Finite Group Databasebeta

← #164592

Subgroups — #164592

Order 512.

1002 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36374C211yesmaximal, characteristic
2#22473C211yesmaximal, characteristic, complemented
3#20720C211yesmaximal, characteristic, complemented
4#7730C211yesmaximal, characteristic, complemented
5#7718C211yesmaximal, characteristic, complemented
6#7710C211yesmaximal, characteristic, complemented
7#7694C211yesmaximal, characteristic, complemented
8#7675C211yesmaximal, characteristic, complemented
9#7661C211yesmaximal, characteristic, complemented
10#7617C211yesmaximal, characteristic, complemented
11#7612C211yesmaximal, characteristic, complemented
12#7609C211yesmaximal, characteristic, complemented
13#7600C211yesmaximal, characteristic, complemented
14#7595C211yesmaximal, characteristic, complemented
15#7563C211yesmaximal, characteristic, complemented
16C2×#548C411yescharacteristic
17C2×C4×#41C2211yescharacteristic
18C2×#436—21no—
19C2×#433—21no—
20#2855C2211yescharacteristic
21#2854C2211yescharacteristic
22#2850C2211yescharacteristic
23#2592C411yescharacteristic
24#2581C411yescharacteristic
25#2477—21no—
26#2474—21no—
27#2465—21no—
28#2459—21no—
29#2444—21no—
30#2430—21no—
31#2416C411yescharacteristic
32#2415C411yescharacteristic
33#2409C411yescharacteristic
34#2407C411yescharacteristic
35#2364—21no—
36#2359—21no—
37#2352C411yescharacteristic
38C4×C22⋊Q8C2211yescharacteristic
39#2297C2211yescharacteristic
40C2×#391C2211yescharacteristic
41#1984—21no—
42#1870—21no—
43#1870—21no—
44#1817C2211yescharacteristic
45#1817C2211yescharacteristic
46#1817C2211yescharacteristic
47#1817C2211yescharacteristic
48#1798—21no—
49#1797C2211yescharacteristic
50#1797C2211yescharacteristic
51#1797C2211yescharacteristic
52#1780—21no—
53#1750—21no—
54#1749C2211yescharacteristic
55C4×C22⋊C8C2211yescharacteristic
56C4×C22⋊C8C2211yescharacteristic
57#1728C2211yescharacteristic
58#1728C2211yescharacteristic
59#1272C2211yescharacteristic
60#1272C2211yescharacteristic
61#1272C2211yescharacteristic
62#1272C2211yescharacteristic
63#1272C2211yescharacteristic
64#1272C2211yescharacteristic
65#1272C2211yescharacteristic
66#1272C2211yescharacteristic
67#1271C2211yescharacteristic
68#1271C2211yescharacteristic
69#1271C2211yescharacteristic
70#1271C2211yescharacteristic
71#1270C2211yescharacteristic
72#1270C2211yescharacteristic
73#1270C2211yescharacteristic
74#1270C2211yescharacteristic
75C22×#41C2×C411yescharacteristic
76C22×#41D411yescharacteristic
77C23×Q8C2×C411yescharacteristic
78C22×M16—21no—
79C22×M16—21no—
80#548—44no—
81C2×#124—21no—
82C2×#124C2×C411yescharacteristic
83C2×#123—21no—
84C2×C22⋊Q8—21no—
85C2×C22⋊Q8C2×C411yescharacteristic
86C2×C22⋊Q8C2×C411yescharacteristic
87C2×C22⋊Q8C2×C411yescharacteristic
88C2×#121—21no—
89C2×#121—21no—
90C2×#121C2×C411yescharacteristic
91C2×#121C2×C411yescharacteristic
92C4×#41—44no—
93C2×C4×Q8C2×C411yescharacteristic
94C2×C4×Q8C2×C411yescharacteristic
95C2×C4×Q8D411yescharacteristic
96C2×C4×D4—21no—
97C2×C4×D4C2×C411yescharacteristic
98C2×C4×D4C2×C411yescharacteristic
99C2×C4×D4C2×C411yescharacteristic
100C2×C4×D4D411yescharacteristic
101C2×C4×D4D411yescharacteristic
102C2×C4×D4D411yescharacteristic
103C2×#117C2×C411yescharacteristic
104C2×#117D411yescharacteristic
105C2×#117D411yescharacteristic
106C2×#117D411yescharacteristic
