Subgroups — C₄₃×#17079 #24937096

Order 11008.

1210 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#391	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#389	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#1446	C₂	1	2	yes	maximal
4	C₄₃×#1445	C₂	1	2	yes	maximal
5	C₄₃×#1442	C₂	1	2	yes	maximal
6	C₄₃×#1442	C₂	1	2	yes	maximal
7	C₄₃×#1441	C₂	1	4	yes	maximal
8	C₄₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
9	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
11	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
16	C₄₃×#391	—	2	4	no	—
17	C₄₃×#389	—	2	4	no	—
18	C₂×#95×C₄₃	C₂²	1	2	yes	—
19	C₂×#95×C₄₃	C₂²	1	2	yes	—
20	C₂×#95×C₄₃	C₂²	1	2	yes	—
21	C₂×#95×C₄₃	C₂²	1	2	yes	—
22	C₂×#95×C₄₃	C₂²	1	2	yes	—
23	C₂×#95×C₄₃	C₂²	1	4	yes	—
24	C₂×#95×C₄₃	C₂²	1	4	yes	—
25	C₂×#95×C₄₃	C₂²	1	4	yes	—
26	C₂×#95×C₄₃	C₂²	1	4	yes	—
27	C₂²×Q₈×C₄₃	—	2	2	no	—
28	C₂²×Q₈×C₄₃	—	2	2	no	—
29	C₂²×Q₈×C₄₃	—	4	2	no	—
30	C₂²×Q₈×C₄₃	—	4	2	no	—
31	C₂²×Q₈×C₄₃	Q₈	1	4	yes	—
32	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
33	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
34	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
35	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
36	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
37	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
38	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
41	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
42	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
43	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
44	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
45	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
46	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
47	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
48	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
49	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
50	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
51	C₂×C₄⋊C₄×C₄₃	Q₈	1	4	yes	complemented
52	C₂×C₄²×C₄₃	—	4	2	no	—
53	C₂×C₄²×C₄₃	D₄	1	4	yes	—
54	#95×C₄₃	—	2	4	no	—
55	#95×C₄₃	—	2	4	no	—
56	#95×C₄₃	—	2	4	no	—
57	#95×C₄₃	—	2	4	no	—
58	#95×C₄₃	—	2	4	no	—
59	#95×C₄₃	—	4	4	no	—
60	#95×C₄₃	—	4	4	no	—
61	#95×C₄₃	—	4	4	no	—
62	#95×C₄₃	—	4	4	no	—
63	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
64	C₂×Q₈×C₄₃	—	2	8	no	—
65	C₂×Q₈×C₄₃	—	4	8	no	—
66	C₂×Q₈×C₄₃	—	4	4	no	—
67	C₂×Q₈×C₄₃	—	4	4	no	—
68	C₂×Q₈×C₄₃	—	4	8	no	—
69	C₂²×C₄×C₄₃	—	2	2	no	—
