Finite Group Databasebeta

← C3×#3265 #85129

Subgroups — C3×#3265 #85129

Order 384.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2C22×C3×SD16C211yesmaximal, characteristic, complemented
3C3×#548C211yesmaximal, characteristic, complemented
4C3×D42C211yesmaximal, characteristic, complemented
5C3×#496C211yesmaximal, characteristic, complemented
6C3×#468C211yesmaximal, characteristic, complemented
7C3×#466C211yesmaximal, characteristic, complemented
8C3×#463C211yesmaximal, characteristic, complemented
9C3×#460C211yesmaximal, characteristic, complemented
10C3×#450C211yesmaximal, characteristic, complemented
11C3×#449C211yesmaximal, characteristic, complemented
12C3×#448C211yesmaximal, characteristic, complemented
13C3×#447C211yesmaximal, characteristic, complemented
14C3×#440C211yesmaximal, characteristic, complemented
15C3×#435C211yesmaximal, characteristic, complemented
16#3265C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×#41C2211yescharacteristic, complemented
18C22×C3×Q8C2211yescharacteristic, complemented
19C22×C3×D4—21no—
20C22×C3×D4C2211yescharacteristic
21C22×C3×D4C2211yescharacteristic
22C3×AGL(1,ℤ/8)—24no—
23C2×C3×SD16—24no—
24C2×C3×SD16C2211yescharacteristic
25C2×C3×SD16C2211yescharacteristic
26C2×C3×SD16C2211yescharacteristic, complemented
27C2×C3×SD16C2211yescharacteristic, complemented
28C2×C3×SD16C2211yescharacteristic, complemented
29C2×C3×SD16C2211yescharacteristic, complemented
30C2×C3×D8C2211yescharacteristic
31C2×C3×D8C2211yescharacteristic, complemented
32C2×C3×D8C2211yescharacteristic, complemented
33C2×C3×M16C2211yescharacteristic, complemented
34C22×C3×C8C2211yescharacteristic, complemented
35C3×#127C2211yescharacteristic
36C3×#124—21no—
37C3×#124C2211yescharacteristic, complemented
38C3×C22⋊Q8—21no—
39C3×C22⋊Q8C2211yescharacteristic, complemented
40C3×#121—21no—
41C3×#121—21no—
42C3×#121C2211yescharacteristic
43C3×#121C2211yescharacteristic
44C3×#121C2211yescharacteristic, complemented
45C3×#120—21no—
46C3×#120—21no—
47C3×C4×Q8C2211yescharacteristic, complemented
48C3×C4×D4—21no—
49C3×C4×D4C2211yescharacteristic
50C3×C4×D4C2211yescharacteristic
51C3×#107C2211yescharacteristic, complemented
52C3×C4⋊C8C2211yescharacteristic, complemented
53C3×#103C2211yescharacteristic, complemented
54C3×#103C2211yescharacteristic, complemented
55C3×#102C2211yescharacteristic
56C3×#102C2211yescharacteristic, complemented
57C3×#102C2211yescharacteristic, complemented
58C3×#102C2211yescharacteristic, complemented
59C3×C22⋊C8C2211yescharacteristic, complemented
60C3×C22⋊C8C2211yescharacteristic, complemented
61C3×#97C2211yescharacteristic, complemented
62C2×AGL(1,ℤ/8)C2×C311yescharacteristic, complemented
63C22×SD16C2×C311yescharacteristic, complemented
64#548C2×C311yescharacteristic, complemented
65D42C2×C311yescharacteristic, complemented
66#496C2×C311yescharacteristic, complemented
67#468C2×C311yescharacteristic, complemented
68#466C2×C311yescharacteristic, complemented
69#463C2×C311yescharacteristic, complemented
70#460C2×C311yescharacteristic, complemented
71#450C2×C311yescharacteristic, complemented
72#449C2×C311yescharacteristic, complemented
73#448C2×C311yescharacteristic, complemented
74#447C2×C311yescharacteristic, complemented
75#440C2×C311yescharacteristic, complemented
76#435C2×C311yescharacteristic, complemented
77C24×C3—21no—
