Subgroups — C₃×#85867 #11904293

Order 1152.

3969 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#1004	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#518	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5554	C₂	1	8	yes	maximal, complemented
5	C₃×D₄×D₁₂	C₂	1	8	yes	maximal, complemented
6	C₃×#5525	C₂	1	2	yes	maximal, complemented
7	C₃×#5524	C₂	1	2	yes	maximal, complemented
8	C₃×#5493	C₂	1	4	yes	maximal, complemented
9	C₂×C₃×#882	C₂	1	4	yes	maximal, complemented
10	C₃×#3484	—	3	1	no	maximal
11	#85867	C₃	1	1	yes	maximal, characteristic, direct product factor
12	C₂⁴×C₃×D₃	C₂²	1	2	yes	complemented
13	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
14	C₂²×C₃×#67	C₂²	1	2	yes	complemented
15	C₂²×C₃×#67	C₂²	1	4	yes	complemented
16	C₃×#1004	—	2	8	no	—
17	C₂×C₃×#237	C₂²	1	4	yes	complemented
18	C₂×C₃×D₃×D₄	—	2	8	no	—
19	C₂×C₃×D₃×D₄	C₂²	1	8	yes	complemented
20	C₂×C₃×D₃×D₄	C₂²	1	4	yes	complemented
21	C₂×C₃×#235	C₂²	1	2	yes	complemented
22	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₃×D₁₂	C₂²	1	8	yes	complemented
24	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic, complemented
25	C₃²×C₄×D₄	C₂²	1	8	yes	complemented
26	C₃²×#117	C₂²	1	2	yes	complemented
27	C₂×C₃²×C₂²⋊C₄	C₂²	1	4	yes	complemented
28	C₃×#930	C₂²	1	16	yes	complemented
29	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	8	yes	complemented
30	C₃×#897	C₂²	1	4	yes	complemented
31	C₃×#895	C₂²	1	4	yes	complemented
32	C₃×#895	C₂²	1	8	yes	complemented
33	C₃×#886	C₂²	1	4	yes	complemented
34	C₃×#886	C₂²	1	8	yes	complemented
35	C₃×#882	C₂²	1	4	yes	complemented
36	C₃×#882	C₂²	1	16	yes	complemented
37	C₃×#882	C₂²	1	8	yes	complemented
38	C₃×#882	C₂²	1	8	yes	complemented
39	C₃×#875	C₂²	1	4	yes	complemented
40	C₃×#874	C₂²	1	4	yes	complemented
41	C₃×C₄×D₁₂	C₂²	1	8	yes	complemented
42	C₂×C₃×H(5,𝔽₂)	—	3	1	no	—
43	C₂³×C₃×D₄	—	3	1	no	—
44	C₂×#1004	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂²×D₃×D₄	C₂×C₃	1	1	yes	characteristic, complemented
46	C₃×#546	—	3	8	no	—
47	C₃×D₄²	—	3	8	no	—
48	C₃×#535	—	3	2	no	—
49	C₃×#534	—	3	4	no	—
50	C₃×#525	—	3	2	no	—
51	C₂×C₃×#120	—	3	4	no	—
52	C₃×#518	—	2	1	no	—
53	C₃×#518	D₃	1	1	yes	characteristic, complemented
54	C₃×#518	C₂×C₃	1	1	yes	characteristic, complemented
55	#5554	C₂×C₃	1	8	yes	complemented
56	D₄×D₁₂	C₂×C₃	1	8	yes	complemented
57	#5525	C₂×C₃	1	2	yes	complemented
58	#5524	C₂×C₃	1	2	yes	complemented
59	#5493	C₂×C₃	1	4	yes	complemented
60	C₂×#882	C₂×C₃	1	4	yes	complemented
61	C₂⁴×C₃²	C₂³	1	2	yes	—
62	C₂³×C₃×D₃	—	2	8	no	—
63	C₂³×C₃×D₃	—	4	8	no	—
64	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
65	C₂³×C₃×D₃	C₂³	1	8	yes	—
66	C₂³×C₃×D₃	C₂³	1	2	yes	—
67	C₂³×C₃×D₃	C₂³	1	4	yes	complemented
68	C₂×C₃²×D₄	D₄	1	8	yes	complemented
69	C₂×C₃²×D₄	C₂³	1	4	yes	—
70	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
71	C₂²×C₃²×C₄	C₂³	1	8	yes	complemented
72	C₂×C₃×#67	—	2	8	no	—
73	C₂×C₃×#67	—	2	16	no	—
74	C₂×C₃×#67	C₂³	1	4	yes	—
75	C₂×C₃×#67	C₂³	1	8	yes	—
76	C₂×C₃×#67	C₂³	1	8	yes	complemented
