Subgroups — C₂×#19149374 #26010437

Order 11008.

11138 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13063371	C₂	1	1	yes	maximal, characteristic, complemented
2	#19149374	C₂	1	32	yes	maximal, direct product factor
3	C₂×#14583707	C₂	1	8	yes	maximal, complemented
4	C₂×#14583702	C₂	1	8	yes	maximal, complemented
5	C₂×#14583697	C₂	1	6	yes	maximal, complemented
6	C₂²×#13063350	C₂	1	6	yes	maximal, complemented
7	C₂×#14583666	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₃×#585	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#13063371	—	2	4	no	—
10	C₂×#13063371	—	2	8	no	—
11	C₂×#13063371	C₂²	1	8	yes	complemented
12	C₂×#13063371	C₂²	1	16	yes	complemented
13	C₂²×#10621902	—	2	1	no	—
14	C₂²×#10621898	C₂²	1	3	yes	complemented
15	C₂³×D₁₇₂	C₂²	1	3	yes	complemented
16	C₂²×D₄×D₄₃	—	2	3	no	—
17	#14583707	C₂²	1	128	yes	complemented
18	#14583702	C₂²	1	128	yes	complemented
19	#14583697	C₂²	1	96	yes	complemented
20	C₂×#13063356	C₂²	1	12	yes	complemented
21	C₂×#13063355	C₂²	1	4	yes	complemented
22	C₂×#13063351	C₂²	1	12	yes	complemented
23	C₂×#13063350	C₂²	1	12	yes	complemented
24	C₂×#13063350	C₂²	1	24	yes	complemented
25	C₂×#13063350	C₂²	1	96	yes	complemented
26	C₂×#13063345	C₂²	1	24	yes	complemented
27	C₂²×#10621884	C₂²	1	12	yes	complemented
28	C₂²×#10621882	C₂²	1	12	yes	complemented
29	#14583666	C₂²	1	16	yes	complemented
30	C₂×#13063332	C₂²	1	8	yes	complemented
31	C₂²×#10621877	C₂²	1	6	yes	complemented
32	C₄₃×#585	—	2	8	no	—
33	C₄₃×#585	C₂²	1	16	yes	complemented
34	C₂×2₋¹⁺⁴×C₄₃	—	2	1	no	—
35	C₂×2₋¹⁺⁴×C₄₃	C₂²	1	4	yes	complemented
36	C₂×H(5,𝔽₂)×C₄₃	—	2	3	no	—
37	C₂×H(5,𝔽₂)×C₄₃	C₂²	1	4	yes	complemented
38	C₂²×#41×C₄₃	—	2	4	no	—
39	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
40	C₂²×#41×C₄₃	C₂²	1	6	yes	complemented
41	C₂⁴×D₄₃	—	2	3	no	—
42	#13063371	—	2	32	no	—
43	#13063371	—	2	64	no	—
44	#13063371	C₂³	1	64	yes	complemented
45	C₂×#10621902	—	2	8	no	—
46	C₂×#10621902	—	2	16	no	—
47	C₂×#10621898	—	2	6	no	—
48	C₂×#10621898	—	2	12	no	—
49	C₂×#10621898	C₂³	1	12	yes	—
50	C₂×#10621898	C₂³	1	24	yes	complemented
51	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
52	C₂²×D₁₇₂	—	2	3	no	—
53	C₂²×D₁₇₂	—	2	6	no	—
54	C₂²×D₁₇₂	—	2	12	no	—
55	C₂²×D₁₇₂	C₂³	1	12	yes	—
56	C₂²×D₁₇₂	C₂³	1	3	yes	—
