Subgroups — C₈×#88073 #15753477

Order 3328.

542 conjugacy classes of subgroups.

The subgroup lattice has 246 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#88073	C₂	1	1	yes	maximal, characteristic
2	#13113157	C₂	1	1	yes	maximal, characteristic
3	C₈×#6099	C₂	1	2	yes	maximal, complemented
4	#13112686	C₂	1	2	yes	maximal, complemented
5	C₂×C₈×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₈×C₁₃	C₄	1	2	yes	—
7	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
8	C₈×D₄×C₁₃	—	2	2	no	—
9	C₈×D₄×C₁₃	—	2	2	no	—
10	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×C₂²⋊C₈	C₄	1	2	yes	—
12	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×#88073	C₄	1	2	yes	—
14	#11718586	C₂²	1	2	yes	—
15	C₄×#6099	C₂²	1	2	yes	—
16	#11718122	C₄	1	2	yes	—
17	#11718117	C₄	1	4	yes	—
18	#11718046	—	2	2	no	—
19	C₈×#1055	—	2	2	no	—
20	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
22	C₂²×C₈×C₁₃	—	2	2	no	—
23	C₂²×C₈×C₁₃	—	2	2	no	—
24	C₂²×C₈×C₁₃	—	4	4	no	—
25	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
27	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₄×D₄×C₁₃	—	2	2	no	—
29	C₄×D₄×C₁₃	—	2	2	no	—
30	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
31	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
32	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
33	C₂×#6099	C₂×C₄	1	4	yes	—
34	C₁₃×C₄⋊C₈	—	2	2	no	—
35	C₁₃×C₂²⋊C₈	—	2	4	no	—
36	C₄×C₈×C₁₃	D₄	1	2	yes	—
37	C₄×C₈×C₁₃	D₄	1	2	yes	—
38	#88073	C₈	1	8	yes	direct product factor
39	C₂²⋊#1055	C₂×C₄	1	4	yes	—
40	C₄⋊#1055	—	2	2	no	—
41	#88043	—	2	2	no	—
42	C₄×#1055	—	2	2	no	—
43	C₄×#1055	—	2	2	no	—
44	C₈×#100	—	13	1	no	maximal, Sylow
45	C₂⁴×C₁₃	C₄²	1	2	yes	—
46	C₂×D₄×C₁₃	—	2	2	no	—
47	C₂×D₄×C₁₃	—	2	2	no	—
48	C₂×D₄×C₁₃	C₂×C₈	1	4	yes	—
49	C₂²×C₄×C₁₃	—	2	2	no	—
50	C₂²×C₄×C₁₃	—	2	2	no	—
51	C₂²×C₄×C₁₃	—	4	2	no	—
52	C₂²×C₄×C₁₃	—	4	2	no	—
53	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
54	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
57	C₂×C₈×C₁₃	—	2	2	no	—
58	C₂×C₈×C₁₃	—	2	2	no	—
59	C₂×C₈×C₁₃	—	4	1	no	—
60	C₂×C₈×C₁₃	—	4	4	no	—
61	C₂×C₈×C₁₃	—	4	4	no	—
62	C₂×C₈×C₁₃	—	4	2	no	—
63	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
64	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
65	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
66	C₁₃×C₄⋊C₄	—	2	2	no	—
67	C₁₃×C₂²⋊C₄	—	2	4	no	—
68	C₄²×C₁₃	C₂×D₄	1	2	yes	—
69	C₄²×C₁₃	#41	1	2	yes	—
70	#6099	—	2	4	no	—
71	#6099	C₂×C₈	1	8	yes	complemented
72	C₂×#1055	—	2	4	no	—
73	C₂×#1055	—	2	4	no	—
74	C₂×C₈×D₄	D₁₃	1	1	yes	characteristic
75	C₄×#100	—	13	1	no	—
76	#1460	—	13	1	no	—
77	C₈×M₁₆	—	13	2	no	—
78	#1283	—	13	2	no	—
79	C₂³×C₁₃	—	2	2	no	—
80	C₂³×C₁₃	—	2	2	no	—
81	C₂³×C₁₃	—	4	2	no	—
82	C₂³×C₁₃	—	4	2	no	—
83	C₂³×C₁₃	C₄×C₈	1	4	yes	—
84	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
