Subgroups — C₈×#10587535 #17952390

Order 4352.

374 conjugacy classes of subgroups.

The subgroup lattice has 224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10587535	C₂	1	1	yes	maximal, characteristic
2	#14544332	C₂	1	1	yes	maximal, characteristic
3	C₈×#63243	C₂	1	2	yes	maximal
4	#14543616	C₂	1	2	yes	maximal
5	C₈²×D₁₇	C₂	1	1	yes	maximal, characteristic
6	#11763828	C₂²	1	2	yes	—
7	C₂×#10587535	C₄	1	2	yes	—
8	C₄×#63243	C₂²	1	2	yes	—
9	#11763685	C₄	1	2	yes	—
10	#11763673	C₄	1	2	yes	—
11	#11763670	C₄	1	2	yes	—
12	#11763651	—	2	2	no	—
13	C₈×#3624	—	2	2	no	—
14	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
15	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
16	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
17	C₈×#3622	C₄	1	1	yes	characteristic
18	C₈×#3622	C₄	1	1	yes	characteristic
19	C₈×#3622	C₄	1	1	yes	characteristic
20	C₈²×C₁₇	C₄	1	1	yes	characteristic
21	C₂×#63243	C₂×C₄	1	4	yes	—
22	C₂×C₈×D₁₇	—	2	1	no	—
23	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×D₁₇	Q₈	1	1	yes	characteristic
26	C₂×C₈×D₁₇	Q₈	1	1	yes	characteristic
27	C₄²×D₁₇	C₂³	1	1	yes	characteristic
28	#10587543	—	2	2	no	—
29	#10587542	—	2	2	no	—
30	C₄⋊#3624	C₂×C₄	1	4	yes	—
31	C₄×#3624	—	2	2	no	—
32	C₄×#3624	—	2	2	no	—
33	#10587535	C₈	1	8	yes	direct product factor
34	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
35	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
36	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
37	C₈×Dic₁₇	—	2	1	no	—
38	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
39	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
40	C₈×Dic₁₇	D₄	1	1	yes	characteristic
41	C₈×Dic₁₇	D₄	1	1	yes	characteristic
42	C₄×#3622	C₂×C₄	1	1	yes	characteristic
43	C₄×#3622	C₂×C₄	1	1	yes	characteristic
44	C₄×#3622	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
46	C₂×C₄×D₁₇	C₂×Q₈	1	1	yes	characteristic
47	C₂×C₄×D₁₇	#41	1	1	yes	characteristic
48	C₂×#3624	—	2	4	no	—
49	C₂×#3624	—	2	4	no	—
50	#63243	—	2	4	no	—
51	#63243	C₂×C₈	1	8	yes	—
52	C₂×C₈×C₁₇	—	2	1	no	—
53	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
54	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
55	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
56	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
57	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
58	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
59	C₄×Dic₁₇	C₂×D₄	1	1	yes	characteristic
60	C₄×Dic₁₇	#41	1	1	yes	characteristic
61	C₂×#3622	—	2	1	no	—
62	C₂×#3622	C₄²	1	1	yes	characteristic
63	C₂×#3622	C₄²	1	1	yes	characteristic
