Subgroups — C₄×#11745345 #16835924

Order 3712.

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×#11745345	C₂	1	2	yes	maximal
2	C₄×C₄⋊#1181	C₂	1	4	yes	maximal, complemented
3	C₄×C₂²⋊#1181	C₂	1	4	yes	maximal
4	#14272099	C₂	1	2	yes	maximal, complemented
5	C₄²×#1181	C₂	1	2	yes	maximal, complemented
6	C₂×C₄²×D₂₉	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₄×D₂₉	C₂²	1	2	yes	—
8	C₂²×C₄×D₂₉	C₂²	1	1	yes	characteristic
9	C₂×C₂²⋊#1181	C₂²	1	4	yes	—
10	#11745345	C₄	1	16	yes	direct product factor
11	C₂×C₄⋊#1181	C₂²	1	4	yes	—
12	C₂×C₄×#1181	C₂²	1	8	yes	—
13	C₂×C₄×#1181	C₂²	1	4	yes	—
14	C₂×C₄²×C₂₉	C₄	1	1	yes	characteristic, complemented
15	C₂×C₄×Dic₂₉	C₄	1	1	yes	characteristic, complemented
16	C₂×C₄×Dic₂₉	C₄	1	2	yes	complemented
17	C₄²×D₂₉	C₄	1	2	yes	complemented
18	C₄²×D₂₉	C₄	1	1	yes	characteristic, complemented
19	C₄²×D₂₉	C₄	1	1	yes	characteristic, complemented
20	C₄²×D₂₉	C₂²	1	1	yes	characteristic
21	C₄²×D₂₉	C₂²	1	1	yes	characteristic
22	C₄²×D₂₉	C₂²	1	2	yes	—
23	(C₂×#1181)⋊C₄	C₂²	1	8	yes	—
24	C₂³×D₂₉	C₂³	1	1	yes	characteristic
25	C₂²×#1181	C₂³	1	8	yes	—
26	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
27	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
28	C₂²×Dic₂₉	C₂×C₄	1	2	yes	—
29	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄×D₂₉	—	2	8	no	—
31	C₂×C₄×D₂₉	C₂×C₄	1	2	yes	—
32	C₂×C₄×D₂₉	C₂×C₄	1	2	yes	—
33	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄×D₂₉	C₂×C₄	1	8	yes	—
36	C₂×C₄×D₂₉	C₂³	1	2	yes	—
37	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
38	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
39	C₂×C₄×D₂₉	C₂³	1	2	yes	—
40	C₂²⋊#1181	C₂×C₄	1	16	yes	—
41	C₄⋊#1181	C₂×C₄	1	16	yes	complemented
42	C₄×#1181	—	2	16	no	—
43	C₄×#1181	C₂×C₄	1	16	yes	complemented
44	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
45	C₄²×C₂₉	C₂×C₄	1	2	yes	—
46	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
47	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
48	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
49	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
50	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
51	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
52	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
53	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
54	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
55	C₂²×D₂₉	—	2	4	no	—
56	C₂²×D₂₉	C₂²×C₄	1	1	yes	characteristic
57	C₂²×D₂₉	C₂²×C₄	1	4	yes	—
58	C₂²×D₂₉	C₂⁴	1	1	yes	characteristic
59	C₂×#1181	—	2	16	no	—
60	C₂×#1181	C₂²×C₄	1	16	yes	—
61	C₂×C₄×C₂₉	—	2	4	no	—
62	C₂×C₄×C₂₉	C₄²	1	4	yes	complemented
63	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
64	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
65	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
66	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
67	C₂×Dic₂₉	—	2	4	no	—
68	C₂×Dic₂₉	C₄²	1	4	yes	complemented
69	C₂×Dic₂₉	C₂²×C₄	1	2	yes	—
70	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
71	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
72	C₂×Dic₂₉	C₂²×C₄	1	2	yes	—
73	C₄×D₂₉	—	2	4	no	—
74	C₄×D₂₉	—	2	4	no	—
75	C₄×D₂₉	—	2	4	no	—
76	C₄×D₂₉	C₄²	1	4	yes	complemented
77	C₄×D₂₉	C₄²	1	4	yes	complemented
78	C₄×D₂₉	C₂²×C₄	1	4	yes	—
79	C₄×D₂₉	C₂²×C₄	1	4	yes	—
80	C₄×D₂₉	#41	1	8	yes	—
