Subgroups — C₄₃×#25733 #24945750

Order 11008.

1566 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#496	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#492	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₃×#449	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₃×#448	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2619	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#2013	C₂	1	2	yes	maximal, complemented
8	C₄₃×#2012	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1960	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1958	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1750	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
13	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
15	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
16	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
17	C₂²×D₈×C₄₃	C₂²	1	2	yes	—
18	C₄₃×#536	—	2	4	no	—
19	C₄₃×#536	—	2	4	no	—
20	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×#123×C₄₃	—	2	2	no	—
26	C₂×C₂²⋊Q₈×C₄₃	—	2	2	no	—
27	C₂×#121×C₄₃	C₂²	1	2	yes	—
28	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
29	C₄₃×#496	—	2	4	no	—
30	C₄₃×#492	—	2	4	no	—
31	C₄₃×#449	—	2	8	no	—
32	C₄₃×#448	—	2	8	no	—
33	C₂×#103×C₄₃	C₂²	1	2	yes	—
34	C₂×#103×C₄₃	C₂²	1	2	yes	—
35	C₂×#103×C₄₃	C₂²	1	2	yes	—
36	C₂×#102×C₄₃	C₂²	1	2	yes	—
37	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
38	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
40	C₄₃×#394	—	2	2	no	—
41	C₄₃×#392	—	2	2	no	—
42	C₄₃×#390	C₂²	1	2	yes	—
43	C₄₃×#382	C₂²	1	1	yes	characteristic
44	C₄₃×#336	C₂²	1	2	yes	—
45	C₂×#41×C₄₃	—	2	2	no	—
46	C₂×#41×C₄₃	—	2	2	no	—
47	C₂×#41×C₄₃	—	2	4	no	—
48	C₂×#41×C₄₃	—	4	2	no	—
49	C₂²×Q₈×C₄₃	—	2	2	no	—
50	C₂²×Q₈×C₄₃	—	2	2	no	—
51	C₂²×Q₈×C₄₃	—	2	1	no	—
52	C₂²×Q₈×C₄₃	—	2	4	no	—
53	C₂²×Q₈×C₄₃	—	4	2	no	—
54	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
55	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
56	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
57	C₂²×D₄×C₄₃	—	2	1	no	—
58	C₂²×D₄×C₄₃	—	2	2	no	—
59	C₂²×D₄×C₄₃	—	2	2	no	—
60	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
61	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₄₃	—	2	1	no	—
63	C₂³×C₄×C₄₃	—	2	1	no	—
64	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
65	C₂×SD₁₆×C₄₃	—	2	4	no	—
66	C₂×SD₁₆×C₄₃	—	2	4	no	—
67	C₂×SD₁₆×C₄₃	—	2	4	no	—
68	C₂×SD₁₆×C₄₃	—	2	4	no	—
69	C₂×SD₁₆×C₄₃	—	2	4	no	—
70	C₂×SD₁₆×C₄₃	—	2	4	no	—
71	C₂×SD₁₆×C₄₃	—	4	2	no	—
72	C₂×SD₁₆×C₄₃	—	4	2	no	—
73	C₂×SD₁₆×C₄₃	—	4	2	no	—
74	C₂×D₈×C₄₃	—	2	4	no	—
75	C₂×D₈×C₄₃	—	2	4	no	—
76	C₂×D₈×C₄₃	—	4	2	no	—
77	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
78	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
79	C₄⋊Q₈×C₄₃	—	2	2	no	—
80	C₄⋊Q₈×C₄₃	—	2	2	no	—
81	C₄⋊Q₈×C₄₃	—	2	2	no	—
82	C₄⋊Q₈×C₄₃	D₄	1	4	yes	complemented
83	#127×C₄₃	—	2	2	no	—
84	#127×C₄₃	—	2	2	no	—
85	#124×C₄₃	—	2	2	no	—
86	#124×C₄₃	—	2	2	no	—
