Subgroups — C₂×D₄×#10621877 #25960499

Order 11008.

3218 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#10621877	C₂	1	2	yes	maximal, complemented
2	D₄×#10621877	C₂	1	16	yes	maximal, direct product factor
3	C₂×#14582977	C₂	1	2	yes	maximal, complemented
4	C₂×#14582971	C₂	1	4	yes	maximal, complemented
5	C₂×D₄×C₄₃⋊C₈	C₂	1	2	yes	maximal, complemented
6	C₂×#14582923	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#14582863	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×#10621877	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₄×D₄×C₄₃	C₂	1	1	yes	maximal, characteristic
10	C₂²×#10621877	—	2	16	no	—
11	C₂²×#10621877	C₂²	1	1	yes	characteristic
12	C₂²×#10621877	C₂²	1	2	yes	—
13	C₂²×#10621877	C₂²	1	1	yes	characteristic
14	C₂²×#10621877	C₂²	1	4	yes	complemented
15	C₂²×#10621877	C₂²	1	16	yes	complemented
16	C₂³×C₄₃⋊C₈	C₂²	1	4	yes	complemented
17	#14582977	C₂²	1	16	yes	complemented
18	#14582971	C₂²	1	32	yes	complemented
19	D₄×C₄₃⋊C₈	C₂²	1	16	yes	complemented
20	#14582923	C₂²	1	8	yes	complemented
21	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	complemented
22	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	complemented
23	#14582863	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	C₄×#10621877	C₂²	1	8	yes	complemented
27	C₂×#13063236	C₂²	1	2	yes	complemented
28	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	complemented
29	C₂³×D₄×C₄₃	C₄	1	1	yes	characteristic
30	C₂⁴×C₄×C₄₃	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₄₃	C₄	1	2	yes	—
32	C₂×C₄×D₄×C₄₃	C₄	1	1	yes	characteristic
33	C₂×C₄×D₄×C₄₃	C₄	1	8	yes	—
34	C₂×C₄×D₄×C₄₃	C₄	1	1	yes	characteristic
35	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₄₃	C₂²	1	8	yes	—
39	C₂²×C₄⋊C₄×C₄₃	C₄	1	1	yes	characteristic
40	C₂²×C₂²⋊C₄×C₄₃	C₄	1	2	yes	—
41	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
42	C₂×#10621877	—	2	8	no	—
43	C₂×#10621877	—	2	4	no	—
44	C₂×#10621877	—	2	64	no	—
45	C₂×#10621877	—	2	16	no	—
46	C₂×#10621877	D₄	1	8	yes	direct product factor
47	C₂×#10621877	C₂³	1	4	yes	—
48	C₂×#10621877	C₂³	1	8	yes	—
49	C₂×#10621877	C₂³	1	4	yes	—
50	C₂×#10621877	C₂³	1	16	yes	complemented
51	C₂²×C₄₃⋊C₈	—	2	16	no	—
52	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
53	C₂²×C₄₃⋊C₈	C₂³	1	4	yes	—
54	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
55	C₂²×C₄₃⋊C₈	C₂³	1	16	yes	complemented
56	C₄⋊(C₄₃⋊C₈)	C₂³	1	8	yes	complemented
57	C₄⋊(C₄₃⋊C₈)	C₂³	1	8	yes	complemented
58	C₂²⋊(C₄₃⋊C₈)	C₂³	1	16	yes	complemented
59	C₂²⋊(C₄₃⋊C₈)	C₂³	1	16	yes	complemented
60	#13063236	C₂³	1	8	yes	complemented
61	C₄×C₄₃⋊C₈	C₂³	1	8	yes	complemented
62	C₂⁵×C₄₃	C₂×C₄	1	2	yes	—
63	C₂²×D₄×C₄₃	—	2	8	no	—
64	C₂²×D₄×C₄₃	C₂×C₄	1	8	yes	—
65	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
66	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
67	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
68	C₂³×C₄×C₄₃	—	2	8	no	—
69	C₂³×C₄×C₄₃	—	2	8	no	—
70	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
