Subgroups — C₄₃×#13818 #24933835

Order 11008.

1690 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×#389	C₂	1	2	yes	maximal
2	C₂×C₄×C₄⋊C₄×C₄₃	C₂	1	2	yes	maximal
3	C₂×C₄×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#1436	C₂	1	4	yes	maximal
5	C₄₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
6	C₄₃×C₄⋊#95	C₂	1	2	yes	maximal
7	C₄×#95×C₄₃	C₂	1	2	yes	maximal
8	C₄×#95×C₄₃	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
10	C₂²×C₄⋊C₄×C₄₃	C₂²	1	4	yes	—
11	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×C₄²×C₄₃	C₂²	1	4	yes	—
14	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
16	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
17	C₄₃×#389	C₄	1	16	yes	complemented
18	C₄×C₄⋊C₄×C₄₃	—	2	8	no	—
19	C₄×C₄⋊C₄×C₄₃	C₄	1	8	yes	complemented
20	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
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	2	yes	—
25	C₂×#95×C₄₃	C₂²	1	4	yes	—
26	C₂×#95×C₄₃	C₂²	1	2	yes	—
27	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
28	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
29	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
30	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
31	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
32	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
33	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
34	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
35	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
36	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
37	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
38	C₂×C₄⋊C₄×C₄₃	—	4	4	no	—
39	C₂×C₄⋊C₄×C₄₃	—	4	4	no	—
40	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
41	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	16	yes	—
42	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
43	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
44	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
45	C₂×C₄⋊C₄×C₄₃	D₄	1	4	yes	—
46	C₂×C₄⋊C₄×C₄₃	Q₈	1	4	yes	—
47	C₂×C₄²×C₄₃	—	2	4	no	—
48	C₂×C₄²×C₄₃	—	2	4	no	—
49	C₂×C₄²×C₄₃	—	2	4	no	—
50	C₂×C₄²×C₄₃	—	2	8	no	—
51	C₂×C₄²×C₄₃	—	2	8	no	—
52	C₂×C₄²×C₄₃	—	4	4	no	—
53	C₂×C₄²×C₄₃	—	4	4	no	—
54	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
55	C₂×C₄²×C₄₃	C₂×C₄	1	8	yes	—
56	C₂×C₄²×C₄₃	C₂×C₄	1	8	yes	—
57	#95×C₄₃	—	2	8	no	—
58	#95×C₄₃	—	2	2	no	—
59	#95×C₄₃	—	2	4	no	—
60	#95×C₄₃	—	2	4	no	—
61	#95×C₄₃	—	4	2	no	—
62	#95×C₄₃	C₂×C₄	1	8	yes	—
63	#95×C₄₃	C₂×C₄	1	16	yes	—
64	#95×C₄₃	Q₈	1	4	yes	—
65	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
66	C₂²×C₄×C₄₃	—	2	2	no	—
67	C₂²×C₄×C₄₃	—	2	2	no	—
68	C₂²×C₄×C₄₃	—	2	4	no	—
69	C₂²×C₄×C₄₃	—	2	2	no	—
70	C₂²×C₄×C₄₃	—	2	2	no	—
71	C₂²×C₄×C₄₃	—	2	4	no	—
72	C₂²×C₄×C₄₃	—	2	2	no	—
73	C₂²×C₄×C₄₃	—	2	2	no	—
74	C₂²×C₄×C₄₃	—	2	2	no	—
75	C₂²×C₄×C₄₃	—	2	4	no	—
76	C₂²×C₄×C₄₃	—	2	2	no	—
77	C₂²×C₄×C₄₃	—	2	2	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	4	no	—
