Subgroups — C₂×#19143712 #25961651

Order 11008.

2154 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143712	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	4	yes	maximal, complemented
5	C₂×#14582956	C₂	1	2	yes	maximal, complemented
6	C₂×#14582952	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#14582923	C₂	1	2	yes	maximal, complemented
8	C₂²×C₄⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×#41×C₄₃	C₂	1	1	yes	maximal, characteristic
10	C₂²×#10621877	C₂²	1	4	yes	—
11	C₂³×C₄₃⋊C₈	C₂²	1	2	yes	—
12	#14583030	C₂²	1	16	yes	complemented
13	#14582977	C₂²	1	16	yes	complemented
14	#14582971	C₂²	1	32	yes	complemented
15	#14582956	C₂²	1	16	yes	complemented
16	#14582952	C₂²	1	8	yes	complemented
17	#14582923	C₂²	1	16	yes	complemented
18	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
21	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	4	yes	—
22	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
23	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	8	yes	complemented
24	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
25	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	4	yes	—
26	C₂×#13063236	C₂²	1	4	yes	—
27	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
28	C₂²×#41×C₄₃	C₄	1	1	yes	characteristic
29	C₄×#41×C₄₃	C₄	1	8	yes	—
30	C₄×#41×C₄₃	C₂²	1	8	yes	—
31	C₂×C₄×Q₈×C₄₃	C₄	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₄₃	C₄	1	2	yes	—
34	C₂×C₄×D₄×C₄₃	C₄	1	1	yes	characteristic
35	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
37	C₂×#117×C₄₃	C₄	1	2	yes	—
38	C₂×#117×C₄₃	C₄	1	1	yes	characteristic
39	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
40	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
41	C₂×#10621877	—	4	8	no	—
42	C₂×#10621877	C₂³	1	16	yes	—
43	C₂²×C₄₃⋊C₈	—	4	4	no	—
44	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
45	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
46	C₂²×C₄₃⋊C₈	C₂³	1	4	yes	—
47	C₂²×C₄₃⋊C₈	C₂³	1	8	yes	—
48	C₄⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
49	C₄⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
50	C₄⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
51	C₄⋊(C₄₃⋊C₈)	C₂³	1	16	yes	—
52	C₄⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
53	C₂²⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
54	C₂²⋊(C₄₃⋊C₈)	C₂³	1	16	yes	—
55	#13063236	C₂³	1	16	yes	—
56	C₄×C₄₃⋊C₈	C₂³	1	8	yes	—
57	C₂×#41×C₄₃	—	2	8	no	—
58	C₂×#41×C₄₃	C₂×C₄	1	8	yes	—
59	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
60	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
61	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
63	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
64	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
65	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
66	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
68	C₄×Q₈×C₄₃	C₂×C₄	1	8	yes	—
69	C₄×Q₈×C₄₃	C₂×C₄	1	4	yes	—
70	C₄×Q₈×C₄₃	C₂³	1	4	yes	—
71	C₄×D₄×C₄₃	C₂×C₄	1	16	yes	—
72	C₄×D₄×C₄₃	C₂×C₄	1	8	yes	—
73	C₄×D₄×C₄₃	C₂×C₄	1	8	yes	—
74	C₄×D₄×C₄₃	C₂×C₄	1	4	yes	—
75	C₄×D₄×C₄₃	C₂³	1	8	yes	—
76	C₄×D₄×C₄₃	C₂³	1	4	yes	—
77	#117×C₄₃	C₂×C₄	1	16	yes	—
78	#117×C₄₃	C₂×C₄	1	8	yes	—
79	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
80	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
82	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
83	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
84	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
85	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
86	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
88	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
89	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₄₃	C₂×C₄	1	8	yes	—
91	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
92	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
95	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
96	C₂×C₄²×C₄₃	C₂³	1	8	yes	—
97	C₂⁴×C₄₃	C₂²×C₄	1	2	yes	—
98	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
99	#41×C₄₃	—	2	32	no	—
100	C₂×Q₈×C₄₃	—	2	4	no	—
