Subgroups — C₃×#5654 #10595751

Order 576.

707 conjugacy classes of subgroups.

The subgroup lattice has 555 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#123	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#939	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#896	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#895	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#894	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#893	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#885	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#884	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#882	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#882	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#67⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×D₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#546	—	3	1	no	maximal
17	#5654	C₃	1	1	yes	maximal, characteristic, direct product factor
18	C₂³×C₃×D₃	C₂²	1	1	yes	characteristic
19	C₂³×C₃×D₃	C₂²	1	1	yes	characteristic
20	C₂×C₃²×D₄	C₂²	1	1	yes	characteristic
21	C₂²×C₃²×C₄	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×#67	C₂²	1	1	yes	characteristic
23	C₂×C₃×#67	C₂²	1	1	yes	characteristic
24	C₂×C₃×#67	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃×#67	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₃×Dic₃	C₂²	1	1	yes	characteristic, complemented
27	C₃×D₃×D₄	—	2	4	no	—
28	C₃×#235	—	2	4	no	—
29	C₂×C₃×D₁₂	C₂²	1	1	yes	characteristic
30	C₂×C₃×D₁₂	C₂²	1	1	yes	characteristic
31	C₂×C₃×D₁₂	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃×D₁₂	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₄×D₃	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₃×C₄×D₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₃×C₄×D₃	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₃×Dic₆	C₂²	1	1	yes	characteristic, complemented
38	C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
39	C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
41	C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
42	C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
43	C₃×#217	C₂²	1	1	yes	characteristic, complemented
44	C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
45	C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
46	C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
47	C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
48	C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
49	C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
50	C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
51	C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
52	C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
