Subgroups — C₂×C₃×#2935 #10678746

Order 768.

2850 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#131	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×#532	C₂	1	1	yes	maximal, characteristic
3	C₃×#2935	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃×#436	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#435	C₂	1	4	yes	maximal, complemented
6	C₂×C₃×C₈×D₄	C₂	1	2	yes	maximal, complemented
7	C₂²×C₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#408	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×C₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#2935	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₂²×C₃×#41	C₂²	1	2	yes	—
12	C₂×C₃×#131	—	2	16	no	—
13	C₂×C₃×#131	C₂²	1	16	yes	complemented
14	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₃×M₁₆	C₂²	1	4	yes	—
16	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
17	C₂³×C₃×C₈	C₂²	1	2	yes	—
18	C₂³×C₃×C₈	C₂²	1	4	yes	—
19	C₃×#532	C₄	1	8	yes	—
20	C₃×#532	C₂²	1	8	yes	—
21	C₂×C₃×C₄⋊Q₈	C₄	1	1	yes	characteristic
22	C₂×C₃×#127	C₄	1	1	yes	characteristic
23	C₂×C₃×#124	C₄	1	2	yes	—
24	C₂×C₃×#121	C₄	1	2	yes	—
25	C₂×C₃×#121	C₄	1	2	yes	—
26	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
27	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
28	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
29	C₃×#436	C₂²	1	16	yes	complemented
30	C₃×#435	C₂²	1	32	yes	complemented
31	C₃×C₈×D₄	C₂²	1	16	yes	complemented
32	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₄⋊C₈	C₂²	1	2	yes	—
34	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₄⋊C₈	C₂²	1	8	yes	complemented
36	C₃×#408	C₂²	1	16	yes	complemented
37	C₂×C₃×C₂²⋊C₈	C₂²	1	4	yes	—
38	C₂×C₃×C₂²⋊C₈	C₂²	1	4	yes	—
39	C₃×C₄×M₁₆	C₂²	1	8	yes	complemented
40	C₂×C₃×#97	C₂²	1	2	yes	—
41	C₂×C₃×C₄×C₈	C₂²	1	2	yes	—
42	C₂²×#131	C₂×C₃	1	2	yes	complemented
43	C₂×#532	C₂×C₃	1	1	yes	characteristic
44	#2935	C₂×C₃	1	16	yes	direct product factor
45	C₂×#436	C₂×C₃	1	2	yes	complemented
46	C₂×#435	C₂×C₃	1	4	yes	complemented
47	C₂×C₈×D₄	C₂×C₃	1	2	yes	complemented
48	C₂²×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
49	C₂×#408	C₂×C₃	1	2	yes	complemented
50	C₂×C₄×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
51	C₂×C₃×#41	—	2	8	no	—
52	C₂×C₃×#41	—	2	8	no	—
53	C₂×C₃×#41	C₂×C₄	1	8	yes	—
54	C₂×C₃×#41	C₂³	1	8	yes	—
55	C₂²×C₃×Q₈	C₂×C₄	1	2	yes	—
56	C₂²×C₃×D₄	C₂×C₄	1	4	yes	—
57	C₂²×C₃×D₄	C₂×C₄	1	2	yes	—
58	C₂²×C₃×D₄	C₂×C₄	1	2	yes	—
59	C₂²×C₃×D₄	C₂×C₄	1	2	yes	—
60	C₂³×C₃×C₄	C₂×C₄	1	1	yes	characteristic
61	C₂³×C₃×C₄	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₃×C₄	C₂³	1	4	yes	—
63	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
64	C₃×#131	—	2	64	no	—
65	C₂×C₃×M₁₆	—	2	4	no	—
66	C₂×C₃×M₁₆	—	2	16	no	—
67	C₂×C₃×M₁₆	D₄	1	8	yes	complemented
68	C₂×C₃×M₁₆	C₂³	1	16	yes	—
69	C₂×C₃×M₁₆	C₂³	1	4	yes	—
70	C₂×C₃×M₁₆	C₂³	1	4	yes	—
