C22×C4C2413yes—
191C22×C4C24124yes—
192C22×C4C24124yescomplemented
193C22×C4C24112yescomplemented
194C4⋊C4C24124yescomplemented
195C4⋊C4C24124yescomplemented
196C4⋊C4C24124yescomplemented
197C22⋊C4C24124yes—
198C22⋊C4C24124yes—
199C22⋊C4C24112yes—
200C22⋊C4C24124yes—
201C22⋊C4C24124yes—
202C22⋊C4C24124yes—
203C22⋊C4C24112yes—
204C22⋊C4C24112yescomplemented
205C22⋊C4C24112yescomplemented
206C22⋊C4C24124yescomplemented
207C22⋊C4C24124yescomplemented
208C42C2414yescomplemented
209C42C24112yescomplemented
210C42C2418yescomplemented
211C23—212no—
212C23—212no—
213C23—26no—
214C23—212no—
215C23—26no—
216C23—248no—
217C23—224no—
218C23—26no—
219C23—212no—
220C23—26no—
221C23—224no—
222C23—412no—
223C23—424no—
224C23—412no—
225C23—424no—
226C23—412no—
227C23—448no—
228C23—448no—
229C23—4128no—
230C23—416no—
231C23—824no—
232C23—88no—
233C23H(5,𝔽2)112yes—
234C23C2516yes—
235C23C2512yes—
236C23C2516yes—
237C23C2516yes—
238C23C2516yes—
239C23C2511yescharacteristic
240Q8—412no—
241D4—248no—
242D4—248no—
243D4—412no—
244D4—412no—
245D4—412no—
246D4—412no—
247D4—424no—
248D4—424no—
249D4—424no—
250D4—412no—
251C2×C4—26no—
252C2×C4—26no—
253C2×C4—224no—
254C2×C4—212no—
255C2×C4—212no—
256C2×C4—424no—
257C2×C4—412no—
258C2×C4—424no—
259C2×C4C2516yes—
260C2×C4C25112yes—
261C2×C4C25112yes—
262C2×C4C2516yes—
263C22—212no—
264C22—224no—
265C22—212no—
266C22—26no—
267C22—212no—
268C22—26no—
269C22—26no—
270C22—212no—
271C22—26no—
272C22—448no—
273C22—448no—
274C22—416no—
275C22—412no—
276C22—44no—
277C22—412no—
278C22—412no—
279C22—824no—
280C22—88no—
281C22C2×H(5,𝔽2)112yes—
282C22C2×H(5,𝔽2)16yes—
283C22C2611yescharacteristic
284C4—26no—
285C4—26no—
286C4—212no—
287C4—212no—
288C2—212no—
289C2—46no—
290C2—42no—
291C2—46no—
292C2—46no—
293C2#353214yesdirect product factor
294C2C22×H(5,𝔽2)13yes—
subgroupG/H
center, socleC23C25
commutator, Frattini, cosocleC22C26
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3532C2direct (N × H)
2. C2×H(3,𝔽4)C2semidirect
3. C2×#560C2semidirect
4. C2×#551C2semidirect
5. C2×#546C2semidirect
6. C2×D42C2semidirect
7. C2×#538C2semidirect
8. C2×#535C2semidirect
9. C2×#534C2semidirect
10. C22×#120C2semidirect
11. C26C22semidirect
12. C22×#41C22semidirect
13. C23×D4C22semidirect
14. C23×D4C22semidirect
15. C23×D4C22semidirect
16. H(3,𝔽4)C22semidirect
17. #560C22semidirect
18. #551C22semidirect
19. #546C22semidirect
20. D42C22semidirect
21. #538C22semidirect
22. #535C22semidirect
23. #534C22semidirect
24. C2×#127C22semidirect
25. C2×#127C22semidirect
26. C2×#126C22semidirect
27. C2×#126C22semidirect
28. C2×#124C22semidirect
29. C2×#124C22semidirect
30. C2×#124C22semidirect
31. C2×#123C22semidirect
32. C2×#123C22semidirect
33. C2×#123C22semidirect
34. C2×#123C22semidirect
35. C2×C22⋊Q8C22semidirect
36. C2×#121C22semidirect
37. C2×#121C22semidirect
38. C2×#121C22semidirect
39. C2×#121C22semidirect
40. C2×#121C22semidirect
42. C2×#120C22semidirect
43. C2×#120C22semidirect
44. C2×#120C22semidirect
45. C2×#120C22semidirect
46. C2×#120C22semidirect
47. C2×#120C22semidirect
48. C2×#120C22semidirect
49. C2×#120C22semidirect
50. C2×#120C22semidirect
51. C2×C4×D4C22semidirect
52. C2×C4×D4C22semidirect
53. C2×#117C22semidirect
54. C22×C22⋊C4C22semidirect
55. C22×C22⋊C4C22semidirect
56. C22×C22⋊C4C22semidirect
62. C25C23semidirect
63. C25C23semidirect
65. C2×#41C23semidirect
66. C22×Q8C23semidirect
78. C22×D4C23semidirect
79. C22×D4C23semidirect
80. C22×D4C23semidirect
81. C22×D4C23semidirect
82. C22×D4C23semidirect
85. C23×C4C23semidirect
86. C23×C4C23semidirect
87. #127C23semidirect
88. #127C23semidirect
89. #126C23semidirect
90. #126C23semidirect
91. #124C23semidirect
92. #124C23semidirect
93. #124C23semidirect
94. #123C23semidirect
95. #123C23semidirect
96. #123C23semidirect
97. #123C23semidirect
98. C22⋊Q8C23semidirect
99. #121C23semidirect
100. #121C23semidirect
101. #121C23semidirect
102. #121C23semidirect
103. #121C23semidirect
105. #120C23semidirect
106. #120C23semidirect
107. #120C23semidirect
108. #120C23semidirect
109. #120C23semidirect
110. #120C23semidirect
111. #120C23semidirect
112. #120C23semidirect
113. C4×D4C23semidirect
114. C4×D4C23semidirect
115. #117C23semidirect
116. C2×C4⋊C4C23semidirect
117. C2×C4⋊C4C23semidirect
118. C2×C4⋊C4C23semidirect
126. C2×C22⋊C4C23semidirect
127. C2×C22⋊C4C23semidirect
128. C2×C22⋊C4C23semidirect
129. C2×C22⋊C4C23semidirect
130. C2×C22⋊C4C23semidirect
131. C2×C22⋊C4C23semidirect
132. C2×C22⋊C4C23semidirect
133. C2×C42C23semidirect
134. C2×C42C23semidirect
135. C2×C42C23semidirect
155. C24C24semidirect
158. C2×Q8C24semidirect
180. C2×D4C24semidirect
181. C2×D4C24semidirect
192. C22×C4C24semidirect
193. C22×C4C24semidirect
194. C4⋊C4C24semidirect
195. C4⋊C4C24semidirect
196. C4⋊C4C24semidirect
204. C22⋊C4C24semidirect
205. C22⋊C4C24semidirect
206. C22⋊C4C24semidirect
207. C22⋊C4C24semidirect
208. C42C24semidirect
209. C42C24semidirect
210. C42C24semidirect
293. C2#3532direct (N × H)

Maximal subgroups

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

subgroupindex
#35322
C2×H(3,𝔽4)2
C2×#5602
C2×#5512
C2×#5462
C2×D422
C2×#5382
C2×#5352
C2×#5342
C22×#1202