Subgroups — #95×#3622 #16939481

Order 4352.

1174 conjugacy classes of subgroups.

The subgroup lattice has 174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×#3622	C₂	1	3	yes	maximal
2	C₂×#11762564	C₂	1	3	yes	maximal
3	C₄×C₁₇×#95	C₂	1	1	yes	maximal, characteristic
4	C₂³×#3622	C₂²	1	3	yes	—
5	C₂³×#3622	C₂²	1	1	yes	characteristic
6	C₂×C₄×#3622	—	2	12	no	—
7	C₂×C₄×#3622	C₄	1	12	yes	complemented
8	#11762564	C₄	1	12	yes	complemented
9	C₂²×C₄²×C₁₇	C₂²	1	3	yes	—
10	C₂×C₁₇×#95	C₄	1	4	yes	—
11	C₂³×C₄×C₁₇	C₂×C₄	1	6	yes	—
12	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
13	C₂×C₄²×C₁₇	—	2	6	no	—
14	C₂×C₄²×C₁₇	—	2	6	no	—
15	C₂×C₄²×C₁₇	C₂×C₄	1	6	yes	—
16	C₂×C₄²×C₁₇	C₂×C₄	1	6	yes	—
17	C₂²×#3622	—	2	6	no	—
18	C₂²×#3622	—	2	3	no	—
19	C₂²×#3622	—	2	3	no	—
20	C₂²×#3622	C₂×C₄	1	6	yes	—
21	C₂²×#3622	C₂×C₄	1	12	yes	—
22	C₂²×#3622	C₂×C₄	1	6	yes	—
23	C₂²×#3622	D₄	1	6	yes	—
24	C₂²×#3622	Q₈	1	2	yes	—
25	C₁₇×#95	C₈	1	16	yes	complemented
26	C₄×#3622	—	2	24	no	—
27	C₂⁴×C₁₇	C₂²×C₄	1	1	yes	characteristic
28	C₂²×C₄×C₁₇	—	2	12	no	—
29	C₂²×C₄×C₁₇	—	2	12	no	—
30	C₂²×C₄×C₁₇	C₄²	1	12	yes	—
31	C₂²×C₄×C₁₇	C₂×C₈	1	24	yes	—
32	C₂²×C₄×C₁₇	C₂²×C₄	1	3	yes	—
33	C₂²×C₄×C₁₇	C₂²×C₄	1	3	yes	—
34	C₂²×C₄×C₁₇	C₂×D₄	1	3	yes	—
35	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
36	C₂²×C₄×C₁₇	#41	1	3	yes	—
37	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
38	C₄²×C₁₇	—	2	6	no	—
39	C₄²×C₁₇	—	2	6	no	—
40	C₄²×C₁₇	—	2	12	no	—
41	C₂×#3622	—	2	6	no	—
42	C₂×#3622	—	2	6	no	—
43	C₂×#3622	—	2	12	no	—
44	C₂×#3622	—	2	12	no	—
45	C₂×#3622	C₄²	1	12	yes	—
46	C₂×#3622	C₄²	1	4	yes	—
47	C₂×#3622	C₂²⋊C₄	1	12	yes	—
48	C₂×#3622	C₄⋊C₄	1	12	yes	—
49	C₈×#95	—	17	1	no	maximal, Sylow
50	C₂³×C₁₇	C₂×C₄²	1	3	yes	—
51	C₂³×C₁₇	C₄×D₄	1	3	yes	—
52	C₂³×C₁₇	C₄×Q₈	1	1	yes	characteristic
53	C₂³×C₁₇	C₂²×C₈	1	4	yes	—
54	C₂³×C₁₇	#131	1	4	yes	—
55	C₂×C₄×C₁₇	—	2	12	no	—
56	C₂×C₄×C₁₇	—	2	12	no	—
57	C₂×C₄×C₁₇	—	2	48	no	—
58	C₂×C₄×C₁₇	C₄×C₈	1	24	yes	complemented
59	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
60	C₂×C₄×C₁₇	C₂×C₄²	1	3	yes	—
