Subgroups — C₂×C₃×#5666 #11910164

Order 1152.

2859 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#123	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#940	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#937	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#930	C₂	1	2	yes	maximal, complemented
5	C₃×#5666	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₃×#898	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#895	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×#884	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×#883	C₂	1	2	yes	maximal, complemented
10	C₂×C₃×#882	C₂	1	2	yes	maximal, complemented
11	C₂×C₃×#560	—	3	1	no	maximal
12	C₂×#5666	C₃	1	1	yes	maximal, characteristic, direct product factor
13	C₂⁴×C₃×D₃	C₂²	1	1	yes	characteristic
14	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
15	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₃×#67	C₂²	1	2	yes	—
17	C₂²×C₃×#67	C₂²	1	2	yes	—
18	C₂²×C₃×#67	C₂²	1	2	yes	complemented
19	C₂²×C₃×D₁₂	C₂²	1	2	yes	—
20	C₂²×C₃×D₁₂	C₂²	1	2	yes	—
21	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	complemented
23	C₃²×#123	C₂²	1	8	yes	complemented
24	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	complemented
25	C₂×C₃²×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃×#217	C₂²	1	1	yes	characteristic
28	C₃×#940	C₂²	1	8	yes	complemented
29	C₃×#937	C₂²	1	8	yes	complemented
30	C₃×#930	C₂²	1	16	yes	complemented
31	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
32	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
33	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
34	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
35	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	complemented
36	C₂×C₃×Dic₃⋊C₄	C₂²	1	2	yes	complemented
37	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
38	C₃×#898	C₂²	1	16	yes	complemented
39	C₃×#895	C₂²	1	16	yes	complemented
40	C₃×#884	C₂²	1	16	yes	complemented
41	C₃×#883	C₂²	1	16	yes	complemented
42	C₃×#882	C₂²	1	16	yes	complemented
43	C₃×#560	—	3	16	no	—
44	C₂×C₃×#127	—	3	1	no	—
45	C₂×C₃×#126	—	3	2	no	—
46	C₂×C₃×#123	—	2	1	no	—
47	C₂×C₃×#123	—	3	2	no	—
48	C₂×C₃×#123	D₃	1	1	yes	characteristic, complemented
49	C₂×C₃×#123	C₂×C₃	1	1	yes	characteristic, complemented
50	C₂×C₃×#121	—	3	2	no	—
51	C₂×C₃×#121	—	3	2	no	—
52	C₂×C₃×#121	—	3	2	no	—
53	C₂×C₃×#120	—	3	1	no	—
54	C₂×C₃×#120	—	3	2	no	—
55	C₂×#940	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂×#937	C₂×C₃	1	1	yes	characteristic, complemented
57	C₂×#930	C₂×C₃	1	2	yes	complemented
58	#5666	C₂×C₃	1	16	yes	direct product factor
59	C₂×#898	C₂×C₃	1	2	yes	complemented
60	C₂×#895	C₂×C₃	1	2	yes	complemented
61	C₂×#884	C₂×C₃	1	2	yes	complemented
62	C₂×#883	C₂×C₃	1	2	yes	complemented
63	C₂×#882	C₂×C₃	1	2	yes	complemented
64	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
65	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
66	C₂³×C₃×D₃	—	4	2	no	—
67	C₂³×C₃×D₃	—	4	4	no	—
68	C₂³×C₃×D₃	C₂³	1	2	yes	—
69	C₂³×C₃×D₃	C₂³	1	2	yes	—
70	C₂³×C₃×D₃	C₂³	1	4	yes	—
71	C₂×C₃²×D₄	—	4	2	no	—
72	C₂×C₃²×D₄	C₂³	1	4	yes	—
73	C₂²×C₃²×C₄	—	4	2	no	—
