Subgroups — C₄₁×#23740 #23799941

Order 10496.

988 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#430	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#2905	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₁×#421	C₂	1	2	yes	maximal
4	C₄₁×#2879	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#2098	C₂	1	8	yes	maximal, complemented
6	C₂×C₄₁×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
8	C₂²×M₁₆×C₄₁	C₂²	1	2	yes	—
9	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
11	C₂×#117×C₄₁	C₂²	1	2	yes	—
12	C₄₁×#430	—	2	2	no	—
13	C₄₁×#430	C₂²	1	4	yes	complemented
14	C₂×#108×C₄₁	—	2	2	no	—
15	C₄₁×#424	—	2	4	no	—
16	C₄₁×#424	C₂²	1	8	yes	complemented
17	C₄₁×#423	—	2	4	no	—
18	C₄₁×#421	—	2	4	no	—
19	C₄₁×#421	C₂²	1	8	yes	—
20	C₂×#104×C₄₁	—	2	4	no	—
21	C₄₁×#408	—	2	2	no	—
22	C₄₁×#408	C₂²	1	4	yes	—
23	C₄₁×#407	—	2	2	no	—
24	C₄₁×H(3,ℤ/4)	C₂²	1	4	yes	complemented
25	C₂×#41×C₄₁	—	2	1	no	—
26	C₂×#41×C₄₁	—	2	1	no	—
27	C₂×#41×C₄₁	—	2	2	no	—
28	C₂×#41×C₄₁	—	2	2	no	—
29	C₂×#41×C₄₁	—	2	2	no	—
30	C₂×#41×C₄₁	—	2	2	no	—
31	C₂×#41×C₄₁	Q₈	1	2	yes	—
32	C₂×#41×C₄₁	C₂³	1	2	yes	—
33	C₂²×Q₈×C₄₁	Q₈	1	1	yes	characteristic
34	C₂²×D₄×C₄₁	—	2	1	no	—
35	C₂²×D₄×C₄₁	Q₈	1	1	yes	characteristic
36	C₂³×C₄×C₄₁	—	2	1	no	—
37	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
38	C₂×M₁₆×C₄₁	—	2	2	no	—
39	C₂×M₁₆×C₄₁	—	2	2	no	—
40	C₂×M₁₆×C₄₁	—	2	1	no	—
41	C₂×M₁₆×C₄₁	—	2	1	no	—
42	C₂×M₁₆×C₄₁	—	2	2	no	—
43	C₂×M₁₆×C₄₁	—	2	2	no	—
44	C₂×M₁₆×C₄₁	—	2	2	no	—
45	C₂×M₁₆×C₄₁	—	2	2	no	—
46	C₂×M₁₆×C₄₁	—	2	2	no	—
47	C₂×M₁₆×C₄₁	—	2	2	no	—
48	C₂×M₁₆×C₄₁	—	2	2	no	—
49	C₂×M₁₆×C₄₁	D₄	1	2	yes	—
50	C₂×M₁₆×C₄₁	C₂³	1	4	yes	—
51	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
52	C₂²×C₈×C₄₁	—	2	2	no	—
53	C₂²×C₈×C₄₁	D₄	1	2	yes	—
54	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
55	#117×C₄₁	—	2	2	no	—
56	#117×C₄₁	—	2	2	no	—
57	#117×C₄₁	D₄	1	4	yes	—
58	#117×C₄₁	C₂³	1	4	yes	—
59	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
61	C₂×C₄²×C₄₁	D₄	1	4	yes	—
62	#108×C₄₁	—	2	8	no	—
63	C₄⋊C₈×C₄₁	—	2	16	no	—
64	#104×C₄₁	—	2	16	no	—
65	C₂²⋊C₈×C₄₁	—	2	8	no	—
66	C₂⁴×C₄₁	—	2	1	no	—
67	C₂⁴×C₄₁	#41	1	1	yes	characteristic
68	#41×C₄₁	—	2	4	no	—
69	#41×C₄₁	—	2	4	no	—
70	#41×C₄₁	—	2	4	no	—
71	#41×C₄₁	—	2	4	no	—
72	#41×C₄₁	—	4	1	no	—
73	#41×C₄₁	—	4	1	no	—
74	#41×C₄₁	—	4	2	no	—
75	#41×C₄₁	—	4	2	no	—
76	#41×C₄₁	—	4	1	no	—
77	#41×C₄₁	—	4	1	no	—
78	C₂×Q₈×C₄₁	—	2	1	no	—
79	C₂×Q₈×C₄₁	—	2	2	no	—
80	C₂×Q₈×C₄₁	—	2	2	no	—
81	C₂×Q₈×C₄₁	C₂×Q₈	1	2	yes	—
82	C₂×D₄×C₄₁	—	2	2	no	—
83	C₂×D₄×C₄₁	—	2	2	no	—
84	C₂×D₄×C₄₁	—	2	2	no	—
85	C₂×D₄×C₄₁	—	2	2	no	—
86	C₂×D₄×C₄₁	—	2	1	no	—
87	C₂×D₄×C₄₁	—	4	2	no	—