70	C₂²×C₄×C₄₃	—	2	2	no	—
71	C₂²×C₄×C₄₃	—	2	2	no	—
72	C₂²×C₄×C₄₃	—	2	2	no	—
73	C₂²×C₄×C₄₃	—	2	2	no	—
74	C₂²×C₄×C₄₃	—	2	4	no	—
75	C₂²×C₄×C₄₃	—	2	2	no	—
76	C₂²×C₄×C₄₃	—	2	4	no	—
77	C₂²×C₄×C₄₃	—	2	4	no	—
78	C₂²×C₄×C₄₃	—	2	4	no	—
79	C₂²×C₄×C₄₃	—	2	4	no	—
80	C₂²×C₄×C₄₃	—	2	2	no	—
81	C₂²×C₄×C₄₃	—	2	2	no	—
82	C₂²×C₄×C₄₃	—	2	2	no	—
83	C₂²×C₄×C₄₃	—	2	1	no	—
84	C₂²×C₄×C₄₃	—	2	2	no	—
85	C₂²×C₄×C₄₃	—	2	4	no	—
86	C₂²×C₄×C₄₃	—	2	4	no	—
87	C₂²×C₄×C₄₃	—	2	4	no	—
88	C₂²×C₄×C₄₃	—	2	4	no	—
89	C₂²×C₄×C₄₃	—	2	2	no	—
90	C₂²×C₄×C₄₃	—	2	2	no	—
91	C₂²×C₄×C₄₃	—	2	4	no	—
92	C₂²×C₄×C₄₃	—	2	4	no	—
93	C₂²×C₄×C₄₃	—	2	4	no	—
94	C₂²×C₄×C₄₃	—	2	4	no	—
95	C₂²×C₄×C₄₃	—	2	2	no	—
96	C₂²×C₄×C₄₃	—	2	1	no	—
97	C₂²×C₄×C₄₃	—	2	4	no	—
98	C₂²×C₄×C₄₃	—	2	4	no	—
99	C₂²×C₄×C₄₃	—	2	2	no	—
100	C₂²×C₄×C₄₃	—	2	2	no	—
101	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
105	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
106	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
107	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
108	C₂²×C₄×C₄₃	#41	1	2	yes	—
109	C₂²×C₄×C₄₃	#41	1	2	yes	—
110	C₂²×C₄×C₄₃	#41	1	4	yes	—
111	C₄⋊C₄×C₄₃	—	2	8	no	—
112	C₄⋊C₄×C₄₃	—	4	4	no	—
113	C₄⋊C₄×C₄₃	—	4	4	no	—
114	C₄⋊C₄×C₄₃	—	4	8	no	—
115	C₄⋊C₄×C₄₃	—	4	8	no	—
116	C₄²×C₄₃	—	4	4	no	—
117	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
118	C₂³×C₄₃	C₂²×Q₈	1	1	yes	characteristic
119	C₂³×C₄₃	C₂²×Q₈	1	1	yes	characteristic
120	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
121	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
122	C₂³×C₄₃	C₂×#41	1	2	yes	—
123	C₂³×C₄₃	H(5,𝔽₂)	1	2	yes	—
124	C₂³×C₄₃	H(5,𝔽₂)	1	2	yes	—
125	C₂³×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
126	C₂³×C₄₃	2₋¹⁺⁴	1	2	yes	—
127	C₂³×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
128	Q₈×C₄₃	—	4	16	no	—
129	C₂×C₄×C₄₃	—	2	2	no	—
130	C₂×C₄×C₄₃	—	2	2	no	—
131	C₂×C₄×C₄₃	—	2	2	no	—
132	C₂×C₄×C₄₃	—	2	2	no	—
133	C₂×C₄×C₄₃	—	2	2	no	—
134	C₂×C₄×C₄₃	—	2	2	no	—
135	C₂×C₄×C₄₃	—	2	4	no	—
136	C₂×C₄×C₄₃	—	2	4	no	—
137	C₂×C₄×C₄₃	—	2	4	no	—
138	C₂×C₄×C₄₃	—	2	4	no	—
139	C₂×C₄×C₄₃	—	2	4	no	—
140	C₂×C₄×C₄₃	—	2	4	no	—
141	C₂×C₄×C₄₃	—	2	4	no	—
142	C₂×C₄×C₄₃	—	2	4	no	—
143	C₂×C₄×C₄₃	—	2	8	no	—
144	C₂×C₄×C₄₃	—	2	8	no	—
145	C₂×C₄×C₄₃	—	4	2	no	—
146	C₂×C₄×C₄₃	—	4	2	no	—
147	C₂×C₄×C₄₃	—	4	2	no	—
148	C₂×C₄×C₄₃	—	4	2	no	—
149	C₂×C₄×C₄₃	—	4	4	no	—
150	C₂×C₄×C₄₃	—	4	4	no	—
151	C₂×C₄×C₄₃	—	4	2	no	—
152	C₂×C₄×C₄₃	—	4	2	no	—
153	C₂×C₄×C₄₃	—	4	2	no	—
154	C₂×C₄×C₄₃	—	4	2	no	—
155	C₂×C₄×C₄₃	—	4	2	no	—
