Subgroups — C₂×#19132689 #25011484

Order 11008.

574 conjugacy classes of subgroups.

The subgroup lattice has 212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13063261	C₂	1	2	yes	maximal
2	#19132689	C₂	1	4	yes	maximal, direct product factor
3	C₂³×C₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×#10621877	—	2	2	no	—
5	C₂×#13063261	—	2	2	no	—
6	C₂×#13063261	—	2	4	no	—
7	C₂×#13063261	C₄	1	8	yes	—
8	C₂×#13063261	C₂²	1	4	yes	—
9	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
10	C₂²×C₁₆×C₄₃	—	2	4	no	—
11	C₂²×C₁₆×C₄₃	C₄	1	2	yes	—
12	C₂²×C₁₆×C₄₃	C₄	1	2	yes	—
13	C₂²×C₁₆×C₄₃	C₂²	1	2	yes	—
14	C₂×#10621877	—	2	8	no	—
15	C₂×#10621877	—	2	4	no	—
16	C₂×#10621877	—	4	2	no	—
17	C₂×#10621877	—	4	4	no	—
18	C₂²×C₄₃⋊C₈	—	4	2	no	—
19	#13063261	—	2	8	no	—
20	#13063261	—	2	4	no	—
21	#13063261	C₂×C₄	1	8	yes	—
22	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
23	C₂²×C₈×C₄₃	C₂×C₄	1	4	yes	—
24	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
27	C₂²×C₈×C₄₃	D₄	1	4	yes	—
28	C₂²×C₈×C₄₃	Q₈	1	1	yes	characteristic
29	C₂²×C₈×C₄₃	Q₈	1	1	yes	characteristic
30	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
31	C₂×C₁₆×C₄₃	—	2	4	no	—
32	C₂×C₁₆×C₄₃	—	2	4	no	—
33	C₂×C₁₆×C₄₃	—	2	4	no	—
34	C₂×C₁₆×C₄₃	C₂×C₄	1	4	yes	—
35	C₂⁴×C₄₃	Q₁₆	1	1	yes	characteristic
36	C₂²×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
37	C₂²×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
38	C₂²×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
39	C₂²×C₄×C₄₃	D₈	1	1	yes	characteristic
40	C₂²×C₄×C₄₃	D₈	1	1	yes	characteristic
41	C₂²×C₄×C₄₃	SD₁₆	1	4	yes	—
42	C₂²×C₄×C₄₃	Q₁₆	1	1	yes	characteristic
43	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
44	C₂×C₈×C₄₃	C₄²	1	2	yes	—
45	C₂×C₈×C₄₃	C₄²	1	2	yes	—
46	C₂×C₈×C₄₃	C₂²⋊C₄	1	4	yes	—
47	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
48	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
49	C₂×C₈×C₄₃	C₄⋊C₄	1	4	yes	—
50	C₂×C₈×C₄₃	C₄⋊C₄	1	4	yes	—
51	C₂×C₈×C₄₃	C₄⋊C₄	1	1	yes	characteristic
52	C₂×C₈×C₄₃	C₄⋊C₄	1	1	yes	characteristic
53	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
54	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
55	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
56	C₂×C₈×C₄₃	C₂×Q₈	1	1	yes	characteristic
57	#10621877	—	2	8	no	—
58	#10621877	—	4	8	no	—
59	#10621877	—	4	4	no	—
60	C₂×C₄₃⋊C₈	—	4	8	no	—
61	C₂×C₄₃⋊C₈	—	4	4	no	—
62	C₁₆×C₄₃	—	2	4	no	—
63	C₂³×C₄₃	—	2	4	no	—
64	C₂³×C₄₃	#103	1	4	yes	—
65	C₂³×C₄₃	#107	1	1	yes	characteristic
66	C₂³×C₄₃	#107	1	1	yes	characteristic
67	C₂³×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
68	C₂×C₄×C₄₃	#95	1	2	yes	—
69	C₂×C₄×C₄₃	#95	1	2	yes	—
70	C₂×C₄×C₄₃	#102	1	4	yes	—
71	C₂×C₄×C₄₃	#102	1	4	yes	—
72	C₂×C₄×C₄₃	#103	1	4	yes	—
73	C₂×C₄×C₄₃	#106	1	2	yes	—
