Subgroups — #25095253

Order 11008.

866 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583028	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Dic₈₆	C₂	1	1	yes	maximal, characteristic
3	#19137071	C₂	1	1	yes	maximal, characteristic
4	#19134470	C₂	1	1	yes	maximal, characteristic
5	#19134468	C₂	1	1	yes	maximal, characteristic
6	#19134463	C₂	1	1	yes	maximal, characteristic
7	#19134463	C₂	1	1	yes	maximal, characteristic
8	#19134456	C₂	1	1	yes	maximal, characteristic
9	#19134454	C₂	1	1	yes	maximal, characteristic
10	#19134451	C₂	1	1	yes	maximal, characteristic
11	#19134443	C₂	1	1	yes	maximal, characteristic
12	#19134283	C₂	1	1	yes	maximal, characteristic
13	#19134281	C₂	1	1	yes	maximal, characteristic
14	#97×Dic₄₃	C₂	1	1	yes	maximal, characteristic
15	C₄₃×#1770	C₂	1	1	yes	maximal, characteristic
16	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
17	#14583028	C₄	1	8	yes	complemented
18	C₈×Dic₈₆	C₄	1	8	yes	complemented
19	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×#13063236	C₂²	1	1	yes	characteristic
25	C₂×#13063236	C₂²	1	1	yes	characteristic
26	C₂×#13063235	C₂²	1	1	yes	characteristic
27	C₂×#13063235	C₂²	1	1	yes	characteristic
28	C₂×#13063235	C₂²	1	1	yes	characteristic
29	C₂×#13063235	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
32	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
35	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
36	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
37	#14582803	C₄	1	2	yes	—
38	#14582794	C₄	1	2	yes	—
39	#14582784	C₄	1	2	yes	—
40	#14582780	C₄	1	2	yes	—
41	C₄×Dic₄₃⋊C₄	C₂²	1	1	yes	characteristic
42	C₄×Dic₄₃⋊C₄	C₂²	1	1	yes	characteristic
43	#14582745	C₂²	1	1	yes	characteristic
44	#14582745	C₂²	1	1	yes	characteristic
45	C₄²×Dic₄₃	C₂²	1	1	yes	characteristic
46	#14582654	C₂²	1	1	yes	characteristic
47	#14582654	C₂²	1	1	yes	characteristic
48	#14582653	C₂²	1	1	yes	characteristic
49	#14582653	C₂²	1	1	yes	characteristic
50	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
51	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
52	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
54	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
55	C₄₃×#336	C₂²	1	1	yes	characteristic
56	C₄₃×#336	C₂²	1	1	yes	characteristic
57	C₂²×Dic₈₆	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
59	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
60	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
62	C₄×Dic₈₆	C₂×C₄	1	4	yes	—
63	C₄×Dic₈₆	C₂×C₄	1	4	yes	—
64	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
65	C₂×Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
66	C₂×Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
67	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
68	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
70	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
71	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
72	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
73	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