156	C₂×C₄×C₄₃	—	4	2	no	—
157	C₂×C₄×C₄₃	—	4	4	no	—
158	C₂×C₄×C₄₃	—	4	4	no	—
159	C₂×C₄×C₄₃	—	4	4	no	—
160	C₂×C₄×C₄₃	—	4	4	no	—
161	C₂×C₄×C₄₃	—	4	4	no	—
162	C₂×C₄×C₄₃	—	4	4	no	—
163	C₂×C₄×C₄₃	—	4	4	no	—
164	C₂×C₄×C₄₃	—	4	4	no	—
165	C₂×C₄×C₄₃	—	4	4	no	—
166	C₂×C₄×C₄₃	—	4	4	no	—
167	C₂×C₄×C₄₃	—	4	4	no	—
168	C₂×C₄×C₄₃	C₂²⋊Q₈	1	4	yes	—
169	C₂×C₄×C₄₃	C₂²⋊Q₈	1	4	yes	—
170	C₂×C₄×C₄₃	#124	1	4	yes	—
171	#17079	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
173	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
174	C₂²×C₄₃	C₂×#124	1	1	yes	characteristic
175	C₂²×C₄₃	#534	1	1	yes	characteristic
176	C₂²×C₄₃	#535	1	1	yes	characteristic
177	C₂²×C₄₃	#536	1	1	yes	characteristic
178	C₂²×C₄₃	#537	1	1	yes	characteristic
179	C₂²×C₄₃	#538	1	2	yes	—
180	C₂²×C₄₃	#538	1	2	yes	—
181	C₂²×C₄₃	#539	1	2	yes	—
182	C₂²×C₄₃	#539	1	2	yes	—
183	C₂²×C₄₃	#543	1	2	yes	—
184	C₂²×C₄₃	#544	1	2	yes	—
185	C₂²×C₄₃	#554	1	2	yes	—
186	C₂²×C₄₃	#555	1	2	yes	—
187	C₂²×C₄₃	#556	1	2	yes	—
188	C₂²×C₄₃	#557	1	2	yes	—
189	C₂²×C₄₃	#557	1	1	yes	characteristic
190	C₂²×C₄₃	#557	1	1	yes	characteristic
191	C₂²×C₄₃	Q₈²	1	1	yes	characteristic
192	C₂²×C₄₃	#559	1	1	yes	characteristic
193	C₂²×C₄₃	#562	1	2	yes	—
194	C₂²×C₄₃	#563	1	2	yes	—
195	C₄×C₄₃	—	2	4	no	—
196	C₄×C₄₃	—	2	4	no	—
197	C₄×C₄₃	—	2	4	no	—
198	C₄×C₄₃	—	4	4	no	—
199	C₄×C₄₃	—	4	4	no	—
200	C₄×C₄₃	—	8	2	no	—
201	C₄×C₄₃	—	8	2	no	—
202	C₄×C₄₃	—	8	4	no	—
203	C₂×#391	C₂×C₄₃	1	1	yes	characteristic
204	C₂×#389	C₂×C₄₃	1	1	yes	characteristic
205	#1446	C₂×C₄₃	1	2	yes	—
206	#1445	C₂×C₄₃	1	2	yes	—
207	#1442	C₂×C₄₃	1	2	yes	—
208	#1442	C₂×C₄₃	1	2	yes	—
209	#1441	C₂×C₄₃	1	4	yes	—
210	C₄⋊#95	C₂×C₄₃	1	1	yes	characteristic
211	C₂×C₄₃	#2563	1	1	yes	characteristic
212	C₂×C₄₃	#2568	1	1	yes	characteristic
213	C₂×C₄₃	#2582	1	1	yes	characteristic
214	C₂×C₄₃	#2626	1	1	yes	characteristic
215	C₂×C₄₃	#2627	1	1	yes	characteristic
216	C₂×C₄₃	#2639	1	1	yes	characteristic
217	C₂×C₄₃	#2805	1	2	yes	—
218	C₂×C₄₃	#2806	1	2	yes	—
219	C₂×C₄₃	#2808	1	2	yes	—
220	C₂×C₄₃	#2809	1	2	yes	—
221	C₂×C₄₃	#2820	1	1	yes	characteristic
222	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic
223	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
224	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
225	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
226	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
227	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
228	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
229	#391	—	2	4	no	—
