Subgroups — C₂×#19133460 #25066153

Order 11008.

838 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582977	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#19133460	C₂	1	8	yes	maximal, direct product factor
4	C₂×#14582650	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#14582621	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₈×C₄₃	C₂	1	1	yes	maximal, characteristic
9	C₂²×#10621877	—	2	1	no	—
10	C₂³×C₄₃⋊C₈	—	2	1	no	—
11	#14582977	—	2	2	no	—
12	#14582977	C₂²	1	4	yes	complemented
13	D₄×C₄₃⋊C₈	—	2	2	no	—
14	D₄×C₄₃⋊C₈	C₂²	1	4	yes	complemented
15	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
18	C₂×C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
19	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
21	#14582650	C₂²	1	4	yes	complemented
22	D₄⋊(C₄₃⋊C₈)	C₂²	1	4	yes	complemented
23	D₄⋊(C₄₃⋊C₈)	C₂²	1	4	yes	complemented
24	#14582621	C₂²	1	4	yes	complemented
25	C₂²×D₈×C₄₃	C₄	1	1	yes	characteristic
26	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
28	C₄×D₈×C₄₃	C₄	1	4	yes	—
29	C₄×D₈×C₄₃	C₂²	1	4	yes	—
30	C₂×#107×C₄₃	C₄	1	1	yes	characteristic
31	C₂×#102×C₄₃	C₄	1	1	yes	characteristic
32	C₂×#102×C₄₃	C₄	1	1	yes	characteristic
33	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
34	C₂×#10621877	—	2	4	no	—
35	C₂×#10621877	—	4	4	no	—
36	C₂²×C₄₃⋊C₈	—	2	1	no	—
37	C₂²×C₄₃⋊C₈	—	2	1	no	—
38	C₂²×C₄₃⋊C₈	—	2	1	no	—
39	C₂²×C₄₃⋊C₈	—	2	4	no	—
40	C₂²×C₄₃⋊C₈	—	4	4	no	—
41	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
42	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
43	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
44	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
45	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
46	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
47	C₂²⋊(C₄₃⋊C₈)	—	2	4	no	—
48	C₂²⋊(C₄₃⋊C₈)	—	2	4	no	—
49	C₄×C₄₃⋊C₈	—	2	1	no	—
50	C₄×C₄₃⋊C₈	D₄	1	2	yes	—
51	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
52	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
53	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
54	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
55	C₂³×C₄×C₄₃	—	2	1	no	—
56	C₂³×C₄×C₄₃	—	2	1	no	—
57	C₂×D₈×C₄₃	—	2	4	no	—
58	C₂×D₈×C₄₃	C₂×C₄	1	4	yes	—
59	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
61	C₄×D₄×C₄₃	—	2	1	no	—
62	C₄×D₄×C₄₃	—	2	1	no	—
63	C₄×D₄×C₄₃	—	2	1	no	—
64	C₄×D₄×C₄₃	—	2	1	no	—
65	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
66	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
67	C₄×D₄×C₄₃	C₂³	1	2	yes	—
68	C₄×D₄×C₄₃	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
