Subgroups — #25257039

Order 11008.

2226 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19137695	C₂	1	4	yes	maximal, complemented
2	#19137685	C₂	1	2	yes	maximal, complemented
3	#19137655	C₂	1	2	yes	maximal, complemented
4	#19137552	C₂	1	4	yes	maximal, complemented
5	#19137552	C₂	1	2	yes	maximal, complemented
6	Q₈×C₄⋊Dic₄₃	C₂	1	2	yes	maximal, complemented
7	#19137330	C₂	1	4	yes	maximal
8	#19137218	C₂	1	2	yes	maximal
9	C₂²⋊Q₈×Dic₄₃	C₂	1	4	yes	maximal
10	#19137002	C₂	1	1	yes	maximal, characteristic
11	#19136951	C₂	1	2	yes	maximal
12	C₂×C₄×C₄⋊Dic₄₃	C₂	1	1	yes	maximal, characteristic
13	C₂×C₄₃×#533	C₂	1	1	yes	maximal, characteristic
14	C₂×Q₈×Dic₄₃	C₂²	1	4	yes	—
15	C₂×#13063284	C₂²	1	2	yes	—
16	C₂²×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄×Dic₄₃	C₂²	1	2	yes	—
19	#14582806	C₂²	1	8	yes	—
20	#14582806	C₂²	1	4	yes	—
21	#14582798	C₂²	1	8	yes	—
22	#14582798	C₂²	1	4	yes	—
23	#14582798	C₂²	1	4	yes	—
24	#14582798	C₂²	1	4	yes	—
25	#14582785	C₂²	1	8	yes	—
26	#14582785	C₂²	1	8	yes	—
27	#14582785	C₂²	1	8	yes	—
28	#14582774	C₂²	1	8	yes	—
29	#14582769	C₂²	1	1	yes	characteristic
30	#14582769	C₂²	1	4	yes	—
31	#14582769	C₂²	1	1	yes	characteristic
32	#14582765	C₂²	1	4	yes	—
33	#14582765	C₂²	1	2	yes	—
34	#14582759	C₂²	1	2	yes	—
35	#14582759	C₂²	1	2	yes	—
36	C₄⋊C₄×Dic₄₃	C₂²	1	4	yes	—
37	C₄⋊C₄×Dic₄₃	C₂²	1	8	yes	—
38	C₄⋊C₄×Dic₄₃	C₂²	1	4	yes	—
39	C₄⋊C₄×Dic₄₃	C₂²	1	4	yes	—
40	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
41	C₄×C₄⋊Dic₄₃	C₂²	1	4	yes	—
42	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
43	C₄×C₄⋊Dic₄₃	C₂²	1	4	yes	—
44	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
45	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
46	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
47	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
48	C₂²⋊C₄×Dic₄₃	C₂²	1	8	yes	—
49	C₂×C₄₃⋊#95	C₂²	1	2	yes	—
50	C₄₃×#533	C₄	1	16	yes	complemented
51	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
52	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
53	C₂×#125×C₄₃	C₂²	1	2	yes	—
54	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
55	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
56	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	—
57	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	—
58	C₂×#117×C₄₃	C₂²	1	2	yes	—
59	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
60	C₂³×Dic₄₃	C₂³	1	2	yes	—
61	C₂³×Dic₄₃	C₂³	1	2	yes	—
62	Q₈×Dic₄₃	—	4	8	no	—
63	#13063284	—	2	8	no	—
64	C₂×C₄⋊Dic₄₃	—	2	4	no	—
65	C₂×C₄⋊Dic₄₃	Q₈	1	8	yes	complemented
66	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
67	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
68	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
