Subgroups — C₂×C₄₃×#1782 #24940600

Order 11008.

4062 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×#99×C₄₃	C₂	1	4	yes	maximal, complemented
3	C₂×C₄₃×#381	C₂	1	2	yes	maximal, complemented
4	C₄₃×#1782	C₂	1	8	yes	maximal, direct product factor
5	C₂²×#41×C₄₃	—	2	16	no	—
6	C₂²×#41×C₄₃	—	2	4	no	—
7	C₂²×#41×C₄₃	—	2	4	no	—
8	C₂²×#41×C₄₃	C₄	1	4	yes	complemented
9	C₂²×#41×C₄₃	C₂²	1	4	yes	—
10	C₂³×Q₈×C₄₃	C₄	1	1	yes	characteristic, complemented
11	C₂³×D₄×C₄₃	C₄	1	1	yes	characteristic, complemented
12	C₂³×D₄×C₄₃	C₂²	1	2	yes	—
13	C₂⁴×C₄×C₄₃	C₄	1	2	yes	complemented
14	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
15	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	4	yes	—
16	C₂×#99×C₄₃	—	2	16	no	—
17	C₂×#99×C₄₃	C₂²	1	16	yes	complemented
18	C₄₃×#381	—	2	4	no	—
19	C₄₃×#381	C₂²	1	8	yes	complemented
20	C₂×#95×C₄₃	—	2	4	no	—
21	C₂⁵×C₄₃	C₂×C₄	1	2	yes	—
22	C₂⁵×C₄₃	C₂³	1	1	yes	characteristic
23	C₂×#41×C₄₃	—	2	64	no	—
24	C₂×#41×C₄₃	—	2	64	no	—
25	C₂×#41×C₄₃	—	2	32	no	—
26	C₂×#41×C₄₃	—	2	32	no	—
27	C₂×#41×C₄₃	—	2	16	no	—
28	C₂×#41×C₄₃	—	2	16	no	—
29	C₂²×Q₈×C₄₃	—	2	8	no	—
30	C₂²×Q₈×C₄₃	—	2	2	no	—
31	C₂²×Q₈×C₄₃	—	2	2	no	—
32	C₂²×Q₈×C₄₃	C₂×C₄	1	4	yes	complemented
33	C₂²×D₄×C₄₃	—	2	8	no	—
34	C₂²×D₄×C₄₃	—	2	8	no	—
35	C₂²×D₄×C₄₃	—	2	4	no	—
36	C₂²×D₄×C₄₃	—	2	4	no	—
37	C₂²×D₄×C₄₃	—	2	2	no	—
38	C₂²×D₄×C₄₃	—	2	2	no	—
39	C₂²×D₄×C₄₃	C₂×C₄	1	4	yes	—
40	C₂²×D₄×C₄₃	C₂×C₄	1	4	yes	complemented
41	C₂²×D₄×C₄₃	D₄	1	16	yes	—
42	C₂²×D₄×C₄₃	C₂³	1	4	yes	—
43	C₂³×C₄×C₄₃	—	2	8	no	—
44	C₂³×C₄×C₄₃	—	2	8	no	—
45	C₂³×C₄×C₄₃	—	2	8	no	—
46	C₂³×C₄×C₄₃	—	2	4	no	—
47	C₂³×C₄×C₄₃	—	2	4	no	—
48	C₂³×C₄×C₄₃	—	2	4	no	—
49	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
51	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
53	C₂³×C₄×C₄₃	C₂×C₄	1	8	yes	complemented
54	C₂³×C₄×C₄₃	D₄	1	4	yes	—
55	C₂³×C₄×C₄₃	D₄	1	4	yes	—
56	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
57	C₂×C₂²⋊C₄×C₄₃	—	2	16	no	—
58	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
59	C₂×C₂²⋊C₄×C₄₃	C₂³	1	8	yes	—
60	#99×C₄₃	—	2	32	no	—
61	#95×C₄₃	—	2	16	no	—
62	C₂⁴×C₄₃	—	2	4	no	—
63	C₂⁴×C₄₃	—	2	2	no	—
64	C₂⁴×C₄₃	—	2	2	no	—
65	C₂⁴×C₄₃	—	4	4	no	—
66	C₂⁴×C₄₃	—	4	8	no	—
67	C₂⁴×C₄₃	C₂²⋊C₄	1	8	yes	—
68	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
69	C₂⁴×C₄₃	C₂²×C₄	1	4	yes	—