71	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
72	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
73	C₂³×C₄×C₄₃	C₂×C₄	1	8	yes	—
74	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
75	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
76	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
77	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
78	C₂³×C₄×C₄₃	C₂³	1	8	yes	—
79	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
80	C₄×D₄×C₄₃	C₂×C₄	1	8	yes	—
81	C₄×D₄×C₄₃	C₂×C₄	1	4	yes	—
82	C₄×D₄×C₄₃	C₂×C₄	1	16	yes	—
83	C₄×D₄×C₄₃	C₂×C₄	1	8	yes	—
84	C₄×D₄×C₄₃	C₂×C₄	1	4	yes	—
85	C₄×D₄×C₄₃	C₂×C₄	1	8	yes	—
86	C₄×D₄×C₄₃	C₂³	1	4	yes	—
87	C₄×D₄×C₄₃	C₂³	1	8	yes	—
88	C₄×D₄×C₄₃	C₂³	1	4	yes	—
89	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
90	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
91	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
93	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
94	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
95	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
96	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
97	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	16	yes	—
98	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
99	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
100	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
101	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
104	C₂⁴×C₄₃	—	2	8	no	—
105	C₂⁴×C₄₃	—	2	8	no	—
106	C₂⁴×C₄₃	—	4	4	no	—
107	C₂⁴×C₄₃	C₂²×C₄	1	2	yes	—
108	C₂⁴×C₄₃	C₂²×C₄	1	8	yes	—
109	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
110	C₂⁴×C₄₃	C₂²×C₄	1	2	yes	—
111	C₂×D₄×C₄₃	—	2	32	no	—
112	C₂×D₄×C₄₃	—	2	4	no	—
113	C₂×D₄×C₄₃	—	2	8	no	—
114	C₂×D₄×C₄₃	M₁₆	1	8	yes	complemented
115	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
116	C₂×D₄×C₄₃	C₂²×C₄	1	8	yes	—
117	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
118	C₂²×C₄×C₄₃	—	2	8	no	—
119	C₂²×C₄×C₄₃	—	2	32	no	—
120	C₂²×C₄×C₄₃	—	2	8	no	—
121	C₂²×C₄×C₄₃	—	2	4	no	—
122	C₂²×C₄×C₄₃	—	2	4	no	—
123	C₂²×C₄×C₄₃	—	2	16	no	—
124	C₂²×C₄×C₄₃	—	2	4	no	—
125	C₂²×C₄×C₄₃	—	2	4	no	—
126	C₂²×C₄×C₄₃	—	2	4	no	—
127	C₂²×C₄×C₄₃	—	2	16	no	—
128	C₂²×C₄×C₄₃	—	2	8	no	—
129	C₂²×C₄×C₄₃	—	4	2	no	—
130	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
133	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
135	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
136	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
137	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
138	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
139	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
140	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
141	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
142	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
143	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
146	C₂²×C₄×C₄₃	#41	1	4	yes	—
