Subgroups — C₂×C₃×#2929 #10678740

Order 768.

3046 conjugacy classes of subgroups.

The subgroup lattice has 488 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	C₂⁴×C₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#525	C₂	1	1	yes	maximal, characteristic
4	C₃×#2929	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃×#435	C₂	1	4	yes	maximal, complemented
6	C₂×C₃×C₈×D₄	C₂	1	4	yes	maximal, complemented
7	C₂×C₃×#424	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#408	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#407	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#2929	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
13	C₂⁴×C₃×C₄	C₂²	1	1	yes	characteristic
14	C₂×C₃×#131	—	2	8	no	—
15	C₂×C₃×#131	C₂²	1	8	yes	complemented
16	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₃×M₁₆	C₂²	1	2	yes	complemented
19	C₂³×C₃×C₈	—	2	8	no	—
20	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
21	C₂³×C₃×C₈	C₂²	1	2	yes	—
22	C₂³×C₃×C₈	C₂²	1	2	yes	—
23	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
24	C₂³×C₃×C₈	C₂²	1	8	yes	complemented
25	C₂³×C₃×C₈	C₂²	1	2	yes	complemented
26	C₃×#525	C₄	1	8	yes	—
27	C₃×#525	C₂²	1	8	yes	—
28	C₂×C₃×#123	C₄	1	2	yes	—
29	C₂×C₃×C₂²⋊Q₈	C₄	1	2	yes	—
30	C₂×C₃×#121	C₄	1	2	yes	—
31	C₂×C₃×#120	C₄	1	2	yes	—
32	C₂×C₃×C₄×D₄	C₂²	1	4	yes	—
33	C₂×C₃×#117	C₂²	1	1	yes	characteristic
34	C₃×#435	C₂²	1	32	yes	complemented
35	C₃×C₈×D₄	C₂²	1	32	yes	complemented
36	C₃×#424	C₂²	1	8	yes	complemented
37	C₂×C₃×C₄⋊C₈	C₂²	1	4	yes	complemented
38	C₃×#408	C₂²	1	8	yes	complemented
39	C₃×#407	C₂²	1	8	yes	complemented
40	C₂×C₃×C₂²⋊C₈	C₂²	1	4	yes	—
41	C₂×C₃×C₂²⋊C₈	C₂²	1	4	yes	complemented
42	C₃×#405	C₂²	1	8	yes	complemented
43	C₂×C₃×#97	C₂²	1	2	yes	complemented
44	C₂×C₃×C₄×C₈	C₂²	1	2	yes	complemented
45	C₂²×#131	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂⁴×C₈	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂×#525	C₂×C₃	1	1	yes	characteristic
48	#2929	C₂×C₃	1	16	yes	direct product factor
49	C₂×#435	C₂×C₃	1	4	yes	complemented
50	C₂×C₈×D₄	C₂×C₃	1	4	yes	complemented
51	C₂×#424	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂×#408	C₂×C₃	1	1	yes	characteristic, complemented
53	C₂×#407	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂×#405	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂⁵×C₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₃×#41	—	2	4	no	—
57	C₂×C₃×#41	—	2	4	no	—
58	C₂×C₃×#41	C₂×C₄	1	4	yes	—
59	C₂×C₃×#41	C₂³	1	4	yes	—
60	C₂²×C₃×Q₈	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₃×D₄	C₂×C₄	1	2	yes	—
62	C₂²×C₃×D₄	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₃×D₄	C₂×C₄	1	4	yes	—
64	C₂³×C₃×C₄	—	2	4	no	—
65	C₂³×C₃×C₄	—	2	4	no	—
66	C₂³×C₃×C₄	C₂×C₄	1	2	yes	—
