Subgroups — #15834898

Order 3328.

612 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13125395	C₂	1	1	yes	maximal, characteristic
2	#13123937	C₂	1	1	yes	maximal, characteristic, complemented
3	#13123902	C₂	1	1	yes	maximal, characteristic
4	#13113725	C₂	1	2	yes	maximal, complemented
5	#13113713	C₂	1	2	yes	maximal, complemented
6	#13113692	C₂	1	2	yes	maximal, complemented
7	#13113635	C₂	1	2	yes	maximal, complemented
8	#13113256	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113252	C₂	1	1	yes	maximal, characteristic
10	C₈×#6099	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1564	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719182	C₂²	1	1	yes	characteristic
13	#11719175	C₂²	1	1	yes	characteristic
14	C₁₃×#431	C₂²	1	1	yes	characteristic
15	C₁₃×#431	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
17	#11718775	C₄	1	2	yes	—
18	#11718775	C₄	1	2	yes	—
19	#11718586	C₂²	1	1	yes	characteristic
20	C₄×#6099	C₂²	1	1	yes	characteristic
21	#11718499	C₂²	1	2	yes	—
22	#11718495	C₂²	1	2	yes	—
23	#11718492	C₂²	1	2	yes	—
24	#11718491	C₂²	1	2	yes	—
25	#11718388	—	2	2	no	—
26	#11718381	—	2	2	no	—
27	#11718355	C₄	1	1	yes	characteristic
28	#11718354	C₄	1	1	yes	characteristic
29	C₄×#6095	C₂²	1	2	yes	—
30	C₄×#6095	C₂²	1	2	yes	—
31	#11718349	—	2	1	no	—
32	C₈×D₅₂	—	2	1	no	—
33	#11718342	C₄	1	1	yes	characteristic
34	#11718341	C₄	1	1	yes	characteristic
35	#11718340	—	2	1	no	—
36	C₈×Dic₂₆	—	2	1	no	—
37	C₁₃×#335	C₂²	1	1	yes	characteristic
38	C₁₃×#335	C₂²	1	1	yes	characteristic
39	C₁₃×#334	C₂²	1	1	yes	characteristic
40	C₁₃×#334	C₂²	1	1	yes	characteristic
41	#11718076	C₂²	1	2	yes	—
42	#11718076	C₂²	1	2	yes	—
43	#11718075	C₂²	1	2	yes	—
44	#11718075	C₂²	1	2	yes	—
45	#11718046	C₂²	1	2	yes	—
46	C₈×#1055	C₂²	1	2	yes	—
47	C₂×#6127	—	2	1	no	—
48	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
51	#88184	—	2	1	no	—
52	#88184	C₂×C₄	1	2	yes	—
53	#88180	—	2	1	no	—
54	#88178	—	2	1	no	—
55	#88178	C₂×C₄	1	2	yes	—
56	C₂×#6099	—	2	1	no	—
57	C₂×#6095	C₂×C₄	1	2	yes	—
58	C₂×#6095	C₂×C₄	1	2	yes	—
59	C₂×#6094	—	2	2	no	—
60	C₂×C₈×D₁₃	—	2	2	no	—
61	#88129	—	2	1	no	—
62	#88128	C₂×C₄	1	1	yes	characteristic
63	C₄×D₅₂	—	2	1	no	—
64	C₄×D₅₂	C₂³	1	2	yes	—
65	#88124	—	2	1	no	—
66	#88123	C₂×C₄	1	1	yes	characteristic
67	#88123	C₂×C₄	1	1	yes	characteristic
68	#88123	C₂×C₄	1	1	yes	characteristic
69	C₄×Dic₂₆	—	2	1	no	—
70	C₄×Dic₂₆	C₂³	1	2	yes	—
71	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
72	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
