Subgroups — #41×C₂²⋊Dic₄₃ #25255802

Order 11008.

5646 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×Dic₄₃	C₂	1	2	yes	maximal, complemented
2	#19137436	C₂	1	2	yes	maximal, complemented
3	Q₈×C₂²⋊Dic₄₃	C₂	1	2	yes	maximal, complemented
4	#19137425	C₂	1	6	yes	maximal, complemented
5	D₄×C₂²⋊Dic₄₃	C₂	1	6	yes	maximal, complemented
6	#19137086	C₂	1	6	yes	maximal, complemented
7	#19136978	C₂	1	3	yes	maximal, complemented
8	C₂×C₄×C₂²⋊Dic₄₃	C₂	1	3	yes	maximal, complemented
9	C₂³×#41×C₄₃	C₂	1	1	yes	maximal, characteristic
10	#41×Dic₄₃	—	2	16	no	—
11	C₂×Q₈×Dic₄₃	C₂²	1	4	yes	complemented
12	C₂×D₄×Dic₄₃	C₂²	1	12	yes	complemented
13	C₂×#13063284	C₂²	1	6	yes	complemented
14	C₂²×C₂²⋊Dic₄₃	C₂²	1	6	yes	—
15	C₂²×C₄×Dic₄₃	C₂²	1	6	yes	complemented
16	#14582806	C₂²	1	12	yes	complemented
17	#14582802	C₂²	1	12	yes	complemented
18	#14582779	C₂²	1	24	yes	complemented
19	#14582762	C₂²	1	6	yes	complemented
20	#14582759	C₂²	1	6	yes	—
21	#14582759	C₂²	1	6	yes	complemented
22	#14582755	C₂²	1	6	yes	—
23	C₄×C₂²⋊Dic₄₃	C₂²	1	6	yes	—
24	C₄×C₂²⋊Dic₄₃	C₂²	1	1	yes	characteristic
25	C₄×C₂²⋊Dic₄₃	C₂²	1	3	yes	—
26	C₄×C₂²⋊Dic₄₃	C₂²	1	6	yes	complemented
27	C₄×C₂²⋊Dic₄₃	C₂²	1	6	yes	complemented
28	C₄×C₂²⋊Dic₄₃	C₂²	1	6	yes	complemented
29	C₂×C₄₃⋊#95	C₂²	1	6	yes	complemented
30	C₂²×#41×C₄₃	—	2	16	no	—
31	C₂²×#41×C₄₃	C₄	1	16	yes	complemented
32	C₂²×#41×C₄₃	C₂²	1	3	yes	—
33	C₂²×#41×C₄₃	C₂²	1	3	yes	—
34	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
35	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
36	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
37	C₂³×D₄×C₄₃	C₂²	1	3	yes	—
38	C₂⁴×C₄×C₄₃	C₂²	1	3	yes	—
39	C₂³×Dic₄₃	C₂³	1	12	yes	—
40	Q₈×Dic₄₃	—	2	16	no	—
41	D₄×Dic₄₃	—	2	48	no	—
42	#13063284	—	2	24	no	—
43	C₂×C₄⋊Dic₄₃	C₂³	1	12	yes	—
44	C₂×C₂²⋊Dic₄₃	—	2	24	no	—
45	C₂×C₂²⋊Dic₄₃	C₂³	1	12	yes	—
46	C₂×C₂²⋊Dic₄₃	C₂³	1	6	yes	—
47	C₂×C₂²⋊Dic₄₃	C₂³	1	12	yes	—
48	C₂×C₂²⋊Dic₄₃	C₂³	1	12	yes	—
49	C₂×C₂²⋊Dic₄₃	C₂³	1	2	yes	—
50	C₂×C₄×Dic₄₃	—	2	24	no	—
51	C₂×C₄×Dic₄₃	C₂³	1	12	yes	—
52	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
53	C₂×C₄×Dic₄₃	C₂³	1	6	yes	—
54	C₄₃⋊#95	C₂³	1	12	yes	—
55	C₄₃⋊#95	C₂³	1	12	yes	—
56	C₄₃⋊#95	C₂³	1	2	yes	—
