Subgroups — #17960973

Order 4352.

398 conjugacy classes of subgroups.

The subgroup lattice has 200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11763731	C₂	1	2	yes	maximal
2	#14544990	C₂	1	2	yes	maximal
3	#14543828	C₂	1	2	yes	maximal
4	C₄×C₈×Dic₁₇	C₂	1	1	yes	maximal, characteristic
5	C₂×#10587538	C₂²	1	4	yes	—
6	#11763731	C₄	1	8	yes	complemented
7	#11763698	—	2	2	no	—
8	#11763695	—	2	2	no	—
9	C₂×C₄×#3622	C₂²	1	1	yes	characteristic
10	C₂×C₈×Dic₁₇	C₄	1	1	yes	characteristic
11	C₂×C₈×Dic₁₇	C₄	1	1	yes	characteristic
12	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
13	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
14	C₄²×Dic₁₇	C₄	1	1	yes	characteristic
15	C₂×C₄×C₈×C₁₇	C₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×Dic₁₇	—	2	2	no	—
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	#10587538	—	2	4	no	—
25	#10587538	C₂×C₄	1	8	yes	—
26	C₂×#63216	—	2	4	no	—
27	C₄×C₈×C₁₇	C₈	1	4	yes	—
28	C₈×Dic₁₇	—	2	2	no	—
29	C₈×Dic₁₇	C₈	1	4	yes	—
30	C₈×Dic₁₇	C₂×C₄	1	4	yes	—
31	C₈×Dic₁₇	D₄	1	1	yes	characteristic
32	C₈×Dic₁₇	D₄	1	1	yes	characteristic
33	C₈×Dic₁₇	Q₈	1	1	yes	characteristic
34	C₈×Dic₁₇	Q₈	1	1	yes	characteristic
35	C₄×#3622	—	2	2	no	—
36	C₂²×C₄×C₁₇	—	2	1	no	—
37	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
38	C₂²×Dic₁₇	—	2	1	no	—
39	C₂²×Dic₁₇	M₁₆	1	2	yes	—
40	C₂×C₈×C₁₇	C₄²	1	2	yes	—
41	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
42	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
43	C₂×C₈×C₁₇	C₂×C₈	1	2	yes	—
44	C₂×C₈×C₁₇	C₂×C₈	1	2	yes	—
45	C₂×C₈×C₁₇	C₂×C₈	1	2	yes	—
46	C₂×C₈×C₁₇	M₁₆	1	2	yes	—
47	C₄²×C₁₇	—	2	1	no	—
48	C₄²×C₁₇	C₂×C₈	1	2	yes	—
49	C₄×Dic₁₇	—	2	8	no	—
50	C₄×Dic₁₇	—	2	1	no	—
51	C₄×Dic₁₇	C₄²	1	2	yes	—
52	C₄×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
53	C₄×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
54	C₄×Dic₁₇	C₂×C₈	1	2	yes	—
55	C₂×#3622	—	2	1	no	—
56	C₂×#3622	—	2	1	no	—
57	C₂×#3622	C₂×C₈	1	2	yes	—
58	C₂×#3622	C₂²×C₄	1	2	yes	—
59	C₂×#3622	C₂×D₄	1	1	yes	characteristic
60	C₂×#3622	C₂×Q₈	1	1	yes	characteristic
61	C₂×#3622	#41	1	2	yes	—
62	#63216	—	2	8	no	—
63	C₄×#364	—	17	1	no	maximal, Sylow
64	C₂³×C₁₇	C₂×M₁₆	1	1	yes	characteristic
65	C₂×C₄×C₁₇	—	2	4	no	—
66	C₂×C₄×C₁₇	—	2	2	no	—
67	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
68	C₂×C₄×C₁₇	C₂×C₄⋊C₄	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	C₂²×C₈	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	2	yes	—
77	C₂×Dic₁₇	C₄⋊C₈	1	2	yes	—
78	C₈×C₁₇	C₄×C₈	1	4	yes	—
79	C₈×C₁₇	C₄⋊C₈	1	2	yes	—
80	C₈×C₁₇	C₄⋊C₈	1	2	yes	—
81	#3622	—	2	2	no	—
82	#3622	C₄×D₄	1	2	yes	—
83	#3622	C₄×Q₈	1	2	yes	—
84	C₂×#364	—	17	2	no	—
85	C₄×M₃₂	—	17	2	no	—
86	C₄²×C₈	—	17	1	no	—
87	#1376	—	17	2	no	—
88	C₂²×C₁₇	—	2	2	no	—
89	C₂²×C₁₇	C₄×M₁₆	1	1	yes	characteristic
90	C₂²×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
91	C₂²×C₁₇	#431	1	1	yes	characteristic
92	C₄×C₁₇	—	2	4	no	—
93	C₄×C₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
94	C₄×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
95	C₄×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
96	C₄×C₁₇	#431	1	1	yes	characteristic
97	Dic₁₇	—	2	4	no	—
98	Dic₁₇	—	2	2	no	—
99	Dic₁₇	#364	1	4	yes	complemented
100	C₂×M₃₂	—	17	4	no	—