57	C₂²×D₁₇₂	C₂³	1	24	yes	complemented
58	C₂²×C₂²⋊D₄₃	—	2	3	no	—
59	C₂×D₄×D₄₃	—	2	24	no	—
60	C₂×D₄×D₄₃	—	2	48	no	—
61	C₂²×C₄×D₄₃	—	2	3	no	—
62	#13063356	C₂³	1	96	yes	complemented
63	#13063355	C₂³	1	32	yes	complemented
64	#13063351	C₂³	1	96	yes	complemented
65	#13063350	C₂³	1	96	yes	complemented
66	#13063350	C₂³	1	192	yes	complemented
67	#13063345	C₂³	1	192	yes	complemented
68	C₂×#10621885	C₂³	1	8	yes	complemented
69	C₂×#10621883	C₂³	1	8	yes	complemented
70	C₂×#10621884	C₂³	1	24	yes	complemented
71	C₂×#10621884	C₂³	1	96	yes	complemented
72	C₂×#10621882	C₂³	1	24	yes	complemented
73	C₂×#10621882	C₂³	1	96	yes	complemented
74	#13063332	C₂³	1	64	yes	complemented
75	C₂×#10621877	C₂³	1	4	yes	—
76	C₂×#10621877	C₂³	1	12	yes	complemented
77	C₂×#10621877	C₂³	1	48	yes	complemented
78	C₂²×C₄₃⋊C₈	C₂³	1	12	yes	complemented
79	2₋¹⁺⁴×C₄₃	—	2	16	no	—
80	2₋¹⁺⁴×C₄₃	—	2	16	no	—
81	2₋¹⁺⁴×C₄₃	C₂³	1	32	yes	complemented
82	H(5,𝔽₂)×C₄₃	—	2	16	no	—
83	H(5,𝔽₂)×C₄₃	—	2	48	no	—
84	H(5,𝔽₂)×C₄₃	C₂³	1	32	yes	complemented
85	C₂×#41×C₄₃	—	2	64	no	—
86	C₂×#41×C₄₃	—	2	4	no	—
87	C₂×#41×C₄₃	—	2	12	no	—
88	C₂×#41×C₄₃	—	2	6	no	—
89	C₂×#41×C₄₃	—	2	6	no	—
90	C₂×#41×C₄₃	—	2	24	no	—
91	C₂×#41×C₄₃	D₄	1	4	yes	—
92	C₂×#41×C₄₃	D₄	1	8	yes	—
93	C₂×#41×C₄₃	C₂³	1	4	yes	—
94	C₂×#41×C₄₃	C₂³	1	4	yes	—
95	C₂×#41×C₄₃	C₂³	1	8	yes	—
96	C₂×#41×C₄₃	C₂³	1	12	yes	complemented
97	C₂×#41×C₄₃	C₂³	1	48	yes	complemented
98	C₂²×Q₈×C₄₃	—	2	4	no	—
99	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
100	C₂²×Q₈×C₄₃	C₂³	1	6	yes	complemented
101	C₂²×D₄×C₄₃	—	2	6	no	—
102	C₂²×D₄×C₄₃	—	2	12	no	—
103	C₂²×D₄×C₄₃	D₄	1	3	yes	—
104	C₂²×D₄×C₄₃	C₂³	1	6	yes	complemented
105	C₂³×C₄×C₄₃	—	2	6	no	—
106	C₂³×C₄×C₄₃	C₂³	1	3	yes	—
107	C₂⁴×C₄₃	—	2	6	no	—
108	C₂⁴×C₄₃	C₂×D₄	1	3	yes	—
109	C₂³×D₄₃	—	2	3	no	—
110	C₂³×D₄₃	—	2	12	no	—
111	C₂³×D₄₃	—	2	24	no	—
112	C₂³×D₄₃	—	8	12	no	—
113	#41×C₄₃	—	2	32	no	—
114	#41×C₄₃	—	2	96	no	—
115	#41×C₄₃	—	2	8	no	—
116	#41×C₄₃	—	2	48	no	—
117	#41×C₄₃	—	2	48	no	—
118	#41×C₄₃	—	2	24	no	—
119	#41×C₄₃	C₂×D₄	1	32	yes	—
120	#41×C₄₃	C₂×D₄	1	16	yes	—
121	#41×C₄₃	C₂⁴	1	16	yes	—
122	#41×C₄₃	C₂⁴	1	16	yes	—
123	#41×C₄₃	C₂⁴	1	48	yes	complemented
124	C₂×Q₈×C₄₃	—	2	32	no	—
125	C₂×Q₈×C₄₃	—	2	6	no	—
126	C₂×Q₈×C₄₃	—	2	12	no	—
127	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