70	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
71	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
72	C₂⁴×C₄₃	C₂×D₄	1	8	yes	—
73	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
74	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
75	#41×C₄₃	—	2	128	no	—
76	#41×C₄₃	—	2	128	no	—
77	C₂×Q₈×C₄₃	—	2	16	no	—
78	C₂×Q₈×C₄₃	—	2	16	no	—
79	C₂×Q₈×C₄₃	—	2	16	no	—
80	C₂×Q₈×C₄₃	—	2	8	no	—
81	C₂×D₄×C₄₃	—	2	16	no	—
82	C₂×D₄×C₄₃	—	2	16	no	—
83	C₂×D₄×C₄₃	—	2	8	no	—
84	C₂×D₄×C₄₃	—	2	8	no	—
85	C₂×D₄×C₄₃	—	2	8	no	—
86	C₂×D₄×C₄₃	—	2	16	no	—
87	C₂×D₄×C₄₃	—	2	32	no	—
88	C₂×D₄×C₄₃	—	2	32	no	—
89	C₂×D₄×C₄₃	—	2	8	no	—
90	C₂×D₄×C₄₃	—	2	8	no	—
91	C₂×D₄×C₄₃	C₂²⋊C₄	1	16	yes	—
92	C₂×D₄×C₄₃	C₂×D₄	1	16	yes	—
93	C₂²×C₄×C₄₃	—	2	32	no	—
94	C₂²×C₄×C₄₃	—	2	32	no	—
95	C₂²×C₄×C₄₃	—	2	16	no	—
96	C₂²×C₄×C₄₃	—	2	16	no	—
97	C₂²×C₄×C₄₃	—	2	4	no	—
98	C₂²×C₄×C₄₃	—	2	4	no	—
99	C₂²×C₄×C₄₃	—	2	4	no	—
100	C₂²×C₄×C₄₃	—	2	2	no	—
101	C₂²×C₄×C₄₃	—	2	8	no	—
102	C₂²×C₄×C₄₃	—	2	16	no	—
103	C₂²×C₄×C₄₃	—	2	2	no	—
104	C₂²×C₄×C₄₃	—	2	16	no	—
105	C₂²×C₄×C₄₃	—	2	16	no	—
106	C₂²×C₄×C₄₃	—	2	8	no	—
107	C₂²×C₄×C₄₃	—	2	8	no	—
108	C₂²×C₄×C₄₃	—	4	16	no	—
109	C₂²×C₄×C₄₃	—	4	8	no	—
110	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
111	C₂²×C₄×C₄₃	C₂²⋊C₄	1	8	yes	—
112	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
113	C₂²×C₄×C₄₃	C₂²⋊C₄	1	8	yes	—
114	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
115	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
116	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
117	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
119	C₂²×C₄×C₄₃	C₂×D₄	1	8	yes	—
120	C₂²⋊C₄×C₄₃	—	2	16	no	—
121	C₂²⋊C₄×C₄₃	—	4	8	no	—
122	C₂³×C₄₃	—	2	8	no	—
123	C₂³×C₄₃	—	2	4	no	—
124	C₂³×C₄₃	—	2	4	no	—
125	C₂³×C₄₃	—	2	4	no	—
126	C₂³×C₄₃	—	2	8	no	—
127	C₂³×C₄₃	—	2	8	no	—
128	C₂³×C₄₃	—	4	2	no	—
129	C₂³×C₄₃	—	4	4	no	—
130	C₂³×C₄₃	—	4	16	no	—
131	C₂³×C₄₃	—	4	2	no	—
132	C₂³×C₄₃	—	4	16	no	—
133	C₂³×C₄₃	—	4	8	no	—
134	C₂³×C₄₃	—	4	8	no	—
135	C₂³×C₄₃	—	4	16	no	—
136	C₂³×C₄₃	—	4	8	no	—
137	C₂³×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
138	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
139	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
140	C₂³×C₄₃	C₂×C₂²⋊C₄	1	8	yes	—
141	C₂³×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
