Subgroups — C₂×#14526855 #16945901

Order 4352.

262 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	C₂×C₄×#63214	C₂	1	1	yes	maximal, characteristic
2	C₂×#11762562	C₂	1	1	yes	maximal, characteristic
3	#14526855	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₇×#335	C₂	1	1	yes	maximal, characteristic
5	C₂²×#63214	C₄	1	1	yes	characteristic
6	C₂²×#63214	C₄	1	1	yes	characteristic
7	C₂×C₄⋊#3622	—	2	1	no	—
8	C₄×#63214	C₄	1	2	yes	—
9	C₄×#63214	C₂²	1	2	yes	—
10	#11762562	—	2	1	no	—
11	#11762562	C₂²	1	2	yes	—
12	C₂×C₁₇×C₄⋊C₈	—	2	1	no	—
13	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
14	C₁₇×#335	—	2	1	no	—
15	C₁₇×#335	C₂²	1	2	yes	—
16	C₂²×C₈×C₁₇	—	4	1	no	—
17	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₇	Q₈	1	1	yes	characteristic
19	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
20	C₂²×#3622	—	4	1	no	—
21	C₁₇×C₄⋊C₈	—	2	2	no	—
22	C₁₇×C₄⋊C₈	—	4	1	no	—
23	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
24	C₄×C₈×C₁₇	D₄	1	1	yes	characteristic
25	C₄×C₈×C₁₇	Q₈	1	1	yes	characteristic
26	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
27	C₂×#63214	—	2	2	no	—
28	C₂×#63214	C₈	1	4	yes	complemented
29	C₂×#63214	C₂×C₄	1	2	yes	—
30	C₂×#63214	C₂×C₄	1	2	yes	—
31	C₄⋊#3622	—	2	2	no	—
32	C₄⋊#3622	—	4	1	no	—
33	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
34	C₂²×C₄×C₁₇	D₈	1	1	yes	characteristic
35	C₂²×C₄×C₁₇	Q₁₆	1	1	yes	characteristic
36	C₂×C₈×C₁₇	—	2	2	no	—
37	C₂×C₈×C₁₇	—	4	2	no	—
38	C₂×C₈×C₁₇	—	8	2	no	—
39	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
40	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
41	C₂×C₈×C₁₇	C₂×C₈	1	2	yes	—
42	C₂×C₈×C₁₇	M₁₆	1	2	yes	—
43	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
44	C₂×C₈×C₁₇	C₂×Q₈	1	1	yes	characteristic
45	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
46	C₄²×C₁₇	D₈	1	1	yes	characteristic
47	C₄²×C₁₇	Q₁₆	1	1	yes	characteristic
48	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
49	C₂×#3622	—	4	2	no	—
50	C₂×#3622	—	8	2	no	—
51	#63214	—	2	2	no	—
52	#63214	C₂×C₈	1	4	yes	complemented
53	C₂×#1371	—	17	1	no	maximal, Sylow
54	C₂³×C₁₇	#107	1	1	yes	characteristic
55	C₂×C₄×C₁₇	—	2	2	no	—
56	C₂×C₄×C₁₇	C₄⋊C₈	1	2	yes	—
57	C₂×C₄×C₁₇	#107	1	1	yes	characteristic
58	C₂×C₄×C₁₇	#107	1	1	yes	characteristic
59	C₂×C₄×C₁₇	#107	1	1	yes	characteristic
60	C₂×C₄×C₁₇	#108	1	2	yes	—
61	C₂×C₄×C₁₇	D₁₆	1	2	yes	—
62	C₂×C₄×C₁₇	Q₃₂	1	2	yes	—
63	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
64	C₂×C₄×C₁₇	C₂×D₈	1	1	yes	characteristic
65	C₂×C₄×C₁₇	C₂×Q₁₆	1	1	yes	characteristic
66	C₈×C₁₇	—	2	1	no	—
67	C₈×C₁₇	—	2	1	no	—
68	C₈×C₁₇	—	8	2	no	—
69	C₈×C₁₇	C₄⋊C₈	1	2	yes	—
70	C₈×C₁₇	C₂²×C₈	1	1	yes	characteristic
71	C₈×C₁₇	C₂×M₁₆	1	1	yes	characteristic
72	#3622	—	8	2	no	—
73	C₂×C₄×C₁₆	—	17	1	no	—
74	C₂×#335	—	17	1	no	—
75	C₂×#335	D₁₇	1	1	yes	characteristic
76	#1371	—	17	4	no	—
77	C₂²×C₁₇	#335	1	2	yes	—
78	C₂²×C₁₇	#366	1	2	yes	—
79	C₂²×C₁₇	#368	1	2	yes	—
80	C₂²×C₁₇	C₂×#107	1	1	yes	characteristic
81	C₄×C₁₇	—	2	1	no	—
82	C₄×C₁₇	—	2	1	no	—
83	C₄×C₁₇	#335	1	2	yes	—
84	C₄×C₁₇	#366	1	2	yes	—
85	C₄×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
86	C₄×C₁₇	C₂×#108	1	1	yes	characteristic
87	C₄×C₁₇	C₂×D₁₆	1	1	yes	characteristic
88	C₄×C₁₇	C₂×Q₃₂	1	1	yes	characteristic
89	C₂²×C₁₆	—	17	1	no	—
90	C₂²×C₁₆	—	17	1	no	—
91	C₂×C₄⋊C₈	—	2	1	no	—
92	C₂×C₄⋊C₈	—	34	1	no	—
93	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
94	C₄×C₁₆	—	17	2	no	—
95	C₄×C₁₆	—	17	2	no	—
96	#335	—	2	1	no	—
97	#335	—	17	2	no	—
