Subgroups — C₂×C₄₃×#2038 #24943508

Order 11008.

1434 conjugacy classes of subgroups.

The subgroup lattice has 646 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
2	C₂×C₄₃×#428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#104×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₃×#417	C₂	1	1	yes	maximal, characteristic
5	C₂²×#101×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄₃×#391	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#2038	C₂	1	8	yes	maximal, direct product factor
8	C₂×C₄₃×#339	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
10	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
13	C₄₃×#536	—	2	2	no	—
14	C₄₃×#536	—	2	2	no	—
15	C₄₃×#536	—	2	2	no	—
16	C₄₃×#536	C₂²	1	4	yes	—
17	C₂×C₄⋊Q₈×C₄₃	—	2	1	no	—
18	C₂×#124×C₄₃	—	2	1	no	—
19	C₂×#123×C₄₃	—	2	2	no	—
20	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
21	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
22	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
25	C₄₃×#428	—	2	2	no	—
26	C₄₃×#428	C₂²	1	4	yes	complemented
27	C₂×#107×C₄₃	—	2	1	no	—
28	C₂×#106×C₄₃	—	2	1	no	—
29	C₂×#104×C₄₃	—	2	4	no	—
30	C₂×#104×C₄₃	C₂²	1	4	yes	—
31	C₄₃×#417	—	2	2	no	—
32	C₄₃×#417	C₂²	1	4	yes	—
33	C₂×#103×C₄₃	—	2	1	no	—
34	C₂×#102×C₄₃	—	2	1	no	—
35	C₂×#101×C₄₃	—	2	4	no	—
36	C₂×#101×C₄₃	C₂²	1	4	yes	complemented
37	C₄₃×#391	—	2	2	no	—
38	C₄₃×#391	C₂²	1	4	yes	complemented
39	C₂×#95×C₄₃	—	2	2	no	—
40	C₄₃×#339	C₂²	1	4	yes	complemented
41	C₂×#41×C₄₃	—	2	1	no	—
42	C₂×#41×C₄₃	—	2	1	no	—
43	C₂×#41×C₄₃	—	2	2	no	—
44	C₂×#41×C₄₃	—	2	2	no	—
45	C₂×#41×C₄₃	—	2	2	no	—
46	C₂×#41×C₄₃	—	2	2	no	—
47	C₂×#41×C₄₃	D₄	1	2	yes	—
48	C₂×#41×C₄₃	C₂³	1	2	yes	—
49	C₂²×Q₈×C₄₃	—	2	1	no	—
50	C₂²×Q₈×C₄₃	—	2	1	no	—
51	C₂²×Q₈×C₄₃	—	2	1	no	—
52	C₂²×Q₈×C₄₃	—	2	1	no	—
53	C₂²×Q₈×C₄₃	—	2	2	no	—
54	C₂²×Q₈×C₄₃	—	2	2	no	—
55	C₂²×Q₈×C₄₃	—	2	2	no	—
56	C₂²×Q₈×C₄₃	—	2	2	no	—
57	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
58	C₂²×Q₈×C₄₃	D₄	1	2	yes	—
59	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
60	C₂²×D₄×C₄₃	—	2	1	no	—
61	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₄₃	—	2	1	no	—
63	C₂³×C₄×C₄₃	—	2	1	no	—
64	C₂³×C₄×C₄₃	—	2	1	no	—
65	C₂³×C₄×C₄₃	D₄	1	2	yes	—
66	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
67	C₂×M₁₆×C₄₃	—	2	1	no	—
68	C₂×M₁₆×C₄₃	—	2	2	no	—
69	C₂×M₁₆×C₄₃	—	2	1	no	—
70	C₂×M₁₆×C₄₃	—	2	2	no	—
71	C₂×M₁₆×C₄₃	—	2	2	no	—
72	C₂×M₁₆×C₄₃	D₄	1	4	yes	—
73	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
74	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
