Subgroups — C₃×#69901 #11790524

Order 1152.

433 conjugacy classes of subgroups.

The subgroup lattice has 286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#405	C₂	1	1	yes	maximal, characteristic
2	C₃×#5124	C₂	1	2	yes	maximal
3	C₂×C₃×#819	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×#819	C₂	1	1	yes	maximal, characteristic
5	C₃×#4533	C₂	1	2	yes	maximal
6	C₃×#1953	—	3	1	no	maximal
7	#69901	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
9	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
10	C₃²×#117	C₂²	1	1	yes	characteristic
11	C₂×C₃×#208	C₂²	1	2	yes	—
12	C₂×C₃×#208	C₂²	1	2	yes	—
13	C₃²×#97	—	2	1	no	—
14	C₃²×C₄×C₈	—	2	1	no	—
15	C₃×#822	—	2	4	no	—
16	C₃×#819	—	2	1	no	—
17	C₃×#819	—	2	1	no	—
18	C₃×#819	C₄	1	4	yes	complemented
19	C₃×#430	—	3	2	no	—
20	C₂×C₃×#108	—	3	1	no	—
21	C₂×C₃×#108	—	3	1	no	—
22	C₃×#405	—	2	1	no	—
23	C₃×#405	D₃	1	1	yes	characteristic
24	C₃×#405	C₂×C₃	1	1	yes	characteristic
25	#5124	C₂×C₃	1	2	yes	—
26	C₂×#819	C₂×C₃	1	1	yes	characteristic
27	C₂×#819	C₂×C₃	1	1	yes	characteristic
28	C₃×#344	—	3	2	no	—
29	#4533	C₂×C₃	1	2	yes	—
30	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
31	C₃²×M₁₆	—	2	1	no	—
32	C₃²×M₁₆	D₄	1	2	yes	—
33	C₂×C₃²×C₈	—	2	1	no	—
34	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
35	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
36	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
37	C₂×C₃²×C₈	Q₈	1	2	yes	—
38	C₃²×C₄⋊C₄	—	2	1	no	—
39	C₃²×C₂²⋊C₄	Q₈	1	2	yes	—
40	C₃²×C₄²	—	2	1	no	—
41	C₃×#208	—	2	2	no	—
42	C₃×#208	—	2	2	no	—
43	C₃×#208	—	2	2	no	—
44	C₃×#208	C₂×C₄	1	4	yes	—
45	C₂×C₃×C₃⋊C₈	—	2	2	no	—
46	C₂×C₃×C₃⋊C₈	—	2	2	no	—
47	#1953	—	3	1	no	Sylow
48	C₂×C₃×M₁₆	—	2	1	no	—
49	C₂×C₃×M₁₆	—	3	2	no	—
50	C₂×C₃×M₁₆	—	3	2	no	—
51	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
52	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
53	C₂²×C₃×C₈	—	2	1	no	—
54	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
55	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
56	C₃×#117	—	2	1	no	—
57	C₃×#117	C₂×D₃	1	1	yes	characteristic
58	C₃×#117	C₂²×C₃	1	1	yes	characteristic
59	C₂×#208	C₂²×C₃	1	2	yes	—
60	C₂×#208	C₂²×C₃	1	2	yes	—
61	C₃×#108	—	3	4	no	—
62	C₃×#108	—	6	4	no	—
63	C₃×#108	—	6	1	no	—
64	C₃×#108	—	6	1	no	—
65	C₃×#97	—	2	2	no	—
66	C₃×#97	—	2	1	no	—
67	C₃×#97	—	2	1	no	—
68	C₃×C₄×C₈	—	2	2	no	—
69	C₃×C₄×C₈	—	2	1	no	—
70	C₃×C₄×C₈	—	2	1	no	—
71	#822	—	2	4	no	—
72	#819	—	2	1	no	—
73	#819	—	2	1	no	—
74	#819	C₃×C₄	1	4	yes	complemented
75	C₂³×C₃²	C₂×Q₈	1	1	yes	characteristic
