Subgroups — C₂×#19143671 #25961380

Order 11008.

2230 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143671	C₂	1	16	yes	maximal, direct product factor
2	C₂×#14582977	C₂	1	2	yes	maximal, complemented
3	C₂×#14582971	C₂	1	4	yes	maximal, complemented
4	C₂×D₄×C₄₃⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₂×#14582956	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14582952	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#14582866	C₂	1	4	yes	maximal, complemented
8	C₂×C₄₃×#532	C₂	1	1	yes	maximal, characteristic
9	C₂²×#10621877	C₂²	1	4	yes	—
10	C₂³×C₄₃⋊C₈	C₂²	1	4	yes	—
11	#14582977	C₂²	1	16	yes	complemented
12	#14582971	C₂²	1	32	yes	complemented
13	D₄×C₄₃⋊C₈	C₂²	1	16	yes	complemented
14	#14582956	C₂²	1	8	yes	complemented
15	#14582952	C₂²	1	8	yes	complemented
16	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
17	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
18	#14582866	C₂²	1	32	yes	complemented
19	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
20	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
21	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	4	yes	—
22	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	4	yes	—
23	C₂×#13063236	C₂²	1	2	yes	—
24	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
26	C₂²×#41×C₄₃	C₂²	1	2	yes	—
27	C₄₃×#532	C₄	1	8	yes	—
28	C₄₃×#532	C₂²	1	8	yes	—
29	C₂×C₄⋊Q₈×C₄₃	C₄	1	1	yes	characteristic
30	C₂×#127×C₄₃	C₄	1	1	yes	characteristic
31	C₂×#124×C₄₃	C₄	1	2	yes	—
32	C₂×#121×C₄₃	C₄	1	2	yes	—
33	C₂×#121×C₄₃	C₄	1	2	yes	—
34	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
36	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
37	C₂×#10621877	—	4	8	no	—
38	C₂×#10621877	C₂³	1	16	yes	—
39	C₂²×C₄₃⋊C₈	—	4	8	no	—
40	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
41	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
42	C₂²×C₄₃⋊C₈	C₂³	1	4	yes	—
43	C₂²×C₄₃⋊C₈	C₂³	1	16	yes	—
44	C₄⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
45	C₄⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
46	C₂²⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
47	C₂²⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
48	C₂²⋊(C₄₃⋊C₈)	C₂³	1	16	yes	—
49	C₂²⋊(C₄₃⋊C₈)	C₂³	1	16	yes	—
50	#13063236	C₂³	1	8	yes	—
51	C₄×C₄₃⋊C₈	C₂³	1	4	yes	—
52	C₄×C₄₃⋊C₈	C₂³	1	4	yes	—
53	C₂×#41×C₄₃	—	4	8	no	—
54	C₂×#41×C₄₃	C₂×C₄	1	8	yes	—
55	C₂×#41×C₄₃	C₂³	1	8	yes	—
56	C₂²×Q₈×C₄₃	C₂×C₄	1	2	yes	—
57	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
58	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
59	C₂²×D₄×C₄₃	C₂×C₄	1	4	yes	—
60	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
61	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
63	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
65	C₄⋊Q₈×C₄₃	C₂×C₄	1	8	yes	—
66	#127×C₄₃	C₂×C₄	1	8	yes	—
67	#124×C₄₃	C₂×C₄	1	16	yes	—
68	#121×C₄₃	C₂×C₄	1	16	yes	—
