Subgroups — C₂×C₄₃×#3092 #24980524

Order 11008.

2650 conjugacy classes of subgroups.

The subgroup lattice has 582 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	C₂³×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#3092	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₄₃×#484	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₃×#481	C₂	1	2	yes	maximal, complemented
6	C₂×C₄₃×#483	C₂	1	2	yes	maximal, complemented
7	C₂×C₄₃×#480	C₂	1	2	yes	maximal, complemented
8	C₂×C₄₃×#428	C₂	1	2	yes	maximal, complemented
9	C₂×C₄₃×#417	C₂	1	2	yes	maximal, complemented
10	C₂×C₄₃×#407	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₄₃	—	2	1	no	—
13	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
15	C₄₃×#525	—	2	4	no	—
16	C₄₃×#525	C₂²	1	8	yes	—
17	C₂×#123×C₄₃	—	2	1	no	—
18	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×#120×C₄₃	—	2	1	no	—
23	C₂×C₄×D₄×C₄₃	—	2	1	no	—
24	C₂×C₄×D₄×C₄₃	—	2	1	no	—
25	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊C₄×C₄₃	—	2	4	no	—
27	C₂²×C₄⋊C₄×C₄₃	—	2	1	no	—
28	C₂²×C₄⋊C₄×C₄₃	—	2	1	no	—
29	C₂²×C₄⋊C₄×C₄₃	—	2	1	no	—
30	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
31	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
32	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
33	C₂²×C₄⋊C₄×C₄₃	C₂²	1	8	yes	complemented
34	C₄₃×#484	C₂²	1	16	yes	complemented
35	C₄₃×#483	C₂²	1	16	yes	complemented
36	C₄₃×#481	C₂²	1	16	yes	complemented
37	C₄₃×#480	C₂²	1	16	yes	complemented
38	C₄₃×#428	C₂²	1	16	yes	complemented
39	C₂×#107×C₄₃	C₂²	1	4	yes	complemented
40	C₂×#106×C₄₃	C₂²	1	4	yes	complemented
41	C₄₃×#417	C₂²	1	16	yes	complemented
42	C₂×#103×C₄₃	C₂²	1	4	yes	complemented
43	C₂×#102×C₄₃	C₂²	1	4	yes	complemented
44	C₄₃×#407	C₂²	1	8	yes	complemented
45	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
46	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
47	C₂⁵×C₄₃	D₄	1	1	yes	characteristic
48	C₂×#41×C₄₃	—	2	2	no	—
49	C₂×#41×C₄₃	—	2	8	no	—
50	C₂×#41×C₄₃	C₂³	1	4	yes	—
51	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₄₃	—	2	1	no	—
53	C₂²×D₄×C₄₃	—	2	1	no	—
54	C₂²×D₄×C₄₃	—	2	1	no	—
55	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₄₃	—	2	8	no	—
57	C₂³×C₄×C₄₃	—	2	2	no	—
58	C₂³×C₄×C₄₃	—	2	2	no	—
59	C₂³×C₄×C₄₃	—	2	2	no	—
60	C₂³×C₄×C₄₃	—	2	8	no	—
61	C₂³×C₄×C₄₃	—	2	1	no	—
62	C₂³×C₄×C₄₃	—	4	8	no	—
63	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
66	C₂³×C₄×C₄₃	D₄	1	4	yes	—
67	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
70	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
71	C₂×M₁₆×C₄₃	—	2	8	no	—
72	C₂×M₁₆×C₄₃	C₂³	1	8	yes	—
73	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
74	#123×C₄₃	—	2	8	no	—
75	C₂²⋊Q₈×C₄₃	—	2	2	no	—
76	C₂²⋊Q₈×C₄₃	—	2	2	no	—
77	C₂²⋊Q₈×C₄₃	C₂³	1	4	yes	—
78	C₂²⋊Q₈×C₄₃	C₂³	1	4	yes	—
79	#121×C₄₃	—	2	2	no	—
80	#121×C₄₃	—	2	2	no	—
81	#121×C₄₃	C₂³	1	4	yes	—
82	#121×C₄₃	C₂³	1	4	yes	—
83	#120×C₄₃	—	2	8	no	—
84	C₄×D₄×C₄₃	—	2	8	no	—
