Subgroups — C₃×#81831 #11885803

Order 1152.

1117 conjugacy classes of subgroups.

The subgroup lattice has 617 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#919	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5676	C₂	1	2	yes	maximal, complemented
4	C₃²×#495	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5188	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5172	C₂	1	2	yes	maximal, complemented
7	C₃×#5169	C₂	1	2	yes	maximal, complemented
8	C₃×#5157	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#5057	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₈×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3280	—	3	1	no	maximal
13	#81831	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃×#239	C₂²	1	2	yes	complemented
15	C₂×C₃×D₃×D₄	C₂²	1	2	yes	—
16	C₂×C₃²×Q₁₆	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₃²×SD₁₆	C₂²	1	2	yes	complemented
18	C₂×C₃²×D₈	C₂²	1	1	yes	characteristic
19	C₃²×#124	C₂²	1	2	yes	complemented
20	C₃×#946	C₂²	1	2	yes	—
21	C₂×C₃×#215	C₂²	1	2	yes	complemented
22	C₃×#938	C₂²	1	2	yes	complemented
23	C₂×C₃×#213	C₂²	1	2	yes	—
24	C₃×#919	—	2	4	no	—
25	C₃×D₃×D₈	—	2	4	no	—
26	C₂×C₃×D₂₄	C₂²	1	1	yes	characteristic
27	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
28	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic, complemented
29	C₃×#884	—	2	2	no	—
30	C₃×#883	—	2	2	no	—
31	C₃×#882	—	2	2	no	—
32	C₃×D₃×C₂²⋊C₄	—	2	2	no	—
33	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
34	C₃×C₄×D₁₂	C₂²	1	2	yes	complemented
35	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
36	C₃×#835	C₂²	1	2	yes	complemented
37	C₃×#832	C₂²	1	2	yes	complemented
38	C₃×#821	C₂²	1	2	yes	complemented
39	C₃×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
40	C₃×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
41	C₃×#818	C₂²	1	1	yes	characteristic, complemented
42	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₃×#135	—	3	1	no	—
44	C₂²×C₃×D₈	—	3	1	no	—
45	C₃×#546	—	3	2	no	—
46	C₂×#919	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂×D₃×D₈	C₂×C₃	1	1	yes	characteristic, complemented
48	#5676	C₂×C₃	1	2	yes	complemented
49	C₃×#495	—	2	1	no	—
50	C₃×#495	D₃	1	1	yes	characteristic, complemented
51	C₃×#495	C₂×C₃	1	1	yes	characteristic, complemented
52	C₃×#467	—	3	1	no	—
53	C₃×#466	—	3	1	no	—
54	C₃×#463	—	3	2	no	—
55	C₃×#450	—	3	2	no	—
56	C₃×#449	—	3	2	no	—
57	C₃×C₄×D₈	—	3	1	no	—
58	C₃×C₈×D₄	—	3	1	no	—
59	#5188	C₂×C₃	1	1	yes	characteristic, complemented
60	#5172	C₂×C₃	1	2	yes	complemented
61	#5169	C₂×C₃	1	2	yes	complemented
62	#5157	C₂×C₃	1	1	yes	characteristic, complemented
63	#5057	C₂×C₃	1	2	yes	complemented
