Subgroups — #15832591

Order 3328.

726 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123877	C₂	1	1	yes	maximal, characteristic, complemented
2	#13123860	C₂	1	1	yes	maximal, characteristic, complemented
3	#13113701	C₂	1	4	yes	maximal, complemented
4	#13113666	C₂	1	4	yes	maximal, complemented
5	#13113584	C₂	1	1	yes	maximal, characteristic, complemented
6	#13113227	C₂	1	1	yes	maximal, characteristic, complemented
7	#13113227	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113128	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₁₃×D₈	C₄	1	1	yes	characteristic
11	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₄×C₁₃×D₈	C₄	1	2	yes	—
14	C₄×C₁₃×D₈	C₄	1	2	yes	—
15	C₄×C₁₃×D₈	C₂²	1	2	yes	—
16	C₄×C₁₃×D₈	C₂²	1	2	yes	—
17	C₂×C₁₃×#107	C₄	1	1	yes	characteristic
18	C₂×C₁₃×#102	C₄	1	1	yes	characteristic
19	C₂×C₁₃×#102	C₄	1	1	yes	characteristic
20	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
21	#11718868	—	2	2	no	—
22	C₂×C₂²⋊#1055	—	2	2	no	—
23	#11718673	—	2	2	no	—
24	#11718673	C₂²	1	4	yes	complemented
25	D₄×#1055	—	2	2	no	—
26	D₄×#1055	C₂²	1	4	yes	complemented
27	#11718586	C₂²	1	1	yes	characteristic
28	#11718586	C₂²	1	1	yes	characteristic
29	#11718586	C₂²	1	1	yes	characteristic
30	#11718586	C₂²	1	1	yes	characteristic
31	D₄⋊#1055	C₂²	1	4	yes	complemented
32	D₄⋊#1055	C₂²	1	4	yes	complemented
33	#11718050	C₂²	1	2	yes	complemented
34	#11718049	C₂²	1	2	yes	complemented
35	#11718046	C₂²	1	2	yes	complemented
36	#11718046	C₂²	1	2	yes	complemented
37	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
38	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₃	—	2	1	no	—
40	C₂³×C₄×C₁₃	—	2	1	no	—
41	C₂×C₁₃×D₈	—	2	4	no	—
42	C₂×C₁₃×D₈	C₂×C₄	1	2	yes	—
43	C₂×C₁₃×D₈	C₂×C₄	1	2	yes	—
44	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
46	C₄×D₄×C₁₃	—	2	1	no	—
47	C₄×D₄×C₁₃	—	2	1	no	—
48	C₄×D₄×C₁₃	—	2	1	no	—
49	C₄×D₄×C₁₃	—	2	1	no	—
50	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
51	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
52	C₄×D₄×C₁₃	C₂³	1	2	yes	—
53	C₄×D₄×C₁₃	C₂³	1	2	yes	—
54	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
55	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
56	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
58	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
59	C₂×#6099	—	2	4	no	—
60	C₂²×#1055	—	2	4	no	—
61	C₁₃×#107	C₂×C₄	1	2	yes	—
62	C₁₃×#107	C₂×C₄	1	2	yes	—
63	C₁₃×#102	C₂×C₄	1	2	yes	—
64	C₁₃×#102	C₂×C₄	1	2	yes	—
65	C₁₃×#102	C₂×C₄	1	2	yes	—
66	C₁₃×#102	C₂×C₄	1	2	yes	—
67	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
68	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
69	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
70	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²⋊#1055	—	2	1	no	—
72	C₂²⋊#1055	—	2	1	no	—
73	C₂²⋊#1055	—	2	1	no	—
74	C₂²⋊#1055	—	2	4	no	—
75	C₂²⋊#1055	—	2	4	no	—
76	C₂²⋊#1055	D₄	1	2	yes	—
77	C₄⋊#1055	—	2	1	no	—
78	C₄⋊#1055	D₄	1	2	yes	—
79	C₄⋊#1055	C₂³	1	2	yes	—
80	C₄⋊#1055	C₂³	1	2	yes	—
81	C₄×#1055	—	2	1	no	—
82	C₄×#1055	—	2	1	no	—
83	C₄×#1055	C₂³	1	2	yes	—
84	C₄×#1055	C₂³	1	2	yes	—
85	#17877	—	13	1	no	maximal, Sylow
