Subgroups — C₂×C₄₁×#2189 #23809716

Order 10496.

1146 conjugacy classes of subgroups.

The subgroup lattice has 400 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
2	C₂²×Q₃₂×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×SD₃₂×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₁×#467	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2189	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	—
14	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
15	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
16	C₂²×SD₁₆×C₄₁	—	2	1	no	—
17	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊Q₈×C₄₁	—	2	1	no	—
20	C₂×Q₃₂×C₄₁	—	2	4	no	—
21	C₂×Q₃₂×C₄₁	C₂²	1	4	yes	complemented
22	C₂×SD₃₂×C₄₁	—	2	4	no	—
23	C₂×SD₃₂×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×#467	—	2	2	no	—
27	C₄₁×#467	C₂²	1	4	yes	complemented
28	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
29	C₂×#103×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×Q₈×C₄₁	—	2	1	no	—
39	C₂²×D₄×C₄₁	—	2	1	no	—
40	C₂²×D₄×C₄₁	—	4	1	no	—
41	C₂³×C₄×C₄₁	—	4	1	no	—
42	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
43	#135×C₄₁	—	2	16	no	—
44	#135×C₄₁	—	2	8	no	—
45	#135×C₄₁	—	2	8	no	—
46	C₂×Q₁₆×C₄₁	—	2	1	no	—
47	C₂×Q₁₆×C₄₁	—	2	2	no	—
48	C₂×Q₁₆×C₄₁	—	2	2	no	—
49	C₂×Q₁₆×C₄₁	—	2	2	no	—
50	C₂×Q₁₆×C₄₁	—	2	1	no	—
51	C₂×Q₁₆×C₄₁	D₄	1	4	yes	—
52	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
53	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
54	C₂×SD₁₆×C₄₁	—	2	8	no	—
55	C₂×SD₁₆×C₄₁	—	2	4	no	—
56	C₂×D₈×C₄₁	—	2	1	no	—
57	C₂×D₈×C₄₁	—	2	2	no	—
58	C₂×D₈×C₄₁	D₄	1	4	yes	—
59	C₂×D₈×C₄₁	C₂³	1	2	yes	—
60	C₂²×C₈×C₄₁	—	2	2	no	—
61	C₂²×C₈×C₄₁	—	2	2	no	—
62	C₂²×C₈×C₄₁	D₄	1	1	yes	characteristic
63	C₂²×C₈×C₄₁	D₄	1	2	yes	—
64	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
65	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
66	C₂²⋊Q₈×C₄₁	—	2	4	no	—
67	C₂²⋊Q₈×C₄₁	—	4	2	no	—
68	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
69	C₂×C₄⋊C₄×C₄₁	—	4	1	no	—
70	C₂×C₂²⋊C₄×C₄₁	—	4	1	no	—
71	Q₃₂×C₄₁	—	2	8	no	—
72	SD₃₂×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	#103×C₄₁	—	2	4	no	—
80	C₂⁴×C₄₁	—	4	1	no	—
81	C₂⁴×C₄₁	D₈	1	1	yes	characteristic
82	#41×C₄₁	—	2	16	no	—
83	#41×C₄₁	—	4	8	no	—
84	#41×C₄₁	—	4	16	no	—
85	C₂×Q₈×C₄₁	—	2	4	no	—
86	C₂×Q₈×C₄₁	—	2	2	no	—
87	C₂×Q₈×C₄₁	—	2	2	no	—
88	C₂×Q₈×C₄₁	—	4	1	no	—
89	C₂×Q₈×C₄₁	—	4	1	no	—
90	C₂×Q₈×C₄₁	—	4	2	no	—
91	C₂×Q₈×C₄₁	—	4	2	no	—
92	C₂×Q₈×C₄₁	—	4	2	no	—
93	C₂×D₄×C₄₁	—	2	4	no	—