101	C₂×Q₈×C₄₃	C₂²×C₄	1	4	yes	—
102	C₂×D₄×C₄₃	—	2	4	no	—
103	C₂×D₄×C₄₃	—	2	8	no	—
104	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
105	C₂×D₄×C₄₃	C₂²×C₄	1	8	yes	—
106	C₂²×C₄×C₄₃	—	2	8	no	—
107	C₂²×C₄×C₄₃	—	2	2	no	—
108	C₂²×C₄×C₄₃	—	2	4	no	—
109	C₂²×C₄×C₄₃	—	2	2	no	—
110	C₂²×C₄×C₄₃	—	2	4	no	—
111	C₂²×C₄×C₄₃	—	4	2	no	—
112	C₂²×C₄×C₄₃	—	4	4	no	—
113	C₂²×C₄×C₄₃	M₁₆	1	8	yes	complemented
114	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
117	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
118	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
123	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
124	C₂²×C₄×C₄₃	C₂²×C₄	1	4	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	4	yes	—
128	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
129	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
130	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
131	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
132	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
133	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
134	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
135	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
136	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
137	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
138	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
139	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
140	C₄²×C₄₃	C₂²×C₄	1	8	yes	—
141	C₄²×C₄₃	C₂²×C₄	1	8	yes	—
142	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
143	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
144	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
145	C₄²×C₄₃	C₂⁴	1	2	yes	—
146	C₄²×C₄₃	C₂⁴	1	2	yes	—
147	C₄²×C₄₃	C₂⁴	1	4	yes	—
148	#10621877	—	4	16	no	—
149	C₂×C₄₃⋊C₈	—	2	8	no	—
150	C₂×C₄₃⋊C₈	—	2	4	no	—
151	C₂×C₄₃⋊C₈	—	2	4	no	—
152	C₂×C₄₃⋊C₈	—	4	8	no	—
153	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
154	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
155	C₂×C₄₃⋊C₈	C₂⁴	1	8	yes	—
156	C₂³×C₄₃	—	2	2	no	—
157	C₂³×C₄₃	—	2	2	no	—
158	C₂³×C₄₃	—	2	4	no	—
159	C₂³×C₄₃	—	2	4	no	—
160	C₂³×C₄₃	—	2	4	no	—
161	C₂³×C₄₃	C₂×M₁₆	1	4	yes	—
162	C₂³×C₄₃	C₂³×C₄	1	4	yes	—
163	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
164	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
165	Q₈×C₄₃	—	2	8	no	—
166	D₄×C₄₃	—	2	16	no	—
167	D₄×C₄₃	—	2	8	no	—
168	C₂×C₄×C₄₃	—	2	2	no	—
169	C₂×C₄×C₄₃	—	2	4	no	—
170	C₂×C₄×C₄₃	—	2	4	no	—
171	C₂×C₄×C₄₃	—	2	2	no	—
172	C₂×C₄×C₄₃	—	2	2	no	—
173	C₂×C₄×C₄₃	—	2	4	no	—
174	C₂×C₄×C₄₃	—	2	4	no	—
175	C₂×C₄×C₄₃	—	2	8	no	—
176	C₂×C₄×C₄₃	—	2	16	no	—
177	C₂×C₄×C₄₃	—	2	2	no	—
178	C₂×C₄×C₄₃	—	2	4	no	—
179	C₂×C₄×C₄₃	—	2	2	no	—
180	C₂×C₄×C₄₃	—	2	4	no	—
181	C₂×C₄×C₄₃	—	4	4	no	—
182	C₂×C₄×C₄₃	—	4	8	no	—
183	C₂×C₄×C₄₃	C₂×M₁₆	1	4	yes	—
184	C₂×C₄×C₄₃	C₂×M₁₆	1	4	yes	—
185	C₂×C₄×C₄₃	C₂×M₁₆	1	16	yes	complemented
186	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
187	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
188	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
189	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
190	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
191	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
192	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
193	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
194	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
195	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
196	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
197	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
198	C₄₃⋊C₈	—	2	8	no	—
199	C₄₃⋊C₈	—	2	4	no	—
200	C₄₃⋊C₈	—	2	4	no	—
201	C₂×#2989	—	43	1	no	maximal, Sylow
202	C₂²×C₄₃	—	2	2	no	—
203	C₂²×C₄₃	—	2	8	no	—
204	C₂²×C₄₃	—	2	2	no	—
205	C₂²×C₄₃	—	2	4	no	—
206	C₂²×C₄₃	—	2	4	no	—
207	C₂²×C₄₃	—	2	4	no	—
208	C₂²×C₄₃	—	4	8	no	—
209	C₂²×C₄₃	#520	1	2	yes	—
210	C₂²×C₄₃	C₂²×M₁₆	1	4	yes	—
211	C₂²×C₄₃	C₂²×M₁₆	1	2	yes	—
212	C₂²×C₄₃	#568	1	2	yes	—
213	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
214	C₄×C₄₃	—	2	2	no	—
