Subgroups — #344×Dic₄₃ #25001804

Order 11008.

906 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×Dic₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆×Dic₄₃	C₂	1	1	yes	maximal, characteristic
3	#117×Dic₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#14582671	C₂	1	1	yes	maximal, characteristic
5	C₂×#14582670	C₂	1	1	yes	maximal, characteristic
6	C₂×#14582669	C₂	1	1	yes	maximal, characteristic
7	C₂×C₄₃×#344	C₂	1	1	yes	maximal, characteristic
8	C₂²×#10621877	C₂²	1	1	yes	characteristic
9	C₂²×#10621877	C₂²	1	1	yes	characteristic
10	C₂×#13063284	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
12	M₁₆×Dic₄₃	—	2	2	no	—
13	M₁₆×Dic₄₃	—	2	1	no	—
14	M₁₆×Dic₄₃	—	2	1	no	—
15	M₁₆×Dic₄₃	—	2	1	no	—
16	M₁₆×Dic₄₃	—	2	1	no	—
17	M₁₆×Dic₄₃	C₄	1	4	yes	complemented
18	C₂×#13063235	—	2	1	no	—
19	C₂×#13063235	C₄	1	2	yes	complemented
20	C₂×C₈×Dic₄₃	—	2	1	no	—
21	C₂×C₈×Dic₄₃	C₄	1	2	yes	complemented
22	C₄⋊C₄×Dic₄₃	—	2	2	no	—
23	C₂²⋊C₄×Dic₄₃	C₄	1	4	yes	—
24	#14582745	—	2	1	no	—
25	C₄²×Dic₄₃	—	2	1	no	—
26	#14582671	C₄	1	4	yes	complemented
27	#14582670	C₄	1	4	yes	complemented
28	#14582669	C₄	1	4	yes	complemented
29	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
31	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
32	C₄₃×#344	C₄	1	4	yes	complemented
33	C₂³×Dic₄₃	C₂×C₄	1	2	yes	—
34	C₂×#10621877	—	2	1	no	—
35	C₂×#10621877	—	2	1	no	—
36	C₂×#10621877	—	2	1	no	—
37	C₂×#10621877	—	2	1	no	—
38	C₂×#10621877	—	2	1	no	—
39	C₂×#10621877	—	2	1	no	—
40	C₂×#10621877	—	2	1	no	—
41	C₂×#10621877	C₂×C₄	1	2	yes	—
42	C₂×#10621877	C₂×C₄	1	2	yes	—
43	C₂×#10621877	C₂×C₄	1	2	yes	—
44	C₂×#10621877	C₂×C₄	1	2	yes	—
45	C₂×#10621877	C₂×C₄	1	2	yes	—
46	C₂²×C₄₃⋊C₈	—	2	1	no	—
47	C₂²×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
48	#13063284	—	2	1	no	—
49	#13063284	—	2	1	no	—
50	#13063284	C₂×C₄	1	2	yes	—
51	#13063284	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊Dic₄₃	—	2	1	no	—
53	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	2	yes	—
54	C₂×C₄×Dic₄₃	—	2	1	no	—
55	C₂×C₄×Dic₄₃	—	2	4	no	—
56	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
59	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
60	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
61	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
62	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
63	C₂×C₄×Dic₄₃	D₄	1	2	yes	—
64	C₂×C₄×Dic₄₃	Q₈	1	2	yes	—
65	#13063235	—	2	4	no	—
66	#13063235	—	2	2	no	—
67	#13063235	—	2	2	no	—
68	C₈×Dic₄₃	—	2	4	no	—
69	C₈×Dic₄₃	—	2	2	no	—
70	C₈×Dic₄₃	—	2	2	no	—
71	C₄₃⋊#95	—	2	4	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	C₂×C₄	1	2	yes	—
83	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
84	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
85	C₂²×C₈×C₄₃	—	2	1	no	—
86	C₂²×C₈×C₄₃	C₂×C₄	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	C₂×C₄	1	2	yes	—
91	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
