Subgroups — C₂×#14583454 #19147884

Order 5504.

1168 conjugacy classes of subgroups.

The subgroup lattice has 232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583454	C₂	1	16	yes	maximal, direct product factor
2	C₂×#13063325	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#13063316	C₂	1	2	yes	maximal, complemented
4	C₂×#13063305	C₂	1	2	yes	maximal
5	C₂×#13063301	C₂	1	2	yes	maximal
6	C₂×Q₈×Dic₄₃	C₂	1	2	yes	maximal, complemented
7	C₂×#13063290	C₂	1	2	yes	maximal, complemented
8	C₂×#13063283	C₂	1	2	yes	maximal
9	C₂×C₄²×D₄₃	C₂	1	1	yes	maximal, characteristic
10	C₂×C₄⋊Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×Dic₈₆	C₂²	1	2	yes	—
12	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic
13	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic
14	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic
15	#13063325	C₂²	1	8	yes	complemented
16	#13063316	C₂²	1	16	yes	complemented
17	#13063305	C₂²	1	16	yes	—
18	#13063301	C₂²	1	16	yes	—
19	Q₈×Dic₄₃	C₂²	1	16	yes	complemented
20	#13063290	C₂²	1	16	yes	complemented
21	#13063283	C₂²	1	16	yes	—
22	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
23	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
24	C₂×C₄⋊Dic₄₃	C₂²	1	4	yes	—
25	C₂×Dic₄₃⋊C₄	C₂²	1	4	yes	—
26	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	4	yes	—
27	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×Dic₄₃	C₂²	1	4	yes	—
31	C₄²×D₄₃	C₂²	1	8	yes	—
32	C₂²×Q₈×C₄₃	C₂²	1	2	yes	—
33	C₄⋊Q₈×C₄₃	C₂²	1	8	yes	complemented
34	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
35	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
36	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
37	C₂³×D₄₃	C₂³	1	1	yes	characteristic
38	C₂×Q₈×C₄₃	—	2	8	no	—
39	C₂×Q₈×C₄₃	C₂³	1	8	yes	—
40	C₂²×C₄×C₄₃	C₂³	1	4	yes	—
41	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
42	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
43	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
44	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
45	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
46	C₂²×Dic₄₃	C₂³	1	4	yes	—
47	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
48	C₂×C₄×D₄₃	—	2	4	no	—
49	C₂×C₄×D₄₃	—	2	4	no	—
50	C₂×C₄×D₄₃	Q₈	1	8	yes	complemented
51	C₂×C₄×D₄₃	C₂³	1	4	yes	—
52	C₂×C₄×D₄₃	C₂³	1	4	yes	—
53	C₂×C₄×D₄₃	C₂³	1	4	yes	—
54	C₂×Dic₈₆	—	2	8	no	—
55	C₂×Dic₈₆	C₂³	1	8	yes	—
56	C₄⋊C₄×C₄₃	C₂³	1	8	yes	—
57	C₄⋊C₄×C₄₃	C₂³	1	8	yes	—
58	C₄²×C₄₃	C₂³	1	4	yes	—
59	(C₂×D₄₃)⋊C₄	C₂³	1	16	yes	—
60	C₄⋊Dic₄₃	C₂³	1	8	yes	—
61	C₄⋊Dic₄₃	C₂³	1	8	yes	—
62	C₄⋊Dic₄₃	C₂³	1	16	yes	—
63	Dic₄₃⋊C₄	C₂³	1	16	yes	—
64	C₄×Dic₄₃	C₂³	1	4	yes	—
65	C₄×Dic₄₃	C₂³	1	4	yes	—
66	C₄×Dic₄₃	C₂³	1	4	yes	—
67	C₄×Dic₄₃	C₂³	1	16	yes	—