88	C₂×D₄×C₄₁	—	4	2	no	—
89	C₂×D₄×C₄₁	C₂×Q₈	1	2	yes	—
90	C₂²×C₄×C₄₁	—	2	1	no	—
91	C₂²×C₄×C₄₁	—	2	4	no	—
92	C₂²×C₄×C₄₁	—	2	2	no	—
93	C₂²×C₄×C₄₁	—	2	2	no	—
94	C₂²×C₄×C₄₁	—	4	2	no	—
95	C₂²×C₄×C₄₁	—	4	2	no	—
96	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₁	C₂×Q₈	1	1	yes	characteristic
101	C₂²×C₄×C₄₁	C₂×Q₈	1	1	yes	characteristic
102	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
103	C₂²×C₄×C₄₁	#41	1	2	yes	—
104	C₂²×C₄×C₄₁	#41	1	2	yes	—
105	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
106	M₁₆×C₄₁	—	2	4	no	—
107	M₁₆×C₄₁	—	2	4	no	—
108	M₁₆×C₄₁	—	2	4	no	—
109	M₁₆×C₄₁	—	2	4	no	—
110	M₁₆×C₄₁	—	4	1	no	—
111	M₁₆×C₄₁	—	4	2	no	—
112	M₁₆×C₄₁	—	4	1	no	—
113	M₁₆×C₄₁	—	4	2	no	—
114	M₁₆×C₄₁	—	4	2	no	—
115	C₂×C₈×C₄₁	—	2	2	no	—
116	C₂×C₈×C₄₁	—	2	2	no	—
117	C₂×C₈×C₄₁	—	2	2	no	—
118	C₂×C₈×C₄₁	—	2	4	no	—
119	C₂×C₈×C₄₁	—	2	4	no	—
120	C₂×C₈×C₄₁	—	4	2	no	—
121	C₂×C₈×C₄₁	—	4	2	no	—
122	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
123	C₄⋊C₄×C₄₁	—	2	4	no	—
124	C₄⋊C₄×C₄₁	—	2	4	no	—
125	C₂²⋊C₄×C₄₁	—	2	4	no	—
126	C₂²⋊C₄×C₄₁	—	2	4	no	—
127	C₄²×C₄₁	—	2	4	no	—
128	C₄²×C₄₁	C₂×D₄	1	8	yes	—
129	C₂³×C₄₁	—	2	2	no	—
130	C₂³×C₄₁	—	4	2	no	—
131	C₂³×C₄₁	—	8	1	no	—
132	C₂³×C₄₁	—	8	2	no	—
133	C₂³×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
134	C₂³×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
135	C₂³×C₄₁	#123	1	2	yes	—
136	C₂³×C₄₁	#123	1	2	yes	—
137	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
138	Q₈×C₄₁	—	2	4	no	—
139	Q₈×C₄₁	—	4	1	no	—
140	Q₈×C₄₁	—	4	1	no	—
141	D₄×C₄₁	—	2	4	no	—
142	D₄×C₄₁	—	4	4	no	—
143	D₄×C₄₁	—	4	2	no	—
144	D₄×C₄₁	—	4	2	no	—
145	D₄×C₄₁	—	4	1	no	—
146	D₄×C₄₁	—	4	1	no	—
147	C₂×C₄×C₄₁	—	2	2	no	—
148	C₂×C₄×C₄₁	—	2	8	no	—
149	C₂×C₄×C₄₁	—	4	2	no	—
150	C₂×C₄×C₄₁	—	4	2	no	—
151	C₂×C₄×C₄₁	—	4	2	no	—
152	C₂×C₄×C₄₁	—	4	4	no	—
153	C₂×C₄×C₄₁	—	8	4	no	—
154	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
155	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
156	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
157	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
158	C₂×C₄×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
159	C₂×C₄×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
160	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
161	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
162	C₂×C₄×C₄₁	#123	1	2	yes	—
163	C₂×C₄×C₄₁	#123	1	2	yes	—
164	C₂×C₄×C₄₁	#123	1	2	yes	—
165	C₂×C₄×C₄₁	#127	1	1	yes	characteristic
166	C₂×C₄×C₄₁	#127	1	2	yes	—
167	C₂×C₄×C₄₁	#127	1	1	yes	characteristic
168	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
