Subgroups — C₄₁×#33856 #23810057

Order 10496.

652 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3416	C₂	1	2	yes	maximal, complemented
2	C₄₁×#3293	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3292	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2248	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2223	C₂	1	2	yes	maximal, complemented
6	C₄₁×#2214	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#2213	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#2194	C₂	1	2	yes	maximal, complemented
9	C₄₁×#2193	C₂	1	2	yes	maximal, complemented
10	C₄₁×#2178	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#2170	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#578	—	2	1	no	—
13	C₄₁×#578	C₂²	1	2	yes	complemented
14	C₄₁×#576	—	2	1	no	—
15	C₄₁×#576	C₂²	1	2	yes	—
16	C₄₁×#510	—	2	2	no	—
17	C₄₁×#510	C₂²	1	2	yes	—
18	C₄₁×#509	—	2	2	no	—
19	C₄₁×#509	C₂²	1	2	yes	complemented
20	C₄₁×#508	—	2	2	no	—
21	C₄₁×#508	C₂²	1	1	yes	characteristic
22	C₂×SD₃₂×C₄₁	—	2	2	no	—
23	C₂×SD₃₂×C₄₁	C₂²	1	2	yes	complemented
24	C₂×SD₃₂×C₄₁	C₂²	1	2	yes	complemented
25	C₄₁×#504	C₂²	1	2	yes	complemented
26	C₄₁×#494	C₂²	1	1	yes	characteristic, complemented
27	C₄₁×#493	C₂²	1	1	yes	characteristic
28	C₄₁×#473	—	2	1	no	—
29	C₄₁×#473	C₂²	1	2	yes	complemented
30	C₄₁×#472	—	2	1	no	—
31	C₄₁×#472	C₂²	1	2	yes	—
32	C₄₁×#456	—	2	2	no	—
33	C₄₁×#453	—	2	2	no	—
34	C₄₁×#443	C₂²	1	1	yes	characteristic
35	C₄₁×#443	C₂²	1	1	yes	characteristic
36	C₄₁×#443	C₂²	1	1	yes	characteristic, complemented
37	C₄₁×#368	C₂²	1	1	yes	characteristic, complemented
38	C₄₁×#364	C₂²	1	1	yes	characteristic, complemented
39	C₄₁×#362	C₂²	1	2	yes	complemented
40	C₄₁×#361	C₂²	1	2	yes	complemented
41	C₄₁×#359	C₂²	1	1	yes	characteristic
42	C₄₁×#359	C₂²	1	1	yes	characteristic, complemented
43	C₄₁×#350	C₂²	1	2	yes	complemented
44	C₄×C₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
45	2₋¹⁺⁴×C₄₁	—	2	2	no	—
46	H(5,𝔽₂)×C₄₁	—	2	2	no	—
47	#137×C₄₁	—	2	2	no	—
48	#137×C₄₁	—	2	2	no	—
49	#137×C₄₁	—	4	2	no	—
50	#137×C₄₁	—	4	2	no	—
51	AGL(1,ℤ/8)×C₄₁	—	2	2	no	—
52	AGL(1,ℤ/8)×C₄₁	—	2	2	no	—
53	AGL(1,ℤ/8)×C₄₁	—	4	2	no	—
54	AGL(1,ℤ/8)×C₄₁	—	4	2	no	—
