Subgroups — C₄×#63510 #11857256

Order 1152.

858 conjugacy classes of subgroups.

The subgroup lattice has 162 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₉×#41	C₂	1	1	yes	maximal, characteristic
2	C₂×#63510	C₂	1	2	yes	maximal
3	#10588675	C₂	1	6	yes	maximal, complemented
4	C₄×#3667	C₂	1	3	yes	maximal, complemented
5	C₂×C₄×C₉⋊C₈	C₂	1	3	yes	maximal, complemented
6	C₄×#948	—	3	1	no	maximal
7	C₂×C₉×#41	C₂²	1	1	yes	characteristic
8	C₄×Q₈×C₉	C₄	1	2	yes	—
9	C₄×D₄×C₉	C₄	1	6	yes	—
10	C₉×#117	C₂²	1	3	yes	—
11	C₂×C₄²×C₉	C₂²	1	3	yes	—
12	#63510	C₄	1	16	yes	direct product factor
13	C₂×#3667	C₂²	1	6	yes	—
14	C₂²×C₉⋊C₈	C₂²	1	6	yes	—
15	#63362	C₂²	1	6	yes	—
16	C₄×C₉⋊C₈	C₂²	1	6	yes	—
17	C₄×C₉⋊C₈	C₂²	1	1	yes	characteristic
18	C₄×C₉⋊C₈	C₂²	1	3	yes	—
19	C₃×C₄×#41	D₃	1	1	yes	characteristic
20	C₂×#948	—	3	2	no	—
21	#4997	—	3	6	no	—
22	C₄×#208	—	3	3	no	—
23	C₂×C₄×C₃⋊C₈	—	3	3	no	—
24	C₉×#41	C₂×C₄	1	8	yes	—
25	C₂×Q₈×C₉	C₂×C₄	1	1	yes	characteristic
26	C₂×D₄×C₉	C₂×C₄	1	3	yes	—
27	C₂²×C₄×C₉	C₂×C₄	1	6	yes	—
28	C₂²×C₄×C₉	C₂³	1	3	yes	—
29	C₉×C₄⋊C₄	C₂×C₄	1	6	yes	—
30	C₉×C₂²⋊C₄	C₂×C₄	1	6	yes	—
31	C₄²×C₉	C₂×C₄	1	6	yes	—
32	C₄²×C₉	C₂³	1	1	yes	characteristic
33	C₄²×C₉	C₂³	1	3	yes	—
34	#3667	C₂×C₄	1	24	yes	complemented
35	C₂×C₉⋊C₈	C₂×C₄	1	24	yes	complemented
36	C₂×C₉⋊C₈	C₂³	1	2	yes	—
37	C₂×C₉⋊C₈	C₂³	1	6	yes	—
38	C₄×#131	—	9	1	no	Sylow
39	C₂×C₃×#41	C₂×D₃	1	1	yes	characteristic
40	C₃×C₄×Q₈	Dic₃	1	2	yes	—
41	C₃×C₄×D₄	Dic₃	1	6	yes	—
42	C₃×#117	C₂×D₃	1	3	yes	—
43	C₂×C₃×C₄²	C₂×D₃	1	3	yes	—
44	#948	—	3	16	no	—
45	C₂×#208	—	3	6	no	—
46	C₂²×C₃⋊C₈	—	3	6	no	—
47	#803	—	3	6	no	—
48	C₄×C₃⋊C₈	—	3	1	no	—
49	C₄×C₃⋊C₈	—	3	3	no	—
50	C₄×C₃⋊C₈	—	3	6	no	—
51	C₂³×C₉	C₂²×C₄	1	3	yes	—
52	Q₈×C₉	C₄²	1	4	yes	—
53	D₄×C₉	C₄²	1	12	yes	—
54	C₂×C₄×C₉	—	2	12	no	—
55	C₂×C₄×C₉	C₂²×C₄	1	12	yes	—
56	C₂×C₄×C₉	C₂²×C₄	1	6	yes	—
57	C₂×C₄×C₉	C₂²×C₄	1	3	yes	—
58	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