128	C₂×Q₈×C₄₃	C₂×D₄	1	8	yes	—
129	C₂×Q₈×C₄₃	C₂⁴	1	4	yes	—
130	C₂×Q₈×C₄₃	C₂⁴	1	24	yes	complemented
131	C₂×D₄×C₄₃	—	2	96	no	—
132	C₂×D₄×C₄₃	—	2	6	no	—
133	C₂×D₄×C₄₃	—	2	12	no	—
134	C₂×D₄×C₄₃	—	2	4	no	—
135	C₂×D₄×C₄₃	—	2	12	no	—
136	C₂×D₄×C₄₃	—	2	48	no	—
137	C₂×D₄×C₄₃	C₂×D₄	1	12	yes	—
138	C₂×D₄×C₄₃	C₂×D₄	1	24	yes	—
139	C₂×D₄×C₄₃	C₂⁴	1	4	yes	—
140	C₂×D₄×C₄₃	C₂⁴	1	24	yes	complemented
141	C₂²×C₄×C₄₃	—	2	4	no	—
142	C₂²×C₄×C₄₃	—	2	12	no	—
143	C₂²×C₄×C₄₃	—	2	48	no	—
144	C₂²×C₄×C₄₃	—	2	6	no	—
145	C₂²×C₄×C₄₃	C₂×D₄	1	6	yes	—
146	C₂²×C₄×C₄₃	C₂×D₄	1	3	yes	—
147	C₂²×C₄×C₄₃	C₂×D₄	1	12	yes	—
148	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
149	C₂²×C₄×C₄₃	C₂⁴	1	6	yes	—
150	C₂²×C₄×C₄₃	C₂⁴	1	12	yes	—
151	C₂×C₂²⋊D₄₃	—	2	12	no	—
152	C₂×C₂²⋊D₄₃	—	2	24	no	—
153	C₂²×Dic₄₃	—	2	1	no	—
154	#10621902	—	2	64	no	—
155	D₄×D₄₃	—	2	192	no	—
156	#10621898	—	2	24	no	—
157	#10621898	—	2	48	no	—
158	#10621898	C₂⁴	1	48	yes	—
159	C₂×D₁₇₂	—	2	12	no	—
160	C₂×D₁₇₂	—	2	24	no	—
161	C₂×D₁₇₂	—	2	3	no	—
162	C₂×D₁₇₂	—	2	6	no	—
163	C₂×D₁₇₂	—	2	24	no	—
164	C₂×D₁₇₂	—	2	48	no	—
165	C₂×D₁₇₂	C₂⁴	1	6	yes	—
166	C₂×D₁₇₂	C₂⁴	1	48	yes	—
167	C₂×D₁₇₂	C₂⁴	1	12	yes	—
168	C₂×C₄×D₄₃	—	2	12	no	—
169	C₂×C₄×D₄₃	—	2	24	no	—
170	C₂×Dic₈₆	—	2	1	no	—
171	C₂×Dic₈₆	—	2	2	no	—
172	C₂×Dic₈₆	C₂⁴	1	2	yes	—
173	C₂×Dic₈₆	C₂⁴	1	4	yes	—
174	#10621885	C₂⁴	1	32	yes	complemented
175	#10621884	C₂⁴	1	96	yes	complemented
176	#10621883	C₂⁴	1	32	yes	complemented
177	#10621882	C₂⁴	1	96	yes	complemented
178	#10621877	C₂⁴	1	16	yes	—
179	#10621877	C₂⁴	1	48	yes	complemented
180	C₂×C₄₃⋊C₈	C₂⁴	1	8	yes	—
181	C₂×C₄₃⋊C₈	C₂⁴	1	48	yes	complemented
182	C₂³×C₄₃	—	2	4	no	—
183	C₂³×C₄₃	—	2	24	no	—
184	C₂³×C₄₃	—	4	6	no	—
185	C₂³×C₄₃	—	8	12	no	—
186	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
187	C₂³×C₄₃	C₂²×D₄	1	6	yes	—
188	C₂³×C₄₃	C₂²×D₄	1	12	yes	—
189	C₂²×D₄₃	—	2	12	no	—
190	C₂²×D₄₃	—	2	6	no	—
191	C₂²×D₄₃	—	2	48	no	—
192	C₂²×D₄₃	—	4	12	no	—
193	C₂²×D₄₃	—	8	24	no	—
194	C₂²×D₄₃	—	8	48	no	—
195	Q₈×C₄₃	—	2	4	no	—
196	Q₈×C₄₃	—	2	24	no	—
197	Q₈×C₄₃	C₂²×D₄	1	16	yes	—
198	Q₈×C₄₃	C₂⁵	1	8	yes	—
199	D₄×C₄₃	—	2	16	no	—
200	D₄×C₄₃	—	2	48	no	—
201	D₄×C₄₃	—	2	4	no	—
202	D₄×C₄₃	—	2	24	no	—
203	D₄×C₄₃	C₂²×D₄	1	48	yes	—
204	D₄×C₄₃	C₂⁵	1	8	yes	—
205	C₂×C₄×C₄₃	—	2	4	no	—
206	C₂×C₄×C₄₃	—	2	24	no	—
207	C₂×C₄×C₄₃	—	2	16	no	—
