Subgroups — C₄×C₄₁×#548 #23810359

Order 10496.

3232 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#548	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#41×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2367	C₂	1	3	yes	maximal, complemented
5	C₄₁×#2362	C₂	1	3	yes	maximal, complemented
6	C₄₁×#2361	C₂	1	3	yes	maximal, complemented
7	C₄₁×#2352	C₂	1	3	yes	maximal, complemented
8	C₄₁×#2351	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#2341	C₂	1	1	yes	maximal, characteristic, complemented
10	Q₈×C₂²⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#124×C₄₁	C₂	1	3	yes	maximal, complemented
12	C₄×C₂²⋊Q₈×C₄₁	C₂	1	3	yes	maximal, complemented
13	C₄×#121×C₄₁	C₂	1	3	yes	maximal, complemented
14	C₄²×Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄²×D₄×C₄₁	C₂	1	3	yes	maximal, complemented
16	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
17	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
18	C₄₁×#548	C₄	1	16	yes	direct product factor
19	C₂×#124×C₄₁	C₂²	1	3	yes	—
20	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	3	yes	—
21	C₂×#121×C₄₁	C₂²	1	3	yes	—
22	C₄×#41×C₄₁	—	2	8	no	—
23	C₂×C₄×Q₈×C₄₁	—	2	8	no	—
24	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₄₁	C₂²	1	3	yes	—
26	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₄₁	C₂²	1	3	yes	—
29	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₄₁	C₂²	1	3	yes	—
32	C₂×C₄×D₄×C₄₁	C₂²	1	3	yes	—
33	C₂×C₄×D₄×C₄₁	C₂²	1	3	yes	—
34	C₂×C₄×D₄×C₄₁	C₂²	1	3	yes	—
35	C₂×C₄×D₄×C₄₁	C₂²	1	3	yes	—
36	C₂×#117×C₄₁	C₂²	1	3	yes	—
37	C₂²×C₄⋊C₄×C₄₁	C₂²	1	3	yes	—
38	C₂²×C₄²×C₄₁	C₂²	1	3	yes	—
39	C₂²×C₄²×C₄₁	C₂²	1	3	yes	—
40	C₄₁×#391	C₂²	1	3	yes	—
41	C₄₁×#391	C₂²	1	3	yes	—
42	C₄₁×#390	C₂²	1	3	yes	—
43	C₄₁×#390	C₂²	1	3	yes	—
44	C₄₁×#389	C₂²	1	3	yes	—
45	C₄₁×#389	C₂²	1	3	yes	—
46	C₄₁×#388	C₂²	1	6	yes	—
47	C₄₁×#388	C₂²	1	6	yes	—
48	C₄₁×#388	C₂²	1	6	yes	—
49	C₄₁×#387	C₂²	1	6	yes	—
50	C₄₁×#386	C₂²	1	6	yes	—
51	C₄₁×#385	C₂²	1	6	yes	—
52	C₄₁×#382	C₂²	1	3	yes	—
53	C₄₁×#380	C₂²	1	3	yes	—
54	C₄₁×#380	C₂²	1	3	yes	—
55	C₄×C₄⋊C₄×C₄₁	C₂²	1	3	yes	—
56	C₄×C₄⋊C₄×C₄₁	C₂²	1	3	yes	—
57	C₄×C₄⋊C₄×C₄₁	C₂²	1	3	yes	—
58	C₄×C₄⋊C₄×C₄₁	C₂²	1	3	yes	—
59	C₄×C₄⋊C₄×C₄₁	C₂²	1	3	yes	—
60	C₄×C₄⋊C₄×C₄₁	C₂²	1	3	yes	—
61	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
62	C₄×C₂²⋊C₄×C₄₁	C₂²	1	3	yes	—
63	C₄×C₂²⋊C₄×C₄₁	C₂²	1	3	yes	—
64	C₄×C₂²⋊C₄×C₄₁	C₂²	1	3	yes	—
65	C₄×C₂²⋊C₄×C₄₁	C₂²	1	3	yes	—
66	C₄×C₂²⋊C₄×C₄₁	C₂²	1	3	yes	—
67	C₄×C₂²⋊C₄×C₄₁	C₂²	1	6	yes	—
68	C₄³×C₄₁	C₂²	1	3	yes	—
69	C₂×#41×C₄₁	—	2	4	no	—
70	C₂×#41×C₄₁	—	2	4	no	—
71	C₂×#41×C₄₁	C₂×C₄	1	8	yes	complemented
72	C₂²×Q₈×C₄₁	—	2	4	no	—
73	C₂²×Q₈×C₄₁	—	2	4	no	—
74	C₂²×Q₈×C₄₁	C₂×C₄	1	8	yes	complemented
75	C₂²×Q₈×C₄₁	C₂³	1	3	yes	—
76	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₄₁	C₂³	1	3	yes	—
78	C₂²×D₄×C₄₁	C₂³	1	3	yes	—
79	C₂³×C₄×C₄₁	C₂³	1	3	yes	—
80	C₂³×C₄×C₄₁	C₂³	1	3	yes	—
81	C₂³×C₄×C₄₁	C₂³	1	3	yes	—
