Subgroups — #16943334

Order 4352.

282 conjugacy classes of subgroups.

The subgroup lattice has 136 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10587483	C₂	1	1	yes	maximal, characteristic
2	#14527067	C₂	1	1	yes	maximal, characteristic
3	#14526706	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₇×#346	C₂	1	1	yes	maximal, characteristic
5	C₂×#10587483	C₄	1	2	yes	—
6	#11762862	C₄	1	2	yes	—
7	#11762585	C₂²	1	2	yes	—
8	C₄×#63214	C₄	1	2	yes	—
9	#11762530	C₂²	1	2	yes	—
10	C₈×#3622	C₄	1	2	yes	—
11	C₂²×C₁₆×C₁₇	C₄	1	2	yes	—
12	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
13	C₁₇×#346	C₄	1	2	yes	—
14	C₁₇×#346	C₂²	1	2	yes	—
15	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
18	C₂×C₁₆×C₁₇	—	2	4	no	—
19	C₂×C₁₆×C₁₇	C₂×C₄	1	4	yes	—
20	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
21	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
22	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
23	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
24	C₂²⋊#3622	—	2	2	no	—
25	#10587483	C₈	1	8	yes	complemented
26	C₂×#63214	C₂×C₄	1	4	yes	—
27	C₄⋊#3622	—	2	2	no	—
28	C₄×#3622	C₂×C₄	1	4	yes	—
29	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
30	C₂²×C₄×C₁₇	M₁₆	1	2	yes	—
31	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
32	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
33	C₂×C₈×C₁₇	C₂×C₈	1	4	yes	—
34	C₂×C₈×C₁₇	M₁₆	1	4	yes	—
35	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
37	C₄²×C₁₇	C₄²	1	1	yes	characteristic
38	C₄²×C₁₇	M₁₆	1	2	yes	—
39	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
40	C₂×#3622	—	2	4	no	—
41	C₁₆×C₁₇	—	2	4	no	—
42	#63214	C₂×C₈	1	8	yes	—
43	#11406	—	17	1	no	maximal, Sylow
44	C₂³×C₁₇	#97	1	1	yes	characteristic
45	C₂×C₄×C₁₇	—	4	2	no	—
46	C₂×C₄×C₁₇	C₄×C₈	1	2	yes	—
47	C₂×C₄×C₁₇	#97	1	2	yes	—
48	C₂×C₄×C₁₇	#97	1	2	yes	—
49	C₂×C₄×C₁₇	#97	1	1	yes	characteristic
50	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
51	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
52	C₈×C₁₇	C₄×C₈	1	2	yes	—
53	C₈×C₁₇	#97	1	2	yes	—
54	C₈×C₁₇	C₂²×C₈	1	2	yes	—
55	C₈×C₁₇	C₂×M₁₆	1	2	yes	—
56	#3622	—	4	4	no	—
57	C₄×M₃₂	—	17	1	no	—
58	C₂×#346	D₁₇	1	1	yes	characteristic
59	#1450	—	17	1	no	—
60	#1313	—	17	4	no	—
61	C₂²×C₁₇	—	2	2	no	—
62	C₂²×C₁₇	#322	1	2	yes	—
63	C₂²×C₁₇	C₂×#97	1	1	yes	characteristic
64	C₄×C₁₇	—	2	2	no	—
65	C₄×C₁₇	—	2	2	no	—
66	C₄×C₁₇	#322	1	2	yes	—
67	C₄×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
68	C₄×C₁₇	C₂×#97	1	1	yes	characteristic
69	C₂×M₃₂	—	17	2	no	—
70	C₂²×C₁₆	Dic₁₇	1	2	yes	—
71	#431	—	17	2	no	—
72	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
73	#346	—	17	2	no	—