87	#124×C₄₃	—	2	2	no	—
88	#124×C₄₃	D₄	1	4	yes	complemented
89	#123×C₄₃	—	2	16	no	—
90	C₂²⋊Q₈×C₄₃	—	2	16	no	—
91	#121×C₄₃	—	2	4	no	—
92	#121×C₄₃	—	2	4	no	—
93	#117×C₄₃	—	2	2	no	—
94	#117×C₄₃	—	2	2	no	—
95	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
96	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
97	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
98	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
99	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
100	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
101	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
102	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
103	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
104	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
106	#103×C₄₃	—	2	4	no	—
107	#103×C₄₃	—	2	4	no	—
108	#103×C₄₃	—	2	4	no	—
109	#102×C₄₃	—	2	4	no	—
110	C₂²⋊C₈×C₄₃	D₄	1	8	yes	complemented
111	#97×C₄₃	—	2	2	no	—
112	C₄×C₈×C₄₃	—	2	2	no	—
113	#95×C₄₃	—	2	2	no	—
114	C₂⁴×C₄₃	—	2	1	no	—
115	C₂⁴×C₄₃	—	2	2	no	—
116	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
117	#41×C₄₃	—	4	8	no	—
118	#41×C₄₃	—	4	8	no	—
119	C₂×Q₈×C₄₃	—	2	4	no	—
120	C₂×Q₈×C₄₃	—	2	1	no	—
121	C₂×Q₈×C₄₃	—	2	1	no	—
122	C₂×Q₈×C₄₃	—	2	1	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	—	2	2	no	—
128	C₂×Q₈×C₄₃	—	2	2	no	—
129	C₂×Q₈×C₄₃	—	4	8	no	—
130	C₂×Q₈×C₄₃	—	4	8	no	—
131	C₂×Q₈×C₄₃	—	4	2	no	—
132	C₂×Q₈×C₄₃	—	4	2	no	—
133	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
134	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
135	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
136	C₂×D₄×C₄₃	—	2	4	no	—
137	C₂×D₄×C₄₃	—	2	1	no	—
138	C₂×D₄×C₄₃	—	2	2	no	—
139	C₂×D₄×C₄₃	—	2	2	no	—
140	C₂×D₄×C₄₃	—	2	2	no	—
141	C₂×D₄×C₄₃	—	2	2	no	—
142	C₂×D₄×C₄₃	—	2	2	no	—
143	C₂×D₄×C₄₃	—	2	2	no	—
144	C₂×D₄×C₄₃	—	2	2	no	—
145	C₂×D₄×C₄₃	—	2	2	no	—
146	C₂×D₄×C₄₃	—	4	2	no	—
147	C₂×D₄×C₄₃	—	4	4	no	—
148	C₂×D₄×C₄₃	—	4	2	no	—
149	C₂×D₄×C₄₃	—	4	4	no	—
150	C₂×D₄×C₄₃	—	8	4	no	—
151	C₂×D₄×C₄₃	—	8	4	no	—
152	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
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	—	2	4	no	—
157	C₂²×C₄×C₄₃	—	2	4	no	—
158	C₂²×C₄×C₄₃	—	2	1	no	—
159	C₂²×C₄×C₄₃	—	2	1	no	—
160	C₂²×C₄×C₄₃	—	2	1	no	—
161	C₂²×C₄×C₄₃	—	2	2	no	—
162	C₂²×C₄×C₄₃	—	4	2	no	—
163	C₂²×C₄×C₄₃	—	4	2	no	—
164	C₂²×C₄×C₄₃	—	4	2	no	—
165	C₂²×C₄×C₄₃	—	4	2	no	—
166	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
167	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
169	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
171	SD₁₆×C₄₃	—	4	8	no	—
172	SD₁₆×C₄₃	—	4	8	no	—
173	SD₁₆×C₄₃	—	4	8	no	—
174	D₈×C₄₃	—	4	8	no	—
175	C₂×C₈×C₄₃	—	2	2	no	—
176	C₂×C₈×C₄₃	—	2	2	no	—
177	C₂×C₈×C₄₃	—	2	2	no	—
178	C₂×C₈×C₄₃	—	2	2	no	—
179	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
180	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
181	C₄⋊C₄×C₄₃	—	2	8	no	—
182	C₄⋊C₄×C₄₃	—	2	8	no	—
