Subgroups — #25961015

Order 11008.

1838 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#10621898	C₂	1	1	yes	maximal, characteristic
2	Q₈×#10621877	C₂	1	1	yes	maximal, characteristic, complemented
3	#19143547	C₂	1	2	yes	maximal, complemented
4	#19143543	C₂	1	2	yes	maximal, complemented
5	#19143540	C₂	1	4	yes	maximal, complemented
6	#19143538	C₂	1	1	yes	maximal, characteristic, complemented
7	#19143538	C₂	1	2	yes	maximal, complemented
8	#19143535	C₂	1	2	yes	maximal, complemented
9	#19143531	C₂	1	4	yes	maximal, complemented
10	#19143529	C₂	1	1	yes	maximal, characteristic, complemented
11	#19143526	C₂	1	2	yes	maximal, complemented
12	#446×D₄₃	C₂	1	2	yes	maximal, complemented
13	#19143160	C₂	1	1	yes	maximal, characteristic
14	#19143160	C₂	1	2	yes	maximal
15	#19143020	C₂	1	2	yes	maximal
16	C₄×#13063331	C₂	1	1	yes	maximal, characteristic
17	C₂×C₄₃×#446	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13063331	C₂²	1	1	yes	characteristic
19	C₂×#13063331	C₂²	1	2	yes	—
20	C₂×#13063331	C₂²	1	1	yes	characteristic
21	Q₈×Dic₈₆	C₄	1	1	yes	characteristic
22	#14583627	C₄	1	1	yes	characteristic
23	#14583627	C₄	1	2	yes	—
24	#14583609	C₄	1	1	yes	characteristic
25	#14583609	C₄	1	2	yes	—
26	#14583604	C₄	1	2	yes	—
27	#14583604	C₄	1	4	yes	—
28	Q₈×D₁₇₂	C₄	1	1	yes	characteristic
29	Q₈×C₂²⋊D₄₃	C₄	1	2	yes	—
30	#14583456	C₂²	1	1	yes	characteristic
31	#14583456	C₂²	1	2	yes	—
32	#14583453	C₂²	1	2	yes	—
33	#14583453	C₂²	1	4	yes	—
34	C₄×#10621898	C₂²	1	1	yes	characteristic
35	C₄×#10621898	C₂²	1	2	yes	—
36	C₄×Q₈×D₄₃	C₂²	1	2	yes	—
37	#14583030	C₂²	1	2	yes	—
38	#14583030	C₂²	1	4	yes	—
39	#14583029	C₂²	1	2	yes	—
40	#14583029	C₂²	1	2	yes	—
41	#14583028	C₂²	1	4	yes	—
42	#14583028	C₂²	1	4	yes	—
43	#14583028	C₂²	1	4	yes	—
44	#14583027	C₂²	1	4	yes	—
45	#14583027	C₂²	1	4	yes	—
46	#14583027	C₂²	1	4	yes	—
47	#14583027	C₂²	1	4	yes	—
48	#14583026	C₂²	1	2	yes	—
49	#14583026	C₂²	1	4	yes	—
50	Q₈×C₄₃⋊C₈	C₂²	1	2	yes	—
51	C₈×Dic₈₆	C₂²	1	2	yes	—
52	C₈×Dic₈₆	C₂²	1	2	yes	—
53	#14583023	C₂²	1	4	yes	—
54	#14583023	C₂²	1	2	yes	—
55	#14582925	C₂²	1	2	yes	—
56	#14582925	C₂²	1	2	yes	—
57	#14582925	C₂²	1	2	yes	—
58	#14582924	C₂²	1	4	yes	—
59	#14582924	C₂²	1	4	yes	—
60	#14582924	C₂²	1	4	yes	—
61	#14582923	C₂²	1	1	yes	characteristic
62	#14582923	C₂²	1	2	yes	—
63	#14582921	C₂²	1	2	yes	—
64	#14582921	C₂²	1	4	yes	—
65	C₄⋊C₈×D₄₃	C₂²	1	4	yes	—
66	C₄⋊C₈×D₄₃	C₂²	1	2	yes	—
67	#14582856	C₂²	1	4	yes	—
68	#14582856	C₂²	1	4	yes	—
69	#14582854	C₂²	1	1	yes	characteristic
70	#14582854	C₂²	1	1	yes	characteristic
71	#14582854	C₂²	1	2	yes	—
72	#14582854	C₂²	1	2	yes	—
73	#14582853	C₂²	1	2	yes	—
74	#14582853	C₂²	1	2	yes	—
75	C₄×#10621877	C₂²	1	1	yes	characteristic
76	C₄×#10621877	C₂²	1	2	yes	—
77	#14582851	C₂²	1	4	yes	—
78	C₄×#10621872	C₂²	1	2	yes	—
79	#97×D₄₃	C₂²	1	4	yes	—
80	C₄×C₈×D₄₃	C₂²	1	2	yes	—
81	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
82	C₄₃×#446	C₂²	1	1	yes	characteristic
83	C₄₃×#446	C₂²	1	1	yes	characteristic
84	C₄₃×#446	C₂²	1	2	yes	—
85	C₄₃×#446	C₂²	1	2	yes	—
86	C₄₃×#446	C₂²	1	1	yes	characteristic
87	C₄₃×#446	C₂²	1	1	yes	characteristic
88	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
89	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
90	C₂×#97×C₄₃	C₂²	1	2	yes	—