75	C₂²×C₈×C₄₃	—	2	1	no	—
76	C₂²×C₈×C₄₃	—	2	1	no	—
77	C₄⋊Q₈×C₄₃	—	2	4	no	—
78	C₄⋊Q₈×C₄₃	—	2	4	no	—
79	#124×C₄₃	—	2	4	no	—
80	#124×C₄₃	—	2	4	no	—
81	#123×C₄₃	—	2	8	no	—
82	#123×C₄₃	—	2	8	no	—
83	C₂²⋊Q₈×C₄₃	—	2	4	no	—
84	C₂²⋊Q₈×C₄₃	—	2	4	no	—
85	C₂²⋊Q₈×C₄₃	—	2	4	no	—
86	C₂²⋊Q₈×C₄₃	—	2	4	no	—
87	#117×C₄₃	—	2	1	no	—
88	#117×C₄₃	—	2	1	no	—
89	#117×C₄₃	D₄	1	2	yes	—
90	#117×C₄₃	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
92	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
93	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
94	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
95	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
96	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
97	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
98	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
101	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
102	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
103	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
104	C₂×C₄²×C₄₃	—	2	1	no	—
105	C₂×C₄²×C₄₃	—	2	2	no	—
106	C₂×C₄²×C₄₃	—	2	2	no	—
107	C₂×C₄²×C₄₃	—	2	1	no	—
108	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
109	#107×C₄₃	—	2	4	no	—
110	#106×C₄₃	—	2	4	no	—
111	#104×C₄₃	—	2	8	no	—
112	#103×C₄₃	—	2	4	no	—
113	#102×C₄₃	—	2	4	no	—
114	#101×C₄₃	—	2	8	no	—
115	#95×C₄₃	—	2	8	no	—
116	C₂⁴×C₄₃	—	2	1	no	—
117	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
118	#41×C₄₃	—	2	4	no	—
119	#41×C₄₃	—	2	4	no	—
120	#41×C₄₃	—	2	2	no	—
121	#41×C₄₃	—	2	2	no	—
122	#41×C₄₃	—	2	2	no	—
123	#41×C₄₃	—	2	2	no	—
124	#41×C₄₃	—	4	2	no	—
125	#41×C₄₃	—	4	2	no	—
126	#41×C₄₃	—	4	2	no	—
127	#41×C₄₃	—	4	2	no	—
128	C₂×Q₈×C₄₃	—	2	2	no	—
129	C₂×Q₈×C₄₃	—	2	2	no	—
130	C₂×Q₈×C₄₃	—	2	1	no	—
131	C₂×Q₈×C₄₃	—	2	4	no	—
132	C₂×Q₈×C₄₃	—	2	4	no	—
133	C₂×Q₈×C₄₃	—	2	2	no	—
134	C₂×Q₈×C₄₃	—	2	2	no	—
135	C₂×Q₈×C₄₃	—	2	2	no	—
136	C₂×Q₈×C₄₃	—	2	2	no	—
137	C₂×Q₈×C₄₃	—	2	2	no	—
138	C₂×Q₈×C₄₃	—	2	2	no	—
139	C₂×Q₈×C₄₃	—	2	2	no	—
140	C₂×Q₈×C₄₃	—	2	2	no	—
141	C₂×Q₈×C₄₃	—	4	2	no	—
142	C₂×Q₈×C₄₃	—	4	2	no	—
143	C₂×Q₈×C₄₃	—	4	2	no	—
144	C₂×Q₈×C₄₃	—	4	2	no	—
145	C₂×Q₈×C₄₃	—	4	2	no	—
146	C₂×Q₈×C₄₃	—	4	2	no	—
147	C₂×Q₈×C₄₃	—	4	2	no	—
148	C₂×Q₈×C₄₃	—	4	2	no	—
149	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
150	C₂×D₄×C₄₃	—	2	1	no	—
151	C₂×D₄×C₄₃	—	2	2	no	—
152	C₂×D₄×C₄₃	—	2	2	no	—
153	C₂×D₄×C₄₃	—	2	2	no	—
154	C₂×D₄×C₄₃	—	2	2	no	—
155	C₂×D₄×C₄₃	—	4	2	no	—
156	C₂×D₄×C₄₃	—	4	2	no	—
