Subgroups — C₂×#10589377 #11797043

Order 1152.

504 conjugacy classes of subgroups.

The subgroup lattice has 177 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#63639	C₂	1	1	yes	maximal, characteristic
4	#10589377	C₂	1	4	yes	maximal, direct product factor
5	C₂×#4511	—	3	4	no	maximal
6	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₃⋊Dic₃	C₄	1	1	yes	characteristic
8	C₂²×C₃⋊(C₃⋊C₈)	C₄	1	1	yes	characteristic
9	C₃²×M₃₂	—	2	1	no	—
10	C₃²×M₃₂	C₂²	1	2	yes	—
11	C₂×C₃²×C₁₆	—	2	1	no	—
12	C₈×C₃⋊Dic₃	C₄	1	2	yes	—
13	C₈×C₃⋊Dic₃	C₂²	1	2	yes	—
14	#63639	—	2	1	no	—
15	#63639	C₂²	1	2	yes	—
16	C₂×C₃⋊(C₃⋊C₁₆)	—	2	1	no	—
17	C₂×C₃×M₃₂	D₃	1	4	yes	—
18	C₂×C₈×Dic₃	—	3	4	no	—
19	C₂×#812	—	3	4	no	—
20	#4511	—	3	16	no	—
21	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₃⋊Dic₃	—	2	1	no	—
23	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
24	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
25	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
26	C₂×C₃²×C₈	Q₈	1	1	yes	characteristic
27	C₂×C₃²×C₈	Q₈	1	1	yes	characteristic
28	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
29	C₄×C₃⋊Dic₃	—	2	1	no	—
30	C₄×C₃⋊Dic₃	C₂×C₄	1	2	yes	—
31	C₂×C₃⋊(C₃⋊C₈)	C₈	1	2	yes	—
32	C₂×C₃⋊(C₃⋊C₈)	C₈	1	2	yes	—
33	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	2	yes	—
34	C₃²×C₁₆	—	2	2	no	—
35	C₃⋊(C₃⋊C₁₆)	—	2	2	no	—
36	C₂×#364	—	9	1	no	Sylow
37	C₂²×C₃×C₈	C₂×D₃	1	4	yes	—
38	C₂×C₄×Dic₃	—	3	4	no	—
39	C₂²×C₃⋊C₈	—	3	4	no	—
40	C₃×M₃₂	—	2	4	no	—
41	C₃×M₃₂	C₂×D₃	1	8	yes	—
42	C₂×C₃×C₁₆	—	2	4	no	—
43	C₈×Dic₃	—	3	8	no	—
44	C₈×Dic₃	—	3	8	no	—
45	#812	—	3	8	no	—
46	#812	—	6	4	no	—
47	C₂×C₃⋊C₁₆	—	6	4	no	—
48	C₂³×C₃²	M₁₆	1	1	yes	characteristic
49	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
50	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
51	C₂×C₃²×C₄	C₂×C₈	1	1	yes	characteristic
52	C₂×C₃²×C₄	C₂×C₈	1	1	yes	characteristic
53	C₂×C₃²×C₄	M₁₆	1	1	yes	characteristic
54	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
55	C₂×C₃⋊Dic₃	—	2	4	no	—
56	C₂×C₃⋊Dic₃	—	2	2	no	—
57	C₃²×C₈	C₄⋊C₄	1	1	yes	characteristic
58	C₃²×C₈	C₄⋊C₄	1	1	yes	characteristic
59	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