74	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
75	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	4	yes	—
76	Dic₄₃⋊C₈	C₂×C₄	1	4	yes	—
77	Dic₄₃⋊C₈	C₂×C₄	1	4	yes	—
78	Dic₄₃⋊C₈	C₂×C₄	1	4	yes	—
79	Dic₄₃⋊C₈	C₂×C₄	1	4	yes	—
80	#13063236	—	2	2	no	—
81	#13063236	C₂×C₄	1	4	yes	—
82	#13063235	—	2	2	no	—
83	#13063235	—	2	2	no	—
84	#13063235	C₂×C₄	1	4	yes	—
85	#13063235	Q₈	1	4	yes	complemented
86	C₄×C₄₃⋊C₈	—	2	2	no	—
87	C₈×Dic₄₃	—	2	2	no	—
88	C₈×Dic₄₃	—	2	2	no	—
89	C₈×Dic₄₃	—	2	2	no	—
90	C₈×Dic₄₃	C₂×C₄	1	4	yes	—
91	C₈×Dic₄₃	C₂×C₄	1	4	yes	—
92	C₈×Dic₄₃	C₂×C₄	1	4	yes	—
93	C₄₃⋊#95	C₂×C₄	1	2	yes	—
94	C₄₃⋊#95	C₂×C₄	1	2	yes	—
95	C₄₃⋊#95	C₂×C₄	1	2	yes	—
96	C₄₃⋊#95	C₂×C₄	1	2	yes	—
97	C₄₃⋊#95	C₂×C₄	1	2	yes	—
98	C₄₃⋊#95	C₂×C₄	1	2	yes	—
99	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
104	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
107	C₄⋊C₈×C₄₃	C₂×C₄	1	4	yes	—
108	#97×C₄₃	—	2	2	no	—
109	#97×C₄₃	—	2	2	no	—
110	C₄×C₈×C₄₃	C₂×C₄	1	4	yes	—
111	#95×C₄₃	C₂×C₄	1	2	yes	—
112	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
117	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
118	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
119	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
120	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
121	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
122	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×Dic₈₆	—	2	4	no	—
124	C₂×Dic₈₆	C₄²	1	4	yes	—
125	C₂×C₈×C₄₃	—	2	1	no	—
126	C₂×C₈×C₄₃	—	2	1	no	—
127	C₂×C₈×C₄₃	—	2	1	no	—
128	C₂×C₈×C₄₃	—	2	1	no	—
129	C₂×C₈×C₄₃	—	2	1	no	—
130	C₂×C₈×C₄₃	—	2	1	no	—
131	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
132	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
135	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
136	C₂×C₈×C₄₃	#41	1	2	yes	—
137	C₄⋊C₄×C₄₃	—	4	2	no	—
138	C₄²×C₄₃	—	2	1	no	—
139	C₄²×C₄₃	—	2	1	no	—
140	C₄²×C₄₃	—	2	1	no	—
141	C₄²×C₄₃	—	2	1	no	—
142	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
143	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
144	C₄⋊Dic₄₃	C₄²	1	4	yes	—
145	Dic₄₃⋊C₄	—	2	4	no	—
146	Dic₄₃⋊C₄	—	4	2	no	—
147	Dic₄₃⋊C₄	C₄²	1	4	yes	—
148	Dic₄₃⋊C₄	C₄²	1	4	yes	—
149	C₄×Dic₄₃	—	2	1	no	—
150	C₄×Dic₄₃	—	2	1	no	—
151	C₄×Dic₄₃	—	2	4	no	—
152	C₄×Dic₄₃	—	4	2	no	—
153	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
154	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
155	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
156	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
157	C₄×Dic₄₃	C₂×Q₈	1	2	yes	—
158	C₄×Dic₄₃	#41	1	2	yes	—
159	C₂×C₄₃⋊C₈	—	2	1	no	—
160	C₂×C₄₃⋊C₈	—	2	1	no	—
161	C₂×C₄₃⋊C₈	—	2	1	no	—
162	C₂×C₄₃⋊C₈	—	2	1	no	—
163	C₂×C₄₃⋊C₈	—	2	1	no	—
164	C₂×C₄₃⋊C₈	—	2	1	no	—
165	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
166	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
167	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
168	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
169	C₂×C₄₃⋊C₈	C₂×Q₈	1	2	yes	—
