Subgroups — #33242762

Order 18688.

652 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22623079	C₂	1	2	yes	maximal, complemented
2	#22621736	C₂	1	1	yes	maximal, characteristic, complemented
3	#22621731	C₂	1	1	yes	maximal, characteristic, complemented
4	#22612187	C₂	1	1	yes	maximal, characteristic, complemented
5	#22612061	C₂	1	2	yes	maximal, complemented
6	#22612013	C₂	1	1	yes	maximal, characteristic, complemented
7	#22612008	C₂	1	1	yes	maximal, characteristic, complemented
8	#22611904	C₂	1	2	yes	maximal, complemented
9	#22611897	C₂	1	2	yes	maximal, complemented
10	#22611813	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#2170	C₂	1	1	yes	maximal, characteristic, complemented
12	#17989404	C₂²	1	2	yes	complemented
13	#17989401	—	2	1	no	—
14	#17989392	C₂²	1	2	yes	—
15	#17989389	—	2	1	no	—
16	#17989030	—	2	2	no	—
17	#17989030	C₂²	1	2	yes	—
18	#17989025	—	2	2	no	—
19	#17989025	C₂²	1	2	yes	complemented
20	#17989019	—	2	2	no	—
21	#17989019	C₂²	1	1	yes	characteristic
22	C₂×#14556536	—	2	2	no	—
23	C₂×#14556536	C₂²	1	2	yes	complemented
24	C₂×#14556536	C₂²	1	2	yes	complemented
25	#17988967	C₂²	1	1	yes	characteristic, complemented
26	#17988964	C₂²	1	1	yes	characteristic
27	#17988863	—	2	1	no	—
28	#17988862	C₂²	1	2	yes	complemented
29	#17988858	—	2	1	no	—
30	#17988857	C₂²	1	2	yes	—
31	#17988771	—	2	2	no	—
32	#17988756	—	2	2	no	—
33	#17988705	C₂²	1	1	yes	characteristic
34	#17988705	C₂²	1	1	yes	characteristic, complemented
35	#17988417	C₂²	1	1	yes	characteristic, complemented
36	#17988404	C₂²	1	2	yes	complemented
37	#17988401	C₂²	1	2	yes	complemented
38	#17988395	C₂²	1	1	yes	characteristic
39	#17988395	C₂²	1	1	yes	characteristic, complemented
40	#504×C₇₃	C₂²	1	2	yes	complemented
41	#443×C₇₃	C₂²	1	1	yes	characteristic
42	#364×C₇₃	C₂²	1	1	yes	characteristic, complemented
43	#350×C₇₃	C₂²	1	2	yes	complemented
44	C₄×C₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
45	#14556638	—	2	2	no	—
46	#14556637	—	2	2	no	—
47	#14556624	—	2	2	no	—
48	#14556624	—	4	2	no	—
49	#14556621	—	2	2	no	—
50	#14556620	—	4	2	no	—
51	#14556619	—	2	2	no	—
52	#14556619	—	4	2	no	—
53	#14556618	—	4	2	no	—
54	#14556616	—	2	2	no	—
55	#14556614	—	4	1	no	—
56	#14556613	—	2	2	no	—
57	#14556613	—	2	2	no	—
