Subgroups — C₂×C₃×#2933 #10678744

Order 768.

2926 conjugacy classes of subgroups.

The subgroup lattice has 638 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	1	yes	maximal, characteristic, complemented
2	C₂³×C₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#525	C₂	1	1	yes	maximal, characteristic
4	C₃×#2933	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃×#436	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#435	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#435	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×C₈×D₄	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×#424	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×#408	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#2933	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
15	C₂⁴×C₃×C₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×#131	—	2	8	no	—
17	C₂×C₃×#131	C₂²	1	8	yes	complemented
18	C₂²×C₃×M₁₆	—	2	8	no	—
19	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₃×M₁₆	C₂²	1	2	yes	—
21	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₃×M₁₆	C₂²	1	8	yes	complemented
23	C₂²×C₃×M₁₆	C₂²	1	2	yes	complemented
24	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
25	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
26	C₂³×C₃×C₈	C₂²	1	2	yes	—
27	C₂³×C₃×C₈	C₂²	1	2	yes	complemented
28	C₃×#525	C₄	1	8	yes	—
29	C₃×#525	C₂²	1	8	yes	—
30	C₂×C₃×#123	C₄	1	2	yes	—
31	C₂×C₃×C₂²⋊Q₈	C₄	1	1	yes	characteristic
32	C₂×C₃×C₂²⋊Q₈	C₄	1	1	yes	characteristic
33	C₂×C₃×#121	C₄	1	1	yes	characteristic
34	C₂×C₃×#121	C₄	1	1	yes	characteristic
35	C₂×C₃×#120	C₄	1	2	yes	—
36	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
37	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
38	C₂×C₃×#117	C₂²	1	1	yes	characteristic
39	C₃×#436	C₂²	1	16	yes	complemented
40	C₃×#435	C₂²	1	16	yes	complemented
41	C₃×#435	C₂²	1	16	yes	complemented
42	C₃×C₈×D₄	C₂²	1	16	yes	complemented
43	C₃×#424	C₂²	1	8	yes	complemented
44	C₂×C₃×C₄⋊C₈	C₂²	1	2	yes	complemented
45	C₂×C₃×C₄⋊C₈	C₂²	1	2	yes	complemented
46	C₃×#408	C₂²	1	8	yes	complemented
47	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
49	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
50	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
51	C₂×C₃×C₂²⋊C₈	C₂²	1	8	yes	complemented
52	C₂×C₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
53	C₂×C₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
54	C₃×#405	C₂²	1	8	yes	complemented
55	C₂×C₃×#97	C₂²	1	2	yes	complemented
56	C₂×C₃×C₄×C₈	C₂²	1	2	yes	complemented
57	C₂²×#131	C₂×C₃	1	1	yes	characteristic, complemented
58	C₂³×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
59	C₂×#525	C₂×C₃	1	1	yes	characteristic
60	#2933	C₂×C₃	1	16	yes	direct product factor
61	C₂×#436	C₂×C₃	1	2	yes	complemented
62	C₂×#435	C₂×C₃	1	2	yes	complemented
63	C₂×#435	C₂×C₃	1	2	yes	complemented
64	C₂×C₈×D₄	C₂×C₃	1	2	yes	complemented
65	C₂×#424	C₂×C₃	1	1	yes	characteristic, complemented
66	C₂×#408	C₂×C₃	1	1	yes	characteristic, complemented
67	C₂²×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
68	C₂×#405	C₂×C₃	1	1	yes	characteristic, complemented
69	C₂⁵×C₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₃×#41	—	2	4	no	—
71	C₂×C₃×#41	—	2	4	no	—