53	C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
54	C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₃×#41	—	3	1	no	—
56	C₂²×C₃×D₄	—	3	1	no	—
57	C₂×D₃×D₄	C₂×C₃	1	1	yes	characteristic, complemented
58	C₂×#235	C₂×C₃	1	1	yes	characteristic, complemented
59	C₃×#124	—	3	1	no	—
60	C₃×#123	—	2	1	no	—
61	C₃×#123	—	3	1	no	—
62	C₃×#123	D₃	1	1	yes	characteristic, complemented
63	C₃×#123	C₂×C₃	1	1	yes	characteristic, complemented
64	C₃×C₂²⋊Q₈	—	3	1	no	—
65	C₃×#121	—	3	1	no	—
66	C₃×#121	—	3	1	no	—
67	C₃×#121	—	3	1	no	—
68	C₃×#120	—	3	1	no	—
69	C₃×#120	—	3	1	no	—
70	C₃×C₄×D₄	—	3	1	no	—
71	C₃×C₄×D₄	—	3	1	no	—
72	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
73	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
74	#939	C₂×C₃	1	1	yes	characteristic, complemented
75	C₂×(C₂×D₃)⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
76	#896	C₂×C₃	1	1	yes	characteristic, complemented
77	#895	C₂×C₃	1	1	yes	characteristic, complemented
78	#894	C₂×C₃	1	1	yes	characteristic, complemented
79	#893	C₂×C₃	1	1	yes	characteristic, complemented
80	#885	C₂×C₃	1	1	yes	characteristic, complemented
81	#884	C₂×C₃	1	1	yes	characteristic, complemented
82	#882	C₂×C₃	1	1	yes	characteristic, complemented
83	#882	C₂×C₃	1	1	yes	characteristic, complemented
84	#67⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
85	D₃×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
86	C₂³×C₃²	C₂³	1	1	yes	characteristic
87	C₂³×C₃²	C₂³	1	1	yes	characteristic
88	C₂²×C₃×D₃	—	2	2	no	—
89	C₂²×C₃×D₃	—	2	2	no	—
90	C₂²×C₃×D₃	—	2	2	no	—
91	C₂²×C₃×D₃	—	2	2	no	—
92	C₂²×C₃×D₃	—	4	1	no	—
93	C₂²×C₃×D₃	—	4	1	no	—
94	C₂²×C₃×D₃	C₂³	1	1	yes	characteristic
95	C₂²×C₃×D₃	C₂³	1	1	yes	characteristic
96	C₂²×C₃×D₃	C₂³	1	1	yes	characteristic
97	C₂²×C₃×D₃	C₂³	1	1	yes	characteristic
98	C₃²×D₄	—	2	2	no	—
99	C₂×C₃²×C₄	—	2	2	no	—
100	C₂×C₃²×C₄	C₂³	1	1	yes	characteristic
101	C₂×C₃²×C₄	C₂³	1	1	yes	characteristic
102	C₂×C₃²×C₄	C₂³	1	1	yes	characteristic
103	C₂×C₃²×C₄	C₂³	1	1	yes	characteristic
104	C₂×C₃²×C₄	C₂³	1	1	yes	characteristic
105	C₃×#67	—	2	2	no	—
106	C₃×#67	—	2	2	no	—
107	C₃×#67	—	4	1	no	—
108	C₃×#67	D₄	1	4	yes	complemented
109	C₂×C₃×Dic₃	—	4	1	no	—
110	C₂×C₃×Dic₃	C₂³	1	1	yes	characteristic
111	C₂×C₃×Dic₃	C₂³	1	1	yes	characteristic
112	C₂×C₃×Dic₃	C₂³	1	1	yes	characteristic
113	C₂×C₃×Dic₃	C₂³	1	1	yes	characteristic
114	C₃×D₁₂	—	2	2	no	—
115	C₃×D₁₂	—	2	2	no	—
116	C₃×D₁₂	—	2	2	no	—
117	C₃×D₁₂	—	4	1	no	—
118	C₃×C₄×D₃	—	2	2	no	—
119	C₃×C₄×D₃	—	2	2	no	—
120	C₃×C₄×D₃	—	2	2	no	—
121	C₃×C₄×D₃	—	4	1	no	—
122	C₃×Dic₆	—	2	2	no	—
123	#546	—	3	1	no	Sylow
124	C₂⁴×C₃	—	3	1	no	—
125	C₂⁴×C₃	—	3	1	no	—
126	C₂³×D₃	C₂²×C₃	1	1	yes	characteristic
127	C₂³×D₃	C₂²×C₃	1	1	yes	characteristic