230	#389	—	2	4	no	—
231	C₂×#95	C₂²×C₄₃	1	2	yes	—
232	C₂×#95	C₂²×C₄₃	1	2	yes	—
233	C₂×#95	C₂²×C₄₃	1	2	yes	—
234	C₂×#95	C₂²×C₄₃	1	2	yes	—
235	C₂×#95	C₂²×C₄₃	1	2	yes	—
236	C₂×#95	C₂²×C₄₃	1	4	yes	—
237	C₂×#95	C₂²×C₄₃	1	4	yes	—
238	C₂×#95	C₂²×C₄₃	1	4	yes	—
239	C₂×#95	C₂²×C₄₃	1	4	yes	—
240	C₄₃	#17079	1	1	yes	characteristic, direct product factor, Sylow
241	C₂²×Q₈	—	2	2	no	—
242	C₂²×Q₈	—	2	2	no	—
243	C₂²×Q₈	—	4	2	no	—
244	C₂²×Q₈	—	4	2	no	—
245	C₂²×Q₈	Q₈×C₄₃	1	4	yes	—
246	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
247	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
248	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
249	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
250	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
251	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
252	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
253	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	4	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	4	no	—
260	C₂×C₄⋊C₄	—	2	8	no	—
261	C₂×C₄⋊C₄	—	4	2	no	—
262	C₂×C₄⋊C₄	—	4	2	no	—
263	C₂×C₄⋊C₄	—	4	2	no	—
264	C₂×C₄⋊C₄	—	4	2	no	—
265	C₂×C₄⋊C₄	Q₈×C₄₃	1	4	yes	complemented
266	C₂×C₄²	—	4	2	no	—
267	C₂×C₄²	D₄×C₄₃	1	4	yes	—
268	#95	—	2	4	no	—
269	#95	—	2	4	no	—
270	#95	—	2	4	no	—
271	#95	—	2	4	no	—
272	#95	—	2	4	no	—
273	#95	—	4	4	no	—
274	#95	—	4	4	no	—
275	#95	—	4	4	no	—
276	#95	—	4	4	no	—
277	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
278	C₂×Q₈	—	2	8	no	—
279	C₂×Q₈	—	4	8	no	—
280	C₂×Q₈	—	4	4	no	—
281	C₂×Q₈	—	4	4	no	—
282	C₂×Q₈	—	4	8	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
316	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
317	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
318	C₂²×C₄	C₂×Q₈×C₄₃	1	4	yes	—
319	C₂²×C₄	C₂×Q₈×C₄₃	1	4	yes	—
320	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
321	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
322	C₂²×C₄	#41×C₄₃	1	2	yes	—
323	C₂²×C₄	#41×C₄₃	1	2	yes	—
324	C₂²×C₄	#41×C₄₃	1	4	yes	—
325	C₄⋊C₄	—	2	8	no	—
326	C₄⋊C₄	—	4	4	no	—
327	C₄⋊C₄	—	4	4	no	—
328	C₄⋊C₄	—	4	8	no	—
329	C₄⋊C₄	—	4	8	no	—
330	C₄²	—	4	4	no	—
331	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
332	C₂³	C₂²×Q₈×C₄₃	1	1	yes	characteristic
333	C₂³	C₂²×Q₈×C₄₃	1	1	yes	characteristic
334	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
335	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
336	C₂³	C₂×#41×C₄₃	1	2	yes	—
337	C₂³	H(5,𝔽₂)×C₄₃	1	2	yes	—
338	C₂³	H(5,𝔽₂)×C₄₃	1	2	yes	—
