Finite Group Databasebeta

← #6615871

Subgroups — #6615871

Order 512.

1665 conjugacy classes of subgroups.

The subgroup lattice has 771 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36209C211yesmaximal, characteristic
2#36134C211yesmaximal, characteristic
3#33232C211yesmaximal, characteristic, complemented
4#33176C211yesmaximal, characteristic, complemented
5#33172C211yesmaximal, characteristic, complemented
6#29207C211yesmaximal, characteristic, complemented
7#28934C214yesmaximal, complemented
8#28920C214yesmaximal, complemented
9#28440C211yesmaximal, characteristic, complemented
10#27892C211yesmaximal, characteristic, complemented
11#27889C211yesmaximal, characteristic, complemented
12#25600C211yesmaximal, characteristic, complemented
13#25600C211yesmaximal, characteristic, complemented
14#25398C214yesmaximal
15#23110C214yesmaximal, complemented
16#21647C211yesmaximal, characteristic, complemented
17#21409C211yesmaximal, characteristic, complemented
18#21400C211yesmaximal, characteristic, complemented
19C4×#435C211yesmaximal, characteristic
20C2×#533C2211yescharacteristic
21C2×#533C2211yescharacteristic
22C2×#494C2211yescharacteristic
23C2×#494C2211yescharacteristic
24C2×#491C2214yes—
25C2×#487C2211yescharacteristic
26C2×#470C2214yes—
27C2×#467C2214yes—
28C2×#462C2214yes—
29C2×#435C2212yes—
30C2×C4×M16C2211yescharacteristic
31C22×C4×C8C2211yescharacteristic
32#2868C2211yescharacteristic
33#2859C2211yescharacteristic
34#2857C2211yescharacteristic
35#2857C2211yescharacteristic
36#2857C2211yescharacteristic
37#2857C2211yescharacteristic
38#2552—21no—
39#2542C2212yes—
40#2538—21no—
41#2536C2212yes—
42#2508—21no—
43#2508—21no—
44#2495—21no—
45#2495—21no—
46#2489C2212yes—
47#2489C2212yes—
48#2485—21no—
49#2485—21no—
50#2441—21no—
51#2441—21no—
52#2429C2212yes—
53#2429C2212yes—
54#2423—21no—
55#2423—21no—
56#2365C2212yes—
57#2356C2212yes—
58#2354—21no—
59Q8×C4⋊C4—21no—
60#2346—21no—
61#2346—21no—
62C4×C4⋊Q8C2211yescharacteristic
63C4×C4⋊Q8C2211yescharacteristic
64#2285C2211yescharacteristic
65#2285C2211yescharacteristic
66C42×D4C2211yescharacteristic
67#2059C2214yes—
68#2036C2214yes—
69#2035C2214yes—
70#2016C2214yes—
71#2001C2214yes—
72#2001C2214yes—
73#1990C2211yescharacteristic
74#1990C2211yescharacteristic
75#1990C2211yescharacteristic
76#1971C2214yes—
77#1969C2214yes—
78#1960C2214yes—
79#1956C2211yescharacteristic
80#1956C2211yescharacteristic
81#1956C2211yescharacteristic
82#1956C2211yescharacteristic
83#1956C2211yescharacteristic
84#1956C2211yescharacteristic
85#1956C2211yescharacteristic
86#1949C2214yes—
87#1935C2214yes—
88#1928C2214yes—
89#1927C2214yes—
90#1894C2214yes—
91#1892C2214yes—
92#1878C2214yes—
93#1878C2214yes—
94#1845C2211yescharacteristic
95#1844C2211yescharacteristic
96#1834C2211yescharacteristic
97#1771C2212yes—
98C4×C4⋊C8C2211yescharacteristic
99#1763C2214yes—
100#1763C2214yes—
101C4×#103C2214yes—
102#1753C2212yes—
103#1752C2212yes—
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106C4×#97C2211yescharacteristic
107C22×Q16C2314yes—
108C22×Q16C2314yes—
109C22×M16C2312yes—
110C23×C8C2312yes—
111#533—24no—
112#533—24no—
113#533—42no—
114#533—42no—
115C2×C4⋊Q8C2311yescharacteristic
116C2×C4⋊Q8C2311yescharacteristic
117C2×C4⋊Q8C2311yescharacteristic
118C2×C4⋊Q8C2312yes—
119C2×C4⋊Q8C2312yes—
