Subgroups — C₄₃×#23977 #24943994

Order 11008.

1286 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#555	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#419	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2409	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2024	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2000	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1895	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1877	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1873	C₂	1	2	yes	maximal, complemented
10	C₄₃×#1870	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1825	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
14	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
15	C₄₃×#555	—	2	4	no	—
16	C₄₃×#555	—	2	4	no	—
17	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×#124×C₄₃	—	2	1	no	—
19	C₂×#124×C₄₃	—	2	1	no	—
20	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
21	C₂×#121×C₄₃	—	2	1	no	—
22	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×#117×C₄₃	—	2	1	no	—
27	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
29	C₄₃×#448	—	2	4	no	—
30	C₄₃×#419	—	2	4	no	—
31	C₂×#103×C₄₃	C₂²	1	2	yes	—
32	C₂×#103×C₄₃	C₂²	1	2	yes	—
33	C₂×#103×C₄₃	C₂²	1	2	yes	—
34	C₂×#102×C₄₃	C₂²	1	2	yes	—
35	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
37	C₄₃×#395	—	2	1	no	—
38	C₄₃×#393	—	2	1	no	—
39	C₄₃×#391	C₂²	1	2	yes	—
40	C₄₃×#386	—	2	1	no	—
41	C₄₃×#385	—	2	1	no	—
42	C₄₃×#380	C₂²	1	1	yes	characteristic
43	C₄₃×#340	C₂²	1	2	yes	—
44	C₄₃×#340	C₂²	1	2	yes	—
45	C₄₃×#340	C₂²	1	2	yes	—
46	C₄₃×#336	C₂²	1	2	yes	—
47	C₂²×Q₈×C₄₃	—	2	1	no	—
48	C₂²×Q₈×C₄₃	—	2	1	no	—
49	C₂²×Q₈×C₄₃	—	2	4	no	—
50	C₂²×Q₈×C₄₃	—	2	2	no	—
51	C₂²×Q₈×C₄₃	—	2	2	no	—
52	C₂²×Q₈×C₄₃	—	4	2	no	—
53	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
54	C₂²×D₄×C₄₃	—	2	1	no	—
55	C₂²×D₄×C₄₃	—	2	1	no	—
56	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
57	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₄₃	—	2	1	no	—
59	C₂³×C₄×C₄₃	—	2	1	no	—
60	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
62	C₂×SD₁₆×C₄₃	—	2	4	no	—
63	C₂×SD₁₆×C₄₃	—	2	4	no	—
64	C₂×SD₁₆×C₄₃	—	4	2	no	—
65	C₂×M₁₆×C₄₃	—	2	2	no	—
66	C₂×M₁₆×C₄₃	—	4	2	no	—
67	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
68	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
69	C₄⋊Q₈×C₄₃	—	2	2	no	—
70	C₄⋊Q₈×C₄₃	—	2	2	no	—
71	#124×C₄₃	—	2	8	no	—
72	#124×C₄₃	—	2	8	no	—
73	C₂²⋊Q₈×C₄₃	—	2	4	no	—
