Subgroups — C₄×#11763741 #17962546

Order 4352.

250 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×#11763741	C₂	1	2	yes	maximal
2	#14543891	C₂	1	2	yes	maximal, complemented
3	C₄×#10587467	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×#63214	C₂	1	1	yes	maximal, characteristic
5	#11763741	C₄	1	8	yes	direct product factor
6	C₂×#10587467	C₂²	1	4	yes	—
7	C₂²×#63214	C₄	1	1	yes	characteristic
8	C₂²×#63214	C₂²	1	1	yes	characteristic
9	C₄×#63214	C₄	1	1	yes	characteristic
10	C₄×#63214	C₄	1	1	yes	characteristic
11	C₄×#63214	C₂²	1	1	yes	characteristic
12	C₄×#63214	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₈×C₁₇	C₄	1	1	yes	characteristic
14	C₂²×C₈×C₁₇	C₈	1	1	yes	characteristic
15	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄²×C₁₇	C₈	1	1	yes	characteristic
17	C₄×C₈×C₁₇	C₈	1	1	yes	characteristic
18	C₄×C₈×C₁₇	C₈	1	1	yes	characteristic
19	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
20	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
21	C₂×#63214	C₈	1	4	yes	—
22	C₂×#63214	C₂×C₄	1	4	yes	—
23	C₂×#63214	C₂×C₄	1	1	yes	characteristic
24	C₂×#63214	C₂×C₄	1	1	yes	characteristic
25	C₂×#63214	C₂×C₄	1	1	yes	characteristic
26	C₂×#63214	C₂³	1	1	yes	characteristic
27	#10587467	C₂×C₄	1	8	yes	complemented
28	C₂²×C₄×C₁₇	C₁₆	1	2	yes	—
29	C₂²×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
30	C₂×C₈×C₁₇	C₁₆	1	4	yes	—
31	C₂×C₈×C₁₇	C₄²	1	2	yes	—
32	C₂×C₈×C₁₇	C₂×C₈	1	2	yes	—
33	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
34	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
35	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
36	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
37	C₄²×C₁₇	C₁₆	1	2	yes	—
38	C₄²×C₁₇	C₂×C₈	1	1	yes	characteristic
39	C₄²×C₁₇	C₂×C₈	1	1	yes	characteristic
40	#63214	C₄²	1	2	yes	—
41	#63214	C₂×C₈	1	2	yes	—
42	#63214	C₂×C₈	1	2	yes	—
43	#63214	C₂²×C₄	1	2	yes	—
44	C₄×M₆₄	—	17	1	no	maximal, Sylow
45	C₂³×C₁₇	C₂×C₁₆	1	1	yes	characteristic
46	C₂×C₄×C₁₇	—	2	4	no	—
47	C₂×C₄×C₁₇	C₄×C₈	1	2	yes	—
48	C₂×C₄×C₁₇	C₂×C₁₆	1	2	yes	—
49	C₂×C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
50	C₂×C₄×C₁₇	C₂×C₁₆	1	2	yes	—
51	C₂×C₄×C₁₇	C₂×C₁₆	1	2	yes	—
52	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
53	C₈×C₁₇	C₄×C₈	1	2	yes	—
54	C₈×C₁₇	C₂×C₁₆	1	2	yes	—
55	C₈×C₁₇	C₂×C₁₆	1	2	yes	—
56	C₈×C₁₇	C₂×C₄²	1	1	yes	characteristic
57	C₈×C₁₇	C₂²×C₈	1	1	yes	characteristic
58	C₂×M₆₄	—	17	2	no	—
59	C₂×C₄×C₁₆	—	17	1	no	—
60	#1397	—	17	2	no	—
61	C₄×C₃₂	—	17	2	no	—
62	C₂²×C₁₇	—	2	2	no	—
63	C₂²×C₁₇	C₄×C₁₆	1	2	yes	—
64	C₂²×C₁₇	C₂²×C₁₆	1	1	yes	characteristic
65	C₄×C₁₇	—	2	2	no	—
66	C₄×C₁₇	C₄×C₁₆	1	2	yes	—
67	C₄×C₁₇	M₆₄	1	4	yes	complemented
68	C₄×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
69	C₄×C₁₇	C₂²×C₁₆	1	1	yes	characteristic
70	C₂²×C₁₆	—	17	1	no	—