71	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
73	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
74	#107×C₄₃	C₂×C₄	1	4	yes	—
75	#102×C₄₃	C₂×C₄	1	4	yes	—
76	#102×C₄₃	C₂×C₄	1	4	yes	—
77	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
78	C₄×C₈×C₄₃	C₂³	1	2	yes	—
79	C₂⁴×C₄₃	—	2	1	no	—
80	C₂⁴×C₄₃	—	2	1	no	—
81	C₂×D₄×C₄₃	—	2	1	no	—
82	C₂×D₄×C₄₃	—	2	1	no	—
83	C₂×D₄×C₄₃	—	2	2	no	—
84	C₂×D₄×C₄₃	—	2	2	no	—
85	C₂×D₄×C₄₃	—	2	2	no	—
86	C₂×D₄×C₄₃	M₁₆	1	4	yes	complemented
87	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
88	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₄₃	—	2	2	no	—
90	C₂²×C₄×C₄₃	—	2	2	no	—
91	C₂²×C₄×C₄₃	—	2	2	no	—
92	C₂²×C₄×C₄₃	—	2	2	no	—
93	C₂²×C₄×C₄₃	—	2	1	no	—
94	C₂²×C₄×C₄₃	—	2	1	no	—
95	C₂²×C₄×C₄₃	—	4	2	no	—
96	C₂²×C₄×C₄₃	—	4	2	no	—
97	C₂²×C₄×C₄₃	—	4	2	no	—
98	C₂²×C₄×C₄₃	—	4	2	no	—
99	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
102	D₈×C₄₃	—	2	8	no	—
103	C₂×C₈×C₄₃	—	2	2	no	—
104	C₂×C₈×C₄₃	—	2	2	no	—
105	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
106	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
107	C₄⋊C₄×C₄₃	—	2	1	no	—
108	C₄⋊C₄×C₄₃	—	2	1	no	—
109	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
110	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
111	C₂²⋊C₄×C₄₃	—	2	2	no	—
112	C₂²⋊C₄×C₄₃	—	2	2	no	—
113	C₂²⋊C₄×C₄₃	—	2	2	no	—
114	C₂²⋊C₄×C₄₃	—	2	2	no	—
115	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₄₃	#41	1	1	yes	characteristic
118	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
119	#10621877	—	4	8	no	—
120	C₂×C₄₃⋊C₈	—	2	4	no	—
121	C₂×C₄₃⋊C₈	—	2	2	no	—
122	C₂×C₄₃⋊C₈	—	2	2	no	—
123	C₂×C₄₃⋊C₈	—	2	2	no	—
124	C₂×C₄₃⋊C₈	—	2	2	no	—
125	C₂×C₄₃⋊C₈	—	2	2	no	—
126	C₂×C₄₃⋊C₈	—	4	8	no	—
127	C₂×C₄₃⋊C₈	—	4	2	no	—
128	C₂×C₄₃⋊C₈	—	4	2	no	—
129	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
130	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
131	C₂³×C₄₃	—	2	2	no	—
132	C₂³×C₄₃	—	2	4	no	—
133	C₂³×C₄₃	—	2	2	no	—
134	C₂³×C₄₃	—	4	2	no	—
135	C₂³×C₄₃	—	4	2	no	—
136	C₂³×C₄₃	—	4	2	no	—
137	C₂³×C₄₃	—	4	2	no	—
138	C₂³×C₄₃	—	4	2	no	—
139	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
140	D₄×C₄₃	—	2	2	no	—
141	D₄×C₄₃	—	2	2	no	—
142	D₄×C₄₃	—	2	2	no	—
143	D₄×C₄₃	—	2	4	no	—
144	D₄×C₄₃	—	4	2	no	—
145	D₄×C₄₃	C₂×M₁₆	1	4	yes	complemented
146	C₂×C₄×C₄₃	—	2	2	no	—
147	C₂×C₄×C₄₃	—	2	2	no	—
148	C₂×C₄×C₄₃	—	2	2	no	—
149	C₂×C₄×C₄₃	—	4	2	no	—
150	C₂×C₄×C₄₃	—	4	2	no	—
151	C₂×C₄×C₄₃	—	4	2	no	—
152	C₂×C₄×C₄₃	—	4	2	no	—
153	C₂×C₄×C₄₃	—	4	2	no	—
154	C₂×C₄×C₄₃	—	4	2	no	—
155	C₂×C₄×C₄₃	—	4	4	no	—
156	C₂×C₄×C₄₃	—	4	4	no	—
157	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₄₃	C₂×M₁₆	1	2	yes	—
