Subgroups — C₂²×#11763893 #17982826

Order 4352.

1182 conjugacy classes of subgroups.

The subgroup lattice has 184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×#3633	C₂	1	2	yes	maximal
2	C₂×#11763893	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₈×#595	C₂	1	1	yes	maximal, characteristic
4	C₂³×#3633	C₄	1	4	yes	—
5	C₂×C₄×#3633	C₄	1	12	yes	—
6	C₂×C₄×#3633	C₂²	1	12	yes	—
7	#11763893	C₂²	1	16	yes	direct product factor
8	C₂²×#63242	C₄	1	1	yes	characteristic
9	C₂²×C₄×#595	C₂²	1	1	yes	characteristic
10	C₂×C₈×#595	C₄	1	6	yes	—
11	C₂×C₈×#595	C₂²	1	6	yes	—
12	C₂²×C₈×D₁₇	C₄	1	1	yes	characteristic
13	C₂³×#595	C₂×C₄	1	2	yes	—
14	C₂²×#3633	—	2	16	no	—
15	C₂²×#3633	C₂×C₄	1	24	yes	—
16	C₂²×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
17	C₂²×#3624	C₈	1	2	yes	complemented
18	C₂×C₄×#595	C₂×C₄	1	6	yes	—
19	C₂×C₄×#595	C₂×C₄	1	3	yes	—
20	C₂×C₄×#595	C₂³	1	3	yes	—
21	C₂×#63242	C₈	1	6	yes	complemented
22	C₂×#63242	C₂×C₄	1	6	yes	—
23	C₄×#3633	C₂×C₄	1	24	yes	—
24	C₄×#3633	C₂³	1	8	yes	—
25	C₂²×C₈×C₁₇	C₈	1	1	yes	characteristic, complemented
26	C₂²×#3622	C₈	1	1	yes	characteristic, complemented
27	C₂×C₈×D₁₇	C₈	1	6	yes	complemented
28	C₂×C₈×D₁₇	C₂×C₄	1	6	yes	—
29	C₈×#595	C₂×C₄	1	12	yes	—
30	C₈×#595	C₂³	1	4	yes	—
31	C₂³×D₁₇	C₄²	1	1	yes	characteristic
32	C₂²×#595	C₄²	1	6	yes	—
33	C₂²×#595	M₁₆	1	16	yes	—
34	C₂²×#595	C₂²×C₄	1	6	yes	—
35	C₂×#3633	—	2	48	no	—
36	C₂×#3633	C₂²×C₄	1	16	yes	—
37	C₂²×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
38	C₂²×Dic₁₇	C₂×C₈	1	1	yes	characteristic
39	C₂×C₄×D₁₇	C₄²	1	3	yes	—
40	C₂×C₄×D₁₇	C₂×C₈	1	3	yes	—
41	C₂×C₄×D₁₇	C₂×C₈	1	3	yes	—
42	C₂×C₄×D₁₇	C₂²×C₄	1	3	yes	—
43	C₂×#3624	C₂×C₈	1	12	yes	complemented
44	C₄×#595	C₄²	1	6	yes	—
45	C₄×#595	C₂²×C₄	1	6	yes	—
46	C₄×#595	C₂²×C₄	1	3	yes	—
47	C₄×#595	C₂⁴	1	1	yes	characteristic
48	#63242	C₂×C₈	1	12	yes	complemented
49	#63242	C₂²×C₄	1	4	yes	—
50	C₂×C₈×C₁₇	C₂×C₈	1	6	yes	complemented
51	C₂×#3622	C₂×C₈	1	6	yes	complemented
52	C₈×D₁₇	C₂×C₈	1	12	yes	complemented
53	C₈×D₁₇	C₂²×C₄	1	4	yes	—
54	C₂²×#322	—	17	1	no	maximal, Sylow
55	C₂³×C₁₇	C₄×C₈	1	1	yes	characteristic
56	C₂²×D₁₇	C₄×C₈	1	3	yes	—
57	C₂²×D₁₇	#97	1	8	yes	—
58	C₂²×D₁₇	C₂×C₄²	1	3	yes	—
59	C₂×#595	#97	1	24	yes	—
60	C₂×#595	C₂×C₄²	1	6	yes	—
61	C₂×#595	C₂×M₁₆	1	24	yes	—
