Subgroups — #384×Dic₄₃ #25017822

Order 11008.

2094 conjugacy classes of subgroups.

The subgroup lattice has 240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582769	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊C₄×Dic₄₃	C₂	1	6	yes	maximal
3	C₂×C₄²×Dic₄₃	C₂	1	1	yes	maximal, characteristic
4	#19132824	C₂	1	6	yes	maximal
5	C₂×C₄₃×#384	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄⋊Dic₄₃	C₂²	1	6	yes	—
7	C₂²×C₄×Dic₄₃	C₂²	1	4	yes	—
8	C₂²×C₄×Dic₄₃	C₂²	1	3	yes	—
9	C₂²×C₄×Dic₄₃	C₂²	1	3	yes	—
10	#14582769	C₄	1	8	yes	complemented
11	C₄⋊C₄×Dic₄₃	—	2	24	no	—
12	C₂×C₄₃⋊#95	C₂²	1	12	yes	—
13	C₄²×Dic₄₃	C₄	1	8	yes	complemented
14	C₂²×C₄⋊C₄×C₄₃	C₂²	1	6	yes	—
15	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
16	C₄₃×#384	C₄	1	8	yes	complemented
17	C₂³×Dic₄₃	C₂³	1	4	yes	—
18	C₂³×Dic₄₃	C₂³	1	3	yes	—
19	C₂³×Dic₄₃	C₂³	1	1	yes	characteristic
20	C₂×C₄⋊Dic₄₃	—	2	12	no	—
21	C₂×C₄⋊Dic₄₃	—	2	12	no	—
22	C₂×C₄⋊Dic₄₃	C₂×C₄	1	24	yes	—
23	C₂×C₄×Dic₄₃	—	2	6	no	—
24	C₂×C₄×Dic₄₃	—	2	6	no	—
25	C₂×C₄×Dic₄₃	—	2	24	no	—
26	C₂×C₄×Dic₄₃	C₂×C₄	1	12	yes	—
27	C₂×C₄×Dic₄₃	C₂×C₄	1	12	yes	—
28	C₂×C₄×Dic₄₃	D₄	1	12	yes	—
29	C₂×C₄×Dic₄₃	Q₈	1	12	yes	—
30	C₄₃⋊#95	—	2	24	no	—
31	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
32	C₂³×C₄×C₄₃	C₂³	1	3	yes	—
33	C₂×C₄⋊C₄×C₄₃	—	2	12	no	—
34	C₂×C₄⋊C₄×C₄₃	—	2	12	no	—
35	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	24	yes	—
36	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
37	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
38	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
39	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
40	C₂²×C₄×C₄₃	—	2	12	no	—
41	C₂²×C₄×C₄₃	—	2	12	no	—
42	C₂²×C₄×C₄₃	C₂²×C₄	1	6	yes	—
43	C₂²×C₄×C₄₃	C₂²×C₄	1	6	yes	—
44	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
45	C₂²×C₄×C₄₃	C₂²×C₄	1	6	yes	—
46	C₂²×C₄×C₄₃	C₂×D₄	1	6	yes	—
47	C₂²×C₄×C₄₃	C₂×Q₈	1	6	yes	—
48	C₂²×C₄×C₄₃	#41	1	6	yes	—
49	C₂²×C₄×C₄₃	#41	1	6	yes	—
50	C₂²×Dic₄₃	—	2	12	no	—
51	C₂²×Dic₄₃	—	2	6	no	—
52	C₂²×Dic₄₃	—	2	6	no	—
53	C₂²×Dic₄₃	—	2	12	no	—
54	C₂²×Dic₄₃	C₂²×C₄	1	8	yes	—
55	C₂²×Dic₄₃	C₂²×C₄	1	6	yes	—
