Subgroups — C₂×#19133344 #25065573

Order 11008.

834 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582951	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊C₈×D₄₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#10621872	C₂	1	1	yes	maximal, characteristic
4	#19133344	C₂	1	8	yes	maximal, direct product factor
5	C₂×#14582652	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14582651	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#14582649	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₃×#334	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#10621872	C₄	1	1	yes	characteristic
10	C₂²×#10621872	C₄	1	1	yes	characteristic
11	C₂²×C₈×D₄₃	—	2	1	no	—
12	C₂×C₄²×D₄₃	C₂²	1	1	yes	characteristic
13	#14582951	—	2	2	no	—
14	#14582951	C₂²	1	4	yes	—
15	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×Dic₄₃⋊C₈	—	2	1	no	—
18	C₄⋊C₈×D₄₃	—	2	2	no	—
19	C₄⋊C₈×D₄₃	C₂²	1	4	yes	—
20	C₂×(C₂×D₄₃)⋊C₈	—	2	1	no	—
21	C₄×#10621872	C₄	1	4	yes	—
22	C₄×#10621872	C₂²	1	4	yes	—
23	C₂×#13063235	C₄	1	1	yes	characteristic
24	C₂×#13063235	C₄	1	1	yes	characteristic
25	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₈×Dic₄₃	—	2	1	no	—
27	#14582652	C₂²	1	4	yes	complemented
28	#14582651	C₂²	1	4	yes	complemented
29	#14582649	C₂²	1	4	yes	complemented
30	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
33	C₄₃×#334	C₂²	1	4	yes	complemented
34	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₄×D₄₃	D₄	1	1	yes	characteristic
36	C₂²×C₄×D₄₃	Q₈	1	1	yes	characteristic
37	C₂×#10621872	—	2	4	no	—
38	C₂×#10621872	C₈	1	8	yes	complemented
39	C₂×#10621872	C₂×C₄	1	4	yes	—
40	C₂×#10621872	C₂×C₄	1	4	yes	—
41	C₂²×C₄₃⋊C₈	—	2	1	no	—
42	C₂²×C₄₃⋊C₈	—	2	1	no	—
43	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
45	C₂×C₈×D₄₃	—	2	4	no	—
46	C₂×C₈×D₄₃	—	4	4	no	—
47	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
49	C₂×C₄×Dic₄₃	Q₈	1	1	yes	characteristic
50	C₄²×D₄₃	C₂×C₄	1	2	yes	—
51	C₄²×D₄₃	D₄	1	2	yes	—
52	C₄²×D₄₃	Q₈	1	2	yes	—
53	C₄²×D₄₃	C₂³	1	2	yes	—
54	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
55	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
56	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
57	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
58	Dic₄₃⋊C₈	—	2	4	no	—
59	(C₂×D₄₃)⋊C₈	—	2	4	no	—
60	#13063235	C₂×C₄	1	4	yes	—
61	#13063235	C₂×C₄	1	4	yes	—
62	C₄×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
63	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
64	C₈×Dic₄₃	—	2	4	no	—
65	C₂²×C₈×C₄₃	—	2	1	no	—
66	C₂²×C₈×C₄₃	—	2	1	no	—
67	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
68	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
