Subgroups — C₂×#19143261 #25960360

Order 11008.

2178 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143261	C₂	1	16	yes	maximal, direct product factor
2	C₂×#14582960	C₂	1	4	yes	maximal, complemented
3	C₂×#14582956	C₂	1	2	yes	maximal, complemented
4	C₂×#14582952	C₂	1	2	yes	maximal, complemented
5	C₂×#14582923	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#14582866	C₂	1	2	yes	maximal
8	C₂×#14582855	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×#41×C₄₃	C₂	1	1	yes	maximal, characteristic
10	C₂²×#10621877	C₂²	1	2	yes	—
11	C₂³×C₄₃⋊C₈	C₂²	1	2	yes	—
12	#14582960	C₂²	1	32	yes	complemented
13	#14582956	C₂²	1	16	yes	complemented
14	#14582952	C₂²	1	16	yes	complemented
15	#14582923	C₂²	1	8	yes	complemented
16	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
18	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
20	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
21	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	8	yes	complemented
22	#14582866	C₂²	1	16	yes	—
23	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	4	yes	—
24	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	4	yes	—
25	#14582855	C₂²	1	16	yes	complemented
26	C₂×#13063236	C₂²	1	4	yes	—
27	C₂×C₄×C₄₃⋊C₈	C₂²	1	4	yes	—
28	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
29	C₄×#41×C₄₃	C₄	1	8	yes	—
30	C₄×#41×C₄₃	C₂²	1	8	yes	—
31	C₂×C₄×Q₈×C₄₃	C₄	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₄₃	C₄	1	1	yes	characteristic
33	C₂×C₄×D₄×C₄₃	C₄	1	2	yes	—
34	C₂×C₄×D₄×C₄₃	C₄	1	1	yes	characteristic
35	C₂×C₄×D₄×C₄₃	C₄	1	2	yes	—
36	C₂×C₄×D₄×C₄₃	C₄	1	1	yes	characteristic
37	C₂×#117×C₄₃	C₂²	1	2	yes	—
38	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
40	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
41	C₂×#10621877	—	2	8	no	—
42	C₂×#10621877	C₂³	1	8	yes	—
43	C₂²×C₄₃⋊C₈	—	2	8	no	—
44	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
45	C₂²×C₄₃⋊C₈	C₂³	1	4	yes	—
46	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
47	C₂²×C₄₃⋊C₈	C₂³	1	8	yes	—
48	C₄⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
49	C₄⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
50	C₄⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
51	C₄⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
52	C₄⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
53	C₂²⋊(C₄₃⋊C₈)	C₂³	1	16	yes	—
54	C₂²⋊(C₄₃⋊C₈)	C₂³	1	16	yes	—
55	#13063236	C₂³	1	16	yes	—
56	C₄×C₄₃⋊C₈	C₂³	1	16	yes	—
57	C₂×#41×C₄₃	—	2	4	no	—
58	C₂×#41×C₄₃	—	2	4	no	—
59	C₂×#41×C₄₃	C₂×C₄	1	4	yes	—
60	C₂×#41×C₄₃	C₂³	1	4	yes	—
61	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
62	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
63	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
64	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
65	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
66	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
67	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
68	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
69	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
70	C₄×Q₈×C₄₃	C₂×C₄	1	8	yes	—
71	C₄×Q₈×C₄₃	C₂×C₄	1	8	yes	—
72	C₄×D₄×C₄₃	C₂×C₄	1	16	yes	—
73	C₄×D₄×C₄₃	C₂×C₄	1	8	yes	—
74	C₄×D₄×C₄₃	C₂×C₄	1	16	yes	—
75	C₄×D₄×C₄₃	C₂×C₄	1	8	yes	—
76	#117×C₄₃	C₂×C₄	1	8	yes	—
77	#117×C₄₃	C₂×C₄	1	4	yes	—
78	#117×C₄₃	C₂³	1	4	yes	—
79	#117×C₄₃	C₂³	1	8	yes	—
80	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
81	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
82	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
84	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
85	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
86	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
87	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
88	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
90	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₄₃	C₂×C₄	1	8	yes	—
92	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
93	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
95	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
97	C₂×C₄²×C₄₃	C₂³	1	8	yes	—
98	C₂⁴×C₄₃	C₂²×C₄	1	2	yes	—
99	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
