Subgroups — C₂×C₄₁×#3482 #23838916

Order 10496.

7706 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3482	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₄₁×#557	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#556	C₂	1	3	yes	maximal, complemented
4	C₂×C₄₁×#552	C₂	1	6	yes	maximal, complemented
5	C₂×D₄×Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄₁×#548	C₂	1	2	yes	maximal, complemented
7	C₂×C₄₁×#547	C₂	1	3	yes	maximal, complemented
8	C₂×C₄₁×#533	C₂	1	3	yes	maximal, complemented
9	C₂×C₄₁×#529	C₂	1	6	yes	maximal, complemented
10	C₂×C₄×#41×C₄₁	C₂	1	3	yes	maximal, complemented
11	C₂×C₄×#41×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₄×Q₈×C₄₁	C₂	1	2	yes	maximal, complemented
13	C₂²×#41×C₄₁	C₂²	1	3	yes	—
14	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
15	C₂³×Q₈×C₄₁	C₂²	1	2	yes	—
16	C₄₁×#557	C₂²	1	16	yes	complemented
17	C₄₁×#556	C₂²	1	48	yes	complemented
18	C₄₁×#552	C₂²	1	96	yes	complemented
19	D₄×Q₈×C₄₁	C₂²	1	16	yes	complemented
20	C₄₁×#548	C₂²	1	32	yes	complemented
21	C₄₁×#547	C₂²	1	48	yes	complemented
22	C₄₁×#533	C₂²	1	48	yes	complemented
23	C₂×C₄⋊Q₈×C₄₁	C₂²	1	3	yes	—
24	C₂×C₄⋊Q₈×C₄₁	C₂²	1	3	yes	—
25	C₄₁×#529	C₂²	1	96	yes	complemented
26	C₂×#126×C₄₁	C₂²	1	12	yes	—
27	C₂×#125×C₄₁	C₂²	1	6	yes	—
28	C₂×#125×C₄₁	C₂²	1	6	yes	—
29	C₂×#124×C₄₁	C₂²	1	6	yes	—
30	C₂×#123×C₄₁	C₂²	1	12	yes	—
31	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	6	yes	—
32	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	6	yes	—
33	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	6	yes	—
34	C₂×#121×C₄₁	C₂²	1	6	yes	—
35	C₄×#41×C₄₁	C₂²	1	48	yes	complemented
36	C₄×#41×C₄₁	C₂²	1	16	yes	complemented
37	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×Q₈×C₄₁	C₂²	1	6	yes	—
39	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
40	C₂×C₄×Q₈×C₄₁	C₂²	1	6	yes	—
41	C₂×C₄×Q₈×C₄₁	C₂²	1	3	yes	—
42	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₄₁	C₂²	1	3	yes	—
44	C₂×C₄×Q₈×C₄₁	C₂²	1	32	yes	complemented
45	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₄₁	C₂²	1	3	yes	—
47	C₂×C₄×D₄×C₄₁	C₂²	1	6	yes	—
48	C₂×C₄×D₄×C₄₁	C₂²	1	3	yes	—
49	C₂×C₄×D₄×C₄₁	C₂²	1	3	yes	—
50	C₂×C₄×D₄×C₄₁	C₂²	1	6	yes	—
51	C₂×#117×C₄₁	C₂²	1	3	yes	—
52	C₂×#117×C₄₁	C₂²	1	6	yes	—
53	C₂×#117×C₄₁	C₂²	1	3	yes	—
54	C₂×#117×C₄₁	C₂²	1	6	yes	—
55	C₂²×C₄⋊C₄×C₄₁	C₂²	1	6	yes	—
56	C₂²×C₄²×C₄₁	C₂²	1	6	yes	—
57	C₂²×C₄²×C₄₁	C₂²	1	3	yes	—
