Subgroups — #25960774

Order 11008.

2706 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13063347	C₂	1	1	yes	maximal, characteristic
2	#19147796	C₂	1	2	yes	maximal, complemented
3	#19143480	C₂	1	4	yes	maximal, complemented
4	#19143472	C₂	1	4	yes	maximal, complemented
5	#19143464	C₂	1	2	yes	maximal, complemented
6	#19143456	C₂	1	4	yes	maximal, complemented
7	#19143448	C₂	1	2	yes	maximal, complemented
8	#19143397	C₂	1	4	yes	maximal, complemented
9	C₄×#13063347	C₂	1	4	yes	maximal, complemented
10	C₂×#14582937	C₂	1	1	yes	maximal, characteristic, complemented
11	#19143115	C₂	1	2	yes	maximal, complemented
12	C₂×C₄₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#10621898	C₂²	1	2	yes	—
14	C₂×#13063347	C₄	1	16	yes	complemented
15	C₂×#13063347	C₂²	1	2	yes	—
16	C₂×#13063347	C₂²	1	2	yes	—
17	C₂×#13063347	C₂²	1	2	yes	—
18	C₂×#13063347	C₂²	1	2	yes	—
19	C₂²×Dic₁₇₂	C₂²	1	1	yes	characteristic
20	C₂²×#10621873	C₂²	1	2	yes	—
21	C₂²×D₃₄₄	C₂²	1	1	yes	characteristic
22	#14583380	—	2	4	no	—
23	#14583379	C₂²	1	8	yes	complemented
24	#14583376	C₂²	1	4	yes	—
25	#14583373	C₂²	1	4	yes	—
26	#14583372	—	2	4	no	—
27	C₄×#10621898	C₂²	1	8	yes	complemented
28	#14583367	—	2	4	no	—
29	C₂×#13063284	C₂²	1	2	yes	—
30	#117×D₄₃	—	2	4	no	—
31	#14583012	C₂²	1	8	yes	complemented
32	#14583007	C₂²	1	8	yes	complemented
33	#14583001	C₂²	1	16	yes	complemented
34	C₄×Dic₁₇₂	C₂²	1	8	yes	complemented
35	C₄×#10621873	C₂²	1	16	yes	complemented
36	C₄×D₃₄₄	C₂²	1	8	yes	complemented
37	#14582937	C₂²	1	2	yes	—
38	#14582937	C₂²	1	2	yes	—
39	#14582937	C₂²	1	2	yes	complemented
40	#14582937	C₂²	1	2	yes	complemented
41	C₂×#13063259	C₂²	1	2	yes	complemented
42	C₂×#13063257	C₂²	1	2	yes	complemented
43	#14582909	C₂²	1	4	yes	—
44	#14582905	C₂²	1	4	yes	—
45	#14582901	C₂²	1	8	yes	complemented
46	#14582896	C₂²	1	8	yes	complemented
47	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
48	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
49	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
50	C₄₃×#405	C₂²	1	2	yes	—
51	C₄₃×#405	C₂²	1	2	yes	—
52	C₄₃×#405	C₂²	1	2	yes	complemented
53	C₄₃×#405	C₂²	1	2	yes	complemented
54	C₂×#97×C₄₃	C₂²	1	2	yes	complemented
55	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	complemented
56	C₂×#10621898	—	2	2	no	—
57	C₂×#10621898	—	2	2	no	—
58	C₂×#10621898	—	2	8	no	—
59	C₂×#10621898	C₂×C₄	1	16	yes	complemented
60	C₂×#10621898	C₂³	1	4	yes	—
61	C₂×#10621898	C₂³	1	4	yes	—
62	C₂²×Dic₈₆	C₂³	1	2	yes	—
63	C₂²×D₁₇₂	C₂³	1	2	yes	—
64	C₂²×C₂²⋊D₄₃	—	2	2	no	—
65	C₂²×C₄×D₄₃	—	2	2	no	—
66	#13063347	C₂×C₄	1	16	yes	complemented
67	#13063347	C₂×C₄	1	16	yes	complemented
68	#13063347	C₂×C₄	1	16	yes	complemented
69	#13063347	C₂×C₄	1	16	yes	complemented
