Subgroups — C₂×C₄₃×#1826 #24940721

Order 11008.

1606 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#117×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#407	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₂²⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#1826	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₄₃×#339	C₂	1	4	yes	maximal, complemented
6	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
8	C₂×#117×C₄₃	—	2	1	no	—
9	C₂×#117×C₄₃	—	2	2	no	—
10	C₂×#117×C₄₃	—	2	2	no	—
11	C₂×#117×C₄₃	—	2	1	no	—
12	C₂×#117×C₄₃	C₄	1	2	yes	complemented
13	C₂×#117×C₄₃	C₄	1	4	yes	complemented
14	C₂×#117×C₄₃	C₂²	1	2	yes	—
15	C₂×#117×C₄₃	C₂²	1	4	yes	—
16	C₂²×C₄⋊C₄×C₄₃	C₄	1	1	yes	characteristic, complemented
17	C₂²×C₄⋊C₄×C₄₃	C₄	1	1	yes	characteristic, complemented
18	C₂²×C₂²⋊C₄×C₄₃	—	2	1	no	—
19	C₂²×C₂²⋊C₄×C₄₃	—	2	1	no	—
20	C₂²×C₄²×C₄₃	—	2	1	no	—
21	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
22	C₄₃×#407	—	2	2	no	—
23	C₄₃×#407	C₂²	1	4	yes	—
24	C₂×C₂²⋊C₈×C₄₃	—	2	1	no	—
25	C₂×C₂²⋊C₈×C₄₃	—	2	1	no	—
26	C₄×C₂²⋊C₄×C₄₃	—	2	2	no	—
27	C₄×C₂²⋊C₄×C₄₃	C₂²	1	4	yes	—
28	C₂×#95×C₄₃	—	2	1	no	—
29	C₄₃×#339	C₂²	1	16	yes	complemented
30	C₂⁵×C₄₃	D₄	1	1	yes	characteristic
31	C₂³×C₄×C₄₃	—	2	8	no	—
32	C₂³×C₄×C₄₃	—	2	1	no	—
33	C₂³×C₄×C₄₃	—	2	1	no	—
34	C₂³×C₄×C₄₃	—	2	2	no	—
35	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
37	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₃	D₄	1	2	yes	—
40	C₂³×C₄×C₄₃	D₄	1	2	yes	—
41	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
44	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
45	C₂×M₁₆×C₄₃	—	2	2	no	—
46	C₂×M₁₆×C₄₃	—	2	8	no	—
47	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
48	C₂²×C₈×C₄₃	—	2	2	no	—
49	#117×C₄₃	—	2	4	no	—
50	#117×C₄₃	—	2	4	no	—
51	#117×C₄₃	—	2	4	no	—
52	#117×C₄₃	—	2	2	no	—
53	#117×C₄₃	—	2	4	no	—
54	#117×C₄₃	—	2	2	no	—
55	#117×C₄₃	—	2	4	no	—
56	#117×C₄₃	C₂×C₄	1	4	yes	—
57	#117×C₄₃	C₂×C₄	1	8	yes	complemented
58	#117×C₄₃	C₂³	1	4	yes	—
59	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
60	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
61	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
64	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
65	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	complemented
66	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	complemented
67	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
68	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
69	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
72	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
73	C₂×C₄²×C₄₃	—	2	4	no	—
74	C₂×C₄²×C₄₃	—	2	2	no	—
75	C₂×C₄²×C₄₃	—	2	4	no	—
76	C₂×C₄²×C₄₃	—	2	2	no	—
77	C₂×C₄²×C₄₃	—	2	8	no	—
78	C₂×C₄²×C₄₃	—	2	2	no	—
79	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
80	C₂²⋊C₈×C₄₃	—	2	4	no	—
81	C₂²⋊C₈×C₄₃	—	2	4	no	—
82	#95×C₄₃	—	2	4	no	—
83	C₂⁴×C₄₃	—	2	4	no	—
84	C₂⁴×C₄₃	—	2	4	no	—
85	C₂⁴×C₄₃	—	4	2	no	—
86	C₂⁴×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
87	C₂⁴×C₄₃	C₂²⋊C₄	1	2	yes	—
88	C₂⁴×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
89	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
