Subgroups — C₄₁×#62824 #23839025

Order 10496.

7330 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3561	C₂	1	8	yes	maximal, complemented
2	C₄₁×#3558	C₂	1	8	yes	maximal, complemented
3	C₄₁×#3545	C₂	1	8	yes	maximal, complemented
4	C₄₁×#3514	C₂	1	16	yes	maximal, complemented
5	C₄₁×#3510	C₂	1	4	yes	maximal, complemented
6	C₄₁×#3500	C₂	1	4	yes	maximal, complemented
7	C₄₁×#3490	C₂	1	8	yes	maximal, complemented
8	C₄₁×#3486	C₂	1	2	yes	maximal, complemented
9	C₄₁×#3484	C₂	1	2	yes	maximal, complemented
10	C₄₁×#3444	C₂	1	2	yes	maximal, complemented
11	C₂²×#124×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×2₋¹⁺⁴×C₄₁	C₂²	1	2	yes	complemented
13	C₂×H(5,𝔽₂)×C₄₁	C₂²	1	2	yes	complemented
14	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
15	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
16	C₄₁×#563	C₂²	1	8	yes	complemented
17	C₄₁×#562	C₂²	1	16	yes	complemented
18	C₄₁×H(3,𝔽₄)	C₂²	1	8	yes	complemented
19	C₄₁×#559	C₂²	1	16	yes	complemented
20	C₄₁×#556	C₂²	1	16	yes	complemented
21	C₄₁×#555	C₂²	1	16	yes	complemented
22	C₄₁×#551	C₂²	1	32	yes	complemented
23	C₄₁×#551	C₂²	1	32	yes	complemented
24	C₄₁×#551	C₂²	1	16	yes	complemented
25	D₄×Q₈×C₄₁	C₂²	1	16	yes	complemented
26	C₄₁×#548	C₂²	1	16	yes	complemented
27	C₄₁×#548	C₂²	1	16	yes	complemented
28	C₄₁×#546	C₂²	1	16	yes	complemented
29	C₄₁×#546	C₂²	1	32	yes	complemented
30	C₄₁×#546	C₂²	1	32	yes	complemented
31	C₄₁×#546	C₂²	1	16	yes	complemented
32	D₄²×C₄₁	C₂²	1	16	yes	complemented
33	C₄₁×#543	C₂²	1	8	yes	complemented
34	C₄₁×#542	C₂²	1	16	yes	complemented
35	C₄₁×#542	C₂²	1	32	yes	complemented
36	C₄₁×#538	C₂²	1	16	yes	complemented
37	C₄₁×#538	C₂²	1	16	yes	complemented
38	C₄₁×#538	C₂²	1	32	yes	complemented
39	C₄₁×#536	C₂²	1	4	yes	complemented
40	C₄₁×#536	C₂²	1	8	yes	complemented
41	C₄₁×#536	C₂²	1	8	yes	complemented
42	C₄₁×#535	C₂²	1	4	yes	—
43	C₄₁×#535	C₂²	1	8	yes	complemented
44	C₄₁×#534	C₂²	1	8	yes	complemented
45	C₄₁×#534	C₂²	1	8	yes	complemented
46	C₄₁×#533	C₂²	1	4	yes	complemented
47	C₄₁×#533	C₂²	1	2	yes	complemented
48	C₄₁×#532	C₂²	1	4	yes	complemented
49	C₄₁×#532	C₂²	1	2	yes	complemented
50	C₄₁×#532	C₂²	1	8	yes	complemented
51	C₄₁×#529	C₂²	1	8	yes	complemented
52	C₄₁×#529	C₂²	1	8	yes	complemented
53	C₄₁×#529	C₂²	1	8	yes	complemented
54	C₄₁×#529	C₂²	1	16	yes	complemented
55	C₂×#124×C₄₁	C₂²	1	8	yes	complemented
56	C₂×#124×C₄₁	C₂²	1	4	yes	complemented
57	C₂×#124×C₄₁	C₂²	1	8	yes	complemented
58	C₂×#124×C₄₁	C₂²	1	4	yes	complemented
59	C₂×#124×C₄₁	C₂²	1	8	yes	complemented
60	C₄₁×#525	C₂²	1	4	yes	complemented
61	C₄₁×#525	C₂²	1	8	yes	complemented
62	C₄₁×#525	C₂²	1	8	yes	complemented
63	C₂×#120×C₄₁	C₂²	1	8	yes	complemented
64	C₄₁×#519	C₂²	1	2	yes	complemented
65	C₄₁×#518	C₂²	1	2	yes	complemented
66	C₄₁×#518	C₂²	1	16	yes	complemented
67	C₄×#41×C₄₁	C₂²	1	4	yes	complemented
68	C₄×#41×C₄₁	C₂²	1	8	yes	complemented
69	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	4	yes	complemented
70	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic, complemented
71	C₂⁵×C₄₁	C₂³	1	2	yes	—
72	2₋¹⁺⁴×C₄₁	—	4	8	no	—
73	H(5,𝔽₂)×C₄₁	—	4	8	no	—
74	C₂×#41×C₄₁	C₂³	1	4	yes	—
75	C₂×#41×C₄₁	C₂³	1	8	yes	—
76	C₂×#41×C₄₁	C₂³	1	8	yes	—
77	C₂×#41×C₄₁	C₂³	1	8	yes	—
78	C₂×#41×C₄₁	C₂³	1	8	yes	complemented
79	C₂²×Q₈×C₄₁	—	4	4	no	—
80	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
81	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
82	C₂²×Q₈×C₄₁	C₂³	1	8	yes	—
83	C₂²×Q₈×C₄₁	C₂³	1	8	yes	complemented
84	C₂²×D₄×C₄₁	—	4	4	no	—
85	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
86	C₂²×D₄×C₄₁	C₂³	1	16	yes	—
87	C₂²×D₄×C₄₁	C₂³	1	8	yes	—
88	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
89	C₂²×D₄×C₄₁	C₂³	1	8	yes	—
