Subgroups — C₂×C₄₃×#1897 #24940995

Order 11008.

1954 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#525	C₂	1	1	yes	maximal, characteristic
2	C₂²×#117×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#104×C₄₃	C₂	1	2	yes	maximal, complemented
4	C₂×C₄₃×#407	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#1897	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₄₃×#339	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
8	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
10	C₄₃×#525	—	2	2	no	—
11	C₄₃×#525	—	2	2	no	—
12	C₄₃×#525	C₄	1	4	yes	complemented
13	C₄₃×#525	C₂²	1	4	yes	—
14	C₂×#123×C₄₃	—	2	1	no	—
15	C₂×C₂²⋊Q₈×C₄₃	C₄	1	2	yes	complemented
16	C₂×#121×C₄₃	C₄	1	2	yes	complemented
17	C₂×#120×C₄₃	—	2	1	no	—
18	C₂×C₄×D₄×C₄₃	—	2	2	no	—
19	C₂×#117×C₄₃	—	2	2	no	—
20	C₂×#117×C₄₃	—	2	8	no	—
21	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×#117×C₄₃	C₂²	1	4	yes	complemented
23	C₂²×C₄⋊C₄×C₄₃	—	2	1	no	—
24	C₂²×C₂²⋊C₄×C₄₃	—	2	1	no	—
25	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
26	C₂×#104×C₄₃	—	2	8	no	—
27	C₂×#104×C₄₃	C₂²	1	8	yes	complemented
28	C₄₃×#407	—	2	2	no	—
29	C₄₃×#407	C₂²	1	4	yes	complemented
30	C₂×C₂²⋊C₈×C₄₃	—	2	2	no	—
31	C₄₃×#339	C₂²	1	8	yes	complemented
32	C₂⁵×C₄₃	D₄	1	1	yes	characteristic
33	C₂×#41×C₄₃	—	2	1	no	—
34	C₂×#41×C₄₃	—	2	1	no	—
35	C₂×#41×C₄₃	—	2	4	no	—
36	C₂×#41×C₄₃	—	2	4	no	—
37	C₂×#41×C₄₃	C₂×C₄	1	2	yes	—
38	C₂×#41×C₄₃	C₂³	1	2	yes	—
39	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×D₄×C₄₃	—	2	2	no	—
41	C₂²×D₄×C₄₃	—	2	1	no	—
42	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₄₃	—	2	4	no	—
44	C₂³×C₄×C₄₃	—	2	4	no	—
45	C₂³×C₄×C₄₃	—	2	2	no	—
46	C₂³×C₄×C₄₃	—	2	1	no	—
47	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
48	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
49	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₃	D₄	1	2	yes	—
51	C₂³×C₄×C₄₃	D₄	1	2	yes	—
52	C₂³×C₄×C₄₃	D₄	1	2	yes	—
53	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
54	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
55	C₂×M₁₆×C₄₃	—	2	2	no	—
56	C₂×M₁₆×C₄₃	—	2	4	no	—
57	C₂×M₁₆×C₄₃	—	2	4	no	—
58	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
59	C₂²×C₈×C₄₃	—	2	2	no	—
60	#123×C₄₃	—	2	4	no	—
61	#123×C₄₃	—	2	4	no	—
62	C₂²⋊Q₈×C₄₃	—	2	4	no	—
63	C₂²⋊Q₈×C₄₃	C₂×C₄	1	8	yes	complemented
64	#121×C₄₃	—	2	4	no	—
65	#121×C₄₃	C₂×C₄	1	8	yes	complemented
66	#120×C₄₃	—	2	4	no	—
67	#120×C₄₃	—	2	4	no	—
68	C₄×D₄×C₄₃	—	2	8	no	—
69	C₄×D₄×C₄₃	—	2	8	no	—
70	#117×C₄₃	—	2	16	no	—
71	#117×C₄₃	—	2	1	no	—
72	#117×C₄₃	—	2	1	no	—