77	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
78	C₂²×C₃×Dic₃	C₂³	1	4	yes	complemented
79	C₃×#237	—	2	16	no	—
80	C₃×D₃×D₄	—	2	32	no	—
81	C₃×D₃×D₄	—	2	16	no	—
82	C₃×#235	—	2	8	no	—
83	C₂×C₃×D₁₂	—	2	4	no	—
84	C₂×C₃×D₁₂	—	4	16	no	—
85	C₂×C₃×D₁₂	C₂³	1	8	yes	—
86	C₂×C₃×D₁₂	C₂³	1	4	yes	—
87	C₂×C₃×D₁₂	C₂³	1	2	yes	complemented
88	C₂×C₃×D₁₂	C₂³	1	16	yes	complemented
89	C₂×C₃×C₄×D₃	—	2	4	no	—
90	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
91	C₂×C₃×C₄×D₃	C₂³	1	4	yes	complemented
92	C₂×C₃×Dic₆	C₂³	1	2	yes	complemented
93	C₃²×C₄⋊C₄	C₂³	1	4	yes	complemented
94	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
95	C₃²×C₂²⋊C₄	C₂³	1	8	yes	complemented
96	C₃²×C₄²	C₂³	1	4	yes	complemented
97	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
98	C₃×(C₂×D₃)⋊C₄	C₂³	1	16	yes	complemented
99	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
100	C₃×C₄⋊Dic₃	C₂³	1	8	yes	complemented
101	#3484	—	3	1	no	Sylow
102	C₂⁵×C₃	—	3	2	no	—
103	C₂⁴×D₃	C₂²×C₃	1	2	yes	complemented
104	C₃×H(5,𝔽₂)	—	6	8	no	—
105	C₂×C₃×#41	—	3	4	no	—
106	C₂×C₃×#41	—	3	2	no	—
107	C₂²×C₃×D₄	—	2	1	no	—
108	C₂²×C₃×D₄	—	3	2	no	—
109	C₂²×C₃×D₄	—	3	4	no	—
110	C₂²×C₃×D₄	—	3	8	no	—
111	C₂²×C₃×D₄	—	3	4	no	—
112	C₂²×C₃×D₄	—	3	1	no	—
113	C₂²×C₃×D₄	—	3	8	no	—
114	C₂²×C₃×D₄	—	6	8	no	—
115	C₂²×C₃×D₄	C₂×D₃	1	1	yes	characteristic
116	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
117	C₂³×C₃×C₄	—	3	1	no	—
118	C₂²×#67	C₂²×C₃	1	2	yes	complemented
119	C₂²×#67	C₂²×C₃	1	4	yes	complemented
120	#1004	—	2	8	no	—
121	C₂×#237	C₂²×C₃	1	4	yes	complemented
122	C₂×D₃×D₄	—	2	8	no	—
123	C₂×D₃×D₄	C₂²×C₃	1	8	yes	complemented
124	C₂×D₃×D₄	C₂²×C₃	1	4	yes	complemented
125	C₂×#235	C₂²×C₃	1	2	yes	complemented
126	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
127	C₂²×D₁₂	C₂²×C₃	1	8	yes	complemented
128	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic, complemented
129	C₃×#127	—	3	4	no	—
130	C₃×#124	—	3	4	no	—
131	C₃×#123	—	3	4	no	—
132	C₃×#123	—	3	8	no	—
133	C₃×C₂²⋊Q₈	—	3	4	no	—
134	C₃×#121	—	3	16	no	—
135	C₃×#121	—	3	4	no	—
136	C₃×#121	—	3	8	no	—
137	C₃×#120	—	3	4	no	—
138	C₃×#120	—	3	8	no	—
139	C₃×#120	—	3	16	no	—
140	C₃×#120	—	3	8	no	—
141	C₃×C₄×D₄	—	2	8	no	—
142	C₃×C₄×D₄	—	3	8	no	—
143	C₃×C₄×D₄	C₂×D₃	1	8	yes	complemented
144	C₃×C₄×D₄	C₂²×C₃	1	8	yes	complemented
145	C₃×#117	—	2	2	no	—
146	C₃×#117	C₂×D₃	1	2	yes	complemented
147	C₃×#117	C₂²×C₃	1	2	yes	complemented
148	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
149	C₂×C₃×C₂²⋊C₄	—	3	8	no	—
150	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	4	yes	complemented
151	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
152	#930	C₂²×C₃	1	16	yes	complemented
153	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	complemented
154	#897	C₂²×C₃	1	4	yes	complemented
155	#895	C₂²×C₃	1	4	yes	complemented
156	#895	C₂²×C₃	1	8	yes	complemented
157	#886	C₂²×C₃	1	4	yes	complemented
158	#886	C₂²×C₃	1	8	yes	complemented
159	#882	C₂²×C₃	1	4	yes	complemented
160	#882	C₂²×C₃	1	16	yes	complemented