74	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
75	C₂²×C₃²×C₄	C₂³	1	2	yes	—
76	C₂²×C₃²×C₄	C₂³	1	2	yes	—
77	C₂²×C₃²×C₄	C₂³	1	4	yes	complemented
78	C₂×C₃×#67	—	4	4	no	—
79	C₂×C₃×#67	—	4	4	no	—
80	C₂×C₃×#67	—	4	4	no	—
81	C₂×C₃×#67	C₂³	1	8	yes	—
82	C₂×C₃×#67	C₂³	1	8	yes	—
83	C₂×C₃×#67	C₂³	1	8	yes	complemented
84	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
85	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
86	C₂×C₃×D₁₂	—	4	4	no	—
87	C₂×C₃×D₁₂	—	4	4	no	—
88	C₂×C₃×D₁₂	—	4	2	no	—
89	C₂×C₃×D₁₂	C₂³	1	8	yes	—
90	C₂×C₃×D₁₂	C₂³	1	8	yes	—
91	C₂×C₃×D₁₂	C₂³	1	4	yes	complemented
92	C₂×C₃×C₄×D₃	—	4	4	no	—
93	C₂×C₃×C₄×D₃	C₂³	1	8	yes	complemented
94	C₃²×C₄⋊C₄	C₂³	1	8	yes	complemented
95	C₃²×C₂²⋊C₄	C₂³	1	8	yes	—
96	C₃²×C₂²⋊C₄	C₂³	1	4	yes	complemented
97	C₃×#217	C₂³	1	4	yes	—
98	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
99	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
100	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
101	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
102	C₃×C₄⋊Dic₃	C₂³	1	8	yes	complemented
103	C₃×Dic₃⋊C₄	C₂³	1	8	yes	complemented
104	C₃×C₄×Dic₃	C₂³	1	4	yes	complemented
105	C₂×#560	—	3	1	no	Sylow
106	C₂⁵×C₃	—	3	1	no	—
107	C₂⁴×D₃	C₂²×C₃	1	1	yes	characteristic
108	C₂²×C₃×D₄	—	2	1	no	—
109	C₂²×C₃×D₄	—	3	2	no	—
110	C₂²×C₃×D₄	—	3	2	no	—
111	C₂²×C₃×D₄	—	3	2	no	—
112	C₂²×C₃×D₄	—	3	2	no	—
113	C₂²×C₃×D₄	—	3	2	no	—
114	C₂²×C₃×D₄	—	3	1	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	—	2	1	no	—
118	C₂³×C₃×C₄	—	3	2	no	—
119	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic, complemented
120	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic, complemented
121	C₂²×#67	C₂²×C₃	1	2	yes	—
122	C₂²×#67	C₂²×C₃	1	2	yes	—
123	C₂²×#67	C₂²×C₃	1	2	yes	complemented
124	C₂²×D₁₂	C₂²×C₃	1	2	yes	—
125	C₂²×D₁₂	C₂²×C₃	1	2	yes	—
126	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
127	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	complemented
128	C₃×#127	—	3	8	no	—
129	C₃×#126	—	3	16	no	—
130	C₃×#123	—	2	8	no	—
131	C₃×#123	—	3	16	no	—
132	C₃×#123	C₂×D₃	1	8	yes	complemented
133	C₃×#123	C₂²×C₃	1	8	yes	complemented
134	C₃×#121	—	3	16	no	—
135	C₃×#121	—	3	16	no	—
136	C₃×#121	—	3	16	no	—
137	C₃×#120	—	3	8	no	—
138	C₃×#120	—	3	16	no	—
139	C₂×C₃×C₄⋊C₄	—	2	2	no	—
140	C₂×C₃×C₄⋊C₄	—	3	2	no	—
141	C₂×C₃×C₄⋊C₄	—	3	2	no	—
142	C₂×C₃×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
143	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
144	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
145	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
146	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
147	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
148	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
149	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
150	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
151	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	2	yes	—
152	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
153	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
154	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
