Subgroups — #28557732

Order 15104.

666 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433213	C₂	1	2	yes	maximal
2	#21422863	C₂	1	4	yes	maximal, complemented
3	#21422859	C₂	1	2	yes	maximal, complemented
4	#21422852	C₂	1	2	yes	maximal, complemented
5	#21422848	C₂	1	2	yes	maximal, complemented
6	#21422844	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16837153	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#131×C₅₉	C₂	1	1	yes	maximal, characteristic
9	#16837533	—	2	2	no	—
10	#16837480	—	2	2	no	—
11	#16837474	—	2	4	no	—
12	#16837459	C₂²	1	4	yes	—
13	#16837455	C₂²	1	2	yes	—
14	#16837426	C₂²	1	4	yes	—
15	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
16	#16837155	C₂²	1	4	yes	—
17	#16837155	C₂²	1	2	yes	—
18	#16837153	C₂²	1	4	yes	—
19	#16837153	C₂²	1	1	yes	characteristic
20	#16837153	C₂²	1	2	yes	—
21	#16837153	C₂²	1	1	yes	characteristic
22	#16837153	C₂²	1	2	yes	—
23	C₂×#131×C₅₉	C₄	1	1	yes	characteristic
24	C₂×#131×C₅₉	C₄	1	1	yes	characteristic
25	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
26	C₅₉×#405	C₄	1	1	yes	characteristic
27	C₅₉×#405	C₄	1	2	yes	—
28	C₅₉×#405	C₄	1	2	yes	—
29	C₅₉×#405	C₄	1	1	yes	characteristic
30	C₄×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
31	C₄×M₁₆×C₅₉	C₂²	1	2	yes	—
32	C₂×C₄×C₈×C₅₉	C₂²	1	2	yes	—
33	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
34	C₂×#11745664	—	2	4	no	—
35	C₂²×C₅₉⋊C₈	—	2	2	no	—
36	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
37	C₄⋊(C₅₉⋊C₈)	—	2	4	no	—
38	C₄⋊(C₅₉⋊C₈)	C₂³	1	4	yes	—
39	C₄⋊(C₅₉⋊C₈)	C₂³	1	2	yes	—
40	C₄⋊(C₅₉⋊C₈)	C₂³	1	2	yes	—
41	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
42	C₂²⋊(C₅₉⋊C₈)	—	2	4	no	—
43	#14273638	—	2	4	no	—
44	C₄×C₅₉⋊C₈	—	2	2	no	—
45	C₂×#41×C₅₉	C₂×C₄	1	1	yes	characteristic
46	#131×C₅₉	—	2	4	no	—
47	#131×C₅₉	—	2	4	no	—
48	C₂×M₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
49	C₂×M₁₆×C₅₉	C₂×C₄	1	2	yes	—
50	C₂×M₁₆×C₅₉	C₂×C₄	1	2	yes	—
51	C₂×M₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₈×C₅₉	C₂×C₄	1	2	yes	—
54	C₂²×C₈×C₅₉	C₂×C₄	1	2	yes	—
55	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
56	C₄×Q₈×C₅₉	D₄	1	1	yes	characteristic
57	C₄×Q₈×C₅₉	Q₈	1	1	yes	characteristic
58	C₄×D₄×C₅₉	D₄	1	2	yes	—
59	C₄×D₄×C₅₉	D₄	1	1	yes	characteristic
60	C₄×D₄×C₅₉	Q₈	1	2	yes	—
61	C₄×D₄×C₅₉	Q₈	1	1	yes	characteristic
62	#117×C₅₉	C₂×C₄	1	2	yes	—
63	#117×C₅₉	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
66	#97×C₅₉	C₂×C₄	1	2	yes	—