58	C₂×#41×C₄₁	—	2	8	no	—
59	C₂×#41×C₄₁	—	2	24	no	—
60	C₂×#41×C₄₁	C₂³	1	24	yes	—
61	C₂×#41×C₄₁	C₂³	1	8	yes	—
62	C₂²×Q₈×C₄₁	—	2	16	no	—
63	C₂²×Q₈×C₄₁	C₂³	1	6	yes	—
64	C₂²×Q₈×C₄₁	C₂³	1	3	yes	—
65	C₂²×Q₈×C₄₁	C₂³	1	16	yes	—
66	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₄₁	C₂³	1	6	yes	—
68	C₂²×D₄×C₄₁	C₂³	1	3	yes	—
69	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₄₁	C₂³	1	6	yes	—
71	C₂³×C₄×C₄₁	C₂³	1	6	yes	—
72	C₂³×C₄×C₄₁	C₂³	1	3	yes	—
73	C₂³×C₄×C₄₁	C₂³	1	3	yes	—
74	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
75	C₂³×C₄×C₄₁	C₂³	1	3	yes	—
76	C₄⋊Q₈×C₄₁	C₂³	1	24	yes	—
77	C₄⋊Q₈×C₄₁	C₂³	1	24	yes	—
78	#126×C₄₁	C₂³	1	96	yes	—
79	#125×C₄₁	C₂³	1	48	yes	—
80	#125×C₄₁	C₂³	1	48	yes	—
81	#124×C₄₁	C₂³	1	48	yes	—
82	#123×C₄₁	C₂³	1	96	yes	—
83	C₂²⋊Q₈×C₄₁	C₂³	1	48	yes	—
84	C₂²⋊Q₈×C₄₁	C₂³	1	48	yes	—
85	C₂²⋊Q₈×C₄₁	C₂³	1	48	yes	—
86	#121×C₄₁	C₂³	1	48	yes	—
87	C₄×Q₈×C₄₁	C₂³	1	8	yes	—
88	C₄×Q₈×C₄₁	C₂³	1	48	yes	—
89	C₄×Q₈×C₄₁	C₂³	1	16	yes	—
90	C₄×Q₈×C₄₁	C₂³	1	48	yes	—
91	C₄×Q₈×C₄₁	C₂³	1	24	yes	—
92	C₄×Q₈×C₄₁	C₂³	1	8	yes	—
93	C₄×Q₈×C₄₁	C₂³	1	24	yes	—
94	C₄×D₄×C₄₁	C₂³	1	8	yes	—
95	C₄×D₄×C₄₁	C₂³	1	24	yes	—
96	C₄×D₄×C₄₁	C₂³	1	48	yes	—
97	C₄×D₄×C₄₁	C₂³	1	24	yes	—
98	C₄×D₄×C₄₁	C₂³	1	24	yes	—
99	C₄×D₄×C₄₁	C₂³	1	48	yes	—
100	#117×C₄₁	C₂³	1	24	yes	—
101	#117×C₄₁	C₂³	1	48	yes	—
102	#117×C₄₁	C₂³	1	24	yes	—
103	#117×C₄₁	C₂³	1	48	yes	—
104	C₂×C₄⋊C₄×C₄₁	C₂³	1	3	yes	—
105	C₂×C₄⋊C₄×C₄₁	C₂³	1	6	yes	—
106	C₂×C₄⋊C₄×C₄₁	C₂³	1	12	yes	—
107	C₂×C₄⋊C₄×C₄₁	C₂³	1	48	yes	—
108	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₄₁	C₂³	1	6	yes	—
110	C₂×C₄⋊C₄×C₄₁	C₂³	1	3	yes	—
111	C₂×C₄⋊C₄×C₄₁	C₂³	1	3	yes	—
112	C₂×C₄⋊C₄×C₄₁	C₂³	1	6	yes	—
113	C₂×C₄⋊C₄×C₄₁	C₂³	1	6	yes	—
114	C₂×C₄⋊C₄×C₄₁	C₂³	1	6	yes	—
115	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
116	C₂×C₂²⋊C₄×C₄₁	C₂³	1	6	yes	—
117	C₂×C₂²⋊C₄×C₄₁	C₂³	1	6	yes	—
118	C₂×C₂²⋊C₄×C₄₁	C₂³	1	6	yes	—
119	C₂×C₂²⋊C₄×C₄₁	C₂³	1	12	yes	—
120	C₂×C₄²×C₄₁	C₂³	1	3	yes	—
121	C₂×C₄²×C₄₁	C₂³	1	6	yes	—
122	C₂×C₄²×C₄₁	C₂³	1	3	yes	—
123	C₂×C₄²×C₄₁	C₂³	1	6	yes	—
124	C₂×C₄²×C₄₁	C₂³	1	48	yes	—
125	C₂×C₄²×C₄₁	C₂³	1	24	yes	—
126	C₂×C₄²×C₄₁	C₂³	1	3	yes	—
127	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₄₁	C₂³	1	6	yes	—
129	C₂⁴×C₄₁	C₂⁴	1	3	yes	—
130	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
131	#41×C₄₁	—	2	32	no	—
132	#41×C₄₁	—	2	96	no	—
133	C₂×Q₈×C₄₁	—	2	64	no	—
