Subgroups — C₂×#19133357 #25065603

Order 11008.

766 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582955	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×D₄₃	C₂	1	1	yes	maximal, characteristic
3	#19133357	C₂	1	8	yes	maximal, direct product factor
4	C₂×#14582652	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#14582649	C₂	1	2	yes	maximal, complemented
6	C₂×C₄₃×#335	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₈×D₄₃	C₄	1	1	yes	characteristic
8	C₂²×C₈×D₄₃	C₄	1	1	yes	characteristic
9	C₂×C₄²×D₄₃	C₂²	1	1	yes	characteristic
10	#14582955	—	2	4	no	—
11	#14582955	C₂²	1	8	yes	—
12	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
13	C₂×(C₂×D₄₃)⋊C₈	—	2	2	no	—
14	C₂×#13063235	—	2	2	no	—
15	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₈×Dic₄₃	C₄	1	1	yes	characteristic
17	C₂×C₈×Dic₄₃	C₄	1	1	yes	characteristic
18	C₄×C₈×D₄₃	C₄	1	4	yes	—
19	C₄×C₈×D₄₃	C₂²	1	4	yes	—
20	#14582652	C₂²	1	4	yes	complemented
21	#14582649	C₂²	1	8	yes	complemented
22	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₄₃×#335	C₂²	1	4	yes	complemented
25	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₄×D₄₃	D₄	1	1	yes	characteristic
27	C₂²×C₄×D₄₃	Q₈	1	1	yes	characteristic
28	C₂²×C₄₃⋊C₈	—	2	2	no	—
29	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
31	C₂×C₈×D₄₃	—	2	4	no	—
32	C₂×C₈×D₄₃	—	2	4	no	—
33	C₂×C₈×D₄₃	C₂×C₄	1	4	yes	—
34	C₂×C₈×D₄₃	C₂×C₄	1	4	yes	—
35	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
37	C₂×C₄×Dic₄₃	Q₈	1	1	yes	characteristic
38	C₄²×D₄₃	C₂×C₄	1	2	yes	—
39	C₄²×D₄₃	D₄	1	2	yes	—
40	C₄²×D₄₃	Q₈	1	2	yes	—
41	C₄²×D₄₃	C₂³	1	2	yes	—
42	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
43	C₄⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
44	(C₂×D₄₃)⋊C₈	—	2	8	no	—
45	#13063235	—	2	8	no	—
46	C₄×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
47	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
48	C₈×Dic₄₃	C₂×C₄	1	4	yes	—
49	C₈×Dic₄₃	C₂×C₄	1	4	yes	—
50	C₂²×C₈×C₄₃	—	2	2	no	—
51	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
54	C₄⋊C₈×C₄₃	—	2	2	no	—
55	C₄⋊C₈×C₄₃	C₂³	1	4	yes	—
56	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
57	C₄×C₈×C₄₃	C₂³	1	2	yes	—
58	C₂³×D₄₃	C₄⋊C₄	1	1	yes	characteristic
59	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
60	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
61	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
62	C₂²×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
63	C₂²×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
64	C₂²×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
65	C₂×C₄×D₄₃	—	2	2	no	—
66	C₂×C₄×D₄₃	—	2	2	no	—
67	C₂×C₄×D₄₃	—	2	2	no	—
68	C₂×C₄×D₄₃	—	2	2	no	—
69	C₂×C₄×D₄₃	—	2	4	no	—
70	C₂×C₄×D₄₃	C₄⋊C₄	1	2	yes	—
71	C₂×C₄×D₄₃	C₄⋊C₄	1	2	yes	—
72	C₂×C₄×D₄₃	C₄⋊C₄	1	2	yes	—
73	C₂×C₄×D₄₃	C₂²×C₄	1	2	yes	—
