Finite Group Databasebeta

← C2×#5829 #87269

Subgroups — C2×#5829 #87269

Order 384.

1900 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#41C211yesmaximal, characteristic, complemented
2C22×D3×D4C211yesmaximal, characteristic, complemented
3#5829C2116yesmaximal, direct product factor
4C2×#947C211yesmaximal, characteristic, complemented
5C2×#946C211yesmaximal, characteristic, complemented
6C2×#939C212yesmaximal, complemented
7C2×#937C212yesmaximal, complemented
8C2×D4×Dic3C211yesmaximal, characteristic, complemented
9C2×#930C211yesmaximal, characteristic, complemented
10C2×#929C212yesmaximal, complemented
11C2×C4×#67C211yesmaximal, characteristic, complemented
12C22×(C2×D3)⋊C4C212yesmaximal, complemented
13C2×#546—31nomaximal, Sylow
14C24×D3C2212yes—
15C2×C3×#41—28no—
16C2×C3×#41C2218yescomplemented
17C22×C3×Q8C2211yescharacteristic, complemented
18C22×C3×D4C2211yescharacteristic
19C22×C3×D4C2212yescomplemented
20C23×C3×C4C2212yescomplemented
21C23×C3×C4C2211yescharacteristic, complemented
22C22×#67C2212yes—
23C22×#67C2211yescharacteristic
24C22×#67C2212yescomplemented
25C23×Dic3C2212yescomplemented
26C2×D3×D4—28no—
27C2×D3×D4C2218yescomplemented
28C22×D12C2211yescharacteristic
29C22×C4×D3C2211yescharacteristic
30C2×#217C2211yescharacteristic, complemented
31C2×#217C2212yescomplemented
32#947C2218yescomplemented
33#946C2218yescomplemented
34#939C22116yescomplemented
35#937C22116yescomplemented
36D4×Dic3C2218yescomplemented
37#930C2218yescomplemented
38#929C22116yescomplemented
39C4×#67C2218yescomplemented
40C2×(C2×D3)⋊C4C2211yescharacteristic
41C2×(C2×D3)⋊C4C2212yes—
42C2×(C2×D3)⋊C4C22116yescomplemented
43C2×(C2×D3)⋊C4C2212yescomplemented
44C2×(C2×D3)⋊C4C2212yescomplemented
45C2×(C2×D3)⋊C4C2212yescomplemented
46C2×C4⋊Dic3C2211yescharacteristic, complemented
47C2×Dic3⋊C4C2211yescharacteristic, complemented
48C2×Dic3⋊C4C2212yescomplemented
49C2×C4×Dic3C2211yescharacteristic, complemented
50C22×#41D311yescharacteristic, complemented
51C23×D4—31no—
52#546—316no—
53C2×#124—31no—
54C2×#123—32no—
55C2×C22⋊Q8—31no—
56C2×#121—32no—
57C2×#121—31no—
58C2×#120—32no—
59C2×C4×D4—31no—
60C2×C4×D4—31no—
61C22×C22⋊C4—32no—
62C24×C3C2311yescharacteristic
63C24×C3C2312yes—
64C23×D3—28no—
65C23×D3—28no—
66C23×D3—44no—
67C23×D3C2312yes—
68C23×D3C2318yes—
69C23×D3C2311yescharacteristic
70C3×#41—232no—
71C2×C3×Q8—24no—
72C2×C3×Q8C2314yescomplemented
73C2×C3×D4—28no—
74C2×C3×D4D418yescomplemented
75C2×C3×D4C2314yes—
76C2×C3×D4C2318yescomplemented
77C22×C3×C4—28no—
78C22×C3×C4—24no—
79C22×C3×C4C2311yescharacteristic
