Subgroups — C₂×C₄₁×#1955 #23797387

Order 10496.

2094 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊C₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₂²⋊C₈×C₄₁	C₂	1	4	yes	maximal, complemented
4	C₂²×#97×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1955	C₂	1	8	yes	maximal, direct product factor
6	C₂³×D₄×C₄₁	C₄	1	1	yes	characteristic
7	C₂⁴×C₄×C₄₁	C₂²	1	2	yes	—
8	C₂³×C₈×C₄₁	C₂²	1	2	yes	—
9	C₂³×C₈×C₄₁	C₂²	1	2	yes	—
10	C₂×C₄×D₄×C₄₁	—	2	4	no	—
11	C₂×C₄×D₄×C₄₁	—	2	4	no	—
12	C₂×C₄×D₄×C₄₁	C₄	1	4	yes	—
13	C₂×C₄×D₄×C₄₁	C₂²	1	4	yes	—
14	C₂²×C₄⋊C₄×C₄₁	C₄	1	1	yes	characteristic
15	C₂²×C₂²⋊C₄×C₄₁	C₄	1	2	yes	—
16	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₈×C₄₁	—	2	4	no	—
18	C₂×C₄⋊C₈×C₄₁	C₂²	1	4	yes	complemented
19	C₂×C₂²⋊C₈×C₄₁	—	2	16	no	—
20	C₂×C₂²⋊C₈×C₄₁	C₂²	1	16	yes	complemented
21	C₂×#97×C₄₁	—	2	4	no	—
22	C₂×#97×C₄₁	C₂²	1	4	yes	complemented
23	C₂⁵×C₄₁	C₂×C₄	1	2	yes	—
24	C₂²×D₄×C₄₁	—	2	8	no	—
25	C₂²×D₄×C₄₁	—	2	4	no	—
26	C₂²×D₄×C₄₁	C₂×C₄	1	4	yes	—
27	C₂³×C₄×C₄₁	—	2	4	no	—
28	C₂³×C₄×C₄₁	—	2	4	no	—
29	C₂³×C₄×C₄₁	—	2	8	no	—
30	C₂³×C₄×C₄₁	—	2	8	no	—
31	C₂³×C₄×C₄₁	C₂×C₄	1	2	yes	—
32	C₂³×C₄×C₄₁	C₂×C₄	1	4	yes	—
33	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
36	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₄₁	—	2	4	no	—
38	C₂²×C₈×C₄₁	—	2	4	no	—
39	C₂²×C₈×C₄₁	—	2	8	no	—
40	C₂²×C₈×C₄₁	—	2	4	no	—
41	C₂²×C₈×C₄₁	D₄	1	8	yes	complemented
42	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
43	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
44	C₄×D₄×C₄₁	—	2	16	no	—
45	C₄×D₄×C₄₁	—	2	8	no	—
46	C₄×D₄×C₄₁	—	2	8	no	—
47	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
48	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	4	yes	—
49	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
50	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	8	yes	—
51	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₄₁	D₄	1	4	yes	—
53	C₂×C₄²×C₄₁	D₄	1	4	yes	—
54	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
55	C₄⋊C₈×C₄₁	—	2	8	no	—
56	C₂²⋊C₈×C₄₁	—	2	32	no	—
57	#97×C₄₁	—	2	8	no	—
58	C₂⁴×C₄₁	—	2	4	no	—
59	C₂⁴×C₄₁	—	2	8	no	—
60	C₂⁴×C₄₁	—	2	4	no	—
61	C₂⁴×C₄₁	—	2	8	no	—
62	C₂⁴×C₄₁	M₁₆	1	8	yes	—
63	C₂⁴×C₄₁	C₂²×C₄	1	4	yes	—
64	C₂⁴×C₄₁	C₂²×C₄	1	1	yes	characteristic
65	C₂×D₄×C₄₁	—	2	32	no	—
66	C₂×D₄×C₄₁	—	2	16	no	—
67	C₂×D₄×C₄₁	—	2	8	no	—
68	C₂²×C₄×C₄₁	—	2	4	no	—
69	C₂²×C₄×C₄₁	—	2	4	no	—
70	C₂²×C₄×C₄₁	—	2	4	no	—
71	C₂²×C₄×C₄₁	—	2	8	no	—
72	C₂²×C₄×C₄₁	—	2	8	no	—
