Subgroups — C₄₃×#13925 #24933942

Order 11008.

1710 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#382	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#1446	C₂	1	2	yes	maximal
5	C₄₃×#1445	C₂	1	2	yes	maximal
6	C₄₃×#1436	C₂	1	4	yes	maximal
7	C₄₃×C₄⋊#95	C₂	1	4	yes	maximal
8	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
9	C₂×C₄×Q₈×C₄₃	—	2	4	no	—
10	C₂×C₄×Q₈×C₄₃	—	2	4	no	—
11	C₂×C₄×Q₈×C₄₃	C₄	1	8	yes	complemented
12	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
16	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
17	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
18	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
19	C₄₃×#382	—	2	4	no	—
20	C₄×C₄⋊C₄×C₄₃	—	2	4	no	—
21	C₂×#95×C₄₃	C₂²	1	8	yes	—
22	C₂×#95×C₄₃	C₂²	1	2	yes	—
23	C₂×#95×C₄₃	C₂²	1	2	yes	—
24	C₂×#95×C₄₃	C₂²	1	2	yes	—
25	C₂×#95×C₄₃	C₂²	1	8	yes	—
26	C₂²×Q₈×C₄₃	—	2	2	no	—
27	C₂²×Q₈×C₄₃	—	2	2	no	—
28	C₂²×Q₈×C₄₃	—	2	8	no	—
29	C₂²×Q₈×C₄₃	C₂×C₄	1	4	yes	—
30	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
31	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
32	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
33	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
34	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
35	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
36	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
37	C₄×Q₈×C₄₃	—	2	32	no	—
38	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
39	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
40	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
41	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
42	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
43	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
44	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
45	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
46	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
47	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
48	C₂×C₄⋊C₄×C₄₃	Q₈	1	8	yes	complemented
49	C₂×C₄²×C₄₃	—	2	4	no	—
50	C₂×C₄²×C₄₃	—	2	4	no	—
51	C₂×C₄²×C₄₃	—	2	4	no	—
52	C₂×C₄²×C₄₃	—	4	4	no	—
53	C₂×C₄²×C₄₃	C₂×C₄	1	8	yes	—
54	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
55	C₂×C₄²×C₄₃	D₄	1	4	yes	—
56	C₂×C₄²×C₄₃	D₄	1	4	yes	—
57	#95×C₄₃	—	2	4	no	—
58	#95×C₄₃	—	2	4	no	—
59	#95×C₄₃	—	2	4	no	—
60	#95×C₄₃	—	2	16	no	—
61	#95×C₄₃	—	4	8	no	—
62	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
63	C₂×Q₈×C₄₃	—	2	16	no	—
64	C₂×Q₈×C₄₃	—	2	16	no	—
65	C₂×Q₈×C₄₃	—	2	8	no	—
66	C₂×Q₈×C₄₃	—	2	16	no	—
67	C₂²×C₄×C₄₃	—	2	2	no	—
68	C₂²×C₄×C₄₃	—	2	2	no	—
69	C₂²×C₄×C₄₃	—	2	4	no	—
70	C₂²×C₄×C₄₃	—	2	2	no	—
71	C₂²×C₄×C₄₃	—	2	2	no	—
72	C₂²×C₄×C₄₃	—	2	4	no	—
73	C₂²×C₄×C₄₃	—	2	4	no	—
74	C₂²×C₄×C₄₃	—	2	4	no	—
75	C₂²×C₄×C₄₃	—	2	8	no	—
76	C₂²×C₄×C₄₃	—	2	4	no	—
77	C₂²×C₄×C₄₃	—	2	8	no	—
78	C₂²×C₄×C₄₃	—	2	8	no	—
79	C₂²×C₄×C₄₃	—	2	2	no	—
80	C₂²×C₄×C₄₃	—	2	4	no	—
81	C₂²×C₄×C₄₃	—	2	8	no	—
82	C₂²×C₄×C₄₃	—	2	4	no	—
83	C₂²×C₄×C₄₃	—	2	2	no	—
84	C₂²×C₄×C₄₃	—	2	4	no	—
85	C₂²×C₄×C₄₃	—	2	4	no	—