67	#97×C₅₉	C₂×C₄	1	2	yes	—
68	#97×C₅₉	C₂×C₄	1	2	yes	—
69	C₄×C₈×C₅₉	C₂×C₄	1	2	yes	—
70	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
71	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
72	C₄×C₈×C₅₉	C₂×C₄	1	2	yes	—
73	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
74	C₄×C₈×C₅₉	C₂³	1	2	yes	—
75	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
76	#41×C₅₉	—	2	2	no	—
77	#41×C₅₉	—	2	2	no	—
78	C₂×Q₈×C₅₉	C₄⋊C₄	1	1	yes	characteristic
79	C₂×D₄×C₅₉	C₄⋊C₄	1	2	yes	—
80	C₂×D₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₅₉	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
85	C₂²×C₄×C₅₉	C₂×Q₈	1	2	yes	—
86	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
87	M₁₆×C₅₉	—	2	2	no	—
88	M₁₆×C₅₉	—	2	4	no	—
89	M₁₆×C₅₉	—	2	4	no	—
90	M₁₆×C₅₉	M₁₆	1	4	yes	complemented
91	C₂×C₈×C₅₉	—	2	2	no	—
92	C₂×C₈×C₅₉	—	2	4	no	—
93	C₂×C₈×C₅₉	—	2	4	no	—
94	C₂×C₈×C₅₉	M₁₆	1	4	yes	complemented
95	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
98	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
100	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
101	C₄⋊C₄×C₅₉	C₄⋊C₄	1	2	yes	—
102	C₄⋊C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
103	C₄⋊C₄×C₅₉	C₄⋊C₄	1	2	yes	—
104	C₄⋊C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
105	C₂²⋊C₄×C₅₉	C₄⋊C₄	1	2	yes	—
106	C₂²⋊C₄×C₅₉	C₄⋊C₄	1	2	yes	—
107	C₂²⋊C₄×C₅₉	C₄⋊C₄	1	2	yes	—
108	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
109	C₄²×C₅₉	C₂²×C₄	1	2	yes	—
110	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₅₉	C₂×D₄	1	2	yes	—
112	C₄²×C₅₉	C₂×Q₈	1	2	yes	—
113	C₄²×C₅₉	C₂×Q₈	1	1	yes	characteristic
114	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
115	#11745664	—	8	4	no	—
116	C₂×C₅₉⋊C₈	—	2	2	no	—
117	C₂×C₅₉⋊C₈	—	2	2	no	—
118	C₂×C₅₉⋊C₈	—	2	4	no	—
119	C₂×C₅₉⋊C₈	—	8	2	no	—
120	C₂³×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
121	C₂³×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
122	Q₈×C₅₉	—	2	2	no	—
123	D₄×C₅₉	—	2	4	no	—
124	D₄×C₅₉	—	2	2	no	—
125	C₂×C₄×C₅₉	—	2	2	no	—
126	C₂×C₄×C₅₉	—	2	2	no	—
127	C₂×C₄×C₅₉	—	2	2	no	—
128	C₂×C₄×C₅₉	—	2	4	no	—
129	C₂×C₄×C₅₉	—	4	1	no	—
130	C₂×C₄×C₅₉	—	4	2	no	—
131	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
132	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
133	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
135	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
136	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₅₉	C₂×M₁₆	1	2	yes	—