74	C₂×C₄×C₄₃	#106	1	2	yes	—
75	C₂×C₄×C₄₃	#107	1	1	yes	characteristic
76	C₂×C₄×C₄₃	#107	1	1	yes	characteristic
77	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
78	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
79	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
80	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
81	C₈×C₄₃	#95	1	2	yes	—
82	C₈×C₄₃	#95	1	2	yes	—
83	C₈×C₄₃	C₂×C₄²	1	1	yes	characteristic
84	C₈×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
85	C₈×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
86	C₄₃⋊C₈	—	4	8	no	—
87	C₂×#1381	—	43	1	no	maximal, Sylow
88	C₂²×C₄₃	—	2	8	no	—
89	C₂²×C₄₃	—	2	2	no	—
90	C₂²×C₄₃	—	2	2	no	—
91	C₂²×C₄₃	#340	1	2	yes	—
92	C₂²×C₄₃	#340	1	2	yes	—
93	C₂²×C₄₃	#368	1	4	yes	—
94	C₂²×C₄₃	C₂×#103	1	2	yes	—
95	C₂²×C₄₃	C₂×#107	1	1	yes	characteristic
96	C₄×C₄₃	#340	1	2	yes	—
97	C₄×C₄₃	#340	1	2	yes	—
98	C₄×C₄₃	C₂×#95	1	1	yes	characteristic
99	C₄×C₄₃	C₂×#102	1	2	yes	—
100	C₄×C₄₃	C₂×#106	1	1	yes	characteristic
101	C₂³×C₁₆	D₄₃	1	1	yes	characteristic
102	C₂²×#108	—	43	2	no	—
103	#1381	—	43	4	no	—
104	C₂×C₄₃	—	2	2	no	—
105	C₂×C₄₃	—	2	2	no	—
106	C₂×C₄₃	#1381	1	4	yes	complemented
107	C₂×C₄₃	C₂×#340	1	1	yes	characteristic
108	C₂×C₄₃	C₂×#368	1	2	yes	—
109	C₂²×M₁₆	—	86	2	no	—
110	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
111	C₂²×C₁₆	—	2	4	no	—
112	C₂²×C₁₆	Dic₄₃	1	2	yes	—
113	C₂²×C₁₆	Dic₄₃	1	2	yes	—
114	C₂²×C₁₆	C₂×D₄₃	1	2	yes	—
115	C₂×#108	—	43	4	no	—
116	C₂×#108	—	43	8	no	—
117	C₂×#108	—	86	2	no	—
118	C₂×#108	—	86	4	no	—
119	C₄₃	C₂×#1381	1	1	yes	characteristic, complemented, Sylow
120	C₂³×C₄	D₁₇₂	1	1	yes	characteristic
121	C₂×M₁₆	—	86	8	no	—
122	C₂×M₁₆	—	86	4	no	—
123	C₂×M₁₆	—	172	4	no	—
124	C₂×M₁₆	—	172	2	no	—
125	C₂²×C₈	—	172	2	no	—
126	C₂²×C₈	Dic₈₆	1	1	yes	characteristic
127	C₂²×C₈	Dic₈₆	1	1	yes	characteristic
128	C₂²×C₈	C₄×D₄₃	1	4	yes	—
129	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
130	C₂²×C₈	C₂×Dic₄₃	1	1	yes	characteristic
131	C₂²×C₈	C₂×Dic₄₃	1	1	yes	characteristic
132	C₂²×C₈	C₂²⋊D₄₃	1	4	yes	—
133	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
134	C₂×C₁₆	—	2	4	no	—
135	C₂×C₁₆	—	2	4	no	—
136	C₂×C₁₆	—	2	4	no	—
137	C₂×C₁₆	C₂×Dic₄₃	1	4	yes	—
138	#108	—	43	8	no	—
139	#108	—	86	8	no	—
140	#108	—	86	4	no	—
141	C₂⁴	Dic₁₇₂	1	1	yes	characteristic
142	C₂²×C₄	#10621873	1	4	yes	—
143	C₂²×C₄	D₃₄₄	1	1	yes	characteristic
144	C₂²×C₄	D₃₄₄	1	1	yes	characteristic
145	C₂²×C₄	Dic₁₇₂	1	1	yes	characteristic
146	C₂²×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
147	C₂²×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
148	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	4	yes	—
149	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
150	M₁₆	—	86	8	no	—
151	M₁₆	—	172	8	no	—
