Subgroups — C₄×#19149758 #36369995

Order 22144.

752 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×#19149758	C₂	1	2	yes	maximal
2	C₄×C₄⋊#10621924	C₂	1	4	yes	maximal, complemented
3	C₄×C₂²⋊#10621924	C₂	1	4	yes	maximal
4	#26012427	C₂	1	2	yes	maximal, complemented
5	C₄²×#10621924	C₂	1	2	yes	maximal, complemented
6	C₂×C₄²×D₁₇₃	C₂	1	1	yes	maximal, characteristic
7	#19149758	C₄	1	16	yes	direct product factor
8	C₂×C₄⋊#10621924	C₂²	1	4	yes	—
9	C₂×C₂²⋊#10621924	C₂²	1	4	yes	—
10	C₂×C₄×#10621924	C₂²	1	8	yes	—
11	C₂×C₄×#10621924	C₂²	1	4	yes	—
12	(C₂×#10621924)⋊C₄	C₂²	1	8	yes	—
13	C₂²×C₄×D₁₇₃	C₂²	1	2	yes	—
14	C₂²×C₄×D₁₇₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×Dic₁₇₃	C₄	1	1	yes	characteristic, complemented
16	C₂×C₄×Dic₁₇₃	C₄	1	2	yes	complemented
17	C₄²×D₁₇₃	C₄	1	1	yes	characteristic, complemented
18	C₄²×D₁₇₃	C₄	1	2	yes	complemented
19	C₄²×D₁₇₃	C₄	1	1	yes	characteristic, complemented
20	C₄²×D₁₇₃	C₂²	1	1	yes	characteristic
21	C₄²×D₁₇₃	C₂²	1	1	yes	characteristic
22	C₄²×D₁₇₃	C₂²	1	2	yes	—
23	C₂×C₄²×C₁₇₃	C₄	1	1	yes	characteristic, complemented
24	C₂²×#10621924	C₂³	1	8	yes	—
25	C₄⋊#10621924	C₂×C₄	1	16	yes	complemented
26	C₂²⋊#10621924	C₂×C₄	1	16	yes	—
27	C₄×#10621924	—	2	16	no	—
28	C₄×#10621924	C₂×C₄	1	16	yes	complemented
29	C₂³×D₁₇₃	C₂³	1	1	yes	characteristic
30	C₂²×Dic₁₇₃	C₂×C₄	1	2	yes	—
31	C₂²×Dic₁₇₃	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄×D₁₇₃	—	2	8	no	—
33	C₂×C₄×D₁₇₃	C₂×C₄	1	8	yes	—
34	C₂×C₄×D₁₇₃	C₂×C₄	1	2	yes	—
35	C₂×C₄×D₁₇₃	C₂×C₄	1	2	yes	—
36	C₂×C₄×D₁₇₃	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄×D₁₇₃	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄×D₁₇₃	C₂³	1	2	yes	—
39	C₂×C₄×D₁₇₃	C₂³	1	1	yes	characteristic
40	C₂×C₄×D₁₇₃	C₂³	1	1	yes	characteristic
41	C₂×C₄×D₁₇₃	C₂³	1	2	yes	—
42	C₄×Dic₁₇₃	C₂×C₄	1	2	yes	—
43	C₄×Dic₁₇₃	C₂×C₄	1	2	yes	—
44	C₄×Dic₁₇₃	C₂×C₄	1	1	yes	characteristic
45	C₄×Dic₁₇₃	C₂×C₄	1	2	yes	—
46	C₄×Dic₁₇₃	C₂×C₄	1	1	yes	characteristic
47	C₄×Dic₁₇₃	C₂×C₄	1	2	yes	—
48	C₄×Dic₁₇₃	C₂×C₄	1	2	yes	—
49	C₂²×C₄×C₁₇₃	C₂×C₄	1	2	yes	—
50	C₂²×C₄×C₁₇₃	C₂×C₄	1	1	yes	characteristic
51	C₄²×C₁₇₃	C₂×C₄	1	1	yes	characteristic
52	C₄²×C₁₇₃	C₂×C₄	1	2	yes	—
53	C₄²×C₁₇₃	C₂×C₄	1	1	yes	characteristic
54	C₂×#10621924	—	2	16	no	—
55	C₂×#10621924	C₂²×C₄	1	16	yes	—
56	C₂²×D₁₇₃	—	2	4	no	—
57	C₂²×D₁₇₃	C₂²×C₄	1	1	yes	characteristic
58	C₂²×D₁₇₃	C₂²×C₄	1	4	yes	—
59	C₂²×D₁₇₃	C₂⁴	1	1	yes	characteristic
60	C₂×Dic₁₇₃	—	2	4	no	—
61	C₂×Dic₁₇₃	C₄²	1	4	yes	complemented
62	C₂×Dic₁₇₃	C₂²×C₄	1	2	yes	—
63	C₂×Dic₁₇₃	C₂²×C₄	1	1	yes	characteristic
64	C₂×Dic₁₇₃	C₂²×C₄	1	1	yes	characteristic
65	C₂×Dic₁₇₃	C₂²×C₄	1	2	yes	—
66	C₄×D₁₇₃	—	2	4	no	—
67	C₄×D₁₇₃	—	2	4	no	—
68	C₄×D₁₇₃	—	2	4	no	—
69	C₄×D₁₇₃	C₄²	1	4	yes	complemented
70	C₄×D₁₇₃	C₄²	1	4	yes	complemented
71	C₄×D₁₇₃	C₂²×C₄	1	4	yes	—
72	C₄×D₁₇₃	C₂²×C₄	1	4	yes	—
73	C₄×D₁₇₃	#41	1	8	yes	—
74	C₂³×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
75	C₂×C₄×C₁₇₃	—	2	4	no	—
76	C₂×C₄×C₁₇₃	C₄²	1	4	yes	complemented
77	C₂×C₄×C₁₇₃	C₂²×C₄	1	2	yes	—
78	C₂×C₄×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
79	C₂×C₄×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
80	C₂×C₄×C₁₇₃	C₂²×C₄	1	2	yes	—
81	C₂²×C₁₇₃	—	2	2	no	—
82	C₂²×C₁₇₃	C₂×C₄²	1	2	yes	—
83	C₂²×C₁₇₃	C₂³×C₄	1	1	yes	characteristic
84	C₂×D₁₇₃	—	2	2	no	—
85	C₂×D₁₇₃	—	2	8	no	—
