Subgroups — C₃×#70857 #11797474

Order 1152.

395 conjugacy classes of subgroups.

The subgroup lattice has 363 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₈×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#812	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#4549	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#4549	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₄⋊(C₃⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#4461	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2168	—	3	1	no	maximal
9	#70857	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
11	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
12	C₃²×C₄×D₄	C₄	1	1	yes	characteristic
13	C₃²×C₄⋊C₈	C₄	1	1	yes	characteristic
14	C₃²×C₂²⋊C₈	C₄	1	1	yes	characteristic
15	C₃²×C₂²⋊C₈	C₄	1	1	yes	characteristic
16	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
17	C₃×#812	—	2	2	no	—
18	C₂×C₃×C₃⋊C₁₆	—	2	2	no	—
19	C₂×C₃×C₃⋊C₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₃⋊C₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₃⋊C₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₃⋊C₁₆	C₂²	1	1	yes	characteristic
23	C₂×C₃×M₃₂	—	3	1	no	—
24	C₂²×C₃×C₁₆	—	3	1	no	—
25	C₃×C₈×D₄	—	2	1	no	—
26	C₃×C₈×D₄	D₃	1	1	yes	characteristic
27	C₃×C₈×D₄	C₂×C₃	1	1	yes	characteristic
28	C₂×#812	C₂×C₃	1	1	yes	characteristic, complemented
29	C₂²×C₃⋊C₁₆	C₂×C₃	1	1	yes	characteristic, complemented
30	C₃×C₄⋊C₁₆	—	3	1	no	—
31	C₃×C₂²⋊C₁₆	—	3	1	no	—
32	C₃×C₂²⋊C₁₆	—	3	1	no	—
33	C₃×#346	—	3	1	no	—
34	#4549	C₂×C₃	1	1	yes	characteristic, complemented
35	#4549	C₂×C₃	1	1	yes	characteristic, complemented
36	C₄⋊(C₃⋊C₁₆)	C₂×C₃	1	1	yes	characteristic, complemented
37	#4461	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂×C₃²×D₄	C₈	1	1	yes	characteristic
39	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
41	C₂×C₃²×C₈	—	2	1	no	—
42	C₂×C₃²×C₈	—	2	1	no	—
43	C₂×C₃²×C₈	—	2	1	no	—
44	C₂×C₃²×C₈	—	2	1	no	—
45	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
46	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
47	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
48	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
49	C₃²×C₄⋊C₄	C₈	1	1	yes	characteristic
50	C₃²×C₂²⋊C₄	C₈	1	1	yes	characteristic
51	C₃²×C₂²⋊C₄	C₈	1	1	yes	characteristic
52	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
53	C₃×C₃⋊C₁₆	—	2	1	no	—
54	C₃×C₃⋊C₁₆	—	2	1	no	—
55	C₃×C₃⋊C₁₆	—	2	1	no	—
56	C₃×C₃⋊C₁₆	D₄	1	2	yes	complemented
57	#2168	—	3	1	no	Sylow
58	C₂²×C₃×C₈	—	2	1	no	—
59	C₂²×C₃×C₈	—	2	1	no	—
60	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
61	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
62	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
