Subgroups — C₄₁×#14155 #23790356

Order 10496.

1910 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#391	C₂	1	4	yes	maximal
3	C₂×C₄×C₄⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₄⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#1445	C₂	1	4	yes	maximal
6	C₄₁×C₄⋊#95	C₂	1	4	yes	maximal
7	C₂³×Q₈×C₄₁	C₂²	1	2	yes	—
8	C₂×C₄⋊Q₈×C₄₁	—	2	4	no	—
9	C₂×C₄⋊Q₈×C₄₁	—	2	4	no	—
10	C₂×C₄⋊Q₈×C₄₁	C₄	1	8	yes	complemented
11	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
12	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
15	C₂²×C₄²×C₄₁	C₂²	1	2	yes	—
16	C₂²×C₄²×C₄₁	C₂²	1	2	yes	—
17	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
18	C₄₁×#391	—	2	16	no	—
19	C₄×C₄⋊C₄×C₄₁	—	2	4	no	—
20	C₄×C₄⋊C₄×C₄₁	—	2	4	no	—
21	C₂×#95×C₄₁	C₂²	1	2	yes	—
22	C₂×#95×C₄₁	C₂²	1	2	yes	—
23	C₂×#95×C₄₁	C₂²	1	16	yes	—
24	C₂²×Q₈×C₄₁	—	2	4	no	—
25	C₂²×Q₈×C₄₁	—	2	4	no	—
26	C₂²×Q₈×C₄₁	—	2	8	no	—
27	C₂²×Q₈×C₄₁	—	2	8	no	—
28	C₂²×Q₈×C₄₁	C₂×C₄	1	8	yes	—
29	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
30	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
31	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
32	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
33	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
34	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
35	C₄⋊Q₈×C₄₁	—	2	32	no	—
36	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
37	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
38	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
39	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
40	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
41	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
42	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
43	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
44	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	8	yes	—
45	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	8	yes	—
46	C₂×C₄⋊C₄×C₄₁	D₄	1	8	yes	—
47	C₂×C₄⋊C₄×C₄₁	Q₈	1	8	yes	complemented
48	C₂×C₄²×C₄₁	—	2	4	no	—
49	C₂×C₄²×C₄₁	—	2	4	no	—
50	C₂×C₄²×C₄₁	—	2	8	no	—
51	C₂×C₄²×C₄₁	—	2	8	no	—
52	C₂×C₄²×C₄₁	C₂×C₄	1	4	yes	—
53	C₂×C₄²×C₄₁	D₄	1	4	yes	—
54	C₂×C₄²×C₄₁	D₄	1	4	yes	—
55	#95×C₄₁	—	2	4	no	—
56	#95×C₄₁	—	2	4	no	—
57	#95×C₄₁	—	2	32	no	—
58	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
59	C₂×Q₈×C₄₁	—	2	16	no	—
60	C₂×Q₈×C₄₁	—	2	32	no	—
61	C₂×Q₈×C₄₁	—	4	16	no	—
62	C₂×Q₈×C₄₁	—	4	8	no	—
63	C₂×Q₈×C₄₁	—	4	8	no	—
64	C₂²×C₄×C₄₁	—	2	4	no	—
65	C₂²×C₄×C₄₁	—	2	8	no	—
66	C₂²×C₄×C₄₁	—	2	8	no	—
67	C₂²×C₄×C₄₁	—	2	4	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	4	no	—
73	C₂²×C₄×C₄₁	—	2	4	no	—
74	C₂²×C₄×C₄₁	—	2	8	no	—
75	C₂²×C₄×C₄₁	—	2	8	no	—
76	C₂²×C₄×C₄₁	—	2	8	no	—
77	C₂²×C₄×C₄₁	C₂²×C₄	1	8	yes	—
78	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
79	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₄₁	C₂×D₄	1	8	yes	—
82	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
83	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
