Subgroups — C₂×#19143183 #25960256

Order 11008.

2878 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#10621872	C₂	1	1	yes	maximal, characteristic
2	C₂×#117×D₄₃	C₂	1	2	yes	maximal
3	#19143183	C₂	1	16	yes	maximal, direct product factor
4	C₂×#14582940	C₂	1	4	yes	maximal, complemented
5	C₂×#14582938	C₂	1	4	yes	maximal, complemented
6	C₂×#14582937	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#14582935	C₂	1	2	yes	maximal, complemented
8	C₂×C₄₃×#427	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×C₄×D₄₃	C₂²	1	1	yes	characteristic
10	C₂²×#10621872	C₄	1	16	yes	complemented
11	C₂²×#10621872	C₂²	1	2	yes	—
12	C₂²×#10621872	C₂²	1	2	yes	—
13	C₂²×#10621872	C₂²	1	8	yes	—
14	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×#13063284	C₂²	1	2	yes	—
16	C₂×#13063283	C₂²	1	4	yes	—
17	C₂×#13063282	—	2	2	no	—
18	C₂×#13063281	—	2	2	no	—
19	#117×D₄₃	—	2	8	no	—
20	#117×D₄₃	C₂²	1	16	yes	—
21	C₂×C₄⋊C₄×D₄₃	C₂²	1	4	yes	—
22	C₂×C₂²⋊C₄×D₄₃	—	2	2	no	—
23	C₂×C₄²×D₄₃	—	2	2	no	—
24	#14582940	C₂²	1	32	yes	complemented
25	#14582938	C₂²	1	32	yes	complemented
26	#14582937	C₂²	1	8	yes	complemented
27	#14582935	C₂²	1	16	yes	complemented
28	C₂×#13063259	C₂²	1	2	yes	complemented
29	C₂×#13063258	C₂²	1	4	yes	complemented
30	C₂×#13063257	C₂²	1	2	yes	complemented
31	C₂×#13063256	C₂²	1	4	yes	complemented
32	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
33	C₂×#117×C₄₃	C₂²	1	2	yes	—
34	C₄₃×#427	C₂²	1	8	yes	complemented
35	C₂×#107×C₄₃	C₂²	1	2	yes	complemented
36	C₂×#106×C₄₃	C₂²	1	2	yes	complemented
37	C₂⁴×D₄₃	D₄	1	1	yes	characteristic
38	C₂³×Dic₄₃	D₄	1	1	yes	characteristic
39	C₂²×C₄×D₄₃	—	2	4	no	—
40	C₂²×C₄×D₄₃	C₂×C₄	1	8	yes	—
41	C₂²×C₄×D₄₃	D₄	1	2	yes	—
42	C₂²×C₄×D₄₃	D₄	1	4	yes	—
43	C₂²×C₄×D₄₃	Q₈	1	8	yes	—
44	C₂²×C₄×D₄₃	C₂³	1	2	yes	—
45	C₂²×C₄×D₄₃	C₂³	1	4	yes	—
46	C₂×#10621872	C₂×C₄	1	16	yes	complemented
47	C₂×#10621872	C₂×C₄	1	16	yes	complemented
48	C₂×#10621872	C₂×C₄	1	64	yes	complemented
49	C₂×#10621872	C₂³	1	8	yes	—
50	C₂×#10621872	C₂³	1	8	yes	—
51	C₂²×C₄₃⋊C₈	C₂×C₄	1	8	yes	complemented
52	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
53	C₂²×C₄₃⋊C₈	C₂³	1	4	yes	—
54	#13063284	—	2	4	no	—
55	#13063284	C₂³	1	8	yes	—
56	#13063283	—	2	8	no	—
57	#13063283	C₂³	1	16	yes	—
58	#13063282	—	2	16	no	—
59	#13063281	—	2	16	no	—
60	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
61	C₂×Dic₄₃⋊C₄	—	2	4	no	—
62	C₄⋊C₄×D₄₃	—	2	8	no	—