208	C₂×C₄×C₄₃	—	2	48	no	—
209	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
211	C₂×C₄×C₄₃	C₂²×D₄	1	6	yes	—
212	C₂×C₄×C₄₃	C₂²×D₄	1	12	yes	—
213	C₂×C₄×C₄₃	C₂²×D₄	1	24	yes	—
214	C₂×C₄×C₄₃	C₂²×D₄	1	12	yes	—
215	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
216	C₂×C₄×C₄₃	C₂⁵	1	12	yes	—
217	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
218	C₂²⋊D₄₃	—	2	48	no	—
219	C₂×Dic₄₃	—	2	4	no	—
220	C₂×Dic₄₃	—	2	2	no	—
221	D₁₇₂	—	2	12	no	—
222	D₁₇₂	—	2	6	no	—
223	D₁₇₂	—	2	48	no	—
224	D₁₇₂	C₂⁵	1	12	yes	—
225	C₄×D₄₃	—	2	48	no	—
226	Dic₈₆	—	2	4	no	—
227	Dic₈₆	—	2	2	no	—
228	Dic₈₆	C₂⁵	1	4	yes	—
229	C₄₃⋊C₈	C₂⁵	1	16	yes	—
230	C₂×#3585	—	43	1	no	maximal, Sylow
231	C₂²×C₄₃	—	2	2	no	—
232	C₂²×C₄₃	—	2	12	no	—
233	C₂²×C₄₃	—	2	8	no	—
234	C₂²×C₄₃	—	4	12	no	—
235	C₂²×C₄₃	—	4	8	no	—
236	C₂²×C₄₃	—	8	24	no	—
237	C₂²×C₄₃	C₂³×D₄	1	2	yes	—
238	C₂²×C₄₃	C₂³×D₄	1	12	yes	—
239	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
240	C₂×D₄₃	—	2	12	no	—
241	C₂×D₄₃	—	4	24	no	—
242	C₂×D₄₃	—	4	12	no	—
243	C₂×D₄₃	—	8	48	no	—
244	C₄×C₄₃	—	2	8	no	—
245	C₄×C₄₃	C₂³×D₄	1	2	yes	—
246	C₄×C₄₃	C₂³×D₄	1	1	yes	characteristic
247	C₄×C₄₃	C₂³×D₄	1	12	yes	—
248	C₄×C₄₃	C₂⁶	1	1	yes	characteristic
249	Dic₄₃	—	2	4	no	—
250	C₂×#585	D₄₃	1	1	yes	characteristic, complemented
251	C₂²×H(5,𝔽₂)	—	43	1	no	—
252	#3585	—	43	32	no	—
253	C₂×#577	—	43	8	no	—
254	C₂×#576	—	43	8	no	—
255	C₂×#575	—	43	6	no	—
256	C₂²×AGL(1,ℤ/8)	—	43	6	no	—
257	C₂×#568	—	43	1	no	—
258	C₂×C₄₃	—	2	2	no	—
259	C₂×C₄₃	—	2	12	no	—
260	C₂×C₄₃	—	4	8	no	—
261	C₂×C₄₃	#3585	1	2	yes	complemented
262	C₂×C₄₃	C₂⁴×D₄	1	1	yes	characteristic
263	D₄₃	—	4	12	no	—
264	#585	—	2	8	no	—
265	#585	C₂×D₄₃	1	16	yes	complemented
266	C₂×2₋¹⁺⁴	—	2	1	no	—
267	C₂×2₋¹⁺⁴	C₂×D₄₃	1	4	yes	complemented
268	C₂×H(5,𝔽₂)	—	2	3	no	—
269	C₂×H(5,𝔽₂)	—	43	16	no	—
270	C₂×H(5,𝔽₂)	—	43	8	no	—
271	C₂×H(5,𝔽₂)	—	86	4	no	—
272	C₂×H(5,𝔽₂)	—	86	8	no	—
273	C₂×H(5,𝔽₂)	C₂×D₄₃	1	4	yes	complemented
274	C₂²×#41	—	2	4	no	—
275	C₂²×#41	—	43	3	no	—
276	C₂²×#41	—	86	1	no	—
277	C₂²×#41	C₂×D₄₃	1	1	yes	characteristic
278	C₂²×#41	C₂×D₄₃	1	6	yes	complemented
279	C₂³×D₄	—	43	3	no	—
280	C₂³×D₄	—	86	3	no	—
281	#577	—	43	128	no	—
282	#576	—	43	128	no	—
283	#575	—	43	96	no	—
284	C₂×#137	—	43	4	no	—
285	C₂×#137	—	43	12	no	—
286	C₂×AGL(1,ℤ/8)	—	43	12	no	—