161	C₂×C₄×C₄₃	#131	1	2	yes	—
162	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
163	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
164	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
167	C₈×C₄₃	—	2	2	no	—
168	C₈×C₄₃	—	2	2	no	—
169	C₄₃⋊C₈	—	2	4	no	—
170	C₄₃⋊C₈	—	2	2	no	—
171	C₄₃⋊C₈	—	2	2	no	—
172	C₄₃⋊C₈	—	4	2	no	—
173	C₄₃⋊C₈	—	4	2	no	—
174	C₂×#1586	—	43	1	no	maximal, Sylow
175	C₂²×C₄₃	—	2	4	no	—
176	C₂²×C₄₃	—	4	8	no	—
177	C₂²×C₄₃	—	4	2	no	—
178	C₂²×C₄₃	—	4	2	no	—
179	C₂²×C₄₃	—	4	2	no	—
180	C₂²×C₄₃	—	4	2	no	—
181	C₂²×C₄₃	—	4	2	no	—
182	C₂²×C₄₃	—	8	4	no	—
183	C₂²×C₄₃	#435	1	2	yes	—
184	C₂²×C₄₃	#442	1	2	yes	—
185	C₂²×C₄₃	#443	1	2	yes	—
186	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
187	C₄×C₄₃	—	2	1	no	—
188	C₄×C₄₃	—	2	1	no	—
189	C₄×C₄₃	—	4	2	no	—
190	C₄×C₄₃	—	4	2	no	—
191	C₄×C₄₃	#435	1	2	yes	—
192	C₄×C₄₃	#442	1	2	yes	—
193	C₄×C₄₃	C₂²×M₁₆	1	1	yes	characteristic
194	C₄×C₄₃	C₂×#131	1	1	yes	characteristic
195	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
196	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
197	C₂×C₄×D₈	D₄₃	1	1	yes	characteristic
198	C₂×#436	—	43	1	no	—
199	C₂×C₈×D₄	—	43	1	no	—
200	#1586	—	43	8	no	—
201	C₂×#334	—	43	1	no	—
202	C₂×D₄⋊C₈	—	43	1	no	—
203	C₂×D₄⋊C₈	—	43	1	no	—
204	C₂×#322	—	43	1	no	—
205	C₂×C₄₃	—	4	4	no	—
206	C₂×C₄₃	—	8	2	no	—
207	C₂×C₄₃	#1586	1	4	yes	complemented
208	C₂×C₄₃	C₂×#435	1	1	yes	characteristic
209	C₂×C₄₃	C₂×#442	1	1	yes	characteristic
210	C₂×C₄₃	C₂×#443	1	1	yes	characteristic
211	C₂²×D₈	Dic₄₃	1	1	yes	characteristic
212	C₂²×M₁₆	—	86	1	no	—
213	C₂³×C₈	—	86	1	no	—
214	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
215	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
216	C₄×D₈	Dic₄₃	1	4	yes	—
217	C₄×D₈	C₂×D₄₃	1	4	yes	—
218	#436	—	43	4	no	—
219	#436	—	86	2	no	—
220	C₈×D₄	—	43	4	no	—
221	C₈×D₄	—	86	2	no	—
222	C₂×#107	Dic₄₃	1	1	yes	characteristic
223	C₂×C₄⋊C₈	—	43	1	no	—
224	C₂×C₄⋊C₈	—	43	1	no	—
225	C₂×#102	Dic₄₃	1	1	yes	characteristic
226	C₂×#102	Dic₄₃	1	1	yes	characteristic
227	C₂×C₂²⋊C₈	—	86	1	no	—
228	C₂×C₂²⋊C₈	—	86	1	no	—
229	C₂×C₄×C₈	—	43	1	no	—
230	C₂×C₄×C₈	—	43	1	no	—
231	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
232	#334	—	43	4	no	—
233	D₄⋊C₈	—	43	4	no	—
234	D₄⋊C₈	—	43	4	no	—
235	#322	—	43	4	no	—
236	C₄₃	C₂×#1586	1	1	yes	characteristic, complemented, Sylow
237	C₂²×D₄	C₂×Dic₄₃	1	1	yes	characteristic
238	C₂²×D₄	C₂×Dic₄₃	1	1	yes	characteristic
239	C₂³×C₄	—	2	1	no	—
240	C₂³×C₄	—	2	1	no	—
241	C₂×D₈	—	2	4	no	—
242	C₂×D₈	C₂×Dic₄₃	1	4	yes	—
243	C₂×M₁₆	—	86	4	no	—
244	C₂×M₁₆	—	172	4	no	—
245	C₂²×C₈	—	43	1	no	—
