Subgroups — C₄×#10587593 #14537208

Order 2176.

572 conjugacy classes of subgroups.

The subgroup lattice has 174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10587593	C₂	1	2	yes	maximal
2	C₄×#63252	C₂	1	1	yes	maximal, characteristic
3	#11762767	C₂	1	2	yes	maximal, complemented
4	#11762766	C₂	1	4	yes	maximal, complemented
5	C₄×#63218	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×#3622	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₈×D₁₇	C₂	1	2	yes	maximal, complemented
8	C₄×M₁₆×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#63252	C₂²	1	1	yes	characteristic
10	C₂×M₁₆×C₁₇	C₂²	1	2	yes	—
11	C₂×C₄²×C₁₇	C₂²	1	1	yes	characteristic
12	C₄×C₂²⋊D₁₇	C₄	1	4	yes	—
13	#10587612	C₂²	1	1	yes	characteristic
14	C₂²×#3622	C₂²	1	2	yes	—
15	#10587593	C₄	1	16	yes	direct product factor
16	C₂×#63218	C₂²	1	4	yes	—
17	C₂×C₈×D₁₇	C₂²	1	4	yes	—
18	C₄×D₆₈	C₄	1	2	yes	—
19	#10587558	C₂²	1	2	yes	—
20	C₄²×D₁₇	C₂²	1	2	yes	—
21	C₄×Dic₃₄	C₄	1	2	yes	—
22	C₁₇×#97	C₂²	1	2	yes	—
23	C₄×C₈×C₁₇	C₂²	1	2	yes	—
24	#10587486	C₂²	1	4	yes	—
25	C₈×Dic₁₇	C₂²	1	4	yes	—
26	C₄×#3622	C₂²	1	1	yes	characteristic
27	C₄×#3622	C₂²	1	1	yes	characteristic
28	C₄×#3622	C₂²	1	2	yes	—
29	C₂²×C₄×C₁₇	C₂×C₄	1	2	yes	—
30	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
31	C₂×C₂²⋊D₁₇	C₂×C₄	1	2	yes	—
32	#63252	C₂×C₄	1	8	yes	—
33	C₂×D₆₈	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄×D₁₇	C₂×C₄	1	4	yes	—
35	C₂×C₄×D₁₇	C₂³	1	2	yes	—
36	C₂×Dic₃₄	C₂×C₄	1	1	yes	characteristic
37	M₁₆×C₁₇	C₂×C₄	1	8	yes	complemented
38	C₂×C₈×C₁₇	C₂³	1	4	yes	—
39	C₄²×C₁₇	C₂×C₄	1	2	yes	—
40	C₄²×C₁₇	C₂³	1	1	yes	characteristic
41	C₄²×C₁₇	C₂³	1	1	yes	characteristic
42	C₂²⋊Dic₁₇	C₂×C₄	1	2	yes	—
43	#63227	C₂×C₄	1	4	yes	—
44	C₄⋊Dic₁₇	C₂×C₄	1	2	yes	—
45	#63225	C₂×C₄	1	4	yes	—
46	C₄×Dic₁₇	C₂×C₄	1	4	yes	—
47	C₄×Dic₁₇	C₂³	1	2	yes	—
48	C₂×#3622	C₂×C₄	1	8	yes	complemented
49	C₂×#3622	C₂³	1	2	yes	—
50	C₂×#3622	C₂³	1	2	yes	—
51	#63218	C₂×C₄	1	16	yes	complemented
52	C₈×D₁₇	C₂×C₄	1	16	yes	complemented
53	C₂³×C₁₇	C₂²×C₄	1	1	yes	characteristic
54	C₂²×D₁₇	C₂²×C₄	1	2	yes	—
55	C₂×C₄×C₁₇	—	2	4	no	—
56	C₂×C₄×C₁₇	C₂²×C₄	1	2	yes	—
57	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
58	C₂×C₄×C₁₇	C₂²×C₄	1	4	yes	—
59	C₂×C₄×C₁₇	C₂²×C₄	1	2	yes	—
60	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
61	C₂²⋊D₁₇	C₄²	1	8	yes	—
62	C₂×Dic₁₇	C₂²×C₄	1	4	yes	—
63	C₂×Dic₁₇	C₂²×C₄	1	2	yes	—
64	D₆₈	C₄²	1	4	yes	—
65	C₄×D₁₇	—	2	8	no	—
66	C₄×D₁₇	C₂²×C₄	1	8	yes	—
67	Dic₃₄	C₄²	1	4	yes	—
68	C₈×C₁₇	C₂²×C₄	1	8	yes	—
69	#3622	C₂²×C₄	1	4	yes	—
70	#3622	C₂²×C₄	1	4	yes	—
71	C₄×#131	—	17	1	no	maximal, Sylow
72	C₂²×C₁₇	—	2	2	no	—
73	C₂²×C₁₇	C₂×C₄²	1	2	yes	—