69	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
70	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
71	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
72	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
73	C₂×C₄⋊Dic₄₃	C₂³	1	8	yes	—
74	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
75	C₂×C₄⋊Dic₄₃	C₂³	1	8	yes	—
76	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
77	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
78	C₂×C₂²⋊Dic₄₃	C₂³	1	4	yes	—
79	C₂×C₄×Dic₄₃	—	4	4	no	—
80	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
81	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
82	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
83	C₂×C₄×Dic₄₃	C₂³	1	8	yes	—
84	C₂×C₄×Dic₄₃	C₂³	1	8	yes	—
85	C₄₃⋊#95	C₂³	1	8	yes	—
86	C₄₃⋊#95	C₂³	1	4	yes	—
87	C₄₃⋊#95	C₂³	1	8	yes	—
88	C₄₃⋊#95	C₂³	1	8	yes	—
89	C₄₃⋊#95	C₂³	1	4	yes	—
90	C₄₃⋊#95	C₂³	1	4	yes	—
91	C₄₃⋊#95	C₂³	1	4	yes	—
92	C₄₃⋊#95	C₂³	1	8	yes	—
93	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
94	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
95	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
98	C₄⋊Q₈×C₄₃	C₂×C₄	1	8	yes	complemented
99	C₄⋊Q₈×C₄₃	C₂×C₄	1	8	yes	complemented
100	#125×C₄₃	C₂×C₄	1	16	yes	complemented
101	C₂²⋊Q₈×C₄₃	C₂×C₄	1	16	yes	—
102	C₂²⋊Q₈×C₄₃	C₂×C₄	1	16	yes	—
103	C₄×Q₈×C₄₃	C₂×C₄	1	16	yes	complemented
104	C₄×Q₈×C₄₃	C₂×C₄	1	16	yes	complemented
105	#117×C₄₃	C₂×C₄	1	16	yes	—
106	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
108	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
109	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
112	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
113	C₂×C₄²×C₄₃	C₂×C₄	1	8	yes	—
114	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
119	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
120	C₂×Q₈×C₄₃	—	2	4	no	—
121	C₂×Q₈×C₄₃	—	2	4	no	—
122	C₂×Q₈×C₄₃	—	4	2	no	—
123	C₂×Q₈×C₄₃	—	4	2	no	—
124	C₂×Q₈×C₄₃	C₂²×C₄	1	8	yes	—
125	C₂×Q₈×C₄₃	C₂²×C₄	1	8	yes	—
126	C₂²×C₄×C₄₃	—	2	2	no	—
127	C₂²×C₄×C₄₃	—	2	2	no	—
128	C₂²×C₄×C₄₃	—	4	1	no	—
129	C₂²×C₄×C₄₃	—	4	1	no	—
130	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
131	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
132	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
133	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
134	C₂²×C₄×C₄₃	#41	1	4	yes	—
135	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
136	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
137	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
138	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
139	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
140	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
