Subgroups — C₂×C₄₁×#1742 #23796558

Order 10496.

2190 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×M₁₆×C₄₁	C₂	1	2	yes	maximal
2	C₂²×#117×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#1742	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₄₁×#343	C₂	1	4	yes	maximal, complemented
5	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
6	C₂²×M₁₆×C₄₁	—	2	8	no	—
7	C₂²×M₁₆×C₄₁	—	2	2	no	—
8	C₂²×M₁₆×C₄₁	—	2	4	no	—
9	C₂²×M₁₆×C₄₁	C₄	1	16	yes	complemented
10	C₂²×M₁₆×C₄₁	C₂²	1	4	yes	—
11	C₂²×M₁₆×C₄₁	C₂²	1	8	yes	—
12	C₂³×C₈×C₄₁	—	2	2	no	—
13	C₂×#117×C₄₁	—	2	2	no	—
14	C₂×#117×C₄₁	—	2	4	no	—
15	C₂×#117×C₄₁	—	2	2	no	—
16	C₂×#117×C₄₁	C₄	1	4	yes	—
17	C₂×#117×C₄₁	C₂²	1	4	yes	—
18	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
19	C₂²×C₂²⋊C₄×C₄₁	C₄	1	2	yes	—
20	C₂²×C₄²×C₄₁	C₄	1	2	yes	—
21	C₄₁×#343	C₂²	1	16	yes	complemented
22	C₂⁵×C₄₁	C₂×C₄	1	1	yes	characteristic
23	C₂³×C₄×C₄₁	C₂×C₄	1	4	yes	—
24	C₂³×C₄×C₄₁	C₂×C₄	1	2	yes	—
25	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₄₁	C₂×C₄	1	8	yes	—
27	C₂³×C₄×C₄₁	D₄	1	4	yes	—
28	C₂³×C₄×C₄₁	D₄	1	2	yes	—
29	C₂³×C₄×C₄₁	D₄	1	4	yes	—
30	C₂³×C₄×C₄₁	D₄	1	2	yes	—
31	C₂³×C₄×C₄₁	Q₈	1	4	yes	—
32	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
33	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
34	C₂×M₁₆×C₄₁	—	2	16	no	—
35	C₂×M₁₆×C₄₁	—	2	32	no	—
36	C₂×M₁₆×C₄₁	—	2	8	no	—
37	C₂×M₁₆×C₄₁	—	2	16	no	—
38	C₂×M₁₆×C₄₁	—	2	4	no	—
39	C₂×M₁₆×C₄₁	—	2	8	no	—
40	C₂×M₁₆×C₄₁	C₂×C₄	1	16	yes	—
41	C₂×M₁₆×C₄₁	C₂×C₄	1	32	yes	complemented
42	C₂×M₁₆×C₄₁	C₂³	1	8	yes	—
43	C₂²×C₈×C₄₁	—	2	16	no	—
44	C₂²×C₈×C₄₁	—	2	4	no	—
45	C₂²×C₈×C₄₁	—	2	8	no	—
46	#117×C₄₁	—	2	8	no	—
47	#117×C₄₁	—	2	8	no	—
48	#117×C₄₁	—	2	8	no	—
49	#117×C₄₁	—	2	8	no	—
50	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
51	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
52	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	4	yes	—
53	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
54	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
55	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
56	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	8	yes	—
57	C₂×C₄²×C₄₁	—	2	2	no	—
58	C₂×C₄²×C₄₁	—	2	4	no	—
59	C₂×C₄²×C₄₁	—	2	2	no	—
60	C₂×C₄²×C₄₁	C₂×C₄	1	8	yes	—
61	C₂⁴×C₄₁	—	4	4	no	—
62	C₂⁴×C₄₁	C₄²	1	4	yes	—
63	C₂⁴×C₄₁	C₂²⋊C₄	1	2	yes	—
64	C₂⁴×C₄₁	C₂²⋊C₄	1	2	yes	—
65	C₂⁴×C₄₁	C₄⋊C₄	1	4	yes	—
66	C₂⁴×C₄₁	C₂²×C₄	1	1	yes	characteristic
67	C₂⁴×C₄₁	C₂²×C₄	1	2	yes	—
68	C₂²×C₄×C₄₁	—	2	4	no	—
69	C₂²×C₄×C₄₁	—	2	4	no	—
70	C₂²×C₄×C₄₁	—	4	8	no	—
71	C₂²×C₄×C₄₁	C₄²	1	8	yes	—
72	C₂²×C₄×C₄₁	C₄²	1	4	yes	—
73	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
75	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
76	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
77	C₂²×C₄×C₄₁	C₂²⋊C₄	1	8	yes	—
78	C₂²×C₄×C₄₁	C₂²⋊C₄	1	8	yes	—
79	C₂²×C₄×C₄₁	C₂²⋊C₄	1	16	yes	—
