Finite Group Databasebeta

← C3×#3267 #85131

Subgroups — C3×#3267 #85131

Order 384.

500 conjugacy classes of subgroups.

The subgroup lattice has 418 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
2C2×C3×#135C211yesmaximal, characteristic, complemented
3C3×#547C211yesmaximal, characteristic, complemented
4C3×#546C211yesmaximal, characteristic, complemented
5C3×#497C211yesmaximal, characteristic, complemented
6C3×#470C211yesmaximal, characteristic, complemented
7C3×#465C211yesmaximal, characteristic, complemented
8C3×#463C211yesmaximal, characteristic, complemented
9C3×#461C211yesmaximal, characteristic, complemented
10C3×#452C211yesmaximal, characteristic, complemented
11C3×#452C211yesmaximal, characteristic, complemented
12C3×#450C211yesmaximal, characteristic, complemented
13C3×#449C211yesmaximal, characteristic, complemented
14C3×#442C211yesmaximal, characteristic, complemented
15C3×#435C211yesmaximal, characteristic, complemented
16#3267C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×#41C2211yescharacteristic
18C2×C3×#41C2211yescharacteristic
19C2×C3×#41C2211yescharacteristic, complemented
20C22×C3×D4C2211yescharacteristic
21C3×AGL(1,ℤ/8)—24no—
22C3×#135—24no—
23C2×C3×Q16C2211yescharacteristic, complemented
24C2×C3×Q16C2211yescharacteristic, complemented
25C2×C3×SD16C2211yescharacteristic
26C2×C3×SD16C2211yescharacteristic
27C2×C3×SD16C2211yescharacteristic
28C2×C3×SD16C2211yescharacteristic
29C2×C3×SD16C2211yescharacteristic, complemented
30C2×C3×D8C2211yescharacteristic
31C2×C3×D8C2211yescharacteristic
32C2×C3×M16C2211yescharacteristic
33C22×C3×C8C2211yescharacteristic, complemented
34C3×C4⋊Q8C2211yescharacteristic, complemented
35C3×#124C2211yescharacteristic
36C3×#123—21no—
37C3×#123—21no—
38C3×#123—21no—
39C3×C22⋊Q8C2211yescharacteristic
40C3×C22⋊Q8C2211yescharacteristic
41C3×C22⋊Q8C2211yescharacteristic, complemented
42C3×#121—21no—
43C3×#121—21no—
44C3×#121C2211yescharacteristic
45C3×#120—21no—
46C3×C4×D4C2211yescharacteristic
47C3×C4×D4C2211yescharacteristic
48C3×C4×D4C2211yescharacteristic, complemented
49C2×C3×C4⋊C4—21no—
50C2×C3×C22⋊C4—21no—
51C3×#106C2211yescharacteristic, complemented
52C3×C4⋊C8C2211yescharacteristic, complemented
53C3×#103C2211yescharacteristic, complemented
54C3×#103C2211yescharacteristic, complemented
55C3×#103C2211yescharacteristic, complemented
56C3×#102C2211yescharacteristic
57C3×#102C2211yescharacteristic
58C3×#102C2211yescharacteristic, complemented
59C3×C22⋊C8C2211yescharacteristic
60C3×C22⋊C8C2211yescharacteristic, complemented
61C3×#97C2211yescharacteristic, complemented
62C2×AGL(1,ℤ/8)C2×C311yescharacteristic, complemented
63C2×#135C2×C311yescharacteristic, complemented
64#547C2×C311yescharacteristic, complemented
65#546C2×C311yescharacteristic, complemented
66#497C2×C311yescharacteristic, complemented
67#470C2×C311yescharacteristic, complemented
68#465C2×C311yescharacteristic, complemented