128	C₃×#41	—	6	4	no	—
129	C₂×C₃×Q₈	—	3	1	no	—
130	C₂×C₃×D₄	—	2	1	no	—
131	C₂×C₃×D₄	—	3	1	no	—
132	C₂×C₃×D₄	—	3	1	no	—
133	C₂×C₃×D₄	—	3	1	no	—
134	C₂×C₃×D₄	—	3	1	no	—
135	C₂×C₃×D₄	—	3	1	no	—
136	C₂×C₃×D₄	—	3	1	no	—
137	C₂×C₃×D₄	—	3	1	no	—
138	C₂×C₃×D₄	—	3	1	no	—
139	C₂×C₃×D₄	—	6	4	no	—
140	C₂×C₃×D₄	C₂×D₃	1	1	yes	characteristic
141	C₂×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
142	C₂²×C₃×C₄	—	2	1	no	—
143	C₂²×C₃×C₄	—	3	1	no	—
144	C₂²×C₃×C₄	—	3	1	no	—
145	C₂²×C₃×C₄	—	3	1	no	—
146	C₂²×C₃×C₄	—	3	1	no	—
147	C₂²×C₃×C₄	—	3	1	no	—
148	C₂²×C₃×C₄	C₂×D₃	1	1	yes	characteristic, complemented
149	C₂²×C₃×C₄	C₂²×C₃	1	1	yes	characteristic, complemented
150	C₂×#67	C₂²×C₃	1	1	yes	characteristic
151	C₂×#67	C₂²×C₃	1	1	yes	characteristic
152	C₂×#67	C₂²×C₃	1	1	yes	characteristic, complemented
153	C₂×#67	C₂²×C₃	1	1	yes	characteristic, complemented
154	C₂²×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
155	D₃×D₄	—	2	4	no	—
156	#235	—	2	4	no	—
157	C₂×D₁₂	C₂²×C₃	1	1	yes	characteristic
158	C₂×D₁₂	C₂²×C₃	1	1	yes	characteristic
159	C₂×D₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
160	C₂×D₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
161	C₂×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
162	C₂×C₄×D₃	C₂²×C₃	1	1	yes	characteristic, complemented
163	C₂×C₄×D₃	C₂²×C₃	1	1	yes	characteristic, complemented
164	C₂×C₄×D₃	C₂²×C₃	1	1	yes	characteristic, complemented
165	C₂×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
166	C₃×C₄⋊C₄	—	2	1	no	—
167	C₃×C₄⋊C₄	—	2	1	no	—
168	C₃×C₄⋊C₄	—	3	1	no	—
169	C₃×C₄⋊C₄	—	3	1	no	—
170	C₃×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
171	C₃×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
172	C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
173	C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
174	C₃×C₂²⋊C₄	—	2	1	no	—
175	C₃×C₂²⋊C₄	—	2	1	no	—
176	C₃×C₂²⋊C₄	—	2	1	no	—
177	C₃×C₂²⋊C₄	—	3	1	no	—
178	C₃×C₂²⋊C₄	—	3	1	no	—
179	C₃×C₂²⋊C₄	—	3	1	no	—
180	C₃×C₂²⋊C₄	—	3	1	no	—
181	C₃×C₂²⋊C₄	—	3	1	no	—
182	C₃×C₂²⋊C₄	—	3	1	no	—
183	C₃×C₂²⋊C₄	—	3	1	no	—
184	C₃×C₂²⋊C₄	—	3	1	no	—
185	C₃×C₂²⋊C₄	—	3	1	no	—
186	C₃×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
187	C₃×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
188	C₃×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
189	C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
190	C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
191	C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
192	C₃×C₄²	—	3	1	no	—
193	#217	C₂²×C₃	1	1	yes	characteristic, complemented
194	(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
195	(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
