Subgroups — C₄₁×#61393 #23837594

Order 10496.

1958 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3480	C₂	1	2	yes	maximal, complemented
2	C₄₁×#3396	C₂	1	3	yes	maximal, complemented
3	C₄₁×#3395	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#3394	C₂	1	6	yes	maximal, complemented
5	C₄₁×#3393	C₂	1	3	yes	maximal, complemented
6	C₄₁×#3392	C₂	1	2	yes	maximal, complemented
7	C₄₁×#3391	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#3147	C₂	1	3	yes	maximal, complemented
9	C₄₁×#3035	C₂	1	6	yes	maximal, complemented
10	C₂×C₈×Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#135×C₄₁	C₂	1	3	yes	maximal, complemented
12	C₂×#135×C₄₁	C₂²	1	3	yes	—
13	C₂×#135×C₄₁	C₂²	1	6	yes	—
14	C₄₁×#559	C₂²	1	6	yes	—
15	C₄₁×#557	C₂²	1	2	yes	—
16	C₄₁×#556	C₂²	1	6	yes	—
17	C₄₁×#553	—	2	6	no	—
18	C₄₁×#550	C₂²	1	2	yes	—
19	C₄₁×#548	—	2	2	no	—
20	C₄₁×#532	C₂²	1	6	yes	—
21	C₄₁×#529	—	2	6	no	—
22	C₄×#41×C₄₁	—	2	2	no	—
23	C₄×#41×C₄₁	C₂²	1	6	yes	—
24	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
25	C₄₁×#495	C₂²	1	6	yes	—
26	C₄₁×#495	C₂²	1	6	yes	—
27	C₄₁×#494	C₂²	1	3	yes	—
28	C₄₁×#493	C₂²	1	3	yes	—
29	C₄₁×#492	C₂²	1	6	yes	—
30	C₄₁×#464	C₂²	1	12	yes	—
31	C₄₁×#463	C₂²	1	12	yes	—
32	C₄₁×#462	C₂²	1	6	yes	—
33	C₄₁×#461	C₂²	1	6	yes	—
34	C₄₁×#460	C₂²	1	6	yes	—
35	C₄₁×#459	C₂²	1	6	yes	—
36	C₈×Q₈×C₄₁	C₂²	1	1	yes	characteristic
37	C₈×Q₈×C₄₁	C₂²	1	1	yes	characteristic
38	C₈×Q₈×C₄₁	C₂²	1	3	yes	—
39	C₈×Q₈×C₄₁	C₂²	1	3	yes	—
40	C₄×Q₁₆×C₄₁	C₂²	1	3	yes	—
41	C₄×Q₁₆×C₄₁	C₂²	1	3	yes	—
42	C₄×SD₁₆×C₄₁	C₂²	1	6	yes	—
43	C₄×SD₁₆×C₄₁	C₂²	1	6	yes	—
44	C₄×D₈×C₄₁	C₂²	1	3	yes	—
45	C₄×D₈×C₄₁	C₂²	1	3	yes	—
46	C₄₁×#427	C₂²	1	1	yes	characteristic
47	C₂×C₄⋊C₈×C₄₁	C₂²	1	3	yes	—
48	C₄₁×#416	C₂²	1	6	yes	—
49	C₂×C₄×C₈×C₄₁	C₂²	1	3	yes	—
50	C₂×#41×C₄₁	—	2	2	no	—
51	C₂×#41×C₄₁	C₂³	1	6	yes	—
52	C₂²×Q₈×C₄₁	D₄	1	1	yes	characteristic
53	#135×C₄₁	—	2	12	no	—
54	#135×C₄₁	—	4	12	no	—
55	C₂×Q₁₆×C₄₁	C₂³	1	3	yes	—
56	C₂×Q₁₆×C₄₁	C₂³	1	6	yes	—
57	C₂×SD₁₆×C₄₁	C₂³	1	6	yes	—
58	C₂×SD₁₆×C₄₁	C₂³	1	12	yes	—
59	C₂×D₈×C₄₁	C₂³	1	3	yes	—
60	C₂×D₈×C₄₁	C₂³	1	6	yes	—
61	C₂²×C₈×C₄₁	C₂³	1	3	yes	—
62	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
63	C₄⋊Q₈×C₄₁	C₂³	1	6	yes	—
64	#127×C₄₁	C₂³	1	6	yes	—
65	#126×C₄₁	—	2	12	no	—
66	#125×C₄₁	—	2	6	no	—
67	#124×C₄₁	—	2	6	no	—
68	#124×C₄₁	C₂³	1	12	yes	—
69	#123×C₄₁	—	2	12	no	—
70	C₂²⋊Q₈×C₄₁	—	2	6	no	—
