Subgroups — Q₃₂×C₂²⋊D₁₃ #16019643

Order 3328.

664 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	Q₁₆×C₂²⋊D₁₃	C₂	1	2	yes	maximal
3	#13117087	C₂	1	1	yes	maximal, characteristic, complemented
4	#13116927	C₂	1	1	yes	maximal, characteristic, complemented
5	#13116924	C₂	1	1	yes	maximal, characteristic, complemented
6	#13116884	C₂	1	2	yes	maximal, complemented
7	#13116770	C₂	1	2	yes	maximal, complemented
8	#13116768	C₂	1	2	yes	maximal, complemented
9	Q₃₂×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₆×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic
11	C₂²×C₁₃×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
13	Q₈×C₂²⋊D₁₃	—	2	2	no	—
14	C₂×Q₁₆×D₁₃	C₂²	1	2	yes	—
15	C₂×C₁₃×Q₃₂	—	2	4	no	—
16	C₂×C₁₃×Q₃₂	C₂²	1	2	yes	—
17	C₂×C₁₃×Q₃₂	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×Q₃₂	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
20	#11718889	—	2	2	no	—
21	#11718849	C₂²	1	2	yes	—
22	#11718847	—	2	2	no	—
23	Q₁₆×Dic₁₃	C₂²	1	2	yes	—
24	#11718843	—	2	2	no	—
25	#11718842	C₂²	1	2	yes	—
26	C₂×#88069	C₂²	1	2	yes	—
27	C₂×#88069	C₂²	1	2	yes	—
28	#11718777	C₂²	1	2	yes	—
29	C₈×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
30	D₁₃×Q₃₂	—	2	4	no	—
31	C₂×Dic₁₀₄	C₂²	1	1	yes	characteristic
32	C₂×C₁₆×D₁₃	C₂²	1	1	yes	characteristic
33	#11718156	C₂²	1	2	yes	—
34	#11718156	C₂²	1	2	yes	—
35	C₂²⋊#6090	C₂²	1	1	yes	characteristic
36	#11718099	C₂²	1	1	yes	characteristic
37	#11718096	C₂²	1	1	yes	characteristic
38	#11718095	C₂²	1	2	yes	—
39	#11718093	C₂²	1	1	yes	characteristic
40	C₁₆×Dic₁₃	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₁₃	—	2	2	no	—
42	C₂×Q₈×D₁₃	—	2	2	no	—
43	C₂×C₁₃×Q₁₆	—	2	4	no	—
44	C₂×C₁₃×Q₁₆	—	2	2	no	—
45	C₂×C₁₃×Q₁₆	—	4	2	no	—
46	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
47	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	#88200	—	2	2	no	—
50	#88200	—	4	2	no	—
51	Q₈×Dic₁₃	—	2	2	no	—
52	#88198	—	2	2	no	—
53	#88198	—	4	2	no	—
54	C₂×#6107	—	2	2	no	—
55	C₂×#6107	—	2	2	no	—
56	C₄×C₂²⋊D₁₃	—	4	2	no	—
57	C₄×C₂²⋊D₁₃	D₄	1	1	yes	characteristic
58	#88178	—	2	2	no	—
59	#88178	—	4	2	no	—
60	Q₁₆×D₁₃	—	2	4	no	—
61	Q₁₆×D₁₃	—	4	2	no	—
62	C₂×Dic₅₂	C₂³	1	2	yes	—
63	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
64	C₁₃×Q₃₂	—	2	4	no	—
65	C₁₃×Q₃₂	—	2	2	no	—
66	C₁₃×Q₃₂	D₄	1	4	yes	complemented
67	C₂×C₁₃×C₁₆	—	2	2	no	—
