Subgroups — #25002973

Order 11008.

994 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13063253	C₂	1	1	yes	maximal, characteristic
2	#19143115	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582872	C₂	1	1	yes	maximal, characteristic
4	C₄×#13063284	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#14582671	C₂	1	1	yes	maximal, characteristic, complemented
6	#19134305	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₃×#339	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10621898	C₂²	1	1	yes	characteristic
9	C₂²×#10621877	C₂²	1	1	yes	characteristic
10	C₂×#13063284	C₂²	1	1	yes	characteristic
11	C₂×#13063284	C₂²	1	1	yes	characteristic
12	C₂×#13063253	—	2	1	no	—
13	C₂×#13063253	—	2	1	no	—
14	C₂×#13063253	—	2	2	no	—
15	C₂×#13063253	C₄	1	4	yes	complemented
16	#14582909	C₄	1	2	yes	complemented
17	#14582905	C₄	1	2	yes	complemented
18	#14582901	—	2	2	no	—
19	#14582896	—	2	2	no	—
20	#14582872	—	2	2	no	—
21	#14582872	C₄	1	4	yes	complemented
22	C₂×#13063239	—	2	2	no	—
23	C₄×C₄⋊Dic₄₃	—	2	2	no	—
24	C₄×C₂²⋊Dic₄₃	—	2	2	no	—
25	#14582745	—	2	1	no	—
26	C₄²×Dic₄₃	—	2	1	no	—
27	#14582671	—	2	2	no	—
28	#14582659	—	2	2	no	—
29	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
30	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
32	C₄₃×#339	—	2	2	no	—
33	C₂×#10621898	—	2	1	no	—
34	C₂×#10621898	—	2	1	no	—
35	C₂×#10621898	—	2	1	no	—
36	C₂×#10621898	—	2	1	no	—
37	C₂×#10621898	—	2	1	no	—
38	C₂×#10621898	—	2	1	no	—
39	C₂×#10621898	—	2	1	no	—
40	C₂×#10621898	—	2	1	no	—
41	C₂×#10621898	—	2	1	no	—
42	C₂×#10621898	—	2	1	no	—
43	C₂×#10621898	C₂×C₄	1	2	yes	—
44	C₂×#10621898	C₂×C₄	1	2	yes	—
45	C₂²×Dic₈₆	C₂×C₄	1	1	yes	characteristic
46	C₂²×D₁₇₂	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₂²⋊D₄₃	—	2	1	no	—
48	C₂²×C₄×D₄₃	—	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	C₂×C₄	1	2	yes	—
55	C₂²×C₄₃⋊C₈	—	2	1	no	—
56	#13063284	—	2	1	no	—
57	#13063284	—	2	1	no	—
58	#13063284	—	2	1	no	—
59	#13063284	—	2	1	no	—
60	#13063284	C₂×C₄	1	2	yes	—
61	#13063284	C₂×C₄	1	2	yes	—
62	#13063284	D₄	1	2	yes	—
63	#13063284	D₄	1	2	yes	—
64	C₂×C₄⋊Dic₄₃	—	2	1	no	—
65	C₂×C₄⋊Dic₄₃	D₄	1	2	yes	—
66	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
67	C₂×C₂²⋊Dic₄₃	D₄	1	2	yes	—
68	C₂×C₄×Dic₄₃	—	2	1	no	—
69	C₂×C₄×Dic₄₃	—	2	1	no	—
70	C₂×C₄×Dic₄₃	—	2	4	no	—
71	#13063253	—	2	4	no	—
72	#13063253	—	2	4	no	—
73	#13063250	—	2	4	no	—
74	#13063247	—	2	4	no	—
75	#13063239	—	2	8	no	—
76	C₄₃⋊#95	—	2	4	no	—
77	C₂³×C₄×C₄₃	—	2	1	no	—
78	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
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	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	C₂×C₄	1	2	yes	—
90	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
92	C₂×C₄²×C₄₃	—	2	1	no	—
93	C₂×C₄²×C₄₃	—	2	1	no	—
