Subgroups — C₂×#19132476 #24986644

Order 11008.

830 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13063236	C₂	1	2	yes	maximal
2	#19132476	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄₃×#382	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₄₃⋊C₈	—	2	2	no	—
5	C₂×#13063236	—	2	4	no	—
6	C₂×#13063236	—	2	2	no	—
7	C₂×#13063236	C₄	1	8	yes	complemented
8	C₂×#13063236	C₂²	1	4	yes	—
9	C₂²×C₄⋊C₄×C₄₃	C₄	1	2	yes	—
10	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
11	C₄₃×#382	—	2	2	no	—
12	C₄₃×#382	C₄	1	2	yes	—
13	C₄₃×#382	C₂²	1	2	yes	—
14	C₂×#95×C₄₃	—	2	2	no	—
15	C₂²×C₄₃⋊C₈	—	2	16	no	—
16	C₂²×C₄₃⋊C₈	—	2	8	no	—
17	C₂²×C₄₃⋊C₈	—	2	4	no	—
18	#13063236	—	2	8	no	—
19	#13063236	—	2	4	no	—
20	#13063236	C₂×C₄	1	8	yes	complemented
21	C₂³×C₄×C₄₃	—	2	2	no	—
22	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
23	C₂³×C₄×C₄₃	D₄	1	2	yes	—
24	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
25	C₂×C₄⋊C₄×C₄₃	—	4	4	no	—
26	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
27	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
28	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄²×C₄₃	D₄	1	2	yes	—
30	C₂×C₄²×C₄₃	D₄	1	2	yes	—
31	C₂×C₄²×C₄₃	Q₈	1	2	yes	—
32	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
33	#95×C₄₃	—	2	4	no	—
34	#95×C₄₃	—	2	4	no	—
35	C₂⁴×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
36	C₂²×C₄×C₄₃	—	2	2	no	—
37	C₂²×C₄×C₄₃	—	2	2	no	—
38	C₂²×C₄×C₄₃	—	2	8	no	—
39	C₂²×C₄×C₄₃	—	2	4	no	—
40	C₂²×C₄×C₄₃	—	4	4	no	—
41	C₂²×C₄×C₄₃	—	4	8	no	—
42	C₂²×C₄×C₄₃	C₄²	1	2	yes	—
43	C₂²×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
44	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
45	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
46	C₂²×C₄×C₄₃	C₄⋊C₄	1	4	yes	—
47	C₂²×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
48	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
49	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
50	C₄⋊C₄×C₄₃	—	4	4	no	—
51	C₄⋊C₄×C₄₃	—	4	4	no	—
52	C₄²×C₄₃	C₄²	1	2	yes	—
53	C₄²×C₄₃	C₂²⋊C₄	1	4	yes	—
54	C₄²×C₄₃	C₄⋊C₄	1	4	yes	—
55	C₄²×C₄₃	C₄⋊C₄	1	2	yes	—
56	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
57	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
58	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
59	C₂×C₄₃⋊C₈	—	2	32	no	—
60	C₂×C₄₃⋊C₈	—	2	16	no	—
61	C₂×C₄₃⋊C₈	—	2	8	no	—
62	C₂³×C₄₃	#95	1	2	yes	—
63	C₂³×C₄₃	#100	1	2	yes	—
64	C₂³×C₄₃	#101	1	2	yes	—
65	C₂³×C₄₃	#104	1	8	yes	—
66	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₄×C₄₃	—	2	8	no	—
68	C₂×C₄×C₄₃	—	2	8	no	—
69	C₂×C₄×C₄₃	—	2	4	no	—
70	C₂×C₄×C₄₃	—	2	4	no	—