67	C₂³×C₃×C₄	C₂×C₄	1	1	yes	characteristic
68	C₂³×C₃×C₄	C₂×C₄	1	4	yes	—
69	C₂³×C₃×C₄	C₂³	1	2	yes	—
70	C₂³×C₃×C₄	C₂³	1	4	yes	—
71	C₂³×C₃×C₄	C₂³	1	2	yes	—
72	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
73	C₃×#131	—	2	32	no	—
74	C₂×C₃×M₁₆	—	2	4	no	—
75	C₂×C₃×M₁₆	—	2	4	no	—
76	C₂×C₃×M₁₆	—	2	8	no	—
77	C₂×C₃×M₁₆	C₂³	1	4	yes	—
78	C₂×C₃×M₁₆	C₂³	1	4	yes	—
79	C₂×C₃×M₁₆	C₂³	1	8	yes	complemented
80	C₂²×C₃×C₈	—	2	4	no	—
81	C₂²×C₃×C₈	—	2	8	no	—
82	C₂²×C₃×C₈	—	2	8	no	—
83	C₂²×C₃×C₈	—	2	8	no	—
84	C₂²×C₃×C₈	—	2	32	no	—
85	C₂²×C₃×C₈	D₄	1	8	yes	complemented
86	C₂²×C₃×C₈	C₂³	1	2	yes	—
87	C₂²×C₃×C₈	C₂³	1	4	yes	—
88	C₂²×C₃×C₈	C₂³	1	8	yes	—
89	C₂²×C₃×C₈	C₂³	1	8	yes	—
90	C₂²×C₃×C₈	C₂³	1	2	yes	—
91	C₂²×C₃×C₈	C₂³	1	2	yes	—
92	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
93	C₂²×C₃×C₈	C₂³	1	4	yes	—
94	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
95	C₂²×C₃×C₈	C₂³	1	8	yes	complemented
96	C₃×#123	C₂×C₄	1	16	yes	—
97	C₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
98	C₃×#121	C₂×C₄	1	16	yes	—
99	C₃×#120	C₂×C₄	1	16	yes	—
100	C₃×C₄×D₄	C₂×C₄	1	16	yes	—
101	C₃×C₄×D₄	C₂³	1	16	yes	—
102	C₃×#117	C₂×C₄	1	4	yes	—
103	C₃×#117	C₂³	1	4	yes	—
104	C₂×C₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
105	C₂×C₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
106	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
107	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
108	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
109	C₂×C₃×C₄²	C₂³	1	2	yes	—
110	C₃×C₄⋊C₈	C₂³	1	16	yes	complemented
111	C₃×C₂²⋊C₈	C₂³	1	16	yes	—
112	C₃×C₂²⋊C₈	C₂³	1	16	yes	complemented
113	C₃×#97	C₂³	1	8	yes	complemented
114	C₃×C₄×C₈	C₂³	1	8	yes	complemented
115	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
116	C₂⁴×C₄	C₂²×C₃	1	1	yes	characteristic
117	C₂×#131	—	2	8	no	—
118	C₂×#131	C₂²×C₃	1	8	yes	complemented
119	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
120	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
121	C₂²×M₁₆	C₂²×C₃	1	2	yes	complemented
122	C₂³×C₈	—	2	8	no	—
123	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
124	C₂³×C₈	C₂²×C₃	1	2	yes	—
125	C₂³×C₈	C₂²×C₃	1	2	yes	—
126	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
127	C₂³×C₈	C₂²×C₃	1	8	yes	complemented
128	C₂³×C₈	C₂²×C₃	1	2	yes	complemented
129	#525	C₃×C₄	1	8	yes	—
130	#525	C₂²×C₃	1	8	yes	—
131	C₂×#123	C₃×C₄	1	2	yes	—
132	C₂×C₂²⋊Q₈	C₃×C₄	1	2	yes	—
133	C₂×#121	C₃×C₄	1	2	yes	—
134	C₂×#120	C₃×C₄	1	2	yes	—
135	C₂×C₄×D₄	C₂²×C₃	1	4	yes	—
136	C₂×#117	C₂²×C₃	1	1	yes	characteristic
137	#435	C₂²×C₃	1	32	yes	complemented
138	C₈×D₄	C₂²×C₃	1	32	yes	complemented
139	#424	C₂²×C₃	1	8	yes	complemented
140	C₂×C₄⋊C₈	C₂²×C₃	1	4	yes	complemented
141	#408	C₂²×C₃	1	8	yes	complemented
