Subgroups — #25064933

Order 11008.

1298 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582952	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14582923	C₂	1	1	yes	maximal, characteristic, complemented
3	#19133272	C₂	1	4	yes	maximal, complemented
4	#19133267	C₂	1	2	yes	maximal, complemented
5	#19133263	C₂	1	2	yes	maximal, complemented
6	#19133244	C₂	1	4	yes	maximal, complemented
7	C₂×C₄₃×#532	C₂	1	1	yes	maximal, characteristic
8	C₂²×#10621877	—	2	1	no	—
9	#14582952	—	2	1	no	—
10	#14582952	—	2	1	no	—
11	#14582952	C₂²	1	2	yes	—
12	#14582952	C₂²	1	2	yes	complemented
13	#14582923	—	2	1	no	—
14	#14582923	—	2	1	no	—
15	#14582923	C₂²	1	2	yes	—
16	#14582923	C₂²	1	2	yes	complemented
17	C₂×C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
18	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	complemented
19	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	complemented
20	C₂×C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
21	C₂×C₄×C₄₃⋊C₈	—	2	1	no	—
22	#14582645	C₂²	1	8	yes	complemented
23	#14582643	C₂²	1	8	yes	complemented
24	C₂²×#41×C₄₃	—	2	1	no	—
25	C₄₃×#532	—	2	1	no	—
26	C₄₃×#532	—	2	1	no	—
27	C₄₃×#532	—	2	1	no	—
28	C₄₃×#532	—	2	1	no	—
29	C₄₃×#532	C₄	1	2	yes	—
30	C₄₃×#532	C₄	1	2	yes	—
31	C₄₃×#532	C₂²	1	2	yes	—
32	C₄₃×#532	C₂²	1	2	yes	—
33	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
34	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
35	C₂×#124×C₄₃	—	2	1	no	—
36	C₂×#121×C₄₃	—	2	1	no	—
37	C₂×#121×C₄₃	C₄	1	2	yes	—
38	C₂×C₄×D₄×C₄₃	—	2	1	no	—
39	C₂×C₄×D₄×C₄₃	C₄	1	2	yes	—
40	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
41	C₂×#10621877	—	2	2	no	—
42	C₂×#10621877	—	2	2	no	—
43	C₂×#10621877	—	4	4	no	—
44	C₂²×C₄₃⋊C₈	—	2	2	no	—
45	C₂²×C₄₃⋊C₈	—	2	2	no	—
46	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
47	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
48	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
49	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
50	C₄⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
51	C₄⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
52	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
53	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
54	C₄×C₄₃⋊C₈	—	2	2	no	—
55	C₄×C₄₃⋊C₈	—	2	2	no	—
56	C₂×#41×C₄₃	—	2	2	no	—
57	C₂×#41×C₄₃	—	2	2	no	—
58	C₂×#41×C₄₃	—	2	2	no	—
59	C₂×#41×C₄₃	—	2	2	no	—
60	C₂×#41×C₄₃	—	4	4	no	—
61	C₂×#41×C₄₃	—	4	4	no	—
62	C₂²×Q₈×C₄₃	—	2	1	no	—
63	C₂²×D₄×C₄₃	—	2	2	no	—
64	C₂²×D₄×C₄₃	—	2	1	no	—
65	C₂²×D₄×C₄₃	—	2	1	no	—
66	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
67	C₂³×C₄×C₄₃	—	2	2	no	—
68	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
69	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
70	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
71	C₄⋊Q₈×C₄₃	—	2	1	no	—
72	C₄⋊Q₈×C₄₃	—	2	1	no	—
73	C₄⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
74	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
75	#127×C₄₃	—	2	1	no	—
76	#127×C₄₃	—	2	1	no	—
77	#127×C₄₃	C₂×C₄	1	2	yes	—
78	#127×C₄₃	C₂³	1	2	yes	—
79	#124×C₄₃	—	2	2	no	—
80	#124×C₄₃	—	2	2	no	—
81	#124×C₄₃	—	2	2	no	—
82	#124×C₄₃	—	2	2	no	—
83	#121×C₄₃	—	2	2	no	—
84	#121×C₄₃	—	2	2	no	—