141	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
142	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
143	C₂²×Dic₄₃	—	2	4	no	—
144	C₂²×Dic₄₃	—	4	2	no	—
145	C₂²×Dic₄₃	—	4	2	no	—
146	C₂²×Dic₄₃	—	4	2	no	—
147	C₂²×Dic₄₃	—	4	2	no	—
148	C₂²×Dic₄₃	C₂×Q₈	1	8	yes	—
149	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
150	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
151	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
152	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
153	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
154	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
155	C₄⋊C₄×C₄₃	C₂²×C₄	1	16	yes	—
156	C₄⋊C₄×C₄₃	C₂²×C₄	1	16	yes	—
157	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
158	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
159	C₂²⋊C₄×C₄₃	C₂²×C₄	1	16	yes	—
160	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
161	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
162	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
163	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
164	C₄²×C₄₃	C₂²×C₄	1	16	yes	—
165	C₂²⋊Dic₄₃	—	2	8	no	—
166	C₄⋊Dic₄₃	—	2	4	no	—
167	C₄⋊Dic₄₃	—	2	4	no	—
168	C₄⋊Dic₄₃	—	2	4	no	—
169	C₄⋊Dic₄₃	—	2	4	no	—
170	C₄⋊Dic₄₃	—	2	4	no	—
171	C₄⋊Dic₄₃	—	2	4	no	—
172	C₄⋊Dic₄₃	—	4	2	no	—
173	C₄⋊Dic₄₃	—	4	2	no	—
174	C₄⋊Dic₄₃	—	4	8	no	—
175	C₄⋊Dic₄₃	—	4	8	no	—
176	C₄⋊Dic₄₃	C₂×Q₈	1	8	yes	—
177	C₄⋊Dic₄₃	C₂×Q₈	1	8	yes	—
178	C₄×Dic₄₃	—	2	8	no	—
179	C₄×Dic₄₃	—	2	8	no	—
180	C₄×Dic₄₃	—	4	4	no	—
181	C₄×Dic₄₃	—	4	8	no	—
182	C₄×Dic₄₃	—	4	8	no	—
183	C₂³×C₄₃	—	2	1	no	—
184	C₂³×C₄₃	—	2	1	no	—
185	C₂³×C₄₃	—	2	1	no	—
186	C₂³×C₄₃	—	2	1	no	—
187	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
188	C₂³×C₄₃	C₂²×Q₈	1	2	yes	—
189	C₂³×C₄₃	C₂×#41	1	2	yes	—
190	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
191	Q₈×C₄₃	—	2	16	no	—
192	Q₈×C₄₃	—	4	8	no	—
193	C₂×C₄×C₄₃	—	2	1	no	—
194	C₂×C₄×C₄₃	—	2	4	no	—
195	C₂×C₄×C₄₃	—	2	1	no	—
196	C₂×C₄×C₄₃	—	2	4	no	—
197	C₂×C₄×C₄₃	—	2	4	no	—
198	C₂×C₄×C₄₃	—	2	1	no	—
199	C₂×C₄×C₄₃	—	2	1	no	—
200	C₂×C₄×C₄₃	—	2	4	no	—
201	C₂×C₄×C₄₃	—	2	1	no	—
202	C₂×C₄×C₄₃	—	2	1	no	—
203	C₂×C₄×C₄₃	—	2	8	no	—
204	C₂×C₄×C₄₃	—	4	4	no	—
205	C₂×C₄×C₄₃	C₄×Q₈	1	16	yes	complemented
206	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
207	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
208	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
209	C₂×C₄×C₄₃	C₂³×C₄	1	8	yes	—
210	C₂×C₄×C₄₃	C₂³×C₄	1	8	yes	—
211	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
212	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
213	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
214	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
215	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