60	C₃²×C₈	C₂×Q₈	1	1	yes	characteristic
61	C₃⋊(C₃⋊C₈)	C₂×C₈	1	4	yes	—
62	C₂×M₃₂	—	9	1	no	—
63	C₂×M₃₂	C₃⋊D₃	1	1	yes	characteristic
64	C₂×C₄×C₈	—	9	1	no	—
65	#364	—	9	4	no	—
66	C₂²×C₃×C₄	C₄×D₃	1	4	yes	—
67	C₂²×Dic₃	—	6	4	no	—
68	C₂×C₃×C₈	Dic₆	1	4	yes	—
69	C₂×C₃×C₈	Dic₆	1	4	yes	—
70	C₂×C₃×C₈	C₄×D₃	1	4	yes	—
71	C₂×C₃×C₈	#67	1	4	yes	—
72	C₂×C₃×C₈	#67	1	4	yes	—
73	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
74	C₄×Dic₃	—	3	8	no	—
75	C₄×Dic₃	—	6	4	no	—
76	C₂×C₃⋊C₈	—	3	8	no	—
77	C₂×C₃⋊C₈	—	3	8	no	—
78	C₂×C₃⋊C₈	—	3	8	no	—
79	C₃×C₁₆	—	2	8	no	—
80	C₃⋊C₁₆	—	6	8	no	—
81	C₂²×C₃²	—	2	2	no	—
82	C₂²×C₃²	C₄⋊C₈	1	1	yes	characteristic
83	C₂²×C₃²	C₄⋊C₈	1	1	yes	characteristic
84	C₂²×C₃²	C₂×M₁₆	1	1	yes	characteristic
85	C₃²×C₄	C₄⋊C₈	1	1	yes	characteristic
86	C₃²×C₄	C₄⋊C₈	1	1	yes	characteristic
87	C₃²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
88	C₃²×C₄	C₂²×C₈	1	1	yes	characteristic
89	C₃⋊Dic₃	—	2	4	no	—
90	C₂²×C₈	—	9	1	no	—
91	C₂²×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
92	C₂×C₄²	—	9	1	no	—
93	M₃₂	—	2	1	no	—
94	M₃₂	—	9	2	no	—
95	M₃₂	—	18	1	no	—
96	M₃₂	C₂×C₃⋊D₃	1	2	yes	—
97	C₂×C₁₆	—	2	1	no	—
98	C₂×C₁₆	—	18	1	no	—
99	C₄×C₈	—	9	2	no	—
100	C₄×C₈	—	9	2	no	—
101	C₂³×C₃	ΓL(1,𝔽₂₅)	1	4	yes	—
102	C₂×C₃×C₄	D₃×C₈	1	4	yes	—
103	C₂×C₃×C₄	D₃×C₈	1	4	yes	—
104	C₂×C₃×C₄	ΓL(1,𝔽₂₅)	1	4	yes	—
105	C₂×C₃×C₄	Dic₃⋊C₄	1	4	yes	—
106	C₂×C₃×C₄	Dic₃⋊C₄	1	4	yes	—
107	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
108	C₂×Dic₃	—	6	16	no	—
109	C₂×Dic₃	—	6	8	no	—
110	C₃×C₈	Dic₃⋊C₄	1	4	yes	—
111	C₃×C₈	Dic₃⋊C₄	1	4	yes	—
112	C₃×C₈	C₂×Dic₆	1	4	yes	—
113	C₃×C₈	C₂×#67	1	4	yes	—
114	C₃⋊C₈	—	3	16	no	—
115	C₂×C₃²	—	2	1	no	—
116	C₂×C₃²	—	2	1	no	—
117	C₂×C₃²	#364	1	2	yes	complemented
118	C₂×C₃²	C₂×C₄⋊C₈	1	1	yes	characteristic
119	C₂²×C₄	—	18	1	no	—
120	C₂²×C₄	C₄×C₃⋊D₃	1	1	yes	characteristic
121	C₂×C₈	—	9	2	no	—
122	C₂×C₈	—	9	2	no	—
123	C₂×C₈	—	9	2	no	—
124	C₂×C₈	#634	1	1	yes	characteristic
125	C₂×C₈	#634	1	1	yes	characteristic
126	C₂×C₈	C₄×C₃⋊D₃	1	1	yes	characteristic
127	C₂×C₈	#638	1	1	yes	characteristic
128	C₂×C₈	#638	1	1	yes	characteristic
129	C₂×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
130	C₄²	—	9	2	no	—
