Subgroups — C₄₁×#3002 #19106782

Order 5248.

764 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#41×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#135×C₄₁	C₂	1	2	yes	maximal, complemented
3	C₄₁×#525	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#452	C₂	1	2	yes	maximal, complemented
5	C₄₁×#451	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#450	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#449	C₂	1	2	yes	maximal, complemented
8	C₄₁×#448	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#447	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#416	C₂	1	2	yes	maximal, complemented
11	C₂×C₂²⋊C₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#41×C₄₁	—	2	8	no	—
13	C₂×#41×C₄₁	—	2	1	no	—
14	C₂×#41×C₄₁	—	2	1	no	—
15	C₂×#41×C₄₁	C₂²	1	2	yes	—
16	C₂×#41×C₄₁	C₂²	1	2	yes	—
17	C₂×#41×C₄₁	C₂²	1	1	yes	characteristic, complemented
18	C₂²×Q₈×C₄₁	C₂²	1	1	yes	characteristic
19	C₂²×D₄×C₄₁	—	2	1	no	—
20	C₂²×D₄×C₄₁	C₂²	1	1	yes	characteristic
21	C₂³×C₄×C₄₁	—	2	1	no	—
22	C₂³×C₄×C₄₁	C₂²	1	1	yes	characteristic
23	#135×C₄₁	—	2	8	no	—
24	C₂×Q₁₆×C₄₁	C₂²	1	2	yes	complemented
25	C₂×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
26	C₂×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
27	C₂×D₈×C₄₁	C₂²	1	2	yes	complemented
28	C₂²×C₈×C₄₁	C₂²	1	2	yes	complemented
29	#123×C₄₁	—	2	1	no	—
30	C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
31	C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
32	#121×C₄₁	C₂²	1	1	yes	characteristic
33	#121×C₄₁	C₂²	1	1	yes	characteristic, complemented
34	#120×C₄₁	—	2	1	no	—
35	C₄×D₄×C₄₁	—	2	1	no	—
36	C₄×D₄×C₄₁	—	2	1	no	—
37	#117×C₄₁	C₂²	1	1	yes	characteristic, complemented
38	#103×C₄₁	C₂²	1	2	yes	complemented
39	#103×C₄₁	C₂²	1	2	yes	complemented
40	#102×C₄₁	C₂²	1	2	yes	complemented
41	#102×C₄₁	C₂²	1	2	yes	complemented
42	C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
43	C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
44	C₂²⋊C₈×C₄₁	C₂²	1	2	yes	complemented
45	C₂⁴×C₄₁	—	2	1	no	—
46	C₂⁴×C₄₁	D₄	1	1	yes	characteristic
47	#41×C₄₁	—	2	8	no	—
48	#41×C₄₁	—	2	8	no	—
49	#41×C₄₁	—	2	4	no	—
50	#41×C₄₁	—	2	4	no	—
51	#41×C₄₁	—	2	4	no	—
52	#41×C₄₁	—	2	4	no	—
53	#41×C₄₁	D₄	1	8	yes	complemented
54	C₂×Q₈×C₄₁	—	2	4	no	—
55	C₂×Q₈×C₄₁	—	2	1	no	—
56	C₂×Q₈×C₄₁	C₂³	1	1	yes	characteristic
57	C₂×Q₈×C₄₁	C₂³	1	2	yes	—
58	C₂×D₄×C₄₁	—	2	8	no	—
59	C₂×D₄×C₄₁	—	2	2	no	—
60	C₂×D₄×C₄₁	—	2	2	no	—
61	C₂×D₄×C₄₁	—	2	4	no	—
62	C₂×D₄×C₄₁	—	2	1	no	—
63	C₂×D₄×C₄₁	—	2	1	no	—
64	C₂×D₄×C₄₁	—	2	1	no	—
65	C₂×D₄×C₄₁	—	2	1	no	—
