Subgroups — #25004112

Order 11008.

950 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582948	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#13063241	C₂	1	1	yes	maximal, characteristic
3	C₂²×#13063241	C₂	1	1	yes	maximal, characteristic
4	C₂²×#13063241	C₂	1	1	yes	maximal, characteristic
5	#19134321	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄₃⋊#338	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1738	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₁₇₂	C₂²	1	1	yes	characteristic
9	C₂²×#10621877	C₂²	1	1	yes	characteristic
10	C₂²×#10621877	C₂²	1	1	yes	characteristic
11	C₂²×#10621877	C₂²	1	1	yes	characteristic
12	#14582948	—	2	2	no	—
13	#14582948	—	2	2	no	—
14	C₂×#13063261	—	2	2	no	—
15	C₂×#13063241	—	2	2	no	—
16	C₂×#13063241	—	2	2	no	—
17	C₂×#13063241	—	2	2	no	—
18	C₂×#13063241	—	2	2	no	—
19	C₂×#13063241	—	2	2	no	—
20	C₂×#13063241	—	2	2	no	—
21	C₂×#13063241	—	2	2	no	—
22	C₂×#13063241	—	2	2	no	—
23	C₂×#13063241	C₄	1	4	yes	—
24	#14582663	—	2	2	no	—
25	C₄₃⋊#338	—	2	2	no	—
26	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
27	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
28	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
29	C₄₃×#341	—	2	2	no	—
30	C₂⁴×D₄₃	Q₈	1	2	yes	—
31	C₂²×D₁₇₂	—	2	1	no	—
32	C₂²×D₁₇₂	—	2	1	no	—
33	C₂²×D₁₇₂	—	2	1	no	—
34	C₂²×D₁₇₂	—	2	1	no	—
35	C₂²×D₁₇₂	—	2	1	no	—
36	C₂²×D₁₇₂	—	2	1	no	—
37	C₂²×D₁₇₂	—	2	1	no	—
38	C₂²×D₁₇₂	—	2	1	no	—
39	C₂²×D₁₇₂	—	2	1	no	—
40	C₂²×D₁₇₂	—	2	1	no	—
41	C₂²×D₁₇₂	—	2	1	no	—
42	C₂²×D₁₇₂	—	2	1	no	—
43	C₂²×D₁₇₂	C₂×C₄	1	2	yes	—
44	C₂²×D₁₇₂	D₄	1	2	yes	—
45	C₂×#10621877	—	2	1	no	—
46	C₂×#10621877	—	2	1	no	—
47	C₂×#10621877	—	2	1	no	—
48	C₂×#10621877	—	2	1	no	—
49	C₂×#10621877	—	2	1	no	—
50	C₂×#10621877	—	2	1	no	—
51	C₂×#10621877	—	2	1	no	—
52	C₂×#10621877	—	2	1	no	—
53	C₂×#10621877	—	2	1	no	—
54	C₂×#10621877	—	2	1	no	—
55	C₂×#10621877	—	2	1	no	—
56	C₂×#10621877	—	2	1	no	—
57	C₂×#10621877	—	2	1	no	—
58	C₂×#10621877	—	2	1	no	—
59	C₂×#10621877	—	2	1	no	—
60	C₂×#10621877	C₂×C₄	1	2	yes	—
61	C₂×#10621877	D₄	1	2	yes	—
62	C₂×#10621877	D₄	1	2	yes	—
63	C₂²×C₄₃⋊C₈	—	2	1	no	—
64	C₂²×C₄₃⋊C₈	—	2	1	no	—
65	C₂²×C₄₃⋊C₈	—	2	1	no	—
66	#13063261	—	2	8	no	—
67	#13063241	—	2	8	no	—
68	#13063241	—	2	8	no	—
69	#13063241	—	2	8	no	—
70	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
71	C₂×M₁₆×C₄₃	—	2	1	no	—
72	C₂×M₁₆×C₄₃	—	2	1	no	—
73	C₂×M₁₆×C₄₃	—	2	1	no	—
74	C₂×M₁₆×C₄₃	—	2	1	no	—
75	C₂×M₁₆×C₄₃	—	2	1	no	—
76	C₂×M₁₆×C₄₃	—	2	1	no	—
77	C₂×M₁₆×C₄₃	—	2	1	no	—
78	C₂×M₁₆×C₄₃	—	2	1	no	—
79	C₂×M₁₆×C₄₃	—	2	1	no	—
