Subgroups — D₁₃⋊#1848 #16798278

Order 3328.

1046 conjugacy classes of subgroups.

The subgroup lattice has 322 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	4	yes	maximal
2	D₁₃⋊#423	C₂	1	2	yes	maximal
3	#13130777	C₂	1	2	yes	maximal, complemented
4	#13130776	C₂	1	4	yes	maximal, complemented
5	#13130775	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
7	C₂×D₁₃⋊M₁₆	C₂²	1	4	yes	—
8	C₂²×C₈×D₁₃	C₂²	1	2	yes	—
9	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
10	#11719129	—	2	4	no	—
11	D₁₃⋊#108	—	2	16	no	—
12	C₂×#88104	C₂²	1	8	yes	—
13	C₂×#88103	C₂²	1	8	yes	—
14	#11719053	C₂²	1	4	yes	—
15	#11719052	C₂²	1	4	yes	—
16	D₁₃⋊(C₄⋊C₈)	—	2	4	no	—
17	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
18	C₂×C₈×Dic₁₃	C₄	1	2	yes	—
19	C₂×C₄×#1055	C₄	1	1	yes	characteristic
20	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
21	C₄×C₈×D₁₃	C₄	1	2	yes	—
22	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
23	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
24	C₄×C₈×D₁₃	C₂²	1	2	yes	—
25	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₁₃	Q₈	1	2	yes	—
27	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
28	C₂×#6122	—	2	4	no	—
29	D₁₃⋊M₁₆	—	2	16	no	—
30	C₂×#6118	C₂³	1	8	yes	—
31	C₂×D₁₃⋊C₈	—	2	4	no	—
32	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
33	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄×Dic₁₃	D₄	1	2	yes	—
36	C₂²×#1055	C₂×C₄	1	2	yes	—
37	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
38	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
39	C₂×C₈×D₁₃	D₄	1	8	yes	—
40	C₂×C₈×D₁₃	Q₈	1	8	yes	—
41	C₂×C₈×D₁₃	C₂³	1	2	yes	—
42	C₂×C₈×D₁₃	C₂³	1	2	yes	—
43	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
44	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
45	C₄²×D₁₃	D₄	1	2	yes	—
46	C₄²×D₁₃	Q₈	1	2	yes	—
47	C₄²×D₁₃	C₂³	1	1	yes	characteristic
48	C₄²×D₁₃	C₂³	1	1	yes	characteristic
49	#88112	—	2	8	no	—
50	C₄⋊#1057	—	2	8	no	—
51	#88104	—	2	16	no	—
52	#88103	—	2	16	no	—
53	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
54	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
55	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
56	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
57	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
58	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
59	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
60	C₄×#1055	C₂×C₄	1	1	yes	characteristic
61	C₄×#1055	C₂×C₄	1	2	yes	—
62	C₄×#1055	C₂×C₄	1	1	yes	characteristic
63	C₂×#1848	—	13	1	no	maximal, Sylow
64	C₂³×D₁₃	C₂×Q₈	1	1	yes	characteristic
65	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
66	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
67	C₂²×Dic₁₃	C₄⋊C₄	1	2	yes	—
68	C₂²×Dic₁₃	C₂×D₄	1	1	yes	characteristic
69	C₂×C₄×D₁₃	—	2	8	no	—