90	C₂²×D₄×C₄₁	C₂³	1	8	yes	—
91	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
93	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
94	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	complemented
95	C₄⋊Q₈×C₄₁	C₂³	1	4	yes	complemented
96	C₄⋊Q₈×C₄₁	C₂³	1	8	yes	complemented
97	C₄⋊Q₈×C₄₁	C₂³	1	16	yes	complemented
98	#127×C₄₁	C₂³	1	8	yes	—
99	#127×C₄₁	C₂³	1	2	yes	complemented
100	#126×C₄₁	C₂³	1	16	yes	complemented
101	#126×C₄₁	C₂³	1	32	yes	complemented
102	#126×C₄₁	C₂³	1	32	yes	complemented
103	#125×C₄₁	C₂³	1	4	yes	complemented
104	#125×C₄₁	C₂³	1	8	yes	complemented
105	#124×C₄₁	C₂³	1	8	yes	—
106	#124×C₄₁	C₂³	1	8	yes	—
107	#124×C₄₁	C₂³	1	16	yes	—
108	#124×C₄₁	C₂³	1	16	yes	—
109	#124×C₄₁	C₂³	1	8	yes	—
110	#124×C₄₁	C₂³	1	8	yes	—
111	#124×C₄₁	C₂³	1	8	yes	—
112	#124×C₄₁	C₂³	1	4	yes	complemented
113	#124×C₄₁	C₂³	1	8	yes	complemented
114	#124×C₄₁	C₂³	1	32	yes	complemented
115	#124×C₄₁	C₂³	1	8	yes	complemented
116	#124×C₄₁	C₂³	1	16	yes	complemented
117	#124×C₄₁	C₂³	1	32	yes	complemented
118	#123×C₄₁	C₂³	1	8	yes	—
119	#123×C₄₁	C₂³	1	16	yes	—
120	#123×C₄₁	C₂³	1	16	yes	—
121	#123×C₄₁	C₂³	1	16	yes	—
122	#123×C₄₁	C₂³	1	32	yes	complemented
123	#123×C₄₁	C₂³	1	32	yes	complemented
124	#123×C₄₁	C₂³	1	32	yes	complemented
125	C₂²⋊Q₈×C₄₁	C₂³	1	8	yes	—
126	C₂²⋊Q₈×C₄₁	C₂³	1	8	yes	—
127	C₂²⋊Q₈×C₄₁	C₂³	1	8	yes	—
128	C₂²⋊Q₈×C₄₁	C₂³	1	16	yes	—
129	C₂²⋊Q₈×C₄₁	C₂³	1	16	yes	complemented
130	C₂²⋊Q₈×C₄₁	C₂³	1	32	yes	complemented
131	C₂²⋊Q₈×C₄₁	C₂³	1	32	yes	complemented
132	C₂²⋊Q₈×C₄₁	C₂³	1	32	yes	complemented
133	#121×C₄₁	C₂³	1	8	yes	—
134	#121×C₄₁	C₂³	1	8	yes	—
135	#121×C₄₁	C₂³	1	8	yes	—
136	#121×C₄₁	C₂³	1	16	yes	—
137	#121×C₄₁	C₂³	1	16	yes	—
138	#121×C₄₁	C₂³	1	32	yes	—
139	#121×C₄₁	C₂³	1	32	yes	complemented
140	#121×C₄₁	C₂³	1	32	yes	complemented
141	#120×C₄₁	C₂³	1	8	yes	—
142	#120×C₄₁	C₂³	1	16	yes	—
143	#120×C₄₁	C₂³	1	32	yes	—
144	#120×C₄₁	C₂³	1	16	yes	—
145	#120×C₄₁	C₂³	1	32	yes	complemented
146	C₄×Q₈×C₄₁	C₂³	1	8	yes	complemented
147	C₄×Q₈×C₄₁	C₂³	1	8	yes	complemented
148	C₄×Q₈×C₄₁	C₂³	1	8	yes	complemented
149	C₄×Q₈×C₄₁	C₂³	1	16	yes	complemented
150	C₄×D₄×C₄₁	C₂³	1	16	yes	—
151	C₄×D₄×C₄₁	C₂³	1	16	yes	—
152	C₄×D₄×C₄₁	C₂³	1	16	yes	—
153	C₄×D₄×C₄₁	C₂³	1	32	yes	—
154	C₄×D₄×C₄₁	C₂³	1	16	yes	—
155	C₄×D₄×C₄₁	C₂³	1	8	yes	complemented
156	C₄×D₄×C₄₁	C₂³	1	8	yes	complemented
157	C₄×D₄×C₄₁	C₂³	1	8	yes	complemented
158	C₄×D₄×C₄₁	C₂³	1	32	yes	complemented
159	C₄×D₄×C₄₁	C₂³	1	32	yes	complemented
160	#117×C₄₁	C₂³	1	4	yes	—
161	#117×C₄₁	C₂³	1	8	yes	—
162	#117×C₄₁	C₂³	1	8	yes	—
163	#117×C₄₁	C₂³	1	8	yes	complemented
164	#117×C₄₁	C₂³	1	16	yes	complemented
165	#117×C₄₁	C₂³	1	32	yes	complemented
166	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
167	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
168	C₂×C₂²⋊C₄×C₄₁	C₂³	1	16	yes	—
169	C₂×C₂²⋊C₄×C₄₁	C₂³	1	16	yes	—
170	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
171	C₂×C₂²⋊C₄×C₄₁	C₂³	1	16	yes	—
172	C₂×C₂²⋊C₄×C₄₁	C₂³	1	32	yes	complemented
173	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
174	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
175	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
176	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
177	C₂×C₄²×C₄₁	C₂³	1	8	yes	complemented
178	C₂⁴×C₄₁	—	4	4	no	—
179	C₂⁴×C₄₁	—	4	8	no	—
180	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
181	C₂⁴×C₄₁	C₂⁴	1	4	yes	—
182	C₂⁴×C₄₁	C₂⁴	1	8	yes	—
183	C₂⁴×C₄₁	C₂⁴	1	8	yes	—
184	#41×C₄₁	—	2	16	no	—
185	#41×C₄₁	—	4	16	no	—
186	#41×C₄₁	—	4	16	no	—
187	#41×C₄₁	—	4	16	no	—
188	#41×C₄₁	—	4	16	no	—
189	C₂×Q₈×C₄₁	—	2	8	no	—
190	C₂×Q₈×C₄₁	—	4	4	no	—
191	C₂×Q₈×C₄₁	—	4	16	no	—
192	C₂×Q₈×C₄₁	—	4	16	no	—
193	C₂×Q₈×C₄₁	C₂⁴	1	4	yes	—