196	(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
197	(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
198	(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
199	(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
200	(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
201	(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
202	Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
203	Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
204	C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
205	C₂²×C₃²	—	2	1	no	—
206	C₂²×C₃²	—	2	1	no	—
207	C₂²×C₃²	—	2	1	no	—
208	C₂²×C₃²	—	2	1	no	—
209	C₂²×C₃²	—	2	1	no	—
210	C₂²×C₃²	C₂×D₄	1	2	yes	—
211	C₂²×C₃²	C₂⁴	1	1	yes	characteristic
212	C₂×C₃×D₃	—	2	1	no	—
213	C₂×C₃×D₃	—	2	1	no	—
214	C₂×C₃×D₃	—	2	1	no	—
215	C₂×C₃×D₃	—	2	1	no	—
216	C₂×C₃×D₃	—	2	1	no	—
217	C₂×C₃×D₃	—	2	1	no	—
218	C₂×C₃×D₃	—	2	1	no	—
219	C₂×C₃×D₃	—	2	1	no	—
220	C₂×C₃×D₃	—	2	1	no	—
221	C₂×C₃×D₃	—	2	1	no	—
222	C₂×C₃×D₃	—	4	4	no	—
223	C₂×C₃×D₃	—	4	4	no	—
224	C₂×C₃×D₃	C₂×D₄	1	2	yes	—
225	C₂×C₃×D₃	#41	1	2	yes	complemented
226	C₃²×C₄	—	2	1	no	—
227	C₃²×C₄	—	2	1	no	—
228	C₃²×C₄	—	2	1	no	—
229	C₃²×C₄	—	2	1	no	—
230	C₃²×C₄	—	2	1	no	—
231	C₃×Dic₃	—	2	1	no	—
232	C₃×Dic₃	—	2	1	no	—
233	C₃×Dic₃	—	2	1	no	—
234	C₃×Dic₃	C₂×D₄	1	2	yes	—
235	C₂×#41	—	3	1	no	—
236	C₂²×D₄	—	3	1	no	—
237	#124	—	3	1	no	—
238	#123	—	3	1	no	—
239	#123	C₃×D₃	1	1	yes	characteristic, complemented
240	C₂²⋊Q₈	—	3	1	no	—
241	#121	—	3	1	no	—
242	#121	—	3	1	no	—
243	#121	—	3	1	no	—
244	#120	—	3	1	no	—
245	#120	—	3	1	no	—
246	C₄×D₄	—	3	1	no	—
247	C₄×D₄	—	3	1	no	—
248	C₂×C₂²⋊C₄	—	3	1	no	—
249	C₂×C₂²⋊C₄	—	3	1	no	—
250	C₂³×C₃	—	2	1	no	—
251	C₂³×C₃	—	2	1	no	—
252	C₂³×C₃	—	3	1	no	—
253	C₂³×C₃	—	3	1	no	—
254	C₂³×C₃	—	3	1	no	—
255	C₂³×C₃	—	3	1	no	—
256	C₂³×C₃	—	6	2	no	—
257	C₂³×C₃	—	6	2	no	—
258	C₂³×C₃	—	6	2	no	—
259	C₂³×C₃	—	6	2	no	—
260	C₂³×C₃	—	12	1	no	—
261	C₂³×C₃	—	12	1	no	—
262	C₂³×C₃	C₂²×D₃	1	1	yes	characteristic
263	C₂³×C₃	C₂²×D₃	1	1	yes	characteristic
264	C₂³×C₃	C₂³×C₃	1	1	yes	characteristic
265	C₂³×C₃	C₂³×C₃	1	1	yes	characteristic
266	C₂²×D₃	—	2	2	no	—
267	C₂²×D₃	—	2	2	no	—
268	C₂²×D₃	—	2	2	no	—
269	C₂²×D₃	—	2	2	no	—
270	C₂²×D₃	—	4	1	no	—
271	C₂²×D₃	—	4	1	no	—
272	C₂²×D₃	C₂³×C₃	1	1	yes	characteristic
273	C₂²×D₃	C₂³×C₃	1	1	yes	characteristic
274	C₂²×D₃	C₂³×C₃	1	1	yes	characteristic
275	C₂²×D₃	C₂³×C₃	1	1	yes	characteristic
276	C₃×Q₈	—	6	2	no	—
277	C₃×D₄	—	2	2	no	—
278	C₃×D₄	—	2	2	no	—
279	C₃×D₄	—	3	4	no	—
280	C₃×D₄	—	4	2	no	—
281	C₃×D₄	—	6	2	no	—
282	C₃×D₄	—	6	2	no	—
283	C₃×D₄	—	6	2	no	—
284	C₃×D₄	—	6	2	no	—
285	C₃×D₄	—	6	2	no	—
286	C₃×D₄	—	12	1	no	—
287	C₃×D₄	—	12	1	no	—
288	C₂×C₃×C₄	—	2	2	no	—
289	C₂×C₃×C₄	—	2	2	no	—
