Subgroups — C₂×#11763675 #14544444

Order 2176.

528 conjugacy classes of subgroups.

The subgroup lattice has 178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#3624	C₂	1	2	yes	maximal
2	#11763675	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₄×Dic₁₇	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₄×C₁₇	C₄	1	1	yes	characteristic
5	C₂³×Dic₁₇	C₄	1	1	yes	characteristic
6	C₂³×Dic₁₇	C₂²	1	1	yes	characteristic
7	C₂²×#3624	—	2	4	no	—
8	C₂²×#3624	—	2	4	no	—
9	C₂²×#3624	C₄	1	8	yes	complemented
10	C₂²×#3624	C₂²	1	4	yes	—
11	C₂×C₄×Dic₁₇	—	2	4	no	—
12	C₂×C₄×Dic₁₇	C₄	1	2	yes	—
13	C₂×C₄×Dic₁₇	C₂²	1	2	yes	—
14	C₂⁴×C₁₇	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₁₇	—	2	2	no	—
16	C₂²×C₄×C₁₇	—	2	2	no	—
17	C₂²×C₄×C₁₇	C₈	1	4	yes	complemented
18	C₂²×C₄×C₁₇	C₂×C₄	1	2	yes	—
19	C₂²×Dic₁₇	—	2	2	no	—
20	C₂²×Dic₁₇	—	2	2	no	—
21	C₂²×Dic₁₇	C₈	1	4	yes	complemented
22	C₂²×Dic₁₇	C₂×C₄	1	2	yes	—
23	C₂²×Dic₁₇	C₂×C₄	1	1	yes	characteristic
24	C₂²×Dic₁₇	C₂×C₄	1	4	yes	—
25	C₂²×Dic₁₇	D₄	1	2	yes	—
26	C₂²×Dic₁₇	D₄	1	4	yes	—
27	C₂²×Dic₁₇	Q₈	1	2	yes	—
28	C₂²×Dic₁₇	C₂³	1	1	yes	characteristic
29	C₂×#3624	—	2	16	no	—
30	C₂×#3624	—	2	4	no	—
31	C₂×#3624	—	2	4	no	—
32	C₂×#3624	C₂×C₄	1	8	yes	complemented
33	C₄×Dic₁₇	—	2	4	no	—
34	C₄×Dic₁₇	—	2	4	no	—
35	C₂³×C₁₇	C₄²	1	2	yes	—
36	C₂³×C₁₇	C₂²⋊C₄	1	2	yes	—
37	C₂³×C₁₇	C₄⋊C₄	1	2	yes	—
38	C₂³×C₁₇	C₂×C₈	1	2	yes	—
39	C₂³×C₁₇	C₂×C₈	1	2	yes	—
40	C₂³×C₁₇	M₁₆	1	2	yes	—
41	C₂³×C₁₇	M₁₆	1	2	yes	—
42	C₂³×C₁₇	C₂²×C₄	1	1	yes	characteristic
43	C₂×C₄×C₁₇	—	2	8	no	—
44	C₂×C₄×C₁₇	—	2	2	no	—
45	C₂×C₄×C₁₇	—	2	2	no	—
46	C₂×C₄×C₁₇	C₂×C₈	1	4	yes	complemented
47	C₂×Dic₁₇	—	2	8	no	—
48	C₂×Dic₁₇	—	2	2	no	—
49	C₂×Dic₁₇	—	2	2	no	—
50	C₂×Dic₁₇	C₄²	1	2	yes	—
51	C₂×Dic₁₇	C₂²⋊C₄	1	2	yes	—
52	C₂×Dic₁₇	C₂²⋊C₄	1	8	yes	—
53	C₂×Dic₁₇	C₄⋊C₄	1	2	yes	—
54	C₂×Dic₁₇	C₄⋊C₄	1	8	yes	—
55	C₂×Dic₁₇	C₂×C₈	1	4	yes	complemented
56	C₂×Dic₁₇	C₂²×C₄	1	2	yes	—
57	C₂×Dic₁₇	C₂×D₄	1	1	yes	characteristic
58	C₂×Dic₁₇	C₂×D₄	1	2	yes	—
59	C₂×Dic₁₇	C₂×Q₈	1	1	yes	characteristic
60	#3624	—	2	8	no	—
61	C₂×#336	—	17	1	no	maximal, Sylow
62	C₂²×C₁₇	#95	1	4	yes	—
63	C₂²×C₁₇	C₄×C₈	1	4	yes	—
