Subgroups — C₄₃×#28554 #24948571

Order 11008.

902 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₈×D₄×C₄₃	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#2415	C₂	1	2	yes	maximal
4	C₄₃×#2086	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2075	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#2056	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#2001	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1933	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1892	C₂	1	2	yes	maximal, complemented
10	C₄₃×#1873	C₂	1	2	yes	maximal, complemented
11	C₄₃×#1735	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
16	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×#117×C₄₃	C₂²	1	2	yes	—
19	C₄₃×#467	—	2	4	no	—
20	C₈×D₄×C₄₃	—	2	4	no	—
21	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×#103×C₄₃	C₂²	1	2	yes	—
24	C₂×#103×C₄₃	C₂²	1	2	yes	—
25	C₂×#103×C₄₃	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
29	C₄₃×#397	—	2	2	no	—
30	C₄₃×#394	—	2	2	no	—
31	C₄₃×#391	C₂²	1	2	yes	—
32	C₄₃×#389	—	2	2	no	—
33	C₄₃×#389	C₂²	1	2	yes	—
34	C₄₃×#388	—	2	2	no	—
35	C₄₃×#380	C₂²	1	2	yes	—
36	C₄₃×#340	C₂²	1	2	yes	—
37	C₄₃×#340	C₂²	1	1	yes	characteristic
38	C₄₃×#340	C₂²	1	2	yes	—
39	C₄₃×#340	C₂²	1	1	yes	characteristic
40	C₄₃×#340	C₂²	1	2	yes	—
41	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
42	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
45	C₂×Q₁₆×C₄₃	—	2	2	no	—
46	C₂×Q₁₆×C₄₃	—	4	2	no	—
47	C₂²×C₈×C₄₃	—	2	2	no	—
48	C₂²×C₈×C₄₃	—	4	2	no	—
49	C₂²×C₈×C₄₃	—	4	2	no	—
50	C₂²×C₈×C₄₃	D₄	1	4	yes	—
51	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
55	C₂²⋊Q₈×C₄₃	—	2	4	no	—
56	C₂²⋊Q₈×C₄₃	—	2	4	no	—
57	C₂²⋊Q₈×C₄₃	—	2	4	no	—
58	C₂²⋊Q₈×C₄₃	—	4	2	no	—
59	C₄×D₄×C₄₃	—	2	2	no	—
60	C₄×D₄×C₄₃	—	2	2	no	—
61	#117×C₄₃	—	2	4	no	—
62	#117×C₄₃	—	4	2	no	—
63	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
64	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
66	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
70	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₄₃	—	2	2	no	—
77	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
78	#107×C₄₃	—	2	2	no	—
79	C₄⋊C₈×C₄₃	—	2	2	no	—
80	#103×C₄₃	—	2	4	no	—
81	#103×C₄₃	—	2	4	no	—
82	#103×C₄₃	—	4	2	no	—
83	C₂²⋊C₈×C₄₃	—	2	2	no	—
84	C₂²⋊C₈×C₄₃	—	2	2	no	—
85	C₄×C₈×C₄₃	—	2	2	no	—
86	#95×C₄₃	—	2	2	no	—
87	#95×C₄₃	—	2	2	no	—
88	#95×C₄₃	—	2	2	no	—
89	#95×C₄₃	—	2	2	no	—
90	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
91	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
92	C₂×Q₈×C₄₃	—	2	2	no	—
93	C₂×Q₈×C₄₃	—	2	2	no	—
