Subgroups — #25002930

Order 11008.

1058 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13063241	C₂	1	1	yes	maximal, characteristic
2	C₂²×#13063241	C₂	1	1	yes	maximal, characteristic
3	#19143013	C₂	1	1	yes	maximal, characteristic, complemented
4	#19137175	C₂	1	1	yes	maximal, characteristic
5	C₂×#14582669	C₂	1	1	yes	maximal, characteristic, complemented
6	#19134333	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₃×#344	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	C₂×#13063284	C₂²	1	1	yes	characteristic
12	C₂×#13063241	—	2	2	no	—
13	C₂×#13063241	—	2	2	no	—
14	C₂×#13063241	—	2	2	no	—
15	C₂×#13063241	—	2	2	no	—
16	C₂×#13063241	C₄	1	4	yes	complemented
17	C₂×#13063241	C₄	1	4	yes	complemented
18	#14582857	—	2	2	no	—
19	#14582854	—	2	2	no	—
20	M₁₆×Dic₄₃	—	2	2	no	—
21	#14582801	—	2	2	no	—
22	#14582800	—	2	2	no	—
23	#14582754	C₄	1	4	yes	—
24	#14582669	—	2	2	no	—
25	#14582667	—	2	2	no	—
26	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
27	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
29	C₄₃×#344	—	2	2	no	—
30	C₂⁴×D₄₃	C₂×C₄	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	C₂×C₄	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	C₂×C₄	1	2	yes	—
54	C₂×#10621877	C₂×C₄	1	2	yes	—
55	C₂×#10621877	D₄	1	2	yes	—
56	C₂×#10621877	D₄	1	2	yes	—
57	C₂²×C₄₃⋊C₈	—	2	1	no	—
58	C₂²×C₄₃⋊C₈	—	2	1	no	—
59	#13063284	—	2	1	no	—
60	#13063284	—	2	1	no	—
61	#13063284	—	2	1	no	—
62	#13063284	—	2	1	no	—
63	C₂×C₄⋊Dic₄₃	D₄	1	2	yes	—
64	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	2	yes	—
65	C₂×(C₂×D₄₃)⋊C₄	—	2	8	no	—
66	C₂×C₄×Dic₄₃	D₄	1	2	yes	—
67	#13063241	—	2	8	no	—
68	#13063241	—	2	8	no	—
69	#13063235	—	2	4	no	—
70	C₈×Dic₄₃	—	2	4	no	—
71	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
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	C₂×C₄	1	2	yes	—
81	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
82	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
83	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
84	C₂²×C₈×C₄₃	—	2	1	no	—
85	C₂²×C₈×C₄₃	—	2	1	no	—
86	#117×C₄₃	—	2	1	no	—
87	#117×C₄₃	—	2	1	no	—
88	#117×C₄₃	—	2	1	no	—
89	#117×C₄₃	—	2	1	no	—
90	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
92	C₂×C₄²×C₄₃	—	2	1	no	—
93	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
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	—	2	2	no	—
100	C₂³×D₄₃	—	8	4	no	—
101	C₂³×D₄₃	C₄²	1	4	yes	—
102	C₂²×C₄×C₄₃	—	2	2	no	—
103	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₃	C₂²×C₄	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	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₃	C₂×D₄	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	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
117	C₂²×Dic₄₃	C₂²⋊C₄	1	4	yes	—
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	—	2	2	no	—
128	C₂×D₁₇₂	—	2	2	no	—
129	C₂×D₁₇₂	—	2	2	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	C₂×D₁₇₂	—	4	1	no	—
144	C₂×D₁₇₂	—	4	1	no	—
145	C₂×D₁₇₂	—	4	1	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	—	2	2	no	—
151	M₁₆×C₄₃	—	4	1	no	—
152	M₁₆×C₄₃	—	4	1	no	—
153	M₁₆×C₄₃	C₂²⋊C₄	1	4	yes	complemented
154	C₂×C₈×C₄₃	—	2	2	no	—
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	—	4	1	no	—
159	C₂×C₈×C₄₃	—	4	1	no	—
160	C₄⋊C₄×C₄₃	—	4	1	no	—
161	C₄⋊C₄×C₄₃	—	4	1	no	—
