Subgroups — C₂×C₄₁×#2186 #23809715

Order 10496.

1198 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#135×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×SD₃₂×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₁×#466	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2186	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₄₁×#358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₁×#357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₁×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₄₁	—	2	1	no	—
10	C₂×#135×C₄₁	—	2	4	no	—
11	C₂×#135×C₄₁	—	2	4	no	—
12	C₂×#135×C₄₁	—	2	2	no	—
13	C₂×#135×C₄₁	C₂²	1	4	yes	complemented
14	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
15	C₂²×SD₁₆×C₄₁	—	2	1	no	—
16	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
17	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×#121×C₄₁	—	2	1	no	—
20	C₂×SD₃₂×C₄₁	—	2	4	no	—
21	C₂×SD₃₂×C₄₁	C₂²	1	4	yes	complemented
22	C₂×D₁₆×C₄₁	—	2	4	no	—
23	C₂×D₁₆×C₄₁	C₂²	1	4	yes	complemented
24	C₂²×C₁₆×C₄₁	C₂²	1	1	yes	characteristic
25	C₂²×C₁₆×C₄₁	C₂²	1	1	yes	characteristic
26	C₄₁×#466	—	2	2	no	—
27	C₄₁×#466	C₂²	1	4	yes	complemented
28	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
29	C₂×#102×C₄₁	—	2	1	no	—
30	C₄₁×#358	C₂²	1	4	yes	complemented
31	C₄₁×#357	C₂²	1	4	yes	complemented
32	C₄₁×C₂²⋊C₁₆	C₂²	1	4	yes	complemented
33	C₂×#41×C₄₁	—	2	8	no	—
34	C₂×#41×C₄₁	—	2	4	no	—
35	C₂×#41×C₄₁	—	4	4	no	—
36	C₂×#41×C₄₁	—	4	2	no	—
37	C₂²×Q₈×C₄₁	—	2	1	no	—
38	C₂²×D₄×C₄₁	—	2	1	no	—
39	C₂²×D₄×C₄₁	—	2	1	no	—
40	C₂²×D₄×C₄₁	—	4	1	no	—
41	C₂²×D₄×C₄₁	—	4	1	no	—
42	C₂³×C₄×C₄₁	—	4	1	no	—
43	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
44	#135×C₄₁	—	2	16	no	—
45	#135×C₄₁	—	2	8	no	—
46	#135×C₄₁	—	2	8	no	—
47	C₂×Q₁₆×C₄₁	—	2	1	no	—
48	C₂×Q₁₆×C₄₁	—	2	2	no	—
49	C₂×Q₁₆×C₄₁	D₄	1	4	yes	complemented
50	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
51	C₂×SD₁₆×C₄₁	—	2	8	no	—
52	C₂×SD₁₆×C₄₁	—	2	4	no	—
53	C₂×D₈×C₄₁	—	2	1	no	—
54	C₂×D₈×C₄₁	—	2	2	no	—
55	C₂×D₈×C₄₁	—	2	2	no	—
56	C₂×D₈×C₄₁	—	2	2	no	—
57	C₂×D₈×C₄₁	—	2	1	no	—
58	C₂×D₈×C₄₁	D₄	1	4	yes	complemented
59	C₂×D₈×C₄₁	C₂³	1	2	yes	—
60	C₂×D₈×C₄₁	C₂³	1	2	yes	—
61	C₂²×C₈×C₄₁	—	2	2	no	—
62	C₂²×C₈×C₄₁	—	2	2	no	—
63	C₂²×C₈×C₄₁	D₄	1	1	yes	characteristic
64	C₂²×C₈×C₄₁	D₄	1	2	yes	—
