Subgroups — C₂×#19143142 #25960196

Order 11008.

4946 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583666	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#41×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#19143142	C₂	1	16	yes	maximal, direct product factor
4	C₂×#14582916	C₂	1	6	yes	maximal, complemented
5	C₂²×#13063252	C₂	1	6	yes	maximal, complemented
6	C₂×C₄₃×#585	C₂	1	1	yes	maximal, characteristic
7	#14583666	—	2	4	no	—
8	#14583666	C₂²	1	8	yes	complemented
9	C₂×#13063332	—	2	4	no	—
10	C₂²×#10621877	C₂²	1	6	yes	complemented
11	#41×Dic₄₃	—	2	4	no	—
12	#41×Dic₄₃	C₂²	1	8	yes	complemented
13	C₂×Q₈×Dic₄₃	—	2	1	no	—
14	C₂×D₄×Dic₄₃	—	2	3	no	—
15	C₂×#13063284	C₂²	1	3	yes	complemented
16	C₂²×C₄×Dic₄₃	C₂²	1	3	yes	complemented
17	#14582916	C₂²	1	48	yes	complemented
18	C₂×#13063252	C₂²	1	4	yes	complemented
19	C₂×#13063252	C₂²	1	12	yes	complemented
20	C₂×#13063252	C₂²	1	48	yes	complemented
21	C₄₃×#585	—	2	4	no	—
22	C₄₃×#585	—	2	4	no	—
23	C₄₃×#585	C₄	1	8	yes	complemented
24	C₄₃×#585	C₂²	1	8	yes	—
25	C₂×2₋¹⁺⁴×C₄₃	—	2	1	no	—
26	C₂×2₋¹⁺⁴×C₄₃	C₄	1	4	yes	complemented
27	C₂×H(5,𝔽₂)×C₄₃	—	2	3	no	—
28	C₂×H(5,𝔽₂)×C₄₃	C₄	1	4	yes	complemented
29	C₂²×#41×C₄₃	—	2	4	no	—
30	C₂²×#41×C₄₃	C₂²	1	6	yes	—
31	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
32	C₂³×Dic₄₃	—	2	3	no	—
33	#13063332	—	2	32	no	—
34	C₂×#10621877	—	2	6	no	—
35	C₂×#10621877	—	2	12	no	—
36	C₂×#10621877	C₂³	1	4	yes	—
37	C₂×#10621877	C₂³	1	24	yes	complemented
38	C₂²×C₄₃⋊C₈	—	2	6	no	—
39	Q₈×Dic₄₃	—	2	8	no	—
40	D₄×Dic₄₃	—	2	24	no	—
41	#13063284	—	2	6	no	—
42	#13063284	C₂³	1	12	yes	complemented
43	C₂×C₄⋊Dic₄₃	—	2	3	no	—
44	C₂×C₂²⋊Dic₄₃	—	2	3	no	—
45	C₂×C₄×Dic₄₃	—	2	3	no	—
46	C₂×C₄×Dic₄₃	—	2	6	no	—
47	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
48	C₂×C₄×Dic₄₃	C₂³	1	3	yes	—
49	C₂×C₄×Dic₄₃	C₂³	1	12	yes	complemented
50	#13063252	C₂³	1	16	yes	complemented
51	#13063252	C₂³	1	48	yes	complemented
52	2₋¹⁺⁴×C₄₃	—	2	16	no	—
53	2₋¹⁺⁴×C₄₃	—	2	8	no	—
54	2₋¹⁺⁴×C₄₃	—	2	8	no	—
55	2₋¹⁺⁴×C₄₃	C₂×C₄	1	32	yes	complemented
56	H(5,𝔽₂)×C₄₃	—	2	16	no	—
57	H(5,𝔽₂)×C₄₃	—	2	24	no	—
58	H(5,𝔽₂)×C₄₃	—	2	24	no	—
59	H(5,𝔽₂)×C₄₃	C₂×C₄	1	32	yes	complemented
60	C₂×#41×C₄₃	—	2	32	no	—
61	C₂×#41×C₄₃	—	2	32	no	—
62	C₂×#41×C₄₃	—	2	4	no	—