68	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
69	C₂²×D₄₃	—	2	2	no	—
70	C₂²×D₄₃	—	2	2	no	—
71	C₂²×D₄₃	C₂×Q₈	1	4	yes	—
72	C₂²×D₄₃	C₂⁴	1	2	yes	—
73	Q₈×C₄₃	—	2	16	no	—
74	C₂×C₄×C₄₃	—	2	8	no	—
75	C₂×C₄×C₄₃	C₂×Q₈	1	4	yes	—
76	C₂×C₄×C₄₃	#41	1	4	yes	—
77	C₂×C₄×C₄₃	#41	1	4	yes	—
78	C₂×C₄×C₄₃	C₂⁴	1	8	yes	—
79	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
80	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
81	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
82	C₂×Dic₄₃	—	2	8	no	—
83	C₂×Dic₄₃	—	2	2	no	—
84	C₂×Dic₄₃	—	2	2	no	—
85	C₂×Dic₄₃	C₂×Q₈	1	4	yes	—
86	C₂×Dic₄₃	C₂⁴	1	2	yes	—
87	C₂×Dic₄₃	C₂⁴	1	2	yes	—
88	C₂×Dic₄₃	C₂⁴	1	8	yes	—
89	C₂×Dic₄₃	C₂⁴	1	2	yes	—
90	C₄×D₄₃	—	2	8	no	—
91	C₄×D₄₃	—	2	8	no	—
92	C₄×D₄₃	C₂×Q₈	1	16	yes	complemented
93	Dic₈₆	—	2	16	no	—
94	C₂²×C₄₃	C₂²×Q₈	1	2	yes	—
95	C₂²×C₄₃	C₂×#41	1	2	yes	—
96	C₂²×C₄₃	C₂×#41	1	2	yes	—
97	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
98	C₂×D₄₃	—	2	8	no	—
99	C₂×D₄₃	—	2	2	no	—
100	C₂×D₄₃	—	2	2	no	—
101	C₂×D₄₃	C₂²×Q₈	1	4	yes	—
102	C₄×C₄₃	—	2	8	no	—
103	C₄×C₄₃	C₂²×Q₈	1	4	yes	—
104	C₄×C₄₃	C₂×#41	1	4	yes	—
105	C₄×C₄₃	C₂×#41	1	4	yes	—
106	Dic₄₃	—	2	8	no	—
107	Dic₄₃	—	2	2	no	—
108	Dic₄₃	—	2	2	no	—
109	Dic₄₃	C₂²×Q₈	1	4	yes	—
110	C₂×#533	—	43	1	no	maximal, Sylow
111	C₂×C₄₃	#533	1	4	yes	complemented
112	C₂×C₄₃	C₂³×Q₈	1	1	yes	characteristic
113	C₂×C₄₃	C₂²×#41	1	1	yes	characteristic
114	C₂×C₄₃	C₂²×#41	1	1	yes	characteristic
115	D₄₃	—	2	4	no	—
116	#533	—	43	16	no	—
117	C₂×C₄⋊Q₈	—	43	1	no	—
118	C₂×C₄⋊Q₈	D₄₃	1	1	yes	characteristic, complemented
119	C₂×#125	—	43	2	no	—
120	C₂×C₂²⋊Q₈	—	43	2	no	—
121	C₂×C₂²⋊Q₈	—	43	2	no	—
122	C₂×C₄×Q₈	—	43	2	no	—
123	C₂×C₄×Q₈	—	43	2	no	—
124	C₂×#117	—	43	2	no	—
125	C₂²×C₄²	—	43	1	no	—
126	C₄₃	C₂×#533	1	1	yes	characteristic, complemented, Sylow
127	C₂²×Q₈	—	43	2	no	—
128	C₂²×Q₈	C₂×D₄₃	1	2	yes	—
129	C₂³×C₄	—	43	1	no	—
130	C₂³×C₄	—	43	1	no	—
131	C₂³×C₄	—	43	1	no	—
132	C₄⋊Q₈	—	43	8	no	—
133	C₄⋊Q₈	C₂×D₄₃	1	8	yes	complemented
134	#125	—	43	16	no	—
135	C₂²⋊Q₈	—	43	16	no	—
136	C₂²⋊Q₈	—	43	16	no	—
137	C₄×Q₈	—	43	16	no	—
138	C₄×Q₈	—	43	16	no	—
139	#117	—	43	16	no	—
140	C₂×C₄⋊C₄	—	43	2	no	—
141	C₂×C₄⋊C₄	—	43	4	no	—
142	C₂×C₄⋊C₄	—	43	4	no	—
143	C₂×C₄⋊C₄	—	43	2	no	—
144	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
145	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
146	C₂×C₂²⋊C₄	—	43	4	no	—
147	C₂×C₄²	—	43	4	no	—
148	C₂×C₄²	—	43	1	no	—
149	C₂×C₄²	—	43	1	no	—
150	C₂×C₄²	—	43	1	no	—
151	C₂×C₄²	—	43	8	no	—
152	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
153	C₂⁴	—	43	1	no	—
154	C₂×Q₈	—	2	8	no	—
155	C₂×Q₈	—	43	8	no	—
156	C₂×Q₈	—	86	8	no	—
157	C₂×Q₈	C₂²×D₄₃	1	8	yes	—
158	C₂²×C₄	—	43	1	no	—
159	C₂²×C₄	—	43	8	no	—
160	C₂²×C₄	—	43	4	no	—
161	C₂²×C₄	—	43	1	no	—
