Subgroups — C₄₁×#11384 #23787585

Order 10496.

1254 conjugacy classes of subgroups.

The subgroup lattice has 372 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×#340	C₂	1	4	yes	maximal
3	C₂×C₄₁×#336	C₂	1	1	yes	maximal, characteristic
4	C₄₁×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
5	C₂³×Q₈×C₄₁	—	2	1	no	—
6	C₂³×C₈×C₄₁	C₂²	1	2	yes	—
7	C₂×C₄⋊Q₈×C₄₁	—	2	8	no	—
8	C₂×C₄⋊Q₈×C₄₁	—	2	2	no	—
9	C₂×C₄⋊Q₈×C₄₁	C₄	1	4	yes	complemented
10	C₂²×C₄⋊C₄×C₄₁	—	2	1	no	—
11	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
12	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
13	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×#95×C₄₁	—	2	1	no	—
15	C₂×#95×C₄₁	—	2	1	no	—
16	C₄₁×#340	—	2	8	no	—
17	C₄₁×#336	—	2	2	no	—
18	C₂²×Q₈×C₄₁	—	2	8	no	—
19	C₂²×Q₈×C₄₁	—	2	4	no	—
20	C₂²×Q₈×C₄₁	—	4	4	no	—
21	C₂²×Q₈×C₄₁	—	4	2	no	—
22	C₂²×Q₈×C₄₁	—	4	2	no	—
23	C₂³×C₄×C₄₁	—	2	2	no	—
24	C₂³×C₄×C₄₁	—	2	2	no	—
25	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
26	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
27	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
28	C₂²×C₈×C₄₁	—	2	2	no	—
29	C₂²×C₈×C₄₁	—	2	4	no	—
30	C₂²×C₈×C₄₁	—	2	2	no	—
31	C₂²×C₈×C₄₁	—	2	4	no	—
32	C₂²×C₈×C₄₁	Q₈	1	4	yes	complemented
33	C₄⋊Q₈×C₄₁	—	2	16	no	—
34	C₄⋊Q₈×C₄₁	—	2	16	no	—
35	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
36	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
37	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
38	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
39	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
40	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
41	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
42	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	4	yes	—
43	C₂×C₄⋊C₄×C₄₁	D₄	1	8	yes	—
44	C₂×C₄⋊C₄×C₄₁	Q₈	1	4	yes	complemented
45	C₂×C₄²×C₄₁	—	2	4	no	—
46	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
47	C₂×C₄²×C₄₁	D₄	1	2	yes	—
48	#95×C₄₁	—	4	2	no	—
49	#95×C₄₁	—	4	2	no	—
50	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
51	C₂×Q₈×C₄₁	—	2	16	no	—
52	C₂×Q₈×C₄₁	—	4	8	no	—
53	C₂×Q₈×C₄₁	—	4	16	no	—
54	C₂×Q₈×C₄₁	—	4	16	no	—
55	C₂×Q₈×C₄₁	—	4	8	no	—
56	C₂²×C₄×C₄₁	—	2	2	no	—
57	C₂²×C₄×C₄₁	—	2	2	no	—
58	C₂²×C₄×C₄₁	—	2	2	no	—
59	C₂²×C₄×C₄₁	—	2	2	no	—
60	C₂²×C₄×C₄₁	—	2	4	no	—
61	C₂²×C₄×C₄₁	—	2	8	no	—
62	C₂²×C₄×C₄₁	—	2	4	no	—
63	C₂²×C₄×C₄₁	—	4	2	no	—
64	C₂²×C₄×C₄₁	—	4	2	no	—
65	C₂²×C₄×C₄₁	—	4	4	no	—
66	C₂²×C₄×C₄₁	—	4	2	no	—
67	C₂²×C₄×C₄₁	—	4	2	no	—
68	C₂²×C₄×C₄₁	—	4	2	no	—
