Subgroups — #30598846

Order 15616.

588 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21461752	C₂	1	1	yes	maximal, characteristic
2	C₄×#14519844	C₂	1	1	yes	maximal, characteristic
3	C₂×#16840612	C₂	1	2	yes	maximal
4	#21460655	C₂	1	2	yes	maximal
5	C₄×#14519742	C₂	1	1	yes	maximal, characteristic
6	C₂×#14519844	—	2	1	no	—
7	C₂×#14519844	—	2	1	no	—
8	C₂×#14519844	—	2	1	no	—
9	C₂×C₄⋊#92420	C₂²	1	2	yes	—
10	C₂×C₄×#92420	C₂²	1	2	yes	—
11	#16840628	—	2	1	no	—
12	#16840612	—	2	4	no	—
13	C₂×C₄×Dic₁₂₂	C₄	1	1	yes	characteristic
14	C₂×#14519742	C₄	1	1	yes	characteristic
15	C₂×#14519742	C₂²	1	1	yes	characteristic
16	C₄⋊C₄×Dic₆₁	C₄	1	1	yes	characteristic
17	C₄⋊C₄×Dic₆₁	C₂²	1	1	yes	characteristic
18	C₄×#11758196	—	2	1	no	—
19	#16839613	—	2	1	no	—
20	#16839613	—	2	1	no	—
21	C₄²×Dic₆₁	—	2	1	no	—
22	C₄²×Dic₆₁	C₂²	1	1	yes	characteristic
23	C₄×C₄⋊C₄×C₆₁	C₄	1	1	yes	characteristic
24	C₂²×#92420	—	2	2	no	—
25	C₂²×#92420	—	2	2	no	—
26	#14519844	—	2	4	no	—
27	#14519844	—	4	2	no	—
28	#14519844	—	4	2	no	—
29	C₄⋊#92420	—	2	2	no	—
30	C₄⋊#92420	—	2	2	no	—
31	C₄×#92420	—	2	2	no	—
32	C₄×#92420	—	2	2	no	—
33	C₂²×Dic₁₂₂	C₂×C₄	1	1	yes	characteristic
34	C₄×Dic₁₂₂	—	2	2	no	—
35	C₄×Dic₁₂₂	—	2	2	no	—
36	#14519742	—	2	2	no	—
37	#14519742	—	2	1	no	—
38	#14519742	—	2	1	no	—
39	#14519742	C₈	1	4	yes	complemented
40	#14519742	D₄	1	2	yes	—
41	#14519742	Q₈	1	2	yes	—
42	C₂×C₄⋊Dic₆₁	C₂×C₄	1	1	yes	characteristic
43	C₂×#11758196	—	2	1	no	—
44	C₂×#11758196	—	2	1	no	—
45	C₂×#11758196	—	2	1	no	—
46	C₂×C₄×Dic₆₁	—	2	1	no	—
47	C₂×C₄×Dic₆₁	—	2	1	no	—
48	C₂×C₄×Dic₆₁	—	2	1	no	—
49	C₂×C₄×Dic₆₁	—	2	1	no	—
50	C₂×C₄×Dic₆₁	—	2	1	no	—
51	C₂×C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄×Dic₆₁	D₄	1	1	yes	characteristic
53	C₂×C₄×Dic₆₁	D₄	1	1	yes	characteristic
54	C₂×C₄×Dic₆₁	D₄	1	1	yes	characteristic
55	C₂×C₄×Dic₆₁	D₄	1	1	yes	characteristic
56	C₂×C₄×Dic₆₁	C₂³	1	1	yes	characteristic
57	#14519684	—	2	1	no	—
58	#14519684	—	2	1	no	—
59	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₆₁	—	2	1	no	—