85	D₄×C₁₃	—	2	8	no	—
86	C₂×C₄×C₁₃	—	2	1	no	—
87	C₂×C₄×C₁₃	—	2	1	no	—
88	C₂×C₄×C₁₃	—	2	2	no	—
89	C₂×C₄×C₁₃	—	4	1	no	—
90	C₂×C₄×C₁₃	—	4	4	no	—
91	C₂×C₄×C₁₃	—	4	2	no	—
92	C₂×C₄×C₁₃	—	4	2	no	—
93	C₂×C₄×C₁₃	—	4	2	no	—
94	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
96	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
97	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
98	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
99	C₂×C₄×C₁₃	#131	1	2	yes	—
100	C₈×C₁₃	—	2	1	no	—
101	C₈×C₁₃	—	2	2	no	—
102	C₈×C₁₃	—	4	2	no	—
103	C₈×C₁₃	#100	1	2	yes	complemented
104	#1055	—	2	8	no	—
105	#1055	—	4	4	no	—
106	C₂³×C₈	Dic₁₃	1	2	yes	—
107	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
108	C₈×D₄	—	2	2	no	—
109	C₈×D₄	—	2	2	no	—
110	#431	—	13	2	no	—
111	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
112	C₂×#100	—	13	2	no	—
113	C₂×C₂²⋊C₈	Dic₁₃	1	2	yes	—
114	C₄×M₁₆	—	13	2	no	—
115	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
116	#343	—	13	2	no	—
117	#323	—	13	4	no	—
118	#322	—	26	2	no	—
119	C₈²	—	26	2	no	—
120	C₂²×C₁₃	—	2	1	no	—
121	C₂²×C₁₃	—	2	1	no	—
122	C₂²×C₁₃	—	2	4	no	—
123	C₂²×C₁₃	—	4	4	no	—
124	C₂²×C₁₃	—	4	4	no	—
125	C₂²×C₁₃	—	4	2	no	—
126	C₂²×C₁₃	—	4	2	no	—
127	C₂²×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
128	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
129	C₂²×C₁₃	#405	1	1	yes	characteristic
130	C₄×C₁₃	—	2	1	no	—
131	C₄×C₁₃	—	2	2	no	—
132	C₄×C₁₃	—	4	2	no	—
133	C₄×C₁₃	C₂×#100	1	1	yes	characteristic
134	C₄×C₁₃	#413	1	1	yes	characteristic
135	C₄×C₁₃	C₈×D₄	1	4	yes	—
136	C₂²×D₄	C₄×D₁₃	1	1	yes	characteristic
137	C₂³×C₄	C₂×Dic₁₃	1	2	yes	—
138	C₂×M₁₆	—	13	4	no	—
139	C₂²×C₈	—	2	2	no	—
140	C₂²×C₈	—	2	2	no	—
141	C₂²×C₈	—	4	4	no	—
142	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
143	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
144	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
145	C₄×D₄	—	2	2	no	—
146	C₄×D₄	—	2	2	no	—
147	C₂×C₄⋊C₄	C₄×D₁₃	1	1	yes	characteristic
148	C₂×C₂²⋊C₄	C₄×D₁₃	1	2	yes	—
149	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
150	C₄⋊C₈	—	2	2	no	—
151	C₄⋊C₈	—	26	2	no	—
152	#100	—	13	8	no	—
153	C₂²⋊C₈	—	2	4	no	—
154	C₂²⋊C₈	—	13	4	no	—
155	#97	—	26	2	no	—
156	C₄×C₈	—	26	2	no	—
157	C₄×C₈	—	26	2	no	—
158	C₄×C₈	C₂²⋊D₁₃	1	2	yes	—
159	C₄×C₈	C₂²⋊D₁₃	1	2	yes	—
160	C₂×C₁₃	—	2	1	no	—
161	C₂×C₁₃	—	2	1	no	—
162	C₂×C₁₃	—	4	4	no	—
163	C₂×C₁₃	C₈×C₂²⋊C₄	1	1	yes	characteristic
164	C₂×C₁₃	C₄×#100	1	1	yes	characteristic
165	C₂×C₁₃	#1757	1	1	yes	characteristic
166	C₂⁴	C₄×Dic₁₃	1	2	yes	—
167	C₂×D₄	—	2	2	no	—
168	C₂×D₄	—	2	2	no	—
169	C₂×D₄	C₈×D₁₃	1	4	yes	—
170	C₂²×C₄	—	2	2	no	—
171	C₂²×C₄	—	2	2	no	—
172	C₂²×C₄	—	4	2	no	—
173	C₂²×C₄	—	4	2	no	—
174	C₂²×C₄	C₄×Dic₁₃	1	2	yes	—
175	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
