Subgroups — C₂×#19143630 #25961332

Order 11008.

2654 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143630	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×#14582863	C₂	1	2	yes	maximal, complemented
8	C₂²×C₂²⋊(C₄₃⋊C₈)	C₂	1	2	yes	maximal, complemented
9	C₂²×C₄×D₄×C₄₃	C₂	1	1	yes	maximal, characteristic
10	C₂²×#10621877	C₂²	1	4	yes	complemented
11	C₂³×C₄₃⋊C₈	C₂²	1	4	yes	complemented
12	#14582977	C₂²	1	16	yes	complemented
13	#14582971	C₂²	1	32	yes	complemented
14	D₄×C₄₃⋊C₈	C₂²	1	16	yes	complemented
15	#14582956	C₂²	1	8	yes	complemented
16	#14582952	C₂²	1	8	yes	complemented
17	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	complemented
18	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	complemented
19	#14582863	C₂²	1	16	yes	complemented
20	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
23	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	16	yes	complemented
24	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	4	yes	complemented
25	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	4	yes	complemented
26	C₂×#13063236	C₂²	1	2	yes	complemented
27	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	complemented
28	C₂³×D₄×C₄₃	C₄	1	1	yes	characteristic
29	C₂⁴×C₄×C₄₃	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₄₃	C₄	1	2	yes	—
31	C₂×C₄×D₄×C₄₃	C₄	1	8	yes	—
32	C₂×C₄×D₄×C₄₃	C₄	1	1	yes	characteristic
33	C₂×C₄×D₄×C₄₃	C₄	1	1	yes	characteristic
34	C₂×C₄×D₄×C₄₃	C₂²	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×C₄×D₄×C₄₃	C₂²	1	8	yes	—
38	C₂²×C₄⋊C₄×C₄₃	C₄	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₄₃	C₄	1	2	yes	—
40	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
41	C₂×#10621877	—	4	8	no	—
42	C₂×#10621877	C₂³	1	16	yes	complemented
43	C₂²×C₄₃⋊C₈	—	4	8	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	16	yes	complemented
48	C₄⋊(C₄₃⋊C₈)	C₂³	1	8	yes	complemented
49	C₄⋊(C₄₃⋊C₈)	C₂³	1	8	yes	complemented
50	C₂²⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
51	C₂²⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
52	C₂²⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
53	C₂²⋊(C₄₃⋊C₈)	C₂³	1	16	yes	complemented
54	C₂²⋊(C₄₃⋊C₈)	C₂³	1	16	yes	complemented
55	#13063236	C₂³	1	8	yes	complemented
56	C₄×C₄₃⋊C₈	C₂³	1	8	yes	complemented
57	C₂⁵×C₄₃	C₂×C₄	1	2	yes	—
58	C₂²×D₄×C₄₃	—	2	8	no	—
59	C₂²×D₄×C₄₃	C₂×C₄	1	8	yes	—
60	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
61	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
62	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
63	C₂³×C₄×C₄₃	—	4	8	no	—
64	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
65	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
66	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
67	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
68	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
69	C₂³×C₄×C₄₃	C₂×C₄	1	8	yes	—
70	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
72	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