59	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
60	C₉⋊C₈	C₂²×C₄	1	4	yes	—
61	C₉⋊C₈	C₂²×C₄	1	12	yes	—
62	C₂×#131	—	9	2	no	—
63	C₄×#41	D₉	1	1	yes	characteristic
64	#405	—	9	6	no	—
65	C₄×M₁₆	—	9	3	no	—
66	C₂×C₄×C₈	—	9	3	no	—
67	C₃×#41	C₄×D₃	1	8	yes	—
68	C₂×C₃×Q₈	C₂×Dic₃	1	1	yes	characteristic
69	C₂×C₃×D₄	C₂×Dic₃	1	3	yes	—
70	C₂²×C₃×C₄	C₂×Dic₃	1	6	yes	—
71	C₂²×C₃×C₄	C₂²×D₃	1	3	yes	—
72	C₃×C₄⋊C₄	C₂×Dic₃	1	6	yes	—
73	C₃×C₂²⋊C₄	C₂×Dic₃	1	6	yes	—
74	C₃×C₄²	C₂×Dic₃	1	6	yes	—
75	C₃×C₄²	C₂²×D₃	1	3	yes	—
76	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
77	#208	—	3	24	no	—
78	C₂×C₃⋊C₈	—	3	24	no	—
79	C₂×C₃⋊C₈	—	3	2	no	—
80	C₂×C₃⋊C₈	—	3	6	no	—
81	C₂²×C₉	—	2	6	no	—
82	C₂²×C₉	C₂×C₄²	1	6	yes	—
83	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
84	C₄×C₉	—	2	6	no	—
85	C₄×C₉	C₂×C₄²	1	6	yes	—
86	C₄×C₉	#131	1	4	yes	complemented
87	C₄×C₉	C₂³×C₄	1	2	yes	—
88	C₂×#41	C₂×D₉	1	1	yes	characteristic
89	#131	—	9	16	no	—
90	C₂×M₁₆	—	9	6	no	—
91	C₂²×C₈	—	9	6	no	—
92	C₄×Q₈	Dic₉	1	2	yes	—
93	C₄×D₄	Dic₉	1	6	yes	—
94	#117	C₂×D₉	1	3	yes	—
95	C₂×C₄²	C₂×D₉	1	3	yes	—
96	#97	—	9	6	no	—
97	C₄×C₈	—	9	6	no	—
98	C₄×C₈	—	9	1	no	—
99	C₄×C₈	—	9	3	no	—
100	C₂³×C₃	C₂²×Dic₃	1	3	yes	—
101	C₃×Q₈	C₄×Dic₃	1	4	yes	—
102	C₃×D₄	C₄×Dic₃	1	12	yes	—
103	C₂×C₃×C₄	—	2	12	no	—
104	C₂×C₃×C₄	C₂×C₄×D₃	1	12	yes	—
105	C₂×C₃×C₄	C₂²×Dic₃	1	6	yes	—
106	C₂×C₃×C₄	C₂²×Dic₃	1	3	yes	—
107	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
108	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
109	C₃⋊C₈	—	3	4	no	—
110	C₃⋊C₈	—	3	12	no	—
111	C₂×C₉	—	2	6	no	—
112	C₂×C₉	C₂²×C₄²	1	1	yes	characteristic
113	C₂×C₉	C₂×#131	1	2	yes	—
114	#41	C₄×D₉	1	8	yes	—
115	C₂×Q₈	C₂×Dic₉	1	1	yes	characteristic
116	C₂×D₄	C₂×Dic₉	1	3	yes	—
117	C₂²×C₄	C₂×Dic₉	1	6	yes	—
118	C₂²×C₄	C₂²×D₉	1	3	yes	—
119	M₁₆	—	9	24	no	—
120	C₂×C₈	—	9	24	no	—
121	C₂×C₈	—	9	2	no	—
122	C₂×C₈	—	9	6	no	—
123	C₄⋊C₄	C₂×Dic₉	1	6	yes	—
124	C₂²⋊C₄	C₂×Dic₉	1	6	yes	—
125	C₄²	C₂×Dic₉	1	6	yes	—