142	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
143	C₂³×C₄₃	#120	1	8	yes	—
144	C₂³×C₄₃	#120	1	8	yes	—
145	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
146	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
147	C₂³×C₄₃	C₂²×D₄	1	4	yes	—
148	Q₈×C₄₃	—	2	32	no	—
149	D₄×C₄₃	—	2	32	no	—
150	D₄×C₄₃	—	2	32	no	—
151	D₄×C₄₃	—	2	32	no	—
152	C₂×C₄×C₄₃	—	2	64	no	—
153	C₂×C₄×C₄₃	—	2	4	no	—
154	C₂×C₄×C₄₃	—	2	4	no	—
155	C₂×C₄×C₄₃	—	2	4	no	—
156	C₂×C₄×C₄₃	—	2	4	no	—
157	C₂×C₄×C₄₃	—	2	16	no	—
158	C₂×C₄×C₄₃	—	2	4	no	—
159	C₂×C₄×C₄₃	—	2	4	no	—
160	C₂×C₄×C₄₃	—	2	8	no	—
161	C₂×C₄×C₄₃	—	2	4	no	—
162	C₂×C₄×C₄₃	—	2	8	no	—
163	C₂×C₄×C₄₃	—	2	4	no	—
164	C₂×C₄×C₄₃	—	2	16	no	—
165	C₂×C₄×C₄₃	—	4	16	no	—
166	C₂×C₄×C₄₃	—	4	8	no	—
167	C₂×C₄×C₄₃	—	8	16	no	—
168	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
169	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	8	yes	—
170	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
171	C₂×#1782	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂²×C₄₃	—	2	2	no	—
173	C₂²×C₄₃	—	2	2	no	—
174	C₂²×C₄₃	—	2	4	no	—
175	C₂²×C₄₃	—	2	4	no	—
176	C₂²×C₄₃	—	2	8	no	—
177	C₂²×C₄₃	—	2	16	no	—
178	C₂²×C₄₃	—	2	8	no	—
179	C₂²×C₄₃	—	4	4	no	—
180	C₂²×C₄₃	—	4	8	no	—
181	C₂²×C₄₃	—	4	4	no	—
182	C₂²×C₄₃	—	4	8	no	—
183	C₂²×C₄₃	—	4	8	no	—
184	C₂²×C₄₃	—	4	16	no	—
185	C₂²×C₄₃	—	4	8	no	—
186	C₂²×C₄₃	—	4	16	no	—
187	C₂²×C₄₃	#379	1	2	yes	—
188	C₂²×C₄₃	#379	1	4	yes	—
189	C₂²×C₄₃	#379	1	2	yes	—
190	C₂²×C₄₃	#410	1	4	yes	—
191	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	2	yes	—
192	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
193	C₂²×C₄₃	C₂×#120	1	4	yes	—
194	C₄×C₄₃	—	2	4	no	—
195	C₄×C₄₃	—	2	8	no	—
196	C₄×C₄₃	—	2	4	no	—
197	C₄×C₄₃	—	8	8	no	—
198	C₂³×#41	C₂×C₄₃	1	1	yes	characteristic
199	C₂²×#99	C₂×C₄₃	1	4	yes	complemented
200	C₂×#381	C₂×C₄₃	1	2	yes	complemented
201	#1782	C₂×C₄₃	1	8	yes	direct product factor
202	C₂×C₄₃	—	2	4	no	—
203	C₂×C₄₃	—	2	2	no	—
204	C₂×C₄₃	—	2	2	no	—
205	C₂×C₄₃	—	2	4	no	—
206	C₂×C₄₃	—	4	8	no	—
207	C₂×C₄₃	#1782	1	4	yes	direct product factor
208	C₂×C₄₃	C₂×#379	1	1	yes	characteristic
209	C₂×C₄₃	C₂×#410	1	2	yes	—
210	C₂²×#41	—	2	16	no	—
211	C₂²×#41	—	2	4	no	—
212	C₂²×#41	—	2	4	no	—
213	C₂²×#41	C₄×C₄₃	1	4	yes	complemented
214	C₂²×#41	C₂²×C₄₃	1	4	yes	—
215	C₂³×Q₈	C₄×C₄₃	1	1	yes	characteristic, complemented