85	#121×C₄₃	—	2	2	no	—
86	#121×C₄₃	—	2	2	no	—
87	#121×C₄₃	—	2	2	no	—
88	#121×C₄₃	—	2	2	no	—
89	#121×C₄₃	C₂×C₄	1	4	yes	—
90	#121×C₄₃	C₂×C₄	1	4	yes	—
91	C₄×D₄×C₄₃	—	2	2	no	—
92	C₄×D₄×C₄₃	—	2	2	no	—
93	C₄×D₄×C₄₃	—	2	2	no	—
94	C₄×D₄×C₄₃	—	2	2	no	—
95	C₄×D₄×C₄₃	—	2	2	no	—
96	C₄×D₄×C₄₃	—	2	2	no	—
97	C₄×D₄×C₄₃	C₂×C₄	1	4	yes	—
98	C₄×D₄×C₄₃	C₂×C₄	1	4	yes	—
99	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
100	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
101	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
102	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
103	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
104	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
105	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
106	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
107	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
108	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
110	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
111	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
112	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
115	C₂⁴×C₄₃	—	2	2	no	—
116	C₂⁴×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
117	#41×C₄₃	—	4	8	no	—
118	#41×C₄₃	—	4	8	no	—
119	#41×C₄₃	—	4	4	no	—
120	#41×C₄₃	—	4	4	no	—
121	#41×C₄₃	—	4	4	no	—
122	#41×C₄₃	—	4	4	no	—
123	C₂×Q₈×C₄₃	—	2	2	no	—
124	C₂×Q₈×C₄₃	—	2	2	no	—
125	C₂×Q₈×C₄₃	—	4	2	no	—
126	C₂×Q₈×C₄₃	—	4	2	no	—
127	C₂×D₄×C₄₃	—	2	2	no	—
128	C₂×D₄×C₄₃	—	2	2	no	—
129	C₂×D₄×C₄₃	—	2	2	no	—
130	C₂×D₄×C₄₃	—	2	2	no	—
131	C₂×D₄×C₄₃	—	2	2	no	—
132	C₂×D₄×C₄₃	—	2	4	no	—
133	C₂×D₄×C₄₃	—	2	4	no	—
134	C₂×D₄×C₄₃	—	4	4	no	—
135	C₂×D₄×C₄₃	—	4	4	no	—
136	C₂×D₄×C₄₃	—	4	2	no	—
137	C₂×D₄×C₄₃	—	4	2	no	—
138	C₂×D₄×C₄₃	—	4	8	no	—
139	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
140	C₂²×C₄×C₄₃	—	2	4	no	—
141	C₂²×C₄×C₄₃	—	2	4	no	—
142	C₂²×C₄×C₄₃	—	2	2	no	—
143	C₂²×C₄×C₄₃	—	4	2	no	—
144	C₂²×C₄×C₄₃	—	4	2	no	—
145	C₂²×C₄×C₄₃	—	4	8	no	—
146	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
148	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
150	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
151	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
153	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
154	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
155	C₂²×C₄×C₄₃	D₈	1	4	yes	—
156	C₂²×C₄×C₄₃	SD₁₆	1	4	yes	—
157	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
166	C₄⋊C₄×C₄₃	—	2	2	no	—
167	C₄⋊C₄×C₄₃	—	2	2	no	—
168	C₄⋊C₄×C₄₃	—	2	2	no	—
169	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
170	C₂²⋊C₄×C₄₃	—	2	4	no	—
171	C₂²⋊C₄×C₄₃	—	2	4	no	—
172	C₂²⋊C₄×C₄₃	—	2	4	no	—
173	C₂²⋊C₄×C₄₃	—	2	4	no	—
174	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
175	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
176	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
177	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
178	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
179	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
180	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
181	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
182	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