161	#882	C₂²×C₃	1	8	yes	complemented
162	#882	C₂²×C₃	1	8	yes	complemented
163	#875	C₂²×C₃	1	4	yes	complemented
164	#874	C₂²×C₃	1	4	yes	complemented
165	C₄×D₁₂	C₂²×C₃	1	8	yes	complemented
166	C₂³×C₃²	—	4	4	no	—
167	C₂³×C₃²	C₂×D₄	1	8	yes	complemented
168	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
169	C₂³×C₃²	C₂⁴	1	4	yes	—
170	C₂²×C₃×D₃	—	2	2	no	—
171	C₂²×C₃×D₃	—	2	4	no	—
172	C₂²×C₃×D₃	—	2	4	no	—
173	C₂²×C₃×D₃	—	2	16	no	—
174	C₂²×C₃×D₃	—	2	8	no	—
175	C₂²×C₃×D₃	—	2	16	no	—
176	C₂²×C₃×D₃	—	4	8	no	—
177	C₂²×C₃×D₃	—	4	4	no	—
178	C₂²×C₃×D₃	—	4	8	no	—
179	C₂²×C₃×D₃	—	4	32	no	—
180	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
181	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
182	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
183	C₃²×D₄	C₂×D₄	1	16	yes	complemented
184	C₂×C₃²×C₄	—	4	8	no	—
185	C₂×C₃²×C₄	C₂×D₄	1	4	yes	complemented
186	C₂×C₃²×C₄	C₂⁴	1	8	yes	—
187	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
188	C₃×#67	—	2	8	no	—
189	C₃×#67	—	2	16	no	—
190	C₃×#67	—	2	16	no	—
191	C₂×C₃×Dic₃	—	2	2	no	—
192	C₂×C₃×Dic₃	—	2	8	no	—
193	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
194	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
195	C₃×D₁₂	—	2	16	no	—
196	C₃×D₁₂	—	2	8	no	—
197	C₃×D₁₂	—	2	4	no	—
198	C₃×D₁₂	—	4	16	no	—
199	C₃×C₄×D₃	—	2	8	no	—
200	C₃×C₄×D₃	—	2	8	no	—
201	C₃×Dic₆	—	2	4	no	—
202	C₂×H(5,𝔽₂)	—	3	1	no	—
203	C₂³×D₄	—	3	1	no	—
204	#546	—	3	8	no	—
205	D₄²	—	3	8	no	—
206	#535	—	3	2	no	—
207	#534	—	3	4	no	—
208	#525	—	3	2	no	—
209	C₂×#120	—	3	4	no	—
210	#518	C₃×D₃	1	1	yes	characteristic, complemented
211	C₂⁴×C₃	—	2	2	no	—
212	C₂⁴×C₃	—	3	1	no	—
213	C₂⁴×C₃	—	3	8	no	—
214	C₂⁴×C₃	—	3	2	no	—
215	C₂⁴×C₃	—	3	4	no	—
216	C₂⁴×C₃	—	6	8	no	—
217	C₂⁴×C₃	—	12	8	no	—
218	C₂⁴×C₃	C₂²×D₃	1	2	yes	—
219	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
220	C₂³×D₃	—	2	8	no	—
221	C₂³×D₃	—	4	8	no	—
222	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
223	C₂³×D₃	C₂³×C₃	1	8	yes	—
224	C₂³×D₃	C₂³×C₃	1	2	yes	—
225	C₂³×D₃	C₂³×C₃	1	4	yes	complemented
226	C₃×#41	—	6	16	no	—
227	C₃×#41	—	6	8	no	—
228	C₂×C₃×Q₈	—	3	2	no	—
229	C₂×C₃×D₄	—	2	8	no	—
230	C₂×C₃×D₄	—	2	4	no	—
231	C₂×C₃×D₄	—	3	4	no	—
232	C₂×C₃×D₄	—	3	8	no	—
233	C₂×C₃×D₄	—	3	8	no	—
234	C₂×C₃×D₄	—	3	8	no	—
235	C₂×C₃×D₄	—	3	4	no	—
236	C₂×C₃×D₄	—	3	2	no	—
237	C₂×C₃×D₄	—	3	16	no	—
238	C₂×C₃×D₄	—	6	8	no	—
239	C₂×C₃×D₄	—	6	16	no	—
240	C₂×C₃×D₄	—	6	32	no	—
241	C₂×C₃×D₄	—	6	16	no	—
242	C₂×C₃×D₄	—	6	4	no	—
243	C₂×C₃×D₄	—	12	16	no	—
244	C₂×C₃×D₄	D₁₂	1	8	yes	complemented
245	C₂×C₃×D₄	C₃×D₄	1	8	yes	complemented
246	C₂×C₃×D₄	C₂²×D₃	1	4	yes	—
247	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
248	C₂²×C₃×C₄	—	2	1	no	—
249	C₂²×C₃×C₄	—	2	8	no	—
250	C₂²×C₃×C₄	—	3	4	no	—
251	C₂²×C₃×C₄	—	3	1	no	—
252	C₂²×C₃×C₄	—	3	4	no	—
253	C₂²×C₃×C₄	—	3	4	no	—
254	C₂²×C₃×C₄	—	6	4	no	—
255	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
256	C₂²×C₃×C₄	C₂²×D₃	1	8	yes	complemented
257	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
