Finite Group Databasebeta

← C2×#5663 #85996

Subgroups — C2×#5663 #85996

Order 384.

1260 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#123C211yesmaximal, characteristic, complemented
2C2×#940C211yesmaximal, characteristic, complemented
3C2×#939C211yesmaximal, characteristic, complemented
4C2×#930C211yesmaximal, characteristic, complemented
5C2×C4×#67C211yesmaximal, characteristic, complemented
6#5663C2116yesmaximal, direct product factor
7C2×#895C211yesmaximal, characteristic, complemented
8C2×#894C211yesmaximal, characteristic, complemented
9C2×#892C211yesmaximal, characteristic, complemented
10C2×#889C211yesmaximal, characteristic, complemented
11C2×#886C211yesmaximal, characteristic, complemented
12C2×#884C211yesmaximal, characteristic, complemented
13C2×#884C211yesmaximal, characteristic, complemented
14C2×#884C211yesmaximal, characteristic, complemented
15C2×#883C211yesmaximal, characteristic, complemented
16C2×#67⋊C4C211yesmaximal, characteristic, complemented
17C2×#540—31nomaximal, Sylow
18C22×C3×D4C2211yescharacteristic
19C23×C3×C4C2211yescharacteristic
20C22×#67C2211yescharacteristic
21C22×#67C2211yescharacteristic
22C22×#67C2211yescharacteristic
23C22×#67C2211yescharacteristic
24C22×#67C2211yescharacteristic
25C22×#67C2211yescharacteristic
26C23×Dic3C2211yescharacteristic
27C22×D12C2211yescharacteristic
28C22×D12C2211yescharacteristic
29C22×D12C2211yescharacteristic
30C22×C4×D3C2211yescharacteristic
31C22×C4×D3C2211yescharacteristic
32C22×C4×D3C2211yescharacteristic
33C3×#123C2218yescomplemented
34C2×C3×C4⋊C4C2211yescharacteristic
35C2×C3×C4⋊C4C2211yescharacteristic
36C2×C3×C22⋊C4C2211yescharacteristic
37C2×C3×C22⋊C4C2211yescharacteristic
38C2×C3×C22⋊C4C2211yescharacteristic
39C2×#217C2211yescharacteristic
40#940C2218yescomplemented
41#939C2218yescomplemented
42#930C2218yescomplemented
43C4×#67C2218yescomplemented
44C2×(C2×D3)⋊C4C2211yescharacteristic
45C2×(C2×D3)⋊C4C2211yescharacteristic
46C2×(C2×D3)⋊C4C2211yescharacteristic
47C2×(C2×D3)⋊C4C2211yescharacteristic
48C2×(C2×D3)⋊C4C2211yescharacteristic
49C2×(C2×D3)⋊C4C2211yescharacteristic
50C2×C4⋊Dic3C2211yescharacteristic
51C2×C4⋊Dic3C2211yescharacteristic
52C2×Dic3⋊C4C2211yescharacteristic
53C2×Dic3⋊C4C2211yescharacteristic
54C2×Dic3⋊C4C2211yescharacteristic
55C2×Dic3⋊C4C2211yescharacteristic
56C2×C4×Dic3C2211yescharacteristic
57C2×C4×Dic3C2211yescharacteristic
58#895C2218yescomplemented
59#894C2218yescomplemented
60#892C2218yescomplemented
61#889C2218yescomplemented
62#886C2218yescomplemented
63#884C2218yescomplemented
64#884C2218yescomplemented
65#884C2218yescomplemented
66#883C2218yescomplemented
67#67⋊C4C2218yescomplemented
68#540—316no—
69C2×#127—31no—
70C2×#125—31no—
71C2×#123—31no—
72C2×#123—31no—
73C2×#123—31no—
