Subgroups — C₄×#11718050 #15754104

Order 3328.

470 conjugacy classes of subgroups.

The subgroup lattice has 186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₄⋊#1055	C₂	1	2	yes	maximal
2	C₂×#11718050	C₂	1	2	yes	maximal
3	#13112671	C₂	1	2	yes	maximal
4	C₄²×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×C₈×C₁₃	C₄	1	2	yes	—
6	C₂×C₄×C₈×C₁₃	C₄	1	2	yes	—
7	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₄³×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊#1055	C₂²	1	4	yes	—
11	C₂×C₄×#1055	—	2	2	no	—
12	#11718116	—	2	2	no	—
13	#11718050	C₄	1	8	yes	direct product factor
14	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
16	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
18	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
19	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
20	C₂×C₄²×C₁₃	Q₈	1	2	yes	—
21	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
22	C₂²×#1055	—	2	4	no	—
23	C₄×C₈×C₁₃	—	2	4	no	—
24	C₄×C₈×C₁₃	—	2	2	no	—
25	C₄×C₈×C₁₃	C₈	1	8	yes	complemented
26	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
27	C₄⋊#1055	—	2	4	no	—
28	C₄⋊#1055	C₂×C₄	1	8	yes	—
29	C₄×#1055	—	4	4	no	—
30	C₄×#335	—	13	1	no	maximal, Sylow
31	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
32	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
33	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
34	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
36	C₂×C₈×C₁₃	—	2	2	no	—
37	C₂×C₈×C₁₃	—	2	2	no	—
38	C₂×C₈×C₁₃	—	2	2	no	—
39	C₂×C₈×C₁₃	C₄²	1	2	yes	—
40	C₂×C₈×C₁₃	C₄²	1	2	yes	—
41	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
42	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
43	C₄²×C₁₃	—	2	4	no	—
44	C₄²×C₁₃	—	2	2	no	—
45	C₄²×C₁₃	C₂×C₈	1	4	yes	—
46	C₄²×C₁₃	M₁₆	1	4	yes	—
47	C₄²×C₁₃	D₈	1	2	yes	—
48	C₄²×C₁₃	Q₁₆	1	2	yes	—
49	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
50	C₄²×C₁₃	#41	1	2	yes	—
51	C₂×#1055	—	2	8	no	—
52	C₂×#1055	—	4	4	no	—
53	C₂×#1055	—	4	4	no	—
54	C₄×C₄⋊C₈	—	13	2	no	—
55	C₄²×C₈	D₁₃	1	1	yes	characteristic
56	C₂×#335	—	13	2	no	—
57	#1277	—	13	2	no	—
58	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
59	C₂×C₄×C₁₃	—	2	2	no	—
60	C₂×C₄×C₁₃	—	2	2	no	—
61	C₂×C₄×C₁₃	—	2	2	no	—
62	C₂×C₄×C₁₃	C₄⋊C₈	1	4	yes	—
63	C₂×C₄×C₁₃	C₄⋊C₈	1	4	yes	—
64	C₂×C₄×C₁₃	#107	1	4	yes	—
65	C₂×C₄×C₁₃	#108	1	4	yes	—
66	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
67	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
68	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
69	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
70	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
71	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
72	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
73	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
74	C₂×C₄×C₁₃	#135	1	2	yes	—
75	C₈×C₁₃	—	2	2	no	—
76	C₈×C₁₃	—	2	4	no	—
77	C₈×C₁₃	C₄×C₈	1	4	yes	complemented
78	#1055	—	4	8	no	—
79	C₂×C₄⋊C₈	—	13	4	no	—
80	C₂×C₄×C₈	—	26	2	no	—
81	C₂×C₄×C₈	Dic₁₃	1	2	yes	—
82	C₂×C₄×C₈	Dic₁₃	1	2	yes	—
83	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
84	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
85	C₄³	C₂×D₁₃	1	1	yes	characteristic
86	#336	—	26	2	no	—
87	#335	—	13	8	no	—
88	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₁₃	C₂×C₄⋊C₈	1	2	yes	—
90	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
91	C₂²×C₁₃	#427	1	1	yes	characteristic
92	C₂²×C₁₃	C₂×#108	1	2	yes	—
93	C₄×C₁₃	—	2	4	no	—
94	C₄×C₁₃	—	2	2	no	—
95	C₄×C₁₃	#335	1	8	yes	complemented
96	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
97	C₄×C₁₃	C₄×M₁₆	1	1	yes	characteristic
98	C₄×C₁₃	#431	1	2	yes	—
99	C₄×C₁₃	C₄×D₈	1	2	yes	—