73	C₂³×C₄×C₄₃	C₂³	1	8	yes	—
74	C₄×D₄×C₄₃	C₂×C₄	1	8	yes	—
75	C₄×D₄×C₄₃	C₂×C₄	1	4	yes	—
76	C₄×D₄×C₄₃	C₂×C₄	1	4	yes	—
77	C₄×D₄×C₄₃	C₂×C₄	1	16	yes	—
78	C₄×D₄×C₄₃	C₂×C₄	1	8	yes	—
79	C₄×D₄×C₄₃	C₂×C₄	1	8	yes	—
80	C₄×D₄×C₄₃	C₂³	1	4	yes	—
81	C₄×D₄×C₄₃	C₂³	1	8	yes	—
82	C₄×D₄×C₄₃	C₂³	1	4	yes	—
83	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
84	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
85	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
87	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
88	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
89	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
90	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
91	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	16	yes	—
92	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
94	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
98	C₂⁴×C₄₃	—	2	8	no	—
99	C₂⁴×C₄₃	—	2	8	no	—
100	C₂⁴×C₄₃	—	4	4	no	—
101	C₂⁴×C₄₃	C₂²×C₄	1	2	yes	—
102	C₂⁴×C₄₃	C₂²×C₄	1	8	yes	—
103	C₂⁴×C₄₃	C₂²×C₄	1	2	yes	—
104	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
105	C₂×D₄×C₄₃	—	2	32	no	—
106	C₂×D₄×C₄₃	—	2	4	no	—
107	C₂×D₄×C₄₃	—	2	8	no	—
108	C₂×D₄×C₄₃	M₁₆	1	8	yes	complemented
109	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
110	C₂×D₄×C₄₃	C₂²×C₄	1	8	yes	—
111	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
112	C₂²×C₄×C₄₃	—	2	4	no	—
113	C₂²×C₄×C₄₃	—	2	4	no	—
114	C₂²×C₄×C₄₃	—	2	8	no	—
115	C₂²×C₄×C₄₃	—	2	8	no	—
116	C₂²×C₄×C₄₃	—	2	4	no	—
117	C₂²×C₄×C₄₃	—	4	4	no	—
118	C₂²×C₄×C₄₃	—	4	4	no	—
119	C₂²×C₄×C₄₃	—	4	4	no	—
120	C₂²×C₄×C₄₃	—	4	16	no	—
121	C₂²×C₄×C₄₃	—	4	16	no	—
122	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
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	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	4	yes	—
132	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
133	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
134	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
135	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
136	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
139	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
140	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
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	4	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	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
149	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
150	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
151	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
152	C₄²×C₄₃	C₂⁴	1	2	yes	—
153	C₄²×C₄₃	C₂⁴	1	2	yes	—
154	#10621877	—	4	16	no	—
155	C₂×C₄₃⋊C₈	—	2	4	no	—
156	C₂×C₄₃⋊C₈	—	2	8	no	—
157	C₂×C₄₃⋊C₈	—	2	4	no	—
158	C₂×C₄₃⋊C₈	—	4	16	no	—
159	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
160	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
161	C₂×C₄₃⋊C₈	C₂⁴	1	8	yes	—
162	C₂³×C₄₃	—	2	2	no	—
163	C₂³×C₄₃	—	2	4	no	—
164	C₂³×C₄₃	—	2	2	no	—
165	C₂³×C₄₃	—	2	4	no	—
166	C₂³×C₄₃	—	2	4	no	—
