Subgroups — #16016330

Order 3328.

652 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13127970	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718361	C₂	1	1	yes	maximal, characteristic, complemented
3	#13116720	C₂	1	4	yes	maximal, complemented
4	#13116715	C₂	1	4	yes	maximal, complemented
5	#13116630	C₂	1	1	yes	maximal, characteristic, complemented
6	#13116564	C₂	1	1	yes	maximal, characteristic, complemented
7	#13116563	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#88052	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#443	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#131	—	2	1	no	—
12	C₂×#88158	C₂²	1	1	yes	characteristic
13	C₂×#88155	—	2	1	no	—
14	C₁₃×#443	—	2	1	no	—
15	C₁₃×#443	—	2	1	no	—
16	C₁₃×#443	C₂²	1	2	yes	complemented
17	C₁₃×#443	C₂²	1	2	yes	complemented
18	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#104	—	2	1	no	—
20	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
21	#11718856	C₄	1	2	yes	complemented
22	#11718855	C₂²	1	4	yes	—
23	#11718854	C₄	1	2	yes	complemented
24	#11718840	C₄	1	2	yes	complemented
25	#11718808	C₄	1	2	yes	complemented
26	C₂×#88059	C₂²	1	1	yes	characteristic
27	C₂×#88052	C₂²	1	1	yes	characteristic
28	C₂×#88052	C₂²	1	1	yes	characteristic
29	C₂×#88045	—	2	1	no	—
30	#11718361	—	2	1	no	—
31	#11718361	—	2	1	no	—
32	#11718361	C₂²	1	2	yes	complemented
33	#11718361	C₂²	1	2	yes	complemented
34	#11718159	C₂²	1	4	yes	complemented
35	#11718089	C₂²	1	4	yes	complemented
36	#11718085	C₂²	1	4	yes	complemented
37	#11718053	C₂²	1	2	yes	complemented
38	C₄×#6090	C₂²	1	2	yes	complemented
39	C₂×C₁₃×#41	—	2	1	no	—
40	C₂×#6127	—	2	1	no	—
41	C₁₃×#135	—	2	1	no	—
42	C₁₃×#135	—	2	1	no	—
43	C₁₃×#135	C₂×C₄	1	2	yes	—
44	C₁₃×#135	C₂³	1	2	yes	—
45	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
46	C₂×C₁₃×SD₁₆	—	2	1	no	—
47	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
48	C₁₃×#131	—	2	2	no	—
49	C₁₃×#131	—	2	2	no	—
50	C₁₃×#131	—	4	1	no	—
51	C₁₃×#131	—	4	1	no	—
52	C₂×C₁₃×M₁₆	—	2	1	no	—
53	C₂×C₁₃×M₁₆	—	4	1	no	—
54	C₂²×C₈×C₁₃	—	4	1	no	—
55	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
58	C₂×#6099	—	2	1	no	—
59	C₂×Dic₅₂	C₂×C₄	1	1	yes	characteristic
60	#88158	—	2	1	no	—
61	#88158	—	2	1	no	—
62	#88158	C₂×C₄	1	2	yes	—
63	#88158	C₂³	1	2	yes	—
64	C₂×D₁₀₄	C₂×C₄	1	1	yes	characteristic
65	C₂×#6095	—	2	1	no	—
66	#88155	—	2	2	no	—
67	#88155	—	2	2	no	—
68	#88155	—	4	1	no	—
69	#88155	—	4	1	no	—
70	C₂×#6094	—	4	1	no	—
71	C₂×C₈×D₁₃	—	4	1	no	—
72	C₁₃×#108	—	2	1	no	—
73	C₁₃×#108	C₂³	1	2	yes	—
74	C₁₃×#104	—	2	2	no	—
75	C₁₃×#104	—	2	2	no	—
76	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
77	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
78	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
80	#88069	C₂×C₄	1	4	yes	complemented
81	#88068	C₂×C₄	1	4	yes	complemented