64	C₄×D₂₄	C₂×C₃	1	1	yes	characteristic, complemented
65	C₈×D₁₂	C₂×C₃	1	1	yes	characteristic, complemented
66	C₂³×C₃×D₃	—	2	2	no	—
67	C₂×C₃²×Q₈	C₂³	1	2	yes	—
68	C₂×C₃²×D₄	C₂³	1	2	yes	—
69	C₂×C₃×#67	—	2	2	no	—
70	C₂×C₃×#67	—	2	2	no	—
71	C₃×#239	—	2	4	no	—
72	C₃×#239	—	4	2	no	—
73	C₃×D₃×D₄	—	2	4	no	—
74	C₃×D₃×D₄	—	4	2	no	—
75	C₂×C₃×D₁₂	—	2	2	no	—
76	C₂×C₃×D₁₂	D₄	1	1	yes	characteristic
77	C₂×C₃×D₁₂	C₂³	1	2	yes	—
78	C₂×C₃×C₄×D₃	—	2	2	no	—
79	C₂×C₃×C₄×D₃	—	2	2	no	—
80	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
81	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
82	C₃²×Q₁₆	—	2	2	no	—
83	C₃²×SD₁₆	—	4	2	no	—
84	C₃²×D₈	—	2	2	no	—
85	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
86	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
87	C₃²×C₂²⋊C₄	—	2	2	no	—
88	C₃²×C₂²⋊C₄	—	2	2	no	—
89	C₃²×C₄²	C₂³	1	1	yes	characteristic
90	C₃×#217	—	2	2	no	—
91	C₃×#215	—	2	4	no	—
92	C₃×#213	—	2	4	no	—
93	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
94	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
95	C₃×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
96	C₃×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
97	C₃×C₄⋊Dic₃	D₄	1	1	yes	characteristic
98	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
99	C₃×Dic₃⋊C₄	—	2	2	no	—
100	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
101	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
102	C₃×D₂₄	D₄	1	4	yes	complemented
103	C₃×D₃×C₈	—	2	2	no	—
104	C₃×D₃×C₈	—	2	2	no	—
105	#3280	—	3	1	no	Sylow
106	C₂×C₃×#41	—	3	2	no	—
107	C₂²×C₃×D₄	—	3	2	no	—
108	C₂×#239	C₂²×C₃	1	2	yes	complemented
109	C₂×D₃×D₄	C₂²×C₃	1	2	yes	—
110	C₃×#135	—	6	4	no	—
111	C₂×C₃×Q₁₆	—	2	1	no	—
112	C₂×C₃×Q₁₆	C₂×D₃	1	1	yes	characteristic, complemented
113	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
114	C₂×C₃×SD₁₆	—	2	2	no	—
115	C₂×C₃×SD₁₆	—	3	2	no	—
116	C₂×C₃×SD₁₆	C₂×D₃	1	2	yes	complemented
117	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	complemented
118	C₂×C₃×D₈	—	2	1	no	—
119	C₂×C₃×D₈	—	3	2	no	—
120	C₂×C₃×D₈	—	3	1	no	—
121	C₂×C₃×D₈	—	6	4	no	—
122	C₂×C₃×D₈	C₂×D₃	1	1	yes	characteristic
123	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic
124	C₂²×C₃×C₈	—	3	1	no	—
125	C₂²×C₃×C₈	—	3	1	no	—
126	C₃×#124	—	2	2	no	—
127	C₃×#124	C₂×D₃	1	2	yes	complemented
128	C₃×#124	C₂²×C₃	1	2	yes	complemented
129	C₃×#123	—	6	2	no	—
130	C₃×C₂²⋊Q₈	—	3	2	no	—
131	C₃×#121	—	3	2	no	—
132	C₃×#121	—	6	2	no	—
133	C₃×#120	—	6	2	no	—
134	C₃×C₄×D₄	—	3	1	no	—
135	C₃×C₄×D₄	—	3	2	no	—
136	C₂×C₃×C₂²⋊C₄	—	6	2	no	—
137	#946	C₂²×C₃	1	2	yes	—
138	C₂×#215	C₂²×C₃	1	2	yes	complemented
139	#938	C₂²×C₃	1	2	yes	complemented
140	C₂×#213	C₂²×C₃	1	2	yes	—
141	#919	—	2	4	no	—
