Subgroups — D₇×C₃⋊#95 #13054243

Order 1344.

660 conjugacy classes of subgroups.

The subgroup lattice has 220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄×D₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₃×D₇	C₂	1	2	yes	maximal
3	#10620670	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×C₃⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
5	#10620529	C₂	1	2	yes	maximal, complemented
6	D₇×#95	—	3	1	no	maximal, Hall
7	C₂³×C₃×D₇	C₂²	1	1	yes	characteristic
8	C₂²×C₃×C₄×C₇	C₂²	1	1	yes	characteristic
9	C₂²×Dic₂₁	C₂²	1	2	yes	—
10	C₂²×C₇×Dic₃	C₂²	1	2	yes	—
11	C₂²×C₃×Dic₇	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₄×D₇	—	2	4	no	—
13	C₂×C₃×C₄×D₇	C₄	1	4	yes	complemented
14	C₂×Dic₃×D₇	—	2	4	no	—
15	C₂×Dic₃×D₇	—	2	4	no	—
16	C₂×Dic₃×D₇	C₄	1	8	yes	complemented
17	C₂²×C₄×D₇	—	3	2	no	—
18	C₂²×C₄×D₇	D₃	1	1	yes	characteristic
19	C₇×#95	—	3	1	no	—
20	C₇⋊#95	—	3	1	no	—
21	C₇⋊#95	—	3	2	no	—
22	C₂×C₃⋊#95	—	7	1	no	maximal, Hall
23	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
24	C₂²×C₃×D₇	C₂×C₄	1	4	yes	—
25	C₂²×C₃×D₇	C₂×C₄	1	2	yes	—
26	C₂²×C₃×D₇	D₄	1	2	yes	—
27	C₂²×C₃×D₇	D₄	1	4	yes	—
28	C₂²×C₃×D₇	Q₈	1	2	yes	—
29	C₂×C₃×C₄×C₇	—	2	2	no	—
30	C₂×C₃×C₄×C₇	C₂×C₄	1	2	yes	complemented
31	C₂×Dic₂₁	—	2	2	no	—
32	C₂×Dic₂₁	—	2	2	no	—
33	C₂×Dic₂₁	C₂×C₄	1	4	yes	complemented
34	C₂×C₇×Dic₃	—	2	2	no	—
35	C₂×C₇×Dic₃	—	2	2	no	—
36	C₂×C₇×Dic₃	C₂×C₄	1	4	yes	complemented
37	C₂×C₃×Dic₇	—	2	2	no	—
38	C₂×C₃×Dic₇	C₂×C₄	1	2	yes	complemented
39	C₃×C₄×D₇	—	2	8	no	—
40	Dic₃×D₇	—	2	16	no	—
41	C₂³×D₇	C₂×D₃	1	1	yes	characteristic
42	C₂²×C₄×C₇	—	3	2	no	—
43	C₂²×C₄×C₇	C₂×D₃	1	1	yes	characteristic
44	C₂²×Dic₇	—	3	2	no	—
45	C₂²×Dic₇	C₂×D₃	1	1	yes	characteristic
46	C₂×C₄×D₇	—	2	4	no	—
47	C₂×C₄×D₇	—	3	8	no	—
48	C₂×C₄×D₇	—	6	4	no	—
49	C₂×C₄×D₇	—	6	4	no	—
50	C₂×C₄×D₇	Dic₃	1	4	yes	complemented
51	C₂³×C₃×C₄	—	7	1	no	—
52	C₂³×Dic₃	—	7	2	no	—
53	C₃⋊#95	—	7	1	no	—
54	C₃⋊#95	—	7	2	no	—
55	C₃⋊#95	D₇	1	1	yes	characteristic, direct product factor
