Subgroups — C₂×#14583408 #19147835

Order 5504.

1880 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10621898	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₄×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583408	C₂	1	16	yes	maximal, direct product factor
4	C₂×#13063310	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#13063307	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#13063303	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#13063302	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#13063298	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#13063297	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#13063295	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#13063293	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×D₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₄×C₂²⋊D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄×C₂²⋊D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#13063282	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×D₄×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂⁴×D₄₃	C₂²	1	1	yes	characteristic
18	C₂×#10621898	—	2	8	no	—
19	C₂×#10621898	C₂²	1	8	yes	complemented
20	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
21	C₂²×D₁₇₂	C₂²	1	1	yes	characteristic
22	C₂²×D₁₇₂	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic, complemented
27	C₂³×Dic₄₃	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₄₃	—	2	8	no	—
29	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic
30	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic
31	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic
32	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic
33	C₂²×C₄×D₄₃	C₂²	1	8	yes	complemented
34	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic, complemented
35	#13063310	C₂²	1	8	yes	complemented
36	#13063307	C₂²	1	8	yes	complemented
37	#13063303	C₂²	1	8	yes	complemented
38	#13063302	C₂²	1	8	yes	complemented
39	#13063298	C₂²	1	8	yes	complemented
40	#13063297	C₂²	1	8	yes	complemented
41	#13063295	C₂²	1	8	yes	complemented
42	#13063293	C₂²	1	8	yes	complemented
43	C₄×D₁₇₂	C₂²	1	8	yes	complemented
44	C₄×C₂²⋊D₄₃	C₂²	1	8	yes	complemented
45	C₄×C₂²⋊D₄₃	C₂²	1	8	yes	complemented
46	#13063282	C₂²	1	8	yes	complemented
47	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic, complemented
48	C₂×Dic₄₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
49	C₂×Dic₄₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
50	C₂×Dic₄₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
