Subgroups — C₂×#19143542 #25960977

Order 11008.

1938 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583456	C₂	1	1	yes	maximal, characteristic
2	#19143542	C₂	1	16	yes	maximal, direct product factor
3	C₂×#14583029	C₂	1	2	yes	maximal, complemented
4	C₂×#14583027	C₂	1	4	yes	maximal, complemented
5	C₂×C₈×Dic₈₆	C₂	1	2	yes	maximal, complemented
6	C₂×#14582927	C₂	1	2	yes	maximal
7	C₂²×C₄⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
8	C₂×#14582857	C₂	1	2	yes	maximal
9	C₂×C₄×M₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
10	C₂³×C₄₃⋊C₈	C₂²	1	2	yes	—
11	#14583456	C₄	1	8	yes	—
12	#14583456	C₂²	1	8	yes	—
13	C₂×#13063325	C₄	1	1	yes	characteristic
14	C₂×#13063325	C₄	1	1	yes	characteristic
15	C₂×#13063317	C₄	1	2	yes	—
16	C₂×#13063304	C₄	1	2	yes	—
17	C₂×#13063304	C₄	1	2	yes	—
18	C₂×C₄×Dic₈₆	C₂²	1	2	yes	—
19	C₂×C₄×Dic₈₆	C₂²	1	2	yes	—
20	C₂×#13063284	C₂²	1	2	yes	—
21	#14583029	C₂²	1	16	yes	complemented
22	#14583027	C₂²	1	32	yes	complemented
23	C₈×Dic₈₆	C₂²	1	16	yes	complemented
24	#14582927	C₂²	1	16	yes	—
25	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
27	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	8	yes	—
29	C₂×Dic₄₃⋊C₈	C₂²	1	4	yes	—
30	C₂×Dic₄₃⋊C₈	C₂²	1	4	yes	—
31	#14582857	C₂²	1	16	yes	—
32	C₂×#13063235	C₂²	1	4	yes	—
33	C₂×C₈×Dic₄₃	C₂²	1	4	yes	—
34	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
35	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
37	C₄×M₁₆×C₄₃	C₂²	1	8	yes	—
38	C₂×#97×C₄₃	C₂²	1	2	yes	—
39	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	—
40	C₂²×Dic₈₆	C₂×C₄	1	2	yes	—
41	C₂²×Dic₈₆	C₂×C₄	1	2	yes	—
42	C₂²×C₄₃⋊C₈	—	2	8	no	—
43	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
44	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
45	C₂²×C₄₃⋊C₈	C₂³	1	8	yes	—
46	#13063325	C₂×C₄	1	8	yes	—
47	#13063325	C₂×C₄	1	8	yes	—
48	#13063317	C₂×C₄	1	16	yes	—
49	#13063304	C₂×C₄	1	16	yes	—
50	#13063304	C₂×C₄	1	16	yes	—
51	C₄×Dic₈₆	C₂×C₄	1	8	yes	—
52	C₄×Dic₈₆	C₂×C₄	1	8	yes	—
53	C₄×Dic₈₆	C₂³	1	8	yes	—
54	C₄×Dic₈₆	C₂³	1	8	yes	—
55	#13063284	C₂×C₄	1	8	yes	—
56	#13063284	C₂³	1	8	yes	—
57	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
58	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
59	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
60	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
61	C₂×Dic₄₃⋊C₄	C₂×C₄	1	4	yes	—
62	C₂×Dic₄₃⋊C₄	C₂×C₄	1	4	yes	—
63	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	4	yes	—
64	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
65	C₄⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
66	C₄⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
67	C₄⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
68	Dic₄₃⋊C₈	C₂³	1	16	yes	—
69	Dic₄₃⋊C₈	C₂³	1	16	yes	—
70	#13063235	C₂³	1	16	yes	—
