Subgroups — C₂×#11763819 #14545435

Order 2176.

512 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	C₂×#10587677	C₂	1	2	yes	maximal
2	#11763819	C₂	1	8	yes	maximal, direct product factor
3	C₂×#10587534	C₂	1	2	yes	maximal, complemented
4	C₂×#10587533	C₂	1	2	yes	maximal, complemented
5	C₂²×C₈×D₁₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄×D₁₇	C₂²	1	1	yes	characteristic
7	C₂×C₂²⋊#595	—	2	2	no	—
8	#10587677	—	2	4	no	—
9	#10587677	C₂²	1	8	yes	—
10	C₂×C₄⋊#595	C₂²	1	4	yes	—
11	C₂×C₄×#595	—	2	2	no	—
12	C₂²×C₈×C₁₇	C₄	1	1	yes	characteristic, complemented
13	C₂²×#3622	C₄	1	1	yes	characteristic, complemented
14	C₂×C₈×D₁₇	C₄	1	1	yes	characteristic, complemented
15	C₂×C₈×D₁₇	C₄	1	1	yes	characteristic, complemented
16	C₂×C₈×D₁₇	C₄	1	4	yes	complemented
17	C₂×C₈×D₁₇	C₂²	1	1	yes	characteristic
18	C₂×C₈×D₁₇	C₂²	1	1	yes	characteristic
19	C₂×C₈×D₁₇	C₂²	1	4	yes	—
20	#10587534	C₂²	1	8	yes	complemented
21	#10587533	C₂²	1	8	yes	complemented
22	C₂³×D₁₇	D₄	1	1	yes	characteristic
23	C₂²×#595	—	2	4	no	—
24	C₂²×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
25	C₂²×Dic₁₇	Q₈	1	1	yes	characteristic
26	C₂×C₄×D₁₇	C₂×C₄	1	2	yes	—
27	C₂×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄×D₁₇	D₄	1	1	yes	characteristic
29	C₂×C₄×D₁₇	D₄	1	2	yes	—
30	C₂×C₄×D₁₇	Q₈	1	2	yes	—
31	C₂×C₄×D₁₇	Q₈	1	1	yes	characteristic
32	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
33	C₂×C₄×D₁₇	C₂³	1	2	yes	—
34	C₂²⋊#595	—	2	8	no	—
35	C₄⋊#595	—	2	4	no	—
36	C₄⋊#595	C₂³	1	8	yes	—
37	C₄×#595	—	2	8	no	—
38	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
39	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
40	C₂×C₈×C₁₇	C₂×C₄	1	4	yes	complemented
41	C₂×#3622	C₂×C₄	1	1	yes	characteristic
42	C₂×#3622	C₂×C₄	1	1	yes	characteristic
43	C₂×#3622	C₂×C₄	1	4	yes	complemented
44	C₈×D₁₇	C₂×C₄	1	2	yes	—
45	C₈×D₁₇	C₂×C₄	1	2	yes	—
46	C₈×D₁₇	C₂×C₄	1	4	yes	complemented
47	C₈×D₁₇	C₂×C₄	1	4	yes	complemented
48	C₈×D₁₇	C₂³	1	2	yes	—
49	C₈×D₁₇	C₂³	1	2	yes	—
50	C₂³×C₁₇	C₄⋊C₄	1	1	yes	characteristic
51	C₂²×D₁₇	—	2	4	no	—
52	C₂²×D₁₇	C₄⋊C₄	1	1	yes	characteristic
53	C₂²×D₁₇	C₄⋊C₄	1	2	yes	—
54	C₂²×D₁₇	C₂×D₄	1	2	yes	—
55	C₂²×D₁₇	C₂×D₄	1	1	yes	characteristic
56	C₂×#595	—	2	8	no	—
57	C₂×#595	—	4	8	no	—
58	C₂×C₄×C₁₇	C₄⋊C₄	1	2	yes	—
59	C₂×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
60	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
61	C₂×C₄×C₁₇	C₂²×C₄	1	2	yes	—
62	C₂×Dic₁₇	C₄⋊C₄	1	2	yes	—
63	C₂×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
64	C₂×Dic₁₇	C₂×Q₈	1	2	yes	—