167	C₂³×C₄₃	—	2	16	no	—
168	C₂³×C₄₃	—	2	4	no	—
169	C₂³×C₄₃	—	2	16	no	—
170	C₂³×C₄₃	—	2	4	no	—
171	C₂³×C₄₃	—	4	8	no	—
172	C₂³×C₄₃	—	4	32	no	—
173	C₂³×C₄₃	C₂×M₁₆	1	8	yes	—
174	C₂³×C₄₃	#131	1	4	yes	—
175	C₂³×C₄₃	C₂³×C₄	1	4	yes	—
176	C₂³×C₄₃	C₂³×C₄	1	4	yes	—
177	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
178	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
179	D₄×C₄₃	—	2	16	no	—
180	D₄×C₄₃	—	2	8	no	—
181	D₄×C₄₃	C₂×M₁₆	1	16	yes	complemented
182	C₂×C₄×C₄₃	—	2	2	no	—
183	C₂×C₄×C₄₃	—	2	4	no	—
184	C₂×C₄×C₄₃	—	2	4	no	—
185	C₂×C₄×C₄₃	—	2	2	no	—
186	C₂×C₄×C₄₃	—	2	8	no	—
187	C₂×C₄×C₄₃	—	2	2	no	—
188	C₂×C₄×C₄₃	—	2	2	no	—
189	C₂×C₄×C₄₃	—	2	4	no	—
190	C₂×C₄×C₄₃	—	2	8	no	—
191	C₂×C₄×C₄₃	—	2	8	no	—
192	C₂×C₄×C₄₃	—	2	8	no	—
193	C₂×C₄×C₄₃	—	2	8	no	—
194	C₂×C₄×C₄₃	—	2	8	no	—
195	C₂×C₄×C₄₃	—	2	4	no	—
196	C₂×C₄×C₄₃	—	4	8	no	—
197	C₂×C₄×C₄₃	—	4	8	no	—
198	C₂×C₄×C₄₃	—	4	8	no	—
199	C₂×C₄×C₄₃	C₂×M₁₆	1	4	yes	—
200	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
201	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
202	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
203	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
204	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
205	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
206	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
207	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
208	C₂×C₄×C₄₃	H(5,𝔽₂)	1	4	yes	—
209	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
210	C₄₃⋊C₈	—	2	4	no	—
211	C₄₃⋊C₈	—	2	8	no	—
212	C₄₃⋊C₈	—	2	4	no	—
213	C₂×#2974	—	43	1	no	maximal, Sylow
214	C₂²×C₄₃	—	2	2	no	—
215	C₂²×C₄₃	—	2	4	no	—
216	C₂²×C₄₃	—	2	8	no	—
217	C₂²×C₄₃	—	2	16	no	—
218	C₂²×C₄₃	—	2	2	no	—
219	C₂²×C₄₃	—	2	4	no	—
220	C₂²×C₄₃	—	2	4	no	—
221	C₂²×C₄₃	—	2	4	no	—
222	C₂²×C₄₃	—	2	4	no	—
223	C₂²×C₄₃	—	4	32	no	—
224	C₂²×C₄₃	—	4	8	no	—
225	C₂²×C₄₃	#518	1	2	yes	—
226	C₂²×C₄₃	C₂²×M₁₆	1	8	yes	—
227	C₂²×C₄₃	C₂²×M₁₆	1	2	yes	—
228	C₂²×C₄₃	C₂×#131	1	4	yes	—
229	C₂²×C₄₃	C₂×#131	1	2	yes	—
230	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
231	C₄×C₄₃	—	2	2	no	—
232	C₄×C₄₃	—	2	4	no	—
233	C₄×C₄₃	—	2	4	no	—
234	C₄×C₄₃	—	2	2	no	—
235	C₄×C₄₃	—	2	2	no	—
236	C₄×C₄₃	—	2	2	no	—
237	C₄×C₄₃	#518	1	2	yes	—
238	C₄×C₄₃	C₂²×M₁₆	1	4	yes	—
239	C₄×C₄₃	C₂×H(5,𝔽₂)	1	2	yes	—
240	C₂²×C₄×D₄	D₄₃	1	1	yes	characteristic
241	#2974	—	43	16	no	—
242	C₂×#436	—	43	2	no	—
243	C₂×#435	—	43	4	no	—
244	C₂×C₈×D₄	—	43	2	no	—
245	C₂×#432	—	43	1	no	—
246	C₂×#431	—	43	1	no	—
247	C₂×#407	—	43	2	no	—
248	C₂²×C₂²⋊C₈	—	43	2	no	—
249	C₂×C₄₃	—	2	4	no	—
250	C₂×C₄₃	—	2	8	no	—
251	C₂×C₄₃	—	4	4	no	—
252	C₂×C₄₃	#2974	1	4	yes	complemented
253	C₂×C₄₃	C₂×#518	1	1	yes	characteristic
254	C₂×C₄₃	C₂³×M₁₆	1	1	yes	characteristic
255	C₂×C₄₃	C₂²×#131	1	1	yes	characteristic
256	C₂³×D₄	Dic₄₃	1	1	yes	characteristic
257	C₂⁴×C₄	C₂×D₄₃	1	2	yes	—
258	C₂²×M₁₆	—	43	4	no	—
259	C₂³×C₈	—	43	4	no	—
260	C₂×C₄×D₄	Dic₄₃	1	2	yes	—
261	C₂×C₄×D₄	Dic₄₃	1	8	yes	—
262	C₂×C₄×D₄	Dic₄₃	1	1	yes	characteristic
263	C₂×C₄×D₄	Dic₄₃	1	1	yes	characteristic
