Subgroups — C₈×#88202 #15828507

Order 3328.

922 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×#1055	C₂	1	1	yes	maximal, characteristic
2	C₄×#88202	C₂	1	1	yes	maximal, characteristic
3	#13113120	C₂	1	3	yes	maximal, complemented
4	#13113117	C₂	1	3	yes	maximal, complemented
5	C₈×#6099	C₂	1	3	yes	maximal, complemented
6	C₂×C₈×#1055	C₂	1	3	yes	maximal, complemented
7	C₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic
8	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
9	C₂×#88202	C₄	1	2	yes	—
10	C₈×Q₈×C₁₃	C₄	1	2	yes	—
11	C₈×D₄×C₁₃	C₄	1	6	yes	—
12	C₁₃×#431	C₂²	1	3	yes	—
13	C₂×C₄×C₈×C₁₃	C₂²	1	3	yes	—
14	Q₈×#1055	C₄	1	2	yes	—
15	D₄×#1055	C₄	1	6	yes	—
16	#11718658	C₄	1	6	yes	—
17	#11718586	C₂²	1	3	yes	—
18	C₄×#6099	C₂²	1	3	yes	—
19	C₂×C₄×#1055	C₂²	1	3	yes	—
20	C₂×C₄×#1055	C₂²	1	3	yes	—
21	#11718046	C₂²	1	6	yes	—
22	C₈×#1055	C₂²	1	1	yes	characteristic
23	C₈×#1055	C₂²	1	3	yes	—
24	C₈×#1055	C₂²	1	3	yes	—
25	C₈×#1055	C₂²	1	3	yes	—
26	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₃	C₂×C₄	1	6	yes	—
28	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
29	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
30	C₄×D₄×C₁₃	C₂×C₄	1	3	yes	—
31	C₄×D₄×C₁₃	C₂×C₄	1	3	yes	—
32	C₁₃×#117	C₂×C₄	1	3	yes	—
33	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
34	#88202	C₈	1	16	yes	direct product factor
35	C₂×#6099	C₂×C₄	1	6	yes	—
36	C₂²×#1055	C₂×C₄	1	6	yes	—
37	C₂²×#1055	C₂×C₄	1	6	yes	—
38	C₁₃×C₄⋊C₈	C₂×C₄	1	6	yes	—
39	C₁₃×C₂²⋊C₈	C₂×C₄	1	6	yes	—
40	C₄×C₈×C₁₃	C₂×C₄	1	6	yes	—
41	C₄×C₈×C₁₃	C₂³	1	3	yes	—
42	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
43	C₂²⋊#1055	C₂×C₄	1	6	yes	—
44	C₄⋊#1055	C₂×C₄	1	6	yes	—
45	#88043	C₂×C₄	1	6	yes	—
46	C₄×#1055	C₂×C₄	1	6	yes	—
47	C₄×#1055	C₂×C₄	1	6	yes	—
48	C₄×#1055	C₂³	1	1	yes	characteristic
49	C₄×#1055	C₂³	1	1	yes	characteristic
50	C₄×#1055	C₂³	1	3	yes	—
51	C₄×#1055	C₂³	1	3	yes	—
52	C₈×#131	—	13	1	no	maximal, Sylow
53	C₁₃×#41	C₂×C₈	1	8	yes	—
54	C₂×Q₈×C₁₃	C₄²	1	1	yes	characteristic
55	C₂×D₄×C₁₃	C₄²	1	3	yes	—
56	C₂²×C₄×C₁₃	C₂²×C₄	1	3	yes	—
57	C₂²×C₄×C₁₃	C₂²×C₄	1	3	yes	—
58	C₂²×C₄×C₁₃	C₂²×C₄	1	3	yes	—
59	C₂×C₈×C₁₃	—	2	12	no	—
60	C₂×C₈×C₁₃	C₂²×C₄	1	6	yes	—
61	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
62	C₁₃×C₄⋊C₄	C₄²	1	3	yes	—
63	C₁₃×C₄⋊C₄	C₄²	1	3	yes	—
64	C₁₃×C₂²⋊C₄	C₄²	1	6	yes	—
65	C₄²×C₁₃	C₂²×C₄	1	3	yes	—
66	C₄²×C₁₃	C₂²×C₄	1	3	yes	—
67	C₄²×C₁₃	C₂²×C₄	1	3	yes	—
68	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
69	#6099	C₂×C₈	1	24	yes	complemented
70	C₂×#1055	—	2	12	no	—
71	C₂×#1055	C₂×C₈	1	24	yes	complemented
72	C₂×#1055	C₂²×C₄	1	6	yes	—
73	C₂×#1055	C₂²×C₄	1	2	yes	—