72	C₂×C₃×#41	C₂×C₄	1	4	yes	—
73	C₂×C₃×#41	C₂³	1	4	yes	—
74	C₂²×C₃×Q₈	C₂×C₄	1	1	yes	characteristic
75	C₂²×C₃×D₄	C₂×C₄	1	2	yes	—
76	C₂²×C₃×D₄	C₂×C₄	1	1	yes	characteristic
77	C₂²×C₃×D₄	C₂×C₄	1	2	yes	—
78	C₂²×C₃×D₄	C₂×C₄	1	2	yes	—
79	C₂³×C₃×C₄	—	2	4	no	—
80	C₂³×C₃×C₄	—	2	4	no	—
81	C₂³×C₃×C₄	C₂×C₄	1	1	yes	characteristic
82	C₂³×C₃×C₄	C₂×C₄	1	1	yes	characteristic
83	C₂³×C₃×C₄	C₂×C₄	1	1	yes	characteristic
84	C₂³×C₃×C₄	C₂×C₄	1	4	yes	—
85	C₂³×C₃×C₄	C₂³	1	4	yes	—
86	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
87	C₂³×C₃×C₄	C₂³	1	2	yes	—
88	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
89	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
90	C₃×#131	—	2	32	no	—
91	C₂×C₃×M₁₆	—	2	4	no	—
92	C₂×C₃×M₁₆	—	2	32	no	—
93	C₂×C₃×M₁₆	—	2	8	no	—
94	C₂×C₃×M₁₆	—	2	8	no	—
95	C₂×C₃×M₁₆	D₄	1	8	yes	complemented
96	C₂×C₃×M₁₆	C₂³	1	4	yes	—
97	C₂×C₃×M₁₆	C₂³	1	8	yes	—
98	C₂×C₃×M₁₆	C₂³	1	4	yes	—
99	C₂×C₃×M₁₆	C₂³	1	8	yes	complemented
100	C₂²×C₃×C₈	—	2	4	no	—
101	C₂²×C₃×C₈	—	2	4	no	—
102	C₂²×C₃×C₈	—	2	8	no	—
103	C₂²×C₃×C₈	—	2	8	no	—
104	C₂²×C₃×C₈	C₂³	1	8	yes	—
105	C₂²×C₃×C₈	C₂³	1	4	yes	—
106	C₂²×C₃×C₈	C₂³	1	4	yes	—
107	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
108	C₂²×C₃×C₈	C₂³	1	2	yes	—
109	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
110	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
111	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
112	C₂²×C₃×C₈	C₂³	1	2	yes	—
113	C₂²×C₃×C₈	C₂³	1	8	yes	complemented
114	C₃×#123	C₂×C₄	1	16	yes	—
115	C₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
116	C₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
117	C₃×#121	C₂×C₄	1	8	yes	—
118	C₃×#121	C₂×C₄	1	8	yes	—
119	C₃×#120	C₂×C₄	1	16	yes	—
120	C₃×C₄×D₄	C₂×C₄	1	8	yes	—
121	C₃×C₄×D₄	C₂×C₄	1	8	yes	—
122	C₃×C₄×D₄	C₂³	1	8	yes	—
123	C₃×C₄×D₄	C₂³	1	8	yes	—
124	C₃×#117	C₂×C₄	1	4	yes	—
125	C₃×#117	C₂³	1	4	yes	—
126	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
127	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
128	C₂×C₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
129	C₂×C₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
130	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
131	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
132	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
133	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
134	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
135	C₂×C₃×C₄²	C₂³	1	2	yes	—
136	C₃×C₄⋊C₈	C₂³	1	8	yes	complemented
137	C₃×C₄⋊C₈	C₂³	1	8	yes	complemented
138	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
139	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
140	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
141	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
142	C₃×C₂²⋊C₈	C₂³	1	8	yes	complemented
143	C₃×C₂²⋊C₈	C₂³	1	8	yes	complemented
144	C₃×#97	C₂³	1	8	yes	complemented
145	C₃×C₄×C₈	C₂³	1	8	yes	complemented
146	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
147	C₂⁴×C₄	C₂²×C₃	1	1	yes	characteristic
148	C₂×#131	—	2	8	no	—
149	C₂×#131	C₂²×C₃	1	8	yes	complemented
150	C₂²×M₁₆	—	2	8	no	—
151	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
152	C₂²×M₁₆	C₂²×C₃	1	2	yes	—
153	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
