Finite Group Databasebeta

← #917560

Subgroups — #917560

Order 512.

3216 conjugacy classes of subgroups.

The subgroup lattice has 823 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2487C211yesmaximal, characteristic, complemented
2C2×#2388C211yesmaximal, characteristic
3#17123C214yesmaximal, complemented
4#17032C212yesmaximal, complemented
5#16932C212yesmaximal, complemented
6#16481C212yesmaximal, complemented
7#16288C212yesmaximal, complemented
8#15501C214yesmaximal, complemented
9#15132C212yesmaximal, complemented
10#15131C212yesmaximal, complemented
11#15129C212yesmaximal, complemented
12#14337C212yesmaximal, complemented
13#13973C212yesmaximal, complemented
14#13906C211yesmaximal, characteristic, complemented
15#13872C212yesmaximal, complemented
16C23×#41C2211yescharacteristic
17C22×C4×D4C2212yes—
18C22×C4×D4C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20#2487—28no—
21C2×#400C2212yes—
22C2×#399C2212yes—
23C2×#397C2214yes—
24C2×#396C2214yes—
25#2388—28no—
26C2×#395C2211yescharacteristic
27C2×#394C2211yescharacteristic
28C2×#394C2212yes—
29C2×#394C2214yes—
30C2×#393C2211yescharacteristic
31C2×#392C2212yes—
32C2×#392C2211yescharacteristic
33C2×#390C2212yes—
34C2×#389C2212yes—
35C2×#389C2212yes—
36C2×#386C2212yes—
37C2×#386C2214yes—
38C2×#385C2212yes—
39C2×#384C2211yescharacteristic
40C2×#380C2212yes—
41C2×#380C2212yes—
42C2×#380C2211yescharacteristic
43C2×#380C2212yes—
44C2×#380C2212yes—
45C2×#380C2212yes—
46C2×#380C2212yes—
47C2×#380C2212yes—
48C2×C4×C4⋊C4C2211yescharacteristic
49C2×C4×C22⋊C4C2212yes—
50C2×C4×C22⋊C4C2211yescharacteristic
51#1446C2214yes—
52#1443C2214yes—
53#1442C2214yes—
54#1442C2214yes—
55#1441C2214yes—
56#1441C2214yes—
57#1441C2214yes—
58#1441C2214yes—
59#1440C2214yes—
60#1440C2214yes—
61#1440C2214yes—
62#1439C2214yes—
63#1439C2214yes—
64#1439C2212yes—
65#1439C2212yes—
66#1439C2214yes—
67#1438C2214yes—
68#1438C2214yes—
69#1438C2214yes—
70#1437C2214yes—
71C4⋊#95C2212yes—
72C4⋊#95C2212yes—
73C4⋊#95C2212yes—
74C4⋊#95C2212yes—
75#1434C2214yes—
76C22⋊#95C2214yes—
77C22×#41—24no—
78C22×#41—28no—
79C22×#41—42no—
80C22×#41—44no—
81C22×#41—42no—
82C23×Q8C2311yescharacteristic
83C23×D4C2312yes—
84C23×D4C2311yescharacteristic
85C23×D4C2311yescharacteristic
86C23×D4C2312yes—
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2312yes—
90C24×C4C2312yes—
91C2×C4×D4—28no—
92C2×C4×D4—28no—
93C2×C4×D4—42no—
94C2×C4×D4—42no—
95C2×C4×D4—44no—
96C2×C4×D4D418yes—
97C22×C4⋊C4—24no—
98C22×C4⋊C4—42no—
99C22×C4⋊C4—42no—
100C22×C4⋊C4C2312yes—
101C22×C4⋊C4C2312yes—
102C22×C4⋊C4C2312yes—
103C22×C4⋊C4C2312yes—
104C22×C4⋊C4C2312yes—
105C22×C4⋊C4C2314yes—
106C22×C4⋊C4C2314yes—
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2311yescharacteristic
111C22×C22⋊C4C2312yes—
112C22×C22⋊C4C2312yes—
113C22×C22⋊C4C2312yes—
114C22×C22⋊C4C2312yes—
115C22×C22⋊C4C2312yes—
116C22×C22⋊C4C2312yes—
117C22×C22⋊C4C2314yes—
118C22×C22⋊C4C2314yes—
119C22×C22⋊C4C2314yes—
120C22×C22⋊C4C2314yes—
121C22×C22⋊C4C2314yes—
122C22×C22⋊C4C2314yes—
123C22×C22⋊C4C2314yes—
124C22×C22⋊C4C2311yescharacteristic
125C22×C22⋊C4C2311yescharacteristic
126C22×C42C2312yes—
127C22×C42C2311yescharacteristic
128C22×C42C2312yes—
129#400—28no—
130#399—28no—
131#397—48no—
132#396—48no—
133#395—24no—
134#394—24no—
135#394—28no—
136#394—48no—