58	#14556613	C₂³	1	1	yes	characteristic
59	#14556613	C₂³	1	1	yes	characteristic
60	#14556610	—	4	1	no	—
61	C₂×Dic₂₉₂	—	2	2	no	—
62	C₂×Dic₂₉₂	—	2	1	no	—
63	C₂×Dic₂₉₂	C₂³	1	2	yes	—
64	Q₁₆×D₇₃	—	4	1	no	—
65	C₂×D₅₈₄	—	2	2	no	—
66	C₂×D₅₈₄	—	2	1	no	—
67	C₂×D₅₈₄	C₂³	1	2	yes	—
68	D₈×D₇₃	—	4	1	no	—
69	#14556597	—	2	1	no	—
70	#14556597	—	2	1	no	—
71	#14556591	—	2	1	no	—
72	#14556588	—	2	1	no	—
73	Dic₅₈₄	—	2	2	no	—
74	Dic₅₈₄	D₄	1	1	yes	characteristic, complemented
75	#14556536	—	2	2	no	—
76	#14556536	—	2	2	no	—
77	#14556536	—	2	2	no	—
78	#14556536	—	2	2	no	—
79	#14556536	—	4	2	no	—
80	#14556536	D₄	1	1	yes	characteristic, complemented
81	#14556536	D₄	1	1	yes	characteristic, complemented
82	D₁₁₆₈	—	2	2	no	—
83	D₁₁₆₈	D₄	1	1	yes	characteristic, complemented
84	#14556527	C₂³	1	1	yes	characteristic
85	#14556527	C₂³	1	1	yes	characteristic
86	#14556519	—	2	1	no	—
87	#14556519	—	2	1	no	—
88	#14556509	—	2	2	no	—
89	#14556507	—	2	2	no	—
90	#135×C₇₃	D₄	1	1	yes	characteristic
91	#131×C₇₃	C₂³	1	2	yes	—
92	M₃₂×C₇₃	—	2	2	no	—
93	M₃₂×C₇₃	C₂³	1	2	yes	—
94	C₂×C₁₆×C₇₃	—	2	2	no	—
95	C₂×C₁₆×C₇₃	C₂³	1	1	yes	characteristic
96	C₂×C₁₆×C₇₃	C₂³	1	1	yes	characteristic
97	#108×C₇₃	D₄	1	1	yes	characteristic
98	#104×C₇₃	D₄	1	2	yes	—
99	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
100	#11924029	—	4	2	no	—
101	#11924028	—	2	1	no	—
102	#11924028	—	2	1	no	—
103	#11924028	—	4	2	no	—
104	#11924028	—	4	2	no	—
105	#11924027	—	4	2	no	—
106	#11924027	—	8	2	no	—
107	C₂×Dic₁₄₆	—	2	2	no	—
108	C₂×Dic₁₄₆	—	4	2	no	—
109	Q₈×D₇₃	—	4	2	no	—
110	C₂×D₂₉₂	—	2	2	no	—
111	C₂×D₂₉₂	—	4	2	no	—
112	C₂×D₂₉₂	—	8	1	no	—
113	D₄×D₇₃	—	4	2	no	—
114	D₄×D₇₃	—	8	2	no	—
115	Dic₂₉₂	—	2	2	no	—
116	Dic₂₉₂	—	2	2	no	—
117	Dic₂₉₂	—	4	2	no	—
118	Dic₂₉₂	—	4	1	no	—
119	Dic₂₉₂	—	4	1	no	—
120	Dic₂₉₂	C₂×D₄	1	1	yes	characteristic
121	Dic₂₉₂	C₂×D₄	1	1	yes	characteristic
122	#11924018	—	4	2	no	—
123	#11924017	—	2	1	no	—
124	#11924017	—	2	1	no	—
125	#11924017	—	4	2	no	—
126	#11924017	—	4	2	no	—
127	#11924016	—	4	2	no	—
128	#11924015	—	4	2	no	—
129	D₅₈₄	—	2	2	no	—
130	D₅₈₄	—	2	2	no	—
131	D₅₈₄	—	4	2	no	—
132	D₅₈₄	—	4	1	no	—
133	D₅₈₄	—	4	1	no	—
134	D₅₈₄	C₂×D₄	1	1	yes	characteristic
135	D₅₈₄	C₂×D₄	1	1	yes	characteristic
136	#11924013	—	4	2	no	—
137	#11924012	—	2	1	no	—
138	#11924012	—	2	1	no	—