66	C₂×D₄×C₄₁	C₂³	1	1	yes	characteristic
67	C₂×D₄×C₄₁	C₂³	1	2	yes	—
68	C₂²×C₄×C₄₁	—	2	8	no	—
69	C₂²×C₄×C₄₁	—	2	1	no	—
70	C₂²×C₄×C₄₁	—	2	2	no	—
71	C₂²×C₄×C₄₁	—	2	4	no	—
72	C₂²×C₄×C₄₁	—	2	2	no	—
73	C₂²×C₄×C₄₁	—	2	1	no	—
74	C₂²×C₄×C₄₁	D₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₁	D₄	1	1	yes	characteristic
76	C₂²×C₄×C₄₁	D₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₁	C₂³	1	1	yes	characteristic
78	C₂²×C₄×C₄₁	C₂³	1	1	yes	characteristic
79	C₂²×C₄×C₄₁	C₂³	1	1	yes	characteristic
80	Q₁₆×C₄₁	—	2	4	no	—
81	SD₁₆×C₄₁	—	2	4	no	—
82	SD₁₆×C₄₁	—	2	4	no	—
83	D₈×C₄₁	—	2	4	no	—
84	C₂×C₈×C₄₁	—	2	4	no	—
85	C₂×C₈×C₄₁	C₂³	1	2	yes	—
86	C₂×C₈×C₄₁	C₂³	1	2	yes	—
87	C₄⋊C₄×C₄₁	—	2	1	no	—
88	C₄⋊C₄×C₄₁	—	2	1	no	—
89	C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
90	C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
91	C₂²⋊C₄×C₄₁	—	2	1	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	C₄²×C₄₁	—	2	1	no	—
97	C₂³×C₄₁	—	2	4	no	—
98	C₂³×C₄₁	—	2	2	no	—
99	C₂³×C₄₁	—	2	2	no	—
100	C₂³×C₄₁	—	2	2	no	—
101	C₂³×C₄₁	—	2	1	no	—
102	C₂³×C₄₁	—	4	1	no	—
103	C₂³×C₄₁	—	4	2	no	—
104	C₂³×C₄₁	—	4	2	no	—
105	C₂³×C₄₁	C₂×D₄	1	1	yes	characteristic
106	C₂³×C₄₁	C₂×D₄	1	1	yes	characteristic
107	C₂³×C₄₁	C₂×D₄	1	1	yes	characteristic
108	Q₈×C₄₁	—	2	4	no	—
109	Q₈×C₄₁	—	2	2	no	—
110	Q₈×C₄₁	—	2	2	no	—
111	Q₈×C₄₁	C₂×D₄	1	4	yes	—
112	D₄×C₄₁	—	2	8	no	—
113	D₄×C₄₁	—	2	4	no	—
114	D₄×C₄₁	—	2	8	no	—
115	D₄×C₄₁	—	2	2	no	—
116	D₄×C₄₁	—	2	2	no	—
117	D₄×C₄₁	—	4	2	no	—
118	D₄×C₄₁	—	4	2	no	—
119	D₄×C₄₁	—	4	2	no	—
120	D₄×C₄₁	C₂×D₄	1	4	yes	—
121	C₂×C₄×C₄₁	—	2	4	no	—
122	C₂×C₄×C₄₁	—	2	8	no	—
123	C₂×C₄×C₄₁	—	2	2	no	—
124	C₂×C₄×C₄₁	—	2	2	no	—
125	C₂×C₄×C₄₁	—	2	2	no	—
126	C₂×C₄×C₄₁	—	2	8	no	—
127	C₂×C₄×C₄₁	—	2	2	no	—
128	C₂×C₄×C₄₁	—	2	2	no	—
129	C₂×C₄×C₄₁	—	2	2	no	—
130	C₂×C₄×C₄₁	—	2	1	no	—
131	C₂×C₄×C₄₁	—	2	1	no	—
132	C₂×C₄×C₄₁	—	2	1	no	—
133	C₂×C₄×C₄₁	—	4	2	no	—
134	C₂×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
135	C₂×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
136	C₂×C₄×C₄₁	C₂×D₄	1	4	yes	—
137	C₂×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
138	C₂×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
139	C₈×C₄₁	—	2	2	no	—
140	C₈×C₄₁	—	2	2	no	—
141	C₂²×C₄₁	—	2	1	no	—
142	C₂²×C₄₁	—	2	1	no	—
143	C₂²×C₄₁	—	2	1	no	—
144	C₂²×C₄₁	—	2	1	no	—
145	C₂²×C₄₁	—	2	1	no	—
146	C₂²×C₄₁	—	2	4	no	—
147	C₂²×C₄₁	—	2	1	no	—
148	C₂²×C₄₁	—	2	1	no	—
149	C₂²×C₄₁	—	4	4	no	—
150	C₂²×C₄₁	—	4	8	no	—
151	C₂²×C₄₁	—	4	2	no	—
152	C₂²×C₄₁	—	4	2	no	—
153	C₂²×C₄₁	—	4	1	no	—
154	C₂²×C₄₁	—	4	1	no	—
155	C₂²×C₄₁	—	4	1	no	—
156	C₂²×C₄₁	#120	1	2	yes	—