157	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₄₃	—	2	4	no	—
159	C₂²×C₄×C₄₃	—	2	2	no	—
160	C₂²×C₄×C₄₃	—	2	2	no	—
161	C₂²×C₄×C₄₃	—	2	2	no	—
162	C₂²×C₄×C₄₃	—	2	1	no	—
163	C₂²×C₄×C₄₃	—	2	1	no	—
164	C₂²×C₄×C₄₃	—	2	2	no	—
165	C₂²×C₄×C₄₃	—	2	1	no	—
166	C₂²×C₄×C₄₃	—	2	4	no	—
167	C₂²×C₄×C₄₃	—	2	4	no	—
168	C₂²×C₄×C₄₃	—	2	2	no	—
169	C₂²×C₄×C₄₃	—	2	2	no	—
170	C₂²×C₄×C₄₃	—	4	2	no	—
171	C₂²×C₄×C₄₃	—	4	4	no	—
172	C₂²×C₄×C₄₃	—	4	2	no	—
173	C₂²×C₄×C₄₃	—	4	2	no	—
174	C₂²×C₄×C₄₃	—	4	1	no	—
175	C₂²×C₄×C₄₃	—	4	1	no	—
176	C₂²×C₄×C₄₃	—	4	2	no	—
177	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
182	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
183	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₄₃	#41	1	2	yes	—
185	C₂²×C₄×C₄₃	#41	1	2	yes	—
186	C₂²×C₄×C₄₃	#41	1	2	yes	—
187	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
188	M₁₆×C₄₃	—	2	4	no	—
189	M₁₆×C₄₃	—	2	2	no	—
190	M₁₆×C₄₃	—	2	2	no	—
191	M₁₆×C₄₃	—	2	2	no	—
192	M₁₆×C₄₃	—	4	2	no	—
193	M₁₆×C₄₃	C₂×D₄	1	4	yes	—
194	C₂×C₈×C₄₃	—	2	4	no	—
195	C₂×C₈×C₄₃	—	2	2	no	—
196	C₂×C₈×C₄₃	—	2	2	no	—
197	C₂×C₈×C₄₃	—	4	2	no	—
198	C₄⋊C₄×C₄₃	—	2	8	no	—
199	C₄⋊C₄×C₄₃	—	2	8	no	—
200	C₄⋊C₄×C₄₃	—	2	1	no	—
201	C₄⋊C₄×C₄₃	—	2	1	no	—
202	C₄⋊C₄×C₄₃	—	2	2	no	—
203	C₄⋊C₄×C₄₃	—	2	2	no	—
204	C₄⋊C₄×C₄₃	—	4	1	no	—
205	C₄⋊C₄×C₄₃	—	4	1	no	—
206	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
207	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
208	C₂²⋊C₄×C₄₃	—	2	8	no	—
209	C₂²⋊C₄×C₄₃	—	2	8	no	—
210	C₂²⋊C₄×C₄₃	—	2	2	no	—
211	C₂²⋊C₄×C₄₃	—	2	2	no	—
212	C₄²×C₄₃	—	2	2	no	—
213	C₄²×C₄₃	—	2	2	no	—
214	C₄²×C₄₃	—	2	2	no	—
215	C₄²×C₄₃	—	2	2	no	—
216	C₄²×C₄₃	—	4	2	no	—
217	C₂³×C₄₃	—	2	2	no	—
218	C₂³×C₄₃	—	2	2	no	—
219	C₂³×C₄₃	—	2	2	no	—
220	C₂³×C₄₃	—	4	2	no	—
221	C₂³×C₄₃	—	4	2	no	—
222	C₂³×C₄₃	—	4	2	no	—
223	C₂³×C₄₃	#120	1	1	yes	characteristic
224	C₂³×C₄₃	#120	1	1	yes	characteristic
225	C₂³×C₄₃	#121	1	2	yes	—
226	C₂³×C₄₃	#123	1	2	yes	—
227	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
228	Q₈×C₄₃	—	2	2	no	—
229	Q₈×C₄₃	—	2	2	no	—
230	Q₈×C₄₃	—	4	2	no	—
231	Q₈×C₄₃	—	4	2	no	—
232	Q₈×C₄₃	—	4	2	no	—
233	Q₈×C₄₃	—	4	2	no	—
234	Q₈×C₄₃	—	4	4	no	—
235	Q₈×C₄₃	—	4	4	no	—
236	Q₈×C₄₃	—	4	2	no	—
237	D₄×C₄₃	—	2	2	no	—
238	D₄×C₄₃	—	2	2	no	—
239	D₄×C₄₃	—	4	2	no	—
240	D₄×C₄₃	—	4	2	no	—
241	D₄×C₄₃	—	4	4	no	—
242	D₄×C₄₃	—	4	2	no	—
243	C₂×C₄×C₄₃	—	2	4	no	—
244	C₂×C₄×C₄₃	—	2	2	no	—
245	C₂×C₄×C₄₃	—	2	2	no	—
246	C₂×C₄×C₄₃	—	2	4	no	—
247	C₂×C₄×C₄₃	—	2	2	no	—
248	C₂×C₄×C₄₃	—	2	4	no	—
249	C₂×C₄×C₄₃	—	2	4	no	—
250	C₂×C₄×C₄₃	—	4	2	no	—