74C2×#123D311yescharacteristic, complemented
75C2×#121—31no—
76C2×#121—31no—
77C2×#121—31no—
78C2×#121—31no—
79C2×#121—31no—
80C2×#121—31no—
81C2×C4×D4—31no—
82C2×C4×D4—31no—
83C2×#117—31no—
84C24×C3C2311yescharacteristic
85C24×C3C2311yescharacteristic
86C23×D3C2311yescharacteristic
87C23×D3C2311yescharacteristic
88C23×D3C2311yescharacteristic
89C2×C3×D4—42no—
90C2×C3×D4C2314yes—
91C22×C3×C4—42no—
92C22×C3×C4C2311yescharacteristic
93C22×C3×C4C2311yescharacteristic
94C22×C3×C4C2311yescharacteristic
95C22×C3×C4C2311yescharacteristic
96C22×C3×C4C2311yescharacteristic
97C22×C3×C4C2314yes—
98C2×#67—24no—
99C2×#67—24no—
100C2×#67—42no—
101C2×#67—42no—
102C2×#67—42no—
103C2×#67—42no—
104C2×#67C2314yes—
105C2×#67C2314yes—
106C2×#67C2314yes—
107C2×#67C2314yes—
108C2×#67C2314yes—
109C2×#67C2314yes—
110C22×Dic3—42no—
111C22×Dic3C2311yescharacteristic
112C22×Dic3C2311yescharacteristic
113C22×Dic3C2311yescharacteristic
114C22×Dic3C2311yescharacteristic
115C22×Dic3C2314yes—
116C22×Dic3C2311yescharacteristic
117C2×D12—42no—
118C2×D12—42no—
119C2×D12—42no—
120C2×D12C2314yes—
121C2×D12C2314yes—
122C2×D12C2314yes—
123C2×C4×D3—24no—
124C2×C4×D3—42no—
125C2×C4×D3—42no—
126C2×C4×D3C2314yes—
127C2×C4×D3C2314yes—
128C2×C4×D3C2314yes—
129C3×C4⋊C4C2314yes—
130C3×C4⋊C4C2314yes—
131C3×C22⋊C4C2314yes—
132C3×C22⋊C4C2314yes—
133C3×C22⋊C4C2314yes—
134#217C2314yes—
135(C2×D3)⋊C4C2314yes—
136(C2×D3)⋊C4C2314yes—
137(C2×D3)⋊C4C2314yes—
138(C2×D3)⋊C4C2314yes—
139(C2×D3)⋊C4C2314yes—
140(C2×D3)⋊C4C2314yes—
141C4⋊Dic3C2314yes—
142C4⋊Dic3C2314yes—
143Dic3⋊C4C2314yes—
144Dic3⋊C4C2314yes—
145Dic3⋊C4C2314yes—
146Dic3⋊C4C2314yes—
147C4×Dic3C2314yes—
148C4×Dic3C2314yes—
149C22×D4—31no—
150C22×D4—31no—
151C22×D4—31no—
152C22×D4—31no—
153C22×D4—31no—
154C22×D4—31no—
155C22×D4—31no—
156C22×D4—31no—
157C22×D4—31no—
158C22×D4C2×D311yescharacteristic
159C23×C4—31no—
160C23×C4—31no—
161C23×C4—31no—
162C23×C4—31no—
163C23×C4C2×D311yescharacteristic
164#127—38no—
165#125—38no—
166#123—38no—
167#123—38no—
168#123—38no—
169#123C2×D318yescomplemented
170#121—38no—
171#121—38no—
172#121—38no—
173#121—38no—
174#121—38no—
175#121—38no—
176C4×D4—38no—
177C4×D4—38no—
178#117—38no—
179C2×C4⋊C4—31no—
180C2×C4⋊C4—31no—
181C2×C4⋊C4—31no—
182C2×C4⋊C4—31no—
183C2×C4⋊C4—31no—
184C2×C4⋊C4—31no—
185C2×C4⋊C4C2×D311yescharacteristic
186C2×C4⋊C4C2×D311yescharacteristic
187C2×C22⋊C4—31no—
188C2×C22⋊C4—31no—
189C2×C22⋊C4—31no—
190C2×C22⋊C4—31no—
191C2×C22⋊C4—31no—
192C2×C22⋊C4—31no—
193C2×C22⋊C4—31no—
194C2×C22⋊C4C2×D311yescharacteristic
195C2×C22⋊C4C2×D311yescharacteristic
196C2×C22⋊C4C2×D311yescharacteristic
197C2×C42—31no—
198C2×C42—31no—
199C23×C3—22no—
200C23×C3—22no—
201C23×C3—22no—
202C23×C3—22no—
203C23×C3—22no—
204C23×C3—22no—
205C23×C3C2412yes—
206C23×C3C2412yes—
