Finite Group Databasebeta

← C2×#31557 #7505071

Subgroups — C2×#31557 #7505071

Order 512.

2448 conjugacy classes of subgroups.

The subgroup lattice has 761 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2420C211yesmaximal, characteristic, complemented
2C2×#2422C211yesmaximal, characteristic, complemented
3#31557C2116yesmaximal, direct product factor
4C2×#2100C211yesmaximal, characteristic, complemented
5C2×#2101C211yesmaximal, characteristic, complemented
6C2×#2077C211yesmaximal, characteristic, complemented
7C2×#2065C211yesmaximal, characteristic, complemented
8C2×#2065C211yesmaximal, characteristic, complemented
9C2×#1999C211yesmaximal, characteristic
10C2×#1893C211yesmaximal, characteristic, complemented
11C2×#1893C211yesmaximal, characteristic, complemented
12C2×#1879C211yesmaximal, characteristic, complemented
13C2×#1879C211yesmaximal, characteristic, complemented
14C2×#1850C211yesmaximal, characteristic, complemented
15C2×#1804C211yesmaximal, characteristic, complemented
16C2×#1802C211yesmaximal, characteristic, complemented
17C23×D8C2211yescharacteristic
18C24×C8C2211yescharacteristic
19C22×#123—21no—
20C22×#121C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24C22×#106C2211yescharacteristic
25C22×C4⋊C8C2211yescharacteristic
26C22×C4⋊C8C2211yescharacteristic
27C22×#102C2211yescharacteristic
28C22×#102C2211yescharacteristic
29C22×#102C2211yescharacteristic
30C22×#102C2211yescharacteristic
31C22×#102C2211yescharacteristic
32C22×#102C2211yescharacteristic
33C22×C22⋊C8C2211yescharacteristic
34#2422—24no—
35#2422C2218yescomplemented
36#2420—24no—
37#2420C2218yescomplemented
38C2×#397—21no—
39C2×#397—21no—
40C2×#394—21no—
41C2×#394—21no—
42C2×#390C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#389C2211yescharacteristic
45C2×#389C2211yescharacteristic
46C2×#386—21no—
47C2×#385—21no—
48C2×#384C2211yescharacteristic
49C2×#382C2211yescharacteristic
50C2×#381—21no—
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×C4×C22⋊C4C2211yescharacteristic
54#2101C2218yescomplemented
55#2100C2218yescomplemented
56#2077C2218yescomplemented
57#2065C2218yescomplemented
58#2065C2218yescomplemented
59#1999C2218yes—
60#1893C2218yescomplemented
61#1893C2218yescomplemented
62#1879C2218yescomplemented
63#1879C2218yescomplemented
64#1850C2218yescomplemented
65#1804C2218yescomplemented
66#1802C2218yescomplemented
67C2×#340C2211yescharacteristic
68C2×#340C2211yescharacteristic
69C2×#340C2211yescharacteristic
70C2×#340C2211yescharacteristic
71C2×#340C2211yescharacteristic
72C2×#340C2211yescharacteristic
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#336C2211yescharacteristic
76C2×#336C2211yescharacteristic
77C23×D4—21no—
78C23×D4—21no—
79C23×D4C2311yescharacteristic
80C23×D4C2311yescharacteristic
81C24×C4—21no—
82C24×C4—21no—
83C24×C4C2311yescharacteristic
84C22×D8—24no—
85C22×D8—24no—
86C22×D8—42no—
87C22×D8C2314yes—
88C23×C8—42no—
89C23×C8—42no—
90C23×C8—42no—
91C23×C8C2311yescharacteristic
92C23×C8C2311yescharacteristic
93C23×C8C2311yescharacteristic
94C23×C8C2311yescharacteristic
95C23×C8C2314yes—
96C2×#123—28no—
97C2×#123—48no—
98C2×#121—22no—
99C2×#121—22no—
100C2×#121—24no—
101C2×#121—24no—
102C2×#121—42no—
103C2×#121—42no—
104C2×#121C2314yes—
105C2×#121C2314yes—
106C2×C4×D4—24no—
107C2×C4×D4—24no—
108C2×C4×D4—22no—
109C2×C4×D4—22no—
