Subgroups — C₂×C₃×#3043 #10679025

Order 768.

2858 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#535	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×#519	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#3043	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₃×#464	C₂	1	4	yes	maximal, complemented
7	C₂×C₃×#460	C₂	1	4	yes	maximal, complemented
8	C₂×C₃×#424	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#418	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×#416	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#3043	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
13	C₂³×C₃×Q₈	C₂²	1	1	yes	characteristic
14	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×#137	—	2	8	no	—
16	C₂×C₃×#137	C₂²	1	8	yes	complemented
17	C₂²×C₃×Q₁₆	C₂²	1	2	yes	complemented
18	C₂²×C₃×SD₁₆	—	2	8	no	—
19	C₂²×C₃×SD₁₆	C₂²	1	4	yes	—
20	C₂²×C₃×SD₁₆	C₂²	1	8	yes	complemented
21	C₂²×C₃×SD₁₆	C₂²	1	2	yes	complemented
22	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
23	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
24	C₃×#535	—	2	4	no	—
25	C₃×#535	C₂²	1	8	yes	—
26	C₂×C₃×#127	C₂²	1	2	yes	—
27	C₂×C₃×#124	C₂²	1	2	yes	—
28	C₂×C₃×#121	—	2	2	no	—
29	C₂×C₃×#120	—	2	2	no	—
30	C₃×#519	—	2	4	no	—
31	C₃×#519	C₂²	1	8	yes	complemented
32	C₂×C₃×C₄×Q₈	—	2	2	no	—
33	C₂×C₃×C₄×Q₈	C₂²	1	4	yes	complemented
34	C₂×C₃×#117	—	2	2	no	—
35	C₂×C₃×#117	C₂²	1	1	yes	characteristic
36	C₂×C₃×#117	C₂²	1	1	yes	characteristic
37	C₃×#464	C₂²	1	32	yes	complemented
38	C₃×#460	C₂²	1	32	yes	complemented
39	C₃×#424	C₂²	1	8	yes	complemented
40	C₂×C₃×C₄⋊C₈	C₂²	1	4	yes	complemented
41	C₃×#418	C₂²	1	8	yes	complemented
42	C₃×#416	C₂²	1	8	yes	complemented
43	C₂×C₃×#103	C₂²	1	2	yes	complemented
44	C₂×C₃×#102	C₂²	1	4	yes	—
45	C₂×C₃×#102	C₂²	1	2	yes	complemented
46	C₂²×#137	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂³×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂×#535	C₂×C₃	1	1	yes	characteristic
49	C₂×#519	C₂×C₃	1	1	yes	characteristic, complemented
50	#3043	C₂×C₃	1	16	yes	direct product factor
51	C₂×#464	C₂×C₃	1	4	yes	complemented
52	C₂×#460	C₂×C₃	1	4	yes	complemented
53	C₂×#424	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂×#418	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂×#416	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂⁵×C₃	—	2	1	no	—
57	C₂×C₃×#41	—	2	2	no	—
58	C₂×C₃×#41	—	2	4	no	—
59	C₂×C₃×#41	—	2	4	no	—
60	C₂×C₃×#41	C₂³	1	4	yes	—
61	C₂²×C₃×Q₈	—	2	1	no	—
62	C₂²×C₃×Q₈	—	2	2	no	—
63	C₂²×C₃×Q₈	—	2	4	no	—
64	C₂²×C₃×Q₈	D₄	1	8	yes	complemented
