Subgroups — #16780944

Order 3328.

446 conjugacy classes of subgroups.

The subgroup lattice has 240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#88102	C₂	1	1	yes	maximal, characteristic
2	#13130629	C₂	1	2	yes	maximal
3	C₈×D₁₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#13129670	C₂	1	2	yes	maximal
5	D₁₃×#335	C₂	1	1	yes	maximal, characteristic
6	C₂×#88102	C₄	1	2	yes	—
7	C₂×C₈×#261	—	2	2	no	—
8	C₄×C₄⋊#261	C₂²	1	2	yes	—
9	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
10	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
11	D₁₃×C₄⋊C₈	C₂²	1	2	yes	—
12	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
13	#11718265	C₄	1	2	yes	—
14	(C₂×#261)⋊C₈	—	2	2	no	—
15	C₈×#1057	C₄	1	2	yes	complemented
16	C₈×#1057	C₄	1	2	yes	complemented
17	C₁₃×#335	C₄	1	1	yes	characteristic, complemented
18	#11718071	C₄	1	2	yes	complemented
19	#11718050	C₄	1	1	yes	characteristic, complemented
20	C₂×C₄⋊#261	C₂×C₄	1	4	yes	—
21	C₂×C₄×#261	—	2	2	no	—
22	C₂×D₁₃⋊C₈	—	2	1	no	—
23	C₂×D₁₃⋊C₈	D₄	1	1	yes	characteristic
24	C₂×D₁₃⋊C₈	D₄	1	1	yes	characteristic
25	C₂×C₈×D₁₃	—	2	2	no	—
26	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
27	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
28	C₄²×D₁₃	C₂³	1	1	yes	characteristic
29	(C₂×#261)⋊C₄	—	2	2	no	—
30	C₄×#1057	—	2	1	no	—
31	C₄×#1057	C₂×C₄	1	2	yes	—
32	C₄×#1057	C₂×C₄	1	2	yes	—
33	C₄×#1057	Q₈	1	2	yes	—
34	#88102	C₈	1	8	yes	complemented
35	C₈×#261	—	4	4	no	—
36	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
37	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
38	#88054	—	2	2	no	—
39	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
40	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
41	C₄⋊#1055	C₂×C₄	1	2	yes	—
42	C₄×#1055	C₂×C₄	1	1	yes	characteristic
43	C₈×#107	—	13	1	no	maximal, Sylow
44	C₂²×#261	—	2	4	no	—
45	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
46	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
48	C₂×#1057	—	2	2	no	—
49	C₂×#1057	C₄⋊C₄	1	2	yes	—
50	C₂×#1057	C₄⋊C₄	1	2	yes	—
51	C₄⋊#261	—	2	4	no	—
52	C₄⋊#261	C₂×C₈	1	8	yes	—
53	C₄×#261	—	4	2	no	—
54	C₄×#261	—	4	2	no	—
55	D₁₃⋊C₈	—	2	4	no	—
56	D₁₃⋊C₈	—	2	1	no	—
57	D₁₃⋊C₈	—	2	1	no	—
58	D₁₃⋊C₈	D₈	1	2	yes	—
59	D₁₃⋊C₈	Q₁₆	1	2	yes	—
60	C₂×C₈×C₁₃	—	2	2	no	—
61	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
62	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
63	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
64	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
65	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
66	C₄×Dic₁₃	#41	1	1	yes	characteristic
67	C₂×#1055	—	2	2	no	—
68	C₂×#1055	C₄²	1	1	yes	characteristic
69	C₂×#1055	C₄²	1	1	yes	characteristic
70	C₈×D₁₃	—	2	2	no	—
71	C₈×D₁₃	—	4	2	no	—
72	C₈×D₁₃	—	4	2	no	—
