Subgroups — C₂×#13117036 #16017708

Order 3328.

630 conjugacy classes of subgroups.

The subgroup lattice has 264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88058	C₂	1	1	yes	maximal, characteristic
2	#13117036	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11718081	C₂	1	2	yes	maximal, complemented
4	C₂×#11718156	C₂	1	2	yes	maximal, complemented
5	C₂×C₂²⋊#6090	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
8	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
10	C₂²×C₄⋊Dic₁₃	—	2	1	no	—
11	C₁₃×#467	—	2	2	no	—
12	C₁₃×#467	C₂²	1	4	yes	—
13	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#103	—	2	1	no	—
15	C₂×#88058	—	2	1	no	—
16	C₂×#88058	—	2	2	no	—
17	C₂×#88058	C₂²	1	4	yes	—
18	C₂×#88058	C₂²	1	2	yes	—
19	C₂²×#6090	C₂²	1	2	yes	—
20	#11718156	C₂²	1	8	yes	complemented
21	C₂²⋊#6090	C₂²	1	4	yes	—
22	#11718081	C₂²	1	8	yes	complemented
23	C₂²×Q₈×C₁₃	—	2	1	no	—
24	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
25	C₂³×Dic₁₃	—	4	1	no	—
26	C₂×C₁₃×Q₁₆	—	2	1	no	—
27	C₂×C₁₃×Q₁₆	—	2	4	no	—
28	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
29	C₂²×C₈×C₁₃	—	2	4	no	—
30	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
31	C₂²×C₈×C₁₃	D₄	1	2	yes	—
32	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
33	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
34	C₁₃×C₂²⋊Q₈	—	2	4	no	—
35	C₁₃×C₂²⋊Q₈	—	4	2	no	—
36	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
37	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
38	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
39	C₂×C₄⋊Dic₁₃	—	2	4	no	—
40	C₂×C₄⋊Dic₁₃	—	2	2	no	—
41	C₂×C₄⋊Dic₁₃	—	4	1	no	—
42	C₂×C₄⋊Dic₁₃	—	4	2	no	—
43	C₁₃×#107	—	2	1	no	—
44	C₁₃×#107	C₂³	1	2	yes	—
45	C₁₃×#103	—	2	4	no	—
46	#88058	—	2	4	no	—
47	#88058	—	2	2	no	—
48	#88058	C₂³	1	4	yes	—
49	C₂×#6090	—	2	4	no	—
50	C₂×#6090	C₂³	1	4	yes	—
51	C₂×#2236	—	13	1	no	maximal, Sylow
52	C₂⁴×C₁₃	D₈	1	1	yes	characteristic
53	C₂×Q₈×C₁₃	—	2	2	no	—
54	C₂×Q₈×C₁₃	—	4	1	no	—
55	C₂×Q₈×C₁₃	—	4	2	no	—
56	C₂×Q₈×C₁₃	—	4	2	no	—
57	C₂²×C₄×C₁₃	—	2	2	no	—
58	C₂²×C₄×C₁₃	—	2	2	no	—
59	C₂²×C₄×C₁₃	—	4	1	no	—
60	C₂²×C₄×C₁₃	—	4	1	no	—
61	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
62	C₂²×C₄×C₁₃	D₈	1	2	yes	—
63	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
64	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
65	C₂²×Dic₁₃	—	4	4	no	—
66	C₂²×Dic₁₃	—	4	2	no	—
67	C₂²×Dic₁₃	—	8	4	no	—
68	C₁₃×Q₁₆	—	2	4	no	—
69	C₁₃×Q₁₆	—	4	2	no	—
70	C₂×C₈×C₁₃	—	2	2	no	—
71	C₂×C₈×C₁₃	—	2	4	no	—
72	C₂×C₈×C₁₃	—	2	4	no	—
73	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
74	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
75	C₂×C₈×C₁₃	#41	1	4	yes	—
76	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
77	C₁₃×C₄⋊C₄	—	2	2	no	—
78	C₁₃×C₄⋊C₄	—	4	1	no	—
79	C₁₃×C₄⋊C₄	—	4	4	no	—
80	C₁₃×C₂²⋊C₄	—	4	4	no	—
81	C₄⋊Dic₁₃	—	2	4	no	—
82	C₄⋊Dic₁₃	—	4	4	no	—
83	C₄⋊Dic₁₃	—	4	2	no	—
84	#6090	—	2	4	no	—
85	C₂×#467	D₁₃	1	1	yes	characteristic
86	C₂²×#107	—	13	1	no	—
87	#2236	—	13	8	no	—
