Subgroups — C₂×C₃×#5745 #11918485

Order 1152.

3069 conjugacy classes of subgroups.

The subgroup lattice has 577 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#235	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃²×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×#208	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5745	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃×#907	C₂	1	4	yes	maximal, complemented
6	C₂×C₃×D₃×M₁₆	C₂	1	4	yes	maximal, complemented
7	C₂×C₃×#901	C₂	1	4	yes	maximal, complemented
8	C₂×C₃×#568	—	3	1	no	maximal
9	C₂×#5745	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
11	C₂²×C₃×#67	C₄	1	2	yes	—
12	C₂×C₃×#235	C₄	1	2	yes	—
13	C₂×C₃×#235	C₄	1	8	yes	—
14	C₂×C₃×#235	C₄	1	2	yes	—
15	C₂×C₃×#235	C₂²	1	2	yes	—
16	C₂×C₃×#235	C₂²	1	8	yes	—
17	C₂×C₃×#235	C₂²	1	2	yes	—
18	C₂²×C₃×D₁₂	C₄	1	1	yes	characteristic
19	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	—
20	C₂²×C₃×Dic₆	C₄	1	1	yes	characteristic
21	C₂×C₃²×M₁₆	C₂²	1	2	yes	—
22	C₂×C₃²×M₁₆	C₂²	1	2	yes	complemented
23	C₂×C₃²×M₁₆	C₂²	1	8	yes	complemented
24	C₂²×C₃²×C₈	C₂²	1	2	yes	complemented
25	C₂×C₃×#208	C₂²	1	2	yes	—
26	C₂×C₃×#208	C₂²	1	2	yes	complemented
27	C₂×C₃×#208	C₂²	1	8	yes	complemented
28	C₂²×C₃×C₃⋊C₈	C₂²	1	2	yes	complemented
29	C₃×#907	C₂²	1	32	yes	complemented
30	C₃×D₃×M₁₆	C₂²	1	32	yes	complemented
31	C₃×#901	C₂²	1	32	yes	complemented
32	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	8	yes	complemented
33	C₂×C₃×D₃×C₈	C₂²	1	8	yes	complemented
34	C₂²×C₃×#41	—	3	1	no	—
35	C₂²×#235	C₂×C₃	1	1	yes	characteristic
36	C₃×#568	—	3	16	no	—
37	C₂×C₃×#131	—	3	4	no	—
38	C₂×C₃×#131	—	3	4	no	—
39	C₂²×C₃×M₁₆	—	2	1	no	—
40	C₂²×C₃×M₁₆	—	3	1	no	—
41	C₂²×C₃×M₁₆	—	3	4	no	—
42	C₂²×C₃×M₁₆	D₃	1	1	yes	characteristic, complemented
43	C₂²×C₃×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂²×#208	C₂×C₃	1	1	yes	characteristic, complemented
45	#5745	C₂×C₃	1	16	yes	direct product factor
46	C₂×#907	C₂×C₃	1	4	yes	complemented
47	C₂×D₃×M₁₆	C₂×C₃	1	4	yes	complemented
48	C₂×#901	C₂×C₃	1	4	yes	complemented
49	C₂⁴×C₃²	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₃×D₃	C₂×C₄	1	2	yes	—
51	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₃²×C₄	C₂×C₄	1	4	yes	—
55	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
56	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
57	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
58	C₂²×C₃²×C₄	C₂³	1	4	yes	—
59	C₂×C₃×#67	C₂×C₄	1	4	yes	—
60	C₂×C₃×#67	C₂×C₄	1	4	yes	—
61	C₂×C₃×#67	C₂×C₄	1	16	yes	—
62	C₂²×C₃×Dic₃	C₂×C₄	1	2	yes	—
63	C₃×#235	C₂×C₄	1	8	yes	—
64	C₃×#235	C₂×C₄	1	16	yes	—
65	C₃×#235	C₂×C₄	1	16	yes	—
66	C₃×#235	C₂×C₄	1	8	yes	—
67	C₃×#235	C₂³	1	8	yes	—
68	C₃×#235	C₂³	1	8	yes	—
69	C₂×C₃×D₁₂	C₂×C₄	1	2	yes	—
70	C₂×C₃×D₁₂	C₂×C₄	1	2	yes	—