154	C₂²×M₁₆	C₂²×C₃	1	8	yes	complemented
155	C₂²×M₁₆	C₂²×C₃	1	2	yes	complemented
156	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
157	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
158	C₂³×C₈	C₂²×C₃	1	2	yes	—
159	C₂³×C₈	C₂²×C₃	1	2	yes	complemented
160	#525	C₃×C₄	1	8	yes	—
161	#525	C₂²×C₃	1	8	yes	—
162	C₂×#123	C₃×C₄	1	2	yes	—
163	C₂×C₂²⋊Q₈	C₃×C₄	1	1	yes	characteristic
164	C₂×C₂²⋊Q₈	C₃×C₄	1	1	yes	characteristic
165	C₂×#121	C₃×C₄	1	1	yes	characteristic
166	C₂×#121	C₃×C₄	1	1	yes	characteristic
167	C₂×#120	C₃×C₄	1	2	yes	—
168	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
169	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
170	C₂×#117	C₂²×C₃	1	1	yes	characteristic
171	#436	C₂²×C₃	1	16	yes	complemented
172	#435	C₂²×C₃	1	16	yes	complemented
173	#435	C₂²×C₃	1	16	yes	complemented
174	C₈×D₄	C₂²×C₃	1	16	yes	complemented
175	#424	C₂²×C₃	1	8	yes	complemented
176	C₂×C₄⋊C₈	C₂²×C₃	1	2	yes	complemented
177	C₂×C₄⋊C₈	C₂²×C₃	1	2	yes	complemented
178	#408	C₂²×C₃	1	8	yes	complemented
179	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
180	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
181	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
182	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
183	C₂×C₂²⋊C₈	C₂²×C₃	1	8	yes	complemented
184	C₂×C₂²⋊C₈	C₂²×C₃	1	2	yes	complemented
185	C₂×C₂²⋊C₈	C₂²×C₃	1	2	yes	complemented
186	#405	C₂²×C₃	1	8	yes	complemented
187	C₂×#97	C₂²×C₃	1	2	yes	complemented
188	C₂×C₄×C₈	C₂²×C₃	1	2	yes	complemented
189	C₂⁴×C₃	—	2	4	no	—
190	C₂⁴×C₃	—	2	4	no	—
191	C₂⁴×C₃	—	4	2	no	—
192	C₂⁴×C₃	C₂²×C₄	1	1	yes	characteristic
193	C₂⁴×C₃	C₂²×C₄	1	2	yes	—
194	C₂⁴×C₃	C₂²×C₄	1	4	yes	—
195	C₂⁴×C₃	C₂²×C₄	1	1	yes	characteristic
196	C₂⁴×C₃	C₂²×C₄	1	1	yes	characteristic
197	C₃×#41	—	2	16	no	—
198	C₃×#41	—	2	8	no	—
199	C₃×#41	—	2	8	no	—
200	C₂×C₃×Q₈	—	2	4	no	—
201	C₂×C₃×Q₈	C₂²×C₄	1	4	yes	—
202	C₂×C₃×D₄	—	2	8	no	—
203	C₂×C₃×D₄	—	2	8	no	—
204	C₂×C₃×D₄	—	2	4	no	—
205	C₂×C₃×D₄	—	4	4	no	—
206	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
207	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
208	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
209	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
210	C₂²×C₃×C₄	—	2	4	no	—
211	C₂²×C₃×C₄	—	2	4	no	—
212	C₂²×C₃×C₄	—	2	4	no	—
213	C₂²×C₃×C₄	—	2	16	no	—
214	C₂²×C₃×C₄	—	2	2	no	—
215	C₂²×C₃×C₄	—	2	4	no	—
216	C₂²×C₃×C₄	—	2	8	no	—
217	C₂²×C₃×C₄	—	2	2	no	—
218	C₂²×C₃×C₄	—	2	2	no	—
219	C₂²×C₃×C₄	—	2	2	no	—
220	C₂²×C₃×C₄	—	2	8	no	—
221	C₂²×C₃×C₄	—	2	4	no	—
222	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
223	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
224	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
225	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
226	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
227	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
228	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
229	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
230	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
231	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
232	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
233	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