194	C₂×Q₈×C₄₁	C₂⁴	1	8	yes	—
195	C₂×Q₈×C₄₁	C₂⁴	1	8	yes	—
196	C₂×Q₈×C₄₁	C₂⁴	1	8	yes	—
197	C₂×Q₈×C₄₁	C₂⁴	1	8	yes	—
198	C₂×D₄×C₄₁	—	2	8	no	—
199	C₂×D₄×C₄₁	—	4	16	no	—
200	C₂×D₄×C₄₁	—	4	16	no	—
201	C₂×D₄×C₄₁	—	4	4	no	—
202	C₂×D₄×C₄₁	—	4	32	no	—
203	C₂×D₄×C₄₁	—	4	16	no	—
204	C₂×D₄×C₄₁	C₂⁴	1	16	yes	—
205	C₂×D₄×C₄₁	C₂⁴	1	8	yes	—
206	C₂×D₄×C₄₁	C₂⁴	1	8	yes	—
207	C₂×D₄×C₄₁	C₂⁴	1	4	yes	—
208	C₂×D₄×C₄₁	C₂⁴	1	32	yes	—
209	C₂×D₄×C₄₁	C₂⁴	1	8	yes	—
210	C₂×D₄×C₄₁	C₂⁴	1	8	yes	—
211	C₂×D₄×C₄₁	C₂⁴	1	16	yes	—
212	C₂×D₄×C₄₁	C₂⁴	1	8	yes	—
213	C₂²×C₄×C₄₁	—	2	4	no	—
214	C₂²×C₄×C₄₁	—	4	4	no	—
215	C₂²×C₄×C₄₁	—	4	4	no	—
216	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
217	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
218	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₄₁	C₂⁴	1	8	yes	—
220	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
221	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
223	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₄₁	C₂⁴	1	16	yes	—
225	C₂²×C₄×C₄₁	C₂⁴	1	8	yes	—
226	C₂²×C₄×C₄₁	C₂⁴	1	16	yes	—
227	C₂²×C₄×C₄₁	C₂⁴	1	8	yes	—
228	C₂²×C₄×C₄₁	C₂⁴	1	16	yes	—
229	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
230	C₄⋊C₄×C₄₁	C₂⁴	1	8	yes	—
231	C₄⋊C₄×C₄₁	C₂⁴	1	8	yes	—
232	C₄⋊C₄×C₄₁	C₂⁴	1	8	yes	—
233	C₄⋊C₄×C₄₁	C₂⁴	1	16	yes	—
234	C₄⋊C₄×C₄₁	C₂⁴	1	16	yes	—
235	C₄⋊C₄×C₄₁	C₂⁴	1	32	yes	—
236	C₄⋊C₄×C₄₁	C₂⁴	1	16	yes	—
237	C₄⋊C₄×C₄₁	C₂⁴	1	16	yes	—
238	C₂²⋊C₄×C₄₁	C₂⁴	1	32	yes	—
239	C₂²⋊C₄×C₄₁	C₂⁴	1	32	yes	—
240	C₂²⋊C₄×C₄₁	C₂⁴	1	8	yes	—
241	C₂²⋊C₄×C₄₁	C₂⁴	1	16	yes	—
242	C₂²⋊C₄×C₄₁	C₂⁴	1	32	yes	—
243	C₂²⋊C₄×C₄₁	C₂⁴	1	16	yes	—
244	C₂²⋊C₄×C₄₁	C₂⁴	1	16	yes	—
245	C₂²⋊C₄×C₄₁	C₂⁴	1	32	yes	—
246	C₂²⋊C₄×C₄₁	C₂⁴	1	16	yes	—
247	C₂²⋊C₄×C₄₁	C₂⁴	1	16	yes	—
248	C₄²×C₄₁	C₂⁴	1	2	yes	—
249	C₄²×C₄₁	C₂⁴	1	2	yes	—
250	C₄²×C₄₁	C₂⁴	1	2	yes	—
251	C₄²×C₄₁	C₂⁴	1	4	yes	—
252	C₄²×C₄₁	C₂⁴	1	4	yes	—
253	C₄²×C₄₁	C₂⁴	1	2	yes	—
254	C₄²×C₄₁	C₂⁴	1	16	yes	—
255	C₄²×C₄₁	C₂⁴	1	8	yes	—
256	C₄²×C₄₁	C₂⁴	1	16	yes	—
257	C₂³×C₄₁	—	2	2	no	—
258	C₂³×C₄₁	—	2	4	no	—
259	C₂³×C₄₁	—	2	8	no	—
260	C₂³×C₄₁	—	2	16	no	—
261	C₂³×C₄₁	—	4	8	no	—
262	C₂³×C₄₁	—	4	8	no	—
263	C₂³×C₄₁	—	4	8	no	—
264	C₂³×C₄₁	—	4	8	no	—
265	C₂³×C₄₁	—	4	16	no	—
266	C₂³×C₄₁	—	8	16	no	—
267	C₂³×C₄₁	C₂⁵	1	8	yes	—
268	C₂³×C₄₁	C₂⁵	1	8	yes	—
269	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
270	C₂³×C₄₁	C₂⁵	1	2	yes	—
271	Q₈×C₄₁	—	2	16	no	—
272	Q₈×C₄₁	—	2	8	no	—
273	Q₈×C₄₁	—	4	8	no	—
274	Q₈×C₄₁	—	4	8	no	—
275	Q₈×C₄₁	—	4	8	no	—
276	D₄×C₄₁	—	2	16	no	—
277	D₄×C₄₁	—	2	32	no	—
278	D₄×C₄₁	—	2	16	no	—
279	D₄×C₄₁	—	2	8	no	—
280	D₄×C₄₁	—	4	8	no	—
281	D₄×C₄₁	—	4	16	no	—
282	D₄×C₄₁	—	4	32	no	—
283	D₄×C₄₁	—	4	8	no	—
284	D₄×C₄₁	—	4	8	no	—
285	C₂×C₄×C₄₁	—	2	2	no	—
286	C₂×C₄×C₄₁	—	2	8	no	—
287	C₂×C₄×C₄₁	—	2	8	no	—
288	C₂×C₄×C₄₁	—	2	8	no	—
289	C₂×C₄×C₄₁	—	2	16	no	—
290	C₂×C₄×C₄₁	—	4	2	no	—
291	C₂×C₄×C₄₁	—	4	4	no	—
292	C₂×C₄×C₄₁	—	4	2	no	—
293	C₂×C₄×C₄₁	—	4	8	no	—
294	C₂×C₄×C₄₁	—	4	16	no	—
295	C₂×C₄×C₄₁	—	4	8	no	—
296	C₂×C₄×C₄₁	—	4	16	no	—
297	C₂×C₄×C₄₁	—	4	16	no	—
298	C₂×C₄×C₄₁	H(5,𝔽₂)	1	4	yes	—
299	C₂×C₄×C₄₁	C₂⁵	1	4	yes	—
300	C₂×C₄×C₄₁	C₂⁵	1	4	yes	—
301	C₂×C₄×C₄₁	C₂⁵	1	16	yes	—
302	C₂×C₄×C₄₁	C₂⁵	1	2	yes	—
303	C₂×C₄×C₄₁	C₂⁵	1	8	yes	—
304	C₂×C₄×C₄₁	C₂⁵	1	8	yes	—
305	C₂×C₄×C₄₁	C₂⁵	1	2	yes	—
306	#62824	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
307	C₂²×C₄₁	—	2	8	no	—
308	C₂²×C₄₁	—	2	2	no	—
309	C₂²×C₄₁	—	2	2	no	—
310	C₂²×C₄₁	—	2	2	no	—
311	C₂²×C₄₁	—	2	8	no	—
312	C₂²×C₄₁	—	2	8	no	—
313	C₂²×C₄₁	—	2	16	no	—
314	C₂²×C₄₁	—	2	16	no	—
315	C₂²×C₄₁	—	8	8	no	—
316	C₂²×C₄₁	—	8	16	no	—
317	C₂²×C₄₁	—	16	8	no	—
318	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	2	yes	—
319	C₂²×C₄₁	#585	1	4	yes	—
320	C₂²×C₄₁	C₂⁶	1	1	yes	characteristic
