Subgroups — #25095037

Order 11008.

1234 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582977	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆×Dic₄₃	C₂	1	2	yes	maximal, complemented
3	C₄×D₄×Dic₄₃	C₂	1	1	yes	maximal, characteristic
4	#19134460	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×C₄⋊Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#19134450	C₂	1	1	yes	maximal, characteristic, complemented
7	#19134381	C₂	1	2	yes	maximal, complemented
8	#19134376	C₂	1	2	yes	maximal, complemented
9	#19134359	C₂	1	2	yes	maximal, complemented
10	C₄×#13063235	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₃×#436	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10621877	C₂²	1	2	yes	—
13	C₂×D₄×Dic₄₃	C₄	1	2	yes	—
14	C₂²×C₄×Dic₄₃	C₂²	1	2	yes	—
15	#14582977	C₄	1	8	yes	complemented
16	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
18	M₁₆×Dic₄₃	—	2	8	no	—
19	C₂×#13063235	C₂²	1	1	yes	characteristic
20	C₂×#13063235	C₂²	1	1	yes	characteristic
21	C₂×#13063235	C₂²	1	1	yes	characteristic
22	C₂×#13063235	C₂²	1	2	yes	—
23	C₂×#13063235	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₈×Dic₄₃	C₂²	1	2	yes	—
26	C₂×C₈×Dic₄₃	C₂²	1	2	yes	—
27	C₄⋊C₄×Dic₄₃	C₄	1	2	yes	—
28	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
29	C₂²⋊C₄×Dic₄₃	C₄	1	4	yes	—
30	C₄×C₂²⋊Dic₄₃	C₂²	1	2	yes	—
31	C₄²×Dic₄₃	C₂²	1	1	yes	characteristic
32	#14582653	C₂²	1	2	yes	—
33	#14582653	C₂²	1	2	yes	—
34	#14582653	C₂²	1	2	yes	—
35	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
37	C₄₃×#436	C₄	1	8	yes	complemented
38	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
40	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
41	C₂³×Dic₄₃	C₂×C₄	1	4	yes	—
42	C₂×#10621877	—	2	4	no	—
43	C₂×#10621877	—	2	4	no	—
44	C₂×#10621877	C₂×C₄	1	8	yes	complemented
45	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
46	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
47	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
48	D₄×Dic₄₃	—	2	8	no	—
49	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
50	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	4	yes	—
51	C₂×C₄×Dic₄₃	—	2	4	no	—
52	C₂×C₄×Dic₄₃	—	2	4	no	—
53	C₂×C₄×Dic₄₃	C₂×C₄	1	4	yes	—
54	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
55	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
56	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
57	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
58	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
59	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	4	yes	complemented
60	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	8	yes	complemented
61	#13063235	—	2	2	no	—
62	#13063235	—	2	4	no	—
63	#13063235	—	2	2	no	—
64	#13063235	—	2	2	no	—
65	#13063235	D₄	1	4	yes	complemented
66	C₄×C₄₃⋊C₈	C₂×C₄	1	4	yes	complemented
67	C₈×Dic₄₃	—	2	4	no	—
68	C₈×Dic₄₃	—	2	4	no	—
69	C₄₃⋊#95	C₂×C₄	1	4	yes	—