91	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
92	C₂×#10621898	C₂³	1	1	yes	characteristic
93	C₂×Q₈×D₄₃	C₂×C₄	1	2	yes	—
94	#13063331	—	2	4	no	—
95	#13063331	—	2	8	no	—
96	#13063331	Q₈	1	8	yes	complemented
97	C₂×#10621877	C₂³	1	1	yes	characteristic
98	C₂×#10621877	C₂³	1	2	yes	—
99	C₂×#10621877	C₂³	1	1	yes	characteristic
100	C₂×#10621872	C₂³	1	2	yes	—
101	C₂×#10621872	C₂³	1	4	yes	—
102	C₂×#10621872	C₂³	1	2	yes	—
103	C₂×C₈×D₄₃	C₂³	1	2	yes	—
104	C₂×C₈×D₄₃	C₂³	1	4	yes	—
105	C₂×C₈×D₄₃	C₂³	1	2	yes	—
106	#13063325	C₂×C₄	1	1	yes	characteristic
107	#13063325	C₂×C₄	1	2	yes	—
108	#13063325	C₂×C₄	1	1	yes	characteristic
109	#13063325	C₂×C₄	1	2	yes	—
110	#13063324	C₂×C₄	1	2	yes	—
111	#13063324	C₂×C₄	1	4	yes	—
112	#13063323	C₂×C₄	1	2	yes	—
113	#13063323	C₂×C₄	1	4	yes	—
114	#13063317	C₂×C₄	1	2	yes	—
115	#13063317	C₂×C₄	1	2	yes	—
116	#13063317	C₂×C₄	1	2	yes	—
117	#13063315	C₂×C₄	1	4	yes	—
118	#13063315	C₂×C₄	1	4	yes	—
119	#13063315	C₂×C₄	1	4	yes	—
120	#13063305	C₂×C₄	1	2	yes	—
121	#13063305	C₂×C₄	1	4	yes	—
122	#13063304	C₂×C₄	1	2	yes	—
123	#13063304	C₂×C₄	1	4	yes	—
124	#13063304	C₂×C₄	1	2	yes	—
125	#13063304	C₂×C₄	1	4	yes	—
126	#13063303	C₂×C₄	1	4	yes	—
127	#13063303	C₂×C₄	1	4	yes	—
128	#13063303	C₂×C₄	1	4	yes	—
129	#13063301	C₂×C₄	1	2	yes	—
130	#13063301	C₂×C₄	1	4	yes	—
131	Q₈×Dic₄₃	C₂×C₄	1	2	yes	—
132	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
133	C₄×Dic₈₆	C₂×C₄	1	2	yes	—
134	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
135	C₄×Dic₈₆	C₂×C₄	1	2	yes	—
136	C₄×Dic₈₆	C₂³	1	2	yes	—
137	C₄×Dic₈₆	C₂³	1	4	yes	—
138	C₄×Dic₈₆	C₂³	1	4	yes	—
139	C₄×Dic₈₆	C₂³	1	2	yes	—
140	#13063290	C₂×C₄	1	2	yes	—
141	#13063290	C₂×C₄	1	4	yes	—
142	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
143	C₄×D₁₇₂	C₂×C₄	1	2	yes	—
144	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
145	C₄×D₁₇₂	C₂×C₄	1	2	yes	—
146	C₄×C₂²⋊D₄₃	C₂×C₄	1	2	yes	—
147	C₄×C₂²⋊D₄₃	C₂×C₄	1	4	yes	—
148	C₄×C₂²⋊D₄₃	C₂×C₄	1	2	yes	—
149	C₄×C₂²⋊D₄₃	C₂×C₄	1	4	yes	—
150	#13063284	C₂³	1	1	yes	characteristic
151	#13063284	C₂³	1	2	yes	—
152	#13063282	C₂³	1	2	yes	—
153	#13063282	C₂³	1	4	yes	—
154	C₄⋊C₄×D₄₃	C₂×C₄	1	2	yes	—
155	C₄⋊C₄×D₄₃	C₂×C₄	1	4	yes	—
156	C₄²×D₄₃	C₂³	1	2	yes	—
157	C₄²×D₄₃	C₂³	1	4	yes	—
158	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
159	C₄⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
160	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
161	C₄⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
162	Dic₄₃⋊C₈	C₂³	1	4	yes	—
163	Dic₄₃⋊C₈	C₂³	1	4	yes	—
164	Dic₄₃⋊C₈	C₂³	1	4	yes	—
165	Dic₄₃⋊C₈	C₂³	1	4	yes	—
166	Dic₄₃⋊C₈	C₂³	1	4	yes	—
167	Dic₄₃⋊C₈	C₂³	1	4	yes	—
168	#13063236	C₂³	1	4	yes	—
169	#13063236	C₂³	1	2	yes	—
170	#13063235	C₂³	1	4	yes	—
171	#13063235	C₂³	1	4	yes	—
172	#13063235	C₂³	1	2	yes	—
173	#13063235	C₂³	1	2	yes	—
174	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
175	C₄×C₄₃⋊C₈	C₂³	1	4	yes	—
176	C₈×Dic₄₃	C₂³	1	2	yes	—
177	C₈×Dic₄₃	C₂³	1	2	yes	—
178	C₈×Dic₄₃	C₂³	1	4	yes	—
179	C₈×Dic₄₃	C₂³	1	4	yes	—
180	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
181	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
182	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
183	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
184	C₄×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
