Subgroups — C₂×#19145124 #25966219

Order 11008.

1854 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583529	C₂	1	2	yes	maximal
2	#19145124	C₂	1	16	yes	maximal, direct product factor
3	C₂×#14583309	C₂	1	2	yes	maximal, complemented
4	C₂×#14583307	C₂	1	2	yes	maximal, complemented
5	C₂×#14583299	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14583297	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#14583296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#14582940	C₂	1	2	yes	maximal
9	C₂×#14582934	C₂	1	1	yes	maximal, characteristic
10	C₂×#106×D₄₃	C₂	1	1	yes	maximal, characteristic
11	C₂×#14582853	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄₃×#499	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#10621872	C₂²	1	1	yes	characteristic
14	C₂²×C₈×D₄₃	C₂²	1	1	yes	characteristic
15	#14583529	—	2	8	no	—
16	#14583529	C₂²	1	16	yes	—
17	C₂×#13063325	C₂²	1	2	yes	—
18	C₂×#13063324	—	2	2	no	—
19	C₂×#13063324	C₂²	1	2	yes	—
20	C₂×#13063316	C₂²	1	2	yes	—
21	C₂×#13063315	—	2	2	no	—
22	C₂×#13063305	—	2	2	no	—
23	C₂×#13063303	—	2	2	no	—
24	C₂×#13063283	C₂²	1	2	yes	—
25	C₂×#13063282	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₄×D₄₃	C₂²	1	2	yes	—
27	#14583309	C₂²	1	16	yes	complemented
28	#14583307	C₂²	1	16	yes	complemented
29	#14583299	C₂²	1	8	yes	complemented
30	#14583297	C₂²	1	8	yes	complemented
31	#14583296	C₂²	1	8	yes	complemented
32	#14582940	C₂²	1	16	yes	—
33	#14582934	C₂²	1	8	yes	—
34	C₂×#13063258	C₂²	1	2	yes	—
35	C₂×#13063258	C₂²	1	2	yes	—
36	C₂×#13063257	C₂²	1	1	yes	characteristic
37	C₂×#13063257	C₂²	1	2	yes	—
38	C₂×#13063257	C₂²	1	1	yes	characteristic
39	C₂×#13063256	C₂²	1	2	yes	—
40	C₂×#13063256	C₂²	1	2	yes	—
41	#106×D₄₃	C₂²	1	8	yes	—
42	#14582853	C₂²	1	8	yes	—
43	C₂×#13063236	C₂²	1	1	yes	characteristic
44	C₂×#13063235	C₂²	1	1	yes	characteristic
45	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
46	C₂×#125×C₄₃	C₂²	1	2	yes	—
47	C₄₃×#499	C₂²	1	8	yes	complemented
48	C₂×#107×C₄₃	C₂²	1	2	yes	—
49	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
50	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
52	C₂²×Dic₈₆	—	2	2	no	—
53	C₂²×Dic₈₆	—	2	2	no	—
54	C₂²×C₄×D₄₃	—	2	2	no	—
55	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
56	C₂×#10621872	Q₈	1	8	yes	complemented
57	C₂×#10621872	C₂³	1	4	yes	—
58	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
59	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