142	#407	C₂²×C₃	1	8	yes	complemented
143	C₂×C₂²⋊C₈	C₂²×C₃	1	4	yes	—
144	C₂×C₂²⋊C₈	C₂²×C₃	1	4	yes	complemented
145	#405	C₂²×C₃	1	8	yes	complemented
146	C₂×#97	C₂²×C₃	1	2	yes	complemented
147	C₂×C₄×C₈	C₂²×C₃	1	2	yes	complemented
148	C₂⁴×C₃	—	2	4	no	—
149	C₂⁴×C₃	—	2	8	no	—
150	C₂⁴×C₃	C₂²×C₄	1	4	yes	—
151	C₂⁴×C₃	C₂²×C₄	1	2	yes	—
152	C₂⁴×C₃	C₂²×C₄	1	1	yes	characteristic
153	C₂⁴×C₃	C₂²×C₄	1	2	yes	—
154	C₃×#41	—	2	16	no	—
155	C₃×#41	—	2	8	no	—
156	C₃×#41	—	2	8	no	—
157	C₂×C₃×Q₈	—	2	4	no	—
158	C₂×C₃×Q₈	C₂²×C₄	1	4	yes	—
159	C₂×C₃×D₄	—	2	8	no	—
160	C₂×C₃×D₄	—	2	16	no	—
161	C₂×C₃×D₄	—	2	4	no	—
162	C₂×C₃×D₄	C₂²×C₄	1	16	yes	—
163	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
164	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
165	C₂²×C₃×C₄	—	2	4	no	—
166	C₂²×C₃×C₄	—	2	8	no	—
167	C₂²×C₃×C₄	—	2	16	no	—
168	C₂²×C₃×C₄	—	2	4	no	—
169	C₂²×C₃×C₄	—	2	8	no	—
170	C₂²×C₃×C₄	—	2	4	no	—
171	C₂²×C₃×C₄	—	2	4	no	—
172	C₂²×C₃×C₄	—	2	8	no	—
173	C₂²×C₃×C₄	—	2	4	no	—
174	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
175	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
176	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
177	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
178	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
179	C₂²×C₃×C₄	C₂²×C₄	1	8	yes	—
180	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
181	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
183	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
184	C₂²×C₃×C₄	#41	1	4	yes	—
185	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
186	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
187	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
188	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
189	C₃×M₁₆	—	2	8	no	—
190	C₃×M₁₆	—	2	8	no	—
191	C₃×M₁₆	—	2	16	no	—
192	C₂×C₃×C₈	—	2	4	no	—
193	C₂×C₃×C₈	—	2	8	no	—
194	C₂×C₃×C₈	—	2	4	no	—
195	C₂×C₃×C₈	—	2	4	no	—
196	C₂×C₃×C₈	—	2	16	no	—
197	C₂×C₃×C₈	—	2	16	no	—
198	C₂×C₃×C₈	—	2	16	no	—
199	C₂×C₃×C₈	C₂×D₄	1	4	yes	—
200	C₂×C₃×C₈	C₂×D₄	1	4	yes	—
201	C₂×C₃×C₈	C₂×D₄	1	16	yes	complemented
202	C₂×C₃×C₈	C₂⁴	1	4	yes	—
203	C₂×C₃×C₈	C₂⁴	1	4	yes	—
204	C₂×C₃×C₈	C₂⁴	1	4	yes	—
205	C₂×C₃×C₈	C₂⁴	1	2	yes	—
206	C₂×C₃×C₈	C₂⁴	1	2	yes	—
207	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
208	C₃×C₄⋊C₄	C₂²×C₄	1	16	yes	—
209	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
210	C₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
211	C₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
212	C₃×C₄²	C₂²×C₄	1	4	yes	—
213	C₃×C₄²	C₂⁴	1	4	yes	—
214	C₂⁵	C₂×C₃×C₄	1	1	yes	characteristic
215	C₂×#41	—	2	4	no	—
216	C₂×#41	—	2	4	no	—
217	C₂×#41	C₂×C₃×C₄	1	4	yes	—
218	C₂×#41	C₂³×C₃	1	4	yes	—