68	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
69	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
70	#88075	—	2	2	no	—
71	#88075	—	2	2	no	—
72	C₂²⋊#1055	D₄	1	1	yes	characteristic
73	#88069	—	2	4	no	—
74	#88069	—	4	2	no	—
75	#88060	D₄	1	1	yes	characteristic
76	#88058	C₂³	1	2	yes	—
77	#88056	—	2	2	no	—
78	#88054	D₄	1	1	yes	characteristic
79	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
80	C₂×#6090	C₂³	1	1	yes	characteristic
81	C₂×#6090	C₂³	1	1	yes	characteristic
82	Dic₁₀₄	—	2	2	no	—
83	C₁₆×D₁₃	—	2	2	no	—
84	D₄×Q₃₂	—	13	1	no	maximal, Sylow
85	C₂×Q₈×C₁₃	—	2	2	no	—
86	C₂×Q₈×C₁₃	—	2	2	no	—
87	C₂×Q₈×C₁₃	—	4	4	no	—
88	C₂×Q₈×C₁₃	—	4	2	no	—
89	C₂×Q₈×C₁₃	—	8	2	no	—
90	C₂²×C₄×C₁₃	—	4	2	no	—
91	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
92	C₂×C₂²⋊D₁₃	D₈	1	1	yes	characteristic
93	Q₈×D₁₃	—	4	4	no	—
94	Q₈×D₁₃	—	8	2	no	—
95	C₂×C₄×D₁₃	—	4	2	no	—
96	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
97	C₂×Dic₂₆	—	2	2	no	—
98	C₂×Dic₂₆	—	4	2	no	—
99	C₁₃×Q₁₆	—	2	2	no	—
100	C₁₃×Q₁₆	—	2	2	no	—
101	C₁₃×Q₁₆	—	2	2	no	—
102	C₁₃×Q₁₆	—	4	4	no	—
103	C₁₃×Q₁₆	C₂×D₄	1	4	yes	—
104	C₂×C₈×C₁₃	—	2	1	no	—
105	C₂×C₈×C₁₃	—	2	1	no	—
106	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
108	C₂²⋊Dic₁₃	—	4	2	no	—
109	C₂²⋊Dic₁₃	D₈	1	1	yes	characteristic
110	#6107	—	4	4	no	—
111	#6107	—	8	2	no	—
112	#6103	—	4	2	no	—
113	#6103	D₈	1	1	yes	characteristic
114	C₄⋊Dic₁₃	—	2	2	no	—
115	C₄⋊Dic₁₃	—	4	2	no	—
116	#6101	—	4	2	no	—
117	#6101	—	4	2	no	—
118	#6101	—	4	2	no	—
119	#6101	—	4	2	no	—
120	#6101	D₈	1	1	yes	characteristic
121	C₄×Dic₁₃	—	4	2	no	—
122	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂×#1055	C₂×D₄	1	1	yes	characteristic
124	C₂×#1055	C₂×D₄	1	1	yes	characteristic
125	Dic₅₂	—	2	2	no	—
126	Dic₅₂	—	2	2	no	—
127	C₈×D₁₃	—	2	1	no	—
128	C₈×D₁₃	—	2	1	no	—
129	C₁₃×C₁₆	—	2	1	no	—
130	C₁₃×C₁₆	C₂×D₄	1	2	yes	—
131	#6090	—	2	1	no	—
132	#6090	—	2	1	no	—
133	C₂²×Q₃₂	—	13	1	no	—
134	C₂²×Q₃₂	D₁₃	1	1	yes	characteristic, complemented
135	D₄×Q₁₆	—	13	2	no	—
136	#2247	—	13	1	no	—
137	#2216	—	13	1	no	—
138	#2216	—	13	1	no	—
139	#2209	—	13	2	no	—
140	#2188	—	13	2	no	—
141	#2188	—	13	2	no	—
142	C₄×Q₃₂	—	13	1	no	—
143	D₄×C₁₆	—	13	1	no	—
144	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
145	C₂²×D₁₃	C₂×D₈	1	1	yes	characteristic
146	Q₈×C₁₃	—	2	4	no	—
147	Q₈×C₁₃	—	4	2	no	—
148	Q₈×C₁₃	—	4	2	no	—