82	#88067	C₂×C₄	1	4	yes	complemented
83	#88066	C₂×C₄	1	4	yes	complemented
84	#88059	—	2	1	no	—
85	#88059	C₂³	1	2	yes	—
86	#88052	—	2	1	no	—
87	#88052	—	2	1	no	—
88	#88052	C₂×C₄	1	2	yes	—
89	#88052	C₂×C₄	1	2	yes	—
90	C₂×#6090	C₂³	1	2	yes	—
91	C₂×#6090	C₂³	1	2	yes	—
92	#88045	—	2	2	no	—
93	#88045	—	2	2	no	—
94	#33463	—	13	1	no	maximal, Sylow
95	C₁₃×#41	—	2	2	no	—
96	C₁₃×#41	—	2	2	no	—
97	C₁₃×#41	—	4	1	no	—
98	C₁₃×#41	—	4	1	no	—
99	C₂×Q₈×C₁₃	—	2	1	no	—
100	C₂×D₄×C₁₃	—	2	1	no	—
101	C₂×D₄×C₁₃	—	4	1	no	—
102	C₂²×C₄×C₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	4	1	no	—
104	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂×C₂²⋊D₁₃	—	4	1	no	—
106	#6127	—	2	2	no	—
107	#6127	—	2	2	no	—
108	#6127	—	4	1	no	—
109	#6127	—	4	1	no	—
110	C₂×D₅₂	—	2	1	no	—
111	C₂×C₄×D₁₃	—	4	1	no	—
112	C₂×Dic₂₆	—	2	1	no	—
113	C₁₃×Q₁₆	—	2	1	no	—
114	C₁₃×Q₁₆	C₂²×C₄	1	2	yes	—
115	C₁₃×SD₁₆	—	2	2	no	—
116	C₁₃×SD₁₆	—	2	2	no	—
117	C₁₃×D₈	—	2	1	no	—
118	C₁₃×D₈	C₂²×C₄	1	2	yes	—
119	C₁₃×M₁₆	—	2	2	no	—
120	C₁₃×M₁₆	—	4	1	no	—
121	C₁₃×M₁₆	—	4	2	no	—
122	C₁₃×M₁₆	—	4	2	no	—
123	C₂×C₈×C₁₃	—	4	1	no	—
124	C₂×C₈×C₁₃	—	4	2	no	—
125	C₂×C₈×C₁₃	—	4	2	no	—
126	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
127	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
128	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
129	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
130	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
136	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
137	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
138	C₄²×C₁₃	—	2	1	no	—
139	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
141	#6099	—	2	2	no	—
142	#6099	—	4	1	no	—
143	C₂×#1055	—	4	1	no	—
144	Dic₅₂	—	2	1	no	—
145	Dic₅₂	C₂²×C₄	1	2	yes	—
146	D₁₀₄	—	2	1	no	—
147	D₁₀₄	C₂²×C₄	1	2	yes	—
148	#6095	—	2	2	no	—
149	#6095	—	2	2	no	—
150	#6094	—	4	2	no	—
151	#6094	—	4	2	no	—
152	C₈×D₁₃	—	4	2	no	—
153	C₈×D₁₃	—	4	2	no	—
154	#6090	—	2	2	no	—
155	#6090	C₂²×C₄	1	4	yes	—
156	#3414	—	13	1	no	—
157	C₂×#443	—	13	1	no	—
158	C₂×#443	D₁₃	1	1	yes	characteristic, complemented
159	#2179	—	13	4	no	—
160	#2178	—	13	4	no	—
161	#2161	—	13	1	no	—
162	#2143	—	13	1	no	—
163	#2143	—	13	1	no	—
164	C₄×M₃₂	—	13	1	no	—
165	C₂³×C₁₃	—	4	1	no	—
166	C₂³×C₁₃	#135	1	1	yes	characteristic
167	C₂²×D₁₃	—	4	1	no	—
168	Q₈×C₁₃	—	2	2	no	—
169	Q₈×C₁₃	—	4	1	no	—
170	D₄×C₁₃	—	2	2	no	—
171	D₄×C₁₃	—	4	2	no	—
172	D₄×C₁₃	—	4	2	no	—
173	D₄×C₁₃	—	4	1	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	4	2	no	—
177	C₂×C₄×C₁₃	—	4	1	no	—
178	C₂×C₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	—	4	2	no	—
180	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
184	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
186	C₂²⋊D₁₃	—	4	2	no	—
187	C₂²⋊D₁₃	—	4	2	no	—
188	C₂×Dic₁₃	—	4	1	no	—
189	D₅₂	—	2	2	no	—
190	D₅₂	—	4	1	no	—
191	C₄×D₁₃	—	4	2	no	—