94	C₂×D₄×C₄₁	—	2	2	no	—
95	C₂×D₄×C₄₁	—	4	8	no	—
96	C₂×D₄×C₄₁	—	4	4	no	—
97	C₂×D₄×C₄₁	—	4	1	no	—
98	C₂×D₄×C₄₁	—	4	2	no	—
99	C₂²×C₄×C₄₁	—	2	2	no	—
100	C₂²×C₄×C₄₁	—	2	2	no	—
101	C₂²×C₄×C₄₁	—	4	8	no	—
102	C₂²×C₄×C₄₁	—	4	1	no	—
103	C₂²×C₄×C₄₁	—	4	4	no	—
104	C₂²×C₄×C₄₁	—	4	1	no	—
105	C₂²×C₄×C₄₁	—	4	1	no	—
106	C₂²×C₄×C₄₁	D₈	1	2	yes	—
107	C₂²×C₄×C₄₁	D₈	1	1	yes	characteristic
108	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
110	Q₁₆×C₄₁	—	2	4	no	—
111	Q₁₆×C₄₁	—	2	2	no	—
112	Q₁₆×C₄₁	—	2	2	no	—
113	Q₁₆×C₄₁	—	2	2	no	—
114	Q₁₆×C₄₁	—	4	2	no	—
115	Q₁₆×C₄₁	C₂×D₄	1	4	yes	—
116	SD₁₆×C₄₁	—	2	16	no	—
117	D₈×C₄₁	—	2	4	no	—
118	D₈×C₄₁	—	2	2	no	—
119	D₈×C₄₁	C₂×D₄	1	4	yes	—
120	C₂×C₈×C₄₁	—	2	2	no	—
121	C₂×C₈×C₄₁	—	2	4	no	—
122	C₂×C₈×C₄₁	—	2	2	no	—
123	C₂×C₈×C₄₁	—	2	2	no	—
124	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
129	C₄⋊C₄×C₄₁	—	2	2	no	—
130	C₄⋊C₄×C₄₁	—	4	1	no	—
131	C₄⋊C₄×C₄₁	—	4	4	no	—
132	C₂²⋊C₄×C₄₁	—	4	4	no	—
133	C₁₆×C₄₁	—	2	2	no	—
134	C₁₆×C₄₁	—	2	2	no	—
135	C₂³×C₄₁	—	2	2	no	—
136	C₂³×C₄₁	—	2	2	no	—
137	C₂³×C₄₁	—	2	2	no	—
138	C₂³×C₄₁	—	4	2	no	—
139	C₂³×C₄₁	—	4	4	no	—
140	C₂³×C₄₁	—	8	2	no	—
141	C₂³×C₄₁	—	8	2	no	—
142	C₂³×C₄₁	C₂×D₈	1	2	yes	—
143	C₂³×C₄₁	C₂×D₈	1	1	yes	characteristic
144	Q₈×C₄₁	—	2	4	no	—
145	Q₈×C₄₁	—	4	2	no	—
146	Q₈×C₄₁	—	4	4	no	—
147	Q₈×C₄₁	—	4	2	no	—
148	Q₈×C₄₁	—	4	2	no	—
149	Q₈×C₄₁	—	8	2	no	—
150	D₄×C₄₁	—	2	4	no	—
151	D₄×C₄₁	—	4	16	no	—
152	D₄×C₄₁	—	4	2	no	—
153	D₄×C₄₁	—	4	4	no	—
154	C₂×C₄×C₄₁	—	2	2	no	—
155	C₂×C₄×C₄₁	—	2	2	no	—
156	C₂×C₄×C₄₁	—	2	2	no	—
157	C₂×C₄×C₄₁	—	2	4	no	—
158	C₂×C₄×C₄₁	—	4	16	no	—
159	C₂×C₄×C₄₁	—	4	2	no	—
160	C₂×C₄×C₄₁	—	4	4	no	—
161	C₂×C₄×C₄₁	—	4	2	no	—
162	C₂×C₄×C₄₁	—	4	2	no	—
163	C₂×C₄×C₄₁	—	8	2	no	—
164	C₂×C₄×C₄₁	—	8	2	no	—
165	C₂×C₄×C₄₁	#120	1	2	yes	—
166	C₂×C₄×C₄₁	C₂×D₈	1	2	yes	—
167	C₂×C₄×C₄₁	C₂×D₈	1	1	yes	characteristic
168	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
169	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
170	C₈×C₄₁	—	2	2	no	—
171	C₈×C₄₁	#120	1	2	yes	—
172	C₈×C₄₁	C₂²×D₄	1	1	yes	characteristic
173	C₈×C₄₁	C₂²×D₄	1	1	yes	characteristic
174	C₂×#2189	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂²×C₄₁	—	2	2	no	—
176	C₂²×C₄₁	—	2	2	no	—
177	C₂²×C₄₁	—	2	2	no	—
178	C₂²×C₄₁	—	4	4	no	—
179	C₂²×C₄₁	—	4	4	no	—
180	C₂²×C₄₁	—	8	2	no	—
181	C₂²×C₄₁	—	8	2	no	—
182	C₂²×C₄₁	—	8	8	no	—
183	C₂²×C₄₁	#447	1	2	yes	—
184	C₂²×C₄₁	#508	1	2	yes	—
185	C₂²×C₄₁	#510	1	2	yes	—
186	C₂²×C₄₁	C₂²×D₈	1	1	yes	characteristic
187	C₄×C₄₁	—	2	2	no	—
