Subgroups — C₄₁×#12739 #23788940

Order 10496.

936 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#575	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#360	C₂	1	2	yes	maximal, complemented
3	C₄₁×#2139	C₂	1	2	yes	maximal, complemented
4	C₂×C₄₁×#349	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1809	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#41×C₄₁	—	2	1	no	—
7	C₄₁×#575	—	2	4	no	—
8	C₄₁×#575	—	2	2	no	—
9	C₄₁×#575	C₄	1	4	yes	complemented
10	C₂×#137×C₄₁	—	2	2	no	—
11	C₂×AGL(1,ℤ/8)×C₄₁	—	2	2	no	—
12	C₂×#135×C₄₁	—	2	1	no	—
13	C₂×#135×C₄₁	C₂²	1	2	yes	—
14	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
15	C₂×M₃₂×C₄₁	C₂²	1	2	yes	complemented
16	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic, complemented
17	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic, complemented
18	C₄₁×#380	—	2	1	no	—
19	C₄₁×#360	—	2	4	no	—
20	C₄₁×#358	—	2	2	no	—
21	C₄₁×#357	—	2	2	no	—
22	C₄₁×#349	—	2	2	no	—
23	C₄₁×#340	—	2	1	no	—
24	C₂×#41×C₄₁	—	2	2	no	—
25	C₂×#41×C₄₁	—	2	4	no	—
26	C₂×#41×C₄₁	—	2	4	no	—
27	C₂×#41×C₄₁	—	2	2	no	—
28	C₂×#41×C₄₁	—	4	1	no	—
29	C₂×#41×C₄₁	—	4	2	no	—
30	C₂×#41×C₄₁	—	4	1	no	—
31	C₂×#41×C₄₁	—	4	2	no	—
32	C₂²×Q₈×C₄₁	—	2	1	no	—
33	C₂²×D₄×C₄₁	—	2	1	no	—
34	C₂²×D₄×C₄₁	—	4	1	no	—
35	C₂³×C₄×C₄₁	—	4	1	no	—
36	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
37	#137×C₄₁	—	2	8	no	—
38	#137×C₄₁	—	2	8	no	—
39	AGL(1,ℤ/8)×C₄₁	—	2	8	no	—
40	AGL(1,ℤ/8)×C₄₁	—	2	8	no	—
41	#135×C₄₁	—	2	4	no	—
42	#135×C₄₁	—	2	4	no	—
43	#135×C₄₁	—	2	2	no	—
44	#135×C₄₁	—	2	2	no	—
45	#135×C₄₁	C₂×C₄	1	4	yes	—
46	#135×C₄₁	D₄	1	4	yes	—
47	C₂×Q₁₆×C₄₁	—	2	1	no	—
48	C₂×Q₁₆×C₄₁	D₄	1	2	yes	—
49	C₂×SD₁₆×C₄₁	—	2	2	no	—
50	C₂×SD₁₆×C₄₁	—	2	2	no	—
51	C₂×D₈×C₄₁	—	2	1	no	—
52	C₂×D₈×C₄₁	D₄	1	2	yes	—
53	C₂×M₁₆×C₄₁	—	2	2	no	—
54	C₂×M₁₆×C₄₁	—	2	2	no	—
55	C₂×M₁₆×C₄₁	C₂×C₄	1	2	yes	—
56	C₂×M₁₆×C₄₁	D₄	1	2	yes	—
57	C₂²×C₈×C₄₁	D₄	1	1	yes	characteristic
58	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
60	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
61	C₂×C₂²⋊C₄×C₄₁	—	4	1	no	—
62	M₃₂×C₄₁	—	2	2	no	—
63	M₃₂×C₄₁	—	2	2	no	—
64	C₂×C₁₆×C₄₁	—	2	2	no	—
65	#107×C₄₁	—	2	2	no	—
66	#106×C₄₁	—	2	2	no	—
67	#95×C₄₁	—	4	1	no	—
68	C₂⁴×C₄₁	—	4	1	no	—
69	C₂⁴×C₄₁	D₈	1	1	yes	characteristic
70	#41×C₄₁	—	2	8	no	—
71	#41×C₄₁	—	2	4	no	—
72	#41×C₄₁	—	2	4	no	—
73	#41×C₄₁	—	4	4	no	—
74	#41×C₄₁	—	4	4	no	—
75	#41×C₄₁	—	4	4	no	—
76	#41×C₄₁	—	4	4	no	—
77	#41×C₄₁	—	4	4	no	—
78	#41×C₄₁	—	4	2	no	—
79	#41×C₄₁	—	4	2	no	—
80	C₂×Q₈×C₄₁	—	2	4	no	—
81	C₂×Q₈×C₄₁	—	2	2	no	—
82	C₂×Q₈×C₄₁	—	4	1	no	—