80	C₂×M₁₆×C₄₃	—	2	1	no	—
81	C₂×M₁₆×C₄₃	—	2	1	no	—
82	C₂×M₁₆×C₄₃	—	2	1	no	—
83	C₂×M₁₆×C₄₃	—	2	1	no	—
84	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
85	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
86	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
87	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
88	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
89	C₂²×C₈×C₄₃	—	2	1	no	—
90	C₂²×C₈×C₄₃	—	2	1	no	—
91	C₂²×C₈×C₄₃	—	2	1	no	—
92	C₂⁴×C₄₃	C₂×Q₈	1	1	yes	characteristic
93	C₂³×D₄₃	—	2	2	no	—
94	C₂³×D₄₃	—	2	2	no	—
95	C₂³×D₄₃	—	2	2	no	—
96	C₂³×D₄₃	—	2	2	no	—
97	C₂³×D₄₃	—	2	2	no	—
98	C₂³×D₄₃	—	2	2	no	—
99	C₂³×D₄₃	—	8	4	no	—
100	C₂³×D₄₃	C₄⋊C₄	1	4	yes	—
101	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
110	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
112	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
114	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
115	C₂×D₁₇₂	—	2	2	no	—
116	C₂×D₁₇₂	—	2	2	no	—
117	C₂×D₁₇₂	—	2	2	no	—
118	C₂×D₁₇₂	—	2	2	no	—
119	C₂×D₁₇₂	—	2	2	no	—
120	C₂×D₁₇₂	—	2	2	no	—
121	C₂×D₁₇₂	—	2	2	no	—
122	C₂×D₁₇₂	—	2	2	no	—
123	C₂×D₁₇₂	—	2	2	no	—
124	C₂×D₁₇₂	—	2	2	no	—
125	C₂×D₁₇₂	—	2	2	no	—
126	C₂×D₁₇₂	—	2	2	no	—
127	C₂×D₁₇₂	—	4	1	no	—
128	C₂×D₁₇₂	—	4	1	no	—
129	C₂×D₁₇₂	—	4	1	no	—
130	C₂×D₁₇₂	—	4	1	no	—
131	C₂×D₁₇₂	—	4	1	no	—
132	C₂×D₁₇₂	—	4	1	no	—
133	C₂×D₁₇₂	—	4	1	no	—
134	C₂×D₁₇₂	—	4	1	no	—
135	C₂×D₁₇₂	—	4	1	no	—
136	C₂×D₁₇₂	—	4	1	no	—
137	C₂×D₁₇₂	—	4	1	no	—
138	C₂×D₁₇₂	—	4	1	no	—
139	C₂×D₁₇₂	—	4	1	no	—
140	C₂×D₁₇₂	—	4	1	no	—
141	C₂×D₁₇₂	—	4	1	no	—
142	C₂×D₁₇₂	—	4	1	no	—
143	M₁₆×C₄₃	—	2	2	no	—
144	M₁₆×C₄₃	—	2	2	no	—
145	M₁₆×C₄₃	—	2	2	no	—
146	M₁₆×C₄₃	—	2	2	no	—
147	M₁₆×C₄₃	—	2	2	no	—
148	M₁₆×C₄₃	—	2	2	no	—
149	M₁₆×C₄₃	—	2	2	no	—
150	M₁₆×C₄₃	—	4	1	no	—
151	M₁₆×C₄₃	—	4	1	no	—
152	M₁₆×C₄₃	—	4	1	no	—
153	M₁₆×C₄₃	—	4	1	no	—
154	M₁₆×C₄₃	C₂²⋊C₄	1	4	yes	—
155	C₂×C₈×C₄₃	—	2	2	no	—
156	C₂×C₈×C₄₃	—	2	2	no	—
157	C₂×C₈×C₄₃	—	2	2	no	—
158	C₂×C₈×C₄₃	—	2	2	no	—
159	C₂×C₈×C₄₃	—	2	2	no	—
160	C₂×C₈×C₄₃	—	4	1	no	—
161	C₂×C₈×C₄₃	—	4	1	no	—
162	C₂×C₈×C₄₃	—	4	1	no	—
163	C₂×C₈×C₄₃	—	4	1	no	—
164	#10621877	—	2	2	no	—
165	#10621877	—	2	2	no	—
166	#10621877	—	2	2	no	—
167	#10621877	—	2	2	no	—
168	#10621877	—	2	2	no	—
169	#10621877	—	2	2	no	—
170	#10621877	—	4	1	no	—
171	#10621877	—	4	1	no	—
172	#10621877	—	4	1	no	—
173	#10621877	—	4	1	no	—
174	#10621877	—	4	1	no	—
175	#10621877	—	4	1	no	—
176	C₂×C₄₃⋊C₈	—	2	2	no	—
177	C₂×C₄₃⋊C₈	—	2	2	no	—
178	C₂×C₄₃⋊C₈	—	2	2	no	—
179	C₂×C₄₃⋊C₈	—	4	1	no	—
180	C₂×C₄₃⋊C₈	—	4	1	no	—
181	C₂×C₄₃⋊C₈	—	4	1	no	—