73	#117×C₄₃	—	2	16	no	—
74	#117×C₄₃	C₂×C₄	1	2	yes	—
75	#117×C₄₃	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
77	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
78	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
79	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
80	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
81	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
83	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
85	C₂×C₄²×C₄₃	—	2	2	no	—
86	C₂×C₄²×C₄₃	—	2	4	no	—
87	C₂×C₄²×C₄₃	—	2	1	no	—
88	C₂×C₄²×C₄₃	D₄	1	8	yes	complemented
89	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
90	#104×C₄₃	—	2	16	no	—
91	C₂²⋊C₈×C₄₃	—	2	8	no	—
92	C₂⁴×C₄₃	—	2	2	no	—
93	C₂⁴×C₄₃	—	2	2	no	—
94	C₂⁴×C₄₃	—	2	1	no	—
95	C₂⁴×C₄₃	—	4	4	no	—
96	C₂⁴×C₄₃	C₂²⋊C₄	1	2	yes	—
97	C₂⁴×C₄₃	C₂²⋊C₄	1	2	yes	—
98	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
99	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
100	#41×C₄₃	—	2	8	no	—
101	#41×C₄₃	—	2	4	no	—
102	#41×C₄₃	—	2	4	no	—
103	#41×C₄₃	—	4	2	no	—
104	#41×C₄₃	—	4	4	no	—
105	#41×C₄₃	—	4	2	no	—
106	C₂×Q₈×C₄₃	—	2	1	no	—
107	C₂×Q₈×C₄₃	—	2	4	no	—
108	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
109	C₂×D₄×C₄₃	—	2	1	no	—
110	C₂×D₄×C₄₃	—	2	8	no	—
111	C₂×D₄×C₄₃	—	2	2	no	—
112	C₂×D₄×C₄₃	—	2	2	no	—
113	C₂×D₄×C₄₃	—	2	4	no	—
114	C₂×D₄×C₄₃	—	4	8	no	—
115	C₂×D₄×C₄₃	—	4	2	no	—
116	C₂×D₄×C₄₃	—	4	2	no	—
117	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₄₃	—	2	8	no	—
119	C₂²×C₄×C₄₃	—	2	8	no	—
120	C₂²×C₄×C₄₃	—	2	4	no	—
121	C₂²×C₄×C₄₃	—	2	8	no	—
122	C₂²×C₄×C₄₃	—	2	8	no	—
123	C₂²×C₄×C₄₃	—	2	4	no	—
124	C₂²×C₄×C₄₃	—	2	4	no	—
125	C₂²×C₄×C₄₃	—	2	4	no	—
126	C₂²×C₄×C₄₃	—	2	2	no	—
127	C₂²×C₄×C₄₃	—	2	2	no	—
128	C₂²×C₄×C₄₃	—	2	2	no	—
129	C₂²×C₄×C₄₃	—	2	1	no	—
130	C₂²×C₄×C₄₃	—	2	2	no	—
131	C₂²×C₄×C₄₃	—	2	8	no	—
132	C₂²×C₄×C₄₃	—	2	2	no	—
133	C₂²×C₄×C₄₃	—	2	4	no	—
134	C₂²×C₄×C₄₃	—	4	8	no	—
135	C₂²×C₄×C₄₃	—	4	4	no	—
136	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
137	C₂²×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
138	C₂²×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
139	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
140	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
141	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
144	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
146	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₃	#41	1	4	yes	—
150	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
151	M₁₆×C₄₃	—	2	4	no	—
152	M₁₆×C₄₃	—	2	4	no	—
153	M₁₆×C₄₃	—	4	4	no	—