94	C₂×Q₈×C₄₃	—	2	2	no	—
95	C₂×Q₈×C₄₃	—	2	2	no	—
96	C₂×Q₈×C₄₃	—	2	2	no	—
97	C₂×Q₈×C₄₃	—	2	2	no	—
98	C₂×D₄×C₄₃	—	2	2	no	—
99	C₂×D₄×C₄₃	—	2	2	no	—
100	C₂×D₄×C₄₃	—	2	2	no	—
101	C₂²×C₄×C₄₃	—	2	2	no	—
102	C₂²×C₄×C₄₃	—	2	2	no	—
103	C₂²×C₄×C₄₃	—	2	1	no	—
104	C₂²×C₄×C₄₃	—	2	1	no	—
105	C₂²×C₄×C₄₃	—	2	2	no	—
106	C₂²×C₄×C₄₃	—	2	2	no	—
107	C₂²×C₄×C₄₃	—	2	2	no	—
108	C₂²×C₄×C₄₃	—	2	2	no	—
109	C₂²×C₄×C₄₃	—	2	2	no	—
110	C₂²×C₄×C₄₃	—	2	2	no	—
111	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	#41	1	2	yes	—
117	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
118	Q₁₆×C₄₃	—	4	4	no	—
119	C₂×C₈×C₄₃	—	2	2	no	—
120	C₂×C₈×C₄₃	—	2	2	no	—
121	C₂×C₈×C₄₃	—	2	1	no	—
122	C₂×C₈×C₄₃	—	2	1	no	—
123	C₂×C₈×C₄₃	—	2	2	no	—
124	C₂×C₈×C₄₃	—	2	2	no	—
125	C₂×C₈×C₄₃	—	4	4	no	—
126	C₂×C₈×C₄₃	—	4	4	no	—
127	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
129	C₄⋊C₄×C₄₃	—	2	2	no	—
130	C₄⋊C₄×C₄₃	—	2	2	no	—
131	C₄⋊C₄×C₄₃	—	2	2	no	—
132	C₄⋊C₄×C₄₃	—	2	2	no	—
133	C₄⋊C₄×C₄₃	—	2	2	no	—
134	C₄⋊C₄×C₄₃	—	2	2	no	—
135	C₄⋊C₄×C₄₃	—	4	4	no	—
136	C₄⋊C₄×C₄₃	—	4	4	no	—
137	C₄⋊C₄×C₄₃	—	4	4	no	—
138	C₄⋊C₄×C₄₃	#41	1	4	yes	—
139	C₂²⋊C₄×C₄₃	—	2	2	no	—
140	C₂²⋊C₄×C₄₃	—	2	2	no	—
141	C₂²⋊C₄×C₄₃	—	4	4	no	—
142	C₂²⋊C₄×C₄₃	—	4	4	no	—
143	C₂²⋊C₄×C₄₃	—	4	4	no	—
144	C₂²⋊C₄×C₄₃	—	4	4	no	—
145	C₄²×C₄₃	—	2	1	no	—
146	C₄²×C₄₃	—	2	1	no	—
147	C₄²×C₄₃	—	4	4	no	—
148	C₂³×C₄₃	—	2	1	no	—
149	C₂³×C₄₃	—	2	2	no	—
150	C₂³×C₄₃	—	2	2	no	—
151	C₂³×C₄₃	—	2	1	no	—
152	C₂³×C₄₃	—	2	1	no	—
153	C₂³×C₄₃	—	2	1	no	—
154	C₂³×C₄₃	—	2	2	no	—
155	C₂³×C₄₃	—	2	2	no	—
156	C₂³×C₄₃	#121	1	2	yes	—
157	C₂³×C₄₃	#135	1	2	yes	—
158	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
159	Q₈×C₄₃	—	4	2	no	—
160	Q₈×C₄₃	—	4	2	no	—
161	Q₈×C₄₃	—	4	2	no	—
162	Q₈×C₄₃	—	4	2	no	—
163	D₄×C₄₃	—	2	8	no	—
164	C₂×C₄×C₄₃	—	2	1	no	—
165	C₂×C₄×C₄₃	—	2	2	no	—
166	C₂×C₄×C₄₃	—	2	1	no	—
167	C₂×C₄×C₄₃	—	2	2	no	—
168	C₂×C₄×C₄₃	—	2	2	no	—
169	C₂×C₄×C₄₃	—	2	4	no	—
170	C₂×C₄×C₄₃	—	2	1	no	—
171	C₂×C₄×C₄₃	—	2	1	no	—
172	C₂×C₄×C₄₃	—	2	4	no	—
173	C₂×C₄×C₄₃	—	2	2	no	—
174	C₂×C₄×C₄₃	—	2	2	no	—
175	C₂×C₄×C₄₃	—	4	2	no	—
176	C₂×C₄×C₄₃	—	4	2	no	—
177	C₂×C₄×C₄₃	—	4	1	no	—
178	C₂×C₄×C₄₃	—	4	1	no	—
179	C₂×C₄×C₄₃	—	4	2	no	—
180	C₂×C₄×C₄₃	—	4	2	no	—
181	C₂×C₄×C₄₃	—	4	2	no	—
182	C₂×C₄×C₄₃	—	4	2	no	—
183	C₂×C₄×C₄₃	—	4	2	no	—
184	C₂×C₄×C₄₃	—	4	2	no	—
185	C₂×C₄×C₄₃	—	4	2	no	—
186	C₂×C₄×C₄₃	—	4	2	no	—
187	C₂×C₄×C₄₃	—	4	2	no	—
188	C₂×C₄×C₄₃	—	4	2	no	—
189	C₂×C₄×C₄₃	#121	1	2	yes	—
190	C₂×C₄×C₄₃	#135	1	2	yes	—
191	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
193	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
