Finite Group Databasebeta

← #6452996

Subgroups — #6452996

Order 512.

4398 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#547C211yesmaximal, characteristic
2C2×#3094C211yesmaximal, characteristic, complemented
3C22×#428C211yesmaximal, characteristic, complemented
4#34809C211yesmaximal, characteristic, complemented
5#24100C218yesmaximal, complemented
6#24089C214yesmaximal, complemented
7#24088C214yesmaximal, complemented
8#23552C212yesmaximal, complemented
9#23480C212yesmaximal, complemented
10#20973C211yesmaximal, characteristic, complemented
11#20898C211yesmaximal, characteristic, complemented
12#20873C212yesmaximal, complemented
13#20844C212yesmaximal, complemented
14#20700C211yesmaximal, characteristic, complemented
15C23×#41—21no—
16C23×M16C2211yescharacteristic
17C2×#547—28no—
18C2×#547—22no—
19C2×#547—22no—
20C2×#547—28no—
21C2×#547C2214yes—
22C2×#547C2214yes—
23C22×C4⋊Q8C2211yescharacteristic
24C22×#123—21no—
25C22×#123—21no—
26C22×C22⋊Q8—21no—
27C22×#121C2211yescharacteristic
28C22×#121C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic
31C22×#117C2211yescharacteristic
32C23×C4⋊C4C2211yescharacteristic
33C23×C4⋊C4C2211yescharacteristic
34#3094—28no—
35C2×#481C2212yescomplemented
36C2×#482C2214yescomplemented
37C2×#480C2212yescomplemented
38C2×#428—28no—
39C2×#428C2212yes—
40C2×#428C2212yes—
41C2×#428C2212yes—
42C2×#428C2214yescomplemented
43C22×#107C2212yescomplemented
44C22×#106C2212yescomplemented
45C2×#418C2212yes—
46C2×#418C2212yes—
47C2×#407C2211yescharacteristic
48C2×#407C2212yes—
49#2487C2212yescomplemented
50#2486C2212yescomplemented
51#2485C2214yescomplemented
52#2484—21no—
53#2483—21no—
54#2482—21no—
55#2405—21no—
56#2395—22no—
57C4×#123—22no—
58#2296C2212yes—
59#2280C2212yes—
60#2280C2211yescharacteristic
61#2058C2218yescomplemented
62#2057C2218yescomplemented
63#2034C2218yescomplemented
64#2033C2218yescomplemented
65#1895C2214yescomplemented
66#1893C2214yescomplemented
67#1870C2214yescomplemented
68#1869C2214yescomplemented
69#1864C2218yescomplemented
70#1862C2218yescomplemented
71#1853C2218yescomplemented
72#1852C2218yescomplemented
73#1824C2214yescomplemented
74#1823C2214yescomplemented
75#1736C2212yes—
76#1736C2212yes—
77#1736C2212yes—
78#1728C2212yes—
79C22×#41—216no—
80C22×#41—24no—
81C22×#41—24no—
82C22×#41—416no—
83C23×Q8—21no—
84C23×D4—21no—
85C23×D4—21no—
86C23×D4D411yescharacteristic
87C23×D4C2311yescharacteristic
88C24×C4—21no—
89C24×C4—21no—
90C24×C4—21no—
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C22×M16—24no—
94C22×M16—28no—
95C22×M16C2312yes—
96C22×M16C2312yes—
97C22×M16C2312yes—
98C23×C8C2312yes—
99#547—232no—
100#547—232no—
101#547—216no—
102#547—216no—
103#547—216no—
104#547—216no—
105C2×C4⋊Q8—24no—
106C2×C4⋊Q8—24no—
107C2×C4⋊Q8—22no—
108C2×C4⋊Q8C2314yes—
109C2×#123—216no—
110C2×#123—216no—
111C2×#123—22no—
112C2×#123—24no—
113C2×#123—24no—
114C2×#123—24no—
115C2×#123—24no—
116C2×C22⋊Q8—216no—
117C2×C22⋊Q8—24no—
118C2×C22⋊Q8—24no—
119C2×#121—24no—
120C2×#121—24no—
121C2×#121—22no—
122C2×#121—21no—
123C2×#121—21no—
124C2×#121—24no—
125C2×#121D418yes—
126C2×#121C2314yes—
127C2×#121C2312yes—
128C2×#121C2312yes—
129C2×C4×D4—24no—
130C2×C4×D4—24no—
131C2×C4×D4—24no—
132C2×C4×D4—24no—
133C2×C4×D4—22no—
134C2×C4×D4D412yes—
135C2×C4×D4D412yes—
136C2×C4×D4C2314yes—
137C2×C4×D4C2312yes—
138C2×C4×D4C2312yes—
139C2×#117—21no—
140C2×#117—21no—
141C2×#117—24no—
142C2×#117—24no—
143C2×#117C2312yes—
144C2×#117C2312yes—
145C2×#117C2312yes—
146C22×C4⋊C4—21no—
147C22×C4⋊C4—21no—
148C22×C4⋊C4—22no—
149C22×C4⋊C4—24no—
150C22×C4⋊C4—21no—
151C22×C4⋊C4—21no—
152C22×C4⋊C4—21no—
153C22×C4⋊C4—24no—
154C22×C4⋊C4—24no—
