Subgroups — C₈×#13093935 #26105631

Order 12032.

606 conjugacy classes of subgroups.

The subgroup lattice has 156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20243134	C₂	1	1	yes	maximal, characteristic
2	C₄×#13093935	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688845	C₂	1	2	yes	maximal
4	C₂×C₈×C₄₇⋊C₈	C₂	1	2	yes	maximal
5	C₄²×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#13093935	C₄	1	4	yes	—
7	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
8	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
9	#15688878	C₄	1	4	yes	—
10	#15688845	C₄	1	8	yes	complemented
11	C₈×C₄₇⋊C₈	C₄	1	8	yes	complemented
12	C₂×C₄×C₈×C₄₇	C₄	1	4	yes	—
13	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₄³×C₄₇	C₂²	1	1	yes	characteristic
16	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
17	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
18	#13093935	C₈	1	16	yes	direct product factor
19	C₄×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
20	C₄×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
21	C₄×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
22	C₄×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
23	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
24	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
25	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
26	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
27	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
28	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
29	C₄×C₈×C₄₇	—	2	8	no	—
30	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	—
31	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	—
32	C₂²×C₄×C₄₇	C₄²	1	4	yes	—
33	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
34	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
35	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₈×C₄₇	—	2	4	no	—
37	C₂×C₈×C₄₇	C₄²	1	4	yes	—
38	C₂×C₈×C₄₇	C₄²	1	4	yes	—
39	C₂×C₈×C₄₇	M₁₆	1	8	yes	—
40	C₄²×C₄₇	—	2	4	no	—
41	C₄²×C₄₇	—	2	4	no	—
42	C₄²×C₄₇	C₂×C₈	1	8	yes	—
43	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
44	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
45	C₂×C₄₇⋊C₈	—	2	8	no	—
46	C₂×C₄₇⋊C₈	C₄²	1	8	yes	—
47	C₂×C₄₇⋊C₈	C₄²	1	8	yes	—
48	C₂×C₄₇⋊C₈	C₂×C₈	1	16	yes	—
49	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
50	C₂×C₄×C₄₇	—	2	4	no	—
51	C₂×C₄×C₄₇	—	2	4	no	—
52	C₂×C₄×C₄₇	C₄×C₈	1	8	yes	—
53	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
54	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
55	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
56	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
57	C₂×C₄×C₄₇	C₂²×C₈	1	4	yes	—
58	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
59	C₂×C₄×C₄₇	#131	1	4	yes	—
60	C₈×C₄₇	—	2	4	no	—
61	C₈×C₄₇	#97	1	8	yes	complemented
62	C₄₇⋊C₈	—	2	8	no	—
63	C₄₇⋊C₈	C₄×C₈	1	16	yes	complemented
64	C₈×#97	—	47	1	no	maximal, Sylow
65	C₂²×C₄₇	C₄³	1	1	yes	characteristic
66	C₂²×C₄₇	C₂×C₄×C₈	1	2	yes	—
67	C₂²×C₄₇	C₄×M₁₆	1	2	yes	—
68	C₂²×C₄₇	#405	1	2	yes	—
69	C₄×C₄₇	—	2	8	no	—
70	C₄×C₄₇	C₂×C₄×C₈	1	4	yes	—
71	C₄×C₄₇	C₂×#97	1	2	yes	—
72	C₄×C₄₇	C₄×M₁₆	1	2	yes	—
73	C₄×C₄₇	#405	1	4	yes	—
74	#1744	—	47	1	no	—
75	C₄×#97	—	47	1	no	—
76	C₄²×C₈	D₄₇	1	1	yes	characteristic
77	C₂×#322	—	47	2	no	—
78	C₂×C₈²	—	47	2	no	—
79	C₂×C₄₇	C₈×M₁₆	1	4	yes	—
