Subgroups — C₄₃×#21881 #24941898

Order 11008.

1018 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#542	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#2921	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2905	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#1997	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1967	C₂	1	2	yes	maximal, complemented
6	C₄₃×#1901	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1900	C₂	1	2	yes	maximal
8	C₄₃×#1801	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1800	C₂	1	2	yes	maximal, complemented
10	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
11	C₄₃×#542	—	2	4	no	—
12	C₄₃×#542	—	2	4	no	—
13	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×#126×C₄₃	C₄	1	2	yes	—
15	C₂×#124×C₄₃	C₄	1	2	yes	—
16	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×#123×C₄₃	C₄	1	2	yes	—
18	C₂×C₂²⋊Q₈×C₄₃	C₄	1	2	yes	—
19	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
24	C₄₃×#433	—	2	4	no	—
25	C₄₃×#424	—	2	4	no	—
26	C₄₃×#423	C₂²	1	2	yes	—
27	C₄₃×#423	C₂²	1	2	yes	—
28	C₄₃×#423	C₂²	1	2	yes	—
29	C₂×#101×C₄₃	C₂²	1	4	yes	—
30	C₂×#100×C₄₃	C₂²	1	4	yes	—
31	C₄₃×#407	C₂²	1	2	yes	—
32	C₄×M₁₆×C₄₃	C₂²	1	2	yes	—
33	C₄₃×#343	C₂²	1	4	yes	—
34	C₄₃×#343	C₂²	1	4	yes	—
35	C₂²×Q₈×C₄₃	C₂×C₄	1	2	yes	—
36	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
37	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
38	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
40	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
41	C₂×M₁₆×C₄₃	—	2	2	no	—
42	C₂×M₁₆×C₄₃	—	4	4	no	—
43	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
44	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
45	C₂²×C₈×C₄₃	—	2	2	no	—
46	C₄⋊Q₈×C₄₃	—	2	2	no	—
47	C₄⋊Q₈×C₄₃	—	2	2	no	—
48	#126×C₄₃	—	2	8	no	—
49	#124×C₄₃	—	2	8	no	—
50	#124×C₄₃	—	2	2	no	—
51	#124×C₄₃	—	2	2	no	—
52	#123×C₄₃	—	2	8	no	—
53	C₂²⋊Q₈×C₄₃	—	2	2	no	—
54	C₂²⋊Q₈×C₄₃	—	2	2	no	—
55	C₂²⋊Q₈×C₄₃	—	2	8	no	—
56	#121×C₄₃	—	2	2	no	—
57	#121×C₄₃	—	2	2	no	—
58	C₄×Q₈×C₄₃	—	2	2	no	—
59	C₄×Q₈×C₄₃	—	2	2	no	—
60	C₄×D₄×C₄₃	—	2	2	no	—
61	C₄×D₄×C₄₃	—	2	2	no	—
62	#117×C₄₃	D₄	1	4	yes	—
63	#117×C₄₃	D₄	1	4	yes	—
64	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
65	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
67	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
72	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
73	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
74	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
75	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
76	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
79	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
81	C₄⋊C₈×C₄₃	—	2	4	no	—
82	C₄⋊C₈×C₄₃	—	2	4	no	—
83	C₄⋊C₈×C₄₃	—	2	4	no	—
84	#101×C₄₃	—	4	4	no	—
85	#100×C₄₃	—	4	4	no	—
86	C₂²⋊C₈×C₄₃	—	2	4	no	—
87	#97×C₄₃	—	2	2	no	—
88	C₄×C₈×C₄₃	—	2	2	no	—
89	C₂⁴×C₄₃	C₂²×C₄	1	2	yes	—
90	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
91	C₂×Q₈×C₄₃	—	2	4	no	—
92	C₂×Q₈×C₄₃	—	2	1	no	—
93	C₂×Q₈×C₄₃	—	2	1	no	—
94	C₂×Q₈×C₄₃	—	2	2	no	—
95	C₂×Q₈×C₄₃	—	2	2	no	—
96	C₂×Q₈×C₄₃	—	8	2	no	—
97	C₂×D₄×C₄₃	—	2	1	no	—
98	C₂×D₄×C₄₃	—	2	1	no	—
99	C₂×D₄×C₄₃	—	2	2	no	—
100	C₂×D₄×C₄₃	—	2	2	no	—
101	C₂×D₄×C₄₃	—	2	4	no	—
102	C₂×D₄×C₄₃	—	8	2	no	—
103	C₂²×C₄×C₄₃	—	2	2	no	—
104	C₂²×C₄×C₄₃	—	2	2	no	—
105	C₂²×C₄×C₄₃	—	2	4	no	—
106	C₂²×C₄×C₄₃	—	8	2	no	—
107	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
113	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
