Subgroups — C₃²×#5674 #13179052

Order 1728.

2308 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#239	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃²×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃³×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#947	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×#940	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×#884	C₂	1	4	yes	maximal, complemented
7	C₃²×#882	C₂	1	4	yes	maximal, complemented
8	C₃²×#874	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃²×#872	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃²×#535	—	3	1	no	maximal
11	C₃×#5674	C₃	1	4	yes	maximal, direct product factor
12	C₂³×C₃²×D₃	C₂²	1	2	yes	—
13	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic, complemented
14	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₃²×#67	C₂²	1	2	yes	—
16	C₂×C₃²×#67	C₂²	1	4	yes	complemented
17	C₃²×#239	—	2	4	no	—
18	C₃²×D₃×D₄	—	2	4	no	—
19	C₂×C₃²×D₁₂	C₂²	1	1	yes	characteristic
20	C₂×C₃²×D₁₂	C₂²	1	2	yes	—
21	C₂×C₃²×D₁₂	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃²×D₁₂	C₂²	1	4	yes	complemented
23	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
24	C₂×C₃²×C₄×D₃	C₂²	1	2	yes	complemented
25	C₃³×C₂²⋊C₄	C₂²	1	4	yes	complemented
26	C₃³×C₄²	C₂²	1	1	yes	characteristic, complemented
27	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
28	C₃²×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
29	C₃²×Dic₃⋊C₄	C₂²	1	2	yes	complemented
30	C₃²×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃²×#41	—	3	1	no	—
32	C₂²×C₃²×D₄	—	3	1	no	—
33	C₂×C₃×#239	C₂×C₃	1	4	yes	complemented
34	C₂×C₃×D₃×D₄	C₂×C₃	1	4	yes	complemented
35	C₃²×#127	—	3	1	no	—
36	C₃²×#127	—	3	1	no	—
37	C₃²×#124	—	2	4	no	—
38	C₃²×#124	—	3	1	no	—
39	C₃²×#124	D₃	1	1	yes	characteristic, complemented
40	C₃²×#124	C₂×C₃	1	4	yes	complemented
41	C₃²×#121	—	3	4	no	—
42	C₃²×#120	—	3	4	no	—
43	C₃²×#117	—	3	1	no	—
44	C₃×#947	C₂×C₃	1	4	yes	complemented
45	C₃×#940	C₂×C₃	1	4	yes	complemented
46	C₃×#884	C₂×C₃	1	16	yes	complemented
47	C₃×#882	C₂×C₃	1	16	yes	complemented
48	C₃×#874	C₂×C₃	1	4	yes	complemented
49	C₃×#872	C₂×C₃	1	4	yes	complemented
50	C₂³×C₃³	C₂³	1	2	yes	—
51	C₂²×C₃²×D₃	—	2	4	no	—
52	C₂²×C₃²×D₃	—	4	4	no	—