65	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
66	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
67	#121×C₄₁	—	2	4	no	—
68	#121×C₄₁	—	4	2	no	—
69	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₄₁	—	4	1	no	—
71	SD₃₂×C₄₁	—	2	8	no	—
72	D₁₆×C₄₁	—	2	8	no	—
73	C₂×C₁₆×C₄₁	—	2	2	no	—
74	C₂×C₁₆×C₄₁	—	2	2	no	—
75	C₂×C₁₆×C₄₁	C₂³	1	2	yes	—
76	C₂×C₁₆×C₄₁	C₂³	1	2	yes	—
77	#107×C₄₁	—	2	1	no	—
78	#107×C₄₁	C₂³	1	2	yes	—
79	#102×C₄₁	—	2	4	no	—
80	C₂⁴×C₄₁	—	4	1	no	—
81	C₂⁴×C₄₁	—	4	1	no	—
82	C₂⁴×C₄₁	D₈	1	1	yes	characteristic
83	#41×C₄₁	—	2	16	no	—
84	#41×C₄₁	—	4	8	no	—
85	#41×C₄₁	—	4	16	no	—
86	C₂×Q₈×C₄₁	—	2	4	no	—
87	C₂×Q₈×C₄₁	—	2	2	no	—
88	C₂×Q₈×C₄₁	—	4	1	no	—
89	C₂×Q₈×C₄₁	—	4	2	no	—
90	C₂×D₄×C₄₁	—	2	4	no	—
91	C₂×D₄×C₄₁	—	2	2	no	—
92	C₂×D₄×C₄₁	—	2	2	no	—
93	C₂×D₄×C₄₁	—	4	8	no	—
94	C₂×D₄×C₄₁	—	4	4	no	—
95	C₂×D₄×C₄₁	—	4	4	no	—
96	C₂×D₄×C₄₁	—	4	2	no	—
97	C₂×D₄×C₄₁	—	4	1	no	—
98	C₂×D₄×C₄₁	—	4	1	no	—
99	C₂×D₄×C₄₁	—	4	2	no	—
100	C₂×D₄×C₄₁	—	4	2	no	—
101	C₂×D₄×C₄₁	—	8	4	no	—
102	C₂²×C₄×C₄₁	—	2	2	no	—
103	C₂²×C₄×C₄₁	—	2	2	no	—
104	C₂²×C₄×C₄₁	—	4	8	no	—
105	C₂²×C₄×C₄₁	—	4	1	no	—
106	C₂²×C₄×C₄₁	—	4	4	no	—
107	C₂²×C₄×C₄₁	—	4	1	no	—
108	C₂²×C₄×C₄₁	D₈	1	2	yes	—
109	C₂²×C₄×C₄₁	D₈	1	1	yes	characteristic
110	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
112	Q₁₆×C₄₁	—	2	4	no	—
113	Q₁₆×C₄₁	—	2	2	no	—
114	Q₁₆×C₄₁	C₂×D₄	1	4	yes	complemented
115	SD₁₆×C₄₁	—	2	16	no	—
116	D₈×C₄₁	—	2	4	no	—
117	D₈×C₄₁	—	2	2	no	—
118	D₈×C₄₁	—	2	2	no	—
119	D₈×C₄₁	—	2	2	no	—
120	D₈×C₄₁	—	4	2	no	—
121	D₈×C₄₁	C₂×D₄	1	4	yes	complemented
122	C₂×C₈×C₄₁	—	2	2	no	—
123	C₂×C₈×C₄₁	—	2	4	no	—
124	C₂×C₈×C₄₁	—	2	2	no	—
125	C₂×C₈×C₄₁	—	2	2	no	—
126	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
131	C₄⋊C₄×C₄₁	—	2	2	no	—
132	C₄⋊C₄×C₄₁	—	4	1	no	—
133	C₂²⋊C₄×C₄₁	—	4	4	no	—
134	C₁₆×C₄₁	—	2	2	no	—
135	C₁₆×C₄₁	—	2	2	no	—
136	C₂³×C₄₁	—	2	2	no	—
137	C₂³×C₄₁	—	2	2	no	—
138	C₂³×C₄₁	—	2	2	no	—
139	C₂³×C₄₁	—	4	2	no	—
140	C₂³×C₄₁	—	4	4	no	—
141	C₂³×C₄₁	—	4	2	no	—
142	C₂³×C₄₁	—	8	2	no	—
143	C₂³×C₄₁	—	8	2	no	—
144	C₂³×C₄₁	—	8	2	no	—
145	C₂³×C₄₁	—	8	2	no	—
146	C₂³×C₄₁	—	8	2	no	—
147	C₂³×C₄₁	C₂×D₈	1	2	yes	—
148	C₂³×C₄₁	C₂×D₈	1	1	yes	characteristic
149	Q₈×C₄₁	—	2	4	no	—
150	Q₈×C₄₁	—	4	2	no	—
151	Q₈×C₄₁	—	4	4	no	—
152	D₄×C₄₁	—	2	4	no	—
153	D₄×C₄₁	—	4	16	no	—
154	D₄×C₄₁	—	4	2	no	—
155	D₄×C₄₁	—	4	2	no	—
