Subgroups — C₂×#19143504 #25960909

Order 11008.

2674 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583699	C₂	1	1	yes	maximal, characteristic
2	C₂×#14583665	C₂	1	2	yes	maximal, complemented
3	#19143504	C₂	1	16	yes	maximal, direct product factor
4	C₂×#14583020	C₂	1	4	yes	maximal, complemented
5	C₂×#14583015	C₂	1	4	yes	maximal, complemented
6	C₂²×#13063251	C₂	1	2	yes	maximal, complemented
7	C₂×M₁₆×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₃×#430	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#10621898	C₂²	1	2	yes	—
10	#14583699	C₄	1	8	yes	complemented
11	#14583699	C₂²	1	8	yes	—
12	C₂×#13063358	C₄	1	4	yes	complemented
13	C₂×#13063353	C₄	1	4	yes	complemented
14	C₂×#13063347	C₂²	1	4	yes	—
15	#14583665	—	2	8	no	—
16	#14583665	C₂²	1	16	yes	complemented
17	C₂×#13063333	C₂²	1	8	yes	complemented
18	C₂×#13063331	—	2	4	no	—
19	C₂²×#10621877	C₂²	1	1	yes	characteristic
20	C₂×M₁₆×D₄₃	—	2	4	no	—
21	C₂²×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
22	#14583020	C₂²	1	32	yes	complemented
23	#14583015	C₂²	1	32	yes	complemented
24	C₂×#13063251	C₂²	1	4	yes	complemented
25	C₂×#13063251	C₂²	1	4	yes	complemented
26	C₂×#13063251	C₂²	1	16	yes	complemented
27	M₁₆×Dic₄₃	C₂²	1	8	yes	complemented
28	C₂×#13063235	C₂²	1	2	yes	complemented
29	C₂×C₈×Dic₄₃	C₂²	1	2	yes	complemented
30	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
31	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
32	C₄₃×#430	C₂²	1	8	yes	complemented
33	C₂×#108×C₄₃	C₂²	1	4	yes	complemented
34	C₂×#10621898	—	2	2	no	—
35	C₂×#10621898	—	2	4	no	—
36	C₂×#10621898	—	2	2	no	—
37	C₂×#10621898	—	2	4	no	—
38	C₂×#10621898	C₂×C₄	1	4	yes	—
39	C₂×#10621898	C₂×C₄	1	8	yes	—
40	C₂×#10621898	C₂³	1	4	yes	—
41	C₂×#10621898	C₂³	1	8	yes	—
42	C₂²×Dic₈₆	C₂×C₄	1	2	yes	—
43	C₂²×D₁₇₂	C₂×C₄	1	2	yes	—
44	C₂²×C₂²⋊D₄₃	—	2	2	no	—
45	C₂³×Dic₄₃	—	2	1	no	—
46	C₂²×C₄×D₄₃	—	2	2	no	—
47	#13063358	C₂×C₄	1	32	yes	complemented
48	#13063353	C₂×C₄	1	32	yes	complemented
49	#13063347	C₂×C₄	1	16	yes	complemented
50	#13063347	C₂³	1	16	yes	—
51	C₂×Dic₁₇₂	C₂×C₄	1	4	yes	complemented
52	C₂×#10621873	C₂×C₄	1	8	yes	complemented
53	C₂×D₃₄₄	C₂×C₄	1	4	yes	complemented
54	#13063333	—	2	16	no	—
55	#13063333	C₂³	1	32	yes	complemented
56	#13063331	—	2	32	no	—
57	C₂×#10621877	D₄	1	4	yes	—
58	C₂×#10621877	D₄	1	4	yes	—
59	C₂×#10621877	C₂³	1	4	yes	—
60	C₂×#10621872	—	2	8	no	—
61	M₁₆×D₄₃	—	2	32	no	—
62	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
63	C₂×C₈×D₄₃	—	2	8	no	—
64	C₂×C₄×Dic₄₃	—	2	1	no	—
65	C₂×C₄×Dic₄₃	—	2	2	no	—