63	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
64	C₃×C₄×D₄	—	2	1	no	—
65	C₃×C₄×D₄	Dic₃	1	1	yes	characteristic
66	C₃×C₄×D₄	C₃×C₄	1	1	yes	characteristic
67	C₃×M₃₂	—	6	2	no	—
68	C₂×C₃×C₁₆	—	3	1	no	—
69	C₂×C₃×C₁₆	—	3	1	no	—
70	C₂×C₃×C₁₆	—	3	1	no	—
71	C₂×C₃×C₁₆	—	3	1	no	—
72	C₂×C₃×C₁₆	—	6	2	no	—
73	C₃×C₄⋊C₈	—	2	1	no	—
74	C₃×C₄⋊C₈	Dic₃	1	1	yes	characteristic
75	C₃×C₄⋊C₈	C₃×C₄	1	1	yes	characteristic
76	C₃×C₂²⋊C₈	—	2	1	no	—
77	C₃×C₂²⋊C₈	—	2	1	no	—
78	C₃×C₂²⋊C₈	Dic₃	1	1	yes	characteristic
79	C₃×C₂²⋊C₈	Dic₃	1	1	yes	characteristic
80	C₃×C₂²⋊C₈	C₃×C₄	1	1	yes	characteristic
81	C₃×C₂²⋊C₈	C₃×C₄	1	1	yes	characteristic
82	C₃×C₄×C₈	—	2	1	no	—
83	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
84	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
85	#812	—	2	2	no	—
86	C₂×C₃⋊C₁₆	—	2	2	no	—
87	C₂×C₃⋊C₁₆	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₃⋊C₁₆	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₃⋊C₁₆	C₂²×C₃	1	1	yes	characteristic
90	C₂×C₃⋊C₁₆	C₂²×C₃	1	1	yes	characteristic
91	C₂³×C₃²	C₂×C₈	1	1	yes	characteristic
92	C₂³×C₃²	C₂×C₈	1	1	yes	characteristic
93	C₃²×D₄	—	2	2	no	—
94	C₂×C₃²×C₄	—	2	1	no	—
95	C₂×C₃²×C₄	—	2	1	no	—
96	C₂×C₃²×C₄	—	2	1	no	—
97	C₂×C₃²×C₄	—	2	1	no	—
98	C₂×C₃²×C₄	C₂×C₈	1	1	yes	characteristic
99	C₂×C₃²×C₄	C₂×C₈	1	1	yes	characteristic
100	C₂×C₃²×C₄	C₂×C₈	1	1	yes	characteristic
101	C₂×C₃²×C₄	C₂×C₈	1	1	yes	characteristic
102	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
103	C₃²×C₈	—	2	1	no	—
104	C₃²×C₈	—	2	1	no	—
105	C₃²×C₈	—	2	1	no	—
106	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
107	C₃²×C₈	#41	1	1	yes	characteristic
108	C₂×M₃₂	—	3	1	no	—
109	C₂²×C₁₆	—	3	1	no	—
110	C₈×D₄	C₃×D₃	1	1	yes	characteristic
111	C₄⋊C₁₆	—	3	1	no	—
112	C₂²⋊C₁₆	—	3	1	no	—
113	C₂²⋊C₁₆	—	3	1	no	—
114	#346	—	3	1	no	—
115	C₂×C₃×D₄	—	2	1	no	—
116	C₂×C₃×D₄	C₃⋊C₈	1	1	yes	characteristic
117	C₂×C₃×D₄	C₃×C₈	1	1	yes	characteristic
118	C₂²×C₃×C₄	—	2	1	no	—
119	C₂²×C₃×C₄	—	2	1	no	—
120	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
121	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
122	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
123	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
124	C₂×C₃×C₈	—	2	1	no	—
125	C₂×C₃×C₈	—	2	1	no	—
126	C₂×C₃×C₈	—	2	1	no	—
127	C₂×C₃×C₈	—	2	1	no	—
128	C₂×C₃×C₈	—	2	1	no	—
129	C₂×C₃×C₈	—	2	1	no	—
130	C₂×C₃×C₈	—	2	1	no	—
131	C₂×C₃×C₈	—	2	1	no	—
132	C₂×C₃×C₈	—	2	1	no	—
133	C₂×C₃×C₈	—	2	1	no	—
134	C₂×C₃×C₈	—	2	1	no	—
135	C₂×C₃×C₈	—	2	1	no	—
136	C₂×C₃×C₈	—	4	1	no	—
137	C₂×C₃×C₈	—	4	1	no	—
138	C₂×C₃×C₈	—	4	1	no	—
139	C₂×C₃×C₈	—	4	1	no	—
140	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
141	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
142	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
