Subgroups — C₄₁×#18992 #23795193

Order 10496.

1152 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×H(3,𝔽₄)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3213	C₂	1	2	yes	maximal, complemented
3	C₄₁×#3153	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1659	C₂	1	4	yes	maximal, complemented
5	C₄₁×#1655	C₂	1	4	yes	maximal, complemented
6	C₄₁×#1533	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1527	C₂	1	2	yes	maximal, complemented
8	C₂×#137×C₄₁	—	2	1	no	—
9	C₂×AGL(1,ℤ/8)×C₄₁	—	2	1	no	—
10	C₄₁×H(3,𝔽₄)	—	2	4	no	—
11	C₄₁×H(3,𝔽₄)	—	2	2	no	—
12	C₄₁×H(3,𝔽₄)	C₂²	1	4	yes	—
13	C₄₁×#532	C₂²	1	1	yes	characteristic, complemented
14	C₂×#124×C₄₁	—	2	1	no	—
15	C₂×#124×C₄₁	—	2	2	no	—
16	C₂×#124×C₄₁	C₂²	1	2	yes	—
17	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×#120×C₄₁	—	2	1	no	—
19	C₂×#120×C₄₁	—	2	2	no	—
20	C₄₁×#497	C₂²	1	2	yes	complemented
21	C₄₁×#496	C₂²	1	2	yes	complemented
22	C₄₁×#496	C₂²	1	4	yes	complemented
23	C₄₁×#495	—	2	2	no	—
24	C₄₁×#489	C₂²	1	4	yes	complemented
25	C₄₁×#463	—	2	4	no	—
26	C₄₁×#448	—	2	2	no	—
27	C₄₁×#447	—	2	2	no	—
28	C₄₁×#432	C₂²	1	2	yes	complemented
29	C₄×M₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
30	C₄₁×#329	C₂²	1	8	yes	complemented
31	C₄₁×#329	C₂²	1	4	yes	complemented
32	C₂⁵×C₄₁	—	2	1	no	—
33	C₂×#41×C₄₁	—	2	1	no	—
34	C₂²×Q₈×C₄₁	D₄	1	1	yes	characteristic
35	C₂²×Q₈×C₄₁	D₄	1	2	yes	—
36	C₂²×D₄×C₄₁	—	2	2	no	—
37	C₂²×D₄×C₄₁	—	2	1	no	—
38	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
39	C₂²×D₄×C₄₁	D₄	1	2	yes	—
40	#137×C₄₁	—	4	4	no	—
41	AGL(1,ℤ/8)×C₄₁	—	4	4	no	—
42	C₂×Q₁₆×C₄₁	—	2	2	no	—
43	C₂×SD₁₆×C₄₁	—	2	2	no	—
44	C₂×SD₁₆×C₄₁	—	2	2	no	—
45	C₂×SD₁₆×C₄₁	—	2	4	no	—
46	C₂×D₈×C₄₁	—	2	2	no	—
47	C₂×D₈×C₄₁	—	2	4	no	—
48	C₂×M₁₆×C₄₁	—	2	1	no	—
49	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic, complemented
50	#127×C₄₁	C₂³	1	1	yes	characteristic, complemented
51	#124×C₄₁	—	2	8	no	—
52	#124×C₄₁	—	2	4	no	—
53	#124×C₄₁	—	2	8	no	—
54	#124×C₄₁	—	2	4	no	—
55	#124×C₄₁	—	2	2	no	—
56	#124×C₄₁	—	2	2	no	—
57	#124×C₄₁	—	2	2	no	—
58	#124×C₄₁	—	2	1	no	—
59	#124×C₄₁	D₄	1	4	yes	—
60	#124×C₄₁	D₄	1	2	yes	—
61	#124×C₄₁	C₂³	1	4	yes	—
62	#124×C₄₁	C₂³	1	2	yes	—
63	#121×C₄₁	—	2	2	no	—
64	#120×C₄₁	—	2	8	no	—
65	#120×C₄₁	—	2	4	no	—
66	#120×C₄₁	—	2	8	no	—
67	#120×C₄₁	—	2	4	no	—
68	C₄×D₄×C₄₁	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
74	C₂×C₄²×C₄₁	—	2	1	no	—
75	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
76	C₄⋊C₈×C₄₁	—	2	2	no	—
77	#103×C₄₁	—	2	4	no	—
78	#102×C₄₁	—	2	4	no	—
79	C₂²⋊C₈×C₄₁	—	2	2	no	—
80	#97×C₄₁	C₂³	1	2	yes	complemented