65	C₂×Dic₁₇	C₂×Q₈	1	1	yes	characteristic
66	C₄×D₁₇	C₄⋊C₄	1	2	yes	—
67	C₄×D₁₇	C₄⋊C₄	1	2	yes	—
68	C₄×D₁₇	C₄⋊C₄	1	2	yes	—
69	C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
70	C₄×D₁₇	C₂²×C₄	1	2	yes	—
71	C₄×D₁₇	C₂×D₄	1	2	yes	—
72	C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
73	C₄×D₁₇	C₂×Q₈	1	2	yes	—
74	C₄×D₁₇	C₂×Q₈	1	1	yes	characteristic
75	C₄×D₁₇	C₂⁴	1	1	yes	characteristic
76	C₈×C₁₇	C₂²×C₄	1	2	yes	—
77	C₈×C₁₇	C₂²×C₄	1	2	yes	—
78	#3622	C₂²×C₄	1	2	yes	—
79	#3622	C₂²×C₄	1	2	yes	—
80	C₂×#427	—	17	1	no	maximal, Sylow
81	C₂²×C₁₇	—	2	2	no	—
82	C₂²×C₁₇	C₂×C₄⋊C₄	1	2	yes	—
83	C₂²×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
84	C₂×D₁₇	—	2	2	no	—
85	C₂×D₁₇	—	2	4	no	—
86	C₂×D₁₇	—	2	4	no	—
87	C₂×D₁₇	C₂×C₄⋊C₄	1	2	yes	—
88	C₂×D₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
89	C₂×D₁₇	#135	1	4	yes	—
90	C₂×D₁₇	C₂²×D₄	1	1	yes	characteristic
91	#595	—	4	8	no	—
92	C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
93	C₄×C₁₇	C₂×C₄⋊C₄	1	2	yes	—
94	C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
95	Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
96	Dic₁₇	C₂×C₄⋊C₄	1	2	yes	—
97	Dic₁₇	C₂²×Q₈	1	1	yes	characteristic
98	C₂³×C₈	—	17	1	no	—
99	C₂×#117	—	17	2	no	—
100	#427	—	17	8	no	—
101	C₂×#107	—	17	2	no	—
102	C₂×#106	—	17	2	no	—
103	C₂×C₁₇	—	2	2	no	—
104	C₂×C₁₇	#427	1	2	yes	complemented
105	C₂×C₁₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
106	D₁₇	—	2	2	no	—
107	D₁₇	#427	1	2	yes	complemented
108	D₁₇	C₂×#135	1	2	yes	—
109	C₂³×C₄	—	17	1	no	—
110	C₂²×C₈	—	17	1	no	—
111	C₂²×C₈	—	17	1	no	—
112	C₂²×C₈	—	17	1	no	—
113	C₂²×C₈	—	17	1	no	—
114	C₂²×C₈	—	17	1	no	—
115	C₂²×C₈	—	17	4	no	—
116	C₂²×C₈	—	17	4	no	—
117	C₂²×C₈	#595	1	1	yes	characteristic, complemented
118	#117	—	17	8	no	—
119	#117	—	34	4	no	—
120	C₂×C₄⋊C₄	—	17	4	no	—
121	C₂×C₂²⋊C₄	—	34	2	no	—
122	C₂×C₄²	—	34	2	no	—
123	#107	—	17	8	no	—
124	#106	—	17	8	no	—
125	C₁₇	C₂×#427	1	1	yes	characteristic, complemented, Sylow
126	C₂⁴	—	17	1	no	—
127	C₂²×C₄	—	17	1	no	—
128	C₂²×C₄	—	17	2	no	—
129	C₂²×C₄	—	17	2	no	—
130	C₂²×C₄	—	17	1	no	—
131	C₂²×C₄	—	17	1	no	—
132	C₂²×C₄	—	17	1	no	—
133	C₂²×C₄	—	17	2	no	—
134	C₂²×C₄	—	17	1	no	—
135	C₂²×C₄	—	17	2	no	—
136	C₂²×C₄	—	34	4	no	—
137	C₂²×C₄	C₂×#595	1	1	yes	characteristic
138	C₂×C₈	—	17	1	no	—
139	C₂×C₈	—	17	1	no	—
140	C₂×C₈	—	17	4	no	—
141	C₂×C₈	—	17	2	no	—
142	C₂×C₈	—	17	2	no	—
143	C₂×C₈	—	17	2	no	—
144	C₂×C₈	—	17	2	no	—
145	C₂×C₈	—	17	4	no	—
146	C₂×C₈	—	17	4	no	—
147	C₂×C₈	C₂×#595	1	1	yes	characteristic
148	C₂×C₈	C₂×#595	1	1	yes	characteristic