120C2×C4⋊Q8C2311yescharacteristic
121C2×#125—21no—
122C2×#125—21no—
123C2×#125C2312yes—
124C2×C22⋊Q8—21no—
125C2×C22⋊Q8—21no—
126C2×C22⋊Q8C2312yes—
127C2×C22⋊Q8C2312yes—
128C2×C22⋊Q8C2312yes—
129C2×C22⋊Q8C2312yes—
130C2×C22⋊Q8C2312yes—
131C2×C22⋊Q8C2312yes—
132C2×C4×Q8—21no—
133C2×C4×Q8—21no—
134C2×C4×Q8—21no—
135C2×C4×Q8C2312yes—
136C2×C4×Q8C2312yes—
137C2×C4×Q8C2312yes—
138C2×C4×D4D411yescharacteristic
139C2×C4×D4D411yescharacteristic
140C2×C4×D4C2311yescharacteristic
141C2×#117—21no—
142C2×#117—21no—
143C2×#117—21no—
144C2×#117—21no—
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147#494—42no—
148#494—42no—
149#491—48no—
150#487—24no—
151#470—48no—
152#467—48no—
153#462—216no—
154#435—28no—
155C2×#107C2314yes—
156C2×#106C2314yes—
157C2×C4⋊C8C2312yes—
158C2×#103C2314yes—
159C2×#103C2314yes—
160C2×#103C2314yes—
161C2×#103C2314yes—
162C2×#103C2314yes—
163C2×#103C2314yes—
164C2×#103C2314yes—
165C2×#103C2314yes—
166C2×C22⋊C8C2312yes—
167C2×C22⋊C8C2312yes—
168C4×M16—42no—
169C2×#97C2312yes—
170C2×#97C2312yes—
171C2×#97C2312yes—
172C2×C4×C8—42no—
173C2×C4×C8C2311yescharacteristic
174C2×C4×C8C2311yescharacteristic
175C2×C4×C8C2311yescharacteristic
176C2×C4×C8C2311yescharacteristic
177C2×C4×C8C2312yes—
178#400—22no—
179#400—22no—
180#399—22no—
181#399—22no—
182#398—22no—
183#398—22no—
184#398—22no—
185#397—22no—
186#397—22no—
187#396—22no—
188#396—22no—
189#394—22no—
190#391—21no—
191#391C2312yes—
192#391C2312yes—
193#391C2312yes—
194#391C2312yes—
195#391C2312yes—
196#390—22no—
197#389—22no—
198#389—21no—
199#389—21no—
200#389—21no—
201#389—21no—
202#389—21no—
203#389—21no—
204#389—21no—
205#389—21no—
206#389—21no—
207#389—21no—
208#389—21no—
209#389—21no—
210#389—21no—
211#389—21no—
212#389—21no—
213#389—22no—
214#389—22no—
215#389C2312yes—
216#388—22no—
217#388—22no—
218#388—22no—
219#388—22no—
220#388—22no—
221#388—22no—
222#387—22no—
223#387—22no—
224#387—22no—
225#387—22no—
226#384—22no—
227#384—21no—
228#384—21no—
229#384—21no—
230#384—21no—
231#384C2311yescharacteristic
232#384C2311yescharacteristic
233#384C2311yescharacteristic
234#384C2311yescharacteristic
235#383—22no—
236#382—21no—
237#382—21no—
238#382—22no—
239#382—22no—
240#382C2312yes—
241#380—21no—
242#380—21no—
243#380—21no—
244#380—21no—
245#380—21no—
246#380—21no—
247#380—21no—
248#380—21no—
249#380—21no—
250#380—21no—
251#380C2312yes—
252#380C2312yes—
253C4×C4⋊C4—22no—
254C4×C4⋊C4—21no—
255C4×C4⋊C4—21no—
256C4×C4⋊C4—21no—
257C4×C4⋊C4—21no—
258C4×C4⋊C4—21no—
259C4×C4⋊C4D411yescharacteristic
260C4×C4⋊C4D411yescharacteristic
261C4×C4⋊C4C2312yes—
262C4×C4⋊C4C2312yes—
263C4×C4⋊C4C2312yes—
264C4×C4⋊C4C2311yescharacteristic
265C4×C22⋊C4D411yescharacteristic
266C4×C22⋊C4D411yescharacteristic
267C4×C22⋊C4D411yescharacteristic
268C4×C22⋊C4D411yescharacteristic
269C4×C22⋊C4C2311yescharacteristic
270C4×C22⋊C4C2311yescharacteristic
271#376—22no—
272C43C2311yescharacteristic
273#340C2314yes—
274#340C2314yes—
275#340C2314yes—
276#340C2314yes—
277#336C2312yes—
278#336C2312yes—
279#336C2312yes—
280C22×Q8—21no—
281C22×Q8C2412yes—
282C22×Q8C2412yes—
283C22×Q8C2412yes—
284C22×D4C2×D411yescharacteristic
285C23×C4C2×D411yescharacteristic
286C23×C4C2×D411yescharacteristic
287C23×C4C2×D411yescharacteristic
288C23×C4C2×D411yescharacteristic
289C23×C4C2411yescharacteristic
290C23×C4C2411yescharacteristic