82	C₂³×C₄×C₄₁	C₂³	1	3	yes	—
83	C₂³×C₄×C₄₁	C₂³	1	3	yes	—
84	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
85	#124×C₄₁	C₂×C₄	1	24	yes	complemented
86	C₂²⋊Q₈×C₄₁	C₂×C₄	1	24	yes	complemented
87	#121×C₄₁	C₂×C₄	1	24	yes	complemented
88	C₄×Q₈×C₄₁	—	2	4	no	—
89	C₄×Q₈×C₄₁	—	2	4	no	—
90	C₄×Q₈×C₄₁	—	2	4	no	—
91	C₄×Q₈×C₄₁	—	2	12	no	—
92	C₄×Q₈×C₄₁	—	2	12	no	—
93	C₄×Q₈×C₄₁	C₂×C₄	1	8	yes	complemented
94	C₄×Q₈×C₄₁	D₄	1	8	yes	complemented
95	C₄×D₄×C₄₁	—	2	12	no	—
96	C₄×D₄×C₄₁	—	2	12	no	—
97	C₄×D₄×C₄₁	—	2	12	no	—
98	C₄×D₄×C₄₁	—	2	12	no	—
99	C₄×D₄×C₄₁	C₂×C₄	1	24	yes	complemented
100	#117×C₄₁	—	2	12	no	—
101	C₂×C₄⋊C₄×C₄₁	—	2	12	no	—
102	C₂×C₄⋊C₄×C₄₁	C₂³	1	3	yes	—
103	C₂×C₄⋊C₄×C₄₁	C₂³	1	6	yes	—
104	C₂×C₄⋊C₄×C₄₁	C₂³	1	3	yes	—
105	C₂×C₄⋊C₄×C₄₁	C₂³	1	3	yes	—
106	C₂×C₄⋊C₄×C₄₁	C₂³	1	3	yes	—
107	C₂×C₄⋊C₄×C₄₁	C₂³	1	3	yes	—
108	C₂×C₄⋊C₄×C₄₁	C₂³	1	3	yes	—
109	C₂×C₄⋊C₄×C₄₁	C₂³	1	3	yes	—
110	C₂×C₄⋊C₄×C₄₁	C₂³	1	3	yes	—
111	C₂×C₂²⋊C₄×C₄₁	C₂³	1	6	yes	—
112	C₂×C₂²⋊C₄×C₄₁	C₂³	1	3	yes	—
113	C₂×C₂²⋊C₄×C₄₁	C₂³	1	3	yes	—
114	C₂×C₂²⋊C₄×C₄₁	C₂³	1	3	yes	—
115	C₂×C₂²⋊C₄×C₄₁	C₂³	1	6	yes	—
116	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
117	C₂×C₂²⋊C₄×C₄₁	C₂³	1	3	yes	—
118	C₂×C₂²⋊C₄×C₄₁	C₂³	1	6	yes	—
119	C₂×C₂²⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₄₁	—	2	12	no	—
121	C₂×C₄²×C₄₁	—	2	12	no	—
122	C₂×C₄²×C₄₁	C₂³	1	3	yes	—
123	C₂×C₄²×C₄₁	C₂³	1	3	yes	—
124	C₂×C₄²×C₄₁	C₂³	1	3	yes	—
125	C₂×C₄²×C₄₁	C₂³	1	3	yes	—
126	C₂×C₄²×C₄₁	C₂³	1	3	yes	—
127	C₂×C₄²×C₄₁	C₂³	1	3	yes	—
128	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₄₁	C₂³	1	3	yes	—
130	C₂×C₄²×C₄₁	C₂³	1	3	yes	—
131	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₄₁	C₂³	1	3	yes	—
133	C₂×C₄²×C₄₁	C₂³	1	3	yes	—
134	C₂×C₄²×C₄₁	C₂³	1	3	yes	—
135	#95×C₄₁	C₂³	1	1	yes	characteristic
136	#95×C₄₁	C₂³	1	1	yes	characteristic
137	#95×C₄₁	C₂³	1	3	yes	—
138	#95×C₄₁	C₂³	1	3	yes	—
139	#95×C₄₁	C₂³	1	3	yes	—
140	#95×C₄₁	C₂³	1	3	yes	—
141	#95×C₄₁	C₂³	1	6	yes	—
142	#95×C₄₁	C₂³	1	6	yes	—
143	#95×C₄₁	C₂³	1	6	yes	—
144	C₂⁴×C₄₁	C₂⁴	1	3	yes	—
145	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
146	#41×C₄₁	—	2	32	no	—
147	C₂×Q₈×C₄₁	—	2	32	no	—
148	C₂×Q₈×C₄₁	—	2	6	no	—
149	C₂×Q₈×C₄₁	—	2	6	no	—
150	C₂×Q₈×C₄₁	C₂²×C₄	1	12	yes	—
151	C₂×Q₈×C₄₁	C₂²×C₄	1	4	yes	—
152	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
153	C₂×Q₈×C₄₁	#41	1	4	yes	—
154	C₂×D₄×C₄₁	—	2	6	no	—
155	C₂×D₄×C₄₁	—	2	6	no	—
156	C₂×D₄×C₄₁	—	2	6	no	—
157	C₂×D₄×C₄₁	—	2	6	no	—
158	C₂×D₄×C₄₁	C₂²×C₄	1	12	yes	—
159	C₂×D₄×C₄₁	C₂²×C₄	1	12	yes	—
160	C₂²×C₄×C₄₁	—	2	2	no	—
161	C₂²×C₄×C₄₁	—	2	6	no	—
162	C₂²×C₄×C₄₁	—	2	6	no	—
163	C₂²×C₄×C₄₁	—	2	6	no	—
164	C₂²×C₄×C₄₁	—	2	6	no	—
165	C₂²×C₄×C₄₁	—	2	2	no	—
166	C₂²×C₄×C₄₁	—	2	6	no	—
167	C₂²×C₄×C₄₁	—	2	6	no	—
168	C₂²×C₄×C₄₁	—	2	6	no	—
169	C₂²×C₄×C₄₁	—	2	6	no	—
170	C₂²×C₄×C₄₁	—	2	6	no	—
171	C₂²×C₄×C₄₁	—	2	6	no	—
172	C₂²×C₄×C₄₁	—	2	6	no	—
173	C₂²×C₄×C₄₁	—	4	3	no	—
174	C₂²×C₄×C₄₁	—	4	3	no	—