287	C₂×AGL(1,ℤ/8)	—	43	96	no	—
288	C₂×AGL(1,ℤ/8)	—	43	24	no	—
289	C₂×AGL(1,ℤ/8)	—	43	12	no	—
290	C₂×#135	—	43	24	no	—
291	C₂²×SD₁₆	—	43	12	no	—
292	C₂²×D₈	—	43	12	no	—
293	#568	—	43	16	no	—
294	C₂×#131	—	43	8	no	—
295	C₂²×M₁₆	—	43	6	no	—
296	C₄₃	C₂×#3585	1	1	yes	characteristic, complemented, Sylow
297	C₂⁵	—	86	3	no	—
298	2₋¹⁺⁴	—	2	16	no	—
299	2₋¹⁺⁴	—	2	16	no	—
300	2₋¹⁺⁴	C₂²×D₄₃	1	32	yes	complemented
301	H(5,𝔽₂)	—	2	16	no	—
302	H(5,𝔽₂)	—	2	48	no	—
303	H(5,𝔽₂)	—	43	64	no	—
304	H(5,𝔽₂)	—	86	64	no	—
305	H(5,𝔽₂)	—	86	32	no	—
306	H(5,𝔽₂)	C₂²×D₄₃	1	32	yes	complemented
307	C₂×#41	—	2	64	no	—
308	C₂×#41	—	2	4	no	—
309	C₂×#41	—	2	12	no	—
310	C₂×#41	—	2	6	no	—
311	C₂×#41	—	2	6	no	—
312	C₂×#41	—	2	24	no	—
313	C₂×#41	—	43	12	no	—
314	C₂×#41	—	43	24	no	—
315	C₂×#41	—	86	8	no	—
316	C₂×#41	—	86	16	no	—
317	C₂×#41	—	86	6	no	—
318	C₂×#41	—	86	12	no	—
319	C₂×#41	C₂²⋊D₄₃	1	4	yes	—
320	C₂×#41	C₂²⋊D₄₃	1	8	yes	—
321	C₂×#41	C₂²×D₄₃	1	4	yes	—
322	C₂×#41	C₂²×D₄₃	1	4	yes	—
323	C₂×#41	C₂²×D₄₃	1	8	yes	—
324	C₂×#41	C₂²×D₄₃	1	12	yes	complemented
325	C₂×#41	C₂²×D₄₃	1	48	yes	complemented
326	C₂²×Q₈	—	2	4	no	—
327	C₂²×Q₈	—	43	1	no	—
328	C₂²×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
329	C₂²×Q₈	C₂²×D₄₃	1	6	yes	complemented
330	C₂²×D₄	—	2	6	no	—
331	C₂²×D₄	—	2	12	no	—
332	C₂²×D₄	—	43	12	no	—
333	C₂²×D₄	—	43	3	no	—
334	C₂²×D₄	—	43	24	no	—
335	C₂²×D₄	—	86	3	no	—
336	C₂²×D₄	—	86	24	no	—
337	C₂²×D₄	—	86	48	no	—
338	C₂²×D₄	—	86	3	no	—
339	C₂²×D₄	—	86	6	no	—
340	C₂²×D₄	—	86	12	no	—
341	C₂²×D₄	C₂²⋊D₄₃	1	3	yes	—
342	C₂²×D₄	C₂²×D₄₃	1	6	yes	complemented
343	C₂³×C₄	—	2	6	no	—
344	C₂³×C₄	—	86	3	no	—
345	C₂³×C₄	C₂²×D₄₃	1	3	yes	—
346	#137	—	43	32	no	—
347	#137	—	43	96	no	—
348	AGL(1,ℤ/8)	—	43	96	no	—
349	AGL(1,ℤ/8)	—	43	192	no	—
350	AGL(1,ℤ/8)	—	43	96	no	—
351	#135	—	43	192	no	—
352	C₂×Q₁₆	—	43	8	no	—
353	C₂×SD₁₆	—	43	24	no	—
354	C₂×SD₁₆	—	43	96	no	—
355	C₂×SD₁₆	—	43	8	no	—
356	C₂×D₈	—	43	24	no	—
357	C₂×D₈	—	43	96	no	—
358	#131	—	43	64	no	—
359	C₂×M₁₆	—	43	4	no	—
360	C₂×M₁₆	—	43	12	no	—
361	C₂×M₁₆	—	43	48	no	—
362	C₂²×C₈	—	43	12	no	—
363	C₂⁴	—	2	6	no	—
364	C₂⁴	—	86	24	no	—
365	C₂⁴	—	86	12	no	—
366	C₂⁴	—	86	3	no	—
367	C₂⁴	—	344	12	no	—
368	C₂⁴	C₂×C₂²⋊D₄₃	1	3	yes	—
369	#41	—	2	32	no	—
370	#41	—	2	96	no	—
371	#41	—	2	8	no	—
372	#41	—	2	48	no	—