107C22×C4⋊C4C2×C411yescharacteristic
108C22×C42C2311yescharacteristic
109C22×C42C2311yescharacteristic
110C22×C42C2311yescharacteristic
111#436—44no—
112#433—44no—
113C2×C4⋊C8—21no—
114C2×C4⋊C8—21no—
115C2×C4⋊C8—21no—
116C2×C22⋊C8—21no—
117C2×C22⋊C8—21no—
118C2×C22⋊C8—21no—
119C2×C22⋊C8—21no—
120C2×C22⋊C8—21no—
121C2×C22⋊C8—21no—
122C2×C22⋊C8—21no—
123C2×C22⋊C8—21no—
124C2×C22⋊C8—21no—
125C2×C22⋊C8—21no—
126C2×#97—21no—
127C2×C4×C8—21no—
128C2×C4×C8—21no—
129#400—21no—
130#397—21no—
131#397—21no—
132#396—21no—
133#395—21no—
134#395—21no—
135#394—21no—
136#394—21no—
137#394—21no—
138#393—21no—
139#393—21no—
140#392—21no—
141#391—21no—
142#391—21no—
143#391C2×C411yescharacteristic
144#391C2×C411yescharacteristic
145#391C2×C411yescharacteristic
146#391C2×C411yescharacteristic
147#391C2311yescharacteristic
148#391C2311yescharacteristic
149#390C2×C411yescharacteristic
150#390C2×C411yescharacteristic
151#390C2311yescharacteristic
152#389—21no—
153#389C2×C411yescharacteristic
154#389C2×C411yescharacteristic
155#389C2311yescharacteristic
156#388—21no—
157#388—21no—
158#388—21no—
159#388—21no—
160#388—21no—
161#388—21no—
162#388—21no—
163#388—21no—
164#387—21no—
165#387—21no—
166#387—21no—
167#387—21no—
168#387—21no—
169#387—21no—
170#386—21no—
171#386—21no—
172#386—21no—
173#386—21no—
174#386—21no—
175#386—21no—
176#386—21no—
177#386—21no—
178#386—21no—
179#385—21no—
180#385—21no—
181#385—21no—
182#385—21no—
183#382C2×C411yescharacteristic
184#381—21no—
185#380C2×C411yescharacteristic
186#380C2×C411yescharacteristic
187#380C2×C411yescharacteristic
188C4×C4⋊C4—21no—
189C4×C4⋊C4C2×C411yescharacteristic
190C4×C22⋊C4—21no—
191C4×C22⋊C4—21no—
192C4×C22⋊C4—21no—
193C4×C22⋊C4—21no—
194C2×#95—21no—
195C2×#95—21no—
196#336—21no—
197#336—21no—
198#336—21no—
199#336—21no—
200#336—21no—
201#336—21no—
202#336C2311yescharacteristic
203#336C2311yescharacteristic
204#336C2311yescharacteristic
205#336C2311yescharacteristic
206#336C2311yescharacteristic
207#336C2311yescharacteristic
208#336C2311yescharacteristic
209#336C2311yescharacteristic
210C2×#41—22no—
211C2×#41—41no—
212C2×#41—41no—
213C2×#41—42no—
214C2×#41—42no—
215C2×#41—41no—
216C2×#41—42no—
217C2×#41—81no—
218C22×Q8—21no—
219C22×Q8—22no—
220C22×Q8—41no—
221C22×Q8—42no—
222C22×Q8—81no—
223C22×Q8C22⋊C411yescharacteristic
224C22×Q8C22×C411yescharacteristic
225C22×Q8C22×C411yescharacteristic
226C22×D4—21no—
227C22×D4—21no—
228C22×D4—21no—
229C22×D4C22⋊C411yescharacteristic
230C22×D4C22⋊C411yescharacteristic
231C22×D4C22⋊C411yescharacteristic
232C22×D4C22×C411yescharacteristic
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4C22×C411yescharacteristic
237C23×C4C22×C411yescharacteristic
238C23×C4C22×C411yescharacteristic
239C23×C4C2×D411yescharacteristic
240C23×C4C2×D411yescharacteristic
241C23×C4C2×D411yescharacteristic
242C23×C4C2×D411yescharacteristic
243C23×C4C2×D411yescharacteristic
244C23×C4C2×D411yescharacteristic
245C2×M16—42no—
246C2×M16—42no—
247C2×M16—42no—
248C2×M16—42no—
249C2×M16—81no—
250C2×M16—81no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—21no—
259#124—42no—
260#124—44no—
261#123—42no—
262#123—42no—
263C22⋊Q8—22no—
264C22⋊Q8—41no—
265C22⋊Q8—44no—
266C22⋊Q8—42no—
267C22⋊Q8—81no—
268#121—42no—
269#121—44no—
270#121—44no—
271#121—81no—
272C4×Q8—42no—
273C4×Q8—42no—
274C4×Q8—42no—
275C4×D4—24no—
276C4×D4—24no—
277C4×D4—42no—