134	C₂×Q₈×C₄₁	—	2	24	no	—
135	C₂×Q₈×C₄₁	—	2	12	no	—
136	C₂×Q₈×C₄₁	#41	1	8	yes	complemented
137	C₂×Q₈×C₄₁	C₂⁴	1	24	yes	—
138	C₂×Q₈×C₄₁	C₂⁴	1	12	yes	—
139	C₂×Q₈×C₄₁	C₂⁴	1	4	yes	—
140	C₂×D₄×C₄₁	—	2	24	no	—
141	C₂×D₄×C₄₁	—	2	12	no	—
142	C₂×D₄×C₄₁	#41	1	8	yes	complemented
143	C₂×D₄×C₄₁	C₂⁴	1	24	yes	—
144	C₂×D₄×C₄₁	C₂⁴	1	12	yes	—
145	C₂×D₄×C₄₁	C₂⁴	1	4	yes	—
146	C₂²×C₄×C₄₁	—	2	24	no	—
147	C₂²×C₄×C₄₁	—	2	24	no	—
148	C₂²×C₄×C₄₁	—	2	12	no	—
149	C₂²×C₄×C₄₁	—	2	12	no	—
150	C₂²×C₄×C₄₁	—	2	8	no	—
151	C₂²×C₄×C₄₁	—	2	12	no	—
152	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
153	C₂²×C₄×C₄₁	C₂⁴	1	8	yes	—
154	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
155	C₂²×C₄×C₄₁	C₂⁴	1	3	yes	—
156	C₂²×C₄×C₄₁	C₂⁴	1	3	yes	—
157	C₂²×C₄×C₄₁	C₂⁴	1	6	yes	—
158	C₂²×C₄×C₄₁	C₂⁴	1	6	yes	—
159	C₂²×C₄×C₄₁	C₂⁴	1	24	yes	—
160	C₂²×C₄×C₄₁	C₂⁴	1	24	yes	—
161	C₂²×C₄×C₄₁	C₂⁴	1	12	yes	—
162	C₂²×C₄×C₄₁	C₂⁴	1	12	yes	—
163	C₂²×C₄×C₄₁	C₂⁴	1	12	yes	—
164	C₂²×C₄×C₄₁	C₂⁴	1	3	yes	—
165	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
166	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
167	C₄⋊C₄×C₄₁	C₂⁴	1	12	yes	—
168	C₄⋊C₄×C₄₁	C₂⁴	1	24	yes	—
169	C₄⋊C₄×C₄₁	C₂⁴	1	48	yes	—
170	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
171	C₄⋊C₄×C₄₁	C₂⁴	1	24	yes	—
172	C₄⋊C₄×C₄₁	C₂⁴	1	12	yes	—
173	C₄⋊C₄×C₄₁	C₂⁴	1	12	yes	—
174	C₄⋊C₄×C₄₁	C₂⁴	1	24	yes	—
175	C₄⋊C₄×C₄₁	C₂⁴	1	24	yes	—
176	C₄⋊C₄×C₄₁	C₂⁴	1	24	yes	—
177	C₂²⋊C₄×C₄₁	C₂⁴	1	8	yes	—
178	C₂²⋊C₄×C₄₁	C₂⁴	1	24	yes	—
179	C₂²⋊C₄×C₄₁	C₂⁴	1	24	yes	—
180	C₂²⋊C₄×C₄₁	C₂⁴	1	24	yes	—
181	C₂²⋊C₄×C₄₁	C₂⁴	1	48	yes	—
182	C₄²×C₄₁	C₂⁴	1	12	yes	—
183	C₄²×C₄₁	C₂⁴	1	4	yes	—
184	C₄²×C₄₁	C₂⁴	1	12	yes	—
185	C₄²×C₄₁	C₂⁴	1	24	yes	—
186	C₄²×C₄₁	C₂⁴	1	24	yes	—
187	C₄²×C₄₁	C₂⁴	1	12	yes	—
188	C₄²×C₄₁	C₂⁴	1	24	yes	—
189	C₂³×C₄₁	—	2	4	no	—
190	C₂³×C₄₁	—	2	4	no	—
191	C₂³×C₄₁	—	2	6	no	—
192	C₂³×C₄₁	—	2	6	no	—
193	C₂³×C₄₁	—	2	6	no	—
194	C₂³×C₄₁	C₂×#41	1	8	yes	—
195	C₂³×C₄₁	C₂⁵	1	6	yes	—
196	C₂³×C₄₁	C₂⁵	1	4	yes	—
197	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
198	Q₈×C₄₁	—	2	48	no	—
199	Q₈×C₄₁	—	2	24	no	—
200	Q₈×C₄₁	C₂×#41	1	16	yes	complemented
201	D₄×C₄₁	—	2	48	no	—
202	D₄×C₄₁	—	2	24	no	—
203	D₄×C₄₁	C₂×#41	1	16	yes	complemented
204	C₂×C₄×C₄₁	—	2	6	no	—
205	C₂×C₄×C₄₁	—	2	2	no	—
206	C₂×C₄×C₄₁	—	2	12	no	—
207	C₂×C₄×C₄₁	—	2	12	no	—
208	C₂×C₄×C₄₁	—	2	48	no	—
209	C₂×C₄×C₄₁	—	2	4	no	—
210	C₂×C₄×C₄₁	—	2	6	no	—
211	C₂×C₄×C₄₁	—	2	48	no	—