118	M₁₆×C₄₃	—	2	4	no	—
119	M₁₆×C₄₃	—	2	4	no	—
120	M₁₆×C₄₃	—	2	4	no	—
121	M₁₆×C₄₃	—	2	4	no	—
122	M₁₆×C₄₃	—	4	4	no	—
123	C₂×C₈×C₄₃	—	2	4	no	—
124	C₂×C₈×C₄₃	—	2	4	no	—
125	C₂×C₈×C₄₃	—	4	4	no	—
126	C₄⋊C₄×C₄₃	—	2	4	no	—
127	C₄⋊C₄×C₄₃	—	2	4	no	—
128	C₄⋊C₄×C₄₃	—	2	4	no	—
129	C₄⋊C₄×C₄₃	—	2	1	no	—
130	C₄⋊C₄×C₄₃	—	2	1	no	—
131	C₄⋊C₄×C₄₃	—	2	1	no	—
132	C₄⋊C₄×C₄₃	—	2	1	no	—
133	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
134	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
135	C₂²⋊C₄×C₄₃	—	2	4	no	—
136	C₂²⋊C₄×C₄₃	—	2	4	no	—
137	C₂²⋊C₄×C₄₃	—	2	4	no	—
138	C₂²⋊C₄×C₄₃	—	2	4	no	—
139	C₂²⋊C₄×C₄₃	—	2	4	no	—
140	C₂²⋊C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
141	C₂²⋊C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
142	C₄²×C₄₃	—	2	4	no	—
143	C₄²×C₄₃	C₂×D₄	1	2	yes	—
144	C₄²×C₄₃	C₂×D₄	1	2	yes	—
145	C₄²×C₄₃	C₂×D₄	1	2	yes	—
146	C₄²×C₄₃	C₂×D₄	1	2	yes	—
147	C₂³×C₄₃	—	2	2	no	—
148	C₂³×C₄₃	—	2	2	no	—
149	C₂³×C₄₃	—	2	4	no	—
150	C₂³×C₄₃	—	4	1	no	—
151	C₂³×C₄₃	—	4	1	no	—
152	C₂³×C₄₃	—	4	2	no	—
153	C₂³×C₄₃	—	4	2	no	—
154	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
156	Q₈×C₄₃	—	4	1	no	—
157	Q₈×C₄₃	—	4	1	no	—
158	Q₈×C₄₃	—	4	2	no	—
159	Q₈×C₄₃	—	8	4	no	—
160	D₄×C₄₃	—	4	1	no	—
161	D₄×C₄₃	—	4	1	no	—
162	D₄×C₄₃	—	4	2	no	—
163	D₄×C₄₃	—	8	4	no	—
164	C₂×C₄×C₄₃	—	2	2	no	—
165	C₂×C₄×C₄₃	—	2	2	no	—
166	C₂×C₄×C₄₃	—	2	2	no	—
167	C₂×C₄×C₄₃	—	2	4	no	—
168	C₂×C₄×C₄₃	—	2	2	no	—
169	C₂×C₄×C₄₃	—	2	2	no	—
170	C₂×C₄×C₄₃	—	2	2	no	—
171	C₂×C₄×C₄₃	—	2	4	no	—
172	C₂×C₄×C₄₃	—	4	1	no	—
173	C₂×C₄×C₄₃	—	4	1	no	—
174	C₂×C₄×C₄₃	—	4	1	no	—
175	C₂×C₄×C₄₃	—	4	1	no	—
176	C₂×C₄×C₄₃	—	4	2	no	—
177	C₂×C₄×C₄₃	—	4	2	no	—
178	C₂×C₄×C₄₃	—	8	4	no	—
179	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
180	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
181	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
182	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
183	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
184	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
187	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
188	C₈×C₄₃	—	4	4	no	—
189	C₈×C₄₃	—	4	4	no	—
190	#21881	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₂²×C₄₃	—	2	1	no	—
192	C₂²×C₄₃	—	2	1	no	—
193	C₂²×C₄₃	—	2	2	no	—
194	C₂²×C₄₃	—	2	2	no	—
195	C₂²×C₄₃	—	2	2	no	—
196	C₂²×C₄₃	—	4	2	no	—
197	C₂²×C₄₃	—	4	2	no	—
198	C₂²×C₄₃	—	4	2	no	—
199	C₂²×C₄₃	—	8	2	no	—
200	C₂²×C₄₃	—	8	4	no	—
201	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
202	C₂²×C₄₃	#520	1	2	yes	—
203	C₄×C₄₃	—	2	2	no	—
204	C₄×C₄₃	—	2	2	no	—
205	C₄×C₄₃	—	2	2	no	—
206	C₄×C₄₃	—	2	2	no	—
207	C₄×C₄₃	—	2	2	no	—
208	C₄×C₄₃	—	4	2	no	—
209	C₄×C₄₃	—	4	2	no	—
210	C₄×C₄₃	—	4	2	no	—
211	C₄×C₄₃	#535	1	1	yes	characteristic
212	C₄×C₄₃	#536	1	1	yes	characteristic
213	C₄×C₄₃	#537	1	2	yes	—
214	C₂×#542	C₂×C₄₃	1	1	yes	characteristic
215	#2921	C₂×C₄₃	1	1	yes	characteristic, complemented
216	#2905	C₂×C₄₃	1	1	yes	characteristic, complemented
217	#1997	C₂×C₄₃	1	2	yes	complemented
218	#1967	C₂×C₄₃	1	2	yes	complemented
219	#1901	C₂×C₄₃	1	2	yes	complemented
220	#1900	C₂×C₄₃	1	2	yes	—
221	#1801	C₂×C₄₃	1	2	yes	complemented
222	#1800	C₂×C₄₃	1	2	yes	complemented
223	C₂×C₄₃	—	2	2	no	—
224	C₂×C₄₃	—	4	2	no	—
225	C₂×C₄₃	—	8	2	no	—
226	C₂×C₄₃	#2311	1	1	yes	characteristic
227	C₂×C₄₃	#2888	1	1	yes	characteristic
228	C₂×C₄₃	#2889	1	1	yes	characteristic
229	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	—
230	#542	—	2	4	no	—
