Subgroups — C₄₁×#20633 #23796834

Order 10496.

1690 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#518	C₂	1	1	yes	maximal, characteristic
2	C₂²×#99×C₄₁	C₂	1	2	yes	maximal
3	C₄₁×#2315	C₂	1	2	yes	maximal, complemented
4	C₄₁×#1799	C₂	1	8	yes	maximal, complemented
5	C₂×C₄₁×#342	C₂	1	2	yes	maximal, complemented
6	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
7	C₄₁×#518	—	2	8	no	—
8	C₂×C₄×D₄×C₄₁	C₄	1	4	yes	complemented
9	C₂×C₄×D₄×C₄₁	C₂²	1	4	yes	—
10	C₂×#117×C₄₁	C₄	1	2	yes	complemented
11	C₂²×C₂²⋊C₄×C₄₁	C₄	1	2	yes	complemented
12	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	4	yes	—
13	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
14	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
15	C₂×#99×C₄₁	—	2	8	no	—
16	C₂×#99×C₄₁	C₂²	1	8	yes	—
17	C₄₁×#385	—	2	8	no	—
18	C₄₁×#380	C₂²	1	8	yes	complemented
19	C₄₁×#342	C₂²	1	8	yes	complemented
20	C₂⁵×C₄₁	C₂×C₄	1	1	yes	characteristic
21	C₂⁵×C₄₁	C₂³	1	1	yes	characteristic
22	C₂²×D₄×C₄₁	—	2	4	no	—
23	C₂²×D₄×C₄₁	—	2	4	no	—
24	C₂²×D₄×C₄₁	C₂×C₄	1	2	yes	—
25	C₂²×D₄×C₄₁	D₄	1	4	yes	—
26	C₂²×D₄×C₄₁	Q₈	1	4	yes	—
27	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
28	C₂³×C₄×C₄₁	—	2	4	no	—
29	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₄₁	C₂×C₄	1	2	yes	—
31	C₂³×C₄×C₄₁	C₂×C₄	1	4	yes	complemented
32	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
33	C₄×D₄×C₄₁	—	2	16	no	—
34	C₄×D₄×C₄₁	—	2	16	no	—
35	#117×C₄₁	—	2	8	no	—
36	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
37	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	4	yes	complemented
38	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
39	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
40	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
41	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
42	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
43	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
44	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
45	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
46	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	4	yes	complemented
47	C₂×C₂²⋊C₄×C₄₁	D₄	1	8	yes	—
48	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
49	C₂×C₂²⋊C₄×C₄₁	C₂³	1	2	yes	—
50	C₂×C₄²×C₄₁	C₂×C₄	1	4	yes	complemented
51	#99×C₄₁	—	2	16	no	—
52	#95×C₄₁	—	2	8	no	—
53	C₂⁴×C₄₁	—	2	2	no	—
54	C₂⁴×C₄₁	—	2	2	no	—
55	C₂⁴×C₄₁	—	8	2	no	—
56	C₂⁴×C₄₁	—	8	2	no	—
57	C₂⁴×C₄₁	C₄⋊C₄	1	4	yes	complemented
58	C₂⁴×C₄₁	C₂²×C₄	1	2	yes	—
59	C₂⁴×C₄₁	C₂²×C₄	1	1	yes	characteristic
60	C₂⁴×C₄₁	C₂²×C₄	1	1	yes	characteristic
61	C₂⁴×C₄₁	C₂×D₄	1	4	yes	—
62	C₂⁴×C₄₁	C₂×D₄	1	2	yes	—
63	C₂⁴×C₄₁	C₂×Q₈	1	2	yes	—
64	C₂⁴×C₄₁	#41	1	4	yes	—