216	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
217	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
218	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
219	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
220	C₂×Dic₄₃	—	2	4	no	—
221	C₂×Dic₄₃	—	2	4	no	—
222	C₂×Dic₄₃	—	2	4	no	—
223	C₂×Dic₄₃	—	2	4	no	—
224	C₂×Dic₄₃	—	2	4	no	—
225	C₂×Dic₄₃	—	2	4	no	—
226	C₂×Dic₄₃	—	2	4	no	—
227	C₂×Dic₄₃	—	2	4	no	—
228	C₂×Dic₄₃	—	2	4	no	—
229	C₂×Dic₄₃	—	2	4	no	—
230	C₂×Dic₄₃	—	2	4	no	—
231	C₂×Dic₄₃	—	4	8	no	—
232	C₂×Dic₄₃	—	4	8	no	—
233	C₂×Dic₄₃	C₂²×Q₈	1	8	yes	—
234	#34213	—	43	1	no	maximal, Sylow
235	C₂²×C₄₃	—	2	2	no	—
236	C₂²×C₄₃	—	2	2	no	—
237	C₂²×C₄₃	—	2	2	no	—
238	C₂²×C₄₃	—	2	2	no	—
239	C₂²×C₄₃	—	2	2	no	—
240	C₂²×C₄₃	—	2	2	no	—
241	C₂²×C₄₃	C₂×C₄×Q₈	1	4	yes	—
242	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
243	C₂²×C₄₃	C₂³×Q₈	1	1	yes	characteristic
244	C₂²×C₄₃	C₂²×#41	1	1	yes	characteristic
245	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
246	C₂²×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
247	C₂²×C₄₃	#585	1	1	yes	characteristic
248	C₂²×C₄₃	#585	1	1	yes	characteristic
249	C₄×C₄₃	—	2	2	no	—
250	C₄×C₄₃	—	2	8	no	—
251	C₄×C₄₃	—	2	2	no	—
252	C₄×C₄₃	—	2	2	no	—
253	C₄×C₄₃	—	2	8	no	—
254	C₄×C₄₃	C₂×C₄×Q₈	1	4	yes	—
255	C₄×C₄₃	C₂×C₄×Q₈	1	4	yes	—
256	C₄×C₄₃	#520	1	4	yes	—
257	Dic₄₃	—	2	8	no	—
258	Dic₄₃	—	4	4	no	—
259	Dic₄₃	—	4	4	no	—
260	Dic₄₃	—	4	4	no	—
261	C₂×#533	D₄₃	1	1	yes	characteristic
262	#2370	—	43	4	no	—
263	#2369	—	43	2	no	—
264	#2365	—	43	2	no	—
265	#2355	—	43	2	no	—
266	#2355	—	43	4	no	—
267	Q₈×C₄⋊C₄	—	43	2	no	—
268	#2329	—	43	4	no	—
269	#2317	—	43	2	no	—
270	C₄×C₂²⋊Q₈	—	43	4	no	—
271	#2285	—	43	1	no	—
272	#2274	—	43	2	no	—
273	C₂×C₄×C₄⋊C₄	—	43	1	no	—
274	C₂×C₄₃	—	2	4	no	—
275	C₂×C₄₃	C₂²×C₄×Q₈	1	1	yes	characteristic
276	C₂×C₄₃	C₂×#520	1	1	yes	characteristic
277	C₂×C₄₃	#3428	1	1	yes	characteristic
278	C₂×C₄₃	#3501	1	1	yes	characteristic
279	C₂×C₄₃	#3502	1	1	yes	characteristic
280	C₂×C₄₃	#3506	1	1	yes	characteristic
281	C₂×C₄₃	#3507	1	1	yes	characteristic
282	#533	Dic₄₃	1	16	yes	complemented
283	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
284	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
285	C₂×#125	C₂×D₄₃	1	2	yes	—
286	C₂×C₂²⋊Q₈	C₂×D₄₃	1	2	yes	—
287	C₂×C₂²⋊Q₈	C₂×D₄₃	1	2	yes	—
288	C₂×C₄×Q₈	—	43	4	no	—
289	C₂×C₄×Q₈	C₂×D₄₃	1	2	yes	—
290	C₂×C₄×Q₈	C₂×D₄₃	1	2	yes	—
291	C₂×#117	—	43	2	no	—
292	C₂×#117	C₂×D₄₃	1	2	yes	—
293	C₂²×C₄⋊C₄	—	43	1	no	—
294	C₂²×C₄⋊C₄	—	43	1	no	—
295	C₂²×C₄²	—	43	2	no	—
296	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
297	#391	—	43	8	no	—
298	#391	—	43	4	no	—
299	#389	—	43	4	no	—
300	#389	—	43	4	no	—
301	#389	—	43	8	no	—
302	#389	—	43	4	no	—
