Subgroups — #595⋊#346 #17982373

Order 4352.

510 conjugacy classes of subgroups.

The subgroup lattice has 200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11763904	C₂	1	2	yes	maximal
2	#14545940	C₂	1	2	yes	maximal
3	C₂×#11763902	C₂	1	2	yes	maximal
4	C₄×C₈×#595	C₂	1	1	yes	maximal, characteristic
5	C₂×#10587665	C₂²	1	4	yes	—
6	#11763904	C₄	1	8	yes	complemented
7	#11763903	C₄	1	8	yes	complemented
8	#11763902	C₄	1	8	yes	complemented
9	C₄×#63242	C₂²	1	1	yes	characteristic
10	C₂×C₈×#595	C₄	1	1	yes	characteristic
11	C₂×C₈×#595	C₄	1	1	yes	characteristic
12	C₂×C₈×#595	C₂²	1	1	yes	characteristic
13	C₂×C₈×#595	C₂²	1	1	yes	characteristic
14	C₄²×#595	C₄	1	1	yes	characteristic
15	C₄×C₈×D₁₇	C₄	1	1	yes	characteristic
16	C₂×C₄×#595	C₈	1	4	yes	—
17	C₂×C₄×#595	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×#595	C₂×C₄	1	1	yes	characteristic
19	C₂×#63242	C₂×C₄	1	1	yes	characteristic
20	C₂×#63242	C₂³	1	1	yes	characteristic
21	C₂×#63241	C₂×C₄	1	8	yes	—
22	#10587665	C₂×C₄	1	8	yes	—
23	#10587665	C₂×C₄	1	8	yes	—
24	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
26	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
27	C₄×#3624	C₂×C₄	1	4	yes	—
28	C₈×#595	C₈	1	4	yes	—
29	C₈×#595	C₈	1	4	yes	—
30	C₈×#595	C₂×C₄	1	4	yes	—
31	C₈×#595	C₂×C₄	1	4	yes	—
32	C₄×C₈×C₁₇	C₈	1	1	yes	characteristic
33	C₈×Dic₁₇	C₈	1	1	yes	characteristic
34	C₈×Dic₁₇	C₈	1	1	yes	characteristic
35	C₄×#3622	C₈	1	1	yes	characteristic
36	C₂²×#595	C₂×C₈	1	2	yes	—
37	C₂²×#595	C₂×C₈	1	2	yes	—
38	C₂×C₄×D₁₇	C₂×C₈	1	2	yes	—
39	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
40	C₂×#3624	C₄²	1	2	yes	—
41	C₂×#3624	C₂²×C₄	1	2	yes	—
42	C₄×#595	—	2	8	no	—
43	C₄×#595	C₄²	1	2	yes	—
44	C₄×#595	C₄²	1	2	yes	—
45	C₄×#595	C₂×C₈	1	2	yes	—
46	C₄×#595	C₂×C₈	1	2	yes	—
47	#63242	C₂×C₈	1	2	yes	—
48	#63242	C₂×C₈	1	2	yes	—
49	#63242	C₂²×C₄	1	2	yes	—
50	#63242	C₂²×C₄	1	2	yes	—
51	#63241	C₄²	1	16	yes	complemented
52	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
53	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
54	C₄²×C₁₇	C₂×C₈	1	1	yes	characteristic
55	C₄×Dic₁₇	C₄²	1	2	yes	—
56	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
57	C₂×#3622	C₂×C₈	1	1	yes	characteristic