251	C₂×C₄×C₄₃	—	4	8	no	—
252	C₂×C₄×C₄₃	—	4	2	no	—
253	C₂×C₄×C₄₃	—	4	4	no	—
254	C₂×C₄×C₄₃	—	4	4	no	—
255	C₂×C₄×C₄₃	—	4	2	no	—
256	C₂×C₄×C₄₃	—	4	2	no	—
257	C₂×C₄×C₄₃	—	4	2	no	—
258	C₂×C₄×C₄₃	—	4	2	no	—
259	C₂×C₄×C₄₃	—	4	2	no	—
260	C₂×C₄×C₄₃	—	4	4	no	—
261	C₂×C₄×C₄₃	—	4	4	no	—
262	C₂×C₄×C₄₃	—	4	2	no	—
263	C₂×C₄×C₄₃	—	8	2	no	—
264	C₂×C₄×C₄₃	—	8	2	no	—
265	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
266	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
267	C₂×C₄×C₄₃	#121	1	2	yes	—
268	C₂×C₄×C₄₃	#121	1	2	yes	—
269	C₂×C₄×C₄₃	#121	1	2	yes	—
270	C₂×C₄×C₄₃	#121	1	2	yes	—
271	C₂×C₄×C₄₃	#121	1	2	yes	—
272	C₂×C₄×C₄₃	#123	1	2	yes	—
273	C₂×C₄×C₄₃	#123	1	2	yes	—
274	C₂×C₄×C₄₃	#123	1	2	yes	—
275	C₂×C₄×C₄₃	#124	1	2	yes	—
276	C₂×C₄×C₄₃	#124	1	2	yes	—
277	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
278	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
279	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
280	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
281	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
282	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
283	C₈×C₄₃	—	2	4	no	—
284	C₈×C₄₃	—	4	2	no	—
285	C₂×#2038	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
286	C₂²×C₄₃	—	2	1	no	—
287	C₂²×C₄₃	—	2	1	no	—
288	C₂²×C₄₃	—	2	1	no	—
289	C₂²×C₄₃	—	2	1	no	—
290	C₂²×C₄₃	—	2	4	no	—
291	C₂²×C₄₃	—	2	4	no	—
292	C₂²×C₄₃	—	4	2	no	—
293	C₂²×C₄₃	—	4	2	no	—
294	C₂²×C₄₃	—	4	2	no	—
295	C₂²×C₄₃	—	8	4	no	—
296	C₂²×C₄₃	#394	1	2	yes	—
297	C₂²×C₄₃	#394	1	2	yes	—
298	C₂²×C₄₃	#454	1	2	yes	—
299	C₂²×C₄₃	#456	1	2	yes	—
300	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
301	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
302	C₂²×C₄₃	C₂×#123	1	1	yes	characteristic
303	C₄×C₄₃	—	4	4	no	—
304	C₄×C₄₃	—	4	4	no	—
305	C₄×C₄₃	—	4	2	no	—
306	C₄×C₄₃	—	4	2	no	—
307	C₄×C₄₃	—	4	2	no	—
308	C₄×C₄₃	—	8	2	no	—
309	C₄×C₄₃	#394	1	2	yes	—
310	C₄×C₄₃	#394	1	2	yes	—
311	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
312	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
313	C₄×C₄₃	C₂×#123	1	1	yes	characteristic
314	C₄×C₄₃	C₂×#124	1	1	yes	characteristic
315	C₂×#536	C₂×C₄₃	1	1	yes	characteristic
316	C₂×#428	C₂×C₄₃	1	1	yes	characteristic, complemented
317	C₂²×#104	C₂×C₄₃	1	1	yes	characteristic
318	C₂×#417	C₂×C₄₃	1	1	yes	characteristic
319	C₂²×#101	C₂×C₄₃	1	1	yes	characteristic, complemented
320	C₂×#391	C₂×C₄₃	1	1	yes	characteristic, complemented
321	#2038	C₂×C₄₃	1	8	yes	direct product factor