93	C₂×C₄²×C₄₃	—	2	1	no	—
94	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₃	—	2	2	no	—
96	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
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×Q₈	1	1	yes	characteristic
106	C₂²×C₄×C₄₃	#41	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×Dic₄₃	—	2	2	no	—
111	C₂²×Dic₄₃	—	4	4	no	—
112	C₂²×Dic₄₃	C₄²	1	2	yes	—
113	C₂²×Dic₄₃	C₄²	1	2	yes	—
114	C₂²×Dic₄₃	C₂²⋊C₄	1	2	yes	—
115	C₂²×Dic₄₃	C₂²⋊C₄	1	2	yes	—
116	C₂²×Dic₄₃	C₄⋊C₄	1	2	yes	—
117	C₂²×Dic₄₃	C₄⋊C₄	1	2	yes	—
118	M₁₆×C₄₃	—	2	2	no	—
119	M₁₆×C₄₃	—	2	2	no	—
120	M₁₆×C₄₃	—	2	2	no	—
121	M₁₆×C₄₃	—	2	2	no	—
122	M₁₆×C₄₃	—	2	2	no	—
123	M₁₆×C₄₃	—	2	2	no	—
124	M₁₆×C₄₃	—	2	2	no	—
125	M₁₆×C₄₃	C₄²	1	4	yes	complemented
126	C₂×C₈×C₄₃	—	2	2	no	—
127	C₂×C₈×C₄₃	—	2	2	no	—
128	C₂×C₈×C₄₃	—	2	2	no	—
129	C₂×C₈×C₄₃	—	2	2	no	—
130	C₂×C₈×C₄₃	—	2	2	no	—
131	C₂×C₈×C₄₃	C₄²	1	4	yes	complemented
132	C₄⋊C₄×C₄₃	—	2	2	no	—
133	C₄⋊C₄×C₄₃	—	2	2	no	—
134	C₂²⋊C₄×C₄₃	—	2	2	no	—
135	C₂²⋊C₄×C₄₃	C₄²	1	4	yes	—
136	C₄²×C₄₃	—	2	2	no	—
137	C₄²×C₄₃	—	2	2	no	—
138	C₂²⋊Dic₄₃	—	2	2	no	—
139	C₂²⋊Dic₄₃	C₄²	1	4	yes	—
140	C₄⋊Dic₄₃	—	2	2	no	—
141	C₄⋊Dic₄₃	—	2	2	no	—
142	C₄×Dic₄₃	—	2	2	no	—
143	C₄×Dic₄₃	—	2	2	no	—
144	C₄×Dic₄₃	—	4	8	no	—
145	C₄×Dic₄₃	C₂²⋊C₄	1	2	yes	—
146	C₄×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
147	C₄×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
148	C₄×Dic₄₃	C₂²⋊C₄	1	2	yes	—
149	C₄×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
150	C₄×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
151	C₄×Dic₄₃	C₄⋊C₄	1	2	yes	—
152	C₄×Dic₄₃	C₄⋊C₄	1	2	yes	—
153	C₄×Dic₄₃	C₄⋊C₄	1	2	yes	—
154	C₄×Dic₄₃	C₄⋊C₄	1	2	yes	—
155	#10621877	—	2	2	no	—
156	#10621877	—	2	2	no	—
157	#10621877	—	2	2	no	—
158	#10621877	—	2	2	no	—
159	#10621877	—	2	2	no	—
160	#10621877	—	2	2	no	—
161	#10621877	—	2	2	no	—
162	#10621877	C₄²	1	4	yes	complemented
163	C₂×C₄₃⋊C₈	—	2	2	no	—
164	C₂×C₄₃⋊C₈	—	2	2	no	—
165	C₂×C₄₃⋊C₈	—	2	2	no	—
166	C₂×C₄₃⋊C₈	—	2	2	no	—
167	C₂×C₄₃⋊C₈	—	2	2	no	—
168	C₂×C₄₃⋊C₈	C₄²	1	4	yes	complemented
169	C₂³×C₄₃	—	4	2	no	—
170	C₂³×C₄₃	C₂×C₄²	1	1	yes	characteristic
171	C₂³×C₄₃	C₂×C₄²	1	1	yes	characteristic
172	C₂³×C₄₃	C₂×C₄²	1	1	yes	characteristic
173	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
174	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂³×C₄₃	#117	1	1	yes	characteristic
176	C₂³×C₄₃	#117	1	1	yes	characteristic
177	C₂×C₄×C₄₃	—	2	4	no	—
178	C₂×C₄×C₄₃	—	4	4	no	—
179	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
180	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
181	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
182	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
183	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
188	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
189	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
190	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
