Subgroups — C₄×#15688968 #26137348

Order 12032.

2302 conjugacy classes of subgroups.

The subgroup lattice has 186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15688968	C₂	1	4	yes	maximal
2	C₂×C₄²×Dic₄₇	C₂	1	3	yes	maximal
3	C₄×C₄₇⋊#95	C₂	1	3	yes	maximal
4	#95×Dic₄₇	C₂	1	4	yes	maximal
5	C₄×#95×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄×Dic₄₇	C₂²	1	6	yes	—
7	C₂²×C₄×Dic₄₇	C₂²	1	3	yes	—
8	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
9	C₂²×C₄×Dic₄₇	C₂²	1	6	yes	—
10	#15688968	C₄	1	32	yes	direct product factor
11	C₂×C₄₇⋊#95	C₂²	1	12	yes	—
12	C₄²×Dic₄₇	C₄	1	24	yes	complemented
13	C₂²×C₄²×C₄₇	C₂²	1	3	yes	—
14	C₂×#95×C₄₇	C₂²	1	4	yes	—
15	C₂³×Dic₄₇	C₂³	1	6	yes	—
16	C₂³×Dic₄₇	C₂³	1	1	yes	characteristic
17	C₂³×Dic₄₇	C₂³	1	1	yes	characteristic
18	C₂×C₄×Dic₄₇	—	2	6	no	—
19	C₂×C₄×Dic₄₇	—	2	6	no	—
20	C₂×C₄×Dic₄₇	—	2	24	no	—
21	C₂×C₄×Dic₄₇	C₂×C₄	1	12	yes	—
22	C₂×C₄×Dic₄₇	C₂×C₄	1	24	yes	—
23	C₂×C₄×Dic₄₇	C₂×C₄	1	12	yes	—
24	C₂×C₄×Dic₄₇	C₂×C₄	1	24	yes	—
25	C₂×C₄×Dic₄₇	C₂×C₄	1	48	yes	—
26	C₄₇⋊#95	C₂×C₄	1	48	yes	—
27	C₂³×C₄×C₄₇	C₂³	1	6	yes	—
28	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
29	C₂×C₄²×C₄₇	—	2	12	no	—
30	C₂×C₄²×C₄₇	C₂×C₄	1	12	yes	—
31	#95×C₄₇	C₂×C₄	1	16	yes	—
32	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
33	C₂²×C₄×C₄₇	—	2	12	no	—
34	C₂²×C₄×C₄₇	—	2	12	no	—
35	C₂²×C₄×C₄₇	C₂²×C₄	1	12	yes	—
36	C₂²×C₄×C₄₇	C₂²×C₄	1	24	yes	—
37	C₂²×C₄×C₄₇	C₂²×C₄	1	6	yes	—
38	C₂²×C₄×C₄₇	#41	1	6	yes	—
39	C₂²×C₄×C₄₇	#41	1	2	yes	—
40	C₂²×Dic₄₇	—	2	12	no	—
41	C₂²×Dic₄₇	—	2	6	no	—
42	C₂²×Dic₄₇	—	2	6	no	—
43	C₂²×Dic₄₇	C₂²×C₄	1	24	yes	—
44	C₂²×Dic₄₇	C₂²×C₄	1	12	yes	—
45	C₂²×Dic₄₇	C₂²×C₄	1	6	yes	—
46	C₂²×Dic₄₇	C₂²×C₄	1	8	yes	—
47	C₂²×Dic₄₇	C₂²×C₄	1	6	yes	—
48	C₂²×Dic₄₇	#41	1	8	yes	—
49	C₄²×C₄₇	—	2	24	no	—
50	C₄×Dic₄₇	—	2	24	no	—
51	C₄×Dic₄₇	—	2	48	no	—
52	C₄×Dic₄₇	C₄²	1	16	yes	—
53	C₄×Dic₄₇	C₄²	1	96	yes	complemented
54	C₂³×C₄₇	C₂³×C₄	1	3	yes	—
55	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
56	C₂³×C₄₇	C₂×#41	1	4	yes	—
57	C₂³×C₄₇	C₂×#41	1	3	yes	—
58	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
59	C₂×C₄×C₄₇	—	2	12	no	—
60	C₂×C₄×C₄₇	—	2	12	no	—
61	C₂×C₄×C₄₇	—	2	48	no	—
