Subgroups — C₂×#14531060 #17189803

Order 4352.

494 conjugacy classes of subgroups.

The subgroup lattice has 188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11763211	C₂	1	1	yes	maximal, characteristic
2	#14531060	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11762636	C₂	1	2	yes	maximal
4	C₂×#11762634	C₂	1	2	yes	maximal
5	C₂×C₄×#63214	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₇×#499	C₂	1	1	yes	maximal, characteristic
7	C₂×#10587556	—	2	1	no	—
8	C₂²×#63214	C₂²	1	1	yes	characteristic
9	C₂²×#63214	C₂²	1	1	yes	characteristic
10	#11763211	—	2	2	no	—
11	#11763211	C₂²	1	4	yes	—
12	C₂×#10587489	C₂²	1	2	yes	—
13	C₂×#10587488	—	2	1	no	—
14	#11762636	C₂²	1	8	yes	—
15	#11762634	C₂²	1	8	yes	—
16	C₄×#63214	C₂²	1	4	yes	—
17	C₂×C₁₇×#125	—	2	1	no	—
18	C₁₇×#499	—	2	2	no	—
19	C₁₇×#499	C₂²	1	4	yes	—
20	C₂×C₁₇×#107	C₂²	1	2	yes	—
21	C₂×C₁₇×#106	—	2	1	no	—
22	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
23	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
24	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
25	C₁₇×#125	—	2	4	no	—
26	C₁₇×#125	—	4	2	no	—
27	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
28	C₂×C₄⋊C₄×C₁₇	—	4	2	no	—
29	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
30	C₂×C₄⋊Dic₁₇	—	2	2	no	—
31	C₂×#63225	—	4	2	no	—
32	#10587556	—	2	4	no	—
33	#10587556	—	4	2	no	—
34	C₁₇×#107	—	2	2	no	—
35	C₁₇×#107	C₂³	1	4	yes	—
36	C₁₇×#106	—	2	4	no	—
37	C₄×C₈×C₁₇	D₄	1	2	yes	—
38	C₄×C₈×C₁₇	C₂³	1	2	yes	—
39	#10587489	—	2	2	no	—
40	#10587489	C₂³	1	4	yes	—
41	#10587488	—	2	4	no	—
42	C₂×#63214	Q₈	1	4	yes	—
43	C₂×#63214	Q₈	1	4	yes	—
44	C₂×#63214	C₂³	1	2	yes	—
45	C₂×#63214	C₂³	1	2	yes	—
46	C₂²×C₄×C₁₇	—	4	2	no	—
47	C₂²×C₄×C₁₇	D₈	1	2	yes	—
48	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
49	C₂²×Dic₁₇	—	4	2	no	—
50	C₂×C₈×C₁₇	Q₁₆	1	4	yes	—
51	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
52	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
53	C₂×C₈×C₁₇	C₂×Q₈	1	2	yes	—
54	C₂×C₈×C₁₇	C₂×Q₈	1	2	yes	—
55	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
56	C₄⋊C₄×C₁₇	—	2	4	no	—
57	C₄⋊C₄×C₁₇	—	4	8	no	—
58	C₄⋊C₄×C₁₇	—	4	2	no	—
59	C₄²×C₁₇	D₈	1	2	yes	—
60	C₄²×C₁₇	C₂×D₄	1	2	yes	—
61	C₄⋊Dic₁₇	—	2	4	no	—
62	C₄⋊Dic₁₇	—	4	2	no	—
63	#63225	—	4	8	no	—
64	#63214	C₂×Q₈	1	4	yes	—
65	#63214	C₂×Q₈	1	4	yes	—
66	C₂×#2253	—	17	1	no	maximal, Sylow
67	C₂³×C₁₇	C₂×D₈	1	1	yes	characteristic
68	C₂×C₄×C₁₇	—	2	4	no	—
69	C₂×C₄×C₁₇	—	4	4	no	—
70	C₂×C₄×C₁₇	—	8	4	no	—
71	C₂×C₄×C₁₇	C₄⋊Q₈	1	2	yes	—
72	C₂×C₄×C₁₇	C₂×D₈	1	4	yes	—
73	C₂×C₄×C₁₇	C₂×D₈	1	1	yes	characteristic
74	C₂×C₄×C₁₇	C₂×Q₁₆	1	2	yes	—
75	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
76	C₂×Dic₁₇	—	4	4	no	—
77	C₂×Dic₁₇	—	8	4	no	—
78	C₈×C₁₇	C₄⋊Q₈	1	2	yes	—
79	C₈×C₁₇	C₂×Q₁₆	1	4	yes	—
80	C₈×C₁₇	C₂²×Q₈	1	1	yes	characteristic
81	C₈×C₁₇	C₂²×Q₈	1	1	yes	characteristic
82	C₂×#499	—	17	1	no	—
83	C₂×#499	D₁₇	1	1	yes	characteristic
84	#2253	—	17	8	no	—
85	C₂×#367	—	17	2	no	—
86	C₂×#366	—	17	2	no	—
87	C₂×C₄×C₁₆	—	17	1	no	—
88	C₂²×C₁₇	#500	1	2	yes	—
89	C₂²×C₁₇	#508	1	4	yes	—
90	C₂²×C₁₇	C₂²×D₈	1	1	yes	characteristic
91	C₄×C₁₇	—	2	4	no	—
92	C₄×C₁₇	—	8	4	no	—
93	C₄×C₁₇	#500	1	2	yes	—
94	C₄×C₁₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
95	C₄×C₁₇	C₂²×Q₁₆	1	1	yes	characteristic
96	Dic₁₇	—	8	4	no	—
97	C₂×#125	—	2	1	no	—
98	C₂×#125	—	34	1	no	—
99	C₂²×C₁₆	—	17	1	no	—