101	C₂×C₄×C₈	—	17	1	no	—
102	C₂×C₄×C₈	—	17	1	no	—
103	C₂×C₄×C₈	—	17	1	no	—
104	C₂×C₄×C₈	—	17	1	no	—
105	C₂×C₄×C₈	—	17	1	no	—
106	C₂×C₄×C₈	#595	1	1	yes	characteristic
107	C₄³	—	17	1	no	—
108	#364	—	17	8	no	—
109	#346	—	34	2	no	—
110	C₄×C₁₆	—	34	2	no	—
111	C₂×C₁₇	—	2	1	no	—
112	C₂×C₁₇	—	2	1	no	—
113	C₂×C₁₇	C₄×C₄⋊C₈	1	1	yes	characteristic
114	C₂×C₁₇	C₂×#364	1	2	yes	—
115	C₂²×C₈	—	17	1	no	—
116	C₂²×C₈	—	17	1	no	—
117	C₂²×C₈	C₂×#595	1	1	yes	characteristic
118	C₂²×C₈	C₂×#595	1	1	yes	characteristic
119	C₂×C₄²	—	17	1	no	—
120	C₂×C₄²	—	17	1	no	—
121	C₂×C₄²	—	34	2	no	—
122	C₂×C₄²	C₂×#595	1	1	yes	characteristic
123	M₃₂	—	17	8	no	—
124	M₃₂	—	34	4	no	—
125	C₂×C₁₆	—	34	4	no	—
126	C₄×C₈	—	17	4	no	—
127	C₄×C₈	—	17	4	no	—
128	C₄×C₈	—	17	1	no	—
129	C₄×C₈	—	17	1	no	—
130	C₄×C₈	—	17	1	no	—
131	C₄×C₈	—	17	1	no	—
132	C₄×C₈	—	34	2	no	—
133	C₄×C₈	—	34	2	no	—
134	C₄×C₈	#3624	1	4	yes	—
135	C₁₇	C₄×#364	1	1	yes	characteristic, complemented, Sylow
136	C₂²×C₄	—	2	1	no	—
137	C₂²×C₄	—	17	2	no	—
138	C₂²×C₄	—	34	1	no	—
139	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
140	C₂×C₈	—	17	2	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	—	34	1	no	—
146	C₂×C₈	—	34	1	no	—
147	C₂×C₈	#63242	1	2	yes	—
148	C₂×C₈	#63243	1	2	yes	—
149	C₂×C₈	C₄×#595	1	2	yes	—
150	C₂×C₈	C₄⋊#595	1	1	yes	characteristic
151	C₂×C₈	C₄⋊#595	1	1	yes	characteristic
152	C₂×C₈	C₂×#3624	1	2	yes	—
153	C₂×C₈	C₂×#3624	1	2	yes	—
154	C₄²	—	2	1	no	—
155	C₄²	—	17	2	no	—
156	C₄²	—	17	1	no	—
157	C₄²	—	17	1	no	—
158	C₄²	—	17	2	no	—
159	C₄²	—	34	8	no	—
160	C₄²	—	34	1	no	—
161	C₄²	C₂×#3624	1	2	yes	—
162	C₁₆	—	34	8	no	—
163	C₂³	D₁₇⋊M₁₆	1	1	yes	characteristic
164	C₂×C₄	—	2	4	no	—
165	C₂×C₄	—	2	2	no	—
166	C₂×C₄	—	17	2	no	—
167	C₂×C₄	—	17	2	no	—
168	C₂×C₄	—	34	4	no	—
169	C₂×C₄	—	34	4	no	—
170	C₂×C₄	—	34	2	no	—
171	C₂×C₄	C₂×#63242	1	1	yes	characteristic
172	C₂×C₄	C₂×#63243	1	1	yes	characteristic
173	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
174	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
175	C₂×C₄	#10587677	1	1	yes	characteristic
176	C₂×C₄	C₂²×#3624	1	1	yes	characteristic
177	C₈	—	17	2	no	—
178	C₈	—	17	2	no	—
179	C₈	—	34	2	no	—
180	C₈	C₄×#3624	1	4	yes	—
181	C₈	C₄⋊#3624	1	2	yes	—
182	C₈	C₄⋊#3624	1	2	yes	—
183	C₂²	—	2	2	no	—
184	C₂²	C₄×#63243	1	1	yes	characteristic
185	C₂²	#11763810	1	1	yes	characteristic
186	C₂²	#11763825	1	1	yes	characteristic
187	C₄	—	2	4	no	—
188	C₄	—	17	4	no	—
189	C₄	—	34	4	no	—
190	C₄	—	34	2	no	—
191	C₄	C₄×C₄⋊#595	1	1	yes	characteristic
192	C₄	C₂×C₄×#3624	1	1	yes	characteristic
193	C₄	C₂×C₄⋊#3624	1	1	yes	characteristic
194	C₄	#11763828	1	1	yes	characteristic
195	C₂	—	2	1	no	—
196	C₂	—	2	1	no	—
197	C₂	C₄×C₄⋊#3624	1	1	yes	characteristic
198	C₂	#14545123	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₄⋊#595
commutator	C₄×C₁₇	C₂×C₄×C₈
Frattini	C₂²×C₄	C₂²×#595
Fitting	C₂×C₄×C₈×C₁₇	C₄
socle	C₂²×C₁₇	C₂×C₄⋊C₈
prime radical	C₂³×C₁₇	C₂×M₁₆
cosocle	C₂²×#3622	C₂³
hypercenter	C₂×C₄×C₈	#595
hypocenter	C₁₇	C₄×#364
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
6. #11763731	C₄	semidirect
99. Dic₁₇	#364	semidirect
135. C₁₇	C₄×#364	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11763731	2
#14544990	2
#14543828	2
C₄×C₈×Dic₁₇	2
C₄×#364	17