Subgroups — #25003007

Order 11008.

916 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582915	C₂	1	1	yes	maximal, characteristic
2	#19143115	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582872	C₂	1	1	yes	maximal, characteristic
4	#19134327	C₂	1	1	yes	maximal, characteristic, complemented
5	#19134306	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14582656	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#2873	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10621898	C₂²	1	1	yes	characteristic
9	C₂×#13063284	C₂²	1	1	yes	characteristic
10	C₂×#13063284	C₂²	1	1	yes	characteristic
11	C₂×#13063284	C₂²	1	1	yes	characteristic
12	#14582915	—	2	2	no	—
13	#14582915	—	2	2	no	—
14	C₂×#13063251	C₄	1	4	yes	complemented
15	#14582909	C₄	1	2	yes	complemented
16	#14582905	C₄	1	2	yes	complemented
17	#14582901	—	2	2	no	—
18	#14582896	—	2	2	no	—
19	#14582872	—	2	2	no	—
20	#14582872	C₄	1	4	yes	complemented
21	C₂×#13063239	—	2	2	no	—
22	#14582665	—	2	2	no	—
23	#14582660	—	2	2	no	—
24	#14582656	—	2	2	no	—
25	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
26	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
28	C₄₃×#405	—	2	2	no	—
29	C₄₃×#405	—	2	2	no	—
30	C₄×M₁₆×C₄₃	—	2	2	no	—
31	C₂×#10621898	—	2	1	no	—
32	C₂×#10621898	—	2	1	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	C₂×C₄	1	2	yes	—
42	C₂×#10621898	C₂×C₄	1	2	yes	—
43	C₂²×Dic₈₆	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₁₇₂	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₂²⋊D₄₃	—	2	1	no	—
46	C₂²×C₄×D₄₃	—	2	1	no	—
47	#13063284	—	2	1	no	—
48	#13063284	—	2	1	no	—
49	#13063284	—	2	1	no	—
50	#13063284	—	2	1	no	—
51	#13063284	—	2	1	no	—
52	#13063284	—	2	1	no	—
53	#13063284	—	2	1	no	—
54	#13063284	—	2	1	no	—
55	#13063284	—	2	1	no	—
56	#13063284	—	2	1	no	—
57	#13063284	C₂×C₄	1	2	yes	—
58	#13063284	C₂×C₄	1	2	yes	—
59	C₂×C₄⋊Dic₄₃	—	2	1	no	—
60	C₂×C₄⋊Dic₄₃	—	2	1	no	—
61	C₂×C₄⋊Dic₄₃	—	2	1	no	—
62	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
63	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
64	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
65	C₂×C₄×Dic₄₃	—	2	1	no	—
66	C₂×C₄×Dic₄₃	—	2	1	no	—
67	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
68	#13063251	—	2	8	no	—
69	#13063250	—	2	4	no	—
70	#13063247	—	2	4	no	—
71	#13063239	—	2	8	no	—
72	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
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	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
85	C₂²×C₈×C₄₃	—	2	1	no	—