155	C₂×C₃×C₄²	—	3	1	no	—
156	C₂×#217	C₂²×C₃	1	1	yes	characteristic
157	#940	C₂²×C₃	1	8	yes	complemented
158	#937	C₂²×C₃	1	8	yes	complemented
159	#930	C₂²×C₃	1	16	yes	complemented
160	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
161	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
162	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
163	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	complemented
164	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	complemented
165	C₂×Dic₃⋊C₄	C₂²×C₃	1	2	yes	complemented
166	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
167	#898	C₂²×C₃	1	16	yes	complemented
168	#895	C₂²×C₃	1	16	yes	complemented
169	#884	C₂²×C₃	1	16	yes	complemented
170	#883	C₂²×C₃	1	16	yes	complemented
171	#882	C₂²×C₃	1	16	yes	complemented
172	C₂³×C₃²	—	2	2	no	—
173	C₂³×C₃²	—	2	4	no	—
174	C₂³×C₃²	—	2	2	no	—
175	C₂³×C₃²	—	2	4	no	—
176	C₂³×C₃²	C₂⁴	1	2	yes	—
177	C₂³×C₃²	C₂⁴	1	2	yes	—
178	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
179	C₂²×C₃×D₃	—	2	4	no	—
180	C₂²×C₃×D₃	—	2	4	no	—
181	C₂²×C₃×D₃	—	2	4	no	—
182	C₂²×C₃×D₃	—	2	4	no	—
183	C₂²×C₃×D₃	—	2	4	no	—
184	C₂²×C₃×D₃	—	2	4	no	—
185	C₂²×C₃×D₃	—	4	4	no	—
186	C₂²×C₃×D₃	—	4	8	no	—
187	C₂²×C₃×D₃	—	4	16	no	—
188	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
189	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
190	C₃²×D₄	—	4	4	no	—
191	C₂×C₃²×C₄	—	2	4	no	—
192	C₂×C₃²×C₄	—	2	4	no	—
193	C₂×C₃²×C₄	—	2	2	no	—
194	C₂×C₃²×C₄	—	4	4	no	—
195	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
196	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
197	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
198	C₃×#67	—	4	8	no	—
199	C₃×#67	—	4	8	no	—
200	C₃×#67	—	4	8	no	—
201	C₂×C₃×Dic₃	—	2	4	no	—
202	C₂×C₃×Dic₃	—	2	4	no	—
203	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
204	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
205	C₃×D₁₂	—	4	8	no	—
206	C₃×D₁₂	—	4	8	no	—
207	C₃×D₁₂	—	4	4	no	—
208	C₃×C₄×D₃	—	4	8	no	—
209	#560	—	3	16	no	—
210	C₂×#127	—	3	1	no	—
211	C₂×#126	—	3	2	no	—
212	C₂×#123	—	3	2	no	—
213	C₂×#123	C₃×D₃	1	1	yes	characteristic, complemented
214	C₂×#121	—	3	2	no	—
215	C₂×#121	—	3	2	no	—
216	C₂×#121	—	3	2	no	—
217	C₂×#120	—	3	1	no	—
218	C₂×#120	—	3	2	no	—
219	C₂⁴×C₃	—	2	1	no	—
220	C₂⁴×C₃	—	2	1	no	—
221	C₂⁴×C₃	—	3	2	no	—
222	C₂⁴×C₃	—	3	2	no	—
223	C₂⁴×C₃	—	3	4	no	—
224	C₂⁴×C₃	—	12	2	no	—
225	C₂⁴×C₃	—	12	4	no	—
226	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
227	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
228	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
229	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
230	C₂³×D₃	—	4	2	no	—
231	C₂³×D₃	—	4	4	no	—
232	C₂³×D₃	C₂³×C₃	1	2	yes	—
233	C₂³×D₃	C₂³×C₃	1	2	yes	—
234	C₂³×D₃	C₂³×C₃	1	4	yes	—
235	C₂×C₃×D₄	—	2	4	no	—
236	C₂×C₃×D₄	—	3	8	no	—
237	C₂×C₃×D₄	—	3	8	no	—
238	C₂×C₃×D₄	—	3	8	no	—
239	C₂×C₃×D₄	—	3	8	no	—
240	C₂×C₃×D₄	—	3	8	no	—
241	C₂×C₃×D₄	—	3	4	no	—
242	C₂×C₃×D₄	—	4	2	no	—
243	C₂×C₃×D₄	—	4	2	no	—
244	C₂×C₃×D₄	—	4	4	no	—
245	C₂×C₃×D₄	—	12	4	no	—
246	C₂×C₃×D₄	—	12	2	no	—
247	C₂×C₃×D₄	—	12	4	no	—