53	C₂²×C₃²×D₃	C₂³	1	2	yes	—
54	C₂²×C₃²×D₃	C₂³	1	2	yes	—
55	C₂²×C₃²×D₃	C₂³	1	1	yes	characteristic
56	C₃³×Q₈	—	2	2	no	—
57	C₃³×D₄	—	2	2	no	—
58	C₂×C₃³×C₄	C₂³	1	2	yes	—
59	C₂×C₃³×C₄	C₂³	1	2	yes	—
60	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
61	C₃²×#67	—	2	4	no	—
62	C₃²×#67	—	4	4	no	—
63	C₂×C₃²×Dic₃	C₂³	1	2	yes	—
64	C₂×C₃²×Dic₃	C₂³	1	1	yes	characteristic
65	C₃²×D₁₂	—	2	4	no	—
66	C₃²×D₁₂	—	2	2	no	—
67	C₃²×D₁₂	—	2	2	no	—
68	C₃²×D₁₂	—	4	4	no	—
69	C₃²×C₄×D₃	—	2	4	no	—
70	C₃²×C₄×D₃	D₄	1	4	yes	complemented
71	C₃×#535	—	3	4	no	—
72	#5674	C₃²	1	1	yes	characteristic, direct product factor
73	C₂⁴×C₃²	—	3	2	no	—
74	C₂³×C₃×D₃	C₂²×C₃	1	8	yes	—
75	C₃²×#41	—	6	4	no	—
76	C₂×C₃²×Q₈	—	2	4	no	—
77	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
78	C₂×C₃²×Q₈	C₂²×C₃	1	4	yes	complemented
79	C₂×C₃²×D₄	—	2	4	no	—
80	C₂×C₃²×D₄	—	3	2	no	—
81	C₂×C₃²×D₄	—	3	4	no	—
82	C₂×C₃²×D₄	—	3	1	no	—
83	C₂×C₃²×D₄	—	3	2	no	—
84	C₂×C₃²×D₄	—	3	1	no	—
85	C₂×C₃²×D₄	—	3	4	no	—
86	C₂×C₃²×D₄	—	6	4	no	—
87	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
88	C₂×C₃²×D₄	C₂²×C₃	1	4	yes	—
89	C₂²×C₃²×C₄	—	3	1	no	—
90	C₂²×C₃²×C₄	—	3	2	no	—
91	C₂×C₃×#67	C₂²×C₃	1	8	yes	—
92	C₂×C₃×#67	C₂²×C₃	1	16	yes	complemented
93	C₃×#239	—	2	16	no	—
94	C₃×D₃×D₄	—	2	16	no	—
95	C₂×C₃×D₁₂	C₂²×C₃	1	8	yes	—
96	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	—
97	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	complemented
98	C₂×C₃×D₁₂	C₂²×C₃	1	16	yes	complemented
99	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
100	C₂×C₃×C₄×D₃	C₂²×C₃	1	8	yes	complemented
101	C₃²×C₄⋊C₄	—	3	2	no	—
102	C₃²×C₂²⋊C₄	—	2	16	no	—
103	C₃²×C₂²⋊C₄	—	3	2	no	—
104	C₃²×C₂²⋊C₄	—	3	4	no	—
105	C₃²×C₂²⋊C₄	C₂×D₃	1	4	yes	complemented
106	C₃²×C₂²⋊C₄	C₂²×C₃	1	16	yes	complemented
107	C₃²×C₄²	—	2	4	no	—
108	C₃²×C₄²	—	3	1	no	—
109	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic, complemented
110	C₃²×C₄²	C₂²×C₃	1	4	yes	complemented
111	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
112	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	16	yes	complemented
113	C₃×Dic₃⋊C₄	C₂²×C₃	1	8	yes	complemented
114	C₃×C₄×Dic₃	C₂²×C₃	1	4	yes	complemented
115	C₂²×C₃³	—	2	2	no	—
116	C₂²×C₃³	—	2	4	no	—
117	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
