Subgroups — C₄₁×#15143 #23791344

Order 10496.

1934 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#395	C₂	1	4	yes	maximal
3	C₂×C₄₁×#389	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₁×#384	C₂	1	2	yes	maximal
5	C₄₁×#1444	C₂	1	4	yes	maximal
6	C₄₁×C₄⋊#95	C₂	1	2	yes	maximal
7	C₄×#95×C₄₁	C₂	1	1	yes	maximal, characteristic
8	C₂³×Q₈×C₄₁	C₂²	1	2	yes	—
9	C₂×C₄⋊Q₈×C₄₁	—	2	8	no	—
10	C₂×C₄⋊Q₈×C₄₁	—	2	4	no	—
11	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₄₁	C₂²	1	8	yes	—
15	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₄₁	C₂²	1	2	yes	—
19	C₄₁×#395	—	2	16	no	—
20	C₄₁×#389	—	2	4	no	—
21	C₄₁×#384	—	2	8	no	—
22	C₂×#95×C₄₁	C₂²	1	2	yes	—
23	C₂×#95×C₄₁	C₂²	1	8	yes	—
24	C₂×#95×C₄₁	C₂²	1	2	yes	—
25	C₂×#95×C₄₁	C₂²	1	2	yes	—
26	C₂²×Q₈×C₄₁	—	2	8	no	—
27	C₂²×Q₈×C₄₁	—	2	4	no	—
28	C₂²×Q₈×C₄₁	—	2	8	no	—
29	C₂²×Q₈×C₄₁	—	4	4	no	—
30	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
31	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
32	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
33	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
34	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
35	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
36	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
37	C₄⋊Q₈×C₄₁	—	2	32	no	—
38	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
39	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
40	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
41	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
42	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
43	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
44	C₂×C₄⋊C₄×C₄₁	—	2	16	no	—
45	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
46	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
47	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
48	C₂×C₄⋊C₄×C₄₁	—	2	16	no	—
49	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
50	C₂×C₄⋊C₄×C₄₁	—	4	8	no	—
51	C₂×C₄⋊C₄×C₄₁	D₄	1	8	yes	—
52	C₂×C₄⋊C₄×C₄₁	Q₈	1	4	yes	complemented
53	C₂×C₄²×C₄₁	—	2	4	no	—
54	C₂×C₄²×C₄₁	—	2	4	no	—
55	C₂×C₄²×C₄₁	—	2	4	no	—
56	C₂×C₄²×C₄₁	D₄	1	4	yes	—
57	C₂×C₄²×C₄₁	Q₈	1	8	yes	complemented
58	#95×C₄₁	—	2	4	no	—
59	#95×C₄₁	—	2	16	no	—
60	#95×C₄₁	D₄	1	8	yes	—
61	#95×C₄₁	Q₈	1	8	yes	complemented
62	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
63	C₂×Q₈×C₄₁	—	2	16	no	—
64	C₂×Q₈×C₄₁	—	4	32	no	—
65	C₂×Q₈×C₄₁	—	4	8	no	—
66	C₂×Q₈×C₄₁	—	4	8	no	—
67	C₂²×C₄×C₄₁	—	2	2	no	—
68	C₂²×C₄×C₄₁	—	2	4	no	—