74	C₂²⋊Q₈×C₄₃	—	4	2	no	—
75	#121×C₄₃	—	2	8	no	—
76	#121×C₄₃	—	2	2	no	—
77	#121×C₄₃	—	2	2	no	—
78	#121×C₄₃	—	2	2	no	—
79	#121×C₄₃	D₄	1	4	yes	—
80	C₄×D₄×C₄₃	—	2	2	no	—
81	C₄×D₄×C₄₃	—	2	2	no	—
82	C₄×D₄×C₄₃	—	2	2	no	—
83	C₄×D₄×C₄₃	—	2	2	no	—
84	#117×C₄₃	—	2	8	no	—
85	#117×C₄₃	—	2	2	no	—
86	#117×C₄₃	—	2	2	no	—
87	#117×C₄₃	—	2	2	no	—
88	#117×C₄₃	D₄	1	4	yes	—
89	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
90	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
91	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
102	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₄₃	—	2	1	no	—
106	C₂×C₄²×C₄₃	—	2	1	no	—
107	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
108	#103×C₄₃	—	2	4	no	—
109	#103×C₄₃	—	2	4	no	—
110	#103×C₄₃	—	2	4	no	—
111	#102×C₄₃	—	4	2	no	—
112	C₂²⋊C₈×C₄₃	—	2	2	no	—
113	C₂²⋊C₈×C₄₃	—	4	2	no	—
114	#95×C₄₃	—	2	1	no	—
115	#95×C₄₃	—	2	2	no	—
116	#95×C₄₃	—	2	2	no	—
117	C₂⁴×C₄₃	—	2	1	no	—
118	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
119	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
120	C₂×Q₈×C₄₃	—	2	4	no	—
121	C₂×Q₈×C₄₃	—	2	2	no	—
122	C₂×Q₈×C₄₃	—	2	8	no	—
123	C₂×Q₈×C₄₃	—	2	2	no	—
124	C₂×Q₈×C₄₃	—	2	2	no	—
125	C₂×Q₈×C₄₃	—	2	2	no	—
126	C₂×Q₈×C₄₃	—	2	2	no	—
127	C₂×Q₈×C₄₃	—	4	4	no	—
128	C₂×Q₈×C₄₃	—	4	8	no	—
129	C₂×Q₈×C₄₃	—	4	4	no	—
130	C₂×Q₈×C₄₃	—	4	2	no	—
131	C₂×Q₈×C₄₃	—	8	2	no	—
132	C₂×Q₈×C₄₃	#41	1	4	yes	—
133	C₂×D₄×C₄₃	—	2	4	no	—
134	C₂×D₄×C₄₃	—	2	2	no	—
135	C₂×D₄×C₄₃	—	2	1	no	—
136	C₂×D₄×C₄₃	—	2	2	no	—
137	C₂×D₄×C₄₃	—	2	4	no	—
138	C₂×D₄×C₄₃	—	2	2	no	—
139	C₂×D₄×C₄₃	—	2	2	no	—
140	C₂×D₄×C₄₃	—	4	1	no	—
141	C₂×D₄×C₄₃	—	8	2	no	—
142	C₂×D₄×C₄₃	—	8	2	no	—
143	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₄₃	—	2	2	no	—
145	C₂²×C₄×C₄₃	—	2	2	no	—
146	C₂²×C₄×C₄₃	—	2	4	no	—
147	C₂²×C₄×C₄₃	—	2	1	no	—
148	C₂²×C₄×C₄₃	—	2	1	no	—
149	C₂²×C₄×C₄₃	—	2	2	no	—
150	C₂²×C₄×C₄₃	—	2	2	no	—
151	C₂²×C₄×C₄₃	—	2	2	no	—
152	C₂²×C₄×C₄₃	—	2	1	no	—
153	C₂²×C₄×C₄₃	—	2	1	no	—
154	C₂²×C₄×C₄₃	—	2	1	no	—
155	C₂²×C₄×C₄₃	—	2	2	no	—
156	C₂²×C₄×C₄₃	—	4	4	no	—
157	C₂²×C₄×C₄₃	—	4	2	no	—
158	C₂²×C₄×C₄₃	—	4	2	no	—
159	C₂²×C₄×C₄₃	—	4	2	no	—
160	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
167	SD₁₆×C₄₃	—	4	8	no	—
168	M₁₆×C₄₃	—	4	4	no	—
169	C₂×C₈×C₄₃	—	2	2	no	—
170	C₂×C₈×C₄₃	—	2	2	no	—
171	C₂×C₈×C₄₃	—	2	2	no	—
172	C₂×C₈×C₄₃	—	2	2	no	—
173	C₂×C₈×C₄₃	—	2	2	no	—
174	C₂×C₈×C₄₃	—	2	2	no	—
175	C₄⋊C₄×C₄₃	—	2	4	no	—
176	C₄⋊C₄×C₄₃	—	2	2	no	—
177	C₄⋊C₄×C₄₃	—	2	1	no	—
178	C₄⋊C₄×C₄₃	—	2	1	no	—
