Subgroups — C₂×#13114976 #15863148

Order 3328.

830 conjugacy classes of subgroups.

The subgroup lattice has 238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718585	C₂	1	1	yes	maximal, characteristic
2	C₂²×#88043	C₂	1	1	yes	maximal, characteristic
3	#13114976	C₂	1	8	yes	maximal, direct product factor
4	C₂×#11718150	C₂	1	4	yes	maximal
5	C₂×C₁₃×#423	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
7	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
8	C₂²×#6099	C₂²	1	2	yes	—
9	C₂³×#1055	C₂²	1	2	yes	—
10	C₁₃×#423	—	2	2	no	—
11	C₁₃×#423	C₂²	1	4	yes	—
12	C₂×C₁₃×C₄⋊C₈	—	2	2	no	—
13	#11718585	—	2	2	no	—
14	#11718585	C₂²	1	4	yes	—
15	C₂×C₄⋊#1055	—	2	2	no	—
16	C₂×#88043	C₄	1	4	yes	—
17	C₂×#88043	C₄	1	4	yes	—
18	C₂×#88043	C₂²	1	4	yes	—
19	#11718150	C₂²	1	16	yes	—
20	C₂³×C₄×C₁₃	Q₈	1	2	yes	—
21	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
22	C₂×C₁₃×M₁₆	—	2	2	no	—
23	C₂×C₁₃×M₁₆	—	2	8	no	—
24	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
25	C₂²×C₈×C₁₃	—	2	2	no	—
26	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
27	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
28	C₂×C₄²×C₁₃	D₄	1	2	yes	—
29	C₂×C₄²×C₁₃	D₄	1	2	yes	—
30	C₂×C₄²×C₁₃	Q₈	1	2	yes	—
31	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
32	C₂×#6099	—	2	2	no	—
33	C₂×#6099	—	2	8	no	—
34	C₂×#6099	C₂³	1	4	yes	—
35	C₂²×#1055	—	2	4	no	—
36	C₂²×#1055	—	2	4	no	—
37	C₂²×#1055	—	2	2	no	—
38	C₂²×#1055	C₂×C₄	1	4	yes	—
39	C₂²×#1055	C₂×C₄	1	4	yes	—
40	C₂²×#1055	C₂³	1	4	yes	—
41	C₁₃×C₄⋊C₈	—	2	8	no	—
42	C₄⋊#1055	—	2	8	no	—
43	#88043	C₂×C₄	1	16	yes	—
44	C₂×#1838	—	13	1	no	maximal, Sylow
45	C₂⁴×C₁₃	C₂×Q₈	1	1	yes	characteristic
46	C₂²×C₄×C₁₃	—	4	4	no	—
47	C₂²×C₄×C₁₃	C₄⋊C₄	1	4	yes	—
48	C₂²×C₄×C₁₃	C₄⋊C₄	1	4	yes	—
49	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
54	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
55	C₂²×C₄×C₁₃	#41	1	4	yes	—
56	C₂²×C₄×C₁₃	#41	1	4	yes	—
57	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
58	C₁₃×M₁₆	—	2	8	no	—
59	C₁₃×M₁₆	—	4	4	no	—
60	C₂×C₈×C₁₃	—	2	4	no	—
61	C₂×C₈×C₁₃	—	4	4	no	—
62	C₄²×C₁₃	C₄⋊C₄	1	4	yes	—
63	C₄²×C₁₃	C₄⋊C₄	1	4	yes	—
64	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
65	C₄²×C₁₃	C₂×D₄	1	4	yes	—
66	#6099	—	2	8	no	—
67	#6099	—	4	4	no	—
68	C₂×#1055	—	2	8	no	—
69	C₂×#1055	—	2	8	no	—
70	C₂×#1055	—	2	4	no	—
71	C₂×#1055	—	2	4	no	—
72	C₂×#1055	—	2	4	no	—
73	C₂×#1055	—	4	4	no	—
74	C₂×#1055	C₂²×C₄	1	8	yes	—
75	C₂×#423	—	13	1	no	—
76	C₂×#423	D₁₃	1	1	yes	characteristic
77	C₂²×#97	—	13	1	no	—
78	#1838	—	13	8	no	—
79	C₂×#341	—	13	4	no	—
80	C₂³×C₁₃	—	2	4	no	—
81	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
82	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
83	C₂³×C₁₃	#125	1	4	yes	—