71	C₈×Dic₄₃	C₂³	1	16	yes	—
72	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
73	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
74	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
75	C₂×M₁₆×C₄₃	—	2	4	no	—
76	C₂×M₁₆×C₄₃	Q₈	1	8	yes	complemented
77	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
78	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
79	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
80	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
81	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
84	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
87	#97×C₄₃	C₂³	1	8	yes	—
88	C₄×C₈×C₄₃	C₂³	1	8	yes	—
89	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₃	—	2	4	no	—
91	C₂²×C₄×C₄₃	—	4	2	no	—
92	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
97	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
101	C₂²×C₄×C₄₃	#41	1	4	yes	—
102	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
103	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
104	C₂²×Dic₄₃	C₂²×C₄	1	4	yes	—
105	C₂²×Dic₄₃	C₂²×C₄	1	4	yes	—
106	C₂×Dic₈₆	—	2	8	no	—
107	C₂×Dic₈₆	—	4	4	no	—
108	C₂×Dic₈₆	C₂²×C₄	1	8	yes	—
109	C₂×Dic₈₆	C₂²×C₄	1	8	yes	—
110	M₁₆×C₄₃	—	2	8	no	—
111	M₁₆×C₄₃	C₂×Q₈	1	16	yes	complemented
112	C₂×C₈×C₄₃	—	2	4	no	—
113	C₂×C₈×C₄₃	C₂×Q₈	1	8	yes	—
114	C₂×C₈×C₄₃	C₂⁴	1	4	yes	—
115	C₂×C₈×C₄₃	C₂⁴	1	4	yes	—
116	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
117	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
118	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
119	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
120	C₄²×C₄₃	C₂⁴	1	2	yes	—
121	C₄²×C₄₃	C₂⁴	1	2	yes	—
122	C₂²⋊Dic₄₃	C₂²×C₄	1	16	yes	—
123	C₄⋊Dic₄₃	C₂²×C₄	1	8	yes	—
124	C₄⋊Dic₄₃	C₂²×C₄	1	8	yes	—
125	C₄⋊Dic₄₃	C₂²×C₄	1	8	yes	—
126	C₄⋊Dic₄₃	C₂²×C₄	1	8	yes	—
127	Dic₄₃⋊C₄	C₂²×C₄	1	16	yes	—
128	Dic₄₃⋊C₄	C₂²×C₄	1	16	yes	—
129	C₄×Dic₄₃	C₂²×C₄	1	8	yes	—
130	C₄×Dic₄₃	C₂⁴	1	8	yes	—
131	C₂×C₄₃⋊C₈	—	2	4	no	—
132	C₂×C₄₃⋊C₈	—	2	4	no	—
133	C₂×C₄₃⋊C₈	—	2	16	no	—
134	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
135	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
136	C₂³×C₄₃	—	2	2	no	—
137	C₂³×C₄₃	—	2	2	no	—
138	C₂³×C₄₃	C₄×Q₈	1	4	yes	—
139	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
140	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
141	C₂×C₄×C₄₃	—	2	2	no	—
142	C₂×C₄×C₄₃	—	2	2	no	—
143	C₂×C₄×C₄₃	—	2	2	no	—
144	C₂×C₄×C₄₃	—	2	8	no	—
145	C₂×C₄×C₄₃	—	4	4	no	—
146	C₂×C₄×C₄₃	C₄×Q₈	1	8	yes	—
147	C₂×C₄×C₄₃	C₄×Q₈	1	4	yes	—
148	C₂×C₄×C₄₃	#131	1	4	yes	—
149	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
150	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
151	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
152	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
