Subgroups — #15756035

Order 3328.

418 conjugacy classes of subgroups.

The subgroup lattice has 252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718340	C₂	1	1	yes	maximal, characteristic
2	#13114838	C₂	1	2	yes	maximal
3	C₂×#11718049	C₂	1	1	yes	maximal, characteristic
4	#13112719	C₂	1	2	yes	maximal
5	C₁₃×#1834	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₂₆	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₁₃×#384	C₂²	1	2	yes	—
9	C₂×#88055	—	2	1	no	—
10	C₂×#88054	—	2	1	no	—
11	C₂×#88050	—	2	2	no	—
12	C₂×C₄⋊#1055	C₂²	1	2	yes	—
13	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
14	#11718340	—	2	2	no	—
15	#11718340	C₄	1	4	yes	complemented
16	C₁₃×#340	—	2	1	no	—
17	C₁₃×#340	—	2	1	no	—
18	#11718121	—	2	2	no	—
19	#11718049	—	2	2	no	—
20	C₂²×Dic₂₆	D₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
24	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
25	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
26	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
27	C₂×C₄⋊Dic₁₃	D₄	1	1	yes	characteristic
28	C₂×#6101	—	2	1	no	—
29	C₂×C₄×Dic₁₃	—	2	1	no	—
30	C₂²×#1055	—	2	1	no	—
31	C₂²×#1055	—	2	2	no	—
32	C₄×Dic₂₆	—	2	1	no	—
33	C₄×Dic₂₆	—	2	1	no	—
34	C₄×Dic₂₆	C₂×C₄	1	2	yes	—
35	C₄×Dic₂₆	Q₈	1	2	yes	—
36	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
37	C₄×C₈×C₁₃	D₄	1	2	yes	—
38	#88055	—	2	4	no	—
39	#88054	—	2	4	no	—
40	#88050	—	4	4	no	—
41	C₄⋊#1055	—	2	1	no	—
42	C₄⋊#1055	—	2	2	no	—
43	C₄⋊#1055	—	2	2	no	—
44	C₄⋊#1055	C₂×C₄	1	2	yes	—
45	#8657	—	13	1	no	maximal, Sylow
46	C₂²×C₄×C₁₃	—	4	2	no	—
47	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
50	C₂²×Dic₁₃	—	2	1	no	—
51	C₂²×Dic₁₃	—	2	1	no	—
52	C₂×Dic₂₆	—	2	2	no	—
53	C₂×Dic₂₆	—	2	2	no	—
54	C₂×Dic₂₆	—	2	1	no	—
55	C₂×Dic₂₆	C₄⋊C₄	1	2	yes	—
56	C₂×C₈×C₁₃	—	2	2	no	—
57	C₂×C₈×C₁₃	—	2	2	no	—
58	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
59	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
60	C₁₃×C₄⋊C₄	—	4	2	no	—
61	C₁₃×C₄⋊C₄	—	4	2	no	—
62	C₁₃×C₄⋊C₄	—	4	2	no	—
63	C₁₃×C₄⋊C₄	—	4	2	no	—
64	C₁₃×C₄⋊C₄	—	8	2	no	—
65	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
66	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
67	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
68	C₄²×C₁₃	#41	1	1	yes	characteristic
69	C₄⋊Dic₁₃	—	2	1	no	—
70	C₄⋊Dic₁₃	C₄⋊C₄	1	2	yes	—
71	#6101	—	2	2	no	—
72	#6101	—	2	2	no	—
73	C₄×Dic₁₃	—	2	2	no	—
74	C₄×Dic₁₃	—	2	2	no	—
75	C₂×#1055	—	2	2	no	—
76	C₂×#1055	—	4	2	no	—
77	C₂×#1055	—	4	2	no	—
78	C₂×#1055	—	4	2	no	—
79	C₂×#1055	—	4	2	no	—
80	C₂×#446	—	13	1	no	—
81	#1834	D₁₃	1	1	yes	characteristic
82	#1803	—	13	2	no	—
83	C₂×#334	—	13	1	no	—
84	#1296	—	13	2	no	—
85	C₂³×C₁₃	#121	1	1	yes	characteristic
