Subgroups — C₂×C₄₁×#2426 #23810906

Order 10496.

3678 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#124×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂²⋊Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#121×C₄₁	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2426	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₄₁×#396	C₂	1	2	yes	maximal, complemented
7	C₂×C₄₁×#394	C₂	1	2	yes	maximal, complemented
8	C₂×C₄₁×#390	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄₁×#390	C₂	1	2	yes	maximal, complemented
10	C₂×C₄₁×#389	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₁×#388	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×C₂²⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
15	C₂³×D₄×C₄₁	C₂²	1	2	yes	—
16	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
17	C₂×#124×C₄₁	—	2	8	no	—
18	C₂×#124×C₄₁	C₂²	1	8	yes	complemented
19	C₂×C₂²⋊Q₈×C₄₁	—	2	8	no	—
20	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	8	yes	complemented
21	C₂×#121×C₄₁	—	2	8	no	—
22	C₂×#121×C₄₁	C₂²	1	8	yes	—
23	C₂×C₄×Q₈×C₄₁	—	2	8	no	—
24	C₂×C₄×Q₈×C₄₁	C₂²	1	8	yes	complemented
25	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
26	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
28	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
29	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
31	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
32	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
33	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
34	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
35	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
36	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
37	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
38	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
40	C₂²×C₄²×C₄₁	C₂²	1	2	yes	—
41	C₄₁×#396	C₂²	1	16	yes	complemented
42	C₄₁×#394	C₂²	1	16	yes	complemented
43	C₄₁×#390	C₂²	1	8	yes	complemented
44	C₄₁×#390	C₂²	1	16	yes	complemented
45	C₄₁×#389	C₂²	1	8	yes	complemented
46	C₄₁×#388	C₂²	1	16	yes	complemented
47	C₄×C₂²⋊C₄×C₄₁	C₂²	1	8	yes	complemented
48	C₂×#95×C₄₁	C₂²	1	1	yes	characteristic
49	C₂×#95×C₄₁	C₂²	1	1	yes	characteristic
50	C₂×#95×C₄₁	C₂²	1	2	yes	—
51	C₂⁵×C₄₁	C₂³	1	2	yes	—
52	C₂⁵×C₄₁	C₂³	1	1	yes	characteristic
53	C₂²×Q₈×C₄₁	—	2	4	no	—
54	C₂²×Q₈×C₄₁	—	2	4	no	—
55	C₂²×Q₈×C₄₁	D₄	1	8	yes	complemented
56	C₂²×Q₈×C₄₁	C₂³	1	4	yes	—
57	C₂²×D₄×C₄₁	—	2	8	no	—
58	C₂²×D₄×C₄₁	—	2	8	no	—
59	C₂²×D₄×C₄₁	—	2	4	no	—
60	C₂²×D₄×C₄₁	—	2	4	no	—
61	C₂²×D₄×C₄₁	—	2	4	no	—
62	C₂²×D₄×C₄₁	—	4	4	no	—
63	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
64	C₂²×D₄×C₄₁	C₂³	1	8	yes	—
65	C₂³×C₄×C₄₁	—	2	4	no	—
66	C₂³×C₄×C₄₁	—	2	4	no	—
67	C₂³×C₄×C₄₁	—	2	4	no	—
68	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
69	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
73	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