321	C₄×C₄₁	—	2	2	no	—
322	C₄×C₄₁	—	2	8	no	—
323	C₄×C₄₁	—	2	8	no	—
324	C₄×C₄₁	—	2	4	no	—
325	C₄×C₄₁	—	2	4	no	—
326	C₄×C₄₁	—	2	16	no	—
327	C₄×C₄₁	C₂×H(5,𝔽₂)	1	4	yes	—
328	#3561	C₂×C₄₁	1	8	yes	complemented
329	#3558	C₂×C₄₁	1	8	yes	complemented
330	#3545	C₂×C₄₁	1	8	yes	complemented
331	#3514	C₂×C₄₁	1	16	yes	complemented
332	#3510	C₂×C₄₁	1	4	yes	complemented
333	#3500	C₂×C₄₁	1	4	yes	complemented
334	#3490	C₂×C₄₁	1	8	yes	complemented
335	#3486	C₂×C₄₁	1	2	yes	complemented
336	#3484	C₂×C₄₁	1	2	yes	complemented
337	#3444	C₂×C₄₁	1	2	yes	complemented
338	C₂²×#124	C₂×C₄₁	1	1	yes	characteristic, complemented
339	C₂×C₄₁	—	2	2	no	—
340	C₂×C₄₁	—	2	4	no	—
341	C₂×C₄₁	—	4	8	no	—
342	C₂×C₄₁	—	4	8	no	—
343	C₂×C₄₁	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
344	C₂×C₄₁	C₂×#585	1	2	yes	—
345	C₂×2₋¹⁺⁴	C₂²×C₄₁	1	2	yes	complemented
346	C₂×H(5,𝔽₂)	C₂²×C₄₁	1	2	yes	complemented
347	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
348	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
349	#563	C₂²×C₄₁	1	8	yes	complemented
350	#562	C₂²×C₄₁	1	16	yes	complemented
351	H(3,𝔽₄)	C₂²×C₄₁	1	8	yes	complemented
352	#559	C₂²×C₄₁	1	16	yes	complemented
353	#556	C₂²×C₄₁	1	16	yes	complemented
354	#555	C₂²×C₄₁	1	16	yes	complemented
355	#551	C₂²×C₄₁	1	32	yes	complemented
356	#551	C₂²×C₄₁	1	32	yes	complemented
357	#551	C₂²×C₄₁	1	16	yes	complemented
358	D₄×Q₈	C₂²×C₄₁	1	16	yes	complemented
359	#548	C₂²×C₄₁	1	16	yes	complemented
360	#548	C₂²×C₄₁	1	16	yes	complemented
361	#546	C₂²×C₄₁	1	16	yes	complemented
362	#546	C₂²×C₄₁	1	32	yes	complemented
363	#546	C₂²×C₄₁	1	32	yes	complemented
364	#546	C₂²×C₄₁	1	16	yes	complemented
365	D₄²	C₂²×C₄₁	1	16	yes	complemented
366	#543	C₂²×C₄₁	1	8	yes	complemented
367	#542	C₂²×C₄₁	1	16	yes	complemented
368	#542	C₂²×C₄₁	1	32	yes	complemented
369	#538	C₂²×C₄₁	1	16	yes	complemented
370	#538	C₂²×C₄₁	1	16	yes	complemented
371	#538	C₂²×C₄₁	1	32	yes	complemented
372	#536	C₂²×C₄₁	1	4	yes	complemented
373	#536	C₂²×C₄₁	1	8	yes	complemented
374	#536	C₂²×C₄₁	1	8	yes	complemented
375	#535	C₂²×C₄₁	1	4	yes	—
376	#535	C₂²×C₄₁	1	8	yes	complemented
377	#534	C₂²×C₄₁	1	8	yes	complemented
378	#534	C₂²×C₄₁	1	8	yes	complemented
379	#533	C₂²×C₄₁	1	2	yes	complemented
380	#533	C₂²×C₄₁	1	4	yes	complemented
381	#532	C₂²×C₄₁	1	2	yes	complemented
382	#532	C₂²×C₄₁	1	4	yes	complemented
383	#532	C₂²×C₄₁	1	8	yes	complemented
384	#529	C₂²×C₄₁	1	8	yes	complemented
385	#529	C₂²×C₄₁	1	8	yes	complemented
386	#529	C₂²×C₄₁	1	8	yes	complemented
387	#529	C₂²×C₄₁	1	16	yes	complemented
388	C₂×#124	C₂²×C₄₁	1	4	yes	complemented
389	C₂×#124	C₂²×C₄₁	1	8	yes	complemented
390	C₂×#124	C₂²×C₄₁	1	4	yes	complemented
391	C₂×#124	C₂²×C₄₁	1	8	yes	complemented
392	C₂×#124	C₂²×C₄₁	1	8	yes	complemented
393	#525	C₂²×C₄₁	1	4	yes	complemented
394	#525	C₂²×C₄₁	1	8	yes	complemented
395	#525	C₂²×C₄₁	1	8	yes	complemented
396	C₂×#120	C₂²×C₄₁	1	8	yes	complemented
397	#519	C₂²×C₄₁	1	2	yes	complemented
398	#518	C₂²×C₄₁	1	2	yes	complemented
399	#518	C₂²×C₄₁	1	16	yes	complemented
400	C₄×#41	C₂²×C₄₁	1	4	yes	complemented
401	C₄×#41	C₂²×C₄₁	1	8	yes	complemented
402	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	4	yes	complemented
403	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic, complemented
404	C₄₁	#62824	1	1	yes	characteristic, direct product factor, Sylow
405	C₂⁵	C₂³×C₄₁	1	2	yes	—
406	2₋¹⁺⁴	—	4	8	no	—
407	H(5,𝔽₂)	—	4	8	no	—
408	C₂×#41	C₂³×C₄₁	1	4	yes	—
409	C₂×#41	C₂³×C₄₁	1	8	yes	—
410	C₂×#41	C₂³×C₄₁	1	8	yes	—
411	C₂×#41	C₂³×C₄₁	1	8	yes	—
412	C₂×#41	C₂³×C₄₁	1	8	yes	complemented
413	C₂²×Q₈	—	4	4	no	—
414	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
415	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