152	M₁₆	—	172	4	no	—
153	C₂×C₈	—	172	8	no	—
154	C₂×C₈	—	172	4	no	—
155	C₂×C₈	C₄×Dic₄₃	1	2	yes	—
156	C₂×C₈	C₄×Dic₄₃	1	2	yes	—
157	C₂×C₈	Dic₄₃⋊C₄	1	4	yes	—
158	C₂×C₈	Dic₄₃⋊C₄	1	4	yes	—
159	C₂×C₈	C₄⋊Dic₄₃	1	1	yes	characteristic
160	C₂×C₈	C₄⋊Dic₄₃	1	1	yes	characteristic
161	C₂×C₈	(C₂×D₄₃)⋊C₄	1	4	yes	—
162	C₂×C₈	C₂²⋊Dic₄₃	1	2	yes	—
163	C₂×C₈	C₂²⋊Dic₄₃	1	2	yes	—
164	C₂×C₈	C₂×Dic₈₆	1	1	yes	characteristic
165	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
166	C₂×C₈	C₂²×Dic₄₃	1	1	yes	characteristic
167	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
168	C₁₆	—	2	4	no	—
169	C₂³	—	2	4	no	—
170	C₂³	#13063250	1	4	yes	—
171	C₂³	#13063259	1	1	yes	characteristic
172	C₂³	#13063259	1	1	yes	characteristic
173	C₂³	C₂×Dic₁₇₂	1	1	yes	characteristic
174	C₂×C₄	C₄₃⋊#95	1	2	yes	—
175	C₂×C₄	C₄₃⋊#95	1	2	yes	—
176	C₂×C₄	#13063247	1	4	yes	—
177	C₂×C₄	#13063247	1	4	yes	—
178	C₂×C₄	#13063250	1	4	yes	—
179	C₂×C₄	#13063257	1	2	yes	—
180	C₂×C₄	#13063257	1	2	yes	—
181	C₂×C₄	#13063259	1	1	yes	characteristic
182	C₂×C₄	#13063259	1	1	yes	characteristic
183	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	2	yes	—
184	C₂×C₄	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
185	C₂×C₄	C₂×D₃₄₄	1	1	yes	characteristic
186	C₂×C₄	C₂×#10621873	1	2	yes	—
187	C₈	—	172	8	no	—
188	C₈	C₄₃⋊#95	1	2	yes	—
189	C₈	C₄₃⋊#95	1	2	yes	—
190	C₈	C₂×C₄×Dic₄₃	1	1	yes	characteristic
191	C₈	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
192	C₈	C₂×Dic₄₃⋊C₄	1	2	yes	—
193	C₂²	—	2	8	no	—
194	C₂²	—	2	2	no	—
195	C₂²	—	2	2	no	—
196	C₂²	#14582662	1	2	yes	—
197	C₂²	#14582662	1	2	yes	—
198	C₂²	#14582729	1	4	yes	—
199	C₂²	C₂×#13063250	1	2	yes	—
200	C₂²	C₂×#13063259	1	1	yes	characteristic
201	C₄	#14582662	1	2	yes	—
202	C₄	#14582662	1	2	yes	—
203	C₄	C₂×C₄₃⋊#95	1	1	yes	characteristic
204	C₄	C₂×#13063247	1	2	yes	—
205	C₄	C₂×#13063257	1	1	yes	characteristic
206	C₂	—	2	2	no	—
207	C₂	—	2	2	no	—
208	C₂	#19132689	1	4	yes	direct product factor
209	C₂	C₂×#14582662	1	1	yes	characteristic
210	C₂	C₂×#14582729	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₃₄₄
commutator	C₈×C₄₃	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₂³×C₁₆×C₄₃	C₂
socle	C₂³×C₄₃	#107
prime radical	C₂⁴×C₄₃	Q₁₆
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	C₂³×C₁₆	D₄₃
hypocenter	C₄₃	C₂×#1381
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂³×C₁₆

Complements

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

N	H ≅ G/N	type
2. #19132689	C₂	direct (N × H)
106. C₂×C₄₃	#1381	semidirect
119. C₄₃	C₂×#1381	semidirect
208. C₂	#19132689	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×#13063261	2
#19132689	2
C₂³×C₁₆×C₄₃	2
C₂×#1381	43

Subgroups — C2×#19132689 #25011484

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19132689 #25011484