183	C₄⋊C₄×C₄₃	—	2	4	no	—
184	C₄⋊C₄×C₄₃	—	2	2	no	—
185	C₄⋊C₄×C₄₃	—	2	2	no	—
186	C₂²⋊C₄×C₄₃	—	2	8	no	—
187	C₂²⋊C₄×C₄₃	—	2	8	no	—
188	C₂²⋊C₄×C₄₃	—	2	4	no	—
189	C₂²⋊C₄×C₄₃	—	4	4	no	—
190	C₂²⋊C₄×C₄₃	—	8	4	no	—
191	C₄²×C₄₃	—	2	1	no	—
192	C₄²×C₄₃	—	2	1	no	—
193	C₄²×C₄₃	C₂×D₄	1	2	yes	—
194	C₄²×C₄₃	C₂×D₄	1	2	yes	—
195	C₂³×C₄₃	—	2	1	no	—
196	C₂³×C₄₃	—	2	1	no	—
197	C₂³×C₄₃	—	2	4	no	—
198	C₂³×C₄₃	—	2	2	no	—
199	C₂³×C₄₃	—	4	1	no	—
200	C₂³×C₄₃	—	4	1	no	—
201	C₂³×C₄₃	—	4	4	no	—
202	C₂³×C₄₃	—	4	2	no	—
203	C₂³×C₄₃	—	4	2	no	—
204	C₂³×C₄₃	—	4	2	no	—
205	C₂³×C₄₃	—	4	4	no	—
206	C₂³×C₄₃	—	4	4	no	—
207	C₂³×C₄₃	#127	1	2	yes	—
208	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
209	Q₈×C₄₃	—	2	4	no	—
210	Q₈×C₄₃	—	2	4	no	—
211	Q₈×C₄₃	—	2	4	no	—
212	Q₈×C₄₃	—	4	8	no	—
213	Q₈×C₄₃	—	4	2	no	—
214	Q₈×C₄₃	—	4	2	no	—
215	Q₈×C₄₃	—	4	2	no	—
216	D₄×C₄₃	—	2	4	no	—
217	D₄×C₄₃	—	4	8	no	—
218	D₄×C₄₃	—	4	2	no	—
219	D₄×C₄₃	—	4	2	no	—
220	D₄×C₄₃	—	4	2	no	—
221	D₄×C₄₃	—	4	2	no	—
222	D₄×C₄₃	—	4	2	no	—
223	D₄×C₄₃	—	8	8	no	—
224	D₄×C₄₃	—	8	8	no	—
225	C₂×C₄×C₄₃	—	2	1	no	—
226	C₂×C₄×C₄₃	—	2	1	no	—
227	C₂×C₄×C₄₃	—	2	4	no	—
228	C₂×C₄×C₄₃	—	2	4	no	—
229	C₂×C₄×C₄₃	—	2	4	no	—
230	C₂×C₄×C₄₃	—	2	2	no	—
231	C₂×C₄×C₄₃	—	2	2	no	—
232	C₂×C₄×C₄₃	—	2	2	no	—
233	C₂×C₄×C₄₃	—	2	2	no	—
234	C₂×C₄×C₄₃	—	2	4	no	—
235	C₂×C₄×C₄₃	—	4	8	no	—
236	C₂×C₄×C₄₃	—	4	8	no	—
237	C₂×C₄×C₄₃	—	4	1	no	—
238	C₂×C₄×C₄₃	—	4	1	no	—
239	C₂×C₄×C₄₃	—	4	1	no	—
240	C₂×C₄×C₄₃	—	4	1	no	—
241	C₂×C₄×C₄₃	—	4	1	no	—
242	C₂×C₄×C₄₃	—	4	1	no	—
243	C₂×C₄×C₄₃	—	4	2	no	—
244	C₂×C₄×C₄₃	—	4	4	no	—
245	C₂×C₄×C₄₃	#120	1	4	yes	—
246	C₂×C₄×C₄₃	#127	1	2	yes	—
247	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
250	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
251	C₈×C₄₃	—	2	4	no	—
252	C₈×C₄₃	—	2	4	no	—
253	#25733	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
254	C₂²×C₄₃	—	2	4	no	—
255	C₂²×C₄₃	—	2	2	no	—
256	C₂²×C₄₃	—	4	2	no	—
257	C₂²×C₄₃	—	4	2	no	—
258	C₂²×C₄₃	—	4	2	no	—
259	C₂²×C₄₃	—	4	4	no	—
260	C₂²×C₄₃	—	8	2	no	—
261	C₂²×C₄₃	—	8	2	no	—
262	C₂²×C₄₃	—	8	2	no	—
263	C₂²×C₄₃	—	8	2	no	—
264	C₂²×C₄₃	—	8	2	no	—
265	C₂²×C₄₃	—	8	4	no	—
266	C₂²×C₄₃	—	8	4	no	—
267	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
268	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
269	C₂²×C₄₃	#535	1	1	yes	characteristic
270	C₂²×C₄₃	#577	1	4	yes	—
271	C₄×C₄₃	—	2	2	no	—
272	C₄×C₄₃	—	2	4	no	—
273	C₄×C₄₃	—	4	2	no	—
274	C₄×C₄₃	—	4	2	no	—
275	C₄×C₄₃	—	4	2	no	—
276	C₄×C₄₃	—	4	2	no	—
277	C₄×C₄₃	—	8	2	no	—
278	C₄×C₄₃	D₄²	1	2	yes	—
279	C₄×C₄₃	D₄²	1	2	yes	—
280	C₂×#536	C₂×C₄₃	1	1	yes	characteristic, complemented
281	C₂×#496	C₂×C₄₃	1	1	yes	characteristic, complemented
282	C₂×#492	C₂×C₄₃	1	1	yes	characteristic, complemented
283	C₂×#449	C₂×C₄₃	1	2	yes	complemented
284	C₂×#448	C₂×C₄₃	1	2	yes	complemented
285	#2619	C₂×C₄₃	1	1	yes	characteristic, complemented
286	#2013	C₂×C₄₃	1	2	yes	complemented
287	#2012	C₂×C₄₃	1	2	yes	complemented