51	C₂×Dic₄₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₂²⋊Dic₄₃	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊Dic₄₃	C₂²	1	1	yes	characteristic, complemented
54	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic
55	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic
56	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic
57	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic
58	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
59	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
61	C₂²×D₄×C₄₃	C₂²	1	1	yes	characteristic
62	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
63	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
64	C₄×D₄×C₄₃	C₂²	1	8	yes	complemented
65	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
68	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic, complemented
69	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
70	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
71	C₂³×D₄₃	—	2	4	no	—
72	C₂³×D₄₃	—	2	4	no	—
73	C₂³×D₄₃	—	2	4	no	—
74	C₂³×D₄₃	C₂³	1	1	yes	characteristic
75	C₂³×D₄₃	C₂³	1	4	yes	—
76	C₂³×D₄₃	C₂³	1	1	yes	characteristic
77	C₂³×D₄₃	C₂³	1	1	yes	characteristic
78	C₂×D₄×C₄₃	—	2	4	no	—
79	C₂×D₄×C₄₃	C₂³	1	4	yes	—
80	C₂²×C₄×C₄₃	—	2	4	no	—
81	C₂²×C₄×C₄₃	—	2	4	no	—
82	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
83	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
84	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
85	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
86	C₂²×C₄×C₄₃	C₂³	1	4	yes	—
87	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₄₃	C₂³	1	4	yes	complemented
89	C₂×C₂²⋊D₄₃	—	2	4	no	—
90	C₂×C₂²⋊D₄₃	—	2	4	no	—
91	C₂×C₂²⋊D₄₃	—	2	4	no	—
92	C₂×C₂²⋊D₄₃	—	2	4	no	—
93	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
94	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
95	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
96	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	complemented
97	C₂²×Dic₄₃	—	2	4	no	—
98	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
99	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
100	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
101	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
102	C₂²×Dic₄₃	C₂³	1	4	yes	—
103	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
104	#10621898	—	2	32	no	—
105	C₂×D₁₇₂	—	2	4	no	—
106	C₂×D₁₇₂	—	2	4	no	—
107	C₂×D₁₇₂	C₂³	1	4	yes	—
108	C₂×D₁₇₂	C₂³	1	4	yes	—
109	C₂×C₄×D₄₃	—	2	4	no	—
110	C₂×C₄×D₄₃	—	2	4	no	—
111	C₂×C₄×D₄₃	—	2	4	no	—
112	C₂×C₄×D₄₃	—	2	32	no	—
113	C₂×C₄×D₄₃	—	2	4	no	—
114	C₂×C₄×D₄₃	D₄	1	8	yes	complemented
115	C₂×C₄×D₄₃	C₂³	1	4	yes	—
116	C₂×C₄×D₄₃	C₂³	1	4	yes	—
117	C₂×C₄×D₄₃	C₂³	1	4	yes	—