71	#121×C₄₁	—	2	6	no	—
72	#121×C₄₁	—	2	6	no	—
73	#121×C₄₁	—	2	6	no	—
74	C₄×Q₈×C₄₁	—	2	2	no	—
75	C₄×Q₈×C₄₁	D₄	1	1	yes	characteristic
76	C₄×Q₈×C₄₁	D₄	1	3	yes	—
77	C₄×Q₈×C₄₁	C₂³	1	6	yes	—
78	C₄×Q₈×C₄₁	C₂³	1	6	yes	—
79	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
80	C₄×Q₈×C₄₁	C₂³	1	3	yes	—
81	C₄×D₄×C₄₁	—	2	6	no	—
82	C₄×D₄×C₄₁	—	2	6	no	—
83	C₄×D₄×C₄₁	—	2	6	no	—
84	C₄×D₄×C₄₁	—	2	6	no	—
85	C₄×D₄×C₄₁	—	2	6	no	—
86	C₄×D₄×C₄₁	C₂³	1	6	yes	—
87	C₄×D₄×C₄₁	C₂³	1	6	yes	—
88	#117×C₄₁	—	2	6	no	—
89	#117×C₄₁	—	2	6	no	—
90	#117×C₄₁	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₄₁	D₄	1	3	yes	—
92	C₂×C₄²×C₄₁	—	2	6	no	—
93	C₂×C₄²×C₄₁	C₂³	1	3	yes	—
94	#107×C₄₁	C₂³	1	1	yes	characteristic
95	#107×C₄₁	C₂³	1	1	yes	characteristic
96	#106×C₄₁	C₂³	1	2	yes	—
97	C₄⋊C₈×C₄₁	C₂³	1	3	yes	—
98	C₄⋊C₈×C₄₁	C₂³	1	3	yes	—
99	C₄⋊C₈×C₄₁	C₂³	1	6	yes	—
100	#103×C₄₁	C₂³	1	6	yes	—
101	#103×C₄₁	C₂³	1	6	yes	—
102	#102×C₄₁	C₂³	1	6	yes	—
103	#102×C₄₁	C₂³	1	6	yes	—
104	C₄×C₈×C₄₁	C₂³	1	3	yes	—
105	C₄×C₈×C₄₁	C₂³	1	3	yes	—
106	C₄×C₈×C₄₁	C₂³	1	3	yes	—
107	C₄×C₈×C₄₁	C₂³	1	3	yes	—
108	#41×C₄₁	—	2	12	no	—
109	#41×C₄₁	—	2	12	no	—
110	#41×C₄₁	—	4	8	no	—
111	C₂×Q₈×C₄₁	—	2	4	no	—
112	C₂×Q₈×C₄₁	C₂×D₄	1	3	yes	—
113	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
114	C₂×Q₈×C₄₁	C₂⁴	1	6	yes	—
115	C₂×D₄×C₄₁	—	2	6	no	—
116	C₂×D₄×C₄₁	—	2	6	no	—
117	C₂×D₄×C₄₁	—	2	6	no	—
118	C₂×D₄×C₄₁	C₂⁴	1	6	yes	—
119	C₂²×C₄×C₄₁	—	2	6	no	—
120	C₂²×C₄×C₄₁	—	2	6	no	—
121	C₂²×C₄×C₄₁	—	2	6	no	—
122	C₂²×C₄×C₄₁	C₂×D₄	1	3	yes	—
123	C₂²×C₄×C₄₁	C₂×D₄	1	3	yes	—
124	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
125	Q₁₆×C₄₁	—	2	6	no	—
126	Q₁₆×C₄₁	—	4	6	no	—
127	SD₁₆×C₄₁	—	2	12	no	—
128	SD₁₆×C₄₁	—	4	12	no	—
129	D₈×C₄₁	—	2	6	no	—
130	D₈×C₄₁	—	4	6	no	—
131	C₂×C₈×C₄₁	—	2	6	no	—
132	C₂×C₈×C₄₁	#41	1	4	yes	complemented
133	C₂×C₈×C₄₁	C₂⁴	1	3	yes	—
134	C₂×C₈×C₄₁	C₂⁴	1	3	yes	—
135	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
136	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
137	C₄⋊C₄×C₄₁	—	2	6	no	—
138	C₄⋊C₄×C₄₁	—	2	6	no	—
139	C₄⋊C₄×C₄₁	—	2	6	no	—
140	C₄⋊C₄×C₄₁	—	2	6	no	—
141	C₄⋊C₄×C₄₁	C₂×D₄	1	3	yes	—
142	C₄⋊C₄×C₄₁	C₂×D₄	1	3	yes	—
143	C₄⋊C₄×C₄₁	C₂×D₄	1	6	yes	—
144	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
145	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
146	C₂²⋊C₄×C₄₁	—	2	2	no	—
147	C₂²⋊C₄×C₄₁	—	2	12	no	—
