Subgroups — #25065644

Order 11008.

666 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143714	C₂	1	2	yes	maximal
2	C₄×#13063331	C₂	1	1	yes	maximal, characteristic
3	#19133363	C₂	1	2	yes	maximal, complemented
4	#19133359	C₂	1	2	yes	maximal, complemented
5	#19133357	C₂	1	1	yes	maximal, characteristic, complemented
6	#19133354	C₂	1	1	yes	maximal, characteristic, complemented
7	#19133352	C₂	1	1	yes	maximal, characteristic, complemented
8	#19133344	C₂	1	2	yes	maximal, complemented
9	#19133342	C₂	1	1	yes	maximal, characteristic, complemented
10	#335×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1568	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063331	C₄	1	1	yes	characteristic
13	C₂×#13063331	C₄	1	1	yes	characteristic
14	C₄×#10621898	C₂²	1	1	yes	characteristic
15	#14583027	—	2	2	no	—
16	#14582974	—	2	2	no	—
17	#14582973	—	2	2	no	—
18	#14582972	—	2	2	no	—
19	#14582955	C₂²	1	2	yes	—
20	#14582951	C₂²	1	2	yes	—
21	#14582923	C₂²	1	2	yes	—
22	#14582921	C₂²	1	2	yes	—
23	C₄⋊C₈×D₄₃	C₂²	1	2	yes	—
24	#14582854	C₄	1	1	yes	characteristic
25	#14582854	C₄	1	1	yes	characteristic
26	#14582853	C₄	1	1	yes	characteristic
27	#14582853	C₄	1	1	yes	characteristic
28	#14582853	C₄	1	1	yes	characteristic
29	#14582853	C₄	1	1	yes	characteristic
30	C₄×#10621877	C₂²	1	1	yes	characteristic
31	C₄×#10621872	C₂²	1	1	yes	characteristic
32	C₄×#10621872	C₂²	1	1	yes	characteristic
33	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
35	#14582652	C₂²	1	1	yes	characteristic
36	#14582652	C₂²	1	1	yes	characteristic
37	#14582652	C₂²	1	2	yes	—
38	#14582651	C₂²	1	2	yes	—
39	#14582651	C₂²	1	2	yes	—
40	#14582649	C₂²	1	2	yes	—
41	#14582649	C₂²	1	2	yes	—
42	C₄₃×#432	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
44	C₄₃×#335	C₂²	1	1	yes	characteristic
45	C₄₃×#335	C₂²	1	1	yes	characteristic
46	C₄₃×#334	C₂²	1	2	yes	—
47	C₂×#10621898	C₂×C₄	1	1	yes	characteristic
48	#13063331	—	2	4	no	—
49	#13063331	—	2	4	no	—
50	C₂×#10621877	—	2	2	no	—
51	C₂×#10621877	C₂×C₄	1	1	yes	characteristic
52	C₂×#10621877	C₂×C₄	1	1	yes	characteristic
53	C₂×#10621872	—	2	2	no	—
54	C₂×#10621872	C₂×C₄	1	1	yes	characteristic
55	C₂×#10621872	C₂×C₄	1	1	yes	characteristic
56	C₂×#10621872	C₂×C₄	1	1	yes	characteristic
57	C₂×#10621872	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₄₃	—	2	2	no	—
59	C₂×C₈×D₄₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₄₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₄₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₄₃	C₂×C₄	1	1	yes	characteristic
63	C₄×Dic₈₆	D₄	1	1	yes	characteristic
64	C₄×Dic₈₆	Q₈	1	1	yes	characteristic
65	C₄×D₁₇₂	D₄	1	1	yes	characteristic
66	C₄×D₁₇₂	Q₈	1	1	yes	characteristic
67	C₄×C₂²⋊D₄₃	D₄	1	1	yes	characteristic