137#393—24no—
138#392—28no—
139#392—24no—
140#390—44no—
141#389—28no—
142#389—44no—
143#386—28no—
144#386—48no—
145#385—28no—
146#384—42no—
147#380—28no—
148#380—24no—
149#380—28no—
150#380—44no—
151#380—44no—
152#380—44no—
153#380—44no—
154#380—44no—
155C4×C4⋊C4—42no—
156C4×C22⋊C4—24no—
157C4×C22⋊C4—28no—
158C2×#95C2312yes—
159C2×#95C2311yescharacteristic
160C2×#95C2312yes—
161C2×#95C2311yescharacteristic
162C2×#95C2314yes—
163C2×#95C2314yes—
164C2×#95C2312yes—
165C2×#95C2314yes—
166C2×#95C2314yes—
167C2×#95C2314yes—
168C2×#95C2314yes—
169C2×#95C2314yes—
170C2×#95C2314yes—
171C2×#95C2314yes—
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2312yes—
178C2×#95C2314yes—
179C25C2411yescharacteristic
180C25C2412yes—
181C25C2411yescharacteristic
182C2×#41—432no—
183C2×#41—416no—
184C2×#41—416no—
185C2×#41—432no—
186C2×#41—416no—
187C22×Q8—22no—
188C22×Q8—24no—
189C22×Q8—42no—
190C22×Q8—41no—
191C22×Q8—41no—
192C22×D4—24no—
193C22×D4—22no—
194C22×D4—22no—
195C22×D4—24no—
196C22×D4—24no—
197C22×D4—24no—
198C22×D4—24no—
199C22×D4—24no—
200C22×D4—24no—
201C22×D4—22no—
202C22×D4—24no—
203C22×D4—24no—
204C22×D4—22no—
205C22×D4—22no—
206C22×D4—41no—
207C22×D4—41no—
208C22×D4—42no—
209C22×D4—42no—
210C22×D4—42no—
211C22×D4—42no—
212C22×D4—42no—
213C22×D4—42no—
214C22×D4—42no—
215C22×D4—41no—
216C22×D4—41no—
217C22×D4C2×D414yes—
218C23×C4—24no—
219C23×C4—24no—
220C23×C4—24no—
221C23×C4—24no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—24no—
227C23×C4—24no—
228C23×C4—24no—
229C23×C4—24no—
230C23×C4—24no—
231C23×C4—24no—
232C23×C4—24no—
233C23×C4—42no—
234C23×C4—42no—
235C23×C4—44no—
236C23×C4—44no—
237C23×C4C2×D414yes—
238C23×C4C2×D414yes—
239C23×C4#4118yes—
240C23×C4C2414yes—
241C23×C4C2414yes—
242C23×C4C2414yes—
243C23×C4C2412yes—
244C23×C4C2414yes—
245C23×C4C2411yescharacteristic
246C23×C4C2411yescharacteristic
247C23×C4C2411yescharacteristic
248C23×C4C2412yes—
249C23×C4C2412yes—
250C23×C4C2411yescharacteristic
251C23×C4C2411yescharacteristic
252C4×D4—416no—
253C4×D4—432no—
254C2×C4⋊C4—24no—
255C2×C4⋊C4—24no—
256C2×C4⋊C4—24no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—24no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—28no—
270C2×C4⋊C4—28no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—42no—
273C2×C4⋊C4—42no—
274C2×C4⋊C4—41no—
275C2×C4⋊C4—41no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—416no—
278C2×C4⋊C4—44no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—44no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—44no—
284C2×C4⋊C4—44no—
285C2×C4⋊C4—44no—
286C2×C4⋊C4C2×D414yes—
287C2×C22⋊C4—24no—
288C2×C22⋊C4—24no—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—24no—
291C2×C22⋊C4—24no—
292C2×C22⋊C4—24no—
293C2×C22⋊C4—24no—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—24no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—28no—
302C2×C22⋊C4—28no—
303C2×C22⋊C4—28no—
304C2×C22⋊C4—42no—
305C2×C22⋊C4—42no—
306C2×C22⋊C4—41no—
307C2×C22⋊C4—41no—
308C2×C22⋊C4—41no—
309C2×C22⋊C4—41no—
310C2×C22⋊C4—42no—
311C2×C22⋊C4—42no—
312C2×C22⋊C4—44no—
313C2×C22⋊C4—44no—
314C2×C22⋊C4—44no—
315C2×C22⋊C4—44no—
316C2×C22⋊C4—44no—
317C2×C22⋊C4—44no—
318C2×C22⋊C4—44no—
319C2×C22⋊C4—44no—
320C2×C22⋊C4—44no—
321C2×C22⋊C4—44no—
322C2×C22⋊C4—44no—
323C2×C22⋊C4—44no—
324C2×C22⋊C4—44no—