142	D₃×D₈	—	2	4	no	—
143	C₂×D₂₄	C₂²×C₃	1	1	yes	characteristic
144	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
145	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
146	#884	—	2	2	no	—
147	#883	—	2	2	no	—
148	#882	—	2	2	no	—
149	D₃×C₂²⋊C₄	—	2	2	no	—
150	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
151	C₄×D₁₂	C₂²×C₃	1	2	yes	complemented
152	C₃×#107	—	3	1	no	—
153	C₃×C₄⋊C₈	—	3	1	no	—
154	C₃×#103	—	3	2	no	—
155	C₃×#102	—	3	2	no	—
156	C₃×#102	—	3	2	no	—
157	C₃×C₂²⋊C₈	—	3	1	no	—
158	C₃×C₂²⋊C₈	—	3	1	no	—
159	C₃×C₄×C₈	—	2	1	no	—
160	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic, complemented
161	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
162	#835	C₂²×C₃	1	2	yes	complemented
163	#832	C₂²×C₃	1	2	yes	complemented
164	#821	C₂²×C₃	1	2	yes	complemented
165	(C₂×D₃)⋊C₈	C₂²×C₃	1	1	yes	characteristic
166	(C₂×D₃)⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
167	#818	C₂²×C₃	1	1	yes	characteristic, complemented
168	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic, complemented
169	C₂³×C₃²	—	2	2	no	—
170	C₂²×C₃×D₃	—	2	2	no	—
171	C₂²×C₃×D₃	—	4	4	no	—
172	C₂²×C₃×D₃	—	4	4	no	—
173	C₂²×C₃×D₃	—	8	2	no	—
174	C₂²×C₃×D₃	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₃×D₃	C₂×D₄	1	1	yes	characteristic
176	C₃²×Q₈	—	2	2	no	—
177	C₃²×Q₈	—	2	2	no	—
178	C₃²×D₄	—	2	2	no	—
179	C₃²×D₄	—	2	2	no	—
180	C₂×C₃²×C₄	—	2	2	no	—
181	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
182	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
183	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
184	C₃×#67	—	4	4	no	—
185	C₃×#67	—	8	2	no	—
186	C₂×C₃×Dic₃	—	2	2	no	—
187	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
188	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
189	C₃×D₁₂	—	2	2	no	—
190	C₃×D₁₂	—	2	2	no	—
191	C₃×D₁₂	—	4	4	no	—
192	C₃×D₁₂	C₂×D₄	1	4	yes	—
193	C₃×C₄×D₃	—	2	1	no	—
194	C₃×C₄×D₃	—	2	1	no	—
195	C₃×C₄×D₃	—	2	1	no	—
196	C₃×C₄×D₃	—	2	1	no	—
197	C₃×C₄×D₃	—	4	4	no	—
198	C₃×C₄×D₃	—	8	2	no	—
199	C₃²×C₈	—	2	1	no	—
200	C₃²×C₈	C₂×D₄	1	2	yes	—
201	C₃×C₃⋊C₈	—	2	1	no	—
202	C₃×C₃⋊C₈	—	2	1	no	—
203	C₂×#135	—	3	1	no	—
204	C₂²×D₈	—	3	1	no	—
205	#546	—	3	2	no	—
206	#495	C₃×D₃	1	1	yes	characteristic, complemented
207	#467	—	3	1	no	—
208	#466	—	3	1	no	—
209	#463	—	3	2	no	—
210	#450	—	3	2	no	—
211	#449	—	3	2	no	—
212	C₄×D₈	—	3	1	no	—
213	C₈×D₄	—	3	1	no	—
214	C₂⁴×C₃	—	6	2	no	—
215	C₂³×D₃	—	2	2	no	—
216	C₃×#41	—	6	4	no	—
217	C₃×#41	—	12	2	no	—
218	C₂×C₃×Q₈	—	2	2	no	—
219	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
220	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
221	C₂×C₃×D₄	—	2	2	no	—
222	C₂×C₃×D₄	—	3	1	no	—
223	C₂×C₃×D₄	—	3	2	no	—