69	#121×C₄₃	C₂×C₄	1	16	yes	—
70	C₄×D₄×C₄₃	C₂×C₄	1	8	yes	—
71	C₄×D₄×C₄₃	C₂×C₄	1	8	yes	—
72	C₄×D₄×C₄₃	C₂³	1	8	yes	—
73	C₄×D₄×C₄₃	C₂³	1	8	yes	—
74	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
75	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
76	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
77	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
78	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
81	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
84	C₂⁴×C₄₃	C₂²×C₄	1	4	yes	—
85	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
86	#41×C₄₃	—	4	16	no	—
87	#41×C₄₃	—	4	16	no	—
88	C₂×Q₈×C₄₃	—	4	4	no	—
89	C₂×Q₈×C₄₃	C₂²×C₄	1	8	yes	—
90	C₂×D₄×C₄₃	—	2	8	no	—
91	C₂×D₄×C₄₃	—	4	4	no	—
92	C₂×D₄×C₄₃	—	4	8	no	—
93	C₂×D₄×C₄₃	—	4	4	no	—
94	C₂×D₄×C₄₃	C₂²×C₄	1	8	yes	—
95	C₂×D₄×C₄₃	C₂²×C₄	1	8	yes	—
96	C₂×D₄×C₄₃	C₂²×C₄	1	16	yes	—
97	C₂×D₄×C₄₃	C₂²×C₄	1	8	yes	—
98	C₂²×C₄×C₄₃	—	2	4	no	—
99	C₂²×C₄×C₄₃	—	2	4	no	—
100	C₂²×C₄×C₄₃	—	2	8	no	—
101	C₂²×C₄×C₄₃	—	2	8	no	—
102	C₂²×C₄×C₄₃	—	4	2	no	—
103	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
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	4	yes	—
110	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
111	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
112	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
114	C₂²×C₄×C₄₃	C₂⁴	1	8	yes	—
115	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
116	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
117	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
118	C₂²⋊C₄×C₄₃	C₂²×C₄	1	16	yes	—
119	C₂²⋊C₄×C₄₃	C₂²×C₄	1	16	yes	—
120	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
121	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
122	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
123	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
124	C₄²×C₄₃	C₂⁴	1	2	yes	—
125	C₄²×C₄₃	C₂⁴	1	2	yes	—
126	#10621877	—	4	16	no	—
127	C₂×C₄₃⋊C₈	—	2	4	no	—
128	C₂×C₄₃⋊C₈	—	2	8	no	—
129	C₂×C₄₃⋊C₈	—	2	4	no	—
130	C₂×C₄₃⋊C₈	—	4	16	no	—
131	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
132	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
133	C₂×C₄₃⋊C₈	C₂⁴	1	8	yes	—
134	C₂³×C₄₃	—	2	2	no	—
135	C₂³×C₄₃	—	2	8	no	—
136	C₂³×C₄₃	—	2	2	no	—
137	C₂³×C₄₃	—	2	8	no	—
138	C₂³×C₄₃	—	2	2	no	—
139	C₂³×C₄₃	—	2	8	no	—
140	C₂³×C₄₃	C₂³×C₄	1	8	yes	—
141	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
142	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
143	Q₈×C₄₃	—	4	8	no	—
144	D₄×C₄₃	—	2	16	no	—
145	D₄×C₄₃	—	4	8	no	—
146	D₄×C₄₃	—	4	8	no	—
147	D₄×C₄₃	—	4	16	no	—
148	C₂×C₄×C₄₃	—	2	2	no	—
149	C₂×C₄×C₄₃	—	2	8	no	—
150	C₂×C₄×C₄₃	—	2	2	no	—
151	C₂×C₄×C₄₃	—	2	2	no	—
152	C₂×C₄×C₄₃	—	2	2	no	—
153	C₂×C₄×C₄₃	—	2	16	no	—
154	C₂×C₄×C₄₃	—	2	4	no	—
155	C₂×C₄×C₄₃	—	2	8	no	—
156	C₂×C₄×C₄₃	—	2	8	no	—
157	C₂×C₄×C₄₃	—	2	8	no	—
158	C₂×C₄×C₄₃	—	2	4	no	—
159	C₂×C₄×C₄₃	—	4	4	no	—