148	C₂²⋊C₄×C₄₁	—	2	6	no	—
149	C₂²⋊C₄×C₄₁	—	2	6	no	—
150	C₂²⋊C₄×C₄₁	—	2	12	no	—
151	C₄²×C₄₁	—	2	6	no	—
152	C₄²×C₄₁	—	2	6	no	—
153	C₄²×C₄₁	—	2	2	no	—
154	C₄²×C₄₁	C₂×D₄	1	3	yes	—
155	C₄²×C₄₁	C₂×D₄	1	3	yes	—
156	C₄²×C₄₁	C₂⁴	1	3	yes	—
157	C₄²×C₄₁	C₂⁴	1	3	yes	—
158	C₂³×C₄₁	—	2	6	no	—
159	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
160	Q₈×C₄₁	—	2	6	no	—
161	Q₈×C₄₁	—	2	6	no	—
162	Q₈×C₄₁	—	2	6	no	—
163	Q₈×C₄₁	#135	1	4	yes	complemented
164	D₄×C₄₁	—	2	6	no	—
165	D₄×C₄₁	—	2	6	no	—
166	D₄×C₄₁	—	4	12	no	—
167	D₄×C₄₁	—	4	12	no	—
168	D₄×C₄₁	—	8	6	no	—
169	C₂×C₄×C₄₁	—	2	6	no	—
170	C₂×C₄×C₄₁	—	2	2	no	—
171	C₂×C₄×C₄₁	—	2	2	no	—
172	C₂×C₄×C₄₁	—	2	6	no	—
173	C₂×C₄×C₄₁	—	4	3	no	—
174	C₂×C₄×C₄₁	—	4	12	no	—
175	C₂×C₄×C₄₁	—	4	12	no	—
176	C₂×C₄×C₄₁	—	8	6	no	—
177	C₂×C₄×C₄₁	C₂²×D₄	1	3	yes	—
178	C₂×C₄×C₄₁	C₂²×D₄	1	3	yes	—
179	C₂×C₄×C₄₁	C₂²×D₄	1	3	yes	—
180	C₂×C₄×C₄₁	C₂²×D₄	1	3	yes	—
181	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
183	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
184	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
185	C₈×C₄₁	—	2	3	no	—
186	C₈×C₄₁	—	2	3	no	—
187	C₈×C₄₁	C₂×#41	1	2	yes	—
188	C₈×C₄₁	C₂×#41	1	2	yes	—
189	#61393	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₂²×C₄₁	—	2	1	no	—
191	C₂²×C₄₁	—	2	1	no	—
192	C₂²×C₄₁	—	4	6	no	—
193	C₂²×C₄₁	—	4	6	no	—
194	C₂²×C₄₁	—	4	6	no	—
195	C₂²×C₄₁	#550	1	2	yes	—
196	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
197	C₄×C₄₁	—	2	3	no	—
198	C₄×C₄₁	—	2	3	no	—
199	C₄×C₄₁	—	2	3	no	—
200	C₄×C₄₁	—	4	2	no	—
201	C₄×C₄₁	—	4	6	no	—
202	C₄×C₄₁	—	4	2	no	—
203	C₄×C₄₁	#550	1	2	yes	—
204	C₄×C₄₁	C₂×#135	1	6	yes	—
205	C₄×C₄₁	C₂²×#41	1	1	yes	characteristic
206	C₄×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
207	#3480	C₂×C₄₁	1	2	yes	complemented
208	#3396	C₂×C₄₁	1	3	yes	complemented
209	#3395	C₂×C₄₁	1	1	yes	characteristic, complemented
210	#3394	C₂×C₄₁	1	6	yes	complemented
211	#3393	C₂×C₄₁	1	3	yes	complemented
212	#3392	C₂×C₄₁	1	2	yes	complemented
213	#3391	C₂×C₄₁	1	1	yes	characteristic, complemented
214	#3147	C₂×C₄₁	1	3	yes	complemented
215	#3035	C₂×C₄₁	1	6	yes	complemented
216	C₂×C₈×Q₈	C₂×C₄₁	1	1	yes	characteristic, complemented
217	C₄×#135	C₂×C₄₁	1	3	yes	complemented
218	C₂×C₄₁	—	2	2	no	—
219	C₂×C₄₁	—	8	6	no	—
220	C₂×C₄₁	C₂×#550	1	1	yes	characteristic
221	C₂×C₄₁	C₂²×#135	1	1	yes	characteristic