100	C₂²×C₁₆	—	17	1	no	—
101	#499	—	2	2	no	—
102	#499	—	17	4	no	—
103	#499	—	34	2	no	—
104	#499	C₂×D₁₇	1	4	yes	—
105	C₂×#107	—	17	2	no	—
106	C₂×#107	C₂×D₁₇	1	2	yes	—
107	C₂×#106	—	2	1	no	—
108	C₂×#106	—	34	1	no	—
109	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
110	#367	—	17	8	no	—
111	#366	—	17	8	no	—
112	C₄×C₁₆	—	17	4	no	—
113	C₂×C₁₇	#2253	1	4	yes	complemented
114	C₂×C₁₇	C₂×#500	1	1	yes	characteristic
115	C₂×C₁₇	C₂×#508	1	2	yes	—
116	C₂²×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
117	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
118	#125	—	2	4	no	—
119	#125	—	4	2	no	—
120	#125	—	34	4	no	—
121	#125	—	68	2	no	—
122	C₂×C₄⋊C₄	—	2	2	no	—
123	C₂×C₄⋊C₄	—	4	2	no	—
124	C₂×C₄⋊C₄	—	34	2	no	—
125	C₂×C₄⋊C₄	—	68	2	no	—
126	C₂×C₄²	C₂²⋊D₁₇	1	1	yes	characteristic
127	C₂×C₁₆	—	17	4	no	—
128	C₂×C₁₆	—	17	4	no	—
129	C₂×C₁₆	—	17	2	no	—
130	C₂×C₁₆	—	17	2	no	—
131	#107	—	2	2	no	—
132	#107	—	17	4	no	—
133	#107	—	34	2	no	—
134	#107	C₂²×D₁₇	1	4	yes	—
135	#106	—	2	4	no	—
136	#106	—	34	4	no	—
137	C₄×C₈	C₂²⋊D₁₇	1	2	yes	—
138	C₄×C₈	C₂²×D₁₇	1	2	yes	—
139	C₁₇	C₂×#2253	1	1	yes	characteristic, complemented, Sylow
140	C₂²×C₄	—	4	2	no	—
141	C₂²×C₄	—	68	2	no	—
142	C₂²×C₄	#63228	1	2	yes	—
143	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
144	C₂×C₈	#63231	1	4	yes	—
145	C₂×C₈	Q₈×D₁₇	1	2	yes	—
146	C₂×C₈	Q₈×D₁₇	1	2	yes	—
147	C₂×C₈	C₂×C₂²⋊D₁₇	1	2	yes	—
148	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
149	C₂×C₈	C₂³×D₁₇	1	1	yes	characteristic
150	C₄⋊C₄	—	2	4	no	—
151	C₄⋊C₄	—	4	2	no	—
152	C₄⋊C₄	—	4	8	no	—
153	C₄⋊C₄	—	34	4	no	—
154	C₄⋊C₄	—	68	2	no	—
155	C₄⋊C₄	—	68	8	no	—
156	C₄²	#63228	1	2	yes	—
157	C₄²	C₂×C₂²⋊D₁₇	1	2	yes	—
158	C₁₆	—	17	4	no	—
159	C₁₆	—	17	4	no	—
160	C₂³	C₂×#63228	1	1	yes	characteristic
161	C₂×C₄	—	2	4	no	—
162	C₂×C₄	—	4	4	no	—
163	C₂×C₄	—	8	4	no	—
164	C₂×C₄	—	68	4	no	—
165	C₂×C₄	—	136	4	no	—
166	C₂×C₄	C₂×#63228	1	4	yes	—
167	C₂×C₄	C₂×#63228	1	1	yes	characteristic
168	C₂×C₄	C₂×#63231	1	2	yes	—
169	C₂×C₄	#10587630	1	2	yes	—
170	C₂×C₄	C₂²×C₂²⋊D₁₇	1	1	yes	characteristic
171	C₈	C₂×#63231	1	4	yes	—
172	C₈	#10587630	1	2	yes	—
173	C₈	C₂×Q₈×D₁₇	1	1	yes	characteristic
174	C₈	C₂×Q₈×D₁₇	1	1	yes	characteristic
175	C₂²	#11763212	1	2	yes	—
176	C₂²	#11763239	1	4	yes	—
177	C₂²	C₂²×#63228	1	1	yes	characteristic
178	C₄	—	2	4	no	—
179	C₄	—	8	4	no	—
180	C₄	—	136	4	no	—
181	C₄	#11763212	1	2	yes	—
182	C₄	C₂×#10587630	1	1	yes	characteristic
183	C₄	C₂²×#63231	1	1	yes	characteristic
184	C₂	#14531060	1	4	yes	direct product factor
185	C₂	C₂×#11763212	1	1	yes	characteristic
186	C₂	C₂×#11763239	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×#63228
commutator, cosocle	C₂×C₈×C₁₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₇
Fitting	C₂×C₁₇×#499	C₂
socle, prime radical	C₂³×C₁₇	C₂×D₈
hypercenter	C₂×#499	D₁₇
hypocenter	C₁₇	C₂×#2253
LCS	G ▷ C₂×C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#499

Complements

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

N	H ≅ G/N	type
2. #14531060	C₂	direct (N × H)
113. C₂×C₁₇	#2253	semidirect
139. C₁₇	C₂×#2253	semidirect
184. C₂	#14531060	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×#11763211	2
#14531060	2
C₂×#11762636	2
C₂×#11762634	2
C₂×C₄×#63214	2
C₂×C₁₇×#499	2
C₂×#2253	17

Subgroups — C2×#14531060 #17189803

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14531060 #17189803