Subgroups — #364×#595 #17960977

Order 4352.

398 conjugacy classes of subgroups.

The subgroup lattice has 250 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545123	C₂	1	1	yes	maximal, characteristic
2	M₃₂×#595	C₂	1	2	yes	maximal
3	C₄×C₈×#595	C₂	1	1	yes	maximal, characteristic
4	#14543827	C₂	1	2	yes	maximal
5	D₁₇×#364	C₂	1	1	yes	maximal, characteristic
6	#11763865	C₂²	1	2	yes	—
7	C₄×#63242	C₄	1	1	yes	characteristic
8	C₂×C₈×#595	C₄	1	1	yes	characteristic
9	C₂×C₈×#595	C₄	1	1	yes	characteristic
10	C₂×C₈×#595	C₂²	1	1	yes	characteristic
11	C₂×C₈×#595	C₂²	1	1	yes	characteristic
12	C₄²×#595	C₄	1	1	yes	characteristic
13	#11763732	C₄	1	2	yes	complemented
14	#11763731	C₄	1	2	yes	complemented
15	#11763696	—	2	2	no	—
16	C₁₆×#595	—	2	2	no	—
17	M₃₂×D₁₇	C₂²	1	2	yes	—
18	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
19	#11762630	C₄	1	1	yes	characteristic, complemented
20	#11762629	C₄	1	2	yes	complemented
21	C₁₇×#364	C₄	1	1	yes	characteristic, complemented
22	C₂×C₄×#595	—	2	2	no	—
23	C₂×C₄×#595	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄×#595	C₂×C₄	1	1	yes	characteristic
25	C₂×#63242	C₂×C₄	1	1	yes	characteristic
26	C₂×#63242	C₂×C₄	1	1	yes	characteristic
27	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
28	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
29	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
30	C₄×#3624	—	2	2	no	—
31	#10587538	C₂×C₄	1	4	yes	—
32	C₈×#595	—	2	1	no	—
33	C₈×#595	—	2	1	no	—
34	C₈×#595	C₈	1	4	yes	—
35	C₈×#595	C₈	1	4	yes	—
36	C₈×#595	D₄	1	1	yes	characteristic
37	C₈×#595	D₄	1	1	yes	characteristic
38	C₈×#595	Q₈	1	1	yes	characteristic
39	C₈×#595	Q₈	1	1	yes	characteristic
40	#10587530	—	2	2	no	—
41	#10587529	—	2	2	no	—
42	C₁₇×M₃₂	C₂×C₄	1	2	yes	—
43	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
44	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
45	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
46	#10587483	C₂×C₄	1	2	yes	—
47	C₄×#3622	C₂×C₄	1	1	yes	characteristic
48	#10587469	—	2	2	no	—
49	C₁₆×D₁₇	—	2	2	no	—
50	C₂²×#595	—	2	1	no	—
51	C₂²×#595	M₁₆	1	2	yes	—
52	C₂×C₄×D₁₇	—	2	1	no	—
53	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
54	C₂×#3624	—	2	1	no	—
55	C₂×#3624	M₁₆	1	2	yes	—
56	C₄×#595	—	2	8	no	—
57	C₄×#595	—	2	1	no	—
58	C₄×#595	C₄⋊C₄	1	1	yes	characteristic
59	C₄×#595	C₄⋊C₄	1	1	yes	characteristic
60	C₄×#595	C₂×C₈	1	2	yes	—
61	C₄×#595	C₂×C₈	1	2	yes	—
62	#63242	—	2	1	no	—
63	#63242	C₄⋊C₄	1	1	yes	characteristic
64	#63242	C₄⋊C₄	1	1	yes	characteristic
65	#63242	C₂×C₈	1	2	yes	—
66	#63242	C₂×C₈	1	2	yes	—
67	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
68	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
69	C₄²×C₁₇	C₄²	1	1	yes	characteristic
70	C₄×Dic₁₇	—	2	1	no	—
71	C₄×Dic₁₇	C₄²	1	1	yes	characteristic