62	C₂×#595	C₂³×C₄	1	2	yes	—
63	#3633	—	2	16	no	—
64	C₂×C₄×C₁₇	C₄×C₈	1	3	yes	—
65	C₂×C₄×C₁₇	C₂²×C₈	1	3	yes	—
66	C₂×Dic₁₇	C₄×C₈	1	3	yes	—
67	C₂×Dic₁₇	C₂²×C₈	1	3	yes	—
68	C₄×D₁₇	C₄×C₈	1	6	yes	—
69	C₄×D₁₇	C₂×C₄²	1	3	yes	—
70	C₄×D₁₇	C₂²×C₈	1	3	yes	—
71	C₄×D₁₇	C₂²×C₈	1	3	yes	—
72	C₄×D₁₇	C₂³×C₄	1	1	yes	characteristic
73	#3624	C₂²×C₈	1	8	yes	complemented
74	C₈×C₁₇	C₂²×C₈	1	4	yes	complemented
75	#3622	C₂²×C₈	1	4	yes	complemented
76	C₂²×C₄×C₈	—	17	2	no	—
77	C₂²×C₄×C₈	—	17	1	no	—
78	C₂×#322	—	17	12	no	—
79	C₂²×C₁₇	#322	1	4	yes	complemented
80	C₂²×C₁₇	C₂×C₄×C₈	1	3	yes	—
81	C₂×D₁₇	#322	1	12	yes	complemented
82	C₂×D₁₇	C₂×C₄×C₈	1	3	yes	—
83	C₂×D₁₇	C₂×#97	1	12	yes	—
84	C₂×D₁₇	C₂²×C₄²	1	1	yes	characteristic
85	#595	C₂×#97	1	12	yes	—
86	#595	C₂²×M₁₆	1	4	yes	—
87	C₄×C₁₇	C₂×C₄×C₈	1	3	yes	—
88	C₄×C₁₇	C₂³×C₈	1	1	yes	characteristic
89	Dic₁₇	C₂×C₄×C₈	1	3	yes	—
90	Dic₁₇	C₂³×C₈	1	1	yes	characteristic
91	C₂³×C₈	—	17	1	no	—
92	C₂³×C₈	—	17	1	no	—
93	C₂³×C₈	—	17	4	no	—
94	C₂²×C₄²	—	17	1	no	—
95	C₂×C₄×C₈	—	17	6	no	—
96	C₂×C₄×C₈	—	17	6	no	—
97	C₂×C₄×C₈	—	17	12	no	—
98	C₂×C₄×C₈	—	17	12	no	—
99	#322	—	17	16	no	—
100	C₂×C₁₇	C₂×#322	1	6	yes	complemented
101	C₂×C₁₇	C₂²×C₄×C₈	1	1	yes	characteristic
102	D₁₇	C₂×#322	1	6	yes	complemented
103	D₁₇	C₂²×#97	1	2	yes	—
104	C₂³×C₄	—	17	2	no	—
105	C₂³×C₄	—	17	1	no	—
106	C₂²×C₈	—	17	6	no	—
107	C₂²×C₈	—	17	6	no	—
108	C₂²×C₈	—	17	2	no	—
109	C₂²×C₈	—	17	1	no	—
110	C₂²×C₈	—	17	6	no	—
111	C₂²×C₈	—	17	6	no	—
112	C₂²×C₈	—	17	24	no	—
113	C₂²×C₈	—	34	16	no	—
114	C₂²×C₈	#3633	1	1	yes	characteristic, complemented
115	C₂×C₄²	—	17	3	no	—
116	C₂×C₄²	—	17	6	no	—
117	C₂×C₄²	—	17	3	no	—
118	C₄×C₈	—	17	24	no	—
119	C₄×C₈	—	17	8	no	—
120	C₄×C₈	—	17	4	no	—
121	C₄×C₈	—	17	12	no	—
122	C₁₇	C₂²×#322	1	1	yes	characteristic, complemented, Sylow
123	C₂⁴	—	17	1	no	—
124	C₂²×C₄	—	17	6	no	—
125	C₂²×C₄	—	17	16	no	—
126	C₂²×C₄	—	17	6	no	—
127	C₂²×C₄	—	17	1	no	—
128	C₂²×C₄	—	17	3	no	—
129	C₂²×C₄	—	17	3	no	—
130	C₂²×C₄	—	17	3	no	—
131	C₂²×C₄	—	17	3	no	—
132	C₂²×C₄	C₂×#3633	1	1	yes	characteristic
133	C₂×C₈	—	17	12	no	—
134	C₂×C₈	—	17	4	no	—
135	C₂×C₈	—	17	12	no	—
136	C₂×C₈	—	17	6	no	—
137	C₂×C₈	—	17	4	no	—
138	C₂×C₈	—	17	12	no	—
139	C₂×C₈	—	17	16	no	—
140	C₂×C₈	—	34	48	no	—
141	C₂×C₈	C₂×#3633	1	6	yes	complemented
