Subgroups — #15832091

Order 3328.

642 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	C₂×#11718587	C₂	1	2	yes	maximal
2	#13113621	C₂	1	8	yes	maximal, complemented
3	#13113599	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
6	C₁₃×#431	C₄	1	4	yes	—
7	C₁₃×#431	C₂²	1	4	yes	—
8	C₂×C₁₃×C₄⋊C₈	C₄	1	2	yes	—
9	C₂×C₁₃×C₂²⋊C₈	C₄	1	2	yes	—
10	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
11	C₂×C₂²⋊#1055	—	2	2	no	—
12	#11718587	—	2	2	no	—
13	#11718587	—	2	2	no	—
14	#11718587	C₂²	1	4	yes	—
15	#11718587	C₂²	1	4	yes	—
16	C₂×C₄⋊#1055	C₂²	1	4	yes	—
17	C₂×#88043	—	2	2	no	—
18	#11718050	C₂²	1	8	yes	complemented
19	#11718049	C₂²	1	8	yes	complemented
20	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₃	Q₈	1	1	yes	characteristic
23	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
24	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
26	C₂×C₄²×C₁₃	D₄	1	2	yes	—
27	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₃	Q₈	1	2	yes	—
29	C₂×C₄²×C₁₃	Q₈	1	1	yes	characteristic
30	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
31	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
32	C₂²×#1055	—	2	4	no	—
33	C₁₃×C₄⋊C₈	C₂×C₄	1	8	yes	—
34	C₁₃×C₂²⋊C₈	C₂×C₄	1	8	yes	—
35	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
36	C₄×C₈×C₁₃	C₂³	1	4	yes	—
37	C₂²⋊#1055	—	2	4	no	—
38	C₂²⋊#1055	—	2	4	no	—
39	C₄⋊#1055	—	2	4	no	—
40	C₄⋊#1055	C₂³	1	8	yes	—
41	#88043	—	2	4	no	—
42	#88043	—	2	4	no	—
43	#17818	—	13	1	no	maximal, Sylow
44	C₂⁴×C₁₃	C₄⋊C₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₃	—	2	4	no	—
46	C₂²×C₄×C₁₃	—	4	2	no	—
47	C₂²×C₄×C₁₃	—	4	2	no	—
48	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
50	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
52	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
53	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
55	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
58	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
59	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
60	C₂×C₈×C₁₃	—	4	4	no	—
61	C₂×C₈×C₁₃	C₂²×C₄	1	8	yes	—
62	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
63	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
64	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
65	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
66	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
67	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
68	C₄²×C₁₃	C₂×D₄	1	2	yes	—
69	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
70	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
71	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
72	C₂×#1055	—	2	8	no	—
73	C₂×#1055	—	4	8	no	—
74	C₂×#432	—	13	2	no	—
75	C₂×#431	D₁₃	1	1	yes	characteristic
76	#1573	—	13	8	no	—
77	#1568	—	13	4	no	—
78	C₂³×C₁₃	—	4	1	no	—
79	C₂³×C₁₃	—	4	1	no	—
80	C₂³×C₁₃	#108	1	4	yes	—
81	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
82	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₁₃	—	2	2	no	—
84	C₂×C₄×C₁₃	—	2	4	no	—
85	C₂×C₄×C₁₃	—	2	2	no	—
86	C₂×C₄×C₁₃	—	2	4	no	—
87	C₂×C₄×C₁₃	—	2	2	no	—
88	C₂×C₄×C₁₃	—	2	4	no	—
89	C₂×C₄×C₁₃	—	2	4	no	—
90	C₂×C₄×C₁₃	—	2	2	no	—
91	C₂×C₄×C₁₃	—	4	2	no	—
92	C₂×C₄×C₁₃	—	4	1	no	—
93	C₂×C₄×C₁₃	—	4	1	no	—
94	C₂×C₄×C₁₃	—	4	2	no	—
95	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
96	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
97	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
98	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
99	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
100	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
101	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
102	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
103	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
104	C₈×C₁₃	—	2	8	no	—
105	#1055	—	4	8	no	—
106	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
107	#432	—	13	4	no	—
108	#432	—	13	4	no	—
109	#432	—	26	2	no	—
110	#432	—	26	2	no	—
111	#431	Dic₁₃	1	4	yes	—
112	#431	C₂×D₁₃	1	4	yes	—
113	C₂×C₄⋊C₈	—	13	4	no	—
114	C₂×C₄⋊C₈	Dic₁₃	1	2	yes	—
115	C₂×C₂²⋊C₈	—	26	2	no	—
116	C₂×C₂²⋊C₈	Dic₁₃	1	2	yes	—
117	C₂×#97	—	26	2	no	—
118	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	—
119	#335	—	13	8	no	—
120	#334	—	13	8	no	—
121	C₂²×C₁₃	—	2	1	no	—
122	C₂²×C₁₃	—	2	2	no	—
123	C₂²×C₁₃	—	2	2	no	—
124	C₂²×C₁₃	—	2	1	no	—
125	C₂²×C₁₃	—	4	4	no	—
126	C₂²×C₁₃	C₂×#108	1	4	yes	—
127	C₂²×C₁₃	C₂×#108	1	2	yes	—
128	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