231	#542	—	2	4	no	—
232	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
233	C₂×#126	C₄×C₄₃	1	2	yes	—
234	C₂×#124	C₄×C₄₃	1	2	yes	—
235	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
236	C₂×#123	C₄×C₄₃	1	2	yes	—
237	C₂×C₂²⋊Q₈	C₄×C₄₃	1	2	yes	—
238	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
239	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
240	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
241	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
242	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
243	#433	—	2	4	no	—
244	#424	—	2	4	no	—
245	#423	C₂²×C₄₃	1	2	yes	—
246	#423	C₂²×C₄₃	1	2	yes	—
247	#423	C₂²×C₄₃	1	2	yes	—
248	C₂×#101	C₂²×C₄₃	1	4	yes	—
249	C₂×#100	C₂²×C₄₃	1	4	yes	—
250	#407	C₂²×C₄₃	1	2	yes	—
251	C₄×M₁₆	C₂²×C₄₃	1	2	yes	—
252	#343	C₂²×C₄₃	1	4	yes	—
253	#343	C₂²×C₄₃	1	4	yes	—
254	C₄₃	#21881	1	1	yes	characteristic, direct product factor, Sylow
255	C₂²×Q₈	C₂×C₄×C₄₃	1	2	yes	—
256	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
257	C₂²×D₄	C₂×C₄×C₄₃	1	2	yes	—
258	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
259	C₂³×C₄	C₂×C₄×C₄₃	1	2	yes	—
260	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
261	C₂×M₁₆	—	2	2	no	—
262	C₂×M₁₆	—	4	4	no	—
263	C₂×M₁₆	C₂³×C₄₃	1	4	yes	—
264	C₂×M₁₆	C₂³×C₄₃	1	4	yes	—
265	C₂²×C₈	—	2	2	no	—
266	C₄⋊Q₈	—	2	2	no	—
267	C₄⋊Q₈	—	2	2	no	—
268	#126	—	2	8	no	—
269	#124	—	2	8	no	—
270	#124	—	2	2	no	—
271	#124	—	2	2	no	—
272	#123	—	2	8	no	—
273	C₂²⋊Q₈	—	2	2	no	—
274	C₂²⋊Q₈	—	2	2	no	—
275	C₂²⋊Q₈	—	2	8	no	—
276	#121	—	2	2	no	—
277	#121	—	2	2	no	—
278	C₄×Q₈	—	2	2	no	—
279	C₄×Q₈	—	2	2	no	—
280	C₄×D₄	—	2	2	no	—
281	C₄×D₄	—	2	2	no	—
282	#117	D₄×C₄₃	1	4	yes	—
283	#117	D₄×C₄₃	1	4	yes	—
284	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
285	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
286	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
287	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
291	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
292	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
293	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
294	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
295	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
296	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
297	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
298	C₂×C₄²	C₂×C₄×C₄₃	1	2	yes	—
299	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
300	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
301	C₄⋊C₈	—	2	4	no	—
302	C₄⋊C₈	—	2	4	no	—
303	C₄⋊C₈	—	2	4	no	—
304	#101	—	4	4	no	—
305	#100	—	4	4	no	—
306	C₂²⋊C₈	—	2	4	no	—
307	#97	—	2	2	no	—
308	C₄×C₈	—	2	2	no	—
309	C₂⁴	C₂²×C₄×C₄₃	1	2	yes	—
310	C₂⁴	C₂²×C₄×C₄₃	1	1	yes	characteristic
311	C₂×Q₈	—	2	4	no	—
312	C₂×Q₈	—	2	1	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	8	2	no	—
317	C₂×D₄	—	2	4	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	8	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	8	2	no	—
327	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
328	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
329	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
330	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
331	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
332	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
333	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
334	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
