Subgroups — C₃×#70789 #11775053

Order 1152.

627 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5477	C₂	1	1	yes	maximal, characteristic
2	C₃²×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#4470	C₂	1	4	yes	maximal, complemented
5	C₃×#1502	—	3	1	no	maximal
6	#70789	C₃	1	1	yes	maximal, characteristic, direct product factor
7	C₂×C₃×#235	—	2	1	no	—
8	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
9	C₃×#930	—	2	1	no	—
10	C₃×#930	C₂²	1	2	yes	—
11	C₂×C₃×C₄⋊Dic₃	—	2	1	no	—
12	C₂×C₃×C₄×Dic₃	—	2	1	no	—
13	C₃×#875	—	2	1	no	—
14	C₃×#874	C₄	1	1	yes	characteristic, complemented
15	C₃×C₄×D₁₂	—	2	1	no	—
16	C₃×C₄×D₁₂	C₄	1	2	yes	complemented
17	C₃×#869	C₄	1	1	yes	characteristic, complemented
18	C₃²×C₄⋊C₈	—	2	1	no	—
19	C₃²×C₂²⋊C₈	C₂²	1	2	yes	—
20	C₃²×C₄×C₈	—	2	1	no	—
21	C₃×C₃⋊#95	C₂²	1	2	yes	—
22	C₃×#532	—	3	1	no	—
23	#5477	C₂×C₃	1	1	yes	characteristic
24	C₃×#431	—	2	1	no	—
25	C₃×#431	D₃	1	1	yes	characteristic, complemented
26	C₃×#431	C₂×C₃	1	1	yes	characteristic, complemented
27	C₃×C₄×C₄⋊C₄	—	3	1	no	—
28	C₄×C₄⋊Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
29	C₃×#327	—	3	4	no	—
30	#4470	C₂×C₃	1	4	yes	complemented
31	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
32	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
33	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
34	C₂×C₃×#67	—	2	2	no	—
35	C₂²×C₃×Dic₃	—	2	2	no	—
36	C₃×#235	—	4	2	no	—
37	C₃×#235	—	4	2	no	—
38	C₂×C₃×D₁₂	—	2	1	no	—
39	C₂×C₃×D₁₂	—	2	1	no	—
40	C₂×C₃×D₁₂	C₂×C₄	1	2	yes	—
41	C₂×C₃×C₄×D₃	—	2	2	no	—
42	C₂×C₃×Dic₆	—	2	1	no	—
43	C₂×C₃²×C₈	—	2	2	no	—
44	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
45	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
46	C₃²×C₄²	D₄	1	1	yes	characteristic
47	C₃²×C₄²	D₄	1	1	yes	characteristic
48	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
49	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
50	C₃×C₄⋊Dic₃	—	2	4	no	—
51	C₃×C₄⋊Dic₃	—	2	1	no	—
52	C₃×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
53	C₃×C₄×Dic₃	—	4	2	no	—
54	#1502	—	3	1	no	Sylow
55	C₂×C₃×#41	—	6	1	no	—
56	C₂×#235	—	2	1	no	—
57	C₃×C₄⋊Q₈	—	3	1	no	—
58	C₃×#127	—	3	1	no	—
59	C₃×#124	—	6	1	no	—
60	C₃×#121	—	3	2	no	—
61	C₃×#121	—	6	1	no	—
62	C₃×C₄×D₄	—	3	2	no	—
63	C₃×C₄×D₄	—	6	1	no	—
64	C₂×C₃×C₄⋊C₄	—	6	1	no	—
65	C₂×C₃×C₄²	—	2	1	no	—
66	C₂×C₃×C₄²	—	6	1	no	—
67	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
68	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
69	#930	—	2	1	no	—
70	#930	C₂²×C₃	1	2	yes	—
71	C₂×C₄⋊Dic₃	—	2	1	no	—
72	C₂×C₄×Dic₃	—	2	1	no	—
73	#875	—	2	1	no	—
74	#874	C₃×C₄	1	1	yes	characteristic, complemented
75	C₄×D₁₂	—	2	1	no	—
76	C₄×D₁₂	C₃×C₄	1	2	yes	complemented