55	#135×C₄₁	—	2	2	no	—
56	#135×C₄₁	—	2	2	no	—
57	#135×C₄₁	—	4	1	no	—
58	#135×C₄₁	—	4	1	no	—
59	#135×C₄₁	D₄	1	1	yes	characteristic
60	#135×C₄₁	C₂³	1	1	yes	characteristic
61	#135×C₄₁	C₂³	1	1	yes	characteristic
62	C₂×Q₁₆×C₄₁	—	2	2	no	—
63	C₂×Q₁₆×C₄₁	—	2	1	no	—
64	C₂×Q₁₆×C₄₁	—	4	1	no	—
65	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
66	C₂×D₈×C₄₁	—	2	2	no	—
67	C₂×D₈×C₄₁	—	2	1	no	—
68	C₂×D₈×C₄₁	—	4	1	no	—
69	C₂×D₈×C₄₁	C₂³	1	2	yes	—
70	#131×C₄₁	—	2	1	no	—
71	#131×C₄₁	—	2	1	no	—
72	#131×C₄₁	C₂³	1	2	yes	—
73	C₄⋊Q₈×C₄₁	—	2	1	no	—
74	#127×C₄₁	—	2	1	no	—
75	Q₃₂×C₄₁	—	2	2	no	—
76	Q₃₂×C₄₁	D₄	1	1	yes	characteristic, complemented
77	SD₃₂×C₄₁	—	2	2	no	—
78	SD₃₂×C₄₁	—	2	2	no	—
79	SD₃₂×C₄₁	—	2	2	no	—
80	SD₃₂×C₄₁	—	2	2	no	—
81	SD₃₂×C₄₁	—	4	2	no	—
82	SD₃₂×C₄₁	D₄	1	1	yes	characteristic, complemented
83	SD₃₂×C₄₁	D₄	1	1	yes	characteristic, complemented
84	D₁₆×C₄₁	—	2	2	no	—
85	D₁₆×C₄₁	D₄	1	1	yes	characteristic, complemented
86	M₃₂×C₄₁	—	2	2	no	—
87	M₃₂×C₄₁	C₂³	1	2	yes	—
88	C₂×C₁₆×C₄₁	—	2	2	no	—
89	C₂×C₁₆×C₄₁	C₂³	1	1	yes	characteristic
90	C₂×C₁₆×C₄₁	C₂³	1	1	yes	characteristic
91	#108×C₄₁	D₄	1	1	yes	characteristic
92	#108×C₄₁	C₂³	1	1	yes	characteristic
93	#108×C₄₁	C₂³	1	1	yes	characteristic
94	#104×C₄₁	—	2	1	no	—
95	#104×C₄₁	—	2	1	no	—
96	#104×C₄₁	D₄	1	2	yes	—
97	#101×C₄₁	—	2	2	no	—
98	#100×C₄₁	—	2	2	no	—
99	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
100	#41×C₄₁	—	2	1	no	—
101	#41×C₄₁	—	2	1	no	—
102	#41×C₄₁	—	4	2	no	—
103	#41×C₄₁	—	4	2	no	—
104	#41×C₄₁	—	4	2	no	—
105	#41×C₄₁	—	4	2	no	—
106	#41×C₄₁	—	8	2	no	—
107	#41×C₄₁	C₂×D₄	1	2	yes	—
108	C₂×Q₈×C₄₁	—	2	2	no	—
109	C₂×Q₈×C₄₁	—	4	2	no	—
110	C₂×Q₈×C₄₁	—	4	2	no	—
111	C₂×D₄×C₄₁	—	2	2	no	—
112	C₂×D₄×C₄₁	—	4	2	no	—
113	C₂×D₄×C₄₁	—	4	2	no	—
114	C₂×D₄×C₄₁	—	8	1	no	—
115	C₂×D₄×C₄₁	—	8	2	no	—
116	Q₁₆×C₄₁	—	2	2	no	—
117	Q₁₆×C₄₁	—	2	2	no	—
118	Q₁₆×C₄₁	—	4	2	no	—
119	Q₁₆×C₄₁	—	4	2	no	—
120	Q₁₆×C₄₁	—	4	1	no	—
121	Q₁₆×C₄₁	—	4	1	no	—
122	Q₁₆×C₄₁	D₈	1	1	yes	characteristic
123	Q₁₆×C₄₁	C₂×D₄	1	1	yes	characteristic
124	Q₁₆×C₄₁	C₂×D₄	1	1	yes	characteristic
125	SD₁₆×C₄₁	—	2	1	no	—
126	SD₁₆×C₄₁	—	2	1	no	—
127	SD₁₆×C₄₁	—	4	2	no	—
128	SD₁₆×C₄₁	—	4	2	no	—
129	SD₁₆×C₄₁	—	4	2	no	—