118	C₂×C₄×D₄₃	C₂³	1	4	yes	—
119	C₂×C₄×D₄₃	C₂³	1	4	yes	complemented
120	C₂×Dic₈₆	—	2	4	no	—
121	C₂×Dic₈₆	C₂³	1	4	yes	complemented
122	C₄⋊C₄×C₄₃	C₂³	1	4	yes	complemented
123	C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
124	C₂²⋊C₄×C₄₃	C₂³	1	4	yes	complemented
125	C₄²×C₄₃	C₂³	1	4	yes	complemented
126	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
127	C₂²⋊Dic₄₃	C₂³	1	4	yes	complemented
128	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
129	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
130	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
131	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
132	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	complemented
133	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	complemented
134	C₄⋊Dic₄₃	C₂³	1	4	yes	complemented
135	Dic₄₃⋊C₄	C₂³	1	4	yes	complemented
136	Dic₄₃⋊C₄	C₂³	1	4	yes	complemented
137	Dic₄₃⋊C₄	C₂³	1	4	yes	complemented
138	Dic₄₃⋊C₄	C₂³	1	4	yes	complemented
139	C₄×Dic₄₃	C₂³	1	4	yes	complemented
140	C₂³×C₄₃	—	2	2	no	—
141	C₂³×C₄₃	—	2	2	no	—
142	C₂³×C₄₃	—	2	2	no	—
143	C₂³×C₄₃	—	2	2	no	—
144	C₂³×C₄₃	—	2	2	no	—
145	C₂³×C₄₃	#41	1	4	yes	complemented
146	C₂³×C₄₃	C₂⁴	1	2	yes	—
147	C₂³×C₄₃	C₂⁴	1	2	yes	—
148	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
149	C₂²×D₄₃	—	2	32	no	—
150	C₂²×D₄₃	—	2	2	no	—
151	C₂²×D₄₃	—	2	2	no	—
152	C₂²×D₄₃	—	2	2	no	—
153	C₂²×D₄₃	—	2	2	no	—
154	C₂²×D₄₃	—	2	8	no	—
155	C₂²×D₄₃	—	2	8	no	—
156	C₂²×D₄₃	—	2	8	no	—
157	C₂²×D₄₃	—	2	2	no	—
158	C₂²×D₄₃	—	2	2	no	—
159	C₂²×D₄₃	—	2	2	no	—
160	C₂²×D₄₃	C₂×D₄	1	4	yes	—
161	C₂²×D₄₃	#41	1	4	yes	complemented
162	C₂²×D₄₃	C₂⁴	1	2	yes	—
163	C₂²×D₄₃	C₂⁴	1	2	yes	—
164	C₂²×D₄₃	C₂⁴	1	2	yes	—
165	D₄×C₄₃	—	2	8	no	—
166	C₂×C₄×C₄₃	—	2	2	no	—
167	C₂×C₄×C₄₃	—	2	2	no	—
168	C₂×C₄×C₄₃	—	2	2	no	—
169	C₂×C₄×C₄₃	—	2	2	no	—
170	C₂×C₄×C₄₃	—	2	8	no	—
171	C₂×C₄×C₄₃	—	2	8	no	—
172	C₂×C₄×C₄₃	C₂×D₄	1	4	yes	—
173	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
174	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
175	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
176	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
177	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
178	C₂²⋊D₄₃	—	2	8	no	—
179	C₂²⋊D₄₃	—	2	8	no	—
180	C₂²⋊D₄₃	—	2	8	no	—
181	C₂²⋊D₄₃	—	2	8	no	—
182	C₂×Dic₄₃	—	2	2	no	—
183	C₂×Dic₄₃	—	2	2	no	—
184	C₂×Dic₄₃	—	2	2	no	—
185	C₂×Dic₄₃	—	2	2	no	—
186	C₂×Dic₄₃	—	2	8	no	—
187	C₂×Dic₄₃	C₂×D₄	1	4	yes	—
188	C₂×Dic₄₃	C₂⁴	1	2	yes	—
189	C₂×Dic₄₃	C₂⁴	1	2	yes	—
190	C₂×Dic₄₃	C₂⁴	1	2	yes	—
191	C₂×Dic₄₃	C₂⁴	1	2	yes	—
192	C₂×Dic₄₃	C₂⁴	1	2	yes	—
193	D₁₇₂	—	2	8	no	—
194	D₁₇₂	—	2	8	no	—