215	C₄×C₄₃	—	2	4	no	—
216	C₄×C₄₃	—	2	4	no	—
217	C₄×C₄₃	—	2	2	no	—
218	C₄×C₄₃	—	2	2	no	—
219	C₄×C₄₃	—	2	4	no	—
220	C₄×C₄₃	#520	1	2	yes	—
221	C₄×C₄₃	C₂²×M₁₆	1	4	yes	—
222	C₄×C₄₃	C₂²×M₁₆	1	4	yes	—
223	C₄×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
224	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
225	C₂×C₄×#41	D₄₃	1	1	yes	characteristic
226	#2989	—	43	16	no	—
227	C₂×#446	—	43	2	no	—
228	C₂×#436	—	43	2	no	—
229	C₂×#435	—	43	4	no	—
230	C₂×#432	—	43	2	no	—
231	C₂×#431	—	43	1	no	—
232	C₂×#423	—	43	2	no	—
233	C₂²×C₄⋊C₈	—	43	1	no	—
234	C₂×C₄₃	—	2	4	no	—
235	C₂×C₄₃	—	4	4	no	—
236	C₂×C₄₃	#2989	1	4	yes	complemented
237	C₂×C₄₃	C₂×#520	1	1	yes	characteristic
238	C₂×C₄₃	C₂³×M₁₆	1	1	yes	characteristic
239	C₂×C₄₃	C₂×#568	1	1	yes	characteristic
240	C₂²×#41	Dic₄₃	1	1	yes	characteristic
241	C₂²×M₁₆	—	43	4	no	—
242	C₂³×C₈	—	43	2	no	—
243	C₄×#41	Dic₄₃	1	8	yes	—
244	C₄×#41	C₂×D₄₃	1	8	yes	—
245	C₂×C₄×Q₈	Dic₄₃	1	1	yes	characteristic
246	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
247	C₂×C₄×D₄	Dic₄₃	1	2	yes	—
248	C₂×C₄×D₄	Dic₄₃	1	1	yes	characteristic
249	C₂×C₄×D₄	C₂×D₄₃	1	2	yes	—
250	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
251	C₂×#117	Dic₄₃	1	2	yes	—
252	C₂×#117	Dic₄₃	1	1	yes	characteristic
253	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
254	C₂²×C₄²	C₂×D₄₃	1	2	yes	—
255	#446	—	43	16	no	—
256	#436	—	43	16	no	—
257	#435	—	43	32	no	—
258	#432	—	43	16	no	—
259	#431	—	43	8	no	—
260	#423	—	43	16	no	—
261	C₂×C₄⋊C₈	—	43	2	no	—
262	C₂×C₄⋊C₈	—	43	2	no	—
263	C₂×C₄⋊C₈	—	43	8	no	—
264	C₂×C₄⋊C₈	—	43	1	no	—
265	C₂×C₄⋊C₈	—	43	4	no	—
266	C₂×C₄⋊C₈	—	43	1	no	—
267	C₂×C₂²⋊C₈	—	43	2	no	—
268	C₂×C₂²⋊C₈	—	43	4	no	—
269	C₂×#97	—	43	4	no	—
270	C₂×C₄×C₈	—	43	2	no	—
271	C₄₃	C₂×#2989	1	1	yes	characteristic, complemented, Sylow
272	C₂×#41	—	2	8	no	—
273	C₂×#41	C₂×Dic₄₃	1	8	yes	—
274	C₂²×Q₈	C₂×Dic₄₃	1	1	yes	characteristic
275	C₂²×D₄	C₂×Dic₄₃	1	2	yes	—
276	C₂²×D₄	C₂×Dic₄₃	1	1	yes	characteristic
277	C₂³×C₄	C₂×Dic₄₃	1	2	yes	—
278	C₂³×C₄	C₂×Dic₄₃	1	2	yes	—
279	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
280	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
281	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
282	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
283	C₂×M₁₆	—	43	16	no	—
284	C₂×M₁₆	—	172	8	no	—
285	C₂²×C₈	—	43	4	no	—
286	C₂²×C₈	—	43	2	no	—
287	C₂²×C₈	—	43	2	no	—
288	C₂²×C₈	—	43	8	no	—
289	C₂²×C₈	—	172	4	no	—
290	C₄×Q₈	C₂×Dic₄₃	1	8	yes	—
291	C₄×Q₈	C₂×Dic₄₃	1	4	yes	—
292	C₄×Q₈	C₂²×D₄₃	1	4	yes	—
293	C₄×D₄	C₂×Dic₄₃	1	16	yes	—
294	C₄×D₄	C₂×Dic₄₃	1	8	yes	—
295	C₄×D₄	C₂×Dic₄₃	1	8	yes	—
296	C₄×D₄	C₂×Dic₄₃	1	4	yes	—
297	C₄×D₄	C₂²×D₄₃	1	8	yes	—
298	C₄×D₄	C₂²×D₄₃	1	4	yes	—
299	#117	C₂×Dic₄₃	1	16	yes	—
300	#117	C₂×Dic₄₃	1	8	yes	—
301	C₂×C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
302	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
304	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
305	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	2	yes	—
306	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	2	yes	—
307	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	2	yes	—
308	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
309	C₂×C₄²	C₂×Dic₄₃	1	2	yes	—
310	C₂×C₄²	C₂×Dic₄₃	1	2	yes	—
311	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
312	C₂×C₄²	C₂×Dic₄₃	1	8	yes	—
313	C₂×C₄²	C₂×Dic₄₃	1	4	yes	—
314	C₂×C₄²	C₂²×D₄₃	1	4	yes	—
315	C₂×C₄²	C₂²×D₄₃	1	8	yes	—
316	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
317	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
318	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
319	C₄⋊C₈	—	43	8	no	—
320	C₄⋊C₈	—	43	8	no	—
321	C₄⋊C₈	—	43	4	no	—
322	C₄⋊C₈	—	43	16	no	—
323	C₄⋊C₈	—	43	4	no	—
324	C₂²⋊C₈	—	43	8	no	—
325	C₂²⋊C₈	—	43	16	no	—
326	#97	—	43	16	no	—
327	C₄×C₈	—	43	8	no	—
328	C₂⁴	C₂²×Dic₄₃	1	2	yes	—
329	C₂⁴	C₂²×Dic₄₃	1	1	yes	characteristic
330	#41	—	2	32	no	—
331	C₂×Q₈	—	2	4	no	—
332	C₂×Q₈	C₂²×Dic₄₃	1	4	yes	—
333	C₂×D₄	—	2	8	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	C₂²×Dic₄₃	1	8	yes	—