179	C₄⋊C₄×C₄₃	—	2	1	no	—
180	C₄⋊C₄×C₄₃	—	2	2	no	—
181	C₄⋊C₄×C₄₃	—	2	2	no	—
182	C₄⋊C₄×C₄₃	—	4	4	no	—
183	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
184	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
185	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
186	C₂²⋊C₄×C₄₃	—	2	4	no	—
187	C₂²⋊C₄×C₄₃	—	2	4	no	—
188	C₂²⋊C₄×C₄₃	—	2	4	no	—
189	C₂²⋊C₄×C₄₃	—	2	4	no	—
190	C₂²⋊C₄×C₄₃	—	2	2	no	—
191	C₂²⋊C₄×C₄₃	—	2	4	no	—
192	C₂²⋊C₄×C₄₃	—	2	2	no	—
193	C₂²⋊C₄×C₄₃	—	4	4	no	—
194	C₂²⋊C₄×C₄₃	—	4	2	no	—
195	C₄²×C₄₃	—	2	4	no	—
196	C₄²×C₄₃	—	2	4	no	—
197	C₄²×C₄₃	—	2	1	no	—
198	C₄²×C₄₃	—	2	1	no	—
199	C₂³×C₄₃	—	2	2	no	—
200	C₂³×C₄₃	—	2	1	no	—
201	C₂³×C₄₃	—	2	1	no	—
202	C₂³×C₄₃	—	2	2	no	—
203	C₂³×C₄₃	—	2	1	no	—
204	C₂³×C₄₃	—	2	2	no	—
205	C₂³×C₄₃	—	2	2	no	—
206	C₂³×C₄₃	—	2	1	no	—
207	C₂³×C₄₃	—	2	1	no	—
208	C₂³×C₄₃	—	2	2	no	—
209	C₂³×C₄₃	—	4	2	no	—
210	C₂³×C₄₃	—	4	1	no	—
211	C₂³×C₄₃	—	4	1	no	—
212	C₂³×C₄₃	—	4	2	no	—
213	C₂³×C₄₃	#120	1	2	yes	—
214	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
215	Q₈×C₄₃	—	2	4	no	—
216	Q₈×C₄₃	—	2	4	no	—
217	Q₈×C₄₃	—	4	8	no	—
218	Q₈×C₄₃	—	4	2	no	—
219	Q₈×C₄₃	—	4	2	no	—
220	Q₈×C₄₃	—	8	4	no	—
221	D₄×C₄₃	—	2	4	no	—
222	D₄×C₄₃	—	4	4	no	—
223	D₄×C₄₃	—	4	1	no	—
224	D₄×C₄₃	—	4	1	no	—
225	D₄×C₄₃	—	8	4	no	—
226	D₄×C₄₃	—	8	4	no	—
227	C₂×C₄×C₄₃	—	2	1	no	—
228	C₂×C₄×C₄₃	—	2	2	no	—
229	C₂×C₄×C₄₃	—	2	1	no	—
230	C₂×C₄×C₄₃	—	2	2	no	—
231	C₂×C₄×C₄₃	—	2	2	no	—
232	C₂×C₄×C₄₃	—	2	4	no	—
233	C₂×C₄×C₄₃	—	2	1	no	—
234	C₂×C₄×C₄₃	—	2	2	no	—
235	C₂×C₄×C₄₃	—	2	1	no	—
236	C₂×C₄×C₄₃	—	2	2	no	—
237	C₂×C₄×C₄₃	—	2	2	no	—
238	C₂×C₄×C₄₃	—	2	4	no	—
239	C₂×C₄×C₄₃	—	2	2	no	—
240	C₂×C₄×C₄₃	—	2	2	no	—
241	C₂×C₄×C₄₃	—	4	8	no	—
242	C₂×C₄×C₄₃	—	4	8	no	—
243	C₂×C₄×C₄₃	—	4	2	no	—
244	C₂×C₄×C₄₃	—	4	2	no	—
245	C₂×C₄×C₄₃	—	4	1	no	—
246	C₂×C₄×C₄₃	—	4	1	no	—
247	C₂×C₄×C₄₃	—	4	2	no	—
248	C₂×C₄×C₄₃	—	4	2	no	—
249	C₂×C₄×C₄₃	—	4	1	no	—
250	C₂×C₄×C₄₃	—	4	1	no	—
251	C₂×C₄×C₄₃	—	4	2	no	—
252	C₂×C₄×C₄₃	—	4	2	no	—
253	C₂×C₄×C₄₃	—	4	2	no	—
254	C₂×C₄×C₄₃	—	4	2	no	—
255	C₂×C₄×C₄₃	#120	1	2	yes	—
256	C₂×C₄×C₄₃	#137	1	2	yes	—
257	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
260	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
261	C₈×C₄₃	—	4	2	no	—
262	C₈×C₄₃	—	4	2	no	—
263	#23977	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
264	C₂²×C₄₃	—	2	2	no	—
265	C₂²×C₄₃	—	2	2	no	—
266	C₂²×C₄₃	—	2	2	no	—
267	C₂²×C₄₃	—	4	2	no	—
268	C₂²×C₄₃	—	4	2	no	—
269	C₂²×C₄₃	—	4	2	no	—
270	C₂²×C₄₃	—	4	1	no	—