169	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₄₁	C₂²×Q₈	1	1	yes	characteristic
171	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
172	C₈×C₄₁	—	2	4	no	—
173	C₈×C₄₁	—	4	2	no	—
174	C₈×C₄₁	—	4	4	no	—
175	#23740	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₂²×C₄₁	—	4	2	no	—
177	C₂²×C₄₁	—	4	1	no	—
178	C₂²×C₄₁	—	4	1	no	—
179	C₂²×C₄₁	—	4	2	no	—
180	C₂²×C₄₁	—	4	1	no	—
181	C₂²×C₄₁	—	4	4	no	—
182	C₂²×C₄₁	—	4	2	no	—
183	C₂²×C₄₁	—	8	4	no	—
184	C₂²×C₄₁	#399	1	2	yes	—
185	C₂²×C₄₁	#399	1	1	yes	characteristic
186	C₂²×C₄₁	#399	1	1	yes	characteristic
187	C₂²×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
188	C₂²×C₄₁	C₂×#123	1	2	yes	—
189	C₄×C₄₁	—	4	8	no	—
190	C₄×C₄₁	—	4	2	no	—
191	C₄×C₄₁	#399	1	2	yes	—
192	C₄×C₄₁	#399	1	1	yes	characteristic
193	C₄×C₄₁	#399	1	1	yes	characteristic
194	C₄×C₄₁	C₂×C₂²⋊Q₈	1	2	yes	—
195	C₄×C₄₁	C₂×#123	1	1	yes	characteristic
196	C₄×C₄₁	C₂×#127	1	1	yes	characteristic
197	C₂×#430	C₂×C₄₁	1	1	yes	characteristic, complemented
198	#2905	C₂×C₄₁	1	2	yes	complemented
199	C₂×#421	C₂×C₄₁	1	2	yes	—
200	#2879	C₂×C₄₁	1	1	yes	characteristic
201	#2098	C₂×C₄₁	1	8	yes	complemented
202	C₂×H(3,ℤ/4)	C₂×C₄₁	1	1	yes	characteristic, complemented
203	C₂×C₄₁	—	2	2	no	—
204	C₂×C₄₁	—	2	1	no	—
205	C₂×C₄₁	—	2	2	no	—
206	C₂×C₄₁	—	2	1	no	—
207	C₂×C₄₁	—	2	1	no	—
208	C₂×C₄₁	—	8	2	no	—
209	C₂×C₄₁	C₂×#399	1	1	yes	characteristic
210	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
211	C₂²×M₁₆	C₂²×C₄₁	1	2	yes	—
212	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
213	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
214	C₂×#117	C₂²×C₄₁	1	2	yes	—
215	#430	—	2	2	no	—
216	#430	C₂²×C₄₁	1	4	yes	complemented
217	C₂×#108	—	2	2	no	—
218	#424	—	2	4	no	—
219	#424	C₂²×C₄₁	1	8	yes	complemented
220	#423	—	2	4	no	—
221	#421	—	2	4	no	—
222	#421	C₂²×C₄₁	1	8	yes	—
223	C₂×#104	—	2	4	no	—
224	#408	—	2	2	no	—
225	#408	C₂²×C₄₁	1	4	yes	—
226	#407	—	2	2	no	—
227	H(3,ℤ/4)	C₂²×C₄₁	1	4	yes	complemented
228	C₄₁	#23740	1	1	yes	characteristic, direct product factor, Sylow
229	C₂×#41	—	2	1	no	—
230	C₂×#41	—	2	1	no	—
231	C₂×#41	—	2	2	no	—
232	C₂×#41	—	2	2	no	—
233	C₂×#41	—	2	2	no	—
234	C₂×#41	—	2	2	no	—
235	C₂×#41	Q₈×C₄₁	1	2	yes	—
236	C₂×#41	C₂³×C₄₁	1	2	yes	—
237	C₂²×Q₈	Q₈×C₄₁	1	1	yes	characteristic
238	C₂²×D₄	—	2	1	no	—
239	C₂²×D₄	Q₈×C₄₁	1	1	yes	characteristic
240	C₂³×C₄	—	2	1	no	—
241	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
242	C₂×M₁₆	—	2	2	no	—
243	C₂×M₁₆	—	2	2	no	—
244	C₂×M₁₆	—	2	1	no	—
245	C₂×M₁₆	—	2	1	no	—
246	C₂×M₁₆	—	2	2	no	—
247	C₂×M₁₆	—	2	2	no	—
248	C₂×M₁₆	—	2	2	no	—
249	C₂×M₁₆	—	2	2	no	—
250	C₂×M₁₆	—	2	2	no	—
251	C₂×M₁₆	—	2	2	no	—
252	C₂×M₁₆	—	2	2	no	—