154	C₂×C₈×C₄₃	—	2	4	no	—
155	C₂×C₈×C₄₃	—	4	4	no	—
156	C₄⋊C₄×C₄₃	—	2	16	no	—
157	C₄⋊C₄×C₄₃	—	2	8	no	—
158	C₄⋊C₄×C₄₃	—	2	2	no	—
159	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
160	C₂²⋊C₄×C₄₃	—	2	16	no	—
161	C₂²⋊C₄×C₄₃	—	2	8	no	—
162	C₂²⋊C₄×C₄₃	—	2	2	no	—
163	C₂²⋊C₄×C₄₃	—	2	8	no	—
164	C₂²⋊C₄×C₄₃	—	2	2	no	—
165	C₄²×C₄₃	—	2	2	no	—
166	C₄²×C₄₃	—	2	8	no	—
167	C₄²×C₄₃	—	2	4	no	—
168	C₄²×C₄₃	—	2	2	no	—
169	C₄²×C₄₃	C₂×D₄	1	8	yes	complemented
170	C₂³×C₄₃	—	2	4	no	—
171	C₂³×C₄₃	—	2	2	no	—
172	C₂³×C₄₃	—	2	2	no	—
173	C₂³×C₄₃	—	2	4	no	—
174	C₂³×C₄₃	—	2	4	no	—
175	C₂³×C₄₃	—	2	4	no	—
176	C₂³×C₄₃	—	2	4	no	—
177	C₂³×C₄₃	—	2	2	no	—
178	C₂³×C₄₃	—	4	4	no	—
179	C₂³×C₄₃	—	4	4	no	—
180	C₂³×C₄₃	—	4	8	no	—
181	C₂³×C₄₃	—	4	8	no	—
182	C₂³×C₄₃	—	4	2	no	—
183	C₂³×C₄₃	—	4	4	no	—
184	C₂³×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
185	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
186	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
187	C₂³×C₄₃	#120	1	2	yes	—
188	C₂³×C₄₃	#123	1	2	yes	—
189	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
190	Q₈×C₄₃	—	2	4	no	—
191	Q₈×C₄₃	—	4	2	no	—
192	D₄×C₄₃	—	2	4	no	—
193	D₄×C₄₃	—	4	16	no	—
194	D₄×C₄₃	—	4	2	no	—
195	D₄×C₄₃	—	4	2	no	—
196	D₄×C₄₃	—	4	4	no	—
197	D₄×C₄₃	—	4	2	no	—
198	C₂×C₄×C₄₃	—	2	2	no	—
199	C₂×C₄×C₄₃	—	2	2	no	—
200	C₂×C₄×C₄₃	—	2	4	no	—
201	C₂×C₄×C₄₃	—	2	4	no	—
202	C₂×C₄×C₄₃	—	2	8	no	—
203	C₂×C₄×C₄₃	—	2	8	no	—
204	C₂×C₄×C₄₃	—	2	8	no	—
205	C₂×C₄×C₄₃	—	2	8	no	—
206	C₂×C₄×C₄₃	—	2	4	no	—
207	C₂×C₄×C₄₃	—	2	2	no	—
208	C₂×C₄×C₄₃	—	2	8	no	—
209	C₂×C₄×C₄₃	—	4	8	no	—
210	C₂×C₄×C₄₃	—	4	16	no	—
211	C₂×C₄×C₄₃	—	4	2	no	—
212	C₂×C₄×C₄₃	—	4	4	no	—
213	C₂×C₄×C₄₃	—	4	4	no	—
214	C₂×C₄×C₄₃	—	4	4	no	—
215	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
216	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
219	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
220	C₂×C₄×C₄₃	#120	1	2	yes	—
221	C₂×C₄×C₄₃	#121	1	4	yes	—
222	C₂×C₄×C₄₃	#121	1	4	yes	—
223	C₂×C₄×C₄₃	#123	1	2	yes	—
224	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
225	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
226	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
228	C₈×C₄₃	—	4	4	no	—
229	C₂×#1897	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₂²×C₄₃	—	2	2	no	—
231	C₂²×C₄₃	—	2	2	no	—
232	C₂²×C₄₃	—	2	4	no	—
233	C₂²×C₄₃	—	2	4	no	—
234	C₂²×C₄₃	—	2	4	no	—
235	C₂²×C₄₃	—	2	4	no	—
236	C₂²×C₄₃	—	2	4	no	—
237	C₂²×C₄₃	—	4	4	no	—
238	C₂²×C₄₃	—	4	4	no	—
239	C₂²×C₄₃	—	4	8	no	—
240	C₂²×C₄₃	—	4	8	no	—
241	C₂²×C₄₃	—	4	4	no	—
