Subgroups — #15833478

Order 3328.

598 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	#13123771	C₂	1	2	yes	maximal
2	#13113745	C₂	1	4	yes	maximal, complemented
3	#13113655	C₂	1	4	yes	maximal, complemented
4	#13113592	C₂	1	1	yes	maximal, characteristic
5	#13113291	C₂	1	2	yes	maximal
6	C₂×#11718047	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#3170	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#533	C₂²	1	2	yes	—
9	C₁₃×#500	C₄	1	1	yes	characteristic
10	C₁₃×#494	C₄	1	1	yes	characteristic
11	C₁₃×#487	C₄	1	2	yes	—
12	C₁₃×#467	C₄	1	4	yes	—
13	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	—
14	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	#11718685	—	2	2	no	—
16	#11718685	C₂²	1	4	yes	—
17	Q₈×#1055	—	2	2	no	—
18	Q₈×#1055	C₂²	1	4	yes	—
19	#11718660	—	2	2	no	—
20	#11718658	—	2	2	no	—
21	#11718585	C₂²	1	2	yes	—
22	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
23	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
24	Q₈⋊#1055	C₂²	1	8	yes	—
25	#11718049	C₂²	1	4	yes	—
26	#11718047	C₂²	1	2	yes	—
27	#11718047	C₂²	1	2	yes	—
28	C₂×C₁₃×Q₁₆	C₂×C₄	1	4	yes	—
29	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
30	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
31	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
32	C₁₃×#125	—	2	2	no	—
33	C₁₃×C₂²⋊Q₈	—	2	2	no	—
34	C₁₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
35	C₄×Q₈×C₁₃	—	2	2	no	—
36	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
37	C₁₃×#117	—	2	2	no	—
38	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
39	C₂×#6099	—	2	2	no	—
40	C₂²×#1055	—	2	1	no	—
41	C₂²×#1055	D₄	1	2	yes	—
42	C₁₃×#107	C₂×C₄	1	4	yes	—
43	C₁₃×#103	C₂×C₄	1	8	yes	—
44	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
46	C₄×C₈×C₁₃	C₂³	1	2	yes	—
47	C₄⋊#1055	—	2	2	no	—
48	C₄⋊#1055	—	2	4	no	—
49	C₄⋊#1055	—	2	4	no	—
50	C₄⋊#1055	C₂³	1	4	yes	—
51	#88043	—	2	4	no	—
52	C₄×#1055	—	2	1	no	—
53	C₄×#1055	—	2	4	no	—
54	C₄×#1055	D₄	1	2	yes	—
55	C₄×#1055	C₂³	1	2	yes	—
56	C₄×#1055	C₂³	1	1	yes	characteristic
57	C₄×#1055	C₂³	1	1	yes	characteristic
58	#17961	—	13	1	no	maximal, Sylow
59	C₂×Q₈×C₁₃	—	2	2	no	—
60	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
61	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
64	C₁₃×Q₁₆	—	2	8	no	—
65	C₂×C₈×C₁₃	—	2	4	no	—
66	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
67	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
68	C₁₃×C₄⋊C₄	—	2	2	no	—
69	C₁₃×C₄⋊C₄	—	2	2	no	—
70	C₁₃×C₄⋊C₄	—	2	2	no	—
71	C₁₃×C₄⋊C₄	—	2	4	no	—
72	C₁₃×C₄⋊C₄	—	2	4	no	—
73	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
74	C₁₃×C₂²⋊C₄	—	2	4	no	—
75	C₄²×C₁₃	—	2	4	no	—
76	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
77	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
78	C₄²×C₁₃	#41	1	1	yes	characteristic
79	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
80	#6099	—	4	4	no	—
81	C₂×#1055	—	2	4	no	—
82	C₂×#1055	—	2	4	no	—
83	C₂×#1055	—	2	2	no	—
84	C₂×#1055	—	4	2	no	—
85	C₂×#1055	C₂×D₄	1	2	yes	—
86	C₂×#1055	C₂×D₄	1	2	yes	—
87	#3170	D₁₃	1	1	yes	characteristic
88	#2960	—	13	2	no	—
89	#1593	—	13	4	no	—
90	#1579	—	13	4	no	—
91	#1566	—	13	1	no	—
92	#1493	—	13	2	no	—
93	C₂×#322	—	13	1	no	—
94	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
95	Q₈×C₁₃	—	2	8	no	—
96	Q₈×C₁₃	—	4	4	no	—
97	C₂×C₄×C₁₃	—	2	2	no	—
98	C₂×C₄×C₁₃	—	2	2	no	—
99	C₂×C₄×C₁₃	—	2	4	no	—
100	C₂×C₄×C₁₃	—	2	4	no	—
101	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
102	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