71	C₂×C₄×C₄₃	—	2	1	no	—
72	C₂×C₄×C₄₃	—	2	1	no	—
73	C₂×C₄×C₄₃	—	2	1	no	—
74	C₂×C₄×C₄₃	—	2	1	no	—
75	C₂×C₄×C₄₃	—	2	4	no	—
76	C₂×C₄×C₄₃	—	2	4	no	—
77	C₂×C₄×C₄₃	—	4	4	no	—
78	C₂×C₄×C₄₃	—	4	8	no	—
79	C₂×C₄×C₄₃	—	8	8	no	—
80	C₂×C₄×C₄₃	#95	1	4	yes	—
81	C₂×C₄×C₄₃	#95	1	2	yes	—
82	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
83	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
84	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
85	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
86	C₄₃⋊C₈	—	2	16	no	—
87	C₂×#1295	—	43	1	no	maximal, Sylow
88	C₂²×C₄₃	#329	1	8	yes	—
89	C₂²×C₄₃	#330	1	8	yes	—
90	C₂²×C₄₃	#339	1	8	yes	—
91	C₂²×C₄₃	#343	1	4	yes	—
92	C₂²×C₄₃	C₂×#95	1	1	yes	characteristic
93	C₂²×C₄₃	C₂×#100	1	1	yes	characteristic
94	C₂²×C₄₃	C₂×#101	1	1	yes	characteristic
95	C₂²×C₄₃	C₂×#104	1	4	yes	—
96	C₄×C₄₃	—	2	2	no	—
97	C₄×C₄₃	—	2	4	no	—
98	C₄×C₄₃	—	2	2	no	—
99	C₄×C₄₃	—	2	2	no	—
100	C₄×C₄₃	—	2	1	no	—
101	C₄×C₄₃	—	2	1	no	—
102	C₄×C₄₃	—	8	4	no	—
103	C₂²×#97	—	43	2	no	—
104	C₂×#382	D₄₃	1	1	yes	characteristic
105	#1295	—	43	4	no	—
106	C₂×C₄₃	#1295	1	8	yes	complemented
107	C₂×C₄₃	C₂×#329	1	2	yes	—
108	C₂×C₄₃	C₂×#330	1	2	yes	—
109	C₂×C₄₃	C₂×#339	1	2	yes	—
110	C₂×C₄₃	C₂×#343	1	1	yes	characteristic
111	C₂³×C₈	—	86	2	no	—
112	C₂²×C₄⋊C₄	Dic₄₃	1	2	yes	—
113	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
114	C₂×#97	—	43	4	no	—
115	C₂×#97	—	43	8	no	—
116	C₂×#97	—	86	4	no	—
117	C₂×#97	—	86	2	no	—
118	#382	—	2	2	no	—
119	#382	Dic₄₃	1	2	yes	—
120	#382	C₂×D₄₃	1	2	yes	—
121	C₂×#95	—	2	2	no	—
122	C₄₃	C₂×#1295	1	1	yes	characteristic, complemented, Sylow
123	C₂³×C₄	—	2	2	no	—
124	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
125	C₂³×C₄	C₂²⋊D₄₃	1	2	yes	—
126	C₂²×C₈	—	86	16	no	—
127	C₂²×C₈	—	86	8	no	—
128	C₂²×C₈	—	86	4	no	—
129	C₂×C₄⋊C₄	—	2	2	no	—
130	C₂×C₄⋊C₄	—	4	4	no	—
131	C₂×C₄⋊C₄	C₂×Dic₄₃	1	4	yes	—
132	C₂×C₄²	Dic₈₆	1	2	yes	—
133	C₂×C₄²	C₄×D₄₃	1	4	yes	—
134	C₂×C₄²	D₁₇₂	1	2	yes	—
135	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
136	C₂×C₄²	C₂²⋊D₄₃	1	2	yes	—
137	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
138	#97	—	43	8	no	—
139	#97	—	86	8	no	—
140	#97	—	86	4	no	—
141	#95	—	2	4	no	—
142	#95	—	2	4	no	—
143	C₂⁴	C₂²⋊Dic₄₃	1	1	yes	characteristic
144	C₂²×C₄	—	2	2	no	—
145	C₂²×C₄	—	2	2	no	—
146	C₂²×C₄	—	2	8	no	—
147	C₂²×C₄	—	2	4	no	—
148	C₂²×C₄	—	4	4	no	—
149	C₂²×C₄	—	4	8	no	—
150	C₂²×C₄	C₄×Dic₄₃	1	2	yes	—
151	C₂²×C₄	Dic₄₃⋊C₄	1	4	yes	—
152	C₂²×C₄	C₄⋊Dic₄₃	1	2	yes	—
153	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	4	yes	—
154	C₂²×C₄	C₂²⋊Dic₄₃	1	2	yes	—
155	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