291C2×Q16—28no—
292C2×Q16—28no—
293C2×Q16—44no—
294C2×Q16—44no—
295C2×Q16—44no—
296C2×Q16—44no—
297C2×M16—24no—
298C2×M16—24no—
299C2×M16—42no—
300C22×C8—24no—
301C22×C8—24no—
302C22×C8—42no—
303C22×C8C2412yes—
304C22×C8C2412yes—
305C22×C8C2412yes—
306C22×C8C2412yes—
307C4⋊Q8—22no—
308C4⋊Q8—22no—
309C4⋊Q8—28no—
310C4⋊Q8—22no—
311C4⋊Q8—22no—
312C4⋊Q8—22no—
313C4⋊Q8—22no—
314C4⋊Q8—22no—
315C4⋊Q8—44no—
316C4⋊Q8#4114yes—
317#125—44no—
318#125—44no—
319#125—44no—
320C22⋊Q8—24no—
321C22⋊Q8—24no—
322C22⋊Q8—42no—
323C22⋊Q8—42no—
324C22⋊Q8—44no—
325C22⋊Q8—44no—
326C22⋊Q8—44no—
327C22⋊Q8—44no—
328C22⋊Q8—44no—
329C22⋊Q8—44no—
330C4×Q8—24no—
331C4×Q8—24no—
332C4×Q8—28no—
333C4×Q8—42no—
334C4×Q8—42no—
335C4×Q8—44no—
336C4×Q8—44no—
337C4×Q8—44no—
338C4×D4—24no—
339C4×D4—24no—
340C4×D4—42no—
341#117—44no—
342#117—44no—
343#117—44no—
344#117—44no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4C2×D411yescharacteristic
377C2×C4⋊C4C2×D411yescharacteristic
378C2×C4⋊C4C2×D411yescharacteristic
379C2×C4⋊C4C2412yes—
380C2×C4⋊C4C2412yes—
381C2×C4⋊C4C2412yes—
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4C2×D411yescharacteristic
393C2×C22⋊C4C2×D411yescharacteristic
394C2×C22⋊C4C2×D411yescharacteristic
395C2×C22⋊C4C2×D411yescharacteristic
396C2×C22⋊C4C2×D411yescharacteristic
397C2×C22⋊C4C2×D411yescharacteristic
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C2×C42C2×D411yescharacteristic
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2411yescharacteristic
417C2×C42C2411yescharacteristic
418C2×C42C2411yescharacteristic
419C2×C42C2411yescharacteristic
420C2×C42C2411yescharacteristic
421#107—44no—
422#106—44no—
423C4⋊C8#4118yes—
424#103—28no—
425#103—28no—
426#103—28no—
427#103—28no—
428#103—28no—
429#103—28no—
430#103—44no—
431#103—44no—
432C22⋊C8—24no—
433C22⋊C8—24no—
434#97—24no—
435#97—24no—
436#97—42no—
437C4×C8—22no—
438C4×C8—22no—
439C4×C8—22no—
440C4×C8—22no—
441C4×C8—42no—
442#95—22no—
443#95—22no—
444#95—22no—
445#95—22no—
446#95—22no—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95C2×D411yescharacteristic
461#95C2×D411yescharacteristic
462#95C2×D411yescharacteristic
463#95C2×D411yescharacteristic
464#95C2×D411yescharacteristic
465#95C2×D411yescharacteristic
466C24C22×D411yescharacteristic
467C24C22×D411yescharacteristic
468C2×Q8—24no—
469C2×Q8—22no—
470C2×Q8—24no—
471C2×Q8—24no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8—24no—
475C2×Q8—24no—
476C2×Q8—24no—
477C2×Q8—24no—
478C2×Q8—22no—
479C2×Q8—22no—
480C2×Q8—22no—
481C2×Q8—42no—
482C2×Q8—42no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—41no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4#13714yes—
514C22×C4C22×D411yescharacteristic
515C22×C4C22×D411yescharacteristic
516C22×C4C22×D411yescharacteristic
517C22×C4C22×D411yescharacteristic
518C22×C4C22×D411yescharacteristic
519C22×C4C22×D411yescharacteristic
520C22×C4C22×D411yescharacteristic
521C22×C4C22×D411yescharacteristic
522C22×C4C22×D411yescharacteristic
523C22×C4C22×D411yescharacteristic
524C22×C4C22×D411yescharacteristic
525C22×C4C22×D411yescharacteristic
526C22×C4C2511yescharacteristic
527Q16—88no—
528Q16—88no—
529M16—48no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8—48no—
540C2×C8C2×#4114yes—
541C2×C8C2×#4114yes—
542C2×C8H(5,𝔽2)14yes—
543C4⋊C4—22no—
