Subgroups — C₄×#11718840 #16016248

Order 3328.

674 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718840	C₂	1	1	yes	maximal, characteristic
2	C₄×#88158	C₂	1	1	yes	maximal, characteristic
3	#13116705	C₂	1	2	yes	maximal, complemented
4	#13116698	C₂	1	2	yes	maximal, complemented
5	C₄×#88069	C₂	1	2	yes	maximal, complemented
6	C₄×#88068	C₂	1	2	yes	maximal, complemented
7	#13116622	C₂	1	1	yes	maximal, characteristic, complemented
8	#13116556	C₂	1	1	yes	maximal, characteristic, complemented
9	#13116546	C₂	1	1	yes	maximal, characteristic
10	C₄×#88052	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
14	C₂×#88158	C₂²	1	1	yes	characteristic
15	C₄×#6127	—	2	1	no	—
16	C₄×C₁₃×Q₁₆	—	2	1	no	—
17	C₄×C₁₃×Q₁₆	—	2	1	no	—
18	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
19	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
20	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#103	—	2	1	no	—
22	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×#88069	C₂²	1	2	yes	—
24	#11718840	C₄	1	8	yes	direct product factor
25	C₂×#88068	C₂²	1	2	yes	—
26	#11718774	—	2	1	no	—
27	#11718767	C₂²	1	1	yes	characteristic
28	C₂×#88052	C₂²	1	1	yes	characteristic
29	C₂×#88052	C₂²	1	1	yes	characteristic
30	C₄×Dic₅₂	C₂²	1	1	yes	characteristic
31	C₄×Dic₅₂	C₂²	1	1	yes	characteristic
32	C₄×D₁₀₄	C₂²	1	1	yes	characteristic
33	C₄×D₁₀₄	C₂²	1	1	yes	characteristic
34	C₄×#6095	—	2	1	no	—
35	C₄×#6095	—	2	1	no	—
36	#11718156	C₂²	1	2	yes	—
37	#11718156	C₂²	1	2	yes	—
38	#11718084	C₂²	1	2	yes	—
39	#11718083	C₂²	1	2	yes	—
40	#11718082	C₂²	1	2	yes	—
41	#11718081	C₂²	1	2	yes	—
42	#11718053	C₂²	1	2	yes	—
43	C₄×#6090	C₂²	1	2	yes	—
44	C₂²×Q₈×C₁₃	—	2	1	no	—
45	C₂×#6127	—	2	1	no	—
46	C₂×C₁₃×Q₁₆	—	2	1	no	—
47	C₂×C₁₃×Q₁₆	—	2	2	no	—
48	C₂×C₁₃×Q₁₆	C₂×C₄	1	4	yes	complemented
49	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₄×Q₈×C₁₃	—	2	2	no	—
53	C₄×Q₈×C₁₃	—	2	2	no	—
54	C₄×Q₈×C₁₃	—	4	1	no	—
55	C₄×Q₈×C₁₃	—	4	1	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
58	C₂×C₄²×C₁₃	—	4	1	no	—
59	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
60	C₄×C₂²⋊D₁₃	—	4	1	no	—
61	C₄×C₂²⋊D₁₃	—	4	1	no	—
62	#88180	—	2	1	no	—
63	C₂×Dic₅₂	C₂³	1	1	yes	characteristic
64	#88158	—	2	2	no	—
65	#88158	C₂×C₄	1	4	yes	—
66	C₂×D₁₀₄	C₂³	1	1	yes	characteristic
67	C₂×#6095	—	2	1	no	—
68	C₄×D₅₂	—	2	1	no	—
69	C₄×D₅₂	—	2	1	no	—
70	#88126	—	4	1	no	—
71	C₄²×D₁₃	—	4	1	no	—
72	C₄×Dic₂₆	—	2	1	no	—
73	C₄×Dic₂₆	—	2	1	no	—
74	C₁₃×#107	—	2	1	no	—
75	C₁₃×#107	C₂³	1	2	yes	—
76	C₁₃×#103	—	2	2	no	—
77	C₁₃×#103	—	2	2	no	—
78	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