76	C₂×C₃²×C₄	—	2	2	no	—
77	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
78	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
79	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
80	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
81	C₂×C₃²×C₄	#41	1	1	yes	characteristic
82	C₂×C₃²×C₄	#41	1	1	yes	characteristic
83	C₃²×C₈	—	2	2	no	—
84	C₃²×C₈	C₄⋊C₄	1	2	yes	—
85	C₃²×C₈	C₄⋊C₄	1	2	yes	—
86	C₃×C₃⋊C₈	—	2	4	no	—
87	C₃×C₃⋊C₈	—	4	2	no	—
88	#430	—	3	2	no	—
89	C₂×#108	—	3	1	no	—
90	C₂×#108	—	3	1	no	—
91	#405	C₃×D₃	1	1	yes	characteristic
92	#344	—	3	2	no	—
93	C₂²×C₃×C₄	—	2	1	no	—
94	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
95	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
96	C₃×M₁₆	—	2	2	no	—
97	C₃×M₁₆	—	2	1	no	—
98	C₃×M₁₆	—	2	1	no	—
99	C₃×M₁₆	—	2	2	no	—
100	C₃×M₁₆	—	3	4	no	—
101	C₃×M₁₆	—	6	2	no	—
102	C₃×M₁₆	—	6	2	no	—
103	C₃×M₁₆	—	6	2	no	—
104	C₃×M₁₆	D₁₂	1	2	yes	—
105	C₃×M₁₆	C₃×D₄	1	2	yes	—
106	C₂×C₃×C₈	—	2	2	no	—
107	C₂×C₃×C₈	—	2	1	no	—
108	C₂×C₃×C₈	—	2	1	no	—
109	C₂×C₃×C₈	—	2	2	no	—
110	C₂×C₃×C₈	—	2	2	no	—
111	C₂×C₃×C₈	—	2	1	no	—
112	C₂×C₃×C₈	—	2	1	no	—
113	C₂×C₃×C₈	—	6	2	no	—
114	C₂×C₃×C₈	—	6	2	no	—
115	C₂×C₃×C₈	Dic₆	1	2	yes	—
116	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
117	C₂×C₃×C₈	#67	1	1	yes	characteristic
118	C₂×C₃×C₈	#67	1	1	yes	characteristic
119	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
120	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
121	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
122	C₂×C₃×C₈	C₃×Q₈	1	2	yes	—
123	C₃×C₄⋊C₄	—	2	2	no	—
124	C₃×C₄⋊C₄	—	2	1	no	—
125	C₃×C₄⋊C₄	—	2	1	no	—
126	C₃×C₂²⋊C₄	—	2	2	no	—
127	C₃×C₂²⋊C₄	Dic₆	1	2	yes	—
128	C₃×C₂²⋊C₄	C₃×Q₈	1	2	yes	—
129	C₃×C₄²	—	2	2	no	—
130	C₃×C₄²	—	2	1	no	—
131	C₃×C₄²	—	2	1	no	—
132	#208	—	2	2	no	—
133	#208	—	2	2	no	—
134	#208	—	2	2	no	—
135	#208	C₂×C₃×C₄	1	4	yes	—
136	C₂×C₃⋊C₈	—	2	2	no	—
137	C₂×C₃⋊C₈	—	2	2	no	—
138	C₂²×C₃²	—	4	1	no	—
139	C₂²×C₃²	C₄×Q₈	1	1	yes	characteristic
140	C₂²×C₃²	C₂²⋊Q₈	1	1	yes	characteristic
141	C₂²×C₃²	C₄⋊Q₈	1	1	yes	characteristic
142	C₃²×C₄	—	4	2	no	—
143	C₃²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
145	C₃²×C₄	#121	1	1	yes	characteristic
146	C₃²×C₄	#125	1	1	yes	characteristic
147	C₂×M₁₆	—	3	2	no	—
148	C₂×M₁₆	—	3	2	no	—
149	C₂×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
150	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
151	#117	C₂×C₃×D₃	1	1	yes	characteristic
152	#108	—	3	4	no	—
153	#108	—	6	4	no	—
154	#108	—	6	1	no	—