82	C₂²×C₄×C₄₃	—	2	2	no	—
83	C₂²×C₄×C₄₃	—	2	4	no	—
84	C₂²×C₄×C₄₃	—	2	2	no	—
85	C₂²×C₄×C₄₃	—	2	1	no	—
86	C₂²×C₄×C₄₃	—	2	4	no	—
87	C₂²×C₄×C₄₃	—	2	4	no	—
88	C₂²×C₄×C₄₃	—	2	2	no	—
89	C₂²×C₄×C₄₃	—	2	2	no	—
90	C₂²×C₄×C₄₃	—	2	2	no	—
91	C₂²×C₄×C₄₃	—	2	2	no	—
92	C₂²×C₄×C₄₃	—	2	1	no	—
93	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
95	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
97	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
98	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
100	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
103	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
104	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
106	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
107	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
108	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
109	C₂²×C₄×C₄₃	#41	1	2	yes	—
110	C₂²×C₄×C₄₃	#41	1	4	yes	—
111	C₂²×C₄×C₄₃	#41	1	4	yes	—
112	C₄⋊C₄×C₄₃	—	2	16	no	—
113	C₄⋊C₄×C₄₃	—	4	16	no	—
114	C₄⋊C₄×C₄₃	C₄²	1	16	yes	complemented
115	C₄⋊C₄×C₄₃	C₄⋊C₄	1	16	yes	complemented
116	C₄²×C₄₃	—	2	8	no	—
117	C₄²×C₄₃	—	2	16	no	—
118	C₄²×C₄₃	—	4	8	no	—
119	C₄²×C₄₃	—	4	16	no	—
120	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
121	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
122	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
123	C₂³×C₄₃	C₂²×Q₈	1	1	yes	characteristic
124	C₂³×C₄₃	C₂²×Q₈	1	1	yes	characteristic
125	C₂³×C₄₃	C₂×#41	1	2	yes	—
126	C₂³×C₄₃	C₂×#41	1	2	yes	—
127	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
128	C₂³×C₄₃	H(5,𝔽₂)	1	2	yes	—
129	C₂³×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
130	C₂³×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
131	C₂×C₄×C₄₃	—	2	2	no	—
132	C₂×C₄×C₄₃	—	2	4	no	—
133	C₂×C₄×C₄₃	—	2	4	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	8	no	—
138	C₂×C₄×C₄₃	—	2	4	no	—
139	C₂×C₄×C₄₃	—	2	4	no	—
140	C₂×C₄×C₄₃	—	2	8	no	—
141	C₂×C₄×C₄₃	—	2	4	no	—
142	C₂×C₄×C₄₃	—	2	8	no	—
143	C₂×C₄×C₄₃	—	2	4	no	—
144	C₂×C₄×C₄₃	—	2	4	no	—
145	C₂×C₄×C₄₃	—	2	4	no	—
146	C₂×C₄×C₄₃	—	2	4	no	—
147	C₂×C₄×C₄₃	—	2	8	no	—
148	C₂×C₄×C₄₃	—	2	4	no	—
149	C₂×C₄×C₄₃	—	2	2	no	—
150	C₂×C₄×C₄₃	—	2	4	no	—
151	C₂×C₄×C₄₃	—	2	8	no	—
152	C₂×C₄×C₄₃	—	2	2	no	—
153	C₂×C₄×C₄₃	—	2	4	no	—
154	C₂×C₄×C₄₃	—	2	8	no	—
155	C₂×C₄×C₄₃	—	2	4	no	—
156	C₂×C₄×C₄₃	—	2	8	no	—
157	C₂×C₄×C₄₃	—	2	2	no	—
158	C₂×C₄×C₄₃	—	4	4	no	—
159	C₂×C₄×C₄₃	—	4	2	no	—
160	C₂×C₄×C₄₃	—	4	2	no	—
161	C₂×C₄×C₄₃	—	4	4	no	—
162	C₂×C₄×C₄₃	—	4	2	no	—
163	C₂×C₄×C₄₃	—	4	2	no	—
164	C₂×C₄×C₄₃	—	4	4	no	—
165	C₂×C₄×C₄₃	—	4	2	no	—
166	C₂×C₄×C₄₃	—	4	2	no	—
167	C₂×C₄×C₄₃	—	4	4	no	—
168	C₂×C₄×C₄₃	C₂×C₄²	1	8	yes	—
169	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
170	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	8	yes	—
171	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
172	C₂×C₄×C₄₃	#117	1	4	yes	—