56	C₂²×C₃×C₇	C₂²×C₄	1	2	yes	—
57	C₂²×C₃×C₇	C₂²×C₄	1	1	yes	characteristic
58	C₂²×C₃×C₇	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₃×C₇	C₂×D₄	1	2	yes	—
60	C₂²×C₃×C₇	C₂×Q₈	1	1	yes	characteristic
61	C₂×C₃×D₇	C₄²	1	4	yes	—
62	C₂×C₃×D₇	C₂²⋊C₄	1	8	yes	—
63	C₂×C₃×D₇	C₂²⋊C₄	1	4	yes	—
64	C₂×C₃×D₇	C₄⋊C₄	1	8	yes	—
65	C₂×C₃×D₇	C₄⋊C₄	1	4	yes	—
66	C₃×C₄×C₇	—	2	2	no	—
67	Dic₂₁	—	2	4	no	—
68	C₃×Dic₇	—	2	2	no	—
69	C₇×Dic₃	—	2	4	no	—
70	C₂×#95	—	21	1	no	Sylow
71	C₂³×C₇	C₂²×D₃	1	1	yes	characteristic
72	C₂²×D₇	Dic₆	1	2	yes	—
73	C₂²×D₇	C₄×D₃	1	4	yes	—
74	C₂²×D₇	D₁₂	1	2	yes	—
75	C₂²×D₇	C₂×Dic₃	1	2	yes	—
76	C₂²×D₇	#67	1	4	yes	—
77	C₂×C₄×C₇	—	2	2	no	—
78	C₂×C₄×C₇	—	3	4	no	—
79	C₂×C₄×C₇	—	6	2	no	—
80	C₂×C₄×C₇	—	6	2	no	—
81	C₂×C₄×C₇	C₂×Dic₃	1	2	yes	complemented
82	C₂×Dic₇	—	2	2	no	—
83	C₂×Dic₇	—	3	4	no	—
84	C₂×Dic₇	—	6	2	no	—
85	C₂×Dic₇	—	6	2	no	—
86	C₂×Dic₇	C₂×Dic₃	1	2	yes	complemented
87	C₄×D₇	—	2	8	no	—
88	C₄×D₇	—	6	16	no	—
89	C₂⁴×C₃	—	7	1	no	—
90	C₂²×C₃×C₄	—	7	1	no	—
91	C₂²×C₃×C₄	—	7	4	no	—
92	C₂²×C₃×C₄	—	14	4	no	—
93	C₂²×C₃×C₄	C₂×D₇	1	1	yes	characteristic
94	C₂²×Dic₃	—	7	2	no	—
95	C₂²×Dic₃	—	7	8	no	—
96	C₂²×Dic₃	—	14	4	no	—
97	C₂²×Dic₃	—	14	4	no	—
98	C₂²×Dic₃	C₂×D₇	1	2	yes	—
99	C₂×C₃×C₇	C₂×C₄²	1	1	yes	characteristic
100	C₂×C₃×C₇	C₂×C₂²⋊C₄	1	2	yes	—
101	C₂×C₃×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₃×C₇	C₂×C₄⋊C₄	1	2	yes	—
103	C₂×C₃×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
104	C₃×D₇	#95	1	8	yes	complemented
105	C₂³×C₄	—	7	1	no	—
106	C₂³×C₄	—	21	2	no	—
107	#95	—	3	1	no	—
108	#95	—	21	2	no	—
109	#95	—	21	1	no	—
110	C₂²×C₇	C₂×Dic₆	1	1	yes	characteristic
111	C₂²×C₇	C₂×C₄×D₃	1	2	yes	—
112	C₂²×C₇	C₂×D₁₂	1	1	yes	characteristic
113	C₂²×C₇	C₂²×Dic₃	1	1	yes	characteristic
114	C₂²×C₇	C₂×#67	1	2	yes	—
115	C₂×D₇	C₄×Dic₃	1	4	yes	—
116	C₂×D₇	Dic₃⋊C₄	1	8	yes	—
117	C₂×D₇	C₄⋊Dic₃	1	4	yes	—
118	C₂×D₇	(C₂×D₃)⋊C₄	1	8	yes	—
119	C₂×D₇	#217	1	4	yes	—
120	C₄×C₇	—	2	2	no	—