70	C₂×C₄×D₁₃	C₄⋊C₄	1	2	yes	—
71	C₂×C₄×D₁₃	C₄⋊C₄	1	2	yes	—
72	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
73	C₂×C₄×D₁₃	C₂×D₄	1	4	yes	—
74	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
75	C₂×C₄×D₁₃	C₂×Q₈	1	2	yes	—
76	C₂×C₄×D₁₃	C₂×Q₈	1	2	yes	—
77	C₂×C₄×D₁₃	C₂×Q₈	1	4	yes	—
78	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
79	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
80	#6122	—	4	8	no	—
81	C₂×#1057	—	2	8	no	—
82	#6118	—	2	16	no	—
83	D₁₃⋊C₈	—	4	8	no	—
84	C₂×C₈×C₁₃	C₄⋊C₄	1	8	yes	—
85	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
86	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
87	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
88	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
89	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
90	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
91	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
92	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
93	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
94	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
95	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
96	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
97	C₂×#1055	C₄⋊C₄	1	8	yes	—
98	C₂×#1055	C₂²×C₄	1	2	yes	—
99	C₂×#1055	C₂²×C₄	1	2	yes	—
100	C₈×D₁₃	C₄⋊C₄	1	8	yes	—
101	C₈×D₁₃	C₄⋊C₄	1	8	yes	—
102	C₈×D₁₃	C₂×D₄	1	4	yes	—
103	C₈×D₁₃	C₂×D₄	1	4	yes	—
104	C₈×D₁₃	C₂×Q₈	1	4	yes	—
105	C₈×D₁₃	C₂×Q₈	1	4	yes	—
106	C₂²×#108	—	13	4	no	—
107	C₂×#423	—	13	2	no	—
108	C₂²×C₄×C₈	—	13	1	no	—
109	#1848	—	13	2	no	—
110	#1848	—	13	4	no	—
111	#1848	—	13	2	no	—
112	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
113	C₂²×D₁₃	—	2	4	no	—
114	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
115	C₂²×D₁₃	C₄⋊Q₈	1	4	yes	—
116	C₂²×D₁₃	C₂²×Q₈	1	1	yes	characteristic
117	C₂×C₄×C₁₃	—	2	4	no	—
118	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
119	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
120	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
121	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
122	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
123	C₂×Dic₁₃	—	2	4	no	—
124	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
125	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
126	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
127	C₂×Dic₁₃	#127	1	2	yes	—
128	C₂×Dic₁₃	C₄⋊Q₈	1	2	yes	—
129	C₂×Dic₁₃	C₂²×D₄	1	1	yes	characteristic
130	C₄×D₁₃	—	2	4	no	—
131	C₄×D₁₃	—	2	4	no	—
132	C₄×D₁₃	—	2	4	no	—
133	C₄×D₁₃	#108	1	8	yes	complemented
134	C₄×D₁₃	C₂×C₄⋊C₄	1	4	yes	—
135	C₄×D₁₃	#127	1	2	yes	—
136	C₄×D₁₃	C₄⋊Q₈	1	2	yes	—
137	C₄×D₁₃	C₄⋊Q₈	1	4	yes	—
138	C₄×D₁₃	C₂²×D₄	1	2	yes	—
139	C₄×D₁₃	C₂²×Q₈	1	2	yes	—
140	#1057	—	4	8	no	—
141	C₈×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