60	C₂×C₈×D₄₃	Q₈	1	8	yes	complemented
61	C₂×C₈×D₄₃	C₂³	1	4	yes	—
62	#13063325	—	2	4	no	—
63	#13063325	C₂³	1	8	yes	—
64	#13063324	—	2	16	no	—
65	#13063324	—	2	4	no	—
66	#13063324	C₂³	1	8	yes	—
67	#13063316	—	2	4	no	—
68	#13063316	C₂³	1	8	yes	—
69	#13063315	—	2	16	no	—
70	#13063305	—	2	16	no	—
71	#13063303	—	2	16	no	—
72	#13063283	—	2	4	no	—
73	#13063283	C₂³	1	8	yes	—
74	#13063282	D₄	1	4	yes	—
75	#13063282	C₂³	1	4	yes	—
76	C₂×C₄⋊Dic₄₃	—	2	2	no	—
77	C₂×C₄⋊Dic₄₃	—	2	2	no	—
78	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
79	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
80	C₂×Dic₄₃⋊C₄	—	2	2	no	—
81	C₂×Dic₄₃⋊C₄	—	2	2	no	—
82	C₂×Dic₄₃⋊C₄	—	2	2	no	—
83	C₂×Dic₄₃⋊C₄	D₄	1	2	yes	—
84	C₄⋊C₄×D₄₃	—	2	4	no	—
85	C₄⋊C₄×D₄₃	C₂³	1	8	yes	—
86	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
87	C₂×(C₂×D₄₃)⋊C₄	D₄	1	2	yes	—
88	C₂×C₄×Dic₄₃	—	2	2	no	—
89	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
90	#13063258	C₂³	1	8	yes	—
91	#13063258	C₂³	1	8	yes	—
92	#13063257	C₂³	1	4	yes	—
93	#13063257	C₂³	1	4	yes	—
94	#13063257	C₂³	1	8	yes	—
95	#13063256	C₂³	1	8	yes	—
96	#13063256	C₂³	1	8	yes	—
97	#13063236	C₂³	1	4	yes	—
98	#13063235	C₂³	1	4	yes	—
99	C₈×Dic₄₃	C₂³	1	4	yes	—
100	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
102	#125×C₄₃	—	2	4	no	—
103	#125×C₄₃	C₂³	1	8	yes	—
104	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
105	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
106	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
108	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
109	#107×C₄₃	C₂³	1	8	yes	—
110	#106×C₄₃	C₂³	1	4	yes	—
111	#106×C₄₃	C₂³	1	4	yes	—
112	C₄×C₈×C₄₃	C₂³	1	4	yes	—
113	C₂³×D₄₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₃	—	2	2	no	—
115	C₂²×C₄×C₄₃	—	2	2	no	—
116	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
118	C₂²×Dic₄₃	—	2	2	no	—
119	C₂²×Dic₄₃	—	2	2	no	—
120	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
121	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
122	C₂×C₄×D₄₃	—	2	8	no	—
123	C₂×C₄×D₄₃	—	8	4	no	—
124	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
125	C₂×C₄×D₄₃	C₂×Q₈	1	4	yes	—
126	C₂×C₄×D₄₃	C₂×Q₈	1	4	yes	—
127	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
128	C₂×Dic₈₆	—	2	8	no	—
129	C₂×Dic₈₆	—	2	8	no	—
130	C₂×Dic₈₆	—	8	4	no	—
131	C₂×Dic₈₆	—	8	4	no	—
132	C₂×C₈×C₄₃	C₂×Q₈	1	4	yes	—
133	C₂×C₈×C₄₃	C₂×Q₈	1	4	yes	—