175	C₂²×C₄×C₄₁	C₂²×C₄	1	12	yes	—
176	C₂²×C₄×C₄₁	C₂²×C₄	1	12	yes	—
177	C₂²×C₄×C₄₁	#41	1	4	yes	complemented
178	C₂²×C₄×C₄₁	C₂⁴	1	3	yes	—
179	C₂²×C₄×C₄₁	C₂⁴	1	3	yes	—
180	C₂²×C₄×C₄₁	C₂⁴	1	3	yes	—
181	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
182	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
183	C₂²×C₄×C₄₁	C₂⁴	1	3	yes	—
184	C₂²×C₄×C₄₁	C₂⁴	1	3	yes	—
185	C₂²×C₄×C₄₁	C₂⁴	1	3	yes	—
186	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
187	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
188	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
189	C₂²×C₄×C₄₁	C₂⁴	1	3	yes	—
190	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
191	C₄⋊C₄×C₄₁	—	2	12	no	—
192	C₄⋊C₄×C₄₁	—	2	6	no	—
193	C₄⋊C₄×C₄₁	—	2	6	no	—
194	C₄⋊C₄×C₄₁	—	2	6	no	—
195	C₄⋊C₄×C₄₁	—	2	6	no	—
196	C₄⋊C₄×C₄₁	—	2	6	no	—
197	C₄⋊C₄×C₄₁	C₂²×C₄	1	12	yes	—
198	C₄⋊C₄×C₄₁	C₂²×C₄	1	12	yes	—
199	C₄⋊C₄×C₄₁	C₂×D₄	1	12	yes	—
200	C₂²⋊C₄×C₄₁	—	2	6	no	—
201	C₂²⋊C₄×C₄₁	—	2	12	no	—
202	C₂²⋊C₄×C₄₁	—	2	6	no	—
203	C₂²⋊C₄×C₄₁	—	2	6	no	—
204	C₂²⋊C₄×C₄₁	—	4	6	no	—
205	C₂²⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
206	C₂²⋊C₄×C₄₁	C₂²×C₄	1	12	yes	—
207	C₂²⋊C₄×C₄₁	C₂²×C₄	1	24	yes	—
208	C₂²⋊C₄×C₄₁	#41	1	4	yes	complemented
209	C₄²×C₄₁	—	2	2	no	—
210	C₄²×C₄₁	—	2	6	no	—
211	C₄²×C₄₁	—	2	6	no	—
212	C₄²×C₄₁	—	2	6	no	—
213	C₄²×C₄₁	—	2	6	no	—
214	C₄²×C₄₁	—	2	6	no	—
215	C₄²×C₄₁	—	2	6	no	—
216	C₄²×C₄₁	—	2	6	no	—
217	C₄²×C₄₁	—	2	6	no	—
218	C₄²×C₄₁	—	2	2	no	—
219	C₄²×C₄₁	—	4	3	no	—
220	C₄²×C₄₁	C₂²×C₄	1	12	yes	—
221	C₄²×C₄₁	C₂×D₄	1	12	yes	—
222	C₂³×C₄₁	—	2	1	no	—
223	C₂³×C₄₁	—	2	1	no	—
224	C₂³×C₄₁	—	2	1	no	—
225	C₂³×C₄₁	—	2	1	no	—
226	C₂³×C₄₁	—	2	3	no	—
227	C₂³×C₄₁	—	2	3	no	—
228	C₂³×C₄₁	—	2	3	no	—
229	C₂³×C₄₁	—	2	3	no	—
230	C₂³×C₄₁	—	2	3	no	—
231	C₂³×C₄₁	—	2	3	no	—
232	C₂³×C₄₁	C₂³×C₄	1	6	yes	—
233	C₂³×C₄₁	C₂³×C₄	1	2	yes	—
234	C₂³×C₄₁	C₂×#41	1	2	yes	—
235	C₂³×C₄₁	C₂×#41	1	2	yes	—
236	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
237	Q₈×C₄₁	—	2	24	no	—
238	Q₈×C₄₁	C₄×D₄	1	16	yes	complemented
239	D₄×C₄₁	—	2	24	no	—
240	D₄×C₄₁	—	2	24	no	—
241	C₂×C₄×C₄₁	—	2	1	no	—
242	C₂×C₄×C₄₁	—	2	1	no	—
243	C₂×C₄×C₄₁	—	2	1	no	—
244	C₂×C₄×C₄₁	—	2	3	no	—
245	C₂×C₄×C₄₁	—	2	1	no	—
246	C₂×C₄×C₄₁	—	2	3	no	—
247	C₂×C₄×C₄₁	—	2	3	no	—
248	C₂×C₄×C₄₁	—	2	3	no	—
249	C₂×C₄×C₄₁	—	2	1	no	—
250	C₂×C₄×C₄₁	—	2	3	no	—
251	C₂×C₄×C₄₁	—	2	1	no	—
252	C₂×C₄×C₄₁	—	2	1	no	—
253	C₂×C₄×C₄₁	—	2	1	no	—
254	C₂×C₄×C₄₁	—	2	1	no	—
255	C₂×C₄×C₄₁	—	2	3	no	—
256	C₂×C₄×C₄₁	—	2	1	no	—
257	C₂×C₄×C₄₁	—	2	24	no	—
258	C₂×C₄×C₄₁	—	2	24	no	—
259	C₂×C₄×C₄₁	—	2	8	no	—
260	C₂×C₄×C₄₁	—	2	3	no	—
261	C₂×C₄×C₄₁	—	2	3	no	—
262	C₂×C₄×C₄₁	—	2	3	no	—
263	C₂×C₄×C₄₁	—	2	3	no	—
264	C₂×C₄×C₄₁	—	2	3	no	—
265	C₂×C₄×C₄₁	—	2	3	no	—
266	C₂×C₄×C₄₁	—	2	3	no	—
267	C₂×C₄×C₄₁	—	2	3	no	—
268	C₂×C₄×C₄₁	—	2	3	no	—
269	C₂×C₄×C₄₁	—	4	12	no	—
270	C₂×C₄×C₄₁	—	4	12	no	—
271	C₂×C₄×C₄₁	—	4	12	no	—