156	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
157	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
158	C₂×C₈	—	86	16	no	—
159	C₂×C₈	—	86	32	no	—
160	C₂×C₈	—	86	8	no	—
161	C₄⋊C₄	—	4	4	no	—
162	C₄⋊C₄	—	4	4	no	—
163	C₄²	C₄×Dic₄₃	1	2	yes	—
164	C₄²	Dic₄₃⋊C₄	1	4	yes	—
165	C₄²	C₄⋊Dic₄₃	1	2	yes	—
166	C₄²	(C₂×D₄₃)⋊C₄	1	4	yes	—
167	C₄²	C₂×Dic₈₆	1	1	yes	characteristic
168	C₄²	C₂×C₄×D₄₃	1	2	yes	—
169	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
170	C₂³	C₄₃⋊#95	1	2	yes	—
171	C₂³	#13063242	1	2	yes	—
172	C₂³	#13063244	1	2	yes	—
173	C₂³	#13063252	1	8	yes	—
174	C₂³	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
175	C₂×C₄	—	2	1	no	—
176	C₂×C₄	—	2	1	no	—
177	C₂×C₄	—	2	1	no	—
178	C₂×C₄	—	2	1	no	—
179	C₂×C₄	—	2	4	no	—
180	C₂×C₄	—	2	4	no	—
181	C₂×C₄	—	2	8	no	—
182	C₂×C₄	—	2	8	no	—
183	C₂×C₄	—	2	4	no	—
184	C₂×C₄	—	2	4	no	—
185	C₂×C₄	—	4	4	no	—
186	C₂×C₄	—	4	8	no	—
187	C₂×C₄	—	8	8	no	—
188	C₂×C₄	C₄₃⋊#95	1	4	yes	—
189	C₂×C₄	C₄₃⋊#95	1	2	yes	—
190	C₂×C₄	C₂×C₄×Dic₄₃	1	1	yes	characteristic
191	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	2	yes	—
192	C₂×C₄	C₂×Dic₄₃⋊C₄	1	2	yes	—
193	C₂×C₄	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
194	C₈	—	86	16	no	—
195	C₂²	#14582639	1	8	yes	—
196	C₂²	#14582641	1	8	yes	—
197	C₂²	#14582658	1	8	yes	—
198	C₂²	#14582668	1	4	yes	—
199	C₂²	C₂×C₄₃⋊#95	1	1	yes	characteristic
200	C₂²	C₂×#13063242	1	1	yes	characteristic
201	C₂²	C₂×#13063244	1	1	yes	characteristic
202	C₂²	C₂×#13063252	1	4	yes	—
203	C₄	—	2	2	no	—
204	C₄	—	2	4	no	—
205	C₄	—	2	2	no	—
206	C₄	—	2	2	no	—
207	C₄	—	2	1	no	—
208	C₄	—	2	1	no	—
209	C₄	—	8	4	no	—
210	C₂	#19132476	1	8	yes	direct product factor
211	C₂	C₂×#14582639	1	2	yes	—
212	C₂	C₂×#14582641	1	2	yes	—
213	C₂	C₂×#14582658	1	2	yes	—
214	C₂	C₂×#14582668	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂²⋊Dic₄₃
commutator	C₂×C₄×C₄₃	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₂×C₄₃×#382	C₂
socle, prime radical	C₂⁴×C₄₃	C₂²⋊C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	C₂×#382	D₄₃
hypocenter	C₄₃	C₂×#1295
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂×#382

Complements

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

N	H ≅ G/N	type
2. #19132476	C₂	direct (N × H)
7. C₂×#13063236	C₄	semidirect
20. #13063236	C₂×C₄	semidirect
106. C₂×C₄₃	#1295	semidirect
122. C₄₃	C₂×#1295	semidirect
210. C₂	#19132476	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#13063236	2
#19132476	2
C₂×C₄₃×#382	2
C₂×#1295	43

Subgroups — C2×#19132476 #24986644

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19132476 #24986644