Subgroups — #15833642

Order 3328.

590 conjugacy classes of subgroups.

The subgroup lattice has 248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123771	C₂	1	2	yes	maximal
2	#13113687	C₂	1	8	yes	maximal, complemented
3	#13113595	C₂	1	1	yes	maximal, characteristic
4	#13113291	C₂	1	2	yes	maximal
5	C₂×#11718046	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#3170	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#533	C₂²	1	2	yes	—
8	C₁₃×#500	C₄	1	1	yes	characteristic
9	C₁₃×#494	C₄	1	1	yes	characteristic
10	C₁₃×#487	C₄	1	2	yes	—
11	C₁₃×#467	C₄	1	4	yes	—
12	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	—
13	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	#11718685	—	2	2	no	—
15	#11718685	C₂²	1	4	yes	—
16	Q₈×#1055	—	2	2	no	—
17	Q₈×#1055	C₂²	1	4	yes	—
18	#11718660	—	2	2	no	—
19	#11718658	—	2	2	no	—
20	#11718585	C₂²	1	2	yes	—
21	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
22	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
23	Q₈⋊#1055	C₂²	1	8	yes	—
24	#11718050	C₂²	1	4	yes	—
25	#11718046	C₂²	1	4	yes	—
26	C₂×C₁₃×Q₁₆	C₂×C₄	1	4	yes	—
27	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
28	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
29	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
30	C₁₃×#125	—	2	2	no	—
31	C₁₃×C₂²⋊Q₈	—	2	2	no	—
32	C₁₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
33	C₄×Q₈×C₁₃	—	2	2	no	—
34	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
35	C₁₃×#117	—	2	2	no	—
36	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
37	C₂×#6099	—	2	2	no	—
38	C₂²×#1055	—	2	1	no	—
39	C₂²×#1055	D₄	1	1	yes	characteristic
40	C₂²×#1055	D₄	1	1	yes	characteristic
41	C₁₃×#107	C₂×C₄	1	4	yes	—
42	C₁₃×#103	C₂×C₄	1	8	yes	—
43	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₄×C₈×C₁₃	C₂³	1	2	yes	—
46	C₄⋊#1055	—	2	2	no	—
47	C₄⋊#1055	—	2	4	no	—
48	C₄⋊#1055	—	2	4	no	—
49	C₄⋊#1055	C₂³	1	4	yes	—
50	#88043	—	2	4	no	—
51	C₄×#1055	—	2	1	no	—
52	C₄×#1055	—	2	4	no	—
53	C₄×#1055	D₄	1	2	yes	—
54	C₄×#1055	C₂³	1	2	yes	—
55	C₄×#1055	C₂³	1	2	yes	—
56	#17977	—	13	1	no	maximal, Sylow
57	C₂×Q₈×C₁₃	—	2	2	no	—
58	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
59	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
62	C₁₃×Q₁₆	—	4	4	no	—
63	C₂×C₈×C₁₃	—	4	2	no	—
64	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
65	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
66	C₁₃×C₄⋊C₄	—	2	2	no	—
67	C₁₃×C₄⋊C₄	—	2	2	no	—
68	C₁₃×C₄⋊C₄	—	2	2	no	—
69	C₁₃×C₄⋊C₄	—	2	4	no	—
70	C₁₃×C₄⋊C₄	—	2	4	no	—
71	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
72	C₁₃×C₂²⋊C₄	—	2	4	no	—
73	C₄²×C₁₃	—	2	4	no	—
74	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
75	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
76	C₄²×C₁₃	#41	1	1	yes	characteristic
77	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
78	#6099	—	4	4	no	—
79	C₂×#1055	—	2	2	no	—
