Finite Group Databasebeta

← C2×#5654 #86008

Subgroups — C2×#5654 #86008

Order 384.

1900 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×D4C211yesmaximal, characteristic, complemented
2C22×#235C211yesmaximal, characteristic, complemented
3C2×C3×#123C211yesmaximal, characteristic, complemented
4C2×#939C211yesmaximal, characteristic, complemented
5C22×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6#5654C2116yesmaximal, direct product factor
7C2×#896C211yesmaximal, characteristic, complemented
8C2×#895C211yesmaximal, characteristic, complemented
9C2×#894C211yesmaximal, characteristic, complemented
10C2×#893C211yesmaximal, characteristic, complemented
11C2×#885C211yesmaximal, characteristic, complemented
12C2×#884C211yesmaximal, characteristic, complemented
13C2×#882C211yesmaximal, characteristic, complemented
14C2×#882C211yesmaximal, characteristic, complemented
15C2×#67⋊C4C211yesmaximal, characteristic, complemented
16C2×D3×C22⋊C4C211yesmaximal, characteristic, complemented
17C2×#546—31nomaximal, Sylow
18C24×D3C2211yescharacteristic
19C24×D3C2211yescharacteristic
20C22×C3×D4C2211yescharacteristic
21C23×C3×C4C2211yescharacteristic, complemented
22C22×#67C2211yescharacteristic
23C22×#67C2211yescharacteristic
24C22×#67C2211yescharacteristic, complemented
25C22×#67C2211yescharacteristic, complemented
26C23×Dic3C2211yescharacteristic, complemented
27C2×D3×D4—28no—
28C2×D3×D4C2218yescomplemented
29C2×#235—28no—
30C2×#235C2218yescomplemented
31C22×D12C2211yescharacteristic
32C22×D12C2211yescharacteristic
33C22×D12C2211yescharacteristic, complemented
34C22×D12C2211yescharacteristic, complemented
35C22×C4×D3C2211yescharacteristic
36C22×C4×D3C2211yescharacteristic, complemented
37C22×C4×D3C2211yescharacteristic, complemented
38C22×C4×D3C2211yescharacteristic, complemented
39C22×Dic6C2211yescharacteristic, complemented
40C3×#123C2218yescomplemented
41C2×C3×C4⋊C4C2211yescharacteristic, complemented
42C2×C3×C4⋊C4C2211yescharacteristic, complemented
43C2×C3×C22⋊C4C2211yescharacteristic, complemented
44C2×C3×C22⋊C4C2211yescharacteristic, complemented
45C2×C3×C22⋊C4C2211yescharacteristic, complemented
46C2×#217C2211yescharacteristic, complemented
47#939C2218yescomplemented
48C2×(C2×D3)⋊C4C2211yescharacteristic
49C2×(C2×D3)⋊C4C2211yescharacteristic
50C2×(C2×D3)⋊C4C2211yescharacteristic
51C2×(C2×D3)⋊C4C2218yescomplemented
52C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
53C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
54C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
55C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
56C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
57C2×Dic3⋊C4C2211yescharacteristic, complemented
58C2×Dic3⋊C4C2211yescharacteristic, complemented
59C2×C4×Dic3C2211yescharacteristic, complemented
60#896C2218yescomplemented
61#895C2218yescomplemented
62#894C2218yescomplemented
63#893C2218yescomplemented
64#885C2218yescomplemented