83	C₂×Q₈×C₄₁	—	4	2	no	—
84	C₂×D₄×C₄₁	—	2	4	no	—
85	C₂×D₄×C₄₁	—	2	2	no	—
86	C₂×D₄×C₄₁	—	4	1	no	—
87	C₂×D₄×C₄₁	—	4	2	no	—
88	C₂×D₄×C₄₁	—	4	4	no	—
89	C₂×D₄×C₄₁	—	4	2	no	—
90	C₂×D₄×C₄₁	—	4	4	no	—
91	C₂×D₄×C₄₁	—	4	2	no	—
92	C₂²×C₄×C₄₁	—	2	1	no	—
93	C₂²×C₄×C₄₁	—	2	1	no	—
94	C₂²×C₄×C₄₁	—	2	1	no	—
95	C₂²×C₄×C₄₁	—	2	1	no	—
96	C₂²×C₄×C₄₁	—	4	2	no	—
97	C₂²×C₄×C₄₁	—	4	4	no	—
98	C₂²×C₄×C₄₁	—	4	4	no	—
99	C₂²×C₄×C₄₁	—	4	1	no	—
100	C₂²×C₄×C₄₁	—	4	2	no	—
101	C₂²×C₄×C₄₁	—	4	1	no	—
102	C₂²×C₄×C₄₁	—	4	1	no	—
103	C₂²×C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
104	C₂²×C₄×C₄₁	D₈	1	1	yes	characteristic
105	C₂²×C₄×C₄₁	SD₁₆	1	2	yes	—
106	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
107	Q₁₆×C₄₁	—	2	4	no	—
108	Q₁₆×C₄₁	—	2	2	no	—
109	Q₁₆×C₄₁	C₂²⋊C₄	1	4	yes	complemented
110	SD₁₆×C₄₁	—	2	8	no	—
111	SD₁₆×C₄₁	—	2	4	no	—
112	SD₁₆×C₄₁	—	2	4	no	—
113	D₈×C₄₁	—	2	4	no	—
114	D₈×C₄₁	—	2	2	no	—
115	D₈×C₄₁	C₂²⋊C₄	1	4	yes	complemented
116	M₁₆×C₄₁	—	2	4	no	—
117	M₁₆×C₄₁	—	2	4	no	—
118	C₂×C₈×C₄₁	—	2	1	no	—
119	C₂×C₈×C₄₁	—	2	1	no	—
120	C₂×C₈×C₄₁	C₂²⋊C₄	1	2	yes	—
121	C₂×C₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
123	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
124	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
125	C₄⋊C₄×C₄₁	—	4	1	no	—
126	C₄⋊C₄×C₄₁	—	4	1	no	—
127	C₄⋊C₄×C₄₁	—	4	1	no	—
128	C₄⋊C₄×C₄₁	—	4	1	no	—
129	C₂²⋊C₄×C₄₁	—	8	2	no	—
130	C₁₆×C₄₁	—	4	2	no	—
131	C₂³×C₄₁	—	2	1	no	—
132	C₂³×C₄₁	—	2	1	no	—
133	C₂³×C₄₁	—	4	1	no	—
134	C₂³×C₄₁	—	4	1	no	—
135	C₂³×C₄₁	—	4	4	no	—
136	C₂³×C₄₁	—	4	2	no	—
137	C₂³×C₄₁	—	8	2	no	—
138	C₂³×C₄₁	—	8	2	no	—
139	C₂³×C₄₁	#102	1	2	yes	—
140	C₂³×C₄₁	C₂×D₈	1	1	yes	characteristic
141	Q₈×C₄₁	—	2	4	no	—
142	Q₈×C₄₁	—	4	4	no	—
143	Q₈×C₄₁	—	4	2	no	—
144	D₄×C₄₁	—	2	4	no	—
145	D₄×C₄₁	—	4	4	no	—
146	D₄×C₄₁	—	4	8	no	—
147	D₄×C₄₁	—	4	4	no	—
148	D₄×C₄₁	—	4	4	no	—
149	D₄×C₄₁	—	4	2	no	—
150	C₂×C₄×C₄₁	—	2	1	no	—
151	C₂×C₄×C₄₁	—	2	1	no	—
152	C₂×C₄×C₄₁	—	2	2	no	—
153	C₂×C₄×C₄₁	—	2	2	no	—
154	C₂×C₄×C₄₁	—	2	2	no	—
155	C₂×C₄×C₄₁	—	2	2	no	—
156	C₂×C₄×C₄₁	—	4	8	no	—
157	C₂×C₄×C₄₁	—	4	4	no	—
158	C₂×C₄×C₄₁	—	4	2	no	—
159	C₂×C₄×C₄₁	—	4	4	no	—
160	C₂×C₄×C₄₁	—	4	4	no	—
161	C₂×C₄×C₄₁	—	8	1	no	—
162	C₂×C₄×C₄₁	—	8	1	no	—
163	C₂×C₄×C₄₁	—	8	1	no	—
164	C₂×C₄×C₄₁	—	8	1	no	—
165	C₂×C₄×C₄₁	—	8	1	no	—
166	C₂×C₄×C₄₁	—	8	1	no	—
167	C₂×C₄×C₄₁	#102	1	2	yes	—
168	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
170	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
171	C₂×C₄×C₄₁	C₂×SD₁₆	1	1	yes	characteristic
172	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	1	yes	characteristic