253	C₂×M₁₆	D₄×C₄₁	1	2	yes	—
254	C₂×M₁₆	C₂³×C₄₁	1	4	yes	—
255	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
256	C₂²×C₈	—	2	2	no	—
257	C₂²×C₈	D₄×C₄₁	1	2	yes	—
258	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
259	#117	—	2	2	no	—
260	#117	—	2	2	no	—
261	#117	D₄×C₄₁	1	4	yes	—
262	#117	C₂³×C₄₁	1	4	yes	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₄²	D₄×C₄₁	1	4	yes	—
266	#108	—	2	8	no	—
267	C₄⋊C₈	—	2	16	no	—
268	#104	—	2	16	no	—
269	C₂²⋊C₈	—	2	8	no	—
270	C₂⁴	—	2	1	no	—
271	C₂⁴	#41×C₄₁	1	1	yes	characteristic
272	#41	—	2	4	no	—
273	#41	—	2	4	no	—
274	#41	—	2	4	no	—
275	#41	—	2	4	no	—
276	#41	—	4	1	no	—
277	#41	—	4	1	no	—
278	#41	—	4	2	no	—
279	#41	—	4	2	no	—
280	#41	—	4	1	no	—
281	#41	—	4	1	no	—
282	C₂×Q₈	—	2	1	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	C₂×Q₈×C₄₁	1	2	yes	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	4	2	no	—
292	C₂×D₄	—	4	2	no	—
293	C₂×D₄	C₂×Q₈×C₄₁	1	2	yes	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	4	2	no	—
299	C₂²×C₄	—	4	2	no	—
300	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
301	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
302	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
304	C₂²×C₄	C₂×Q₈×C₄₁	1	1	yes	characteristic
305	C₂²×C₄	C₂×Q₈×C₄₁	1	1	yes	characteristic
306	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
307	C₂²×C₄	#41×C₄₁	1	2	yes	—
308	C₂²×C₄	#41×C₄₁	1	2	yes	—
309	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
310	M₁₆	—	2	4	no	—
311	M₁₆	—	2	4	no	—
312	M₁₆	—	2	4	no	—
313	M₁₆	—	2	4	no	—
314	M₁₆	—	4	1	no	—
315	M₁₆	—	4	2	no	—
316	M₁₆	—	4	1	no	—
317	M₁₆	—	4	2	no	—
318	M₁₆	—	4	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	4	no	—
323	C₂×C₈	—	2	4	no	—
324	C₂×C₈	—	4	2	no	—
325	C₂×C₈	—	4	2	no	—
326	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	—	2	4	no	—
329	C₂²⋊C₄	—	2	4	no	—
330	C₂²⋊C₄	—	2	4	no	—
331	C₄²	—	2	4	no	—
332	C₄²	C₂×D₄×C₄₁	1	8	yes	—
333	C₂³	—	2	2	no	—
334	C₂³	—	4	2	no	—
335	C₂³	—	8	1	no	—
336	C₂³	—	8	2	no	—
337	C₂³	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
338	C₂³	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
339	C₂³	#123×C₄₁	1	2	yes	—
340	C₂³	#123×C₄₁	1	2	yes	—
341	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
342	Q₈	—	2	4	no	—
343	Q₈	—	4	1	no	—
344	Q₈	—	4	1	no	—
345	D₄	—	2	4	no	—
346	D₄	—	4	4	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	1	no	—
350	D₄	—	4	1	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	8	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	8	4	no	—
358	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
359	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