63	C₂×#41×C₄₃	—	2	12	no	—
64	C₂×#41×C₄₃	—	2	6	no	—
65	C₂×#41×C₄₃	—	2	6	no	—
66	C₂×#41×C₄₃	—	2	12	no	—
67	C₂×#41×C₄₃	—	2	12	no	—
68	C₂×#41×C₄₃	C₂×C₄	1	4	yes	—
69	C₂×#41×C₄₃	C₂×C₄	1	4	yes	—
70	C₂×#41×C₄₃	C₂×C₄	1	12	yes	complemented
71	C₂×#41×C₄₃	C₂×C₄	1	24	yes	complemented
72	C₂×#41×C₄₃	D₄	1	4	yes	—
73	C₂×#41×C₄₃	D₄	1	4	yes	—
74	C₂×#41×C₄₃	D₄	1	4	yes	—
75	C₂×#41×C₄₃	C₂³	1	4	yes	—
76	C₂×#41×C₄₃	C₂³	1	24	yes	—
77	C₂×#41×C₄₃	C₂³	1	4	yes	—
78	C₂²×Q₈×C₄₃	—	2	4	no	—
79	C₂²×Q₈×C₄₃	C₂×C₄	1	6	yes	complemented
80	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
81	C₂²×D₄×C₄₃	—	2	6	no	—
82	C₂²×D₄×C₄₃	—	2	12	no	—
83	C₂²×D₄×C₄₃	C₂×C₄	1	6	yes	complemented
84	C₂²×D₄×C₄₃	D₄	1	3	yes	—
85	C₂³×C₄×C₄₃	—	2	6	no	—
86	C₂³×C₄×C₄₃	C₂³	1	3	yes	—
87	C₂⁴×C₄₃	—	2	6	no	—
88	C₂⁴×C₄₃	C₂×D₄	1	3	yes	—
89	#41×C₄₃	—	2	32	no	—
90	#41×C₄₃	—	2	96	no	—
91	#41×C₄₃	—	2	24	no	—
92	#41×C₄₃	—	2	24	no	—
93	#41×C₄₃	—	2	24	no	—
94	#41×C₄₃	—	2	4	no	—
95	#41×C₄₃	—	2	24	no	—
96	#41×C₄₃	—	2	4	no	—
97	#41×C₄₃	—	2	24	no	—
98	#41×C₄₃	C₂²⋊C₄	1	16	yes	—
99	#41×C₄₃	C₂²⋊C₄	1	16	yes	—
100	#41×C₄₃	C₂²×C₄	1	8	yes	—
101	#41×C₄₃	C₂²×C₄	1	16	yes	—
102	#41×C₄₃	C₂²×C₄	1	48	yes	complemented
103	#41×C₄₃	C₂×D₄	1	16	yes	—
104	#41×C₄₃	C₂⁴	1	8	yes	—
105	C₂×Q₈×C₄₃	—	2	32	no	—
106	C₂×Q₈×C₄₃	—	2	6	no	—
107	C₂×Q₈×C₄₃	—	2	12	no	—
108	C₂×Q₈×C₄₃	C₂²⋊C₄	1	4	yes	—
109	C₂×Q₈×C₄₃	C₂²⋊C₄	1	4	yes	—
110	C₂×Q₈×C₄₃	C₂²×C₄	1	4	yes	—
111	C₂×Q₈×C₄₃	C₂²×C₄	1	24	yes	complemented
112	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
113	C₂×D₄×C₄₃	—	2	96	no	—
114	C₂×D₄×C₄₃	—	2	6	no	—
115	C₂×D₄×C₄₃	—	2	12	no	—
116	C₂×D₄×C₄₃	—	2	12	no	—
117	C₂×D₄×C₄₃	—	2	24	no	—
118	C₂×D₄×C₄₃	—	2	4	no	—
119	C₂×D₄×C₄₃	—	2	24	no	—
120	C₂×D₄×C₄₃	C₂²⋊C₄	1	12	yes	—
121	C₂×D₄×C₄₃	C₂²⋊C₄	1	12	yes	—
122	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
123	C₂×D₄×C₄₃	C₂²×C₄	1	24	yes	complemented
124	C₂×D₄×C₄₃	C₂×D₄	1	12	yes	—
125	C₂²×C₄×C₄₃	—	2	12	no	—
126	C₂²×C₄×C₄₃	—	2	24	no	—
127	C₂²×C₄×C₄₃	—	2	4	no	—
128	C₂²×C₄×C₄₃	—	2	24	no	—
129	C₂²×C₄×C₄₃	—	2	6	no	—
130	C₂²×C₄×C₄₃	C₂²×C₄	1	6	yes	—
131	C₂²×C₄×C₄₃	C₂²×C₄	1	6	yes	—
132	C₂²×C₄×C₄₃	C₂×D₄	1	6	yes	—
133	C₂²×C₄×C₄₃	C₂×D₄	1	6	yes	—
134	C₂²×C₄×C₄₃	C₂×D₄	1	3	yes	—
135	C₂²×C₄×C₄₃	C₂×D₄	1	6	yes	—
136	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