86	C₂×D₁₇₃	C₂×C₄²	1	2	yes	—
87	C₂×D₁₇₃	C₂³×C₄	1	2	yes	—
88	C₂×D₁₇₃	C₂×#41	1	4	yes	—
89	#10621924	—	2	16	no	—
90	C₄×C₁₇₃	—	2	2	no	—
91	C₄×C₁₇₃	C₂×C₄²	1	2	yes	—
92	C₄×C₁₇₃	C₂×C₄²	1	2	yes	—
93	C₄×C₁₇₃	#117	1	4	yes	complemented
94	Dic₁₇₃	—	2	2	no	—
95	Dic₁₇₃	C₂×C₄²	1	2	yes	—
96	Dic₁₇₃	C₂×C₄²	1	2	yes	—
97	Dic₁₇₃	#117	1	4	yes	complemented
98	C₂×C₁₇₃	—	2	2	no	—
99	C₂×C₁₇₃	C₂²×C₄²	1	1	yes	characteristic
100	C₂×C₁₇₃	C₂×#117	1	2	yes	—
101	D₁₇₃	—	2	2	no	—
102	D₁₇₃	C₄×#41	1	4	yes	—
103	C₁₇₃	C₄×#117	1	1	yes	characteristic, complemented, Sylow
104	C₄×#117	—	173	1	no	maximal, Sylow
105	C₂×#117	—	173	2	no	—
106	C₂²×C₄²	—	173	1	no	—
107	C₄×C₄⋊C₄	—	173	4	no	—
108	C₄×C₂²⋊C₄	—	173	4	no	—
109	#376	—	173	2	no	—
110	C₄³	—	173	2	no	—
111	C₂³×C₄	—	173	2	no	—
112	C₂³×C₄	—	173	1	no	—
113	#117	—	173	16	no	—
114	C₂×C₄⋊C₄	—	173	4	no	—
115	C₂×C₂²⋊C₄	—	173	4	no	—
116	C₂×C₄²	—	173	8	no	—
117	C₂×C₄²	—	173	4	no	—
118	C₂×C₄²	—	173	1	no	—
119	C₂×C₄²	—	173	2	no	—
120	C₂×C₄²	—	173	2	no	—
121	C₂×C₄²	—	173	1	no	—
122	C₂×C₄²	—	173	1	no	—
123	C₂×C₄²	—	173	2	no	—
124	C₂×C₄²	—	173	1	no	—
125	C₂×C₄²	—	173	1	no	—
126	C₂×C₄²	#10621924	1	1	yes	characteristic, complemented
127	#95	—	173	8	no	—
128	C₂⁴	—	173	1	no	—
129	C₂²×C₄	—	346	8	no	—
130	C₂²×C₄	—	173	8	no	—
131	C₂²×C₄	—	173	2	no	—
132	C₂²×C₄	—	173	2	no	—
133	C₂²×C₄	—	173	2	no	—
134	C₂²×C₄	—	173	2	no	—
135	C₂²×C₄	—	173	1	no	—
136	C₂²×C₄	—	173	8	no	—
137	C₂²×C₄	—	173	1	no	—
138	C₂²×C₄	—	173	1	no	—
139	C₂²×C₄	—	173	1	no	—
140	C₂²×C₄	—	173	2	no	—
141	C₂²×C₄	—	173	1	no	—
142	C₂²×C₄	C₂×#10621924	1	2	yes	—
143	C₂²×C₄	C₂×#10621924	1	1	yes	characteristic
144	C₄⋊C₄	—	173	16	no	—
145	C₂²⋊C₄	—	173	16	no	—
146	C₄²	—	346	16	no	—
147	C₄²	—	173	16	no	—
148	C₄²	—	173	1	no	—
149	C₄²	—	173	2	no	—
150	C₄²	—	173	2	no	—
151	C₄²	—	173	2	no	—
152	C₄²	—	173	2	no	—
153	C₄²	—	173	1	no	—
154	C₄²	—	173	2	no	—
155	C₄²	C₂×#10621924	1	1	yes	characteristic
156	C₄²	C₂×#10621924	1	2	yes	—
157	C₄²	C₂×#10621924	1	1	yes	characteristic
158	C₂³	—	346	4	no	—
159	C₂³	—	173	4	no	—
160	C₂³	—	173	1	no	—
161	C₂³	—	173	1	no	—
162	C₂³	C₂²×#10621924	1	1	yes	characteristic
163	C₂×C₄	—	2	4	no	—
164	C₂×C₄	—	346	4	no	—
165	C₂×C₄	—	346	4	no	—
166	C₂×C₄	—	346	16	no	—
167	C₂×C₄	—	346	4	no	—
168	C₂×C₄	—	346	4	no	—
169	C₂×C₄	—	173	16	no	—
170	C₂×C₄	—	173	2	no	—
171	C₂×C₄	—	173	4	no	—
172	C₂×C₄	—	173	1	no	—
173	C₂×C₄	—	173	1	no	—
174	C₂×C₄	—	173	2	no	—
175	C₂×C₄	—	173	4	no	—
176	C₂×C₄	—	173	4	no	—
177	C₂×C₄	—	173	4	no	—
178	C₂×C₄	—	173	4	no	—
179	C₂×C₄	—	173	8	no	—
180	C₂×C₄	C₄×#10621924	1	4	yes	complemented
181	C₂×C₄	C₂²×#10621924	1	2	yes	—
182	C₂×C₄	C₂²×#10621924	1	1	yes	characteristic
183	C₂×C₄	C₂²×#10621924	1	1	yes	characteristic
184	C₂×C₄	C₂²×#10621924	1	2	yes	—
185	C₂²	—	2	2	no	—
186	C₂²	—	346	8	no	—
187	C₂²	—	346	2	no	—
188	C₂²	—	173	2	no	—
189	C₂²	—	173	2	no	—
190	C₂²	—	173	4	no	—
191	C₂²	C₂×C₄×#10621924	1	2	yes	—
192	C₂²	C₂³×#10621924	1	1	yes	characteristic
193	C₄	—	2	2	no	—
194	C₄	—	346	16	no	—
195	C₄	—	346	2	no	—
196	C₄	—	173	2	no	—
197	C₄	—	173	2	no	—
198	C₄	—	173	4	no	—
199	C₄	C₂×C₄×#10621924	1	2	yes	—
200	C₄	C₂×C₄×#10621924	1	2	yes	—
201	C₄	#19149758	1	4	yes	direct product factor
202	C₂	—	2	2	no	—
203	C₂	—	346	2	no	—
204	C₂	—	173	4	no	—
205	C₂	C₂²×C₄×#10621924	1	1	yes	characteristic
206	C₂	C₂×#19149758	1	2	yes	—