86	C₂×C₄×C₁₃	—	2	2	no	—
87	C₂×C₄×C₁₃	—	8	2	no	—
88	C₂×C₄×C₁₃	—	8	2	no	—
89	C₂×C₄×C₁₃	—	8	2	no	—
90	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
92	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
93	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
94	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
95	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
96	C₂×C₄×C₁₃	#135	1	2	yes	—
97	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
98	C₂×C₄×C₁₃	#137	1	2	yes	—
99	C₂×C₄×C₁₃	#137	1	2	yes	—
100	C₂×Dic₁₃	—	2	2	no	—
101	C₂×Dic₁₃	—	2	2	no	—
102	C₂×Dic₁₃	—	4	1	no	—
103	C₂×Dic₁₃	—	4	1	no	—
104	C₂×Dic₁₃	—	4	2	no	—
105	Dic₂₆	—	2	4	no	—
106	Dic₂₆	—	4	2	no	—
107	C₈×C₁₃	—	2	2	no	—
108	C₈×C₁₃	—	2	2	no	—
109	#1055	—	4	2	no	—
110	#1055	—	8	2	no	—
111	C₂×C₄×Q₈	—	13	1	no	—
112	#446	—	13	4	no	—
113	#446	—	26	2	no	—
114	C₂×C₄⋊C₈	—	13	1	no	—
115	C₂×C₄⋊C₈	—	13	2	no	—
116	C₂×C₄⋊C₈	—	26	1	no	—
117	C₂×#103	—	26	2	no	—
118	C₂×#97	—	26	1	no	—
119	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
120	#384	C₂×D₁₃	1	2	yes	—
121	#340	—	2	1	no	—
122	#340	—	2	1	no	—
123	#340	—	26	2	no	—
124	#334	—	26	2	no	—
125	C₂²×C₁₃	#380	1	1	yes	characteristic
126	C₂²×C₁₃	#464	1	2	yes	—
127	C₂²×C₁₃	#469	1	1	yes	characteristic
128	C₂²×C₁₃	#470	1	1	yes	characteristic
129	C₂²×C₁₃	#471	1	2	yes	—
130	C₄×C₁₃	—	2	1	no	—
131	C₄×C₁₃	—	2	1	no	—
132	C₄×C₁₃	—	16	2	no	—
133	C₄×C₁₃	#416	1	1	yes	characteristic
134	C₄×C₁₃	#419	1	1	yes	characteristic
135	C₄×C₁₃	#428	1	2	yes	—
136	C₄×C₁₃	#468	1	2	yes	—
137	C₄×C₁₃	#479	1	2	yes	—
138	Dic₁₃	—	4	2	no	—
139	Dic₁₃	—	4	2	no	—
140	C₂²×Q₈	—	13	1	no	—
141	C₂²×C₈	—	26	1	no	—
142	C₂²×C₈	—	26	2	no	—
143	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
144	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
145	C₄×Q₈	—	13	2	no	—
146	C₄×Q₈	—	13	2	no	—
147	C₄×Q₈	—	26	1	no	—
148	C₄×Q₈	—	26	1	no	—
149	C₂×C₄⋊C₄	—	2	2	no	—
150	C₂×C₄⋊C₄	—	2	2	no	—
151	C₂×C₄⋊C₄	—	2	2	no	—
152	C₂×C₄⋊C₄	—	13	1	no	—
153	C₂×C₄⋊C₄	—	26	1	no	—
154	C₂×C₄²	—	26	1	no	—
155	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
156	C₄⋊C₈	—	13	2	no	—
157	C₄⋊C₈	—	26	4	no	—
158	C₄⋊C₈	—	26	1	no	—
159	C₄⋊C₈	—	26	2	no	—
160	C₄⋊C₈	—	26	2	no	—
161	#103	—	52	4	no	—
162	#97	—	26	4	no	—
163	C₄×C₈	C₄×D₁₃	1	2	yes	—
164	C₄×C₈	D₅₂	1	2	yes	—
165	C₂×C₁₃	#1702	1	2	yes	—
166	C₂×C₁₃	#1704	1	2	yes	—
167	C₂×C₁₃	#1805	1	1	yes	characteristic
168	C₂×C₁₃	#1809	1	1	yes	characteristic
169	C₂×C₁₃	#1815	1	1	yes	characteristic
170	C₂×Q₈	—	13	2	no	—
171	C₂×Q₈	—	26	1	no	—
172	C₂×Q₈	—	26	2	no	—
173	C₂×Q₈	—	26	2	no	—
174	C₂²×C₄	—	4	2	no	—
175	C₂²×C₄	—	26	1	no	—
176	C₂²×C₄	—	26	1	no	—
177	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
