Finite Group Databasebeta

← #382809

Subgroups — #382809

Order 512.

1616 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#525C211yesmaximal, characteristic
2#20682C211yesmaximal, characteristic, complemented
3C4×#380C211yesmaximal, characteristic, complemented
4#11226C212yesmaximal, complemented
5#11201C212yesmaximal, complemented
6#11075C212yesmaximal, complemented
7#10971C212yesmaximal
8#10808C212yesmaximal, complemented
9#10790C212yesmaximal, complemented
10C2×#525C2211yescharacteristic
11C2×C4×#41C2211yescharacteristic
12C23×C42C2211yescharacteristic
13C22×#104C2214yes—
14C2×#407C2212yes—
15C4×C22⋊Q8C411yescharacteristic, complemented
16C4×C22⋊Q8C411yescharacteristic, complemented
17C4×C22⋊Q8C411yescharacteristic, complemented
18C4×C22⋊Q8C411yescharacteristic, complemented
19C4×#123—21no—
20C4×#123—21no—
21C4×#121C411yescharacteristic, complemented
22C4×#121C411yescharacteristic, complemented
23C4×#121C411yescharacteristic, complemented
24C4×#121C411yescharacteristic, complemented
25C4×#120—21no—
26C4×#120—21no—
27#2297C2211yescharacteristic
28#2296C2211yescharacteristic
29#2290—21no—
30#2290—21no—
31#2280C2211yescharacteristic
32C2×#380—21no—
33C42×D4—21no—
34C42×D4—21no—
35C4×#117C2211yescharacteristic
36C2×C4×C4⋊C4C2212yes—
37C2×C4×C22⋊C4C2212yes—
38#1817—21no—
39#1817—21no—
40#1817—21no—
41#1817—21no—
42C2×#339C2214yes—
43C2×#339C2214yes—
44C2×#339C2214yes—
45#1728C2212yes—
46#1728C2212yes—
47C4⋊#95—21no—
48#1434—21no—
49C22⋊#95—21no—
50C4×#95C2212yes—
51C22×#41C2311yescharacteristic
52C24×C4D411yescharacteristic
53C24×C4D411yescharacteristic
54C24×C4C2311yescharacteristic
55C22×M16C2314yes—
56#525—24no—
57#525—24no—
58C2×#123—21no—
59C2×C22⋊Q8C2×C411yescharacteristic
60C2×C22⋊Q8C2×C411yescharacteristic
61C2×#121C2×C411yescharacteristic
62C2×#121C2×C411yescharacteristic
63C2×#120—21no—
64C4×#41—44no—
65C2×C4×Q8C2×C411yescharacteristic
66C2×C4×Q8C2×C411yescharacteristic
67C2×C4×D4—21no—
68C2×C4×D4—21no—
69C2×C4×D4—21no—
70C2×C4×D4—21no—
71C2×C4×D4—21no—
72C2×C4×D4—21no—
73C2×C4×D4—21no—
74C2×C4×D4—21no—
75C2×C4×D4C2×C411yescharacteristic
76C2×C4×D4C2×C411yescharacteristic
77C2×#117—21no—
78C2×#117C2311yescharacteristic
79C2×#117C2311yescharacteristic
80C2×#117C2311yescharacteristic
81C22×C4⋊C4—22no—
82C22×C22⋊C4—22no—
83C22×C42—21no—
84C22×C42—44no—
85C22×C42C2×C411yescharacteristic
86C22×C42C2×C411yescharacteristic
87C22×C42C2×C411yescharacteristic
88C22×C42C2×C411yescharacteristic
89C22×C42D411yescharacteristic
90C22×C42D411yescharacteristic
91C22×C42D411yescharacteristic
92C22×C42D411yescharacteristic
93C22×C42D411yescharacteristic
94C22×C42D411yescharacteristic
95C22×C42C2314yes—
96C22×C42C2311yescharacteristic
97C22×C42C2311yescharacteristic
98C2×#104—28no—
99C2×#104—44no—
100C2×#104—44no—
101#407—44no—
102C2×C22⋊C8—22no—
103C2×C22⋊C8—22no—
104#391C2×C411yescharacteristic
105#391C2×C411yescharacteristic
106#390C2×C411yescharacteristic
107#390C2×C411yescharacteristic
108#389C2×C411yescharacteristic
109#389C2×C411yescharacteristic
110#389C2×C411yescharacteristic
111#389C2×C411yescharacteristic
112#388—21no—
113#388—21no—
114#388—21no—
115#388—21no—
116#387—21no—
117#387—21no—
118#387—21no—
119#387—21no—
120#386—21no—
121#386—21no—
122#386—21no—
123#386—21no—
124#386—21no—
125#386—21no—
126#385—21no—
127#385—21no—
128#385—21no—