90	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₃	—	2	4	no	—
92	C₂²×C₄×C₄₃	—	2	8	no	—
93	C₂²×C₄×C₄₃	—	2	4	no	—
94	C₂²×C₄×C₄₃	—	2	4	no	—
95	C₂²×C₄×C₄₃	—	2	8	no	—
96	C₂²×C₄×C₄₃	—	2	4	no	—
97	C₂²×C₄×C₄₃	—	2	8	no	—
98	C₂²×C₄×C₄₃	—	2	8	no	—
99	C₂²×C₄×C₄₃	—	2	8	no	—
100	C₂²×C₄×C₄₃	—	2	2	no	—
101	C₂²×C₄×C₄₃	—	2	2	no	—
102	C₂²×C₄×C₄₃	—	2	4	no	—
103	C₂²×C₄×C₄₃	—	2	4	no	—
104	C₂²×C₄×C₄₃	—	2	4	no	—
105	C₂²×C₄×C₄₃	—	2	4	no	—
106	C₂²×C₄×C₄₃	—	4	4	no	—
107	C₂²×C₄×C₄₃	—	4	4	no	—
108	C₂²×C₄×C₄₃	—	4	4	no	—
109	C₂²×C₄×C₄₃	—	4	4	no	—
110	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
111	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
113	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
115	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
116	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
117	C₂²×C₄×C₄₃	C₂²×C₄	1	2	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	1	yes	characteristic
121	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₃	#41	1	8	yes	—
128	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
129	M₁₆×C₄₃	—	2	8	no	—
130	M₁₆×C₄₃	—	4	4	no	—
131	C₂×C₈×C₄₃	—	2	4	no	—
132	C₂×C₈×C₄₃	—	4	4	no	—
133	C₄⋊C₄×C₄₃	—	2	2	no	—
134	C₄⋊C₄×C₄₃	—	2	2	no	—
135	C₄⋊C₄×C₄₃	—	2	4	no	—
136	C₄⋊C₄×C₄₃	—	2	4	no	—
137	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
138	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
139	C₂²⋊C₄×C₄₃	—	2	16	no	—
140	C₂²⋊C₄×C₄₃	—	2	4	no	—
141	C₂²⋊C₄×C₄₃	—	2	8	no	—
142	C₂²⋊C₄×C₄₃	—	2	4	no	—
143	C₄²×C₄₃	—	2	4	no	—
144	C₄²×C₄₃	—	2	8	no	—
145	C₄²×C₄₃	—	2	4	no	—
146	C₄²×C₄₃	—	2	8	no	—
147	C₄²×C₄₃	—	4	4	no	—
148	C₂³×C₄₃	—	2	2	no	—
149	C₂³×C₄₃	—	2	2	no	—
150	C₂³×C₄₃	—	2	2	no	—
151	C₂³×C₄₃	—	2	2	no	—
152	C₂³×C₄₃	—	2	4	no	—
153	C₂³×C₄₃	—	2	4	no	—
154	C₂³×C₄₃	—	2	2	no	—
155	C₂³×C₄₃	—	2	4	no	—
156	C₂³×C₄₃	—	2	4	no	—
157	C₂³×C₄₃	—	2	2	no	—
158	C₂³×C₄₃	—	2	2	no	—
159	C₂³×C₄₃	—	4	2	no	—
160	C₂³×C₄₃	—	4	2	no	—
161	C₂³×C₄₃	—	4	16	no	—
162	C₂³×C₄₃	#104	1	4	yes	—
163	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
164	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
165	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
167	C₂³×C₄₃	#123	1	4	yes	—
168	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
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	4	no	—
176	C₂×C₄×C₄₃	—	2	4	no	—
177	C₂×C₄×C₄₃	—	2	4	no	—
178	C₂×C₄×C₄₃	—	2	4	no	—
179	C₂×C₄×C₄₃	—	2	4	no	—
180	C₂×C₄×C₄₃	—	2	4	no	—
181	C₂×C₄×C₄₃	—	2	8	no	—
182	C₂×C₄×C₄₃	—	2	4	no	—
183	C₂×C₄×C₄₃	—	2	4	no	—
184	C₂×C₄×C₄₃	—	4	16	no	—
185	C₂×C₄×C₄₃	—	4	4	no	—
186	C₂×C₄×C₄₃	—	4	8	no	—
187	C₂×C₄×C₄₃	—	4	4	no	—
188	C₂×C₄×C₄₃	—	4	8	no	—
189	C₂×C₄×C₄₃	—	4	4	no	—
190	C₂×C₄×C₄₃	—	4	4	no	—
191	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
192	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
193	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
194	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	C₂×C₄×C₄₃	#117	1	4	yes	—
196	C₂×C₄×C₄₃	#117	1	4	yes	—
197	C₂×C₄×C₄₃	#123	1	4	yes	—
198	C₂×C₄×C₄₃	#123	1	4	yes	—
199	C₂×C₄×C₄₃	#123	1	4	yes	—
200	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
201	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
