Subgroups — C₂×#19143307 #25960471

Order 11008.

2894 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13063332	C₂	1	2	yes	maximal, complemented
2	#19143307	C₂	1	16	yes	maximal, direct product factor
3	C₂×#14582977	C₂	1	4	yes	maximal, complemented
4	C₂×D₄×C₄₃⋊C₈	C₂	1	4	yes	maximal, complemented
5	C₂×#14582923	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14582866	C₂	1	2	yes	maximal, complemented
7	C₂²×C₄×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₃×#532	C₂	1	1	yes	maximal, characteristic
9	C₂×#13063332	—	2	16	no	—
10	C₂×#13063332	C₂²	1	16	yes	complemented
11	C₂²×#10621877	C₂²	1	4	yes	—
12	C₂²×#10621877	C₂²	1	2	yes	—
13	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₂³×C₄₃⋊C₈	C₂²	1	4	yes	—
15	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
16	#14582977	C₂²	1	32	yes	complemented
17	D₄×C₄₃⋊C₈	C₂²	1	32	yes	complemented
18	#14582923	C₂²	1	8	yes	complemented
19	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	4	yes	—
20	#14582866	C₂²	1	16	yes	complemented
21	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	8	yes	—
22	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
23	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
24	C₂×C₄×C₄₃⋊C₈	C₂²	1	8	yes	complemented
25	C₂²×#41×C₄₃	C₂²	1	2	yes	—
26	C₄₃×#532	C₄	1	8	yes	—
27	C₄₃×#532	C₂²	1	8	yes	—
28	C₂×C₄⋊Q₈×C₄₃	C₄	1	1	yes	characteristic
29	C₂×#127×C₄₃	C₄	1	1	yes	characteristic
30	C₂×#124×C₄₃	C₄	1	2	yes	—
31	C₂×#121×C₄₃	C₄	1	4	yes	—
32	C₂×C₄×D₄×C₄₃	C₂²	1	4	yes	—
33	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
34	#13063332	—	2	64	no	—
35	C₂×#10621877	—	2	8	no	—
36	C₂×#10621877	—	2	16	no	—
37	C₂×#10621877	C₂³	1	8	yes	—
38	C₂×#10621877	C₂³	1	16	yes	—
39	C₂²×C₄₃⋊C₈	—	2	4	no	—
40	C₂²×C₄₃⋊C₈	—	2	16	no	—
41	C₂²×C₄₃⋊C₈	D₄	1	8	yes	complemented
42	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
43	C₂²×C₄₃⋊C₈	C₂³	1	4	yes	—
44	C₂²×C₄₃⋊C₈	C₂³	1	4	yes	—
45	C₂²×C₄₃⋊C₈	C₂³	1	16	yes	—
46	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
47	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₄₃⋊C₈	C₂³	1	4	yes	—
49	C₄⋊(C₄₃⋊C₈)	C₂³	1	16	yes	—
50	C₂²⋊(C₄₃⋊C₈)	C₂³	1	32	yes	—
51	C₄×C₄₃⋊C₈	C₂³	1	8	yes	—
52	C₄×C₄₃⋊C₈	C₂³	1	8	yes	—
53	C₂×#41×C₄₃	—	2	8	no	—
54	C₂×#41×C₄₃	—	2	8	no	—
55	C₂×#41×C₄₃	C₂×C₄	1	8	yes	—
56	C₂×#41×C₄₃	C₂³	1	8	yes	—
57	C₂²×Q₈×C₄₃	C₂×C₄	1	2	yes	—
58	C₂²×D₄×C₄₃	C₂×C₄	1	4	yes	—
59	C₂²×D₄×C₄₃	C₂×C₄	1	4	yes	—
60	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
61	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
62	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
63	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
64	C₄⋊Q₈×C₄₃	C₂×C₄	1	8	yes	—
