Subgroups — C₃×#87088 #11918325

Order 1152.

2046 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×H(3,𝔽₄)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5680	C₂	1	3	yes	maximal, complemented
3	C₃×#5672	C₂	1	3	yes	maximal, complemented
4	C₃×#5671	C₂	1	6	yes	maximal, complemented
5	C₃×#5669	C₂	1	6	yes	maximal, complemented
6	C₃×#5593	C₂	1	6	yes	maximal, complemented
7	C₃×#5587	C₂	1	6	yes	maximal, complemented
8	C₃×#3568	—	3	1	no	maximal
9	#87088	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₃²×#124	C₂²	1	6	yes	—
11	C₃²×#124	C₂²	1	3	yes	—
12	C₃²×#120	C₂²	1	6	yes	—
13	C₃×#953	C₂²	1	2	yes	complemented
14	C₂×C₃×#217	C₂²	1	6	yes	complemented
15	C₃×#946	C₂²	1	3	yes	complemented
16	C₃×Q₈×Dic₃	C₂²	1	3	yes	complemented
17	C₃×#944	C₂²	1	6	yes	complemented
18	C₃×#939	C₂²	1	6	yes	—
19	C₃×#938	C₂²	1	3	yes	—
20	C₃×#936	C₂²	1	6	yes	—
21	C₃×#935	C₂²	1	6	yes	—
22	C₃×#935	C₂²	1	6	yes	—
23	C₃×D₄×Dic₃	C₂²	1	3	yes	—
24	C₃×D₄×Dic₃	C₂²	1	6	yes	—
25	C₃×#885	C₂²	1	6	yes	complemented
26	C₃×#883	C₂²	1	6	yes	complemented
27	C₃×#67⋊C₄	C₂²	1	6	yes	complemented
28	C₃×#879	C₂²	1	6	yes	complemented
29	C₃×#879	C₂²	1	6	yes	complemented
30	C₃×#879	C₂²	1	6	yes	complemented
31	C₃×#879	C₂²	1	6	yes	complemented
32	C₃×#878	C₂²	1	6	yes	complemented
33	C₃×#878	C₂²	1	6	yes	complemented
34	C₃×#878	C₂²	1	6	yes	complemented
35	C₃×#877	C₂²	1	6	yes	complemented
36	C₃×#877	C₂²	1	6	yes	complemented
37	C₃×#876	C₂²	1	2	yes	complemented
38	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic, complemented
39	C₃×#870	C₂²	1	3	yes	complemented
40	C₃×C₄×Dic₆	C₂²	1	6	yes	complemented
41	C₃×#563	—	3	3	no	—
42	C₃×H(3,𝔽₄)	—	2	1	no	—
43	C₃×H(3,𝔽₄)	D₃	1	1	yes	characteristic, complemented
44	C₃×H(3,𝔽₄)	C₂×C₃	1	1	yes	characteristic, complemented
45	C₃×#556	—	3	6	no	—
46	C₃×#551	—	3	6	no	—
47	C₃×#542	—	3	6	no	—
48	C₃×#538	—	3	6	no	—
49	C₃×#529	—	3	3	no	—
50	#5680	C₂×C₃	1	3	yes	complemented
51	#5672	C₂×C₃	1	3	yes	complemented
52	#5671	C₂×C₃	1	6	yes	complemented
53	#5669	C₂×C₃	1	6	yes	complemented
54	#5593	C₂×C₃	1	6	yes	complemented
55	#5587	C₂×C₃	1	6	yes	complemented