70	C₂×Dic₁₇₂	C₂×C₄	1	8	yes	complemented
71	C₂×Dic₁₇₂	C₂³	1	2	yes	—
72	C₂×Dic₁₇₂	C₂³	1	2	yes	—
73	C₂×#10621873	C₂×C₄	1	16	yes	complemented
74	C₂×#10621873	C₂³	1	4	yes	—
75	C₂×#10621873	C₂³	1	4	yes	—
76	C₂×D₃₄₄	C₂×C₄	1	8	yes	complemented
77	C₂×D₃₄₄	C₂³	1	2	yes	—
78	C₂×D₃₄₄	C₂³	1	2	yes	—
79	C₄×Dic₈₆	C₂³	1	16	yes	—
80	#13063290	—	2	8	no	—
81	C₄×D₁₇₂	C₂³	1	16	yes	—
82	#13063287	—	2	8	no	—
83	C₄×C₂²⋊D₄₃	—	2	16	no	—
84	(C₂²⋊D₄₃)⋊C₄	—	2	16	no	—
85	#13063284	—	2	2	no	—
86	#13063284	—	2	2	no	—
87	#13063284	C₂³	1	4	yes	—
88	#13063284	C₂³	1	4	yes	—
89	#13063283	—	2	8	no	—
90	#13063282	—	2	8	no	—
91	#13063281	—	2	8	no	—
92	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
93	C₄⋊C₄×D₄₃	—	2	8	no	—
94	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
95	C₂²⋊C₄×D₄₃	—	2	8	no	—
96	C₂×C₄×Dic₄₃	—	2	2	no	—
97	C₄²×D₄₃	—	2	8	no	—
98	#13063259	C₂³	1	4	yes	—
99	#13063259	C₂³	1	4	yes	—
100	#13063257	C₂³	1	4	yes	—
101	#13063257	C₂³	1	4	yes	—
102	#13063250	C₂³	1	16	yes	—
103	#13063247	C₂³	1	16	yes	—
104	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
105	C₂×M₁₆×C₄₃	—	2	4	no	—
106	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
107	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
108	C₂²×C₈×C₄₃	C₂×C₄	1	8	yes	complemented
109	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
110	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
116	#117×C₄₃	D₄	1	2	yes	—
117	#117×C₄₃	D₄	1	2	yes	—
118	#117×C₄₃	C₂³	1	2	yes	—
119	#117×C₄₃	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
121	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
122	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
123	#97×C₄₃	C₂³	1	4	yes	—
124	#97×C₄₃	C₂³	1	4	yes	—
125	C₄×C₈×C₄₃	C₂³	1	4	yes	—
126	C₄×C₈×C₄₃	C₂³	1	4	yes	—
127	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
128	C₂³×D₄₃	—	2	2	no	—
129	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
130	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
131	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₃	#41	1	4	yes	—
135	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
136	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
137	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
138	C₂×C₂²⋊D₄₃	—	2	16	no	—
139	C₂×C₂²⋊D₄₃	—	2	4	no	—
140	C₂×C₂²⋊D₄₃	—	2	4	no	—
141	C₂²×Dic₄₃	—	2	2	no	—
142	C₂²×Dic₄₃	—	2	4	no	—
143	#10621898	—	2	16	no	—
144	#10621898	—	2	16	no	—
145	#10621898	—	2	8	no	—
146	#10621898	—	2	8	no	—
147	#10621898	C₂²×C₄	1	16	yes	—
148	#10621898	C₂²×C₄	1	16	yes	—
149	C₂×D₁₇₂	—	2	2	no	—
150	C₂×D₁₇₂	—	2	4	no	—
151	C₂×D₁₇₂	C₂²×C₄	1	8	yes	—
152	C₂×D₁₇₂	C₂⁴	1	4	yes	—
153	C₂×C₄×D₄₃	—	2	16	no	—
154	C₂×C₄×D₄₃	—	2	4	no	—
155	C₂×C₄×D₄₃	—	2	4	no	—