219	C₂²×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
220	C₂²×D₄	C₂×C₃×C₄	1	4	yes	—
221	C₂²×D₄	C₂×C₃×C₄	1	2	yes	—
222	C₂²×D₄	C₂×C₃×C₄	1	1	yes	characteristic
223	C₂³×C₄	—	2	4	no	—
224	C₂³×C₄	—	2	4	no	—
225	C₂³×C₄	C₂×C₃×C₄	1	2	yes	—
226	C₂³×C₄	C₂×C₃×C₄	1	1	yes	characteristic
227	C₂³×C₄	C₂×C₃×C₄	1	4	yes	—
228	C₂³×C₄	C₂³×C₃	1	2	yes	—
229	C₂³×C₄	C₂³×C₃	1	2	yes	—
230	C₂³×C₄	C₂³×C₃	1	4	yes	—
231	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
232	#131	—	2	32	no	—
233	C₂×M₁₆	—	2	4	no	—
234	C₂×M₁₆	—	2	4	no	—
235	C₂×M₁₆	—	2	8	no	—
236	C₂×M₁₆	C₂³×C₃	1	4	yes	—
237	C₂×M₁₆	C₂³×C₃	1	4	yes	—
238	C₂×M₁₆	C₂³×C₃	1	8	yes	complemented
239	C₂²×C₈	—	2	4	no	—
240	C₂²×C₈	—	2	8	no	—
241	C₂²×C₈	—	2	8	no	—
242	C₂²×C₈	—	2	8	no	—
243	C₂²×C₈	—	2	32	no	—
244	C₂²×C₈	C₃×D₄	1	8	yes	complemented
245	C₂²×C₈	C₂³×C₃	1	2	yes	—
246	C₂²×C₈	C₂³×C₃	1	4	yes	—
247	C₂²×C₈	C₂³×C₃	1	8	yes	—
248	C₂²×C₈	C₂³×C₃	1	8	yes	—
249	C₂²×C₈	C₂³×C₃	1	2	yes	—
250	C₂²×C₈	C₂³×C₃	1	2	yes	—
251	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
252	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
253	C₂²×C₈	C₂³×C₃	1	4	yes	—
254	C₂²×C₈	C₂³×C₃	1	8	yes	complemented
255	#123	C₂×C₃×C₄	1	16	yes	—
256	C₂²⋊Q₈	C₂×C₃×C₄	1	16	yes	—
257	#121	C₂×C₃×C₄	1	16	yes	—
258	#120	C₂×C₃×C₄	1	16	yes	—
259	C₄×D₄	C₂×C₃×C₄	1	16	yes	—
260	C₄×D₄	C₂³×C₃	1	16	yes	—
261	#117	C₂×C₃×C₄	1	4	yes	—
262	#117	C₂³×C₃	1	4	yes	—
263	C₂×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
264	C₂×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
265	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
266	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	4	yes	—
267	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	4	yes	—
268	C₂×C₄²	C₂³×C₃	1	2	yes	—
269	C₄⋊C₈	C₂³×C₃	1	16	yes	complemented
270	C₂²⋊C₈	C₂³×C₃	1	16	yes	—
271	C₂²⋊C₈	C₂³×C₃	1	16	yes	complemented
272	#97	C₂³×C₃	1	8	yes	complemented
273	C₄×C₈	C₂³×C₃	1	8	yes	complemented
274	C₂³×C₃	—	2	32	no	—
275	C₂³×C₃	—	2	8	no	—
276	C₂³×C₃	—	2	4	no	—
277	C₂³×C₃	—	2	4	no	—
278	C₂³×C₃	—	2	4	no	—
279	C₂³×C₃	—	2	16	no	—
280	C₂³×C₃	—	2	4	no	—
281	C₂³×C₃	—	2	8	no	—
282	C₂³×C₃	C₄×D₄	1	4	yes	—
283	C₂³×C₃	#131	1	8	yes	complemented
284	C₂³×C₃	C₂³×C₄	1	4	yes	—
285	C₂³×C₃	C₂³×C₄	1	2	yes	—
286	C₂³×C₃	C₂³×C₄	1	4	yes	—
287	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
288	C₃×Q₈	—	2	8	no	—
289	C₃×D₄	—	2	16	no	—
290	C₃×D₄	—	2	32	no	—
291	C₃×D₄	—	2	8	no	—
292	C₂×C₃×C₄	—	2	8	no	—
293	C₂×C₃×C₄	—	2	4	no	—
294	C₂×C₃×C₄	—	2	4	no	—
295	C₂×C₃×C₄	—	2	8	no	—
296	C₂×C₃×C₄	—	2	8	no	—
297	C₂×C₃×C₄	—	2	16	no	—
298	C₂×C₃×C₄	—	2	8	no	—
299	C₂×C₃×C₄	—	2	4	no	—
300	C₂×C₃×C₄	—	2	4	no	—
301	C₂×C₃×C₄	—	2	4	no	—
302	C₂×C₃×C₄	—	2	4	no	—
303	C₂×C₃×C₄	C₄×D₄	1	4	yes	—
304	C₂×C₃×C₄	C₄×D₄	1	8	yes	—