62	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
63	#95×C₆₁	—	2	1	no	—
64	C₂²×C₄×C₆₁	—	2	1	no	—
65	C₂²×C₄×C₆₁	—	2	1	no	—
66	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
67	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
69	C₂²×Dic₆₁	—	2	1	no	—
70	C₂²×Dic₆₁	—	2	1	no	—
71	C₂²×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×Dic₆₁	C₂×D₄	1	1	yes	characteristic
74	C₂²×Dic₆₁	C₂×D₄	1	1	yes	characteristic
75	C₂×Dic₁₂₂	—	2	1	no	—
76	C₂×Dic₁₂₂	—	2	1	no	—
77	C₂×Dic₁₂₂	—	2	1	no	—
78	C₂×Dic₁₂₂	C₄⋊C₄	1	2	yes	—
79	C₂×Dic₁₂₂	C₂×C₈	1	2	yes	—
80	C₂×Dic₁₂₂	M₁₆	1	2	yes	—
81	C₂×#92420	—	2	4	no	—
82	C₂×#92420	—	4	2	no	—
83	C₂×#92420	—	4	2	no	—
84	C₂×#92420	—	4	2	no	—
85	C₂×#92420	—	4	2	no	—
86	C₂×#92420	—	4	2	no	—
87	C₄⋊C₄×C₆₁	—	2	1	no	—
88	C₄⋊C₄×C₆₁	—	2	1	no	—
89	C₄⋊C₄×C₆₁	C₄⋊C₄	1	2	yes	—
90	C₄⋊C₄×C₆₁	C₂×C₈	1	2	yes	—
91	C₄²×C₆₁	—	2	1	no	—
92	C₄²×C₆₁	—	2	1	no	—
93	C₄²×C₆₁	—	4	2	no	—
94	C₄⋊Dic₆₁	—	2	1	no	—
95	C₄⋊Dic₆₁	M₁₆	1	2	yes	—
96	#11758196	—	2	4	no	—
97	#11758196	—	2	4	no	—
98	#11758196	—	2	2	no	—
99	#11758196	—	2	2	no	—
100	C₄×Dic₆₁	—	2	4	no	—
101	C₄×Dic₆₁	—	2	4	no	—
102	C₄×Dic₆₁	—	2	2	no	—
103	C₄×Dic₆₁	—	2	2	no	—
104	C₄×Dic₆₁	—	2	2	no	—
105	C₄×Dic₆₁	—	2	1	no	—
106	C₄×Dic₆₁	—	2	1	no	—
107	C₄×Dic₆₁	—	4	1	no	—
108	C₄×Dic₆₁	—	4	2	no	—
109	C₄×Dic₆₁	—	4	1	no	—
110	C₄×Dic₆₁	—	4	1	no	—
111	C₄×Dic₆₁	C₂×C₈	1	2	yes	—
112	C₄×Dic₆₁	M₁₆	1	2	yes	—
113	C₄×Dic₆₁	SD₁₆	1	2	yes	—
114	C₄×Dic₆₁	Q₁₆	1	2	yes	—
115	C₄×Dic₆₁	C₂×D₄	1	1	yes	characteristic
116	C₄×Dic₆₁	C₂×Q₈	1	1	yes	characteristic
117	C₄×Dic₆₁	#41	1	1	yes	characteristic
118	C₄×Dic₆₁	#41	1	1	yes	characteristic
119	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	C₂×C₄×C₆₁	—	2	1	no	—
121	C₂×C₄×C₆₁	—	2	1	no	—
122	C₂×C₄×C₆₁	—	2	2	no	—
123	C₂×C₄×C₆₁	—	2	2	no	—
124	C₂×C₄×C₆₁	—	2	1	no	—
125	C₂×C₄×C₆₁	—	2	1	no	—
126	C₂×C₄×C₆₁	—	2	1	no	—
127	C₂×C₄×C₆₁	—	4	1	no	—
128	C₂×C₄×C₆₁	—	4	1	no	—
129	C₂×C₄×C₆₁	—	4	1	no	—
130	C₂×C₄×C₆₁	—	4	1	no	—