156	C₂×C₄×D₄₃	—	2	16	no	—
157	C₂×Dic₈₆	—	2	2	no	—
158	C₂×Dic₈₆	—	2	4	no	—
159	C₂×Dic₈₆	C₂²×C₄	1	8	yes	—
160	C₂×Dic₈₆	C₂⁴	1	4	yes	—
161	M₁₆×C₄₃	—	2	4	no	—
162	M₁₆×C₄₃	—	2	4	no	—
163	C₂×C₈×C₄₃	—	2	4	no	—
164	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
165	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
166	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
167	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
168	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
169	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
170	C₂×C₈×C₄₃	C₂⁴	1	4	yes	—
171	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
172	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
173	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
174	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
175	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
176	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
177	C₂²⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
178	C₂²⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
179	C₄²×C₄₃	C₂×D₄	1	4	yes	—
180	C₄²×C₄₃	C₂⁴	1	4	yes	—
181	C₂²⋊Dic₄₃	—	2	4	no	—
182	C₂²⋊Dic₄₃	—	2	4	no	—
183	(C₂×D₄₃)⋊C₄	—	2	16	no	—
184	C₄⋊Dic₄₃	—	2	4	no	—
185	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
186	Dic₄₃⋊C₄	—	2	16	no	—
187	C₄×Dic₄₃	—	2	4	no	—
188	C₄×Dic₄₃	—	2	16	no	—
189	C₄×Dic₄₃	—	2	4	no	—
190	Dic₁₇₂	C₂²×C₄	1	8	yes	—
191	Dic₁₇₂	C₂²×C₄	1	8	yes	—
192	D₃₄₄	C₂²×C₄	1	8	yes	—
193	D₃₄₄	C₂²×C₄	1	8	yes	—
194	#10621873	C₂²×C₄	1	16	yes	—
195	#10621873	C₂²×C₄	1	16	yes	—
196	C₂³×C₄₃	—	4	2	no	—
197	C₂³×C₄₃	C₄×D₄	1	4	yes	—
198	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
199	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
200	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
201	C₂²×D₄₃	—	2	4	no	—
202	C₂²×D₄₃	—	2	8	no	—
203	C₂²×D₄₃	—	8	4	no	—
204	C₂×C₄×C₄₃	—	4	4	no	—
205	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
206	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
207	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
208	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
209	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
210	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
211	C₂×C₄×C₄₃	C₂²×D₄	1	8	yes	—
212	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
216	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
217	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
218	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
219	C₂²⋊D₄₃	—	2	16	no	—
220	C₂²⋊D₄₃	—	2	16	no	—
221	C₂×Dic₄₃	—	2	8	no	—
222	C₂×Dic₄₃	—	2	4	no	—
223	C₂×Dic₄₃	—	2	8	no	—
224	C₂×Dic₄₃	—	8	4	no	—
225	D₁₇₂	—	2	8	no	—
226	D₁₇₂	—	2	4	no	—