56	C₂⁴×C₃²	C₂³	1	2	yes	—
57	C₂×C₃²×Q₈	C₂³	1	3	yes	—
58	C₂×C₃²×D₄	C₂³	1	3	yes	—
59	C₂×C₃²×D₄	C₂³	1	6	yes	—
60	C₂×C₃×#67	C₂³	1	6	yes	—
61	C₂²×C₃×Dic₃	C₂³	1	6	yes	—
62	C₂²×C₃×Dic₃	C₂³	1	6	yes	—
63	C₂×C₃×C₄×D₃	C₂³	1	3	yes	—
64	C₂×C₃×Dic₆	C₂³	1	6	yes	—
65	C₃²×C₂²⋊C₄	C₂³	1	6	yes	—
66	C₃²×C₂²⋊C₄	C₂³	1	6	yes	—
67	C₃²×C₂²⋊C₄	C₂³	1	6	yes	—
68	C₃²×C₄²	C₂³	1	2	yes	—
69	C₃²×C₄²	C₂³	1	1	yes	characteristic
70	C₃×#217	C₂³	1	6	yes	—
71	C₃×#217	C₂³	1	6	yes	—
72	C₃×#217	C₂³	1	6	yes	—
73	C₃×#217	C₂³	1	6	yes	—
74	C₃×#217	C₂³	1	6	yes	—
75	C₃×(C₂×D₃)⋊C₄	C₂³	1	6	yes	—
76	C₃×C₄⋊Dic₃	C₂³	1	3	yes	—
77	C₃×C₄⋊Dic₃	C₂³	1	3	yes	—
78	C₃×C₄⋊Dic₃	C₂³	1	6	yes	—
79	C₃×Dic₃⋊C₄	C₂³	1	6	yes	—
80	C₃×Dic₃⋊C₄	C₂³	1	6	yes	—
81	C₃×Dic₃⋊C₄	C₂³	1	6	yes	—
82	C₃×Dic₃⋊C₄	C₂³	1	6	yes	—
83	C₃×Dic₃⋊C₄	C₂³	1	6	yes	—
84	C₃×C₄×Dic₃	C₂³	1	3	yes	—
85	C₃×C₄×Dic₃	C₂³	1	6	yes	—
86	C₃×C₄×Dic₃	C₂³	1	6	yes	—
87	#3568	—	3	1	no	Sylow
88	C₃×C₄⋊Q₈	—	3	6	no	—
89	C₃×#126	—	3	6	no	—
90	C₃×#126	—	3	6	no	—
91	C₃×#126	—	3	6	no	—
92	C₃×#126	—	3	6	no	—
93	C₃×#126	—	3	2	no	—
94	C₃×#125	—	3	3	no	—
95	C₃×#124	—	2	3	no	—
96	C₃×#124	—	2	6	no	—
97	C₃×#124	—	3	6	no	—
98	C₃×#124	—	3	6	no	—
99	C₃×#124	C₂×D₃	1	3	yes	—
100	C₃×#124	C₂×D₃	1	6	yes	—
101	C₃×#124	C₂²×C₃	1	6	yes	—
102	C₃×#124	C₂²×C₃	1	3	yes	—
103	C₃×#123	—	3	6	no	—
104	C₃×#123	—	3	6	no	—
105	C₃×#123	—	3	6	no	—
106	C₃×C₂²⋊Q₈	—	3	3	no	—
107	C₃×C₂²⋊Q₈	—	3	6	no	—
108	C₃×C₂²⋊Q₈	—	3	6	no	—
109	C₃×C₂²⋊Q₈	—	3	6	no	—
110	C₃×#121	—	3	3	no	—
111	C₃×#121	—	3	6	no	—
112	C₃×#120	—	2	6	no	—
113	C₃×#120	—	3	2	no	—
114	C₃×#120	C₂×D₃	1	6	yes	—
115	C₃×#120	C₂²×C₃	1	6	yes	—
116	C₃×C₄×Q₈	—	3	3	no	—
117	C₃×C₄×Q₈	—	3	6	no	—
118	C₃×C₄×D₄	—	3	3	no	—
119	C₃×C₄×D₄	—	3	6	no	—
120	C₃×C₄×D₄	—	3	6	no	—
121	C₃×#117	—	3	6	no	—
122	C₃×#117	—	3	6	no	—
123	C₂×C₃×C₂²⋊C₄	—	3	6	no	—
124	C₂×C₃×C₄²	—	3	1	no	—
125	#953	C₂²×C₃	1	2	yes	complemented
126	C₂×#217	C₂²×C₃	1	6	yes	complemented
127	#946	C₂²×C₃	1	3	yes	complemented
128	Q₈×Dic₃	C₂²×C₃	1	3	yes	complemented
129	#944	C₂²×C₃	1	6	yes	complemented
130	#939	C₂²×C₃	1	6	yes	—
131	#938	C₂²×C₃	1	3	yes	—
132	#936	C₂²×C₃	1	6	yes	—