325C2×C22⋊C4—44no—
326C2×C22⋊C4—44no—
327C2×C22⋊C4—44no—
328C2×C22⋊C4—44no—
329C2×C22⋊C4—44no—
330C2×C22⋊C4C2×D414yes—
331C2×C22⋊C4C2×D414yes—
332C2×C42—22no—
333C2×C42—22no—
334C2×C42—24no—
335C2×C42—24no—
336C2×C42—24no—
337C2×C42—24no—
338C2×C42—42no—
339C2×C42—42no—
340C2×C42C2×D414yes—
341#95—22no—
342#95—24no—
343#95—24no—
344#95—22no—
345#95—28no—
346#95—24no—
347#95—28no—
348#95—28no—
349#95—28no—
350#95—28no—
351#95—44no—
352#95—42no—
353#95—44no—
354#95—44no—
355#95—44no—
356#95—44no—
357#95—44no—
358#95—44no—
359#95—44no—
360#95—44no—
361#95—44no—
362C24—22no—
363C24—22no—
364C24—22no—
365C24—21no—
366C24—21no—
367C24—21no—
368C24—21no—
369C24—22no—
370C24—22no—
371C24—22no—
372C24—22no—
373C24—22no—
374C24—22no—
375C24—21no—
376C24—22no—
377C24—22no—
378C24—22no—
379C24—22no—
380C24—22no—
381C24—22no—
382C24—21no—
383C24—21no—
384C24—22no—
385C24—22no—
386C24—22no—
387C24—21no—
388C24—21no—
389C24—21no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24C22×D412yes—
395C24C22×D412yes—
396C24C2×#4114yes—
397C24H(5,𝔽2)12yes—
398C242−1+412yes—
399C24C2511yescharacteristic
400#41—4128no—
401C2×Q8—48no—
402C2×Q8—44no—
403C2×Q8—44no—
404C2×Q8—48no—
405C2×Q8—44no—
406C2×D4—216no—
407C2×D4—28no—
408C2×D4—28no—
409C2×D4—44no—
410C2×D4—44no—
411C2×D4—44no—
412C2×D4—44no—
413C2×D4—44no—
414C2×D4—48no—
415C2×D4—48no—
416C2×D4—48no—
417C2×D4—48no—
418C2×D4—48no—
419C2×D4—44no—
420C2×D4—48no—
421C2×D4—48no—
422C2×D4—48no—
423C2×D4—48no—
424C2×D4—44no—
425C2×D4—48no—
426C2×D4—48no—
427C2×D4—48no—
428C2×D4—48no—
429C2×D4—44no—
430C2×D4—48no—
431C2×D4—48no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—28no—
461C22×C4—28no—
462C22×C4—216no—
463C22×C4—216no—
464C22×C4—216no—
465C22×C4—216no—
466C22×C4—216no—
467C22×C4—24no—
468C22×C4—22no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—22no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—48no—
503C22×C4—48no—
504C22×C4—48no—
505C22×C4—48no—
506C22×C4—48no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—48no—
512C22×C4—48no—
513C22×C4—88no—
514C22×C4—88no—
515C22×C4—84no—
516C22×C4—84no—
517C22×C4C22×D412yes—
518C22×C4C22×D412yes—
519C22×C4C22×D412yes—
520C22×C4C22×D412yes—
521C22×C4C22×D412yes—
522C22×C4C2×#4114yes—
523C22×C4C2×#4114yes—
524C22×C4H(5,𝔽2)14yes—
525C22×C4H(5,𝔽2)12yes—
526C22×C4H(5,𝔽2)12yes—
527C22×C4H(5,𝔽2)14yes—
528C22×C42−1+412yes—
529C22×C42−1+412yes—
530C4⋊C4—44no—
531C4⋊C4—48no—
532C4⋊C4—48no—
533C4⋊C4—48no—
534C4⋊C4—48no—
535C4⋊C4—48no—
536C4⋊C4—48no—
537C4⋊C4—84no—
538C4⋊C4—88no—
539C4⋊C4—88no—
540C4⋊C4—84no—
541C22⋊C4—44no—
542C22⋊C4—44no—
543C22⋊C4—48no—
544C22⋊C4—48no—
545C22⋊C4—48no—
546C22⋊C4—48no—
547C22⋊C4—48no—
548C22⋊C4—48no—
549C22⋊C4—88no—
550C22⋊C4—88no—
551C22⋊C4—88no—
552C22⋊C4—88no—
553C22⋊C4—88no—
554C22⋊C4—88no—
555C22⋊C4—88no—
556C42—28no—
557C42—48no—
558C42—84no—
559C23—22no—
560C23—22no—
561C23—24no—
562C23—24no—
563C23—24no—
564C23—24no—
565C23—22no—
566C23—22no—
567C23—24no—
568C23—22no—
569C23—22no—
570C23—24no—
571C23—22no—
572C23—22no—
573C23—22no—
574C23—24no—
575C23—24no—
576C23—24no—
577C23—24no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—42no—
584C23—41no—
585C23—42no—
586C23—42no—
587C23—41no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—41no—