71	C₂×C₃×D₁₂	C₂×C₄	1	8	yes	—
72	C₂×C₃×C₄×D₃	C₂×C₄	1	4	yes	—
73	C₂×C₃×C₄×D₃	C₂×C₄	1	8	yes	—
74	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
75	C₂×C₃×C₄×D₃	C₂³	1	8	yes	—
76	C₂×C₃×Dic₆	C₂×C₄	1	2	yes	—
77	C₂×C₃×Dic₆	C₂×C₄	1	8	yes	—
78	C₂×C₃×Dic₆	C₂×C₄	1	2	yes	—
79	C₃²×M₁₆	C₂³	1	8	yes	—
80	C₃²×M₁₆	C₂³	1	8	yes	complemented
81	C₂×C₃²×C₈	C₂³	1	4	yes	—
82	C₂×C₃²×C₈	C₂³	1	8	yes	complemented
83	C₃×#208	C₂³	1	8	yes	—
84	C₃×#208	C₂³	1	8	yes	complemented
85	C₂×C₃×C₃⋊C₈	C₂³	1	4	yes	—
86	C₂×C₃×C₃⋊C₈	C₂³	1	8	yes	complemented
87	C₃×ΓL(1,𝔽₂₅)	C₂³	1	32	yes	complemented
88	C₃×D₃×C₈	C₂³	1	32	yes	complemented
89	C₂×#568	—	3	1	no	Sylow
90	C₂×C₃×#41	—	3	2	no	—
91	C₂×C₃×#41	—	3	2	no	—
92	C₂×C₃×#41	—	3	8	no	—
93	C₂×C₃×#41	—	3	2	no	—
94	C₂×C₃×#41	—	3	2	no	—
95	C₂×C₃×#41	—	3	8	no	—
96	C₂²×C₃×Q₈	—	3	1	no	—
97	C₂²×C₃×D₄	—	3	2	no	—
98	C₂²×C₃×D₄	—	3	1	no	—
99	C₂³×C₃×C₄	—	2	1	no	—
100	C₂³×C₃×C₄	—	3	2	no	—
101	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
102	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
103	C₂²×#67	C₃×C₄	1	2	yes	—
104	C₂×#235	C₃×C₄	1	2	yes	—
105	C₂×#235	C₃×C₄	1	2	yes	—
106	C₂×#235	C₃×C₄	1	8	yes	—
107	C₂×#235	C₂²×C₃	1	2	yes	—
108	C₂×#235	C₂²×C₃	1	2	yes	—
109	C₂×#235	C₂²×C₃	1	8	yes	—
110	C₂²×D₁₂	C₃×C₄	1	1	yes	characteristic
111	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	—
112	C₂²×Dic₆	C₃×C₄	1	1	yes	characteristic
113	C₃×#131	—	3	32	no	—
114	C₃×#131	—	3	32	no	—
115	C₂×C₃×M₁₆	—	2	2	no	—
116	C₂×C₃×M₁₆	—	2	2	no	—
117	C₂×C₃×M₁₆	—	2	8	no	—
118	C₂×C₃×M₁₆	—	3	2	no	—
119	C₂×C₃×M₁₆	—	3	2	no	—
120	C₂×C₃×M₁₆	—	3	8	no	—
121	C₂×C₃×M₁₆	—	3	32	no	—
122	C₂×C₃×M₁₆	—	3	8	no	—
123	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
124	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	complemented
125	C₂×C₃×M₁₆	C₂×D₃	1	8	yes	complemented
126	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
127	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	complemented
128	C₂×C₃×M₁₆	C₂²×C₃	1	8	yes	complemented
129	C₂²×C₃×C₈	—	2	2	no	—
130	C₂²×C₃×C₈	—	3	2	no	—
131	C₂²×C₃×C₈	—	3	8	no	—
132	C₂²×C₃×C₈	C₂×D₃	1	2	yes	complemented
133	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	complemented
134	C₂×#208	C₂²×C₃	1	2	yes	—
135	C₂×#208	C₂²×C₃	1	2	yes	complemented
136	C₂×#208	C₂²×C₃	1	8	yes	complemented
137	C₂²×C₃⋊C₈	C₂²×C₃	1	2	yes	complemented
138	#907	C₂²×C₃	1	32	yes	complemented
139	D₃×M₁₆	C₂²×C₃	1	32	yes	complemented
140	#901	C₂²×C₃	1	32	yes	complemented
141	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	8	yes	complemented
142	C₂×D₃×C₈	C₂²×C₃	1	8	yes	complemented
143	C₂³×C₃²	—	4	2	no	—
144	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
145	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
146	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
147	C₂³×C₃²	C₂²×C₄	1	4	yes	—