75	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
76	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
78	#124×C₄₁	—	2	32	no	—
79	C₂²⋊Q₈×C₄₁	—	2	32	no	—
80	#121×C₄₁	—	2	32	no	—
81	C₄×Q₈×C₄₁	—	2	32	no	—
82	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
83	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
84	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
85	C₂×C₄⋊C₄×C₄₁	—	4	4	no	—
86	C₂×C₄⋊C₄×C₄₁	D₄	1	8	yes	—
87	C₂×C₄⋊C₄×C₄₁	C₂³	1	8	yes	—
88	C₂×C₄⋊C₄×C₄₁	C₂³	1	8	yes	—
89	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
90	C₂×C₄⋊C₄×C₄₁	C₂³	1	8	yes	—
91	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
92	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
93	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
94	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
95	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
96	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
97	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
98	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
99	C₂×C₂²⋊C₄×C₄₁	—	4	4	no	—
100	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
101	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
102	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
103	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
104	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
105	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
106	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
107	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
108	C₂×C₄²×C₄₁	—	2	8	no	—
109	C₂×C₄²×C₄₁	—	2	4	no	—
110	C₂×C₄²×C₄₁	—	2	4	no	—
111	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
112	C₂×C₄²×C₄₁	C₂³	1	8	yes	—
113	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
114	#95×C₄₁	C₂³	1	4	yes	—
115	#95×C₄₁	C₂³	1	4	yes	—
116	#95×C₄₁	C₂³	1	8	yes	—
117	C₂⁴×C₄₁	—	2	2	no	—
118	C₂⁴×C₄₁	—	2	2	no	—
119	C₂⁴×C₄₁	—	2	2	no	—
120	C₂⁴×C₄₁	—	2	2	no	—
121	C₂⁴×C₄₁	—	2	2	no	—
122	C₂⁴×C₄₁	—	2	2	no	—
123	C₂⁴×C₄₁	—	2	4	no	—
124	C₂⁴×C₄₁	—	2	4	no	—
125	C₂⁴×C₄₁	—	2	4	no	—
126	C₂⁴×C₄₁	—	2	4	no	—
127	C₂⁴×C₄₁	—	2	4	no	—
128	C₂⁴×C₄₁	—	2	4	no	—
129	C₂⁴×C₄₁	—	2	4	no	—
130	C₂⁴×C₄₁	#41	1	4	yes	—
131	C₂⁴×C₄₁	C₂⁴	1	4	yes	—
132	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
133	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
134	C₂×Q₈×C₄₁	—	2	32	no	—
135	C₂×Q₈×C₄₁	—	2	8	no	—
136	C₂×Q₈×C₄₁	—	2	8	no	—
137	C₂×Q₈×C₄₁	C₂×D₄	1	16	yes	complemented
138	C₂×D₄×C₄₁	—	2	16	no	—
139	C₂×D₄×C₄₁	—	2	16	no	—
140	C₂×D₄×C₄₁	—	2	8	no	—
141	C₂×D₄×C₄₁	—	2	8	no	—
142	C₂×D₄×C₄₁	—	2	8	no	—
143	C₂×D₄×C₄₁	—	4	8	no	—
144	C₂×D₄×C₄₁	—	4	32	no	—
145	C₂×D₄×C₄₁	—	4	16	no	—
146	C₂²×C₄×C₄₁	—	2	2	no	—
147	C₂²×C₄×C₄₁	—	2	4	no	—
148	C₂²×C₄×C₄₁	—	2	4	no	—
149	C₂²×C₄×C₄₁	—	2	4	no	—
150	C₂²×C₄×C₄₁	—	2	4	no	—
151	C₂²×C₄×C₄₁	—	2	2	no	—
152	C₂²×C₄×C₄₁	—	2	2	no	—
153	C₂²×C₄×C₄₁	—	2	2	no	—
