Subgroups — #16950682

Order 4352.

314 conjugacy classes of subgroups.

The subgroup lattice has 182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11762630	C₂	1	2	yes	maximal
2	#14526868	C₂	1	2	yes	maximal
3	#14526864	C₂	1	2	yes	maximal
4	C₄×C₁₇×#97	C₂	1	1	yes	maximal, characteristic
5	C₂×#10587483	C₂²	1	4	yes	—
6	#11762630	—	2	4	no	—
7	C₂×C₁₇×#97	C₄	1	1	yes	characteristic
8	C₂×C₁₇×#97	C₄	1	1	yes	characteristic
9	C₂×C₁₇×#97	C₂²	1	1	yes	characteristic
10	C₂×C₁₇×#97	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₈×C₁₇	C₄	1	1	yes	characteristic
12	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
13	C₄³×C₁₇	C₄	1	1	yes	characteristic
14	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
18	C₂×C₄²×C₁₇	—	2	2	no	—
19	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
22	C₁₇×#97	—	2	2	no	—
23	C₁₇×#97	—	2	2	no	—
24	C₁₇×#97	—	2	2	no	—
25	C₁₇×#97	C₈	1	4	yes	—
26	C₄×C₈×C₁₇	—	2	2	no	—
27	C₄×C₈×C₁₇	D₄	1	2	yes	—
28	C₄×C₈×C₁₇	Q₈	1	2	yes	—
29	#10587483	—	2	4	no	—
30	#10587483	—	2	4	no	—
31	C₂×#63214	—	2	4	no	—
32	C₂²×C₄×C₁₇	—	2	1	no	—
33	C₂²×C₄×C₁₇	—	2	1	no	—
34	C₂²×C₄×C₁₇	M₁₆	1	2	yes	—
35	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₈×C₁₇	—	2	1	no	—
37	C₂×C₈×C₁₇	—	2	1	no	—
38	C₂×C₈×C₁₇	—	2	1	no	—
39	C₂×C₈×C₁₇	—	2	1	no	—
40	C₂×C₈×C₁₇	C₄⋊C₄	1	2	yes	—
41	C₂×C₈×C₁₇	C₂×C₈	1	2	yes	—
42	C₂×C₈×C₁₇	C₂×C₈	1	2	yes	—
43	C₂×C₈×C₁₇	M₁₆	1	2	yes	—
44	C₂×C₈×C₁₇	M₁₆	1	2	yes	—
45	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
46	C₂×C₈×C₁₇	C₂×Q₈	1	1	yes	characteristic
47	C₂×C₈×C₁₇	#41	1	2	yes	—
48	C₂×C₈×C₁₇	#41	1	2	yes	—
49	C₄²×C₁₇	—	2	1	no	—
50	C₄²×C₁₇	—	2	1	no	—
51	C₄²×C₁₇	—	2	1	no	—
52	C₄²×C₁₇	—	2	1	no	—
53	C₄²×C₁₇	—	4	4	no	—
54	C₄²×C₁₇	C₄⋊C₄	1	2	yes	—
55	C₄²×C₁₇	C₂×C₈	1	2	yes	—
56	#63214	—	4	4	no	—
57	#12882	—	17	1	no	maximal, Sylow
58	C₂³×C₁₇	C₂×M₁₆	1	1	yes	characteristic
59	C₂×C₄×C₁₇	—	2	4	no	—
60	C₂×C₄×C₁₇	—	2	2	no	—
61	C₂×C₄×C₁₇	—	2	2	no	—
62	C₂×C₄×C₁₇	—	2	2	no	—
63	C₂×C₄×C₁₇	—	4	2	no	—
64	C₂×C₄×C₁₇	—	4	2	no	—
65	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
66	C₂×C₄×C₁₇	#117	1	1	yes	characteristic
67	C₂×C₄×C₁₇	#117	1	1	yes	characteristic
68	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
69	C₂×C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
70	C₂×C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
71	C₈×C₁₇	—	2	2	no	—
72	C₈×C₁₇	—	2	2	no	—
73	C₈×C₁₇	C₄⋊C₈	1	4	yes	—
74	C₈×C₁₇	#124	1	2	yes	—
75	C₈×C₁₇	#125	1	2	yes	—
76	C₂×#364	—	17	2	no	—
77	C₄×#97	D₁₇	1	1	yes	characteristic
78	#1377	—	17	2	no	—
79	#1375	—	17	2	no	—
80	C₂²×C₁₇	—	2	2	no	—
81	C₂²×C₁₇	#423	1	1	yes	characteristic
82	C₂²×C₁₇	#431	1	1	yes	characteristic
83	C₂²×C₁₇	#432	1	1	yes	characteristic
84	C₄×C₁₇	—	2	4	no	—
85	C₄×C₁₇	—	4	2	no	—
86	C₄×C₁₇	—	4	2	no	—
87	C₄×C₁₇	#382	1	1	yes	characteristic
88	C₄×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
89	C₄×C₁₇	#431	1	1	yes	characteristic
90	C₄×C₁₇	#432	1	1	yes	characteristic
91	C₂×M₃₂	—	17	4	no	—
92	C₂×#97	Dic₁₇	1	1	yes	characteristic
93	C₂×#97	Dic₁₇	1	1	yes	characteristic
94	C₂×#97	C₂×D₁₇	1	1	yes	characteristic
95	C₂×#97	C₂×D₁₇	1	1	yes	characteristic
96	C₂×C₄×C₈	Dic₁₇	1	1	yes	characteristic