118	C₂×C₃²×D₃	—	2	2	no	—
119	C₂×C₃²×D₃	—	2	2	no	—
120	C₂×C₃²×D₃	—	2	2	no	—
121	C₂×C₃²×D₃	—	2	4	no	—
122	C₂×C₃²×D₃	—	2	4	no	—
123	C₂×C₃²×D₃	—	4	8	no	—
124	C₂×C₃²×D₃	C₂×D₄	1	2	yes	—
125	C₃³×C₄	—	2	2	no	—
126	C₃³×C₄	—	2	2	no	—
127	C₃³×C₄	C₂×D₄	1	2	yes	—
128	C₃²×Dic₃	—	2	2	no	—
129	C₃²×Dic₃	C₂×D₄	1	2	yes	—
130	C₂×C₃×#41	—	3	4	no	—
131	C₂²×C₃×D₄	—	3	4	no	—
132	C₂×#239	C₂×C₃²	1	1	yes	characteristic, complemented
133	C₂×D₃×D₄	C₂×C₃²	1	1	yes	characteristic, complemented
134	C₃×#127	—	3	4	no	—
135	C₃×#127	—	3	4	no	—
136	C₃×#124	—	2	4	no	—
137	C₃×#124	—	3	4	no	—
138	C₃×#124	C₃×D₃	1	4	yes	complemented
139	C₃×#124	C₂×C₃²	1	1	yes	characteristic, complemented
140	C₃×#121	—	3	16	no	—
141	C₃×#120	—	3	16	no	—
142	C₃×#117	—	3	4	no	—
143	#947	C₂×C₃²	1	1	yes	characteristic, complemented
144	#940	C₂×C₃²	1	1	yes	characteristic, complemented
145	#884	C₂×C₃²	1	4	yes	complemented
146	#882	C₂×C₃²	1	4	yes	complemented
147	#874	C₂×C₃²	1	1	yes	characteristic, complemented
148	#872	C₂×C₃²	1	1	yes	characteristic, complemented
149	C₂³×C₃²	—	2	8	no	—
150	C₂³×C₃²	—	3	1	no	—
151	C₂³×C₃²	—	3	2	no	—
152	C₂³×C₃²	—	3	2	no	—
153	C₂³×C₃²	—	6	4	no	—
154	C₂³×C₃²	—	12	4	no	—
155	C₂³×C₃²	C₂²×D₃	1	2	yes	—
156	C₂³×C₃²	C₂³×C₃	1	8	yes	—
157	C₂²×C₃×D₃	—	2	16	no	—
158	C₂²×C₃×D₃	—	4	16	no	—
159	C₂²×C₃×D₃	C₂³×C₃	1	8	yes	—
160	C₂²×C₃×D₃	C₂³×C₃	1	8	yes	—
161	C₂²×C₃×D₃	C₂³×C₃	1	4	yes	—
162	C₃²×Q₈	—	2	2	no	—
163	C₃²×Q₈	—	2	8	no	—
164	C₃²×Q₈	—	4	8	no	—
165	C₃²×D₄	—	2	2	no	—
166	C₃²×D₄	—	2	8	no	—
167	C₃²×D₄	—	4	8	no	—
168	C₃²×D₄	—	6	4	no	—
169	C₃²×D₄	—	6	4	no	—
170	C₃²×D₄	—	6	2	no	—
171	C₃²×D₄	—	6	2	no	—
172	C₃²×D₄	—	12	4	no	—
173	C₃²×D₄	—	12	4	no	—
174	C₂×C₃²×C₄	—	2	4	no	—
175	C₂×C₃²×C₄	—	2	8	no	—
176	C₂×C₃²×C₄	—	2	8	no	—
177	C₂×C₃²×C₄	—	3	1	no	—
178	C₂×C₃²×C₄	—	3	4	no	—
179	C₂×C₃²×C₄	—	3	2	no	—
180	C₂×C₃²×C₄	—	6	4	no	—
181	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
182	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
183	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
184	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
185	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
186	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
187	C₃×#67	—	2	16	no	—
188	C₃×#67	—	4	16	no	—