69#463C2×C311yescharacteristic, complemented
70#461C2×C311yescharacteristic, complemented
71#452C2×C311yescharacteristic, complemented
72#452C2×C311yescharacteristic, complemented
73#450C2×C311yescharacteristic, complemented
74#449C2×C311yescharacteristic, complemented
75#442C2×C311yescharacteristic, complemented
76#435C2×C311yescharacteristic, complemented
77C24×C3—21no—
78C3×#41—22no—
79C3×#41—22no—
80C3×#41—22no—
81C3×#41—41no—
82C3×#41—41no—
83C3×#41—41no—
84C2×C3×Q8C2311yescharacteristic
85C2×C3×Q8C2311yescharacteristic
86C2×C3×Q8C2311yescharacteristic
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—41no—
94C2×C3×D4D411yescharacteristic
95C2×C3×D4C2311yescharacteristic
96C2×C3×D4C2311yescharacteristic
97C2×C3×D4C2311yescharacteristic
98C22×C3×C4—21no—
99C22×C3×C4—21no—
100C22×C3×C4—21no—
101C22×C3×C4—21no—
102C22×C3×C4—21no—
103C22×C3×C4C2311yescharacteristic
104C22×C3×C4C2311yescharacteristic
105C3×Q16—22no—
106C3×Q16—41no—
107C3×SD16—22no—
108C3×SD16—22no—
109C3×SD16—22no—
110C3×SD16—22no—
111C3×SD16—41no—
112C3×D8—22no—
113C3×D8D414yescomplemented
114C3×M16—22no—
115C2×C3×C8—22no—
116C2×C3×C8C2311yescharacteristic
117C2×C3×C8C2311yescharacteristic
118C2×C3×C8C2311yescharacteristic
119C2×C3×C8C2311yescharacteristic
120C3×C4⋊C4—21no—
121C3×C4⋊C4—21no—
122C3×C4⋊C4—21no—
123C3×C4⋊C4—21no—
124C3×C4⋊C4—21no—
125C3×C4⋊C4D411yescharacteristic
126C3×C4⋊C4C2311yescharacteristic
127C3×C4⋊C4C2311yescharacteristic
128C3×C22⋊C4—21no—
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×C42C2311yescharacteristic
139C2×#41C22×C311yescharacteristic
140C2×#41C22×C311yescharacteristic
141C2×#41C22×C311yescharacteristic, complemented
142C22×D4C22×C311yescharacteristic
143AGL(1,ℤ/8)—24no—
144#135—24no—
145C2×Q16C22×C311yescharacteristic, complemented
146C2×Q16C22×C311yescharacteristic, complemented
147C2×SD16C22×C311yescharacteristic
148C2×SD16C22×C311yescharacteristic
149C2×SD16C22×C311yescharacteristic
150C2×SD16C22×C311yescharacteristic
151C2×SD16C22×C311yescharacteristic, complemented
152C2×D8C22×C311yescharacteristic
153C2×D8C22×C311yescharacteristic
154C2×M16C22×C311yescharacteristic
155C22×C8C22×C311yescharacteristic, complemented
156C4⋊Q8C22×C311yescharacteristic, complemented
157#124C22×C311yescharacteristic
158#123—21no—
159#123—21no—
160#123—21no—
161C22⋊Q8C22×C311yescharacteristic
162C22⋊Q8C22×C311yescharacteristic
163C22⋊Q8C22×C311yescharacteristic, complemented
164#121—21no—
165#121—21no—
166#121C22×C311yescharacteristic
167#120—21no—
168C4×D4C22×C311yescharacteristic
169C4×D4C22×C311yescharacteristic
170C4×D4C22×C311yescharacteristic, complemented
171C2×C4⋊C4—21no—
172C2×C22⋊C4—21no—
173#106C22×C311yescharacteristic, complemented
174C4⋊C8C22×C311yescharacteristic, complemented
175#103C22×C311yescharacteristic, complemented
176#103C22×C311yescharacteristic, complemented
177#103C22×C311yescharacteristic, complemented
178#102C22×C311yescharacteristic
179#102C22×C311yescharacteristic
