Subgroups — C₂×#19136833 #25251905

Order 11008.

634 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583303	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14583284	C₂	1	1	yes	maximal, characteristic
3	#19136833	C₂	1	8	yes	maximal, direct product factor
4	C₂×#14582703	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#14582701	C₂	1	1	yes	maximal, characteristic
6	C₂×#14582699	C₂	1	1	yes	maximal, characteristic
7	C₂×#14582674	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₃×#358	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#10621884	—	2	1	no	—
10	C₂²×D₃₄₄	C₂²	1	1	yes	characteristic
11	C₂×#13063324	—	2	1	no	—
12	C₂×#13063314	—	2	1	no	—
13	C₂²×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
14	#14583303	—	2	2	no	—
15	#14583303	C₂²	1	4	yes	complemented
16	#14583284	—	2	2	no	—
17	#14583284	C₂²	1	4	yes	—
18	C₂×#13063259	C₂²	1	1	yes	characteristic
19	C₂×#13063258	—	2	1	no	—
20	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
21	#14582703	C₂²	1	4	yes	complemented
22	#14582701	C₂²	1	4	yes	—
23	#14582699	C₂²	1	4	yes	—
24	#14582674	C₂²	1	4	yes	complemented
25	C₂²×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
26	C₂²×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
28	C₄₃×#358	C₂²	1	4	yes	complemented
29	C₂²×Dic₈₆	—	4	1	no	—
30	C₂²×D₁₇₂	—	2	1	no	—
31	C₂×#10621884	—	2	4	no	—
32	C₂×#10621884	—	4	4	no	—
33	C₂×D₃₄₄	—	2	2	no	—
34	C₂×D₃₄₄	—	2	2	no	—
35	C₂×D₃₄₄	—	2	1	no	—
36	C₂×D₃₄₄	C₂³	1	2	yes	—
37	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
38	#13063324	—	2	4	no	—
39	#13063324	—	4	2	no	—
40	#13063314	—	2	4	no	—
41	#13063314	—	4	2	no	—
42	C₂×C₄⋊Dic₄₃	—	2	1	no	—
43	C₂×Dic₄₃⋊C₄	—	4	1	no	—
44	C₂×(C₂×D₄₃)⋊C₄	—	4	1	no	—
45	C₂×(C₂×D₄₃)⋊C₄	—	4	1	no	—
46	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
47	C₂×C₄₃⋊C₁₆	—	2	2	no	—
48	C₂×C₄₃⋊C₁₆	C₂³	1	2	yes	—
49	#13063259	—	2	1	no	—
50	#13063259	C₂³	1	2	yes	—
51	#13063258	—	2	4	no	—
52	C₈×Dic₄₃	D₄	1	2	yes	—
53	C₈×Dic₄₃	C₂³	1	2	yes	—
54	C₂²×Q₈×C₄₃	—	2	1	no	—
55	C₂×Q₁₆×C₄₃	—	2	1	no	—
56	C₂×Q₁₆×C₄₃	—	2	2	no	—
57	C₂×Q₁₆×C₄₃	—	2	2	no	—
58	C₂×Q₁₆×C₄₃	C₂³	1	2	yes	—
59	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
61	C₂×C₁₆×C₄₃	—	2	2	no	—
62	C₂×C₁₆×C₄₃	C₂³	1	2	yes	—
63	#107×C₄₃	—	2	1	no	—
64	#107×C₄₃	C₂³	1	2	yes	—
65	C₂³×D₄₃	—	4	1	no	—
66	C₂×Q₈×C₄₃	—	2	2	no	—
67	C₂×Q₈×C₄₃	—	4	1	no	—
68	C₂×Q₈×C₄₃	—	4	2	no	—
69	C₂×Q₈×C₄₃	—	4	2	no	—
70	C₂²×C₄×C₄₃	—	4	1	no	—
71	C₂²×C₄×C₄₃	—	4	1	no	—
72	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
73	C₂²×Dic₄₃	—	4	1	no	—
74	C₂²×Dic₄₃	D₈	1	1	yes	characteristic