58	C₂×#3622	C₂×C₈	1	1	yes	characteristic
59	C₈×D₁₇	C₄²	1	2	yes	—
60	C₈×D₁₇	C₄²	1	2	yes	—
61	C₈×D₁₇	C₂×C₈	1	2	yes	—
62	C₈×D₁₇	C₂×C₈	1	2	yes	—
63	C₄×#346	—	17	1	no	maximal, Sylow
64	C₂²×D₁₇	C₂²×C₈	1	1	yes	characteristic
65	C₂×#595	—	2	4	no	—
66	C₂×#595	C₄×C₈	1	4	yes	—
67	C₂×#595	C₄×C₈	1	4	yes	—
68	C₂×#595	M₃₂	1	8	yes	—
69	C₂×C₄×C₁₇	C₄×C₈	1	2	yes	—
70	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
71	C₂×Dic₁₇	C₄×C₈	1	2	yes	—
72	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
73	C₄×D₁₇	—	2	4	no	—
74	C₄×D₁₇	C₂×C₄²	1	1	yes	characteristic
75	C₄×D₁₇	C₂×C₄²	1	1	yes	characteristic
76	C₄×D₁₇	C₂²×C₈	1	1	yes	characteristic
77	C₄×D₁₇	C₂²×C₈	1	1	yes	characteristic
78	#3624	C₄×C₈	1	4	yes	—
79	#3624	C₂×C₄²	1	4	yes	—
80	C₈×C₁₇	C₄×C₈	1	2	yes	—
81	C₈×C₁₇	C₄×C₈	1	2	yes	—
82	#3622	C₄×C₈	1	2	yes	—
83	#3622	C₄×C₈	1	2	yes	—
84	C₂×#346	—	17	2	no	—
85	C₂×#346	—	17	2	no	—
86	C₂×C₄×C₁₆	—	17	2	no	—
87	C₄²×C₈	—	17	1	no	—
88	C₂²×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
89	C₂×D₁₇	C₂×C₄×C₈	1	1	yes	characteristic
90	C₂×D₁₇	C₂×C₄×C₈	1	1	yes	characteristic
91	C₂×D₁₇	C₂×M₃₂	1	4	yes	—
92	#595	—	2	4	no	—
93	#595	#346	1	8	yes	complemented
94	C₄×C₁₇	—	2	2	no	—
95	C₄×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
96	C₄×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
97	Dic₁₇	—	2	2	no	—
98	Dic₁₇	C₄³	1	1	yes	characteristic
99	Dic₁₇	C₂×C₄×C₈	1	1	yes	characteristic
100	C₂²×C₁₆	—	17	4	no	—
101	C₂×C₄×C₈	—	17	1	no	—
102	C₂×C₄×C₈	—	17	1	no	—
103	C₂×C₄×C₈	—	17	1	no	—
104	C₂×C₄×C₈	—	17	1	no	—
105	C₂×C₄×C₈	—	17	1	no	—
106	C₂×C₄×C₈	—	17	1	no	—
107	C₄³	—	17	1	no	—
108	#346	—	17	8	no	—
109	#346	—	17	8	no	—
110	C₄×C₁₆	—	17	8	no	—
111	C₂×C₁₇	C₄²×C₈	1	1	yes	characteristic
112	C₂×C₁₇	C₄×M₃₂	1	2	yes	—
113	D₁₇	C₂×#346	1	2	yes	—
114	D₁₇	C₄×M₃₂	1	2	yes	—
115	C₂²×C₈	—	17	1	no	—
116	C₂²×C₈	—	17	1	no	—
117	C₂²×C₈	—	17	1	no	—
118	C₂²×C₈	—	17	1	no	—
119	C₂×C₄²	—	17	1	no	—
120	C₂×C₄²	—	17	1	no	—
121	C₂×C₄²	—	17	1	no	—
122	C₂×C₄²	—	17	4	no	—
123	C₂×C₁₆	—	17	8	no	—
124	C₂×C₁₆	—	17	8	no	—
125	C₂×C₁₆	—	17	8	no	—
126	C₄×C₈	—	17	4	no	—
127	C₄×C₈	—	17	4	no	—
128	C₄×C₈	—	17	4	no	—
129	C₄×C₈	—	17	4	no	—
130	C₄×C₈	—	17	4	no	—
131	C₄×C₈	—	17	1	no	—
132	C₄×C₈	—	17	1	no	—
133	C₄×C₈	—	17	1	no	—