212	C₂×C₄×C₄₁	—	2	24	no	—
213	C₂×C₄×C₄₁	—	2	24	no	—
214	C₂×C₄×C₄₁	—	2	16	no	—
215	C₂×C₄×C₄₁	—	2	24	no	—
216	C₂×C₄×C₄₁	C₂×#41	1	12	yes	—
217	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
218	C₂×C₄×C₄₁	2₋¹⁺⁴	1	4	yes	—
219	C₂×C₄×C₄₁	C₂⁵	1	4	yes	—
220	C₂×C₄×C₄₁	C₂⁵	1	2	yes	—
221	C₂×C₄×C₄₁	C₂⁵	1	6	yes	—
222	C₂×C₄×C₄₁	C₂⁵	1	6	yes	—
223	C₂×C₄×C₄₁	C₂⁵	1	12	yes	—
224	C₂×C₄×C₄₁	C₂⁵	1	12	yes	—
225	C₂×C₄×C₄₁	C₂⁵	1	6	yes	—
226	C₂×C₄×C₄₁	C₂⁵	1	2	yes	—
227	C₂×C₄×C₄₁	C₂⁵	1	2	yes	—
228	C₂×#3482	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂²×C₄₁	—	2	4	no	—
230	C₂²×C₄₁	—	2	4	no	—
231	C₂²×C₄₁	—	2	16	no	—
232	C₂²×C₄₁	—	2	6	no	—
233	C₂²×C₄₁	—	2	6	no	—
234	C₂²×C₄₁	—	2	6	no	—
235	C₂²×C₄₁	—	4	12	no	—
236	C₂²×C₄₁	C₂²×#41	1	8	yes	—
237	C₂²×C₄₁	C₂²×#41	1	2	yes	—
238	C₂²×C₄₁	C₂²×#41	1	2	yes	—
239	C₂²×C₄₁	C₂×2₋¹⁺⁴	1	2	yes	—
240	C₂²×C₄₁	C₂⁶	1	1	yes	characteristic
241	C₄×C₄₁	—	2	6	no	—
242	C₄×C₄₁	—	2	2	no	—
243	C₄×C₄₁	—	2	12	no	—
244	C₄×C₄₁	—	2	12	no	—
245	C₄×C₄₁	—	2	4	no	—
246	C₄×C₄₁	—	2	6	no	—
247	C₄×C₄₁	C₂²×#41	1	12	yes	—
248	C₄×C₄₁	C₂²×#41	1	4	yes	—
249	C₄×C₄₁	C₂×2₋¹⁺⁴	1	4	yes	—
250	#3482	C₂×C₄₁	1	32	yes	direct product factor
251	C₂×#557	C₂×C₄₁	1	1	yes	characteristic, complemented
252	C₂×#556	C₂×C₄₁	1	3	yes	complemented
253	C₂×#552	C₂×C₄₁	1	6	yes	complemented
254	C₂×D₄×Q₈	C₂×C₄₁	1	1	yes	characteristic, complemented
255	C₂×#548	C₂×C₄₁	1	2	yes	complemented
256	C₂×#547	C₂×C₄₁	1	3	yes	complemented
257	C₂×#533	C₂×C₄₁	1	3	yes	complemented
258	C₂×#529	C₂×C₄₁	1	6	yes	complemented
259	C₂×C₄×#41	C₂×C₄₁	1	1	yes	characteristic, complemented
260	C₂×C₄×#41	C₂×C₄₁	1	3	yes	complemented
261	C₂²×C₄×Q₈	C₂×C₄₁	1	2	yes	complemented
262	C₂×C₄₁	—	2	8	no	—
263	C₂×C₄₁	—	4	6	no	—
264	C₂×C₄₁	#3482	1	4	yes	direct product factor
265	C₂×C₄₁	C₂³×#41	1	1	yes	characteristic
266	C₂×C₄₁	C₂³×#41	1	1	yes	characteristic
267	C₂×C₄₁	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
268	C₂²×#41	C₂²×C₄₁	1	3	yes	—
269	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
270	C₂³×Q₈	C₂²×C₄₁	1	2	yes	—
271	#557	C₂²×C₄₁	1	16	yes	complemented
272	#556	C₂²×C₄₁	1	48	yes	complemented
273	#552	C₂²×C₄₁	1	96	yes	complemented
274	D₄×Q₈	C₂²×C₄₁	1	16	yes	complemented
275	#548	C₂²×C₄₁	1	32	yes	complemented
276	#547	C₂²×C₄₁	1	48	yes	complemented
277	#533	C₂²×C₄₁	1	48	yes	complemented
278	C₂×C₄⋊Q₈	C₂²×C₄₁	1	3	yes	—
279	C₂×C₄⋊Q₈	C₂²×C₄₁	1	3	yes	—