121	C₄×C₇	—	6	4	no	—
122	Dic₇	—	2	2	no	—
123	Dic₇	—	6	4	no	—
124	C₂³×C₃	—	7	4	no	—
125	C₂³×C₃	—	7	2	no	—
126	C₂³×C₃	—	7	2	no	—
127	C₂³×C₃	—	7	4	no	—
128	C₂³×C₃	—	7	2	no	—
129	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
130	C₂×C₃×C₄	—	2	2	no	—
131	C₂×C₃×C₄	—	7	2	no	—
132	C₂×C₃×C₄	—	14	8	no	—
133	C₂×C₃×C₄	—	14	2	no	—
134	C₂×C₃×C₄	C₄×D₇	1	2	yes	complemented
135	C₂×Dic₃	—	2	2	no	—
136	C₂×Dic₃	—	2	2	no	—
137	C₂×Dic₃	—	7	4	no	—
138	C₂×Dic₃	—	14	16	no	—
139	C₂×Dic₃	—	14	2	no	—
140	C₂×Dic₃	—	14	2	no	—
141	C₂×Dic₃	C₄×D₇	1	4	yes	complemented
142	C₃×C₇	C₂×#95	1	1	yes	characteristic, complemented, Hall
143	C₂⁴	—	7	1	no	—
144	C₂²×C₄	—	3	2	no	—
145	C₂²×C₄	—	7	1	no	—
146	C₂²×C₄	—	7	4	no	—
147	C₂²×C₄	—	14	4	no	—
148	C₂²×C₄	—	21	8	no	—
149	C₂²×C₄	—	21	2	no	—
150	C₂²×C₄	—	42	4	no	—
151	C₂²×C₄	—	42	4	no	—
152	C₂²×C₄	D₃×D₇	1	1	yes	characteristic
153	C₂×C₇	C₂×C₄×Dic₃	1	1	yes	characteristic
154	C₂×C₇	C₂×Dic₃⋊C₄	1	2	yes	—
155	C₂×C₇	C₂×C₄⋊Dic₃	1	1	yes	characteristic
156	C₂×C₇	C₂×(C₂×D₃)⋊C₄	1	2	yes	—
157	C₂×C₇	C₂×#217	1	1	yes	characteristic
158	D₇	C₃⋊#95	1	8	yes	direct product factor
159	C₂²×C₃	—	7	4	no	—
160	C₂²×C₃	—	7	8	no	—
161	C₂²×C₃	—	7	4	no	—
162	C₂²×C₃	—	7	8	no	—
163	C₂²×C₃	—	7	4	no	—
164	C₂²×C₃	C₂×C₄×D₇	1	2	yes	—
165	C₂²×C₃	C₂×C₄×D₇	1	1	yes	characteristic
166	C₂²×C₃	D₄×D₇	1	1	yes	characteristic
167	C₂²×C₃	D₄×D₇	1	2	yes	—
168	C₂²×C₃	Q₈×D₇	1	1	yes	characteristic
169	C₃×C₄	—	2	2	no	—
170	C₃×C₄	—	14	2	no	—
171	Dic₃	—	2	4	no	—
172	Dic₃	—	14	4	no	—
173	C₂³	—	7	2	no	—
174	C₂³	—	7	4	no	—
175	C₂³	—	7	2	no	—
176	C₂³	—	7	2	no	—
177	C₂³	—	7	4	no	—
178	C₂³	C₂×D₃×D₇	1	1	yes	characteristic
179	C₂×C₄	—	2	2	no	—
180	C₂×C₄	—	3	4	no	—
181	C₂×C₄	—	6	2	no	—
182	C₂×C₄	—	6	2	no	—
183	C₂×C₄	—	7	2	no	—
184	C₂×C₄	—	14	8	no	—
185	C₂×C₄	—	14	2	no	—
186	C₂×C₄	—	21	4	no	—
187	C₂×C₄	—	42	16	no	—
188	C₂×C₄	—	42	2	no	—
189	C₂×C₄	—	42	2	no	—
190	C₂×C₄	Dic₃×D₇	1	2	yes	complemented
191	C₇	C₂×C₃⋊#95	1	1	yes	characteristic, complemented, Sylow