147	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
150	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
151	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
152	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
153	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
154	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
155	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
156	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
157	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
158	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
159	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
160	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
161	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
162	C₄²×C₄₃	C₂⁴	1	2	yes	—
163	C₄²×C₄₃	C₂⁴	1	2	yes	—
164	#10621877	—	2	16	no	—
165	#10621877	—	2	8	no	—
166	#10621877	—	2	32	no	—
167	#10621877	C₂×D₄	1	16	yes	direct product factor
168	C₂×C₄₃⋊C₈	—	2	8	no	—
169	C₂×C₄₃⋊C₈	—	2	4	no	—
170	C₂×C₄₃⋊C₈	—	2	32	no	—
171	C₂×C₄₃⋊C₈	C₂×D₄	1	8	yes	complemented
172	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
173	C₂×C₄₃⋊C₈	C₂⁴	1	8	yes	—
174	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
175	C₂³×C₄₃	—	2	4	no	—
176	C₂³×C₄₃	—	2	2	no	—
177	C₂³×C₄₃	—	2	2	no	—
178	C₂³×C₄₃	—	2	4	no	—
179	C₂³×C₄₃	—	2	16	no	—
180	C₂³×C₄₃	—	2	4	no	—
181	C₂³×C₄₃	—	2	4	no	—
182	C₂³×C₄₃	—	2	16	no	—
183	C₂³×C₄₃	—	2	4	no	—
184	C₂³×C₄₃	—	4	8	no	—
185	C₂³×C₄₃	—	4	32	no	—
186	C₂³×C₄₃	C₄×D₄	1	4	yes	—
187	C₂³×C₄₃	C₂×M₁₆	1	8	yes	complemented
188	C₂³×C₄₃	C₂³×C₄	1	4	yes	—
189	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
190	C₂³×C₄₃	C₂³×C₄	1	4	yes	—
191	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
192	D₄×C₄₃	—	2	16	no	—
193	D₄×C₄₃	—	2	8	no	—
194	D₄×C₄₃	C₂×M₁₆	1	16	yes	complemented
195	C₂×C₄×C₄₃	—	2	16	no	—
196	C₂×C₄×C₄₃	—	2	4	no	—
197	C₂×C₄×C₄₃	—	2	4	no	—
198	C₂×C₄×C₄₃	—	2	2	no	—
199	C₂×C₄×C₄₃	—	2	2	no	—
200	C₂×C₄×C₄₃	—	2	2	no	—
201	C₂×C₄×C₄₃	—	2	8	no	—
202	C₂×C₄×C₄₃	—	2	16	no	—
203	C₂×C₄×C₄₃	—	2	16	no	—
204	C₂×C₄×C₄₃	—	2	8	no	—
205	C₂×C₄×C₄₃	—	2	8	no	—
206	C₂×C₄×C₄₃	—	2	4	no	—
207	C₂×C₄×C₄₃	—	2	4	no	—
208	C₂×C₄×C₄₃	—	2	4	no	—
209	C₂×C₄×C₄₃	—	2	4	no	—
210	C₂×C₄×C₄₃	—	4	4	no	—
211	C₂×C₄×C₄₃	C₄×D₄	1	8	yes	—
212	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
213	C₂×C₄×C₄₃	C₂×M₁₆	1	4	yes	complemented
214	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
215	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
216	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
217	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
218	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
219	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
220	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
221	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
222	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
223	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