322	C₂×#339	C₂×C₄₃	1	1	yes	characteristic, complemented
323	C₂×C₄₃	—	2	1	no	—
324	C₂×C₄₃	—	2	1	no	—
325	C₂×C₄₃	—	2	2	no	—
326	C₂×C₄₃	—	8	2	no	—
327	C₂×C₄₃	#2038	1	4	yes	direct product factor
328	C₂×C₄₃	C₂×#394	1	1	yes	characteristic
329	C₂×C₄₃	C₂×#454	1	1	yes	characteristic
330	C₂×C₄₃	C₂×#456	1	1	yes	characteristic
331	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
332	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic
333	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
334	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
335	#536	—	2	2	no	—
336	#536	—	2	2	no	—
337	#536	—	2	2	no	—
338	#536	C₂²×C₄₃	1	4	yes	—
339	C₂×C₄⋊Q₈	—	2	1	no	—
340	C₂×#124	—	2	1	no	—
341	C₂×#123	—	2	2	no	—
342	C₂×C₂²⋊Q₈	—	2	1	no	—
343	C₂×C₂²⋊Q₈	—	2	1	no	—
344	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
345	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
346	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
347	#428	—	2	2	no	—
348	#428	C₂²×C₄₃	1	4	yes	complemented
349	C₂×#107	—	2	1	no	—
350	C₂×#106	—	2	1	no	—
351	C₂×#104	—	2	4	no	—
352	C₂×#104	C₂²×C₄₃	1	4	yes	—
353	#417	—	2	2	no	—
354	#417	C₂²×C₄₃	1	4	yes	—
355	C₂×#103	—	2	1	no	—
356	C₂×#102	—	2	1	no	—
357	C₂×#101	—	2	4	no	—
358	C₂×#101	C₂²×C₄₃	1	4	yes	complemented
359	#391	—	2	2	no	—
360	#391	C₂²×C₄₃	1	4	yes	complemented
361	C₂×#95	—	2	2	no	—
362	#339	C₂²×C₄₃	1	4	yes	complemented
363	C₄₃	C₂×#2038	1	1	yes	characteristic, direct product factor, Sylow
364	C₂×#41	—	2	1	no	—
365	C₂×#41	—	2	1	no	—
366	C₂×#41	—	2	2	no	—
367	C₂×#41	—	2	2	no	—
368	C₂×#41	—	2	2	no	—
369	C₂×#41	—	2	2	no	—
370	C₂×#41	D₄×C₄₃	1	2	yes	—
371	C₂×#41	C₂³×C₄₃	1	2	yes	—
372	C₂²×Q₈	—	2	1	no	—
373	C₂²×Q₈	—	2	1	no	—
374	C₂²×Q₈	—	2	1	no	—
375	C₂²×Q₈	—	2	1	no	—
376	C₂²×Q₈	—	2	2	no	—
377	C₂²×Q₈	—	2	2	no	—
378	C₂²×Q₈	—	2	2	no	—
379	C₂²×Q₈	—	2	2	no	—
380	C₂²×Q₈	D₄×C₄₃	1	1	yes	characteristic
381	C₂²×Q₈	D₄×C₄₃	1	2	yes	—
382	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
383	C₂²×D₄	—	2	1	no	—
384	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
385	C₂³×C₄	—	2	1	no	—
386	C₂³×C₄	—	2	1	no	—
387	C₂³×C₄	—	2	1	no	—
388	C₂³×C₄	D₄×C₄₃	1	2	yes	—
389	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
390	C₂×M₁₆	—	2	1	no	—
391	C₂×M₁₆	—	2	2	no	—
392	C₂×M₁₆	—	2	1	no	—
393	C₂×M₁₆	—	2	2	no	—
394	C₂×M₁₆	—	2	2	no	—
395	C₂×M₁₆	D₄×C₄₃	1	4	yes	—
396	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
397	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
398	C₂²×C₈	—	2	1	no	—
399	C₂²×C₈	—	2	1	no	—
400	C₄⋊Q₈	—	2	4	no	—