222	C₂×C₄₁	#3584	1	1	yes	characteristic
223	C₂×#135	C₂²×C₄₁	1	3	yes	—
224	C₂×#135	C₂²×C₄₁	1	6	yes	—
225	#559	C₂²×C₄₁	1	6	yes	—
226	#557	C₂²×C₄₁	1	2	yes	—
227	#556	C₂²×C₄₁	1	6	yes	—
228	#553	—	2	6	no	—
229	#550	C₂²×C₄₁	1	2	yes	—
230	#548	—	2	2	no	—
231	#532	C₂²×C₄₁	1	6	yes	—
232	#529	—	2	6	no	—
233	C₄×#41	—	2	2	no	—
234	C₄×#41	C₂²×C₄₁	1	6	yes	—
235	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
236	#495	C₂²×C₄₁	1	6	yes	—
237	#495	C₂²×C₄₁	1	6	yes	—
238	#494	C₂²×C₄₁	1	3	yes	—
239	#493	C₂²×C₄₁	1	3	yes	—
240	#492	C₂²×C₄₁	1	6	yes	—
241	#464	C₂²×C₄₁	1	12	yes	—
242	#463	C₂²×C₄₁	1	12	yes	—
243	#462	C₂²×C₄₁	1	6	yes	—
244	#461	C₂²×C₄₁	1	6	yes	—
245	#460	C₂²×C₄₁	1	6	yes	—
246	#459	C₂²×C₄₁	1	6	yes	—
247	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic
248	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic
249	C₈×Q₈	C₂²×C₄₁	1	3	yes	—
250	C₈×Q₈	C₂²×C₄₁	1	3	yes	—
251	C₄×Q₁₆	C₂²×C₄₁	1	3	yes	—
252	C₄×Q₁₆	C₂²×C₄₁	1	3	yes	—
253	C₄×SD₁₆	C₂²×C₄₁	1	6	yes	—
254	C₄×SD₁₆	C₂²×C₄₁	1	6	yes	—
255	C₄×D₈	C₂²×C₄₁	1	3	yes	—
256	C₄×D₈	C₂²×C₄₁	1	3	yes	—
257	#427	C₂²×C₄₁	1	1	yes	characteristic
258	C₂×C₄⋊C₈	C₂²×C₄₁	1	3	yes	—
259	#416	C₂²×C₄₁	1	6	yes	—
260	C₂×C₄×C₈	C₂²×C₄₁	1	3	yes	—
261	C₄₁	#61393	1	1	yes	characteristic, direct product factor, Sylow
262	C₂×#41	—	2	2	no	—
263	C₂×#41	C₂³×C₄₁	1	6	yes	—
264	C₂²×Q₈	D₄×C₄₁	1	1	yes	characteristic
265	#135	—	2	12	no	—
266	#135	—	4	12	no	—
267	C₂×Q₁₆	C₂³×C₄₁	1	3	yes	—
268	C₂×Q₁₆	C₂³×C₄₁	1	6	yes	—
269	C₂×SD₁₆	C₂³×C₄₁	1	6	yes	—
270	C₂×SD₁₆	C₂³×C₄₁	1	12	yes	—
271	C₂×D₈	C₂³×C₄₁	1	3	yes	—
272	C₂×D₈	C₂³×C₄₁	1	6	yes	—
273	C₂²×C₈	C₂³×C₄₁	1	3	yes	—
274	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
275	C₄⋊Q₈	C₂³×C₄₁	1	6	yes	—
276	#127	C₂³×C₄₁	1	6	yes	—
277	#126	—	2	12	no	—
278	#125	—	2	6	no	—
279	#124	—	2	6	no	—
280	#124	C₂³×C₄₁	1	12	yes	—
281	#123	—	2	12	no	—
282	C₂²⋊Q₈	—	2	6	no	—
283	#121	—	2	6	no	—
284	#121	—	2	6	no	—
285	#121	—	2	6	no	—
286	C₄×Q₈	—	2	2	no	—
287	C₄×Q₈	D₄×C₄₁	1	1	yes	characteristic
288	C₄×Q₈	D₄×C₄₁	1	3	yes	—
289	C₄×Q₈	C₂³×C₄₁	1	6	yes	—
290	C₄×Q₈	C₂³×C₄₁	1	6	yes	—
291	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
292	C₄×Q₈	C₂³×C₄₁	1	3	yes	—
293	C₄×D₄	—	2	6	no	—
294	C₄×D₄	—	2	6	no	—
295	C₄×D₄	—	2	6	no	—
296	C₄×D₄	—	2	6	no	—
297	C₄×D₄	—	2	6	no	—
298	C₄×D₄	C₂³×C₄₁	1	6	yes	—
299	C₄×D₄	C₂³×C₄₁	1	6	yes	—
300	#117	—	2	6	no	—
301	#117	—	2	6	no	—
