Subgroups — C₄₁×#33372 #23809573

Order 10496.

1176 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3499	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2889	C₂	1	2	yes	maximal, complemented
3	C₄₁×#2135	C₂	1	2	yes	maximal, complemented
4	C₄₁×#2133	C₂	1	4	yes	maximal, complemented
5	C₄₁×#2132	C₂	1	2	yes	maximal, complemented
6	C₂×C₄₁×#356	C₂	1	4	yes	maximal, complemented
7	C₂×2₋¹⁺⁴×C₄₁	C₄	1	1	yes	characteristic
8	C₂×2₋¹⁺⁴×C₄₁	C₂²	1	1	yes	characteristic
9	C₄₁×#568	—	2	2	no	—
10	D₄×Q₈×C₄₁	—	2	2	no	—
11	C₄₁×#547	—	2	4	no	—
12	C₄₁×#547	—	2	2	no	—
13	C₄₁×#536	C₄	1	1	yes	characteristic
14	C₄₁×#536	C₄	1	2	yes	—
15	C₄₁×#536	C₂²	1	1	yes	characteristic
16	C₄₁×#536	C₂²	1	2	yes	—
17	C₄₁×#532	C₄	1	2	yes	—
18	C₄₁×#532	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊Q₈×C₄₁	C₄	1	1	yes	characteristic
20	C₂×C₄⋊Q₈×C₄₁	C₂²	1	2	yes	—
21	C₄×#41×C₄₁	C₄	1	1	yes	characteristic
22	C₄₁×#413	—	2	4	no	—
23	C₄₁×#413	C₂²	1	4	yes	—
24	C₂×#101×C₄₁	—	2	2	no	—
25	C₂×#101×C₄₁	C₂²	1	8	yes	—
26	C₄₁×#356	C₂²	1	4	yes	—
27	C₄₁×#356	C₂²	1	8	yes	—
28	C₄₁×#355	C₂²	1	4	yes	—
29	2₋¹⁺⁴×C₄₁	—	4	4	no	—
30	2₋¹⁺⁴×C₄₁	—	4	4	no	—
31	C₂×#41×C₄₁	—	2	2	no	—
32	C₂×#41×C₄₁	—	2	1	no	—
33	C₂×#41×C₄₁	C₂×C₄	1	2	yes	—
34	C₂×#41×C₄₁	C₂×C₄	1	1	yes	characteristic
35	C₂×#41×C₄₁	C₂×C₄	1	2	yes	—
36	C₂×#41×C₄₁	C₂×C₄	1	1	yes	characteristic
37	C₂×#41×C₄₁	D₄	1	4	yes	—
38	C₂×#41×C₄₁	D₄	1	2	yes	—
39	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
40	C₂²×Q₈×C₄₁	—	2	1	no	—
41	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
42	C₂²×Q₈×C₄₁	C₂×C₄	1	2	yes	—
43	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
44	C₂²×Q₈×C₄₁	D₄	1	2	yes	—
45	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
46	#131×C₄₁	—	4	8	no	—
47	C₂×M₁₆×C₄₁	—	2	4	no	—
48	C₂×M₁₆×C₄₁	—	2	8	no	—
49	C₄⋊Q₈×C₄₁	—	2	2	no	—
50	C₄⋊Q₈×C₄₁	—	2	4	no	—
51	C₄⋊Q₈×C₄₁	C₂×C₄	1	2	yes	—
52	C₄⋊Q₈×C₄₁	C₂×C₄	1	2	yes	—
53	C₄⋊Q₈×C₄₁	C₂×C₄	1	2	yes	—
54	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
55	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
56	#127×C₄₁	C₂×C₄	1	1	yes	characteristic
57	#124×C₄₁	C₂×C₄	1	2	yes	—
58	#124×C₄₁	C₂×C₄	1	2	yes	—
59	#124×C₄₁	C₂×C₄	1	1	yes	characteristic
60	#124×C₄₁	C₂³	1	1	yes	characteristic
61	#123×C₄₁	—	2	4	no	—
62	#123×C₄₁	—	2	2	no	—
63	#123×C₄₁	—	2	2	no	—
64	#123×C₄₁	—	2	4	no	—
65	C₂²⋊Q₈×C₄₁	—	2	2	no	—
66	C₂²⋊Q₈×C₄₁	—	2	4	no	—
67	C₂²⋊Q₈×C₄₁	—	2	4	no	—
68	C₂²⋊Q₈×C₄₁	—	2	2	no	—
69	#121×C₄₁	—	2	4	no	—
70	#121×C₄₁	—	2	2	no	—
71	C₄×Q₈×C₄₁	—	2	1	no	—
72	C₄×D₄×C₄₁	—	2	2	no	—
73	C₄×D₄×C₄₁	—	2	1	no	—
74	C₄×D₄×C₄₁	—	2	4	no	—
75	C₄×D₄×C₄₁	—	2	2	no	—
76	#117×C₄₁	C₂×C₄	1	1	yes	characteristic
77	#117×C₄₁	C₂×C₄	1	2	yes	—
78	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
79	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
80	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