373	#41	—	2	48	no	—
374	#41	—	2	24	no	—
375	#41	—	43	48	no	—
376	#41	—	86	64	no	—
377	#41	—	86	48	no	—
378	#41	—	86	24	no	—
379	#41	C₂×C₂²⋊D₄₃	1	32	yes	—
380	#41	C₂×C₂²⋊D₄₃	1	16	yes	—
381	#41	C₂³×D₄₃	1	16	yes	—
382	#41	C₂³×D₄₃	1	16	yes	—
383	#41	C₂³×D₄₃	1	48	yes	complemented
384	C₂×Q₈	—	2	32	no	—
385	C₂×Q₈	—	2	6	no	—
386	C₂×Q₈	—	2	12	no	—
387	C₂×Q₈	—	43	2	no	—
388	C₂×Q₈	—	43	4	no	—
389	C₂×Q₈	—	86	2	no	—
390	C₂×Q₈	—	86	1	no	—
391	C₂×Q₈	C₂×C₂²⋊D₄₃	1	4	yes	—
392	C₂×Q₈	C₂×C₂²⋊D₄₃	1	8	yes	—
393	C₂×Q₈	C₂³×D₄₃	1	4	yes	—
394	C₂×Q₈	C₂³×D₄₃	1	24	yes	complemented
395	C₂×D₄	—	2	4	no	—
396	C₂×D₄	—	2	12	no	—
397	C₂×D₄	—	2	48	no	—
398	C₂×D₄	—	2	96	no	—
399	C₂×D₄	—	2	6	no	—
400	C₂×D₄	—	2	12	no	—
401	C₂×D₄	—	43	6	no	—
402	C₂×D₄	—	43	48	no	—
403	C₂×D₄	—	43	12	no	—
404	C₂×D₄	—	86	24	no	—
405	C₂×D₄	—	86	12	no	—
406	C₂×D₄	—	86	192	no	—
407	C₂×D₄	—	86	24	no	—
408	C₂×D₄	—	86	6	no	—
409	C₂×D₄	—	86	3	no	—
410	C₂×D₄	—	86	12	no	—
411	C₂×D₄	—	86	48	no	—
412	C₂×D₄	—	86	24	no	—
413	C₂×D₄	C₂×C₂²⋊D₄₃	1	12	yes	—
414	C₂×D₄	C₂×C₂²⋊D₄₃	1	24	yes	—
415	C₂×D₄	C₂³×D₄₃	1	4	yes	—
416	C₂×D₄	C₂³×D₄₃	1	24	yes	complemented
417	C₂²×C₄	—	2	6	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	2	12	no	—
420	C₂²×C₄	—	2	48	no	—
421	C₂²×C₄	—	86	1	no	—
422	C₂²×C₄	—	86	24	no	—
423	C₂²×C₄	—	86	12	no	—
424	C₂²×C₄	C₂×C₂²⋊D₄₃	1	6	yes	—
425	C₂²×C₄	C₂×C₂²⋊D₄₃	1	3	yes	—
426	C₂²×C₄	C₂×C₂²⋊D₄₃	1	12	yes	—
427	C₂²×C₄	C₂³×D₄₃	1	6	yes	—
428	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
429	C₂²×C₄	C₂³×D₄₃	1	12	yes	—
430	Q₁₆	—	43	32	no	—
431	SD₁₆	—	43	96	no	—
432	SD₁₆	—	43	32	no	—
433	D₈	—	43	96	no	—
434	M₁₆	—	43	16	no	—
435	M₁₆	—	43	48	no	—
436	C₂×C₈	—	43	8	no	—
437	C₂×C₈	—	43	48	no	—
438	C₂³	—	2	4	no	—
439	C₂³	—	2	24	no	—
440	C₂³	—	4	6	no	—
441	C₂³	—	8	12	no	—
442	C₂³	—	86	48	no	—
443	C₂³	—	86	12	no	—
444	C₂³	—	86	6	no	—
445	C₂³	—	344	24	no	—
446	C₂³	—	344	48	no	—
447	C₂³	—	172	12	no	—
448	C₂³	C₂²×C₂²⋊D₄₃	1	6	yes	—
449	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
450	C₂³	C₂²×C₂²⋊D₄₃	1	12	yes	—
451	Q₈	—	2	4	no	—
452	Q₈	—	2	24	no	—
453	Q₈	—	43	4	no	—
454	Q₈	—	86	4	no	—
455	Q₈	—	86	2	no	—
456	Q₈	C₂²×C₂²⋊D₄₃	1	16	yes	—
457	Q₈	C₂⁴×D₄₃	1	8	yes	—
458	D₄	—	2	16	no	—
459	D₄	—	2	48	no	—
460	D₄	—	2	4	no	—
461	D₄	—	2	24	no	—
462	D₄	—	43	12	no	—
463	D₄	—	86	48	no	—