74	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
75	C₂×C₄×D₄₃	C₂×Q₈	1	2	yes	—
76	C₂×C₈×C₄₃	—	2	2	no	—
77	C₂×C₈×C₄₃	—	2	4	no	—
78	C₂×C₈×C₄₃	—	4	4	no	—
79	C₂×C₈×C₄₃	M₁₆	1	4	yes	—
80	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
81	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
82	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
83	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
84	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
85	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
86	C₄×Dic₄₃	C₄⋊C₄	1	2	yes	—
87	C₄×Dic₄₃	C₄⋊C₄	1	2	yes	—
88	C₄×Dic₄₃	C₄⋊C₄	1	2	yes	—
89	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
90	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
91	C₄×Dic₄₃	C₂×Q₈	1	2	yes	—
92	C₂×C₄₃⋊C₈	—	2	2	no	—
93	C₂×C₄₃⋊C₈	—	2	4	no	—
94	C₂×C₄₃⋊C₈	—	4	4	no	—
95	C₂×C₄₃⋊C₈	M₁₆	1	4	yes	—
96	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
97	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
98	C₈×D₄₃	—	2	8	no	—
99	C₈×D₄₃	—	2	8	no	—
100	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
101	C₂²×D₄₃	—	2	2	no	—
102	C₂²×D₄₃	—	2	2	no	—
103	C₂²×D₄₃	#108	1	4	yes	—
104	C₂²×D₄₃	C₂×C₄⋊C₄	1	2	yes	—
105	C₂×C₄×C₄₃	—	2	2	no	—
106	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
108	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
109	C₂×C₄×C₄₃	C₂×M₁₆	1	2	yes	—
110	C₂×C₄×C₄₃	C₂×M₁₆	1	2	yes	—
111	C₂×C₄×C₄₃	#135	1	2	yes	—
112	C₂×C₄×C₄₃	#135	1	2	yes	—
113	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
114	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
115	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
116	C₂×Dic₄₃	—	2	2	no	—
117	C₂×Dic₄₃	—	2	2	no	—
118	C₂×Dic₄₃	—	2	2	no	—
119	C₂×Dic₄₃	C₂×C₄⋊C₄	1	2	yes	—
120	C₂×Dic₄₃	C₂×C₄⋊C₄	1	2	yes	—
121	C₂×Dic₄₃	C₂×C₄⋊C₄	1	2	yes	—
122	C₄×D₄₃	—	2	4	no	—
123	C₄×D₄₃	—	2	4	no	—
124	C₄×D₄₃	—	2	2	no	—
125	C₄×D₄₃	—	2	2	no	—
126	C₄×D₄₃	—	2	2	no	—
127	C₄×D₄₃	—	2	2	no	—
128	C₄×D₄₃	—	2	4	no	—
129	C₄×D₄₃	—	2	4	no	—
130	C₈×C₄₃	—	2	2	no	—
131	C₈×C₄₃	—	4	4	no	—
132	C₈×C₄₃	C₂×M₁₆	1	4	yes	—
133	C₄₃⋊C₈	—	2	2	no	—
134	C₄₃⋊C₈	—	4	4	no	—
135	C₄₃⋊C₈	C₂×M₁₆	1	4	yes	—
136	C₂×#1568	—	43	1	no	maximal, Sylow
137	C₂²×C₄₃	#423	1	2	yes	—
138	C₂²×C₄₃	#427	1	2	yes	—
139	C₂²×C₄₃	C₂×#108	1	2	yes	—
140	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
141	C₂×D₄₃	—	2	8	no	—
142	C₂×D₄₃	—	2	2	no	—
143	C₂×D₄₃	—	2	2	no	—
144	C₂×D₄₃	C₂×#108	1	4	yes	—
145	C₄×C₄₃	—	2	1	no	—
146	C₄×C₄₃	—	2	1	no	—
147	C₄×C₄₃	#423	1	2	yes	—
148	C₄×C₄₃	#427	1	2	yes	—
149	C₄×C₄₃	C₂²×M₁₆	1	1	yes	characteristic
150	C₄×C₄₃	C₂²×M₁₆	1	1	yes	characteristic
151	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
152	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
153	Dic₄₃	—	2	2	no	—
154	Dic₄₃	—	2	2	no	—
155	Dic₄₃	—	2	2	no	—
156	C₂×#432	—	43	2	no	—
157	C₂²×C₄×C₈	—	43	1	no	—
158	#1568	—	43	8	no	—