133	#935	C₂²×C₃	1	6	yes	—
134	#935	C₂²×C₃	1	6	yes	—
135	D₄×Dic₃	C₂²×C₃	1	6	yes	—
136	D₄×Dic₃	C₂²×C₃	1	3	yes	—
137	#885	C₂²×C₃	1	6	yes	complemented
138	#883	C₂²×C₃	1	6	yes	complemented
139	#67⋊C₄	C₂²×C₃	1	6	yes	complemented
140	#879	C₂²×C₃	1	6	yes	complemented
141	#879	C₂²×C₃	1	6	yes	complemented
142	#879	C₂²×C₃	1	6	yes	complemented
143	#879	C₂²×C₃	1	6	yes	complemented
144	#878	C₂²×C₃	1	6	yes	complemented
145	#878	C₂²×C₃	1	6	yes	complemented
146	#878	C₂²×C₃	1	6	yes	complemented
147	#877	C₂²×C₃	1	6	yes	complemented
148	#877	C₂²×C₃	1	6	yes	complemented
149	#876	C₂²×C₃	1	2	yes	complemented
150	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic, complemented
151	#870	C₂²×C₃	1	3	yes	complemented
152	C₄×Dic₆	C₂²×C₃	1	6	yes	complemented
153	C₂³×C₃²	—	4	6	no	—
154	C₂³×C₃²	C₂⁴	1	6	yes	—
155	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
156	C₃²×Q₈	—	4	3	no	—
157	C₃²×D₄	—	4	6	no	—
158	C₃²×D₄	—	4	3	no	—
159	C₂×C₃²×C₄	C₂⁴	1	6	yes	—
160	C₂×C₃²×C₄	C₂⁴	1	3	yes	—
161	C₃×#67	—	4	6	no	—
162	C₂×C₃×Dic₃	—	4	6	no	—
163	C₂×C₃×Dic₃	—	4	6	no	—
164	C₂×C₃×Dic₃	C₂⁴	1	3	yes	—
165	C₂×C₃×Dic₃	C₂⁴	1	6	yes	—
166	C₂×C₃×Dic₃	C₂⁴	1	6	yes	—
167	C₃×C₄×D₃	—	4	3	no	—
168	C₃×Dic₆	—	4	6	no	—
169	#563	—	3	3	no	—
170	H(3,𝔽₄)	C₃×D₃	1	1	yes	characteristic, complemented
171	#556	—	3	6	no	—
172	#551	—	3	6	no	—
173	#542	—	3	6	no	—
174	#538	—	3	6	no	—
175	#529	—	3	3	no	—
176	C₂⁴×C₃	—	2	2	no	—
177	C₂⁴×C₃	C₂²×D₃	1	2	yes	—
178	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
179	C₂×C₃×Q₈	—	2	3	no	—
180	C₂×C₃×Q₈	—	3	6	no	—
181	C₂×C₃×Q₈	C₂²×D₃	1	3	yes	—
182	C₂×C₃×Q₈	C₂³×C₃	1	3	yes	—
183	C₂×C₃×D₄	—	2	3	no	—
184	C₂×C₃×D₄	—	2	6	no	—
185	C₂×C₃×D₄	—	3	6	no	—
186	C₂×C₃×D₄	C₂²×D₃	1	3	yes	—
187	C₂×C₃×D₄	C₂²×D₃	1	6	yes	—
188	C₂×C₃×D₄	C₂³×C₃	1	3	yes	—
189	C₂×C₃×D₄	C₂³×C₃	1	6	yes	—
190	C₂²×C₃×C₄	—	3	6	no	—
191	C₂²×C₃×C₄	—	3	6	no	—
192	C₂²×C₃×C₄	—	3	3	no	—
193	C₂×#67	C₂³×C₃	1	6	yes	—
194	C₂²×Dic₃	C₂³×C₃	1	6	yes	—
195	C₂²×Dic₃	C₂³×C₃	1	6	yes	—
196	C₂×C₄×D₃	C₂³×C₃	1	3	yes	—
197	C₂×Dic₆	C₂³×C₃	1	6	yes	—
198	C₃×C₄⋊C₄	—	3	6	no	—
199	C₃×C₄⋊C₄	—	3	6	no	—