100	#41×C₄₃	—	2	16	no	—
101	#41×C₄₃	—	2	8	no	—
102	#41×C₄₃	—	2	8	no	—
103	C₂×Q₈×C₄₃	—	2	4	no	—
104	C₂×Q₈×C₄₃	C₂²×C₄	1	4	yes	—
105	C₂×D₄×C₄₃	—	2	4	no	—
106	C₂×D₄×C₄₃	—	2	8	no	—
107	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
108	C₂×D₄×C₄₃	C₂²×C₄	1	8	yes	—
109	C₂²×C₄×C₄₃	—	2	4	no	—
110	C₂²×C₄×C₄₃	—	2	8	no	—
111	C₂²×C₄×C₄₃	—	2	4	no	—
112	C₂²×C₄×C₄₃	—	2	4	no	—
113	C₂²×C₄×C₄₃	—	4	2	no	—
114	C₂²×C₄×C₄₃	—	4	4	no	—
115	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
117	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
118	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
123	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
124	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
125	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
126	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
128	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₃	#41	1	4	yes	—
130	C₂²×C₄×C₄₃	#41	1	4	yes	—
131	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
132	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
133	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
134	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
135	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
136	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
137	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
138	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
139	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
140	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
141	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
142	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
143	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
144	C₄²×C₄₃	C₂²×C₄	1	8	yes	—
145	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
146	C₄²×C₄₃	C₂²×C₄	1	8	yes	—
147	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
148	C₄²×C₄₃	C₂⁴	1	2	yes	—
149	C₄²×C₄₃	C₂⁴	1	4	yes	—
150	C₄²×C₄₃	C₂⁴	1	2	yes	—
151	#10621877	—	2	16	no	—
152	C₂×C₄₃⋊C₈	—	2	4	no	—
153	C₂×C₄₃⋊C₈	—	2	4	no	—
154	C₂×C₄₃⋊C₈	—	2	16	no	—
155	C₂×C₄₃⋊C₈	—	2	8	no	—
156	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
157	C₂×C₄₃⋊C₈	C₂⁴	1	8	yes	—
158	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
159	C₂³×C₄₃	—	2	2	no	—
160	C₂³×C₄₃	—	2	2	no	—
161	C₂³×C₄₃	—	2	4	no	—
162	C₂³×C₄₃	—	2	4	no	—
163	C₂³×C₄₃	—	2	4	no	—
164	C₂³×C₄₃	#117	1	4	yes	—
165	C₂³×C₄₃	C₂³×C₄	1	4	yes	—
166	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
167	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
168	Q₈×C₄₃	—	2	8	no	—
169	D₄×C₄₃	—	2	16	no	—
170	D₄×C₄₃	—	2	8	no	—
171	C₂×C₄×C₄₃	—	2	4	no	—
172	C₂×C₄×C₄₃	—	2	2	no	—
173	C₂×C₄×C₄₃	—	2	4	no	—
174	C₂×C₄×C₄₃	—	2	2	no	—
175	C₂×C₄×C₄₃	—	2	2	no	—
176	C₂×C₄×C₄₃	—	2	4	no	—
177	C₂×C₄×C₄₃	—	2	8	no	—
178	C₂×C₄×C₄₃	—	2	8	no	—
179	C₂×C₄×C₄₃	—	2	16	no	—
180	C₂×C₄×C₄₃	—	2	4	no	—
181	C₂×C₄×C₄₃	—	2	4	no	—
182	C₂×C₄×C₄₃	—	4	4	no	—
183	C₂×C₄×C₄₃	—	4	8	no	—
184	C₂×C₄×C₄₃	#117	1	4	yes	—
185	C₂×C₄×C₄₃	#117	1	8	yes	—
186	C₂×C₄×C₄₃	#131	1	4	yes	—
187	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
188	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
189	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
190	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
191	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
192	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
193	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
195	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
196	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
197	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
198	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
199	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
200	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
201	C₄₃⋊C₈	—	2	4	no	—
202	C₄₃⋊C₈	—	2	4	no	—
203	C₄₃⋊C₈	—	2	8	no	—
204	C₂×#2925	—	43	1	no	maximal, Sylow
205	C₂²×C₄₃	—	2	8	no	—
206	C₂²×C₄₃	—	2	2	no	—
207	C₂²×C₄₃	—	2	2	no	—
208	C₂²×C₄₃	—	2	4	no	—
209	C₂²×C₄₃	—	2	4	no	—
210	C₂²×C₄₃	—	2	4	no	—
211	C₂²×C₄₃	—	4	8	no	—
212	C₂²×C₄₃	C₂×#117	1	4	yes	—
213	C₂²×C₄₃	C₂×#117	1	2	yes	—
214	C₂²×C₄₃	C₂×#131	1	2	yes	—
