Subgroups — C₂×C₈×#10621898 #25961029

Order 11008.

2566 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#10621898	C₂	1	1	yes	maximal, characteristic
2	C₈×#10621898	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₈×Dic₈₆	C₂	1	2	yes	maximal, complemented
4	C₂×C₈×D₁₇₂	C₂	1	2	yes	maximal, complemented
5	C₂×C₈×C₂²⋊D₄₃	C₂	1	4	yes	maximal, complemented
6	C₂×#14582952	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#14582950	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₈×D₄₃	C₂	1	2	yes	maximal, complemented
9	C₂²×C₄×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#10621898	C₄	1	1	yes	characteristic
11	C₂²×C₈×D₄₃	C₂²	1	4	yes	—
12	C₄×#10621898	C₄	1	8	yes	—
13	C₄×#10621898	C₂²	1	8	yes	—
14	C₂×C₄×Dic₈₆	C₄	1	1	yes	characteristic
15	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₁₇₂	C₄	1	1	yes	characteristic
17	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₂²⋊D₄₃	C₄	1	2	yes	—
19	C₂×C₄×C₂²⋊D₄₃	C₂²	1	2	yes	—
20	C₂×#13063284	C₄	1	1	yes	characteristic
21	C₂×#13063282	C₄	1	2	yes	—
22	C₂×C₄²×D₄₃	C₂²	1	2	yes	—
23	C₈×Dic₈₆	C₂²	1	16	yes	complemented
24	C₈×D₁₇₂	C₂²	1	16	yes	complemented
25	C₈×C₂²⋊D₄₃	C₂²	1	32	yes	complemented
26	#14582952	C₂²	1	8	yes	complemented
27	#14582950	C₂²	1	16	yes	complemented
28	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
29	C₂×Dic₄₃⋊C₈	C₂²	1	4	yes	—
30	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
31	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	4	yes	—
32	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
33	C₂×C₈×Dic₄₃	C₂²	1	4	yes	—
34	C₄×C₈×D₄₃	C₂²	1	16	yes	complemented
35	C₂³×C₈×C₄₃	C₂²	1	2	yes	—
36	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	—
39	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₄₃	C₂²	1	8	yes	complemented
41	C₂×#10621898	C₈	1	16	yes	direct product factor
42	C₂×#10621898	C₂×C₄	1	8	yes	—
43	C₂²×Dic₈₆	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₁₇₂	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₂²⋊D₄₃	C₂×C₄	1	2	yes	—
46	C₂²×C₄×D₄₃	C₂×C₄	1	2	yes	—
47	C₂²×C₄×D₄₃	C₂×C₄	1	2	yes	—
48	C₂²×C₄×D₄₃	C₂³	1	2	yes	—
49	C₂²×C₄₃⋊C₈	C₂³	1	4	yes	—
50	C₂×C₈×D₄₃	—	2	16	no	—
51	C₂×C₈×D₄₃	C₂³	1	16	yes	—
52	C₄×Dic₈₆	C₂×C₄	1	8	yes	—
53	C₄×Dic₈₆	C₂×C₄	1	4	yes	—
54	C₄×Dic₈₆	C₂³	1	4	yes	—
55	C₄×D₁₇₂	C₂×C₄	1	8	yes	—
56	C₄×D₁₇₂	C₂×C₄	1	4	yes	—
57	C₄×D₁₇₂	C₂³	1	4	yes	—
58	C₄×C₂²⋊D₄₃	C₂×C₄	1	16	yes	—
59	C₄×C₂²⋊D₄₃	C₂×C₄	1	8	yes	—
60	C₄×C₂²⋊D₄₃	C₂³	1	8	yes	—
61	#13063284	C₂×C₄	1	8	yes	—
62	#13063282	C₂×C₄	1	16	yes	—
63	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
65	C₂×Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
66	C₂×Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
67	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	2	yes	—
68	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	2	yes	—
