Subgroups — #25093941

Order 11008.

1470 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582857	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582855	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582854	C₂	1	1	yes	maximal, characteristic
4	C₂×M₁₆×Dic₄₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×#13063235	C₂	1	1	yes	maximal, characteristic
6	#117×Dic₄₃	C₂	1	1	yes	maximal, characteristic
7	#19134283	C₂	1	2	yes	maximal, complemented
8	#19134281	C₂	1	2	yes	maximal, complemented
9	C₄×#13063235	C₂	1	2	yes	maximal, complemented
10	#97×Dic₄₃	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₃×#405	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10621877	C₂²	1	1	yes	characteristic
13	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×#13063284	C₂²	1	1	yes	characteristic
15	C₂²×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
16	#14582857	C₄	1	8	yes	complemented
17	#14582855	C₄	1	8	yes	complemented
18	#14582854	C₄	1	8	yes	complemented
19	M₁₆×Dic₄₃	C₄	1	8	yes	complemented
20	C₂×#13063236	C₂²	1	2	yes	—
21	C₂×#13063235	C₄	1	8	yes	complemented
22	C₂×#13063235	C₂²	1	1	yes	characteristic
23	C₂×#13063235	C₂²	1	2	yes	—
24	C₂×#13063235	C₂²	1	1	yes	characteristic
25	C₂×#13063235	C₂²	1	1	yes	characteristic
26	C₂×#13063235	C₂²	1	1	yes	characteristic
27	C₂×#13063235	C₂²	1	2	yes	—
28	C₂×#13063235	C₂²	1	2	yes	—
29	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
30	C₂×C₈×Dic₄₃	C₂²	1	2	yes	—
31	C₂×C₈×Dic₄₃	C₂²	1	2	yes	—
32	C₂×C₈×Dic₄₃	C₂²	1	2	yes	—
33	C₄⋊C₄×Dic₄₃	C₄	1	4	yes	—
34	C₂²⋊C₄×Dic₄₃	C₄	1	4	yes	—
35	#14582745	C₂²	1	2	yes	—
36	C₄²×Dic₄₃	C₂²	1	2	yes	—
37	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
38	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
39	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
40	C₄₃×#405	C₄	1	8	yes	complemented
41	C₂×#97×C₄₃	C₂²	1	2	yes	—
42	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	—
43	C₂³×Dic₄₃	C₂×C₄	1	2	yes	—
44	C₂×#10621877	C₂×C₄	1	4	yes	—
45	C₂×#10621877	C₂×C₄	1	4	yes	—
46	C₂×#10621877	C₂×C₄	1	4	yes	—
47	C₂²×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
48	C₂²×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
49	C₂²×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
50	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
51	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
52	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
53	#13063284	C₂×C₄	1	4	yes	—
54	#13063284	C₂×C₄	1	4	yes	—
55	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
56	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	2	yes	—
57	C₂×C₄×Dic₄₃	C₂×C₄	1	8	yes	—
58	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
59	C₂×C₄×Dic₄₃	C₂×C₄	1	4	yes	—
60	C₂×C₄×Dic₄₃	C₂×C₄	1	4	yes	—
61	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
62	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
63	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
64	#13063236	C₂×C₄	1	8	yes	complemented
65	#13063235	C₂×C₄	1	4	yes	—
66	#13063235	C₂×C₄	1	4	yes	—
67	#13063235	C₂×C₄	1	4	yes	—
68	#13063235	C₂×C₄	1	4	yes	—