70	C₄⋊C₈×C₄₃	—	2	1	no	—
71	C₄⋊C₈×C₄₃	—	2	1	no	—
72	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
73	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
74	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
75	C₄×C₈×C₄₃	C₂³	1	2	yes	—
76	C₂³×D₄₃	C₄⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
80	C₂²×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
83	C₂×C₄×D₄₃	—	2	2	no	—
84	C₂×C₄×D₄₃	—	2	2	no	—
85	C₂×C₄×D₄₃	—	4	2	no	—
86	C₂×C₄×D₄₃	C₄⋊C₄	1	2	yes	—
87	C₂×C₄×D₄₃	C₄⋊C₄	1	2	yes	—
88	C₂×C₄×D₄₃	C₄⋊C₄	1	2	yes	—
89	C₂×C₄×D₄₃	C₂×C₈	1	4	yes	—
90	C₂×C₄×D₄₃	M₁₆	1	4	yes	—
91	C₂×C₄×D₄₃	C₂²×C₄	1	2	yes	—
92	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
93	C₂×C₄×D₄₃	C₂×Q₈	1	2	yes	—
94	C₂×C₈×C₄₃	—	2	2	no	—
95	C₂×C₈×C₄₃	—	2	2	no	—
96	C₂×C₈×C₄₃	—	2	2	no	—
97	C₂×C₈×C₄₃	—	4	2	no	—
98	C₂×C₈×C₄₃	—	4	2	no	—
99	C₂×C₈×C₄₃	C₂×C₈	1	4	yes	complemented
100	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
101	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
102	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
103	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
104	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
105	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
106	C₄×Dic₄₃	C₄⋊C₄	1	2	yes	—
107	C₄×Dic₄₃	C₄⋊C₄	1	2	yes	—
108	C₄×Dic₄₃	C₄⋊C₄	1	2	yes	—
109	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
110	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
111	C₄×Dic₄₃	C₂×Q₈	1	2	yes	—
112	C₂×C₄₃⋊C₈	—	2	2	no	—
113	C₂×C₄₃⋊C₈	—	2	2	no	—
114	C₂×C₄₃⋊C₈	—	2	2	no	—
115	C₂×C₄₃⋊C₈	—	4	2	no	—
116	C₂×C₄₃⋊C₈	—	4	2	no	—
117	C₂×C₄₃⋊C₈	C₂×C₈	1	4	yes	complemented
118	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
119	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
120	#10621872	—	2	8	no	—
121	#10621872	C₂×C₈	1	16	yes	complemented
122	C₈×D₄₃	—	4	8	no	—
123	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
124	C₂²×D₄₃	—	2	2	no	—
125	C₂²×D₄₃	—	2	2	no	—
126	C₂²×D₄₃	C₄⋊C₈	1	4	yes	—
127	C₂²×D₄₃	C₂×C₄⋊C₄	1	2	yes	—
128	C₂×C₄×C₄₃	—	2	2	no	—
129	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
131	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
132	C₂×C₄×C₄₃	C₂²×C₈	1	2	yes	—
133	C₂×C₄×C₄₃	C₂×M₁₆	1	2	yes	—
134	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
135	C₂×C₄×C₄₃	#137	1	2	yes	—
136	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
137	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
138	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
139	C₂×Dic₄₃	—	2	2	no	—
140	C₂×Dic₄₃	—	2	2	no	—
141	C₂×Dic₄₃	C₄⋊C₈	1	4	yes	—
142	C₂×Dic₄₃	C₂×C₄⋊C₄	1	2	yes	—
143	C₂×Dic₄₃	C₂×C₄⋊C₄	1	2	yes	—