79	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
80	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	#88069	C₂×C₄	1	8	yes	complemented
83	#88068	C₂×C₄	1	8	yes	complemented
84	#88061	—	2	1	no	—
85	#88061	—	2	1	no	—
86	#88058	C₂³	1	1	yes	characteristic
87	#88058	C₂³	1	1	yes	characteristic
88	#88057	—	2	1	no	—
89	#88056	—	2	1	no	—
90	#88056	—	2	1	no	—
91	#88052	—	2	2	no	—
92	#88052	C₂×C₄	1	4	yes	complemented
93	C₂×#6090	C₂³	1	2	yes	—
94	C₂×#6090	C₂³	1	2	yes	—
95	C₄×#510	—	13	1	no	maximal, Sylow
96	C₂×Q₈×C₁₃	—	2	4	no	—
97	C₂×Q₈×C₁₃	—	2	2	no	—
98	C₂×Q₈×C₁₃	—	4	1	no	—
99	C₂×Q₈×C₁₃	—	4	2	no	—
100	C₂²×C₄×C₁₃	—	4	1	no	—
101	C₂²×C₄×C₁₃	—	4	1	no	—
102	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂×C₂²⋊D₁₃	—	4	1	no	—
106	#6127	—	2	4	no	—
107	#6127	—	4	2	no	—
108	C₂×D₅₂	—	2	1	no	—
109	C₂×C₄×D₁₃	—	4	1	no	—
110	C₂×C₄×D₁₃	—	4	1	no	—
111	C₂×C₄×D₁₃	—	4	1	no	—
112	C₂×Dic₂₆	—	2	1	no	—
113	C₁₃×Q₁₆	—	2	4	no	—
114	C₁₃×Q₁₆	—	2	2	no	—
115	C₁₃×Q₁₆	C₂²×C₄	1	4	yes	—
116	C₂×C₈×C₁₃	—	2	2	no	—
117	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₁₃	#41	1	2	yes	—
122	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
123	C₁₃×C₄⋊C₄	—	2	2	no	—
124	C₁₃×C₄⋊C₄	—	4	1	no	—
125	C₁₃×C₄⋊C₄	—	4	2	no	—
126	C₁₃×C₄⋊C₄	—	4	2	no	—
127	C₄²×C₁₃	—	4	2	no	—
128	C₄²×C₁₃	—	4	2	no	—
129	C₄²×C₁₃	D₈	1	1	yes	characteristic
130	C₄²×C₁₃	D₈	1	1	yes	characteristic
131	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²⋊Dic₁₃	—	4	1	no	—
134	#6103	—	4	1	no	—
135	#6103	—	4	1	no	—
136	C₄⋊Dic₁₃	—	2	1	no	—
137	C₄⋊Dic₁₃	—	2	1	no	—
138	#6101	—	4	1	no	—
139	#6101	—	4	1	no	—
140	C₄×Dic₁₃	—	4	1	no	—
141	C₄×Dic₁₃	—	4	1	no	—
142	C₄×Dic₁₃	—	4	1	no	—
143	Dic₅₂	—	2	1	no	—
144	Dic₅₂	C₂²×C₄	1	2	yes	—
145	D₁₀₄	—	2	1	no	—
146	D₁₀₄	C₂²×C₄	1	2	yes	—
147	#6095	—	2	4	no	—
148	#6090	—	2	2	no	—
149	#6090	C₂²×C₄	1	4	yes	—
150	C₂×#510	—	13	1	no	—
151	C₄×#135	—	13	1	no	—
152	C₂×C₄×Q₁₆	D₁₃	1	1	yes	characteristic, complemented
153	#2176	—	13	2	no	—
154	#2175	—	13	2	no	—
155	C₄×Q₃₂	—	13	2	no	—
156	C₄×SD₃₂	—	13	2	no	—
157	#2159	—	13	1	no	—
158	#2141	—	13	1	no	—
159	#2139	—	13	1	no	—
160	C₄×M₃₂	—	13	1	no	—
161	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
162	C₂²×D₁₃	—	4	1	no	—
163	Q₈×C₁₃	—	2	4	no	—
164	Q₈×C₁₃	—	4	2	no	—
165	Q₈×C₁₃	—	4	4	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	4	1	no	—
168	C₂×C₄×C₁₃	—	4	2	no	—
169	C₂×C₄×C₁₃	—	4	4	no	—
170	C₂×C₄×C₁₃	—	4	2	no	—
171	C₂×C₄×C₁₃	—	8	2	no	—
172	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
173	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
178	C₂×C₄×C₁₃	#135	1	2	yes	—