66	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
67	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
68	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
69	#13063251	C₂³	1	16	yes	complemented
70	#13063251	C₂³	1	16	yes	complemented
71	#13063235	C₂³	1	8	yes	complemented
72	C₈×Dic₄₃	C₂³	1	8	yes	complemented
73	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
74	C₂×M₁₆×C₄₃	—	2	2	no	—
75	C₂×M₁₆×C₄₃	—	2	4	no	—
76	C₂×M₁₆×C₄₃	C₂×C₄	1	4	yes	—
77	C₂×M₁₆×C₄₃	C₂×C₄	1	4	yes	—
78	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
79	C₂×M₁₆×C₄₃	C₂³	1	8	yes	—
80	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
81	C₂²×C₈×C₄₃	—	2	2	no	—
82	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
83	#108×C₄₃	C₂³	1	16	yes	complemented
84	C₂⁴×C₄₃	#41	1	1	yes	characteristic
85	C₂³×D₄₃	—	2	2	no	—
86	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
91	C₂²×C₄×C₄₃	#41	1	2	yes	—
92	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
93	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
94	C₂×C₂²⋊D₄₃	—	2	4	no	—
95	C₂×C₂²⋊D₄₃	—	2	8	no	—
96	C₂×C₂²⋊D₄₃	—	2	4	no	—
97	C₂×C₂²⋊D₄₃	—	2	8	no	—
98	C₂²×Dic₄₃	—	2	2	no	—
99	C₂²×Dic₄₃	—	2	1	no	—
100	C₂²×Dic₄₃	—	2	1	no	—
101	C₂²×Dic₄₃	—	2	4	no	—
102	C₂²×Dic₄₃	—	4	4	no	—
103	#10621898	—	2	8	no	—
104	#10621898	—	2	8	no	—
105	#10621898	—	2	8	no	—
106	#10621898	—	2	8	no	—
107	#10621898	—	2	4	no	—
108	#10621898	—	2	4	no	—
109	#10621898	—	2	8	no	—
110	#10621898	C₂²×C₄	1	8	yes	—
111	#10621898	C₂²×C₄	1	16	yes	—
112	#10621898	C₂⁴	1	8	yes	—
113	C₂×D₁₇₂	—	2	2	no	—
114	C₂×D₁₇₂	—	2	4	no	—
115	C₂×D₁₇₂	C₂²×C₄	1	4	yes	—
116	C₂×D₁₇₂	C₂²×C₄	1	8	yes	—
117	C₂×C₄×D₄₃	—	2	4	no	—
118	C₂×C₄×D₄₃	—	2	8	no	—
119	C₂×C₄×D₄₃	—	2	4	no	—
120	C₂×C₄×D₄₃	—	2	8	no	—
121	C₂×Dic₈₆	—	2	2	no	—
122	C₂×Dic₈₆	—	2	4	no	—
123	C₂×Dic₈₆	C₂²×C₄	1	4	yes	—
124	C₂×Dic₈₆	C₂²×C₄	1	8	yes	—
125	M₁₆×C₄₃	—	2	8	no	—
126	M₁₆×C₄₃	—	2	4	no	—
127	M₁₆×C₄₃	C₂²×C₄	1	16	yes	—
128	M₁₆×C₄₃	C₂⁴	1	8	yes	—
129	C₂×C₈×C₄₃	—	2	4	no	—
130	C₂×C₈×C₄₃	—	2	8	no	—
131	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
132	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
133	C₂×C₈×C₄₃	C₂⁴	1	4	yes	—
134	C₄×Dic₄₃	—	2	1	no	—
135	C₄×Dic₄₃	—	2	4	no	—
136	C₄×Dic₄₃	—	2	1	no	—
137	C₄×Dic₄₃	C₂⁴	1	2	yes	—
138	C₄×Dic₄₃	C₂⁴	1	2	yes	—
139	#10621877	C₂×D₄	1	16	yes	—
140	C₂×C₄₃⋊C₈	C₂×D₄	1	4	yes	—
141	C₂×C₄₃⋊C₈	C₂×D₄	1	4	yes	—
142	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
143	Dic₁₇₂	C₂²×C₄	1	16	yes	complemented
144	D₃₄₄	C₂²×C₄	1	16	yes	complemented
145	#10621873	C₂²×C₄	1	32	yes	complemented
146	#10621872	—	2	32	no	—