224	C₂×C₃×D₄	—	6	2	no	—
225	C₂×C₃×D₄	—	6	2	no	—
226	C₂×C₃×D₄	—	6	4	no	—
227	C₂×C₃×D₄	—	6	2	no	—
228	C₂×C₃×D₄	—	12	2	no	—
229	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
230	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
231	C₂²×C₃×C₄	—	3	1	no	—
232	C₂²×C₃×C₄	—	3	1	no	—
233	C₂²×C₃×C₄	—	6	2	no	—
234	C₂²×C₃×C₄	—	6	2	no	—
235	C₂×#67	—	2	2	no	—
236	C₂×#67	—	2	2	no	—
237	#239	—	2	4	no	—
238	#239	—	4	2	no	—
239	D₃×D₄	—	2	4	no	—
240	D₃×D₄	—	4	2	no	—
241	C₂×D₁₂	—	2	2	no	—
242	C₂×D₁₂	C₃×D₄	1	1	yes	characteristic
243	C₂×D₁₂	C₂³×C₃	1	2	yes	—
244	C₂×C₄×D₃	—	2	2	no	—
245	C₂×C₄×D₃	—	2	2	no	—
246	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
247	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
248	C₃×Q₁₆	—	2	2	no	—
249	C₃×Q₁₆	—	2	2	no	—
250	C₃×Q₁₆	—	4	2	no	—
251	C₃×SD₁₆	—	4	2	no	—
252	C₃×SD₁₆	—	4	2	no	—
253	C₃×SD₁₆	—	4	4	no	—
254	C₃×SD₁₆	—	6	4	no	—
255	C₃×D₈	—	2	2	no	—
256	C₃×D₈	—	2	2	no	—
257	C₃×D₈	—	3	4	no	—
258	C₃×D₈	—	4	2	no	—
259	C₃×D₈	—	6	4	no	—
260	C₂×C₃×C₈	—	2	1	no	—
261	C₂×C₃×C₈	—	2	1	no	—
262	C₂×C₃×C₈	—	3	1	no	—
263	C₂×C₃×C₈	—	3	1	no	—
264	C₂×C₃×C₈	—	6	2	no	—
265	C₂×C₃×C₈	—	6	2	no	—
266	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
267	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
268	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
269	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
270	C₃×C₄⋊C₄	—	3	1	no	—
271	C₃×C₄⋊C₄	—	3	2	no	—
272	C₃×C₄⋊C₄	—	6	2	no	—
273	C₃×C₂²⋊C₄	—	2	2	no	—
274	C₃×C₂²⋊C₄	—	2	2	no	—
275	C₃×C₂²⋊C₄	—	2	2	no	—
276	C₃×C₂²⋊C₄	—	2	2	no	—
277	C₃×C₂²⋊C₄	—	3	1	no	—
278	C₃×C₂²⋊C₄	—	3	1	no	—
279	C₃×C₂²⋊C₄	—	4	2	no	—
280	C₃×C₂²⋊C₄	—	4	2	no	—
281	C₃×C₂²⋊C₄	—	6	2	no	—
282	C₃×C₂²⋊C₄	—	6	2	no	—
283	C₃×C₂²⋊C₄	—	6	2	no	—
284	C₃×C₄²	—	2	1	no	—
285	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
286	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
287	#217	—	2	2	no	—
288	#215	—	2	4	no	—
289	#213	—	2	4	no	—
290	(C₂×D₃)⋊C₄	—	2	2	no	—
291	(C₂×D₃)⋊C₄	—	2	2	no	—
292	(C₂×D₃)⋊C₄	C₃×D₄	1	1	yes	characteristic
293	(C₂×D₃)⋊C₄	C₃×D₄	1	1	yes	characteristic
294	C₄⋊Dic₃	C₃×D₄	1	1	yes	characteristic
295	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
296	Dic₃⋊C₄	—	2	2	no	—
297	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
298	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
299	D₂₄	C₃×D₄	1	4	yes	complemented
300	D₃×C₈	—	2	2	no	—
301	D₃×C₈	—	2	2	no	—
302	C₂²×C₃²	—	4	2	no	—
303	C₂²×C₃²	—	4	2	no	—
304	C₂²×C₃²	—	4	2	no	—
305	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₃×D₃	—	2	1	no	—
307	C₂×C₃×D₃	—	2	1	no	—
308	C₂×C₃×D₃	—	2	1	no	—
309	C₂×C₃×D₃	—	2	4	no	—
310	C₂×C₃×D₃	—	2	1	no	—
311	C₂×C₃×D₃	—	2	1	no	—