73	C₈×D₁₃	C₂×C₈	1	4	yes	—
74	C₄×#107	—	13	1	no	—
75	C₈×C₄⋊C₄	—	13	2	no	—
76	C₂×#335	—	13	1	no	—
77	C₂×C₈²	—	13	1	no	—
78	#1279	—	13	2	no	—
79	C₂²×D₁₃	C₄×D₄	1	1	yes	characteristic
80	C₂×#261	—	2	8	no	—
81	C₂×#261	—	4	4	no	—
82	C₂×#261	—	4	4	no	—
83	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
84	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
85	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
86	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
87	C₂×Dic₁₃	#117	1	1	yes	characteristic
88	C₂×Dic₁₃	C₄×Q₈	1	1	yes	characteristic
89	C₄×D₁₃	—	2	2	no	—
90	C₄×D₁₃	C₂²×C₈	1	2	yes	—
91	C₄×D₁₃	#131	1	2	yes	—
92	C₄×D₁₃	C₂×D₈	1	1	yes	characteristic
93	C₄×D₁₃	C₂×Q₁₆	1	1	yes	characteristic
94	C₄×D₁₃	#135	1	1	yes	characteristic
95	C₄×D₁₃	#135	1	1	yes	characteristic
96	#1057	—	2	4	no	—
97	#1057	—	2	2	no	—
98	#1057	#107	1	4	yes	complemented
99	C₈×C₁₃	—	2	1	no	—
100	C₈×C₁₃	—	4	2	no	—
101	C₈×C₁₃	C₄×C₈	1	2	yes	complemented
102	#1055	—	2	1	no	—
103	#1055	—	4	2	no	—
104	#1055	C₄×C₈	1	2	yes	complemented
105	C₂×#107	—	13	2	no	—
106	C₂×C₄⋊C₈	—	13	2	no	—
107	C₂×C₄×C₈	—	13	1	no	—
108	C₂×C₄×C₈	—	13	1	no	—
109	C₂×C₄×C₈	—	13	1	no	—
110	C₂×C₄×C₈	—	26	2	no	—
111	C₄×C₄⋊C₄	—	13	2	no	—
112	#340	—	13	2	no	—
113	#336	—	26	2	no	—
114	#335	—	13	2	no	—
115	#335	—	13	1	no	—
116	#335	#261	1	1	yes	characteristic, complemented
117	C₈²	—	13	2	no	—
118	C₈²	—	13	2	no	—
119	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
120	C₂×D₁₃	C₈×D₄	1	2	yes	—
121	C₂×D₁₃	C₄×D₈	1	1	yes	characteristic
122	C₂×D₁₃	C₄×Q₁₆	1	1	yes	characteristic
123	C₂×D₁₃	#443	1	2	yes	—
124	#261	—	4	8	no	—
125	C₄×C₁₃	—	2	1	no	—
126	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
127	C₄×C₁₃	#405	1	1	yes	characteristic
128	C₄×C₁₃	C₄×D₈	1	1	yes	characteristic
129	C₄×C₁₃	C₄×Q₁₆	1	1	yes	characteristic
130	Dic₁₃	—	2	1	no	—
131	Dic₁₃	C₂×#107	1	1	yes	characteristic
132	Dic₁₃	#427	1	1	yes	characteristic
133	Dic₁₃	C₈×Q₈	1	2	yes	—
134	C₂²×C₈	—	13	1	no	—
135	C₂²×C₈	—	13	1	no	—
136	C₂²×C₈	—	13	1	no	—
137	C₂²×C₈	—	13	1	no	—
138	C₂²×C₈	—	26	2	no	—
139	C₂²×C₈	—	26	1	no	—
140	C₂×C₄⋊C₄	—	13	4	no	—
141	C₂×C₄²	—	13	1	no	—
142	C₂×C₄²	—	26	2	no	—
143	#107	—	13	8	no	—
144	C₄⋊C₈	—	13	2	no	—
145	C₄⋊C₈	—	26	2	no	—
146	C₄⋊C₈	C₂×#261	1	2	yes	—
147	C₄×C₈	—	13	2	no	—
148	C₄×C₈	—	13	2	no	—
149	C₄×C₈	—	13	1	no	—
150	C₄×C₈	—	13	1	no	—
151	C₄×C₈	—	13	2	no	—
152	C₄×C₈	—	13	1	no	—
153	C₄×C₈	—	26	1	no	—
154	C₄×C₈	—	52	4	no	—
155	C₄×C₈	C₂×#261	1	1	yes	characteristic
156	#95	—	26	2	no	—
157	C₂×C₁₃	C₈×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₁₃	#1772	1	1	yes	characteristic
159	C₂×C₁₃	C₄×#107	1	1	yes	characteristic
160	D₁₃	C₈×D₈	1	2	yes	—
161	D₁₃	C₈×Q₁₆	1	2	yes	—
162	C₂²×C₄	—	13	1	no	—
163	C₂²×C₄	—	13	1	no	—
164	C₂²×C₄	—	13	1	no	—
165	C₂²×C₄	—	26	4	no	—
