Subgroups — C₂×#14545208 #17978841

Order 4352.

470 conjugacy classes of subgroups.

The subgroup lattice has 180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545208	C₂	1	8	yes	maximal, direct product factor
2	C₂×#11763742	C₂	1	2	yes	maximal, complemented
3	C₂×#11763741	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11763740	C₂	1	2	yes	maximal, complemented
5	C₂²×#10587467	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11763227	C₂	1	1	yes	maximal, characteristic
7	#11763742	C₂²	1	8	yes	complemented
8	#11763741	C₂²	1	4	yes	complemented
9	#11763740	C₂²	1	8	yes	complemented
10	C₂×#10587467	C₂²	1	1	yes	characteristic
11	C₂×#10587467	C₂²	1	1	yes	characteristic
12	C₂×#10587467	C₂²	1	2	yes	—
13	C₂×#10587467	C₂²	1	4	yes	complemented
14	C₂×#10587587	C₄	1	1	yes	characteristic
15	#11763227	C₄	1	4	yes	—
16	#11763227	C₂²	1	4	yes	—
17	C₂×#10587469	C₄	1	2	yes	—
18	C₂²×#63214	C₂²	1	1	yes	characteristic
19	C₂×C₁₆×D₁₇	C₂²	1	2	yes	—
20	C₂×C₁₇×M₃₂	C₄	1	1	yes	characteristic
21	C₂×#63252	C₈	1	1	yes	characteristic
22	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
23	C₂×#63223	C₈	1	1	yes	characteristic
24	#10587587	C₈	1	4	yes	—
25	#10587587	C₂×C₄	1	4	yes	—
26	C₂×#63218	C₈	1	2	yes	—
27	C₂×C₈×D₁₇	C₂×C₄	1	2	yes	—
28	C₁₇×M₃₂	C₂×C₄	1	4	yes	—
29	C₂×C₁₆×C₁₇	C₂×C₄	1	2	yes	—
30	C₂×#63214	C₂×C₄	1	1	yes	characteristic
31	C₂×#63214	C₂×C₄	1	2	yes	—
32	C₂×#63214	C₂³	1	1	yes	characteristic
33	C₂×#63214	C₂³	1	2	yes	—
34	#10587469	C₂×C₄	1	8	yes	—
35	C₁₆×D₁₇	C₂×C₄	1	4	yes	—
36	C₁₆×D₁₇	C₂³	1	4	yes	—
37	#10587467	C₂³	1	2	yes	—
38	#10587467	C₂³	1	2	yes	—
39	#10587467	C₂³	1	4	yes	—
40	C₂²×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
41	C₂×C₂²⋊D₁₇	C₁₆	1	2	yes	—
42	#63252	C₁₆	1	4	yes	—
43	#63252	C₂×C₈	1	4	yes	—
44	C₂×D₆₈	C₁₆	1	1	yes	characteristic
45	C₂×C₄×D₁₇	C₂×C₈	1	2	yes	—
46	C₂×Dic₃₄	C₁₆	1	1	yes	characteristic
47	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
48	C₂×C₈×C₁₇	C₂×C₈	1	2	yes	—
49	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
50	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
51	#63223	C₂×C₈	1	4	yes	—
52	C₂×#3622	C₂×C₈	1	2	yes	—
53	#63218	C₂×C₈	1	8	yes	—
54	C₈×D₁₇	C₂×C₈	1	4	yes	—
55	C₈×D₁₇	C₂²×C₄	1	4	yes	—