80C22×C3×C4C2312yes—
81C22×C3×C4C2311yescharacteristic
82C22×C3×C4C2318yescomplemented
83C22×C3×C4C2314yescomplemented
84C2×#67—28no—
85C2×#67—24no—
86C2×#67—44no—
87C2×#67C2314yes—
88C2×#67C2318yes—
89C2×#67C2318yescomplemented
90C22×Dic3—44no—
91C22×Dic3C2311yescharacteristic
92C22×Dic3C2311yescharacteristic
93C22×Dic3C2311yescharacteristic
94C22×Dic3C2312yes—
95C22×Dic3C2318yescomplemented
96D3×D4—232no—
97C2×D12—24no—
98C2×D12C2314yes—
99C2×C4×D3—24no—
100C2×C4×D3C2314yes—
101#217C2314yescomplemented
102#217C2318yescomplemented
103(C2×D3)⋊C4C2314yes—
104(C2×D3)⋊C4C2318yes—
105(C2×D3)⋊C4C2318yescomplemented
106(C2×D3)⋊C4C2318yescomplemented
107(C2×D3)⋊C4C2318yescomplemented
108C4⋊Dic3C2314yescomplemented
109Dic3⋊C4C2314yescomplemented
110Dic3⋊C4C2318yescomplemented
111C4×Dic3C2314yescomplemented
112C25—32no—
113C2×#41—28no—
114C2×#41C2×D318yescomplemented
115C22×Q8C2×D311yescharacteristic, complemented
116C22×D4—31no—
117C22×D4—32no—
118C22×D4—32no—
119C22×D4—38no—
120C22×D4—31no—
121C22×D4—68no—
122C22×D4C2×D311yescharacteristic
123C22×D4C2×D312yescomplemented
124C23×C4—32no—
125C23×C4—31no—
126C23×C4C2×D312yescomplemented
127C23×C4C2×D311yescharacteristic, complemented
128#124—38no—
129#123—316no—
130C22⋊Q8—38no—
131#121—316no—
132#121—38no—
133#120—316no—
134C4×D4—38no—
135C4×D4—38no—
136C2×C4⋊C4—31no—
137C2×C4⋊C4—31no—
138C2×C4⋊C4—32no—
139C2×C22⋊C4—32no—
140C2×C22⋊C4—31no—
141C2×C22⋊C4—31no—
142C2×C22⋊C4—32no—
143C2×C22⋊C4—32no—
144C2×C22⋊C4—32no—
145C2×C22⋊C4—32no—
146C2×C22⋊C4—316no—
147C2×C42—31no—
148C23×C3—24no—
149C23×C3—24no—
150C23×C3—22no—
151C23×C3—22no—
152C23×C3—22no—
153C23×C3C2×D418yes—
154C23×C3C2412yes—
155C23×C3C2414yes—
156C23×C3C2411yescharacteristic
157C22×D3—22no—
158C22×D3—22no—
159C22×D3—24no—
160C22×D3—216no—
161C22×D3—24no—
162C22×D3—24no—
163C22×D3—216no—
164C22×D3—48no—
165C22×D3—432no—
166C22×D3#4114yescomplemented
167C22×D3C2414yes—
168C22×D3C2412yes—
169C3×Q8—28no—
170C3×D4—216no—
171C3×D4C2×D4116yescomplemented
172C2×C3×C4—22no—
173C2×C3×C4—24no—
174C2×C3×C4—216no—
175C2×C3×C4—28no—
176C2×C3×C4C2×D414yes—
177C2×C3×C4C2412yes—
178C2×C3×C4C2414yes—
179C2×C3×C4C2412yes—
180#67—216no—
181#67—28no—
182#67—48no—
183C2×Dic3—22no—
184C2×Dic3—22no—
185C2×Dic3—22no—
186C2×Dic3—24no—
187C2×Dic3—48no—
188C2×Dic3C2412yes—
189C2×Dic3C2412yes—
190C2×Dic3C2412yes—
191C2×Dic3C2414yes—
192D12—28no—
193C4×D3—28no—
194C24—31no—
195C24—32no—
196C24—38no—
197C24—68no—
198C24—68no—
199C24—124no—
200C24C22×D311yescharacteristic
201C24C22×D312yes—
202#41—232no—