71	C₂²×C₃×C₈	—	2	8	no	—
72	C₂²×C₃×C₈	—	2	16	no	—
73	C₂²×C₃×C₈	C₂³	1	8	yes	—
74	C₂²×C₃×C₈	C₂³	1	16	yes	—
75	C₂²×C₃×C₈	C₂³	1	2	yes	—
76	C₂²×C₃×C₈	C₂³	1	2	yes	—
77	C₂²×C₃×C₈	C₂³	1	2	yes	—
78	C₂²×C₃×C₈	C₂³	1	2	yes	—
79	C₃×C₄⋊Q₈	C₂×C₄	1	8	yes	—
80	C₃×#127	C₂×C₄	1	8	yes	—
81	C₃×#124	C₂×C₄	1	16	yes	—
82	C₃×#121	C₂×C₄	1	16	yes	—
83	C₃×#121	C₂×C₄	1	16	yes	—
84	C₃×C₄×D₄	C₂×C₄	1	8	yes	—
85	C₃×C₄×D₄	C₂×C₄	1	8	yes	—
86	C₃×C₄×D₄	C₂³	1	8	yes	—
87	C₃×C₄×D₄	C₂³	1	8	yes	—
88	C₂×C₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
89	C₂×C₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
90	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
91	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
92	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
93	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
94	C₂×C₃×C₄²	C₂×C₄	1	4	yes	—
95	C₂×C₃×C₄²	C₂³	1	4	yes	—
96	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
97	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
98	C₃×C₄⋊C₈	C₂³	1	4	yes	—
99	C₃×C₄⋊C₈	C₂³	1	8	yes	—
100	C₃×C₄⋊C₈	C₂³	1	4	yes	—
101	C₃×C₂²⋊C₈	C₂³	1	16	yes	—
102	C₃×C₂²⋊C₈	C₂³	1	16	yes	—
103	C₃×#97	C₂³	1	8	yes	—
104	C₃×C₄×C₈	C₂³	1	8	yes	—
105	C₂²×#41	C₂²×C₃	1	2	yes	—
106	C₂×#131	—	2	16	no	—
107	C₂×#131	C₂²×C₃	1	16	yes	complemented
108	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
109	C₂²×M₁₆	C₂²×C₃	1	4	yes	—
110	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
111	C₂³×C₈	C₂²×C₃	1	2	yes	—
112	C₂³×C₈	C₂²×C₃	1	4	yes	—
113	#532	C₃×C₄	1	8	yes	—
114	#532	C₂²×C₃	1	8	yes	—
115	C₂×C₄⋊Q₈	C₃×C₄	1	1	yes	characteristic
116	C₂×#127	C₃×C₄	1	1	yes	characteristic
117	C₂×#124	C₃×C₄	1	2	yes	—
118	C₂×#121	C₃×C₄	1	2	yes	—
119	C₂×#121	C₃×C₄	1	2	yes	—
120	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
121	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
122	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
123	#436	C₂²×C₃	1	16	yes	complemented
124	#435	C₂²×C₃	1	32	yes	complemented
125	C₈×D₄	C₂²×C₃	1	16	yes	complemented
126	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₄⋊C₈	C₂²×C₃	1	2	yes	—
128	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
129	C₂×C₄⋊C₈	C₂²×C₃	1	8	yes	complemented
130	#408	C₂²×C₃	1	16	yes	complemented
131	C₂×C₂²⋊C₈	C₂²×C₃	1	4	yes	—
132	C₂×C₂²⋊C₈	C₂²×C₃	1	4	yes	—
133	C₄×M₁₆	C₂²×C₃	1	8	yes	complemented
134	C₂×#97	C₂²×C₃	1	2	yes	—
135	C₂×C₄×C₈	C₂²×C₃	1	2	yes	—
136	C₂⁴×C₃	C₂²×C₄	1	4	yes	—
137	C₂⁴×C₃	C₂²×C₄	1	1	yes	characteristic
138	C₃×#41	—	2	32	no	—
139	C₃×#41	—	2	16	no	—
140	C₃×#41	—	2	16	no	—
141	C₂×C₃×Q₈	—	2	8	no	—
142	C₂×C₃×Q₈	C₂²×C₄	1	8	yes	—
143	C₂×C₃×D₄	—	2	16	no	—
144	C₂×C₃×D₄	—	2	8	no	—
145	C₂×C₃×D₄	—	2	8	no	—
146	C₂×C₃×D₄	—	4	4	no	—
147	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
148	C₂×C₃×D₄	C₂²×C₄	1	16	yes	—
149	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