72	C₂×#3622	C₄²	1	1	yes	characteristic
73	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
74	C₈×D₁₇	C₂×C₈	1	2	yes	—
75	C₈×D₁₇	C₂×C₈	1	2	yes	—
76	C₈×D₁₇	C₂×D₄	1	1	yes	characteristic
77	C₈×D₁₇	C₂×Q₈	1	1	yes	characteristic
78	C₈×D₁₇	#41	1	1	yes	characteristic
79	C₈×D₁₇	#41	1	1	yes	characteristic
80	#63216	—	2	4	no	—
81	C₁₆×C₁₇	—	2	2	no	—
82	#63214	—	2	2	no	—
83	C₄×#364	—	17	1	no	maximal, Sylow
84	C₂²×D₁₇	C₂×M₁₆	1	1	yes	characteristic
85	C₂×#595	—	2	4	no	—
86	C₂×#595	—	2	2	no	—
87	C₂×#595	—	2	4	no	—
88	C₂×#595	C₄⋊C₈	1	2	yes	—
89	C₂×#595	C₄⋊C₈	1	2	yes	—
90	C₂×C₄×C₁₇	—	2	1	no	—
91	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
92	C₂×Dic₁₇	—	2	1	no	—
93	C₂×Dic₁₇	C₂×M₁₆	1	1	yes	characteristic
94	C₄×D₁₇	—	2	4	no	—
95	C₄×D₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
96	C₄×D₁₇	#117	1	1	yes	characteristic
97	C₄×D₁₇	C₂²×C₈	1	1	yes	characteristic
98	C₄×D₁₇	C₂²×C₈	1	1	yes	characteristic
99	#3624	—	2	2	no	—
100	#3624	C₄⋊C₈	1	2	yes	—
101	#3624	C₄⋊C₈	1	2	yes	—
102	C₈×C₁₇	C₄×C₈	1	2	yes	—
103	C₈×C₁₇	C₄×D₄	1	1	yes	characteristic
104	C₈×C₁₇	C₄×Q₈	1	1	yes	characteristic
105	#3622	C₄×C₈	1	2	yes	—
106	#3622	C₄×D₄	1	1	yes	characteristic
107	#3622	C₄×Q₈	1	1	yes	characteristic
108	C₂×#364	—	17	1	no	—
109	C₂×#364	—	17	1	no	—
110	C₄×M₃₂	—	17	2	no	—
111	C₄²×C₈	—	17	1	no	—
112	#1376	—	17	2	no	—
113	C₂²×C₁₇	C₄×M₁₆	1	1	yes	characteristic
114	C₂×D₁₇	—	2	2	no	—
115	C₂×D₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
116	C₂×D₁₇	#431	1	1	yes	characteristic
117	#595	—	2	4	no	—
118	#595	—	2	2	no	—
119	#595	#364	1	4	yes	direct product factor
120	C₄×C₁₇	—	2	2	no	—
121	C₄×C₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
122	C₄×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
123	Dic₁₇	—	2	2	no	—
124	Dic₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
125	Dic₁₇	#431	1	1	yes	characteristic
126	C₂×M₃₂	—	17	2	no	—
127	C₂×M₃₂	—	17	2	no	—
128	C₂×C₄×C₈	—	17	1	no	—
129	C₂×C₄×C₈	—	17	1	no	—
130	C₂×C₄×C₈	—	17	1	no	—
131	C₂×C₄×C₈	—	17	1	no	—
132	C₂×C₄×C₈	—	17	1	no	—
133	C₂×C₄×C₈	—	17	1	no	—
134	C₄³	—	17	1	no	—
135	#364	—	17	2	no	—
136	#364	—	17	2	no	—
137	#364	—	17	2	no	—
138	#364	—	17	1	no	—
139	#364	#595	1	1	yes	characteristic, direct product factor
140	#346	—	34	2	no	—
141	C₄×C₁₆	—	34	2	no	—
142	C₂×C₁₇	—	2	1	no	—
143	C₂×C₁₇	C₄×C₄⋊C₈	1	1	yes	characteristic
144	D₁₇	—	2	1	no	—
145	D₁₇	C₂×#364	1	2	yes	—
146	C₂²×C₈	—	17	1	no	—
147	C₂²×C₈	—	17	1	no	—
148	C₂²×C₈	—	17	1	no	—
149	C₂²×C₈	—	17	1	no	—
150	C₂×C₄²	—	17	1	no	—
151	C₂×C₄²	—	17	1	no	—
152	C₂×C₄²	—	17	1	no	—
153	C₂×C₄²	—	34	2	no	—
154	M₃₂	—	17	4	no	—
155	M₃₂	—	17	2	no	—
156	M₃₂	—	34	2	no	—
157	M₃₂	—	34	2	no	—
158	M₃₂	C₂×#595	1	2	yes	—
159	C₂×C₁₆	—	34	2	no	—
160	C₂×C₁₆	—	34	2	no	—
161	C₄×C₈	—	17	1	no	—