185	C₄×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
186	C₄×Q₈×C₄₃	C₂×C₄	1	2	yes	—
187	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
188	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
189	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
192	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
194	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
195	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
196	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
197	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
198	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
199	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
200	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
201	#97×C₄₃	C₂³	1	2	yes	—
202	#97×C₄₃	C₂³	1	2	yes	—
203	#97×C₄₃	C₂³	1	2	yes	—
204	#97×C₄₃	C₂³	1	2	yes	—
205	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
206	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
207	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
208	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
209	C₂×Q₈×C₄₃	—	4	2	no	—
210	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
211	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
212	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
213	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
214	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
215	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
216	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
217	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
218	C₂×C₂²⋊D₄₃	C₂²×C₄	1	2	yes	—
219	Q₈×D₄₃	—	4	4	no	—
220	#10621898	C₂×Q₈	1	4	yes	—
221	#10621898	#41	1	4	yes	—
222	C₂×D₁₇₂	C₂²×C₄	1	1	yes	characteristic
223	C₂×C₄×D₄₃	C₂²×C₄	1	2	yes	—
224	C₂×C₄×D₄₃	C₂²×C₄	1	2	yes	—
225	C₂×C₄×D₄₃	C₂²×C₄	1	4	yes	—
226	C₂×C₄×D₄₃	C₂²×C₄	1	4	yes	—
227	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
228	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
229	C₂×Dic₈₆	C₂²×C₄	1	4	yes	—
230	C₂×Dic₈₆	C₂²×C₄	1	4	yes	—
231	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
232	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
233	C₂×C₈×C₄₃	—	2	2	no	—
234	C₂×C₈×C₄₃	—	2	4	no	—
235	C₂×C₈×C₄₃	C₂×Q₈	1	4	yes	complemented
236	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
237	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
238	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
239	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
240	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
241	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
242	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
243	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
244	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
245	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
246	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
247	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
248	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
249	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
250	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
251	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
252	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