56	C₁₆×C₁₇	C₂²×C₄	1	4	yes	—
57	#63214	C₂²×C₄	1	1	yes	characteristic
58	#63214	C₂²×C₄	1	2	yes	—
59	#63214	C₂⁴	1	1	yes	characteristic
60	C₂×#2258	—	17	1	no	maximal, Sylow
61	C₂³×C₁₇	C₂×C₁₆	1	1	yes	characteristic
62	C₂²×D₁₇	C₂×C₁₆	1	2	yes	—
63	C₂×C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
64	C₂×C₄×C₁₇	C₂×C₁₆	1	2	yes	—
65	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
66	C₂×C₄×C₁₇	C₂²×C₈	1	2	yes	—
67	C₂²⋊D₁₇	C₂×C₁₆	1	8	yes	—
68	C₂×Dic₁₇	C₂×C₁₆	1	2	yes	—
69	D₆₈	C₂×C₁₆	1	4	yes	—
70	C₄×D₁₇	C₂×C₁₆	1	4	yes	—
71	C₄×D₁₇	C₂²×C₈	1	4	yes	—
72	Dic₃₄	C₂×C₁₆	1	4	yes	—
73	C₈×C₁₇	C₂²×C₈	1	1	yes	characteristic
74	C₈×C₁₇	C₂²×C₈	1	2	yes	—
75	C₈×C₁₇	C₂³×C₄	1	1	yes	characteristic
76	#3622	C₂²×C₈	1	4	yes	—
77	C₂×#504	—	17	1	no	—
78	#2258	—	17	8	no	—
79	C₂×M₆₄	—	17	1	no	—
80	C₂×M₆₄	—	17	2	no	—
81	C₂²×C₃₂	—	17	1	no	—
82	C₂²×C₃₂	—	17	2	no	—
83	C₂²×C₁₇	—	2	2	no	—
84	C₂²×C₁₇	C₂²×C₁₆	1	2	yes	—
85	C₂²×C₁₇	C₂²×C₁₆	1	1	yes	characteristic
86	C₂×D₁₇	—	2	4	no	—
87	C₂×D₁₇	C₂²×C₁₆	1	4	yes	—
88	C₄×C₁₇	C₂²×C₁₆	1	2	yes	—
89	C₄×C₁₇	C₂²×C₁₆	1	1	yes	characteristic
90	C₄×C₁₇	C₂³×C₈	1	1	yes	characteristic
91	Dic₁₇	C₂²×C₁₆	1	4	yes	—
92	C₂×#131	—	17	1	no	—
93	#504	—	17	4	no	—
94	#504	—	17	4	no	—
95	C₂×M₃₂	—	17	2	no	—
96	C₂×M₃₂	#595	1	1	yes	characteristic
97	C₂²×C₁₆	—	17	1	no	—
98	C₂²×C₁₆	—	17	2	no	—
99	M₆₄	—	17	4	no	—
100	M₆₄	—	17	8	no	—
101	C₂×C₃₂	—	17	1	no	—
102	C₂×C₃₂	—	17	1	no	—
103	C₂×C₃₂	—	17	2	no	—
104	C₂×C₃₂	—	17	4	no	—
105	C₂×C₃₂	—	17	8	no	—
106	C₂×C₁₇	—	2	2	no	—
107	C₂×C₁₇	#2258	1	2	yes	complemented
108	C₂×C₁₇	C₂³×C₁₆	1	1	yes	characteristic
109	D₁₇	—	2	4	no	—
110	C₂×#41	—	17	1	no	—
111	#131	—	17	4	no	—
112	#131	—	17	4	no	—
113	C₂×M₁₆	—	17	1	no	—
114	C₂×M₁₆	—	17	2	no	—
115	C₂²×C₈	—	17	2	no	—
116	C₂²×C₈	C₂×#595	1	1	yes	characteristic
117	M₃₂	—	17	8	no	—
118	M₃₂	C₂×#595	1	4	yes	—
119	C₂×C₁₆	—	17	2	no	—
120	C₂×C₁₆	—	17	2	no	—
121	C₂×C₁₆	—	17	1	no	—
122	C₂×C₁₆	—	17	1	no	—
123	C₂×C₁₆	—	17	4	no	—
124	C₂×C₁₆	—	17	4	no	—
125	C₂×C₁₆	C₂×#595	1	2	yes	—
126	C₃₂	—	17	2	no	—
127	C₃₂	—	17	2	no	—
128	C₃₂	—	17	4	no	—
129	C₁₇	C₂×#2258	1	1	yes	characteristic, complemented, Sylow
130	#41	—	17	4	no	—
131	#41	—	17	4	no	—
132	C₂×Q₈	—	17	1	no	—
133	C₂×D₄	—	17	2	no	—
134	C₂×D₄	—	17	1	no	—