416	C₂²×Q₈	C₂³×C₄₁	1	8	yes	—
417	C₂²×Q₈	C₂³×C₄₁	1	8	yes	complemented
418	C₂²×D₄	—	4	4	no	—
419	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
420	C₂²×D₄	C₂³×C₄₁	1	16	yes	—
421	C₂²×D₄	C₂³×C₄₁	1	8	yes	—
422	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
423	C₂²×D₄	C₂³×C₄₁	1	8	yes	—
424	C₂²×D₄	C₂³×C₄₁	1	8	yes	—
425	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
426	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
427	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
428	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	complemented
429	C₄⋊Q₈	C₂³×C₄₁	1	4	yes	complemented
430	C₄⋊Q₈	C₂³×C₄₁	1	8	yes	complemented
431	C₄⋊Q₈	C₂³×C₄₁	1	16	yes	complemented
432	#127	C₂³×C₄₁	1	8	yes	—
433	#127	C₂³×C₄₁	1	2	yes	complemented
434	#126	C₂³×C₄₁	1	16	yes	complemented
435	#126	C₂³×C₄₁	1	32	yes	complemented
436	#126	C₂³×C₄₁	1	32	yes	complemented
437	#125	C₂³×C₄₁	1	4	yes	complemented
438	#125	C₂³×C₄₁	1	8	yes	complemented
439	#124	C₂³×C₄₁	1	8	yes	—
440	#124	C₂³×C₄₁	1	8	yes	—
441	#124	C₂³×C₄₁	1	16	yes	—
442	#124	C₂³×C₄₁	1	16	yes	—
443	#124	C₂³×C₄₁	1	8	yes	—
444	#124	C₂³×C₄₁	1	8	yes	—
445	#124	C₂³×C₄₁	1	8	yes	—
446	#124	C₂³×C₄₁	1	4	yes	complemented
447	#124	C₂³×C₄₁	1	8	yes	complemented
448	#124	C₂³×C₄₁	1	32	yes	complemented
449	#124	C₂³×C₄₁	1	8	yes	complemented
450	#124	C₂³×C₄₁	1	16	yes	complemented
451	#124	C₂³×C₄₁	1	32	yes	complemented
452	#123	C₂³×C₄₁	1	8	yes	—
453	#123	C₂³×C₄₁	1	16	yes	—
454	#123	C₂³×C₄₁	1	16	yes	—
455	#123	C₂³×C₄₁	1	16	yes	—
456	#123	C₂³×C₄₁	1	32	yes	complemented
457	#123	C₂³×C₄₁	1	32	yes	complemented
458	#123	C₂³×C₄₁	1	32	yes	complemented
459	C₂²⋊Q₈	C₂³×C₄₁	1	8	yes	—
460	C₂²⋊Q₈	C₂³×C₄₁	1	8	yes	—
461	C₂²⋊Q₈	C₂³×C₄₁	1	8	yes	—
462	C₂²⋊Q₈	C₂³×C₄₁	1	16	yes	—
463	C₂²⋊Q₈	C₂³×C₄₁	1	16	yes	complemented
464	C₂²⋊Q₈	C₂³×C₄₁	1	32	yes	complemented
465	C₂²⋊Q₈	C₂³×C₄₁	1	32	yes	complemented
466	C₂²⋊Q₈	C₂³×C₄₁	1	32	yes	complemented
467	#121	C₂³×C₄₁	1	8	yes	—
468	#121	C₂³×C₄₁	1	8	yes	—
469	#121	C₂³×C₄₁	1	8	yes	—
470	#121	C₂³×C₄₁	1	16	yes	—
471	#121	C₂³×C₄₁	1	16	yes	—
472	#121	C₂³×C₄₁	1	32	yes	—
473	#121	C₂³×C₄₁	1	32	yes	complemented
474	#121	C₂³×C₄₁	1	32	yes	complemented
475	#120	C₂³×C₄₁	1	8	yes	—
476	#120	C₂³×C₄₁	1	16	yes	—
477	#120	C₂³×C₄₁	1	32	yes	—
478	#120	C₂³×C₄₁	1	16	yes	—
479	#120	C₂³×C₄₁	1	32	yes	complemented
480	C₄×Q₈	C₂³×C₄₁	1	8	yes	complemented
481	C₄×Q₈	C₂³×C₄₁	1	8	yes	complemented
482	C₄×Q₈	C₂³×C₄₁	1	8	yes	complemented
483	C₄×Q₈	C₂³×C₄₁	1	16	yes	complemented
484	C₄×D₄	C₂³×C₄₁	1	16	yes	—
485	C₄×D₄	C₂³×C₄₁	1	16	yes	—
486	C₄×D₄	C₂³×C₄₁	1	16	yes	—
487	C₄×D₄	C₂³×C₄₁	1	32	yes	—
488	C₄×D₄	C₂³×C₄₁	1	16	yes	—
489	C₄×D₄	C₂³×C₄₁	1	8	yes	complemented
490	C₄×D₄	C₂³×C₄₁	1	8	yes	complemented
491	C₄×D₄	C₂³×C₄₁	1	8	yes	complemented
492	C₄×D₄	C₂³×C₄₁	1	32	yes	complemented
493	C₄×D₄	C₂³×C₄₁	1	32	yes	complemented
494	#117	C₂³×C₄₁	1	4	yes	—
495	#117	C₂³×C₄₁	1	8	yes	—
496	#117	C₂³×C₄₁	1	8	yes	—
497	#117	C₂³×C₄₁	1	8	yes	complemented
498	#117	C₂³×C₄₁	1	16	yes	complemented
499	#117	C₂³×C₄₁	1	32	yes	complemented
500	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₄₁	1	16	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₄₁	1	16	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₄₁	1	16	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₄₁	1	32	yes	complemented
507	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
508	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
509	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
510	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
511	C₂×C₄²	C₂³×C₄₁	1	8	yes	complemented
512	C₂⁴	—	4	4	no	—
513	C₂⁴	—	4	8	no	—
514	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
515	C₂⁴	C₂⁴×C₄₁	1	4	yes	—