103	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
104	C₂×C₄×C₁₃	#137	1	4	yes	—
105	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
106	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
107	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
108	C₈×C₁₃	—	2	2	no	—
109	C₈×C₁₃	#131	1	4	yes	—
110	#1055	—	2	2	no	—
111	#1055	—	2	2	no	—
112	#1055	—	4	2	no	—
113	#1055	—	4	4	no	—
114	#533	C₂×D₁₃	1	2	yes	—
115	#500	Dic₁₃	1	1	yes	characteristic
116	#494	Dic₁₃	1	1	yes	characteristic
117	#487	Dic₁₃	1	2	yes	—
118	#467	Dic₁₃	1	4	yes	—
119	#446	—	13	4	no	—
120	#446	—	26	2	no	—
121	C₈×Q₈	—	13	4	no	—
122	C₈×Q₈	—	26	2	no	—
123	C₄×Q₁₆	C₂×D₁₃	1	4	yes	—
124	#424	—	26	2	no	—
125	#423	—	13	2	no	—
126	#405	—	26	2	no	—
127	C₂×C₄×C₈	—	13	1	no	—
128	C₂×C₄×C₈	—	13	1	no	—
129	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
130	#334	—	13	4	no	—
131	Q₈⋊C₈	—	13	8	no	—
132	#322	—	13	2	no	—
133	#322	—	13	2	no	—
134	C₂²×C₁₃	—	2	1	no	—
135	C₂²×C₁₃	—	2	1	no	—
136	C₂²×C₁₃	#441	1	2	yes	—
137	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
138	C₄×C₁₃	—	2	1	no	—
139	C₄×C₁₃	—	2	1	no	—
140	C₄×C₁₃	—	4	4	no	—
141	C₄×C₁₃	—	4	4	no	—
142	C₄×C₁₃	#441	1	2	yes	—
143	C₄×C₁₃	#444	1	2	yes	—
144	C₄×C₁₃	C₂×#131	1	2	yes	—
145	C₄×C₁₃	C₂×#137	1	2	yes	—
146	C₂×Q₁₆	C₂×Dic₁₃	1	4	yes	—
147	C₂×M₁₆	—	26	2	no	—
148	C₂²×C₈	—	13	2	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	1	no	—
169	C₄×C₈	—	13	1	no	—
170	C₄×C₈	—	13	2	no	—
171	C₄×C₈	—	26	4	no	—
172	C₄×C₈	—	26	1	no	—
173	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
174	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
175	C₄×C₈	C₂²×D₁₃	1	2	yes	—
176	C₂×C₁₃	—	2	2	no	—
177	C₂×C₁₃	#2931	1	1	yes	characteristic
178	C₂×C₁₃	C₂×#441	1	1	yes	characteristic
179	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
180	C₂×Q₈	—	2	2	no	—
181	C₂×Q₈	C₂²×Dic₁₃	1	4	yes	—
182	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
183	C₂²×C₄	#6129	1	1	yes	characteristic
184	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
185	Q₁₆	—	2	8	no	—
186	M₁₆	—	52	4	no	—
187	C₂×C₈	—	2	4	no	—
188	C₂×C₈	—	13	2	no	—
189	C₂×C₈	—	13	2	no	—
190	C₂×C₈	—	26	4	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	#17961	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	#88172	1	4	yes	—
217	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
218	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
219	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
220	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
221	C₂×C₄	C₂×#6129	1	1	yes	characteristic
222	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
223	C₈	—	2	2	no	—
224	C₈	—	26	2	no	—
225	C₈	—	26	2	no	—
226	C₈	—	52	2	no	—
227	C₈	—	52	4	no	—
228	C₈	#88202	1	4	yes	—
229	C₂²	—	2	1	no	—
230	C₂²	—	2	1	no	—
231	C₂²	#11718845	1	2	yes	—
232	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
233	C₄	—	2	1	no	—
234	C₄	—	2	1	no	—
235	C₄	—	4	4	no	—
236	C₄	—	4	4	no	—
237	C₄	#11718845	1	2	yes	—
238	C₄	#11718858	1	2	yes	—
239	C₄	C₂×#88172	1	2	yes	—
240	C₄	C₂×#88202	1	2	yes	—
241	C₂	—	2	2	no	—
242	C₂	#13123548	1	1	yes	characteristic
243	C₂	C₂×#11718845	1	1	yes	characteristic
244	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	#17961
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. #13113745	C₂	semidirect
3. #13113655	C₂	semidirect
208. C₁₃	#17961	semidirect

Maximal subgroups

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

subgroup	index
#13123771	2
#13113745	2
#13113655	2
#13113592	2
#13113291	2
C₂×#11718047	2
C₁₃×#3170	2
#17961	13