Subgroups — C₄×D₁₃⋊#108 #16797210

Order 3328.

1086 conjugacy classes of subgroups.

The subgroup lattice has 344 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	C₄×D₁₃⋊M₁₆	C₂	1	2	yes	maximal
3	C₄×#88104	C₂	1	4	yes	maximal, complemented
4	C₄×#88103	C₂	1	4	yes	maximal, complemented
5	#13130528	C₂	1	2	yes	maximal
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	1	yes	characteristic
9	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
11	C₄×#6122	—	2	4	no	—
12	D₁₃⋊#108	C₄	1	16	yes	direct product factor
13	C₂×#88104	C₂²	1	4	yes	—
14	C₂×#88103	C₂²	1	4	yes	—
15	C₄×#6118	C₂²	1	8	yes	—
16	#11719047	—	2	2	no	—
17	C₄×D₁₃⋊C₈	—	2	2	no	—
18	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
19	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
20	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
21	C₂×C₄×#1055	C₄	1	1	yes	characteristic
22	C₄×C₈×D₁₃	C₄	1	2	yes	—
23	C₄×C₈×D₁₃	C₄	1	2	yes	—
24	C₄×C₈×D₁₃	C₂²	1	2	yes	—
25	C₄×C₈×D₁₃	C₂²	1	2	yes	—
26	#11718268	C₂²	1	8	yes	—
27	C₂²×C₄×D₁₃	Q₈	1	2	yes	—
28	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
29	C₂×#6122	—	2	4	no	—
30	D₁₃⋊M₁₆	—	2	8	no	—
31	D₁₃⋊M₁₆	C₂×C₄	1	16	yes	—
32	C₂×#6118	C₂³	1	8	yes	—
33	C₂×D₁₃⋊C₈	—	2	4	no	—
34	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄×Dic₁₃	D₄	1	2	yes	—
39	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
40	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
41	C₂×C₈×D₁₃	—	2	4	no	—
42	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
43	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₈×D₁₃	C₂×C₄	1	8	yes	—
46	C₂×C₈×D₁₃	C₂³	1	2	yes	—
47	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
48	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
49	C₄²×D₁₃	C₂×C₄	1	2	yes	—
50	C₄²×D₁₃	D₄	1	1	yes	characteristic
51	C₄²×D₁₃	D₄	1	1	yes	characteristic
52	C₄²×D₁₃	Q₈	1	1	yes	characteristic
53	C₄²×D₁₃	Q₈	1	1	yes	characteristic
54	C₄²×D₁₃	C₂³	1	2	yes	—
55	#88110	—	2	8	no	—
56	C₄×#1057	—	2	8	no	—
57	#88104	C₂×C₄	1	16	yes	complemented
58	#88103	C₂×C₄	1	16	yes	complemented
59	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
60	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
61	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
62	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
63	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
64	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
65	C₄×#1055	C₂×C₄	1	2	yes	—
66	C₄×#1055	C₂×C₄	1	2	yes	—
67	C₂×C₄×#108	—	13	1	no	maximal, Sylow
68	C₂³×D₁₃	C₂×Q₈	1	1	yes	characteristic
69	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
70	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
71	C₂²×Dic₁₃	C₄⋊C₄	1	2	yes	—
72	C₂²×Dic₁₃	C₂×D₄	1	1	yes	characteristic
73	C₂×C₄×D₁₃	—	2	8	no	—
74	C₂×C₄×D₁₃	C₄⋊C₄	1	2	yes	—
75	C₂×C₄×D₁₃	C₄⋊C₄	1	2	yes	—
76	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