178	C₂²×C₄	#6129	1	1	yes	characteristic
179	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
180	C₂×C₈	—	2	2	no	—
181	C₂×C₈	—	2	2	no	—
182	C₂×C₈	—	26	2	no	—
183	C₂×C₈	—	52	2	no	—
184	C₂×C₈	—	52	2	no	—
185	C₂×C₈	—	52	2	no	—
186	C₂×C₈	—	52	2	no	—
187	C₂×C₈	#6103	1	2	yes	—
188	C₂×C₈	#6103	1	2	yes	—
189	C₄⋊C₄	—	4	2	no	—
190	C₄⋊C₄	—	4	2	no	—
191	C₄⋊C₄	—	4	2	no	—
192	C₄⋊C₄	—	4	2	no	—
193	C₄⋊C₄	—	8	2	no	—
194	C₄⋊C₄	—	13	2	no	—
195	C₄⋊C₄	—	26	2	no	—
196	C₄⋊C₄	—	26	1	no	—
197	C₄⋊C₄	—	26	2	no	—
198	C₄²	—	26	2	no	—
199	C₄²	—	26	2	no	—
200	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
201	C₄²	C₂×D₅₂	1	1	yes	characteristic
202	C₄²	Q₈×D₁₃	1	1	yes	characteristic
203	C₄²	#6131	1	1	yes	characteristic
204	C₁₃	#8657	1	1	yes	characteristic, complemented, Sylow
205	C₂³	#88192	1	1	yes	characteristic
206	Q₈	—	26	4	no	—
207	Q₈	—	52	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	8	2	no	—
210	C₂×C₄	—	8	2	no	—
211	C₂×C₄	—	8	2	no	—
212	C₂×C₄	—	26	2	no	—
213	C₂×C₄	—	26	2	no	—
214	C₂×C₄	—	52	1	no	—
215	C₂×C₄	—	52	2	no	—
216	C₂×C₄	—	52	1	no	—
217	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
218	C₂×C₄	#88146	1	1	yes	characteristic
219	C₂×C₄	#88149	1	1	yes	characteristic
220	C₂×C₄	#88151	1	1	yes	characteristic
221	C₂×C₄	#88165	1	2	yes	—
222	C₂×C₄	#88172	1	2	yes	—
223	C₂×C₄	C₂×#6103	1	1	yes	characteristic
224	C₂×C₄	#88200	1	1	yes	characteristic
225	C₂×C₄	#88204	1	2	yes	—
226	C₂×C₄	#88205	1	2	yes	—
227	C₈	—	2	2	no	—
228	C₈	—	2	2	no	—
229	C₈	—	52	2	no	—
230	C₈	—	104	2	no	—
231	C₂²	#11718648	1	1	yes	characteristic
232	C₂²	#11718715	1	2	yes	—
233	C₂²	#11718820	1	1	yes	characteristic
234	C₂²	#11718838	1	2	yes	—
235	C₂²	#11718850	1	1	yes	characteristic
236	C₄	—	2	1	no	—
237	C₄	—	2	1	no	—
238	C₄	—	16	2	no	—
239	C₄	—	52	2	no	—
240	C₄	—	52	2	no	—
241	C₄	#11718542	1	2	yes	—
242	C₄	#11718547	1	2	yes	—
243	C₄	#11718663	1	1	yes	characteristic
244	C₄	#11718665	1	1	yes	characteristic
245	C₄	#11718724	1	2	yes	—
246	C₂	#13114401	1	2	yes	—
247	C₂	#13114415	1	2	yes	—
248	C₂	#13114848	1	1	yes	characteristic
249	C₂	#13114870	1	1	yes	characteristic
250	C₂	#13114896	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#88192
commutator	C₄²×C₁₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1834	C₂
socle, prime radical	C₂³×C₁₃	#121
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#1834	D₁₃
hypocenter	C₁₃	#8657
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1834

Complements

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

N	H ≅ G/N	type
15. #11718340	C₄	semidirect
204. C₁₃	#8657	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718340	2
#13114838	2
C₂×#11718049	2
#13112719	2
C₁₃×#1834	2
#8657	13