69	C₂²×C₄×C₄₁	—	4	2	no	—
70	C₂²×C₄×C₄₁	—	4	2	no	—
71	C₂²×C₄×C₄₁	—	4	2	no	—
72	C₂²×C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
73	C₂²×C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
74	C₂²×C₄×C₄₁	D₈	1	2	yes	—
75	C₂²×C₄×C₄₁	SD₁₆	1	2	yes	—
76	C₂²×C₄×C₄₁	SD₁₆	1	2	yes	—
77	C₂²×C₄×C₄₁	Q₁₆	1	2	yes	—
78	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
80	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₁	C₂×Q₈	1	2	yes	—
82	C₂²×C₄×C₄₁	C₂×Q₈	1	2	yes	—
83	C₂²×C₄×C₄₁	#41	1	2	yes	—
84	C₂²×C₄×C₄₁	#41	1	2	yes	—
85	C₂×C₈×C₄₁	—	2	8	no	—
86	C₂×C₈×C₄₁	—	2	4	no	—
87	C₂×C₈×C₄₁	—	4	2	no	—
88	C₂×C₈×C₄₁	—	4	4	no	—
89	C₂×C₈×C₄₁	—	4	2	no	—
90	C₄⋊C₄×C₄₁	—	2	16	no	—
91	C₄⋊C₄×C₄₁	—	2	4	no	—
92	C₄⋊C₄×C₄₁	—	2	8	no	—
93	C₄⋊C₄×C₄₁	—	2	8	no	—
94	C₄⋊C₄×C₄₁	—	4	4	no	—
95	C₄⋊C₄×C₄₁	C₂²⋊C₄	1	8	yes	—
96	C₄²×C₄₁	—	2	4	no	—
97	C₄²×C₄₁	—	2	4	no	—
98	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
99	C₂³×C₄₁	#120	1	2	yes	—
100	C₂³×C₄₁	C₂²⋊Q₈	1	2	yes	—
101	C₂³×C₄₁	#124	1	1	yes	characteristic
102	C₂³×C₄₁	C₄⋊Q₈	1	1	yes	characteristic
103	C₂³×C₄₁	C₂×D₈	1	1	yes	characteristic
104	C₂³×C₄₁	C₂×SD₁₆	1	1	yes	characteristic
105	C₂³×C₄₁	C₂×SD₁₆	1	1	yes	characteristic
106	C₂³×C₄₁	C₂×Q₁₆	1	1	yes	characteristic
107	C₂³×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
108	C₂³×C₄₁	#137	1	2	yes	—
109	Q₈×C₄₁	—	4	32	no	—
110	C₂×C₄×C₄₁	—	2	2	no	—
111	C₂×C₄×C₄₁	—	2	2	no	—
112	C₂×C₄×C₄₁	—	2	2	no	—
113	C₂×C₄×C₄₁	—	2	2	no	—
114	C₂×C₄×C₄₁	—	2	4	no	—
115	C₂×C₄×C₄₁	—	2	4	no	—
116	C₂×C₄×C₄₁	—	2	4	no	—
117	C₂×C₄×C₄₁	—	2	4	no	—
118	C₂×C₄×C₄₁	—	2	8	no	—
119	C₂×C₄×C₄₁	—	4	4	no	—
120	C₂×C₄×C₄₁	—	4	4	no	—
121	C₂×C₄×C₄₁	—	4	8	no	—
122	C₂×C₄×C₄₁	—	4	8	no	—
123	C₂×C₄×C₄₁	—	4	4	no	—
124	C₂×C₄×C₄₁	—	4	4	no	—
125	C₂×C₄×C₄₁	—	4	4	no	—
126	C₂×C₄×C₄₁	—	8	2	no	—
127	C₂×C₄×C₄₁	—	8	2	no	—
128	C₂×C₄×C₄₁	—	8	2	no	—
129	C₂×C₄×C₄₁	—	8	2	no	—
130	C₂×C₄×C₄₁	#102	1	4	yes	—
131	C₂×C₄×C₄₁	#103	1	4	yes	—
132	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
133	C₂×C₄×C₄₁	C₄×Q₈	1	2	yes	—
134	C₂×C₄×C₄₁	C₄×Q₈	1	2	yes	—
135	C₂×C₄×C₄₁	#120	1	2	yes	—
136	C₂×C₄×C₄₁	C₂²⋊Q₈	1	4	yes	—
137	C₂×C₄×C₄₁	C₂²⋊Q₈	1	4	yes	—
138	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
139	C₂×C₄×C₄₁	#124	1	4	yes	—
140	C₂×C₄×C₄₁	#124	1	1	yes	characteristic
141	C₂×C₄×C₄₁	C₄⋊Q₈	1	4	yes	—
142	C₂×C₄×C₄₁	C₄⋊Q₈	1	1	yes	characteristic
143	C₈×C₄₁	—	4	4	no	—
144	#11384	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂²×C₄₁	#379	1	1	yes	characteristic
146	C₂²×C₄₁	#391	1	1	yes	characteristic