173	C₂×C₄×C₄₃	C₄×D₄	1	8	yes	—
174	C₂×C₄×C₄₃	C₄×Q₈	1	4	yes	—
175	C₂×C₄×C₄₃	C₄×Q₈	1	8	yes	—
176	C₂×C₄×C₄₃	C₄×Q₈	1	8	yes	—
177	#13818	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂²×C₄₃	C₂²×C₄²	1	1	yes	characteristic
179	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
180	C₂²×C₄₃	C₂×#117	1	1	yes	characteristic
181	C₂²×C₄₃	C₂×C₄×D₄	1	2	yes	—
182	C₂²×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
183	C₂²×C₄₃	C₂×C₄×Q₈	1	2	yes	—
184	C₂²×C₄₃	C₂×C₄×Q₈	1	2	yes	—
185	C₂²×C₄₃	C₄×#41	1	1	yes	characteristic
186	C₂²×C₄₃	C₄×#41	1	2	yes	—
187	C₂²×C₄₃	#518	1	1	yes	characteristic
188	C₂²×C₄₃	#518	1	2	yes	—
189	C₂²×C₄₃	#520	1	1	yes	characteristic
190	C₂²×C₄₃	#520	1	2	yes	—
191	C₂²×C₄₃	#546	1	2	yes	—
192	C₂²×C₄₃	D₄×Q₈	1	1	yes	characteristic
193	C₂²×C₄₃	#550	1	1	yes	characteristic
194	C₂²×C₄₃	#552	1	2	yes	—
195	C₂²×C₄₃	#553	1	2	yes	—
196	C₂²×C₄₃	#554	1	2	yes	—
197	C₂²×C₄₃	#554	1	2	yes	—
198	C₂²×C₄₃	#555	1	2	yes	—
199	C₂²×C₄₃	#557	1	1	yes	characteristic
200	C₂²×C₄₃	Q₈²	1	1	yes	characteristic
201	C₄×C₄₃	—	2	4	no	—
202	C₄×C₄₃	—	2	8	no	—
203	C₄×C₄₃	—	2	8	no	—
204	C₄×C₄₃	—	2	8	no	—
205	C₄×C₄₃	—	4	2	no	—
206	C₄×C₄₃	—	4	4	no	—
207	C₄×C₄₃	—	4	8	no	—
208	C₄×C₄₃	C₄×C₄⋊C₄	1	8	yes	—
209	C₂×#389	C₂×C₄₃	1	2	yes	—
210	C₂×C₄×C₄⋊C₄	C₂×C₄₃	1	2	yes	—
211	C₂×C₄×C₄⋊C₄	C₂×C₄₃	1	1	yes	characteristic
212	#1436	C₂×C₄₃	1	4	yes	—
213	C₄⋊#95	C₂×C₄₃	1	1	yes	characteristic
214	C₄⋊#95	C₂×C₄₃	1	2	yes	—
215	C₄×#95	C₂×C₄₃	1	1	yes	characteristic
216	C₄×#95	C₂×C₄₃	1	2	yes	—
217	C₂×C₄₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
218	C₂×C₄₃	C₄²×Q₈	1	1	yes	characteristic
219	C₂×C₄₃	#2275	1	1	yes	characteristic
220	C₂×C₄₃	#2345	1	1	yes	characteristic
221	C₂×C₄₃	#2346	1	1	yes	characteristic
222	C₂×C₄₃	#2349	1	1	yes	characteristic
223	C₂×C₄₃	Q₈×C₄⋊C₄	1	1	yes	characteristic
224	C₂×C₄₃	#2360	1	2	yes	—
225	C₂×C₄₃	#2363	1	2	yes	—
226	C₂×C₄₃	#2369	1	2	yes	—
227	C₂×C₄₃	#2370	1	2	yes	—
228	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
229	C₂²×C₄⋊C₄	C₂²×C₄₃	1	4	yes	—
230	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
231	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
232	C₂²×C₄²	C₂²×C₄₃	1	4	yes	—
233	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
234	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
235	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
236	#389	C₄×C₄₃	1	16	yes	complemented
237	C₄×C₄⋊C₄	—	2	8	no	—
238	C₄×C₄⋊C₄	C₄×C₄₃	1	8	yes	complemented
239	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
240	C₂×#95	C₂²×C₄₃	1	2	yes	—
241	C₂×#95	C₂²×C₄₃	1	2	yes	—
242	C₂×#95	C₂²×C₄₃	1	4	yes	—
243	C₂×#95	C₂²×C₄₃	1	2	yes	—
244	C₂×#95	C₂²×C₄₃	1	4	yes	—
245	C₂×#95	C₂²×C₄₃	1	2	yes	—
246	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
247	C₄₃	#13818	1	1	yes	characteristic, direct product factor, Sylow
248	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
249	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