69	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	2	yes	—
70	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
71	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
72	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
73	C₄²×D₄₃	C₂×C₄	1	8	yes	—
74	C₄²×D₄₃	C₂³	1	8	yes	—
75	C₄⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
76	Dic₄₃⋊C₈	C₂³	1	16	yes	—
77	C₂²⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
78	(C₂×D₄₃)⋊C₈	C₂³	1	16	yes	—
79	C₄×C₄₃⋊C₈	C₂³	1	8	yes	—
80	C₈×Dic₄₃	C₂³	1	16	yes	—
81	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
82	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
83	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₄₃	—	2	8	no	—
85	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
86	C₂²×C₈×C₄₃	C₂³	1	8	yes	—
87	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
88	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
91	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
94	C₄×C₈×C₄₃	C₂³	1	4	yes	—
95	C₄×C₈×C₄₃	C₂³	1	4	yes	—
96	C₄×C₈×C₄₃	C₂³	1	8	yes	—
97	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
98	C₂³×D₄₃	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₄₃	—	2	4	no	—
100	C₂²×C₄×C₄₃	—	2	4	no	—
101	C₂²×C₄×C₄₃	C₂×C₈	1	8	yes	complemented
102	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
106	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
109	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
111	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
112	C₂×C₂²⋊D₄₃	C₂×C₈	1	16	yes	complemented
113	C₂×C₂²⋊D₄₃	C₂²×C₄	1	8	yes	—
114	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
115	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
116	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
117	#10621898	C₂×C₈	1	64	yes	direct product factor
118	C₂×D₁₇₂	C₂×C₈	1	8	yes	complemented
119	C₂×D₁₇₂	C₂²×C₄	1	4	yes	—
120	C₂×C₄×D₄₃	—	2	8	no	—
121	C₂×C₄×D₄₃	—	2	8	no	—
122	C₂×C₄×D₄₃	C₂×C₈	1	16	yes	complemented
123	C₂×C₄×D₄₃	C₂²×C₄	1	4	yes	—
124	C₂×C₄×D₄₃	C₂²×C₄	1	8	yes	—
125	C₂×C₄×D₄₃	C₂²×C₄	1	8	yes	—
126	C₂×C₄×D₄₃	C₂⁴	1	4	yes	—
127	C₂×Dic₈₆	C₂×C₈	1	8	yes	complemented
128	C₂×Dic₈₆	C₂²×C₄	1	4	yes	—
129	C₂×C₈×C₄₃	—	2	4	no	—
130	C₂×C₈×C₄₃	—	2	16	no	—
131	C₂×C₈×C₄₃	#41	1	8	yes	complemented
132	C₂×C₈×C₄₃	C₂⁴	1	4	yes	—
133	C₂×C₈×C₄₃	C₂⁴	1	4	yes	—
134	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
135	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
136	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
137	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
138	C₄²×C₄₃	C₂⁴	1	2	yes	—
139	C₄²×C₄₃	C₂⁴	1	2	yes	—
140	C₂²⋊Dic₄₃	C₂²×C₄	1	8	yes	—
141	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	8	yes	—
142	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	8	yes	—
143	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