65	#127×C₄₃	C₂×C₄	1	8	yes	—
66	#124×C₄₃	C₂×C₄	1	16	yes	—
67	#121×C₄₃	C₂×C₄	1	32	yes	—
68	C₄×D₄×C₄₃	C₂×C₄	1	16	yes	—
69	C₄×D₄×C₄₃	C₂³	1	16	yes	—
70	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
71	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
72	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
75	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
76	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
77	C₂⁴×C₄₃	C₂²×C₄	1	4	yes	—
78	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
79	#41×C₄₃	—	2	32	no	—
80	#41×C₄₃	—	2	16	no	—
81	#41×C₄₃	—	2	16	no	—
82	C₂×Q₈×C₄₃	—	2	8	no	—
83	C₂×Q₈×C₄₃	C₂²×C₄	1	8	yes	—
84	C₂×D₄×C₄₃	—	2	8	no	—
85	C₂×D₄×C₄₃	—	2	16	no	—
86	C₂×D₄×C₄₃	—	2	16	no	—
87	C₂×D₄×C₄₃	C₂²×C₄	1	16	yes	—
88	C₂×D₄×C₄₃	C₂²×C₄	1	16	yes	—
89	C₂×D₄×C₄₃	C₂²×C₄	1	8	yes	—
90	C₂²×C₄×C₄₃	—	2	8	no	—
91	C₂²×C₄×C₄₃	—	2	8	no	—
92	C₂²×C₄×C₄₃	—	2	8	no	—
93	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
95	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
97	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
101	C₂²×C₄×C₄₃	#41	1	4	yes	—
102	C₂²×C₄×C₄₃	C₂⁴	1	8	yes	—
103	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
104	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
105	C₄⋊C₄×C₄₃	C₂²×C₄	1	16	yes	—
106	C₂²⋊C₄×C₄₃	C₂²×C₄	1	32	yes	—
107	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
108	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
109	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
110	C₄²×C₄₃	C₂⁴	1	4	yes	—
111	#10621877	—	2	16	no	—
112	#10621877	—	2	32	no	—
113	C₂×C₄₃⋊C₈	—	2	8	no	—
114	C₂×C₄₃⋊C₈	—	2	4	no	—
115	C₂×C₄₃⋊C₈	—	2	8	no	—
116	C₂×C₄₃⋊C₈	—	2	32	no	—
117	C₂×C₄₃⋊C₈	C₂×D₄	1	4	yes	—
118	C₂×C₄₃⋊C₈	C₂×D₄	1	4	yes	—
119	C₂×C₄₃⋊C₈	C₂×D₄	1	16	yes	complemented
120	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
121	C₂×C₄₃⋊C₈	C₂⁴	1	8	yes	—
122	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
123	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
124	C₂³×C₄₃	—	2	4	no	—
125	C₂³×C₄₃	—	2	8	no	—
126	C₂³×C₄₃	—	2	16	no	—
127	C₂³×C₄₃	C₄×D₄	1	4	yes	—
128	C₂³×C₄₃	C₂³×C₄	1	8	yes	—
129	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
130	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
131	Q₈×C₄₃	—	2	16	no	—
132	D₄×C₄₃	—	2	32	no	—
133	D₄×C₄₃	—	2	16	no	—
134	D₄×C₄₃	—	2	32	no	—
135	C₂×C₄×C₄₃	—	2	8	no	—
136	C₂×C₄×C₄₃	—	2	4	no	—
137	C₂×C₄×C₄₃	—	2	16	no	—
138	C₂×C₄×C₄₃	—	2	16	no	—
139	C₂×C₄×C₄₃	—	2	8	no	—
140	C₂×C₄×C₄₃	—	2	8	no	—
141	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
142	C₂×C₄×C₄₃	C₄×D₄	1	8	yes	—
143	C₂×C₄×C₄₃	#131	1	8	yes	complemented
