Subgroups — #15832741

Order 3328.

636 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123949	C₂	1	1	yes	maximal, characteristic
2	#13123919	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#88163	C₂	1	1	yes	maximal, characteristic
4	#13113746	C₂	1	2	yes	maximal, complemented
5	#13113740	C₂	1	2	yes	maximal, complemented
6	#13113734	C₂	1	2	yes	maximal, complemented
7	#13113728	C₂	1	2	yes	maximal, complemented
8	#13113588	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113219	C₂	1	1	yes	maximal, characteristic
10	C₂×#11718048	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#88163	C₄	1	1	yes	characteristic
13	C₄×#6127	C₂²	1	1	yes	characteristic
14	C₂×C₄×Dic₂₆	C₂²	1	1	yes	characteristic
15	C₁₃×#431	C₂²	1	1	yes	characteristic
16	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
18	#11718794	C₄	1	1	yes	characteristic
19	#11718782	C₄	1	1	yes	characteristic
20	#11718781	C₄	1	1	yes	characteristic
21	#11718586	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
23	#11718498	—	2	1	no	—
24	#11718496	—	2	1	no	—
25	#11718492	—	2	1	no	—
26	#11718492	—	2	1	no	—
27	#11718391	—	2	2	no	—
28	#11718380	—	2	2	no	—
29	#11718377	C₄	1	2	yes	—
30	#11718371	C₄	1	2	yes	—
31	C₄×Dic₅₂	C₂²	1	2	yes	—
32	C₄×#6095	C₂²	1	2	yes	—
33	#11718349	C₂²	1	2	yes	—
34	#11718340	C₂²	1	2	yes	—
35	#11718340	C₂²	1	2	yes	—
36	#11718340	C₂²	1	2	yes	—
37	C₁₃×#322	C₂²	1	2	yes	—
38	C₈²×C₁₃	C₂²	1	2	yes	—
39	#11718051	C₂²	1	1	yes	characteristic
40	#11718051	C₂²	1	1	yes	characteristic
41	#11718050	C₂²	1	2	yes	—
42	#11718049	C₂²	1	2	yes	—
43	#11718048	C₂²	1	2	yes	—
44	#11718048	C₂²	1	2	yes	—
45	#11718048	C₂²	1	1	yes	characteristic
46	#11718048	C₂²	1	1	yes	characteristic
47	C₂×#6127	C₂×C₄	1	1	yes	characteristic
48	C₂²×Dic₂₆	C₂×C₄	1	1	yes	characteristic
49	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
50	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	—	2	1	no	—
52	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
53	C₄×C₂²⋊D₁₃	—	2	1	no	—
54	C₄×C₂²⋊D₁₃	—	2	1	no	—
55	#88180	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
57	C₂×#6101	—	2	1	no	—
58	C₂×C₄×Dic₁₃	—	2	1	no	—
59	C₂²×#1055	—	2	1	no	—
60	#88163	—	2	4	no	—
61	C₂×Dic₅₂	C₂×C₄	1	2	yes	—
62	C₂×#6095	C₂×C₄	1	2	yes	—
63	C₂×#6094	—	2	2	no	—
64	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
65	C₄×D₅₂	C₂³	1	1	yes	characteristic
66	#88126	—	2	1	no	—
67	C₄²×D₁₃	—	2	1	no	—
68	C₄×Dic₂₆	—	2	1	no	—
69	C₄×Dic₂₆	—	2	1	no	—
70	C₄×Dic₂₆	C₂×C₄	1	2	yes	—
71	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
72	C₄×Dic₂₆	C₂³	1	2	yes	—
73	C₄×Dic₂₆	C₂³	1	1	yes	characteristic
74	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