147	C₈×D₄₃	—	2	32	no	—
148	C₂³×C₄₃	—	4	2	no	—
149	C₂³×C₄₃	C₄×D₄	1	2	yes	—
150	C₂³×C₄₃	C₄×D₄	1	2	yes	—
151	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
152	C₂³×C₄₃	C₂×#41	1	2	yes	—
153	C₂²×D₄₃	—	2	4	no	—
154	C₂²×D₄₃	—	2	8	no	—
155	C₂²×D₄₃	—	8	4	no	—
156	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
157	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
158	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
159	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
160	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
163	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
165	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
167	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
168	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
169	C₂²⋊D₄₃	—	2	16	no	—
170	C₂²⋊D₄₃	—	2	8	no	—
171	C₂²⋊D₄₃	—	2	8	no	—
172	C₂×Dic₄₃	—	2	4	no	—
173	C₂×Dic₄₃	—	2	8	no	—
174	C₂×Dic₄₃	—	2	4	no	—
175	C₂×Dic₄₃	—	2	2	no	—
176	C₂×Dic₄₃	—	2	2	no	—
177	C₂×Dic₄₃	—	4	8	no	—
178	C₂×Dic₄₃	—	4	2	no	—
179	D₁₇₂	—	2	4	no	—
180	D₁₇₂	—	2	8	no	—
181	D₁₇₂	C₂³×C₄	1	8	yes	—
182	C₄×D₄₃	—	2	16	no	—
183	C₄×D₄₃	—	2	8	no	—
184	C₄×D₄₃	—	2	8	no	—
185	Dic₈₆	—	2	4	no	—
186	Dic₈₆	—	2	8	no	—
187	Dic₈₆	C₂³×C₄	1	8	yes	—
188	C₈×C₄₃	—	2	8	no	—
189	C₈×C₄₃	C₂³×C₄	1	8	yes	—
190	C₄₃⋊C₈	C₂²×D₄	1	8	yes	—
191	C₂×#2956	—	43	1	no	maximal, Sylow
192	C₂²×C₄₃	—	2	4	no	—
193	C₂²×C₄₃	—	2	2	no	—
194	C₂²×C₄₃	—	4	2	no	—
195	C₂²×C₄₃	—	4	2	no	—
196	C₂²×C₄₃	C₂×C₄×D₄	1	4	yes	—
197	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
198	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
199	C₂²×C₄₃	C₂²×#41	1	1	yes	characteristic
200	C₂×D₄₃	—	2	8	no	—
201	C₂×D₄₃	—	4	8	no	—
202	C₂×D₄₃	—	8	8	no	—
203	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
204	C₄×C₄₃	C₂×C₄×D₄	1	4	yes	—
205	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
206	C₄×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
207	C₄×C₄₃	C₂³×D₄	1	1	yes	characteristic
208	Dic₄₃	—	2	4	no	—
209	Dic₄₃	—	2	8	no	—
210	Dic₄₃	—	4	2	no	—
211	C₂×#575	—	43	1	no	—
212	C₂×#568	—	43	2	no	—
213	#2956	—	43	16	no	—
214	C₂×#444	—	43	4	no	—
215	C₂×#443	—	43	4	no	—
216	C₂×#430	D₄₃	1	1	yes	characteristic, complemented
217	C₂²×#104	—	43	2	no	—
218	C₂×C₄×M₁₆	—	43	1	no	—
219	C₂×C₄₃	—	2	1	no	—
220	C₂×C₄₃	—	2	4	no	—
221	C₂×C₄₃	—	2	1	no	—
222	C₂×C₄₃	#2956	1	2	yes	complemented
223	C₂×C₄₃	C₂²×C₄×D₄	1	1	yes	characteristic
224	D₄₃	—	4	8	no	—
225	C₂²×#41	—	43	2	no	—
226	#575	—	43	8	no	—
227	#575	—	43	8	no	—
228	C₂×#137	—	43	4	no	—
229	C₂×AGL(1,ℤ/8)	—	43	4	no	—