68	C₄×C₂²⋊D₄₃	D₄	1	1	yes	characteristic
69	C₄×C₂²⋊D₄₃	Q₈	1	1	yes	characteristic
70	C₄×C₂²⋊D₄₃	Q₈	1	1	yes	characteristic
71	#13063284	C₂×C₄	1	1	yes	characteristic
72	#13063282	C₂×C₄	1	1	yes	characteristic
73	#13063282	C₂×C₄	1	1	yes	characteristic
74	C₄²×D₄₃	C₂³	1	1	yes	characteristic
75	C₄²×D₄₃	C₂³	1	1	yes	characteristic
76	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
77	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
78	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
79	Dic₄₃⋊C₈	—	2	2	no	—
80	Dic₄₃⋊C₈	—	2	2	no	—
81	(C₂×D₄₃)⋊C₈	—	2	2	no	—
82	(C₂×D₄₃)⋊C₈	—	2	2	no	—
83	#13063236	C₂×C₄	1	1	yes	characteristic
84	#13063236	C₂×C₄	1	1	yes	characteristic
85	#13063235	—	2	2	no	—
86	#13063235	C₂×C₄	1	1	yes	characteristic
87	#13063235	C₂×C₄	1	1	yes	characteristic
88	#13063235	C₂×C₄	1	1	yes	characteristic
89	#13063235	C₂×C₄	1	1	yes	characteristic
90	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
91	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
92	C₈×Dic₄₃	—	2	2	no	—
93	C₈×Dic₄₃	C₂×C₄	1	1	yes	characteristic
94	C₈×Dic₄₃	C₂×C₄	1	1	yes	characteristic
95	C₈×Dic₄₃	C₂×C₄	1	1	yes	characteristic
96	C₈×Dic₄₃	C₂×C₄	1	1	yes	characteristic
97	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
98	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
99	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
100	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
101	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
102	C₂²⋊C₈×C₄₃	—	2	2	no	—
103	#97×C₄₃	—	2	2	no	—
104	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
105	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
106	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
107	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
108	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
111	C₂×C₂²⋊D₄₃	C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₂²⋊D₄₃	C₄⋊C₄	1	1	yes	characteristic
113	#10621898	—	2	2	no	—
114	#10621898	—	2	2	no	—
115	C₂×D₁₇₂	C₄⋊C₄	1	1	yes	characteristic
116	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₄×D₄₃	C₂×Q₈	1	1	yes	characteristic
121	C₂×C₄×D₄₃	C₂×Q₈	1	1	yes	characteristic
122	C₂×Dic₈₆	C₄⋊C₄	1	1	yes	characteristic
123	C₂×C₈×C₄₃	—	2	2	no	—
124	C₂×C₈×C₄₃	—	2	2	no	—
125	C₂×C₈×C₄₃	—	2	2	no	—
126	C₂×C₈×C₄₃	—	2	2	no	—
127	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
134	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
135	C₂²⋊Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
136	C₂²⋊Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
137	(C₂×D₄₃)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
138	(C₂×D₄₃)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