78C24×C3—21no—
79C3×#41—22no—
80C3×#41—41no—
81C2×C3×Q8—21no—
82C2×C3×Q8—22no—
83C2×C3×Q8—41no—
84C2×C3×Q8C2311yescharacteristic
85C2×C3×Q8C2311yescharacteristic
86C2×C3×D4—22no—
87C2×C3×D4—22no—
88C2×C3×D4—21no—
89C2×C3×D4—21no—
90C2×C3×D4—21no—
91C2×C3×D4—21no—
92C2×C3×D4—21no—
93C2×C3×D4—21no—
94C2×C3×D4—21no—
95C2×C3×D4—21no—
96C2×C3×D4—41no—
97C2×C3×D4—41no—
98C2×C3×D4—44no—
99C2×C3×D4D411yescharacteristic
100C2×C3×D4C2311yescharacteristic
101C2×C3×D4C2311yescharacteristic
102C2×C3×D4C2311yescharacteristic
103C2×C3×D4C2311yescharacteristic
104C22×C3×C4—21no—
105C22×C3×C4—21no—
106C22×C3×C4—21no—
107C22×C3×C4C2311yescharacteristic
108C22×C3×C4C2311yescharacteristic
109C3×SD16—22no—
110C3×SD16—22no—
111C3×SD16—22no—
112C3×SD16—22no—
113C3×SD16—41no—
114C3×SD16D414yescomplemented
115C3×D8—22no—
116C3×D8—22no—
117C3×D8—41no—
118C3×M16—22no—
119C2×C3×C8—22no—
120C2×C3×C8C2311yescharacteristic
121C2×C3×C8C2311yescharacteristic
122C2×C3×C8C2311yescharacteristic
123C2×C3×C8C2311yescharacteristic
124C3×C4⋊C4—21no—
125C3×C4⋊C4—21no—
126C3×C4⋊C4D411yescharacteristic
127C3×C4⋊C4C2311yescharacteristic
128C3×C4⋊C4C2311yescharacteristic
129C3×C22⋊C4—21no—
130C3×C22⋊C4—21no—
131C3×C22⋊C4—21no—
132C3×C22⋊C4—21no—
133C3×C22⋊C4—21no—
134C3×C22⋊C4—21no—
135C3×C22⋊C4—21no—
136C3×C22⋊C4D411yescharacteristic
137C3×C22⋊C4D411yescharacteristic
138C3×C42—21no—
139C3×C42C2311yescharacteristic
140C2×#41C22×C311yescharacteristic, complemented
141C22×Q8C22×C311yescharacteristic, complemented
142C22×D4—21no—
143C22×D4C22×C311yescharacteristic
144C22×D4C22×C311yescharacteristic
145AGL(1,ℤ/8)—24no—
146C2×SD16—24no—
147C2×SD16C22×C311yescharacteristic
148C2×SD16C22×C311yescharacteristic
149C2×SD16C22×C311yescharacteristic, complemented
150C2×SD16C22×C311yescharacteristic, complemented
151C2×SD16C22×C311yescharacteristic, complemented
152C2×SD16C22×C311yescharacteristic, complemented
153C2×D8C22×C311yescharacteristic
154C2×D8C22×C311yescharacteristic, complemented
155C2×D8C22×C311yescharacteristic, complemented
156C2×M16C22×C311yescharacteristic, complemented
157C22×C8C22×C311yescharacteristic, complemented
158#127C22×C311yescharacteristic
159#124—21no—
160#124C22×C311yescharacteristic, complemented
161C22⋊Q8—21no—
162C22⋊Q8C22×C311yescharacteristic, complemented
163#121—21no—
164#121—21no—
165#121C22×C311yescharacteristic
166#121C22×C311yescharacteristic
167#121C22×C311yescharacteristic, complemented
168#120—21no—
169#120—21no—
170C4×Q8C22×C311yescharacteristic, complemented
171C4×D4—21no—
172C4×D4C22×C311yescharacteristic
173C4×D4C22×C311yescharacteristic
174#107C22×C311yescharacteristic, complemented
175C4⋊C8C22×C311yescharacteristic, complemented
176#103C22×C311yescharacteristic, complemented
177#103C22×C311yescharacteristic, complemented
178#102C22×C311yescharacteristic
179#102C22×C311yescharacteristic, complemented
180#102C22×C311yescharacteristic, complemented
181#102C22×C311yescharacteristic, complemented
182C22⋊C8C22×C311yescharacteristic, complemented
183C22⋊C8C22×C311yescharacteristic, complemented
184#97C22×C311yescharacteristic, complemented
185C23×C3—21no—
186C23×C3—21no—
187C23×C3—21no—
188C23×C3—21no—
189C23×C3—42no—
190C23×C3—42no—
191C23×C3—42no—
192C23×C3—42no—
193C23×C3—81no—
194C23×C3—81no—
195C23×C3C2×D411yescharacteristic
196C23×C3C2×D411yescharacteristic