182	C₂×C₄₃⋊C₈	—	4	1	no	—
183	C₂×C₄₃⋊C₈	—	4	1	no	—
184	C₂×C₄₃⋊C₈	—	4	1	no	—
185	C₂³×C₄₃	—	4	2	no	—
186	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂³×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
188	C₂³×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
189	C₂³×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
190	C₂³×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
191	C₂³×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
192	C₂³×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
193	C₂²×D₄₃	—	2	4	no	—
194	C₂²×D₄₃	—	2	4	no	—
195	C₂²×D₄₃	—	2	4	no	—
196	C₂²×D₄₃	—	4	2	no	—
197	C₂²×D₄₃	—	4	2	no	—
198	C₂²×D₄₃	—	4	2	no	—
199	C₂²×D₄₃	—	4	2	no	—
200	C₂²×D₄₃	—	8	4	no	—
201	C₂²×D₄₃	—	8	4	no	—
202	C₂²×D₄₃	—	8	4	no	—
203	C₂²×D₄₃	—	8	4	no	—
204	C₂²×D₄₃	—	8	4	no	—
205	C₂²×D₄₃	—	8	4	no	—
206	C₂²×D₄₃	—	8	4	no	—
207	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
209	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
210	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
211	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
212	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
213	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
214	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
215	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
216	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
217	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
218	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
219	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
220	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
221	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
222	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
223	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
224	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
225	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
226	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
227	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
228	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
229	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
230	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
231	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
232	C₂×C₄×C₄₃	#126	1	1	yes	characteristic
233	C₂×C₄×C₄₃	#126	1	1	yes	characteristic
234	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
235	D₁₇₂	—	4	2	no	—
236	D₁₇₂	—	4	2	no	—
237	D₁₇₂	—	4	2	no	—
238	D₁₇₂	—	4	2	no	—
239	D₁₇₂	—	4	2	no	—
240	D₁₇₂	—	4	2	no	—
241	D₁₇₂	—	4	2	no	—