94	C₂×C₄²×C₄₃	—	2	1	no	—
95	C₂×C₄²×C₄₃	—	2	1	no	—
96	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
97	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₄₃	D₄	1	2	yes	—
100	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
101	C₂³×D₄₃	—	2	1	no	—
102	C₂²×C₄×C₄₃	—	2	2	no	—
103	C₂²×C₄×C₄₃	—	2	1	no	—
104	C₂²×C₄×C₄₃	—	2	1	no	—
105	C₂²×C₄×C₄₃	—	2	2	no	—
106	C₂²×C₄×C₄₃	—	4	4	no	—
107	C₂²×C₄×C₄₃	—	4	1	no	—
108	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
117	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
118	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
120	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
121	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
122	C₂×C₂²⋊D₄₃	—	2	2	no	—
123	C₂×C₂²⋊D₄₃	—	2	2	no	—
124	C₂×C₂²⋊D₄₃	—	4	1	no	—
125	C₂×C₂²⋊D₄₃	—	4	1	no	—
126	C₂×C₂²⋊D₄₃	—	4	1	no	—
127	C₂×C₂²⋊D₄₃	—	4	1	no	—
128	C₂²×Dic₄₃	—	2	1	no	—
129	C₂²×Dic₄₃	—	2	2	no	—
130	C₂²×Dic₄₃	—	2	2	no	—
131	#10621898	—	2	2	no	—
132	#10621898	—	2	2	no	—
133	#10621898	—	2	2	no	—
134	#10621898	—	2	2	no	—
135	#10621898	—	2	2	no	—
136	#10621898	—	2	2	no	—
137	#10621898	—	2	2	no	—
138	#10621898	—	2	2	no	—
139	#10621898	—	4	1	no	—
140	#10621898	—	4	1	no	—
141	#10621898	—	4	1	no	—
142	#10621898	—	4	1	no	—
143	#10621898	—	4	1	no	—
144	#10621898	—	4	1	no	—
145	#10621898	—	4	1	no	—
146	#10621898	—	4	1	no	—
147	C₂×D₁₇₂	—	2	1	no	—
148	C₂×D₁₇₂	—	2	1	no	—
149	C₂×D₁₇₂	—	2	1	no	—
150	C₂×D₁₇₂	—	2	1	no	—
151	C₂×D₁₇₂	—	2	1	no	—
152	C₂×D₁₇₂	C₄²	1	2	yes	complemented
153	C₂×C₄×D₄₃	—	2	2	no	—
154	C₂×C₄×D₄₃	—	2	2	no	—
155	C₂×C₄×D₄₃	—	4	1	no	—
156	C₂×C₄×D₄₃	—	4	1	no	—
157	C₂×C₄×D₄₃	—	4	1	no	—
158	C₂×C₄×D₄₃	—	4	1	no	—
159	C₂×Dic₈₆	—	2	1	no	—
160	C₂×Dic₈₆	—	2	1	no	—
161	C₂×Dic₈₆	—	2	1	no	—
162	C₂×Dic₈₆	—	2	1	no	—
163	C₂×Dic₈₆	—	2	1	no	—
164	C₂×Dic₈₆	C₄²	1	2	yes	complemented
165	M₁₆×C₄₃	—	2	2	no	—
166	M₁₆×C₄₃	—	2	2	no	—
167	M₁₆×C₄₃	—	4	1	no	—
168	M₁₆×C₄₃	—	4	1	no	—
169	C₂×C₈×C₄₃	—	2	2	no	—
170	C₂×C₈×C₄₃	—	4	1	no	—
171	C₂×C₈×C₄₃	—	4	1	no	—
172	C₄⋊C₄×C₄₃	—	2	2	no	—
173	C₄⋊C₄×C₄₃	—	4	1	no	—
174	C₂²⋊C₄×C₄₃	—	2	2	no	—
175	C₂²⋊C₄×C₄₃	—	4	1	no	—
176	C₄²×C₄₃	—	2	2	no	—
177	C₄²×C₄₃	—	2	2	no	—
178	C₄²×C₄₃	—	2	1	no	—
179	C₄²×C₄₃	—	2	1	no	—
180	C₄²×C₄₃	—	2	2	no	—
181	C₄²×C₄₃	—	4	1	no	—
182	C₄²×C₄₃	C₂²⋊C₄	1	2	yes	—
183	C₄²×C₄₃	C₂²⋊C₄	1	2	yes	—
184	C₂²⋊Dic₄₃	—	2	2	no	—
185	C₂²⋊Dic₄₃	—	2	2	no	—
186	C₂²⋊Dic₄₃	—	2	2	no	—
187	C₂²⋊Dic₄₃	C₂²⋊C₄	1	4	yes	—
188	C₄⋊Dic₄₃	—	2	2	no	—
189	C₄⋊Dic₄₃	—	2	2	no	—
190	C₄⋊Dic₄₃	—	2	2	no	—
191	C₄⋊Dic₄₃	C₂²⋊C₄	1	4	yes	—
192	C₄×Dic₄₃	—	2	2	no	—
193	C₄×Dic₄₃	—	2	2	no	—
194	C₄×Dic₄₃	—	2	2	no	—
195	C₄×Dic₄₃	—	2	2	no	—
196	C₄×Dic₄₃	—	4	8	no	—
197	#10621877	—	2	2	no	—
198	#10621877	—	2	2	no	—
199	#10621877	—	4	1	no	—
200	#10621877	—	4	1	no	—
201	C₂×C₄₃⋊C₈	—	2	2	no	—