84	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
85	C₂×C₄×C₁₃	—	2	8	no	—
86	C₂×C₄×C₁₃	—	4	4	no	—
87	C₂×C₄×C₁₃	—	4	4	no	—
88	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	8	yes	—
89	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
90	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
91	C₂×C₄×C₁₃	#117	1	4	yes	—
92	C₂×C₄×C₁₃	#117	1	4	yes	—
93	C₂×C₄×C₁₃	#124	1	2	yes	—
94	C₂×C₄×C₁₃	#124	1	2	yes	—
95	C₂×C₄×C₁₃	#124	1	2	yes	—
96	C₂×C₄×C₁₃	#124	1	2	yes	—
97	C₂×C₄×C₁₃	#125	1	4	yes	—
98	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
99	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
100	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
101	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
102	C₈×C₁₃	—	4	4	no	—
103	#1055	—	2	8	no	—
104	#1055	—	4	4	no	—
105	C₂²×M₁₆	—	13	2	no	—
106	C₂²×M₁₆	C₂×D₁₃	1	2	yes	—
107	C₂³×C₈	—	13	2	no	—
108	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
109	#423	—	2	2	no	—
110	#423	—	13	4	no	—
111	#423	—	26	2	no	—
112	#423	C₂×D₁₃	1	4	yes	—
113	C₂×C₄⋊C₈	—	2	2	no	—
114	C₂×C₄⋊C₈	—	26	2	no	—
115	C₂×#97	—	13	4	no	—
116	C₂×#97	—	13	4	no	—
117	C₂×#97	—	13	4	no	—
118	#341	—	13	16	no	—
119	C₂²×C₁₃	—	2	8	no	—
120	C₂²×C₁₃	—	2	2	no	—
121	C₂²×C₁₃	—	2	2	no	—
122	C₂²×C₁₃	#382	1	2	yes	—
123	C₂²×C₁₃	#382	1	2	yes	—
124	C₂²×C₁₃	#430	1	4	yes	—
125	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
126	C₂²×C₁₃	C₂×#125	1	2	yes	—
127	C₄×C₁₃	—	2	8	no	—
128	C₄×C₁₃	#382	1	2	yes	—
129	C₄×C₁₃	#382	1	2	yes	—
130	C₄×C₁₃	C₂×#117	1	2	yes	—
131	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
132	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
133	C₂³×C₄	Dic₂₆	1	2	yes	—
134	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
135	C₂×M₁₆	—	2	2	no	—
136	C₂×M₁₆	—	2	8	no	—
137	C₂×M₁₆	—	13	4	no	—
138	C₂×M₁₆	—	26	2	no	—
139	C₂×M₁₆	—	26	8	no	—
140	C₂×M₁₆	C₂²×D₁₃	1	4	yes	—
141	C₂²×C₈	—	2	2	no	—
142	C₂²×C₈	—	13	4	no	—
143	C₂²×C₈	—	13	4	no	—
144	C₂²×C₈	—	13	4	no	—
145	C₂²×C₈	—	26	4	no	—
146	C₂²×C₈	—	26	4	no	—
147	C₂²×C₈	—	26	2	no	—
148	C₂×C₄²	Dic₂₆	1	2	yes	—
149	C₂×C₄²	C₄×D₁₃	1	2	yes	—
150	C₂×C₄²	C₄×D₁₃	1	2	yes	—
151	C₂×C₄²	C₂²⋊D₁₃	1	2	yes	—
152	C₂×C₄²	C₂²⋊D₁₃	1	2	yes	—
153	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
154	C₄⋊C₈	—	2	8	no	—
155	C₄⋊C₈	—	26	8	no	—
156	#97	—	13	16	no	—
157	C₂×C₁₃	—	2	2	no	—
158	C₂×C₁₃	—	2	2	no	—
159	C₂×C₁₃	#1838	1	4	yes	complemented
160	C₂×C₁₃	C₂×#382	1	1	yes	characteristic
161	C₂×C₁₃	C₂×#430	1	2	yes	—
162	C₂⁴	C₂×Dic₂₆	1	1	yes	characteristic
163	C₂²×C₄	—	4	4	no	—
164	C₂²×C₄	#6101	1	4	yes	—
165	C₂²×C₄	#6101	1	4	yes	—
166	C₂²×C₄	C₂×Dic₂₆	1	4	yes	—
167	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
168	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