234	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
235	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
236	C₂²×C₃×C₄	#41	1	4	yes	—
237	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
238	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
239	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
240	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
241	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
242	C₃×M₁₆	—	2	8	no	—
243	C₃×M₁₆	—	2	16	no	—
244	C₃×M₁₆	—	2	16	no	—
245	C₃×M₁₆	C₂×D₄	1	16	yes	complemented
246	C₂×C₃×C₈	—	2	2	no	—
247	C₂×C₃×C₈	—	2	2	no	—
248	C₂×C₃×C₈	—	2	4	no	—
249	C₂×C₃×C₈	—	2	8	no	—
250	C₂×C₃×C₈	—	2	2	no	—
251	C₂×C₃×C₈	—	2	2	no	—
252	C₂×C₃×C₈	—	2	8	no	—
253	C₂×C₃×C₈	—	2	16	no	—
254	C₂×C₃×C₈	—	2	16	no	—
255	C₂×C₃×C₈	C₂×D₄	1	8	yes	—
256	C₂×C₃×C₈	C₂⁴	1	2	yes	—
257	C₂×C₃×C₈	C₂⁴	1	2	yes	—
258	C₂×C₃×C₈	C₂⁴	1	2	yes	—
259	C₂×C₃×C₈	C₂⁴	1	2	yes	—
260	C₂×C₃×C₈	C₂⁴	1	4	yes	—
261	C₂×C₃×C₈	C₂⁴	1	4	yes	—
262	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
263	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
264	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
265	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
266	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
267	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
268	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
269	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
270	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
271	C₃×C₄²	C₂²×C₄	1	4	yes	—
272	C₃×C₄²	C₂⁴	1	4	yes	—
273	C₂⁵	C₂×C₃×C₄	1	1	yes	characteristic
274	C₂×#41	—	2	4	no	—
275	C₂×#41	—	2	4	no	—
276	C₂×#41	C₂×C₃×C₄	1	4	yes	—
277	C₂×#41	C₂³×C₃	1	4	yes	—
278	C₂²×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
279	C₂²×D₄	C₂×C₃×C₄	1	2	yes	—
280	C₂²×D₄	C₂×C₃×C₄	1	2	yes	—
281	C₂²×D₄	C₂×C₃×C₄	1	1	yes	characteristic
282	C₂²×D₄	C₂×C₃×C₄	1	2	yes	—
283	C₂³×C₄	—	2	4	no	—
284	C₂³×C₄	—	2	4	no	—
285	C₂³×C₄	C₂×C₃×C₄	1	1	yes	characteristic
286	C₂³×C₄	C₂×C₃×C₄	1	1	yes	characteristic
287	C₂³×C₄	C₂×C₃×C₄	1	1	yes	characteristic
288	C₂³×C₄	C₂×C₃×C₄	1	4	yes	—
289	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
290	C₂³×C₄	C₂³×C₃	1	2	yes	—
291	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
292	C₂³×C₄	C₂³×C₃	1	4	yes	—
293	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
294	#131	—	2	32	no	—
295	C₂×M₁₆	—	2	4	no	—
296	C₂×M₁₆	—	2	32	no	—
297	C₂×M₁₆	—	2	8	no	—
298	C₂×M₁₆	—	2	8	no	—
299	C₂×M₁₆	C₃×D₄	1	8	yes	complemented
300	C₂×M₁₆	C₂³×C₃	1	4	yes	—
301	C₂×M₁₆	C₂³×C₃	1	8	yes	—
302	C₂×M₁₆	C₂³×C₃	1	4	yes	—
303	C₂×M₁₆	C₂³×C₃	1	8	yes	complemented
304	C₂²×C₈	—	2	4	no	—
305	C₂²×C₈	—	2	4	no	—
306	C₂²×C₈	—	2	8	no	—
307	C₂²×C₈	—	2	8	no	—
308	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
309	C₂²×C₈	C₂³×C₃	1	2	yes	—
310	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
311	C₂²×C₈	C₂³×C₃	1	8	yes	—
312	C₂²×C₈	C₂³×C₃	1	4	yes	—
313	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
314	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
315	C₂²×C₈	C₂³×C₃	1	4	yes	—
316	C₂²×C₈	C₂³×C₃	1	2	yes	—
317	C₂²×C₈	C₂³×C₃	1	8	yes	complemented
318	#123	C₂×C₃×C₄	1	16	yes	—
319	C₂²⋊Q₈	C₂×C₃×C₄	1	8	yes	—
320	C₂²⋊Q₈	C₂×C₃×C₄	1	8	yes	—