147	C₂²×C₄₁	#391	1	1	yes	characteristic
148	C₂²×C₄₁	#393	1	2	yes	—
149	C₂²×C₄₁	#395	1	2	yes	—
150	C₂²×C₄₁	C₂×#102	1	1	yes	characteristic
151	C₂²×C₄₁	C₂×#103	1	1	yes	characteristic
152	C₂²×C₄₁	#418	1	1	yes	characteristic
153	C₂²×C₄₁	#419	1	1	yes	characteristic
154	C₂²×C₄₁	#447	1	2	yes	—
155	C₂²×C₄₁	#448	1	2	yes	—
156	C₂²×C₄₁	#450	1	2	yes	—
157	C₂²×C₄₁	#451	1	2	yes	—
158	C₂²×C₄₁	#474	1	2	yes	—
159	C₂²×C₄₁	#475	1	2	yes	—
160	C₂²×C₄₁	#476	1	2	yes	—
161	C₂²×C₄₁	#477	1	2	yes	—
162	C₂²×C₄₁	#486	1	1	yes	characteristic
163	C₂²×C₄₁	#487	1	1	yes	characteristic
164	C₂²×C₄₁	#489	1	2	yes	—
165	C₂²×C₄₁	#498	1	1	yes	characteristic
166	C₂²×C₄₁	#500	1	1	yes	characteristic
167	C₂²×C₄₁	#501	1	2	yes	—
168	C₄×C₄₁	—	2	4	no	—
169	C₄×C₄₁	—	2	4	no	—
170	C₄×C₄₁	—	4	8	no	—
171	C₄×C₄₁	—	8	4	no	—
172	C₄×C₄₁	#391	1	4	yes	—
173	C₄×C₄₁	#393	1	2	yes	—
174	C₄×C₄₁	#395	1	2	yes	—
175	C₂²×C₄⋊Q₈	C₂×C₄₁	1	1	yes	characteristic
176	C₂×#340	C₂×C₄₁	1	4	yes	—
177	C₂×#336	C₂×C₄₁	1	1	yes	characteristic
178	C₄⋊#95	C₂×C₄₁	1	1	yes	characteristic
179	C₂×C₄₁	#1446	1	1	yes	characteristic
180	C₂×C₄₁	#1786	1	1	yes	characteristic
181	C₂×C₄₁	#1787	1	1	yes	characteristic
182	C₂×C₄₁	#1987	1	1	yes	characteristic
183	C₂×C₄₁	#1988	1	1	yes	characteristic
184	C₂×C₄₁	#1990	1	1	yes	characteristic
185	C₂×C₄₁	#1993	1	1	yes	characteristic
186	C₂×C₄₁	#2023	1	2	yes	—
187	C₂×C₄₁	#2024	1	2	yes	—
188	C₂×C₄₁	#2057	1	2	yes	—
189	C₂×C₄₁	#2058	1	2	yes	—
190	C₂³×Q₈	—	2	1	no	—
191	C₂³×C₈	C₂²×C₄₁	1	2	yes	—
192	C₂×C₄⋊Q₈	—	2	8	no	—
193	C₂×C₄⋊Q₈	—	2	2	no	—
194	C₂×C₄⋊Q₈	C₄×C₄₁	1	4	yes	complemented
195	C₂²×C₄⋊C₄	—	2	1	no	—
196	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
197	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
198	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
199	C₂×#95	—	2	1	no	—
200	C₂×#95	—	2	1	no	—
201	#340	—	2	8	no	—
202	#336	—	2	2	no	—
203	C₄₁	#11384	1	1	yes	characteristic, direct product factor, Sylow
204	C₂²×Q₈	—	2	8	no	—
205	C₂²×Q₈	—	2	4	no	—
206	C₂²×Q₈	—	4	4	no	—
207	C₂²×Q₈	—	4	2	no	—
208	C₂²×Q₈	—	4	2	no	—
209	C₂³×C₄	—	2	2	no	—
210	C₂³×C₄	—	2	2	no	—
211	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
212	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
213	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
214	C₂²×C₈	—	2	2	no	—
215	C₂²×C₈	—	2	4	no	—
216	C₂²×C₈	—	2	2	no	—
217	C₂²×C₈	—	2	4	no	—
218	C₂²×C₈	Q₈×C₄₁	1	4	yes	complemented
219	C₄⋊Q₈	—	2	16	no	—
220	C₄⋊Q₈	—	2	16	no	—
221	C₂×C₄⋊C₄	—	2	8	no	—
222	C₂×C₄⋊C₄	—	2	4	no	—
223	C₂×C₄⋊C₄	—	2	4	no	—
