Finite Group Databasebeta

← C3×#5637 #10595734

Subgroups — C3×#5637 #10595734

Order 576.

533 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C22⋊Q8C211yesmaximal, characteristic, complemented
2C3×#947C211yesmaximal, characteristic, complemented
3C3×#946C211yesmaximal, characteristic, complemented
4C3×C4×#67C211yesmaximal, characteristic, complemented
5C2×C3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6C3×#898C211yesmaximal, characteristic, complemented
7C3×#898C211yesmaximal, characteristic, complemented
8C3×#894C211yesmaximal, characteristic, complemented
9C3×#894C211yesmaximal, characteristic, complemented
10C3×#893C211yesmaximal, characteristic, complemented
11C3×#892C211yesmaximal, characteristic, complemented
12C3×#886C211yesmaximal, characteristic, complemented
13C3×#882C211yesmaximal, characteristic
14C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
15C3×#877C211yesmaximal, characteristic, complemented
16C3×#551—31nomaximal
17#5637C311yesmaximal, characteristic, direct product factor
18C23×C3×D3C2211yescharacteristic
19C2×C32×Q8C2211yescharacteristic, complemented
20C22×C32×C4C2211yescharacteristic
21C2×C3×#67C2211yescharacteristic
22C22×C3×Dic3C2211yescharacteristic
23C2×C3×D12C2211yescharacteristic
24C2×C3×D12C2211yescharacteristic
25C2×C3×C4×D3C2211yescharacteristic
26C2×C3×C4×D3C2211yescharacteristic
27C2×C3×C4×D3C2211yescharacteristic, complemented
28C32×C4⋊C4C2211yescharacteristic, complemented
29C32×C4⋊C4C2211yescharacteristic, complemented
30C32×C4⋊C4C2211yescharacteristic, complemented
31C32×C22⋊C4C2211yescharacteristic
32C32×C22⋊C4C2211yescharacteristic
33C3×#217C2211yescharacteristic
34C3×(C2×D3)⋊C4C2211yescharacteristic
35C3×(C2×D3)⋊C4C2211yescharacteristic
36C3×(C2×D3)⋊C4C2211yescharacteristic
37C3×(C2×D3)⋊C4C2211yescharacteristic
38C3×(C2×D3)⋊C4C2211yescharacteristic
39C3×(C2×D3)⋊C4C2211yescharacteristic
40C3×(C2×D3)⋊C4C2211yescharacteristic
41C3×(C2×D3)⋊C4C2211yescharacteristic
42C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C3×C4⋊Dic3C2211yescharacteristic, complemented
46C3×C4⋊Dic3C2211yescharacteristic, complemented
47C3×Dic3⋊C4C2211yescharacteristic, complemented
48C3×Dic3⋊C4C2211yescharacteristic, complemented
49C3×Dic3⋊C4C2211yescharacteristic, complemented
50C3×C4×Dic3C2211yescharacteristic, complemented
51C3×C4×Dic3C2211yescharacteristic, complemented
52C3×C4×Dic3C2211yescharacteristic, complemented
53C3×#126—31no—
54C3×#126—31no—
55C3×#124—31no—
56C3×#123—31no—
57C3×#123—31no—
58C3×#123—31no—
59C3×C22⋊Q8—21no—
60C3×C22⋊Q8—31no—
61C3×C22⋊Q8D311yescharacteristic, complemented
62C3×C22⋊Q8C2×C311yescharacteristic, complemented
63C3×#120—31no—
64C3×C4×D4—31no—
65C3×C4×D4—31no—
66C3×#117—31no—
67C3×#117—31no—
68C2×C3×C22⋊C4—31no—
69C2×C3×C22⋊C4—31no—
70#947C2×C311yescharacteristic, complemented
71#946C2×C311yescharacteristic, complemented
72C4×#67C2×C311yescharacteristic, complemented