65#884C2218yescomplemented
66#882C2218yescomplemented
67#882C2218yescomplemented
68#67⋊C4C2218yescomplemented
69D3×C22⋊C4C2218yescomplemented
70C22×#41—31no—
71C23×D4—31no—
72#546—316no—
73C2×#124—31no—
74C2×#123—31no—
75C2×#123D311yescharacteristic, complemented
76C2×C22⋊Q8—31no—
77C2×#121—31no—
78C2×#121—31no—
79C2×#121—31no—
80C2×#120—31no—
81C2×#120—31no—
82C2×C4×D4—31no—
83C2×C4×D4—31no—
84C22×C22⋊C4—31no—
85C22×C22⋊C4—31no—
86C24×C3C2311yescharacteristic
87C24×C3C2311yescharacteristic
88C23×D3—24no—
89C23×D3—24no—
90C23×D3—24no—
91C23×D3—24no—
92C23×D3—42no—
93C23×D3—42no—
94C23×D3C2311yescharacteristic
95C23×D3C2311yescharacteristic
96C23×D3C2314yes—
97C23×D3C2314yes—
98C23×D3C2311yescharacteristic
99C23×D3C2311yescharacteristic
100C2×C3×D4—24no—
101C2×C3×D4C2314yes—
102C22×C3×C4—24no—
103C22×C3×C4C2311yescharacteristic
104C22×C3×C4C2311yescharacteristic
105C22×C3×C4C2311yescharacteristic
106C22×C3×C4C2311yescharacteristic
107C22×C3×C4C2311yescharacteristic
108C22×C3×C4C2314yescomplemented
109C2×#67—24no—
110C2×#67—24no—
111C2×#67—42no—
112C2×#67D418yescomplemented
113C2×#67C2314yes—
114C2×#67C2314yes—
115C2×#67C2314yescomplemented
116C2×#67C2314yescomplemented
117C22×Dic3—42no—
118C22×Dic3C2311yescharacteristic
119C22×Dic3C2311yescharacteristic
120C22×Dic3C2311yescharacteristic
121C22×Dic3C2311yescharacteristic
122C22×Dic3C2314yescomplemented
123D3×D4—232no—
124#235—232no—
125C2×D12—24no—
126C2×D12—24no—
127C2×D12—24no—
128C2×D12—42no—
129C2×D12C2314yes—
130C2×D12C2314yes—
131C2×D12C2314yescomplemented
132C2×D12C2314yescomplemented
133C2×C4×D3—24no—
134C2×C4×D3—24no—
135C2×C4×D3—24no—
136C2×C4×D3—42no—
137C2×C4×D3C2314yes—
138C2×C4×D3C2314yescomplemented
139C2×C4×D3C2314yescomplemented
140C2×C4×D3C2314yescomplemented
141C2×Dic6—24no—
142C2×Dic6C2314yescomplemented
143C3×C4⋊C4C2314yescomplemented
144C3×C4⋊C4C2314yescomplemented
145C3×C22⋊C4C2314yescomplemented
146C3×C22⋊C4C2314yescomplemented
147C3×C22⋊C4C2314yescomplemented
148#217C2314yescomplemented
149(C2×D3)⋊C4C2314yes—
150(C2×D3)⋊C4C2314yes—
151(C2×D3)⋊C4C2314yes—
152(C2×D3)⋊C4C2314yescomplemented
153(C2×D3)⋊C4C2314yescomplemented
154(C2×D3)⋊C4C2314yescomplemented
155(C2×D3)⋊C4C2314yescomplemented
156(C2×D3)⋊C4C2314yescomplemented
157Dic3⋊C4C2314yescomplemented
158Dic3⋊C4C2314yescomplemented
159C4×Dic3C2314yescomplemented
160C25—31no—
161C25—31no—
162C2×#41—38no—
163C2×#41—68no—
164C22×Q8—31no—
165C22×D4—31no—
166C22×D4—31no—
167C22×D4—31no—
168C22×D4—31no—
169C22×D4—38no—
170C22×D4—31no—
171C22×D4—31no—
172C22×D4—31no—
173C22×D4—31no—
174C22×D4—68no—
175C22×D4C2×D311yescharacteristic
176C23×C4—31no—
177C23×C4—31no—
178C23×C4—31no—
179C23×C4—31no—
180C23×C4—31no—
181C23×C4C2×D311yescharacteristic, complemented
182#124—38no—
183#123—38no—
184#123C2×D318yescomplemented
185C22⋊Q8—38no—
186#121—38no—
187#121—38no—
188#121—38no—
189#120—38no—
190#120—38no—
191C4×D4—38no—
192C4×D4—38no—
193C2×C4⋊C4—31no—
