Subgroups — C₂×#14543814 #17960080

Order 4352.

286 conjugacy classes of subgroups.

The subgroup lattice has 172 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	#14543814	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×#3622	C₂	1	1	yes	maximal, characteristic
4	C₂²×#63216	—	2	2	no	—
5	C₄⋊#63216	—	2	2	no	—
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	—	2	1	no	—
13	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
14	C₂²×#3622	C₈	1	1	yes	characteristic
15	C₂²×#3622	C₈	1	1	yes	characteristic
16	C₂²×#3622	D₄	1	1	yes	characteristic
17	C₂²×#3622	Q₈	1	1	yes	characteristic
18	C₂×#63216	—	2	4	no	—
19	C₂×#63216	—	4	4	no	—
20	C₄×C₈×C₁₇	—	2	1	no	—
21	C₄×C₈×C₁₇	C₂×C₄	1	2	yes	—
22	C₄×#3622	C₈	1	2	yes	—
23	C₄×#3622	C₂×C₄	1	1	yes	characteristic
24	C₄×#3622	C₂×C₄	1	2	yes	—
25	C₄×#3622	D₄	1	1	yes	characteristic
26	C₄×#3622	Q₈	1	1	yes	characteristic
27	C₄×#3622	C₂³	1	1	yes	characteristic
28	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
29	C₂²×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
30	C₂²×C₄×C₁₇	M₁₆	1	1	yes	characteristic
31	C₂×C₈×C₁₇	—	2	4	no	—
32	C₂×C₈×C₁₇	—	2	2	no	—
33	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
34	C₄²×C₁₇	C₂×C₈	1	1	yes	characteristic
35	C₄²×C₁₇	M₁₆	1	1	yes	characteristic
36	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
37	C₂×#3622	—	2	2	no	—
38	C₂×#3622	—	2	2	no	—
39	C₂×#3622	C₁₆	1	4	yes	complemented
40	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
41	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
42	C₂×#3622	C₂×C₈	1	2	yes	—
43	C₂×#3622	C₂×C₈	1	2	yes	—
44	C₂×#3622	D₈	1	2	yes	—
45	C₂×#3622	Q₁₆	1	2	yes	—
46	C₂×#3622	C₂×D₄	1	1	yes	characteristic
47	C₂×#3622	C₂×Q₈	1	1	yes	characteristic
48	#63216	—	4	4	no	—
49	C₂×#1370	—	17	1	no	maximal, Sylow
50	C₂³×C₁₇	C₄⋊C₈	1	1	yes	characteristic
51	C₂×C₄×C₁₇	—	2	2	no	—
52	C₂×C₄×C₁₇	C₄⋊C₈	1	1	yes	characteristic
53	C₂×C₄×C₁₇	C₄⋊C₈	1	1	yes	characteristic
54	C₂×C₄×C₁₇	C₄⋊C₈	1	1	yes	characteristic
55	C₂×C₄×C₁₇	#107	1	2	yes	—
56	C₂×C₄×C₁₇	#108	1	2	yes	—
57	C₂×C₄×C₁₇	C₂×C₁₆	1	2	yes	—
58	C₂×C₄×C₁₇	M₃₂	1	2	yes	—
59	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
60	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
61	C₂×C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
62	C₈×C₁₇	—	2	4	no	—
63	#3622	—	2	1	no	—
64	#3622	—	2	1	no	—
65	#3622	—	2	2	no	—
66	#3622	#107	1	2	yes	—
67	#3622	C₂×C₁₆	1	4	yes	complemented
68	#3622	C₂×D₈	1	1	yes	characteristic
69	#3622	C₂×Q₁₆	1	1	yes	characteristic
70	C₂×C₄⋊C₁₆	—	17	2	no	—
71	C₂×C₈²	—	17	1	no	—
72	#1370	—	17	4	no	—
73	C₂²×C₁₇	#335	1	2	yes	—
74	C₂²×C₁₇	C₄⋊C₁₆	1	2	yes	—
75	C₂²×C₁₇	#364	1	2	yes	—
76	C₂²×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
77	C₄×C₁₇	—	2	1	no	—
78	C₄×C₁₇	—	2	1	no	—
79	C₄×C₁₇	#335	1	2	yes	—
80	C₄×C₁₇	C₄⋊C₁₆	1	2	yes	—
81	C₄×C₁₇	C₂×#107	1	1	yes	characteristic
82	C₄×C₁₇	C₂×#108	1	1	yes	characteristic
83	C₄×C₁₇	C₂²×C₁₆	1	1	yes	characteristic
84	C₄×C₁₇	C₂×M₃₂	1	1	yes	characteristic
85	C₂²×C₁₆	—	34	2	no	—
86	C₂×C₄×C₈	—	17	1	no	—
87	C₂×C₄×C₈	—	17	1	no	—
88	C₂×C₄×C₈	#595	1	1	yes	characteristic
89	C₄⋊C₁₆	—	17	4	no	—
