Subgroups — #17960424

Order 4352.

478 conjugacy classes of subgroups.

The subgroup lattice has 164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11763698	C₂	1	2	yes	maximal
2	C₂×#11763697	C₂	1	1	yes	maximal, characteristic
3	C₂×#11763695	C₂	1	2	yes	maximal
4	C₂×C₄×#63216	C₂	1	1	yes	maximal, characteristic
5	#14528472	C₂	1	1	yes	maximal, characteristic
6	C₂²×#63216	C₂²	1	1	yes	characteristic
7	C₂²×#63216	C₂²	1	1	yes	characteristic
8	C₂²×#63216	C₂²	1	2	yes	—
9	#11763698	C₄	1	8	yes	complemented
10	#11763697	C₄	1	4	yes	complemented
11	#11763695	C₄	1	8	yes	complemented
12	C₄×#63216	C₄	1	4	yes	complemented
13	C₂×#10587486	C₄	1	2	yes	—
14	C₂×C₄×#3622	C₂²	1	1	yes	characteristic
15	C₂×C₈×Dic₁₇	C₂²	1	2	yes	—
16	#11762655	C₄	1	1	yes	characteristic
17	C₂×C₁₇×#97	C₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₇	C₂×C₄	1	2	yes	—
19	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×Dic₁₇	C₂×C₄	1	2	yes	—
21	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
22	C₂²×#3622	C₂³	1	1	yes	characteristic
23	C₂×#63216	C₂×C₄	1	2	yes	—
24	C₂×#63216	C₂×C₄	1	2	yes	—
25	C₂×#63216	C₂×C₄	1	4	yes	—
26	C₂×#63216	C₂×C₄	1	4	yes	—
27	C₂×#63216	C₂×C₄	1	4	yes	—
28	C₂×#63216	C₂×C₄	1	4	yes	—
29	C₂×#63216	C₂×C₄	1	4	yes	—
30	C₁₇×#97	C₈	1	4	yes	—
31	#10587502	C₈	1	4	yes	—
32	#10587486	C₈	1	8	yes	—
33	C₈×Dic₁₇	C₂×C₄	1	4	yes	—
34	C₈×Dic₁₇	C₂×C₄	1	4	yes	—
35	C₄×#3622	C₂×C₄	1	2	yes	—
36	C₄×#3622	C₂×C₄	1	2	yes	—
37	C₂²×C₄×C₁₇	C₂×C₈	1	2	yes	—
38	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
39	C₂²×Dic₁₇	C₂×C₈	1	4	yes	—
40	C₂×C₈×C₁₇	C₄²	1	4	yes	—
41	C₂×C₈×C₁₇	C₂×C₈	1	4	yes	—
42	C₂×C₈×C₁₇	C₂×C₈	1	4	yes	—
43	C₄²×C₁₇	C₄²	1	2	yes	—
44	C₄²×C₁₇	C₂×C₈	1	2	yes	—
45	C₄×Dic₁₇	C₄²	1	4	yes	—
46	C₄×Dic₁₇	C₂×C₈	1	4	yes	—
47	C₂×#3622	C₄²	1	2	yes	—
48	C₂×#3622	C₂×C₈	1	4	yes	—
49	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
50	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
51	C₂×#3622	C₂²×C₄	1	2	yes	—
52	C₂×#3622	C₂²×C₄	1	2	yes	—
53	#63216	C₄²	1	4	yes	—
54	#63216	C₄²	1	4	yes	—
55	#63216	C₄²	1	8	yes	—
56	#12539	—	17	1	no	maximal, Sylow
57	C₂³×C₁₇	C₂²×C₈	1	1	yes	characteristic
58	C₂×C₄×C₁₇	—	2	4	no	—
59	C₂×C₄×C₁₇	C₄×C₈	1	4	yes	—
60	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
61	C₂×C₄×C₁₇	C₂×C₄²	1	2	yes	—
62	C₂×C₄×C₁₇	C₂²×C₈	1	2	yes	—
63	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
64	C₂×Dic₁₇	—	2	8	no	—
65	C₂×Dic₁₇	C₄×C₈	1	8	yes	—
66	C₈×C₁₇	C₄×C₈	1	8	yes	—
67	#3622	C₄×C₈	1	4	yes	—
68	#3622	C₂×C₄²	1	1	yes	characteristic
69	#3622	C₂×C₄²	1	1	yes	characteristic
70	#3622	C₂×C₄²	1	2	yes	—
71	C₂×#346	—	17	1	no	—
72	C₂×#346	—	17	2	no	—
73	C₂×C₄×C₁₆	—	17	1	no	—
74	C₂×C₄×C₁₆	—	17	2	no	—
75	#1726	—	17	1	no	—
76	C₂²×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
77	C₂²×C₁₇	C₂×C₄×C₈	1	2	yes	—
78	C₂²×C₁₇	#504	1	4	yes	—