516	C₂⁴	C₂⁴×C₄₁	1	8	yes	—
517	C₂⁴	C₂⁴×C₄₁	1	8	yes	—
518	#41	—	2	16	no	—
519	#41	—	4	16	no	—
520	#41	—	4	16	no	—
521	#41	—	4	16	no	—
522	#41	—	4	16	no	—
523	C₂×Q₈	—	2	8	no	—
524	C₂×Q₈	—	4	4	no	—
525	C₂×Q₈	—	4	16	no	—
526	C₂×Q₈	—	4	16	no	—
527	C₂×Q₈	C₂⁴×C₄₁	1	4	yes	—
528	C₂×Q₈	C₂⁴×C₄₁	1	8	yes	—
529	C₂×Q₈	C₂⁴×C₄₁	1	8	yes	—
530	C₂×Q₈	C₂⁴×C₄₁	1	8	yes	—
531	C₂×Q₈	C₂⁴×C₄₁	1	8	yes	—
532	C₂×D₄	—	2	8	no	—
533	C₂×D₄	—	4	16	no	—
534	C₂×D₄	—	4	16	no	—
535	C₂×D₄	—	4	4	no	—
536	C₂×D₄	—	4	16	no	—
537	C₂×D₄	—	4	32	no	—
538	C₂×D₄	C₂⁴×C₄₁	1	16	yes	—
539	C₂×D₄	C₂⁴×C₄₁	1	8	yes	—
540	C₂×D₄	C₂⁴×C₄₁	1	8	yes	—
541	C₂×D₄	C₂⁴×C₄₁	1	4	yes	—
542	C₂×D₄	C₂⁴×C₄₁	1	32	yes	—
543	C₂×D₄	C₂⁴×C₄₁	1	8	yes	—
544	C₂×D₄	C₂⁴×C₄₁	1	8	yes	—
545	C₂×D₄	C₂⁴×C₄₁	1	16	yes	—
546	C₂×D₄	C₂⁴×C₄₁	1	8	yes	—
547	C₂²×C₄	—	2	4	no	—
548	C₂²×C₄	—	4	4	no	—
549	C₂²×C₄	—	4	4	no	—
550	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
551	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
552	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
553	C₂²×C₄	C₂⁴×C₄₁	1	8	yes	—
554	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
555	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
556	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
557	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
558	C₂²×C₄	C₂⁴×C₄₁	1	16	yes	—
559	C₂²×C₄	C₂⁴×C₄₁	1	8	yes	—
560	C₂²×C₄	C₂⁴×C₄₁	1	16	yes	—
561	C₂²×C₄	C₂⁴×C₄₁	1	8	yes	—
562	C₂²×C₄	C₂⁴×C₄₁	1	16	yes	—
563	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
564	C₄⋊C₄	C₂⁴×C₄₁	1	8	yes	—
565	C₄⋊C₄	C₂⁴×C₄₁	1	8	yes	—
566	C₄⋊C₄	C₂⁴×C₄₁	1	8	yes	—
567	C₄⋊C₄	C₂⁴×C₄₁	1	16	yes	—
568	C₄⋊C₄	C₂⁴×C₄₁	1	16	yes	—
569	C₄⋊C₄	C₂⁴×C₄₁	1	32	yes	—
570	C₄⋊C₄	C₂⁴×C₄₁	1	16	yes	—
571	C₄⋊C₄	C₂⁴×C₄₁	1	16	yes	—
572	C₂²⋊C₄	C₂⁴×C₄₁	1	32	yes	—
573	C₂²⋊C₄	C₂⁴×C₄₁	1	32	yes	—
574	C₂²⋊C₄	C₂⁴×C₄₁	1	8	yes	—
575	C₂²⋊C₄	C₂⁴×C₄₁	1	16	yes	—
576	C₂²⋊C₄	C₂⁴×C₄₁	1	32	yes	—
577	C₂²⋊C₄	C₂⁴×C₄₁	1	16	yes	—
578	C₂²⋊C₄	C₂⁴×C₄₁	1	16	yes	—
579	C₂²⋊C₄	C₂⁴×C₄₁	1	32	yes	—
580	C₂²⋊C₄	C₂⁴×C₄₁	1	16	yes	—
581	C₂²⋊C₄	C₂⁴×C₄₁	1	16	yes	—
582	C₄²	C₂⁴×C₄₁	1	2	yes	—
583	C₄²	C₂⁴×C₄₁	1	2	yes	—
584	C₄²	C₂⁴×C₄₁	1	2	yes	—
585	C₄²	C₂⁴×C₄₁	1	4	yes	—
586	C₄²	C₂⁴×C₄₁	1	4	yes	—
587	C₄²	C₂⁴×C₄₁	1	2	yes	—
588	C₄²	C₂⁴×C₄₁	1	16	yes	—
589	C₄²	C₂⁴×C₄₁	1	8	yes	—
590	C₄²	C₂⁴×C₄₁	1	16	yes	—
591	C₂³	—	2	2	no	—
592	C₂³	—	2	4	no	—
593	C₂³	—	2	8	no	—
594	C₂³	—	2	16	no	—
595	C₂³	—	4	8	no	—
596	C₂³	—	4	8	no	—
597	C₂³	—	4	8	no	—
598	C₂³	—	4	8	no	—
599	C₂³	—	4	16	no	—
600	C₂³	—	8	16	no	—
601	C₂³	C₂⁵×C₄₁	1	8	yes	—
602	C₂³	C₂⁵×C₄₁	1	8	yes	—
603	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
604	C₂³	C₂⁵×C₄₁	1	2	yes	—
605	Q₈	—	2	16	no	—
606	Q₈	—	2	8	no	—
607	Q₈	—	4	8	no	—
608	Q₈	—	4	8	no	—
609	Q₈	—	4	8	no	—
610	D₄	—	2	16	no	—
611	D₄	—	2	32	no	—
612	D₄	—	2	16	no	—
613	D₄	—	2	8	no	—
614	D₄	—	4	8	no	—
615	D₄	—	4	16	no	—
616	D₄	—	4	32	no	—
617	D₄	—	4	8	no	—
618	D₄	—	4	8	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	8	no	—
621	C₂×C₄	—	2	8	no	—
622	C₂×C₄	—	2	8	no	—
623	C₂×C₄	—	2	16	no	—
624	C₂×C₄	—	4	8	no	—
625	C₂×C₄	—	4	2	no	—
626	C₂×C₄	—	4	4	no	—
627	C₂×C₄	—	4	2	no	—
628	C₂×C₄	—	4	8	no	—
629	C₂×C₄	—	4	16	no	—
630	C₂×C₄	—	4	16	no	—
631	C₂×C₄	—	4	16	no	—
632	C₂×C₄	H(5,𝔽₂)×C₄₁	1	4	yes	—
633	C₂×C₄	C₂⁵×C₄₁	1	4	yes	—
634	C₂×C₄	C₂⁵×C₄₁	1	4	yes	—
635	C₂×C₄	C₂⁵×C₄₁	1	16	yes	—
636	C₂×C₄	C₂⁵×C₄₁	1	2	yes	—
637	C₂×C₄	C₂⁵×C₄₁	1	8	yes	—
638	C₂×C₄	C₂⁵×C₄₁	1	8	yes	—
639	C₂×C₄	C₂⁵×C₄₁	1	2	yes	—
640	C₂²	—	2	8	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	8	no	—
645	C₂²	—	2	8	no	—
646	C₂²	—	2	16	no	—
647	C₂²	—	2	16	no	—
648	C₂²	—	8	8	no	—
649	C₂²	—	8	16	no	—
650	C₂²	—	16	8	no	—
651	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	2	yes	—
652	C₂²	C₄₁×#585	1	4	yes	—