86	C₂²×C₈×C₄₃	D₄	1	2	yes	—
87	#117×C₄₃	—	2	1	no	—
88	#117×C₄₃	—	2	1	no	—
89	#117×C₄₃	C₂×C₄	1	2	yes	—
90	#117×C₄₃	D₄	1	2	yes	—
91	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
93	C₂×C₄²×C₄₃	—	2	1	no	—
94	#97×C₄₃	—	2	4	no	—
95	C₄×C₈×C₄₃	—	2	4	no	—
96	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
97	C₂³×D₄₃	—	2	1	no	—
98	C₂²×C₄×C₄₃	—	2	2	no	—
99	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
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	#41	1	1	yes	characteristic
108	C₂²×C₄×C₄₃	#41	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	C₂×C₂²⋊D₄₃	—	2	2	no	—
114	C₂×C₂²⋊D₄₃	—	2	2	no	—
115	C₂×C₂²⋊D₄₃	—	4	1	no	—
116	C₂×C₂²⋊D₄₃	—	4	1	no	—
117	C₂×C₂²⋊D₄₃	—	4	1	no	—
118	C₂×C₂²⋊D₄₃	—	4	1	no	—
119	C₂²×Dic₄₃	—	2	1	no	—
120	C₂²×Dic₄₃	—	2	2	no	—
121	C₂²×Dic₄₃	—	4	1	no	—
122	C₂²×Dic₄₃	—	4	1	no	—
123	#10621898	—	2	2	no	—
124	#10621898	—	2	2	no	—
125	#10621898	—	2	2	no	—
126	#10621898	—	2	2	no	—
127	#10621898	—	2	2	no	—
128	#10621898	—	2	2	no	—
129	#10621898	—	2	2	no	—
130	#10621898	—	2	2	no	—
131	#10621898	—	4	1	no	—
132	#10621898	—	4	1	no	—
133	#10621898	—	4	1	no	—
134	#10621898	—	4	1	no	—
135	#10621898	—	4	1	no	—
136	#10621898	—	4	1	no	—
137	#10621898	—	4	1	no	—
138	#10621898	—	4	1	no	—
139	C₂×D₁₇₂	—	2	1	no	—
140	C₂×D₁₇₂	—	2	1	no	—
141	C₂×D₁₇₂	—	2	1	no	—
142	C₂×D₁₇₂	—	2	1	no	—
143	C₂×D₁₇₂	—	2	1	no	—
144	C₂×D₁₇₂	C₄²	1	2	yes	—
145	C₂×C₄×D₄₃	—	2	2	no	—
146	C₂×C₄×D₄₃	—	2	2	no	—
147	C₂×C₄×D₄₃	—	4	1	no	—
148	C₂×C₄×D₄₃	—	4	1	no	—
149	C₂×C₄×D₄₃	—	4	1	no	—
150	C₂×C₄×D₄₃	—	4	1	no	—
151	C₂×Dic₈₆	—	2	1	no	—
152	C₂×Dic₈₆	—	2	1	no	—
153	C₂×Dic₈₆	—	2	1	no	—
154	C₂×Dic₈₆	—	2	1	no	—
155	C₂×Dic₈₆	—	2	1	no	—
156	C₂×Dic₈₆	C₄²	1	2	yes	—
157	M₁₆×C₄₃	—	2	2	no	—
158	M₁₆×C₄₃	—	2	2	no	—
159	M₁₆×C₄₃	—	2	2	no	—
160	M₁₆×C₄₃	—	2	2	no	—
161	M₁₆×C₄₃	—	2	2	no	—
162	M₁₆×C₄₃	—	2	2	no	—
163	M₁₆×C₄₃	—	2	2	no	—
164	M₁₆×C₄₃	C₂²⋊C₄	1	4	yes	—
165	C₂×C₈×C₄₃	—	2	2	no	—
166	C₂×C₈×C₄₃	—	2	2	no	—
167	C₂×C₈×C₄₃	—	2	2	no	—
168	C₂×C₈×C₄₃	—	2	2	no	—
169	C₂×C₈×C₄₃	—	2	2	no	—
170	C₂×C₈×C₄₃	C₂²⋊C₄	1	4	yes	—
171	C₄⋊C₄×C₄₃	—	2	2	no	—
172	C₄⋊C₄×C₄₃	—	2	2	no	—
173	C₂²⋊C₄×C₄₃	—	2	2	no	—
174	C₂²⋊C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
175	C₄²×C₄₃	—	2	2	no	—
176	C₄²×C₄₃	—	2	2	no	—
177	C₂²⋊Dic₄₃	—	2	2	no	—
178	C₂²⋊Dic₄₃	—	2	2	no	—
179	C₂²⋊Dic₄₃	—	4	1	no	—
180	C₂²⋊Dic₄₃	—	4	1	no	—
181	C₂²⋊Dic₄₃	—	4	1	no	—
182	C₂²⋊Dic₄₃	—	4	1	no	—
183	C₄⋊Dic₄₃	—	2	2	no	—
184	C₄⋊Dic₄₃	—	2	2	no	—
185	C₄⋊Dic₄₃	—	4	1	no	—
186	C₄⋊Dic₄₃	—	4	1	no	—
187	C₄⋊Dic₄₃	—	4	1	no	—
