Subgroups — C₂×D₁₃⋊#368 #16807034

Order 3328.

662 conjugacy classes of subgroups.

The subgroup lattice has 290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃⋊#108	C₂	1	2	yes	maximal
2	C₂×#11718224	C₂	1	2	yes	maximal, complemented
3	D₁₃⋊#368	C₂	1	8	yes	maximal, direct product factor
4	C₂×#11718223	C₂	1	2	yes	maximal, complemented
5	C₂²×C₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic
6	C₂×D₁₃⋊M₁₆	—	2	2	no	—
7	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
8	D₁₃⋊#108	—	2	4	no	—
9	D₁₃⋊#108	C₂²	1	8	yes	—
10	C₂×#88104	C₂²	1	4	yes	—
11	C₂×#88103	—	2	2	no	—
12	C₂²×C₁₃×C₁₆	C₄	1	1	yes	characteristic
13	C₂²×#6090	C₄	1	1	yes	characteristic
14	C₂×C₁₆×D₁₃	C₄	1	1	yes	characteristic
15	C₂×C₁₆×D₁₃	C₄	1	4	yes	—
16	C₂×C₁₆×D₁₃	C₄	1	1	yes	characteristic
17	C₂×C₁₆×D₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₆×D₁₃	C₂²	1	4	yes	—
19	C₂×C₁₆×D₁₃	C₂²	1	1	yes	characteristic
20	#11718224	C₂²	1	8	yes	complemented
21	#11718223	C₂²	1	8	yes	complemented
22	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
23	C₂×#6122	—	4	2	no	—
24	D₁₃⋊M₁₆	—	2	8	no	—
25	D₁₃⋊M₁₆	—	4	4	no	—
26	C₂×#6118	—	2	4	no	—
27	C₂×D₁₃⋊C₈	—	4	2	no	—
28	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
29	C₂²×#1055	Q₈	1	1	yes	characteristic
30	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
31	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
33	C₂×C₈×D₁₃	D₄	1	2	yes	—
34	C₂×C₈×D₁₃	Q₈	1	2	yes	—
35	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
36	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
37	C₂×C₈×D₁₃	C₂³	1	2	yes	—
38	#88104	—	2	4	no	—
39	#88104	C₂³	1	8	yes	—
40	#88103	—	2	8	no	—
41	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
42	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
43	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
44	C₂×#6090	C₂×C₄	1	1	yes	characteristic
45	C₂×#6090	C₂×C₄	1	4	yes	—
46	C₂×#6090	C₂×C₄	1	1	yes	characteristic
47	C₁₆×D₁₃	C₂×C₄	1	2	yes	—
48	C₁₆×D₁₃	C₂×C₄	1	4	yes	—
49	C₁₆×D₁₃	C₂×C₄	1	4	yes	—
50	C₁₆×D₁₃	C₂×C₄	1	2	yes	—
51	C₁₆×D₁₃	C₂³	1	2	yes	—
52	C₁₆×D₁₃	C₂³	1	2	yes	—
53	C₂²×#368	—	13	1	no	maximal, Sylow
54	C₂³×D₁₃	Q₁₆	1	1	yes	characteristic
55	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
56	C₂²×Dic₁₃	D₈	1	1	yes	characteristic
57	C₂×C₄×D₁₃	C₄⋊C₄	1	2	yes	—
58	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
59	C₂×C₄×D₁₃	D₈	1	1	yes	characteristic
60	C₂×C₄×D₁₃	D₈	1	2	yes	—
61	C₂×C₄×D₁₃	Q₁₆	1	2	yes	—
62	C₂×C₄×D₁₃	Q₁₆	1	1	yes	characteristic
63	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