135	C₂²×C₄	—	17	2	no	—
136	C₂²×C₄	#63242	1	1	yes	characteristic
137	M₁₆	—	17	4	no	—
138	M₁₆	—	17	8	no	—
139	C₂×C₈	—	17	2	no	—
140	C₂×C₈	—	17	4	no	—
141	C₂×C₈	—	17	4	no	—
142	C₂×C₈	#63242	1	1	yes	characteristic
143	C₂×C₈	#63242	1	2	yes	—
144	C₂×C₈	C₂²×#595	1	2	yes	—
145	C₂×C₈	C₂²×#595	1	1	yes	characteristic
146	C₁₆	—	17	1	no	—
147	C₁₆	—	17	1	no	—
148	C₁₆	—	17	2	no	—
149	C₁₆	C₂²×#595	1	4	yes	—
150	C₂³	—	17	2	no	—
151	C₂³	#10587529	1	1	yes	characteristic
152	Q₈	—	17	4	no	—
153	D₄	—	17	8	no	—
154	D₄	—	17	4	no	—
155	C₂×C₄	—	17	2	no	—
156	C₂×C₄	—	17	4	no	—
157	C₂×C₄	—	17	4	no	—
158	C₂×C₄	#10587529	1	1	yes	characteristic
159	C₂×C₄	#10587529	1	2	yes	—
160	C₂×C₄	C₂×#63242	1	1	yes	characteristic
161	C₂×C₄	C₂×#63242	1	2	yes	—
162	C₈	—	17	4	no	—
163	C₈	C₂×#63242	1	1	yes	characteristic
164	C₈	C₂×#63242	1	2	yes	—
165	C₈	C₂³×#595	1	1	yes	characteristic
166	C₂²	—	2	2	no	—
167	C₂²	—	17	4	no	—
168	C₂²	—	34	4	no	—
169	C₂²	C₂×#10587529	1	2	yes	—
170	C₂²	C₂×#10587529	1	1	yes	characteristic
171	C₄	—	17	4	no	—
172	C₄	C₂×#10587529	1	1	yes	characteristic
173	C₄	C₂×#10587529	1	2	yes	—
174	C₄	C₂²×#63242	1	1	yes	characteristic
175	C₂	—	2	2	no	—
176	C₂	—	34	4	no	—
177	C₂	#14545208	1	2	yes	direct product factor
178	C₂	C₂²×#10587529	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×#595
commutator	C₂×C₁₇	C₂³×C₁₆
Frattini	C₈	C₂³×#595
Fitting	C₂×C₁₇×M₃₂	C₄
socle	C₂²×C₁₇	C₂²×C₁₆
prime radical	C₂×#63252	C₈
cosocle	#63214	C₂⁴
hypercenter	C₂×M₃₂	#595
hypocenter	C₁₇	C₂×#2258
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
1. #14545208	C₂	direct (N × H)
2. C₂×#11763742	C₂	semidirect
3. C₂×#11763741	C₂	semidirect
4. C₂×#11763740	C₂	semidirect
5. C₂²×#10587467	C₂	semidirect
7. #11763742	C₂²	semidirect
8. #11763741	C₂²	semidirect
9. #11763740	C₂²	semidirect
13. C₂×#10587467	C₂²	semidirect
107. C₂×C₁₇	#2258	semidirect
129. C₁₇	C₂×#2258	semidirect
177. C₂	#14545208	direct (N × H)

Maximal subgroups

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

subgroup	index
#14545208	2
C₂×#11763742	2
C₂×#11763741	2
C₂×#11763740	2
C₂²×#10587467	2
C₂×#11763227	2
C₂×#2258	17

Subgroups — C2×#14545208 #17978841

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14545208 #17978841