156	D₄×C₄₁	—	4	2	no	—
157	D₄×C₄₁	—	4	4	no	—
158	D₄×C₄₁	—	8	8	no	—
159	D₄×C₄₁	—	8	2	no	—
160	C₂×C₄×C₄₁	—	2	2	no	—
161	C₂×C₄×C₄₁	—	2	2	no	—
162	C₂×C₄×C₄₁	—	2	2	no	—
163	C₂×C₄×C₄₁	—	2	4	no	—
164	C₂×C₄×C₄₁	—	4	16	no	—
165	C₂×C₄×C₄₁	—	4	2	no	—
166	C₂×C₄×C₄₁	—	4	4	no	—
167	C₂×C₄×C₄₁	—	4	2	no	—
168	C₂×C₄×C₄₁	—	8	2	no	—
169	C₂×C₄×C₄₁	#120	1	2	yes	—
170	C₂×C₄×C₄₁	C₂×D₈	1	2	yes	—
171	C₂×C₄×C₄₁	C₂×D₈	1	1	yes	characteristic
172	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
173	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
174	C₈×C₄₁	—	2	2	no	—
175	C₈×C₄₁	#120	1	2	yes	—
176	C₈×C₄₁	C₂²×D₄	1	1	yes	characteristic
177	C₈×C₄₁	C₂²×D₄	1	1	yes	characteristic
178	C₂×#2186	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂²×C₄₁	—	2	2	no	—
180	C₂²×C₄₁	—	2	2	no	—
181	C₂²×C₄₁	—	2	2	no	—
182	C₂²×C₄₁	—	4	4	no	—
183	C₂²×C₄₁	—	4	4	no	—
184	C₂²×C₄₁	—	8	2	no	—
185	C₂²×C₄₁	—	8	2	no	—
186	C₂²×C₄₁	—	8	8	no	—
187	C₂²×C₄₁	—	8	2	no	—
188	C₂²×C₄₁	—	8	2	no	—
189	C₂²×C₄₁	—	8	2	no	—
190	C₂²×C₄₁	—	16	4	no	—
191	C₂²×C₄₁	#447	1	2	yes	—
192	C₂²×C₄₁	#508	1	2	yes	—
193	C₂²×C₄₁	#509	1	2	yes	—
194	C₂²×C₄₁	C₂²×D₈	1	1	yes	characteristic
195	C₄×C₄₁	—	2	2	no	—
196	C₄×C₄₁	—	4	4	no	—
197	C₄×C₄₁	—	8	2	no	—
198	C₄×C₄₁	#447	1	2	yes	—
199	C₄×C₄₁	C₂×#120	1	1	yes	characteristic
200	C₄×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
201	C₂²×#135	C₂×C₄₁	1	1	yes	characteristic, complemented
202	C₂²×SD₃₂	C₂×C₄₁	1	1	yes	characteristic, complemented
203	C₂²×D₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
204	C₂×#466	C₂×C₄₁	1	1	yes	characteristic, complemented
205	#2186	C₂×C₄₁	1	8	yes	direct product factor
206	C₂×#358	C₂×C₄₁	1	1	yes	characteristic, complemented
207	C₂×#357	C₂×C₄₁	1	1	yes	characteristic, complemented
208	C₂×C₂²⋊C₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
209	C₂×C₄₁	—	4	2	no	—
210	C₂×C₄₁	—	8	4	no	—
211	C₂×C₄₁	—	16	2	no	—
212	C₂×C₄₁	#2186	1	4	yes	direct product factor
213	C₂×C₄₁	C₂×#447	1	1	yes	characteristic
214	C₂×C₄₁	C₂×#508	1	1	yes	characteristic
215	C₂×C₄₁	C₂×#509	1	1	yes	characteristic
216	C₂²×#41	—	2	1	no	—
217	C₂×#135	—	2	4	no	—
218	C₂×#135	—	2	4	no	—
219	C₂×#135	—	2	2	no	—
220	C₂×#135	C₂²×C₄₁	1	4	yes	complemented
221	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
222	C₂²×SD₁₆	—	2	1	no	—
