Subgroups — #17961021

Order 4352.

334 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11763731	C₂	1	1	yes	maximal, characteristic
2	#14544993	C₂	1	2	yes	maximal
3	C₂×#11763695	C₂	1	1	yes	maximal, characteristic
4	#14543838	C₂	1	2	yes	maximal
5	#14528665	C₂	1	1	yes	maximal, characteristic
6	C₂×#10587538	C₂²	1	2	yes	—
7	C₂²×#63216	C₂²	1	1	yes	characteristic
8	C₂²×#63216	C₂²	1	1	yes	characteristic
9	#11763731	C₄	1	4	yes	complemented
10	#11763697	—	2	2	no	—
11	#11763695	C₄	1	4	yes	complemented
12	C₄×#63216	—	2	2	no	—
13	C₂×#10587490	C₄	1	1	yes	characteristic
14	#11762765	C₂²	1	2	yes	—
15	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
16	#11762568	C₄	1	2	yes	—
17	C₁₇×#427	C₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
19	C₁₇×#117	C₂×C₄	1	2	yes	—
20	C₂×C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
21	C₂×#63223	C₂×C₄	1	2	yes	—
22	C₂²×#3622	C₂³	1	1	yes	characteristic
23	#10587538	—	2	2	no	—
24	#10587538	C₂×C₄	1	4	yes	—
25	C₂×#63216	—	2	2	no	—
26	C₂×#63216	—	2	1	no	—
27	C₂×#63216	—	2	1	no	—
28	C₂×#63216	C₂×C₄	1	2	yes	—
29	C₂×#63216	C₂×C₄	1	2	yes	—
30	C₂×#63216	D₄	1	1	yes	characteristic
31	C₂×#63216	D₄	1	1	yes	characteristic
32	C₂×#63216	Q₈	1	2	yes	—
33	C₁₇×#107	C₈	1	2	yes	—
34	C₁₇×#106	C₈	1	2	yes	—
35	#10587490	C₈	1	4	yes	—
36	C₈×Dic₁₇	C₂×C₄	1	2	yes	—
37	C₈×Dic₁₇	C₂×C₄	1	2	yes	—
38	#10587474	—	2	2	no	—
39	C₄×#3622	—	2	2	no	—
40	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
41	C₂²×Dic₁₇	—	2	1	no	—
42	C₂×C₈×C₁₇	C₄²	1	2	yes	—
43	C₂×C₈×C₁₇	C₂×C₈	1	2	yes	—
44	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
45	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
46	C₄⋊C₄×C₁₇	C₂×C₈	1	4	yes	—
47	C₂²⋊C₄×C₁₇	—	2	2	no	—
48	C₄²×C₁₇	—	2	2	no	—
49	C₄×Dic₁₇	—	2	1	no	—
50	C₄×Dic₁₇	C₄²	1	2	yes	—
51	#63223	—	2	2	no	—
52	#63223	C₂×C₈	1	4	yes	—
53	C₂×#3622	—	2	2	no	—
54	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
55	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
56	C₂×#3622	C₂×D₄	1	1	yes	characteristic
57	C₂×#3622	C₂×Q₈	1	1	yes	characteristic
58	C₂×#3622	#41	1	1	yes	characteristic
59	C₂×#3622	#41	1	1	yes	characteristic
60	#63216	—	2	2	no	—
61	#63216	—	2	4	no	—
62	#63216	C₄⋊C₄	1	2	yes	—
63	#63216	C₄⋊C₄	1	2	yes	—
64	#12664	—	17	1	no	maximal, Sylow
65	C₂³×C₁₇	#131	1	1	yes	characteristic
66	C₂×C₄×C₁₇	—	2	4	no	—
67	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
68	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
69	C₂×C₄×C₁₇	C₄×Q₈	1	1	yes	characteristic
70	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
71	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
72	C₂×C₄×C₁₇	#131	1	1	yes	characteristic
73	C₂×Dic₁₇	—	2	4	no	—
74	C₂×Dic₁₇	—	2	2	no	—
75	C₈×C₁₇	C₄×C₈	1	2	yes	—
76	C₈×C₁₇	C₄×C₈	1	2	yes	—
77	#3622	—	2	4	no	—
78	#3622	C₂×C₄⋊C₄	1	1	yes	characteristic
79	#3622	#117	1	1	yes	characteristic
80	#3622	C₄×D₄	1	1	yes	characteristic
81	#3622	C₄×Q₈	1	1	yes	characteristic
82	C₂×#364	—	17	1	no	—
83	#2108	—	17	2	no	—
84	C₂×C₄×C₁₆	—	17	1	no	—
85	#1772	—	17	1	no	—
86	#1379	—	17	2	no	—
87	C₂²×C₁₇	—	2	2	no	—
88	C₂²×C₁₇	#405	1	1	yes	characteristic
89	C₂²×C₁₇	C₈×D₄	1	1	yes	characteristic
90	C₂²×C₁₇	C₈×Q₈	1	1	yes	characteristic
91	C₄×C₁₇	—	4	4	no	—
92	C₄×C₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
93	C₄×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
