Subgroups — #17960660

Order 4352.

358 conjugacy classes of subgroups.

The subgroup lattice has 194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11763698	C₂	1	1	yes	maximal, characteristic
2	C₂×#11763695	C₂	1	1	yes	maximal, characteristic
3	#14543823	C₂	1	2	yes	maximal
4	#14543822	C₂	1	2	yes	maximal
5	#14528472	C₂	1	1	yes	maximal, characteristic
6	C₂²×#63216	C₂²	1	2	yes	—
7	C₂²×#63216	C₂²	1	2	yes	—
8	#11763698	C₄	1	4	yes	complemented
9	#11763695	C₄	1	4	yes	complemented
10	C₂×#10587486	C₄	1	1	yes	characteristic
11	C₂×#10587486	C₄	1	1	yes	characteristic
12	C₂×C₄×#3622	C₂²	1	1	yes	characteristic
13	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
14	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
15	#11762655	C₄	1	1	yes	characteristic
16	C₂×C₁₇×#97	C₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
22	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
23	C₂²×#3622	C₂³	1	1	yes	characteristic
24	C₂×#63216	—	2	2	no	—
25	C₂×#63216	—	2	2	no	—
26	C₂×#63216	—	2	2	no	—
27	C₂×#63216	—	2	2	no	—
28	C₂×#63216	C₂×C₄	1	4	yes	—
29	C₂×#63216	C₂×C₄	1	4	yes	—
30	C₁₇×#97	—	2	2	no	—
31	#10587502	C₈	1	4	yes	—
32	#10587486	—	2	2	no	—
33	#10587486	C₈	1	4	yes	—
34	C₈×Dic₁₇	—	2	2	no	—
35	C₈×Dic₁₇	C₂×C₄	1	2	yes	—
36	C₈×Dic₁₇	C₂×C₄	1	2	yes	—
37	C₄×#3622	—	2	2	no	—
38	C₂²×C₄×C₁₇	C₂×C₈	1	2	yes	—
39	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
40	C₂²×Dic₁₇	C₂×C₈	1	2	yes	—
41	C₂²×Dic₁₇	C₂×C₈	1	2	yes	—
42	C₂×C₈×C₁₇	—	2	1	no	—
43	C₂×C₈×C₁₇	—	2	1	no	—
44	C₂×C₈×C₁₇	C₄²	1	2	yes	—
45	C₂×C₈×C₁₇	C₂×C₈	1	2	yes	—
46	C₂×C₈×C₁₇	M₁₆	1	2	yes	—
47	C₂×C₈×C₁₇	M₁₆	1	2	yes	—
48	C₄²×C₁₇	—	2	1	no	—
49	C₄²×C₁₇	—	2	1	no	—
50	C₄×Dic₁₇	—	2	1	no	—
51	C₄×Dic₁₇	—	2	1	no	—
52	C₄×Dic₁₇	C₄²	1	2	yes	—
53	C₄×Dic₁₇	C₂×C₈	1	2	yes	—
54	C₂×#3622	—	2	1	no	—
55	C₂×#3622	—	2	1	no	—
56	C₂×#3622	C₂×C₈	1	2	yes	—
57	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
58	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
59	C₂×#3622	#41	1	2	yes	—
60	C₂×#3622	#41	1	2	yes	—
61	#63216	—	2	4	no	—
62	#63216	—	2	4	no	—
63	#12592	—	17	1	no	maximal, Sylow
64	C₂³×C₁₇	C₂²×C₈	1	1	yes	characteristic
65	C₂×C₄×C₁₇	—	2	2	no	—
66	C₂×C₄×C₁₇	—	2	4	no	—
67	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
68	C₂×C₄×C₁₇	#117	1	1	yes	characteristic
69	C₂×C₄×C₁₇	#117	1	1	yes	characteristic
70	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
71	C₂×C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
72	C₂×C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
73	C₂×Dic₁₇	—	2	4	no	—
74	C₂×Dic₁₇	—	2	2	no	—
75	C₂×Dic₁₇	—	2	4	no	—
76	C₂×Dic₁₇	C₄×C₈	1	4	yes	—
77	C₈×C₁₇	—	2	2	no	—
78	C₈×C₁₇	#97	1	4	yes	—
79	#3622	—	2	2	no	—
80	#3622	#117	1	2	yes	—
81	#3622	#117	1	2	yes	—
82	C₂×#346	—	17	1	no	—
83	C₂×C₄×C₁₆	—	17	1	no	—
84	#1726	—	17	1	no	—
85	#1374	—	17	2	no	—
86	#1374	—	17	2	no	—
87	C₂²×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
88	C₂²×C₁₇	#431	1	1	yes	characteristic
89	C₂²×C₁₇	#431	1	1	yes	characteristic
90	C₂²×C₁₇	#504	1	4	yes	—
91	C₄×C₁₇	—	4	2	no	—
92	C₄×C₁₇	#376	1	1	yes	characteristic
93	C₄×C₁₇	C₂×#97	1	1	yes	characteristic
94	C₄×C₁₇	#431	1	1	yes	characteristic
95	C₄×C₁₇	#431	1	1	yes	characteristic