653	C₂²	C₂⁶×C₄₁	1	1	yes	characteristic
654	C₄	—	2	2	no	—
655	C₄	—	2	8	no	—
656	C₄	—	2	8	no	—
657	C₄	—	2	4	no	—
658	C₄	—	2	4	no	—
659	C₄	—	2	16	no	—
660	C₄	C₂×H(5,𝔽₂)×C₄₁	1	4	yes	—
661	C₂	—	2	2	no	—
662	C₂	—	2	4	no	—
663	C₂	—	4	8	no	—
664	C₂	—	4	8	no	—
665	C₂	C₂²×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
666	C₂	C₂×C₄₁×#585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₄₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3561	C₂	semidirect
2. C₄₁×#3558	C₂	semidirect
3. C₄₁×#3545	C₂	semidirect
4. C₄₁×#3514	C₂	semidirect
5. C₄₁×#3510	C₂	semidirect
6. C₄₁×#3500	C₂	semidirect
7. C₄₁×#3490	C₂	semidirect
8. C₄₁×#3486	C₂	semidirect
9. C₄₁×#3484	C₂	semidirect
10. C₄₁×#3444	C₂	semidirect
11. C₂²×#124×C₄₁	C₂	semidirect
12. C₂×2₋¹⁺⁴×C₄₁	C₂²	semidirect
13. C₂×H(5,𝔽₂)×C₄₁	C₂²	semidirect
14. C₂³×Q₈×C₄₁	C₂²	semidirect
16. C₄₁×#563	C₂²	semidirect
17. C₄₁×#562	C₂²	semidirect
18. C₄₁×H(3,𝔽₄)	C₂²	semidirect
19. C₄₁×#559	C₂²	semidirect
20. C₄₁×#556	C₂²	semidirect
21. C₄₁×#555	C₂²	semidirect
22. C₄₁×#551	C₂²	semidirect
23. C₄₁×#551	C₂²	semidirect
24. C₄₁×#551	C₂²	semidirect
25. D₄×Q₈×C₄₁	C₂²	semidirect
26. C₄₁×#548	C₂²	semidirect
27. C₄₁×#548	C₂²	semidirect
28. C₄₁×#546	C₂²	semidirect
29. C₄₁×#546	C₂²	semidirect
30. C₄₁×#546	C₂²	semidirect
31. C₄₁×#546	C₂²	semidirect
32. D₄²×C₄₁	C₂²	semidirect
33. C₄₁×#543	C₂²	semidirect
34. C₄₁×#542	C₂²	semidirect
35. C₄₁×#542	C₂²	semidirect
36. C₄₁×#538	C₂²	semidirect
37. C₄₁×#538	C₂²	semidirect
38. C₄₁×#538	C₂²	semidirect
39. C₄₁×#536	C₂²	semidirect
40. C₄₁×#536	C₂²	semidirect
41. C₄₁×#536	C₂²	semidirect
43. C₄₁×#535	C₂²	semidirect
44. C₄₁×#534	C₂²	semidirect
45. C₄₁×#534	C₂²	semidirect
46. C₄₁×#533	C₂²	semidirect
47. C₄₁×#533	C₂²	semidirect
48. C₄₁×#532	C₂²	semidirect
49. C₄₁×#532	C₂²	semidirect
50. C₄₁×#532	C₂²	semidirect
51. C₄₁×#529	C₂²	semidirect
52. C₄₁×#529	C₂²	semidirect
53. C₄₁×#529	C₂²	semidirect
54. C₄₁×#529	C₂²	semidirect
55. C₂×#124×C₄₁	C₂²	semidirect
56. C₂×#124×C₄₁	C₂²	semidirect
57. C₂×#124×C₄₁	C₂²	semidirect
58. C₂×#124×C₄₁	C₂²	semidirect
59. C₂×#124×C₄₁	C₂²	semidirect
60. C₄₁×#525	C₂²	semidirect
61. C₄₁×#525	C₂²	semidirect
62. C₄₁×#525	C₂²	semidirect
63. C₂×#120×C₄₁	C₂²	semidirect
64. C₄₁×#519	C₂²	semidirect
65. C₄₁×#518	C₂²	semidirect
66. C₄₁×#518	C₂²	semidirect
67. C₄×#41×C₄₁	C₂²	semidirect
68. C₄×#41×C₄₁	C₂²	semidirect
69. C₂²×C₂²⋊C₄×C₄₁	C₂²	semidirect
70. C₂²×C₄²×C₄₁	C₂²	semidirect
78. C₂×#41×C₄₁	C₂³	semidirect
83. C₂²×Q₈×C₄₁	C₂³	semidirect
94. C₄⋊Q₈×C₄₁	C₂³	semidirect
95. C₄⋊Q₈×C₄₁	C₂³	semidirect
96. C₄⋊Q₈×C₄₁	C₂³	semidirect
97. C₄⋊Q₈×C₄₁	C₂³	semidirect
99. #127×C₄₁	C₂³	semidirect
100. #126×C₄₁	C₂³	semidirect
101. #126×C₄₁	C₂³	semidirect
102. #126×C₄₁	C₂³	semidirect
103. #125×C₄₁	C₂³	semidirect
104. #125×C₄₁	C₂³	semidirect
112. #124×C₄₁	C₂³	semidirect
113. #124×C₄₁	C₂³	semidirect
114. #124×C₄₁	C₂³	semidirect
115. #124×C₄₁	C₂³	semidirect
116. #124×C₄₁	C₂³	semidirect
117. #124×C₄₁	C₂³	semidirect
122. #123×C₄₁	C₂³	semidirect
123. #123×C₄₁	C₂³	semidirect
124. #123×C₄₁	C₂³	semidirect
129. C₂²⋊Q₈×C₄₁	C₂³	semidirect
130. C₂²⋊Q₈×C₄₁	C₂³	semidirect
131. C₂²⋊Q₈×C₄₁	C₂³	semidirect
132. C₂²⋊Q₈×C₄₁	C₂³	semidirect
139. #121×C₄₁	C₂³	semidirect
140. #121×C₄₁	C₂³	semidirect
145. #120×C₄₁	C₂³	semidirect
146. C₄×Q₈×C₄₁	C₂³	semidirect
147. C₄×Q₈×C₄₁	C₂³	semidirect
148. C₄×Q₈×C₄₁	C₂³	semidirect
149. C₄×Q₈×C₄₁	C₂³	semidirect
155. C₄×D₄×C₄₁	C₂³	semidirect
156. C₄×D₄×C₄₁	C₂³	semidirect
157. C₄×D₄×C₄₁	C₂³	semidirect
158. C₄×D₄×C₄₁	C₂³	semidirect
159. C₄×D₄×C₄₁	C₂³	semidirect
163. #117×C₄₁	C₂³	semidirect
164. #117×C₄₁	C₂³	semidirect
165. #117×C₄₁	C₂³	semidirect
172. C₂×C₂²⋊C₄×C₄₁	C₂³	semidirect
177. C₂×C₄²×C₄₁	C₂³	semidirect