192	C₄×D₁₃	—	4	2	no	—
193	Dic₂₆	—	2	2	no	—
194	Dic₂₆	—	4	1	no	—
195	C₈×C₁₃	—	4	2	no	—
196	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
197	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
198	C₈×C₁₃	C₂×D₈	1	1	yes	characteristic
199	C₈×C₁₃	C₂×D₈	1	1	yes	characteristic
200	C₈×C₁₃	C₂×D₈	1	1	yes	characteristic
201	C₈×C₁₃	C₂×D₈	1	1	yes	characteristic
202	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
203	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
204	#1055	—	4	2	no	—
205	C₂×#135	—	13	1	no	—
206	C₂×#135	C₂×D₁₃	1	1	yes	characteristic
207	C₂×#131	—	2	1	no	—
208	C₂×#131	—	26	1	no	—
209	#510	—	13	2	no	—
210	#510	—	13	2	no	—
211	#509	—	13	2	no	—
212	#509	—	13	2	no	—
213	#508	—	13	4	no	—
214	C₂×M₃₂	—	13	1	no	—
215	C₂×M₃₂	—	13	1	no	—
216	#443	—	2	1	no	—
217	#443	—	2	1	no	—
218	#443	—	13	2	no	—
219	#443	—	13	2	no	—
220	#443	—	26	1	no	—
221	#443	—	26	1	no	—
222	#443	C₂×D₁₃	1	2	yes	complemented
223	#443	C₂×D₁₃	1	2	yes	complemented
224	C₂×#108	—	13	1	no	—
225	C₂×#108	C₂×D₁₃	1	1	yes	characteristic
226	C₂×#104	—	2	1	no	—
227	C₂×#104	—	26	1	no	—
228	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
229	#368	—	13	4	no	—
230	#359	—	13	4	no	—
231	#359	—	13	4	no	—
232	#346	—	13	2	no	—
233	C₄×C₁₆	—	13	2	no	—
234	C₂²×C₁₃	—	4	1	no	—
235	C₂²×C₁₃	—	4	2	no	—
236	C₂²×C₁₃	—	8	2	no	—
237	C₂²×C₁₃	C₄×D₈	1	1	yes	characteristic
238	C₂²×C₁₃	C₄×D₈	1	1	yes	characteristic
239	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
240	C₂×D₁₃	—	4	2	no	—
241	C₂×D₁₃	—	8	2	no	—
242	C₄×C₁₃	—	2	2	no	—
243	C₄×C₁₃	—	4	1	no	—
244	C₄×C₁₃	—	4	2	no	—
245	C₄×C₁₃	C₄×D₈	1	1	yes	characteristic
246	C₄×C₁₃	C₄×D₈	1	1	yes	characteristic
247	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
248	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
249	Dic₁₃	—	4	2	no	—
250	C₂×#41	—	2	1	no	—
251	C₂×#41	—	26	1	no	—
252	#135	—	2	1	no	—
253	#135	—	2	1	no	—
254	#135	—	13	2	no	—
255	#135	—	13	2	no	—
256	#135	—	26	1	no	—
257	#135	—	26	1	no	—
258	#135	C₄×D₁₃	1	2	yes	—
259	#135	C₂²×D₁₃	1	2	yes	—
260	C₂×Q₁₆	—	13	1	no	—
261	C₂×Q₁₆	C₄×D₁₃	1	1	yes	characteristic
262	C₂×SD₁₆	—	2	1	no	—
263	C₂×SD₁₆	—	26	1	no	—
264	C₂×D₈	—	13	1	no	—
265	C₂×D₈	C₄×D₁₃	1	1	yes	characteristic
266	#131	—	2	2	no	—
267	#131	—	2	2	no	—
268	#131	—	4	1	no	—
269	#131	—	4	1	no	—
270	#131	—	26	2	no	—
271	#131	—	26	2	no	—
272	#131	—	52	1	no	—
273	#131	—	52	1	no	—
274	C₂×M₁₆	—	2	1	no	—
275	C₂×M₁₆	—	4	1	no	—
276	C₂×M₁₆	—	26	1	no	—
277	C₂×M₁₆	—	52	1	no	—
278	C₂²×C₈	—	4	1	no	—
279	C₂²×C₈	—	52	1	no	—
280	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
281	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
282	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
283	Q₃₂	—	13	4	no	—
284	SD₃₂	—	13	4	no	—
285	SD₃₂	—	13	4	no	—
286	D₁₆	—	13	4	no	—
287	M₃₂	—	13	2	no	—
288	M₃₂	—	13	2	no	—
289	M₃₂	—	26	1	no	—