216	C₂³×D₄	C₄×C₄₃	1	1	yes	characteristic, complemented
217	C₂³×D₄	C₂²×C₄₃	1	2	yes	—
218	C₂⁴×C₄	C₄×C₄₃	1	2	yes	complemented
219	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
220	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	4	yes	—
221	C₂×#99	—	2	16	no	—
222	C₂×#99	C₂²×C₄₃	1	16	yes	complemented
223	#381	—	2	4	no	—
224	#381	C₂²×C₄₃	1	8	yes	complemented
225	C₂×#95	—	2	4	no	—
226	C₄₃	C₂×#1782	1	1	yes	characteristic, direct product factor, Sylow
227	C₂⁵	C₂×C₄×C₄₃	1	2	yes	—
228	C₂⁵	C₂³×C₄₃	1	1	yes	characteristic
229	C₂×#41	—	2	64	no	—
230	C₂×#41	—	2	64	no	—
231	C₂×#41	—	2	32	no	—
232	C₂×#41	—	2	32	no	—
233	C₂×#41	—	2	16	no	—
234	C₂×#41	—	2	16	no	—
235	C₂²×Q₈	—	2	8	no	—
236	C₂²×Q₈	—	2	2	no	—
237	C₂²×Q₈	—	2	2	no	—
238	C₂²×Q₈	C₂×C₄×C₄₃	1	4	yes	complemented
239	C₂²×D₄	—	2	8	no	—
240	C₂²×D₄	—	2	4	no	—
241	C₂²×D₄	—	2	8	no	—
242	C₂²×D₄	—	2	4	no	—
243	C₂²×D₄	—	2	2	no	—
244	C₂²×D₄	—	2	2	no	—
245	C₂²×D₄	C₂×C₄×C₄₃	1	4	yes	—
246	C₂²×D₄	C₂×C₄×C₄₃	1	4	yes	complemented
247	C₂²×D₄	D₄×C₄₃	1	16	yes	—
248	C₂²×D₄	C₂³×C₄₃	1	4	yes	—
249	C₂³×C₄	—	2	8	no	—
250	C₂³×C₄	—	2	8	no	—
251	C₂³×C₄	—	2	8	no	—
252	C₂³×C₄	—	2	4	no	—
253	C₂³×C₄	—	2	4	no	—
254	C₂³×C₄	—	2	4	no	—
255	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
256	C₂³×C₄	C₂×C₄×C₄₃	1	2	yes	—
257	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
258	C₂³×C₄	C₂×C₄×C₄₃	1	2	yes	—
259	C₂³×C₄	C₂×C₄×C₄₃	1	8	yes	complemented
260	C₂³×C₄	D₄×C₄₃	1	4	yes	—
261	C₂³×C₄	D₄×C₄₃	1	4	yes	—
262	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
263	C₂×C₂²⋊C₄	—	2	16	no	—
264	C₂×C₂²⋊C₄	—	2	4	no	—
265	C₂×C₂²⋊C₄	C₂³×C₄₃	1	8	yes	—
266	#99	—	2	32	no	—
267	#95	—	2	16	no	—
268	C₂⁴	—	2	4	no	—
269	C₂⁴	—	2	2	no	—
270	C₂⁴	—	2	2	no	—
271	C₂⁴	—	4	4	no	—
272	C₂⁴	—	4	8	no	—
273	C₂⁴	C₂²⋊C₄×C₄₃	1	8	yes	—
274	C₂⁴	C₂²×C₄×C₄₃	1	1	yes	characteristic
275	C₂⁴	C₂²×C₄×C₄₃	1	4	yes	—
276	C₂⁴	C₂²×C₄×C₄₃	1	1	yes	characteristic
277	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
278	C₂⁴	C₂×D₄×C₄₃	1	8	yes	—
279	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
280	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
281	#41	—	2	128	no	—
282	#41	—	2	128	no	—
283	C₂×Q₈	—	2	16	no	—
284	C₂×Q₈	—	2	16	no	—
285	C₂×Q₈	—	2	16	no	—
286	C₂×Q₈	—	2	8	no	—
287	C₂×D₄	—	2	16	no	—
288	C₂×D₄	—	2	16	no	—
289	C₂×D₄	—	2	8	no	—
290	C₂×D₄	—	2	8	no	—
