Subgroups — C₄×C₄₃×#419 #24940430

Order 11008.

1586 conjugacy classes of subgroups.

The subgroup lattice has 398 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×#419	C₂	1	2	yes	maximal
3	C₂×C₄×M₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₄×#117×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#1763	C₂	1	4	yes	maximal, complemented
6	C₄×#103×C₄₃	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1736	C₂	1	2	yes	maximal
8	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
10	C₂×C₄×Q₈×C₄₃	—	2	4	no	—
11	C₂×C₄×Q₈×C₄₃	—	2	1	no	—
12	C₂×C₄×Q₈×C₄₃	—	2	1	no	—
13	C₂×C₄×Q₈×C₄₃	C₄	1	8	yes	complemented
14	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	—
16	C₂×#117×C₄₃	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₄₃	—	2	1	no	—
18	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₄₃	—	2	1	no	—
20	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
21	C₄₃×#419	C₄	1	16	yes	direct product factor
22	C₂×#103×C₄₃	C₂²	1	8	yes	—
23	C₄×M₁₆×C₄₃	—	2	4	no	—
24	C₂×#97×C₄₃	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	—
26	C₄×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
27	C₄×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
28	C₄×C₂²⋊C₄×C₄₃	—	2	1	no	—
29	C₄×C₂²⋊C₄×C₄₃	—	2	1	no	—
30	C₄₃×#376	—	2	1	no	—
31	C₄³×C₄₃	—	2	1	no	—
32	C₄₃×#340	C₂²	1	8	yes	—
33	C₂²×Q₈×C₄₃	—	2	2	no	—
34	C₂²×Q₈×C₄₃	—	2	1	no	—
35	C₂²×Q₈×C₄₃	—	2	4	no	—
36	C₂²×Q₈×C₄₃	C₂×C₄	1	4	yes	—
37	C₂²×Q₈×C₄₃	C₂×C₄	1	8	yes	—
38	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
39	C₂³×C₄×C₄₃	—	2	1	no	—
40	C₂³×C₄×C₄₃	—	2	1	no	—
41	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
44	C₂×M₁₆×C₄₃	—	2	4	no	—
45	C₂×M₁₆×C₄₃	—	2	4	no	—
46	C₂×M₁₆×C₄₃	C₂×C₄	1	8	yes	—
47	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
48	C₄×Q₈×C₄₃	—	2	8	no	—
49	C₄×Q₈×C₄₃	—	2	8	no	—
50	C₄×Q₈×C₄₃	—	2	4	no	—
51	C₄×Q₈×C₄₃	—	2	4	no	—
52	C₄×Q₈×C₄₃	C₂×C₄	1	8	yes	—
53	C₄×Q₈×C₄₃	C₂×C₄	1	8	yes	—
54	#117×C₄₃	—	2	4	no	—
55	#117×C₄₃	C₂×C₄	1	8	yes	—
56	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
57	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
58	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
59	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
60	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
61	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
62	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
64	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
65	C₂×C₄²×C₄₃	—	2	8	no	—
66	C₂×C₄²×C₄₃	—	2	2	no	—
67	C₂×C₄²×C₄₃	—	2	2	no	—
68	C₂×C₄²×C₄₃	—	2	2	no	—
69	C₂×C₄²×C₄₃	—	2	2	no	—
70	C₂×C₄²×C₄₃	—	2	2	no	—
71	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
72	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₄₃	D₄	1	4	yes	—