202	C₂×C₄₃⋊C₈	—	4	1	no	—
203	C₂×C₄₃⋊C₈	—	4	1	no	—
204	C₂³×C₄₃	—	4	2	no	—
205	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
207	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
208	C₂³×C₄₃	#120	1	1	yes	characteristic
209	C₂³×C₄₃	#121	1	1	yes	characteristic
210	C₂³×C₄₃	#121	1	1	yes	characteristic
211	C₂³×C₄₃	#123	1	1	yes	characteristic
212	C₂²×D₄₃	—	2	2	no	—
213	C₂²×D₄₃	—	4	1	no	—
214	C₂²×D₄₃	—	4	1	no	—
215	C₂²×D₄₃	—	8	2	no	—
216	C₂×C₄×C₄₃	—	2	4	no	—
217	C₂×C₄×C₄₃	—	2	2	no	—
218	C₂×C₄×C₄₃	—	2	2	no	—
219	C₂×C₄×C₄₃	—	4	4	no	—
220	C₂×C₄×C₄₃	—	4	4	no	—
221	C₂×C₄×C₄₃	—	4	2	no	—
222	C₂×C₄×C₄₃	—	4	2	no	—
223	C₂×C₄×C₄₃	—	8	2	no	—
224	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
225	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
228	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
229	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
230	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
233	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
234	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
235	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
236	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
237	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
238	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
239	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
240	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
241	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
242	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
243	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
244	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
245	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
246	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
247	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
248	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
249	C₂×C₄×C₄₃	#126	1	1	yes	characteristic
250	C₂×C₄×C₄₃	#126	1	1	yes	characteristic
251	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
252	C₂²⋊D₄₃	—	4	2	no	—
253	C₂²⋊D₄₃	—	4	2	no	—
254	C₂²⋊D₄₃	—	4	2	no	—
255	C₂²⋊D₄₃	—	4	2	no	—
256	C₂×Dic₄₃	—	2	2	no	—
257	C₂×Dic₄₃	—	2	4	no	—
258	C₂×Dic₄₃	—	2	4	no	—
259	C₂×Dic₄₃	—	4	4	no	—
260	C₂×Dic₄₃	—	4	4	no	—
261	C₂×Dic₄₃	—	4	1	no	—
262	C₂×Dic₄₃	—	4	1	no	—
263	D₁₇₂	—	2	2	no	—
264	D₁₇₂	—	2	2	no	—
265	D₁₇₂	—	4	1	no	—
266	D₁₇₂	—	4	1	no	—
267	C₄×D₄₃	—	4	2	no	—
268	C₄×D₄₃	—	4	2	no	—
269	C₄×D₄₃	—	4	2	no	—
270	C₄×D₄₃	—	4	2	no	—
271	Dic₈₆	—	2	2	no	—
272	Dic₈₆	—	2	2	no	—
273	Dic₈₆	—	4	1	no	—
274	Dic₈₆	—	4	1	no	—
275	C₈×C₄₃	—	4	2	no	—
276	C₄₃⋊C₈	—	4	2	no	—
277	#10945	—	43	1	no	maximal, Sylow
278	C₂²×C₄₃	—	2	2	no	—
279	C₂²×C₄₃	—	2	2	no	—
280	C₂²×C₄₃	—	2	2	no	—
281	C₂²×C₄₃	—	4	1	no	—
282	C₂²×C₄₃	—	4	1	no	—