183	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
184	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
185	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
186	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
187	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
189	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
190	#10621877	—	4	4	no	—
191	#10621877	—	4	4	no	—
192	C₂×C₄₃⋊C₈	—	2	4	no	—
193	C₂×C₄₃⋊C₈	—	2	4	no	—
194	C₂×C₄₃⋊C₈	—	4	4	no	—
195	C₂×C₄₃⋊C₈	—	4	4	no	—
196	C₂³×C₄₃	—	2	4	no	—
197	C₂³×C₄₃	—	4	1	no	—
198	C₂³×C₄₃	—	4	1	no	—
199	C₂³×C₄₃	—	4	4	no	—
200	C₂³×C₄₃	—	4	4	no	—
201	C₂³×C₄₃	—	4	4	no	—
202	C₂³×C₄₃	#102	1	4	yes	—
203	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
204	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	Q₈×C₄₃	—	4	2	no	—
207	Q₈×C₄₃	—	4	2	no	—
208	Q₈×C₄₃	—	4	4	no	—
209	D₄×C₄₃	—	4	4	no	—
210	D₄×C₄₃	—	4	4	no	—
211	D₄×C₄₃	—	4	8	no	—
212	D₄×C₄₃	—	4	8	no	—
213	D₄×C₄₃	—	4	2	no	—
214	D₄×C₄₃	—	4	2	no	—
215	D₄×C₄₃	—	4	4	no	—
216	D₄×C₄₃	—	4	4	no	—
217	D₄×C₄₃	—	4	4	no	—
218	C₂×C₄×C₄₃	—	2	2	no	—
219	C₂×C₄×C₄₃	—	2	2	no	—
220	C₂×C₄×C₄₃	—	2	2	no	—
221	C₂×C₄×C₄₃	—	2	2	no	—
222	C₂×C₄×C₄₃	—	2	2	no	—
223	C₂×C₄×C₄₃	—	2	2	no	—
224	C₂×C₄×C₄₃	—	2	4	no	—
225	C₂×C₄×C₄₃	—	4	1	no	—
226	C₂×C₄×C₄₃	—	4	1	no	—
227	C₂×C₄×C₄₃	—	4	1	no	—
228	C₂×C₄×C₄₃	—	4	1	no	—
229	C₂×C₄×C₄₃	—	4	1	no	—
230	C₂×C₄×C₄₃	—	4	1	no	—
231	C₂×C₄×C₄₃	—	4	4	no	—
232	C₂×C₄×C₄₃	—	4	8	no	—
233	C₂×C₄×C₄₃	—	4	8	no	—
234	C₂×C₄×C₄₃	#102	1	4	yes	—
235	C₂×C₄×C₄₃	#102	1	4	yes	—
236	C₂×C₄×C₄₃	#102	1	4	yes	—
237	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
238	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
247	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
248	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
249	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
250	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
251	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
252	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
253	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
255	C₄₃⋊C₈	—	4	4	no	—
256	C₄₃⋊C₈	—	4	4	no	—
257	#17704	—	43	1	no	maximal, Sylow
258	C₂²×C₄₃	—	2	1	no	—
259	C₂²×C₄₃	—	2	1	no	—
260	C₂²×C₄₃	—	2	1	no	—
261	C₂²×C₄₃	—	2	1	no	—
262	C₂²×C₄₃	—	2	1	no	—
263	C₂²×C₄₃	—	2	1	no	—
264	C₂²×C₄₃	—	4	4	no	—
265	C₂²×C₄₃	—	4	4	no	—
266	C₂²×C₄₃	—	4	4	no	—
267	C₂²×C₄₃	—	4	4	no	—
268	C₂²×C₄₃	—	8	8	no	—
269	C₂²×C₄₃	C₂×#102	1	2	yes	—
270	C₂²×C₄₃	C₂×#102	1	2	yes	—
271	C₂²×C₄₃	C₂×#102	1	2	yes	—
272	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
273	C₄×C₄₃	—	2	1	no	—
274	C₄×C₄₃	—	2	1	no	—
275	C₄×C₄₃	—	2	1	no	—
276	C₄×C₄₃	—	2	1	no	—
277	C₄×C₄₃	—	2	1	no	—
278	C₄×C₄₃	—	2	1	no	—
279	C₄×C₄₃	—	4	4	no	—
280	C₄×C₄₃	#413	1	2	yes	—
281	C₄×C₄₃	C₂×#102	1	2	yes	—
282	C₄×C₄₃	C₂×#102	1	2	yes	—
283	C₄×C₄₃	C₂×#102	1	2	yes	—
284	C₄×C₄₃	C₂²×D₈	1	1	yes	characteristic
285	C₄×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
286	C₄×C₄₃	#575	1	2	yes	—
287	C₂×#532	D₄₃	1	1	yes	characteristic
288	C₂×#431	—	43	1	no	—
289	C₂×#423	—	43	1	no	—
290	#1547	—	43	4	no	—
291	#1546	—	43	2	no	—
292	#1545	—	43	2	no	—
293	#1540	—	43	4	no	—
294	C₂×C₄₃	—	2	2	no	—