271	C₂²×C₄₃	—	4	2	no	—
272	C₂²×C₄₃	—	4	1	no	—
273	C₂²×C₄₃	—	4	2	no	—
274	C₂²×C₄₃	—	4	1	no	—
275	C₂²×C₄₃	—	4	2	no	—
276	C₂²×C₄₃	—	4	2	no	—
277	C₂²×C₄₃	—	8	2	no	—
278	C₂²×C₄₃	—	8	2	no	—
279	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
280	C₂²×C₄₃	#546	1	2	yes	—
281	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
282	C₂²×C₄₃	#575	1	1	yes	characteristic
283	C₂²×C₄₃	#577	1	2	yes	—
284	C₄×C₄₃	—	2	2	no	—
285	C₄×C₄₃	—	2	2	no	—
286	C₄×C₄₃	—	4	1	no	—
287	C₄×C₄₃	—	4	4	no	—
288	C₄×C₄₃	—	4	2	no	—
289	C₄×C₄₃	—	4	1	no	—
290	C₄×C₄₃	—	4	2	no	—
291	C₄×C₄₃	—	4	2	no	—
292	C₄×C₄₃	—	8	2	no	—
293	C₄×C₄₃	#525	1	1	yes	characteristic
294	C₄×C₄₃	#535	1	1	yes	characteristic
295	C₄×C₄₃	#546	1	2	yes	—
296	C₂×#555	C₂×C₄₃	1	1	yes	characteristic
297	C₂×#448	C₂×C₄₃	1	1	yes	characteristic, complemented
298	C₂×#419	C₂×C₄₃	1	1	yes	characteristic, complemented
299	#2409	C₂×C₄₃	1	1	yes	characteristic, complemented
300	#2024	C₂×C₄₃	1	2	yes	complemented
301	#2000	C₂×C₄₃	1	2	yes	complemented
302	#1895	C₂×C₄₃	1	1	yes	characteristic, complemented
303	#1877	C₂×C₄₃	1	2	yes	complemented
304	#1873	C₂×C₄₃	1	2	yes	complemented
305	#1870	C₂×C₄₃	1	1	yes	characteristic, complemented
306	#1825	C₂×C₄₃	1	1	yes	characteristic, complemented
307	C₂×C₄₃	—	4	2	no	—
308	C₂×C₄₃	—	8	1	no	—
309	C₂×C₄₃	—	8	2	no	—
310	C₂×C₄₃	#2404	1	1	yes	characteristic
311	C₂×C₄₃	#3007	1	1	yes	characteristic
312	C₂×C₄₃	#3009	1	1	yes	characteristic
313	C₂×C₄₃	#3321	1	2	yes	—
314	C₂×C₄₃	#3329	1	2	yes	—
315	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic
316	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
317	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
318	#555	—	2	4	no	—
319	#555	—	2	4	no	—
320	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
321	C₂×#124	—	2	1	no	—
322	C₂×#124	—	2	1	no	—
323	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
324	C₂×#121	—	2	1	no	—
325	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
326	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
327	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
328	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
329	C₂×#117	—	2	1	no	—
330	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
331	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
332	#448	—	2	4	no	—
333	#419	—	2	4	no	—
334	C₂×#103	C₂²×C₄₃	1	2	yes	—
335	C₂×#103	C₂²×C₄₃	1	2	yes	—
336	C₂×#103	C₂²×C₄₃	1	2	yes	—
337	C₂×#102	C₂²×C₄₃	1	2	yes	—