90	C₄⋊C₁₆	—	34	2	no	—
91	C₈²	—	17	2	no	—
92	C₈²	—	17	2	no	—
93	C₂×C₁₇	#1370	1	4	yes	complemented
94	C₂×C₁₇	C₂×#335	1	1	yes	characteristic
95	C₂×C₁₇	C₂×C₄⋊C₁₆	1	1	yes	characteristic
96	C₂×C₁₇	C₂×#364	1	1	yes	characteristic
97	C₂²×C₈	—	2	1	no	—
98	C₂²×C₈	—	17	1	no	—
99	C₂²×C₈	—	17	1	no	—
100	C₂²×C₈	—	17	1	no	—
101	C₂²×C₈	—	17	1	no	—
102	C₂×C₄²	C₂×#595	1	1	yes	characteristic
103	C₂×C₁₆	—	34	4	no	—
104	C₂×C₁₆	—	68	4	no	—
105	C₄×C₈	—	2	1	no	—
106	C₄×C₈	—	17	2	no	—
107	C₄×C₈	—	17	1	no	—
108	C₄×C₈	—	17	1	no	—
109	C₄×C₈	—	17	2	no	—
110	C₄×C₈	—	17	1	no	—
111	C₄×C₈	—	17	1	no	—
112	C₄×C₈	C₂×#595	1	2	yes	—
113	C₁₇	C₂×#1370	1	1	yes	characteristic, complemented, Sylow
114	C₂²×C₄	#63242	1	1	yes	characteristic
115	C₂²×C₄	C₄⋊#595	1	1	yes	characteristic
116	C₂²×C₄	#63247	1	1	yes	characteristic
117	C₂×C₈	—	2	4	no	—
118	C₂×C₈	—	2	2	no	—
119	C₂×C₈	—	17	2	no	—
120	C₂×C₈	—	17	1	no	—
121	C₂×C₈	—	17	1	no	—
122	C₂×C₈	—	17	4	no	—
123	C₂×C₈	—	17	2	no	—
124	C₂×C₈	—	17	2	no	—
125	C₂×C₈	—	17	2	no	—
126	C₂×C₈	—	17	1	no	—
127	C₂×C₈	—	17	1	no	—
128	C₂×C₈	—	34	2	no	—
129	C₂×C₈	—	34	2	no	—
130	C₄²	#63242	1	1	yes	characteristic
131	C₄²	C₄⋊#595	1	1	yes	characteristic
132	C₄²	#63247	1	1	yes	characteristic
133	C₄²	C₂²×#595	1	1	yes	characteristic
134	C₁₆	—	68	4	no	—
135	C₂³	#10587544	1	1	yes	characteristic
136	C₂×C₄	—	2	2	no	—
137	C₂×C₄	#10587529	1	2	yes	—
138	C₂×C₄	#10587530	1	2	yes	—
139	C₂×C₄	#10587534	1	2	yes	—
140	C₂×C₄	#10587535	1	2	yes	—
141	C₂×C₄	#10587544	1	1	yes	characteristic
142	C₂×C₄	#10587544	1	1	yes	characteristic
143	C₂×C₄	#10587544	1	1	yes	characteristic
144	C₂×C₄	C₂×#63242	1	1	yes	characteristic
145	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
146	C₂×C₄	C₂×#63247	1	1	yes	characteristic
147	C₈	—	2	4	no	—
148	C₈	—	17	1	no	—
149	C₈	—	17	2	no	—
150	C₈	—	17	1	no	—
151	C₈	—	17	4	no	—
152	C₈	—	34	1	no	—
153	C₈	—	34	1	no	—
154	C₈	—	34	2	no	—
155	C₂²	#11763673	1	2	yes	—
156	C₂²	#11763730	1	2	yes	—
157	C₂²	#11763732	1	2	yes	—
158	C₂²	C₂×#10587544	1	1	yes	characteristic
159	C₄	—	2	1	no	—
160	C₄	—	2	1	no	—
161	C₄	#11763673	1	2	yes	—
162	C₄	#11763730	1	2	yes	—
163	C₄	C₂×#10587534	1	1	yes	characteristic
164	C₄	C₂×#10587535	1	1	yes	characteristic
165	C₄	C₂×#10587529	1	1	yes	characteristic
166	C₄	C₂×#10587530	1	1	yes	characteristic
167	C₂	#14543814	1	4	yes	direct product factor
168	C₂	C₂×#11763673	1	1	yes	characteristic
169	C₂	C₂×#11763730	1	1	yes	characteristic
170	C₂	C₂×#11763732	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₄⋊#595
commutator	C₄×C₁₇	C₂²×C₁₆
Frattini	C₄²	C₂²×#595
Fitting	C₂×C₄×C₈×C₁₇	C₄
socle, prime radical	C₂³×C₁₇	C₄⋊C₈
cosocle	C₄×#3622	C₂³
hypercenter	C₂×C₄×C₈	#595
hypocenter	C₁₇	C₂×#1370
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #14543814	C₂	direct (N × H)
39. C₂×#3622	C₁₆	semidirect
67. #3622	C₂×C₁₆	semidirect
93. C₂×C₁₇	#1370	semidirect
113. C₁₇	C₂×#1370	semidirect
167. C₂	#14543814	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
#14543814	2
C₂×C₈×#3622	2
C₂×#1370	17

Subgroups — C2×#14543814 #17960080

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14543814 #17960080