73	C₂²×C₄×C₄₁	—	2	16	no	—
74	C₂²×C₄×C₄₁	—	2	8	no	—
75	C₂²×C₄×C₄₁	—	2	4	no	—
76	C₂²×C₄×C₄₁	—	2	4	no	—
77	C₂²×C₄×C₄₁	—	2	8	no	—
78	C₂²×C₄×C₄₁	—	4	16	no	—
79	C₂²×C₄×C₄₁	—	4	8	no	—
80	C₂²×C₄×C₄₁	—	4	8	no	—
81	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
82	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
83	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
84	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
90	C₂²×C₄×C₄₁	#41	1	4	yes	—
91	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
92	C₂×C₈×C₄₁	—	2	16	no	—
93	C₂×C₈×C₄₁	—	2	4	no	—
94	C₂×C₈×C₄₁	—	2	4	no	—
95	C₂×C₈×C₄₁	—	2	8	no	—
96	C₂×C₈×C₄₁	—	2	4	no	—
97	C₂×C₈×C₄₁	—	4	8	no	—
98	C₂×C₈×C₄₁	C₂×D₄	1	8	yes	complemented
99	C₄⋊C₄×C₄₁	—	2	8	no	—
100	C₂²⋊C₄×C₄₁	—	2	16	no	—
101	C₄²×C₄₁	C₂²⋊C₄	1	8	yes	—
102	C₄²×C₄₁	C₂×D₄	1	4	yes	—
103	C₄²×C₄₁	C₂×D₄	1	4	yes	—
104	C₂³×C₄₁	—	2	4	no	—
105	C₂³×C₄₁	—	2	8	no	—
106	C₂³×C₄₁	—	2	4	no	—
107	C₂³×C₄₁	—	2	8	no	—
108	C₂³×C₄₁	—	2	16	no	—
109	C₂³×C₄₁	—	2	32	no	—
110	C₂³×C₄₁	—	4	8	no	—
111	C₂³×C₄₁	—	4	8	no	—
112	C₂³×C₄₁	—	4	16	no	—
113	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
114	C₂³×C₄₁	C₄×D₄	1	4	yes	—
115	C₂³×C₄₁	C₂×M₁₆	1	8	yes	—
116	C₂³×C₄₁	C₂×M₁₆	1	4	yes	—
117	C₂³×C₄₁	#131	1	4	yes	—
118	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
119	D₄×C₄₁	—	2	32	no	—
120	C₂×C₄×C₄₁	—	2	4	no	—
121	C₂×C₄×C₄₁	—	2	4	no	—
122	C₂×C₄×C₄₁	—	2	8	no	—
123	C₂×C₄×C₄₁	—	2	8	no	—
124	C₂×C₄×C₄₁	—	2	4	no	—
125	C₂×C₄×C₄₁	—	2	8	no	—
126	C₂×C₄×C₄₁	—	4	8	no	—
127	C₂×C₄×C₄₁	—	4	8	no	—
128	C₂×C₄×C₄₁	—	4	4	no	—
129	C₂×C₄×C₄₁	—	4	4	no	—
130	C₂×C₄×C₄₁	—	4	16	no	—
131	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
132	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
133	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
134	C₂×C₄×C₄₁	C₄×D₄	1	4	yes	—
135	C₂×C₄×C₄₁	#121	1	8	yes	—
136	C₂×C₄×C₄₁	#124	1	4	yes	—
137	C₂×C₄×C₄₁	#127	1	4	yes	—
138	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
139	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
140	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
141	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
142	C₈×C₄₁	—	2	8	no	—
143	C₈×C₄₁	—	4	4	no	—
144	C₂×#1955	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂²×C₄₁	—	2	8	no	—
146	C₂²×C₄₁	—	2	16	no	—
147	C₂²×C₄₁	—	4	4	no	—
148	C₂²×C₄₁	—	4	8	no	—
149	C₂²×C₄₁	—	4	32	no	—
150	C₂²×C₄₁	—	4	4	no	—
151	C₂²×C₄₁	#390	1	4	yes	—
152	C₂²×C₄₁	#407	1	4	yes	—
153	C₂²×C₄₁	#408	1	4	yes	—