64	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
65	#6122	—	4	8	no	—
66	C₂×#1057	—	4	4	no	—
67	#6118	—	2	8	no	—
68	#6118	—	4	4	no	—
69	D₁₃⋊C₈	—	4	8	no	—
70	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
71	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
72	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
73	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
74	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
75	C₂×#1055	C₄⋊C₄	1	2	yes	—
76	C₂×#1055	C₂×Q₈	1	1	yes	characteristic
77	C₂×#1055	C₂×Q₈	1	2	yes	—
78	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
79	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
80	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
81	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
82	C₈×D₁₃	C₂²×C₄	1	2	yes	—
83	C₈×D₁₃	C₂×D₄	1	2	yes	—
84	C₈×D₁₃	C₂×D₄	1	1	yes	characteristic
85	C₈×D₁₃	C₂×Q₈	1	1	yes	characteristic
86	C₈×D₁₃	C₂×Q₈	1	2	yes	—
87	C₈×D₁₃	C₂⁴	1	1	yes	characteristic
88	C₁₃×C₁₆	C₂²×C₄	1	2	yes	—
89	C₁₃×C₁₆	C₂²×C₄	1	2	yes	—
90	#6090	C₂²×C₄	1	2	yes	—
91	#6090	C₂²×C₄	1	2	yes	—
92	C₂³×C₁₆	—	13	1	no	—
93	C₂²×#108	—	13	2	no	—
94	C₂×#368	—	13	2	no	—
95	C₂×#368	—	13	8	no	—
96	C₂×#368	—	13	2	no	—
97	C₂³×C₁₃	#107	1	1	yes	characteristic
98	C₂²×D₁₃	—	2	4	no	—
99	C₂²×D₁₃	#107	1	2	yes	—
100	C₂²×D₁₃	#107	1	1	yes	characteristic
101	C₂²×D₁₃	C₂×Q₁₆	1	1	yes	characteristic
102	C₂²×D₁₃	C₂×Q₁₆	1	2	yes	—
103	C₂×C₄×C₁₃	#107	1	2	yes	—
104	C₂×C₄×C₁₃	#107	1	1	yes	characteristic
105	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
106	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
107	C₂×Dic₁₃	#107	1	2	yes	—
108	C₂×Dic₁₃	#107	1	1	yes	characteristic
109	C₂×Dic₁₃	C₂×D₈	1	1	yes	characteristic
110	C₂×Dic₁₃	C₂×D₈	1	2	yes	—
111	C₄×D₁₃	#107	1	2	yes	—
112	C₄×D₁₃	#107	1	2	yes	—
113	C₄×D₁₃	#107	1	2	yes	—
114	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
115	C₄×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
116	C₄×D₁₃	C₂×D₈	1	2	yes	—
117	C₄×D₁₃	C₂×D₈	1	1	yes	characteristic
118	C₄×D₁₃	C₂×Q₁₆	1	1	yes	characteristic
119	C₄×D₁₃	C₂×Q₁₆	1	2	yes	—
120	C₄×D₁₃	C₂²×D₄	1	1	yes	characteristic
121	#1057	—	4	8	no	—
122	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
123	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
124	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
125	#1055	C₂×C₄⋊C₄	1	2	yes	—
126	#1055	C₂×C₄⋊C₄	1	1	yes	characteristic
127	#1055	C₂²×Q₈	1	1	yes	characteristic
128	C₂²×M₁₆	—	26	2	no	—
129	C₂³×C₈	—	13	1	no	—
130	C₂²×C₁₆	—	13	1	no	—