82	#101×C₄₁	—	2	8	no	—
83	#101×C₄₁	C₂³	1	8	yes	—
84	#100×C₄₁	—	2	4	no	—
85	#41×C₄₁	—	2	8	no	—
86	#41×C₄₁	—	2	4	no	—
87	#41×C₄₁	—	4	2	no	—
88	#41×C₄₁	—	4	4	no	—
89	#41×C₄₁	—	4	8	no	—
90	#41×C₄₁	—	4	4	no	—
91	#41×C₄₁	—	4	2	no	—
92	#41×C₄₁	—	4	8	no	—
93	#41×C₄₁	—	4	4	no	—
94	C₂×Q₈×C₄₁	—	2	2	no	—
95	C₂×Q₈×C₄₁	—	2	1	no	—
96	C₂×Q₈×C₄₁	—	4	4	no	—
97	C₂×Q₈×C₄₁	—	4	2	no	—
98	C₂×Q₈×C₄₁	—	4	4	no	—
99	C₂×Q₈×C₄₁	—	4	2	no	—
100	C₂×Q₈×C₄₁	—	4	4	no	—
101	C₂×Q₈×C₄₁	—	4	4	no	—
102	C₂×Q₈×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
103	C₂×Q₈×C₄₁	C₂²⋊C₄	1	2	yes	—
104	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
105	C₂×Q₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
106	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
107	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
108	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
109	C₂×D₄×C₄₁	—	2	2	no	—
110	C₂×D₄×C₄₁	—	2	1	no	—
111	C₂×D₄×C₄₁	—	2	2	no	—
112	C₂×D₄×C₄₁	C₂²⋊C₄	1	2	yes	—
113	C₂×D₄×C₄₁	C₂²⋊C₄	1	4	yes	—
114	C₂×D₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
115	C₂×D₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
116	C₂×D₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
117	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₄₁	—	2	1	no	—
119	C₂²×C₄×C₄₁	—	2	2	no	—
120	C₂²×C₄×C₄₁	—	2	1	no	—
121	C₂²×C₄×C₄₁	—	2	2	no	—
122	C₂²×C₄×C₄₁	—	2	2	no	—
123	C₂²×C₄×C₄₁	—	2	1	no	—
124	C₂²×C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
125	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
126	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
128	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
129	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
130	M₁₆×C₄₁	—	2	8	no	—
131	M₁₆×C₄₁	—	4	8	no	—
132	M₁₆×C₄₁	—	4	4	no	—
133	C₂×C₈×C₄₁	—	4	8	no	—
134	C₂×C₈×C₄₁	—	4	4	no	—
135	C₄⋊C₄×C₄₁	—	2	4	no	—
136	C₄⋊C₄×C₄₁	—	2	4	no	—
137	C₄⋊C₄×C₄₁	—	2	4	no	—
138	C₄⋊C₄×C₄₁	—	2	2	no	—
139	C₄⋊C₄×C₄₁	—	2	1	no	—
140	C₄⋊C₄×C₄₁	—	2	2	no	—
141	C₄⋊C₄×C₄₁	—	2	4	no	—
142	C₂²⋊C₄×C₄₁	—	2	1	no	—
143	C₂²⋊C₄×C₄₁	—	2	2	no	—
144	C₂²⋊C₄×C₄₁	—	2	4	no	—
145	C₂²⋊C₄×C₄₁	—	2	2	no	—
146	C₂²⋊C₄×C₄₁	—	2	4	no	—
147	C₂²⋊C₄×C₄₁	—	2	2	no	—
148	C₄²×C₄₁	—	2	2	no	—
149	C₄²×C₄₁	—	2	1	no	—
150	C₄²×C₄₁	C₂²×C₄	1	1	yes	characteristic
151	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
152	C₄²×C₄₁	C₂²×C₄	1	1	yes	characteristic
153	C₂³×C₄₁	—	2	1	no	—
154	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
157	Q₈×C₄₁	—	2	2	no	—
158	Q₈×C₄₁	—	2	4	no	—
159	Q₈×C₄₁	—	4	2	no	—
160	Q₈×C₄₁	—	4	4	no	—
161	Q₈×C₄₁	—	4	1	no	—
162	Q₈×C₄₁	—	4	2	no	—
163	Q₈×C₄₁	—	4	1	no	—
164	Q₈×C₄₁	—	4	4	no	—
165	Q₈×C₄₁	—	4	2	no	—
166	D₄×C₄₁	—	2	8	no	—
167	D₄×C₄₁	—	2	4	no	—
168	D₄×C₄₁	—	4	1	no	—
169	D₄×C₄₁	—	4	2	no	—
170	D₄×C₄₁	—	4	1	no	—
171	D₄×C₄₁	—	4	4	no	—
172	D₄×C₄₁	—	4	2	no	—
173	D₄×C₄₁	—	4	4	no	—
174	D₄×C₄₁	#99	1	4	yes	—