195	C₈×C₄₃	—	2	2	no	—
196	C₈×C₄₃	—	2	2	no	—
197	C₈×C₄₃	—	4	1	no	—
198	C₈×C₄₃	—	4	1	no	—
199	#28554	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂²×C₄₃	—	2	4	no	—
201	C₂²×C₄₃	—	2	2	no	—
202	C₂²×C₄₃	—	2	2	no	—
203	C₂²×C₄₃	—	2	2	no	—
204	C₂²×C₄₃	—	2	2	no	—
205	C₂²×C₄₃	—	4	2	no	—
206	C₂²×C₄₃	—	4	2	no	—
207	C₂²×C₄₃	—	4	2	no	—
208	C₂²×C₄₃	—	4	1	no	—
209	C₂²×C₄₃	—	4	1	no	—
210	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
211	C₂²×C₄₃	#546	1	2	yes	—
212	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
213	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
214	C₂²×C₄₃	#578	1	2	yes	—
215	C₄×C₄₃	—	2	2	no	—
216	C₄×C₄₃	—	2	2	no	—
217	C₄×C₄₃	—	4	4	no	—
218	C₄×C₄₃	—	4	1	no	—
219	C₄×C₄₃	—	4	1	no	—
220	C₄×C₄₃	—	8	2	no	—
221	C₄×C₄₃	—	8	2	no	—
222	C₄×C₄₃	—	8	2	no	—
223	C₄×C₄₃	#532	1	1	yes	characteristic
224	C₄×C₄₃	#534	1	1	yes	characteristic
225	C₄×C₄₃	#553	1	2	yes	—
226	C₂×#467	C₂×C₄₃	1	1	yes	characteristic, complemented
227	C₂×C₈×D₄	C₂×C₄₃	1	1	yes	characteristic
228	#2415	C₂×C₄₃	1	2	yes	—
229	#2086	C₂×C₄₃	1	1	yes	characteristic, complemented
230	#2075	C₂×C₄₃	1	1	yes	characteristic, complemented
231	#2056	C₂×C₄₃	1	1	yes	characteristic, complemented
232	#2001	C₂×C₄₃	1	1	yes	characteristic, complemented
233	#1933	C₂×C₄₃	1	2	yes	complemented
234	#1892	C₂×C₄₃	1	2	yes	complemented
235	#1873	C₂×C₄₃	1	2	yes	complemented
236	#1735	C₂×C₄₃	1	1	yes	characteristic, complemented
237	C₂×C₄₃	—	4	2	no	—
238	C₂×C₄₃	—	4	2	no	—
239	C₂×C₄₃	#2543	1	1	yes	characteristic
240	C₂×C₄₃	#3050	1	1	yes	characteristic
241	C₂×C₄₃	#3059	1	1	yes	characteristic
242	C₂×C₄₃	#3300	1	2	yes	—
243	C₂×C₄₃	#3302	1	2	yes	—
244	C₂²×Q₁₆	C₂²×C₄₃	1	1	yes	characteristic
245	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
246	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
247	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
248	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
249	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
250	C₂×#117	C₂²×C₄₃	1	2	yes	—
251	#467	—	2	4	no	—
252	C₈×D₄	—	2	4	no	—
253	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
254	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
255	C₂×#103	C₂²×C₄₃	1	2	yes	—
256	C₂×#103	C₂²×C₄₃	1	2	yes	—
257	C₂×#103	C₂²×C₄₃	1	2	yes	—
258	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
259	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
260	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
261	#397	—	2	2	no	—
262	#394	—	2	2	no	—
263	#391	C₂²×C₄₃	1	2	yes	—
264	#389	—	2	2	no	—
265	#389	C₂²×C₄₃	1	2	yes	—
266	#388	—	2	2	no	—