57	C₄₃⋊#95	C₂³	1	6	yes	—
58	C₂⁵×C₄₃	C₂³	1	3	yes	—
59	C₂×#41×C₄₃	—	2	128	no	—
60	C₂×#41×C₄₃	—	2	8	no	—
61	C₂×#41×C₄₃	—	2	24	no	—
62	C₂×#41×C₄₃	—	2	24	no	—
63	C₂×#41×C₄₃	C₂×C₄	1	8	yes	—
64	C₂×#41×C₄₃	C₂×C₄	1	8	yes	complemented
65	C₂×#41×C₄₃	C₂×C₄	1	24	yes	complemented
66	C₂×#41×C₄₃	C₂×C₄	1	24	yes	complemented
67	C₂×#41×C₄₃	D₄	1	16	yes	—
68	C₂²×Q₈×C₄₃	—	2	8	no	—
69	C₂²×Q₈×C₄₃	C₂×C₄	1	8	yes	complemented
70	C₂²×Q₈×C₄₃	C₂³	1	3	yes	—
71	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₄₃	—	2	24	no	—
73	C₂²×D₄×C₄₃	C₂×C₄	1	24	yes	complemented
74	C₂²×D₄×C₄₃	C₂³	1	3	yes	—
75	C₂²×D₄×C₄₃	C₂³	1	6	yes	—
76	C₂²×D₄×C₄₃	C₂³	1	3	yes	—
77	C₂³×C₄×C₄₃	—	2	24	no	—
78	C₂³×C₄×C₄₃	C₂×C₄	1	24	yes	complemented
79	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₄₃	C₂³	1	3	yes	—
81	C₂³×C₄×C₄₃	C₂³	1	3	yes	—
82	C₂³×C₄×C₄₃	C₂³	1	3	yes	—
83	C₂³×C₄×C₄₃	C₂³	1	3	yes	—
84	C₂³×C₄×C₄₃	C₂³	1	3	yes	—
85	C₂⁴×C₄₃	—	2	12	no	—
86	C₂⁴×C₄₃	—	2	12	no	—
87	C₂⁴×C₄₃	—	4	6	no	—
88	C₂⁴×C₄₃	C₂²×C₄	1	12	yes	—
89	C₂⁴×C₄₃	C₂⁴	1	3	yes	—
90	C₂⁴×C₄₃	C₂⁴	1	3	yes	—
91	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
92	#41×C₄₃	—	2	32	no	—
93	#41×C₄₃	—	2	96	no	—
94	#41×C₄₃	—	2	96	no	—
95	#41×C₄₃	C₂²⋊C₄	1	64	yes	complemented
96	C₂×Q₈×C₄₃	—	2	32	no	—
97	C₂×Q₈×C₄₃	—	2	12	no	—
98	C₂×Q₈×C₄₃	C₂²×C₄	1	12	yes	—
99	C₂×Q₈×C₄₃	C₂²×C₄	1	4	yes	—
100	C₂×Q₈×C₄₃	C₂×D₄	1	8	yes	—
101	C₂×D₄×C₄₃	—	2	96	no	—
102	C₂×D₄×C₄₃	—	2	12	no	—
103	C₂×D₄×C₄₃	—	2	24	no	—
104	C₂×D₄×C₄₃	C₂²×C₄	1	12	yes	—
105	C₂×D₄×C₄₃	C₂²×C₄	1	24	yes	—
106	C₂×D₄×C₄₃	C₂²×C₄	1	12	yes	—
107	C₂×D₄×C₄₃	C₂×D₄	1	24	yes	—
108	C₂²×C₄×C₄₃	—	2	96	no	—
109	C₂²×C₄×C₄₃	—	2	4	no	—
110	C₂²×C₄×C₄₃	—	2	12	no	—
111	C₂²×C₄×C₄₃	—	2	12	no	—
112	C₂²×C₄×C₄₃	—	2	12	no	—
113	C₂²×C₄×C₄₃	—	2	12	no	—
114	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
115	C₂²×C₄×C₄₃	C₂²×C₄	1	12	yes	—
116	C₂²×C₄×C₄₃	C₂²×C₄	1	12	yes	—
117	C₂²×C₄×C₄₃	C₂²×C₄	1	12	yes	—
118	C₂²×C₄×C₄₃	C₂²×C₄	1	12	yes	—
119	C₂²×C₄×C₄₃	C₂²×C₄	1	12	yes	—
120	C₂²×C₄×C₄₃	C₂×D₄	1	24	yes	—
121	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
122	C₂²×C₄×C₄₃	C₂⁴	1	3	yes	—
123	C₂²×C₄×C₄₃	C₂⁴	1	3	yes	—
124	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
125	C₂²×Dic₄₃	—	2	24	no	—