170	C₂×C₄₃⋊C₈	#41	1	2	yes	—
171	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₄₃	—	2	2	no	—
173	C₂×C₄×C₄₃	—	2	2	no	—
174	C₂×C₄×C₄₃	—	2	2	no	—
175	C₂×C₄×C₄₃	—	2	2	no	—
176	C₂×C₄×C₄₃	—	2	2	no	—
177	C₂×C₄×C₄₃	—	2	2	no	—
178	C₂×C₄×C₄₃	—	2	2	no	—
179	C₂×C₄×C₄₃	—	2	2	no	—
180	C₂×C₄×C₄₃	C₂×C₄²	1	2	yes	—
181	C₂×C₄×C₄₃	C₂×C₄²	1	2	yes	—
182	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
184	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
185	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
188	C₂×Dic₄₃	—	2	2	no	—
189	C₂×Dic₄₃	—	2	2	no	—
190	C₂×Dic₄₃	—	2	2	no	—
191	C₂×Dic₄₃	—	2	2	no	—
192	C₂×Dic₄₃	—	2	2	no	—
193	C₂×Dic₄₃	—	2	2	no	—
194	C₂×Dic₄₃	—	2	2	no	—
195	C₂×Dic₄₃	—	2	2	no	—
196	C₂×Dic₄₃	C₂×C₄²	1	2	yes	—
197	C₂×Dic₄₃	C₂×C₄²	1	2	yes	—
198	C₂×Dic₄₃	C₂×C₄²	1	2	yes	—
199	C₂×Dic₄₃	C₂×C₄²	1	2	yes	—
200	C₂×Dic₄₃	C₄×Q₈	1	4	yes	—
201	C₂×Dic₄₃	#131	1	4	yes	—
202	Dic₈₆	—	2	8	no	—
203	C₈×C₄₃	—	2	2	no	—
204	C₈×C₄₃	—	2	2	no	—
205	C₈×C₄₃	—	2	2	no	—
206	C₈×C₄₃	C₄×Q₈	1	4	yes	—
207	C₄₃⋊C₈	—	2	2	no	—
208	C₄₃⋊C₈	—	2	2	no	—
209	C₄₃⋊C₈	—	2	2	no	—
210	C₄₃⋊C₈	C₄×Q₈	1	4	yes	—
211	#20521	—	43	1	no	maximal, Sylow
212	C₂²×C₄₃	C₂²×C₄²	1	1	yes	characteristic
213	C₂²×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
214	C₂²×C₄₃	C₄×#41	1	1	yes	characteristic
215	C₂²×C₄₃	C₂×#131	1	2	yes	—
216	C₂²×C₄₃	#568	1	2	yes	—
217	C₄×C₄₃	—	2	2	no	—
218	C₄×C₄₃	—	2	2	no	—
219	C₄×C₄₃	—	4	2	no	—
220	C₄×C₄₃	—	4	2	no	—
221	C₄×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
222	C₄×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
223	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
224	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
225	Dic₄₃	—	2	2	no	—
226	Dic₄₃	—	2	2	no	—
227	Dic₄₃	—	2	2	no	—
228	Dic₄₃	—	2	4	no	—
229	Dic₄₃	—	4	2	no	—
230	Dic₄₃	#405	1	4	yes	—
231	C₂×#446	—	43	1	no	—
232	C₂×C₈×Q₈	—	43	1	no	—
233	#2295	—	43	1	no	—
234	#1771	—	43	1	no	—
235	#1771	—	43	1	no	—
236	#1770	—	43	1	no	—
237	#1770	—	43	1	no	—
238	#1770	D₄₃	1	1	yes	characteristic
239	C₈×C₄⋊C₄	—	43	1	no	—
240	#1768	—	43	1	no	—
241	#1768	—	43	1	no	—
242	C₄×C₄⋊C₈	—	43	1	no	—
243	#1726	—	43	1	no	—
244	#1726	—	43	1	no	—
245	C₄×#97	—	43	1	no	—
246	C₂×C₄₃	C₄²×Q₈	1	1	yes	characteristic
247	C₂×C₄₃	C₂×#405	1	1	yes	characteristic
248	C₂×C₄₃	#2875	1	1	yes	characteristic
249	C₂×C₄₃	#2962	1	2	yes	—
250	C₂×C₄₃	#2969	1	2	yes	—
251	C₂×C₄×Q₈	—	43	1	no	—
252	#446	—	43	8	no	—
253	C₈×Q₈	—	43	8	no	—
254	C₂×C₄⋊C₈	—	43	1	no	—
255	C₂×C₄⋊C₈	—	43	1	no	—
256	C₂×C₄⋊C₈	—	43	1	no	—
257	C₂×C₄⋊C₈	—	43	1	no	—
258	C₂×C₄⋊C₈	—	43	1	no	—
259	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
260	C₂×#97	—	43	1	no	—
261	C₂×#97	—	43	1	no	—
262	C₂×#97	—	43	1	no	—
263	C₂×#97	—	43	1	no	—
264	C₂×#97	—	43	1	no	—
265	C₂×#97	—	43	1	no	—
266	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
267	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
268	C₂×C₄×C₈	—	43	1	no	—
269	C₂×C₄×C₈	—	43	1	no	—
270	C₂×C₄×C₈	—	43	1	no	—
271	C₂×C₄×C₈	—	43	1	no	—
272	C₂×C₄×C₈	—	43	1	no	—