134	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
135	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
136	C₄⋊C₄×C₄₃	—	2	8	no	—
137	C₄⋊C₄×C₄₃	—	2	8	no	—
138	C₄⋊C₄×C₄₃	—	2	2	no	—
139	C₄⋊C₄×C₄₃	—	2	2	no	—
140	C₄⋊C₄×C₄₃	C₂⁴	1	4	yes	—
141	C₄⋊C₄×C₄₃	C₂⁴	1	4	yes	—
142	C₄²×C₄₃	C₂×D₄	1	2	yes	—
143	C₄²×C₄₃	C₂⁴	1	2	yes	—
144	(C₂×D₄₃)⋊C₄	—	2	8	no	—
145	(C₂×D₄₃)⋊C₄	C₂×D₄	1	8	yes	—
146	C₄⋊Dic₄₃	—	2	2	no	—
147	C₄⋊Dic₄₃	—	2	8	no	—
148	C₄⋊Dic₄₃	—	2	2	no	—
149	C₄⋊Dic₄₃	—	2	8	no	—
150	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
151	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
152	Dic₄₃⋊C₄	—	2	8	no	—
153	Dic₄₃⋊C₄	—	2	8	no	—
154	Dic₄₃⋊C₄	—	2	8	no	—
155	Dic₄₃⋊C₄	C₂×D₄	1	8	yes	—
156	C₄×Dic₄₃	—	2	8	no	—
157	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
158	C₄×Dic₄₃	C₂⁴	1	2	yes	—
159	C₂×C₄₃⋊C₈	C₂×Q₈	1	4	yes	—
160	C₂×C₄₃⋊C₈	C₂×Q₈	1	4	yes	—
161	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
162	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
163	#10621872	C₂×Q₈	1	16	yes	complemented
164	C₈×D₄₃	C₂×Q₈	1	16	yes	complemented
165	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
166	C₂²×D₄₃	—	2	4	no	—
167	C₂²×D₄₃	C₄⋊Q₈	1	4	yes	—
168	C₂²×D₄₃	C₂²×D₄	1	2	yes	—
169	C₂×C₄×C₄₃	—	2	4	no	—
170	C₂×C₄×C₄₃	—	2	4	no	—
171	C₂×C₄×C₄₃	—	2	4	no	—
172	C₂×C₄×C₄₃	—	4	4	no	—
173	C₂×C₄×C₄₃	—	4	4	no	—
174	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
175	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
177	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
178	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
179	C₂×Dic₄₃	—	2	4	no	—
180	C₂×Dic₄₃	—	2	4	no	—
181	C₂×Dic₄₃	—	2	4	no	—
182	C₂×Dic₄₃	—	4	4	no	—
183	C₂×Dic₄₃	—	4	4	no	—
184	C₂×Dic₄₃	C₄⋊Q₈	1	4	yes	—
185	C₂×Dic₄₃	C₂²×D₄	1	4	yes	—
186	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
187	C₄×D₄₃	—	8	8	no	—
188	C₄×D₄₃	C₄⋊Q₈	1	8	yes	—
189	C₄×D₄₃	C₂²×Q₈	1	4	yes	—
190	C₄×D₄₃	C₂²×Q₈	1	4	yes	—
191	Dic₈₆	—	8	8	no	—
192	Dic₈₆	—	8	8	no	—
193	C₈×C₄₃	C₂²×Q₈	1	4	yes	—
194	C₈×C₄₃	C₂²×Q₈	1	4	yes	—
195	C₄₃⋊C₈	C₂²×Q₈	1	4	yes	—
196	C₄₃⋊C₈	C₂²×Q₈	1	4	yes	—
197	C₂×#3163	—	43	1	no	maximal, Sylow
198	C₂²×C₄₃	C₂×C₄⋊Q₈	1	2	yes	—
199	C₂²×C₄₃	#577	1	4	yes	—
200	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
201	C₂×D₄₃	—	2	8	no	—
202	C₂×D₄₃	—	2	4	no	—
203	C₂×D₄₃	C₂×C₄⋊Q₈	1	4	yes	—
204	C₄×C₄₃	—	2	4	no	—
205	C₄×C₄₃	—	4	4	no	—
206	C₄×C₄₃	—	4	4	no	—
207	C₄×C₄₃	C₂×C₄⋊Q₈	1	2	yes	—