272	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
273	C₂×C₄×C₄₁	C₂³×C₄	1	6	yes	—
274	C₂×C₄×C₄₁	C₂³×C₄	1	6	yes	—
275	C₂×C₄×C₄₁	C₂³×C₄	1	2	yes	—
276	C₂×C₄×C₄₁	C₂³×C₄	1	6	yes	—
277	C₂×C₄×C₄₁	C₂²×D₄	1	6	yes	—
278	C₂×C₄×C₄₁	C₂²×D₄	1	6	yes	—
279	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
280	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
281	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
282	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
283	C₂×C₄×C₄₁	C₂×#41	1	6	yes	—
284	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
285	C₂×C₄×C₄₁	2₋¹⁺⁴	1	2	yes	—
286	C₄×#548	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
287	C₂²×C₄₁	—	2	2	no	—
288	C₂²×C₄₁	—	2	2	no	—
289	C₂²×C₄₁	—	2	2	no	—
290	C₂²×C₄₁	—	2	2	no	—
291	C₂²×C₄₁	—	2	2	no	—
292	C₂²×C₄₁	—	2	2	no	—
293	C₂²×C₄₁	—	2	6	no	—
294	C₂²×C₄₁	—	2	6	no	—
295	C₂²×C₄₁	—	2	6	no	—
296	C₂²×C₄₁	—	4	3	no	—
297	C₂²×C₄₁	—	4	3	no	—
298	C₂²×C₄₁	—	4	3	no	—
299	C₂²×C₄₁	—	4	3	no	—
300	C₂²×C₄₁	C₄×#41	1	4	yes	complemented
301	C₂²×C₄₁	C₂⁴×C₄	1	1	yes	characteristic
302	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
303	C₂²×C₄₁	C₂²×#41	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	C₂×2₋¹⁺⁴	1	1	yes	characteristic
307	C₂²×C₄₁	#585	1	1	yes	characteristic
308	C₄×C₄₁	—	2	2	no	—
309	C₄×C₄₁	—	2	6	no	—
310	C₄×C₄₁	—	2	6	no	—
311	C₄×C₄₁	—	2	2	no	—
312	C₄×C₄₁	—	2	2	no	—
313	C₄×C₄₁	—	2	2	no	—
314	C₄×C₄₁	—	2	6	no	—
315	C₄×C₄₁	—	2	2	no	—
316	C₄×C₄₁	—	4	3	no	—
317	C₄×C₄₁	—	4	3	no	—
318	C₄×C₄₁	—	4	3	no	—
319	C₄×C₄₁	C₂×C₄×D₄	1	12	yes	—
320	C₄×C₄₁	#548	1	4	yes	direct product factor
321	C₂×#548	C₂×C₄₁	1	1	yes	characteristic
322	C₂×C₄×#41	C₂×C₄₁	1	1	yes	characteristic, complemented
323	C₂²×C₄×Q₈	C₂×C₄₁	1	1	yes	characteristic, complemented
324	#2367	C₂×C₄₁	1	3	yes	complemented
325	#2362	C₂×C₄₁	1	3	yes	complemented
326	#2361	C₂×C₄₁	1	3	yes	complemented
327	#2352	C₂×C₄₁	1	3	yes	complemented
328	#2351	C₂×C₄₁	1	1	yes	characteristic, complemented
329	#2341	C₂×C₄₁	1	1	yes	characteristic, complemented
330	Q₈×C₂²⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
331	C₄×#124	C₂×C₄₁	1	3	yes	complemented
332	C₄×C₂²⋊Q₈	C₂×C₄₁	1	3	yes	complemented
333	C₄×#121	C₂×C₄₁	1	3	yes	complemented
334	C₄²×Q₈	C₂×C₄₁	1	1	yes	characteristic, complemented
335	C₄²×D₄	C₂×C₄₁	1	3	yes	complemented
336	C₂×C₄₁	—	2	4	no	—
337	C₂×C₄₁	—	4	6	no	—
338	C₂×C₄₁	C₂²×C₄×D₄	1	1	yes	characteristic
339	C₂×C₄₁	C₂×C₄×#41	1	1	yes	characteristic
340	C₂×C₄₁	C₄×2₋¹⁺⁴	1	1	yes	characteristic
341	C₂×C₄₁	C₂×#548	1	1	yes	characteristic
342	C₂×C₄₁	D₄×#41	1	1	yes	characteristic
343	C₂×C₄₁	#3480	1	1	yes	characteristic
344	C₂×C₄₁	#3482	1	1	yes	characteristic
345	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
346	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
347	#548	C₄×C₄₁	1	16	yes	direct product factor
348	C₂×#124	C₂²×C₄₁	1	3	yes	—
349	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	3	yes	—