250	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
251	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
252	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
253	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
254	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
255	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
256	C₂×C₄⋊C₄	—	2	4	no	—
257	C₂×C₄⋊C₄	—	2	4	no	—
258	C₂×C₄⋊C₄	—	4	4	no	—
259	C₂×C₄⋊C₄	—	4	4	no	—
260	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	8	yes	—
261	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	16	yes	—
262	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
263	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	8	yes	—
264	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
265	C₂×C₄⋊C₄	D₄×C₄₃	1	4	yes	—
266	C₂×C₄⋊C₄	Q₈×C₄₃	1	4	yes	—
267	C₂×C₄²	—	2	4	no	—
268	C₂×C₄²	—	2	4	no	—
269	C₂×C₄²	—	2	4	no	—
270	C₂×C₄²	—	2	8	no	—
271	C₂×C₄²	—	2	8	no	—
272	C₂×C₄²	—	4	4	no	—
273	C₂×C₄²	—	4	4	no	—
274	C₂×C₄²	C₂×C₄×C₄₃	1	4	yes	—
275	C₂×C₄²	C₂×C₄×C₄₃	1	8	yes	—
276	C₂×C₄²	C₂×C₄×C₄₃	1	8	yes	—
277	#95	—	2	8	no	—
278	#95	—	2	2	no	—
279	#95	—	2	4	no	—
280	#95	—	2	4	no	—
281	#95	—	4	2	no	—
282	#95	C₂×C₄×C₄₃	1	8	yes	—
283	#95	C₂×C₄×C₄₃	1	16	yes	—
284	#95	Q₈×C₄₃	1	4	yes	—
285	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
314	C₂²×C₄	C₂²×C₄×C₄₃	1	8	yes	—
315	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
316	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
317	C₂²×C₄	C₂²×C₄×C₄₃	1	8	yes	—
318	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
319	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
320	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
321	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
322	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
323	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
324	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
325	C₂²×C₄	C₂×Q₈×C₄₃	1	4	yes	—
326	C₂²×C₄	C₂×Q₈×C₄₃	1	4	yes	—
327	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
328	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
329	C₂²×C₄	#41×C₄₃	1	2	yes	—
330	C₂²×C₄	#41×C₄₃	1	4	yes	—
331	C₂²×C₄	#41×C₄₃	1	4	yes	—
332	C₄⋊C₄	—	2	16	no	—
333	C₄⋊C₄	—	4	16	no	—
334	C₄⋊C₄	C₄²×C₄₃	1	16	yes	complemented
335	C₄⋊C₄	C₄⋊C₄×C₄₃	1	16	yes	complemented
336	C₄²	—	2	8	no	—
337	C₄²	—	2	16	no	—
338	C₄²	—	4	8	no	—
339	C₄²	—	4	16	no	—
340	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
341	C₂³	C₂³×C₄×C₄₃	1	2	yes	—
342	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
343	C₂³	C₂²×Q₈×C₄₃	1	1	yes	characteristic
344	C₂³	C₂²×Q₈×C₄₃	1	1	yes	characteristic
345	C₂³	C₂×#41×C₄₃	1	2	yes	—
346	C₂³	C₂×#41×C₄₃	1	2	yes	—
347	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
348	C₂³	H(5,𝔽₂)×C₄₃	1	2	yes	—
349	C₂³	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