134	C₄×C₈	#3633	1	1	yes	characteristic
135	C₁₇	C₄×#346	1	1	yes	characteristic, complemented, Sylow
136	C₂²×C₄	—	17	2	no	—
137	C₂²×C₄	—	17	1	no	—
138	C₂²×C₄	—	17	2	no	—
139	C₂²×C₄	—	17	2	no	—
140	C₂×C₈	—	17	2	no	—
141	C₂×C₈	—	17	2	no	—
142	C₂×C₈	—	17	2	no	—
143	C₂×C₈	—	17	2	no	—
144	C₂×C₈	—	17	2	no	—
145	C₂×C₈	—	17	2	no	—
146	C₂×C₈	—	17	1	no	—
147	C₂×C₈	—	17	1	no	—
148	C₂×C₈	—	17	2	no	—
149	C₂×C₈	—	17	2	no	—
150	C₂×C₈	—	17	2	no	—
151	C₂×C₈	—	17	2	no	—
152	C₂×C₈	C₂×#3633	1	1	yes	characteristic
153	C₂×C₈	C₂×#3633	1	1	yes	characteristic
154	C₄²	—	17	2	no	—
155	C₄²	—	17	2	no	—
156	C₄²	—	17	2	no	—
157	C₄²	—	17	2	no	—
158	C₄²	—	17	2	no	—
159	C₄²	—	17	1	no	—
160	C₄²	—	34	8	no	—
161	C₄²	C₂×#3633	1	1	yes	characteristic
162	C₁₆	—	17	16	no	—
163	C₂³	—	17	1	no	—
164	C₂×C₄	—	17	4	no	—
165	C₂×C₄	—	17	8	no	—
166	C₂×C₄	—	17	1	no	—
167	C₂×C₄	—	17	1	no	—
168	C₂×C₄	—	17	1	no	—
169	C₂×C₄	—	17	1	no	—
170	C₂×C₄	—	17	1	no	—
171	C₂×C₄	—	17	4	no	—
172	C₂×C₄	—	17	2	no	—
173	C₂×C₄	—	34	4	no	—
174	C₂×C₄	—	34	4	no	—
175	C₂×C₄	C₄×#3633	1	2	yes	—
176	C₂×C₄	C₂²×#3633	1	1	yes	characteristic
177	C₈	—	17	4	no	—
178	C₈	—	17	4	no	—
179	C₈	—	17	2	no	—
180	C₈	—	17	2	no	—
181	C₈	C₄×#3633	1	2	yes	—
182	C₈	C₄×#3633	1	2	yes	—
183	C₂²	—	17	4	no	—
184	C₂²	—	17	1	no	—
185	C₂²	—	17	1	no	—
186	C₂²	C₂×C₄×#3633	1	1	yes	characteristic
187	C₄	—	2	2	no	—
188	C₄	—	17	8	no	—
189	C₄	—	17	1	no	—
190	C₄	—	17	1	no	—
191	C₄	—	34	4	no	—
192	C₄	—	34	2	no	—
193	C₄	C₂×C₄×#3633	1	1	yes	characteristic
194	C₄	C₂×C₄×#3633	1	1	yes	characteristic
195	C₂	—	17	2	no	—
196	C₂	—	17	2	no	—
197	C₂	C₄²×#3633	1	1	yes	characteristic
198	C₂	#595⋊M₃₂	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₂×#3633
commutator	C₂×C₁₇	C₄²×C₈
Frattini	C₂×C₄	C₂²×#3633
Fitting	C₄×C₈×C₁₇	C₈
socle	C₂²×C₁₇	C₂×C₄×C₈
prime radical	C₂²×D₁₇	C₂²×C₈
cosocle	C₂×#63242	C₂³
hypercenter	C₄×C₈	#3633
hypocenter	C₁₇	C₄×#346
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
6. #11763904	C₄	semidirect
7. #11763903	C₄	semidirect
8. #11763902	C₄	semidirect
51. #63241	C₄²	semidirect
93. #595	#346	semidirect
135. C₁₇	C₄×#346	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11763904	2
#14545940	2
C₂×#11763902	2
C₄×C₈×#595	2
C₄×#346	17