80	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₁	C₄⋊C₄	1	8	yes	—
82	C₂²×C₄×C₄₁	C₄⋊C₄	1	4	yes	—
83	C₂²×C₄×C₄₁	C₄⋊C₄	1	8	yes	—
84	C₂²×C₄×C₄₁	C₄⋊C₄	1	16	yes	—
85	C₂²×C₄×C₄₁	C₄⋊C₄	1	8	yes	—
86	C₂²×C₄×C₄₁	C₂²×C₄	1	8	yes	—
87	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
90	C₂²×C₄×C₄₁	C₂²×C₄	1	8	yes	—
91	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
93	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
96	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
97	C₂²×C₄×C₄₁	C₂×Q₈	1	2	yes	—
98	C₂²×C₄×C₄₁	C₂×Q₈	1	4	yes	—
99	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
100	M₁₆×C₄₁	—	2	16	no	—
101	M₁₆×C₄₁	—	2	32	no	—
102	M₁₆×C₄₁	—	2	8	no	—
103	M₁₆×C₄₁	C₂²×C₄	1	16	yes	—
104	C₂×C₈×C₄₁	—	2	16	no	—
105	C₂×C₈×C₄₁	—	2	32	no	—
106	C₂×C₈×C₄₁	—	2	8	no	—
107	C₄⋊C₄×C₄₁	—	2	8	no	—
108	C₄⋊C₄×C₄₁	—	2	8	no	—
109	C₂²⋊C₄×C₄₁	—	2	16	no	—
110	C₄²×C₄₁	—	2	8	no	—
111	C₄²×C₄₁	—	2	8	no	—
112	C₂³×C₄₁	—	2	4	no	—
113	C₂³×C₄₁	—	2	8	no	—
114	C₂³×C₄₁	—	4	8	no	—
115	C₂³×C₄₁	—	4	4	no	—
116	C₂³×C₄₁	—	4	8	no	—
117	C₂³×C₄₁	—	4	4	no	—
118	C₂³×C₄₁	#95	1	8	yes	—
119	C₂³×C₄₁	#95	1	8	yes	—
120	C₂³×C₄₁	C₂×C₄²	1	2	yes	—
121	C₂³×C₄₁	C₂×C₄²	1	4	yes	—
122	C₂³×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
123	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
124	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
125	C₂³×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
126	C₂³×C₄₁	C₂×C₄⋊C₄	1	4	yes	—
127	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
128	C₂×C₄×C₄₁	—	2	8	no	—
129	C₂×C₄×C₄₁	—	4	8	no	—
130	C₂×C₄×C₄₁	—	4	8	no	—
131	C₂×C₄×C₄₁	—	4	8	no	—
132	C₂×C₄×C₄₁	#95	1	8	yes	—
133	C₂×C₄×C₄₁	#95	1	16	yes	—
134	C₂×C₄×C₄₁	#95	1	16	yes	—
135	C₂×C₄×C₄₁	#95	1	4	yes	—
136	C₂×C₄×C₄₁	#95	1	4	yes	—
137	C₂×C₄×C₄₁	C₂×C₄²	1	4	yes	—
138	C₂×C₄×C₄₁	C₂×C₄²	1	2	yes	—
139	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	8	yes	—
140	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
141	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
142	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	8	yes	—
143	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
144	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
145	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
146	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	4	yes	—
147	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	8	yes	—
148	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	8	yes	—
149	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	4	yes	—
150	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	4	yes	—
151	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
152	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
153	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
155	C₂×C₄×C₄₁	C₂²×Q₈	1	1	yes	characteristic
156	C₈×C₄₁	—	2	16	no	—