148	C₂²×C₃×D₃	—	4	4	no	—
149	C₂²×C₃×D₃	C₂²×C₄	1	4	yes	—
150	C₂²×C₃×D₃	C₂²×C₄	1	8	yes	—
151	C₂×C₃²×C₄	C₂²×C₄	1	4	yes	—
152	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
155	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
157	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
158	C₂×C₃²×C₄	C₂²×C₄	1	4	yes	—
159	C₂×C₃²×C₄	C₂²×C₄	1	4	yes	—
160	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
161	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
162	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
163	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
164	C₃×#67	C₂²×C₄	1	16	yes	—
165	C₃×#67	C₂²×C₄	1	16	yes	—
166	C₂×C₃×Dic₃	C₂²×C₄	1	8	yes	—
167	C₂×C₃×Dic₃	C₂²×C₄	1	4	yes	—
168	C₃×D₁₂	C₂²×C₄	1	8	yes	—
169	C₃×D₁₂	C₂²×C₄	1	8	yes	—
170	C₃×C₄×D₃	C₂²×C₄	1	8	yes	—
171	C₃×C₄×D₃	C₂²×C₄	1	16	yes	—
172	C₃×C₄×D₃	C₂⁴	1	8	yes	—
173	C₃×Dic₆	C₂²×C₄	1	8	yes	—
174	C₃×Dic₆	C₂²×C₄	1	8	yes	—
175	C₃²×C₈	C₂⁴	1	8	yes	—
176	C₃×C₃⋊C₈	C₂⁴	1	8	yes	—
177	C₂²×#41	—	3	1	no	—
178	#568	—	3	16	no	—
179	C₂×#131	—	3	4	no	—
180	C₂×#131	—	3	4	no	—
181	C₂²×M₁₆	—	3	1	no	—
182	C₂²×M₁₆	—	3	4	no	—
183	C₂²×M₁₆	C₃×D₃	1	1	yes	characteristic, complemented
184	C₂⁴×C₃	—	2	1	no	—
185	C₂⁴×C₃	—	3	2	no	—
186	C₂⁴×C₃	C₄×D₃	1	1	yes	characteristic
187	C₂⁴×C₃	C₂×C₃×C₄	1	1	yes	characteristic
188	C₂³×D₃	C₂×C₃×C₄	1	2	yes	—
189	C₃×#41	—	3	8	no	—
190	C₃×#41	—	3	8	no	—
191	C₃×#41	—	3	16	no	—
192	C₃×#41	—	3	16	no	—
193	C₃×#41	—	3	8	no	—
194	C₃×#41	—	3	8	no	—
195	C₂×C₃×Q₈	—	3	2	no	—
196	C₂×C₃×Q₈	—	3	2	no	—
197	C₂×C₃×Q₈	—	3	8	no	—
198	C₂×C₃×D₄	—	3	4	no	—
199	C₂×C₃×D₄	—	3	4	no	—
200	C₂×C₃×D₄	—	3	16	no	—
201	C₂×C₃×D₄	—	3	2	no	—
202	C₂×C₃×D₄	—	3	2	no	—
203	C₂×C₃×D₄	—	3	8	no	—
204	C₂²×C₃×C₄	—	2	1	no	—
205	C₂²×C₃×C₄	—	2	1	no	—
206	C₂²×C₃×C₄	—	2	1	no	—
207	C₂²×C₃×C₄	—	2	4	no	—
208	C₂²×C₃×C₄	—	2	1	no	—
209	C₂²×C₃×C₄	—	2	1	no	—
210	C₂²×C₃×C₄	—	2	1	no	—
211	C₂²×C₃×C₄	—	2	4	no	—
212	C₂²×C₃×C₄	—	3	2	no	—
213	C₂²×C₃×C₄	—	3	4	no	—
214	C₂²×C₃×C₄	—	3	8	no	—
215	C₂²×C₃×C₄	—	3	8	no	—
216	C₂²×C₃×C₄	—	3	4	no	—
217	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
218	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
219	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
220	C₂²×C₃×C₄	C₄×D₃	1	4	yes	—
221	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
222	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
223	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
224	C₂²×C₃×C₄	C₂×C₃×C₄	1	4	yes	—
225	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
226	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
227	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
228	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
229	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
230	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