305	C₂×C₃×C₄	C₂³×C₄	1	8	yes	—
306	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
307	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
308	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
309	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
310	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
311	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
312	C₂×C₃×C₄	C₂×#41	1	2	yes	—
313	C₂×C₃×C₄	C₂×#41	1	4	yes	—
314	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
315	C₃×C₈	—	2	4	no	—
316	C₃×C₈	—	2	4	no	—
317	C₃×C₈	—	2	4	no	—
318	C₃×C₈	C₂²×D₄	1	4	yes	—
319	C₃×C₈	C₂²×D₄	1	4	yes	—
320	C₂⁴	—	2	4	no	—
321	C₂⁴	—	2	8	no	—
322	C₂⁴	C₂²×C₃×C₄	1	2	yes	—
323	C₂⁴	C₂²×C₃×C₄	1	4	yes	—
324	C₂⁴	C₂²×C₃×C₄	1	1	yes	characteristic
325	C₂⁴	C₂²×C₃×C₄	1	2	yes	—
326	#41	—	2	16	no	—
327	#41	—	2	8	no	—
328	#41	—	2	8	no	—
329	C₂×Q₈	—	2	4	no	—
330	C₂×Q₈	C₂²×C₃×C₄	1	4	yes	—
331	C₂×D₄	—	2	8	no	—
332	C₂×D₄	—	2	16	no	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	C₂²×C₃×C₄	1	16	yes	—
335	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
336	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	8	no	—
339	C₂²×C₄	—	2	16	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	8	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	8	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
347	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
348	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
349	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
350	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
351	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	—
352	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
353	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
354	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
355	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
356	C₂²×C₄	C₃×#41	1	4	yes	—
357	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
358	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
359	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
360	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
361	M₁₆	—	2	8	no	—
362	M₁₆	—	2	8	no	—
363	M₁₆	—	2	16	no	—
364	C₂×C₈	—	2	4	no	—
365	C₂×C₈	—	2	8	no	—
366	C₂×C₈	—	2	4	no	—
367	C₂×C₈	—	2	4	no	—
368	C₂×C₈	—	2	16	no	—
369	C₂×C₈	—	2	16	no	—
370	C₂×C₈	—	2	16	no	—
371	C₂×C₈	C₂×C₃×D₄	1	4	yes	—
372	C₂×C₈	C₂×C₃×D₄	1	4	yes	—
373	C₂×C₈	C₂×C₃×D₄	1	16	yes	complemented
374	C₂×C₈	C₂⁴×C₃	1	4	yes	—
375	C₂×C₈	C₂⁴×C₃	1	4	yes	—
376	C₂×C₈	C₂⁴×C₃	1	4	yes	—
377	C₂×C₈	C₂⁴×C₃	1	2	yes	—
378	C₂×C₈	C₂⁴×C₃	1	2	yes	—
379	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
380	C₄⋊C₄	C₂²×C₃×C₄	1	16	yes	—
381	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
