Subgroups — C₂×#14543698 #17957995

Order 4352.

350 conjugacy classes of subgroups.

The subgroup lattice has 182 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	#14543698	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	1	yes	characteristic
7	C₂×C₄×#3624	C₄	1	1	yes	characteristic
8	#11763695	C₄	1	2	yes	—
9	#11763695	C₂²	1	2	yes	—
10	C₈×#3624	C₄	1	2	yes	—
11	C₈×#3624	C₂²	1	2	yes	—
12	C₂²×#63214	C₄	1	1	yes	characteristic
13	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
14	C₁₆×Dic₁₇	C₄	1	2	yes	—
15	C₁₆×Dic₁₇	C₂²	1	2	yes	—
16	C₂²×C₁₆×C₁₇	C₄	1	1	yes	characteristic
17	C₂²×#3624	C₈	1	2	yes	—
18	C₂²×#3624	C₈	1	2	yes	—
19	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
21	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
22	C₄×#3624	C₈	1	2	yes	—
23	C₄×#3624	C₈	1	2	yes	—
24	C₄×#3624	C₂×C₄	1	2	yes	—
25	C₄×#3624	C₂×C₄	1	2	yes	—
26	C₂×#63216	—	2	4	no	—
27	C₂×#63216	C₂×C₄	1	4	yes	—
28	C₂×C₁₆×C₁₇	—	2	2	no	—
29	C₂×C₁₆×C₁₇	C₂×C₄	1	2	yes	—
30	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
31	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
32	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
33	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
34	C₂×#63214	—	2	2	no	—
35	C₂×#63214	C₂×C₄	1	2	yes	—
36	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
37	C₂²×Dic₁₇	C₂×C₈	1	1	yes	characteristic
38	C₂²×Dic₁₇	C₂×C₈	1	1	yes	characteristic
39	C₂×#3624	—	2	4	no	—
40	C₂×#3624	C₁₆	1	8	yes	complemented
41	C₂×#3624	C₂×C₈	1	4	yes	—
42	C₂×#3624	C₂×C₈	1	4	yes	—
43	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
44	C₂×C₈×C₁₇	M₁₆	1	2	yes	—
45	C₂×C₈×C₁₇	M₁₆	1	2	yes	—
46	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
47	C₄×Dic₁₇	C₄²	1	1	yes	characteristic
48	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
49	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
50	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
51	C₂×#3622	C₄²	1	1	yes	characteristic
52	C₂×#3622	M₁₆	1	4	yes	—
53	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
54	#63216	—	2	4	no	—
55	C₁₆×C₁₇	—	2	2	no	—
56	#63214	—	2	2	no	—
57	C₂×#1312	—	17	1	no	maximal, Sylow
58	C₂³×C₁₇	C₄×C₈	1	1	yes	characteristic
59	C₂×C₄×C₁₇	C₄×C₈	1	1	yes	characteristic
60	C₂×C₄×C₁₇	#97	1	2	yes	—
61	C₂×C₄×C₁₇	#97	1	2	yes	—
62	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
63	C₂×Dic₁₇	C₄×C₈	1	1	yes	characteristic
64	C₂×Dic₁₇	C₄×C₈	1	1	yes	characteristic
65	C₂×Dic₁₇	C₂×C₁₆	1	4	yes	—
66	C₂×Dic₁₇	M₃₂	1	4	yes	—
67	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
68	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
69	#3624	—	2	4	no	—
70	#3624	C₂×C₁₆	1	8	yes	complemented
71	C₈×C₁₇	#97	1	2	yes	—
72	C₈×C₁₇	C₂×M₁₆	1	1	yes	characteristic
73	C₈×C₁₇	C₂×M₁₆	1	1	yes	characteristic
74	#3622	#97	1	2	yes	—
75	#3622	C₂×M₁₆	1	2	yes	—
76	C₂×C₄×C₁₆	—	17	1	no	—
77	C₂×C₄×C₁₆	—	17	1	no	—
78	C₂×C₈²	—	17	1	no	—
79	#1312	—	17	4	no	—
80	C₂²×C₁₇	#322	1	2	yes	—
81	C₂²×C₁₇	C₄×C₁₆	1	2	yes	—
82	C₂²×C₁₇	#346	1	2	yes	—
83	C₂²×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
84	C₄×C₁₇	#322	1	2	yes	—
85	C₄×C₁₇	C₂×#97	1	1	yes	characteristic
86	C₄×C₁₇	C₂×#97	1	1	yes	characteristic
87	Dic₁₇	C₄×C₁₆	1	2	yes	—