306. #62824	C₄₁	direct (N × H)
328. #3561	C₂×C₄₁	semidirect
329. #3558	C₂×C₄₁	semidirect
330. #3545	C₂×C₄₁	semidirect
331. #3514	C₂×C₄₁	semidirect
332. #3510	C₂×C₄₁	semidirect
333. #3500	C₂×C₄₁	semidirect
334. #3490	C₂×C₄₁	semidirect
335. #3486	C₂×C₄₁	semidirect
336. #3484	C₂×C₄₁	semidirect
337. #3444	C₂×C₄₁	semidirect
338. C₂²×#124	C₂×C₄₁	semidirect
345. C₂×2₋¹⁺⁴	C₂²×C₄₁	semidirect
346. C₂×H(5,𝔽₂)	C₂²×C₄₁	semidirect
347. C₂³×Q₈	C₂²×C₄₁	semidirect
349. #563	C₂²×C₄₁	semidirect
350. #562	C₂²×C₄₁	semidirect
351. H(3,𝔽₄)	C₂²×C₄₁	semidirect
352. #559	C₂²×C₄₁	semidirect
353. #556	C₂²×C₄₁	semidirect
354. #555	C₂²×C₄₁	semidirect
355. #551	C₂²×C₄₁	semidirect
356. #551	C₂²×C₄₁	semidirect
357. #551	C₂²×C₄₁	semidirect
358. D₄×Q₈	C₂²×C₄₁	semidirect
359. #548	C₂²×C₄₁	semidirect
360. #548	C₂²×C₄₁	semidirect
361. #546	C₂²×C₄₁	semidirect
362. #546	C₂²×C₄₁	semidirect
363. #546	C₂²×C₄₁	semidirect
364. #546	C₂²×C₄₁	semidirect
365. D₄²	C₂²×C₄₁	semidirect
366. #543	C₂²×C₄₁	semidirect
367. #542	C₂²×C₄₁	semidirect
368. #542	C₂²×C₄₁	semidirect
369. #538	C₂²×C₄₁	semidirect
370. #538	C₂²×C₄₁	semidirect
371. #538	C₂²×C₄₁	semidirect
372. #536	C₂²×C₄₁	semidirect
373. #536	C₂²×C₄₁	semidirect
374. #536	C₂²×C₄₁	semidirect
376. #535	C₂²×C₄₁	semidirect
377. #534	C₂²×C₄₁	semidirect
378. #534	C₂²×C₄₁	semidirect
379. #533	C₂²×C₄₁	semidirect
380. #533	C₂²×C₄₁	semidirect
381. #532	C₂²×C₄₁	semidirect
382. #532	C₂²×C₄₁	semidirect
383. #532	C₂²×C₄₁	semidirect
384. #529	C₂²×C₄₁	semidirect
385. #529	C₂²×C₄₁	semidirect
386. #529	C₂²×C₄₁	semidirect
387. #529	C₂²×C₄₁	semidirect
388. C₂×#124	C₂²×C₄₁	semidirect
389. C₂×#124	C₂²×C₄₁	semidirect
390. C₂×#124	C₂²×C₄₁	semidirect
391. C₂×#124	C₂²×C₄₁	semidirect
392. C₂×#124	C₂²×C₄₁	semidirect
393. #525	C₂²×C₄₁	semidirect
394. #525	C₂²×C₄₁	semidirect
395. #525	C₂²×C₄₁	semidirect
396. C₂×#120	C₂²×C₄₁	semidirect
397. #519	C₂²×C₄₁	semidirect
398. #518	C₂²×C₄₁	semidirect
399. #518	C₂²×C₄₁	semidirect
400. C₄×#41	C₂²×C₄₁	semidirect
401. C₄×#41	C₂²×C₄₁	semidirect
402. C₂²×C₂²⋊C₄	C₂²×C₄₁	semidirect
403. C₂²×C₄²	C₂²×C₄₁	semidirect
404. C₄₁	#62824	direct (N × H)
412. C₂×#41	C₂³×C₄₁	semidirect
417. C₂²×Q₈	C₂³×C₄₁	semidirect
428. C₄⋊Q₈	C₂³×C₄₁	semidirect
429. C₄⋊Q₈	C₂³×C₄₁	semidirect
430. C₄⋊Q₈	C₂³×C₄₁	semidirect
431. C₄⋊Q₈	C₂³×C₄₁	semidirect
433. #127	C₂³×C₄₁	semidirect
434. #126	C₂³×C₄₁	semidirect
435. #126	C₂³×C₄₁	semidirect
436. #126	C₂³×C₄₁	semidirect
437. #125	C₂³×C₄₁	semidirect
438. #125	C₂³×C₄₁	semidirect
446. #124	C₂³×C₄₁	semidirect
447. #124	C₂³×C₄₁	semidirect
448. #124	C₂³×C₄₁	semidirect
449. #124	C₂³×C₄₁	semidirect
450. #124	C₂³×C₄₁	semidirect
451. #124	C₂³×C₄₁	semidirect
456. #123	C₂³×C₄₁	semidirect
457. #123	C₂³×C₄₁	semidirect
458. #123	C₂³×C₄₁	semidirect
463. C₂²⋊Q₈	C₂³×C₄₁	semidirect
464. C₂²⋊Q₈	C₂³×C₄₁	semidirect
465. C₂²⋊Q₈	C₂³×C₄₁	semidirect
466. C₂²⋊Q₈	C₂³×C₄₁	semidirect
473. #121	C₂³×C₄₁	semidirect
474. #121	C₂³×C₄₁	semidirect
479. #120	C₂³×C₄₁	semidirect
480. C₄×Q₈	C₂³×C₄₁	semidirect
481. C₄×Q₈	C₂³×C₄₁	semidirect
482. C₄×Q₈	C₂³×C₄₁	semidirect
483. C₄×Q₈	C₂³×C₄₁	semidirect
489. C₄×D₄	C₂³×C₄₁	semidirect
490. C₄×D₄	C₂³×C₄₁	semidirect
491. C₄×D₄	C₂³×C₄₁	semidirect
492. C₄×D₄	C₂³×C₄₁	semidirect
493. C₄×D₄	C₂³×C₄₁	semidirect
497. #117	C₂³×C₄₁	semidirect
498. #117	C₂³×C₄₁	semidirect
499. #117	C₂³×C₄₁	semidirect
506. C₂×C₂²⋊C₄	C₂³×C₄₁	semidirect
511. C₂×C₄²	C₂³×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3561	2
C₄₁×#3558	2
C₄₁×#3545	2
C₄₁×#3514	2
C₄₁×#3510	2
C₄₁×#3500	2
C₄₁×#3490	2
C₄₁×#3486	2
C₄₁×#3484	2
C₄₁×#3444	2
C₂²×#124×C₄₁	2
#62824	41

Subgroups — C41×#62824 #23839025

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#62824 #23839025