130	SD₁₆×C₄₁	—	4	2	no	—
131	SD₁₆×C₄₁	D₈	1	2	yes	—
132	D₈×C₄₁	—	2	2	no	—
133	D₈×C₄₁	—	2	2	no	—
134	D₈×C₄₁	—	4	2	no	—
135	D₈×C₄₁	—	4	2	no	—
136	D₈×C₄₁	—	4	1	no	—
137	D₈×C₄₁	—	4	1	no	—
138	D₈×C₄₁	D₈	1	1	yes	characteristic
139	D₈×C₄₁	C₂×D₄	1	1	yes	characteristic
140	D₈×C₄₁	C₂×D₄	1	1	yes	characteristic
141	M₁₆×C₄₁	—	2	2	no	—
142	M₁₆×C₄₁	—	2	1	no	—
143	M₁₆×C₄₁	—	2	1	no	—
144	M₁₆×C₄₁	—	4	1	no	—
145	M₁₆×C₄₁	—	4	1	no	—
146	M₁₆×C₄₁	C₂×D₄	1	2	yes	—
147	C₂×C₈×C₄₁	—	2	2	no	—
148	C₂×C₈×C₄₁	—	4	1	no	—
149	C₂×C₈×C₄₁	—	4	1	no	—
150	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
152	C₄⋊C₄×C₄₁	—	8	1	no	—
153	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
154	C₁₆×C₄₁	—	2	2	no	—
155	C₁₆×C₄₁	—	2	1	no	—
156	C₁₆×C₄₁	C₂×D₄	1	1	yes	characteristic
157	C₁₆×C₄₁	C₂×D₄	1	1	yes	characteristic
158	C₂³×C₄₁	—	4	2	no	—
159	C₂³×C₄₁	—	8	2	no	—
160	Q₈×C₄₁	—	2	1	no	—
161	Q₈×C₄₁	—	2	1	no	—
162	Q₈×C₄₁	—	4	2	no	—
163	Q₈×C₄₁	—	4	2	no	—
164	Q₈×C₄₁	—	8	2	no	—
165	Q₈×C₄₁	C₂×D₈	1	2	yes	—
166	D₄×C₄₁	—	2	2	no	—
167	D₄×C₄₁	—	2	1	no	—
168	D₄×C₄₁	—	2	1	no	—
169	D₄×C₄₁	—	4	1	no	—
170	D₄×C₄₁	—	4	1	no	—
171	D₄×C₄₁	—	4	2	no	—
172	D₄×C₄₁	—	4	2	no	—
173	D₄×C₄₁	—	8	2	no	—
174	D₄×C₄₁	—	8	2	no	—
175	D₄×C₄₁	—	8	2	no	—
176	D₄×C₄₁	—	16	2	no	—
177	D₄×C₄₁	C₂×D₈	1	2	yes	—
178	C₂×C₄×C₄₁	—	2	1	no	—
179	C₂×C₄×C₄₁	—	2	2	no	—
180	C₂×C₄×C₄₁	—	4	1	no	—
181	C₂×C₄×C₄₁	—	4	1	no	—
182	C₂×C₄×C₄₁	—	4	2	no	—
183	C₂×C₄×C₄₁	—	8	2	no	—
184	C₂×C₄×C₄₁	—	8	2	no	—
185	C₂×C₄×C₄₁	—	8	2	no	—
186	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
187	C₈×C₄₁	—	2	2	no	—
188	C₈×C₄₁	—	4	1	no	—
189	C₈×C₄₁	—	4	1	no	—
190	C₈×C₄₁	C₂×D₈	1	1	yes	characteristic
191	C₈×C₄₁	C₂×D₈	1	1	yes	characteristic
192	C₈×C₄₁	C₂²×D₄	1	1	yes	characteristic
193	C₈×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
194	#33856	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂²×C₄₁	—	2	2	no	—
196	C₂²×C₄₁	—	4	1	no	—
197	C₂²×C₄₁	—	4	1	no	—
198	C₂²×C₄₁	—	8	2	no	—
199	C₂²×C₄₁	—	16	2	no	—
200	C₂²×C₄₁	—	32	2	no	—
201	C₂²×C₄₁	#576	1	1	yes	characteristic
202	C₄×C₄₁	—	2	2	no	—
203	C₄×C₄₁	—	2	2	no	—
204	C₄×C₄₁	—	4	1	no	—
205	C₄×C₄₁	—	4	1	no	—
206	C₄×C₄₁	—	8	2	no	—
207	C₄×C₄₁	D₄²	1	1	yes	characteristic