80	C₂×#1055	—	2	4	no	—
81	C₂×#1055	—	2	2	no	—
82	C₂×#1055	—	4	2	no	—
83	C₂×#1055	Q₁₆	1	4	yes	complemented
84	C₂×#1055	C₂×D₄	1	2	yes	—
85	C₂×#1055	C₂×D₄	1	2	yes	—
86	#3170	D₁₃	1	1	yes	characteristic
87	#2960	—	13	2	no	—
88	#1584	—	13	8	no	—
89	#1567	—	13	1	no	—
90	#1493	—	13	2	no	—
91	C₂×#322	—	13	1	no	—
92	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
93	Q₈×C₁₃	—	2	8	no	—
94	Q₈×C₁₃	—	4	4	no	—
95	C₂×C₄×C₁₃	—	2	2	no	—
96	C₂×C₄×C₁₃	—	2	2	no	—
97	C₂×C₄×C₁₃	—	2	4	no	—
98	C₂×C₄×C₁₃	—	2	4	no	—
99	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
100	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
101	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
102	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
103	C₂×C₄×C₁₃	#135	1	2	yes	—
104	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
105	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
106	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
107	C₈×C₁₃	—	2	2	no	—
108	C₈×C₁₃	—	2	2	no	—
109	#1055	—	2	2	no	—
110	#1055	—	4	2	no	—
111	#1055	—	4	4	no	—
112	#1055	C₂×Q₁₆	1	4	yes	—
113	#533	C₂×D₁₃	1	2	yes	—
114	#500	Dic₁₃	1	1	yes	characteristic
115	#494	Dic₁₃	1	1	yes	characteristic
116	#487	Dic₁₃	1	2	yes	—
117	#467	Dic₁₃	1	4	yes	—
118	#446	—	13	4	no	—
119	#446	—	26	2	no	—
120	C₈×Q₈	—	13	4	no	—
121	C₈×Q₈	—	26	2	no	—
122	C₄×Q₁₆	C₂×D₁₃	1	4	yes	—
123	#424	—	26	2	no	—
124	#423	—	13	2	no	—
125	#405	—	26	2	no	—
126	C₂×C₄×C₈	—	13	1	no	—
127	C₂×C₄×C₈	—	13	1	no	—
128	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
129	#335	—	13	4	no	—
130	Q₈⋊C₈	—	13	8	no	—
131	#322	—	13	4	no	—
132	C₂²×C₁₃	—	2	1	no	—
133	C₂²×C₁₃	—	2	1	no	—
134	C₂²×C₁₃	C₄×Q₁₆	1	2	yes	—
135	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
136	C₄×C₁₃	—	2	1	no	—
137	C₄×C₁₃	—	2	1	no	—
138	C₄×C₁₃	—	4	4	no	—
139	C₄×C₁₃	—	4	4	no	—
140	C₄×C₁₃	C₄×Q₁₆	1	2	yes	—
141	C₄×C₁₃	#444	1	2	yes	—
142	C₄×C₁₃	#568	1	2	yes	—
143	C₄×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
144	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
145	C₂×Q₁₆	C₂×Dic₁₃	1	4	yes	—
146	C₂×M₁₆	—	26	2	no	—
147	C₂²×C₈	—	13	1	no	—
148	C₂²×C₈	—	13	1	no	—
149	C₂²×C₈	—	26	1	no	—
150	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
151	C₄⋊Q₈	C₂×Dic₁₃	1	2	yes	—
152	C₄⋊Q₈	C₂×Dic₁₃	1	2	yes	—
153	#125	—	2	2	no	—
154	C₂²⋊Q₈	—	2	2	no	—
155	C₂²⋊Q₈	C₂×Dic₁₃	1	4	yes	—
156	C₄×Q₈	—	2	2	no	—
157	C₄×Q₈	C₂²×D₁₃	1	4	yes	—
158	#117	—	2	2	no	—
159	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
160	#107	C₂×Dic₁₃	1	4	yes	—
161	C₄⋊C₈	—	13	4	no	—
162	C₄⋊C₈	—	26	4	no	—
163	C₄⋊C₈	—	26	4	no	—
164	C₄⋊C₈	—	26	2	no	—
165	#103	C₂×Dic₁₃	1	8	yes	—
166	#97	—	26	4	no	—
167	C₄×C₈	—	13	2	no	—
168	C₄×C₈	—	13	2	no	—
169	C₄×C₈	—	13	2	no	—
170	C₄×C₈	—	26	4	no	—
171	C₄×C₈	—	26	1	no	—
172	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
173	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
174	C₄×C₈	C₂²×D₁₃	1	2	yes	—