86	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
87	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
90	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₄₃	C₂×Q₈	1	8	yes	—
98	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
99	C₂²×C₄×C₄₃	#41	1	8	yes	—
100	C₂²×C₄×C₄₃	#41	1	4	yes	—
101	C₄⋊C₄×C₄₃	—	2	16	no	—
102	C₄⋊C₄×C₄₃	—	2	8	no	—
103	C₄⋊C₄×C₄₃	—	2	16	no	—
104	C₄⋊C₄×C₄₃	—	4	8	no	—
105	C₄²×C₄₃	—	2	16	no	—
106	C₄²×C₄₃	—	4	8	no	—
107	C₄²×C₄₃	C₂²⋊C₄	1	16	yes	—
108	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
109	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
110	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
111	C₂³×C₄₃	C₂²×Q₈	1	2	yes	—
112	C₂³×C₄₃	C₂×#41	1	4	yes	—
113	C₂³×C₄₃	C₂×#41	1	2	yes	—
114	C₂³×C₄₃	H(5,𝔽₂)	1	2	yes	—
115	C₂³×C₄₃	2₋¹⁺⁴	1	2	yes	—
116	Q₈×C₄₃	—	2	32	no	—
117	C₂×C₄×C₄₃	—	2	4	no	—
118	C₂×C₄×C₄₃	—	2	4	no	—
119	C₂×C₄×C₄₃	—	2	4	no	—
120	C₂×C₄×C₄₃	—	2	4	no	—
121	C₂×C₄×C₄₃	—	2	4	no	—
122	C₂×C₄×C₄₃	—	2	4	no	—
123	C₂×C₄×C₄₃	—	2	8	no	—
124	C₂×C₄×C₄₃	—	2	8	no	—
125	C₂×C₄×C₄₃	—	2	2	no	—
126	C₂×C₄×C₄₃	—	2	2	no	—
127	C₂×C₄×C₄₃	—	2	4	no	—
128	C₂×C₄×C₄₃	—	2	4	no	—
129	C₂×C₄×C₄₃	—	2	8	no	—
130	C₂×C₄×C₄₃	—	2	8	no	—
131	C₂×C₄×C₄₃	—	2	16	no	—
132	C₂×C₄×C₄₃	—	4	4	no	—
133	C₂×C₄×C₄₃	—	4	4	no	—
134	C₂×C₄×C₄₃	—	4	2	no	—
135	C₂×C₄×C₄₃	—	4	2	no	—
136	C₂×C₄×C₄₃	—	4	4	no	—
137	C₂×C₄×C₄₃	—	4	8	no	—
138	C₂×C₄×C₄₃	—	4	4	no	—
139	C₂×C₄×C₄₃	—	4	4	no	—
140	C₂×C₄×C₄₃	—	4	4	no	—
141	C₂×C₄×C₄₃	—	4	8	no	—
142	C₂×C₄×C₄₃	—	4	8	no	—
143	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
144	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
145	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
146	C₂×C₄×C₄₃	#117	1	8	yes	—
147	C₂×C₄×C₄₃	C₄×Q₈	1	8	yes	—
148	C₂×C₄×C₄₃	C₂²⋊Q₈	1	8	yes	—
149	C₂×C₄×C₄₃	#124	1	4	yes	—
150	C₂×C₄×C₄₃	C₄⋊Q₈	1	4	yes	—
151	#13925	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
153	C₂²×C₄₃	C₂×#117	1	2	yes	—
154	C₂²×C₄₃	C₂×C₄×Q₈	1	2	yes	—
155	C₂²×C₄₃	#520	1	2	yes	—
156	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	2	yes	—
157	C₂²×C₄₃	#525	1	2	yes	—
158	C₂²×C₄₃	#525	1	2	yes	—
159	C₂²×C₄₃	C₂×#124	1	1	yes	characteristic
160	C₂²×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
161	C₂²×C₄₃	#535	1	1	yes	characteristic
162	C₂²×C₄₃	#536	1	1	yes	characteristic
163	C₂²×C₄₃	#537	1	2	yes	—
164	C₂²×C₄₃	#554	1	4	yes	—
165	C₂²×C₄₃	#556	1	4	yes	—
166	C₂²×C₄₃	#557	1	4	yes	—
167	C₂²×C₄₃	#559	1	4	yes	—
168	C₄×C₄₃	—	2	4	no	—
169	C₄×C₄₃	—	2	4	no	—
170	C₄×C₄₃	—	2	8	no	—
171	C₄×C₄₃	—	4	4	no	—
172	C₄×C₄₃	—	4	8	no	—
173	C₄×C₄₃	—	8	4	no	—
174	C₄×C₄₃	#391	1	8	yes	—
175	C₂²×C₄×Q₈	C₂×C₄₃	1	1	yes	characteristic
176	C₂×#382	C₂×C₄₃	1	1	yes	characteristic
177	C₂×C₄×C₄⋊C₄	C₂×C₄₃	1	1	yes	characteristic
178	#1446	C₂×C₄₃	1	2	yes	—
179	#1445	C₂×C₄₃	1	2	yes	—
180	#1436	C₂×C₄₃	1	4	yes	—
181	C₄⋊#95	C₂×C₄₃	1	4	yes	—
182	C₂×C₄₃	#2280	1	1	yes	characteristic
183	C₂×C₄₃	C₂×#391	1	1	yes	characteristic
184	C₂×C₄₃	#2311	1	1	yes	characteristic
185	C₂×C₄₃	#2355	1	4	yes	—