64	C₂²×C₁₇	#97	1	4	yes	—
65	C₂²×C₁₇	C₂²⋊C₈	1	4	yes	—
66	C₂²×C₁₇	C₂²⋊C₈	1	4	yes	—
67	C₂²×C₁₇	C₄⋊C₈	1	4	yes	—
68	C₂²×C₁₇	C₄⋊C₈	1	4	yes	—
69	C₂²×C₁₇	C₂×C₄²	1	1	yes	characteristic
70	C₂²×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
72	C₂²×C₁₇	C₂²×C₈	1	1	yes	characteristic
73	C₂²×C₁₇	C₂²×C₈	1	1	yes	characteristic
74	C₂²×C₁₇	C₂×M₁₆	1	1	yes	characteristic
75	C₂²×C₁₇	C₂×M₁₆	1	1	yes	characteristic
76	C₄×C₁₇	—	2	4	no	—
77	Dic₁₇	—	2	4	no	—
78	Dic₁₇	#95	1	4	yes	—
79	Dic₁₇	C₂×C₂²⋊C₄	1	2	yes	—
80	Dic₁₇	C₂×C₄⋊C₄	1	2	yes	—
81	C₂³×C₈	—	17	2	no	—
82	C₂²×C₄²	—	17	1	no	—
83	#336	—	17	4	no	—
84	C₂×C₁₇	#336	1	8	yes	complemented
85	C₂×C₁₇	C₂×#95	1	1	yes	characteristic
86	C₂×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
87	C₂×C₁₇	C₂×#97	1	1	yes	characteristic
88	C₂×C₁₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
89	C₂×C₁₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
90	C₂×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
91	C₂×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
92	C₂³×C₄	—	17	1	no	—
93	C₂³×C₄	—	17	1	no	—
94	C₂³×C₄	#595	1	1	yes	characteristic
95	C₂²×C₈	—	17	8	no	—
96	C₂²×C₈	—	17	4	no	—
97	C₂²×C₈	—	34	4	no	—
98	C₂²×C₈	—	34	4	no	—
99	C₂×C₄²	—	17	2	no	—
100	C₂×C₄²	—	17	2	no	—
101	C₂×C₄²	—	34	4	no	—
102	C₁₇	C₂×#336	1	1	yes	characteristic, complemented, Sylow
103	C₂⁴	C₂×#595	1	1	yes	characteristic
104	C₂²×C₄	—	2	2	no	—
105	C₂²×C₄	—	2	2	no	—
106	C₂²×C₄	—	17	4	no	—
107	C₂²×C₄	—	17	2	no	—
108	C₂²×C₄	—	17	2	no	—
109	C₂²×C₄	—	17	4	no	—
110	C₂²×C₄	—	17	1	no	—
111	C₂²×C₄	—	17	1	no	—
112	C₂²×C₄	—	17	4	no	—
113	C₂²×C₄	—	17	2	no	—
114	C₂²×C₄	—	34	2	no	—
115	C₂²×C₄	—	34	2	no	—
116	C₂²×C₄	#3624	1	4	yes	complemented
117	C₂²×C₄	C₂×#595	1	2	yes	—
118	C₂×C₈	—	17	8	no	—
119	C₂×C₈	—	34	4	no	—
120	C₂×C₈	—	34	4	no	—
121	C₂×C₈	—	34	16	no	—
122	C₄²	—	34	4	no	—
123	C₄²	—	34	4	no	—
124	C₂³	#63242	1	2	yes	—
125	C₂³	#63243	1	2	yes	—
126	C₂³	C₄×#595	1	2	yes	—
127	C₂³	C₄⋊#595	1	2	yes	—
128	C₂³	C₂×#3624	1	2	yes	—
129	C₂³	#63247	1	2	yes	—
130	C₂³	C₂²⋊#595	1	2	yes	—
131	C₂³	C₂²×#595	1	1	yes	characteristic
132	C₂×C₄	—	2	2	no	—
133	C₂×C₄	—	2	2	no	—
134	C₂×C₄	—	2	8	no	—