100	C₄×C₁₃	C₄×Q₁₆	1	2	yes	—
101	C₂²×C₈	—	26	4	no	—
102	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
103	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
104	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
105	C₂×C₄²	Dic₂₆	1	2	yes	—
106	C₂×C₄²	D₅₂	1	1	yes	characteristic
107	C₂×C₄²	D₅₂	1	1	yes	characteristic
108	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
109	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
110	C₄⋊C₈	—	13	8	no	—
111	C₄⋊C₈	—	26	4	no	—
112	C₄×C₈	—	2	4	no	—
113	C₄×C₈	—	2	2	no	—
114	C₄×C₈	—	52	4	no	—
115	C₄×C₈	#1055	1	8	yes	complemented
116	C₄×C₈	C₄×D₁₃	1	4	yes	—
117	C₂×C₁₃	C₂×#335	1	2	yes	—
118	C₂×C₁₃	#1564	1	2	yes	—
119	C₂×C₁₃	C₄×C₄⋊C₈	1	1	yes	characteristic
120	C₂×C₁₃	C₄×#107	1	1	yes	characteristic
121	C₂×C₁₃	C₄×#108	1	1	yes	characteristic
122	C₂²×C₄	C₄⋊Dic₁₃	1	2	yes	—
123	C₂²×C₄	C₄⋊Dic₁₃	1	2	yes	—
124	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
125	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
126	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
127	C₂×C₈	—	2	2	no	—
128	C₂×C₈	—	2	2	no	—
129	C₂×C₈	—	2	2	no	—
130	C₂×C₈	—	26	8	no	—
131	C₂×C₈	—	52	4	no	—
132	C₂×C₈	—	52	4	no	—
133	C₂×C₈	C₂×#1055	1	4	yes	—
134	C₂×C₈	C₂×#1055	1	4	yes	—
135	C₂×C₈	C₄×Dic₁₃	1	2	yes	—
136	C₂×C₈	C₄×Dic₁₃	1	2	yes	—
137	C₄²	—	2	2	no	—
138	C₄²	—	2	4	no	—
139	C₄²	D₁₀₄	1	2	yes	—
140	C₄²	Dic₅₂	1	2	yes	—
141	C₄²	C₂×#1055	1	4	yes	—
142	C₄²	#6099	1	4	yes	—
143	C₄²	C₂×C₄×D₁₃	1	2	yes	—
144	C₄²	#6127	1	2	yes	—
145	C₁₃	C₄×#335	1	1	yes	characteristic, complemented, Sylow
146	C₂³	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
147	C₂×C₄	—	2	2	no	—
148	C₂×C₄	—	2	2	no	—
149	C₂×C₄	—	2	2	no	—
150	C₂×C₄	C₄⋊#1055	1	4	yes	—
151	C₂×C₄	C₄⋊#1055	1	4	yes	—
152	C₂×C₄	#88058	1	4	yes	—
153	C₂×C₄	#88059	1	4	yes	—
154	C₂×C₄	C₄×Dic₂₆	1	2	yes	—
155	C₂×C₄	C₄×D₅₂	1	2	yes	—
156	C₂×C₄	C₂×D₁₀₄	1	1	yes	characteristic
157	C₂×C₄	#88158	1	2	yes	—
158	C₂×C₄	C₂×Dic₅₂	1	1	yes	characteristic
159	C₂×C₄	C₂²×#1055	1	2	yes	—
160	C₂×C₄	C₂×#6099	1	2	yes	—
161	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
162	C₂×C₄	#88180	1	1	yes	characteristic
163	C₈	—	2	2	no	—
164	C₈	—	2	4	no	—
165	C₈	—	52	8	no	—
166	C₈	C₄×#1055	1	4	yes	complemented
167	C₂²	C₂×C₄⋊#1055	1	2	yes	—
168	C₂²	C₄×C₄⋊Dic₁₃	1	1	yes	characteristic
169	C₂²	C₂×#88058	1	1	yes	characteristic
170	C₂²	#11718767	1	1	yes	characteristic
171	C₂²	C₂×#88059	1	2	yes	—
172	C₄	—	2	2	no	—
173	C₄	—	2	4	no	—
174	C₄	#11718050	1	8	yes	direct product factor
175	C₄	C₄×D₁₀₄	1	2	yes	—
176	C₄	C₄×Dic₅₂	1	2	yes	—
177	C₄	C₂×C₄×#1055	1	1	yes	characteristic
178	C₄	C₄×#6099	1	1	yes	characteristic
179	C₄	#11718586	1	2	yes	—
180	C₂	C₂×#11718050	1	2	yes	—
181	C₂	#13113584	1	2	yes	—
182	C₂	C₄×C₄⋊#1055	1	1	yes	characteristic
183	C₂	C₄×#88058	1	1	yes	characteristic
184	C₂	C₄×#88059	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄²	D₅₂
commutator	C₄×C₁₃	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₄²×C₈×C₁₃	C₂
socle, prime radical	C₂³×C₁₃	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	C₄²×C₈	D₁₃
hypocenter	C₁₃	C₄×#335
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄² ◁ C₄³ ◁ C₄²×C₈

Complements

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

N	H ≅ G/N	type
13. #11718050	C₄	direct (N × H)
25. C₄×C₈×C₁₃	C₈	semidirect
77. C₈×C₁₃	C₄×C₈	semidirect
95. C₄×C₁₃	#335	semidirect
115. C₄×C₈	#1055	semidirect
145. C₁₃	C₄×#335	semidirect
166. C₈	C₄×#1055	semidirect
174. C₄	#11718050	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₄⋊#1055	2
C₂×#11718050	2
#13112671	2
C₄²×C₈×C₁₃	2
C₄×#335	13

Subgroups — C4×#11718050 #15754104

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11718050 #15754104