350	C₂×#121	C₂²×C₄₁	1	3	yes	—
351	C₄×#41	—	2	8	no	—
352	C₂×C₄×Q₈	—	2	8	no	—
353	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
354	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
355	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
356	C₂×C₄×Q₈	C₂²×C₄₁	1	3	yes	—
357	C₂×C₄×Q₈	C₂²×C₄₁	1	3	yes	—
358	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
359	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
360	C₂×C₄×D₄	C₂²×C₄₁	1	3	yes	—
361	C₂×C₄×D₄	C₂²×C₄₁	1	3	yes	—
362	C₂×C₄×D₄	C₂²×C₄₁	1	3	yes	—
363	C₂×C₄×D₄	C₂²×C₄₁	1	3	yes	—
364	C₂×C₄×D₄	C₂²×C₄₁	1	3	yes	—
365	C₂×#117	C₂²×C₄₁	1	3	yes	—
366	C₂²×C₄⋊C₄	C₂²×C₄₁	1	3	yes	—
367	C₂²×C₄²	C₂²×C₄₁	1	3	yes	—
368	C₂²×C₄²	C₂²×C₄₁	1	3	yes	—
369	#391	C₂²×C₄₁	1	3	yes	—
370	#391	C₂²×C₄₁	1	3	yes	—
371	#390	C₂²×C₄₁	1	3	yes	—
372	#390	C₂²×C₄₁	1	3	yes	—
373	#389	C₂²×C₄₁	1	3	yes	—
374	#389	C₂²×C₄₁	1	3	yes	—
375	#388	C₂²×C₄₁	1	6	yes	—
376	#388	C₂²×C₄₁	1	6	yes	—
377	#388	C₂²×C₄₁	1	6	yes	—
378	#387	C₂²×C₄₁	1	6	yes	—
379	#386	C₂²×C₄₁	1	6	yes	—
380	#385	C₂²×C₄₁	1	6	yes	—
381	#382	C₂²×C₄₁	1	3	yes	—
382	#380	C₂²×C₄₁	1	3	yes	—
383	#380	C₂²×C₄₁	1	3	yes	—
384	C₄×C₄⋊C₄	C₂²×C₄₁	1	3	yes	—
385	C₄×C₄⋊C₄	C₂²×C₄₁	1	3	yes	—
386	C₄×C₄⋊C₄	C₂²×C₄₁	1	3	yes	—
387	C₄×C₄⋊C₄	C₂²×C₄₁	1	3	yes	—
388	C₄×C₄⋊C₄	C₂²×C₄₁	1	3	yes	—
389	C₄×C₄⋊C₄	C₂²×C₄₁	1	3	yes	—
390	C₄×C₂²⋊C₄	C₂²×C₄₁	1	3	yes	—
391	C₄×C₂²⋊C₄	C₂²×C₄₁	1	3	yes	—
392	C₄×C₂²⋊C₄	C₂²×C₄₁	1	3	yes	—
393	C₄×C₂²⋊C₄	C₂²×C₄₁	1	3	yes	—
394	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
395	C₄×C₂²⋊C₄	C₂²×C₄₁	1	3	yes	—
396	C₄×C₂²⋊C₄	C₂²×C₄₁	1	6	yes	—
397	C₄³	C₂²×C₄₁	1	3	yes	—
398	C₄₁	C₄×#548	1	1	yes	characteristic, direct product factor, Sylow
399	C₂×#41	—	2	4	no	—
400	C₂×#41	—	2	4	no	—
401	C₂×#41	C₂×C₄×C₄₁	1	8	yes	complemented
402	C₂²×Q₈	—	2	4	no	—
403	C₂²×Q₈	—	2	4	no	—
404	C₂²×Q₈	C₂×C₄×C₄₁	1	8	yes	complemented
405	C₂²×Q₈	C₂³×C₄₁	1	3	yes	—
406	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
407	C₂²×D₄	C₂³×C₄₁	1	3	yes	—
408	C₂²×D₄	C₂³×C₄₁	1	3	yes	—
409	C₂³×C₄	C₂³×C₄₁	1	3	yes	—
410	C₂³×C₄	C₂³×C₄₁	1	3	yes	—
411	C₂³×C₄	C₂³×C₄₁	1	3	yes	—
412	C₂³×C₄	C₂³×C₄₁	1	3	yes	—
413	C₂³×C₄	C₂³×C₄₁	1	3	yes	—
414	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
415	#124	C₂×C₄×C₄₁	1	24	yes	complemented
416	C₂²⋊Q₈	C₂×C₄×C₄₁	1	24	yes	complemented
417	#121	C₂×C₄×C₄₁	1	24	yes	complemented
418	C₄×Q₈	—	2	4	no	—
419	C₄×Q₈	—	2	4	no	—
420	C₄×Q₈	—	2	4	no	—
421	C₄×Q₈	—	2	12	no	—
422	C₄×Q₈	—	2	12	no	—
423	C₄×Q₈	C₂×C₄×C₄₁	1	8	yes	complemented
424	C₄×Q₈	D₄×C₄₁	1	8	yes	complemented
425	C₄×D₄	—	2	12	no	—
426	C₄×D₄	—	2	12	no	—
427	C₄×D₄	—	2	12	no	—
428	C₄×D₄	—	2	12	no	—
429	C₄×D₄	C₂×C₄×C₄₁	1	24	yes	complemented
430	#117	—	2	12	no	—
431	C₂×C₄⋊C₄	—	2	12	no	—
432	C₂×C₄⋊C₄	C₂³×C₄₁	1	3	yes	—
433	C₂×C₄⋊C₄	C₂³×C₄₁	1	6	yes	—
434	C₂×C₄⋊C₄	C₂³×C₄₁	1	3	yes	—
435	C₂×C₄⋊C₄	C₂³×C₄₁	1	3	yes	—
436	C₂×C₄⋊C₄	C₂³×C₄₁	1	3	yes	—
437	C₂×C₄⋊C₄	C₂³×C₄₁	1	3	yes	—
