Finite Group Databasebeta

← C2×D3×#135 #87182

Subgroups — C2×D3×#135 #87182

Order 384.

1504 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#41C212yesmaximal, complemented
2C2×C3×#135C211yesmaximal, characteristic, complemented
3C2×#950C212yesmaximal, complemented
4D3×#135C2116yesmaximal, direct product factor
5C2×#919C211yesmaximal, characteristic, complemented
6C2×D3×Q16C211yesmaximal, characteristic, complemented
7C2×#916C212yesmaximal, complemented
8C2×D3×SD16C212yesmaximal, complemented
9C2×#912C211yesmaximal, characteristic, complemented
10C2×D3×D8C211yesmaximal, characteristic, complemented
11C2×#904C211yesmaximal, characteristic, complemented
12C22×D3×C8C211yesmaximal, characteristic, complemented
13C22×#135—31nomaximal, Sylow
14C2×C3×#41C2212yescomplemented
15D3×#41—28no—
16D3×#41C22116yescomplemented
17C2×#239C2212yescomplemented
18C2×D3×Q8C2212yes—
19C2×#237—22no—
20C2×#237C2212yescomplemented
21C2×D3×D4—22no—
22C2×D3×D4C2212yes—
23C2×#235—22no—
24C2×#235C2212yescomplemented
25C22×C4×D3—22no—
26C22×C4×D3C2211yescharacteristic
27C3×#135C2218yescomplemented
28C2×C3×Q16C2211yescharacteristic, complemented
29C2×C3×SD16C2212yescomplemented
30C2×C3×D8C2211yescharacteristic, complemented
31C22×C3×C8C2211yescharacteristic, complemented
32#950C22116yescomplemented
33C2×#216C2212yescomplemented
34C2×#215C2212yescomplemented
35C2×#214C2212yescomplemented
36C2×#213C2212yescomplemented
37C22×C3⋊C8C2211yescharacteristic, complemented
38#919C2218yescomplemented
39D3×Q16C2218yescomplemented
40#916C22116yescomplemented
41D3×SD16C22116yescomplemented
42#912C2218yescomplemented
43D3×D8C2218yescomplemented
44C2×Dic12C2211yescharacteristic, complemented
45#904C2218yescomplemented
46C2×D24C2211yescharacteristic, complemented
47C2×#204C2212yescomplemented
48C2×D3×C8C2211yescharacteristic
49C2×D3×C8C2211yescharacteristic
50C2×D3×C8C2218yescomplemented
51C2×D3×C8C2211yescharacteristic, complemented
52C2×D3×C8C2211yescharacteristic, complemented
53C22×#41—32no—
54C2×#135—32no—
55C2×#135—316no—
56C2×#135—31no—
57C2×#135—32no—
58C2×#135—31no—
59C2×#135—31no—
60C2×#135D311yescharacteristic, direct product factor
61C22×Q16—31no—
62C22×SD16—32no—
63C22×D8—31no—
64C23×C8—31no—
65C23×D3—22no—
66C23×D3D411yescharacteristic
67C3×#41—24no—
68C3×#41C2318yescomplemented
69C2×C3×Q8C2312yes—
70C2×C3×D4—22no—
71C2×C3×D4C2312yes—
72C22×C3×C4—22no—
73C22×C3×C4C2311yescharacteristic
74C2×#67—22no—
75C2×#67—22no—
76C2×#67—22no—
77C22×Dic3—22no—
78C22×Dic3D411yescharacteristic
79#239—24no—
80#239C2318yescomplemented
81D3×Q8—24no—
82D3×Q8C2318yes—
83#237—216no—
84#237—24no—
85#237C2318yescomplemented