64	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
65	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
66	C₈×D₁₇	—	2	4	no	—
67	C₈×D₁₇	—	2	2	no	—
68	C₈×D₁₇	—	2	2	no	—
69	C₈×D₁₇	—	2	2	no	—
70	C₈×D₁₇	C₂×C₈	1	4	yes	—
71	C₈×#108	—	17	1	no	maximal, Sylow
72	C₂²×D₁₇	C₄×Q₈	1	1	yes	characteristic
73	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
74	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
75	C₂×C₄×C₁₇	#117	1	1	yes	characteristic
76	C₂×Dic₁₇	C₄×D₄	1	1	yes	characteristic
77	C₂×Dic₁₇	C₄×D₄	1	1	yes	characteristic
78	C₂×Dic₁₇	C₄×Q₈	1	1	yes	characteristic
79	C₄×D₁₇	—	2	1	no	—
80	C₄×D₁₇	—	2	1	no	—
81	C₄×D₁₇	—	2	2	no	—
82	C₄×D₁₇	C₂²×C₈	1	2	yes	—
83	C₄×D₁₇	#131	1	2	yes	—
84	#3624	—	2	8	no	—
85	#3624	—	4	4	no	—
86	C₈×C₁₇	—	2	2	no	—
87	C₈×C₁₇	—	2	1	no	—
88	C₈×C₁₇	—	2	1	no	—
89	C₈×C₁₇	C₄×C₈	1	2	yes	—
90	C₈×C₁₇	#108	1	2	yes	complemented
91	#3622	—	2	2	no	—
92	#3622	—	2	1	no	—
93	#3622	—	2	1	no	—
94	#3622	C₄×C₈	1	2	yes	—
95	#3622	#108	1	2	yes	complemented
96	C₄×#108	—	17	1	no	—
97	#1564	—	17	1	no	—
98	C₈×M₁₆	—	17	2	no	—
99	C₂×C₈²	—	17	1	no	—
100	#1278	—	17	2	no	—
101	C₂²×C₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
102	C₂×D₁₇	—	2	1	no	—
103	C₂×D₁₇	—	2	1	no	—
104	C₂×D₁₇	C₈×Q₈	1	2	yes	—
105	C₄×C₁₇	—	2	1	no	—
106	C₄×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
107	C₄×C₁₇	#405	1	1	yes	characteristic
108	C₄×C₁₇	C₂×#108	1	1	yes	characteristic
109	C₄×C₁₇	C₂×#108	1	1	yes	characteristic
110	Dic₁₇	—	2	1	no	—
111	Dic₁₇	C₈×D₄	1	2	yes	—
112	Dic₁₇	#443	1	2	yes	—
113	#431	—	17	2	no	—
114	C₂×#108	—	17	2	no	—
115	C₄×M₁₆	—	17	2	no	—
116	C₂×C₄×C₈	—	17	1	no	—
117	C₂×C₄×C₈	—	17	1	no	—
118	C₂×C₄×C₈	—	17	1	no	—
119	#341	—	17	2	no	—
120	#335	—	17	2	no	—
121	#334	—	17	2	no	—
122	#322	—	34	2	no	—
123	C₈²	—	17	1	no	—
124	C₈²	—	17	1	no	—
125	C₈²	—	17	1	no	—
126	C₈²	—	34	2	no	—
127	C₈²	#595	1	1	yes	characteristic
128	C₂×C₁₇	C₈×C₄⋊C₄	1	1	yes	characteristic
129	C₂×C₁₇	#1772	1	1	yes	characteristic
130	C₂×C₁₇	C₄×#108	1	1	yes	characteristic
131	D₁₇	—	2	2	no	—
132	C₂×M₁₆	—	17	4	no	—
133	C₂²×C₈	—	17	1	no	—
134	C₂²×C₈	—	17	1	no	—
135	C₂²×C₈	—	17	1	no	—
136	C₂²×C₈	—	17	1	no	—
137	C₂²×C₈	—	34	1	no	—
138	C₂×C₄²	—	17	1	no	—
139	#108	—	17	8	no	—
140	C₄⋊C₈	—	17	4	no	—
141	C₂²⋊C₈	—	34	2	no	—
142	#97	—	34	2	no	—
143	C₄×C₈	—	17	1	no	—
144	C₄×C₈	—	17	1	no	—
145	C₄×C₈	—	17	1	no	—
146	C₄×C₈	—	17	1	no	—
147	C₄×C₈	—	17	1	no	—
148	C₄×C₈	—	17	1	no	—
149	C₄×C₈	—	17	1	no	—
150	C₄×C₈	—	34	1	no	—
151	C₄×C₈	—	34	2	no	—
152	C₄×C₈	—	34	2	no	—
153	C₄×C₈	C₂×#595	1	1	yes	characteristic
154	C₄×C₈	C₂×#595	1	1	yes	characteristic
155	C₄×C₈	C₂×#595	1	1	yes	characteristic