321	#121	C₂×C₃×C₄	1	8	yes	—
322	#121	C₂×C₃×C₄	1	8	yes	—
323	#120	C₂×C₃×C₄	1	16	yes	—
324	C₄×D₄	C₂×C₃×C₄	1	8	yes	—
325	C₄×D₄	C₂×C₃×C₄	1	8	yes	—
326	C₄×D₄	C₂³×C₃	1	8	yes	—
327	C₄×D₄	C₂³×C₃	1	8	yes	—
328	#117	C₂×C₃×C₄	1	4	yes	—
329	#117	C₂³×C₃	1	4	yes	—
330	C₂×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
331	C₂×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
332	C₂×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
333	C₂×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
334	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
335	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
336	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
337	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
338	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
339	C₂×C₄²	C₂³×C₃	1	2	yes	—
340	C₄⋊C₈	C₂³×C₃	1	8	yes	complemented
341	C₄⋊C₈	C₂³×C₃	1	8	yes	complemented
342	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
343	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
344	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
345	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
346	C₂²⋊C₈	C₂³×C₃	1	8	yes	complemented
347	C₂²⋊C₈	C₂³×C₃	1	8	yes	complemented
348	#97	C₂³×C₃	1	8	yes	complemented
349	C₄×C₈	C₂³×C₃	1	8	yes	complemented
350	C₂³×C₃	—	2	2	no	—
351	C₂³×C₃	—	2	2	no	—
352	C₂³×C₃	—	2	2	no	—
353	C₂³×C₃	—	2	2	no	—
354	C₂³×C₃	—	2	8	no	—
355	C₂³×C₃	—	2	2	no	—
356	C₂³×C₃	—	2	4	no	—
357	C₂³×C₃	—	2	4	no	—
358	C₂³×C₃	—	2	2	no	—
359	C₂³×C₃	—	2	8	no	—
360	C₂³×C₃	—	2	2	no	—
361	C₂³×C₃	—	2	4	no	—
362	C₂³×C₃	—	4	4	no	—
363	C₂³×C₃	—	4	16	no	—
364	C₂³×C₃	C₄×D₄	1	4	yes	—
365	C₂³×C₃	#131	1	4	yes	complemented
366	C₂³×C₃	C₂³×C₄	1	2	yes	—
367	C₂³×C₃	C₂³×C₄	1	4	yes	—
368	C₂³×C₃	C₂³×C₄	1	2	yes	—
369	C₂³×C₃	C₂³×C₄	1	2	yes	—
370	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
371	C₃×Q₈	—	2	8	no	—
372	C₃×D₄	—	2	16	no	—
373	C₃×D₄	—	2	16	no	—
374	C₃×D₄	—	2	8	no	—
375	C₃×D₄	—	4	8	no	—
376	C₂×C₃×C₄	—	2	8	no	—
377	C₂×C₃×C₄	—	2	2	no	—
378	C₂×C₃×C₄	—	2	2	no	—
379	C₂×C₃×C₄	—	2	4	no	—
380	C₂×C₃×C₄	—	2	4	no	—
381	C₂×C₃×C₄	—	2	4	no	—
382	C₂×C₃×C₄	—	2	4	no	—
383	C₂×C₃×C₄	—	2	4	no	—
384	C₂×C₃×C₄	—	2	8	no	—
385	C₂×C₃×C₄	—	2	8	no	—
386	C₂×C₃×C₄	—	2	8	no	—
387	C₂×C₃×C₄	—	2	2	no	—
388	C₂×C₃×C₄	—	2	4	no	—
389	C₂×C₃×C₄	—	2	2	no	—
390	C₂×C₃×C₄	—	2	2	no	—
391	C₂×C₃×C₄	—	2	2	no	—
392	C₂×C₃×C₄	—	2	4	no	—
393	C₂×C₃×C₄	C₄×D₄	1	4	yes	—
394	C₂×C₃×C₄	C₄×D₄	1	8	yes	—
395	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
396	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
397	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
398	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
399	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
400	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
401	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
402	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
403	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
404	C₂×C₃×C₄	C₂×#41	1	2	yes	—
405	C₂×C₃×C₄	C₂×#41	1	4	yes	—
406	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
407	C₃×C₈	—	2	2	no	—
408	C₃×C₈	—	2	2	no	—
409	C₃×C₈	—	2	4	no	—
410	C₃×C₈	—	2	2	no	—
411	C₃×C₈	—	2	2	no	—
412	C₃×C₈	C₂²×D₄	1	8	yes	—
413	C₂⁴	—	2	4	no	—