162	C₂²×C₄	—	43	1	no	—
163	C₂²×C₄	—	43	4	no	—
164	C₂²×C₄	—	43	4	no	—
165	C₂²×C₄	—	43	4	no	—
166	C₂²×C₄	—	86	4	no	—
167	C₂²×C₄	—	86	4	no	—
168	C₂²×C₄	C₂²×D₄₃	1	4	yes	—
169	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
170	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
171	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
172	C₄⋊C₄	—	43	8	no	—
173	C₄⋊C₄	—	43	16	no	—
174	C₄⋊C₄	—	43	16	no	—
175	C₄⋊C₄	—	43	8	no	—
176	C₄⋊C₄	C₂²×D₄₃	1	8	yes	—
177	C₄⋊C₄	C₂²×D₄₃	1	8	yes	—
178	C₂²⋊C₄	—	43	16	no	—
179	C₄²	—	43	4	no	—
180	C₄²	—	43	4	no	—
181	C₄²	—	43	4	no	—
182	C₄²	—	43	16	no	—
183	C₄²	C₂²×D₄₃	1	4	yes	—
184	C₂³	—	43	4	no	—
185	C₂³	—	43	2	no	—
186	C₂³	—	86	2	no	—
187	C₂³	—	86	2	no	—
188	C₂³	C₂³×D₄₃	1	1	yes	characteristic
189	Q₈	—	2	16	no	—
190	Q₈	—	86	16	no	—
191	C₂×C₄	—	2	8	no	—
192	C₂×C₄	—	43	4	no	—
193	C₂×C₄	—	43	2	no	—
194	C₂×C₄	—	43	16	no	—
195	C₂×C₄	—	43	2	no	—
196	C₂×C₄	—	43	2	no	—
197	C₂×C₄	—	43	8	no	—
198	C₂×C₄	—	86	2	no	—
199	C₂×C₄	—	86	2	no	—
200	C₂×C₄	—	86	8	no	—
201	C₂×C₄	—	86	8	no	—
202	C₂×C₄	—	86	8	no	—
203	C₂×C₄	#10621900	1	4	yes	—
204	C₂×C₄	Q₈×D₄₃	1	4	yes	—
205	C₂×C₄	#10621902	1	4	yes	—
206	C₂×C₄	C₂³×D₄₃	1	8	yes	—
207	C₂×C₄	C₂³×D₄₃	1	2	yes	—
208	C₂×C₄	C₂³×D₄₃	1	2	yes	—
209	C₂×C₄	C₂³×D₄₃	1	2	yes	—
210	C₂²	—	43	4	no	—
211	C₂²	—	86	8	no	—
212	C₂²	—	86	2	no	—
213	C₂²	—	86	2	no	—
214	C₂²	C₂×Q₈×D₄₃	1	2	yes	—
215	C₂²	C₂×#10621900	1	2	yes	—
216	C₂²	C₂×#10621902	1	2	yes	—
217	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
218	C₄	—	2	8	no	—
219	C₄	—	43	4	no	—
220	C₄	—	86	2	no	—
221	C₄	—	86	2	no	—
222	C₄	—	86	8	no	—
223	C₄	C₂×Q₈×D₄₃	1	4	yes	—
224	C₄	C₂×#10621900	1	4	yes	—
225	C₄	C₂×#10621902	1	4	yes	—
226	C₂	—	86	4	no	—
227	C₂	#14583454	1	4	yes	direct product factor
228	C₂	C₂²×Q₈×D₄₃	1	1	yes	characteristic
229	C₂	C₂²×#10621900	1	1	yes	characteristic
230	C₂	C₂²×#10621902	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₄₃
commutator	C₂²×C₄₃	C₂⁵
Frattini	C₂²	C₂⁴×D₄₃
Fitting	C₂×C₄⋊Q₈×C₄₃	C₂
socle	C₂³×C₄₃	C₂⁴
hypercenter	C₂×C₄⋊Q₈	D₄₃
hypocenter	C₄₃	C₂×#533
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. #14583454	C₂	direct (N × H)
2. C₂×#13063325	C₂	semidirect
3. C₂×#13063316	C₂	semidirect
6. C₂×Q₈×Dic₄₃	C₂	semidirect
7. C₂×#13063290	C₂	semidirect
10. C₂×C₄⋊Q₈×C₄₃	C₂	semidirect
15. #13063325	C₂²	semidirect
16. #13063316	C₂²	semidirect
19. Q₈×Dic₄₃	C₂²	semidirect
20. #13063290	C₂²	semidirect
33. C₄⋊Q₈×C₄₃	C₂²	semidirect
50. C₂×C₄×D₄₃	Q₈	semidirect
92. C₄×D₄₃	C₂×Q₈	semidirect
111. C₂×C₄₃	#533	semidirect
118. C₂×C₄⋊Q₈	D₄₃	semidirect
126. C₄₃	C₂×#533	semidirect
133. C₄⋊Q₈	C₂×D₄₃	semidirect
227. C₂	#14583454	direct (N × H)

Subgroups — C2×#14583454 #19147884

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#14583454 #19147884