Subgroups — C₂×C₈×#63216 #17957977

Order 4352.

398 conjugacy classes of subgroups.

The subgroup lattice has 138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#63216	C₂	1	2	yes	maximal
2	C₈×#63216	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×#3622	C₂	1	1	yes	maximal, characteristic
4	C₂²×#63216	C₄	1	4	yes	—
5	C₄×#63216	C₄	1	4	yes	—
6	C₄×#63216	C₂²	1	4	yes	—
7	C₂×C₄×#3622	C₄	1	1	yes	characteristic
8	C₂×C₄×#3622	C₂²	1	1	yes	characteristic
9	C₈×#3622	C₄	1	2	yes	—
10	C₈×#3622	C₂²	1	2	yes	—
11	C₂×C₄×C₈×C₁₇	C₄	1	1	yes	characteristic
12	C₂²×C₈×C₁₇	C₈	1	2	yes	—
13	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
14	C₂²×#3622	C₈	1	2	yes	—
15	C₂²×#3622	C₂×C₄	1	2	yes	—
16	C₂×#63216	C₈	1	16	yes	direct product factor
17	C₂×#63216	C₂×C₄	1	8	yes	—
18	C₄×C₈×C₁₇	C₈	1	2	yes	—
19	C₄×C₈×C₁₇	C₂×C₄	1	2	yes	—
20	C₄×#3622	C₈	1	2	yes	—
21	C₄×#3622	C₂×C₄	1	2	yes	—
22	C₄×#3622	C₂×C₄	1	1	yes	characteristic
23	C₄×#3622	C₂×C₄	1	2	yes	—
24	C₄×#3622	C₂³	1	1	yes	characteristic
25	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
26	C₂²×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
27	C₂²×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
28	C₂×C₈×C₁₇	C₁₆	1	8	yes	complemented
29	C₂×C₈×C₁₇	C₂×C₈	1	4	yes	—
30	C₄²×C₁₇	C₄²	1	1	yes	characteristic
31	C₄²×C₁₇	C₂×C₈	1	1	yes	characteristic
32	C₄²×C₁₇	C₂×C₈	1	1	yes	characteristic
33	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
34	C₂×#3622	C₁₆	1	8	yes	complemented
35	C₂×#3622	C₄²	1	2	yes	—
36	C₂×#3622	C₂×C₈	1	8	yes	—
37	C₂×#3622	C₂×C₈	1	4	yes	—
38	C₂×#3622	C₂²×C₄	1	2	yes	—
39	#63216	C₂×C₈	1	16	yes	direct product factor
40	C₂×C₈×C₁₆	—	17	1	no	maximal, Sylow
41	C₂³×C₁₇	C₄×C₈	1	1	yes	characteristic
42	C₂×C₄×C₁₇	C₄×C₈	1	4	yes	—
43	C₂×C₄×C₁₇	C₄×C₈	1	1	yes	characteristic
44	C₂×C₄×C₁₇	C₄×C₈	1	1	yes	characteristic
45	C₂×C₄×C₁₇	C₄×C₈	1	1	yes	characteristic
46	C₂×C₄×C₁₇	C₂×C₁₆	1	4	yes	—
47	C₂×C₄×C₁₇	C₂×C₁₆	1	4	yes	—
48	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
49	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
50	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
51	C₈×C₁₇	C₂×C₁₆	1	8	yes	complemented
52	#3622	C₄×C₈	1	4	yes	—
53	#3622	C₂×C₁₆	1	8	yes	complemented
54	#3622	C₂²×C₈	1	4	yes	—
55	C₂×C₄×C₁₆	—	17	2	no	—
56	C₂×C₈²	—	17	1	no	—
57	C₈×C₁₆	—	17	4	no	—
58	C₂²×C₁₇	C₈²	1	2	yes	—
59	C₂²×C₁₇	C₄×C₁₆	1	2	yes	—
60	C₂²×C₁₇	C₄×C₁₆	1	2	yes	—
61	C₂²×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
62	C₄×C₁₇	C₈²	1	2	yes	—
63	C₄×C₁₇	C₄×C₁₆	1	2	yes	—
64	C₄×C₁₇	C₄×C₁₆	1	2	yes	—
65	C₄×C₁₇	C₂×C₄×C₈	1	2	yes	—
66	C₄×C₁₇	C₂²×C₁₆	1	2	yes	—
67	C₄×C₁₇	C₂²×C₁₆	1	2	yes	—
68	C₂²×C₁₆	—	17	4	no	—
69	C₂×C₄×C₈	—	17	1	no	—
70	C₂×C₄×C₈	—	17	1	no	—
71	C₂×C₄×C₈	#595	1	1	yes	characteristic
72	C₄×C₁₆	—	17	4	no	—
73	C₄×C₁₆	—	17	4	no	—
74	C₈²	—	17	2	no	—
75	C₈²	—	17	2	no	—