273	C₂×C₄×C₈	—	43	1	no	—
274	C₂×C₄×C₈	—	43	1	no	—
275	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
276	#391	—	43	2	no	—
277	#389	—	43	2	no	—
278	#387	—	43	2	no	—
279	#387	—	43	2	no	—
280	C₄×C₄⋊C₄	—	43	1	no	—
281	C₄×C₄⋊C₄	—	43	1	no	—
282	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
283	#376	—	43	1	no	—
284	#376	—	43	1	no	—
285	C₄³	—	43	1	no	—
286	#336	—	43	1	no	—
287	#336	—	43	1	no	—
288	#336	—	43	1	no	—
289	#336	—	43	1	no	—
290	#336	C₂×D₄₃	1	1	yes	characteristic
291	#336	C₂×D₄₃	1	1	yes	characteristic
292	C₄₃	#20521	1	1	yes	characteristic, complemented, Sylow
293	C₂²×Q₈	—	43	1	no	—
294	C₂²×C₈	—	43	1	no	—
295	C₂²×C₈	—	43	1	no	—
296	C₂²×C₈	—	43	1	no	—
297	C₂²×C₈	—	43	1	no	—
298	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
299	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
300	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
301	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
302	C₄×Q₈	—	43	4	no	—
303	C₄×Q₈	—	43	4	no	—
304	C₂×C₄⋊C₄	—	43	1	no	—
305	C₂×C₄⋊C₄	—	43	1	no	—
306	C₂×C₄⋊C₄	—	43	1	no	—
307	C₂×C₄⋊C₄	—	43	2	no	—
308	C₂×C₄⋊C₄	—	43	2	no	—
309	C₂×C₄⋊C₄	C₄×D₄₃	1	2	yes	—
310	C₂×C₄²	—	43	1	no	—
311	C₂×C₄²	—	43	1	no	—
312	C₂×C₄²	—	43	1	no	—
313	C₂×C₄²	—	43	2	no	—
314	C₂×C₄²	—	43	1	no	—
315	C₂×C₄²	—	43	2	no	—
316	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
317	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
318	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
319	C₄⋊C₈	—	43	4	no	—
320	C₄⋊C₈	—	43	4	no	—
321	C₄⋊C₈	—	43	4	no	—
322	C₄⋊C₈	—	43	4	no	—
323	C₄⋊C₈	—	43	4	no	—
324	C₄⋊C₈	C₄×D₄₃	1	4	yes	—
325	#97	—	2	2	no	—
326	#97	—	2	2	no	—
327	#97	—	43	4	no	—
328	#97	—	43	4	no	—
329	#97	—	43	4	no	—
330	#97	—	86	2	no	—
331	#97	—	86	2	no	—
332	#97	—	86	2	no	—
333	C₄×C₈	—	43	4	no	—
334	C₄×C₈	—	43	4	no	—
335	C₄×C₈	—	43	4	no	—
336	C₄×C₈	—	86	2	no	—
337	C₄×C₈	—	86	2	no	—
338	C₄×C₈	—	86	2	no	—
339	C₄×C₈	—	86	2	no	—
340	C₄×C₈	C₄×D₄₃	1	4	yes	—
341	#95	—	43	2	no	—
342	#95	—	43	2	no	—
343	#95	—	43	2	no	—
344	#95	—	43	2	no	—
345	#95	—	43	2	no	—
346	#95	—	43	2	no	—
347	#95	C₄×D₄₃	1	2	yes	—
348	C₂×Q₈	—	43	4	no	—
349	C₂×Q₈	—	86	4	no	—
350	C₂²×C₄	—	43	1	no	—
351	C₂²×C₄	—	43	2	no	—
352	C₂²×C₄	—	43	1	no	—
353	C₂²×C₄	—	43	1	no	—
354	C₂²×C₄	—	43	1	no	—
355	C₂²×C₄	—	43	2	no	—
356	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
357	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
358	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
359	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
360	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	43	2	no	—
368	C₂×C₈	—	43	2	no	—
369	C₂×C₈	—	43	2	no	—
370	C₂×C₈	—	43	2	no	—
371	C₂×C₈	—	43	2	no	—
372	C₂×C₈	—	43	2	no	—
373	C₂×C₈	—	86	1	no	—
374	C₂×C₈	—	86	1	no	—
375	C₂×C₈	—	86	1	no	—
376	C₂×C₈	—	86	1	no	—
377	C₂×C₈	—	86	1	no	—
378	C₂×C₈	—	86	1	no	—
379	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
380	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
381	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