544C4⋊C4—24no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—24no—
548C4⋊C4—24no—
549C4⋊C4—24no—
550C4⋊C4—24no—
551C4⋊C4—41no—
552C4⋊C4—44no—
553C4⋊C4—44no—
554C4⋊C4—44no—
555C4⋊C4—44no—
556C4⋊C4—44no—
557C4⋊C4—44no—
558C4⋊C4—44no—
559C4⋊C4—44no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—42no—
564C4⋊C4—42no—
565C4⋊C4—42no—
566C4⋊C4—42no—
567C4⋊C4—42no—
568C4⋊C4—42no—
569C4⋊C4—42no—
570C4⋊C4—42no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—42no—
574C4⋊C4—82no—
575C4⋊C4—82no—
576C4⋊C4—82no—
577C4⋊C4—82no—
578C4⋊C4—82no—
579C4⋊C4—82no—
580C4⋊C4—82no—
581C4⋊C4—82no—
582C4⋊C4C2×#4114yes—
583C22⋊C4—22no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—41no—
588C22⋊C4—41no—
589C22⋊C4—44no—
590C22⋊C4—44no—
591C22⋊C4—44no—
592C22⋊C4—44no—
593C22⋊C4—82no—
594C22⋊C4—82no—
595C22⋊C4—82no—
596C22⋊C4—82no—
597C42—22no—
598C42—22no—
599C42—22no—
600C42—22no—
601C42—22no—
602C42—22no—
603C42—22no—
604C42—22no—
605C42—21no—
606C42—21no—
607C42—21no—
608C42—22no—
609C42—21no—
610C42—44no—
611C42—44no—
612C42—44no—
613C42—44no—
614C42—44no—
615C42—44no—
616C42C2×#4114yes—
617C42C2×#4112yes—
618C42H(5,𝔽2)12yes—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23C2×#13712yes—
633C23C23×D411yescharacteristic
634Q8—48no—
635Q8—44no—
636Q8—44no—
637Q8—44no—
638Q8—44no—
639Q8—44no—
640Q8—44no—
641D4—44no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—28no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—24no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—44no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4#53212yes—
702C2×C4#53212yes—
703C2×C4#54612yes—
704C2×C4#54612yes—
705C2×C4C2×#13712yes—
706C2×C4C2×#13712yes—
707C2×C4#57512yes—
708C2×C4#57812yes—
709C2×C4#57812yes—
710C2×C4C22×#4111yescharacteristic
711C2×C4C22×#4112yes—
712C2×C4C2×H(5,𝔽2)12yes—
713C2×C4C2×H(5,𝔽2)11yescharacteristic
714C8—24no—
715C8—24no—
716C8—24no—
717C8—42no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22C2×#53211yescharacteristic
733C22C2×#54611yescharacteristic
734C22#349811yescharacteristic
735C22C22×#13711yescharacteristic
736C22C2×#57511yescharacteristic
737C22C2×#57811yescharacteristic
738C22C2×#57811yescharacteristic
739C4—22no—
740C4—22no—
741C4—22no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4—41no—
746C4—41no—
747C4—44no—
748C4—41no—
749C4—41no—
750C4—82no—
751C4—82no—
752C4—82no—
753C4—82no—
754C4—82no—
755C4—82no—
756C4—82no—
757C4#331214yes—
758C4#331514yes—
759C4#348312yes—
760C4#351912yes—
761C2—42no—
762C2—81no—
763C2#3641211yescharacteristic
764C2#6070111yescharacteristic
765C2#6071511yescharacteristic
766C2C2×#331211yescharacteristic
767C2C2×#331511yescharacteristic
768C2#6242411yescharacteristic
769C2#6242511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #33232C2semidirect
4. #33176C2semidirect
5. #33172C2semidirect
6. #29207C2semidirect
7. #28934C2semidirect
8. #28920C2semidirect
9. #28440C2semidirect
10. #27892C2semidirect
11. #27889C2semidirect
12. #25600C2semidirect
13. #25600C2semidirect
15. #23110C2semidirect
16. #21647C2semidirect
17. #21409C2semidirect
18. #21400C2semidirect

Maximal subgroups

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

subgroupindex
#362092
#361342
#332322
#331762
#331722
#292072
#289342
#289202
#284402
#278922
#278892
#256002
#253982
#231102
#216472
#214092
#214002
C4×#4352