253	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
254	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
255	C₄²×C₄₃	C₂⁴	1	2	yes	—
256	C₄²×C₄₃	C₂⁴	1	2	yes	—
257	C₂²⋊Dic₄₃	C₂²×C₄	1	4	yes	—
258	C₂²⋊Dic₄₃	C₂²×C₄	1	2	yes	—
259	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	2	yes	—
260	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	4	yes	—
261	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	2	yes	—
262	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	4	yes	—
263	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
264	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
265	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
266	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
267	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
268	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
269	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
270	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
271	Dic₄₃⋊C₄	C₂²×C₄	1	4	yes	—
272	Dic₄₃⋊C₄	C₂²×C₄	1	4	yes	—
273	Dic₄₃⋊C₄	C₂²×C₄	1	4	yes	—
274	Dic₄₃⋊C₄	C₂²×C₄	1	2	yes	—
275	Dic₄₃⋊C₄	C₂²×C₄	1	4	yes	—
276	Dic₄₃⋊C₄	C₂²×C₄	1	2	yes	—
277	Dic₄₃⋊C₄	C₂²×C₄	1	4	yes	—
278	Dic₄₃⋊C₄	C₂²×C₄	1	4	yes	—
279	Dic₄₃⋊C₄	C₂²×C₄	1	4	yes	—
280	Dic₄₃⋊C₄	C₂²×C₄	1	4	yes	—
281	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
282	C₄×Dic₄₃	C₂²×C₄	1	4	yes	—
283	C₄×Dic₄₃	C₂²×C₄	1	4	yes	—
284	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
285	C₄×Dic₄₃	C₂⁴	1	2	yes	—
286	C₄×Dic₄₃	C₂⁴	1	4	yes	—
287	#10621877	—	2	2	no	—
288	#10621877	—	2	4	no	—
289	#10621877	C₂×Q₈	1	4	yes	complemented
290	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
291	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
292	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
293	#10621872	—	2	4	no	—
294	#10621872	—	2	8	no	—
295	#10621872	C₂×Q₈	1	8	yes	complemented
296	C₈×D₄₃	—	2	4	no	—
297	C₈×D₄₃	—	2	8	no	—
298	C₈×D₄₃	C₂×Q₈	1	8	yes	complemented
299	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
300	C₂²×D₄₃	C₂³×C₄	1	2	yes	—
301	Q₈×C₄₃	—	2	2	no	—
302	Q₈×C₄₃	—	2	2	no	—
303	Q₈×C₄₃	—	4	2	no	—
304	C₂×C₄×C₄₃	—	2	2	no	—
305	C₂×C₄×C₄₃	—	4	1	no	—
306	C₂×C₄×C₄₃	—	4	2	no	—
307	C₂×C₄×C₄₃	—	4	2	no	—
308	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
309	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
310	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
311	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
312	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
313	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
314	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
315	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
316	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
317	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
318	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
319	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
320	C₂²⋊D₄₃	C₄×Q₈	1	8	yes	—
321	C₂×Dic₄₃	C₂³×C₄	1	4	yes	—
322	C₂×Dic₄₃	C₂³×C₄	1	2	yes	—
323	C₂×Dic₄₃	C₂³×C₄	1	4	yes	—
324	C₂×Dic₄₃	C₂³×C₄	1	2	yes	—
325	C₂×Dic₄₃	C₂³×C₄	1	2	yes	—
326	D₁₇₂	C₄×Q₈	1	4	yes	—
327	C₄×D₄₃	—	2	4	no	—
328	C₄×D₄₃	—	4	2	no	—
329	C₄×D₄₃	—	4	4	no	—
330	C₄×D₄₃	—	4	4	no	—
331	C₄×D₄₃	C₂²×Q₈	1	4	yes	—
332	C₄×D₄₃	C₂×#41	1	4	yes	—