75	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
76	C₁₃×C₂²⋊C₈	D₄	1	2	yes	—
77	C₁₃×#97	C₂×C₄	1	2	yes	—
78	C₄×C₈×C₁₃	—	2	1	no	—
79	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₄×C₈×C₁₃	C₂³	1	2	yes	—
82	C₄×C₈×C₁₃	C₂³	1	2	yes	—
83	C₂²⋊#1055	—	2	1	no	—
84	#88061	C₂×C₄	1	2	yes	—
85	#88060	—	2	2	no	—
86	#88058	C₂×C₄	1	2	yes	—
87	#88057	C₂×C₄	1	2	yes	—
88	#88056	C₂×C₄	1	2	yes	—
89	#88056	C₂×C₄	1	2	yes	—
90	#88056	C₂×C₄	1	2	yes	—
91	#88055	—	2	2	no	—
92	#88055	—	2	2	no	—
93	#88055	—	2	2	no	—
94	#88054	—	2	2	no	—
95	#88054	—	2	2	no	—
96	#88054	—	2	2	no	—
97	C₄⋊#1055	—	2	1	no	—
98	C₄⋊#1055	C₂³	1	2	yes	—
99	C₄⋊#1055	C₂³	1	1	yes	characteristic
100	C₄⋊#1055	C₂³	1	1	yes	characteristic
101	C₄×#1055	—	2	1	no	—
102	#17894	—	13	1	no	maximal, Sylow
103	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
106	C₂×C₂²⋊D₁₃	—	2	1	no	—
107	C₂²×Dic₁₃	—	2	1	no	—
108	C₂²×Dic₁₃	—	2	1	no	—
109	#6127	—	2	2	no	—
110	#6127	—	2	2	no	—
111	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₄×D₁₃	—	2	1	no	—
113	C₂×C₄×D₁₃	—	2	1	no	—
114	C₂×C₄×D₁₃	—	2	1	no	—
115	C₂×Dic₂₆	—	2	2	no	—
116	C₂×Dic₂₆	—	2	2	no	—
117	C₂×Dic₂₆	—	2	1	no	—
118	C₂×Dic₂₆	C₂²×C₄	1	2	yes	—
119	C₂×Dic₂₆	C₂²×C₄	1	1	yes	characteristic
120	C₁₃×M₁₆	—	2	2	no	—
121	C₁₃×M₁₆	M₁₆	1	4	yes	complemented
122	C₂×C₈×C₁₃	—	2	1	no	—
123	C₂×C₈×C₁₃	—	2	1	no	—
124	C₂×C₈×C₁₃	—	4	2	no	—
125	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
129	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₁₃	#41	1	1	yes	characteristic
132	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
133	C₂²⋊Dic₁₃	—	2	1	no	—
134	#6103	—	2	1	no	—
135	#6103	—	2	1	no	—
136	C₄⋊Dic₁₃	—	2	1	no	—
137	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
138	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
140	#6101	—	2	2	no	—
141	#6101	—	2	1	no	—
142	#6101	—	2	2	no	—
143	#6101	—	2	1	no	—
144	C₄×Dic₁₃	—	2	2	no	—
145	C₄×Dic₁₃	—	2	1	no	—
146	C₄×Dic₁₃	—	2	1	no	—
147	C₄×Dic₁₃	—	2	2	no	—
148	C₄×Dic₁₃	—	2	1	no	—
149	C₂×#1055	—	2	1	no	—
150	C₂×#1055	—	2	1	no	—
151	C₂×#1055	—	2	2	no	—
152	C₂×#1055	—	8	1	no	—
153	Dic₅₂	—	2	4	no	—
154	#6095	—	2	4	no	—
155	#6094	—	8	2	no	—
156	#2989	—	13	1	no	—
157	#2983	—	13	1	no	—
158	C₄×#137	—	13	1	no	—
159	#1593	—	13	2	no	—
160	#1592	—	13	2	no	—
161	#1591	—	13	2	no	—
162	#1590	—	13	2	no	—
163	#1565	—	13	1	no	—
164	#1476	—	13	1	no	—
165	C₂×Q₈⋊C₈	—	13	1	no	—
166	C₈×M₁₆	D₁₃	1	1	yes	characteristic, complemented
167	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
168	C₂²×D₁₃	—	2	1	no	—
169	C₂×C₄×C₁₃	—	2	1	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	4	1	no	—