129#385—21no—
130#385—21no—
131#385—21no—
132#381—21no—
133#380—28no—
134#380C2×C411yescharacteristic
135#380C2×C411yescharacteristic
136#380C2×C411yescharacteristic
137#380C2×C411yescharacteristic
138#379—21no—
139C4×C4⋊C4—21no—
140C4×C4⋊C4—21no—
141C4×C4⋊C4—21no—
142C4×C4⋊C4—21no—
143C4×C4⋊C4—21no—
144C4×C4⋊C4—21no—
145C4×C4⋊C4—44no—
146C4×C4⋊C4C2×C411yescharacteristic
147C4×C4⋊C4C2×C411yescharacteristic
148C4×C4⋊C4C2×C411yescharacteristic
149C4×C4⋊C4C2×C411yescharacteristic
150C4×C22⋊C4—21no—
151C4×C22⋊C4—21no—
152C4×C22⋊C4—21no—
153C4×C22⋊C4—21no—
154C4×C22⋊C4—21no—
155C4×C22⋊C4—21no—
156C4×C22⋊C4—21no—
157C4×C22⋊C4—21no—
158C4×C22⋊C4—21no—
159C4×C22⋊C4—21no—
160C4×C22⋊C4—21no—
161C4×C22⋊C4—21no—
162C4×C22⋊C4—21no—
163C4×C22⋊C4—21no—
164C4×C22⋊C4—44no—
165#376—21no—
166C2×#95—22no—
167C2×#95—22no—
168C2×#95—22no—
169C2×#95—22no—
170C43—21no—
171#339—28no—
172#339—44no—
173#339—44no—
174#336—22no—
175#336—22no—
176#336—22no—
177#336—22no—
178C25C2×D411yescharacteristic
179C2×#41—22no—
180C2×#41—24no—
181C2×#41—22no—
182C2×#41—22no—
183C2×#41#4114yes—
184C22×Q8C22×C411yescharacteristic
185C22×D4—21no—
186C22×D4—21no—
187C22×D4—21no—
188C22×D4C22×C411yescharacteristic
189C23×C4—24no—
190C23×C4—21no—
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—22no—
194C23×C4—24no—
195C23×C4—22no—
196C23×C4—24no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—42no—
200C23×C4—42no—
201C23×C4—42no—
202C23×C4—42no—
203C23×C4—42no—
204C23×C4C22⋊C411yescharacteristic
205C23×C4C22⋊C411yescharacteristic
206C23×C4C22⋊C411yescharacteristic
207C23×C4C22⋊C411yescharacteristic
208C23×C4C22⋊C411yescharacteristic
209C23×C4C22⋊C411yescharacteristic
210C23×C4C22⋊C411yescharacteristic
211C23×C4C22⋊C411yescharacteristic
212C23×C4C22×C411yescharacteristic
213C23×C4C22×C411yescharacteristic
214C23×C4C2×D411yescharacteristic
215C23×C4C2×D411yescharacteristic
216C23×C4C2×D411yescharacteristic
217C23×C4C2×D411yescharacteristic
218C23×C4C2×D411yescharacteristic
219C23×C4C2×D411yescharacteristic
220C23×C4C2×D411yescharacteristic
221C23×C4C2411yescharacteristic
222C2×M16—24no—
223C2×M16—24no—
224C2×M16—24no—
225C2×M16—24no—
226C2×M16—24no—
227C2×M16—24no—
228C22×C8—24no—
229#123—28no—
230C22⋊Q8—22no—
231C22⋊Q8—22no—
232C22⋊Q8—22no—
233C22⋊Q8—22no—
234#121—22no—
235#121—22no—
236#121—22no—
237#121—22no—
238#120—28no—
239C4×Q8—42no—
240C4×Q8—42no—
241C4×D4—28no—
242C4×D4—28no—
243C4×D4—42no—
244C4×D4—42no—
245C4×D4—44no—
246C4×D4—44no—
247C4×D4—44no—
248C4×D4—44no—
249C4×D4—44no—
250C4×D4—44no—
251#117—22no—
252#117—24no—
253#117—22no—
254#117—22no—
255#117—44no—
256#117#4114yes—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—28no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—44no—
267C2×C4⋊C4—44no—
268C2×C4⋊C4C22×C411yescharacteristic
269C2×C4⋊C4C22×C411yescharacteristic
270C2×C4⋊C4C22×C411yescharacteristic
271C2×C4⋊C4C22×C411yescharacteristic
272C2×C4⋊C4C22×C411yescharacteristic
273C2×C4⋊C4C22×C411yescharacteristic
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—28no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—44no—
293C2×C22⋊C4—44no—
294C2×C42—21no—
295C2×C42—24no—
296C2×C42—24no—
297C2×C42—21no—
298C2×C42—21no—
299C2×C42—21no—
300C2×C42—21no—
301C2×C42—21no—
302C2×C42—21no—
303C2×C42—21no—
304C2×C42—21no—
305C2×C42—24no—
306C2×C42—24no—
307C2×C42—24no—