290	C₂×C₃×C₄	—	2	1	no	—
291	C₂×C₃×C₄	—	2	1	no	—
292	C₂×C₃×C₄	—	2	1	no	—
293	C₂×C₃×C₄	—	2	1	no	—
294	C₂×C₃×C₄	—	2	1	no	—
295	C₂×C₃×C₄	—	3	1	no	—
296	C₂×C₃×C₄	—	3	1	no	—
297	C₂×C₃×C₄	—	3	1	no	—
298	C₂×C₃×C₄	—	3	1	no	—
299	C₂×C₃×C₄	—	4	2	no	—
300	C₂×C₃×C₄	—	6	2	no	—
301	C₂×C₃×C₄	—	6	2	no	—
302	C₂×C₃×C₄	—	6	2	no	—
303	C₂×C₃×C₄	—	12	1	no	—
304	C₂×C₃×C₄	—	12	1	no	—
305	C₂×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
306	C₂×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
307	C₂×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
308	C₂×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
309	C₂×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
310	C₂×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
311	C₂×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
312	C₂×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
313	C₂×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
314	C₂×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
315	#67	—	2	2	no	—
316	#67	—	2	2	no	—
317	#67	—	4	1	no	—
318	#67	C₃×D₄	1	4	yes	complemented
319	C₂×Dic₃	—	4	1	no	—
320	C₂×Dic₃	C₂³×C₃	1	1	yes	characteristic
321	C₂×Dic₃	C₂³×C₃	1	1	yes	characteristic
322	C₂×Dic₃	C₂³×C₃	1	1	yes	characteristic
323	C₂×Dic₃	C₂³×C₃	1	1	yes	characteristic
324	D₁₂	—	2	2	no	—
325	D₁₂	—	2	2	no	—
326	D₁₂	—	2	2	no	—
327	D₁₂	—	4	1	no	—
328	C₄×D₃	—	2	2	no	—
329	C₄×D₃	—	2	2	no	—
330	C₄×D₃	—	2	2	no	—
331	C₄×D₃	—	4	1	no	—
332	Dic₆	—	2	2	no	—
333	C₂×C₃²	—	2	2	no	—
334	C₂×C₃²	—	4	1	no	—
335	C₂×C₃²	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₃²	C₂×#41	1	1	yes	characteristic
337	C₂×C₃²	H(5,𝔽₂)	1	1	yes	characteristic
338	C₃×D₃	—	2	2	no	—
339	C₃×D₃	—	2	2	no	—
340	C₃×D₃	—	4	1	no	—
341	C₃×D₃	—	4	1	no	—
342	C₂⁴	—	3	1	no	—
343	C₂⁴	—	3	1	no	—
344	#41	—	6	4	no	—
345	C₂×Q₈	—	3	1	no	—
346	C₂×D₄	—	3	1	no	—
347	C₂×D₄	—	3	1	no	—
348	C₂×D₄	—	3	1	no	—
349	C₂×D₄	—	3	1	no	—
350	C₂×D₄	—	3	1	no	—
351	C₂×D₄	—	3	1	no	—
352	C₂×D₄	—	3	1	no	—
353	C₂×D₄	—	3	1	no	—
354	C₂×D₄	—	6	4	no	—
355	C₂×D₄	C₂×C₃×D₃	1	1	yes	characteristic
356	C₂²×C₄	—	3	1	no	—
357	C₂²×C₄	—	3	1	no	—
358	C₂²×C₄	—	3	1	no	—
359	C₂²×C₄	—	3	1	no	—
360	C₂²×C₄	—	3	1	no	—
361	C₂²×C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
362	C₄⋊C₄	—	3	1	no	—
363	C₄⋊C₄	—	3	1	no	—
364	C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
365	C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
366	C₂²⋊C₄	—	3	1	no	—
367	C₂²⋊C₄	—	3	1	no	—
368	C₂²⋊C₄	—	3	1	no	—
369	C₂²⋊C₄	—	3	1	no	—
370	C₂²⋊C₄	—	3	1	no	—
371	C₂²⋊C₄	—	3	1	no	—
372	C₂²⋊C₄	—	3	1	no	—
373	C₂²⋊C₄	—	3	1	no	—
374	C₂²⋊C₄	—	3	1	no	—
375	C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
376	C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