172	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
176	C₂×C₄×C₁₃	#131	1	2	yes	—
177	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
180	C₂²⋊D₁₃	—	4	2	no	—
181	C₂×Dic₁₃	—	2	2	no	—
182	C₂×Dic₁₃	—	2	2	no	—
183	C₂×Dic₁₃	—	2	1	no	—
184	C₂×Dic₁₃	—	2	1	no	—
185	C₂×Dic₁₃	—	2	1	no	—
186	C₂×Dic₁₃	—	4	2	no	—
187	C₂×Dic₁₃	—	8	1	no	—
188	D₅₂	—	2	1	no	—
189	D₅₂	—	2	1	no	—
190	C₄×D₁₃	—	4	1	no	—
191	C₄×D₁₃	—	4	1	no	—
192	C₄×D₁₃	—	4	2	no	—
193	C₄×D₁₃	—	8	1	no	—
194	Dic₂₆	—	2	2	no	—
195	Dic₂₆	—	2	1	no	—
196	Dic₂₆	—	2	2	no	—
197	Dic₂₆	—	2	1	no	—
198	Dic₂₆	—	4	2	no	—
199	C₈×C₁₃	—	2	2	no	—
200	C₈×C₁₃	—	2	2	no	—
201	C₈×C₁₃	—	2	2	no	—
202	C₈×C₁₃	—	2	2	no	—
203	C₈×C₁₃	—	4	1	no	—
204	C₈×C₁₃	C₂×M₁₆	1	4	yes	—
205	#1055	—	4	2	no	—
206	#1055	—	4	1	no	—
207	#1055	—	4	1	no	—
208	C₂×#137	—	13	1	no	—
209	C₄×#41	—	13	1	no	—
210	C₂×C₄×Q₈	—	13	1	no	—
211	#446	—	13	2	no	—
212	#446	—	13	2	no	—
213	#446	—	13	2	no	—
214	#446	—	26	1	no	—
215	#446	—	26	1	no	—
216	#441	—	13	2	no	—
217	#440	—	13	2	no	—
218	C₄×Q₁₆	—	13	2	no	—
219	C₄×SD₁₆	—	13	2	no	—
220	#436	—	13	2	no	—
221	#435	—	26	2	no	—
222	#432	—	26	1	no	—
223	#432	—	26	2	no	—
224	#431	—	13	1	no	—
225	#431	C₂×D₁₃	1	1	yes	characteristic
226	#428	—	13	1	no	—
227	#423	—	26	1	no	—
228	C₂×C₄⋊C₈	—	13	1	no	—
229	#419	—	13	1	no	—
230	#417	—	13	1	no	—
231	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
232	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
233	#335	—	13	2	no	—
234	#334	—	13	2	no	—
235	Q₈⋊C₈	—	13	2	no	—
236	Q₈⋊C₈	—	13	1	no	—
237	Q₈⋊C₈	—	13	2	no	—
238	Q₈⋊C₈	—	13	1	no	—
239	D₄⋊C₈	—	13	1	no	—
240	D₄⋊C₈	—	13	1	no	—
241	#322	C₂×D₁₃	1	2	yes	—
242	C₈²	C₂×D₁₃	1	2	yes	—
243	C₂²×C₁₃	—	2	1	no	—
244	C₂²×C₁₃	—	2	1	no	—
245	C₂²×C₁₃	#436	1	2	yes	—
246	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
247	C₂×D₁₃	—	4	1	no	—
248	C₂×D₁₃	—	4	1	no	—
249	C₂×D₁₃	—	4	1	no	—
250	C₄×C₁₃	—	2	1	no	—
251	C₄×C₁₃	—	2	1	no	—
252	C₄×C₁₃	—	2	1	no	—
253	C₄×C₁₃	#436	1	2	yes	—
254	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
255	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
256	C₄×C₁₃	#577	1	1	yes	characteristic
257	C₄×C₁₃	#578	1	1	yes	characteristic
258	Dic₁₃	—	4	2	no	—
259	Dic₁₃	—	4	1	no	—
260	Dic₁₃	—	4	1	no	—
261	Dic₁₃	—	4	1	no	—
262	Dic₁₃	—	4	2	no	—
263	C₂×#41	—	13	1	no	—
264	C₂²×Q₈	—	13	1	no	—
265	#137	—	26	4	no	—
266	C₂×Q₁₆	—	13	2	no	—
267	C₂×SD₁₆	—	13	2	no	—
268	C₂×M₁₆	—	26	2	no	—
269	C₂×M₁₆	C₄×D₁₃	1	1	yes	characteristic
270	C₂×M₁₆	C₄×D₁₃	1	1	yes	characteristic
271	C₂²×C₈	—	2	1	no	—
272	C₂²×C₈	—	26	1	no	—
273	C₄×Q₈	—	13	2	no	—
274	C₄×Q₈	—	13	1	no	—
275	C₄×Q₈	—	13	2	no	—
276	C₄×Q₈	—	13	1	no	—
277	C₄×Q₈	—	26	1	no	—
278	C₄×Q₈	—	26	1	no	—
