Subgroups — C₂²×C₃×#435 #10678738

Order 768.

3350 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂³×C₃×C₄	C₂³
commutator	C₂²	C₂⁴×C₃×C₄
Frattini, cosocle	C₂×C₄	C₂⁵×C₃
socle	C₂⁴×C₃	C₂²×C₄
prime radical	C₂³×C₃×D₄	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×M₁₆	C₂	semidirect
2. C₂⁴×C₃×C₈	C₂	semidirect
4. C₂×C₃×#435	C₂	direct (N × H)
5. C₂²×C₃×C₄⋊C₈	C₂	semidirect
6. C₂²×C₃×C₂²⋊C₈	C₂	semidirect
7. C₂²×C₃×C₂²⋊C₈	C₂	semidirect
8. C₂²×C₃×#97	C₂	semidirect
9. C₂²×#435	C₃	direct (N × H)
14. C₂²×C₃×M₁₆	C₂²	semidirect
20. C₂³×C₃×C₈	C₂²	semidirect
27. C₃×#435	C₂²	direct (N × H)
28. C₂×C₃×C₄⋊C₈	C₂²	semidirect
29. C₂×C₃×C₂²⋊C₈	C₂²	semidirect
30. C₂×C₃×C₂²⋊C₈	C₂²	semidirect
31. C₂×C₃×#97	C₂²	semidirect
32. C₂³×M₁₆	C₂×C₃	semidirect
33. C₂⁴×C₈	C₂×C₃	semidirect
35. C₂×#435	C₂×C₃	direct (N × H)
36. C₂²×C₄⋊C₈	C₂×C₃	semidirect
37. C₂²×C₂²⋊C₈	C₂×C₃	semidirect
38. C₂²×C₂²⋊C₈	C₂×C₃	semidirect
39. C₂²×#97	C₂×C₃	semidirect
58. C₂×C₃×M₁₆	C₂³	semidirect
63. C₂²×C₃×C₈	D₄	semidirect
68. C₂²×C₃×C₈	C₂³	semidirect
76. C₃×C₄⋊C₈	C₂³	semidirect
77. C₃×C₂²⋊C₈	C₂³	semidirect
78. C₃×C₂²⋊C₈	C₂³	semidirect
79. C₃×#97	C₂³	semidirect
84. C₂²×M₁₆	C₂²×C₃	semidirect
90. C₂³×C₈	C₂²×C₃	semidirect
97. #435	C₂²×C₃	direct (N × H)
98. C₂×C₄⋊C₈	C₂²×C₃	semidirect
99. C₂×C₂²⋊C₈	C₂²×C₃	semidirect
100. C₂×C₂²⋊C₈	C₂²×C₃	semidirect
101. C₂×#97	C₂²×C₃	semidirect
107. C₂⁴×C₃	M₁₆	semidirect
140. C₂×C₃×C₈	C₂×D₄	semidirect
168. C₂×M₁₆	C₂³×C₃	semidirect
173. C₂²×C₈	C₃×D₄	semidirect
178. C₂²×C₈	C₂³×C₃	semidirect
186. C₄⋊C₈	C₂³×C₃	semidirect
187. C₂²⋊C₈	C₂³×C₃	semidirect
188. C₂²⋊C₈	C₂³×C₃	semidirect
189. #97	C₂³×C₃	semidirect
199. C₂³×C₃	C₂×M₁₆	semidirect
227. C₃×C₈	C₂²×D₄	semidirect
233. C₂⁴	C₃×M₁₆	semidirect
266. C₂×C₈	C₂×C₃×D₄	semidirect
283. C₂²×C₃	#435	direct (N × H)
286. C₂²×C₃	C₂²×M₁₆	semidirect
305. C₂³	C₂×C₃×M₁₆	semidirect
333. C₈	C₂²×C₃×D₄	semidirect
336. C₂×C₃	C₂×#435	direct (N × H)
347. C₂²	C₃×#435	direct (N × H)
350. C₂²	C₂²×C₃×M₁₆	semidirect
360. C₃	C₂²×#435	direct (N × H)
363. C₂	C₂×C₃×#435	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×M₁₆	2
C₂⁴×C₃×C₈	2
C₂²×C₃×C₄×D₄	2
C₂×C₃×#435	2
C₂²×C₃×C₄⋊C₈	2
C₂²×C₃×C₂²⋊C₈	2
C₂²×C₃×#97	2
C₂²×#435	3

Subgroups — C22×C3×#435 #10678738

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#435 #10678738