Subgroups — Dic₇×#376 #13274867

Order 1792.

2302 conjugacy classes of subgroups.

The subgroup lattice has 152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#376	C₂	1	1	yes	maximal, characteristic
2	C₂×#89704	C₂	1	3	yes	maximal
3	C₂×C₄²×Dic₇	C₂	1	3	yes	maximal
4	Dic₇×#95	C₂	1	8	yes	maximal
5	C₂²×C₄²×C₇	C₂²	1	3	yes	—
6	C₂²×C₄×Dic₇	C₂²	1	12	yes	—
7	C₂²×C₄×Dic₇	C₂²	1	1	yes	characteristic
8	C₂²×C₄×Dic₇	C₂²	1	3	yes	—
9	C₇×#376	C₄	1	8	yes	complemented
10	C₂×C₇×#95	C₂²	1	4	yes	—
11	C₂×C₇⋊#95	C₂²	1	12	yes	—
12	#89704	C₄	1	24	yes	complemented
13	C₄²×Dic₇	C₄	1	24	yes	complemented
14	C₄×#376	—	7	1	no	maximal, Sylow
15	C₂³×C₄×C₇	C₂³	1	6	yes	—
16	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
17	C₂³×Dic₇	C₂³	1	6	yes	—
18	C₂³×Dic₇	C₂³	1	2	yes	—
19	C₂×C₄²×C₇	C₂×C₄	1	12	yes	—
20	C₂×C₄²×C₇	C₂×C₄	1	12	yes	—
21	C₂×C₄²×C₇	C₂×C₄	1	12	yes	—
22	C₂×C₄×Dic₇	—	2	48	no	—
23	C₂×C₄×Dic₇	C₂×C₄	1	48	yes	—
24	C₂×C₄×Dic₇	C₂×C₄	1	12	yes	—
25	C₂×C₄×Dic₇	C₂×C₄	1	12	yes	—
26	C₂×C₄×Dic₇	C₂×C₄	1	24	yes	—
27	C₇×#95	C₂×C₄	1	16	yes	—
28	C₇⋊#95	C₂×C₄	1	48	yes	—
29	C₂×#376	—	7	3	no	—
30	C₂×#376	D₇	1	1	yes	characteristic
31	C₂×C₄³	—	7	3	no	—
32	C₄×#95	—	7	8	no	—
33	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
34	C₂²×C₄×C₇	—	2	24	no	—
35	C₂²×C₄×C₇	C₂²×C₄	1	12	yes	—
36	C₂²×C₄×C₇	C₂²×C₄	1	12	yes	—
37	C₂²×C₄×C₇	C₂²×C₄	1	12	yes	—
38	C₂²×C₄×C₇	C₂²×C₄	1	6	yes	—
39	C₂²×C₄×C₇	C₂²×C₄	1	6	yes	—
40	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
41	C₂²×Dic₇	—	2	24	no	—
42	C₂²×Dic₇	C₂²×C₄	1	24	yes	—
43	C₂²×Dic₇	C₂²×C₄	1	12	yes	—
44	C₂²×Dic₇	C₂²×C₄	1	12	yes	—
45	C₂²×Dic₇	#41	1	16	yes	—
46	C₄²×C₇	C₄²	1	48	yes	complemented
47	C₄×Dic₇	—	2	96	no	—
48	C₄×Dic₇	C₄²	1	16	yes	—
49	C₄×Dic₇	C₄²	1	48	yes	complemented
50	C₂²×C₄²	—	7	1	no	—
51	C₂²×C₄²	—	7	3	no	—
52	C₂²×C₄²	—	7	12	no	—
53	C₂²×C₄²	C₂×D₇	1	3	yes	—
54	#376	—	7	24	no	—
55	#376	Dic₇	1	8	yes	direct product factor
56	C₂×#95	—	7	12	no	—
57	C₂×#95	C₂×D₇	1	4	yes	—
58	C₄³	—	7	24	no	—
59	C₂³×C₇	C₂³×C₄	1	3	yes	—
60	C₂³×C₇	C₂³×C₄	1	3	yes	—
61	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
62	C₂³×C₇	C₂×#41	1	8	yes	—
63	C₂×C₄×C₇	—	2	24	no	—
64	C₂×C₄×C₇	—	2	24	no	—
65	C₂×C₄×C₇	—	2	24	no	—
66	C₂×C₄×C₇	C₂×C₄²	1	4	yes	—
67	C₂×C₄×C₇	C₂×C₄²	1	12	yes	—
68	C₂×C₄×C₇	C₂×C₄²	1	24	yes	—
69	C₂×C₄×C₇	C₂×C₄²	1	12	yes	—
70	C₂×Dic₇	—	2	24	no	—
71	C₂×Dic₇	—	2	48	no	—
72	C₂×Dic₇	C₂×C₄²	1	24	yes	—
73	C₂×Dic₇	C₂×C₄²	1	8	yes	—
74	C₂×Dic₇	#117	1	48	yes	—
75	C₂³×C₄	—	7	2	no	—
76	C₂³×C₄	—	7	6	no	—
77	C₂³×C₄	C₂²×D₇	1	6	yes	—
78	C₂³×C₄	C₂²×D₇	1	1	yes	characteristic
79	C₂×C₄²	—	7	12	no	—
80	C₂×C₄²	—	7	12	no	—
81	C₂×C₄²	—	7	24	no	—
82	C₂×C₄²	—	7	48	no	—
83	C₂×C₄²	—	14	48	no	—
84	C₂×C₄²	C₄×D₇	1	12	yes	—