230	C₂×#135	—	43	4	no	—
231	#568	—	43	16	no	—
232	#568	—	86	8	no	—
233	C₂×#131	—	43	8	no	—
234	C₂×#131	—	86	4	no	—
235	C₂²×M₁₆	—	43	1	no	—
236	C₂²×M₁₆	—	86	4	no	—
237	C₂²×M₁₆	C₂×D₄₃	1	2	yes	—
238	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
239	C₂²×C₄²	—	43	1	no	—
240	#444	—	43	32	no	—
241	#443	—	43	32	no	—
242	#430	C₂×D₄₃	1	8	yes	complemented
243	C₂×#108	C₂×D₄₃	1	4	yes	complemented
244	C₂×#104	—	43	4	no	—
245	C₂×#104	—	43	4	no	—
246	C₂×#104	—	43	16	no	—
247	C₄×M₁₆	—	43	8	no	—
248	C₂×#97	—	43	2	no	—
249	C₂×C₄×C₈	—	43	2	no	—
250	C₄₃	C₂×#2956	1	1	yes	characteristic, complemented, Sylow
251	C₂×#41	—	43	4	no	—
252	C₂×#41	—	43	8	no	—
253	C₂×#41	—	43	4	no	—
254	C₂×#41	—	43	8	no	—
255	C₂×#41	—	86	2	no	—
256	C₂×#41	—	86	4	no	—
257	C₂×#41	—	86	2	no	—
258	C₂×#41	—	86	4	no	—
259	C₂²×Q₈	—	43	2	no	—
260	C₂²×D₄	—	43	2	no	—
261	C₂²×D₄	—	86	2	no	—
262	C₂³×C₄	—	86	2	no	—
263	C₂³×C₄	—	86	1	no	—
264	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
265	#137	—	43	32	no	—
266	AGL(1,ℤ/8)	—	43	32	no	—
267	#135	—	43	16	no	—
268	#135	—	43	16	no	—
269	C₂×Q₁₆	—	43	4	no	—
270	C₂×SD₁₆	—	43	8	no	—
271	C₂×D₈	—	43	4	no	—
272	#131	—	43	32	no	—
273	#131	—	86	32	no	—
274	#131	—	86	16	no	—
275	C₂×M₁₆	—	2	2	no	—
276	C₂×M₁₆	—	2	4	no	—
277	C₂×M₁₆	—	43	4	no	—
278	C₂×M₁₆	—	43	4	no	—
279	C₂×M₁₆	—	43	4	no	—
280	C₂×M₁₆	—	86	8	no	—
281	C₂×M₁₆	—	86	32	no	—
282	C₂×M₁₆	C₄×D₄₃	1	4	yes	—
283	C₂×M₁₆	C₄×D₄₃	1	4	yes	—
284	C₂×M₁₆	C₂²×D₄₃	1	4	yes	—
285	C₂×M₁₆	C₂²×D₄₃	1	8	yes	—
286	C₂×M₁₆	C₂²×D₄₃	1	4	yes	—
287	C₂²×C₈	—	2	2	no	—
288	C₂²×C₈	—	43	2	no	—
289	C₂²×C₈	—	86	8	no	—
290	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
291	C₂×C₄²	—	43	1	no	—
292	C₂×C₄²	—	43	1	no	—
293	C₂×C₄²	—	43	4	no	—
294	C₂×C₄²	—	86	1	no	—
295	C₂×C₄²	—	86	2	no	—
296	#108	C₂²×D₄₃	1	16	yes	complemented
297	#104	—	43	16	no	—
298	#104	—	43	16	no	—
299	#97	—	43	8	no	—
300	C₄×C₈	—	43	8	no	—
301	C₂⁴	—	86	2	no	—
302	C₂⁴	#10621902	1	1	yes	characteristic
303	#41	—	43	8	no	—
304	#41	—	43	16	no	—
305	#41	—	43	8	no	—
306	#41	—	86	8	no	—
307	#41	—	86	8	no	—
308	#41	—	86	8	no	—
309	#41	—	86	8	no	—
310	#41	—	86	4	no	—
311	#41	—	86	4	no	—
312	#41	—	86	8	no	—
313	C₂×Q₈	—	43	4	no	—
314	C₂×Q₈	—	43	8	no	—
315	C₂×Q₈	—	86	2	no	—
316	C₂×Q₈	—	86	4	no	—
317	C₂×D₄	—	43	4	no	—
318	C₂×D₄	—	43	8	no	—
319	C₂×D₄	—	86	8	no	—
320	C₂×D₄	—	86	4	no	—
321	C₂×D₄	—	86	8	no	—
322	C₂×D₄	—	86	4	no	—
323	C₂×D₄	—	86	2	no	—
324	C₂×D₄	—	86	4	no	—
325	C₂²×C₄	—	86	2	no	—
326	C₂²×C₄	—	86	1	no	—
327	C₂²×C₄	—	86	4	no	—
328	C₂²×C₄	—	86	8	no	—
329	C₂²×C₄	—	86	8	no	—