308C2×C42—24no—
309C2×C42—24no—
310C2×C42—24no—
311C2×C42—42no—
312C2×C42—42no—
313C2×C42—42no—
314C2×C42—42no—
315C2×C42—42no—
316C2×C42—42no—
317C2×C42—42no—
318C2×C42—42no—
319C2×C42—44no—
320C2×C42—42no—
321C2×C42—42no—
322C2×C42C22⋊C411yescharacteristic
323C2×C42C22⋊C411yescharacteristic
324C2×C42C22⋊C411yescharacteristic
325C2×C42C22⋊C411yescharacteristic
326C2×C42C22⋊C411yescharacteristic
327C2×C42C22⋊C411yescharacteristic
328C2×C42C22⋊C411yescharacteristic
329C2×C42C22⋊C411yescharacteristic
330C2×C42C22×C411yescharacteristic
331C2×C42C22×C411yescharacteristic
332C2×C42C22×C411yescharacteristic
333C2×C42C22×C411yescharacteristic
334C2×C42C2×D411yescharacteristic
335C2×C42C2×D411yescharacteristic
336C2×C42C2×D411yescharacteristic
337C2×C42C2×D411yescharacteristic
338#104—416no—
339C22⋊C8—44no—
340C22⋊C8—44no—
341#95—28no—
342#95—21no—
343#95—21no—
344#95—21no—
345#95—21no—
346#95—21no—
347#95—21no—
348#95—21no—
349#95—21no—
350#95—21no—
351#95—21no—
352#95—21no—
353#95—21no—
354#95—21no—
355#95—21no—
356#95—21no—
357#95—21no—
358#95—44no—
359#95—44no—
360#95—44no—
361C24—21no—
362C24—21no—
363C24—22no—
364C24—22no—
365C24—21no—
366C24—22no—
367C24—22no—
368C24—41no—
369C24—41no—
370C24C2×C22⋊C411yescharacteristic
371C24C2×C22⋊C411yescharacteristic
372C24C22×D411yescharacteristic
373#41—28no—
374#41—28no—
375#41—44no—
376#41—44no—
377C2×Q8—21no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8#11712yes—
381C2×D4—24no—
382C2×D4—24no—
383C2×D4—24no—
384C2×D4—21no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—42no—
388C2×D4—42no—
389C2×D4—42no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4—42no—
393C2×D4—42no—
394C2×D4#11712yes—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—24no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—28no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—416no—
458C22×C4—42no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—416no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—44no—
466C22×C4—44no—
467C22×C4—44no—
468C22×C4—44no—
469C22×C4—44no—
470C22×C4—44no—
471C22×C4—44no—
472C22×C4—44no—
473C22×C4—44no—
474C22×C4—44no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4#10414yescomplemented
478C22×C4C2×C22⋊C411yescharacteristic
479C22×C4C2×C22⋊C411yescharacteristic
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×C4C23×C411yescharacteristic
489C22×C4C22×D411yescharacteristic
490C22×C4C2×#4112yes—
491C22×C4C2×#4112yes—
492C22×C4H(5,𝔽2)14yes—
493C22×C4H(5,𝔽2)12yes—
494C22×C42−1+412yes—
495M16—44no—
496M16—44no—
497M16—44no—
498M16—44no—
499C2×C8—44no—
500C2×C8—44no—
501C2×C8—44no—
502C4⋊C4—24no—
503C4⋊C4—24no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—416no—
511C4⋊C4—42no—
512C4⋊C4—42no—
513C4⋊C4—42no—
514C4⋊C4—42no—
515C4⋊C4—42no—
516C4⋊C4—42no—
517C4⋊C4#11712yes—
518C4⋊C4#11712yes—
519C22⋊C4—24no—
520C22⋊C4—24no—
521C22⋊C4—24no—
522C22⋊C4—24no—
523C22⋊C4—24no—
524C22⋊C4—42no—
525C22⋊C4—42no—
526C22⋊C4—42no—
527C22⋊C4—42no—
528C22⋊C4—416no—
529C22⋊C4—42no—
530C22⋊C4—42no—
531C22⋊C4—42no—
532C22⋊C4—41no—
533C22⋊C4—41no—
534C22⋊C4—42no—
535C22⋊C4—42no—
536C22⋊C4—42no—
537C22⋊C4—42no—
538C42—22no—
539C42—22no—
540C42—22no—
541C42—22no—
542C42—24no—
543C42—22no—
544C42—22no—
545C42—22no—
546C42—22no—
547C42—41no—
548C42—41no—
549C42—41no—
550C42—41no—
551C42—41no—