126	C₂²×Dic₄₃	—	2	24	no	—
127	C₂²×Dic₄₃	—	4	12	no	—
128	C₂²×Dic₄₃	C₂⁴	1	12	yes	—
129	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
130	C₂²⋊Dic₄₃	—	2	24	no	—
131	C₂²⋊Dic₄₃	—	2	24	no	—
132	C₂²⋊Dic₄₃	—	2	12	no	—
133	C₂²⋊Dic₄₃	—	4	12	no	—
134	C₂²⋊Dic₄₃	#41	1	8	yes	direct product factor
135	C₄⋊Dic₄₃	—	2	24	no	—
136	C₄×Dic₄₃	—	2	4	no	—
137	C₄×Dic₄₃	—	2	12	no	—
138	C₄×Dic₄₃	—	2	24	no	—
139	C₂³×C₄₃	—	2	2	no	—
140	C₂³×C₄₃	—	2	6	no	—
141	C₂³×C₄₃	—	2	6	no	—
142	C₂³×C₄₃	—	2	2	no	—
143	C₂³×C₄₃	—	2	24	no	—
144	C₂³×C₄₃	—	2	24	no	—
145	C₂³×C₄₃	—	2	6	no	—
146	C₂³×C₄₃	—	2	6	no	—
147	C₂³×C₄₃	—	2	6	no	—
148	C₂³×C₄₃	—	4	12	no	—
149	C₂³×C₄₃	—	4	48	no	—
150	C₂³×C₄₃	C₂³×C₄	1	6	yes	—
151	C₂³×C₄₃	C₂³×C₄	1	6	yes	—
152	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
153	C₂³×C₄₃	C₂²×D₄	1	12	yes	—
154	C₂³×C₄₃	C₂×#41	1	4	yes	—
155	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
156	Q₈×C₄₃	—	2	24	no	—
157	Q₈×C₄₃	C₂×C₂²⋊C₄	1	16	yes	complemented
158	D₄×C₄₃	—	2	48	no	—
159	D₄×C₄₃	—	2	24	no	—
160	D₄×C₄₃	C₂×C₂²⋊C₄	1	48	yes	complemented
161	C₂×C₄×C₄₃	—	2	24	no	—
162	C₂×C₄×C₄₃	—	2	2	no	—
163	C₂×C₄×C₄₃	—	2	6	no	—
164	C₂×C₄×C₄₃	—	2	8	no	—
165	C₂×C₄×C₄₃	—	2	24	no	—
166	C₂×C₄×C₄₃	—	2	24	no	—
167	C₂×C₄×C₄₃	—	2	24	no	—
168	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	48	yes	complemented
169	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
170	C₂×C₄×C₄₃	C₂³×C₄	1	6	yes	—
171	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
172	C₂×C₄×C₄₃	C₂³×C₄	1	6	yes	—
173	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
174	C₂×C₄×C₄₃	C₂²×D₄	1	12	yes	—
175	C₂×Dic₄₃	—	2	4	no	—
176	C₂×Dic₄₃	—	2	4	no	—
177	C₂×Dic₄₃	—	2	12	no	—
178	C₂×Dic₄₃	—	2	12	no	—
179	C₂×Dic₄₃	—	2	12	no	—
180	C₂×Dic₄₃	—	4	48	no	—
181	C₂×Dic₄₃	C₂×#41	1	8	yes	complemented
182	C₂²⋊C₄×#41	—	43	1	no	maximal, Sylow
183	C₂²×C₄₃	—	2	2	no	—
184	C₂²×C₄₃	—	2	6	no	—
185	C₂²×C₄₃	—	2	2	no	—
186	C₂²×C₄₃	—	2	6	no	—
187	C₂²×C₄₃	—	2	8	no	—
188	C₂²×C₄₃	—	2	24	no	—
189	C₂²×C₄₃	—	2	6	no	—
190	C₂²×C₄₃	—	2	6	no	—
191	C₂²×C₄₃	—	2	6	no	—
192	C₂²×C₄₃	—	4	48	no	—
193	C₂²×C₄₃	—	4	12	no	—
194	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	12	yes	—
195	C₂²×C₄₃	C₄×#41	1	4	yes	complemented