85	C₄×D₄×C₄₃	—	2	8	no	—
86	#117×C₄₃	—	2	2	no	—
87	#117×C₄₃	C₂³	1	4	yes	—
88	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
89	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
90	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
91	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
92	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
93	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
94	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
95	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
96	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
97	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
98	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
99	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
100	C₂×C₄⋊C₄×C₄₃	C₂³	1	8	yes	—
101	C₂×C₄⋊C₄×C₄₃	C₂³	1	8	yes	—
102	C₂×C₄⋊C₄×C₄₃	C₂³	1	8	yes	—
103	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
110	C₂×C₄²×C₄₃	—	2	1	no	—
111	#107×C₄₃	C₂³	1	16	yes	complemented
112	#106×C₄₃	C₂³	1	16	yes	complemented
113	#103×C₄₃	C₂³	1	16	yes	complemented
114	#102×C₄₃	C₂³	1	16	yes	complemented
115	C₂²⋊C₈×C₄₃	C₂³	1	8	yes	—
116	C₂²⋊C₈×C₄₃	C₂³	1	8	yes	—
117	C₂⁴×C₄₃	—	2	4	no	—
118	C₂⁴×C₄₃	—	2	4	no	—
119	C₂⁴×C₄₃	—	2	4	no	—
120	C₂⁴×C₄₃	—	2	1	no	—
121	C₂⁴×C₄₃	C₂×D₄	1	4	yes	—
122	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
123	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
124	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
125	#41×C₄₃	—	2	16	no	—
126	#41×C₄₃	—	4	8	no	—
127	C₂×Q₈×C₄₃	—	2	1	no	—
128	C₂×Q₈×C₄₃	—	2	4	no	—
129	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
130	C₂×D₄×C₄₃	—	2	1	no	—
131	C₂×D₄×C₄₃	—	2	4	no	—
132	C₂×D₄×C₄₃	—	2	4	no	—
133	C₂×D₄×C₄₃	—	2	4	no	—
134	C₂×D₄×C₄₃	—	2	4	no	—
135	C₂×D₄×C₄₃	—	4	4	no	—
136	C₂×D₄×C₄₃	—	4	4	no	—
137	C₂×D₄×C₄₃	—	4	4	no	—
138	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
139	C₂²×C₄×C₄₃	—	2	4	no	—
140	C₂²×C₄×C₄₃	—	2	4	no	—
141	C₂²×C₄×C₄₃	—	2	16	no	—
142	C₂²×C₄×C₄₃	—	2	4	no	—
143	C₂²×C₄×C₄₃	—	2	4	no	—
144	C₂²×C₄×C₄₃	—	2	16	no	—
145	C₂²×C₄×C₄₃	—	2	4	no	—
146	C₂²×C₄×C₄₃	—	2	4	no	—
147	C₂²×C₄×C₄₃	—	2	8	no	—
148	C₂²×C₄×C₄₃	—	2	8	no	—
149	C₂²×C₄×C₄₃	—	2	8	no	—
150	C₂²×C₄×C₄₃	—	2	1	no	—
151	C₂²×C₄×C₄₃	—	2	1	no	—
152	C₂²×C₄×C₄₃	—	2	1	no	—
153	C₂²×C₄×C₄₃	—	2	4	no	—
154	C₂²×C₄×C₄₃	—	4	8	no	—
155	C₂²×C₄×C₄₃	—	4	8	no	—
156	C₂²×C₄×C₄₃	—	4	32	no	—
157	C₂²×C₄×C₄₃	—	4	4	no	—
158	C₂²×C₄×C₄₃	—	4	8	no	—
159	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
160	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
161	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
163	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
164	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
165	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₄₃	#41	1	8	yes	—
169	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
170	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