62	C₂×C₄×C₄₇	C₂×C₄²	1	24	yes	—
63	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
64	C₂×C₄×C₄₇	#117	1	12	yes	—
65	C₂×C₄×C₄₇	#117	1	12	yes	—
66	C₂×Dic₄₇	—	2	12	no	—
67	C₂×Dic₄₇	—	2	12	no	—
68	C₂×Dic₄₇	—	2	24	no	—
69	C₂×Dic₄₇	—	2	24	no	—
70	C₂×Dic₄₇	C₂×C₄²	1	24	yes	—
71	C₂×Dic₄₇	C₂×C₄²	1	4	yes	—
72	C₂×Dic₄₇	C₂×C₄²	1	24	yes	—
73	C₂×Dic₄₇	C₂×C₄²	1	4	yes	—
74	C₂×Dic₄₇	#117	1	24	yes	—
75	C₄×#376	—	47	1	no	maximal, Sylow
76	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
77	C₂²×C₄₇	C₂²×C₄²	1	6	yes	—
78	C₂²×C₄₇	C₂×#117	1	6	yes	—
79	C₂²×C₄₇	C₂×#117	1	3	yes	—
80	C₂²×C₄₇	C₂×#117	1	3	yes	—
81	C₂²×C₄₇	C₄×#41	1	12	yes	—
82	C₂²×C₄₇	C₄×#41	1	4	yes	—
83	C₄×C₄₇	—	2	24	no	—
84	C₄×C₄₇	#376	1	8	yes	complemented
85	Dic₄₇	—	2	24	no	—
86	Dic₄₇	C₄³	1	8	yes	—
87	Dic₄₇	#376	1	8	yes	complemented
88	C₂×#376	—	47	4	no	—
89	C₂×C₄³	—	47	3	no	—
90	C₄×#95	—	47	3	no	—
91	C₄×#95	—	47	4	no	—
92	C₄×#95	D₄₇	1	1	yes	characteristic
93	C₂×C₄₇	C₂×C₄³	1	1	yes	characteristic
94	C₂×C₄₇	C₂×#376	1	1	yes	characteristic
95	C₂×C₄₇	C₂×#376	1	1	yes	characteristic
96	C₂×C₄₇	C₄×#117	1	6	yes	—
97	C₂×C₄₇	C₄×#117	1	6	yes	—
98	C₂²×C₄²	—	47	6	no	—
99	C₂²×C₄²	—	47	1	no	—
100	C₂²×C₄²	—	47	6	no	—
101	C₂²×C₄²	—	47	3	no	—
102	C₂²×C₄²	C₂×D₄₇	1	3	yes	—
103	#376	—	47	32	no	—
104	C₂×#95	—	47	12	no	—
105	C₂×#95	C₂×D₄₇	1	4	yes	—
106	C₄³	—	47	24	no	—
107	C₄₇	C₄×#376	1	1	yes	characteristic, complemented, Sylow
108	C₂³×C₄	—	47	1	no	—
109	C₂³×C₄	—	47	1	no	—
110	C₂³×C₄	—	47	6	no	—
111	C₂³×C₄	C₂²×D₄₇	1	6	yes	—
112	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
113	C₂×C₄²	—	2	12	no	—
114	C₂×C₄²	—	47	12	no	—
115	C₂×C₄²	—	47	24	no	—
116	C₂×C₄²	—	47	48	no	—
117	C₂×C₄²	—	47	24	no	—
118	C₂×C₄²	—	47	12	no	—
119	C₂×C₄²	—	94	24	no	—
120	C₂×C₄²	—	94	6	no	—
121	C₂×C₄²	—	94	6	no	—
122	C₂×C₄²	C₄×D₄₇	1	12	yes	—
123	#95	—	47	48	no	—
124	#95	C₄×D₄₇	1	16	yes	—
125	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
126	C₂²×C₄	—	2	12	no	—
127	C₂²×C₄	—	2	12	no	—
128	C₂²×C₄	—	47	6	no	—
129	C₂²×C₄	—	47	8	no	—
130	C₂²×C₄	—	47	6	no	—
131	C₂²×C₄	—	47	8	no	—
132	C₂²×C₄	—	47	24	no	—
133	C₂²×C₄	—	47	12	no	—
134	C₂²×C₄	—	94	12	no	—
135	C₂²×C₄	—	94	6	no	—
136	C₂²×C₄	—	94	6	no	—