143	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
144	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
145	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
146	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
147	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
148	C₃×C₄⋊C₄	—	2	1	no	—
149	C₃×C₄⋊C₄	C₃⋊C₈	1	1	yes	characteristic
150	C₃×C₄⋊C₄	C₃×C₈	1	1	yes	characteristic
151	C₃×C₂²⋊C₄	—	2	1	no	—
152	C₃×C₂²⋊C₄	—	2	1	no	—
153	C₃×C₂²⋊C₄	C₃⋊C₈	1	1	yes	characteristic
154	C₃×C₂²⋊C₄	C₃⋊C₈	1	1	yes	characteristic
155	C₃×C₂²⋊C₄	C₃×C₈	1	1	yes	characteristic
156	C₃×C₂²⋊C₄	C₃×C₈	1	1	yes	characteristic
157	C₃×C₄²	—	2	1	no	—
158	C₃×C₄²	C₂×Dic₃	1	1	yes	characteristic
159	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
160	C₃×C₁₆	—	3	2	no	—
161	C₃×C₁₆	—	6	1	no	—
162	C₃×C₁₆	—	6	1	no	—
163	C₃×C₁₆	—	6	1	no	—
164	C₃⋊C₁₆	—	2	1	no	—
165	C₃⋊C₁₆	—	2	1	no	—
166	C₃⋊C₁₆	—	2	1	no	—
167	C₃⋊C₁₆	C₃×D₄	1	2	yes	complemented
168	C₂²×C₃²	—	2	1	no	—
169	C₂²×C₃²	—	2	1	no	—
170	C₂²×C₃²	—	2	1	no	—
171	C₂²×C₃²	—	2	1	no	—
172	C₂²×C₃²	—	2	1	no	—
173	C₂²×C₃²	M₃₂	1	2	yes	complemented
174	C₂²×C₃²	C₂²×C₈	1	1	yes	characteristic
175	C₃²×C₄	—	2	1	no	—
176	C₃²×C₄	—	2	1	no	—
177	C₃²×C₄	—	2	1	no	—
178	C₃²×C₄	—	2	1	no	—
179	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
180	C₃²×C₄	#131	1	1	yes	characteristic
181	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
182	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
183	C₄×D₄	C₃×Dic₃	1	1	yes	characteristic
184	M₃₂	—	6	2	no	—
185	C₂×C₁₆	—	3	1	no	—
186	C₂×C₁₆	—	3	1	no	—
187	C₂×C₁₆	—	3	1	no	—
188	C₂×C₁₆	—	3	1	no	—
189	C₂×C₁₆	—	6	2	no	—
190	C₄⋊C₈	C₃×Dic₃	1	1	yes	characteristic
191	C₂²⋊C₈	C₃×Dic₃	1	1	yes	characteristic
192	C₂²⋊C₈	C₃×Dic₃	1	1	yes	characteristic
193	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic
194	C₂³×C₃	—	2	1	no	—
195	C₂³×C₃	—	2	1	no	—
196	C₂³×C₃	C₂×C₃⋊C₈	1	1	yes	characteristic
197	C₂³×C₃	C₂×C₃⋊C₈	1	1	yes	characteristic
198	C₂³×C₃	C₂×C₃×C₈	1	1	yes	characteristic
199	C₂³×C₃	C₂×C₃×C₈	1	1	yes	characteristic
200	C₃×D₄	—	2	4	no	—
201	C₃×D₄	—	2	2	no	—
202	C₃×D₄	—	2	2	no	—
203	C₂×C₃×C₄	—	2	1	no	—
204	C₂×C₃×C₄	—	2	1	no	—
205	C₂×C₃×C₄	—	2	1	no	—
206	C₂×C₃×C₄	—	2	1	no	—
207	C₂×C₃×C₄	—	2	1	no	—
208	C₂×C₃×C₄	—	2	1	no	—
209	C₂×C₃×C₄	—	2	1	no	—
210	C₂×C₃×C₄	—	2	1	no	—
211	C₂×C₃×C₄	—	2	1	no	—
212	C₂×C₃×C₄	—	2	1	no	—
213	C₂×C₃×C₄	—	2	1	no	—
214	C₂×C₃×C₄	—	2	1	no	—
215	C₂×C₃×C₄	—	2	1	no	—
216	C₂×C₃×C₄	—	4	1	no	—
217	C₂×C₃×C₄	—	4	1	no	—
218	C₂×C₃×C₄	—	4	1	no	—
219	C₂×C₃×C₄	—	4	1	no	—
220	C₂×C₃×C₄	C₂×C₃⋊C₈	1	1	yes	characteristic
221	C₂×C₃×C₄	C₂×C₃⋊C₈	1	1	yes	characteristic
222	C₂×C₃×C₄	C₂×C₃⋊C₈	1	1	yes	characteristic
223	C₂×C₃×C₄	C₂×C₃⋊C₈	1	1	yes	characteristic