153	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
154	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
155	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
156	C₂×C₄×C₄₃	C₂²×Q₈	1	4	yes	—
157	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
158	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
159	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
160	C₂×Dic₄₃	—	2	8	no	—
161	C₂×Dic₄₃	—	2	8	no	—
162	C₂×Dic₄₃	C₂³×C₄	1	8	yes	—
163	C₂×Dic₄₃	C₂³×C₄	1	8	yes	—
164	Dic₈₆	—	2	16	no	—
165	Dic₈₆	—	4	8	no	—
166	C₈×C₄₃	—	2	4	no	—
167	C₈×C₄₃	C₂²×Q₈	1	8	yes	—
168	C₄₃⋊C₈	—	2	4	no	—
169	C₄₃⋊C₈	—	2	4	no	—
170	C₂×#2962	—	43	1	no	maximal, Sylow
171	C₂²×C₄₃	—	2	8	no	—
172	C₂²×C₄₃	—	2	2	no	—
173	C₂²×C₄₃	—	2	2	no	—
174	C₂²×C₄₃	C₂×C₄×Q₈	1	4	yes	—
175	C₂²×C₄₃	C₂×C₄×Q₈	1	2	yes	—
176	C₂²×C₄₃	C₂×#131	1	2	yes	—
177	C₂²×C₄₃	#568	1	2	yes	—
178	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
179	C₄×C₄₃	—	2	2	no	—
180	C₄×C₄₃	—	2	2	no	—
181	C₄×C₄₃	—	2	2	no	—
182	C₄×C₄₃	C₂×C₄×Q₈	1	2	yes	—
183	C₄×C₄₃	C₂×C₄×Q₈	1	4	yes	—
184	C₄×C₄₃	C₂×#131	1	4	yes	—
185	C₄×C₄₃	C₂³×Q₈	1	1	yes	characteristic
186	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
187	Dic₄₃	—	2	8	no	—
188	Dic₄₃	—	2	8	no	—
189	C₂×#533	—	43	1	no	—
190	#2962	—	43	16	no	—
191	C₂×#446	—	43	4	no	—
192	C₂×#446	—	43	2	no	—
193	C₂×C₈×Q₈	—	43	2	no	—
194	C₂×#424	—	43	2	no	—
195	C₂²×C₄⋊C₈	—	43	1	no	—
196	C₂×#405	—	43	2	no	—
197	C₂×C₄×M₁₆	D₄₃	1	1	yes	characteristic
198	C₂×C₄₃	—	2	4	no	—
199	C₂×C₄₃	#2962	1	4	yes	complemented
200	C₂×C₄₃	C₂²×C₄×Q₈	1	1	yes	characteristic
201	C₂×C₄₃	C₂²×#131	1	1	yes	characteristic
202	C₂×C₄₃	C₂×#568	1	1	yes	characteristic
203	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
204	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
205	C₂³×C₈	—	43	2	no	—
206	#533	—	43	8	no	—
207	#533	—	43	8	no	—
208	C₂×C₄⋊Q₈	—	43	1	no	—
209	C₂×C₄⋊Q₈	—	43	1	no	—
210	C₂×#125	—	43	2	no	—
211	C₂×C₂²⋊Q₈	—	43	2	no	—
212	C₂×C₂²⋊Q₈	—	43	2	no	—
213	C₂×C₄×Q₈	—	43	2	no	—
214	C₂×C₄×Q₈	—	43	2	no	—
215	C₂×#117	—	43	2	no	—
216	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
217	#446	—	43	32	no	—
218	#446	—	43	16	no	—
219	C₈×Q₈	—	43	16	no	—
220	#424	—	43	16	no	—
221	C₂×C₄⋊C₈	—	43	4	no	—
222	C₂×C₄⋊C₈	—	43	4	no	—
223	C₂×C₄⋊C₈	—	43	1	no	—
224	C₂×C₄⋊C₈	—	43	1	no	—
225	C₂×C₄⋊C₈	—	43	2	no	—
226	C₂×C₄⋊C₈	—	43	8	no	—
227	#405	—	43	16	no	—
228	C₄×M₁₆	C₂×D₄₃	1	8	yes	—
229	C₂×#97	—	43	4	no	—
230	C₂×#97	C₂×D₄₃	1	2	yes	—
231	C₂×C₄×C₈	—	43	4	no	—
232	C₂×C₄×C₈	C₂×D₄₃	1	2	yes	—
233	C₄₃	C₂×#2962	1	1	yes	characteristic, complemented, Sylow
234	C₂²×Q₈	—	43	2	no	—
235	C₂²×Q₈	—	43	2	no	—
236	C₂³×C₄	C₄×D₄₃	1	1	yes	characteristic
237	C₂³×C₄	C₄×D₄₃	1	1	yes	characteristic
238	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