200	C₃×C₄⋊C₄	—	3	6	no	—
201	C₃×C₄⋊C₄	—	3	6	no	—
202	C₃×C₄⋊C₄	—	3	6	no	—
203	C₃×C₄⋊C₄	—	3	6	no	—
204	C₃×C₄⋊C₄	—	3	3	no	—
205	C₃×C₄⋊C₄	—	3	3	no	—
206	C₃×C₂²⋊C₄	—	2	6	no	—
207	C₃×C₂²⋊C₄	—	2	6	no	—
208	C₃×C₂²⋊C₄	—	2	6	no	—
209	C₃×C₂²⋊C₄	—	3	6	no	—
210	C₃×C₂²⋊C₄	—	3	6	no	—
211	C₃×C₂²⋊C₄	—	3	6	no	—
212	C₃×C₂²⋊C₄	—	3	6	no	—
213	C₃×C₂²⋊C₄	—	3	6	no	—
214	C₃×C₂²⋊C₄	—	3	6	no	—
215	C₃×C₂²⋊C₄	C₂²×D₃	1	6	yes	—
216	C₃×C₂²⋊C₄	C₂²×D₃	1	6	yes	—
217	C₃×C₂²⋊C₄	C₂²×D₃	1	6	yes	—
218	C₃×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
219	C₃×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
220	C₃×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
221	C₃×C₄²	—	2	1	no	—
222	C₃×C₄²	—	2	2	no	—
223	C₃×C₄²	—	3	3	no	—
224	C₃×C₄²	—	3	6	no	—
225	C₃×C₄²	—	3	6	no	—
226	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
227	C₃×C₄²	C₂²×D₃	1	2	yes	—
228	C₃×C₄²	C₂³×C₃	1	2	yes	—
229	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
230	#217	C₂³×C₃	1	6	yes	—
231	#217	C₂³×C₃	1	6	yes	—
232	#217	C₂³×C₃	1	6	yes	—
233	#217	C₂³×C₃	1	6	yes	—
234	#217	C₂³×C₃	1	6	yes	—
235	(C₂×D₃)⋊C₄	C₂³×C₃	1	6	yes	—
236	C₄⋊Dic₃	C₂³×C₃	1	6	yes	—
237	C₄⋊Dic₃	C₂³×C₃	1	3	yes	—
238	C₄⋊Dic₃	C₂³×C₃	1	3	yes	—
239	Dic₃⋊C₄	C₂³×C₃	1	6	yes	—
240	Dic₃⋊C₄	C₂³×C₃	1	6	yes	—
241	Dic₃⋊C₄	C₂³×C₃	1	6	yes	—
242	Dic₃⋊C₄	C₂³×C₃	1	6	yes	—
243	Dic₃⋊C₄	C₂³×C₃	1	6	yes	—
244	C₄×Dic₃	C₂³×C₃	1	6	yes	—
245	C₄×Dic₃	C₂³×C₃	1	6	yes	—
246	C₄×Dic₃	C₂³×C₃	1	3	yes	—
247	C₂²×C₃²	—	2	6	no	—
248	C₂²×C₃²	—	2	6	no	—
249	C₂²×C₃²	—	2	6	no	—
250	C₂²×C₃²	—	8	4	no	—
251	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
252	C₂×C₃×D₃	—	2	3	no	—
253	C₃²×C₄	—	2	6	no	—
254	C₃²×C₄	—	2	3	no	—
255	C₃×Dic₃	—	2	6	no	—
256	C₃×Dic₃	—	2	6	no	—
257	C₃×Dic₃	—	2	3	no	—
258	C₄⋊Q₈	—	3	6	no	—
259	#126	—	3	6	no	—
260	#126	—	3	6	no	—
261	#126	—	3	6	no	—
262	#126	—	3	6	no	—
263	#126	—	3	2	no	—
264	#125	—	3	3	no	—
265	#124	—	3	6	no	—
266	#124	—	3	6	no	—
267	#124	C₂×C₃×D₃	1	3	yes	—
268	#124	C₂×C₃×D₃	1	6	yes	—
269	#123	—	3	6	no	—
270	#123	—	3	6	no	—
271	#123	—	3	6	no	—
272	C₂²⋊Q₈	—	3	3	no	—
273	C₂²⋊Q₈	—	3	6	no	—
274	C₂²⋊Q₈	—	3	6	no	—