312	C₂×C₃×D₃	—	4	2	no	—
313	C₂×C₃×D₃	—	4	2	no	—
314	C₂×C₃×D₃	—	8	8	no	—
315	C₂×C₃×D₃	#135	1	2	yes	complemented
316	C₃²×C₄	—	2	1	no	—
317	C₃²×C₄	—	2	1	no	—
318	C₃²×C₄	—	4	2	no	—
319	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
320	C₃²×C₄	H(5,𝔽₂)	1	1	yes	characteristic
321	C₃×Dic₃	—	2	1	no	—
322	C₃×Dic₃	—	2	1	no	—
323	C₃×Dic₃	—	4	2	no	—
324	C₂×#41	—	3	2	no	—
325	C₂²×D₄	—	3	2	no	—
326	#135	—	6	4	no	—
327	C₂×Q₁₆	C₂×C₃×D₃	1	1	yes	characteristic, complemented
328	C₂×SD₁₆	—	3	2	no	—
329	C₂×SD₁₆	C₂×C₃×D₃	1	2	yes	complemented
330	C₂×D₈	—	3	2	no	—
331	C₂×D₈	—	3	1	no	—
332	C₂×D₈	—	6	4	no	—
333	C₂×D₈	C₂×C₃×D₃	1	1	yes	characteristic
334	C₂²×C₈	—	3	1	no	—
335	C₂²×C₈	—	3	1	no	—
336	#124	C₂×C₃×D₃	1	2	yes	complemented
337	#123	—	6	2	no	—
338	C₂²⋊Q₈	—	3	2	no	—
339	#121	—	3	2	no	—
340	#121	—	6	2	no	—
341	#120	—	6	2	no	—
342	C₄×D₄	—	3	1	no	—
343	C₄×D₄	—	3	2	no	—
344	C₂×C₂²⋊C₄	—	6	2	no	—
345	#107	—	3	1	no	—
346	C₄⋊C₈	—	3	1	no	—
347	#103	—	3	2	no	—
348	#102	—	3	2	no	—
349	#102	—	3	2	no	—
350	C₂²⋊C₈	—	3	1	no	—
351	C₂²⋊C₈	—	3	1	no	—
352	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
353	C₂³×C₃	—	2	2	no	—
354	C₂³×C₃	—	2	2	no	—
355	C₂³×C₃	—	3	1	no	—
356	C₂³×C₃	—	3	1	no	—
357	C₂³×C₃	—	4	2	no	—
358	C₂³×C₃	—	6	2	no	—
359	C₂³×C₃	—	12	4	no	—
360	C₂³×C₃	—	12	4	no	—
361	C₂³×C₃	—	24	2	no	—
362	C₂²×D₃	—	2	2	no	—
363	C₂²×D₃	—	4	4	no	—
364	C₂²×D₃	—	4	4	no	—
365	C₂²×D₃	—	8	2	no	—
366	C₂²×D₃	C₂×C₃×D₄	1	1	yes	characteristic
367	C₂²×D₃	C₂×C₃×D₄	1	1	yes	characteristic
368	C₃×Q₈	—	2	2	no	—
369	C₃×Q₈	—	2	2	no	—
370	C₃×Q₈	—	2	2	no	—
371	C₃×Q₈	—	2	2	no	—
372	C₃×Q₈	—	4	2	no	—
373	C₃×Q₈	—	4	2	no	—
374	C₃×D₄	—	2	2	no	—
375	C₃×D₄	—	2	2	no	—
376	C₃×D₄	—	2	2	no	—
377	C₃×D₄	—	2	2	no	—
378	C₃×D₄	—	3	4	no	—
379	C₃×D₄	—	4	2	no	—
380	C₃×D₄	—	4	2	no	—
381	C₃×D₄	—	6	2	no	—
382	C₃×D₄	—	6	2	no	—
383	C₃×D₄	—	12	4	no	—
384	C₃×D₄	—	12	4	no	—
385	C₃×D₄	—	24	2	no	—
386	C₂×C₃×C₄	—	2	2	no	—
387	C₂×C₃×C₄	—	2	2	no	—
388	C₂×C₃×C₄	—	2	1	no	—
389	C₂×C₃×C₄	—	2	1	no	—
390	C₂×C₃×C₄	—	2	1	no	—
391	C₂×C₃×C₄	—	3	1	no	—
392	C₂×C₃×C₄	—	3	1	no	—
393	C₂×C₃×C₄	—	4	2	no	—
394	C₂×C₃×C₄	—	6	1	no	—
395	C₂×C₃×C₄	—	6	1	no	—
396	C₂×C₃×C₄	—	6	1	no	—
397	C₂×C₃×C₄	—	6	1	no	—
398	C₂×C₃×C₄	—	6	2	no	—
399	C₂×C₃×C₄	—	12	4	no	—
400	C₂×C₃×C₄	—	24	2	no	—
401	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
402	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
403	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
404	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
405	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
406	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
407	#67	—	4	4	no	—
408	#67	—	8	2	no	—
409	C₂×Dic₃	—	2	2	no	—