157	C₂²×C₄₁	#135	1	2	yes	complemented
158	C₂²×C₄₁	C₂²×D₄	1	1	yes	characteristic
159	C₄×C₄₁	—	2	1	no	—
160	C₄×C₄₁	—	2	4	no	—
161	C₄×C₄₁	—	2	1	no	—
162	C₄×C₄₁	—	4	1	no	—
163	C₄×C₄₁	—	4	1	no	—
164	C₄×C₄₁	—	4	1	no	—
165	C₄×C₄₁	#120	1	2	yes	—
166	C₄×C₄₁	C₂²×D₄	1	2	yes	—
167	#3002	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂×C₄₁	—	2	2	no	—
169	C₂×C₄₁	—	2	2	no	—
170	C₂×C₄₁	—	4	1	no	—
171	C₂×C₄₁	—	4	4	no	—
172	C₂×C₄₁	—	8	1	no	—
173	C₂×C₄₁	C₂×#120	1	1	yes	characteristic
174	C₂×C₄₁	C₂×#135	1	1	yes	characteristic
175	C₂×C₄₁	#575	1	1	yes	characteristic
176	C₂²×#41	C₂×C₄₁	1	1	yes	characteristic, complemented
177	C₂×#135	C₂×C₄₁	1	2	yes	complemented
178	#525	C₂×C₄₁	1	1	yes	characteristic, complemented
179	#452	C₂×C₄₁	1	2	yes	complemented
180	#451	C₂×C₄₁	1	1	yes	characteristic, complemented
181	#450	C₂×C₄₁	1	1	yes	characteristic, complemented
182	#449	C₂×C₄₁	1	2	yes	complemented
183	#448	C₂×C₄₁	1	1	yes	characteristic, complemented
184	#447	C₂×C₄₁	1	1	yes	characteristic, complemented
185	#416	C₂×C₄₁	1	2	yes	complemented
186	C₂×C₂²⋊C₈	C₂×C₄₁	1	1	yes	characteristic, complemented
187	C₄₁	#3002	1	1	yes	characteristic, direct product factor, Sylow
188	C₂×#41	—	2	8	no	—
189	C₂×#41	—	2	1	no	—
190	C₂×#41	—	2	1	no	—
191	C₂×#41	C₂²×C₄₁	1	2	yes	—
192	C₂×#41	C₂²×C₄₁	1	2	yes	—
193	C₂×#41	C₂²×C₄₁	1	1	yes	characteristic, complemented
194	C₂²×Q₈	C₂²×C₄₁	1	1	yes	characteristic
195	C₂²×D₄	—	2	1	no	—
196	C₂²×D₄	C₂²×C₄₁	1	1	yes	characteristic
197	C₂³×C₄	—	2	1	no	—
198	C₂³×C₄	C₂²×C₄₁	1	1	yes	characteristic
199	#135	—	2	8	no	—
200	C₂×Q₁₆	C₂²×C₄₁	1	2	yes	complemented
201	C₂×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
202	C₂×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
203	C₂×D₈	C₂²×C₄₁	1	2	yes	complemented
204	C₂²×C₈	C₂²×C₄₁	1	2	yes	complemented
205	#123	—	2	1	no	—
206	C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
207	C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
208	#121	C₂²×C₄₁	1	1	yes	characteristic
209	#121	C₂²×C₄₁	1	1	yes	characteristic, complemented
210	#120	—	2	1	no	—
211	C₄×D₄	—	2	1	no	—
212	C₄×D₄	—	2	1	no	—
213	#117	C₂²×C₄₁	1	1	yes	characteristic, complemented
214	#103	C₂²×C₄₁	1	2	yes	complemented
215	#103	C₂²×C₄₁	1	2	yes	complemented
216	#102	C₂²×C₄₁	1	2	yes	complemented
217	#102	C₂²×C₄₁	1	2	yes	complemented
218	C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
219	C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
220	C₂²⋊C₈	C₂²×C₄₁	1	2	yes	complemented
221	C₂⁴	—	2	1	no	—
222	C₂⁴	D₄×C₄₁	1	1	yes	characteristic
223	#41	—	2	8	no	—