69	#13063235	C₂×C₄	1	8	yes	—
70	#13063235	C₂×C₄	1	8	yes	complemented
71	#13063235	C₂×C₄	1	8	yes	complemented
72	C₄×C₄₃⋊C₈	C₂×C₄	1	8	yes	complemented
73	C₈×Dic₄₃	C₂×C₄	1	8	yes	—
74	C₈×Dic₄₃	C₂×C₄	1	8	yes	complemented
75	C₈×Dic₄₃	C₂×C₄	1	8	yes	complemented
76	C₄₃⋊#95	C₂×C₄	1	8	yes	—
77	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
78	C₂×M₁₆×C₄₃	C₂×C₄	1	4	yes	—
79	C₂×M₁₆×C₄₃	C₂×C₄	1	4	yes	—
80	C₂×M₁₆×C₄₃	C₂×C₄	1	4	yes	—
81	C₂²×C₈×C₄₃	C₂×C₄	1	4	yes	—
82	C₂²×C₈×C₄₃	C₂×C₄	1	4	yes	—
83	C₂²×C₈×C₄₃	C₂×C₄	1	4	yes	—
84	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
86	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
87	#117×C₄₃	C₂×C₄	1	4	yes	—
88	#117×C₄₃	C₂×C₄	1	4	yes	—
89	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
90	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
91	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
92	#97×C₄₃	C₂×C₄	1	8	yes	complemented
93	C₄×C₈×C₄₃	C₂×C₄	1	8	yes	complemented
94	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
102	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
104	C₂²×Dic₄₃	—	4	4	no	—
105	C₂²×Dic₄₃	C₄²	1	8	yes	—
106	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
107	C₂²×Dic₄₃	C₂²×C₄	1	4	yes	—
108	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
109	M₁₆×C₄₃	C₄²	1	16	yes	complemented
110	C₂×C₈×C₄₃	C₄²	1	16	yes	complemented
111	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
112	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
113	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
114	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
115	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
116	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
117	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
119	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
120	C₄⋊C₄×C₄₃	C₄²	1	8	yes	—
121	C₂²⋊C₄×C₄₃	C₄²	1	8	yes	—
122	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
123	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
124	C₂²⋊Dic₄₃	C₄²	1	8	yes	—
125	C₄⋊Dic₄₃	C₄²	1	8	yes	—
126	C₄×Dic₄₃	—	4	8	no	—
127	C₄×Dic₄₃	C₄²	1	8	yes	—
128	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
129	C₄×Dic₄₃	C₂²×C₄	1	4	yes	—
130	C₄×Dic₄₃	C₂²×C₄	1	4	yes	—
131	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
132	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
133	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
134	#10621877	C₄²	1	16	yes	complemented
135	C₂×C₄₃⋊C₈	C₄²	1	16	yes	complemented
136	C₂×C₄₃⋊C₈	C₂²×C₄	1	4	yes	—
137	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
138	C₂×C₄₃⋊C₈	C₂²×C₄	1	4	yes	—
139	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
140	C₂×C₄₃⋊C₈	C₂²×C₄	1	4	yes	—
141	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
142	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
143	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
144	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
145	C₂³×C₄₃	—	2	4	no	—
146	C₂³×C₄₃	C₂×C₄²	1	2	yes	—
147	C₂³×C₄₃	C₂×C₄²	1	2	yes	—
148	C₂³×C₄₃	C₂×C₄²	1	2	yes	—