382	C₂²⋊C₄	C₂²×C₃×C₄	1	16	yes	—
383	C₂²⋊C₄	C₂²×C₃×C₄	1	16	yes	—
384	C₄²	C₂²×C₃×C₄	1	4	yes	—
385	C₄²	C₂⁴×C₃	1	4	yes	—
386	C₂²×C₃	—	2	32	no	—
387	C₂²×C₃	—	2	4	no	—
388	C₂²×C₃	—	2	8	no	—
389	C₂²×C₃	—	2	16	no	—
390	C₂²×C₃	—	2	4	no	—
391	C₂²×C₃	—	2	4	no	—
392	C₂²×C₃	—	2	4	no	—
393	C₂²×C₃	—	2	8	no	—
394	C₂²×C₃	—	4	8	no	—
395	C₂²×C₃	C₂×C₄×D₄	1	4	yes	—
396	C₂²×C₃	C₂×C₄×D₄	1	2	yes	—
397	C₂²×C₃	C₂×#131	1	4	yes	—
398	C₂²×C₃	C₂×#131	1	8	yes	complemented
399	C₂²×C₃	C₂⁴×C₄	1	1	yes	characteristic
400	C₃×C₄	—	2	4	no	—
401	C₃×C₄	—	2	4	no	—
402	C₃×C₄	—	2	8	no	—
403	C₃×C₄	C₂×C₄×D₄	1	2	yes	—
404	C₃×C₄	C₂×C₄×D₄	1	4	yes	—
405	C₃×C₄	C₂³×D₄	1	1	yes	characteristic
406	C₃×C₄	C₂²×#41	1	1	yes	characteristic
407	C₂³	—	2	32	no	—
408	C₂³	—	2	4	no	—
409	C₂³	—	2	4	no	—
410	C₂³	—	2	16	no	—
411	C₂³	—	2	8	no	—
412	C₂³	—	2	4	no	—
413	C₂³	—	2	8	no	—
414	C₂³	—	2	4	no	—
415	C₂³	C₃×C₄×D₄	1	4	yes	—
416	C₂³	C₃×#131	1	8	yes	complemented
417	C₂³	C₂³×C₃×C₄	1	4	yes	—
418	C₂³	C₂³×C₃×C₄	1	4	yes	—
419	C₂³	C₂³×C₃×C₄	1	2	yes	—
420	C₂³	C₂³×C₃×C₄	1	1	yes	characteristic
421	Q₈	—	2	8	no	—
422	D₄	—	2	32	no	—
423	D₄	—	2	16	no	—
424	D₄	—	2	8	no	—
425	C₂×C₄	—	2	8	no	—
426	C₂×C₄	—	2	8	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	8	no	—
434	C₂×C₄	—	2	16	no	—
435	C₂×C₄	—	2	8	no	—
436	C₂×C₄	C₃×C₄×D₄	1	4	yes	—
437	C₂×C₄	C₃×C₄×D₄	1	8	yes	—
438	C₂×C₄	C₂³×C₃×C₄	1	8	yes	—
439	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
440	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
441	C₂×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
442	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
443	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
444	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
445	C₂×C₄	C₂×C₃×#41	1	2	yes	—
446	C₂×C₄	C₂×C₃×#41	1	4	yes	—
447	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
448	C₈	—	2	4	no	—
449	C₈	—	2	4	no	—
450	C₈	—	2	4	no	—
451	C₈	C₂²×C₃×D₄	1	4	yes	—
452	C₈	C₂²×C₃×D₄	1	4	yes	—
453	C₂×C₃	—	2	4	no	—
454	C₂×C₃	—	2	8	no	—
455	C₂×C₃	—	4	4	no	—
456	C₂×C₃	#2929	1	4	yes	direct product factor
457	C₂×C₃	C₂²×C₄×D₄	1	1	yes	characteristic
458	C₂×C₃	C₂²×#131	1	2	yes	—
459	C₂²	—	2	32	no	—
460	C₂²	—	2	4	no	—
461	C₂²	—	2	8	no	—
462	C₂²	—	2	16	no	—
463	C₂²	—	2	4	no	—
464	C₂²	—	2	4	no	—
465	C₂²	—	2	4	no	—
466	C₂²	—	2	8	no	—
467	C₂²	—	4	8	no	—
468	C₂²	C₂×C₃×C₄×D₄	1	4	yes	—
469	C₂²	C₂×C₃×C₄×D₄	1	2	yes	—
470	C₂²	C₂×C₃×#131	1	4	yes	—
471	C₂²	C₂×C₃×#131	1	8	yes	complemented
472	C₂²	C₂⁴×C₃×C₄	1	1	yes	characteristic
473	C₄	—	2	4	no	—
474	C₄	—	2	4	no	—
475	C₄	—	2	8	no	—
476	C₄	C₂×C₃×C₄×D₄	1	2	yes	—
477	C₄	C₂×C₃×C₄×D₄	1	4	yes	—
478	C₄	C₂³×C₃×D₄	1	1	yes	characteristic
479	C₄	C₂²×C₃×#41	1	1	yes	characteristic
480	C₃	C₂×#2929	1	1	yes	characteristic, direct product factor, Sylow