77	#869	C₃×C₄	1	1	yes	characteristic, complemented
78	C₃×C₄⋊C₈	—	2	2	no	—
79	C₃×C₄⋊C₈	—	2	1	no	—
80	C₃×C₄⋊C₈	—	2	1	no	—
81	C₃×C₂²⋊C₈	—	2	2	no	—
82	C₃×C₂²⋊C₈	C₂×D₃	1	2	yes	—
83	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
84	C₃×C₄×C₈	—	2	2	no	—
85	C₃×C₄×C₈	—	2	1	no	—
86	C₃×C₄×C₈	—	2	1	no	—
87	C₃×#95	—	3	2	no	—
88	C₃⋊#95	C₂²×C₃	1	2	yes	—
89	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₃×D₃	—	2	2	no	—
91	C₂×C₃²×C₄	—	2	2	no	—
92	C₂×C₃²×C₄	—	4	1	no	—
93	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₃²×C₄	D₈	1	2	yes	—
98	C₂×C₃²×C₄	SD₁₆	1	2	yes	—
99	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
101	C₃×#67	—	4	2	no	—
102	C₃×#67	—	4	2	no	—
103	C₂×C₃×Dic₃	—	2	4	no	—
104	C₂×C₃×Dic₃	—	2	2	no	—
105	C₂×C₃×Dic₃	—	4	2	no	—
106	C₂×C₃×Dic₃	—	4	2	no	—
107	C₃×D₁₂	—	4	2	no	—
108	C₃×D₁₂	—	4	2	no	—
109	C₃×D₁₂	—	4	2	no	—
110	C₃×C₄×D₃	—	4	4	no	—
111	C₃×Dic₆	—	4	2	no	—
112	C₃²×C₈	—	4	2	no	—
113	#532	—	3	1	no	—
114	#431	C₃×D₃	1	1	yes	characteristic, complemented
115	C₄×C₄⋊C₄	—	3	1	no	—
116	#327	—	3	4	no	—
117	C₃×#41	—	12	2	no	—
118	C₃×#41	—	12	2	no	—
119	C₂×C₃×Q₈	—	6	1	no	—
120	C₂×C₃×D₄	—	3	2	no	—
121	C₂×C₃×D₄	—	6	2	no	—
122	C₂×C₃×D₄	—	6	1	no	—
123	C₂×C₃×D₄	—	6	1	no	—
124	C₂²×C₃×C₄	—	2	1	no	—
125	C₂²×C₃×C₄	—	2	1	no	—
126	C₂²×C₃×C₄	—	2	1	no	—
127	C₂²×C₃×C₄	—	6	2	no	—
128	C₂²×C₃×C₄	—	6	2	no	—
129	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
130	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
131	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
132	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
133	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
134	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
135	C₂×#67	—	2	2	no	—
136	C₂²×Dic₃	—	2	2	no	—
137	#235	—	4	2	no	—
138	#235	—	4	2	no	—
139	C₂×D₁₂	—	2	1	no	—
140	C₂×D₁₂	—	2	1	no	—
141	C₂×D₁₂	C₂×C₃×C₄	1	2	yes	—
142	C₂×C₄×D₃	—	2	2	no	—
143	C₂×Dic₆	—	2	1	no	—
144	C₂×C₃×C₈	—	2	4	no	—
145	C₂×C₃×C₈	—	2	2	no	—
146	C₂×C₃×C₈	—	2	2	no	—
147	C₃×C₄⋊C₄	—	3	2	no	—
148	C₃×C₄⋊C₄	—	6	4	no	—
149	C₃×C₄⋊C₄	—	6	1	no	—
150	C₃×C₂²⋊C₄	—	6	2	no	—
151	C₃×C₂²⋊C₄	—	6	2	no	—
152	C₃×C₄²	—	2	1	no	—
153	C₃×C₄²	—	2	1	no	—
154	C₃×C₄²	—	2	1	no	—
155	C₃×C₄²	—	2	1	no	—
156	C₃×C₄²	—	12	2	no	—
157	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
158	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
159	C₃×C₄²	#67	1	1	yes	characteristic
160	C₃×C₄²	#67	1	1	yes	characteristic
161	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
162	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
163	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
164	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
165	(C₂×D₃)⋊C₄	—	2	2	no	—
166	(C₂×D₃)⋊C₄	—	2	2	no	—