215	C₂²×C₄₃	#568	1	2	yes	—
216	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
217	C₄×C₄₃	—	2	4	no	—
218	C₄×C₄₃	—	2	2	no	—
219	C₄×C₄₃	—	2	4	no	—
220	C₄×C₄₃	—	2	2	no	—
221	C₄×C₄₃	—	2	2	no	—
222	C₄×C₄₃	—	2	4	no	—
223	C₄×C₄₃	C₂×#117	1	2	yes	—
224	C₄×C₄₃	C₂×#117	1	4	yes	—
225	C₄×C₄₃	C₂×#131	1	4	yes	—
226	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
227	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
228	C₂×C₄×#41	D₄₃	1	1	yes	characteristic
229	#2925	—	43	16	no	—
230	C₂×#433	—	43	4	no	—
231	C₂×#432	—	43	2	no	—
232	C₂×#431	—	43	2	no	—
233	C₂×#423	—	43	1	no	—
234	C₂²×C₄⋊C₈	—	43	1	no	—
235	C₂×#408	—	43	2	no	—
236	C₂×#405	—	43	2	no	—
237	C₂×C₄₃	—	2	4	no	—
238	C₂×C₄₃	—	4	4	no	—
239	C₂×C₄₃	#2925	1	4	yes	complemented
240	C₂×C₄₃	C₂²×#117	1	1	yes	characteristic
241	C₂×C₄₃	C₂²×#131	1	1	yes	characteristic
242	C₂×C₄₃	C₂×#568	1	1	yes	characteristic
243	C₂²×#41	C₂×D₄₃	1	1	yes	characteristic
244	C₂²×M₁₆	—	43	2	no	—
245	C₂³×C₈	—	43	2	no	—
246	C₄×#41	Dic₄₃	1	8	yes	—
247	C₄×#41	C₂×D₄₃	1	8	yes	—
248	C₂×C₄×Q₈	Dic₄₃	1	1	yes	characteristic
249	C₂×C₄×Q₈	Dic₄₃	1	1	yes	characteristic
250	C₂×C₄×D₄	Dic₄₃	1	2	yes	—
251	C₂×C₄×D₄	Dic₄₃	1	1	yes	characteristic
252	C₂×C₄×D₄	Dic₄₃	1	2	yes	—
253	C₂×C₄×D₄	Dic₄₃	1	1	yes	characteristic
254	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
255	C₂×#117	C₂×D₄₃	1	2	yes	—
256	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
257	C₂²×C₄²	C₂×D₄₃	1	2	yes	—
258	#433	—	43	32	no	—
259	#432	—	43	16	no	—
260	#431	—	43	16	no	—
261	#423	—	43	8	no	—
262	C₂×C₄⋊C₈	—	43	1	no	—
263	C₂×C₄⋊C₈	—	43	1	no	—
264	C₂×C₄⋊C₈	—	43	2	no	—
265	C₂×C₄⋊C₈	—	43	8	no	—
266	C₂×C₄⋊C₈	—	43	2	no	—
267	C₂×C₄⋊C₈	—	43	2	no	—
268	#408	—	43	16	no	—
269	C₂×C₂²⋊C₈	—	43	4	no	—
270	C₂×C₂²⋊C₈	—	43	4	no	—
271	#405	—	43	16	no	—
272	C₂×#97	—	43	4	no	—
273	C₂×C₄×C₈	—	43	4	no	—
274	C₄₃	C₂×#2925	1	1	yes	characteristic, complemented, Sylow
275	C₂×#41	—	2	4	no	—
276	C₂×#41	—	2	4	no	—
277	C₂×#41	C₂×Dic₄₃	1	4	yes	—
278	C₂×#41	C₂²×D₄₃	1	4	yes	—
279	C₂²×Q₈	C₂×Dic₄₃	1	1	yes	characteristic
280	C₂²×D₄	C₂×Dic₄₃	1	2	yes	—
281	C₂²×D₄	C₂×Dic₄₃	1	1	yes	characteristic
282	C₂³×C₄	C₂×Dic₄₃	1	2	yes	—
283	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
284	C₂³×C₄	C₂×Dic₄₃	1	2	yes	—
285	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
286	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
287	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
288	C₂×M₁₆	—	43	8	no	—
289	C₂×M₁₆	—	86	8	no	—
290	C₂²×C₈	—	43	8	no	—
291	C₂²×C₈	—	43	2	no	—
292	C₂²×C₈	—	43	2	no	—
293	C₂²×C₈	—	43	4	no	—
294	C₂²×C₈	—	86	8	no	—
295	C₄×Q₈	C₂×Dic₄₃	1	8	yes	—
296	C₄×Q₈	C₂×Dic₄₃	1	8	yes	—
297	C₄×D₄	C₂×Dic₄₃	1	16	yes	—
298	C₄×D₄	C₂×Dic₄₃	1	8	yes	—
299	C₄×D₄	C₂×Dic₄₃	1	16	yes	—
300	C₄×D₄	C₂×Dic₄₃	1	8	yes	—
301	#117	C₂×Dic₄₃	1	8	yes	—
302	#117	C₂×Dic₄₃	1	4	yes	—
303	#117	C₂²×D₄₃	1	4	yes	—
304	#117	C₂²×D₄₃	1	8	yes	—
305	C₂×C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
306	C₂×C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
307	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	2	yes	—
310	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	2	yes	—
311	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	2	yes	—
312	C₂×C₄²	C₂×Dic₄₃	1	2	yes	—
313	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
314	C₂×C₄²	C₂×Dic₄₃	1	2	yes	—
315	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
316	C₂×C₄²	C₂×Dic₄₃	1	8	yes	—
317	C₂×C₄²	C₂×Dic₄₃	1	4	yes	—
318	C₂×C₄²	C₂²×D₄₃	1	4	yes	—
319	C₂×C₄²	C₂²×D₄₃	1	8	yes	—
320	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
321	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
322	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
323	C₄⋊C₈	—	43	4	no	—
324	C₄⋊C₈	—	43	4	no	—
325	C₄⋊C₈	—	43	8	no	—
326	C₄⋊C₈	—	43	8	no	—
327	C₄⋊C₈	—	43	8	no	—
328	C₂²⋊C₈	—	43	16	no	—
329	C₂²⋊C₈	—	43	16	no	—
330	#97	—	43	16	no	—
331	C₄×C₈	—	43	16	no	—
332	C₂⁴	C₂²×Dic₄₃	1	2	yes	—
333	C₂⁴	C₂²×Dic₄₃	1	1	yes	characteristic
334	#41	—	2	16	no	—
335	#41	—	2	8	no	—
336	#41	—	2	8	no	—
337	C₂×Q₈	—	2	4	no	—
338	C₂×Q₈	C₂²×Dic₄₃	1	4	yes	—
339	C₂×D₄	—	2	8	no	—
340	C₂×D₄	—	2	4	no	—
341	C₂×D₄	C₂²×Dic₄₃	1	8	yes	—