410	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
411	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
412	D₁₂	—	2	2	no	—
413	D₁₂	—	2	2	no	—
414	D₁₂	—	4	4	no	—
415	D₁₂	C₂×C₃×D₄	1	4	yes	—
416	C₄×D₃	—	2	1	no	—
417	C₄×D₃	—	2	1	no	—
418	C₄×D₃	—	2	1	no	—
419	C₄×D₃	—	2	1	no	—
420	C₄×D₃	—	4	4	no	—
421	C₄×D₃	—	8	2	no	—
422	C₃×C₈	—	2	2	no	—
423	C₃×C₈	—	2	1	no	—
424	C₃×C₈	—	2	1	no	—
425	C₃×C₈	—	2	2	no	—
426	C₃×C₈	—	6	1	no	—
427	C₃×C₈	—	6	1	no	—
428	C₃×C₈	D₃×D₄	1	2	yes	—
429	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
430	C₃⋊C₈	—	2	1	no	—
431	C₃⋊C₈	—	2	1	no	—
432	C₂×C₃²	—	8	2	no	—
433	C₂×C₃²	D₄²	1	1	yes	characteristic
434	C₂×C₃²	C₂×#135	1	1	yes	characteristic
435	C₂×C₃²	#576	1	1	yes	characteristic
436	C₃×D₃	—	2	2	no	—
437	C₃×D₃	—	4	1	no	—
438	C₃×D₃	—	4	4	no	—
439	C₂⁴	—	6	2	no	—
440	#41	—	6	4	no	—
441	#41	—	12	2	no	—
442	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
443	C₂×D₄	—	3	2	no	—
444	C₂×D₄	—	3	1	no	—
445	C₂×D₄	—	6	2	no	—
446	C₂×D₄	—	6	2	no	—
447	C₂×D₄	—	6	4	no	—
448	C₂×D₄	—	6	2	no	—
449	C₂×D₄	—	12	2	no	—
450	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
451	C₂²×C₄	—	3	1	no	—
452	C₂²×C₄	—	3	1	no	—
453	C₂²×C₄	—	6	2	no	—
454	C₂²×C₄	—	6	2	no	—
455	Q₁₆	—	2	2	no	—
456	SD₁₆	—	4	2	no	—
457	SD₁₆	—	6	4	no	—
458	D₈	—	2	2	no	—
459	D₈	—	3	4	no	—
460	D₈	—	6	4	no	—
461	C₂×C₈	—	3	1	no	—
462	C₂×C₈	—	3	1	no	—
463	C₂×C₈	—	6	2	no	—
464	C₂×C₈	—	6	2	no	—
465	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
466	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
467	C₄⋊C₄	—	3	1	no	—
468	C₄⋊C₄	—	3	2	no	—
469	C₄⋊C₄	—	6	2	no	—
470	C₂²⋊C₄	—	2	2	no	—
471	C₂²⋊C₄	—	2	2	no	—
472	C₂²⋊C₄	—	3	1	no	—
473	C₂²⋊C₄	—	3	1	no	—
474	C₂²⋊C₄	—	6	2	no	—
475	C₂²⋊C₄	—	6	2	no	—
476	C₂²⋊C₄	—	6	2	no	—
477	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
478	C₂²×C₃	—	2	1	no	—
479	C₂²×C₃	—	3	2	no	—
480	C₂²×C₃	—	4	2	no	—
481	C₂²×C₃	—	4	2	no	—
482	C₂²×C₃	—	4	2	no	—
483	C₂²×C₃	—	4	2	no	—
484	C₂²×C₃	—	4	2	no	—
485	C₂²×C₃	—	4	2	no	—
486	C₂²×C₃	—	6	1	no	—
487	C₂²×C₃	—	6	1	no	—
488	C₂²×C₃	—	6	1	no	—
489	C₂²×C₃	—	6	4	no	—
490	C₂²×C₃	—	6	1	no	—
491	C₂²×C₃	—	6	1	no	—
492	C₂²×C₃	—	8	2	no	—
493	C₂²×C₃	—	8	2	no	—
494	C₂²×C₃	—	8	2	no	—
495	C₂²×C₃	—	12	2	no	—
496	C₂²×C₃	—	12	2	no	—
497	C₂²×C₃	—	24	8	no	—
498	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
499	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
500	C₂×D₃	—	2	1	no	—
501	C₂×D₃	—	2	1	no	—
502	C₂×D₃	—	2	1	no	—
503	C₂×D₃	—	2	1	no	—
504	C₂×D₃	—	2	1	no	—
505	C₂×D₃	—	2	4	no	—
506	C₂×D₃	—	4	2	no	—
507	C₂×D₃	—	4	2	no	—
508	C₂×D₃	—	8	8	no	—
509	C₂×D₃	C₃×#135	1	2	yes	complemented
510	C₃×C₄	—	2	1	no	—
511	C₃×C₄	—	2	1	no	—
512	C₃×C₄	—	2	1	no	—