333	Dic₈₆	—	2	4	no	—
334	Dic₈₆	—	4	4	no	—
335	Dic₈₆	—	4	2	no	—
336	Dic₈₆	—	4	4	no	—
337	Dic₈₆	C₄×Q₈	1	4	yes	—
338	C₈×C₄₃	—	2	1	no	—
339	C₈×C₄₃	—	2	2	no	—
340	C₈×C₄₃	—	2	1	no	—
341	C₈×C₄₃	—	2	2	no	—
342	C₈×C₄₃	C₂²×Q₈	1	2	yes	—
343	C₈×C₄₃	C₂²×Q₈	1	2	yes	—
344	C₄₃⋊C₈	—	2	2	no	—
345	C₄₃⋊C₈	—	2	4	no	—
346	C₄₃⋊C₈	C₂²×Q₈	1	4	yes	—
347	#60195	—	43	1	no	maximal, Sylow
348	C₂²×C₄₃	—	2	1	no	—
349	C₂²×C₄₃	—	2	1	no	—
350	C₂²×C₄₃	C₂×C₄×Q₈	1	2	yes	—
351	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
352	C₂×D₄₃	—	2	2	no	—
353	C₂×D₄₃	—	2	2	no	—
354	C₂×D₄₃	C₂×C₄×Q₈	1	4	yes	—
355	C₄×C₄₃	—	2	2	no	—
356	C₄×C₄₃	—	2	1	no	—
357	C₄×C₄₃	—	2	2	no	—
358	C₄×C₄₃	—	2	1	no	—
359	C₄×C₄₃	—	2	2	no	—
360	C₄×C₄₃	—	2	1	no	—
361	C₄×C₄₃	—	2	2	no	—
362	C₄×C₄₃	C₂×C₄×Q₈	1	2	yes	—
363	C₄×C₄₃	#568	1	2	yes	—
364	C₄×C₄₃	C₂³×Q₈	1	1	yes	characteristic
365	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
366	Dic₄₃	—	2	4	no	—
367	Dic₄₃	—	2	2	no	—
368	Dic₄₃	—	2	2	no	—
369	Dic₄₃	—	2	4	no	—
370	Dic₄₃	C₂×C₄×Q₈	1	4	yes	—
371	Q₈×#41	—	43	1	no	—
372	Q₈×M₁₆	—	43	2	no	—
373	Q₈×M₁₆	—	43	1	no	—
374	#2962	—	43	4	no	—
375	#2962	—	43	2	no	—
376	#2962	—	43	1	no	—
377	#2962	—	43	2	no	—
378	#2961	—	43	4	no	—
379	#2961	—	43	2	no	—
380	#2960	—	43	2	no	—
381	#2960	—	43	1	no	—
382	C₂×#446	—	43	2	no	—
383	C₂×#446	D₄₃	1	1	yes	characteristic, complemented
384	#2906	—	43	1	no	—
385	#2906	—	43	2	no	—
386	#2875	—	43	2	no	—
387	C₄×#131	—	43	1	no	—
388	C₂×C₄₃	—	2	2	no	—
389	C₂×C₄₃	C₂²×C₄×Q₈	1	1	yes	characteristic
390	C₂×C₄₃	C₂×#568	1	1	yes	characteristic
391	C₂×C₄₃	#3573	1	1	yes	characteristic
392	D₄₃	—	2	4	no	—
393	C₂×#131	—	43	1	no	—
394	C₂×#131	—	43	1	no	—
395	C₂×#131	—	43	2	no	—
396	Q₈²	—	43	1	no	—
397	#557	—	43	1	no	—
398	#557	—	43	2	no	—
399	#554	—	43	1	no	—
400	#554	—	43	2	no	—
401	#554	—	43	2	no	—
402	#554	—	43	4	no	—
403	D₄×Q₈	—	43	2	no	—
404	D₄×Q₈	—	43	1	no	—
405	#533	—	43	2	no	—
406	#533	—	43	4	no	—
407	#533	—	43	1	no	—
408	#533	—	43	2	no	—
409	C₄×#41	—	43	1	no	—
410	C₄×#41	—	43	2	no	—
411	C₂×C₄×Q₈	—	43	2	no	—
412	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
413	#446	—	43	2	no	—
414	#446	—	43	4	no	—
415	#446	—	43	2	no	—
416	#446	—	43	4	no	—
417	#446	—	43	4	no	—
418	#446	—	43	4	no	—
419	#446	—	43	4	no	—
420	#446	—	43	4	no	—
421	#446	—	43	4	no	—
422	#446	—	43	4	no	—
423	#446	—	43	4	no	—
424	#446	—	43	2	no	—
425	#446	—	43	2	no	—
426	#446	C₂×D₄₃	1	1	yes	characteristic
427	#446	C₂×D₄₃	1	1	yes	characteristic
428	#446	C₂×D₄₃	1	2	yes	—
429	#446	C₂×D₄₃	1	1	yes	characteristic
430	#446	C₂×D₄₃	1	2	yes	—
431	#446	C₂×D₄₃	1	1	yes	characteristic
432	C₈×Q₈	—	43	2	no	—
433	C₈×Q₈	—	43	4	no	—
434	C₈×Q₈	—	43	2	no	—
435	C₈×Q₈	—	43	2	no	—
436	C₈×Q₈	—	43	2	no	—
437	#424	—	43	2	no	—
438	#424	—	43	2	no	—
439	#424	—	43	2	no	—
440	#424	—	43	4	no	—
441	#424	—	43	4	no	—
442	#424	—	43	4	no	—
443	#423	—	43	1	no	—
444	#423	—	43	2	no	—
445	#423	—	43	2	no	—
446	#423	—	43	4	no	—
447	C₂×C₄⋊C₈	—	43	4	no	—
448	C₂×C₄⋊C₈	—	43	2	no	—
449	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
450	C₂×C₄⋊C₈	C₂×D₄₃	1	2	yes	—
451	#405	—	43	1	no	—
452	#405	—	43	1	no	—
453	#405	—	43	2	no	—
454	#405	—	43	2	no	—
455	#405	—	43	4	no	—
456	#405	—	43	4	no	—
457	#405	—	43	2	no	—
458	#405	—	43	2	no	—
459	C₄×M₁₆	—	43	1	no	—
460	C₄×M₁₆	—	43	2	no	—