155	#108	—	6	1	no	—
156	#97	—	2	1	no	—
157	C₄×C₈	—	2	1	no	—
158	C₂³×C₃	—	2	1	no	—
159	C₂³×C₃	C₂×Dic₆	1	1	yes	characteristic
160	C₂³×C₃	C₂×C₃×Q₈	1	1	yes	characteristic
161	C₂×C₃×C₄	—	2	4	no	—
162	C₂×C₃×C₄	—	2	2	no	—
163	C₂×C₃×C₄	—	2	2	no	—
164	C₂×C₃×C₄	—	2	1	no	—
165	C₂×C₃×C₄	—	2	1	no	—
166	C₂×C₃×C₄	—	2	1	no	—
167	C₂×C₃×C₄	—	2	1	no	—
168	C₂×C₃×C₄	—	2	1	no	—
169	C₂×C₃×C₄	—	2	1	no	—
170	C₂×C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
171	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
172	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
173	C₂×C₃×C₄	#235	1	1	yes	characteristic
174	C₂×C₃×C₄	#235	1	1	yes	characteristic
175	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
176	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
177	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
178	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
179	C₂×C₃×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
180	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
181	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
182	C₃×C₈	—	2	4	no	—
183	C₃×C₈	—	2	2	no	—
184	C₃×C₈	—	2	2	no	—
185	C₃×C₈	—	2	2	no	—
186	C₃×C₈	—	2	2	no	—
187	C₃×C₈	—	6	4	no	—
188	C₃×C₈	—	12	2	no	—
189	C₃×C₈	Dic₃⋊C₄	1	2	yes	—
190	C₃×C₈	Dic₃⋊C₄	1	2	yes	—
191	C₃×C₈	C₃×C₄⋊C₄	1	2	yes	—
192	C₃×C₈	C₃×C₄⋊C₄	1	2	yes	—
193	C₃⋊C₈	—	2	4	no	—
194	C₃⋊C₈	—	4	2	no	—
195	C₂×C₃²	—	2	1	no	—
196	C₂×C₃²	—	2	1	no	—
197	C₂×C₃²	—	2	1	no	—
198	C₂×C₃²	#389	1	1	yes	characteristic
199	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
200	M₁₆	—	2	1	no	—
201	M₁₆	—	3	4	no	—
202	M₁₆	—	6	2	no	—
203	M₁₆	—	6	2	no	—
204	M₁₆	—	6	2	no	—
205	M₁₆	C₃×D₁₂	1	2	yes	—
206	C₂×C₈	—	2	1	no	—
207	C₂×C₈	—	6	2	no	—
208	C₂×C₈	—	6	2	no	—
209	C₂×C₈	C₃×Dic₆	1	2	yes	—
210	C₂×C₈	C₃×C₄×D₃	1	2	yes	—
211	C₂×C₈	C₃×#67	1	1	yes	characteristic
212	C₂×C₈	C₃×#67	1	1	yes	characteristic
213	C₄⋊C₄	—	2	1	no	—
214	C₂²⋊C₄	C₃×Dic₆	1	2	yes	—
215	C₄²	—	2	1	no	—
216	C₂²×C₃	—	2	1	no	—
217	C₂²×C₃	—	2	1	no	—
218	C₂²×C₃	—	2	1	no	—
219	C₂²×C₃	—	4	1	no	—
220	C₂²×C₃	—	4	1	no	—
221	C₂²×C₃	—	4	2	no	—
222	C₂²×C₃	C₄×Dic₆	1	1	yes	characteristic
223	C₂²×C₃	#869	1	1	yes	characteristic
224	C₂²×C₃	#924	1	1	yes	characteristic
225	C₂²×C₃	C₃×C₄×Q₈	1	1	yes	characteristic
226	C₂²×C₃	C₃×C₂²⋊Q₈	1	1	yes	characteristic
227	C₂²×C₃	C₃×C₄⋊Q₈	1	1	yes	characteristic
228	C₃×C₄	—	2	1	no	—
229	C₃×C₄	—	2	1	no	—
230	C₃×C₄	—	2	1	no	—
231	C₃×C₄	—	2	1	no	—
232	C₃×C₄	—	4	4	no	—
233	C₃×C₄	—	4	2	no	—
234	C₃×C₄	—	4	2	no	—
235	C₃×C₄	#870	1	1	yes	characteristic