70	C₄₃⋊#95	C₂×C₄	1	2	yes	—
71	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
72	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
73	C₂×M₁₆×C₄₃	—	2	4	no	—
74	C₂×M₁₆×C₄₃	—	2	4	no	—
75	C₂×M₁₆×C₄₃	C₂×C₄	1	8	yes	complemented
76	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
77	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
79	C₄×D₄×C₄₃	C₂×C₄	1	4	yes	—
80	C₄×D₄×C₄₃	C₂×C₄	1	4	yes	—
81	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
83	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
84	C₄⋊C₈×C₄₃	C₂×C₄	1	4	yes	complemented
85	C₂²⋊C₈×C₄₃	C₂×C₄	1	8	yes	complemented
86	C₄×C₈×C₄₃	C₂×C₄	1	4	yes	complemented
87	C₂⁴×C₄₃	C₂²×C₄	1	2	yes	—
88	C₂×D₄×C₄₃	—	2	4	no	—
89	C₂×D₄×C₄₃	C₄²	1	4	yes	—
90	C₂²×C₄×C₄₃	—	2	2	no	—
91	C₂²×C₄×C₄₃	—	2	2	no	—
92	C₂²×C₄×C₄₃	—	2	2	no	—
93	C₂²×C₄×C₄₃	—	2	2	no	—
94	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
95	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
100	C₂²×Dic₄₃	—	2	8	no	—
101	C₂²×Dic₄₃	—	2	8	no	—
102	C₂²×Dic₄₃	—	4	4	no	—
103	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
104	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
105	C₂²×Dic₄₃	C₂²×C₄	1	4	yes	—
106	M₁₆×C₄₃	—	2	16	no	—
107	C₂×C₈×C₄₃	—	2	2	no	—
108	C₂×C₈×C₄₃	—	2	2	no	—
109	C₂×C₈×C₄₃	—	2	1	no	—
110	C₂×C₈×C₄₃	—	2	1	no	—
111	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
112	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
113	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
114	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
115	C₂×C₈×C₄₃	#41	1	2	yes	—
116	C₄⋊C₄×C₄₃	C₄²	1	4	yes	—
117	C₂²⋊C₄×C₄₃	C₄²	1	8	yes	—
118	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
119	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
120	C₂²⋊Dic₄₃	—	2	8	no	—
121	C₄⋊Dic₄₃	M₁₆	1	8	yes	complemented
122	C₄×Dic₄₃	—	2	4	no	—
123	C₄×Dic₄₃	—	2	2	no	—
124	C₄×Dic₄₃	—	2	1	no	—
125	C₄×Dic₄₃	—	2	1	no	—
126	C₄×Dic₄₃	—	2	2	no	—
127	C₄×Dic₄₃	—	2	8	no	—
128	C₄×Dic₄₃	—	4	2	no	—
129	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
130	C₄×Dic₄₃	#41	1	2	yes	—
131	#10621877	—	2	16	no	—
132	C₂×C₄₃⋊C₈	—	2	2	no	—
133	C₂×C₄₃⋊C₈	—	2	1	no	—
134	C₂×C₄₃⋊C₈	—	2	1	no	—
135	C₂×C₄₃⋊C₈	—	2	2	no	—
136	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
137	C₂×C₄₃⋊C₈	C₂²×C₄	1	4	yes	—
138	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
139	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
140	C₂×C₄₃⋊C₈	#41	1	2	yes	—
141	C₂³×C₄₃	—	2	2	no	—
142	C₂³×C₄₃	—	2	2	no	—
143	C₂³×C₄₃	—	2	4	no	—
144	C₂³×C₄₃	—	2	4	no	—
145	C₂³×C₄₃	C₂×C₄²	1	4	yes	—
146	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
147	D₄×C₄₃	—	2	8	no	—
148	C₂×C₄×C₄₃	—	2	2	no	—
149	C₂×C₄×C₄₃	—	2	2	no	—
150	C₂×C₄×C₄₃	—	2	2	no	—
151	C₂×C₄×C₄₃	—	2	4	no	—
152	C₂×C₄×C₄₃	—	2	4	no	—
153	C₂×C₄×C₄₃	—	2	4	no	—
154	C₂×C₄×C₄₃	—	2	4	no	—
155	C₂×C₄×C₄₃	C₂×C₄²	1	2	yes	—
156	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
157	C₂×C₄×C₄₃	C₂×C₄²	1	2	yes	—