131	C₂×C₄×C₆₁	#103	1	2	yes	—
132	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₆₁	#117	1	1	yes	characteristic
134	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
135	C₂×C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
136	C₂×C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
137	C₂×C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
138	C₂×Dic₆₁	—	2	2	no	—
139	C₂×Dic₆₁	—	2	2	no	—
140	C₂×Dic₆₁	—	2	2	no	—
141	C₂×Dic₆₁	—	2	1	no	—
142	C₂×Dic₆₁	—	2	1	no	—
143	C₂×Dic₆₁	—	2	1	no	—
144	C₂×Dic₆₁	—	2	1	no	—
145	C₂×Dic₆₁	—	2	2	no	—
146	C₂×Dic₆₁	—	4	1	no	—
147	C₂×Dic₆₁	—	4	1	no	—
148	C₂×Dic₆₁	C₂²⋊C₈	1	2	yes	—
149	C₂×Dic₆₁	C₂²⋊C₈	1	2	yes	—
150	C₂×Dic₆₁	#103	1	2	yes	—
151	C₂×Dic₆₁	#104	1	2	yes	—
152	C₂×Dic₆₁	#121	1	1	yes	characteristic
153	C₂×Dic₆₁	#121	1	1	yes	characteristic
154	C₂×Dic₆₁	C₂²⋊Q₈	1	1	yes	characteristic
155	C₂×Dic₆₁	C₂²⋊Q₈	1	1	yes	characteristic
156	C₂×Dic₆₁	C₂×SD₁₆	1	1	yes	characteristic
157	C₂×Dic₆₁	C₂×Q₁₆	1	1	yes	characteristic
158	C₂×Dic₆₁	AGL(1,ℤ/8)	1	1	yes	characteristic
159	C₂×Dic₆₁	#137	1	1	yes	characteristic
160	Dic₁₂₂	—	2	2	no	—
161	Dic₁₂₂	—	2	2	no	—
162	Dic₁₂₂	—	2	2	no	—
163	Dic₁₂₂	C₄⋊C₈	1	4	yes	complemented
164	#92420	—	4	4	no	—
165	#92420	—	8	2	no	—
166	#8564	—	61	1	no	maximal, Sylow
167	C₂²×C₆₁	#380	1	1	yes	characteristic
168	C₂²×C₆₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
169	C₂²×C₆₁	#407	1	1	yes	characteristic
170	C₂²×C₆₁	C₂×#103	1	1	yes	characteristic
171	C₂²×C₆₁	#417	1	1	yes	characteristic
172	C₂²×C₆₁	C₂×#104	1	1	yes	characteristic
173	C₂²×C₆₁	#421	1	1	yes	characteristic
174	C₄×C₆₁	—	2	2	no	—
175	C₄×C₆₁	—	4	2	no	—
176	C₄×C₆₁	—	4	2	no	—
177	C₄×C₆₁	—	4	1	no	—
178	C₄×C₆₁	C₂×C₄⋊C₈	1	1	yes	characteristic
179	C₄×C₆₁	#423	1	1	yes	characteristic
180	C₄×C₆₁	#431	1	1	yes	characteristic
181	C₄×C₆₁	#432	1	1	yes	characteristic
182	Dic₆₁	—	2	4	no	—
183	Dic₆₁	—	2	1	no	—
184	Dic₆₁	—	2	1	no	—
185	Dic₆₁	—	2	2	no	—
186	Dic₆₁	—	4	2	no	—
187	Dic₆₁	Q₈⋊C₈	1	4	yes	complemented