242	C₂²×C₄₃	—	4	2	no	—
243	C₂²×C₄₃	—	8	4	no	—
244	C₂²×C₄₃	#386	1	2	yes	—
245	C₂²×C₄₃	#386	1	2	yes	—
246	C₂²×C₄₃	#421	1	4	yes	—
247	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
248	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
249	C₂²×C₄₃	C₂×#123	1	1	yes	characteristic
250	C₄×C₄₃	—	2	4	no	—
251	C₄×C₄₃	—	4	8	no	—
252	C₄×C₄₃	—	4	4	no	—
253	C₄×C₄₃	—	4	2	no	—
254	C₄×C₄₃	#386	1	2	yes	—
255	C₄×C₄₃	#386	1	2	yes	—
256	C₄×C₄₃	C₂×C₄×D₄	1	2	yes	—
257	C₄×C₄₃	C₂×#121	1	2	yes	—
258	C₂×#525	C₂×C₄₃	1	1	yes	characteristic
259	C₂²×#117	C₂×C₄₃	1	1	yes	characteristic, complemented
260	C₂²×#104	C₂×C₄₃	1	2	yes	complemented
261	C₂×#407	C₂×C₄₃	1	1	yes	characteristic, complemented
262	#1897	C₂×C₄₃	1	8	yes	direct product factor
263	C₂×#339	C₂×C₄₃	1	2	yes	complemented
264	C₂×C₄₃	—	2	1	no	—
265	C₂×C₄₃	—	2	1	no	—
266	C₂×C₄₃	—	2	2	no	—
267	C₂×C₄₃	—	4	4	no	—
268	C₂×C₄₃	—	8	2	no	—
269	C₂×C₄₃	#1897	1	4	yes	direct product factor
270	C₂×C₄₃	C₂×#386	1	1	yes	characteristic
271	C₂×C₄₃	C₂×#421	1	2	yes	—
272	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
273	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
274	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	—
275	#525	—	2	2	no	—
276	#525	—	2	2	no	—
277	#525	C₄×C₄₃	1	4	yes	complemented
278	#525	C₂²×C₄₃	1	4	yes	—
279	C₂×#123	—	2	1	no	—
280	C₂×C₂²⋊Q₈	C₄×C₄₃	1	2	yes	complemented
281	C₂×#121	C₄×C₄₃	1	2	yes	complemented
282	C₂×#120	—	2	1	no	—
283	C₂×C₄×D₄	—	2	2	no	—
284	C₂×#117	—	2	2	no	—
285	C₂×#117	—	2	8	no	—
286	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
287	C₂×#117	C₂²×C₄₃	1	4	yes	complemented
288	C₂²×C₄⋊C₄	—	2	1	no	—
289	C₂²×C₂²⋊C₄	—	2	1	no	—
290	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
291	C₂×#104	—	2	8	no	—
292	C₂×#104	C₂²×C₄₃	1	8	yes	complemented
293	#407	—	2	2	no	—
294	#407	C₂²×C₄₃	1	4	yes	complemented
295	C₂×C₂²⋊C₈	—	2	2	no	—
296	#339	C₂²×C₄₃	1	8	yes	complemented
297	C₄₃	C₂×#1897	1	1	yes	characteristic, direct product factor, Sylow
298	C₂⁵	D₄×C₄₃	1	1	yes	characteristic
299	C₂×#41	—	2	1	no	—
300	C₂×#41	—	2	1	no	—
301	C₂×#41	—	2	4	no	—
302	C₂×#41	—	2	4	no	—
303	C₂×#41	C₂×C₄×C₄₃	1	2	yes	—
304	C₂×#41	C₂³×C₄₃	1	2	yes	—
305	C₂²×Q₈	C₂×C₄×C₄₃	1	1	yes	characteristic
306	C₂²×D₄	—	2	2	no	—
307	C₂²×D₄	—	2	1	no	—
308	C₂²×D₄	C₂×C₄×C₄₃	1	1	yes	characteristic
309	C₂³×C₄	—	2	4	no	—
310	C₂³×C₄	—	2	4	no	—
311	C₂³×C₄	—	2	2	no	—
312	C₂³×C₄	—	2	1	no	—
313	C₂³×C₄	C₂×C₄×C₄₃	1	2	yes	—
314	C₂³×C₄	C₂×C₄×C₄₃	1	2	yes	—
315	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
316	C₂³×C₄	D₄×C₄₃	1	2	yes	—
317	C₂³×C₄	D₄×C₄₃	1	2	yes	—