303	#387	—	43	8	no	—
304	#387	—	43	8	no	—
305	#387	—	43	8	no	—
306	#385	—	43	8	no	—
307	#384	—	43	4	no	—
308	#384	—	43	1	no	—
309	#384	—	43	1	no	—
310	#382	—	43	4	no	—
311	#382	—	43	2	no	—
312	#380	—	43	2	no	—
313	#380	—	43	2	no	—
314	C₄×C₄⋊C₄	—	43	4	no	—
315	C₄×C₄⋊C₄	—	43	8	no	—
316	C₄×C₄⋊C₄	—	43	4	no	—
317	C₄×C₄⋊C₄	—	43	4	no	—
318	C₄×C₄⋊C₄	—	43	2	no	—
319	C₄×C₄⋊C₄	—	43	4	no	—
320	C₄×C₄⋊C₄	—	43	2	no	—
321	C₄×C₄⋊C₄	—	43	4	no	—
322	C₄×C₄⋊C₄	—	43	2	no	—
323	C₄×C₄⋊C₄	—	43	2	no	—
324	C₄×C₄⋊C₄	—	43	2	no	—
325	C₄×C₄⋊C₄	—	43	2	no	—
326	C₄×C₂²⋊C₄	—	43	8	no	—
327	C₂×#95	—	43	2	no	—
328	C₄₃	#34213	1	1	yes	characteristic, complemented, Sylow
329	C₂²×Q₈	C₂²×D₄₃	1	2	yes	—
330	C₂²×Q₈	C₂²×D₄₃	1	2	yes	—
331	C₂³×C₄	—	43	2	no	—
332	C₂³×C₄	—	43	2	no	—
333	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
334	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
335	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
336	C₄⋊Q₈	C₂×Dic₄₃	1	8	yes	complemented
337	C₄⋊Q₈	C₂×Dic₄₃	1	8	yes	complemented
338	#125	C₂×Dic₄₃	1	16	yes	complemented
339	C₂²⋊Q₈	C₂×Dic₄₃	1	16	yes	—
340	C₂²⋊Q₈	C₂×Dic₄₃	1	16	yes	—
341	C₄×Q₈	—	172	8	no	—
342	C₄×Q₈	C₂×Dic₄₃	1	16	yes	complemented
343	C₄×Q₈	C₂×Dic₄₃	1	16	yes	complemented
344	#117	—	86	8	no	—
345	#117	C₂×Dic₄₃	1	16	yes	—
346	C₂×C₄⋊C₄	—	43	8	no	—
347	C₂×C₄⋊C₄	—	43	2	no	—
348	C₂×C₄⋊C₄	—	43	2	no	—
349	C₂×C₄⋊C₄	—	43	2	no	—
350	C₂×C₄⋊C₄	—	43	2	no	—
351	C₂×C₄⋊C₄	—	43	2	no	—
352	C₂×C₄⋊C₄	—	43	2	no	—
353	C₂×C₄⋊C₄	—	43	2	no	—
354	C₂×C₄⋊C₄	—	43	2	no	—
355	C₂×C₄⋊C₄	—	43	8	no	—
356	C₂×C₄⋊C₄	—	43	2	no	—
357	C₂×C₄⋊C₄	—	43	2	no	—
358	C₂×C₄⋊C₄	—	43	8	no	—
359	C₂×C₄⋊C₄	—	86	4	no	—
360	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
361	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
362	C₂×C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
363	C₂×C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
364	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
365	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
366	C₂×C₂²⋊C₄	—	43	4	no	—
367	C₂×C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
368	C₂×C₄²	—	43	4	no	—
369	C₂×C₄²	—	43	4	no	—
370	C₂×C₄²	—	43	8	no	—
371	C₂×C₄²	—	43	8	no	—
372	C₂×C₄²	—	43	4	no	—
373	C₂×C₄²	—	172	4	no	—
374	C₂×C₄²	C₂×Dic₄₃	1	8	yes	—
375	C₂×C₄²	C₂²×D₄₃	1	4	yes	—
376	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
377	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
378	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
379	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
380	#95	—	43	4	no	—
381	#95	—	43	4	no	—
382	#95	—	43	8	no	—
383	#95	—	43	8	no	—
384	#95	—	43	4	no	—
385	#95	—	43	4	no	—
386	#95	—	43	8	no	—
387	#95	—	43	8	no	—
388	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