73C2×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
74#898C2×C311yescharacteristic, complemented
75#898C2×C311yescharacteristic, complemented
76#894C2×C311yescharacteristic, complemented
77#894C2×C311yescharacteristic, complemented
78#893C2×C311yescharacteristic, complemented
79#892C2×C311yescharacteristic, complemented
80#886C2×C311yescharacteristic, complemented
81#882C2×C311yescharacteristic
82D3×C22⋊C4C2×C311yescharacteristic, complemented
83#877C2×C311yescharacteristic, complemented
84C23×C32C2311yescharacteristic
85C22×C3×D3—22no—
86C22×C3×D3—22no—
87C22×C3×D3—41no—
88C22×C3×D3C2311yescharacteristic
89C22×C3×D3C2311yescharacteristic
90C22×C3×D3C2311yescharacteristic
91C32×Q8—41no—
92C2×C32×C4—41no—
93C2×C32×C4C2311yescharacteristic
94C2×C32×C4C2311yescharacteristic
95C2×C32×C4C2311yescharacteristic
96C2×C32×C4C2311yescharacteristic
97C2×C32×C4C2311yescharacteristic
98C2×C32×C4C2311yescharacteristic
99C3×#67—22no—
100C2×C3×Dic3—22no—
101C2×C3×Dic3C2311yescharacteristic
102C2×C3×Dic3C2311yescharacteristic
103C2×C3×Dic3C2311yescharacteristic
104C2×C3×Dic3C2311yescharacteristic
105C2×C3×Dic3C2311yescharacteristic
106C3×D12—22no—
107C3×D12—41no—
108C3×C4×D3—22no—
109C3×C4×D3—41no—
110C3×C4×D3—41no—
111#551—31noSylow
112C24×C3—31no—
113C23×D3C22×C311yescharacteristic
114C2×C3×Q8—21no—
115C2×C3×Q8C2×D311yescharacteristic, complemented
116C2×C3×Q8C22×C311yescharacteristic, complemented
117C2×C3×D4—31no—
118C2×C3×D4—31no—
119C2×C3×D4—31no—
120C22×C3×C4—21no—
121C22×C3×C4—31no—
122C22×C3×C4—31no—
123C22×C3×C4—31no—
124C22×C3×C4—31no—
125C22×C3×C4C2×D311yescharacteristic
126C22×C3×C4C22×C311yescharacteristic
127C2×#67C22×C311yescharacteristic
128C22×Dic3C22×C311yescharacteristic
129C2×D12C22×C311yescharacteristic
130C2×D12C22×C311yescharacteristic
131C2×C4×D3C22×C311yescharacteristic
132C2×C4×D3C22×C311yescharacteristic
133C2×C4×D3C22×C311yescharacteristic, complemented
134C3×C4⋊C4—21no—
135C3×C4⋊C4—21no—
136C3×C4⋊C4—21no—
137C3×C4⋊C4—31no—
138C3×C4⋊C4—31no—
139C3×C4⋊C4—31no—
140C3×C4⋊C4—31no—
141C3×C4⋊C4—31no—
142C3×C4⋊C4C2×D311yescharacteristic, complemented
143C3×C4⋊C4C2×D311yescharacteristic, complemented
144C3×C4⋊C4C2×D311yescharacteristic, complemented
145C3×C4⋊C4C22×C311yescharacteristic, complemented
146C3×C4⋊C4C22×C311yescharacteristic, complemented
147C3×C4⋊C4C22×C311yescharacteristic, complemented
148C3×C22⋊C4—21no—
149C3×C22⋊C4—21no—
150C3×C22⋊C4—31no—
151C3×C22⋊C4—31no—
152C3×C22⋊C4—31no—
153C3×C22⋊C4—31no—
154C3×C22⋊C4—31no—
155C3×C22⋊C4—31no—
156C3×C22⋊C4—31no—
157C3×C22⋊C4—31no—
158C3×C22⋊C4—31no—
159C3×C22⋊C4—31no—
160C3×C22⋊C4—31no—
161C3×C22⋊C4—31no—
162C3×C22⋊C4C2×D311yescharacteristic
163C3×C22⋊C4C2×D311yescharacteristic
164C3×C22⋊C4C22×C311yescharacteristic
165C3×C22⋊C4C22×C311yescharacteristic
166C3×C42—31no—
167C3×C42—31no—
168C3×C42—31no—
169#217C22×C311yescharacteristic
170(C2×D3)⋊C4C22×C311yescharacteristic
171(C2×D3)⋊C4C22×C311yescharacteristic