63	C₄⋊C₄×D₄₃	C₂³	1	16	yes	—
64	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
65	C₂×(C₂×D₄₃)⋊C₄	—	2	4	no	—
66	C₂²⋊C₄×D₄₃	—	2	16	no	—
67	C₂×C₄×Dic₄₃	—	2	2	no	—
68	C₂×C₄×Dic₄₃	—	2	4	no	—
69	C₄²×D₄₃	—	2	16	no	—
70	#13063259	C₂³	1	8	yes	complemented
71	#13063258	C₂³	1	16	yes	complemented
72	#13063257	C₂³	1	8	yes	complemented
73	#13063256	C₂³	1	16	yes	complemented
74	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₄₃	C₂×C₄	1	8	yes	complemented
76	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
79	#117×C₄₃	—	2	4	no	—
80	#117×C₄₃	C₂³	1	8	yes	—
81	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
82	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
83	C₂×C₄²×C₄₃	—	2	2	no	—
84	#107×C₄₃	C₂³	1	8	yes	complemented
85	#106×C₄₃	C₂³	1	8	yes	complemented
86	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
87	C₂³×D₄₃	—	4	4	no	—
88	C₂³×D₄₃	C₄⋊C₄	1	8	yes	—
89	C₂³×D₄₃	C₂×D₄	1	2	yes	—
90	C₂³×D₄₃	C₂×D₄	1	4	yes	—
91	C₂²×C₄×C₄₃	—	2	4	no	—
92	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
93	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
96	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
97	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
98	C₂²×Dic₄₃	—	2	4	no	—
99	C₂²×Dic₄₃	C₄⋊C₄	1	8	yes	—
100	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
101	C₂²×Dic₄₃	C₂×D₄	1	4	yes	—
102	C₂×C₄×D₄₃	—	2	16	no	—
103	C₂×C₄×D₄₃	—	4	16	no	—
104	C₂×C₄×D₄₃	C₄⋊C₄	1	16	yes	—
105	C₂×C₄×D₄₃	C₄⋊C₄	1	32	yes	—
106	C₂×C₄×D₄₃	C₂²×C₄	1	8	yes	—
107	C₂×C₄×D₄₃	C₂²×C₄	1	16	yes	—
108	C₂×C₄×D₄₃	C₂×D₄	1	8	yes	—
109	C₂×C₄×D₄₃	C₂×D₄	1	4	yes	—
110	C₂×C₄×D₄₃	C₂×Q₈	1	8	yes	—
111	C₂×C₄×D₄₃	C₂×Q₈	1	16	yes	—
112	C₂×C₄×D₄₃	C₂⁴	1	4	yes	—
113	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
114	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
115	C₂×C₈×C₄₃	C₂²×C₄	1	16	yes	complemented
116	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
117	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
118	C₄⋊C₄×C₄₃	—	2	4	no	—
119	C₄⋊C₄×C₄₃	C₂⁴	1	8	yes	—
120	C₂²⋊C₄×C₄₃	—	2	8	no	—
121	C₄²×C₄₃	—	2	8	no	—
122	C₂²⋊Dic₄₃	—	2	8	no	—
123	(C₂×D₄₃)⋊C₄	—	2	16	no	—
124	C₄⋊Dic₄₃	—	2	4	no	—
125	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
126	Dic₄₃⋊C₄	—	2	16	no	—
127	C₄×Dic₄₃	—	2	8	no	—
128	C₄×Dic₄₃	—	2	16	no	—
129	C₂×C₄₃⋊C₈	C₂²×C₄	1	8	yes	—
130	C₂×C₄₃⋊C₈	C₂²×C₄	1	16	yes	complemented
131	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
