Subgroups — #15772894

Order 3328.

358 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	#13116635	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11718050	C₂	1	1	yes	maximal, characteristic, complemented
3	#13112797	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3169	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#532	—	2	1	no	—
6	C₁₃×#500	C₄	1	1	yes	characteristic
7	C₁₃×#493	C₄	1	1	yes	characteristic
8	C₁₃×#486	—	2	1	no	—
9	C₁₃×#466	—	2	1	no	—
10	C₁₃×#466	C₄	1	2	yes	—
11	C₄×C₁₃×D₈	—	2	1	no	—
12	C₄×C₁₃×D₈	C₂²	1	2	yes	—
13	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊#1055	—	2	1	no	—
15	C₂²⋊#6090	—	2	1	no	—
16	C₄⋊#6090	—	2	1	no	—
17	C₄×#6090	C₂²	1	2	yes	—
18	#11718050	—	2	1	no	—
19	#11718050	C₂²	1	2	yes	—
20	C₂×C₁₃×#41	—	4	1	no	—
21	C₂×C₁₃×D₈	—	2	1	no	—
22	C₂×C₁₃×D₈	C₂×C₄	1	2	yes	—
23	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
25	C₁₃×C₄⋊Q₈	—	2	1	no	—
26	C₁₃×#127	—	2	1	no	—
27	C₁₃×#124	—	4	1	no	—
28	C₁₃×#121	—	2	2	no	—
29	C₁₃×#121	—	4	1	no	—
30	C₄×D₄×C₁₃	—	2	2	no	—
31	C₄×D₄×C₁₃	—	4	1	no	—
32	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
33	C₂²×#1055	—	4	1	no	—
34	C₁₃×#107	—	2	1	no	—
35	C₁₃×#107	C₂×C₄	1	2	yes	—
36	C₁₃×#102	—	2	2	no	—
37	C₁₃×#102	—	2	2	no	—
38	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
39	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
40	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
41	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
42	C₂×#6090	—	2	2	no	—
43	C₄⋊#1055	—	2	2	no	—
44	C₄⋊#1055	—	4	1	no	—
45	#11645	—	13	1	no	maximal, Sylow
46	C₁₃×#41	—	8	2	no	—
47	C₁₃×#41	—	8	2	no	—
48	C₂×Q₈×C₁₃	—	4	1	no	—
49	C₂×D₄×C₁₃	—	2	2	no	—
50	C₂×D₄×C₁₃	—	4	2	no	—
51	C₂×D₄×C₁₃	—	4	1	no	—
52	C₂×D₄×C₁₃	—	4	1	no	—
53	C₂²×C₄×C₁₃	—	4	2	no	—
54	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
56	C₂²×C₄×C₁₃	SD₁₆	1	1	yes	characteristic
57	C₁₃×D₈	—	2	4	no	—
58	C₁₃×D₈	—	4	2	no	—
59	C₂×C₈×C₁₃	—	2	2	no	—
60	C₂×C₈×C₁₃	—	4	1	no	—
61	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
62	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
63	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
64	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
65	C₁₃×C₄⋊C₄	—	2	2	no	—
66	C₁₃×C₄⋊C₄	—	4	1	no	—
67	C₁₃×C₂²⋊C₄	—	4	2	no	—
68	C₁₃×C₂²⋊C₄	—	4	2	no	—
69	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
70	C₄²×C₁₃	D₈	1	1	yes	characteristic
71	C₄²×C₁₃	SD₁₆	1	1	yes	characteristic
72	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
73	C₂×#1055	—	4	2	no	—
74	C₂×#1055	—	8	2	no	—
75	#6090	—	4	2	no	—
76	#3169	D₁₃	1	1	yes	characteristic
77	#2162	—	13	1	no	—
78	C₂×#335	—	13	1	no	—
79	#1331	—	13	4	no	—
80	C₂³×C₁₃	—	4	2	no	—
81	C₂³×C₁₃	#102	1	1	yes	characteristic
82	Q₈×C₁₃	—	8	2	no	—
83	D₄×C₁₃	—	4	2	no	—