	subgroup	G/H
center	C₄²	C₂×#10621924
commutator	C₂×C₁₇₃	C₂²×C₄²
Frattini	C₂²	C₂³×#10621924
Fitting	C₂×C₄²×C₁₇₃	C₄
socle	C₂²×C₁₇₃	C₂³×C₄
prime radical	C₂³×D₁₇₃	C₂³
cosocle	C₂²×D₁₇₃	C₂⁴
hypercenter	C₂×C₄²	#10621924
hypocenter	C₁₇₃	C₄×#117
LCS	G ▷ C₂×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₄² ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. C₄×C₄⋊#10621924	C₂	semidirect
4. #26012427	C₂	semidirect
5. C₄²×#10621924	C₂	semidirect
7. #19149758	C₄	direct (N × H)
15. C₂×C₄×Dic₁₇₃	C₄	semidirect
16. C₂×C₄×Dic₁₇₃	C₄	semidirect
17. C₄²×D₁₇₃	C₄	semidirect
18. C₄²×D₁₇₃	C₄	semidirect
19. C₄²×D₁₇₃	C₄	semidirect
23. C₂×C₄²×C₁₇₃	C₄	semidirect
25. C₄⋊#10621924	C₂×C₄	semidirect
28. C₄×#10621924	C₂×C₄	semidirect
61. C₂×Dic₁₇₃	C₄²	semidirect
69. C₄×D₁₇₃	C₄²	semidirect
70. C₄×D₁₇₃	C₄²	semidirect
76. C₂×C₄×C₁₇₃	C₄²	semidirect
93. C₄×C₁₇₃	#117	semidirect
97. Dic₁₇₃	#117	semidirect
103. C₁₇₃	C₄×#117	semidirect
126. C₂×C₄²	#10621924	semidirect
180. C₂×C₄	C₄×#10621924	semidirect
201. C₄	#19149758	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×#19149758	2
C₄×C₄⋊#10621924	2
C₄×C₂²⋊#10621924	2
#26012427	2
C₄²×#10621924	2
C₂×C₄²×D₁₇₃	2
C₄×#117	173

Subgroups — C4×#19149758 #36369995

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#19149758 #36369995