149	Q₈×C₁₃	—	4	2	no	—
150	Q₈×C₁₃	—	8	4	no	—
151	C₂×C₄×C₁₃	—	2	1	no	—
152	C₂×C₄×C₁₃	—	2	1	no	—
153	C₂×C₄×C₁₃	—	4	2	no	—
154	C₂×C₄×C₁₃	—	4	2	no	—
155	C₂×C₄×C₁₃	—	8	4	no	—
156	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
157	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
158	C₂²⋊D₁₃	Q₃₂	1	4	yes	direct product factor
159	C₂×Dic₁₃	—	4	2	no	—
160	C₂×Dic₁₃	—	4	2	no	—
161	C₂×Dic₁₃	C₂×D₈	1	1	yes	characteristic
162	C₂×Dic₁₃	C₂×D₈	1	1	yes	characteristic
163	C₂×Dic₁₃	C₂×D₈	1	1	yes	characteristic
164	C₄×D₁₃	—	2	1	no	—
165	C₄×D₁₃	—	2	1	no	—
166	C₄×D₁₃	—	8	4	no	—
167	Dic₂₆	—	4	2	no	—
168	Dic₂₆	—	4	2	no	—
169	Dic₂₆	—	8	4	no	—
170	C₈×C₁₃	—	2	1	no	—
171	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
172	C₈×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
173	#1055	—	2	1	no	—
174	#1055	—	2	1	no	—
175	C₂²×Q₁₆	—	13	2	no	—
176	C₂²×Q₁₆	C₂×D₁₃	1	2	yes	—
177	D₄×Q₈	—	26	2	no	—
178	C₂×Q₃₂	—	2	4	no	—
179	C₂×Q₃₂	—	13	2	no	—
180	C₂×Q₃₂	—	13	2	no	—
181	C₂×Q₃₂	—	13	1	no	—
182	C₂×Q₃₂	—	26	4	no	—
183	C₂×Q₃₂	C₂×D₁₃	1	2	yes	—
184	C₂×Q₃₂	C₂×D₁₃	1	1	yes	characteristic
185	C₂×Q₃₂	C₂×D₁₃	1	1	yes	characteristic
186	C₂²×C₁₆	—	13	1	no	—
187	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
188	#494	—	13	2	no	—
189	#467	—	13	2	no	—
190	#467	—	13	2	no	—
191	#462	—	26	2	no	—
192	#451	—	26	2	no	—
193	#451	—	26	2	no	—
194	C₄×Q₁₆	—	13	2	no	—
195	C₈×D₄	—	13	1	no	—
196	#366	—	13	1	no	—
197	C₄⋊C₁₆	—	13	1	no	—
198	#358	—	13	2	no	—
199	#358	—	13	2	no	—
200	#358	—	13	2	no	—
201	C₂²⋊C₁₆	—	13	1	no	—
202	C₂²⋊C₁₆	—	13	1	no	—
203	C₄×C₁₆	—	13	1	no	—
204	C₂²×C₁₃	—	2	1	no	—
205	C₂²×C₁₃	—	2	1	no	—
206	C₂²×C₁₃	C₂×Q₃₂	1	2	yes	complemented
207	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
208	C₂×D₁₃	—	2	1	no	—
209	C₂×D₁₃	—	2	1	no	—
210	C₂×D₁₃	C₂×Q₃₂	1	2	yes	complemented
211	C₄×C₁₃	—	2	1	no	—
212	C₄×C₁₃	—	4	4	no	—
213	C₄×C₁₃	—	8	2	no	—
214	C₄×C₁₃	D₄²	1	1	yes	characteristic
215	C₄×C₁₃	#576	1	1	yes	characteristic
216	Dic₁₃	—	2	1	no	—
217	Dic₁₃	—	2	1	no	—
218	Dic₁₃	—	8	2	no	—
219	Dic₁₃	—	8	2	no	—
220	Dic₁₃	C₂×Q₃₂	1	2	yes	complemented
221	C₂²×Q₈	—	2	2	no	—
222	C₂²×Q₈	—	26	2	no	—
223	C₂×Q₁₆	—	2	4	no	—
224	C₂×Q₁₆	—	2	2	no	—
225	C₂×Q₁₆	—	4	2	no	—
226	C₂×Q₁₆	—	13	2	no	—
227	C₂×Q₁₆	—	26	2	no	—
228	C₂×Q₁₆	—	26	2	no	—
229	C₂×Q₁₆	—	26	4	no	—
230	C₂×Q₁₆	—	52	2	no	—
231	C₂×Q₁₆	C₂²×D₁₃	1	2	yes	—
