Subgroups — C₂×#14545751 #17981023

Order 4352.

2074 conjugacy classes of subgroups.

The subgroup lattice has 196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545751	C₂	1	16	yes	maximal, direct product factor
2	C₂×#11763867	C₂	1	8	yes	maximal, complemented
3	C₂²×#10587538	C₂	1	6	yes	maximal, complemented
4	C₂²×#10587634	C₂	1	1	yes	maximal, characteristic
5	#11763867	C₂²	1	64	yes	complemented
6	C₂×#10587538	C₂²	1	4	yes	—
7	C₂×#10587538	C₂²	1	12	yes	complemented
8	C₂×#10587538	C₂²	1	48	yes	complemented
9	C₂²×#63216	C₂²	1	12	yes	complemented
10	C₂×#10587634	C₄	1	4	yes	—
11	C₂×#10587634	C₄	1	8	yes	—
12	C₂×#10587634	C₂²	1	4	yes	—
13	C₂×#10587634	C₂²	1	8	yes	—
14	C₂²×#63223	C₄	1	3	yes	—
15	C₂³×#3622	C₂²	1	3	yes	—
16	C₂²×#41×C₁₇	C₄	1	1	yes	characteristic
17	C₂×#41×C₁₇	C₈	1	4	yes	—
18	C₂×#41×C₁₇	C₈	1	8	yes	—
19	C₂×#41×C₁₇	C₂×C₄	1	4	yes	—
20	C₂×#41×C₁₇	C₂×C₄	1	8	yes	—
21	C₂²×Q₈×C₁₇	C₈	1	1	yes	characteristic
22	C₂²×D₄×C₁₇	C₈	1	3	yes	—
23	C₂³×C₄×C₁₇	C₂×C₄	1	3	yes	—
24	#10587634	C₂×C₄	1	16	yes	—
25	#10587634	C₂×C₄	1	32	yes	—
26	#10587634	C₂³	1	16	yes	—
27	C₂×#63223	C₂×C₄	1	12	yes	—
28	C₂×#63223	C₂×C₄	1	24	yes	—
29	C₂²×#3622	C₂×C₄	1	3	yes	—
30	C₂²×#3622	C₂×C₄	1	12	yes	—
31	C₂²×#3622	C₂×C₄	1	6	yes	—
32	C₂²×#3622	C₂³	1	1	yes	characteristic
33	C₂²×#3622	C₂³	1	6	yes	—
34	C₂²×#3622	C₂³	1	12	yes	—
35	#10587538	C₂³	1	16	yes	—
36	#10587538	C₂³	1	48	yes	complemented
37	C₂×#63216	C₂³	1	8	yes	—
38	C₂×#63216	C₂³	1	48	yes	complemented
39	C₂⁴×C₁₇	C₂×C₈	1	3	yes	—
40	#41×C₁₇	C₂×C₈	1	16	yes	—
41	#41×C₁₇	C₂×C₈	1	32	yes	—
42	#41×C₁₇	C₂²×C₄	1	16	yes	—
43	C₂×Q₈×C₁₇	C₂×C₈	1	8	yes	—
44	C₂×Q₈×C₁₇	C₂×C₈	1	4	yes	—
45	C₂×D₄×C₁₇	C₂×C₈	1	12	yes	—
46	C₂×D₄×C₁₇	C₂×C₈	1	24	yes	—
47	C₂²×C₄×C₁₇	C₂×C₈	1	3	yes	—
48	C₂²×C₄×C₁₇	C₂×C₈	1	6	yes	—
49	C₂²×C₄×C₁₇	C₂×C₈	1	12	yes	—
50	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₇	C₂²×C₄	1	12	yes	—
52	C₂²×C₄×C₁₇	C₂²×C₄	1	6	yes	—
53	#63223	C₂²×C₄	1	48	yes	—
54	C₂×#3622	C₂²×C₄	1	2	yes	—
55	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
56	C₂×#3622	C₂²×C₄	1	12	yes	—
57	C₂×#3622	C₂²×C₄	1	6	yes	—
58	C₂×#3622	C₂²×C₄	1	12	yes	—
59	C₂×#3622	C₂²×C₄	1	24	yes	—
60	C₂×#3622	C₂⁴	1	1	yes	characteristic
61	C₂×#3622	C₂⁴	1	12	yes	—
62	C₂×#3622	C₂⁴	1	2	yes	—
63	#63216	C₂⁴	1	16	yes	—
64	C₂×#3407	—	17	1	no	maximal, Sylow
65	C₂³×C₁₇	—	4	6	no	—
66	C₂³×C₁₇	C₂²×C₈	1	1	yes	characteristic
