Subgroups — #97×#3633 #17981559

Order 4352.

606 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545918	C₂	1	1	yes	maximal, characteristic
2	C₄²×#3633	C₂	1	1	yes	maximal, characteristic
3	C₂×#11763893	C₂	1	2	yes	maximal
4	C₂×C₈×#3633	C₂	1	2	yes	maximal
5	#97×#595	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×#3633	C₄	1	4	yes	—
7	C₂×C₄×#3633	C₂²	1	1	yes	characteristic
8	C₂×C₄×#3633	C₂²	1	2	yes	—
9	C₂×C₄×#3633	C₂²	1	1	yes	characteristic
10	(C₂×#3633)⋊C₄	C₄	1	4	yes	—
11	#11763893	C₄	1	8	yes	complemented
12	C₈×#3633	C₄	1	8	yes	complemented
13	#11763768	C₄	1	1	yes	characteristic
14	C₂×#10587532	C₄	1	2	yes	—
15	C₂×C₈×#595	C₂²	1	2	yes	—
16	C₄²×#595	C₂²	1	1	yes	characteristic
17	#97×D₁₇	C₄	1	1	yes	characteristic
18	C₂²×#3633	C₂×C₄	1	4	yes	—
19	C₂²×#3633	C₂×C₄	1	2	yes	—
20	C₂²×#3633	C₂×C₄	1	2	yes	—
21	C₂×C₄×#595	C₂×C₄	1	2	yes	—
22	C₂×C₄×#595	C₂×C₄	1	2	yes	—
23	C₂×C₄×#595	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄×#595	C₂³	1	1	yes	characteristic
25	C₂×#63242	C₂×C₄	1	2	yes	—
26	C₄×#3633	—	2	8	no	—
27	C₄×#3633	C₂×C₄	1	4	yes	—
28	C₄×#3633	C₂×C₄	1	4	yes	—
29	C₄×#3633	C₂×C₄	1	4	yes	—
30	C₄×#3633	C₂×C₄	1	4	yes	—
31	C₂×C₈×D₁₇	C₂×C₄	1	2	yes	—
32	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
33	#10587542	C₈	1	4	yes	complemented
34	#10587532	C₈	1	8	yes	complemented
35	C₈×#595	C₂×C₄	1	4	yes	—
36	C₈×#595	C₂×C₄	1	4	yes	—
37	C₁₇×#97	C₈	1	1	yes	characteristic, complemented
38	#10587486	C₈	1	2	yes	complemented
39	#10587474	C₈	1	1	yes	characteristic, complemented
40	C₂²×#595	C₄²	1	2	yes	—
41	C₂²×#595	C₂²×C₄	1	1	yes	characteristic
42	C₂²×#595	C₂²×C₄	1	1	yes	characteristic
43	C₂×#3633	—	2	4	no	—
44	C₂×#3633	—	2	8	no	—
45	C₂×#3633	C₄²	1	4	yes	—
46	C₂×#3633	C₄²	1	8	yes	—
47	C₂×#3633	C₄²	1	4	yes	—
48	C₂×#3633	M₁₆	1	8	yes	—
49	C₂×C₄×D₁₇	C₄²	1	2	yes	—
50	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
51	C₂×#3624	C₂×C₈	1	4	yes	—
52	C₄×#595	—	2	4	no	—
53	C₄×#595	—	2	4	no	—
54	C₄×#595	C₂×C₈	1	4	yes	—
55	C₄×#595	C₂²×C₄	1	2	yes	—
56	C₄×#595	C₂²×C₄	1	2	yes	—
57	#63242	C₄²	1	4	yes	—
58	#63242	C₂×C₈	1	4	yes	—
59	C₂×C₈×C₁₇	C₂×C₈	1	2	yes	—
60	C₄²×C₁₇	C₂×C₈	1	1	yes	characteristic
61	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
62	C₄×Dic₁₇	C₂×C₈	1	2	yes	—
63	C₂×#3622	C₂×C₈	1	2	yes	—
64	C₈×D₁₇	C₄²	1	4	yes	—
65	C₈×D₁₇	C₂×C₈	1	4	yes	—
66	C₈×#97	—	17	1	no	maximal, Sylow
67	C₂²×D₁₇	C₂×C₄²	1	1	yes	characteristic