139	(C₂×D₄₃)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
140	(C₂×D₄₃)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
141	C₄⋊Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
142	C₄⋊Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
143	Dic₄₃⋊C₄	C₄⋊C₄	1	1	yes	characteristic
144	Dic₄₃⋊C₄	C₄⋊C₄	1	1	yes	characteristic
145	Dic₄₃⋊C₄	C₄⋊C₄	1	1	yes	characteristic
146	Dic₄₃⋊C₄	C₄⋊C₄	1	1	yes	characteristic
147	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
148	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
149	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
150	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
151	C₄×Dic₄₃	C₂×Q₈	1	1	yes	characteristic
152	C₄×Dic₄₃	C₂×Q₈	1	1	yes	characteristic
153	#10621877	—	2	2	no	—
154	#10621877	—	2	2	no	—
155	#10621877	—	8	2	no	—
156	C₂×C₄₃⋊C₈	—	2	2	no	—
157	C₂×C₄₃⋊C₈	—	2	2	no	—
158	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
162	#10621872	—	2	2	no	—
163	#10621872	—	2	2	no	—
164	#10621872	—	2	2	no	—
165	#10621872	—	8	2	no	—
166	#10621872	M₁₆	1	4	yes	complemented
167	C₈×D₄₃	—	2	2	no	—
168	C₈×D₄₃	—	2	2	no	—
169	C₈×D₄₃	—	2	2	no	—
170	C₈×D₄₃	—	8	2	no	—
171	C₈×D₄₃	M₁₆	1	4	yes	complemented
172	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂²×D₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂²×D₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₄₃	—	2	1	no	—
176	C₂×C₄×C₄₃	—	2	1	no	—
177	C₂×C₄×C₄₃	—	2	1	no	—
178	C₂×C₄×C₄₃	—	2	1	no	—
179	C₂×C₄×C₄₃	—	4	1	no	—
180	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
184	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
186	C₂²⋊D₄₃	—	2	2	no	—
187	C₂²⋊D₄₃	—	2	2	no	—
188	C₂×Dic₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×Dic₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂×Dic₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₂×Dic₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
192	C₂×Dic₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
193	C₂×Dic₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
194	D₁₇₂	—	2	2	no	—
195	C₄×D₄₃	—	2	1	no	—
196	C₄×D₄₃	—	2	1	no	—
197	C₄×D₄₃	—	2	1	no	—
198	C₄×D₄₃	—	2	1	no	—
199	C₄×D₄₃	—	2	1	no	—
200	C₄×D₄₃	—	2	1	no	—
201	C₄×D₄₃	—	4	1	no	—
202	C₄×D₄₃	—	4	1	no	—
203	C₄×D₄₃	C₂×M₁₆	1	2	yes	—
204	C₄×D₄₃	C₂×M₁₆	1	2	yes	—
205	Dic₈₆	—	2	2	no	—
206	C₈×C₄₃	—	2	1	no	—
207	C₈×C₄₃	—	2	1	no	—
208	C₈×C₄₃	—	4	2	no	—
209	C₈×C₄₃	—	4	2	no	—
210	C₈×C₄₃	C₂×M₁₆	1	2	yes	—
211	C₈×C₄₃	C₂×M₁₆	1	2	yes	—
212	C₄₃⋊C₈	—	2	1	no	—
213	C₄₃⋊C₈	—	2	1	no	—
214	C₄₃⋊C₈	—	4	2	no	—
215	C₄₃⋊C₈	—	4	2	no	—
216	C₄₃⋊C₈	C₂×M₁₆	1	2	yes	—
217	C₄₃⋊C₈	C₂×M₁₆	1	2	yes	—
218	#17799	—	43	1	no	maximal, Sylow
219	C₂²×C₄₃	—	2	1	no	—
220	C₂²×C₄₃	—	2	1	no	—
221	C₂²×C₄₃	—	2	1	no	—
222	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
