Subgroups — C₂×#19134396 #25094296

Order 11008.

1474 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13063331	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582881	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582872	C₂	1	1	yes	maximal, characteristic
4	C₂×#14582854	C₂	1	1	yes	maximal, characteristic, complemented
5	#19134396	C₂	1	8	yes	maximal, direct product factor
6	C₂×#14582671	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#14582669	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#10621898	C₂²	1	1	yes	characteristic
10	C₂×#13063331	—	2	1	no	—
11	C₂×#13063331	—	2	1	no	—
12	C₂×#13063331	—	2	2	no	—
13	C₂×#13063331	—	2	1	no	—
14	C₂×#13063331	—	2	1	no	—
15	C₂×#13063331	—	2	2	no	—
16	C₂×#13063331	C₄	1	4	yes	complemented
17	C₂×#13063331	C₂²	1	4	yes	—
18	C₂²×#10621877	C₂²	1	1	yes	characteristic
19	C₂²×#10621877	C₂²	1	1	yes	characteristic
20	C₂²×#10621872	C₄	1	2	yes	complemented
21	C₂²×C₈×D₄₃	C₄	1	2	yes	complemented
22	C₂×#13063284	C₂²	1	1	yes	characteristic
23	#14582881	C₄	1	4	yes	complemented
24	#14582881	C₂²	1	4	yes	—
25	C₂×#13063243	C₄	1	2	yes	complemented
26	C₂×#13063241	C₄	1	2	yes	complemented
27	#14582872	C₄	1	4	yes	—
28	#14582872	C₂²	1	4	yes	—
29	C₂×#13063239	C₄	1	4	yes	—
30	#14582854	—	2	2	no	—
31	#14582854	C₂²	1	4	yes	complemented
32	C₂×#13063235	—	2	1	no	—
33	C₂×C₈×Dic₄₃	—	2	1	no	—
34	#14582671	C₂²	1	4	yes	complemented
35	#14582669	C₂²	1	4	yes	complemented
36	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
37	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
38	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
39	C₄₃×#405	—	2	2	no	—
40	C₄₃×#405	C₂²	1	4	yes	complemented
41	C₂×#97×C₄₃	—	2	1	no	—
42	C₂×C₄×C₈×C₄₃	—	2	1	no	—
43	C₂×#10621898	—	2	1	no	—
44	C₂×#10621898	—	2	1	no	—
45	C₂×#10621898	—	2	1	no	—
46	C₂×#10621898	—	2	1	no	—
47	C₂×#10621898	—	2	1	no	—
48	C₂×#10621898	—	2	1	no	—
49	C₂×#10621898	—	2	1	no	—
50	C₂×#10621898	—	2	1	no	—
51	C₂×#10621898	C₂×C₄	1	2	yes	—
52	C₂×#10621898	C₂×C₄	1	2	yes	—
53	C₂×#10621898	C₂×C₄	1	2	yes	—
54	C₂×#10621898	C₂³	1	2	yes	—
55	C₂²×Dic₈₆	C₂×C₄	1	1	yes	characteristic
56	C₂²×D₁₇₂	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₂²⋊D₄₃	C₂×C₄	1	2	yes	—
58	C₂²×C₄×D₄₃	C₂×C₄	1	2	yes	—
59	#13063331	—	2	4	no	—
60	#13063331	—	2	4	no	—
61	#13063331	—	2	4	no	—
62	#13063331	—	2	4	no	—
63	#13063331	—	2	4	no	—
64	#13063331	—	2	4	no	—
65	#13063331	—	2	4	no	—
66	#13063331	—	2	4	no	—
67	C₂×#10621877	—	2	1	no	—
68	C₂×#10621877	—	2	1	no	—
69	C₂×#10621877	—	2	1	no	—
70	C₂×#10621877	—	2	1	no	—
71	C₂×#10621877	—	2	1	no	—
72	C₂×#10621877	—	2	1	no	—
73	C₂×#10621877	—	2	1	no	—
74	C₂×#10621877	C₂×C₄	1	2	yes	—
75	C₂×#10621877	C₂×C₄	1	2	yes	—
76	C₂×#10621877	C₂×C₄	1	2	yes	—
77	C₂×#10621877	C₂³	1	2	yes	—
78	C₂×#10621877	C₂³	1	2	yes	—
79	C₂×#10621872	—	2	2	no	—
80	C₂×#10621872	—	2	2	no	—
81	C₂×#10621872	—	2	4	no	—
82	C₂×#10621872	C₂×C₄	1	8	yes	complemented
83	C₂²×C₄₃⋊C₈	—	2	1	no	—
84	C₂²×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
85	C₂×C₈×D₄₃	—	2	2	no	—
86	C₂×C₈×D₄₃	—	2	4	no	—
87	C₂×C₈×D₄₃	—	2	2	no	—
88	C₂×C₈×D₄₃	C₂×C₄	1	8	yes	complemented
89	#13063284	—	2	1	no	—