142	C₈×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
143	#1055	C₂×C₄⋊C₄	1	4	yes	—
144	#1055	C₂×C₄⋊C₄	1	4	yes	—
145	C₂²×M₁₆	—	13	4	no	—
146	C₂³×C₈	—	13	2	no	—
147	C₂²×C₄²	—	13	1	no	—
148	C₂×#108	—	13	8	no	—
149	C₂×#108	—	13	8	no	—
150	C₂×#108	—	26	16	no	—
151	#423	—	13	4	no	—
152	#423	—	13	4	no	—
153	#423	—	26	4	no	—
154	C₂×C₄⋊C₈	—	26	4	no	—
155	C₂×C₄×C₈	—	13	2	no	—
156	C₂×C₄×C₈	—	13	1	no	—
157	C₂×C₄×C₈	—	13	1	no	—
158	C₂×C₄×C₈	—	13	2	no	—
159	C₂×C₄×C₈	—	13	1	no	—
160	C₂×C₄×C₈	—	13	1	no	—
161	C₂×C₄×C₈	—	13	1	no	—
162	C₂×C₄×C₈	—	13	2	no	—
163	C₂×C₄×C₈	#261	1	1	yes	characteristic
164	C₂²×C₁₃	—	2	2	no	—
165	C₂²×C₁₃	#384	1	2	yes	—
166	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
167	C₂×D₁₃	—	2	2	no	—
168	C₂×D₁₃	—	2	8	no	—
169	C₂×D₁₃	#384	1	2	yes	—
170	C₂×D₁₃	C₂×#108	1	4	yes	—
171	C₂×D₁₃	C₂×C₄⋊Q₈	1	2	yes	—
172	C₄×C₁₃	—	2	2	no	—
173	C₄×C₁₃	#384	1	2	yes	—
174	C₄×C₁₃	C₂×#108	1	4	yes	complemented
175	C₄×C₁₃	C₂²×C₄⋊C₄	1	2	yes	—
176	Dic₁₃	—	2	2	no	—
177	Dic₁₃	#384	1	2	yes	—
178	Dic₁₃	C₂×#108	1	4	yes	complemented
179	Dic₁₃	C₂×#127	1	1	yes	characteristic
180	Dic₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
181	C₂³×C₄	—	13	1	no	—
182	C₂³×C₄	—	13	2	no	—
183	C₂×M₁₆	—	13	8	no	—
184	C₂×M₁₆	—	26	4	no	—
185	C₂×M₁₆	—	26	16	no	—
186	C₂²×C₈	—	13	2	no	—
187	C₂²×C₈	—	13	8	no	—
188	C₂²×C₈	—	13	8	no	—
189	C₂²×C₈	—	13	2	no	—
190	C₂²×C₈	—	13	2	no	—
191	C₂²×C₈	—	13	2	no	—
192	C₂²×C₈	—	13	2	no	—
193	C₂²×C₈	—	26	4	no	—
194	C₂²×C₈	C₂×#261	1	2	yes	—
195	C₂×C₄²	—	13	2	no	—
196	C₂×C₄²	—	13	1	no	—
197	C₂×C₄²	—	13	2	no	—
198	C₂×C₄²	—	13	2	no	—
199	C₂×C₄²	—	13	1	no	—
200	C₂×C₄²	—	13	1	no	—
201	C₂×C₄²	—	13	1	no	—
202	C₂×C₄²	—	13	1	no	—
203	C₂×C₄²	C₂×#261	1	1	yes	characteristic
204	#108	—	26	16	no	—
205	#108	—	26	16	no	—
206	C₄⋊C₈	—	26	8	no	—
207	C₄⋊C₈	—	26	8	no	—
208	C₄×C₈	—	13	2	no	—
209	C₄×C₈	—	13	2	no	—
210	C₄×C₈	—	13	2	no	—
211	C₄×C₈	—	13	2	no	—
212	C₄×C₈	—	13	2	no	—
213	C₄×C₈	—	13	1	no	—
214	C₄×C₈	—	13	1	no	—
215	C₄×C₈	C₂×#261	1	2	yes	—
216	C₄×C₈	C₂×#261	1	1	yes	characteristic
217	C₄×C₈	C₂×#261	1	1	yes	characteristic
218	C₂×C₁₃	—	2	2	no	—
219	C₂×C₁₃	C₂×#384	1	1	yes	characteristic
220	C₂×C₁₃	C₂²×#108	1	2	yes	—
221	D₁₃	—	2	2	no	—
222	D₁₃	#1848	1	4	yes	complemented
223	C₂⁴	—	13	1	no	—
224	C₂²×C₄	—	13	1	no	—
225	C₂²×C₄	—	13	2	no	—
226	C₂²×C₄	—	13	4	no	—
227	C₂²×C₄	—	13	4	no	—
228	C₂²×C₄	—	13	1	no	—
229	C₂²×C₄	—	13	1	no	—
230	C₂²×C₄	—	13	1	no	—
231	C₂²×C₄	—	13	1	no	—
232	C₂²×C₄	—	13	2	no	—
233	C₂²×C₄	—	13	2	no	—
234	C₂²×C₄	—	13	2	no	—
235	C₂²×C₄	—	13	2	no	—
236	C₂²×C₄	—	26	8	no	—
237	C₂²×C₄	C₄⋊#261	1	2	yes	—
238	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
239	M₁₆	—	26	16	no	—
240	M₁₆	—	52	8	no	—
241	C₂×C₈	—	13	8	no	—
242	C₂×C₈	—	13	2	no	—
243	C₂×C₈	—	13	2	no	—
244	C₂×C₈	—	13	4	no	—