195	C₄×D₄₃	—	2	8	no	—
196	C₄×D₄₃	—	2	8	no	—
197	C₄×D₄₃	—	2	8	no	—
198	C₄×D₄₃	—	2	8	no	—
199	C₄×D₄₃	C₂×D₄	1	16	yes	complemented
200	Dic₈₆	—	2	8	no	—
201	C₂²×C₄₃	—	2	8	no	—
202	C₂²×C₄₃	—	2	2	no	—
203	C₂²×C₄₃	—	2	2	no	—
204	C₂²×C₄₃	—	2	2	no	—
205	C₂²×C₄₃	—	2	2	no	—
206	C₂²×C₄₃	—	2	2	no	—
207	C₂²×C₄₃	—	4	4	no	—
208	C₂²×C₄₃	C₂²×D₄	1	2	yes	—
209	C₂²×C₄₃	C₂×#41	1	2	yes	—
210	C₂²×C₄₃	C₂×#41	1	2	yes	—
211	C₂²×C₄₃	C₂×#41	1	4	yes	complemented
212	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
213	C₂×D₄₃	—	2	32	no	—
214	C₂×D₄₃	—	2	8	no	—
215	C₂×D₄₃	—	2	8	no	—
216	C₂×D₄₃	—	2	2	no	—
217	C₂×D₄₃	—	2	2	no	—
218	C₂×D₄₃	—	2	2	no	—
219	C₂×D₄₃	—	2	2	no	—
220	C₂×D₄₃	—	2	2	no	—
221	C₂×D₄₃	—	2	2	no	—
222	C₂×D₄₃	—	2	2	no	—
223	C₂×D₄₃	—	4	4	no	—
224	C₂×D₄₃	C₂²×D₄	1	4	yes	—
225	C₂×D₄₃	C₂×#41	1	4	yes	complemented
226	C₄×C₄₃	—	2	2	no	—
227	C₄×C₄₃	—	2	2	no	—
228	C₄×C₄₃	—	2	2	no	—
229	C₄×C₄₃	—	2	2	no	—
230	C₄×C₄₃	C₂²×D₄	1	4	yes	—
231	Dic₄₃	—	2	2	no	—
232	Dic₄₃	—	2	2	no	—
233	Dic₄₃	—	2	2	no	—
234	Dic₄₃	—	2	2	no	—
235	Dic₄₃	C₂²×D₄	1	4	yes	—
236	C₂×#525	—	43	1	no	maximal, Sylow
237	C₂×C₄₃	—	2	4	no	—
238	C₂×C₄₃	—	4	2	no	—
239	C₂×C₄₃	#525	1	4	yes	complemented
240	C₂×C₄₃	C₂³×D₄	1	1	yes	characteristic
241	C₂×C₄₃	C₂²×#41	1	1	yes	characteristic
242	C₂×C₄₃	C₂²×#41	1	1	yes	characteristic
243	D₄₃	—	2	4	no	—
244	D₄₃	—	2	4	no	—
245	D₄₃	—	4	2	no	—
246	C₂²×#41	—	43	1	no	—
247	C₂⁴×C₄	—	43	1	no	—
248	#525	—	43	16	no	—
249	C₂×#123	—	43	1	no	—
250	C₂×#123	—	43	1	no	—
251	C₂×C₂²⋊Q₈	—	43	1	no	—
252	C₂×C₂²⋊Q₈	—	43	1	no	—
253	C₂×#121	—	43	1	no	—
254	C₂×#121	—	43	1	no	—
255	C₂×#120	—	43	1	no	—
256	C₂×#120	—	43	1	no	—
257	C₂×C₄×D₄	—	43	1	no	—
258	C₂×C₄×D₄	—	43	1	no	—
259	C₂×C₄×D₄	—	43	1	no	—
260	C₂×C₄×D₄	D₄₃	1	1	yes	characteristic, complemented
261	C₂×#117	—	43	1	no	—
262	C₄₃	C₂×#525	1	1	yes	characteristic, complemented, Sylow
263	C₂⁵	—	43	1	no	—
264	C₂×#41	—	43	8	no	—
265	C₂×#41	—	86	8	no	—
266	C₂²×Q₈	—	43	1	no	—
267	C₂²×D₄	—	43	1	no	—
268	C₂²×D₄	—	43	1	no	—
269	C₂²×D₄	—	43	1	no	—
270	C₂²×D₄	—	43	1	no	—
271	C₂²×D₄	—	43	1	no	—
272	C₂²×D₄	—	43	1	no	—
273	C₂²×D₄	C₂×D₄₃	1	1	yes	characteristic
274	C₂³×C₄	—	43	1	no	—
275	C₂³×C₄	—	43	1	no	—
276	C₂³×C₄	—	43	1	no	—
277	C₂³×C₄	—	43	1	no	—
278	C₂³×C₄	—	43	8	no	—
279	C₂³×C₄	—	43	1	no	—
280	C₂³×C₄	—	43	1	no	—
281	C₂³×C₄	—	86	8	no	—
282	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
283	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic, complemented
284	#123	—	43	8	no	—
285	#123	—	43	8	no	—
286	C₂²⋊Q₈	—	43	8	no	—
287	C₂²⋊Q₈	—	43	8	no	—
288	#121	—	43	8	no	—
289	#121	—	43	8	no	—
290	#120	—	43	8	no	—
291	#120	—	43	8	no	—
292	C₄×D₄	—	43	8	no	—