188	C₄×C₄₁	—	4	4	no	—
189	C₄×C₄₁	—	8	2	no	—
190	C₄×C₄₁	—	8	2	no	—
191	C₄×C₄₁	#447	1	2	yes	—
192	C₄×C₄₁	C₂×#120	1	1	yes	characteristic
193	C₄×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
194	C₂²×#135	C₂×C₄₁	1	1	yes	characteristic
195	C₂²×Q₃₂	C₂×C₄₁	1	1	yes	characteristic, complemented
196	C₂²×SD₃₂	C₂×C₄₁	1	1	yes	characteristic, complemented
197	C₂×#467	C₂×C₄₁	1	1	yes	characteristic, complemented
198	#2189	C₂×C₄₁	1	8	yes	direct product factor
199	C₂×#358	C₂×C₄₁	1	1	yes	characteristic, complemented
200	C₂×#357	C₂×C₄₁	1	1	yes	characteristic, complemented
201	C₂×C₂²⋊C₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
202	C₂×C₄₁	—	4	2	no	—
203	C₂×C₄₁	—	8	4	no	—
204	C₂×C₄₁	#2189	1	4	yes	direct product factor
205	C₂×C₄₁	C₂×#447	1	1	yes	characteristic
206	C₂×C₄₁	C₂×#508	1	1	yes	characteristic
207	C₂×C₄₁	C₂×#510	1	1	yes	characteristic
208	C₂²×#41	—	2	1	no	—
209	C₂×#135	—	2	4	no	—
210	C₂×#135	—	2	4	no	—
211	C₂×#135	—	2	2	no	—
212	C₂×#135	C₂²×C₄₁	1	4	yes	—
213	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
214	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
215	C₂²×SD₁₆	—	2	1	no	—
216	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
217	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
218	C₂×C₂²⋊Q₈	—	2	1	no	—
219	C₂×Q₃₂	—	2	4	no	—
220	C₂×Q₃₂	C₂²×C₄₁	1	4	yes	complemented
221	C₂×SD₃₂	—	2	4	no	—
222	C₂×SD₃₂	C₂²×C₄₁	1	4	yes	complemented
223	C₂²×C₁₆	C₂²×C₄₁	1	1	yes	characteristic
224	C₂²×C₁₆	C₂²×C₄₁	1	1	yes	characteristic
225	#467	—	2	2	no	—
226	#467	C₂²×C₄₁	1	4	yes	complemented
227	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
228	C₂×#103	—	2	1	no	—
229	#358	C₂²×C₄₁	1	4	yes	complemented
230	#357	C₂²×C₄₁	1	4	yes	complemented
231	C₂²⋊C₁₆	C₂²×C₄₁	1	4	yes	complemented
232	C₄₁	C₂×#2189	1	1	yes	characteristic, direct product factor, Sylow
233	C₂×#41	—	2	8	no	—
234	C₂×#41	—	2	4	no	—
235	C₂×#41	—	4	4	no	—
236	C₂×#41	—	4	2	no	—
237	C₂²×Q₈	—	2	1	no	—
238	C₂²×Q₈	—	2	1	no	—
239	C₂²×D₄	—	2	1	no	—
240	C₂²×D₄	—	4	1	no	—
241	C₂³×C₄	—	4	1	no	—
242	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
243	#135	—	2	16	no	—
244	#135	—	2	8	no	—
245	#135	—	2	8	no	—
246	C₂×Q₁₆	—	2	1	no	—
247	C₂×Q₁₆	—	2	2	no	—
248	C₂×Q₁₆	—	2	2	no	—
249	C₂×Q₁₆	—	2	2	no	—
250	C₂×Q₁₆	—	2	1	no	—
251	C₂×Q₁₆	D₄×C₄₁	1	4	yes	—
252	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
253	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
254	C₂×SD₁₆	—	2	8	no	—
255	C₂×SD₁₆	—	2	4	no	—
256	C₂×D₈	—	2	1	no	—
257	C₂×D₈	—	2	2	no	—