97	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
98	C₄³	Dic₁₇	1	1	yes	characteristic
99	#364	—	34	4	no	—
100	C₂×C₁₇	—	2	1	no	—
101	C₂×C₁₇	—	2	1	no	—
102	C₂×C₁₇	#1831	1	1	yes	characteristic
103	C₂×C₁₇	#2165	1	2	yes	—
104	C₂²×C₈	C₂×Dic₁₇	1	1	yes	characteristic
105	C₂²×C₈	C₂×Dic₁₇	1	1	yes	characteristic
106	C₂²×C₈	C₂×Dic₁₇	1	1	yes	characteristic
107	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
108	C₂×C₄²	—	2	2	no	—
109	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
110	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
111	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
112	M₃₂	—	34	4	no	—
113	M₃₂	—	34	4	no	—
114	C₂×C₁₆	—	34	4	no	—
115	#97	—	2	2	no	—
116	#97	—	2	2	no	—
117	#97	—	2	2	no	—
118	#97	#3622	1	4	yes	—
119	C₄×C₈	—	2	2	no	—
120	C₄×C₈	Dic₃₄	1	2	yes	—
121	C₄×C₈	D₆₈	1	2	yes	—
122	C₁₇	#12882	1	1	yes	characteristic, complemented, Sylow
123	C₂²×C₄	—	2	1	no	—
124	C₂²×C₄	—	2	1	no	—
125	C₂²×C₄	#63223	1	2	yes	—
126	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
127	C₂×C₈	—	2	1	no	—
128	C₂×C₈	—	2	1	no	—
129	C₂×C₈	—	2	1	no	—
130	C₂×C₈	—	2	1	no	—
131	C₂×C₈	C₂×#3622	1	2	yes	—
132	C₂×C₈	C₂×#3622	1	2	yes	—
133	C₂×C₈	#63223	1	2	yes	—
134	C₂×C₈	#63223	1	2	yes	—
135	C₂×C₈	C₄⋊Dic₁₇	1	2	yes	—
136	C₂×C₈	C₂×Dic₃₄	1	1	yes	characteristic
137	C₂×C₈	C₂×D₆₈	1	1	yes	characteristic
138	C₂×C₈	#63252	1	2	yes	—
139	C₂×C₈	#63252	1	2	yes	—
140	C₄²	—	2	1	no	—
141	C₄²	—	2	1	no	—
142	C₄²	—	2	1	no	—
143	C₄²	—	2	1	no	—
144	C₄²	—	4	4	no	—
145	C₄²	C₂×#3622	1	2	yes	—
146	C₄²	C₄⋊Dic₁₇	1	2	yes	—
147	C₁₆	—	68	4	no	—
148	C₂³	C₂×#63223	1	1	yes	characteristic
149	C₂×C₄	—	2	4	no	—
150	C₂×C₄	—	2	2	no	—
151	C₂×C₄	—	2	2	no	—
152	C₂×C₄	—	2	2	no	—
153	C₂×C₄	—	4	2	no	—
154	C₂×C₄	—	4	2	no	—
155	C₂×C₄	C₂²×#3622	1	1	yes	characteristic
156	C₂×C₄	C₂×#63223	1	1	yes	characteristic
157	C₂×C₄	C₂×#63223	1	1	yes	characteristic
158	C₂×C₄	C₂×C₄⋊Dic₁₇	1	1	yes	characteristic
159	C₂×C₄	#10587612	1	1	yes	characteristic
160	C₂×C₄	#10587612	1	1	yes	characteristic
161	C₈	—	2	2	no	—
162	C₈	—	2	2	no	—
163	C₈	C₄⋊#3622	1	4	yes	—
164	C₈	#10587556	1	2	yes	—
165	C₈	#10587561	1	2	yes	—
166	C₂²	—	2	2	no	—
167	C₂²	#11762833	1	1	yes	characteristic
168	C₂²	#11762862	1	1	yes	characteristic
169	C₂²	#11762866	1	1	yes	characteristic
170	C₄	—	2	4	no	—
171	C₄	—	4	2	no	—
172	C₄	—	4	2	no	—
173	C₄	#11762675	1	1	yes	characteristic
174	C₄	C₂×C₄⋊#3622	1	1	yes	characteristic
175	C₄	#11762862	1	1	yes	characteristic
176	C₄	#11762866	1	1	yes	characteristic
177	C₂	—	2	1	no	—
178	C₂	—	2	1	no	—
179	C₂	#14528901	1	1	yes	characteristic
180	C₂	#14530596	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#10587612
commutator	C₂×C₄×C₁₇	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₁₇
Fitting	C₄×C₁₇×#97	C₂
socle	C₂²×C₁₇	#432
prime radical	C₂³×C₁₇	C₂×M₁₆
cosocle	C₂²×C₈×C₁₇	C₂³
hypercenter	C₄×#97	D₁₇
hypocenter	C₁₇	#12882
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#97 ◁ C₄×#97

Complements

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

N	H ≅ G/N	type
122. C₁₇	#12882	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11762630	2
#14526868	2
#14526864	2
C₄×C₁₇×#97	2
#12882	17