197C3×Q8—21no—
198C3×Q8—21no—
199C3×Q8—21no—
200C3×Q8—42no—
201C3×Q8C2×D412yescomplemented
202C3×D4—22no—
203C3×D4—21no—
204C3×D4—21no—
205C3×D4—21no—
206C3×D4—21no—
207C3×D4—21no—
208C3×D4—21no—
209C3×D4—21no—
210C3×D4—42no—
211C3×D4—42no—
212C3×D4—42no—
213C3×D4—42no—
214C3×D4—42no—
215C3×D4—42no—
216C3×D4—42no—
217C3×D4—81no—
218C3×D4C2×D412yes—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—42no—
228C2×C3×C4—42no—
229C2×C3×C4—42no—
230C2×C3×C4C2×D411yescharacteristic
231C2×C3×C4C2×D411yescharacteristic
232C2×C3×C4C2×D411yescharacteristic
233C2×C3×C4C2×D411yescharacteristic
234C2×C3×C4C2411yescharacteristic
235C3×C8—21no—
236C3×C8—21no—
237C3×C8—21no—
238C3×C8C2×D412yescomplemented
239C24—21no—
240C24—21no—
241#41—22no—
242#41—41no—
243C2×Q8—21no—
244C2×Q8—22no—
245C2×Q8—41no—
246C2×Q8C23×C311yescharacteristic
247C2×Q8C23×C311yescharacteristic
248C2×D4—22no—
249C2×D4—22no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—41no—
259C2×D4—41no—
260C2×D4—44no—
261C2×D4C3×D411yescharacteristic
262C2×D4C23×C311yescharacteristic
263C2×D4C23×C311yescharacteristic
264C2×D4C23×C311yescharacteristic
265C2×D4C23×C311yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4C23×C311yescharacteristic
270C22×C4C23×C311yescharacteristic
271SD16—22no—
272SD16—22no—
273SD16—22no—
274SD16—22no—
275SD16—41no—
276SD16C3×D414yescomplemented
277D8—22no—
278D8—22no—
279D8—41no—
280M16—22no—
281C2×C8—22no—
282C2×C8C23×C311yescharacteristic
283C2×C8C23×C311yescharacteristic
284C2×C8C23×C311yescharacteristic
285C2×C8C23×C311yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4C3×D411yescharacteristic
289C4⋊C4C23×C311yescharacteristic
290C4⋊C4C23×C311yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—21no—
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4C3×D411yescharacteristic
299C22⋊C4C3×D411yescharacteristic
300C42—21no—
301C42C23×C311yescharacteristic
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—21no—
305C22×C3—22no—
306C22×C3—21no—
307C22×C3—21no—
308C22×C3—41no—
309C22×C3—41no—
310C22×C3—41no—
311C22×C3—41no—
312C22×C3—41no—
313C22×C3—41no—
314C22×C3—41no—
315C22×C3—41no—
316C22×C3—41no—
317C22×C3—41no—
318C22×C3—41no—
319C22×C3—84no—
320C22×C3—84no—
321C22×C3AGL(1,ℤ/8)12yescomplemented
322C22×C3C22×D411yescharacteristic
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—22no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—41no—
329C3×C4—41no—
330C3×C4—41no—
331C3×C4C22×D411yescharacteristic
332C3×C4H(5,𝔽2)11yescharacteristic
333C23—21no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—42no—
338C23—42no—
339C23—42no—
340C23—42no—
341C23—81no—
342C23—81no—
343C23C2×C3×D411yescharacteristic
344C23C2×C3×D411yescharacteristic
345Q8—21no—
346Q8—21no—
347Q8—21no—
348Q8—42no—
349Q8C2×C3×D412yescomplemented
350D4—22no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—42no—
359D4—42no—
360D4—42no—
361D4—42no—
362D4—42no—
363D4—42no—
364D4—42no—
365D4—81no—
366D4C2×C3×D412yes—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4C2×C3×D411yescharacteristic
379C2×C4C2×C3×D411yescharacteristic
380C2×C4C2×C3×D411yescharacteristic
381C2×C4C2×C3×D411yescharacteristic
382C2×C4C24×C311yescharacteristic
383C8—21no—
384C8—21no—
385C8—21no—
386C8C2×C3×D412yescomplemented
387C2×C3—22no—
388C2×C3—41no—
389C2×C3—42no—
390C2×C3—81no—
391C2×C3—81no—
392C2×C3—81no—