68	C₂×#595	—	2	2	no	—
69	C₂×#595	—	2	2	no	—
70	C₂×#595	C₄×C₈	1	4	yes	—
71	C₂×#595	C₂×C₄²	1	1	yes	characteristic
72	C₂×#595	C₂×C₄²	1	1	yes	characteristic
73	C₂×#595	C₂×C₄²	1	2	yes	—
74	C₂×#595	C₂×M₁₆	1	4	yes	—
75	C₂×#595	#131	1	4	yes	—
76	#3633	—	2	4	no	—
77	#3633	—	2	8	no	—
78	#3633	#97	1	8	yes	direct product factor
79	C₂×C₄×C₁₇	C₄×C₈	1	2	yes	—
80	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
81	C₂×Dic₁₇	C₄×C₈	1	2	yes	—
82	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
83	C₄×D₁₇	—	2	2	no	—
84	C₄×D₁₇	—	2	2	no	—
85	C₄×D₁₇	C₂×C₄²	1	2	yes	—
86	C₄×D₁₇	C₂²×C₈	1	2	yes	—
87	#3624	C₄×C₈	1	8	yes	complemented
88	C₈×C₁₇	C₄×C₈	1	4	yes	complemented
89	#3622	C₄×C₈	1	4	yes	complemented
90	#1744	—	17	1	no	—
91	C₄×#97	—	17	1	no	—
92	C₄²×C₈	—	17	1	no	—
93	C₂×#322	—	17	2	no	—
94	C₂×C₈²	—	17	2	no	—
95	C₂²×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
96	C₂×D₁₇	C₄³	1	1	yes	characteristic
97	C₂×D₁₇	C₂×C₄×C₈	1	1	yes	characteristic
98	C₂×D₁₇	C₄×M₁₆	1	2	yes	—
99	C₂×D₁₇	#405	1	2	yes	—
100	#595	—	2	4	no	—
101	#595	C₂×#97	1	2	yes	—
102	#595	C₄×M₁₆	1	2	yes	—
103	#595	#405	1	4	yes	—
104	C₄×C₁₇	—	2	2	no	—
105	C₄×C₁₇	C₂×C₄×C₈	1	2	yes	—
106	Dic₁₇	—	2	2	no	—
107	Dic₁₇	C₂×C₄×C₈	1	2	yes	—
108	C₂×#97	—	17	2	no	—
109	C₂×#97	—	17	1	no	—
110	C₂×#97	—	17	1	no	—
111	C₂×C₄×C₈	—	17	2	no	—
112	C₂×C₄×C₈	—	17	1	no	—
113	C₂×C₄×C₈	—	17	2	no	—
114	C₂×C₄×C₈	—	17	1	no	—
115	C₂×C₄×C₈	—	17	4	no	—
116	C₄³	—	17	1	no	—
117	#336	—	17	4	no	—
118	#322	—	17	8	no	—
119	C₈²	—	17	8	no	—
120	C₂×C₁₇	C₈×M₁₆	1	2	yes	—
121	C₂×C₁₇	C₄²×C₈	1	1	yes	characteristic
122	D₁₇	C₈×M₁₆	1	2	yes	—
123	D₁₇	C₄×#97	1	1	yes	characteristic
124	D₁₇	#1726	1	1	yes	characteristic
125	C₂²×C₈	—	17	2	no	—
126	C₂²×C₈	—	17	2	no	—
127	C₂²×C₈	—	17	2	no	—
128	C₂²×C₈	—	17	4	no	—
129	C₂²×C₈	—	17	2	no	—
130	C₂×C₄²	—	17	1	no	—
131	C₂×C₄²	—	17	1	no	—
132	C₂×C₄²	—	17	1	no	—
133	C₂×C₄²	—	17	2	no	—
134	C₂×C₄²	—	17	2	no	—
135	#97	—	17	8	no	—
136	#97	—	17	4	no	—
137	#97	—	17	2	no	—
138	#97	—	17	1	no	—
139	#97	#3633	1	1	yes	characteristic, direct product factor
140	C₄×C₈	—	17	4	no	—
141	C₄×C₈	—	17	4	no	—
142	C₄×C₈	—	17	4	no	—
143	C₄×C₈	—	17	4	no	—
144	C₄×C₈	—	17	4	no	—
145	C₄×C₈	—	17	4	no	—
146	C₄×C₈	—	34	8	no	—
147	C₁₇	C₈×#97	1	1	yes	characteristic, complemented, Sylow
148	C₂²×C₄	—	17	1	no	—
149	C₂²×C₄	—	17	1	no	—
150	C₂²×C₄	—	17	1	no	—
151	C₂²×C₄	—	17	2	no	—