162	C₂²⋊C₄×C₄₃	—	2	2	no	—
163	C₂²⋊C₄×C₄₃	—	2	2	no	—
164	C₄²×C₄₃	—	4	1	no	—
165	C₄²×C₄₃	—	4	1	no	—
166	C₂²⋊Dic₄₃	—	2	2	no	—
167	C₂²⋊Dic₄₃	—	2	2	no	—
168	(C₂×D₄₃)⋊C₄	—	8	8	no	—
169	C₄⋊Dic₄₃	—	2	2	no	—
170	C₄⋊Dic₄₃	—	2	2	no	—
171	C₄×Dic₄₃	—	2	2	no	—
172	C₄×Dic₄₃	—	2	2	no	—
173	#10621877	—	2	2	no	—
174	#10621877	—	2	2	no	—
175	#10621877	—	2	2	no	—
176	#10621877	—	2	2	no	—
177	#10621877	—	2	2	no	—
178	#10621877	—	4	1	no	—
179	#10621877	—	4	1	no	—
180	#10621877	C₂²⋊C₄	1	4	yes	complemented
181	C₂×C₄₃⋊C₈	—	2	2	no	—
182	C₂×C₄₃⋊C₈	—	2	2	no	—
183	C₂×C₄₃⋊C₈	—	2	2	no	—
184	C₂×C₄₃⋊C₈	—	2	2	no	—
185	C₂×C₄₃⋊C₈	—	4	1	no	—
186	C₂×C₄₃⋊C₈	—	4	1	no	—
187	C₂³×C₄₃	—	4	2	no	—
188	C₂³×C₄₃	C₂×C₄²	1	1	yes	characteristic
189	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	C₂³×C₄₃	#117	1	1	yes	characteristic
191	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
192	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
193	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
194	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
195	C₂²×D₄₃	—	2	4	no	—
196	C₂²×D₄₃	—	2	4	no	—
197	C₂²×D₄₃	—	2	4	no	—
198	C₂²×D₄₃	—	4	8	no	—
199	C₂²×D₄₃	—	4	2	no	—
200	C₂²×D₄₃	—	4	2	no	—
201	C₂²×D₄₃	—	4	2	no	—
202	C₂²×D₄₃	—	4	2	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	C₂²×D₄₃	—	8	4	no	—
208	C₂²×D₄₃	—	8	4	no	—
209	C₂×C₄×C₄₃	—	4	4	no	—
210	C₂×C₄×C₄₃	—	4	2	no	—
211	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
212	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
214	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
215	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
216	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
217	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
218	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
219	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
220	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
221	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
222	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
223	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
224	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
225	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
226	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
227	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
228	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
229	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
230	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
231	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
232	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
233	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
234	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
235	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
236	C₂×C₄×C₄₃	#126	1	1	yes	characteristic
237	C₂×C₄×C₄₃	#126	1	1	yes	characteristic
238	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
239	C₂×Dic₄₃	—	2	4	no	—
240	C₂×Dic₄₃	—	4	4	no	—
241	D₁₇₂	—	4	2	no	—
242	D₁₇₂	—	4	2	no	—
243	D₁₇₂	—	4	2	no	—
244	D₁₇₂	—	4	2	no	—
245	D₁₇₂	—	4	2	no	—
246	D₁₇₂	—	4	2	no	—
247	D₁₇₂	—	4	2	no	—
248	D₁₇₂	—	4	2	no	—
249	C₈×C₄₃	—	2	4	no	—
250	C₈×C₄₃	—	4	2	no	—
251	C₄₃⋊C₈	—	2	4	no	—
252	C₄₃⋊C₈	—	4	2	no	—
253	#10939	—	43	1	no	maximal, Sylow