258	C₂×D₈	D₄×C₄₁	1	4	yes	—
259	C₂×D₈	C₂³×C₄₁	1	2	yes	—
260	C₂²×C₈	—	2	2	no	—
261	C₂²×C₈	—	2	2	no	—
262	C₂²×C₈	D₄×C₄₁	1	1	yes	characteristic
263	C₂²×C₈	D₄×C₄₁	1	2	yes	—
264	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
265	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
266	C₂²⋊Q₈	—	2	4	no	—
267	C₂²⋊Q₈	—	4	2	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	4	1	no	—
270	C₂×C₂²⋊C₄	—	4	1	no	—
271	Q₃₂	—	2	8	no	—
272	SD₃₂	—	2	8	no	—
273	C₂×C₁₆	—	2	2	no	—
274	C₂×C₁₆	—	2	2	no	—
275	C₂×C₁₆	C₂³×C₄₁	1	2	yes	—
276	C₂×C₁₆	C₂³×C₄₁	1	2	yes	—
277	#107	—	2	1	no	—
278	#107	C₂³×C₄₁	1	2	yes	—
279	#103	—	2	4	no	—
280	C₂⁴	—	4	1	no	—
281	C₂⁴	D₈×C₄₁	1	1	yes	characteristic
282	#41	—	2	16	no	—
283	#41	—	4	8	no	—
284	#41	—	4	16	no	—
285	C₂×Q₈	—	2	4	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	4	1	no	—
289	C₂×Q₈	—	4	1	no	—
290	C₂×Q₈	—	4	2	no	—
291	C₂×Q₈	—	4	2	no	—
292	C₂×Q₈	—	4	2	no	—
293	C₂×D₄	—	2	4	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	4	8	no	—
296	C₂×D₄	—	4	4	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂×D₄	—	4	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	4	8	no	—
302	C₂²×C₄	—	4	1	no	—
303	C₂²×C₄	—	4	4	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	D₈×C₄₁	1	1	yes	characteristic
307	C₂²×C₄	D₈×C₄₁	1	2	yes	—
308	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
309	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
310	Q₁₆	—	2	4	no	—
311	Q₁₆	—	2	2	no	—
312	Q₁₆	—	2	2	no	—
313	Q₁₆	—	2	2	no	—
314	Q₁₆	—	4	2	no	—
315	Q₁₆	C₂×D₄×C₄₁	1	4	yes	—
316	SD₁₆	—	2	16	no	—
317	D₈	—	2	4	no	—
318	D₈	—	2	2	no	—
319	D₈	C₂×D₄×C₄₁	1	4	yes	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	4	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
325	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
326	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
327	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
328	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	4	1	no	—
331	C₄⋊C₄	—	4	4	no	—
332	C₂²⋊C₄	—	4	4	no	—
333	C₁₆	—	2	2	no	—
334	C₁₆	—	2	2	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	2	2	no	—
338	C₂³	—	4	2	no	—
339	C₂³	—	4	4	no	—
340	C₂³	—	8	2	no	—
341	C₂³	—	8	2	no	—
342	C₂³	C₂×D₈×C₄₁	1	2	yes	—
343	C₂³	C₂×D₈×C₄₁	1	1	yes	characteristic
344	Q₈	—	2	4	no	—
345	Q₈	—	4	2	no	—
346	Q₈	—	4	4	no	—
347	Q₈	—	4	2	no	—
348	Q₈	—	4	2	no	—
349	Q₈	—	8	2	no	—
350	D₄	—	2	4	no	—
351	D₄	—	4	16	no	—
352	D₄	—	4	2	no	—