288	#1960	C₂×C₄₃	1	1	yes	characteristic, complemented
289	#1958	C₂×C₄₃	1	1	yes	characteristic, complemented
290	#1750	C₂×C₄₃	1	1	yes	characteristic, complemented
291	C₂×C₄₃	—	4	2	no	—
292	C₂×C₄₃	—	8	2	no	—
293	C₂×C₄₃	—	16	2	no	—
294	C₂×C₄₃	#2433	1	1	yes	characteristic
295	C₂×C₄₃	#3010	1	2	yes	—
296	C₂×C₄₃	#3154	1	2	yes	—
297	C₂×C₄₃	#3221	1	2	yes	—
298	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
299	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic
300	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
301	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
302	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
303	C₂²×D₈	C₂²×C₄₃	1	2	yes	—
304	#536	—	2	4	no	—
305	#536	—	2	4	no	—
306	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
307	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
308	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
309	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
310	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
311	C₂×#123	—	2	2	no	—
312	C₂×C₂²⋊Q₈	—	2	2	no	—
313	C₂×#121	C₂²×C₄₃	1	2	yes	—
314	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
315	#496	—	2	4	no	—
316	#492	—	2	4	no	—
317	#449	—	2	8	no	—
318	#448	—	2	8	no	—
319	C₂×#103	C₂²×C₄₃	1	2	yes	—
320	C₂×#103	C₂²×C₄₃	1	2	yes	—
321	C₂×#103	C₂²×C₄₃	1	2	yes	—
322	C₂×#102	C₂²×C₄₃	1	2	yes	—
323	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
324	C₂×#97	C₂²×C₄₃	1	1	yes	characteristic
325	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
326	#394	—	2	2	no	—
327	#392	—	2	2	no	—
328	#390	C₂²×C₄₃	1	2	yes	—
329	#382	C₂²×C₄₃	1	1	yes	characteristic
330	#336	C₂²×C₄₃	1	2	yes	—
331	C₄₃	#25733	1	1	yes	characteristic, direct product factor, Sylow
332	C₂×#41	—	2	2	no	—
333	C₂×#41	—	2	2	no	—
334	C₂×#41	—	2	4	no	—
335	C₂×#41	—	4	2	no	—
336	C₂²×Q₈	—	2	2	no	—
337	C₂²×Q₈	—	2	2	no	—
338	C₂²×Q₈	—	2	1	no	—
339	C₂²×Q₈	—	2	4	no	—
340	C₂²×Q₈	—	4	2	no	—
341	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
342	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
343	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
344	C₂²×D₄	—	2	1	no	—
345	C₂²×D₄	—	2	2	no	—
346	C₂²×D₄	—	2	2	no	—
347	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
348	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
349	C₂³×C₄	—	2	1	no	—
350	C₂³×C₄	—	2	1	no	—
351	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
352	C₂×SD₁₆	—	2	4	no	—
353	C₂×SD₁₆	—	2	4	no	—
354	C₂×SD₁₆	—	2	4	no	—
355	C₂×SD₁₆	—	2	4	no	—
356	C₂×SD₁₆	—	2	4	no	—
357	C₂×SD₁₆	—	2	4	no	—
358	C₂×SD₁₆	—	4	2	no	—
359	C₂×SD₁₆	—	4	2	no	—
360	C₂×SD₁₆	—	4	2	no	—
361	C₂×D₈	—	2	4	no	—
362	C₂×D₈	—	2	4	no	—
363	C₂×D₈	—	4	2	no	—
364	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
365	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
366	C₄⋊Q₈	—	2	2	no	—
367	C₄⋊Q₈	—	2	2	no	—
368	C₄⋊Q₈	—	2	2	no	—
369	C₄⋊Q₈	D₄×C₄₃	1	4	yes	complemented
370	#127	—	2	2	no	—