61	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	3	yes	—
62	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	3	yes	—
63	C₂×C₄×C₁₇	#117	1	3	yes	—
64	C₂×C₄×C₁₇	#117	1	3	yes	—
65	C₂×C₄×C₁₇	C₄×D₄	1	6	yes	—
66	C₂×C₄×C₁₇	C₄×D₄	1	3	yes	—
67	C₂×C₄×C₁₇	C₄×Q₈	1	3	yes	—
68	#3622	—	2	12	no	—
69	#3622	#95	1	8	yes	direct product factor
70	C₂²×C₄×C₈	—	17	3	no	—
71	C₂×#336	—	17	3	no	—
72	C₄×#95	D₁₇	1	1	yes	characteristic
73	C₂²×C₁₇	C₄³	1	1	yes	characteristic
74	C₂²×C₁₇	C₄×C₂²⋊C₄	1	3	yes	—
75	C₂²×C₁₇	C₄×C₄⋊C₄	1	3	yes	—
76	C₂²×C₁₇	C₂×C₄×C₈	1	6	yes	—
77	C₂²×C₁₇	#405	1	6	yes	—
78	C₂²×C₁₇	C₈×D₄	1	12	yes	—
79	C₂²×C₁₇	C₈×Q₈	1	4	yes	—
80	C₄×C₁₇	—	2	24	no	—
81	C₄×C₁₇	C₂×#95	1	1	yes	characteristic
82	C₄×C₁₇	#376	1	1	yes	characteristic
83	C₄×C₁₇	C₄×C₂²⋊C₄	1	3	yes	—
84	C₄×C₁₇	C₄×C₄⋊C₄	1	3	yes	—
85	C₂³×C₈	—	17	1	no	—
86	C₂³×C₈	—	17	3	no	—
87	C₂²×C₄²	C₂×D₁₇	1	3	yes	—
88	C₂×C₄×C₈	—	17	12	no	—
89	C₂×C₄×C₈	—	34	12	no	—
90	C₂×#95	Dic₁₇	1	4	yes	—
91	#336	—	17	12	no	—
92	C₂×C₁₇	C₄×#95	1	1	yes	characteristic
93	C₂×C₁₇	C₄²×C₈	1	1	yes	characteristic
94	C₂×C₁₇	#1726	1	1	yes	characteristic
95	C₂×C₁₇	C₈×C₂²⋊C₄	1	6	yes	—
96	C₂×C₁₇	C₈×C₄⋊C₄	1	6	yes	—
97	C₂³×C₄	C₂×Dic₁₇	1	6	yes	—
98	C₂³×C₄	C₂²×D₁₇	1	1	yes	characteristic
99	C₂²×C₈	—	17	6	no	—
100	C₂²×C₈	—	17	6	no	—
101	C₂²×C₈	—	17	2	no	—
102	C₂²×C₈	—	17	12	no	—
103	C₂²×C₈	—	17	6	no	—
104	C₂²×C₈	—	34	6	no	—
105	C₂²×C₈	—	34	3	no	—
106	C₂²×C₈	—	34	3	no	—
107	C₂×C₄²	—	2	6	no	—
108	C₂×C₄²	—	2	6	no	—
109	C₂×C₄²	C₄×D₁₇	1	6	yes	—
110	C₂×C₄²	C₄×D₁₇	1	6	yes	—
111	C₄×C₈	—	34	24	no	—
112	#95	#3622	1	16	yes	direct product factor
113	C₁₇	C₈×#95	1	1	yes	characteristic, complemented, Sylow
114	C₂⁴	C₂²×Dic₁₇	1	1	yes	characteristic
115	C₂²×C₄	—	2	12	no	—
116	C₂²×C₄	—	2	12	no	—
117	C₂²×C₄	C₂×#3622	1	24	yes	—
118	C₂²×C₄	C₄×Dic₁₇	1	12	yes	—
119	C₂²×C₄	C₂×C₄×D₁₇	1	3	yes	—
120	C₂²×C₄	C₂×C₄×D₁₇	1	3	yes	—
121	C₂²×C₄	D₄×D₁₇	1	3	yes	—
122	C₂²×C₄	#63254	1	3	yes	—
123	C₂²×C₄	Q₈×D₁₇	1	1	yes	characteristic
124	C₂²×C₄	#63256	1	1	yes	characteristic
125	C₂×C₈	—	17	4	no	—
126	C₂×C₈	—	17	12	no	—