191	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
192	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
195	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
197	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
198	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
199	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
200	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
201	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
202	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
203	C₂×C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
204	C₂×C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
205	C₂×C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
206	C₂×C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
207	C₂×Dic₄₃	—	2	4	no	—
208	C₂×Dic₄₃	—	2	4	no	—
209	C₂×Dic₄₃	—	2	4	no	—
210	C₂×Dic₄₃	—	2	4	no	—
211	C₂×Dic₄₃	—	4	2	no	—
212	C₂×Dic₄₃	—	4	2	no	—
213	C₂×Dic₄₃	—	4	2	no	—
214	C₂×Dic₄₃	—	4	4	no	—
215	C₂×Dic₄₃	#95	1	2	yes	—
216	C₂×Dic₄₃	#95	1	2	yes	—
217	C₂×Dic₄₃	#95	1	2	yes	—
218	C₂×Dic₄₃	#95	1	2	yes	—
219	C₈×C₄₃	—	2	4	no	—
220	C₈×C₄₃	—	2	4	no	—
221	C₄₃⋊C₈	—	2	4	no	—
222	C₄₃⋊C₈	—	2	4	no	—
223	C₄×#344	—	43	1	no	maximal, Sylow
224	C₂²×C₄₃	—	2	2	no	—
225	C₂²×C₄₃	—	2	2	no	—
226	C₂²×C₄₃	—	2	2	no	—
227	C₂²×C₄₃	—	4	1	no	—
228	C₂²×C₄₃	—	4	1	no	—
229	C₂²×C₄₃	—	4	1	no	—
230	C₂²×C₄₃	—	4	1	no	—
231	C₂²×C₄₃	C₄³	1	1	yes	characteristic
232	C₂²×C₄₃	C₂×#95	1	1	yes	characteristic
233	C₂²×C₄₃	#376	1	1	yes	characteristic
234	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
235	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
236	C₂²×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
237	C₂²×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
238	C₄×C₄₃	—	4	4	no	—
239	C₄×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
240	C₄×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
241	C₄×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
242	C₄×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
243	C₄×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
244	C₄×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
245	C₄×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
246	C₄×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
247	Dic₄₃	—	2	2	no	—
248	Dic₄₃	—	2	2	no	—
249	Dic₄₃	—	2	2	no	—
250	Dic₄₃	—	4	4	no	—
251	Dic₄₃	#344	1	4	yes	direct product factor
252	C₂×C₄×M₁₆	—	43	1	no	—
253	C₂×C₄×M₁₆	—	43	1	no	—
254	C₄×#117	—	43	1	no	—
255	C₂×#344	—	43	1	no	—
256	C₂×#344	—	43	1	no	—
257	C₂×#344	—	43	1	no	—
258	C₂×#344	D₄₃	1	1	yes	characteristic
259	C₂×C₄₃	—	2	1	no	—
260	C₂×C₄₃	—	2	1	no	—
261	C₂×C₄₃	—	2	1	no	—
262	C₂×C₄₃	—	2	1	no	—
263	C₂×C₄₃	—	2	1	no	—
264	C₂×C₄₃	—	2	1	no	—
265	C₂×C₄₃	C₄×#95	1	1	yes	characteristic
266	C₂×C₄₃	C₂×#344	1	2	yes	—
267	C₂²×M₁₆	—	43	1	no	—
268	C₂²×M₁₆	—	43	1	no	—
269	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