242	D₁₇₂	—	4	2	no	—
243	C₈×C₄₃	—	2	4	no	—
244	C₈×C₄₃	—	4	2	no	—
245	C₈×C₄₃	—	4	2	no	—
246	C₄₃⋊C₈	—	4	2	no	—
247	C₄₃⋊C₈	—	4	2	no	—
248	C₄₃⋊C₈	—	4	2	no	—
249	#11139	—	43	1	no	maximal, Sylow
250	C₂²×C₄₃	—	2	2	no	—
251	C₂²×C₄₃	—	2	2	no	—
252	C₂²×C₄₃	—	2	2	no	—
253	C₂²×C₄₃	—	4	1	no	—
254	C₂²×C₄₃	—	4	1	no	—
255	C₂²×C₄₃	—	4	1	no	—
256	C₂²×C₄₃	—	4	1	no	—
257	C₂²×C₄₃	#380	1	1	yes	characteristic
258	C₂²×C₄₃	#385	1	1	yes	characteristic
259	C₂²×C₄₃	#385	1	1	yes	characteristic
260	C₂²×C₄₃	#393	1	1	yes	characteristic
261	C₂²×C₄₃	#396	1	1	yes	characteristic
262	C₂²×C₄₃	#396	1	1	yes	characteristic
263	C₂²×C₄₃	#399	1	1	yes	characteristic
264	C₂×D₄₃	—	4	4	no	—
265	C₂×D₄₃	—	8	4	no	—
266	C₂×D₄₃	—	8	4	no	—
267	C₂×D₄₃	—	8	4	no	—
268	C₂×D₄₃	—	8	4	no	—
269	C₂×D₄₃	—	8	4	no	—
270	C₂×D₄₃	—	8	4	no	—
271	C₂×D₄₃	—	8	4	no	—
272	C₄×C₄₃	#386	1	1	yes	characteristic
273	C₄×C₄₃	#388	1	1	yes	characteristic
274	C₄×C₄₃	#388	1	1	yes	characteristic
275	C₄×C₄₃	#390	1	1	yes	characteristic
276	C₄×C₄₃	#392	1	1	yes	characteristic
277	C₄×C₄₃	#394	1	1	yes	characteristic
278	C₄×C₄₃	#394	1	1	yes	characteristic
279	C₄×C₄₃	#397	1	1	yes	characteristic
280	C₂×#430	—	43	1	no	—
281	C₂²×#100	—	43	1	no	—
282	C₂²×#100	—	43	1	no	—
283	C₂²×#100	—	43	1	no	—
284	#1738	—	43	1	no	—
285	#1738	D₄₃	1	1	yes	characteristic, complemented
286	C₂×#338	—	43	1	no	—
287	C₂×C₄₃	—	2	1	no	—
288	C₂×C₄₃	—	2	1	no	—
289	C₂×C₄₃	—	2	1	no	—
290	C₂×C₄₃	—	2	1	no	—
291	C₂×C₄₃	—	2	1	no	—
292	C₂×C₄₃	—	2	1	no	—
293	C₂×C₄₃	#1439	1	1	yes	characteristic
294	C₂×C₄₃	#2069	1	2	yes	—
295	D₄₃	—	8	4	no	—
296	C₂³×D₄	—	43	1	no	—
297	C₂²×M₁₆	—	43	1	no	—
298	C₂²×M₁₆	—	43	1	no	—
299	C₂²×M₁₆	—	43	1	no	—
300	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
301	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
302	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
303	#430	—	86	2	no	—
304	#430	—	86	2	no	—
305	C₂×#108	—	86	2	no	—
306	C₂×#100	—	43	4	no	—
307	C₂×#100	—	86	2	no	—
308	C₂×#100	—	86	2	no	—
309	C₂×#100	—	86	2	no	—
310	C₂×#100	—	86	2	no	—
311	C₂×#100	—	86	2	no	—
312	C₂×#100	—	86	2	no	—
313	C₂×#100	—	86	2	no	—
314	C₂×#100	—	86	2	no	—
315	#341	—	2	2	no	—
316	#341	—	86	2	no	—
317	#338	—	86	2	no	—
318	C₄₃	#11139	1	1	yes	characteristic, complemented, Sylow
319	C₂⁵	—	43	2	no	—
320	C₂²×D₄	—	43	2	no	—
321	C₂²×D₄	—	43	2	no	—
322	C₂²×D₄	—	86	1	no	—
323	C₂²×D₄	—	86	1	no	—
324	C₂²×D₄	—	86	1	no	—
325	C₂²×D₄	—	86	1	no	—
326	C₂²×D₄	—	86	1	no	—
327	C₂²×D₄	—	86	1	no	—
328	C₂²×D₄	—	86	1	no	—
329	C₂²×D₄	—	86	1	no	—
330	C₂²×D₄	—	86	1	no	—
331	C₂²×D₄	—	86	1	no	—
332	C₂²×D₄	—	86	1	no	—