393C2×C3D4211yescharacteristic
394C2×C3C2×AGL(1,ℤ/8)11yescharacteristic
395C2×C3#57711yescharacteristic
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—22no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—84no—
414C22—84no—
415C22C3×AGL(1,ℤ/8)12yescomplemented
416C22C22×C3×D411yescharacteristic
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—22no—
422C4—41no—
423C4—41no—
424C4—41no—
425C4C22×C3×D411yescharacteristic
426C4C3×H(5,𝔽2)11yescharacteristic
427C3#326511yescharacteristic, direct product factor, Sylow
428C2—22no—
429C2—41no—
430C2—42no—
431C2—81no—
432C2—81no—
433C2—81no—
434C2C3×D4211yescharacteristic
435C2C2×C3×AGL(1,ℤ/8)11yescharacteristic
436C2C3×#57711yescharacteristic
subgroupG/H
center, socleC22×C3C22×D4
commutator, Frattini, cosocleC2×C4C24×C3
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×AGL(1,ℤ/8)C2semidirect
2. C22×C3×SD16C2semidirect
3. C3×#548C2semidirect
4. C3×D42C2semidirect
5. C3×#496C2semidirect
6. C3×#468C2semidirect
7. C3×#466C2semidirect
8. C3×#463C2semidirect
9. C3×#460C2semidirect
10. C3×#450C2semidirect
11. C3×#449C2semidirect
12. C3×#448C2semidirect
13. C3×#447C2semidirect
14. C3×#440C2semidirect
15. C3×#435C2semidirect
16. #3265C3direct (N × H)
17. C2×C3×#41C22semidirect
18. C22×C3×Q8C22semidirect
26. C2×C3×SD16C22semidirect
27. C2×C3×SD16C22semidirect
28. C2×C3×SD16C22semidirect
29. C2×C3×SD16C22semidirect
31. C2×C3×D8C22semidirect
32. C2×C3×D8C22semidirect
33. C2×C3×M16C22semidirect
34. C22×C3×C8C22semidirect
37. C3×#124C22semidirect
39. C3×C22⋊Q8C22semidirect
44. C3×#121C22semidirect
47. C3×C4×Q8C22semidirect
51. C3×#107C22semidirect
52. C3×C4⋊C8C22semidirect
53. C3×#103C22semidirect
54. C3×#103C22semidirect
56. C3×#102C22semidirect
57. C3×#102C22semidirect
58. C3×#102C22semidirect
59. C3×C22⋊C8C22semidirect
60. C3×C22⋊C8C22semidirect
61. C3×#97C22semidirect
62. C2×AGL(1,ℤ/8)C2×C3semidirect
63. C22×SD16C2×C3semidirect
64. #548C2×C3semidirect
65. D42C2×C3semidirect
66. #496C2×C3semidirect
67. #468C2×C3semidirect
68. #466C2×C3semidirect
69. #463C2×C3semidirect
70. #460C2×C3semidirect
71. #450C2×C3semidirect
72. #449C2×C3semidirect
73. #448C2×C3semidirect
74. #447C2×C3semidirect
75. #440C2×C3semidirect
76. #435C2×C3semidirect
114. C3×SD16D4semidirect
140. C2×#41C22×C3semidirect
141. C22×Q8C22×C3semidirect
149. C2×SD16C22×C3semidirect
150. C2×SD16C22×C3semidirect
151. C2×SD16C22×C3semidirect
152. C2×SD16C22×C3semidirect
154. C2×D8C22×C3semidirect
155. C2×D8C22×C3semidirect
156. C2×M16C22×C3semidirect
157. C22×C8C22×C3semidirect
160. #124C22×C3semidirect
162. C22⋊Q8C22×C3semidirect
167. #121C22×C3semidirect
170. C4×Q8C22×C3semidirect
174. #107C22×C3semidirect
175. C4⋊C8C22×C3semidirect
176. #103C22×C3semidirect
177. #103C22×C3semidirect
179. #102C22×C3semidirect
180. #102C22×C3semidirect
181. #102C22×C3semidirect
182. C22⋊C8C22×C3semidirect
183. C22⋊C8C22×C3semidirect
184. #97C22×C3semidirect
201. C3×Q8C2×D4semidirect
238. C3×C8C2×D4semidirect
276. SD16C3×D4semidirect
321. C22×C3AGL(1,ℤ/8)semidirect
349. Q8C2×C3×D4semidirect
386. C8C2×C3×D4semidirect
415. C22C3×AGL(1,ℤ/8)semidirect
427. C3#3265direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×AGL(1,ℤ/8)2
C22×C3×SD162
C3×#5482
C3×D422
C3×#4962
C3×#4682
C3×#4662
C3×#4632
C3×#4602
C3×#4502
C3×#4492
C3×#4482
C3×#4472
C3×#4402
C3×#4352
#32653