152	C₂²×C₄	—	17	2	no	—
153	C₂×C₈	—	17	4	no	—
154	C₂×C₈	—	17	4	no	—
155	C₂×C₈	—	17	4	no	—
156	C₂×C₈	—	17	4	no	—
157	C₂×C₈	—	17	8	no	—
158	C₂×C₈	—	17	2	no	—
159	C₂×C₈	—	17	4	no	—
160	C₂×C₈	—	17	4	no	—
161	C₂×C₈	—	17	8	no	—
162	C₂×C₈	—	17	4	no	—
163	C₂×C₈	—	34	4	no	—
164	C₂×C₈	—	34	8	no	—
165	C₂×C₈	C₂×#3633	1	2	yes	—
166	C₄²	—	17	4	no	—
167	C₄²	—	17	2	no	—
168	C₄²	—	17	2	no	—
169	C₄²	—	17	2	no	—
170	C₄²	—	17	1	no	—
171	C₄²	—	34	4	no	—
172	C₄²	—	34	4	no	—
173	C₄²	C₂×#3633	1	1	yes	characteristic
174	C₂³	—	17	1	no	—
175	C₂×C₄	—	17	1	no	—
176	C₂×C₄	—	17	1	no	—
177	C₂×C₄	—	17	2	no	—
178	C₂×C₄	—	17	4	no	—
179	C₂×C₄	—	17	4	no	—
180	C₂×C₄	—	17	1	no	—
181	C₂×C₄	—	17	2	no	—
182	C₂×C₄	—	17	2	no	—
183	C₂×C₄	—	17	4	no	—
184	C₂×C₄	—	17	2	no	—
185	C₂×C₄	—	34	2	no	—
186	C₂×C₄	—	34	2	no	—
187	C₂×C₄	—	34	2	no	—
188	C₂×C₄	—	34	2	no	—
189	C₂×C₄	C₄×#3633	1	2	yes	—
190	C₂×C₄	C₂²×#3633	1	1	yes	characteristic
191	C₈	—	17	8	no	—
192	C₈	—	17	8	no	—
193	C₈	—	17	4	no	—
194	C₈	—	34	4	no	—
195	C₈	—	34	8	no	—
196	C₈	C₄×#3633	1	4	yes	complemented
197	C₂²	—	17	2	no	—
198	C₂²	—	17	2	no	—
199	C₂²	—	17	1	no	—
200	C₂²	—	17	1	no	—
201	C₂²	C₂×C₄×#3633	1	1	yes	characteristic
202	C₄	—	2	2	no	—
203	C₄	—	17	2	no	—
204	C₄	—	17	2	no	—
205	C₄	—	17	4	no	—
206	C₄	—	17	2	no	—
207	C₄	—	34	4	no	—
208	C₄	—	34	2	no	—
209	C₄	C₂×C₄×#3633	1	2	yes	—
210	C₂	—	17	1	no	—
211	C₂	—	17	1	no	—
212	C₂	—	17	2	no	—
213	C₂	M₁₆×#3633	1	2	yes	—
214	C₂	C₄²×#3633	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#3633
commutator	C₂×C₁₇	C₄²×C₈
Fitting	C₁₇×#97	C₈
socle	C₂²×C₁₇	C₂×C₄×C₈
prime radical	C₂²×D₁₇	C₂×C₄²
cosocle	C₂×C₄×#595	C₂³
hypercenter	#97	#3633
hypocenter	C₁₇	C₈×#97
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ #97

Complements

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

N	H ≅ G/N	type
11. #11763893	C₄	semidirect
12. C₈×#3633	C₄	semidirect
33. #10587542	C₈	semidirect
34. #10587532	C₈	semidirect
37. C₁₇×#97	C₈	semidirect
38. #10587486	C₈	semidirect
39. #10587474	C₈	semidirect
78. #3633	#97	direct (N × H)
87. #3624	C₄×C₈	semidirect
88. C₈×C₁₇	C₄×C₈	semidirect
89. #3622	C₄×C₈	semidirect
139. #97	#3633	direct (N × H)
147. C₁₇	C₈×#97	semidirect
196. C₈	C₄×#3633	semidirect

Maximal subgroups

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

subgroup	index
#14545918	2
C₄²×#3633	2
C₂×#11763893	2
C₂×C₈×#3633	2
#97×#595	2
C₈×#97	17