139	#11924011	—	4	1	no	—
140	#11924011	—	4	1	no	—
141	C₈×D₇₃	—	4	1	no	—
142	C₈×D₇₃	—	4	1	no	—
143	C₄⋊Dic₇₃	—	8	1	no	—
144	#41×C₇₃	C₂×D₄	1	2	yes	—
145	Q₁₆×C₇₃	D₈	1	1	yes	characteristic
146	SD₁₆×C₇₃	D₈	1	2	yes	—
147	D₈×C₇₃	D₈	1	1	yes	characteristic
148	M₁₆×C₇₃	—	2	2	no	—
149	M₁₆×C₇₃	C₂×D₄	1	2	yes	—
150	C₂×C₈×C₇₃	—	2	2	no	—
151	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
152	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
153	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
154	C₁₆×C₇₃	—	2	2	no	—
155	C₁₆×C₇₃	—	2	1	no	—
156	C₁₆×C₇₃	C₂×D₄	1	1	yes	characteristic
157	C₁₆×C₇₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×D₇₃	—	4	2	no	—
159	C₂²×D₇₃	—	8	2	no	—
160	Q₈×C₇₃	C₂×D₈	1	2	yes	—
161	D₄×C₇₃	—	2	2	no	—
162	D₄×C₇₃	C₂×D₈	1	2	yes	—
163	C₂×C₄×C₇₃	—	2	1	no	—
164	C₂×C₄×C₇₃	—	2	2	no	—
165	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
166	C₂²⋊D₇₃	—	4	1	no	—
167	C₂²⋊D₇₃	—	4	1	no	—
168	C₂²⋊D₇₃	—	8	2	no	—
169	C₂²⋊D₇₃	—	8	2	no	—
170	C₂×Dic₇₃	—	4	2	no	—
171	C₂×Dic₇₃	—	8	2	no	—
172	D₂₉₂	—	2	1	no	—
173	D₂₉₂	—	2	1	no	—
174	D₂₉₂	—	4	2	no	—
175	D₂₉₂	—	4	2	no	—
176	D₂₉₂	—	8	2	no	—
177	D₂₉₂	—	16	2	no	—
178	C₄×D₇₃	—	4	1	no	—
179	C₄×D₇₃	—	4	1	no	—
180	C₄×D₇₃	—	8	2	no	—
181	C₄×D₇₃	—	8	2	no	—
182	Dic₁₄₆	—	2	1	no	—
183	Dic₁₄₆	—	2	1	no	—
184	Dic₁₄₆	—	4	2	no	—
185	Dic₁₄₆	—	4	2	no	—
186	Dic₁₄₆	—	8	2	no	—
187	C₈×C₇₃	—	2	2	no	—
188	C₈×C₇₃	C₂×D₈	1	1	yes	characteristic
189	C₈×C₇₃	C₂×D₈	1	1	yes	characteristic
190	C₈×C₇₃	C₂²×D₄	1	1	yes	characteristic
191	C₈×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
192	#10596831	—	4	1	no	—
193	#10596831	—	4	1	no	—
194	C₂²×C₇₃	—	2	2	no	—
195	C₂²×C₇₃	#576	1	1	yes	characteristic
196	C₂×D₇₃	—	4	1	no	—
197	C₂×D₇₃	—	4	1	no	—
198	C₂×D₇₃	—	8	2	no	—
199	C₂×D₇₃	—	16	2	no	—
200	C₂×D₇₃	—	32	2	no	—
201	C₄×C₇₃	—	2	2	no	—
202	C₄×C₇₃	—	2	2	no	—
203	C₄×C₇₃	D₄²	1	1	yes	characteristic
204	C₄×C₇₃	C₂²×D₈	1	1	yes	characteristic
205	Dic₇₃	—	4	1	no	—
206	Dic₇₃	—	4	1	no	—
207	Dic₇₃	—	8	2	no	—
208	#33856	—	73	1	no	maximal, Sylow
209	C₂×C₇₃	—	2	1	no	—
210	C₂×C₇₃	—	4	2	no	—
211	C₂×C₇₃	D₄×D₈	1	1	yes	characteristic
212	D₇₃	—	8	1	no	—
213	D₇₃	—	8	1	no	—
214	D₇₃	—	16	2	no	—
215	#3416	—	73	2	no	—
216	#3293	—	73	1	no	—
217	#3292	—	73	1	no	—
218	#2248	—	73	1	no	—
219	#2223	—	73	2	no	—