231	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
232	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
233	C₂×#67	C₂×C₃×C₄	1	4	yes	—
234	C₂×#67	C₂×C₃×C₄	1	4	yes	—
235	C₂×#67	C₂×C₃×C₄	1	16	yes	—
236	C₂²×Dic₃	C₂×C₃×C₄	1	2	yes	—
237	#235	C₂×C₃×C₄	1	8	yes	—
238	#235	C₂×C₃×C₄	1	8	yes	—
239	#235	C₂×C₃×C₄	1	16	yes	—
240	#235	C₂×C₃×C₄	1	16	yes	—
241	#235	C₂³×C₃	1	8	yes	—
242	#235	C₂³×C₃	1	8	yes	—
243	C₂×D₁₂	C₂×C₃×C₄	1	2	yes	—
244	C₂×D₁₂	C₂×C₃×C₄	1	2	yes	—
245	C₂×D₁₂	C₂×C₃×C₄	1	8	yes	—
246	C₂×C₄×D₃	C₂×C₃×C₄	1	4	yes	—
247	C₂×C₄×D₃	C₂×C₃×C₄	1	8	yes	—
248	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
249	C₂×C₄×D₃	C₂³×C₃	1	8	yes	—
250	C₂×Dic₆	C₂×C₃×C₄	1	2	yes	—
251	C₂×Dic₆	C₂×C₃×C₄	1	2	yes	—
252	C₂×Dic₆	C₂×C₃×C₄	1	8	yes	—
253	C₃×M₁₆	—	2	8	no	—
254	C₃×M₁₆	—	2	8	no	—
255	C₃×M₁₆	—	3	8	no	—
256	C₃×M₁₆	—	3	8	no	—
257	C₃×M₁₆	—	3	32	no	—
258	C₃×M₁₆	C₂²×D₃	1	8	yes	—
259	C₃×M₁₆	C₂²×D₃	1	8	yes	complemented
260	C₃×M₁₆	C₂³×C₃	1	8	yes	—
261	C₃×M₁₆	C₂³×C₃	1	8	yes	complemented
262	C₂×C₃×C₈	—	2	4	no	—
263	C₂×C₃×C₈	—	2	8	no	—
264	C₂×C₃×C₈	—	3	8	no	—
265	C₂×C₃×C₈	—	3	4	no	—
266	C₂×C₃×C₈	—	3	32	no	—
267	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
268	C₂×C₃×C₈	C₂²×D₃	1	8	yes	complemented
269	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
270	C₂×C₃×C₈	C₂³×C₃	1	8	yes	complemented
271	#208	C₂³×C₃	1	8	yes	—
272	#208	C₂³×C₃	1	8	yes	complemented
273	C₂×C₃⋊C₈	C₂³×C₃	1	4	yes	—
274	C₂×C₃⋊C₈	C₂³×C₃	1	8	yes	complemented
275	ΓL(1,𝔽₂₅)	C₂³×C₃	1	32	yes	complemented
276	D₃×C₈	C₂³×C₃	1	32	yes	complemented
277	C₂²×C₃²	—	2	2	no	—
278	C₂²×C₃²	—	2	2	no	—
279	C₂²×C₃²	—	2	2	no	—
280	C₂²×C₃²	—	4	4	no	—
281	C₂²×C₃²	C₂³×C₄	1	2	yes	—
282	C₂²×C₃²	C₂³×C₄	1	2	yes	—
283	C₂²×C₃²	C₂³×C₄	1	2	yes	—
284	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
285	C₂×C₃×D₃	—	2	8	no	—
286	C₂×C₃×D₃	—	4	8	no	—
287	C₂×C₃×D₃	C₂³×C₄	1	8	yes	—
288	C₃²×C₄	C₂³×C₄	1	2	yes	—
289	C₃²×C₄	C₂³×C₄	1	2	yes	—
290	C₃²×C₄	C₂³×C₄	1	2	yes	—
291	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
292	C₃²×C₄	C₂⁵	1	1	yes	characteristic
293	C₃×Dic₃	C₂³×C₄	1	8	yes	—
294	C₂×#41	—	3	2	no	—
295	C₂×#41	—	3	2	no	—
296	C₂×#41	—	3	8	no	—
297	C₂×#41	—	3	2	no	—
298	C₂×#41	—	3	2	no	—
299	C₂×#41	—	3	8	no	—
300	C₂²×Q₈	—	3	1	no	—
301	C₂²×D₄	—	3	2	no	—
302	C₂²×D₄	—	3	1	no	—
303	C₂³×C₄	—	3	2	no	—
304	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
305	#131	—	3	32	no	—
306	#131	—	3	32	no	—
307	C₂×M₁₆	—	3	2	no	—
308	C₂×M₁₆	—	3	2	no	—
309	C₂×M₁₆	—	3	8	no	—
310	C₂×M₁₆	—	3	32	no	—
311	C₂×M₁₆	—	3	8	no	—
312	C₂×M₁₆	C₂×C₃×D₃	1	2	yes	—
313	C₂×M₁₆	C₂×C₃×D₃	1	2	yes	complemented
314	C₂×M₁₆	C₂×C₃×D₃	1	8	yes	complemented
315	C₂²×C₈	—	3	2	no	—
316	C₂²×C₈	—	3	8	no	—
317	C₂²×C₈	C₂×C₃×D₃	1	2	yes	complemented
318	C₂³×C₃	—	2	1	no	—
319	C₂³×C₃	—	2	1	no	—