80	C₂×C₄₇	C₄²×C₈	1	1	yes	characteristic
81	C₂×C₄₇	C₄×#97	1	1	yes	characteristic
82	C₂×C₄₇	#1726	1	1	yes	characteristic
83	C₂×#97	—	47	4	no	—
84	C₂×C₄×C₈	—	47	2	no	—
85	C₂×C₄×C₈	—	47	2	no	—
86	C₂×C₄×C₈	Dic₄₇	1	4	yes	—
87	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
88	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
89	C₄³	C₂×D₄₇	1	1	yes	characteristic
90	#336	—	47	4	no	—
91	#322	—	47	8	no	—
92	C₈²	—	47	8	no	—
93	C₄₇	C₈×#97	1	1	yes	characteristic, complemented, Sylow
94	C₂²×C₈	—	47	4	no	—
95	C₂²×C₈	—	47	4	no	—
96	C₂²×C₈	C₂×Dic₄₇	1	2	yes	—
97	C₂²×C₈	C₂×Dic₄₇	1	2	yes	—
98	C₂×C₄²	C₄×D₄₇	1	2	yes	—
99	C₂×C₄²	C₄×D₄₇	1	2	yes	—
100	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
101	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
102	#97	—	47	16	no	—
103	C₄×C₈	—	2	8	no	—
104	C₄×C₈	—	47	4	no	—
105	C₄×C₈	—	47	4	no	—
106	C₄×C₈	—	47	4	no	—
107	C₄×C₈	—	47	4	no	—
108	C₄×C₈	C₄×D₄₇	1	4	yes	—
109	C₄×C₈	C₄×D₄₇	1	4	yes	—
110	C₂²×C₄	C₄×Dic₄₇	1	4	yes	—
111	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
112	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
113	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
114	C₂×C₈	—	2	4	no	—
115	C₂×C₈	—	47	8	no	—
116	C₂×C₈	—	47	16	no	—
117	C₂×C₈	—	47	8	no	—
118	C₂×C₈	—	94	8	no	—
119	C₂×C₈	#10625329	1	8	yes	—
120	C₂×C₈	C₄×Dic₄₇	1	4	yes	—
121	C₂×C₈	C₄×Dic₄₇	1	4	yes	—
122	C₄²	—	2	4	no	—
123	C₄²	—	2	4	no	—
124	C₄²	C₈×D₄₇	1	8	yes	—
125	C₄²	C₂×C₄×D₄₇	1	2	yes	—
126	C₄²	C₂×C₄×D₄₇	1	2	yes	—
127	C₂³	C₂×C₄×Dic₄₇	1	1	yes	characteristic
128	C₂×C₄	—	2	4	no	—
129	C₂×C₄	—	2	4	no	—
130	C₂×C₄	C₈×Dic₄₇	1	8	yes	—
131	C₂×C₄	C₄²×D₄₇	1	2	yes	—
132	C₂×C₄	C₄²×D₄₇	1	2	yes	—
133	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
134	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
135	C₂×C₄	C₂×C₈×D₄₇	1	4	yes	—
136	C₂×C₄	C₂×#10625329	1	4	yes	—
137	C₂×C₄	#13094030	1	4	yes	—
138	C₈	—	2	4	no	—
139	C₈	—	47	16	no	—
140	C₈	—	94	8	no	—
141	C₈	#13093935	1	8	yes	direct product factor
142	C₂²	C₄²×Dic₄₇	1	1	yes	characteristic
143	C₂²	C₂×C₈×Dic₄₇	1	2	yes	—
144	C₂²	C₄×#10625329	1	2	yes	—
145	C₂²	#15689078	1	2	yes	—
146	C₄	—	2	8	no	—
147	C₄	C₄×C₈×D₄₇	1	4	yes	—
148	C₄	C₂×#13093935	1	2	yes	—
149	C₄	C₄×#10625329	1	2	yes	—
150	C₄	#15689077	1	4	yes	—
151	C₂	C₈×#10625329	1	4	yes	—
152	C₂	C₄×C₈×Dic₄₇	1	1	yes	characteristic
153	C₂	C₄×#13093935	1	1	yes	characteristic
154	C₂	#20243074	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₈	C₂×D₄₇
commutator	C₂×C₄₇	C₄²×C₈
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄²×C₈×C₄₇	C₂
socle, prime radical	C₂³×C₄₇	C₂×C₄²
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₄²×C₈	D₄₇
hypocenter	C₄₇	C₈×#97
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄×C₈ ◁ C₄²×C₈

Complements

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

N	H ≅ G/N	type
10. #15688845	C₄	semidirect
11. C₈×C₄₇⋊C₈	C₄	semidirect
18. #13093935	C₈	direct (N × H)
61. C₈×C₄₇	#97	semidirect
63. C₄₇⋊C₈	C₄×C₈	semidirect
93. C₄₇	C₈×#97	semidirect
141. C₈	#13093935	direct (N × H)

Maximal subgroups

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

subgroup	index
#20243134	2
C₄×#13093935	2
C₂×#15688845	2
C₂×C₈×C₄₇⋊C₈	2
C₄²×C₈×C₄₇	2
C₈×#97	47

Subgroups — C8×#13093935 #26105631

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#13093935 #26105631