171	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
172	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
173	M₁₆×C₄₃	—	2	16	no	—
174	C₂×C₈×C₄₃	—	2	8	no	—
175	C₂×C₈×C₄₃	C₂⁴	1	8	yes	—
176	C₄⋊C₄×C₄₃	—	2	8	no	—
177	C₄⋊C₄×C₄₃	—	2	8	no	—
178	C₄⋊C₄×C₄₃	—	2	8	no	—
179	C₄⋊C₄×C₄₃	—	2	4	no	—
180	C₄⋊C₄×C₄₃	—	2	4	no	—
181	C₄⋊C₄×C₄₃	—	2	4	no	—
182	C₄⋊C₄×C₄₃	—	2	1	no	—
183	C₄⋊C₄×C₄₃	—	2	1	no	—
184	C₄⋊C₄×C₄₃	C₂⁴	1	8	yes	—
185	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
186	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
187	C₂²⋊C₄×C₄₃	—	2	4	no	—
188	C₂²⋊C₄×C₄₃	—	2	4	no	—
189	C₂²⋊C₄×C₄₃	—	2	4	no	—
190	C₂²⋊C₄×C₄₃	—	2	4	no	—
191	C₂²⋊C₄×C₄₃	—	2	4	no	—
192	C₄²×C₄₃	—	2	4	no	—
193	C₂³×C₄₃	—	2	32	no	—
194	C₂³×C₄₃	—	2	8	no	—
195	C₂³×C₄₃	—	2	2	no	—
196	C₂³×C₄₃	—	2	2	no	—
197	C₂³×C₄₃	—	2	8	no	—
198	C₂³×C₄₃	—	2	2	no	—
199	C₂³×C₄₃	—	2	2	no	—
200	C₂³×C₄₃	—	2	8	no	—
201	C₂³×C₄₃	—	2	2	no	—
202	C₂³×C₄₃	—	2	2	no	—
203	C₂³×C₄₃	—	2	2	no	—
204	C₂³×C₄₃	—	4	2	no	—
205	C₂³×C₄₃	—	4	2	no	—
206	C₂³×C₄₃	—	4	2	no	—
207	C₂³×C₄₃	#123	1	4	yes	—
208	C₂³×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
209	C₂³×C₄₃	#137	1	4	yes	—
210	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
211	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
212	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
213	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
214	Q₈×C₄₃	—	2	4	no	—
215	Q₈×C₄₃	—	4	2	no	—
216	D₄×C₄₃	—	2	4	no	—
217	D₄×C₄₃	—	4	8	no	—
218	D₄×C₄₃	—	4	8	no	—
219	D₄×C₄₃	—	4	8	no	—
220	D₄×C₄₃	—	4	2	no	—
221	C₂×C₄×C₄₃	—	2	8	no	—
222	C₂×C₄×C₄₃	—	2	2	no	—
223	C₂×C₄×C₄₃	—	2	2	no	—
224	C₂×C₄×C₄₃	—	2	8	no	—
225	C₂×C₄×C₄₃	—	2	8	no	—
226	C₂×C₄×C₄₃	—	2	4	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	8	no	—
234	C₂×C₄×C₄₃	—	4	16	no	—
235	C₂×C₄×C₄₃	—	4	16	no	—
236	C₂×C₄×C₄₃	—	4	2	no	—
237	C₂×C₄×C₄₃	—	4	16	no	—
238	C₂×C₄×C₄₃	—	4	8	no	—
239	C₂×C₄×C₄₃	—	4	2	no	—
240	C₂×C₄×C₄₃	—	4	2	no	—
241	C₂×C₄×C₄₃	—	4	8	no	—
242	C₂×C₄×C₄₃	#123	1	4	yes	—
243	C₂×C₄×C₄₃	#123	1	8	yes	—
244	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
245	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
246	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
247	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
249	C₂×C₄×C₄₃	C₂×#41	1	8	yes	—
250	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
251	C₈×C₄₃	—	2	8	no	—
252	C₂×#3092	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
253	C₂²×C₄₃	—	2	32	no	—
254	C₂²×C₄₃	—	2	8	no	—
255	C₂²×C₄₃	—	2	8	no	—
256	C₂²×C₄₃	—	2	8	no	—
257	C₂²×C₄₃	—	2	2	no	—
258	C₂²×C₄₃	—	2	2	no	—
259	C₂²×C₄₃	—	2	2	no	—
260	C₂²×C₄₃	—	2	2	no	—
261	C₂²×C₄₃	—	2	2	no	—
262	C₂²×C₄₃	—	2	2	no	—
263	C₂²×C₄₃	—	4	2	no	—
264	C₂²×C₄₃	—	4	2	no	—
265	C₂²×C₄₃	—	4	2	no	—
266	C₂²×C₄₃	—	8	4	no	—
267	C₂²×C₄₃	C₂×#123	1	4	yes	—
268	C₂²×C₄₃	C₂×#123	1	2	yes	—
269	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