157	C₂×#1742	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
158	C₂²×C₄₁	—	2	2	no	—
159	C₂²×C₄₁	—	2	2	no	—
160	C₂²×C₄₁	—	2	8	no	—
161	C₂²×C₄₁	—	2	16	no	—
162	C₂²×C₄₁	—	2	4	no	—
163	C₂²×C₄₁	—	2	4	no	—
164	C₂²×C₄₁	—	4	8	no	—
165	C₂²×C₄₁	—	4	4	no	—
166	C₂²×C₄₁	—	4	4	no	—
167	C₂²×C₄₁	C₂×#95	1	8	yes	—
168	C₂²×C₄₁	C₂×#95	1	2	yes	—
169	C₂²×C₄₁	C₂×#95	1	2	yes	—
170	C₂²×C₄₁	#413	1	4	yes	—
171	C₂²×C₄₁	C₂²×C₄²	1	1	yes	characteristic
172	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
173	C₂²×C₄₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
174	C₄×C₄₁	—	4	8	no	—
175	C₄×C₄₁	C₂×#95	1	4	yes	—
176	C₄×C₄₁	C₂×#95	1	4	yes	—
177	C₄×C₄₁	C₂×#95	1	4	yes	—
178	C₄×C₄₁	C₂²×C₂²⋊C₄	1	2	yes	—
179	C₄×C₄₁	C₂²×C₄⋊C₄	1	2	yes	—
180	C₂³×M₁₆	C₂×C₄₁	1	2	yes	—
181	C₂²×#117	C₂×C₄₁	1	1	yes	characteristic
182	#1742	C₂×C₄₁	1	8	yes	direct product factor
183	C₂×#343	C₂×C₄₁	1	4	yes	complemented
184	C₂×C₄₁	—	2	1	no	—
185	C₂×C₄₁	—	2	2	no	—
186	C₂×C₄₁	—	2	8	no	—
187	C₂×C₄₁	—	2	1	no	—
188	C₂×C₄₁	#1742	1	4	yes	direct product factor
189	C₂×C₄₁	C₂²×#95	1	1	yes	characteristic
190	C₂×C₄₁	C₂×#413	1	2	yes	—
191	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
192	C₂²×M₁₆	—	2	8	no	—
193	C₂²×M₁₆	—	2	2	no	—
194	C₂²×M₁₆	—	2	4	no	—
195	C₂²×M₁₆	C₄×C₄₁	1	16	yes	complemented
196	C₂²×M₁₆	C₂²×C₄₁	1	4	yes	—
197	C₂²×M₁₆	C₂²×C₄₁	1	8	yes	—
198	C₂³×C₈	—	2	2	no	—
199	C₂×#117	—	2	2	no	—
200	C₂×#117	—	2	2	no	—
201	C₂×#117	—	2	4	no	—
202	C₂×#117	C₄×C₄₁	1	4	yes	—
203	C₂×#117	C₂²×C₄₁	1	4	yes	—
204	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
205	C₂²×C₂²⋊C₄	C₄×C₄₁	1	2	yes	—
206	C₂²×C₄²	C₄×C₄₁	1	2	yes	—
207	#343	C₂²×C₄₁	1	16	yes	complemented
208	C₄₁	C₂×#1742	1	1	yes	characteristic, direct product factor, Sylow
209	C₂⁵	C₂×C₄×C₄₁	1	1	yes	characteristic
210	C₂³×C₄	C₂×C₄×C₄₁	1	4	yes	—
211	C₂³×C₄	C₂×C₄×C₄₁	1	2	yes	—
212	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
213	C₂³×C₄	C₂×C₄×C₄₁	1	8	yes	—
214	C₂³×C₄	D₄×C₄₁	1	4	yes	—
215	C₂³×C₄	D₄×C₄₁	1	2	yes	—
216	C₂³×C₄	D₄×C₄₁	1	2	yes	—
217	C₂³×C₄	D₄×C₄₁	1	4	yes	—
218	C₂³×C₄	Q₈×C₄₁	1	4	yes	—
219	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
220	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
221	C₂×M₁₆	—	2	16	no	—
222	C₂×M₁₆	—	2	32	no	—
223	C₂×M₁₆	—	2	8	no	—
224	C₂×M₁₆	—	2	16	no	—
225	C₂×M₁₆	—	2	4	no	—
226	C₂×M₁₆	—	2	8	no	—
227	C₂×M₁₆	C₂×C₄×C₄₁	1	16	yes	—
228	C₂×M₁₆	C₂×C₄×C₄₁	1	32	yes	complemented
229	C₂×M₁₆	C₂³×C₄₁	1	8	yes	—
230	C₂²×C₈	—	2	16	no	—
231	C₂²×C₈	—	2	4	no	—
232	C₂²×C₈	—	2	8	no	—
233	#117	—	2	8	no	—
234	#117	—	2	8	no	—
235	#117	—	2	8	no	—
236	#117	—	2	8	no	—
237	C₂×C₄⋊C₄	—	2	4	no	—
238	C₂×C₄⋊C₄	—	2	4	no	—
239	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	4	yes	—
240	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
241	C₂×C₂²⋊C₄	—	2	4	no	—
242	C₂×C₂²⋊C₄	—	2	4	no	—