248	C₂×C₃×D₄	—	12	4	no	—
249	C₂×C₃×D₄	—	12	4	no	—
250	C₂×C₃×D₄	—	12	4	no	—
251	C₂×C₃×D₄	C₂²×D₃	1	4	yes	—
252	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
253	C₂²×C₃×C₄	—	2	2	no	—
254	C₂²×C₃×C₄	—	2	2	no	—
255	C₂²×C₃×C₄	—	2	1	no	—
256	C₂²×C₃×C₄	—	2	4	no	—
257	C₂²×C₃×C₄	—	3	2	no	—
258	C₂²×C₃×C₄	—	3	2	no	—
259	C₂²×C₃×C₄	—	3	8	no	—
260	C₂²×C₃×C₄	—	4	2	no	—
261	C₂²×C₃×C₄	—	4	2	no	—
262	C₂²×C₃×C₄	—	4	4	no	—
263	C₂²×C₃×C₄	—	12	4	no	—
264	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
265	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
266	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
267	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	complemented
268	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
269	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
270	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
271	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	complemented
272	C₂×#67	—	4	4	no	—
273	C₂×#67	—	4	4	no	—
274	C₂×#67	—	4	4	no	—
275	C₂×#67	C₂³×C₃	1	8	yes	—
276	C₂×#67	C₂³×C₃	1	8	yes	—
277	C₂×#67	C₂³×C₃	1	8	yes	complemented
278	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
279	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
280	C₂×D₁₂	—	4	4	no	—
281	C₂×D₁₂	—	4	4	no	—
282	C₂×D₁₂	—	4	2	no	—
283	C₂×D₁₂	C₂³×C₃	1	8	yes	—
284	C₂×D₁₂	C₂³×C₃	1	8	yes	—
285	C₂×D₁₂	C₂³×C₃	1	4	yes	complemented
286	C₂×C₄×D₃	—	4	4	no	—
287	C₂×C₄×D₃	C₂³×C₃	1	8	yes	complemented
288	C₃×C₄⋊C₄	—	2	8	no	—
289	C₃×C₄⋊C₄	—	3	8	no	—
290	C₃×C₄⋊C₄	—	3	8	no	—
291	C₃×C₄⋊C₄	C₂²×D₃	1	8	yes	complemented
292	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	complemented
293	C₃×C₂²⋊C₄	—	2	8	no	—
294	C₃×C₂²⋊C₄	—	2	4	no	—
295	C₃×C₂²⋊C₄	—	3	4	no	—
296	C₃×C₂²⋊C₄	—	3	8	no	—
297	C₃×C₂²⋊C₄	—	3	8	no	—
298	C₃×C₂²⋊C₄	—	3	8	no	—
299	C₃×C₂²⋊C₄	—	3	8	no	—
300	C₃×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
301	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	complemented
302	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
303	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	complemented
304	C₃×C₄²	—	3	4	no	—
305	#217	C₂³×C₃	1	4	yes	—
306	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	—
307	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	—
308	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	—
309	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	complemented
310	C₄⋊Dic₃	C₂³×C₃	1	8	yes	complemented
311	Dic₃⋊C₄	C₂³×C₃	1	8	yes	complemented
312	C₄×Dic₃	C₂³×C₃	1	4	yes	complemented
313	C₂²×C₃²	—	2	2	no	—
314	C₂²×C₃²	—	2	4	no	—
315	C₂²×C₃²	—	2	4	no	—
316	C₂²×C₃²	—	2	2	no	—
317	C₂²×C₃²	—	4	4	no	—
318	C₂²×C₃²	—	4	4	no	—
319	C₂²×C₃²	H(5,𝔽₂)	1	2	yes	—
320	C₂²×C₃²	H(5,𝔽₂)	1	4	yes	—
321	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
322	C₂×C₃×D₃	—	2	4	no	—
323	C₂×C₃×D₃	—	2	4	no	—
324	C₂×C₃×D₃	—	2	4	no	—
325	C₂×C₃×D₃	—	2	4	no	—
326	C₂×C₃×D₃	—	2	4	no	—
327	C₂×C₃×D₃	—	2	4	no	—
328	C₂×C₃×D₃	—	4	16	no	—
329	C₂×C₃×D₃	—	4	8	no	—
330	C₂×C₃×D₃	—	4	8	no	—
331	C₃²×C₄	—	2	4	no	—
332	C₃²×C₄	—	2	4	no	—
333	C₃²×C₄	—	2	2	no	—
334	C₃×Dic₃	—	2	4	no	—
335	C₃×Dic₃	—	2	4	no	—
336	C₂⁵	—	3	1	no	—