338	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
339	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
340	#395	—	2	1	no	—
341	#393	—	2	1	no	—
342	#391	C₂²×C₄₃	1	2	yes	—
343	#386	—	2	1	no	—
344	#385	—	2	1	no	—
345	#380	C₂²×C₄₃	1	1	yes	characteristic
346	#340	C₂²×C₄₃	1	2	yes	—
347	#340	C₂²×C₄₃	1	2	yes	—
348	#340	C₂²×C₄₃	1	2	yes	—
349	#336	C₂²×C₄₃	1	2	yes	—
350	C₄₃	#23977	1	1	yes	characteristic, direct product factor, Sylow
351	C₂²×Q₈	—	2	1	no	—
352	C₂²×Q₈	—	2	1	no	—
353	C₂²×Q₈	—	2	4	no	—
354	C₂²×Q₈	—	2	2	no	—
355	C₂²×Q₈	—	2	2	no	—
356	C₂²×Q₈	—	4	2	no	—
357	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
358	C₂²×D₄	—	2	1	no	—
359	C₂²×D₄	—	2	1	no	—
360	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
361	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
362	C₂³×C₄	—	2	1	no	—
363	C₂³×C₄	—	2	1	no	—
364	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
365	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
366	C₂×SD₁₆	—	2	4	no	—
367	C₂×SD₁₆	—	2	4	no	—
368	C₂×SD₁₆	—	4	2	no	—
369	C₂×M₁₆	—	2	2	no	—
370	C₂×M₁₆	—	4	2	no	—
371	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
372	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
373	C₄⋊Q₈	—	2	2	no	—
374	C₄⋊Q₈	—	2	2	no	—
375	#124	—	2	8	no	—
376	#124	—	2	8	no	—
377	C₂²⋊Q₈	—	2	4	no	—
378	C₂²⋊Q₈	—	4	2	no	—
379	#121	—	2	8	no	—
380	#121	—	2	2	no	—
381	#121	—	2	2	no	—
382	#121	—	2	2	no	—
383	#121	D₄×C₄₃	1	4	yes	—
384	C₄×D₄	—	2	2	no	—
385	C₄×D₄	—	2	2	no	—
386	C₄×D₄	—	2	2	no	—
387	C₄×D₄	—	2	2	no	—
388	#117	—	2	8	no	—
389	#117	—	2	2	no	—
390	#117	—	2	2	no	—
391	#117	—	2	2	no	—
392	#117	D₄×C₄₃	1	4	yes	—
393	C₂×C₄⋊C₄	—	2	1	no	—
394	C₂×C₄⋊C₄	—	2	2	no	—
395	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
397	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
400	C₂×C₂²⋊C₄	—	2	1	no	—
401	C₂×C₂²⋊C₄	—	2	1	no	—
402	C₂×C₂²⋊C₄	—	2	1	no	—
403	C₂×C₂²⋊C₄	—	2	1	no	—
404	C₂×C₂²⋊C₄	—	2	1	no	—
405	C₂×C₂²⋊C₄	—	2	2	no	—
406	C₂×C₂²⋊C₄	—	2	1	no	—
407	C₂×C₂²⋊C₄	D₄×C₄₃	1	1	yes	characteristic
408	C₂×C₂²⋊C₄	D₄×C₄₃	1	1	yes	characteristic
409	C₂×C₄²	—	2	1	no	—
410	C₂×C₄²	—	2	1	no	—
411	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
412	#103	—	2	4	no	—
413	#103	—	2	4	no	—
414	#103	—	2	4	no	—
415	#102	—	4	2	no	—
416	C₂²⋊C₈	—	2	2	no	—
417	C₂²⋊C₈	—	4	2	no	—
418	#95	—	2	1	no	—
419	#95	—	2	2	no	—
420	#95	—	2	2	no	—
421	C₂⁴	—	2	1	no	—
422	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
423	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