224	C₂×C₃×C₄	C₂×C₃×C₈	1	1	yes	characteristic
225	C₂×C₃×C₄	C₂×C₃×C₈	1	1	yes	characteristic
226	C₂×C₃×C₄	C₂×C₃×C₈	1	1	yes	characteristic
227	C₂×C₃×C₄	C₂×C₃×C₈	1	1	yes	characteristic
228	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
229	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
230	C₃×C₈	—	2	1	no	—
231	C₃×C₈	—	2	1	no	—
232	C₃×C₈	—	2	1	no	—
233	C₃×C₈	—	2	1	no	—
234	C₃×C₈	—	2	1	no	—
235	C₃×C₈	—	2	1	no	—
236	C₃×C₈	—	2	1	no	—
237	C₃×C₈	—	2	1	no	—
238	C₃×C₈	—	4	1	no	—
239	C₃×C₈	—	4	1	no	—
240	C₃×C₈	—	4	1	no	—
241	C₃×C₈	D₃×D₄	1	1	yes	characteristic
242	C₃×C₈	#237	1	1	yes	characteristic
243	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
244	C₃×C₈	C₃×#41	1	1	yes	characteristic
245	C₂×C₃²	—	2	2	no	—
246	C₂×C₃²	—	4	1	no	—
247	C₂×C₃²	C₈×D₄	1	1	yes	characteristic
248	C₂×C₃²	C₂×M₃₂	1	1	yes	characteristic
249	C₂×C₃²	#504	1	1	yes	characteristic
250	C₂×D₄	C₃×C₃⋊C₈	1	1	yes	characteristic
251	C₂²×C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
252	C₂²×C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
253	C₂×C₈	—	2	1	no	—
254	C₂×C₈	—	2	1	no	—
255	C₂×C₈	—	2	1	no	—
256	C₂×C₈	—	2	1	no	—
257	C₂×C₈	C₂×C₃×Dic₃	1	1	yes	characteristic
258	C₂×C₈	C₂×C₃×Dic₃	1	1	yes	characteristic
259	C₂×C₈	C₂×C₃×Dic₃	1	1	yes	characteristic
260	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
261	C₄⋊C₄	C₃×C₃⋊C₈	1	1	yes	characteristic
262	C₂²⋊C₄	C₃×C₃⋊C₈	1	1	yes	characteristic
263	C₂²⋊C₄	C₃×C₃⋊C₈	1	1	yes	characteristic
264	C₄²	C₂×C₃×Dic₃	1	1	yes	characteristic
265	C₁₆	—	3	2	no	—
266	C₁₆	—	6	1	no	—
267	C₁₆	—	6	1	no	—
268	C₁₆	—	6	1	no	—
269	C₂²×C₃	—	2	1	no	—
270	C₂²×C₃	—	2	1	no	—
271	C₂²×C₃	—	2	1	no	—
272	C₂²×C₃	—	2	1	no	—
273	C₂²×C₃	—	2	2	no	—
274	C₂²×C₃	—	2	1	no	—
275	C₂²×C₃	—	2	1	no	—
276	C₂²×C₃	—	2	1	no	—
277	C₂²×C₃	—	2	1	no	—
278	C₂²×C₃	—	2	1	no	—
279	C₂²×C₃	—	2	1	no	—
280	C₂²×C₃	—	2	1	no	—
281	C₂²×C₃	—	2	2	no	—
282	C₂²×C₃	—	4	1	no	—
283	C₂²×C₃	—	4	1	no	—
284	C₂²×C₃	—	4	1	no	—
285	C₂²×C₃	—	4	1	no	—
286	C₂²×C₃	#812	1	2	yes	complemented
287	C₂²×C₃	C₃×M₃₂	1	2	yes	complemented
288	C₂²×C₃	C₂²×C₃⋊C₈	1	1	yes	characteristic
289	C₂²×C₃	C₂²×C₃×C₈	1	1	yes	characteristic
290	C₃×C₄	—	2	2	no	—
291	C₃×C₄	—	2	1	no	—
292	C₃×C₄	—	2	1	no	—
293	C₃×C₄	—	2	1	no	—
294	C₃×C₄	—	2	1	no	—
295	C₃×C₄	—	2	1	no	—
296	C₃×C₄	—	2	1	no	—
297	C₃×C₄	—	2	1	no	—
298	C₃×C₄	—	2	1	no	—
299	C₃×C₄	—	2	1	no	—
300	C₃×C₄	—	2	1	no	—
301	C₃×C₄	—	4	1	no	—
302	C₃×C₄	—	4	1	no	—
303	C₃×C₄	—	4	1	no	—
304	C₃×C₄	D₄×Dic₃	1	1	yes	characteristic
305	C₃×C₄	#948	1	1	yes	characteristic
306	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
307	C₃×C₄	C₃×#131	1	1	yes	characteristic
308	C₃²	#2168	1	1	yes	characteristic, complemented, Sylow
309	C₂³	C₂×C₃×C₃⋊C₈	1	1	yes	characteristic