137	C₂²×C₄×C₄₃	C₂⁴	1	6	yes	—
138	C₂²×Dic₄₃	—	2	1	no	—
139	C₂²×Dic₄₃	—	2	3	no	—
140	C₂²×Dic₄₃	—	2	12	no	—
141	C₂²×Dic₄₃	—	4	12	no	—
142	C₂²⋊Dic₄₃	—	2	12	no	—
143	C₄⋊Dic₄₃	—	2	12	no	—
144	C₄×Dic₄₃	—	2	1	no	—
145	C₄×Dic₄₃	—	2	3	no	—
146	C₄×Dic₄₃	—	2	12	no	—
147	C₄×Dic₄₃	C₂⁴	1	2	yes	—
148	C₄×Dic₄₃	C₂⁴	1	6	yes	—
149	#10621877	—	2	4	no	—
150	#10621877	—	2	24	no	—
151	#10621877	C₂⁴	1	8	yes	—
152	C₂×C₄₃⋊C₈	—	2	4	no	—
153	C₂×C₄₃⋊C₈	—	2	24	no	—
154	C₂³×C₄₃	—	2	4	no	—
155	C₂³×C₄₃	—	2	24	no	—
156	C₂³×C₄₃	—	4	6	no	—
157	C₂³×C₄₃	—	8	12	no	—
158	C₂³×C₄₃	C₂×C₂²⋊C₄	1	6	yes	—
159	C₂³×C₄₃	C₂×C₂²⋊C₄	1	6	yes	—
160	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
161	C₂³×C₄₃	C₂²×D₄	1	6	yes	—
162	Q₈×C₄₃	—	2	4	no	—
163	Q₈×C₄₃	—	2	24	no	—
164	Q₈×C₄₃	C₂×C₂²⋊C₄	1	16	yes	—
165	Q₈×C₄₃	C₂³×C₄	1	8	yes	—
166	D₄×C₄₃	—	2	8	no	—
167	D₄×C₄₃	—	2	48	no	—
168	D₄×C₄₃	—	2	8	no	—
169	D₄×C₄₃	—	2	4	no	—
170	D₄×C₄₃	—	2	24	no	—
171	D₄×C₄₃	C₂×C₂²⋊C₄	1	48	yes	—
172	D₄×C₄₃	C₂³×C₄	1	8	yes	—
173	C₂×C₄×C₄₃	—	2	4	no	—
174	C₂×C₄×C₄₃	—	2	24	no	—
175	C₂×C₄×C₄₃	—	2	8	no	—
176	C₂×C₄×C₄₃	—	2	48	no	—
177	C₂×C₄×C₄₃	—	2	8	no	—
178	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	6	yes	—
179	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	12	yes	—
180	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	12	yes	—
181	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	6	yes	—
182	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
184	C₂×C₄×C₄₃	C₂³×C₄	1	12	yes	—
185	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₃	C₂²×D₄	1	6	yes	—
187	C₂×C₄×C₄₃	C₂²×D₄	1	12	yes	—
188	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
191	C₂×Dic₄₃	—	2	4	no	—
192	C₂×Dic₄₃	—	2	2	no	—
193	C₂×Dic₄₃	—	2	6	no	—
194	C₂×Dic₄₃	—	4	24	no	—
195	C₂×Dic₄₃	—	4	6	no	—
196	C₄₃⋊C₈	—	2	8	no	—
197	C₂×#2901	—	43	1	no	maximal, Sylow
198	C₂²×C₄₃	—	2	2	no	—
199	C₂²×C₄₃	—	2	12	no	—
200	C₂²×C₄₃	—	2	8	no	—
201	C₂²×C₄₃	—	4	6	no	—
202	C₂²×C₄₃	—	4	6	no	—
203	C₂²×C₄₃	—	4	8	no	—
204	C₂²×C₄₃	—	8	24	no	—
205	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	12	yes	—
206	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
207	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
208	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