67	C₂³×C₁₇	C₂²×C₈	1	6	yes	—
68	C₂³×C₁₇	C₂²×C₈	1	12	yes	—
69	Q₈×C₁₇	C₂²×C₈	1	16	yes	—
70	D₄×C₁₇	C₂²×C₈	1	48	yes	—
71	C₂×C₄×C₁₇	C₂²×C₈	1	2	yes	—
72	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
73	C₂×C₄×C₁₇	C₂²×C₈	1	12	yes	—
74	C₂×C₄×C₁₇	C₂²×C₈	1	6	yes	—
75	C₂×C₄×C₁₇	C₂²×C₈	1	24	yes	—
76	C₂×C₄×C₁₇	C₂²×C₈	1	12	yes	—
77	C₂×C₄×C₁₇	C₂³×C₄	1	2	yes	—
78	C₂×C₄×C₁₇	C₂³×C₄	1	12	yes	—
79	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
80	#3622	C₂³×C₄	1	1	yes	characteristic
81	#3622	C₂³×C₄	1	2	yes	—
82	#3622	C₂³×C₄	1	12	yes	—
83	#3622	C₂⁵	1	1	yes	characteristic
84	C₂²×#131	—	17	1	no	—
85	#3407	—	17	16	no	—
86	C₂×#504	—	17	8	no	—
87	C₂²×M₃₂	—	17	6	no	—
88	C₂²×C₁₇	—	2	2	no	—
89	C₂²×C₁₇	—	2	12	no	—
90	C₂²×C₁₇	—	4	12	no	—
91	C₂²×C₁₇	C₂³×C₈	1	2	yes	—
92	C₂²×C₁₇	C₂³×C₈	1	12	yes	—
93	C₂²×C₁₇	C₂³×C₈	1	1	yes	characteristic
94	C₄×C₁₇	C₂³×C₈	1	2	yes	—
95	C₄×C₁₇	C₂³×C₈	1	1	yes	characteristic
96	C₄×C₁₇	C₂³×C₈	1	12	yes	—
97	C₄×C₁₇	C₂⁴×C₄	1	1	yes	characteristic
98	C₂²×#41	#595	1	1	yes	characteristic
99	C₂×#131	—	17	4	no	—
100	C₂×#131	—	17	8	no	—
101	C₂×#131	—	17	8	no	—
102	C₂×#131	—	17	4	no	—
103	C₂²×M₁₆	—	17	3	no	—
104	C₂³×C₈	—	17	3	no	—
105	#504	—	17	64	no	—
106	C₂×M₃₂	—	17	4	no	—
107	C₂×M₃₂	—	17	12	no	—
108	C₂×M₃₂	—	17	48	no	—
109	C₂²×C₁₆	—	17	12	no	—
110	C₂×C₁₇	—	2	2	no	—
111	C₂×C₁₇	—	2	12	no	—
112	C₂×C₁₇	#3407	1	2	yes	complemented
113	C₂×C₁₇	C₂⁴×C₈	1	1	yes	characteristic
114	C₂×#41	#3624	1	4	yes	—
115	C₂×#41	#3624	1	8	yes	—
116	C₂×#41	C₂×#595	1	8	yes	—
117	C₂×#41	C₂×#595	1	4	yes	—
118	C₂²×Q₈	#3624	1	1	yes	characteristic
119	C₂²×D₄	#3624	1	3	yes	—
120	C₂³×C₄	C₂×#595	1	3	yes	—
121	#131	—	17	16	no	—
122	#131	—	17	32	no	—
123	#131	—	17	16	no	—
124	C₂×M₁₆	—	17	24	no	—
125	C₂×M₁₆	—	17	12	no	—
126	C₂²×C₈	—	17	1	no	—
127	C₂²×C₈	—	17	3	no	—
128	C₂²×C₈	—	17	12	no	—
129	C₂²×C₈	—	17	6	no	—
130	C₂²×C₈	—	17	6	no	—
131	C₂²×C₈	—	17	12	no	—
132	M₃₂	—	17	16	no	—
133	M₃₂	—	17	48	no	—
134	C₂×C₁₆	—	17	8	no	—
135	C₂×C₁₆	—	17	48	no	—
136	C₁₇	C₂×#3407	1	1	yes	characteristic, complemented, Sylow
137	C₂⁴	C₂×#3624	1	3	yes	—
138	#41	C₂×#3624	1	32	yes	—
139	#41	C₂×#3624	1	16	yes	—
140	#41	C₂²×#595	1	16	yes	—
141	C₂×Q₈	C₂×#3624	1	8	yes	—
142	C₂×Q₈	C₂×#3624	1	4	yes	—
143	C₂×D₄	C₂×#3624	1	12	yes	—
144	C₂×D₄	C₂×#3624	1	24	yes	—
145	C₂²×C₄	C₂×#3624	1	3	yes	—
146	C₂²×C₄	C₂×#3624	1	6	yes	—
147	C₂²×C₄	C₂×#3624	1	12	yes	—