155C22×C4⋊C4D411yescharacteristic
156C22×C4⋊C4D418yes—
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2314yes—
160C22×C4⋊C4C2312yes—
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C22⋊C4—21no—
166C22×C22⋊C4—21no—
167C22×C22⋊C4—21no—
168C22×C22⋊C4—21no—
169C22×C22⋊C4D411yescharacteristic
170C22×C22⋊C4D411yescharacteristic
171C22×C42—21no—
172C22×C42C2311yescharacteristic
173#482—216no—
174#481—28no—
175#480—28no—
176#428—28no—
177#428—28no—
178#428—28no—
179#428—216no—
180C2×#107—28no—
181C2×#107C2314yes—
182C2×#107C2314yes—
183C2×#107C2314yes—
184C2×#106—28no—
185C2×#106C2314yes—
186C2×#106C2314yes—
187C2×#106C2314yes—
188#418—28no—
189#418—28no—
190C2×#102C2314yes—
191C2×#102C2314yes—
192C2×#102C2318yes—
193#407—24no—
194#407—28no—
195C2×C22⋊C8C2312yes—
196C2×C22⋊C8C2312yes—
197C2×C22⋊C8C2318yes—
198#400—22no—
199#399—22no—
200#398—22no—
201#397—22no—
202#397—24no—
203#394—24no—
204#389C2314yes—
205#389C2314yes—
206#388—24no—
207#387—24no—
208#386—22no—
209#385—22no—
210#385—22no—
211#385—22no—
212#381—21no—
213#381—22no—
214#381—22no—
215#380C2312yes—
216#380C2312yes—
217#380C2314yes—
218#380C2314yes—
219#379—22no—
220#379—21no—
221C4×C4⋊C4—24no—
222C4×C22⋊C4—21no—
223C4×C22⋊C4—24no—
224C4×C22⋊C4—21no—
225#340C2318yes—
226#340C2318yes—
227#340C2318yes—
228#336C2318yes—
229C25—21no—
230C25C2×D411yescharacteristic
231C25C2×D411yescharacteristic
232C2×#41—232no—
233C2×#41—232no—
234C2×#41—4128no—
235C2×#41—416no—
236C2×#41—416no—
237C2×#41—416no—
238C2×#41—416no—
239C22×Q8—28no—
240C22×Q8—24no—
241C22×Q8—48no—
242C22×D4—24no—
243C22×D4—28no—
244C22×D4—28no—
245C22×D4—28no—
246C22×D4—24no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—21no—
250C22×D4—22no—
251C22×D4—24no—
252C22×D4—24no—
253C22×D4—48no—
254C22×D4—48no—
255C22×D4C2×D412yes—
256C22×D4C2×D414yes—
257C22×D4C2×D412yes—
258C22×D4C2412yes—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—28no—
262C23×C4—28no—
263C23×C4—28no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—24no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—48no—
278C23×C4—48no—
279C23×C4—48no—
280C23×C4C2×D411yescharacteristic
281C23×C4C2×D412yes—
282C23×C4C2×D411yescharacteristic
283C23×C4C2×D411yescharacteristic
284C23×C4C2×D411yescharacteristic
285C23×C4C2×D411yescharacteristic
286C23×C4C2×D414yes—
287C23×C4C2×D414yes—
288C23×C4C2×D411yescharacteristic
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
291C23×C4C2411yescharacteristic
292C23×C4C2411yescharacteristic
293C2×M16—232no—
294C2×M16—24no—
295C2×M16—24no—
296C2×M16—24no—
297C2×M16—24no—
298C2×M16—24no—
299C2×M16—24no—
300C2×M16—28no—
301C2×M16#4118yescomplemented
302C22×C8—24no—
303C22×C8—28no—
304C22×C8C2414yes—
305C22×C8C2414yes—
306C4⋊Q8—216no—
307C4⋊Q8—28no—
308C4⋊Q8—28no—
309#123—232no—
310#123—232no—
311#123—232no—
312#123—232no—
313#123—48no—
314C22⋊Q8—232no—
315C22⋊Q8—232no—
316#121—216no—
317#121—28no—
318#121—28no—
319#121—28no—
320#121—24no—
321#121—24no—
322#121—28no—
323#121C2×D418yes—
324#121C2×D418yes—
325C4×D4—216no—
326C4×D4—28no—
327C4×D4—28no—
328C4×D4—28no—
329C4×D4—24no—
330C4×D4—24no—
331C4×D4—24no—
332C4×D4—24no—
333C4×D4—28no—
334#117—24no—
335#117—24no—
336#117—24no—
337#117—24no—
338#117—24no—
339#117—24no—
340#117—44no—
341#117—44no—
342C2×C4⋊C4—28no—
343C2×C4⋊C4—216no—
344C2×C4⋊C4—28no—
345C2×C4⋊C4—28no—
346C2×C4⋊C4—28no—
347C2×C4⋊C4—28no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—28no—
362C2×C4⋊C4—28no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4C2×D412yes—
372C2×C4⋊C4C2×D412yes—
373C2×C4⋊C4C2×D414yes—
374C2×C4⋊C4C2×D414yes—
375C2×C4⋊C4C2×D414yes—
376C2×C4⋊C4C2×D418yes—
377C2×C4⋊C4C2×D418yes—