224	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
225	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
226	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
227	C₄₃⋊C₈	—	2	8	no	—
228	C₄₃⋊C₈	—	2	4	no	—
229	C₄₃⋊C₈	C₂²×D₄	1	8	yes	complemented
230	C₂×D₄×M₁₆	—	43	1	no	maximal, Sylow
231	C₂²×C₄₃	—	2	4	no	—
232	C₂²×C₄₃	—	2	8	no	—
233	C₂²×C₄₃	—	2	16	no	—
234	C₂²×C₄₃	—	2	2	no	—
235	C₂²×C₄₃	—	2	2	no	—
236	C₂²×C₄₃	—	2	4	no	—
237	C₂²×C₄₃	—	2	4	no	—
238	C₂²×C₄₃	—	2	4	no	—
239	C₂²×C₄₃	—	2	4	no	—
240	C₂²×C₄₃	—	4	32	no	—
241	C₂²×C₄₃	—	4	8	no	—
242	C₂²×C₄₃	C₂×C₄×D₄	1	4	yes	—
243	C₂²×C₄₃	C₂×C₄×D₄	1	2	yes	—
244	C₂²×C₄₃	C₂²×M₁₆	1	2	yes	—
245	C₂²×C₄₃	C₂²×M₁₆	1	8	yes	complemented
246	C₂²×C₄₃	#568	1	2	yes	—
247	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
248	C₄×C₄₃	—	2	4	no	—
249	C₄×C₄₃	—	2	4	no	—
250	C₄×C₄₃	—	2	2	no	—
251	C₄×C₄₃	—	2	2	no	—
252	C₄×C₄₃	—	2	2	no	—
253	C₄×C₄₃	C₂×C₄×D₄	1	2	yes	—
254	C₄×C₄₃	C₂×C₄×D₄	1	4	yes	—
255	C₄×C₄₃	C₂²×M₁₆	1	4	yes	complemented
256	C₄×C₄₃	C₂³×D₄	1	1	yes	characteristic
257	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
258	C₂³×M₁₆	—	43	2	no	—
259	C₂²×C₄×D₄	D₄₃	1	1	yes	characteristic
260	D₄×M₁₆	—	43	16	no	—
261	C₂×#436	—	43	2	no	—
262	C₂×#435	—	43	4	no	—
263	C₂×C₈×D₄	—	43	2	no	—
264	C₂×#423	—	43	1	no	—
265	C₂×#407	—	43	2	no	—
266	C₂×C₄×M₁₆	—	43	1	no	—
267	C₂×C₄₃	—	2	4	no	—
268	C₂×C₄₃	—	2	8	no	—
269	C₂×C₄₃	—	4	4	no	—
270	C₂×C₄₃	D₄×M₁₆	1	4	yes	complemented
271	C₂×C₄₃	C₂²×C₄×D₄	1	1	yes	characteristic
272	C₂×C₄₃	C₂³×M₁₆	1	1	yes	characteristic
273	C₂×C₄₃	C₂×#568	1	1	yes	characteristic
274	C₂³×D₄	Dic₄₃	1	1	yes	characteristic
275	C₂⁴×C₄	C₂×D₄₃	1	2	yes	—
276	C₂²×M₁₆	—	43	1	no	—
277	C₂²×M₁₆	—	43	1	no	—
278	C₂²×M₁₆	—	43	2	no	—
279	C₂²×M₁₆	—	43	4	no	—
280	C₂²×M₁₆	—	43	16	no	—
281	C₂²×M₁₆	—	86	16	no	—
282	C₂³×C₈	—	43	4	no	—
283	C₂×C₄×D₄	Dic₄₃	1	2	yes	—
284	C₂×C₄×D₄	Dic₄₃	1	1	yes	characteristic
285	C₂×C₄×D₄	Dic₄₃	1	8	yes	—
286	C₂×C₄×D₄	Dic₄₃	1	1	yes	characteristic
287	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
288	C₂×C₄×D₄	C₂×D₄₃	1	2	yes	—
289	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
290	C₂×C₄×D₄	C₂×D₄₃	1	8	yes	—
291	C₂²×C₄⋊C₄	Dic₄₃	1	1	yes	characteristic
292	C₂²×C₂²⋊C₄	Dic₄₃	1	2	yes	—
293	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
294	#436	—	43	16	no	—
295	#435	—	43	32	no	—
296	C₈×D₄	—	43	16	no	—
297	#423	—	43	8	no	—
298	C₂×C₄⋊C₈	—	43	2	no	—
299	C₂×C₄⋊C₈	—	43	2	no	—
300	#407	—	43	16	no	—
301	C₂×C₂²⋊C₈	—	43	4	no	—
302	C₂×C₂²⋊C₈	—	43	4	no	—
303	C₄×M₁₆	—	43	8	no	—
304	C₂×#97	—	43	2	no	—
305	C₂×C₄×C₈	—	43	2	no	—
306	C₄₃	C₂×D₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
307	C₂⁵	C₂×Dic₄₃	1	2	yes	—
308	C₂²×D₄	—	2	8	no	—
309	C₂²×D₄	C₂×Dic₄₃	1	2	yes	—
310	C₂²×D₄	C₂×Dic₄₃	1	8	yes	—
311	C₂²×D₄	C₂×Dic₄₃	1	1	yes	characteristic
312	C₂²×D₄	C₂×Dic₄₃	1	1	yes	characteristic
313	C₂³×C₄	—	2	8	no	—
314	C₂³×C₄	—	2	8	no	—
315	C₂³×C₄	C₂×Dic₄₃	1	2	yes	—
316	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