279	C₄×D₄	—	13	1	no	—
280	C₄×D₄	—	13	1	no	—
281	C₄×D₄	—	26	1	no	—
282	C₄×D₄	—	26	1	no	—
283	#117	—	13	1	no	—
284	#117	—	26	1	no	—
285	C₂×C₄⋊C₄	—	13	1	no	—
286	C₂×C₄⋊C₄	—	26	1	no	—
287	C₂×C₄²	—	26	1	no	—
288	C₂×C₄²	—	26	1	no	—
289	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
290	#107	—	13	2	no	—
291	#106	—	13	2	no	—
292	C₄⋊C₈	—	13	1	no	—
293	C₄⋊C₈	—	13	1	no	—
294	C₄⋊C₈	—	13	2	no	—
295	C₄⋊C₈	—	26	2	no	—
296	C₄⋊C₈	—	26	2	no	—
297	C₄⋊C₈	—	26	2	no	—
298	C₄⋊C₈	—	26	1	no	—
299	C₄⋊C₈	D₅₂	1	1	yes	characteristic
300	C₄⋊C₈	D₅₂	1	1	yes	characteristic
301	#103	—	13	2	no	—
302	#103	—	13	2	no	—
303	#103	—	13	2	no	—
304	#102	—	13	2	no	—
305	C₂²⋊C₈	—	26	1	no	—
306	C₂²⋊C₈	—	26	2	no	—
307	C₂²⋊C₈	D₅₂	1	2	yes	—
308	#97	—	26	2	no	—
309	#97	—	26	2	no	—
310	#97	—	26	2	no	—
311	#97	C₄×D₁₃	1	2	yes	—
312	C₄×C₈	—	2	1	no	—
313	C₄×C₈	—	26	1	no	—
314	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
315	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
316	C₄×C₈	C₂²×D₁₃	1	2	yes	—
317	C₄×C₈	C₂²×D₁₃	1	2	yes	—
318	C₂×C₁₃	—	2	2	no	—
319	C₂×C₁₃	C₂×#436	1	1	yes	characteristic
320	C₂×C₁₃	#2947	1	1	yes	characteristic
321	C₂×C₁₃	#2956	1	1	yes	characteristic
322	D₁₃	—	8	1	no	—
323	#41	—	26	2	no	—
324	#41	—	26	2	no	—
325	C₂×Q₈	—	13	2	no	—
326	C₂×Q₈	—	13	1	no	—
327	C₂×Q₈	—	26	1	no	—
328	C₂×Q₈	—	26	2	no	—
329	C₂×Q₈	—	26	2	no	—
330	C₂×D₄	—	13	1	no	—
331	C₂×D₄	—	26	1	no	—
332	C₂²×C₄	—	26	1	no	—
333	C₂²×C₄	—	26	1	no	—
334	C₂²×C₄	—	26	1	no	—
335	C₂²×C₄	—	26	1	no	—
336	C₂²×C₄	—	26	1	no	—
337	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
339	C₂²×C₄	#6127	1	1	yes	characteristic
340	Q₁₆	—	26	4	no	—
341	SD₁₆	—	26	4	no	—
342	M₁₆	—	2	2	no	—
343	M₁₆	—	104	2	no	—
344	M₁₆	#6094	1	4	yes	complemented
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	4	2	no	—
348	C₂×C₈	—	26	1	no	—
349	C₂×C₈	—	26	1	no	—
350	C₂×C₈	—	26	2	no	—
351	C₂×C₈	—	104	1	no	—
352	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
353	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
354	C₂×C₈	C₂×D₅₂	1	2	yes	—
355	C₂×C₈	C₂×D₅₂	1	2	yes	—
356	C₄⋊C₄	—	13	2	no	—
357	C₄⋊C₄	—	13	1	no	—
358	C₄⋊C₄	—	13	1	no	—
359	C₄⋊C₄	—	26	1	no	—
360	C₄⋊C₄	—	26	2	no	—
361	C₄⋊C₄	—	26	1	no	—
362	C₄⋊C₄	—	26	2	no	—
363	C₄⋊C₄	—	26	1	no	—
364	C₂²⋊C₄	—	26	1	no	—
365	C₂²⋊C₄	—	26	1	no	—
366	C₂²⋊C₄	—	26	1	no	—
367	C₄²	—	26	1	no	—
368	C₄²	—	26	1	no	—
369	C₄²	—	26	2	no	—
370	C₄²	—	26	1	no	—
371	C₄²	—	26	2	no	—
372	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
373	C₄²	C₂×D₅₂	1	1	yes	characteristic
374	C₄²	#6127	1	1	yes	characteristic
375	C₄²	C₂³×D₁₃	1	1	yes	characteristic
376	C₁₃	#17894	1	1	yes	characteristic, complemented, Sylow