98	#335	—	34	1	no	—
99	#335	C₂×D₁₇	1	2	yes	—
100	C₂×C₁₇	#1371	1	4	yes	complemented
101	C₂×C₁₇	C₂×#335	1	1	yes	characteristic
102	C₂×C₁₇	C₂×#366	1	1	yes	characteristic
103	C₂×C₁₇	C₂×#368	1	1	yes	characteristic
104	C₂²×C₈	—	4	1	no	—
105	C₂²×C₈	—	68	1	no	—
106	C₂²×C₈	Dic₃₄	1	1	yes	characteristic
107	C₂²×C₈	C₄×D₁₇	1	1	yes	characteristic
108	C₂×C₄²	C₂²⋊D₁₇	1	1	yes	characteristic
109	C₂×C₁₆	—	17	2	no	—
110	C₂×C₁₆	—	17	4	no	—
111	C₂×C₁₆	—	17	2	no	—
112	C₂×C₁₆	—	34	2	no	—
113	C₄⋊C₈	—	2	2	no	—
114	C₄⋊C₈	—	4	1	no	—
115	C₄⋊C₈	—	34	2	no	—
116	C₄⋊C₈	—	68	1	no	—
117	C₄×C₈	Dic₃₄	1	1	yes	characteristic
118	C₄×C₈	C₄×D₁₇	1	1	yes	characteristic
119	C₄×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
120	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
121	C₁₇	C₂×#1371	1	1	yes	characteristic, complemented, Sylow
122	C₂²×C₄	#63225	1	1	yes	characteristic
123	C₂²×C₄	#63228	1	1	yes	characteristic
124	C₂²×C₄	#63231	1	1	yes	characteristic
125	C₂×C₈	—	2	2	no	—
126	C₂×C₈	—	4	2	no	—
127	C₂×C₈	—	8	2	no	—
128	C₂×C₈	—	68	2	no	—
129	C₂×C₈	—	136	2	no	—
130	C₂×C₈	C₈×D₁₇	1	2	yes	—
131	C₂×C₈	#63218	1	2	yes	—
132	C₂×C₈	#63225	1	1	yes	characteristic
133	C₂×C₈	#63225	1	1	yes	characteristic
134	C₂×C₈	C₂×Dic₃₄	1	1	yes	characteristic
135	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
136	C₄²	#63225	1	1	yes	characteristic
137	C₄²	#63228	1	1	yes	characteristic
138	C₄²	#63231	1	1	yes	characteristic
139	C₄²	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
140	C₁₆	—	17	4	no	—
141	C₁₆	—	34	2	no	—
142	C₂³	#10587478	1	1	yes	characteristic
143	C₂×C₄	—	2	2	no	—
144	C₂×C₄	#10587478	1	1	yes	characteristic
145	C₂×C₄	#10587478	1	1	yes	characteristic
146	C₂×C₄	#10587478	1	1	yes	characteristic
147	C₂×C₄	#10587485	1	2	yes	—
148	C₂×C₄	#10587493	1	2	yes	—
149	C₂×C₄	#10587497	1	2	yes	—
150	C₂×C₄	#10587500	1	2	yes	—
151	C₂×C₄	C₂×#63225	1	1	yes	characteristic
152	C₂×C₄	C₂×#63228	1	1	yes	characteristic
153	C₂×C₄	C₂×#63231	1	1	yes	characteristic
154	C₈	—	2	1	no	—
155	C₈	—	2	1	no	—
156	C₈	—	8	2	no	—
157	C₈	—	136	2	no	—
158	C₈	#10587485	1	2	yes	—
159	C₈	C₂×C₈×D₁₇	1	1	yes	characteristic
160	C₈	C₂×#63218	1	1	yes	characteristic
161	C₂²	#11762561	1	2	yes	—
162	C₂²	#11762634	1	2	yes	—
163	C₂²	#11762638	1	2	yes	—
164	C₂²	C₂×#10587478	1	1	yes	characteristic
165	C₄	—	2	1	no	—
166	C₄	—	2	1	no	—
167	C₄	#11762561	1	2	yes	—
168	C₄	#11762634	1	2	yes	—
169	C₄	C₂×#10587485	1	1	yes	characteristic
170	C₄	C₂×#10587493	1	1	yes	characteristic
171	C₄	C₂×#10587497	1	1	yes	characteristic
172	C₄	C₂×#10587500	1	1	yes	characteristic
173	C₂	#14526855	1	4	yes	direct product factor
174	C₂	C₂×#11762561	1	1	yes	characteristic
175	C₂	C₂×#11762634	1	1	yes	characteristic
176	C₂	C₂×#11762638	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	#63228
commutator	C₈×C₁₇	C₂²×C₈
Frattini	C₄×C₈	C₂²×D₁₇
Fitting	C₂×C₁₇×#335	C₂
socle, prime radical	C₂³×C₁₇	#107
cosocle	C₄×C₈×C₁₇	C₂³
hypercenter	C₂×#335	D₁₇
hypocenter	C₁₇	C₂×#1371
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#335

Complements

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

N	H ≅ G/N	type
3. #14526855	C₂	direct (N × H)
28. C₂×#63214	C₈	semidirect
52. #63214	C₂×C₈	semidirect
100. C₂×C₁₇	#1371	semidirect
121. C₁₇	C₂×#1371	semidirect
173. C₂	#14526855	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×C₄×#63214	2
C₂×#11762562	2
#14526855	2
C₂×C₁₇×#335	2
C₂×#1371	17

Subgroups — C2×#14526855 #16945901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14526855 #16945901