138	C₂×C₄×C₅₉	C₂×M₁₆	1	2	yes	—
139	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
140	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
141	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
142	C₈×C₅₉	—	2	1	no	—
143	C₈×C₅₉	—	2	1	no	—
144	C₈×C₅₉	—	2	2	no	—
145	C₈×C₅₉	C₂×M₁₆	1	2	yes	—
146	C₈×C₅₉	C₂×M₁₆	1	4	yes	—
147	C₈×C₅₉	C₂×M₁₆	1	2	yes	—
148	C₅₉⋊C₈	—	4	2	no	—
149	C₅₉⋊C₈	—	4	4	no	—
150	C₅₉⋊C₈	—	4	2	no	—
151	#17798	—	59	1	no	maximal, Sylow
152	C₂²×C₅₉	—	2	1	no	—
153	C₂²×C₅₉	—	2	1	no	—
154	C₂²×C₅₉	—	2	2	no	—
155	C₂²×C₅₉	—	2	2	no	—
156	C₂²×C₅₉	—	2	2	no	—
157	C₂²×C₅₉	#423	1	2	yes	—
158	C₂²×C₅₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
159	C₄×C₅₉	—	2	2	no	—
160	C₄×C₅₉	—	2	1	no	—
161	C₄×C₅₉	—	2	2	no	—
162	C₄×C₅₉	—	2	1	no	—
163	C₄×C₅₉	—	2	1	no	—
164	C₄×C₅₉	—	2	2	no	—
165	C₄×C₅₉	#423	1	2	yes	—
166	C₄×C₅₉	C₂²×M₁₆	1	1	yes	characteristic
167	C₄×C₅₉	C₂²×M₁₆	1	1	yes	characteristic
168	C₄×C₅₉	#577	1	2	yes	—
169	#2989	—	59	2	no	—
170	C₄×#131	D₅₉	1	1	yes	characteristic
171	#1569	—	59	4	no	—
172	#1568	—	59	2	no	—
173	#1566	—	59	2	no	—
174	#1565	—	59	2	no	—
175	#1564	—	59	1	no	—
176	C₂×#334	—	59	1	no	—
177	C₂×C₅₉	—	2	2	no	—
178	C₂×C₅₉	—	4	2	no	—
179	C₂×C₅₉	C₂×#423	1	1	yes	characteristic
180	C₂×C₅₉	#2912	1	1	yes	characteristic
181	C₂×C₅₉	#2916	1	1	yes	characteristic
182	C₂×#131	Dic₅₉	1	1	yes	characteristic
183	C₂×#131	Dic₅₉	1	1	yes	characteristic
184	C₄×#41	C₂×D₅₉	1	1	yes	characteristic
185	#446	—	118	2	no	—
186	#436	—	118	2	no	—
187	#435	—	118	4	no	—
188	#432	—	59	4	no	—
189	#431	—	59	2	no	—
190	#423	—	59	4	no	—
191	C₂×C₄⋊C₈	—	59	2	no	—
192	#405	Dic₅₉	1	1	yes	characteristic
193	#405	Dic₅₉	1	2	yes	—
194	#405	Dic₅₉	1	2	yes	—
195	#405	Dic₅₉	1	1	yes	characteristic
196	C₄×M₁₆	C₂×D₅₉	1	1	yes	characteristic
197	C₄×M₁₆	C₂×D₅₉	1	2	yes	—
198	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
199	C₂×C₄×C₈	C₂×D₅₉	1	2	yes	—
200	#335	—	59	2	no	—
201	#335	—	59	4	no	—
202	#334	—	59	2	no	—
203	#334	—	59	2	no	—
204	#334	—	59	1	no	—
205	#334	—	59	1	no	—
206	#334	—	59	4	no	—
207	C₅₉	#17798	1	1	yes	characteristic, complemented, Sylow
208	C₂×#41	C₂×Dic₅₉	1	1	yes	characteristic
209	#131	—	2	4	no	—
210	#131	—	2	4	no	—
211	C₂×M₁₆	—	118	4	no	—
212	C₂×M₁₆	C₂×Dic₅₉	1	1	yes	characteristic
213	C₂×M₁₆	C₂×Dic₅₉	1	2	yes	—
214	C₂×M₁₆	C₂×Dic₅₉	1	2	yes	—
215	C₂×M₁₆	C₂×Dic₅₉	1	1	yes	characteristic
216	C₂²×C₈	—	118	2	no	—
217	C₂²×C₈	C₂×Dic₅₉	1	1	yes	characteristic
218	C₂²×C₈	C₂×Dic₅₉	1	2	yes	—