196	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
197	C₂²×C₄₃	C₂³×D₄	1	2	yes	—
198	C₂²×C₄₃	C₂²×#41	1	2	yes	—
199	C₂²×C₄₃	#585	1	2	yes	—
200	C₄×C₄₃	—	2	2	no	—
201	C₄×C₄₃	—	2	6	no	—
202	C₄×C₄₃	C₂²×C₂²⋊C₄	1	4	yes	—
203	C₄×C₄₃	C₂²×C₂²⋊C₄	1	12	yes	—
204	Dic₄₃	—	2	8	no	—
205	Dic₄₃	—	4	12	no	—
206	C₂³×#41	D₄₃	1	1	yes	characteristic
207	C₂×C₄×#41	—	43	2	no	—
208	#2341	—	43	2	no	—
209	Q₈×C₂²⋊C₄	—	43	2	no	—
210	#2339	—	43	6	no	—
211	D₄×C₂²⋊C₄	—	43	6	no	—
212	#2297	—	43	6	no	—
213	#2280	—	43	3	no	—
214	C₂×C₄×C₂²⋊C₄	—	43	3	no	—
215	C₂×C₄₃	—	2	4	no	—
216	C₂×C₄₃	—	2	12	no	—
217	C₂×C₄₃	—	4	6	no	—
218	C₂×C₄₃	C₂³×C₂²⋊C₄	1	1	yes	characteristic
219	C₂×C₄₃	C₂×C₄×#41	1	1	yes	characteristic
220	C₂×C₄₃	#3428	1	1	yes	characteristic
221	C₂×C₄₃	D₄×#41	1	4	yes	—
222	C₂²×#41	—	2	16	no	—
223	C₂²×#41	Dic₄₃	1	16	yes	complemented
224	C₂²×#41	C₂×D₄₃	1	3	yes	—
225	C₂²×#41	C₂×D₄₃	1	1	yes	characteristic
226	C₂²×#41	C₂×D₄₃	1	3	yes	—
227	C₂²×#41	C₂×D₄₃	1	1	yes	characteristic
228	C₂³×Q₈	C₂×D₄₃	1	1	yes	characteristic
229	C₂³×D₄	C₂×D₄₃	1	3	yes	—
230	C₂⁴×C₄	C₂×D₄₃	1	3	yes	—
231	C₄×#41	—	86	16	no	—
232	C₂×C₄×Q₈	—	43	4	no	—
233	C₂×C₄×D₄	—	43	12	no	—
234	C₂×#117	—	43	6	no	—
235	C₂²×C₂²⋊C₄	—	43	6	no	—
236	C₂²×C₄²	—	43	6	no	—
237	#391	—	43	12	no	—
238	#390	—	43	12	no	—
239	#386	—	43	24	no	—
240	#381	—	43	6	no	—
241	#380	—	43	6	no	—
242	#380	—	43	6	no	—
243	#379	—	43	6	no	—
244	C₄×C₂²⋊C₄	—	43	6	no	—
245	C₄×C₂²⋊C₄	—	43	6	no	—
246	C₄×C₂²⋊C₄	—	43	1	no	—
247	C₄×C₂²⋊C₄	—	43	3	no	—
248	C₄×C₂²⋊C₄	—	43	6	no	—
249	C₄×C₂²⋊C₄	—	43	6	no	—
250	C₂×#95	—	43	6	no	—
251	C₄₃	C₂²⋊C₄×#41	1	1	yes	characteristic, complemented, Sylow
252	C₂⁵	C₂²×D₄₃	1	3	yes	—
253	C₂×#41	—	2	128	no	—
254	C₂×#41	—	2	8	no	—
255	C₂×#41	—	2	24	no	—
256	C₂×#41	—	2	24	no	—
257	C₂×#41	C₂×Dic₄₃	1	8	yes	—
258	C₂×#41	C₂×Dic₄₃	1	8	yes	complemented
259	C₂×#41	C₂×Dic₄₃	1	24	yes	complemented
260	C₂×#41	C₂×Dic₄₃	1	24	yes	complemented
261	C₂×#41	C₂²⋊D₄₃	1	16	yes	—
262	C₂²×Q₈	—	2	8	no	—
263	C₂²×Q₈	C₂×Dic₄₃	1	8	yes	complemented
264	C₂²×Q₈	C₂²×D₄₃	1	3	yes	—
265	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
266	C₂²×D₄	—	2	24	no	—
267	C₂²×D₄	C₂×Dic₄₃	1	24	yes	complemented
268	C₂²×D₄	C₂²×D₄₃	1	6	yes	—
269	C₂²×D₄	C₂²×D₄₃	1	3	yes	—