186	C₂×C₄₃	#2580	1	2	yes	—
187	C₂×C₄₃	#2581	1	2	yes	—
188	C₂×C₄₃	#2584	1	2	yes	—
189	C₂×C₄₃	#2592	1	2	yes	—
190	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic
191	C₂×C₄×Q₈	—	2	4	no	—
192	C₂×C₄×Q₈	—	2	4	no	—
193	C₂×C₄×Q₈	C₄×C₄₃	1	8	yes	complemented
194	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
195	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
196	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
197	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
198	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
199	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
200	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
201	#382	—	2	4	no	—
202	C₄×C₄⋊C₄	—	2	4	no	—
203	C₂×#95	C₂²×C₄₃	1	8	yes	—
204	C₂×#95	C₂²×C₄₃	1	2	yes	—
205	C₂×#95	C₂²×C₄₃	1	2	yes	—
206	C₂×#95	C₂²×C₄₃	1	2	yes	—
207	C₂×#95	C₂²×C₄₃	1	8	yes	—
208	C₄₃	#13925	1	1	yes	characteristic, direct product factor, Sylow
209	C₂²×Q₈	—	2	2	no	—
210	C₂²×Q₈	—	2	2	no	—
211	C₂²×Q₈	—	2	8	no	—
212	C₂²×Q₈	C₂×C₄×C₄₃	1	4	yes	—
213	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
214	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
215	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
216	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
217	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
218	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
219	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
220	C₄×Q₈	—	2	32	no	—
221	C₂×C₄⋊C₄	—	2	4	no	—
222	C₂×C₄⋊C₄	—	2	4	no	—
223	C₂×C₄⋊C₄	—	2	2	no	—
224	C₂×C₄⋊C₄	—	2	2	no	—
225	C₂×C₄⋊C₄	—	2	4	no	—
226	C₂×C₄⋊C₄	—	2	4	no	—
227	C₂×C₄⋊C₄	—	2	4	no	—
228	C₂×C₄⋊C₄	—	2	8	no	—
229	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
230	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	8	yes	—
231	C₂×C₄⋊C₄	Q₈×C₄₃	1	8	yes	complemented
232	C₂×C₄²	—	2	4	no	—
233	C₂×C₄²	—	2	4	no	—
234	C₂×C₄²	—	2	4	no	—
235	C₂×C₄²	—	4	4	no	—
236	C₂×C₄²	C₂×C₄×C₄₃	1	8	yes	—
237	C₂×C₄²	C₂×C₄×C₄₃	1	4	yes	—
238	C₂×C₄²	D₄×C₄₃	1	4	yes	—
239	C₂×C₄²	D₄×C₄₃	1	4	yes	—
240	#95	—	2	4	no	—
241	#95	—	2	4	no	—
242	#95	—	2	4	no	—
243	#95	—	2	16	no	—
244	#95	—	4	8	no	—
245	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
246	C₂×Q₈	—	2	16	no	—
247	C₂×Q₈	—	2	16	no	—
248	C₂×Q₈	—	2	8	no	—
249	C₂×Q₈	—	2	16	no	—
250	C₂²×C₄	—	2	2	no	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	2	4	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	8	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	2	8	no	—
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	2	8	no	—
266	C₂²×C₄	—	2	8	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
270	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
271	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
272	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
273	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
274	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
275	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
276	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