74	C₂×#1055	C₂²×C₄	1	6	yes	—
75	C₂×#1055	C₂²×C₄	1	2	yes	—
76	C₈×#41	—	13	1	no	—
77	C₈×#41	D₁₃	1	1	yes	characteristic
78	C₄×#131	—	13	1	no	—
79	#1450	—	13	3	no	—
80	C₈×M₁₆	—	13	3	no	—
81	C₈×M₁₆	—	13	3	no	—
82	C₂×C₈²	—	13	3	no	—
83	C₂³×C₁₃	C₂×C₄²	1	3	yes	—
84	Q₈×C₁₃	C₄×C₈	1	4	yes	—
85	D₄×C₁₃	C₄×C₈	1	12	yes	—
86	C₂×C₄×C₁₃	—	2	6	no	—
87	C₂×C₄×C₁₃	—	2	6	no	—
88	C₂×C₄×C₁₃	C₂×C₄²	1	3	yes	—
89	C₂×C₄×C₁₃	C₂×C₄²	1	3	yes	—
90	C₂×C₄×C₁₃	C₂×C₄²	1	3	yes	—
91	C₂×C₄×C₁₃	C₂²×C₈	1	12	yes	—
92	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
93	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
94	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
95	C₈×C₁₃	—	2	6	no	—
96	C₈×C₁₃	#131	1	4	yes	complemented
97	#1055	—	2	6	no	—
98	#1055	C₂²×C₈	1	4	yes	—
99	#1055	C₂²×C₈	1	12	yes	—
100	#1055	#131	1	4	yes	complemented
101	C₂×#131	—	13	2	no	—
102	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
103	C₈×Q₈	—	13	2	no	—
104	C₈×Q₈	Dic₁₃	1	2	yes	—
105	C₈×D₄	—	13	6	no	—
106	C₈×D₄	Dic₁₃	1	6	yes	—
107	#431	—	13	3	no	—
108	#431	C₂×D₁₃	1	3	yes	—
109	#405	—	13	6	no	—
110	C₄×M₁₆	—	13	3	no	—
111	C₂×C₄×C₈	—	13	3	no	—
112	C₂×C₄×C₈	—	13	3	no	—
113	C₂×C₄×C₈	C₂×D₁₃	1	3	yes	—
114	#322	—	13	6	no	—
115	C₈²	—	13	3	no	—
116	C₈²	—	13	3	no	—
117	C₈²	—	13	1	no	—
118	C₈²	—	13	3	no	—
119	C₂²×C₁₃	—	2	3	no	—
120	C₂²×C₁₃	—	2	3	no	—
121	C₂²×C₁₃	C₂×C₄×C₈	1	6	yes	—
122	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
123	C₄×C₁₃	—	2	3	no	—
124	C₄×C₁₃	—	2	3	no	—
125	C₄×C₁₃	C₂×C₄×C₈	1	6	yes	—
126	C₄×C₁₃	C₂³×C₈	1	2	yes	—
127	C₄×C₁₃	C₂×#131	1	2	yes	—
128	C₄×C₁₃	C₂×#131	1	2	yes	—
129	C₂×#41	C₄×D₁₃	1	1	yes	characteristic
130	#131	—	13	16	no	—
131	C₂×M₁₆	—	13	6	no	—
132	C₂²×C₈	—	13	6	no	—
133	C₂²×C₈	—	13	6	no	—
134	C₂²×C₈	C₂×Dic₁₃	1	6	yes	—
135	C₄×Q₈	C₄×D₁₃	1	1	yes	characteristic
136	C₄×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
137	C₄×D₄	C₄×D₁₃	1	3	yes	—
138	C₄×D₄	C₂×Dic₁₃	1	3	yes	—
139	#117	C₄×D₁₃	1	3	yes	—
140	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
141	C₄⋊C₈	—	13	6	no	—
142	C₄⋊C₈	C₂×Dic₁₃	1	6	yes	—
143	C₂²⋊C₈	—	13	6	no	—
144	C₂²⋊C₈	C₂×Dic₁₃	1	6	yes	—
145	#97	—	13	6	no	—
146	C₄×C₈	—	13	6	no	—
147	C₄×C₈	—	13	6	no	—
148	C₄×C₈	—	13	1	no	—
149	C₄×C₈	—	13	1	no	—
150	C₄×C₈	—	13	3	no	—
151	C₄×C₈	—	13	3	no	—
152	C₄×C₈	C₂×Dic₁₃	1	6	yes	—
153	C₄×C₈	C₂²×D₁₃	1	3	yes	—
154	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
155	C₂×C₁₃	—	2	6	no	—
156	C₂×C₁₃	C₂²×C₄×C₈	1	1	yes	characteristic
157	C₂×C₁₃	C₄×#131	1	1	yes	characteristic
158	C₂×C₁₃	C₄×#131	1	1	yes	characteristic
159	#41	C₈×D₁₃	1	8	yes	—
160	C₂×Q₈	C₄×Dic₁₃	1	1	yes	characteristic
161	C₂×D₄	C₄×Dic₁₃	1	3	yes	—