135	C₂×C₄	—	17	2	no	—
136	C₂×C₄	—	17	2	no	—
137	C₂×C₄	—	17	1	no	—
138	C₂×C₄	—	17	2	no	—
139	C₂×C₄	—	17	1	no	—
140	C₂×C₄	—	17	2	no	—
141	C₂×C₄	—	17	2	no	—
142	C₂×C₄	—	17	8	no	—
143	C₂×C₄	—	17	8	no	—
144	C₂×C₄	—	17	4	no	—
145	C₂×C₄	—	34	2	no	—
146	C₂×C₄	—	34	2	no	—
147	C₂×C₄	—	34	8	no	—
148	C₂×C₄	C₂×#3624	1	4	yes	complemented
149	C₈	—	34	8	no	—
150	C₂²	C₄×#3624	1	4	yes	—
151	C₂²	C₄⋊#3624	1	4	yes	—
152	C₂²	#10587542	1	4	yes	—
153	C₂²	#10587543	1	4	yes	—
154	C₂²	#10587544	1	4	yes	—
155	C₂²	(C₂×#595)⋊C₄	1	4	yes	—
156	C₂²	C₂²⋊#3624	1	4	yes	—
157	C₂²	C₂×#63242	1	1	yes	characteristic
158	C₂²	C₂×#63243	1	1	yes	characteristic
159	C₂²	C₂×C₄×#595	1	1	yes	characteristic
160	C₂²	C₂×C₄⋊#595	1	1	yes	characteristic
161	C₂²	C₂²×#3624	1	1	yes	characteristic
162	C₂²	C₂×#63247	1	1	yes	characteristic
163	C₂²	C₂×C₂²⋊#595	1	1	yes	characteristic
164	C₄	—	2	4	no	—
165	C₄	—	17	2	no	—
166	C₄	—	17	4	no	—
167	C₄	—	17	2	no	—
168	C₄	—	34	4	no	—
169	C₂	#11763675	1	8	yes	direct product factor
170	C₂	C₂×(C₂×#595)⋊C₄	1	1	yes	characteristic
171	C₂	C₂×C₄×#3624	1	1	yes	characteristic
172	C₂	C₂×#10587542	1	1	yes	characteristic
173	C₂	C₂×C₂²⋊#3624	1	1	yes	characteristic
174	C₂	C₂×#10587543	1	1	yes	characteristic
175	C₂	C₂×C₄⋊#3624	1	1	yes	characteristic
176	C₂	C₂×#10587544	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×#595
commutator	C₂×C₁₇	C₂×C₄×C₈
Frattini	C₂³	C₂²×#595
Fitting	C₂³×C₄×C₁₇	C₄
socle, prime radical	C₂⁴×C₁₇	C₂×C₄
cosocle	C₂²×Dic₁₇	C₂³
hypercenter	C₂³×C₄	#595
hypocenter	C₁₇	C₂×#336
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
2. #11763675	C₂	direct (N × H)
9. C₂²×#3624	C₄	semidirect
17. C₂²×C₄×C₁₇	C₈	semidirect
21. C₂²×Dic₁₇	C₈	semidirect
32. C₂×#3624	C₂×C₄	semidirect
46. C₂×C₄×C₁₇	C₂×C₈	semidirect
55. C₂×Dic₁₇	C₂×C₈	semidirect
84. C₂×C₁₇	#336	semidirect
102. C₁₇	C₂×#336	semidirect
116. C₂²×C₄	#3624	semidirect
148. C₂×C₄	C₂×#3624	semidirect
169. C₂	#11763675	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#3624	2
#11763675	2
C₂²×C₄×Dic₁₇	2
C₂×#336	17

Subgroups — C2×#11763675 #14544444

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11763675 #14544444