81	C₄×#117	—	29	1	no	maximal, Sylow
82	C₂²×C₂₉	—	2	2	no	—
83	C₂²×C₂₉	C₂×C₄²	1	2	yes	—
84	C₂²×C₂₉	C₂³×C₄	1	1	yes	characteristic
85	C₂×D₂₉	—	2	2	no	—
86	C₂×D₂₉	—	2	8	no	—
87	C₂×D₂₉	C₂×C₄²	1	2	yes	—
88	C₂×D₂₉	C₂³×C₄	1	2	yes	—
89	C₂×D₂₉	C₂×#41	1	4	yes	—
90	#1181	—	2	16	no	—
91	C₄×C₂₉	—	2	2	no	—
92	C₄×C₂₉	C₂×C₄²	1	2	yes	—
93	C₄×C₂₉	C₂×C₄²	1	2	yes	—
94	C₄×C₂₉	#117	1	4	yes	complemented
95	Dic₂₉	—	2	2	no	—
96	Dic₂₉	C₂×C₄²	1	2	yes	—
97	Dic₂₉	C₂×C₄²	1	2	yes	—
98	Dic₂₉	#117	1	4	yes	complemented
99	C₂×#117	—	29	2	no	—
100	C₂²×C₄²	—	29	1	no	—
101	C₄×C₄⋊C₄	—	29	4	no	—
102	C₄×C₂²⋊C₄	—	29	4	no	—
103	#376	—	29	2	no	—
104	C₄³	—	29	2	no	—
105	C₂×C₂₉	—	2	2	no	—
106	C₂×C₂₉	C₂²×C₄²	1	1	yes	characteristic
107	C₂×C₂₉	C₂×#117	1	2	yes	—
108	D₂₉	—	2	2	no	—
109	D₂₉	C₄×#41	1	4	yes	—
110	C₂³×C₄	—	29	1	no	—
111	C₂³×C₄	—	29	2	no	—
112	#117	—	29	16	no	—
113	C₂×C₄⋊C₄	—	29	4	no	—
114	C₂×C₂²⋊C₄	—	29	4	no	—
115	C₂×C₄²	—	29	4	no	—
116	C₂×C₄²	—	29	2	no	—
117	C₂×C₄²	—	29	1	no	—
118	C₂×C₄²	—	29	1	no	—
119	C₂×C₄²	—	29	2	no	—
120	C₂×C₄²	—	29	1	no	—
121	C₂×C₄²	—	29	2	no	—
122	C₂×C₄²	—	29	1	no	—
123	C₂×C₄²	—	29	1	no	—
124	C₂×C₄²	—	29	8	no	—
125	C₂×C₄²	#1181	1	1	yes	characteristic, complemented
126	#95	—	29	8	no	—
127	C₂₉	C₄×#117	1	1	yes	characteristic, complemented, Sylow
128	C₂⁴	—	29	1	no	—
129	C₂²×C₄	—	29	1	no	—
130	C₂²×C₄	—	29	8	no	—
131	C₂²×C₄	—	29	1	no	—
132	C₂²×C₄	—	29	2	no	—
133	C₂²×C₄	—	29	1	no	—
134	C₂²×C₄	—	29	1	no	—
135	C₂²×C₄	—	29	1	no	—
136	C₂²×C₄	—	29	8	no	—
137	C₂²×C₄	—	29	2	no	—
138	C₂²×C₄	—	29	2	no	—
139	C₂²×C₄	—	29	2	no	—
140	C₂²×C₄	—	29	2	no	—
141	C₂²×C₄	—	58	8	no	—
142	C₂²×C₄	C₂×#1181	1	2	yes	—
143	C₂²×C₄	C₂×#1181	1	1	yes	characteristic
144	C₄⋊C₄	—	29	16	no	—
145	C₂²⋊C₄	—	29	16	no	—
146	C₄²	—	29	16	no	—
147	C₄²	—	29	2	no	—
148	C₄²	—	29	1	no	—
149	C₄²	—	29	2	no	—
150	C₄²	—	29	2	no	—
151	C₄²	—	29	2	no	—
152	C₄²	—	29	2	no	—
153	C₄²	—	29	1	no	—
154	C₄²	—	58	16	no	—
155	C₄²	C₂×#1181	1	1	yes	characteristic
156	C₄²	C₂×#1181	1	2	yes	—
157	C₄²	C₂×#1181	1	1	yes	characteristic
158	C₂³	—	29	1	no	—
159	C₂³	—	29	4	no	—
160	C₂³	—	29	1	no	—
161	C₂³	—	58	4	no	—
162	C₂³	C₂²×#1181	1	1	yes	characteristic
163	C₂×C₄	—	2	4	no	—
164	C₂×C₄	—	29	4	no	—
165	C₂×C₄	—	29	1	no	—
166	C₂×C₄	—	29	1	no	—
167	C₂×C₄	—	29	2	no	—
168	C₂×C₄	—	29	4	no	—
169	C₂×C₄	—	29	4	no	—
170	C₂×C₄	—	29	4	no	—
171	C₂×C₄	—	29	4	no	—
172	C₂×C₄	—	29	8	no	—
173	C₂×C₄	—	29	16	no	—
174	C₂×C₄	—	29	2	no	—
175	C₂×C₄	—	58	4	no	—
176	C₂×C₄	—	58	4	no	—
177	C₂×C₄	—	58	4	no	—
178	C₂×C₄	—	58	16	no	—
179	C₂×C₄	—	58	4	no	—
180	C₂×C₄	C₄×#1181	1	4	yes	complemented
181	C₂×C₄	C₂²×#1181	1	2	yes	—
182	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
183	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
184	C₂×C₄	C₂²×#1181	1	2	yes	—
185	C₂²	—	2	2	no	—
186	C₂²	—	29	2	no	—
187	C₂²	—	29	4	no	—
188	C₂²	—	29	2	no	—
189	C₂²	—	58	8	no	—
190	C₂²	—	58	2	no	—
191	C₂²	C₂×C₄×#1181	1	2	yes	—
192	C₂²	C₂³×#1181	1	1	yes	characteristic
193	C₄	—	2	2	no	—
194	C₄	—	29	2	no	—
195	C₄	—	29	2	no	—
196	C₄	—	29	4	no	—
197	C₄	—	58	16	no	—
198	C₄	—	58	2	no	—
199	C₄	C₂×C₄×#1181	1	2	yes	—
200	C₄	C₂×C₄×#1181	1	2	yes	—
201	C₄	#11745345	1	4	yes	direct product factor
202	C₂	—	2	2	no	—
203	C₂	—	29	4	no	—
204	C₂	—	58	2	no	—
205	C₂	C₂²×C₄×#1181	1	1	yes	characteristic
206	C₂	C₂×#11745345	1	2	yes	—