71	C₂²×C₁₆	—	17	1	no	—
72	C₂×C₄×C₈	#595	1	1	yes	characteristic
73	M₆₄	—	17	8	no	—
74	C₂×C₃₂	—	17	4	no	—
75	C₄×C₁₆	—	17	1	no	—
76	C₄×C₁₆	—	17	1	no	—
77	C₄×C₁₆	—	17	1	no	—
78	C₄×C₁₆	—	17	1	no	—
79	C₂×C₁₇	—	2	2	no	—
80	C₂×C₁₇	C₂×C₄×C₁₆	1	1	yes	characteristic
81	C₂×C₁₇	C₂×M₆₄	1	2	yes	—
82	C₂²×C₈	#3624	1	1	yes	characteristic
83	C₂²×C₈	C₂×#595	1	1	yes	characteristic
84	C₂×C₄²	#3624	1	1	yes	characteristic
85	C₂×C₁₆	—	17	4	no	—
86	C₂×C₁₆	—	17	4	no	—
87	C₂×C₁₆	—	17	1	no	—
88	C₂×C₁₆	—	17	1	no	—
89	C₂×C₁₆	—	17	1	no	—
90	C₂×C₁₆	—	17	1	no	—
91	C₄×C₈	#3624	1	1	yes	characteristic
92	C₄×C₈	#3624	1	1	yes	characteristic
93	C₄×C₈	C₂×#595	1	1	yes	characteristic
94	C₄×C₈	C₂×#595	1	1	yes	characteristic
95	C₃₂	—	17	8	no	—
96	C₁₇	C₄×M₆₄	1	1	yes	characteristic, complemented, Sylow
97	C₂²×C₄	#63216	1	2	yes	—
98	C₂²×C₄	C₂×#3624	1	1	yes	characteristic
99	C₂×C₈	#63216	1	4	yes	—
100	C₂×C₈	#63242	1	2	yes	—
101	C₂×C₈	C₄×#595	1	2	yes	—
102	C₂×C₈	C₂×#3624	1	1	yes	characteristic
103	C₂×C₈	C₂×#3624	1	1	yes	characteristic
104	C₂×C₈	C₂×#3624	1	1	yes	characteristic
105	C₂×C₈	C₂²×#595	1	1	yes	characteristic
106	C₄²	#63216	1	2	yes	—
107	C₄²	C₂×#3624	1	1	yes	characteristic
108	C₄²	C₂×#3624	1	1	yes	characteristic
109	C₁₆	—	17	2	no	—
110	C₁₆	—	17	2	no	—
111	C₁₆	—	17	2	no	—
112	C₁₆	—	17	2	no	—
113	C₂³	C₂×#63216	1	1	yes	characteristic
114	C₂×C₄	—	2	4	no	—
115	C₂×C₄	C₂×#63216	1	2	yes	—
116	C₂×C₄	C₂×#63216	1	2	yes	—
117	C₂×C₄	C₂×#63216	1	2	yes	—
118	C₂×C₄	C₂×#63216	1	1	yes	characteristic
119	C₂×C₄	C₄×#3624	1	2	yes	—
120	C₂×C₄	C₂²×#3624	1	1	yes	characteristic
121	C₈	C₂×#63216	1	2	yes	—
122	C₈	C₂×#63216	1	2	yes	—
123	C₈	C₄×#3624	1	2	yes	—
124	C₈	C₂×#63242	1	1	yes	characteristic
125	C₈	C₂×C₄×#595	1	1	yes	characteristic
126	C₂²	—	2	2	no	—
127	C₂²	C₄×#63216	1	2	yes	—
128	C₂²	C₂²×#63216	1	1	yes	characteristic
129	C₄	—	2	2	no	—
130	C₄	C₄×#63216	1	2	yes	—
131	C₄	#11763741	1	4	yes	direct product factor
132	C₄	C₂×C₄×#3624	1	1	yes	characteristic
133	C₄	C₂²×#63216	1	1	yes	characteristic
134	C₂	—	2	2	no	—
135	C₂	C₂×C₄×#63216	1	1	yes	characteristic
136	C₂	C₂×#11763741	1	2	yes	—

	subgroup	G/H
center	C₄×C₈	C₂×#595
commutator	C₂×C₁₇	C₂×C₄×C₁₆
Frattini	C₂×C₈	C₂²×#595
Fitting	C₂×C₄×C₈×C₁₇	C₄
socle	C₂²×C₁₇	C₂²×C₁₆
prime radical	C₂³×C₁₇	C₂×C₁₆
cosocle	C₂×#63214	C₂³
hypercenter	C₂×C₄×C₈	#595
hypocenter	C₁₇	C₄×M₆₄
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #14543891	C₂	semidirect
3. C₄×#10587467	C₂	semidirect
5. #11763741	C₄	direct (N × H)
27. #10587467	C₂×C₄	semidirect
67. C₄×C₁₇	M₆₄	semidirect
96. C₁₇	C₄×M₆₄	semidirect
131. C₄	#11763741	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×#11763741	2
#14543891	2
C₄×#10587467	2
C₂×C₄×#63214	2
C₄×M₆₄	17

Subgroups — C4×#11763741 #17962546

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11763741 #17962546