414	C₂⁴	—	2	4	no	—
415	C₂⁴	—	4	2	no	—
416	C₂⁴	C₂²×C₃×C₄	1	1	yes	characteristic
417	C₂⁴	C₂²×C₃×C₄	1	2	yes	—
418	C₂⁴	C₂²×C₃×C₄	1	4	yes	—
419	C₂⁴	C₂²×C₃×C₄	1	1	yes	characteristic
420	C₂⁴	C₂²×C₃×C₄	1	1	yes	characteristic
421	#41	—	2	16	no	—
422	#41	—	2	8	no	—
423	#41	—	2	8	no	—
424	C₂×Q₈	—	2	4	no	—
425	C₂×Q₈	C₂²×C₃×C₄	1	4	yes	—
426	C₂×D₄	—	2	8	no	—
427	C₂×D₄	—	2	8	no	—
428	C₂×D₄	—	2	4	no	—
429	C₂×D₄	—	4	4	no	—
430	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
431	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
432	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
433	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	16	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	2	8	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	8	no	—
445	C₂²×C₄	—	2	4	no	—
446	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
447	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
448	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
449	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
450	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
451	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
452	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
453	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
454	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
455	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
456	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
457	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
458	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
459	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
460	C₂²×C₄	C₃×#41	1	4	yes	—
461	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
462	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
463	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
464	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
465	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
466	M₁₆	—	2	8	no	—
467	M₁₆	—	2	16	no	—
468	M₁₆	—	2	16	no	—
469	M₁₆	C₂×C₃×D₄	1	16	yes	complemented
470	C₂×C₈	—	2	2	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	2	4	no	—
473	C₂×C₈	—	2	8	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	2	8	no	—
477	C₂×C₈	—	2	16	no	—
478	C₂×C₈	—	2	16	no	—
479	C₂×C₈	C₂×C₃×D₄	1	8	yes	—
480	C₂×C₈	C₂⁴×C₃	1	2	yes	—
481	C₂×C₈	C₂⁴×C₃	1	2	yes	—
482	C₂×C₈	C₂⁴×C₃	1	2	yes	—
483	C₂×C₈	C₂⁴×C₃	1	2	yes	—
484	C₂×C₈	C₂⁴×C₃	1	4	yes	—
485	C₂×C₈	C₂⁴×C₃	1	4	yes	—
486	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
487	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
488	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
489	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
490	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
491	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
492	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
493	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
494	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
495	C₄²	C₂²×C₃×C₄	1	4	yes	—
496	C₄²	C₂⁴×C₃	1	4	yes	—
497	C₂²×C₃	—	2	2	no	—
498	C₂²×C₃	—	2	8	no	—
499	C₂²×C₃	—	2	8	no	—
500	C₂²×C₃	—	2	2	no	—
501	C₂²×C₃	—	2	2	no	—
502	C₂²×C₃	—	2	2	no	—
503	C₂²×C₃	—	2	2	no	—
504	C₂²×C₃	—	2	4	no	—
505	C₂²×C₃	—	2	4	no	—