295	C₂×C₄₃	—	2	2	no	—
296	C₂×C₄₃	—	2	2	no	—
297	C₂×C₄₃	—	8	4	no	—
298	C₂×C₄₃	C₂×#413	1	1	yes	characteristic
299	C₂×C₄₃	C₂²×#102	1	1	yes	characteristic
300	C₂×C₄₃	#2896	1	1	yes	characteristic
301	C₂²×#41	—	2	1	no	—
302	C₂²×M₁₆	—	86	1	no	—
303	#532	—	2	1	no	—
304	#532	—	2	1	no	—
305	#532	—	2	1	no	—
306	#532	—	2	1	no	—
307	#532	Dic₄₃	1	2	yes	—
308	#532	Dic₄₃	1	2	yes	—
309	#532	C₂×D₄₃	1	2	yes	—
310	#532	C₂×D₄₃	1	2	yes	—
311	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
312	C₂×#127	C₂×D₄₃	1	1	yes	characteristic
313	C₂×#124	—	2	1	no	—
314	C₂×#121	—	2	1	no	—
315	C₂×#121	Dic₄₃	1	2	yes	—
316	C₂×C₄×D₄	—	2	1	no	—
317	C₂×C₄×D₄	Dic₄₃	1	2	yes	—
318	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
319	#431	—	43	2	no	—
320	#431	—	43	2	no	—
321	#431	—	86	1	no	—
322	#431	—	86	1	no	—
323	#423	—	43	2	no	—
324	#423	—	43	2	no	—
325	#423	—	86	1	no	—
326	#423	—	86	1	no	—
327	C₂×C₄⋊C₈	—	43	2	no	—
328	C₂×C₄⋊C₈	—	43	2	no	—
329	C₂×C₄⋊C₈	—	86	1	no	—
330	C₂×C₂²⋊C₈	—	86	1	no	—
331	C₂×C₄×C₈	—	86	1	no	—
332	#332	—	43	8	no	—
333	#331	—	43	8	no	—
334	C₄₃	#17704	1	1	yes	characteristic, complemented, Sylow
335	C₂×#41	—	2	2	no	—
336	C₂×#41	—	2	2	no	—
337	C₂×#41	—	2	2	no	—
338	C₂×#41	—	2	2	no	—
339	C₂×#41	—	4	4	no	—
340	C₂×#41	—	4	4	no	—
341	C₂²×Q₈	—	2	1	no	—
342	C₂²×D₄	—	2	2	no	—
343	C₂²×D₄	—	2	1	no	—
344	C₂²×D₄	—	2	1	no	—
345	C₂²×D₄	C₂×Dic₄₃	1	2	yes	—
346	C₂³×C₄	—	2	2	no	—
347	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
348	C₂³×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
349	C₂³×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
350	C₂×M₁₆	—	86	2	no	—
351	C₂×M₁₆	—	86	2	no	—
352	C₂×M₁₆	—	172	4	no	—
353	C₂²×C₈	—	86	2	no	—
354	C₂²×C₈	—	86	2	no	—
355	C₄⋊Q₈	—	2	1	no	—
356	C₄⋊Q₈	—	2	1	no	—
357	C₄⋊Q₈	C₂×Dic₄₃	1	2	yes	—
358	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
359	#127	—	2	1	no	—
360	#127	—	2	1	no	—
361	#127	C₂×Dic₄₃	1	2	yes	—
362	#127	C₂²×D₄₃	1	2	yes	—
363	#124	—	2	2	no	—
364	#124	—	2	2	no	—
365	#124	—	2	2	no	—
366	#124	—	2	2	no	—
367	#121	—	2	2	no	—
368	#121	—	2	2	no	—
369	#121	—	2	2	no	—
370	#121	—	2	2	no	—
371	#121	—	2	2	no	—
372	#121	—	2	2	no	—
373	#121	C₂×Dic₄₃	1	4	yes	—
374	#121	C₂×Dic₄₃	1	4	yes	—
375	C₄×D₄	—	2	2	no	—
376	C₄×D₄	—	2	2	no	—
377	C₄×D₄	—	2	2	no	—
378	C₄×D₄	—	2	2	no	—
379	C₄×D₄	—	2	2	no	—
380	C₄×D₄	—	2	2	no	—
381	C₄×D₄	C₂×Dic₄₃	1	4	yes	—
382	C₄×D₄	C₂×Dic₄₃	1	4	yes	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
385	C₂×C₂²⋊C₄	—	2	2	no	—
386	C₂×C₂²⋊C₄	—	2	2	no	—
387	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
388	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
389	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
390	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
391	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
392	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
393	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
394	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
395	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
396	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
397	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
398	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