144	C₂×Dic₄₃	C₂×C₄⋊C₄	1	2	yes	—
145	C₄×D₄₃	—	2	2	no	—
146	C₄×D₄₃	—	2	2	no	—
147	C₄×D₄₃	—	2	4	no	—
148	C₄×D₄₃	—	4	2	no	—
149	C₄×D₄₃	—	4	2	no	—
150	C₄×D₄₃	C₄⋊C₈	1	8	yes	—
151	C₄×D₄₃	C₂²×C₈	1	4	yes	—
152	C₄×D₄₃	C₂×M₁₆	1	4	yes	—
153	C₈×C₄₃	—	2	2	no	—
154	C₈×C₄₃	—	4	2	no	—
155	C₈×C₄₃	—	4	2	no	—
156	C₈×C₄₃	C₂²×C₈	1	4	yes	complemented
157	C₄₃⋊C₈	—	2	2	no	—
158	C₄₃⋊C₈	—	4	2	no	—
159	C₄₃⋊C₈	—	4	2	no	—
160	C₄₃⋊C₈	C₂²×C₈	1	4	yes	complemented
161	C₂×#1565	—	43	1	no	maximal, Sylow
162	C₂²×C₄₃	C₂×C₄⋊C₈	1	2	yes	—
163	C₂²×C₄₃	#428	1	2	yes	—
164	C₂²×C₄₃	#430	1	2	yes	—
165	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
166	C₂×D₄₃	—	2	8	no	—
167	C₂×D₄₃	—	2	2	no	—
168	C₂×D₄₃	—	2	2	no	—
169	C₂×D₄₃	C₂×C₄⋊C₈	1	4	yes	—
170	C₄×C₄₃	—	2	1	no	—
171	C₄×C₄₃	—	2	1	no	—
172	C₄×C₄₃	C₂×C₄⋊C₈	1	2	yes	—
173	C₄×C₄₃	#428	1	2	yes	—
174	C₄×C₄₃	C₂³×C₈	1	1	yes	characteristic
175	C₄×C₄₃	C₂²×M₁₆	1	1	yes	characteristic
176	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
177	C₄×C₄₃	C₂×#137	1	1	yes	characteristic
178	Dic₄₃	—	2	2	no	—
179	Dic₄₃	—	2	2	no	—
180	Dic₄₃	C₂×C₄⋊C₈	1	4	yes	—
181	C₂×#431	—	43	1	no	—
182	C₂²×C₄⋊C₈	—	43	1	no	—
183	C₂×C₄×M₁₆	—	43	1	no	—
184	#1565	—	43	8	no	—
185	C₂×#335	—	43	1	no	—
186	C₂×#335	—	43	1	no	—
187	C₂×#334	—	43	1	no	—
188	C₂×#334	D₄₃	1	1	yes	characteristic, complemented
189	C₂×C₄₃	#1565	1	4	yes	complemented
190	C₂×C₄₃	C₂²×C₄⋊C₈	1	1	yes	characteristic
191	C₂×C₄₃	C₂×#428	1	1	yes	characteristic
192	C₂×C₄₃	C₂×#430	1	1	yes	characteristic
193	D₄₃	—	2	4	no	—
194	C₂²×M₁₆	—	43	1	no	—
195	C₂²×M₁₆	—	43	1	no	—
196	C₂³×C₈	—	86	1	no	—
197	C₂²×C₄²	—	43	1	no	—
198	#431	—	43	4	no	—
199	#431	—	86	2	no	—
200	C₂×C₄⋊C₈	—	43	1	no	—
201	C₂×C₄⋊C₈	—	43	1	no	—
202	C₂×C₄⋊C₈	—	43	4	no	—
203	C₂×C₄⋊C₈	—	86	2	no	—
204	C₂×C₄⋊C₈	—	86	1	no	—
205	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
206	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
207	C₂×C₂²⋊C₈	—	86	1	no	—
208	C₄×M₁₆	—	43	4	no	—
209	C₄×M₁₆	—	43	4	no	—
210	C₂×#97	—	43	1	no	—
211	C₂×#97	—	43	1	no	—
212	C₂×C₄×C₈	—	43	1	no	—
213	C₂×C₄×C₈	—	86	1	no	—
214	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
215	#335	—	43	4	no	—
216	#335	—	43	4	no	—
217	#334	—	43	4	no	—
218	#334	C₂×D₄₃	1	4	yes	complemented
219	C₄₃	C₂×#1565	1	1	yes	characteristic, complemented, Sylow
220	C₂³×C₄	—	43	1	no	—
221	C₂³×C₄	—	43	1	no	—
222	C₂³×C₄	—	43	1	no	—
223	C₂×M₁₆	—	43	8	no	—
224	C₂×M₁₆	—	43	4	no	—
225	C₂×M₁₆	—	43	4	no	—
226	C₂×M₁₆	—	86	4	no	—
227	C₂²×C₈	—	2	1	no	—
228	C₂²×C₈	—	2	1	no	—
229	C₂²×C₈	—	43	1	no	—
230	C₂²×C₈	—	43	1	no	—
231	C₂²×C₈	—	86	4	no	—
232	C₂²×C₈	—	86	1	no	—
233	C₂²×C₈	—	86	1	no	—
234	C₂²×C₈	—	172	4	no	—