189	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
190	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
191	C₃×D₁₂	—	2	16	no	—
192	C₃×D₁₂	—	2	8	no	—
193	C₃×D₁₂	—	2	8	no	—
194	C₃×D₁₂	—	4	16	no	—
195	C₃×C₄×D₃	—	2	16	no	—
196	C₃×C₄×D₃	C₃×D₄	1	16	yes	complemented
197	#535	—	3	1	no	Sylow
198	C₂×C₃³	—	4	2	no	—
199	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₃³	H(5,𝔽₂)	1	2	yes	—
201	C₃²×D₃	—	2	2	no	—
202	C₃²×D₃	—	4	2	no	—
203	C₃²×D₃	—	4	2	no	—
204	C₂⁴×C₃	—	3	8	no	—
205	C₂³×D₃	C₂²×C₃²	1	2	yes	—
206	C₃×#41	—	6	16	no	—
207	C₂×C₃×Q₈	—	2	4	no	—
208	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	complemented
209	C₂×C₃×Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
210	C₂×C₃×D₄	—	2	4	no	—
211	C₂×C₃×D₄	—	3	8	no	—
212	C₂×C₃×D₄	—	3	16	no	—
213	C₂×C₃×D₄	—	3	8	no	—
214	C₂×C₃×D₄	—	3	4	no	—
215	C₂×C₃×D₄	—	3	4	no	—
216	C₂×C₃×D₄	—	3	16	no	—
217	C₂×C₃×D₄	—	6	16	no	—
218	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	—
219	C₂×C₃×D₄	C₂²×C₃²	1	1	yes	characteristic
220	C₂²×C₃×C₄	—	3	4	no	—
221	C₂²×C₃×C₄	—	3	8	no	—
222	C₂×#67	C₂²×C₃²	1	2	yes	—
223	C₂×#67	C₂²×C₃²	1	4	yes	complemented
224	#239	—	2	4	no	—
225	D₃×D₄	—	2	4	no	—
226	C₂×D₁₂	C₂²×C₃²	1	1	yes	characteristic
227	C₂×D₁₂	C₂²×C₃²	1	2	yes	—
228	C₂×D₁₂	C₂²×C₃²	1	1	yes	characteristic, complemented
229	C₂×D₁₂	C₂²×C₃²	1	4	yes	complemented
230	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
231	C₂×C₄×D₃	C₂²×C₃²	1	2	yes	complemented
232	C₃×C₄⋊C₄	—	3	8	no	—
233	C₃×C₂²⋊C₄	—	2	16	no	—
234	C₃×C₂²⋊C₄	—	3	8	no	—
235	C₃×C₂²⋊C₄	—	3	16	no	—
236	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	16	yes	complemented
237	C₃×C₂²⋊C₄	C₂²×C₃²	1	4	yes	complemented
238	C₃×C₄²	—	2	4	no	—
239	C₃×C₄²	—	3	4	no	—
240	C₃×C₄²	C₂×C₃×D₃	1	4	yes	complemented
241	C₃×C₄²	C₂²×C₃²	1	1	yes	characteristic, complemented
242	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	—
243	(C₂×D₃)⋊C₄	C₂²×C₃²	1	4	yes	complemented
244	Dic₃⋊C₄	C₂²×C₃²	1	2	yes	complemented
245	C₄×Dic₃	C₂²×C₃²	1	1	yes	characteristic, complemented
246	C₂²×C₃²	—	2	2	no	—
247	C₂²×C₃²	—	2	4	no	—
248	C₂²×C₃²	—	2	4	no	—
249	C₂²×C₃²	—	2	8	no	—
250	C₂²×C₃²	—	2	16	no	—
251	C₂²×C₃²	—	3	2	no	—
252	C₂²×C₃²	—	4	8	no	—
253	C₂²×C₃²	—	4	16	no	—
254	C₂²×C₃²	—	6	2	no	—