90	#13063284	—	2	1	no	—
91	#13063284	C₂×C₄	1	2	yes	—
92	#13063284	C₂³	1	2	yes	—
93	C₂×C₄⋊Dic₄₃	—	2	1	no	—
94	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	2	yes	—
95	C₂×C₄×Dic₄₃	—	2	1	no	—
96	#13063243	C₂×C₄	1	8	yes	complemented
97	#13063241	C₂×C₄	1	8	yes	complemented
98	#13063239	C₂×C₄	1	16	yes	—
99	#13063235	—	2	4	no	—
100	C₈×Dic₄₃	—	2	4	no	—
101	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
102	C₂×M₁₆×C₄₃	—	2	1	no	—
103	C₂×M₁₆×C₄₃	—	2	1	no	—
104	C₂×M₁₆×C₄₃	—	2	1	no	—
105	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
106	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
107	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
108	C₂²×C₈×C₄₃	—	2	1	no	—
109	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
110	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
111	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
112	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
113	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
114	C₂²×C₈×C₄₃	D₄	1	2	yes	—
115	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
116	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
117	C₂²×C₈×C₄₃	D₄	1	2	yes	—
118	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
119	#117×C₄₃	—	2	1	no	—
120	#117×C₄₃	—	2	1	no	—
121	#117×C₄₃	C₂×C₄	1	2	yes	—
122	#117×C₄₃	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
125	C₂×C₄²×C₄₃	—	2	1	no	—
126	#97×C₄₃	—	2	4	no	—
127	C₄×C₈×C₄₃	—	2	4	no	—
128	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
129	C₂³×D₄₃	C₄²	1	2	yes	—
130	C₂²×C₄×C₄₃	—	2	2	no	—
131	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
141	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
142	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
143	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
144	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
145	C₂×C₂²⋊D₄₃	—	2	2	no	—
146	C₂×C₂²⋊D₄₃	—	2	2	no	—
147	C₂×C₂²⋊D₄₃	—	2	2	no	—
148	C₂×C₂²⋊D₄₃	—	2	2	no	—
149	C₂×C₂²⋊D₄₃	C₄²	1	4	yes	—
150	C₂×C₂²⋊D₄₃	C₂²×C₄	1	4	yes	—
151	C₂²×Dic₄₃	—	2	2	no	—
152	C₂²×Dic₄₃	C₄²	1	2	yes	—
153	#10621898	—	2	2	no	—
154	#10621898	—	2	2	no	—
155	#10621898	—	2	2	no	—
156	#10621898	—	2	2	no	—
157	#10621898	—	2	2	no	—
158	#10621898	—	2	2	no	—
159	#10621898	—	2	2	no	—
160	#10621898	—	2	2	no	—
161	#10621898	—	2	2	no	—
162	#10621898	—	2	2	no	—
163	#10621898	—	2	2	no	—
164	#10621898	—	2	2	no	—
165	#10621898	—	2	2	no	—
166	#10621898	—	2	2	no	—
167	#10621898	—	2	2	no	—
168	#10621898	—	2	2	no	—
169	C₂×D₁₇₂	—	2	1	no	—
170	C₂×D₁₇₂	—	2	1	no	—
171	C₂×D₁₇₂	—	2	1	no	—
172	C₂×D₁₇₂	—	2	1	no	—
173	C₂×D₁₇₂	C₄²	1	2	yes	—
174	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
175	C₂×C₄×D₄₃	—	2	2	no	—
176	C₂×C₄×D₄₃	—	2	2	no	—
177	C₂×C₄×D₄₃	—	2	2	no	—
178	C₂×C₄×D₄₃	—	2	2	no	—
179	C₂×C₄×D₄₃	C₄²	1	4	yes	—
180	C₂×C₄×D₄₃	C₂²×C₄	1	4	yes	—
181	C₂×Dic₈₆	—	2	1	no	—
182	C₂×Dic₈₆	—	2	1	no	—
183	C₂×Dic₈₆	—	2	1	no	—
184	C₂×Dic₈₆	—	2	1	no	—
185	C₂×Dic₈₆	C₄²	1	2	yes	—
186	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
187	M₁₆×C₄₃	—	2	2	no	—
188	M₁₆×C₄₃	—	2	2	no	—
189	M₁₆×C₄₃	—	2	2	no	—
190	M₁₆×C₄₃	C₂²×C₄	1	4	yes	—