180#102C22×C311yescharacteristic, complemented
181C22⋊C8C22×C311yescharacteristic
182C22⋊C8C22×C311yescharacteristic, complemented
183#97C22×C311yescharacteristic, complemented
184C23×C3—21no—
185C23×C3—21no—
186C23×C3—21no—
187C23×C3—42no—
188C23×C3—42no—
189C23×C3—81no—
190C23×C3C2×D411yescharacteristic
191C23×C3C2×D411yescharacteristic
192C3×Q8—21no—
193C3×Q8—21no—
194C3×Q8—21no—
195C3×Q8—21no—
196C3×Q8—21no—
197C3×Q8—21no—
198C3×D4—21no—
199C3×D4—21no—
200C3×D4—21no—
201C3×D4—21no—
202C3×D4—41no—
203C3×D4—42no—
204C3×D4—42no—
205C3×D4—42no—
206C3×D4—42no—
207C3×D4—81no—
208C3×D4C2×D412yes—
209C3×D4C2×D412yes—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—42no—
220C2×C3×C4—42no—
221C2×C3×C4—42no—
222C2×C3×C4—42no—
223C2×C3×C4—81no—
224C2×C3×C4C2×D411yescharacteristic
225C2×C3×C4C2×D411yescharacteristic
226C2×C3×C4C2×D411yescharacteristic
227C2×C3×C4C2×D411yescharacteristic
228C2×C3×C4C2411yescharacteristic
229C3×C8—21no—
230C3×C8—21no—
231C3×C8—21no—
232C3×C8C2×D412yes—
233C24—21no—
234#41—22no—
235#41—22no—
236#41—22no—
237#41—41no—
238#41—41no—
239#41—41no—
240C2×Q8C23×C311yescharacteristic
241C2×Q8C23×C311yescharacteristic
242C2×Q8C23×C311yescharacteristic
243C2×D4—22no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—21no—
249C2×D4—41no—
250C2×D4C3×D411yescharacteristic
251C2×D4C23×C311yescharacteristic
252C2×D4C23×C311yescharacteristic
253C2×D4C23×C311yescharacteristic
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4C23×C311yescharacteristic
260C22×C4C23×C311yescharacteristic
261Q16—22no—
262Q16—41no—
263SD16—22no—
264SD16—22no—
265SD16—22no—
266SD16—22no—
267SD16—41no—
268D8—22no—
269D8C3×D414yescomplemented
270M16—22no—
271C2×C8—22no—
272C2×C8C23×C311yescharacteristic
273C2×C8C23×C311yescharacteristic
274C2×C8C23×C311yescharacteristic
275C2×C8C23×C311yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4C3×D411yescharacteristic
282C4⋊C4C23×C311yescharacteristic
283C4⋊C4C23×C311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4C3×D411yescharacteristic
293C22⋊C4C3×D411yescharacteristic
294C42C23×C311yescharacteristic
295C22×C3—21no—
296C22×C3—21no—
297C22×C3—22no—
298C22×C3—22no—
299C22×C3—21no—
300C22×C3—21no—
301C22×C3—21no—
302C22×C3—21no—
303C22×C3—41no—
304C22×C3—41no—
305C22×C3—41no—
306C22×C3—41no—
307C22×C3—41no—
308C22×C3—41no—
309C22×C3—41no—
310C22×C3—84no—
311C22×C3C22×D411yescharacteristic
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—41no—
317C3×C4—41no—
318C3×C4—41no—
319C3×C4—41no—
320C3×C4—41no—
321C3×C4C22×D411yescharacteristic
322C3×C4H(5,𝔽2)11yescharacteristic
323C23—21no—
324C23—21no—
325C23—21no—
326C23—42no—
327C23—42no—
328C23—81no—
329C23C2×C3×D411yescharacteristic
330C23C2×C3×D411yescharacteristic
331Q8—21no—
332Q8—21no—
333Q8—21no—
334Q8—21no—
335Q8—21no—
336Q8—21no—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—41no—
342D4—42no—
343D4—42no—
344D4—42no—
345D4—42no—
346D4—81no—