401	C₄⋊Q₈	—	2	4	no	—
402	#124	—	2	4	no	—
403	#124	—	2	4	no	—
404	#123	—	2	8	no	—
405	#123	—	2	8	no	—
406	C₂²⋊Q₈	—	2	4	no	—
407	C₂²⋊Q₈	—	2	4	no	—
408	C₂²⋊Q₈	—	2	4	no	—
409	C₂²⋊Q₈	—	2	4	no	—
410	#117	—	2	1	no	—
411	#117	—	2	1	no	—
412	#117	D₄×C₄₃	1	2	yes	—
413	#117	C₂³×C₄₃	1	2	yes	—
414	C₂×C₄⋊C₄	—	2	2	no	—
415	C₂×C₄⋊C₄	—	2	2	no	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	—	2	1	no	—
418	C₂×C₄⋊C₄	—	2	1	no	—
419	C₂×C₄⋊C₄	—	2	1	no	—
420	C₂×C₄⋊C₄	—	2	1	no	—
421	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
422	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
424	C₂×C₂²⋊C₄	—	2	2	no	—
425	C₂×C₂²⋊C₄	—	2	2	no	—
426	C₂×C₂²⋊C₄	—	2	1	no	—
427	C₂×C₄²	—	2	1	no	—
428	C₂×C₄²	—	2	2	no	—
429	C₂×C₄²	—	2	2	no	—
430	C₂×C₄²	—	2	1	no	—
431	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
432	#107	—	2	4	no	—
433	#106	—	2	4	no	—
434	#104	—	2	8	no	—
435	#103	—	2	4	no	—
436	#102	—	2	4	no	—
437	#101	—	2	8	no	—
438	#95	—	2	8	no	—
439	C₂⁴	—	2	1	no	—
440	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
441	#41	—	2	4	no	—
442	#41	—	2	4	no	—
443	#41	—	2	2	no	—
444	#41	—	2	2	no	—
445	#41	—	2	2	no	—
446	#41	—	2	2	no	—
447	#41	—	4	2	no	—
448	#41	—	4	2	no	—
449	#41	—	4	2	no	—
450	#41	—	4	2	no	—
451	C₂×Q₈	—	2	2	no	—
452	C₂×Q₈	—	2	2	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	—	2	4	no	—
455	C₂×Q₈	—	2	4	no	—
456	C₂×Q₈	—	2	2	no	—
457	C₂×Q₈	—	2	2	no	—
458	C₂×Q₈	—	2	2	no	—
459	C₂×Q₈	—	2	2	no	—
460	C₂×Q₈	—	2	2	no	—
461	C₂×Q₈	—	2	2	no	—
462	C₂×Q₈	—	2	2	no	—
463	C₂×Q₈	—	2	2	no	—
464	C₂×Q₈	—	4	2	no	—
465	C₂×Q₈	—	4	2	no	—
466	C₂×Q₈	—	4	2	no	—
467	C₂×Q₈	—	4	2	no	—
468	C₂×Q₈	—	4	2	no	—
469	C₂×Q₈	—	4	2	no	—
470	C₂×Q₈	—	4	2	no	—
471	C₂×Q₈	—	4	2	no	—
472	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
473	C₂×D₄	—	2	2	no	—
474	C₂×D₄	—	2	2	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	2	no	—
477	C₂×D₄	—	2	2	no	—
478	C₂×D₄	—	4	2	no	—
479	C₂×D₄	—	4	2	no	—
480	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
481	C₂²×C₄	—	2	4	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	—	2	4	no	—
488	C₂²×C₄	—	2	4	no	—
489	C₂²×C₄	—	2	2	no	—
490	C₂²×C₄	—	2	2	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	2	no	—
493	C₂²×C₄	—	4	2	no	—
494	C₂²×C₄	—	4	2	no	—
495	C₂²×C₄	—	4	2	no	—
496	C₂²×C₄	—	4	2	no	—
497	C₂²×C₄	—	4	4	no	—
498	C₂²×C₄	—	4	1	no	—
499	C₂²×C₄	—	4	1	no	—
500	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
501	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
502	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