223	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
224	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
225	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
226	C₂×#121	—	2	1	no	—
227	C₂×SD₃₂	—	2	4	no	—
228	C₂×SD₃₂	C₂²×C₄₁	1	4	yes	complemented
229	C₂×D₁₆	—	2	4	no	—
230	C₂×D₁₆	C₂²×C₄₁	1	4	yes	complemented
231	C₂²×C₁₆	C₂²×C₄₁	1	1	yes	characteristic
232	C₂²×C₁₆	C₂²×C₄₁	1	1	yes	characteristic
233	#466	—	2	2	no	—
234	#466	C₂²×C₄₁	1	4	yes	complemented
235	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
236	C₂×#102	—	2	1	no	—
237	#358	C₂²×C₄₁	1	4	yes	complemented
238	#357	C₂²×C₄₁	1	4	yes	complemented
239	C₂²⋊C₁₆	C₂²×C₄₁	1	4	yes	complemented
240	C₄₁	C₂×#2186	1	1	yes	characteristic, direct product factor, Sylow
241	C₂×#41	—	2	8	no	—
242	C₂×#41	—	2	4	no	—
243	C₂×#41	—	4	4	no	—
244	C₂×#41	—	4	2	no	—
245	C₂²×Q₈	—	2	1	no	—
246	C₂²×D₄	—	2	1	no	—
247	C₂²×D₄	—	2	1	no	—
248	C₂²×D₄	—	4	1	no	—
249	C₂²×D₄	—	4	1	no	—
250	C₂³×C₄	—	4	1	no	—
251	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
252	#135	—	2	16	no	—
253	#135	—	2	8	no	—
254	#135	—	2	8	no	—
255	C₂×Q₁₆	—	2	1	no	—
256	C₂×Q₁₆	—	2	2	no	—
257	C₂×Q₁₆	D₄×C₄₁	1	4	yes	complemented
258	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
259	C₂×SD₁₆	—	2	8	no	—
260	C₂×SD₁₆	—	2	4	no	—
261	C₂×D₈	—	2	1	no	—
262	C₂×D₈	—	2	2	no	—
263	C₂×D₈	—	2	2	no	—
264	C₂×D₈	—	2	2	no	—
265	C₂×D₈	—	2	1	no	—
266	C₂×D₈	D₄×C₄₁	1	4	yes	complemented
267	C₂×D₈	C₂³×C₄₁	1	2	yes	—
268	C₂×D₈	C₂³×C₄₁	1	2	yes	—
269	C₂²×C₈	—	2	2	no	—
270	C₂²×C₈	—	2	2	no	—
271	C₂²×C₈	D₄×C₄₁	1	1	yes	characteristic
272	C₂²×C₈	D₄×C₄₁	1	2	yes	—
273	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
274	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
275	#121	—	2	4	no	—
276	#121	—	4	2	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₂²⋊C₄	—	4	1	no	—
279	SD₃₂	—	2	8	no	—
280	D₁₆	—	2	8	no	—
281	C₂×C₁₆	—	2	2	no	—
282	C₂×C₁₆	—	2	2	no	—
283	C₂×C₁₆	C₂³×C₄₁	1	2	yes	—
284	C₂×C₁₆	C₂³×C₄₁	1	2	yes	—
285	#107	—	2	1	no	—
286	#107	C₂³×C₄₁	1	2	yes	—
287	#102	—	2	4	no	—
288	C₂⁴	—	4	1	no	—
289	C₂⁴	—	4	1	no	—
290	C₂⁴	D₈×C₄₁	1	1	yes	characteristic
291	#41	—	2	16	no	—
292	#41	—	4	8	no	—
293	#41	—	4	16	no	—
294	C₂×Q₈	—	2	4	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	4	1	no	—
297	C₂×Q₈	—	4	2	no	—
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	4	8	no	—