154	C₂²×C₄×C₄₁	—	2	2	no	—
155	C₂²×C₄×C₄₁	—	2	2	no	—
156	C₂²×C₄×C₄₁	—	2	4	no	—
157	C₂²×C₄×C₄₁	—	2	2	no	—
158	C₂²×C₄×C₄₁	—	2	2	no	—
159	C₂²×C₄×C₄₁	—	2	2	no	—
160	C₂²×C₄×C₄₁	—	2	2	no	—
161	C₂²×C₄×C₄₁	—	2	4	no	—
162	C₂²×C₄×C₄₁	—	2	2	no	—
163	C₂²×C₄×C₄₁	—	2	2	no	—
164	C₂²×C₄×C₄₁	—	2	4	no	—
165	C₂²×C₄×C₄₁	—	2	2	no	—
166	C₂²×C₄×C₄₁	—	2	2	no	—
167	C₂²×C₄×C₄₁	—	2	8	no	—
168	C₂²×C₄×C₄₁	—	2	8	no	—
169	C₂²×C₄×C₄₁	—	2	8	no	—
170	C₂²×C₄×C₄₁	—	4	16	no	—
171	C₂²×C₄×C₄₁	C₂×D₄	1	8	yes	—
172	C₂²×C₄×C₄₁	C₂×D₄	1	8	yes	—
173	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
174	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
175	C₂²×C₄×C₄₁	#41	1	4	yes	—
176	C₂²×C₄×C₄₁	#41	1	4	yes	—
177	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
182	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
183	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
184	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
186	C₄⋊C₄×C₄₁	—	2	16	no	—
187	C₄⋊C₄×C₄₁	—	2	8	no	—
188	C₄⋊C₄×C₄₁	—	2	16	no	—
189	C₄⋊C₄×C₄₁	—	4	8	no	—
190	C₄⋊C₄×C₄₁	C₂×D₄	1	16	yes	—
191	C₂²⋊C₄×C₄₁	—	2	8	no	—
192	C₂²⋊C₄×C₄₁	—	2	16	no	—
193	C₂²⋊C₄×C₄₁	—	2	16	no	—
194	C₂²⋊C₄×C₄₁	—	2	16	no	—
195	C₂²⋊C₄×C₄₁	—	2	16	no	—
196	C₂²⋊C₄×C₄₁	—	2	8	no	—
197	C₂²⋊C₄×C₄₁	—	2	16	no	—
198	C₂²⋊C₄×C₄₁	—	4	8	no	—
199	C₄²×C₄₁	—	2	16	no	—
200	C₄²×C₄₁	—	2	8	no	—
201	C₄²×C₄₁	—	2	8	no	—
202	C₂³×C₄₁	—	2	8	no	—
203	C₂³×C₄₁	—	2	8	no	—
204	C₂³×C₄₁	—	2	8	no	—
205	C₂³×C₄₁	—	2	2	no	—
206	C₂³×C₄₁	—	2	2	no	—
207	C₂³×C₄₁	—	2	2	no	—
208	C₂³×C₄₁	—	2	2	no	—
209	C₂³×C₄₁	—	2	2	no	—
210	C₂³×C₄₁	—	2	2	no	—
211	C₂³×C₄₁	—	2	4	no	—
212	C₂³×C₄₁	—	2	4	no	—
213	C₂³×C₄₁	—	2	4	no	—
214	C₂³×C₄₁	—	2	4	no	—
215	C₂³×C₄₁	—	2	4	no	—
216	C₂³×C₄₁	—	2	4	no	—
217	C₂³×C₄₁	—	2	4	no	—
218	C₂³×C₄₁	—	4	4	no	—
219	C₂³×C₄₁	—	4	4	no	—
220	C₂³×C₄₁	—	4	4	no	—
221	C₂³×C₄₁	—	4	4	no	—
222	C₂³×C₄₁	—	4	8	no	—
223	C₂³×C₄₁	—	4	8	no	—
224	C₂³×C₄₁	—	4	8	no	—
225	C₂³×C₄₁	—	4	8	no	—
226	C₂³×C₄₁	—	4	8	no	—
227	C₂³×C₄₁	—	4	8	no	—
228	C₂³×C₄₁	—	4	8	no	—
229	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
230	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
231	C₂³×C₄₁	C₂×#41	1	4	yes	—
232	C₂³×C₄₁	C₂×#41	1	2	yes	—
233	C₂³×C₄₁	C₂×#41	1	2	yes	—
234	C₂³×C₄₁	C₂×#41	1	2	yes	—
235	C₂³×C₄₁	H(5,𝔽₂)	1	2	yes	—
236	C₂³×C₄₁	2₋¹⁺⁴	1	2	yes	—
237	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
238	Q₈×C₄₁	—	2	32	no	—
239	D₄×C₄₁	—	4	32	no	—
240	D₄×C₄₁	—	4	16	no	—
241	C₂×C₄×C₄₁	—	2	16	no	—
242	C₂×C₄×C₄₁	—	2	16	no	—
243	C₂×C₄×C₄₁	—	2	8	no	—
244	C₂×C₄×C₄₁	—	2	2	no	—
245	C₂×C₄×C₄₁	—	2	4	no	—
246	C₂×C₄×C₄₁	—	2	4	no	—
247	C₂×C₄×C₄₁	—	2	4	no	—
248	C₂×C₄×C₄₁	—	2	4	no	—
249	C₂×C₄×C₄₁	—	2	2	no	—
250	C₂×C₄×C₄₁	—	2	2	no	—
251	C₂×C₄×C₄₁	—	2	2	no	—
252	C₂×C₄×C₄₁	—	2	2	no	—
253	C₂×C₄×C₄₁	—	2	2	no	—
254	C₂×C₄×C₄₁	—	2	4	no	—
255	C₂×C₄×C₄₁	—	2	2	no	—
256	C₂×C₄×C₄₁	—	2	2	no	—
257	C₂×C₄×C₄₁	—	2	2	no	—
258	C₂×C₄×C₄₁	—	2	2	no	—
259	C₂×C₄×C₄₁	—	2	4	no	—
260	C₂×C₄×C₄₁	—	2	2	no	—