481	C₂	—	2	8	no	—
482	C₂	—	2	4	no	—
483	C₂	—	4	4	no	—
484	C₂	C₃×#2929	1	4	yes	direct product factor
485	C₂	C₂²×C₃×C₄×D₄	1	1	yes	characteristic
486	C₂	C₂²×C₃×#131	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃×C₈	C₂³
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×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×#131	C₂	semidirect
2. C₂⁴×C₃×C₈	C₂	semidirect
4. C₃×#2929	C₂	direct (N × H)
5. C₂×C₃×#435	C₂	semidirect
6. C₂×C₃×C₈×D₄	C₂	semidirect
7. C₂×C₃×#424	C₂	semidirect
8. C₂×C₃×#408	C₂	semidirect
9. C₂×C₃×#407	C₂	semidirect
10. C₂×C₃×#405	C₂	semidirect
11. C₂×#2929	C₃	direct (N × H)
15. C₂×C₃×#131	C₂²	semidirect
18. C₂²×C₃×M₁₆	C₂²	semidirect
24. C₂³×C₃×C₈	C₂²	semidirect
25. C₂³×C₃×C₈	C₂²	semidirect
34. C₃×#435	C₂²	semidirect
35. C₃×C₈×D₄	C₂²	semidirect
36. C₃×#424	C₂²	semidirect
37. C₂×C₃×C₄⋊C₈	C₂²	semidirect
38. C₃×#408	C₂²	semidirect
39. C₃×#407	C₂²	semidirect
41. C₂×C₃×C₂²⋊C₈	C₂²	semidirect
42. C₃×#405	C₂²	semidirect
43. C₂×C₃×#97	C₂²	semidirect
44. C₂×C₃×C₄×C₈	C₂²	semidirect
45. C₂²×#131	C₂×C₃	semidirect
46. C₂⁴×C₈	C₂×C₃	semidirect
48. #2929	C₂×C₃	direct (N × H)
49. C₂×#435	C₂×C₃	semidirect
50. C₂×C₈×D₄	C₂×C₃	semidirect
51. C₂×#424	C₂×C₃	semidirect
52. C₂×#408	C₂×C₃	semidirect
53. C₂×#407	C₂×C₃	semidirect
54. C₂×#405	C₂×C₃	semidirect
79. C₂×C₃×M₁₆	C₂³	semidirect
85. C₂²×C₃×C₈	D₄	semidirect
95. C₂²×C₃×C₈	C₂³	semidirect
110. C₃×C₄⋊C₈	C₂³	semidirect
112. C₃×C₂²⋊C₈	C₂³	semidirect
113. C₃×#97	C₂³	semidirect
114. C₃×C₄×C₈	C₂³	semidirect
118. C₂×#131	C₂²×C₃	semidirect
121. C₂²×M₁₆	C₂²×C₃	semidirect
127. C₂³×C₈	C₂²×C₃	semidirect
128. C₂³×C₈	C₂²×C₃	semidirect
137. #435	C₂²×C₃	semidirect
138. C₈×D₄	C₂²×C₃	semidirect
139. #424	C₂²×C₃	semidirect
140. C₂×C₄⋊C₈	C₂²×C₃	semidirect
141. #408	C₂²×C₃	semidirect
142. #407	C₂²×C₃	semidirect
144. C₂×C₂²⋊C₈	C₂²×C₃	semidirect
145. #405	C₂²×C₃	semidirect
146. C₂×#97	C₂²×C₃	semidirect
147. C₂×C₄×C₈	C₂²×C₃	semidirect
201. C₂×C₃×C₈	C₂×D₄	semidirect
238. C₂×M₁₆	C₂³×C₃	semidirect
244. C₂²×C₈	C₃×D₄	semidirect
254. C₂²×C₈	C₂³×C₃	semidirect
269. C₄⋊C₈	C₂³×C₃	semidirect
271. C₂²⋊C₈	C₂³×C₃	semidirect
272. #97	C₂³×C₃	semidirect
273. C₄×C₈	C₂³×C₃	semidirect
283. C₂³×C₃	#131	semidirect
373. C₂×C₈	C₂×C₃×D₄	semidirect
398. C₂²×C₃	C₂×#131	semidirect
416. C₂³	C₃×#131	semidirect
456. C₂×C₃	#2929	direct (N × H)
471. C₂²	C₂×C₃×#131	semidirect
480. C₃	C₂×#2929	direct (N × H)
484. C₂	C₃×#2929	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
C₂⁴×C₃×C₈	2
C₂×C₃×#525	2
C₃×#2929	2
C₂×C₃×#435	2
C₂×C₃×C₈×D₄	2
C₂×C₃×#424	2
C₂×C₃×#408	2
C₂×C₃×#407	2
C₂×C₃×#405	2
C₂×#2929	3

Subgroups — C2×C3×#2929 #10678740

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#2929 #10678740