75	C₂²×Dic₄₃	D₈	1	1	yes	characteristic
76	C₂×D₁₇₂	—	2	2	no	—
77	C₂×D₁₇₂	—	4	1	no	—
78	C₂×D₁₇₂	—	4	2	no	—
79	C₂×D₁₇₂	—	4	2	no	—
80	C₂×Dic₈₆	—	4	4	no	—
81	C₂×Dic₈₆	—	8	4	no	—
82	Q₁₆×C₄₃	—	2	2	no	—
83	Q₁₆×C₄₃	—	2	2	no	—
84	Q₁₆×C₄₃	—	4	2	no	—
85	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
86	C₂×C₈×C₄₃	#41	1	2	yes	—
87	C₂×C₈×C₄₃	#41	1	2	yes	—
88	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
89	C₄⋊C₄×C₄₃	—	2	2	no	—
90	C₄⋊C₄×C₄₃	—	4	1	no	—
91	#10621884	—	4	8	no	—
92	(C₂×D₄₃)⋊C₄	—	4	4	no	—
93	(C₂×D₄₃)⋊C₄	—	4	4	no	—
94	C₄⋊Dic₄₃	—	2	2	no	—
95	C₄⋊Dic₄₃	—	4	1	no	—
96	Dic₄₃⋊C₄	—	4	4	no	—
97	C₄×Dic₄₃	D₈	1	2	yes	—
98	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
99	C₂×C₄₃⋊C₈	SD₁₆	1	4	yes	—
100	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
101	D₃₄₄	—	2	2	no	—
102	D₃₄₄	—	2	2	no	—
103	D₃₄₄	—	4	2	no	—
104	C₁₆×C₄₃	—	2	2	no	—
105	C₄₃⋊C₁₆	—	2	2	no	—
106	C₂³×C₄₃	C₂×D₈	1	1	yes	characteristic
107	C₂²×D₄₃	—	4	2	no	—
108	C₂²×D₄₃	—	8	2	no	—
109	C₂²×D₄₃	—	8	2	no	—
110	C₂²×D₄₃	—	8	2	no	—
111	Q₈×C₄₃	—	4	2	no	—
112	Q₈×C₄₃	—	4	2	no	—
113	Q₈×C₄₃	—	8	2	no	—
114	C₂×C₄×C₄₃	—	4	2	no	—
115	C₂×C₄×C₄₃	—	4	2	no	—
116	C₂×C₄×C₄₃	—	8	2	no	—
117	C₂×C₄×C₄₃	—	8	2	no	—
118	C₂×C₄×C₄₃	#124	1	2	yes	—
119	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
120	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
121	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
122	C₂×Dic₄₃	—	2	2	no	—
123	C₂×Dic₄₃	—	2	2	no	—
124	C₂×Dic₄₃	—	4	2	no	—
125	C₂×Dic₄₃	—	8	2	no	—
126	C₂×Dic₄₃	C₂×D₈	1	2	yes	—
127	C₂×Dic₄₃	C₂×D₈	1	2	yes	—
128	D₁₇₂	—	4	2	no	—
129	D₁₇₂	—	4	2	no	—
130	D₁₇₂	—	8	2	no	—
131	Dic₈₆	—	8	8	no	—
132	C₈×C₄₃	#124	1	2	yes	—
133	C₈×C₄₃	C₂×#41	1	1	yes	characteristic
134	C₈×C₄₃	C₂×#41	1	1	yes	characteristic
135	C₄₃⋊C₈	C₂×SD₁₆	1	4	yes	—
136	C₂×#2243	—	43	1	no	maximal, Sylow
137	C₂²×C₄₃	#486	1	2	yes	—
138	C₂²×C₄₃	#509	1	2	yes	—
139	C₂²×C₄₃	#510	1	2	yes	—
140	C₂²×C₄₃	C₂²×D₈	1	1	yes	characteristic
141	C₂×D₄₃	—	8	2	no	—
142	C₂×D₄₃	—	8	2	no	—
143	C₂×D₄₃	—	8	2	no	—
144	C₂×D₄₃	—	16	4	no	—
145	C₄×C₄₃	—	8	2	no	—
146	C₄×C₄₃	—	8	2	no	—
147	C₄×C₄₃	#486	1	2	yes	—
148	C₄×C₄₃	C₂×#124	1	1	yes	characteristic
149	C₄×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
150	Dic₄₃	—	2	2	no	—
151	Dic₄₃	—	2	2	no	—
152	Dic₄₃	—	8	2	no	—
153	C₂×#500	—	43	1	no	—
154	C₂×#495	—	43	1	no	—
155	#2243	—	43	8	no	—
156	C₂×#358	—	43	1	no	—
157	C₂×#358	D₄₃	1	1	yes	characteristic, complemented
158	C₂×#357	—	43	1	no	—
159	C₂×#357	—	43	1	no	—
160	C₂×#346	—	43	1	no	—
161	C₂×C₄₃	#2243	1	4	yes	complemented
162	C₂×C₄₃	C₂×#486	1	1	yes	characteristic