261	C₂×C₄×C₄₁	—	2	2	no	—
262	C₂×C₄×C₄₁	—	2	4	no	—
263	C₂×C₄×C₄₁	—	2	2	no	—
264	C₂×C₄×C₄₁	—	2	2	no	—
265	C₂×C₄×C₄₁	—	4	4	no	—
266	C₂×C₄×C₄₁	—	4	4	no	—
267	C₂×C₄×C₄₁	—	4	4	no	—
268	C₂×C₄×C₄₁	—	4	4	no	—
269	C₂×C₄×C₄₁	—	4	8	no	—
270	C₂×C₄×C₄₁	—	4	16	no	—
271	C₂×C₄×C₄₁	#121	1	16	yes	—
272	C₂×C₄×C₄₁	C₂²×D₄	1	8	yes	—
273	C₂×C₄×C₄₁	C₂²×D₄	1	8	yes	—
274	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
275	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
276	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
277	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
278	C₂×#2426	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
279	C₂²×C₄₁	—	2	4	no	—
280	C₂²×C₄₁	—	2	4	no	—
281	C₂²×C₄₁	—	2	4	no	—
282	C₂²×C₄₁	—	4	2	no	—
283	C₂²×C₄₁	—	4	16	no	—
284	C₂²×C₄₁	—	4	2	no	—
285	C₂²×C₄₁	—	4	2	no	—
286	C₂²×C₄₁	—	4	2	no	—
287	C₂²×C₄₁	—	4	4	no	—
288	C₂²×C₄₁	—	4	4	no	—
289	C₂²×C₄₁	—	4	4	no	—
290	C₂²×C₄₁	—	4	4	no	—
291	C₂²×C₄₁	—	4	4	no	—
292	C₂²×C₄₁	—	4	4	no	—
293	C₂²×C₄₁	—	4	4	no	—
294	C₂²×C₄₁	—	8	16	no	—
295	C₂²×C₄₁	C₂×#121	1	4	yes	—
296	C₂²×C₄₁	#529	1	4	yes	—
297	C₂²×C₄₁	#542	1	4	yes	—
298	C₂²×C₄₁	#546	1	4	yes	—
299	C₂²×C₄₁	#548	1	4	yes	—
300	C₂²×C₄₁	#548	1	4	yes	—
301	C₂²×C₄₁	#550	1	4	yes	—
302	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
303	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
304	C₂²×C₄₁	C₂²×#41	1	1	yes	characteristic
305	C₂²×C₄₁	C₂²×#41	1	1	yes	characteristic
306	C₂²×C₄₁	C₂²×#41	1	1	yes	characteristic
307	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
308	C₂²×C₄₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
309	C₄×C₄₁	—	2	8	no	—
310	C₄×C₄₁	—	2	8	no	—
311	C₄×C₄₁	—	2	4	no	—
312	C₄×C₄₁	—	4	2	no	—
313	C₄×C₄₁	—	4	2	no	—
314	C₄×C₄₁	—	4	2	no	—
315	C₄×C₄₁	—	4	2	no	—
316	C₄×C₄₁	—	4	4	no	—
317	C₄×C₄₁	C₂×#121	1	8	yes	—
318	C₂²×#124	C₂×C₄₁	1	1	yes	characteristic, complemented
319	C₂²×C₂²⋊Q₈	C₂×C₄₁	1	1	yes	characteristic, complemented
320	C₂²×#121	C₂×C₄₁	1	1	yes	characteristic
321	C₂²×C₄×Q₈	C₂×C₄₁	1	1	yes	characteristic, complemented
322	#2426	C₂×C₄₁	1	16	yes	direct product factor
323	C₂×#396	C₂×C₄₁	1	2	yes	complemented
324	C₂×#394	C₂×C₄₁	1	2	yes	complemented
325	C₂×#390	C₂×C₄₁	1	2	yes	complemented
326	C₂×#390	C₂×C₄₁	1	1	yes	characteristic, complemented
327	C₂×#389	C₂×C₄₁	1	1	yes	characteristic, complemented
328	C₂×#388	C₂×C₄₁	1	2	yes	complemented
329	C₂×C₄×C₂²⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
330	C₂×C₄₁	—	4	4	no	—
331	C₂×C₄₁	—	8	4	no	—
332	C₂×C₄₁	#2426	1	8	yes	direct product factor
333	C₂×C₄₁	C₂²×#121	1	1	yes	characteristic
334	C₂×C₄₁	C₂×#529	1	1	yes	characteristic
335	C₂×C₄₁	C₂×#542	1	1	yes	characteristic
336	C₂×C₄₁	C₂×#546	1	1	yes	characteristic
337	C₂×C₄₁	C₂×#548	1	1	yes	characteristic
338	C₂×C₄₁	C₂×#548	1	1	yes	characteristic
339	C₂×C₄₁	C₂×#550	1	1	yes	characteristic
340	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