310	C₂³	C₂×C₃×C₃⋊C₈	1	1	yes	characteristic
311	D₄	—	2	2	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	C₂×C₃×C₃⋊C₈	1	1	yes	characteristic
317	C₂×C₄	C₂×C₃×C₃⋊C₈	1	1	yes	characteristic
318	C₂×C₄	C₂×C₃×C₃⋊C₈	1	1	yes	characteristic
319	C₂×C₄	C₂×C₃×C₃⋊C₈	1	1	yes	characteristic
320	C₂×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
321	C₈	—	2	1	no	—
322	C₈	—	2	1	no	—
323	C₈	—	2	1	no	—
324	C₈	C₃×D₃×D₄	1	1	yes	characteristic
325	C₈	C₃×#237	1	1	yes	characteristic
326	C₂×C₃	—	2	2	no	—
327	C₂×C₃	—	2	2	no	—
328	C₂×C₃	—	2	1	no	—
329	C₂×C₃	—	2	1	no	—
330	C₂×C₃	—	2	1	no	—
331	C₂×C₃	—	4	2	no	—
332	C₂×C₃	—	4	2	no	—
333	C₂×C₃	—	4	1	no	—
334	C₂×C₃	—	4	1	no	—
335	C₂×C₃	D₄×C₃⋊C₈	1	1	yes	characteristic
336	C₂×C₃	C₂×#812	1	1	yes	characteristic
337	C₂×C₃	#5140	1	1	yes	characteristic
338	C₂×C₃	C₃×C₈×D₄	1	1	yes	characteristic
339	C₂×C₃	C₂×C₃×M₃₂	1	1	yes	characteristic
340	C₂×C₃	C₃×#504	1	1	yes	characteristic
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	C₃×#812	1	2	yes	complemented
347	C₂²	C₂²×C₃×C₃⋊C₈	1	1	yes	characteristic
348	C₄	—	2	1	no	—
349	C₄	—	2	1	no	—
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	C₃×D₄×Dic₃	1	1	yes	characteristic
353	C₄	C₃×#948	1	1	yes	characteristic
354	C₃	—	2	1	no	—
355	C₃	#70857	1	1	yes	characteristic, direct product factor
356	C₃	C₃×#2168	1	1	yes	characteristic, complemented
357	C₂	—	2	2	no	—
358	C₂	—	4	1	no	—
359	C₂	C₃×D₄×C₃⋊C₈	1	1	yes	characteristic
360	C₂	C₂×C₃×#812	1	1	yes	characteristic
361	C₂	C₃×#5140	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₈	C₂²×D₃
commutator	C₂²×C₃	C₂²×C₃×C₈
Frattini	C₂×C₈	C₂²×C₃×D₃
Fitting	C₃²×C₈×D₄	C₂
socle	C₂²×C₃²	C₂²×C₈
prime radical	C₂×C₃²×D₄	C₈
cosocle	C₂×C₃×C₈	C₂³×C₃
hypercenter	C₃×C₈×D₄	D₃
hypocenter	C₃	C₃×#2168
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₈ ◁ C₃×C₈×D₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#812	C₂	semidirect
3. C₂²×C₃×C₃⋊C₁₆	C₂	semidirect
4. C₃×#4549	C₂	semidirect
5. C₃×#4549	C₂	semidirect
6. C₃×C₄⋊(C₃⋊C₁₆)	C₂	semidirect
7. C₃×#4461	C₂	semidirect
9. #70857	C₃	direct (N × H)
28. C₂×#812	C₂×C₃	semidirect
29. C₂²×C₃⋊C₁₆	C₂×C₃	semidirect
34. #4549	C₂×C₃	semidirect
35. #4549	C₂×C₃	semidirect
36. C₄⋊(C₃⋊C₁₆)	C₂×C₃	semidirect
37. #4461	C₂×C₃	semidirect
56. C₃×C₃⋊C₁₆	D₄	semidirect
167. C₃⋊C₁₆	C₃×D₄	semidirect
173. C₂²×C₃²	M₃₂	semidirect
286. C₂²×C₃	#812	semidirect
287. C₂²×C₃	C₃×M₃₂	semidirect
308. C₃²	#2168	semidirect
346. C₂²	C₃×#812	semidirect
355. C₃	#70857	direct (N × H)
356. C₃	C₃×#2168	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₈×D₄	2
C₂×C₃×#812	2
C₂²×C₃×C₃⋊C₁₆	2
C₃×#4549	2
C₃×C₄⋊(C₃⋊C₁₆)	2
C₃×#4461	2
C₃×#2168	3
#70857	3

Subgroups — C3×#70857 #11797474

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#70857 #11797474