389	C₂×Q₈	—	2	4	no	—
390	C₂×Q₈	—	2	4	no	—
391	C₂×Q₈	—	4	2	no	—
392	C₂×Q₈	—	4	2	no	—
393	C₂×Q₈	C₂²×Dic₄₃	1	8	yes	—
394	C₂×Q₈	C₂²×Dic₄₃	1	8	yes	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	4	1	no	—
398	C₂²×C₄	—	4	1	no	—
399	C₂²×C₄	—	43	4	no	—
400	C₂²×C₄	—	43	8	no	—
401	C₂²×C₄	—	43	4	no	—
402	C₂²×C₄	—	43	4	no	—
403	C₂²×C₄	—	43	4	no	—
404	C₂²×C₄	—	86	4	no	—
405	C₂²×C₄	—	172	2	no	—
406	C₂²×C₄	—	172	2	no	—
407	C₂²×C₄	—	172	2	no	—
408	C₂²×C₄	—	172	2	no	—
409	C₂²×C₄	Q₈×D₄₃	1	4	yes	—
410	C₂²×C₄	#10621902	1	4	yes	—
411	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
412	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
413	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
414	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
415	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
416	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
417	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
418	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
419	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
420	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
421	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
422	C₄⋊C₄	—	43	8	no	—
423	C₄⋊C₄	—	43	8	no	—
424	C₄⋊C₄	—	86	4	no	—
425	C₄⋊C₄	—	86	4	no	—
426	C₄⋊C₄	—	86	4	no	—
427	C₄⋊C₄	—	86	4	no	—
428	C₄⋊C₄	—	86	4	no	—
429	C₄⋊C₄	—	86	4	no	—
430	C₄⋊C₄	—	172	8	no	—
431	C₄⋊C₄	—	172	2	no	—
432	C₄⋊C₄	—	172	2	no	—
433	C₄⋊C₄	—	172	8	no	—
434	C₄⋊C₄	C₂²×Dic₄₃	1	8	yes	—
435	C₄⋊C₄	C₂²×Dic₄₃	1	8	yes	—
436	C₄⋊C₄	C₂²×Dic₄₃	1	16	yes	—
437	C₄⋊C₄	C₂²×Dic₄₃	1	16	yes	—
438	C₄⋊C₄	C₂²×Dic₄₃	1	8	yes	—
439	C₄⋊C₄	C₂²×Dic₄₃	1	8	yes	—
440	C₂²⋊C₄	—	86	8	no	—
441	C₂²⋊C₄	C₂²×Dic₄₃	1	16	yes	—
442	C₄²	—	86	8	no	—
443	C₄²	—	86	8	no	—
444	C₄²	—	172	4	no	—
445	C₄²	—	172	8	no	—
446	C₄²	—	172	8	no	—
447	C₄²	C₂²×Dic₄₃	1	4	yes	—
448	C₄²	C₂²×Dic₄₃	1	4	yes	—
449	C₄²	C₂²×Dic₄₃	1	4	yes	—
450	C₄²	C₂²×Dic₄₃	1	4	yes	—
451	C₄²	C₂²×Dic₄₃	1	16	yes	—
452	C₂³	—	2	1	no	—
453	C₂³	—	2	1	no	—
454	C₂³	—	2	1	no	—
455	C₂³	—	2	1	no	—
456	C₂³	C₂³×Dic₄₃	1	2	yes	—
457	C₂³	C₂×Q₈×D₄₃	1	2	yes	—
458	C₂³	C₂×#10621902	1	2	yes	—
459	C₂³	C₂⁴×D₄₃	1	1	yes	characteristic
460	Q₈	—	2	16	no	—
461	Q₈	—	4	8	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	8	no	—
473	C₂×C₄	—	4	4	no	—
474	C₂×C₄	—	43	8	no	—
475	C₂×C₄	—	86	4	no	—
476	C₂×C₄	—	86	4	no	—
477	C₂×C₄	—	86	4	no	—
478	C₂×C₄	—	86	4	no	—
479	C₂×C₄	—	86	4	no	—
480	C₂×C₄	—	86	4	no	—
481	C₂×C₄	—	86	4	no	—
482	C₂×C₄	—	86	4	no	—
483	C₂×C₄	—	86	4	no	—
484	C₂×C₄	—	86	4	no	—
485	C₂×C₄	—	86	4	no	—
486	C₂×C₄	—	172	8	no	—
487	C₂×C₄	—	172	8	no	—
488	C₂×C₄	Q₈×Dic₄₃	1	16	yes	complemented
489	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
490	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
