Subgroups — D₁₇⋊#446 #14545570

Order 2176.

400 conjugacy classes of subgroups.

The subgroup lattice has 208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763861	C₂	1	4	yes	maximal, complemented
2	#11763860	C₂	1	2	yes	maximal, complemented
3	#11763859	C₂	1	2	yes	maximal, complemented
4	#11763810	C₂	1	2	yes	maximal
5	#11763810	C₂	1	1	yes	maximal, characteristic
6	#11763768	C₂	1	2	yes	maximal
7	C₄×#63242	C₂	1	1	yes	maximal, characteristic
8	C₄×Q₈×D₁₇	C₂	1	1	yes	maximal, characteristic
9	C₂×Q₈×D₁₇	C₄	1	1	yes	characteristic
10	C₂×#63242	C₂²	1	1	yes	characteristic
11	C₂×#63242	C₂²	1	2	yes	—
12	C₂×#63242	C₂²	1	1	yes	characteristic
13	C₄×Q₈×C₁₇	C₄	1	1	yes	characteristic
14	Q₈×Dic₁₇	C₂²	1	1	yes	characteristic
15	C₄⋊C₄×D₁₇	C₄	1	2	yes	—
16	C₄⋊C₄×D₁₇	C₄	1	1	yes	characteristic
17	#10587573	C₂²	1	1	yes	characteristic
18	#10587573	C₂²	1	2	yes	—
19	C₄²×D₁₇	C₂²	1	1	yes	characteristic
20	C₄²×D₁₇	C₂²	1	2	yes	—
21	C₄×Dic₃₄	C₄	1	2	yes	—
22	C₄×Dic₃₄	C₄	1	1	yes	characteristic
23	#10587544	C₂²	1	4	yes	—
24	#10587544	C₂²	1	2	yes	—
25	#10587542	C₂²	1	4	yes	—
26	#10587542	C₂²	1	4	yes	—
27	C₄⋊#3624	C₂²	1	2	yes	—
28	C₄⋊#3624	C₂²	1	4	yes	—
29	C₄×#3624	C₂²	1	2	yes	—
30	C₄×#3624	C₂²	1	2	yes	—
31	C₂×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
32	Q₈×D₁₇	—	2	4	no	—
33	C₂×C₄×D₁₇	C₂×C₄	1	2	yes	—
34	C₂×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄×D₁₇	C₂×C₄	1	2	yes	—
36	C₂×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
38	C₂×Dic₃₄	C₂×C₄	1	1	yes	characteristic
39	C₂×Dic₃₄	C₂×C₄	1	2	yes	—
40	C₂×#3624	C₂³	1	2	yes	—
41	C₂×#3624	C₂³	1	4	yes	—
42	C₂×#3624	C₂³	1	2	yes	—
43	#63242	—	2	2	no	—
44	#63242	—	2	4	no	—
45	#63242	Q₈	1	4	yes	complemented
46	C₄⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
47	C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
48	C₄²×C₁₇	C₂×C₄	1	2	yes	—
49	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
50	C₄⋊Dic₁₇	C₂×C₄	1	2	yes	—
51	C₄⋊Dic₁₇	C₂×C₄	1	1	yes	characteristic
52	#63225	C₂×C₄	1	2	yes	—
53	#63225	C₂×C₄	1	2	yes	—
54	#63225	C₂×C₄	1	2	yes	—
55	C₄×Dic₁₇	C₂×C₄	1	2	yes	—
56	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
57	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
58	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
59	C₄×Dic₁₇	C₂³	1	2	yes	—
60	C₄×Dic₁₇	C₂³	1	2	yes	—
61	C₂²×D₁₇	C₂²×C₄	1	1	yes	characteristic