110C2×C4×D4—42no—
111C2×C4×D4—42no—
112C2×C4×D4C2314yes—
113C2×C4×D4C2314yes—
114C22×C4⋊C4—21no—
115C22×C4⋊C4—21no—
116C22×C4⋊C4—21no—
117C22×C4⋊C4—21no—
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C22⋊C4—21no—
125C22×C22⋊C4—21no—
126C22×C22⋊C4—21no—
127C22×C22⋊C4—21no—
128C22×C22⋊C4—21no—
129C22×C22⋊C4—21no—
130C22×C22⋊C4—21no—
131C22×C22⋊C4—21no—
132C22×C22⋊C4—21no—
133C22×C22⋊C4—21no—
134C22×C22⋊C4D411yescharacteristic
135C22×C22⋊C4D411yescharacteristic
136C22×C42C2311yescharacteristic
137C22×C42C2311yescharacteristic
138C2×#106—42no—
139C2×#106C2314yes—
140C2×C4⋊C8—42no—
141C2×C4⋊C8—42no—
142C2×C4⋊C8C2314yes—
143C2×C4⋊C8C2314yes—
144C2×#102—42no—
145C2×#102—42no—
146C2×#102—42no—
147C2×#102—42no—
148C2×#102—42no—
149C2×#102—42no—
150C2×#102C2314yes—
151C2×#102C2314yes—
152C2×#102C2314yes—
153C2×#102C2314yes—
154C2×#102C2314yes—
155C2×#102C2314yes—
156C2×C22⋊C8—42no—
157C2×C22⋊C8C2314yes—
158#397—28no—
159#397—28no—
160#394—28no—
161#394—28no—
162#390—22no—
163#390—22no—
164#390C2314yes—
165#390C2314yes—
166#389—22no—
167#389—22no—
168#389C2314yes—
169#389C2314yes—
170#386—28no—
171#385—28no—
172#384—22no—
173#384C2314yes—
174#382—22no—
175#382C2314yes—
176#381—28no—
177#380—22no—
178#380—22no—
179#380C2314yes—
180#380C2314yes—
181C4×C22⋊C4D414yes—
182C4×C22⋊C4C2314yes—
183C2×#95—21no—
184C2×#95—21no—
185C2×#95—21no—
186C2×#95—21no—
187C2×#95—21no—
188C2×#95—21no—
189C2×#95D411yescharacteristic
190C2×#95D411yescharacteristic
191#340C2314yes—
192#340C2314yes—
193#340C2314yes—
194#340C2314yes—
195#340C2314yes—
196#340C2314yes—
197#340C2314yes—
198#340C2314yes—
199#336C2314yes—
200#336C2314yes—
201C25—21no—
202C25—21no—
203C25C2×D411yescharacteristic
204C22×D4—24no—
205C22×D4—24no—
206C22×D4—21no—
207C22×D4—21no—
208C22×D4—22no—
209C22×D4—22no—
210C22×D4—22no—
211C22×D4—22no—
212C22×D4—22no—
213C22×D4—22no—
214C22×D4—22no—
215C22×D4—22no—
216C22×D4—22no—
217C22×D4—22no—
218C22×D4—44no—
219C22×D4—44no—
220C22×D4—44no—
221C22×D4—44no—
222C22×D4—82no—
223C22×D4—82no—
224C22×D4#4114yes—
225C22×D4#4114yes—
226C22×D4C2412yes—
227C22×D4C2412yes—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—44no—
243C23×C4—44no—
244C23×C4—44no—
245C23×C4—44no—
246C23×C4—82no—
247C23×C4—82no—
248C23×C4C2×D412yes—
249C23×C4C2×D411yescharacteristic
250C23×C4C2×D411yescharacteristic
251C23×C4C2×D411yescharacteristic
252C23×C4C2×D411yescharacteristic
253C23×C4C2×D411yescharacteristic
254C23×C4C2412yes—
255C23×C4C2411yescharacteristic
256C2×D8—28no—
257C2×D8—28no—
258C2×D8—44no—
259C2×D8—416no—
260C22×C8—22no—
261C22×C8—22no—
262C22×C8—22no—
263C22×C8—22no—
264C22×C8—22no—
265C22×C8—22no—
266C22×C8—22no—
267C22×C8—22no—
268C22×C8—22no—
269C22×C8—22no—
270C22×C8—22no—
271C22×C8—22no—
272C22×C8—44no—
273C22×C8—44no—
274C22×C8—44no—
275C22×C8—416no—
276C22×C8C2412yes—
277C22×C8C2412yes—
278C22×C8C2412yes—
279C22×C8C2412yes—
280#123—432no—
281#121—28no—
282#121—28no—
283#121—44no—
284#121—44no—
285#121—48no—
286#121—48no—
287C4×D4—28no—
288C4×D4—28no—
289C4×D4—44no—
290C4×D4—44no—
291C4×D4—48no—
292C4×D4—48no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4—44no—
317C2×C4⋊C4—82no—
318C2×C4⋊C4—82no—
319C2×C4⋊C4C2412yes—
320C2×C4⋊C4C2412yes—
321C2×C4⋊C4C2412yes—
322C2×C4⋊C4C2412yes—
323C2×C4⋊C4C2412yes—