280	#529	C₂²×C₄₁	1	96	yes	complemented
281	C₂×#126	C₂²×C₄₁	1	12	yes	—
282	C₂×#125	C₂²×C₄₁	1	6	yes	—
283	C₂×#125	C₂²×C₄₁	1	6	yes	—
284	C₂×#124	C₂²×C₄₁	1	6	yes	—
285	C₂×#123	C₂²×C₄₁	1	12	yes	—
286	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	6	yes	—
287	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	6	yes	—
288	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	6	yes	—
289	C₂×#121	C₂²×C₄₁	1	6	yes	—
290	C₄×#41	C₂²×C₄₁	1	48	yes	complemented
291	C₄×#41	C₂²×C₄₁	1	16	yes	complemented
292	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
293	C₂×C₄×Q₈	C₂²×C₄₁	1	6	yes	—
294	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
295	C₂×C₄×Q₈	C₂²×C₄₁	1	6	yes	—
296	C₂×C₄×Q₈	C₂²×C₄₁	1	3	yes	—
297	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
298	C₂×C₄×Q₈	C₂²×C₄₁	1	3	yes	—
299	C₂×C₄×Q₈	C₂²×C₄₁	1	32	yes	complemented
300	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
301	C₂×C₄×D₄	C₂²×C₄₁	1	6	yes	—
302	C₂×C₄×D₄	C₂²×C₄₁	1	3	yes	—
303	C₂×C₄×D₄	C₂²×C₄₁	1	3	yes	—
304	C₂×C₄×D₄	C₂²×C₄₁	1	3	yes	—
305	C₂×C₄×D₄	C₂²×C₄₁	1	6	yes	—
306	C₂×#117	C₂²×C₄₁	1	3	yes	—
307	C₂×#117	C₂²×C₄₁	1	6	yes	—
308	C₂×#117	C₂²×C₄₁	1	3	yes	—
309	C₂×#117	C₂²×C₄₁	1	6	yes	—
310	C₂²×C₄⋊C₄	C₂²×C₄₁	1	6	yes	—
311	C₂²×C₄²	C₂²×C₄₁	1	6	yes	—
312	C₂²×C₄²	C₂²×C₄₁	1	3	yes	—
313	C₄₁	C₂×#3482	1	1	yes	characteristic, direct product factor, Sylow
314	C₂×#41	—	2	8	no	—
315	C₂×#41	—	2	24	no	—
316	C₂×#41	C₂³×C₄₁	1	24	yes	—
317	C₂×#41	C₂³×C₄₁	1	8	yes	—
318	C₂²×Q₈	—	2	16	no	—
319	C₂²×Q₈	C₂³×C₄₁	1	6	yes	—
320	C₂²×Q₈	C₂³×C₄₁	1	3	yes	—
321	C₂²×Q₈	C₂³×C₄₁	1	16	yes	—
322	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
323	C₂²×D₄	C₂³×C₄₁	1	6	yes	—
324	C₂²×D₄	C₂³×C₄₁	1	3	yes	—
325	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
326	C₂³×C₄	C₂³×C₄₁	1	6	yes	—
327	C₂³×C₄	C₂³×C₄₁	1	6	yes	—
328	C₂³×C₄	C₂³×C₄₁	1	3	yes	—
329	C₂³×C₄	C₂³×C₄₁	1	3	yes	—
330	C₂³×C₄	C₂³×C₄₁	1	3	yes	—
331	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
332	C₄⋊Q₈	C₂³×C₄₁	1	24	yes	—
333	C₄⋊Q₈	C₂³×C₄₁	1	24	yes	—
334	#126	C₂³×C₄₁	1	96	yes	—
335	#125	C₂³×C₄₁	1	48	yes	—
336	#125	C₂³×C₄₁	1	48	yes	—
337	#124	C₂³×C₄₁	1	48	yes	—
338	#123	C₂³×C₄₁	1	96	yes	—
339	C₂²⋊Q₈	C₂³×C₄₁	1	48	yes	—
340	C₂²⋊Q₈	C₂³×C₄₁	1	48	yes	—
341	C₂²⋊Q₈	C₂³×C₄₁	1	48	yes	—
342	#121	C₂³×C₄₁	1	48	yes	—
343	C₄×Q₈	C₂³×C₄₁	1	8	yes	—
344	C₄×Q₈	C₂³×C₄₁	1	48	yes	—
345	C₄×Q₈	C₂³×C₄₁	1	16	yes	—
346	C₄×Q₈	C₂³×C₄₁	1	48	yes	—