270	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
271	C₂²×C₄₃	C₂×#137	1	4	yes	—
272	C₂²×C₄₃	C₂×#137	1	2	yes	—
273	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
274	C₄×C₄₃	—	2	2	no	—
275	C₄×C₄₃	—	2	2	no	—
276	C₄×C₄₃	—	4	2	no	—
277	C₄×C₄₃	—	4	8	no	—
278	C₄×C₄₃	—	4	2	no	—
279	C₄×C₄₃	—	4	2	no	—
280	C₄×C₄₃	C₂×#123	1	4	yes	—
281	C₄×C₄₃	C₂×#123	1	2	yes	—
282	C₄×C₄₃	C₂²×#41	1	2	yes	—
283	C₂×#525	C₂×C₄₃	1	1	yes	characteristic
284	C₂³×C₄⋊C₄	C₂×C₄₃	1	1	yes	characteristic, complemented
285	#3092	C₂×C₄₃	1	16	yes	direct product factor
286	C₂×#484	C₂×C₄₃	1	2	yes	complemented
287	C₂×#481	C₂×C₄₃	1	2	yes	complemented
288	C₂×#483	C₂×C₄₃	1	2	yes	complemented
289	C₂×#480	C₂×C₄₃	1	2	yes	complemented
290	C₂×#428	C₂×C₄₃	1	2	yes	complemented
291	C₂×#417	C₂×C₄₃	1	2	yes	complemented
292	C₂×#407	C₂×C₄₃	1	1	yes	characteristic, complemented
293	C₂×C₄₃	—	2	4	no	—
294	C₂×C₄₃	—	2	4	no	—
295	C₂×C₄₃	—	2	4	no	—
296	C₂×C₄₃	—	8	2	no	—
297	C₂×C₄₃	#3092	1	4	yes	direct product factor
298	C₂×C₄₃	C₂²×#123	1	1	yes	characteristic
299	C₂×C₄₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
300	C₂×C₄₃	C₂²×#137	1	1	yes	characteristic
301	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
302	C₂⁴×C₄	—	2	1	no	—
303	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
304	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	—
305	#525	—	2	4	no	—
306	#525	C₂²×C₄₃	1	8	yes	—
307	C₂×#123	—	2	1	no	—
308	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
309	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
310	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
311	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
312	C₂×#120	—	2	1	no	—
313	C₂×C₄×D₄	—	2	1	no	—
314	C₂×C₄×D₄	—	2	1	no	—
315	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
316	C₂²×C₄⋊C₄	—	2	4	no	—
317	C₂²×C₄⋊C₄	—	2	1	no	—
318	C₂²×C₄⋊C₄	—	2	1	no	—
319	C₂²×C₄⋊C₄	—	2	1	no	—
320	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
321	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
322	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
323	C₂²×C₄⋊C₄	C₂²×C₄₃	1	8	yes	complemented
324	#484	C₂²×C₄₃	1	16	yes	complemented
325	#483	C₂²×C₄₃	1	16	yes	complemented
326	#481	C₂²×C₄₃	1	16	yes	complemented
327	#480	C₂²×C₄₃	1	16	yes	complemented
328	#428	C₂²×C₄₃	1	16	yes	complemented
329	C₂×#107	C₂²×C₄₃	1	4	yes	complemented
330	C₂×#106	C₂²×C₄₃	1	4	yes	complemented
331	#417	C₂²×C₄₃	1	16	yes	complemented
332	C₂×#103	C₂²×C₄₃	1	4	yes	complemented
333	C₂×#102	C₂²×C₄₃	1	4	yes	complemented
334	#407	C₂²×C₄₃	1	8	yes	complemented
335	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
336	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
337	C₄₃	C₂×#3092	1	1	yes	characteristic, direct product factor, Sylow
338	C₂⁵	D₄×C₄₃	1	1	yes	characteristic
339	C₂×#41	—	2	2	no	—
340	C₂×#41	—	2	8	no	—
341	C₂×#41	C₂³×C₄₃	1	4	yes	—
342	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