74	C₂²×C₁₇	C₂³×C₄	1	1	yes	characteristic
75	C₂×D₁₇	—	2	4	no	—
76	C₂×D₁₇	C₂×C₄²	1	4	yes	—
77	C₄×C₁₇	—	2	2	no	—
78	C₄×C₁₇	C₂×C₄²	1	2	yes	—
79	C₄×C₁₇	#131	1	4	yes	complemented
80	C₄×C₁₇	C₂³×C₄	1	2	yes	—
81	Dic₁₇	—	2	4	no	—
82	Dic₁₇	C₂×C₄²	1	4	yes	—
83	C₂×#131	—	17	2	no	—
84	C₄×#41	—	17	1	no	—
85	#405	—	17	2	no	—
86	#405	—	17	4	no	—
87	C₄×M₁₆	—	17	2	no	—
88	C₄×M₁₆	D₁₇	1	1	yes	characteristic, complemented
89	C₂×C₄×C₈	—	17	1	no	—
90	C₂×C₄×C₈	—	17	2	no	—
91	C₂×C₁₇	—	2	2	no	—
92	C₂×C₁₇	C₂²×C₄²	1	1	yes	characteristic
93	C₂×C₁₇	C₂×#131	1	2	yes	—
94	D₁₇	—	2	4	no	—
95	C₂×#41	—	17	1	no	—
96	#131	—	17	16	no	—
97	C₂×M₁₆	—	17	4	no	—
98	C₂×M₁₆	C₂×D₁₇	1	2	yes	—
99	C₂²×C₈	—	17	2	no	—
100	C₂²×C₈	—	17	4	no	—
101	C₄×Q₈	—	17	2	no	—
102	C₄×D₄	—	17	4	no	—
103	C₄×D₄	—	17	2	no	—
104	#117	—	17	1	no	—
105	#117	—	17	2	no	—
106	C₂×C₄²	—	17	2	no	—
107	C₂×C₄²	C₂×D₁₇	1	1	yes	characteristic
108	#97	—	17	4	no	—
109	#97	C₂×D₁₇	1	2	yes	—
110	C₄×C₈	—	17	4	no	—
111	C₄×C₈	—	17	2	no	—
112	C₄×C₈	—	17	1	no	—
113	C₄×C₈	—	17	1	no	—
114	C₄×C₈	C₂×D₁₇	1	2	yes	—
115	C₁₇	C₄×#131	1	1	yes	characteristic, complemented, Sylow
116	#41	—	17	8	no	—
117	C₂×Q₈	—	17	1	no	—
118	C₂×D₄	—	17	2	no	—
119	C₂×D₄	—	17	1	no	—
120	C₂²×C₄	—	17	2	no	—
121	C₂²×C₄	—	17	4	no	—
122	C₂²×C₄	C₄×D₁₇	1	2	yes	—
123	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
124	M₁₆	—	17	16	no	—
125	M₁₆	C₄×D₁₇	1	8	yes	complemented
126	C₂×C₈	—	17	8	no	—
127	C₂×C₈	—	17	2	no	—
128	C₂×C₈	—	17	2	no	—
129	C₂×C₈	—	17	16	no	—
130	C₂×C₈	C₂²×D₁₇	1	4	yes	—
131	C₄⋊C₄	—	17	4	no	—
132	C₄⋊C₄	—	17	2	no	—
133	C₂²⋊C₄	—	17	2	no	—
134	C₂²⋊C₄	—	17	4	no	—
135	C₄²	—	17	4	no	—
136	C₄²	—	17	2	no	—
137	C₄²	C₄×D₁₇	1	2	yes	—
138	C₄²	C₂²×D₁₇	1	1	yes	characteristic
139	C₄²	C₂²×D₁₇	1	1	yes	characteristic
140	C₂³	—	17	2	no	—
141	C₂³	C₂×C₄×D₁₇	1	1	yes	characteristic
142	Q₈	—	17	4	no	—
143	D₄	—	17	8	no	—
144	D₄	—	17	4	no	—
145	C₂×C₄	—	2	4	no	—
146	C₂×C₄	—	17	2	no	—
147	C₂×C₄	—	17	8	no	—
148	C₂×C₄	—	17	4	no	—
149	C₂×C₄	—	34	8	no	—
150	C₂×C₄	C₂×C₄×D₁₇	1	2	yes	—
151	C₂×C₄	C₂×C₄×D₁₇	1	4	yes	—
152	C₂×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
153	C₂×C₄	C₂×C₄×D₁₇	1	2	yes	—
154	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
155	C₈	—	17	4	no	—
156	C₈	—	17	4	no	—
157	C₈	C₂×C₄×D₁₇	1	8	yes	—
158	C₂²	—	2	2	no	—
159	C₂²	—	17	4	no	—
160	C₂²	—	34	4	no	—
161	C₂²	C₄²×D₁₇	1	2	yes	—
162	C₂²	C₂²×C₄×D₁₇	1	1	yes	characteristic
163	C₄	—	2	2	no	—
164	C₄	—	17	4	no	—
165	C₄	—	34	4	no	—
166	C₄	C₄²×D₁₇	1	2	yes	—
167	C₄	#10587593	1	4	yes	direct product factor
168	C₄	C₂²×C₄×D₁₇	1	2	yes	—
169	C₂	—	2	2	no	—
170	C₂	—	34	4	no	—
171	C₂	C₂×C₄²×D₁₇	1	1	yes	characteristic
172	C₂	C₂×#10587593	1	2	yes	—