188	C₄⋊Dic₄₃	—	4	1	no	—
189	C₄×Dic₄₃	—	2	2	no	—
190	C₄×Dic₄₃	—	2	2	no	—
191	C₄×Dic₄₃	—	2	2	no	—
192	C₄×Dic₄₃	—	2	2	no	—
193	C₄×Dic₄₃	—	4	1	no	—
194	C₄×Dic₄₃	—	4	1	no	—
195	C₂³×C₄₃	—	8	1	no	—
196	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
197	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
198	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
199	C₂³×C₄₃	#121	1	1	yes	characteristic
200	C₂³×C₄₃	#121	1	1	yes	characteristic
201	C₂³×C₄₃	#124	1	1	yes	characteristic
202	C₂³×C₄₃	#127	1	1	yes	characteristic
203	C₂²×D₄₃	—	2	2	no	—
204	C₂²×D₄₃	—	4	1	no	—
205	C₂²×D₄₃	—	4	1	no	—
206	C₂²×D₄₃	—	8	2	no	—
207	C₂×C₄×C₄₃	—	2	4	no	—
208	C₂×C₄×C₄₃	—	8	2	no	—
209	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
210	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
212	C₂×C₄×C₄₃	#117	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	C₄×D₄	1	1	yes	characteristic
224	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
225	C₂×C₄×C₄₃	#120	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	#126	1	1	yes	characteristic
236	C₂×C₄×C₄₃	#126	1	1	yes	characteristic
237	C₂²⋊D₄₃	—	4	2	no	—
238	C₂²⋊D₄₃	—	4	2	no	—
239	C₂²⋊D₄₃	—	4	2	no	—
240	C₂²⋊D₄₃	—	4	2	no	—
241	C₂×Dic₄₃	—	2	2	no	—
242	C₂×Dic₄₃	—	4	1	no	—
243	C₂×Dic₄₃	—	4	1	no	—
244	C₂×Dic₄₃	—	4	2	no	—
245	C₂×Dic₄₃	—	4	2	no	—
246	C₂×Dic₄₃	—	4	2	no	—
247	C₂×Dic₄₃	—	8	2	no	—
248	C₂×Dic₄₃	—	8	2	no	—
249	C₂×Dic₄₃	—	8	2	no	—
250	D₁₇₂	—	2	2	no	—
251	D₁₇₂	—	2	2	no	—
252	D₁₇₂	—	4	1	no	—
253	D₁₇₂	—	4	1	no	—
254	C₄×D₄₃	—	4	2	no	—
255	C₄×D₄₃	—	4	2	no	—
256	C₄×D₄₃	—	4	2	no	—
257	C₄×D₄₃	—	4	2	no	—
258	Dic₈₆	—	2	2	no	—
259	Dic₈₆	—	2	2	no	—
260	Dic₈₆	—	4	1	no	—
261	Dic₈₆	—	4	1	no	—
262	C₈×C₄₃	—	2	4	no	—
263	C₈×C₄₃	—	2	4	no	—
264	#10951	—	43	1	no	maximal, Sylow
265	C₂²×C₄₃	—	4	1	no	—
266	C₂²×C₄₃	—	4	1	no	—
267	C₂²×C₄₃	—	4	1	no	—
268	C₂²×C₄₃	—	4	1	no	—
269	C₂²×C₄₃	—	4	1	no	—
270	C₂²×C₄₃	—	4	1	no	—
271	C₂²×C₄₃	—	4	1	no	—
272	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
273	C₂²×C₄₃	#386	1	1	yes	characteristic
274	C₂²×C₄₃	#388	1	1	yes	characteristic
275	C₂²×C₄₃	#388	1	1	yes	characteristic
276	C₂²×C₄₃	#390	1	1	yes	characteristic
277	C₂²×C₄₃	#390	1	1	yes	characteristic
278	C₂²×C₄₃	#390	1	1	yes	characteristic
279	C₂×D₄₃	—	4	2	no	—
280	C₂×D₄₃	—	8	2	no	—
281	C₂×D₄₃	—	8	2	no	—
282	C₂×D₄₃	—	8	2	no	—
283	C₄×C₄₃	—	4	4	no	—
284	C₄×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
285	C₄×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
286	C₄×C₄₃	#386	1	1	yes	characteristic
