Subgroups — C₈×#88103 #16780985

Order 3328.

374 conjugacy classes of subgroups.

The subgroup lattice has 224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#88103	C₂	1	1	yes	maximal, characteristic
2	#13130384	C₂	1	1	yes	maximal, characteristic
3	C₈×#6118	C₂	1	2	yes	maximal
4	#13129668	C₂	1	2	yes	maximal
5	C₈²×D₁₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#88103	C₄	1	2	yes	—
7	#11719051	C₂²	1	2	yes	—
8	C₄×#6118	C₂²	1	2	yes	—
9	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
10	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
11	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
12	#11718268	C₄	1	2	yes	—
13	#11718256	C₄	1	2	yes	—
14	#11718253	C₄	1	2	yes	—
15	#1057⋊C₈	—	2	2	no	—
16	C₈×#1057	—	2	2	no	—
17	C₈²×C₁₃	C₄	1	1	yes	characteristic
18	C₈×#1055	C₄	1	1	yes	characteristic
19	C₈×#1055	C₄	1	1	yes	characteristic
20	C₈×#1055	C₄	1	1	yes	characteristic
21	C₂×#6118	C₂×C₄	1	4	yes	—
22	C₂×C₈×D₁₃	—	2	1	no	—
23	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
26	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
27	C₄²×D₁₃	C₂³	1	1	yes	characteristic
28	#88111	—	2	2	no	—
29	#88110	—	2	2	no	—
30	C₄⋊#1057	C₂×C₄	1	4	yes	—
31	C₄×#1057	—	2	2	no	—
32	C₄×#1057	—	2	2	no	—
33	#88103	C₈	1	8	yes	direct product factor
34	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
35	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
36	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
37	C₈×Dic₁₃	—	2	1	no	—
38	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
39	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
40	C₈×Dic₁₃	D₄	1	1	yes	characteristic
41	C₈×Dic₁₃	D₄	1	1	yes	characteristic
42	C₄×#1055	C₂×C₄	1	1	yes	characteristic
43	C₄×#1055	C₂×C₄	1	1	yes	characteristic
44	C₄×#1055	C₂×C₄	1	1	yes	characteristic
45	C₈×#108	—	13	1	no	maximal, Sylow
46	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
47	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
48	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
49	C₂×#1057	—	2	4	no	—
50	C₂×#1057	—	2	4	no	—
51	#6118	—	2	4	no	—
52	#6118	C₂×C₈	1	8	yes	—
53	C₂×C₈×C₁₃	—	2	1	no	—
54	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
55	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
56	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
57	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
58	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
59	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
60	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
61	C₄×Dic₁₃	#41	1	1	yes	characteristic
62	C₂×#1055	—	2	1	no	—
63	C₂×#1055	C₄²	1	1	yes	characteristic