65	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
66	C₂²×C₃×Q₈	C₂³	1	2	yes	—
67	C₂²×C₃×Q₈	C₂³	1	4	yes	—
68	C₂²×C₃×D₄	—	2	1	no	—
69	C₂²×C₃×D₄	—	2	4	no	—
70	C₂²×C₃×D₄	—	2	1	no	—
71	C₂²×C₃×D₄	—	2	2	no	—
72	C₂²×C₃×D₄	—	2	4	no	—
73	C₂²×C₃×D₄	—	2	4	no	—
74	C₂²×C₃×D₄	C₂³	1	2	yes	—
75	C₂²×C₃×D₄	C₂³	1	4	yes	—
76	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
77	C₂³×C₃×C₄	—	2	1	no	—
78	C₂³×C₃×C₄	—	2	1	no	—
79	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
80	C₃×#137	—	2	32	no	—
81	C₂×C₃×Q₁₆	—	2	8	no	—
82	C₂×C₃×Q₁₆	C₂³	1	8	yes	complemented
83	C₂×C₃×SD₁₆	—	2	16	no	—
84	C₂×C₃×SD₁₆	—	2	8	no	—
85	C₂×C₃×SD₁₆	—	2	32	no	—
86	C₂×C₃×SD₁₆	C₂³	1	16	yes	—
87	C₂×C₃×SD₁₆	C₂³	1	8	yes	complemented
88	C₂×C₃×M₁₆	—	2	4	no	—
89	C₂×C₃×M₁₆	C₂³	1	4	yes	—
90	C₂²×C₃×C₈	—	2	4	no	—
91	C₂²×C₃×C₈	C₂³	1	2	yes	—
92	C₂²×C₃×C₈	C₂³	1	4	yes	—
93	C₂²×C₃×C₈	C₂³	1	2	yes	—
94	C₃×#127	—	2	4	no	—
95	C₃×#127	C₂³	1	8	yes	—
96	C₃×#124	—	2	4	no	—
97	C₃×#124	C₂³	1	8	yes	—
98	C₃×#121	—	2	16	no	—
99	C₃×#120	—	2	16	no	—
100	C₃×C₄×Q₈	—	2	16	no	—
101	C₃×C₄×Q₈	—	2	8	no	—
102	C₃×C₄×Q₈	C₂³	1	16	yes	complemented
103	C₃×#117	—	2	2	no	—
104	C₃×#117	—	2	16	no	—
105	C₃×#117	D₄	1	4	yes	—
106	C₃×#117	C₂³	1	4	yes	—
107	C₃×#117	C₂³	1	4	yes	—
108	C₂×C₃×C₄⋊C₄	—	2	4	no	—
109	C₂×C₃×C₄⋊C₄	D₄	1	2	yes	—
110	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
111	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
112	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
113	C₂×C₃×C₂²⋊C₄	D₄	1	2	yes	—
114	C₂×C₃×C₄²	—	2	4	no	—
115	C₂×C₃×C₄²	—	2	1	no	—
116	C₂×C₃×C₄²	C₂³	1	2	yes	—
117	C₃×C₄⋊C₈	C₂³	1	16	yes	complemented
118	C₃×#103	C₂³	1	8	yes	complemented
119	C₃×#102	C₂³	1	16	yes	—
120	C₃×#102	C₂³	1	8	yes	complemented
121	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
122	C₂³×Q₈	C₂²×C₃	1	1	yes	characteristic
123	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
124	C₂×#137	—	2	8	no	—
125	C₂×#137	C₂²×C₃	1	8	yes	complemented
126	C₂²×Q₁₆	C₂²×C₃	1	2	yes	complemented
127	C₂²×SD₁₆	—	2	8	no	—
128	C₂²×SD₁₆	C₂²×C₃	1	4	yes	—
129	C₂²×SD₁₆	C₂²×C₃	1	8	yes	complemented
130	C₂²×SD₁₆	C₂²×C₃	1	2	yes	complemented
131	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
132	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
133	#535	—	2	4	no	—
134	#535	C₂²×C₃	1	8	yes	—
135	C₂×#127	C₂²×C₃	1	2	yes	—
136	C₂×#124	C₂²×C₃	1	2	yes	—
137	C₂×#121	—	2	2	no	—
138	C₂×#120	—	2	2	no	—
139	#519	—	2	4	no	—
140	#519	C₂²×C₃	1	8	yes	complemented
141	C₂×C₄×Q₈	—	2	2	no	—
142	C₂×C₄×Q₈	C₂²×C₃	1	4	yes	complemented
143	C₂×#117	—	2	2	no	—
144	C₂×#117	C₂²×C₃	1	1	yes	characteristic
145	C₂×#117	C₂²×C₃	1	1	yes	characteristic