236	C₃×C₄	C₄×D₁₂	1	1	yes	characteristic
237	C₃×C₄	C₂×Dic₃⋊C₄	1	1	yes	characteristic
238	C₃×C₄	#930	1	1	yes	characteristic
239	C₃×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
240	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
241	C₃×C₄	C₃×#121	1	1	yes	characteristic
242	C₃×C₄	C₃×#125	1	1	yes	characteristic
243	C₃²	#1953	1	1	yes	characteristic, complemented, Sylow
244	C₂³	C₂×C₃×Dic₆	1	1	yes	characteristic
245	C₂×C₄	—	2	2	no	—
246	C₂×C₄	C₂×C₃×Dic₆	1	1	yes	characteristic
247	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
248	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
249	C₂×C₄	C₃×#235	1	1	yes	characteristic
250	C₂×C₄	C₃×#235	1	1	yes	characteristic
251	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
252	C₈	—	2	2	no	—
253	C₈	—	6	4	no	—
254	C₈	—	12	2	no	—
255	C₈	C₃×Dic₃⋊C₄	1	2	yes	—
256	C₈	C₃×Dic₃⋊C₄	1	2	yes	—
257	C₂×C₃	—	2	2	no	—
258	C₂×C₃	—	2	1	no	—
259	C₂×C₃	—	2	1	no	—
260	C₂×C₃	—	2	1	no	—
261	C₂×C₃	—	2	1	no	—
262	C₂×C₃	—	2	1	no	—
263	C₂×C₃	—	2	1	no	—
264	C₂×C₃	—	2	1	no	—
265	C₂×C₃	—	4	1	no	—
266	C₂×C₃	—	4	1	no	—
267	C₂×C₃	#4928	1	1	yes	characteristic
268	C₂×C₃	C₃×#389	1	1	yes	characteristic
269	C₂²	—	4	1	no	—
270	C₂²	C₃×C₄×Dic₆	1	1	yes	characteristic
271	C₂²	C₃×#869	1	1	yes	characteristic
272	C₂²	C₃×#924	1	1	yes	characteristic
273	C₄	—	4	2	no	—
274	C₄	C₃×#870	1	1	yes	characteristic
275	C₄	C₃×C₄×D₁₂	1	1	yes	characteristic
276	C₄	C₂×C₃×Dic₃⋊C₄	1	1	yes	characteristic
277	C₄	C₃×#930	1	1	yes	characteristic
278	C₃	—	2	1	no	—
279	C₃	#69901	1	1	yes	characteristic, direct product factor
280	C₃	C₃×#1953	1	1	yes	characteristic, complemented
281	C₂	—	2	1	no	—
282	C₂	—	2	1	no	—
283	C₂	—	2	1	no	—
284	C₂	C₃×#4928	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	#930
commutator	C₂×C₃×C₄	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₃
Fitting	C₃²×#405	C₂
socle	C₂×C₃²	#389
prime radical	C₂³×C₃²	C₂×Q₈
cosocle	C₂²×C₃×C₄	C₂³×C₃
hypercenter	C₃×#405	D₃
hypocenter	C₃	C₃×#1953
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₃×#405

Complements

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

N	H ≅ G/N	type
7. #69901	C₃	direct (N × H)
18. C₃×#819	C₄	semidirect
74. #819	C₃×C₄	semidirect
243. C₃²	#1953	semidirect
279. C₃	#69901	direct (N × H)
280. C₃	C₃×#1953	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#405	2
C₃×#5124	2
C₂×C₃×#819	2
C₃×#4533	2
C₃×#1953	3
#69901	3

Subgroups — C3×#69901 #11790524

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#69901 #11790524