207C23×C3C2411yescharacteristic
208C22×D3—22no—
209C22×D3—22no—
210C22×D3—22no—
211C22×D3—22no—
212C22×D3—22no—
213C22×D3—22no—
214C22×D3—22no—
215C22×D3—22no—
216C22×D3—22no—
217C22×D3C2412yes—
218C22×D3C2412yes—
219C22×D3C2412yes—
220C3×D4—44no—
221C2×C3×C4—22no—
222C2×C3×C4—22no—
223C2×C3×C4—22no—
224C2×C3×C4—22no—
225C2×C3×C4—22no—
226C2×C3×C4—44no—
227C2×C3×C4C2412yes—
228C2×C3×C4C2412yes—
229C2×C3×C4C2412yes—
230C2×C3×C4C2412yes—
231C2×C3×C4C2412yes—
232#67—28no—
233#67—28no—
234#67—44no—
235#67—44no—
236#67—44no—
237#67—44no—
238C2×Dic3—22no—
239C2×Dic3—22no—
240C2×Dic3—22no—
241C2×Dic3—22no—
242C2×Dic3—44no—
243C2×Dic3#4114yes—
244C2×Dic3C2412yes—
245C2×Dic3C2412yes—
246C2×Dic3C2412yes—
247C2×Dic3C2412yes—
248C2×Dic3C2412yes—
249D12—44no—
250D12—44no—
251D12—44no—
252C4×D3—28no—
253C4×D3—44no—
254C4×D3—44no—
255C24—31no—
256C24—31no—
257C24—31no—
258C24C22×D311yescharacteristic
259C24C22×D311yescharacteristic
260C2×D4—34no—
261C2×D4—34no—
262C2×D4—34no—
263C2×D4—34no—
264C2×D4—34no—
265C2×D4—34no—
266C2×D4—34no—
267C2×D4—34no—
268C2×D4—34no—
269C2×D4—42no—
270C2×D4—64no—
271C2×D4—64no—
272C2×D4—122no—
273C2×D4—122no—
274C2×D4—122no—
275C2×D4—122no—
276C2×D4—122no—
277C2×D4—122no—
278C2×D4—122no—
279C2×D4C22×D314yes—
280C22×C4—31no—
281C22×C4—31no—
282C22×C4—31no—
283C22×C4—31no—
284C22×C4—31no—
285C22×C4—34no—
286C22×C4—34no—
287C22×C4—34no—
288C22×C4—34no—
289C22×C4—42no—
290C22×C4—64no—
291C22×C4—122no—
292C22×C4—122no—
293C22×C4—122no—
294C22×C4C22×D311yescharacteristic
295C22×C4C22×D311yescharacteristic
296C22×C4C22×D311yescharacteristic
297C22×C4C22×D311yescharacteristic
298C22×C4C22×D311yescharacteristic
299C22×C4C22×D314yes—
300C4⋊C4—34no—
301C4⋊C4—34no—
302C4⋊C4—34no—
303C4⋊C4—34no—
304C4⋊C4—34no—
305C4⋊C4—34no—
306C4⋊C4C22×D314yes—
307C4⋊C4C22×D314yes—
308C22⋊C4—34no—
309C22⋊C4—34no—
310C22⋊C4—34no—
311C22⋊C4—34no—
312C22⋊C4—34no—
313C22⋊C4—34no—
314C22⋊C4—34no—
315C22⋊C4C22×D314yes—
316C22⋊C4C22×D314yes—
317C22⋊C4C22×D314yes—
318C42—34no—
319C42—34no—
320C22×C3—22no—
321C22×C3—22no—
322C22×C3—22no—
323C22×C3—22no—
324C22×C3—22no—
325C22×C3—22no—
326C22×C3—44no—
327C22×C3—44no—
328C22×C3C2×#4112yes—
329C22×C3H(5,𝔽2)12yes—
330C22×C3H(5,𝔽2)12yes—
331C22×C3C2511yescharacteristic
332C2×D3—22no—
333C2×D3—22no—
334C2×D3—22no—
335C2×D3—22no—
336C2×D3—22no—
337C2×D3—22no—
338C2×D3—22no—
339C2×D3—22no—
340C2×D3—22no—
341C2×D3—44no—
342C2×D3—44no—
343C2×D3—44no—
344C3×C4—22no—
345C3×C4—22no—
346C3×C4—22no—
347C3×C4—22no—
348C3×C4—22no—
349Dic3—22no—
350Dic3—22no—
351Dic3—22no—
352Dic3—22no—
353Dic3C2×#4114yes—
354C23—22no—
355C23—22no—
356C23—22no—
357C23—22no—
358C23—22no—
359C23—22no—
360C23—32no—
361C23—32no—
362C23—32no—
363C23—62no—
364C23—62no—
365C23—62no—
366C23—62no—
367C23—62no—
368C23—62no—
369C23—62no—