377	C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
378	C₄²	—	3	1	no	—
379	C₂²×C₃	—	2	1	no	—
380	C₂²×C₃	—	2	1	no	—
381	C₂²×C₃	—	2	1	no	—
382	C₂²×C₃	—	2	1	no	—
383	C₂²×C₃	—	2	1	no	—
384	C₂²×C₃	—	2	1	no	—
385	C₂²×C₃	—	2	1	no	—
386	C₂²×C₃	—	2	1	no	—
387	C₂²×C₃	—	2	1	no	—
388	C₂²×C₃	—	2	1	no	—
389	C₂²×C₃	—	2	1	no	—
390	C₂²×C₃	—	2	2	no	—
391	C₂²×C₃	—	3	2	no	—
392	C₂²×C₃	—	3	2	no	—
393	C₂²×C₃	—	4	1	no	—
394	C₂²×C₃	—	4	1	no	—
395	C₂²×C₃	—	4	1	no	—
396	C₂²×C₃	—	4	1	no	—
397	C₂²×C₃	—	4	1	no	—
398	C₂²×C₃	—	6	1	no	—
399	C₂²×C₃	—	6	1	no	—
400	C₂²×C₃	—	6	1	no	—
401	C₂²×C₃	—	6	1	no	—
402	C₂²×C₃	—	6	1	no	—
403	C₂²×C₃	—	6	1	no	—
404	C₂²×C₃	—	6	1	no	—
405	C₂²×C₃	—	6	1	no	—
406	C₂²×C₃	—	6	1	no	—
407	C₂²×C₃	—	6	1	no	—
408	C₂²×C₃	—	12	4	no	—
409	C₂²×C₃	—	12	4	no	—
410	C₂²×C₃	D₃×D₄	1	2	yes	—
411	C₂²×C₃	C₂×C₃×D₄	1	2	yes	—
412	C₂²×C₃	C₂³×D₃	1	1	yes	characteristic
413	C₂²×C₃	C₂⁴×C₃	1	1	yes	characteristic
414	C₂×D₃	—	2	1	no	—
415	C₂×D₃	—	2	1	no	—
416	C₂×D₃	—	2	1	no	—
417	C₂×D₃	—	2	1	no	—
418	C₂×D₃	—	2	1	no	—
419	C₂×D₃	—	2	1	no	—
420	C₂×D₃	—	2	1	no	—
421	C₂×D₃	—	2	1	no	—
422	C₂×D₃	—	2	1	no	—
423	C₂×D₃	—	2	1	no	—
424	C₂×D₃	—	4	4	no	—
425	C₂×D₃	—	4	4	no	—
426	C₂×D₃	C₂×C₃×D₄	1	2	yes	—
427	C₂×D₃	C₃×#41	1	2	yes	complemented
428	C₃×C₄	—	2	1	no	—
429	C₃×C₄	—	2	1	no	—
430	C₃×C₄	—	2	1	no	—
431	C₃×C₄	—	2	1	no	—
432	C₃×C₄	—	2	1	no	—
433	C₃×C₄	—	2	1	no	—
434	C₃×C₄	—	2	1	no	—
435	C₃×C₄	—	2	1	no	—
436	C₃×C₄	—	2	1	no	—
437	C₃×C₄	—	2	1	no	—
438	C₃×C₄	—	3	2	no	—
439	C₃×C₄	—	4	1	no	—
440	C₃×C₄	—	4	1	no	—
441	C₃×C₄	—	4	1	no	—
442	C₃×C₄	—	4	1	no	—
443	C₃×C₄	—	4	1	no	—
444	C₃×C₄	—	6	1	no	—
445	C₃×C₄	—	6	1	no	—
446	C₃×C₄	—	6	1	no	—
447	Dic₃	—	2	1	no	—
448	Dic₃	—	2	1	no	—
449	Dic₃	—	2	1	no	—
450	Dic₃	C₂×C₃×D₄	1	2	yes	—
451	C₃²	#546	1	1	yes	characteristic, complemented, Sylow
452	C₂³	—	3	1	no	—
453	C₂³	—	3	1	no	—
454	C₂³	—	3	1	no	—
455	C₂³	—	3	1	no	—
456	C₂³	—	6	2	no	—
457	C₂³	—	6	2	no	—
458	C₂³	—	6	2	no	—
459	C₂³	—	6	2	no	—
460	C₂³	—	12	1	no	—
461	C₂³	—	12	1	no	—
462	C₂³	C₂²×C₃×D₃	1	1	yes	characteristic
463	C₂³	C₂²×C₃×D₃	1	1	yes	characteristic
464	Q₈	—	6	2	no	—
465	D₄	—	2	2	no	—
466	D₄	—	3	4	no	—
467	D₄	—	6	2	no	—
468	D₄	—	6	2	no	—
469	D₄	—	6	2	no	—
470	D₄	—	6	2	no	—
471	D₄	—	6	2	no	—
472	D₄	—	12	1	no	—
473	D₄	—	12	1	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	3	1	no	—
476	C₂×C₄	—	3	1	no	—
477	C₂×C₄	—	3	1	no	—
478	C₂×C₄	—	3	1	no	—
479	C₂×C₄	—	6	2	no	—
480	C₂×C₄	—	6	2	no	—
481	C₂×C₄	—	6	2	no	—
482	C₂×C₄	—	12	1	no	—
483	C₂×C₄	—	12	1	no	—
484	C₂×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
485	C₂×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
486	C₂×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
487	C₂×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
