Subgroups — C₂×#14543695 #17957979

Order 4352.

366 conjugacy classes of subgroups.

The subgroup lattice has 150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11763695	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×#3624	C₂	1	1	yes	maximal, characteristic
3	#14543695	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₆×Dic₁₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×#63216	C₄	1	2	yes	—
6	C₂×C₄×#3624	C₄	1	2	yes	—
7	#11763695	C₄	1	2	yes	—
8	#11763695	C₂²	1	2	yes	—
9	C₈×#3624	C₄	1	2	yes	—
10	C₈×#3624	C₂²	1	2	yes	—
11	C₂²×#63214	C₄	1	1	yes	characteristic
12	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
13	C₁₆×Dic₁₇	C₄	1	2	yes	—
14	C₁₆×Dic₁₇	C₂²	1	2	yes	—
15	C₂²×C₁₆×C₁₇	C₄	1	1	yes	characteristic
16	C₂²×#3624	C₈	1	4	yes	—
17	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
19	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
20	C₄×#3624	C₈	1	4	yes	—
21	C₄×#3624	C₂×C₄	1	4	yes	—
22	C₂×#63216	C₈	1	8	yes	complemented
23	C₂×#63216	C₂×C₄	1	4	yes	—
24	C₂×C₁₆×C₁₇	C₈	1	4	yes	complemented
25	C₂×C₁₆×C₁₇	C₂×C₄	1	2	yes	—
26	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
27	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
28	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
29	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
30	C₂×#63214	C₈	1	4	yes	complemented
31	C₂×#63214	C₂×C₄	1	2	yes	—
32	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
33	C₂²×Dic₁₇	C₂×C₈	1	2	yes	—
34	C₂×#3624	—	2	8	no	—
35	C₂×#3624	C₂×C₈	1	8	yes	—
36	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
37	C₂×C₈×C₁₇	C₂×C₈	1	2	yes	—
38	C₂×C₈×C₁₇	C₂×C₈	1	2	yes	—
39	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
40	C₄×Dic₁₇	C₄²	1	1	yes	characteristic
41	C₄×Dic₁₇	C₂×C₈	1	2	yes	—
42	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
43	C₂×#3622	C₄²	1	1	yes	characteristic
44	C₂×#3622	C₂×C₈	1	4	yes	—
45	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
46	#63216	C₂×C₈	1	8	yes	complemented
47	C₁₆×C₁₇	C₂×C₈	1	4	yes	complemented
48	#63214	C₂×C₈	1	4	yes	complemented
49	C₂×#1311	—	17	1	no	maximal, Sylow
50	C₂³×C₁₇	C₄×C₈	1	1	yes	characteristic
51	C₂×C₄×C₁₇	C₄×C₈	1	1	yes	characteristic
52	C₂×C₄×C₁₇	C₄×C₈	1	2	yes	—
53	C₂×C₄×C₁₇	C₄×C₈	1	2	yes	—
54	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
55	C₂×Dic₁₇	C₄×C₈	1	2	yes	—
56	C₂×Dic₁₇	M₃₂	1	8	yes	—
57	C₂×Dic₁₇	C₂²×C₈	1	2	yes	—
58	#3624	—	2	8	no	—
59	C₈×C₁₇	C₄×C₈	1	2	yes	—
60	C₈×C₁₇	C₂²×C₈	1	1	yes	characteristic
61	C₈×C₁₇	C₂²×C₈	1	1	yes	characteristic
62	#3622	C₄×C₈	1	2	yes	—
63	#3622	C₂²×C₈	1	2	yes	—
64	C₂×C₄×C₁₆	—	17	1	no	—
65	C₂×C₄×C₁₆	—	17	1	no	—
66	C₂×C₈²	—	17	1	no	—
67	#1311	—	17	4	no	—
68	C₂²×C₁₇	C₈²	1	2	yes	—
69	C₂²×C₁₇	#346	1	4	yes	—
70	C₂²×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
71	C₄×C₁₇	C₈²	1	2	yes	—
72	C₄×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
73	C₄×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
74	Dic₁₇	#346	1	4	yes	—
75	Dic₁₇	C₂×M₃₂	1	4	yes	—
76	C₂²×C₁₆	—	17	2	no	—
77	C₂²×C₁₆	—	17	1	no	—
78	C₂²×C₁₆	#595	1	1	yes	characteristic
79	C₂×C₄×C₈	—	17	2	no	—
80	C₂×C₄×C₈	—	17	1	no	—
81	C₄×C₁₆	—	17	2	no	—
82	C₄×C₁₆	—	17	2	no	—
83	C₄×C₁₆	—	17	2	no	—
84	C₄×C₁₆	—	17	2	no	—
85	C₈²	—	17	2	no	—
86	C₈²	—	17	2	no	—
87	C₂×C₁₇	#1311	1	4	yes	complemented
88	C₂×C₁₇	C₂×C₈²	1	1	yes	characteristic
89	C₂×C₁₇	C₂×#346	1	2	yes	—
90	C₂²×C₈	—	17	1	no	—
91	C₂²×C₈	—	17	4	no	—
92	C₂²×C₈	C₂×#595	1	1	yes	characteristic
93	C₂×C₄²	—	17	1	no	—
94	C₂×C₁₆	—	17	4	no	—
95	C₂×C₁₆	—	17	8	no	—
96	C₂×C₁₆	—	17	4	no	—
97	C₂×C₁₆	—	17	2	no	—
98	C₂×C₁₆	#3624	1	4	yes	complemented
99	C₂×C₁₆	C₂×#595	1	2	yes	—
100	C₄×C₈	—	17	4	no	—
101	C₄×C₈	—	17	4	no	—
102	C₄×C₈	—	17	1	no	—
103	C₄×C₈	—	17	1	no	—
104	C₄×C₈	—	17	1	no	—
105	C₄×C₈	—	17	1	no	—
106	C₁₇	C₂×#1311	1	1	yes	characteristic, complemented, Sylow
107	C₂²×C₄	—	17	2	no	—
108	C₂²×C₄	C₄×#595	1	1	yes	characteristic
109	C₂×C₈	—	17	1	no	—
110	C₂×C₈	—	17	1	no	—
111	C₂×C₈	—	17	4	no	—
112	C₂×C₈	—	17	8	no	—
113	C₂×C₈	—	34	8	no	—
114	C₂×C₈	#63242	1	2	yes	—
115	C₂×C₈	C₄×#595	1	1	yes	characteristic
116	C₂×C₈	C₂×#3624	1	2	yes	—
117	C₂×C₈	C₂²×#595	1	1	yes	characteristic
118	C₄²	—	17	1	no	—
119	C₄²	—	17	1	no	—
120	C₄²	—	17	2	no	—
121	C₁₆	—	17	8	no	—
122	C₁₆	—	17	4	no	—
123	C₁₆	C₂×#3624	1	4	yes	complemented
124	C₂³	C₈×#595	1	1	yes	characteristic
125	C₂×C₄	—	17	2	no	—
126	C₂×C₄	—	17	2	no	—
127	C₂×C₄	—	17	8	no	—
128	C₂×C₄	C₈×#595	1	2	yes	—
129	C₂×C₄	C₈×#595	1	1	yes	characteristic
130	C₂×C₄	C₄×#3624	1	2	yes	—
131	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
132	C₈	—	17	2	no	—
133	C₈	—	17	2	no	—
134	C₈	—	34	8	no	—
135	C₈	C₄×#3624	1	2	yes	—
136	C₈	C₂×#63242	1	1	yes	characteristic
137	C₈	C₂²×#3624	1	1	yes	characteristic
138	C₂²	C₈×#3624	1	2	yes	—
139	C₂²	#11763696	1	4	yes	—
140	C₂²	C₂×C₈×#595	1	1	yes	characteristic
141	C₄	—	17	4	no	—
142	C₄	—	17	4	no	—
143	C₄	C₈×#3624	1	2	yes	—
144	C₄	C₂×C₈×#595	1	1	yes	characteristic
145	C₄	C₂×C₄×#3624	1	1	yes	characteristic
146	C₂	#14543695	1	4	yes	direct product factor
147	C₂	C₂×C₈×#3624	1	1	yes	characteristic
148	C₂	C₂×#11763696	1	2	yes	—