227	D₁₇₂	C₂³×C₄	1	8	yes	—
228	C₄×D₄₃	—	2	16	no	—
229	C₄×D₄₃	—	2	16	no	—
230	C₄×D₄₃	—	8	16	no	—
231	Dic₈₆	—	2	8	no	—
232	Dic₈₆	—	2	4	no	—
233	Dic₈₆	C₂³×C₄	1	8	yes	—
234	C₈×C₄₃	—	2	4	no	—
235	C₈×C₄₃	C₂³×C₄	1	2	yes	—
236	C₈×C₄₃	C₂³×C₄	1	2	yes	—
237	C₈×C₄₃	C₂³×C₄	1	2	yes	—
238	C₈×C₄₃	C₂³×C₄	1	2	yes	—
239	#60167	—	43	1	no	maximal, Sylow
240	C₂²×C₄₃	—	2	2	no	—
241	C₂²×C₄₃	—	2	2	no	—
242	C₂²×C₄₃	—	2	2	no	—
243	C₂²×C₄₃	—	4	4	no	—
244	C₂²×C₄₃	C₂×C₄×D₄	1	2	yes	—
245	C₂²×C₄₃	C₂×C₄×D₄	1	2	yes	—
246	C₂²×C₄₃	C₂×C₄×D₄	1	2	yes	—
247	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
248	C₂×D₄₃	—	2	8	no	—
249	C₂×D₄₃	—	4	8	no	—
250	C₂×D₄₃	—	8	8	no	—
251	C₄×C₄₃	—	2	8	no	—
252	C₄×C₄₃	C₂×C₄×D₄	1	2	yes	—
253	C₄×C₄₃	C₂×C₄×D₄	1	2	yes	—
254	C₄×C₄₃	C₂×C₄×D₄	1	2	yes	—
255	C₄×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
256	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
257	Dic₄₃	—	2	8	no	—
258	Dic₄₃	—	4	8	no	—
259	C₂²×#135	—	43	1	no	—
260	#3428	—	43	2	no	—
261	#2952	—	43	4	no	—
262	#2951	—	43	4	no	—
263	#2950	—	43	2	no	—
264	#2949	—	43	4	no	—
265	#2948	—	43	2	no	—
266	#2943	—	43	4	no	—
267	C₄×#135	—	43	4	no	—
268	C₂×#427	—	43	1	no	—
269	#2896	—	43	2	no	—
270	C₂×#405	D₄₃	1	1	yes	characteristic, complemented
271	C₂×C₄₃	—	2	2	no	—
272	C₂×C₄₃	—	2	2	no	—
273	C₂×C₄₃	—	2	2	no	—
274	C₂×C₄₃	C₂²×C₄×D₄	1	1	yes	characteristic
275	C₂×C₄₃	#3584	1	2	yes	—
276	D₄₃	—	4	8	no	—
277	C₂²×#41	—	43	2	no	—
278	C₂×#135	—	43	2	no	—
279	C₂×#135	—	43	2	no	—
280	C₂×#135	—	43	2	no	—
281	C₂×#135	—	43	2	no	—
282	C₂×#135	—	43	16	no	—
283	C₂²×Q₁₆	—	43	1	no	—
284	C₂²×SD₁₆	—	43	2	no	—
285	C₂²×D₈	—	43	1	no	—
286	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
287	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
288	#520	—	43	8	no	—
289	#520	—	86	4	no	—
290	#519	—	43	4	no	—
291	#518	—	43	4	no	—
292	#518	—	86	4	no	—
293	C₄×#41	—	43	8	no	—
294	C₄×#41	—	86	4	no	—
295	C₂×#117	—	43	2	no	—
296	C₂×#117	—	86	4	no	—
297	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
298	#442	—	43	8	no	—
299	#441	—	43	8	no	—
300	#440	—	43	16	no	—
301	C₄×Q₁₆	—	43	8	no	—
302	C₄×SD₁₆	—	43	16	no	—
303	C₄×D₈	—	43	8	no	—
304	#427	—	43	2	no	—
305	#427	—	43	2	no	—
306	#427	—	43	2	no	—
307	#427	—	43	2	no	—
308	C₂×#107	—	43	2	no	—
309	C₂×#106	—	43	2	no	—
310	#419	—	43	4	no	—
311	#418	—	43	4	no	—
312	#417	—	43	8	no	—
313	#416	—	43	8	no	—
314	#405	C₂×D₄₃	1	2	yes	—
315	#405	C₂×D₄₃	1	2	yes	—
316	#405	C₂×D₄₃	1	2	yes	complemented
317	#405	C₂×D₄₃	1	2	yes	complemented
318	C₂×#97	C₂×D₄₃	1	2	yes	complemented
319	C₂×C₄×C₈	C₂×D₄₃	1	2	yes	complemented
320	C₄₃	#60167	1	1	yes	characteristic, complemented, Sylow
321	C₂×#41	—	43	16	no	—
322	C₂×#41	—	43	4	no	—
323	C₂×#41	—	43	4	no	—
324	C₂×#41	—	86	2	no	—
