Subgroups — C₄×#13063313 #19137139

Order 5504.

652 conjugacy classes of subgroups.

The subgroup lattice has 226 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13063313	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₈₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×D₁₇₂	C₂	1	1	yes	maximal, characteristic
4	#14582805	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582801	C₂	1	1	yes	maximal, characteristic
6	#14582790	C₂	1	4	yes	maximal, complemented
7	#14582765	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×(C₂×D₄₃)⋊C₄	C₂	1	4	yes	maximal, complemented
9	C₄³×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic
11	C₂²×D₁₇₂	C₂²	1	1	yes	characteristic
12	C₂²×C₄×D₄₃	C₂²	1	2	yes	—
13	#13063313	C₄	1	8	yes	direct product factor
14	C₄×Dic₈₆	—	2	4	no	—
15	C₄×D₁₇₂	—	2	4	no	—
16	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
18	C₂×Dic₄₃⋊C₄	C₂²	1	2	yes	—
19	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	2	yes	—
20	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	4	yes	—
21	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	4	yes	—
22	C₂×C₄×Dic₄₃	C₂²	1	2	yes	—
23	C₄₃⋊#95	C₂²	1	4	yes	—
24	C₄₃⋊#95	C₂²	1	4	yes	—
25	C₂×C₄²×C₄₃	C₂²	1	2	yes	—
26	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×C₄²×C₄₃	C₂²	1	2	yes	—
28	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
29	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
30	C₂³×D₄₃	C₂³	1	2	yes	—
31	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
32	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
33	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
34	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
35	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
36	C₂²×Dic₄₃	C₂³	1	2	yes	—
37	C₂²×Dic₄₃	C₂³	1	2	yes	—
38	C₂²×Dic₄₃	C₂³	1	2	yes	—
39	C₂×D₁₇₂	—	2	2	no	—
40	C₂×D₁₇₂	—	2	2	no	—
41	C₂×D₁₇₂	C₂×C₄	1	4	yes	—
42	C₂×C₄×D₄₃	—	2	4	no	—
43	C₂×C₄×D₄₃	—	2	8	no	—
44	C₂×Dic₈₆	—	2	2	no	—
45	C₂×Dic₈₆	—	2	2	no	—
46	C₂×Dic₈₆	C₂×C₄	1	4	yes	complemented
47	C₄²×C₄₃	—	2	4	no	—
48	C₄²×C₄₃	—	2	2	no	—
49	C₄²×C₄₃	—	2	4	no	—
50	C₄²×C₄₃	C₂×C₄	1	4	yes	complemented
51	C₄²×C₄₃	D₄	1	4	yes	—
52	(C₂×D₄₃)⋊C₄	—	2	4	no	—
53	(C₂×D₄₃)⋊C₄	—	2	8	no	—
54	(C₂×D₄₃)⋊C₄	C₂×C₄	1	16	yes	complemented
55	C₄⋊Dic₄₃	—	2	2	no	—
56	C₄⋊Dic₄₃	—	2	2	no	—
57	Dic₄₃⋊C₄	—	2	4	no	—
58	C₄×Dic₄₃	—	2	4	no	—
59	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
60	C₂²×D₄₃	—	2	2	no	—
61	C₂²×D₄₃	—	2	4	no	—
62	C₂²×D₄₃	—	2	4	no	—
63	C₂²×D₄₃	—	2	2	no	—
64	C₂²×D₄₃	C₂²×C₄	1	4	yes	—
65	C₂×C₄×C₄₃	—	2	2	no	—
66	C₂×C₄×C₄₃	—	2	2	no	—
67	C₂×C₄×C₄₃	—	2	2	no	—
68	C₂×C₄×C₄₃	—	2	2	no	—
69	C₂×C₄×C₄₃	—	2	2	no	—