65	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
66	C₂×D₄×C₄₁	—	2	4	no	—
67	C₂×D₄×C₄₁	—	2	4	no	—
68	C₂×D₄×C₄₁	—	2	16	no	—
69	C₂×D₄×C₄₁	—	2	16	no	—
70	C₂×D₄×C₄₁	—	2	4	no	—
71	C₂×D₄×C₄₁	—	2	4	no	—
72	C₂×D₄×C₄₁	C₄⋊C₄	1	8	yes	complemented
73	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
74	C₂×D₄×C₄₁	C₂×Q₈	1	4	yes	—
75	C₂²×C₄×C₄₁	—	2	2	no	—
76	C₂²×C₄×C₄₁	—	2	2	no	—
77	C₂²×C₄×C₄₁	—	2	4	no	—
78	C₂²×C₄×C₄₁	—	2	8	no	—
79	C₂²×C₄×C₄₁	—	2	8	no	—
80	C₂²×C₄×C₄₁	—	4	8	no	—
81	C₂²×C₄×C₄₁	—	8	2	no	—
82	C₂²×C₄×C₄₁	—	8	8	no	—
83	C₂²×C₄×C₄₁	—	8	2	no	—
84	C₂²×C₄×C₄₁	—	8	4	no	—
85	C₂²×C₄×C₄₁	C₄⋊C₄	1	4	yes	complemented
86	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
88	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
89	C₂²×C₄×C₄₁	C₂×D₄	1	8	yes	—
90	C₄⋊C₄×C₄₁	—	2	8	no	—
91	C₄⋊C₄×C₄₁	—	8	8	no	—
92	C₂²⋊C₄×C₄₁	—	2	4	no	—
93	C₂²⋊C₄×C₄₁	—	2	4	no	—
94	C₂²⋊C₄×C₄₁	—	2	8	no	—
95	C₂²⋊C₄×C₄₁	—	2	8	no	—
96	C₂²⋊C₄×C₄₁	—	2	8	no	—
97	C₂²⋊C₄×C₄₁	—	4	8	no	—
98	C₂²⋊C₄×C₄₁	C₂²⋊C₄	1	8	yes	—
99	C₂²⋊C₄×C₄₁	C₂²⋊C₄	1	8	yes	—
100	C₄²×C₄₁	—	2	8	no	—
101	C₂³×C₄₁	—	2	2	no	—
102	C₂³×C₄₁	—	2	2	no	—
103	C₂³×C₄₁	—	2	8	no	—
104	C₂³×C₄₁	—	4	2	no	—
105	C₂³×C₄₁	—	4	8	no	—
106	C₂³×C₄₁	—	4	2	no	—
107	C₂³×C₄₁	—	4	2	no	—
108	C₂³×C₄₁	—	4	4	no	—
109	C₂³×C₄₁	—	8	4	no	—
110	C₂³×C₄₁	—	8	2	no	—
111	C₂³×C₄₁	—	8	2	no	—
112	C₂³×C₄₁	—	8	4	no	—
113	C₂³×C₄₁	—	8	4	no	—
114	C₂³×C₄₁	—	8	4	no	—
115	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
116	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
117	C₂³×C₄₁	C₂×C₄⋊C₄	1	4	yes	—
118	C₂³×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
119	C₂³×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
120	C₂³×C₄₁	#117	1	2	yes	—
121	C₂³×C₄₁	#117	1	2	yes	—
122	C₂³×C₄₁	#121	1	8	yes	—
123	C₂³×C₄₁	C₂²⋊Q₈	1	8	yes	—
124	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
125	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
126	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
127	C₂³×C₄₁	C₂²×Q₈	1	1	yes	characteristic
128	C₂³×C₄₁	C₂×#41	1	2	yes	—
129	D₄×C₄₁	—	2	8	no	—
130	D₄×C₄₁	—	2	8	no	—
131	D₄×C₄₁	—	2	16	no	—
132	C₂×C₄×C₄₁	—	2	2	no	—
133	C₂×C₄×C₄₁	—	2	2	no	—
134	C₂×C₄×C₄₁	—	2	8	no	—
135	C₂×C₄×C₄₁	—	2	4	no	—
136	C₂×C₄×C₄₁	—	4	8	no	—
137	C₂×C₄×C₄₁	—	4	4	no	—
138	C₂×C₄×C₄₁	—	4	4	no	—
139	C₂×C₄×C₄₁	—	4	16	no	—
140	C₂×C₄×C₄₁	—	4	8	no	—
141	C₂×C₄×C₄₁	—	8	8	no	—
142	C₂×C₄×C₄₁	—	8	4	no	—
143	C₂×C₄×C₄₁	—	8	16	no	—
144	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	8	yes	—
145	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	4	yes	—
146	#20633	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
147	C₂²×C₄₁	—	2	4	no	—
148	C₂²×C₄₁	—	2	2	no	—