144	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
145	Dic₄₃⋊C₄	C₂²×C₄	1	8	yes	—
146	Dic₄₃⋊C₄	C₂²×C₄	1	8	yes	—
147	C₄×Dic₄₃	C₂²×C₄	1	4	yes	—
148	C₄×Dic₄₃	C₂²×C₄	1	8	yes	—
149	C₄×Dic₄₃	C₂²×C₄	1	8	yes	—
150	C₄×Dic₄₃	C₂⁴	1	4	yes	—
151	C₂×C₄₃⋊C₈	—	2	8	no	—
152	C₂×C₄₃⋊C₈	C₂⁴	1	8	yes	—
153	C₈×D₄₃	—	2	32	no	—
154	C₂³×C₄₃	—	2	2	no	—
155	C₂³×C₄₃	—	2	2	no	—
156	C₂³×C₄₃	C₂²×C₈	1	4	yes	—
157	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
158	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
159	C₂²×D₄₃	—	2	4	no	—
160	C₂²×D₄₃	—	2	4	no	—
161	C₂²×D₄₃	C₂²×C₈	1	8	yes	—
162	C₂²×D₄₃	C₂³×C₄	1	4	yes	—
163	C₂×C₄×C₄₃	—	2	2	no	—
164	C₂×C₄×C₄₃	—	2	2	no	—
165	C₂×C₄×C₄₃	—	2	4	no	—
166	C₂×C₄×C₄₃	—	2	8	no	—
167	C₂×C₄×C₄₃	—	2	4	no	—
168	C₂×C₄×C₄₃	C₂²×C₈	1	4	yes	—
169	C₂×C₄×C₄₃	C₂²×C₈	1	4	yes	—
170	C₂×C₄×C₄₃	C₂²×C₈	1	16	yes	complemented
171	C₂×C₄×C₄₃	#131	1	4	yes	—
172	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
173	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
174	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
176	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
177	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
178	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
179	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
180	C₂²⋊D₄₃	C₂²×C₈	1	32	yes	complemented
181	C₂×Dic₄₃	—	2	4	no	—
182	C₂×Dic₄₃	—	2	4	no	—
183	C₂×Dic₄₃	C₂²×C₈	1	8	yes	—
184	C₂×Dic₄₃	C₂³×C₄	1	4	yes	—
185	C₂×Dic₄₃	C₂³×C₄	1	4	yes	—
186	C₂×Dic₄₃	C₂³×C₄	1	4	yes	—
187	D₁₇₂	C₂²×C₈	1	16	yes	complemented
188	C₄×D₄₃	—	2	8	no	—
189	C₄×D₄₃	—	2	16	no	—
190	C₄×D₄₃	—	2	8	no	—
191	C₄×D₄₃	C₂²×C₈	1	32	yes	complemented
192	Dic₈₆	C₂²×C₈	1	16	yes	complemented
193	C₈×C₄₃	—	2	4	no	—
194	C₈×C₄₃	C₂×#41	1	8	yes	complemented
195	C₄₃⋊C₈	—	2	8	no	—
196	C₂×C₈×#41	—	43	1	no	maximal, Sylow
197	C₂²×C₄₃	—	2	2	no	—
198	C₂²×C₄₃	—	2	8	no	—
199	C₂²×C₄₃	—	2	2	no	—
200	C₂²×C₄₃	C₄×#41	1	2	yes	—
201	C₂²×C₄₃	C₂³×C₈	1	4	yes	—
202	C₂²×C₄₃	C₂³×C₈	1	2	yes	—
203	C₂²×C₄₃	C₂×#131	1	2	yes	—
204	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
205	C₂×D₄₃	—	2	4	no	—
206	C₂×D₄₃	—	2	16	no	—
207	C₂×D₄₃	—	2	4	no	—
208	C₂×D₄₃	C₂³×C₈	1	8	yes	—
209	C₄×C₄₃	—	2	2	no	—
210	C₄×C₄₃	—	2	2	no	—
211	C₄×C₄₃	C₄×#41	1	2	yes	—
212	C₄×C₄₃	C₂³×C₈	1	4	yes	—
213	C₄×C₄₃	C₂³×C₈	1	4	yes	—
214	C₄×C₄₃	C₂×#131	1	4	yes	—
215	C₄×C₄₃	C₂²×#41	1	2	yes	—
216	Dic₄₃	—	2	4	no	—
217	Dic₄₃	—	2	4	no	—
218	Dic₄₃	C₂³×C₈	1	8	yes	—
219	C₂×C₄×#41	—	43	1	no	—
220	C₈×#41	—	43	16	no	—
221	C₂×C₈×Q₈	—	43	2	no	—
222	C₂×C₈×D₄	—	43	2	no	—
223	C₂×C₈×D₄	—	43	4	no	—
224	C₂×#431	—	43	1	no	—
225	C₂×#431	—	43	2	no	—
226	C₂²×C₄×C₈	—	43	2	no	—
227	C₂²×C₄×C₈	D₄₃	1	1	yes	characteristic, complemented
228	C₂×C₄₃	—	2	4	no	—
229	C₂×C₄₃	C₈×#41	1	4	yes	complemented
230	C₂×C₄₃	C₂×C₄×#41	1	1	yes	characteristic