290	M₃₂	—	26	1	no	—
291	C₂×C₁₆	—	13	2	no	—
292	C₂×C₁₆	—	13	2	no	—
293	#108	—	2	1	no	—
294	#108	—	13	2	no	—
295	#108	—	26	1	no	—
296	#108	C₂²×D₁₃	1	2	yes	—
297	#104	—	2	2	no	—
298	#104	—	2	2	no	—
299	#104	—	26	2	no	—
300	#104	—	26	2	no	—
301	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
302	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
303	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
304	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
305	C₂×C₁₃	—	2	1	no	—
306	C₂×C₁₃	—	2	1	no	—
307	C₂×C₁₃	—	2	1	no	—
308	C₂×C₁₃	—	8	2	no	—
309	C₂×C₁₃	C₂×C₄×D₈	1	1	yes	characteristic
310	D₁₃	—	8	2	no	—
311	#41	—	2	2	no	—
312	#41	—	2	2	no	—
313	#41	—	4	1	no	—
314	#41	—	4	1	no	—
315	#41	—	26	2	no	—
316	#41	—	26	2	no	—
317	#41	—	52	1	no	—
318	#41	—	52	1	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	26	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	4	1	no	—
323	C₂×D₄	—	26	1	no	—
324	C₂×D₄	—	52	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	4	1	no	—
327	C₂²×C₄	—	52	1	no	—
328	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
329	Q₁₆	—	2	1	no	—
330	Q₁₆	—	13	2	no	—
331	Q₁₆	—	26	1	no	—
332	Q₁₆	C₂×C₄×D₁₃	1	2	yes	—
333	SD₁₆	—	2	2	no	—
334	SD₁₆	—	2	2	no	—
335	SD₁₆	—	26	2	no	—
336	SD₁₆	—	26	2	no	—
337	D₈	—	2	1	no	—
338	D₈	—	13	2	no	—
339	D₈	—	26	1	no	—
340	D₈	C₂×C₄×D₁₃	1	2	yes	—
341	M₁₆	—	2	2	no	—
342	M₁₆	—	4	1	no	—
343	M₁₆	—	4	2	no	—
344	M₁₆	—	4	2	no	—
345	M₁₆	—	26	2	no	—
346	M₁₆	—	52	1	no	—
347	M₁₆	—	52	2	no	—
348	M₁₆	—	52	2	no	—
349	C₂×C₈	—	4	1	no	—
350	C₂×C₈	—	4	2	no	—
351	C₂×C₈	—	4	2	no	—
352	C₂×C₈	—	52	1	no	—
353	C₂×C₈	—	52	2	no	—
354	C₂×C₈	—	52	2	no	—
355	C₂×C₈	#6104	1	1	yes	characteristic
356	C₂×C₈	#6104	1	1	yes	characteristic
357	C₂×C₈	#6104	1	1	yes	characteristic
358	C₂×C₈	#6104	1	1	yes	characteristic
359	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
360	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
361	C₂×C₈	#6127	1	1	yes	characteristic
362	C₂×C₈	#6127	1	1	yes	characteristic
363	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
364	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
365	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
366	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
367	C₄²	—	2	1	no	—
368	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
369	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
370	C₁₆	—	13	4	no	—
371	C₁₆	—	26	2	no	—
372	C₁₃	#33463	1	1	yes	characteristic, complemented, Sylow
373	C₂³	—	4	1	no	—
374	C₂³	—	52	1	no	—
375	C₂³	#88204	1	1	yes	characteristic
376	Q₈	—	2	2	no	—
377	Q₈	—	4	1	no	—
378	Q₈	—	26	2	no	—
379	Q₈	—	52	1	no	—
380	D₄	—	2	2	no	—
381	D₄	—	4	2	no	—
382	D₄	—	4	2	no	—
383	D₄	—	4	1	no	—
384	D₄	—	26	2	no	—
385	D₄	—	52	2	no	—
386	D₄	—	52	2	no	—
387	D₄	—	52	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	52	1	no	—