146	#464	C₂²×C₃	1	32	yes	complemented
147	#460	C₂²×C₃	1	32	yes	complemented
148	#424	C₂²×C₃	1	8	yes	complemented
149	C₂×C₄⋊C₈	C₂²×C₃	1	4	yes	complemented
150	#418	C₂²×C₃	1	8	yes	complemented
151	#416	C₂²×C₃	1	8	yes	complemented
152	C₂×#103	C₂²×C₃	1	2	yes	complemented
153	C₂×#102	C₂²×C₃	1	4	yes	—
154	C₂×#102	C₂²×C₃	1	2	yes	complemented
155	C₂⁴×C₃	—	2	2	no	—
156	C₂⁴×C₃	—	2	1	no	—
157	C₂⁴×C₃	—	2	4	no	—
158	C₂⁴×C₃	—	4	4	no	—
159	C₂⁴×C₃	—	8	4	no	—
160	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
161	C₃×#41	—	2	8	no	—
162	C₃×#41	—	2	8	no	—
163	C₃×#41	—	4	8	no	—
164	C₂×C₃×Q₈	—	2	8	no	—
165	C₂×C₃×Q₈	—	2	16	no	—
166	C₂×C₃×Q₈	—	2	4	no	—
167	C₂×C₃×Q₈	—	2	2	no	—
168	C₂×C₃×Q₈	—	2	1	no	—
169	C₂×C₃×Q₈	—	2	4	no	—
170	C₂×C₃×Q₈	—	2	8	no	—
171	C₂×C₃×Q₈	—	2	2	no	—
172	C₂×C₃×Q₈	—	2	2	no	—
173	C₂×C₃×Q₈	C₂×D₄	1	8	yes	—
174	C₂×C₃×Q₈	C₂×D₄	1	16	yes	complemented
175	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
176	C₂×C₃×Q₈	C₂⁴	1	4	yes	—
177	C₂×C₃×D₄	—	2	4	no	—
178	C₂×C₃×D₄	—	2	4	no	—
179	C₂×C₃×D₄	—	2	8	no	—
180	C₂×C₃×D₄	—	2	2	no	—
181	C₂×C₃×D₄	—	2	4	no	—
182	C₂×C₃×D₄	—	2	2	no	—
183	C₂×C₃×D₄	—	2	1	no	—
184	C₂×C₃×D₄	—	2	16	no	—
185	C₂×C₃×D₄	—	2	4	no	—
186	C₂×C₃×D₄	—	2	8	no	—
187	C₂×C₃×D₄	—	2	2	no	—
188	C₂×C₃×D₄	—	4	4	no	—
189	C₂×C₃×D₄	—	4	4	no	—
190	C₂×C₃×D₄	—	4	8	no	—
191	C₂×C₃×D₄	—	8	8	no	—
192	C₂×C₃×D₄	C₂⁴	1	4	yes	—
193	C₂×C₃×D₄	C₂⁴	1	2	yes	—
194	C₂²×C₃×C₄	—	2	8	no	—
195	C₂²×C₃×C₄	—	2	4	no	—
196	C₂²×C₃×C₄	—	2	2	no	—
197	C₂²×C₃×C₄	—	2	2	no	—
198	C₂²×C₃×C₄	—	2	1	no	—
199	C₂²×C₃×C₄	—	2	4	no	—
200	C₂²×C₃×C₄	—	4	4	no	—
201	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
202	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
203	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
205	C₂²×C₃×C₄	#41	1	4	yes	—
206	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
207	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
208	C₃×Q₁₆	—	2	16	no	—
209	C₃×SD₁₆	—	2	32	no	—
210	C₃×SD₁₆	—	2	16	no	—
211	C₃×M₁₆	—	2	8	no	—
212	C₂×C₃×C₈	—	2	4	no	—
213	C₂×C₃×C₈	—	2	8	no	—
214	C₂×C₃×C₈	—	2	4	no	—
215	C₂×C₃×C₈	C₂⁴	1	4	yes	—
216	C₂×C₃×C₈	C₂⁴	1	4	yes	—
217	C₃×C₄⋊C₄	—	2	16	no	—
218	C₃×C₄⋊C₄	—	2	2	no	—
219	C₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
220	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
221	C₃×C₂²⋊C₄	—	2	4	no	—
222	C₃×C₂²⋊C₄	—	2	16	no	—
223	C₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
224	C₃×C₄²	—	2	16	no	—
225	C₃×C₄²	—	2	4	no	—
226	C₃×C₄²	C₂×D₄	1	4	yes	—
227	C₃×C₄²	C₂⁴	1	4	yes	—
228	C₂⁵	—	2	1	no	—
229	C₂×#41	—	2	2	no	—
230	C₂×#41	—	2	4	no	—