191	C₂×C₈×C₄₃	—	2	2	no	—
192	C₂×C₈×C₄₃	—	2	2	no	—
193	C₂×C₈×C₄₃	—	2	2	no	—
194	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
195	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
196	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
197	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
198	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
199	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
200	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
201	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
202	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
203	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
204	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
205	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
206	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
207	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
208	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
209	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
210	C₄⋊C₄×C₄₃	—	2	2	no	—
211	C₄⋊C₄×C₄₃	—	2	2	no	—
212	C₂²⋊C₄×C₄₃	—	2	2	no	—
213	C₂²⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
214	C₄²×C₄₃	—	2	2	no	—
215	C₄²×C₄₃	—	2	2	no	—
216	C₂²⋊Dic₄₃	—	2	2	no	—
217	C₂²⋊Dic₄₃	C₂²×C₄	1	4	yes	—
218	C₄⋊Dic₄₃	—	2	2	no	—
219	C₄⋊Dic₄₃	—	2	2	no	—
220	C₄×Dic₄₃	—	2	2	no	—
221	C₄×Dic₄₃	—	2	2	no	—
222	#10621877	—	2	2	no	—
223	#10621877	—	2	2	no	—
224	#10621877	—	2	2	no	—
225	#10621877	—	2	2	no	—
226	#10621877	—	2	2	no	—
227	#10621877	—	2	2	no	—
228	#10621877	—	2	2	no	—
229	#10621877	C₂²×C₄	1	4	yes	—
230	C₂×C₄₃⋊C₈	—	2	2	no	—
231	C₂×C₄₃⋊C₈	—	2	2	no	—
232	C₂×C₄₃⋊C₈	—	2	2	no	—
233	C₂×C₄₃⋊C₈	—	2	2	no	—
234	C₂×C₄₃⋊C₈	—	2	2	no	—
235	C₂×C₄₃⋊C₈	C₂²×C₄	1	4	yes	—
236	#10621872	—	2	8	no	—
237	#10621872	—	2	8	no	—
238	C₈×D₄₃	—	2	8	no	—
239	C₈×D₄₃	—	2	8	no	—
240	C₂³×C₄₃	—	4	2	no	—
241	C₂³×C₄₃	C₂×C₄²	1	1	yes	characteristic
242	C₂³×C₄₃	C₂×C₄²	1	1	yes	characteristic
243	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
244	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
245	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
246	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
247	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
248	C₂²×D₄₃	—	2	2	no	—
249	C₂²×D₄₃	—	2	2	no	—
250	C₂²×D₄₃	—	4	4	no	—
251	C₂²×D₄₃	C₂×C₄²	1	4	yes	—
252	C₂×C₄×C₄₃	—	2	4	no	—
253	C₂×C₄×C₄₃	—	4	4	no	—
254	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
255	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
256	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
257	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
258	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
261	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
262	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
263	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
264	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
265	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
266	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
267	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
268	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