343	C₂²×D₄	—	2	1	no	—
344	C₂²×D₄	—	2	1	no	—
345	C₂²×D₄	—	2	1	no	—
346	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
347	C₂³×C₄	—	2	8	no	—
348	C₂³×C₄	—	2	2	no	—
349	C₂³×C₄	—	2	2	no	—
350	C₂³×C₄	—	2	2	no	—
351	C₂³×C₄	—	2	8	no	—
352	C₂³×C₄	—	2	1	no	—
353	C₂³×C₄	—	4	8	no	—
354	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
355	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
356	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
357	C₂³×C₄	D₄×C₄₃	1	4	yes	—
358	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
359	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
360	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
361	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
362	C₂×M₁₆	—	2	8	no	—
363	C₂×M₁₆	C₂³×C₄₃	1	8	yes	—
364	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
365	#123	—	2	8	no	—
366	C₂²⋊Q₈	—	2	2	no	—
367	C₂²⋊Q₈	—	2	2	no	—
368	C₂²⋊Q₈	C₂³×C₄₃	1	4	yes	—
369	C₂²⋊Q₈	C₂³×C₄₃	1	4	yes	—
370	#121	—	2	2	no	—
371	#121	—	2	2	no	—
372	#121	C₂³×C₄₃	1	4	yes	—
373	#121	C₂³×C₄₃	1	4	yes	—
374	#120	—	2	8	no	—
375	C₄×D₄	—	2	8	no	—
376	C₄×D₄	—	2	8	no	—
377	#117	—	2	2	no	—
378	#117	C₂³×C₄₃	1	4	yes	—
379	C₂×C₄⋊C₄	—	2	2	no	—
380	C₂×C₄⋊C₄	—	2	2	no	—
381	C₂×C₄⋊C₄	—	2	4	no	—
382	C₂×C₄⋊C₄	—	2	4	no	—
383	C₂×C₄⋊C₄	—	2	2	no	—
384	C₂×C₄⋊C₄	—	2	4	no	—
385	C₂×C₄⋊C₄	—	2	8	no	—
386	C₂×C₄⋊C₄	—	2	8	no	—
387	C₂×C₄⋊C₄	—	2	8	no	—
388	C₂×C₄⋊C₄	—	2	1	no	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
391	C₂×C₄⋊C₄	C₂³×C₄₃	1	8	yes	—
392	C₂×C₄⋊C₄	C₂³×C₄₃	1	8	yes	—
393	C₂×C₄⋊C₄	C₂³×C₄₃	1	8	yes	—
394	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
396	C₂×C₂²⋊C₄	—	2	1	no	—
397	C₂×C₂²⋊C₄	—	2	1	no	—
398	C₂×C₂²⋊C₄	—	2	1	no	—
399	C₂×C₂²⋊C₄	—	2	1	no	—
400	C₂×C₂²⋊C₄	—	2	1	no	—
401	C₂×C₄²	—	2	1	no	—
402	#107	C₂³×C₄₃	1	16	yes	complemented
403	#106	C₂³×C₄₃	1	16	yes	complemented
404	#103	C₂³×C₄₃	1	16	yes	complemented
405	#102	C₂³×C₄₃	1	16	yes	complemented
406	C₂²⋊C₈	C₂³×C₄₃	1	8	yes	—
407	C₂²⋊C₈	C₂³×C₄₃	1	8	yes	—
408	C₂⁴	—	2	4	no	—
409	C₂⁴	—	2	4	no	—
410	C₂⁴	—	2	4	no	—
411	C₂⁴	—	2	1	no	—
412	C₂⁴	C₂×D₄×C₄₃	1	4	yes	—
413	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
414	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
415	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
416	#41	—	2	16	no	—
417	#41	—	4	8	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	4	no	—
420	C₂×Q₈	C₂⁴×C₄₃	1	2	yes	—
421	C₂×D₄	—	2	4	no	—
422	C₂×D₄	—	2	4	no	—
423	C₂×D₄	—	2	4	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	2	4	no	—
426	C₂×D₄	—	4	4	no	—
427	C₂×D₄	—	4	4	no	—
428	C₂×D₄	—	4	4	no	—
429	C₂×D₄	C₂⁴×C₄₃	1	2	yes	—
430	C₂²×C₄	—	2	4	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	2	16	no	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	16	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	8	no	—
441	C₂²×C₄	—	2	8	no	—
442	C₂²×C₄	—	2	8	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	4	8	no	—