506	C₂²×C₃	—	2	2	no	—
507	C₂²×C₃	—	2	2	no	—
508	C₂²×C₃	—	2	4	no	—
509	C₂²×C₃	—	4	16	no	—
510	C₂²×C₃	—	4	8	no	—
511	C₂²×C₃	—	4	4	no	—
512	C₂²×C₃	C₂×C₄×D₄	1	4	yes	—
513	C₂²×C₃	C₂×C₄×D₄	1	2	yes	—
514	C₂²×C₃	C₂×#131	1	2	yes	—
515	C₂²×C₃	C₂×#131	1	4	yes	complemented
516	C₂²×C₃	#568	1	2	yes	—
517	C₂²×C₃	C₂⁴×C₄	1	1	yes	characteristic
518	C₃×C₄	—	2	2	no	—
519	C₃×C₄	—	2	2	no	—
520	C₃×C₄	—	2	4	no	—
521	C₃×C₄	—	2	4	no	—
522	C₃×C₄	—	2	4	no	—
523	C₃×C₄	C₂×C₄×D₄	1	2	yes	—
524	C₃×C₄	C₂×C₄×D₄	1	4	yes	—
525	C₃×C₄	C₂³×D₄	1	1	yes	characteristic
526	C₃×C₄	C₂²×#41	1	1	yes	characteristic
527	C₂³	—	2	2	no	—
528	C₂³	—	2	2	no	—
529	C₂³	—	2	2	no	—
530	C₂³	—	2	2	no	—
531	C₂³	—	2	4	no	—
532	C₂³	—	2	2	no	—
533	C₂³	—	2	8	no	—
534	C₂³	—	2	2	no	—
535	C₂³	—	2	4	no	—
536	C₂³	—	2	8	no	—
537	C₂³	—	2	2	no	—
538	C₂³	—	2	4	no	—
539	C₂³	—	4	4	no	—
540	C₂³	—	4	16	no	—
541	C₂³	C₃×C₄×D₄	1	4	yes	—
542	C₂³	C₃×#131	1	4	yes	complemented
543	C₂³	C₂³×C₃×C₄	1	2	yes	—
544	C₂³	C₂³×C₃×C₄	1	4	yes	—
545	C₂³	C₂³×C₃×C₄	1	2	yes	—
546	C₂³	C₂³×C₃×C₄	1	2	yes	—
547	C₂³	C₂³×C₃×C₄	1	1	yes	characteristic
548	Q₈	—	2	8	no	—
549	D₄	—	2	16	no	—
550	D₄	—	2	16	no	—
551	D₄	—	2	8	no	—
552	D₄	—	4	8	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	2	8	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	4	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	4	no	—
567	C₂×C₄	—	2	8	no	—
568	C₂×C₄	—	2	8	no	—
569	C₂×C₄	—	2	8	no	—
570	C₂×C₄	C₃×C₄×D₄	1	4	yes	—
571	C₂×C₄	C₃×C₄×D₄	1	8	yes	—
572	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
573	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
574	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
575	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
576	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
577	C₂×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
578	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
579	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
580	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
581	C₂×C₄	C₂×C₃×#41	1	2	yes	—
582	C₂×C₄	C₂×C₃×#41	1	4	yes	—
583	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
584	C₈	—	2	2	no	—
585	C₈	—	2	2	no	—
586	C₈	—	2	4	no	—
587	C₈	—	2	2	no	—
588	C₈	—	2	2	no	—
589	C₈	C₂²×C₃×D₄	1	8	yes	—
590	C₂×C₃	—	2	4	no	—
591	C₂×C₃	—	2	4	no	—
592	C₂×C₃	—	4	4	no	—
593	C₂×C₃	—	4	2	no	—
594	C₂×C₃	#2933	1	4	yes	direct product factor
595	C₂×C₃	C₂²×C₄×D₄	1	1	yes	characteristic
596	C₂×C₃	C₂²×#131	1	1	yes	characteristic
597	C₂×C₃	C₂×#568	1	1	yes	characteristic
598	C₂²	—	2	2	no	—
599	C₂²	—	2	8	no	—
600	C₂²	—	2	8	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	2	4	no	—
606	C₂²	—	2	4	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	2	4	no	—
610	C₂²	—	4	16	no	—
611	C₂²	—	4	4	no	—
612	C₂²	—	4	8	no	—
613	C₂²	C₂×C₃×C₄×D₄	1	4	yes	—
614	C₂²	C₂×C₃×C₄×D₄	1	2	yes	—
615	C₂²	C₂×C₃×#131	1	2	yes	—
616	C₂²	C₂×C₃×#131	1	4	yes	complemented
617	C₂²	C₃×#568	1	2	yes	—
618	C₂²	C₂⁴×C₃×C₄	1	1	yes	characteristic
619	C₄	—	2	2	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	4	no	—
622	C₄	—	2	4	no	—
623	C₄	—	2	4	no	—
624	C₄	C₂×C₃×C₄×D₄	1	2	yes	—
625	C₄	C₂×C₃×C₄×D₄	1	4	yes	—
626	C₄	C₂³×C₃×D₄	1	1	yes	characteristic
627	C₄	C₂²×C₃×#41	1	1	yes	characteristic