231	C₂×#41	—	2	4	no	—
232	C₂×#41	C₂³×C₃	1	4	yes	—
233	C₂²×Q₈	—	2	1	no	—
234	C₂²×Q₈	—	2	2	no	—
235	C₂²×Q₈	—	2	4	no	—
236	C₂²×Q₈	C₃×D₄	1	8	yes	complemented
237	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
238	C₂²×Q₈	C₂³×C₃	1	2	yes	—
239	C₂²×Q₈	C₂³×C₃	1	4	yes	—
240	C₂²×D₄	—	2	1	no	—
241	C₂²×D₄	—	2	4	no	—
242	C₂²×D₄	—	2	1	no	—
243	C₂²×D₄	—	2	2	no	—
244	C₂²×D₄	—	2	4	no	—
245	C₂²×D₄	—	2	4	no	—
246	C₂²×D₄	C₂³×C₃	1	2	yes	—
247	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
248	C₂²×D₄	C₂³×C₃	1	4	yes	—
249	C₂³×C₄	—	2	1	no	—
250	C₂³×C₄	—	2	1	no	—
251	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
252	#137	—	2	32	no	—
253	C₂×Q₁₆	—	2	8	no	—
254	C₂×Q₁₆	C₂³×C₃	1	8	yes	complemented
255	C₂×SD₁₆	—	2	16	no	—
256	C₂×SD₁₆	—	2	8	no	—
257	C₂×SD₁₆	—	2	32	no	—
258	C₂×SD₁₆	C₂³×C₃	1	16	yes	—
259	C₂×SD₁₆	C₂³×C₃	1	8	yes	complemented
260	C₂×M₁₆	—	2	4	no	—
261	C₂×M₁₆	C₂³×C₃	1	4	yes	—
262	C₂²×C₈	—	2	4	no	—
263	C₂²×C₈	C₂³×C₃	1	2	yes	—
264	C₂²×C₈	C₂³×C₃	1	4	yes	—
265	C₂²×C₈	C₂³×C₃	1	2	yes	—
266	#127	—	2	4	no	—
267	#127	C₂³×C₃	1	8	yes	—
268	#124	—	2	4	no	—
269	#124	C₂³×C₃	1	8	yes	—
270	#121	—	2	16	no	—
271	#120	—	2	16	no	—
272	C₄×Q₈	—	2	16	no	—
273	C₄×Q₈	—	2	8	no	—
274	C₄×Q₈	C₂³×C₃	1	16	yes	complemented
275	#117	—	2	2	no	—
276	#117	—	2	16	no	—
277	#117	C₃×D₄	1	4	yes	—
278	#117	C₂³×C₃	1	4	yes	—
279	#117	C₂³×C₃	1	4	yes	—
280	C₂×C₄⋊C₄	—	2	4	no	—
281	C₂×C₄⋊C₄	C₃×D₄	1	2	yes	—
282	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
283	C₂×C₂²⋊C₄	—	2	1	no	—
284	C₂×C₂²⋊C₄	—	2	4	no	—
285	C₂×C₂²⋊C₄	C₃×D₄	1	2	yes	—
286	C₂×C₄²	—	2	4	no	—
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	C₂³×C₃	1	2	yes	—
289	C₄⋊C₈	C₂³×C₃	1	16	yes	complemented
290	#103	C₂³×C₃	1	8	yes	complemented
291	#102	C₂³×C₃	1	16	yes	—
292	#102	C₂³×C₃	1	8	yes	complemented
293	C₂³×C₃	—	2	4	no	—
294	C₂³×C₃	—	2	4	no	—
295	C₂³×C₃	—	2	2	no	—
296	C₂³×C₃	—	4	2	no	—
297	C₂³×C₃	—	4	8	no	—
298	C₂³×C₃	—	4	4	no	—
299	C₂³×C₃	—	4	4	no	—
300	C₂³×C₃	—	4	8	no	—
301	C₂³×C₃	—	8	8	no	—
302	C₂³×C₃	—	8	16	no	—
303	C₂³×C₃	#121	1	4	yes	—
304	C₂³×C₃	C₂²×D₄	1	2	yes	—
305	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
306	C₃×Q₈	—	2	8	no	—
307	C₃×Q₈	—	2	16	no	—
308	C₃×Q₈	—	2	4	no	—
309	C₃×Q₈	—	2	2	no	—
310	C₃×Q₈	—	2	2	no	—
311	C₃×Q₈	—	4	2	no	—
312	C₃×Q₈	C₂²×D₄	1	8	yes	—
313	C₃×D₄	—	2	4	no	—
314	C₃×D₄	—	2	2	no	—
315	C₃×D₄	—	2	4	no	—
316	C₃×D₄	—	2	2	no	—
317	C₃×D₄	—	4	8	no	—
318	C₃×D₄	—	4	8	no	—
319	C₃×D₄	—	4	4	no	—
320	C₃×D₄	—	4	2	no	—
321	C₃×D₄	—	8	16	no	—
322	C₂×C₃×C₄	—	2	8	no	—
323	C₂×C₃×C₄	—	2	16	no	—
324	C₂×C₃×C₄	—	2	8	no	—
325	C₂×C₃×C₄	—	2	4	no	—