94	C₄×C₁₇	C₈×D₄	1	1	yes	characteristic
95	C₄×C₁₇	C₈×Q₈	1	1	yes	characteristic
96	Dic₁₇	—	2	4	no	—
97	C₂×M₃₂	—	17	2	no	—
98	C₂²×C₁₆	—	17	1	no	—
99	C₂²×C₁₆	—	17	1	no	—
100	C₂×#108	—	17	1	no	—
101	#427	#595	1	1	yes	characteristic
102	#405	—	17	2	no	—
103	C₂×C₄×C₈	—	17	1	no	—
104	#364	—	17	4	no	—
105	#346	—	34	2	no	—
106	C₄×C₁₆	—	17	4	no	—
107	C₄×C₁₆	—	34	2	no	—
108	#339	—	17	2	no	—
109	C₂×C₁₇	—	2	1	no	—
110	C₂×C₁₇	—	2	1	no	—
111	C₂×C₁₇	C₈×C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₁₇	#2170	1	2	yes	—
113	C₂×M₁₆	—	17	2	no	—
114	C₂²×C₈	—	17	1	no	—
115	C₂²×C₈	C₂×#595	1	1	yes	characteristic
116	#117	C₂×#595	1	2	yes	—
117	C₂×C₄²	—	17	1	no	—
118	M₃₂	—	17	4	no	—
119	M₃₂	—	34	2	no	—
120	C₂×C₁₆	—	17	2	no	—
121	C₂×C₁₆	—	17	1	no	—
122	C₂×C₁₆	—	17	1	no	—
123	C₂×C₁₆	—	17	2	no	—
124	C₂×C₁₆	—	17	2	no	—
125	C₂×C₁₆	—	34	2	no	—
126	C₂×C₁₆	—	34	1	no	—
127	C₂×C₁₆	—	34	1	no	—
128	#108	—	17	4	no	—
129	#107	#3624	1	2	yes	—
130	#106	#3624	1	2	yes	—
131	#97	—	34	2	no	—
132	C₄×C₈	—	17	2	no	—
133	C₄×C₈	—	17	2	no	—
134	C₄×C₈	—	34	2	no	—
135	C₁₇	#12664	1	1	yes	characteristic, complemented, Sylow
136	C₂²×C₄	—	34	1	no	—
137	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
138	M₁₆	—	17	4	no	—
139	M₁₆	—	34	2	no	—
140	C₂×C₈	—	17	1	no	—
141	C₂×C₈	—	17	1	no	—
142	C₂×C₈	—	17	1	no	—
143	C₂×C₈	—	17	1	no	—
144	C₂×C₈	—	17	1	no	—
145	C₂×C₈	—	17	1	no	—
146	C₂×C₈	—	34	2	no	—
147	C₂×C₈	#63242	1	2	yes	—
148	C₂×C₈	C₄×#595	1	2	yes	—
149	C₂×C₈	C₂×#3624	1	1	yes	characteristic
150	C₂×C₈	C₂×#3624	1	1	yes	characteristic
151	C₄⋊C₄	C₂×#3624	1	4	yes	—
152	C₂²⋊C₄	—	2	2	no	—
153	C₄²	—	2	2	no	—
154	C₄²	—	17	2	no	—
155	C₄²	—	34	1	no	—
156	C₁₆	—	17	2	no	—
157	C₁₆	—	17	2	no	—
158	C₁₆	—	34	2	no	—
159	C₁₆	—	34	4	no	—
160	C₂³	#10587678	1	1	yes	characteristic
161	C₂×C₄	—	2	4	no	—
162	C₂×C₄	—	34	4	no	—
163	C₂×C₄	—	34	2	no	—
164	C₂×C₄	C₂×#63242	1	1	yes	characteristic
165	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
166	C₂×C₄	D₄×#595	1	1	yes	characteristic
167	C₂×C₄	#10587680	1	1	yes	characteristic
168	C₂×C₄	Q₈×#595	1	1	yes	characteristic
169	C₂×C₄	C₂²×#3624	1	1	yes	characteristic
170	C₈	—	17	1	no	—
171	C₈	—	17	1	no	—
172	C₈	—	17	1	no	—
173	C₈	—	17	1	no	—
174	C₈	—	34	4	no	—
175	C₈	C₄×#3624	1	2	yes	—
176	C₈	C₄×#3624	1	2	yes	—
177	C₂²	—	2	2	no	—
178	C₂²	#11763774	1	1	yes	characteristic
179	C₂²	D₄×#3624	1	1	yes	characteristic
180	C₂²	#11763858	1	1	yes	characteristic
181	C₄	—	4	4	no	—
182	C₄	—	34	4	no	—
183	C₄	C₄⋊C₄×#595	1	1	yes	characteristic
184	C₄	C₂×C₄×#3624	1	1	yes	characteristic
185	C₄	#11763837	1	1	yes	characteristic
186	C₄	Q₈×#3624	1	1	yes	characteristic
187	C₂	—	2	1	no	—
188	C₂	—	2	1	no	—
189	C₂	C₄⋊C₄×#3624	1	1	yes	characteristic
190	C₂	#14545171	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	D₄×#595
commutator	C₄×C₁₇	C₂×C₄×C₈
Frattini	C₂²×C₄	C₂²×#595
Fitting	C₁₇×#427	C₄
socle	C₂²×C₁₇	C₈×D₄
prime radical	C₂³×C₁₇	#131
cosocle	C₂²×#3622	C₂³
hypercenter	#427	#595
hypocenter	C₁₇	#12664
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #427

Complements

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

N	H ≅ G/N	type
9. #11763731	C₄	semidirect
11. #11763695	C₄	semidirect
135. C₁₇	#12664	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11763731	2
#14544993	2
C₂×#11763695	2
#14543838	2
#14528665	2
#12664	17