317	C₂³×C₄	C₂×Dic₄₃	1	2	yes	—
318	C₂³×C₄	C₂×Dic₄₃	1	8	yes	—
319	C₂³×C₄	C₂×Dic₄₃	1	2	yes	—
320	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
321	C₂³×C₄	C₂²×D₄₃	1	8	yes	—
322	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
323	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
324	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
325	C₂×M₁₆	—	43	8	no	—
326	C₂×M₁₆	—	43	4	no	—
327	C₂×M₁₆	—	43	8	no	—
328	C₂×M₁₆	—	43	16	no	—
329	C₂×M₁₆	—	43	4	no	—
330	C₂×M₁₆	—	86	16	no	—
331	C₂×M₁₆	—	86	64	no	—
332	C₂×M₁₆	—	86	8	no	—
333	C₂×M₁₆	—	86	4	no	—
334	C₂²×C₈	—	43	2	no	—
335	C₂²×C₈	—	43	16	no	—
336	C₂²×C₈	—	43	4	no	—
337	C₂²×C₈	—	43	2	no	—
338	C₂²×C₈	—	86	16	no	—
339	C₄×D₄	C₂×Dic₄₃	1	8	yes	—
340	C₄×D₄	C₂×Dic₄₃	1	4	yes	—
341	C₄×D₄	C₂×Dic₄₃	1	16	yes	—
342	C₄×D₄	C₂×Dic₄₃	1	8	yes	—
343	C₄×D₄	C₂×Dic₄₃	1	4	yes	—
344	C₄×D₄	C₂×Dic₄₃	1	8	yes	—
345	C₄×D₄	C₂²×D₄₃	1	4	yes	—
346	C₄×D₄	C₂²×D₄₃	1	8	yes	—
347	C₄×D₄	C₂²×D₄₃	1	4	yes	—
348	C₂×C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
349	C₂×C₄⋊C₄	C₂×Dic₄₃	1	8	yes	—
350	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
352	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	2	yes	—
353	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	2	yes	—
354	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	2	yes	—
355	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	2	yes	—
356	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	16	yes	—
357	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
358	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
359	C₂×C₄²	C₂×Dic₄₃	1	4	yes	—
360	C₂×C₄²	C₂²×D₄₃	1	4	yes	—
361	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
362	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
363	C₄⋊C₈	—	43	8	no	—
364	C₄⋊C₈	—	43	8	no	—
365	C₂²⋊C₈	—	43	16	no	—
366	C₂²⋊C₈	—	43	16	no	—
367	#97	—	43	8	no	—
368	C₄×C₈	—	43	8	no	—
369	C₂⁴	—	2	8	no	—
370	C₂⁴	—	2	8	no	—
371	C₂⁴	—	4	4	no	—
372	C₂⁴	C₂²×Dic₄₃	1	2	yes	—
373	C₂⁴	C₂²×Dic₄₃	1	8	yes	—
374	C₂⁴	C₂²×Dic₄₃	1	1	yes	characteristic
375	C₂⁴	C₂²×Dic₄₃	1	2	yes	—
376	C₂×D₄	—	2	8	no	—
377	C₂×D₄	—	2	32	no	—
378	C₂×D₄	—	2	4	no	—
379	C₂×D₄	#10621877	1	8	yes	direct product factor
380	C₂×D₄	C₂²×Dic₄₃	1	8	yes	—
381	C₂×D₄	C₂²×Dic₄₃	1	4	yes	—
382	C₂×D₄	C₂²×Dic₄₃	1	4	yes	—
383	C₂²×C₄	—	2	8	no	—
384	C₂²×C₄	—	2	8	no	—
385	C₂²×C₄	—	2	32	no	—
386	C₂²×C₄	—	2	8	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	16	no	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	2	16	no	—
394	C₂²×C₄	—	4	2	no	—
395	C₂²×C₄	D₄×D₄₃	1	4	yes	—
396	C₂²×C₄	#10621900	1	4	yes	—
397	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
398	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
399	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
400	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
401	C₂²×C₄	C₂²×Dic₄₃	1	8	yes	—
402	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
403	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