438	C₂×C₄⋊C₄	C₂³×C₄₁	1	3	yes	—
439	C₂×C₄⋊C₄	C₂³×C₄₁	1	3	yes	—
440	C₂×C₄⋊C₄	C₂³×C₄₁	1	3	yes	—
441	C₂×C₂²⋊C₄	C₂³×C₄₁	1	6	yes	—
442	C₂×C₂²⋊C₄	C₂³×C₄₁	1	3	yes	—
443	C₂×C₂²⋊C₄	C₂³×C₄₁	1	3	yes	—
444	C₂×C₂²⋊C₄	C₂³×C₄₁	1	3	yes	—
445	C₂×C₂²⋊C₄	C₂³×C₄₁	1	6	yes	—
446	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
447	C₂×C₂²⋊C₄	C₂³×C₄₁	1	3	yes	—
448	C₂×C₂²⋊C₄	C₂³×C₄₁	1	6	yes	—
449	C₂×C₂²⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
450	C₂×C₄²	—	2	12	no	—
451	C₂×C₄²	—	2	12	no	—
452	C₂×C₄²	C₂³×C₄₁	1	3	yes	—
453	C₂×C₄²	C₂³×C₄₁	1	3	yes	—
454	C₂×C₄²	C₂³×C₄₁	1	3	yes	—
455	C₂×C₄²	C₂³×C₄₁	1	3	yes	—
456	C₂×C₄²	C₂³×C₄₁	1	3	yes	—
457	C₂×C₄²	C₂³×C₄₁	1	3	yes	—
458	C₂×C₄²	C₂³×C₄₁	1	3	yes	—
459	C₂×C₄²	C₂³×C₄₁	1	3	yes	—
460	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
461	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
462	C₂×C₄²	C₂³×C₄₁	1	3	yes	—
463	C₂×C₄²	C₂³×C₄₁	1	3	yes	—
464	C₂×C₄²	C₂³×C₄₁	1	3	yes	—
465	#95	C₂³×C₄₁	1	1	yes	characteristic
466	#95	C₂³×C₄₁	1	1	yes	characteristic
467	#95	C₂³×C₄₁	1	3	yes	—
468	#95	C₂³×C₄₁	1	3	yes	—
469	#95	C₂³×C₄₁	1	3	yes	—
470	#95	C₂³×C₄₁	1	3	yes	—
471	#95	C₂³×C₄₁	1	6	yes	—
472	#95	C₂³×C₄₁	1	6	yes	—
473	#95	C₂³×C₄₁	1	6	yes	—
474	C₂⁴	C₂⁴×C₄₁	1	3	yes	—
475	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
476	#41	—	2	32	no	—
477	C₂×Q₈	—	2	32	no	—
478	C₂×Q₈	—	2	6	no	—
479	C₂×Q₈	—	2	6	no	—
480	C₂×Q₈	C₂²×C₄×C₄₁	1	12	yes	—
481	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	—
482	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
483	C₂×Q₈	#41×C₄₁	1	4	yes	—
484	C₂×D₄	—	2	6	no	—
485	C₂×D₄	—	2	6	no	—
486	C₂×D₄	—	2	6	no	—
487	C₂×D₄	—	2	6	no	—
488	C₂×D₄	C₂²×C₄×C₄₁	1	12	yes	—
489	C₂×D₄	C₂²×C₄×C₄₁	1	12	yes	—
490	C₂²×C₄	—	2	2	no	—
491	C₂²×C₄	—	2	6	no	—
492	C₂²×C₄	—	2	6	no	—
493	C₂²×C₄	—	2	6	no	—
494	C₂²×C₄	—	2	6	no	—
495	C₂²×C₄	—	2	2	no	—
496	C₂²×C₄	—	2	6	no	—
497	C₂²×C₄	—	2	6	no	—
498	C₂²×C₄	—	2	6	no	—
499	C₂²×C₄	—	2	6	no	—
500	C₂²×C₄	—	2	6	no	—
501	C₂²×C₄	—	2	6	no	—
502	C₂²×C₄	—	2	6	no	—
503	C₂²×C₄	—	4	3	no	—
504	C₂²×C₄	—	4	3	no	—
505	C₂²×C₄	C₂²×C₄×C₄₁	1	12	yes	—
506	C₂²×C₄	C₂²×C₄×C₄₁	1	12	yes	—
507	C₂²×C₄	#41×C₄₁	1	4	yes	complemented
508	C₂²×C₄	C₂⁴×C₄₁	1	3	yes	—
509	C₂²×C₄	C₂⁴×C₄₁	1	3	yes	—
510	C₂²×C₄	C₂⁴×C₄₁	1	3	yes	—
511	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
512	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
513	C₂²×C₄	C₂⁴×C₄₁	1	3	yes	—
514	C₂²×C₄	C₂⁴×C₄₁	1	3	yes	—
515	C₂²×C₄	C₂⁴×C₄₁	1	3	yes	—
516	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
517	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
518	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
519	C₂²×C₄	C₂⁴×C₄₁	1	3	yes	—
520	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
521	C₄⋊C₄	—	2	12	no	—
522	C₄⋊C₄	—	2	6	no	—
523	C₄⋊C₄	—	2	6	no	—
524	C₄⋊C₄	—	2	6	no	—
525	C₄⋊C₄	—	2	6	no	—
526	C₄⋊C₄	—	2	6	no	—
527	C₄⋊C₄	C₂²×C₄×C₄₁	1	12	yes	—
528	C₄⋊C₄	C₂²×C₄×C₄₁	1	12	yes	—