258	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	complemented
259	C₂×#67	—	2	8	no	—
260	C₂×#67	—	2	16	no	—
261	C₂×#67	C₂³×C₃	1	4	yes	—
262	C₂×#67	C₂³×C₃	1	8	yes	—
263	C₂×#67	C₂³×C₃	1	8	yes	complemented
264	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
265	C₂²×Dic₃	C₂³×C₃	1	4	yes	complemented
266	#237	—	2	16	no	—
267	D₃×D₄	—	2	32	no	—
268	D₃×D₄	—	2	16	no	—
269	#235	—	2	8	no	—
270	C₂×D₁₂	—	2	4	no	—
271	C₂×D₁₂	—	4	16	no	—
272	C₂×D₁₂	C₂³×C₃	1	8	yes	—
273	C₂×D₁₂	C₂³×C₃	1	4	yes	—
274	C₂×D₁₂	C₂³×C₃	1	2	yes	complemented
275	C₂×D₁₂	C₂³×C₃	1	16	yes	complemented
276	C₂×C₄×D₃	—	2	4	no	—
277	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
278	C₂×C₄×D₃	C₂³×C₃	1	4	yes	complemented
279	C₂×Dic₆	C₂³×C₃	1	2	yes	complemented
280	C₃×C₄⋊C₄	—	2	4	no	—
281	C₃×C₄⋊C₄	—	3	8	no	—
282	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	complemented
283	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	complemented
284	C₃×C₂²⋊C₄	—	2	4	no	—
285	C₃×C₂²⋊C₄	—	2	8	no	—
286	C₃×C₂²⋊C₄	—	3	8	no	—
287	C₃×C₂²⋊C₄	—	3	16	no	—
288	C₃×C₂²⋊C₄	—	3	8	no	—
289	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
290	C₃×C₂²⋊C₄	C₂²×D₃	1	8	yes	complemented
291	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
292	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	complemented
293	C₃×C₄²	—	2	4	no	—
294	C₃×C₄²	C₂²×D₃	1	4	yes	complemented
295	C₃×C₄²	C₂³×C₃	1	4	yes	complemented
296	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	—
297	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	complemented
298	(C₂×D₃)⋊C₄	C₂³×C₃	1	16	yes	complemented
299	C₄⋊Dic₃	C₂³×C₃	1	8	yes	complemented
300	C₂²×C₃²	—	2	8	no	—
301	C₂²×C₃²	—	2	2	no	—
302	C₂²×C₃²	—	4	8	no	—
303	C₂²×C₃²	C₂²×D₄	1	2	yes	—
304	C₂²×C₃²	C₂²×D₄	1	8	yes	—
305	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
306	C₂×C₃×D₃	—	2	8	no	—
307	C₂×C₃×D₃	—	2	2	no	—
308	C₂×C₃×D₃	—	2	2	no	—
309	C₂×C₃×D₃	—	2	4	no	—
310	C₂×C₃×D₃	—	2	4	no	—
311	C₂×C₃×D₃	—	2	8	no	—
312	C₂×C₃×D₃	—	2	8	no	—
313	C₂×C₃×D₃	—	4	32	no	—
314	C₂×C₃×D₃	—	4	8	no	—
315	C₂×C₃×D₃	—	8	8	no	—
316	C₂×C₃×D₃	H(5,𝔽₂)	1	4	yes	complemented
317	C₃²×C₄	—	2	8	no	—
318	C₃²×C₄	C₂²×D₄	1	4	yes	—
319	C₃×Dic₃	—	2	4	no	—
320	C₃×Dic₃	—	2	2	no	—
321	C₂⁵	—	3	2	no	—
322	H(5,𝔽₂)	—	6	8	no	—
323	C₂×#41	—	3	4	no	—
324	C₂×#41	—	3	2	no	—
325	C₂²×D₄	—	3	4	no	—
326	C₂²×D₄	—	3	2	no	—
327	C₂²×D₄	—	3	4	no	—
328	C₂²×D₄	—	3	8	no	—
329	C₂²×D₄	—	3	1	no	—
330	C₂²×D₄	—	3	8	no	—
331	C₂²×D₄	—	6	8	no	—
332	C₂²×D₄	C₂×C₃×D₃	1	1	yes	characteristic
333	C₂³×C₄	—	3	1	no	—
334	#127	—	3	4	no	—
335	#124	—	3	4	no	—
336	#123	—	3	4	no	—
337	#123	—	3	8	no	—
338	C₂²⋊Q₈	—	3	4	no	—
339	#121	—	3	16	no	—
340	#121	—	3	4	no	—
341	#121	—	3	8	no	—
342	#120	—	3	4	no	—
343	#120	—	3	8	no	—
344	#120	—	3	16	no	—
345	#120	—	3	8	no	—
346	C₄×D₄	—	3	8	no	—
347	C₄×D₄	C₂×C₃×D₃	1	8	yes	complemented
348	#117	C₂×C₃×D₃	1	2	yes	complemented
349	C₂×C₂²⋊C₄	—	3	8	no	—
350	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	4	yes	complemented
351	C₂³×C₃	—	2	1	no	—
352	C₂³×C₃	—	2	4	no	—