203	C₈×C₄₃	—	4	4	no	—
204	C₂×#1826	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂²×C₄₃	—	2	8	no	—
206	C₂²×C₄₃	—	2	8	no	—
207	C₂²×C₄₃	—	2	1	no	—
208	C₂²×C₄₃	—	2	1	no	—
209	C₂²×C₄₃	—	2	1	no	—
210	C₂²×C₄₃	—	2	2	no	—
211	C₂²×C₄₃	—	2	1	no	—
212	C₂²×C₄₃	—	2	2	no	—
213	C₂²×C₄₃	—	2	2	no	—
214	C₂²×C₄₃	—	2	2	no	—
215	C₂²×C₄₃	—	2	2	no	—
216	C₂²×C₄₃	—	4	8	no	—
217	C₂²×C₄₃	—	4	8	no	—
218	C₂²×C₄₃	—	4	4	no	—
219	C₂²×C₄₃	#381	1	2	yes	—
220	C₂²×C₄₃	#381	1	2	yes	—
221	C₂²×C₄₃	C₂×#104	1	4	yes	—
222	C₂²×C₄₃	C₂×#104	1	2	yes	—
223	C₂²×C₄₃	#421	1	2	yes	—
224	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
225	C₂²×C₄₃	C₂×#123	1	2	yes	—
226	C₄×C₄₃	—	2	2	no	—
227	C₄×C₄₃	—	2	2	no	—
228	C₄×C₄₃	—	4	8	no	—
229	C₄×C₄₃	—	4	4	no	—
230	C₄×C₄₃	—	4	4	no	—
231	C₄×C₄₃	#381	1	2	yes	—
232	C₄×C₄₃	#381	1	2	yes	—
233	C₄×C₄₃	C₂×#117	1	2	yes	—
234	C₄×C₄₃	C₂×#123	1	2	yes	—
235	C₂²×#117	C₂×C₄₃	1	1	yes	characteristic
236	C₂×#407	C₂×C₄₃	1	1	yes	characteristic
237	C₂×C₄×C₂²⋊C₄	C₂×C₄₃	1	1	yes	characteristic
238	#1826	C₂×C₄₃	1	8	yes	direct product factor
239	C₂×#339	C₂×C₄₃	1	4	yes	complemented
240	C₂×C₄₃	—	2	2	no	—
241	C₂×C₄₃	—	2	2	no	—
242	C₂×C₄₃	—	2	4	no	—
243	C₂×C₄₃	—	4	2	no	—
244	C₂×C₄₃	#1826	1	4	yes	direct product factor
245	C₂×C₄₃	C₂×#381	1	1	yes	characteristic
246	C₂×C₄₃	C₂²×#104	1	1	yes	characteristic
247	C₂×C₄₃	C₂×#421	1	1	yes	characteristic
248	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
249	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	—
250	C₂×#117	—	2	1	no	—
251	C₂×#117	—	2	2	no	—
252	C₂×#117	—	2	1	no	—
253	C₂×#117	—	2	2	no	—
254	C₂×#117	C₄×C₄₃	1	2	yes	complemented
255	C₂×#117	C₄×C₄₃	1	4	yes	complemented
256	C₂×#117	C₂²×C₄₃	1	2	yes	—
257	C₂×#117	C₂²×C₄₃	1	4	yes	—
258	C₂²×C₄⋊C₄	C₄×C₄₃	1	1	yes	characteristic, complemented
259	C₂²×C₄⋊C₄	C₄×C₄₃	1	1	yes	characteristic, complemented
260	C₂²×C₂²⋊C₄	—	2	1	no	—
261	C₂²×C₂²⋊C₄	—	2	1	no	—
262	C₂²×C₄²	—	2	1	no	—
263	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
264	#407	—	2	2	no	—
265	#407	C₂²×C₄₃	1	4	yes	—
266	C₂×C₂²⋊C₈	—	2	1	no	—
267	C₂×C₂²⋊C₈	—	2	1	no	—
268	C₄×C₂²⋊C₄	—	2	2	no	—
269	C₄×C₂²⋊C₄	C₂²×C₄₃	1	4	yes	—
270	C₂×#95	—	2	1	no	—
271	#339	C₂²×C₄₃	1	16	yes	complemented
272	C₄₃	C₂×#1826	1	1	yes	characteristic, direct product factor, Sylow
273	C₂⁵	D₄×C₄₃	1	1	yes	characteristic
274	C₂³×C₄	—	2	8	no	—
275	C₂³×C₄	—	2	1	no	—
276	C₂³×C₄	—	2	1	no	—
277	C₂³×C₄	—	2	2	no	—
278	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
279	C₂³×C₄	C₂×C₄×C₄₃	1	2	yes	—
280	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
281	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
282	C₂³×C₄	D₄×C₄₃	1	2	yes	—
283	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
284	C₂³×C₄	D₄×C₄₃	1	2	yes	—
285	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
286	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
287	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
288	C₂×M₁₆	—	2	2	no	—
289	C₂×M₁₆	—	2	8	no	—
290	C₂×M₁₆	C₂³×C₄₃	1	4	yes	—
291	C₂²×C₈	—	2	2	no	—
292	#117	—	2	4	no	—
293	#117	—	2	4	no	—
294	#117	—	2	4	no	—
295	#117	—	2	2	no	—
296	#117	—	2	4	no	—
297	#117	—	2	2	no	—
298	#117	—	2	4	no	—
299	#117	C₂×C₄×C₄₃	1	4	yes	—