56	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
57	C₂²×Dic₄₃	C₂×D₄	1	6	yes	—
58	C₂²×Dic₄₃	C₂×D₄	1	6	yes	—
59	C₂²×Dic₄₃	C₂×Q₈	1	6	yes	—
60	C₂²×Dic₄₃	C₂×Q₈	1	6	yes	—
61	C₄⋊C₄×C₄₃	—	2	48	no	—
62	C₄²×C₄₃	C₄²	1	16	yes	complemented
63	C₄⋊Dic₄₃	—	2	48	no	—
64	C₄×Dic₄₃	—	2	24	no	—
65	C₄×Dic₄₃	—	4	16	no	—
66	C₄×Dic₄₃	C₄⋊C₄	1	48	yes	complemented
67	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
68	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
69	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
70	C₂³×C₄₃	C₂²×D₄	1	3	yes	—
71	C₂³×C₄₃	C₂²×Q₈	1	3	yes	—
72	C₂³×C₄₃	C₂×#41	1	3	yes	—
73	C₂³×C₄₃	C₂×#41	1	3	yes	—
74	C₂×C₄×C₄₃	—	2	24	no	—
75	C₂×C₄×C₄₃	—	4	4	no	—
76	C₂×C₄×C₄₃	—	4	12	no	—
77	C₂×C₄×C₄₃	C₂×C₄²	1	12	yes	—
78	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	12	yes	—
79	C₂×C₄×C₄₃	#117	1	12	yes	—
80	C₂×C₄×C₄₃	C₄×D₄	1	12	yes	—
81	C₂×C₄×C₄₃	C₄×D₄	1	12	yes	—
82	C₂×C₄×C₄₃	C₄×Q₈	1	12	yes	—
83	C₂×C₄×C₄₃	C₄×Q₈	1	12	yes	—
84	C₂×Dic₄₃	—	2	12	no	—
85	C₂×Dic₄₃	—	2	6	no	—
86	C₂×Dic₄₃	—	2	6	no	—
87	C₂×Dic₄₃	—	2	12	no	—
88	C₂×Dic₄₃	—	2	24	no	—
89	C₂×Dic₄₃	—	4	4	no	—
90	C₂×Dic₄₃	—	4	12	no	—
91	C₂×Dic₄₃	C₂×C₄⋊C₄	1	12	yes	—
92	C₂×Dic₄₃	C₂×C₄⋊C₄	1	12	yes	—
93	C₂×Dic₄₃	#127	1	4	yes	—
94	C₂×Dic₄₃	C₄⋊Q₈	1	12	yes	—
95	C₄×#384	—	43	1	no	maximal, Sylow
96	C₂²×C₄₃	C₂²×C₄²	1	1	yes	characteristic
97	C₂²×C₄₃	C₂²×C₄⋊C₄	1	3	yes	—
98	C₂²×C₄₃	C₂×#117	1	3	yes	—
99	C₂²×C₄₃	C₂×C₄×D₄	1	3	yes	—
100	C₂²×C₄₃	C₂×C₄×D₄	1	3	yes	—
101	C₂²×C₄₃	C₂×C₄×Q₈	1	3	yes	—
102	C₂²×C₄₃	C₂×C₄×Q₈	1	3	yes	—
103	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
104	C₂²×C₄₃	C₂×C₄⋊Q₈	1	3	yes	—
105	C₂²×C₄₃	#532	1	3	yes	—
106	C₂²×C₄₃	#532	1	3	yes	—
107	C₂²×C₄₃	#533	1	6	yes	—
108	C₄×C₄₃	—	4	8	no	—
109	C₄×C₄₃	C₄×C₄⋊C₄	1	24	yes	complemented
110	Dic₄₃	—	2	12	no	—
111	Dic₄₃	—	4	8	no	—
112	Dic₄₃	#384	1	8	yes	direct product factor
113	C₂×#384	—	43	1	no	—
114	C₂×#384	D₄₃	1	1	yes	characteristic
115	C₂×C₄×C₄⋊C₄	—	43	6	no	—
116	C₂×C₄³	—	43	1	no	—
117	C₄⋊#95	—	43	6	no	—
118	C₂×C₄₃	C₂×C₄×C₄⋊C₄	1	3	yes	—
119	C₂×C₄₃	C₂×#384	1	1	yes	characteristic
120	C₂×C₄₃	#2285	1	3	yes	—
121	C₂×C₄₃	C₄×#127	1	1	yes	characteristic
122	C₂×C₄₃	C₄×#127	1	1	yes	characteristic