353	C₂³×C₃	—	2	8	no	—
354	C₂³×C₃	—	3	2	no	—
355	C₂³×C₃	—	3	4	no	—
356	C₂³×C₃	—	3	4	no	—
357	C₂³×C₃	—	4	4	no	—
358	C₂³×C₃	—	4	4	no	—
359	C₂³×C₃	—	6	4	no	—
360	C₂³×C₃	—	6	16	no	—
361	C₂³×C₃	—	6	2	no	—
362	C₂³×C₃	—	6	16	no	—
363	C₂³×C₃	—	6	4	no	—
364	C₂³×C₃	—	6	8	no	—
365	C₂³×C₃	—	8	4	no	—
366	C₂³×C₃	—	12	8	no	—
367	C₂³×C₃	—	12	4	no	—
368	C₂³×C₃	—	12	8	no	—
369	C₂³×C₃	—	12	32	no	—
370	C₂³×C₃	C₂×D₁₂	1	8	yes	complemented
371	C₂³×C₃	C₂×C₃×D₄	1	8	yes	complemented
372	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
373	C₂³×C₃	C₂³×D₃	1	4	yes	—
374	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
375	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
376	C₂²×D₃	—	2	2	no	—
377	C₂²×D₃	—	2	4	no	—
378	C₂²×D₃	—	2	4	no	—
379	C₂²×D₃	—	2	16	no	—
380	C₂²×D₃	—	2	8	no	—
381	C₂²×D₃	—	2	16	no	—
382	C₂²×D₃	—	4	8	no	—
383	C₂²×D₃	—	4	4	no	—
384	C₂²×D₃	—	4	8	no	—
385	C₂²×D₃	—	4	32	no	—
386	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
387	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
388	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
389	C₃×Q₈	—	6	4	no	—
390	C₃×D₄	—	2	16	no	—
391	C₃×D₄	—	6	16	no	—
392	C₃×D₄	—	6	16	no	—
393	C₃×D₄	—	6	8	no	—
394	C₃×D₄	—	6	16	no	—
395	C₃×D₄	—	6	8	no	—
396	C₃×D₄	—	6	4	no	—
397	C₃×D₄	—	12	16	no	—
398	C₃×D₄	C₂×D₁₂	1	16	yes	complemented
399	C₃×D₄	C₂×C₃×D₄	1	16	yes	complemented
400	C₂×C₃×C₄	—	2	2	no	—
401	C₂×C₃×C₄	—	2	8	no	—
402	C₂×C₃×C₄	—	2	4	no	—
403	C₂×C₃×C₄	—	3	4	no	—
404	C₂×C₃×C₄	—	3	2	no	—
405	C₂×C₃×C₄	—	4	8	no	—
406	C₂×C₃×C₄	—	4	8	no	—
407	C₂×C₃×C₄	—	6	2	no	—
408	C₂×C₃×C₄	—	6	8	no	—
409	C₂×C₃×C₄	—	6	8	no	—
410	C₂×C₃×C₄	—	6	8	no	—
411	C₂×C₃×C₄	—	8	8	no	—
412	C₂×C₃×C₄	C₂×D₁₂	1	4	yes	complemented
413	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	complemented
414	C₂×C₃×C₄	C₂³×D₃	1	8	yes	—
415	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
416	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
417	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
418	#67	—	2	8	no	—
419	#67	—	2	16	no	—
420	#67	—	2	16	no	—
421	C₂×Dic₃	—	2	2	no	—
422	C₂×Dic₃	—	2	8	no	—
423	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
424	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
425	D₁₂	—	2	16	no	—
426	D₁₂	—	2	8	no	—
427	D₁₂	—	2	4	no	—
428	D₁₂	—	4	16	no	—
429	C₄×D₃	—	2	8	no	—
430	C₄×D₃	—	2	8	no	—
431	Dic₆	—	2	4	no	—
432	C₂×C₃²	—	2	2	no	—
433	C₂×C₃²	—	2	8	no	—
434	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
435	C₂×C₃²	C₂×H(5,𝔽₂)	1	2	yes	—
436	C₃×D₃	—	2	4	no	—
437	C₃×D₃	—	4	4	no	—
438	C₃×D₃	—	4	4	no	—
439	C₂⁴	—	3	1	no	—
440	C₂⁴	—	3	8	no	—
441	C₂⁴	—	3	2	no	—
442	C₂⁴	—	3	4	no	—
443	C₂⁴	—	6	8	no	—
444	C₂⁴	—	12	8	no	—
445	C₂⁴	C₂²×C₃×D₃	1	2	yes	—
446	#41	—	6	16	no	—
447	#41	—	6	8	no	—
448	C₂×Q₈	—	3	2	no	—
449	C₂×D₄	—	3	4	no	—
450	C₂×D₄	—	3	8	no	—
451	C₂×D₄	—	3	8	no	—
452	C₂×D₄	—	3	8	no	—
453	C₂×D₄	—	3	4	no	—
454	C₂×D₄	—	3	2	no	—
455	C₂×D₄	—	3	16	no	—
456	C₂×D₄	—	6	8	no	—
457	C₂×D₄	—	6	16	no	—
458	C₂×D₄	—	6	32	no	—
459	C₂×D₄	—	6	16	no	—
460	C₂×D₄	—	6	4	no	—