231	C₂×C₄₃	C₂⁴×C₈	1	1	yes	characteristic
232	C₂×C₄₃	C₂²×#131	1	1	yes	characteristic
233	D₄₃	—	2	8	no	—
234	C₂²×#41	—	43	1	no	—
235	C₂³×C₈	—	43	4	no	—
236	C₂³×C₈	C₂×D₄₃	1	2	yes	—
237	C₄×#41	—	43	8	no	—
238	C₄×#41	—	43	8	no	—
239	C₂×C₄×Q₈	—	43	1	no	—
240	C₂×C₄×Q₈	—	43	1	no	—
241	C₂×C₄×D₄	—	43	2	no	—
242	C₂×C₄×D₄	—	43	2	no	—
243	C₂×C₄×D₄	—	43	1	no	—
244	C₂×C₄×D₄	—	43	1	no	—
245	C₂×#117	—	43	1	no	—
246	C₂×#117	—	43	2	no	—
247	C₂²×C₄²	—	43	2	no	—
248	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
249	C₈×Q₈	—	43	16	no	—
250	C₈×D₄	—	43	32	no	—
251	C₈×D₄	—	43	16	no	—
252	#431	—	43	8	no	—
253	#431	—	43	16	no	—
254	C₂×C₄⋊C₈	—	43	4	no	—
255	C₂×C₄⋊C₈	—	43	2	no	—
256	C₂×C₂²⋊C₈	—	43	2	no	—
257	C₂×C₂²⋊C₈	—	43	4	no	—
258	C₂×C₄×C₈	—	43	4	no	—
259	C₂×C₄×C₈	—	43	2	no	—
260	C₂×C₄×C₈	—	43	16	no	—
261	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
262	C₂×C₄×C₈	C₂×D₄₃	1	2	yes	—
263	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
264	C₂×C₄×C₈	C₂×D₄₃	1	8	yes	complemented
265	C₄₃	C₂×C₈×#41	1	1	yes	characteristic, complemented, Sylow
266	C₂×#41	—	43	16	no	—
267	C₂×#41	—	43	8	no	—
268	C₂²×Q₈	—	43	1	no	—
269	C₂²×D₄	—	43	2	no	—
270	C₂²×D₄	—	43	1	no	—
271	C₂³×C₄	—	43	2	no	—
272	C₂³×C₄	—	43	2	no	—
273	C₂³×C₄	—	43	2	no	—
274	C₂³×C₄	C₄×D₄₃	1	1	yes	characteristic
275	C₂³×C₄	C₄×D₄₃	1	1	yes	characteristic
276	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
277	C₂²×C₈	—	2	8	no	—
278	C₂²×C₈	—	43	4	no	—
279	C₂²×C₈	—	43	16	no	—
280	C₂²×C₈	—	86	16	no	—
281	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
282	C₂²×C₈	C₂²×D₄₃	1	8	yes	—
283	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
284	C₄×Q₈	—	43	4	no	—
285	C₄×Q₈	—	43	8	no	—
286	C₄×Q₈	—	43	4	no	—
287	C₄×D₄	—	43	16	no	—
288	C₄×D₄	—	43	8	no	—
289	C₄×D₄	—	43	8	no	—
290	C₄×D₄	—	43	4	no	—
291	C₄×D₄	—	43	8	no	—
292	C₄×D₄	—	43	4	no	—
293	#117	—	43	8	no	—
294	#117	—	43	16	no	—
295	C₂×C₄⋊C₄	—	43	2	no	—
296	C₂×C₄⋊C₄	—	43	2	no	—
297	C₂×C₄⋊C₄	—	43	1	no	—
298	C₂×C₄⋊C₄	—	43	1	no	—
299	C₂×C₂²⋊C₄	—	43	2	no	—
300	C₂×C₂²⋊C₄	—	43	2	no	—
301	C₂×C₂²⋊C₄	—	43	2	no	—
302	C₂×C₄²	—	43	2	no	—
303	C₂×C₄²	—	43	2	no	—
304	C₂×C₄²	—	43	2	no	—
305	C₂×C₄²	—	43	8	no	—
306	C₂×C₄²	—	43	8	no	—
307	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
308	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
309	C₂×C₄²	C₄×D₄₃	1	4	yes	—
310	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
311	C₂×C₄²	C₂²×D₄₃	1	4	yes	—
312	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
313	C₄⋊C₈	—	43	16	no	—
314	C₄⋊C₈	—	43	8	no	—
315	C₂²⋊C₈	—	43	8	no	—
316	C₂²⋊C₈	—	43	16	no	—
317	C₄×C₈	—	43	16	no	—
318	C₄×C₈	—	43	8	no	—
319	C₄×C₈	C₂²×D₄₃	1	4	yes	—
320	C₄×C₈	C₂²×D₄₃	1	4	yes	—
321	C₄×C₈	C₂²×D₄₃	1	8	yes	—
322	C₂⁴	—	43	2	no	—
323	C₂⁴	C₂×C₄×D₄₃	1	1	yes	characteristic
324	#41	—	43	64	no	—