269	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
270	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
271	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
272	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
273	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
274	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
275	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
276	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
277	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
278	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
279	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
280	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
281	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
282	C₂²⋊D₄₃	—	2	4	no	—
283	C₂²⋊D₄₃	—	2	4	no	—
284	C₂²⋊D₄₃	—	2	4	no	—
285	C₂²⋊D₄₃	—	2	4	no	—
286	C₂×Dic₄₃	—	2	2	no	—
287	C₂×Dic₄₃	—	2	2	no	—
288	C₂×Dic₄₃	—	2	4	no	—
289	C₂×Dic₄₃	—	4	4	no	—
290	C₂×Dic₄₃	C₂×C₄²	1	4	yes	—
291	D₁₇₂	—	2	2	no	—
292	D₁₇₂	—	2	2	no	—
293	D₁₇₂	—	2	2	no	—
294	D₁₇₂	—	2	2	no	—
295	C₄×D₄₃	—	2	4	no	—
296	C₄×D₄₃	—	2	4	no	—
297	C₄×D₄₃	—	2	4	no	—
298	C₄×D₄₃	—	2	4	no	—
299	Dic₈₆	—	2	2	no	—
300	Dic₈₆	—	2	2	no	—
301	Dic₈₆	—	2	2	no	—
302	Dic₈₆	—	2	2	no	—
303	C₈×C₄₃	—	2	4	no	—
304	C₈×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
305	C₈×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
306	C₈×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
307	C₈×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
308	C₄₃⋊C₈	—	2	4	no	—
309	C₄₃⋊C₈	—	2	4	no	—
310	C₂×#1757	—	43	1	no	maximal, Sylow
311	C₂²×C₄₃	—	2	2	no	—
312	C₂²×C₄₃	—	2	2	no	—
313	C₂²×C₄₃	—	2	2	no	—
314	C₂²×C₄₃	—	4	1	no	—
315	C₂²×C₄₃	—	4	1	no	—
316	C₂²×C₄₃	—	4	1	no	—
317	C₂²×C₄₃	—	4	1	no	—
318	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
319	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
320	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
321	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
322	C₂²×C₄₃	C₂²×C₄²	1	1	yes	characteristic
323	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
324	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
325	C₂×D₄₃	—	2	4	no	—
326	C₂×D₄₃	—	4	4	no	—
327	C₂×D₄₃	—	4	4	no	—
328	C₂×D₄₃	—	4	4	no	—
329	C₄×C₄₃	—	4	4	no	—
330	C₄×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
331	C₄×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
332	C₄×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
333	C₄×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
334	C₄×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
335	C₄×C₄₃	C₂×#117	1	1	yes	characteristic
336	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
337	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
338	Dic₄₃	—	2	4	no	—
339	Dic₄₃	—	4	4	no	—
340	C₂²×#131	—	43	1	no	—
341	C₂×#413	—	43	1	no	—
342	C₂×#410	—	43	1	no	—
343	C₂×#405	—	43	1	no	—
344	C₂×#405	D₄₃	1	1	yes	characteristic, complemented
345	#1757	—	43	8	no	—
346	C₂×#344	—	43	1	no	—
347	C₂×#344	—	43	1	no	—
348	C₂×C₄₃	—	2	1	no	—
349	C₂×C₄₃	—	2	1	no	—
350	C₂×C₄₃	—	2	1	no	—
351	C₂×C₄₃	—	2	1	no	—