194C2×C4⋊C4—31no—
195C2×C4⋊C4C2×D311yescharacteristic, complemented
196C2×C4⋊C4C2×D311yescharacteristic, complemented
197C2×C22⋊C4—31no—
198C2×C22⋊C4—31no—
199C2×C22⋊C4—31no—
200C2×C22⋊C4—31no—
201C2×C22⋊C4—31no—
202C2×C22⋊C4—31no—
203C2×C22⋊C4—31no—
204C2×C22⋊C4—31no—
205C2×C22⋊C4—31no—
206C2×C22⋊C4—38no—
207C2×C22⋊C4—38no—
208C2×C22⋊C4C2×D311yescharacteristic, complemented
209C2×C22⋊C4C2×D311yescharacteristic, complemented
210C2×C22⋊C4C2×D311yescharacteristic, complemented
211C2×C42—31no—
212C23×C3—22no—
213C23×C3—22no—
214C23×C3—22no—
215C23×C3—22no—
216C23×C3—22no—
217C23×C3C2×D414yes—
218C23×C3C2412yes—
219C23×C3C2412yes—
220C23×C3C2411yescharacteristic
221C22×D3—22no—
222C22×D3—22no—
223C22×D3—22no—
224C22×D3—22no—
225C22×D3—22no—
226C22×D3—22no—
227C22×D3—28no—
228C22×D3—22no—
229C22×D3—22no—
230C22×D3—22no—
231C22×D3—22no—
232C22×D3—28no—
233C22×D3—28no—
234C22×D3—28no—
235C22×D3—44no—
236C22×D3—44no—
237C22×D3—416no—
238C22×D3—416no—
239C22×D3C2×D414yes—
240C22×D3#4114yescomplemented
241C22×D3C2412yes—
242C22×D3C2412yes—
243C22×D3C2412yes—
244C22×D3C2412yes—
245C3×D4—28no—
246C2×C3×C4—22no—
247C2×C3×C4—22no—
248C2×C3×C4—22no—
249C2×C3×C4—28no—
250C2×C3×C4—22no—
251C2×C3×C4—22no—
252C2×C3×C4C2412yes—
253C2×C3×C4C2412yes—
254C2×C3×C4C2412yes—
255C2×C3×C4C2412yes—
256C2×C3×C4C2412yes—
257#67—28no—
258#67—28no—
259#67—44no—
260#67C2×D4116yescomplemented
261C2×Dic3—22no—
262C2×Dic3—22no—
263C2×Dic3—22no—
264C2×Dic3—44no—
265C2×Dic3C2×D414yes—
266C2×Dic3C2412yes—
267C2×Dic3C2412yes—
268C2×Dic3C2412yes—
269C2×Dic3C2412yes—
270D12—28no—
271D12—28no—
272D12—28no—
273D12—44no—
274C4×D3—28no—
275C4×D3—28no—
276C4×D3—28no—
277C4×D3—44no—
278Dic6—28no—
279C24—31no—
280C24—31no—
281C24—31no—
282C24—31no—
283C24—34no—
284C24—34no—
285C24—64no—
286C24—64no—
287C24—64no—
288C24—64no—
289C24—122no—
290C24—122no—
291C24C22×D311yescharacteristic
292C24C22×D311yescharacteristic
293#41—632no—
294C2×Q8—34no—
295C2×Q8—64no—
296C2×D4—24no—
297C2×D4—38no—
298C2×D4—34no—
299C2×D4—34no—
300C2×D4—34no—
301C2×D4—34no—
302C2×D4—34no—
303C2×D4—34no—
304C2×D4—34no—
305C2×D4—34no—
306C2×D4—64no—
307C2×D4—64no—
308C2×D4—64no—
309C2×D4—64no—
310C2×D4—632no—
311C2×D4—64no—
312C2×D4—122no—
313C2×D4—122no—
314C2×D4C22×D314yes—
315C22×C4—24no—
316C22×C4—31no—
317C22×C4—31no—
318C22×C4—31no—
319C22×C4—31no—
320C22×C4—34no—
321C22×C4—34no—
322C22×C4—34no—
323C22×C4—34no—
324C22×C4—34no—
325C22×C4—64no—
326C22×C4—64no—
327C22×C4—64no—
328C22×C4—122no—
329C22×C4—122no—
330C22×C4C22×D311yescharacteristic
331C22×C4C22×D311yescharacteristic
332C22×C4C22×D311yescharacteristic
333C22×C4C22×D311yescharacteristic
334C22×C4C22×D311yescharacteristic
335C22×C4C22×D314yescomplemented
336C4⋊C4—34no—
337C4⋊C4—34no—
338C4⋊C4C22×D314yescomplemented
339C4⋊C4C22×D314yescomplemented
340C22⋊C4—34no—
341C22⋊C4—34no—
342C22⋊C4—34no—
343C22⋊C4—34no—
344C22⋊C4—34no—
345C22⋊C4—34no—
346C22⋊C4—34no—
347C22⋊C4—34no—
348C22⋊C4—34no—