86D3×D4—216no—
87D3×D4—24no—
88D3×D4C2318yes—
89#235—24no—
90#235—216no—
91#235C2318yescomplemented
92C2×D12—22no—
93C2×D12C2312yes—
94C2×C4×D3—22no—
95C2×C4×D3—22no—
96C2×C4×D3—22no—
97C2×C4×D3—216no—
98C2×C4×D3D411yescharacteristic
99C2×C4×D3D411yescharacteristic
100C2×C4×D3D414yes—
101C2×C4×D3C2311yescharacteristic
102C2×C4×D3C2311yescharacteristic
103C2×C4×D3C2314yes—
104C2×Dic6—22no—
105C2×Dic6C2312yes—
106C3×Q16C2314yescomplemented
107C3×SD16C2318yescomplemented
108C3×D8C2314yescomplemented
109C2×C3×C8C2311yescharacteristic
110C2×C3×C8C2311yescharacteristic
111C2×C3×C8C2314yescomplemented
112#216C2318yescomplemented
113#215C2318yescomplemented
114#214C2318yescomplemented
115#213C2318yescomplemented
116C2×C3⋊C8C2311yescharacteristic
117C2×C3⋊C8C2311yescharacteristic
118C2×C3⋊C8C2314yescomplemented
119Dic12C2314yescomplemented
120D24C2314yescomplemented
121#204C2318yescomplemented
122D3×C8C2314yes—
123D3×C8C2314yes—
124D3×C8C2314yescomplemented
125D3×C8C2314yescomplemented
126C2×#41—316no—
127C2×#41—32no—
128C2×#41—32no—
129C2×#41—32no—
130C2×#41—62no—
131C2×#41—62no—
132C2×#41—68no—
133C2×#41C2×D312yescomplemented
134C22×Q8—32no—
135C22×D4—32no—
136C22×D4—62no—
137C23×C4—31no—
138C23×C4—62no—
139#135—316no—
140#135—38no—
141#135—316no—
142#135—38no—
143#135—38no—
144#135C2×D318yesdirect product factor
145C2×Q16—32no—
146C2×Q16—38no—
147C2×Q16—31no—
148C2×Q16C2×D311yescharacteristic, complemented
149C2×SD16—32no—
150C2×SD16—32no—
151C2×SD16—316no—
152C2×SD16—32no—
153C2×SD16C2×D312yescomplemented
154C2×D8—32no—
155C2×D8—38no—
156C2×D8—31no—
157C2×D8C2×D311yescharacteristic, complemented
158C22×C8—31no—
159C22×C8—31no—
160C22×C8—31no—
161C22×C8—31no—
162C22×C8—31no—
163C22×C8—38no—
164C22×C8C2×D311yescharacteristic, complemented
165C23×C3—22no—
166C23×C3C2×D411yescharacteristic
167C22×D3—24no—
168C22×D3—22no—
169C22×D3—28no—
170C22×D3—48no—
171C22×D3C2×D411yescharacteristic
172C22×D3C2×D414yes—
173C22×D3C2×D411yescharacteristic
174C3×Q8—22no—
175C3×Q8C2414yes—
176C3×D4—28no—
177C3×D4—22no—
178C3×D4C2414yes—
179C2×C3×C4—22no—
180C2×C3×C4—28no—
181C2×C3×C4C2×D412yes—
182C2×C3×C4C2×D411yescharacteristic
183C2×C3×C4C2411yescharacteristic
184C2×C3×C4C2412yes—
185#67—28no—
186#67—28no—
187#67—28no—
188C2×Dic3—22no—
189C2×Dic3—28no—
190C2×Dic3C2×D411yescharacteristic
191C2×Dic3C2×D411yescharacteristic
192C2×Dic3C2×D414yes—
193D12—28no—
194D12—22no—
195D12C2414yes—
196C4×D3—28no—
197C4×D3—28no—
198C4×D3—28no—
199C4×D3C2×D414yes—
200C4×D3C2×D414yes—
201C4×D3C2×D412yes—
202C4×D3C2×D412yes—
203C4×D3C2412yes—
204C4×D3C2412yes—
205Dic6—22no—
206Dic6—28no—
207Dic6C2414yes—