352	C₂×C₄₃	—	2	1	no	—
353	C₂×C₄₃	—	2	1	no	—
354	C₂×C₄₃	#1757	1	2	yes	complemented
355	C₂×C₄₃	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
356	D₄₃	—	4	4	no	—
357	C₂²×#41	—	43	1	no	—
358	C₂×#131	—	43	4	no	—
359	C₂×#131	—	43	4	no	—
360	C₂×#131	—	86	1	no	—
361	C₂×#131	—	86	2	no	—
362	C₂×#131	—	86	1	no	—
363	C₂×#131	—	86	1	no	—
364	C₂×#131	—	86	2	no	—
365	C₂×#131	—	86	1	no	—
366	C₂²×M₁₆	—	43	1	no	—
367	C₂²×M₁₆	—	43	2	no	—
368	C₂²×M₁₆	—	43	1	no	—
369	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
370	C₂³×C₈	—	43	2	no	—
371	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
372	C₂×#117	—	43	1	no	—
373	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
374	#413	—	43	4	no	—
375	#413	—	43	4	no	—
376	C₂×#101	—	43	2	no	—
377	C₂×#100	—	43	2	no	—
378	#410	—	43	4	no	—
379	#410	—	43	4	no	—
380	C₂×#99	—	43	4	no	—
381	#405	—	2	2	no	—
382	#405	—	43	4	no	—
383	#405	—	86	2	no	—
384	#405	C₂×D₄₃	1	4	yes	complemented
385	C₂×#97	—	2	1	no	—
386	C₂×#97	—	86	1	no	—
387	C₂×C₄×C₈	—	2	1	no	—
388	C₂×C₄×C₈	—	86	1	no	—
389	#344	—	43	4	no	—
390	#344	—	43	4	no	—
391	C₄₃	C₂×#1757	1	1	yes	characteristic, complemented, Sylow
392	C₂×#41	—	43	2	no	—
393	C₂×#41	—	43	2	no	—
394	C₂×#41	—	43	2	no	—
395	C₂×#41	—	43	2	no	—
396	C₂×#41	—	86	1	no	—
397	C₂×#41	—	86	1	no	—
398	C₂×#41	—	86	1	no	—
399	C₂×#41	—	86	1	no	—
400	C₂×#41	—	86	1	no	—
401	C₂×#41	—	86	1	no	—
402	C₂×#41	—	86	1	no	—
403	C₂×#41	—	86	1	no	—
404	C₂²×Q₈	—	43	1	no	—
405	C₂²×D₄	—	43	2	no	—
406	C₂²×D₄	—	43	1	no	—
407	C₂³×C₄	—	43	2	no	—
408	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
409	#131	—	86	4	no	—
410	#131	—	86	4	no	—
411	#131	—	86	4	no	—
412	#131	—	86	4	no	—
413	#131	—	86	4	no	—
414	#131	—	86	4	no	—
415	#131	—	86	4	no	—
416	#131	—	86	4	no	—
417	C₂×M₁₆	—	2	1	no	—
418	C₂×M₁₆	—	2	1	no	—
419	C₂×M₁₆	—	2	1	no	—
420	C₂×M₁₆	—	43	2	no	—
421	C₂×M₁₆	—	43	2	no	—
422	C₂×M₁₆	—	43	8	no	—
423	C₂×M₁₆	—	43	2	no	—
424	C₂×M₁₆	—	43	2	no	—
425	C₂×M₁₆	—	43	2	no	—
426	C₂×M₁₆	—	86	1	no	—
427	C₂×M₁₆	—	86	1	no	—
428	C₂×M₁₆	—	86	1	no	—
429	C₂×M₁₆	—	86	1	no	—
430	C₂×M₁₆	—	86	1	no	—
431	C₂×M₁₆	—	86	1	no	—
432	C₂×M₁₆	—	86	1	no	—
433	C₂×M₁₆	—	86	4	no	—
434	C₂×M₁₆	—	86	2	no	—
435	C₂×M₁₆	—	86	2	no	—
436	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
437	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
438	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
439	C₂²×C₈	—	2	1	no	—
440	C₂²×C₈	—	43	2	no	—
441	C₂²×C₈	—	43	8	no	—
442	C₂²×C₈	—	86	1	no	—
443	C₂²×C₈	—	86	4	no	—
444	C₂²×C₈	—	86	2	no	—
445	C₂²×C₈	—	86	2	no	—
446	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
447	C₂²×C₈	C₄×D₄₃	1	2	yes	—
448	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
449	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
450	C₂²×C₈	D₁₇₂	1	2	yes	—
451	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
452	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
453	C₂²×C₈	C₂²⋊D₄₃	1	2	yes	—
454	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
455	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
456	#117	—	2	1	no	—
457	#117	—	2	1	no	—
458	#117	—	43	2	no	—
459	#117	—	43	2	no	—
460	#117	—	86	1	no	—