245	C₂×C₈	—	13	4	no	—
246	C₂×C₈	—	13	8	no	—
247	C₂×C₈	—	13	8	no	—
248	C₂×C₈	—	13	4	no	—
249	C₂×C₈	—	13	4	no	—
250	C₂×C₈	—	26	8	no	—
251	C₂×C₈	—	52	8	no	—
252	C₂×C₈	C₄⋊#261	1	8	yes	—
253	C₂×C₈	C₂²×#261	1	2	yes	—
254	C₂×C₈	C₂²×#261	1	2	yes	—
255	C₄²	—	13	2	no	—
256	C₄²	—	13	2	no	—
257	C₄²	—	13	2	no	—
258	C₄²	—	13	2	no	—
259	C₄²	—	13	2	no	—
260	C₄²	—	13	1	no	—
261	C₄²	—	13	1	no	—
262	C₄²	C₄⋊#261	1	2	yes	—
263	C₄²	C₂²×#261	1	1	yes	characteristic
264	C₄²	C₂²×#261	1	1	yes	characteristic
265	C₁₃	C₂×#1848	1	1	yes	characteristic, complemented, Sylow
266	C₂³	—	13	1	no	—
267	C₂³	—	13	4	no	—
268	C₂³	—	13	1	no	—
269	C₂³	—	26	4	no	—
270	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
271	C₂×C₄	—	2	4	no	—
272	C₂×C₄	—	13	2	no	—
273	C₂×C₄	—	13	2	no	—
274	C₂×C₄	—	13	1	no	—
275	C₂×C₄	—	13	1	no	—
276	C₂×C₄	—	13	2	no	—
277	C₂×C₄	—	13	2	no	—
278	C₂×C₄	—	13	2	no	—
279	C₂×C₄	—	13	4	no	—
280	C₂×C₄	—	13	8	no	—
281	C₂×C₄	—	13	2	no	—
282	C₂×C₄	—	13	4	no	—
283	C₂×C₄	—	13	2	no	—
284	C₂×C₄	—	13	2	no	—
285	C₂×C₄	—	26	4	no	—
286	C₂×C₄	—	26	4	no	—
287	C₂×C₄	—	26	4	no	—
288	C₂×C₄	—	26	4	no	—
289	C₂×C₄	C₂×C₄⋊#261	1	2	yes	—
290	C₂×C₄	C₂×C₄⋊#261	1	4	yes	—
291	C₂×C₄	C₂×C₄⋊#261	1	2	yes	—
292	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
293	C₂×C₄	C₂³×#261	1	1	yes	characteristic
294	C₈	—	13	4	no	—
295	C₈	—	13	4	no	—
296	C₈	—	52	8	no	—
297	C₈	C₂×C₄⋊#261	1	4	yes	—
298	C₈	C₂×C₄⋊#261	1	4	yes	—
299	C₂²	—	2	2	no	—
300	C₂²	—	13	2	no	—
301	C₂²	—	13	4	no	—
302	C₂²	—	13	2	no	—
303	C₂²	—	26	8	no	—
304	C₂²	—	26	2	no	—
305	C₂²	#11719059	1	2	yes	—
306	C₂²	C₂²×C₄⋊#261	1	1	yes	characteristic
307	C₄	—	2	2	no	—
308	C₄	—	13	1	no	—
309	C₄	—	13	1	no	—
310	C₄	—	13	2	no	—
311	C₄	—	13	4	no	—
312	C₄	—	26	2	no	—
313	C₄	#11719059	1	2	yes	—
314	C₄	D₁₃⋊#108	1	4	yes	complemented
315	C₄	C₂²×C₄⋊#261	1	2	yes	—
316	C₂	—	2	2	no	—
317	C₂	—	13	4	no	—
318	C₂	—	26	2	no	—
319	C₂	C₂×#11719059	1	1	yes	characteristic
320	C₂	C₂×D₁₃⋊#108	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×C₄⋊#261
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#261
Fitting	C₂×C₄×C₈×C₁₃	C₄
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₃	C₂×Q₈
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	C₂×C₄×C₈	#261
hypocenter	C₁₃	C₂×#1848
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
3. #13130777	C₂	semidirect
4. #13130776	C₂	semidirect
5. #13130775	C₂	semidirect
133. C₄×D₁₃	#108	semidirect
174. C₄×C₁₃	C₂×#108	semidirect
178. Dic₁₃	C₂×#108	semidirect
222. D₁₃	#1848	semidirect
265. C₁₃	C₂×#1848	semidirect
314. C₄	D₁₃⋊#108	semidirect

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
D₁₃⋊#423	2
#13130777	2
#13130776	2
#13130775	2
C₂×C₄×C₈×D₁₃	2
C₂×#1848	13

Subgroups — D13⋊#1848 #16798278

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃⋊#1848 #16798278