86	C₂⁴×C₁₃	—	2	1	no	—
87	C₂⁴×C₁₃	—	2	1	no	—
88	C₂×D₄×C₁₃	—	2	1	no	—
89	C₂×D₄×C₁₃	—	2	1	no	—
90	C₂×D₄×C₁₃	—	2	2	no	—
91	C₂×D₄×C₁₃	—	2	2	no	—
92	C₂×D₄×C₁₃	—	2	2	no	—
93	C₂×D₄×C₁₃	M₁₆	1	4	yes	complemented
94	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
95	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₁₃	—	2	1	no	—
97	C₂²×C₄×C₁₃	—	2	1	no	—
98	C₂²×C₄×C₁₃	—	2	2	no	—
99	C₂²×C₄×C₁₃	—	2	2	no	—
100	C₂²×C₄×C₁₃	—	2	2	no	—
101	C₂²×C₄×C₁₃	—	2	2	no	—
102	C₂²×C₄×C₁₃	—	8	2	no	—
103	C₂²×C₄×C₁₃	—	8	2	no	—
104	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
107	C₁₃×D₈	—	2	4	no	—
108	C₁₃×D₈	—	2	4	no	—
109	C₂×C₈×C₁₃	—	2	2	no	—
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₁₃×C₄⋊C₄	—	2	1	no	—
116	C₁₃×C₄⋊C₄	—	2	1	no	—
117	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
118	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
119	C₁₃×C₂²⋊C₄	—	2	2	no	—
120	C₁₃×C₂²⋊C₄	—	2	2	no	—
121	C₁₃×C₂²⋊C₄	—	2	2	no	—
122	C₁₃×C₂²⋊C₄	—	2	2	no	—
123	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₁₃	#41	1	1	yes	characteristic
126	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
127	#6099	—	8	4	no	—
128	C₂×#1055	—	2	2	no	—
129	C₂×#1055	—	2	2	no	—
130	C₂×#1055	—	2	2	no	—
131	C₂×#1055	—	8	4	no	—
132	C₂×#1055	C₂×D₄	1	4	yes	—
133	#2975	—	13	1	no	—
134	#2972	—	13	1	no	—
135	C₂×C₄×D₈	D₁₃	1	1	yes	characteristic
136	#1586	—	13	4	no	—
137	#1581	—	13	4	no	—
138	#1564	—	13	1	no	—
139	#1478	—	13	1	no	—
140	#1478	—	13	1	no	—
141	#1452	—	13	1	no	—
142	C₂³×C₁₃	—	2	2	no	—
143	C₂³×C₁₃	—	2	4	no	—
144	C₂³×C₁₃	—	2	2	no	—
145	C₂³×C₁₃	—	4	2	no	—
146	C₂³×C₁₃	—	8	1	no	—
147	C₂³×C₁₃	—	8	1	no	—
148	C₂³×C₁₃	—	8	1	no	—
149	C₂³×C₁₃	—	8	1	no	—
150	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
151	D₄×C₁₃	—	2	2	no	—
152	D₄×C₁₃	—	2	2	no	—
153	D₄×C₁₃	—	2	2	no	—
154	D₄×C₁₃	—	2	4	no	—
155	D₄×C₁₃	—	4	2	no	—
156	D₄×C₁₃	C₂×M₁₆	1	4	yes	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	4	1	no	—
161	C₂×C₄×C₁₃	—	4	4	no	—
162	C₂×C₄×C₁₃	—	4	4	no	—
163	C₂×C₄×C₁₃	—	8	2	no	—
164	C₂×C₄×C₁₃	—	8	2	no	—
165	C₂×C₄×C₁₃	—	8	1	no	—
166	C₂×C₄×C₁₃	—	8	1	no	—
167	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
171	C₂×C₄×C₁₃	#131	1	2	yes	—
172	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
175	C₈×C₁₃	—	2	1	no	—
176	C₈×C₁₃	—	2	1	no	—
177	C₈×C₁₃	—	2	1	no	—
178	C₈×C₁₃	—	2	1	no	—
179	#1055	—	2	4	no	—
180	#1055	—	4	2	no	—
181	#1055	—	4	2	no	—
182	#1055	—	4	2	no	—
183	C₂²×D₈	Dic₁₃	1	1	yes	characteristic
184	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
185	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
186	C₄×D₈	Dic₁₃	1	2	yes	—
187	C₄×D₈	Dic₁₃	1	2	yes	—
188	C₄×D₈	C₂×D₁₃	1	2	yes	—
189	C₄×D₈	C₂×D₁₃	1	2	yes	—
190	#436	—	13	4	no	—
191	#436	—	26	2	no	—
192	C₈×D₄	—	13	4	no	—
193	C₈×D₄	—	26	2	no	—
194	#431	—	13	1	no	—
195	#431	—	13	1	no	—
196	#431	—	13	1	no	—
197	#431	—	13	1	no	—
198	C₂×#107	Dic₁₃	1	1	yes	characteristic
199	C₂×#102	Dic₁₃	1	1	yes	characteristic
200	C₂×#102	Dic₁₃	1	1	yes	characteristic
201	#407	—	26	2	no	—
202	C₂×C₂²⋊C₈	—	26	2	no	—
203	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
204	#335	—	13	2	no	—