325	C₂×Q₈	—	43	8	no	—
326	C₂×Q₈	—	43	4	no	—
327	C₂×D₄	—	43	16	no	—
328	C₂×D₄	—	43	8	no	—
329	C₂×D₄	—	43	8	no	—
330	C₂×D₄	—	43	4	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	43	2	no	—
334	C₂²×C₄	—	43	16	no	—
335	C₂²×C₄	—	43	8	no	—
336	C₂²×C₄	—	43	2	no	—
337	C₂²×C₄	—	43	2	no	—
338	C₂²×C₄	—	43	4	no	—
339	C₂²×C₄	—	43	8	no	—
340	C₂²×C₄	—	43	4	no	—
341	C₂²×C₄	—	86	8	no	—
342	C₂²×C₄	—	86	8	no	—
343	C₂²×C₄	C₈×D₄₃	1	8	yes	complemented
344	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
345	C₂²×C₄	C₂×C₄×D₄₃	1	4	yes	—
346	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
347	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
348	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
349	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
350	C₂²×C₄	C₂×C₄×D₄₃	1	4	yes	—
351	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
352	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
353	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
354	C₂×C₈	—	2	4	no	—
355	C₂×C₈	—	2	16	no	—
356	C₂×C₈	—	43	8	no	—
357	C₂×C₈	—	86	8	no	—
358	C₂×C₈	—	86	32	no	—
359	C₂×C₈	#10621898	1	8	yes	direct product factor
360	C₂×C₈	C₂³×D₄₃	1	4	yes	—
361	C₂×C₈	C₂³×D₄₃	1	4	yes	—
362	C₄⋊C₄	—	43	8	no	—
363	C₄⋊C₄	—	43	8	no	—
364	C₄⋊C₄	—	43	4	no	—
365	C₄⋊C₄	—	43	4	no	—
366	C₂²⋊C₄	—	43	8	no	—
367	C₂²⋊C₄	—	43	8	no	—
368	C₂²⋊C₄	—	43	8	no	—
369	C₄²	—	43	8	no	—
370	C₄²	—	43	4	no	—
371	C₄²	—	43	8	no	—
372	C₄²	—	43	4	no	—
373	C₄²	C₂×C₄×D₄₃	1	2	yes	—
374	C₄²	C₂×C₄×D₄₃	1	4	yes	—
375	C₄²	C₂×C₄×D₄₃	1	4	yes	—
376	C₄²	C₂×C₄×D₄₃	1	2	yes	—
377	C₄²	C₂³×D₄₃	1	2	yes	—
378	C₄²	C₂³×D₄₃	1	2	yes	—
379	C₂³	—	2	2	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	43	8	no	—
382	C₂³	—	43	4	no	—
383	C₂³	—	86	4	no	—
384	C₂³	—	86	4	no	—
385	C₂³	C₂×C₈×D₄₃	1	4	yes	—
386	C₂³	C₂²×C₄×D₄₃	1	2	yes	—
387	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
388	Q₈	—	43	16	no	—
389	D₄	—	43	32	no	—
390	D₄	—	43	16	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	8	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	43	8	no	—
397	C₂×C₄	—	43	4	no	—
398	C₂×C₄	—	43	32	no	—
399	C₂×C₄	—	43	4	no	—
400	C₂×C₄	—	43	4	no	—
401	C₂×C₄	—	86	4	no	—
402	C₂×C₄	—	86	4	no	—
403	C₂×C₄	—	86	8	no	—
404	C₂×C₄	—	86	16	no	—
405	C₂×C₄	—	86	8	no	—
406	C₂×C₄	C₂×C₈×D₄₃	1	4	yes	—
407	C₂×C₄	C₂×C₈×D₄₃	1	4	yes	—
408	C₂×C₄	C₂×C₈×D₄₃	1	16	yes	complemented
409	C₂×C₄	#13063331	1	4	yes	—
410	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
411	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
412	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
413	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
414	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
415	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
416	C₂×C₄	C₂×#10621898	1	4	yes	—
417	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