399	C₄⋊C₈	—	43	4	no	—
400	C₄⋊C₈	—	43	4	no	—
401	C₄⋊C₈	—	86	2	no	—
402	C₄⋊C₈	—	86	2	no	—
403	C₄⋊C₈	—	86	2	no	—
404	C₄⋊C₈	—	86	2	no	—
405	C₂²⋊C₈	—	86	2	no	—
406	C₂²⋊C₈	—	86	2	no	—
407	C₄×C₈	—	86	2	no	—
408	C₄×C₈	—	86	2	no	—
409	C₂⁴	—	2	2	no	—
410	C₂⁴	C₂²⋊Dic₄₃	1	1	yes	characteristic
411	#41	—	4	8	no	—
412	#41	—	4	8	no	—
413	#41	—	4	4	no	—
414	#41	—	4	4	no	—
415	#41	—	4	4	no	—
416	#41	—	4	4	no	—
417	C₂×Q₈	—	2	2	no	—
418	C₂×Q₈	—	2	2	no	—
419	C₂×Q₈	—	4	2	no	—
420	C₂×Q₈	—	4	2	no	—
421	C₂×D₄	—	2	4	no	—
422	C₂×D₄	—	2	4	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	4	4	no	—
429	C₂×D₄	—	4	4	no	—
430	C₂×D₄	—	4	8	no	—
431	C₂×D₄	—	4	2	no	—
432	C₂×D₄	—	4	2	no	—
433	C₂×D₄	C₂²×Dic₄₃	1	4	yes	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	4	2	no	—
438	C₂²×C₄	—	4	2	no	—
439	C₂²×C₄	—	4	8	no	—
440	C₂²×C₄	#10621882	1	4	yes	—
441	C₂²×C₄	#10621883	1	4	yes	—
442	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
443	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
444	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
445	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
446	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
447	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
448	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
449	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
450	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
451	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
452	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
453	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
454	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
455	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
456	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
457	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
458	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
459	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
460	M₁₆	—	172	4	no	—
461	M₁₆	—	172	4	no	—
462	C₂×C₈	—	86	4	no	—
463	C₂×C₈	—	86	4	no	—
464	C₂×C₈	—	172	4	no	—
465	C₂×C₈	—	172	4	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	C₂²×Dic₄₃	1	4	yes	—
470	C₂²⋊C₄	—	2	4	no	—
471	C₂²⋊C₄	—	2	4	no	—
472	C₂²⋊C₄	—	2	4	no	—
473	C₂²⋊C₄	—	2	4	no	—
474	C₄²	C₂²⋊Dic₄₃	1	1	yes	characteristic
475	C₄²	C₂²⋊Dic₄₃	1	1	yes	characteristic
476	C₄²	C₂²⋊Dic₄₃	1	1	yes	characteristic
477	C₄²	C₂²⋊Dic₄₃	1	1	yes	characteristic
478	C₄²	C₂²⋊Dic₄₃	1	1	yes	characteristic
479	C₄²	C₂²⋊Dic₄₃	1	1	yes	characteristic
480	C₄²	C₂²×Dic₄₃	1	1	yes	characteristic
481	C₄²	C₂²×Dic₄₃	1	1	yes	characteristic
482	C₄²	C₂²×Dic₄₃	1	1	yes	characteristic
483	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
484	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
485	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
486	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
487	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
488	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
489	C₄²	C₂³×D₄₃	1	1	yes	characteristic
490	C₂³	—	2	4	no	—
491	C₂³	—	4	1	no	—
492	C₂³	—	4	1	no	—
493	C₂³	—	4	4	no	—
494	C₂³	—	4	4	no	—
495	C₂³	—	4	4	no	—
496	C₂³	#13063246	1	4	yes	—
497	C₂³	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