144	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
145	C₂×C₄×C₄₃	C₂³×C₄	1	8	yes	—
146	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
148	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
149	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
150	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
151	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
152	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
153	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
154	C₄₃⋊C₈	—	2	8	no	—
155	C₄₃⋊C₈	—	2	4	no	—
156	C₄₃⋊C₈	C₂²×D₄	1	4	yes	—
157	C₄₃⋊C₈	C₂²×D₄	1	4	yes	—
158	C₂×#2931	—	43	1	no	maximal, Sylow
159	C₂²×C₄₃	—	2	8	no	—
160	C₂²×C₄₃	—	2	4	no	—
161	C₂²×C₄₃	—	2	8	no	—
162	C₂²×C₄₃	—	2	16	no	—
163	C₂²×C₄₃	—	4	16	no	—
164	C₂²×C₄₃	C₂×C₄×D₄	1	4	yes	—
165	C₂²×C₄₃	C₂×C₄×D₄	1	2	yes	—
166	C₂²×C₄₃	C₂×#131	1	4	yes	—
167	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
168	C₄×C₄₃	—	2	8	no	—
169	C₄×C₄₃	—	2	4	no	—
170	C₄×C₄₃	C₂×C₄×D₄	1	2	yes	—
171	C₄×C₄₃	C₂×C₄×D₄	1	4	yes	—
172	C₄×C₄₃	C₂×#131	1	8	yes	complemented
173	C₄×C₄₃	C₂³×D₄	1	1	yes	characteristic
174	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
175	C₂²×#131	—	43	2	no	—
176	C₂×#532	D₄₃	1	1	yes	characteristic
177	#2931	—	43	16	no	—
178	C₂×#436	—	43	4	no	—
179	C₂×C₈×D₄	—	43	4	no	—
180	C₂×#423	—	43	1	no	—
181	C₂×#408	—	43	2	no	—
182	C₂²×C₄×C₈	—	43	1	no	—
183	C₂×C₄₃	—	2	4	no	—
184	C₂×C₄₃	—	4	8	no	—
185	C₂×C₄₃	#2931	1	4	yes	complemented
186	C₂×C₄₃	C₂²×C₄×D₄	1	1	yes	characteristic
187	C₂×C₄₃	C₂²×#131	1	2	yes	—
188	C₂²×#41	C₂×D₄₃	1	2	yes	—
189	C₂×#131	—	43	16	no	—
190	C₂×#131	—	86	16	no	—
191	C₂²×M₁₆	—	43	2	no	—
192	C₂²×M₁₆	—	43	4	no	—
193	C₂³×C₈	—	43	1	no	—
194	C₂³×C₈	—	43	1	no	—
195	C₂³×C₈	—	43	4	no	—
196	#532	Dic₄₃	1	8	yes	—
197	#532	C₂×D₄₃	1	8	yes	—
198	C₂×C₄⋊Q₈	Dic₄₃	1	1	yes	characteristic
199	C₂×#127	Dic₄₃	1	1	yes	characteristic
200	C₂×#124	Dic₄₃	1	2	yes	—
201	C₂×#121	Dic₄₃	1	4	yes	—
202	C₂×C₄×D₄	C₂×D₄₃	1	4	yes	—
203	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
204	#436	—	43	32	no	—
205	C₈×D₄	—	43	32	no	—
206	#423	—	43	8	no	—
207	C₂×C₄⋊C₈	—	43	4	no	—
208	#408	—	43	16	no	—
209	C₂×C₂²⋊C₈	—	43	8	no	—
210	C₂×C₄×C₈	—	43	2	no	—
211	C₂×C₄×C₈	—	43	2	no	—
212	C₂×C₄×C₈	—	43	8	no	—
213	C₄₃	C₂×#2931	1	1	yes	characteristic, complemented, Sylow
214	C₂×#41	—	2	8	no	—
215	C₂×#41	—	2	8	no	—
216	C₂×#41	C₂×Dic₄₃	1	8	yes	—
217	C₂×#41	C₂²×D₄₃	1	8	yes	—
218	C₂²×Q₈	C₂×Dic₄₃	1	2	yes	—
219	C₂²×D₄	C₂×Dic₄₃	1	4	yes	—
220	C₂²×D₄	C₂×Dic₄₃	1	4	yes	—
221	C₂²×D₄	C₂×Dic₄₃	1	2	yes	—
222	C₂³×C₄	C₂×Dic₄₃	1	2	yes	—
223	C₂³×C₄	C₂²×D₄₃	1	4	yes	—
224	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
225	#131	—	86	64	no	—