220	#2214	—	73	1	no	—
221	#2213	—	73	1	no	—
222	#2194	—	73	2	no	—
223	#2193	—	73	2	no	—
224	#2178	—	73	1	no	—
225	#2170	D₇₃	1	1	yes	characteristic, complemented
226	C₇₃	#33856	1	1	yes	characteristic, complemented, Sylow
227	#578	—	73	2	no	—
228	#578	—	146	1	no	—
229	#576	—	73	2	no	—
230	#576	—	146	1	no	—
231	#510	—	73	2	no	—
232	#510	—	146	2	no	—
233	#509	—	73	2	no	—
234	#509	—	146	2	no	—
235	#508	—	73	1	no	—
236	#508	—	146	2	no	—
237	C₂×SD₃₂	—	73	2	no	—
238	C₂×SD₃₂	—	73	2	no	—
239	C₂×SD₃₂	—	146	2	no	—
240	#504	C₂×D₇₃	1	2	yes	complemented
241	#494	—	73	1	no	—
242	#493	—	73	1	no	—
243	#473	—	73	2	no	—
244	#473	—	146	1	no	—
245	#472	—	73	2	no	—
246	#472	—	146	1	no	—
247	#456	—	146	2	no	—
248	#453	—	146	2	no	—
249	#443	—	73	1	no	—
250	#443	—	73	1	no	—
251	#443	C₂×D₇₃	1	1	yes	characteristic
252	#368	—	73	1	no	—
253	#364	C₂×D₇₃	1	1	yes	characteristic, complemented
254	#362	—	73	2	no	—
255	#361	—	73	2	no	—
256	#359	—	73	1	no	—
257	#359	—	73	1	no	—
258	#350	C₂×D₇₃	1	2	yes	complemented
259	C₄×C₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
260	2₋¹⁺⁴	—	146	2	no	—
261	H(5,𝔽₂)	—	146	2	no	—
262	#137	—	292	2	no	—
263	#137	—	292	2	no	—
264	#137	—	146	2	no	—
265	#137	—	146	2	no	—
266	AGL(1,ℤ/8)	—	292	2	no	—
267	AGL(1,ℤ/8)	—	292	2	no	—
268	AGL(1,ℤ/8)	—	146	2	no	—
269	AGL(1,ℤ/8)	—	146	2	no	—
270	#135	—	292	1	no	—
271	#135	—	292	1	no	—
272	#135	—	73	1	no	—
273	#135	—	73	1	no	—
274	#135	—	146	2	no	—
275	#135	—	146	2	no	—
276	#135	D₂₉₂	1	1	yes	characteristic
277	C₂×Q₁₆	—	292	1	no	—
278	C₂×Q₁₆	—	73	2	no	—
279	C₂×Q₁₆	—	146	2	no	—
280	C₂×Q₁₆	—	146	1	no	—
281	C₂×D₈	—	292	1	no	—
282	C₂×D₈	—	73	2	no	—
283	C₂×D₈	—	146	2	no	—
284	C₂×D₈	—	146	1	no	—
285	#131	—	146	1	no	—
286	#131	—	146	1	no	—
287	#131	C₂²×D₇₃	1	2	yes	—
288	C₄⋊Q₈	—	146	1	no	—
289	#127	—	146	1	no	—
290	Q₃₂	—	73	1	no	—
291	Q₃₂	—	146	2	no	—
292	SD₃₂	—	292	2	no	—
293	SD₃₂	—	73	1	no	—
294	SD₃₂	—	73	1	no	—
295	SD₃₂	—	146	2	no	—
296	SD₃₂	—	146	2	no	—
297	SD₃₂	—	146	2	no	—
298	SD₃₂	—	146	2	no	—
299	D₁₆	—	73	1	no	—
300	D₁₆	—	146	2	no	—
301	M₃₂	—	2	2	no	—
302	M₃₂	C₂²×D₇₃	1	2	yes	—
303	C₂×C₁₆	—	2	2	no	—
304	C₂×C₁₆	C₂²×D₇₃	1	1	yes	characteristic
305	C₂×C₁₆	C₂²×D₇₃	1	1	yes	characteristic
306	#108	—	73	1	no	—
307	#108	—	73	1	no	—