172(C2×D3)⋊C4C22×C311yescharacteristic
173(C2×D3)⋊C4C22×C311yescharacteristic
174(C2×D3)⋊C4C22×C311yescharacteristic
175(C2×D3)⋊C4C22×C311yescharacteristic
176(C2×D3)⋊C4C22×C311yescharacteristic
177(C2×D3)⋊C4C22×C311yescharacteristic
178(C2×D3)⋊C4C22×C311yescharacteristic, complemented
179(C2×D3)⋊C4C22×C311yescharacteristic, complemented
180(C2×D3)⋊C4C22×C311yescharacteristic, complemented
181C4⋊Dic3C22×C311yescharacteristic, complemented
182C4⋊Dic3C22×C311yescharacteristic, complemented
183Dic3⋊C4C22×C311yescharacteristic, complemented
184Dic3⋊C4C22×C311yescharacteristic, complemented
185Dic3⋊C4C22×C311yescharacteristic, complemented
186C4×Dic3C22×C311yescharacteristic, complemented
187C4×Dic3C22×C311yescharacteristic, complemented
188C4×Dic3C22×C311yescharacteristic, complemented
189C22×C32—21no—
190C22×C32—21no—
191C22×C32#4112yes—
192C22×C32C2411yescharacteristic
193C2×C3×D3—21no—
194C2×C3×D3—21no—
195C2×C3×D3—21no—
196C2×C3×D3—21no—
197C2×C3×D3—21no—
198C2×C3×D3—21no—
199C2×C3×D3—21no—
200C2×C3×D3—21no—
201C2×C3×D3—44no—
202C2×C3×D3#4112yes—
203C32×C4—21no—
204C32×C4—21no—
205C32×C4—21no—
206C32×C4—21no—
207C32×C4—21no—
208C32×C4—21no—
209C3×Dic3—21no—
210C3×Dic3—21no—
211C3×Dic3—21no—
212C3×Dic3—21no—
213C3×Dic3—21no—
214#126—31no—
215#126—31no—
216#124—31no—
217#123—31no—
218#123—31no—
219#123—31no—
220C22⋊Q8—31no—
221C22⋊Q8C3×D311yescharacteristic, complemented
222#120—31no—
223C4×D4—31no—
224C4×D4—31no—
225#117—31no—
226#117—31no—
227C2×C22⋊C4—31no—
228C2×C22⋊C4—31no—
229C23×C3—21no—
230C23×C3—31no—
231C23×C3—31no—
232C23×C3—31no—
233C23×C3—62no—
234C23×C3—62no—
235C23×C3—121no—
236C23×C3C22×D311yescharacteristic
237C23×C3C23×C311yescharacteristic
238C22×D3—22no—
239C22×D3—22no—
240C22×D3—41no—
241C22×D3C23×C311yescharacteristic
242C22×D3C23×C311yescharacteristic
243C22×D3C23×C311yescharacteristic
244C3×Q8—41no—
245C3×Q8—41no—
246C3×Q8—42no—
247C3×D4—62no—
248C3×D4—62no—
249C3×D4—121no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—31no—
257C2×C3×C4—31no—
258C2×C3×C4—31no—
259C2×C3×C4—31no—
260C2×C3×C4—31no—
261C2×C3×C4—41no—
262C2×C3×C4—41no—
263C2×C3×C4—42no—
264C2×C3×C4—62no—
265C2×C3×C4—62no—
266C2×C3×C4—121no—
267C2×C3×C4—121no—
268C2×C3×C4C22×D311yescharacteristic
269C2×C3×C4C22×D311yescharacteristic
270C2×C3×C4C22×D311yescharacteristic
271C2×C3×C4C22×D311yescharacteristic
272C2×C3×C4C22×D311yescharacteristic
273C2×C3×C4C22×D311yescharacteristic
274C2×C3×C4C23×C311yescharacteristic
275C2×C3×C4C23×C311yescharacteristic
276C2×C3×C4C23×C311yescharacteristic
277C2×C3×C4C23×C311yescharacteristic
278C2×C3×C4C23×C311yescharacteristic
279C2×C3×C4C23×C311yescharacteristic
280#67—22no—
281C2×Dic3—22no—
282C2×Dic3C23×C311yescharacteristic
283C2×Dic3C23×C311yescharacteristic
284C2×Dic3C23×C311yescharacteristic
285C2×Dic3C23×C311yescharacteristic
286C2×Dic3C23×C311yescharacteristic
287D12—22no—
288D12—41no—
289C4×D3—22no—
290C4×D3—41no—
291C4×D3—41no—