69	C₂²×C₄×C₄₁	—	2	2	no	—
70	C₂²×C₄×C₄₁	—	2	4	no	—
71	C₂²×C₄×C₄₁	—	2	4	no	—
72	C₂²×C₄×C₄₁	—	2	2	no	—
73	C₂²×C₄×C₄₁	—	2	2	no	—
74	C₂²×C₄×C₄₁	—	2	4	no	—
75	C₂²×C₄×C₄₁	—	2	4	no	—
76	C₂²×C₄×C₄₁	—	2	2	no	—
77	C₂²×C₄×C₄₁	—	2	8	no	—
78	C₂²×C₄×C₄₁	—	2	4	no	—
79	C₂²×C₄×C₄₁	—	2	4	no	—
80	C₂²×C₄×C₄₁	—	2	2	no	—
81	C₂²×C₄×C₄₁	—	2	8	no	—
82	C₂²×C₄×C₄₁	—	2	4	no	—
83	C₂²×C₄×C₄₁	—	2	2	no	—
84	C₂²×C₄×C₄₁	—	2	4	no	—
85	C₂²×C₄×C₄₁	—	2	4	no	—
86	C₂²×C₄×C₄₁	—	2	4	no	—
87	C₂²×C₄×C₄₁	C₂×D₄	1	8	yes	—
88	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
89	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₄₁	C₂×D₄	1	8	yes	—
92	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
93	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₄₁	C₂×Q₈	1	4	yes	—
95	C₂²×C₄×C₄₁	C₂×Q₈	1	4	yes	—
96	C₂²×C₄×C₄₁	C₂×Q₈	1	8	yes	—
97	C₂²×C₄×C₄₁	C₂×Q₈	1	8	yes	—
98	C₂²×C₄×C₄₁	C₂×Q₈	1	4	yes	—
99	C₂²×C₄×C₄₁	C₂×Q₈	1	2	yes	—
100	C₂²×C₄×C₄₁	#41	1	2	yes	—
101	C₄⋊C₄×C₄₁	—	2	16	no	—
102	C₄⋊C₄×C₄₁	—	2	16	no	—
103	C₄⋊C₄×C₄₁	—	2	8	no	—
104	C₄⋊C₄×C₄₁	—	4	32	no	—
105	C₄⋊C₄×C₄₁	—	4	4	no	—
106	C₄⋊C₄×C₄₁	—	4	8	no	—
107	C₄²×C₄₁	—	2	8	no	—
108	C₄²×C₄₁	—	2	16	no	—
109	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
110	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
111	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
112	C₂³×C₄₁	C₂²×Q₈	1	2	yes	—
113	C₂³×C₄₁	C₂²×Q₈	1	1	yes	characteristic
114	C₂³×C₄₁	C₂²×Q₈	1	2	yes	—
115	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
116	C₂³×C₄₁	H(5,𝔽₂)	1	2	yes	—
117	C₂³×C₄₁	2₋¹⁺⁴	1	2	yes	—
118	Q₈×C₄₁	—	4	32	no	—
119	C₂×C₄×C₄₁	—	2	2	no	—
120	C₂×C₄×C₄₁	—	2	2	no	—
121	C₂×C₄×C₄₁	—	2	8	no	—
122	C₂×C₄×C₄₁	—	2	2	no	—
123	C₂×C₄×C₄₁	—	2	2	no	—
124	C₂×C₄×C₄₁	—	2	8	no	—
125	C₂×C₄×C₄₁	—	2	8	no	—
126	C₂×C₄×C₄₁	—	2	8	no	—
127	C₂×C₄×C₄₁	—	2	8	no	—
128	C₂×C₄×C₄₁	—	2	8	no	—
129	C₂×C₄×C₄₁	—	2	8	no	—
130	C₂×C₄×C₄₁	—	2	8	no	—
131	C₂×C₄×C₄₁	—	2	8	no	—
132	C₂×C₄×C₄₁	—	2	4	no	—
133	C₂×C₄×C₄₁	—	2	16	no	—
134	C₂×C₄×C₄₁	—	2	8	no	—
135	C₂×C₄×C₄₁	—	4	2	no	—
136	C₂×C₄×C₄₁	—	4	4	no	—
137	C₂×C₄×C₄₁	—	4	4	no	—
138	C₂×C₄×C₄₁	—	4	2	no	—
139	C₂×C₄×C₄₁	—	4	8	no	—
140	C₂×C₄×C₄₁	—	4	4	no	—
141	C₂×C₄×C₄₁	—	4	2	no	—
142	C₂×C₄×C₄₁	—	4	2	no	—
143	C₂×C₄×C₄₁	—	4	2	no	—
144	C₂×C₄×C₄₁	—	4	8	no	—
145	C₂×C₄×C₄₁	#120	1	4	yes	—
146	C₂×C₄×C₄₁	C₂²⋊Q₈	1	8	yes	—
147	C₂×C₄×C₄₁	C₂²⋊Q₈	1	4	yes	—
148	C₂×C₄×C₄₁	#127	1	4	yes	—
149	C₂×C₄×C₄₁	C₄⋊Q₈	1	4	yes	—
150	C₂×C₄×C₄₁	C₄⋊Q₈	1	4	yes	—
151	C₂×C₄×C₄₁	C₄⋊Q₈	1	8	yes	—
152	C₂×C₄×C₄₁	C₄⋊Q₈	1	16	yes	complemented