488	C₂×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
489	C₂×C₃	—	2	2	no	—
490	C₂×C₃	—	2	2	no	—
491	C₂×C₃	—	2	1	no	—
492	C₂×C₃	—	2	1	no	—
493	C₂×C₃	—	2	1	no	—
494	C₂×C₃	—	4	2	no	—
495	C₂×C₃	—	4	1	no	—
496	C₂×C₃	—	4	1	no	—
497	C₂×C₃	—	6	2	no	—
498	C₂×C₃	—	6	2	no	—
499	C₂×C₃	—	8	1	no	—
500	C₂×C₃	—	12	1	no	—
501	C₂×C₃	—	12	1	no	—
502	C₂×C₃	C₂×D₃×D₄	1	1	yes	characteristic
503	C₂×C₃	D₃×#41	1	1	yes	characteristic
504	C₂×C₃	#1009	1	1	yes	characteristic
505	C₂×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
506	C₂×C₃	C₂×C₃×#41	1	1	yes	characteristic
507	C₂×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
508	D₃	—	2	2	no	—
509	D₃	—	2	2	no	—
510	D₃	—	4	1	no	—
511	D₃	—	4	1	no	—
512	C₂²	—	2	1	no	—
513	C₂²	—	2	1	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	2	1	no	—
517	C₂²	—	3	2	no	—
518	C₂²	—	3	2	no	—
519	C₂²	—	6	1	no	—
520	C₂²	—	6	1	no	—
521	C₂²	—	6	1	no	—
522	C₂²	—	6	1	no	—
523	C₂²	—	6	1	no	—
524	C₂²	—	6	1	no	—
525	C₂²	—	6	1	no	—
526	C₂²	—	6	1	no	—
527	C₂²	—	6	1	no	—
528	C₂²	—	6	1	no	—
529	C₂²	—	12	4	no	—
530	C₂²	—	12	4	no	—
531	C₂²	C₃×D₃×D₄	1	2	yes	—
532	C₂²	C₂³×C₃×D₃	1	1	yes	characteristic
533	C₄	—	2	1	no	—
534	C₄	—	2	1	no	—
535	C₄	—	2	1	no	—
536	C₄	—	2	1	no	—
537	C₄	—	2	1	no	—
538	C₄	—	3	2	no	—
539	C₄	—	6	1	no	—
540	C₄	—	6	1	no	—
541	C₄	—	6	1	no	—
542	C₃	—	2	1	no	—
543	C₃	#5654	1	1	yes	characteristic, direct product factor
544	C₃	C₃×#546	1	1	yes	characteristic, complemented
545	C₂	—	2	2	no	—
546	C₂	—	4	1	no	—
547	C₂	—	6	2	no	—
548	C₂	—	6	2	no	—
549	C₂	—	12	1	no	—
550	C₂	—	12	1	no	—
551	C₂	C₂×C₃×D₃×D₄	1	1	yes	characteristic
552	C₂	C₃×D₃×#41	1	1	yes	characteristic
553	C₂	C₃×#1009	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×D₃
Fitting	C₃²×#123	C₂
socle	C₂²×C₃²	C₂⁴
hypercenter	C₃×#123	D₃
hypocenter	C₃	C₃×#546
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#123

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₃×D₄	C₂	semidirect
2. C₂×C₃×#235	C₂	semidirect
3. C₃²×#123	C₂	semidirect
4. C₃×#939	C₂	semidirect
5. C₂×C₃×(C₂×D₃)⋊C₄	C₂	semidirect
6. C₃×#896	C₂	semidirect
7. C₃×#895	C₂	semidirect
8. C₃×#894	C₂	semidirect
9. C₃×#893	C₂	semidirect
10. C₃×#885	C₂	semidirect
11. C₃×#884	C₂	semidirect
12. C₃×#882	C₂	semidirect
13. C₃×#882	C₂	semidirect
14. C₃×#67⋊C₄	C₂	semidirect
15. C₃×D₃×C₂²⋊C₄	C₂	semidirect
17. #5654	C₃	direct (N × H)
21. C₂²×C₃²×C₄	C₂²	semidirect
24. C₂×C₃×#67	C₂²	semidirect
25. C₂×C₃×#67	C₂²	semidirect
26. C₂²×C₃×Dic₃	C₂²	semidirect
31. C₂×C₃×D₁₂	C₂²	semidirect
32. C₂×C₃×D₁₂	C₂²	semidirect
34. C₂×C₃×C₄×D₃	C₂²	semidirect
35. C₂×C₃×C₄×D₃	C₂²	semidirect
36. C₂×C₃×C₄×D₃	C₂²	semidirect
37. C₂×C₃×Dic₆	C₂²	semidirect
38. C₃²×C₄⋊C₄	C₂²	semidirect