287	C₄×C₄₃	#386	1	1	yes	characteristic
288	C₄×C₄₃	#388	1	1	yes	characteristic
289	C₄×C₄₃	#388	1	1	yes	characteristic
290	C₄×C₄₃	#388	1	1	yes	characteristic
291	C₄×C₄₃	#388	1	1	yes	characteristic
292	Dic₄₃	—	4	2	no	—
293	Dic₄₃	—	8	2	no	—
294	Dic₄₃	—	8	2	no	—
295	Dic₄₃	—	8	2	no	—
296	C₂×#421	—	43	1	no	—
297	#2896	—	43	1	no	—
298	C₂×#410	—	43	1	no	—
299	#2873	D₄₃	1	1	yes	characteristic, complemented
300	#1740	—	43	1	no	—
301	#1733	—	43	1	no	—
302	C₂×H(3,ℤ/4)	—	43	1	no	—
303	C₂×C₄₃	—	2	1	no	—
304	C₂×C₄₃	—	2	1	no	—
305	C₂×C₄₃	—	2	1	no	—
306	C₂×C₄₃	—	2	1	no	—
307	C₂×C₄₃	—	2	1	no	—
308	C₂×C₄₃	—	2	1	no	—
309	C₂×C₄₃	—	2	1	no	—
310	C₂×C₄₃	#1437	1	1	yes	characteristic
311	D₄₃	—	8	2	no	—
312	C₂²×#41	—	43	1	no	—
313	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
314	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
315	C₂×#117	—	43	1	no	—
316	C₂×#117	—	43	1	no	—
317	C₂×#117	—	43	1	no	—
318	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
319	#421	—	86	2	no	—
320	#421	—	86	2	no	—
321	C₂×#104	—	43	4	no	—
322	#419	—	43	2	no	—
323	#418	—	43	2	no	—
324	#417	—	86	2	no	—
325	#416	—	86	2	no	—
326	#410	—	43	4	no	—
327	#410	—	86	2	no	—
328	C₂×#99	—	86	2	no	—
329	#405	—	2	2	no	—
330	#405	—	2	2	no	—
331	C₄×M₁₆	—	2	2	no	—
332	#342	—	86	2	no	—
333	#339	—	86	2	no	—
334	H(3,ℤ/4)	—	86	2	no	—
335	C₄₃	#10951	1	1	yes	characteristic, complemented, Sylow
336	C₂×#41	—	43	2	no	—
337	C₂×#41	—	43	2	no	—
338	C₂×#41	—	86	1	no	—
339	C₂×#41	—	86	1	no	—
340	C₂×#41	—	86	1	no	—
341	C₂×#41	—	86	1	no	—
342	C₂×#41	—	86	1	no	—
343	C₂×#41	—	86	1	no	—
344	C₂×#41	—	86	1	no	—
345	C₂×#41	—	86	1	no	—
346	C₂×#41	—	86	1	no	—
347	C₂×#41	—	86	1	no	—
348	C₂²×Q₈	—	43	1	no	—
349	C₂²×D₄	—	43	1	no	—
350	C₂²×D₄	—	86	1	no	—
351	C₂³×C₄	—	86	1	no	—
352	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
353	C₂×M₁₆	—	2	1	no	—
354	C₂×M₁₆	—	2	1	no	—
355	C₂×M₁₆	—	2	1	no	—
356	C₂×M₁₆	—	2	1	no	—
357	C₂×M₁₆	—	2	1	no	—
358	C₂×M₁₆	—	2	1	no	—
359	C₂×M₁₆	—	2	1	no	—
360	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
361	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
362	C₂×M₁₆	D₁₇₂	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	C₂²⋊D₄₃	1	2	yes	—
367	#117	—	2	1	no	—
368	#117	—	2	1	no	—
369	#117	—	43	2	no	—
370	#117	—	43	2	no	—
371	#117	—	86	1	no	—
372	#117	—	86	1	no	—
373	#117	—	86	1	no	—
374	#117	—	86	1	no	—
375	#117	—	86	1	no	—
376	#117	—	86	1	no	—
377	#117	—	86	1	no	—
378	#117	—	86	1	no	—
379	#117	—	86	1	no	—
380	#117	—	86	1	no	—
381	#117	C₄×D₄₃	1	2	yes	—