341	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
342	C₂³×D₄	C₂²×C₄₁	1	2	yes	—
343	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
344	C₂×#124	—	2	8	no	—
345	C₂×#124	C₂²×C₄₁	1	8	yes	complemented
346	C₂×C₂²⋊Q₈	—	2	8	no	—
347	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	8	yes	complemented
348	C₂×#121	—	2	8	no	—
349	C₂×#121	C₂²×C₄₁	1	8	yes	—
350	C₂×C₄×Q₈	—	2	8	no	—
351	C₂×C₄×Q₈	C₂²×C₄₁	1	8	yes	complemented
352	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
353	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
354	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
355	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
356	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
357	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
358	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
359	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
360	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
361	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
362	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
363	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
364	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
365	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
366	C₂²×C₄²	C₂²×C₄₁	1	2	yes	—
367	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
368	#396	C₂²×C₄₁	1	16	yes	complemented
369	#394	C₂²×C₄₁	1	16	yes	complemented
370	#390	C₂²×C₄₁	1	8	yes	complemented
371	#390	C₂²×C₄₁	1	16	yes	complemented
372	#389	C₂²×C₄₁	1	8	yes	complemented
373	#388	C₂²×C₄₁	1	16	yes	complemented
374	C₄×C₂²⋊C₄	C₂²×C₄₁	1	8	yes	complemented
375	C₂×#95	C₂²×C₄₁	1	2	yes	—
376	C₂×#95	C₂²×C₄₁	1	1	yes	characteristic
377	C₂×#95	C₂²×C₄₁	1	1	yes	characteristic
378	C₄₁	C₂×#2426	1	1	yes	characteristic, direct product factor, Sylow
379	C₂⁵	C₂³×C₄₁	1	2	yes	—
380	C₂⁵	C₂³×C₄₁	1	1	yes	characteristic
381	C₂²×Q₈	—	2	4	no	—
382	C₂²×Q₈	—	2	4	no	—
383	C₂²×Q₈	D₄×C₄₁	1	8	yes	complemented
384	C₂²×Q₈	C₂³×C₄₁	1	4	yes	—
385	C₂²×D₄	—	2	8	no	—
386	C₂²×D₄	—	2	8	no	—
387	C₂²×D₄	—	2	4	no	—
388	C₂²×D₄	—	2	4	no	—
389	C₂²×D₄	—	2	4	no	—
390	C₂²×D₄	—	4	4	no	—
391	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
392	C₂²×D₄	C₂³×C₄₁	1	8	yes	—
393	C₂³×C₄	—	2	4	no	—
394	C₂³×C₄	—	2	4	no	—
395	C₂³×C₄	—	2	4	no	—
396	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
397	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
398	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
399	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
400	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
401	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
402	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
403	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
404	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
405	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
406	#124	—	2	32	no	—
