Subgroups — C₂×#19143582 #25961062

Order 11008.

1970 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143582	C₂	1	16	yes	maximal, direct product factor
2	C₂×#14583030	C₂	1	2	yes	maximal, complemented
3	C₂×#14582977	C₂	1	2	yes	maximal, complemented
4	C₂×#14582971	C₂	1	2	yes	maximal, complemented
5	C₂×#14582971	C₂	1	2	yes	maximal, complemented
6	C₂×#14582960	C₂	1	2	yes	maximal, complemented
7	C₂×#14582956	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#14582855	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×#10621877	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄₃×#529	C₂	1	1	yes	maximal, characteristic
11	C₂²×#10621877	C₂²	1	2	yes	—
12	C₂²×#10621877	C₂²	1	2	yes	—
13	C₂³×C₄₃⋊C₈	C₂²	1	2	yes	—
14	#14583030	C₂²	1	16	yes	complemented
15	#14582977	C₂²	1	16	yes	complemented
16	#14582971	C₂²	1	16	yes	complemented
17	#14582971	C₂²	1	16	yes	complemented
18	#14582960	C₂²	1	16	yes	complemented
19	#14582956	C₂²	1	8	yes	complemented
20	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
21	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
22	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
23	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
26	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
27	#14582855	C₂²	1	16	yes	complemented
28	C₄×#10621877	C₂²	1	8	yes	complemented
29	C₂×#13063236	C₂²	1	2	yes	—
30	C₂×#13063236	C₂²	1	2	yes	—
31	C₂×#13063236	C₂²	1	2	yes	—
32	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
35	C₄₃×#529	C₄	1	8	yes	—
36	C₄₃×#529	C₂²	1	8	yes	—
37	C₂×#126×C₄₃	C₄	1	2	yes	—
38	C₂×#125×C₄₃	C₄	1	1	yes	characteristic
39	C₂×#124×C₄₃	C₄	1	1	yes	characteristic
40	C₂×#123×C₄₃	C₄	1	2	yes	—
41	C₂×C₂²⋊Q₈×C₄₃	C₄	1	1	yes	characteristic
42	C₂×#121×C₄₃	C₄	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
46	C₂×#117×C₄₃	C₂²	1	2	yes	—
47	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
48	C₂×#10621877	—	2	8	no	—
49	C₂×#10621877	—	2	8	no	—
50	C₂×#10621877	C₂³	1	8	yes	—
51	C₂×#10621877	C₂³	1	8	yes	—
52	C₂²×C₄₃⋊C₈	—	2	8	no	—
53	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
54	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
55	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
56	C₂²×C₄₃⋊C₈	C₂³	1	8	yes	—
57	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
58	C₄⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
59	C₄⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
60	C₄⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
61	C₂²⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
62	C₂²⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
63	C₂²⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
64	C₂²⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
65	#13063236	C₂³	1	8	yes	—
66	#13063236	C₂³	1	8	yes	—
67	#13063236	C₂³	1	8	yes	—
68	C₄×C₄₃⋊C₈	C₂³	1	4	yes	—
69	C₄×C₄₃⋊C₈	C₂³	1	4	yes	—
70	C₄×C₄₃⋊C₈	C₂³	1	8	yes	—
71	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
72	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
73	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
74	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
75	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
76	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
78	#126×C₄₃	C₂×C₄	1	16	yes	—
79	#125×C₄₃	C₂×C₄	1	8	yes	—
80	#124×C₄₃	C₂×C₄	1	8	yes	—
81	#123×C₄₃	C₂×C₄	1	16	yes	—
82	C₂²⋊Q₈×C₄₃	C₂×C₄	1	8	yes	—
83	#121×C₄₃	C₂×C₄	1	8	yes	—
84	C₄×Q₈×C₄₃	C₂×C₄	1	4	yes	—
85	C₄×Q₈×C₄₃	C₂³	1	4	yes	—
86	C₄×D₄×C₄₃	C₂×C₄	1	4	yes	—
87	C₄×D₄×C₄₃	C₂×C₄	1	8	yes	—
88	C₄×D₄×C₄₃	C₂³	1	4	yes	—
89	C₄×D₄×C₄₃	C₂³	1	8	yes	—
90	#117×C₄₃	C₂×C₄	1	8	yes	—
91	#117×C₄₃	C₂³	1	8	yes	—
92	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
93	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
94	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
96	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
98	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
99	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
100	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
101	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
102	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
103	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