353	D₄	—	4	4	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	4	16	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	8	2	no	—
364	C₂×C₄	—	8	2	no	—
365	C₂×C₄	#120×C₄₁	1	2	yes	—
366	C₂×C₄	C₂×D₈×C₄₁	1	2	yes	—
367	C₂×C₄	C₂×D₈×C₄₁	1	1	yes	characteristic
368	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
369	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
370	C₈	—	2	2	no	—
371	C₈	#120×C₄₁	1	2	yes	—
372	C₈	C₂²×D₄×C₄₁	1	1	yes	characteristic
373	C₈	C₂²×D₄×C₄₁	1	1	yes	characteristic
374	C₂²	—	2	2	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	4	4	no	—
378	C₂²	—	4	4	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	8	2	no	—
381	C₂²	—	8	8	no	—
382	C₂²	C₄₁×#447	1	2	yes	—
383	C₂²	C₄₁×#508	1	2	yes	—
384	C₂²	C₄₁×#510	1	2	yes	—
385	C₂²	C₂²×D₈×C₄₁	1	1	yes	characteristic
386	C₄	—	2	2	no	—
387	C₄	—	4	4	no	—
388	C₄	—	8	2	no	—
389	C₄	—	8	2	no	—
390	C₄	C₄₁×#447	1	2	yes	—
391	C₄	C₂×#120×C₄₁	1	1	yes	characteristic
392	C₄	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
393	C₂	—	4	2	no	—
394	C₂	—	8	4	no	—
395	C₂	C₄₁×#2189	1	4	yes	direct product factor
396	C₂	C₂×C₄₁×#447	1	1	yes	characteristic
397	C₂	C₂×C₄₁×#508	1	1	yes	characteristic
398	C₂	C₂×C₄₁×#510	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₄₁
prime radical	C₂²×#135×C₄₁	C₂
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
2. C₂²×Q₃₂×C₄₁	C₂	semidirect
3. C₂²×SD₃₂×C₄₁	C₂	semidirect
4. C₂×C₄₁×#467	C₂	semidirect
5. C₄₁×#2189	C₂	direct (N × H)
6. C₂×C₄₁×#358	C₂	semidirect
7. C₂×C₄₁×#357	C₂	semidirect
8. C₂×C₄₁×C₂²⋊C₁₆	C₂	semidirect
21. C₂×Q₃₂×C₄₁	C₂²	semidirect
23. C₂×SD₃₂×C₄₁	C₂²	semidirect
27. C₄₁×#467	C₂²	semidirect
30. C₄₁×#358	C₂²	semidirect
31. C₄₁×#357	C₂²	semidirect
32. C₄₁×C₂²⋊C₁₆	C₂²	semidirect
174. C₂×#2189	C₄₁	direct (N × H)
195. C₂²×Q₃₂	C₂×C₄₁	semidirect
196. C₂²×SD₃₂	C₂×C₄₁	semidirect
197. C₂×#467	C₂×C₄₁	semidirect
198. #2189	C₂×C₄₁	direct (N × H)
199. C₂×#358	C₂×C₄₁	semidirect
200. C₂×#357	C₂×C₄₁	semidirect
201. C₂×C₂²⋊C₁₆	C₂×C₄₁	semidirect
204. C₂×C₄₁	#2189	direct (N × H)
220. C₂×Q₃₂	C₂²×C₄₁	semidirect
222. C₂×SD₃₂	C₂²×C₄₁	semidirect
226. #467	C₂²×C₄₁	semidirect
229. #358	C₂²×C₄₁	semidirect
230. #357	C₂²×C₄₁	semidirect
231. C₂²⋊C₁₆	C₂²×C₄₁	semidirect
232. C₄₁	C₂×#2189	direct (N × H)
395. C₂	C₄₁×#2189	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×Q₃₂×C₄₁	2
C₂²×SD₃₂×C₄₁	2
C₂×C₄₁×#467	2
C₄₁×#2189	2
C₂×C₄₁×#358	2
C₂×C₄₁×#357	2
C₂×C₄₁×C₂²⋊C₁₆	2
C₂×#2189	41

Subgroups — C2×C41×#2189 #23809716

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#2189 #23809716