81	#97×C₄₁	C₂³	1	4	yes	complemented
82	C₄×C₈×C₄₁	—	2	1	no	—
83	C₂⁴×C₄₁	—	2	4	no	—
84	C₂⁴×C₄₁	—	2	1	no	—
85	C₂⁴×C₄₁	—	2	2	no	—
86	C₂⁴×C₄₁	—	8	4	no	—
87	C₂⁴×C₄₁	—	8	2	no	—
88	#41×C₄₁	—	4	2	no	—
89	#41×C₄₁	—	4	2	no	—
90	C₂×Q₈×C₄₁	—	2	2	no	—
91	C₂×Q₈×C₄₁	—	2	1	no	—
92	C₂×Q₈×C₄₁	—	2	1	no	—
93	C₂×Q₈×C₄₁	—	4	2	no	—
94	C₂×Q₈×C₄₁	—	8	2	no	—
95	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
96	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
97	C₂×D₄×C₄₁	—	2	4	no	—
98	C₂×D₄×C₄₁	—	2	8	no	—
99	C₂×D₄×C₄₁	—	2	2	no	—
100	C₂×D₄×C₄₁	—	2	1	no	—
101	C₂×D₄×C₄₁	—	2	2	no	—
102	C₂×D₄×C₄₁	—	2	1	no	—
103	C₂×D₄×C₄₁	—	4	2	no	—
104	C₂×D₄×C₄₁	—	4	1	no	—
105	C₂×D₄×C₄₁	—	8	2	no	—
106	C₂×D₄×C₄₁	—	8	4	no	—
107	C₂×D₄×C₄₁	—	8	2	no	—
108	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
109	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₄₁	—	2	2	no	—
111	C₂²×C₄×C₄₁	—	2	1	no	—
112	C₂²×C₄×C₄₁	—	4	1	no	—
113	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
115	Q₁₆×C₄₁	—	4	4	no	—
116	SD₁₆×C₄₁	—	4	4	no	—
117	SD₁₆×C₄₁	—	4	4	no	—
118	SD₁₆×C₄₁	—	8	4	no	—
119	D₈×C₄₁	—	4	4	no	—
120	D₈×C₄₁	—	8	4	no	—
121	M₁₆×C₄₁	—	2	4	no	—
122	C₂×C₈×C₄₁	—	2	2	no	—
123	C₂×C₈×C₄₁	—	2	4	no	—
124	C₄⋊C₄×C₄₁	—	2	2	no	—
125	C₂²⋊C₄×C₄₁	—	2	8	no	—
126	C₂²⋊C₄×C₄₁	—	2	4	no	—
127	C₂²⋊C₄×C₄₁	—	2	4	no	—
128	C₂²⋊C₄×C₄₁	—	2	4	no	—
129	C₂²⋊C₄×C₄₁	—	2	4	no	—
130	C₂²⋊C₄×C₄₁	—	2	4	no	—
131	C₂²⋊C₄×C₄₁	—	2	4	no	—
132	C₂²⋊C₄×C₄₁	—	2	4	no	—
133	C₂²⋊C₄×C₄₁	—	4	2	no	—
134	C₄²×C₄₁	—	2	4	no	—
135	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₄₁	C₂×D₄	1	2	yes	—
137	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
138	C₂³×C₄₁	—	2	2	no	—
139	C₂³×C₄₁	—	2	4	no	—
140	C₂³×C₄₁	—	4	4	no	—
141	C₂³×C₄₁	—	4	4	no	—
142	C₂³×C₄₁	—	4	4	no	—
143	C₂³×C₄₁	—	4	2	no	—
144	C₂³×C₄₁	—	4	4	no	—
145	C₂³×C₄₁	—	4	1	no	—
146	C₂³×C₄₁	—	8	4	no	—
147	C₂³×C₄₁	—	8	8	no	—
148	C₂³×C₄₁	—	8	16	no	—
149	C₂³×C₄₁	#120	1	1	yes	characteristic
150	Q₈×C₄₁	—	4	2	no	—
151	Q₈×C₄₁	—	4	4	no	—
152	Q₈×C₄₁	—	4	1	no	—
153	Q₈×C₄₁	—	4	1	no	—
154	Q₈×C₄₁	—	8	1	no	—
155	Q₈×C₄₁	—	8	2	no	—
156	D₄×C₄₁	—	4	2	no	—
157	D₄×C₄₁	—	4	4	no	—
158	D₄×C₄₁	—	4	1	no	—
159	D₄×C₄₁	—	4	4	no	—
160	D₄×C₄₁	—	4	1	no	—
161	D₄×C₄₁	—	8	1	no	—
162	D₄×C₄₁	—	8	2	no	—
163	D₄×C₄₁	—	8	4	no	—
164	D₄×C₄₁	—	8	8	no	—
165	D₄×C₄₁	—	8	2	no	—
166	C₂×C₄×C₄₁	—	2	2	no	—
167	C₂×C₄×C₄₁	—	2	2	no	—
168	C₂×C₄×C₄₁	—	2	4	no	—
169	C₂×C₄×C₄₁	—	4	2	no	—
170	C₂×C₄×C₄₁	—	4	4	no	—
171	C₂×C₄×C₄₁	—	4	2	no	—
172	C₂×C₄×C₄₁	—	4	1	no	—
173	C₂×C₄×C₄₁	—	8	2	no	—
174	C₂×C₄×C₄₁	#120	1	2	yes	—
175	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