318	C₂³×C₄	D₄×C₄₃	1	2	yes	—
319	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
320	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
321	C₂×M₁₆	—	2	2	no	—
322	C₂×M₁₆	—	2	4	no	—
323	C₂×M₁₆	—	2	4	no	—
324	C₂×M₁₆	C₂³×C₄₃	1	4	yes	—
325	C₂²×C₈	—	2	2	no	—
326	#123	—	2	4	no	—
327	#123	—	2	4	no	—
328	C₂²⋊Q₈	—	2	4	no	—
329	C₂²⋊Q₈	C₂×C₄×C₄₃	1	8	yes	complemented
330	#121	—	2	4	no	—
331	#121	C₂×C₄×C₄₃	1	8	yes	complemented
332	#120	—	2	4	no	—
333	#120	—	2	4	no	—
334	C₄×D₄	—	2	8	no	—
335	C₄×D₄	—	2	8	no	—
336	#117	—	2	16	no	—
337	#117	—	2	1	no	—
338	#117	—	2	1	no	—
339	#117	—	2	16	no	—
340	#117	C₂×C₄×C₄₃	1	2	yes	—
341	#117	C₂³×C₄₃	1	2	yes	—
342	C₂×C₄⋊C₄	—	2	8	no	—
343	C₂×C₄⋊C₄	—	2	2	no	—
344	C₂×C₄⋊C₄	—	2	4	no	—
345	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
346	C₂×C₂²⋊C₄	—	2	8	no	—
347	C₂×C₂²⋊C₄	—	2	2	no	—
348	C₂×C₂²⋊C₄	—	2	4	no	—
349	C₂×C₂²⋊C₄	—	2	1	no	—
350	C₂×C₂²⋊C₄	—	2	2	no	—
351	C₂×C₄²	—	2	2	no	—
352	C₂×C₄²	—	2	4	no	—
353	C₂×C₄²	—	2	1	no	—
354	C₂×C₄²	D₄×C₄₃	1	8	yes	complemented
355	C₂×C₄²	C₂³×C₄₃	1	4	yes	—
356	#104	—	2	16	no	—
357	C₂²⋊C₈	—	2	8	no	—
358	C₂⁴	—	2	2	no	—
359	C₂⁴	—	2	2	no	—
360	C₂⁴	—	2	1	no	—
361	C₂⁴	—	4	4	no	—
362	C₂⁴	C₂²⋊C₄×C₄₃	1	2	yes	—
363	C₂⁴	C₂²⋊C₄×C₄₃	1	2	yes	—
364	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
365	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
366	#41	—	2	8	no	—
367	#41	—	2	4	no	—
368	#41	—	2	4	no	—
369	#41	—	4	2	no	—
370	#41	—	4	4	no	—
371	#41	—	4	2	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	—	2	4	no	—
374	C₂×Q₈	C₂²×C₄×C₄₃	1	2	yes	—
375	C₂×D₄	—	2	8	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	2	4	no	—
380	C₂×D₄	—	4	8	no	—
381	C₂×D₄	—	4	2	no	—
382	C₂×D₄	—	4	2	no	—
383	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	8	no	—
387	C₂²×C₄	—	2	8	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	8	no	—
390	C₂²×C₄	—	2	8	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	8	no	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	4	8	no	—
401	C₂²×C₄	—	4	4	no	—
402	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
403	C₂²×C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
404	C₂²×C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
405	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
406	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
407	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
408	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
409	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
410	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