255	C₂²×C₃²	—	6	2	no	—
256	C₂²×C₃²	—	6	2	no	—
257	C₂²×C₃²	—	6	4	no	—
258	C₂²×C₃²	—	6	4	no	—
259	C₂²×C₃²	—	12	8	no	—
260	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
261	C₂²×C₃²	C₂⁴×C₃	1	4	yes	—
262	C₂×C₃×D₃	—	2	8	no	—
263	C₂×C₃×D₃	—	2	8	no	—
264	C₂×C₃×D₃	—	2	8	no	—
265	C₂×C₃×D₃	—	2	16	no	—
266	C₂×C₃×D₃	—	2	16	no	—
267	C₂×C₃×D₃	—	4	32	no	—
268	C₂×C₃×D₃	C₂×C₃×D₄	1	8	yes	—
269	C₃²×C₄	—	2	2	no	—
270	C₃²×C₄	—	2	2	no	—
271	C₃²×C₄	—	2	8	no	—
272	C₃²×C₄	—	2	8	no	—
273	C₃²×C₄	—	2	8	no	—
274	C₃²×C₄	—	3	2	no	—
275	C₃²×C₄	—	4	8	no	—
276	C₃²×C₄	—	4	8	no	—
277	C₃²×C₄	—	6	2	no	—
278	C₃²×C₄	D₃×D₄	1	2	yes	—
279	C₃²×C₄	C₂×C₃×D₄	1	8	yes	—
280	C₃×Dic₃	—	2	8	no	—
281	C₃×Dic₃	C₂×C₃×D₄	1	8	yes	—
282	C₂×#41	—	3	1	no	—
283	C₂²×D₄	—	3	1	no	—
284	#127	—	3	1	no	—
285	#127	—	3	1	no	—
286	#124	—	3	1	no	—
287	#124	C₃²×D₃	1	1	yes	characteristic, complemented
288	#121	—	3	4	no	—
289	#120	—	3	4	no	—
290	#117	—	3	1	no	—
291	C₃³	#535	1	1	yes	characteristic, complemented, Sylow
292	C₂³×C₃	—	2	8	no	—
293	C₂³×C₃	—	3	4	no	—
294	C₂³×C₃	—	3	8	no	—
295	C₂³×C₃	—	3	8	no	—
296	C₂³×C₃	—	6	16	no	—
297	C₂³×C₃	—	12	16	no	—
298	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
299	C₂³×C₃	C₂³×C₃²	1	2	yes	—
300	C₂²×D₃	—	2	4	no	—
301	C₂²×D₃	—	4	4	no	—
302	C₂²×D₃	C₂³×C₃²	1	2	yes	—
303	C₂²×D₃	C₂³×C₃²	1	2	yes	—
304	C₂²×D₃	C₂³×C₃²	1	1	yes	characteristic
305	C₃×Q₈	—	2	8	no	—
306	C₃×Q₈	—	2	2	no	—
307	C₃×Q₈	—	4	8	no	—
308	C₃×D₄	—	2	8	no	—
309	C₃×D₄	—	2	2	no	—
310	C₃×D₄	—	4	8	no	—
311	C₃×D₄	—	6	16	no	—
312	C₃×D₄	—	6	16	no	—
313	C₃×D₄	—	6	8	no	—
314	C₃×D₄	—	6	8	no	—
315	C₃×D₄	—	12	16	no	—
316	C₃×D₄	—	12	16	no	—
317	C₂×C₃×C₄	—	2	4	no	—
318	C₂×C₃×C₄	—	2	8	no	—
319	C₂×C₃×C₄	—	2	8	no	—
320	C₂×C₃×C₄	—	3	4	no	—
321	C₂×C₃×C₄	—	3	16	no	—
322	C₂×C₃×C₄	—	3	8	no	—
323	C₂×C₃×C₄	—	6	16	no	—
324	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
325	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
326	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
327	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
328	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
329	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
330	#67	—	2	4	no	—
331	#67	—	4	4	no	—
332	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