302	#117	C₂³×C₄₁	1	2	yes	—
303	C₂×C₄⋊C₄	D₄×C₄₁	1	3	yes	—
304	C₂×C₄²	—	2	6	no	—
305	C₂×C₄²	C₂³×C₄₁	1	3	yes	—
306	#107	C₂³×C₄₁	1	1	yes	characteristic
307	#107	C₂³×C₄₁	1	1	yes	characteristic
308	#106	C₂³×C₄₁	1	2	yes	—
309	C₄⋊C₈	C₂³×C₄₁	1	3	yes	—
310	C₄⋊C₈	C₂³×C₄₁	1	3	yes	—
311	C₄⋊C₈	C₂³×C₄₁	1	6	yes	—
312	#103	C₂³×C₄₁	1	6	yes	—
313	#103	C₂³×C₄₁	1	6	yes	—
314	#102	C₂³×C₄₁	1	6	yes	—
315	#102	C₂³×C₄₁	1	6	yes	—
316	C₄×C₈	C₂³×C₄₁	1	3	yes	—
317	C₄×C₈	C₂³×C₄₁	1	3	yes	—
318	C₄×C₈	C₂³×C₄₁	1	3	yes	—
319	C₄×C₈	C₂³×C₄₁	1	3	yes	—
320	#41	—	2	12	no	—
321	#41	—	2	12	no	—
322	#41	—	4	8	no	—
323	C₂×Q₈	—	2	4	no	—
324	C₂×Q₈	C₂×D₄×C₄₁	1	3	yes	—
325	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
326	C₂×Q₈	C₂⁴×C₄₁	1	6	yes	—
327	C₂×D₄	—	2	6	no	—
328	C₂×D₄	—	2	6	no	—
329	C₂×D₄	—	2	6	no	—
330	C₂×D₄	C₂⁴×C₄₁	1	6	yes	—
331	C₂²×C₄	—	2	6	no	—
332	C₂²×C₄	—	2	6	no	—
333	C₂²×C₄	—	2	6	no	—
334	C₂²×C₄	C₂×D₄×C₄₁	1	3	yes	—
335	C₂²×C₄	C₂×D₄×C₄₁	1	3	yes	—
336	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
337	Q₁₆	—	2	6	no	—
338	Q₁₆	—	4	6	no	—
339	SD₁₆	—	2	12	no	—
340	SD₁₆	—	4	12	no	—
341	D₈	—	2	6	no	—
342	D₈	—	4	6	no	—
343	C₂×C₈	—	2	6	no	—
344	C₂×C₈	#41×C₄₁	1	4	yes	complemented
345	C₂×C₈	C₂⁴×C₄₁	1	3	yes	—
346	C₂×C₈	C₂⁴×C₄₁	1	3	yes	—
347	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
348	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
349	C₄⋊C₄	—	2	6	no	—
350	C₄⋊C₄	—	2	6	no	—
351	C₄⋊C₄	—	2	6	no	—
352	C₄⋊C₄	—	2	6	no	—
353	C₄⋊C₄	C₂×D₄×C₄₁	1	3	yes	—
354	C₄⋊C₄	C₂×D₄×C₄₁	1	3	yes	—
355	C₄⋊C₄	C₂×D₄×C₄₁	1	6	yes	—
356	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
357	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₂²⋊C₄	—	2	12	no	—
360	C₂²⋊C₄	—	2	6	no	—
361	C₂²⋊C₄	—	2	6	no	—
362	C₂²⋊C₄	—	2	12	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	2	6	no	—
365	C₄²	—	2	6	no	—
366	C₄²	C₂×D₄×C₄₁	1	3	yes	—
367	C₄²	C₂×D₄×C₄₁	1	3	yes	—
368	C₄²	C₂⁴×C₄₁	1	3	yes	—
369	C₄²	C₂⁴×C₄₁	1	3	yes	—
370	C₂³	—	2	6	no	—
371	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
372	Q₈	—	2	6	no	—
373	Q₈	—	2	6	no	—
374	Q₈	—	2	6	no	—
375	Q₈	#135×C₄₁	1	4	yes	complemented
376	D₄	—	2	6	no	—
377	D₄	—	2	6	no	—
378	D₄	—	4	12	no	—
379	D₄	—	4	12	no	—
380	D₄	—	8	6	no	—
381	C₂×C₄	—	2	6	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	6	no	—
385	C₂×C₄	—	4	3	no	—
386	C₂×C₄	—	4	12	no	—
387	C₂×C₄	—	4	12	no	—