325	C₂×#41	—	86	2	no	—
326	C₂×#41	—	86	8	no	—
327	C₂²×Q₈	—	43	2	no	—
328	C₂²×D₄	—	43	2	no	—
329	C₂²×D₄	—	86	2	no	—
330	C₂³×C₄	—	86	2	no	—
331	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
332	#135	—	43	16	no	—
333	#135	—	43	16	no	—
334	#135	—	43	16	no	—
335	#135	—	43	16	no	—
336	C₂×Q₁₆	—	43	8	no	—
337	C₂×Q₁₆	—	43	2	no	—
338	C₂×Q₁₆	—	43	2	no	—
339	C₂×SD₁₆	—	43	16	no	—
340	C₂×SD₁₆	—	43	4	no	—
341	C₂×SD₁₆	—	43	4	no	—
342	C₂×D₈	—	43	8	no	—
343	C₂×D₈	—	43	2	no	—
344	C₂×D₈	—	43	2	no	—
345	C₂×M₁₆	—	2	4	no	—
346	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
347	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
348	C₂²×C₈	C₄×D₄₃	1	8	yes	complemented
349	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
350	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
351	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
352	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
353	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
354	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
355	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
356	C₄×Q₈	—	43	16	no	—
357	C₄×Q₈	—	86	8	no	—
358	C₄×D₄	—	43	16	no	—
359	C₄×D₄	—	86	16	no	—
360	C₄×D₄	—	86	8	no	—
361	C₄×D₄	—	86	16	no	—
362	#117	—	43	4	no	—
363	#117	—	43	4	no	—
364	#117	—	86	2	no	—
365	#117	—	86	2	no	—
366	#117	—	86	8	no	—
367	#117	—	86	8	no	—
368	#117	—	86	8	no	—
369	#117	D₁₇₂	1	2	yes	—
370	#117	D₁₇₂	1	2	yes	—
371	#117	C₂²×D₄₃	1	2	yes	—
372	#117	C₂²×D₄₃	1	2	yes	—
373	C₂×C₄⋊C₄	—	43	4	no	—
374	C₂×C₄⋊C₄	—	86	8	no	—
375	C₂×C₄⋊C₄	D₁₇₂	1	2	yes	—
376	C₂×C₂²⋊C₄	—	86	2	no	—
377	C₂×C₂²⋊C₄	—	86	8	no	—
378	C₂×C₂²⋊C₄	D₁₇₂	1	2	yes	—
379	C₂×C₄²	—	86	2	no	—
380	C₂×C₄²	—	86	8	no	—
381	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
382	#107	—	43	4	no	—
383	#107	—	43	4	no	—
384	#106	—	43	4	no	—
385	#106	—	43	4	no	—
386	#103	—	43	16	no	—
387	#102	—	43	16	no	—
388	#97	C₂²×D₄₃	1	4	yes	—
389	#97	C₂²×D₄₃	1	4	yes	—
390	C₄×C₈	C₂²×D₄₃	1	4	yes	—
391	C₄×C₈	C₂²×D₄₃	1	4	yes	—
392	C₂⁴	—	86	2	no	—
393	C₂⁴	C₂×D₁₇₂	1	1	yes	characteristic
394	#41	—	43	16	no	—
395	#41	—	43	16	no	—
396	#41	—	86	16	no	—
397	#41	—	86	16	no	—
398	#41	—	86	8	no	—
399	#41	—	86	8	no	—
400	C₂×Q₈	—	43	8	no	—
401	C₂×Q₈	—	43	4	no	—
402	C₂×Q₈	—	86	2	no	—
403	C₂×Q₈	—	86	4	no	—
404	C₂×D₄	—	43	8	no	—
405	C₂×D₄	—	43	4	no	—
406	C₂×D₄	—	86	16	no	—
407	C₂×D₄	—	86	4	no	—
408	C₂×D₄	—	86	4	no	—
409	C₂×D₄	—	86	2	no	—
410	C₂×D₄	—	86	4	no	—
411	C₂²×C₄	—	86	2	no	—
412	C₂²×C₄	—	86	16	no	—
413	C₂²×C₄	—	86	4	no	—
414	C₂²×C₄	—	86	4	no	—
415	C₂²×C₄	—	86	4	no	—
416	C₂²×C₄	—	86	16	no	—
417	C₂²×C₄	C₂×C₄×D₄₃	1	4	yes	—
418	C₂²×C₄	C₂×D₁₇₂	1	4	yes	—
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	4	yes	—