175	C₂×C₄×C₄₁	—	2	1	no	—
176	C₂×C₄×C₄₁	—	2	8	no	—
177	C₂×C₄×C₄₁	—	2	4	no	—
178	C₂×C₄×C₄₁	—	2	4	no	—
179	C₂×C₄×C₄₁	—	2	2	no	—
180	C₂×C₄×C₄₁	—	2	2	no	—
181	C₂×C₄×C₄₁	—	2	1	no	—
182	C₂×C₄×C₄₁	—	2	2	no	—
183	C₂×C₄×C₄₁	—	2	1	no	—
184	C₂×C₄×C₄₁	—	4	4	no	—
185	C₂×C₄×C₄₁	—	4	2	no	—
186	C₂×C₄×C₄₁	—	4	4	no	—
187	C₂×C₄×C₄₁	—	4	2	no	—
188	C₂×C₄×C₄₁	—	4	4	no	—
189	C₂×C₄×C₄₁	—	4	2	no	—
190	C₂×C₄×C₄₁	—	4	4	no	—
191	C₂×C₄×C₄₁	—	4	2	no	—
192	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
193	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
194	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
196	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
197	C₈×C₄₁	—	4	8	no	—
198	#33372	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂²×C₄₁	—	2	1	no	—
200	C₂²×C₄₁	—	2	2	no	—
201	C₂²×C₄₁	—	4	2	no	—
202	C₂²×C₄₁	—	4	1	no	—
203	C₂²×C₄₁	—	4	2	no	—
204	C₂²×C₄₁	—	4	2	no	—
205	C₂²×C₄₁	—	4	1	no	—
206	C₂²×C₄₁	C₂×#99	1	4	yes	—
207	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
208	C₄×C₄₁	—	2	2	no	—
209	C₄×C₄₁	—	2	2	no	—
210	C₄×C₄₁	—	2	1	no	—
211	C₄×C₄₁	—	2	2	no	—
212	C₄×C₄₁	—	2	4	no	—
213	C₄×C₄₁	—	4	2	no	—
214	C₄×C₄₁	—	4	1	no	—
215	C₄×C₄₁	—	4	2	no	—
216	C₄×C₄₁	—	4	1	no	—
217	C₄×C₄₁	C₂×#99	1	2	yes	—
218	#3499	C₂×C₄₁	1	1	yes	characteristic
219	#2889	C₂×C₄₁	1	2	yes	complemented
220	#2135	C₂×C₄₁	1	2	yes	complemented
221	#2133	C₂×C₄₁	1	4	yes	complemented
222	#2132	C₂×C₄₁	1	2	yes	complemented
223	C₂×#356	C₂×C₄₁	1	4	yes	complemented
224	C₂×C₄₁	—	2	1	no	—
225	C₂×C₄₁	—	2	4	no	—
226	C₂×C₄₁	—	4	1	no	—
227	C₂×C₄₁	—	4	2	no	—
228	C₂×C₄₁	—	8	1	no	—
229	C₂×C₄₁	C₂²×#99	1	1	yes	characteristic
230	C₂×2₋¹⁺⁴	C₄×C₄₁	1	1	yes	characteristic
231	C₂×2₋¹⁺⁴	C₂²×C₄₁	1	1	yes	characteristic
232	#568	—	2	2	no	—
233	D₄×Q₈	—	2	2	no	—
234	#547	—	2	4	no	—
235	#547	—	2	2	no	—
236	#536	C₄×C₄₁	1	1	yes	characteristic
237	#536	C₄×C₄₁	1	2	yes	—
238	#536	C₂²×C₄₁	1	1	yes	characteristic
239	#536	C₂²×C₄₁	1	2	yes	—
240	#532	C₄×C₄₁	1	2	yes	—
241	#532	C₂²×C₄₁	1	1	yes	characteristic
242	C₂×C₄⋊Q₈	C₄×C₄₁	1	1	yes	characteristic
243	C₂×C₄⋊Q₈	C₂²×C₄₁	1	2	yes	—
244	C₄×#41	C₄×C₄₁	1	1	yes	characteristic
245	#413	—	2	4	no	—
246	#413	C₂²×C₄₁	1	4	yes	—
247	C₂×#101	—	2	2	no	—
248	C₂×#101	C₂²×C₄₁	1	8	yes	—
249	#356	C₂²×C₄₁	1	4	yes	—
250	#356	C₂²×C₄₁	1	8	yes	—
251	#355	C₂²×C₄₁	1	4	yes	—
252	C₄₁	#33372	1	1	yes	characteristic, direct product factor, Sylow
253	2₋¹⁺⁴	—	4	4	no	—
254	2₋¹⁺⁴	—	4	4	no	—
255	C₂×#41	—	2	2	no	—
256	C₂×#41	—	2	1	no	—
257	C₂×#41	C₂×C₄×C₄₁	1	2	yes	—
258	C₂×#41	C₂×C₄×C₄₁	1	1	yes	characteristic
259	C₂×#41	C₂×C₄×C₄₁	1	2	yes	—
260	C₂×#41	C₂×C₄×C₄₁	1	1	yes	characteristic
261	C₂×#41	D₄×C₄₁	1	4	yes	—
262	C₂×#41	D₄×C₄₁	1	2	yes	—
263	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
264	C₂²×Q₈	—	2	1	no	—
265	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