404	C₂²×C₄	C₂²×Dic₄₃	1	8	yes	—
405	C₂²×C₄	C₂²×Dic₄₃	1	8	yes	—
406	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
407	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
408	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
409	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
410	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
411	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
412	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
413	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
414	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
415	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
416	M₁₆	—	43	16	no	—
417	M₁₆	—	86	32	no	—
418	M₁₆	—	86	16	no	—
419	M₁₆	—	86	8	no	—
420	C₂×C₈	—	43	8	no	—
421	C₂×C₈	—	43	4	no	—
422	C₂×C₈	—	43	4	no	—
423	C₂×C₈	—	43	8	no	—
424	C₂×C₈	—	86	32	no	—
425	C₂×C₈	—	86	8	no	—
426	C₂×C₈	—	86	4	no	—
427	C₄⋊C₄	C₂²×Dic₄₃	1	8	yes	—
428	C₄⋊C₄	C₂²×Dic₄₃	1	4	yes	—
429	C₄⋊C₄	C₂²×Dic₄₃	1	4	yes	—
430	C₂²⋊C₄	C₂²×Dic₄₃	1	8	yes	—
431	C₂²⋊C₄	C₂²×Dic₄₃	1	8	yes	—
432	C₂²⋊C₄	C₂²×Dic₄₃	1	8	yes	—
433	C₂²⋊C₄	C₂²×Dic₄₃	1	8	yes	—
434	C₄²	C₂²×Dic₄₃	1	4	yes	—
435	C₄²	C₂²×Dic₄₃	1	2	yes	—
436	C₄²	C₂²×Dic₄₃	1	4	yes	—
437	C₄²	C₂²×Dic₄₃	1	2	yes	—
438	C₄²	C₂³×D₄₃	1	2	yes	—
439	C₄²	C₂³×D₄₃	1	2	yes	—
440	C₂³	—	2	4	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	4	no	—
444	C₂³	—	2	16	no	—
445	C₂³	—	2	4	no	—
446	C₂³	—	2	4	no	—
447	C₂³	—	2	16	no	—
448	C₂³	—	2	4	no	—
449	C₂³	—	4	8	no	—
450	C₂³	—	4	32	no	—
451	C₂³	D₄×Dic₄₃	1	4	yes	—
452	C₂³	C₂×#10621877	1	8	yes	complemented
453	C₂³	C₂³×Dic₄₃	1	4	yes	—
454	C₂³	C₂³×Dic₄₃	1	2	yes	—
455	C₂³	C₂³×Dic₄₃	1	4	yes	—
456	C₂³	C₂³×Dic₄₃	1	1	yes	characteristic
457	D₄	—	2	16	no	—
458	D₄	—	2	8	no	—
459	D₄	C₂×#10621877	1	16	yes	direct product factor
460	C₂×C₄	—	2	16	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	8	no	—
467	C₂×C₄	—	2	16	no	—
468	C₂×C₄	—	2	16	no	—
469	C₂×C₄	—	2	8	no	—
470	C₂×C₄	—	2	8	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	4	4	no	—
476	C₂×C₄	D₄×Dic₄₃	1	8	yes	—
477	C₂×C₄	D₄×Dic₄₃	1	4	yes	—
478	C₂×C₄	C₂×#10621877	1	4	yes	complemented
479	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
480	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
481	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
482	C₂×C₄	C₂³×Dic₄₃	1	4	yes	—
483	C₂×C₄	C₂³×Dic₄₃	1	4	yes	—
484	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
485	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
486	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
487	C₂×C₄	C₂×D₄×D₄₃	1	2	yes	—
488	C₂×C₄	C₂×D₄×D₄₃	1	4	yes	—
489	C₂×C₄	C₂×#10621900	1	2	yes	—
490	C₂×C₄	C₂×#10621900	1	4	yes	—
491	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
492	C₈	—	43	8	no	—
493	C₈	—	86	8	no	—
494	C₈	—	86	4	no	—
495	C₂²	—	2	8	no	—
496	C₂²	—	2	16	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	4	no	—
499	C₂²	—	2	2	no	—
500	C₂²	—	2	4	no	—
