Subgroups — C₂×C₇⋊#1273 #13243175

Order 1792.

982 conjugacy classes of subgroups.

The subgroup lattice has 224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₇×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₇⋊C₈	C₂	1	2	yes	maximal
3	C₇⋊#1273	C₂	1	4	yes	maximal, direct product factor
4	C₂³×C₇×C₈	C₄	1	2	yes	—
5	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
6	C₂³×C₇⋊C₈	C₄	1	4	yes	—
7	C₂×C₄×C₇×C₈	—	2	4	no	—
8	C₂×C₄×C₇×C₈	C₄	1	2	yes	—
9	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
10	C₂×C₄×C₇⋊C₈	—	2	4	no	—
11	C₂×C₄×C₇⋊C₈	—	2	4	no	—
12	C₂×C₄×C₇⋊C₈	C₄	1	4	yes	—
13	C₂×C₄×C₇⋊C₈	C₂²	1	4	yes	—
14	C₂×#1273	—	7	1	no	maximal, Sylow
15	C₂³×C₄×C₇	C₂×C₄	1	2	yes	—
16	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₇×C₈	—	2	4	no	—
18	C₂²×C₇×C₈	—	2	4	no	—
19	C₂²×C₇×C₈	C₈	1	8	yes	complemented
20	C₂²×C₇×C₈	C₂×C₄	1	4	yes	—
21	C₂×C₄²×C₇	C₂×C₄	1	2	yes	—
22	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄²×C₇	D₄	1	2	yes	—
24	C₂×C₄²×C₇	D₄	1	4	yes	—
25	C₂×C₄²×C₇	Q₈	1	2	yes	—
26	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
27	C₂²×C₇⋊C₈	—	2	8	no	—
28	C₂²×C₇⋊C₈	—	2	8	no	—
29	C₂²×C₇⋊C₈	C₈	1	16	yes	complemented
30	C₂²×C₇⋊C₈	C₂×C₄	1	8	yes	—
31	C₄×C₇×C₈	—	2	4	no	—
32	C₄×C₇×C₈	—	2	4	no	—
33	C₄×C₇⋊C₈	—	2	8	no	—
34	C₄×C₇⋊C₈	—	2	4	no	—
35	C₄×C₇⋊C₈	—	2	4	no	—
36	C₂²×C₄×C₈	—	7	2	no	—
37	C₂²×C₄×C₈	D₇	1	1	yes	characteristic
38	#1273	—	7	4	no	—
39	C₂⁴×C₇	C₄²	1	1	yes	characteristic
40	C₂²×C₄×C₇	C₄²	1	1	yes	characteristic
41	C₂²×C₄×C₇	C₄²	1	2	yes	—
42	C₂²×C₄×C₇	C₂²⋊C₄	1	4	yes	—
43	C₂²×C₄×C₇	C₂²⋊C₄	1	2	yes	—
44	C₂²×C₄×C₇	C₄⋊C₄	1	4	yes	—
45	C₂²×C₄×C₇	C₄⋊C₄	1	2	yes	—
46	C₂²×C₄×C₇	C₂×C₈	1	8	yes	—
47	C₂²×C₄×C₇	C₂×C₈	1	4	yes	—
48	C₂²×C₄×C₇	M₁₆	1	8	yes	—
49	C₂²×C₄×C₇	M₁₆	1	4	yes	—
50	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
51	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
52	C₂×C₇×C₈	—	2	16	no	—
53	C₂×C₇×C₈	—	2	4	no	—
54	C₂×C₇×C₈	—	2	4	no	—
55	C₂×C₇×C₈	C₂×C₈	1	8	yes	complemented
56	C₄²×C₇	C₂²⋊C₄	1	4	yes	—