291	C₂×D₄	—	2	16	no	—
292	C₂×D₄	—	2	32	no	—
293	C₂×D₄	—	2	32	no	—
294	C₂×D₄	—	2	8	no	—
295	C₂×D₄	—	2	8	no	—
296	C₂×D₄	—	2	8	no	—
297	C₂×D₄	C₂²⋊C₄×C₄₃	1	16	yes	—
298	C₂×D₄	C₂×D₄×C₄₃	1	16	yes	—
299	C₂²×C₄	—	2	32	no	—
300	C₂²×C₄	—	2	32	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	8	no	—
307	C₂²×C₄	—	2	16	no	—
308	C₂²×C₄	—	2	16	no	—
309	C₂²×C₄	—	2	16	no	—
310	C₂²×C₄	—	2	8	no	—
311	C₂²×C₄	—	2	16	no	—
312	C₂²×C₄	—	2	16	no	—
313	C₂²×C₄	—	2	8	no	—
314	C₂²×C₄	—	4	16	no	—
315	C₂²×C₄	—	4	8	no	—
316	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
317	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
318	C₂²×C₄	C₂²⋊C₄×C₄₃	1	8	yes	—
319	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
320	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
321	C₂²×C₄	C₂²⋊C₄×C₄₃	1	8	yes	—
322	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
323	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
324	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
325	C₂²×C₄	C₂×D₄×C₄₃	1	8	yes	—
326	C₂²⋊C₄	—	2	16	no	—
327	C₂²⋊C₄	—	4	8	no	—
328	C₂³	—	2	8	no	—
329	C₂³	—	2	4	no	—
330	C₂³	—	2	4	no	—
331	C₂³	—	2	4	no	—
332	C₂³	—	2	8	no	—
333	C₂³	—	2	8	no	—
334	C₂³	—	4	2	no	—
335	C₂³	—	4	4	no	—
336	C₂³	—	4	16	no	—
337	C₂³	—	4	2	no	—
338	C₂³	—	4	16	no	—
339	C₂³	—	4	8	no	—
340	C₂³	—	4	8	no	—
341	C₂³	—	4	16	no	—
342	C₂³	—	4	8	no	—
343	C₂³	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
344	C₂³	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
345	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
346	C₂³	C₂×C₂²⋊C₄×C₄₃	1	8	yes	—
347	C₂³	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
348	C₂³	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
349	C₂³	#120×C₄₃	1	8	yes	—
350	C₂³	#120×C₄₃	1	8	yes	—
351	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
352	C₂³	C₂²×D₄×C₄₃	1	2	yes	—
353	C₂³	C₂²×D₄×C₄₃	1	4	yes	—
354	Q₈	—	2	32	no	—
355	D₄	—	2	32	no	—
356	D₄	—	2	32	no	—
357	D₄	—	2	32	no	—
358	C₂×C₄	—	2	64	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	16	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	8	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	8	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	16	no	—
371	C₂×C₄	—	4	16	no	—
372	C₂×C₄	—	4	8	no	—
373	C₂×C₄	—	8	16	no	—
374	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