104	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
105	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
106	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
109	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
110	C₂⁴×C₄₃	C₂²×C₄	1	2	yes	—
111	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×Q₈×C₄₃	—	4	2	no	—
113	C₂×Q₈×C₄₃	C₂²×C₄	1	4	yes	—
114	C₂×D₄×C₄₃	—	4	4	no	—
115	C₂×D₄×C₄₃	—	4	2	no	—
116	C₂×D₄×C₄₃	C₂²×C₄	1	8	yes	—
117	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
118	C₂²×C₄×C₄₃	—	2	4	no	—
119	C₂²×C₄×C₄₃	—	2	4	no	—
120	C₂²×C₄×C₄₃	—	2	4	no	—
121	C₂²×C₄×C₄₃	—	4	2	no	—
122	C₂²×C₄×C₄₃	—	4	2	no	—
123	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
125	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
130	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
131	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
132	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
133	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
134	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
135	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
136	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
137	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
138	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
139	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
140	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
141	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
142	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
143	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
144	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
145	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
146	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
147	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
148	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
149	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
150	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
151	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
152	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
153	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
154	C₄²×C₄₃	C₂⁴	1	2	yes	—
155	C₄²×C₄₃	C₂⁴	1	2	yes	—
156	C₄²×C₄₃	C₂⁴	1	4	yes	—
157	#10621877	—	2	16	no	—
158	#10621877	—	2	16	no	—
159	C₂×C₄₃⋊C₈	—	2	4	no	—
160	C₂×C₄₃⋊C₈	—	2	4	no	—
161	C₂×C₄₃⋊C₈	—	2	4	no	—
162	C₂×C₄₃⋊C₈	—	2	16	no	—
163	C₂×C₄₃⋊C₈	#41	1	8	yes	—
164	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
165	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
166	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
167	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
168	C₂³×C₄₃	—	2	4	no	—
169	C₂³×C₄₃	—	2	2	no	—
170	C₂³×C₄₃	—	2	2	no	—
171	C₂³×C₄₃	—	2	2	no	—
172	C₂³×C₄₃	—	2	4	no	—
173	C₂³×C₄₃	—	2	4	no	—
174	C₂³×C₄₃	C₂³×C₄	1	4	yes	—
175	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
176	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
177	Q₈×C₄₃	—	4	4	no	—
178	D₄×C₄₃	—	4	4	no	—
179	D₄×C₄₃	—	4	8	no	—
180	C₂×C₄×C₄₃	—	2	4	no	—
181	C₂×C₄×C₄₃	—	2	2	no	—
182	C₂×C₄×C₄₃	—	2	2	no	—
183	C₂×C₄×C₄₃	—	2	2	no	—
184	C₂×C₄×C₄₃	—	2	2	no	—
185	C₂×C₄×C₄₃	—	2	2	no	—
186	C₂×C₄×C₄₃	—	2	4	no	—
187	C₂×C₄×C₄₃	—	2	4	no	—
188	C₂×C₄×C₄₃	—	2	8	no	—
189	C₂×C₄×C₄₃	—	2	4	no	—
190	C₂×C₄×C₄₃	—	2	4	no	—
191	C₂×C₄×C₄₃	—	2	4	no	—
192	C₂×C₄×C₄₃	—	2	4	no	—
193	C₂×C₄×C₄₃	—	4	4	no	—
194	C₂×C₄×C₄₃	—	4	4	no	—
195	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
196	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
197	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
198	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
199	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
200	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
201	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
202	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
203	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
204	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
205	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
206	C₄₃⋊C₈	—	2	4	no	—
207	C₄₃⋊C₈	—	2	4	no	—
208	C₄₃⋊C₈	—	2	4	no	—
209	C₄₃⋊C₈	C₂×#41	1	8	yes	—
210	C₂×#2967	—	43	1	no	maximal, Sylow
211	C₂²×C₄₃	—	2	4	no	—
212	C₂²×C₄₃	—	2	2	no	—
213	C₂²×C₄₃	—	2	2	no	—