158	C₂×C₄×C₄₃	C₂×M₁₆	1	4	yes	—
159	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
165	C₂×Dic₄₃	—	2	4	no	—
166	C₂×Dic₄₃	—	2	2	no	—
167	C₂×Dic₄₃	—	2	2	no	—
168	C₂×Dic₄₃	—	2	4	no	—
169	C₂×Dic₄₃	—	2	2	no	—
170	C₂×Dic₄₃	—	2	2	no	—
171	C₂×Dic₄₃	—	2	2	no	—
172	C₂×Dic₄₃	—	4	16	no	—
173	C₂×Dic₄₃	C₄×D₄	1	4	yes	—
174	C₂×Dic₄₃	C₂×M₁₆	1	8	yes	—
175	C₈×C₄₃	—	2	4	no	—
176	C₈×C₄₃	—	2	2	no	—
177	C₈×C₄₃	C₄×D₄	1	4	yes	complemented
178	C₄₃⋊C₈	—	2	4	no	—
179	C₄₃⋊C₈	—	2	2	no	—
180	C₄₃⋊C₈	C₄×D₄	1	4	yes	complemented
181	#20494	—	43	1	no	maximal, Sylow
182	C₂²×C₄₃	—	2	4	no	—
183	C₂²×C₄₃	—	2	4	no	—
184	C₂²×C₄₃	—	2	4	no	—
185	C₂²×C₄₃	—	4	4	no	—
186	C₂²×C₄₃	—	4	4	no	—
187	C₂²×C₄₃	C₂²×C₄²	1	1	yes	characteristic
188	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
189	C₂²×C₄₃	C₄×#41	1	1	yes	characteristic
190	C₂²×C₄₃	C₂²×M₁₆	1	2	yes	—
191	C₂²×C₄₃	#568	1	2	yes	—
192	C₄×C₄₃	—	2	2	no	—
193	C₄×C₄₃	—	2	4	no	—
194	C₄×C₄₃	C₄×M₁₆	1	4	yes	complemented
195	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
196	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
197	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
198	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
199	Dic₄₃	—	2	4	no	—
200	Dic₄₃	—	2	8	no	—
201	Dic₄₃	—	4	2	no	—
202	C₂×#436	—	43	1	no	—
203	C₂×#436	D₄₃	1	1	yes	characteristic
204	C₂×C₄×M₁₆	—	43	2	no	—
205	C₄²×D₄	—	43	1	no	—
206	C₈×C₄⋊C₄	—	43	1	no	—
207	C₈×C₄⋊C₄	—	43	1	no	—
208	#1767	—	43	1	no	—
209	#1753	—	43	2	no	—
210	#1753	—	43	2	no	—
211	#1749	—	43	2	no	—
212	C₄×#97	—	43	1	no	—
213	C₂×C₄₃	—	4	4	no	—
214	C₂×C₄₃	C₄²×D₄	1	1	yes	characteristic
215	C₂×C₄₃	C₂×C₄×M₁₆	1	1	yes	characteristic
216	C₂×C₄₃	#2875	1	1	yes	characteristic
217	C₂×C₄₃	D₄×M₁₆	1	2	yes	—
218	C₂×C₄₃	#2971	1	2	yes	—
219	C₂²×M₁₆	—	43	2	no	—
220	C₂²×M₁₆	C₂×D₄₃	1	2	yes	—
221	C₂×C₄×D₄	—	43	2	no	—
222	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
223	C₂²×C₄²	—	43	2	no	—
224	#436	—	43	8	no	—
225	#436	Dic₄₃	1	8	yes	complemented
226	C₂×C₄⋊C₈	—	43	1	no	—
227	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
228	C₂×C₂²⋊C₈	—	43	2	no	—
229	C₂×C₂²⋊C₈	C₂×D₄₃	1	2	yes	—
230	C₄×M₁₆	—	86	8	no	—
231	C₂×#97	—	43	1	no	—
232	C₂×#97	—	43	2	no	—
233	C₂×#97	—	43	1	no	—
234	C₂×#97	—	43	1	no	—
235	C₂×#97	—	43	1	no	—
236	C₂×C₄×C₈	—	43	1	no	—
237	C₂×C₄×C₈	—	43	2	no	—
238	C₂×C₄×C₈	—	43	2	no	—
239	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
240	C₄×C₄⋊C₄	—	43	2	no	—
241	C₄×C₄⋊C₄	—	43	1	no	—
242	C₄×C₂²⋊C₄	—	43	2	no	—
243	C₄×C₂²⋊C₄	—	43	4	no	—
244	C₄³	—	43	1	no	—
245	#336	—	43	2	no	—
246	#336	—	43	2	no	—
247	#336	—	43	2	no	—
248	C₄₃	#20494	1	1	yes	characteristic, complemented, Sylow
249	C₂²×D₄	C₄×D₄₃	1	1	yes	characteristic
250	C₂³×C₄	—	43	4	no	—
251	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
252	C₂×M₁₆	—	2	4	no	—
253	C₂×M₁₆	—	2	4	no	—
254	C₂×M₁₆	—	43	8	no	—
255	C₂×M₁₆	—	86	4	no	—
256	C₂×M₁₆	—	86	4	no	—
257	C₂×M₁₆	C₂×Dic₄₃	1	8	yes	complemented
