Subgroups — C₃×#89480 #13055142

Order 1344.

260 conjugacy classes of subgroups.

The subgroup lattice has 168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#1131	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₈×D₇	C₂	1	1	yes	maximal, characteristic
3	C₃×#6435	C₂	1	1	yes	maximal, characteristic
4	C₃×C₇×#97	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#6389	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₈×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₄×C₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#89480	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₇×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₇×C₈	C₂²	1	1	yes	characteristic
12	C₃×C₄²×C₇	C₂²	1	1	yes	characteristic
13	C₃×(C₂×D₇)⋊C₄	C₄	1	2	yes	—
14	C₃×Dic₇⋊C₄	C₄	1	2	yes	—
15	C₃×C₄×Dic₇	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₇⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₇⋊C₈	C₂²	1	1	yes	characteristic
18	C₃×#1131	C₄	1	4	yes	complemented
19	C₃×C₈×D₇	C₄	1	4	yes	complemented
20	C₂×#1131	C₂×C₃	1	1	yes	characteristic
21	C₂×C₈×D₇	C₂×C₃	1	1	yes	characteristic
22	#6435	C₂×C₃	1	1	yes	characteristic
23	C₇×#97	C₂×C₃	1	1	yes	characteristic, complemented
24	#6389	C₂×C₃	1	1	yes	characteristic, complemented
25	C₈×Dic₇	C₂×C₃	1	1	yes	characteristic, complemented
26	C₄×C₇⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
27	C₃×#405	—	7	1	no	maximal, Hall
28	C₂²×C₃×D₇	C₂×C₄	1	1	yes	characteristic
29	C₂×C₃×C₄×C₇	C₂×C₄	1	2	yes	—
30	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
31	C₂×C₃×Dic₇	C₂×C₄	1	2	yes	—
32	C₂×C₃×Dic₇	C₂×C₄	1	1	yes	characteristic
33	C₃×C₄×D₇	C₂×C₄	1	2	yes	—
34	C₃×C₄×D₇	C₂×C₄	1	2	yes	—
35	C₃×C₇×C₈	C₂×C₄	1	2	yes	—
36	C₃×C₇×C₈	C₂×C₄	1	2	yes	—
37	C₃×C₇⋊C₈	C₂×C₄	1	2	yes	—
38	C₃×C₇⋊C₈	C₂×C₄	1	2	yes	—
39	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
40	C₂×C₇×C₈	C₂²×C₃	1	1	yes	characteristic
41	C₂×C₇×C₈	C₂²×C₃	1	1	yes	characteristic
42	C₄²×C₇	C₂²×C₃	1	1	yes	characteristic
43	(C₂×D₇)⋊C₄	C₃×C₄	1	2	yes	—
44	Dic₇⋊C₄	C₃×C₄	1	2	yes	—
45	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic
46	C₂×C₇⋊C₈	C₂²×C₃	1	1	yes	characteristic
47	C₂×C₇⋊C₈	C₂²×C₃	1	1	yes	characteristic
48	#1131	C₃×C₄	1	4	yes	complemented
49	C₈×D₇	C₃×C₄	1	4	yes	complemented
50	C₂×C₃×M₁₆	—	7	1	no	—
51	C₂²×C₃×C₈	—	7	1	no	—
52	C₃×#117	—	7	1	no	—
53	C₃×#97	—	7	1	no	—
54	C₃×#97	D₇	1	1	yes	characteristic, complemented
55	C₃×C₄×C₈	—	7	1	no	—
56	C₃×C₄×C₈	—	7	1	no	—
57	C₂²×C₃×C₇	C₂²×C₄	1	1	yes	characteristic
58	C₂×C₃×D₇	—	2	2	no	—
59	C₂×C₃×D₇	C₄²	1	2	yes	—
60	C₃×C₄×C₇	—	2	2	no	—
61	C₃×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
62	C₃×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
63	C₃×Dic₇	—	2	2	no	—
64	C₃×Dic₇	C₄²	1	2	yes	—
65	#405	—	7	1	no	Sylow
66	C₂²×D₇	C₂×C₃×C₄	1	1	yes	characteristic
67	C₂×C₄×C₇	C₂×C₃×C₄	1	2	yes	—
68	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
69	C₂×Dic₇	C₂×C₃×C₄	1	2	yes	—
70	C₂×Dic₇	C₂×C₃×C₄	1	1	yes	characteristic
71	C₄×D₇	C₂×C₃×C₄	1	2	yes	—
72	C₄×D₇	C₂×C₃×C₄	1	2	yes	—