142	C₄²	—	17	6	no	—
143	C₄²	—	17	6	no	—
144	C₄²	—	17	3	no	—
145	C₄²	—	17	1	no	—
146	C₂³	—	17	8	no	—
147	C₂³	—	17	3	no	—
148	C₂³	—	17	3	no	—
149	C₂³	C₄×#3633	1	1	yes	characteristic
150	C₂×C₄	—	17	2	no	—
151	C₂×C₄	—	17	6	no	—
152	C₂×C₄	—	17	24	no	—
153	C₂×C₄	—	17	24	no	—
154	C₂×C₄	—	17	3	no	—
155	C₂×C₄	—	17	3	no	—
156	C₂×C₄	—	17	3	no	—
157	C₂×C₄	—	17	3	no	—
158	C₂×C₄	—	17	6	no	—
159	C₂×C₄	—	17	1	no	—
160	C₂×C₄	—	17	3	no	—
161	C₂×C₄	C₄×#3633	1	3	yes	—
162	C₂×C₄	C₂²×#3633	1	3	yes	—
163	C₈	—	17	8	no	—
164	C₈	—	17	4	no	—
165	C₈	—	34	16	no	—
166	C₈	C₂²×#3633	1	4	yes	complemented
167	C₂²	—	17	1	no	—
168	C₂²	—	17	3	no	—
169	C₂²	—	17	12	no	—
170	C₂²	—	17	12	no	—
171	C₂²	#11763893	1	4	yes	direct product factor
172	C₂²	C₂×C₄×#3633	1	3	yes	—
173	C₄	—	17	4	no	—
174	C₄	—	17	12	no	—
175	C₄	—	17	1	no	—
176	C₄	—	17	3	no	—
177	C₄	C₂×C₄×#3633	1	3	yes	—
178	C₄	C₂³×#3633	1	1	yes	characteristic
179	C₂	—	17	2	no	—
180	C₂	—	17	6	no	—
181	C₂	C₂×#11763893	1	6	yes	direct product factor
182	C₂	C₂²×C₄×#3633	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×#3633
commutator	C₂×C₁₇	C₂²×C₄×C₈
Frattini	C₄	C₂³×#3633
Fitting	C₂²×C₈×C₁₇	C₈
socle	C₂³×C₁₇	C₄×C₈
prime radical	C₂³×D₁₇	C₄²
cosocle	C₄×#595	C₂⁴
hypercenter	C₂²×C₈	#3633
hypocenter	C₁₇	C₂²×#322
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×#11763893	C₂	direct (N × H)
7. #11763893	C₂²	direct (N × H)
17. C₂²×#3624	C₈	semidirect
21. C₂×#63242	C₈	semidirect
25. C₂²×C₈×C₁₇	C₈	semidirect
26. C₂²×#3622	C₈	semidirect
27. C₂×C₈×D₁₇	C₈	semidirect
43. C₂×#3624	C₂×C₈	semidirect
48. #63242	C₂×C₈	semidirect
50. C₂×C₈×C₁₇	C₂×C₈	semidirect
51. C₂×#3622	C₂×C₈	semidirect
52. C₈×D₁₇	C₂×C₈	semidirect
73. #3624	C₂²×C₈	semidirect
74. C₈×C₁₇	C₂²×C₈	semidirect
75. #3622	C₂²×C₈	semidirect
79. C₂²×C₁₇	#322	semidirect
81. C₂×D₁₇	#322	semidirect
100. C₂×C₁₇	C₂×#322	semidirect
102. D₁₇	C₂×#322	semidirect
114. C₂²×C₈	#3633	semidirect
122. C₁₇	C₂²×#322	semidirect
141. C₂×C₈	C₂×#3633	semidirect
166. C₈	C₂²×#3633	semidirect
171. C₂²	#11763893	direct (N × H)
181. C₂	C₂×#11763893	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×#3633	2
C₂×#11763893	2
C₂²×C₈×#595	2
C₂²×#322	17

Subgroups — C22×#11763893 #17982826

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11763893 #17982826