326	C₂×C₃×C₄	—	2	4	no	—
327	C₂×C₃×C₄	—	2	2	no	—
328	C₂×C₃×C₄	—	4	2	no	—
329	C₂×C₃×C₄	—	4	4	no	—
330	C₂×C₃×C₄	—	4	8	no	—
331	C₂×C₃×C₄	#121	1	4	yes	—
332	C₂×C₃×C₄	#121	1	8	yes	—
333	C₂×C₃×C₄	C₂²×D₄	1	8	yes	—
334	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
335	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
337	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
338	C₂×C₃×C₄	C₂×#41	1	2	yes	—
339	C₂×C₃×C₄	C₂×#41	1	4	yes	—
340	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
341	C₃×C₈	—	2	4	no	—
342	C₃×C₈	—	2	4	no	—
343	C₂⁴	—	2	2	no	—
344	C₂⁴	—	2	1	no	—
345	C₂⁴	—	2	4	no	—
346	C₂⁴	—	4	4	no	—
347	C₂⁴	—	8	4	no	—
348	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
349	#41	—	2	8	no	—
350	#41	—	2	8	no	—
351	#41	—	4	8	no	—
352	C₂×Q₈	—	2	8	no	—
353	C₂×Q₈	—	2	16	no	—
354	C₂×Q₈	—	2	4	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	4	no	—
358	C₂×Q₈	—	2	8	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	C₂×C₃×D₄	1	8	yes	—
362	C₂×Q₈	C₂×C₃×D₄	1	16	yes	complemented
363	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
364	C₂×Q₈	C₂⁴×C₃	1	4	yes	—
365	C₂×D₄	—	2	4	no	—
366	C₂×D₄	—	2	4	no	—
367	C₂×D₄	—	2	8	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	4	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	—	2	16	no	—
373	C₂×D₄	—	2	4	no	—
374	C₂×D₄	—	2	8	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	4	4	no	—
377	C₂×D₄	—	4	4	no	—
378	C₂×D₄	—	4	8	no	—
379	C₂×D₄	—	8	8	no	—
380	C₂×D₄	C₂⁴×C₃	1	4	yes	—
381	C₂×D₄	C₂⁴×C₃	1	2	yes	—
382	C₂²×C₄	—	2	8	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	4	4	no	—
389	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
390	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
391	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
392	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
393	C₂²×C₄	C₃×#41	1	4	yes	—
394	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
395	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
396	Q₁₆	—	2	16	no	—
397	SD₁₆	—	2	32	no	—
398	SD₁₆	—	2	16	no	—
399	M₁₆	—	2	8	no	—
400	C₂×C₈	—	2	4	no	—
401	C₂×C₈	—	2	8	no	—
402	C₂×C₈	—	2	4	no	—
403	C₂×C₈	C₂⁴×C₃	1	4	yes	—
404	C₂×C₈	C₂⁴×C₃	1	4	yes	—
405	C₄⋊C₄	—	2	16	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	C₂×C₃×D₄	1	8	yes	—
408	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
409	C₂²⋊C₄	—	2	4	no	—
410	C₂²⋊C₄	—	2	16	no	—
411	C₂²⋊C₄	C₂×C₃×D₄	1	8	yes	—
412	C₄²	—	2	16	no	—
413	C₄²	—	2	4	no	—
414	C₄²	C₂×C₃×D₄	1	4	yes	—
415	C₄²	C₂⁴×C₃	1	4	yes	—
416	C₂²×C₃	—	2	8	no	—
417	C₂²×C₃	—	2	4	no	—
418	C₂²×C₃	—	4	2	no	—
419	C₂²×C₃	—	4	4	no	—