243	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	8	yes	—
244	C₂×C₄²	—	2	4	no	—
245	C₂×C₄²	—	2	2	no	—
246	C₂×C₄²	—	2	2	no	—
247	C₂×C₄²	C₂×C₄×C₄₁	1	8	yes	—
248	C₂⁴	—	4	4	no	—
249	C₂⁴	C₄²×C₄₁	1	4	yes	—
250	C₂⁴	C₂²⋊C₄×C₄₁	1	2	yes	—
251	C₂⁴	C₂²⋊C₄×C₄₁	1	2	yes	—
252	C₂⁴	C₄⋊C₄×C₄₁	1	4	yes	—
253	C₂⁴	C₂²×C₄×C₄₁	1	1	yes	characteristic
254	C₂⁴	C₂²×C₄×C₄₁	1	2	yes	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	4	8	no	—
258	C₂²×C₄	C₄²×C₄₁	1	4	yes	—
259	C₂²×C₄	C₄²×C₄₁	1	8	yes	—
260	C₂²×C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
261	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
262	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
263	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
264	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
265	C₂²×C₄	C₂²⋊C₄×C₄₁	1	8	yes	—
266	C₂²×C₄	C₂²⋊C₄×C₄₁	1	8	yes	—
267	C₂²×C₄	C₂²⋊C₄×C₄₁	1	16	yes	—
268	C₂²×C₄	C₄⋊C₄×C₄₁	1	4	yes	—
269	C₂²×C₄	C₄⋊C₄×C₄₁	1	8	yes	—
270	C₂²×C₄	C₄⋊C₄×C₄₁	1	8	yes	—
271	C₂²×C₄	C₄⋊C₄×C₄₁	1	8	yes	—
272	C₂²×C₄	C₄⋊C₄×C₄₁	1	16	yes	—
273	C₂²×C₄	C₂²×C₄×C₄₁	1	8	yes	—
274	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
275	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
276	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
277	C₂²×C₄	C₂²×C₄×C₄₁	1	8	yes	—
278	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
279	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
280	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
281	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
282	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
283	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
284	C₂²×C₄	C₂×Q₈×C₄₁	1	2	yes	—
285	C₂²×C₄	C₂×Q₈×C₄₁	1	4	yes	—
286	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
287	M₁₆	—	2	16	no	—
288	M₁₆	—	2	32	no	—
289	M₁₆	—	2	8	no	—
290	M₁₆	C₂²×C₄×C₄₁	1	16	yes	—
291	C₂×C₈	—	2	16	no	—
292	C₂×C₈	—	2	32	no	—
293	C₂×C₈	—	2	8	no	—
294	C₄⋊C₄	—	2	8	no	—
295	C₄⋊C₄	—	2	8	no	—
296	C₂²⋊C₄	—	2	16	no	—
297	C₄²	—	2	8	no	—
298	C₄²	—	2	8	no	—
299	C₂³	—	2	4	no	—
300	C₂³	—	2	8	no	—
301	C₂³	—	4	8	no	—
302	C₂³	—	4	4	no	—
303	C₂³	—	4	8	no	—
304	C₂³	—	4	4	no	—
305	C₂³	#95×C₄₁	1	8	yes	—
306	C₂³	#95×C₄₁	1	8	yes	—
307	C₂³	C₂×C₄²×C₄₁	1	2	yes	—
308	C₂³	C₂×C₄²×C₄₁	1	4	yes	—
309	C₂³	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
310	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
311	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
312	C₂³	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
313	C₂³	C₂×C₄⋊C₄×C₄₁	1	4	yes	—
314	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
315	C₂×C₄	—	2	8	no	—
316	C₂×C₄	—	4	8	no	—
317	C₂×C₄	—	4	8	no	—
318	C₂×C₄	—	4	8	no	—
319	C₂×C₄	#95×C₄₁	1	8	yes	—
320	C₂×C₄	#95×C₄₁	1	16	yes	—
321	C₂×C₄	#95×C₄₁	1	16	yes	—
322	C₂×C₄	#95×C₄₁	1	4	yes	—
323	C₂×C₄	#95×C₄₁	1	4	yes	—
324	C₂×C₄	C₂×C₄²×C₄₁	1	4	yes	—