149	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
150	C₂×C₄×C₄₃	—	2	8	no	—
151	C₂×C₄×C₄₃	C₂×C₄²	1	2	yes	—
152	C₂×C₄×C₄₃	C₂×C₄²	1	2	yes	—
153	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
154	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
155	C₂×C₄×C₄₃	C₂×C₄²	1	8	yes	—
156	C₂×C₄×C₄₃	C₂×C₄²	1	2	yes	—
157	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
158	C₂×C₄×C₄₃	C₂×C₄²	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	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
163	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
164	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
165	C₂×Dic₄₃	—	2	4	no	—
166	C₂×Dic₄₃	—	2	8	no	—
167	C₂×Dic₄₃	—	2	4	no	—
168	C₂×Dic₄₃	—	4	8	no	—
169	C₂×Dic₄₃	C₂×C₄²	1	4	yes	—
170	C₂×Dic₄₃	C₂×C₄²	1	4	yes	—
171	C₂×Dic₄₃	C₂×C₄²	1	8	yes	—
172	C₈×C₄₃	C₂×C₄²	1	4	yes	—
173	C₈×C₄₃	C₂×C₄²	1	4	yes	—
174	C₈×C₄₃	C₂×C₄²	1	8	yes	—
175	C₄₃⋊C₈	C₂×C₄²	1	4	yes	—
176	C₄₃⋊C₈	C₂×C₄²	1	4	yes	—
177	C₄₃⋊C₈	C₂×C₄²	1	8	yes	—
178	#20331	—	43	1	no	maximal, Sylow
179	C₂²×C₄₃	—	2	4	no	—
180	C₂²×C₄₃	—	2	4	no	—
181	C₂²×C₄₃	—	2	4	no	—
182	C₂²×C₄₃	C₄³	1	4	yes	—
183	C₂²×C₄₃	C₂²×C₄²	1	1	yes	characteristic
184	C₂²×C₄₃	C₂²×C₄²	1	1	yes	characteristic
185	C₂²×C₄₃	C₂²×C₄²	1	1	yes	characteristic
186	C₂²×C₄₃	#568	1	4	yes	—
187	C₄×C₄₃	—	2	8	no	—
188	C₄×C₄₃	C₄³	1	4	yes	—
189	C₄×C₄₃	C₂²×C₄²	1	1	yes	characteristic
190	C₄×C₄₃	C₂²×C₄²	1	1	yes	characteristic
191	C₄×C₄₃	C₂²×C₄²	1	1	yes	characteristic
192	C₄×C₄₃	C₂²×C₄²	1	1	yes	characteristic
193	Dic₄₃	—	2	4	no	—
194	Dic₄₃	—	2	4	no	—
195	Dic₄₃	—	2	8	no	—
196	C₂×#405	—	43	1	no	—
197	C₂×#405	—	43	1	no	—
198	C₂×#405	—	43	1	no	—
199	C₂×#405	D₄₃	1	1	yes	characteristic
200	C₂×C₄×M₁₆	—	43	1	no	—
201	C₂²×#97	—	43	1	no	—
202	C₄×#117	—	43	1	no	—
203	#1726	—	43	2	no	—
204	#1726	—	43	2	no	—
205	C₄×#97	—	43	2	no	—
206	C₄×#97	—	43	2	no	—
207	C₂×C₄₃	—	2	4	no	—
208	C₂×C₄₃	C₂×C₄³	1	1	yes	characteristic
209	C₂×C₄₃	#2873	1	2	yes	—
210	C₂×C₄₃	#2875	1	2	yes	—
211	C₂×C₄₃	#2875	1	2	yes	—
212	C₂²×M₁₆	—	43	1	no	—
213	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
214	C₂³×C₈	—	43	1	no	—
215	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
216	C₂×#117	—	43	1	no	—
217	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
218	C₂²×C₄²	—	43	1	no	—
219	#405	—	43	8	no	—
220	#405	—	43	8	no	—
221	#405	—	43	8	no	—
222	#405	Dic₄₃	1	8	yes	complemented
223	C₄×M₁₆	—	43	8	no	—
224	C₂×#97	—	43	1	no	—
225	C₂×#97	—	43	1	no	—
226	C₂×#97	—	43	1	no	—
227	C₂×#97	—	43	1	no	—
228	C₂×#97	—	43	2	no	—
229	C₂×#97	—	43	2	no	—
230	C₂×#97	—	43	2	no	—
231	C₂×#97	—	43	8	no	—
232	C₂×#97	—	43	2	no	—
233	C₂×#97	C₂×D₄₃	1	2	yes	—
234	C₂×C₄×C₈	—	43	2	no	—
235	C₂×C₄×C₈	—	43	2	no	—
236	C₂×C₄×C₈	—	43	2	no	—
237	C₂×C₄×C₈	—	43	2	no	—
238	C₂×C₄×C₈	C₂×D₄₃	1	2	yes	—
239	C₄×C₄⋊C₄	—	43	4	no	—
240	C₄×C₂²⋊C₄	—	43	4	no	—
241	#376	—	43	2	no	—
242	C₄³	—	43	2	no	—
243	C₄₃	#20331	1	1	yes	characteristic, complemented, Sylow
244	C₂³×C₄	—	43	2	no	—
245	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
246	C₂×M₁₆	—	43	4	no	—
247	C₂×M₁₆	—	43	4	no	—
248	C₂×M₁₆	—	43	4	no	—
249	C₂×M₁₆	C₄×D₄₃	1	4	yes	—