208	C₄×C₄₁	C₂²×D₈	1	1	yes	characteristic
209	#3416	C₂×C₄₁	1	2	yes	complemented
210	#3293	C₂×C₄₁	1	1	yes	characteristic, complemented
211	#3292	C₂×C₄₁	1	1	yes	characteristic, complemented
212	#2248	C₂×C₄₁	1	1	yes	characteristic, complemented
213	#2223	C₂×C₄₁	1	2	yes	complemented
214	#2214	C₂×C₄₁	1	1	yes	characteristic, complemented
215	#2213	C₂×C₄₁	1	1	yes	characteristic, complemented
216	#2194	C₂×C₄₁	1	2	yes	complemented
217	#2193	C₂×C₄₁	1	2	yes	complemented
218	#2178	C₂×C₄₁	1	1	yes	characteristic, complemented
219	#2170	C₂×C₄₁	1	1	yes	characteristic, complemented
220	C₂×C₄₁	—	2	1	no	—
221	C₂×C₄₁	—	4	2	no	—
222	C₂×C₄₁	—	8	1	no	—
223	C₂×C₄₁	—	8	1	no	—
224	C₂×C₄₁	—	16	2	no	—
225	C₂×C₄₁	D₄×D₈	1	1	yes	characteristic
226	#578	—	2	1	no	—
227	#578	C₂²×C₄₁	1	2	yes	complemented
228	#576	—	2	1	no	—
229	#576	C₂²×C₄₁	1	2	yes	—
230	#510	—	2	2	no	—
231	#510	C₂²×C₄₁	1	2	yes	—
232	#509	—	2	2	no	—
233	#509	C₂²×C₄₁	1	2	yes	complemented
234	#508	—	2	2	no	—
235	#508	C₂²×C₄₁	1	1	yes	characteristic
236	C₂×SD₃₂	—	2	2	no	—
237	C₂×SD₃₂	C₂²×C₄₁	1	2	yes	complemented
238	C₂×SD₃₂	C₂²×C₄₁	1	2	yes	complemented
239	#504	C₂²×C₄₁	1	2	yes	complemented
240	#494	C₂²×C₄₁	1	1	yes	characteristic, complemented
241	#493	C₂²×C₄₁	1	1	yes	characteristic
242	#473	—	2	1	no	—
243	#473	C₂²×C₄₁	1	2	yes	complemented
244	#472	—	2	1	no	—
245	#472	C₂²×C₄₁	1	2	yes	—
246	#456	—	2	2	no	—
247	#453	—	2	2	no	—
248	#443	C₂²×C₄₁	1	1	yes	characteristic
249	#443	C₂²×C₄₁	1	1	yes	characteristic
250	#443	C₂²×C₄₁	1	1	yes	characteristic, complemented
251	#368	C₂²×C₄₁	1	1	yes	characteristic, complemented
252	#364	C₂²×C₄₁	1	1	yes	characteristic, complemented
253	#362	C₂²×C₄₁	1	2	yes	complemented
254	#361	C₂²×C₄₁	1	2	yes	complemented
255	#359	C₂²×C₄₁	1	1	yes	characteristic
256	#359	C₂²×C₄₁	1	1	yes	characteristic, complemented
257	#350	C₂²×C₄₁	1	2	yes	complemented
258	C₄×C₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
259	C₄₁	#33856	1	1	yes	characteristic, direct product factor, Sylow
260	2₋¹⁺⁴	—	2	2	no	—
261	H(5,𝔽₂)	—	2	2	no	—
262	#137	—	2	2	no	—
263	#137	—	2	2	no	—
264	#137	—	4	2	no	—
265	#137	—	4	2	no	—
266	AGL(1,ℤ/8)	—	2	2	no	—