377	C₂³	—	26	1	no	—
378	C₂³	C₄×D₅₂	1	1	yes	characteristic
379	Q₈	—	26	2	no	—
380	Q₈	—	26	1	no	—
381	Q₈	—	26	2	no	—
382	Q₈	—	26	1	no	—
383	Q₈	—	52	2	no	—
384	D₄	—	26	1	no	—
385	D₄	—	26	1	no	—
386	D₄	—	52	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	26	1	no	—
391	C₂×C₄	—	26	1	no	—
392	C₂×C₄	—	26	2	no	—
393	C₂×C₄	—	26	1	no	—
394	C₂×C₄	—	26	2	no	—
395	C₂×C₄	—	52	2	no	—
396	C₂×C₄	—	52	1	no	—
397	C₂×C₄	—	52	1	no	—
398	C₂×C₄	—	52	2	no	—
399	C₂×C₄	—	104	1	no	—
400	C₂×C₄	—	104	1	no	—
401	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
402	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
403	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
404	C₂×C₄	C₂×#6094	1	2	yes	—
405	C₂×C₄	#88155	1	2	yes	—
406	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
407	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
408	C₂×C₄	C₂×#6127	1	1	yes	characteristic
409	C₈	—	2	2	no	—
410	C₈	—	2	2	no	—
411	C₈	—	2	2	no	—
412	C₈	—	2	2	no	—
413	C₈	—	4	1	no	—
414	C₈	—	52	1	no	—
415	C₈	—	52	2	no	—
416	C₈	—	52	1	no	—
417	C₈	C₂×#6094	1	4	yes	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	52	1	no	—
421	C₂²	—	52	1	no	—
422	C₂²	—	52	1	no	—
423	C₂²	#11718349	1	2	yes	—
424	C₂²	C₂×C₄×D₅₂	1	1	yes	characteristic
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	52	1	no	—
429	C₄	—	52	1	no	—
430	C₄	—	52	2	no	—
431	C₄	—	52	1	no	—
432	C₄	—	52	2	no	—
433	C₄	#11718349	1	2	yes	—
434	C₄	C₂²×#6094	1	1	yes	characteristic
435	C₄	C₂×#88155	1	1	yes	characteristic
436	C₄	#11719456	1	1	yes	characteristic
437	C₄	#11719458	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	104	1	no	—
440	C₂	C₂×#11718349	1	1	yes	characteristic
441	C₂	#13123681	1	1	yes	characteristic
442	C₂	#13123747	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₅₂
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₈×C₁₃×M₁₆	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×#6127	C₂×C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₈×M₁₆	D₁₃
hypocenter	C₁₃	#17894
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
2. #13123919	C₂	semidirect
4. #13113746	C₂	semidirect
5. #13113740	C₂	semidirect
6. #13113734	C₂	semidirect
7. #13113728	C₂	semidirect
8. #13113588	C₂	semidirect
10. C₂×#11718048	C₂	semidirect
11. C₈×C₁₃×M₁₆	C₂	semidirect
121. C₁₃×M₁₆	M₁₆	semidirect
166. C₈×M₁₆	D₁₃	semidirect
344. M₁₆	#6094	semidirect
376. C₁₃	#17894	semidirect

Maximal subgroups

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

subgroup	index
#13123949	2
#13123919	2
C₄×#88163	2
#13113746	2
#13113740	2
#13113734	2
#13113728	2
#13113588	2
#13113219	2
C₂×#11718048	2
C₈×C₁₃×M₁₆	2
#17894	13