293	C₄×D₄	—	43	8	no	—
294	C₄×D₄	—	43	8	no	—
295	C₄×D₄	C₂×D₄₃	1	8	yes	complemented
296	#117	—	43	8	no	—
297	C₂×C₄⋊C₄	—	43	1	no	—
298	C₂×C₄⋊C₄	—	43	1	no	—
299	C₂×C₄⋊C₄	—	43	1	no	—
300	C₂×C₄⋊C₄	—	43	1	no	—
301	C₂×C₄⋊C₄	—	43	1	no	—
302	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic, complemented
303	C₂×C₂²⋊C₄	—	43	1	no	—
304	C₂×C₂²⋊C₄	—	43	1	no	—
305	C₂×C₂²⋊C₄	—	43	1	no	—
306	C₂×C₂²⋊C₄	—	43	1	no	—
307	C₂×C₂²⋊C₄	—	43	1	no	—
308	C₂×C₂²⋊C₄	—	43	1	no	—
309	C₂×C₂²⋊C₄	—	43	1	no	—
310	C₂×C₂²⋊C₄	—	43	1	no	—
311	C₂×C₂²⋊C₄	C₂×D₄₃	1	1	yes	characteristic
312	C₂×C₂²⋊C₄	C₂×D₄₃	1	1	yes	characteristic, complemented
313	C₂×C₄²	—	43	1	no	—
314	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic, complemented
315	C₂⁴	—	43	1	no	—
316	C₂⁴	—	43	1	no	—
317	C₂⁴	—	43	1	no	—
318	C₂⁴	—	43	4	no	—
319	C₂⁴	—	86	4	no	—
320	C₂⁴	—	86	4	no	—
321	C₂⁴	—	86	4	no	—
322	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
323	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
324	#41	—	86	32	no	—
325	C₂×Q₈	—	43	4	no	—
326	C₂×Q₈	—	86	4	no	—
327	C₂×D₄	—	2	4	no	—
328	C₂×D₄	—	43	4	no	—
329	C₂×D₄	—	43	4	no	—
330	C₂×D₄	—	43	4	no	—
331	C₂×D₄	—	43	4	no	—
332	C₂×D₄	—	43	4	no	—
333	C₂×D₄	—	43	4	no	—
334	C₂×D₄	—	86	4	no	—
335	C₂×D₄	—	86	4	no	—
336	C₂×D₄	—	86	4	no	—
337	C₂×D₄	—	86	4	no	—
338	C₂×D₄	—	86	4	no	—
339	C₂×D₄	—	86	4	no	—
340	C₂×D₄	C₂²×D₄₃	1	4	yes	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	43	1	no	—
344	C₂²×C₄	—	43	8	no	—
345	C₂²×C₄	—	43	4	no	—
346	C₂²×C₄	—	43	1	no	—
347	C₂²×C₄	—	43	1	no	—
348	C₂²×C₄	—	43	1	no	—
349	C₂²×C₄	—	43	1	no	—
350	C₂²×C₄	—	43	4	no	—
351	C₂²×C₄	—	43	4	no	—
352	C₂²×C₄	—	43	4	no	—
353	C₂²×C₄	—	43	4	no	—
354	C₂²×C₄	—	43	4	no	—
355	C₂²×C₄	—	86	4	no	—
356	C₂²×C₄	—	86	32	no	—
357	C₂²×C₄	—	86	4	no	—
358	C₂²×C₄	—	86	4	no	—
359	C₂²×C₄	—	86	4	no	—
360	C₂²×C₄	—	86	4	no	—
361	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
362	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
363	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
364	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
365	C₂²×C₄	C₂²×D₄₃	1	4	yes	—
366	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
367	C₂²×C₄	C₂²×D₄₃	1	4	yes	complemented
368	C₄⋊C₄	—	43	4	no	—
369	C₄⋊C₄	—	43	4	no	—
370	C₄⋊C₄	—	43	4	no	—
371	C₄⋊C₄	—	43	4	no	—
372	C₄⋊C₄	—	43	4	no	—
373	C₄⋊C₄	C₂²×D₄₃	1	4	yes	complemented
374	C₂²⋊C₄	—	43	4	no	—
375	C₂²⋊C₄	—	43	4	no	—
376	C₂²⋊C₄	—	43	4	no	—
377	C₂²⋊C₄	—	43	4	no	—
378	C₂²⋊C₄	—	43	4	no	—
379	C₂²⋊C₄	—	43	4	no	—
380	C₂²⋊C₄	—	43	4	no	—
381	C₂²⋊C₄	—	43	4	no	—
382	C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
383	C₂²⋊C₄	C₂²×D₄₃	1	4	yes	complemented
