Subgroups — C₄×#11718144 #15768106

Order 3328.

910 conjugacy classes of subgroups.

The subgroup lattice has 188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#6099	C₂	1	2	yes	maximal
2	C₂×#11718144	C₂	1	4	yes	maximal
3	C₂²×C₄×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
5	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
6	C₂²×#6099	C₂²	1	4	yes	—
7	C₂×C₄×C₈×C₁₃	—	2	4	no	—
8	C₂×C₄×C₈×C₁₃	C₄	1	4	yes	—
9	C₄×#6099	—	2	4	no	—
10	C₄×#6099	C₄	1	8	yes	—
11	C₂×#88043	—	2	2	no	—
12	C₂×C₄×#1055	—	2	2	no	—
13	#11718144	C₄	1	16	yes	direct product factor
14	C₂³×C₄×C₁₃	Q₈	1	2	yes	—
15	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
16	C₂²×C₈×C₁₃	—	2	4	no	—
17	C₂²×C₈×C₁₃	—	2	4	no	—
18	C₂²×C₈×C₁₃	C₂×C₄	1	8	yes	—
19	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
20	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
21	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
22	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
23	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
24	C₂×C₄²×C₁₃	D₄	1	4	yes	—
25	C₂×#6099	—	2	4	no	—
26	C₂×#6099	—	2	8	no	—
27	C₂×#6099	C₂×C₄	1	16	yes	—
28	C₂×#6099	C₂×C₄	1	8	yes	—
29	C₂²×#1055	—	2	4	no	—
30	C₄×C₈×C₁₃	—	2	8	no	—
31	#88043	—	2	8	no	—
32	C₄×#1055	—	2	8	no	—
33	C₄×#341	—	13	1	no	maximal, Sylow
34	C₂⁴×C₁₃	C₂×Q₈	1	1	yes	characteristic
35	C₂²×C₄×C₁₃	—	2	8	no	—
36	C₂²×C₄×C₁₃	C₄⋊C₄	1	8	yes	—
37	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
38	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
39	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
40	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
41	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
44	C₂²×C₄×C₁₃	#41	1	4	yes	—
45	C₂×C₈×C₁₃	—	2	4	no	—
46	C₂×C₈×C₁₃	—	2	4	no	—
47	C₂×C₈×C₁₃	—	2	16	no	—
48	C₂×C₈×C₁₃	C₄²	1	8	yes	—
49	C₄²×C₁₃	C₄²	1	4	yes	—
50	C₄²×C₁₃	C₂²⋊C₄	1	4	yes	—
51	C₄²×C₁₃	C₂²⋊C₄	1	4	yes	—
52	C₄²×C₁₃	C₂²⋊C₄	1	4	yes	—
53	#6099	—	2	8	no	—
54	#6099	—	2	16	no	—
55	#6099	C₄²	1	16	yes	—
56	C₂×#1055	—	2	8	no	—
57	C₂×#1055	—	2	16	no	—
58	C₂×C₄×M₁₆	—	13	2	no	—
59	C₂²×C₄×C₈	D₁₃	1	1	yes	characteristic
60	C₂×#341	—	13	4	no	—
61	C₂³×C₁₃	—	2	4	no	—
62	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
63	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
64	C₂³×C₁₃	C₄×Q₈	1	4	yes	—
65	C₂×C₄×C₁₃	—	2	4	no	—
66	C₂×C₄×C₁₃	—	2	16	no	—
67	C₂×C₄×C₁₃	#95	1	4	yes	—
68	C₂×C₄×C₁₃	#95	1	4	yes	—
69	C₂×C₄×C₁₃	#108	1	8	yes	—
70	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
71	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
72	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
73	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
74	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
75	C₂×C₄×C₁₃	#117	1	4	yes	—
76	C₂×C₄×C₁₃	#117	1	2	yes	—
77	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
78	C₂×C₄×C₁₃	C₄×D₄	1	8	yes	—
79	C₈×C₁₃	—	2	8	no	—
80	#1055	—	2	16	no	—
81	C₂²×M₁₆	—	13	4	no	—
82	C₂³×C₈	C₂×D₁₃	1	2	yes	—
83	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
84	C₄×M₁₆	—	13	8	no	—
85	C₄×M₁₆	—	26	4	no	—
86	C₂×#97	—	26	2	no	—
87	C₂×C₄×C₈	—	2	4	no	—
88	C₂×C₄×C₈	—	26	2	no	—
89	C₂×C₄×C₈	Dic₁₃	1	4	yes	—
90	#341	—	13	16	no	—
91	C₂²×C₁₃	—	2	4	no	—
92	C₂²×C₁₃	—	2	8	no	—
93	C₂²×C₁₃	C₂×#95	1	1	yes	characteristic
94	C₂²×C₁₃	C₄×C₄⋊C₄	1	4	yes	—
95	C₂²×C₁₃	C₄×C₄⋊C₄	1	2	yes	—
96	C₂²×C₁₃	C₂×#108	1	4	yes	—
97	C₄×C₁₃	—	2	4	no	—
98	C₄×C₁₃	#341	1	8	yes	complemented
99	C₄×C₁₃	C₄³	1	1	yes	characteristic