407	C₂²⋊Q₈	—	2	32	no	—
408	#121	—	2	32	no	—
409	C₄×Q₈	—	2	32	no	—
410	C₂×C₄⋊C₄	—	2	8	no	—
411	C₂×C₄⋊C₄	—	2	4	no	—
412	C₂×C₄⋊C₄	—	2	8	no	—
413	C₂×C₄⋊C₄	—	4	4	no	—
414	C₂×C₄⋊C₄	D₄×C₄₁	1	8	yes	—
415	C₂×C₄⋊C₄	C₂³×C₄₁	1	8	yes	—
416	C₂×C₄⋊C₄	C₂³×C₄₁	1	8	yes	—
417	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
418	C₂×C₄⋊C₄	C₂³×C₄₁	1	8	yes	—
419	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
420	C₂×C₂²⋊C₄	—	2	4	no	—
421	C₂×C₂²⋊C₄	—	2	8	no	—
422	C₂×C₂²⋊C₄	—	2	8	no	—
423	C₂×C₂²⋊C₄	—	2	8	no	—
424	C₂×C₂²⋊C₄	—	2	8	no	—
425	C₂×C₂²⋊C₄	—	2	4	no	—
426	C₂×C₂²⋊C₄	—	2	8	no	—
427	C₂×C₂²⋊C₄	—	4	4	no	—
428	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
430	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
432	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
433	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
436	C₂×C₄²	—	2	8	no	—
437	C₂×C₄²	—	2	4	no	—
438	C₂×C₄²	—	2	4	no	—
439	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
440	C₂×C₄²	C₂³×C₄₁	1	8	yes	—
441	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
442	#95	C₂³×C₄₁	1	4	yes	—
443	#95	C₂³×C₄₁	1	4	yes	—
444	#95	C₂³×C₄₁	1	8	yes	—
445	C₂⁴	—	2	2	no	—
446	C₂⁴	—	2	2	no	—
447	C₂⁴	—	2	2	no	—
448	C₂⁴	—	2	2	no	—
449	C₂⁴	—	2	2	no	—
450	C₂⁴	—	2	2	no	—
451	C₂⁴	—	2	4	no	—
452	C₂⁴	—	2	4	no	—
453	C₂⁴	—	2	4	no	—
454	C₂⁴	—	2	4	no	—
455	C₂⁴	—	2	4	no	—
456	C₂⁴	—	2	4	no	—
457	C₂⁴	—	2	4	no	—
458	C₂⁴	#41×C₄₁	1	4	yes	—
459	C₂⁴	C₂⁴×C₄₁	1	4	yes	—
460	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
461	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
462	C₂×Q₈	—	2	32	no	—
463	C₂×Q₈	—	2	8	no	—
464	C₂×Q₈	—	2	8	no	—
465	C₂×Q₈	C₂×D₄×C₄₁	1	16	yes	complemented
466	C₂×D₄	—	2	16	no	—
467	C₂×D₄	—	2	16	no	—
468	C₂×D₄	—	2	8	no	—
469	C₂×D₄	—	2	8	no	—
470	C₂×D₄	—	2	8	no	—
471	C₂×D₄	—	4	8	no	—
472	C₂×D₄	—	4	32	no	—
473	C₂×D₄	—	4	16	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	4	no	—
477	C₂²×C₄	—	2	4	no	—
478	C₂²×C₄	—	2	4	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	2	no	—
484	C₂²×C₄	—	2	4	no	—
485	C₂²×C₄	—	2	2	no	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	2	4	no	—
489	C₂²×C₄	—	2	2	no	—
490	C₂²×C₄	—	2	2	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	4	no	—
493	C₂²×C₄	—	2	2	no	—
494	C₂²×C₄	—	2	2	no	—
495	C₂²×C₄	—	2	8	no	—
496	C₂²×C₄	—	2	8	no	—
497	C₂²×C₄	—	2	8	no	—
498	C₂²×C₄	—	4	16	no	—
499	C₂²×C₄	C₂×D₄×C₄₁	1	8	yes	—
500	C₂²×C₄	C₂×D₄×C₄₁	1	8	yes	—
501	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
502	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
503	C₂²×C₄	#41×C₄₁	1	4	yes	—
504	C₂²×C₄	#41×C₄₁	1	4	yes	—
505	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
506	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
507	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
508	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
509	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