461	C₄×M₁₆	—	43	4	no	—
462	C₄×M₁₆	—	43	2	no	—
463	C₂×#97	—	43	4	no	—
464	C₂×#97	C₂×D₄₃	1	2	yes	—
465	C₂×C₄×C₈	—	43	2	no	—
466	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
467	C₄₃	#60195	1	1	yes	characteristic, complemented, Sylow
468	C₂×#41	—	43	1	no	—
469	C₂²×Q₈	—	43	2	no	—
470	C₂²×Q₈	C₄×D₄₃	1	1	yes	characteristic
471	#131	—	43	8	no	—
472	#131	—	86	4	no	—
473	#131	—	86	8	no	—
474	C₂×M₁₆	—	43	1	no	—
475	C₂×M₁₆	—	43	1	no	—
476	C₂×M₁₆	—	43	2	no	—
477	C₂×M₁₆	—	43	2	no	—
478	C₂×M₁₆	—	43	4	no	—
479	C₂×M₁₆	—	43	2	no	—
480	C₂²×C₈	—	43	2	no	—
481	C₂²×C₈	—	43	2	no	—
482	C₂²×C₈	—	43	4	no	—
483	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
484	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
485	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
486	C₄⋊Q₈	—	43	2	no	—
487	C₄⋊Q₈	—	43	4	no	—
488	C₄⋊Q₈	—	43	2	no	—
489	C₄⋊Q₈	—	43	4	no	—
490	C₄⋊Q₈	—	43	1	no	—
491	C₄⋊Q₈	—	43	2	no	—
492	C₄⋊Q₈	—	43	1	no	—
493	C₄⋊Q₈	—	43	2	no	—
494	#125	—	43	4	no	—
495	#125	—	43	4	no	—
496	#125	—	43	4	no	—
497	#125	—	43	2	no	—
498	#125	—	43	2	no	—
499	#125	—	43	2	no	—
500	C₂²⋊Q₈	—	43	2	no	—
501	C₂²⋊Q₈	—	43	4	no	—
502	C₂²⋊Q₈	—	43	2	no	—
503	C₂²⋊Q₈	—	43	4	no	—
504	C₂²⋊Q₈	—	43	2	no	—
505	C₂²⋊Q₈	—	43	4	no	—
506	C₂²⋊Q₈	—	43	2	no	—
507	C₂²⋊Q₈	—	43	4	no	—
508	C₂²⋊Q₈	—	43	4	no	—
509	C₂²⋊Q₈	—	43	4	no	—
510	C₂²⋊Q₈	—	43	4	no	—
511	C₄×Q₈	—	43	2	no	—
512	C₄×Q₈	—	43	2	no	—
513	C₄×Q₈	—	43	4	no	—
514	C₄×Q₈	—	43	1	no	—
515	C₄×Q₈	—	43	2	no	—
516	C₄×Q₈	—	43	1	no	—
517	C₄×Q₈	—	43	2	no	—
518	C₄×Q₈	—	43	2	no	—
519	C₄×Q₈	—	43	4	no	—
520	C₄×Q₈	—	43	4	no	—
521	C₄×Q₈	—	43	2	no	—
522	C₄×Q₈	C₄×D₄₃	1	1	yes	characteristic
523	C₄×Q₈	C₄×D₄₃	1	1	yes	characteristic
524	C₄×Q₈	C₄×D₄₃	1	2	yes	—
525	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
526	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
527	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
528	C₄×D₄	—	43	2	no	—
529	C₄×D₄	—	43	4	no	—
530	C₄×D₄	—	43	2	no	—
531	C₄×D₄	—	43	4	no	—
532	C₄×D₄	—	43	1	no	—
533	C₄×D₄	—	43	2	no	—
534	C₄×D₄	—	43	1	no	—
535	C₄×D₄	—	43	2	no	—
536	#117	—	43	1	no	—
537	#117	—	43	2	no	—
538	#117	—	43	4	no	—
539	#117	—	43	2	no	—
540	C₂×C₄⋊C₄	—	43	2	no	—
541	C₂×C₄⋊C₄	—	43	4	no	—
542	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
543	C₂×C₄⋊C₄	C₄×D₄₃	1	2	yes	—
544	C₂×C₄²	—	43	2	no	—
545	C₂×C₄²	—	43	4	no	—
546	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
547	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
548	C₄⋊C₈	—	43	4	no	—
549	C₄⋊C₈	—	43	4	no	—
550	C₄⋊C₈	—	43	4	no	—
551	C₄⋊C₈	—	43	4	no	—
552	C₄⋊C₈	—	43	4	no	—
553	C₄⋊C₈	—	43	4	no	—
554	C₄⋊C₈	—	43	2	no	—
555	C₄⋊C₈	—	43	4	no	—
556	C₄⋊C₈	—	43	4	no	—
557	C₄⋊C₈	—	43	2	no	—
558	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
559	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
560	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
561	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
562	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
563	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
564	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
565	#97	—	43	4	no	—
566	#97	—	43	4	no	—
567	#97	—	43	2	no	—
568	#97	—	43	2	no	—
569	#97	—	43	4	no	—
570	#97	—	43	2	no	—
571	#97	C₂²×D₄₃	1	2	yes	—
572	#97	C₂²×D₄₃	1	2	yes	—
573	#97	C₂²×D₄₃	1	2	yes	—