123	C₂×C₄₃	C₄×C₄⋊Q₈	1	3	yes	—
124	C₂×C₄₃	C₄×C₄⋊Q₈	1	3	yes	—
125	C₂²×C₄⋊C₄	—	43	6	no	—
126	C₂²×C₄⋊C₄	C₂×D₄₃	1	6	yes	—
127	C₂²×C₄²	—	43	3	no	—
128	C₂²×C₄²	—	43	3	no	—
129	C₂²×C₄²	—	43	4	no	—
130	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
131	#384	—	43	8	no	—
132	#384	Dic₄₃	1	8	yes	direct product factor
133	C₄×C₄⋊C₄	—	86	24	no	—
134	C₂×#95	—	43	12	no	—
135	C₄³	—	43	8	no	—
136	C₄₃	C₄×#384	1	1	yes	characteristic, complemented, Sylow
137	C₂³×C₄	—	43	1	no	—
138	C₂³×C₄	—	43	3	no	—
139	C₂³×C₄	—	43	4	no	—
140	C₂³×C₄	C₂²×D₄₃	1	4	yes	—
141	C₂³×C₄	C₂²×D₄₃	1	3	yes	—
142	C₂×C₄⋊C₄	—	2	12	no	—
143	C₂×C₄⋊C₄	—	2	12	no	—
144	C₂×C₄⋊C₄	—	43	24	no	—
145	C₂×C₄⋊C₄	—	86	12	no	—
146	C₂×C₄⋊C₄	—	86	12	no	—
147	C₂×C₄⋊C₄	C₂×Dic₄₃	1	24	yes	—
148	C₂×C₄²	—	43	12	no	—
149	C₂×C₄²	—	43	12	no	—
150	C₂×C₄²	—	43	12	no	—
151	C₂×C₄²	—	43	12	no	—
152	C₂×C₄²	—	86	6	no	—
153	C₂×C₄²	—	86	6	no	—
154	C₂×C₄²	—	86	24	no	—
155	C₂×C₄²	C₄×D₄₃	1	4	yes	—
156	C₂×C₄²	C₄×D₄₃	1	4	yes	—
157	C₂×C₄²	C₂×Dic₄₃	1	4	yes	—
158	#95	—	86	24	no	—
159	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
160	C₂²×C₄	—	2	12	no	—
161	C₂²×C₄	—	2	12	no	—
162	C₂²×C₄	—	43	2	no	—
163	C₂²×C₄	—	43	6	no	—
164	C₂²×C₄	—	43	6	no	—
165	C₂²×C₄	—	43	6	no	—
166	C₂²×C₄	—	43	6	no	—
167	C₂²×C₄	—	43	6	no	—
168	C₂²×C₄	—	43	8	no	—
169	C₂²×C₄	—	86	6	no	—
170	C₂²×C₄	—	86	6	no	—
171	C₂²×C₄	—	86	12	no	—
172	C₂²×C₄	—	86	12	no	—
173	C₂²×C₄	C₂×C₄×D₄₃	1	6	yes	—
174	C₂²×C₄	C₂×C₄×D₄₃	1	6	yes	—
175	C₂²×C₄	D₄×D₄₃	1	6	yes	—
176	C₂²×C₄	#10621900	1	6	yes	—
177	C₂²×C₄	Q₈×D₄₃	1	6	yes	—
178	C₂²×C₄	#10621902	1	6	yes	—
179	C₂²×C₄	C₂²×Dic₄₃	1	8	yes	—
180	C₂²×C₄	C₂²×Dic₄₃	1	6	yes	—
181	C₄⋊C₄	—	2	48	no	—
182	C₄⋊C₄	—	86	48	no	—
183	C₄²	—	43	48	no	—
184	C₄²	—	86	24	no	—
185	C₄²	—	172	16	no	—
186	C₄²	C₄×Dic₄₃	1	16	yes	complemented
187	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
188	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
189	C₂³	C₂³×Dic₄₃	1	1	yes	characteristic
190	C₂³	C₂×D₄×D₄₃	1	3	yes	—
191	C₂³	C₂×Q₈×D₄₃	1	3	yes	—
192	C₂³	C₂×#10621900	1	3	yes	—
193	C₂³	C₂×#10621902	1	3	yes	—
194	C₂×C₄	—	2	24	no	—
195	C₂×C₄	—	4	4	no	—
196	C₂×C₄	—	4	12	no	—