176	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
177	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
178	C₈×C₄₁	—	2	4	no	—
179	C₈×C₄₁	—	4	4	no	—
180	#18992	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₂²×C₄₁	—	2	2	no	—
182	C₂²×C₄₁	—	4	2	no	—
183	C₂²×C₄₁	—	4	4	no	—
184	C₂²×C₄₁	—	4	4	no	—
185	C₂²×C₄₁	—	4	4	no	—
186	C₂²×C₄₁	—	4	4	no	—
187	C₂²×C₄₁	—	8	4	no	—
188	C₂²×C₄₁	—	8	8	no	—
189	C₂²×C₄₁	—	8	16	no	—
190	C₂²×C₄₁	—	8	1	no	—
191	C₂²×C₄₁	—	8	2	no	—
192	C₂²×C₄₁	#453	1	2	yes	—
193	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
194	C₄×C₄₁	—	2	1	no	—
195	C₄×C₄₁	—	2	1	no	—
196	C₄×C₄₁	—	2	2	no	—
197	C₄×C₄₁	—	2	2	no	—
198	C₄×C₄₁	—	4	2	no	—
199	C₄×C₄₁	—	4	4	no	—
200	C₄×C₄₁	—	8	1	no	—
201	C₂×H(3,𝔽₄)	C₂×C₄₁	1	1	yes	characteristic, complemented
202	#3213	C₂×C₄₁	1	2	yes	complemented
203	#3153	C₂×C₄₁	1	1	yes	characteristic, complemented
204	#1659	C₂×C₄₁	1	4	yes	complemented
205	#1655	C₂×C₄₁	1	4	yes	complemented
206	#1533	C₂×C₄₁	1	1	yes	characteristic, complemented
207	#1527	C₂×C₄₁	1	2	yes	complemented
208	C₂×C₄₁	—	2	2	no	—
209	C₂×C₄₁	—	8	2	no	—
210	C₂×C₄₁	—	8	4	no	—
211	C₂×C₄₁	—	16	1	no	—
212	C₂×C₄₁	C₂×#453	1	1	yes	characteristic
213	C₂×C₄₁	#3019	1	2	yes	—
214	C₂×#137	—	2	1	no	—
215	C₂×AGL(1,ℤ/8)	—	2	1	no	—
216	H(3,𝔽₄)	—	2	4	no	—
217	H(3,𝔽₄)	—	2	2	no	—
218	H(3,𝔽₄)	C₂²×C₄₁	1	4	yes	—
219	#532	C₂²×C₄₁	1	1	yes	characteristic, complemented
220	C₂×#124	—	2	1	no	—
221	C₂×#124	—	2	2	no	—
222	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
223	C₂×#124	C₂²×C₄₁	1	2	yes	—
224	C₂×#120	—	2	1	no	—
225	C₂×#120	—	2	2	no	—
226	#497	C₂²×C₄₁	1	2	yes	complemented
227	#496	C₂²×C₄₁	1	2	yes	complemented
228	#496	C₂²×C₄₁	1	4	yes	complemented
229	#495	—	2	2	no	—
230	#489	C₂²×C₄₁	1	4	yes	complemented
231	#463	—	2	4	no	—
232	#448	—	2	2	no	—
233	#447	—	2	2	no	—
234	#432	C₂²×C₄₁	1	2	yes	complemented
235	C₄×M₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
236	#329	C₂²×C₄₁	1	8	yes	complemented
237	#329	C₂²×C₄₁	1	4	yes	complemented
238	C₄₁	#18992	1	1	yes	characteristic, direct product factor, Sylow
239	C₂⁵	—	2	1	no	—
240	C₂×#41	—	2	1	no	—
241	C₂²×Q₈	D₄×C₄₁	1	1	yes	characteristic
242	C₂²×Q₈	D₄×C₄₁	1	2	yes	—
243	C₂²×D₄	—	2	2	no	—
244	C₂²×D₄	—	2	1	no	—
245	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
246	C₂²×D₄	D₄×C₄₁	1	2	yes	—
247	#137	—	4	4	no	—
248	AGL(1,ℤ/8)	—	4	4	no	—
249	C₂×Q₁₆	—	2	2	no	—
250	C₂×SD₁₆	—	2	2	no	—
251	C₂×SD₁₆	—	2	2	no	—
252	C₂×SD₁₆	—	2	4	no	—
253	C₂×D₈	—	2	2	no	—
254	C₂×D₈	—	2	4	no	—
255	C₂×M₁₆	—	2	1	no	—
256	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic, complemented