370C23—62no—
371C23—62no—
372C23C23×D312yes—
373C23C23×D312yes—
374C23C23×D311yescharacteristic
375D4—44no—
376D4—68no—
377D4—68no—
378D4—124no—
379D4—124no—
380D4—124no—
381D4—124no—
382D4—124no—
383D4—124no—
384D4—124no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—34no—
391C2×C4—32no—
392C2×C4—32no—
393C2×C4—32no—
394C2×C4—32no—
395C2×C4—32no—
396C2×C4—44no—
397C2×C4—68no—
398C2×C4—62no—
399C2×C4—62no—
400C2×C4—62no—
401C2×C4—62no—
402C2×C4—124no—
403C2×C4—124no—
404C2×C4—124no—
405C2×C4C23×D312yes—
406C2×C4C23×D312yes—
407C2×C4C23×D312yes—
408C2×C4C23×D312yes—
409C2×C4C23×D312yes—
410C2×C3—42no—
411C2×C3—42no—
412C2×C3#54014yescomplemented
413C2×C3C22×#4111yescharacteristic
414C2×C3C2×H(5,𝔽2)11yescharacteristic
415C2×C3C2×H(5,𝔽2)11yescharacteristic
416D3—42no—
417D3—42no—
418D3—42no—
419C22—22no—
420C22—22no—
421C22—22no—
422C22—22no—
423C22—22no—
424C22—22no—
425C22—44no—
426C22—44no—
427C22—62no—
428C22—62no—
429C22—62no—
430C22—62no—
431C22—62no—
432C22—62no—
433C22—62no—
434C22—62no—
435C22—62no—
436C22—124no—
437C22—124no—
438C22—124no—
439C22#100412yes—
440C22D3×#4112yes—
441C22#100912yes—
442C22C24×D311yescharacteristic
443C4—22no—
444C4—22no—
445C4—22no—
446C4—22no—
447C4—22no—
448C4—34no—
449C4—62no—
450C4—62no—
451C4—62no—
452C4—62no—
453C3C2×#54011yescharacteristic, complemented, Sylow
454C2—42no—
455C2—42no—
456C2—122no—
457C2—122no—
458C2—122no—
459C2#566314yesdirect product factor
460C2C2×#100411yescharacteristic
461C2C2×D3×#4111yescharacteristic
462C2C2×#100911yescharacteristic
subgroupG/H
centerC23C23×D3
commutator, cosocleC22×C3C25
FrattiniC22C24×D3
FittingC2×C3×#123C2
socleC23×C3C24
hypercenterC2×#123D3
hypocenterC3C2×#540
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×C3×#123C2semidirect
2. C2×#940C2semidirect
3. C2×#939C2semidirect
4. C2×#930C2semidirect
5. C2×C4×#67C2semidirect
6. #5663C2direct (N × H)
7. C2×#895C2semidirect
8. C2×#894C2semidirect
9. C2×#892C2semidirect
10. C2×#889C2semidirect
11. C2×#886C2semidirect
12. C2×#884C2semidirect
13. C2×#884C2semidirect
14. C2×#884C2semidirect
15. C2×#883C2semidirect
16. C2×#67⋊C4C2semidirect
33. C3×#123C22semidirect
40. #940C22semidirect
41. #939C22semidirect
42. #930C22semidirect
43. C4×#67C22semidirect
58. #895C22semidirect
59. #894C22semidirect
60. #892C22semidirect
61. #889C22semidirect
62. #886C22semidirect
63. #884C22semidirect
64. #884C22semidirect
65. #884C22semidirect
66. #883C22semidirect
67. #67⋊C4C22semidirect
74. C2×#123D3semidirect
169. #123C2×D3semidirect
412. C2×C3#540semidirect
453. C3C2×#540semidirect
459. C2#5663direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#1232
C2×#9402
C2×#9392
C2×#9302
C2×C4×#672
#56632
C2×#8952
C2×#8942
C2×#8922
C2×#8892
C2×#8862
C2×#8842
C2×#8832
C2×#67⋊C42
C2×#5403