203C2×Q8—24no—
204C2×Q8C22×D314yescomplemented
205C2×D4—28no—
206C2×D4—34no—
207C2×D4—38no—
208C2×D4—38no—
209C2×D4—34no—
210C2×D4—64no—
211C2×D4—68no—
212C2×D4—632no—
213C2×D4—64no—
214C2×D4—124no—
215C2×D4#6718yescomplemented
216C2×D4C22×D314yes—
217C2×D4C22×D318yescomplemented
218C22×C4—28no—
219C22×C4—24no—
220C22×C4—31no—
221C22×C4—31no—
222C22×C4—32no—
223C22×C4—31no—
224C22×C4—38no—
225C22×C4—34no—
226C22×C4—64no—
227C22×C4—124no—
228C22×C4C22×D311yescharacteristic
229C22×C4C22×D312yes—
230C22×C4C22×D311yescharacteristic
231C22×C4C22×D318yescomplemented
232C22×C4C22×D314yescomplemented
233C4⋊C4—34no—
234C4⋊C4—34no—
235C4⋊C4—38no—
236C22⋊C4—38no—
237C22⋊C4—34no—
238C22⋊C4—34no—
239C22⋊C4—38no—
240C22⋊C4—38no—
241C22⋊C4—38no—
242C22⋊C4—38no—
243C42—34no—
244C22×C3—216no—
245C22×C3—24no—
246C22×C3—24no—
247C22×C3—22no—
248C22×C3—22no—
249C22×C3—22no—
250C22×C3—44no—
251C22×C3C22×D418yes—
252C22×C3C22×D412yes—
253C22×C3C2×#4112yes—
254C22×C3H(5,𝔽2)12yes—
255C22×C3C2511yescharacteristic
256C2×D3—28no—
257C2×D3—22no—
258C2×D3—22no—
259C2×D3—24no—
260C2×D3—24no—
261C2×D3—24no—
262C2×D3—432no—
263C2×D3—48no—
264C2×D3C2×#4114yescomplemented
265C3×C4—22no—
266C3×C4—24no—
267C3×C4C22×D414yes—
268Dic3—22no—
269Dic3—22no—
270Dic3—22no—
271Dic3—24no—
272C23—24no—
273C23—24no—
274C23—22no—
275C23—22no—
276C23—22no—
277C23—34no—
278C23—32no—
279C23—34no—
280C23—616no—
281C23—62no—
282C23—62no—
283C23—64no—
284C23—64no—
285C23—616no—
286C23—64no—
287C23—128no—
288C23—1232no—
289C23C2×#6718yes—
290C23C23×D312yes—
291C23C23×D314yes—
292C23C23×D311yescharacteristic
293Q8—28no—
294D4—216no—
295D4—68no—
296D4—616no—
297D4—68no—
298D4—128no—
299D4C2×#67116yescomplemented
300C2×C4—22no—
301C2×C4—24no—
302C2×C4—216no—
303C2×C4—28no—
304C2×C4—32no—
305C2×C4—32no—
306C2×C4—34no—
307C2×C4—32no—
308C2×C4—62no—
309C2×C4—62no—
310C2×C4—64no—
311C2×C4—62no—
312C2×C4—68no—
313C2×C4—128no—
314C2×C4C2×#6714yes—
315C2×C4C23×D312yes—
316C2×C4C23×D314yes—
317C2×C4C23×D312yes—
318C2×C3—28no—
319C2×C3—42no—
320C2×C3#54614yescomplemented
321C2×C3C23×D411yescharacteristic
322C2×C3C22×#4111yescharacteristic
323C2×C3C2×H(5,𝔽2)11yescharacteristic
324D3—24no—
325D3—44no—
326C22—24no—
327C22—24no—
328C22—216no—
329C22—22no—
330C22—22no—
331C22—22no—
332C22—34no—
333C22—44no—
334C22—62no—
335C22—62no—
336C22—68no—
337C22—64no—
338C22—64no—
339C22—64no—
340C22—1232no—
341C22—128no—
342C22D3×#4112yes—
343C22#100912yes—
344C22C22×#6718yes—
345C22C22×#6712yes—
346C22C24×D311yescharacteristic
347C4—22no—
348C4—24no—
349C4—62no—