160	C₂×C₄×C₄₃	#131	1	4	yes	—
161	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
162	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
163	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
164	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
165	C₂×C₄×C₄₃	C₂³×C₄	1	8	yes	—
166	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
167	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
168	C₂×C₄×C₄₃	H(5,𝔽₂)	1	4	yes	—
169	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
170	C₄₃⋊C₈	—	2	4	no	—
171	C₄₃⋊C₈	—	2	8	no	—
172	C₄₃⋊C₈	—	2	4	no	—
173	C₂×#2981	—	43	1	no	maximal, Sylow
174	C₂²×C₄₃	—	2	8	no	—
175	C₂²×C₄₃	—	2	2	no	—
176	C₂²×C₄₃	—	2	2	no	—
177	C₂²×C₄₃	—	2	8	no	—
178	C₂²×C₄₃	—	2	2	no	—
179	C₂²×C₄₃	—	2	8	no	—
180	C₂²×C₄₃	—	4	4	no	—
181	C₂²×C₄₃	—	4	16	no	—
182	C₂²×C₄₃	#518	1	2	yes	—
183	C₂²×C₄₃	C₂×#131	1	2	yes	—
184	C₂²×C₄₃	#568	1	2	yes	—
185	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
186	C₄×C₄₃	—	2	2	no	—
187	C₄×C₄₃	—	2	8	no	—
188	C₄×C₄₃	—	2	2	no	—
189	C₄×C₄₃	—	2	2	no	—
190	C₄×C₄₃	—	2	2	no	—
191	C₄×C₄₃	#518	1	2	yes	—
192	C₄×C₄₃	C₂×#131	1	4	yes	—
193	C₄×C₄₃	C₂×H(5,𝔽₂)	1	2	yes	—
194	C₂×#532	D₄₃	1	1	yes	characteristic
195	#2981	—	43	16	no	—
196	C₂×#436	—	43	2	no	—
197	C₂×#435	—	43	4	no	—
198	C₂×C₈×D₄	—	43	2	no	—
199	C₂×#432	—	43	1	no	—
200	C₂×#431	—	43	1	no	—
201	C₂×#408	—	43	4	no	—
202	C₂×C₄₃	—	4	8	no	—
203	C₂×C₄₃	—	4	2	no	—
204	C₂×C₄₃	#2981	1	4	yes	complemented
205	C₂×C₄₃	C₂×#518	1	1	yes	characteristic
206	C₂×C₄₃	C₂²×#131	1	1	yes	characteristic
207	C₂×C₄₃	C₂×#568	1	1	yes	characteristic
208	C₂²×#41	C₂×D₄₃	1	2	yes	—
209	C₂²×M₁₆	—	43	4	no	—
210	C₂³×C₈	—	43	4	no	—
211	#532	Dic₄₃	1	8	yes	—
212	#532	C₂×D₄₃	1	8	yes	—
213	C₂×C₄⋊Q₈	Dic₄₃	1	1	yes	characteristic
214	C₂×#127	Dic₄₃	1	1	yes	characteristic
215	C₂×#124	Dic₄₃	1	2	yes	—
216	C₂×#121	Dic₄₃	1	2	yes	—
217	C₂×#121	Dic₄₃	1	2	yes	—
218	C₂×C₄×D₄	C₂×D₄₃	1	2	yes	—
219	C₂×C₄×D₄	C₂×D₄₃	1	2	yes	—
220	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
221	#436	—	43	16	no	—
222	#435	—	43	32	no	—
223	C₈×D₄	—	43	16	no	—
224	#432	—	43	8	no	—
225	#431	—	43	8	no	—
226	C₂×C₄⋊C₈	—	43	2	no	—
227	C₂×C₄⋊C₈	—	43	2	no	—
228	#408	—	43	32	no	—
229	C₂×C₂²⋊C₈	—	43	2	no	—
230	C₂×C₂²⋊C₈	—	43	2	no	—
231	C₂×C₂²⋊C₈	—	43	4	no	—
232	C₂×C₂²⋊C₈	—	43	4	no	—
233	C₂×#97	—	43	2	no	—
234	C₂×C₄×C₈	—	43	1	no	—
235	C₂×C₄×C₈	—	43	1	no	—
236	C₄₃	C₂×#2981	1	1	yes	characteristic, complemented, Sylow
237	C₂×#41	—	4	8	no	—
238	C₂×#41	C₂×Dic₄₃	1	8	yes	—
239	C₂×#41	C₂²×D₄₃	1	8	yes	—
240	C₂²×Q₈	C₂×Dic₄₃	1	2	yes	—
241	C₂²×D₄	C₂×Dic₄₃	1	2	yes	—
242	C₂²×D₄	C₂×Dic₄₃	1	2	yes	—
243	C₂²×D₄	C₂×Dic₄₃	1	4	yes	—
244	C₂²×D₄	C₂×Dic₄₃	1	2	yes	—
245	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
246	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
247	C₂³×C₄	C₂²×D₄₃	1	4	yes	—
248	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
249	C₂×M₁₆	—	43	16	no	—