339	C₂³	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
340	C₂³	2₋¹⁺⁴×C₄₃	1	2	yes	—
341	C₂³	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
342	Q₈	—	4	16	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	8	no	—
358	C₂×C₄	—	2	8	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	—	4	4	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	—	4	4	no	—
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	—	4	4	no	—
380	C₂×C₄	—	4	4	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	C₂²⋊Q₈×C₄₃	1	4	yes	—
383	C₂×C₄	C₂²⋊Q₈×C₄₃	1	4	yes	—
384	C₂×C₄	#124×C₄₃	1	4	yes	—
385	C₂²	C₂×C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
386	C₂²	C₂×C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
387	C₂²	C₂×#124×C₄₃	1	1	yes	characteristic
388	C₂²	C₄₃×#534	1	1	yes	characteristic
389	C₂²	C₄₃×#535	1	1	yes	characteristic
390	C₂²	C₄₃×#536	1	1	yes	characteristic
391	C₂²	C₄₃×#537	1	1	yes	characteristic
392	C₂²	C₄₃×#538	1	2	yes	—
393	C₂²	C₄₃×#538	1	2	yes	—
394	C₂²	C₄₃×#539	1	2	yes	—
395	C₂²	C₄₃×#539	1	2	yes	—
396	C₂²	C₄₃×#543	1	2	yes	—
397	C₂²	C₄₃×#544	1	2	yes	—
398	C₂²	C₄₃×#554	1	2	yes	—
399	C₂²	C₄₃×#555	1	2	yes	—
400	C₂²	C₄₃×#556	1	2	yes	—
401	C₂²	C₄₃×#557	1	1	yes	characteristic
402	C₂²	C₄₃×#557	1	1	yes	characteristic
403	C₂²	C₄₃×#557	1	2	yes	—
404	C₂²	Q₈²×C₄₃	1	1	yes	characteristic
405	C₂²	C₄₃×#559	1	1	yes	characteristic
406	C₂²	C₄₃×#562	1	2	yes	—
407	C₂²	C₄₃×#563	1	2	yes	—
408	C₄	—	2	4	no	—
409	C₄	—	2	4	no	—
410	C₄	—	2	4	no	—
411	C₄	—	4	4	no	—
412	C₄	—	4	4	no	—
413	C₄	—	8	2	no	—
414	C₄	—	8	4	no	—
415	C₄	—	8	2	no	—
416	C₂	C₄₃×#2563	1	1	yes	characteristic
417	C₂	C₄₃×#2568	1	1	yes	characteristic
418	C₂	C₄₃×#2582	1	1	yes	characteristic
419	C₂	C₄₃×#2626	1	1	yes	characteristic
420	C₂	C₄₃×#2627	1	1	yes	characteristic
421	C₂	C₄₃×#2639	1	1	yes	characteristic
422	C₂	C₄₃×#2805	1	2	yes	—
423	C₂	C₄₃×#2806	1	2	yes	—
424	C₂	C₄₃×#2808	1	2	yes	—
425	C₂	C₄₃×#2809	1	2	yes	—
426	C₂	C₄₃×#2820	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₄₃	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₄₃
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
51. C₂×C₄⋊C₄×C₄₃	Q₈	semidirect
171. #17079	C₄₃	direct (N × H)
240. C₄₃	#17079	direct (N × H)
265. C₂×C₄⋊C₄	Q₈×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#391	2
C₂×C₄₃×#389	2
C₄₃×#1446	2
C₄₃×#1445	2
C₄₃×#1442	2
C₄₃×#1441	2
C₄₃×C₄⋊#95	2
#17079	43

Subgroups — C43×#17079 #24937096

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#17079 #24937096