77	C₂×C₄×D₁₃	C₂²×C₄	1	4	yes	—
78	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
79	C₂×C₄×D₁₃	C₂×Q₈	1	2	yes	—
80	C₂×C₄×D₁₃	C₂×Q₈	1	2	yes	—
81	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
82	C₂×C₄×D₁₃	#41	1	4	yes	—
83	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
84	#6122	—	2	16	no	—
85	C₂×#1057	—	2	8	no	—
86	#6118	—	2	8	no	—
87	#6118	C₂²×C₄	1	16	yes	—
88	D₁₃⋊C₈	—	2	16	no	—
89	C₂×C₈×C₁₃	—	2	2	no	—
90	C₂×C₈×C₁₃	C₄²	1	4	yes	—
91	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
92	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
94	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
95	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
96	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
97	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
98	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
99	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
100	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
101	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
102	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
103	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
104	C₂×#1055	—	2	2	no	—
105	C₂×#1055	C₄²	1	4	yes	—
106	C₂×#1055	C₂²×C₄	1	2	yes	—
107	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
108	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
109	C₈×D₁₃	—	2	4	no	—
110	C₈×D₁₃	—	2	4	no	—
111	C₈×D₁₃	C₄²	1	4	yes	—
112	C₈×D₁₃	C₄²	1	4	yes	—
113	C₈×D₁₃	C₂²×C₄	1	4	yes	—
114	C₈×D₁₃	C₂²×C₄	1	4	yes	—
115	C₂²×#108	—	13	2	no	—
116	C₂×C₄×M₁₆	—	13	2	no	—
117	C₂²×C₄×C₈	—	13	1	no	—
118	C₄×#108	—	13	4	no	—
119	C₄×#108	—	13	4	no	—
120	C₂×#341	—	13	2	no	—
121	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
122	C₂²×D₁₃	—	2	4	no	—
123	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
124	C₂²×D₁₃	C₄×Q₈	1	4	yes	—
125	C₂²×D₁₃	C₂²×Q₈	1	1	yes	characteristic
126	C₂×C₄×C₁₃	—	2	4	no	—
127	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
128	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
129	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
131	C₂×C₄×C₁₃	#117	1	2	yes	—
132	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
133	C₂×Dic₁₃	—	2	4	no	—
134	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
135	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
137	C₂×Dic₁₃	C₄×D₄	1	4	yes	—
138	C₂×Dic₁₃	C₂²×D₄	1	1	yes	characteristic
139	C₄×D₁₃	—	2	4	no	—
140	C₄×D₁₃	—	2	4	no	—
141	C₄×D₁₃	—	2	4	no	—
142	C₄×D₁₃	#108	1	8	yes	complemented
143	C₄×D₁₃	C₂×C₄²	1	2	yes	—
144	C₄×D₁₃	#117	1	2	yes	—
145	C₄×D₁₃	C₄×D₄	1	4	yes	—
146	C₄×D₁₃	C₄×Q₈	1	4	yes	—
147	C₄×D₁₃	C₂³×C₄	1	2	yes	—
148	C₄×D₁₃	C₂×#41	1	2	yes	—
149	#1057	—	2	16	no	—
150	C₈×C₁₃	—	2	2	no	—
151	C₈×C₁₃	C₂×C₄²	1	2	yes	—
152	C₈×C₁₃	C₂×C₄²	1	2	yes	—
153	#1055	—	2	2	no	—
154	#1055	C₂×C₄²	1	2	yes	—
155	#1055	C₂×C₄²	1	2	yes	—