337	C₂²×D₄	—	3	2	no	—
338	C₂²×D₄	—	3	2	no	—
339	C₂²×D₄	—	3	2	no	—
340	C₂²×D₄	—	3	2	no	—
341	C₂²×D₄	—	3	2	no	—
342	C₂²×D₄	—	3	1	no	—
343	C₂²×D₄	C₂×C₃×D₃	1	1	yes	characteristic
344	C₂³×C₄	—	3	2	no	—
345	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
346	#127	—	3	8	no	—
347	#126	—	3	16	no	—
348	#123	—	3	16	no	—
349	#123	C₂×C₃×D₃	1	8	yes	complemented
350	#121	—	3	16	no	—
351	#121	—	3	16	no	—
352	#121	—	3	16	no	—
353	#120	—	3	8	no	—
354	#120	—	3	16	no	—
355	C₂×C₄⋊C₄	—	3	2	no	—
356	C₂×C₄⋊C₄	—	3	2	no	—
357	C₂×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	complemented
358	C₂×C₂²⋊C₄	—	3	1	no	—
359	C₂×C₂²⋊C₄	—	3	2	no	—
360	C₂×C₂²⋊C₄	—	3	2	no	—
361	C₂×C₂²⋊C₄	—	3	2	no	—
362	C₂×C₂²⋊C₄	—	3	2	no	—
363	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
364	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
365	C₂×C₄²	—	3	1	no	—
366	C₂³×C₃	—	2	4	no	—
367	C₂³×C₃	—	2	2	no	—
368	C₂³×C₃	—	2	2	no	—
369	C₂³×C₃	—	2	4	no	—
370	C₂³×C₃	—	2	4	no	—
371	C₂³×C₃	—	2	4	no	—
372	C₂³×C₃	—	2	4	no	—
373	C₂³×C₃	—	2	2	no	—
374	C₂³×C₃	—	2	2	no	—
375	C₂³×C₃	—	2	1	no	—
376	C₂³×C₃	—	2	2	no	—
377	C₂³×C₃	—	2	2	no	—
378	C₂³×C₃	—	3	4	no	—
379	C₂³×C₃	—	3	4	no	—
380	C₂³×C₃	—	4	4	no	—
381	C₂³×C₃	—	4	2	no	—
382	C₂³×C₃	—	4	4	no	—
383	C₂³×C₃	—	6	4	no	—
384	C₂³×C₃	—	6	4	no	—
385	C₂³×C₃	—	6	4	no	—
386	C₂³×C₃	—	6	4	no	—
387	C₂³×C₃	—	6	4	no	—
388	C₂³×C₃	—	6	4	no	—
389	C₂³×C₃	—	12	4	no	—
390	C₂³×C₃	—	12	8	no	—
391	C₂³×C₃	—	12	16	no	—
392	C₂³×C₃	C₂³×D₃	1	2	yes	—
393	C₂³×C₃	C₂³×D₃	1	2	yes	—
394	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
395	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
396	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
397	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
398	C₂²×D₃	—	2	4	no	—
399	C₂²×D₃	—	2	4	no	—
400	C₂²×D₃	—	2	4	no	—
401	C₂²×D₃	—	2	4	no	—
402	C₂²×D₃	—	2	4	no	—
403	C₂²×D₃	—	2	4	no	—
404	C₂²×D₃	—	4	4	no	—
405	C₂²×D₃	—	4	8	no	—
406	C₂²×D₃	—	4	16	no	—
407	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
408	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
409	C₃×D₄	—	4	4	no	—
410	C₃×D₄	—	4	4	no	—
411	C₃×D₄	—	4	8	no	—
412	C₃×D₄	—	12	8	no	—
413	C₃×D₄	—	12	4	no	—
414	C₃×D₄	—	12	8	no	—
415	C₃×D₄	—	12	8	no	—
416	C₃×D₄	—	12	8	no	—
417	C₃×D₄	—	12	8	no	—
418	C₂×C₃×C₄	—	2	4	no	—
419	C₂×C₃×C₄	—	2	2	no	—
420	C₂×C₃×C₄	—	2	4	no	—
421	C₂×C₃×C₄	—	2	4	no	—
422	C₂×C₃×C₄	—	2	4	no	—
423	C₂×C₃×C₄	—	2	2	no	—
424	C₂×C₃×C₄	—	2	4	no	—
425	C₂×C₃×C₄	—	2	4	no	—
426	C₂×C₃×C₄	—	2	2	no	—
427	C₂×C₃×C₄	—	3	4	no	—
428	C₂×C₃×C₄	—	3	4	no	—
429	C₂×C₃×C₄	—	4	4	no	—
430	C₂×C₃×C₄	—	4	4	no	—
431	C₂×C₃×C₄	—	4	2	no	—
432	C₂×C₃×C₄	—	4	4	no	—
433	C₂×C₃×C₄	—	4	4	no	—
434	C₂×C₃×C₄	—	4	8	no	—
435	C₂×C₃×C₄	—	6	4	no	—
436	C₂×C₃×C₄	—	6	4	no	—
437	C₂×C₃×C₄	—	12	8	no	—
438	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
439	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
440	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
441	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
442	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
443	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