333	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
334	D₁₂	—	2	4	no	—
335	D₁₂	—	2	2	no	—
336	D₁₂	—	2	2	no	—
337	D₁₂	—	4	4	no	—
338	C₄×D₃	—	2	4	no	—
339	C₄×D₃	C₃²×D₄	1	4	yes	complemented
340	C₂×C₃²	—	2	4	no	—
341	C₂×C₃²	—	2	8	no	—
342	C₂×C₃²	—	4	2	no	—
343	C₂×C₃²	—	4	8	no	—
344	C₂×C₃²	—	6	2	no	—
345	C₂×C₃²	—	8	8	no	—
346	C₂×C₃²	—	12	2	no	—
347	C₂×C₃²	—	12	2	no	—
348	C₂×C₃²	C₂×D₃×D₄	1	1	yes	characteristic
349	C₂×C₃²	#1009	1	2	yes	—
350	C₂×C₃²	C₂²×C₃×D₄	1	4	yes	—
351	C₂×C₃²	C₃×H(5,𝔽₂)	1	8	yes	—
352	C₃×D₃	—	2	8	no	—
353	C₃×D₃	—	4	8	no	—
354	C₃×D₃	—	4	8	no	—
355	C₂⁴	—	3	2	no	—
356	#41	—	6	4	no	—
357	C₂×Q₈	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
358	C₂×D₄	—	3	2	no	—
359	C₂×D₄	—	3	4	no	—
360	C₂×D₄	—	3	2	no	—
361	C₂×D₄	—	3	1	no	—
362	C₂×D₄	—	3	1	no	—
363	C₂×D₄	—	3	4	no	—
364	C₂×D₄	—	6	4	no	—
365	C₂×D₄	C₂×C₃²×D₃	1	1	yes	characteristic
366	C₂²×C₄	—	3	1	no	—
367	C₂²×C₄	—	3	2	no	—
368	C₄⋊C₄	—	3	2	no	—
369	C₂²⋊C₄	—	3	2	no	—
370	C₂²⋊C₄	—	3	4	no	—
371	C₂²⋊C₄	C₂×C₃²×D₃	1	4	yes	complemented
372	C₄²	—	3	1	no	—
373	C₄²	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
374	C₂²×C₃	—	2	8	no	—
375	C₂²×C₃	—	2	16	no	—
376	C₂²×C₃	—	2	2	no	—
377	C₂²×C₃	—	2	4	no	—
378	C₂²×C₃	—	2	4	no	—
379	C₂²×C₃	—	3	8	no	—
380	C₂²×C₃	—	4	8	no	—
381	C₂²×C₃	—	4	16	no	—
382	C₂²×C₃	—	6	8	no	—
383	C₂²×C₃	—	6	8	no	—
384	C₂²×C₃	—	6	8	no	—
385	C₂²×C₃	—	6	16	no	—
386	C₂²×C₃	—	6	16	no	—
387	C₂²×C₃	—	12	32	no	—
388	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
389	C₂²×C₃	C₂⁴×C₃²	1	1	yes	characteristic
390	C₂×D₃	—	2	2	no	—
391	C₂×D₃	—	2	2	no	—
392	C₂×D₃	—	2	2	no	—
393	C₂×D₃	—	2	4	no	—
394	C₂×D₃	—	2	4	no	—
395	C₂×D₃	—	4	8	no	—
396	C₂×D₃	C₂×C₃²×D₄	1	2	yes	—
397	C₃×C₄	—	2	8	no	—
398	C₃×C₄	—	2	8	no	—
399	C₃×C₄	—	2	2	no	—
400	C₃×C₄	—	2	2	no	—
401	C₃×C₄	—	2	8	no	—
402	C₃×C₄	—	3	8	no	—
403	C₃×C₄	—	4	8	no	—
404	C₃×C₄	—	4	8	no	—
405	C₃×C₄	—	6	8	no	—
406	C₃×C₄	C₃×D₃×D₄	1	8	yes	—
407	C₃×C₄	C₂×C₃²×D₄	1	2	yes	—
408	Dic₃	—	2	2	no	—
409	Dic₃	C₂×C₃²×D₄	1	2	yes	—
410	C₃²	—	2	4	no	—
411	C₃²	#5674	1	1	yes	characteristic, direct product factor
412	C₃²	C₃×#535	1	4	yes	complemented
413	C₂³	—	3	1	no	—
414	C₂³	—	3	2	no	—
415	C₂³	—	3	2	no	—
416	C₂³	—	6	4	no	—
417	C₂³	—	12	4	no	—
418	C₂³	C₂²×C₃²×D₃	1	2	yes	—