258	C₂²×C₈	—	43	1	no	—
259	C₂²×C₈	—	43	2	no	—
260	C₂²×C₈	—	43	1	no	—
261	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
262	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
263	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
264	C₄×D₄	—	86	8	no	—
265	C₄×D₄	C₄×D₄₃	1	4	yes	—
266	C₄×D₄	C₂×Dic₄₃	1	4	yes	—
267	C₂×C₄⋊C₄	—	43	2	no	—
268	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	—	43	4	no	—
270	C₂×C₂²⋊C₄	C₄×D₄₃	1	2	yes	—
271	C₂×C₄²	—	43	1	no	—
272	C₂×C₄²	—	43	2	no	—
273	C₂×C₄²	—	43	4	no	—
274	C₂×C₄²	—	43	1	no	—
275	C₂×C₄²	—	43	2	no	—
276	C₂×C₄²	—	43	2	no	—
277	C₂×C₄²	—	86	4	no	—
278	C₂×C₄²	—	86	4	no	—
279	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
280	C₄⋊C₈	—	43	4	no	—
281	C₄⋊C₈	C₂×Dic₄₃	1	4	yes	complemented
282	C₂²⋊C₈	—	43	8	no	—
283	C₂²⋊C₈	C₂×Dic₄₃	1	8	yes	complemented
284	#97	—	43	4	no	—
285	#97	—	86	2	no	—
286	#97	—	86	4	no	—
287	#97	—	86	2	no	—
288	#97	—	86	2	no	—
289	C₄×C₈	—	43	4	no	—
290	C₄×C₈	—	86	4	no	—
291	C₄×C₈	—	86	4	no	—
292	C₄×C₈	C₂×Dic₄₃	1	4	yes	complemented
293	#95	—	43	2	no	—
294	#95	—	43	4	no	—
295	C₂⁴	C₂×C₄×D₄₃	1	2	yes	—
296	C₂×D₄	—	2	4	no	—
297	C₂×D₄	C₄×Dic₄₃	1	4	yes	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	43	4	no	—
303	C₂²×C₄	—	43	2	no	—
304	C₂²×C₄	—	43	2	no	—
305	C₂²×C₄	—	86	8	no	—
306	C₂²×C₄	—	86	8	no	—
307	C₂²×C₄	—	172	4	no	—
308	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
310	C₂²×C₄	C₂×C₄×D₄₃	1	4	yes	—
311	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
312	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
313	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
314	M₁₆	—	2	16	no	—
315	M₁₆	—	86	16	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	43	2	no	—
321	C₂×C₈	—	43	2	no	—
322	C₂×C₈	—	43	2	no	—
323	C₂×C₈	—	43	2	no	—
324	C₂×C₈	—	43	4	no	—
325	C₂×C₈	—	86	2	no	—
326	C₂×C₈	—	86	1	no	—
327	C₂×C₈	—	86	2	no	—
328	C₂×C₈	—	86	1	no	—
329	C₂×C₈	D₄×D₄₃	1	2	yes	—
330	C₂×C₈	#10621900	1	2	yes	—
331	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
332	C₂×C₈	C₂²×Dic₄₃	1	4	yes	—
333	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
334	C₄⋊C₄	—	43	8	no	—
335	C₄⋊C₄	C₄×Dic₄₃	1	4	yes	—
336	C₂²⋊C₄	—	86	8	no	—
337	C₂²⋊C₄	C₄×Dic₄₃	1	8	yes	—
338	C₄²	—	43	2	no	—
339	C₄²	—	43	2	no	—
340	C₄²	—	86	8	no	—
341	C₄²	—	86	4	no	—
342	C₄²	—	86	2	no	—
343	C₄²	—	86	1	no	—
344	C₄²	—	86	2	no	—
345	C₄²	—	86	1	no	—
346	C₄²	—	172	2	no	—
347	C₄²	C₂×C₄×D₄₃	1	2	yes	—
348	C₄²	C₂²×Dic₄₃	1	2	yes	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	4	no	—
352	C₂³	—	2	4	no	—
353	C₂³	C₂×C₄×Dic₄₃	1	4	yes	—
354	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
355	D₄	—	2	8	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	43	4	no	—
364	C₂×C₄	—	43	8	no	—
365	C₂×C₄	—	86	4	no	—
366	C₂×C₄	—	86	2	no	—
367	C₂×C₄	—	86	2	no	—
368	C₂×C₄	—	86	4	no	—
369	C₂×C₄	—	86	2	no	—
370	C₂×C₄	—	86	2	no	—
371	C₂×C₄	—	86	2	no	—
372	C₂×C₄	—	172	16	no	—