491	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
492	C₂×C₄	C₂³×Dic₄₃	1	8	yes	—
493	C₂×C₄	C₂³×Dic₄₃	1	8	yes	—
494	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
495	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
496	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
497	C₂×C₄	C₂×Q₈×D₄₃	1	2	yes	—
498	C₂×C₄	C₂×Q₈×D₄₃	1	2	yes	—
499	C₂×C₄	C₂×#10621902	1	2	yes	—
500	C₂×C₄	C₂×#10621902	1	2	yes	—
501	C₂×C₄	#13063371	1	2	yes	—
502	C₂×C₄	#13063372	1	2	yes	—
503	C₂²	—	2	2	no	—
504	C₂²	—	2	2	no	—
505	C₂²	—	2	2	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	2	2	no	—
509	C₂²	C₂×Q₈×Dic₄₃	1	4	yes	—
510	C₂²	C₂⁴×Dic₄₃	1	1	yes	characteristic
511	C₂²	C₂²×Q₈×D₄₃	1	1	yes	characteristic
512	C₂²	C₂²×#10621902	1	1	yes	characteristic
513	C₂²	C₂×#13063371	1	1	yes	characteristic
514	C₂²	C₂×#13063372	1	1	yes	characteristic
515	C₂²	#14583735	1	1	yes	characteristic
516	C₂²	#14583735	1	1	yes	characteristic
517	C₄	—	2	2	no	—
518	C₄	—	2	8	no	—
519	C₄	—	2	2	no	—
520	C₄	—	2	2	no	—
521	C₄	—	2	8	no	—
522	C₄	—	86	8	no	—
523	C₄	—	172	4	no	—
524	C₄	—	172	4	no	—
525	C₄	—	172	4	no	—
526	C₄	C₂×Q₈×Dic₄₃	1	4	yes	—
527	C₄	C₂×Q₈×Dic₄₃	1	4	yes	—
528	C₄	#14583382	1	4	yes	—
529	C₂	—	2	4	no	—
530	C₂	C₂²×Q₈×Dic₄₃	1	1	yes	characteristic
531	C₂	C₂×#14583382	1	1	yes	characteristic
532	C₂	#19147798	1	1	yes	characteristic
533	C₂	#19148396	1	1	yes	characteristic
534	C₂	#19148400	1	1	yes	characteristic
535	C₂	#19148449	1	1	yes	characteristic
536	C₂	#19148462	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₄₃
commutator	C₂²×C₄₃	C₂⁴×C₄
Fitting	C₂×C₄₃×#533	C₂
socle, cosocle	C₂³×C₄₃	C₂⁵
prime radical	C₂⁴×C₄₃	C₂⁴
hypercenter	C₂×#533	D₄₃
hypocenter	C₄₃	#34213
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×#533

Complements

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

N	H ≅ G/N	type
1. #19137695	C₂	semidirect
2. #19137685	C₂	semidirect
3. #19137655	C₂	semidirect
4. #19137552	C₂	semidirect
5. #19137552	C₂	semidirect
6. Q₈×C₄⋊Dic₄₃	C₂	semidirect
50. C₄₃×#533	C₄	semidirect
65. C₂×C₄⋊Dic₄₃	Q₈	semidirect
98. C₄⋊Q₈×C₄₃	C₂×C₄	semidirect
99. C₄⋊Q₈×C₄₃	C₂×C₄	semidirect
100. #125×C₄₃	C₂×C₄	semidirect
103. C₄×Q₈×C₄₃	C₂×C₄	semidirect
104. C₄×Q₈×C₄₃	C₂×C₄	semidirect
205. C₂×C₄×C₄₃	C₄×Q₈	semidirect
282. #533	Dic₄₃	semidirect
328. C₄₃	#34213	semidirect
336. C₄⋊Q₈	C₂×Dic₄₃	semidirect
337. C₄⋊Q₈	C₂×Dic₄₃	semidirect
338. #125	C₂×Dic₄₃	semidirect
342. C₄×Q₈	C₂×Dic₄₃	semidirect
343. C₄×Q₈	C₂×Dic₄₃	semidirect
488. C₂×C₄	Q₈×Dic₄₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#19137695	2
#19137685	2
#19137655	2
#19137552	2
Q₈×C₄⋊Dic₄₃	2
#19137330	2
#19137218	2
C₂²⋊Q₈×Dic₄₃	2
#19137002	2
#19136951	2
C₂×C₄×C₄⋊Dic₄₃	2
C₂×C₄₃×#533	2
#34213	43