84	D₄×C₁₃	—	4	2	no	—
85	D₄×C₁₃	—	8	2	no	—
86	D₄×C₁₃	—	8	4	no	—
87	D₄×C₁₃	—	8	2	no	—
88	C₂×C₄×C₁₃	—	2	1	no	—
89	C₂×C₄×C₁₃	—	2	1	no	—
90	C₂×C₄×C₁₃	—	4	1	no	—
91	C₂×C₄×C₁₃	—	4	2	no	—
92	C₂×C₄×C₁₃	—	8	2	no	—
93	C₂×C₄×C₁₃	—	8	2	no	—
94	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
95	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
96	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
97	C₂×C₄×C₁₃	D₁₆	1	2	yes	—
98	C₂×C₄×C₁₃	SD₃₂	1	2	yes	—
99	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
101	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
102	C₈×C₁₃	—	2	1	no	—
103	C₈×C₁₃	—	2	1	no	—
104	C₈×C₁₃	—	2	1	no	—
105	C₈×C₁₃	#131	1	2	yes	—
106	#1055	—	8	2	no	—
107	#532	—	2	1	no	—
108	#500	Dic₁₃	1	1	yes	characteristic
109	#493	Dic₁₃	1	1	yes	characteristic
110	#486	—	2	1	no	—
111	#466	—	2	1	no	—
112	#466	Dic₁₃	1	2	yes	—
113	C₄×D₈	—	2	1	no	—
114	C₄×D₈	C₂×D₁₃	1	2	yes	—
115	C₂×C₄⋊C₈	—	26	1	no	—
116	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
117	C₄⋊C₁₆	—	26	1	no	—
118	C₂²⋊C₁₆	—	26	1	no	—
119	C₄×C₁₆	—	13	2	no	—
120	#335	—	13	2	no	—
121	#335	—	26	1	no	—
122	C₂²×C₁₃	—	2	1	no	—
123	C₂²×C₁₃	—	2	1	no	—
124	C₂²×C₁₃	—	8	2	no	—
125	C₂²×C₁₃	—	8	2	no	—
126	C₂²×C₁₃	—	8	2	no	—
127	C₂²×C₁₃	#357	1	2	yes	—
128	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
129	C₄×C₁₃	—	2	1	no	—
130	C₄×C₁₃	—	2	1	no	—
131	C₄×C₁₃	—	2	1	no	—
132	C₄×C₁₃	—	8	2	no	—
133	C₄×C₁₃	#357	1	2	yes	—
134	C₄×C₁₃	#408	1	1	yes	characteristic
135	C₄×C₁₃	#421	1	1	yes	characteristic
136	C₄×C₁₃	C₂×D₁₆	1	1	yes	characteristic
137	C₄×C₁₃	C₂×SD₃₂	1	1	yes	characteristic
138	C₂×#41	—	4	1	no	—
139	C₂×D₈	—	2	1	no	—
140	C₂×D₈	C₂×Dic₁₃	1	2	yes	—
141	C₂²×C₈	—	52	1	no	—
142	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
143	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
144	C₄⋊Q₈	—	2	1	no	—
145	#127	—	2	1	no	—
146	#124	—	4	1	no	—
147	#121	—	2	2	no	—
148	#121	—	4	1	no	—
149	C₄×D₄	—	2	2	no	—
150	C₄×D₄	—	4	1	no	—
151	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
152	C₂×C₁₆	—	26	2	no	—
153	#107	—	2	1	no	—
154	#107	C₂×Dic₁₃	1	2	yes	—
155	C₄⋊C₈	—	26	2	no	—
156	C₄⋊C₈	—	52	1	no	—
157	#102	—	2	2	no	—
158	#102	—	2	2	no	—
159	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
160	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
161	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
162	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
163	C₂×C₁₃	—	2	2	no	—
164	C₂×C₁₃	—	16	2	no	—
165	C₂×C₁₃	#1480	1	1	yes	characteristic
166	C₂×C₁₃	C₂×#357	1	1	yes	characteristic
167	C₂×C₁₃	#2143	1	1	yes	characteristic
168	#41	—	8	2	no	—
169	#41	—	8	2	no	—
170	C₂×Q₈	—	4	1	no	—
171	C₂×D₄	—	2	2	no	—
172	C₂×D₄	—	4	2	no	—
173	C₂×D₄	—	4	1	no	—
174	C₂×D₄	—	4	1	no	—
175	C₂²×C₄	—	4	2	no	—