275	C₂²⋊Q₈	—	3	6	no	—
276	#121	—	3	3	no	—
277	#121	—	3	6	no	—
278	#120	—	3	2	no	—
279	#120	C₂×C₃×D₃	1	6	yes	—
280	C₄×Q₈	—	3	3	no	—
281	C₄×Q₈	—	3	6	no	—
282	C₄×D₄	—	3	3	no	—
283	C₄×D₄	—	3	6	no	—
284	C₄×D₄	—	3	6	no	—
285	#117	—	3	6	no	—
286	#117	—	3	6	no	—
287	C₂×C₂²⋊C₄	—	3	6	no	—
288	C₂×C₄²	—	3	1	no	—
289	C₂³×C₃	—	2	6	no	—
290	C₂³×C₃	—	3	1	no	—
291	C₂³×C₃	—	4	6	no	—
292	C₂³×C₃	—	4	6	no	—
293	C₂³×C₃	—	8	6	no	—
294	C₂³×C₃	C₂³×D₃	1	6	yes	—
295	C₂³×C₃	C₂⁴×C₃	1	6	yes	—
296	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
297	C₃×Q₈	—	4	3	no	—
298	C₃×Q₈	—	4	3	no	—
299	C₃×Q₈	—	8	3	no	—
300	C₃×Q₈	—	12	6	no	—
301	C₃×D₄	—	4	3	no	—
302	C₃×D₄	—	4	6	no	—
303	C₃×D₄	—	4	6	no	—
304	C₃×D₄	—	4	3	no	—
305	C₃×D₄	—	8	3	no	—
306	C₃×D₄	—	8	6	no	—
307	C₃×D₄	—	12	6	no	—
308	C₂×C₃×C₄	—	2	6	no	—
309	C₂×C₃×C₄	—	2	3	no	—
310	C₂×C₃×C₄	—	3	3	no	—
311	C₂×C₃×C₄	—	3	6	no	—
312	C₂×C₃×C₄	—	3	6	no	—
313	C₂×C₃×C₄	—	12	3	no	—
314	C₂×C₃×C₄	—	12	6	no	—
315	C₂×C₃×C₄	—	12	6	no	—
316	C₂×C₃×C₄	C₂³×D₃	1	6	yes	—
317	C₂×C₃×C₄	C₂³×D₃	1	3	yes	—
318	C₂×C₃×C₄	C₂⁴×C₃	1	6	yes	—
319	C₂×C₃×C₄	C₂⁴×C₃	1	3	yes	—
320	#67	—	4	6	no	—
321	C₂×Dic₃	—	4	6	no	—
322	C₂×Dic₃	—	4	6	no	—
323	C₂×Dic₃	C₂⁴×C₃	1	3	yes	—
324	C₂×Dic₃	C₂⁴×C₃	1	6	yes	—
325	C₂×Dic₃	C₂⁴×C₃	1	6	yes	—
326	C₄×D₃	—	4	3	no	—
327	Dic₆	—	4	6	no	—
328	C₂×C₃²	—	4	6	no	—
329	C₂×C₃²	#585	1	3	yes	—
330	C₃×D₃	—	4	1	no	—
331	C₂⁴	C₂²×C₃×D₃	1	2	yes	—
332	C₂×Q₈	—	3	6	no	—
333	C₂×Q₈	C₂²×C₃×D₃	1	3	yes	—
334	C₂×D₄	—	3	6	no	—
335	C₂×D₄	C₂²×C₃×D₃	1	3	yes	—
336	C₂×D₄	C₂²×C₃×D₃	1	6	yes	—
337	C₂²×C₄	—	3	6	no	—
338	C₂²×C₄	—	3	6	no	—
339	C₂²×C₄	—	3	3	no	—
340	C₄⋊C₄	—	3	6	no	—
341	C₄⋊C₄	—	3	6	no	—
342	C₄⋊C₄	—	3	6	no	—
343	C₄⋊C₄	—	3	6	no	—
344	C₄⋊C₄	—	3	3	no	—
345	C₄⋊C₄	—	3	6	no	—
346	C₄⋊C₄	—	3	3	no	—
347	C₄⋊C₄	—	3	6	no	—
348	C₂²⋊C₄	—	3	6	no	—
349	C₂²⋊C₄	—	3	6	no	—
350	C₂²⋊C₄	—	3	6	no	—
351	C₂²⋊C₄	—	3	6	no	—
352	C₂²⋊C₄	—	3	6	no	—
353	C₂²⋊C₄	—	3	6	no	—
354	C₂²⋊C₄	C₂²×C₃×D₃	1	6	yes	—
355	C₂²⋊C₄	C₂²×C₃×D₃	1	6	yes	—
356	C₂²⋊C₄	C₂²×C₃×D₃	1	6	yes	—
357	C₄²	—	3	3	no	—
358	C₄²	—	3	6	no	—
359	C₄²	—	3	6	no	—