395	C₂×C₄	—	52	2	no	—
396	C₂×C₄	—	52	2	no	—
397	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
398	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
399	C₂×C₄	C₂×#6104	1	1	yes	characteristic
400	C₂×C₄	C₂×#6104	1	1	yes	characteristic
401	C₂×C₄	#88204	1	1	yes	characteristic
402	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
403	C₈	—	4	2	no	—
404	C₈	—	52	2	no	—
405	C₈	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
406	C₈	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
407	C₈	C₂×#6104	1	1	yes	characteristic
408	C₈	C₂×#6104	1	1	yes	characteristic
409	C₈	C₂×#6104	1	1	yes	characteristic
410	C₈	C₂×#6104	1	1	yes	characteristic
411	C₈	C₂²×C₄×D₁₃	1	1	yes	characteristic
412	C₈	C₂×#6127	1	1	yes	characteristic
413	C₂²	—	4	1	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	52	2	no	—
417	C₂²	—	104	2	no	—
418	C₂²	C₄×#6104	1	1	yes	characteristic
419	C₂²	C₄×#6104	1	1	yes	characteristic
420	C₂²	C₂×#88204	1	1	yes	characteristic
421	C₄	—	2	2	no	—
422	C₄	—	4	1	no	—
423	C₄	—	4	2	no	—
424	C₄	—	52	2	no	—
425	C₄	C₄×#6104	1	1	yes	characteristic
426	C₄	C₄×#6104	1	1	yes	characteristic
427	C₄	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
428	C₄	C₂²×#6104	1	1	yes	characteristic
429	C₂	—	2	1	no	—
430	C₂	—	2	1	no	—
431	C₂	—	2	1	no	—
432	C₂	—	8	2	no	—
433	C₂	—	104	2	no	—
434	C₂	C₂×C₄×#6104	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×#6104
commutator	C₈×C₁₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂×C₁₃×#443	C₂
socle	C₂×C₁₃	C₂×C₄×D₈
prime radical	#13127970	C₂
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₂×#443	D₁₃
hypocenter	C₁₃	#33463
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ C₂×C₄×C₈ ◁ C₂×#443

Complements

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

N	H ≅ G/N	type
2. C₂×#11718361	C₂	semidirect
3. #13116720	C₂	semidirect
4. #13116715	C₂	semidirect
5. #13116630	C₂	semidirect
6. #13116564	C₂	semidirect
7. #13116563	C₂	semidirect
8. C₄×#88052	C₂	semidirect
9. C₂×C₁₃×#443	C₂	semidirect
16. C₁₃×#443	C₂²	semidirect
17. C₁₃×#443	C₂²	semidirect
21. #11718856	C₄	semidirect
23. #11718854	C₄	semidirect
24. #11718840	C₄	semidirect
25. #11718808	C₄	semidirect
32. #11718361	C₂²	semidirect
33. #11718361	C₂²	semidirect
34. #11718159	C₂²	semidirect
35. #11718089	C₂²	semidirect
36. #11718085	C₂²	semidirect
37. #11718053	C₂²	semidirect
38. C₄×#6090	C₂²	semidirect
80. #88069	C₂×C₄	semidirect
81. #88068	C₂×C₄	semidirect
82. #88067	C₂×C₄	semidirect
83. #88066	C₂×C₄	semidirect
158. C₂×#443	D₁₃	semidirect
222. #443	C₂×D₁₃	semidirect
223. #443	C₂×D₁₃	semidirect
372. C₁₃	#33463	semidirect

Maximal subgroups

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

subgroup	index
#13127970	2
C₂×#11718361	2
#13116720	2
#13116715	2
#13116630	2
#13116564	2
#13116563	2
C₄×#88052	2
C₂×C₁₃×#443	2
#33463	13