336	C₂×D₄	C₂²×Dic₄₃	1	4	yes	—
337	C₂²×C₄	—	2	8	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	4	2	no	—
343	C₂²×C₄	—	4	4	no	—
344	C₂²×C₄	#10621877	1	8	yes	complemented
345	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
346	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
347	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
348	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
349	C₂²×C₄	C₂²×Dic₄₃	1	8	yes	—
350	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
351	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
352	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
353	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
354	C₂²×C₄	C₂²×Dic₄₃	1	8	yes	—
355	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
356	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
357	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
358	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
359	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
360	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
361	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
362	M₁₆	—	172	16	no	—
363	C₂×C₈	—	43	4	no	—
364	C₂×C₈	—	43	4	no	—
365	C₂×C₈	—	43	8	no	—
366	C₂×C₈	—	86	8	no	—
367	C₂×C₈	—	86	4	no	—
368	C₂×C₈	—	86	4	no	—
369	C₂×C₈	—	172	8	no	—
370	C₄⋊C₄	C₂²×Dic₄₃	1	8	yes	—
371	C₄⋊C₄	C₂²×Dic₄₃	1	4	yes	—
372	C₄⋊C₄	C₂²×Dic₄₃	1	8	yes	—
373	C₄⋊C₄	C₂²×Dic₄₃	1	4	yes	—
374	C₂²⋊C₄	C₂²×Dic₄₃	1	8	yes	—
375	C₂²⋊C₄	C₂²×Dic₄₃	1	8	yes	—
376	C₂²⋊C₄	C₂²×Dic₄₃	1	8	yes	—
377	C₄²	C₂²×Dic₄₃	1	2	yes	—
378	C₄²	C₂²×Dic₄₃	1	4	yes	—
379	C₄²	C₂²×Dic₄₃	1	8	yes	—
380	C₄²	C₂²×Dic₄₃	1	8	yes	—
381	C₄²	C₂²×Dic₄₃	1	4	yes	—
382	C₄²	C₂²×Dic₄₃	1	4	yes	—
383	C₄²	C₂²×Dic₄₃	1	2	yes	—
384	C₄²	C₂³×D₄₃	1	2	yes	—
385	C₄²	C₂³×D₄₃	1	4	yes	—
386	C₄²	C₂³×D₄₃	1	2	yes	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	4	no	—
390	C₂³	—	2	4	no	—
391	C₂³	—	2	4	no	—
392	C₂³	C₂×#10621877	1	4	yes	—
393	C₂³	C₂³×Dic₄₃	1	4	yes	—
394	C₂³	C₂³×Dic₄₃	1	2	yes	—
395	C₂³	C₂³×Dic₄₃	1	1	yes	characteristic
396	Q₈	—	2	8	no	—
397	D₄	—	2	16	no	—
398	D₄	—	2	8	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	8	no	—
407	C₂×C₄	—	2	16	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	—	4	8	no	—
414	C₂×C₄	C₂×#10621877	1	4	yes	—
415	C₂×C₄	C₂×#10621877	1	4	yes	—
416	C₂×C₄	C₂×#10621877	1	16	yes	complemented
417	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
418	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
419	C₂×C₄	C₂³×Dic₄₃	1	4	yes	—
420	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
421	C₂×C₄	C₂³×Dic₄₃	1	4	yes	—
422	C₂×C₄	C₂³×Dic₄₃	1	4	yes	—
423	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
424	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
425	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
426	C₂×C₄	#13063371	1	2	yes	—
427	C₂×C₄	#13063372	1	2	yes	—
428	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
429	C₈	—	86	8	no	—
430	C₈	—	86	4	no	—
431	C₈	—	86	4	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	8	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	4	no	—
436	C₂²	—	2	4	no	—
437	C₂²	—	2	4	no	—
438	C₂²	—	4	8	no	—
439	C₂²	#14583382	1	2	yes	—
440	C₂²	C₂²×#10621877	1	4	yes	—
441	C₂²	C₂²×#10621877	1	2	yes	—
442	C₂²	#14583666	1	2	yes	—
443	C₂²	C₂⁴×Dic₄₃	1	1	yes	characteristic
444	C₄	—	2	2	no	—
445	C₄	—	2	4	no	—
446	C₄	—	2	4	no	—
447	C₄	—	2	2	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	4	no	—
450	C₄	#14583382	1	2	yes	—
451	C₄	C₂²×#10621877	1	4	yes	—
452	C₄	C₂²×#10621877	1	4	yes	—
453	C₄	C₂×#13063371	1	1	yes	characteristic
454	C₄	C₂×#13063372	1	1	yes	characteristic
455	C₂	—	2	4	no	—
456	C₂	—	4	4	no	—
457	C₂	#19143712	1	4	yes	direct product factor
458	C₂	C₂×#14583382	1	1	yes	characteristic
459	C₂	C₂³×#10621877	1	1	yes	characteristic
460	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×C₄×#41×C₄₃	C₂
socle	C₂³×C₄₃	C₂³×C₄
prime radical	C₂²×#41×C₄₃	C₄
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	C₂×C₄×#41	D₄₃
hypocenter	C₄₃	C₂×#2989
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×#41