148	C₂²×C₄	C₂²×#595	1	12	yes	—
149	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
150	C₂²×C₄	C₂²×#595	1	6	yes	—
151	M₁₆	—	17	48	no	—
152	C₂×C₈	—	17	12	no	—
153	C₂×C₈	—	17	2	no	—
154	C₂×C₈	—	17	2	no	—
155	C₂×C₈	—	17	12	no	—
156	C₂×C₈	—	17	12	no	—
157	C₂×C₈	—	17	24	no	—
158	C₂×C₈	—	17	1	no	—
159	C₂×C₈	—	17	1	no	—
160	C₂×C₈	—	17	6	no	—
161	C₁₆	—	17	16	no	—
162	C₂³	—	4	6	no	—
163	C₂³	C₂²×#3624	1	1	yes	characteristic
164	C₂³	C₂²×#3624	1	6	yes	—
165	C₂³	C₂²×#3624	1	12	yes	—
166	Q₈	C₂²×#3624	1	16	yes	—
167	D₄	C₂²×#3624	1	48	yes	—
168	C₂×C₄	C₂²×#3624	1	1	yes	characteristic
169	C₂×C₄	C₂²×#3624	1	2	yes	—
170	C₂×C₄	C₂²×#3624	1	12	yes	—
171	C₂×C₄	C₂²×#3624	1	6	yes	—
172	C₂×C₄	C₂²×#3624	1	24	yes	—
173	C₂×C₄	C₂²×#3624	1	12	yes	—
174	C₂×C₄	C₂³×#595	1	2	yes	—
175	C₂×C₄	C₂³×#595	1	12	yes	—
176	C₂×C₄	C₂³×#595	1	1	yes	characteristic
177	C₈	—	17	1	no	—
178	C₈	—	17	2	no	—
179	C₈	—	17	1	no	—
180	C₈	—	17	12	no	—
181	C₂²	—	2	2	no	—
182	C₂²	—	2	12	no	—
183	C₂²	—	4	12	no	—
184	C₂²	C₂³×#3624	1	2	yes	—
185	C₂²	C₂³×#3624	1	12	yes	—
186	C₂²	C₂³×#3624	1	1	yes	characteristic
187	C₄	C₂³×#3624	1	2	yes	—
188	C₄	C₂³×#3624	1	1	yes	characteristic
189	C₄	C₂³×#3624	1	12	yes	—
190	C₄	C₂⁴×#595	1	1	yes	characteristic
191	C₂	—	2	2	no	—
192	C₂	—	2	12	no	—
193	C₂	#14545751	1	2	yes	direct product factor
194	C₂	C₂⁴×#3624	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×#595
commutator	C₂×C₁₇	C₂⁴×C₈
Frattini	C₄	C₂⁴×#595
Fitting, prime radical	C₂²×#41×C₁₇	C₄
socle	C₂²×C₁₇	C₂³×C₈
cosocle	#3622	C₂⁵
hypercenter	C₂²×#41	#595
hypocenter	C₁₇	C₂×#3407
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×#41

Complements

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

N	H ≅ G/N	type
1. #14545751	C₂	direct (N × H)
2. C₂×#11763867	C₂	semidirect
3. C₂²×#10587538	C₂	semidirect
5. #11763867	C₂²	semidirect
7. C₂×#10587538	C₂²	semidirect
8. C₂×#10587538	C₂²	semidirect
9. C₂²×#63216	C₂²	semidirect
36. #10587538	C₂³	semidirect
38. C₂×#63216	C₂³	semidirect
112. C₂×C₁₇	#3407	semidirect
136. C₁₇	C₂×#3407	semidirect
193. C₂	#14545751	direct (N × H)

Maximal subgroups

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

subgroup	index
#14545751	2
C₂×#11763867	2
C₂²×#10587538	2
C₂²×#10587634	2
C₂×#3407	17

Subgroups — C2×#14545751 #17981023

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14545751 #17981023