267	#380	C₂²×C₄₃	1	2	yes	—
268	#340	C₂²×C₄₃	1	1	yes	characteristic
269	#340	C₂²×C₄₃	1	2	yes	—
270	#340	C₂²×C₄₃	1	2	yes	—
271	#340	C₂²×C₄₃	1	1	yes	characteristic
272	#340	C₂²×C₄₃	1	2	yes	—
273	C₄₃	#28554	1	1	yes	characteristic, direct product factor, Sylow
274	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
275	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
276	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
277	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
278	C₂×Q₁₆	—	2	2	no	—
279	C₂×Q₁₆	—	4	2	no	—
280	C₂²×C₈	—	2	2	no	—
281	C₂²×C₈	—	4	2	no	—
282	C₂²×C₈	—	4	2	no	—
283	C₂²×C₈	D₄×C₄₃	1	4	yes	—
284	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
285	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
286	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
287	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
288	C₂²⋊Q₈	—	2	4	no	—
289	C₂²⋊Q₈	—	2	4	no	—
290	C₂²⋊Q₈	—	2	4	no	—
291	C₂²⋊Q₈	—	4	2	no	—
292	C₄×D₄	—	2	2	no	—
293	C₄×D₄	—	2	2	no	—
294	#117	—	2	4	no	—
295	#117	—	4	2	no	—
296	C₂×C₄⋊C₄	—	2	2	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
300	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
301	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
302	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
303	C₂×C₂²⋊C₄	—	2	2	no	—
304	C₂×C₂²⋊C₄	—	2	2	no	—
305	C₂×C₂²⋊C₄	—	2	2	no	—
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₂²⋊C₄	D₄×C₄₃	1	1	yes	characteristic
308	C₂×C₂²⋊C₄	D₄×C₄₃	1	1	yes	characteristic
309	C₂×C₄²	—	2	2	no	—
310	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
311	#107	—	2	2	no	—
312	C₄⋊C₈	—	2	2	no	—
313	#103	—	2	4	no	—
314	#103	—	2	4	no	—
315	#103	—	4	2	no	—
316	C₂²⋊C₈	—	2	2	no	—
317	C₂²⋊C₈	—	2	2	no	—
318	C₄×C₈	—	2	2	no	—
319	#95	—	2	2	no	—
320	#95	—	2	2	no	—
321	#95	—	2	2	no	—
322	#95	—	2	2	no	—
323	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
324	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
345	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
348	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
349	C₂²×C₄	#41×C₄₃	1	2	yes	—
350	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
351	Q₁₆	—	4	4	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	4	4	no	—
359	C₂×C₈	—	4	4	no	—
360	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
361	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	4	4	no	—
369	C₄⋊C₄	—	4	4	no	—
370	C₄⋊C₄	—	4	4	no	—
371	C₄⋊C₄	#41×C₄₃	1	4	yes	—
372	C₂²⋊C₄	—	2	2	no	—
373	C₂²⋊C₄	—	2	2	no	—
374	C₂²⋊C₄	—	4	4	no	—
375	C₂²⋊C₄	—	4	4	no	—
376	C₂²⋊C₄	—	4	4	no	—