159	C₂×#335	—	43	1	no	—
160	C₂×#335	D₄₃	1	1	yes	characteristic, complemented
161	C₂×#334	—	43	2	no	—
162	C₂×C₄₃	#1568	1	4	yes	complemented
163	C₂×C₄₃	C₂×#423	1	1	yes	characteristic
164	C₂×C₄₃	C₂×#427	1	1	yes	characteristic
165	C₂×C₄₃	C₂²×#108	1	1	yes	characteristic
166	D₄₃	—	2	4	no	—
167	C₂³×C₈	—	43	1	no	—
168	C₂³×C₈	—	43	1	no	—
169	C₂²×C₄²	—	43	1	no	—
170	#432	—	43	8	no	—
171	#432	—	86	4	no	—
172	C₂×C₄⋊C₈	—	43	2	no	—
173	C₂×C₄⋊C₈	C₂×D₄₃	1	2	yes	—
174	C₂×C₂²⋊C₈	—	86	2	no	—
175	C₂×#97	—	86	2	no	—
176	C₂×C₄×C₈	—	43	1	no	—
177	C₂×C₄×C₈	—	43	1	no	—
178	C₂×C₄×C₈	—	43	1	no	—
179	C₂×C₄×C₈	—	43	4	no	—
180	C₂×C₄×C₈	—	43	4	no	—
181	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
182	#335	—	43	4	no	—
183	#335	C₂×D₄₃	1	4	yes	complemented
184	#334	—	43	8	no	—
185	C₄₃	C₂×#1568	1	1	yes	characteristic, complemented, Sylow
186	C₂³×C₄	—	43	1	no	—
187	C₂³×C₄	—	43	1	no	—
188	C₂³×C₄	—	43	1	no	—
189	C₂²×C₈	—	2	2	no	—
190	C₂²×C₈	—	43	1	no	—
191	C₂²×C₈	—	43	1	no	—
192	C₂²×C₈	—	43	4	no	—
193	C₂²×C₈	—	43	4	no	—
194	C₂²×C₈	—	86	4	no	—
195	C₂²×C₈	—	86	4	no	—
196	C₂²×C₈	—	86	2	no	—
197	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
198	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
199	C₂×C₄²	—	43	1	no	—
200	C₂×C₄²	—	43	1	no	—
201	C₂×C₄²	—	43	1	no	—
202	C₂×C₄²	—	43	2	no	—
203	C₂×C₄²	—	43	2	no	—
204	C₂×C₄²	—	43	2	no	—
205	C₂×C₄²	—	43	2	no	—
206	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
207	C₄⋊C₈	—	2	2	no	—
208	C₄⋊C₈	—	43	4	no	—
209	C₄⋊C₈	—	86	2	no	—
210	C₄⋊C₈	C₂²×D₄₃	1	4	yes	—
211	C₂²⋊C₈	—	86	8	no	—
212	#97	—	86	8	no	—
213	C₄×C₈	—	43	4	no	—
214	C₄×C₈	—	43	4	no	—
215	C₄×C₈	—	43	2	no	—
216	C₄×C₈	—	43	2	no	—
217	C₄×C₈	C₄×D₄₃	1	2	yes	—
218	C₄×C₈	C₂²×D₄₃	1	2	yes	—
219	C₂⁴	—	43	1	no	—
220	C₂²×C₄	—	43	1	no	—
221	C₂²×C₄	—	43	1	no	—
222	C₂²×C₄	—	43	1	no	—
223	C₂²×C₄	—	43	2	no	—
224	C₂²×C₄	—	43	2	no	—
225	C₂²×C₄	—	43	2	no	—
226	C₂²×C₄	—	43	2	no	—
227	C₂²×C₄	—	43	2	no	—
228	C₂²×C₄	—	43	2	no	—
229	C₂²×C₄	—	86	4	no	—
230	C₂²×C₄	—	86	2	no	—
231	C₂²×C₄	—	86	2	no	—
232	C₂²×C₄	—	86	2	no	—
233	C₂²×C₄	—	86	2	no	—
234	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
235	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
236	C₂²×C₄	Q₈×D₄₃	1	1	yes	characteristic
237	C₂×C₈	—	2	2	no	—
238	C₂×C₈	—	2	4	no	—
239	C₂×C₈	—	4	4	no	—
240	C₂×C₈	—	43	4	no	—
241	C₂×C₈	—	43	2	no	—
242	C₂×C₈	—	43	2	no	—
243	C₂×C₈	—	86	8	no	—
244	C₂×C₈	—	86	2	no	—
245	C₂×C₈	—	86	8	no	—
246	C₂×C₈	—	86	4	no	—
247	C₂×C₈	—	172	4	no	—
248	C₂×C₈	#10621872	1	4	yes	—
249	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
250	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
251	C₄²	—	43	2	no	—
252	C₄²	—	43	2	no	—
253	C₄²	—	43	2	no	—
254	C₄²	—	43	2	no	—
255	C₄²	—	43	2	no	—
256	C₄²	—	43	2	no	—
257	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
258	C₄²	D₄×D₄₃	1	1	yes	characteristic