162	C₄×C₈	—	17	1	no	—
163	C₄×C₈	—	17	4	no	—
164	C₄×C₈	—	17	4	no	—
165	C₄×C₈	—	17	1	no	—
166	C₄×C₈	—	17	1	no	—
167	C₄×C₈	—	17	1	no	—
168	C₄×C₈	—	17	1	no	—
169	C₄×C₈	—	17	1	no	—
170	C₄×C₈	—	34	1	no	—
171	C₄×C₈	—	34	1	no	—
172	C₄×C₈	—	34	2	no	—
173	C₄×C₈	C₂×#595	1	1	yes	characteristic
174	C₁₇	C₄×#364	1	1	yes	characteristic, complemented, Sylow
175	C₂²×C₄	—	17	1	no	—
176	C₂²×C₄	—	17	2	no	—
177	C₂²×C₄	—	34	1	no	—
178	C₂²×C₄	—	34	1	no	—
179	C₂×C₈	—	17	1	no	—
180	C₂×C₈	—	17	1	no	—
181	C₂×C₈	—	17	2	no	—
182	C₂×C₈	—	17	2	no	—
183	C₂×C₈	—	17	1	no	—
184	C₂×C₈	—	17	1	no	—
185	C₂×C₈	—	17	1	no	—
186	C₂×C₈	—	17	1	no	—
187	C₂×C₈	—	17	1	no	—
188	C₂×C₈	—	17	1	no	—
189	C₂×C₈	—	17	2	no	—
190	C₂×C₈	—	17	2	no	—
191	C₂×C₈	—	17	2	no	—
192	C₂×C₈	—	34	1	no	—
193	C₂×C₈	—	34	1	no	—
194	C₂×C₈	C₄×#595	1	1	yes	characteristic
195	C₂×C₈	C₂²×#595	1	1	yes	characteristic
196	C₄²	—	17	1	no	—
197	C₄²	—	17	1	no	—
198	C₄²	—	17	2	no	—
199	C₄²	—	17	2	no	—
200	C₄²	—	17	1	no	—
201	C₄²	—	34	1	no	—
202	C₄²	—	34	1	no	—
203	C₄²	—	34	8	no	—
204	C₄²	C₄×#595	1	1	yes	characteristic
205	C₁₆	—	2	2	no	—
206	C₁₆	—	34	4	no	—
207	C₁₆	—	34	2	no	—
208	C₂³	—	17	1	no	—
209	C₂×C₄	—	2	1	no	—
210	C₂×C₄	—	17	2	no	—
211	C₂×C₄	—	17	1	no	—
212	C₂×C₄	—	17	1	no	—
213	C₂×C₄	—	17	1	no	—
214	C₂×C₄	—	17	1	no	—
215	C₂×C₄	—	17	1	no	—
216	C₂×C₄	—	17	2	no	—
217	C₂×C₄	—	34	4	no	—
218	C₂×C₄	—	34	4	no	—
219	C₂×C₄	—	34	2	no	—
220	C₂×C₄	—	34	4	no	—
221	C₂×C₄	—	34	1	no	—
222	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
223	C₈	—	17	2	no	—
224	C₈	—	17	2	no	—
225	C₈	—	17	1	no	—
226	C₈	—	17	1	no	—
227	C₈	—	17	2	no	—
228	C₈	—	34	2	no	—
229	C₈	C₈×#595	1	2	yes	—
230	C₈	D₄×#595	1	1	yes	characteristic
231	C₈	Q₈×#595	1	1	yes	characteristic
232	C₂²	—	17	1	no	—
233	C₂²	—	17	1	no	—
234	C₂²	—	34	2	no	—
235	C₂²	M₁₆×#595	1	1	yes	characteristic
236	C₄	—	2	2	no	—
237	C₄	—	17	4	no	—
238	C₄	—	17	1	no	—
239	C₄	—	17	1	no	—
240	C₄	—	34	2	no	—
241	C₄	—	34	2	no	—
242	C₄	—	34	4	no	—
243	C₄	C₄⋊C₄×#595	1	1	yes	characteristic
244	C₄	C₂×C₈×#595	1	1	yes	characteristic
245	C₂	—	2	1	no	—
246	C₂	—	17	2	no	—
247	C₂	—	34	1	no	—
248	C₂	C₄⋊C₈×#595	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₄×#595
commutator	C₄×C₁₇	C₂×C₄×C₈
Frattini	C₂×C₈	C₂²×#595
Fitting	C₁₇×#364	C₄
socle	C₂×C₁₇	C₄×C₄⋊C₈
prime radical	C₂²×D₁₇	C₂×M₁₆
cosocle	C₂×C₈×D₁₇	C₂³
hypercenter	#364	#595
hypocenter	C₁₇	C₄×#364
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
13. #11763732	C₄	semidirect
14. #11763731	C₄	semidirect
19. #11762630	C₄	semidirect
20. #11762629	C₄	semidirect
21. C₁₇×#364	C₄	semidirect
119. #595	#364	direct (N × H)
139. #364	#595	direct (N × H)
174. 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
#14545123	2
M₃₂×#595	2
C₄×C₈×#595	2
#14543827	2
D₁₇×#364	2
C₄×#364	17