320	C₂³×C₃	—	2	1	no	—
321	C₂³×C₃	—	2	4	no	—
322	C₂³×C₃	—	3	4	no	—
323	C₂³×C₃	—	3	8	no	—
324	C₂³×C₃	—	4	2	no	—
325	C₂³×C₃	—	4	2	no	—
326	C₂³×C₃	—	4	4	no	—
327	C₂³×C₃	—	12	4	no	—
328	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
329	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
330	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
331	C₂³×C₃	C₂×C₄×D₃	1	4	yes	—
332	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
333	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
334	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
335	C₂³×C₃	C₂²×C₃×C₄	1	4	yes	—
336	C₂²×D₃	—	4	4	no	—
337	C₂²×D₃	C₂²×C₃×C₄	1	4	yes	—
338	C₂²×D₃	C₂²×C₃×C₄	1	8	yes	—
339	C₃×Q₈	—	3	8	no	—
340	C₃×Q₈	—	3	8	no	—
341	C₃×D₄	—	3	16	no	—
342	C₃×D₄	—	3	16	no	—
343	C₃×D₄	—	3	8	no	—
344	C₃×D₄	—	3	8	no	—
345	C₂×C₃×C₄	—	2	1	no	—
346	C₂×C₃×C₄	—	2	2	no	—
347	C₂×C₃×C₄	—	2	2	no	—
348	C₂×C₃×C₄	—	2	2	no	—
349	C₂×C₃×C₄	—	2	1	no	—
350	C₂×C₃×C₄	—	2	2	no	—
351	C₂×C₃×C₄	—	2	1	no	—
352	C₂×C₃×C₄	—	2	1	no	—
353	C₂×C₃×C₄	—	2	4	no	—
354	C₂×C₃×C₄	—	2	2	no	—
355	C₂×C₃×C₄	—	2	4	no	—
356	C₂×C₃×C₄	—	2	2	no	—
357	C₂×C₃×C₄	—	2	4	no	—
358	C₂×C₃×C₄	—	3	8	no	—
359	C₂×C₃×C₄	—	3	4	no	—
360	C₂×C₃×C₄	—	3	16	no	—
361	C₂×C₃×C₄	—	3	8	no	—
362	C₂×C₃×C₄	—	3	8	no	—
363	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
364	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
365	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
366	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
367	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
368	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
369	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
370	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
371	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
372	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
373	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
374	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
375	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
376	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
377	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
378	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
379	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
380	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
381	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
382	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
383	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
384	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
385	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
386	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
387	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
388	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