461	C₂×D₄	—	12	16	no	—
462	C₂×D₄	C₃×D₁₂	1	8	yes	complemented
463	C₂×D₄	C₂²×C₃×D₃	1	4	yes	—
464	C₂²×C₄	—	3	4	no	—
465	C₂²×C₄	—	3	1	no	—
466	C₂²×C₄	—	3	4	no	—
467	C₂²×C₄	—	3	4	no	—
468	C₂²×C₄	—	6	4	no	—
469	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
470	C₂²×C₄	C₂²×C₃×D₃	1	8	yes	complemented
471	C₄⋊C₄	—	3	8	no	—
472	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	complemented
473	C₂²⋊C₄	—	3	8	no	—
474	C₂²⋊C₄	—	3	16	no	—
475	C₂²⋊C₄	—	3	8	no	—
476	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
477	C₂²⋊C₄	C₂²×C₃×D₃	1	8	yes	complemented
478	C₄²	C₂²×C₃×D₃	1	4	yes	complemented
479	C₂²×C₃	—	2	8	no	—
480	C₂²×C₃	—	2	2	no	—
481	C₂²×C₃	—	2	8	no	—
482	C₂²×C₃	—	2	2	no	—
483	C₂²×C₃	—	2	2	no	—
484	C₂²×C₃	—	2	8	no	—
485	C₂²×C₃	—	2	1	no	—
486	C₂²×C₃	—	3	4	no	—
487	C₂²×C₃	—	4	8	no	—
488	C₂²×C₃	—	4	2	no	—
489	C₂²×C₃	—	4	8	no	—
490	C₂²×C₃	—	4	8	no	—
491	C₂²×C₃	—	6	8	no	—
492	C₂²×C₃	—	6	2	no	—
493	C₂²×C₃	—	6	2	no	—
494	C₂²×C₃	—	6	4	no	—
495	C₂²×C₃	—	6	4	no	—
496	C₂²×C₃	—	6	8	no	—
497	C₂²×C₃	—	6	8	no	—
498	C₂²×C₃	—	8	8	no	—
499	C₂²×C₃	—	12	32	no	—
500	C₂²×C₃	—	12	8	no	—
501	C₂²×C₃	—	24	8	no	—
502	C₂²×C₃	C₂²×D₁₂	1	2	yes	—
503	C₂²×C₃	C₂²×D₁₂	1	8	yes	—
504	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
505	C₂²×C₃	C₂²×C₃×D₄	1	8	yes	—
506	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
507	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
508	C₂×D₃	—	2	8	no	—
509	C₂×D₃	—	2	2	no	—
510	C₂×D₃	—	2	2	no	—
511	C₂×D₃	—	2	4	no	—
512	C₂×D₃	—	2	4	no	—
513	C₂×D₃	—	2	8	no	—
514	C₂×D₃	—	2	8	no	—
515	C₂×D₃	—	4	32	no	—
516	C₂×D₃	—	4	8	no	—
517	C₂×D₃	—	8	8	no	—
518	C₂×D₃	C₃×H(5,𝔽₂)	1	4	yes	complemented
519	C₃×C₄	—	2	8	no	—
520	C₃×C₄	—	2	8	no	—
521	C₃×C₄	—	2	4	no	—
522	C₃×C₄	—	4	8	no	—
523	C₃×C₄	—	6	2	no	—
524	C₃×C₄	—	6	4	no	—
525	C₃×C₄	C₂²×D₁₂	1	4	yes	—
526	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
527	Dic₃	—	2	4	no	—
528	Dic₃	—	2	2	no	—
529	C₃²	#3484	1	1	yes	characteristic, complemented, Sylow
530	C₂³	—	3	2	no	—
531	C₂³	—	3	4	no	—
532	C₂³	—	3	4	no	—
533	C₂³	—	4	4	no	—
534	C₂³	—	6	4	no	—
535	C₂³	—	6	16	no	—
536	C₂³	—	6	2	no	—
537	C₂³	—	6	16	no	—
538	C₂³	—	6	4	no	—
539	C₂³	—	6	8	no	—
540	C₂³	—	12	8	no	—
541	C₂³	—	12	4	no	—
542	C₂³	—	12	8	no	—
543	C₂³	—	12	32	no	—
544	C₂³	C₂×C₃×D₁₂	1	8	yes	complemented
545	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
546	C₂³	C₂³×C₃×D₃	1	4	yes	—
547	Q₈	—	6	4	no	—
548	D₄	—	6	16	no	—
549	D₄	—	6	16	no	—
550	D₄	—	6	8	no	—
551	D₄	—	6	16	no	—
552	D₄	—	6	8	no	—
553	D₄	—	6	4	no	—
554	D₄	—	12	16	no	—
555	D₄	C₂×C₃×D₁₂	1	16	yes	complemented
556	C₂×C₄	—	3	4	no	—
557	C₂×C₄	—	3	2	no	—
558	C₂×C₄	—	4	8	no	—
559	C₂×C₄	—	6	2	no	—
560	C₂×C₄	—	6	8	no	—
561	C₂×C₄	—	6	8	no	—
562	C₂×C₄	—	6	8	no	—
563	C₂×C₄	C₂×C₃×D₁₂	1	4	yes	complemented
564	C₂×C₄	C₂³×C₃×D₃	1	8	yes	—
565	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
566	C₂×C₃	—	2	2	no	—
567	C₂×C₃	—	2	8	no	—
568	C₂×C₃	—	2	2	no	—
569	C₂×C₃	—	2	8	no	—
570	C₂×C₃	—	2	1	no	—
571	C₂×C₃	—	2	2	no	—
572	C₂×C₃	—	4	2	no	—