513	C₃×C₄	—	2	1	no	—
514	C₃×C₄	—	2	1	no	—
515	C₃×C₄	—	2	1	no	—
516	C₃×C₄	—	4	1	no	—
517	C₃×C₄	—	4	1	no	—
518	C₃×C₄	—	4	2	no	—
519	C₃×C₄	—	4	2	no	—
520	C₃×C₄	—	6	1	no	—
521	C₃×C₄	—	6	1	no	—
522	C₃×C₄	—	8	2	no	—
523	C₃×C₄	—	12	2	no	—
524	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
525	C₃×C₄	#1004	1	1	yes	characteristic
526	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
527	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
528	Dic₃	—	2	1	no	—
529	Dic₃	—	2	1	no	—
530	Dic₃	—	4	2	no	—
531	C₃²	#3280	1	1	yes	characteristic, complemented, Sylow
532	C₂³	—	2	2	no	—
533	C₂³	—	3	1	no	—
534	C₂³	—	3	1	no	—
535	C₂³	—	6	2	no	—
536	C₂³	—	12	4	no	—
537	C₂³	—	12	4	no	—
538	C₂³	—	24	2	no	—
539	Q₈	—	2	2	no	—
540	Q₈	—	2	2	no	—
541	D₄	—	2	2	no	—
542	D₄	—	2	2	no	—
543	D₄	—	3	4	no	—
544	D₄	—	6	2	no	—
545	D₄	—	6	2	no	—
546	D₄	—	12	4	no	—
547	D₄	—	12	4	no	—
548	D₄	—	24	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	3	1	no	—
551	C₂×C₄	—	3	1	no	—
552	C₂×C₄	—	6	1	no	—
553	C₂×C₄	—	6	1	no	—
554	C₂×C₄	—	6	1	no	—
555	C₂×C₄	—	6	1	no	—
556	C₂×C₄	—	6	2	no	—
557	C₂×C₄	—	12	4	no	—
558	C₂×C₄	—	24	2	no	—
559	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
560	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
561	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
562	C₈	—	2	1	no	—
563	C₈	—	6	1	no	—
564	C₈	—	6	1	no	—
565	C₈	C₃×D₃×D₄	1	2	yes	—
566	C₂×C₃	—	2	1	no	—
567	C₂×C₃	—	2	1	no	—
568	C₂×C₃	—	2	1	no	—
569	C₂×C₃	—	6	2	no	—
570	C₂×C₃	—	8	2	no	—
571	C₂×C₃	—	8	2	no	—
572	C₂×C₃	—	12	1	no	—
573	C₂×C₃	—	12	4	no	—
574	C₂×C₃	—	16	2	no	—
575	C₂×C₃	#5717	1	1	yes	characteristic
576	C₂×C₃	D₃×#135	1	1	yes	characteristic
577	C₂×C₃	#5769	1	1	yes	characteristic
578	C₂×C₃	C₃×D₄²	1	1	yes	characteristic
579	C₂×C₃	C₂×C₃×#135	1	1	yes	characteristic
580	C₂×C₃	C₃×#576	1	1	yes	characteristic
581	D₃	—	2	2	no	—
582	D₃	—	4	1	no	—
583	D₃	—	4	4	no	—
584	C₂²	—	3	2	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	2	no	—
587	C₂²	—	4	2	no	—
588	C₂²	—	6	1	no	—
589	C₂²	—	6	1	no	—
590	C₂²	—	6	1	no	—
591	C₂²	—	6	1	no	—
592	C₂²	—	6	1	no	—
593	C₂²	—	6	4	no	—
594	C₂²	—	12	2	no	—
595	C₂²	—	12	2	no	—
596	C₂²	—	24	8	no	—
597	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
598	C₄	—	2	1	no	—
599	C₄	—	2	1	no	—
600	C₄	—	4	2	no	—
601	C₄	—	6	1	no	—
602	C₄	—	6	1	no	—
603	C₄	—	12	2	no	—
604	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
605	C₄	C₃×#1004	1	1	yes	characteristic
606	C₃	—	2	1	no	—
607	C₃	#81831	1	1	yes	characteristic, direct product factor
608	C₃	C₃×#3280	1	1	yes	characteristic, complemented
609	C₂	—	6	2	no	—
610	C₂	—	8	2	no	—
611	C₂	—	12	1	no	—
612	C₂	—	12	4	no	—
613	C₂	C₃×#5717	1	1	yes	characteristic