88	C₂×#366	—	13	2	no	—
89	C₂×#358	—	13	2	no	—
90	C₂×C₂²⋊C₁₆	—	13	1	no	—
91	C₂³×C₁₃	—	2	2	no	—
92	C₂³×C₁₃	—	2	2	no	—
93	C₂³×C₁₃	Q₃₂	1	4	yes	—
94	C₂³×C₁₃	C₂×D₈	1	2	yes	—
95	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
96	Q₈×C₁₃	—	4	2	no	—
97	Q₈×C₁₃	—	4	2	no	—
98	Q₈×C₁₃	—	8	2	no	—
99	C₂×C₄×C₁₃	—	2	2	no	—
100	C₂×C₄×C₁₃	—	2	2	no	—
101	C₂×C₄×C₁₃	—	2	2	no	—
102	C₂×C₄×C₁₃	—	2	4	no	—
103	C₂×C₄×C₁₃	—	4	2	no	—
104	C₂×C₄×C₁₃	—	4	2	no	—
105	C₂×C₄×C₁₃	—	8	2	no	—
106	C₂×C₄×C₁₃	—	8	2	no	—
107	C₂×C₄×C₁₃	#123	1	2	yes	—
108	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
109	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
110	C₂×C₄×C₁₃	#137	1	2	yes	—
111	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
112	C₂×Dic₁₃	—	4	4	no	—
113	C₂×Dic₁₃	—	8	8	no	—
114	C₂×Dic₁₃	—	8	4	no	—
115	C₈×C₁₃	—	2	2	no	—
116	C₈×C₁₃	#123	1	2	yes	—
117	C₈×C₁₃	C₂×#41	1	2	yes	—
118	C₂²×Q₁₆	C₂×D₁₃	1	1	yes	characteristic
119	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
120	C₂×C₂²⋊Q₈	—	2	1	no	—
121	C₂²×C₄⋊C₄	—	26	1	no	—
122	C₂²×C₁₆	—	13	2	no	—
123	#467	—	2	2	no	—
124	#467	C₂×D₁₃	1	4	yes	—
125	C₂×#107	—	13	2	no	—
126	C₂×#107	—	13	4	no	—
127	C₂×#107	—	26	1	no	—
128	C₂×#107	—	26	2	no	—
129	C₂×#107	C₂×D₁₃	1	1	yes	characteristic
130	C₂×#103	—	2	1	no	—
131	#366	—	13	8	no	—
132	#358	—	13	8	no	—
133	C₂²⋊C₁₆	—	13	4	no	—
134	C₂²×C₁₃	—	2	2	no	—
135	C₂²×C₁₃	—	2	2	no	—
136	C₂²×C₁₃	—	2	8	no	—
137	C₂²×C₁₃	#480	1	2	yes	—
138	C₂²×C₁₃	C₂×Q₃₂	1	4	yes	—
139	C₂²×C₁₃	C₂×Q₃₂	1	2	yes	—
140	C₂²×C₁₃	#509	1	2	yes	—
141	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
142	C₄×C₁₃	—	2	2	no	—
143	C₄×C₁₃	—	8	2	no	—
144	C₄×C₁₃	—	8	2	no	—
145	C₄×C₁₃	#480	1	2	yes	—
146	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
147	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
148	Dic₁₃	—	8	4	no	—
149	C₂²×Q₈	—	2	1	no	—
150	C₂³×C₄	—	52	1	no	—
151	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
152	C₂×Q₁₆	—	2	4	no	—
153	C₂×Q₁₆	—	2	1	no	—
154	C₂×Q₁₆	C₂²×D₁₃	1	2	yes	—
155	C₂²×C₈	—	2	4	no	—
156	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
157	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
158	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
159	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
160	C₂²⋊Q₈	—	2	4	no	—
161	C₂²⋊Q₈	—	4	2	no	—
162	C₂×C₄⋊C₄	—	2	1	no	—
163	C₂×C₄⋊C₄	—	4	1	no	—
164	C₂×C₄⋊C₄	—	26	4	no	—
165	C₂×C₄⋊C₄	—	26	2	no	—
166	C₂×C₄⋊C₄	—	52	2	no	—
167	C₂×C₄⋊C₄	—	52	1	no	—
168	C₂×C₂²⋊C₄	—	4	1	no	—
169	C₂×C₁₆	—	13	4	no	—
170	C₂×C₁₆	—	26	4	no	—
171	#107	—	2	1	no	—
172	#107	—	13	4	no	—
173	#107	—	26	4	no	—
174	#107	—	26	2	no	—
175	#107	C₂²×D₁₃	1	2	yes	—
176	#103	—	2	4	no	—
177	C₂×C₁₃	—	2	4	no	—
178	C₂×C₁₃	#2236	1	4	yes	complemented
179	C₂×C₁₃	C₂×#480	1	1	yes	characteristic
180	C₂×C₁₃	C₂²×Q₃₂	1	1	yes	characteristic
181	C₂×C₁₃	C₂×#509	1	1	yes	characteristic
182	C₂⁴	#6104	1	1	yes	characteristic
183	C₂×Q₈	—	2	2	no	—
184	C₂×Q₈	—	4	1	no	—
185	C₂×Q₈	—	4	2	no	—
186	C₂×Q₈	—	4	2	no	—
187	C₂²×C₄	—	2	2	no	—
188	C₂²×C₄	—	2	2	no	—