205	#334	—	13	2	no	—
206	D₄⋊C₈	—	13	4	no	—
207	D₄⋊C₈	—	13	4	no	—
208	#322	—	13	2	no	—
209	#322	—	13	2	no	—
210	C₂²×C₁₃	—	2	1	no	—
211	C₂²×C₁₃	—	2	1	no	—
212	C₂²×C₁₃	—	2	4	no	—
213	C₂²×C₁₃	—	4	2	no	—
214	C₂²×C₁₃	—	4	2	no	—
215	C₂²×C₁₃	—	4	2	no	—
216	C₂²×C₁₃	—	4	2	no	—
217	C₂²×C₁₃	—	4	2	no	—
218	C₂²×C₁₃	—	8	4	no	—
219	C₂²×C₁₃	—	8	4	no	—
220	C₂²×C₁₃	#435	1	2	yes	—
221	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
222	C₄×C₁₃	—	2	1	no	—
223	C₄×C₁₃	—	2	1	no	—
224	C₄×C₁₃	—	2	1	no	—
225	C₄×C₁₃	—	4	2	no	—
226	C₄×C₁₃	—	4	2	no	—
227	C₄×C₁₃	#435	1	2	yes	—
228	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
229	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
230	C₄×C₁₃	#576	1	2	yes	—
231	C₂²×D₄	C₂×Dic₁₃	1	1	yes	characteristic
232	C₂²×D₄	C₂×Dic₁₃	1	1	yes	characteristic
233	C₂³×C₄	—	2	1	no	—
234	C₂³×C₄	—	2	1	no	—
235	C₂×D₈	—	2	4	no	—
236	C₂×D₈	C₂×Dic₁₃	1	2	yes	—
237	C₂×D₈	C₂×Dic₁₃	1	2	yes	—
238	C₂×M₁₆	—	26	4	no	—
239	C₂²×C₈	—	26	4	no	—
240	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
241	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	—	2	1	no	—
244	C₄×D₄	—	2	1	no	—
245	C₄×D₄	—	2	1	no	—
246	C₄×D₄	C₂×Dic₁₃	1	2	yes	—
247	C₄×D₄	C₂×Dic₁₃	1	2	yes	—
248	C₄×D₄	C₂²×D₁₃	1	2	yes	—
249	C₄×D₄	C₂²×D₁₃	1	2	yes	—
250	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
252	C₂×C₂²⋊C₄	—	2	1	no	—
253	C₂×C₂²⋊C₄	—	2	1	no	—
254	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
255	#107	C₂×Dic₁₃	1	2	yes	—
256	#107	C₂×Dic₁₃	1	2	yes	—
257	C₄⋊C₈	—	13	2	no	—
258	C₄⋊C₈	—	13	2	no	—
259	C₄⋊C₈	—	13	2	no	—
260	C₄⋊C₈	—	26	1	no	—
261	#102	C₂×Dic₁₃	1	2	yes	—
262	#102	C₂×Dic₁₃	1	2	yes	—
263	#102	C₂×Dic₁₃	1	2	yes	—
264	#102	C₂×Dic₁₃	1	2	yes	—
265	C₂²⋊C₈	—	13	2	no	—
266	C₂²⋊C₈	—	26	4	no	—
267	C₂²⋊C₈	—	26	4	no	—
268	C₂²⋊C₈	—	26	1	no	—
269	C₂²⋊C₈	—	26	1	no	—
270	C₂²⋊C₈	—	26	1	no	—
271	C₄×C₈	—	13	2	no	—
272	C₄×C₈	—	13	2	no	—
273	C₄×C₈	—	26	1	no	—
274	C₄×C₈	—	26	1	no	—
275	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
276	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
277	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
278	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
279	C₂×C₁₃	—	2	2	no	—
280	C₂×C₁₃	—	4	4	no	—
281	C₂×C₁₃	—	8	2	no	—
282	C₂×C₁₃	C₂×#435	1	1	yes	characteristic
283	C₂×C₁₃	#2948	1	1	yes	characteristic
284	C₂×C₁₃	#2957	1	1	yes	characteristic
285	C₂⁴	—	2	1	no	—
286	C₂⁴	—	2	1	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	#6099	1	4	yes	complemented
293	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
294	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	8	2	no	—
302	C₂²×C₄	—	8	2	no	—
303	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
304	C₂²×C₄	#6129	1	1	yes	characteristic
305	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
306	D₈	—	2	4	no	—
307	D₈	—	2	4	no	—
308	M₁₆	—	104	4	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	13	4	no	—
312	C₂×C₈	—	26	2	no	—
313	C₂×C₈	—	26	2	no	—
314	C₂×C₈	—	26	2	no	—
315	C₂×C₈	—	104	4	no	—
316	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
317	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
318	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