250	C₂×M₁₆	C₄×D₄₃	1	4	yes	—
251	C₂×M₁₆	C₂×Dic₄₃	1	4	yes	—
252	C₂²×C₈	—	43	4	no	—
253	C₂²×C₈	—	43	4	no	—
254	C₂²×C₈	—	43	4	no	—
255	C₂²×C₈	—	43	1	no	—
256	C₂²×C₈	—	43	1	no	—
257	C₂²×C₈	—	43	2	no	—
258	C₂²×C₈	C₄×D₄₃	1	4	yes	—
259	C₂²×C₈	C₄×D₄₃	1	4	yes	—
260	C₂²×C₈	C₂×Dic₄₃	1	4	yes	—
261	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
262	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
263	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
264	#117	—	43	4	no	—
265	#117	—	43	4	no	—
266	#117	C₄×D₄₃	1	4	yes	—
267	#117	C₂×Dic₄₃	1	4	yes	—
268	C₂×C₄⋊C₄	—	43	2	no	—
269	C₂×C₄⋊C₄	C₄×D₄₃	1	2	yes	—
270	C₂×C₂²⋊C₄	—	43	2	no	—
271	C₂×C₂²⋊C₄	C₄×D₄₃	1	2	yes	—
272	C₂×C₄²	—	43	2	no	—
273	C₂×C₄²	—	43	4	no	—
274	C₂×C₄²	—	43	4	no	—
275	C₂×C₄²	—	43	2	no	—
276	C₂×C₄²	—	43	1	no	—
277	C₂×C₄²	—	43	1	no	—
278	C₂×C₄²	—	43	8	no	—
279	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
280	#97	—	43	4	no	—
281	#97	—	43	4	no	—
282	#97	—	43	4	no	—
283	#97	—	43	4	no	—
284	#97	—	43	8	no	—
285	#97	—	43	8	no	—
286	#97	—	43	8	no	—
287	#97	—	43	8	no	—
288	#97	C₂×Dic₄₃	1	8	yes	complemented
289	C₄×C₈	—	43	8	no	—
290	C₄×C₈	—	43	8	no	—
291	C₄×C₈	—	43	8	no	—
292	C₄×C₈	—	43	8	no	—
293	C₄×C₈	C₂×Dic₄₃	1	8	yes	complemented
294	#95	—	43	8	no	—
295	C₂⁴	C₂×C₄×D₄₃	1	1	yes	characteristic
296	C₂²×C₄	—	43	2	no	—
297	C₂²×C₄	—	43	4	no	—
298	C₂²×C₄	—	43	2	no	—
299	C₂²×C₄	—	43	8	no	—
300	C₂²×C₄	—	172	4	no	—
301	C₂²×C₄	C₂×C₄×D₄₃	1	4	yes	—
302	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
303	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
304	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
305	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
306	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
307	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
308	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
309	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
310	M₁₆	—	43	16	no	—
311	M₁₆	C₄×Dic₄₃	1	16	yes	complemented
312	C₂×C₈	—	43	16	no	—
313	C₂×C₈	—	43	2	no	—
314	C₂×C₈	—	43	2	no	—
315	C₂×C₈	—	43	4	no	—
316	C₂×C₈	—	43	4	no	—
317	C₂×C₈	—	43	4	no	—
318	C₂×C₈	—	43	2	no	—
319	C₂×C₈	—	43	2	no	—
320	C₂×C₈	—	43	2	no	—
321	C₂×C₈	—	43	2	no	—
322	C₂×C₈	C₄×Dic₄₃	1	16	yes	complemented
323	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
324	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
325	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
326	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
327	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
328	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
329	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
330	C₂×C₈	C₂²×Dic₄₃	1	4	yes	—
331	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
332	C₄⋊C₄	—	43	8	no	—
333	C₄⋊C₄	C₄×Dic₄₃	1	8	yes	—
334	C₂²⋊C₄	—	43	8	no	—
335	C₂²⋊C₄	C₄×Dic₄₃	1	8	yes	—
336	C₄²	—	43	8	no	—
337	C₄²	—	43	2	no	—
338	C₄²	—	43	4	no	—
339	C₄²	—	43	4	no	—
340	C₄²	—	43	2	no	—
341	C₄²	—	43	2	no	—
342	C₄²	—	43	2	no	—
343	C₄²	—	172	8	no	—
344	C₄²	C₂×C₄×D₄₃	1	4	yes	—
345	C₄²	C₂²×Dic₄₃	1	4	yes	—