73	C₇×C₈	C₂×C₃×C₄	1	2	yes	—
74	C₇×C₈	C₂×C₃×C₄	1	2	yes	—
75	C₇⋊C₈	C₂×C₃×C₄	1	2	yes	—
76	C₇⋊C₈	C₂×C₃×C₄	1	2	yes	—
77	C₂²×C₃×C₄	—	7	1	no	—
78	C₃×M₁₆	—	7	4	no	—
79	C₂×C₃×C₈	—	7	1	no	—
80	C₂×C₃×C₈	—	7	1	no	—
81	C₂×C₃×C₈	—	7	4	no	—
82	C₂×C₃×C₈	C₂×D₇	1	1	yes	characteristic
83	C₂×C₃×C₈	C₂×D₇	1	1	yes	characteristic
84	C₃×C₄⋊C₄	—	7	2	no	—
85	C₃×C₂²⋊C₄	—	7	2	no	—
86	C₃×C₄²	—	7	1	no	—
87	C₃×C₄²	C₂×D₇	1	1	yes	characteristic
88	C₂×C₃×C₇	C₂×C₄²	1	1	yes	characteristic
89	C₂×C₃×C₇	#131	1	2	yes	—
90	C₃×D₇	—	2	2	no	—
91	C₂×M₁₆	—	7	1	no	—
92	C₂²×C₈	—	7	1	no	—
93	#117	—	7	1	no	—
94	#97	—	7	1	no	—
95	#97	C₃×D₇	1	1	yes	characteristic, complemented
96	C₄×C₈	—	7	1	no	—
97	C₄×C₈	—	7	1	no	—
98	C₂²×C₇	C₂²×C₃×C₄	1	1	yes	characteristic
99	C₂×D₇	—	2	2	no	—
100	C₂×D₇	C₃×C₄²	1	2	yes	—
101	C₄×C₇	—	2	2	no	—
102	C₄×C₇	C₂²×C₃×C₄	1	1	yes	characteristic
103	C₄×C₇	C₂²×C₃×C₄	1	1	yes	characteristic
104	Dic₇	—	2	2	no	—
105	Dic₇	C₃×C₄²	1	2	yes	—
106	C₂³×C₃	—	7	1	no	—
107	C₂×C₃×C₄	—	7	1	no	—
108	C₂×C₃×C₄	—	7	2	no	—
109	C₂×C₃×C₄	—	7	2	no	—
110	C₂×C₃×C₄	—	7	2	no	—
111	C₂×C₃×C₄	C₄×D₇	1	2	yes	—
112	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
113	C₃×C₈	—	7	2	no	—
114	C₃×C₈	—	7	2	no	—
115	C₃×C₈	C₄×D₇	1	2	yes	—
116	C₃×C₈	C₄×D₇	1	2	yes	—
117	C₃×C₇	#405	1	1	yes	characteristic, complemented, Hall
118	C₂²×C₄	—	7	1	no	—
119	M₁₆	—	7	4	no	—
120	C₂×C₈	—	7	1	no	—
121	C₂×C₈	—	7	1	no	—
122	C₂×C₈	—	7	4	no	—
123	C₂×C₈	C₂×C₃×D₇	1	1	yes	characteristic
124	C₂×C₈	C₂×C₃×D₇	1	1	yes	characteristic
125	C₄⋊C₄	—	7	2	no	—
126	C₂²⋊C₄	—	7	2	no	—
127	C₄²	—	7	1	no	—
128	C₄²	C₂×C₃×D₇	1	1	yes	characteristic
129	C₂×C₇	C₂×C₃×C₄²	1	1	yes	characteristic
130	C₂×C₇	C₃×#131	1	2	yes	—
131	D₇	—	2	2	no	—
132	C₂²×C₃	—	7	2	no	—
133	C₂²×C₃	—	14	2	no	—
134	C₂²×C₃	C₂×C₄×D₇	1	1	yes	characteristic
135	C₃×C₄	—	2	2	no	—
136	C₃×C₄	—	7	2	no	—
137	C₃×C₄	—	14	2	no	—
138	C₃×C₄	C₂×C₄×D₇	1	1	yes	characteristic
139	C₃×C₄	C₂×C₄×D₇	1	1	yes	characteristic
140	C₂³	—	7	1	no	—
141	C₂×C₄	—	7	1	no	—
142	C₂×C₄	—	7	2	no	—
143	C₂×C₄	—	7	2	no	—
144	C₂×C₄	—	7	2	no	—
145	C₂×C₄	C₃×C₄×D₇	1	2	yes	—
146	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
147	C₈	—	7	2	no	—
148	C₈	—	7	2	no	—
149	C₈	C₃×C₄×D₇	1	2	yes	—
150	C₈	C₃×C₄×D₇	1	2	yes	—
151	C₇	C₃×#405	1	1	yes	characteristic, complemented, Sylow
152	C₂×C₃	—	14	2	no	—
153	C₂×C₃	C₄²×D₇	1	1	yes	characteristic
154	C₂×C₃	#6470	1	2	yes	—
155	C₂²	—	7	2	no	—
156	C₂²	—	14	2	no	—
157	C₂²	C₂×C₃×C₄×D₇	1	1	yes	characteristic
158	C₄	—	2	2	no	—
159	C₄	—	7	2	no	—
160	C₄	—	14	2	no	—
161	C₄	C₂×C₃×C₄×D₇	1	1	yes	characteristic
162	C₄	C₂×C₃×C₄×D₇	1	1	yes	characteristic
163	C₃	#89480	1	1	yes	characteristic, direct product factor, Sylow
164	C₂	—	14	2	no	—
165	C₂	C₃×C₄²×D₇	1	1	yes	characteristic
166	C₂	C₃×#6470	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×D₇
commutator	C₂×C₇	C₂×C₃×C₄²
Frattini	C₂×C₄	C₂²×C₃×D₇
Fitting	C₃×C₇×#97	C₂
socle	C₂²×C₃×C₇	C₂²×C₄
prime radical	C₂²×C₃×D₇	C₂×C₄
cosocle	C₂×C₄×C₇	C₂³×C₃
hypercenter	C₃×#97	D₇
hypocenter	C₇	C₃×#405
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#97