270	C₂²×D₄	C₂²×D₄₃	1	3	yes	—
271	C₂³×C₄	—	2	24	no	—
272	C₂³×C₄	—	43	12	no	—
273	C₂³×C₄	C₂×Dic₄₃	1	24	yes	complemented
274	C₂³×C₄	C₂²×D₄₃	1	3	yes	—
275	C₂³×C₄	C₂²×D₄₃	1	3	yes	—
276	C₂³×C₄	C₂²×D₄₃	1	3	yes	—
277	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
278	C₂³×C₄	C₂²×D₄₃	1	3	yes	—
279	C₂³×C₄	C₂²×D₄₃	1	3	yes	—
280	C₄×Q₈	—	86	16	no	—
281	C₄×D₄	—	86	48	no	—
282	#117	—	86	24	no	—
283	C₂×C₄⋊C₄	—	43	12	no	—
284	C₂×C₂²⋊C₄	—	43	2	no	—
285	C₂×C₂²⋊C₄	—	43	6	no	—
286	C₂×C₂²⋊C₄	—	43	12	no	—
287	C₂×C₂²⋊C₄	—	43	12	no	—
288	C₂×C₂²⋊C₄	—	43	12	no	—
289	C₂×C₂²⋊C₄	—	86	24	no	—
290	C₂×C₄²	—	43	12	no	—
291	C₂×C₄²	—	43	6	no	—
292	C₂×C₄²	—	43	2	no	—
293	C₂×C₄²	—	86	24	no	—
294	#95	—	43	2	no	—
295	#95	—	43	6	no	—
296	#95	—	43	12	no	—
297	#95	—	43	12	no	—
298	C₂⁴	—	2	12	no	—
299	C₂⁴	—	2	12	no	—
300	C₂⁴	—	4	6	no	—
301	C₂⁴	C₂²×Dic₄₃	1	12	yes	—
302	C₂⁴	C₂³×D₄₃	1	3	yes	—
303	C₂⁴	C₂³×D₄₃	1	3	yes	—
304	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
305	#41	—	2	32	no	—
306	#41	—	2	96	no	—
307	#41	—	2	96	no	—
308	#41	C₂²⋊Dic₄₃	1	64	yes	direct product factor
309	C₂×Q₈	—	2	32	no	—
310	C₂×Q₈	—	2	12	no	—
311	C₂×Q₈	C₂²×Dic₄₃	1	12	yes	—
312	C₂×Q₈	C₂²×Dic₄₃	1	4	yes	—
313	C₂×Q₈	C₂×C₂²⋊D₄₃	1	8	yes	—
314	C₂×D₄	—	2	24	no	—
315	C₂×D₄	—	2	96	no	—
316	C₂×D₄	—	2	12	no	—
317	C₂×D₄	C₂²×Dic₄₃	1	24	yes	—
318	C₂×D₄	C₂²×Dic₄₃	1	12	yes	—
319	C₂×D₄	C₂²×Dic₄₃	1	12	yes	—
320	C₂×D₄	C₂×C₂²⋊D₄₃	1	24	yes	—
321	C₂²×C₄	—	2	12	no	—
322	C₂²×C₄	—	2	96	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	12	no	—
325	C₂²×C₄	—	2	12	no	—
326	C₂²×C₄	—	2	12	no	—
327	C₂²×C₄	—	43	4	no	—
328	C₂²×C₄	—	43	12	no	—
329	C₂²×C₄	—	86	24	no	—
330	C₂²×C₄	—	86	24	no	—
331	C₂²×C₄	—	172	12	no	—
332	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
333	C₂²×C₄	C₂²×Dic₄₃	1	12	yes	—
334	C₂²×C₄	C₂²×Dic₄₃	1	12	yes	—
335	C₂²×C₄	C₂²×Dic₄₃	1	12	yes	—
336	C₂²×C₄	C₂²×Dic₄₃	1	12	yes	—
337	C₂²×C₄	C₂²×Dic₄₃	1	12	yes	—
338	C₂²×C₄	C₂×C₂²⋊D₄₃	1	24	yes	—
339	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
340	C₂²×C₄	C₂³×D₄₃	1	3	yes	—
341	C₂²×C₄	C₂³×D₄₃	1	3	yes	—
342	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
343	C₄⋊C₄	—	86	24	no	—
344	C₂²⋊C₄	—	43	8	no	—
345	C₂²⋊C₄	—	86	24	no	—