498	C₂³	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
499	C₂³	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
500	Q₈	—	4	4	no	—
501	Q₈	—	4	2	no	—
502	Q₈	—	4	2	no	—
503	D₄	—	4	4	no	—
504	D₄	—	4	4	no	—
505	D₄	—	4	8	no	—
506	D₄	—	4	8	no	—
507	D₄	—	4	4	no	—
508	D₄	—	4	4	no	—
509	D₄	—	4	2	no	—
510	D₄	—	4	2	no	—
511	D₄	—	4	4	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	4	no	—
526	C₂×C₄	—	4	8	no	—
527	C₂×C₄	—	4	8	no	—
528	C₂×C₄	#13063246	1	4	yes	—
529	C₂×C₄	#13063246	1	4	yes	—
530	C₂×C₄	#13063246	1	4	yes	—
531	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
532	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
533	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
534	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
535	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
536	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
537	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
538	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
539	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
540	C₂×C₄	C₂×#10621882	1	2	yes	—
541	C₂×C₄	C₂×#10621882	1	2	yes	—
542	C₂×C₄	C₂×#10621882	1	2	yes	—
543	C₂×C₄	C₂×#10621883	1	2	yes	—
544	C₂×C₄	C₂×#10621883	1	2	yes	—
545	C₂×C₄	C₂×#10621883	1	2	yes	—
546	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
547	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
548	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
549	C₈	—	172	4	no	—
550	C₈	—	172	4	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	2	1	no	—
556	C₂²	—	2	1	no	—
557	C₂²	—	4	4	no	—
558	C₂²	—	4	4	no	—
559	C₂²	—	4	4	no	—
560	C₂²	—	4	4	no	—
561	C₂²	—	8	8	no	—
562	C₂²	C₂×#13063246	1	2	yes	—
563	C₂²	C₂×#13063246	1	2	yes	—
564	C₂²	C₂×#13063246	1	2	yes	—
565	C₂²	C₂²×C₂²⋊Dic₄₃	1	1	yes	characteristic
566	C₄	—	2	1	no	—
567	C₄	—	2	1	no	—
568	C₄	—	2	1	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	1	no	—
572	C₄	—	4	4	no	—
573	C₄	#14582883	1	2	yes	—
574	C₄	C₂×#13063246	1	2	yes	—
575	C₄	C₂×#13063246	1	2	yes	—
576	C₄	C₂×#13063246	1	2	yes	—
577	C₄	C₂²×#10621882	1	1	yes	characteristic
578	C₄	C₂²×#10621883	1	1	yes	characteristic
579	C₄	#14583697	1	2	yes	—
580	C₂	—	2	2	no	—
581	C₂	—	2	2	no	—
582	C₂	—	2	2	no	—
583	C₂	—	8	4	no	—
584	C₂	C₂×#14582883	1	1	yes	characteristic
585	C₂	C₂²×#13063246	1	1	yes	characteristic
586	C₂	#19143114	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊Dic₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting, prime radical	C₂×C₄₃×#532	C₂
socle	C₂²×C₄₃	C₂²×C₂²⋊C₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	C₂×#532	D₄₃
hypocenter	C₄₃	#17704
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. C₂×#14582952	C₂	semidirect
2. C₂×#14582923	C₂	semidirect
3. #19133272	C₂	semidirect
4. #19133267	C₂	semidirect
5. #19133263	C₂	semidirect
6. #19133244	C₂	semidirect
12. #14582952	C₂²	semidirect
16. #14582923	C₂²	semidirect
18. C₂×C₄⋊(C₄₃⋊C₈)	C₂²	semidirect
19. C₂×C₄⋊(C₄₃⋊C₈)	C₂²	semidirect
22. #14582645	C₂²	semidirect
23. #14582643	C₂²	semidirect
334. C₄₃	#17704	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582952	2
C₂×#14582923	2
#19133272	2
#19133267	2
#19133263	2
#19133244	2
C₂×C₄₃×#532	2
#17704	43