423	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
424	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
425	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
426	Q₁₆	—	43	8	no	—
427	Q₁₆	—	43	8	no	—
428	SD₁₆	—	43	16	no	—
429	SD₁₆	—	43	16	no	—
430	D₈	—	43	8	no	—
431	D₈	—	43	8	no	—
432	M₁₆	—	2	4	no	—
433	M₁₆	—	2	4	no	—
434	C₂×C₈	—	2	4	no	—
435	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
436	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
437	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
438	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
439	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
440	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
441	C₂×C₈	C₂³×D₄₃	1	4	yes	—
442	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
443	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
444	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
445	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
446	C₄⋊C₄	—	43	8	no	—
447	C₄⋊C₄	—	86	4	no	—
448	C₄⋊C₄	—	86	16	no	—
449	C₄⋊C₄	C₂×D₁₇₂	1	4	yes	—
450	C₄⋊C₄	C₂×D₁₇₂	1	4	yes	—
451	C₂²⋊C₄	—	86	4	no	—
452	C₂²⋊C₄	—	86	4	no	—
453	C₂²⋊C₄	—	86	16	no	—
454	C₂²⋊C₄	C₂×D₁₇₂	1	4	yes	—
455	C₂²⋊C₄	C₂×D₁₇₂	1	4	yes	—
456	C₄²	—	86	4	no	—
457	C₄²	—	86	16	no	—
458	C₄²	—	86	4	no	—
459	C₄²	C₂×D₁₇₂	1	4	yes	—
460	C₄²	C₂³×D₄₃	1	4	yes	—
461	C₂³	—	4	2	no	—
462	C₂³	—	86	8	no	—
463	C₂³	—	86	4	no	—
464	C₂³	—	344	4	no	—
465	C₂³	C₄×D₁₇₂	1	4	yes	—
466	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
467	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
468	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
469	Q₈	—	43	8	no	—
470	Q₈	—	86	8	no	—
471	Q₈	—	86	4	no	—
472	D₄	—	43	8	no	—
473	D₄	—	86	16	no	—
474	D₄	—	86	16	no	—
475	D₄	—	86	8	no	—
476	D₄	—	86	4	no	—
477	C₂×C₄	—	4	4	no	—
478	C₂×C₄	—	86	8	no	—
479	C₂×C₄	—	86	4	no	—
480	C₂×C₄	—	86	16	no	—
481	C₂×C₄	—	86	16	no	—
482	C₂×C₄	—	86	8	no	—
483	C₂×C₄	—	344	16	no	—
484	C₂×C₄	—	344	4	no	—
485	C₂×C₄	C₄×D₁₇₂	1	4	yes	—
486	C₂×C₄	C₄×D₁₇₂	1	4	yes	—
487	C₂×C₄	C₄×D₁₇₂	1	4	yes	—
488	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
489	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
490	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
491	C₂×C₄	C₂²×D₁₇₂	1	8	yes	—
492	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
493	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
494	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
495	C₂×C₄	C₂×#10621898	1	2	yes	—
496	C₂×C₄	C₂×#10621898	1	2	yes	—
497	C₂×C₄	C₂×#10621898	1	2	yes	—
498	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
499	C₈	—	2	4	no	—
500	C₈	C₂²×C₄×D₄₃	1	2	yes	—
501	C₈	C₂²×C₄×D₄₃	1	2	yes	—
502	C₈	C₂²×C₄×D₄₃	1	2	yes	—