418	C₈	—	2	4	no	—
419	C₈	—	86	8	no	—
420	C₈	C₂×#10621898	1	8	yes	direct product factor
421	C₂²	—	2	8	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	2	2	no	—
424	C₂²	—	43	8	no	—
425	C₂²	—	86	16	no	—
426	C₂²	—	86	4	no	—
427	C₂²	—	86	4	no	—
428	C₂²	C₄×#10621898	1	2	yes	—
429	C₂²	C₂²×C₈×D₄₃	1	4	yes	—
430	C₂²	C₂²×C₈×D₄₃	1	2	yes	—
431	C₂²	C₂×#13063331	1	2	yes	—
432	C₂²	C₂³×C₄×D₄₃	1	1	yes	characteristic
433	C₄	—	2	2	no	—
434	C₄	—	2	2	no	—
435	C₄	—	43	8	no	—
436	C₄	—	86	4	no	—
437	C₄	—	86	4	no	—
438	C₄	C₄×#10621898	1	2	yes	—
439	C₄	C₂²×C₈×D₄₃	1	4	yes	—
440	C₄	C₂²×C₈×D₄₃	1	4	yes	—
441	C₄	C₂×#13063331	1	4	yes	—
442	C₄	C₂²×#10621898	1	2	yes	—
443	C₂	—	2	4	no	—
444	C₂	—	86	8	no	—
445	C₂	C₈×#10621898	1	4	yes	direct product factor
446	C₂	C₂×C₄×#10621898	1	1	yes	characteristic
447	C₂	C₂³×C₈×D₄₃	1	1	yes	characteristic
448	C₂	C₂²×#13063331	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₈	C₂×D₄₃
commutator	C₂×C₄₃	C₂⁴×C₈
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₂²×C₄×C₈×C₄₃	C₂
socle	C₂³×C₄₃	C₂³×C₄
prime radical	C₂²×#10621898	C₄
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	C₂²×C₄×C₈	D₄₃
hypocenter	C₄₃	C₂×C₈×#41
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄×C₈ ◁ C₂²×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. C₈×#10621898	C₂	direct (N × H)
3. C₂×C₈×Dic₈₆	C₂	semidirect
4. C₂×C₈×D₁₇₂	C₂	semidirect
5. C₂×C₈×C₂²⋊D₄₃	C₂	semidirect
6. C₂×#14582952	C₂	semidirect
7. C₂×#14582950	C₂	semidirect
8. C₂×C₄×C₈×D₄₃	C₂	semidirect
9. C₂²×C₄×C₈×C₄₃	C₂	semidirect
23. C₈×Dic₈₆	C₂²	semidirect
24. C₈×D₁₇₂	C₂²	semidirect
25. C₈×C₂²⋊D₄₃	C₂²	semidirect
26. #14582952	C₂²	semidirect
27. #14582950	C₂²	semidirect
34. C₄×C₈×D₄₃	C₂²	semidirect
40. C₂×C₄×C₈×C₄₃	C₂²	semidirect
41. C₂×#10621898	C₈	direct (N × H)
101. C₂²×C₄×C₄₃	C₂×C₈	semidirect
112. C₂×C₂²⋊D₄₃	C₂×C₈	semidirect
117. #10621898	C₂×C₈	direct (N × H)
118. C₂×D₁₇₂	C₂×C₈	semidirect
122. C₂×C₄×D₄₃	C₂×C₈	semidirect
127. C₂×Dic₈₆	C₂×C₈	semidirect
131. C₂×C₈×C₄₃	#41	semidirect
170. C₂×C₄×C₄₃	C₂²×C₈	semidirect
180. C₂²⋊D₄₃	C₂²×C₈	semidirect
187. D₁₇₂	C₂²×C₈	semidirect
191. C₄×D₄₃	C₂²×C₈	semidirect
192. Dic₈₆	C₂²×C₈	semidirect
194. C₈×C₄₃	C₂×#41	semidirect
227. C₂²×C₄×C₈	D₄₃	semidirect
229. C₂×C₄₃	C₈×#41	semidirect
264. C₂×C₄×C₈	C₂×D₄₃	semidirect
265. C₄₃	C₂×C₈×#41	semidirect
343. C₂²×C₄	C₈×D₄₃	semidirect
359. C₂×C₈	#10621898	direct (N × H)
408. C₂×C₄	C₂×C₈×D₄₃	semidirect
420. C₈	C₂×#10621898	direct (N × H)
445. C₂	C₈×#10621898	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×#10621898	2
C₈×#10621898	2
C₂×C₈×Dic₈₆	2
C₂×C₈×D₁₇₂	2
C₂×C₈×C₂²⋊D₄₃	2
C₂×#14582952	2
C₂×#14582950	2
C₂×C₄×C₈×D₄₃	2
C₂²×C₄×C₈×C₄₃	2
C₂×C₈×#41	43

Subgroups — C2×C8×#10621898 #25961029

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×#10621898 #25961029