278C4×D4—42no—
279C4×D4—42no—
280C4×D4—42no—
281C4×D4—44no—
282#117—24no—
283#117—42no—
284#117—42no—
285#117—81no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—81no—
295C2×C4⋊C4C22⋊C411yescharacteristic
296C2×C4⋊C4C22⋊C411yescharacteristic
297C2×C4⋊C4C22⋊C411yescharacteristic
298C2×C4⋊C4C22⋊C411yescharacteristic
299C2×C4⋊C4C22⋊C411yescharacteristic
300C2×C4⋊C4C22⋊C411yescharacteristic
301C2×C4⋊C4C22×C411yescharacteristic
302C2×C4⋊C4C22×C411yescharacteristic
303C2×C4⋊C4C22×C411yescharacteristic
304C2×C4⋊C4C22×C411yescharacteristic
305C2×C4⋊C4C22×C411yescharacteristic
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4C22⋊C411yescharacteristic
324C2×C22⋊C4C22⋊C411yescharacteristic
325C2×C22⋊C4C22⋊C411yescharacteristic
326C2×C22⋊C4C22⋊C411yescharacteristic
327C2×C22⋊C4C22⋊C411yescharacteristic
328C2×C22⋊C4C22⋊C411yescharacteristic
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—42no—
333C2×C42—42no—
334C2×C42—42no—
335C2×C42C22×C411yescharacteristic
336C2×C42C22×C411yescharacteristic
337C2×C42C22×C411yescharacteristic
338C2×C42C2×D411yescharacteristic
339C2×C42C2×D411yescharacteristic
340C2×C42C2×D411yescharacteristic
341C2×C42C2×D411yescharacteristic
342C2×C42C2×D411yescharacteristic
343C2×C42C2×D411yescharacteristic
344C2×C42C2411yescharacteristic
345C4⋊C8—42no—
346C4⋊C8—42no—
347C4⋊C8—42no—
348C22⋊C8—42no—
349C22⋊C8—42no—
350C22⋊C8—42no—
351C22⋊C8—42no—
352C22⋊C8—42no—
353C22⋊C8—42no—
354C22⋊C8—42no—
355C22⋊C8—42no—
356C22⋊C8—42no—
357C22⋊C8—81no—
358#97—42no—
359C4×C8—42no—
360C4×C8—42no—
361#95—21no—
362#95—21no—
363#95—21no—
364#95—21no—
365#95—21no—
366#95—21no—
367#95—21no—
368#95—21no—
369#95—21no—
370#95—21no—
371#95—21no—
372#95—21no—
373#95—21no—
374#95—21no—
375#95—21no—
376#95—21no—
377#95—21no—
378#95—21no—
379#95—21no—
380#95—21no—
381#95—21no—
382C24—21no—
383C24C2×C22⋊C411yescharacteristic
384C24C2×C22⋊C411yescharacteristic
385C24C2×C22⋊C411yescharacteristic
386#41—48no—
387#41—48no—
388#41—84no—
389#41—84no—
390C2×Q8—21no—
391C2×Q8—22no—
392C2×Q8—21no—
393C2×Q8—21no—
394C2×Q8—41no—
395C2×Q8—41no—
396C2×Q8—42no—
397C2×Q8—42no—
398C2×Q8—41no—
399C2×Q8—41no—
400C2×Q8—41no—
401C2×Q8—41no—
402C2×Q8—81no—
403C2×Q8—84no—
404C2×Q8—84no—
405C2×Q8#13112yes—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—22no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4—41no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—42no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—42no—
421C2×D4—42no—
422C2×D4—42no—
423C2×D4—42no—
424C2×D4—42no—
425C2×D4—81no—
426C2×D4—81no—
427C2×D4—81no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—81no—
477C22×C4—81no—
478C22×C4—81no—
479C22×C4—81no—
480C22×C4C2×C22⋊C411yescharacteristic
481C22×C4C2×C22⋊C411yescharacteristic
482C22×C4C2×C22⋊C411yescharacteristic
483C22×C4C2×C22⋊C411yescharacteristic
484C22×C4C2×C22⋊C411yescharacteristic
485C22×C4C2×C22⋊C411yescharacteristic
486C22×C4C2×C22⋊C411yescharacteristic
487C22×C4C2×C22⋊C411yescharacteristic
488C22×C4C2×C22⋊C411yescharacteristic
489C22×C4C23×C411yescharacteristic
490C22×C4C22×D411yescharacteristic
491C22×C4C22×D411yescharacteristic
492M16—84no—
493M16—84no—
494C2×C8—22no—
495C2×C8—41no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—41no—
499C2×C8—41no—
500C2×C8—41no—
501C2×C8—41no—
502C2×C8—41no—
503C2×C8—41no—
504C2×C8—41no—
505C2×C8—41no—
506C2×C8—41no—