73	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
74	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
75	C₁₃×C₂²⋊C₈	—	2	1	no	—
76	C₁₃×C₂²⋊C₈	—	2	1	no	—
77	C₄×C₈×C₁₃	—	2	1	no	—
78	C₄×C₈×C₁₃	—	2	1	no	—
79	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
80	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
81	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
83	C₂²⋊#1055	D₄	1	2	yes	—
84	#88061	C₂×C₄	1	2	yes	—
85	#88061	C₂×C₄	1	2	yes	—
86	#88060	—	2	2	no	—
87	#88060	—	2	2	no	—
88	#88057	C₂×C₄	1	2	yes	—
89	#88057	C₂×C₄	1	2	yes	—
90	#88056	C₂×C₄	1	2	yes	—
91	#88056	C₂×C₄	1	2	yes	—
92	#88055	—	2	2	no	—
93	#88054	—	2	2	no	—
94	#88054	—	2	2	no	—
95	C₈×Dic₁₃	—	2	2	no	—
96	C₄⋊#1055	D₄	1	1	yes	characteristic
97	C₄⋊#1055	D₄	1	1	yes	characteristic
98	#88043	—	2	1	no	—
99	C₄×#1055	C₂³	1	2	yes	—
100	C₄×#1055	C₂³	1	2	yes	—
101	#18085	—	13	1	no	maximal, Sylow
102	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
105	C₂×C₂²⋊D₁₃	—	2	2	no	—
106	#6127	—	8	1	no	—
107	#6127	—	8	1	no	—
108	C₂×D₅₂	—	2	1	no	—
109	C₂×D₅₂	—	2	1	no	—
110	C₂×D₅₂	C₂²×C₄	1	2	yes	—
111	C₂×C₄×D₁₃	—	2	2	no	—
112	C₂×Dic₂₆	—	2	1	no	—
113	C₂×Dic₂₆	—	2	1	no	—
114	C₂×Dic₂₆	C₂²×C₄	1	2	yes	—
115	C₂×C₈×C₁₃	—	2	2	no	—
116	C₂×C₈×C₁₃	—	2	1	no	—
117	C₂×C₈×C₁₃	—	2	1	no	—
118	C₂×C₈×C₁₃	—	2	1	no	—
119	C₂×C₈×C₁₃	—	2	1	no	—
120	C₂×C₈×C₁₃	—	4	1	no	—
121	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₁₃	#41	1	1	yes	characteristic
128	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
129	C₂²⋊Dic₁₃	—	2	2	no	—
130	#6103	—	2	2	no	—
131	#6103	—	2	2	no	—
132	C₄⋊Dic₁₃	—	2	1	no	—
133	C₄⋊Dic₁₃	—	2	1	no	—
134	C₄⋊Dic₁₃	—	2	1	no	—
135	C₄⋊Dic₁₃	—	2	1	no	—
136	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
137	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
138	#6101	—	2	2	no	—
139	#6101	—	2	2	no	—
140	C₄×Dic₁₃	—	2	2	no	—
141	#6099	—	2	4	no	—
142	C₂×#1055	—	2	2	no	—
143	C₂×#1055	C₂×D₄	1	2	yes	—
144	C₂×#1055	C₂×D₄	1	2	yes	—
145	#6095	—	2	4	no	—
146	#6095	—	4	2	no	—
147	#6094	—	8	2	no	—
148	C₈×D₁₃	—	8	2	no	—
149	#3167	—	13	1	no	—
150	#2986	—	13	1	no	—
151	#2979	—	13	1	no	—
152	#1590	—	13	2	no	—
153	#1588	—	13	2	no	—
154	#1585	—	13	2	no	—
155	C₈×SD₁₆	—	13	2	no	—
156	#1564	D₁₃	1	1	yes	characteristic, complemented
157	#1485	—	13	1	no	—
158	#1484	—	13	1	no	—
159	C₈×M₁₆	—	13	1	no	—
160	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
161	C₂²×D₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	2	1	no	—
163	C₂×C₄×C₁₃	—	2	1	no	—