154	C₂²×C₄₁	#435	1	16	yes	—
155	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
156	C₂²×C₄₁	C₂×C₄×D₄	1	2	yes	—
157	C₂²×C₄₁	C₂²×M₁₆	1	2	yes	—
158	C₂²×C₄₁	C₂×#131	1	2	yes	—
159	C₄×C₄₁	—	2	4	no	—
160	C₄×C₄₁	—	2	4	no	—
161	C₄×C₄₁	—	4	4	no	—
162	C₄×C₄₁	#390	1	4	yes	—
163	C₄×C₄₁	C₂×#121	1	2	yes	—
164	C₄×C₄₁	C₂×#124	1	1	yes	characteristic
165	C₄×C₄₁	C₂×#127	1	1	yes	characteristic
166	C₂²×C₄×D₄	C₂×C₄₁	1	1	yes	characteristic
167	C₂²×C₄⋊C₈	C₂×C₄₁	1	1	yes	characteristic, complemented
168	C₂²×C₂²⋊C₈	C₂×C₄₁	1	4	yes	complemented
169	C₂²×#97	C₂×C₄₁	1	1	yes	characteristic, complemented
170	#1955	C₂×C₄₁	1	8	yes	direct product factor
171	C₂×C₄₁	—	4	8	no	—
172	C₂×C₄₁	#1955	1	8	yes	direct product factor
173	C₂×C₄₁	C₂×#390	1	1	yes	characteristic
174	C₂×C₄₁	C₂×#407	1	1	yes	characteristic
175	C₂×C₄₁	C₂×#408	1	1	yes	characteristic
176	C₂×C₄₁	C₂×#435	1	4	yes	—
177	C₂³×D₄	C₄×C₄₁	1	1	yes	characteristic
178	C₂⁴×C₄	C₂²×C₄₁	1	2	yes	—
179	C₂³×C₈	C₂²×C₄₁	1	2	yes	—
180	C₂³×C₈	C₂²×C₄₁	1	2	yes	—
181	C₂×C₄×D₄	—	2	4	no	—
182	C₂×C₄×D₄	—	2	4	no	—
183	C₂×C₄×D₄	C₄×C₄₁	1	4	yes	—
184	C₂×C₄×D₄	C₂²×C₄₁	1	4	yes	—
185	C₂²×C₄⋊C₄	C₄×C₄₁	1	1	yes	characteristic
186	C₂²×C₂²⋊C₄	C₄×C₄₁	1	2	yes	—
187	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
188	C₂×C₄⋊C₈	—	2	4	no	—
189	C₂×C₄⋊C₈	C₂²×C₄₁	1	4	yes	complemented
190	C₂×C₂²⋊C₈	—	2	16	no	—
191	C₂×C₂²⋊C₈	C₂²×C₄₁	1	16	yes	complemented
192	C₂×#97	—	2	4	no	—
193	C₂×#97	C₂²×C₄₁	1	4	yes	complemented
194	C₄₁	C₂×#1955	1	1	yes	characteristic, direct product factor, Sylow
195	C₂⁵	C₂×C₄×C₄₁	1	2	yes	—
196	C₂²×D₄	—	2	8	no	—
197	C₂²×D₄	—	2	4	no	—
198	C₂²×D₄	C₂×C₄×C₄₁	1	4	yes	—
199	C₂³×C₄	—	2	4	no	—
200	C₂³×C₄	—	2	4	no	—
201	C₂³×C₄	—	2	8	no	—
202	C₂³×C₄	—	2	8	no	—
203	C₂³×C₄	C₂×C₄×C₄₁	1	2	yes	—
204	C₂³×C₄	C₂×C₄×C₄₁	1	4	yes	—
205	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
206	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
207	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
208	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
209	C₂²×C₈	—	2	4	no	—
210	C₂²×C₈	—	2	4	no	—
211	C₂²×C₈	—	2	8	no	—
212	C₂²×C₈	—	2	4	no	—
213	C₂²×C₈	D₄×C₄₁	1	8	yes	complemented
214	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
215	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
216	C₄×D₄	—	2	16	no	—
217	C₄×D₄	—	2	8	no	—
218	C₄×D₄	—	2	8	no	—
219	C₂×C₄⋊C₄	—	2	4	no	—
220	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	4	yes	—
221	C₂×C₂²⋊C₄	—	2	8	no	—
222	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	8	yes	—