149	C₂²×C₄₁	—	2	4	no	—
150	C₂²×C₄₁	—	2	4	no	—
151	C₂²×C₄₁	—	2	4	no	—
152	C₂²×C₄₁	—	4	8	no	—
153	C₂²×C₄₁	—	4	2	no	—
154	C₂²×C₄₁	—	4	2	no	—
155	C₂²×C₄₁	—	4	2	no	—
156	C₂²×C₄₁	—	4	2	no	—
157	C₂²×C₄₁	—	4	8	no	—
158	C₂²×C₄₁	—	4	1	no	—
159	C₂²×C₄₁	—	4	1	no	—
160	C₂²×C₄₁	—	4	2	no	—
161	C₂²×C₄₁	—	4	4	no	—
162	C₂²×C₄₁	—	4	4	no	—
163	C₂²×C₄₁	—	4	4	no	—
164	C₂²×C₄₁	—	8	8	no	—
165	C₂²×C₄₁	#380	1	4	yes	—
166	C₂²×C₄₁	#380	1	4	yes	—
167	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
168	C₂²×C₄₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
169	C₂²×C₄₁	C₂×#117	1	1	yes	characteristic
170	C₂²×C₄₁	C₂×#121	1	2	yes	—
171	C₂²×C₄₁	C₂×C₂²⋊Q₈	1	2	yes	—
172	C₄×C₄₁	—	2	8	no	—
173	C₄×C₄₁	—	2	4	no	—
174	C₄×C₄₁	—	4	4	no	—
175	C₄×C₄₁	—	8	8	no	—
176	C₂×#518	C₂×C₄₁	1	1	yes	characteristic
177	C₂²×#99	C₂×C₄₁	1	2	yes	—
178	#2315	C₂×C₄₁	1	2	yes	complemented
179	#1799	C₂×C₄₁	1	8	yes	complemented
180	C₂×#342	C₂×C₄₁	1	2	yes	complemented
181	C₂×C₄₁	—	2	2	no	—
182	C₂×C₄₁	—	2	1	no	—
183	C₂×C₄₁	—	2	1	no	—
184	C₂×C₄₁	—	2	4	no	—
185	C₂×C₄₁	—	2	2	no	—
186	C₂×C₄₁	—	2	4	no	—
187	C₂×C₄₁	—	4	4	no	—
188	C₂×C₄₁	C₂×#380	1	1	yes	characteristic
189	C₂×C₄₁	#2883	1	2	yes	—
190	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
191	#518	—	2	8	no	—
192	C₂×C₄×D₄	C₄×C₄₁	1	4	yes	complemented
193	C₂×C₄×D₄	C₂²×C₄₁	1	4	yes	—
194	C₂×#117	C₄×C₄₁	1	2	yes	complemented
195	C₂²×C₂²⋊C₄	C₄×C₄₁	1	2	yes	complemented
196	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	4	yes	—
197	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
198	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
199	C₂×#99	—	2	8	no	—
200	C₂×#99	C₂²×C₄₁	1	8	yes	—
201	#385	—	2	8	no	—
202	#380	C₂²×C₄₁	1	8	yes	complemented
203	#342	C₂²×C₄₁	1	8	yes	complemented
204	C₄₁	#20633	1	1	yes	characteristic, direct product factor, Sylow
205	C₂⁵	C₂×C₄×C₄₁	1	1	yes	characteristic
206	C₂⁵	C₂³×C₄₁	1	1	yes	characteristic
207	C₂²×D₄	—	2	4	no	—
208	C₂²×D₄	—	2	4	no	—
209	C₂²×D₄	C₂×C₄×C₄₁	1	2	yes	—
210	C₂²×D₄	D₄×C₄₁	1	4	yes	—
211	C₂²×D₄	Q₈×C₄₁	1	4	yes	—
212	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
213	C₂³×C₄	—	2	4	no	—
214	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
215	C₂³×C₄	C₂×C₄×C₄₁	1	2	yes	—
216	C₂³×C₄	C₂×C₄×C₄₁	1	4	yes	complemented
217	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
218	C₄×D₄	—	2	16	no	—
219	C₄×D₄	—	2	16	no	—
220	#117	—	2	8	no	—
221	C₂×C₄⋊C₄	—	2	8	no	—
222	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	4	yes	complemented
223	C₂×C₂²⋊C₄	—	2	4	no	—
224	C₂×C₂²⋊C₄	—	2	8	no	—
225	C₂×C₂²⋊C₄	—	2	8	no	—
226	C₂×C₂²⋊C₄	—	2	8	no	—
227	C₂×C₂²⋊C₄	—	2	4	no	—
228	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