614	C₂	C₃×D₃×#135	1	1	yes	characteristic
615	C₂	C₃×#5769	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#495	C₂
socle	C₂²×C₃²	C₂²×D₄
hypercenter	C₃×#495	D₃
hypocenter	C₃	C₃×#3280
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#495

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#919	C₂	semidirect
2. C₂×C₃×D₃×D₈	C₂	semidirect
3. C₃×#5676	C₂	semidirect
4. C₃²×#495	C₂	semidirect
5. C₃×#5188	C₂	semidirect
6. C₃×#5172	C₂	semidirect
7. C₃×#5169	C₂	semidirect
8. C₃×#5157	C₂	semidirect
9. C₃×#5057	C₂	semidirect
10. C₃×C₄×D₂₄	C₂	semidirect
11. C₃×C₈×D₁₂	C₂	semidirect
13. #81831	C₃	direct (N × H)
14. C₂×C₃×#239	C₂²	semidirect
16. C₂×C₃²×Q₁₆	C₂²	semidirect
17. C₂×C₃²×SD₁₆	C₂²	semidirect
19. C₃²×#124	C₂²	semidirect
21. C₂×C₃×#215	C₂²	semidirect
22. C₃×#938	C₂²	semidirect
28. C₂×C₃×D₃×C₈	C₂²	semidirect
34. C₃×C₄×D₁₂	C₂²	semidirect
35. C₃²×C₄×C₈	C₂²	semidirect
36. C₃×#835	C₂²	semidirect
37. C₃×#832	C₂²	semidirect
38. C₃×#821	C₂²	semidirect
40. C₃×(C₂×D₃)⋊C₈	C₂²	semidirect
41. C₃×#818	C₂²	semidirect
42. C₃×C₄⋊(C₃⋊C₈)	C₂²	semidirect
46. C₂×#919	C₂×C₃	semidirect
47. C₂×D₃×D₈	C₂×C₃	semidirect
48. #5676	C₂×C₃	semidirect
50. C₃×#495	D₃	semidirect
51. C₃×#495	C₂×C₃	semidirect
59. #5188	C₂×C₃	semidirect
60. #5172	C₂×C₃	semidirect
61. #5169	C₂×C₃	semidirect
62. #5157	C₂×C₃	semidirect
63. #5057	C₂×C₃	semidirect
64. C₄×D₂₄	C₂×C₃	semidirect
65. C₈×D₁₂	C₂×C₃	semidirect
102. C₃×D₂₄	D₄	semidirect
108. C₂×#239	C₂²×C₃	semidirect
112. C₂×C₃×Q₁₆	C₂×D₃	semidirect
113. C₂×C₃×Q₁₆	C₂²×C₃	semidirect
116. C₂×C₃×SD₁₆	C₂×D₃	semidirect
117. C₂×C₃×SD₁₆	C₂²×C₃	semidirect
127. C₃×#124	C₂×D₃	semidirect
128. C₃×#124	C₂²×C₃	semidirect
138. C₂×#215	C₂²×C₃	semidirect
139. #938	C₂²×C₃	semidirect
145. C₂×D₃×C₈	C₂²×C₃	semidirect
151. C₄×D₁₂	C₂²×C₃	semidirect
160. C₃×C₄×C₈	C₂×D₃	semidirect
161. C₃×C₄×C₈	C₂²×C₃	semidirect
162. #835	C₂²×C₃	semidirect
163. #832	C₂²×C₃	semidirect
164. #821	C₂²×C₃	semidirect
166. (C₂×D₃)⋊C₈	C₂²×C₃	semidirect
167. #818	C₂²×C₃	semidirect
168. C₄⋊(C₃⋊C₈)	C₂²×C₃	semidirect
206. #495	C₃×D₃	semidirect
299. D₂₄	C₃×D₄	semidirect
315. C₂×C₃×D₃	#135	semidirect
327. C₂×Q₁₆	C₂×C₃×D₃	semidirect
329. C₂×SD₁₆	C₂×C₃×D₃	semidirect
336. #124	C₂×C₃×D₃	semidirect
352. C₄×C₈	C₂×C₃×D₃	semidirect
509. C₂×D₃	C₃×#135	semidirect
531. C₃²	#3280	semidirect
607. C₃	#81831	direct (N × H)
608. C₃	C₃×#3280	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#919	2
C₂×C₃×D₃×D₈	2
C₃×#5676	2
C₃²×#495	2
C₃×#5188	2
C₃×#5172	2
C₃×#5169	2
C₃×#5157	2
C₃×#5057	2
C₃×C₄×D₂₄	2
C₃×C₈×D₁₂	2
C₃×#3280	3
#81831	3

Subgroups — C3×#81831 #11885803

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#81831 #11885803