Subgroups — C₄₁×#26440 #23802641

Order 10496.

738 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	C₄₁×#2551	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2365	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#2086	C₂	1	2	yes	maximal
4	C₄₁×#2057	C₂	1	2	yes	maximal
5	C₄₁×#1990	C₂	1	1	yes	maximal, characteristic
6	C₄₁×#1988	C₂	1	2	yes	maximal
7	C₄₁×#1988	C₂	1	1	yes	maximal, characteristic
8	C₄₁×#1947	C₂	1	1	yes	maximal, characteristic
9	C₄₁×#1939	C₂	1	1	yes	maximal, characteristic
10	C₄₁×#1918	C₂	1	2	yes	maximal
11	C₄×#107×C₄₁	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄⋊Q₈×C₄₁	—	2	1	no	—
13	C₂×C₄⋊Q₈×C₄₁	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₄₁	—	2	1	no	—
16	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
17	C₂×#107×C₄₁	C₂²	1	2	yes	—
18	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
22	C₄₁×#395	—	2	2	no	—
23	C₄₁×#391	—	2	1	no	—
24	C₄₁×#389	—	2	1	no	—
25	C₄₁×#389	C₂²	1	2	yes	—
26	C₄₁×#389	C₂²	1	2	yes	—
27	C₄₁×#387	—	2	2	no	—
28	C₄₁×#384	C₂²	1	1	yes	characteristic
29	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
30	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
32	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
33	C₄₁×#340	C₂²	1	1	yes	characteristic
34	C₄₁×#340	C₂²	1	1	yes	characteristic
35	C₄₁×#340	C₂²	1	2	yes	—
36	C₄₁×#340	C₂²	1	2	yes	—
37	C₄₁×#340	C₂²	1	2	yes	—
38	C₄₁×#340	C₂²	1	2	yes	—
39	C₄₁×#340	C₂²	1	2	yes	—
40	C₄₁×#336	C₂²	1	2	yes	—
41	C₂²×Q₈×C₄₁	—	2	1	no	—
42	C₂²×Q₈×C₄₁	—	2	2	no	—
43	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
44	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
46	C₄⋊Q₈×C₄₁	—	2	4	no	—
47	C₄⋊Q₈×C₄₁	—	2	2	no	—
48	C₄⋊Q₈×C₄₁	—	4	2	no	—
49	C₄⋊Q₈×C₄₁	—	4	4	no	—
50	C₄⋊Q₈×C₄₁	Q₈	1	4	yes	complemented
51	C₄×Q₈×C₄₁	—	4	4	no	—
52	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
53	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
54	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
55	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
56	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
58	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₄₁	—	2	2	no	—
67	C₂×C₄²×C₄₁	—	2	1	no	—
68	C₂×C₄²×C₄₁	—	2	1	no	—
69	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
70	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
71	#107×C₄₁	—	2	2	no	—
72	#107×C₄₁	—	4	2	no	—
73	#107×C₄₁	Q₈	1	4	yes	complemented
74	C₄⋊C₈×C₄₁	—	2	2	no	—
75	C₄⋊C₈×C₄₁	—	4	2	no	—
76	C₄×C₈×C₄₁	—	2	2	no	—
77	#95×C₄₁	—	2	1	no	—
78	#95×C₄₁	—	2	2	no	—
79	#95×C₄₁	—	2	1	no	—
80	#95×C₄₁	—	2	2	no	—
81	#95×C₄₁	—	2	2	no	—
82	#95×C₄₁	D₄	1	2	yes	—
83	C₂×Q₈×C₄₁	—	2	4	no	—
84	C₂×Q₈×C₄₁	—	4	4	no	—
85	C₂×Q₈×C₄₁	—	4	2	no	—
86	C₂×Q₈×C₄₁	—	4	4	no	—
87	C₂×Q₈×C₄₁	—	4	2	no	—
88	C₂×Q₈×C₄₁	—	8	2	no	—
89	C₂²×C₄×C₄₁	—	2	1	no	—
90	C₂²×C₄×C₄₁	—	2	1	no	—
91	C₂²×C₄×C₄₁	—	2	2	no	—
92	C₂²×C₄×C₄₁	—	2	1	no	—
93	C₂²×C₄×C₄₁	—	2	1	no	—
94	C₂²×C₄×C₄₁	—	2	2	no	—
95	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
100	C₂×C₈×C₄₁	—	2	1	no	—
101	C₂×C₈×C₄₁	—	2	1	no	—