574	#97	C₂²×D₄₃	1	2	yes	—
575	C₄×C₈	—	43	2	no	—
576	C₄×C₈	—	43	2	no	—
577	C₄×C₈	—	43	4	no	—
578	C₄×C₈	—	43	4	no	—
579	C₄×C₈	—	43	2	no	—
580	C₄×C₈	—	43	4	no	—
581	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
582	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
583	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
584	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
585	#41	—	43	4	no	—
586	#41	—	43	4	no	—
587	C₂×Q₈	—	4	2	no	—
588	C₂×Q₈	—	43	1	no	—
589	C₂×Q₈	—	43	2	no	—
590	C₂×Q₈	—	43	4	no	—
591	C₂×Q₈	—	43	4	no	—
592	C₂×Q₈	—	43	2	no	—
593	C₂×Q₈	—	172	4	no	—
594	C₂×Q₈	C₂×C₄×D₄₃	1	1	yes	characteristic
595	C₂×Q₈	C₂×C₄×D₄₃	1	1	yes	characteristic
596	C₂×Q₈	C₂×C₄×D₄₃	1	2	yes	—
597	C₂×D₄	—	43	2	no	—
598	C₂×D₄	—	43	1	no	—
599	C₂²×C₄	—	43	2	no	—
600	C₂²×C₄	—	43	2	no	—
601	C₂²×C₄	—	43	2	no	—
602	C₂²×C₄	—	43	4	no	—
603	C₂²×C₄	—	43	4	no	—
604	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
605	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
606	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
607	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
608	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
609	M₁₆	—	43	4	no	—
610	M₁₆	—	43	8	no	—
611	M₁₆	—	86	8	no	—
612	M₁₆	—	86	4	no	—
613	M₁₆	—	86	2	no	—
614	M₁₆	—	86	4	no	—
615	C₂×C₈	—	2	2	no	—
616	C₂×C₈	—	2	4	no	—
617	C₂×C₈	—	43	2	no	—
618	C₂×C₈	—	43	8	no	—
619	C₂×C₈	—	43	2	no	—
620	C₂×C₈	—	43	4	no	—
621	C₂×C₈	—	86	4	no	—
622	C₂×C₈	—	86	8	no	—
623	C₂×C₈	Q₈×D₄₃	1	4	yes	complemented
624	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
625	C₂×C₈	C₂³×D₄₃	1	2	yes	—
626	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
627	C₂×C₈	C₂³×D₄₃	1	2	yes	—
628	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
629	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
630	C₄⋊C₄	—	43	4	no	—
631	C₄⋊C₄	—	43	4	no	—
632	C₄⋊C₄	—	43	4	no	—
633	C₄⋊C₄	—	43	4	no	—
634	C₄⋊C₄	—	43	2	no	—
635	C₄⋊C₄	—	43	2	no	—
636	C₄⋊C₄	—	43	4	no	—
637	C₄⋊C₄	—	43	4	no	—
638	C₄⋊C₄	—	43	2	no	—
639	C₄⋊C₄	—	43	1	no	—
640	C₄⋊C₄	—	43	2	no	—
641	C₄⋊C₄	—	43	1	no	—
642	C₄⋊C₄	—	43	2	no	—
643	C₄⋊C₄	—	43	4	no	—
644	C₄⋊C₄	—	43	4	no	—
645	C₄⋊C₄	—	43	4	no	—
646	C₄⋊C₄	—	43	4	no	—
647	C₄⋊C₄	—	43	2	no	—
648	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
649	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
650	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
651	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
652	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
653	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
654	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
655	C₂²⋊C₄	—	43	2	no	—
656	C₂²⋊C₄	—	43	4	no	—
657	C₂²⋊C₄	—	43	2	no	—
658	C₂²⋊C₄	—	43	4	no	—
659	C₂²⋊C₄	—	43	2	no	—
660	C₂²⋊C₄	—	43	4	no	—
661	C₄²	—	43	2	no	—
662	C₄²	—	43	4	no	—
663	C₄²	—	43	4	no	—
664	C₄²	—	43	2	no	—
665	C₄²	—	43	2	no	—
666	C₄²	—	43	4	no	—
667	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
668	C₄²	C₂×C₄×D₄₃	1	2	yes	—
669	C₄²	C₂×C₄×D₄₃	1	2	yes	—
670	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
671	C₄²	C₂³×D₄₃	1	1	yes	characteristic
672	C₄²	C₂³×D₄₃	1	2	yes	—
673	C₄²	C₂³×D₄₃	1	1	yes	characteristic
674	C₄²	C₂³×D₄₃	1	2	yes	—
675	C₂³	—	43	2	no	—
676	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