444	#67	—	4	8	no	—
445	#67	—	4	8	no	—
446	#67	—	4	8	no	—
447	C₂×Dic₃	—	2	4	no	—
448	C₂×Dic₃	—	2	4	no	—
449	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
450	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
451	D₁₂	—	4	8	no	—
452	D₁₂	—	4	8	no	—
453	D₁₂	—	4	4	no	—
454	C₄×D₃	—	4	8	no	—
455	C₂×C₃²	—	4	2	no	—
456	C₂×C₃²	—	4	2	no	—
457	C₂×C₃²	#560	1	4	yes	complemented
458	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
459	C₂×C₃²	C₂×H(5,𝔽₂)	1	2	yes	—
460	C₃×D₃	—	4	4	no	—
461	C₃×D₃	—	4	4	no	—
462	C₂⁴	—	3	2	no	—
463	C₂⁴	—	3	2	no	—
464	C₂⁴	—	3	4	no	—
465	C₂⁴	—	12	2	no	—
466	C₂⁴	—	12	4	no	—
467	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
468	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
469	C₂×D₄	—	3	8	no	—
470	C₂×D₄	—	3	8	no	—
471	C₂×D₄	—	3	8	no	—
472	C₂×D₄	—	3	8	no	—
473	C₂×D₄	—	3	8	no	—
474	C₂×D₄	—	3	4	no	—
475	C₂×D₄	—	4	2	no	—
476	C₂×D₄	—	12	4	no	—
477	C₂×D₄	—	12	2	no	—
478	C₂×D₄	—	12	4	no	—
479	C₂×D₄	—	12	4	no	—
480	C₂×D₄	—	12	4	no	—
481	C₂×D₄	—	12	4	no	—
482	C₂×D₄	C₂²×C₃×D₃	1	4	yes	—
483	C₂²×C₄	—	3	2	no	—
484	C₂²×C₄	—	3	2	no	—
485	C₂²×C₄	—	3	8	no	—
486	C₂²×C₄	—	4	2	no	—
487	C₂²×C₄	—	12	4	no	—
488	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
489	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
490	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
491	C₂²×C₄	C₂²×C₃×D₃	1	4	yes	complemented
492	C₄⋊C₄	—	3	8	no	—
493	C₄⋊C₄	—	3	8	no	—
494	C₄⋊C₄	C₂²×C₃×D₃	1	8	yes	complemented
495	C₂²⋊C₄	—	3	4	no	—
496	C₂²⋊C₄	—	3	8	no	—
497	C₂²⋊C₄	—	3	8	no	—
498	C₂²⋊C₄	—	3	8	no	—
499	C₂²⋊C₄	—	3	8	no	—
500	C₂²⋊C₄	C₂²×C₃×D₃	1	8	yes	—
501	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	complemented
502	C₄²	—	3	4	no	—
503	C₂²×C₃	—	2	4	no	—
504	C₂²×C₃	—	2	2	no	—
505	C₂²×C₃	—	2	2	no	—
506	C₂²×C₃	—	2	4	no	—
507	C₂²×C₃	—	2	4	no	—
508	C₂²×C₃	—	2	4	no	—
509	C₂²×C₃	—	2	4	no	—
510	C₂²×C₃	—	2	2	no	—
511	C₂²×C₃	—	2	2	no	—
512	C₂²×C₃	—	2	2	no	—
513	C₂²×C₃	—	2	4	no	—
514	C₂²×C₃	—	2	1	no	—
515	C₂²×C₃	—	4	4	no	—
516	C₂²×C₃	—	4	2	no	—
517	C₂²×C₃	—	4	4	no	—
518	C₂²×C₃	—	4	8	no	—
519	C₂²×C₃	—	4	4	no	—
520	C₂²×C₃	—	4	4	no	—
521	C₂²×C₃	—	4	4	no	—
522	C₂²×C₃	—	4	4	no	—
523	C₂²×C₃	—	6	4	no	—
524	C₂²×C₃	—	6	4	no	—
525	C₂²×C₃	—	6	4	no	—
526	C₂²×C₃	—	6	4	no	—
527	C₂²×C₃	—	6	4	no	—
528	C₂²×C₃	—	6	4	no	—
529	C₂²×C₃	—	8	4	no	—
530	C₂²×C₃	—	12	16	no	—
531	C₂²×C₃	—	12	8	no	—
532	C₂²×C₃	—	12	8	no	—
533	C₂²×C₃	#1004	1	2	yes	—
534	C₂²×C₃	#1009	1	4	yes	—
535	C₂²×C₃	C₃×H(5,𝔽₂)	1	2	yes	—
536	C₂²×C₃	C₃×H(5,𝔽₂)	1	4	yes	—
537	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
538	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
539	C₂×D₃	—	2	4	no	—
540	C₂×D₃	—	2	4	no	—
541	C₂×D₃	—	2	4	no	—
542	C₂×D₃	—	2	4	no	—
543	C₂×D₃	—	2	4	no	—
544	C₂×D₃	—	2	4	no	—
545	C₂×D₃	—	4	16	no	—
546	C₂×D₃	—	4	8	no	—
547	C₂×D₃	—	4	8	no	—
548	C₃×C₄	—	2	4	no	—
549	C₃×C₄	—	2	2	no	—
550	C₃×C₄	—	2	4	no	—
551	C₃×C₄	—	2	4	no	—
552	C₃×C₄	—	2	4	no	—
553	C₃×C₄	—	2	2	no	—
554	C₃×C₄	—	4	4	no	—
555	C₃×C₄	—	4	2	no	—
556	C₃×C₄	—	4	4	no	—
557	C₃×C₄	—	6	4	no	—
558	C₃×C₄	—	6	4	no	—
559	Dic₃	—	2	4	no	—
560	Dic₃	—	2	4	no	—
561	C₃²	C₂×#560	1	1	yes	characteristic, complemented, Sylow