164	C₂×C₄×C₁₃	—	2	1	no	—
165	C₂×C₄×C₁₃	—	2	1	no	—
166	C₂×C₄×C₁₃	—	2	2	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	C₂³×C₄	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
173	C₂²⋊D₁₃	—	8	2	no	—
174	C₂×Dic₁₃	—	2	2	no	—
175	C₂×Dic₁₃	—	2	2	no	—
176	C₂×Dic₁₃	—	2	2	no	—
177	D₅₂	—	2	2	no	—
178	D₅₂	—	2	2	no	—
179	D₅₂	—	4	2	no	—
180	D₅₂	—	8	1	no	—
181	C₄×D₁₃	—	4	2	no	—
182	C₄×D₁₃	—	4	2	no	—
183	Dic₂₆	—	2	2	no	—
184	Dic₂₆	—	2	2	no	—
185	Dic₂₆	—	4	2	no	—
186	Dic₂₆	—	8	1	no	—
187	C₈×C₁₃	—	2	1	no	—
188	C₈×C₁₃	—	2	1	no	—
189	C₈×C₁₃	—	2	1	no	—
190	C₈×C₁₃	—	4	1	no	—
191	C₈×C₁₃	—	4	1	no	—
192	C₈×C₁₃	—	4	1	no	—
193	C₈×C₁₃	—	4	1	no	—
194	C₈×C₁₃	#131	1	2	yes	—
195	#1055	—	2	4	no	—
196	#1055	—	2	2	no	—
197	#1055	—	2	2	no	—
198	#533	—	13	1	no	—
199	#532	—	13	1	no	—
200	#498	—	13	1	no	—
201	#492	—	13	1	no	—
202	#487	—	13	1	no	—
203	#486	—	13	1	no	—
204	#465	—	13	2	no	—
205	#465	—	13	2	no	—
206	#446	—	13	2	no	—
207	#446	—	26	1	no	—
208	C₈×Q₈	—	13	2	no	—
209	C₈×Q₈	—	26	1	no	—
210	C₄×SD₁₆	—	13	2	no	—
211	C₄×SD₁₆	—	13	2	no	—
212	#436	—	13	2	no	—
213	#436	—	26	1	no	—
214	C₈×D₄	—	13	2	no	—
215	C₈×D₄	—	26	1	no	—
216	#433	—	26	2	no	—
217	#431	—	13	1	no	—
218	#431	C₂×D₁₃	1	1	yes	characteristic
219	#431	C₂×D₁₃	1	1	yes	characteristic
220	#408	—	26	2	no	—
221	C₄×M₁₆	—	13	1	no	—
222	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
223	#335	C₂×D₁₃	1	1	yes	characteristic
224	#335	C₂×D₁₃	1	1	yes	characteristic
225	#334	C₂×D₁₃	1	1	yes	characteristic
226	#334	C₂×D₁₃	1	1	yes	characteristic
227	Q₈⋊C₈	—	13	2	no	—
228	Q₈⋊C₈	—	13	2	no	—
229	D₄⋊C₈	—	13	2	no	—
230	D₄⋊C₈	—	13	2	no	—
231	#322	—	13	2	no	—
232	C₈²	—	13	2	no	—
233	C₂²×C₁₃	—	2	1	no	—
234	C₂²×C₁₃	—	2	1	no	—
235	C₂²×C₁₃	—	2	1	no	—
236	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
237	C₂×D₁₃	—	4	2	no	—
238	C₂×D₁₃	—	4	2	no	—
239	C₂×D₁₃	—	4	2	no	—
240	C₄×C₁₃	—	2	1	no	—
241	C₄×C₁₃	—	2	1	no	—
242	C₄×C₁₃	—	2	1	no	—
243	C₄×C₁₃	#443	1	2	yes	—
244	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
245	C₄×C₁₃	#568	1	1	yes	characteristic
246	C₄×C₁₃	#577	1	1	yes	characteristic
247	C₄×C₁₃	#577	1	1	yes	characteristic
248	Dic₁₃	—	4	2	no	—
249	Dic₁₃	—	4	2	no	—
250	Dic₁₃	—	4	2	no	—
251	C₂×#41	—	26	1	no	—
252	C₂×SD₁₆	—	13	2	no	—
253	C₂×SD₁₆	—	13	2	no	—
254	C₂×M₁₆	—	26	2	no	—
255	C₂×M₁₆	—	26	1	no	—
256	C₂²×C₈	—	26	2	no	—
257	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
258	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
259	C₄⋊Q₈	—	13	1	no	—
260	C₄⋊Q₈	—	13	1	no	—
261	C₄⋊Q₈	—	13	1	no	—