342	C₂×D₄	C₂²×Dic₄₃	1	4	yes	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	8	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	—	4	4	no	—
349	C₂²×C₄	#10621898	1	4	yes	—
350	C₂²×C₄	#10621898	1	4	yes	—
351	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
352	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
353	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
354	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
355	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
356	C₂²×C₄	C₂²×Dic₄₃	1	8	yes	—
357	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
358	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
359	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
360	C₂²×C₄	C₂²×Dic₄₃	1	8	yes	—
361	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
362	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
363	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
364	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
365	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
366	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
367	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
368	M₁₆	—	86	16	no	—
369	C₂×C₈	—	43	4	no	—
370	C₂×C₈	—	43	8	no	—
371	C₂×C₈	—	43	4	no	—
372	C₂×C₈	—	86	4	no	—
373	C₂×C₈	—	86	4	no	—
374	C₂×C₈	—	86	16	no	—
375	C₂×C₈	—	86	8	no	—
376	C₄⋊C₄	C₂²×Dic₄₃	1	8	yes	—
377	C₄⋊C₄	C₂²×Dic₄₃	1	8	yes	—
378	C₄⋊C₄	C₂²×Dic₄₃	1	4	yes	—
379	C₄⋊C₄	C₂²×Dic₄₃	1	4	yes	—
380	C₂²⋊C₄	C₂²×Dic₄₃	1	8	yes	—
381	C₂²⋊C₄	C₂²×Dic₄₃	1	8	yes	—
382	C₂²⋊C₄	C₂²×Dic₄₃	1	8	yes	—
383	C₄²	C₂²×Dic₄₃	1	2	yes	—
384	C₄²	C₂²×Dic₄₃	1	4	yes	—
385	C₄²	C₂²×Dic₄₃	1	2	yes	—
386	C₄²	C₂²×Dic₄₃	1	8	yes	—
387	C₄²	C₂²×Dic₄₃	1	4	yes	—
388	C₄²	C₂²×Dic₄₃	1	8	yes	—
389	C₄²	C₂²×Dic₄₃	1	4	yes	—
390	C₄²	C₂³×D₄₃	1	4	yes	—
391	C₄²	C₂³×D₄₃	1	2	yes	—
392	C₄²	C₂³×D₄₃	1	2	yes	—
393	C₂³	—	2	2	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	4	no	—
396	C₂³	—	2	4	no	—
397	C₂³	—	2	4	no	—
398	C₂³	#13063284	1	4	yes	—
399	C₂³	C₂³×Dic₄₃	1	4	yes	—
400	C₂³	C₂³×Dic₄₃	1	2	yes	—
401	C₂³	C₂³×Dic₄₃	1	1	yes	characteristic
402	Q₈	—	2	8	no	—
403	D₄	—	2	16	no	—
404	D₄	—	2	8	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	8	no	—
412	C₂×C₄	—	2	8	no	—
413	C₂×C₄	—	2	16	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	4	8	no	—
418	C₂×C₄	#13063284	1	4	yes	—
419	C₂×C₄	#13063284	1	8	yes	—
420	C₂×C₄	#13063332	1	4	yes	—
421	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
422	C₂×C₄	C₂³×Dic₄₃	1	4	yes	—
423	C₂×C₄	C₂³×Dic₄₃	1	4	yes	—
424	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
425	C₂×C₄	C₂³×Dic₄₃	1	4	yes	—
426	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
427	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
428	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
429	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
430	C₂×C₄	C₂×#10621898	1	2	yes	—
431	C₂×C₄	C₂×#10621898	1	2	yes	—
432	C₂×C₄	C₂×#10621898	1	4	yes	—
433	C₂×C₄	C₂×#10621898	1	4	yes	—
434	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
435	C₈	—	86	4	no	—
436	C₈	—	86	4	no	—
437	C₈	—	86	8	no	—
438	C₂²	—	2	8	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	4	no	—
442	C₂²	—	2	4	no	—
443	C₂²	—	2	4	no	—
444	C₂²	—	4	8	no	—
445	C₂²	C₂×#13063284	1	4	yes	—
446	C₂²	C₂×#13063284	1	2	yes	—
447	C₂²	C₂×#13063332	1	2	yes	—
448	C₂²	#14583666	1	2	yes	—
449	C₂²	C₂⁴×Dic₄₃	1	1	yes	characteristic
450	C₄	—	2	4	no	—
451	C₄	—	2	2	no	—
452	C₄	—	2	4	no	—
453	C₄	—	2	2	no	—
454	C₄	—	2	2	no	—
455	C₄	—	2	4	no	—
456	C₄	C₂×#13063284	1	2	yes	—
457	C₄	C₂×#13063284	1	4	yes	—
458	C₄	C₂×#13063332	1	4	yes	—
459	C₄	C₂²×#10621898	1	1	yes	characteristic
460	C₄	C₂²×#10621898	1	1	yes	characteristic
461	C₂	—	2	4	no	—
462	C₂	—	4	4	no	—
463	C₂	#19143261	1	4	yes	direct product factor
464	C₂	C₂²×#13063284	1	1	yes	characteristic
465	C₂	C₂²×#13063332	1	1	yes	characteristic
466	C₂	C₂×#14583666	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₄₃
commutator	C₂²×C₄₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₂×C₄×#41×C₄₃	C₂
socle	C₂³×C₄₃	C₂³×C₄
prime radical	C₂²×#41×C₄₃	C₂²
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	C₂×C₄×#41	D₄₃
hypocenter	C₄₃	C₂×#2925
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×#41