	subgroup	G/H
center	C₄²	C₂²×D₁₇
commutator	C₂×C₁₇	C₂²×C₄²
Frattini	C₂×C₄	C₂³×D₁₇
Fitting	C₄×M₁₆×C₁₇	C₂
socle	C₂²×C₁₇	C₂³×C₄
prime radical	C₂×#63252	C₂²
cosocle	C₂×C₄×C₁₇	C₂⁴
hypercenter	C₄×M₁₆	D₁₇
hypocenter	C₁₇	C₄×#131
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄² ◁ C₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. #11762767	C₂	semidirect
4. #11762766	C₂	semidirect
5. C₄×#63218	C₂	semidirect
6. C₂×C₄×#3622	C₂	semidirect
7. C₄×C₈×D₁₇	C₂	semidirect
8. C₄×M₁₆×C₁₇	C₂	semidirect
15. #10587593	C₄	direct (N × H)
37. M₁₆×C₁₇	C₂×C₄	semidirect
48. C₂×#3622	C₂×C₄	semidirect
51. #63218	C₂×C₄	semidirect
52. C₈×D₁₇	C₂×C₄	semidirect
79. C₄×C₁₇	#131	semidirect
88. C₄×M₁₆	D₁₇	semidirect
115. C₁₇	C₄×#131	semidirect
125. M₁₆	C₄×D₁₇	semidirect
167. C₄	#10587593	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×#10587593	2
C₄×#63252	2
#11762767	2
#11762766	2
C₄×#63218	2
C₂×C₄×#3622	2
C₄×C₈×D₁₇	2
C₄×M₁₆×C₁₇	2
C₄×#131	17

Subgroups — C4×#10587593 #14537208

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#10587593 #14537208