529	C₄⋊C₄	C₂×D₄×C₄₁	1	12	yes	—
530	C₂²⋊C₄	—	2	6	no	—
531	C₂²⋊C₄	—	2	12	no	—
532	C₂²⋊C₄	—	2	6	no	—
533	C₂²⋊C₄	—	2	6	no	—
534	C₂²⋊C₄	—	4	6	no	—
535	C₂²⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
536	C₂²⋊C₄	C₂²×C₄×C₄₁	1	12	yes	—
537	C₂²⋊C₄	C₂²×C₄×C₄₁	1	24	yes	—
538	C₂²⋊C₄	#41×C₄₁	1	4	yes	complemented
539	C₄²	—	2	2	no	—
540	C₄²	—	2	6	no	—
541	C₄²	—	2	6	no	—
542	C₄²	—	2	6	no	—
543	C₄²	—	2	6	no	—
544	C₄²	—	2	6	no	—
545	C₄²	—	2	6	no	—
546	C₄²	—	2	6	no	—
547	C₄²	—	2	6	no	—
548	C₄²	—	2	2	no	—
549	C₄²	—	4	3	no	—
550	C₄²	C₂²×C₄×C₄₁	1	12	yes	—
551	C₄²	C₂×D₄×C₄₁	1	12	yes	—
552	C₂³	—	2	1	no	—
553	C₂³	—	2	1	no	—
554	C₂³	—	2	1	no	—
555	C₂³	—	2	1	no	—
556	C₂³	—	2	3	no	—
557	C₂³	—	2	3	no	—
558	C₂³	—	2	3	no	—
559	C₂³	—	2	3	no	—
560	C₂³	—	2	3	no	—
561	C₂³	—	2	3	no	—
562	C₂³	C₂³×C₄×C₄₁	1	6	yes	—
563	C₂³	C₂³×C₄×C₄₁	1	2	yes	—
564	C₂³	C₂×#41×C₄₁	1	2	yes	—
565	C₂³	C₂×#41×C₄₁	1	2	yes	—
566	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
567	Q₈	—	2	24	no	—
568	Q₈	C₄×D₄×C₄₁	1	16	yes	complemented
569	D₄	—	2	24	no	—
570	D₄	—	2	24	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	3	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	3	no	—
577	C₂×C₄	—	2	3	no	—
578	C₂×C₄	—	2	3	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	3	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	3	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	24	no	—
588	C₂×C₄	—	2	24	no	—
589	C₂×C₄	—	2	8	no	—
590	C₂×C₄	—	2	3	no	—
591	C₂×C₄	—	2	3	no	—
592	C₂×C₄	—	2	3	no	—
593	C₂×C₄	—	2	3	no	—
594	C₂×C₄	—	2	3	no	—
595	C₂×C₄	—	2	3	no	—
596	C₂×C₄	—	2	3	no	—
597	C₂×C₄	—	2	3	no	—
598	C₂×C₄	—	2	3	no	—
599	C₂×C₄	—	4	12	no	—
600	C₂×C₄	—	4	12	no	—
601	C₂×C₄	—	4	12	no	—
602	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
603	C₂×C₄	C₂³×C₄×C₄₁	1	6	yes	—
604	C₂×C₄	C₂³×C₄×C₄₁	1	6	yes	—
605	C₂×C₄	C₂³×C₄×C₄₁	1	2	yes	—
606	C₂×C₄	C₂³×C₄×C₄₁	1	6	yes	—
607	C₂×C₄	C₂²×D₄×C₄₁	1	6	yes	—
608	C₂×C₄	C₂²×D₄×C₄₁	1	6	yes	—
609	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
610	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
611	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
612	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
613	C₂×C₄	C₂×#41×C₄₁	1	6	yes	—
614	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
615	C₂×C₄	2₋¹⁺⁴×C₄₁	1	2	yes	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	2	6	no	—
623	C₂²	—	2	6	no	—
624	C₂²	—	2	6	no	—
625	C₂²	—	4	3	no	—
626	C₂²	—	4	3	no	—
627	C₂²	—	4	3	no	—
628	C₂²	—	4	3	no	—
629	C₂²	C₄×#41×C₄₁	1	4	yes	complemented
630	C₂²	C₂⁴×C₄×C₄₁	1	1	yes	characteristic
631	C₂²	C₂³×D₄×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	C₂²×#41×C₄₁	1	1	yes	characteristic
635	C₂²	C₂×2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
636	C₂²	C₄₁×#585	1	1	yes	characteristic
637	C₄	—	2	2	no	—
638	C₄	—	2	6	no	—
639	C₄	—	2	6	no	—
640	C₄	—	2	2	no	—
641	C₄	—	2	2	no	—
642	C₄	—	2	2	no	—
643	C₄	—	2	6	no	—