552C42—41no—
553C42—41no—
554C42—41no—
555C42—42no—
556C42—42no—
557C42—42no—
558C42—42no—
559C42—42no—
560C42—42no—
561C42—42no—
562C42—42no—
563C42—44no—
564C42—44no—
565C42—44no—
566C42—44no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—24no—
572C23—24no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—22no—
586C23—44no—
587C23—44no—
588C23—44no—
589C23—44no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23C2×#10412yes—
601C23#42112yes—
602C23C22×C22⋊C411yescharacteristic
603C23#52512yes—
604C23#53412yes—
605C23#53511yescharacteristic
606C23#53611yescharacteristic
607Q8—24no—
608Q8—42no—
609D4—24no—
610D4—48no—
611D4—48no—
612D4—44no—
613D4—44no—
614D4—42no—
615C2×C4—28no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
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—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—44no—
646C2×C4—44no—
647C2×C4—44no—
648C2×C4—44no—
649C2×C4—44no—
650C2×C4—44no—
651C2×C4—44no—
652C2×C4—44no—
653C2×C4—44no—
654C2×C4—44no—
655C2×C4—44no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—44no—
669C2×C4—44no—
670C2×C4—48no—
671C2×C4—48no—
672C2×C4—48no—
673C2×C4—48no—
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—41no—
686C2×C4—84no—
687C2×C4—84no—
688C2×C4—84no—
689C2×C4—84no—
690C2×C4—84no—
691C2×C4—84no—
692C2×C4C2×#10412yes—
693C2×C4C2×#10412yes—
694C2×C4#42112yes—
695C2×C4#42112yes—
696C2×C4C2×#11711yescharacteristic
697C2×C4C2×#11711yescharacteristic
698C2×C4#51812yes—
699C2×C4#52012yes—
700C2×C4#52512yes—
701C2×C4#53412yes—
702C2×C4#53712yes—
703C2×C4#53814yes—
704C2×C4#53914yes—
705C2×C4#54014yes—
706C2×C4#54214yes—
707C8—84no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—48no—
723C22—48no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22—81no—
739C22#228011yescharacteristic
740C22#230811yescharacteristic
741C22#231111yescharacteristic
742C22#263512yes—
743C22#263812yes—
744C22C22×#10411yescharacteristic
745C22C2×#42111yescharacteristic
746C22C2×#42111yescharacteristic
747C22C2×#42111yescharacteristic
748C4—22no—
749C4—22no—
750C4—22no—
751C4—22no—
752C4—41no—
753C4—41no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—41no—
758C4—41no—
759C4—41no—
760C4—41no—
761C4—88no—
762C4—81no—
763C4—81no—
764C4—81no—
765C4—81no—
766C4#231812yes—
767C4#231912yes—
768C4#263014yes—
769C2—22no—
770C2—22no—
771C2—42no—
772C2—42no—
773C2—82no—
774C2#1434411yescharacteristic
775C2#2074711yescharacteristic
776C2#2074811yescharacteristic
777C2#2177311yescharacteristic
778C2#2177411yescharacteristic
779C2#2189911yescharacteristic
780C2#2190011yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC23C22×C22⋊C4
prime radicalC2×#525C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C23×C42 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #20682C2semidirect
3. C4×#380C2semidirect
4. #11226C2semidirect
5. #11201C2semidirect
6. #11075C2semidirect
8. #10808C2semidirect
9. #10790C2semidirect
15. C4×C22⋊Q8C4semidirect
16. C4×C22⋊Q8C4semidirect
17. C4×C22⋊Q8C4semidirect
18. C4×C22⋊Q8C4semidirect
21. C4×#121C4semidirect
22. C4×#121C4semidirect
23. C4×#121C4semidirect
24. C4×#121C4semidirect
477. C22×C4#104semidirect

Maximal subgroups

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

subgroupindex
C4×#5252
#206822
C4×#3802
#112262
#112012
#110752
#109712
#108082
#107902