150	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
151	C₂²×C₃×C₄	—	2	4	no	—
152	C₂²×C₃×C₄	—	2	8	no	—
153	C₂²×C₃×C₄	—	2	8	no	—
154	C₂²×C₃×C₄	—	4	2	no	—
155	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
159	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
160	C₂²×C₃×C₄	C₂²×C₄	1	8	yes	—
161	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
162	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
164	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
166	C₂²×C₃×C₄	#41	1	4	yes	—
167	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
168	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
169	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
170	C₃×M₁₆	—	2	8	no	—
171	C₃×M₁₆	—	2	32	no	—
172	C₃×M₁₆	C₂×D₄	1	16	yes	complemented
173	C₂×C₃×C₈	—	2	4	no	—
174	C₂×C₃×C₈	—	2	4	no	—
175	C₂×C₃×C₈	—	2	16	no	—
176	C₂×C₃×C₈	—	2	4	no	—
177	C₂×C₃×C₈	—	2	32	no	—
178	C₂×C₃×C₈	C₂×D₄	1	8	yes	—
179	C₂×C₃×C₈	C₂⁴	1	4	yes	—
180	C₂×C₃×C₈	C₂⁴	1	4	yes	—
181	C₂×C₃×C₈	C₂⁴	1	4	yes	—
182	C₂×C₃×C₈	C₂⁴	1	4	yes	—
183	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
184	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
185	C₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
186	C₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
187	C₃×C₄²	C₂²×C₄	1	2	yes	—
188	C₃×C₄²	C₂²×C₄	1	2	yes	—
189	C₃×C₄²	C₂²×C₄	1	4	yes	—
190	C₃×C₄²	C₂²×C₄	1	4	yes	—
191	C₃×C₄²	C₂⁴	1	2	yes	—
192	C₃×C₄²	C₂⁴	1	2	yes	—
193	C₂×#41	—	2	8	no	—
194	C₂×#41	—	2	8	no	—
195	C₂×#41	C₂×C₃×C₄	1	8	yes	—
196	C₂×#41	C₂³×C₃	1	8	yes	—
197	C₂²×Q₈	C₂×C₃×C₄	1	2	yes	—
198	C₂²×D₄	C₂×C₃×C₄	1	2	yes	—
199	C₂²×D₄	C₂×C₃×C₄	1	4	yes	—
200	C₂²×D₄	C₂×C₃×C₄	1	2	yes	—
201	C₂²×D₄	C₂×C₃×C₄	1	2	yes	—
202	C₂³×C₄	C₂×C₃×C₄	1	1	yes	characteristic
203	C₂³×C₄	C₂×C₃×C₄	1	1	yes	characteristic
204	C₂³×C₄	C₂³×C₃	1	4	yes	—
205	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
206	#131	—	2	64	no	—
207	C₂×M₁₆	—	2	4	no	—
208	C₂×M₁₆	—	2	16	no	—
209	C₂×M₁₆	C₃×D₄	1	8	yes	complemented
210	C₂×M₁₆	C₂³×C₃	1	16	yes	—
211	C₂×M₁₆	C₂³×C₃	1	4	yes	—
212	C₂×M₁₆	C₂³×C₃	1	4	yes	—
213	C₂²×C₈	—	2	8	no	—
214	C₂²×C₈	—	2	16	no	—
215	C₂²×C₈	C₂³×C₃	1	2	yes	—
216	C₂²×C₈	C₂³×C₃	1	2	yes	—
217	C₂²×C₈	C₂³×C₃	1	8	yes	—
218	C₂²×C₈	C₂³×C₃	1	16	yes	—
219	C₂²×C₈	C₂³×C₃	1	2	yes	—
220	C₂²×C₈	C₂³×C₃	1	2	yes	—
221	C₄⋊Q₈	C₂×C₃×C₄	1	8	yes	—
222	#127	C₂×C₃×C₄	1	8	yes	—
223	#124	C₂×C₃×C₄	1	16	yes	—
224	#121	C₂×C₃×C₄	1	16	yes	—
225	#121	C₂×C₃×C₄	1	16	yes	—
226	C₄×D₄	C₂×C₃×C₄	1	8	yes	—
227	C₄×D₄	C₂×C₃×C₄	1	8	yes	—
228	C₄×D₄	C₂³×C₃	1	8	yes	—
229	C₄×D₄	C₂³×C₃	1	8	yes	—
230	C₂×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
231	C₂×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
232	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	4	yes	—
233	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	4	yes	—
234	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