503	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
504	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
505	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
506	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
507	C₂²×C₄	#41×C₄₃	1	2	yes	—
508	C₂²×C₄	#41×C₄₃	1	2	yes	—
509	C₂²×C₄	#41×C₄₃	1	2	yes	—
510	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
511	M₁₆	—	2	4	no	—
512	M₁₆	—	2	2	no	—
513	M₁₆	—	2	2	no	—
514	M₁₆	—	2	2	no	—
515	M₁₆	—	4	2	no	—
516	M₁₆	C₂×D₄×C₄₃	1	4	yes	—
517	C₂×C₈	—	2	4	no	—
518	C₂×C₈	—	2	2	no	—
519	C₂×C₈	—	2	2	no	—
520	C₂×C₈	—	4	2	no	—
521	C₄⋊C₄	—	2	8	no	—
522	C₄⋊C₄	—	2	8	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	2	no	—
526	C₄⋊C₄	—	2	2	no	—
527	C₄⋊C₄	—	4	1	no	—
528	C₄⋊C₄	—	4	1	no	—
529	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
530	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
531	C₂²⋊C₄	—	2	8	no	—
532	C₂²⋊C₄	—	2	8	no	—
533	C₂²⋊C₄	—	2	2	no	—
534	C₂²⋊C₄	—	2	2	no	—
535	C₄²	—	2	2	no	—
536	C₄²	—	2	2	no	—
537	C₄²	—	2	2	no	—
538	C₄²	—	2	2	no	—
539	C₄²	—	4	2	no	—
540	C₂³	—	2	2	no	—
541	C₂³	—	2	2	no	—
542	C₂³	—	2	2	no	—
543	C₂³	—	4	2	no	—
544	C₂³	—	4	2	no	—
545	C₂³	—	4	2	no	—
546	C₂³	#120×C₄₃	1	1	yes	characteristic
547	C₂³	#120×C₄₃	1	1	yes	characteristic
548	C₂³	#121×C₄₃	1	2	yes	—
549	C₂³	#123×C₄₃	1	2	yes	—
550	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
551	Q₈	—	2	2	no	—
552	Q₈	—	2	2	no	—
553	Q₈	—	4	2	no	—
554	Q₈	—	4	2	no	—
555	Q₈	—	4	2	no	—
556	Q₈	—	4	2	no	—
557	Q₈	—	4	4	no	—
558	Q₈	—	4	4	no	—
559	Q₈	—	4	2	no	—
560	D₄	—	2	2	no	—
561	D₄	—	2	2	no	—
562	D₄	—	4	2	no	—
563	D₄	—	4	2	no	—
564	D₄	—	4	4	no	—
565	D₄	—	4	2	no	—
566	C₂×C₄	—	2	4	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	4	8	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	4	4	no	—
577	C₂×C₄	—	4	4	no	—
578	C₂×C₄	—	4	2	no	—
579	C₂×C₄	—	4	2	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	4	no	—
584	C₂×C₄	—	4	4	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	8	2	no	—
587	C₂×C₄	—	8	2	no	—
588	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
589	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
590	C₂×C₄	#121×C₄₃	1	2	yes	—
591	C₂×C₄	#121×C₄₃	1	2	yes	—
592	C₂×C₄	#121×C₄₃	1	2	yes	—
593	C₂×C₄	#121×C₄₃	1	2	yes	—
594	C₂×C₄	#121×C₄₃	1	2	yes	—
595	C₂×C₄	#123×C₄₃	1	2	yes	—
596	C₂×C₄	#123×C₄₃	1	2	yes	—
597	C₂×C₄	#123×C₄₃	1	2	yes	—
598	C₂×C₄	#124×C₄₃	1	2	yes	—
599	C₂×C₄	#124×C₄₃	1	2	yes	—
600	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