131	C₂²×C₁₆	—	13	1	no	—
132	C₂²×C₁₆	—	13	4	no	—
133	C₂²×C₁₆	—	13	1	no	—
134	C₂²×C₁₆	—	13	1	no	—
135	C₂²×C₁₆	—	13	4	no	—
136	C₂²×C₁₆	—	13	1	no	—
137	C₂²×C₁₆	#261	1	1	yes	characteristic
138	C₂×#108	—	13	4	no	—
139	C₂×#108	—	13	8	no	—
140	C₂×#108	—	26	2	no	—
141	C₂×#108	—	26	4	no	—
142	#368	—	13	8	no	—
143	#368	—	13	8	no	—
144	C₂²×C₁₃	—	2	2	no	—
145	C₂²×C₁₃	C₂×#107	1	2	yes	—
146	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
147	C₂×D₁₃	—	2	2	no	—
148	C₂×D₁₃	—	2	4	no	—
149	C₂×D₁₃	—	2	4	no	—
150	C₂×D₁₃	#368	1	4	yes	complemented
151	C₂×D₁₃	C₂×#107	1	1	yes	characteristic
152	C₂×D₁₃	C₂×#107	1	2	yes	—
153	C₂×D₁₃	C₂²×Q₁₆	1	1	yes	characteristic
154	C₄×C₁₃	C₂×#107	1	1	yes	characteristic
155	C₄×C₁₃	C₂×#107	1	2	yes	—
156	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
157	Dic₁₃	C₂×#107	1	1	yes	characteristic
158	Dic₁₃	C₂×#107	1	2	yes	—
159	Dic₁₃	C₂²×D₈	1	1	yes	characteristic
160	C₂³×C₄	—	13	1	no	—
161	C₂×M₁₆	—	26	4	no	—
162	C₂×M₁₆	—	26	8	no	—
163	C₂×M₁₆	—	52	4	no	—
164	C₂×M₁₆	—	52	2	no	—
165	C₂²×C₈	—	13	1	no	—
166	C₂²×C₈	—	13	1	no	—
167	C₂²×C₈	—	13	2	no	—
168	C₂²×C₈	—	13	1	no	—
169	C₂²×C₈	—	13	2	no	—
170	C₂²×C₈	—	13	1	no	—
171	C₂²×C₈	—	13	2	no	—
172	C₂²×C₈	—	13	1	no	—
173	C₂²×C₈	—	13	2	no	—
174	C₂²×C₈	—	52	2	no	—
175	C₂²×C₈	C₂×#261	1	1	yes	characteristic
176	C₂×C₁₆	—	13	1	no	—
177	C₂×C₁₆	—	13	4	no	—
178	C₂×C₁₆	—	13	1	no	—
179	C₂×C₁₆	—	13	2	no	—
180	C₂×C₁₆	—	13	2	no	—
181	C₂×C₁₆	—	13	2	no	—
182	C₂×C₁₆	—	13	4	no	—
183	C₂×C₁₆	—	13	4	no	—
184	C₂×C₁₆	—	13	2	no	—
185	C₂×C₁₆	C₂×#261	1	1	yes	characteristic
186	C₂×C₁₆	C₂×#261	1	4	yes	—
187	C₂×C₁₆	C₂×#261	1	1	yes	characteristic
188	#108	—	13	8	no	—
189	#108	—	26	8	no	—
190	#108	—	26	4	no	—
191	C₂×C₁₃	—	2	2	no	—
192	C₂×C₁₃	C₂×#368	1	2	yes	complemented
193	C₂×C₁₃	C₂²×#107	1	1	yes	characteristic
194	D₁₃	—	2	1	no	—
195	D₁₃	—	2	1	no	—
196	D₁₃	C₂×#368	1	4	yes	complemented
197	C₂⁴	—	13	1	no	—
198	C₂²×C₄	—	13	1	no	—
199	C₂²×C₄	—	13	2	no	—
200	C₂²×C₄	—	13	2	no	—
201	C₂²×C₄	—	13	1	no	—
202	C₂²×C₄	—	13	1	no	—
203	C₂²×C₄	—	13	1	no	—
204	C₂²×C₄	—	13	2	no	—
205	C₂²×C₄	—	13	1	no	—
206	C₂²×C₄	—	13	2	no	—
207	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
208	M₁₆	—	26	8	no	—
209	M₁₆	—	52	4	no	—
210	M₁₆	—	52	8	no	—
211	C₂×C₈	—	13	1	no	—
212	C₂×C₈	—	13	2	no	—
213	C₂×C₈	—	13	1	no	—
214	C₂×C₈	—	13	2	no	—
215	C₂×C₈	—	13	2	no	—
216	C₂×C₈	—	13	1	no	—
217	C₂×C₈	—	13	2	no	—
218	C₂×C₈	—	13	2	no	—
219	C₂×C₈	—	13	2	no	—
220	C₂×C₈	—	13	2	no	—
221	C₂×C₈	—	13	1	no	—
222	C₂×C₈	—	13	1	no	—
223	C₂×C₈	—	13	2	no	—