283	C₂²×C₄₃	—	4	1	no	—
284	C₂²×C₄₃	—	4	1	no	—
285	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
286	C₂²×C₄₃	#386	1	1	yes	characteristic
287	C₂²×C₄₃	#386	1	1	yes	characteristic
288	C₂²×C₄₃	#386	1	1	yes	characteristic
289	C₂²×C₄₃	#388	1	1	yes	characteristic
290	C₂²×C₄₃	#388	1	1	yes	characteristic
291	C₂²×C₄₃	#390	1	1	yes	characteristic
292	C₂×D₄₃	—	4	2	no	—
293	C₂×D₄₃	—	8	2	no	—
294	C₂×D₄₃	—	8	2	no	—
295	C₂×D₄₃	—	8	2	no	—
296	C₄×C₄₃	—	2	4	no	—
297	C₄×C₄₃	—	4	2	no	—
298	C₄×C₄₃	—	8	2	no	—
299	C₄×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
300	C₄×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
301	C₄×C₄₃	#388	1	1	yes	characteristic
302	C₄×C₄₃	#388	1	1	yes	characteristic
303	C₄×C₄₃	#388	1	1	yes	characteristic
304	C₄×C₄₃	#388	1	1	yes	characteristic
305	C₄×C₄₃	#390	1	1	yes	characteristic
306	C₄×C₄₃	#390	1	1	yes	characteristic
307	Dic₄₃	—	4	4	no	—
308	Dic₄₃	—	4	4	no	—
309	Dic₄₃	—	4	2	no	—
310	C₂²×#104	—	43	1	no	—
311	#2896	—	43	1	no	—
312	C₂×#410	—	43	1	no	—
313	C₄×#117	—	43	1	no	—
314	C₂×#344	—	43	1	no	—
315	#1733	—	43	1	no	—
316	C₂×#339	D₄₃	1	1	yes	characteristic, complemented
317	C₂×C₄₃	—	2	1	no	—
318	C₂×C₄₃	—	2	1	no	—
319	C₂×C₄₃	—	2	1	no	—
320	C₂×C₄₃	—	2	1	no	—
321	C₂×C₄₃	—	2	1	no	—
322	C₂×C₄₃	—	2	1	no	—
323	C₂×C₄₃	#1437	1	1	yes	characteristic
324	C₂×C₄₃	#1906	1	2	yes	—
325	D₄₃	—	8	2	no	—
326	C₂²×#41	—	43	1	no	—
327	C₂²×M₁₆	—	43	1	no	—
328	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
329	C₂×#117	—	43	1	no	—
330	C₂×#117	—	43	1	no	—
331	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
332	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
333	C₂×#104	—	43	4	no	—
334	C₂×#104	—	86	1	no	—
335	C₂×#104	—	86	1	no	—
336	C₂×#104	—	86	2	no	—
337	#419	—	43	2	no	—
338	#418	—	43	2	no	—
339	#417	—	86	2	no	—
340	#416	—	86	2	no	—
341	#410	—	43	4	no	—
342	#410	—	86	2	no	—
343	C₂×#99	—	86	2	no	—
344	C₄×C₄⋊C₄	—	86	2	no	—
345	C₄×C₂²⋊C₄	—	86	2	no	—
346	#376	—	86	1	no	—
347	C₄³	—	86	1	no	—
348	#344	—	86	2	no	—
349	#339	—	2	2	no	—
350	#339	—	86	2	no	—
351	C₄₃	#10945	1	1	yes	characteristic, complemented, Sylow
352	C₂×#41	—	43	2	no	—
353	C₂×#41	—	43	2	no	—
354	C₂×#41	—	86	1	no	—
355	C₂×#41	—	86	1	no	—
356	C₂×#41	—	86	1	no	—
357	C₂×#41	—	86	1	no	—
358	C₂×#41	—	86	1	no	—
359	C₂×#41	—	86	1	no	—
360	C₂×#41	—	86	1	no	—
361	C₂×#41	—	86	1	no	—
362	C₂×#41	—	86	1	no	—
363	C₂×#41	—	86	1	no	—
364	C₂²×Q₈	—	43	1	no	—
365	C₂²×D₄	—	43	1	no	—
366	C₂²×D₄	—	86	1	no	—
367	C₂³×C₄	—	2	1	no	—
368	C₂³×C₄	—	86	1	no	—
369	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
370	C₂×M₁₆	—	2	1	no	—
371	C₂×M₁₆	—	2	1	no	—
372	C₂×M₁₆	—	2	1	no	—
373	C₂×M₁₆	—	2	1	no	—
374	C₂×M₁₆	—	2	1	no	—
375	C₂×M₁₆	—	43	2	no	—
376	C₂×M₁₆	—	86	1	no	—
377	C₂×M₁₆	—	86	1	no	—
378	C₂×M₁₆	—	86	1	no	—