377	C₂²⋊C₄	—	4	4	no	—
378	C₄²	—	2	1	no	—
379	C₄²	—	2	1	no	—
380	C₄²	—	4	4	no	—
381	C₂³	—	2	1	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	#121×C₄₃	1	2	yes	—
390	C₂³	#135×C₄₃	1	2	yes	—
391	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
392	Q₈	—	4	2	no	—
393	Q₈	—	4	2	no	—
394	Q₈	—	4	2	no	—
395	Q₈	—	4	2	no	—
396	D₄	—	2	8	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	#121×C₄₃	1	2	yes	—
423	C₂×C₄	#135×C₄₃	1	2	yes	—
424	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
425	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
426	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
427	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
428	C₈	—	2	2	no	—
429	C₈	—	2	2	no	—
430	C₈	—	4	1	no	—
431	C₈	—	4	1	no	—
432	C₂²	—	2	4	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	4	2	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	1	no	—
441	C₂²	—	4	1	no	—
442	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
443	C₂²	C₄₃×#546	1	2	yes	—
444	C₂²	C₂×#135×C₄₃	1	1	yes	characteristic
445	C₂²	C₂×#135×C₄₃	1	1	yes	characteristic
446	C₂²	C₄₃×#578	1	2	yes	—
447	C₄	—	2	2	no	—
448	C₄	—	2	2	no	—
449	C₄	—	4	4	no	—
450	C₄	—	4	1	no	—
451	C₄	—	4	1	no	—
452	C₄	—	8	2	no	—
453	C₄	—	8	2	no	—
454	C₄	—	8	2	no	—
455	C₄	C₄₃×#532	1	1	yes	characteristic
456	C₄	C₄₃×#534	1	1	yes	characteristic
457	C₄	C₄₃×#553	1	2	yes	—
458	C₂	—	4	2	no	—
459	C₂	—	4	2	no	—
460	C₂	C₄₃×#2543	1	1	yes	characteristic
461	C₂	C₄₃×#3050	1	1	yes	characteristic
462	C₂	C₄₃×#3059	1	1	yes	characteristic
463	C₂	C₄₃×#3300	1	2	yes	—
464	C₂	C₄₃×#3302	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂²×D₄×C₄₃	D₄
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
1. C₂×C₄₃×#467	C₂	semidirect
4. C₄₃×#2086	C₂	semidirect
5. C₄₃×#2075	C₂	semidirect
6. C₄₃×#2056	C₂	semidirect
7. C₄₃×#2001	C₂	semidirect
8. C₄₃×#1933	C₂	semidirect
9. C₄₃×#1892	C₂	semidirect
10. C₄₃×#1873	C₂	semidirect
11. C₄₃×#1735	C₂	semidirect
199. #28554	C₄₃	direct (N × H)
226. C₂×#467	C₂×C₄₃	semidirect
229. #2086	C₂×C₄₃	semidirect
230. #2075	C₂×C₄₃	semidirect
231. #2056	C₂×C₄₃	semidirect
232. #2001	C₂×C₄₃	semidirect
233. #1933	C₂×C₄₃	semidirect
234. #1892	C₂×C₄₃	semidirect
235. #1873	C₂×C₄₃	semidirect
236. #1735	C₂×C₄₃	semidirect
273. C₄₃	#28554	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×#467	2
C₂×C₈×D₄×C₄₃	2
C₄₃×#2415	2
C₄₃×#2086	2
C₄₃×#2075	2
C₄₃×#2056	2
C₄₃×#2001	2
C₄₃×#1933	2
C₄₃×#1892	2
C₄₃×#1873	2
C₄₃×#1735	2
#28554	43

Subgroups — C43×#28554 #24948571

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#28554 #24948571