239	C₂×M₁₆	—	2	4	no	—
240	C₂×M₁₆	Dic₈₆	1	8	yes	complemented
241	C₂×M₁₆	C₂²×D₄₃	1	4	yes	—
242	C₂×M₁₆	C₂²×D₄₃	1	4	yes	—
243	C₂²×C₈	—	43	8	no	—
244	C₂²×C₈	—	43	2	no	—
245	C₂²×C₈	—	43	2	no	—
246	C₂²×C₈	—	86	8	no	—
247	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
248	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
249	C₄⋊Q₈	—	43	8	no	—
250	C₄⋊Q₈	—	43	8	no	—
251	#125	—	43	16	no	—
252	C₂²⋊Q₈	—	43	16	no	—
253	C₂²⋊Q₈	—	43	16	no	—
254	C₄×Q₈	—	43	8	no	—
255	C₄×Q₈	—	43	8	no	—
256	C₄×Q₈	—	43	8	no	—
257	C₄×Q₈	—	43	8	no	—
258	#117	—	43	8	no	—
259	#117	—	43	8	no	—
260	C₂×C₄⋊C₄	—	43	2	no	—
261	C₂×C₄⋊C₄	—	43	2	no	—
262	C₂×C₄⋊C₄	—	43	4	no	—
263	C₂×C₄⋊C₄	—	43	4	no	—
264	C₂×C₄⋊C₄	—	43	2	no	—
265	C₂×C₄⋊C₄	—	43	2	no	—
266	C₂×C₂²⋊C₄	—	43	4	no	—
267	C₂×C₄²	—	43	4	no	—
268	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
269	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
270	C₂×C₄²	C₄×D₄₃	1	4	yes	—
271	C₂×C₄²	C₂²×D₄₃	1	4	yes	—
272	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
273	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
274	C₄⋊C₈	—	43	16	no	—
275	C₄⋊C₈	—	43	16	no	—
276	C₄⋊C₈	—	43	4	no	—
277	C₄⋊C₈	—	43	4	no	—
278	C₄⋊C₈	—	43	8	no	—
279	#97	—	43	16	no	—
280	#97	C₂²×D₄₃	1	8	yes	—
281	C₄×C₈	—	43	16	no	—
282	C₄×C₈	C₂²×D₄₃	1	8	yes	—
283	C₂⁴	C₂×C₄×D₄₃	1	1	yes	characteristic
284	C₂×Q₈	—	43	8	no	—
285	C₂×Q₈	—	43	8	no	—
286	C₂×Q₈	—	86	8	no	—
287	C₂×Q₈	—	172	4	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	4	2	no	—
290	C₂²×C₄	—	43	4	no	—
291	C₂²×C₄	—	43	4	no	—
292	C₂²×C₄	C₂×Dic₈₆	1	4	yes	—
293	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
294	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
295	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
296	C₂²×C₄	C₂×C₄×D₄₃	1	4	yes	—
297	C₂²×C₄	C₂×C₄×D₄₃	1	4	yes	—
298	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
300	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
301	C₂²×C₄	#10621898	1	4	yes	—
302	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
303	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
304	M₁₆	—	2	8	no	—
305	M₁₆	C₂×Dic₈₆	1	16	yes	complemented
306	C₂×C₈	—	2	4	no	—
307	C₂×C₈	—	43	4	no	—
308	C₂×C₈	—	43	4	no	—
309	C₂×C₈	—	86	4	no	—
310	C₂×C₈	—	86	4	no	—
311	C₂×C₈	—	86	16	no	—
312	C₂×C₈	C₂×Dic₈₆	1	8	yes	—
313	C₂×C₈	C₂³×D₄₃	1	4	yes	—
314	C₂×C₈	C₂³×D₄₃	1	4	yes	—
315	C₄⋊C₄	—	43	8	no	—
316	C₄⋊C₄	—	43	8	no	—
317	C₄⋊C₄	—	43	16	no	—
318	C₄⋊C₄	—	43	16	no	—
319	C₄⋊C₄	—	43	8	no	—
320	C₄⋊C₄	—	43	8	no	—
321	C₂²⋊C₄	—	43	16	no	—
322	C₄²	—	43	8	no	—
323	C₄²	—	43	8	no	—
324	C₄²	C₂×C₄×D₄₃	1	2	yes	—
325	C₄²	C₂×C₄×D₄₃	1	2	yes	—
326	C₄²	C₂×C₄×D₄₃	1	4	yes	—
327	C₄²	C₂×C₄×D₄₃	1	4	yes	—
328	C₄²	C₂³×D₄₃	1	2	yes	—
329	C₄²	C₂³×D₄₃	1	2	yes	—
330	C₂³	—	2	2	no	—
331	C₂³	—	2	2	no	—
332	C₂³	C₄×Dic₈₆	1	4	yes	—