382	#117	C₂²⋊D₄₃	1	2	yes	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	—	86	1	no	—
385	C₂×C₄⋊C₄	—	86	1	no	—
386	C₂×C₄⋊C₄	—	86	1	no	—
387	C₂×C₂²⋊C₄	—	86	1	no	—
388	C₂×C₂²⋊C₄	—	86	1	no	—
389	C₂×C₂²⋊C₄	—	86	1	no	—
390	C₂×C₂²⋊C₄	D₁₇₂	1	2	yes	—
391	C₂×C₄²	—	2	1	no	—
392	C₂×C₄²	—	43	2	no	—
393	C₂×C₄²	—	86	1	no	—
394	C₂×C₄²	—	86	1	no	—
395	#104	—	86	8	no	—
396	#103	—	86	4	no	—
397	#102	—	86	4	no	—
398	#99	—	86	8	no	—
399	#97	—	2	4	no	—
400	C₄×C₈	—	2	4	no	—
401	C₂⁴	—	86	1	no	—
402	C₂⁴	C₂×D₁₇₂	1	1	yes	characteristic
403	#41	—	86	2	no	—
404	#41	—	86	2	no	—
405	#41	—	86	2	no	—
406	#41	—	86	2	no	—
407	#41	—	86	2	no	—
408	#41	—	86	2	no	—
409	#41	—	86	2	no	—
410	#41	—	86	2	no	—
411	#41	—	172	1	no	—
412	#41	—	172	1	no	—
413	#41	—	172	1	no	—
414	#41	—	172	1	no	—
415	#41	—	172	1	no	—
416	#41	—	172	1	no	—
417	#41	—	172	1	no	—
418	#41	—	172	1	no	—
419	C₂×Q₈	—	43	2	no	—
420	C₂×Q₈	—	86	1	no	—
421	C₂×Q₈	—	86	1	no	—
422	C₂×Q₈	—	86	1	no	—
423	C₂×Q₈	—	86	1	no	—
424	C₂×Q₈	—	86	1	no	—
425	C₂×D₄	—	43	2	no	—
426	C₂×D₄	—	86	2	no	—
427	C₂×D₄	—	86	2	no	—
428	C₂×D₄	—	86	1	no	—
429	C₂×D₄	—	86	1	no	—
430	C₂×D₄	—	86	1	no	—
431	C₂×D₄	—	86	1	no	—
432	C₂×D₄	—	86	1	no	—
433	C₂×D₄	—	172	1	no	—
434	C₂×D₄	—	172	1	no	—
435	C₂×D₄	—	172	1	no	—
436	C₂×D₄	—	172	1	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	86	1	no	—
439	C₂²×C₄	—	86	2	no	—
440	C₂²×C₄	—	86	2	no	—
441	C₂²×C₄	—	86	2	no	—
442	C₂²×C₄	—	172	1	no	—
443	C₂²×C₄	—	172	1	no	—
444	C₂²×C₄	—	172	1	no	—
445	C₂²×C₄	—	172	1	no	—
446	C₂²×C₄	—	172	1	no	—
447	C₂²×C₄	—	172	1	no	—
448	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
449	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
450	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
451	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
453	C₂²×C₄	#10621898	1	1	yes	characteristic
454	C₂²×C₄	#10621898	1	1	yes	characteristic
455	C₂²×C₄	#10621898	1	1	yes	characteristic
456	C₂²×C₄	#10621898	1	1	yes	characteristic
457	C₂²×C₄	#10621898	1	1	yes	characteristic
458	C₂²×C₄	#10621898	1	1	yes	characteristic
459	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
460	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
461	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
462	M₁₆	—	2	2	no	—
463	M₁₆	—	2	2	no	—
464	M₁₆	—	2	2	no	—
465	M₁₆	—	2	2	no	—
466	M₁₆	—	2	2	no	—
467	M₁₆	—	2	2	no	—
468	M₁₆	—	2	2	no	—
469	M₁₆	(C₂×D₄₃)⋊C₄	1	4	yes	—
470	C₂×C₈	—	2	2	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	2	2	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	(C₂×D₄₃)⋊C₄	1	4	yes	—