85	C₂×C₄²	C₄×D₇	1	12	yes	—
86	C₂×C₄²	C₂×Dic₇	1	12	yes	—
87	#95	—	7	48	no	—
88	#95	C₂×Dic₇	1	16	yes	—
89	C₂²×C₇	C₂²×C₄²	1	1	yes	characteristic
90	C₂²×C₇	C₂²×C₄²	1	3	yes	—
91	C₂²×C₇	C₂²×C₄²	1	3	yes	—
92	C₂²×C₇	C₂×#117	1	12	yes	—
93	C₂²×C₇	C₄×#41	1	12	yes	—
94	C₂²×C₇	C₄×#41	1	4	yes	—
95	C₄×C₇	—	2	24	no	—
96	C₄×C₇	C₄³	1	8	yes	—
97	Dic₇	—	2	24	no	—
98	Dic₇	#376	1	16	yes	direct product factor
99	C₂⁴	C₂³×D₇	1	1	yes	characteristic
100	C₂²×C₄	—	2	24	no	—
101	C₂²×C₄	—	7	12	no	—
102	C₂²×C₄	—	7	16	no	—
103	C₂²×C₄	—	7	24	no	—
104	C₂²×C₄	—	7	12	no	—
105	C₂²×C₄	—	14	24	no	—
106	C₂²×C₄	C₂×C₄×D₇	1	12	yes	—
107	C₂²×C₄	C₂×C₄×D₇	1	12	yes	—
108	C₂²×C₄	C₂×C₄×D₇	1	6	yes	—
109	C₂²×C₄	C₂×C₄×D₇	1	6	yes	—
110	C₂²×C₄	C₂²×Dic₇	1	12	yes	—
111	C₂²×C₄	C₂²×Dic₇	1	2	yes	—
112	C₄²	—	7	16	no	—
113	C₄²	—	7	48	no	—
114	C₄²	—	14	96	no	—
115	C₄²	C₄×Dic₇	1	48	yes	complemented
116	C₂×C₇	C₂×C₄³	1	1	yes	characteristic
117	C₂×C₇	C₂×#376	1	2	yes	—
118	C₂×C₇	C₄×#117	1	6	yes	—
119	C₂×C₇	C₄×#117	1	6	yes	—
120	C₂³	C₂²×C₄×D₇	1	3	yes	—
121	C₂³	C₂²×C₄×D₇	1	3	yes	—
122	C₂³	D₇×#41	1	8	yes	—
123	C₂³	C₂³×Dic₇	1	1	yes	characteristic
124	C₂×C₄	—	2	24	no	—
125	C₂×C₄	—	2	24	no	—
126	C₂×C₄	—	2	24	no	—
127	C₂×C₄	—	7	8	no	—
128	C₂×C₄	—	7	48	no	—
129	C₂×C₄	—	7	24	no	—
130	C₂×C₄	—	14	24	no	—
131	C₂×C₄	—	14	48	no	—
132	C₂×C₄	C₄²×D₇	1	12	yes	—
133	C₂×C₄	C₄²×D₇	1	4	yes	—
134	C₂×C₄	C₂×C₄×Dic₇	1	24	yes	—
135	C₂×C₄	C₂×C₄×Dic₇	1	12	yes	—
136	C₇	C₄×#376	1	1	yes	characteristic, complemented, Sylow
137	C₂²	C₂×C₄²×D₇	1	3	yes	—
138	C₂²	C₂×C₄²×D₇	1	1	yes	characteristic
139	C₂²	D₇×#117	1	12	yes	—
140	C₂²	#90213	1	12	yes	—
141	C₂²	C₂²×C₄×Dic₇	1	3	yes	—
142	C₂²	#41×Dic₇	1	4	yes	—
143	C₄	—	2	24	no	—
144	C₄	—	7	16	no	—
145	C₄	—	14	24	no	—
146	C₄	C₄²×Dic₇	1	8	yes	—
147	C₂	#11730827	1	6	yes	—
148	C₂	D₇×#376	1	2	yes	—
149	C₂	C₂×C₄²×Dic₇	1	1	yes	characteristic
150	C₂	Dic₇×#117	1	6	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂²×D₇
commutator	C₂×C₇	C₂×C₄³
Frattini	C₂⁴	C₂³×D₇
Fitting	C₂×C₇×#376	C₂
socle, prime radical, cosocle	C₂⁴×C₇	C₂⁴
hypercenter	C₂×#376	D₇
hypocenter	C₇	C₄×#376
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂³×C₄ ◁ C₂×#376

Complements

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

N	H ≅ G/N	type
9. C₇×#376	C₄	semidirect
12. #89704	C₄	semidirect
13. C₄²×Dic₇	C₄	semidirect
46. C₄²×C₇	C₄²	semidirect
49. C₄×Dic₇	C₄²	semidirect
55. #376	Dic₇	direct (N × H)
98. Dic₇	#376	direct (N × H)
115. C₄²	C₄×Dic₇	semidirect
136. C₇	C₄×#376	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#376	2
C₂×#89704	2
C₂×C₄²×Dic₇	2
Dic₇×#95	2
C₄×#376	7

Subgroups — Dic7×#376 #13274867

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₇×#376 #13274867