308	#108	D₂₉₂	1	1	yes	characteristic
309	#104	—	146	1	no	—
310	#104	—	146	1	no	—
311	#104	D₂₉₂	1	2	yes	—
312	#101	—	146	2	no	—
313	#100	—	146	2	no	—
314	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
315	#41	—	292	2	no	—
316	#41	—	292	2	no	—
317	#41	—	292	2	no	—
318	#41	—	292	2	no	—
319	#41	—	584	2	no	—
320	#41	—	146	1	no	—
321	#41	—	146	1	no	—
322	#41	C₂×D₂₉₂	1	2	yes	—
323	C₂×Q₈	—	292	2	no	—
324	C₂×Q₈	—	292	2	no	—
325	C₂×Q₈	—	146	2	no	—
326	C₂×D₄	—	292	2	no	—
327	C₂×D₄	—	292	2	no	—
328	C₂×D₄	—	584	1	no	—
329	C₂×D₄	—	584	2	no	—
330	C₂×D₄	—	146	2	no	—
331	Q₁₆	—	292	2	no	—
332	Q₁₆	—	292	2	no	—
333	Q₁₆	—	292	1	no	—
334	Q₁₆	—	292	1	no	—
335	Q₁₆	—	73	1	no	—
336	Q₁₆	—	73	1	no	—
337	Q₁₆	—	146	2	no	—
338	Q₁₆	—	146	2	no	—
339	Q₁₆	D₅₈₄	1	1	yes	characteristic
340	SD₁₆	—	292	2	no	—
341	SD₁₆	—	292	2	no	—
342	SD₁₆	—	292	2	no	—
343	SD₁₆	—	292	2	no	—
344	SD₁₆	—	146	1	no	—
345	SD₁₆	—	146	1	no	—
346	SD₁₆	D₅₈₄	1	2	yes	—
347	D₈	—	292	2	no	—
348	D₈	—	292	2	no	—
349	D₈	—	292	1	no	—
350	D₈	—	292	1	no	—
351	D₈	—	73	1	no	—
352	D₈	—	73	1	no	—
353	D₈	—	146	2	no	—
354	D₈	—	146	2	no	—
355	D₈	D₅₈₄	1	1	yes	characteristic
356	M₁₆	—	2	2	no	—
357	M₁₆	—	292	1	no	—
358	M₁₆	—	292	1	no	—
359	M₁₆	—	146	1	no	—
360	M₁₆	—	146	1	no	—
361	M₁₆	C₂×D₂₉₂	1	2	yes	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	292	1	no	—
364	C₂×C₈	—	292	1	no	—
365	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
366	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
367	C₄⋊C₄	—	584	1	no	—
368	C₄²	C₂×D₂₉₂	1	1	yes	characteristic
369	C₁₆	—	2	2	no	—
370	C₁₆	—	2	1	no	—
371	C₁₆	D₄×D₇₃	1	1	yes	characteristic
372	C₁₆	D₄×D₇₃	1	1	yes	characteristic
373	C₂³	—	292	2	no	—
374	C₂³	—	584	2	no	—
375	Q₈	—	292	2	no	—
376	Q₈	—	292	2	no	—
377	Q₈	—	584	2	no	—
378	Q₈	—	146	1	no	—
379	Q₈	—	146	1	no	—
380	Q₈	C₂×D₅₈₄	1	2	yes	—
381	D₄	—	2	2	no	—
382	D₄	—	292	1	no	—
383	D₄	—	292	1	no	—
384	D₄	—	292	2	no	—
385	D₄	—	292	2	no	—
386	D₄	—	584	2	no	—
387	D₄	—	584	2	no	—
388	D₄	—	584	2	no	—
389	D₄	—	1168	2	no	—
390	D₄	—	146	1	no	—
391	D₄	—	146	1	no	—
392	D₄	C₂×D₅₈₄	1	2	yes	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	292	1	no	—
396	C₂×C₄	—	292	1	no	—
397	C₂×C₄	—	292	2	no	—
398	C₂×C₄	—	584	2	no	—
399	C₂×C₄	—	584	2	no	—
400	C₂×C₄	—	584	2	no	—
401	C₂×C₄	C₂²×D₂₉₂	1	1	yes	characteristic