464	D₄	—	86	12	no	—
465	D₄	—	86	48	no	—
466	D₄	—	86	6	no	—
467	D₄	C₂²×C₂²⋊D₄₃	1	48	yes	—
468	D₄	C₂⁴×D₄₃	1	8	yes	—
469	C₂×C₄	—	2	24	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	16	no	—
472	C₂×C₄	—	2	48	no	—
473	C₂×C₄	—	86	4	no	—
474	C₂×C₄	—	86	2	no	—
475	C₂×C₄	—	86	48	no	—
476	C₂×C₄	C₂²×C₂²⋊D₄₃	1	24	yes	—
477	C₂×C₄	C₂²×C₂²⋊D₄₃	1	12	yes	—
478	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
479	C₂×C₄	C₂²×C₂²⋊D₄₃	1	12	yes	—
480	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
481	C₂×C₄	C₂²×C₂²⋊D₄₃	1	6	yes	—
482	C₂×C₄	C₂⁴×D₄₃	1	12	yes	—
483	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
484	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
485	C₈	—	43	16	no	—
486	C₂²	—	2	2	no	—
487	C₂²	—	2	12	no	—
488	C₂²	—	2	8	no	—
489	C₂²	—	4	12	no	—
490	C₂²	—	4	8	no	—
491	C₂²	—	8	24	no	—
492	C₂²	—	86	12	no	—
493	C₂²	—	344	48	no	—
494	C₂²	—	172	24	no	—
495	C₂²	—	172	12	no	—
496	C₂²	C₂³×C₂²⋊D₄₃	1	12	yes	—
497	C₂²	C₂³×C₂²⋊D₄₃	1	2	yes	—
498	C₂²	C₂³×C₂²⋊D₄₃	1	1	yes	characteristic
499	C₄	—	2	8	no	—
500	C₄	—	86	4	no	—
501	C₄	C₂³×C₂²⋊D₄₃	1	2	yes	—
502	C₄	C₂³×C₂²⋊D₄₃	1	12	yes	—
503	C₄	C₂³×C₂²⋊D₄₃	1	1	yes	characteristic
504	C₄	C₂⁵×D₄₃	1	1	yes	characteristic
505	C₂	—	2	2	no	—
506	C₂	—	2	12	no	—
507	C₂	—	4	8	no	—
508	C₂	—	172	12	no	—
509	C₂	#19149374	1	2	yes	direct product factor
510	C₂	C₂⁴×C₂²⋊D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×C₂²⋊D₄₃
commutator, cosocle	C₄×C₄₃	C₂⁶
Frattini	C₄	C₂⁵×D₄₃
Fitting	C₂×C₄₃×#585	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	C₂×#585	D₄₃
hypocenter	C₄₃	C₂×#3585
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×#41 ◁ C₂×#585

Complements

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

N	H ≅ G/N	type
1. C₂²×#13063371	C₂	semidirect
2. #19149374	C₂	direct (N × H)
3. C₂×#14583707	C₂	semidirect
4. C₂×#14583702	C₂	semidirect
5. C₂×#14583697	C₂	semidirect
6. C₂²×#13063350	C₂	semidirect
7. C₂×#14583666	C₂	semidirect
8. C₂×C₄₃×#585	C₂	semidirect
11. C₂×#13063371	C₂²	semidirect
12. C₂×#13063371	C₂²	semidirect
14. C₂²×#10621898	C₂²	semidirect
15. C₂³×D₁₇₂	C₂²	semidirect
17. #14583707	C₂²	semidirect
18. #14583702	C₂²	semidirect
19. #14583697	C₂²	semidirect
20. C₂×#13063356	C₂²	semidirect
21. C₂×#13063355	C₂²	semidirect
22. C₂×#13063351	C₂²	semidirect