562	C₂³	—	2	2	no	—
563	C₂³	—	2	2	no	—
564	C₂³	—	2	4	no	—
565	C₂³	—	2	4	no	—
566	C₂³	—	3	4	no	—
567	C₂³	—	3	4	no	—
568	C₂³	—	6	4	no	—
569	C₂³	—	6	4	no	—
570	C₂³	—	6	4	no	—
571	C₂³	—	6	4	no	—
572	C₂³	—	6	4	no	—
573	C₂³	—	6	4	no	—
574	C₂³	—	12	4	no	—
575	C₂³	—	12	8	no	—
576	C₂³	—	12	16	no	—
577	C₂³	C₂³×C₃×D₃	1	2	yes	—
578	C₂³	C₂³×C₃×D₃	1	2	yes	—
579	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
580	D₄	—	4	4	no	—
581	D₄	—	12	8	no	—
582	D₄	—	12	4	no	—
583	D₄	—	12	8	no	—
584	D₄	—	12	8	no	—
585	D₄	—	12	8	no	—
586	D₄	—	12	8	no	—
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	4	no	—
590	C₂×C₄	—	3	4	no	—
591	C₂×C₄	—	3	4	no	—
592	C₂×C₄	—	4	4	no	—
593	C₂×C₄	—	6	4	no	—
594	C₂×C₄	—	6	4	no	—
595	C₂×C₄	—	12	8	no	—
596	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
597	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
598	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
599	C₂×C₃	—	2	1	no	—
600	C₂×C₃	—	2	2	no	—
601	C₂×C₃	—	2	4	no	—
602	C₂×C₃	—	4	4	no	—
603	C₂×C₃	—	4	2	no	—
604	C₂×C₃	—	4	2	no	—
605	C₂×C₃	—	4	2	no	—
606	C₂×C₃	—	4	2	no	—
607	C₂×C₃	—	8	2	no	—
608	C₂×C₃	—	12	4	no	—
609	C₂×C₃	—	12	4	no	—
610	C₂×C₃	#5666	1	4	yes	direct product factor
611	C₂×C₃	C₃×#560	1	4	yes	complemented
612	C₂×C₃	C₂×#1004	1	1	yes	characteristic
613	C₂×C₃	C₂×#1009	1	2	yes	—
614	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
615	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
616	D₃	—	4	4	no	—
617	D₃	—	4	4	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	2	4	no	—
621	C₂²	—	2	4	no	—
622	C₂²	—	4	4	no	—
623	C₂²	—	4	4	no	—
624	C₂²	—	6	4	no	—
625	C₂²	—	6	4	no	—
626	C₂²	—	6	4	no	—
627	C₂²	—	6	4	no	—
628	C₂²	—	6	4	no	—
629	C₂²	—	6	4	no	—
630	C₂²	—	12	16	no	—
631	C₂²	—	12	8	no	—
632	C₂²	—	12	8	no	—
633	C₂²	C₃×#1004	1	2	yes	—
634	C₂²	C₃×#1009	1	4	yes	—
635	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
636	C₄	—	2	4	no	—
637	C₄	—	2	2	no	—
638	C₄	—	2	4	no	—
639	C₄	—	6	4	no	—
640	C₄	—	6	4	no	—
641	C₃	—	2	1	no	—
642	C₃	C₂×#5666	1	1	yes	characteristic, direct product factor
643	C₃	C₂×C₃×#560	1	1	yes	characteristic, complemented
644	C₂	—	4	2	no	—
645	C₂	—	4	2	no	—
646	C₂	—	12	4	no	—
647	C₂	—	12	4	no	—
648	C₂	C₃×#5666	1	4	yes	direct product factor
649	C₂	C₂×C₃×#1004	1	1	yes	characteristic
650	C₂	C₂×C₃×#1009	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₂×C₃²×#123	C₂
socle	C₂³×C₃²	C₂⁴
hypercenter	C₂×C₃×#123	D₃
hypocenter	C₃	C₂×C₃×#560
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#123

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×#123	C₂	semidirect
2. C₂×C₃×#940	C₂	semidirect
3. C₂×C₃×#937	C₂	semidirect
4. C₂×C₃×#930	C₂	semidirect
5. C₃×#5666	C₂	direct (N × H)
6. C₂×C₃×#898	C₂	semidirect
7. C₂×C₃×#895	C₂	semidirect
8. C₂×C₃×#884	C₂	semidirect
9. C₂×C₃×#883	C₂	semidirect
10. C₂×C₃×#882	C₂	semidirect
12. C₂×#5666	C₃	direct (N × H)
15. C₂³×C₃²×C₄	C₂²	semidirect
18. C₂²×C₃×#67	C₂²	semidirect
21. C₂²×C₃×D₁₂	C₂²	semidirect
22. C₂²×C₃×C₄×D₃	C₂²	semidirect
23. C₃²×#123	C₂²	semidirect
24. C₂×C₃²×C₄⋊C₄	C₂²	semidirect
26. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