223	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
224	C₂×C₄²	D₄×C₄₁	1	4	yes	—
225	C₂×C₄²	D₄×C₄₁	1	4	yes	—
226	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
227	C₄⋊C₈	—	2	8	no	—
228	C₂²⋊C₈	—	2	32	no	—
229	#97	—	2	8	no	—
230	C₂⁴	—	2	4	no	—
231	C₂⁴	—	2	8	no	—
232	C₂⁴	—	2	4	no	—
233	C₂⁴	—	2	8	no	—
234	C₂⁴	M₁₆×C₄₁	1	8	yes	—
235	C₂⁴	C₂²×C₄×C₄₁	1	4	yes	—
236	C₂⁴	C₂²×C₄×C₄₁	1	1	yes	characteristic
237	C₂×D₄	—	2	32	no	—
238	C₂×D₄	—	2	16	no	—
239	C₂×D₄	—	2	8	no	—
240	C₂²×C₄	—	2	4	no	—
241	C₂²×C₄	—	2	4	no	—
242	C₂²×C₄	—	2	4	no	—
243	C₂²×C₄	—	2	8	no	—
244	C₂²×C₄	—	2	8	no	—
245	C₂²×C₄	—	2	16	no	—
246	C₂²×C₄	—	2	8	no	—
247	C₂²×C₄	—	2	4	no	—
248	C₂²×C₄	—	2	4	no	—
249	C₂²×C₄	—	2	8	no	—
250	C₂²×C₄	—	4	16	no	—
251	C₂²×C₄	—	4	8	no	—
252	C₂²×C₄	—	4	8	no	—
253	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
254	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
255	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
256	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
257	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
258	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
259	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
260	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
261	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
262	C₂²×C₄	#41×C₄₁	1	4	yes	—
263	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
264	C₂×C₈	—	2	16	no	—
265	C₂×C₈	—	2	4	no	—
266	C₂×C₈	—	2	4	no	—
267	C₂×C₈	—	2	8	no	—
268	C₂×C₈	—	2	4	no	—
269	C₂×C₈	—	4	8	no	—
270	C₂×C₈	C₂×D₄×C₄₁	1	8	yes	complemented
271	C₄⋊C₄	—	2	8	no	—
272	C₂²⋊C₄	—	2	16	no	—
273	C₄²	C₂²⋊C₄×C₄₁	1	8	yes	—
274	C₄²	C₂×D₄×C₄₁	1	4	yes	—
275	C₄²	C₂×D₄×C₄₁	1	4	yes	—
276	C₂³	—	2	4	no	—
277	C₂³	—	2	8	no	—
278	C₂³	—	2	4	no	—
279	C₂³	—	2	8	no	—
280	C₂³	—	2	16	no	—
281	C₂³	—	2	32	no	—
282	C₂³	—	4	8	no	—
283	C₂³	—	4	8	no	—
284	C₂³	—	4	16	no	—
285	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
286	C₂³	C₄×D₄×C₄₁	1	4	yes	—
287	C₂³	C₂×M₁₆×C₄₁	1	8	yes	—
288	C₂³	C₂×M₁₆×C₄₁	1	4	yes	—
289	C₂³	#131×C₄₁	1	4	yes	—
290	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
291	D₄	—	2	32	no	—
292	C₂×C₄	—	2	4	no	—
293	C₂×C₄	—	2	4	no	—
294	C₂×C₄	—	2	8	no	—
295	C₂×C₄	—	2	8	no	—
296	C₂×C₄	—	2	4	no	—
297	C₂×C₄	—	2	8	no	—
298	C₂×C₄	—	4	8	no	—
299	C₂×C₄	—	4	8	no	—
300	C₂×C₄	—	4	4	no	—
301	C₂×C₄	—	4	4	no	—
302	C₂×C₄	—	4	16	no	—
303	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