254	C₂²×C₄₃	—	2	2	no	—
255	C₂²×C₄₃	—	2	2	no	—
256	C₂²×C₄₃	—	2	2	no	—
257	C₂²×C₄₃	—	4	1	no	—
258	C₂²×C₄₃	—	4	1	no	—
259	C₂²×C₄₃	—	4	1	no	—
260	C₂²×C₄₃	—	4	1	no	—
261	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
262	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
263	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
264	C₂²×C₄₃	#386	1	1	yes	characteristic
265	C₂²×C₄₃	#388	1	1	yes	characteristic
266	C₂²×C₄₃	#388	1	1	yes	characteristic
267	C₂²×C₄₃	#390	1	1	yes	characteristic
268	C₂×D₄₃	—	4	8	no	—
269	C₂×D₄₃	—	4	4	no	—
270	C₂×D₄₃	—	8	4	no	—
271	C₂×D₄₃	—	8	4	no	—
272	C₂×D₄₃	—	8	4	no	—
273	C₂×D₄₃	—	8	4	no	—
274	C₂×D₄₃	—	8	4	no	—
275	C₂×D₄₃	—	8	4	no	—
276	C₄×C₄₃	—	8	2	no	—
277	C₄×C₄₃	#386	1	1	yes	characteristic
278	C₄×C₄₃	#386	1	1	yes	characteristic
279	C₄×C₄₃	#388	1	1	yes	characteristic
280	C₄×C₄₃	#388	1	1	yes	characteristic
281	C₄×C₄₃	#388	1	1	yes	characteristic
282	C₄×C₄₃	#388	1	1	yes	characteristic
283	C₄×C₄₃	#390	1	1	yes	characteristic
284	C₄×C₄₃	#390	1	1	yes	characteristic
285	Dic₄₃	—	4	4	no	—
286	C₂²×#100	—	43	1	no	—
287	C₂²×#100	—	43	1	no	—
288	#2873	—	43	1	no	—
289	#2309	—	43	1	no	—
290	C₂×#344	—	43	1	no	—
291	C₂×#344	D₄₃	1	1	yes	characteristic, complemented
292	#1742	—	43	1	no	—
293	C₂×C₄₃	—	2	1	no	—
294	C₂×C₄₃	—	2	1	no	—
295	C₂×C₄₃	—	2	1	no	—
296	C₂×C₄₃	—	2	1	no	—
297	C₂×C₄₃	—	2	1	no	—
298	C₂×C₄₃	—	2	1	no	—
299	C₂×C₄₃	#1437	1	1	yes	characteristic
300	C₂×C₄₃	#1914	1	2	yes	—
301	D₄₃	—	8	4	no	—
302	C₂³×D₄	—	43	1	no	—
303	C₂²×M₁₆	—	43	1	no	—
304	C₂²×M₁₆	—	43	1	no	—
305	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
306	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
307	C₂×#117	—	43	1	no	—
308	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
309	C₂×#100	—	43	4	no	—
310	C₂×#100	—	43	4	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	#405	—	86	2	no	—
316	#405	—	86	2	no	—
317	C₄×M₁₆	—	86	2	no	—
318	#390	—	86	2	no	—
319	#390	—	86	2	no	—
320	#379	—	43	4	no	—
321	#344	—	2	2	no	—
322	#344	—	86	2	no	—
323	#343	—	86	2	no	—
324	C₄₃	#10939	1	1	yes	characteristic, complemented, Sylow
325	C₂⁵	—	43	2	no	—
326	C₂²×D₄	—	43	2	no	—
327	C₂²×D₄	—	43	2	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	C₂²×D₄	—	86	1	no	—
335	C₂²×D₄	—	86	1	no	—
336	C₂²×D₄	—	86	1	no	—
337	C₂²×D₄	—	86	1	no	—
338	C₂²×D₄	—	86	1	no	—
339	C₂²×D₄	—	86	1	no	—
340	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
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	—	2	1	no	—
349	C₂×M₁₆	—	43	2	no	—
350	C₂×M₁₆	—	43	2	no	—
351	C₂×M₁₆	—	43	2	no	—
352	C₂×M₁₆	—	43	2	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	C₄×D₄₃	1	2	yes	—
362	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
363	C₂×M₁₆	D₁₇₂	1	2	yes	—
364	C₂×M₁₆	C₂²⋊D₄₃	1	2	yes	—
365	C₂²×C₈	—	2	1	no	—
366	C₂²×C₈	—	2	1	no	—
367	C₂²×C₈	—	86	1	no	—
368	C₂²×C₈	—	86	1	no	—
369	#117	—	2	1	no	—
370	#117	—	2	1	no	—
371	#117	—	2	1	no	—
372	#117	—	2	1	no	—
373	#117	—	86	1	no	—
374	#117	—	86	1	no	—
375	#117	—	86	1	no	—
376	#117	—	86	1	no	—
377	C₂×C₄⋊C₄	—	2	1	no	—
378	C₂×C₄⋊C₄	—	43	2	no	—
379	C₂×C₂²⋊C₄	—	43	2	no	—
380	C₂×C₂²⋊C₄	—	86	8	no	—
381	C₂×C₂²⋊C₄	C₄×D₄₃	1	2	yes	—
382	C₂×C₄²	—	2	1	no	—
383	C₂×C₄²	—	43	2	no	—
384	#100	—	86	8	no	—
385	#100	—	86	8	no	—
386	#97	—	86	4	no	—
387	C₄×C₈	—	86	4	no	—
388	C₂⁴	—	43	4	no	—
389	C₂⁴	—	86	2	no	—