300	#117	C₂×C₄×C₄₃	1	8	yes	complemented
301	#117	C₂³×C₄₃	1	4	yes	—
302	C₂×C₄⋊C₄	—	2	2	no	—
303	C₂×C₄⋊C₄	—	2	2	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
307	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
308	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	4	yes	complemented
309	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	4	yes	complemented
310	C₂×C₂²⋊C₄	—	2	8	no	—
311	C₂×C₂²⋊C₄	—	2	4	no	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	—	2	4	no	—
315	C₂×C₂²⋊C₄	—	2	4	no	—
316	C₂×C₄²	—	2	4	no	—
317	C₂×C₄²	—	2	2	no	—
318	C₂×C₄²	—	2	2	no	—
319	C₂×C₄²	—	2	4	no	—
320	C₂×C₄²	—	2	8	no	—
321	C₂×C₄²	—	2	2	no	—
322	C₂×C₄²	C₂³×C₄₃	1	4	yes	—
323	C₂²⋊C₈	—	2	4	no	—
324	C₂²⋊C₈	—	2	4	no	—
325	#95	—	2	4	no	—
326	C₂⁴	—	2	4	no	—
327	C₂⁴	—	2	4	no	—
328	C₂⁴	—	4	2	no	—
329	C₂⁴	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
330	C₂⁴	C₂²⋊C₄×C₄₃	1	2	yes	—
331	C₂⁴	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
332	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
333	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	2	8	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	8	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	8	no	—
342	C₂²×C₄	—	2	8	no	—
343	C₂²×C₄	—	2	8	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	4	4	no	—
350	C₂²×C₄	—	4	4	no	—
351	C₂²×C₄	—	4	4	no	—
352	C₂²×C₄	—	4	4	no	—
353	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
354	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
355	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
356	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
357	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
358	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
359	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
360	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
361	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
362	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
363	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
364	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
365	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
366	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
367	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
370	C₂²×C₄	#41×C₄₃	1	8	yes	—
371	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
372	M₁₆	—	2	8	no	—
373	M₁₆	—	4	4	no	—
374	C₂×C₈	—	2	4	no	—
375	C₂×C₈	—	4	4	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	4	no	—
379	C₄⋊C₄	—	2	4	no	—
380	C₄⋊C₄	C₂²×C₄×C₄₃	1	4	yes	—
381	C₄⋊C₄	C₂²×C₄×C₄₃	1	4	yes	—
382	C₂²⋊C₄	—	2	16	no	—
383	C₂²⋊C₄	—	2	4	no	—
384	C₂²⋊C₄	—	2	8	no	—
385	C₂²⋊C₄	—	2	4	no	—
386	C₄²	—	2	4	no	—
387	C₄²	—	2	8	no	—
388	C₄²	—	2	4	no	—
389	C₄²	—	2	8	no	—
390	C₄²	—	4	4	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	2	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	4	no	—
396	C₂³	—	2	4	no	—
397	C₂³	—	2	2	no	—
398	C₂³	—	2	4	no	—
399	C₂³	—	2	4	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	2	2	no	—
402	C₂³	—	4	2	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	4	16	no	—
405	C₂³	#104×C₄₃	1	4	yes	—
406	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