70	C₂×C₄×C₄₃	C₂²×C₄	1	4	yes	—
71	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
72	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
73	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
74	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
75	C₂×C₄×C₄₃	#41	1	4	yes	—
76	C₂×C₄×C₄₃	#41	1	2	yes	—
77	C₂×C₄×C₄₃	#41	1	4	yes	—
78	C₂×Dic₄₃	—	2	2	no	—
79	C₂×Dic₄₃	—	2	2	no	—
80	C₂×Dic₄₃	—	2	2	no	—
81	C₂×Dic₄₃	—	2	2	no	—
82	C₂×Dic₄₃	—	2	4	no	—
83	C₂×Dic₄₃	—	2	4	no	—
84	C₂×Dic₄₃	C₂²×C₄	1	4	yes	—
85	D₁₇₂	—	2	8	no	—
86	C₄×D₄₃	—	4	8	no	—
87	Dic₈₆	—	2	8	no	—
88	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
89	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
90	C₂²×C₄₃	C₂×#41	1	1	yes	characteristic
91	C₂²×C₄₃	C₂×#41	1	2	yes	—
92	C₂²×C₄₃	C₂×#41	1	2	yes	—
93	C₂×D₄₃	—	2	4	no	—
94	C₂×D₄₃	—	2	8	no	—
95	C₂×D₄₃	—	4	2	no	—
96	C₂×D₄₃	—	4	4	no	—
97	C₂×D₄₃	—	4	2	no	—
98	C₄×C₄₃	—	2	4	no	—
99	C₄×C₄₃	—	2	4	no	—
100	C₄×C₄₃	—	2	2	no	—
101	C₄×C₄₃	C₄×D₄	1	4	yes	—
102	C₄×C₄₃	#124	1	4	yes	complemented
103	Dic₄₃	—	2	4	no	—
104	Dic₄₃	—	4	2	no	—
105	Dic₄₃	—	4	2	no	—
106	C₄×#124	—	43	1	no	maximal, Sylow
107	C₂×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
108	C₂×C₄₃	C₄×#41	1	2	yes	—
109	C₂×C₄₃	C₂×#124	1	1	yes	characteristic
110	C₂×C₄₃	#529	1	2	yes	—
111	C₂×C₄₃	#532	1	1	yes	characteristic
112	D₄₃	—	4	4	no	—
113	C₂×#124	—	43	1	no	—
114	C₂×C₄×Q₈	—	43	1	no	—
115	C₂×C₄×D₄	—	43	1	no	—
116	#391	—	43	1	no	—
117	#390	—	43	1	no	—
118	#388	—	43	4	no	—
119	#382	—	43	1	no	—
120	C₄×C₂²⋊C₄	—	43	4	no	—
121	C₄³	D₄₃	1	1	yes	characteristic, complemented
122	C₄₃	C₄×#124	1	1	yes	characteristic, complemented, Sylow
123	C₂²×Q₈	—	43	1	no	—
124	C₂²×D₄	—	43	1	no	—
125	C₂³×C₄	—	43	2	no	—
126	#124	—	43	8	no	—
127	C₄×Q₈	—	86	4	no	—
128	C₄×D₄	—	86	4	no	—
129	C₂×C₄⋊C₄	—	43	1	no	—
130	C₂×C₄⋊C₄	—	43	2	no	—
131	C₂×C₄⋊C₄	—	43	1	no	—
132	C₂×C₂²⋊C₄	—	43	4	no	—
133	C₂×C₂²⋊C₄	—	43	2	no	—
134	C₂×C₂²⋊C₄	—	43	4	no	—
135	C₂×C₄²	—	43	2	no	—
136	C₂×C₄²	C₂×D₄₃	1	2	yes	—
137	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
138	C₂×C₄²	C₂×D₄₃	1	2	yes	—
139	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
140	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
141	#95	—	43	4	no	—
142	#95	—	43	4	no	—
143	C₂⁴	—	43	2	no	—
144	C₂×Q₈	—	43	4	no	—
145	C₂×Q₈	—	86	2	no	—
146	C₂×Q₈	—	86	2	no	—
147	C₂×D₄	—	43	4	no	—
148	C₂×D₄	—	86	2	no	—
149	C₂×D₄	—	86	2	no	—
150	C₂²×C₄	—	43	2	no	—
151	C₂²×C₄	—	43	2	no	—
152	C₂²×C₄	—	43	2	no	—
153	C₂²×C₄	—	86	4	no	—
154	C₂²×C₄	—	86	8	no	—
155	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
156	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