102	C₂×C₈×C₄₁	—	2	1	no	—
103	C₂×C₈×C₄₁	—	2	2	no	—
104	C₂×C₈×C₄₁	—	2	1	no	—
105	C₂×C₈×C₄₁	—	2	2	no	—
106	C₂×C₈×C₄₁	—	2	2	no	—
107	C₂×C₈×C₄₁	—	2	1	no	—
108	C₂×C₈×C₄₁	C₂×Q₈	1	2	yes	—
109	C₄⋊C₄×C₄₁	—	2	4	no	—
110	C₄⋊C₄×C₄₁	—	2	2	no	—
111	C₄⋊C₄×C₄₁	—	2	2	no	—
112	C₄⋊C₄×C₄₁	—	2	1	no	—
113	C₄⋊C₄×C₄₁	—	2	1	no	—
114	C₄⋊C₄×C₄₁	—	2	1	no	—
115	C₄⋊C₄×C₄₁	—	2	1	no	—
116	C₄⋊C₄×C₄₁	—	2	2	no	—
117	C₄⋊C₄×C₄₁	—	2	1	no	—
118	C₄⋊C₄×C₄₁	—	2	2	no	—
119	C₄⋊C₄×C₄₁	—	4	4	no	—
120	C₄⋊C₄×C₄₁	—	4	4	no	—
121	C₄⋊C₄×C₄₁	—	4	4	no	—
122	C₄⋊C₄×C₄₁	—	4	2	no	—
123	C₄⋊C₄×C₄₁	—	8	1	no	—
124	C₄⋊C₄×C₄₁	D₈	1	4	yes	—
125	C₄⋊C₄×C₄₁	C₂×Q₈	1	2	yes	—
126	C₄⋊C₄×C₄₁	C₂×Q₈	1	2	yes	—
127	C₄⋊C₄×C₄₁	C₂×Q₈	1	4	yes	—
128	C₄⋊C₄×C₄₁	#41	1	2	yes	—
129	C₄²×C₄₁	—	2	2	no	—
130	C₄²×C₄₁	—	2	2	no	—
131	C₄²×C₄₁	—	4	4	no	—
132	C₄²×C₄₁	—	4	2	no	—
133	C₄²×C₄₁	—	4	2	no	—
134	C₄²×C₄₁	C₂×Q₈	1	2	yes	—
135	C₄²×C₄₁	#41	1	2	yes	—
136	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
137	Q₈×C₄₁	—	4	8	no	—
138	Q₈×C₄₁	—	8	8	no	—
139	C₂×C₄×C₄₁	—	2	2	no	—
140	C₂×C₄×C₄₁	—	2	1	no	—
141	C₂×C₄×C₄₁	—	2	2	no	—
142	C₂×C₄×C₄₁	—	2	1	no	—
143	C₂×C₄×C₄₁	—	2	4	no	—
144	C₂×C₄×C₄₁	—	2	2	no	—
145	C₂×C₄×C₄₁	—	2	2	no	—
146	C₂×C₄×C₄₁	—	2	2	no	—
147	C₂×C₄×C₄₁	—	2	2	no	—
148	C₂×C₄×C₄₁	—	2	2	no	—
149	C₂×C₄×C₄₁	—	2	2	no	—
150	C₂×C₄×C₄₁	—	4	1	no	—
151	C₂×C₄×C₄₁	—	4	1	no	—
152	C₂×C₄×C₄₁	—	4	2	no	—
153	C₂×C₄×C₄₁	—	4	1	no	—
154	C₂×C₄×C₄₁	—	4	2	no	—
155	C₂×C₄×C₄₁	—	4	1	no	—
156	C₂×C₄×C₄₁	—	4	1	no	—
157	C₂×C₄×C₄₁	—	4	1	no	—
158	C₂×C₄×C₄₁	—	4	2	no	—
159	C₂×C₄×C₄₁	—	4	1	no	—
160	C₂×C₄×C₄₁	—	4	1	no	—
161	C₂×C₄×C₄₁	—	4	2	no	—
162	C₂×C₄×C₄₁	—	4	2	no	—
163	C₂×C₄×C₄₁	—	4	1	no	—
164	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
165	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
166	C₂×C₄×C₄₁	C₂×D₈	1	4	yes	—
167	C₂×C₄×C₄₁	C₂×D₈	1	2	yes	—
168	C₂×C₄×C₄₁	#137	1	2	yes	—
169	C₂×C₄×C₄₁	C₂²×Q₈	1	1	yes	characteristic
170	C₂×C₄×C₄₁	C₂²×Q₈	1	1	yes	characteristic
171	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
172	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
174	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
175	C₈×C₄₁	—	2	2	no	—
176	C₈×C₄₁	—	4	1	no	—
177	C₈×C₄₁	—	4	2	no	—
178	#26440	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂²×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
180	C₂²×C₄₁	#546	1	1	yes	characteristic
181	C₂²×C₄₁	D₄×Q₈	1	1	yes	characteristic
182	C₂²×C₄₁	C₂²×D₈	1	1	yes	characteristic
183	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
184	C₂²×C₄₁	#577	1	1	yes	characteristic
185	C₂²×C₄₁	#578	1	1	yes	characteristic
186	C₄×C₄₁	—	2	2	no	—
187	C₄×C₄₁	—	2	4	no	—
188	C₄×C₄₁	—	4	2	no	—
189	C₄×C₄₁	—	4	2	no	—
190	C₄×C₄₁	—	4	2	no	—
191	C₄×C₄₁	—	4	2	no	—
192	C₄×C₄₁	—	4	4	no	—
193	C₄×C₄₁	—	8	1	no	—
194	C₄×C₄₁	—	8	2	no	—
195	C₄×C₄₁	#474	1	4	yes	—
196	C₄×C₄₁	#533	1	1	yes	characteristic
197	C₄×C₄₁	#542	1	1	yes	characteristic
198	C₄×C₄₁	#557	1	1	yes	characteristic
199	C₄×C₄₁	Q₈²	1	1	yes	characteristic
200	#2551	C₂×C₄₁	1	1	yes	characteristic