419	Q₈	—	2	2	no	—
420	D₄	—	2	2	no	—
421	D₄	—	6	4	no	—
422	D₄	—	6	4	no	—
423	D₄	—	6	2	no	—
424	D₄	—	6	2	no	—
425	D₄	—	12	4	no	—
426	D₄	—	12	4	no	—
427	C₂×C₄	—	3	1	no	—
428	C₂×C₄	—	3	4	no	—
429	C₂×C₄	—	3	2	no	—
430	C₂×C₄	—	6	4	no	—
431	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
432	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
433	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
434	C₂×C₃	—	2	4	no	—
435	C₂×C₃	—	2	8	no	—
436	C₂×C₃	—	4	8	no	—
437	C₂×C₃	—	4	2	no	—
438	C₂×C₃	—	6	8	no	—
439	C₂×C₃	—	8	8	no	—
440	C₂×C₃	—	12	8	no	—
441	C₂×C₃	—	12	8	no	—
442	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
443	C₂×C₃	C₃×#1009	1	8	yes	—
444	C₂×C₃	C₂²×C₃²×D₄	1	1	yes	characteristic
445	C₂×C₃	C₃²×H(5,𝔽₂)	1	2	yes	—
446	D₃	—	2	2	no	—
447	D₃	—	4	2	no	—
448	D₃	—	4	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	2	4	no	—
451	C₂²	—	3	2	no	—
452	C₂²	—	6	2	no	—
453	C₂²	—	6	2	no	—
454	C₂²	—	6	2	no	—
455	C₂²	—	6	4	no	—
456	C₂²	—	6	4	no	—
457	C₂²	—	12	8	no	—
458	C₂²	C₂³×C₃²×D₃	1	1	yes	characteristic
459	C₄	—	2	2	no	—
460	C₄	—	2	2	no	—
461	C₄	—	3	2	no	—
462	C₄	—	6	2	no	—
463	C₄	C₃²×D₃×D₄	1	2	yes	—
464	C₃	—	2	4	no	—
465	C₃	C₃×#5674	1	4	yes	direct product factor
466	C₃	C₃²×#535	1	1	yes	characteristic, complemented
467	C₂	—	4	2	no	—
468	C₂	—	6	2	no	—
469	C₂	—	12	2	no	—
470	C₂	—	12	2	no	—
471	C₂	C₂×C₃²×D₃×D₄	1	1	yes	characteristic
472	C₂	C₃²×#1009	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃²	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₃²
Frattini	C₂²	C₂³×C₃²×D₃
Fitting	C₃³×#124	C₂
socle	C₂²×C₃³	C₂⁴
hypercenter	C₃²×#124	D₃
hypocenter	C₃	C₃²×#535
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃² ◁ C₃²×#124

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×#239	C₂	semidirect
2. C₂×C₃²×D₃×D₄	C₂	semidirect
3. C₃³×#124	C₂	semidirect
4. C₃²×#947	C₂	semidirect
5. C₃²×#940	C₂	semidirect
6. C₃²×#884	C₂	semidirect
7. C₃²×#882	C₂	semidirect
8. C₃²×#874	C₂	semidirect
9. C₃²×#872	C₂	semidirect
11. C₃×#5674	C₃	direct (N × H)
13. C₂×C₃³×Q₈	C₂²	semidirect
16. C₂×C₃²×#67	C₂²	semidirect
21. C₂×C₃²×D₁₂	C₂²	semidirect
22. C₂×C₃²×D₁₂	C₂²	semidirect
24. C₂×C₃²×C₄×D₃	C₂²	semidirect
25. C₃³×C₂²⋊C₄	C₂²	semidirect
26. C₃³×C₄²	C₂²	semidirect