270	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
271	C₂×#117	—	43	1	no	—
272	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
273	C₂²×C₄²	—	43	1	no	—
274	C₄×M₁₆	—	43	4	no	—
275	C₄×M₁₆	—	86	1	no	—
276	C₄×M₁₆	—	86	1	no	—
277	C₄×M₁₆	—	86	1	no	—
278	C₄×M₁₆	—	86	1	no	—
279	C₄×M₁₆	—	86	2	no	—
280	C₂×#97	—	43	2	no	—
281	C₂×#97	—	86	1	no	—
282	C₂×C₄×C₈	—	43	2	no	—
283	C₂×C₄×C₈	—	86	1	no	—
284	C₄×C₄⋊C₄	—	86	2	no	—
285	C₄×C₂²⋊C₄	—	43	4	no	—
286	#376	—	86	1	no	—
287	C₄³	—	86	1	no	—
288	#344	—	43	4	no	—
289	#344	—	43	4	no	—
290	#344	—	43	4	no	—
291	#344	Dic₄₃	1	4	yes	direct product factor
292	C₄₃	C₄×#344	1	1	yes	characteristic, complemented, Sylow
293	C₂³×C₄	—	43	2	no	—
294	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
295	C₂×M₁₆	—	2	1	no	—
296	C₂×M₁₆	—	2	1	no	—
297	C₂×M₁₆	—	2	1	no	—
298	C₂×M₁₆	—	2	1	no	—
299	C₂×M₁₆	—	2	1	no	—
300	C₂×M₁₆	—	2	1	no	—
301	C₂×M₁₆	—	2	1	no	—
302	C₂×M₁₆	—	43	2	no	—
303	C₂×M₁₆	—	43	2	no	—
304	C₂×M₁₆	—	43	2	no	—
305	C₂×M₁₆	—	43	2	no	—
306	C₂×M₁₆	—	43	2	no	—
307	C₂×M₁₆	—	86	1	no	—
308	C₂×M₁₆	—	86	1	no	—
309	C₂×M₁₆	—	86	1	no	—
310	C₂×M₁₆	—	86	1	no	—
311	C₂×M₁₆	—	86	1	no	—
312	C₂×M₁₆	—	86	1	no	—
313	C₂×M₁₆	—	86	1	no	—
314	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
315	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
316	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
317	C₂×M₁₆	C₂×Dic₄₃	1	2	yes	—
318	C₂×M₁₆	C₂×Dic₄₃	1	2	yes	—
319	C₂²×C₈	—	2	1	no	—
320	C₂²×C₈	—	43	2	no	—
321	C₂²×C₈	—	86	1	no	—
322	C₂²×C₈	C₄×D₄₃	1	2	yes	—
323	#117	—	2	1	no	—
324	#117	—	2	1	no	—
325	#117	—	43	2	no	—
326	#117	—	43	2	no	—
327	#117	—	86	1	no	—
328	#117	—	86	1	no	—
329	#117	C₄×D₄₃	1	2	yes	—
330	#117	C₂×Dic₄₃	1	2	yes	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	—	86	1	no	—
333	C₂×C₂²⋊C₄	—	43	2	no	—
334	C₂×C₂²⋊C₄	C₄×D₄₃	1	2	yes	—
335	C₂×C₄²	—	2	1	no	—
336	C₂×C₄²	—	43	1	no	—
337	C₂×C₄²	—	43	1	no	—
338	C₂×C₄²	—	43	2	no	—
339	C₂×C₄²	—	43	1	no	—
340	C₂×C₄²	—	43	1	no	—
341	C₂×C₄²	—	43	2	no	—
342	C₂×C₄²	—	43	1	no	—
343	C₂×C₄²	—	43	1	no	—
344	C₂×C₄²	—	43	2	no	—
345	C₂×C₄²	—	86	1	no	—
346	C₂×C₄²	—	86	4	no	—
347	#97	—	86	2	no	—
348	#97	—	86	2	no	—
349	#97	—	86	4	no	—
350	C₄×C₈	—	86	2	no	—
351	C₄×C₈	—	86	2	no	—
352	C₄×C₈	—	86	4	no	—
353	#95	—	86	4	no	—
354	C₂⁴	C₂×C₄×D₄₃	1	1	yes	characteristic
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	43	2	no	—
357	C₂²×C₄	—	43	2	no	—
358	C₂²×C₄	—	43	2	no	—
359	C₂²×C₄	—	43	2	no	—
360	C₂²×C₄	—	43	2	no	—
361	C₂²×C₄	—	43	2	no	—
362	C₂²×C₄	—	86	2	no	—
363	C₂²×C₄	—	172	4	no	—
364	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
365	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
366	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
367	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
368	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
369	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