75	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
77	#103×C₄₃	C₂×C₄	1	32	yes	complemented
78	#97×C₄₃	—	2	4	no	—
79	C₄×C₈×C₄₃	—	2	4	no	—
80	#95×C₄₃	—	2	2	no	—
81	#95×C₄₃	—	2	2	no	—
82	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
83	C₂×Q₈×C₄₃	—	2	4	no	—
84	C₂×Q₈×C₄₃	—	2	8	no	—
85	C₂×Q₈×C₄₃	—	2	8	no	—
86	C₂×Q₈×C₄₃	—	2	16	no	—
87	C₂×Q₈×C₄₃	—	2	2	no	—
88	C₂×Q₈×C₄₃	—	2	4	no	—
89	C₂×Q₈×C₄₃	C₄²	1	16	yes	complemented
90	C₂×Q₈×C₄₃	C₂²×C₄	1	8	yes	—
91	C₂×Q₈×C₄₃	C₂²×C₄	1	4	yes	—
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	8	no	—
96	C₂²×C₄×C₄₃	—	2	2	no	—
97	C₂²×C₄×C₄₃	—	2	4	no	—
98	C₂²×C₄×C₄₃	—	2	2	no	—
99	C₂²×C₄×C₄₃	—	4	2	no	—
100	C₂²×C₄×C₄₃	—	4	4	no	—
101	C₂²×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
102	C₂²×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
103	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
105	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	#41	1	4	yes	—
112	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
113	M₁₆×C₄₃	—	2	16	no	—
114	C₂×C₈×C₄₃	—	2	4	no	—
115	C₂×C₈×C₄₃	—	2	4	no	—
116	C₂×C₈×C₄₃	C₂²×C₄	1	8	yes	—
117	C₄⋊C₄×C₄₃	—	2	8	no	—
118	C₄⋊C₄×C₄₃	—	2	8	no	—
119	C₄⋊C₄×C₄₃	—	2	4	no	—
120	C₄⋊C₄×C₄₃	—	2	2	no	—
121	C₄⋊C₄×C₄₃	—	2	4	no	—
122	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
123	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
124	C₂²⋊C₄×C₄₃	—	2	8	no	—
125	C₄²×C₄₃	—	2	8	no	—
126	C₄²×C₄₃	—	2	8	no	—
127	C₄²×C₄₃	—	2	8	no	—
128	C₄²×C₄₃	—	4	4	no	—
129	C₄²×C₄₃	—	4	4	no	—
130	C₄²×C₄₃	C₂²⋊C₄	1	4	yes	—
131	C₄²×C₄₃	C₂²⋊C₄	1	4	yes	—
132	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
133	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
134	C₄²×C₄₃	C₂×D₄	1	2	yes	—
135	C₄²×C₄₃	C₂×D₄	1	2	yes	—
136	C₂³×C₄₃	—	2	2	no	—
137	C₂³×C₄₃	—	2	2	no	—
138	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
139	C₂³×C₄₃	C₄×D₄	1	4	yes	—
140	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
141	Q₈×C₄₃	—	2	4	no	—
142	Q₈×C₄₃	—	2	8	no	—
143	Q₈×C₄₃	—	2	16	no	—
144	Q₈×C₄₃	C₂×C₄²	1	8	yes	—
145	C₂×C₄×C₄₃	—	2	4	no	—
146	C₂×C₄×C₄₃	—	2	8	no	—
147	C₂×C₄×C₄₃	—	2	2	no	—
148	C₂×C₄×C₄₃	—	2	2	no	—
149	C₂×C₄×C₄₃	—	2	2	no	—
150	C₂×C₄×C₄₃	—	2	16	no	—
151	C₂×C₄×C₄₃	—	2	8	no	—
152	C₂×C₄×C₄₃	—	2	4	no	—
153	C₂×C₄×C₄₃	—	2	8	no	—
154	C₂×C₄×C₄₃	—	4	4	no	—
155	C₂×C₄×C₄₃	—	4	8	no	—
156	C₂×C₄×C₄₃	—	4	4	no	—
157	C₂×C₄×C₄₃	—	4	4	no	—
158	C₂×C₄×C₄₃	—	4	4	no	—
159	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
160	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
161	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
162	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
163	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
164	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂×C₄×C₄₃	#117	1	4	yes	—