100	C₄×C₁₃	#376	1	1	yes	characteristic
101	C₄×C₁₃	C₄×C₂²⋊C₄	1	4	yes	—
102	C₄×C₁₃	C₄×C₂²⋊C₄	1	2	yes	—
103	C₂³×C₄	Dic₂₆	1	2	yes	—
104	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
105	C₂×M₁₆	—	13	16	no	—
106	C₂×M₁₆	—	13	8	no	—
107	C₂×M₁₆	—	26	8	no	—
108	C₂×M₁₆	—	26	4	no	—
109	C₂²×C₈	—	2	4	no	—
110	C₂²×C₈	—	2	4	no	—
111	C₂²×C₈	—	26	4	no	—
112	C₂²×C₈	C₄×D₁₃	1	8	yes	—
113	C₂²×C₈	C₂×Dic₁₃	1	4	yes	—
114	C₂×C₄²	C₄×D₁₃	1	4	yes	—
115	C₂×C₄²	D₅₂	1	1	yes	characteristic
116	C₂×C₄²	D₅₂	1	1	yes	characteristic
117	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
118	C₂×C₄²	C₂²⋊D₁₃	1	4	yes	—
119	#97	—	26	8	no	—
120	C₄×C₈	—	2	8	no	—
121	C₄×C₈	—	26	8	no	—
122	C₂×C₁₃	—	2	4	no	—
123	C₂×C₁₃	C₄×#95	1	1	yes	characteristic
124	C₂×C₁₃	C₂×#341	1	2	yes	—
125	C₂×C₁₃	C₄×#108	1	4	yes	—
126	C₂⁴	C₂×Dic₂₆	1	1	yes	characteristic
127	C₂²×C₄	—	2	8	no	—
128	C₂²×C₄	#6101	1	8	yes	—
129	C₂²×C₄	C₄⋊Dic₁₃	1	2	yes	—
130	C₂²×C₄	C₄⋊Dic₁₃	1	2	yes	—
131	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
132	C₂²×C₄	C₂×C₄×D₁₃	1	4	yes	—
133	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
134	C₂²×C₄	#6127	1	4	yes	—
135	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
136	C₂²×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
137	M₁₆	—	13	16	no	—
138	M₁₆	—	26	8	no	—
139	M₁₆	—	26	16	no	—
140	C₂×C₈	—	2	4	no	—
141	C₂×C₈	—	2	16	no	—
142	C₂×C₈	—	2	4	no	—
143	C₂×C₈	—	26	16	no	—
144	C₂×C₈	—	26	8	no	—
145	C₂×C₈	C₄×Dic₁₃	1	8	yes	—
146	C₄²	C₄×Dic₁₃	1	4	yes	—
147	C₄²	#6103	1	4	yes	—
148	C₄²	#6103	1	4	yes	—
149	C₄²	C₂²⋊Dic₁₃	1	4	yes	—
150	C₁₃	C₄×#341	1	1	yes	characteristic, complemented, Sylow
151	C₂³	—	2	4	no	—
152	C₂³	C₄×Dic₂₆	1	4	yes	—
153	C₂³	C₂×#6101	1	2	yes	—
154	C₂³	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
155	C₂×C₄	—	2	4	no	—
156	C₂×C₄	—	2	16	no	—
157	C₂×C₄	#88059	1	8	yes	—
158	C₂×C₄	#88071	1	4	yes	—
159	C₂×C₄	#88071	1	4	yes	—
160	C₂×C₄	C₄²×D₁₃	1	4	yes	—
161	C₂×C₄	#88126	1	4	yes	—
162	C₂×C₄	C₄×D₅₂	1	4	yes	—
163	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
164	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
165	C₂×C₄	#88180	1	2	yes	—
166	C₂×C₄	C₂×#6103	1	2	yes	—
167	C₂×C₄	C₄×C₂²⋊D₁₃	1	8	yes	—
168	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
169	C₈	—	2	8	no	—
170	C₈	—	26	16	no	—
171	C₂²	—	2	8	no	—
172	C₂²	—	2	4	no	—
173	C₂²	C₄×#6101	1	4	yes	—
174	C₂²	C₄×C₄⋊Dic₁₃	1	2	yes	—
175	C₂²	C₂×#88059	1	4	yes	—
176	C₂²	C₂×#88071	1	1	yes	characteristic
177	C₄	—	2	4	no	—
178	C₄	#11718144	1	8	yes	direct product factor
179	C₄	C₄²×Dic₁₃	1	1	yes	characteristic
180	C₄	#11718593	1	1	yes	characteristic
181	C₄	C₄×#6103	1	4	yes	—
182	C₄	C₄×C₂²⋊Dic₁₃	1	2	yes	—
183	C₂	—	2	4	no	—
184	C₂	C₄×#88071	1	1	yes	characteristic
185	C₂	C₂×#11718144	1	2	yes	—
186	C₂	C₄×#88059	1	4	yes	—

	subgroup	G/H
center	C₂×C₄²	D₅₂
commutator	C₄×C₁₃	C₄³
Frattini	C₂³×C₄	C₂²×D₁₃
Fitting	C₂²×C₄×C₈×C₁₃	C₂
socle	C₂³×C₁₃	C₂×C₄⋊C₄
prime radical	C₂⁴×C₁₃	C₂×Q₈
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	C₂²×C₄×C₈	D₁₃
hypocenter	C₁₃	C₄×#341
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄² ◁ C₂²×C₄² ◁ C₂²×C₄×C₈

Complements

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

N	H ≅ G/N	type
13. #11718144	C₄	direct (N × H)
98. C₄×C₁₃	#341	semidirect
150. C₁₃	C₄×#341	semidirect
178. C₄	#11718144	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×#6099	2
C₂×#11718144	2
C₂²×C₄×C₈×C₁₃	2
C₄×#341	13

Subgroups — C4×#11718144 #15768106

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11718144 #15768106