126	C₄²	C₂²×D₉	1	3	yes	—
127	C₄²	C₂²×D₉	1	1	yes	characteristic
128	C₂²×C₃	—	2	6	no	—
129	C₂²×C₃	C₂×C₄×Dic₃	1	6	yes	—
130	C₂²×C₃	C₂³×Dic₃	1	1	yes	characteristic
131	C₃×C₄	—	2	6	no	—
132	C₃×C₄	C₂×C₄×Dic₃	1	6	yes	—
133	C₃×C₄	#948	1	4	yes	—
134	C₃×C₄	C₂²×C₄×D₃	1	2	yes	—
135	C₉	C₄×#131	1	1	yes	characteristic, complemented, Sylow
136	C₂³	C₂²×Dic₉	1	3	yes	—
137	Q₈	C₄×Dic₉	1	4	yes	—
138	D₄	C₄×Dic₉	1	12	yes	—
139	C₂×C₄	—	2	12	no	—
140	C₂×C₄	C₂×C₄×D₉	1	12	yes	—
141	C₂×C₄	C₂²×Dic₉	1	6	yes	—
142	C₂×C₄	C₂²×Dic₉	1	2	yes	—
143	C₂×C₄	C₂²×Dic₉	1	3	yes	—
144	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
145	C₈	—	9	4	no	—
146	C₈	—	9	12	no	—
147	C₂×C₃	—	2	6	no	—
148	C₂×C₃	C₂²×C₄×Dic₃	1	1	yes	characteristic
149	C₂×C₃	C₂×#948	1	2	yes	—
150	C₂²	—	2	6	no	—
151	C₂²	C₂×C₄×Dic₉	1	6	yes	—
152	C₂²	C₂³×Dic₉	1	1	yes	characteristic
153	C₄	—	2	6	no	—
154	C₄	C₂×C₄×Dic₉	1	6	yes	—
155	C₄	#63510	1	4	yes	direct product factor
156	C₄	C₂²×C₄×D₉	1	2	yes	—
157	C₃	C₄×#948	1	1	yes	characteristic
158	C₂	—	2	6	no	—
159	C₂	C₂²×C₄×Dic₉	1	1	yes	characteristic
160	C₂	C₂×#63510	1	2	yes	—

	subgroup	G/H
center	C₄²	C₂²×D₉
commutator	C₂×C₉	C₂²×C₄²
Frattini	C₂×C₃×C₄	C₂³×D₃
Fitting	C₄×C₉×#41	C₂
socle	C₂²×C₃	C₂³×Dic₃
prime radical	C₂×C₃×#41	C₂×D₃
cosocle	C₂×C₄×C₉	C₂⁴
hypercenter	C₄×#41	D₉
hypocenter	C₉	C₄×#131
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₄² ◁ C₄×#41

Complements

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

N	H ≅ G/N	type
3. #10588675	C₂	semidirect
4. C₄×#3667	C₂	semidirect
5. C₂×C₄×C₉⋊C₈	C₂	semidirect
12. #63510	C₄	direct (N × H)
34. #3667	C₂×C₄	semidirect
35. C₂×C₉⋊C₈	C₂×C₄	semidirect
86. C₄×C₉	#131	semidirect
135. C₉	C₄×#131	semidirect
155. C₄	#63510	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₉×#41	2
C₂×#63510	2
#10588675	2
C₄×#3667	2
C₂×C₄×C₉⋊C₈	2
C₄×#948	3

Subgroups — C4×#63510 #11857256

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#63510 #11857256