402	C₈	—	2	2	no	—
403	C₈	—	292	1	no	—
404	C₈	—	292	1	no	—
405	C₈	C₂×D₅₈₄	1	1	yes	characteristic
406	C₈	C₂×D₅₈₄	1	1	yes	characteristic
407	C₈	C₂×D₄×D₇₃	1	1	yes	characteristic
408	C₈	#14556637	1	1	yes	characteristic
409	C₂²	—	2	2	no	—
410	C₂²	—	2336	2	no	—
411	C₂²	—	292	1	no	—
412	C₂²	—	292	1	no	—
413	C₂²	—	584	2	no	—
414	C₂²	—	1168	2	no	—
415	C₂²	#17989392	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	292	1	no	—
419	C₄	—	292	1	no	—
420	C₄	—	584	2	no	—
421	C₄	D₄×D₂₉₂	1	1	yes	characteristic
422	C₄	C₂²×D₅₈₄	1	1	yes	characteristic
423	C₂	—	2	1	no	—
424	C₂	—	4	2	no	—
425	C₂	—	584	1	no	—
426	C₂	—	584	1	no	—
427	C₂	—	1168	2	no	—
428	C₂	D₄×D₅₈₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₅₈₄
commutator, cosocle	C₂×C₈×C₇₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₇₃
Fitting	C₇₃×#2170	C₂
socle	C₂×C₇₃	D₄×D₈
hypercenter	#2170	D₇₃
hypocenter	C₇₃	#33856
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #443 ◁ #2170

Complements

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

N	H ≅ G/N	type
1. #22623079	C₂	semidirect
2. #22621736	C₂	semidirect
3. #22621731	C₂	semidirect
4. #22612187	C₂	semidirect
5. #22612061	C₂	semidirect
6. #22612013	C₂	semidirect
7. #22612008	C₂	semidirect
8. #22611904	C₂	semidirect
9. #22611897	C₂	semidirect
10. #22611813	C₂	semidirect
11. C₇₃×#2170	C₂	semidirect
12. #17989404	C₂²	semidirect
19. #17989025	C₂²	semidirect
23. C₂×#14556536	C₂²	semidirect
24. C₂×#14556536	C₂²	semidirect
25. #17988967	C₂²	semidirect
28. #17988862	C₂²	semidirect
34. #17988705	C₂²	semidirect
35. #17988417	C₂²	semidirect
36. #17988404	C₂²	semidirect
37. #17988401	C₂²	semidirect
39. #17988395	C₂²	semidirect
40. #504×C₇₃	C₂²	semidirect
42. #364×C₇₃	C₂²	semidirect
43. #350×C₇₃	C₂²	semidirect
44. C₄×C₁₆×C₇₃	C₂²	semidirect
74. Dic₅₈₄	D₄	semidirect
80. #14556536	D₄	semidirect
81. #14556536	D₄	semidirect
83. D₁₁₆₈	D₄	semidirect
225. #2170	D₇₃	semidirect
226. C₇₃	#33856	semidirect
240. #504	C₂×D₇₃	semidirect
253. #364	C₂×D₇₃	semidirect
258. #350	C₂×D₇₃	semidirect
259. C₄×C₁₆	C₂×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#22623079	2
#22621736	2
#22621731	2
#22612187	2
#22612061	2
#22612013	2
#22612008	2
#22611904	2
#22611897	2
#22611813	2
C₇₃×#2170	2
#33856	73