232	C₂×Q₁₆	C₂²×D₁₃	1	2	yes	—
233	C₂²×C₈	—	13	1	no	—
234	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
235	C₄⋊Q₈	—	26	2	no	—
236	C₄⋊Q₈	—	52	2	no	—
237	C₂²⋊Q₈	—	26	2	no	—
238	C₂²⋊Q₈	—	26	2	no	—
239	C₂²⋊Q₈	—	52	2	no	—
240	C₂²⋊Q₈	—	52	2	no	—
241	C₄×Q₈	—	26	2	no	—
242	C₄×D₄	—	13	1	no	—
243	C₄×D₄	—	52	2	no	—
244	Q₃₂	—	2	4	no	—
245	Q₃₂	—	2	2	no	—
246	Q₃₂	—	26	4	no	—
247	Q₃₂	—	26	2	no	—
248	Q₃₂	—	52	2	no	—
249	Q₃₂	C₂²⋊D₁₃	1	4	yes	direct product factor
250	C₂×C₁₆	—	2	2	no	—
251	C₂×C₁₆	—	13	1	no	—
252	C₂×C₁₆	—	13	1	no	—
253	C₂×C₁₆	—	26	2	no	—
254	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
255	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
256	#107	—	13	2	no	—
257	C₄⋊C₈	—	13	1	no	—
258	#103	—	26	2	no	—
259	#103	—	26	2	no	—
260	#103	—	26	2	no	—
261	C₂²⋊C₈	—	13	1	no	—
262	C₂²⋊C₈	—	13	1	no	—
263	C₄×C₈	—	13	1	no	—
264	C₂×C₁₃	—	2	2	no	—
265	C₂×C₁₃	D₄×D₈	1	1	yes	characteristic
266	C₂×C₁₃	C₂²×Q₃₂	1	1	yes	characteristic
267	C₂×C₁₃	#3417	1	1	yes	characteristic
268	D₁₃	—	2	2	no	—
269	C₂×Q₈	—	2	2	no	—
270	C₂×Q₈	—	2	2	no	—
271	C₂×Q₈	—	4	4	no	—
272	C₂×Q₈	—	4	2	no	—
273	C₂×Q₈	—	8	2	no	—
274	C₂×Q₈	—	26	2	no	—
275	C₂×Q₈	—	52	2	no	—
276	C₂×Q₈	—	52	4	no	—
277	C₂×Q₈	—	104	2	no	—
278	C₂×D₄	—	13	1	no	—
279	C₂²×C₄	—	4	2	no	—
280	C₂²×C₄	—	13	1	no	—
281	C₂²×C₄	—	52	2	no	—
282	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
283	Q₁₆	—	2	2	no	—
284	Q₁₆	—	2	2	no	—
285	Q₁₆	—	2	2	no	—
286	Q₁₆	—	4	4	no	—
287	Q₁₆	—	26	2	no	—
288	Q₁₆	—	26	2	no	—
289	Q₁₆	—	52	4	no	—
290	Q₁₆	—	104	2	no	—
291	Q₁₆	C₂×C₂²⋊D₁₃	1	4	yes	—
292	C₂×C₈	—	2	1	no	—
293	C₂×C₈	—	2	1	no	—
294	C₂×C₈	—	13	1	no	—
295	C₂×C₈	—	13	1	no	—
296	C₂×C₈	—	26	1	no	—
297	C₂×C₈	—	26	1	no	—
298	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
299	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
300	C₄⋊C₄	—	13	1	no	—
301	C₄⋊C₄	—	26	2	no	—
302	C₄⋊C₄	—	52	2	no	—
303	C₄⋊C₄	—	52	2	no	—
304	C₄⋊C₄	—	52	2	no	—
305	C₄⋊C₄	—	52	2	no	—
306	C₄⋊C₄	—	52	2	no	—
307	C₂²⋊C₄	—	13	1	no	—
308	C₂²⋊C₄	—	13	1	no	—
309	C₂²⋊C₄	—	52	2	no	—
310	C₂²⋊C₄	—	52	2	no	—
311	C₄²	—	13	1	no	—
312	C₄²	—	52	2	no	—
313	C₁₆	—	2	1	no	—
314	C₁₆	—	26	1	no	—
315	C₁₆	—	26	1	no	—
316	C₁₆	C₂×C₂²⋊D₁₃	1	2	yes	—
317	C₁₃	D₄×Q₃₂	1	1	yes	characteristic, complemented, Sylow
318	C₂³	—	13	1	no	—
319	C₂³	D₈×D₁₃	1	1	yes	characteristic
320	Q₈	—	2	4	no	—
321	Q₈	—	4	2	no	—