384	C₄²	—	43	4	no	—
385	C₄²	C₂²×D₄₃	1	4	yes	complemented
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	43	4	no	—
392	C₂³	—	43	4	no	—
393	C₂³	—	43	2	no	—
394	C₂³	—	43	2	no	—
395	C₂³	—	43	2	no	—
396	C₂³	—	86	8	no	—
397	C₂³	—	86	8	no	—
398	C₂³	—	86	32	no	—
399	C₂³	—	86	2	no	—
400	C₂³	—	86	2	no	—
401	C₂³	—	86	2	no	—
402	C₂³	—	86	2	no	—
403	C₂³	—	86	8	no	—
404	C₂³	—	86	2	no	—
405	C₂³	—	86	2	no	—
406	C₂³	—	86	2	no	—
407	C₂³	#10621898	1	4	yes	complemented
408	C₂³	C₂³×D₄₃	1	2	yes	—
409	C₂³	C₂³×D₄₃	1	2	yes	—
410	C₂³	C₂³×D₄₃	1	1	yes	characteristic
411	Q₈	—	86	8	no	—
412	D₄	—	2	8	no	—
413	D₄	—	86	8	no	—
414	D₄	—	86	8	no	—
415	D₄	—	86	8	no	—
416	D₄	—	86	8	no	—
417	D₄	—	86	8	no	—
418	D₄	—	86	8	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	8	no	—
424	C₂×C₄	—	2	8	no	—
425	C₂×C₄	—	43	4	no	—
426	C₂×C₄	—	43	2	no	—
427	C₂×C₄	—	43	16	no	—
428	C₂×C₄	—	43	2	no	—
429	C₂×C₄	—	43	2	no	—
430	C₂×C₄	—	43	2	no	—
431	C₂×C₄	—	43	2	no	—
432	C₂×C₄	—	86	8	no	—
433	C₂×C₄	—	86	8	no	—
434	C₂×C₄	—	86	8	no	—
435	C₂×C₄	—	86	2	no	—
436	C₂×C₄	—	86	2	no	—
437	C₂×C₄	—	86	2	no	—
438	C₂×C₄	—	86	2	no	—
439	C₂×C₄	—	86	8	no	—
440	C₂×C₄	—	86	8	no	—
441	C₂×C₄	D₄×D₄₃	1	4	yes	—
442	C₂×C₄	C₂³×D₄₃	1	2	yes	—
443	C₂×C₄	C₂³×D₄₃	1	2	yes	—
444	C₂×C₄	C₂³×D₄₃	1	2	yes	—
445	C₂×C₄	C₂³×D₄₃	1	2	yes	—
446	C₂×C₄	C₂³×D₄₃	1	2	yes	—
447	C₂²	—	2	8	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	4	4	no	—
454	C₂²	—	43	4	no	—
455	C₂²	—	43	4	no	—
456	C₂²	—	86	32	no	—
457	C₂²	—	86	8	no	—
458	C₂²	—	86	8	no	—
459	C₂²	—	86	2	no	—
460	C₂²	—	86	2	no	—
461	C₂²	—	86	2	no	—
462	C₂²	—	86	2	no	—
463	C₂²	—	86	2	no	—
464	C₂²	—	86	2	no	—
465	C₂²	—	86	2	no	—
466	C₂²	—	172	4	no	—
467	C₂²	C₂×D₄×D₄₃	1	2	yes	—
468	C₂²	#41×D₄₃	1	2	yes	—
469	C₂²	C₂×#10621898	1	2	yes	—
470	C₂²	C₂×#10621898	1	4	yes	complemented
471	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
472	C₄	—	2	2	no	—
473	C₄	—	2	2	no	—
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	43	4	no	—
477	C₄	—	86	2	no	—
478	C₄	—	86	2	no	—
479	C₄	—	86	2	no	—
480	C₄	—	86	2	no	—
481	C₄	C₂×D₄×D₄₃	1	4	yes	—
482	C₂	—	2	4	no	—
483	C₂	—	4	2	no	—
484	C₂	—	86	4	no	—
485	C₂	—	86	4	no	—
486	C₂	—	172	2	no	—
487	C₂	#14583408	1	4	yes	direct product factor
488	C₂	C₂²×D₄×D₄₃	1	1	yes	characteristic
489	C₂	C₂×#41×D₄₃	1	1	yes	characteristic
490	C₂	C₂²×#10621898	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₄₃
commutator	C₂²×C₄₃	C₂⁵
Frattini	C₂²	C₂⁴×D₄₃
Fitting	C₂×C₄×D₄×C₄₃	C₂
socle	C₂³×C₄₃	C₂⁴
hypercenter	C₂×C₄×D₄	D₄₃
hypocenter	C₄₃	C₂×#525
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#10621898	C₂	semidirect
2. C₂³×C₄×D₄₃	C₂	semidirect