644	C₄	—	2	2	no	—
645	C₄	—	4	3	no	—
646	C₄	—	4	3	no	—
647	C₄	—	4	3	no	—
648	C₄	C₂×C₄×D₄×C₄₁	1	12	yes	—
649	C₄	C₄₁×#548	1	4	yes	direct product factor
650	C₂	—	2	4	no	—
651	C₂	—	4	6	no	—
652	C₂	C₂²×C₄×D₄×C₄₁	1	1	yes	characteristic
653	C₂	C₂×C₄×#41×C₄₁	1	1	yes	characteristic
654	C₂	C₄×2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
655	C₂	C₂×C₄₁×#548	1	1	yes	characteristic
656	C₂	D₄×#41×C₄₁	1	1	yes	characteristic
657	C₂	C₄₁×#3480	1	1	yes	characteristic
658	C₂	C₄₁×#3482	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₄₁	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₄₁
Frattini, cosocle	C₂³	C₂⁵×C₄₁
socle	C₂³×C₄₁	C₂⁵
prime radical	C₂×C₄₁×#548	C₂
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
2. C₂×C₄×#41×C₄₁	C₂	semidirect
3. C₂²×C₄×Q₈×C₄₁	C₂	semidirect
4. C₄₁×#2367	C₂	semidirect
5. C₄₁×#2362	C₂	semidirect
6. C₄₁×#2361	C₂	semidirect
7. C₄₁×#2352	C₂	semidirect
8. C₄₁×#2351	C₂	semidirect
9. C₄₁×#2341	C₂	semidirect
10. Q₈×C₂²⋊C₄×C₄₁	C₂	semidirect
11. C₄×#124×C₄₁	C₂	semidirect
12. C₄×C₂²⋊Q₈×C₄₁	C₂	semidirect
13. C₄×#121×C₄₁	C₂	semidirect
14. C₄²×Q₈×C₄₁	C₂	semidirect
15. C₄²×D₄×C₄₁	C₂	semidirect
18. C₄₁×#548	C₄	direct (N × H)
71. C₂×#41×C₄₁	C₂×C₄	semidirect
74. C₂²×Q₈×C₄₁	C₂×C₄	semidirect
85. #124×C₄₁	C₂×C₄	semidirect
86. C₂²⋊Q₈×C₄₁	C₂×C₄	semidirect
87. #121×C₄₁	C₂×C₄	semidirect
93. C₄×Q₈×C₄₁	C₂×C₄	semidirect
94. C₄×Q₈×C₄₁	D₄	semidirect
99. C₄×D₄×C₄₁	C₂×C₄	semidirect
177. C₂²×C₄×C₄₁	#41	semidirect
208. C₂²⋊C₄×C₄₁	#41	semidirect
238. Q₈×C₄₁	C₄×D₄	semidirect
286. C₄×#548	C₄₁	direct (N × H)
300. C₂²×C₄₁	C₄×#41	semidirect
320. C₄×C₄₁	#548	direct (N × H)
322. C₂×C₄×#41	C₂×C₄₁	semidirect
323. C₂²×C₄×Q₈	C₂×C₄₁	semidirect
324. #2367	C₂×C₄₁	semidirect
325. #2362	C₂×C₄₁	semidirect
326. #2361	C₂×C₄₁	semidirect
327. #2352	C₂×C₄₁	semidirect
328. #2351	C₂×C₄₁	semidirect
329. #2341	C₂×C₄₁	semidirect
330. Q₈×C₂²⋊C₄	C₂×C₄₁	semidirect
331. C₄×#124	C₂×C₄₁	semidirect
332. C₄×C₂²⋊Q₈	C₂×C₄₁	semidirect
333. C₄×#121	C₂×C₄₁	semidirect
334. C₄²×Q₈	C₂×C₄₁	semidirect
335. C₄²×D₄	C₂×C₄₁	semidirect
347. #548	C₄×C₄₁	direct (N × H)
398. C₄₁	C₄×#548	direct (N × H)
401. C₂×#41	C₂×C₄×C₄₁	semidirect
404. C₂²×Q₈	C₂×C₄×C₄₁	semidirect
415. #124	C₂×C₄×C₄₁	semidirect
416. C₂²⋊Q₈	C₂×C₄×C₄₁	semidirect
417. #121	C₂×C₄×C₄₁	semidirect
423. C₄×Q₈	C₂×C₄×C₄₁	semidirect
424. C₄×Q₈	D₄×C₄₁	semidirect
429. C₄×D₄	C₂×C₄×C₄₁	semidirect
507. C₂²×C₄	#41×C₄₁	semidirect
538. C₂²⋊C₄	#41×C₄₁	semidirect
568. Q₈	C₄×D₄×C₄₁	semidirect
629. C₂²	C₄×#41×C₄₁	semidirect
649. C₄	C₄₁×#548	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#548	2
C₂×C₄×#41×C₄₁	2
C₂²×C₄×Q₈×C₄₁	2
C₄₁×#2367	2
C₄₁×#2362	2
C₄₁×#2361	2
C₄₁×#2352	2
C₄₁×#2351	2
C₄₁×#2341	2
Q₈×C₂²⋊C₄×C₄₁	2
C₄×#124×C₄₁	2
C₄×C₂²⋊Q₈×C₄₁	2
C₄×#121×C₄₁	2
C₄²×Q₈×C₄₁	2
C₄²×D₄×C₄₁	2
C₄×#548	41

Subgroups — C4×C41×#548 #23810359

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₄₁×#548 #23810359