224	C₂×C₈	—	13	1	no	—
225	C₂×C₈	—	52	8	no	—
226	C₂×C₈	—	52	4	no	—
227	C₂×C₈	C₄⋊#261	1	1	yes	characteristic
228	C₂×C₈	C₄⋊#261	1	2	yes	—
229	C₂×C₈	C₂²×#261	1	1	yes	characteristic
230	C₂×C₈	C₂²×#261	1	2	yes	—
231	C₁₆	—	13	2	no	—
232	C₁₆	—	13	2	no	—
233	C₁₆	C₂²×#261	1	2	yes	—
234	C₁₆	C₂²×#261	1	2	yes	—
235	C₁₃	C₂²×#368	1	1	yes	characteristic, complemented, Sylow
236	C₂³	—	13	1	no	—
237	C₂³	—	13	2	no	—
238	C₂³	—	13	2	no	—
239	C₂³	—	13	1	no	—
240	C₂³	—	26	4	no	—
241	C₂³	#88102	1	1	yes	characteristic
242	C₂×C₄	—	13	1	no	—
243	C₂×C₄	—	13	2	no	—
244	C₂×C₄	—	13	2	no	—
245	C₂×C₄	—	13	1	no	—
246	C₂×C₄	—	13	2	no	—
247	C₂×C₄	—	13	1	no	—
248	C₂×C₄	—	13	2	no	—
249	C₂×C₄	—	13	2	no	—
250	C₂×C₄	—	13	2	no	—
251	C₂×C₄	—	13	1	no	—
252	C₂×C₄	—	13	2	no	—
253	C₂×C₄	—	13	1	no	—
254	C₂×C₄	—	13	2	no	—
255	C₂×C₄	—	13	1	no	—
256	C₂×C₄	#88102	1	2	yes	—
257	C₂×C₄	#88102	1	1	yes	characteristic
258	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
259	C₂×C₄	C₂×C₄⋊#261	1	2	yes	—
260	C₈	—	13	2	no	—
261	C₈	—	13	1	no	—
262	C₈	—	13	1	no	—
263	C₈	—	52	8	no	—
264	C₈	C₂×C₄⋊#261	1	2	yes	—
265	C₈	C₂×C₄⋊#261	1	1	yes	characteristic
266	C₈	C₂³×#261	1	1	yes	characteristic
267	C₂²	—	2	2	no	—
268	C₂²	—	13	4	no	—
269	C₂²	—	13	2	no	—
270	C₂²	—	13	1	no	—
271	C₂²	—	13	1	no	—
272	C₂²	—	26	4	no	—
273	C₂²	—	26	4	no	—
274	C₂²	—	26	2	no	—
275	C₂²	C₂×#88102	1	2	yes	—
276	C₂²	C₂×#88102	1	1	yes	characteristic
277	C₄	—	13	1	no	—
278	C₄	—	13	1	no	—
279	C₄	—	13	2	no	—
280	C₄	C₂×#88102	1	1	yes	characteristic
281	C₄	C₂×#88102	1	2	yes	—
282	C₄	C₂²×C₄⋊#261	1	1	yes	characteristic
283	C₂	—	2	2	no	—
284	C₂	—	13	4	no	—
285	C₂	—	26	1	no	—
286	C₂	—	26	1	no	—
287	C₂	D₁₃⋊#368	1	2	yes	direct product factor
288	C₂	C₂²×#88102	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#88102
commutator	C₈×C₁₃	C₂³×C₄
Frattini	C₈	C₂³×#261
Fitting	C₂²×C₁₃×C₁₆	C₄
socle	C₂²×C₁₃	C₂×#107
prime radical	C₂³×D₁₃	Q₁₆
cosocle	C₈×D₁₃	C₂⁴
hypercenter	C₂²×C₁₆	#261
hypocenter	C₁₃	C₂²×#368
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×#11718224	C₂	semidirect
3. D₁₃⋊#368	C₂	direct (N × H)
4. C₂×#11718223	C₂	semidirect
20. #11718224	C₂²	semidirect
21. #11718223	C₂²	semidirect
150. C₂×D₁₃	#368	semidirect
192. C₂×C₁₃	C₂×#368	semidirect
196. D₁₃	C₂×#368	semidirect
235. C₁₃	C₂²×#368	semidirect
287. C₂	D₁₃⋊#368	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×D₁₃⋊#108	2
C₂×#11718224	2
D₁₃⋊#368	2
C₂×#11718223	2
C₂²×C₁₆×D₁₃	2
C₂²×#368	13

Subgroups — C2×D13⋊#368 #16807034

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₃⋊#368 #16807034