333	C₂²×D₄	—	86	1	no	—
334	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
335	C₂×M₁₆	—	2	1	no	—
336	C₂×M₁₆	—	2	1	no	—
337	C₂×M₁₆	—	2	1	no	—
338	C₂×M₁₆	—	2	1	no	—
339	C₂×M₁₆	—	2	1	no	—
340	C₂×M₁₆	—	2	1	no	—
341	C₂×M₁₆	—	2	1	no	—
342	C₂×M₁₆	—	2	1	no	—
343	C₂×M₁₆	—	2	1	no	—
344	C₂×M₁₆	—	2	1	no	—
345	C₂×M₁₆	—	2	1	no	—
346	C₂×M₁₆	—	2	1	no	—
347	C₂×M₁₆	—	2	1	no	—
348	C₂×M₁₆	—	43	2	no	—
349	C₂×M₁₆	—	43	2	no	—
350	C₂×M₁₆	—	43	2	no	—
351	C₂×M₁₆	—	86	1	no	—
352	C₂×M₁₆	—	86	1	no	—
353	C₂×M₁₆	—	86	1	no	—
354	C₂×M₁₆	—	86	1	no	—
355	C₂×M₁₆	—	86	1	no	—
356	C₂×M₁₆	—	86	1	no	—
357	C₂×M₁₆	—	86	1	no	—
358	C₂×M₁₆	—	86	1	no	—
359	C₂×M₁₆	—	86	1	no	—
360	C₂×M₁₆	—	86	1	no	—
361	C₂×M₁₆	—	86	1	no	—
362	C₂×M₁₆	—	86	1	no	—
363	C₂×M₁₆	—	86	1	no	—
364	C₂×M₁₆	—	86	1	no	—
365	C₂×M₁₆	—	86	1	no	—
366	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
367	C₂×M₁₆	D₁₇₂	1	2	yes	—
368	C₂×M₁₆	D₁₇₂	1	2	yes	—
369	C₂×M₁₆	D₁₇₂	1	2	yes	—
370	C₂×M₁₆	C₂²⋊D₄₃	1	2	yes	—
371	C₂²×C₈	—	2	1	no	—
372	C₂²×C₈	—	2	1	no	—
373	C₂²×C₈	—	2	1	no	—
374	C₂²×C₈	—	86	1	no	—
375	C₂²×C₈	—	86	1	no	—
376	C₂²×C₈	—	86	1	no	—
377	#108	—	86	8	no	—
378	#100	—	86	8	no	—
379	#100	—	86	8	no	—
380	#100	—	86	8	no	—
381	C₂⁴	—	43	4	no	—
382	C₂⁴	—	86	2	no	—
383	C₂⁴	—	86	2	no	—
384	C₂⁴	—	86	2	no	—
385	C₂⁴	—	86	2	no	—
386	C₂⁴	—	86	2	no	—
387	C₂⁴	—	86	2	no	—
388	C₂⁴	—	344	4	no	—
389	C₂⁴	Q₈×D₄₃	1	1	yes	characteristic
390	C₂×D₄	—	86	2	no	—
391	C₂×D₄	—	86	2	no	—
392	C₂×D₄	—	86	2	no	—
393	C₂×D₄	—	86	2	no	—
394	C₂×D₄	—	86	2	no	—
395	C₂×D₄	—	86	2	no	—
396	C₂×D₄	—	86	2	no	—
397	C₂×D₄	—	86	2	no	—
398	C₂×D₄	—	86	2	no	—
399	C₂×D₄	—	86	2	no	—
400	C₂×D₄	—	86	2	no	—
401	C₂×D₄	—	86	2	no	—
402	C₂×D₄	—	172	1	no	—
403	C₂×D₄	—	172	1	no	—
404	C₂×D₄	—	172	1	no	—
405	C₂×D₄	—	172	1	no	—
406	C₂×D₄	—	172	1	no	—
407	C₂×D₄	—	172	1	no	—
408	C₂×D₄	—	172	1	no	—
409	C₂×D₄	—	172	1	no	—
410	C₂×D₄	—	172	1	no	—
411	C₂×D₄	—	172	1	no	—
412	C₂×D₄	—	172	1	no	—
413	C₂×D₄	—	172	1	no	—
414	C₂×D₄	—	172	1	no	—
415	C₂×D₄	—	172	1	no	—
416	C₂×D₄	—	172	1	no	—
417	C₂×D₄	—	172	1	no	—
418	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
419	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
420	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
421	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
422	C₂²×C₄	#10621898	1	1	yes	characteristic
423	C₂²×C₄	#10621898	1	1	yes	characteristic
424	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
425	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
426	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
427	C₂²×C₄	#10621900	1	1	yes	characteristic