169	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
170	C₂²×C₄	#6129	1	4	yes	—
171	C₂²×C₄	#6131	1	4	yes	—
172	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
173	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
174	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
175	M₁₆	—	2	8	no	—
176	M₁₆	—	4	4	no	—
177	M₁₆	—	26	8	no	—
178	M₁₆	—	52	4	no	—
179	C₂×C₈	—	2	4	no	—
180	C₂×C₈	—	4	4	no	—
181	C₂×C₈	—	13	8	no	—
182	C₂×C₈	—	26	8	no	—
183	C₂×C₈	—	26	8	no	—
184	C₂×C₈	—	26	4	no	—
185	C₂×C₈	—	26	4	no	—
186	C₂×C₈	—	26	4	no	—
187	C₂×C₈	—	52	4	no	—
188	C₄²	#6101	1	4	yes	—
189	C₄²	#6101	1	4	yes	—
190	C₄²	C₂×C₄×D₁₃	1	4	yes	—
191	C₄²	C₂×C₂²⋊D₁₃	1	4	yes	—
192	C₁₃	C₂×#1838	1	1	yes	characteristic, complemented, Sylow
193	C₂³	—	2	4	no	—
194	C₂³	#88144	1	4	yes	—
195	C₂³	C₂×#6101	1	1	yes	characteristic
196	C₂³	C₂×#6101	1	1	yes	characteristic
197	C₂³	C₂²×Dic₂₆	1	1	yes	characteristic
198	C₂×C₄	—	2	8	no	—
199	C₂×C₄	—	4	4	no	—
200	C₂×C₄	—	4	4	no	—
201	C₂×C₄	#88144	1	4	yes	—
202	C₂×C₄	#88146	1	4	yes	—
203	C₂×C₄	#88146	1	4	yes	—
204	C₂×C₄	C₂×#6101	1	8	yes	—
205	C₂×C₄	C₂×#6101	1	1	yes	characteristic
206	C₂×C₄	C₂×#6101	1	1	yes	characteristic
207	C₂×C₄	#88190	1	2	yes	—
208	C₂×C₄	#88190	1	2	yes	—
209	C₂×C₄	#88201	1	2	yes	—
210	C₂×C₄	#88201	1	2	yes	—
211	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
212	C₂×C₄	C₂×#6129	1	2	yes	—
213	C₂×C₄	C₂×#6131	1	2	yes	—
214	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
215	C₈	—	4	4	no	—
216	C₈	—	26	8	no	—
217	C₈	—	52	4	no	—
218	C₂²	—	2	8	no	—
219	C₂²	—	2	2	no	—
220	C₂²	—	2	2	no	—
221	C₂²	#11718638	1	2	yes	—
222	C₂²	#11718638	1	2	yes	—
223	C₂²	#11718785	1	4	yes	—
224	C₂²	C₂×#88144	1	2	yes	—
225	C₂²	C₂²×#6101	1	1	yes	characteristic
226	C₄	—	2	8	no	—
227	C₄	#11718638	1	2	yes	—
228	C₄	#11718638	1	2	yes	—
229	C₄	C₂×#88146	1	2	yes	—
230	C₄	C₂×#88190	1	1	yes	characteristic
231	C₄	C₂×#88201	1	1	yes	characteristic
232	C₂	—	2	2	no	—
233	C₂	—	2	2	no	—
234	C₂	#13114976	1	4	yes	direct product factor
235	C₂	C₂×#11718638	1	1	yes	characteristic
236	C₂	C₂×#11718785	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂×C₁₃×#423	C₂
socle	C₂³×C₁₃	C₂×C₄⋊C₄
prime radical	C₂⁴×C₁₃	C₂×Q₈
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂×#423	D₁₃
hypocenter	C₁₃	C₂×#1838
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×#423

Complements

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

N	H ≅ G/N	type
3. #13114976	C₂	direct (N × H)
159. C₂×C₁₃	#1838	semidirect
192. C₁₃	C₂×#1838	semidirect
234. C₂	#13114976	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#11718585	2
C₂²×#88043	2
#13114976	2
C₂×#11718150	2
C₂×C₁₃×#423	2
C₂×#1838	13

Subgroups — C2×#13114976 #15863148

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13114976 #15863148