Complements

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

N	H ≅ G/N	type
1. #19143261	C₂	direct (N × H)
2. C₂×#14582960	C₂	semidirect
3. C₂×#14582956	C₂	semidirect
4. C₂×#14582952	C₂	semidirect
5. C₂×#14582923	C₂	semidirect
6. C₂²×C₄⋊(C₄₃⋊C₈)	C₂	semidirect
8. C₂×#14582855	C₂	semidirect
12. #14582960	C₂²	semidirect
13. #14582956	C₂²	semidirect
14. #14582952	C₂²	semidirect
15. #14582923	C₂²	semidirect
21. C₂×C₄⋊(C₄₃⋊C₈)	C₂²	semidirect
25. #14582855	C₂²	semidirect
239. C₂×C₄₃	#2925	semidirect
274. C₄₃	C₂×#2925	semidirect
463. C₂	#19143261	direct (N × H)

Maximal subgroups

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

subgroup	index
#19143261	2
C₂×#14582960	2
C₂×#14582956	2
C₂×#14582952	2
C₂×#14582923	2
C₂²×C₄⋊(C₄₃⋊C₈)	2
C₂×#14582866	2
C₂×#14582855	2
C₂×C₄×#41×C₄₃	2
C₂×#2925	43

Subgroups — C2×#19143261 #25960360

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19143261 #25960360