64	C₂×#1055	C₄²	1	1	yes	characteristic
65	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
66	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
67	C₈×D₁₃	—	2	4	no	—
68	C₈×D₁₃	—	2	2	no	—
69	C₈×D₁₃	—	2	2	no	—
70	C₈×D₁₃	—	2	2	no	—
71	C₈×D₁₃	C₂×C₈	1	4	yes	—
72	C₄×#108	—	13	1	no	—
73	#1564	—	13	1	no	—
74	C₈×M₁₆	—	13	2	no	—
75	C₂×C₈²	—	13	1	no	—
76	#1278	—	13	2	no	—
77	C₂²×D₁₃	C₄×Q₈	1	1	yes	characteristic
78	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
79	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
80	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
81	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
82	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
83	C₂×Dic₁₃	C₄×Q₈	1	1	yes	characteristic
84	C₄×D₁₃	—	2	1	no	—
85	C₄×D₁₃	—	2	1	no	—
86	C₄×D₁₃	—	2	2	no	—
87	C₄×D₁₃	C₂²×C₈	1	2	yes	—
88	C₄×D₁₃	#131	1	2	yes	—
89	#1057	—	2	8	no	—
90	#1057	—	4	4	no	—
91	C₈×C₁₃	—	2	2	no	—
92	C₈×C₁₃	—	2	1	no	—
93	C₈×C₁₃	—	2	1	no	—
94	C₈×C₁₃	C₄×C₈	1	2	yes	—
95	C₈×C₁₃	#108	1	2	yes	complemented
96	#1055	—	2	2	no	—
97	#1055	—	2	1	no	—
98	#1055	—	2	1	no	—
99	#1055	C₄×C₈	1	2	yes	—
100	#1055	#108	1	2	yes	complemented
101	#431	—	13	2	no	—
102	C₂×#108	—	13	2	no	—
103	C₄×M₁₆	—	13	2	no	—
104	C₂×C₄×C₈	—	13	1	no	—
105	C₂×C₄×C₈	—	13	1	no	—
106	C₂×C₄×C₈	—	13	1	no	—
107	#341	—	13	2	no	—
108	#335	—	13	2	no	—
109	#334	—	13	2	no	—
110	#322	—	26	2	no	—
111	C₈²	—	13	1	no	—
112	C₈²	—	13	1	no	—
113	C₈²	—	13	1	no	—
114	C₈²	—	26	2	no	—
115	C₈²	#261	1	1	yes	characteristic
116	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
117	C₂×D₁₃	—	2	1	no	—
118	C₂×D₁₃	—	2	1	no	—
119	C₂×D₁₃	C₈×Q₈	1	2	yes	—
120	C₄×C₁₃	—	2	1	no	—
121	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
122	C₄×C₁₃	#405	1	1	yes	characteristic
123	C₄×C₁₃	C₂×#108	1	1	yes	characteristic
124	C₄×C₁₃	C₂×#108	1	1	yes	characteristic
125	Dic₁₃	—	2	1	no	—
126	Dic₁₃	C₈×D₄	1	2	yes	—
127	Dic₁₃	#443	1	2	yes	—
128	C₂×M₁₆	—	13	4	no	—
129	C₂²×C₈	—	13	1	no	—
130	C₂²×C₈	—	13	1	no	—
131	C₂²×C₈	—	13	1	no	—
132	C₂²×C₈	—	13	1	no	—
133	C₂²×C₈	—	26	1	no	—
134	C₂×C₄²	—	13	1	no	—
135	#108	—	13	8	no	—
136	C₄⋊C₈	—	13	4	no	—
137	C₂²⋊C₈	—	26	2	no	—
138	#97	—	26	2	no	—
139	C₄×C₈	—	13	1	no	—
140	C₄×C₈	—	13	1	no	—
141	C₄×C₈	—	13	1	no	—
142	C₄×C₈	—	13	1	no	—
143	C₄×C₈	—	13	1	no	—
144	C₄×C₈	—	13	1	no	—
145	C₄×C₈	—	13	1	no	—
146	C₄×C₈	—	26	1	no	—
147	C₄×C₈	—	26	2	no	—
148	C₄×C₈	—	26	2	no	—
149	C₄×C₈	C₂×#261	1	1	yes	characteristic
150	C₄×C₈	C₂×#261	1	1	yes	characteristic
151	C₄×C₈	C₂×#261	1	1	yes	characteristic
152	C₂×C₁₃	C₈×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₁₃	#1772	1	1	yes	characteristic