461	#117	—	86	1	no	—
462	#117	C₄×D₄₃	1	2	yes	—
463	#117	C₂²×D₄₃	1	2	yes	—
464	C₂×C₄⋊C₄	—	2	1	no	—
465	C₂×C₄⋊C₄	—	86	1	no	—
466	C₂×C₂²⋊C₄	—	43	2	no	—
467	C₂×C₂²⋊C₄	C₄×D₄₃	1	2	yes	—
468	C₂×C₄²	—	2	1	no	—
469	C₂×C₄²	—	86	1	no	—
470	#101	—	43	8	no	—
471	#100	—	43	8	no	—
472	#99	—	43	16	no	—
473	#97	—	2	4	no	—
474	#97	—	86	4	no	—
475	C₄×C₈	—	2	4	no	—
476	C₄×C₈	—	86	4	no	—
477	C₂⁴	—	43	2	no	—
478	C₂⁴	C₂×C₄×D₄₃	1	1	yes	characteristic
479	#41	—	86	2	no	—
480	#41	—	86	2	no	—
481	#41	—	86	2	no	—
482	#41	—	86	2	no	—
483	#41	—	86	2	no	—
484	#41	—	86	2	no	—
485	#41	—	86	2	no	—
486	#41	—	86	2	no	—
487	#41	—	86	2	no	—
488	#41	—	86	2	no	—
489	#41	—	86	2	no	—
490	#41	—	86	2	no	—
491	#41	—	86	2	no	—
492	#41	—	86	2	no	—
493	#41	—	86	2	no	—
494	#41	—	86	2	no	—
495	C₂×Q₈	—	43	2	no	—
496	C₂×Q₈	—	43	2	no	—
497	C₂×Q₈	—	86	1	no	—
498	C₂×Q₈	—	86	1	no	—
499	C₂×Q₈	—	86	1	no	—
500	C₂×Q₈	—	86	1	no	—
501	C₂×D₄	—	43	4	no	—
502	C₂×D₄	—	43	4	no	—
503	C₂×D₄	—	43	2	no	—
504	C₂×D₄	—	43	2	no	—
505	C₂×D₄	—	86	2	no	—
506	C₂×D₄	—	86	2	no	—
507	C₂×D₄	—	86	2	no	—
508	C₂×D₄	—	86	2	no	—
509	C₂×D₄	—	86	1	no	—
510	C₂×D₄	—	86	1	no	—
511	C₂×D₄	—	86	1	no	—
512	C₂×D₄	—	86	1	no	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	—	43	2	no	—
515	C₂²×C₄	—	43	4	no	—
516	C₂²×C₄	—	43	4	no	—
517	C₂²×C₄	—	86	2	no	—
518	C₂²×C₄	—	86	2	no	—
519	C₂²×C₄	—	86	2	no	—
520	C₂²×C₄	—	86	2	no	—
521	C₂²×C₄	—	86	2	no	—
522	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
523	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
524	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
525	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
526	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
527	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
528	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
529	C₂²×C₄	#10621898	1	1	yes	characteristic
530	C₂²×C₄	#10621898	1	1	yes	characteristic
531	C₂²×C₄	#10621898	1	1	yes	characteristic
532	C₂²×C₄	#10621898	1	1	yes	characteristic
533	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
534	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
535	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
536	M₁₆	—	2	2	no	—
537	M₁₆	—	2	2	no	—
538	M₁₆	—	2	2	no	—
539	M₁₆	—	43	4	no	—
540	M₁₆	—	86	2	no	—
541	M₁₆	—	86	2	no	—
542	M₁₆	—	86	2	no	—
543	M₁₆	—	86	2	no	—
544	M₁₆	—	86	2	no	—
545	M₁₆	—	86	2	no	—
546	M₁₆	—	86	2	no	—
547	M₁₆	—	86	8	no	—
548	M₁₆	—	86	8	no	—
549	M₁₆	C₂×C₄×D₄₃	1	4	yes	—
550	C₂×C₈	—	2	2	no	—
551	C₂×C₈	—	2	2	no	—
552	C₂×C₈	—	2	2	no	—
553	C₂×C₈	—	43	4	no	—
554	C₂×C₈	—	86	2	no	—
555	C₂×C₈	—	86	2	no	—
556	C₂×C₈	—	86	2	no	—
557	C₂×C₈	—	86	2	no	—
558	C₂×C₈	—	86	2	no	—
559	C₂×C₈	—	86	8	no	—
560	C₂×C₈	—	86	8	no	—
561	C₂×C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
562	C₂×C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
563	C₂×C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
564	C₂×C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
565	C₂×C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
566	C₂×C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
567	C₂×C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