96	Dic₁₇	—	2	4	no	—
97	Dic₁₇	—	4	2	no	—
98	C₂²×C₁₆	—	17	2	no	—
99	C₂²×C₁₆	—	17	2	no	—
100	C₂×#97	—	17	1	no	—
101	C₂×#97	—	17	1	no	—
102	C₂×#97	#595	1	1	yes	characteristic
103	C₂×C₄×C₈	—	17	1	no	—
104	C₂×C₄×C₈	—	17	1	no	—
105	C₂×C₄×C₈	—	17	1	no	—
106	#376	—	17	1	no	—
107	#346	—	17	4	no	—
108	C₄×C₁₆	—	17	4	no	—
109	C₂×C₁₇	#1744	1	1	yes	characteristic
110	C₂×C₁₇	#2108	1	2	yes	—
111	C₂×C₁₇	#2164	1	2	yes	—
112	C₂×C₁₇	#2164	1	2	yes	—
113	C₂²×C₈	—	17	1	no	—
114	C₂²×C₈	—	17	1	no	—
115	C₂²×C₈	C₂×#595	1	1	yes	characteristic
116	C₂²×C₈	C₂×#595	1	1	yes	characteristic
117	C₂×C₄²	—	17	1	no	—
118	C₂×C₄²	—	17	1	no	—
119	C₂×C₄²	C₂×#595	1	1	yes	characteristic
120	C₂×C₁₆	—	17	4	no	—
121	C₂×C₁₆	—	17	4	no	—
122	C₂×C₁₆	—	34	2	no	—
123	C₂×C₁₆	—	34	2	no	—
124	C₂×C₁₆	—	34	2	no	—
125	C₂×C₁₆	—	34	2	no	—
126	#97	—	2	2	no	—
127	#97	—	17	4	no	—
128	#97	—	34	2	no	—
129	C₄×C₈	—	17	2	no	—
130	C₄×C₈	—	17	2	no	—
131	C₄×C₈	—	34	2	no	—
132	C₄×C₈	—	34	2	no	—
133	#95	—	17	4	no	—
134	C₁₇	#12592	1	1	yes	characteristic, complemented, Sylow
135	C₂²×C₄	—	17	2	no	—
136	C₂²×C₄	—	17	2	no	—
137	C₂²×C₄	#63242	1	2	yes	—
138	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
139	C₂×C₈	—	2	1	no	—
140	C₂×C₈	—	2	1	no	—
141	C₂×C₈	—	17	1	no	—
142	C₂×C₈	—	17	1	no	—
143	C₂×C₈	—	17	2	no	—
144	C₂×C₈	—	17	2	no	—
145	C₂×C₈	—	17	2	no	—
146	C₂×C₈	—	34	1	no	—
147	C₂×C₈	—	34	1	no	—
148	C₂×C₈	#63242	1	2	yes	—
149	C₂×C₈	#63243	1	2	yes	—
150	C₂×C₈	C₄×#595	1	2	yes	—
151	C₂×C₈	#63247	1	2	yes	—
152	C₄²	—	2	1	no	—
153	C₄²	—	2	1	no	—
154	C₄²	—	17	2	no	—
155	C₄²	—	17	2	no	—
156	C₄²	—	34	1	no	—
157	C₄²	—	34	1	no	—
158	C₁₆	—	34	4	no	—
159	C₁₆	—	34	4	no	—
160	C₂³	C₂×#63242	1	1	yes	characteristic
161	C₂×C₄	—	2	2	no	—
162	C₂×C₄	—	2	4	no	—
163	C₂×C₄	—	17	4	no	—
164	C₂×C₄	—	34	4	no	—
165	C₂×C₄	—	34	2	no	—
166	C₂×C₄	—	34	4	no	—
167	C₂×C₄	C₂×#63242	1	1	yes	characteristic
168	C₂×C₄	C₂×#63243	1	1	yes	characteristic
169	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
170	C₂×C₄	#10587677	1	1	yes	characteristic
171	C₂×C₄	#10587677	1	1	yes	characteristic
172	C₂×C₄	C₂×#63247	1	1	yes	characteristic
173	C₈	—	2	2	no	—
174	C₈	—	17	2	no	—
175	C₈	—	17	2	no	—
176	C₈	—	34	2	no	—
177	C₈	#10587542	1	4	yes	—
178	C₂²	C₄×#63242	1	1	yes	characteristic
179	C₂²	#11763826	1	1	yes	characteristic
180	C₂²	#11763828	1	1	yes	characteristic
181	C₂²	#11763868	1	4	yes	—
182	C₄	—	4	2	no	—
183	C₄	—	34	4	no	—
184	C₄	—	68	2	no	—
185	C₄	#11763745	1	1	yes	characteristic
186	C₄	C₂×#10587542	1	1	yes	characteristic
187	C₄	#11763826	1	1	yes	characteristic
188	C₄	#11763828	1	1	yes	characteristic
189	C₂	#14544499	1	1	yes	characteristic
190	C₂	#14544994	1	2	yes	—
191	C₂	#14545150	1	2	yes	—
192	C₂	#14545152	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×#595
commutator	C₂²×C₁₇	C₂×C₄×C₈
Fitting	C₂×C₁₇×#97	C₄
socle, prime radical	C₂³×C₁₇	C₂²×C₈
cosocle	C₂²×#3622	C₂³
hypercenter	C₂×#97	#595
hypocenter	C₁₇	#12592
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
8. #11763698	C₄	semidirect
9. #11763695	C₄	semidirect
134. C₁₇	#12592	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#11763698	2
C₂×#11763695	2
#14543823	2
#14543822	2
#14528472	2
#12592	17