208	C₄×C₄₃	C₂³×Q₈	1	1	yes	characteristic
209	C₄×C₄₃	C₂³×Q₈	1	1	yes	characteristic
210	Dic₄₃	—	2	4	no	—
211	Dic₄₃	—	4	4	no	—
212	Dic₄₃	—	4	4	no	—
213	Dic₄₃	C₂×C₄⋊Q₈	1	4	yes	—
214	C₂×#544	—	43	2	no	—
215	#3163	—	43	16	no	—
216	C₂×#501	—	43	2	no	—
217	C₂×#501	—	43	2	no	—
218	C₂×#499	—	43	1	no	—
219	C₂×#499	D₄₃	1	1	yes	characteristic, complemented
220	C₂×#498	—	43	1	no	—
221	C₂×#498	—	43	1	no	—
222	C₂×#428	—	43	2	no	—
223	C₂×#427	—	43	1	no	—
224	C₂²×#106	—	43	1	no	—
225	C₂×#405	—	43	1	no	—
226	C₂×C₄₃	#3163	1	4	yes	complemented
227	C₂×C₄₃	C₂²×C₄⋊Q₈	1	1	yes	characteristic
228	C₂×C₄₃	C₂×#577	1	2	yes	—
229	D₄₃	—	2	4	no	—
230	C₂²×M₁₆	—	43	1	no	—
231	C₂³×C₈	—	43	1	no	—
232	#544	—	43	16	no	—
233	#544	—	86	8	no	—
234	C₂×C₄⋊Q₈	—	43	2	no	—
235	C₂×C₄⋊Q₈	—	43	2	no	—
236	C₂×C₄⋊Q₈	—	86	2	no	—
237	C₂×#125	—	43	2	no	—
238	C₂×#125	—	86	2	no	—
239	C₂×#125	C₂×D₄₃	1	2	yes	—
240	C₂×C₂²⋊Q₈	—	86	2	no	—
241	C₂×C₂²⋊Q₈	—	86	2	no	—
242	C₂×#117	—	43	1	no	—
243	C₂×#117	—	43	2	no	—
244	C₂²×C₄⋊C₄	—	43	2	no	—
245	#501	—	43	16	no	—
246	#501	—	43	16	no	—
247	#499	—	43	8	no	—
248	#499	C₂×D₄₃	1	8	yes	complemented
249	#498	—	43	8	no	—
250	#498	—	43	8	no	—
251	#428	—	43	16	no	—
252	#427	—	43	8	no	—
253	C₂×#107	—	43	2	no	—
254	C₂×#107	—	43	2	no	—
255	C₂×#107	C₂×D₄₃	1	2	yes	—
256	C₂×#106	—	43	1	no	—
257	C₂×#106	—	43	1	no	—
258	C₂×#106	—	43	2	no	—
259	C₂×#106	—	43	2	no	—
260	C₂×#106	—	43	2	no	—
261	C₂×#106	—	43	8	no	—
262	C₂×#106	C₂×D₄₃	1	1	yes	characteristic
263	C₂×#106	C₂×D₄₃	1	1	yes	characteristic
264	#405	—	43	8	no	—
265	C₂×#97	—	43	1	no	—
266	C₂×#97	—	43	1	no	—
267	C₂×C₄×C₈	—	43	1	no	—
268	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
269	C₄₃	C₂×#3163	1	1	yes	characteristic, complemented, Sylow
270	C₂²×Q₈	—	86	2	no	—
271	C₂²×Q₈	—	86	2	no	—
272	C₂³×C₄	—	43	1	no	—
273	C₂³×C₄	—	86	2	no	—
274	C₂×M₁₆	—	43	8	no	—
275	C₂×M₁₆	—	43	4	no	—
276	C₂²×C₈	—	43	1	no	—
277	C₂²×C₈	—	43	1	no	—
278	C₂²×C₈	—	43	8	no	—
279	C₂²×C₈	—	43	4	no	—
280	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
281	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
282	C₄⋊Q₈	—	43	8	no	—
283	C₄⋊Q₈	—	43	8	no	—
284	C₄⋊Q₈	—	86	4	no	—
285	C₄⋊Q₈	—	86	16	no	—
286	C₄⋊Q₈	—	86	4	no	—
287	#125	—	2	4	no	—
288	#125	—	43	8	no	—
289	#125	—	86	4	no	—
290	#125	—	86	16	no	—
291	#125	C₂²×D₄₃	1	8	yes	—
292	C₂²⋊Q₈	—	86	16	no	—
293	C₂²⋊Q₈	—	86	16	no	—
294	#117	—	43	4	no	—
295	#117	—	43	4	no	—
296	#117	—	43	8	no	—