266	C₂²×Q₈	C₂×C₄×C₄₁	1	2	yes	—
267	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
268	C₂²×Q₈	D₄×C₄₁	1	2	yes	—
269	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
270	#131	—	4	8	no	—
271	C₂×M₁₆	—	2	4	no	—
272	C₂×M₁₆	—	2	8	no	—
273	C₄⋊Q₈	—	2	2	no	—
274	C₄⋊Q₈	—	2	4	no	—
275	C₄⋊Q₈	C₂×C₄×C₄₁	1	2	yes	—
276	C₄⋊Q₈	C₂×C₄×C₄₁	1	2	yes	—
277	C₄⋊Q₈	C₂×C₄×C₄₁	1	2	yes	—
278	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
279	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
280	#127	C₂×C₄×C₄₁	1	1	yes	characteristic
281	#124	C₂×C₄×C₄₁	1	2	yes	—
282	#124	C₂×C₄×C₄₁	1	2	yes	—
283	#124	C₂×C₄×C₄₁	1	1	yes	characteristic
284	#124	C₂³×C₄₁	1	1	yes	characteristic
285	#123	—	2	4	no	—
286	#123	—	2	2	no	—
287	#123	—	2	2	no	—
288	#123	—	2	4	no	—
289	C₂²⋊Q₈	—	2	2	no	—
290	C₂²⋊Q₈	—	2	4	no	—
291	C₂²⋊Q₈	—	2	4	no	—
292	C₂²⋊Q₈	—	2	2	no	—
293	#121	—	2	4	no	—
294	#121	—	2	2	no	—
295	C₄×Q₈	—	2	1	no	—
296	C₄×D₄	—	2	2	no	—
297	C₄×D₄	—	2	1	no	—
298	C₄×D₄	—	2	4	no	—
299	C₄×D₄	—	2	2	no	—
300	#117	C₂×C₄×C₄₁	1	1	yes	characteristic
301	#117	C₂×C₄×C₄₁	1	2	yes	—
302	C₂×C₄⋊C₄	—	2	2	no	—
303	C₂×C₄⋊C₄	—	2	4	no	—
304	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
305	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
306	#101	—	2	8	no	—
307	#101	C₂³×C₄₁	1	8	yes	—
308	#100	—	2	4	no	—
309	#41	—	2	8	no	—
310	#41	—	2	4	no	—
311	#41	—	4	2	no	—
312	#41	—	4	4	no	—
313	#41	—	4	8	no	—
314	#41	—	4	4	no	—
315	#41	—	4	2	no	—
316	#41	—	4	8	no	—
317	#41	—	4	4	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	4	4	no	—
321	C₂×Q₈	—	4	2	no	—
322	C₂×Q₈	—	4	4	no	—
323	C₂×Q₈	—	4	2	no	—
324	C₂×Q₈	—	4	4	no	—
325	C₂×Q₈	—	4	4	no	—
326	C₂×Q₈	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
327	C₂×Q₈	C₂²⋊C₄×C₄₁	1	2	yes	—
328	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
329	C₂×Q₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
330	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
331	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
332	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	C₂²⋊C₄×C₄₁	1	2	yes	—
337	C₂×D₄	C₂²⋊C₄×C₄₁	1	4	yes	—
338	C₂×D₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
339	C₂×D₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
340	C₂×D₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
341	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
349	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
350	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
351	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
352	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
353	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
354	M₁₆	—	2	8	no	—
355	M₁₆	—	4	8	no	—
356	M₁₆	—	4	4	no	—
357	C₂×C₈	—	4	8	no	—
358	C₂×C₈	—	4	4	no	—
359	C₄⋊C₄	—	2	4	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	4	no	—
366	C₂²⋊C₄	—	2	1	no	—