322	Q₈	—	4	2	no	—
323	Q₈	—	4	2	no	—
324	Q₈	—	8	4	no	—
325	Q₈	—	52	2	no	—
326	Q₈	—	52	2	no	—
327	Q₈	—	104	4	no	—
328	D₄	—	13	4	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	8	4	no	—
334	C₂×C₄	—	13	1	no	—
335	C₂×C₄	—	13	1	no	—
336	C₂×C₄	—	13	1	no	—
337	C₂×C₄	—	26	1	no	—
338	C₂×C₄	—	26	1	no	—
339	C₂×C₄	—	52	2	no	—
340	C₂×C₄	—	52	2	no	—
341	C₂×C₄	—	104	4	no	—
342	C₂×C₄	D₈×D₁₃	1	1	yes	characteristic
343	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
344	C₈	—	2	1	no	—
345	C₈	—	26	1	no	—
346	C₈	—	26	1	no	—
347	C₈	#88251	1	1	yes	characteristic
348	C₈	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	13	2	no	—
352	C₂²	—	26	1	no	—
353	C₂²	—	26	1	no	—
354	C₂²	D₁₃×Q₃₂	1	2	yes	complemented
355	C₂²	C₂×D₈×D₁₃	1	1	yes	characteristic
356	C₄	—	2	1	no	—
357	C₄	—	4	4	no	—
358	C₄	—	8	2	no	—
359	C₄	—	13	2	no	—
360	C₄	—	26	1	no	—
361	C₄	—	26	1	no	—
362	C₄	—	104	2	no	—
363	C₄	—	104	2	no	—
364	C₄	#11719462	1	1	yes	characteristic
365	C₄	D₄×C₂²⋊D₁₃	1	1	yes	characteristic
366	C₂	—	2	2	no	—
367	C₂	—	26	2	no	—
368	C₂	D₈×C₂²⋊D₁₃	1	1	yes	characteristic
369	C₂	C₂×D₁₃×Q₃₂	1	1	yes	characteristic
370	C₂	#13127985	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₈×D₁₃
commutator, cosocle	C₂×C₈×C₁₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂²×C₁₃×Q₃₂	C₂
socle	C₂²×C₁₃	C₂²×D₈
prime radical	C₂×C₂²⋊D₁₃	D₈
hypercenter	C₂²×Q₃₂	D₁₃
hypocenter	C₁₃	D₄×Q₃₂
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₃₂

Complements

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

N	H ≅ G/N	type
1. C₂×D₁₃×Q₃₂	C₂	semidirect
3. #13117087	C₂	semidirect
4. #13116927	C₂	semidirect
5. #13116924	C₂	semidirect
6. #13116884	C₂	semidirect
7. #13116770	C₂	semidirect
8. #13116768	C₂	semidirect
9. Q₃₂×Dic₁₃	C₂	semidirect
11. C₂²×C₁₃×Q₃₂	C₂	semidirect
66. C₁₃×Q₃₂	D₄	semidirect
134. C₂²×Q₃₂	D₁₃	semidirect
158. C₂²⋊D₁₃	Q₃₂	direct (N × H)
206. C₂²×C₁₃	C₂×Q₃₂	semidirect
210. C₂×D₁₃	C₂×Q₃₂	semidirect
220. Dic₁₃	C₂×Q₃₂	semidirect
249. Q₃₂	C₂²⋊D₁₃	direct (N × H)
317. C₁₃	D₄×Q₃₂	semidirect
354. C₂²	D₁₃×Q₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₃×Q₃₂	2
Q₁₆×C₂²⋊D₁₃	2
#13117087	2
#13116927	2
#13116924	2
#13116884	2
#13116770	2
#13116768	2
Q₃₂×Dic₁₃	2
C₁₆×C₂²⋊D₁₃	2
C₂²×C₁₃×Q₃₂	2
D₄×Q₃₂	13

Subgroups — Q32×C22⋊D13 #16019643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₃₂×C₂²⋊D₁₃ #16019643