214	C₂²×C₄₃	—	2	2	no	—
215	C₂²×C₄₃	—	2	4	no	—
216	C₂²×C₄₃	—	2	4	no	—
217	C₂²×C₄₃	—	4	4	no	—
218	C₂²×C₄₃	—	4	8	no	—
219	C₂²×C₄₃	C₄×#41	1	2	yes	—
220	C₂²×C₄₃	#568	1	2	yes	—
221	C₂²×C₄₃	#568	1	2	yes	—
222	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
223	C₄×C₄₃	—	2	4	no	—
224	C₄×C₄₃	—	2	2	no	—
225	C₄×C₄₃	—	2	2	no	—
226	C₄×C₄₃	—	2	2	no	—
227	C₄×C₄₃	—	2	2	no	—
228	C₄×C₄₃	—	2	2	no	—
229	C₄×C₄₃	—	2	4	no	—
230	C₄×C₄₃	—	2	4	no	—
231	C₄×C₄₃	C₄×#41	1	2	yes	—
232	C₄×C₄₃	C₂²×#41	1	2	yes	—
233	C₂×#529	D₄₃	1	1	yes	characteristic
234	#2967	—	43	16	no	—
235	C₂×#446	—	43	2	no	—
236	C₂×#436	—	43	2	no	—
237	C₂×#435	—	43	2	no	—
238	C₂×#435	—	43	2	no	—
239	C₂×#433	—	43	2	no	—
240	C₂×#432	—	43	1	no	—
241	C₂×#405	—	43	2	no	—
242	C₂×C₄×M₁₆	—	43	1	no	—
243	C₂×C₄₃	—	4	2	no	—
244	C₂×C₄₃	—	4	4	no	—
245	C₂×C₄₃	#2967	1	4	yes	complemented
246	C₂×C₄₃	C₂×C₄×#41	1	1	yes	characteristic
247	C₂×C₄₃	C₂×#568	1	1	yes	characteristic
248	C₂×C₄₃	C₂×#568	1	1	yes	characteristic
249	C₂²×M₁₆	—	43	2	no	—
250	C₂²×M₁₆	—	43	2	no	—
251	C₂³×C₈	—	43	2	no	—
252	#529	Dic₄₃	1	8	yes	—
253	#529	C₂×D₄₃	1	8	yes	—
254	C₂×#126	Dic₄₃	1	2	yes	—
255	C₂×#125	Dic₄₃	1	1	yes	characteristic
256	C₂×#124	Dic₄₃	1	1	yes	characteristic
257	C₂×#123	Dic₄₃	1	2	yes	—
258	C₂×C₂²⋊Q₈	Dic₄₃	1	1	yes	characteristic
259	C₂×#121	Dic₄₃	1	1	yes	characteristic
260	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
261	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
262	C₂×C₄×D₄	C₂×D₄₃	1	2	yes	—
263	C₂×#117	C₂×D₄₃	1	2	yes	—
264	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
265	#446	—	43	16	no	—
266	#436	—	43	16	no	—
267	#435	—	43	16	no	—
268	#435	—	43	16	no	—
269	#433	—	43	16	no	—
270	#432	—	43	8	no	—
271	C₂×C₄⋊C₈	—	43	2	no	—
272	C₂×C₄⋊C₈	—	43	2	no	—
273	C₂×C₄⋊C₈	—	43	2	no	—
274	C₂×C₂²⋊C₈	—	43	1	no	—
275	C₂×C₂²⋊C₈	—	43	1	no	—
276	C₂×C₂²⋊C₈	—	43	2	no	—
277	C₂×C₂²⋊C₈	—	43	2	no	—
278	#405	—	43	16	no	—
279	C₄×M₁₆	—	43	8	no	—
280	C₂×#97	—	43	2	no	—
281	C₂×#97	—	43	2	no	—
282	C₂×#97	—	43	2	no	—
283	C₂×C₄×C₈	—	43	1	no	—
284	C₂×C₄×C₈	—	43	1	no	—
285	C₂×C₄×C₈	—	43	2	no	—
286	C₄₃	C₂×#2967	1	1	yes	characteristic, complemented, Sylow
287	C₂²×Q₈	C₂×Dic₄₃	1	1	yes	characteristic
288	C₂²×D₄	C₂×Dic₄₃	1	2	yes	—
289	C₂²×D₄	C₂×Dic₄₃	1	1	yes	characteristic
290	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
291	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
292	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
293	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
294	C₂×M₁₆	—	43	8	no	—
295	C₂×M₁₆	—	43	8	no	—
296	C₂×M₁₆	—	86	8	no	—
297	C₂×M₁₆	—	86	8	no	—
298	C₂²×C₈	—	43	2	no	—
299	C₂²×C₈	—	43	8	no	—
300	C₂²×C₈	—	43	2	no	—
301	C₂²×C₈	—	43	2	no	—
302	C₂²×C₈	—	43	2	no	—
303	C₂²×C₈	—	86	8	no	—
304	#126	C₂×Dic₄₃	1	16	yes	—
305	#125	C₂×Dic₄₃	1	8	yes	—
306	#124	C₂×Dic₄₃	1	8	yes	—
307	#123	C₂×Dic₄₃	1	16	yes	—
308	C₂²⋊Q₈	C₂×Dic₄₃	1	8	yes	—
309	#121	C₂×Dic₄₃	1	8	yes	—
310	C₄×Q₈	C₂×Dic₄₃	1	4	yes	—
311	C₄×Q₈	C₂²×D₄₃	1	4	yes	—
312	C₄×D₄	C₂×Dic₄₃	1	4	yes	—
313	C₄×D₄	C₂×Dic₄₃	1	8	yes	—
314	C₄×D₄	C₂²×D₄₃	1	4	yes	—
315	C₄×D₄	C₂²×D₄₃	1	8	yes	—
316	#117	C₂×Dic₄₃	1	8	yes	—
317	#117	C₂²×D₄₃	1	8	yes	—
318	C₂×C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
319	C₂×C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
320	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
321	C₂×C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
322	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
323	C₂×C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
324	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	2	yes	—
325	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	2	yes	—
326	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	2	yes	—
327	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	2	yes	—
328	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	2	yes	—
329	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
330	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
331	C₂×C₄²	C₂×Dic₄₃	1	4	yes	—
332	C₂×C₄²	C₂²×D₄₃	1	4	yes	—
333	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
334	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
335	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
336	C₄⋊C₈	—	43	8	no	—
337	C₄⋊C₈	—	43	8	no	—
338	C₄⋊C₈	—	43	8	no	—