264	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
265	C₂×C₄×D₄	C₂×D₄₃	1	2	yes	—
266	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
267	C₂×C₄×D₄	C₂×D₄₃	1	8	yes	—
268	C₂²×C₄⋊C₄	Dic₄₃	1	1	yes	characteristic
269	C₂²×C₂²⋊C₄	Dic₄₃	1	2	yes	—
270	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
271	#436	—	43	16	no	—
272	#435	—	43	32	no	—
273	C₈×D₄	—	43	16	no	—
274	#432	—	43	8	no	—
275	#431	—	43	8	no	—
276	C₂×C₄⋊C₈	—	43	2	no	—
277	C₂×C₄⋊C₈	—	43	2	no	—
278	#407	—	43	16	no	—
279	C₂×C₂²⋊C₈	—	43	1	no	—
280	C₂×C₂²⋊C₈	—	43	2	no	—
281	C₂×C₂²⋊C₈	—	43	4	no	—
282	C₂×C₂²⋊C₈	—	43	16	no	—
283	C₂×C₂²⋊C₈	—	43	1	no	—
284	C₂×C₂²⋊C₈	—	43	4	no	—
285	C₂×#97	—	43	2	no	—
286	C₂×C₄×C₈	—	43	2	no	—
287	C₄₃	C₂×#2974	1	1	yes	characteristic, complemented, Sylow
288	C₂⁵	C₂×Dic₄₃	1	2	yes	—
289	C₂²×D₄	—	2	8	no	—
290	C₂²×D₄	C₂×Dic₄₃	1	2	yes	—
291	C₂²×D₄	C₂×Dic₄₃	1	8	yes	—
292	C₂²×D₄	C₂×Dic₄₃	1	1	yes	characteristic
293	C₂²×D₄	C₂×Dic₄₃	1	1	yes	characteristic
294	C₂³×C₄	—	4	8	no	—
295	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
296	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
297	C₂³×C₄	C₂×Dic₄₃	1	2	yes	—
298	C₂³×C₄	C₂×Dic₄₃	1	8	yes	—
299	C₂³×C₄	C₂×Dic₄₃	1	2	yes	—
300	C₂³×C₄	C₂×Dic₄₃	1	2	yes	—
301	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
302	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
303	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
304	C₂³×C₄	C₂²×D₄₃	1	8	yes	—
305	C₂×M₁₆	—	43	16	no	—
306	C₂×M₁₆	—	172	8	no	—
307	C₂²×C₈	—	43	2	no	—
308	C₂²×C₈	—	43	4	no	—
309	C₂²×C₈	—	43	2	no	—
310	C₂²×C₈	—	43	16	no	—
311	C₂²×C₈	—	172	8	no	—
312	C₄×D₄	C₂×Dic₄₃	1	8	yes	—
313	C₄×D₄	C₂×Dic₄₃	1	4	yes	—
314	C₄×D₄	C₂×Dic₄₃	1	4	yes	—
315	C₄×D₄	C₂×Dic₄₃	1	16	yes	—
316	C₄×D₄	C₂×Dic₄₃	1	8	yes	—
317	C₄×D₄	C₂×Dic₄₃	1	8	yes	—
318	C₄×D₄	C₂²×D₄₃	1	4	yes	—
319	C₄×D₄	C₂²×D₄₃	1	8	yes	—
320	C₄×D₄	C₂²×D₄₃	1	4	yes	—
321	C₂×C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
322	C₂×C₄⋊C₄	C₂×Dic₄₃	1	8	yes	—
323	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
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×C₂²⋊C₄	C₂×Dic₄₃	1	16	yes	—
330	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
331	C₂×C₄²	C₂×Dic₄₃	1	4	yes	—
332	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
333	C₂×C₄²	C₂²×D₄₃	1	4	yes	—
334	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
335	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
336	C₄⋊C₈	—	43	8	no	—
337	C₄⋊C₈	—	43	8	no	—
338	C₂²⋊C₈	—	43	4	no	—
339	C₂²⋊C₈	—	43	8	no	—
340	C₂²⋊C₈	—	43	4	no	—
341	C₂²⋊C₈	—	43	16	no	—
342	C₂²⋊C₈	—	43	16	no	—
343	#97	—	43	8	no	—
344	C₄×C₈	—	43	8	no	—
345	C₂⁴	—	2	8	no	—
346	C₂⁴	—	2	8	no	—
347	C₂⁴	—	4	4	no	—
348	C₂⁴	C₂²×Dic₄₃	1	2	yes	—
349	C₂⁴	C₂²×Dic₄₃	1	8	yes	—
350	C₂⁴	C₂²×Dic₄₃	1	2	yes	—
351	C₂⁴	C₂²×Dic₄₃	1	1	yes	characteristic
352	C₂×D₄	—	2	8	no	—
353	C₂×D₄	—	2	32	no	—
354	C₂×D₄	—	2	4	no	—
355	C₂×D₄	#10621877	1	8	yes	complemented
356	C₂×D₄	C₂²×Dic₄₃	1	8	yes	—
357	C₂×D₄	C₂²×Dic₄₃	1	4	yes	—