156	C₂²×M₁₆	—	13	4	no	—
157	C₂³×C₈	—	13	1	no	—
158	C₂³×C₈	—	13	1	no	—
159	C₂²×C₄²	—	13	1	no	—
160	C₂×#108	—	13	4	no	—
161	C₂×#108	—	13	4	no	—
162	C₂×#108	—	13	16	no	—
163	C₄×M₁₆	—	13	8	no	—
164	C₄×M₁₆	—	26	4	no	—
165	C₂×#97	—	26	2	no	—
166	C₂×C₄×C₈	—	13	1	no	—
167	C₂×C₄×C₈	—	13	1	no	—
168	C₂×C₄×C₈	—	13	1	no	—
169	C₂×C₄×C₈	—	13	2	no	—
170	C₂×C₄×C₈	—	13	2	no	—
171	C₂×C₄×C₈	—	13	2	no	—
172	C₂×C₄×C₈	—	13	2	no	—
173	C₂×C₄×C₈	—	26	2	no	—
174	C₂×C₄×C₈	#261	1	1	yes	characteristic
175	#341	—	13	8	no	—
176	C₂²×C₁₃	—	2	2	no	—
177	C₂²×C₁₃	C₄×C₄⋊C₄	1	2	yes	—
178	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
179	C₂×D₁₃	—	2	2	no	—
180	C₂×D₁₃	—	2	8	no	—
181	C₂×D₁₃	C₄×C₄⋊C₄	1	2	yes	—
182	C₂×D₁₃	C₂×#108	1	4	yes	—
183	C₂×D₁₃	C₂×C₄×Q₈	1	2	yes	—
184	C₄×C₁₃	—	2	2	no	—
185	C₄×C₁₃	C₄×C₄⋊C₄	1	2	yes	—
186	C₄×C₁₃	C₂×#108	1	4	yes	complemented
187	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
188	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
189	Dic₁₃	—	2	2	no	—
190	Dic₁₃	C₄×C₄⋊C₄	1	2	yes	—
191	Dic₁₃	C₂×#108	1	4	yes	complemented
192	Dic₁₃	C₂×C₄×D₄	1	2	yes	—
193	C₂³×C₄	—	13	1	no	—
194	C₂³×C₄	—	13	2	no	—
195	C₂×M₁₆	—	13	8	no	—
196	C₂×M₁₆	—	13	16	no	—
197	C₂×M₁₆	—	26	4	no	—
198	C₂×M₁₆	—	26	8	no	—
199	C₂²×C₈	—	13	1	no	—
200	C₂²×C₈	—	13	8	no	—
201	C₂²×C₈	—	13	1	no	—
202	C₂²×C₈	—	13	1	no	—
203	C₂²×C₈	—	13	1	no	—
204	C₂²×C₈	—	13	1	no	—
205	C₂²×C₈	—	13	1	no	—
206	C₂²×C₈	—	13	2	no	—
207	C₂²×C₈	—	13	2	no	—
208	C₂²×C₈	—	26	4	no	—
209	C₂²×C₈	—	26	4	no	—
210	C₂²×C₈	C₂×#261	1	1	yes	characteristic
211	C₂²×C₈	C₂×#261	1	1	yes	characteristic
212	C₂×C₄²	—	13	2	no	—
213	C₂×C₄²	—	13	1	no	—
214	C₂×C₄²	—	13	1	no	—
215	C₂×C₄²	—	13	1	no	—
216	C₂×C₄²	—	13	1	no	—
217	C₂×C₄²	—	13	1	no	—
218	C₂×C₄²	—	13	2	no	—
219	C₂×C₄²	—	13	2	no	—
220	C₂×C₄²	C₂×#261	1	1	yes	characteristic
221	#108	—	13	16	no	—
222	#108	—	13	16	no	—
223	#97	—	26	8	no	—
224	C₄×C₈	—	13	2	no	—
225	C₄×C₈	—	13	2	no	—
226	C₄×C₈	—	13	2	no	—
227	C₄×C₈	—	13	2	no	—
228	C₄×C₈	—	13	2	no	—
229	C₄×C₈	—	13	2	no	—
230	C₄×C₈	—	26	8	no	—
231	C₄×C₈	C₂×#261	1	2	yes	—
232	C₄×C₈	C₂×#261	1	2	yes	—
233	C₂×C₁₃	—	2	2	no	—
234	C₂×C₁₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
235	C₂×C₁₃	C₂²×#108	1	2	yes	—
236	D₁₃	—	2	2	no	—
237	D₁₃	C₄×#108	1	4	yes	complemented
238	C₂⁴	—	13	1	no	—
239	C₂²×C₄	—	13	1	no	—
240	C₂²×C₄	—	13	4	no	—
241	C₂²×C₄	—	13	1	no	—
242	C₂²×C₄	—	13	2	no	—
243	C₂²×C₄	—	13	1	no	—
244	C₂²×C₄	—	13	4	no	—
245	C₂²×C₄	—	13	1	no	—
246	C₂²×C₄	—	13	1	no	—
247	C₂²×C₄	—	13	2	no	—
248	C₂²×C₄	—	13	2	no	—
249	C₂²×C₄	—	13	2	no	—
250	C₂²×C₄	—	13	2	no	—
251	C₂²×C₄	—	26	8	no	—
252	C₂²×C₄	C₄⋊#261	1	2	yes	—
253	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
254	M₁₆	—	13	16	no	—
255	M₁₆	—	26	8	no	—
256	M₁₆	—	26	16	no	—
257	C₂×C₈	—	2	2	no	—
258	C₂×C₈	—	13	4	no	—
259	C₂×C₈	—	13	1	no	—
260	C₂×C₈	—	13	1	no	—
261	C₂×C₈	—	13	4	no	—
262	C₂×C₈	—	13	4	no	—