370	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
371	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
372	C₂²×C₄	#10621900	1	1	yes	characteristic
373	C₂²×C₄	#10621900	1	1	yes	characteristic
374	C₂²×C₄	#10621900	1	1	yes	characteristic
375	C₂²×C₄	Q₈×D₄₃	1	1	yes	characteristic
376	C₂²×C₄	#10621902	1	1	yes	characteristic
377	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
378	M₁₆	—	2	2	no	—
379	M₁₆	—	2	2	no	—
380	M₁₆	—	2	2	no	—
381	M₁₆	—	2	2	no	—
382	M₁₆	—	2	2	no	—
383	M₁₆	—	2	2	no	—
384	M₁₆	—	2	2	no	—
385	M₁₆	—	43	4	no	—
386	M₁₆	—	86	2	no	—
387	M₁₆	—	86	2	no	—
388	M₁₆	—	86	2	no	—
389	M₁₆	—	86	2	no	—
390	M₁₆	—	86	2	no	—
391	M₁₆	—	86	2	no	—
392	M₁₆	—	86	2	no	—
393	M₁₆	C₄×Dic₄₃	1	4	yes	complemented
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	43	4	no	—
400	C₂×C₈	—	86	2	no	—
401	C₂×C₈	—	86	2	no	—
402	C₂×C₈	—	86	2	no	—
403	C₂×C₈	—	86	2	no	—
404	C₂×C₈	—	86	2	no	—
405	C₂×C₈	C₄×Dic₄₃	1	4	yes	complemented
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	86	2	no	—
409	C₄⋊C₄	—	86	2	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₂²⋊C₄	—	43	4	no	—
412	C₂²⋊C₄	—	86	2	no	—
413	C₂²⋊C₄	C₄×Dic₄₃	1	4	yes	—
414	C₄²	—	2	2	no	—
415	C₄²	—	2	2	no	—
416	C₄²	—	43	2	no	—
417	C₄²	—	43	2	no	—
418	C₄²	—	43	1	no	—
419	C₄²	—	43	1	no	—
420	C₄²	—	43	1	no	—
421	C₄²	—	43	1	no	—
422	C₄²	—	43	2	no	—
423	C₄²	—	43	2	no	—
424	C₄²	—	43	2	no	—
425	C₄²	—	43	2	no	—
426	C₄²	—	86	2	no	—
427	C₄²	—	86	2	no	—
428	C₄²	—	172	8	no	—
429	C₂³	—	4	2	no	—
430	C₂³	C₄²×D₄₃	1	1	yes	characteristic
431	C₂³	C₄²×D₄₃	1	1	yes	characteristic
432	C₂³	C₂×C₄×Dic₄₃	1	1	yes	characteristic
433	C₂³	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
434	C₂³	C₄⋊C₄×D₄₃	1	1	yes	characteristic
435	C₂³	#13063281	1	1	yes	characteristic
436	C₂³	#13063283	1	1	yes	characteristic
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	4	4	no	—
439	C₂×C₄	—	43	2	no	—
440	C₂×C₄	—	43	2	no	—
441	C₂×C₄	—	43	2	no	—
442	C₂×C₄	—	43	2	no	—
443	C₂×C₄	—	86	4	no	—
444	C₂×C₄	—	86	4	no	—
445	C₂×C₄	—	86	4	no	—
446	C₂×C₄	—	86	4	no	—
447	C₂×C₄	—	172	2	no	—
448	C₂×C₄	—	172	2	no	—
449	C₂×C₄	—	172	2	no	—
450	C₂×C₄	—	172	4	no	—
451	C₂×C₄	C₄²×D₄₃	1	1	yes	characteristic
452	C₂×C₄	C₄²×D₄₃	1	1	yes	characteristic
453	C₂×C₄	C₂×C₄×Dic₄₃	1	1	yes	characteristic
454	C₂×C₄	C₂×C₄×Dic₄₃	1	1	yes	characteristic
455	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
456	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
457	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
458	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
459	C₂×C₄	#13063281	1	1	yes	characteristic
460	C₂×C₄	#13063281	1	1	yes	characteristic
461	C₂×C₄	#13063283	1	1	yes	characteristic
462	C₂×C₄	#13063283	1	1	yes	characteristic
463	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
464	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
465	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
466	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