167	C₄⋊Dic₃	—	2	4	no	—
168	C₄⋊Dic₃	—	2	1	no	—
169	C₄⋊Dic₃	C₂×C₃×C₄	1	2	yes	—
170	C₄×Dic₃	—	4	2	no	—
171	C₂²×C₃²	—	2	1	no	—
172	C₂²×C₃²	—	2	1	no	—
173	C₂²×C₃²	C₂×C₂²⋊C₄	1	1	yes	characteristic
174	C₂²×C₃²	C₂×D₈	1	1	yes	characteristic
175	C₂²×C₃²	C₂×SD₁₆	1	1	yes	characteristic
176	C₂×C₃×D₃	—	4	2	no	—
177	C₂×C₃×D₃	—	4	2	no	—
178	C₂×C₃×D₃	—	4	2	no	—
179	C₃²×C₄	—	2	1	no	—
180	C₃²×C₄	—	2	1	no	—
181	C₃²×C₄	—	2	1	no	—
182	C₃²×C₄	#102	1	2	yes	—
183	C₃²×C₄	#102	1	2	yes	—
184	C₃²×C₄	#104	1	2	yes	—
185	C₃×Dic₃	—	4	4	no	—
186	C₃×Dic₃	—	4	2	no	—
187	C₂×#41	—	6	1	no	—
188	C₄⋊Q₈	—	3	1	no	—
189	#127	—	3	1	no	—
190	#124	—	6	1	no	—
191	#121	—	3	2	no	—
192	#121	—	6	1	no	—
193	C₄×D₄	—	3	2	no	—
194	C₄×D₄	—	6	1	no	—
195	C₂×C₄⋊C₄	—	6	1	no	—
196	C₂×C₄²	—	6	1	no	—
197	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
198	C₄⋊C₈	—	2	1	no	—
199	C₂²⋊C₈	C₂×C₃×D₃	1	2	yes	—
200	C₄×C₈	—	2	1	no	—
201	#95	—	3	2	no	—
202	C₂³×C₃	—	2	1	no	—
203	C₂³×C₃	—	6	2	no	—
204	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
205	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
206	C₂²×D₃	—	2	2	no	—
207	C₃×Q₈	—	12	2	no	—
208	C₃×D₄	—	12	2	no	—
209	C₃×D₄	—	12	2	no	—
210	C₃×D₄	—	12	2	no	—
211	C₃×D₄	—	12	2	no	—
212	C₃×D₄	—	12	2	no	—
213	C₂×C₃×C₄	—	2	2	no	—
214	C₂×C₃×C₄	—	2	2	no	—
215	C₂×C₃×C₄	—	2	2	no	—
216	C₂×C₃×C₄	—	2	2	no	—
217	C₂×C₃×C₄	—	2	1	no	—
218	C₂×C₃×C₄	—	2	1	no	—
219	C₂×C₃×C₄	—	2	1	no	—
220	C₂×C₃×C₄	—	2	1	no	—
221	C₂×C₃×C₄	—	2	1	no	—
222	C₂×C₃×C₄	—	2	1	no	—
223	C₂×C₃×C₄	—	4	2	no	—
224	C₂×C₃×C₄	—	4	1	no	—
225	C₂×C₃×C₄	—	4	1	no	—
226	C₂×C₃×C₄	—	4	2	no	—
227	C₂×C₃×C₄	—	6	4	no	—
228	C₂×C₃×C₄	—	6	2	no	—
229	C₂×C₃×C₄	—	12	2	no	—
230	C₂×C₃×C₄	—	12	2	no	—
231	C₂×C₃×C₄	—	12	4	no	—
232	C₂×C₃×C₄	#204	1	2	yes	—
233	C₂×C₃×C₄	D₂₄	1	2	yes	—
234	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
235	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
236	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
237	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
238	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
239	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
240	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
241	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
242	C₂×C₃×C₄	C₃×D₈	1	2	yes	—
243	C₂×C₃×C₄	C₃×SD₁₆	1	2	yes	—
244	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
245	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
246	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
247	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
248	#67	—	4	2	no	—
249	#67	—	4	2	no	—
250	C₂×Dic₃	—	2	4	no	—
251	C₂×Dic₃	—	2	2	no	—
252	C₂×Dic₃	—	4	2	no	—
253	C₂×Dic₃	—	4	2	no	—
254	D₁₂	—	4	2	no	—
