Subgroups — C₂×#14583626 #19148166

Order 5504.

1048 conjugacy classes of subgroups.

The subgroup lattice has 260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583626	C₂	1	16	yes	maximal, direct product factor
2	C₂×#13063324	C₂	1	1	yes	maximal, characteristic
3	C₂×#13063324	C₂	1	2	yes	maximal
4	C₂×#13063316	C₂	1	1	yes	maximal, characteristic
5	C₂×#13063315	C₂	1	2	yes	maximal
6	C₂×#13063315	C₂	1	2	yes	maximal
7	C₂×C₄×Dic₈₆	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄×Dic₈₆	C₂	1	1	yes	maximal, characteristic
9	C₂×#13063290	C₂	1	2	yes	maximal
10	C₂×#13063290	C₂	1	1	yes	maximal, characteristic
11	C₂×#13063290	C₂	1	1	yes	maximal, characteristic
12	C₂×#125×C₄₃	C₂	1	1	yes	maximal, characteristic
13	C₂²×Dic₈₆	C₂²	1	2	yes	—
14	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic
15	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic
16	#13063324	C₂²	1	16	yes	—
17	#13063324	C₂²	1	8	yes	—
18	#13063316	C₂²	1	8	yes	—
19	#13063315	C₂²	1	16	yes	—
20	#13063315	C₂²	1	16	yes	—
21	C₄×Dic₈₆	C₂²	1	8	yes	—
22	C₄×Dic₈₆	C₂²	1	8	yes	—
23	#13063290	C₂²	1	8	yes	—
24	#13063290	C₂²	1	16	yes	—
25	#13063290	C₂²	1	8	yes	—
26	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
29	C₂×Dic₄₃⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×Dic₄₃⋊C₄	C₂²	1	2	yes	—
31	C₂×Dic₄₃⋊C₄	C₂²	1	2	yes	—
32	C₂×Dic₄₃⋊C₄	C₂²	1	2	yes	—
33	C₂×Dic₄₃⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×Dic₄₃⋊C₄	C₂²	1	2	yes	—
35	C₂×Dic₄₃⋊C₄	C₂²	1	2	yes	—
36	C₂×C₄×Dic₄₃	C₂²	1	2	yes	—
37	C₂×C₄×Dic₄₃	C₂²	1	2	yes	—
38	C₂×C₄×Dic₄₃	C₂²	1	2	yes	—
39	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
41	#125×C₄₃	C₂²	1	8	yes	—
42	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
43	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
46	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
47	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
48	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
49	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
50	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
51	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
52	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
53	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
54	C₂²×Dic₄₃	C₂³	1	2	yes	—
55	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
56	C₂²×Dic₄₃	C₂³	1	2	yes	—
57	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
58	C₂×Dic₈₆	—	2	8	no	—
59	C₂×Dic₈₆	—	2	4	no	—
60	C₂×Dic₈₆	Q₈	1	8	yes	complemented
61	C₂×Dic₈₆	C₂³	1	8	yes	—
62	C₂×Dic₈₆	C₂³	1	4	yes	—
63	C₂×Dic₈₆	C₂³	1	4	yes	—
64	C₄⋊C₄×C₄₃	C₂³	1	8	yes	—
65	C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
66	C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
67	C₄⋊C₄×C₄₃	C₂³	1	8	yes	—
68	C₄²×C₄₃	C₂³	1	4	yes	—
69	C₄⋊Dic₄₃	C₂³	1	4	yes	—
70	C₄⋊Dic₄₃	C₂³	1	4	yes	—
71	C₄⋊Dic₄₃	C₂³	1	8	yes	—
72	Dic₄₃⋊C₄	C₂³	1	4	yes	—
73	Dic₄₃⋊C₄	C₂³	1	8	yes	—
74	Dic₄₃⋊C₄	C₂³	1	8	yes	—
75	Dic₄₃⋊C₄	C₂³	1	8	yes	—