324C2×C4⋊C4C2412yes—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—44no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4—44no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4—44no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4—82no—
345C2×C22⋊C4—82no—
346C2×C22⋊C4—82no—
347C2×C22⋊C4C2×D414yes—
348C2×C22⋊C4C2×D414yes—
349C2×C42—22no—
350C2×C42—22no—
351C2×C42—22no—
352C2×C42—22no—
353C2×C42C2×D412yes—
354C2×C42C2×D412yes—
355C2×C42C2412yes—
356C2×C42C2412yes—
357#106—44no—
358C4⋊C8—44no—
359C4⋊C8—44no—
360#102—44no—
361#102—44no—
362#102—44no—
363#102—44no—
364#102—44no—
365#102—44no—
366C22⋊C8—44no—
367#95—24no—
368#95—24no—
369#95—24no—
370#95—24no—
371#95—24no—
372#95—24no—
373#95C2×D414yes—
374#95C2×D414yes—
375C24—22no—
376C24—22no—
377C24—22no—
378C24—22no—
379C24—22no—
380C24—22no—
381C24—24no—
382C24—24no—
383C24—22no—
384C24—22no—
385C24—42no—
386C24—42no—
387C24—42no—
388C24—42no—
389C24—42no—
390C24—42no—
391C24—42no—
392C24—42no—
393C24—42no—
394C24—42no—
395C24—42no—
396C24—42no—
397C24AGL(1,ℤ/8)14yes—
398C24C22×D412yes—
399C24C22×D411yescharacteristic
400C2×D4—28no—
401C2×D4—28no—
402C2×D4—24no—
403C2×D4—24no—
404C2×D4—28no—
405C2×D4—28no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—48no—
417C2×D4—48no—
418C2×D4—48no—
419C2×D4—48no—
420C2×D4—42no—
421C2×D4—42no—
422C2×D4—44no—
423C2×D4—44no—
424C2×D4—42no—
425C2×D4—42no—
426C2×D4—44no—
427C2×D4—44no—
428C2×D4—84no—
429C2×D4—84no—
430C2×D4—816no—
431C2×D4—816no—
432C2×D4C2×#4114yes—
433C2×D4C2×#4114yes—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—48no—
464C22×C4—48no—
465C22×C4—48no—
466C22×C4—44no—
467C22×C4—44no—
468C22×C4—44no—
469C22×C4—44no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—48no—
489C22×C4—84no—
490C22×C4—84no—
491C22×C4—816no—
492C22×C4—816no—
493C22×C4#13514yes—
494C22×C4C22×D412yes—
495C22×C4C22×D412yes—
496C22×C4C22×D412yes—
497C22×C4C22×D412yes—
498C22×C4C22×D412yes—
499C22×C4C22×D411yescharacteristic
500C22×C4C2×#4112yes—
501C22×C4C2×#4112yes—
502C22×C4H(5,𝔽2)12yes—
503C22×C4H(5,𝔽2)12yes—
504C22×C4H(5,𝔽2)12yes—
505C22×C42−1+412yes—
506C22×C4C2511yescharacteristic
507D8—416no—
508C2×C8—22no—
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8—22no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—416no—
521C2×C8—44no—
522C2×C8—44no—
523C2×C8—44no—
524C2×C8—44no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—48no—
538C4⋊C4—48no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—42no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4—42no—
545C4⋊C4—84no—
546C4⋊C4—84no—
547C22⋊C4—28no—
548C22⋊C4—28no—
549C22⋊C4—48no—
550C22⋊C4—48no—
551C22⋊C4—48no—
552C22⋊C4—48no—
553C22⋊C4—48no—
554C22⋊C4—48no—
555C22⋊C4—48no—
556C22⋊C4—84no—
557C22⋊C4—84no—
558C22⋊C4—84no—
559C42—24no—
560C42—24no—
561C42—22no—
562C42—22no—
563C42—22no—
564C42—22no—
565C23—22no—
566C23—22no—
567C23—22no—
568C23—28no—
569C23—28no—
570C23—28no—
571C23—22no—
572C23—22no—
573C23—22no—
574C23—24no—
575C23—24no—
576C23—44no—
577C23—44no—
578C23—44no—
579C23—44no—
580C23—42no—
581C23—42no—
582C23—48no—
583C23—48no—
584C23—42no—
585C23—42no—
586C23—48no—
587C23—48no—
588C23—48no—
589C23—48no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—84no—
599C23—84no—
600C23—84no—
601C23—84no—
602C23—84no—
603C23—84no—
604C23—84no—
605C23—84no—
606C23#53712yes—
607C23#54612yes—