371	#127	—	2	2	no	—
372	#124	—	2	2	no	—
373	#124	—	2	2	no	—
374	#124	—	2	2	no	—
375	#124	D₄×C₄₃	1	4	yes	complemented
376	#123	—	2	16	no	—
377	C₂²⋊Q₈	—	2	16	no	—
378	#121	—	2	4	no	—
379	#121	—	2	4	no	—
380	#117	—	2	2	no	—
381	#117	—	2	2	no	—
382	C₂×C₄⋊C₄	—	2	2	no	—
383	C₂×C₄⋊C₄	—	2	2	no	—
384	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
385	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
386	C₂×C₂²⋊C₄	—	2	2	no	—
387	C₂×C₂²⋊C₄	—	2	2	no	—
388	C₂×C₂²⋊C₄	—	2	2	no	—
389	C₂×C₂²⋊C₄	—	2	4	no	—
390	C₂×C₂²⋊C₄	D₄×C₄₃	1	2	yes	—
391	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
392	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
393	#103	—	2	4	no	—
394	#103	—	2	4	no	—
395	#103	—	2	4	no	—
396	#102	—	2	4	no	—
397	C₂²⋊C₈	D₄×C₄₃	1	8	yes	complemented
398	#97	—	2	2	no	—
399	C₄×C₈	—	2	2	no	—
400	#95	—	2	2	no	—
401	C₂⁴	—	2	1	no	—
402	C₂⁴	—	2	2	no	—
403	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
404	#41	—	4	8	no	—
405	#41	—	4	8	no	—
406	C₂×Q₈	—	2	4	no	—
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	—	2	1	no	—
409	C₂×Q₈	—	2	1	no	—
410	C₂×Q₈	—	2	2	no	—
411	C₂×Q₈	—	2	2	no	—
412	C₂×Q₈	—	2	2	no	—
413	C₂×Q₈	—	2	2	no	—
414	C₂×Q₈	—	2	2	no	—
415	C₂×Q₈	—	2	2	no	—
416	C₂×Q₈	—	4	8	no	—
417	C₂×Q₈	—	4	8	no	—
418	C₂×Q₈	—	4	2	no	—
419	C₂×Q₈	—	4	2	no	—
420	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
421	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
422	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
423	C₂×D₄	—	2	4	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	1	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	4	2	no	—
434	C₂×D₄	—	4	2	no	—
435	C₂×D₄	—	4	4	no	—
436	C₂×D₄	—	4	4	no	—
437	C₂×D₄	—	8	4	no	—
438	C₂×D₄	—	8	4	no	—
439	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	4	2	no	—
450	C₂²×C₄	—	4	2	no	—
451	C₂²×C₄	—	4	2	no	—
452	C₂²×C₄	—	4	2	no	—
453	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
454	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
455	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
456	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
457	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
458	SD₁₆	—	4	8	no	—
459	SD₁₆	—	4	8	no	—
460	SD₁₆	—	4	8	no	—
461	D₈	—	4	8	no	—
462	C₂×C₈	—	2	2	no	—
463	C₂×C₈	—	2	2	no	—
464	C₂×C₈	—	2	2	no	—
465	C₂×C₈	—	2	2	no	—
466	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
467	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
468	C₄⋊C₄	—	2	8	no	—
469	C₄⋊C₄	—	2	8	no	—
470	C₄⋊C₄	—	2	4	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₂²⋊C₄	—	2	8	no	—
474	C₂²⋊C₄	—	2	8	no	—
475	C₂²⋊C₄	—	2	4	no	—
476	C₂²⋊C₄	—	4	4	no	—
477	C₂²⋊C₄	—	8	4	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	C₂×D₄×C₄₃	1	2	yes	—
481	C₄²	C₂×D₄×C₄₃	1	2	yes	—
482	C₂³	—	2	1	no	—
483	C₂³	—	2	1	no	—
484	C₂³	—	2	4	no	—
485	C₂³	—	2	2	no	—
486	C₂³	—	4	1	no	—
487	C₂³	—	4	1	no	—
488	C₂³	—	4	4	no	—
489	C₂³	—	4	2	no	—
490	C₂³	—	4	2	no	—