339	C₂²⋊C₈	—	43	4	no	—
340	C₂²⋊C₈	—	43	4	no	—
341	C₂²⋊C₈	—	43	8	no	—
342	C₂²⋊C₈	—	43	8	no	—
343	#97	—	43	8	no	—
344	#97	—	43	8	no	—
345	#97	—	43	8	no	—
346	C₄×C₈	—	43	4	no	—
347	C₄×C₈	—	43	4	no	—
348	C₄×C₈	—	43	8	no	—
349	C₂⁴	C₂²×Dic₄₃	1	2	yes	—
350	C₂⁴	C₂²×Dic₄₃	1	1	yes	characteristic
351	C₂×Q₈	—	4	2	no	—
352	C₂×Q₈	C₂²×Dic₄₃	1	4	yes	—
353	C₂×D₄	—	4	2	no	—
354	C₂×D₄	—	4	4	no	—
355	C₂×D₄	C₂²×Dic₄₃	1	8	yes	—
356	C₂×D₄	C₂²×Dic₄₃	1	4	yes	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	4	2	no	—
361	C₂²×C₄	—	4	2	no	—
362	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
363	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
364	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
365	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
366	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
367	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
368	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
369	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
370	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
371	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
372	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
373	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
374	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
375	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
376	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
377	M₁₆	—	86	16	no	—
378	M₁₆	—	86	16	no	—
379	C₂×C₈	—	43	8	no	—
380	C₂×C₈	—	43	4	no	—
381	C₂×C₈	—	43	4	no	—
382	C₂×C₈	—	43	4	no	—
383	C₂×C₈	—	43	4	no	—
384	C₂×C₈	—	86	16	no	—
385	C₂×C₈	—	86	4	no	—
386	C₂×C₈	—	86	4	no	—
387	C₂×C₈	—	86	4	no	—
388	C₄⋊C₄	C₂²×Dic₄₃	1	8	yes	—
389	C₄⋊C₄	C₂²×Dic₄₃	1	8	yes	—
390	C₄⋊C₄	C₂²×Dic₄₃	1	4	yes	—
391	C₄⋊C₄	C₂²×Dic₄₃	1	8	yes	—
392	C₄⋊C₄	C₂²×Dic₄₃	1	4	yes	—
393	C₄⋊C₄	C₂²×Dic₄₃	1	8	yes	—
394	C₂²⋊C₄	C₂²×Dic₄₃	1	8	yes	—
395	C₂²⋊C₄	C₂²×Dic₄₃	1	8	yes	—
396	C₂²⋊C₄	C₂²×Dic₄₃	1	8	yes	—
397	C₂²⋊C₄	C₂²×Dic₄₃	1	8	yes	—
398	C₂²⋊C₄	C₂²×Dic₄₃	1	8	yes	—
399	C₄²	C₂²×Dic₄₃	1	2	yes	—
400	C₄²	C₂²×Dic₄₃	1	2	yes	—
401	C₄²	C₂²×Dic₄₃	1	4	yes	—
402	C₄²	C₂²×Dic₄₃	1	4	yes	—
403	C₄²	C₂²×Dic₄₃	1	4	yes	—
404	C₄²	C₂³×D₄₃	1	2	yes	—
405	C₄²	C₂³×D₄₃	1	4	yes	—
406	C₄²	C₂³×D₄₃	1	2	yes	—
407	C₂³	—	2	4	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	4	no	—
412	C₂³	—	2	4	no	—
413	C₂³	C₂³×Dic₄₃	1	4	yes	—
414	C₂³	C₂³×Dic₄₃	1	2	yes	—
415	C₂³	C₂³×Dic₄₃	1	1	yes	characteristic
416	Q₈	—	4	4	no	—
417	D₄	—	4	4	no	—
418	D₄	—	4	8	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	8	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	—	4	4	no	—
433	C₂×C₄	—	4	4	no	—
434	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
435	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
436	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
437	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
438	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
439	C₂×C₄	C₂³×Dic₄₃	1	4	yes	—
440	C₂×C₄	C₂³×Dic₄₃	1	4	yes	—
441	C₂×C₄	C₂³×Dic₄₃	1	4	yes	—
442	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
443	C₂×C₄	#41×D₄₃	1	4	yes	—
444	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
445	C₈	—	43	8	no	—
446	C₈	—	86	4	no	—
447	C₈	—	86	4	no	—
448	C₈	—	86	4	no	—
449	C₂²	—	2	4	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	4	no	—
454	C₂²	—	2	4	no	—
455	C₂²	—	4	4	no	—
456	C₂²	—	4	8	no	—
457	C₂²	#41×Dic₄₃	1	2	yes	—
458	C₂²	#14583666	1	2	yes	—
459	C₂²	#14583666	1	2	yes	—
460	C₂²	C₂⁴×Dic₄₃	1	1	yes	characteristic
461	C₄	—	2	4	no	—
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	2	2	no	—
465	C₄	—	2	2	no	—
466	C₄	—	2	2	no	—
467	C₄	—	2	4	no	—
468	C₄	—	2	4	no	—
469	C₄	#41×Dic₄₃	1	2	yes	—
470	C₄	C₂×#41×D₄₃	1	2	yes	—
471	C₂	—	4	2	no	—
472	C₂	—	4	4	no	—
473	C₂	#19143582	1	4	yes	direct product factor
474	C₂	C₂×#41×Dic₄₃	1	1	yes	characteristic
475	C₂	C₂×#14583666	1	1	yes	characteristic
476	C₂	C₂×#14583666	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₄₃
commutator	C₂²×C₄₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₂×C₄₃×#529	C₂
socle	C₂³×C₄₃	C₂³×C₄
prime radical	C₂×#121×C₄₃	C₄
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	C₂×#529	D₄₃
hypocenter	C₄₃	C₂×#2967
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#529