446	C₂²×C₄	—	4	8	no	—
447	C₂²×C₄	—	4	32	no	—
448	C₂²×C₄	—	4	8	no	—
449	C₂²×C₄	—	4	4	no	—
450	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
451	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
453	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
454	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
455	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
456	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
457	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
458	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
459	C₂²×C₄	#41×C₄₃	1	8	yes	—
460	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
461	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
462	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
463	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
464	M₁₆	—	2	16	no	—
465	C₂×C₈	—	2	8	no	—
466	C₂×C₈	C₂⁴×C₄₃	1	8	yes	—
467	C₄⋊C₄	—	2	8	no	—
468	C₄⋊C₄	—	2	8	no	—
469	C₄⋊C₄	—	2	8	no	—
470	C₄⋊C₄	—	2	4	no	—
471	C₄⋊C₄	—	2	4	no	—
472	C₄⋊C₄	—	2	4	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	C₂⁴×C₄₃	1	8	yes	—
476	C₄⋊C₄	C₂⁴×C₄₃	1	2	yes	—
477	C₄⋊C₄	C₂⁴×C₄₃	1	2	yes	—
478	C₂²⋊C₄	—	2	4	no	—
479	C₂²⋊C₄	—	2	4	no	—
480	C₂²⋊C₄	—	2	4	no	—
481	C₂²⋊C₄	—	2	4	no	—
482	C₂²⋊C₄	—	2	4	no	—
483	C₄²	—	2	4	no	—
484	C₂³	—	2	32	no	—
485	C₂³	—	2	8	no	—
486	C₂³	—	2	2	no	—
487	C₂³	—	2	2	no	—
488	C₂³	—	2	8	no	—
489	C₂³	—	2	2	no	—
490	C₂³	—	2	2	no	—
491	C₂³	—	2	8	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	2	2	no	—
494	C₂³	—	2	2	no	—
495	C₂³	—	4	2	no	—
496	C₂³	—	4	2	no	—
497	C₂³	—	4	2	no	—
498	C₂³	#123×C₄₃	1	4	yes	—
499	C₂³	AGL(1,ℤ/8)×C₄₃	1	4	yes	—
500	C₂³	#137×C₄₃	1	4	yes	—
501	C₂³	C₂²×D₄×C₄₃	1	2	yes	—
502	C₂³	C₂²×D₄×C₄₃	1	2	yes	—
503	C₂³	C₂²×D₄×C₄₃	1	2	yes	—
504	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
505	Q₈	—	2	4	no	—
506	Q₈	—	4	2	no	—
507	D₄	—	2	4	no	—
508	D₄	—	4	8	no	—
509	D₄	—	4	8	no	—
510	D₄	—	4	8	no	—
511	D₄	—	4	2	no	—
512	C₂×C₄	—	2	8	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	8	no	—
516	C₂×C₄	—	2	8	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	8	no	—
525	C₂×C₄	—	4	16	no	—
526	C₂×C₄	—	4	16	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	16	no	—
529	C₂×C₄	—	4	8	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	8	no	—
533	C₂×C₄	#123×C₄₃	1	4	yes	—
534	C₂×C₄	#123×C₄₃	1	8	yes	—
535	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
536	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
537	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
538	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
539	C₂×C₄	C₂×#41×C₄₃	1	4	yes	—
540	C₂×C₄	C₂×#41×C₄₃	1	8	yes	—
541	C₂×C₄	C₂⁵×C₄₃	1	1	yes	characteristic
542	C₈	—	2	8	no	—
543	C₂²	—	2	32	no	—
544	C₂²	—	2	8	no	—
545	C₂²	—	2	8	no	—
546	C₂²	—	2	8	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	2	2	no	—
550	C₂²	—	2	2	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	4	2	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	8	4	no	—