137	C₂²×C₄	C₂×C₄×D₄₇	1	24	yes	—
138	C₂²×C₄	C₂×C₄×D₄₇	1	12	yes	—
139	C₂²×C₄	C₂×C₄×D₄₇	1	6	yes	—
140	C₂²×C₄	#10625352	1	6	yes	—
141	C₂²×C₄	#10625354	1	2	yes	—
142	C₄²	—	2	24	no	—
143	C₄²	—	47	16	no	—
144	C₄²	—	47	96	no	—
145	C₄²	—	94	48	no	—
146	C₄²	—	94	24	no	—
147	C₂³	C₂²×C₄×D₄₇	1	3	yes	—
148	C₂³	C₂²×C₄×D₄₇	1	4	yes	—
149	C₂³	#41×D₄₇	1	4	yes	—
150	C₂³	C₂×#10625352	1	3	yes	—
151	C₂³	C₂×#10625354	1	1	yes	characteristic
152	C₂×C₄	—	2	12	no	—
153	C₂×C₄	—	2	12	no	—
154	C₂×C₄	—	2	48	no	—
155	C₂×C₄	—	47	4	no	—
156	C₂×C₄	—	47	24	no	—
157	C₂×C₄	—	47	4	no	—
158	C₂×C₄	—	47	24	no	—
159	C₂×C₄	—	47	24	no	—
160	C₂×C₄	—	94	12	no	—
161	C₂×C₄	—	94	12	no	—
162	C₂×C₄	—	94	24	no	—
163	C₂×C₄	—	94	24	no	—
164	C₂×C₄	C₄²×D₄₇	1	24	yes	—
165	C₂×C₄	C₄²×D₄₇	1	4	yes	—
166	C₂×C₄	#13093980	1	12	yes	—
167	C₂×C₄	#13093982	1	12	yes	—
168	C₂²	C₂×C₄²×D₄₇	1	1	yes	characteristic
169	C₂²	C₂×C₄²×D₄₇	1	6	yes	—
170	C₂²	#117×D₄₇	1	6	yes	—
171	C₂²	C₂×#13093980	1	3	yes	—
172	C₂²	C₂×#13093982	1	3	yes	—
173	C₂²	C₄×#10625352	1	12	yes	—
174	C₂²	C₄×#10625354	1	4	yes	—
175	C₄	—	2	24	no	—
176	C₄	—	47	8	no	—
177	C₄	—	47	8	no	—
178	C₄	—	94	24	no	—
179	C₄	#15688968	1	8	yes	direct product factor
180	C₂	C₄³×D₄₇	1	1	yes	characteristic
181	C₂	#376×D₄₇	1	1	yes	characteristic
182	C₂	C₂×#15688968	1	1	yes	characteristic
183	C₂	C₄×#13093980	1	6	yes	—
184	C₂	C₄×#13093982	1	6	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂²×D₄₇
commutator	C₂×C₄₇	C₂×C₄³
Frattini	C₂⁴	C₂³×D₄₇
Fitting	C₄×#95×C₄₇	C₂
socle, prime radical, cosocle	C₂⁴×C₄₇	C₂⁴
hypercenter	C₄×#95	D₄₇
hypocenter	C₄₇	C₄×#376
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³×C₄ ◁ C₄×#95

Complements

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

N	H ≅ G/N	type
10. #15688968	C₄	direct (N × H)
12. C₄²×Dic₄₇	C₄	semidirect
53. C₄×Dic₄₇	C₄²	semidirect
84. C₄×C₄₇	#376	semidirect
87. Dic₄₇	#376	semidirect
107. C₄₇	C₄×#376	semidirect
179. C₄	#15688968	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×#15688968	2
C₂×C₄²×Dic₄₇	2
C₄×C₄₇⋊#95	2
#95×Dic₄₇	2
C₄×#95×C₄₇	2
C₄×#376	47

Subgroups — C4×#15688968 #26137348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#15688968 #26137348