277	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
278	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
279	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
280	C₂²×C₄	C₂×Q₈×C₄₃	1	8	yes	—
281	C₂²×C₄	C₂×Q₈×C₄₃	1	4	yes	—
282	C₂²×C₄	#41×C₄₃	1	8	yes	—
283	C₂²×C₄	#41×C₄₃	1	4	yes	—
284	C₄⋊C₄	—	2	16	no	—
285	C₄⋊C₄	—	2	8	no	—
286	C₄⋊C₄	—	2	16	no	—
287	C₄⋊C₄	—	4	8	no	—
288	C₄²	—	2	16	no	—
289	C₄²	—	4	8	no	—
290	C₄²	C₂²⋊C₄×C₄₃	1	16	yes	—
291	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
292	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
293	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
294	C₂³	C₂²×Q₈×C₄₃	1	2	yes	—
295	C₂³	C₂×#41×C₄₃	1	4	yes	—
296	C₂³	C₂×#41×C₄₃	1	2	yes	—
297	C₂³	H(5,𝔽₂)×C₄₃	1	2	yes	—
298	C₂³	2₋¹⁺⁴×C₄₃	1	2	yes	—
299	Q₈	—	2	32	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	8	no	—
307	C₂×C₄	—	2	8	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	8	no	—
313	C₂×C₄	—	2	8	no	—
314	C₂×C₄	—	2	16	no	—
315	C₂×C₄	—	4	4	no	—
316	C₂×C₄	—	4	4	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	4	4	no	—
320	C₂×C₄	—	4	8	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	—	4	4	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	—	4	8	no	—
325	C₂×C₄	—	4	8	no	—
326	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
327	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
328	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
329	C₂×C₄	#117×C₄₃	1	8	yes	—
330	C₂×C₄	C₄×Q₈×C₄₃	1	8	yes	—
331	C₂×C₄	C₂²⋊Q₈×C₄₃	1	8	yes	—
332	C₂×C₄	#124×C₄₃	1	4	yes	—
333	C₂×C₄	C₄⋊Q₈×C₄₃	1	4	yes	—
334	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
335	C₂²	C₂×#117×C₄₃	1	2	yes	—
336	C₂²	C₂×C₄×Q₈×C₄₃	1	2	yes	—
337	C₂²	C₄₃×#520	1	2	yes	—
338	C₂²	C₂×C₂²⋊Q₈×C₄₃	1	2	yes	—
339	C₂²	C₄₃×#525	1	2	yes	—
340	C₂²	C₄₃×#525	1	2	yes	—
341	C₂²	C₂×#124×C₄₃	1	1	yes	characteristic
342	C₂²	C₂×C₄⋊Q₈×C₄₃	1	1	yes	characteristic
343	C₂²	C₄₃×#535	1	1	yes	characteristic
344	C₂²	C₄₃×#536	1	1	yes	characteristic
345	C₂²	C₄₃×#537	1	2	yes	—
346	C₂²	C₄₃×#554	1	4	yes	—
347	C₂²	C₄₃×#556	1	4	yes	—
348	C₂²	C₄₃×#557	1	4	yes	—
349	C₂²	C₄₃×#559	1	4	yes	—
350	C₄	—	2	4	no	—
351	C₄	—	2	8	no	—
352	C₄	—	2	4	no	—
353	C₄	—	4	8	no	—
354	C₄	—	4	4	no	—
355	C₄	—	8	4	no	—
356	C₄	C₄₃×#391	1	8	yes	—
357	C₂	C₄₃×#2280	1	1	yes	characteristic
358	C₂	C₂×C₄₃×#391	1	1	yes	characteristic
359	C₂	C₄₃×#2311	1	1	yes	characteristic
360	C₂	C₄₃×#2355	1	4	yes	—
361	C₂	C₄₃×#2580	1	2	yes	—
362	C₂	C₄₃×#2581	1	2	yes	—
363	C₂	C₄₃×#2584	1	2	yes	—
364	C₂	C₄₃×#2592	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
11. C₂×C₄×Q₈×C₄₃	C₄	semidirect
48. C₂×C₄⋊C₄×C₄₃	Q₈	semidirect
151. #13925	C₄₃	direct (N × H)
193. C₂×C₄×Q₈	C₄×C₄₃	semidirect
208. C₄₃	#13925	direct (N × H)
231. 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
C₂²×C₄×Q₈×C₄₃	2
C₂×C₄₃×#382	2
C₂×C₄×C₄⋊C₄×C₄₃	2
C₄₃×#1446	2
C₄₃×#1445	2
C₄₃×#1436	2
C₄₃×C₄⋊#95	2
#13925	43

Subgroups — C43×#13925 #24933942

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#13925 #24933942