153	#15143	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
154	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
155	C₂²×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
156	C₂²×C₄₁	C₂×C₂²⋊Q₈	1	2	yes	—
157	C₂²×C₄₁	C₂×#127	1	1	yes	characteristic
158	C₂²×C₄₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
159	C₂²×C₄₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
160	C₂²×C₄₁	C₂×C₄⋊Q₈	1	4	yes	—
161	C₂²×C₄₁	C₂×C₄⋊Q₈	1	2	yes	—
162	C₂²×C₄₁	#535	1	1	yes	characteristic
163	C₂²×C₄₁	#536	1	1	yes	characteristic
164	C₂²×C₄₁	#544	1	4	yes	—
165	C₂²×C₄₁	D₄²	1	4	yes	—
166	C₂²×C₄₁	#547	1	2	yes	—
167	C₂²×C₄₁	D₄×Q₈	1	4	yes	—
168	C₂²×C₄₁	D₄×Q₈	1	2	yes	—
169	C₂²×C₄₁	#554	1	2	yes	—
170	C₂²×C₄₁	Q₈²	1	2	yes	—
171	C₄×C₄₁	—	2	4	no	—
172	C₄×C₄₁	—	2	4	no	—
173	C₄×C₄₁	—	2	16	no	—
174	C₄×C₄₁	—	4	8	no	—
175	C₄×C₄₁	—	4	4	no	—
176	C₄×C₄₁	—	8	2	no	—
177	C₄×C₄₁	#395	1	8	yes	complemented
178	C₂²×C₄⋊Q₈	C₂×C₄₁	1	1	yes	characteristic
179	C₂×#395	C₂×C₄₁	1	4	yes	—
180	C₂×#389	C₂×C₄₁	1	1	yes	characteristic
181	C₂×#384	C₂×C₄₁	1	2	yes	—
182	#1444	C₂×C₄₁	1	4	yes	—
183	C₄⋊#95	C₂×C₄₁	1	2	yes	—
184	C₄×#95	C₂×C₄₁	1	1	yes	characteristic
185	C₂×C₄₁	C₂×#395	1	1	yes	characteristic
186	C₂×C₄₁	#2433	1	1	yes	characteristic
187	C₂×C₄₁	#2434	1	1	yes	characteristic
188	C₂×C₄₁	#2440	1	4	yes	—
189	C₂×C₄₁	#2542	1	1	yes	characteristic
190	C₂×C₄₁	#2551	1	4	yes	—
191	C₂×C₄₁	#2567	1	1	yes	characteristic
192	C₂×C₄₁	#2660	1	1	yes	characteristic
193	C₂×C₄₁	#2868	1	1	yes	characteristic
194	C₂³×Q₈	C₂²×C₄₁	1	2	yes	—
195	C₂×C₄⋊Q₈	—	2	8	no	—
196	C₂×C₄⋊Q₈	—	2	4	no	—
197	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
198	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
199	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
200	C₂²×C₄⋊C₄	C₂²×C₄₁	1	8	yes	—
201	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
202	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
203	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
204	C₂²×C₄²	C₂²×C₄₁	1	2	yes	—
205	#395	—	2	16	no	—
206	#389	—	2	4	no	—
207	#384	—	2	8	no	—
208	C₂×#95	C₂²×C₄₁	1	8	yes	—
209	C₂×#95	C₂²×C₄₁	1	2	yes	—
210	C₂×#95	C₂²×C₄₁	1	2	yes	—
211	C₂×#95	C₂²×C₄₁	1	2	yes	—
212	C₄₁	#15143	1	1	yes	characteristic, direct product factor, Sylow
213	C₂²×Q₈	—	2	8	no	—
214	C₂²×Q₈	—	2	4	no	—
215	C₂²×Q₈	—	2	8	no	—
216	C₂²×Q₈	—	4	4	no	—
217	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
218	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
219	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