226	C₂×M₁₆	—	43	8	no	—
227	C₂×M₁₆	—	43	16	no	—
228	C₂×M₁₆	—	86	16	no	—
229	C₂×M₁₆	—	86	8	no	—
230	C₂²×C₈	—	43	8	no	—
231	C₂²×C₈	—	43	4	no	—
232	C₂²×C₈	—	43	1	no	—
233	C₂²×C₈	—	43	1	no	—
234	C₂²×C₈	—	43	16	no	—
235	C₂²×C₈	—	43	4	no	—
236	C₂²×C₈	—	43	4	no	—
237	C₂²×C₈	—	43	2	no	—
238	C₂²×C₈	—	86	16	no	—
239	C₂²×C₈	—	86	4	no	—
240	C₄⋊Q₈	C₂×Dic₄₃	1	8	yes	—
241	#127	C₂×Dic₄₃	1	8	yes	—
242	#124	C₂×Dic₄₃	1	16	yes	—
243	#121	C₂×Dic₄₃	1	32	yes	—
244	C₄×D₄	C₂×Dic₄₃	1	16	yes	—
245	C₄×D₄	C₂²×D₄₃	1	16	yes	—
246	C₂×C₄⋊C₄	C₂×Dic₄₃	1	4	yes	—
247	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	8	yes	—
248	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
249	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
250	C₂×C₄²	C₂×Dic₄₃	1	4	yes	—
251	C₂×C₄²	C₂²×D₄₃	1	4	yes	—
252	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
253	C₄⋊C₈	—	43	16	no	—
254	C₂²⋊C₈	—	43	32	no	—
255	C₄×C₈	—	43	8	no	—
256	C₄×C₈	—	43	8	no	—
257	C₂⁴	C₂²×Dic₄₃	1	4	yes	—
258	C₂⁴	C₂²×Dic₄₃	1	1	yes	characteristic
259	#41	—	2	32	no	—
260	#41	—	2	16	no	—
261	#41	—	2	16	no	—
262	C₂×Q₈	—	2	8	no	—
263	C₂×Q₈	C₂²×Dic₄₃	1	8	yes	—
264	C₂×D₄	—	2	16	no	—
265	C₂×D₄	—	2	8	no	—
266	C₂×D₄	—	2	16	no	—
267	C₂×D₄	C₂²×Dic₄₃	1	16	yes	—
268	C₂×D₄	C₂²×Dic₄₃	1	16	yes	—
269	C₂×D₄	C₂²×Dic₄₃	1	8	yes	—
270	C₂²×C₄	—	2	8	no	—
271	C₂²×C₄	—	2	8	no	—
272	C₂²×C₄	—	2	8	no	—
273	C₂²×C₄	D₄×D₄₃	1	4	yes	—
274	C₂²×C₄	#10621900	1	4	yes	—
275	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
276	C₂²×C₄	C₂²×Dic₄₃	1	8	yes	—
277	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
278	C₂²×C₄	C₂²×Dic₄₃	1	8	yes	—
279	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
280	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
281	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
282	C₂²×C₄	C₂³×D₄₃	1	8	yes	—
283	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
284	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
285	M₁₆	—	86	32	no	—
286	M₁₆	—	86	16	no	—
287	C₂×C₈	—	43	4	no	—
288	C₂×C₈	—	43	4	no	—
289	C₂×C₈	—	43	16	no	—
290	C₂×C₈	—	43	2	no	—
291	C₂×C₈	—	43	2	no	—
292	C₂×C₈	—	43	4	no	—
293	C₂×C₈	—	43	8	no	—
294	C₂×C₈	—	86	32	no	—
295	C₂×C₈	—	86	8	no	—
296	C₂×C₈	—	86	4	no	—
297	C₂×C₈	—	86	8	no	—
298	C₄⋊C₄	C₂²×Dic₄₃	1	16	yes	—
299	C₂²⋊C₄	C₂²×Dic₄₃	1	32	yes	—
300	C₄²	C₂²×Dic₄₃	1	4	yes	—
301	C₄²	C₂²×Dic₄₃	1	4	yes	—
302	C₄²	C₂²×Dic₄₃	1	4	yes	—
303	C₄²	C₂³×D₄₃	1	4	yes	—
304	C₂³	—	2	4	no	—
305	C₂³	—	2	8	no	—
306	C₂³	—	2	16	no	—
307	C₂³	D₄×Dic₄₃	1	4	yes	—
308	C₂³	C₂³×Dic₄₃	1	8	yes	—
309	C₂³	C₂³×Dic₄₃	1	2	yes	—
310	C₂³	C₂³×Dic₄₃	1	1	yes	characteristic
311	Q₈	—	2	16	no	—
312	D₄	—	2	32	no	—
313	D₄	—	2	16	no	—