201	#2365	C₂×C₄₁	1	1	yes	characteristic
202	#2086	C₂×C₄₁	1	2	yes	—
203	#2057	C₂×C₄₁	1	2	yes	—
204	#1990	C₂×C₄₁	1	1	yes	characteristic
205	#1988	C₂×C₄₁	1	2	yes	—
206	#1988	C₂×C₄₁	1	1	yes	characteristic
207	#1947	C₂×C₄₁	1	1	yes	characteristic
208	#1939	C₂×C₄₁	1	1	yes	characteristic
209	#1918	C₂×C₄₁	1	2	yes	—
210	C₄×#107	C₂×C₄₁	1	1	yes	characteristic
211	C₂×C₄₁	#2451	1	1	yes	characteristic
212	C₂×C₄₁	C₂×#474	1	1	yes	characteristic
213	C₂×C₄₁	#3082	1	1	yes	characteristic
214	C₂×C₄₁	#3294	1	1	yes	characteristic
215	C₂×C₄₁	#3328	1	1	yes	characteristic
216	C₂×C₄₁	Q₈×D₈	1	1	yes	characteristic
217	C₂×C₄₁	#3387	1	1	yes	characteristic
218	C₂×C₄⋊Q₈	—	2	1	no	—
219	C₂×C₄⋊Q₈	C₂²×C₄₁	1	2	yes	—
220	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
221	C₂×C₄×Q₈	—	2	1	no	—
222	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
223	C₂×#107	C₂²×C₄₁	1	2	yes	—
224	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
225	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
226	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
227	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
228	#395	—	2	2	no	—
229	#391	—	2	1	no	—
230	#389	—	2	1	no	—
231	#389	C₂²×C₄₁	1	2	yes	—
232	#389	C₂²×C₄₁	1	2	yes	—
233	#387	—	2	2	no	—
234	#384	C₂²×C₄₁	1	1	yes	characteristic
235	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
236	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
237	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
238	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
239	#340	C₂²×C₄₁	1	2	yes	—
240	#340	C₂²×C₄₁	1	2	yes	—
241	#340	C₂²×C₄₁	1	1	yes	characteristic
242	#340	C₂²×C₄₁	1	2	yes	—
243	#340	C₂²×C₄₁	1	2	yes	—
244	#340	C₂²×C₄₁	1	2	yes	—
245	#340	C₂²×C₄₁	1	1	yes	characteristic
246	#336	C₂²×C₄₁	1	2	yes	—
247	C₄₁	#26440	1	1	yes	characteristic, direct product factor, Sylow
248	C₂²×Q₈	—	2	1	no	—
249	C₂²×Q₈	—	2	2	no	—
250	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
251	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
252	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
253	C₄⋊Q₈	—	2	4	no	—
254	C₄⋊Q₈	—	2	2	no	—
255	C₄⋊Q₈	—	4	2	no	—
256	C₄⋊Q₈	—	4	4	no	—
257	C₄⋊Q₈	Q₈×C₄₁	1	4	yes	complemented
258	C₄×Q₈	—	4	4	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
266	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
267	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
268	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
269	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
270	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
273	C₂×C₄²	—	2	2	no	—
274	C₂×C₄²	—	2	1	no	—
275	C₂×C₄²	—	2	1	no	—
276	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
277	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
278	#107	—	2	2	no	—
279	#107	—	4	2	no	—
280	#107	Q₈×C₄₁	1	4	yes	complemented
281	C₄⋊C₈	—	2	2	no	—
282	C₄⋊C₈	—	4	2	no	—
283	C₄×C₈	—	2	2	no	—
284	#95	—	2	1	no	—
285	#95	—	2	2	no	—
286	#95	—	2	1	no	—
287	#95	—	2	2	no	—
288	#95	—	2	2	no	—
289	#95	D₄×C₄₁	1	2	yes	—
290	C₂×Q₈	—	2	4	no	—