132	#10621872	C₂²×C₄	1	32	yes	complemented
133	#10621872	C₂²×C₄	1	32	yes	complemented
134	C₂³×C₄₃	—	2	4	no	—
135	C₂³×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
136	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
137	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
138	C₂²×D₄₃	—	2	8	no	—
139	C₂²×D₄₃	—	4	16	no	—
140	C₂²×D₄₃	—	4	8	no	—
141	C₂²×D₄₃	C₂×C₄⋊C₄	1	8	yes	—
142	C₂²×D₄₃	C₂×C₄⋊C₄	1	16	yes	—
143	C₂²×D₄₃	C₂²×D₄	1	4	yes	—
144	C₂×C₄×C₄₃	—	2	8	no	—
145	C₂×C₄×C₄₃	—	4	8	no	—
146	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	8	yes	—
147	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
148	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
149	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
150	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
151	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₄×C₄₃	C₂²×Q₈	1	4	yes	—
153	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
154	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
155	C₂×Dic₄₃	—	2	8	no	—
156	C₂×Dic₄₃	—	4	8	no	—
157	C₂×Dic₄₃	C₂×C₄⋊C₄	1	16	yes	—
158	C₂×Dic₄₃	C₂×C₄⋊C₄	1	8	yes	—
159	C₂×Dic₄₃	C₂²×D₄	1	4	yes	—
160	C₄×D₄₃	—	4	32	no	—
161	C₄×D₄₃	C₂×C₄⋊C₄	1	32	yes	—
162	C₄×D₄₃	C₂×C₄⋊C₄	1	16	yes	—
163	C₄×D₄₃	C₂³×C₄	1	8	yes	—
164	C₄×D₄₃	C₂²×Q₈	1	8	yes	—
165	C₈×C₄₃	C₂³×C₄	1	4	yes	—
166	C₈×C₄₃	C₂³×C₄	1	4	yes	—
167	C₄₃⋊C₈	C₂³×C₄	1	8	yes	—
168	C₂×#2911	—	43	1	no	maximal, Sylow
169	C₂²×C₄₃	—	2	8	no	—
170	C₂²×C₄₃	—	2	4	no	—
171	C₂²×C₄₃	C₂²×C₄⋊C₄	1	4	yes	—
172	C₂²×C₄₃	C₂²×C₄⋊C₄	1	2	yes	—
173	C₂²×C₄₃	#575	1	4	yes	—
174	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
175	C₂×D₄₃	—	2	16	no	—
176	C₂×D₄₃	—	2	8	no	—
177	C₂×D₄₃	—	4	16	no	—
178	C₂×D₄₃	C₂²×C₄⋊C₄	1	8	yes	—
179	C₄×C₄₃	—	4	8	no	—
180	C₄×C₄₃	C₂²×C₄⋊C₄	1	2	yes	—
181	C₄×C₄₃	C₂²×C₄⋊C₄	1	4	yes	—
182	C₄×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
183	C₄×C₄₃	C₂³×Q₈	1	1	yes	characteristic
184	Dic₄₃	—	4	8	no	—
185	Dic₄₃	C₂²×C₄⋊C₄	1	8	yes	—
186	C₂³×M₁₆	—	43	1	no	—
187	C₂²×#117	—	43	2	no	—
188	#2911	—	43	16	no	—
189	C₂×#428	—	43	4	no	—
190	C₂×#428	—	43	4	no	—
191	C₂×#427	—	43	1	no	—
192	C₂×#427	—	43	2	no	—
193	C₂×#427	D₄₃	1	1	yes	characteristic, complemented
194	C₂×C₄₃	—	2	4	no	—
195	C₂×C₄₃	#2911	1	4	yes	complemented
196	C₂×C₄₃	C₂³×C₄⋊C₄	1	1	yes	characteristic
197	C₂×C₄₃	C₂×#575	1	2	yes	—
198	D₄₃	—	2	8	no	—
199	C₂⁴×C₄	—	43	1	no	—
200	C₂²×M₁₆	—	43	2	no	—