	subgroup	G/H
center	C₂²×C₈	C₂×#595
commutator	C₂×C₁₇	C₂×C₈²
Frattini	C₂×C₈	C₂²×#595
Fitting	C₂²×C₁₆×C₁₇	C₄
socle, prime radical	C₂³×C₁₇	C₄×C₈
cosocle	C₈×Dic₁₇	C₂³
hypercenter	C₂²×C₁₆	#595
hypocenter	C₁₇	C₂×#1311
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
3. #14543695	C₂	direct (N × H)
22. C₂×#63216	C₈	semidirect
24. C₂×C₁₆×C₁₇	C₈	semidirect
30. C₂×#63214	C₈	semidirect
46. #63216	C₂×C₈	semidirect
47. C₁₆×C₁₇	C₂×C₈	semidirect
48. #63214	C₂×C₈	semidirect
87. C₂×C₁₇	#1311	semidirect
98. C₂×C₁₆	#3624	semidirect
106. C₁₇	C₂×#1311	semidirect
123. C₁₆	C₂×#3624	semidirect
146. C₂	#14543695	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×#11763695	2
C₂×C₈×#3624	2
#14543695	2
C₂×C₁₆×Dic₁₇	2
C₂×#1311	17

Subgroups — C2×#14543695 #17957979

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14543695 #17957979