347	C₄×Q₈	C₂³×C₄₁	1	24	yes	—
348	C₄×Q₈	C₂³×C₄₁	1	8	yes	—
349	C₄×Q₈	C₂³×C₄₁	1	24	yes	—
350	C₄×D₄	C₂³×C₄₁	1	8	yes	—
351	C₄×D₄	C₂³×C₄₁	1	24	yes	—
352	C₄×D₄	C₂³×C₄₁	1	48	yes	—
353	C₄×D₄	C₂³×C₄₁	1	24	yes	—
354	C₄×D₄	C₂³×C₄₁	1	24	yes	—
355	C₄×D₄	C₂³×C₄₁	1	48	yes	—
356	#117	C₂³×C₄₁	1	24	yes	—
357	#117	C₂³×C₄₁	1	48	yes	—
358	#117	C₂³×C₄₁	1	24	yes	—
359	#117	C₂³×C₄₁	1	48	yes	—
360	C₂×C₄⋊C₄	C₂³×C₄₁	1	3	yes	—
361	C₂×C₄⋊C₄	C₂³×C₄₁	1	6	yes	—
362	C₂×C₄⋊C₄	C₂³×C₄₁	1	12	yes	—
363	C₂×C₄⋊C₄	C₂³×C₄₁	1	48	yes	—
364	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
365	C₂×C₄⋊C₄	C₂³×C₄₁	1	6	yes	—
366	C₂×C₄⋊C₄	C₂³×C₄₁	1	3	yes	—
367	C₂×C₄⋊C₄	C₂³×C₄₁	1	3	yes	—
368	C₂×C₄⋊C₄	C₂³×C₄₁	1	6	yes	—
369	C₂×C₄⋊C₄	C₂³×C₄₁	1	6	yes	—
370	C₂×C₄⋊C₄	C₂³×C₄₁	1	6	yes	—
371	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
372	C₂×C₂²⋊C₄	C₂³×C₄₁	1	6	yes	—
373	C₂×C₂²⋊C₄	C₂³×C₄₁	1	6	yes	—
374	C₂×C₂²⋊C₄	C₂³×C₄₁	1	6	yes	—
375	C₂×C₂²⋊C₄	C₂³×C₄₁	1	12	yes	—
376	C₂×C₄²	C₂³×C₄₁	1	3	yes	—
377	C₂×C₄²	C₂³×C₄₁	1	6	yes	—
378	C₂×C₄²	C₂³×C₄₁	1	6	yes	—
379	C₂×C₄²	C₂³×C₄₁	1	3	yes	—
380	C₂×C₄²	C₂³×C₄₁	1	6	yes	—
381	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
382	C₂×C₄²	C₂³×C₄₁	1	3	yes	—
383	C₂×C₄²	C₂³×C₄₁	1	48	yes	—
384	C₂×C₄²	C₂³×C₄₁	1	24	yes	—
385	C₂⁴	C₂⁴×C₄₁	1	3	yes	—
386	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
387	#41	—	2	32	no	—
388	#41	—	2	96	no	—
389	C₂×Q₈	—	2	64	no	—
390	C₂×Q₈	—	2	24	no	—
391	C₂×Q₈	—	2	12	no	—
392	C₂×Q₈	#41×C₄₁	1	8	yes	complemented
393	C₂×Q₈	C₂⁴×C₄₁	1	24	yes	—
394	C₂×Q₈	C₂⁴×C₄₁	1	12	yes	—
395	C₂×Q₈	C₂⁴×C₄₁	1	4	yes	—
396	C₂×D₄	—	2	24	no	—
397	C₂×D₄	—	2	12	no	—
398	C₂×D₄	#41×C₄₁	1	8	yes	complemented
399	C₂×D₄	C₂⁴×C₄₁	1	24	yes	—
400	C₂×D₄	C₂⁴×C₄₁	1	12	yes	—
401	C₂×D₄	C₂⁴×C₄₁	1	4	yes	—
402	C₂²×C₄	—	2	24	no	—
403	C₂²×C₄	—	2	24	no	—
404	C₂²×C₄	—	2	12	no	—
405	C₂²×C₄	—	2	12	no	—
406	C₂²×C₄	—	2	8	no	—
407	C₂²×C₄	—	2	12	no	—
408	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
409	C₂²×C₄	C₂⁴×C₄₁	1	8	yes	—
410	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
411	C₂²×C₄	C₂⁴×C₄₁	1	3	yes	—
412	C₂²×C₄	C₂⁴×C₄₁	1	3	yes	—
413	C₂²×C₄	C₂⁴×C₄₁	1	6	yes	—
414	C₂²×C₄	C₂⁴×C₄₁	1	6	yes	—
415	C₂²×C₄	C₂⁴×C₄₁	1	24	yes	—
416	C₂²×C₄	C₂⁴×C₄₁	1	24	yes	—
417	C₂²×C₄	C₂⁴×C₄₁	1	12	yes	—
418	C₂²×C₄	C₂⁴×C₄₁	1	12	yes	—
419	C₂²×C₄	C₂⁴×C₄₁	1	12	yes	—
420	C₂²×C₄	C₂⁴×C₄₁	1	3	yes	—
421	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