388	C₂×C₄	—	8	6	no	—
389	C₂×C₄	C₂²×D₄×C₄₁	1	3	yes	—
390	C₂×C₄	C₂²×D₄×C₄₁	1	3	yes	—
391	C₂×C₄	C₂²×D₄×C₄₁	1	3	yes	—
392	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
393	C₂×C₄	C₂²×D₄×C₄₁	1	3	yes	—
394	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
395	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
396	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
397	C₈	—	2	3	no	—
398	C₈	—	2	3	no	—
399	C₈	C₂×#41×C₄₁	1	2	yes	—
400	C₈	C₂×#41×C₄₁	1	2	yes	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	4	6	no	—
404	C₂²	—	4	6	no	—
405	C₂²	—	4	6	no	—
406	C₂²	C₄₁×#550	1	2	yes	—
407	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
408	C₄	—	2	3	no	—
409	C₄	—	2	3	no	—
410	C₄	—	2	3	no	—
411	C₄	—	4	2	no	—
412	C₄	—	4	2	no	—
413	C₄	—	4	6	no	—
414	C₄	C₄₁×#550	1	2	yes	—
415	C₄	C₂×#135×C₄₁	1	6	yes	—
416	C₄	C₂²×#41×C₄₁	1	1	yes	characteristic
417	C₄	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
418	C₂	—	2	2	no	—
419	C₂	—	8	6	no	—
420	C₂	C₂×C₄₁×#550	1	1	yes	characteristic
421	C₂	C₂²×#135×C₄₁	1	1	yes	characteristic
422	C₂	C₄₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
socle	C₂²×C₄₁	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁ ◁ C₂×C₄×Q₈×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3480	C₂	semidirect
2. C₄₁×#3396	C₂	semidirect
3. C₄₁×#3395	C₂	semidirect
4. C₄₁×#3394	C₂	semidirect
5. C₄₁×#3393	C₂	semidirect
6. C₄₁×#3392	C₂	semidirect
7. C₄₁×#3391	C₂	semidirect
8. C₄₁×#3147	C₂	semidirect
9. C₄₁×#3035	C₂	semidirect
10. C₂×C₈×Q₈×C₄₁	C₂	semidirect
11. C₄×#135×C₄₁	C₂	semidirect
132. C₂×C₈×C₄₁	#41	semidirect
163. Q₈×C₄₁	#135	semidirect
189. #61393	C₄₁	direct (N × H)
207. #3480	C₂×C₄₁	semidirect
208. #3396	C₂×C₄₁	semidirect
209. #3395	C₂×C₄₁	semidirect
210. #3394	C₂×C₄₁	semidirect
211. #3393	C₂×C₄₁	semidirect
212. #3392	C₂×C₄₁	semidirect
213. #3391	C₂×C₄₁	semidirect
214. #3147	C₂×C₄₁	semidirect
215. #3035	C₂×C₄₁	semidirect
216. C₂×C₈×Q₈	C₂×C₄₁	semidirect
217. C₄×#135	C₂×C₄₁	semidirect
261. C₄₁	#61393	direct (N × H)
344. C₂×C₈	#41×C₄₁	semidirect
375. Q₈	#135×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3480	2
C₄₁×#3396	2
C₄₁×#3395	2
C₄₁×#3394	2
C₄₁×#3393	2
C₄₁×#3392	2
C₄₁×#3391	2
C₄₁×#3147	2
C₄₁×#3035	2
C₂×C₈×Q₈×C₄₁	2
C₄×#135×C₄₁	2
#61393	41

Subgroups — C41×#61393 #23837594

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61393 #23837594