350C4—62no—
351C4—64no—
352C4—62no—
353C4C22×#6714yes—
354C3C2×#54611yescharacteristic, complemented, Sylow
355C2—28no—
356C2—42no—
357C2—64no—
358C2—124no—
359C2#582914yesdirect product factor
360C2C2×D3×#4111yescharacteristic
361C2C2×#100911yescharacteristic
362C2C23×#6711yescharacteristic
subgroupG/H
centerC23C23×D3
commutator, cosocleC22×C3C25
FrattiniC22C24×D3
FittingC22×C3×#41C2
socleC23×C3C24
hypercenterC22×#41D3
hypocenterC3C2×#546
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×C3×#41C2semidirect
2. C22×D3×D4C2semidirect
3. #5829C2direct (N × H)
4. C2×#947C2semidirect
5. C2×#946C2semidirect
6. C2×#939C2semidirect
7. C2×#937C2semidirect
8. C2×D4×Dic3C2semidirect
9. C2×#930C2semidirect
10. C2×#929C2semidirect
11. C2×C4×#67C2semidirect
12. C22×(C2×D3)⋊C4C2semidirect
16. C2×C3×#41C22semidirect
17. C22×C3×Q8C22semidirect
19. C22×C3×D4C22semidirect
20. C23×C3×C4C22semidirect
21. C23×C3×C4C22semidirect
24. C22×#67C22semidirect
25. C23×Dic3C22semidirect
27. C2×D3×D4C22semidirect
30. C2×#217C22semidirect
31. C2×#217C22semidirect
32. #947C22semidirect
33. #946C22semidirect
34. #939C22semidirect
35. #937C22semidirect
36. D4×Dic3C22semidirect
37. #930C22semidirect
38. #929C22semidirect
39. C4×#67C22semidirect
42. C2×(C2×D3)⋊C4C22semidirect
43. C2×(C2×D3)⋊C4C22semidirect
44. C2×(C2×D3)⋊C4C22semidirect
45. C2×(C2×D3)⋊C4C22semidirect
46. C2×C4⋊Dic3C22semidirect
47. C2×Dic3⋊C4C22semidirect
48. C2×Dic3⋊C4C22semidirect
49. C2×C4×Dic3C22semidirect
50. C22×#41D3semidirect
72. C2×C3×Q8C23semidirect
74. C2×C3×D4D4semidirect
76. C2×C3×D4C23semidirect
82. C22×C3×C4C23semidirect
83. C22×C3×C4C23semidirect
89. C2×#67C23semidirect
95. C22×Dic3C23semidirect
101. #217C23semidirect
102. #217C23semidirect
105. (C2×D3)⋊C4C23semidirect
106. (C2×D3)⋊C4C23semidirect
107. (C2×D3)⋊C4C23semidirect
108. C4⋊Dic3C23semidirect
109. Dic3⋊C4C23semidirect
110. Dic3⋊C4C23semidirect
111. C4×Dic3C23semidirect
114. C2×#41C2×D3semidirect
115. C22×Q8C2×D3semidirect
123. C22×D4C2×D3semidirect
126. C23×C4C2×D3semidirect
127. C23×C4C2×D3semidirect
166. C22×D3#41semidirect
171. C3×D4C2×D4semidirect
204. C2×Q8C22×D3semidirect
215. C2×D4#67semidirect
217. C2×D4C22×D3semidirect
231. C22×C4C22×D3semidirect
232. C22×C4C22×D3semidirect
264. C2×D3C2×#41semidirect
299. D4C2×#67semidirect
320. C2×C3#546semidirect
354. C3C2×#546semidirect
359. C2#5829direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#412
C22×D3×D42
#58292
C2×#9472
C2×#9462
C2×#9392
C2×#9372
C2×D4×Dic32
C2×#9302
C2×#9292
C2×C4×#672
C22×(C2×D3)⋊C42
C2×#5463