209	C₄×C₄₃	—	2	8	no	—
210	C₄×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
211	C₄×C₄₃	C₂²×C₂²⋊C₄	1	12	yes	—
212	C₄×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
213	C₄×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
214	C₄×C₄₃	C₂³×D₄	1	1	yes	characteristic
215	Dic₄₃	—	2	4	no	—
216	Dic₄₃	—	4	6	no	—
217	C₂×#585	D₄₃	1	1	yes	characteristic
218	C₂×#568	—	43	1	no	—
219	C₂×C₄×#41	—	43	1	no	—
220	#2901	—	43	16	no	—
221	C₂×#421	—	43	6	no	—
222	C₂²×#104	—	43	6	no	—
223	C₂×C₄₃	—	2	1	no	—
224	C₂×C₄₃	—	2	1	no	—
225	C₂×C₄₃	—	2	12	no	—
226	C₂×C₄₃	—	4	8	no	—
227	C₂×C₄₃	#2901	1	2	yes	complemented
228	C₂×C₄₃	C₂³×C₂²⋊C₄	1	1	yes	characteristic
229	#585	—	2	4	no	—
230	#585	—	2	4	no	—
231	#585	Dic₄₃	1	8	yes	complemented
232	#585	C₂×D₄₃	1	8	yes	—
233	C₂×2₋¹⁺⁴	—	2	1	no	—
234	C₂×2₋¹⁺⁴	Dic₄₃	1	4	yes	complemented
235	C₂×H(5,𝔽₂)	—	2	3	no	—
236	C₂×H(5,𝔽₂)	Dic₄₃	1	4	yes	complemented
237	C₂²×#41	—	2	4	no	—
238	C₂²×#41	C₂×D₄₃	1	6	yes	—
239	C₂²×#41	C₂×D₄₃	1	1	yes	characteristic
240	#568	—	43	8	no	—
241	#568	—	86	4	no	—
242	C₂×#131	—	86	4	no	—
243	C₂²×M₁₆	—	43	6	no	—
244	C₄×#41	—	43	8	no	—
245	C₄×#41	—	86	4	no	—
246	C₂×C₄×Q₈	—	86	1	no	—
247	C₂×C₄×D₄	—	86	3	no	—
248	C₂×#117	—	43	3	no	—
249	C₂²×C₄²	—	43	3	no	—
250	#421	—	43	48	no	—
251	C₂×#104	—	43	4	no	—
252	C₂×#104	—	43	12	no	—
253	C₂×#104	—	43	48	no	—
254	C₄₃	C₂×#2901	1	1	yes	characteristic, complemented, Sylow
255	2₋¹⁺⁴	—	2	16	no	—
256	2₋¹⁺⁴	—	2	8	no	—
257	2₋¹⁺⁴	—	2	8	no	—
258	2₋¹⁺⁴	C₂×Dic₄₃	1	32	yes	complemented
259	H(5,𝔽₂)	—	2	16	no	—
260	H(5,𝔽₂)	—	2	24	no	—
261	H(5,𝔽₂)	—	2	24	no	—
262	H(5,𝔽₂)	C₂×Dic₄₃	1	32	yes	complemented
263	C₂×#41	—	2	32	no	—
264	C₂×#41	—	2	32	no	—
265	C₂×#41	—	2	4	no	—
266	C₂×#41	—	2	12	no	—
267	C₂×#41	—	2	6	no	—
268	C₂×#41	—	2	6	no	—
269	C₂×#41	—	2	12	no	—
270	C₂×#41	—	2	12	no	—
271	C₂×#41	C₂×Dic₄₃	1	4	yes	—
272	C₂×#41	C₂×Dic₄₃	1	4	yes	—
273	C₂×#41	C₂×Dic₄₃	1	12	yes	complemented
274	C₂×#41	C₂×Dic₄₃	1	24	yes	complemented
275	C₂×#41	C₂²⋊D₄₃	1	4	yes	—
276	C₂×#41	C₂²⋊D₄₃	1	4	yes	—
277	C₂×#41	C₂²⋊D₄₃	1	4	yes	—
278	C₂×#41	C₂²×D₄₃	1	4	yes	—
279	C₂×#41	C₂²×D₄₃	1	24	yes	—
280	C₂×#41	C₂²×D₄₃	1	4	yes	—
281	C₂²×Q₈	—	2	4	no	—
282	C₂²×Q₈	C₂×Dic₄₃	1	6	yes	complemented
283	C₂²×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