229	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
230	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
231	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	4	yes	complemented
232	C₂×C₂²⋊C₄	D₄×C₄₁	1	8	yes	—
233	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
234	C₂×C₂²⋊C₄	C₂³×C₄₁	1	2	yes	—
235	C₂×C₄²	C₂×C₄×C₄₁	1	4	yes	complemented
236	#99	—	2	16	no	—
237	#95	—	2	8	no	—
238	C₂⁴	—	2	2	no	—
239	C₂⁴	—	2	2	no	—
240	C₂⁴	—	8	2	no	—
241	C₂⁴	—	8	2	no	—
242	C₂⁴	C₄⋊C₄×C₄₁	1	4	yes	complemented
243	C₂⁴	C₂²×C₄×C₄₁	1	2	yes	—
244	C₂⁴	C₂²×C₄×C₄₁	1	1	yes	characteristic
245	C₂⁴	C₂²×C₄×C₄₁	1	1	yes	characteristic
246	C₂⁴	C₂×D₄×C₄₁	1	4	yes	—
247	C₂⁴	C₂×D₄×C₄₁	1	2	yes	—
248	C₂⁴	C₂×Q₈×C₄₁	1	2	yes	—
249	C₂⁴	#41×C₄₁	1	4	yes	—
250	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
251	C₂×D₄	—	2	4	no	—
252	C₂×D₄	—	2	4	no	—
253	C₂×D₄	—	2	16	no	—
254	C₂×D₄	—	2	16	no	—
255	C₂×D₄	—	2	4	no	—
256	C₂×D₄	—	2	4	no	—
257	C₂×D₄	C₄⋊C₄×C₄₁	1	8	yes	complemented
258	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
259	C₂×D₄	C₂×Q₈×C₄₁	1	4	yes	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	8	no	—
264	C₂²×C₄	—	2	8	no	—
265	C₂²×C₄	—	4	8	no	—
266	C₂²×C₄	—	8	2	no	—
267	C₂²×C₄	—	8	8	no	—
268	C₂²×C₄	—	8	2	no	—
269	C₂²×C₄	—	8	4	no	—
270	C₂²×C₄	C₄⋊C₄×C₄₁	1	4	yes	complemented
271	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
272	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
273	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
274	C₂²×C₄	C₂×D₄×C₄₁	1	8	yes	—
275	C₄⋊C₄	—	2	8	no	—
276	C₄⋊C₄	—	8	8	no	—
277	C₂²⋊C₄	—	2	4	no	—
278	C₂²⋊C₄	—	2	4	no	—
279	C₂²⋊C₄	—	2	8	no	—
280	C₂²⋊C₄	—	2	8	no	—
281	C₂²⋊C₄	—	2	8	no	—
282	C₂²⋊C₄	—	4	8	no	—
283	C₂²⋊C₄	C₂²⋊C₄×C₄₁	1	8	yes	—
284	C₂²⋊C₄	C₂²⋊C₄×C₄₁	1	8	yes	—
285	C₄²	—	2	8	no	—
286	C₂³	—	2	2	no	—
287	C₂³	—	2	2	no	—
288	C₂³	—	2	8	no	—
289	C₂³	—	4	2	no	—
290	C₂³	—	4	8	no	—
291	C₂³	—	4	2	no	—
292	C₂³	—	4	2	no	—
293	C₂³	—	4	4	no	—
294	C₂³	—	8	4	no	—
295	C₂³	—	8	2	no	—
296	C₂³	—	8	2	no	—
297	C₂³	—	8	4	no	—
298	C₂³	—	8	4	no	—
299	C₂³	—	8	4	no	—
300	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
301	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
302	C₂³	C₂×C₄⋊C₄×C₄₁	1	4	yes	—
303	C₂³	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
304	C₂³	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
305	C₂³	#117×C₄₁	1	2	yes	—
306	C₂³	#117×C₄₁	1	2	yes	—
307	C₂³	#121×C₄₁	1	8	yes	—
308	C₂³	C₂²⋊Q₈×C₄₁	1	8	yes	—
309	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
310	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
311	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
312	C₂³	C₂²×Q₈×C₄₁	1	1	yes	characteristic