173	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	1	yes	characteristic
174	C₈×C₄₁	—	2	2	no	—
175	C₈×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
176	C₈×C₄₁	#120	1	2	yes	—
177	#12739	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂²×C₄₁	—	2	1	no	—
179	C₂²×C₄₁	—	2	1	no	—
180	C₂²×C₄₁	—	2	2	no	—
181	C₂²×C₄₁	—	4	2	no	—
182	C₂²×C₄₁	—	4	1	no	—
183	C₂²×C₄₁	—	4	1	no	—
184	C₂²×C₄₁	—	4	4	no	—
185	C₂²×C₄₁	—	8	1	no	—
186	C₂²×C₄₁	—	8	8	no	—
187	C₂²×C₄₁	—	8	2	no	—
188	C₂²×C₄₁	—	8	2	no	—
189	C₂²×C₄₁	C₂×#102	1	1	yes	characteristic
190	C₂²×C₄₁	#447	1	1	yes	characteristic
191	C₂²×C₄₁	#447	1	1	yes	characteristic
192	C₄×C₄₁	—	2	2	no	—
193	C₄×C₄₁	—	4	4	no	—
194	C₄×C₄₁	—	16	1	no	—
195	C₄×C₄₁	—	16	1	no	—
196	C₄×C₄₁	#379	1	1	yes	characteristic
197	C₄×C₄₁	#418	1	1	yes	characteristic
198	C₄×C₄₁	#450	1	1	yes	characteristic
199	C₄×C₄₁	#450	1	1	yes	characteristic
200	C₂×#575	C₂×C₄₁	1	1	yes	characteristic
201	C₂×#360	C₂×C₄₁	1	2	yes	complemented
202	#2139	C₂×C₄₁	1	2	yes	complemented
203	C₂×#349	C₂×C₄₁	1	1	yes	characteristic, complemented
204	#1809	C₂×C₄₁	1	1	yes	characteristic, complemented
205	C₂×C₄₁	—	2	1	no	—
206	C₂×C₄₁	—	2	1	no	—
207	C₂×C₄₁	—	4	2	no	—
208	C₂×C₄₁	—	8	4	no	—
209	C₂×C₄₁	#1786	1	1	yes	characteristic
210	C₂×C₄₁	#2190	1	1	yes	characteristic
211	C₂×C₄₁	#2191	1	1	yes	characteristic
212	C₂²×#41	—	2	1	no	—
213	#575	—	2	4	no	—
214	#575	—	2	2	no	—
215	#575	C₄×C₄₁	1	4	yes	complemented
216	C₂×#137	—	2	2	no	—
217	C₂×AGL(1,ℤ/8)	—	2	2	no	—
218	C₂×#135	—	2	1	no	—
219	C₂×#135	C₂²×C₄₁	1	2	yes	—
220	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
221	C₂×M₃₂	C₂²×C₄₁	1	2	yes	complemented
222	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic, complemented
223	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic, complemented
224	#380	—	2	1	no	—
225	#360	—	2	4	no	—
226	#358	—	2	2	no	—
227	#357	—	2	2	no	—
228	#349	—	2	2	no	—
229	#340	—	2	1	no	—
230	C₄₁	#12739	1	1	yes	characteristic, direct product factor, Sylow
231	C₂×#41	—	2	2	no	—
232	C₂×#41	—	2	4	no	—
233	C₂×#41	—	2	4	no	—
234	C₂×#41	—	2	2	no	—
235	C₂×#41	—	4	1	no	—
236	C₂×#41	—	4	2	no	—
237	C₂×#41	—	4	1	no	—
238	C₂×#41	—	4	2	no	—
239	C₂²×Q₈	—	2	1	no	—
240	C₂²×D₄	—	2	1	no	—
241	C₂²×D₄	—	4	1	no	—
242	C₂³×C₄	—	4	1	no	—
243	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
244	#137	—	2	8	no	—
245	#137	—	2	8	no	—
246	AGL(1,ℤ/8)	—	2	8	no	—
247	AGL(1,ℤ/8)	—	2	8	no	—
248	#135	—	2	4	no	—
249	#135	—	2	4	no	—
250	#135	—	2	2	no	—
251	#135	—	2	2	no	—
252	#135	C₂×C₄×C₄₁	1	4	yes	—
253	#135	D₄×C₄₁	1	4	yes	—