28. C₃²×(C₂×D₃)⋊C₄	C₂²	semidirect
29. C₃²×Dic₃⋊C₄	C₂²	semidirect
30. C₃²×C₄×Dic₃	C₂²	semidirect
33. C₂×C₃×#239	C₂×C₃	semidirect
34. C₂×C₃×D₃×D₄	C₂×C₃	semidirect
39. C₃²×#124	D₃	semidirect
40. C₃²×#124	C₂×C₃	semidirect
44. C₃×#947	C₂×C₃	semidirect
45. C₃×#940	C₂×C₃	semidirect
46. C₃×#884	C₂×C₃	semidirect
47. C₃×#882	C₂×C₃	semidirect
48. C₃×#874	C₂×C₃	semidirect
49. C₃×#872	C₂×C₃	semidirect
70. C₃²×C₄×D₃	D₄	semidirect
72. #5674	C₃²	direct (N × H)
77. C₂×C₃²×Q₈	C₂×D₃	semidirect
78. C₂×C₃²×Q₈	C₂²×C₃	semidirect
92. C₂×C₃×#67	C₂²×C₃	semidirect
97. C₂×C₃×D₁₂	C₂²×C₃	semidirect
98. C₂×C₃×D₁₂	C₂²×C₃	semidirect
100. C₂×C₃×C₄×D₃	C₂²×C₃	semidirect
105. C₃²×C₂²⋊C₄	C₂×D₃	semidirect
106. C₃²×C₂²⋊C₄	C₂²×C₃	semidirect
109. C₃²×C₄²	C₂×D₃	semidirect
110. C₃²×C₄²	C₂²×C₃	semidirect
112. C₃×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
113. C₃×Dic₃⋊C₄	C₂²×C₃	semidirect
114. C₃×C₄×Dic₃	C₂²×C₃	semidirect
132. C₂×#239	C₂×C₃²	semidirect
133. C₂×D₃×D₄	C₂×C₃²	semidirect
138. C₃×#124	C₃×D₃	semidirect
139. C₃×#124	C₂×C₃²	semidirect
143. #947	C₂×C₃²	semidirect
144. #940	C₂×C₃²	semidirect
145. #884	C₂×C₃²	semidirect
146. #882	C₂×C₃²	semidirect
147. #874	C₂×C₃²	semidirect
148. #872	C₂×C₃²	semidirect
196. C₃×C₄×D₃	C₃×D₄	semidirect
208. C₂×C₃×Q₈	C₂×C₃×D₃	semidirect
209. C₂×C₃×Q₈	C₂²×C₃²	semidirect
223. C₂×#67	C₂²×C₃²	semidirect
228. C₂×D₁₂	C₂²×C₃²	semidirect
229. C₂×D₁₂	C₂²×C₃²	semidirect
231. C₂×C₄×D₃	C₂²×C₃²	semidirect
236. C₃×C₂²⋊C₄	C₂×C₃×D₃	semidirect
237. C₃×C₂²⋊C₄	C₂²×C₃²	semidirect
240. C₃×C₄²	C₂×C₃×D₃	semidirect
241. C₃×C₄²	C₂²×C₃²	semidirect
243. (C₂×D₃)⋊C₄	C₂²×C₃²	semidirect
244. Dic₃⋊C₄	C₂²×C₃²	semidirect
245. C₄×Dic₃	C₂²×C₃²	semidirect
287. #124	C₃²×D₃	semidirect
291. C₃³	#535	semidirect
339. C₄×D₃	C₃²×D₄	semidirect
357. C₂×Q₈	C₂×C₃²×D₃	semidirect
371. C₂²⋊C₄	C₂×C₃²×D₃	semidirect
373. C₄²	C₂×C₃²×D₃	semidirect
411. C₃²	#5674	direct (N × H)
412. C₃²	C₃×#535	semidirect
465. C₃	C₃×#5674	direct (N × H)
466. C₃	C₃²×#535	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×#239	2
C₂×C₃²×D₃×D₄	2
C₃³×#124	2
C₃²×#947	2
C₃²×#940	2
C₃²×#884	2
C₃²×#882	2
C₃²×#874	2
C₃²×#872	2
C₃²×#535	3
C₃×#5674	3

Subgroups — C32×#5674 #13179052

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#5674 #13179052