424	C₂×Q₈	—	2	4	no	—
425	C₂×Q₈	—	2	2	no	—
426	C₂×Q₈	—	2	8	no	—
427	C₂×Q₈	—	2	2	no	—
428	C₂×Q₈	—	2	2	no	—
429	C₂×Q₈	—	2	2	no	—
430	C₂×Q₈	—	2	2	no	—
431	C₂×Q₈	—	4	4	no	—
432	C₂×Q₈	—	4	8	no	—
433	C₂×Q₈	—	4	4	no	—
434	C₂×Q₈	—	4	2	no	—
435	C₂×Q₈	—	8	2	no	—
436	C₂×Q₈	#41×C₄₃	1	4	yes	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	4	no	—
439	C₂×D₄	—	2	4	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	2	no	—
444	C₂×D₄	—	4	1	no	—
445	C₂×D₄	—	8	2	no	—
446	C₂×D₄	—	8	2	no	—
447	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	4	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	4	4	no	—
461	C₂²×C₄	—	4	2	no	—
462	C₂²×C₄	—	4	2	no	—
463	C₂²×C₄	—	4	2	no	—
464	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
465	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
466	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
467	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
468	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
469	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
470	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
471	SD₁₆	—	4	8	no	—
472	M₁₆	—	4	4	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	2	2	no	—
477	C₂×C₈	—	2	2	no	—
478	C₂×C₈	—	2	2	no	—
479	C₄⋊C₄	—	2	4	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	4	4	no	—
487	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
488	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
489	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
490	C₂²⋊C₄	—	2	4	no	—
491	C₂²⋊C₄	—	2	4	no	—
492	C₂²⋊C₄	—	2	4	no	—
493	C₂²⋊C₄	—	2	4	no	—
494	C₂²⋊C₄	—	2	2	no	—
495	C₂²⋊C₄	—	2	4	no	—
496	C₂²⋊C₄	—	2	2	no	—
497	C₂²⋊C₄	—	4	4	no	—
498	C₂²⋊C₄	—	4	2	no	—
499	C₄²	—	2	4	no	—
500	C₄²	—	2	4	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	2	1	no	—
503	C₂³	—	2	2	no	—
504	C₂³	—	2	1	no	—
505	C₂³	—	2	1	no	—
506	C₂³	—	2	2	no	—
507	C₂³	—	2	1	no	—
508	C₂³	—	2	2	no	—
509	C₂³	—	2	2	no	—
510	C₂³	—	2	1	no	—
511	C₂³	—	2	1	no	—
512	C₂³	—	2	2	no	—
513	C₂³	—	4	2	no	—
514	C₂³	—	4	1	no	—
515	C₂³	—	4	1	no	—
516	C₂³	—	4	2	no	—
517	C₂³	#120×C₄₃	1	2	yes	—
518	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
519	Q₈	—	2	4	no	—
520	Q₈	—	2	4	no	—
521	Q₈	—	4	8	no	—
522	Q₈	—	4	2	no	—
523	Q₈	—	4	2	no	—
524	Q₈	—	8	4	no	—
525	D₄	—	2	4	no	—
526	D₄	—	4	4	no	—
527	D₄	—	4	1	no	—
528	D₄	—	4	1	no	—
529	D₄	—	8	4	no	—
530	D₄	—	8	4	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	4	8	no	—