	subgroup	G/H
center	C₄²	C₂×#1181
commutator	C₂×C₂₉	C₂²×C₄²
Frattini	C₂²	C₂³×#1181
Fitting	C₂×C₄²×C₂₉	C₄
socle	C₂²×C₂₉	C₂³×C₄
prime radical	C₂³×D₂₉	C₂³
cosocle	C₂²×D₂₉	C₂⁴
hypercenter	C₂×C₄²	#1181
hypocenter	C₂₉	C₄×#117
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄² ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. C₄×C₄⋊#1181	C₂	semidirect
4. #14272099	C₂	semidirect
5. C₄²×#1181	C₂	semidirect
10. #11745345	C₄	direct (N × H)
14. C₂×C₄²×C₂₉	C₄	semidirect
15. C₂×C₄×Dic₂₉	C₄	semidirect
16. C₂×C₄×Dic₂₉	C₄	semidirect
17. C₄²×D₂₉	C₄	semidirect
18. C₄²×D₂₉	C₄	semidirect
19. C₄²×D₂₉	C₄	semidirect
41. C₄⋊#1181	C₂×C₄	semidirect
43. C₄×#1181	C₂×C₄	semidirect
62. C₂×C₄×C₂₉	C₄²	semidirect
68. C₂×Dic₂₉	C₄²	semidirect
76. C₄×D₂₉	C₄²	semidirect
77. C₄×D₂₉	C₄²	semidirect
94. C₄×C₂₉	#117	semidirect
98. Dic₂₉	#117	semidirect
125. C₂×C₄²	#1181	semidirect
127. C₂₉	C₄×#117	semidirect
180. C₂×C₄	C₄×#1181	semidirect
201. C₄	#11745345	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×#11745345	2
C₄×C₄⋊#1181	2
C₄×C₂²⋊#1181	2
#14272099	2
C₄²×#1181	2
C₂×C₄²×D₂₉	2
C₄×#117	29

Subgroups — C4×#11745345 #16835924

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11745345 #16835924