382	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
383	C₂×C₈	#10621900	1	2	yes	—
384	C₂×C₈	Q₈×D₄₃	1	2	yes	—
385	C₄⋊C₄	—	4	2	no	—
386	C₄⋊C₄	—	43	4	no	—
387	C₄⋊C₄	—	43	4	no	—
388	C₄⋊C₄	—	43	4	no	—
389	C₄⋊C₄	—	86	4	no	—
390	C₄⋊C₄	—	172	2	no	—
391	C₄²	—	2	1	no	—
392	C₄²	—	2	1	no	—
393	C₄²	—	2	1	no	—
394	C₄²	—	2	1	no	—
395	C₄²	—	43	2	no	—
396	C₄²	—	43	2	no	—
397	C₄²	—	43	2	no	—
398	C₄²	—	43	2	no	—
399	C₄²	—	43	2	no	—
400	C₄²	—	43	2	no	—
401	C₄²	—	86	4	no	—
402	C₄²	—	86	1	no	—
403	C₄²	—	86	1	no	—
404	C₄²	—	172	2	no	—
405	C₄²	C₂×C₄×D₄₃	1	2	yes	—
406	C₄²	C₂×C₄×D₄₃	1	2	yes	—
407	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
408	Q₈	—	86	8	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	43	2	no	—
418	C₂×C₄	—	43	4	no	—
419	C₂×C₄	—	43	2	no	—
420	C₂×C₄	—	43	2	no	—
421	C₂×C₄	—	43	2	no	—
422	C₂×C₄	—	43	4	no	—
423	C₂×C₄	—	86	2	no	—
424	C₂×C₄	—	86	2	no	—
425	C₂×C₄	—	86	2	no	—
426	C₂×C₄	—	86	2	no	—
427	C₂×C₄	—	86	2	no	—
428	C₂×C₄	—	86	2	no	—
429	C₂×C₄	—	86	2	no	—
430	C₂×C₄	—	86	2	no	—
431	C₂×C₄	C₄²×D₄₃	1	2	yes	—
432	C₂×C₄	C₄²×D₄₃	1	2	yes	—
433	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
434	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
435	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
436	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
437	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
438	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
439	C₈	—	2	2	no	—
440	C₈	—	2	2	no	—
441	C₈	—	2	2	no	—
442	C₈	—	43	4	no	—
443	C₈	—	86	2	no	—
444	C₈	—	86	2	no	—
445	C₈	—	86	2	no	—
446	C₈	#13063290	1	4	yes	—
447	C₂²	C₂×C₄²×D₄₃	1	1	yes	characteristic
448	C₂²	C₄×Q₈×D₄₃	1	1	yes	characteristic
449	C₂²	C₄×#10621900	1	1	yes	characteristic
450	C₂²	#131×D₄₃	1	2	yes	—
451	C₂²	#14583665	1	2	yes	—
452	C₄	—	2	2	no	—
453	C₄	—	2	2	no	—
454	C₄	—	4	2	no	—
455	C₄	—	4	2	no	—
456	C₄	—	43	4	no	—
457	C₄	—	86	2	no	—
458	C₄	—	86	2	no	—
459	C₄	—	86	2	no	—
460	C₄	—	86	4	no	—
461	C₄	—	172	2	no	—
462	C₄	C₄×Q₈×D₄₃	1	1	yes	characteristic
463	C₄	C₂×#13063290	1	1	yes	characteristic
464	C₄	C₄×#10621900	1	1	yes	characteristic
465	C₄	#14583367	1	1	yes	characteristic
466	C₂	C₄×#13063290	1	1	yes	characteristic
467	C₂	#405×D₄₃	1	1	yes	characteristic
468	C₂	#19143020	1	1	yes	characteristic
469	C₂	#19143540	1	2	yes	—
470	C₂	#19143594	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₃
commutator	C₂²×C₄₃	C₂²×C₄²
Fitting	C₄₃×#1770	C₂
socle, prime radical	C₂³×C₄₃	C₂³×C₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1770	D₄₃
hypocenter	C₄₃	#20521
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1770

Complements

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

N	H ≅ G/N	type
17. #14583028	C₄	semidirect
18. C₈×Dic₈₆	C₄	semidirect
85. #13063235	Q₈	semidirect
292. C₄₃	#20521	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583028	2
C₂×C₈×Dic₈₆	2
#19137071	2
#19134470	2
#19134468	2
#19134463	2
#19134456	2
#19134454	2
#19134451	2
#19134443	2
#19134283	2
#19134281	2
#97×Dic₄₃	2
C₄₃×#1770	2
#20521	43