390	C₂⁴	—	86	2	no	—
391	C₂⁴	—	86	2	no	—
392	C₂⁴	—	86	2	no	—
393	C₂⁴	—	86	2	no	—
394	C₂⁴	—	86	2	no	—
395	C₂⁴	—	344	4	no	—
396	C₂⁴	C₂×C₄×D₄₃	1	1	yes	characteristic
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	—	86	2	no	—
403	C₂×D₄	—	86	2	no	—
404	C₂×D₄	—	86	2	no	—
405	C₂×D₄	—	86	2	no	—
406	C₂×D₄	—	86	2	no	—
407	C₂×D₄	—	86	2	no	—
408	C₂×D₄	—	86	2	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	C₂×D₄	—	172	1	no	—
419	C₂×D₄	—	172	1	no	—
420	C₂×D₄	—	172	1	no	—
421	C₂×D₄	—	172	1	no	—
422	C₂×D₄	—	172	1	no	—
423	C₂×D₄	—	172	1	no	—
424	C₂×D₄	—	172	1	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	43	4	no	—
427	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
428	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
429	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
430	C₂²×C₄	#10621898	1	1	yes	characteristic
431	C₂²×C₄	#10621898	1	1	yes	characteristic
432	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
433	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
434	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
435	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
436	C₂²×C₄	#10621900	1	1	yes	characteristic
437	C₂²×C₄	#10621900	1	1	yes	characteristic
438	C₂²×C₄	#10621902	1	1	yes	characteristic
439	C₂²×C₄	#10621902	1	1	yes	characteristic
440	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
441	M₁₆	—	2	2	no	—
442	M₁₆	—	2	2	no	—
443	M₁₆	—	2	2	no	—
444	M₁₆	—	2	2	no	—
445	M₁₆	—	2	2	no	—
446	M₁₆	—	4	1	no	—
447	M₁₆	—	4	1	no	—
448	M₁₆	—	43	4	no	—
449	M₁₆	—	86	2	no	—
450	M₁₆	—	86	2	no	—
451	M₁₆	—	86	2	no	—
452	M₁₆	—	86	2	no	—
453	M₁₆	—	86	2	no	—
454	M₁₆	—	172	1	no	—
455	M₁₆	—	172	1	no	—
456	M₁₆	(C₂×D₄₃)⋊C₄	1	4	yes	complemented
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	—	86	2	no	—
464	C₂×C₈	—	86	2	no	—
465	C₂×C₈	—	86	2	no	—
466	C₂×C₈	—	86	2	no	—
467	C₂×C₈	—	172	1	no	—
468	C₂×C₈	—	172	1	no	—
469	C₄⋊C₄	—	4	1	no	—
470	C₄⋊C₄	—	4	1	no	—
471	C₄⋊C₄	—	86	2	no	—
472	C₄⋊C₄	—	86	2	no	—
473	C₂²⋊C₄	—	2	2	no	—
474	C₂²⋊C₄	—	2	2	no	—
475	C₂²⋊C₄	—	86	2	no	—
476	C₂²⋊C₄	—	86	2	no	—
477	C₂²⋊C₄	—	344	8	no	—
478	C₄²	—	4	1	no	—
479	C₄²	—	4	1	no	—
480	C₄²	—	86	2	no	—
481	C₄²	—	86	2	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	86	4	no	—
484	C₂³	—	86	4	no	—
485	C₂³	—	86	4	no	—
486	C₂³	—	344	4	no	—
487	C₂³	—	344	4	no	—
488	C₂³	—	344	4	no	—
489	C₂³	—	344	4	no	—
490	C₂³	—	344	4	no	—
491	C₂³	—	344	4	no	—
492	C₂³	—	172	8	no	—
493	C₂³	—	172	2	no	—
494	C₂³	—	172	2	no	—
495	C₂³	—	172	2	no	—
496	C₂³	—	172	2	no	—
497	C₂³	C₄²×D₄₃	1	1	yes	characteristic
498	C₂³	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
499	C₂³	#13063283	1	1	yes	characteristic
500	C₂³	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
501	C₂³	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
502	C₂³	#13063287	1	1	yes	characteristic
503	C₂³	C₄×D₁₇₂	1	1	yes	characteristic
504	D₄	—	172	2	no	—
505	D₄	—	172	2	no	—
506	D₄	—	172	2	no	—
507	D₄	—	172	2	no	—
508	D₄	—	172	2	no	—
509	D₄	—	172	2	no	—
510	D₄	—	172	2	no	—
511	D₄	—	172	2	no	—
512	C₂×C₄	—	4	4	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	86	4	no	—
515	C₂×C₄	—	172	4	no	—
516	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
517	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
518	C₂×C₄	#13063282	1	1	yes	characteristic