176	C₂²×C₄	#6104	1	1	yes	characteristic
177	C₂²×C₄	#6105	1	1	yes	characteristic
178	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
179	D₈	—	2	4	no	—
180	D₈	—	4	2	no	—
181	C₂×C₈	—	2	2	no	—
182	C₂×C₈	—	4	1	no	—
183	C₂×C₈	—	52	2	no	—
184	C₂×C₈	—	104	2	no	—
185	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
186	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
187	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
188	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
189	C₄⋊C₄	—	2	2	no	—
190	C₄⋊C₄	—	4	1	no	—
191	C₂²⋊C₄	—	4	2	no	—
192	C₂²⋊C₄	—	4	2	no	—
193	C₄²	#6104	1	1	yes	characteristic
194	C₄²	#6105	1	1	yes	characteristic
195	C₄²	C₂²⋊Dic₁₃	1	1	yes	characteristic
196	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
197	C₁₆	—	52	2	no	—
198	C₁₃	#11645	1	1	yes	characteristic, complemented, Sylow
199	C₂³	—	4	2	no	—
200	C₂³	#88072	1	1	yes	characteristic
201	Q₈	—	8	2	no	—
202	D₄	—	4	2	no	—
203	D₄	—	4	2	no	—
204	D₄	—	8	2	no	—
205	D₄	—	8	4	no	—
206	D₄	—	8	2	no	—
207	C₂×C₄	—	2	1	no	—
208	C₂×C₄	—	2	1	no	—
209	C₂×C₄	—	4	1	no	—
210	C₂×C₄	—	4	2	no	—
211	C₂×C₄	—	8	2	no	—
212	C₂×C₄	—	8	2	no	—
213	C₂×C₄	#88066	1	2	yes	—
214	C₂×C₄	#88067	1	2	yes	—
215	C₂×C₄	#88072	1	1	yes	characteristic
216	C₂×C₄	#88072	1	1	yes	characteristic
217	C₂×C₄	#88072	1	1	yes	characteristic
218	C₂×C₄	C₂×#6104	1	1	yes	characteristic
219	C₂×C₄	C₂×#6105	1	1	yes	characteristic
220	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
221	C₈	—	2	1	no	—
222	C₈	—	2	1	no	—
223	C₈	—	2	1	no	—
224	C₈	—	104	2	no	—
225	C₈	#88202	1	2	yes	—
226	C₂²	—	2	1	no	—
227	C₂²	—	2	1	no	—
228	C₂²	—	8	2	no	—
229	C₂²	—	8	2	no	—
230	C₂²	—	8	2	no	—
231	C₂²	#11718154	1	2	yes	—
232	C₂²	C₂×#88072	1	1	yes	characteristic
233	C₄	—	2	1	no	—
234	C₄	—	2	1	no	—
235	C₄	—	2	1	no	—
236	C₄	—	8	2	no	—
237	C₄	#11718154	1	2	yes	—
238	C₄	C₂×#88066	1	1	yes	characteristic
239	C₄	C₂×#88067	1	1	yes	characteristic
240	C₄	#11718895	1	1	yes	characteristic
241	C₄	#11718897	1	1	yes	characteristic
242	C₂	—	2	2	no	—
243	C₂	—	16	2	no	—
244	C₂	#13113235	1	1	yes	characteristic
245	C₂	C₂×#11718154	1	1	yes	characteristic
246	C₂	#13116564	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#6104
commutator	C₂×C₈×C₁₃	C₂²×C₄
Frattini	C₄×C₈	C₂²×D₁₃
Fitting, prime radical	C₁₃×#3169	C₂
socle	C₂²×C₁₃	C₂×#102
cosocle	C₄×C₈×C₁₃	C₂³
hypercenter	#3169	D₁₃
hypocenter	C₁₃	#11645
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #3169

Complements

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

N	H ≅ G/N	type
1. #13116635	C₂	semidirect
2. C₂×#11718050	C₂	semidirect
3. #13112797	C₂	semidirect
198. C₁₃	#11645	semidirect

Maximal subgroups

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

subgroup	index
#13116635	2
C₂×#11718050	2
#13112797	2
C₁₃×#3169	2
#11645	13