346	C₂³	—	2	4	no	—
347	C₂³	C₄²×D₄₃	1	2	yes	—
348	C₂³	C₄²×D₄₃	1	2	yes	—
349	C₂³	C₂×C₄×Dic₄₃	1	2	yes	—
350	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
351	C₂×C₄	—	2	8	no	—
352	C₂×C₄	—	43	4	no	—
353	C₂×C₄	—	43	4	no	—
354	C₂×C₄	—	43	8	no	—
355	C₂×C₄	—	86	4	no	—
356	C₂×C₄	—	86	8	no	—
357	C₂×C₄	—	86	4	no	—
358	C₂×C₄	—	172	8	no	—
359	C₂×C₄	C₄²×D₄₃	1	4	yes	—
360	C₂×C₄	C₄²×D₄₃	1	4	yes	—
361	C₂×C₄	C₄²×D₄₃	1	2	yes	—
362	C₂×C₄	C₄²×D₄₃	1	2	yes	—
363	C₂×C₄	C₂×C₄×Dic₄₃	1	8	yes	—
364	C₂×C₄	C₂×C₄×Dic₄₃	1	4	yes	—
365	C₂×C₄	C₂×C₄×Dic₄₃	1	4	yes	—
366	C₂×C₄	C₂×C₄×Dic₄₃	1	2	yes	—
367	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
368	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
369	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
370	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
371	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
372	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
373	C₈	—	43	4	no	—
374	C₈	—	43	4	no	—
375	C₈	—	43	8	no	—
376	C₈	C₂×C₄×Dic₄₃	1	4	yes	—
377	C₈	C₂×C₄×Dic₄₃	1	4	yes	—
378	C₈	C₂×C₄×Dic₄₃	1	8	yes	—
379	C₂²	—	2	4	no	—
380	C₂²	—	2	4	no	—
381	C₂²	—	2	4	no	—
382	C₂²	C₄²×Dic₄₃	1	4	yes	—
383	C₂²	C₂×C₄²×D₄₃	1	1	yes	characteristic
384	C₂²	C₂×C₄²×D₄₃	1	1	yes	characteristic
385	C₂²	C₂²×C₄×Dic₄₃	1	1	yes	characteristic
386	C₂²	#14583664	1	4	yes	—
387	C₄	—	2	8	no	—
388	C₄	—	86	4	no	—
389	C₄	—	86	4	no	—
390	C₄	—	86	8	no	—
391	C₄	C₄²×Dic₄₃	1	4	yes	—
392	C₄	C₂×C₄²×D₄₃	1	1	yes	characteristic
393	C₄	C₂×C₄²×D₄₃	1	1	yes	characteristic
394	C₄	C₂²×C₄×Dic₄₃	1	1	yes	characteristic
395	C₄	C₂²×C₄×Dic₄₃	1	1	yes	characteristic
396	C₂	—	2	4	no	—
397	C₂	C₂×C₄²×Dic₄₃	1	1	yes	characteristic
398	C₂	#19143011	1	2	yes	—
399	C₂	#19143021	1	2	yes	—
400	C₂	#19143022	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₃
commutator	C₂×C₄₃	C₂×C₄³
Fitting	C₂×C₄₃×#405	C₂
socle	C₂³×C₄₃	C₂³×C₄
prime radical	C₂⁴×C₄₃	C₂²×C₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×#405	D₄₃
hypocenter	C₄₃	#20331
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
7. #19134283	C₂	semidirect
8. #19134281	C₂	semidirect
9. C₄×#13063235	C₂	semidirect
10. #97×Dic₄₃	C₂	semidirect
16. #14582857	C₄	semidirect
17. #14582855	C₄	semidirect
18. #14582854	C₄	semidirect
19. M₁₆×Dic₄₃	C₄	semidirect
21. C₂×#13063235	C₄	semidirect
40. C₄₃×#405	C₄	semidirect
64. #13063236	C₂×C₄	semidirect
70. #13063235	C₂×C₄	semidirect
71. #13063235	C₂×C₄	semidirect
72. C₄×C₄₃⋊C₈	C₂×C₄	semidirect
74. C₈×Dic₄₃	C₂×C₄	semidirect
75. C₈×Dic₄₃	C₂×C₄	semidirect
92. #97×C₄₃	C₂×C₄	semidirect
93. C₄×C₈×C₄₃	C₂×C₄	semidirect
109. M₁₆×C₄₃	C₄²	semidirect
110. C₂×C₈×C₄₃	C₄²	semidirect
134. #10621877	C₄²	semidirect
135. C₂×C₄₃⋊C₈	C₄²	semidirect
222. #405	Dic₄₃	semidirect
243. C₄₃	#20331	semidirect
288. #97	C₂×Dic₄₃	semidirect
293. C₄×C₈	C₂×Dic₄₃	semidirect
311. M₁₆	C₄×Dic₄₃	semidirect
322. C₂×C₈	C₄×Dic₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582857	2
C₂×#14582855	2
C₂×#14582854	2
C₂×M₁₆×Dic₄₃	2
C₂²×#13063235	2
#117×Dic₄₃	2
#19134283	2
#19134281	2
C₄×#13063235	2
#97×Dic₄₃	2
C₂×C₄₃×#405	2
#20331	43