349C22⋊C4C22×D314yescomplemented
350C22⋊C4C22×D314yescomplemented
351C22⋊C4C22×D314yescomplemented
352C42—34no—
353C22×C3—28no—
354C22×C3—22no—
355C22×C3—22no—
356C22×C3—22no—
357C22×C3—22no—
358C22×C3—22no—
359C22×C3—44no—
360C22×C3C22×D414yes—
361C22×C3C22×D412yes—
362C22×C3C2×#4112yes—
363C22×C3H(5,𝔽2)12yes—
364C22×C3C2511yescharacteristic
365C2×D3—28no—
366C2×D3—28no—
367C2×D3—22no—
368C2×D3—22no—
369C2×D3—22no—
370C2×D3—22no—
371C2×D3—22no—
372C2×D3—22no—
373C2×D3—22no—
374C2×D3—22no—
375C2×D3—22no—
376C2×D3—22no—
377C2×D3—416no—
378C2×D3—416no—
379C2×D3—44no—
380C2×D3—44no—
381C2×D3C22×D414yes—
382C2×D3C2×#4114yescomplemented
383C3×C4—22no—
384C3×C4—22no—
385C3×C4—22no—
386C3×C4—22no—
387C3×C4—22no—
388Dic3—22no—
389Dic3—22no—
390Dic3—22no—
391Dic3C22×D414yes—
392C23—22no—
393C23—22no—
394C23—22no—
395C23—22no—
396C23—22no—
397C23—34no—
398C23—34no—
399C23—32no—
400C23—32no—
401C23—32no—
402C23—32no—
403C23—68no—
404C23—68no—
405C23—68no—
406C23—62no—
407C23—62no—
408C23—62no—
409C23—62no—
410C23—62no—
411C23—68no—
412C23—62no—
413C23—62no—
414C23—62no—
415C23—62no—
416C23—62no—
417C23—124no—
418C23—124no—
419C23—1216no—
420C23—1216no—
421C23D3×D414yes—
422C23C23×D312yes—
423C23C23×D312yes—
424C23C23×D311yescharacteristic
425Q8—68no—
426D4—28no—
427D4—316no—
428D4—68no—
429D4—68no—
430D4—68no—
431D4—68no—
432D4—68no—
433D4—124no—
434D4—124no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—28no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—34no—
442C2×C4—32no—
443C2×C4—32no—
444C2×C4—32no—
445C2×C4—32no—
446C2×C4—68no—
447C2×C4—68no—
448C2×C4—68no—
449C2×C4—62no—
450C2×C4—62no—
451C2×C4—62no—
452C2×C4—124no—
453C2×C4—124no—
454C2×C4C23×D312yes—
455C2×C4C23×D312yes—
456C2×C4C23×D312yes—
457C2×C4C23×D312yes—
458C2×C4C23×D312yes—
459C2×C3—24no—
460C2×C3—42no—
461C2×C3#54614yescomplemented
462C2×C3C23×D411yescharacteristic
463C2×C3C22×#4111yescharacteristic
464C2×C3C2×H(5,𝔽2)11yescharacteristic
465D3—24no—
466D3—24no—
467D3—42no—
468D3—42no—
469C22—28no—
470C22—22no—
471C22—22no—
472C22—22no—
473C22—22no—
474C22—22no—
475C22—34no—
476C22—34no—
477C22—44no—
478C22—68no—
479C22—68no—
480C22—62no—
481C22—62no—
482C22—62no—
483C22—62no—
484C22—62no—
485C22—62no—
486C22—62no—
487C22—62no—
488C22—62no—
489C22—62no—
490C22—1216no—
491C22—1216no—
492C22—124no—
493C22—124no—
494C22C2×D3×D414yes—
495C22C2×D3×D412yes—
496C22D3×#4112yes—
497C22#100912yes—
498C22C24×D311yescharacteristic
499C4—22no—
500C4—22no—
501C4—22no—
502C4—22no—
503C4—22no—
504C4—34no—
505C4—62no—
506C4—62no—
507C4—62no—
508C3C2×#54611yescharacteristic, complemented, Sylow
509C2—24no—
510C2—42no—
511C2—64no—
512C2—64no—
513C2—122no—
514C2—122no—
515C2#565414yesdirect product factor
516C2C22×D3×D411yescharacteristic
517C2C2×D3×#4111yescharacteristic
518C2C2×#100911yescharacteristic
subgroupG/H
centerC23C23×D3
commutator, cosocleC22×C3C25
FrattiniC22C24×D3
FittingC2×C3×#123C2
socleC23×C3C24