360	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
361	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
362	C₂×C₄	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
363	C₂×C₄	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
364	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
365	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
366	C₂×C₄	#123×C₄₁	1	2	yes	—
367	C₂×C₄	#123×C₄₁	1	2	yes	—
368	C₂×C₄	#123×C₄₁	1	2	yes	—
369	C₂×C₄	#127×C₄₁	1	1	yes	characteristic
370	C₂×C₄	#127×C₄₁	1	2	yes	—
371	C₂×C₄	#127×C₄₁	1	1	yes	characteristic
372	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
373	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
374	C₂×C₄	C₂²×Q₈×C₄₁	1	1	yes	characteristic
375	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
376	C₈	—	2	4	no	—
377	C₈	—	4	2	no	—
378	C₈	—	4	4	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	1	no	—
381	C₂²	—	4	1	no	—
382	C₂²	—	4	2	no	—
383	C₂²	—	4	1	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	8	4	no	—
387	C₂²	C₄₁×#399	1	2	yes	—
388	C₂²	C₄₁×#399	1	1	yes	characteristic
389	C₂²	C₄₁×#399	1	1	yes	characteristic
390	C₂²	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
391	C₂²	C₂×#123×C₄₁	1	2	yes	—
392	C₄	—	4	8	no	—
393	C₄	—	4	2	no	—
394	C₄	C₄₁×#399	1	2	yes	—
395	C₄	C₄₁×#399	1	1	yes	characteristic
396	C₄	C₄₁×#399	1	1	yes	characteristic
397	C₄	C₂×C₂²⋊Q₈×C₄₁	1	2	yes	—
398	C₄	C₂×#123×C₄₁	1	1	yes	characteristic
399	C₄	C₂×#127×C₄₁	1	1	yes	characteristic
400	C₂	—	2	2	no	—
401	C₂	—	2	1	no	—
402	C₂	—	2	2	no	—
403	C₂	—	2	1	no	—
404	C₂	—	2	1	no	—
405	C₂	—	8	2	no	—
406	C₂	C₂×C₄₁×#399	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₄₁	C₂×#127
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
socle	C₂×C₄₁	C₂×#399
prime radical	C₂²×#41×C₄₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₄₁ ◁ C₂³×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#430	C₂	semidirect
2. C₄₁×#2905	C₂	semidirect
5. C₄₁×#2098	C₂	semidirect
6. C₂×C₄₁×H(3,ℤ/4)	C₂	semidirect
13. C₄₁×#430	C₂²	semidirect
16. C₄₁×#424	C₂²	semidirect
24. C₄₁×H(3,ℤ/4)	C₂²	semidirect
175. #23740	C₄₁	direct (N × H)
197. C₂×#430	C₂×C₄₁	semidirect
198. #2905	C₂×C₄₁	semidirect
201. #2098	C₂×C₄₁	semidirect
202. C₂×H(3,ℤ/4)	C₂×C₄₁	semidirect
216. #430	C₂²×C₄₁	semidirect
219. #424	C₂²×C₄₁	semidirect
227. H(3,ℤ/4)	C₂²×C₄₁	semidirect
228. C₄₁	#23740	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#430	2
C₄₁×#2905	2
C₂×C₄₁×#421	2
C₄₁×#2879	2
C₄₁×#2098	2
C₂×C₄₁×H(3,ℤ/4)	2
#23740	41

Subgroups — C41×#23740 #23799941

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#23740 #23799941