284	C₂²×D₄	—	2	6	no	—
285	C₂²×D₄	—	2	12	no	—
286	C₂²×D₄	C₂×Dic₄₃	1	6	yes	complemented
287	C₂²×D₄	C₂²⋊D₄₃	1	3	yes	—
288	C₂³×C₄	—	2	6	no	—
289	C₂³×C₄	—	86	3	no	—
290	C₂³×C₄	C₂²×D₄₃	1	3	yes	—
291	#131	—	86	32	no	—
292	C₂×M₁₆	—	43	4	no	—
293	C₂×M₁₆	—	43	24	no	—
294	C₂×M₁₆	—	86	6	no	—
295	C₂×M₁₆	—	86	12	no	—
296	C₂²×C₈	—	86	6	no	—
297	C₄×Q₈	—	86	8	no	—
298	C₄×D₄	—	86	24	no	—
299	#117	—	43	12	no	—
300	#117	—	86	6	no	—
301	C₂×C₄⋊C₄	—	86	3	no	—
302	C₂×C₂²⋊C₄	—	86	3	no	—
303	C₂×C₄²	—	43	3	no	—
304	C₂×C₄²	—	43	12	no	—
305	C₂×C₄²	—	43	1	no	—
306	C₂×C₄²	—	86	3	no	—
307	C₂×C₄²	—	86	6	no	—
308	#104	—	43	16	no	—
309	#104	—	43	48	no	—
310	C₂⁴	—	2	6	no	—
311	C₂⁴	C₂×C₂²⋊D₄₃	1	3	yes	—
312	#41	—	2	32	no	—
313	#41	—	2	96	no	—
314	#41	—	2	24	no	—
315	#41	—	2	24	no	—
316	#41	—	2	24	no	—
317	#41	—	2	4	no	—
318	#41	—	2	24	no	—
319	#41	—	2	4	no	—
320	#41	—	2	24	no	—
321	#41	C₂²⋊Dic₄₃	1	16	yes	—
322	#41	C₂²⋊Dic₄₃	1	16	yes	—
323	#41	C₂²×Dic₄₃	1	8	yes	—
324	#41	C₂²×Dic₄₃	1	16	yes	—
325	#41	C₂²×Dic₄₃	1	48	yes	complemented
326	#41	C₂×C₂²⋊D₄₃	1	16	yes	—
327	#41	C₂³×D₄₃	1	8	yes	—
328	C₂×Q₈	—	2	32	no	—
329	C₂×Q₈	—	2	6	no	—
330	C₂×Q₈	—	2	12	no	—
331	C₂×Q₈	C₂²⋊Dic₄₃	1	4	yes	—
332	C₂×Q₈	C₂²⋊Dic₄₃	1	4	yes	—
333	C₂×Q₈	C₂²×Dic₄₃	1	4	yes	—
334	C₂×Q₈	C₂²×Dic₄₃	1	24	yes	complemented
335	C₂×Q₈	C₂×C₂²⋊D₄₃	1	4	yes	—
336	C₂×D₄	—	2	12	no	—
337	C₂×D₄	—	2	24	no	—
338	C₂×D₄	—	2	4	no	—
339	C₂×D₄	—	2	24	no	—
340	C₂×D₄	—	2	96	no	—
341	C₂×D₄	—	2	6	no	—
342	C₂×D₄	—	2	12	no	—
343	C₂×D₄	C₂²⋊Dic₄₃	1	12	yes	—
344	C₂×D₄	C₂²⋊Dic₄₃	1	12	yes	—
345	C₂×D₄	C₂²×Dic₄₃	1	4	yes	—
346	C₂×D₄	C₂²×Dic₄₃	1	24	yes	complemented
347	C₂×D₄	C₂×C₂²⋊D₄₃	1	12	yes	—
348	C₂²×C₄	—	2	6	no	—
349	C₂²×C₄	—	2	12	no	—
350	C₂²×C₄	—	2	24	no	—
351	C₂²×C₄	—	2	24	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	86	1	no	—
354	C₂²×C₄	—	86	3	no	—
355	C₂²×C₄	—	86	12	no	—
356	C₂²×C₄	—	172	12	no	—
357	C₂²×C₄	C₂²×Dic₄₃	1	6	yes	—
358	C₂²×C₄	C₂²×Dic₄₃	1	6	yes	—
359	C₂²×C₄	C₂×C₂²⋊D₄₃	1	3	yes	—
360	C₂²×C₄	C₂×C₂²⋊D₄₃	1	6	yes	—
361	C₂²×C₄	C₂×C₂²⋊D₄₃	1	6	yes	—
362	C₂²×C₄	C₂×C₂²⋊D₄₃	1	6	yes	—
363	C₂²×C₄	C₂³×D₄₃	1	6	yes	—
364	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
365	M₁₆	—	43	8	no	—
366	M₁₆	—	86	4	no	—
367	M₁₆	—	86	24	no	—
368	C₂×C₈	—	86	24	no	—