224	#41	—	2	8	no	—
225	#41	—	2	4	no	—
226	#41	—	2	4	no	—
227	#41	—	2	4	no	—
228	#41	—	2	4	no	—
229	#41	D₄×C₄₁	1	8	yes	complemented
230	C₂×Q₈	—	2	4	no	—
231	C₂×Q₈	—	2	1	no	—
232	C₂×Q₈	C₂³×C₄₁	1	1	yes	characteristic
233	C₂×Q₈	C₂³×C₄₁	1	2	yes	—
234	C₂×D₄	—	2	8	no	—
235	C₂×D₄	—	2	2	no	—
236	C₂×D₄	—	2	2	no	—
237	C₂×D₄	—	2	4	no	—
238	C₂×D₄	—	2	1	no	—
239	C₂×D₄	—	2	1	no	—
240	C₂×D₄	—	2	1	no	—
241	C₂×D₄	—	2	1	no	—
242	C₂×D₄	C₂³×C₄₁	1	1	yes	characteristic
243	C₂×D₄	C₂³×C₄₁	1	2	yes	—
244	C₂²×C₄	—	2	8	no	—
245	C₂²×C₄	—	2	1	no	—
246	C₂²×C₄	—	2	2	no	—
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	—	2	4	no	—
249	C₂²×C₄	—	2	1	no	—
250	C₂²×C₄	D₄×C₄₁	1	1	yes	characteristic
251	C₂²×C₄	D₄×C₄₁	1	1	yes	characteristic
252	C₂²×C₄	D₄×C₄₁	1	1	yes	characteristic
253	C₂²×C₄	C₂³×C₄₁	1	1	yes	characteristic
254	C₂²×C₄	C₂³×C₄₁	1	1	yes	characteristic
255	C₂²×C₄	C₂³×C₄₁	1	1	yes	characteristic
256	Q₁₆	—	2	4	no	—
257	SD₁₆	—	2	4	no	—
258	SD₁₆	—	2	4	no	—
259	D₈	—	2	4	no	—
260	C₂×C₈	—	2	4	no	—
261	C₂×C₈	C₂³×C₄₁	1	2	yes	—
262	C₂×C₈	C₂³×C₄₁	1	2	yes	—
263	C₄⋊C₄	—	2	1	no	—
264	C₄⋊C₄	—	2	1	no	—
265	C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
266	C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
267	C₂²⋊C₄	—	2	1	no	—
268	C₂²⋊C₄	—	2	1	no	—
269	C₂²⋊C₄	—	2	1	no	—
270	C₂²⋊C₄	—	2	1	no	—
271	C₂²⋊C₄	—	2	1	no	—
272	C₄²	—	2	1	no	—
273	C₂³	—	2	4	no	—
274	C₂³	—	2	2	no	—
275	C₂³	—	2	2	no	—
276	C₂³	—	2	2	no	—
277	C₂³	—	2	1	no	—
278	C₂³	—	4	1	no	—
279	C₂³	—	4	2	no	—
280	C₂³	—	4	2	no	—
281	C₂³	C₂×D₄×C₄₁	1	1	yes	characteristic
282	C₂³	C₂×D₄×C₄₁	1	1	yes	characteristic
283	C₂³	C₂×D₄×C₄₁	1	1	yes	characteristic
284	Q₈	—	2	4	no	—
285	Q₈	—	2	2	no	—
286	Q₈	—	2	2	no	—
287	Q₈	C₂×D₄×C₄₁	1	4	yes	—
288	D₄	—	2	8	no	—
289	D₄	—	2	4	no	—
290	D₄	—	2	8	no	—
291	D₄	—	2	2	no	—
292	D₄	—	2	2	no	—
293	D₄	—	4	2	no	—
294	D₄	—	4	2	no	—
295	D₄	—	4	2	no	—
296	D₄	C₂×D₄×C₄₁	1	4	yes	—
297	C₂×C₄	—	2	4	no	—
298	C₂×C₄	—	2	8	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	8	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	4	2	no	—
310	C₂×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
311	C₂×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
312	C₂×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
313	C₂×C₄	C₂×D₄×C₄₁	1	4	yes	—
314	C₂×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
315	C₈	—	2	2	no	—
316	C₈	—	2	2	no	—
317	C₂²	—	2	1	no	—
318	C₂²	—	2	1	no	—
319	C₂²	—	2	1	no	—
320	C₂²	—	2	1	no	—
321	C₂²	—	2	1	no	—
322	C₂²	—	2	4	no	—
323	C₂²	—	2	1	no	—
324	C₂²	—	2	1	no	—
325	C₂²	—	4	4	no	—
326	C₂²	—	4	8	no	—