208C3×C8C2412yes—
209C3×C8C2412yes—
210C3⋊C8C2412yes—
211C3⋊C8C2412yes—
212C24—31no—
213C24—62no—
214#41—24no—
215#41—38no—
216#41—38no—
217#41—38no—
218#41—616no—
219#41—616no—
220#41—64no—
221#41—64no—
222#41—64no—
223#41C22×D318yescomplemented
224C2×Q8—38no—
225C2×Q8—32no—
226C2×Q8—62no—
227C2×Q8—64no—
228C2×Q8C22×D312yes—
229C2×D4—22no—
230C2×D4—38no—
231C2×D4—32no—
232C2×D4—62no—
233C2×D4—64no—
234C2×D4—62no—
235C2×D4—616no—
236C2×D4—62no—
237C2×D4—62no—
238C2×D4C22×D312yes—
239C22×C4—22no—
240C22×C4—31no—
241C22×C4—34no—
242C22×C4—31no—
243C22×C4—31no—
244C22×C4—31no—
245C22×C4—31no—
246C22×C4—34no—
247C22×C4—62no—
248C22×C4—616no—
249C22×C4—62no—
250C22×C4—62no—
251C22×C4—62no—
252C22×C4C22×D311yescharacteristic
253Q16—38no—
254Q16—34no—
255Q16C22×D314yescomplemented
256SD16—38no—
257SD16—38no—
258SD16—38no—
259SD16C22×D318yescomplemented
260D8—38no—
261D8—34no—
262D8C22×D314yescomplemented
263C2×C8—31no—
264C2×C8—31no—
265C2×C8—34no—
266C2×C8—34no—
267C2×C8—34no—
268C2×C8—34no—
269C2×C8—34no—
270C2×C8C22×D311yescharacteristic
271C2×C8C22×D311yescharacteristic
272C2×C8C22×D314yescomplemented
273C22×C3—22no—
274C22×C3—24no—
275C22×C3—44no—
276C22×C3C22×D412yes—
277C22×C3C22×D411yescharacteristic
278C2×D3—22no—
279C2×D3—28no—
280C2×D3—24no—
281C2×D3—44no—
282C2×D3—416no—
283C2×D3#13514yesdirect product factor
284C2×D3C22×D412yes—
285C2×D3C22×D412yes—
286C3×C4—24no—
287C3×C4C22×D411yescharacteristic
288C3×C4C22×D412yes—
289C3×C4C2511yescharacteristic
290Dic3—24no—
291Dic3C22×D412yes—
292Dic3C22×D412yes—
293C23—22no—
294C23—31no—
295C23—34no—
296C23—31no—
297C23—64no—
298C23—68no—
299C23—62no—
300C23—128no—
301C23D3×D411yescharacteristic
302Q8—22no—
303Q8—34no—
304Q8—68no—
305Q8—62no—
306Q8C23×D314yes—
307D4—28no—
308D4—22no—
309D4—34no—
310D4—68no—
311D4—68no—
312D4—68no—
313D4—68no—
314D4—62no—
315D4C23×D314yes—
316C2×C4—22no—
317C2×C4—28no—
318C2×C4—31no—
319C2×C4—31no—
320C2×C4—34no—
321C2×C4—34no—
322C2×C4—32no—
323C2×C4—32no—
324C2×C4—34no—
325C2×C4—32no—
326C2×C4—32no—
327C2×C4—68no—
328C2×C4—68no—
329C2×C4—68no—
330C2×C4—62no—
331C2×C4—68no—
332C2×C4D3×D412yes—
333C2×C4D3×D411yescharacteristic
334C2×C4C23×D311yescharacteristic
335C2×C4C23×D312yes—
336C8—32no—
337C8—32no—
338C8C23×D312yes—
339C8C23×D312yes—
340C2×C3—22no—
341C2×C3—44no—
342C2×C3C2×#13512yescomplemented
343C2×C3C23×D411yescharacteristic
344D3—22no—
345D3—44no—
346D3C2×#13514yesdirect product factor
347C22—22no—
348C22—24no—
349C22—32no—
350C22—34no—
351C22—32no—
352C22—44no—
353C22—68no—
354C22—62no—
355C22—64no—
356C22—1216no—
357C22—124no—
358C22C2×D3×D412yes—
359C22C2×D3×D411yescharacteristic