336	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
337	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
338	M₁₆	—	2	4	no	—
339	M₁₆	—	2	4	no	—
340	M₁₆	—	2	4	no	—
341	M₁₆	—	2	4	no	—
342	M₁₆	—	4	4	no	—
343	C₂×C₈	—	2	4	no	—
344	C₂×C₈	—	2	4	no	—
345	C₂×C₈	—	4	4	no	—
346	C₄⋊C₄	—	2	4	no	—
347	C₄⋊C₄	—	2	4	no	—
348	C₄⋊C₄	—	2	4	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
354	C₄⋊C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
355	C₂²⋊C₄	—	2	4	no	—
356	C₂²⋊C₄	—	2	4	no	—
357	C₂²⋊C₄	—	2	4	no	—
358	C₂²⋊C₄	—	2	4	no	—
359	C₂²⋊C₄	—	2	4	no	—
360	C₂²⋊C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
361	C₂²⋊C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
362	C₄²	—	2	4	no	—
363	C₄²	C₂×D₄×C₄₃	1	2	yes	—
364	C₄²	C₂×D₄×C₄₃	1	2	yes	—
365	C₄²	C₂×D₄×C₄₃	1	2	yes	—
366	C₄²	C₂×D₄×C₄₃	1	2	yes	—
367	C₂³	—	2	2	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	2	4	no	—
370	C₂³	—	4	1	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	4	2	no	—
373	C₂³	—	4	2	no	—
374	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
375	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
376	Q₈	—	4	1	no	—
377	Q₈	—	4	1	no	—
378	Q₈	—	4	2	no	—
379	Q₈	—	8	4	no	—
380	D₄	—	4	1	no	—
381	D₄	—	4	1	no	—
382	D₄	—	4	2	no	—
383	D₄	—	8	4	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	8	4	no	—
399	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
400	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
401	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
402	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
403	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
404	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
405	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
406	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
407	C₂×C₄	2₋¹⁺⁴×C₄₃	1	2	yes	—
408	C₈	—	4	4	no	—
409	C₈	—	4	4	no	—
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	4	2	no	—
417	C₂²	—	4	2	no	—
418	C₂²	—	8	2	no	—
419	C₂²	—	8	4	no	—
420	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
421	C₂²	C₄₃×#520	1	2	yes	—
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	2	2	no	—
427	C₄	—	4	2	no	—
428	C₄	—	4	2	no	—
429	C₄	—	4	2	no	—
430	C₄	C₄₃×#535	1	1	yes	characteristic
431	C₄	C₄₃×#536	1	1	yes	characteristic
432	C₄	C₄₃×#537	1	2	yes	—
433	C₂	—	2	2	no	—
434	C₂	—	4	2	no	—
435	C₂	—	8	2	no	—
436	C₂	C₄₃×#2311	1	1	yes	characteristic
437	C₂	C₄₃×#2888	1	1	yes	characteristic
438	C₂	C₄₃×#2889	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₃	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₄₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×#121×C₄₃	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₃ ◁ C₂×#117×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₃×#2921	C₂	semidirect
3. C₄₃×#2905	C₂	semidirect
4. C₄₃×#1997	C₂	semidirect
5. C₄₃×#1967	C₂	semidirect
6. C₄₃×#1901	C₂	semidirect
8. C₄₃×#1801	C₂	semidirect
9. C₄₃×#1800	C₂	semidirect
190. #21881	C₄₃	direct (N × H)
215. #2921	C₂×C₄₃	semidirect
216. #2905	C₂×C₄₃	semidirect
217. #1997	C₂×C₄₃	semidirect
218. #1967	C₂×C₄₃	semidirect
219. #1901	C₂×C₄₃	semidirect
221. #1801	C₂×C₄₃	semidirect
222. #1800	C₂×C₄₃	semidirect
254. C₄₃	#21881	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#542	2
C₄₃×#2921	2
C₄₃×#2905	2
C₄₃×#1997	2
C₄₃×#1967	2
C₄₃×#1901	2
C₄₃×#1900	2
C₄₃×#1801	2
C₄₃×#1800	2
#21881	43

Subgroups — C43×#21881 #24941898

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#21881 #24941898