262	#127	—	13	1	no	—
263	#125	—	26	1	no	—
264	#124	—	26	1	no	—
265	C₂²⋊Q₈	—	13	2	no	—
266	C₂²⋊Q₈	—	26	1	no	—
267	#121	—	13	2	no	—
268	#121	—	26	1	no	—
269	C₄×Q₈	—	13	2	no	—
270	C₄×Q₈	—	26	1	no	—
271	C₄×D₄	—	13	2	no	—
272	C₄×D₄	—	26	1	no	—
273	#117	—	26	1	no	—
274	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
275	#106	—	13	2	no	—
276	#106	—	13	2	no	—
277	C₄⋊C₈	—	13	1	no	—
278	C₄⋊C₈	—	13	1	no	—
279	C₄⋊C₈	—	26	2	no	—
280	C₄⋊C₈	—	26	2	no	—
281	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
282	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
283	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
284	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
285	#103	—	13	2	no	—
286	#103	—	13	2	no	—
287	#102	—	13	2	no	—
288	#102	—	13	2	no	—
289	C₂²⋊C₈	—	2	1	no	—
290	C₂²⋊C₈	—	2	1	no	—
291	C₂²⋊C₈	—	13	2	no	—
292	C₂²⋊C₈	—	26	2	no	—
293	C₂²⋊C₈	—	26	2	no	—
294	#97	—	26	2	no	—
295	#97	—	26	1	no	—
296	C₄×C₈	—	2	1	no	—
297	C₄×C₈	—	2	1	no	—
298	C₄×C₈	—	13	2	no	—
299	C₄×C₈	—	13	2	no	—
300	C₄×C₈	—	26	2	no	—
301	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
302	C₄×C₈	C₄×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	—	4	1	no	—
306	C₂×C₁₃	#2935	1	1	yes	characteristic
307	C₂×C₁₃	#2949	1	1	yes	characteristic
308	C₂×C₁₃	C₂×#443	1	1	yes	characteristic
309	D₁₃	—	8	2	no	—
310	#41	—	104	1	no	—
311	#41	—	104	1	no	—
312	C₂×Q₈	—	13	2	no	—
313	C₂×Q₈	—	26	1	no	—
314	C₂×Q₈	—	26	1	no	—
315	C₂×D₄	—	13	2	no	—
316	C₂×D₄	—	26	2	no	—
317	C₂×D₄	—	26	1	no	—
318	C₂×D₄	—	26	1	no	—
319	C₂²×C₄	—	26	2	no	—
320	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
321	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
322	C₂²×C₄	#6131	1	1	yes	characteristic
323	SD₁₆	—	26	4	no	—
324	SD₁₆	—	52	2	no	—
325	M₁₆	—	26	4	no	—
326	M₁₆	—	104	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	4	1	no	—
333	C₂×C₈	—	13	2	no	—
334	C₂×C₈	—	13	2	no	—
335	C₂×C₈	—	26	2	no	—
336	C₂×C₈	—	104	2	no	—
337	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
338	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
339	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
340	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
341	C₄⋊C₄	—	13	2	no	—
342	C₄⋊C₄	—	13	2	no	—
343	C₄⋊C₄	—	26	1	no	—
344	C₄⋊C₄	—	26	1	no	—
345	C₄⋊C₄	—	26	1	no	—
346	C₄⋊C₄	—	26	2	no	—
347	C₄⋊C₄	—	26	1	no	—
348	C₄⋊C₄	—	26	2	no	—
349	C₂²⋊C₄	—	26	2	no	—
350	C₂²⋊C₄	—	26	2	no	—
351	C₂²⋊C₄	—	26	2	no	—
352	C₄²	—	26	2	no	—
353	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