573	C₂×C₃	—	4	8	no	—
574	C₂×C₃	—	6	4	no	—
575	C₂×C₃	—	12	4	no	—
576	C₂×C₃	—	12	4	no	—
577	C₂×C₃	C₂³×D₁₂	1	1	yes	characteristic
578	C₂×C₃	D₃×H(5,𝔽₂)	1	2	yes	—
579	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
580	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
581	D₃	—	2	4	no	—
582	D₃	—	4	4	no	—
583	D₃	—	4	4	no	—
584	C₂²	—	2	8	no	—
585	C₂²	—	2	2	no	—
586	C₂²	—	3	4	no	—
587	C₂²	—	4	8	no	—
588	C₂²	—	6	8	no	—
589	C₂²	—	6	2	no	—
590	C₂²	—	6	2	no	—
591	C₂²	—	6	4	no	—
592	C₂²	—	6	4	no	—
593	C₂²	—	6	8	no	—
594	C₂²	—	6	8	no	—
595	C₂²	—	12	32	no	—
596	C₂²	—	12	8	no	—
597	C₂²	—	24	8	no	—
598	C₂²	C₂²×C₃×D₁₂	1	2	yes	—
599	C₂²	C₂²×C₃×D₁₂	1	8	yes	—
600	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
601	C₄	—	2	8	no	—
602	C₄	—	6	2	no	—
603	C₄	—	6	4	no	—
604	C₄	C₂²×C₃×D₁₂	1	4	yes	—
605	C₃	—	2	1	no	—
606	C₃	#85867	1	1	yes	characteristic, direct product factor
607	C₃	C₃×#3484	1	1	yes	characteristic, complemented
608	C₂	—	2	2	no	—
609	C₂	—	2	8	no	—
610	C₂	—	6	4	no	—
611	C₂	—	12	4	no	—
612	C₂	—	12	4	no	—
613	C₂	C₂³×C₃×D₁₂	1	1	yes	characteristic
614	C₂	C₃×D₃×H(5,𝔽₂)	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₃²×#518	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×#518	D₃
hypocenter	C₃	C₃×#3484
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#518

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#1004	C₂	semidirect
2. C₂²×C₃×D₃×D₄	C₂	semidirect
3. C₃²×#518	C₂	semidirect
4. C₃×#5554	C₂	semidirect
5. C₃×D₄×D₁₂	C₂	semidirect
6. C₃×#5525	C₂	semidirect
7. C₃×#5524	C₂	semidirect
8. C₃×#5493	C₂	semidirect
9. C₂×C₃×#882	C₂	semidirect
11. #85867	C₃	direct (N × H)
12. C₂⁴×C₃×D₃	C₂²	semidirect
14. C₂²×C₃×#67	C₂²	semidirect
15. C₂²×C₃×#67	C₂²	semidirect
17. C₂×C₃×#237	C₂²	semidirect
19. C₂×C₃×D₃×D₄	C₂²	semidirect
20. C₂×C₃×D₃×D₄	C₂²	semidirect
21. C₂×C₃×#235	C₂²	semidirect
22. C₂²×C₃×D₁₂	C₂²	semidirect
23. C₂²×C₃×D₁₂	C₂²	semidirect
24. C₂²×C₃×C₄×D₃	C₂²	semidirect
25. C₃²×C₄×D₄	C₂²	semidirect
26. C₃²×#117	C₂²	semidirect
27. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
28. C₃×#930	C₂²	semidirect
29. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
30. C₃×#897	C₂²	semidirect
31. C₃×#895	C₂²	semidirect
32. C₃×#895	C₂²	semidirect
33. C₃×#886	C₂²	semidirect
34. C₃×#886	C₂²	semidirect
35. C₃×#882	C₂²	semidirect
36. C₃×#882	C₂²	semidirect
37. C₃×#882	C₂²	semidirect
38. C₃×#882	C₂²	semidirect
39. C₃×#875	C₂²	semidirect
40. C₃×#874	C₂²	semidirect
41. C₃×C₄×D₁₂	C₂²	semidirect
44. C₂×#1004	C₂×C₃	semidirect
45. C₂²×D₃×D₄	C₂×C₃	semidirect
53. C₃×#518	D₃	semidirect
54. C₃×#518	C₂×C₃	semidirect
55. #5554	C₂×C₃	semidirect
56. D₄×D₁₂	C₂×C₃	semidirect
57. #5525	C₂×C₃	semidirect
58. #5524	C₂×C₃	semidirect
59. #5493	C₂×C₃	semidirect
60. C₂×#882	C₂×C₃	semidirect
67. C₂³×C₃×D₃	C₂³	semidirect
68. C₂×C₃²×D₄	D₄	semidirect
71. C₂²×C₃²×C₄	C₂³	semidirect
76. C₂×C₃×#67	C₂³	semidirect
78. C₂²×C₃×Dic₃	C₂³	semidirect
87. C₂×C₃×D₁₂	C₂³	semidirect
88. C₂×C₃×D₁₂	C₂³	semidirect
91. C₂×C₃×C₄×D₃	C₂³	semidirect