292C2×C32—22no—
293C2×C32C2×#4111yescharacteristic
294C2×C32C2×#4111yescharacteristic
295C2×C32H(5,𝔽2)11yescharacteristic
296C3×D3—22no—
297C3×D3—41no—
298C3×D3—41no—
299C24—31no—
300C2×Q8C2×C3×D311yescharacteristic, complemented
301C2×D4—31no—
302C2×D4—31no—
303C2×D4—31no—
304C22×C4—31no—
305C22×C4—31no—
306C22×C4—31no—
307C22×C4—31no—
308C22×C4C2×C3×D311yescharacteristic
309C4⋊C4—31no—
310C4⋊C4—31no—
311C4⋊C4—31no—
312C4⋊C4—31no—
313C4⋊C4—31no—
314C4⋊C4C2×C3×D311yescharacteristic, complemented
315C4⋊C4C2×C3×D311yescharacteristic, complemented
316C4⋊C4C2×C3×D311yescharacteristic, complemented
317C22⋊C4—31no—
318C22⋊C4—31no—
319C22⋊C4—31no—
320C22⋊C4—31no—
321C22⋊C4—31no—
322C22⋊C4—31no—
323C22⋊C4—31no—
324C22⋊C4—31no—
325C22⋊C4—31no—
326C22⋊C4—31no—
327C22⋊C4—31no—
328C22⋊C4—31no—
329C22⋊C4C2×C3×D311yescharacteristic
330C22⋊C4C2×C3×D311yescharacteristic
331C42—31no—
332C42—31no—
333C42—31no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—22no—
340C22×C3—32no—
341C22×C3—41no—
342C22×C3—41no—
343C22×C3—61no—
344C22×C3—61no—
345C22×C3—61no—
346C22×C3—61no—
347C22×C3—61no—
348C22×C3—61no—
349C22×C3—61no—
350C22×C3—61no—
351C22×C3—124no—
352C22×C3#23912yes—
353C22×C3C3×#4112yes—
354C22×C3C23×D311yescharacteristic
355C22×C3C24×C311yescharacteristic
356C2×D3—21no—
357C2×D3—21no—
358C2×D3—21no—
359C2×D3—21no—
360C2×D3—21no—
361C2×D3—21no—
362C2×D3—21no—
363C2×D3—21no—
364C2×D3—44no—
365C2×D3C3×#4112yes—
366C3×C4—22no—
367C3×C4—21no—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—41no—
380C3×C4—41no—
381C3×C4—41no—
382C3×C4—41no—
383C3×C4—41no—
384C3×C4—61no—
385C3×C4—61no—
386C3×C4—61no—
387C3×C4—61no—
388C3×C4—61no—
389Dic3—21no—
390Dic3—21no—
391Dic3—21no—
392Dic3—21no—
393Dic3—21no—
394C32#55111yescharacteristic, complemented, Sylow
395C23—31no—
396C23—31no—
397C23—31no—
398C23—62no—
399C23—62no—
400C23—121no—
401C23C22×C3×D311yescharacteristic
402Q8—41no—
403D4—62no—
404D4—62no—
405D4—121no—
406C2×C4—31no—
407C2×C4—31no—
408C2×C4—31no—
409C2×C4—31no—
410C2×C4—31no—
411C2×C4—41no—
412C2×C4—62no—
413C2×C4—62no—
414C2×C4—121no—
415C2×C4—121no—
416C2×C4C22×C3×D311yescharacteristic
417C2×C4C22×C3×D311yescharacteristic
418C2×C4C22×C3×D311yescharacteristic
419C2×C4C22×C3×D311yescharacteristic
420C2×C4C22×C3×D311yescharacteristic
421C2×C4C22×C3×D311yescharacteristic
422C2×C3—22no—
423C2×C3—22no—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—21no—
427C2×C3—42no—
428C2×C3—62no—
429C2×C3—121no—
430C2×C3—121no—
431C2×C3#100411yescharacteristic
432C2×C3C2×#23911yescharacteristic
433C2×C3D3×#4111yescharacteristic
434C2×C3C2×C3×#4111yescharacteristic
435C2×C3C2×C3×#4111yescharacteristic
436C2×C3C3×H(5,𝔽2)11yescharacteristic
437D3—22no—
438D3—41no—
439D3—41no—
440C22—21no—
441C22—21no—
442C22—32no—
443C22—61no—
444C22—61no—
445C22—61no—
446C22—61no—
447C22—61no—
448C22—61no—
449C22—61no—
450C22—61no—
451C22—124no—
452C22C3×#23912yes—
453C22C23×C3×D311yescharacteristic