369	C₂×C₈	—	86	4	no	—
370	C₄⋊C₄	—	86	12	no	—
371	C₂²⋊C₄	—	86	12	no	—
372	C₄²	—	43	2	no	—
373	C₄²	—	43	6	no	—
374	C₄²	—	86	1	no	—
375	C₄²	—	86	3	no	—
376	C₄²	—	86	12	no	—
377	C₂³	—	2	4	no	—
378	C₂³	—	2	24	no	—
379	C₂³	—	4	6	no	—
380	C₂³	—	8	12	no	—
381	C₂³	C₂×C₂²⋊Dic₄₃	1	6	yes	—
382	C₂³	C₂×C₂²⋊Dic₄₃	1	6	yes	—
383	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
384	C₂³	C₂²×C₂²⋊D₄₃	1	6	yes	—
385	Q₈	—	2	4	no	—
386	Q₈	—	2	24	no	—
387	Q₈	C₂×C₂²⋊Dic₄₃	1	16	yes	—
388	Q₈	C₂³×Dic₄₃	1	8	yes	—
389	D₄	—	2	8	no	—
390	D₄	—	2	48	no	—
391	D₄	—	2	8	no	—
392	D₄	—	2	4	no	—
393	D₄	—	2	24	no	—
394	D₄	C₂×C₂²⋊Dic₄₃	1	48	yes	—
395	D₄	C₂³×Dic₄₃	1	8	yes	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	24	no	—
398	C₂×C₄	—	2	8	no	—
399	C₂×C₄	—	2	48	no	—
400	C₂×C₄	—	2	8	no	—
401	C₂×C₄	—	86	4	no	—
402	C₂×C₄	—	86	2	no	—
403	C₂×C₄	—	86	6	no	—
404	C₂×C₄	—	172	24	no	—
405	C₂×C₄	—	172	6	no	—
406	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	6	yes	—
407	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	12	yes	—
408	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	12	yes	—
409	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	6	yes	—
410	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
411	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
412	C₂×C₄	C₂³×Dic₄₃	1	12	yes	—
413	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
414	C₂×C₄	C₂²×C₂²⋊D₄₃	1	6	yes	—
415	C₂×C₄	C₂²×C₂²⋊D₄₃	1	12	yes	—
416	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
417	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
418	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
419	C₈	—	86	8	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	12	no	—
422	C₂²	—	2	8	no	—
423	C₂²	—	4	6	no	—
424	C₂²	—	4	6	no	—
425	C₂²	—	4	8	no	—
426	C₂²	—	8	24	no	—
427	C₂²	C₂²×C₂²⋊Dic₄₃	1	12	yes	—
428	C₂²	C₂²×C₂²⋊Dic₄₃	1	1	yes	characteristic
429	C₂²	C₂²×C₂²⋊Dic₄₃	1	1	yes	characteristic
430	C₂²	C₂³×C₂²⋊D₄₃	1	1	yes	characteristic
431	C₄	—	2	8	no	—
432	C₄	—	86	4	no	—
433	C₄	—	172	6	no	—
434	C₄	C₂²×C₂²⋊Dic₄₃	1	1	yes	characteristic
435	C₄	C₂²×C₂²⋊Dic₄₃	1	12	yes	—
436	C₄	C₂²×C₂²⋊Dic₄₃	1	1	yes	characteristic
437	C₄	C₂⁴×Dic₄₃	1	1	yes	characteristic
438	C₄	C₂³×C₂²⋊D₄₃	1	1	yes	characteristic
439	C₂	—	2	1	no	—
440	C₂	—	2	1	no	—