601	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
602	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
603	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
604	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
605	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
606	C₈	—	2	4	no	—
607	C₈	—	4	2	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	2	1	no	—
610	C₂²	—	2	1	no	—
611	C₂²	—	2	1	no	—
612	C₂²	—	2	4	no	—
613	C₂²	—	2	4	no	—
614	C₂²	—	4	2	no	—
615	C₂²	—	4	2	no	—
616	C₂²	—	4	2	no	—
617	C₂²	—	8	4	no	—
618	C₂²	C₄₃×#394	1	2	yes	—
619	C₂²	C₄₃×#394	1	2	yes	—
620	C₂²	C₄₃×#454	1	2	yes	—
621	C₂²	C₄₃×#456	1	2	yes	—
622	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
623	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
624	C₂²	C₂×#123×C₄₃	1	1	yes	characteristic
625	C₄	—	4	4	no	—
626	C₄	—	4	4	no	—
627	C₄	—	4	2	no	—
628	C₄	—	4	2	no	—
629	C₄	—	4	2	no	—
630	C₄	—	8	2	no	—
631	C₄	C₄₃×#394	1	2	yes	—
632	C₄	C₄₃×#394	1	2	yes	—
633	C₄	C₂×#121×C₄₃	1	1	yes	characteristic
634	C₄	C₂×#121×C₄₃	1	1	yes	characteristic
635	C₄	C₂×#123×C₄₃	1	1	yes	characteristic
636	C₄	C₂×#124×C₄₃	1	1	yes	characteristic
637	C₂	—	2	1	no	—
638	C₂	—	2	1	no	—
639	C₂	—	2	2	no	—
640	C₂	—	8	2	no	—
641	C₂	C₄₃×#2038	1	4	yes	direct product factor
642	C₂	C₂×C₄₃×#394	1	1	yes	characteristic
643	C₂	C₂×C₄₃×#454	1	1	yes	characteristic
644	C₂	C₂×C₄₃×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂²×#41×C₄₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂³×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₃×#428	C₂	semidirect
5. C₂²×#101×C₄₃	C₂	semidirect
6. C₂×C₄₃×#391	C₂	semidirect
7. C₄₃×#2038	C₂	direct (N × H)
8. C₂×C₄₃×#339	C₂	semidirect
26. C₄₃×#428	C₂²	semidirect
36. C₂×#101×C₄₃	C₂²	semidirect
38. C₄₃×#391	C₂²	semidirect
40. C₄₃×#339	C₂²	semidirect
285. C₂×#2038	C₄₃	direct (N × H)
316. C₂×#428	C₂×C₄₃	semidirect
319. C₂²×#101	C₂×C₄₃	semidirect
320. C₂×#391	C₂×C₄₃	semidirect
321. #2038	C₂×C₄₃	direct (N × H)
322. C₂×#339	C₂×C₄₃	semidirect
327. C₂×C₄₃	#2038	direct (N × H)
348. #428	C₂²×C₄₃	semidirect
358. C₂×#101	C₂²×C₄₃	semidirect
360. #391	C₂²×C₄₃	semidirect
362. #339	C₂²×C₄₃	semidirect
363. C₄₃	C₂×#2038	direct (N × H)
641. C₂	C₄₃×#2038	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×#536	2
C₂×C₄₃×#428	2
C₂²×#104×C₄₃	2
C₂×C₄₃×#417	2
C₂²×#101×C₄₃	2
C₂×C₄₃×#391	2
C₄₃×#2038	2
C₂×C₄₃×#339	2
C₂×#2038	43

Subgroups — C2×C43×#2038 #24943508

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₃×#2038 #24943508