39. C₃²×C₄⋊C₄	C₂²	semidirect
40. C₃²×C₂²⋊C₄	C₂²	semidirect
41. C₃²×C₂²⋊C₄	C₂²	semidirect
42. C₃²×C₂²⋊C₄	C₂²	semidirect
43. C₃×#217	C₂²	semidirect
47. C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
48. C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
49. C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
50. C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
51. C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
52. C₃×Dic₃⋊C₄	C₂²	semidirect
53. C₃×Dic₃⋊C₄	C₂²	semidirect
54. C₃×C₄×Dic₃	C₂²	semidirect
57. C₂×D₃×D₄	C₂×C₃	semidirect
58. C₂×#235	C₂×C₃	semidirect
62. C₃×#123	D₃	semidirect
63. C₃×#123	C₂×C₃	semidirect
74. #939	C₂×C₃	semidirect
75. C₂×(C₂×D₃)⋊C₄	C₂×C₃	semidirect
76. #896	C₂×C₃	semidirect
77. #895	C₂×C₃	semidirect
78. #894	C₂×C₃	semidirect
79. #893	C₂×C₃	semidirect
80. #885	C₂×C₃	semidirect
81. #884	C₂×C₃	semidirect
82. #882	C₂×C₃	semidirect
83. #882	C₂×C₃	semidirect
84. #67⋊C₄	C₂×C₃	semidirect
85. D₃×C₂²⋊C₄	C₂×C₃	semidirect
108. C₃×#67	D₄	semidirect
148. C₂²×C₃×C₄	C₂×D₃	semidirect
149. C₂²×C₃×C₄	C₂²×C₃	semidirect
152. C₂×#67	C₂²×C₃	semidirect
153. C₂×#67	C₂²×C₃	semidirect
154. C₂²×Dic₃	C₂²×C₃	semidirect
159. C₂×D₁₂	C₂²×C₃	semidirect
160. C₂×D₁₂	C₂²×C₃	semidirect
162. C₂×C₄×D₃	C₂²×C₃	semidirect
163. C₂×C₄×D₃	C₂²×C₃	semidirect
164. C₂×C₄×D₃	C₂²×C₃	semidirect
165. C₂×Dic₆	C₂²×C₃	semidirect
170. C₃×C₄⋊C₄	C₂×D₃	semidirect
171. C₃×C₄⋊C₄	C₂×D₃	semidirect
172. C₃×C₄⋊C₄	C₂²×C₃	semidirect
173. C₃×C₄⋊C₄	C₂²×C₃	semidirect
186. C₃×C₂²⋊C₄	C₂×D₃	semidirect
187. C₃×C₂²⋊C₄	C₂×D₃	semidirect
188. C₃×C₂²⋊C₄	C₂×D₃	semidirect
189. C₃×C₂²⋊C₄	C₂²×C₃	semidirect
190. C₃×C₂²⋊C₄	C₂²×C₃	semidirect
191. C₃×C₂²⋊C₄	C₂²×C₃	semidirect
193. #217	C₂²×C₃	semidirect
197. (C₂×D₃)⋊C₄	C₂²×C₃	semidirect
198. (C₂×D₃)⋊C₄	C₂²×C₃	semidirect
199. (C₂×D₃)⋊C₄	C₂²×C₃	semidirect
200. (C₂×D₃)⋊C₄	C₂²×C₃	semidirect
201. (C₂×D₃)⋊C₄	C₂²×C₃	semidirect
202. Dic₃⋊C₄	C₂²×C₃	semidirect
203. Dic₃⋊C₄	C₂²×C₃	semidirect
204. C₄×Dic₃	C₂²×C₃	semidirect
225. C₂×C₃×D₃	#41	semidirect
239. #123	C₃×D₃	semidirect
318. #67	C₃×D₄	semidirect
361. C₂²×C₄	C₂×C₃×D₃	semidirect
364. C₄⋊C₄	C₂×C₃×D₃	semidirect
365. C₄⋊C₄	C₂×C₃×D₃	semidirect
375. C₂²⋊C₄	C₂×C₃×D₃	semidirect
376. C₂²⋊C₄	C₂×C₃×D₃	semidirect
377. C₂²⋊C₄	C₂×C₃×D₃	semidirect
427. C₂×D₃	C₃×#41	semidirect
451. C₃²	#546	semidirect
543. C₃	#5654	direct (N × H)
544. C₃	C₃×#546	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₃×D₄	2
C₂×C₃×#235	2
C₃²×#123	2
C₃×#939	2
C₂×C₃×(C₂×D₃)⋊C₄	2
C₃×#896	2
C₃×#895	2
C₃×#894	2
C₃×#893	2
C₃×#885	2
C₃×#884	2
C₃×#882	2
C₃×#67⋊C₄	2
C₃×D₃×C₂²⋊C₄	2
C₃×#546	3
#5654	3

Subgroups — C3×#5654 #10595751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#5654 #10595751