223	C₂×D₄₃	—	2	1	no	—
224	C₂×D₄₃	—	2	1	no	—
225	C₂×D₄₃	—	2	1	no	—
226	C₂×D₄₃	—	2	1	no	—
227	C₂×D₄₃	—	2	1	no	—
228	C₂×D₄₃	#423	1	2	yes	—
229	C₄×C₄₃	—	2	1	no	—
230	C₄×C₄₃	—	2	1	no	—
231	C₄×C₄₃	—	2	1	no	—
232	C₄×C₄₃	—	2	1	no	—
233	C₄×C₄₃	C₂²×M₁₆	1	1	yes	characteristic
234	C₄×C₄₃	C₂²×M₁₆	1	1	yes	characteristic
235	C₄×C₄₃	#576	1	1	yes	characteristic
236	C₄×C₄₃	#578	1	1	yes	characteristic
237	Dic₄₃	—	2	1	no	—
238	Dic₄₃	—	2	1	no	—
239	Dic₄₃	—	2	1	no	—
240	Dic₄₃	—	2	1	no	—
241	Dic₄₃	—	2	1	no	—
242	Dic₄₃	#423	1	2	yes	—
243	#2989	—	43	2	no	—
244	C₄×#131	—	43	1	no	—
245	#1569	—	43	2	no	—
246	#1569	—	43	2	no	—
247	#1568	—	43	1	no	—
248	#1568	D₄₃	1	1	yes	characteristic, complemented
249	#1567	—	43	1	no	—
250	#1567	—	43	1	no	—
251	#1565	—	43	2	no	—
252	#1564	—	43	1	no	—
253	C₂×#335	—	43	1	no	—
254	C₂×C₄₃	—	4	1	no	—
255	C₂×C₄₃	C₂×#423	1	1	yes	characteristic
256	C₂×C₄₃	#2913	1	1	yes	characteristic
257	C₂×C₄₃	#2916	1	1	yes	characteristic
258	D₄₃	—	2	2	no	—
259	D₄₃	—	4	1	no	—
260	C₂×#131	—	43	1	no	—
261	C₂×#131	—	43	1	no	—
262	C₄×#41	—	43	1	no	—
263	#446	—	86	2	no	—
264	#436	—	86	2	no	—
265	#435	—	86	2	no	—
266	#435	—	86	2	no	—
267	#432	—	43	2	no	—
268	#432	C₂×D₄₃	1	2	yes	—
269	#431	—	43	2	no	—
270	#423	—	43	2	no	—
271	#423	—	43	2	no	—
272	C₂×C₄⋊C₈	—	43	2	no	—
273	#405	—	43	1	no	—
274	#405	—	43	1	no	—
275	#405	—	43	1	no	—
276	#405	—	43	1	no	—
277	#405	—	43	1	no	—
278	#405	—	43	1	no	—
279	C₄×M₁₆	—	43	1	no	—
280	C₄×M₁₆	—	43	1	no	—
281	C₄×M₁₆	—	43	1	no	—
282	C₂×C₄×C₈	—	43	1	no	—
283	C₂×C₄×C₈	—	43	1	no	—
284	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
285	#335	—	43	2	no	—
286	#335	—	43	2	no	—
287	#335	—	43	1	no	—
288	#335	—	43	1	no	—
289	#335	—	43	2	no	—
290	#335	C₂×D₄₃	1	1	yes	characteristic
291	#335	C₂×D₄₃	1	1	yes	characteristic
292	#334	—	43	2	no	—
293	#334	—	43	2	no	—
294	#334	C₂×D₄₃	1	2	yes	—
295	C₄₃	#17799	1	1	yes	characteristic, complemented, Sylow
296	C₂×#41	—	43	1	no	—
297	#131	—	86	4	no	—
298	#131	—	86	4	no	—
299	C₂×M₁₆	—	43	1	no	—
300	C₂×M₁₆	—	43	1	no	—
301	C₂×M₁₆	—	43	1	no	—
302	C₂×M₁₆	—	43	1	no	—
303	C₂×M₁₆	—	43	1	no	—
304	C₂×M₁₆	—	43	1	no	—
305	C₂×M₁₆	—	86	2	no	—
306	C₂×M₁₆	—	86	2	no	—
307	C₂²×C₈	—	43	1	no	—
308	C₂²×C₈	—	43	1	no	—
309	C₂²×C₈	—	43	1	no	—
310	C₂²×C₈	—	43	1	no	—
311	C₂²×C₈	—	86	2	no	—
312	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
313	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
314	C₄×Q₈	—	43	1	no	—
315	C₄×Q₈	—	43	1	no	—
316	C₄×D₄	—	43	1	no	—
317	C₄×D₄	—	43	1	no	—
318	C₄×D₄	—	43	1	no	—
319	C₄×D₄	—	43	1	no	—
320	C₄×D₄	—	43	1	no	—
321	C₄×D₄	—	43	1	no	—
322	#117	—	43	1	no	—
323	#117	—	43	1	no	—
324	#117	—	43	1	no	—
325	C₂×C₄²	—	43	1	no	—
326	C₂×C₄²	—	43	1	no	—