257	#127	C₂³×C₄₁	1	1	yes	characteristic, complemented
258	#124	—	2	8	no	—
259	#124	—	2	4	no	—
260	#124	—	2	8	no	—
261	#124	—	2	4	no	—
262	#124	—	2	2	no	—
263	#124	—	2	2	no	—
264	#124	—	2	2	no	—
265	#124	—	2	1	no	—
266	#124	D₄×C₄₁	1	4	yes	—
267	#124	D₄×C₄₁	1	2	yes	—
268	#124	C₂³×C₄₁	1	4	yes	—
269	#124	C₂³×C₄₁	1	2	yes	—
270	#121	—	2	2	no	—
271	#120	—	2	8	no	—
272	#120	—	2	4	no	—
273	#120	—	2	8	no	—
274	#120	—	2	4	no	—
275	C₄×D₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	—	2	1	no	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₄²	—	2	1	no	—
282	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
283	C₄⋊C₈	—	2	2	no	—
284	#103	—	2	4	no	—
285	#102	—	2	4	no	—
286	C₂²⋊C₈	—	2	2	no	—
287	#97	C₂³×C₄₁	1	2	yes	complemented
288	#97	C₂³×C₄₁	1	4	yes	complemented
289	C₄×C₈	—	2	1	no	—
290	C₂⁴	—	2	4	no	—
291	C₂⁴	—	2	1	no	—
292	C₂⁴	—	2	2	no	—
293	C₂⁴	—	8	4	no	—
294	C₂⁴	—	8	2	no	—
295	#41	—	4	2	no	—
296	#41	—	4	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	1	no	—
299	C₂×Q₈	—	2	1	no	—
300	C₂×Q₈	—	4	2	no	—
301	C₂×Q₈	—	8	2	no	—
302	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
303	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	2	8	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	1	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	1	no	—
310	C₂×D₄	—	4	2	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂×D₄	—	8	2	no	—
313	C₂×D₄	—	8	4	no	—
314	C₂×D₄	—	8	2	no	—
315	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
316	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	4	1	no	—
320	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
322	Q₁₆	—	4	4	no	—
323	SD₁₆	—	4	4	no	—
324	SD₁₆	—	4	4	no	—
325	SD₁₆	—	8	4	no	—
326	D₈	—	4	4	no	—
327	D₈	—	8	4	no	—
328	M₁₆	—	2	4	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	4	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₂²⋊C₄	—	2	8	no	—
333	C₂²⋊C₄	—	2	4	no	—
334	C₂²⋊C₄	—	2	4	no	—
335	C₂²⋊C₄	—	2	4	no	—
336	C₂²⋊C₄	—	2	4	no	—
337	C₂²⋊C₄	—	2	4	no	—
338	C₂²⋊C₄	—	2	4	no	—
339	C₂²⋊C₄	—	2	4	no	—
340	C₂²⋊C₄	—	4	2	no	—
341	C₄²	—	2	4	no	—
342	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
343	C₄²	C₂×D₄×C₄₁	1	2	yes	—
344	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
345	C₂³	—	2	2	no	—
346	C₂³	—	2	4	no	—
347	C₂³	—	4	4	no	—
348	C₂³	—	4	4	no	—
349	C₂³	—	4	4	no	—
350	C₂³	—	4	2	no	—
351	C₂³	—	4	4	no	—
352	C₂³	—	4	1	no	—
353	C₂³	—	8	4	no	—
354	C₂³	—	8	8	no	—
355	C₂³	—	8	16	no	—
356	C₂³	#120×C₄₁	1	1	yes	characteristic
357	Q₈	—	4	2	no	—
358	Q₈	—	4	4	no	—
359	Q₈	—	4	1	no	—
360	Q₈	—	4	1	no	—
361	Q₈	—	8	1	no	—
362	Q₈	—	8	2	no	—