350	C₂³	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	8	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	8	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	8	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	8	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	8	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	8	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	8	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	4	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	C₂×C₄²×C₄₃	1	8	yes	—
389	C₂×C₄	C₂×C₄²×C₄₃	1	4	yes	—
390	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	8	yes	—
391	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	4	yes	—
392	C₂×C₄	#117×C₄₃	1	4	yes	—
393	C₂×C₄	C₄×D₄×C₄₃	1	8	yes	—
394	C₂×C₄	C₄×Q₈×C₄₃	1	4	yes	—
395	C₂×C₄	C₄×Q₈×C₄₃	1	8	yes	—
396	C₂×C₄	C₄×Q₈×C₄₃	1	8	yes	—
397	C₂²	C₂²×C₄²×C₄₃	1	1	yes	characteristic
398	C₂²	C₂²×C₄⋊C₄×C₄₃	1	1	yes	characteristic
399	C₂²	C₂×#117×C₄₃	1	1	yes	characteristic
400	C₂²	C₂×C₄×D₄×C₄₃	1	2	yes	—
401	C₂²	C₂×C₄×Q₈×C₄₃	1	1	yes	characteristic
402	C₂²	C₂×C₄×Q₈×C₄₃	1	2	yes	—
403	C₂²	C₂×C₄×Q₈×C₄₃	1	2	yes	—
404	C₂²	C₄×#41×C₄₃	1	1	yes	characteristic
405	C₂²	C₄×#41×C₄₃	1	2	yes	—
406	C₂²	C₄₃×#518	1	1	yes	characteristic
407	C₂²	C₄₃×#518	1	2	yes	—
408	C₂²	C₄₃×#520	1	1	yes	characteristic
409	C₂²	C₄₃×#520	1	2	yes	—
410	C₂²	C₄₃×#546	1	2	yes	—
411	C₂²	D₄×Q₈×C₄₃	1	1	yes	characteristic
412	C₂²	C₄₃×#550	1	1	yes	characteristic
413	C₂²	C₄₃×#552	1	2	yes	—
414	C₂²	C₄₃×#553	1	2	yes	—
415	C₂²	C₄₃×#554	1	2	yes	—
416	C₂²	C₄₃×#554	1	2	yes	—
417	C₂²	C₄₃×#555	1	2	yes	—
418	C₂²	C₄₃×#557	1	1	yes	characteristic
419	C₂²	Q₈²×C₄₃	1	1	yes	characteristic
420	C₄	—	2	4	no	—
421	C₄	—	2	8	no	—
422	C₄	—	2	8	no	—
423	C₄	—	2	8	no	—
424	C₄	—	4	2	no	—
425	C₄	—	4	4	no	—
426	C₄	—	4	8	no	—
427	C₄	C₄×C₄⋊C₄×C₄₃	1	8	yes	—
428	C₂	C₂×C₄×C₄⋊C₄×C₄₃	1	1	yes	characteristic
429	C₂	C₄²×Q₈×C₄₃	1	1	yes	characteristic
430	C₂	C₄₃×#2275	1	1	yes	characteristic
431	C₂	C₄₃×#2345	1	1	yes	characteristic
432	C₂	C₄₃×#2346	1	1	yes	characteristic
433	C₂	C₄₃×#2349	1	1	yes	characteristic
434	C₂	Q₈×C₄⋊C₄×C₄₃	1	1	yes	characteristic
435	C₂	C₄₃×#2360	1	2	yes	—
436	C₂	C₄₃×#2363	1	2	yes	—
437	C₂	C₄₃×#2369	1	2	yes	—
438	C₂	C₄₃×#2370	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₄₃	C₂⁴
commutator	C₂²	C₂²×C₄²×C₄₃
Frattini, cosocle	C₂⁴	C₂⁴×C₄₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
17. C₄₃×#389	C₄	semidirect
19. C₄×C₄⋊C₄×C₄₃	C₄	semidirect
114. C₄⋊C₄×C₄₃	C₄²	semidirect
115. C₄⋊C₄×C₄₃	C₄⋊C₄	semidirect
177. #13818	C₄₃	direct (N × H)
236. #389	C₄×C₄₃	semidirect
238. C₄×C₄⋊C₄	C₄×C₄₃	semidirect
247. C₄₃	#13818	direct (N × H)
334. C₄⋊C₄	C₄²×C₄₃	semidirect
335. C₄⋊C₄	C₄⋊C₄×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×#389	2
C₂×C₄×C₄⋊C₄×C₄₃	2
C₄₃×#1436	2
C₄₃×C₄⋊#95	2
C₄×#95×C₄₃	2
#13818	43

Subgroups — C43×#13818 #24933835

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#13818 #24933835