201	C₂²×M₁₆	—	43	2	no	—
202	C₂²×M₁₆	—	43	8	no	—
203	C₂²×M₁₆	—	43	16	no	—
204	C₂³×C₈	—	43	1	no	—
205	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
206	C₂×#117	—	43	2	no	—
207	C₂×#117	—	43	16	no	—
208	C₂×#117	—	43	4	no	—
209	C₂×#117	—	86	2	no	—
210	C₂×#117	—	86	2	no	—
211	C₂×#117	—	86	8	no	—
212	C₂×#117	C₂×D₄₃	1	2	yes	—
213	C₂²×C₄⋊C₄	—	43	4	no	—
214	C₂²×C₂²⋊C₄	—	86	2	no	—
215	C₂²×C₄²	—	86	2	no	—
216	#428	—	43	32	no	—
217	#428	—	43	32	no	—
218	#427	—	43	8	no	—
219	#427	—	43	16	no	—
220	#427	C₂×D₄₃	1	8	yes	complemented
221	C₂×#107	—	43	2	no	—
222	C₂×#107	—	43	4	no	—
223	C₂×#107	C₂×D₄₃	1	2	yes	complemented
224	C₂×#106	—	43	2	no	—
225	C₂×#106	—	43	4	no	—
226	C₂×#106	C₂×D₄₃	1	2	yes	complemented
227	C₄₃	C₂×#2911	1	1	yes	characteristic, complemented, Sylow
228	C₂⁵	—	43	1	no	—
229	C₂³×C₄	—	43	1	no	—
230	C₂³×C₄	—	43	8	no	—
231	C₂³×C₄	—	43	4	no	—
232	C₂³×C₄	—	43	2	no	—
233	C₂³×C₄	—	43	8	no	—
234	C₂³×C₄	—	43	2	no	—
235	C₂³×C₄	—	43	4	no	—
236	C₂³×C₄	—	86	4	no	—
237	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
238	C₂×M₁₆	—	43	16	no	—
239	C₂×M₁₆	—	43	16	no	—
240	C₂×M₁₆	—	43	64	no	—
241	C₂×M₁₆	—	43	8	no	—
242	C₂×M₁₆	—	43	8	no	—
243	C₂²×C₈	—	43	8	no	—
244	C₂²×C₈	—	43	2	no	—
245	C₂²×C₈	—	43	4	no	—
246	C₂²×C₈	C₄×D₄₃	1	8	yes	complemented
247	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
248	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
249	C₂²×C₈	C₂²×D₄₃	1	4	yes	—
250	#117	—	2	4	no	—
251	#117	—	43	8	no	—
252	#117	—	43	16	no	—
253	#117	—	86	16	no	—
254	#117	—	86	16	no	—
255	#117	—	86	8	no	—
256	#117	—	86	4	no	—
257	#117	C₂²×D₄₃	1	8	yes	—
258	C₂×C₄⋊C₄	—	43	4	no	—
259	C₂×C₄⋊C₄	—	43	16	no	—
260	C₂×C₄⋊C₄	—	86	8	no	—
261	C₂×C₄⋊C₄	—	86	4	no	—
262	C₂×C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
263	C₂×C₂²⋊C₄	—	2	2	no	—
264	C₂×C₂²⋊C₄	—	86	16	no	—
265	C₂×C₂²⋊C₄	—	86	4	no	—
266	C₂×C₂²⋊C₄	—	86	2	no	—
267	C₂×C₄²	—	2	2	no	—
268	C₂×C₄²	—	86	16	no	—
269	C₂×C₄²	—	86	4	no	—
270	C₂×C₄²	—	86	2	no	—
271	#107	—	43	8	no	—
272	#107	—	43	16	no	—
273	#107	C₂²×D₄₃	1	8	yes	complemented
274	#106	—	43	8	no	—
275	#106	—	43	16	no	—
276	#106	C₂²×D₄₃	1	8	yes	complemented
277	C₂⁴	—	43	2	no	—
278	C₂⁴	—	43	8	no	—
279	C₂⁴	—	43	4	no	—
280	C₂⁴	—	172	4	no	—
281	C₂⁴	D₄×D₄₃	1	1	yes	characteristic
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	43	8	no	—
284	C₂²×C₄	—	43	2	no	—
285	C₂²×C₄	—	43	4	no	—
286	C₂²×C₄	—	43	32	no	—