347D4C2×C3×D412yes—
348D4C2×C3×D412yes—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—81no—
363C2×C4C2×C3×D411yescharacteristic
364C2×C4C2×C3×D411yescharacteristic
365C2×C4C2×C3×D411yescharacteristic
366C2×C4C2×C3×D411yescharacteristic
367C2×C4C24×C311yescharacteristic
368C8—21no—
369C8—21no—
370C8—21no—
371C8C2×C3×D412yes—
372C2×C3—41no—
373C2×C3—41no—
374C2×C3—42no—
375C2×C3—42no—
376C2×C3—81no—
377C2×C3D4211yescharacteristic
378C2×C3#57511yescharacteristic
379C2×C3#57711yescharacteristic
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—22no—
387C22—22no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—84no—
396C22C22×C3×D411yescharacteristic
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—41no—
402C4—41no—
403C4—41no—
404C4—41no—
405C4—41no—
406C4C22×C3×D411yescharacteristic
407C4C3×H(5,𝔽2)11yescharacteristic
408C3#326711yescharacteristic, direct product factor, Sylow
409C2—41no—
410C2—41no—
411C2—42no—
412C2—42no—
413C2—81no—
414C2C3×D4211yescharacteristic
415C2C3×#57511yescharacteristic
416C2C3×#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. C2×C3×#135C2semidirect
3. C3×#547C2semidirect
4. C3×#546C2semidirect
5. C3×#497C2semidirect
6. C3×#470C2semidirect
7. C3×#465C2semidirect
8. C3×#463C2semidirect
9. C3×#461C2semidirect
10. C3×#452C2semidirect
11. C3×#452C2semidirect
12. C3×#450C2semidirect
13. C3×#449C2semidirect
14. C3×#442C2semidirect
15. C3×#435C2semidirect
16. #3267C3direct (N × H)
19. C2×C3×#41C22semidirect
23. C2×C3×Q16C22semidirect
24. C2×C3×Q16C22semidirect
29. C2×C3×SD16C22semidirect
33. C22×C3×C8C22semidirect
34. C3×C4⋊Q8C22semidirect
41. C3×C22⋊Q8C22semidirect
48. C3×C4×D4C22semidirect
51. C3×#106C22semidirect
52. C3×C4⋊C8C22semidirect
53. C3×#103C22semidirect
54. C3×#103C22semidirect
55. C3×#103C22semidirect
58. C3×#102C22semidirect
60. C3×C22⋊C8C22semidirect
61. C3×#97C22semidirect
62. C2×AGL(1,ℤ/8)C2×C3semidirect
63. C2×#135C2×C3semidirect
64. #547C2×C3semidirect
65. #546C2×C3semidirect
66. #497C2×C3semidirect
67. #470C2×C3semidirect
68. #465C2×C3semidirect
69. #463C2×C3semidirect
70. #461C2×C3semidirect
71. #452C2×C3semidirect
72. #452C2×C3semidirect
73. #450C2×C3semidirect
74. #449C2×C3semidirect
75. #442C2×C3semidirect
76. #435C2×C3semidirect
113. C3×D8D4semidirect
141. C2×#41C22×C3semidirect
145. C2×Q16C22×C3semidirect
146. C2×Q16C22×C3semidirect
151. C2×SD16C22×C3semidirect
155. C22×C8C22×C3semidirect
156. C4⋊Q8C22×C3semidirect
163. C22⋊Q8C22×C3semidirect
170. C4×D4C22×C3semidirect
173. #106C22×C3semidirect
174. C4⋊C8C22×C3semidirect
175. #103C22×C3semidirect
176. #103C22×C3semidirect
177. #103C22×C3semidirect
180. #102C22×C3semidirect
182. C22⋊C8C22×C3semidirect
183. #97C22×C3semidirect
269. D8C3×D4semidirect
408. C3#3267direct (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
C2×C3×#1352
C3×#5472
C3×#5462
C3×#4972
C3×#4702
C3×#4652
C3×#4632
C3×#4612
C3×#4522
C3×#4502
C3×#4492
C3×#4422
C3×#4352
#32673