302	C₂×D₄	—	4	4	no	—
303	C₂×D₄	—	4	4	no	—
304	C₂×D₄	—	4	2	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	4	2	no	—
308	C₂×D₄	—	4	2	no	—
309	C₂×D₄	—	8	4	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	4	8	no	—
313	C₂²×C₄	—	4	1	no	—
314	C₂²×C₄	—	4	4	no	—
315	C₂²×C₄	—	4	1	no	—
316	C₂²×C₄	D₈×C₄₁	1	1	yes	characteristic
317	C₂²×C₄	D₈×C₄₁	1	2	yes	—
318	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
319	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
320	Q₁₆	—	2	4	no	—
321	Q₁₆	—	2	2	no	—
322	Q₁₆	C₂×D₄×C₄₁	1	4	yes	complemented
323	SD₁₆	—	2	16	no	—
324	D₈	—	2	4	no	—
325	D₈	—	2	2	no	—
326	D₈	—	2	2	no	—
327	D₈	—	2	2	no	—
328	D₈	—	4	2	no	—
329	D₈	C₂×D₄×C₄₁	1	4	yes	complemented
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	4	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
335	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
336	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
337	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
338	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	4	1	no	—
341	C₂²⋊C₄	—	4	4	no	—
342	C₁₆	—	2	2	no	—
343	C₁₆	—	2	2	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	4	4	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	8	2	no	—
351	C₂³	—	8	2	no	—
352	C₂³	—	8	2	no	—
353	C₂³	—	8	2	no	—
354	C₂³	—	8	2	no	—
355	C₂³	C₂×D₈×C₄₁	1	2	yes	—
356	C₂³	C₂×D₈×C₄₁	1	1	yes	characteristic
357	Q₈	—	2	4	no	—
358	Q₈	—	4	2	no	—
359	Q₈	—	4	4	no	—
360	D₄	—	2	4	no	—
361	D₄	—	4	16	no	—
362	D₄	—	4	2	no	—
363	D₄	—	4	2	no	—
364	D₄	—	4	2	no	—
365	D₄	—	4	4	no	—
366	D₄	—	8	8	no	—
367	D₄	—	8	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	4	16	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	8	2	no	—
377	C₂×C₄	#120×C₄₁	1	2	yes	—
378	C₂×C₄	C₂×D₈×C₄₁	1	2	yes	—
379	C₂×C₄	C₂×D₈×C₄₁	1	1	yes	characteristic
380	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
381	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
382	C₈	—	2	2	no	—
383	C₈	#120×C₄₁	1	2	yes	—
384	C₈	C₂²×D₄×C₄₁	1	1	yes	characteristic
385	C₈	C₂²×D₄×C₄₁	1	1	yes	characteristic
386	C₂²	—	2	2	no	—
387	C₂²	—	2	2	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	4	4	no	—
390	C₂²	—	4	4	no	—
391	C₂²	—	8	2	no	—
392	C₂²	—	8	2	no	—
393	C₂²	—	8	8	no	—
394	C₂²	—	8	2	no	—
395	C₂²	—	8	2	no	—
396	C₂²	—	8	2	no	—