259	C₄²	Q₈×D₄₃	1	1	yes	characteristic
260	C₄²	C₂³×D₄₃	1	1	yes	characteristic
261	C₂³	—	43	2	no	—
262	C₂³	—	43	4	no	—
263	C₂³	—	86	2	no	—
264	C₂³	—	86	2	no	—
265	C₂³	C₄⋊C₄×D₄₃	1	1	yes	characteristic
266	C₂×C₄	—	2	2	no	—
267	C₂×C₄	—	43	2	no	—
268	C₂×C₄	—	43	2	no	—
269	C₂×C₄	—	43	2	no	—
270	C₂×C₄	—	86	4	no	—
271	C₂×C₄	—	86	4	no	—
272	C₂×C₄	—	86	2	no	—
273	C₂×C₄	—	86	2	no	—
274	C₂×C₄	—	86	2	no	—
275	C₂×C₄	—	86	2	no	—
276	C₂×C₄	—	86	2	no	—
277	C₂×C₄	—	86	2	no	—
278	C₂×C₄	—	86	2	no	—
279	C₂×C₄	—	86	4	no	—
280	C₂×C₄	—	86	4	no	—
281	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
282	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
283	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
284	C₂×C₄	M₁₆×D₄₃	1	2	yes	—
285	C₂×C₄	C₂×#10621872	1	2	yes	—
286	C₂×C₄	#13063344	1	2	yes	—
287	C₂×C₄	#13063348	1	2	yes	—
288	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
289	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
290	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
291	C₈	—	2	2	no	—
292	C₈	—	4	4	no	—
293	C₈	—	43	4	no	—
294	C₈	—	86	2	no	—
295	C₈	—	172	4	no	—
296	C₈	C₂×#10621872	1	4	yes	—
297	C₂²	—	43	4	no	—
298	C₂²	—	86	2	no	—
299	C₂²	—	86	8	no	—
300	C₂²	—	86	2	no	—
301	C₂²	#14582921	1	2	yes	—
302	C₂²	#14582936	1	2	yes	—
303	C₂²	#108×D₄₃	1	2	yes	—
304	C₂²	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
305	C₄	—	2	1	no	—
306	C₄	—	2	1	no	—
307	C₄	—	86	2	no	—
308	C₄	—	86	2	no	—
309	C₄	—	86	2	no	—
310	C₄	#14582921	1	2	yes	—
311	C₄	#14582936	1	2	yes	—
312	C₄	C₂×M₁₆×D₄₃	1	1	yes	characteristic
313	C₄	C₂²×#10621872	1	1	yes	characteristic
314	C₄	C₂×#13063344	1	1	yes	characteristic
315	C₄	C₂×#13063348	1	1	yes	characteristic
316	C₂	—	86	4	no	—
317	C₂	#19133357	1	4	yes	direct product factor
318	C₂	C₂×#14582921	1	1	yes	characteristic
319	C₂	C₂×#14582936	1	1	yes	characteristic
320	C₂	C₂×#108×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₂×C₄₃×#335	C₂
socle	C₂³×C₄₃	C₂×C₄⋊C₄
prime radical	C₂³×D₄₃	C₄⋊C₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	C₂×#335	D₄₃
hypocenter	C₄₃	C₂×#1568
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#335

Complements

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

N	H ≅ G/N	type
3. #19133357	C₂	direct (N × H)
4. C₂×#14582652	C₂	semidirect
5. C₂×#14582649	C₂	semidirect
6. C₂×C₄₃×#335	C₂	semidirect
20. #14582652	C₂²	semidirect
21. #14582649	C₂²	semidirect
24. C₄₃×#335	C₂²	semidirect
160. C₂×#335	D₄₃	semidirect
162. C₂×C₄₃	#1568	semidirect
183. #335	C₂×D₄₃	semidirect
185. C₄₃	C₂×#1568	semidirect
317. C₂	#19133357	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×#14582955	2
C₂×C₄×C₈×D₄₃	2
#19133357	2
C₂×#14582652	2
C₂×#14582649	2
C₂×C₄₃×#335	2
C₂×#1568	43

Subgroups — C2×#19133357 #25065603

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19133357 #25065603