379	C₂×M₁₆	—	86	1	no	—
380	C₂×M₁₆	—	86	1	no	—
381	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
382	C₂²×C₈	—	2	1	no	—
383	C₂²×C₈	—	86	1	no	—
384	#117	—	2	1	no	—
385	#117	—	2	1	no	—
386	#117	—	2	1	no	—
387	#117	—	43	2	no	—
388	#117	—	43	2	no	—
389	#117	—	43	2	no	—
390	#117	—	43	2	no	—
391	#117	—	86	1	no	—
392	#117	—	86	1	no	—
393	#117	—	86	1	no	—
394	#117	—	86	1	no	—
395	#117	C₄×D₄₃	1	2	yes	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	—	43	2	no	—
398	C₂×C₄⋊C₄	—	86	1	no	—
399	C₂×C₂²⋊C₄	—	2	1	no	—
400	C₂×C₂²⋊C₄	—	43	2	no	—
401	C₂×C₂²⋊C₄	—	86	1	no	—
402	C₂×C₄²	—	2	1	no	—
403	C₂×C₄²	—	2	1	no	—
404	C₂×C₄²	—	2	1	no	—
405	C₂×C₄²	—	2	1	no	—
406	C₂×C₄²	—	86	1	no	—
407	C₂×C₄²	—	86	1	no	—
408	C₂×C₄²	—	86	4	no	—
409	C₂×C₄²	C₄×D₄₃	1	2	yes	—
410	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
411	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
412	C₂×C₄²	C₂²⋊D₄₃	1	2	yes	—
413	#104	—	86	4	no	—
414	#104	—	86	4	no	—
415	#103	—	86	4	no	—
416	#102	—	86	4	no	—
417	#99	—	86	8	no	—
418	#95	—	86	4	no	—
419	C₂⁴	—	86	1	no	—
420	C₂⁴	D₄×D₄₃	1	1	yes	characteristic
421	#41	—	86	2	no	—
422	#41	—	86	2	no	—
423	#41	—	86	2	no	—
424	#41	—	86	2	no	—
425	#41	—	86	2	no	—
426	#41	—	86	2	no	—
427	#41	—	86	2	no	—
428	#41	—	86	2	no	—
429	#41	—	172	1	no	—
430	#41	—	172	1	no	—
431	#41	—	172	1	no	—
432	#41	—	172	1	no	—
433	#41	—	172	1	no	—
434	#41	—	172	1	no	—
435	#41	—	172	1	no	—
436	#41	—	172	1	no	—
437	C₂×Q₈	—	43	2	no	—
438	C₂×Q₈	—	86	1	no	—
439	C₂×Q₈	—	86	1	no	—
440	C₂×Q₈	—	86	1	no	—
441	C₂×Q₈	—	86	1	no	—
442	C₂×Q₈	—	86	1	no	—
443	C₂×D₄	—	43	2	no	—
444	C₂×D₄	—	86	2	no	—
445	C₂×D₄	—	86	2	no	—
446	C₂×D₄	—	86	1	no	—
447	C₂×D₄	—	86	1	no	—
448	C₂×D₄	—	86	1	no	—
449	C₂×D₄	—	86	1	no	—
450	C₂×D₄	—	86	1	no	—
451	C₂×D₄	—	172	1	no	—
452	C₂×D₄	—	172	1	no	—
453	C₂×D₄	—	172	1	no	—
454	C₂×D₄	—	172	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	4	4	no	—
460	C₂²×C₄	—	4	1	no	—
461	C₂²×C₄	—	86	1	no	—
462	C₂²×C₄	—	86	2	no	—
463	C₂²×C₄	—	86	2	no	—
464	C₂²×C₄	—	86	2	no	—
465	C₂²×C₄	—	86	2	no	—
466	C₂²×C₄	—	172	1	no	—
467	C₂²×C₄	—	172	1	no	—
468	C₂²×C₄	—	172	1	no	—
469	C₂²×C₄	—	172	1	no	—
470	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
471	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
472	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
473	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
474	C₂²×C₄	#10621898	1	1	yes	characteristic
475	C₂²×C₄	#10621898	1	1	yes	characteristic
476	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
477	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
478	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
479	C₂²×C₄	#10621900	1	1	yes	characteristic
480	C₂²×C₄	#10621900	1	1	yes	characteristic
481	C₂²×C₄	#10621902	1	1	yes	characteristic