389	#67	C₂²×C₃×C₄	1	16	yes	—
390	#67	C₂²×C₃×C₄	1	16	yes	—
391	C₂×Dic₃	C₂²×C₃×C₄	1	8	yes	—
392	C₂×Dic₃	C₂²×C₃×C₄	1	4	yes	—
393	D₁₂	C₂²×C₃×C₄	1	8	yes	—
394	D₁₂	C₂²×C₃×C₄	1	8	yes	—
395	C₄×D₃	C₂²×C₃×C₄	1	8	yes	—
396	C₄×D₃	C₂²×C₃×C₄	1	16	yes	—
397	C₄×D₃	C₂⁴×C₃	1	8	yes	—
398	Dic₆	C₂²×C₃×C₄	1	8	yes	—
399	Dic₆	C₂²×C₃×C₄	1	8	yes	—
400	C₃×C₈	—	2	8	no	—
401	C₃×C₈	—	3	8	no	—
402	C₃×C₈	C₂³×D₃	1	8	yes	—
403	C₃×C₈	C₂⁴×C₃	1	8	yes	—
404	C₃⋊C₈	C₂⁴×C₃	1	8	yes	—
405	C₂×C₃²	—	2	2	no	—
406	C₂×C₃²	—	2	2	no	—
407	C₂×C₃²	—	2	2	no	—
408	C₂×C₃²	#568	1	2	yes	complemented
409	C₂×C₃²	C₂⁴×C₄	1	1	yes	characteristic
410	C₃×D₃	—	2	8	no	—
411	C₂⁴	—	3	2	no	—
412	C₂⁴	C₃×C₄×D₃	1	1	yes	characteristic
413	#41	—	3	8	no	—
414	#41	—	3	8	no	—
415	#41	—	3	8	no	—
416	#41	—	3	8	no	—
417	#41	—	3	16	no	—
418	#41	—	3	16	no	—
419	C₂×Q₈	—	3	2	no	—
420	C₂×Q₈	—	3	2	no	—
421	C₂×Q₈	—	3	8	no	—
422	C₂×D₄	—	3	4	no	—
423	C₂×D₄	—	3	4	no	—
424	C₂×D₄	—	3	16	no	—
425	C₂×D₄	—	3	2	no	—
426	C₂×D₄	—	3	2	no	—
427	C₂×D₄	—	3	8	no	—
428	C₂²×C₄	—	3	2	no	—
429	C₂²×C₄	—	3	4	no	—
430	C₂²×C₄	—	3	8	no	—
431	C₂²×C₄	—	3	4	no	—
432	C₂²×C₄	—	3	8	no	—
433	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
434	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
435	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
436	C₂²×C₄	C₃×C₄×D₃	1	4	yes	—
437	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
438	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
439	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
440	C₂²×C₄	C₂²×C₃×D₃	1	4	yes	—
441	M₁₆	—	3	8	no	—
442	M₁₆	—	3	8	no	—
443	M₁₆	—	3	32	no	—
444	M₁₆	C₂²×C₃×D₃	1	8	yes	—
445	M₁₆	C₂²×C₃×D₃	1	8	yes	complemented
446	C₂×C₈	—	3	4	no	—
447	C₂×C₈	—	3	8	no	—
448	C₂×C₈	—	3	32	no	—
449	C₂×C₈	C₂²×C₃×D₃	1	4	yes	—
450	C₂×C₈	C₂²×C₃×D₃	1	8	yes	complemented
451	C₂²×C₃	—	2	4	no	—
452	C₂²×C₃	—	2	2	no	—
453	C₂²×C₃	—	2	2	no	—
454	C₂²×C₃	—	2	2	no	—
455	C₂²×C₃	—	2	2	no	—
456	C₂²×C₃	—	2	2	no	—
457	C₂²×C₃	—	2	2	no	—
458	C₂²×C₃	—	2	2	no	—
459	C₂²×C₃	—	2	1	no	—
460	C₂²×C₃	—	2	2	no	—
461	C₂²×C₃	—	2	2	no	—
462	C₂²×C₃	—	3	8	no	—
463	C₂²×C₃	—	4	2	no	—
464	C₂²×C₃	—	4	2	no	—
465	C₂²×C₃	—	4	4	no	—
466	C₂²×C₃	—	4	4	no	—
467	C₂²×C₃	—	4	8	no	—
468	C₂²×C₃	—	6	8	no	—
469	C₂²×C₃	—	12	8	no	—
470	C₂²×C₃	C₂²×C₄×D₃	1	2	yes	—
471	C₂²×C₃	C₂²×C₄×D₃	1	2	yes	—
472	C₂²×C₃	C₂²×C₄×D₃	1	2	yes	—
473	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
474	C₂²×C₃	C₂³×C₃×C₄	1	2	yes	—
475	C₂²×C₃	C₂³×C₃×C₄	1	2	yes	—
476	C₂²×C₃	C₂³×C₃×C₄	1	2	yes	—
477	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
478	C₂×D₃	—	2	8	no	—
479	C₂×D₃	—	4	8	no	—
480	C₂×D₃	C₂³×C₃×C₄	1	8	yes	—
481	C₃×C₄	—	2	1	no	—
482	C₃×C₄	—	2	2	no	—
483	C₃×C₄	—	2	2	no	—
484	C₃×C₄	—	2	2	no	—
485	C₃×C₄	—	2	1	no	—
486	C₃×C₄	—	3	8	no	—
487	C₃×C₄	C₂²×C₄×D₃	1	2	yes	—
488	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