503	C₈	C₂²×C₄×D₄₃	1	2	yes	—
504	C₂²	—	2	2	no	—
505	C₂²	—	2	2	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	4	4	no	—
508	C₂²	—	86	8	no	—
509	C₂²	—	344	8	no	—
510	C₂²	—	172	8	no	—
511	C₂²	C₂×C₄×D₁₇₂	1	2	yes	—
512	C₂²	C₂×C₄×D₁₇₂	1	2	yes	—
513	C₂²	C₂×C₄×D₁₇₂	1	2	yes	—
514	C₂²	C₂³×D₁₇₂	1	1	yes	characteristic
515	C₄	—	2	8	no	—
516	C₄	—	86	8	no	—
517	C₄	—	172	8	no	—
518	C₄	C₂×C₄×D₁₇₂	1	2	yes	—
519	C₄	C₂×C₄×D₁₇₂	1	2	yes	—
520	C₄	C₂×C₄×D₁₇₂	1	2	yes	—
521	C₄	C₂³×C₄×D₄₃	1	1	yes	characteristic
522	C₄	C₂²×#10621898	1	1	yes	characteristic
523	C₂	—	2	2	no	—
524	C₂	—	2	2	no	—
525	C₂	—	2	2	no	—
526	C₂	—	172	8	no	—
527	C₂	C₂²×C₄×D₁₇₂	1	1	yes	characteristic
528	C₂	#19149369	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₇₂
commutator	C₄×C₄₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₂×C₄₃×#405	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	C₂²×#13063347	C₂
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	C₂×#405	D₄₃
hypocenter	C₄₃	#60167
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#117 ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
2. #19147796	C₂	semidirect
3. #19143480	C₂	semidirect
4. #19143472	C₂	semidirect
5. #19143464	C₂	semidirect
6. #19143456	C₂	semidirect
7. #19143448	C₂	semidirect
8. #19143397	C₂	semidirect
9. C₄×#13063347	C₂	semidirect
10. C₂×#14582937	C₂	semidirect
11. #19143115	C₂	semidirect
12. C₂×C₄₃×#405	C₂	semidirect
14. C₂×#13063347	C₄	semidirect
23. #14583379	C₂²	semidirect
27. C₄×#10621898	C₂²	semidirect
31. #14583012	C₂²	semidirect
32. #14583007	C₂²	semidirect
33. #14583001	C₂²	semidirect
34. C₄×Dic₁₇₂	C₂²	semidirect
35. C₄×#10621873	C₂²	semidirect
36. C₄×D₃₄₄	C₂²	semidirect
39. #14582937	C₂²	semidirect
40. #14582937	C₂²	semidirect
41. C₂×#13063259	C₂²	semidirect
42. C₂×#13063257	C₂²	semidirect
45. #14582901	C₂²	semidirect
46. #14582896	C₂²	semidirect
52. C₄₃×#405	C₂²	semidirect
53. C₄₃×#405	C₂²	semidirect
54. C₂×#97×C₄₃	C₂²	semidirect
55. C₂×C₄×C₈×C₄₃	C₂²	semidirect
59. C₂×#10621898	C₂×C₄	semidirect
66. #13063347	C₂×C₄	semidirect
67. #13063347	C₂×C₄	semidirect
68. #13063347	C₂×C₄	semidirect
69. #13063347	C₂×C₄	semidirect
70. C₂×Dic₁₇₂	C₂×C₄	semidirect
73. C₂×#10621873	C₂×C₄	semidirect
76. C₂×D₃₄₄	C₂×C₄	semidirect
108. C₂²×C₈×C₄₃	C₂×C₄	semidirect
270. C₂×#405	D₄₃	semidirect
316. #405	C₂×D₄₃	semidirect
317. #405	C₂×D₄₃	semidirect
318. C₂×#97	C₂×D₄₃	semidirect
319. C₂×C₄×C₈	C₂×D₄₃	semidirect
320. C₄₃	#60167	semidirect
348. C₂²×C₈	C₄×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13063347	2
#19147796	2
#19143480	2
#19143472	2
#19143464	2
#19143456	2
#19143448	2
#19143397	2
C₄×#13063347	2
C₂×#14582937	2
#19143115	2
C₂×C₄₃×#405	2
#60167	43