156	C₁₇	C₈×#108	1	1	yes	characteristic, complemented, Sylow
157	C₂²×C₄	—	17	1	no	—
158	C₂²×C₄	—	17	1	no	—
159	C₂²×C₄	—	17	1	no	—
160	M₁₆	—	17	8	no	—
161	M₁₆	—	34	4	no	—
162	C₂×C₈	—	2	1	no	—
163	C₂×C₈	—	17	1	no	—
164	C₂×C₈	—	17	1	no	—
165	C₂×C₈	—	17	4	no	—
166	C₂×C₈	—	17	1	no	—
167	C₂×C₈	—	17	1	no	—
168	C₂×C₈	—	34	2	no	—
169	C₂×C₈	—	34	2	no	—
170	C₂×C₈	—	34	4	no	—
171	C₂×C₈	—	34	4	no	—
172	C₂×C₈	—	34	1	no	—
173	C₂×C₈	—	34	2	no	—
174	C₂×C₈	—	34	4	no	—
175	C₂×C₈	C₄×#595	1	1	yes	characteristic
176	C₂×C₈	C₄×#595	1	1	yes	characteristic
177	C₂×C₈	C₄⋊#595	1	1	yes	characteristic
178	C₂×C₈	C₄⋊#595	1	1	yes	characteristic
179	C₄²	—	17	1	no	—
180	C₄²	—	17	1	no	—
181	C₄²	—	17	1	no	—
182	C₄²	C₂²×#595	1	1	yes	characteristic
183	C₂³	—	17	1	no	—
184	C₂×C₄	—	17	1	no	—
185	C₂×C₄	—	17	1	no	—
186	C₂×C₄	—	17	2	no	—
187	C₂×C₄	—	17	2	no	—
188	C₂×C₄	—	17	1	no	—
189	C₂×C₄	—	34	2	no	—
190	C₂×C₄	—	34	1	no	—
191	C₂×C₄	—	34	1	no	—
192	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
193	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
194	C₂×C₄	#10587677	1	1	yes	characteristic
195	C₈	—	2	2	no	—
196	C₈	—	2	1	no	—
197	C₈	—	2	1	no	—
198	C₈	—	17	2	no	—
199	C₈	—	17	2	no	—
200	C₈	—	34	2	no	—
201	C₈	—	34	8	no	—
202	C₈	—	34	1	no	—
203	C₈	—	34	1	no	—
204	C₈	—	68	4	no	—
205	C₈	C₈×#595	1	2	yes	—
206	C₈	#10587535	1	2	yes	direct product factor
207	C₂²	—	17	2	no	—
208	C₂²	—	34	1	no	—
209	C₂²	—	34	1	no	—
210	C₂²	C₄×C₄⋊#595	1	1	yes	characteristic
211	C₄	—	2	1	no	—
212	C₄	—	17	2	no	—
213	C₄	—	17	2	no	—
214	C₄	—	34	1	no	—
215	C₄	C₂×C₈×#595	1	1	yes	characteristic
216	C₄	#11763772	1	1	yes	characteristic
217	C₄	C₂×#10587535	1	1	yes	characteristic
218	C₄	D₁₇⋊#108	1	1	yes	characteristic
219	C₂	—	34	2	no	—
220	C₂	C₈×C₄⋊#595	1	1	yes	characteristic
221	C₂	#14544586	1	1	yes	characteristic
222	C₂	C₄×#10587535	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₄⋊#595
commutator	C₄×C₁₇	C₂×C₄×C₈
Frattini	C₄²	C₂²×#595
Fitting	C₈²×C₁₇	C₄
socle	C₂²×C₁₇	C₄×C₄⋊C₄
prime radical	C₂²×D₁₇	C₄×Q₈
cosocle	C₄²×D₁₇	C₂³
hypercenter	C₈²	#595
hypocenter	C₁₇	C₈×#108
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈²

Complements

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

N	H ≅ G/N	type
33. #10587535	C₈	direct (N × H)
90. C₈×C₁₇	#108	semidirect
95. #3622	#108	semidirect
156. C₁₇	C₈×#108	semidirect
206. C₈	#10587535	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×#10587535	2
#14544332	2
C₈×#63243	2
#14543616	2
C₈²×D₁₇	2
C₈×#108	17

Subgroups — C8×#10587535 #17952390

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#10587535 #17952390