62	Q₈×C₁₇	—	2	2	no	—
63	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
64	C₂×C₄×C₁₇	C₂²×C₄	1	2	yes	—
65	C₂×C₄×C₁₇	C₂²×C₄	1	2	yes	—
66	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
67	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
68	C₂×Dic₁₇	C₂²×C₄	1	2	yes	—
69	C₂×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
70	C₂×Dic₁₇	C₂²×C₄	1	2	yes	—
71	C₂×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
72	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
73	C₄×D₁₇	—	2	4	no	—
74	C₄×D₁₇	—	2	2	no	—
75	C₄×D₁₇	—	2	4	no	—
76	C₄×D₁₇	M₁₆	1	4	yes	—
77	C₄×D₁₇	C₂×Q₈	1	2	yes	—
78	C₄×D₁₇	#41	1	2	yes	—
79	Dic₃₄	—	2	2	no	—
80	Dic₃₄	—	2	4	no	—
81	#3624	—	2	2	no	—
82	#3624	—	2	4	no	—
83	#3624	C₂×Q₈	1	4	yes	complemented
84	C₂×#446	—	17	1	no	maximal, Sylow
85	C₂²×C₁₇	C₂³×C₄	1	1	yes	characteristic
86	C₂×D₁₇	C₄×Q₈	1	2	yes	—
87	C₂×D₁₇	C₂×M₁₆	1	2	yes	—
88	C₂×D₁₇	#131	1	2	yes	—
89	C₄×C₁₇	—	2	2	no	—
90	C₄×C₁₇	—	2	1	no	—
91	C₄×C₁₇	—	2	2	no	—
92	C₄×C₁₇	C₄×Q₈	1	2	yes	—
93	C₄×C₁₇	C₂×M₁₆	1	2	yes	—
94	Dic₁₇	—	2	2	no	—
95	Dic₁₇	—	2	1	no	—
96	Dic₁₇	—	2	2	no	—
97	Dic₁₇	C₂×M₁₆	1	2	yes	—
98	Dic₁₇	C₂²×Q₈	1	1	yes	characteristic
99	Dic₁₇	C₂×#41	1	1	yes	characteristic
100	C₂×C₄×Q₈	—	17	1	no	—
101	#446	—	17	2	no	—
102	#446	—	17	2	no	—
103	#446	—	17	4	no	—
104	C₂×C₄⋊C₈	—	17	1	no	—
105	C₂×C₄⋊C₈	—	17	2	no	—
106	C₂×#97	—	17	2	no	—
107	C₂×C₄×C₈	—	17	1	no	—
108	C₂×C₁₇	C₂×C₄×Q₈	1	1	yes	characteristic
109	C₂×C₁₇	C₂²×M₁₆	1	1	yes	characteristic
110	C₂×C₁₇	C₂×#131	1	1	yes	characteristic
111	D₁₇	#446	1	4	yes	complemented
112	C₂²×Q₈	—	17	1	no	—
113	C₂²×C₈	—	17	1	no	—
114	C₂²×C₈	—	17	1	no	—
115	C₂²×C₈	—	17	2	no	—
116	C₄×Q₈	—	17	1	no	—
117	C₄×Q₈	—	17	1	no	—
118	C₄×Q₈	—	17	2	no	—
119	C₄×Q₈	—	17	2	no	—
120	C₄×Q₈	—	17	1	no	—
121	C₄×Q₈	#595	1	1	yes	characteristic
122	C₂×C₄⋊C₄	—	17	1	no	—
123	C₂×C₄⋊C₄	—	17	2	no	—
124	C₂×C₄²	—	17	1	no	—
125	C₂×C₄²	—	17	2	no	—
126	C₄⋊C₈	—	17	2	no	—
127	C₄⋊C₈	—	17	4	no	—
128	C₄⋊C₈	—	17	2	no	—
129	C₄⋊C₈	—	17	4	no	—
130	#97	—	17	4	no	—
131	#97	—	17	4	no	—
132	C₄×C₈	—	17	2	no	—
133	C₄×C₈	—	17	2	no	—
134	C₁₇	C₂×#446	1	1	yes	characteristic, complemented, Sylow
135	C₂×Q₈	—	17	2	no	—
136	C₂×Q₈	—	17	1	no	—
137	C₂×Q₈	—	34	4	no	—
138	C₂×Q₈	C₂×#595	1	1	yes	characteristic
139	C₂²×C₄	—	17	1	no	—
140	C₂²×C₄	—	17	1	no	—
141	C₂²×C₄	—	17	1	no	—