235	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
236	C₂×C₄²	C₂×C₃×C₄	1	4	yes	—
237	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
238	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
239	C₂×C₄²	C₂³×C₃	1	4	yes	—
240	C₄⋊C₈	C₂³×C₃	1	4	yes	—
241	C₄⋊C₈	C₂³×C₃	1	8	yes	—
242	C₄⋊C₈	C₂³×C₃	1	4	yes	—
243	C₂²⋊C₈	C₂³×C₃	1	16	yes	—
244	C₂²⋊C₈	C₂³×C₃	1	16	yes	—
245	#97	C₂³×C₃	1	8	yes	—
246	C₄×C₈	C₂³×C₃	1	8	yes	—
247	C₂³×C₃	—	2	2	no	—
248	C₂³×C₃	—	2	2	no	—
249	C₂³×C₃	—	2	8	no	—
250	C₂³×C₃	—	2	8	no	—
251	C₂³×C₃	—	2	8	no	—
252	C₂³×C₃	C₄×D₄	1	4	yes	—
253	C₂³×C₃	C₂³×C₄	1	8	yes	—
254	C₂³×C₃	C₂³×C₄	1	2	yes	—
255	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
256	C₃×Q₈	—	2	16	no	—
257	C₃×D₄	—	2	32	no	—
258	C₃×D₄	—	2	16	no	—
259	C₃×D₄	—	2	16	no	—
260	C₃×D₄	—	4	8	no	—
261	C₂×C₃×C₄	—	2	8	no	—
262	C₂×C₃×C₄	—	2	2	no	—
263	C₂×C₃×C₄	—	2	2	no	—
264	C₂×C₃×C₄	—	2	2	no	—
265	C₂×C₃×C₄	—	2	16	no	—
266	C₂×C₃×C₄	—	2	8	no	—
267	C₂×C₃×C₄	—	2	8	no	—
268	C₂×C₃×C₄	—	2	8	no	—
269	C₂×C₃×C₄	—	4	4	no	—
270	C₂×C₃×C₄	C₄×D₄	1	4	yes	—
271	C₂×C₃×C₄	C₄×D₄	1	8	yes	—
272	C₂×C₃×C₄	#131	1	4	yes	complemented
273	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
274	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
275	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
276	C₂×C₃×C₄	C₂³×C₄	1	8	yes	—
277	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
278	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
279	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
280	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
281	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
282	C₂×C₃×C₄	C₂×#41	1	2	yes	—
283	C₂×C₃×C₄	C₂×#41	1	4	yes	—
284	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
285	C₃×C₈	—	2	4	no	—
286	C₃×C₈	—	2	4	no	—
287	C₃×C₈	—	2	4	no	—
288	C₃×C₈	C₂²×D₄	1	8	yes	—
289	C₂⁴	C₂²×C₃×C₄	1	4	yes	—
290	C₂⁴	C₂²×C₃×C₄	1	1	yes	characteristic
291	#41	—	2	32	no	—
292	#41	—	2	16	no	—
293	#41	—	2	16	no	—
294	C₂×Q₈	—	2	8	no	—
295	C₂×Q₈	C₂²×C₃×C₄	1	8	yes	—
296	C₂×D₄	—	2	16	no	—
297	C₂×D₄	—	2	8	no	—
298	C₂×D₄	—	2	8	no	—
299	C₂×D₄	—	4	4	no	—
300	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
301	C₂×D₄	C₂²×C₃×C₄	1	16	yes	—
302	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
303	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	8	no	—
306	C₂²×C₄	—	2	8	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
309	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
310	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
311	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
312	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
313	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	—
314	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
315	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
316	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