149	C₂×C₈	C₂×#595	1	4	yes	complemented
150	C₄⋊C₄	—	17	8	no	—
151	C₄⋊C₄	—	34	4	no	—
152	C₂²⋊C₄	—	34	8	no	—
153	C₄²	—	34	8	no	—
154	C₂³	—	17	1	no	—
155	C₂³	—	17	2	no	—
156	C₂³	—	17	2	no	—
157	C₂³	—	17	1	no	—
158	C₂³	—	34	4	no	—
159	C₂³	C₄⋊#595	1	1	yes	characteristic
160	C₂×C₄	—	17	2	no	—
161	C₂×C₄	—	17	1	no	—
162	C₂×C₄	—	17	2	no	—
163	C₂×C₄	—	17	1	no	—
164	C₂×C₄	—	17	2	no	—
165	C₂×C₄	—	17	1	no	—
166	C₂×C₄	—	17	2	no	—
167	C₂×C₄	—	17	2	no	—
168	C₂×C₄	—	17	2	no	—
169	C₂×C₄	—	17	1	no	—
170	C₂×C₄	—	17	2	no	—
171	C₂×C₄	—	17	1	no	—
172	C₂×C₄	—	17	1	no	—
173	C₂×C₄	—	17	2	no	—
174	C₂×C₄	—	34	8	no	—
175	C₂×C₄	—	68	8	no	—
176	C₂×C₄	C₄⋊#595	1	2	yes	—
177	C₂×C₄	C₄⋊#595	1	1	yes	characteristic
178	C₂×C₄	C₂²×#595	1	1	yes	characteristic
179	C₂×C₄	C₂²×#595	1	2	yes	—
180	C₈	—	17	2	no	—
181	C₈	—	17	2	no	—
182	C₈	C₂²×#595	1	2	yes	—
183	C₈	C₂²×#595	1	2	yes	—
184	C₂²	—	2	2	no	—
185	C₂²	—	17	4	no	—
186	C₂²	—	17	1	no	—
187	C₂²	—	17	1	no	—
188	C₂²	—	17	2	no	—
189	C₂²	—	34	4	no	—
190	C₂²	—	34	4	no	—
191	C₂²	—	34	2	no	—
192	C₂²	C₂×C₄⋊#595	1	2	yes	—
193	C₂²	C₂×C₄⋊#595	1	1	yes	characteristic
194	C₄	—	17	2	no	—
195	C₄	—	17	1	no	—
196	C₄	—	17	1	no	—
197	C₄	—	68	8	no	—
198	C₄	C₂×C₄⋊#595	1	1	yes	characteristic
199	C₄	C₂×C₄⋊#595	1	2	yes	—
200	C₄	C₂³×#595	1	1	yes	characteristic
201	C₂	—	2	2	no	—
202	C₂	—	17	2	no	—
203	C₂	—	17	2	no	—
204	C₂	—	34	2	no	—
205	C₂	#11763819	1	2	yes	direct product factor
206	C₂	C₂²×C₄⋊#595	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₄⋊#595
commutator	C₄×C₁₇	C₂³×C₄
Frattini	C₄	C₂³×#595
Fitting	C₂²×C₈×C₁₇	C₄
socle	C₂²×C₁₇	C₂×C₄⋊C₄
prime radical	C₂³×D₁₇	D₄
cosocle	C₄×D₁₇	C₂⁴
hypercenter	C₂²×C₈	#595
hypocenter	C₁₇	C₂×#427
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. #11763819	C₂	direct (N × H)
3. C₂×#10587534	C₂	semidirect
4. C₂×#10587533	C₂	semidirect
12. C₂²×C₈×C₁₇	C₄	semidirect
13. C₂²×#3622	C₄	semidirect
14. C₂×C₈×D₁₇	C₄	semidirect
15. C₂×C₈×D₁₇	C₄	semidirect
16. C₂×C₈×D₁₇	C₄	semidirect
20. #10587534	C₂²	semidirect
21. #10587533	C₂²	semidirect
40. C₂×C₈×C₁₇	C₂×C₄	semidirect
43. C₂×#3622	C₂×C₄	semidirect
46. C₈×D₁₇	C₂×C₄	semidirect
47. C₈×D₁₇	C₂×C₄	semidirect
104. C₂×C₁₇	#427	semidirect
107. D₁₇	#427	semidirect
117. C₂²×C₈	#595	semidirect
125. C₁₇	C₂×#427	semidirect
149. C₂×C₈	C₂×#595	semidirect
205. C₂	#11763819	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#10587677	2
#11763819	2
C₂×#10587534	2
C₂×#10587533	2
C₂²×C₈×D₁₇	2
C₂×#427	17

Subgroups — C2×#11763819 #14545435

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11763819 #14545435