428	C₂²×C₄	#10621900	1	1	yes	characteristic
429	C₂²×C₄	#10621900	1	1	yes	characteristic
430	C₂²×C₄	#10621902	1	1	yes	characteristic
431	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
432	M₁₆	—	2	2	no	—
433	M₁₆	—	2	2	no	—
434	M₁₆	—	2	2	no	—
435	M₁₆	—	2	2	no	—
436	M₁₆	—	2	2	no	—
437	M₁₆	—	2	2	no	—
438	M₁₆	—	2	2	no	—
439	M₁₆	—	4	1	no	—
440	M₁₆	—	4	1	no	—
441	M₁₆	—	4	1	no	—
442	M₁₆	—	4	1	no	—
443	M₁₆	—	86	2	no	—
444	M₁₆	—	86	2	no	—
445	M₁₆	—	86	2	no	—
446	M₁₆	—	86	2	no	—
447	M₁₆	—	86	2	no	—
448	M₁₆	—	86	2	no	—
449	M₁₆	—	172	1	no	—
450	M₁₆	—	172	1	no	—
451	M₁₆	—	172	1	no	—
452	M₁₆	—	172	1	no	—
453	M₁₆	—	172	1	no	—
454	M₁₆	—	172	1	no	—
455	M₁₆	(C₂×D₄₃)⋊C₄	1	4	yes	—
456	C₂×C₈	—	2	2	no	—
457	C₂×C₈	—	2	2	no	—
458	C₂×C₈	—	2	2	no	—
459	C₂×C₈	—	2	2	no	—
460	C₂×C₈	—	2	2	no	—
461	C₂×C₈	—	4	1	no	—
462	C₂×C₈	—	4	1	no	—
463	C₂×C₈	—	4	1	no	—
464	C₂×C₈	—	4	1	no	—
465	C₂×C₈	—	86	2	no	—
466	C₂×C₈	—	86	2	no	—
467	C₂×C₈	—	86	2	no	—
468	C₂×C₈	—	172	1	no	—
469	C₂×C₈	—	172	1	no	—
470	C₂×C₈	—	172	1	no	—
471	C₂×C₈	—	172	1	no	—
472	C₂×C₈	—	172	1	no	—
473	C₂×C₈	—	172	1	no	—
474	C₂³	—	4	2	no	—
475	C₂³	—	86	4	no	—
476	C₂³	—	86	4	no	—
477	C₂³	—	86	4	no	—
478	C₂³	—	344	4	no	—
479	C₂³	—	344	4	no	—
480	C₂³	—	344	4	no	—
481	C₂³	—	344	4	no	—
482	C₂³	—	344	4	no	—
483	C₂³	—	344	4	no	—
484	C₂³	—	344	4	no	—
485	C₂³	—	172	2	no	—
486	C₂³	—	172	2	no	—
487	C₂³	—	172	2	no	—
488	C₂³	—	172	2	no	—
489	C₂³	C₄⋊C₄×D₄₃	1	1	yes	characteristic
490	C₂³	#13063301	1	1	yes	characteristic
491	C₂³	#13063303	1	1	yes	characteristic
492	C₂³	#13063303	1	1	yes	characteristic
493	C₂³	#13063305	1	1	yes	characteristic
494	C₂³	#13063305	1	1	yes	characteristic
495	C₂³	#13063305	1	1	yes	characteristic
496	D₄	—	172	2	no	—
497	D₄	—	172	2	no	—
498	D₄	—	172	2	no	—
499	D₄	—	172	2	no	—
500	D₄	—	172	2	no	—
501	D₄	—	172	2	no	—
502	D₄	—	172	2	no	—
503	D₄	—	172	2	no	—
504	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
505	C₂×C₄	#13063283	1	1	yes	characteristic
506	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
507	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
508	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
509	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
510	C₂×C₄	#13063295	1	1	yes	characteristic
511	C₂×C₄	#13063295	1	1	yes	characteristic
512	C₂×C₄	#13063295	1	1	yes	characteristic
513	C₂×C₄	#13063296	1	1	yes	characteristic
514	C₂×C₄	#13063297	1	1	yes	characteristic
515	C₂×C₄	#13063297	1	1	yes	characteristic
516	C₂×C₄	#13063299	1	1	yes	characteristic
517	C₂×C₄	#13063299	1	1	yes	characteristic