255	D₁₂	—	4	2	no	—
256	D₁₂	—	4	2	no	—
257	C₄×D₃	—	4	4	no	—
258	Dic₆	—	4	2	no	—
259	C₃×C₈	—	4	4	no	—
260	C₃×C₈	—	4	2	no	—
261	C₃×C₈	—	4	2	no	—
262	C₂×C₃²	—	2	1	no	—
263	C₂×C₃²	—	2	1	no	—
264	C₂×C₃²	#410	1	1	yes	characteristic
265	C₂×C₃²	C₂×#102	1	1	yes	characteristic
266	C₂×C₃²	C₂×#104	1	1	yes	characteristic
267	C₃×D₃	—	8	2	no	—
268	#41	—	12	2	no	—
269	#41	—	12	2	no	—
270	C₂×Q₈	—	6	1	no	—
271	C₂×D₄	—	3	2	no	—
272	C₂×D₄	—	6	2	no	—
273	C₂×D₄	—	6	1	no	—
274	C₂×D₄	—	6	1	no	—
275	C₂²×C₄	—	6	2	no	—
276	C₂²×C₄	—	6	2	no	—
277	C₂²×C₄	C₃×D₁₂	1	1	yes	characteristic
278	C₂²×C₄	C₃×D₁₂	1	1	yes	characteristic
279	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
280	C₂×C₈	—	2	2	no	—
281	C₄⋊C₄	—	3	2	no	—
282	C₄⋊C₄	—	6	4	no	—
283	C₄⋊C₄	—	6	1	no	—
284	C₂²⋊C₄	—	6	2	no	—
285	C₂²⋊C₄	—	6	2	no	—
286	C₄²	—	12	2	no	—
287	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
288	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
289	C₄²	C₃×#67	1	1	yes	characteristic
290	C₄²	C₃×#67	1	1	yes	characteristic
291	C₂²×C₃	—	2	1	no	—
292	C₂²×C₃	—	2	1	no	—
293	C₂²×C₃	—	2	1	no	—
294	C₂²×C₃	—	2	1	no	—
295	C₂²×C₃	—	2	1	no	—
296	C₂²×C₃	—	2	1	no	—
297	C₂²×C₃	—	2	1	no	—
298	C₂²×C₃	—	4	1	no	—
299	C₂²×C₃	—	4	1	no	—
300	C₂²×C₃	—	12	2	no	—
301	C₂²×C₃	—	12	2	no	—
302	C₂²×C₃	—	12	2	no	—
303	C₂²×C₃	C₂×#204	1	1	yes	characteristic
304	C₂²×C₃	C₂×D₂₄	1	1	yes	characteristic
305	C₂²×C₃	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
306	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
307	C₂²×C₃	C₂×C₃×D₈	1	1	yes	characteristic
308	C₂²×C₃	C₂×C₃×SD₁₆	1	1	yes	characteristic
309	C₂×D₃	—	4	2	no	—
310	C₂×D₃	—	4	2	no	—
311	C₂×D₃	—	4	2	no	—
312	C₃×C₄	—	2	2	no	—
313	C₃×C₄	—	2	1	no	—
314	C₃×C₄	—	2	1	no	—
315	C₃×C₄	—	2	1	no	—
316	C₃×C₄	—	2	1	no	—
317	C₃×C₄	—	2	1	no	—
318	C₃×C₄	—	2	1	no	—
319	C₃×C₄	—	2	2	no	—
320	C₃×C₄	—	2	2	no	—
321	C₃×C₄	—	2	2	no	—
322	C₃×C₄	—	4	1	no	—
323	C₃×C₄	—	4	1	no	—
324	C₃×C₄	—	12	4	no	—
325	C₃×C₄	—	12	2	no	—
326	C₃×C₄	#821	1	2	yes	—
327	C₃×C₄	#821	1	2	yes	—
328	C₃×C₄	#825	1	2	yes	—
329	C₃×C₄	C₃×#102	1	2	yes	—
330	C₃×C₄	C₃×#102	1	2	yes	—
331	C₃×C₄	C₃×#104	1	2	yes	—
332	Dic₃	—	4	4	no	—
333	Dic₃	—	4	2	no	—
334	C₃²	#1502	1	1	yes	characteristic, complemented, Sylow
335	C₂³	—	6	2	no	—
336	C₂³	C₂×C₃×D₁₂	1	1	yes	characteristic
337	Q₈	—	12	2	no	—
338	D₄	—	12	2	no	—
339	D₄	—	12	2	no	—
340	D₄	—	12	2	no	—
341	D₄	—	12	2	no	—
342	D₄	—	12	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	6	4	no	—
346	C₂×C₄	—	6	2	no	—
347	C₂×C₄	—	12	2	no	—
348	C₂×C₄	—	12	2	no	—
349	C₂×C₄	—	12	4	no	—
350	C₂×C₄	C₃×#204	1	2	yes	—
351	C₂×C₄	C₃×D₂₄	1	2	yes	—
352	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
353	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