482	C₂²×C₄	#10621902	1	1	yes	characteristic
483	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
484	M₁₆	—	2	2	no	—
485	M₁₆	—	2	2	no	—
486	M₁₆	—	4	1	no	—
487	M₁₆	—	4	1	no	—
488	M₁₆	—	86	2	no	—
489	M₁₆	—	86	2	no	—
490	M₁₆	—	172	1	no	—
491	M₁₆	—	172	1	no	—
492	C₂×C₈	—	2	2	no	—
493	C₂×C₈	—	4	1	no	—
494	C₂×C₈	—	4	1	no	—
495	C₂×C₈	—	86	2	no	—
496	C₂×C₈	—	172	1	no	—
497	C₂×C₈	—	172	1	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	4	1	no	—
500	C₄⋊C₄	—	43	4	no	—
501	C₄⋊C₄	—	86	2	no	—
502	C₄⋊C₄	—	86	2	no	—
503	C₄⋊C₄	—	86	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	4	1	no	—
506	C₂²⋊C₄	—	43	4	no	—
507	C₂²⋊C₄	—	86	2	no	—
508	C₂²⋊C₄	—	86	2	no	—
509	C₂²⋊C₄	—	86	2	no	—
510	C₄²	—	2	2	no	—
511	C₄²	—	2	2	no	—
512	C₄²	—	2	1	no	—
513	C₄²	—	2	1	no	—
514	C₄²	—	2	2	no	—
515	C₄²	—	4	1	no	—
516	C₄²	—	86	2	no	—
517	C₄²	—	86	2	no	—
518	C₄²	—	86	2	no	—
519	C₄²	—	86	2	no	—
520	C₄²	—	172	8	no	—
521	C₄²	(C₂×D₄₃)⋊C₄	1	2	yes	—
522	C₄²	(C₂×D₄₃)⋊C₄	1	2	yes	—
523	C₂³	—	4	2	no	—
524	C₂³	—	86	2	no	—
525	C₂³	—	344	2	no	—
526	C₂³	—	172	1	no	—
527	C₂³	—	172	1	no	—
528	C₂³	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
529	C₂³	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
530	C₂³	#13063287	1	1	yes	characteristic
531	C₂³	#13063295	1	1	yes	characteristic
532	C₂³	#13063297	1	1	yes	characteristic
533	C₂³	#13063298	1	1	yes	characteristic
534	C₂³	#13063310	1	1	yes	characteristic
535	Q₈	—	86	2	no	—
536	Q₈	—	86	2	no	—
537	Q₈	—	172	1	no	—
538	Q₈	—	172	1	no	—
539	D₄	—	86	2	no	—
540	D₄	—	86	2	no	—
541	D₄	—	172	2	no	—
542	D₄	—	172	2	no	—
543	D₄	—	172	2	no	—
544	D₄	—	172	2	no	—
545	D₄	—	172	1	no	—
546	D₄	—	172	1	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	4	4	no	—
551	C₂×C₄	—	4	4	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	8	2	no	—
555	C₂×C₄	—	86	2	no	—
556	C₂×C₄	—	86	4	no	—
557	C₂×C₄	—	86	4	no	—
558	C₂×C₄	—	172	4	no	—
559	C₂×C₄	—	172	4	no	—
560	C₂×C₄	—	172	1	no	—
561	C₂×C₄	—	172	1	no	—
562	C₂×C₄	—	172	2	no	—
563	C₂×C₄	—	172	2	no	—
564	C₂×C₄	—	172	2	no	—
565	C₂×C₄	—	172	2	no	—
566	C₂×C₄	C₄²×D₄₃	1	1	yes	characteristic
567	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
568	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
569	C₂×C₄	#13063282	1	1	yes	characteristic
570	C₂×C₄	#13063283	1	1	yes	characteristic
571	C₂×C₄	#13063283	1	1	yes	characteristic
572	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
573	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
574	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
575	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
576	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
577	C₂×C₄	#13063287	1	1	yes	characteristic
578	C₂×C₄	#13063287	1	1	yes	characteristic
579	C₂×C₄	#13063287	1	1	yes	characteristic