250	C₂×M₁₆	—	172	8	no	—
251	C₂²×C₈	—	43	2	no	—
252	C₂²×C₈	—	43	4	no	—
253	C₂²×C₈	—	43	2	no	—
254	C₂²×C₈	—	43	16	no	—
255	C₂²×C₈	—	172	8	no	—
256	C₄⋊Q₈	C₂×Dic₄₃	1	8	yes	—
257	#127	C₂×Dic₄₃	1	8	yes	—
258	#124	C₂×Dic₄₃	1	16	yes	—
259	#121	C₂×Dic₄₃	1	16	yes	—
260	#121	C₂×Dic₄₃	1	16	yes	—
261	C₄×D₄	C₂×Dic₄₃	1	8	yes	—
262	C₄×D₄	C₂×Dic₄₃	1	8	yes	—
263	C₄×D₄	C₂²×D₄₃	1	8	yes	—
264	C₄×D₄	C₂²×D₄₃	1	8	yes	—
265	C₂×C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
266	C₂×C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
267	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	4	yes	—
268	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	4	yes	—
269	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
270	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
271	C₂×C₄²	C₂×Dic₄₃	1	4	yes	—
272	C₂×C₄²	C₂²×D₄₃	1	4	yes	—
273	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
274	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
275	C₄⋊C₈	—	43	8	no	—
276	C₄⋊C₈	—	43	8	no	—
277	C₂²⋊C₈	—	43	8	no	—
278	C₂²⋊C₈	—	43	8	no	—
279	C₂²⋊C₈	—	43	16	no	—
280	C₂²⋊C₈	—	43	16	no	—
281	#97	—	43	8	no	—
282	C₄×C₈	—	43	4	no	—
283	C₄×C₈	—	43	4	no	—
284	C₂⁴	C₂²×Dic₄₃	1	4	yes	—
285	C₂⁴	C₂²×Dic₄₃	1	1	yes	characteristic
286	#41	—	4	16	no	—
287	#41	—	4	16	no	—
288	C₂×Q₈	—	4	4	no	—
289	C₂×Q₈	C₂²×Dic₄₃	1	8	yes	—
290	C₂×D₄	—	2	8	no	—
291	C₂×D₄	—	4	4	no	—
292	C₂×D₄	—	4	8	no	—
293	C₂×D₄	—	4	4	no	—
294	C₂×D₄	C₂²×Dic₄₃	1	8	yes	—
295	C₂×D₄	C₂²×Dic₄₃	1	8	yes	—
296	C₂×D₄	C₂²×Dic₄₃	1	16	yes	—
297	C₂×D₄	C₂²×Dic₄₃	1	8	yes	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	8	no	—
300	C₂²×C₄	—	2	8	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	4	2	no	—
303	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
304	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
305	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
306	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
307	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
308	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
309	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
310	C₂²×C₄	C₂²×Dic₄₃	1	8	yes	—
311	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
312	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
313	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
314	C₂²×C₄	C₂³×D₄₃	1	8	yes	—
315	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
316	M₁₆	—	172	16	no	—
317	C₂×C₈	—	43	4	no	—
318	C₂×C₈	—	43	4	no	—
319	C₂×C₈	—	43	8	no	—
320	C₂×C₈	—	86	4	no	—
321	C₂×C₈	—	86	8	no	—
322	C₂×C₈	—	86	4	no	—
323	C₂×C₈	—	172	16	no	—
324	C₄⋊C₄	C₂²×Dic₄₃	1	8	yes	—
325	C₄⋊C₄	C₂²×Dic₄₃	1	8	yes	—
326	C₂²⋊C₄	C₂²×Dic₄₃	1	16	yes	—
327	C₂²⋊C₄	C₂²×Dic₄₃	1	16	yes	—
328	C₄²	C₂²×Dic₄₃	1	2	yes	—
329	C₄²	C₂²×Dic₄₃	1	2	yes	—
330	C₄²	C₂²×Dic₄₃	1	4	yes	—
331	C₄²	C₂²×Dic₄₃	1	4	yes	—
332	C₄²	C₂³×D₄₃	1	2	yes	—
333	C₄²	C₂³×D₄₃	1	2	yes	—
334	C₂³	—	2	2	no	—