297	#117	—	86	4	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	—	43	2	no	—
301	C₂×C₄⋊C₄	—	43	2	no	—
302	C₂×C₄⋊C₄	—	43	2	no	—
303	C₂×C₄⋊C₄	—	43	8	no	—
304	C₂×C₄⋊C₄	—	86	4	no	—
305	C₂×C₄⋊C₄	—	86	2	no	—
306	C₂×C₄⋊C₄	—	86	2	no	—
307	C₂×C₄⋊C₄	—	86	2	no	—
308	C₂×C₄⋊C₄	—	86	2	no	—
309	C₂×C₄⋊C₄	—	86	2	no	—
310	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
311	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
312	C₂×C₂²⋊C₄	—	43	2	no	—
313	C₂×C₂²⋊C₄	—	86	2	no	—
314	C₂×C₄²	—	43	1	no	—
315	C₂×C₄²	—	86	2	no	—
316	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
317	#107	—	43	8	no	—
318	#107	—	43	8	no	—
319	#107	C₂²×D₄₃	1	8	yes	—
320	#106	—	43	4	no	—
321	#106	—	43	4	no	—
322	#106	—	43	8	no	—
323	#106	—	43	8	no	—
324	#106	—	43	8	no	—
325	#106	C₂²×D₄₃	1	4	yes	—
326	#106	C₂²×D₄₃	1	4	yes	—
327	#97	—	43	4	no	—
328	#97	—	43	4	no	—
329	C₄×C₈	—	43	4	no	—
330	C₄×C₈	C₂²×D₄₃	1	4	yes	—
331	C₂⁴	—	43	1	no	—
332	C₂×Q₈	—	86	8	no	—
333	C₂×Q₈	—	86	8	no	—
334	C₂×Q₈	—	344	4	no	—
335	C₂×Q₈	—	344	4	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	43	1	no	—
339	C₂²×C₄	—	43	2	no	—
340	C₂²×C₄	—	43	4	no	—
341	C₂²×C₄	—	43	4	no	—
342	C₂²×C₄	—	43	2	no	—
343	C₂²×C₄	—	43	2	no	—
344	C₂²×C₄	—	86	8	no	—
345	C₂²×C₄	—	86	2	no	—
346	C₂²×C₄	—	86	2	no	—
347	C₂²×C₄	—	344	4	no	—
348	C₂²×C₄	D₄×D₄₃	1	2	yes	—
349	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
350	M₁₆	—	43	16	no	—
351	C₂×C₈	—	43	4	no	—
352	C₂×C₈	—	43	4	no	—
353	C₂×C₈	—	43	2	no	—
354	C₂×C₈	—	43	2	no	—
355	C₂×C₈	—	43	16	no	—
356	C₂×C₈	Q₈×D₄₃	1	4	yes	—
357	C₂×C₈	Q₈×D₄₃	1	4	yes	—
358	C₂×C₈	C₂³×D₄₃	1	2	yes	—
359	C₂×C₈	C₂³×D₄₃	1	2	yes	—
360	C₄⋊C₄	—	2	8	no	—
361	C₄⋊C₄	—	2	8	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	43	8	no	—
365	C₄⋊C₄	—	43	4	no	—
366	C₄⋊C₄	—	43	4	no	—
367	C₄⋊C₄	—	86	8	no	—
368	C₄⋊C₄	—	86	8	no	—
369	C₄⋊C₄	—	86	8	no	—
370	C₄⋊C₄	—	86	8	no	—
371	C₄⋊C₄	—	86	2	no	—
372	C₄⋊C₄	—	86	2	no	—
373	C₄⋊C₄	—	86	8	no	—
374	C₄⋊C₄	C₂³×D₄₃	1	4	yes	—
375	C₄⋊C₄	C₂³×D₄₃	1	4	yes	—
376	C₂²⋊C₄	—	43	8	no	—
377	C₂²⋊C₄	—	86	8	no	—
378	C₄²	—	43	2	no	—
379	C₄²	—	43	2	no	—
380	C₄²	—	86	8	no	—
381	C₄²	D₄×D₄₃	1	2	yes	—
382	C₄²	C₂³×D₄₃	1	2	yes	—
383	C₂³	—	43	4	no	—
384	C₂³	—	43	2	no	—
385	C₂³	—	86	4	no	—
386	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
387	Q₈	—	344	8	no	—
388	Q₈	—	344	8	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	4	no	—
394	C₂×C₄	—	43	4	no	—
395	C₂×C₄	—	43	2	no	—