Complements

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

N	H ≅ G/N	type
4. C₃×C₇×#97	C₂	semidirect
5. C₃×#6389	C₂	semidirect
6. C₃×C₈×Dic₇	C₂	semidirect
7. C₃×C₄×C₇⋊C₈	C₂	semidirect
8. #89480	C₃	direct (N × H)
18. C₃×#1131	C₄	semidirect
19. C₃×C₈×D₇	C₄	semidirect
23. C₇×#97	C₂×C₃	semidirect
24. #6389	C₂×C₃	semidirect
25. C₈×Dic₇	C₂×C₃	semidirect
26. C₄×C₇⋊C₈	C₂×C₃	semidirect
48. #1131	C₃×C₄	semidirect
49. C₈×D₇	C₃×C₄	semidirect
54. C₃×#97	D₇	semidirect
95. #97	C₃×D₇	semidirect
117. C₃×C₇	#405	semidirect
151. C₇	C₃×#405	semidirect
163. C₃	#89480	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×C₃×#1131	2
C₂×C₃×C₈×D₇	2
C₃×#6435	2
C₃×C₇×#97	2
C₃×#6389	2
C₃×C₈×Dic₇	2
C₃×C₄×C₇⋊C₈	2
#89480	3
C₃×#405	7

Subgroups — C3×#89480 #13055142

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#89480 #13055142