28. C₃×#940	C₂²	semidirect
29. C₃×#937	C₂²	semidirect
30. C₃×#930	C₂²	semidirect
34. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
35. C₂×C₃×C₄⋊Dic₃	C₂²	semidirect
36. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
37. C₂×C₃×C₄×Dic₃	C₂²	semidirect
38. C₃×#898	C₂²	semidirect
39. C₃×#895	C₂²	semidirect
40. C₃×#884	C₂²	semidirect
41. C₃×#883	C₂²	semidirect
42. C₃×#882	C₂²	semidirect
48. C₂×C₃×#123	D₃	semidirect
49. C₂×C₃×#123	C₂×C₃	semidirect
55. C₂×#940	C₂×C₃	semidirect
56. C₂×#937	C₂×C₃	semidirect
57. C₂×#930	C₂×C₃	semidirect
58. #5666	C₂×C₃	direct (N × H)
59. C₂×#898	C₂×C₃	semidirect
60. C₂×#895	C₂×C₃	semidirect
61. C₂×#884	C₂×C₃	semidirect
62. C₂×#883	C₂×C₃	semidirect
63. C₂×#882	C₂×C₃	semidirect
77. C₂²×C₃²×C₄	C₂³	semidirect
83. C₂×C₃×#67	C₂³	semidirect
91. C₂×C₃×D₁₂	C₂³	semidirect
93. C₂×C₃×C₄×D₃	C₂³	semidirect
94. C₃²×C₄⋊C₄	C₂³	semidirect
96. C₃²×C₂²⋊C₄	C₂³	semidirect
101. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
102. C₃×C₄⋊Dic₃	C₂³	semidirect
103. C₃×Dic₃⋊C₄	C₂³	semidirect
104. C₃×C₄×Dic₃	C₂³	semidirect
119. C₂³×C₃×C₄	C₂×D₃	semidirect
120. C₂³×C₃×C₄	C₂²×C₃	semidirect
123. C₂²×#67	C₂²×C₃	semidirect
126. C₂²×D₁₂	C₂²×C₃	semidirect
127. C₂²×C₄×D₃	C₂²×C₃	semidirect
132. C₃×#123	C₂×D₃	semidirect
133. C₃×#123	C₂²×C₃	semidirect
142. C₂×C₃×C₄⋊C₄	C₂×D₃	semidirect
143. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
152. C₂×C₃×C₂²⋊C₄	C₂×D₃	semidirect
154. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
157. #940	C₂²×C₃	semidirect
158. #937	C₂²×C₃	semidirect
159. #930	C₂²×C₃	semidirect
163. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
164. C₂×C₄⋊Dic₃	C₂²×C₃	semidirect
165. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
166. C₂×C₄×Dic₃	C₂²×C₃	semidirect
167. #898	C₂²×C₃	semidirect
168. #895	C₂²×C₃	semidirect
169. #884	C₂²×C₃	semidirect
170. #883	C₂²×C₃	semidirect
171. #882	C₂²×C₃	semidirect
213. C₂×#123	C₃×D₃	semidirect
267. C₂²×C₃×C₄	C₂²×D₃	semidirect
271. C₂²×C₃×C₄	C₂³×C₃	semidirect
277. C₂×#67	C₂³×C₃	semidirect
285. C₂×D₁₂	C₂³×C₃	semidirect
287. C₂×C₄×D₃	C₂³×C₃	semidirect
291. C₃×C₄⋊C₄	C₂²×D₃	semidirect
292. C₃×C₄⋊C₄	C₂³×C₃	semidirect
301. C₃×C₂²⋊C₄	C₂²×D₃	semidirect
303. C₃×C₂²⋊C₄	C₂³×C₃	semidirect
309. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
310. C₄⋊Dic₃	C₂³×C₃	semidirect
311. Dic₃⋊C₄	C₂³×C₃	semidirect
312. C₄×Dic₃	C₂³×C₃	semidirect
345. C₂³×C₄	C₂×C₃×D₃	semidirect
349. #123	C₂×C₃×D₃	semidirect
357. C₂×C₄⋊C₄	C₂×C₃×D₃	semidirect
364. C₂×C₂²⋊C₄	C₂×C₃×D₃	semidirect
457. C₂×C₃²	#560	semidirect
491. C₂²×C₄	C₂²×C₃×D₃	semidirect
494. C₄⋊C₄	C₂²×C₃×D₃	semidirect
501. C₂²⋊C₄	C₂²×C₃×D₃	semidirect
561. C₃²	C₂×#560	semidirect
610. C₂×C₃	#5666	direct (N × H)
611. C₂×C₃	C₃×#560	semidirect
642. C₃	C₂×#5666	direct (N × H)
643. C₃	C₂×C₃×#560	semidirect
648. C₂	C₃×#5666	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃²×#123	2
C₂×C₃×#940	2
C₂×C₃×#937	2
C₂×C₃×#930	2
C₃×#5666	2
C₂×C₃×#898	2
C₂×C₃×#895	2
C₂×C₃×#884	2
C₂×C₃×#883	2
C₂×C₃×#882	2
C₂×C₃×#560	3
C₂×#5666	3

Subgroups — C2×C3×#5666 #11910164

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5666 #11910164