254	C₂×Q₁₆	—	2	1	no	—
255	C₂×Q₁₆	D₄×C₄₁	1	2	yes	—
256	C₂×SD₁₆	—	2	2	no	—
257	C₂×SD₁₆	—	2	2	no	—
258	C₂×D₈	—	2	1	no	—
259	C₂×D₈	D₄×C₄₁	1	2	yes	—
260	C₂×M₁₆	—	2	2	no	—
261	C₂×M₁₆	—	2	2	no	—
262	C₂×M₁₆	C₂×C₄×C₄₁	1	2	yes	—
263	C₂×M₁₆	D₄×C₄₁	1	2	yes	—
264	C₂²×C₈	D₄×C₄₁	1	1	yes	characteristic
265	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₂²⋊C₄	—	4	1	no	—
269	M₃₂	—	2	2	no	—
270	M₃₂	—	2	2	no	—
271	C₂×C₁₆	—	2	2	no	—
272	#107	—	2	2	no	—
273	#106	—	2	2	no	—
274	#95	—	4	1	no	—
275	C₂⁴	—	4	1	no	—
276	C₂⁴	D₈×C₄₁	1	1	yes	characteristic
277	#41	—	2	8	no	—
278	#41	—	2	4	no	—
279	#41	—	2	4	no	—
280	#41	—	4	4	no	—
281	#41	—	4	4	no	—
282	#41	—	4	4	no	—
283	#41	—	4	4	no	—
284	#41	—	4	4	no	—
285	#41	—	4	2	no	—
286	#41	—	4	2	no	—
287	C₂×Q₈	—	2	4	no	—
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	4	1	no	—
290	C₂×Q₈	—	4	2	no	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	4	1	no	—
294	C₂×D₄	—	4	2	no	—
295	C₂×D₄	—	4	4	no	—
296	C₂×D₄	—	4	2	no	—
297	C₂×D₄	—	4	4	no	—
298	C₂×D₄	—	4	2	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	4	2	no	—
304	C₂²×C₄	—	4	4	no	—
305	C₂²×C₄	—	4	4	no	—
306	C₂²×C₄	—	4	1	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	—	4	1	no	—
309	C₂²×C₄	—	4	1	no	—
310	C₂²×C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
311	C₂²×C₄	D₈×C₄₁	1	1	yes	characteristic
312	C₂²×C₄	SD₁₆×C₄₁	1	2	yes	—
313	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
314	Q₁₆	—	2	4	no	—
315	Q₁₆	—	2	2	no	—
316	Q₁₆	C₂²⋊C₄×C₄₁	1	4	yes	complemented
317	SD₁₆	—	2	8	no	—
318	SD₁₆	—	2	4	no	—
319	SD₁₆	—	2	4	no	—
320	D₈	—	2	4	no	—
321	D₈	—	2	2	no	—
322	D₈	C₂²⋊C₄×C₄₁	1	4	yes	complemented
323	M₁₆	—	2	4	no	—
324	M₁₆	—	2	4	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	C₂²⋊C₄×C₄₁	1	2	yes	—
328	C₂×C₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
329	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
330	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
331	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
332	C₄⋊C₄	—	4	1	no	—
333	C₄⋊C₄	—	4	1	no	—
334	C₄⋊C₄	—	4	1	no	—
335	C₄⋊C₄	—	4	1	no	—
336	C₂²⋊C₄	—	8	2	no	—
337	C₁₆	—	4	2	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	4	1	no	—
341	C₂³	—	4	1	no	—
342	C₂³	—	4	4	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	8	2	no	—
345	C₂³	—	8	2	no	—
346	C₂³	#102×C₄₁	1	2	yes	—
347	C₂³	C₂×D₈×C₄₁	1	1	yes	characteristic
348	Q₈	—	2	4	no	—
349	Q₈	—	4	4	no	—
350	Q₈	—	4	2	no	—
351	D₄	—	2	4	no	—
352	D₄	—	4	4	no	—
353	D₄	—	4	8	no	—
354	D₄	—	4	4	no	—
355	D₄	—	4	4	no	—