628	C₃	C₂×#2933	1	1	yes	characteristic, direct product factor, Sylow
629	C₂	—	2	4	no	—
630	C₂	—	2	4	no	—
631	C₂	—	4	2	no	—
632	C₂	—	4	4	no	—
633	C₂	C₃×#2933	1	4	yes	direct product factor
634	C₂	C₂²×C₃×C₄×D₄	1	1	yes	characteristic
635	C₂	C₂²×C₃×#131	1	1	yes	characteristic
636	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×#525	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
2. C₂³×C₃×M₁₆	C₂	semidirect
4. C₃×#2933	C₂	direct (N × H)
5. C₂×C₃×#436	C₂	semidirect
6. C₂×C₃×#435	C₂	semidirect
7. C₂×C₃×#435	C₂	semidirect
8. C₂×C₃×C₈×D₄	C₂	semidirect
9. C₂×C₃×#424	C₂	semidirect
10. C₂×C₃×#408	C₂	semidirect
11. C₂²×C₃×C₂²⋊C₈	C₂	semidirect
12. C₂×C₃×#405	C₂	semidirect
13. C₂×#2933	C₃	direct (N × H)
17. C₂×C₃×#131	C₂²	semidirect
22. C₂²×C₃×M₁₆	C₂²	semidirect
23. C₂²×C₃×M₁₆	C₂²	semidirect
27. C₂³×C₃×C₈	C₂²	semidirect
39. C₃×#436	C₂²	semidirect
40. C₃×#435	C₂²	semidirect
41. C₃×#435	C₂²	semidirect
42. C₃×C₈×D₄	C₂²	semidirect
43. C₃×#424	C₂²	semidirect
44. C₂×C₃×C₄⋊C₈	C₂²	semidirect
45. C₂×C₃×C₄⋊C₈	C₂²	semidirect
46. C₃×#408	C₂²	semidirect
51. C₂×C₃×C₂²⋊C₈	C₂²	semidirect
52. C₂×C₃×C₂²⋊C₈	C₂²	semidirect
53. C₂×C₃×C₂²⋊C₈	C₂²	semidirect
54. C₃×#405	C₂²	semidirect
55. C₂×C₃×#97	C₂²	semidirect
56. C₂×C₃×C₄×C₈	C₂²	semidirect
57. C₂²×#131	C₂×C₃	semidirect
58. C₂³×M₁₆	C₂×C₃	semidirect
60. #2933	C₂×C₃	direct (N × H)
61. C₂×#436	C₂×C₃	semidirect
62. C₂×#435	C₂×C₃	semidirect
63. C₂×#435	C₂×C₃	semidirect
64. C₂×C₈×D₄	C₂×C₃	semidirect
65. C₂×#424	C₂×C₃	semidirect
66. C₂×#408	C₂×C₃	semidirect
67. C₂²×C₂²⋊C₈	C₂×C₃	semidirect
68. C₂×#405	C₂×C₃	semidirect
95. C₂×C₃×M₁₆	D₄	semidirect
99. C₂×C₃×M₁₆	C₂³	semidirect
113. C₂²×C₃×C₈	C₂³	semidirect
136. C₃×C₄⋊C₈	C₂³	semidirect
137. C₃×C₄⋊C₈	C₂³	semidirect
142. C₃×C₂²⋊C₈	C₂³	semidirect
143. C₃×C₂²⋊C₈	C₂³	semidirect
144. C₃×#97	C₂³	semidirect
145. C₃×C₄×C₈	C₂³	semidirect
149. C₂×#131	C₂²×C₃	semidirect
154. C₂²×M₁₆	C₂²×C₃	semidirect
155. C₂²×M₁₆	C₂²×C₃	semidirect
159. C₂³×C₈	C₂²×C₃	semidirect
171. #436	C₂²×C₃	semidirect
172. #435	C₂²×C₃	semidirect
173. #435	C₂²×C₃	semidirect
174. C₈×D₄	C₂²×C₃	semidirect
175. #424	C₂²×C₃	semidirect
176. C₂×C₄⋊C₈	C₂²×C₃	semidirect
177. C₂×C₄⋊C₈	C₂²×C₃	semidirect
178. #408	C₂²×C₃	semidirect
183. C₂×C₂²⋊C₈	C₂²×C₃	semidirect
184. C₂×C₂²⋊C₈	C₂²×C₃	semidirect
185. C₂×C₂²⋊C₈	C₂²×C₃	semidirect
186. #405	C₂²×C₃	semidirect
187. C₂×#97	C₂²×C₃	semidirect
188. C₂×C₄×C₈	C₂²×C₃	semidirect
245. C₃×M₁₆	C₂×D₄	semidirect
299. C₂×M₁₆	C₃×D₄	semidirect
303. C₂×M₁₆	C₂³×C₃	semidirect
317. C₂²×C₈	C₂³×C₃	semidirect
340. C₄⋊C₈	C₂³×C₃	semidirect
341. C₄⋊C₈	C₂³×C₃	semidirect
346. C₂²⋊C₈	C₂³×C₃	semidirect
347. C₂²⋊C₈	C₂³×C₃	semidirect
348. #97	C₂³×C₃	semidirect
349. C₄×C₈	C₂³×C₃	semidirect
365. C₂³×C₃	#131	semidirect
469. M₁₆	C₂×C₃×D₄	semidirect
515. C₂²×C₃	C₂×#131	semidirect
542. C₂³	C₃×#131	semidirect
594. C₂×C₃	#2933	direct (N × H)
616. C₂²	C₂×C₃×#131	semidirect
628. C₃	C₂×#2933	direct (N × H)
633. C₂	C₃×#2933	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
C₂³×C₃×M₁₆	2
C₂×C₃×#525	2
C₃×#2933	2
C₂×C₃×#436	2
C₂×C₃×#435	2
C₂×C₃×C₈×D₄	2
C₂×C₃×#424	2
C₂×C₃×#408	2
C₂²×C₃×C₂²⋊C₈	2
C₂×C₃×#405	2
C₂×#2933	3

Subgroups — C2×C3×#2933 #10678744

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#2933 #10678744