92. C₂×C₃×Dic₆	C₂³	semidirect
93. C₃²×C₄⋊C₄	C₂³	semidirect
95. C₃²×C₂²⋊C₄	C₂³	semidirect
96. C₃²×C₄²	C₂³	semidirect
98. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
99. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
100. C₃×C₄⋊Dic₃	C₂³	semidirect
103. C₂⁴×D₃	C₂²×C₃	semidirect
118. C₂²×#67	C₂²×C₃	semidirect
119. C₂²×#67	C₂²×C₃	semidirect
121. C₂×#237	C₂²×C₃	semidirect
123. C₂×D₃×D₄	C₂²×C₃	semidirect
124. C₂×D₃×D₄	C₂²×C₃	semidirect
125. C₂×#235	C₂²×C₃	semidirect
126. C₂²×D₁₂	C₂²×C₃	semidirect
127. C₂²×D₁₂	C₂²×C₃	semidirect
128. C₂²×C₄×D₃	C₂²×C₃	semidirect
143. C₃×C₄×D₄	C₂×D₃	semidirect
144. C₃×C₄×D₄	C₂²×C₃	semidirect
146. C₃×#117	C₂×D₃	semidirect
147. C₃×#117	C₂²×C₃	semidirect
150. C₂×C₃×C₂²⋊C₄	C₂×D₃	semidirect
151. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
152. #930	C₂²×C₃	semidirect
153. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
154. #897	C₂²×C₃	semidirect
155. #895	C₂²×C₃	semidirect
156. #895	C₂²×C₃	semidirect
157. #886	C₂²×C₃	semidirect
158. #886	C₂²×C₃	semidirect
159. #882	C₂²×C₃	semidirect
160. #882	C₂²×C₃	semidirect
161. #882	C₂²×C₃	semidirect
162. #882	C₂²×C₃	semidirect
163. #875	C₂²×C₃	semidirect
164. #874	C₂²×C₃	semidirect
165. C₄×D₁₂	C₂²×C₃	semidirect
167. C₂³×C₃²	C₂×D₄	semidirect
183. C₃²×D₄	C₂×D₄	semidirect
185. C₂×C₃²×C₄	C₂×D₄	semidirect
210. #518	C₃×D₃	semidirect
225. C₂³×D₃	C₂³×C₃	semidirect
244. C₂×C₃×D₄	D₁₂	semidirect
245. C₂×C₃×D₄	C₃×D₄	semidirect
256. C₂²×C₃×C₄	C₂²×D₃	semidirect
258. C₂²×C₃×C₄	C₂³×C₃	semidirect
263. C₂×#67	C₂³×C₃	semidirect
265. C₂²×Dic₃	C₂³×C₃	semidirect
274. C₂×D₁₂	C₂³×C₃	semidirect
275. C₂×D₁₂	C₂³×C₃	semidirect
278. C₂×C₄×D₃	C₂³×C₃	semidirect
279. C₂×Dic₆	C₂³×C₃	semidirect
282. C₃×C₄⋊C₄	C₂²×D₃	semidirect
283. C₃×C₄⋊C₄	C₂³×C₃	semidirect
290. C₃×C₂²⋊C₄	C₂²×D₃	semidirect
292. C₃×C₂²⋊C₄	C₂³×C₃	semidirect
294. C₃×C₄²	C₂²×D₃	semidirect
295. C₃×C₄²	C₂³×C₃	semidirect
297. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
298. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
299. C₄⋊Dic₃	C₂³×C₃	semidirect
316. C₂×C₃×D₃	H(5,𝔽₂)	semidirect
347. C₄×D₄	C₂×C₃×D₃	semidirect
348. #117	C₂×C₃×D₃	semidirect
350. C₂×C₂²⋊C₄	C₂×C₃×D₃	semidirect
370. C₂³×C₃	C₂×D₁₂	semidirect
371. C₂³×C₃	C₂×C₃×D₄	semidirect
398. C₃×D₄	C₂×D₁₂	semidirect
399. C₃×D₄	C₂×C₃×D₄	semidirect
412. C₂×C₃×C₄	C₂×D₁₂	semidirect
413. C₂×C₃×C₄	C₂×C₃×D₄	semidirect
462. C₂×D₄	C₃×D₁₂	semidirect
470. C₂²×C₄	C₂²×C₃×D₃	semidirect
472. C₄⋊C₄	C₂²×C₃×D₃	semidirect
477. C₂²⋊C₄	C₂²×C₃×D₃	semidirect
478. C₄²	C₂²×C₃×D₃	semidirect
518. C₂×D₃	C₃×H(5,𝔽₂)	semidirect
529. C₃²	#3484	semidirect
544. C₂³	C₂×C₃×D₁₂	semidirect
555. D₄	C₂×C₃×D₁₂	semidirect
563. C₂×C₄	C₂×C₃×D₁₂	semidirect
606. C₃	#85867	direct (N × H)
607. C₃	C₃×#3484	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#1004	2
C₂²×C₃×D₃×D₄	2
C₃²×#518	2
C₃×#5554	2
C₃×D₄×D₁₂	2
C₃×#5525	2
C₃×#5524	2
C₃×#5493	2
C₂×C₃×#882	2
C₃×#3484	3
#85867	3

Subgroups — C3×#85867 #11904293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#85867 #11904293