179	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
180	C₂²⋊D₁₃	—	4	4	no	—
181	C₂×Dic₁₃	—	4	1	no	—
182	C₂×Dic₁₃	—	4	1	no	—
183	C₂×Dic₁₃	—	4	1	no	—
184	D₅₂	—	2	2	no	—
185	D₅₂	—	4	1	no	—
186	C₄×D₁₃	—	4	4	no	—
187	C₄×D₁₃	—	8	2	no	—
188	C₄×D₁₃	—	8	2	no	—
189	Dic₂₆	—	2	2	no	—
190	Dic₂₆	—	4	1	no	—
191	C₈×C₁₃	—	2	1	no	—
192	C₈×C₁₃	—	2	1	no	—
193	C₈×C₁₃	C₄×D₄	1	2	yes	—
194	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
195	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
196	C₂×#135	—	13	1	no	—
197	C₂²×Q₁₆	C₂×D₁₃	1	1	yes	characteristic
198	C₄×#41	—	26	1	no	—
199	C₂×C₄×Q₈	—	2	1	no	—
200	#510	—	13	8	no	—
201	C₂×Q₃₂	—	13	2	no	—
202	C₂×SD₃₂	—	13	2	no	—
203	C₂×M₃₂	—	13	1	no	—
204	C₂×M₃₂	—	13	1	no	—
205	C₄×Q₁₆	—	2	1	no	—
206	C₄×Q₁₆	—	2	1	no	—
207	C₄×Q₁₆	—	13	1	no	—
208	C₄×Q₁₆	—	13	1	no	—
209	C₄×Q₁₆	C₂×D₁₃	1	2	yes	—
210	C₄×Q₁₆	C₂×D₁₃	1	2	yes	—
211	C₄×SD₁₆	—	26	1	no	—
212	C₄×SD₁₆	—	26	1	no	—
213	C₄×D₈	—	13	1	no	—
214	C₄×D₈	—	13	1	no	—
215	#427	—	13	1	no	—
216	C₂×#107	C₂×D₁₃	1	1	yes	characteristic
217	#416	—	26	1	no	—
218	C₂×#103	—	2	1	no	—
219	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
220	#367	—	13	2	no	—
221	#366	—	13	2	no	—
222	#358	—	13	2	no	—
223	#358	—	13	2	no	—
224	#358	—	13	2	no	—
225	#357	—	13	2	no	—
226	#346	—	13	2	no	—
227	C₄×C₁₆	—	13	2	no	—
228	C₂²×C₁₃	—	2	1	no	—
229	C₂²×C₁₃	—	2	1	no	—
230	C₂²×C₁₃	C₄×D₈	1	2	yes	—
231	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
232	C₂×D₁₃	—	4	2	no	—
233	C₂×D₁₃	—	8	1	no	—
234	C₂×D₁₃	—	8	1	no	—
235	C₄×C₁₃	—	2	1	no	—
236	C₄×C₁₃	—	2	1	no	—
237	C₄×C₁₃	—	2	1	no	—
238	C₄×C₁₃	—	4	4	no	—
239	C₄×C₁₃	—	8	2	no	—
240	C₄×C₁₃	C₄×D₈	1	2	yes	—
241	C₄×C₁₃	#510	1	2	yes	complemented
242	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
243	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
244	Dic₁₃	—	4	2	no	—
245	Dic₁₃	—	8	1	no	—
246	Dic₁₃	—	8	1	no	—
247	C₂×#41	—	26	1	no	—
248	C₂²×Q₈	—	2	1	no	—
249	#135	—	13	4	no	—
250	#135	—	26	2	no	—
251	C₂×Q₁₆	—	2	2	no	—
252	C₂×Q₁₆	—	2	1	no	—
253	C₂×Q₁₆	—	13	1	no	—
254	C₂×Q₁₆	C₄×D₁₃	1	4	yes	complemented
255	C₂×Q₁₆	C₂²×D₁₃	1	2	yes	—
256	C₂×SD₁₆	—	26	1	no	—
257	C₂×D₈	—	13	1	no	—
258	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
259	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
260	C₄×Q₈	—	2	2	no	—
261	C₄×Q₈	—	2	2	no	—
262	C₄×Q₈	—	4	1	no	—
263	C₄×Q₈	—	4	1	no	—
264	C₄×Q₈	—	26	1	no	—
265	C₄×Q₈	—	26	1	no	—
266	C₄×D₄	—	26	1	no	—
267	C₄×D₄	—	26	1	no	—
268	C₄×D₄	—	52	1	no	—
269	C₄×D₄	—	52	1	no	—
270	#117	—	26	1	no	—
271	#117	—	52	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	4	1	no	—