519	C₂×C₄	#13063283	1	1	yes	characteristic
520	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
521	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
522	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
523	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
524	C₂×C₄	#13063287	1	1	yes	characteristic
525	C₂×C₄	#13063287	1	1	yes	characteristic
526	C₂×C₄	#13063287	1	1	yes	characteristic
527	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
528	C₂×C₄	#13063295	1	1	yes	characteristic
529	C₂×C₄	#13063297	1	1	yes	characteristic
530	C₂×C₄	#13063297	1	1	yes	characteristic
531	C₂×C₄	#13063298	1	1	yes	characteristic
532	C₂×C₄	#13063298	1	1	yes	characteristic
533	C₂×C₄	#13063300	1	1	yes	characteristic
534	C₂×C₄	#13063300	1	1	yes	characteristic
535	C₂×C₄	#13063309	1	1	yes	characteristic
536	C₂×C₄	#13063310	1	1	yes	characteristic
537	C₂×C₄	#13063310	1	1	yes	characteristic
538	C₂×C₄	#13063311	1	1	yes	characteristic
539	C₂×C₄	#13063311	1	1	yes	characteristic
540	C₂×C₄	#13063314	1	1	yes	characteristic
541	C₂×C₄	#13063320	1	1	yes	characteristic
542	C₂×C₄	#13063320	1	1	yes	characteristic
543	C₂×C₄	#13063321	1	1	yes	characteristic
544	C₈	—	2	4	no	—
545	C₈	—	4	2	no	—
546	C₈	—	86	4	no	—
547	C₈	—	172	2	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	2	2	no	—
550	C₂²	—	2	2	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	344	4	no	—
556	C₂²	—	344	4	no	—
557	C₂²	—	344	4	no	—
558	C₂²	—	344	4	no	—
559	C₂²	—	344	4	no	—
560	C₂²	—	344	4	no	—
561	C₂²	—	172	8	no	—
562	C₂²	—	172	4	no	—
563	C₂²	#14582746	1	1	yes	characteristic
564	C₂²	#14582746	1	1	yes	characteristic
565	C₂²	C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
566	C₂²	#14582777	1	1	yes	characteristic
567	C₂²	#14582789	1	1	yes	characteristic
568	C₂²	#14582791	1	1	yes	characteristic
569	C₂²	#14582799	1	1	yes	characteristic
570	C₄	—	8	2	no	—
571	C₄	—	172	4	no	—
572	C₄	#14582776	1	1	yes	characteristic
573	C₄	#14582777	1	1	yes	characteristic
574	C₄	#14582788	1	1	yes	characteristic
575	C₄	#14582788	1	1	yes	characteristic
576	C₄	#14582789	1	1	yes	characteristic
577	C₄	#14582791	1	1	yes	characteristic
578	C₄	#14582799	1	1	yes	characteristic
579	C₄	#14582800	1	1	yes	characteristic
580	C₂	—	2	1	no	—
581	C₂	—	2	1	no	—
582	C₂	—	2	1	no	—
583	C₂	—	2	1	no	—
584	C₂	—	2	1	no	—
585	C₂	—	2	1	no	—
586	C₂	—	344	4	no	—
587	C₂	#19132831	1	1	yes	characteristic
588	C₂	#19135141	1	2	yes	—

	subgroup	G/H
center	C₂²	#14582777
commutator	C₂³×C₄₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₃
Fitting	C₂×C₄₃×#344	C₂
socle	C₂²×C₄₃	#386
prime radical	C₂³×D₁₇₂	C₂²
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	C₂×#344	D₄₃
hypocenter	C₄₃	#10939
LCS	G ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#344

Complements

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

N	H ≅ G/N	type
3. #19143013	C₂	semidirect
5. C₂×#14582669	C₂	semidirect
6. #19134333	C₂	semidirect
7. C₂×C₄₃×#344	C₂	semidirect
16. C₂×#13063241	C₄	semidirect
17. C₂×#13063241	C₄	semidirect
153. M₁₆×C₄₃	C₂²⋊C₄	semidirect
180. #10621877	C₂²⋊C₄	semidirect
291. C₂×#344	D₄₃	semidirect
324. C₄₃	#10939	semidirect
456. M₁₆	(C₂×D₄₃)⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13063241	2
#19143013	2
#19137175	2
C₂×#14582669	2
#19134333	2
C₂×C₄₃×#344	2
#10939	43