546	C₂×C₄	—	4	8	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	#120×C₄₃	1	2	yes	—
560	C₂×C₄	#137×C₄₃	1	2	yes	—
561	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
562	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
563	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
564	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
565	C₈	—	4	2	no	—
566	C₈	—	4	2	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	4	2	no	—
571	C₂²	—	4	2	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	2	no	—
574	C₂²	—	4	2	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	2	no	—
578	C₂²	—	4	2	no	—
579	C₂²	—	4	2	no	—
580	C₂²	—	8	2	no	—
581	C₂²	—	8	2	no	—
582	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
583	C₂²	C₄₃×#546	1	2	yes	—
584	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
585	C₂²	C₄₃×#575	1	1	yes	characteristic
586	C₂²	C₄₃×#577	1	2	yes	—
587	C₄	—	2	2	no	—
588	C₄	—	2	2	no	—
589	C₄	—	4	1	no	—
590	C₄	—	4	4	no	—
591	C₄	—	4	2	no	—
592	C₄	—	4	1	no	—
593	C₄	—	4	2	no	—
594	C₄	—	4	2	no	—
595	C₄	—	8	2	no	—
596	C₄	C₄₃×#525	1	1	yes	characteristic
597	C₄	C₄₃×#535	1	1	yes	characteristic
598	C₄	C₄₃×#546	1	2	yes	—
599	C₂	—	4	2	no	—
600	C₂	—	8	1	no	—
601	C₂	—	8	2	no	—
602	C₂	C₄₃×#2404	1	1	yes	characteristic
603	C₂	C₄₃×#3007	1	1	yes	characteristic
604	C₂	C₄₃×#3009	1	1	yes	characteristic
605	C₂	C₄₃×#3321	1	2	yes	—
606	C₂	C₄₃×#3329	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×C₄₃×#555	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂×C₄×D₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₃×#448	C₂	semidirect
3. C₂×C₄₃×#419	C₂	semidirect
4. C₄₃×#2409	C₂	semidirect
5. C₄₃×#2024	C₂	semidirect
6. C₄₃×#2000	C₂	semidirect
7. C₄₃×#1895	C₂	semidirect
8. C₄₃×#1877	C₂	semidirect
9. C₄₃×#1873	C₂	semidirect
10. C₄₃×#1870	C₂	semidirect
11. C₄₃×#1825	C₂	semidirect
263. #23977	C₄₃	direct (N × H)
297. C₂×#448	C₂×C₄₃	semidirect
298. C₂×#419	C₂×C₄₃	semidirect
299. #2409	C₂×C₄₃	semidirect
300. #2024	C₂×C₄₃	semidirect
301. #2000	C₂×C₄₃	semidirect
302. #1895	C₂×C₄₃	semidirect
303. #1877	C₂×C₄₃	semidirect
304. #1873	C₂×C₄₃	semidirect
305. #1870	C₂×C₄₃	semidirect
306. #1825	C₂×C₄₃	semidirect
350. C₄₃	#23977	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×#555	2
C₂×C₄₃×#448	2
C₂×C₄₃×#419	2
C₄₃×#2409	2
C₄₃×#2024	2
C₄₃×#2000	2
C₄₃×#1895	2
C₄₃×#1877	2
C₄₃×#1873	2
C₄₃×#1870	2
C₄₃×#1825	2
#23977	43

Subgroups — C43×#23977 #24943994

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#23977 #24943994