491	C₂³	—	4	2	no	—
492	C₂³	—	4	4	no	—
493	C₂³	—	4	4	no	—
494	C₂³	#127×C₄₃	1	2	yes	—
495	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
496	Q₈	—	2	4	no	—
497	Q₈	—	2	4	no	—
498	Q₈	—	2	4	no	—
499	Q₈	—	4	8	no	—
500	Q₈	—	4	2	no	—
501	Q₈	—	4	2	no	—
502	Q₈	—	4	2	no	—
503	D₄	—	2	4	no	—
504	D₄	—	4	8	no	—
505	D₄	—	4	2	no	—
506	D₄	—	4	2	no	—
507	D₄	—	4	2	no	—
508	D₄	—	4	2	no	—
509	D₄	—	4	2	no	—
510	D₄	—	8	8	no	—
511	D₄	—	8	8	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	4	8	no	—
523	C₂×C₄	—	4	8	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	4	no	—
532	C₂×C₄	#120×C₄₃	1	4	yes	—
533	C₂×C₄	#127×C₄₃	1	2	yes	—
534	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
535	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
536	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
537	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
538	C₈	—	2	4	no	—
539	C₈	—	2	4	no	—
540	C₂²	—	2	4	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	4	4	no	—
546	C₂²	—	8	2	no	—
547	C₂²	—	8	2	no	—
548	C₂²	—	8	2	no	—
549	C₂²	—	8	2	no	—
550	C₂²	—	8	2	no	—
551	C₂²	—	8	4	no	—
552	C₂²	—	8	4	no	—
553	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
554	C₂²	C₂×#127×C₄₃	1	1	yes	characteristic
555	C₂²	C₄₃×#535	1	1	yes	characteristic
556	C₂²	C₄₃×#577	1	4	yes	—
557	C₄	—	2	2	no	—
558	C₄	—	2	4	no	—
559	C₄	—	4	2	no	—
560	C₄	—	4	2	no	—
561	C₄	—	4	2	no	—
562	C₄	—	4	2	no	—
563	C₄	—	8	2	no	—
564	C₄	D₄²×C₄₃	1	2	yes	—
565	C₄	D₄²×C₄₃	1	2	yes	—
566	C₂	—	4	2	no	—
567	C₂	—	8	2	no	—
568	C₂	—	16	2	no	—
569	C₂	C₄₃×#2433	1	1	yes	characteristic
570	C₂	C₄₃×#3010	1	2	yes	—
571	C₂	C₄₃×#3154	1	2	yes	—
572	C₂	C₄₃×#3221	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂×#117×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#536	C₂	semidirect
2. C₂×C₄₃×#496	C₂	semidirect
3. C₂×C₄₃×#492	C₂	semidirect
4. C₂×C₄₃×#449	C₂	semidirect
5. C₂×C₄₃×#448	C₂	semidirect
6. C₄₃×#2619	C₂	semidirect
7. C₄₃×#2013	C₂	semidirect
8. C₄₃×#2012	C₂	semidirect
9. C₄₃×#1960	C₂	semidirect
10. C₄₃×#1958	C₂	semidirect
11. C₄₃×#1750	C₂	semidirect
82. C₄⋊Q₈×C₄₃	D₄	semidirect
88. #124×C₄₃	D₄	semidirect
110. C₂²⋊C₈×C₄₃	D₄	semidirect
253. #25733	C₄₃	direct (N × H)
280. C₂×#536	C₂×C₄₃	semidirect
281. C₂×#496	C₂×C₄₃	semidirect
282. C₂×#492	C₂×C₄₃	semidirect
283. C₂×#449	C₂×C₄₃	semidirect
284. C₂×#448	C₂×C₄₃	semidirect
285. #2619	C₂×C₄₃	semidirect
286. #2013	C₂×C₄₃	semidirect
287. #2012	C₂×C₄₃	semidirect
288. #1960	C₂×C₄₃	semidirect
289. #1958	C₂×C₄₃	semidirect
290. #1750	C₂×C₄₃	semidirect
331. C₄₃	#25733	direct (N × H)
369. C₄⋊Q₈	D₄×C₄₃	semidirect
375. #124	D₄×C₄₃	semidirect
397. C₂²⋊C₈	D₄×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×#536	2
C₂×C₄₃×#496	2
C₂×C₄₃×#492	2
C₂×C₄₃×#449	2
C₂×C₄₃×#448	2
C₄₃×#2619	2
C₄₃×#2013	2
C₄₃×#2012	2
C₄₃×#1960	2
C₄₃×#1958	2
C₄₃×#1750	2
#25733	43

Subgroups — C43×#25733 #24945750

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#25733 #24945750