319	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
323	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
324	C₂²⋊C₄	—	2	2	no	—
325	C₂²⋊C₄	—	2	2	no	—
326	C₂²⋊C₄	—	2	2	no	—
327	C₂²⋊C₄	—	2	2	no	—
328	C₄²	D₄×D₁₃	1	1	yes	characteristic
329	C₄²	#6129	1	1	yes	characteristic
330	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
331	C₄²	C₂³×D₁₃	1	1	yes	characteristic
332	C₁₃	#17877	1	1	yes	characteristic, complemented, Sylow
333	C₂³	—	2	2	no	—
334	C₂³	—	2	4	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	4	2	no	—
337	C₂³	—	8	1	no	—
338	C₂³	—	8	1	no	—
339	C₂³	—	8	1	no	—
340	C₂³	—	8	1	no	—
341	C₂³	D₄×Dic₁₃	1	1	yes	characteristic
342	D₄	—	2	4	no	—
343	D₄	—	2	2	no	—
344	D₄	—	2	2	no	—
345	D₄	—	2	2	no	—
346	D₄	—	4	2	no	—
347	D₄	C₂×#6099	1	4	yes	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	8	2	no	—
355	C₂×C₄	—	8	2	no	—
356	C₂×C₄	—	8	1	no	—
357	C₂×C₄	—	8	1	no	—
358	C₂×C₄	C₂×#6099	1	2	yes	—
359	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
360	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
361	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
362	C₂×C₄	#88202	1	2	yes	—
363	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
364	C₂×C₄	C₂×#6129	1	1	yes	characteristic
365	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
366	C₈	—	2	1	no	—
367	C₈	—	2	1	no	—
368	C₈	—	2	1	no	—
369	C₈	—	2	1	no	—
370	C₈	—	26	4	no	—
371	C₈	—	52	2	no	—
372	C₈	—	52	2	no	—
373	C₈	—	52	2	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	4	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	8	4	no	—
383	C₂²	—	8	4	no	—
384	C₂²	#11718672	1	2	yes	—
385	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	4	2	no	—
390	C₄	—	4	2	no	—
391	C₄	#11718672	1	2	yes	—
392	C₄	#11719462	1	2	yes	—
393	C₄	C₂²×#6099	1	1	yes	characteristic
394	C₄	C₂×#88202	1	1	yes	characteristic
395	C₂	—	2	2	no	—
396	C₂	—	4	4	no	—
397	C₂	—	8	2	no	—
398	C₂	C₂×#11718672	1	1	yes	characteristic
399	C₂	#13123688	1	1	yes	characteristic
400	C₂	#13123753	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₂×C₄×C₁₃×D₈	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂²×C₁₃×D₈	C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₂×C₄×D₈	D₁₃
hypocenter	C₁₃	#17877
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×D₈

Complements

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

N	H ≅ G/N	type
1. #13123877	C₂	semidirect
2. #13123860	C₂	semidirect
3. #13113701	C₂	semidirect
4. #13113666	C₂	semidirect
5. #13113584	C₂	semidirect
6. #13113227	C₂	semidirect
7. #13113227	C₂	semidirect
8. #13113128	C₂	semidirect
24. #11718673	C₂²	semidirect
26. D₄×#1055	C₂²	semidirect
31. D₄⋊#1055	C₂²	semidirect
32. D₄⋊#1055	C₂²	semidirect
33. #11718050	C₂²	semidirect
34. #11718049	C₂²	semidirect
35. #11718046	C₂²	semidirect
36. #11718046	C₂²	semidirect
93. C₂×D₄×C₁₃	M₁₆	semidirect
292. C₂×D₄	#6099	semidirect
332. C₁₃	#17877	semidirect

Maximal subgroups

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

subgroup	index
#13123877	2
#13123860	2
#13113701	2
#13113666	2
#13113584	2
#13113227	2
#13113128	2
C₂×C₄×C₁₃×D₈	2
#17877	13