373	C₂×C₄	C₂×C₄×Dic₄₃	1	2	yes	—
374	C₂×C₄	C₂×C₄×Dic₄₃	1	4	yes	—
375	C₂×C₄	C₂×C₄×Dic₄₃	1	2	yes	—
376	C₂×C₄	M₁₆×D₄₃	1	4	yes	—
377	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
378	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
379	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
380	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
381	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
382	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
383	C₈	—	2	4	no	—
384	C₈	—	2	2	no	—
385	C₈	—	43	4	no	—
386	C₈	—	86	4	no	—
387	C₈	—	86	2	no	—
388	C₈	D₄×Dic₄₃	1	4	yes	complemented
389	C₂²	—	2	4	no	—
390	C₂²	—	2	4	no	—
391	C₂²	—	2	4	no	—
392	C₂²	—	4	4	no	—
393	C₂²	—	4	4	no	—
394	C₂²	C₂²×C₄×Dic₄₃	1	1	yes	characteristic
395	C₂²	C₄×D₄×D₄₃	1	1	yes	characteristic
396	C₂²	C₄×#10621900	1	1	yes	characteristic
397	C₂²	C₂×M₁₆×D₄₃	1	2	yes	—
398	C₂²	#14583664	1	2	yes	—
399	C₄	—	2	2	no	—
400	C₄	—	2	4	no	—
401	C₄	—	86	4	no	—
402	C₄	—	86	8	no	—
403	C₄	—	172	2	no	—
404	C₄	M₁₆×Dic₄₃	1	4	yes	complemented
405	C₄	C₄×D₄×D₄₃	1	1	yes	characteristic
406	C₄	C₂×D₄×Dic₄₃	1	1	yes	characteristic
407	C₄	C₄×#10621900	1	1	yes	characteristic
408	C₄	#41×Dic₄₃	1	1	yes	characteristic
409	C₂	—	4	4	no	—
410	C₂	C₄×D₄×Dic₄₃	1	1	yes	characteristic
411	C₂	C₂×M₁₆×Dic₄₃	1	1	yes	characteristic
412	C₂	#19143021	1	1	yes	characteristic
413	C₂	#19143331	1	2	yes	—
414	C₂	#19143611	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₃
commutator	C₂²×C₄₃	C₂²×C₄²
Fitting	C₂×C₄₃×#436	C₂
socle	C₂³×C₄₃	C₂³×C₄
prime radical	C₂²×D₄×C₄₃	C₂×C₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×#436	D₄₃
hypocenter	C₄₃	#20494
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#436

Complements

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

N	H ≅ G/N	type
2. C₂×M₁₆×Dic₄₃	C₂	semidirect
4. #19134460	C₂	semidirect
5. C₈×C₄⋊Dic₄₃	C₂	semidirect
6. #19134450	C₂	semidirect
7. #19134381	C₂	semidirect
8. #19134376	C₂	semidirect
9. #19134359	C₂	semidirect
10. C₄×#13063235	C₂	semidirect
15. #14582977	C₄	semidirect
37. C₄₃×#436	C₄	semidirect
44. C₂×#10621877	C₂×C₄	semidirect
59. C₄⋊(C₄₃⋊C₈)	C₂×C₄	semidirect
60. C₂²⋊(C₄₃⋊C₈)	C₂×C₄	semidirect
65. #13063235	D₄	semidirect
66. C₄×C₄₃⋊C₈	C₂×C₄	semidirect
75. C₂×M₁₆×C₄₃	C₂×C₄	semidirect
84. C₄⋊C₈×C₄₃	C₂×C₄	semidirect
85. C₂²⋊C₈×C₄₃	C₂×C₄	semidirect
86. C₄×C₈×C₄₃	C₂×C₄	semidirect
121. C₄⋊Dic₄₃	M₁₆	semidirect
177. C₈×C₄₃	C₄×D₄	semidirect
180. C₄₃⋊C₈	C₄×D₄	semidirect
194. C₄×C₄₃	C₄×M₁₆	semidirect
225. #436	Dic₄₃	semidirect
248. C₄₃	#20494	semidirect
257. C₂×M₁₆	C₂×Dic₄₃	semidirect
281. C₄⋊C₈	C₂×Dic₄₃	semidirect
283. C₂²⋊C₈	C₂×Dic₄₃	semidirect
292. C₄×C₈	C₂×Dic₄₃	semidirect
388. C₈	D₄×Dic₄₃	semidirect
404. C₄	M₁₆×Dic₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582977	2
C₂×M₁₆×Dic₄₃	2
C₄×D₄×Dic₄₃	2
#19134460	2
C₈×C₄⋊Dic₄₃	2
#19134450	2
#19134381	2
#19134376	2
#19134359	2
C₄×#13063235	2
C₂×C₄₃×#436	2
#20494	43