166	C₂×C₄×C₄₃	C₄×D₄	1	8	yes	—
167	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
168	C₂×C₄×C₄₃	#137	1	4	yes	—
169	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
171	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
173	C₈×C₄₃	—	2	8	no	—
174	C₄×#419	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂²×C₄₃	—	2	2	no	—
176	C₂²×C₄₃	—	2	2	no	—
177	C₂²×C₄₃	—	2	8	no	—
178	C₂²×C₄₃	C₄×C₂²⋊C₄	1	4	yes	—
179	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
180	C₂²×C₄₃	C₂×C₄×D₄	1	2	yes	—
181	C₂²×C₄₃	C₂×#137	1	2	yes	—
182	C₂²×C₄₃	#575	1	2	yes	—
183	C₄×C₄₃	—	2	2	no	—
184	C₄×C₄₃	—	2	2	no	—
185	C₄×C₄₃	—	2	2	no	—
186	C₄×C₄₃	—	2	8	no	—
187	C₄×C₄₃	—	4	4	no	—
188	C₄×C₄₃	—	4	8	no	—
189	C₄×C₄₃	C₄×C₂²⋊C₄	1	4	yes	—
190	C₄×C₄₃	#419	1	4	yes	direct product factor
191	C₄×C₄₃	C₂²×C₄²	1	1	yes	characteristic
192	C₄×C₄₃	C₂×#117	1	1	yes	characteristic
193	C₄×C₄₃	C₂×C₄×D₄	1	2	yes	—
194	C₂²×C₄×Q₈	C₂×C₄₃	1	1	yes	characteristic
195	C₂×#419	C₂×C₄₃	1	2	yes	—
196	C₂×C₄×M₁₆	C₂×C₄₃	1	1	yes	characteristic
197	C₄×#117	C₂×C₄₃	1	1	yes	characteristic
198	#1763	C₂×C₄₃	1	4	yes	complemented
199	C₄×#103	C₂×C₄₃	1	4	yes	complemented
200	#1736	C₂×C₄₃	1	2	yes	—
201	C₂×C₄₃	—	2	4	no	—
202	C₂×C₄₃	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
203	C₂×C₄₃	C₂×#419	1	1	yes	characteristic
204	C₂×C₄₃	#2896	1	1	yes	characteristic
205	C₂×C₄₃	C₄×#137	1	4	yes	—
206	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic
207	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	—
208	C₂×C₄×Q₈	—	2	4	no	—
209	C₂×C₄×Q₈	—	2	1	no	—
210	C₂×C₄×Q₈	—	2	1	no	—
211	C₂×C₄×Q₈	C₄×C₄₃	1	8	yes	complemented
212	C₂×C₄×Q₈	C₂²×C₄₃	1	2	yes	—
213	C₂×C₄×Q₈	C₂²×C₄₃	1	2	yes	—
214	C₂×#117	C₂²×C₄₃	1	2	yes	—
215	C₂²×C₄⋊C₄	—	2	1	no	—
216	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
217	C₂²×C₄²	—	2	1	no	—
218	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
219	#419	C₄×C₄₃	1	16	yes	direct product factor
220	C₂×#103	C₂²×C₄₃	1	8	yes	—
221	C₄×M₁₆	—	2	4	no	—
222	C₂×#97	C₂²×C₄₃	1	2	yes	—
223	C₂×C₄×C₈	C₂²×C₄₃	1	2	yes	—
224	C₄×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
225	C₄×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
226	C₄×C₂²⋊C₄	—	2	1	no	—
227	C₄×C₂²⋊C₄	—	2	1	no	—
228	#376	—	2	1	no	—
229	C₄³	—	2	1	no	—
230	#340	C₂²×C₄₃	1	8	yes	—
231	C₄₃	C₄×#419	1	1	yes	characteristic, direct product factor, Sylow
232	C₂²×Q₈	—	2	2	no	—
233	C₂²×Q₈	—	2	1	no	—
234	C₂²×Q₈	—	2	4	no	—
235	C₂²×Q₈	C₂×C₄×C₄₃	1	4	yes	—
236	C₂²×Q₈	C₂×C₄×C₄₃	1	8	yes	—
237	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
238	C₂³×C₄	—	2	1	no	—
239	C₂³×C₄	—	2	1	no	—
240	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
241	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
242	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