407	C₂³	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
408	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
409	C₂³	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
410	C₂³	#123×C₄₃	1	4	yes	—
411	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	8	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	4	16	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	4	8	no	—
430	C₂×C₄	—	4	4	no	—
431	C₂×C₄	—	4	8	no	—
432	C₂×C₄	—	4	4	no	—
433	C₂×C₄	—	4	4	no	—
434	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
435	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
436	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
437	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
438	C₂×C₄	#117×C₄₃	1	4	yes	—
439	C₂×C₄	#117×C₄₃	1	4	yes	—
440	C₂×C₄	#123×C₄₃	1	4	yes	—
441	C₂×C₄	#123×C₄₃	1	4	yes	—
442	C₂×C₄	#123×C₄₃	1	4	yes	—
443	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
444	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
445	C₂×C₄	C₂×#41×C₄₃	1	4	yes	—
446	C₈	—	4	4	no	—
447	C₂²	—	2	8	no	—
448	C₂²	—	2	8	no	—
449	C₂²	—	2	1	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	2	2	no	—
458	C₂²	—	4	8	no	—
459	C₂²	—	4	8	no	—
460	C₂²	—	4	4	no	—
461	C₂²	C₄₃×#381	1	2	yes	—
462	C₂²	C₄₃×#381	1	2	yes	—
463	C₂²	C₂×#104×C₄₃	1	4	yes	—
464	C₂²	C₂×#104×C₄₃	1	2	yes	—
465	C₂²	C₄₃×#421	1	2	yes	—
466	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
467	C₂²	C₂×#123×C₄₃	1	2	yes	—
468	C₄	—	2	2	no	—
469	C₄	—	2	2	no	—
470	C₄	—	4	8	no	—
471	C₄	—	4	4	no	—
472	C₄	—	4	4	no	—
473	C₄	C₄₃×#381	1	2	yes	—
474	C₄	C₄₃×#381	1	2	yes	—
475	C₄	C₂×#117×C₄₃	1	2	yes	—
476	C₄	C₂×#123×C₄₃	1	2	yes	—
477	C₂	—	2	2	no	—
478	C₂	—	2	2	no	—
479	C₂	—	2	4	no	—
480	C₂	—	4	2	no	—
481	C₂	C₄₃×#1826	1	4	yes	direct product factor
482	C₂	C₂×C₄₃×#381	1	1	yes	characteristic
483	C₂	C₂²×#104×C₄₃	1	1	yes	characteristic
484	C₂	C₂×C₄₃×#421	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₄₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
socle	C₂³×C₄₃	C₂×C₂²⋊C₄
prime radical	C₂⁵×C₄₃	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₃ ◁ C₂⁴×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₄₃×#1826	C₂	direct (N × H)
5. C₂×C₄₃×#339	C₂	semidirect
12. C₂×#117×C₄₃	C₄	semidirect
13. C₂×#117×C₄₃	C₄	semidirect
16. C₂²×C₄⋊C₄×C₄₃	C₄	semidirect
17. C₂²×C₄⋊C₄×C₄₃	C₄	semidirect
29. C₄₃×#339	C₂²	semidirect
57. #117×C₄₃	C₂×C₄	semidirect
65. C₂×C₄⋊C₄×C₄₃	C₂×C₄	semidirect
66. C₂×C₄⋊C₄×C₄₃	C₂×C₄	semidirect
204. C₂×#1826	C₄₃	direct (N × H)
238. #1826	C₂×C₄₃	direct (N × H)
239. C₂×#339	C₂×C₄₃	semidirect
244. C₂×C₄₃	#1826	direct (N × H)
254. C₂×#117	C₄×C₄₃	semidirect
255. C₂×#117	C₄×C₄₃	semidirect
258. C₂²×C₄⋊C₄	C₄×C₄₃	semidirect
259. C₂²×C₄⋊C₄	C₄×C₄₃	semidirect
271. #339	C₂²×C₄₃	semidirect
272. C₄₃	C₂×#1826	direct (N × H)
300. #117	C₂×C₄×C₄₃	semidirect
308. C₂×C₄⋊C₄	C₂×C₄×C₄₃	semidirect
309. C₂×C₄⋊C₄	C₂×C₄×C₄₃	semidirect
481. C₂	C₄₃×#1826	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#117×C₄₃	2
C₂×C₄₃×#407	2
C₂×C₄×C₂²⋊C₄×C₄₃	2
C₄₃×#1826	2
C₂×C₄₃×#339	2
C₂×#1826	43

Subgroups — C2×C43×#1826 #24940721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₃×#1826 #24940721