304	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
305	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
306	C₂×C₄	C₄×D₄×C₄₁	1	4	yes	—
307	C₂×C₄	#121×C₄₁	1	8	yes	—
308	C₂×C₄	#124×C₄₁	1	4	yes	—
309	C₂×C₄	#127×C₄₁	1	4	yes	—
310	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
311	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
312	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
313	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
314	C₈	—	2	8	no	—
315	C₈	—	4	4	no	—
316	C₂²	—	2	8	no	—
317	C₂²	—	2	16	no	—
318	C₂²	—	4	4	no	—
319	C₂²	—	4	4	no	—
320	C₂²	—	4	8	no	—
321	C₂²	—	4	32	no	—
322	C₂²	C₄₁×#390	1	4	yes	—
323	C₂²	C₄₁×#407	1	4	yes	—
324	C₂²	C₄₁×#408	1	4	yes	—
325	C₂²	C₄₁×#435	1	16	yes	—
326	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
327	C₂²	C₂×C₄×D₄×C₄₁	1	2	yes	—
328	C₂²	C₂²×M₁₆×C₄₁	1	2	yes	—
329	C₂²	C₂×#131×C₄₁	1	2	yes	—
330	C₄	—	2	4	no	—
331	C₄	—	2	4	no	—
332	C₄	—	4	4	no	—
333	C₄	C₄₁×#390	1	4	yes	—
334	C₄	C₂×#121×C₄₁	1	2	yes	—
335	C₄	C₂×#124×C₄₁	1	1	yes	characteristic
336	C₄	C₂×#127×C₄₁	1	1	yes	characteristic
337	C₂	—	4	8	no	—
338	C₂	C₄₁×#1955	1	8	yes	direct product factor
339	C₂	C₂×C₄₁×#390	1	1	yes	characteristic
340	C₂	C₂×C₄₁×#407	1	1	yes	characteristic
341	C₂	C₂×C₄₁×#408	1	1	yes	characteristic
342	C₂	C₂×C₄₁×#435	1	4	yes	—

	subgroup	G/H
center	C₂³×C₄×C₄₁	C₂³
commutator	C₂³	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
socle	C₂⁴×C₄₁	C₂²×C₄
prime radical	C₂³×D₄×C₄₁	C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄⋊C₈×C₄₁	C₂	semidirect
3. C₂²×C₂²⋊C₈×C₄₁	C₂	semidirect
4. C₂²×#97×C₄₁	C₂	semidirect
5. C₄₁×#1955	C₂	direct (N × H)
18. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
20. C₂×C₂²⋊C₈×C₄₁	C₂²	semidirect
22. C₂×#97×C₄₁	C₂²	semidirect
41. C₂²×C₈×C₄₁	D₄	semidirect
98. C₂×C₈×C₄₁	C₂×D₄	semidirect
144. C₂×#1955	C₄₁	direct (N × H)
167. C₂²×C₄⋊C₈	C₂×C₄₁	semidirect
168. C₂²×C₂²⋊C₈	C₂×C₄₁	semidirect
169. C₂²×#97	C₂×C₄₁	semidirect
170. #1955	C₂×C₄₁	direct (N × H)
172. C₂×C₄₁	#1955	direct (N × H)
189. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
191. C₂×C₂²⋊C₈	C₂²×C₄₁	semidirect
193. C₂×#97	C₂²×C₄₁	semidirect
194. C₄₁	C₂×#1955	direct (N × H)
213. C₂²×C₈	D₄×C₄₁	semidirect
270. C₂×C₈	C₂×D₄×C₄₁	semidirect
338. C₂	C₄₁×#1955	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₄₁	2
C₂²×C₄⋊C₈×C₄₁	2
C₂²×C₂²⋊C₈×C₄₁	2
C₂²×#97×C₄₁	2
C₄₁×#1955	2
C₂×#1955	41

Subgroups — C2×C41×#1955 #23797387

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#1955 #23797387