246	C₂²×C₈	—	43	1	no	—
247	C₂²×C₈	—	86	4	no	—
248	C₂²×C₈	—	86	1	no	—
249	C₂²×C₈	—	86	1	no	—
250	C₂²×C₈	—	86	1	no	—
251	C₂²×C₈	—	172	4	no	—
252	C₂²×C₈	C₂×Dic₄₃	1	1	yes	characteristic
253	C₂²×C₈	C₂×Dic₄₃	1	1	yes	characteristic
254	C₄×D₄	—	2	1	no	—
255	C₄×D₄	—	2	1	no	—
256	C₄×D₄	—	2	1	no	—
257	C₄×D₄	—	2	1	no	—
258	C₄×D₄	C₂×Dic₄₃	1	2	yes	—
259	C₄×D₄	C₂×Dic₄₃	1	2	yes	—
260	C₄×D₄	C₂²×D₄₃	1	2	yes	—
261	C₄×D₄	C₂²×D₄₃	1	2	yes	—
262	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
264	C₂×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₂²⋊C₄	—	2	1	no	—
266	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
267	#107	C₂×Dic₄₃	1	4	yes	—
268	C₄⋊C₈	—	43	2	no	—
269	C₄⋊C₈	—	43	2	no	—
270	C₄⋊C₈	—	86	1	no	—
271	C₄⋊C₈	—	86	1	no	—
272	#102	C₂×Dic₄₃	1	4	yes	—
273	#102	C₂×Dic₄₃	1	4	yes	—
274	C₂²⋊C₈	—	86	4	no	—
275	C₂²⋊C₈	—	86	4	no	—
276	C₄×C₈	—	43	2	no	—
277	C₄×C₈	—	43	2	no	—
278	C₄×C₈	—	43	2	no	—
279	C₄×C₈	—	86	1	no	—
280	C₄×C₈	C₂×Dic₄₃	1	2	yes	—
281	C₄×C₈	C₂²×D₄₃	1	2	yes	—
282	C₂⁴	—	2	1	no	—
283	C₂⁴	—	2	1	no	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	—	2	1	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	#10621877	1	4	yes	complemented
290	C₂×D₄	C₂²×Dic₄₃	1	2	yes	—
291	C₂×D₄	C₂²×Dic₄₃	1	2	yes	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	4	2	no	—
299	C₂²×C₄	—	4	2	no	—
300	C₂²×C₄	—	4	2	no	—
301	C₂²×C₄	—	4	2	no	—
302	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
303	C₂²×C₄	#10621900	1	1	yes	characteristic
304	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
305	D₈	—	2	8	no	—
306	M₁₆	—	172	8	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	43	2	no	—
310	C₂×C₈	—	43	2	no	—
311	C₂×C₈	—	86	4	no	—
312	C₂×C₈	—	86	2	no	—
313	C₂×C₈	—	86	2	no	—
314	C₂×C₈	—	86	2	no	—
315	C₂×C₈	—	86	2	no	—
316	C₂×C₈	—	86	2	no	—
317	C₂×C₈	—	172	8	no	—
318	C₂×C₈	—	172	2	no	—
319	C₂×C₈	—	172	2	no	—
320	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
321	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	C₂²×Dic₄₃	1	2	yes	—
325	C₄⋊C₄	C₂²×Dic₄₃	1	2	yes	—
326	C₂²⋊C₄	—	2	2	no	—
327	C₂²⋊C₄	—	2	2	no	—
328	C₂²⋊C₄	—	2	2	no	—
329	C₂²⋊C₄	—	2	2	no	—
330	C₄²	D₄×D₄₃	1	1	yes	characteristic
331	C₄²	#10621900	1	1	yes	characteristic
332	C₄²	C₂²×Dic₄₃	1	1	yes	characteristic
333	C₄²	C₂³×D₄₃	1	1	yes	characteristic
334	C₂³	—	2	2	no	—
335	C₂³	—	2	4	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	4	2	no	—
338	C₂³	—	4	2	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	D₄×Dic₄₃	1	1	yes	characteristic
343	D₄	—	2	2	no	—
344	D₄	—	2	2	no	—
345	D₄	—	2	2	no	—
346	D₄	—	2	4	no	—
347	D₄	—	4	2	no	—
348	D₄	C₂×#10621877	1	4	yes	complemented