608C23#54612yes—
609C23C2×#13512yes—
610C23C2×AGL(1,ℤ/8)14yes—
611C23C2×AGL(1,ℤ/8)12yes—
612C23#57612yes—
613C23#57712yes—
614C23C23×D411yescharacteristic
615D4—24no—
616D4—24no—
617D4—24no—
618D4—24no—
619D4—42no—
620D4—42no—
621D4—48no—
622D4—48no—
623D4—42no—
624D4—42no—
625D4—816no—
626D4—816no—
627C2×C4—22no—
628C2×C4—28no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—48no—
649C2×C4—42no—
650C2×C4—42no—
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—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—816no—
670C2×C4—816no—
671C2×C4—84no—
672C2×C4—84no—
673C2×C4—84no—
674C2×C4—84no—
675C2×C4—84no—
676C2×C4—84no—
677C2×C4#53712yes—
678C2×C4#53914yes—
679C2×C4#53914yes—
680C2×C4#54612yes—
681C2×C4#54612yes—
682C2×C4#55114yes—
683C2×C4#56014yes—
684C2×C4C2×#13514yes—
685C2×C4C22×#4111yescharacteristic
686C2×C4C22×#4111yescharacteristic
687C2×C4C2×H(5,𝔽2)11yescharacteristic
688C2×C4C2×H(5,𝔽2)11yescharacteristic
689C2×C4C2×H(5,𝔽2)11yescharacteristic
690C2×C4C2×2−1+411yescharacteristic
691C8—42no—
692C8—42no—
693C8—42no—
694C8—42no—
695C22—24no—
696C22—24no—
697C22—24no—
698C22—416no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—44no—
704C22—44no—
705C22—44no—
706C22—44no—
707C22—44no—
708C22—44no—
709C22—816no—
710C22—816no—
711C22—82no—
712C22—82no—
713C22—82no—
714C22—82no—
715C22—82no—
716C22—82no—
717C22—82no—
718C22—82no—
719C22#269314yes—
720C22#324714yes—
721C22#325714yes—
722C22#329714yes—
723C22#330314yes—
724C22#330614yes—
725C22#331814yes—
726C22C2×#53711yescharacteristic
727C22C2×#54611yescharacteristic
728C22C2×#54611yescharacteristic
729C22C22×#13511yescharacteristic
730C22C22×AGL(1,ℤ/8)11yescharacteristic
731C22C2×#57611yescharacteristic
732C22C2×#57711yescharacteristic
733C4—24no—
734C4—42no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—82no—
739C4—82no—
740C4—82no—
741C4—82no—
742C4—82no—
743C4—82no—
744C4#269314yes—
745C4C2×#53911yescharacteristic
746C4C2×#53911yescharacteristic
747C4C2×#55111yescharacteristic
748C4C2×#56011yescharacteristic
749C2—44no—
750C2—84no—
751C2—84no—
752C2#3155718yesdirect product factor
753C2C2×#269311yescharacteristic
754C2C2×#324711yescharacteristic
755C2C2×#325711yescharacteristic
756C2C2×#329711yescharacteristic
757C2C2×#330311yescharacteristic
758C2C2×#330611yescharacteristic
759C2C2×#331811yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#1999C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2420C2semidirect
2. C2×#2422C2semidirect
3. #31557C2direct (N × H)
4. C2×#2100C2semidirect
5. C2×#2101C2semidirect
6. C2×#2077C2semidirect
7. C2×#2065C2semidirect
8. C2×#2065C2semidirect
10. C2×#1893C2semidirect
11. C2×#1893C2semidirect
12. C2×#1879C2semidirect
13. C2×#1879C2semidirect
14. C2×#1850C2semidirect
15. C2×#1804C2semidirect
16. C2×#1802C2semidirect
35. #2422C22semidirect
37. #2420C22semidirect
54. #2101C22semidirect
55. #2100C22semidirect
56. #2077C22semidirect
57. #2065C22semidirect
58. #2065C22semidirect
60. #1893C22semidirect
61. #1893C22semidirect
62. #1879C22semidirect
63. #1879C22semidirect
64. #1850C22semidirect
65. #1804C22semidirect
66. #1802C22semidirect
752. C2#31557direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#24202
C2×#24222
#315572
C2×#21002
C2×#21012
C2×#20772
C2×#20652
C2×#19992
C2×#18932
C2×#18792
C2×#18502
C2×#18042
C2×#18022