Complements

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

N	H ≅ G/N	type
1. #19143712	C₂	direct (N × H)
2. C₂×#14583030	C₂	semidirect
3. C₂×#14582977	C₂	semidirect
4. C₂×#14582971	C₂	semidirect
5. C₂×#14582956	C₂	semidirect
6. C₂×#14582952	C₂	semidirect
7. C₂×#14582923	C₂	semidirect
8. C₂²×C₄⋊(C₄₃⋊C₈)	C₂	semidirect
12. #14583030	C₂²	semidirect
13. #14582977	C₂²	semidirect
14. #14582971	C₂²	semidirect
15. #14582956	C₂²	semidirect
16. #14582952	C₂²	semidirect
17. #14582923	C₂²	semidirect
23. C₂×C₄⋊(C₄₃⋊C₈)	C₂²	semidirect
113. C₂²×C₄×C₄₃	M₁₆	semidirect
185. C₂×C₄×C₄₃	C₂×M₁₆	semidirect
236. C₂×C₄₃	#2989	semidirect
271. C₄₃	C₂×#2989	semidirect
344. C₂²×C₄	#10621877	semidirect
416. C₂×C₄	C₂×#10621877	semidirect
457. C₂	#19143712	direct (N × H)

Maximal subgroups

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

subgroup	index
#19143712	2
C₂×#14583030	2
C₂×#14582977	2
C₂×#14582971	2
C₂×#14582956	2
C₂×#14582952	2
C₂×#14582923	2
C₂²×C₄⋊(C₄₃⋊C₈)	2
C₂×C₄×#41×C₄₃	2
C₂×#2989	43

Subgroups — C2×#19143712 #25961651

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19143712 #25961651