358	C₂×D₄	C₂²×Dic₄₃	1	4	yes	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	2	8	no	—
362	C₂²×C₄	—	2	8	no	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	—	4	16	no	—
365	C₂²×C₄	—	4	16	no	—
366	C₂²×C₄	—	4	4	no	—
367	C₂²×C₄	—	4	4	no	—
368	C₂²×C₄	—	4	4	no	—
369	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
370	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
371	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
372	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
373	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
374	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
375	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
376	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
377	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
378	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
379	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
380	C₂²×C₄	C₂²×Dic₄₃	1	8	yes	—
381	C₂²×C₄	C₂²×Dic₄₃	1	8	yes	—
382	C₂²×C₄	C₂²×Dic₄₃	1	8	yes	—
383	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
384	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
385	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
386	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
387	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
388	M₁₆	—	172	16	no	—
389	C₂×C₈	—	43	4	no	—
390	C₂×C₈	—	43	4	no	—
391	C₂×C₈	—	43	8	no	—
392	C₂×C₈	—	86	4	no	—
393	C₂×C₈	—	86	8	no	—
394	C₂×C₈	—	86	4	no	—
395	C₂×C₈	—	172	16	no	—
396	C₄⋊C₄	C₂²×Dic₄₃	1	8	yes	—
397	C₄⋊C₄	C₂²×Dic₄₃	1	4	yes	—
398	C₄⋊C₄	C₂²×Dic₄₃	1	4	yes	—
399	C₂²⋊C₄	C₂²×Dic₄₃	1	8	yes	—
400	C₂²⋊C₄	C₂²×Dic₄₃	1	8	yes	—
401	C₂²⋊C₄	C₂²×Dic₄₃	1	8	yes	—
402	C₂²⋊C₄	C₂²×Dic₄₃	1	8	yes	—
403	C₄²	C₂²×Dic₄₃	1	4	yes	—
404	C₄²	C₂²×Dic₄₃	1	4	yes	—
405	C₄²	C₂²×Dic₄₃	1	2	yes	—
406	C₄²	C₂²×Dic₄₃	1	2	yes	—
407	C₄²	C₂³×D₄₃	1	2	yes	—
408	C₄²	C₂³×D₄₃	1	2	yes	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	4	no	—
411	C₂³	—	2	2	no	—
412	C₂³	—	2	4	no	—
413	C₂³	—	2	4	no	—
414	C₂³	—	2	16	no	—
415	C₂³	—	2	4	no	—
416	C₂³	—	2	16	no	—
417	C₂³	—	2	4	no	—
418	C₂³	—	4	8	no	—
419	C₂³	—	4	32	no	—
420	C₂³	C₂×#10621877	1	8	yes	—
421	C₂³	#13063332	1	4	yes	—
422	C₂³	C₂³×Dic₄₃	1	4	yes	—
423	C₂³	C₂³×Dic₄₃	1	4	yes	—
424	C₂³	C₂³×Dic₄₃	1	2	yes	—
425	C₂³	C₂³×Dic₄₃	1	1	yes	characteristic
426	D₄	—	2	16	no	—
427	D₄	—	2	8	no	—
428	D₄	C₂×#10621877	1	16	yes	complemented
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	8	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	8	no	—
438	C₂×C₄	—	2	8	no	—
439	C₂×C₄	—	2	8	no	—
440	C₂×C₄	—	2	8	no	—
441	C₂×C₄	—	2	8	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	4	8	no	—
444	C₂×C₄	—	4	8	no	—
445	C₂×C₄	—	4	8	no	—
446	C₂×C₄	C₂×#10621877	1	4	yes	—
447	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
448	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
449	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
450	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
451	C₂×C₄	C₂³×Dic₄₃	1	4	yes	—
452	C₂×C₄	C₂³×Dic₄₃	1	4	yes	—