411	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
413	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
414	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
415	C₂²×C₄	#41×C₄₃	1	4	yes	—
416	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
417	M₁₆	—	2	4	no	—
418	M₁₆	—	2	4	no	—
419	M₁₆	—	4	4	no	—
420	C₂×C₈	—	2	4	no	—
421	C₂×C₈	—	4	4	no	—
422	C₄⋊C₄	—	2	16	no	—
423	C₄⋊C₄	—	2	8	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	C₂²×C₄×C₄₃	1	4	yes	—
426	C₂²⋊C₄	—	2	16	no	—
427	C₂²⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	—	2	8	no	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₂²⋊C₄	—	2	8	no	—
431	C₄²	—	2	2	no	—
432	C₄²	—	2	8	no	—
433	C₄²	—	2	4	no	—
434	C₄²	—	2	2	no	—
435	C₄²	C₂×D₄×C₄₃	1	8	yes	complemented
436	C₂³	—	2	4	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	4	no	—
440	C₂³	—	2	4	no	—
441	C₂³	—	2	4	no	—
442	C₂³	—	2	4	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	4	4	no	—
445	C₂³	—	4	4	no	—
446	C₂³	—	4	8	no	—
447	C₂³	—	4	8	no	—
448	C₂³	—	4	2	no	—
449	C₂³	—	4	4	no	—
450	C₂³	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
451	C₂³	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
452	C₂³	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
453	C₂³	#120×C₄₃	1	2	yes	—
454	C₂³	#123×C₄₃	1	2	yes	—
455	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
456	Q₈	—	2	4	no	—
457	Q₈	—	4	2	no	—
458	D₄	—	2	4	no	—
459	D₄	—	4	16	no	—
460	D₄	—	4	2	no	—
461	D₄	—	4	2	no	—
462	D₄	—	4	4	no	—
463	D₄	—	4	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	8	no	—
469	C₂×C₄	—	2	8	no	—
470	C₂×C₄	—	2	8	no	—
471	C₂×C₄	—	2	8	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	8	no	—
475	C₂×C₄	—	4	8	no	—
476	C₂×C₄	—	4	16	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	4	no	—
479	C₂×C₄	—	4	4	no	—
480	C₂×C₄	—	4	4	no	—
481	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
482	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
483	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
484	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
485	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
486	C₂×C₄	#120×C₄₃	1	2	yes	—
487	C₂×C₄	#121×C₄₃	1	4	yes	—
488	C₂×C₄	#121×C₄₃	1	4	yes	—
489	C₂×C₄	#123×C₄₃	1	2	yes	—
490	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
491	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
492	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
493	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
494	C₈	—	4	4	no	—