154	C₂×C₁₃	C₄×#108	1	1	yes	characteristic
155	D₁₃	—	2	2	no	—
156	C₂²×C₄	—	13	1	no	—
157	C₂²×C₄	—	13	1	no	—
158	C₂²×C₄	—	13	1	no	—
159	M₁₆	—	13	8	no	—
160	M₁₆	—	26	4	no	—
161	C₂×C₈	—	2	1	no	—
162	C₂×C₈	—	13	1	no	—
163	C₂×C₈	—	13	1	no	—
164	C₂×C₈	—	13	4	no	—
165	C₂×C₈	—	13	1	no	—
166	C₂×C₈	—	13	1	no	—
167	C₂×C₈	—	26	2	no	—
168	C₂×C₈	—	26	2	no	—
169	C₂×C₈	—	26	4	no	—
170	C₂×C₈	—	26	4	no	—
171	C₂×C₈	—	26	1	no	—
172	C₂×C₈	—	26	2	no	—
173	C₂×C₈	—	26	4	no	—
174	C₂×C₈	C₄×#261	1	1	yes	characteristic
175	C₂×C₈	C₄×#261	1	1	yes	characteristic
176	C₂×C₈	C₄⋊#261	1	1	yes	characteristic
177	C₂×C₈	C₄⋊#261	1	1	yes	characteristic
178	C₄²	—	13	1	no	—
179	C₄²	—	13	1	no	—
180	C₄²	—	13	1	no	—
181	C₄²	C₂²×#261	1	1	yes	characteristic
182	C₁₃	C₈×#108	1	1	yes	characteristic, complemented, Sylow
183	C₂³	—	13	1	no	—
184	C₂×C₄	—	13	1	no	—
185	C₂×C₄	—	13	1	no	—
186	C₂×C₄	—	13	2	no	—
187	C₂×C₄	—	13	2	no	—
188	C₂×C₄	—	13	1	no	—
189	C₂×C₄	—	26	2	no	—
190	C₂×C₄	—	26	1	no	—
191	C₂×C₄	—	26	1	no	—
192	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
193	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
194	C₂×C₄	#88237	1	1	yes	characteristic
195	C₈	—	2	2	no	—
196	C₈	—	2	1	no	—
197	C₈	—	2	1	no	—
198	C₈	—	13	2	no	—
199	C₈	—	13	2	no	—
200	C₈	—	26	2	no	—
201	C₈	—	26	8	no	—
202	C₈	—	26	1	no	—
203	C₈	—	26	1	no	—
204	C₈	—	52	4	no	—
205	C₈	C₈×#261	1	2	yes	—
206	C₈	#88103	1	2	yes	direct product factor
207	C₂²	—	13	2	no	—
208	C₂²	—	26	1	no	—
209	C₂²	—	26	1	no	—
210	C₂²	C₄×C₄⋊#261	1	1	yes	characteristic
211	C₄	—	2	1	no	—
212	C₄	—	13	2	no	—
213	C₄	—	13	2	no	—
214	C₄	—	26	1	no	—
215	C₄	C₂×C₈×#261	1	1	yes	characteristic
216	C₄	#11719089	1	1	yes	characteristic
217	C₄	C₂×#88103	1	1	yes	characteristic
218	C₄	D₁₃⋊#108	1	1	yes	characteristic
219	C₂	—	26	2	no	—
220	C₂	C₈×C₄⋊#261	1	1	yes	characteristic
221	C₂	#13130638	1	1	yes	characteristic
222	C₂	C₄×#88103	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₄⋊#261
commutator	C₄×C₁₃	C₂×C₄×C₈
Frattini	C₄²	C₂²×#261
Fitting	C₈²×C₁₃	C₄
socle	C₂²×C₁₃	C₄×C₄⋊C₄
prime radical	C₂²×D₁₃	C₄×Q₈
cosocle	C₄²×D₁₃	C₂³
hypercenter	C₈²	#261
hypocenter	C₁₃	C₈×#108
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈²

Complements

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

N	H ≅ G/N	type
33. #88103	C₈	direct (N × H)
95. C₈×C₁₃	#108	semidirect
100. #1055	#108	semidirect
182. C₁₃	C₈×#108	semidirect
206. C₈	#88103	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×#88103	2
#13130384	2
C₈×#6118	2
#13129668	2
C₈²×D₁₃	2
C₈×#108	13

Subgroups — C8×#88103 #16780985

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#88103 #16780985