327	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
328	C₄⋊C₈	—	43	2	no	—
329	C₄⋊C₈	—	43	2	no	—
330	C₄⋊C₈	—	86	2	no	—
331	C₄⋊C₈	—	86	2	no	—
332	C₄⋊C₈	—	86	2	no	—
333	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
334	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
335	C₂²⋊C₈	—	2	2	no	—
336	C₂²⋊C₈	—	86	2	no	—
337	C₂²⋊C₈	—	86	2	no	—
338	#97	—	2	2	no	—
339	#97	—	43	1	no	—
340	#97	—	43	1	no	—
341	#97	—	43	1	no	—
342	#97	—	43	1	no	—
343	#97	—	43	1	no	—
344	#97	—	43	1	no	—
345	#97	—	86	2	no	—
346	C₄×C₈	—	43	1	no	—
347	C₄×C₈	—	43	1	no	—
348	C₄×C₈	—	43	1	no	—
349	C₄×C₈	—	43	1	no	—
350	C₄×C₈	—	43	1	no	—
351	C₄×C₈	—	43	1	no	—
352	C₄×C₈	—	86	2	no	—
353	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
354	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
355	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
356	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
357	#41	—	86	2	no	—
358	#41	—	86	2	no	—
359	C₂×Q₈	—	43	1	no	—
360	C₂×D₄	—	43	1	no	—
361	C₂×D₄	—	43	1	no	—
362	C₂×D₄	—	43	1	no	—
363	C₂²×C₄	—	43	1	no	—
364	C₂²×C₄	—	43	1	no	—
365	C₂²×C₄	—	43	1	no	—
366	C₂²×C₄	—	43	1	no	—
367	C₂²×C₄	—	43	1	no	—
368	C₂²×C₄	—	43	1	no	—
369	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
370	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
371	C₂²×C₄	Q₈×D₄₃	1	1	yes	characteristic
372	M₁₆	—	43	4	no	—
373	M₁₆	—	86	2	no	—
374	M₁₆	—	86	2	no	—
375	M₁₆	—	86	2	no	—
376	M₁₆	—	86	2	no	—
377	M₁₆	—	86	2	no	—
378	M₁₆	—	344	2	no	—
379	M₁₆	—	344	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	43	1	no	—
385	C₂×C₈	—	43	1	no	—
386	C₂×C₈	—	43	4	no	—
387	C₂×C₈	—	43	1	no	—
388	C₂×C₈	—	43	1	no	—
389	C₂×C₈	—	86	2	no	—
390	C₂×C₈	—	86	2	no	—
391	C₂×C₈	—	86	2	no	—
392	C₂×C₈	—	86	2	no	—
393	C₂×C₈	—	86	2	no	—
394	C₂×C₈	—	344	2	no	—
395	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
396	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
397	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
398	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
399	C₄⋊C₄	—	43	1	no	—
400	C₄⋊C₄	—	43	1	no	—
401	C₄⋊C₄	—	43	1	no	—
402	C₄⋊C₄	—	43	1	no	—
403	C₄⋊C₄	—	43	1	no	—
404	C₄⋊C₄	—	43	1	no	—
405	C₂²⋊C₄	—	43	1	no	—
406	C₂²⋊C₄	—	43	1	no	—
407	C₂²⋊C₄	—	43	1	no	—
408	C₂²⋊C₄	—	43	1	no	—
409	C₂²⋊C₄	—	43	1	no	—
410	C₂²⋊C₄	—	43	1	no	—
411	C₄²	—	43	1	no	—
412	C₄²	—	43	1	no	—
413	C₄²	—	43	1	no	—
414	C₄²	—	43	1	no	—
415	C₄²	—	43	1	no	—
416	C₄²	—	43	1	no	—
417	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
418	C₄²	D₄×D₄₃	1	1	yes	characteristic
419	C₄²	Q₈×D₄₃	1	1	yes	characteristic
420	C₄²	C₂³×D₄₃	1	1	yes	characteristic
421	C₂³	—	43	1	no	—
422	C₂³	—	43	1	no	—
423	C₂³	C₄⋊C₄×D₄₃	1	1	yes	characteristic
424	Q₈	—	86	2	no	—
425	D₄	—	86	2	no	—