360	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
361	C₄²	C₂²×C₃×D₃	1	2	yes	—
362	C₂²×C₃	—	2	6	no	—
363	C₂²×C₃	—	2	6	no	—
364	C₂²×C₃	—	2	6	no	—
365	C₂²×C₃	—	2	6	no	—
366	C₂²×C₃	—	2	6	no	—
367	C₂²×C₃	—	2	6	no	—
368	C₂²×C₃	—	2	1	no	—
369	C₂²×C₃	—	4	6	no	—
370	C₂²×C₃	—	4	6	no	—
371	C₂²×C₃	—	4	6	no	—
372	C₂²×C₃	—	6	3	no	—
373	C₂²×C₃	—	8	4	no	—
374	C₂²×C₃	—	8	4	no	—
375	C₂²×C₃	—	8	8	no	—
376	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
377	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
378	C₂×D₃	—	2	3	no	—
379	C₃×C₄	—	2	3	no	—
380	C₃×C₄	—	2	6	no	—
381	C₃×C₄	—	2	6	no	—
382	C₃×C₄	—	2	3	no	—
383	C₃×C₄	—	4	3	no	—
384	C₃×C₄	—	4	6	no	—
385	C₃×C₄	—	6	3	no	—
386	C₃×C₄	—	6	6	no	—
387	C₃×C₄	—	6	6	no	—
388	Dic₃	—	2	6	no	—
389	Dic₃	—	2	6	no	—
390	Dic₃	—	2	3	no	—
391	C₃²	#3568	1	1	yes	characteristic, complemented, Sylow
392	C₂³	—	3	1	no	—
393	C₂³	—	4	6	no	—
394	C₂³	C₂³×C₃×D₃	1	6	yes	—
395	Q₈	—	4	3	no	—
396	Q₈	—	12	6	no	—
397	D₄	—	4	3	no	—
398	D₄	—	4	6	no	—
399	D₄	—	12	6	no	—
400	C₂×C₄	—	3	3	no	—
401	C₂×C₄	—	3	6	no	—
402	C₂×C₄	—	3	6	no	—
403	C₂×C₄	—	12	3	no	—
404	C₂×C₄	—	12	6	no	—
405	C₂×C₄	—	12	6	no	—
406	C₂×C₄	C₂³×C₃×D₃	1	6	yes	—
407	C₂×C₄	C₂³×C₃×D₃	1	3	yes	—
408	C₂×C₃	—	2	3	no	—
409	C₂×C₃	—	4	6	no	—
410	C₂×C₃	—	4	6	no	—
411	C₂×C₃	—	8	6	no	—
412	C₂×C₃	—	12	1	no	—
413	C₂×C₃	#5966	1	3	yes	—
414	C₂×C₃	C₃×#585	1	3	yes	—
415	D₃	—	4	1	no	—
416	C₂²	—	2	6	no	—
417	C₂²	—	2	6	no	—
418	C₂²	—	2	6	no	—
419	C₂²	—	6	3	no	—
420	C₂²	—	8	4	no	—
421	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
422	C₄	—	2	3	no	—
423	C₄	—	2	6	no	—
424	C₄	—	6	3	no	—
425	C₄	—	6	6	no	—
426	C₄	—	6	6	no	—
427	C₃	—	2	1	no	—
428	C₃	#87088	1	1	yes	characteristic, direct product factor
429	C₃	C₃×#3568	1	1	yes	characteristic, complemented
430	C₂	—	4	6	no	—
431	C₂	—	12	1	no	—
432	C₂	C₃×#5966	1	3	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₃²×H(3,𝔽₄)	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×H(3,𝔽₄)	D₃
hypocenter	C₃	C₃×#3568
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×H(3,𝔽₄)

Complements

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