263	C₂×C₈	—	13	4	no	—
264	C₂×C₈	—	13	4	no	—
265	C₂×C₈	—	13	2	no	—
266	C₂×C₈	—	26	4	no	—
267	C₂×C₈	—	26	4	no	—
268	C₂×C₈	—	26	8	no	—
269	C₂×C₈	—	26	16	no	—
270	C₂×C₈	—	26	2	no	—
271	C₂×C₈	C₄×#261	1	4	yes	—
272	C₂×C₈	C₂²×#261	1	2	yes	—
273	C₂×C₈	C₂²×#261	1	1	yes	characteristic
274	C₂×C₈	C₂²×#261	1	1	yes	characteristic
275	C₄²	—	13	2	no	—
276	C₄²	—	13	2	no	—
277	C₄²	—	13	2	no	—
278	C₄²	—	13	1	no	—
279	C₄²	—	13	2	no	—
280	C₄²	—	13	1	no	—
281	C₄²	—	13	2	no	—
282	C₄²	C₄⋊#261	1	1	yes	characteristic
283	C₄²	C₄⋊#261	1	1	yes	characteristic
284	C₄²	C₂²×#261	1	2	yes	—
285	C₁₃	C₂×C₄×#108	1	1	yes	characteristic, complemented, Sylow
286	C₂³	—	13	1	no	—
287	C₂³	—	13	4	no	—
288	C₂³	—	13	1	no	—
289	C₂³	—	26	4	no	—
290	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
291	C₂×C₄	—	2	4	no	—
292	C₂×C₄	—	13	4	no	—
293	C₂×C₄	—	13	1	no	—
294	C₂×C₄	—	13	1	no	—
295	C₂×C₄	—	13	2	no	—
296	C₂×C₄	—	13	4	no	—
297	C₂×C₄	—	13	4	no	—
298	C₂×C₄	—	13	8	no	—
299	C₂×C₄	—	13	2	no	—
300	C₂×C₄	—	13	2	no	—
301	C₂×C₄	—	13	2	no	—
302	C₂×C₄	—	13	2	no	—
303	C₂×C₄	—	13	2	no	—
304	C₂×C₄	—	26	4	no	—
305	C₂×C₄	—	26	4	no	—
306	C₂×C₄	—	26	4	no	—
307	C₂×C₄	—	26	4	no	—
308	C₂×C₄	C₂×C₄×#261	1	2	yes	—
309	C₂×C₄	C₂×C₄⋊#261	1	2	yes	—
310	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
311	C₂×C₄	C₂×C₄⋊#261	1	2	yes	—
312	C₂×C₄	#88237	1	2	yes	—
313	C₂×C₄	C₂³×#261	1	1	yes	characteristic
314	C₈	—	2	2	no	—
315	C₈	—	13	2	no	—
316	C₈	—	13	2	no	—
317	C₈	—	26	16	no	—
318	C₈	—	26	2	no	—
319	C₈	C₂×C₄×#261	1	2	yes	—
320	C₈	C₂×C₄×#261	1	2	yes	—
321	C₂²	—	2	2	no	—
322	C₂²	—	13	2	no	—
323	C₂²	—	13	4	no	—
324	C₂²	—	13	2	no	—
325	C₂²	—	26	8	no	—
326	C₂²	—	26	2	no	—
327	C₂²	C₄×C₄⋊#261	1	2	yes	—
328	C₂²	C₂²×C₄⋊#261	1	1	yes	characteristic
329	C₄	—	2	2	no	—
330	C₄	—	13	2	no	—
331	C₄	—	13	2	no	—
332	C₄	—	13	4	no	—
333	C₄	—	26	2	no	—
334	C₄	C₄×C₄⋊#261	1	2	yes	—
335	C₄	D₁₃⋊#108	1	4	yes	direct product factor
336	C₄	C₂²×C₄×#261	1	1	yes	characteristic
337	C₄	C₂×#88237	1	1	yes	characteristic
338	C₂	—	2	2	no	—
339	C₂	—	13	4	no	—
340	C₂	—	26	2	no	—
341	C₂	C₂×C₄×C₄⋊#261	1	1	yes	characteristic
342	C₂	C₂×D₁₃⋊#108	1	2	yes	—

	subgroup	G/H
center	C₄²	C₄⋊#261
commutator	C₄×C₁₃	C₂²×C₄²
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×C₄×#108
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
3. C₄×#88104	C₂	semidirect
4. C₄×#88103	C₂	semidirect
12. D₁₃⋊#108	C₄	direct (N × H)
57. #88104	C₂×C₄	semidirect
58. #88103	C₂×C₄	semidirect
142. C₄×D₁₃	#108	semidirect
186. C₄×C₁₃	C₂×#108	semidirect
191. Dic₁₃	C₂×#108	semidirect
237. D₁₃	C₄×#108	semidirect
285. C₁₃	C₂×C₄×#108	semidirect
335. C₄	D₁₃⋊#108	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
C₄×D₁₃⋊M₁₆	2
C₄×#88104	2
C₄×#88103	2
#13130528	2
C₂×C₄×C₈×D₁₃	2
C₂×C₄×#108	13

Subgroups — C4×D13⋊#108 #16797210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₁₃⋊#108 #16797210