495	C₂²	—	2	2	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	2	4	no	—
498	C₂²	—	2	4	no	—
499	C₂²	—	2	4	no	—
500	C₂²	—	2	4	no	—
501	C₂²	—	2	4	no	—
502	C₂²	—	4	4	no	—
503	C₂²	—	4	4	no	—
504	C₂²	—	4	8	no	—
505	C₂²	—	4	8	no	—
506	C₂²	—	4	4	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	8	4	no	—
509	C₂²	C₄₃×#386	1	2	yes	—
510	C₂²	C₄₃×#386	1	2	yes	—
511	C₂²	C₄₃×#421	1	4	yes	—
512	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
513	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
514	C₂²	C₂×#123×C₄₃	1	1	yes	characteristic
515	C₄	—	2	4	no	—
516	C₄	—	4	8	no	—
517	C₄	—	4	4	no	—
518	C₄	—	4	2	no	—
519	C₄	C₄₃×#386	1	2	yes	—
520	C₄	C₄₃×#386	1	2	yes	—
521	C₄	C₂×C₄×D₄×C₄₃	1	2	yes	—
522	C₄	C₂×#121×C₄₃	1	2	yes	—
523	C₂	—	2	1	no	—
524	C₂	—	2	1	no	—
525	C₂	—	2	2	no	—
526	C₂	—	4	4	no	—
527	C₂	—	8	2	no	—
528	C₂	C₄₃×#1897	1	4	yes	direct product factor
529	C₂	C₂×C₄₃×#386	1	1	yes	characteristic
530	C₂	C₂×C₄₃×#421	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₄₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
socle	C₂³×C₄₃	C₂×C₂²⋊C₄
prime radical	C₂×C₄₃×#525	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₃ ◁ C₂⁴×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#117×C₄₃	C₂	semidirect
3. C₂²×#104×C₄₃	C₂	semidirect
4. C₂×C₄₃×#407	C₂	semidirect
5. C₄₃×#1897	C₂	direct (N × H)
6. C₂×C₄₃×#339	C₂	semidirect
12. C₄₃×#525	C₄	semidirect
15. C₂×C₂²⋊Q₈×C₄₃	C₄	semidirect
16. C₂×#121×C₄₃	C₄	semidirect
22. C₂×#117×C₄₃	C₂²	semidirect
27. C₂×#104×C₄₃	C₂²	semidirect
29. C₄₃×#407	C₂²	semidirect
31. C₄₃×#339	C₂²	semidirect
63. C₂²⋊Q₈×C₄₃	C₂×C₄	semidirect
65. #121×C₄₃	C₂×C₄	semidirect
88. C₂×C₄²×C₄₃	D₄	semidirect
169. C₄²×C₄₃	C₂×D₄	semidirect
229. C₂×#1897	C₄₃	direct (N × H)
259. C₂²×#117	C₂×C₄₃	semidirect
260. C₂²×#104	C₂×C₄₃	semidirect
261. C₂×#407	C₂×C₄₃	semidirect
262. #1897	C₂×C₄₃	direct (N × H)
263. C₂×#339	C₂×C₄₃	semidirect
269. C₂×C₄₃	#1897	direct (N × H)
277. #525	C₄×C₄₃	semidirect
280. C₂×C₂²⋊Q₈	C₄×C₄₃	semidirect
281. C₂×#121	C₄×C₄₃	semidirect
287. C₂×#117	C₂²×C₄₃	semidirect
292. C₂×#104	C₂²×C₄₃	semidirect
294. #407	C₂²×C₄₃	semidirect
296. #339	C₂²×C₄₃	semidirect
297. C₄₃	C₂×#1897	direct (N × H)
329. C₂²⋊Q₈	C₂×C₄×C₄₃	semidirect
331. #121	C₂×C₄×C₄₃	semidirect
354. C₂×C₄²	D₄×C₄₃	semidirect
435. C₄²	C₂×D₄×C₄₃	semidirect
528. C₂	C₄₃×#1897	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×#525	2
C₂²×#117×C₄₃	2
C₂²×#104×C₄₃	2
C₂×C₄₃×#407	2
C₄₃×#1897	2
C₂×C₄₃×#339	2
C₂×#1897	43

Subgroups — C2×C43×#1897 #24940995

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₃×#1897 #24940995