518	C₂×C₄	#13063300	1	1	yes	characteristic
519	C₂×C₄	#13063300	1	1	yes	characteristic
520	C₂×C₄	#13063300	1	1	yes	characteristic
521	C₂×C₄	#13063307	1	1	yes	characteristic
522	C₂×C₄	#13063307	1	1	yes	characteristic
523	C₂×C₄	#13063309	1	1	yes	characteristic
524	C₂×C₄	#13063309	1	1	yes	characteristic
525	C₂×C₄	#13063309	1	1	yes	characteristic
526	C₂×C₄	#13063311	1	1	yes	characteristic
527	C₂×C₄	#13063311	1	1	yes	characteristic
528	C₂×C₄	#13063313	1	1	yes	characteristic
529	C₂×C₄	#13063320	1	1	yes	characteristic
530	C₂×C₄	#13063320	1	1	yes	characteristic
531	C₂×C₄	#13063322	1	1	yes	characteristic
532	C₈	—	2	4	no	—
533	C₈	—	4	2	no	—
534	C₈	—	4	2	no	—
535	C₈	—	172	2	no	—
536	C₈	—	172	2	no	—
537	C₈	—	172	2	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	2	2	no	—
541	C₂²	—	4	1	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	4	1	no	—
544	C₂²	—	4	1	no	—
545	C₂²	—	344	4	no	—
546	C₂²	—	344	4	no	—
547	C₂²	—	344	4	no	—
548	C₂²	—	344	4	no	—
549	C₂²	—	344	4	no	—
550	C₂²	—	344	4	no	—
551	C₂²	—	344	4	no	—
552	C₂²	—	172	4	no	—
553	C₂²	#14582756	1	1	yes	characteristic
554	C₂²	#14582773	1	1	yes	characteristic
555	C₂²	#14582773	1	1	yes	characteristic
556	C₂²	#14582812	1	1	yes	characteristic
557	C₂²	#14582821	1	1	yes	characteristic
558	C₂²	#14582821	1	1	yes	characteristic
559	C₂²	#14582836	1	1	yes	characteristic
560	C₄	#14582776	1	1	yes	characteristic
561	C₄	#14582791	1	1	yes	characteristic
562	C₄	#14582791	1	1	yes	characteristic
563	C₄	#14582801	1	1	yes	characteristic
564	C₄	#14582809	1	1	yes	characteristic
565	C₄	#14582815	1	1	yes	characteristic
566	C₄	#14582815	1	1	yes	characteristic
567	C₄	#14582826	1	1	yes	characteristic
568	C₂	—	2	1	no	—
569	C₂	—	2	1	no	—
570	C₂	—	2	1	no	—
571	C₂	—	2	1	no	—
572	C₂	—	2	1	no	—
573	C₂	—	2	1	no	—
574	C₂	—	344	4	no	—
575	C₂	#19132841	1	1	yes	characteristic
576	C₂	#19135992	1	2	yes	—

	subgroup	G/H
center	C₂²	#14582821
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₃
Fitting	C₄₃×#1738	C₂
socle	C₂²×C₄₃	#396
prime radical	C₂³×D₁₇₂	C₂²
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	#1738	D₄₃
hypocenter	C₄₃	#11139
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #1738

Complements

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

N	H ≅ G/N	type
1. C₂×#14582948	C₂	semidirect
5. #19134321	C₂	semidirect
6. C₂×C₄₃⋊#338	C₂	semidirect
7. C₄₃×#1738	C₂	semidirect
285. #1738	D₄₃	semidirect
318. C₄₃	#11139	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582948	2
C₂²×#13063241	2
#19134321	2
C₂×C₄₃⋊#338	2
C₄₃×#1738	2
#11139	43