88	Dic₁₇	#346	1	2	yes	—
89	Dic₁₇	C₂²×C₁₆	1	2	yes	—
90	Dic₁₇	C₂×M₃₂	1	2	yes	—
91	C₂²×C₁₆	—	17	2	no	—
92	C₂²×C₁₆	—	17	1	no	—
93	C₂²×C₁₆	#595	1	1	yes	characteristic
94	C₂×C₄×C₈	—	17	1	no	—
95	C₂×C₄×C₈	—	17	1	no	—
96	C₂×C₄×C₈	—	17	1	no	—
97	C₄×C₁₆	—	17	2	no	—
98	C₄×C₁₆	—	17	2	no	—
99	C₄×C₁₆	—	17	2	no	—
100	C₄×C₁₆	—	17	2	no	—
101	C₈²	—	17	2	no	—
102	C₈²	—	17	2	no	—
103	C₂×C₁₇	#1312	1	4	yes	complemented
104	C₂×C₁₇	C₂×#322	1	1	yes	characteristic
105	C₂×C₁₇	C₂×C₄×C₁₆	1	1	yes	characteristic
106	C₂×C₁₇	C₂×#346	1	1	yes	characteristic
107	C₂²×C₈	—	17	2	no	—
108	C₂²×C₈	—	17	1	no	—
109	C₂²×C₈	—	17	2	no	—
110	C₂²×C₈	C₂×#595	1	1	yes	characteristic
111	C₂×C₄²	—	17	1	no	—
112	C₂×C₁₆	—	2	2	no	—
113	C₂×C₁₆	—	17	4	no	—
114	C₂×C₁₆	—	17	2	no	—
115	C₂×C₁₆	—	34	4	no	—
116	C₂×C₁₆	—	34	2	no	—
117	C₂×C₁₆	C₂×#595	1	2	yes	—
118	C₄×C₈	—	17	2	no	—
119	C₄×C₈	—	17	2	no	—
120	C₄×C₈	—	17	2	no	—
121	C₄×C₈	—	17	2	no	—
122	C₄×C₈	—	17	1	no	—
123	C₄×C₈	—	17	1	no	—
124	C₄×C₈	—	17	1	no	—
125	C₄×C₈	—	17	1	no	—
126	C₁₇	C₂×#1312	1	1	yes	characteristic, complemented, Sylow
127	C₂²×C₄	—	17	1	no	—
128	C₂²×C₄	—	17	1	no	—
129	C₂²×C₄	C₄×#595	1	1	yes	characteristic
130	C₂×C₈	—	17	8	no	—
131	C₂×C₈	—	17	4	no	—
132	C₂×C₈	—	17	1	no	—
133	C₂×C₈	—	17	1	no	—
134	C₂×C₈	—	17	4	no	—
135	C₂×C₈	—	17	4	no	—
136	C₂×C₈	—	34	4	no	—
137	C₂×C₈	#63243	1	2	yes	—
138	C₂×C₈	C₄×#595	1	1	yes	characteristic
139	C₂×C₈	#63247	1	2	yes	—
140	C₂×C₈	C₂²×#595	1	1	yes	characteristic
141	C₄²	—	17	1	no	—
142	C₄²	—	17	1	no	—
143	C₄²	—	17	1	no	—
144	C₄²	—	17	1	no	—
145	C₁₆	—	2	2	no	—
146	C₁₆	—	34	4	no	—
147	C₁₆	—	34	2	no	—
148	C₂³	C₈×#595	1	1	yes	characteristic
149	C₂×C₄	—	17	1	no	—
150	C₂×C₄	—	17	1	no	—
151	C₂×C₄	—	17	1	no	—
152	C₂×C₄	—	17	1	no	—
153	C₂×C₄	—	17	4	no	—
154	C₂×C₄	—	17	4	no	—
155	C₂×C₄	C₈×#595	1	1	yes	characteristic
156	C₂×C₄	#10587532	1	2	yes	—
157	C₂×C₄	#10587542	1	2	yes	—
158	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
159	C₈	—	17	8	no	—
160	C₈	—	17	2	no	—
161	C₈	—	17	2	no	—
162	C₈	—	34	4	no	—
163	C₈	#10587542	1	2	yes	—
164	C₈	C₂×#63243	1	1	yes	characteristic
165	C₈	C₂×#63247	1	1	yes	characteristic
166	C₂²	#11763651	1	2	yes	—
167	C₂²	C₁₆×#595	1	2	yes	—
168	C₂²	#11763696	1	2	yes	—
169	C₂²	C₂×C₈×#595	1	1	yes	characteristic
170	C₄	—	17	2	no	—
171	C₄	—	17	2	no	—
172	C₄	—	17	2	no	—
173	C₄	—	17	2	no	—
174	C₄	#11763651	1	2	yes	—
175	C₄	C₂×#10587532	1	1	yes	characteristic
176	C₄	C₂×#10587542	1	1	yes	characteristic
177	C₂	#14543698	1	4	yes	direct product factor
178	C₂	C₂×#11763651	1	1	yes	characteristic
179	C₂	C₂×C₁₆×#595	1	1	yes	characteristic
180	C₂	C₂×#11763696	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈	C₂×#595
commutator	C₂×C₁₇	C₂×C₄×C₁₆
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×#1312
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. #14543698	C₂	direct (N × H)
40. C₂×#3624	C₁₆	semidirect
70. #3624	C₂×C₁₆	semidirect
103. C₂×C₁₇	#1312	semidirect
126. C₁₇	C₂×#1312	semidirect
177. C₂	#14543698	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
#14543698	2
C₂×C₁₆×Dic₁₇	2
C₂×#1312	17

Subgroups — C2×#14543698 #17957995

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14543698 #17957995