476	C₄⋊C₄	—	2	2	no	—
477	C₄⋊C₄	—	2	2	no	—
478	C₄⋊C₄	—	86	2	no	—
479	C₄⋊C₄	—	86	2	no	—
480	C₄⋊C₄	—	172	1	no	—
481	C₄⋊C₄	—	172	1	no	—
482	C₄⋊C₄	—	172	1	no	—
483	C₄⋊C₄	—	172	1	no	—
484	C₂²⋊C₄	—	2	2	no	—
485	C₂²⋊C₄	—	86	2	no	—
486	C₂²⋊C₄	—	86	2	no	—
487	C₂²⋊C₄	—	172	1	no	—
488	C₂²⋊C₄	—	172	1	no	—
489	C₂²⋊C₄	—	172	1	no	—
490	C₂²⋊C₄	—	172	1	no	—
491	C₂²⋊C₄	(C₂×D₄₃)⋊C₄	1	4	yes	—
492	C₄²	—	2	2	no	—
493	C₄²	—	2	2	no	—
494	C₄²	—	86	2	no	—
495	C₄²	—	86	2	no	—
496	C₄²	—	86	2	no	—
497	C₄²	—	86	2	no	—
498	C₄²	—	172	1	no	—
499	C₄²	—	172	1	no	—
500	C₂³	—	8	1	no	—
501	C₂³	—	86	2	no	—
502	C₂³	—	344	2	no	—
503	C₂³	—	172	1	no	—
504	C₂³	—	172	1	no	—
505	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
506	C₂³	C₄×D₁₇₂	1	1	yes	characteristic
507	C₂³	C₄×D₁₇₂	1	1	yes	characteristic
508	C₂³	#13063299	1	1	yes	characteristic
509	C₂³	#13063299	1	1	yes	characteristic
510	C₂³	#13063313	1	1	yes	characteristic
511	C₂³	#13063322	1	1	yes	characteristic
512	Q₈	—	86	2	no	—
513	Q₈	—	86	2	no	—
514	Q₈	—	172	1	no	—
515	Q₈	—	172	1	no	—
516	D₄	—	86	2	no	—
517	D₄	—	86	2	no	—
518	D₄	—	172	2	no	—
519	D₄	—	172	2	no	—
520	D₄	—	172	2	no	—
521	D₄	—	172	2	no	—
522	D₄	—	172	1	no	—
523	D₄	—	172	1	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	8	2	no	—
526	C₂×C₄	—	86	2	no	—
527	C₂×C₄	—	344	2	no	—
528	C₂×C₄	—	344	2	no	—
529	C₂×C₄	—	344	2	no	—
530	C₂×C₄	—	172	2	no	—
531	C₂×C₄	—	172	2	no	—
532	C₂×C₄	—	172	2	no	—
533	C₂×C₄	—	172	1	no	—
534	C₂×C₄	—	172	1	no	—
535	C₂×C₄	—	172	2	no	—
536	C₂×C₄	—	172	2	no	—
537	C₂×C₄	—	172	2	no	—
538	C₂×C₄	—	172	2	no	—
539	C₂×C₄	C₄²×D₄₃	1	1	yes	characteristic
540	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
541	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
542	C₂×C₄	#13063282	1	1	yes	characteristic
543	C₂×C₄	#13063282	1	1	yes	characteristic
544	C₂×C₄	#13063282	1	1	yes	characteristic
545	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
546	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
547	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
548	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
549	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
550	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
551	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
552	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
553	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
554	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
555	C₂×C₄	#13063294	1	1	yes	characteristic