188	Dic₆₁	#460	1	1	yes	characteristic
189	Dic₆₁	#462	1	1	yes	characteristic
190	Dic₆₁	#475	1	1	yes	characteristic
191	Dic₆₁	#477	1	1	yes	characteristic
192	C₄²×Q₈	—	61	1	no	—
193	#1842	—	61	1	no	—
194	C₄×C₄⋊C₈	—	61	1	no	—
195	C₂×Q₈⋊C₈	—	61	2	no	—
196	#1279	—	61	2	no	—
197	C₂×C₆₁	C₂×Q₈⋊C₈	1	1	yes	characteristic
198	C₂×C₆₁	#1477	1	1	yes	characteristic
199	C₂×C₆₁	#1487	1	1	yes	characteristic
200	C₂×C₆₁	#1489	1	1	yes	characteristic
201	C₂×C₆₁	#1797	1	1	yes	characteristic
202	C₂×C₆₁	#1803	1	1	yes	characteristic
203	C₂×C₆₁	#1806	1	1	yes	characteristic
204	C₂×C₄×Q₈	—	61	1	no	—
205	C₂×C₄×Q₈	—	61	1	no	—
206	C₂×C₄×Q₈	—	61	1	no	—
207	C₂×C₄⋊C₈	—	61	2	no	—
208	C₂×C₄⋊C₈	—	122	1	no	—
209	C₂×C₄⋊C₈	—	122	1	no	—
210	C₂×C₄⋊C₈	—	122	1	no	—
211	C₂×C₄×C₈	—	61	2	no	—
212	C₄×C₄⋊C₄	—	61	1	no	—
213	C₄×C₄⋊C₄	—	61	1	no	—
214	C₄×C₄⋊C₄	—	122	1	no	—
215	C₄×C₄⋊C₄	—	122	1	no	—
216	C₄×C₄⋊C₄	—	122	1	no	—
217	C₄×C₄⋊C₄	#6923	1	1	yes	characteristic
218	C₄³	—	61	1	no	—
219	C₄³	—	122	1	no	—
220	#336	—	122	1	no	—
221	Q₈⋊C₈	—	122	4	no	—
222	C₆₁	#8564	1	1	yes	characteristic, complemented, Sylow
223	C₂²×Q₈	—	61	1	no	—
224	C₂²×C₈	—	122	2	no	—
225	C₂²×C₈	—	122	2	no	—
226	C₄×Q₈	—	61	4	no	—
227	C₄×Q₈	—	61	2	no	—
228	C₄×Q₈	—	61	2	no	—
229	C₄×Q₈	—	122	2	no	—
230	C₄×Q₈	—	122	2	no	—
231	C₄×Q₈	—	122	1	no	—
232	C₄×Q₈	—	122	1	no	—
233	C₄×Q₈	—	122	2	no	—
234	C₂×C₄⋊C₄	—	61	1	no	—
235	C₂×C₄⋊C₄	—	122	1	no	—
236	C₂×C₄⋊C₄	—	122	1	no	—
237	C₂×C₄⋊C₄	—	122	1	no	—
238	C₂×C₄⋊C₄	C₂×#6923	1	1	yes	characteristic
239	C₂×C₄⋊C₄	C₂×#6923	1	1	yes	characteristic
240	C₂×C₄²	—	2	1	no	—
241	C₂×C₄²	—	61	1	no	—
242	C₂×C₄²	—	61	1	no	—
243	C₂×C₄²	—	61	1	no	—
244	C₂×C₄²	—	61	1	no	—
245	C₂×C₄²	—	61	1	no	—
246	C₂×C₄²	—	61	1	no	—
247	C₂×C₄²	—	122	1	no	—
248	C₂×C₄²	—	122	1	no	—
249	C₂×C₄²	—	122	1	no	—
250	C₂×C₄²	—	122	1	no	—
251	C₂×C₄²	—	122	1	no	—
252	C₂×C₄²	C₂×#6923	1	1	yes	characteristic
253	C₄⋊C₈	—	122	2	no	—
254	C₄⋊C₈	—	122	2	no	—
255	C₄⋊C₈	—	122	4	no	—
256	C₄⋊C₈	—	244	2	no	—
257	C₄⋊C₈	—	244	2	no	—
258	C₄×C₈	—	122	2	no	—