hypercenterC2×#123D3
hypocenterC3C2×#546
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C22×D3×D4C2semidirect
2. C22×#235C2semidirect
3. C2×C3×#123C2semidirect
4. C2×#939C2semidirect
5. C22×(C2×D3)⋊C4C2semidirect
6. #5654C2direct (N × H)
7. C2×#896C2semidirect
8. C2×#895C2semidirect
9. C2×#894C2semidirect
10. C2×#893C2semidirect
11. C2×#885C2semidirect
12. C2×#884C2semidirect
13. C2×#882C2semidirect
14. C2×#882C2semidirect
15. C2×#67⋊C4C2semidirect
16. C2×D3×C22⋊C4C2semidirect
21. C23×C3×C4C22semidirect
24. C22×#67C22semidirect
25. C22×#67C22semidirect
26. C23×Dic3C22semidirect
28. C2×D3×D4C22semidirect
30. C2×#235C22semidirect
33. C22×D12C22semidirect
34. C22×D12C22semidirect
36. C22×C4×D3C22semidirect
37. C22×C4×D3C22semidirect
38. C22×C4×D3C22semidirect
39. C22×Dic6C22semidirect
40. C3×#123C22semidirect
41. C2×C3×C4⋊C4C22semidirect
42. C2×C3×C4⋊C4C22semidirect
43. C2×C3×C22⋊C4C22semidirect
44. C2×C3×C22⋊C4C22semidirect
45. C2×C3×C22⋊C4C22semidirect
46. C2×#217C22semidirect
47. #939C22semidirect
51. C2×(C2×D3)⋊C4C22semidirect
52. C2×(C2×D3)⋊C4C22semidirect
53. C2×(C2×D3)⋊C4C22semidirect
54. C2×(C2×D3)⋊C4C22semidirect
55. C2×(C2×D3)⋊C4C22semidirect
56. C2×(C2×D3)⋊C4C22semidirect
57. C2×Dic3⋊C4C22semidirect
58. C2×Dic3⋊C4C22semidirect
59. C2×C4×Dic3C22semidirect
60. #896C22semidirect
61. #895C22semidirect
62. #894C22semidirect
63. #893C22semidirect
64. #885C22semidirect
65. #884C22semidirect
66. #882C22semidirect
67. #882C22semidirect
68. #67⋊C4C22semidirect
69. D3×C22⋊C4C22semidirect
75. C2×#123D3semidirect
108. C22×C3×C4C23semidirect
112. C2×#67D4semidirect
115. C2×#67C23semidirect
116. C2×#67C23semidirect
122. C22×Dic3C23semidirect
131. C2×D12C23semidirect
132. C2×D12C23semidirect
138. C2×C4×D3C23semidirect
139. C2×C4×D3C23semidirect
140. C2×C4×D3C23semidirect
142. C2×Dic6C23semidirect
143. C3×C4⋊C4C23semidirect
144. C3×C4⋊C4C23semidirect
145. C3×C22⋊C4C23semidirect
146. C3×C22⋊C4C23semidirect
147. C3×C22⋊C4C23semidirect
148. #217C23semidirect
152. (C2×D3)⋊C4C23semidirect
153. (C2×D3)⋊C4C23semidirect
154. (C2×D3)⋊C4C23semidirect
155. (C2×D3)⋊C4C23semidirect
156. (C2×D3)⋊C4C23semidirect
157. Dic3⋊C4C23semidirect
158. Dic3⋊C4C23semidirect
159. C4×Dic3C23semidirect
181. C23×C4C2×D3semidirect
184. #123C2×D3semidirect
195. C2×C4⋊C4C2×D3semidirect
196. C2×C4⋊C4C2×D3semidirect
208. C2×C22⋊C4C2×D3semidirect
209. C2×C22⋊C4C2×D3semidirect
210. C2×C22⋊C4C2×D3semidirect
240. C22×D3#41semidirect
260. #67C2×D4semidirect
335. C22×C4C22×D3semidirect
338. C4⋊C4C22×D3semidirect
339. C4⋊C4C22×D3semidirect
349. C22⋊C4C22×D3semidirect
350. C22⋊C4C22×D3semidirect
351. C22⋊C4C22×D3semidirect
382. C2×D3C2×#41semidirect
461. C2×C3#546semidirect
508. C3C2×#546semidirect
515. C2#5654direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×D42
C22×#2352
C2×C3×#1232
C2×#9392
C22×(C2×D3)⋊C42
#56542
C2×#8962
C2×#8952
C2×#8942
C2×#8932
C2×#8852
C2×#8842
C2×#8822
C2×#67⋊C42
C2×D3×C22⋊C42
C2×#5463