274	C₂×C₄²	—	4	1	no	—
275	C₂×C₄²	—	52	1	no	—
276	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
277	Q₃₂	—	13	8	no	—
278	SD₃₂	—	13	8	no	—
279	M₃₂	—	13	4	no	—
280	M₃₂	—	26	2	no	—
281	C₂×C₁₆	—	13	2	no	—
282	C₂×C₁₆	—	13	2	no	—
283	#107	—	2	1	no	—
284	#107	—	13	1	no	—
285	#107	—	13	1	no	—
286	#107	C₂²×D₁₃	1	2	yes	—
287	#106	—	26	1	no	—
288	#103	—	2	2	no	—
289	#103	—	2	2	no	—
290	#103	—	26	1	no	—
291	#103	—	26	1	no	—
292	#102	—	26	1	no	—
293	#102	—	26	1	no	—
294	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
295	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
296	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
297	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
298	C₂×C₁₃	—	2	2	no	—
299	C₂×C₁₃	C₂×C₄×D₈	1	1	yes	characteristic
300	C₂×C₁₃	C₂×#510	1	1	yes	characteristic
301	C₂×C₁₃	#3414	1	1	yes	characteristic
302	D₁₃	—	8	2	no	—
303	#41	—	26	4	no	—
304	#41	—	52	2	no	—
305	C₂×Q₈	—	2	4	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	4	1	no	—
308	C₂×Q₈	—	4	2	no	—
309	C₂×Q₈	—	26	1	no	—
310	C₂×D₄	—	26	1	no	—
311	C₂×D₄	—	52	1	no	—
312	C₂²×C₄	—	4	1	no	—
313	C₂²×C₄	—	4	1	no	—
314	C₂²×C₄	—	52	1	no	—
315	C₂²×C₄	—	52	1	no	—
316	C₂²×C₄	—	52	1	no	—
317	C₂²×C₄	#6104	1	1	yes	characteristic
318	C₂²×C₄	#6104	1	1	yes	characteristic
319	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
320	Q₁₆	—	2	4	no	—
321	Q₁₆	—	2	2	no	—
322	Q₁₆	—	13	2	no	—
323	Q₁₆	—	26	1	no	—
324	Q₁₆	C₂×C₄×D₁₃	1	4	yes	—
325	SD₁₆	—	26	4	no	—
326	D₈	—	13	2	no	—
327	D₈	—	26	1	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
330	C₂×C₈	#6127	1	2	yes	—
331	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
332	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
333	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
334	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	4	1	no	—
337	C₄⋊C₄	—	4	2	no	—
338	C₄⋊C₄	—	4	2	no	—
339	C₄⋊C₄	—	26	1	no	—
340	C₄⋊C₄	—	26	1	no	—
341	C₄⋊C₄	—	52	1	no	—
342	C₄⋊C₄	—	52	1	no	—
343	C₂²⋊C₄	—	52	1	no	—
344	C₂²⋊C₄	—	52	1	no	—
345	C₂²⋊C₄	—	52	1	no	—
346	C₄²	—	4	2	no	—
347	C₄²	—	4	2	no	—
348	C₄²	—	52	1	no	—
349	C₄²	—	52	1	no	—
350	C₄²	—	52	1	no	—
351	C₄²	#6104	1	1	yes	characteristic
352	C₄²	#6104	1	1	yes	characteristic
353	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
354	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
355	C₁₆	—	13	4	no	—
356	C₁₆	—	26	2	no	—
357	C₁₃	C₄×#510	1	1	yes	characteristic, complemented, Sylow
358	C₂³	—	52	1	no	—
359	C₂³	C₂×#6104	1	1	yes	characteristic
360	Q₈	—	2	4	no	—
361	Q₈	—	4	4	no	—
362	Q₈	—	4	2	no	—