76	Dic₄₃⋊C₄	C₂³	1	4	yes	—
77	Dic₄₃⋊C₄	C₂³	1	8	yes	—
78	Dic₄₃⋊C₄	C₂³	1	8	yes	—
79	C₄×Dic₄₃	C₂³	1	8	yes	—
80	C₄×Dic₄₃	C₂³	1	8	yes	—
81	C₄×Dic₄₃	C₂³	1	8	yes	—
82	C₄×Dic₄₃	C₂³	1	4	yes	—
83	C₄×Dic₄₃	C₂³	1	4	yes	—
84	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
85	C₂×C₄×C₄₃	—	2	2	no	—
86	C₂×C₄×C₄₃	—	2	4	no	—
87	C₂×C₄×C₄₃	—	2	2	no	—
88	C₂×C₄×C₄₃	—	2	4	no	—
89	C₂×C₄×C₄₃	C₂×Q₈	1	4	yes	—
90	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
91	C₂×C₄×C₄₃	C₂⁴	1	4	yes	—
92	C₂×C₄×C₄₃	C₂⁴	1	4	yes	—
93	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
94	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
95	C₂×Dic₄₃	—	2	4	no	—
96	C₂×Dic₄₃	—	2	2	no	—
97	C₂×Dic₄₃	—	2	2	no	—
98	C₂×Dic₄₃	—	2	2	no	—
99	C₂×Dic₄₃	C₂×Q₈	1	8	yes	—
100	C₂×Dic₄₃	#41	1	4	yes	—
101	C₂×Dic₄₃	C₂⁴	1	2	yes	—
102	C₂×Dic₄₃	C₂⁴	1	2	yes	—
103	C₂×Dic₄₃	C₂⁴	1	4	yes	—
104	C₂×Dic₄₃	C₂⁴	1	2	yes	—
105	C₂×Dic₄₃	C₂⁴	1	4	yes	—
106	C₂×Dic₄₃	C₂⁴	1	2	yes	—
107	Dic₈₆	—	2	16	no	—
108	Dic₈₆	—	2	8	no	—
109	Dic₈₆	C₂×Q₈	1	16	yes	complemented
110	C₂²×C₄₃	C₂²×Q₈	1	2	yes	—
111	C₂²×C₄₃	C₂×#41	1	2	yes	—
112	C₂²×C₄₃	2₋¹⁺⁴	1	2	yes	—
113	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
114	C₄×C₄₃	—	2	4	no	—
115	C₄×C₄₃	—	2	2	no	—
116	C₄×C₄₃	—	2	2	no	—
117	C₄×C₄₃	—	2	4	no	—
118	C₄×C₄₃	C₂²×Q₈	1	4	yes	—
119	Dic₄₃	—	2	4	no	—
120	Dic₄₃	—	2	2	no	—
121	Dic₄₃	—	2	2	no	—
122	Dic₄₃	—	2	2	no	—
123	Dic₄₃	C₂²×Q₈	1	8	yes	—
124	Dic₄₃	C₂×#41	1	4	yes	—
125	C₂×#557	—	43	1	no	maximal, Sylow
126	C₂×C₄₃	#557	1	4	yes	complemented
127	C₂×C₄₃	C₂³×Q₈	1	1	yes	characteristic
128	C₂×C₄₃	C₂²×#41	1	1	yes	characteristic
129	C₂×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
130	#557	—	43	16	no	—
131	C₂×C₄⋊Q₈	—	43	2	no	—
132	C₂×C₄⋊Q₈	—	43	1	no	—
133	C₂×#125	—	43	2	no	—
134	C₂×#125	—	43	2	no	—
135	C₂×#125	—	43	1	no	—
136	C₂×#125	D₄₃	1	1	yes	characteristic
137	C₂×C₄×Q₈	—	43	1	no	—
138	C₂×C₄×Q₈	—	43	2	no	—
139	C₂×C₄×Q₈	—	43	1	no	—
140	C₂×C₄×Q₈	—	43	1	no	—
141	C₂×C₄×Q₈	—	43	1	no	—
142	C₄₃	C₂×#557	1	1	yes	characteristic, complemented, Sylow
143	C₂²×Q₈	—	43	1	no	—
144	C₂²×Q₈	—	43	2	no	—
145	C₂²×Q₈	—	43	1	no	—
146	C₄⋊Q₈	—	43	16	no	—
147	C₄⋊Q₈	—	43	8	no	—
148	#125	—	43	16	no	—
149	#125	—	43	16	no	—
150	#125	—	43	8	no	—
151	#125	C₂×D₄₃	1	8	yes	—
152	C₄×Q₈	—	43	8	no	—
153	C₄×Q₈	—	43	16	no	—
154	C₄×Q₈	—	43	8	no	—
155	C₄×Q₈	—	43	8	no	—
156	C₄×Q₈	—	43	8	no	—
157	C₂×C₄⋊C₄	—	43	1	no	—
158	C₂×C₄⋊C₄	—	43	2	no	—
159	C₂×C₄⋊C₄	—	43	2	no	—
160	C₂×C₄⋊C₄	—	43	1	no	—
161	C₂×C₄⋊C₄	—	43	1	no	—
162	C₂×C₄⋊C₄	—	43	2	no	—
163	C₂×C₄⋊C₄	—	43	2	no	—
164	C₂×C₄⋊C₄	—	43	1	no	—
165	C₂×C₄⋊C₄	—	43	2	no	—
166	C₂×C₄⋊C₄	—	43	2	no	—
167	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
168	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
169	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
170	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
171	C₂×C₄²	—	43	2	no	—
172	C₂×C₄²	—	43	2	no	—
173	C₂×C₄²	—	43	1	no	—
174	C₂×C₄²	—	43	2	no	—