453	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
454	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
455	C₂×C₄	#13063370	1	4	yes	—
456	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
457	C₈	—	86	4	no	—
458	C₈	—	86	8	no	—
459	C₈	—	86	4	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	2	4	no	—
462	C₂²	—	2	8	no	—
463	C₂²	—	2	16	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	2	4	no	—
466	C₂²	—	2	4	no	—
467	C₂²	—	2	4	no	—
468	C₂²	—	2	4	no	—
469	C₂²	—	4	32	no	—
470	C₂²	—	4	8	no	—
471	C₂²	#14583374	1	2	yes	—
472	C₂²	C₂²×#10621877	1	8	yes	—
473	C₂²	C₂²×#10621877	1	2	yes	—
474	C₂²	C₂×#13063332	1	4	yes	—
475	C₂²	C₂×#13063332	1	2	yes	—
476	C₂²	C₂⁴×Dic₄₃	1	1	yes	characteristic
477	C₄	—	2	2	no	—
478	C₄	—	2	4	no	—
479	C₄	—	2	4	no	—
480	C₄	—	2	2	no	—
481	C₄	—	2	2	no	—
482	C₄	—	2	2	no	—
483	C₄	#14583374	1	2	yes	—
484	C₄	C₂²×#10621877	1	4	yes	—
485	C₄	C₂×#13063370	1	2	yes	—
486	C₂	—	2	4	no	—
487	C₂	—	2	8	no	—
488	C₂	—	4	4	no	—
489	C₂	#19143630	1	4	yes	direct product factor
490	C₂	C₂×#14583374	1	1	yes	characteristic
491	C₂	C₂³×#10621877	1	1	yes	characteristic
492	C₂	C₂²×#13063332	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₄₃
commutator	C₂²×C₄₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₂²×C₄×D₄×C₄₃	C₂
socle	C₂³×C₄₃	C₂³×C₄
prime radical	C₂³×D₄×C₄₃	C₄
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	C₂²×C₄×D₄	D₄₃
hypocenter	C₄₃	C₂×#2974
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #19143630	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×#14582863	C₂	semidirect
8. C₂²×C₂²⋊(C₄₃⋊C₈)	C₂	semidirect
10. C₂²×#10621877	C₂²	semidirect
11. C₂³×C₄₃⋊C₈	C₂²	semidirect
12. #14582977	C₂²	semidirect
13. #14582971	C₂²	semidirect
14. D₄×C₄₃⋊C₈	C₂²	semidirect
15. #14582956	C₂²	semidirect
16. #14582952	C₂²	semidirect
17. C₂×C₄⋊(C₄₃⋊C₈)	C₂²	semidirect
18. C₂×C₄⋊(C₄₃⋊C₈)	C₂²	semidirect
19. #14582863	C₂²	semidirect
23. C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	semidirect
24. C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	semidirect
25. C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	semidirect
26. C₂×#13063236	C₂²	semidirect
27. C₂×C₄×C₄₃⋊C₈	C₂²	semidirect
42. C₂×#10621877	C₂³	semidirect
47. C₂²×C₄₃⋊C₈	C₂³	semidirect
48. C₄⋊(C₄₃⋊C₈)	C₂³	semidirect
49. C₄⋊(C₄₃⋊C₈)	C₂³	semidirect
53. C₂²⋊(C₄₃⋊C₈)	C₂³	semidirect
54. C₂²⋊(C₄₃⋊C₈)	C₂³	semidirect
55. #13063236	C₂³	semidirect
56. C₄×C₄₃⋊C₈	C₂³	semidirect
108. C₂×D₄×C₄₃	M₁₆	semidirect
181. D₄×C₄₃	C₂×M₁₆	semidirect
252. C₂×C₄₃	#2974	semidirect
287. C₄₃	C₂×#2974	semidirect
355. C₂×D₄	#10621877	semidirect
428. D₄	C₂×#10621877	semidirect
489. C₂	#19143630	direct (N × H)

Maximal subgroups

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

subgroup	index
#19143630	2
C₂×#14582977	2
C₂×#14582971	2
C₂×D₄×C₄₃⋊C₈	2
C₂×#14582956	2
C₂×#14582952	2
C₂×#14582863	2
C₂²×C₂²⋊(C₄₃⋊C₈)	2
C₂²×C₄×D₄×C₄₃	2
C₂×#2974	43

Subgroups — C2×#19143630 #25961332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19143630 #25961332