235	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
236	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
237	C₂×C₄²	—	43	1	no	—
238	C₂×C₄²	—	43	1	no	—
239	C₂×C₄²	—	43	1	no	—
240	C₂×C₄²	—	43	2	no	—
241	C₂×C₄²	—	43	2	no	—
242	C₂×C₄²	—	43	2	no	—
243	C₂×C₄²	—	43	2	no	—
244	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
245	C₄⋊C₈	—	2	1	no	—
246	C₄⋊C₈	—	2	1	no	—
247	C₄⋊C₈	—	43	2	no	—
248	C₄⋊C₈	—	43	2	no	—
249	C₄⋊C₈	—	86	4	no	—
250	C₄⋊C₈	—	86	1	no	—
251	C₄⋊C₈	—	86	1	no	—
252	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
253	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
254	C₂²⋊C₈	—	86	4	no	—
255	#97	—	43	4	no	—
256	#97	—	43	4	no	—
257	C₄×C₈	—	43	2	no	—
258	C₄×C₈	—	43	2	no	—
259	C₄×C₈	—	86	4	no	—
260	C₄×C₈	C₄×D₄₃	1	2	yes	—
261	C₄×C₈	C₂²×D₄₃	1	2	yes	—
262	C₂⁴	—	43	1	no	—
263	C₂²×C₄	—	43	1	no	—
264	C₂²×C₄	—	43	2	no	—
265	C₂²×C₄	—	43	4	no	—
266	C₂²×C₄	—	43	4	no	—
267	C₂²×C₄	—	43	2	no	—
268	C₂²×C₄	—	43	1	no	—
269	C₂²×C₄	—	43	1	no	—
270	C₂²×C₄	—	43	2	no	—
271	C₂²×C₄	—	43	2	no	—
272	C₂²×C₄	—	43	2	no	—
273	C₂²×C₄	—	43	2	no	—
274	C₂²×C₄	—	86	2	no	—
275	C₂²×C₄	—	86	2	no	—
276	C₂²×C₄	—	172	2	no	—
277	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
278	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
279	C₂²×C₄	Q₈×D₄₃	1	1	yes	characteristic
280	M₁₆	—	43	16	no	—
281	M₁₆	—	86	8	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	4	2	no	—
286	C₂×C₈	—	4	2	no	—
287	C₂×C₈	—	43	4	no	—
288	C₂×C₈	—	43	2	no	—
289	C₂×C₈	—	43	2	no	—
290	C₂×C₈	—	86	2	no	—
291	C₂×C₈	—	86	2	no	—
292	C₂×C₈	—	86	2	no	—
293	C₂×C₈	—	172	8	no	—
294	C₂×C₈	—	172	2	no	—
295	C₂×C₈	—	172	2	no	—
296	C₂×C₈	C₈×D₄₃	1	4	yes	complemented
297	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
298	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
299	C₄²	—	43	2	no	—
300	C₄²	—	43	2	no	—
301	C₄²	—	43	2	no	—
302	C₄²	—	43	2	no	—
303	C₄²	—	43	2	no	—
304	C₄²	—	43	2	no	—
305	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
306	C₄²	D₄×D₄₃	1	1	yes	characteristic
307	C₄²	Q₈×D₄₃	1	1	yes	characteristic
308	C₄²	C₂³×D₄₃	1	1	yes	characteristic
309	C₂³	—	43	2	no	—
310	C₂³	—	43	4	no	—
311	C₂³	—	86	2	no	—
312	C₂³	—	86	2	no	—
313	C₂³	C₄⋊C₄×D₄₃	1	1	yes	characteristic
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	43	2	no	—
316	C₂×C₄	—	43	4	no	—
317	C₂×C₄	—	43	4	no	—
318	C₂×C₄	—	43	4	no	—
319	C₂×C₄	—	43	8	no	—
320	C₂×C₄	—	43	2	no	—
321	C₂×C₄	—	43	2	no	—
322	C₂×C₄	—	86	2	no	—
323	C₂×C₄	—	86	2	no	—
324	C₂×C₄	—	86	2	no	—
325	C₂×C₄	—	86	2	no	—
326	C₂×C₄	—	86	4	no	—
327	C₂×C₄	—	172	2	no	—
328	C₂×C₄	—	172	2	no	—
329	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