84	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
85	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
86	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
87	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
89	C₂²×C₄×C₄₁	C₂×Q₈	1	8	yes	—
90	C₂²×C₄×C₄₁	C₂×Q₈	1	4	yes	—
91	C₂²×C₄×C₄₁	#41	1	4	yes	—
92	C₂²×C₄×C₄₁	#41	1	4	yes	—
93	C₄⋊C₄×C₄₁	—	2	16	no	—
94	C₄⋊C₄×C₄₁	—	2	16	no	—
95	C₄⋊C₄×C₄₁	—	2	16	no	—
96	C₄⋊C₄×C₄₁	—	2	16	no	—
97	C₄²×C₄₁	—	4	8	no	—
98	C₄²×C₄₁	—	4	8	no	—
99	C₄²×C₄₁	C₂²⋊C₄	1	16	yes	—
100	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
101	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
102	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
103	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
104	C₂³×C₄₁	C₂²×Q₈	1	2	yes	—
105	C₂³×C₄₁	C₂×#41	1	2	yes	—
106	C₂³×C₄₁	C₂×#41	1	2	yes	—
107	C₂³×C₄₁	2₋¹⁺⁴	1	4	yes	—
108	Q₈×C₄₁	—	4	32	no	—
109	C₂×C₄×C₄₁	—	2	4	no	—
110	C₂×C₄×C₄₁	—	2	4	no	—
111	C₂×C₄×C₄₁	—	2	4	no	—
112	C₂×C₄×C₄₁	—	2	8	no	—
113	C₂×C₄×C₄₁	—	2	16	no	—
114	C₂×C₄×C₄₁	—	2	8	no	—
115	C₂×C₄×C₄₁	—	2	8	no	—
116	C₂×C₄×C₄₁	—	2	16	no	—
117	C₂×C₄×C₄₁	—	2	16	no	—
118	C₂×C₄×C₄₁	—	4	8	no	—
119	C₂×C₄×C₄₁	—	4	4	no	—
120	C₂×C₄×C₄₁	—	4	4	no	—
121	C₂×C₄×C₄₁	—	4	4	no	—
122	C₂×C₄×C₄₁	—	4	4	no	—
123	C₂×C₄×C₄₁	—	4	4	no	—
124	C₂×C₄×C₄₁	—	4	4	no	—
125	C₂×C₄×C₄₁	—	4	8	no	—
126	C₂×C₄×C₄₁	—	4	8	no	—
127	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
128	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
129	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
130	C₂×C₄×C₄₁	C₄×D₄	1	8	yes	—
131	C₂×C₄×C₄₁	C₄×Q₈	1	8	yes	—
132	C₂×C₄×C₄₁	#121	1	8	yes	—
133	C₂×C₄×C₄₁	C₂²⋊Q₈	1	8	yes	—
134	C₂×C₄×C₄₁	#124	1	4	yes	—
135	C₂×C₄×C₄₁	#124	1	4	yes	—
136	C₂×C₄×C₄₁	#127	1	4	yes	—
137	C₂×C₄×C₄₁	C₄⋊Q₈	1	4	yes	—
138	#14155	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
140	C₂²×C₄₁	C₂×C₄×D₄	1	2	yes	—
141	C₂²×C₄₁	C₂×C₄×Q₈	1	2	yes	—
142	C₂²×C₄₁	#519	1	2	yes	—
143	C₂²×C₄₁	C₂×#121	1	2	yes	—
144	C₂²×C₄₁	C₂×C₂²⋊Q₈	1	2	yes	—
145	C₂²×C₄₁	C₂×#124	1	1	yes	characteristic
146	C₂²×C₄₁	C₂×#124	1	1	yes	characteristic
147	C₂²×C₄₁	C₂×#127	1	1	yes	characteristic
148	C₂²×C₄₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
149	C₂²×C₄₁	#536	1	2	yes	—
150	C₂²×C₄₁	#536	1	2	yes	—
151	C₂²×C₄₁	#547	1	4	yes	—
152	C₂²×C₄₁	D₄×Q₈	1	4	yes	—
153	C₂²×C₄₁	#556	1	4	yes	—
154	C₂²×C₄₁	#557	1	4	yes	—
155	C₄×C₄₁	—	2	4	no	—
156	C₄×C₄₁	—	4	8	no	—
157	C₄×C₄₁	—	4	8	no	—
158	C₄×C₄₁	—	4	8	no	—
159	C₄×C₄₁	#390	1	8	yes	—
160	C₄×C₄₁	#391	1	8	yes	complemented
161	C₂²×C₄⋊Q₈	C₂×C₄₁	1	1	yes	characteristic
162	C₂×#391	C₂×C₄₁	1	4	yes	—
163	C₂×C₄×C₄⋊C₄	C₂×C₄₁	1	1	yes	characteristic
164	C₂×C₄×C₄⋊C₄	C₂×C₄₁	1	1	yes	characteristic
165	#1445	C₂×C₄₁	1	4	yes	—
166	C₄⋊#95	C₂×C₄₁	1	4	yes	—
167	C₂×C₄₁	C₂×#390	1	1	yes	characteristic
168	C₂×C₄₁	C₂×#391	1	1	yes	characteristic
169	C₂×C₄₁	#2310	1	1	yes	characteristic
170	C₂×C₄₁	#2365	1	4	yes	—
171	C₂×C₄₁	#2542	1	2	yes	—