580	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
581	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
582	C₂×C₄	#13063297	1	1	yes	characteristic
583	C₂×C₄	#13063298	1	1	yes	characteristic
584	C₂×C₄	#13063300	1	1	yes	characteristic
585	C₂×C₄	#13063300	1	1	yes	characteristic
586	C₂×C₄	#13063309	1	1	yes	characteristic
587	C₂×C₄	#13063310	1	1	yes	characteristic
588	C₂×C₄	#13063311	1	1	yes	characteristic
589	C₂×C₄	#13063311	1	1	yes	characteristic
590	C₂×C₄	#13063314	1	1	yes	characteristic
591	C₂×C₄	#13063320	1	1	yes	characteristic
592	C₂×C₄	#13063320	1	1	yes	characteristic
593	C₂×C₄	#13063321	1	1	yes	characteristic
594	C₈	—	4	2	no	—
595	C₈	—	172	2	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	4	1	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	344	2	no	—
604	C₂²	—	344	2	no	—
605	C₂²	—	344	2	no	—
606	C₂²	—	172	2	no	—
607	C₂²	#14582746	1	1	yes	characteristic
608	C₂²	#14582776	1	1	yes	characteristic
609	C₂²	#14582777	1	1	yes	characteristic
610	C₂²	#14582777	1	1	yes	characteristic
611	C₂²	#14582788	1	1	yes	characteristic
612	C₂²	#14582789	1	1	yes	characteristic
613	C₂²	#14582799	1	1	yes	characteristic
614	C₄	—	2	4	no	—
615	C₄	—	4	2	no	—
616	C₄	—	8	2	no	—
617	C₄	—	172	4	no	—
618	C₄	—	172	4	no	—
619	C₄	—	172	2	no	—
620	C₄	#14582746	1	1	yes	characteristic
621	C₄	C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
622	C₄	#14582788	1	1	yes	characteristic
623	C₄	#14582789	1	1	yes	characteristic
624	C₄	#14582791	1	1	yes	characteristic
625	C₄	#14582791	1	1	yes	characteristic
626	C₄	#14582799	1	1	yes	characteristic
627	C₄	#14582800	1	1	yes	characteristic
628	C₂	—	2	1	no	—
629	C₂	—	2	1	no	—
630	C₂	—	2	1	no	—
631	C₂	—	2	1	no	—
632	C₂	—	2	1	no	—
633	C₂	—	2	1	no	—
634	C₂	—	344	2	no	—
635	C₂	#19132831	1	1	yes	characteristic
636	C₂	#19135095	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#13063300
commutator	C₂×C₄×C₄₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₃
Fitting	C₂×C₄₃×#339	C₂
socle	C₂²×C₄₃	#386
prime radical	C₂²×#10621898	C₂²
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	C₂×#339	D₄₃
hypocenter	C₄₃	#10945
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#339

Complements

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

N	H ≅ G/N	type
4. C₄×#13063284	C₂	semidirect
5. C₂×#14582671	C₂	semidirect
6. #19134305	C₂	semidirect
7. C₂×C₄₃×#339	C₂	semidirect
15. C₂×#13063253	C₄	semidirect
16. #14582909	C₄	semidirect
17. #14582905	C₄	semidirect
21. #14582872	C₄	semidirect
152. C₂×D₁₇₂	C₄²	semidirect
164. C₂×Dic₈₆	C₄²	semidirect
316. C₂×#339	D₄₃	semidirect
351. C₄₃	#10945	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13063253	2
#19143115	2
C₂×#14582872	2
C₄×#13063284	2
C₂×#14582671	2
#19134305	2
C₂×C₄₃×#339	2
#10945	43