330	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
331	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
332	C₂×C₄	C₂×C₈×D₄₃	1	2	yes	—
333	C₂×C₄	M₁₆×D₄₃	1	2	yes	—
334	C₂×C₄	#13063352	1	2	yes	—
335	C₂×C₄	#13063354	1	2	yes	—
336	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
337	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
338	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
339	C₈	—	2	2	no	—
340	C₈	—	4	2	no	—
341	C₈	—	4	2	no	—
342	C₈	—	43	4	no	—
343	C₈	—	86	2	no	—
344	C₈	—	172	2	no	—
345	C₈	—	172	2	no	—
346	C₈	C₂×C₈×D₄₃	1	4	yes	complemented
347	C₂²	—	43	4	no	—
348	C₂²	—	86	2	no	—
349	C₂²	—	86	2	no	—
350	C₂²	—	86	8	no	—
351	C₂²	C₄⋊C₈×D₄₃	1	2	yes	—
352	C₂²	#14582938	1	2	yes	—
353	C₂²	#14582946	1	2	yes	—
354	C₂²	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	43	4	no	—
358	C₄	—	86	2	no	—
359	C₄	—	86	2	no	—
360	C₄	C₄⋊C₈×D₄₃	1	2	yes	—
361	C₄	#14582938	1	2	yes	—
362	C₄	C₂²×C₈×D₄₃	1	1	yes	characteristic
363	C₄	C₂×M₁₆×D₄₃	1	1	yes	characteristic
364	C₄	C₂×#13063352	1	1	yes	characteristic
365	C₄	C₂×#13063354	1	1	yes	characteristic
366	C₂	—	86	4	no	—
367	C₂	#19133344	1	4	yes	direct product factor
368	C₂	C₂×C₄⋊C₈×D₄₃	1	1	yes	characteristic
369	C₂	C₂×#14582938	1	1	yes	characteristic
370	C₂	C₂×#14582946	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₃
commutator	C₄×C₄₃	C₂³×C₈
Frattini	C₄²	C₂³×D₄₃
Fitting	C₂×C₄₃×#334	C₂
socle	C₂³×C₄₃	C₂×C₄⋊C₄
prime radical	C₂³×D₄₃	C₄⋊C₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	C₂×#334	D₄₃
hypocenter	C₄₃	C₂×#1565
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#334

Complements

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

N	H ≅ G/N	type
4. #19133344	C₂	direct (N × H)
5. C₂×#14582652	C₂	semidirect
6. C₂×#14582651	C₂	semidirect
7. C₂×#14582649	C₂	semidirect
8. C₂×C₄₃×#334	C₂	semidirect
27. #14582652	C₂²	semidirect
28. #14582651	C₂²	semidirect
29. #14582649	C₂²	semidirect
33. C₄₃×#334	C₂²	semidirect
38. C₂×#10621872	C₈	semidirect
99. C₂×C₈×C₄₃	C₂×C₈	semidirect
117. C₂×C₄₃⋊C₈	C₂×C₈	semidirect
121. #10621872	C₂×C₈	semidirect
156. C₈×C₄₃	C₂²×C₈	semidirect
160. C₄₃⋊C₈	C₂²×C₈	semidirect
188. C₂×#334	D₄₃	semidirect
189. C₂×C₄₃	#1565	semidirect
218. #334	C₂×D₄₃	semidirect
219. C₄₃	C₂×#1565	semidirect
296. C₂×C₈	C₈×D₄₃	semidirect
346. C₈	C₂×C₈×D₄₃	semidirect
367. C₂	#19133344	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×#14582951	2
C₂×C₄⋊C₈×D₄₃	2
C₂×C₄×#10621872	2
#19133344	2
C₂×#14582652	2
C₂×#14582651	2
C₂×#14582649	2
C₂×C₄₃×#334	2
C₂×#1565	43

Subgroups — C2×#19133344 #25065573

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19133344 #25065573