441	C₂	—	2	12	no	—
442	C₂	—	4	8	no	—
443	C₂	#19143142	1	2	yes	direct product factor
444	C₂	C₂³×C₂²⋊Dic₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₃
commutator	C₄×C₄₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting, prime radical	C₂×C₄₃×#585	C₂
socle	C₂²×C₄₃	C₂²×C₂²⋊C₄
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	C₂×#585	D₄₃
hypocenter	C₄₃	C₂×#2901
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×#41 ◁ C₂×#585

Complements

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

N	H ≅ G/N	type
1. C₂×#14583666	C₂	semidirect
2. C₂×#41×Dic₄₃	C₂	semidirect
3. #19143142	C₂	direct (N × H)
4. C₂×#14582916	C₂	semidirect
5. C₂²×#13063252	C₂	semidirect
8. #14583666	C₂²	semidirect
10. C₂²×#10621877	C₂²	semidirect
12. #41×Dic₄₃	C₂²	semidirect
15. C₂×#13063284	C₂²	semidirect
16. C₂²×C₄×Dic₄₃	C₂²	semidirect
17. #14582916	C₂²	semidirect
18. C₂×#13063252	C₂²	semidirect
19. C₂×#13063252	C₂²	semidirect
20. C₂×#13063252	C₂²	semidirect
23. C₄₃×#585	C₄	semidirect
26. C₂×2₋¹⁺⁴×C₄₃	C₄	semidirect
28. C₂×H(5,𝔽₂)×C₄₃	C₄	semidirect
37. C₂×#10621877	C₂³	semidirect
42. #13063284	C₂³	semidirect
49. C₂×C₄×Dic₄₃	C₂³	semidirect
50. #13063252	C₂³	semidirect
51. #13063252	C₂³	semidirect
55. 2₋¹⁺⁴×C₄₃	C₂×C₄	semidirect
59. H(5,𝔽₂)×C₄₃	C₂×C₄	semidirect
70. C₂×#41×C₄₃	C₂×C₄	semidirect
71. C₂×#41×C₄₃	C₂×C₄	semidirect
79. C₂²×Q₈×C₄₃	C₂×C₄	semidirect
83. C₂²×D₄×C₄₃	C₂×C₄	semidirect
102. #41×C₄₃	C₂²×C₄	semidirect
111. C₂×Q₈×C₄₃	C₂²×C₄	semidirect
123. C₂×D₄×C₄₃	C₂²×C₄	semidirect
227. C₂×C₄₃	#2901	semidirect
231. #585	Dic₄₃	semidirect
234. C₂×2₋¹⁺⁴	Dic₄₃	semidirect
236. C₂×H(5,𝔽₂)	Dic₄₃	semidirect
254. C₄₃	C₂×#2901	semidirect
258. 2₋¹⁺⁴	C₂×Dic₄₃	semidirect
262. H(5,𝔽₂)	C₂×Dic₄₃	semidirect
273. C₂×#41	C₂×Dic₄₃	semidirect
274. C₂×#41	C₂×Dic₄₃	semidirect
282. C₂²×Q₈	C₂×Dic₄₃	semidirect
286. C₂²×D₄	C₂×Dic₄₃	semidirect
325. #41	C₂²×Dic₄₃	semidirect
334. C₂×Q₈	C₂²×Dic₄₃	semidirect
346. C₂×D₄	C₂²×Dic₄₃	semidirect
443. C₂	#19143142	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×#14583666	2
C₂×#41×Dic₄₃	2
#19143142	2
C₂×#14582916	2
C₂²×#13063252	2
C₂×C₄₃×#585	2
C₂×#2901	43

Subgroups — C2×#19143142 #25960196

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19143142 #25960196