224	C₂×C₄⋊C₄	—	2	2	no	—
225	C₂×C₄⋊C₄	—	2	4	no	—
226	C₂×C₄⋊C₄	—	2	4	no	—
227	C₂×C₄⋊C₄	—	2	2	no	—
228	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	4	yes	—
229	C₂×C₄⋊C₄	D₄×C₄₁	1	8	yes	—
230	C₂×C₄⋊C₄	Q₈×C₄₁	1	4	yes	complemented
231	C₂×C₄²	—	2	4	no	—
232	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
233	C₂×C₄²	D₄×C₄₁	1	2	yes	—
234	#95	—	4	2	no	—
235	#95	—	4	2	no	—
236	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
237	C₂×Q₈	—	2	16	no	—
238	C₂×Q₈	—	4	8	no	—
239	C₂×Q₈	—	4	16	no	—
240	C₂×Q₈	—	4	16	no	—
241	C₂×Q₈	—	4	8	no	—
242	C₂²×C₄	—	2	2	no	—
243	C₂²×C₄	—	2	2	no	—
244	C₂²×C₄	—	2	2	no	—
245	C₂²×C₄	—	2	2	no	—
246	C₂²×C₄	—	2	4	no	—
247	C₂²×C₄	—	2	8	no	—
248	C₂²×C₄	—	2	4	no	—
249	C₂²×C₄	—	4	2	no	—
250	C₂²×C₄	—	4	2	no	—
251	C₂²×C₄	—	4	4	no	—
252	C₂²×C₄	—	4	2	no	—
253	C₂²×C₄	—	4	2	no	—
254	C₂²×C₄	—	4	2	no	—
255	C₂²×C₄	—	4	2	no	—
256	C₂²×C₄	—	4	2	no	—
257	C₂²×C₄	—	4	2	no	—
258	C₂²×C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
259	C₂²×C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
260	C₂²×C₄	D₈×C₄₁	1	2	yes	—
261	C₂²×C₄	SD₁₆×C₄₁	1	2	yes	—
262	C₂²×C₄	SD₁₆×C₄₁	1	2	yes	—
263	C₂²×C₄	Q₁₆×C₄₁	1	2	yes	—
264	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
265	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
266	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
267	C₂²×C₄	C₂×Q₈×C₄₁	1	2	yes	—
268	C₂²×C₄	C₂×Q₈×C₄₁	1	2	yes	—
269	C₂²×C₄	#41×C₄₁	1	2	yes	—
270	C₂²×C₄	#41×C₄₁	1	2	yes	—
271	C₂×C₈	—	2	8	no	—
272	C₂×C₈	—	2	4	no	—
273	C₂×C₈	—	4	2	no	—
274	C₂×C₈	—	4	4	no	—
275	C₂×C₈	—	4	2	no	—
276	C₄⋊C₄	—	2	16	no	—
277	C₄⋊C₄	—	2	4	no	—
278	C₄⋊C₄	—	2	8	no	—
279	C₄⋊C₄	—	2	8	no	—
280	C₄⋊C₄	—	4	4	no	—
281	C₄⋊C₄	C₂²⋊C₄×C₄₁	1	8	yes	—
282	C₄²	—	2	4	no	—
283	C₄²	—	2	4	no	—
284	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
285	C₂³	#120×C₄₁	1	2	yes	—
286	C₂³	C₂²⋊Q₈×C₄₁	1	2	yes	—
287	C₂³	#124×C₄₁	1	1	yes	characteristic
288	C₂³	C₄⋊Q₈×C₄₁	1	1	yes	characteristic
289	C₂³	C₂×D₈×C₄₁	1	1	yes	characteristic
290	C₂³	C₂×SD₁₆×C₄₁	1	1	yes	characteristic
291	C₂³	C₂×SD₁₆×C₄₁	1	1	yes	characteristic
292	C₂³	C₂×Q₁₆×C₄₁	1	1	yes	characteristic
293	C₂³	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
294	C₂³	#137×C₄₁	1	2	yes	—
295	Q₈	—	4	32	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	2	8	no	—
305	C₂×C₄	—	4	4	no	—
306	C₂×C₄	—	4	4	no	—
307	C₂×C₄	—	4	8	no	—
308	C₂×C₄	—	4	8	no	—
309	C₂×C₄	—	4	4	no	—
310	C₂×C₄	—	4	4	no	—
311	C₂×C₄	—	4	4	no	—
312	C₂×C₄	—	8	2	no	—
313	C₂×C₄	—	8	2	no	—