219	C₂²×C₈	C₂×Dic₅₉	1	2	yes	—
220	C₂²×C₈	C₂×Dic₅₉	1	1	yes	characteristic
221	C₄×Q₈	Dic₁₁₈	1	1	yes	characteristic
222	C₄×Q₈	D₂₃₆	1	1	yes	characteristic
223	C₄×D₄	Dic₁₁₈	1	2	yes	—
224	C₄×D₄	Dic₁₁₈	1	1	yes	characteristic
225	C₄×D₄	D₂₃₆	1	2	yes	—
226	C₄×D₄	D₂₃₆	1	1	yes	characteristic
227	#117	C₂×Dic₅₉	1	2	yes	—
228	#117	C₂×Dic₅₉	1	1	yes	characteristic
229	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
230	C₂×C₄²	C₂²×D₅₉	1	2	yes	—
231	C₄⋊C₈	—	59	4	no	—
232	C₄⋊C₈	—	59	2	no	—
233	C₄⋊C₈	—	59	2	no	—
234	C₄⋊C₈	—	118	2	no	—
235	C₄⋊C₈	—	118	4	no	—
236	C₂²⋊C₈	—	118	2	no	—
237	C₂²⋊C₈	—	118	4	no	—
238	#97	—	118	4	no	—
239	#97	C₂×Dic₅₉	1	2	yes	—
240	#97	C₂×Dic₅₉	1	2	yes	—
241	#97	C₂×Dic₅₉	1	2	yes	—
242	C₄×C₈	—	118	2	no	—
243	C₄×C₈	C₂×Dic₅₉	1	2	yes	—
244	C₄×C₈	C₂×Dic₅₉	1	1	yes	characteristic
245	C₄×C₈	C₂×Dic₅₉	1	1	yes	characteristic
246	C₄×C₈	C₂×Dic₅₉	1	2	yes	—
247	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
248	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
249	C₄×C₈	C₂²×D₅₉	1	2	yes	—
250	#41	—	2	2	no	—
251	#41	—	2	2	no	—
252	C₂×Q₈	C₄⋊Dic₅₉	1	1	yes	characteristic
253	C₂×D₄	C₄⋊Dic₅₉	1	2	yes	—
254	C₂×D₄	C₄⋊Dic₅₉	1	1	yes	characteristic
255	C₂²×C₄	C₂×Dic₁₁₈	1	2	yes	—
256	C₂²×C₄	C₂×Dic₁₁₈	1	1	yes	characteristic
257	C₂²×C₄	C₂×D₂₃₆	1	1	yes	characteristic
258	C₂²×C₄	C₂×D₂₃₆	1	2	yes	—
259	C₂²×C₄	C₂²×Dic₅₉	1	2	yes	—
260	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
261	M₁₆	—	2	2	no	—
262	M₁₆	—	2	4	no	—
263	M₁₆	—	2	4	no	—
264	M₁₆	—	472	4	no	—
265	M₁₆	#11745664	1	4	yes	complemented
266	C₂×C₈	—	2	2	no	—
267	C₂×C₈	—	2	4	no	—
268	C₂×C₈	—	2	4	no	—
269	C₂×C₈	—	118	2	no	—
270	C₂×C₈	—	118	2	no	—
271	C₂×C₈	—	118	4	no	—
272	C₂×C₈	—	472	2	no	—
273	C₂×C₈	#11745664	1	4	yes	complemented
274	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
275	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
276	C₂×C₈	C₂²×Dic₅₉	1	2	yes	—
277	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
278	C₂×C₈	C₂²×Dic₅₉	1	2	yes	—
279	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
280	C₄⋊C₄	C₄⋊Dic₅₉	1	2	yes	—
281	C₄⋊C₄	C₄⋊Dic₅₉	1	1	yes	characteristic
282	C₄⋊C₄	C₄⋊Dic₅₉	1	2	yes	—
283	C₄⋊C₄	C₄⋊Dic₅₉	1	1	yes	characteristic
284	C₂²⋊C₄	C₄⋊Dic₅₉	1	2	yes	—
285	C₂²⋊C₄	C₄⋊Dic₅₉	1	2	yes	—
286	C₂²⋊C₄	C₄⋊Dic₅₉	1	2	yes	—
287	C₄²	C₂×Dic₁₁₈	1	2	yes	—
288	C₄²	C₂×Dic₁₁₈	1	1	yes	characteristic
289	C₄²	C₂×D₂₃₆	1	1	yes	characteristic
290	C₄²	C₂×D₂₃₆	1	2	yes	—
291	C₄²	C₂²×Dic₅₉	1	1	yes	characteristic