267	AGL(1,ℤ/8)	—	2	2	no	—
268	AGL(1,ℤ/8)	—	4	2	no	—
269	AGL(1,ℤ/8)	—	4	2	no	—
270	#135	—	2	2	no	—
271	#135	—	2	2	no	—
272	#135	—	4	1	no	—
273	#135	—	4	1	no	—
274	#135	D₄×C₄₁	1	1	yes	characteristic
275	#135	C₂³×C₄₁	1	1	yes	characteristic
276	#135	C₂³×C₄₁	1	1	yes	characteristic
277	C₂×Q₁₆	—	2	2	no	—
278	C₂×Q₁₆	—	2	1	no	—
279	C₂×Q₁₆	—	4	1	no	—
280	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
281	C₂×D₈	—	2	2	no	—
282	C₂×D₈	—	2	1	no	—
283	C₂×D₈	—	4	1	no	—
284	C₂×D₈	C₂³×C₄₁	1	2	yes	—
285	#131	—	2	1	no	—
286	#131	—	2	1	no	—
287	#131	C₂³×C₄₁	1	2	yes	—
288	C₄⋊Q₈	—	2	1	no	—
289	#127	—	2	1	no	—
290	Q₃₂	—	2	2	no	—
291	Q₃₂	D₄×C₄₁	1	1	yes	characteristic, complemented
292	SD₃₂	—	2	2	no	—
293	SD₃₂	—	2	2	no	—
294	SD₃₂	—	2	2	no	—
295	SD₃₂	—	2	2	no	—
296	SD₃₂	—	4	2	no	—
297	SD₃₂	D₄×C₄₁	1	1	yes	characteristic, complemented
298	SD₃₂	D₄×C₄₁	1	1	yes	characteristic, complemented
299	D₁₆	—	2	2	no	—
300	D₁₆	D₄×C₄₁	1	1	yes	characteristic, complemented
301	M₃₂	—	2	2	no	—
302	M₃₂	C₂³×C₄₁	1	2	yes	—
303	C₂×C₁₆	—	2	2	no	—
304	C₂×C₁₆	C₂³×C₄₁	1	1	yes	characteristic
305	C₂×C₁₆	C₂³×C₄₁	1	1	yes	characteristic
306	#108	D₄×C₄₁	1	1	yes	characteristic
307	#108	C₂³×C₄₁	1	1	yes	characteristic
308	#108	C₂³×C₄₁	1	1	yes	characteristic
309	#104	—	2	1	no	—
310	#104	—	2	1	no	—
311	#104	D₄×C₄₁	1	2	yes	—
312	#101	—	2	2	no	—
313	#100	—	2	2	no	—
314	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
315	#41	—	2	1	no	—
316	#41	—	2	1	no	—
317	#41	—	4	2	no	—
318	#41	—	4	2	no	—
319	#41	—	4	2	no	—
320	#41	—	4	2	no	—
321	#41	—	8	2	no	—
322	#41	C₂×D₄×C₄₁	1	2	yes	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	4	2	no	—
325	C₂×Q₈	—	4	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	4	2	no	—
328	C₂×D₄	—	4	2	no	—
329	C₂×D₄	—	8	1	no	—
330	C₂×D₄	—	8	2	no	—
331	Q₁₆	—	2	2	no	—
332	Q₁₆	—	2	2	no	—
333	Q₁₆	—	4	2	no	—
334	Q₁₆	—	4	2	no	—
335	Q₁₆	—	4	1	no	—
336	Q₁₆	—	4	1	no	—
337	Q₁₆	D₈×C₄₁	1	1	yes	characteristic
338	Q₁₆	C₂×D₄×C₄₁	1	1	yes	characteristic
339	Q₁₆	C₂×D₄×C₄₁	1	1	yes	characteristic
340	SD₁₆	—	2	1	no	—
341	SD₁₆	—	2	1	no	—
342	SD₁₆	—	4	2	no	—
343	SD₁₆	—	4	2	no	—
344	SD₁₆	—	4	2	no	—
345	SD₁₆	—	4	2	no	—
346	SD₁₆	D₈×C₄₁	1	2	yes	—