375	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	8	yes	—
376	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
377	C₂²	—	2	4	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	4	no	—
381	C₂²	—	2	16	no	—
382	C₂²	—	2	8	no	—
383	C₂²	—	2	8	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	4	8	no	—
386	C₂²	—	4	4	no	—
387	C₂²	—	4	8	no	—
388	C₂²	—	4	8	no	—
389	C₂²	—	4	16	no	—
390	C₂²	—	4	8	no	—
391	C₂²	—	4	16	no	—
392	C₂²	C₄₃×#379	1	2	yes	—
393	C₂²	C₄₃×#379	1	4	yes	—
394	C₂²	C₄₃×#379	1	2	yes	—
395	C₂²	C₄₃×#410	1	4	yes	—
396	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	2	yes	—
397	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
398	C₂²	C₂×#120×C₄₃	1	4	yes	—
399	C₄	—	2	4	no	—
400	C₄	—	2	8	no	—
401	C₄	—	2	4	no	—
402	C₄	—	8	8	no	—
403	C₂	—	2	4	no	—
404	C₂	—	2	2	no	—
405	C₂	—	2	2	no	—
406	C₂	—	2	4	no	—
407	C₂	—	4	8	no	—
408	C₂	C₄₃×#1782	1	4	yes	direct product factor
409	C₂	C₂×C₄₃×#379	1	1	yes	characteristic
410	C₂	C₂×C₄₃×#410	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₄₃
Frattini, cosocle	C₂⁴	C₂⁴×C₄₃
prime radical	C₂³×#41×C₄₃	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂⁴×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#99×C₄₃	C₂	semidirect
3. C₂×C₄₃×#381	C₂	semidirect
4. C₄₃×#1782	C₂	direct (N × H)
8. C₂²×#41×C₄₃	C₄	semidirect
10. C₂³×Q₈×C₄₃	C₄	semidirect
11. C₂³×D₄×C₄₃	C₄	semidirect
13. C₂⁴×C₄×C₄₃	C₄	semidirect
17. C₂×#99×C₄₃	C₂²	semidirect
19. C₄₃×#381	C₂²	semidirect
32. C₂²×Q₈×C₄₃	C₂×C₄	semidirect
40. C₂²×D₄×C₄₃	C₂×C₄	semidirect
53. C₂³×C₄×C₄₃	C₂×C₄	semidirect
171. C₂×#1782	C₄₃	direct (N × H)
199. C₂²×#99	C₂×C₄₃	semidirect
200. C₂×#381	C₂×C₄₃	semidirect
201. #1782	C₂×C₄₃	direct (N × H)
207. C₂×C₄₃	#1782	direct (N × H)
213. C₂²×#41	C₄×C₄₃	semidirect
215. C₂³×Q₈	C₄×C₄₃	semidirect
216. C₂³×D₄	C₄×C₄₃	semidirect
218. C₂⁴×C₄	C₄×C₄₃	semidirect
222. C₂×#99	C₂²×C₄₃	semidirect
224. #381	C₂²×C₄₃	semidirect
226. C₄₃	C₂×#1782	direct (N × H)
238. C₂²×Q₈	C₂×C₄×C₄₃	semidirect
246. C₂²×D₄	C₂×C₄×C₄₃	semidirect
259. C₂³×C₄	C₂×C₄×C₄₃	semidirect
408. C₂	C₄₃×#1782	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×#41×C₄₃	2
C₂²×#99×C₄₃	2
C₂×C₄₃×#381	2
C₄₃×#1782	2
C₂×#1782	43

Subgroups — C2×C43×#1782 #24940600

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₃×#1782 #24940600