259	C₄×C₈	—	122	2	no	—
260	#95	—	2	1	no	—
261	#95	—	122	1	no	—
262	#95	—	122	1	no	—
263	C₂×Q₈	—	61	2	no	—
264	C₂×Q₈	—	61	2	no	—
265	C₂×Q₈	—	61	2	no	—
266	C₂×Q₈	—	122	1	no	—
267	C₂×Q₈	—	122	1	no	—
268	C₂×Q₈	—	122	1	no	—
269	C₂²×C₄	—	2	1	no	—
270	C₂²×C₄	—	2	1	no	—
271	C₂²×C₄	—	61	1	no	—
272	C₂²×C₄	—	61	1	no	—
273	C₂²×C₄	—	61	1	no	—
274	C₂²×C₄	—	61	1	no	—
275	C₂²×C₄	—	122	1	no	—
276	C₂²×C₄	—	122	1	no	—
277	C₂²×C₄	C₂²⋊#6923	1	1	yes	characteristic
278	C₂²×C₄	C₂²⋊#6923	1	1	yes	characteristic
279	C₂²×C₄	C₂²×#6923	1	1	yes	characteristic
280	C₂×C₈	—	122	4	no	—
281	C₂×C₈	—	244	2	no	—
282	C₂×C₈	—	244	2	no	—
283	C₂×C₈	—	244	2	no	—
284	C₂×C₈	—	244	2	no	—
285	C₂×C₈	—	244	2	no	—
286	C₄⋊C₄	—	2	1	no	—
287	C₄⋊C₄	—	2	1	no	—
288	C₄⋊C₄	—	61	2	no	—
289	C₄⋊C₄	—	122	2	no	—
290	C₄⋊C₄	—	122	2	no	—
291	C₄⋊C₄	—	122	4	no	—
292	C₄⋊C₄	—	122	4	no	—
293	C₄⋊C₄	—	122	1	no	—
294	C₄⋊C₄	D₆₁⋊C₈	1	2	yes	—
295	C₄⋊C₄	C₄⋊#6923	1	2	yes	—
296	C₄²	—	2	1	no	—
297	C₄²	—	2	1	no	—
298	C₄²	—	4	2	no	—
299	C₄²	—	61	2	no	—
300	C₄²	—	61	2	no	—
301	C₄²	—	61	1	no	—
302	C₄²	—	61	1	no	—
303	C₄²	—	61	1	no	—
304	C₄²	—	61	1	no	—
305	C₄²	—	61	2	no	—
306	C₄²	—	61	2	no	—
307	C₄²	—	122	2	no	—
308	C₄²	—	122	1	no	—
309	C₄²	—	122	1	no	—
310	C₄²	—	122	2	no	—
311	C₄²	—	122	2	no	—
312	C₄²	—	122	4	no	—
313	C₄²	—	122	4	no	—
314	C₄²	—	244	1	no	—
315	C₄²	—	244	1	no	—
316	C₄²	—	244	1	no	—
317	C₄²	—	244	2	no	—
318	C₂³	C₂×C₂²⋊#6923	1	1	yes	characteristic
319	Q₈	—	61	4	no	—
320	Q₈	—	122	2	no	—
321	Q₈	—	122	2	no	—
322	Q₈	—	122	2	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	61	1	no	—
335	C₂×C₄	—	61	1	no	—
336	C₂×C₄	—	61	2	no	—
337	C₂×C₄	—	61	2	no	—
338	C₂×C₄	—	61	1	no	—
339	C₂×C₄	—	61	1	no	—
340	C₂×C₄	—	61	1	no	—
341	C₂×C₄	—	61	1	no	—
342	C₂×C₄	—	61	2	no	—
343	C₂×C₄	—	61	1	no	—
344	C₂×C₄	—	61	1	no	—
345	C₂×C₄	—	61	2	no	—
346	C₂×C₄	—	122	2	no	—
347	C₂×C₄	—	122	2	no	—
348	C₂×C₄	—	122	2	no	—
349	C₂×C₄	—	122	1	no	—
350	C₂×C₄	—	122	1	no	—
351	C₂×C₄	—	122	1	no	—
352	C₂×C₄	—	122	1	no	—