367	C₂²⋊C₄	—	2	2	no	—
368	C₂²⋊C₄	—	2	4	no	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	2	4	no	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	1	no	—
374	C₄²	C₂²×C₄×C₄₁	1	1	yes	characteristic
375	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
376	C₄²	C₂²×C₄×C₄₁	1	1	yes	characteristic
377	C₂³	—	2	1	no	—
378	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
379	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
380	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
381	Q₈	—	2	2	no	—
382	Q₈	—	2	4	no	—
383	Q₈	—	4	2	no	—
384	Q₈	—	4	4	no	—
385	Q₈	—	4	1	no	—
386	Q₈	—	4	2	no	—
387	Q₈	—	4	1	no	—
388	Q₈	—	4	4	no	—
389	Q₈	—	4	2	no	—
390	D₄	—	2	4	no	—
391	D₄	—	2	8	no	—
392	D₄	—	4	1	no	—
393	D₄	—	4	2	no	—
394	D₄	—	4	1	no	—
395	D₄	—	4	4	no	—
396	D₄	—	4	2	no	—
397	D₄	—	4	4	no	—
398	D₄	#99×C₄₁	1	4	yes	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	8	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	4	4	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	4	no	—
411	C₂×C₄	—	4	4	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
417	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
418	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
419	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
420	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
421	C₈	—	4	8	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	2	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	4	1	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	1	no	—
429	C₂²	C₂×#99×C₄₁	1	4	yes	—
430	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
431	C₄	—	2	2	no	—
432	C₄	—	2	2	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	4	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	1	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	1	no	—
440	C₄	C₂×#99×C₄₁	1	2	yes	—
441	C₂	—	2	1	no	—
442	C₂	—	2	4	no	—
443	C₂	—	4	1	no	—
444	C₂	—	4	2	no	—
445	C₂	—	8	1	no	—
446	C₂	C₂²×#99×C₄₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₄₁	C₂²×#99
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂×Q₈	C₂⁴×C₄₁
prime radical	C₄₁×#3499	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄₁ ◁ C₂×D₄×C₄₁ ◁ C₂×2₋¹⁺⁴×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#2889	C₂	semidirect
3. C₄₁×#2135	C₂	semidirect
4. C₄₁×#2133	C₂	semidirect
5. C₄₁×#2132	C₂	semidirect
6. C₂×C₄₁×#356	C₂	semidirect
198. #33372	C₄₁	direct (N × H)
219. #2889	C₂×C₄₁	semidirect
220. #2135	C₂×C₄₁	semidirect
221. #2133	C₂×C₄₁	semidirect
222. #2132	C₂×C₄₁	semidirect
223. C₂×#356	C₂×C₄₁	semidirect
252. C₄₁	#33372	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₁×#3499	2
C₄₁×#2889	2
C₄₁×#2135	2
C₄₁×#2133	2
C₄₁×#2132	2
C₂×C₄₁×#356	2
#33372	41

Subgroups — C41×#33372 #23809573

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#33372 #23809573