568	C₂×C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
569	C₂×C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
570	C₂×C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
571	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
572	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
573	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
574	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
575	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
576	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
577	C₄⋊C₄	—	2	2	no	—
578	C₄⋊C₄	—	2	2	no	—
579	C₄⋊C₄	—	86	2	no	—
580	C₄⋊C₄	—	86	2	no	—
581	C₂²⋊C₄	—	2	2	no	—
582	C₂²⋊C₄	—	43	4	no	—
583	C₂²⋊C₄	—	86	2	no	—
584	C₂²⋊C₄	C₂×C₄×D₄₃	1	4	yes	—
585	C₄²	—	2	2	no	—
586	C₄²	—	2	2	no	—
587	C₄²	—	86	2	no	—
588	C₄²	—	86	2	no	—
589	C₂³	—	4	2	no	—
590	C₂³	—	43	4	no	—
591	C₂³	—	86	2	no	—
592	C₂³	—	86	2	no	—
593	C₂³	—	172	4	no	—
594	C₂³	C₄²×D₄₃	1	1	yes	characteristic
595	C₂³	C₄²×D₄₃	1	1	yes	characteristic
596	C₂³	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
597	C₂³	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
598	C₂³	C₄×D₁₇₂	1	1	yes	characteristic
599	C₂³	C₄×D₁₇₂	1	1	yes	characteristic
600	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
601	Q₈	—	86	2	no	—
602	Q₈	—	86	2	no	—
603	Q₈	—	86	2	no	—
604	Q₈	—	86	2	no	—
605	D₄	—	86	4	no	—
606	D₄	—	86	4	no	—
607	D₄	—	86	4	no	—
608	D₄	—	86	4	no	—
609	D₄	—	86	2	no	—
610	D₄	—	86	2	no	—
611	D₄	—	86	2	no	—
612	D₄	—	86	2	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	4	4	no	—
615	C₂×C₄	—	43	4	no	—
616	C₂×C₄	—	86	2	no	—
617	C₂×C₄	—	86	2	no	—
618	C₂×C₄	—	86	4	no	—
619	C₂×C₄	—	86	4	no	—
620	C₂×C₄	—	86	4	no	—
621	C₂×C₄	—	86	4	no	—
622	C₂×C₄	—	86	4	no	—
623	C₂×C₄	—	172	4	no	—
624	C₂×C₄	C₄²×D₄₃	1	1	yes	characteristic
625	C₂×C₄	C₄²×D₄₃	1	1	yes	characteristic
626	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
627	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
628	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
629	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
630	C₂×C₄	#13063282	1	1	yes	characteristic
631	C₂×C₄	#13063282	1	1	yes	characteristic
632	C₂×C₄	#13063282	1	1	yes	characteristic
633	C₂×C₄	#13063282	1	1	yes	characteristic
634	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
635	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
636	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
637	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
638	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
639	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
640	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
641	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
642	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
643	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
644	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
645	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
646	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
647	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
648	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