347	D₈	—	2	2	no	—
348	D₈	—	2	2	no	—
349	D₈	—	4	2	no	—
350	D₈	—	4	2	no	—
351	D₈	—	4	1	no	—
352	D₈	—	4	1	no	—
353	D₈	D₈×C₄₁	1	1	yes	characteristic
354	D₈	C₂×D₄×C₄₁	1	1	yes	characteristic
355	D₈	C₂×D₄×C₄₁	1	1	yes	characteristic
356	M₁₆	—	2	2	no	—
357	M₁₆	—	2	1	no	—
358	M₁₆	—	2	1	no	—
359	M₁₆	—	4	1	no	—
360	M₁₆	—	4	1	no	—
361	M₁₆	C₂×D₄×C₄₁	1	2	yes	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	4	1	no	—
364	C₂×C₈	—	4	1	no	—
365	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
366	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
367	C₄⋊C₄	—	8	1	no	—
368	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
369	C₁₆	—	2	2	no	—
370	C₁₆	—	2	1	no	—
371	C₁₆	C₂×D₄×C₄₁	1	1	yes	characteristic
372	C₁₆	C₂×D₄×C₄₁	1	1	yes	characteristic
373	C₂³	—	4	2	no	—
374	C₂³	—	8	2	no	—
375	Q₈	—	2	1	no	—
376	Q₈	—	2	1	no	—
377	Q₈	—	4	2	no	—
378	Q₈	—	4	2	no	—
379	Q₈	—	8	2	no	—
380	Q₈	C₂×D₈×C₄₁	1	2	yes	—
381	D₄	—	2	2	no	—
382	D₄	—	2	1	no	—
383	D₄	—	2	1	no	—
384	D₄	—	4	1	no	—
385	D₄	—	4	1	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	2	no	—
388	D₄	—	8	2	no	—
389	D₄	—	8	2	no	—
390	D₄	—	8	2	no	—
391	D₄	—	16	2	no	—
392	D₄	C₂×D₈×C₄₁	1	2	yes	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	8	2	no	—
399	C₂×C₄	—	8	2	no	—
400	C₂×C₄	—	8	2	no	—
401	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
402	C₈	—	2	2	no	—
403	C₈	—	4	1	no	—
404	C₈	—	4	1	no	—
405	C₈	C₂×D₈×C₄₁	1	1	yes	characteristic
406	C₈	C₂×D₈×C₄₁	1	1	yes	characteristic
407	C₈	C₂²×D₄×C₄₁	1	1	yes	characteristic
408	C₈	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
409	C₂²	—	2	2	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	8	2	no	—
413	C₂²	—	16	2	no	—
414	C₂²	—	32	2	no	—
415	C₂²	C₄₁×#576	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	4	1	no	—
419	C₄	—	4	1	no	—
420	C₄	—	8	2	no	—
421	C₄	D₄²×C₄₁	1	1	yes	characteristic
422	C₄	C₂²×D₈×C₄₁	1	1	yes	characteristic
423	C₂	—	2	1	no	—
424	C₂	—	4	2	no	—
425	C₂	—	8	1	no	—
426	C₂	—	8	1	no	—
427	C₂	—	16	2	no	—
428	C₂	D₄×D₈×C₄₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₄₁	D₄×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₄₁