330	C₂²×C₄	—	86	4	no	—
331	C₂²×C₄	—	86	4	no	—
332	C₂²×C₄	—	86	1	no	—
333	C₂²×C₄	—	172	4	no	—
334	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
335	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
336	C₂²×C₄	D₄×D₄₃	1	2	yes	—
337	C₂²×C₄	D₄×D₄₃	1	2	yes	—
338	C₂²×C₄	#10621902	1	1	yes	characteristic
339	C₂²×C₄	#10621902	1	2	yes	—
340	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
341	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
342	Q₁₆	—	43	16	no	—
343	SD₁₆	—	43	32	no	—
344	D₈	—	43	16	no	—
345	M₁₆	—	2	8	no	—
346	M₁₆	—	2	4	no	—
347	M₁₆	—	43	16	no	—
348	M₁₆	—	86	32	no	—
349	M₁₆	C₂×C₄×D₄₃	1	16	yes	—
350	M₁₆	C₂³×D₄₃	1	8	yes	—
351	C₂×C₈	—	2	8	no	—
352	C₂×C₈	—	2	4	no	—
353	C₂×C₈	—	43	4	no	—
354	C₂×C₈	—	43	4	no	—
355	C₂×C₈	—	43	4	no	—
356	C₂×C₈	—	86	32	no	—
357	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
358	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
359	C₂×C₈	C₂³×D₄₃	1	4	yes	—
360	C₄²	—	43	2	no	—
361	C₄²	—	43	2	no	—
362	C₄²	—	86	1	no	—
363	C₄²	—	86	4	no	—
364	C₄²	—	86	1	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	86	8	no	—
367	C₂³	—	86	4	no	—
368	C₂³	—	344	4	no	—
369	C₂³	#13063287	1	2	yes	—
370	C₂³	#13063287	1	2	yes	—
371	C₂³	C₂×#10621902	1	1	yes	characteristic
372	C₂³	C₂×#10621902	1	2	yes	—
373	Q₈	—	43	8	no	—
374	Q₈	—	86	8	no	—
375	Q₈	—	86	4	no	—
376	D₄	—	43	8	no	—
377	D₄	—	86	16	no	—
378	D₄	—	86	8	no	—
379	D₄	—	86	8	no	—
380	D₄	—	86	8	no	—
381	D₄	—	86	4	no	—
382	C₂×C₄	—	86	4	no	—
383	C₂×C₄	—	86	8	no	—
384	C₂×C₄	—	86	4	no	—
385	C₂×C₄	—	86	2	no	—
386	C₂×C₄	—	86	8	no	—
387	C₂×C₄	—	86	16	no	—
388	C₂×C₄	—	86	8	no	—
389	C₂×C₄	—	86	2	no	—
390	C₂×C₄	—	172	8	no	—
391	C₂×C₄	—	172	2	no	—
392	C₂×C₄	#13063287	1	2	yes	—
393	C₂×C₄	#13063287	1	4	yes	—
394	C₂×C₄	#13063287	1	4	yes	—
395	C₂×C₄	#13063287	1	2	yes	—
396	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
397	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
398	C₂×C₄	C₂²×C₄×D₄₃	1	4	yes	—
399	C₂×C₄	C₂×D₄×D₄₃	1	4	yes	—
400	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
401	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
402	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
403	C₂×C₄	C₂×#10621902	1	2	yes	—
404	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
405	C₈	—	2	8	no	—
406	C₈	—	43	8	no	—
407	C₈	C₂²×C₄×D₄₃	1	8	yes	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	4	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	86	8	no	—
413	C₂²	—	344	8	no	—
414	C₂²	—	172	8	no	—
415	C₂²	C₂×#13063287	1	4	yes	—
416	C₂²	C₂×#13063287	1	1	yes	characteristic