317	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
318	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
319	C₂²×C₄	C₃×#41	1	4	yes	—
320	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
321	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
322	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
323	M₁₆	—	2	8	no	—
324	M₁₆	—	2	32	no	—
325	M₁₆	C₂×C₃×D₄	1	16	yes	complemented
326	C₂×C₈	—	2	4	no	—
327	C₂×C₈	—	2	4	no	—
328	C₂×C₈	—	2	16	no	—
329	C₂×C₈	—	2	4	no	—
330	C₂×C₈	—	2	32	no	—
331	C₂×C₈	C₂×C₃×D₄	1	8	yes	—
332	C₂×C₈	C₂⁴×C₃	1	4	yes	—
333	C₂×C₈	C₂⁴×C₃	1	4	yes	—
334	C₂×C₈	C₂⁴×C₃	1	4	yes	—
335	C₂×C₈	C₂⁴×C₃	1	4	yes	—
336	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
337	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
338	C₂²⋊C₄	C₂²×C₃×C₄	1	16	yes	—
339	C₂²⋊C₄	C₂²×C₃×C₄	1	16	yes	—
340	C₄²	C₂²×C₃×C₄	1	2	yes	—
341	C₄²	C₂²×C₃×C₄	1	2	yes	—
342	C₄²	C₂²×C₃×C₄	1	4	yes	—
343	C₄²	C₂²×C₃×C₄	1	4	yes	—
344	C₄²	C₂⁴×C₃	1	2	yes	—
345	C₄²	C₂⁴×C₃	1	2	yes	—
346	C₂²×C₃	—	2	8	no	—
347	C₂²×C₃	—	2	2	no	—
348	C₂²×C₃	—	2	2	no	—
349	C₂²×C₃	—	2	8	no	—
350	C₂²×C₃	—	2	8	no	—
351	C₂²×C₃	—	2	8	no	—
352	C₂²×C₃	—	4	16	no	—
353	C₂²×C₃	C₂×C₄×D₄	1	4	yes	—
354	C₂²×C₃	C₂×C₄×D₄	1	2	yes	—
355	C₂²×C₃	C₂×#131	1	2	yes	—
356	C₂²×C₃	#568	1	2	yes	—
357	C₂²×C₃	C₂⁴×C₄	1	1	yes	characteristic
358	C₃×C₄	—	2	8	no	—
359	C₃×C₄	—	2	2	no	—
360	C₃×C₄	—	2	2	no	—
361	C₃×C₄	—	2	2	no	—
362	C₃×C₄	C₂×C₄×D₄	1	2	yes	—
363	C₃×C₄	C₂×C₄×D₄	1	4	yes	—
364	C₃×C₄	C₂×#131	1	4	yes	complemented
365	C₃×C₄	C₂³×D₄	1	1	yes	characteristic
366	C₃×C₄	C₂²×#41	1	1	yes	characteristic
367	C₂³	—	2	2	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	2	8	no	—
370	C₂³	—	2	8	no	—
371	C₂³	—	2	8	no	—
372	C₂³	C₃×C₄×D₄	1	4	yes	—
373	C₂³	C₂³×C₃×C₄	1	8	yes	—
374	C₂³	C₂³×C₃×C₄	1	2	yes	—
375	C₂³	C₂³×C₃×C₄	1	1	yes	characteristic
376	Q₈	—	2	16	no	—
377	D₄	—	2	32	no	—
378	D₄	—	2	16	no	—
379	D₄	—	2	16	no	—
380	D₄	—	4	8	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	8	no	—
385	C₂×C₄	—	2	8	no	—
386	C₂×C₄	—	2	8	no	—
387	C₂×C₄	—	2	8	no	—
388	C₂×C₄	—	2	16	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	C₃×C₄×D₄	1	4	yes	—
391	C₂×C₄	C₃×C₄×D₄	1	8	yes	—
392	C₂×C₄	C₃×#131	1	4	yes	complemented
393	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
394	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
395	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
396	C₂×C₄	C₂³×C₃×C₄	1	8	yes	—
397	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
398	C₂×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
399	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
400	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
401	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
402	C₂×C₄	C₂×C₃×#41	1	2	yes	—
403	C₂×C₄	C₂×C₃×#41	1	4	yes	—
404	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