76	C₂×C₁₇	C₈×C₁₆	1	4	yes	complemented
77	C₂×C₁₇	C₂×C₈²	1	1	yes	characteristic
78	C₂×C₁₇	C₂×C₄×C₁₆	1	1	yes	characteristic
79	C₂×C₁₇	C₂×C₄×C₁₆	1	1	yes	characteristic
80	C₂²×C₈	—	17	2	no	—
81	C₂²×C₈	—	17	2	no	—
82	C₂²×C₈	#3624	1	2	yes	—
83	C₂×C₄²	C₂×#595	1	1	yes	characteristic
84	C₂×C₁₆	—	17	8	no	—
85	C₂×C₁₆	—	17	16	no	—
86	C₄×C₈	—	17	2	no	—
87	C₄×C₈	—	17	2	no	—
88	C₄×C₈	—	17	2	no	—
89	C₄×C₈	—	17	1	no	—
90	C₄×C₈	—	17	1	no	—
91	C₄×C₈	#3624	1	2	yes	—
92	C₄×C₈	C₂×#595	1	2	yes	—
93	C₁₇	C₂×C₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
94	C₂²×C₄	#63242	1	1	yes	characteristic
95	C₂²×C₄	C₄×#595	1	1	yes	characteristic
96	C₂²×C₄	C₂×#3624	1	1	yes	characteristic
97	C₂×C₈	—	17	4	no	—
98	C₂×C₈	—	17	2	no	—
99	C₂×C₈	—	17	2	no	—
100	C₂×C₈	—	17	8	no	—
101	C₂×C₈	—	17	8	no	—
102	C₂×C₈	#63216	1	8	yes	direct product factor
103	C₂×C₈	C₂×#3624	1	4	yes	—
104	C₄²	#63242	1	1	yes	characteristic
105	C₄²	C₄×#595	1	1	yes	characteristic
106	C₄²	C₂×#3624	1	1	yes	characteristic
107	C₄²	C₂²×#595	1	1	yes	characteristic
108	C₁₆	—	17	16	no	—
109	C₂³	C₄×#3624	1	1	yes	characteristic
110	C₂×C₄	#10587529	1	4	yes	—
111	C₂×C₄	C₈×#595	1	4	yes	—
112	C₂×C₄	C₂×#63216	1	4	yes	—
113	C₂×C₄	C₄×#3624	1	1	yes	characteristic
114	C₂×C₄	C₄×#3624	1	1	yes	characteristic
115	C₂×C₄	C₄×#3624	1	1	yes	characteristic
116	C₂×C₄	C₂×#63242	1	1	yes	characteristic
117	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
118	C₂×C₄	C₂²×#3624	1	1	yes	characteristic
119	C₈	—	17	4	no	—
120	C₈	—	17	4	no	—
121	C₈	—	17	8	no	—
122	C₈	C₂×#63216	1	8	yes	direct product factor
123	C₂²	C₈×#3624	1	2	yes	—
124	C₂²	C₄×#63216	1	2	yes	—
125	C₂²	#11763695	1	2	yes	—
126	C₂²	C₂×C₄×#3624	1	1	yes	characteristic
127	C₄	C₈×#3624	1	2	yes	—
128	C₄	C₄×#63216	1	2	yes	—
129	C₄	#11763695	1	2	yes	—
130	C₄	C₂×C₈×#595	1	2	yes	—
131	C₄	C₂²×#63216	1	2	yes	—
132	C₄	C₂×#10587529	1	2	yes	—
133	C₂	C₈×#63216	1	4	yes	direct product factor
134	C₂	C₂×C₈×#3624	1	1	yes	characteristic
135	C₂	C₂×C₄×#63216	1	1	yes	characteristic
136	C₂	C₂×#11763695	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄×C₈	#595
commutator, hypocenter	C₁₇	C₂×C₈×C₁₆
Frattini	C₄²	C₂²×#595
Fitting	C₂×C₄×C₈×C₁₇	C₄
socle, prime radical	C₂³×C₁₇	C₄×C₈
cosocle	C₄×#3622	C₂³
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. C₈×#63216	C₂	direct (N × H)
16. C₂×#63216	C₈	direct (N × H)
28. C₂×C₈×C₁₇	C₁₆	semidirect
34. C₂×#3622	C₁₆	semidirect
39. #63216	C₂×C₈	direct (N × H)
51. C₈×C₁₇	C₂×C₁₆	semidirect
53. #3622	C₂×C₁₆	semidirect
76. C₂×C₁₇	C₈×C₁₆	semidirect
93. C₁₇	C₂×C₈×C₁₆	semidirect
102. C₂×C₈	#63216	direct (N × H)
122. C₈	C₂×#63216	direct (N × H)
133. C₂	C₈×#63216	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×C₄×#63216	2
C₈×#63216	2
C₂×C₈×#3622	2
C₂×C₈×C₁₆	17

Subgroups — C2×C8×#63216 #17957977

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×#63216 #17957977