420	C₂²×C₃	—	4	4	no	—
421	C₂²×C₃	—	4	8	no	—
422	C₂²×C₃	—	8	16	no	—
423	C₂²×C₃	—	8	4	no	—
424	C₂²×C₃	—	8	8	no	—
425	C₂²×C₃	C₂×#121	1	4	yes	—
426	C₂²×C₃	C₂×#121	1	2	yes	—
427	C₂²×C₃	#577	1	4	yes	—
428	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
429	C₃×C₄	—	2	8	no	—
430	C₃×C₄	—	2	8	no	—
431	C₃×C₄	—	4	2	no	—
432	C₃×C₄	—	4	4	no	—
433	C₃×C₄	C₂×#121	1	4	yes	—
434	C₃×C₄	C₂×#121	1	2	yes	—
435	C₃×C₄	C₂³×D₄	1	1	yes	characteristic
436	C₃×C₄	C₂²×#41	1	1	yes	characteristic
437	C₂³	—	2	4	no	—
438	C₂³	—	2	4	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	4	4	no	—
441	C₂³	—	4	8	no	—
442	C₂³	—	4	2	no	—
443	C₂³	—	4	8	no	—
444	C₂³	—	4	4	no	—
445	C₂³	—	8	8	no	—
446	C₂³	—	8	16	no	—
447	C₂³	C₃×#121	1	4	yes	—
448	C₂³	C₂²×C₃×D₄	1	2	yes	—
449	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
450	Q₈	—	2	4	no	—
451	Q₈	—	2	8	no	—
452	Q₈	—	2	16	no	—
453	Q₈	—	2	2	no	—
454	Q₈	—	2	2	no	—
455	Q₈	—	4	2	no	—
456	Q₈	C₂²×C₃×D₄	1	8	yes	—
457	D₄	—	2	4	no	—
458	D₄	—	2	2	no	—
459	D₄	—	2	4	no	—
460	D₄	—	2	2	no	—
461	D₄	—	4	8	no	—
462	D₄	—	4	8	no	—
463	D₄	—	4	4	no	—
464	D₄	—	4	2	no	—
465	D₄	—	8	16	no	—
466	C₂×C₄	—	2	8	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	8	no	—
469	C₂×C₄	—	2	16	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	4	4	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	8	no	—
475	C₂×C₄	C₃×#121	1	4	yes	—
476	C₂×C₄	C₃×#121	1	8	yes	—
477	C₂×C₄	C₂²×C₃×D₄	1	8	yes	—
478	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
479	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
480	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
481	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
482	C₂×C₄	C₂×C₃×#41	1	2	yes	—
483	C₂×C₄	C₂×C₃×#41	1	4	yes	—
484	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
485	C₈	—	2	4	no	—
486	C₈	—	2	4	no	—
487	C₂×C₃	—	2	4	no	—
488	C₂×C₃	—	8	2	no	—
489	C₂×C₃	—	8	4	no	—
490	C₂×C₃	#3043	1	4	yes	direct product factor
491	C₂×C₃	C₂²×#121	1	1	yes	characteristic
492	C₂×C₃	C₂×#577	1	2	yes	—
493	C₂²	—	2	4	no	—
494	C₂²	—	2	8	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	4	4	no	—
497	C₂²	—	4	4	no	—
498	C₂²	—	4	8	no	—
499	C₂²	—	8	16	no	—
500	C₂²	—	8	8	no	—
501	C₂²	—	8	4	no	—
502	C₂²	C₂×C₃×#121	1	4	yes	—
503	C₂²	C₂×C₃×#121	1	2	yes	—
504	C₂²	C₃×#577	1	4	yes	—
505	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
506	C₄	—	2	8	no	—
507	C₄	—	2	8	no	—
508	C₄	—	4	2	no	—
509	C₄	—	4	4	no	—
510	C₄	C₂×C₃×#121	1	4	yes	—
511	C₄	C₂×C₃×#121	1	2	yes	—
512	C₄	C₂³×C₃×D₄	1	1	yes	characteristic
513	C₄	C₂²×C₃×#41	1	1	yes	characteristic