405	C₈	—	2	4	no	—
406	C₈	—	2	4	no	—
407	C₈	—	2	4	no	—
408	C₈	C₂²×C₃×D₄	1	8	yes	—
409	C₂×C₃	—	2	4	no	—
410	C₂×C₃	—	4	8	no	—
411	C₂×C₃	#2935	1	4	yes	direct product factor
412	C₂×C₃	C₂²×C₄×D₄	1	1	yes	characteristic
413	C₂×C₃	C₂²×#131	1	1	yes	characteristic
414	C₂×C₃	C₂×#568	1	1	yes	characteristic
415	C₂²	—	2	8	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	8	no	—
419	C₂²	—	2	8	no	—
420	C₂²	—	2	8	no	—
421	C₂²	—	4	16	no	—
422	C₂²	C₂×C₃×C₄×D₄	1	4	yes	—
423	C₂²	C₂×C₃×C₄×D₄	1	2	yes	—
424	C₂²	C₂×C₃×#131	1	2	yes	—
425	C₂²	C₃×#568	1	2	yes	—
426	C₂²	C₂⁴×C₃×C₄	1	1	yes	characteristic
427	C₄	—	2	8	no	—
428	C₄	—	2	2	no	—
429	C₄	—	2	2	no	—
430	C₄	—	2	2	no	—
431	C₄	C₂×C₃×C₄×D₄	1	2	yes	—
432	C₄	C₂×C₃×C₄×D₄	1	4	yes	—
433	C₄	C₂×C₃×#131	1	4	yes	complemented
434	C₄	C₂³×C₃×D₄	1	1	yes	characteristic
435	C₄	C₂²×C₃×#41	1	1	yes	characteristic
436	C₃	C₂×#2935	1	1	yes	characteristic, direct product factor, Sylow
437	C₂	—	2	4	no	—
438	C₂	—	4	8	no	—
439	C₂	C₃×#2935	1	4	yes	direct product factor
440	C₂	C₂²×C₃×C₄×D₄	1	1	yes	characteristic
441	C₂	C₂²×C₃×#131	1	1	yes	characteristic
442	C₂	C₂×C₃×#568	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	C₂⁴
commutator	C₂²	C₂⁴×C₃×C₄
Frattini, cosocle	C₂×C₄	C₂⁵×C₃
socle	C₂³×C₃	C₂³×C₄
prime radical	C₂×C₃×#532	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×#131	C₂	semidirect
3. C₃×#2935	C₂	direct (N × H)
4. C₂×C₃×#436	C₂	semidirect
5. C₂×C₃×#435	C₂	semidirect
6. C₂×C₃×C₈×D₄	C₂	semidirect
7. C₂²×C₃×C₄⋊C₈	C₂	semidirect
8. C₂×C₃×#408	C₂	semidirect
9. C₂×C₃×C₄×M₁₆	C₂	semidirect
10. C₂×#2935	C₃	direct (N × H)
13. C₂×C₃×#131	C₂²	semidirect
29. C₃×#436	C₂²	semidirect
30. C₃×#435	C₂²	semidirect
31. C₃×C₈×D₄	C₂²	semidirect
35. C₂×C₃×C₄⋊C₈	C₂²	semidirect
36. C₃×#408	C₂²	semidirect
39. C₃×C₄×M₁₆	C₂²	semidirect
42. C₂²×#131	C₂×C₃	semidirect
44. #2935	C₂×C₃	direct (N × H)
45. C₂×#436	C₂×C₃	semidirect
46. C₂×#435	C₂×C₃	semidirect
47. C₂×C₈×D₄	C₂×C₃	semidirect
48. C₂²×C₄⋊C₈	C₂×C₃	semidirect
49. C₂×#408	C₂×C₃	semidirect
50. C₂×C₄×M₁₆	C₂×C₃	semidirect
67. C₂×C₃×M₁₆	D₄	semidirect
107. C₂×#131	C₂²×C₃	semidirect
123. #436	C₂²×C₃	semidirect
124. #435	C₂²×C₃	semidirect
125. C₈×D₄	C₂²×C₃	semidirect
129. C₂×C₄⋊C₈	C₂²×C₃	semidirect
130. #408	C₂²×C₃	semidirect
133. C₄×M₁₆	C₂²×C₃	semidirect
172. C₃×M₁₆	C₂×D₄	semidirect
209. C₂×M₁₆	C₃×D₄	semidirect
272. C₂×C₃×C₄	#131	semidirect
325. M₁₆	C₂×C₃×D₄	semidirect
364. C₃×C₄	C₂×#131	semidirect
392. C₂×C₄	C₃×#131	semidirect
411. C₂×C₃	#2935	direct (N × H)
433. C₄	C₂×C₃×#131	semidirect
436. C₃	C₂×#2935	direct (N × H)
439. C₂	C₃×#2935	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×#131	2
C₂×C₃×#532	2
C₃×#2935	2
C₂×C₃×#436	2
C₂×C₃×#435	2
C₂×C₃×C₈×D₄	2
C₂²×C₃×C₄⋊C₈	2
C₂×C₃×#408	2
C₂×C₃×C₄×M₁₆	2
C₂×#2935	3

Subgroups — C2×C3×#2935 #10678746

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#2935 #10678746