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
361	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
362	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
363	C₂×C₄	C₂×#10621877	1	2	yes	—
364	C₂×C₄	#13063332	1	2	yes	—
365	C₂×C₄	#13063349	1	2	yes	—
366	C₂×C₄	#13063349	1	2	yes	—
367	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
368	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
369	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
370	C₈	—	2	2	no	—
371	C₈	—	2	2	no	—
372	C₈	—	86	4	no	—
373	C₈	—	86	2	no	—
374	C₈	—	86	2	no	—
375	C₈	—	172	2	no	—
376	C₈	—	172	2	no	—
377	C₂²	—	2	4	no	—
378	C₂²	—	4	8	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	4	2	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	8	4	no	—
385	C₂²	#14582971	1	2	yes	—
386	C₂²	#14583011	1	2	yes	—
387	C₂²	#14583016	1	2	yes	—
388	C₂²	C₂×D₄×Dic₄₃	1	1	yes	characteristic
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	2	no	—
393	C₄	#14582971	1	2	yes	—
394	C₄	#14583011	1	2	yes	—
395	C₄	C₂²×#10621877	1	1	yes	characteristic
396	C₄	C₂×#13063332	1	1	yes	characteristic
397	C₄	C₂×#13063349	1	1	yes	characteristic
398	C₄	C₂×#13063349	1	1	yes	characteristic
399	C₂	—	4	4	no	—
400	C₂	—	8	2	no	—
401	C₂	#19133460	1	4	yes	direct product factor
402	C₂	C₂×#14582971	1	1	yes	characteristic
403	C₂	C₂×#14583011	1	1	yes	characteristic
404	C₂	C₂×#14583016	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₂×C₄×D₈×C₄₃	C₂
socle	C₂³×C₄₃	C₄×D₄
prime radical	C₂²×D₈×C₄₃	C₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	C₂×C₄×D₈	D₄₃
hypocenter	C₄₃	C₂×#1586
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×D₈

Complements

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

N	H ≅ G/N	type
1. C₂×#14582977	C₂	semidirect
2. C₂×D₄×C₄₃⋊C₈	C₂	semidirect
3. #19133460	C₂	direct (N × H)
4. C₂×#14582650	C₂	semidirect
5. C₂×D₄⋊(C₄₃⋊C₈)	C₂	semidirect
6. C₂×D₄⋊(C₄₃⋊C₈)	C₂	semidirect
7. C₂×#14582621	C₂	semidirect
12. #14582977	C₂²	semidirect
14. D₄×C₄₃⋊C₈	C₂²	semidirect
21. #14582650	C₂²	semidirect
22. D₄⋊(C₄₃⋊C₈)	C₂²	semidirect
23. D₄⋊(C₄₃⋊C₈)	C₂²	semidirect
24. #14582621	C₂²	semidirect
86. C₂×D₄×C₄₃	M₁₆	semidirect
145. D₄×C₄₃	C₂×M₁₆	semidirect
207. C₂×C₄₃	#1586	semidirect
236. C₄₃	C₂×#1586	semidirect
289. C₂×D₄	#10621877	semidirect
348. D₄	C₂×#10621877	semidirect
401. C₂	#19133460	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×#14582977	2
C₂×D₄×C₄₃⋊C₈	2
#19133460	2
C₂×#14582650	2
C₂×D₄⋊(C₄₃⋊C₈)	2
C₂×#14582621	2
C₂×C₄×D₈×C₄₃	2
C₂×#1586	43

Subgroups — C2×#19133460 #25066153

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19133460 #25066153