489	C₃×C₄	C₂²×C₄×D₃	1	2	yes	—
490	C₃×C₄	C₂²×C₄×D₃	1	2	yes	—
491	C₃×C₄	C₂³×C₃×C₄	1	2	yes	—
492	C₃×C₄	C₂³×C₃×C₄	1	2	yes	—
493	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
494	C₃×C₄	C₂³×C₃×C₄	1	2	yes	—
495	C₃×C₄	C₂⁴×D₃	1	1	yes	characteristic
496	C₃×C₄	C₂⁵×C₃	1	1	yes	characteristic
497	Dic₃	C₂³×C₃×C₄	1	8	yes	—
498	C₃²	C₂×#568	1	1	yes	characteristic, complemented, Sylow
499	C₂³	—	3	4	no	—
500	C₂³	—	3	8	no	—
501	C₂³	—	4	2	no	—
502	C₂³	—	12	4	no	—
503	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
504	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
505	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
506	C₂³	C₂×C₃×C₄×D₃	1	4	yes	—
507	Q₈	—	3	8	no	—
508	Q₈	—	3	8	no	—
509	D₄	—	3	16	no	—
510	D₄	—	3	16	no	—
511	D₄	—	3	8	no	—
512	D₄	—	3	8	no	—
513	C₂×C₄	—	3	8	no	—
514	C₂×C₄	—	3	4	no	—
515	C₂×C₄	—	3	8	no	—
516	C₂×C₄	—	3	16	no	—
517	C₂×C₄	—	3	8	no	—
518	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
519	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
520	C₂×C₄	C₂×C₃×C₄×D₃	1	4	yes	—
521	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
522	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
523	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
524	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
525	C₂×C₄	C₂×C₃×C₄×D₃	1	4	yes	—
526	C₂×C₄	C₂×C₃×C₄×D₃	1	4	yes	—
527	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
528	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
529	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
530	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
531	C₈	—	3	8	no	—
532	C₈	C₂³×C₃×D₃	1	8	yes	—
533	C₂×C₃	—	2	4	no	—
534	C₂×C₃	—	2	2	no	—
535	C₂×C₃	—	2	2	no	—
536	C₂×C₃	—	2	2	no	—
537	C₂×C₃	—	2	2	no	—
538	C₂×C₃	—	2	2	no	—
539	C₂×C₃	—	2	2	no	—
540	C₂×C₃	—	2	2	no	—
541	C₂×C₃	—	2	1	no	—
542	C₂×C₃	—	4	2	no	—
543	C₂×C₃	—	4	2	no	—
544	C₂×C₃	—	6	8	no	—
545	C₂×C₃	#5745	1	2	yes	direct product factor
546	C₂×C₃	C₃×#568	1	2	yes	complemented
547	C₂×C₃	C₂³×C₄×D₃	1	1	yes	characteristic
548	C₂×C₃	C₂⁴×C₃×C₄	1	1	yes	characteristic
549	D₃	—	2	8	no	—
550	C₂²	—	2	2	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	3	8	no	—
554	C₂²	—	4	4	no	—
555	C₂²	—	6	8	no	—
556	C₂²	—	12	8	no	—
557	C₂²	C₂²×C₃×C₄×D₃	1	2	yes	—
558	C₂²	C₂²×C₃×C₄×D₃	1	2	yes	—
559	C₂²	C₂²×C₃×C₄×D₃	1	2	yes	—
560	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
561	C₄	—	3	8	no	—
562	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
563	C₄	C₂²×C₃×C₄×D₃	1	2	yes	—
564	C₄	C₂²×C₃×C₄×D₃	1	2	yes	—
565	C₄	C₂²×C₃×C₄×D₃	1	2	yes	—
566	C₄	C₂⁴×C₃×D₃	1	1	yes	characteristic
567	C₃	—	2	1	no	—
568	C₃	C₂×#5745	1	1	yes	characteristic, direct product factor
569	C₃	C₂×C₃×#568	1	1	yes	characteristic, complemented
570	C₂	—	2	2	no	—
571	C₂	—	2	2	no	—