417	C₂²	C₂×#13063287	1	1	yes	characteristic
418	C₂²	C₂²×#10621902	1	1	yes	characteristic
419	C₄	—	86	4	no	—
420	C₄	—	86	8	no	—
421	C₄	—	172	2	no	—
422	C₄	C₂×#13063287	1	1	yes	characteristic
423	C₄	C₂×#13063287	1	4	yes	—
424	C₄	C₂×#13063287	1	1	yes	characteristic
425	C₄	C₂³×C₄×D₄₃	1	1	yes	characteristic
426	C₄	C₂²×D₄×D₄₃	1	1	yes	characteristic
427	C₂	—	2	1	no	—
428	C₂	—	2	4	no	—
429	C₂	—	2	1	no	—
430	C₂	—	172	8	no	—
431	C₂	#19143504	1	2	yes	direct product factor
432	C₂	C₂²×#13063287	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₄×C₄₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₂×C₄₃×#430	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂×#14583699	C₂
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	C₂×#430	D₄₃
hypocenter	C₄₃	C₂×#2956
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#430

Complements

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

N	H ≅ G/N	type
2. C₂×#14583665	C₂	semidirect
3. #19143504	C₂	direct (N × H)
4. C₂×#14583020	C₂	semidirect
5. C₂×#14583015	C₂	semidirect
6. C₂²×#13063251	C₂	semidirect
7. C₂×M₁₆×Dic₄₃	C₂	semidirect
8. C₂×C₄₃×#430	C₂	semidirect
10. #14583699	C₄	semidirect
12. C₂×#13063358	C₄	semidirect
13. C₂×#13063353	C₄	semidirect
16. #14583665	C₂²	semidirect
17. C₂×#13063333	C₂²	semidirect
22. #14583020	C₂²	semidirect
23. #14583015	C₂²	semidirect
24. C₂×#13063251	C₂²	semidirect
25. C₂×#13063251	C₂²	semidirect
26. C₂×#13063251	C₂²	semidirect
27. M₁₆×Dic₄₃	C₂²	semidirect
28. C₂×#13063235	C₂²	semidirect
29. C₂×C₈×Dic₄₃	C₂²	semidirect
32. C₄₃×#430	C₂²	semidirect
33. C₂×#108×C₄₃	C₂²	semidirect
47. #13063358	C₂×C₄	semidirect
48. #13063353	C₂×C₄	semidirect
49. #13063347	C₂×C₄	semidirect
51. C₂×Dic₁₇₂	C₂×C₄	semidirect
52. C₂×#10621873	C₂×C₄	semidirect
53. C₂×D₃₄₄	C₂×C₄	semidirect
55. #13063333	C₂³	semidirect
69. #13063251	C₂³	semidirect
70. #13063251	C₂³	semidirect
71. #13063235	C₂³	semidirect
72. C₈×Dic₄₃	C₂³	semidirect
83. #108×C₄₃	C₂³	semidirect
143. Dic₁₇₂	C₂²×C₄	semidirect
144. D₃₄₄	C₂²×C₄	semidirect
145. #10621873	C₂²×C₄	semidirect
216. C₂×#430	D₄₃	semidirect
222. C₂×C₄₃	#2956	semidirect
242. #430	C₂×D₄₃	semidirect
243. C₂×#108	C₂×D₄₃	semidirect
250. C₄₃	C₂×#2956	semidirect
296. #108	C₂²×D₄₃	semidirect
431. C₂	#19143504	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×#14583699	2
C₂×#14583665	2
#19143504	2
C₂×#14583020	2
C₂×#14583015	2
C₂²×#13063251	2
C₂×M₁₆×Dic₄₃	2
C₂×C₄₃×#430	2
C₂×#2956	43

Subgroups — C2×#19143504 #25960909

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19143504 #25960909