327	C₂²	—	4	2	no	—
328	C₂²	—	4	2	no	—
329	C₂²	—	4	1	no	—
330	C₂²	—	4	1	no	—
331	C₂²	—	4	1	no	—
332	C₂²	#120×C₄₁	1	2	yes	—
333	C₂²	#135×C₄₁	1	2	yes	complemented
334	C₂²	C₂²×D₄×C₄₁	1	1	yes	characteristic
335	C₄	—	2	1	no	—
336	C₄	—	2	4	no	—
337	C₄	—	2	1	no	—
338	C₄	—	4	1	no	—
339	C₄	—	4	1	no	—
340	C₄	—	4	1	no	—
341	C₄	#120×C₄₁	1	2	yes	—
342	C₄	C₂²×D₄×C₄₁	1	2	yes	—
343	C₂	—	2	2	no	—
344	C₂	—	2	2	no	—
345	C₂	—	4	1	no	—
346	C₂	—	4	4	no	—
347	C₂	—	8	1	no	—
348	C₂	C₂×#120×C₄₁	1	1	yes	characteristic
349	C₂	C₂×#135×C₄₁	1	1	yes	characteristic
350	C₂	C₄₁×#575	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂²×#41×C₄₁	C₂	semidirect
2. C₂×#135×C₄₁	C₂	semidirect
3. C₄₁×#525	C₂	semidirect
4. C₄₁×#452	C₂	semidirect
5. C₄₁×#451	C₂	semidirect
6. C₄₁×#450	C₂	semidirect
7. C₄₁×#449	C₂	semidirect
8. C₄₁×#448	C₂	semidirect
9. C₄₁×#447	C₂	semidirect
10. C₄₁×#416	C₂	semidirect
11. C₂×C₂²⋊C₈×C₄₁	C₂	semidirect
17. C₂×#41×C₄₁	C₂²	semidirect
24. C₂×Q₁₆×C₄₁	C₂²	semidirect
25. C₂×SD₁₆×C₄₁	C₂²	semidirect
26. C₂×SD₁₆×C₄₁	C₂²	semidirect
27. C₂×D₈×C₄₁	C₂²	semidirect
28. C₂²×C₈×C₄₁	C₂²	semidirect
31. C₂²⋊Q₈×C₄₁	C₂²	semidirect
33. #121×C₄₁	C₂²	semidirect
37. #117×C₄₁	C₂²	semidirect
38. #103×C₄₁	C₂²	semidirect
39. #103×C₄₁	C₂²	semidirect
40. #102×C₄₁	C₂²	semidirect
41. #102×C₄₁	C₂²	semidirect
44. C₂²⋊C₈×C₄₁	C₂²	semidirect
53. #41×C₄₁	D₄	semidirect
157. C₂²×C₄₁	#135	semidirect
167. #3002	C₄₁	direct (N × H)
176. C₂²×#41	C₂×C₄₁	semidirect
177. C₂×#135	C₂×C₄₁	semidirect
178. #525	C₂×C₄₁	semidirect
179. #452	C₂×C₄₁	semidirect
180. #451	C₂×C₄₁	semidirect
181. #450	C₂×C₄₁	semidirect
182. #449	C₂×C₄₁	semidirect
183. #448	C₂×C₄₁	semidirect
184. #447	C₂×C₄₁	semidirect
185. #416	C₂×C₄₁	semidirect
186. C₂×C₂²⋊C₈	C₂×C₄₁	semidirect
187. C₄₁	#3002	direct (N × H)
193. C₂×#41	C₂²×C₄₁	semidirect
200. C₂×Q₁₆	C₂²×C₄₁	semidirect
201. C₂×SD₁₆	C₂²×C₄₁	semidirect
202. C₂×SD₁₆	C₂²×C₄₁	semidirect
203. C₂×D₈	C₂²×C₄₁	semidirect
204. C₂²×C₈	C₂²×C₄₁	semidirect
207. C₂²⋊Q₈	C₂²×C₄₁	semidirect
209. #121	C₂²×C₄₁	semidirect
213. #117	C₂²×C₄₁	semidirect
214. #103	C₂²×C₄₁	semidirect
215. #103	C₂²×C₄₁	semidirect
216. #102	C₂²×C₄₁	semidirect
217. #102	C₂²×C₄₁	semidirect
220. C₂²⋊C₈	C₂²×C₄₁	semidirect
229. #41	D₄×C₄₁	semidirect
333. C₂²	#135×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#41×C₄₁	2
C₂×#135×C₄₁	2
C₄₁×#525	2
C₄₁×#452	2
C₄₁×#451	2
C₄₁×#450	2
C₄₁×#449	2
C₄₁×#448	2
C₄₁×#447	2
C₄₁×#416	2
C₂×C₂²⋊C₈×C₄₁	2
#3002	41

Subgroups — C41×#3002 #19106782

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#3002 #19106782