325	C₂×C₄	C₂×C₄²×C₄₁	1	2	yes	—
326	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	8	yes	—
327	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
328	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
329	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	8	yes	—
330	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
331	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
332	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
333	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	4	yes	—
334	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	8	yes	—
335	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	8	yes	—
336	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	4	yes	—
337	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	4	yes	—
338	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
339	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
340	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
341	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
342	C₂×C₄	C₂²×Q₈×C₄₁	1	1	yes	characteristic
343	C₈	—	2	16	no	—
344	C₂²	—	2	2	no	—
345	C₂²	—	2	2	no	—
346	C₂²	—	2	8	no	—
347	C₂²	—	2	16	no	—
348	C₂²	—	2	4	no	—
349	C₂²	—	2	4	no	—
350	C₂²	—	4	8	no	—
351	C₂²	—	4	4	no	—
352	C₂²	—	4	4	no	—
353	C₂²	C₂×#95×C₄₁	1	8	yes	—
354	C₂²	C₂×#95×C₄₁	1	2	yes	—
355	C₂²	C₂×#95×C₄₁	1	2	yes	—
356	C₂²	C₄₁×#413	1	4	yes	—
357	C₂²	C₂²×C₄²×C₄₁	1	1	yes	characteristic
358	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
359	C₂²	C₂²×C₄⋊C₄×C₄₁	1	1	yes	characteristic
360	C₄	—	4	8	no	—
361	C₄	C₂×#95×C₄₁	1	4	yes	—
362	C₄	C₂×#95×C₄₁	1	4	yes	—
363	C₄	C₂×#95×C₄₁	1	4	yes	—
364	C₄	C₂²×C₂²⋊C₄×C₄₁	1	2	yes	—
365	C₄	C₂²×C₄⋊C₄×C₄₁	1	2	yes	—
366	C₂	—	2	1	no	—
367	C₂	—	2	1	no	—
368	C₂	—	2	2	no	—
369	C₂	—	2	8	no	—
370	C₂	C₄₁×#1742	1	4	yes	direct product factor
371	C₂	C₂²×#95×C₄₁	1	1	yes	characteristic
372	C₂	C₂×C₄₁×#413	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₄₁	C₂²⋊C₄
commutator	C₂²	C₂²×C₄²×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
socle	C₂³×C₄₁	C₂×C₂²⋊C₄
prime radical	C₂⁵×C₄₁	C₂×C₄
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₁ ◁ C₂⁴×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄₁×#1742	C₂	direct (N × H)
4. C₂×C₄₁×#343	C₂	semidirect
9. C₂²×M₁₆×C₄₁	C₄	semidirect
21. C₄₁×#343	C₂²	semidirect
41. C₂×M₁₆×C₄₁	C₂×C₄	semidirect
157. C₂×#1742	C₄₁	direct (N × H)
182. #1742	C₂×C₄₁	direct (N × H)
183. C₂×#343	C₂×C₄₁	semidirect
188. C₂×C₄₁	#1742	direct (N × H)
195. C₂²×M₁₆	C₄×C₄₁	semidirect
207. #343	C₂²×C₄₁	semidirect
208. C₄₁	C₂×#1742	direct (N × H)
228. C₂×M₁₆	C₂×C₄×C₄₁	semidirect
370. C₂	C₄₁×#1742	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×M₁₆×C₄₁	2
C₂²×#117×C₄₁	2
C₄₁×#1742	2
C₂×C₄₁×#343	2
C₂×#1742	41

Subgroups — C2×C41×#1742 #23796558

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#1742 #23796558