220	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
221	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
222	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
223	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
224	C₄⋊Q₈	—	2	32	no	—
225	C₂×C₄⋊C₄	—	2	8	no	—
226	C₂×C₄⋊C₄	—	2	4	no	—
227	C₂×C₄⋊C₄	—	2	4	no	—
228	C₂×C₄⋊C₄	—	2	4	no	—
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄⋊C₄	—	2	2	no	—
231	C₂×C₄⋊C₄	—	2	16	no	—
232	C₂×C₄⋊C₄	—	2	4	no	—
233	C₂×C₄⋊C₄	—	2	2	no	—
234	C₂×C₄⋊C₄	—	2	4	no	—
235	C₂×C₄⋊C₄	—	2	16	no	—
236	C₂×C₄⋊C₄	—	2	8	no	—
237	C₂×C₄⋊C₄	—	4	8	no	—
238	C₂×C₄⋊C₄	D₄×C₄₁	1	8	yes	—
239	C₂×C₄⋊C₄	Q₈×C₄₁	1	4	yes	complemented
240	C₂×C₄²	—	2	4	no	—
241	C₂×C₄²	—	2	4	no	—
242	C₂×C₄²	—	2	4	no	—
243	C₂×C₄²	D₄×C₄₁	1	4	yes	—
244	C₂×C₄²	Q₈×C₄₁	1	8	yes	complemented
245	#95	—	2	4	no	—
246	#95	—	2	16	no	—
247	#95	D₄×C₄₁	1	8	yes	—
248	#95	Q₈×C₄₁	1	8	yes	complemented
249	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
250	C₂×Q₈	—	2	16	no	—
251	C₂×Q₈	—	4	32	no	—
252	C₂×Q₈	—	4	8	no	—
253	C₂×Q₈	—	4	8	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	8	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	8	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	C₂×D₄×C₄₁	1	8	yes	—
275	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
276	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
277	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
278	C₂²×C₄	C₂×D₄×C₄₁	1	8	yes	—
279	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
280	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
281	C₂²×C₄	C₂×Q₈×C₄₁	1	4	yes	—
282	C₂²×C₄	C₂×Q₈×C₄₁	1	4	yes	—
283	C₂²×C₄	C₂×Q₈×C₄₁	1	8	yes	—
284	C₂²×C₄	C₂×Q₈×C₄₁	1	8	yes	—
285	C₂²×C₄	C₂×Q₈×C₄₁	1	4	yes	—
286	C₂²×C₄	C₂×Q₈×C₄₁	1	2	yes	—
287	C₂²×C₄	#41×C₄₁	1	2	yes	—
288	C₄⋊C₄	—	2	16	no	—
289	C₄⋊C₄	—	2	16	no	—
290	C₄⋊C₄	—	2	8	no	—
291	C₄⋊C₄	—	4	32	no	—
292	C₄⋊C₄	—	4	4	no	—
293	C₄⋊C₄	—	4	8	no	—
294	C₄²	—	2	8	no	—
295	C₄²	—	2	16	no	—
296	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
297	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
298	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
299	C₂³	C₂²×Q₈×C₄₁	1	2	yes	—
300	C₂³	C₂²×Q₈×C₄₁	1	1	yes	characteristic
301	C₂³	C₂²×Q₈×C₄₁	1	2	yes	—
302	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
303	C₂³	H(5,𝔽₂)×C₄₁	1	2	yes	—
304	C₂³	2₋¹⁺⁴×C₄₁	1	2	yes	—
305	Q₈	—	4	32	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	8	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	8	no	—