287	C₂²×C₄	—	43	16	no	—
288	C₂²×C₄	—	43	8	no	—
289	C₂²×C₄	—	43	16	no	—
290	C₂²×C₄	—	43	8	no	—
291	C₂²×C₄	—	43	4	no	—
292	C₂²×C₄	—	43	8	no	—
293	C₂²×C₄	—	43	16	no	—
294	C₂²×C₄	—	43	4	no	—
295	C₂²×C₄	—	86	16	no	—
296	C₂²×C₄	—	86	4	no	—
297	C₂²×C₄	—	172	16	no	—
298	C₂²×C₄	C₂×C₄×D₄₃	1	4	yes	—
299	C₂²×C₄	D₄×D₄₃	1	2	yes	—
300	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
301	C₂²×C₄	Q₈×D₄₃	1	4	yes	—
302	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
303	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
304	M₁₆	—	43	32	no	—
305	M₁₆	—	43	32	no	—
306	C₂×C₈	—	43	8	no	—
307	C₂×C₈	—	43	16	no	—
308	C₂×C₈	—	43	4	no	—
309	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
310	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
311	C₂×C₈	C₂×C₄×D₄₃	1	16	yes	complemented
312	C₂×C₈	C₂³×D₄₃	1	2	yes	—
313	C₂×C₈	C₂³×D₄₃	1	2	yes	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	43	8	no	—
316	C₄⋊C₄	—	86	16	no	—
317	C₄⋊C₄	—	86	4	no	—
318	C₄⋊C₄	C₂³×D₄₃	1	8	yes	—
319	C₂²⋊C₄	—	2	8	no	—
320	C₂²⋊C₄	—	86	16	no	—
321	C₂²⋊C₄	—	86	8	no	—
322	C₄²	—	2	8	no	—
323	C₄²	—	86	16	no	—
324	C₄²	—	86	8	no	—
325	C₂³	—	2	4	no	—
326	C₂³	—	43	8	no	—
327	C₂³	—	43	4	no	—
328	C₂³	—	43	16	no	—
329	C₂³	—	86	8	no	—
330	C₂³	—	172	16	no	—
331	C₂³	—	172	8	no	—
332	C₂³	C₄⋊C₄×D₄₃	1	4	yes	—
333	C₂³	C₂×D₄×D₄₃	1	2	yes	—
334	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
335	C₂×C₄	—	2	8	no	—
336	C₂×C₄	—	4	8	no	—
337	C₂×C₄	—	43	16	no	—
338	C₂×C₄	—	43	8	no	—
339	C₂×C₄	—	43	4	no	—
340	C₂×C₄	—	43	32	no	—
341	C₂×C₄	—	43	16	no	—
342	C₂×C₄	—	43	8	no	—
343	C₂×C₄	—	43	8	no	—
344	C₂×C₄	—	86	8	no	—
345	C₂×C₄	—	172	32	no	—
346	C₂×C₄	—	172	8	no	—
347	C₂×C₄	C₄⋊C₄×D₄₃	1	8	yes	—
348	C₂×C₄	C₄⋊C₄×D₄₃	1	4	yes	—
349	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
350	C₂×C₄	C₂²×C₄×D₄₃	1	4	yes	—
351	C₂×C₄	C₂×D₄×D₄₃	1	2	yes	—
352	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
353	C₂×C₄	C₂×Q₈×D₄₃	1	4	yes	—
354	C₂×C₄	C₂×Q₈×D₄₃	1	2	yes	—
355	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
356	C₈	—	43	8	no	—
357	C₈	C₂²×C₄×D₄₃	1	4	yes	—
358	C₈	C₂²×C₄×D₄₃	1	4	yes	—
359	C₂²	—	2	8	no	—
360	C₂²	—	2	4	no	—
361	C₂²	—	43	8	no	—
362	C₂²	—	86	16	no	—
363	C₂²	—	86	8	no	—
364	C₂²	—	172	16	no	—
365	C₂²	C₂×C₄⋊C₄×D₄₃	1	4	yes	—
366	C₂²	C₂×C₄⋊C₄×D₄₃	1	2	yes	—
367	C₂²	#14583696	1	4	yes	—
368	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
369	C₄	—	4	8	no	—
370	C₄	—	43	8	no	—