197	C₂×C₄	—	43	12	no	—
198	C₂×C₄	—	43	4	no	—
199	C₂×C₄	—	43	12	no	—
200	C₂×C₄	—	43	12	no	—
201	C₂×C₄	—	86	12	no	—
202	C₂×C₄	—	86	6	no	—
203	C₂×C₄	—	86	6	no	—
204	C₂×C₄	—	86	12	no	—
205	C₂×C₄	—	86	24	no	—
206	C₂×C₄	—	172	4	no	—
207	C₂×C₄	—	172	12	no	—
208	C₂×C₄	C₂×C₄×Dic₄₃	1	12	yes	—
209	C₂×C₄	C₄⋊C₄×D₄₃	1	12	yes	—
210	C₂×C₄	#13063283	1	12	yes	—
211	C₂×C₄	#13063287	1	12	yes	—
212	C₂×C₄	D₄×Dic₄₃	1	12	yes	—
213	C₂×C₄	#13063290	1	12	yes	—
214	C₂×C₄	Q₈×Dic₄₃	1	12	yes	—
215	C₂²	C₂²×C₄×Dic₄₃	1	1	yes	characteristic
216	C₂²	C₂×C₄⋊C₄×D₄₃	1	3	yes	—
217	C₂²	C₂×#13063283	1	3	yes	—
218	C₂²	C₂×#13063287	1	3	yes	—
219	C₂²	C₂×D₄×Dic₄₃	1	3	yes	—
220	C₂²	C₂×#13063290	1	3	yes	—
221	C₂²	C₂×Q₈×Dic₄₃	1	3	yes	—
222	C₂²	#127×D₄₃	1	1	yes	characteristic
223	C₂²	C₄⋊Q₈×D₄₃	1	3	yes	—
224	C₂²	#14583447	1	3	yes	—
225	C₂²	#14583450	1	3	yes	—
226	C₂²	#14583454	1	6	yes	—
227	C₄	—	4	8	no	—
228	C₄	—	43	8	no	—
229	C₄	—	86	12	no	—
230	C₄	—	172	8	no	—
231	C₄	C₄⋊C₄×Dic₄₃	1	24	yes	complemented
232	C₂	C₂×C₄⋊C₄×Dic₄₃	1	3	yes	—
233	C₂	#384×D₄₃	1	1	yes	characteristic
234	C₂	#19137000	1	3	yes	—
235	C₂	#19137157	1	1	yes	characteristic
236	C₂	#127×Dic₄₃	1	1	yes	characteristic
237	C₂	#19137162	1	3	yes	—
238	C₂	C₄⋊Q₈×Dic₄₃	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂⁴	C₂³×D₄₃
commutator	C₂²×C₄₃	C₂²×C₄²
Fitting	C₂×C₄₃×#384	C₂
socle, prime radical, cosocle	C₂⁴×C₄₃	C₂⁴
hypercenter	C₂×#384	D₄₃
hypocenter	C₄₃	C₄×#384
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂⁴ ◁ C₂×#384

Complements

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

N	H ≅ G/N	type
10. #14582769	C₄	semidirect
13. C₄²×Dic₄₃	C₄	semidirect
16. C₄₃×#384	C₄	semidirect
62. C₄²×C₄₃	C₄²	semidirect
66. C₄×Dic₄₃	C₄⋊C₄	semidirect
109. C₄×C₄₃	C₄×C₄⋊C₄	semidirect
112. Dic₄₃	#384	direct (N × H)
132. #384	Dic₄₃	direct (N × H)
136. C₄₃	C₄×#384	semidirect
186. C₄²	C₄×Dic₄₃	semidirect
231. C₄	C₄⋊C₄×Dic₄₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#14582769	2
C₂×C₄⋊C₄×Dic₄₃	2
C₂×C₄²×Dic₄₃	2
#19132824	2
C₂×C₄₃×#384	2
C₄×#384	43

Subgroups — #384×Dic43 #25017822

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #384×Dic₄₃ #25017822