312	C₂×C₄	—	2	8	no	—
313	C₂×C₄	—	2	8	no	—
314	C₂×C₄	—	2	8	no	—
315	C₂×C₄	—	2	8	no	—
316	C₂×C₄	—	2	8	no	—
317	C₂×C₄	—	2	8	no	—
318	C₂×C₄	—	2	8	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	16	no	—
321	C₂×C₄	—	2	8	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	8	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	8	no	—
332	C₂×C₄	#120×C₄₁	1	4	yes	—
333	C₂×C₄	C₂²⋊Q₈×C₄₁	1	8	yes	—
334	C₂×C₄	C₂²⋊Q₈×C₄₁	1	4	yes	—
335	C₂×C₄	#127×C₄₁	1	4	yes	—
336	C₂×C₄	C₄⋊Q₈×C₄₁	1	4	yes	—
337	C₂×C₄	C₄⋊Q₈×C₄₁	1	8	yes	—
338	C₂×C₄	C₄⋊Q₈×C₄₁	1	4	yes	—
339	C₂×C₄	C₄⋊Q₈×C₄₁	1	16	yes	complemented
340	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
341	C₂²	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
342	C₂²	C₂×C₂²⋊Q₈×C₄₁	1	2	yes	—
343	C₂²	C₂×#127×C₄₁	1	1	yes	characteristic
344	C₂²	C₂×C₄⋊Q₈×C₄₁	1	2	yes	—
345	C₂²	C₂×C₄⋊Q₈×C₄₁	1	4	yes	—
346	C₂²	C₂×C₄⋊Q₈×C₄₁	1	1	yes	characteristic
347	C₂²	C₂×C₄⋊Q₈×C₄₁	1	1	yes	characteristic
348	C₂²	C₄₁×#535	1	1	yes	characteristic
349	C₂²	C₄₁×#536	1	1	yes	characteristic
350	C₂²	C₄₁×#544	1	4	yes	—
351	C₂²	D₄²×C₄₁	1	4	yes	—
352	C₂²	C₄₁×#547	1	2	yes	—
353	C₂²	D₄×Q₈×C₄₁	1	2	yes	—
354	C₂²	D₄×Q₈×C₄₁	1	4	yes	—
355	C₂²	C₄₁×#554	1	2	yes	—
356	C₂²	Q₈²×C₄₁	1	2	yes	—
357	C₄	—	2	4	no	—
358	C₄	—	2	4	no	—
359	C₄	—	2	16	no	—
360	C₄	—	4	4	no	—
361	C₄	—	4	8	no	—
362	C₄	—	8	2	no	—
363	C₄	C₄₁×#395	1	8	yes	complemented
364	C₂	C₂×C₄₁×#395	1	1	yes	characteristic
365	C₂	C₄₁×#2433	1	1	yes	characteristic
366	C₂	C₄₁×#2434	1	1	yes	characteristic
367	C₂	C₄₁×#2440	1	4	yes	—
368	C₂	C₄₁×#2542	1	1	yes	characteristic
369	C₂	C₄₁×#2551	1	4	yes	—
370	C₂	C₄₁×#2567	1	1	yes	characteristic
371	C₂	C₄₁×#2660	1	1	yes	characteristic
372	C₂	C₄₁×#2868	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₄₁	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₄₁
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
52. C₂×C₄⋊C₄×C₄₁	Q₈	semidirect
57. C₂×C₄²×C₄₁	Q₈	semidirect
61. #95×C₄₁	Q₈	semidirect
152. C₂×C₄×C₄₁	C₄⋊Q₈	semidirect
153. #15143	C₄₁	direct (N × H)
177. C₄×C₄₁	#395	semidirect
212. C₄₁	#15143	direct (N × H)
239. C₂×C₄⋊C₄	Q₈×C₄₁	semidirect
244. C₂×C₄²	Q₈×C₄₁	semidirect
248. #95	Q₈×C₄₁	semidirect
339. C₂×C₄	C₄⋊Q₈×C₄₁	semidirect
363. C₄	C₄₁×#395	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊Q₈×C₄₁	2
C₂×C₄₁×#395	2
C₂×C₄₁×#389	2
C₂×C₄₁×#384	2
C₄₁×#1444	2
C₄₁×C₄⋊#95	2
C₄×#95×C₄₁	2
#15143	41

Subgroups — C41×#15143 #23791344

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#15143 #23791344