172	C₂×C₄₁	#2546	1	2	yes	—
173	C₂×C₄₁	#2547	1	2	yes	—
174	C₂×C₄₁	#2568	1	2	yes	—
175	C₂³×Q₈	C₂²×C₄₁	1	2	yes	—
176	C₂×C₄⋊Q₈	—	2	4	no	—
177	C₂×C₄⋊Q₈	—	2	4	no	—
178	C₂×C₄⋊Q₈	C₄×C₄₁	1	8	yes	complemented
179	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
180	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
181	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
182	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
183	C₂²×C₄²	C₂²×C₄₁	1	2	yes	—
184	C₂²×C₄²	C₂²×C₄₁	1	2	yes	—
185	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
186	#391	—	2	16	no	—
187	C₄×C₄⋊C₄	—	2	4	no	—
188	C₄×C₄⋊C₄	—	2	4	no	—
189	C₂×#95	C₂²×C₄₁	1	16	yes	—
190	C₂×#95	C₂²×C₄₁	1	2	yes	—
191	C₂×#95	C₂²×C₄₁	1	2	yes	—
192	C₄₁	#14155	1	1	yes	characteristic, direct product factor, Sylow
193	C₂²×Q₈	—	2	4	no	—
194	C₂²×Q₈	—	2	4	no	—
195	C₂²×Q₈	—	2	8	no	—
196	C₂²×Q₈	—	2	8	no	—
197	C₂²×Q₈	C₂×C₄×C₄₁	1	8	yes	—
198	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
199	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
200	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
201	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
202	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
203	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
204	C₄⋊Q₈	—	2	32	no	—
205	C₂×C₄⋊C₄	—	2	4	no	—
206	C₂×C₄⋊C₄	—	2	4	no	—
207	C₂×C₄⋊C₄	—	2	4	no	—
208	C₂×C₄⋊C₄	—	2	4	no	—
209	C₂×C₄⋊C₄	—	2	4	no	—
210	C₂×C₄⋊C₄	—	2	4	no	—
211	C₂×C₄⋊C₄	—	2	4	no	—
212	C₂×C₄⋊C₄	—	2	4	no	—
213	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	8	yes	—
214	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	8	yes	—
215	C₂×C₄⋊C₄	D₄×C₄₁	1	8	yes	—
216	C₂×C₄⋊C₄	Q₈×C₄₁	1	8	yes	complemented
217	C₂×C₄²	—	2	4	no	—
218	C₂×C₄²	—	2	4	no	—
219	C₂×C₄²	—	2	8	no	—
220	C₂×C₄²	—	2	8	no	—
221	C₂×C₄²	C₂×C₄×C₄₁	1	4	yes	—
222	C₂×C₄²	D₄×C₄₁	1	4	yes	—
223	C₂×C₄²	D₄×C₄₁	1	4	yes	—
224	#95	—	2	4	no	—
225	#95	—	2	4	no	—
226	#95	—	2	32	no	—
227	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
228	C₂×Q₈	—	2	16	no	—
229	C₂×Q₈	—	2	32	no	—
230	C₂×Q₈	—	4	16	no	—
231	C₂×Q₈	—	4	8	no	—
232	C₂×Q₈	—	4	8	no	—
233	C₂²×C₄	—	2	4	no	—
234	C₂²×C₄	—	2	8	no	—
235	C₂²×C₄	—	2	8	no	—
236	C₂²×C₄	—	2	4	no	—
237	C₂²×C₄	—	2	4	no	—
238	C₂²×C₄	—	2	4	no	—
239	C₂²×C₄	—	2	4	no	—
240	C₂²×C₄	—	2	8	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	8	no	—
246	C₂²×C₄	C₂²×C₄×C₄₁	1	8	yes	—
247	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
248	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
249	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
250	C₂²×C₄	C₂×D₄×C₄₁	1	8	yes	—
251	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
252	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
253	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
254	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
255	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
256	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
257	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