3. #14583408	C₂	direct (N × H)
4. C₂×#13063310	C₂	semidirect
5. C₂×#13063307	C₂	semidirect
6. C₂×#13063303	C₂	semidirect
7. C₂×#13063302	C₂	semidirect
8. C₂×#13063298	C₂	semidirect
9. C₂×#13063297	C₂	semidirect
10. C₂×#13063295	C₂	semidirect
11. C₂×#13063293	C₂	semidirect
12. C₂×C₄×D₁₇₂	C₂	semidirect
13. C₂×C₄×C₂²⋊D₄₃	C₂	semidirect
14. C₂×C₄×C₂²⋊D₄₃	C₂	semidirect
15. C₂×#13063282	C₂	semidirect
16. C₂×C₄×D₄×C₄₃	C₂	semidirect
19. C₂×#10621898	C₂²	semidirect
20. C₂²×Dic₈₆	C₂²	semidirect
26. C₂²×C₂²⋊D₄₃	C₂²	semidirect
33. C₂²×C₄×D₄₃	C₂²	semidirect
34. C₂²×C₄×D₄₃	C₂²	semidirect
35. #13063310	C₂²	semidirect
36. #13063307	C₂²	semidirect
37. #13063303	C₂²	semidirect
38. #13063302	C₂²	semidirect
39. #13063298	C₂²	semidirect
40. #13063297	C₂²	semidirect
41. #13063295	C₂²	semidirect
42. #13063293	C₂²	semidirect
43. C₄×D₁₇₂	C₂²	semidirect
44. C₄×C₂²⋊D₄₃	C₂²	semidirect
45. C₄×C₂²⋊D₄₃	C₂²	semidirect
46. #13063282	C₂²	semidirect
47. C₂×C₄⋊Dic₄₃	C₂²	semidirect
48. C₂×Dic₄₃⋊C₄	C₂²	semidirect
49. C₂×Dic₄₃⋊C₄	C₂²	semidirect
50. C₂×Dic₄₃⋊C₄	C₂²	semidirect
51. C₂×Dic₄₃⋊C₄	C₂²	semidirect
53. C₂×C₂²⋊Dic₄₃	C₂²	semidirect
58. C₂×(C₂×D₄₃)⋊C₄	C₂²	semidirect
59. C₂×(C₂×D₄₃)⋊C₄	C₂²	semidirect
60. C₂×C₄×Dic₄₃	C₂²	semidirect
63. C₂³×C₄×C₄₃	C₂²	semidirect
64. C₄×D₄×C₄₃	C₂²	semidirect
65. C₂×C₄⋊C₄×C₄₃	C₂²	semidirect
67. C₂×C₂²⋊C₄×C₄₃	C₂²	semidirect
68. C₂×C₄²×C₄₃	C₂²	semidirect
88. C₂²×C₄×C₄₃	C₂³	semidirect
96. C₂×C₂²⋊D₄₃	C₂³	semidirect
114. C₂×C₄×D₄₃	D₄	semidirect
119. C₂×C₄×D₄₃	C₂³	semidirect
121. C₂×Dic₈₆	C₂³	semidirect
122. C₄⋊C₄×C₄₃	C₂³	semidirect
124. C₂²⋊C₄×C₄₃	C₂³	semidirect
125. C₄²×C₄₃	C₂³	semidirect
127. C₂²⋊Dic₄₃	C₂³	semidirect
132. (C₂×D₄₃)⋊C₄	C₂³	semidirect
133. (C₂×D₄₃)⋊C₄	C₂³	semidirect
134. C₄⋊Dic₄₃	C₂³	semidirect
135. Dic₄₃⋊C₄	C₂³	semidirect
136. Dic₄₃⋊C₄	C₂³	semidirect
137. Dic₄₃⋊C₄	C₂³	semidirect
138. Dic₄₃⋊C₄	C₂³	semidirect
139. C₄×Dic₄₃	C₂³	semidirect
145. C₂³×C₄₃	#41	semidirect
161. C₂²×D₄₃	#41	semidirect
199. C₄×D₄₃	C₂×D₄	semidirect
211. C₂²×C₄₃	C₂×#41	semidirect
225. C₂×D₄₃	C₂×#41	semidirect
239. C₂×C₄₃	#525	semidirect
260. C₂×C₄×D₄	D₄₃	semidirect
262. C₄₃	C₂×#525	semidirect
283. C₂³×C₄	C₂×D₄₃	semidirect
295. C₄×D₄	C₂×D₄₃	semidirect
302. C₂×C₄⋊C₄	C₂×D₄₃	semidirect
312. C₂×C₂²⋊C₄	C₂×D₄₃	semidirect
314. C₂×C₄²	C₂×D₄₃	semidirect
367. C₂²×C₄	C₂²×D₄₃	semidirect
373. C₄⋊C₄	C₂²×D₄₃	semidirect
383. C₂²⋊C₄	C₂²×D₄₃	semidirect
385. C₄²	C₂²×D₄₃	semidirect
407. C₂³	#10621898	semidirect
470. C₂²	C₂×#10621898	semidirect
487. C₂	#14583408	direct (N × H)

Subgroups — C2×#14583408 #19147835

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#14583408 #19147835