346	C₂²⋊C₄	—	86	24	no	—
347	C₂²⋊C₄	—	86	12	no	—
348	C₂²⋊C₄	—	172	12	no	—
349	C₄²	—	86	4	no	—
350	C₄²	—	86	12	no	—
351	C₄²	—	86	24	no	—
352	C₂³	—	2	2	no	—
353	C₂³	—	2	6	no	—
354	C₂³	—	2	6	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	2	24	no	—
357	C₂³	—	2	24	no	—
358	C₂³	—	2	6	no	—
359	C₂³	—	2	6	no	—
360	C₂³	—	2	6	no	—
361	C₂³	—	4	12	no	—
362	C₂³	—	4	48	no	—
363	C₂³	C₂³×Dic₄₃	1	6	yes	—
364	C₂³	C₂³×Dic₄₃	1	6	yes	—
365	C₂³	C₂³×Dic₄₃	1	2	yes	—
366	C₂³	C₂²×C₂²⋊D₄₃	1	12	yes	—
367	C₂³	#41×D₄₃	1	4	yes	—
368	C₂³	C₂⁴×D₄₃	1	1	yes	characteristic
369	Q₈	—	2	24	no	—
370	Q₈	C₂×C₂²⋊Dic₄₃	1	16	yes	complemented
371	D₄	—	2	48	no	—
372	D₄	—	2	24	no	—
373	D₄	C₂×C₂²⋊Dic₄₃	1	48	yes	complemented
374	C₂×C₄	—	2	24	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	6	no	—
377	C₂×C₄	—	2	8	no	—
378	C₂×C₄	—	2	24	no	—
379	C₂×C₄	—	2	24	no	—
380	C₂×C₄	—	2	24	no	—
381	C₂×C₄	—	43	8	no	—
382	C₂×C₄	—	86	4	no	—
383	C₂×C₄	—	86	4	no	—
384	C₂×C₄	—	86	12	no	—
385	C₂×C₄	—	86	12	no	—
386	C₂×C₄	—	86	12	no	—
387	C₂×C₄	—	172	48	no	—
388	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	48	yes	complemented
389	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
390	C₂×C₄	C₂³×Dic₄₃	1	6	yes	—
391	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
392	C₂×C₄	C₂³×Dic₄₃	1	6	yes	—
393	C₂×C₄	C₂²×C₂²⋊D₄₃	1	4	yes	—
394	C₂×C₄	C₂²×C₂²⋊D₄₃	1	12	yes	—
395	C₂²	—	2	6	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	6	no	—
398	C₂²	—	2	24	no	—
399	C₂²	—	2	8	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	6	no	—
402	C₂²	—	2	6	no	—
403	C₂²	—	2	6	no	—
404	C₂²	—	4	48	no	—
405	C₂²	—	4	12	no	—
406	C₂²	C₂²×C₂²⋊Dic₄₃	1	12	yes	—
407	C₂²	#41×Dic₄₃	1	4	yes	complemented
408	C₂²	C₂⁴×Dic₄₃	1	1	yes	characteristic
409	C₂²	C₂³×C₂²⋊D₄₃	1	2	yes	—
410	C₂²	C₂×#41×D₄₃	1	2	yes	—
411	C₂²	#14583735	1	2	yes	—
412	C₄	—	2	2	no	—
413	C₄	—	2	6	no	—
414	C₄	—	86	8	no	—
415	C₄	—	172	12	no	—
416	C₄	C₂²×C₂²⋊Dic₄₃	1	4	yes	—
417	C₄	C₂²×C₂²⋊Dic₄₃	1	12	yes	—
418	C₂	—	2	4	no	—
419	C₂	—	2	12	no	—
420	C₂	—	4	6	no	—
421	C₂	C₂³×C₂²⋊Dic₄₃	1	1	yes	characteristic
422	C₂	C₂×#41×Dic₄₃	1	1	yes	characteristic
423	C₂	#19147798	1	1	yes	characteristic
424	C₂	#41×C₂²⋊D₄₃	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂³×D₄₃