422	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
423	C₄⋊C₄	C₂⁴×C₄₁	1	12	yes	—
424	C₄⋊C₄	C₂⁴×C₄₁	1	24	yes	—
425	C₄⋊C₄	C₂⁴×C₄₁	1	48	yes	—
426	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
427	C₄⋊C₄	C₂⁴×C₄₁	1	24	yes	—
428	C₄⋊C₄	C₂⁴×C₄₁	1	12	yes	—
429	C₄⋊C₄	C₂⁴×C₄₁	1	12	yes	—
430	C₄⋊C₄	C₂⁴×C₄₁	1	24	yes	—
431	C₄⋊C₄	C₂⁴×C₄₁	1	24	yes	—
432	C₄⋊C₄	C₂⁴×C₄₁	1	24	yes	—
433	C₂²⋊C₄	C₂⁴×C₄₁	1	8	yes	—
434	C₂²⋊C₄	C₂⁴×C₄₁	1	24	yes	—
435	C₂²⋊C₄	C₂⁴×C₄₁	1	24	yes	—
436	C₂²⋊C₄	C₂⁴×C₄₁	1	24	yes	—
437	C₂²⋊C₄	C₂⁴×C₄₁	1	48	yes	—
438	C₄²	C₂⁴×C₄₁	1	12	yes	—
439	C₄²	C₂⁴×C₄₁	1	4	yes	—
440	C₄²	C₂⁴×C₄₁	1	12	yes	—
441	C₄²	C₂⁴×C₄₁	1	24	yes	—
442	C₄²	C₂⁴×C₄₁	1	24	yes	—
443	C₄²	C₂⁴×C₄₁	1	12	yes	—
444	C₄²	C₂⁴×C₄₁	1	24	yes	—
445	C₂³	—	2	4	no	—
446	C₂³	—	2	4	no	—
447	C₂³	—	2	6	no	—
448	C₂³	—	2	6	no	—
449	C₂³	—	2	6	no	—
450	C₂³	C₂×#41×C₄₁	1	8	yes	—
451	C₂³	C₂⁵×C₄₁	1	6	yes	—
452	C₂³	C₂⁵×C₄₁	1	4	yes	—
453	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
454	Q₈	—	2	48	no	—
455	Q₈	—	2	24	no	—
456	Q₈	C₂×#41×C₄₁	1	16	yes	complemented
457	D₄	—	2	48	no	—
458	D₄	—	2	24	no	—
459	D₄	C₂×#41×C₄₁	1	16	yes	complemented
460	C₂×C₄	—	2	6	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	12	no	—
463	C₂×C₄	—	2	12	no	—
464	C₂×C₄	—	2	48	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	6	no	—
467	C₂×C₄	—	2	48	no	—
468	C₂×C₄	—	2	24	no	—
469	C₂×C₄	—	2	24	no	—
470	C₂×C₄	—	2	16	no	—
471	C₂×C₄	—	2	24	no	—
472	C₂×C₄	C₂×#41×C₄₁	1	12	yes	—
473	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
474	C₂×C₄	2₋¹⁺⁴×C₄₁	1	4	yes	—
475	C₂×C₄	C₂⁵×C₄₁	1	4	yes	—
476	C₂×C₄	C₂⁵×C₄₁	1	2	yes	—
477	C₂×C₄	C₂⁵×C₄₁	1	6	yes	—
478	C₂×C₄	C₂⁵×C₄₁	1	6	yes	—
479	C₂×C₄	C₂⁵×C₄₁	1	12	yes	—
480	C₂×C₄	C₂⁵×C₄₁	1	12	yes	—
481	C₂×C₄	C₂⁵×C₄₁	1	6	yes	—
482	C₂×C₄	C₂⁵×C₄₁	1	2	yes	—
483	C₂×C₄	C₂⁵×C₄₁	1	2	yes	—
484	C₂²	—	2	4	no	—
485	C₂²	—	2	4	no	—
486	C₂²	—	2	16	no	—
487	C₂²	—	2	6	no	—
488	C₂²	—	2	6	no	—
489	C₂²	—	2	6	no	—
490	C₂²	—	4	12	no	—
491	C₂²	C₂²×#41×C₄₁	1	8	yes	—
492	C₂²	C₂²×#41×C₄₁	1	2	yes	—
493	C₂²	C₂²×#41×C₄₁	1	2	yes	—
494	C₂²	C₂×2₋¹⁺⁴×C₄₁	1	2	yes	—
495	C₂²	C₂⁶×C₄₁	1	1	yes	characteristic
496	C₄	—	2	6	no	—
497	C₄	—	2	2	no	—
498	C₄	—	2	12	no	—
499	C₄	—	2	12	no	—
500	C₄	—	2	4	no	—
501	C₄	—	2	6	no	—
502	C₄	C₂²×#41×C₄₁	1	12	yes	—
503	C₄	C₂²×#41×C₄₁	1	4	yes	—
504	C₄	C₂×2₋¹⁺⁴×C₄₁	1	4	yes	—
505	C₂	—	2	8	no	—
506	C₂	—	4	6	no	—
507	C₂	C₄₁×#3482	1	4	yes	direct product factor