175	C₂×C₄²	—	43	1	no	—
176	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
177	C₂×Q₈	—	43	8	no	—
178	C₂×Q₈	—	43	4	no	—
179	C₂×Q₈	—	43	8	no	—
180	C₂×Q₈	—	43	4	no	—
181	C₂×Q₈	—	86	8	no	—
182	C₂×Q₈	—	86	4	no	—
183	C₂²×C₄	—	43	2	no	—
184	C₂²×C₄	—	43	1	no	—
185	C₂²×C₄	—	43	1	no	—
186	C₂²×C₄	—	43	1	no	—
187	C₂²×C₄	—	43	1	no	—
188	C₂²×C₄	—	43	2	no	—
189	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
190	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
191	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
192	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
193	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
194	C₄⋊C₄	—	43	4	no	—
195	C₄⋊C₄	—	43	8	no	—
196	C₄⋊C₄	—	43	8	no	—
197	C₄⋊C₄	—	43	4	no	—
198	C₄⋊C₄	—	43	4	no	—
199	C₄⋊C₄	—	43	8	no	—
200	C₄⋊C₄	—	43	8	no	—
201	C₄⋊C₄	—	43	4	no	—
202	C₄⋊C₄	—	43	8	no	—
203	C₄⋊C₄	—	43	8	no	—
204	C₄⋊C₄	C₂²×D₄₃	1	8	yes	—
205	C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
206	C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
207	C₄⋊C₄	C₂²×D₄₃	1	8	yes	—
208	C₄²	—	43	8	no	—
209	C₄²	—	43	8	no	—
210	C₄²	—	43	4	no	—
211	C₄²	—	43	8	no	—
212	C₄²	—	43	4	no	—
213	C₄²	C₂²×D₄₃	1	4	yes	—
214	C₂³	C₂³×D₄₃	1	1	yes	characteristic
215	Q₈	—	43	16	no	—
216	Q₈	—	86	16	no	—
217	Q₈	—	86	8	no	—
218	C₂×C₄	—	2	4	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	2	4	no	—
222	C₂×C₄	—	43	8	no	—
223	C₂×C₄	—	43	4	no	—
224	C₂×C₄	—	43	4	no	—
225	C₂×C₄	—	43	2	no	—
226	C₂×C₄	—	43	2	no	—
227	C₂×C₄	—	43	2	no	—
228	C₂×C₄	—	43	2	no	—
229	C₂×C₄	—	43	4	no	—
230	C₂×C₄	—	86	2	no	—
231	C₂×C₄	—	86	4	no	—
232	C₂×C₄	—	86	2	no	—
233	C₂×C₄	—	86	2	no	—
234	C₂×C₄	Q₈×D₄₃	1	4	yes	—
235	C₂×C₄	C₂³×D₄₃	1	2	yes	—
236	C₂×C₄	C₂³×D₄₃	1	4	yes	—
237	C₂×C₄	C₂³×D₄₃	1	4	yes	—
238	C₂×C₄	C₂³×D₄₃	1	2	yes	—
239	C₂×C₄	C₂³×D₄₃	1	2	yes	—
240	C₂²	C₂×Q₈×D₄₃	1	2	yes	—
241	C₂²	#41×D₄₃	1	2	yes	—
242	C₂²	#13063372	1	2	yes	—
243	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
244	C₄	—	2	4	no	—
245	C₄	—	2	2	no	—
246	C₄	—	2	2	no	—
247	C₄	—	2	4	no	—
248	C₄	—	43	8	no	—
249	C₄	—	43	4	no	—
250	C₄	—	86	2	no	—
251	C₄	—	86	4	no	—
252	C₄	—	86	2	no	—
253	C₄	—	86	2	no	—
254	C₄	C₂×Q₈×D₄₃	1	4	yes	—
255	C₂	#14583626	1	4	yes	direct product factor
256	C₂	C₂²×Q₈×D₄₃	1	1	yes	characteristic
257	C₂	C₂×#41×D₄₃	1	1	yes	characteristic
258	C₂	C₂×#13063372	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₄₃
commutator	C₂²×C₄₃	C₂⁵
Frattini	C₂²	C₂⁴×D₄₃
Fitting	C₂×#125×C₄₃	C₂
socle	C₂³×C₄₃	C₂⁴
hypercenter	C₂×#125	D₄₃
hypocenter	C₄₃	C₂×#557
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×#125

Complements

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

N	H ≅ G/N	type
1. #14583626	C₂	direct (N × H)
60. C₂×Dic₈₆	Q₈	semidirect
109. Dic₈₆	C₂×Q₈	semidirect
126. C₂×C₄₃	#557	semidirect
142. C₄₃	C₂×#557	semidirect
255. C₂	#14583626	direct (N × H)

Subgroups — C2×#14583626 #19148166

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#14583626 #19148166