commutator	C₂²×C₄₃	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₄₃
Fitting, prime radical	C₂³×#41×C₄₃	C₂
socle, cosocle	C₂³×C₄₃	C₂⁵
hypercenter	C₂³×#41	D₄₃
hypocenter	C₄₃	C₂²⋊C₄×#41
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×#41

Complements

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

N	H ≅ G/N	type
1. C₂×#41×Dic₄₃	C₂	semidirect
2. #19137436	C₂	semidirect
3. Q₈×C₂²⋊Dic₄₃	C₂	semidirect
4. #19137425	C₂	semidirect
5. D₄×C₂²⋊Dic₄₃	C₂	semidirect
6. #19137086	C₂	semidirect
7. #19136978	C₂	semidirect
8. C₂×C₄×C₂²⋊Dic₄₃	C₂	semidirect
11. C₂×Q₈×Dic₄₃	C₂²	semidirect
12. C₂×D₄×Dic₄₃	C₂²	semidirect
13. C₂×#13063284	C₂²	semidirect
15. C₂²×C₄×Dic₄₃	C₂²	semidirect
16. #14582806	C₂²	semidirect
17. #14582802	C₂²	semidirect
18. #14582779	C₂²	semidirect
19. #14582762	C₂²	semidirect
21. #14582759	C₂²	semidirect
26. C₄×C₂²⋊Dic₄₃	C₂²	semidirect
27. C₄×C₂²⋊Dic₄₃	C₂²	semidirect
28. C₄×C₂²⋊Dic₄₃	C₂²	semidirect
29. C₂×C₄₃⋊#95	C₂²	semidirect
31. C₂²×#41×C₄₃	C₄	semidirect
64. C₂×#41×C₄₃	C₂×C₄	semidirect
65. C₂×#41×C₄₃	C₂×C₄	semidirect
66. C₂×#41×C₄₃	C₂×C₄	semidirect
69. C₂²×Q₈×C₄₃	C₂×C₄	semidirect
73. C₂²×D₄×C₄₃	C₂×C₄	semidirect
78. C₂³×C₄×C₄₃	C₂×C₄	semidirect
95. #41×C₄₃	C₂²⋊C₄	semidirect
134. C₂²⋊Dic₄₃	#41	direct (N × H)
157. Q₈×C₄₃	C₂×C₂²⋊C₄	semidirect
160. D₄×C₄₃	C₂×C₂²⋊C₄	semidirect
168. C₂×C₄×C₄₃	C₂×C₂²⋊C₄	semidirect
181. C₂×Dic₄₃	C₂×#41	semidirect
195. C₂²×C₄₃	C₄×#41	semidirect
223. C₂²×#41	Dic₄₃	semidirect
251. C₄₃	C₂²⋊C₄×#41	semidirect
258. C₂×#41	C₂×Dic₄₃	semidirect
259. C₂×#41	C₂×Dic₄₃	semidirect
260. C₂×#41	C₂×Dic₄₃	semidirect
263. C₂²×Q₈	C₂×Dic₄₃	semidirect
267. C₂²×D₄	C₂×Dic₄₃	semidirect
273. C₂³×C₄	C₂×Dic₄₃	semidirect
308. #41	C₂²⋊Dic₄₃	direct (N × H)
370. Q₈	C₂×C₂²⋊Dic₄₃	semidirect
373. D₄	C₂×C₂²⋊Dic₄₃	semidirect
388. C₂×C₄	C₂×C₂²⋊Dic₄₃	semidirect
407. C₂²	#41×Dic₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×Dic₄₃	2
#19137436	2
Q₈×C₂²⋊Dic₄₃	2
#19137425	2
D₄×C₂²⋊Dic₄₃	2
#19137086	2
#19136978	2
C₂×C₄×C₂²⋊Dic₄₃	2
C₂³×#41×C₄₃	2
C₂²⋊C₄×#41	43

Subgroups — #41×C22⋊Dic43 #25255802

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #41×C₂²⋊Dic₄₃ #25255802