592C23—41no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—41no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—41no—
611C23—42no—
612C23—41no—
613C23—41no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—41no—
620C23—41no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—41no—
637C23—42no—
638C23—41no—
639C23#53714yes—
640C23C23×D411yescharacteristic
641C23C22×#4112yes—
642C23C2×H(5,𝔽2)11yescharacteristic
643C23C2×H(5,𝔽2)11yescharacteristic
644C23C2×H(5,𝔽2)11yescharacteristic
645C23C2×H(5,𝔽2)12yes—
646C23C2×H(5,𝔽2)12yes—
647C23C2×2−1+411yescharacteristic
648C23C2×2−1+411yescharacteristic
649C23C2×2−1+411yescharacteristic
650C23#58512yes—
651Q8—416no—
652D4—416no—
653D4—432no—
654D4—416no—
655D4—432no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—416no—
692C2×C4—416no—
693C2×C4—432no—
694C2×C4—44no—
695C2×C4—42no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—42no—
699C2×C4—44no—
700C2×C4—42no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—42no—
722C2×C4—44no—
723C2×C4—42no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—816no—
730C2×C4#53414yes—
731C2×C4#53614yes—
732C2×C4#53818yes—
733C2×C4#54618yes—
734C2×C4#55114yes—
735C2×C4#56014yes—
736C22—24no—
737C22—28no—
738C22—42no—
739C22—44no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—44no—
745C22—42no—
746C22—44no—
747C22—44no—
748C22—44no—
749C22—44no—
750C22—42no—
751C22—44no—
752C22—42no—
753C22—44no—
754C22—42no—
755C22—44no—
756C22—44no—
757C22—44no—
758C22—44no—
759C22—81no—
760C22—82no—
761C22—82no—
762C22—81no—
763C22—82no—
764C22—81no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—81no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22C2×#53411yescharacteristic
774C22C2×#53611yescharacteristic
775C22C2×#53711yescharacteristic
776C22C2×#53812yes—
777C22C2×#54612yes—
778C22C2×#55111yescharacteristic
779C22#348812yes—
780C22#349212yes—
781C22#349412yes—
782C22#350712yes—
783C22#351112yes—
784C22C2×#56011yescharacteristic
785C22#353611yescharacteristic
786C22#353611yescharacteristic
787C22#353712yes—
788C22#353811yescharacteristic
789C22#353811yescharacteristic
790C22#354112yes—
791C22#354612yes—
792C22#354712yes—
793C22#354812yes—
794C22#354911yescharacteristic
795C22#355111yescharacteristic
796C4—24no—
797C4—42no—
798C4—42no—
799C4—44no—
800C4—42no—
801C4—44no—
802C4—82no—
803C4—84no—
804C4—84no—
805C4—84no—
806C4—84no—
807C4#269718yes—
808C2—44no—
809C2—82no—
810C2—84no—
811C2#3727311yescharacteristic
812C2#3744211yescharacteristic
813C2#3783612yes—
814C2#3947012yes—
815C2#4244912yes—
816C2#4298912yes—
817C2#4491411yescharacteristic
818C2#4511511yescharacteristic
819C2C2×#269711yescharacteristic
820C2#5295711yescharacteristic
821C2#5300611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2388C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2487C2semidirect
3. #17123C2semidirect
4. #17032C2semidirect
5. #16932C2semidirect
6. #16481C2semidirect
7. #16288C2semidirect
8. #15501C2semidirect
9. #15132C2semidirect
10. #15131C2semidirect
11. #15129C2semidirect
12. #14337C2semidirect
13. #13973C2semidirect
14. #13906C2semidirect
15. #13872C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24872
C2×#23882
#171232
#170322
#169322
#164812
#162882
#155012
#151322
#151312
#151292
#143372
#139732
#139062
#138722