454C4—21no—
455C4—21no—
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—61no—
461C4—61no—
462C4—61no—
463C4—61no—
464C4—61no—
465C3—21no—
466C3#563711yescharacteristic, direct product factor
467C3C3×#55111yescharacteristic, complemented
468C2—22no—
469C2—62no—
470C2—121no—
471C2—121no—
472C2C3×#100411yescharacteristic
473C2C2×C3×#23911yescharacteristic
474C2C3×D3×#4111yescharacteristic
subgroupG/H
centerC22×C3C23×D3
commutator, cosocleC22×C3C24×C3
FrattiniC22C23×C3×D3
FittingC32×C22⋊Q8C2
socleC22×C32C24
prime radicalC3×#882C2
hypercenterC3×C22⋊Q8D3
hypocenterC3C3×#551
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C32×C22⋊Q8C2semidirect
2. C3×#947C2semidirect
3. C3×#946C2semidirect
4. C3×C4×#67C2semidirect
5. C2×C3×(C2×D3)⋊C4C2semidirect
6. C3×#898C2semidirect
7. C3×#898C2semidirect
8. C3×#894C2semidirect
9. C3×#894C2semidirect
10. C3×#893C2semidirect
11. C3×#892C2semidirect
12. C3×#886C2semidirect
14. C3×D3×C22⋊C4C2semidirect
15. C3×#877C2semidirect
17. #5637C3direct (N × H)
19. C2×C32×Q8C22semidirect
27. C2×C3×C4×D3C22semidirect
28. C32×C4⋊C4C22semidirect
29. C32×C4⋊C4C22semidirect
30. C32×C4⋊C4C22semidirect
42. C3×(C2×D3)⋊C4C22semidirect
43. C3×(C2×D3)⋊C4C22semidirect
44. C3×(C2×D3)⋊C4C22semidirect
45. C3×C4⋊Dic3C22semidirect
46. C3×C4⋊Dic3C22semidirect
47. C3×Dic3⋊C4C22semidirect
48. C3×Dic3⋊C4C22semidirect
49. C3×Dic3⋊C4C22semidirect
50. C3×C4×Dic3C22semidirect
51. C3×C4×Dic3C22semidirect
52. C3×C4×Dic3C22semidirect
61. C3×C22⋊Q8D3semidirect
62. C3×C22⋊Q8C2×C3semidirect
70. #947C2×C3semidirect
71. #946C2×C3semidirect
72. C4×#67C2×C3semidirect
73. C2×(C2×D3)⋊C4C2×C3semidirect
74. #898C2×C3semidirect
75. #898C2×C3semidirect
76. #894C2×C3semidirect
77. #894C2×C3semidirect
78. #893C2×C3semidirect
79. #892C2×C3semidirect
80. #886C2×C3semidirect
82. D3×C22⋊C4C2×C3semidirect
83. #877C2×C3semidirect
115. C2×C3×Q8C2×D3semidirect
116. C2×C3×Q8C22×C3semidirect
133. C2×C4×D3C22×C3semidirect
142. C3×C4⋊C4C2×D3semidirect
143. C3×C4⋊C4C2×D3semidirect
144. C3×C4⋊C4C2×D3semidirect
145. C3×C4⋊C4C22×C3semidirect
146. C3×C4⋊C4C22×C3semidirect
147. C3×C4⋊C4C22×C3semidirect
178. (C2×D3)⋊C4C22×C3semidirect
179. (C2×D3)⋊C4C22×C3semidirect
180. (C2×D3)⋊C4C22×C3semidirect
181. C4⋊Dic3C22×C3semidirect
182. C4⋊Dic3C22×C3semidirect
183. Dic3⋊C4C22×C3semidirect
184. Dic3⋊C4C22×C3semidirect
185. Dic3⋊C4C22×C3semidirect
186. C4×Dic3C22×C3semidirect
187. C4×Dic3C22×C3semidirect
188. C4×Dic3C22×C3semidirect
221. C22⋊Q8C3×D3semidirect
300. C2×Q8C2×C3×D3semidirect
314. C4⋊C4C2×C3×D3semidirect
315. C4⋊C4C2×C3×D3semidirect
316. C4⋊C4C2×C3×D3semidirect
394. C32#551semidirect
466. C3#5637direct (N × H)
467. C3C3×#551semidirect

Maximal subgroups

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

subgroupindex
C32×C22⋊Q82
C3×#9472
C3×#9462
C3×C4×#672
C2×C3×(C2×D3)⋊C42
C3×#8982
C3×#8942
C3×#8932
C3×#8922
C3×#8862
C3×#8822
C3×D3×C22⋊C42
C3×#8772
C3×#5513
#56373