514	C₃	C₂×#3043	1	1	yes	characteristic, direct product factor, Sylow
515	C₂	—	2	4	no	—
516	C₂	—	8	4	no	—
517	C₂	—	8	2	no	—
518	C₂	C₃×#3043	1	4	yes	direct product factor
519	C₂	C₂²×C₃×#121	1	1	yes	characteristic
520	C₂	C₂×C₃×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
prime radical	C₂×C₃×#535	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×#137	C₂	semidirect
2. C₂³×C₃×SD₁₆	C₂	semidirect
4. C₂×C₃×#519	C₂	semidirect
5. C₃×#3043	C₂	direct (N × H)
6. C₂×C₃×#464	C₂	semidirect
7. C₂×C₃×#460	C₂	semidirect
8. C₂×C₃×#424	C₂	semidirect
9. C₂×C₃×#418	C₂	semidirect
10. C₂×C₃×#416	C₂	semidirect
11. C₂×#3043	C₃	direct (N × H)
16. C₂×C₃×#137	C₂²	semidirect
17. C₂²×C₃×Q₁₆	C₂²	semidirect
20. C₂²×C₃×SD₁₆	C₂²	semidirect
21. C₂²×C₃×SD₁₆	C₂²	semidirect
31. C₃×#519	C₂²	semidirect
33. C₂×C₃×C₄×Q₈	C₂²	semidirect
37. C₃×#464	C₂²	semidirect
38. C₃×#460	C₂²	semidirect
39. C₃×#424	C₂²	semidirect
40. C₂×C₃×C₄⋊C₈	C₂²	semidirect
41. C₃×#418	C₂²	semidirect
42. C₃×#416	C₂²	semidirect
43. C₂×C₃×#103	C₂²	semidirect
45. C₂×C₃×#102	C₂²	semidirect
46. C₂²×#137	C₂×C₃	semidirect
47. C₂³×SD₁₆	C₂×C₃	semidirect
49. C₂×#519	C₂×C₃	semidirect
50. #3043	C₂×C₃	direct (N × H)
51. C₂×#464	C₂×C₃	semidirect
52. C₂×#460	C₂×C₃	semidirect
53. C₂×#424	C₂×C₃	semidirect
54. C₂×#418	C₂×C₃	semidirect
55. C₂×#416	C₂×C₃	semidirect
64. C₂²×C₃×Q₈	D₄	semidirect
82. C₂×C₃×Q₁₆	C₂³	semidirect
87. C₂×C₃×SD₁₆	C₂³	semidirect
102. C₃×C₄×Q₈	C₂³	semidirect
117. C₃×C₄⋊C₈	C₂³	semidirect
118. C₃×#103	C₂³	semidirect
120. C₃×#102	C₂³	semidirect
125. C₂×#137	C₂²×C₃	semidirect
126. C₂²×Q₁₆	C₂²×C₃	semidirect
129. C₂²×SD₁₆	C₂²×C₃	semidirect
130. C₂²×SD₁₆	C₂²×C₃	semidirect
140. #519	C₂²×C₃	semidirect
142. C₂×C₄×Q₈	C₂²×C₃	semidirect
146. #464	C₂²×C₃	semidirect
147. #460	C₂²×C₃	semidirect
148. #424	C₂²×C₃	semidirect
149. C₂×C₄⋊C₈	C₂²×C₃	semidirect
150. #418	C₂²×C₃	semidirect
151. #416	C₂²×C₃	semidirect
152. C₂×#103	C₂²×C₃	semidirect
154. C₂×#102	C₂²×C₃	semidirect
174. C₂×C₃×Q₈	C₂×D₄	semidirect
236. C₂²×Q₈	C₃×D₄	semidirect
254. C₂×Q₁₆	C₂³×C₃	semidirect
259. C₂×SD₁₆	C₂³×C₃	semidirect
274. C₄×Q₈	C₂³×C₃	semidirect
289. C₄⋊C₈	C₂³×C₃	semidirect
290. #103	C₂³×C₃	semidirect
292. #102	C₂³×C₃	semidirect
362. C₂×Q₈	C₂×C₃×D₄	semidirect
490. C₂×C₃	#3043	direct (N × H)
514. C₃	C₂×#3043	direct (N × H)
518. C₂	C₃×#3043	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×#137	2
C₂³×C₃×SD₁₆	2
C₂×C₃×#535	2
C₂×C₃×#519	2
C₃×#3043	2
C₂×C₃×#464	2
C₂×C₃×#460	2
C₂×C₃×#424	2
C₂×C₃×#418	2
C₂×C₃×#416	2
C₂×#3043	3

Subgroups — C2×C3×#3043 #10679025

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#3043 #10679025