649	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
650	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
651	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
652	C₈	—	2	4	no	—
653	C₈	—	86	4	no	—
654	C₈	—	86	4	no	—
655	C₈	C₂×(C₂×D₄₃)⋊C₄	1	2	yes	—
656	C₈	C₂×(C₂×D₄₃)⋊C₄	1	2	yes	—
657	C₈	C₂×(C₂×D₄₃)⋊C₄	1	2	yes	—
658	C₈	C₂×(C₂×D₄₃)⋊C₄	1	2	yes	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	4	1	no	—
663	C₂²	—	4	1	no	—
664	C₂²	—	4	1	no	—
665	C₂²	—	4	1	no	—
666	C₂²	—	86	4	no	—
667	C₂²	—	172	4	no	—
668	C₂²	—	172	4	no	—
669	C₂²	—	172	4	no	—
670	C₂²	C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
671	C₂²	C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
672	C₂²	C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
673	C₂²	C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
674	C₂²	C₂×C₄²×D₄₃	1	1	yes	characteristic
675	C₂²	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
676	C₂²	C₂×C₄×D₁₇₂	1	1	yes	characteristic
677	C₄	—	4	4	no	—
678	C₄	—	86	4	no	—
679	C₄	—	172	4	no	—
680	C₄	C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
681	C₄	C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
682	C₄	C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
683	C₄	C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
684	C₄	C₂²×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
685	C₄	C₂×#13063282	1	1	yes	characteristic
686	C₄	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
687	C₄	C₂×C₄×D₁₇₂	1	1	yes	characteristic
688	C₂	—	2	1	no	—
689	C₂	—	2	1	no	—
690	C₂	—	2	1	no	—
691	C₂	—	2	1	no	—
692	C₂	—	2	1	no	—
693	C₂	—	2	1	no	—
694	C₂	—	172	4	no	—
695	C₂	#19134396	1	2	yes	direct product factor
696	C₂	C₂×C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	(C₂×D₄₃)⋊C₄
commutator	C₂²×C₄₃	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂×C₄₃×#405	C₂
socle	C₂²×C₄₃	C₄×C₂²⋊C₄
prime radical	C₂²×#10621898	C₂²
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×#405	D₄₃
hypocenter	C₄₃	C₂×#1757
LCS	G ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂³×C₈ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
4. C₂×#14582854	C₂	semidirect
5. #19134396	C₂	direct (N × H)
6. C₂×#14582671	C₂	semidirect
7. C₂×#14582669	C₂	semidirect
8. C₂×C₄₃×#405	C₂	semidirect
16. C₂×#13063331	C₄	semidirect
20. C₂²×#10621872	C₄	semidirect
21. C₂²×C₈×D₄₃	C₄	semidirect
23. #14582881	C₄	semidirect
25. C₂×#13063243	C₄	semidirect
26. C₂×#13063241	C₄	semidirect
31. #14582854	C₂²	semidirect
34. #14582671	C₂²	semidirect
35. #14582669	C₂²	semidirect
40. C₄₃×#405	C₂²	semidirect
82. C₂×#10621872	C₂×C₄	semidirect
88. C₂×C₈×D₄₃	C₂×C₄	semidirect
96. #13063243	C₂×C₄	semidirect
97. #13063241	C₂×C₄	semidirect
344. C₂×#405	D₄₃	semidirect
354. C₂×C₄₃	#1757	semidirect
384. #405	C₂×D₄₃	semidirect
391. C₄₃	C₂×#1757	semidirect
695. C₂	#19134396	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×#13063331	2
C₂×#14582881	2
C₂×#14582872	2
C₂×#14582854	2
#19134396	2
C₂×#14582671	2
C₂×#14582669	2
C₂×C₄₃×#405	2
C₂×#1757	43

Subgroups — C2×#19134396 #25094296

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19134396 #25094296