572	C₂	—	2	2	no	—
573	C₂	—	6	8	no	—
574	C₂	C₃×#5745	1	2	yes	direct product factor
575	C₂	C₂³×C₃×C₄×D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₃
commutator	C₂×C₃	C₂⁴×C₃×C₄
Frattini	C₄	C₂⁴×C₃×D₃
Fitting	C₂²×C₃²×M₁₆	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₂²×C₃×#235	C₂
cosocle	C₃×C₄	C₂⁵×C₃
hypercenter	C₂²×C₃×M₁₆	D₃
hypocenter	C₃	C₂×C₃×#568
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃²×M₁₆	C₂	semidirect
3. C₂²×C₃×#208	C₂	semidirect
4. C₃×#5745	C₂	direct (N × H)
5. C₂×C₃×#907	C₂	semidirect
6. C₂×C₃×D₃×M₁₆	C₂	semidirect
7. C₂×C₃×#901	C₂	semidirect
9. C₂×#5745	C₃	direct (N × H)
22. C₂×C₃²×M₁₆	C₂²	semidirect
23. C₂×C₃²×M₁₆	C₂²	semidirect
24. C₂²×C₃²×C₈	C₂²	semidirect
26. C₂×C₃×#208	C₂²	semidirect
27. C₂×C₃×#208	C₂²	semidirect
28. C₂²×C₃×C₃⋊C₈	C₂²	semidirect
29. C₃×#907	C₂²	semidirect
30. C₃×D₃×M₁₆	C₂²	semidirect
31. C₃×#901	C₂²	semidirect
32. C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	semidirect
33. C₂×C₃×D₃×C₈	C₂²	semidirect
42. C₂²×C₃×M₁₆	D₃	semidirect
43. C₂²×C₃×M₁₆	C₂×C₃	semidirect
44. C₂²×#208	C₂×C₃	semidirect
45. #5745	C₂×C₃	direct (N × H)
46. C₂×#907	C₂×C₃	semidirect
47. C₂×D₃×M₁₆	C₂×C₃	semidirect
48. C₂×#901	C₂×C₃	semidirect
80. C₃²×M₁₆	C₂³	semidirect
82. C₂×C₃²×C₈	C₂³	semidirect
84. C₃×#208	C₂³	semidirect
86. C₂×C₃×C₃⋊C₈	C₂³	semidirect
87. C₃×ΓL(1,𝔽₂₅)	C₂³	semidirect
88. C₃×D₃×C₈	C₂³	semidirect
124. C₂×C₃×M₁₆	C₂×D₃	semidirect
125. C₂×C₃×M₁₆	C₂×D₃	semidirect
127. C₂×C₃×M₁₆	C₂²×C₃	semidirect
128. C₂×C₃×M₁₆	C₂²×C₃	semidirect
132. C₂²×C₃×C₈	C₂×D₃	semidirect
133. C₂²×C₃×C₈	C₂²×C₃	semidirect
135. C₂×#208	C₂²×C₃	semidirect
136. C₂×#208	C₂²×C₃	semidirect
137. C₂²×C₃⋊C₈	C₂²×C₃	semidirect
138. #907	C₂²×C₃	semidirect
139. D₃×M₁₆	C₂²×C₃	semidirect
140. #901	C₂²×C₃	semidirect
141. C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	semidirect
142. C₂×D₃×C₈	C₂²×C₃	semidirect
183. C₂²×M₁₆	C₃×D₃	semidirect
259. C₃×M₁₆	C₂²×D₃	semidirect
261. C₃×M₁₆	C₂³×C₃	semidirect
268. C₂×C₃×C₈	C₂²×D₃	semidirect
270. C₂×C₃×C₈	C₂³×C₃	semidirect
272. #208	C₂³×C₃	semidirect
274. C₂×C₃⋊C₈	C₂³×C₃	semidirect
275. ΓL(1,𝔽₂₅)	C₂³×C₃	semidirect
276. D₃×C₈	C₂³×C₃	semidirect
313. C₂×M₁₆	C₂×C₃×D₃	semidirect
314. C₂×M₁₆	C₂×C₃×D₃	semidirect
317. C₂²×C₈	C₂×C₃×D₃	semidirect
408. C₂×C₃²	#568	semidirect
445. M₁₆	C₂²×C₃×D₃	semidirect
450. C₂×C₈	C₂²×C₃×D₃	semidirect
498. C₃²	C₂×#568	semidirect
545. C₂×C₃	#5745	direct (N × H)
546. C₂×C₃	C₃×#568	semidirect
568. C₃	C₂×#5745	direct (N × H)
569. C₃	C₂×C₃×#568	semidirect
574. C₂	C₃×#5745	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×#235	2
C₂²×C₃²×M₁₆	2
C₂²×C₃×#208	2
C₃×#5745	2
C₂×C₃×#907	2
C₂×C₃×D₃×M₁₆	2
C₂×C₃×#901	2
C₂×C₃×#568	3
C₂×#5745	3

Subgroups — C2×C3×#5745 #11918485

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5745 #11918485