131	C₄²	—	18	1	no	—
132	C₁₆	—	2	2	no	—
133	C₁₆	—	18	2	no	—
134	C₂²×C₃	—	2	8	no	—
135	C₂²×C₃	Dic₃⋊C₈	1	4	yes	—
136	C₂²×C₃	Dic₃⋊C₈	1	4	yes	—
137	C₂²×C₃	C₂×ΓL(1,𝔽₂₅)	1	4	yes	—
138	C₃×C₄	Dic₃⋊C₈	1	4	yes	—
139	C₃×C₄	Dic₃⋊C₈	1	4	yes	—
140	C₃×C₄	C₂×D₃×C₈	1	4	yes	—
141	C₃×C₄	C₂×Dic₃⋊C₄	1	4	yes	—
142	Dic₃	—	6	16	no	—
143	C₃²	C₂×#364	1	1	yes	characteristic, complemented, Sylow
144	C₂³	#3743	1	1	yes	characteristic
145	C₂×C₄	—	18	4	no	—
146	C₂×C₄	—	18	2	no	—
147	C₂×C₄	C₈×C₃⋊D₃	1	1	yes	characteristic
148	C₂×C₄	C₈×C₃⋊D₃	1	1	yes	characteristic
149	C₂×C₄	#3743	1	1	yes	characteristic
150	C₂×C₄	#3750	1	1	yes	characteristic
151	C₂×C₄	#3750	1	1	yes	characteristic
152	C₂×C₄	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
153	C₈	—	9	4	no	—
154	C₈	#3750	1	1	yes	characteristic
155	C₈	#3750	1	1	yes	characteristic
156	C₈	C₂×#634	1	1	yes	characteristic
157	C₈	C₂×#638	1	1	yes	characteristic
158	C₂×C₃	—	2	4	no	—
159	C₂×C₃	—	2	4	no	—
160	C₂×C₃	#4511	1	8	yes	complemented
161	C₂×C₃	C₂×Dic₃⋊C₈	1	4	yes	—
162	C₂²	—	2	2	no	—
163	C₂²	#63641	1	1	yes	characteristic
164	C₂²	#63641	1	1	yes	characteristic
165	C₂²	C₂×#3743	1	1	yes	characteristic
166	C₄	—	18	4	no	—
167	C₄	#63641	1	1	yes	characteristic
168	C₄	#63641	1	1	yes	characteristic
169	C₄	C₂×C₈×C₃⋊D₃	1	1	yes	characteristic
170	C₄	C₂×#3750	1	1	yes	characteristic
171	C₃	C₂×#4511	1	4	yes	complemented
172	C₂	—	2	1	no	—
173	C₂	—	2	1	no	—
174	C₂	#10589377	1	2	yes	direct product factor
175	C₂	C₂×#63641	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	#638
commutator	C₃²×C₄	C₂²×C₈
Frattini	C₂×C₈	C₂²×C₃⋊D₃
Fitting	C₂×C₃²×M₃₂	C₂
socle	C₂²×C₃²	C₄⋊C₈
prime radical	C₂³×C₃²	M₁₆
cosocle	C₂×C₃²×C₈	C₂³
hypercenter	C₂×M₃₂	C₃⋊D₃
hypocenter	C₃²	C₂×#364
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
4. #10589377	C₂	direct (N × H)
117. C₂×C₃²	#364	semidirect
143. C₃²	C₂×#364	semidirect
160. C₂×C₃	#4511	semidirect
171. C₃	C₂×#4511	semidirect
174. C₂	#10589377	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃²×M₃₂	2
C₂×C₈×C₃⋊Dic₃	2
C₂×#63639	2
#10589377	2
C₂×#4511	3

Subgroups — C2×#10589377 #11797043

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10589377 #11797043