501	C₂²	—	2	4	no	—
502	C₂²	—	2	4	no	—
503	C₂²	—	2	4	no	—
504	C₂²	—	4	32	no	—
505	C₂²	—	4	8	no	—
506	C₂²	C₂×D₄×Dic₄₃	1	4	yes	—
507	C₂²	C₂×D₄×Dic₄₃	1	2	yes	—
508	C₂²	C₂²×#10621877	1	2	yes	—
509	C₂²	C₂²×#10621877	1	8	yes	complemented
510	C₂²	#14583666	1	2	yes	—
511	C₂²	C₂⁴×Dic₄₃	1	1	yes	characteristic
512	C₄	—	2	2	no	—
513	C₄	—	2	4	no	—
514	C₄	—	2	4	no	—
515	C₄	—	2	2	no	—
516	C₄	—	2	2	no	—
517	C₄	C₂×D₄×Dic₄₃	1	4	yes	—
518	C₄	C₂×D₄×Dic₄₃	1	2	yes	—
519	C₄	C₂²×#10621877	1	4	yes	complemented
520	C₄	C₂²×D₄×D₄₃	1	1	yes	characteristic
521	C₄	C₂²×#10621900	1	1	yes	characteristic
522	C₂	—	2	4	no	—
523	C₂	—	2	8	no	—
524	C₂	—	4	4	no	—
525	C₂	D₄×#10621877	1	4	yes	direct product factor
526	C₂	C₂²×D₄×Dic₄₃	1	1	yes	characteristic
527	C₂	C₂³×#10621877	1	1	yes	characteristic
528	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	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×D₄×M₁₆
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. C₂³×#10621877	C₂	semidirect
2. D₄×#10621877	C₂	direct (N × H)
3. C₂×#14582977	C₂	semidirect
4. C₂×#14582971	C₂	semidirect
5. C₂×D₄×C₄₃⋊C₈	C₂	semidirect
6. C₂×#14582923	C₂	semidirect
7. C₂×#14582863	C₂	semidirect
8. C₂×C₄×#10621877	C₂	semidirect
14. C₂²×#10621877	C₂²	semidirect
15. C₂²×#10621877	C₂²	semidirect
16. C₂³×C₄₃⋊C₈	C₂²	semidirect
17. #14582977	C₂²	semidirect
18. #14582971	C₂²	semidirect
19. D₄×C₄₃⋊C₈	C₂²	semidirect
20. #14582923	C₂²	semidirect
21. C₂×C₄⋊(C₄₃⋊C₈)	C₂²	semidirect
22. C₂×C₄⋊(C₄₃⋊C₈)	C₂²	semidirect
23. #14582863	C₂²	semidirect
24. C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	semidirect
25. C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	semidirect
26. C₄×#10621877	C₂²	semidirect
27. C₂×#13063236	C₂²	semidirect
28. C₂×C₄×C₄₃⋊C₈	C₂²	semidirect
46. C₂×#10621877	D₄	direct (N × H)
50. C₂×#10621877	C₂³	semidirect
55. C₂²×C₄₃⋊C₈	C₂³	semidirect
56. C₄⋊(C₄₃⋊C₈)	C₂³	semidirect
57. C₄⋊(C₄₃⋊C₈)	C₂³	semidirect
58. C₂²⋊(C₄₃⋊C₈)	C₂³	semidirect
59. C₂²⋊(C₄₃⋊C₈)	C₂³	semidirect
60. #13063236	C₂³	semidirect
61. C₄×C₄₃⋊C₈	C₂³	semidirect
114. C₂×D₄×C₄₃	M₁₆	semidirect
167. #10621877	C₂×D₄	direct (N × H)
171. C₂×C₄₃⋊C₈	C₂×D₄	semidirect
187. C₂³×C₄₃	C₂×M₁₆	semidirect
194. D₄×C₄₃	C₂×M₁₆	semidirect
213. C₂×C₄×C₄₃	C₂×M₁₆	semidirect
229. C₄₃⋊C₈	C₂²×D₄	semidirect
245. C₂²×C₄₃	C₂²×M₁₆	semidirect
255. C₄×C₄₃	C₂²×M₁₆	semidirect
270. C₂×C₄₃	D₄×M₁₆	semidirect
306. C₄₃	C₂×D₄×M₁₆	semidirect
379. C₂×D₄	#10621877	direct (N × H)
452. C₂³	C₂×#10621877	semidirect
459. D₄	C₂×#10621877	direct (N × H)
478. C₂×C₄	C₂×#10621877	semidirect
509. C₂²	C₂²×#10621877	semidirect
519. C₄	C₂²×#10621877	semidirect
525. C₂	D₄×#10621877	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#10621877	2
D₄×#10621877	2
C₂×#14582977	2
C₂×#14582971	2
C₂×D₄×C₄₃⋊C₈	2
C₂×#14582923	2
C₂×#14582863	2
C₂×C₄×#10621877	2
C₂²×C₄×D₄×C₄₃	2
C₂×D₄×M₁₆	43

Subgroups — C2×D4×#10621877 #25960499

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄×#10621877 #25960499