313	C₂³	C₂×#41×C₄₁	1	2	yes	—
314	D₄	—	2	8	no	—
315	D₄	—	2	8	no	—
316	D₄	—	2	16	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	8	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	4	8	no	—
322	C₂×C₄	—	4	4	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	—	4	16	no	—
325	C₂×C₄	—	4	8	no	—
326	C₂×C₄	—	8	8	no	—
327	C₂×C₄	—	8	4	no	—
328	C₂×C₄	—	8	16	no	—
329	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	8	yes	—
330	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	4	yes	—
331	C₂²	—	2	4	no	—
332	C₂²	—	2	2	no	—
333	C₂²	—	2	4	no	—
334	C₂²	—	2	4	no	—
335	C₂²	—	2	4	no	—
336	C₂²	—	4	8	no	—
337	C₂²	—	4	2	no	—
338	C₂²	—	4	2	no	—
339	C₂²	—	4	2	no	—
340	C₂²	—	4	2	no	—
341	C₂²	—	4	8	no	—
342	C₂²	—	4	1	no	—
343	C₂²	—	4	1	no	—
344	C₂²	—	4	2	no	—
345	C₂²	—	4	4	no	—
346	C₂²	—	4	4	no	—
347	C₂²	—	4	4	no	—
348	C₂²	—	8	8	no	—
349	C₂²	C₄₁×#380	1	4	yes	—
350	C₂²	C₄₁×#380	1	4	yes	—
351	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
352	C₂²	C₂²×C₄⋊C₄×C₄₁	1	1	yes	characteristic
353	C₂²	C₂×#117×C₄₁	1	1	yes	characteristic
354	C₂²	C₂×#121×C₄₁	1	2	yes	—
355	C₂²	C₂×C₂²⋊Q₈×C₄₁	1	2	yes	—
356	C₄	—	2	4	no	—
357	C₄	—	2	8	no	—
358	C₄	—	4	4	no	—
359	C₄	—	8	8	no	—
360	C₂	—	2	2	no	—
361	C₂	—	2	1	no	—
362	C₂	—	2	1	no	—
363	C₂	—	2	4	no	—
364	C₂	—	2	2	no	—
365	C₂	—	2	4	no	—
366	C₂	—	4	4	no	—
367	C₂	C₂×C₄₁×#380	1	1	yes	characteristic
368	C₂	C₄₁×#2883	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₄₁×#2315	C₂	semidirect
4. C₄₁×#1799	C₂	semidirect
5. C₂×C₄₁×#342	C₂	semidirect
8. C₂×C₄×D₄×C₄₁	C₄	semidirect
10. C₂×#117×C₄₁	C₄	semidirect
11. C₂²×C₂²⋊C₄×C₄₁	C₄	semidirect
18. C₄₁×#380	C₂²	semidirect
19. C₄₁×#342	C₂²	semidirect
31. C₂³×C₄×C₄₁	C₂×C₄	semidirect
37. C₂×C₄⋊C₄×C₄₁	C₂×C₄	semidirect
46. C₂×C₂²⋊C₄×C₄₁	C₂×C₄	semidirect
50. C₂×C₄²×C₄₁	C₂×C₄	semidirect
57. C₂⁴×C₄₁	C₄⋊C₄	semidirect
72. C₂×D₄×C₄₁	C₄⋊C₄	semidirect
85. C₂²×C₄×C₄₁	C₄⋊C₄	semidirect
146. #20633	C₄₁	direct (N × H)
178. #2315	C₂×C₄₁	semidirect
179. #1799	C₂×C₄₁	semidirect
180. C₂×#342	C₂×C₄₁	semidirect
192. C₂×C₄×D₄	C₄×C₄₁	semidirect
194. C₂×#117	C₄×C₄₁	semidirect
195. C₂²×C₂²⋊C₄	C₄×C₄₁	semidirect
202. #380	C₂²×C₄₁	semidirect
203. #342	C₂²×C₄₁	semidirect
204. C₄₁	#20633	direct (N × H)
216. C₂³×C₄	C₂×C₄×C₄₁	semidirect
222. C₂×C₄⋊C₄	C₂×C₄×C₄₁	semidirect
231. C₂×C₂²⋊C₄	C₂×C₄×C₄₁	semidirect
235. C₂×C₄²	C₂×C₄×C₄₁	semidirect
242. C₂⁴	C₄⋊C₄×C₄₁	semidirect
257. C₂×D₄	C₄⋊C₄×C₄₁	semidirect
270. C₂²×C₄	C₄⋊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×#518	2
C₂²×#99×C₄₁	2
C₄₁×#2315	2
C₄₁×#1799	2
C₂×C₄₁×#342	2
#20633	41

Subgroups — C41×#20633 #23796834

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#20633 #23796834