360C4—24no—
361C4—32no—
362C4—32no—
363C4—64no—
364C4C2×D3×D412yes—
365C4C2×D3×D411yescharacteristic
366C4C24×D311yescharacteristic
367C3C22×#13511yescharacteristic, complemented, Sylow
368C2—22no—
369C2—34no—
370C2—44no—
371C2—62no—
372C2—124no—
373C2D3×#13512yesdirect product factor
374C2C22×D3×D411yescharacteristic
subgroupG/H
centerC2×C4D3×D4
commutator, cosocleC3×C4C25
FrattiniC4C24×D3
FittingC2×C3×#135C2
socleC22×C3C22×D4
hypercenterC2×#135D3
hypocenterC3C22×#135
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×D3×#41C2semidirect
2. C2×C3×#135C2semidirect
3. C2×#950C2semidirect
4. D3×#135C2direct (N × H)
5. C2×#919C2semidirect
6. C2×D3×Q16C2semidirect
7. C2×#916C2semidirect
8. C2×D3×SD16C2semidirect
9. C2×#912C2semidirect
10. C2×D3×D8C2semidirect
11. C2×#904C2semidirect
12. C22×D3×C8C2semidirect
14. C2×C3×#41C22semidirect
16. D3×#41C22semidirect
17. C2×#239C22semidirect
20. C2×#237C22semidirect
24. C2×#235C22semidirect
27. C3×#135C22semidirect
28. C2×C3×Q16C22semidirect
29. C2×C3×SD16C22semidirect
30. C2×C3×D8C22semidirect
31. C22×C3×C8C22semidirect
32. #950C22semidirect
33. C2×#216C22semidirect
34. C2×#215C22semidirect
35. C2×#214C22semidirect
36. C2×#213C22semidirect
37. C22×C3⋊C8C22semidirect
38. #919C22semidirect
39. D3×Q16C22semidirect
40. #916C22semidirect
41. D3×SD16C22semidirect
42. #912C22semidirect
43. D3×D8C22semidirect
44. C2×Dic12C22semidirect
45. #904C22semidirect
46. C2×D24C22semidirect
47. C2×#204C22semidirect
50. C2×D3×C8C22semidirect
51. C2×D3×C8C22semidirect
52. C2×D3×C8C22semidirect
60. C2×#135D3direct (N × H)
68. C3×#41C23semidirect
80. #239C23semidirect
85. #237C23semidirect
91. #235C23semidirect
106. C3×Q16C23semidirect
107. C3×SD16C23semidirect
108. C3×D8C23semidirect
111. C2×C3×C8C23semidirect
112. #216C23semidirect
113. #215C23semidirect
114. #214C23semidirect
115. #213C23semidirect
118. C2×C3⋊C8C23semidirect
119. Dic12C23semidirect
120. D24C23semidirect
121. #204C23semidirect
124. D3×C8C23semidirect
125. D3×C8C23semidirect
133. C2×#41C2×D3semidirect
144. #135C2×D3direct (N × H)
148. C2×Q16C2×D3semidirect
153. C2×SD16C2×D3semidirect
157. C2×D8C2×D3semidirect
164. C22×C8C2×D3semidirect
223. #41C22×D3semidirect
255. Q16C22×D3semidirect
259. SD16C22×D3semidirect
262. D8C22×D3semidirect
272. C2×C8C22×D3semidirect
283. C2×D3#135direct (N × H)
342. C2×C3C2×#135semidirect
346. D3C2×#135direct (N × H)
367. C3C22×#135semidirect
373. C2D3×#135direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D3×#412
C2×C3×#1352
C2×#9502
D3×#1352
C2×#9192
C2×D3×Q162
C2×#9162
C2×D3×SD162
C2×#9122
C2×D3×D82
C2×#9042
C22×D3×C82
C22×#1353