508	C₂	C₂³×#41×C₄₁	1	1	yes	characteristic
509	C₂	C₂³×#41×C₄₁	1	1	yes	characteristic
510	C₂	C₂²×2₋¹⁺⁴×C₄₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₄₁	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₄₁
socle	C₂³×C₄₁	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3482	C₂	direct (N × H)
2. C₂×C₄₁×#557	C₂	semidirect
3. C₂×C₄₁×#556	C₂	semidirect
4. C₂×C₄₁×#552	C₂	semidirect
5. C₂×D₄×Q₈×C₄₁	C₂	semidirect
6. C₂×C₄₁×#548	C₂	semidirect
7. C₂×C₄₁×#547	C₂	semidirect
8. C₂×C₄₁×#533	C₂	semidirect
9. C₂×C₄₁×#529	C₂	semidirect
10. C₂×C₄×#41×C₄₁	C₂	semidirect
11. C₂×C₄×#41×C₄₁	C₂	semidirect
12. C₂²×C₄×Q₈×C₄₁	C₂	semidirect
16. C₄₁×#557	C₂²	semidirect
17. C₄₁×#556	C₂²	semidirect
18. C₄₁×#552	C₂²	semidirect
19. D₄×Q₈×C₄₁	C₂²	semidirect
20. C₄₁×#548	C₂²	semidirect
21. C₄₁×#547	C₂²	semidirect
22. C₄₁×#533	C₂²	semidirect
25. C₄₁×#529	C₂²	semidirect
35. C₄×#41×C₄₁	C₂²	semidirect
36. C₄×#41×C₄₁	C₂²	semidirect
44. C₂×C₄×Q₈×C₄₁	C₂²	semidirect
136. C₂×Q₈×C₄₁	#41	semidirect
142. C₂×D₄×C₄₁	#41	semidirect
200. Q₈×C₄₁	C₂×#41	semidirect
203. D₄×C₄₁	C₂×#41	semidirect
228. C₂×#3482	C₄₁	direct (N × H)
250. #3482	C₂×C₄₁	direct (N × H)
251. C₂×#557	C₂×C₄₁	semidirect
252. C₂×#556	C₂×C₄₁	semidirect
253. C₂×#552	C₂×C₄₁	semidirect
254. C₂×D₄×Q₈	C₂×C₄₁	semidirect
255. C₂×#548	C₂×C₄₁	semidirect
256. C₂×#547	C₂×C₄₁	semidirect
257. C₂×#533	C₂×C₄₁	semidirect
258. C₂×#529	C₂×C₄₁	semidirect
259. C₂×C₄×#41	C₂×C₄₁	semidirect
260. C₂×C₄×#41	C₂×C₄₁	semidirect
261. C₂²×C₄×Q₈	C₂×C₄₁	semidirect
264. C₂×C₄₁	#3482	direct (N × H)
271. #557	C₂²×C₄₁	semidirect
272. #556	C₂²×C₄₁	semidirect
273. #552	C₂²×C₄₁	semidirect
274. D₄×Q₈	C₂²×C₄₁	semidirect
275. #548	C₂²×C₄₁	semidirect
276. #547	C₂²×C₄₁	semidirect
277. #533	C₂²×C₄₁	semidirect
280. #529	C₂²×C₄₁	semidirect
290. C₄×#41	C₂²×C₄₁	semidirect
291. C₄×#41	C₂²×C₄₁	semidirect
299. C₂×C₄×Q₈	C₂²×C₄₁	semidirect
313. C₄₁	C₂×#3482	direct (N × H)
392. C₂×Q₈	#41×C₄₁	semidirect
398. C₂×D₄	#41×C₄₁	semidirect
456. Q₈	C₂×#41×C₄₁	semidirect
459. D₄	C₂×#41×C₄₁	semidirect
507. C₂	C₄₁×#3482	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×#3482	2
C₂×C₄₁×#557	2
C₂×C₄₁×#556	2
C₂×C₄₁×#552	2
C₂×D₄×Q₈×C₄₁	2
C₂×C₄₁×#548	2
C₂×C₄₁×#547	2
C₂×C₄₁×#533	2
C₂×C₄₁×#529	2
C₂×C₄×#41×C₄₁	2
C₂²×C₄×Q₈×C₄₁	2
C₂×#3482	41

Subgroups — C2×C41×#3482 #23838916

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#3482 #23838916