163	C₂×C₄₃	C₂×#509	1	1	yes	characteristic
164	C₂×C₄₃	C₂×#510	1	1	yes	characteristic
165	D₄₃	—	16	2	no	—
166	C₂²×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
167	C₂²×SD₁₆	—	86	1	no	—
168	C₂²×D₈	—	43	1	no	—
169	C₂×C₄⋊Q₈	—	86	1	no	—
170	C₂×#124	—	86	1	no	—
171	C₂²×C₁₆	—	43	1	no	—
172	C₂²×C₁₆	C₂×D₄₃	1	1	yes	characteristic
173	#500	—	43	4	no	—
174	#500	—	86	2	no	—
175	#495	—	43	4	no	—
176	#495	—	86	2	no	—
177	C₂×#107	—	43	1	no	—
178	C₂×#107	—	86	1	no	—
179	C₂×#107	C₂×D₄₃	1	1	yes	characteristic
180	C₂×C₄×C₈	—	43	1	no	—
181	#358	—	43	4	no	—
182	#358	C₂×D₄₃	1	4	yes	complemented
183	#357	—	43	4	no	—
184	#357	—	43	4	no	—
185	#346	—	43	4	no	—
186	C₄₃	C₂×#2243	1	1	yes	characteristic, complemented, Sylow
187	C₂²×Q₈	—	2	1	no	—
188	C₂²×Q₈	—	172	1	no	—
189	C₂²×D₄	—	86	1	no	—
190	C₂×Q₁₆	—	2	2	no	—
191	C₂×Q₁₆	—	2	1	no	—
192	C₂×Q₁₆	—	2	2	no	—
193	C₂×Q₁₆	C₂²×D₄₃	1	2	yes	—
194	C₂×SD₁₆	—	86	4	no	—
195	C₂×SD₁₆	—	172	4	no	—
196	C₂×D₈	—	43	2	no	—
197	C₂×D₈	—	86	2	no	—
198	C₂×D₈	—	86	1	no	—
199	C₂×D₈	—	86	2	no	—
200	C₂²×C₈	—	43	1	no	—
201	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
202	C₄⋊Q₈	—	86	4	no	—
203	C₄⋊Q₈	—	172	2	no	—
204	#124	—	86	4	no	—
205	#124	—	172	2	no	—
206	C₂×C₄⋊C₄	—	2	1	no	—
207	C₂×C₄⋊C₄	—	86	1	no	—
208	C₂×C₄⋊C₄	—	172	1	no	—
209	C₂×C₂²⋊C₄	—	172	1	no	—
210	C₂×C₂²⋊C₄	—	172	1	no	—
211	C₂×C₄²	—	43	1	no	—
212	C₂×C₁₆	—	2	2	no	—
213	C₂×C₁₆	—	43	2	no	—
214	C₂×C₁₆	—	86	2	no	—
215	C₂×C₁₆	C₂²×D₄₃	1	2	yes	—
216	#107	—	2	1	no	—
217	#107	—	43	2	no	—
218	#107	—	86	4	no	—
219	#107	—	86	1	no	—
220	#107	C₂²×D₄₃	1	2	yes	—
221	C₄×C₈	—	43	2	no	—
222	C₄×C₈	—	43	2	no	—
223	C₂⁴	—	172	1	no	—
224	C₂×Q₈	—	2	2	no	—
225	C₂×Q₈	—	4	1	no	—
226	C₂×Q₈	—	4	2	no	—
227	C₂×Q₈	—	4	2	no	—
228	C₂×Q₈	—	344	4	no	—
229	C₂×Q₈	—	172	4	no	—
230	C₂×D₄	—	86	2	no	—
231	C₂×D₄	—	172	2	no	—
232	C₂×D₄	—	172	1	no	—
233	C₂×D₄	—	172	2	no	—
234	C₂²×C₄	—	4	1	no	—
235	C₂²×C₄	—	4	1	no	—
236	C₂²×C₄	—	43	1	no	—
237	C₂²×C₄	—	43	1	no	—
238	C₂²×C₄	—	172	1	no	—
239	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
240	Q₁₆	—	2	2	no	—
241	Q₁₆	—	2	2	no	—
242	Q₁₆	—	4	2	no	—
243	SD₁₆	—	172	8	no	—
244	D₈	—	86	2	no	—
245	D₈	—	86	2	no	—
246	D₈	—	172	2	no	—
247	C₂×C₈	—	43	4	no	—
248	C₂×C₈	—	43	2	no	—
249	C₂×C₈	#10621898	1	2	yes	—
250	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
251	C₂×C₈	#10621900	1	2	yes	—
252	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
253	C₄⋊C₄	—	2	2	no	—
254	C₄⋊C₄	—	4	1	no	—
255	C₄⋊C₄	—	86	2	no	—
256	C₄⋊C₄	—	172	4	no	—
257	C₄⋊C₄	—	172	1	no	—
258	C₂²⋊C₄	—	172	4	no	—
259	C₂²⋊C₄	—	172	4	no	—