314	C₂×C₄	—	8	2	no	—
315	C₂×C₄	—	8	2	no	—
316	C₂×C₄	#102×C₄₁	1	4	yes	—
317	C₂×C₄	#103×C₄₁	1	4	yes	—
318	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
319	C₂×C₄	C₄×Q₈×C₄₁	1	2	yes	—
320	C₂×C₄	C₄×Q₈×C₄₁	1	2	yes	—
321	C₂×C₄	#120×C₄₁	1	2	yes	—
322	C₂×C₄	C₂²⋊Q₈×C₄₁	1	4	yes	—
323	C₂×C₄	C₂²⋊Q₈×C₄₁	1	4	yes	—
324	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
325	C₂×C₄	#124×C₄₁	1	4	yes	—
326	C₂×C₄	#124×C₄₁	1	1	yes	characteristic
327	C₂×C₄	C₄⋊Q₈×C₄₁	1	4	yes	—
328	C₂×C₄	C₄⋊Q₈×C₄₁	1	1	yes	characteristic
329	C₈	—	4	4	no	—
330	C₂²	C₄₁×#379	1	1	yes	characteristic
331	C₂²	C₄₁×#391	1	1	yes	characteristic
332	C₂²	C₄₁×#391	1	1	yes	characteristic
333	C₂²	C₄₁×#393	1	2	yes	—
334	C₂²	C₄₁×#395	1	2	yes	—
335	C₂²	C₂×#102×C₄₁	1	1	yes	characteristic
336	C₂²	C₂×#103×C₄₁	1	1	yes	characteristic
337	C₂²	C₄₁×#418	1	1	yes	characteristic
338	C₂²	C₄₁×#419	1	1	yes	characteristic
339	C₂²	C₄₁×#447	1	2	yes	—
340	C₂²	C₄₁×#448	1	2	yes	—
341	C₂²	C₄₁×#450	1	2	yes	—
342	C₂²	C₄₁×#451	1	2	yes	—
343	C₂²	C₄₁×#474	1	2	yes	—
344	C₂²	C₄₁×#475	1	2	yes	—
345	C₂²	C₄₁×#476	1	2	yes	—
346	C₂²	C₄₁×#477	1	2	yes	—
347	C₂²	C₄₁×#486	1	1	yes	characteristic
348	C₂²	C₄₁×#487	1	1	yes	characteristic
349	C₂²	C₄₁×#489	1	2	yes	—
350	C₂²	C₄₁×#498	1	1	yes	characteristic
351	C₂²	C₄₁×#500	1	1	yes	characteristic
352	C₂²	C₄₁×#501	1	2	yes	—
353	C₄	—	2	4	no	—
354	C₄	—	2	4	no	—
355	C₄	—	4	8	no	—
356	C₄	—	8	4	no	—
357	C₄	C₄₁×#391	1	4	yes	—
358	C₄	C₄₁×#393	1	2	yes	—
359	C₄	C₄₁×#395	1	2	yes	—
360	C₂	C₄₁×#1446	1	1	yes	characteristic
361	C₂	C₄₁×#1786	1	1	yes	characteristic
362	C₂	C₄₁×#1787	1	1	yes	characteristic
363	C₂	C₄₁×#1987	1	1	yes	characteristic
364	C₂	C₄₁×#1988	1	1	yes	characteristic
365	C₂	C₄₁×#1990	1	1	yes	characteristic
366	C₂	C₄₁×#1993	1	1	yes	characteristic
367	C₂	C₄₁×#2023	1	2	yes	—
368	C₂	C₄₁×#2024	1	2	yes	—
369	C₂	C₄₁×#2057	1	2	yes	—
370	C₂	C₄₁×#2058	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₄₁	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₄₁
Frattini, cosocle	C₂³×C₄	C₂³×C₄₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
9. C₂×C₄⋊Q₈×C₄₁	C₄	semidirect
32. C₂²×C₈×C₄₁	Q₈	semidirect
44. C₂×C₄⋊C₄×C₄₁	Q₈	semidirect
144. #11384	C₄₁	direct (N × H)
194. C₂×C₄⋊Q₈	C₄×C₄₁	semidirect
203. C₄₁	#11384	direct (N × H)
218. C₂²×C₈	Q₈×C₄₁	semidirect
230. C₂×C₄⋊C₄	Q₈×C₄₁	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×#340	2
C₂×C₄₁×#336	2
C₄₁×C₄⋊#95	2
#11384	41

Subgroups — C41×#11384 #23787585

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#11384 #23787585