243	C₂×M₁₆	—	2	4	no	—
244	C₂×M₁₆	—	2	4	no	—
245	C₂×M₁₆	C₂×C₄×C₄₃	1	8	yes	—
246	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
247	C₄×Q₈	—	2	8	no	—
248	C₄×Q₈	—	2	8	no	—
249	C₄×Q₈	—	2	4	no	—
250	C₄×Q₈	—	2	4	no	—
251	C₄×Q₈	C₂×C₄×C₄₃	1	8	yes	—
252	C₄×Q₈	C₂×C₄×C₄₃	1	8	yes	—
253	#117	—	2	4	no	—
254	#117	C₂×C₄×C₄₃	1	8	yes	—
255	C₂×C₄⋊C₄	—	2	8	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
261	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
262	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
263	C₂×C₂²⋊C₄	—	2	2	no	—
264	C₂×C₄²	—	2	8	no	—
265	C₂×C₄²	—	2	2	no	—
266	C₂×C₄²	—	2	2	no	—
267	C₂×C₄²	—	2	2	no	—
268	C₂×C₄²	—	2	2	no	—
269	C₂×C₄²	—	2	2	no	—
270	C₂×C₄²	C₂×C₄×C₄₃	1	4	yes	—
271	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
272	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
273	C₂×C₄²	D₄×C₄₃	1	4	yes	—
274	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
276	#103	C₂×C₄×C₄₃	1	32	yes	complemented
277	#97	—	2	4	no	—
278	C₄×C₈	—	2	4	no	—
279	#95	—	2	2	no	—
280	#95	—	2	2	no	—
281	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
282	C₂×Q₈	—	2	4	no	—
283	C₂×Q₈	—	2	8	no	—
284	C₂×Q₈	—	2	8	no	—
285	C₂×Q₈	—	2	16	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	4	no	—
288	C₂×Q₈	C₄²×C₄₃	1	16	yes	complemented
289	C₂×Q₈	C₂²×C₄×C₄₃	1	8	yes	—
290	C₂×Q₈	C₂²×C₄×C₄₃	1	4	yes	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	8	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	4	2	no	—
299	C₂²×C₄	—	4	4	no	—
300	C₂²×C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
301	C₂²×C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
302	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
303	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
304	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
310	C₂²×C₄	#41×C₄₃	1	4	yes	—
311	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
312	M₁₆	—	2	16	no	—
313	C₂×C₈	—	2	4	no	—
314	C₂×C₈	—	2	4	no	—
315	C₂×C₈	C₂²×C₄×C₄₃	1	8	yes	—
316	C₄⋊C₄	—	2	8	no	—
317	C₄⋊C₄	—	2	8	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	4	no	—
321	C₄⋊C₄	C₂²×C₄×C₄₃	1	8	yes	—
322	C₄⋊C₄	C₂²×C₄×C₄₃	1	4	yes	—
323	C₂²⋊C₄	—	2	8	no	—
324	C₄²	—	2	8	no	—
325	C₄²	—	2	8	no	—
326	C₄²	—	2	8	no	—
327	C₄²	—	4	4	no	—
328	C₄²	—	4	4	no	—
329	C₄²	C₂²⋊C₄×C₄₃	1	4	yes	—
330	C₄²	C₂²⋊C₄×C₄₃	1	4	yes	—
331	C₄²	C₂²×C₄×C₄₃	1	2	yes	—
332	C₄²	C₂²×C₄×C₄₃	1	2	yes	—
333	C₄²	C₂×D₄×C₄₃	1	2	yes	—
334	C₄²	C₂×D₄×C₄₃	1	2	yes	—
335	C₂³	—	2	2	no	—
336	C₂³	—	2	2	no	—
337	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
338	C₂³	C₄×D₄×C₄₃	1	4	yes	—
339	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
340	Q₈	—	2	4	no	—
341	Q₈	—	2	8	no	—
342	Q₈	—	2	16	no	—