356	D₄	—	4	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	4	8	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	8	1	no	—
369	C₂×C₄	—	8	1	no	—
370	C₂×C₄	—	8	1	no	—
371	C₂×C₄	—	8	1	no	—
372	C₂×C₄	—	8	1	no	—
373	C₂×C₄	—	8	1	no	—
374	C₂×C₄	#102×C₄₁	1	2	yes	—
375	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
376	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
377	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
378	C₂×C₄	C₂×SD₁₆×C₄₁	1	1	yes	characteristic
379	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
380	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
381	C₈	—	2	2	no	—
382	C₈	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
383	C₈	#120×C₄₁	1	2	yes	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	1	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	4	4	no	—
391	C₂²	—	8	1	no	—
392	C₂²	—	8	8	no	—
393	C₂²	—	8	2	no	—
394	C₂²	—	8	2	no	—
395	C₂²	C₂×#102×C₄₁	1	1	yes	characteristic
396	C₂²	C₄₁×#447	1	1	yes	characteristic
397	C₂²	C₄₁×#447	1	1	yes	characteristic
398	C₄	—	2	2	no	—
399	C₄	—	4	4	no	—
400	C₄	—	16	1	no	—
401	C₄	—	16	1	no	—
402	C₄	C₄₁×#379	1	1	yes	characteristic
403	C₄	C₄₁×#418	1	1	yes	characteristic
404	C₄	C₄₁×#450	1	1	yes	characteristic
405	C₄	C₄₁×#450	1	1	yes	characteristic
406	C₂	—	2	1	no	—
407	C₂	—	2	1	no	—
408	C₂	—	4	2	no	—
409	C₂	—	8	4	no	—
410	C₂	C₄₁×#1786	1	1	yes	characteristic
411	C₂	C₄₁×#2190	1	1	yes	characteristic
412	C₂	C₄₁×#2191	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	#447
commutator	C₂×C₈	C₂²×C₄×C₄₁
Frattini, cosocle	C₂²×C₈	C₂³×C₄₁
prime radical	C₂×C₄₁×#575	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂²×C₄×C₄₁ ◁ C₂²×M₁₆×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#360	C₂	semidirect
3. C₄₁×#2139	C₂	semidirect
4. C₂×C₄₁×#349	C₂	semidirect
5. C₄₁×#1809	C₂	semidirect
9. C₄₁×#575	C₄	semidirect
15. C₂×M₃₂×C₄₁	C₂²	semidirect
16. C₂×#107×C₄₁	C₂²	semidirect
17. C₂×#106×C₄₁	C₂²	semidirect
109. Q₁₆×C₄₁	C₂²⋊C₄	semidirect
115. D₈×C₄₁	C₂²⋊C₄	semidirect
177. #12739	C₄₁	direct (N × H)
201. C₂×#360	C₂×C₄₁	semidirect
202. #2139	C₂×C₄₁	semidirect
203. C₂×#349	C₂×C₄₁	semidirect
204. #1809	C₂×C₄₁	semidirect
215. #575	C₄×C₄₁	semidirect
221. C₂×M₃₂	C₂²×C₄₁	semidirect
222. C₂×#107	C₂²×C₄₁	semidirect
223. C₂×#106	C₂²×C₄₁	semidirect
230. C₄₁	#12739	direct (N × H)
316. Q₁₆	C₂²⋊C₄×C₄₁	semidirect
322. D₈	C₂²⋊C₄×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#575	2
C₂×C₄₁×#360	2
C₄₁×#2139	2
C₂×C₄₁×#349	2
C₄₁×#1809	2
#12739	41

Subgroups — C41×#12739 #23788940

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#12739 #23788940