396	C₂×C₄	—	43	8	no	—
397	C₂×C₄	—	43	4	no	—
398	C₂×C₄	—	43	4	no	—
399	C₂×C₄	—	43	4	no	—
400	C₂×C₄	—	86	4	no	—
401	C₂×C₄	—	86	4	no	—
402	C₂×C₄	—	86	4	no	—
403	C₂×C₄	—	344	8	no	—
404	C₂×C₄	—	172	4	no	—
405	C₂×C₄	—	172	4	no	—
406	C₂×C₄	C₂×D₄×D₄₃	1	4	yes	—
407	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
408	C₂×C₄	C₂×Q₈×D₄₃	1	2	yes	—
409	C₂×C₄	C₂×Q₈×D₄₃	1	2	yes	—
410	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
411	C₈	—	43	4	no	—
412	C₈	—	43	4	no	—
413	C₈	C₂×Q₈×D₄₃	1	4	yes	—
414	C₈	C₂×Q₈×D₄₃	1	4	yes	—
415	C₂²	—	43	4	no	—
416	C₂²	—	86	4	no	—
417	C₂²	—	86	8	no	—
418	C₂²	C₄⋊Q₈×D₄₃	1	2	yes	—
419	C₂²	#14583706	1	4	yes	—
420	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
421	C₄	—	2	4	no	—
422	C₄	—	4	4	no	—
423	C₄	—	4	4	no	—
424	C₄	—	43	4	no	—
425	C₄	—	86	4	no	—
426	C₄	—	172	4	no	—
427	C₄	—	172	4	no	—
428	C₄	C₄⋊Q₈×D₄₃	1	2	yes	—
429	C₄	C₂²×Q₈×D₄₃	1	1	yes	characteristic
430	C₄	C₂²×Q₈×D₄₃	1	1	yes	characteristic
431	C₂	—	86	4	no	—
432	C₂	#19145124	1	4	yes	direct product factor
433	C₂	C₂×C₄⋊Q₈×D₄₃	1	1	yes	characteristic
434	C₂	C₂×#14583706	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₂×C₄₃×#499	C₂
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂³×D₄₃	C₂×D₄
hypercenter	C₂×#499	D₄₃
hypocenter	C₄₃	C₂×#3163
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#499

Complements

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

N	H ≅ G/N	type
2. #19145124	C₂	direct (N × H)
3. C₂×#14583309	C₂	semidirect
4. C₂×#14583307	C₂	semidirect
5. C₂×#14583299	C₂	semidirect
6. C₂×#14583297	C₂	semidirect
7. C₂×#14583296	C₂	semidirect
12. C₂×C₄₃×#499	C₂	semidirect
27. #14583309	C₂²	semidirect
28. #14583307	C₂²	semidirect
29. #14583299	C₂²	semidirect
30. #14583297	C₂²	semidirect
31. #14583296	C₂²	semidirect
47. C₄₃×#499	C₂²	semidirect
56. C₂×#10621872	Q₈	semidirect
60. C₂×C₈×D₄₃	Q₈	semidirect
163. #10621872	C₂×Q₈	semidirect
164. C₈×D₄₃	C₂×Q₈	semidirect
219. C₂×#499	D₄₃	semidirect
226. C₂×C₄₃	#3163	semidirect
248. #499	C₂×D₄₃	semidirect
269. C₄₃	C₂×#3163	semidirect
432. C₂	#19145124	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×#14583529	2
#19145124	2
C₂×#14583309	2
C₂×#14583307	2
C₂×#14583299	2
C₂×#14583297	2
C₂×#14583296	2
C₂×#14582940	2
C₂×#14582934	2
C₂×#106×D₄₃	2
C₂×#14582853	2
C₂×C₄₃×#499	2
C₂×#3163	43

Subgroups — C2×#19145124 #25966219

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19145124 #25966219