258	C₂²×C₄	C₂×Q₈×C₄₁	1	8	yes	—
259	C₂²×C₄	C₂×Q₈×C₄₁	1	4	yes	—
260	C₂²×C₄	#41×C₄₁	1	4	yes	—
261	C₂²×C₄	#41×C₄₁	1	4	yes	—
262	C₄⋊C₄	—	2	16	no	—
263	C₄⋊C₄	—	2	16	no	—
264	C₄⋊C₄	—	2	16	no	—
265	C₄⋊C₄	—	2	16	no	—
266	C₄²	—	4	8	no	—
267	C₄²	—	4	8	no	—
268	C₄²	C₂²⋊C₄×C₄₁	1	16	yes	—
269	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
270	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
271	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
272	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
273	C₂³	C₂²×Q₈×C₄₁	1	2	yes	—
274	C₂³	C₂×#41×C₄₁	1	2	yes	—
275	C₂³	C₂×#41×C₄₁	1	2	yes	—
276	C₂³	2₋¹⁺⁴×C₄₁	1	4	yes	—
277	Q₈	—	4	32	no	—
278	C₂×C₄	—	2	4	no	—
279	C₂×C₄	—	2	4	no	—
280	C₂×C₄	—	2	4	no	—
281	C₂×C₄	—	2	8	no	—
282	C₂×C₄	—	2	16	no	—
283	C₂×C₄	—	2	8	no	—
284	C₂×C₄	—	2	8	no	—
285	C₂×C₄	—	2	16	no	—
286	C₂×C₄	—	2	16	no	—
287	C₂×C₄	—	4	8	no	—
288	C₂×C₄	—	4	4	no	—
289	C₂×C₄	—	4	4	no	—
290	C₂×C₄	—	4	4	no	—
291	C₂×C₄	—	4	4	no	—
292	C₂×C₄	—	4	4	no	—
293	C₂×C₄	—	4	4	no	—
294	C₂×C₄	—	4	8	no	—
295	C₂×C₄	—	4	8	no	—
296	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
297	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
298	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
299	C₂×C₄	C₄×D₄×C₄₁	1	8	yes	—
300	C₂×C₄	C₄×Q₈×C₄₁	1	8	yes	—
301	C₂×C₄	#121×C₄₁	1	8	yes	—
302	C₂×C₄	C₂²⋊Q₈×C₄₁	1	8	yes	—
303	C₂×C₄	#124×C₄₁	1	4	yes	—
304	C₂×C₄	#124×C₄₁	1	4	yes	—
305	C₂×C₄	#127×C₄₁	1	4	yes	—
306	C₂×C₄	C₄⋊Q₈×C₄₁	1	4	yes	—
307	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
308	C₂²	C₂×C₄×D₄×C₄₁	1	2	yes	—
309	C₂²	C₂×C₄×Q₈×C₄₁	1	2	yes	—
310	C₂²	C₄₁×#519	1	2	yes	—
311	C₂²	C₂×#121×C₄₁	1	2	yes	—
312	C₂²	C₂×C₂²⋊Q₈×C₄₁	1	2	yes	—
313	C₂²	C₂×#124×C₄₁	1	1	yes	characteristic
314	C₂²	C₂×#124×C₄₁	1	1	yes	characteristic
315	C₂²	C₂×#127×C₄₁	1	1	yes	characteristic
316	C₂²	C₂×C₄⋊Q₈×C₄₁	1	1	yes	characteristic
317	C₂²	C₄₁×#536	1	2	yes	—
318	C₂²	C₄₁×#536	1	2	yes	—
319	C₂²	C₄₁×#547	1	4	yes	—
320	C₂²	D₄×Q₈×C₄₁	1	4	yes	—
321	C₂²	C₄₁×#556	1	4	yes	—
322	C₂²	C₄₁×#557	1	4	yes	—
323	C₄	—	2	4	no	—
324	C₄	—	4	8	no	—
325	C₄	—	4	8	no	—
326	C₄	—	4	8	no	—
327	C₄	C₄₁×#390	1	8	yes	—
328	C₄	C₄₁×#391	1	8	yes	complemented
329	C₂	C₂×C₄₁×#390	1	1	yes	characteristic
330	C₂	C₂×C₄₁×#391	1	1	yes	characteristic
331	C₂	C₄₁×#2310	1	1	yes	characteristic
332	C₂	C₄₁×#2365	1	4	yes	—
333	C₂	C₄₁×#2542	1	2	yes	—
334	C₂	C₄₁×#2546	1	2	yes	—
335	C₂	C₄₁×#2547	1	2	yes	—
336	C₂	C₄₁×#2568	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
10. C₂×C₄⋊Q₈×C₄₁	C₄	semidirect
47. C₂×C₄⋊C₄×C₄₁	Q₈	semidirect
138. #14155	C₄₁	direct (N × H)
160. C₄×C₄₁	#391	semidirect
178. C₂×C₄⋊Q₈	C₄×C₄₁	semidirect
192. C₄₁	#14155	direct (N × H)
216. C₂×C₄⋊C₄	Q₈×C₄₁	semidirect
328. C₄	C₄₁×#391	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊Q₈×C₄₁	2
C₂×C₄₁×#391	2
C₂×C₄×C₄⋊C₄×C₄₁	2
C₄₁×#1445	2
C₄₁×C₄⋊#95	2
#14155	41

Subgroups — C41×#14155 #23790356

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#14155 #23790356