166	C₂×C₈	—	2	2	no	—
167	C₂×C₈	—	13	2	no	—
168	C₂×C₈	—	13	2	no	—
169	C₂×C₈	—	13	2	no	—
170	C₂×C₈	—	13	1	no	—
171	C₂×C₈	—	13	4	no	—
172	C₂×C₈	—	13	2	no	—
173	C₂×C₈	—	13	1	no	—
174	C₂×C₈	—	26	2	no	—
175	C₂×C₈	—	26	2	no	—
176	C₂×C₈	—	26	1	no	—
177	C₂×C₈	—	26	1	no	—
178	C₂×C₈	—	26	4	no	—
179	C₂×C₈	—	26	2	no	—
180	C₂×C₈	—	52	2	no	—
181	C₂×C₈	—	52	2	no	—
182	C₂×C₈	C₄×#261	1	1	yes	characteristic
183	C₂×C₈	C₄×#261	1	1	yes	characteristic
184	C₄⋊C₄	—	13	8	no	—
185	C₄⋊C₄	—	26	4	no	—
186	C₄²	—	13	1	no	—
187	C₄²	—	13	1	no	—
188	C₄²	—	13	1	no	—
189	C₄²	—	52	2	no	—
190	C₄²	—	52	2	no	—
191	C₄²	C₂²×#261	1	1	yes	characteristic
192	C₁₃	C₈×#107	1	1	yes	characteristic, complemented, Sylow
193	C₂³	—	13	1	no	—
194	C₂×C₄	—	13	1	no	—
195	C₂×C₄	—	13	1	no	—
196	C₂×C₄	—	13	2	no	—
197	C₂×C₄	—	13	2	no	—
198	C₂×C₄	—	13	1	no	—
199	C₂×C₄	—	13	1	no	—
200	C₂×C₄	—	13	1	no	—
201	C₂×C₄	—	13	1	no	—
202	C₂×C₄	—	13	1	no	—
203	C₂×C₄	—	26	2	no	—
204	C₂×C₄	—	26	8	no	—
205	C₂×C₄	—	52	4	no	—
206	C₂×C₄	—	52	4	no	—
207	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
208	C₂×C₄	D₄×#261	1	1	yes	characteristic
209	C₂×C₄	Q₈×#261	1	1	yes	characteristic
210	C₈	—	2	1	no	—
211	C₈	—	4	2	no	—
212	C₈	—	13	4	no	—
213	C₈	—	13	2	no	—
214	C₈	—	26	2	no	—
215	C₈	—	26	4	no	—
216	C₈	—	26	1	no	—
217	C₈	—	52	2	no	—
218	C₈	C₈×#261	1	2	yes	complemented
219	C₂²	—	13	2	no	—
220	C₂²	—	13	2	no	—
221	C₂²	—	13	1	no	—
222	C₂²	—	13	1	no	—
223	C₂²	C₄⋊C₄×#261	1	1	yes	characteristic
224	C₄	—	2	1	no	—
225	C₄	—	13	2	no	—
226	C₄	—	13	1	no	—
227	C₄	—	13	1	no	—
228	C₄	—	26	1	no	—
229	C₄	—	52	8	no	—
230	C₄	C₂×C₈×#261	1	1	yes	characteristic
231	C₄	#11719099	1	1	yes	characteristic
232	C₄	D₈×#261	1	1	yes	characteristic
233	C₄	Q₁₆×#261	1	1	yes	characteristic
234	C₂	—	13	2	no	—
235	C₂	—	13	2	no	—
236	C₂	#13130629	1	1	yes	characteristic
237	C₂	#13130641	1	1	yes	characteristic
238	C₂	#107×#261	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×#261
commutator	C₄×C₁₃	C₂×C₄×C₈
Frattini	C₄²	C₂²×#261
Fitting	C₁₃×#335	C₄
socle	C₂²×C₁₃	C₄×C₄⋊C₄
prime radical	C₂²×D₁₃	C₄×D₄
cosocle	C₄²×D₁₃	C₂³
hypercenter	#335	#261
hypocenter	C₁₃	C₈×#107
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ #335

Complements

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

N	H ≅ G/N	type
15. C₈×#1057	C₄	semidirect
16. C₈×#1057	C₄	semidirect
17. C₁₃×#335	C₄	semidirect
18. #11718071	C₄	semidirect
19. #11718050	C₄	semidirect
34. #88102	C₈	semidirect
98. #1057	#107	semidirect
101. C₈×C₁₃	C₄×C₈	semidirect
104. #1055	C₄×C₈	semidirect
116. #335	#261	semidirect
192. C₁₃	C₈×#107	semidirect
218. C₈	C₈×#261	semidirect

Maximal subgroups

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

subgroup	index
C₄×#88102	2
#13130629	2
C₈×D₁₃⋊C₈	2
#13129670	2
D₁₃×#335	2
C₈×#107	13