397	C₂²	—	16	4	no	—
398	C₂²	C₄₁×#447	1	2	yes	—
399	C₂²	C₄₁×#508	1	2	yes	—
400	C₂²	C₄₁×#509	1	2	yes	—
401	C₂²	C₂²×D₈×C₄₁	1	1	yes	characteristic
402	C₄	—	2	2	no	—
403	C₄	—	4	4	no	—
404	C₄	—	8	2	no	—
405	C₄	C₄₁×#447	1	2	yes	—
406	C₄	C₂×#120×C₄₁	1	1	yes	characteristic
407	C₄	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
408	C₂	—	4	2	no	—
409	C₂	—	8	4	no	—
410	C₂	—	16	2	no	—
411	C₂	C₄₁×#2186	1	4	yes	direct product factor
412	C₂	C₂×C₄₁×#447	1	1	yes	characteristic
413	C₂	C₂×C₄₁×#508	1	1	yes	characteristic
414	C₂	C₂×C₄₁×#509	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₄₁
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂³×C₄×C₄₁ ◁ C₂³×C₈×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#135×C₄₁	C₂	semidirect
2. C₂²×SD₃₂×C₄₁	C₂	semidirect
3. C₂²×D₁₆×C₄₁	C₂	semidirect
4. C₂×C₄₁×#466	C₂	semidirect
5. C₄₁×#2186	C₂	direct (N × H)
6. C₂×C₄₁×#358	C₂	semidirect
7. C₂×C₄₁×#357	C₂	semidirect
8. C₂×C₄₁×C₂²⋊C₁₆	C₂	semidirect
13. C₂×#135×C₄₁	C₂²	semidirect
21. C₂×SD₃₂×C₄₁	C₂²	semidirect
23. C₂×D₁₆×C₄₁	C₂²	semidirect
27. C₄₁×#466	C₂²	semidirect
30. C₄₁×#358	C₂²	semidirect
31. C₄₁×#357	C₂²	semidirect
32. C₄₁×C₂²⋊C₁₆	C₂²	semidirect
49. C₂×Q₁₆×C₄₁	D₄	semidirect
58. C₂×D₈×C₄₁	D₄	semidirect
114. Q₁₆×C₄₁	C₂×D₄	semidirect
121. D₈×C₄₁	C₂×D₄	semidirect
178. C₂×#2186	C₄₁	direct (N × H)
201. C₂²×#135	C₂×C₄₁	semidirect
202. C₂²×SD₃₂	C₂×C₄₁	semidirect
203. C₂²×D₁₆	C₂×C₄₁	semidirect
204. C₂×#466	C₂×C₄₁	semidirect
205. #2186	C₂×C₄₁	direct (N × H)
206. C₂×#358	C₂×C₄₁	semidirect
207. C₂×#357	C₂×C₄₁	semidirect
208. C₂×C₂²⋊C₁₆	C₂×C₄₁	semidirect
212. C₂×C₄₁	#2186	direct (N × H)
220. C₂×#135	C₂²×C₄₁	semidirect
228. C₂×SD₃₂	C₂²×C₄₁	semidirect
230. C₂×D₁₆	C₂²×C₄₁	semidirect
234. #466	C₂²×C₄₁	semidirect
237. #358	C₂²×C₄₁	semidirect
238. #357	C₂²×C₄₁	semidirect
239. C₂²⋊C₁₆	C₂²×C₄₁	semidirect
240. C₄₁	C₂×#2186	direct (N × H)
257. C₂×Q₁₆	D₄×C₄₁	semidirect
266. C₂×D₈	D₄×C₄₁	semidirect
322. Q₁₆	C₂×D₄×C₄₁	semidirect
329. D₈	C₂×D₄×C₄₁	semidirect
411. C₂	C₄₁×#2186	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#135×C₄₁	2
C₂²×SD₃₂×C₄₁	2
C₂²×D₁₆×C₄₁	2
C₂×C₄₁×#466	2
C₄₁×#2186	2
C₂×C₄₁×#358	2
C₂×C₄₁×#357	2
C₂×C₄₁×C₂²⋊C₁₆	2
C₂×#2186	41

Subgroups — C2×C41×#2186 #23809715

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#2186 #23809715