129	C₄×C₁₃	—	2	1	no	—
130	C₄×C₁₃	—	2	2	no	—
131	C₄×C₁₃	—	2	2	no	—
132	C₄×C₁₃	—	2	1	no	—
133	C₄×C₁₃	—	2	1	no	—
134	C₄×C₁₃	—	2	2	no	—
135	C₄×C₁₃	—	2	1	no	—
136	C₄×C₁₃	#568	1	2	yes	—
137	C₄×C₁₃	#575	1	2	yes	—
138	C₂³×C₄	Dic₂₆	1	1	yes	characteristic
139	C₂³×C₄	D₅₂	1	1	yes	characteristic
140	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
141	C₂²×C₈	—	26	4	no	—
142	C₂²×C₈	C₂×Dic₁₃	1	4	yes	—
143	C₂×C₄²	Dic₂₆	1	2	yes	—
144	C₂×C₄²	Dic₂₆	1	1	yes	characteristic
145	C₂×C₄²	D₅₂	1	2	yes	—
146	C₂×C₄²	D₅₂	1	1	yes	characteristic
147	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
148	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
149	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
150	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
151	C₄⋊C₈	—	13	8	no	—
152	C₄⋊C₈	—	26	4	no	—
153	C₄⋊C₈	C₂×Dic₁₃	1	8	yes	—
154	C₂²⋊C₈	—	26	4	no	—
155	C₂²⋊C₈	—	26	4	no	—
156	C₂²⋊C₈	C₂×Dic₁₃	1	8	yes	—
157	#97	—	26	4	no	—
158	#97	—	26	4	no	—
159	C₄×C₈	C₂×Dic₁₃	1	4	yes	—
160	C₄×C₈	C₂²×D₁₃	1	4	yes	—
161	C₂×C₁₃	—	2	2	no	—
162	C₂×C₁₃	—	2	4	no	—
163	C₂×C₁₃	#2905	1	1	yes	characteristic
164	C₂×C₁₃	#2911	1	1	yes	characteristic
165	C₂×C₁₃	C₂²×#108	1	1	yes	characteristic
166	C₂⁴	C₄⋊Dic₁₃	1	1	yes	characteristic
167	C₂²×C₄	—	2	4	no	—
168	C₂²×C₄	—	4	2	no	—
169	C₂²×C₄	—	4	2	no	—
170	C₂²×C₄	C₄⋊Dic₁₃	1	2	yes	—
171	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
172	C₂²×C₄	C₄⋊Dic₁₃	1	2	yes	—
173	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
174	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
175	C₂²×C₄	C₄⋊Dic₁₃	1	2	yes	—
176	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
177	C₂²×C₄	C₂×Dic₂₆	1	2	yes	—
178	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
179	C₂²×C₄	C₂×D₅₂	1	2	yes	—
180	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
181	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
182	C₂×C₈	—	4	4	no	—
183	C₂×C₈	—	26	8	no	—
184	C₂×C₈	—	52	8	no	—
185	C₂×C₈	C₂²×Dic₁₃	1	8	yes	—
186	C₄²	C₄⋊Dic₁₃	1	2	yes	—
187	C₄²	C₄⋊Dic₁₃	1	2	yes	—
188	C₄²	C₄⋊Dic₁₃	1	2	yes	—
189	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
190	C₄²	C₂×Dic₂₆	1	2	yes	—
191	C₄²	C₂×D₅₂	1	1	yes	characteristic
192	C₄²	C₂×D₅₂	1	2	yes	—
193	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
194	C₄²	C₂²×Dic₁₃	1	2	yes	—
195	C₄²	C₂³×D₁₃	1	1	yes	characteristic
196	C₁₃	#17818	1	1	yes	characteristic, complemented, Sylow
197	C₂³	—	4	1	no	—
198	C₂³	—	4	1	no	—
199	C₂³	#88059	1	4	yes	—
200	C₂³	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
201	C₂³	C₂×C₄⋊Dic₁₃	1	2	yes	—
202	C₂×C₄	—	2	4	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	4	no	—
206	C₂×C₄	—	2	4	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	4	no	—
210	C₂×C₄	—	4	2	no	—
211	C₂×C₄	—	4	1	no	—
212	C₂×C₄	—	4	1	no	—
213	C₂×C₄	—	4	2	no	—
214	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
215	C₂×C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
216	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
217	C₂×C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
218	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
219	C₂×C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
220	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
221	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
222	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
223	C₈	—	2	8	no	—
224	C₈	—	52	8	no	—
225	C₂²	—	2	1	no	—
226	C₂²	—	2	2	no	—
227	C₂²	—	2	2	no	—
228	C₂²	—	2	1	no	—
229	C₂²	—	4	4	no	—
230	C₂²	C₂×#88059	1	2	yes	—
231	C₂²	C₂×#88059	1	4	yes	—
232	C₂²	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic
233	C₄	—	2	1	no	—
234	C₄	—	2	2	no	—
235	C₄	—	2	2	no	—
236	C₄	—	2	1	no	—
237	C₄	—	2	1	no	—
238	C₄	—	2	2	no	—
239	C₄	—	2	1	no	—
240	C₄	#11719453	1	2	yes	—
241	C₄	#11719524	1	2	yes	—
242	C₂	—	2	2	no	—
243	C₂	—	2	4	no	—
244	C₂	#13123400	1	1	yes	characteristic
245	C₂	#13123426	1	1	yes	characteristic
246	C₂	C₂²×#88059	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₅₂
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₂×C₁₃×#431	C₂
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₁₃	C₄⋊C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₂×#431	D₁₃
hypocenter	C₁₃	#17818
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
2. #13113621	C₂	semidirect
3. #13113599	C₂	semidirect
18. #11718050	C₂²	semidirect
19. #11718049	C₂²	semidirect
196. C₁₃	#17818	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718587	2
#13113621	2
#13113599	2
C₂×C₁₃×#431	2
#17818	13