57	C₄²×C₇	C₂²⋊C₄	1	2	yes	—
58	C₄²×C₇	C₄⋊C₄	1	4	yes	—
59	C₄²×C₇	C₄⋊C₄	1	2	yes	—
60	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
61	C₄²×C₇	C₂×D₄	1	2	yes	—
62	C₄²×C₇	C₂×Q₈	1	1	yes	characteristic
63	C₂×C₇⋊C₈	—	2	32	no	—
64	C₂×C₇⋊C₈	—	2	8	no	—
65	C₂×C₇⋊C₈	—	2	8	no	—
66	C₂×C₇⋊C₈	C₂×C₈	1	16	yes	complemented
67	C₂³×C₈	—	7	4	no	—
68	C₂³×C₈	Dic₇	1	2	yes	—
69	C₂²×C₄²	C₂×D₇	1	1	yes	characteristic
70	C₂×C₄×C₈	—	2	4	no	—
71	C₂×C₄×C₈	—	7	4	no	—
72	C₂×C₄×C₈	—	7	4	no	—
73	C₂×C₄×C₈	—	14	4	no	—
74	C₂×C₄×C₈	—	14	4	no	—
75	C₂×C₄×C₈	Dic₇	1	2	yes	—
76	C₂×C₄×C₈	C₂×D₇	1	2	yes	—
77	C₂³×C₇	#95	1	2	yes	—
78	C₂³×C₇	C₄×C₈	1	2	yes	—
79	C₂³×C₇	C₄×C₈	1	4	yes	—
80	C₂³×C₇	#97	1	2	yes	—
81	C₂³×C₇	#97	1	4	yes	—
82	C₂³×C₇	C₂×C₄²	1	1	yes	characteristic
83	C₂×C₄×C₇	#95	1	4	yes	—
84	C₂×C₄×C₇	#95	1	2	yes	—
85	C₂×C₄×C₇	C₄×C₈	1	2	yes	—
86	C₂×C₄×C₇	C₄×C₈	1	4	yes	—
87	C₂×C₄×C₇	#97	1	2	yes	—
88	C₂×C₄×C₇	#97	1	4	yes	—
89	C₂×C₄×C₇	C₂²⋊C₈	1	8	yes	—
90	C₂×C₄×C₇	C₂²⋊C₈	1	16	yes	—
91	C₂×C₄×C₇	C₄⋊C₈	1	8	yes	—
92	C₂×C₄×C₇	C₄⋊C₈	1	16	yes	—
93	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
94	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
96	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
97	C₂×C₄×C₇	C₂²×C₈	1	4	yes	—
98	C₂×C₄×C₇	C₂²×C₈	1	2	yes	—
99	C₂×C₄×C₇	C₂×M₁₆	1	4	yes	—
100	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
101	C₇×C₈	—	2	8	no	—
102	C₇⋊C₈	—	2	16	no	—
103	C₂³×C₄	C₄×D₇	1	2	yes	—
104	C₂³×C₄	C₂×Dic₇	1	1	yes	characteristic
105	C₂²×C₈	—	2	4	no	—
106	C₂²×C₈	—	2	4	no	—
107	C₂²×C₈	—	7	16	no	—
108	C₂²×C₈	—	7	8	no	—
109	C₂²×C₈	—	14	8	no	—
110	C₂²×C₈	—	14	8	no	—
111	C₂²×C₈	C₇⋊C₈	1	8	yes	complemented
112	C₂²×C₈	C₂×Dic₇	1	4	yes	—
113	C₂×C₄²	Dic₁₄	1	2	yes	—
114	C₂×C₄²	C₄×D₇	1	2	yes	—
115	C₂×C₄²	D₂₈	1	2	yes	—
116	C₂×C₄²	C₂×Dic₇	1	1	yes	characteristic
117	C₂×C₄²	C₂²⋊D₇	1	4	yes	—
118	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
119	C₄×C₈	—	2	4	no	—
120	C₄×C₈	—	2	4	no	—
121	C₄×C₈	—	14	8	no	—
122	C₄×C₈	—	14	4	no	—
123	C₄×C₈	—	14	4	no	—