74	#346	Dic₁₇	1	2	yes	—
75	#346	C₂×D₁₇	1	2	yes	—
76	C₄×C₁₆	—	17	2	no	—
77	#322	—	17	2	no	—
78	C₈²	—	17	2	no	—
79	C₂×C₁₇	—	2	2	no	—
80	C₂×C₁₇	C₂×#322	1	1	yes	characteristic
81	C₂×C₁₇	#2110	1	2	yes	—
82	C₂²×C₈	C₄×D₁₇	1	1	yes	characteristic
83	C₂²×C₈	C₂×Dic₁₇	1	1	yes	characteristic
84	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
85	M₃₂	—	17	8	no	—
86	C₂×C₁₆	—	2	4	no	—
87	C₂×C₁₆	—	17	4	no	—
88	C₂×C₁₆	C₂×Dic₁₇	1	4	yes	—
89	C₄⋊C₈	—	34	2	no	—
90	C₂²⋊C₈	—	34	2	no	—
91	C₄×C₈	—	17	4	no	—
92	C₄×C₈	C₄×D₁₇	1	1	yes	characteristic
93	C₄×C₈	C₄×D₁₇	1	1	yes	characteristic
94	C₄×C₈	C₂×Dic₁₇	1	1	yes	characteristic
95	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
96	C₁₇	#11406	1	1	yes	characteristic, complemented, Sylow
97	C₂²×C₄	#63218	1	2	yes	—
98	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
99	C₂×C₈	—	34	4	no	—
100	C₂×C₈	C₈×D₁₇	1	4	yes	—
101	C₂×C₈	#63223	1	4	yes	—
102	C₂×C₈	C₄×Dic₁₇	1	1	yes	characteristic
103	C₂×C₈	C₄×Dic₁₇	1	1	yes	characteristic
104	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
105	C₂×C₈	C₂²×Dic₁₇	1	1	yes	characteristic
106	C₄²	#63218	1	2	yes	—
107	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
108	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
109	C₁₆	—	2	4	no	—
110	C₁₆	—	17	8	no	—
111	C₂³	#10587486	1	1	yes	characteristic
112	C₂×C₄	—	4	2	no	—
113	C₂×C₄	#10587474	1	2	yes	—
114	C₂×C₄	C₈×Dic₁₇	1	2	yes	—
115	C₂×C₄	#10587486	1	2	yes	—
116	C₂×C₄	#10587486	1	1	yes	characteristic
117	C₂×C₄	C₂×#63218	1	2	yes	—
118	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
119	C₈	—	68	4	no	—
120	C₈	#10587474	1	2	yes	—
121	C₈	C₈×Dic₁₇	1	2	yes	—
122	C₈	C₂×C₈×D₁₇	1	2	yes	—
123	C₈	C₂×#63223	1	2	yes	—
124	C₂²	—	2	2	no	—
125	C₂²	#11762531	1	2	yes	—
126	C₂²	C₂×#10587486	1	1	yes	characteristic
127	C₄	—	2	2	no	—
128	C₄	—	2	2	no	—
129	C₄	#11762531	1	2	yes	—
130	C₄	C₂×C₈×Dic₁₇	1	1	yes	characteristic
131	C₄	C₂×#10587474	1	1	yes	characteristic
132	C₂	—	2	2	no	—
133	C₂	C₂×#11762531	1	1	yes	characteristic
134	C₂	#14530388	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₄×Dic₁₇
commutator	C₄×C₁₇	C₂×C₄×C₈
Frattini	C₄×C₈	C₂²×D₁₇
Fitting	C₂×C₁₇×#346	C₂
socle	C₂²×C₁₇	C₂×#97
prime radical	C₂³×C₁₇	#97
cosocle	C₄×C₈×C₁₇	C₂³
hypercenter	C₂×#346	D₁₇
hypocenter	C₁₇	#11406
LCS	G ▷ C₄×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×#346

Complements

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

N	H ≅ G/N	type
3. #14526706	C₂	semidirect
25. #10587483	C₈	semidirect
96. C₁₇	#11406	semidirect

Maximal subgroups

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

subgroup	index
C₄×#10587483	2
#14527067	2
#14526706	2
C₂×C₁₇×#346	2
#11406	17