363	D₄	—	4	2	no	—
364	D₄	—	4	4	no	—
365	D₄	—	4	1	no	—
366	D₄	—	4	4	no	—
367	D₄	—	4	1	no	—
368	D₄	—	8	1	no	—
369	D₄	—	8	2	no	—
370	D₄	—	8	4	no	—
371	D₄	—	8	8	no	—
372	D₄	—	8	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	8	2	no	—
381	C₂×C₄	#120×C₄₁	1	2	yes	—
382	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
383	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
384	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
385	C₈	—	2	4	no	—
386	C₈	—	4	4	no	—
387	C₂²	—	2	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	4	no	—
390	C₂²	—	4	4	no	—
391	C₂²	—	4	4	no	—
392	C₂²	—	4	4	no	—
393	C₂²	—	8	4	no	—
394	C₂²	—	8	8	no	—
395	C₂²	—	8	16	no	—
396	C₂²	—	8	1	no	—
397	C₂²	—	8	2	no	—
398	C₂²	C₄₁×#453	1	2	yes	—
399	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	2	no	—
403	C₄	—	2	2	no	—
404	C₄	—	4	2	no	—
405	C₄	—	4	4	no	—
406	C₄	—	8	1	no	—
407	C₂	—	2	2	no	—
408	C₂	—	8	2	no	—
409	C₂	—	8	4	no	—
410	C₂	—	16	1	no	—
411	C₂	C₂×C₄₁×#453	1	1	yes	characteristic
412	C₂	C₄₁×#3019	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₁
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×H(3,𝔽₄)	C₂	semidirect
2. C₄₁×#3213	C₂	semidirect
3. C₄₁×#3153	C₂	semidirect
4. C₄₁×#1659	C₂	semidirect
5. C₄₁×#1655	C₂	semidirect
6. C₄₁×#1533	C₂	semidirect
7. C₄₁×#1527	C₂	semidirect
13. C₄₁×#532	C₂²	semidirect
20. C₄₁×#497	C₂²	semidirect
21. C₄₁×#496	C₂²	semidirect
22. C₄₁×#496	C₂²	semidirect
24. C₄₁×#489	C₂²	semidirect
28. C₄₁×#432	C₂²	semidirect
29. C₄×M₁₆×C₄₁	C₂²	semidirect
30. C₄₁×#329	C₂²	semidirect
31. C₄₁×#329	C₂²	semidirect
49. C₄⋊Q₈×C₄₁	C₂³	semidirect
50. #127×C₄₁	C₂³	semidirect
80. #97×C₄₁	C₂³	semidirect
81. #97×C₄₁	C₂³	semidirect
180. #18992	C₄₁	direct (N × H)
201. C₂×H(3,𝔽₄)	C₂×C₄₁	semidirect
202. #3213	C₂×C₄₁	semidirect
203. #3153	C₂×C₄₁	semidirect
204. #1659	C₂×C₄₁	semidirect
205. #1655	C₂×C₄₁	semidirect
206. #1533	C₂×C₄₁	semidirect
207. #1527	C₂×C₄₁	semidirect
219. #532	C₂²×C₄₁	semidirect
226. #497	C₂²×C₄₁	semidirect
227. #496	C₂²×C₄₁	semidirect
228. #496	C₂²×C₄₁	semidirect
230. #489	C₂²×C₄₁	semidirect
234. #432	C₂²×C₄₁	semidirect
235. C₄×M₁₆	C₂²×C₄₁	semidirect
236. #329	C₂²×C₄₁	semidirect
237. #329	C₂²×C₄₁	semidirect
238. C₄₁	#18992	direct (N × H)
256. C₄⋊Q₈	C₂³×C₄₁	semidirect
257. #127	C₂³×C₄₁	semidirect
287. #97	C₂³×C₄₁	semidirect
288. #97	C₂³×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×H(3,𝔽₄)	2
C₄₁×#3213	2
C₄₁×#3153	2
C₄₁×#1659	2
C₄₁×#1655	2
C₄₁×#1533	2
C₄₁×#1527	2
#18992	41

Subgroups — C41×#18992 #23795193

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#18992 #23795193