124	C₂²×C₇	C₈²	1	4	yes	—
125	C₂²×C₇	#322	1	8	yes	—
126	C₂²×C₇	#322	1	4	yes	—
127	C₂²×C₇	#336	1	8	yes	—
128	C₂²×C₇	#336	1	4	yes	—
129	C₂²×C₇	C₂×#95	1	1	yes	characteristic
130	C₂²×C₇	C₂×C₄×C₈	1	2	yes	—
131	C₂²×C₇	C₂×C₄×C₈	1	1	yes	characteristic
132	C₂²×C₇	C₂×#97	1	2	yes	—
133	C₂²×C₇	C₂×#97	1	1	yes	characteristic
134	C₄×C₇	#336	1	8	yes	—
135	C₄×C₇	#336	1	4	yes	—
136	C₄×C₇	C₂×C₂²⋊C₈	1	4	yes	—
137	C₄×C₇	C₂×C₂²⋊C₈	1	2	yes	—
138	C₄×C₇	C₂×C₄⋊C₈	1	4	yes	—
139	C₄×C₇	C₂×C₄⋊C₈	1	2	yes	—
140	C₂⁴	C₄×Dic₇	1	1	yes	characteristic
141	C₂²×C₄	C₈×D₇	1	8	yes	—
142	C₂²×C₄	#1131	1	8	yes	—
143	C₂²×C₄	C₂×C₇⋊C₈	1	4	yes	—
144	C₂²×C₄	#1136	1	4	yes	—
145	C₂²×C₄	C₄×Dic₇	1	1	yes	characteristic
146	C₂²×C₄	C₄×Dic₇	1	2	yes	—
147	C₂²×C₄	Dic₇⋊C₄	1	4	yes	—
148	C₂²×C₄	C₄⋊Dic₇	1	2	yes	—
149	C₂²×C₄	(C₂×D₇)⋊C₄	1	4	yes	—
150	C₂²×C₄	C₂²⋊Dic₇	1	2	yes	—
151	C₂²×C₄	C₂×C₄×D₇	1	2	yes	—
152	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
153	C₂×C₈	—	2	16	no	—
154	C₂×C₈	—	2	4	no	—
155	C₂×C₈	—	2	4	no	—
156	C₂×C₈	—	7	16	no	—
157	C₂×C₈	—	14	8	no	—
158	C₂×C₈	—	14	8	no	—
159	C₂×C₈	—	14	32	no	—
160	C₂×C₈	C₂×C₇⋊C₈	1	8	yes	complemented
161	C₄²	Dic₇⋊C₄	1	4	yes	—
162	C₄²	C₄⋊Dic₇	1	2	yes	—
163	C₄²	(C₂×D₇)⋊C₄	1	4	yes	—
164	C₄²	C₂²⋊Dic₇	1	2	yes	—
165	C₄²	C₂×Dic₁₄	1	1	yes	characteristic
166	C₄²	C₂×D₂₈	1	1	yes	characteristic
167	C₄²	C₂×C₂²⋊D₇	1	2	yes	—
168	C₂×C₇	#1273	1	8	yes	complemented
169	C₂×C₇	C₂×C₈²	1	1	yes	characteristic
170	C₂×C₇	C₂×#322	1	2	yes	—
171	C₂×C₇	C₂×#322	1	1	yes	characteristic
172	C₂×C₇	C₂×#336	1	2	yes	—
173	C₂×C₇	C₂×#336	1	1	yes	characteristic
174	C₂³	C₄×C₇⋊C₈	1	2	yes	—
175	C₂³	#6377	1	2	yes	—
176	C₂³	C₈×Dic₇	1	4	yes	—
177	C₂³	#6389	1	4	yes	—
178	C₂³	C₇⋊#95	1	2	yes	—
179	C₂³	C₂×C₄×Dic₇	1	1	yes	characteristic
180	C₂×C₄	C₄×C₇⋊C₈	1	2	yes	—
181	C₂×C₄	#6377	1	2	yes	—
182	C₂×C₄	C₄⋊(C₇⋊C₈)	1	8	yes	—
183	C₂×C₄	C₈×Dic₇	1	4	yes	—
184	C₂×C₄	Dic₇⋊C₈	1	16	yes	—
185	C₂×C₄	#6389	1	4	yes	—
186	C₂×C₄	(C₂×D₇)⋊C₈	1	16	yes	—
187	C₂×C₄	C₂²⋊(C₇⋊C₈)	1	8	yes	—
188	C₂×C₄	C₇⋊#95	1	4	yes	—