N	H ≅ G/N	type
1. C₃²×H(3,𝔽₄)	C₂	semidirect
2. C₃×#5680	C₂	semidirect
3. C₃×#5672	C₂	semidirect
4. C₃×#5671	C₂	semidirect
5. C₃×#5669	C₂	semidirect
6. C₃×#5593	C₂	semidirect
7. C₃×#5587	C₂	semidirect
9. #87088	C₃	direct (N × H)
13. C₃×#953	C₂²	semidirect
14. C₂×C₃×#217	C₂²	semidirect
15. C₃×#946	C₂²	semidirect
16. C₃×Q₈×Dic₃	C₂²	semidirect
17. C₃×#944	C₂²	semidirect
25. C₃×#885	C₂²	semidirect
26. C₃×#883	C₂²	semidirect
27. C₃×#67⋊C₄	C₂²	semidirect
28. C₃×#879	C₂²	semidirect
29. C₃×#879	C₂²	semidirect
30. C₃×#879	C₂²	semidirect
31. C₃×#879	C₂²	semidirect
32. C₃×#878	C₂²	semidirect
33. C₃×#878	C₂²	semidirect
34. C₃×#878	C₂²	semidirect
35. C₃×#877	C₂²	semidirect
36. C₃×#877	C₂²	semidirect
37. C₃×#876	C₂²	semidirect
38. C₃×C₄²×D₃	C₂²	semidirect
39. C₃×#870	C₂²	semidirect
40. C₃×C₄×Dic₆	C₂²	semidirect
43. C₃×H(3,𝔽₄)	D₃	semidirect
44. C₃×H(3,𝔽₄)	C₂×C₃	semidirect
50. #5680	C₂×C₃	semidirect
51. #5672	C₂×C₃	semidirect
52. #5671	C₂×C₃	semidirect
53. #5669	C₂×C₃	semidirect
54. #5593	C₂×C₃	semidirect
55. #5587	C₂×C₃	semidirect
125. #953	C₂²×C₃	semidirect
126. C₂×#217	C₂²×C₃	semidirect
127. #946	C₂²×C₃	semidirect
128. Q₈×Dic₃	C₂²×C₃	semidirect
129. #944	C₂²×C₃	semidirect
137. #885	C₂²×C₃	semidirect
138. #883	C₂²×C₃	semidirect
139. #67⋊C₄	C₂²×C₃	semidirect
140. #879	C₂²×C₃	semidirect
141. #879	C₂²×C₃	semidirect
142. #879	C₂²×C₃	semidirect
143. #879	C₂²×C₃	semidirect
144. #878	C₂²×C₃	semidirect
145. #878	C₂²×C₃	semidirect
146. #878	C₂²×C₃	semidirect
147. #877	C₂²×C₃	semidirect
148. #877	C₂²×C₃	semidirect
149. #876	C₂²×C₃	semidirect
150. C₄²×D₃	C₂²×C₃	semidirect
151. #870	C₂²×C₃	semidirect
152. C₄×Dic₆	C₂²×C₃	semidirect
170. H(3,𝔽₄)	C₃×D₃	semidirect
391. C₃²	#3568	semidirect
428. C₃	#87088	direct (N × H)
429. C₃	C₃×#3568	semidirect

Maximal subgroups

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

subgroup	index
C₃²×H(3,𝔽₄)	2
C₃×#5680	2
C₃×#5672	2
C₃×#5671	2
C₃×#5669	2
C₃×#5593	2
C₃×#5587	2
C₃×#3568	3
#87088	3

Subgroups — C3×#87088 #11918325

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#87088 #11918325