371	C₄	—	172	8	no	—
372	C₄	C₂×C₄⋊C₄×D₄₃	1	2	yes	—
373	C₄	C₂×C₄⋊C₄×D₄₃	1	4	yes	—
374	C₄	C₂³×C₄×D₄₃	1	1	yes	characteristic
375	C₄	C₂²×Q₈×D₄₃	1	1	yes	characteristic
376	C₂	—	2	4	no	—
377	C₂	—	86	8	no	—
378	C₂	#19143183	1	4	yes	direct product factor
379	C₂	C₂²×C₄⋊C₄×D₄₃	1	1	yes	characteristic
380	C₂	C₂×#14583696	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₃
commutator	C₄×C₄₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₂×C₄₃×#427	C₂
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂⁴×D₄₃	D₄
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	C₂×#427	D₄₃
hypocenter	C₄₃	C₂×#2911
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂×#427

Complements

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

N	H ≅ G/N	type
3. #19143183	C₂	direct (N × H)
4. C₂×#14582940	C₂	semidirect
5. C₂×#14582938	C₂	semidirect
6. C₂×#14582937	C₂	semidirect
7. C₂×#14582935	C₂	semidirect
8. C₂×C₄₃×#427	C₂	semidirect
10. C₂²×#10621872	C₄	semidirect
24. #14582940	C₂²	semidirect
25. #14582938	C₂²	semidirect
26. #14582937	C₂²	semidirect
27. #14582935	C₂²	semidirect
28. C₂×#13063259	C₂²	semidirect
29. C₂×#13063258	C₂²	semidirect
30. C₂×#13063257	C₂²	semidirect
31. C₂×#13063256	C₂²	semidirect
34. C₄₃×#427	C₂²	semidirect
35. C₂×#107×C₄₃	C₂²	semidirect
36. C₂×#106×C₄₃	C₂²	semidirect
46. C₂×#10621872	C₂×C₄	semidirect
47. C₂×#10621872	C₂×C₄	semidirect
48. C₂×#10621872	C₂×C₄	semidirect
51. C₂²×C₄₃⋊C₈	C₂×C₄	semidirect
70. #13063259	C₂³	semidirect
71. #13063258	C₂³	semidirect
72. #13063257	C₂³	semidirect
73. #13063256	C₂³	semidirect
75. C₂²×C₈×C₄₃	C₂×C₄	semidirect
84. #107×C₄₃	C₂³	semidirect
85. #106×C₄₃	C₂³	semidirect
115. C₂×C₈×C₄₃	C₂²×C₄	semidirect
130. C₂×C₄₃⋊C₈	C₂²×C₄	semidirect
132. #10621872	C₂²×C₄	semidirect
133. #10621872	C₂²×C₄	semidirect
193. C₂×#427	D₄₃	semidirect
195. C₂×C₄₃	#2911	semidirect
220. #427	C₂×D₄₃	semidirect
223. C₂×#107	C₂×D₄₃	semidirect
226. C₂×#106	C₂×D₄₃	semidirect
227. C₄₃	C₂×#2911	semidirect
246. C₂²×C₈	C₄×D₄₃	semidirect
273. #107	C₂²×D₄₃	semidirect
276. #106	C₂²×D₄₃	semidirect
311. C₂×C₈	C₂×C₄×D₄₃	semidirect
378. C₂	#19143183	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#10621872	2
C₂×#117×D₄₃	2
#19143183	2
C₂×#14582940	2
C₂×#14582938	2
C₂×#14582937	2
C₂×#14582935	2
C₂×C₄₃×#427	2
C₂×#2911	43

Subgroups — C2×#19143183 #25960256

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19143183 #25960256