556	C₂×C₄	#13063299	1	1	yes	characteristic
557	C₂×C₄	#13063299	1	1	yes	characteristic
558	C₂×C₄	#13063299	1	1	yes	characteristic
559	C₂×C₄	#13063299	1	1	yes	characteristic
560	C₂×C₄	#13063308	1	1	yes	characteristic
561	C₂×C₄	#13063308	1	1	yes	characteristic
562	C₂×C₄	#13063308	1	1	yes	characteristic
563	C₂×C₄	#13063313	1	1	yes	characteristic
564	C₂×C₄	#13063313	1	1	yes	characteristic
565	C₂×C₄	#13063319	1	1	yes	characteristic
566	C₂×C₄	#13063319	1	1	yes	characteristic
567	C₈	—	2	4	no	—
568	C₈	—	2	4	no	—
569	C₂²	—	4	1	no	—
570	C₂²	—	4	1	no	—
571	C₂²	—	4	1	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	344	2	no	—
577	C₂²	—	344	2	no	—
578	C₂²	—	344	2	no	—
579	C₂²	—	172	2	no	—
580	C₂²	C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
581	C₂²	#14582778	1	1	yes	characteristic
582	C₂²	#14582790	1	1	yes	characteristic
583	C₂²	#14582790	1	1	yes	characteristic
584	C₂²	#14582801	1	1	yes	characteristic
585	C₂²	#14582801	1	1	yes	characteristic
586	C₂²	#14582801	1	1	yes	characteristic
587	C₄	—	4	4	no	—
588	C₄	—	344	2	no	—
589	C₄	—	344	2	no	—
590	C₄	—	344	2	no	—
591	C₄	—	172	2	no	—
592	C₄	C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
593	C₄	C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
594	C₄	#14582778	1	1	yes	characteristic
595	C₄	#14582778	1	1	yes	characteristic
596	C₄	#14582790	1	1	yes	characteristic
597	C₄	#14582790	1	1	yes	characteristic
598	C₄	#14582790	1	1	yes	characteristic
599	C₄	#14582790	1	1	yes	characteristic
600	C₂	—	2	1	no	—
601	C₂	—	2	1	no	—
602	C₂	—	2	1	no	—
603	C₂	—	2	1	no	—
604	C₂	—	2	1	no	—
605	C₂	—	2	1	no	—
606	C₂	—	2	1	no	—
607	C₂	—	344	2	no	—
608	C₂	#19132833	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14582778
commutator	C₂×C₄×C₄₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₃
Fitting	C₄₃×#2873	C₂
socle	C₂×C₄₃	#1437
prime radical	C₂²×#10621898	C₂²
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	#2873	D₄₃
hypocenter	C₄₃	#10951
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ #2873

Complements

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

N	H ≅ G/N	type
4. #19134327	C₂	semidirect
5. #19134306	C₂	semidirect
6. C₂×#14582656	C₂	semidirect
7. C₄₃×#2873	C₂	semidirect
14. C₂×#13063251	C₄	semidirect
15. #14582909	C₄	semidirect
16. #14582905	C₄	semidirect
20. #14582872	C₄	semidirect
299. #2873	D₄₃	semidirect
335. C₄₃	#10951	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582915	2
#19143115	2
C₂×#14582872	2
#19134327	2
#19134306	2
C₂×#14582656	2
C₄₃×#2873	2
#10951	43