189	C₂²×C₄	—	4	1	no	—
190	C₂²×C₄	—	4	1	no	—
191	C₂²×C₄	—	52	4	no	—
192	C₂²×C₄	—	52	2	no	—
193	C₂²×C₄	—	104	4	no	—
194	C₂²×C₄	#6104	1	2	yes	—
195	C₂²×C₄	#6104	1	1	yes	characteristic
196	C₂²×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
197	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
198	Q₁₆	—	2	4	no	—
199	Q₁₆	—	4	2	no	—
200	C₂×C₈	—	2	2	no	—
201	C₂×C₈	—	2	4	no	—
202	C₂×C₈	—	2	4	no	—
203	C₂×C₈	#6129	1	4	yes	—
204	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
205	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
206	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
207	C₄⋊C₄	—	2	2	no	—
208	C₄⋊C₄	—	4	1	no	—
209	C₄⋊C₄	—	4	4	no	—
210	C₄⋊C₄	—	26	4	no	—
211	C₄⋊C₄	—	52	4	no	—
212	C₄⋊C₄	—	52	2	no	—
213	C₂²⋊C₄	—	4	4	no	—
214	C₁₆	—	26	4	no	—
215	C₁₃	C₂×#2236	1	1	yes	characteristic, complemented, Sylow
216	C₂³	—	2	2	no	—
217	C₂³	—	2	2	no	—
218	C₂³	#88069	1	4	yes	—
219	C₂³	C₂×#6104	1	2	yes	—
220	C₂³	C₂×#6104	1	1	yes	characteristic
221	Q₈	—	4	2	no	—
222	Q₈	—	4	2	no	—
223	Q₈	—	8	2	no	—
224	C₂×C₄	—	2	2	no	—
225	C₂×C₄	—	2	4	no	—
226	C₂×C₄	—	2	2	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	4	2	no	—
229	C₂×C₄	—	4	2	no	—
230	C₂×C₄	—	8	2	no	—
231	C₂×C₄	—	8	2	no	—
232	C₂×C₄	—	52	4	no	—
233	C₂×C₄	—	104	8	no	—
234	C₂×C₄	—	104	4	no	—
235	C₂×C₄	C₂×#6104	1	2	yes	—
236	C₂×C₄	C₂×#6104	1	1	yes	characteristic
237	C₂×C₄	#88189	1	2	yes	—
238	C₂×C₄	#88205	1	2	yes	—
239	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
240	C₈	—	2	2	no	—
241	C₈	#88189	1	2	yes	—
242	C₈	C₂×#6129	1	2	yes	—
243	C₂²	—	2	2	no	—
244	C₂²	—	2	2	no	—
245	C₂²	—	2	8	no	—
246	C₂²	#11718694	1	2	yes	—
247	C₂²	C₂×#88069	1	4	yes	—
248	C₂²	C₂×#88069	1	2	yes	—
249	C₂²	#11718854	1	2	yes	—
250	C₂²	C₂²×#6104	1	1	yes	characteristic
251	C₄	—	2	2	no	—
252	C₄	—	8	2	no	—
253	C₄	—	8	2	no	—
254	C₄	—	104	4	no	—
255	C₄	#11718694	1	2	yes	—
256	C₄	C₂×#88189	1	1	yes	characteristic
257	C₄	C₂×#88205	1	1	yes	characteristic
258	C₂	—	2	4	no	—
259	C₂	#13117036	1	4	yes	direct product factor
260	C₂	C₂×#11718694	1	1	yes	characteristic
261	C₂	C₂²×#88069	1	1	yes	characteristic
262	C₂	C₂×#11718854	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#6104
commutator, cosocle	C₂×C₈×C₁₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂×C₁₃×#467	C₂
socle	C₂³×C₁₃	C₂×D₈
prime radical	C₂⁴×C₁₃	D₈
hypercenter	C₂×#467	D₁₃
hypocenter	C₁₃	C₂×#2236
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂×#467

Complements

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

N	H ≅ G/N	type
2. #13117036	C₂	direct (N × H)
3. C₂×#11718081	C₂	semidirect
4. C₂×#11718156	C₂	semidirect
20. #11718156	C₂²	semidirect
22. #11718081	C₂²	semidirect
178. C₂×C₁₃	#2236	semidirect
215. C₁₃	C₂×#2236	semidirect
259. C₂	#13117036	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#88058	2
#13117036	2
C₂×#11718081	2
C₂×#11718156	2
C₂×C₂²⋊#6090	2
C₂×C₁₃×#467	2
C₂×#2236	13

Subgroups — C2×#13117036 #16017708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13117036 #16017708