353	C₂×C₄	—	122	2	no	—
354	C₂×C₄	—	244	1	no	—
355	C₂×C₄	—	244	1	no	—
356	C₂×C₄	#14519840	1	2	yes	—
357	C₂×C₄	C₂×C₄⋊#6923	1	1	yes	characteristic
358	C₂×C₄	#14519856	1	1	yes	characteristic
359	C₂×C₄	C₂×D₆₁⋊C₈	1	1	yes	characteristic
360	C₂×C₄	D₆₁⋊M₁₆	1	1	yes	characteristic
361	C₂×C₄	D₆₁⋊M₁₆	1	1	yes	characteristic
362	C₂×C₄	D₆₁⋊M₁₆	1	1	yes	characteristic
363	C₈	—	488	2	no	—
364	C₈	—	244	4	no	—
365	C₂²	#16840704	1	1	yes	characteristic
366	C₂²	D₆₁⋊(C₂²⋊C₈)	1	1	yes	characteristic
367	C₂²	#16840734	1	1	yes	characteristic
368	C₂²	C₂×#14519840	1	1	yes	characteristic
369	C₂²	#16840753	1	1	yes	characteristic
370	C₂²	D₆₁⋊#104	1	1	yes	characteristic
371	C₂²	#16840760	1	1	yes	characteristic
372	C₄	—	2	2	no	—
373	C₄	—	4	2	no	—
374	C₄	—	4	1	no	—
375	C₄	—	4	2	no	—
376	C₄	—	61	4	no	—
377	C₄	—	61	1	no	—
378	C₄	—	61	1	no	—
379	C₄	—	61	1	no	—
380	C₄	—	61	1	no	—
381	C₄	—	122	2	no	—
382	C₄	—	122	4	no	—
383	C₄	—	122	1	no	—
384	C₄	—	122	1	no	—
385	C₄	—	244	2	no	—
386	C₄	D₆₁⋊(C₄⋊C₈)	1	1	yes	characteristic
387	C₄	#16840767	1	1	yes	characteristic
388	C₄	#16840780	1	1	yes	characteristic
389	C₄	#16840785	1	1	yes	characteristic
390	C₂	D₆₁⋊(Q₈⋊C₈)	1	1	yes	characteristic
391	C₂	#21461115	1	1	yes	characteristic
392	C₂	#21461149	1	1	yes	characteristic
393	C₂	#21461156	1	1	yes	characteristic
394	C₂	#21461676	1	1	yes	characteristic
395	C₂	#21461688	1	1	yes	characteristic
396	C₂	#21461693	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊#6923
commutator	C₂×C₄×C₆₁	C₂²×C₈
Frattini	C₂²×C₄	C₂²×#6923
Fitting	C₄×C₄⋊C₄×C₆₁	C₄
socle, prime radical	C₂³×C₆₁	C₂×C₂²⋊C₄
cosocle	C₂×C₄×Dic₆₁	C₂³
hypercenter	C₄×C₄⋊C₄	#6923
hypocenter	C₆₁	#8564
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
39. #14519742	C₈	semidirect
163. Dic₁₂₂	C₄⋊C₈	semidirect
187. Dic₆₁	Q₈⋊C₈	semidirect
222. C₆₁	#8564	semidirect

Maximal subgroups

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

subgroup	index
#21461752	2
C₄×#14519844	2
C₂×#16840612	2
#21460655	2
C₄×#14519742	2
#8564	61