335	C₂³	—	2	8	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	2	8	no	—
338	C₂³	—	2	2	no	—
339	C₂³	—	2	8	no	—
340	C₂³	C₂³×Dic₄₃	1	8	yes	—
341	C₂³	C₂³×Dic₄₃	1	2	yes	—
342	C₂³	C₂³×Dic₄₃	1	1	yes	characteristic
343	Q₈	—	4	8	no	—
344	D₄	—	2	16	no	—
345	D₄	—	4	8	no	—
346	D₄	—	4	16	no	—
347	D₄	—	4	8	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	8	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	16	no	—
355	C₂×C₄	—	2	8	no	—
356	C₂×C₄	—	2	8	no	—
357	C₂×C₄	—	2	8	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	#13063332	1	4	yes	—
361	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
362	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
363	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
364	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
365	C₂×C₄	C₂³×Dic₄₃	1	8	yes	—
366	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
367	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
368	C₂×C₄	#13063370	1	4	yes	—
369	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
370	C₈	—	86	4	no	—
371	C₈	—	86	8	no	—
372	C₈	—	86	4	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	8	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	8	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	8	no	—
379	C₂²	—	4	4	no	—
380	C₂²	—	4	16	no	—
381	C₂²	#14583374	1	2	yes	—
382	C₂²	C₂×#13063332	1	2	yes	—
383	C₂²	#14583666	1	2	yes	—
384	C₂²	C₂⁴×Dic₄₃	1	1	yes	characteristic
385	C₄	—	2	2	no	—
386	C₄	—	2	8	no	—
387	C₄	—	2	2	no	—
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	#14583374	1	2	yes	—
391	C₄	C₂×#13063332	1	4	yes	—
392	C₄	C₂×#13063370	1	2	yes	—
393	C₂	—	4	2	no	—
394	C₂	—	4	8	no	—
395	C₂	#19143671	1	4	yes	direct product factor
396	C₂	C₂×#14583374	1	1	yes	characteristic
397	C₂	C₂²×#13063332	1	1	yes	characteristic
398	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, prime radical	C₂×C₄₃×#532	C₂
socle	C₂³×C₄₃	C₂³×C₄
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	C₂×#532	D₄₃
hypocenter	C₄₃	C₂×#2981
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. #19143671	C₂	direct (N × H)
2. C₂×#14582977	C₂	semidirect
3. C₂×#14582971	C₂	semidirect
4. C₂×D₄×C₄₃⋊C₈	C₂	semidirect
5. C₂×#14582956	C₂	semidirect
6. C₂×#14582952	C₂	semidirect
7. C₂×#14582866	C₂	semidirect
11. #14582977	C₂²	semidirect
12. #14582971	C₂²	semidirect
13. D₄×C₄₃⋊C₈	C₂²	semidirect
14. #14582956	C₂²	semidirect
15. #14582952	C₂²	semidirect
18. #14582866	C₂²	semidirect
204. C₂×C₄₃	#2981	semidirect
236. C₄₃	C₂×#2981	semidirect
395. C₂	#19143671	direct (N × H)

Maximal subgroups

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

subgroup	index
#19143671	2
C₂×#14582977	2
C₂×#14582971	2
C₂×D₄×C₄₃⋊C₈	2
C₂×#14582956	2
C₂×#14582952	2
C₂×#14582866	2
C₂×C₄₃×#532	2
C₂×#2981	43

Subgroups — C2×#19143671 #25961380

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19143671 #25961380