162	C₂²×C₄	C₂×C₄×D₁₃	1	3	yes	—
163	C₂²×C₄	C₂×C₄×D₁₃	1	3	yes	—
164	C₂²×C₄	C₂²×Dic₁₃	1	3	yes	—
165	M₁₆	—	13	24	no	—
166	C₂×C₈	—	2	12	no	—
167	C₂×C₈	—	13	24	no	—
168	C₂×C₈	—	13	2	no	—
169	C₂×C₈	—	13	2	no	—
170	C₂×C₈	—	13	6	no	—
171	C₂×C₈	—	13	6	no	—
172	C₂×C₈	—	26	12	no	—
173	C₂×C₈	C₂²×Dic₁₃	1	6	yes	—
174	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
175	C₄⋊C₄	C₄×Dic₁₃	1	3	yes	—
176	C₄⋊C₄	C₄×Dic₁₃	1	3	yes	—
177	C₂²⋊C₄	C₄×Dic₁₃	1	6	yes	—
178	C₄²	C₂×C₄×D₁₃	1	3	yes	—
179	C₄²	C₂×C₄×D₁₃	1	3	yes	—
180	C₄²	C₂²×Dic₁₃	1	3	yes	—
181	C₄²	C₂³×D₁₃	1	1	yes	characteristic
182	C₁₃	C₈×#131	1	1	yes	characteristic, complemented, Sylow
183	C₂³	C₂×C₄×Dic₁₃	1	3	yes	—
184	Q₈	C₈×Dic₁₃	1	4	yes	—
185	D₄	C₈×Dic₁₃	1	12	yes	—
186	C₂×C₄	—	2	6	no	—
187	C₂×C₄	—	2	6	no	—
188	C₂×C₄	C₂×C₈×D₁₃	1	12	yes	—
189	C₂×C₄	C₂×C₄×Dic₁₃	1	3	yes	—
190	C₂×C₄	C₂×C₄×Dic₁₃	1	3	yes	—
191	C₂×C₄	C₂×C₄×Dic₁₃	1	3	yes	—
192	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
193	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
194	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
195	C₈	—	2	6	no	—
196	C₈	—	13	4	no	—
197	C₈	—	13	12	no	—
198	C₈	—	13	4	no	—
199	C₈	—	26	6	no	—
200	C₈	#88202	1	4	yes	direct product factor
201	C₂²	—	2	3	no	—
202	C₂²	—	2	3	no	—
203	C₂²	C₂×C₈×Dic₁₃	1	6	yes	—
204	C₂²	C₂²×C₄×Dic₁₃	1	1	yes	characteristic
205	C₄	—	2	3	no	—
206	C₄	—	2	3	no	—
207	C₄	C₂×C₈×Dic₁₃	1	6	yes	—
208	C₄	C₂²×C₈×D₁₃	1	2	yes	—
209	C₄	D₁₃×#131	1	2	yes	—
210	C₄	C₂×#88202	1	2	yes	—
211	C₂	—	2	6	no	—
212	C₂	C₂²×C₈×Dic₁₃	1	1	yes	characteristic
213	C₂	#131×Dic₁₃	1	1	yes	characteristic
214	C₂	C₄×#88202	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₈	C₂²×D₁₃
commutator	C₂×C₁₃	C₂²×C₄×C₈
Frattini	C₄²	C₂³×D₁₃
Fitting	C₈×C₁₃×#41	C₂
socle	C₂²×C₁₃	C₂²×C₄²
prime radical	C₂×C₁₃×#41	C₂×C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₈×#41	D₁₃
hypocenter	C₁₃	C₈×#131
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄×C₈ ◁ C₈×#41

Complements

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

N	H ≅ G/N	type
3. #13113120	C₂	semidirect
4. #13113117	C₂	semidirect
5. C₈×#6099	C₂	semidirect
6. C₂×C₈×#1055	C₂	semidirect
34. #88202	C₈	direct (N × H)
69. #6099	C₂×C₈	semidirect
71. C₂×#1055	C₂×C₈	semidirect
96. C₈×C₁₃	#131	semidirect
100. #1055	#131	semidirect
182. C₁₃	C₈×#131	semidirect
200. C₈	#88202	direct (N × H)

Maximal subgroups

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

subgroup	index
#41×#1055	2
C₄×#88202	2
#13113120	2
#13113117	2
C₈×#6099	2
C₂×C₈×#1055	2
C₈×C₁₃×#41	2
C₈×#131	13

Subgroups — C8×#88202 #15828507

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#88202 #15828507