79	C₄×C₁₇	—	2	4	no	—
80	C₄×C₁₇	C₄³	1	1	yes	characteristic
81	C₄×C₁₇	C₂×C₄×C₈	1	2	yes	—
82	C₄×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
83	Dic₁₇	—	2	8	no	—
84	C₂²×C₁₆	—	17	1	no	—
85	C₂²×C₁₆	—	17	1	no	—
86	C₂²×C₁₆	—	17	2	no	—
87	C₂×#97	—	17	2	no	—
88	C₂×#97	#595	1	1	yes	characteristic
89	C₂×C₄×C₈	—	17	2	no	—
90	C₂×C₄×C₈	—	17	1	no	—
91	#376	—	17	1	no	—
92	#346	—	17	4	no	—
93	#346	—	17	8	no	—
94	C₄×C₁₆	—	17	4	no	—
95	C₄×C₁₆	—	17	8	no	—
96	C₂×C₁₇	C₄²×C₈	1	1	yes	characteristic
97	C₂×C₁₇	#2108	1	4	yes	—
98	C₂×C₁₇	#2108	1	2	yes	—
99	C₂²×C₈	—	17	1	no	—
100	C₂²×C₈	—	17	1	no	—
101	C₂²×C₈	C₂×#595	1	2	yes	—
102	C₂×C₄²	—	17	2	no	—
103	C₂×C₄²	C₂×#595	1	1	yes	characteristic
104	C₂×C₁₆	—	17	2	no	—
105	C₂×C₁₆	—	17	2	no	—
106	C₂×C₁₆	—	17	4	no	—
107	C₂×C₁₆	—	17	4	no	—
108	C₂×C₁₆	—	17	4	no	—
109	C₂×C₁₆	—	17	4	no	—
110	C₂×C₁₆	—	17	4	no	—
111	#97	—	17	8	no	—
112	#97	#3624	1	4	yes	—
113	C₄×C₈	—	17	4	no	—
114	C₄×C₈	—	17	4	no	—
115	C₄×C₈	—	17	2	no	—
116	C₄×C₈	—	17	2	no	—
117	#95	—	17	4	no	—
118	C₁₇	#12539	1	1	yes	characteristic, complemented, Sylow
119	C₂²×C₄	—	17	4	no	—
120	C₂²×C₄	#63242	1	2	yes	—
121	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
122	C₂×C₈	—	17	4	no	—
123	C₂×C₈	—	17	2	no	—
124	C₂×C₈	—	17	2	no	—
125	C₂×C₈	—	17	1	no	—
126	C₂×C₈	—	17	1	no	—
127	C₂×C₈	—	17	2	no	—
128	C₂×C₈	#63242	1	4	yes	—
129	C₂×C₈	C₄×#595	1	4	yes	—
130	C₂×C₈	C₂×#3624	1	4	yes	—
131	C₄²	—	17	4	no	—
132	C₄²	—	17	4	no	—
133	C₄²	C₄×#595	1	2	yes	—
134	C₄²	C₂×#3624	1	2	yes	—
135	C₁₆	—	17	4	no	—
136	C₁₆	—	17	4	no	—
137	C₁₆	—	17	8	no	—
138	C₂³	C₂×#63242	1	1	yes	characteristic
139	C₂×C₄	—	2	4	no	—
140	C₂×C₄	—	17	8	no	—
141	C₂×C₄	—	34	8	no	—
142	C₂×C₄	C₄×#3624	1	4	yes	—
143	C₂×C₄	C₂×#63242	1	2	yes	—
144	C₂×C₄	C₂×C₄×#595	1	2	yes	—
145	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
146	C₂×C₄	C₂²×#3624	1	1	yes	characteristic
147	C₈	—	17	1	no	—
148	C₈	—	17	2	no	—
149	C₈	—	17	1	no	—
150	C₈	—	17	4	no	—
151	C₈	C₄×#3624	1	8	yes	—
152	C₂²	C₂×C₄×#3624	1	1	yes	characteristic
153	C₂²	C₄×#63242	1	2	yes	—
154	C₂²	#11763868	1	4	yes	—
155	C₄	—	2	4	no	—
156	C₄	—	34	8	no	—
157	C₄	C₄²×#595	1	1	yes	characteristic
158	C₄	C₂×C₄×#3624	1	2	yes	—
159	C₄	C₄×#63242	1	1	yes	characteristic
160	C₂	C₄²×#3624	1	1	yes	characteristic
161	C₂	#14544994	1	4	yes	—
162	C₂	#14544995	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×#595
commutator	C₂×C₁₇	C₄²×C₈
Fitting	C₂×C₁₇×#97	C₄
socle, prime radical	C₂³×C₁₇	C₂²×C₈
cosocle	C₂²×#3622	C₂³
hypercenter	C₂×#97	#595
hypocenter	C₁₇	#12539
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
9. #11763698	C₄	semidirect
10. #11763697	C₄	semidirect
11. #11763695	C₄	semidirect
12. C₄×#63216	C₄	semidirect
118. C₁₇	#12539	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11763698	2
C₂×#11763697	2
C₂×#11763695	2
C₂×C₄×#63216	2
#14528472	2
#12539	17