426	D₄	—	86	2	no	—
427	D₄	—	86	2	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	43	1	no	—
434	C₂×C₄	—	43	2	no	—
435	C₂×C₄	—	43	2	no	—
436	C₂×C₄	—	43	1	no	—
437	C₂×C₄	—	43	1	no	—
438	C₂×C₄	—	43	1	no	—
439	C₂×C₄	—	43	1	no	—
440	C₂×C₄	—	43	1	no	—
441	C₂×C₄	—	86	1	no	—
442	C₂×C₄	—	86	1	no	—
443	C₂×C₄	—	86	1	no	—
444	C₂×C₄	—	86	1	no	—
445	C₂×C₄	—	86	1	no	—
446	C₂×C₄	—	86	1	no	—
447	C₂×C₄	—	172	1	no	—
448	C₂×C₄	—	172	1	no	—
449	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
450	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
451	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
452	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
453	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
454	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
455	C₈	—	2	1	no	—
456	C₈	—	2	1	no	—
457	C₈	—	4	2	no	—
458	C₈	—	4	2	no	—
459	C₈	—	43	2	no	—
460	C₈	—	43	2	no	—
461	C₈	—	86	1	no	—
462	C₈	—	86	1	no	—
463	C₈	—	172	2	no	—
464	C₈	—	172	2	no	—
465	C₈	M₁₆×D₄₃	1	2	yes	—
466	C₈	M₁₆×D₄₃	1	2	yes	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	43	2	no	—
471	C₂²	—	86	1	no	—
472	C₂²	—	86	1	no	—
473	C₂²	—	86	1	no	—
474	C₂²	—	86	1	no	—
475	C₂²	—	86	1	no	—
476	C₂²	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
477	C₄	—	2	1	no	—
478	C₄	—	2	1	no	—
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	43	2	no	—
482	C₄	—	86	1	no	—
483	C₄	—	86	1	no	—
484	C₄	—	86	1	no	—
485	C₄	—	86	1	no	—
486	C₄	—	86	1	no	—
487	C₄	C₂×M₁₆×D₄₃	1	1	yes	characteristic
488	C₄	C₂×M₁₆×D₄₃	1	1	yes	characteristic
489	C₄	#14583701	1	1	yes	characteristic
490	C₄	#14583713	1	1	yes	characteristic
491	C₂	—	4	1	no	—
492	C₂	—	86	2	no	—
493	C₂	—	172	1	no	—
494	C₂	#423×D₄₃	1	1	yes	characteristic
495	C₂	#19143192	1	1	yes	characteristic
496	C₂	#19143203	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#1568	C₂
socle	C₂²×C₄₃	C₂²×C₄⋊C₄
prime radical	C₂×#10621898	C₂×C₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#1568	D₄₃
hypocenter	C₄₃	#17799
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1568

Complements

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

N	H ≅ G/N	type
3. #19133363	C₂	semidirect
4. #19133359	C₂	semidirect
5. #19133357	C₂	semidirect
6. #19133354	C₂	semidirect
7. #19133352	C₂	semidirect
8. #19133344	C₂	semidirect
9. #19133342	C₂	semidirect
10. #335×D₄₃	C₂	semidirect
11. C₄₃×#1568	C₂	semidirect
166. #10621872	M₁₆	semidirect
171. C₈×D₄₃	M₁₆	semidirect
248. #1568	D₄₃	semidirect
295. C₄₃	#17799	semidirect

Maximal subgroups

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

subgroup	index
#19143714	2
C₄×#13063331	2
#19133363	2
#19133359	2
#19133357	2
#19133354	2
#19133352	2
#19133344	2
#19133342	2
#335×D₄₃	2
C₄₃×#1568	2
#17799	43