175	C₂×C₁₃	—	2	2	no	—
176	C₂×C₁₃	#2932	1	1	yes	characteristic
177	C₂×C₁₃	C₂×C₄×Q₁₆	1	1	yes	characteristic
178	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
179	C₂×Q₈	—	2	2	no	—
180	C₂×Q₈	C₂²×Dic₁₃	1	4	yes	—
181	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
182	C₂²×C₄	#6129	1	1	yes	characteristic
183	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
184	Q₁₆	—	4	4	no	—
185	M₁₆	—	52	4	no	—
186	C₂×C₈	—	4	2	no	—
187	C₂×C₈	—	13	4	no	—
188	C₂×C₈	—	13	2	no	—
189	C₂×C₈	—	13	2	no	—
190	C₂×C₈	—	26	2	no	—
191	C₂×C₈	—	26	4	no	—
192	C₂×C₈	—	26	2	no	—
193	C₂×C₈	—	52	2	no	—
194	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
195	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
196	C₄⋊C₄	—	2	2	no	—
197	C₄⋊C₄	—	2	2	no	—
198	C₄⋊C₄	—	2	2	no	—
199	C₄⋊C₄	—	2	4	no	—
200	C₄⋊C₄	—	2	4	no	—
201	C₄⋊C₄	C₂²×Dic₁₃	1	4	yes	—
202	C₂²⋊C₄	—	2	4	no	—
203	C₄²	—	2	4	no	—
204	C₄²	D₄×D₁₃	1	1	yes	characteristic
205	C₄²	#6129	1	1	yes	characteristic
206	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
207	C₄²	C₂³×D₁₃	1	1	yes	characteristic
208	C₁₃	#17977	1	1	yes	characteristic, complemented, Sylow
209	C₂³	D₄×Dic₁₃	1	1	yes	characteristic
210	Q₈	—	2	8	no	—
211	Q₈	—	4	4	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	2	4	no	—
215	C₂×C₄	—	2	4	no	—
216	C₂×C₄	Q₁₆×D₁₃	1	2	yes	—
217	C₂×C₄	#88173	1	2	yes	—
218	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
219	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
220	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
221	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
222	C₂×C₄	C₂×#6129	1	1	yes	characteristic
223	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
224	C₈	—	2	2	no	—
225	C₈	—	2	2	no	—
226	C₈	—	13	4	no	—
227	C₈	—	26	2	no	—
228	C₈	—	52	2	no	—
229	C₈	—	52	4	no	—
230	C₂²	—	2	1	no	—
231	C₂²	—	2	1	no	—
232	C₂²	Q₁₆×Dic₁₃	1	2	yes	—
233	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
234	C₄	—	2	1	no	—
235	C₄	—	2	1	no	—
236	C₄	—	4	4	no	—
237	C₄	—	4	4	no	—
238	C₄	Q₁₆×Dic₁₃	1	2	yes	—
239	C₄	#11718858	1	2	yes	—
240	C₄	C₂×Q₁₆×D₁₃	1	1	yes	characteristic
241	C₄	C₂×#88173	1	1	yes	characteristic
242	C₄	#11719524	1	2	yes	—
243	C₂	—	2	2	no	—
244	C₂	#13123554	1	1	yes	characteristic
245	C₂	C₂×Q₁₆×Dic₁₃	1	1	yes	characteristic
246	C₂	C₂×#11718858	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#3170	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂³×C₁₃	C₄×D₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#3170	D₁₃
hypocenter	C₁₃	#17977
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3170

Complements

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

N	H ≅ G/N	type
2. #13113687	C₂	semidirect
83. C₂×#1055	Q₁₆	semidirect
208. C₁₃	#17977	semidirect

Maximal subgroups

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

subgroup	index
#13123771	2
#13113687	2
#13113595	2
#13113291	2
C₂×#11718046	2
C₁₃×#3170	2
#17977	13