157	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
158	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
159	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
160	C₄⋊C₄	—	86	2	no	—
161	C₄⋊C₄	—	86	4	no	—
162	C₄⋊C₄	—	86	2	no	—
163	C₂²⋊C₄	—	43	16	no	—
164	C₂²⋊C₄	—	86	4	no	—
165	C₂²⋊C₄	—	86	8	no	—
166	C₄²	—	2	4	no	—
167	C₄²	—	2	2	no	—
168	C₄²	—	2	4	no	—
169	C₄²	—	86	4	no	—
170	C₄²	C₄×D₄₃	1	4	yes	complemented
171	C₄²	D₁₇₂	1	4	yes	—
172	C₂³	—	43	4	no	—
173	C₂³	—	86	2	no	—
174	C₂³	—	86	4	no	—
175	C₂³	—	86	4	no	—
176	C₂³	—	86	2	no	—
177	C₂³	C₂³×D₄₃	1	1	yes	characteristic
178	Q₈	—	86	8	no	—
179	D₄	—	86	8	no	—
180	C₂×C₄	—	2	2	no	—
181	C₂×C₄	—	2	2	no	—
182	C₂×C₄	—	2	2	no	—
183	C₂×C₄	—	2	2	no	—
184	C₂×C₄	—	2	2	no	—
185	C₂×C₄	—	43	4	no	—
186	C₂×C₄	—	86	2	no	—
187	C₂×C₄	—	86	2	no	—
188	C₂×C₄	—	86	2	no	—
189	C₂×C₄	—	86	2	no	—
190	C₂×C₄	—	86	4	no	—
191	C₂×C₄	—	86	4	no	—
192	C₂×C₄	—	172	8	no	—
193	C₂×C₄	C₂×C₄×D₄₃	1	4	yes	—
194	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
195	C₂×C₄	C₂×D₁₇₂	1	2	yes	—
196	C₂×C₄	C₂×D₁₇₂	1	2	yes	—
197	C₂×C₄	C₂×D₁₇₂	1	2	yes	—
198	C₂×C₄	#10621898	1	4	yes	—
199	C₂×C₄	#10621898	1	2	yes	—
200	C₂×C₄	#10621898	1	4	yes	—
201	C₂²	—	86	4	no	—
202	C₂²	—	86	8	no	—
203	C₂²	—	172	2	no	—
204	C₂²	—	172	4	no	—
205	C₂²	—	172	2	no	—
206	C₂²	C₂²×C₄×D₄₃	1	1	yes	characteristic
207	C₂²	C₂²×D₁₇₂	1	1	yes	characteristic
208	C₂²	C₂×#10621898	1	1	yes	characteristic
209	C₂²	C₂×#10621898	1	2	yes	—
210	C₂²	C₂×#10621898	1	2	yes	—
211	C₄	—	2	4	no	—
212	C₄	—	2	4	no	—
213	C₄	—	2	2	no	—
214	C₄	—	86	4	no	—
215	C₄	—	172	2	no	—
216	C₄	—	172	2	no	—
217	C₄	C₄×D₁₇₂	1	4	yes	—
218	C₄	#13063313	1	4	yes	direct product factor
219	C₂	—	172	4	no	—
220	C₂	C₂×C₄×D₁₇₂	1	1	yes	characteristic
221	C₂	C₄×#10621898	1	2	yes	—
222	C₂	C₂×#13063313	1	1	yes	characteristic
223	C₂	#14583433	1	2	yes	—
224	C₂	#14583449	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₄₃
commutator	C₂²×C₄₃	C₂³×C₄
Frattini	C₂³	C₂³×D₄₃
Fitting	C₄³×C₄₃	C₂
socle	C₂³×C₄₃	C₂⁴
hypercenter	C₄³	D₄₃
hypocenter	C₄₃	C₄×#124
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×Dic₈₆	C₂	semidirect
4. #14582805	C₂	semidirect
6. #14582790	C₂	semidirect
7. #14582765	C₂	semidirect
8. C₄×(C₂×D₄₃)⋊C₄	C₂	semidirect
9. C₄³×C₄₃	C₂	semidirect
13. #13063313	C₄	direct (N × H)
46. C₂×Dic₈₆	C₂×C₄	semidirect
50. C₄²×C₄₃	C₂×C₄	semidirect
54. (C₂×D₄₃)⋊C₄	C₂×C₄	semidirect
102. C₄×C₄₃	#124	semidirect
121. C₄³	D₄₃	semidirect
122. C₄₃	C₄×#124	semidirect
170. C₄²	C₄×D₄₃	semidirect
218. C₄	#13063313	direct (N × H)

Subgroups — C4×#13063313 #19137139

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#13063313 #19137139