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄₁ ◁ C₂×C₄×C₄₁ ◁ C₄₁×#443 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3416	C₂	semidirect
2. C₄₁×#3293	C₂	semidirect
3. C₄₁×#3292	C₂	semidirect
4. C₄₁×#2248	C₂	semidirect
5. C₄₁×#2223	C₂	semidirect
6. C₄₁×#2214	C₂	semidirect
7. C₄₁×#2213	C₂	semidirect
8. C₄₁×#2194	C₂	semidirect
9. C₄₁×#2193	C₂	semidirect
10. C₄₁×#2178	C₂	semidirect
11. C₄₁×#2170	C₂	semidirect
13. C₄₁×#578	C₂²	semidirect
19. C₄₁×#509	C₂²	semidirect
23. C₂×SD₃₂×C₄₁	C₂²	semidirect
24. C₂×SD₃₂×C₄₁	C₂²	semidirect
25. C₄₁×#504	C₂²	semidirect
26. C₄₁×#494	C₂²	semidirect
29. C₄₁×#473	C₂²	semidirect
36. C₄₁×#443	C₂²	semidirect
37. C₄₁×#368	C₂²	semidirect
38. C₄₁×#364	C₂²	semidirect
39. C₄₁×#362	C₂²	semidirect
40. C₄₁×#361	C₂²	semidirect
42. C₄₁×#359	C₂²	semidirect
43. C₄₁×#350	C₂²	semidirect
44. C₄×C₁₆×C₄₁	C₂²	semidirect
76. Q₃₂×C₄₁	D₄	semidirect
82. SD₃₂×C₄₁	D₄	semidirect
83. SD₃₂×C₄₁	D₄	semidirect
85. D₁₆×C₄₁	D₄	semidirect
194. #33856	C₄₁	direct (N × H)
209. #3416	C₂×C₄₁	semidirect
210. #3293	C₂×C₄₁	semidirect
211. #3292	C₂×C₄₁	semidirect
212. #2248	C₂×C₄₁	semidirect
213. #2223	C₂×C₄₁	semidirect
214. #2214	C₂×C₄₁	semidirect
215. #2213	C₂×C₄₁	semidirect
216. #2194	C₂×C₄₁	semidirect
217. #2193	C₂×C₄₁	semidirect
218. #2178	C₂×C₄₁	semidirect
219. #2170	C₂×C₄₁	semidirect
227. #578	C₂²×C₄₁	semidirect
233. #509	C₂²×C₄₁	semidirect
237. C₂×SD₃₂	C₂²×C₄₁	semidirect
238. C₂×SD₃₂	C₂²×C₄₁	semidirect
239. #504	C₂²×C₄₁	semidirect
240. #494	C₂²×C₄₁	semidirect
243. #473	C₂²×C₄₁	semidirect
250. #443	C₂²×C₄₁	semidirect
251. #368	C₂²×C₄₁	semidirect
252. #364	C₂²×C₄₁	semidirect
253. #362	C₂²×C₄₁	semidirect
254. #361	C₂²×C₄₁	semidirect
256. #359	C₂²×C₄₁	semidirect
257. #350	C₂²×C₄₁	semidirect
258. C₄×C₁₆	C₂²×C₄₁	semidirect
259. C₄₁	#33856	direct (N × H)
291. Q₃₂	D₄×C₄₁	semidirect
297. SD₃₂	D₄×C₄₁	semidirect
298. SD₃₂	D₄×C₄₁	semidirect
300. D₁₆	D₄×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3416	2
C₄₁×#3293	2
C₄₁×#3292	2
C₄₁×#2248	2
C₄₁×#2223	2
C₄₁×#2214	2
C₄₁×#2213	2
C₄₁×#2194	2
C₄₁×#2193	2
C₄₁×#2178	2
C₄₁×#2170	2
#33856	41

Subgroups — C41×#33856 #23810057

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#33856 #23810057