Complements

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

N	H ≅ G/N	type
1. #19143582	C₂	direct (N × H)
2. C₂×#14583030	C₂	semidirect
3. C₂×#14582977	C₂	semidirect
4. C₂×#14582971	C₂	semidirect
5. C₂×#14582971	C₂	semidirect
6. C₂×#14582960	C₂	semidirect
7. C₂×#14582956	C₂	semidirect
8. C₂×#14582855	C₂	semidirect
9. C₂×C₄×#10621877	C₂	semidirect
14. #14583030	C₂²	semidirect
15. #14582977	C₂²	semidirect
16. #14582971	C₂²	semidirect
17. #14582971	C₂²	semidirect
18. #14582960	C₂²	semidirect
19. #14582956	C₂²	semidirect
27. #14582855	C₂²	semidirect
28. C₄×#10621877	C₂²	semidirect
245. C₂×C₄₃	#2967	semidirect
286. C₄₃	C₂×#2967	semidirect
473. C₂	#19143582	direct (N × H)

Maximal subgroups

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

subgroup	index
#19143582	2
C₂×#14583030	2
C₂×#14582977	2
C₂×#14582971	2
C₂×#14582960	2
C₂×#14582956	2
C₂×#14582855	2
C₂×C₄×#10621877	2
C₂×C₄₃×#529	2
C₂×#2967	43

Subgroups — C2×#19143582 #25961062

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19143582 #25961062