467	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
468	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
469	C₂×C₄	#13063287	1	1	yes	characteristic
470	C₂×C₄	#13063287	1	1	yes	characteristic
471	C₂×C₄	#13063287	1	1	yes	characteristic
472	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
473	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
474	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
475	C₂×C₄	#13063290	1	1	yes	characteristic
476	C₂×C₄	#13063290	1	1	yes	characteristic
477	C₂×C₄	#13063290	1	1	yes	characteristic
478	C₂×C₄	Q₈×Dic₄₃	1	1	yes	characteristic
479	C₈	—	2	4	no	—
480	C₈	—	2	4	no	—
481	C₈	—	86	4	no	—
482	C₈	—	86	4	no	—
483	C₂²	—	2	2	no	—
484	C₂²	—	2	2	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	4	1	no	—
487	C₂²	—	4	1	no	—
488	C₂²	—	4	1	no	—
489	C₂²	—	4	1	no	—
490	C₂²	C₄²×Dic₄₃	1	1	yes	characteristic
491	C₂²	#95×D₄₃	1	1	yes	characteristic
492	C₂²	#14582744	1	1	yes	characteristic
493	C₂²	#14582746	1	1	yes	characteristic
494	C₂²	C₂²⋊C₄×Dic₄₃	1	1	yes	characteristic
495	C₂²	#14582750	1	1	yes	characteristic
496	C₂²	C₄⋊C₄×Dic₄₃	1	1	yes	characteristic
497	C₄	—	4	4	no	—
498	C₄	—	43	4	no	—
499	C₄	—	86	2	no	—
500	C₄	—	86	2	no	—
501	C₄	—	86	2	no	—
502	C₄	—	172	4	no	—
503	C₄	#14582746	1	1	yes	characteristic
504	C₄	#14582746	1	1	yes	characteristic
505	C₄	C₂²⋊C₄×Dic₄₃	1	1	yes	characteristic
506	C₄	C₂²⋊C₄×Dic₄₃	1	1	yes	characteristic
507	C₄	#14582750	1	1	yes	characteristic
508	C₄	#14582750	1	1	yes	characteristic
509	C₄	C₄⋊C₄×Dic₄₃	1	1	yes	characteristic
510	C₄	C₄⋊C₄×Dic₄₃	1	1	yes	characteristic
511	C₂	—	2	1	no	—
512	C₂	—	2	1	no	—
513	C₂	—	2	1	no	—
514	C₂	—	2	1	no	—
515	C₂	—	2	1	no	—
516	C₂	—	2	1	no	—
517	C₂	#95×Dic₄₃	1	1	yes	characteristic
518	C₂	#344×D₄₃	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₄₃
commutator	C₂²×C₄₃	C₄³
Frattini	C₂³×C₄	C₂²×D₄₃
Fitting	C₂×C₄₃×#344	C₂
socle	C₂²×C₄₃	C₂×#95
prime radical	C₂⁴×C₄₃	C₂²×C₄
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	C₂×#344	D₄₃
hypocenter	C₄₃	C₄×#344
LCS	G ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#344

Complements

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

N	H ≅ G/N	type
17. M₁₆×Dic₄₃	C₄	semidirect
19. C₂×#13063235	C₄	semidirect
21. C₂×C₈×Dic₄₃	C₄	semidirect
26. #14582671	C₄	semidirect
27. #14582670	C₄	semidirect
28. #14582669	C₄	semidirect
32. C₄₃×#344	C₄	semidirect
125. M₁₆×C₄₃	C₄²	semidirect
131. C₂×C₈×C₄₃	C₄²	semidirect
162. #10621877	C₄²	semidirect
168. C₂×C₄₃⋊C₈	C₄²	semidirect
251. Dic₄₃	#344	direct (N × H)
291. #344	Dic₄₃	direct (N × H)
292. C₄₃	C₄×#344	semidirect
393. M₁₆	C₄×Dic₄₃	semidirect
405. C₂×C₈	C₄×Dic₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₁₆×Dic₄₃	2
#117×Dic₄₃	2
C₂×#14582671	2
C₂×#14582670	2
C₂×#14582669	2
C₂×C₄₃×#344	2
C₄×#344	43

Subgroups — #344×Dic43 #25001804

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #344×Dic₄₃ #25001804