314	D₄	—	2	32	no	—
315	C₂×C₄	—	2	8	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	16	no	—
318	C₂×C₄	—	2	16	no	—
319	C₂×C₄	—	2	8	no	—
320	C₂×C₄	—	2	8	no	—
321	C₂×C₄	D₄×Dic₄₃	1	4	yes	—
322	C₂×C₄	D₄×Dic₄₃	1	8	yes	—
323	C₂×C₄	#13063332	1	8	yes	complemented
324	C₂×C₄	C₂³×Dic₄₃	1	4	yes	—
325	C₂×C₄	C₂³×Dic₄₃	1	8	yes	—
326	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
327	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
328	C₂×C₄	C₂³×Dic₄₃	1	4	yes	—
329	C₂×C₄	C₂×D₄×D₄₃	1	2	yes	—
330	C₂×C₄	C₂×D₄×D₄₃	1	4	yes	—
331	C₂×C₄	C₂×#10621900	1	2	yes	—
332	C₂×C₄	C₂×#10621900	1	4	yes	—
333	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
334	C₈	—	43	4	no	—
335	C₈	—	43	4	no	—
336	C₈	—	86	8	no	—
337	C₈	—	86	4	no	—
338	C₂²	—	2	8	no	—
339	C₂²	—	2	4	no	—
340	C₂²	—	2	16	no	—
341	C₂²	—	2	8	no	—
342	C₂²	—	4	16	no	—
343	C₂²	C₂×D₄×Dic₄₃	1	4	yes	—
344	C₂²	C₂×D₄×Dic₄₃	1	2	yes	—
345	C₂²	C₂×#13063332	1	4	yes	—
346	C₂²	C₂⁴×Dic₄₃	1	1	yes	characteristic
347	C₄	—	2	4	no	—
348	C₄	—	2	8	no	—
349	C₄	C₂×D₄×Dic₄₃	1	2	yes	—
350	C₄	C₂×D₄×Dic₄₃	1	4	yes	—
351	C₄	C₂×#13063332	1	8	yes	complemented
352	C₄	C₂²×D₄×D₄₃	1	1	yes	characteristic
353	C₄	C₂²×#10621900	1	1	yes	characteristic
354	C₂	—	2	4	no	—
355	C₂	—	4	8	no	—
356	C₂	#19143307	1	4	yes	direct product factor
357	C₂	C₂²×D₄×Dic₄₃	1	1	yes	characteristic
358	C₂	C₂²×#13063332	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂³×D₄₃
commutator	C₂²×C₄₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting, prime radical	C₂×C₄₃×#532	C₂
socle	C₂³×C₄₃	C₂³×C₄
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	C₂×#532	D₄₃
hypocenter	C₄₃	C₂×#2931
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. C₂²×#13063332	C₂	semidirect
2. #19143307	C₂	direct (N × H)
3. C₂×#14582977	C₂	semidirect
4. C₂×D₄×C₄₃⋊C₈	C₂	semidirect
5. C₂×#14582923	C₂	semidirect
6. C₂×#14582866	C₂	semidirect
7. C₂²×C₄×C₄₃⋊C₈	C₂	semidirect
10. C₂×#13063332	C₂²	semidirect
16. #14582977	C₂²	semidirect
17. D₄×C₄₃⋊C₈	C₂²	semidirect
18. #14582923	C₂²	semidirect
20. #14582866	C₂²	semidirect
24. C₂×C₄×C₄₃⋊C₈	C₂²	semidirect
41. C₂²×C₄₃⋊C₈	D₄	semidirect
119. C₂×C₄₃⋊C₈	C₂×D₄	semidirect
143. C₂×C₄×C₄₃	#131	semidirect
172. C₄×C₄₃	C₂×#131	semidirect
185. C₂×C₄₃	#2931	semidirect
213. C₄₃	C₂×#2931	semidirect
323. C₂×C₄	#13063332	semidirect
351. C₄	C₂×#13063332	semidirect
356. C₂	#19143307	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#13063332	2
#19143307	2
C₂×#14582977	2
C₂×D₄×C₄₃⋊C₈	2
C₂×#14582923	2
C₂×#14582866	2
C₂²×C₄×C₄₃⋊C₈	2
C₂×C₄₃×#532	2
C₂×#2931	43

Subgroups — C2×#19143307 #25960471

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19143307 #25960471