260	C₄²	—	43	2	no	—
261	C₄²	—	43	2	no	—
262	C₁₆	—	2	2	no	—
263	C₁₆	—	86	2	no	—
264	C₂³	—	344	2	no	—
265	C₂³	—	344	2	no	—
266	C₂³	—	344	2	no	—
267	C₂³	—	172	2	no	—
268	C₂³	D₈×D₄₃	1	1	yes	characteristic
269	Q₈	—	4	2	no	—
270	Q₈	—	4	2	no	—
271	Q₈	—	8	2	no	—
272	Q₈	—	344	8	no	—
273	D₄	—	344	2	no	—
274	D₄	—	172	2	no	—
275	D₄	—	172	2	no	—
276	C₂×C₄	—	4	2	no	—
277	C₂×C₄	—	4	2	no	—
278	C₂×C₄	—	8	2	no	—
279	C₂×C₄	—	8	2	no	—
280	C₂×C₄	—	43	2	no	—
281	C₂×C₄	—	43	2	no	—
282	C₂×C₄	—	86	2	no	—
283	C₂×C₄	—	86	2	no	—
284	C₂×C₄	—	344	2	no	—
285	C₂×C₄	—	172	2	no	—
286	C₂×C₄	#13063311	1	2	yes	—
287	C₂×C₄	D₈×D₄₃	1	1	yes	characteristic
288	C₂×C₄	SD₁₆×D₄₃	1	2	yes	—
289	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
290	C₈	—	43	4	no	—
291	C₈	#13063311	1	2	yes	—
292	C₈	C₂×#10621900	1	1	yes	characteristic
293	C₈	C₂×#10621898	1	1	yes	characteristic
294	C₂²	—	344	2	no	—
295	C₂²	—	344	2	no	—
296	C₂²	—	344	2	no	—
297	C₂²	—	688	4	no	—
298	C₂²	#14583244	1	2	yes	—
299	C₂²	#14583336	1	2	yes	—
300	C₂²	#14583341	1	2	yes	—
301	C₂²	C₂×D₈×D₄₃	1	1	yes	characteristic
302	C₄	—	8	2	no	—
303	C₄	—	8	2	no	—
304	C₄	—	86	2	no	—
305	C₄	—	86	2	no	—
306	C₄	—	344	2	no	—
307	C₄	#14583244	1	2	yes	—
308	C₄	C₂×#13063311	1	1	yes	characteristic
309	C₄	C₂×SD₁₆×D₄₃	1	1	yes	characteristic
310	C₂	—	688	2	no	—
311	C₂	#19136833	1	4	yes	direct product factor
312	C₂	C₂×#14583244	1	1	yes	characteristic
313	C₂	C₂×#14583336	1	1	yes	characteristic
314	C₂	C₂×#14583341	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₈×D₄₃
commutator, cosocle	C₂×C₈×C₄₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₄₃
Fitting	C₂×C₄₃×#358	C₂
socle	C₂³×C₄₃	C₂×D₈
prime radical	C₂²×D₃₄₄	C₂²
hypercenter	C₂×#358	D₄₃
hypocenter	C₄₃	C₂×#2243
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#358

Complements

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

N	H ≅ G/N	type
1. C₂×#14583303	C₂	semidirect
3. #19136833	C₂	direct (N × H)
4. C₂×#14582703	C₂	semidirect
7. C₂×#14582674	C₂	semidirect
8. C₂×C₄₃×#358	C₂	semidirect
15. #14583303	C₂²	semidirect
21. #14582703	C₂²	semidirect
24. #14582674	C₂²	semidirect
28. C₄₃×#358	C₂²	semidirect
157. C₂×#358	D₄₃	semidirect
161. C₂×C₄₃	#2243	semidirect
182. #358	C₂×D₄₃	semidirect
186. C₄₃	C₂×#2243	semidirect
311. C₂	#19136833	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×#14583303	2
C₂×#14583284	2
#19136833	2
C₂×#14582703	2
C₂×#14582701	2
C₂×#14582699	2
C₂×#14582674	2
C₂×C₄₃×#358	2
C₂×#2243	43

Subgroups — C2×#19136833 #25251905

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19136833 #25251905