677	Q₈	—	2	2	no	—
678	Q₈	—	2	2	no	—
679	Q₈	—	4	2	no	—
680	Q₈	—	43	4	no	—
681	Q₈	—	86	4	no	—
682	Q₈	—	172	4	no	—
683	Q₈	—	172	4	no	—
684	Q₈	—	172	2	no	—
685	D₄	—	43	8	no	—
686	D₄	—	43	4	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	4	2	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	2	no	—
691	C₂×C₄	—	43	2	no	—
692	C₂×C₄	—	43	4	no	—
693	C₂×C₄	—	43	4	no	—
694	C₂×C₄	—	43	2	no	—
695	C₂×C₄	—	43	4	no	—
696	C₂×C₄	—	43	4	no	—
697	C₂×C₄	—	43	2	no	—
698	C₂×C₄	—	86	4	no	—
699	C₂×C₄	—	172	4	no	—
700	C₂×C₄	—	172	2	no	—
701	C₂×C₄	—	172	4	no	—
702	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
703	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
704	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
705	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
706	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
707	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
708	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
709	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
710	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
711	C₂×C₄	C₂×Q₈×D₄₃	1	2	yes	—
712	C₂×C₄	#41×D₄₃	1	2	yes	—
713	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
714	C₈	—	2	1	no	—
715	C₈	—	2	2	no	—
716	C₈	—	2	2	no	—
717	C₈	—	2	1	no	—
718	C₈	—	43	4	no	—
719	C₈	—	86	2	no	—
720	C₈	—	86	4	no	—
721	C₈	C₂×Q₈×D₄₃	1	2	yes	—
722	C₈	C₂×Q₈×D₄₃	1	2	yes	—
723	C₂²	—	2	1	no	—
724	C₂²	—	2	1	no	—
725	C₂²	—	43	4	no	—
726	C₂²	—	86	2	no	—
727	C₂²	—	86	2	no	—
728	C₂²	C₄×Q₈×D₄₃	1	2	yes	—
729	C₂²	C₂³×C₄×D₄₃	1	1	yes	characteristic
730	C₄	—	2	1	no	—
731	C₄	—	2	2	no	—
732	C₄	—	2	2	no	—
733	C₄	—	2	1	no	—
734	C₄	—	2	2	no	—
735	C₄	—	2	2	no	—
736	C₄	—	2	1	no	—
737	C₄	—	43	4	no	—
738	C₄	—	86	2	no	—
739	C₄	—	86	4	no	—
740	C₄	—	86	4	no	—
741	C₄	—	86	2	no	—
742	C₄	C₄×Q₈×D₄₃	1	2	yes	—
743	C₄	#14583665	1	2	yes	—
744	C₄	C₂²×Q₈×D₄₃	1	1	yes	characteristic
745	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
746	C₂	—	2	2	no	—
747	C₂	—	86	4	no	—
748	C₂	C₂×C₄×Q₈×D₄₃	1	1	yes	characteristic
749	C₂	C₂×#14583665	1	1	yes	characteristic
750	C₂	#19149306	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁴×C₄
Fitting	C₂×C₄₃×#446	C₂
prime radical	C₂×#10621898	C₂³
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	C₂×#446	D₄₃
hypocenter	C₄₃	#60195
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#446

Complements

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

N	H ≅ G/N	type
2. Q₈×#10621877	C₂	semidirect
3. #19143547	C₂	semidirect
4. #19143543	C₂	semidirect
5. #19143540	C₂	semidirect
6. #19143538	C₂	semidirect
7. #19143538	C₂	semidirect
8. #19143535	C₂	semidirect
9. #19143531	C₂	semidirect
10. #19143529	C₂	semidirect
11. #19143526	C₂	semidirect
12. #446×D₄₃	C₂	semidirect
17. C₂×C₄₃×#446	C₂	semidirect
96. #13063331	Q₈	semidirect
235. C₂×C₈×C₄₃	C₂×Q₈	semidirect
289. #10621877	C₂×Q₈	semidirect
295. #10621872	C₂×Q₈	semidirect
298. C₈×D₄₃	C₂×Q₈	semidirect
383. C₂×#446	D₄₃	semidirect
467. C₄₃	#60195	semidirect
623. C₂×C₈	Q₈×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
Q₈×#10621898	2
Q₈×#10621877	2
#19143547	2
#19143543	2
#19143540	2
#19143538	2
#19143535	2
#19143531	2
#19143529	2
#19143526	2
#446×D₄₃	2
#19143160	2
#19143020	2
C₄×#13063331	2
C₂×C₄₃×#446	2
#60195	43