354	C₄²	D₄×D₁₃	1	1	yes	characteristic
355	C₄²	#6131	1	1	yes	characteristic
356	C₄²	C₂³×D₁₃	1	1	yes	characteristic
357	C₁₃	#18085	1	1	yes	characteristic, complemented, Sylow
358	C₂³	—	26	2	no	—
359	C₂³	#88147	1	1	yes	characteristic
360	Q₈	—	26	2	no	—
361	Q₈	—	26	2	no	—
362	Q₈	—	52	2	no	—
363	Q₈	—	104	1	no	—
364	D₄	—	26	2	no	—
365	D₄	—	26	2	no	—
366	D₄	—	52	2	no	—
367	D₄	—	104	1	no	—
368	D₄	—	104	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	26	2	no	—
375	C₂×C₄	—	26	2	no	—
376	C₂×C₄	—	26	2	no	—
377	C₂×C₄	—	52	2	no	—
378	C₂×C₄	—	52	2	no	—
379	C₂×C₄	#88147	1	1	yes	characteristic
380	C₂×C₄	#88147	1	1	yes	characteristic
381	C₂×C₄	#88147	1	1	yes	characteristic
382	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
383	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
384	C₂×C₄	C₂×#6131	1	1	yes	characteristic
385	C₈	—	2	1	no	—
386	C₈	—	2	1	no	—
387	C₈	—	2	1	no	—
388	C₈	—	4	1	no	—
389	C₈	—	4	1	no	—
390	C₈	—	4	1	no	—
391	C₈	—	4	1	no	—
392	C₈	—	26	4	no	—
393	C₈	—	26	2	no	—
394	C₈	—	26	2	no	—
395	C₈	#88155	1	2	yes	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	52	2	no	—
400	C₂²	—	52	2	no	—
401	C₂²	—	52	2	no	—
402	C₂²	C₂×#88147	1	1	yes	characteristic
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	52	2	no	—
407	C₄	—	52	2	no	—
408	C₄	—	52	2	no	—
409	C₄	#11718556	1	2	yes	—
410	C₄	C₂×#88155	1	1	yes	characteristic
411	C₄	#11719450	1	1	yes	characteristic
412	C₄	#11719475	1	1	yes	characteristic
413	C₄	#11719475	1	1	yes	characteristic
414	C₂	—	4	1	no	—
415	C₂	—	104	2	no	—
416	C₂	#13123579	1	1	yes	characteristic
417	C₂	#13123694	1	1	yes	characteristic
418	C₂	C₂×#11718556	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#1564	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	#11719182	C₂²
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1564	D₁₃
hypocenter	C₁₃	#18085
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

Complements

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

N	H ≅ G/N	type
2. #13123937	C₂	semidirect
4. #13113725	C₂	semidirect
5. #13113713	C₂	semidirect
6. #13113692	C₂	semidirect
7. #13113635	C₂	semidirect
8. #13113256	C₂	semidirect
10. C₈×#6099	C₂	semidirect
11. C₁₃×#1564	C₂	semidirect
156. #1564	D₁₃	semidirect
357. C₁₃	#18085	semidirect

Maximal subgroups

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

subgroup	index
#13125395	2
#13123937	2
#13123902	2
#13113725	2
#13113713	2
#13113692	2
#13113635	2
#13113256	2
#13113252	2
C₈×#6099	2
C₁₃×#1564	2
#18085	13