354	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
355	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
356	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
357	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
358	C₈	—	4	2	no	—
359	C₂×C₃	—	2	1	no	—
360	C₂×C₃	—	2	1	no	—
361	C₂×C₃	—	2	1	no	—
362	C₂×C₃	—	2	1	no	—
363	C₂×C₃	—	2	1	no	—
364	C₂×C₃	—	2	1	no	—
365	C₂×C₃	—	2	1	no	—
366	C₂×C₃	—	4	1	no	—
367	C₂×C₃	—	4	1	no	—
368	C₂×C₃	—	24	2	no	—
369	C₂×C₃	#5006	1	1	yes	characteristic
370	C₂×C₃	C₂×#821	1	1	yes	characteristic
371	C₂×C₃	C₂×#825	1	1	yes	characteristic
372	C₂×C₃	C₃×#410	1	1	yes	characteristic
373	C₂×C₃	C₂×C₃×#102	1	1	yes	characteristic
374	C₂×C₃	C₂×C₃×#104	1	1	yes	characteristic
375	D₃	—	8	2	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	12	2	no	—
379	C₂²	—	12	2	no	—
380	C₂²	—	12	2	no	—
381	C₂²	C₂×C₃×#204	1	1	yes	characteristic
382	C₂²	C₂×C₃×D₂₄	1	1	yes	characteristic
383	C₂²	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
384	C₄	—	2	1	no	—
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	12	4	no	—
388	C₄	—	12	2	no	—
389	C₄	C₃×#821	1	2	yes	—
390	C₄	C₃×#821	1	2	yes	—
391	C₄	C₃×#825	1	2	yes	—
392	C₃	—	2	1	no	—
393	C₃	#70789	1	1	yes	characteristic, direct product factor
394	C₃	C₃×#1502	1	1	yes	characteristic, complemented
395	C₂	—	2	1	no	—
396	C₂	—	2	1	no	—
397	C₂	—	24	2	no	—
398	C₂	C₃×#5006	1	1	yes	characteristic
399	C₂	C₂×C₃×#821	1	1	yes	characteristic
400	C₂	C₂×C₃×#825	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	(C₂×D₃)⋊C₄
commutator	C₂×C₃×C₄	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₃
Fitting	C₃²×#431	C₂
socle	C₂²×C₃²	C₂×C₂²⋊C₄
prime radical	C₃×#5477	C₂
cosocle	C₂²×C₃×C₄	C₂³×C₃
hypercenter	C₃×#431	D₃
hypocenter	C₃	C₃×#1502
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₃×#431

Complements

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

N	H ≅ G/N	type
2. C₃²×#431	C₂	semidirect
3. C₃×C₄×C₄⋊Dic₃	C₂	semidirect
4. C₃×#4470	C₂	semidirect
6. #70789	C₃	direct (N × H)
14. C₃×#874	C₄	semidirect
16. C₃×C₄×D₁₂	C₄	semidirect
17. C₃×#869	C₄	semidirect
25. C₃×#431	D₃	semidirect
26. C₃×#431	C₂×C₃	semidirect
28. C₄×C₄⋊Dic₃	C₂×C₃	semidirect
30. #4470	C₂×C₃	semidirect
74. #874	C₃×C₄	semidirect
76. C₄×D₁₂	C₃×C₄	semidirect
77. #869	C₃×C₄	semidirect
114. #431	C₃×D₃	semidirect
334. C₃²	#1502	semidirect
393. C₃	#70789	direct (N × H)
394. C₃	C₃×#1502	semidirect

Maximal subgroups

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

subgroup	index
C₃×#5477	2
C₃²×#431	2
C₃×C₄×C₄⋊Dic₃	2
C₃×#4470	2
C₃×#1502	3
#70789	3

Subgroups — C3×#70789 #11775053

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#70789 #11775053