510	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
511	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
512	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
513	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
514	C₄⋊C₄	—	2	16	no	—
515	C₄⋊C₄	—	2	8	no	—
516	C₄⋊C₄	—	2	16	no	—
517	C₄⋊C₄	—	4	8	no	—
518	C₄⋊C₄	C₂×D₄×C₄₁	1	16	yes	—
519	C₂²⋊C₄	—	2	8	no	—
520	C₂²⋊C₄	—	2	16	no	—
521	C₂²⋊C₄	—	2	16	no	—
522	C₂²⋊C₄	—	2	16	no	—
523	C₂²⋊C₄	—	2	16	no	—
524	C₂²⋊C₄	—	2	8	no	—
525	C₂²⋊C₄	—	2	16	no	—
526	C₂²⋊C₄	—	4	8	no	—
527	C₄²	—	2	16	no	—
528	C₄²	—	2	8	no	—
529	C₄²	—	2	8	no	—
530	C₂³	—	2	8	no	—
531	C₂³	—	2	8	no	—
532	C₂³	—	2	8	no	—
533	C₂³	—	2	2	no	—
534	C₂³	—	2	2	no	—
535	C₂³	—	2	2	no	—
536	C₂³	—	2	2	no	—
537	C₂³	—	2	2	no	—
538	C₂³	—	2	2	no	—
539	C₂³	—	2	4	no	—
540	C₂³	—	2	4	no	—
541	C₂³	—	2	4	no	—
542	C₂³	—	2	4	no	—
543	C₂³	—	2	4	no	—
544	C₂³	—	2	4	no	—
545	C₂³	—	2	4	no	—
546	C₂³	—	4	4	no	—
547	C₂³	—	4	4	no	—
548	C₂³	—	4	4	no	—
549	C₂³	—	4	4	no	—
550	C₂³	—	4	8	no	—
551	C₂³	—	4	8	no	—
552	C₂³	—	4	8	no	—
553	C₂³	—	4	8	no	—
554	C₂³	—	4	8	no	—
555	C₂³	—	4	8	no	—
556	C₂³	—	4	8	no	—
557	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
558	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
559	C₂³	C₂×#41×C₄₁	1	4	yes	—
560	C₂³	C₂×#41×C₄₁	1	2	yes	—
561	C₂³	C₂×#41×C₄₁	1	2	yes	—
562	C₂³	C₂×#41×C₄₁	1	2	yes	—
563	C₂³	H(5,𝔽₂)×C₄₁	1	2	yes	—
564	C₂³	2₋¹⁺⁴×C₄₁	1	2	yes	—
565	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
566	Q₈	—	2	32	no	—
567	D₄	—	4	32	no	—
568	D₄	—	4	16	no	—
569	C₂×C₄	—	2	16	no	—
570	C₂×C₄	—	2	16	no	—
571	C₂×C₄	—	2	8	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	4	no	—
576	C₂×C₄	—	2	4	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	4	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	4	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	4	4	no	—
594	C₂×C₄	—	4	4	no	—
595	C₂×C₄	—	4	4	no	—
596	C₂×C₄	—	4	4	no	—
597	C₂×C₄	—	4	8	no	—
598	C₂×C₄	—	4	16	no	—
599	C₂×C₄	#121×C₄₁	1	16	yes	—
600	C₂×C₄	C₂²×D₄×C₄₁	1	8	yes	—
601	C₂×C₄	C₂²×D₄×C₄₁	1	8	yes	—
602	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
603	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
604	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
605	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
606	C₂²	—	2	4	no	—
607	C₂²	—	2	4	no	—
608	C₂²	—	2	4	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	16	no	—
611	C₂²	—	4	2	no	—
612	C₂²	—	4	2	no	—
613	C₂²	—	4	2	no	—
614	C₂²	—	4	4	no	—
615	C₂²	—	4	4	no	—
616	C₂²	—	4	4	no	—
617	C₂²	—	4	4	no	—
618	C₂²	—	4	4	no	—
619	C₂²	—	4	4	no	—
620	C₂²	—	4	4	no	—
621	C₂²	—	8	16	no	—
622	C₂²	C₂×#121×C₄₁	1	4	yes	—
623	C₂²	C₄₁×#529	1	4	yes	—
624	C₂²	C₄₁×#542	1	4	yes	—
625	C₂²	C₄₁×#546	1	4	yes	—
626	C₂²	C₄₁×#548	1	4	yes	—
627	C₂²	C₄₁×#548	1	4	yes	—
628	C₂²	C₄₁×#550	1	4	yes	—
629	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
630	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