23. C₂×#13063350	C₂²	semidirect
24. C₂×#13063350	C₂²	semidirect
25. C₂×#13063350	C₂²	semidirect
26. C₂×#13063345	C₂²	semidirect
27. C₂²×#10621884	C₂²	semidirect
28. C₂²×#10621882	C₂²	semidirect
29. #14583666	C₂²	semidirect
30. C₂×#13063332	C₂²	semidirect
31. C₂²×#10621877	C₂²	semidirect
33. C₄₃×#585	C₂²	semidirect
35. C₂×2₋¹⁺⁴×C₄₃	C₂²	semidirect
37. C₂×H(5,𝔽₂)×C₄₃	C₂²	semidirect
40. C₂²×#41×C₄₃	C₂²	semidirect
44. #13063371	C₂³	semidirect
50. C₂×#10621898	C₂³	semidirect
57. C₂²×D₁₇₂	C₂³	semidirect
62. #13063356	C₂³	semidirect
63. #13063355	C₂³	semidirect
64. #13063351	C₂³	semidirect
65. #13063350	C₂³	semidirect
66. #13063350	C₂³	semidirect
67. #13063345	C₂³	semidirect
68. C₂×#10621885	C₂³	semidirect
69. C₂×#10621883	C₂³	semidirect
70. C₂×#10621884	C₂³	semidirect
71. C₂×#10621884	C₂³	semidirect
72. C₂×#10621882	C₂³	semidirect
73. C₂×#10621882	C₂³	semidirect
74. #13063332	C₂³	semidirect
76. C₂×#10621877	C₂³	semidirect
77. C₂×#10621877	C₂³	semidirect
78. C₂²×C₄₃⋊C₈	C₂³	semidirect
81. 2₋¹⁺⁴×C₄₃	C₂³	semidirect
84. H(5,𝔽₂)×C₄₃	C₂³	semidirect
96. C₂×#41×C₄₃	C₂³	semidirect
97. C₂×#41×C₄₃	C₂³	semidirect
100. C₂²×Q₈×C₄₃	C₂³	semidirect
104. C₂²×D₄×C₄₃	C₂³	semidirect
123. #41×C₄₃	C₂⁴	semidirect
130. C₂×Q₈×C₄₃	C₂⁴	semidirect
140. C₂×D₄×C₄₃	C₂⁴	semidirect
174. #10621885	C₂⁴	semidirect
175. #10621884	C₂⁴	semidirect
176. #10621883	C₂⁴	semidirect
177. #10621882	C₂⁴	semidirect
179. #10621877	C₂⁴	semidirect
181. C₂×C₄₃⋊C₈	C₂⁴	semidirect
250. C₂×#585	D₄₃	semidirect
261. C₂×C₄₃	#3585	semidirect
265. #585	C₂×D₄₃	semidirect
267. C₂×2₋¹⁺⁴	C₂×D₄₃	semidirect
273. C₂×H(5,𝔽₂)	C₂×D₄₃	semidirect
278. C₂²×#41	C₂×D₄₃	semidirect
296. C₄₃	C₂×#3585	semidirect
300. 2₋¹⁺⁴	C₂²×D₄₃	semidirect
306. H(5,𝔽₂)	C₂²×D₄₃	semidirect
324. C₂×#41	C₂²×D₄₃	semidirect
325. C₂×#41	C₂²×D₄₃	semidirect
329. C₂²×Q₈	C₂²×D₄₃	semidirect
342. C₂²×D₄	C₂²×D₄₃	semidirect
383. #41	C₂³×D₄₃	semidirect
394. C₂×Q₈	C₂³×D₄₃	semidirect
416. C₂×D₄	C₂³×D₄₃	semidirect
509. C₂	#19149374	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×#13063371	2
#19149374	2
C₂×#14583707	2
C₂×#14583702	2
C₂×#14583697	2
C₂²×#13063350	2
C₂×#14583666	2
C₂×C₄₃×#585	2
C₂×#3585	43

Subgroups — C2×#19149374 #26010437

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19149374 #26010437