142	C₂²×C₄	—	17	2	no	—
143	C₂²×C₄	—	17	2	no	—
144	C₂×C₈	—	17	4	no	—
145	C₂×C₈	—	17	2	no	—
146	C₂×C₈	—	17	2	no	—
147	C₂×C₈	—	17	4	no	—
148	C₂×C₈	—	34	2	no	—
149	C₂×C₈	—	34	4	no	—
150	C₄⋊C₄	—	17	2	no	—
151	C₄⋊C₄	—	17	2	no	—
152	C₄⋊C₄	—	17	2	no	—
153	C₄⋊C₄	—	17	2	no	—
154	C₄⋊C₄	—	17	1	no	—
155	C₄⋊C₄	C₂×#595	1	2	yes	—
156	C₄⋊C₄	C₂×#595	1	1	yes	characteristic
157	C₄²	—	17	1	no	—
158	C₄²	—	17	1	no	—
159	C₄²	—	17	2	no	—
160	C₄²	—	17	2	no	—
161	C₄²	—	17	1	no	—
162	C₄²	—	17	2	no	—
163	C₄²	C₂×#595	1	2	yes	—
164	C₄²	C₂×#595	1	1	yes	characteristic
165	C₂³	—	17	1	no	—
166	Q₈	—	2	2	no	—
167	Q₈	—	34	4	no	—
168	Q₈	—	34	2	no	—
169	C₂×C₄	—	17	1	no	—
170	C₂×C₄	—	17	1	no	—
171	C₂×C₄	—	17	4	no	—
172	C₂×C₄	—	17	2	no	—
173	C₂×C₄	—	17	2	no	—
174	C₂×C₄	—	17	1	no	—
175	C₂×C₄	—	17	2	no	—
176	C₂×C₄	—	17	2	no	—
177	C₂×C₄	—	34	4	no	—
178	C₂×C₄	—	34	2	no	—
179	C₂×C₄	—	34	4	no	—
180	C₂×C₄	C₂²×#595	1	1	yes	characteristic
181	C₂×C₄	C₂²×#595	1	2	yes	—
182	C₂×C₄	C₂²×#595	1	2	yes	—
183	C₂×C₄	C₂²×#595	1	1	yes	characteristic
184	C₂×C₄	C₂²×#595	1	1	yes	characteristic
185	C₈	—	17	4	no	—
186	C₈	—	34	2	no	—
187	C₈	—	34	4	no	—
188	C₂²	—	17	2	no	—
189	C₂²	—	17	2	no	—
190	C₂²	—	17	2	no	—
191	C₂²	C₂³×#595	1	1	yes	characteristic
192	C₄	—	2	2	no	—
193	C₄	—	2	1	no	—
194	C₄	—	2	2	no	—
195	C₄	—	17	1	no	—
196	C₄	—	17	1	no	—
197	C₄	—	17	2	no	—
198	C₄	—	34	2	no	—
199	C₄	—	34	1	no	—
200	C₄	—	34	2	no	—
201	C₄	D₁₇⋊M₁₆	1	2	yes	—
202	C₄	Q₈×#595	1	2	yes	—
203	C₂	—	17	4	no	—
204	C₂	C₂×Q₈×#595	1	1	yes	characteristic
205	C₂	C₂×D₁₇⋊M₁₆	1	1	yes	characteristic
206	C₂	D₁₇⋊#131	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×#595
commutator, socle	C₂²×C₁₇	C₂³×C₄
Frattini	C₂²	C₂³×#595
Fitting	C₄×Q₈×C₁₇	C₄
prime radical	C₂²×D₁₇	C₂²×C₄
cosocle	C₂×Dic₁₇	C₂⁴
hypercenter	C₄×Q₈	#595
hypocenter	C₁₇	C₂×#446
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
1. #11763861	C₂	semidirect
2. #11763860	C₂	semidirect
3. #11763859	C₂	semidirect
45. #63242	Q₈	semidirect
83. #3624	C₂×Q₈	semidirect
111. D₁₇	#446	semidirect
134. C₁₇	C₂×#446	semidirect

Maximal subgroups

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

subgroup	index
#11763861	2
#11763860	2
#11763859	2
#11763810	2
#11763768	2
C₄×#63242	2
C₄×Q₈×D₁₇	2
C₂×#446	17

Subgroups — D17⋊#446 #14545570

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₇⋊#446 #14545570