189	C₂×C₄	C₇⋊#95	1	2	yes	—
190	C₂×C₄	C₂×C₈×D₇	1	4	yes	—
191	C₂×C₄	C₂×#1131	1	4	yes	—
192	C₂×C₄	C₂²×C₇⋊C₈	1	2	yes	—
193	C₂×C₄	C₂×#1136	1	2	yes	—
194	C₂×C₄	C₂×Dic₇⋊C₄	1	2	yes	—
195	C₂×C₄	C₂×C₄⋊Dic₇	1	1	yes	characteristic
196	C₂×C₄	C₂×(C₂×D₇)⋊C₄	1	2	yes	—
197	C₂×C₄	C₂×C₂²⋊Dic₇	1	1	yes	characteristic
198	C₈	—	2	8	no	—
199	C₈	—	14	16	no	—
200	C₇	C₂×#1273	1	1	yes	characteristic, complemented, Sylow
201	C₂²	C₈×C₇⋊C₈	1	4	yes	—
202	C₂²	#89249	1	8	yes	—
203	C₂²	#89250	1	4	yes	—
204	C₂²	#89319	1	4	yes	—
205	C₂²	#89345	1	8	yes	—
206	C₂²	C₂×C₄×C₇⋊C₈	1	1	yes	characteristic
207	C₂²	C₂×#6377	1	1	yes	characteristic
208	C₂²	C₂×C₈×Dic₇	1	2	yes	—
209	C₂²	C₂×#6389	1	2	yes	—
210	C₂²	C₂×C₇⋊#95	1	1	yes	characteristic
211	C₄	#89319	1	4	yes	—
212	C₄	#89345	1	8	yes	—
213	C₄	C₂×C₄⋊(C₇⋊C₈)	1	2	yes	—
214	C₄	C₂×Dic₇⋊C₈	1	4	yes	—
215	C₄	C₂×(C₂×D₇)⋊C₈	1	4	yes	—
216	C₄	C₂×C₂²⋊(C₇⋊C₈)	1	2	yes	—
217	C₂	C₇⋊#1273	1	8	yes	direct product factor
218	C₂	C₂×C₈×C₇⋊C₈	1	1	yes	characteristic
219	C₂	C₂×#89249	1	2	yes	—
220	C₂	C₂×#89250	1	1	yes	characteristic
221	C₂	C₂×#89319	1	1	yes	characteristic
222	C₂	C₂×#89345	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄²	C₂×D₇
commutator	C₂×C₇	C₂×C₈²
Frattini	C₂×C₄²	C₂²×D₇
Fitting	C₂²×C₄×C₇×C₈	C₂
socle, prime radical	C₂⁴×C₇	C₄²
cosocle	C₂×C₄²×C₇	C₂³
hypercenter	C₂²×C₄×C₈	D₇
hypocenter	C₇	C₂×#1273
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₄² ◁ C₂²×C₄×C₈

Complements

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

N	H ≅ G/N	type
3. C₇⋊#1273	C₂	direct (N × H)
19. C₂²×C₇×C₈	C₈	semidirect
29. C₂²×C₇⋊C₈	C₈	semidirect
55. C₂×C₇×C₈	C₂×C₈	semidirect
66. C₂×C₇⋊C₈	C₂×C₈	semidirect
111. C₂²×C₈	C₇⋊C₈	semidirect
160. C₂×C₈	C₂×C₇⋊C₈	semidirect
168. C₂×C₇	#1273	semidirect
200. C₇	C₂×#1273	semidirect
217. C₂	C₇⋊#1273	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×C₇×C₈	2
C₂²×C₄×C₇⋊C₈	2
C₇⋊#1273	2
C₂×#1273	7

Subgroups — C2×C7⋊#1273 #13243175

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇⋊#1273 #13243175