333	C₂³	C₂²×C₄×D₄₃	1	2	yes	—
334	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
335	Q₈	—	86	16	no	—
336	Q₈	—	172	8	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	8	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	43	8	no	—
343	C₂×C₄	—	43	8	no	—
344	C₂×C₄	—	86	8	no	—
345	C₂×C₄	—	86	8	no	—
346	C₂×C₄	C₄×Dic₈₆	1	8	yes	—
347	C₂×C₄	C₄×Dic₈₆	1	4	yes	—
348	C₂×C₄	#13063333	1	4	yes	—
349	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
350	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
351	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
352	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
353	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
354	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
355	C₂×C₄	C₂²×Dic₈₆	1	2	yes	—
356	C₂×C₄	C₂²×Dic₈₆	1	4	yes	—
357	C₂×C₄	C₂×#10621898	1	2	yes	—
358	C₂×C₄	C₂×#10621898	1	4	yes	—
359	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
360	C₈	—	2	4	no	—
361	C₈	—	86	4	no	—
362	C₈	—	86	4	no	—
363	C₈	C₂²×Dic₈₆	1	8	yes	—
364	C₂²	—	2	8	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	C₂×C₄×Dic₈₆	1	4	yes	—
368	C₂²	C₂×C₄×Dic₈₆	1	2	yes	—
369	C₂²	C₂×#13063333	1	2	yes	—
370	C₂²	#14583665	1	2	yes	—
371	C₂²	C₂³×C₄×D₄₃	1	1	yes	characteristic
372	C₄	—	2	2	no	—
373	C₄	—	2	2	no	—
374	C₄	—	2	2	no	—
375	C₄	—	86	8	no	—
376	C₄	—	86	8	no	—
377	C₄	C₂×C₄×Dic₈₆	1	2	yes	—
378	C₄	C₂×C₄×Dic₈₆	1	4	yes	—
379	C₄	C₂×#13063333	1	4	yes	—
380	C₄	C₂³×Dic₈₆	1	1	yes	characteristic
381	C₄	C₂²×#10621898	1	1	yes	characteristic
382	C₂	—	2	4	no	—
383	C₂	#19143542	1	4	yes	direct product factor
384	C₂	C₂²×C₄×Dic₈₆	1	1	yes	characteristic
385	C₂	C₂²×#13063333	1	1	yes	characteristic
386	C₂	C₂×#14583665	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₄₃
commutator	C₂²×C₄₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₂×C₄×M₁₆×C₄₃	C₂
socle	C₂³×C₄₃	C₂³×C₄
prime radical	C₂⁴×C₄₃	C₂²×C₄
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	C₂×C₄×M₁₆	D₄₃
hypocenter	C₄₃	C₂×#2962
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
2. #19143542	C₂	direct (N × H)
3. C₂×#14583029	C₂	semidirect
4. C₂×#14583027	C₂	semidirect
5. C₂×C₈×Dic₈₆	C₂	semidirect
21. #14583029	C₂²	semidirect
22. #14583027	C₂²	semidirect
23. C₈×Dic₈₆	C₂²	semidirect
76. C₂×M₁₆×C₄₃	Q₈	semidirect
111. M₁₆×C₄₃	C₂×Q₈	semidirect
199. C₂×C₄₃	#2962	semidirect
233. C₄₃	C₂×#2962	semidirect
240. C₂×M₁₆	Dic₈₆	semidirect
305. M₁₆	C₂×Dic₈₆	semidirect
383. C₂	#19143542	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×#14583456	2
#19143542	2
C₂×#14583029	2
C₂×#14583027	2
C₂×C₈×Dic₈₆	2
C₂×#14582927	2
C₂²×C₄⋊(C₄₃⋊C₈)	2
C₂×#14582857	2
C₂×C₄×M₁₆×C₄₃	2
C₂×#2962	43

Subgroups — C2×#19143542 #25960977

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19143542 #25960977