363	Q₈	—	26	2	no	—
364	Q₈	—	52	1	no	—
365	D₄	—	26	2	no	—
366	D₄	—	52	4	no	—
367	D₄	—	52	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	8	2	no	—
374	C₂×C₄	—	52	1	no	—
375	C₂×C₄	—	52	4	no	—
376	C₂×C₄	—	52	1	no	—
377	C₂×C₄	—	52	1	no	—
378	C₂×C₄	—	104	2	no	—
379	C₂×C₄	—	104	2	no	—
380	C₂×C₄	C₄×C₂²⋊D₁₃	1	2	yes	—
381	C₂×C₄	C₂×#6104	1	1	yes	characteristic
382	C₂×C₄	C₂×#6104	1	1	yes	characteristic
383	C₂×C₄	C₂×#6104	1	1	yes	characteristic
384	C₂×C₄	C₂×#6104	1	1	yes	characteristic
385	C₂×C₄	C₂×#6104	1	1	yes	characteristic
386	C₂×C₄	#88204	1	2	yes	—
387	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
388	C₈	—	2	1	no	—
389	C₈	—	2	1	no	—
390	C₈	C₄×C₂²⋊D₁₃	1	2	yes	—
391	C₈	C₂²×C₄×D₁₃	1	1	yes	characteristic
392	C₈	C₂×#6127	1	1	yes	characteristic
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	52	2	no	—
396	C₂²	—	104	1	no	—
397	C₂²	—	104	1	no	—
398	C₂²	C₄×#6104	1	2	yes	—
399	C₂²	C₂²×#6104	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	4	4	no	—
404	C₄	—	8	2	no	—
405	C₄	—	52	2	no	—
406	C₄	—	104	1	no	—
407	C₄	—	104	1	no	—
408	C₄	C₄×#6104	1	2	yes	—
409	C₄	#11718840	1	2	yes	direct product factor
410	C₄	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
411	C₄	C₂×#88204	1	1	yes	characteristic
412	C₂	—	2	2	no	—
413	C₂	—	104	2	no	—
414	C₂	C₂×C₄×#6104	1	1	yes	characteristic
415	C₂	C₂×#11718840	1	1	yes	characteristic
416	C₂	#13127970	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#6104
commutator	C₈×C₁₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂×C₄×C₁₃×Q₁₆	C₂
socle	C₂²×C₁₃	C₂²×D₈
prime radical	C₂×#88158	C₂²
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₂×C₄×Q₁₆	D₁₃
hypocenter	C₁₃	C₄×#510
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
3. #13116705	C₂	semidirect
4. #13116698	C₂	semidirect
5. C₄×#88069	C₂	semidirect
6. C₄×#88068	C₂	semidirect
7. #13116622	C₂	semidirect
8. #13116556	C₂	semidirect
10. C₄×#88052	C₂	semidirect
11. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
24. #11718840	C₄	direct (N × H)
48. C₂×C₁₃×Q₁₆	C₂×C₄	semidirect
82. #88069	C₂×C₄	semidirect
83. #88068	C₂×C₄	semidirect
92. #88052	C₂×C₄	semidirect
152. C₂×C₄×Q₁₆	D₁₃	semidirect
241. C₄×C₁₃	#510	semidirect
254. C₂×Q₁₆	C₄×D₁₃	semidirect
357. C₁₃	C₄×#510	semidirect
409. C₄	#11718840	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×#11718840	2
C₄×#88158	2
#13116705	2
#13116698	2
C₄×#88069	2
C₄×#88068	2
#13116622	2
#13116556	2
#13116546	2
C₄×#88052	2
C₂×C₄×C₁₃×Q₁₆	2
C₄×#510	13

Subgroups — C4×#11718840 #16016248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11718840 #16016248