631	C₂²	C₂²×#41×C₄₁	1	1	yes	characteristic
632	C₂²	C₂²×#41×C₄₁	1	1	yes	characteristic
633	C₂²	C₂²×#41×C₄₁	1	1	yes	characteristic
634	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
635	C₂²	C₂×2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
636	C₄	—	2	8	no	—
637	C₄	—	2	8	no	—
638	C₄	—	2	4	no	—
639	C₄	—	4	2	no	—
640	C₄	—	4	2	no	—
641	C₄	—	4	2	no	—
642	C₄	—	4	2	no	—
643	C₄	—	4	4	no	—
644	C₄	C₂×#121×C₄₁	1	8	yes	—
645	C₂	—	4	4	no	—
646	C₂	—	8	4	no	—
647	C₂	C₄₁×#2426	1	8	yes	direct product factor
648	C₂	C₂²×#121×C₄₁	1	1	yes	characteristic
649	C₂	C₂×C₄₁×#529	1	1	yes	characteristic
650	C₂	C₂×C₄₁×#542	1	1	yes	characteristic
651	C₂	C₂×C₄₁×#546	1	1	yes	characteristic
652	C₂	C₂×C₄₁×#548	1	1	yes	characteristic
653	C₂	C₂×C₄₁×#548	1	1	yes	characteristic
654	C₂	C₂×C₄₁×#550	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₄₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₁
prime radical	C₂²×#121×C₄₁	C₂
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
1. C₂²×#124×C₄₁	C₂	semidirect
2. C₂²×C₂²⋊Q₈×C₄₁	C₂	semidirect
4. C₂²×C₄×Q₈×C₄₁	C₂	semidirect
5. C₄₁×#2426	C₂	direct (N × H)
6. C₂×C₄₁×#396	C₂	semidirect
7. C₂×C₄₁×#394	C₂	semidirect
8. C₂×C₄₁×#390	C₂	semidirect
9. C₂×C₄₁×#390	C₂	semidirect
10. C₂×C₄₁×#389	C₂	semidirect
11. C₂×C₄₁×#388	C₂	semidirect
12. C₂×C₄×C₂²⋊C₄×C₄₁	C₂	semidirect
18. C₂×#124×C₄₁	C₂²	semidirect
20. C₂×C₂²⋊Q₈×C₄₁	C₂²	semidirect
24. C₂×C₄×Q₈×C₄₁	C₂²	semidirect
41. C₄₁×#396	C₂²	semidirect
42. C₄₁×#394	C₂²	semidirect
43. C₄₁×#390	C₂²	semidirect
44. C₄₁×#390	C₂²	semidirect
45. C₄₁×#389	C₂²	semidirect
46. C₄₁×#388	C₂²	semidirect
47. C₄×C₂²⋊C₄×C₄₁	C₂²	semidirect
55. C₂²×Q₈×C₄₁	D₄	semidirect
137. C₂×Q₈×C₄₁	C₂×D₄	semidirect
278. C₂×#2426	C₄₁	direct (N × H)
318. C₂²×#124	C₂×C₄₁	semidirect
319. C₂²×C₂²⋊Q₈	C₂×C₄₁	semidirect
321. C₂²×C₄×Q₈	C₂×C₄₁	semidirect
322. #2426	C₂×C₄₁	direct (N × H)
323. C₂×#396	C₂×C₄₁	semidirect
324. C₂×#394	C₂×C₄₁	semidirect
325. C₂×#390	C₂×C₄₁	semidirect
326. C₂×#390	C₂×C₄₁	semidirect
327. C₂×#389	C₂×C₄₁	semidirect
328. C₂×#388	C₂×C₄₁	semidirect
329. C₂×C₄×C₂²⋊C₄	C₂×C₄₁	semidirect
332. C₂×C₄₁	#2426	direct (N × H)
345. C₂×#124	C₂²×C₄₁	semidirect
347. C₂×C₂²⋊Q₈	C₂²×C₄₁	semidirect
351. C₂×C₄×Q₈	C₂²×C₄₁	semidirect
368. #396	C₂²×C₄₁	semidirect
369. #394	C₂²×C₄₁	semidirect
370. #390	C₂²×C₄₁	semidirect
371. #390	C₂²×C₄₁	semidirect
372. #389	C₂²×C₄₁	semidirect
373. #388	C₂²×C₄₁	semidirect
374. C₄×C₂²⋊C₄	C₂²×C₄₁	semidirect
378. C₄₁	C₂×#2426	direct (N × H)
383. C₂²×Q₈	D₄×C₄₁	semidirect
465. C₂×Q₈	C₂×D₄×C₄₁	semidirect
647. C₂	C₄₁×#2426	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#124×C₄₁	2
C₂²×C₂²⋊Q₈×C₄₁	2
C₂²×#121×C₄₁	2
C₂²×C₄×Q₈×C₄₁	2
C₄₁×#2426	2
C₂×C₄₁×#396	2
C₂×C₄₁×#394	2
C₂×C₄₁×#390	2
C₂×C₄₁×#389	2
C₂×C₄₁×#388	2
C₂×C₄×C₂²⋊C₄×C₄₁	2
C₂×#2426	41

Subgroups — C2×C41×#2426 #23810906

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#2426 #23810906