291	C₂×Q₈	—	4	4	no	—
292	C₂×Q₈	—	4	2	no	—
293	C₂×Q₈	—	4	4	no	—
294	C₂×Q₈	—	4	2	no	—
295	C₂×Q₈	—	8	2	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
303	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
305	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
306	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	C₂×Q₈×C₄₁	1	2	yes	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	4	4	no	—
327	C₄⋊C₄	—	4	4	no	—
328	C₄⋊C₄	—	4	4	no	—
329	C₄⋊C₄	—	4	2	no	—
330	C₄⋊C₄	—	8	1	no	—
331	C₄⋊C₄	D₈×C₄₁	1	4	yes	—
332	C₄⋊C₄	C₂×Q₈×C₄₁	1	2	yes	—
333	C₄⋊C₄	C₂×Q₈×C₄₁	1	2	yes	—
334	C₄⋊C₄	C₂×Q₈×C₄₁	1	4	yes	—
335	C₄⋊C₄	#41×C₄₁	1	2	yes	—
336	C₄²	—	2	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	4	4	no	—
339	C₄²	—	4	2	no	—
340	C₄²	—	4	2	no	—
341	C₄²	C₂×Q₈×C₄₁	1	2	yes	—
342	C₄²	#41×C₄₁	1	2	yes	—
343	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
344	Q₈	—	4	8	no	—
345	Q₈	—	8	8	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
372	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
373	C₂×C₄	C₂×D₈×C₄₁	1	4	yes	—
374	C₂×C₄	C₂×D₈×C₄₁	1	2	yes	—
375	C₂×C₄	#137×C₄₁	1	2	yes	—
376	C₂×C₄	C₂²×Q₈×C₄₁	1	1	yes	characteristic
377	C₂×C₄	C₂²×Q₈×C₄₁	1	1	yes	characteristic
378	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
379	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
380	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
381	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
382	C₈	—	2	2	no	—
383	C₈	—	4	1	no	—
384	C₈	—	4	2	no	—
385	C₂²	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
386	C₂²	C₄₁×#546	1	1	yes	characteristic
387	C₂²	D₄×Q₈×C₄₁	1	1	yes	characteristic
388	C₂²	C₂²×D₈×C₄₁	1	1	yes	characteristic
389	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
390	C₂²	C₄₁×#577	1	1	yes	characteristic
391	C₂²	C₄₁×#578	1	1	yes	characteristic
392	C₄	—	2	4	no	—
393	C₄	—	2	2	no	—
394	C₄	—	4	2	no	—
395	C₄	—	4	4	no	—
396	C₄	—	4	2	no	—
397	C₄	—	4	2	no	—
398	C₄	—	4	2	no	—
399	C₄	—	8	2	no	—
400	C₄	—	8	1	no	—
401	C₄	C₄₁×#474	1	4	yes	—
402	C₄	C₄₁×#533	1	1	yes	characteristic
403	C₄	C₄₁×#542	1	1	yes	characteristic
404	C₄	C₄₁×#557	1	1	yes	characteristic
405	C₄	Q₈²×C₄₁	1	1	yes	characteristic
406	C₂	C₄₁×#2451	1	1	yes	characteristic
407	C₂	C₂×C₄₁×#474	1	1	yes	characteristic
408	C₂	C₄₁×#3082	1	1	yes	characteristic
409	C₂	C₄₁×#3294	1	1	yes	characteristic
410	C₂	C₄₁×#3328	1	1	yes	characteristic
411	C₂	Q₈×D₈×C₄₁	1	1	yes	characteristic
412	C₂	C₄₁×#3387	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₄×C₄⋊C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
50. C₄⋊Q₈×C₄₁	Q₈	semidirect
73. #107×C₄₁	Q₈	semidirect
178. #26440	C₄₁	direct (N × H)
247. C₄₁	#26440	direct (N × H)
257. C₄⋊Q₈	Q₈×C₄₁	semidirect
280. #107	Q₈×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#2551	2
C₄₁×#2365	2
C₄₁×#2086	2
C₄₁×#2057	2
C₄₁×#1990	2
C₄₁×#1988	2
C₄₁×#1947	2
C₄₁×#1939	2
C₄₁×#1918	2
C₄×#107×C₄₁	2
#26440	41

Subgroups — C41×#26440 #23802641

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#26440 #23802641