507C2×C8—41no—
508C2×C8—41no—
509C2×C8—41no—
510C2×C8—41no—
511C2×C8—41no—
512C2×C8—41no—
513C2×C8—41no—
514C2×C8—41no—
515C2×C8—41no—
516C2×C8—41no—
517C2×C8—41no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—41no—
525C4⋊C4—41no—
526C4⋊C4—42no—
527C4⋊C4—41no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—42no—
532C4⋊C4—42no—
533C4⋊C4—41no—
534C4⋊C4—41no—
535C4⋊C4—42no—
536C4⋊C4—42no—
537C4⋊C4—81no—
538C4⋊C4—81no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—41no—
543C22⋊C4—41no—
544C22⋊C4—42no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C22⋊C4—42no—
548C22⋊C4—42no—
549C22⋊C4—42no—
550C22⋊C4—42no—
551C22⋊C4—41no—
552C22⋊C4—41no—
553C22⋊C4—41no—
554C22⋊C4—41no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—81no—
558C22⋊C4—81no—
559C22⋊C4—81no—
560C22⋊C4—81no—
561C22⋊C4—81no—
562C22⋊C4—81no—
563C22⋊C4#9914yes—
564C42—22no—
565C42—22no—
566C42—22no—
567C42—22no—
568C42—41no—
569C42—41no—
570C42—41no—
571C42—41no—
572C42—41no—
573C42—41no—
574C42—42no—
575C42—81no—
576C42—81no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23C2×#9912yes—
605C23C22×C22⋊C411yescharacteristic
606Q8—42no—
607Q8—42no—
608Q8—44no—
609Q8—81no—
610Q8—81no—
611Q8—84no—
612D4—44no—
613D4—44no—
614D4—44no—
615D4—81no—
616D4—81no—
617D4—84no—
618D4—84no—
619D4—162no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—22no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—81no—
686C2×C4—81no—
687C2×C4—81no—
688C2×C4—81no—
689C2×C4—84no—
690C2×C4—84no—
691C2×C4—162no—
692C2×C4C2×#9912yes—
693C2×C4C2×#9912yes—
694C2×C4#42112yes—
695C2×C4C2×#13111yescharacteristic
696C2×C4#56811yescharacteristic
697C2×C4#57511yescharacteristic
698C2×C4#57511yescharacteristic
699C2×C4#57711yescharacteristic
700C2×C4#57811yescharacteristic
701C8—42no—
702C8—81no—
703C8—81no—
704C8—81no—
705C8—81no—
706C8—81no—
707C8—81no—
708C8—81no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22#288011yescharacteristic
738C22C22×#9911yescharacteristic
739C22#288811yescharacteristic
740C22#289611yescharacteristic
741C22#289811yescharacteristic
742C22C2×#42111yescharacteristic
743C22#290111yescharacteristic
744C4—21no—
745C4—21no—
746C4—22no—
747C4—21no—
748C4—21no—
749C4—22no—
750C4—21no—
751C4—21no—
752C4—22no—
753C4—41no—
754C4—41no—
755C4—42no—
756C4—41no—
757C4—41no—
758C4—41no—
759C4—41no—
760C4—81no—
761C4—81no—
762C4—81no—
763C4—81no—
764C4—81no—
765C4—81no—
766C2—42no—
767C2—81no—
768C2—81no—
769C2—161no—
770C2#1741111yescharacteristic
771C2#1751611yescharacteristic
772C2#1752511yescharacteristic
773C2#1755911yescharacteristic
774C2#1760811yescharacteristic
775C2#1768111yescharacteristic
776C2#1776811yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
prime radical#36374C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×#41 ◁ G
LECSG ▷ C2×C42 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #22473C2semidirect
3. #20720C2semidirect
4. #7730C2semidirect
5. #7718C2semidirect
6. #7710C2semidirect
7. #7694C2semidirect
8. #7675C2semidirect
9. #7661C2semidirect
10. #7617C2semidirect
11. #7612C2semidirect
12. #7609C2semidirect
13. #7600C2semidirect
14. #7595C2semidirect
15. #7563C2semidirect

Maximal subgroups

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

subgroupindex
#363742
#224732
#207202
#77302
#77182
#77102
#76942
#76752
#76612
#76172
#76122
#76092
#76002
#75952
#75632