192	C₂×C₃	—	7	8	no	—
193	C₂×C₃	C₄²×D₇	1	1	yes	characteristic
194	C₂×C₃	D₇×C₂²⋊C₄	1	2	yes	—
195	C₂×C₃	D₇×C₂²⋊C₄	1	1	yes	characteristic
196	C₂×C₃	D₇×C₄⋊C₄	1	2	yes	—
197	C₂×C₃	D₇×C₄⋊C₄	1	1	yes	characteristic
198	C₂²	—	7	4	no	—
199	C₂²	—	7	8	no	—
200	C₂²	—	7	4	no	—
201	C₂²	—	7	8	no	—
202	C₂²	—	7	4	no	—
203	C₂²	D₇×Dic₆	1	1	yes	characteristic
204	C₂²	C₄×D₃×D₇	1	2	yes	—
205	C₂²	D₇×D₁₂	1	1	yes	characteristic
206	C₂²	C₂×Dic₃×D₇	1	1	yes	characteristic
207	C₂²	D₇×#67	1	2	yes	—
208	C₄	—	2	2	no	—
209	C₄	—	6	4	no	—
210	C₄	—	14	2	no	—
211	C₄	—	42	4	no	—
212	C₃	D₇×#95	1	1	yes	characteristic, complemented, Sylow
213	C₂	—	7	8	no	—
214	C₂	C₄×Dic₃×D₇	1	1	yes	characteristic
215	C₂	D₇×Dic₃⋊C₄	1	2	yes	—
216	C₂	D₇×C₄⋊Dic₃	1	1	yes	characteristic
217	C₂	D₇×(C₂×D₃)⋊C₄	1	2	yes	—
218	C₂	D₇×#217	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂×D₃×D₇
commutator	C₂×C₃×C₇	C₂×C₄²
Fitting	C₂²×C₃×C₄×C₇	C₂²
socle, cosocle	C₂³×C₃×C₇	C₂³
prime radical	C₂³×C₃×D₇	C₂²
hypercenter	C₂²×C₄	D₃×D₇
hypocenter	C₃×C₇	C₂×#95
LCS	G ▷ C₂×C₃×C₇ ▷ C₃×C₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
3. #10620670	C₂	semidirect
4. C₇×C₃⋊#95	C₂	semidirect
5. #10620529	C₂	semidirect
13. C₂×C₃×C₄×D₇	C₄	semidirect
16. C₂×Dic₃×D₇	C₄	semidirect
30. C₂×C₃×C₄×C₇	C₂×C₄	semidirect
33. C₂×Dic₂₁	C₂×C₄	semidirect
36. C₂×C₇×Dic₃	C₂×C₄	semidirect
38. C₂×C₃×Dic₇	C₂×C₄	semidirect
50. C₂×C₄×D₇	Dic₃	semidirect
55. C₃⋊#95	D₇	direct (N × H)
81. C₂×C₄×C₇	C₂×Dic₃	semidirect
86. C₂×Dic₇	C₂×Dic₃	semidirect
104. C₃×D₇	#95	semidirect
134. C₂×C₃×C₄	C₄×D₇	semidirect
141. C₂×Dic₃	C₄×D₇	semidirect
142. C₃×C₇	C₂×#95	semidirect
158. D₇	C₃⋊#95	direct (N × H)
190. C₂×C₄	Dic₃×D₇	semidirect
191. C₇	C₂×C₃⋊#95	semidirect
212. C₃	D₇×#95	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₄×D₇	2
C₂²×Dic₃×D₇	2
#10620670	2
C₇×C₃⋊#95	2
#10620529	2
D₇×#95	3
C₂×C₃⋊#95	7

Subgroups — D7×C3⋊#95 #13054243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×C₃⋊#95 #13054243