127	C₂×C₈	—	17	12	no	—
128	C₂×C₈	—	17	12	no	—
129	C₂×C₈	—	34	6	no	—
130	C₂×C₈	—	34	12	no	—
131	C₂×C₈	—	34	6	no	—
132	C₂×C₈	—	34	12	no	—
133	C₄²	—	2	6	no	—
134	C₄²	—	2	6	no	—
135	C₄²	—	2	12	no	—
136	C₂³	C₂²×#3622	1	4	yes	—
137	C₂³	C₂×C₄×Dic₁₇	1	3	yes	—
138	C₂³	D₄×Dic₁₇	1	3	yes	—
139	C₂³	Q₈×Dic₁₇	1	1	yes	characteristic
140	C₂³	#10587634	1	4	yes	—
141	C₂×C₄	—	2	12	no	—
142	C₂×C₄	—	2	48	no	—
143	C₂×C₄	—	2	12	no	—
144	C₂×C₄	C₄×#3622	1	24	yes	complemented
145	C₂×C₄	C₄²×D₁₇	1	1	yes	characteristic
146	C₂×C₄	C₄²×D₁₇	1	3	yes	—
147	C₂×C₄	#10587563	1	3	yes	—
148	C₂×C₄	C₂²⋊C₄×D₁₇	1	3	yes	—
149	C₂×C₄	#10587567	1	6	yes	—
150	C₂×C₄	#10587573	1	3	yes	—
151	C₂×C₄	C₄⋊C₄×D₁₇	1	3	yes	—
152	C₂×C₄	#10587578	1	3	yes	—
153	C₂×C₄	#10587579	1	3	yes	—
154	C₈	—	17	8	no	—
155	C₈	—	34	12	no	—
156	C₂²	C₄²×Dic₁₇	1	1	yes	characteristic
157	C₂²	C₂²⋊C₄×Dic₁₇	1	3	yes	—
158	C₂²	C₄⋊C₄×Dic₁₇	1	3	yes	—
159	C₂²	C₂×C₄×#3622	1	6	yes	—
160	C₂²	#11762765	1	6	yes	—
161	C₂²	D₄×#3622	1	12	yes	—
162	C₂²	Q₈×#3622	1	4	yes	—
163	C₄	—	2	24	no	—
164	C₄	#95×D₁₇	1	1	yes	characteristic
165	C₄	#11762654	1	1	yes	characteristic
166	C₄	#11762656	1	3	yes	—
167	C₄	#11762660	1	3	yes	—
168	C₂	#95×Dic₁₇	1	1	yes	characteristic
169	C₂	C₄²×#3622	1	1	yes	characteristic
170	C₂	#14528471	1	1	yes	characteristic
171	C₂	C₂²⋊C₄×#3622	1	6	yes	—
172	C₂	C₄⋊C₄×#3622	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂³×C₄	C₂²×D₁₇
commutator	C₂×C₁₇	C₄²×C₈
Fitting	C₄×C₁₇×#95	C₂
socle, prime radical	C₂⁴×C₁₇	C₂²×C₄
cosocle	C₂³×C₄×C₁₇	C₂³
hypercenter	C₄×#95	D₁₇
hypocenter	C₁₇	C₈×#95
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂³×C₄ ◁ C₄×#95

Complements

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

N	H ≅ G/N	type
7. C₂×C₄×#3622	C₄	semidirect
8. #11762564	C₄	semidirect
25. C₁₇×#95	C₈	semidirect
58. C₂×C₄×C₁₇	C₄×C₈	semidirect
69. #3622	#95	direct (N × H)
112. #95	#3622	direct (N × H)
113. C₁₇	C₈×#95	semidirect
144. C₂×C₄	C₄×#3622	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×#3622	2
C₂×#11762564	2
C₄×C₁₇×#95	2
C₈×#95	17