176	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
177	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
178	M₁₆	—	13	8	no	—
179	M₁₆	—	26	4	no	—
180	C₂×C₈	—	2	2	no	—
181	C₂×C₈	—	2	2	no	—
182	C₂×C₈	—	4	1	no	—
183	C₂×C₈	—	4	4	no	—
184	C₂×C₈	—	4	4	no	—
185	C₂×C₈	—	4	2	no	—
186	C₂×C₈	—	26	4	no	—
187	C₂×C₈	—	26	4	no	—
188	C₂×C₈	C₂²⋊Dic₁₃	1	2	yes	—
189	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
190	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
191	C₄⋊C₄	—	2	2	no	—
192	C₂²⋊C₄	—	2	4	no	—
193	C₄²	#6127	1	2	yes	—
194	C₄²	C₂×C₂²⋊D₁₃	1	2	yes	—
195	C₁₃	C₈×#100	1	1	yes	characteristic, complemented, Sylow
196	C₂³	—	2	2	no	—
197	C₂³	—	2	2	no	—
198	C₂³	—	4	2	no	—
199	C₂³	—	4	2	no	—
200	C₂³	C₈×Dic₁₃	1	4	yes	—
201	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
202	D₄	—	2	8	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	4	4	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	4	2	no	—
210	C₂×C₄	—	4	2	no	—
211	C₂×C₄	C₂×C₈×D₁₃	1	2	yes	—
212	C₂×C₄	#88155	1	2	yes	—
213	C₂×C₄	#88180	1	1	yes	characteristic
214	C₂×C₄	C₄×C₂²⋊D₁₃	1	2	yes	—
215	C₂×C₄	C₄×C₂²⋊D₁₃	1	2	yes	—
216	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
217	C₈	—	2	1	no	—
218	C₈	—	2	2	no	—
219	C₈	—	4	2	no	—
220	C₈	—	26	8	no	—
221	C₈	—	52	4	no	—
222	C₈	#88073	1	2	yes	direct product factor
223	C₂²	—	2	1	no	—
224	C₂²	—	2	1	no	—
225	C₂²	—	2	4	no	—
226	C₂²	—	4	4	no	—
227	C₂²	—	4	4	no	—
228	C₂²	—	4	2	no	—
229	C₂²	—	4	2	no	—
230	C₂²	C₂×C₈×Dic₁₃	1	1	yes	characteristic
231	C₂²	#11718762	1	1	yes	characteristic
232	C₂²	C₄×C₂²⋊Dic₁₃	1	1	yes	characteristic
233	C₄	—	2	1	no	—
234	C₄	—	2	2	no	—
235	C₄	—	4	2	no	—
236	C₄	C₈×C₂²⋊D₁₃	1	4	yes	—
237	C₄	C₂×#88073	1	1	yes	characteristic
238	C₄	#11718898	1	1	yes	characteristic
239	C₂	—	2	1	no	—
240	C₂	—	2	1	no	—
241	C₂	—	4	4	no	—
242	C₂	C₈×C₂²⋊Dic₁₃	1	1	yes	characteristic
243	C₂	C₄×#88073	1	1	yes	characteristic
244	C₂	#13114636	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²⋊Dic₁₃
commutator	C₂²×C₁₃	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₂×C₈×D₄×C₁₃	C₂
socle	C₂²×C₁₃	C₄×C₂²⋊C₄
prime radical	C₂²×D₄×C₁₃	C₂×C₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	C₂×C₈×D₄	D₁₃
hypocenter	C₁₃	C₈×#100
LCS	G ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₂×C₈×D₄

Complements

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

N	H ≅ G/N	type
3. C₈×#6099	C₂	semidirect
4. #13112686	C₂	semidirect
38. #88073	C₈	direct (N × H)
71. #6099	C₂×C₈	semidirect
103. C₈×C₁₃	#100	semidirect
195. C₁₃	C₈×#100	semidirect
222. C₈	#88073	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×#88073	2
#13113157	2
C₈×#6099	2
#13112686	2
C₂×C₈×D₄×C₁₃	2
C₈×#100	13

Subgroups — C8×#88073 #15753477

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#88073 #15753477