292	C₄²	C₂²×Dic₅₉	1	2	yes	—
293	C₄²	C₂³×D₅₉	1	1	yes	characteristic
294	C₂³	C₂×C₄⋊Dic₅₉	1	2	yes	—
295	C₂³	C₂×C₄⋊Dic₅₉	1	1	yes	characteristic
296	Q₈	—	2	2	no	—
297	D₄	—	2	4	no	—
298	D₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	4	1	no	—
304	C₂×C₄	—	4	2	no	—
305	C₂×C₄	C₂×C₄⋊Dic₅₉	1	2	yes	—
306	C₂×C₄	C₂×C₄⋊Dic₅₉	1	1	yes	characteristic
307	C₂×C₄	C₂×C₄⋊Dic₅₉	1	2	yes	—
308	C₂×C₄	C₂×C₄⋊Dic₅₉	1	1	yes	characteristic
309	C₂×C₄	C₂×C₄⋊Dic₅₉	1	2	yes	—
310	C₂×C₄	C₂×C₄⋊Dic₅₉	1	1	yes	characteristic
311	C₂×C₄	C₂×#11745664	1	2	yes	—
312	C₂×C₄	C₂×#11745664	1	2	yes	—
313	C₂×C₄	C₂³×Dic₅₉	1	1	yes	characteristic
314	C₂×C₄	C₂²×D₂₃₆	1	1	yes	characteristic
315	C₂×C₄	C₂²×Dic₁₁₈	1	1	yes	characteristic
316	C₈	—	2	1	no	—
317	C₈	—	2	1	no	—
318	C₈	—	2	2	no	—
319	C₈	—	236	2	no	—
320	C₈	—	236	4	no	—
321	C₈	—	236	2	no	—
322	C₈	C₂×#11745664	1	2	yes	—
323	C₈	C₂×#11745664	1	4	yes	—
324	C₈	C₂×#11745664	1	2	yes	—
325	C₂²	—	2	1	no	—
326	C₂²	—	2	1	no	—
327	C₂²	—	2	2	no	—
328	C₂²	—	2	2	no	—
329	C₂²	—	2	2	no	—
330	C₂²	#16837426	1	2	yes	—
331	C₂²	C₂²×C₄⋊Dic₅₉	1	1	yes	characteristic
332	C₄	—	2	2	no	—
333	C₄	—	2	1	no	—
334	C₄	—	2	2	no	—
335	C₄	—	2	1	no	—
336	C₄	—	2	1	no	—
337	C₄	—	2	2	no	—
338	C₄	#16837426	1	2	yes	—
339	C₄	C₂²×#11745664	1	1	yes	characteristic
340	C₄	C₂²×#11745664	1	1	yes	characteristic
341	C₄	#16838214	1	2	yes	—
342	C₂	—	2	2	no	—
343	C₂	—	4	2	no	—
344	C₂	C₂×#16837426	1	1	yes	characteristic
345	C₂	#21432691	1	1	yes	characteristic
346	C₂	#21432707	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₃₆
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₄²	C₂³×D₅₉
Fitting	C₄×#131×C₅₉	C₂
socle	C₂²×C₅₉	C₂²×C₄⋊C₄
prime radical	C₂×#41×C₅₉	C₂×C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	C₄×#131	D₅₉
hypocenter	C₅₉	#17798
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ C₄×#131

Complements

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

N	H ≅ G/N	type
2. #21422863	C₂	semidirect
3. #21422859	C₂	semidirect
4. #21422852	C₂	semidirect
5. #21422848	C₂	semidirect
6. #21422844	C₂	semidirect
7. C₂×#16837153	C₂	semidirect
90. M₁₆×C₅₉	M₁₆	semidirect
94. C₂×C₈×C₅₉	M₁₆	semidirect
207. C₅₉	#17798	semidirect
265. M₁₆	#11745664	semidirect
273. C₂×C₈	#11745664	semidirect

Maximal subgroups

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

subgroup	index
#21433213	2
#21422863	2
#21422859	2
#21422852	2
#21422848	2
#21422844	2
C₂×#16837153	2
C₄×#131×C₅₉	2
#17798	59