343	Q₈	C₂×C₄²×C₄₃	1	8	yes	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	8	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	16	no	—
350	C₂×C₄	—	2	8	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	8	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	4	8	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	C₂×C₄²×C₄₃	1	4	yes	—
359	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
360	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
361	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
362	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
363	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
364	C₂×C₄	#117×C₄₃	1	4	yes	—
365	C₂×C₄	C₄×D₄×C₄₃	1	8	yes	—
366	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
367	C₂×C₄	#137×C₄₃	1	4	yes	—
368	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
369	C₂×C₄	C₂³×C₄×C₄₃	1	2	yes	—
370	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
371	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
372	C₈	—	2	8	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	8	no	—
376	C₂²	C₄×C₂²⋊C₄×C₄₃	1	4	yes	—
377	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
378	C₂²	C₂×C₄×D₄×C₄₃	1	2	yes	—
379	C₂²	C₂×#137×C₄₃	1	2	yes	—
380	C₂²	C₄₃×#575	1	2	yes	—
381	C₄	—	2	2	no	—
382	C₄	—	2	2	no	—
383	C₄	—	2	2	no	—
384	C₄	—	2	8	no	—
385	C₄	—	4	4	no	—
386	C₄	—	4	8	no	—
387	C₄	C₄×C₂²⋊C₄×C₄₃	1	4	yes	—
388	C₄	C₄₃×#419	1	4	yes	direct product factor
389	C₄	C₂²×C₄²×C₄₃	1	1	yes	characteristic
390	C₄	C₂×#117×C₄₃	1	1	yes	characteristic
391	C₄	C₂×C₄×D₄×C₄₃	1	2	yes	—
392	C₂	—	2	4	no	—
393	C₂	C₂×C₄×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
394	C₂	C₂×C₄₃×#419	1	1	yes	characteristic
395	C₂	C₄₃×#2896	1	1	yes	characteristic
396	C₂	C₄×#137×C₄₃	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₄₃	C₂×D₄
commutator	C₄	C₂²×C₄²×C₄₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂⁴×C₄₃	C₂×D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₃ ◁ C₂²×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₄₃×#1763	C₂	semidirect
6. C₄×#103×C₄₃	C₂	semidirect
13. C₂×C₄×Q₈×C₄₃	C₄	semidirect
21. C₄₃×#419	C₄	direct (N × H)
77. #103×C₄₃	C₂×C₄	semidirect
89. C₂×Q₈×C₄₃	C₄²	semidirect
174. C₄×#419	C₄₃	direct (N × H)
190. C₄×C₄₃	#419	direct (N × H)
198. #1763	C₂×C₄₃	semidirect
199. C₄×#103	C₂×C₄₃	semidirect
211. C₂×C₄×Q₈	C₄×C₄₃	semidirect
219. #419	C₄×C₄₃	direct (N × H)
231. C₄₃	C₄×#419	direct (N × H)
276. #103	C₂×C₄×C₄₃	semidirect
288. C₂×Q₈	C₄²×C₄₃	semidirect
388. C₄	C₄₃×#419	direct (N × H)

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×#419	2
C₂×C₄×M₁₆×C₄₃	2
C₄×#117×C₄₃	2
C₄₃×#1763	2
C₄×#103×C₄₃	2
C₄₃×#1736	2
C₄×#419	43

Subgroups — C4×C43×#419 #24940430

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₄₃×#419 #24940430