557	C₂²	C₂×#123×C₄₃	1	4	yes	—
558	C₂²	C₂×#123×C₄₃	1	2	yes	—
559	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	4	yes	—
560	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	2	yes	—
561	C₂²	C₂×#137×C₄₃	1	4	yes	—
562	C₂²	C₂×#137×C₄₃	1	2	yes	—
563	C₂²	C₂³×D₄×C₄₃	1	1	yes	characteristic
564	C₄	—	2	2	no	—
565	C₄	—	2	2	no	—
566	C₄	—	4	2	no	—
567	C₄	—	4	8	no	—
568	C₄	—	4	2	no	—
569	C₄	—	4	2	no	—
570	C₄	C₂×#123×C₄₃	1	4	yes	—
571	C₄	C₂×#123×C₄₃	1	2	yes	—
572	C₄	C₂²×#41×C₄₃	1	2	yes	—
573	C₂	—	2	4	no	—
574	C₂	—	2	4	no	—
575	C₂	—	2	4	no	—
576	C₂	—	8	2	no	—
577	C₂	C₄₃×#3092	1	4	yes	direct product factor
578	C₂	C₂²×#123×C₄₃	1	1	yes	characteristic
579	C₂	C₂²×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
580	C₂	C₂²×#137×C₄₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₃
prime radical	C₂×C₄₃×#525	C₂
LCS	G ▷ C₂×C₄ ▷ 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. C₂³×C₄⋊C₄×C₄₃	C₂	semidirect
3. C₄₃×#3092	C₂	direct (N × H)
4. C₂×C₄₃×#484	C₂	semidirect
5. C₂×C₄₃×#481	C₂	semidirect
6. C₂×C₄₃×#483	C₂	semidirect
7. C₂×C₄₃×#480	C₂	semidirect
8. C₂×C₄₃×#428	C₂	semidirect
9. C₂×C₄₃×#417	C₂	semidirect
10. C₂×C₄₃×#407	C₂	semidirect
33. C₂²×C₄⋊C₄×C₄₃	C₂²	semidirect
34. C₄₃×#484	C₂²	semidirect
35. C₄₃×#483	C₂²	semidirect
36. C₄₃×#481	C₂²	semidirect
37. C₄₃×#480	C₂²	semidirect
38. C₄₃×#428	C₂²	semidirect
39. C₂×#107×C₄₃	C₂²	semidirect
40. C₂×#106×C₄₃	C₂²	semidirect
41. C₄₃×#417	C₂²	semidirect
42. C₂×#103×C₄₃	C₂²	semidirect
43. C₂×#102×C₄₃	C₂²	semidirect
44. C₄₃×#407	C₂²	semidirect
111. #107×C₄₃	C₂³	semidirect
112. #106×C₄₃	C₂³	semidirect
113. #103×C₄₃	C₂³	semidirect
114. #102×C₄₃	C₂³	semidirect
252. C₂×#3092	C₄₃	direct (N × H)
284. C₂³×C₄⋊C₄	C₂×C₄₃	semidirect
285. #3092	C₂×C₄₃	direct (N × H)
286. C₂×#484	C₂×C₄₃	semidirect
287. C₂×#481	C₂×C₄₃	semidirect
288. C₂×#483	C₂×C₄₃	semidirect
289. C₂×#480	C₂×C₄₃	semidirect
290. C₂×#428	C₂×C₄₃	semidirect
291. C₂×#417	C₂×C₄₃	semidirect
292. C₂×#407	C₂×C₄₃	semidirect
297. C₂×C₄₃	#3092	direct (N × H)
323. C₂²×C₄⋊C₄	C₂²×C₄₃	semidirect
324. #484	C₂²×C₄₃	semidirect
325. #483	C₂²×C₄₃	semidirect
326. #481	C₂²×C₄₃	semidirect
327. #480	C₂²×C₄₃	semidirect
328. #428	C₂²×C₄₃	semidirect
329. C₂×#107	C₂²×C₄₃	semidirect
330. C₂×#106	C₂²×C₄₃	semidirect
331. #417	C₂²×C₄₃	semidirect
332. C₂×#103	C₂²×C₄₃	semidirect
333. C₂×#102	C₂²×C₄₃	semidirect
334. #407	C₂²×C₄₃	semidirect
337. C₄₃	C₂×#3092	direct (N × H)
402. #107	C₂³×C₄₃	semidirect
403. #106	C₂³×C₄₃	semidirect
404. #103	C₂³×C₄₃	semidirect
405. #102	C₂³×C₄₃	semidirect
577. C₂	C₄₃×#3092	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
C₂³×C₄⋊C₄×C₄₃	2
C₄₃×#3092	2
C₂×C₄₃×#484	2
C₂×C₄₃×#481	2
C₂×C₄₃×#483	2
C₂×C₄₃×#480	2
C₂×C₄₃×#428	2
C₂×C₄₃×#417	2
C₂×C₄₃×#407	2
C₂×#3092	43

Subgroups — C2×C43×#3092 #24980524

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₃×#3092 #24980524