378C2×C4⋊C4C2412yes—
379C2×C4⋊C4C2412yes—
380C2×C4⋊C4C2414yes—
381C2×C4⋊C4C2412yes—
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—28no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—28no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—44no—
401C2×C22⋊C4C2×D412yes—
402C2×C22⋊C4C2×D412yes—
403C2×C22⋊C4C2×D412yes—
404C2×C22⋊C4C2×D412yes—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—44no—
411C2×C42C2×D412yes—
412C2×C42C2412yes—
413#107—28no—
414#107—28no—
415#107—28no—
416#106—28no—
417#106—28no—
418#106—28no—
419#102—28no—
420#102—28no—
421#102—216no—
422C22⋊C8—24no—
423C22⋊C8—24no—
424C22⋊C8—216no—
425#95—24no—
426#95—24no—
427#95—22no—
428#95—22no—
429#95—24no—
430#95—24no—
431C24—22no—
432C24—24no—
433C24—24no—
434C24—24no—
435C24—24no—
436C24—24no—
437C24—22no—
438C24—42no—
439C24—42no—
440C24—44no—
441C24—44no—
442C24—44no—
443C24#12014yes—
444C24C22×D411yescharacteristic
445C24C22×D412yes—
446C24C22×D411yescharacteristic
447C24C22×D411yescharacteristic
448#41—4128no—
449#41—4128no—
450C2×Q8—216no—
451C2×Q8—432no—
452C2×Q8—48no—
453C2×Q8—48no—
454C2×D4—232no—
455C2×D4—24no—
456C2×D4—24no—
457C2×D4—24no—
458C2×D4—24no—
459C2×D4—216no—
460C2×D4—28no—
461C2×D4—28no—
462C2×D4—24no—
463C2×D4—216no—
464C2×D4—24no—
465C2×D4—22no—
466C2×D4—24no—
467C2×D4—24no—
468C2×D4—432no—
469C2×D4—432no—
470C2×D4—48no—
471C2×D4—48no—
472C2×D4—48no—
473C2×D4—48no—
474C2×D4—44no—
475C2×D4—44no—
476C2×D4—44no—
477C2×D4AGL(1,ℤ/8)18yes—
478C2×D4C22×D414yes—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—28no—
482C22×C4—28no—
483C22×C4—216no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—216no—
492C22×C4—216no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—28no—
499C22×C4—28no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—28no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—42no—
514C22×C4—432no—
515C22×C4—48no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4—44no—
519C22×C4—432no—
520C22×C4—432no—
521C22×C4—48no—
522C22×C4—48no—
523C22×C4—48no—
524C22×C4—48no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—48no—
528C22×C4—48no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—44no—
532C22×C4—82no—
533C22×C4#12014yes—
534C22×C4#12014yes—
535C22×C4#12014yes—
536C22×C4C22×D412yes—
537C22×C4C22×D412yes—
538C22×C4C22×D411yescharacteristic
539C22×C4C22×D411yescharacteristic
540C22×C4C22×D412yes—
541C22×C4C22×D412yes—
542C22×C4C22×D412yes—
543C22×C4C22×D412yes—
544C22×C4C22×D412yes—
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D412yes—
547C22×C4C22×D412yes—
548C22×C4C2×#4114yes—
549C22×C42−1+414yes—
550C22×C4C2511yescharacteristic
551M16—216no—
552M16—216no—
553M16—48no—
554C2×C8—216no—
555C2×C8—24no—
556C2×C8—24no—
557C2×C8—24no—
558C2×C8—24no—
559C2×C8—24no—
560C2×C8C2×#4118yescomplemented
561C4⋊C4—216no—
562C4⋊C4—216no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—28no—
567C4⋊C4—28no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—48no—
582C4⋊C4—84no—
583C4⋊C4C22×D414yes—
584C4⋊C4C22×D414yes—
585C4⋊C4C22×D414yes—
586C22⋊C4—216no—
587C22⋊C4—216no—
588C22⋊C4—24no—
589C22⋊C4—24no—
590C22⋊C4—28no—
591C22⋊C4—28no—
592C22⋊C4—24no—
593C22⋊C4—24no—
594C22⋊C4—44no—
595C22⋊C4—44no—
596C22⋊C4—44no—
597C22⋊C4—44no—
598C22⋊C4—48no—
599C22⋊C4—82no—
600C22⋊C4—84no—
601C42—24no—
602C42—22no—
603C42—22no—
604C42—44no—
605C42—44no—
606C42—44no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—28no—
612C23—24no—
613C23—22no—
614C23—28no—
615C23—22no—
616C23—24no—
617C23—22no—
618C23—28no—
619C23—22no—
620C23—22no—
621C23—24no—
622C23—44no—
623C23—416no—
624C23—416no—
625C23—44no—
626C23—48no—
627C23—48no—
628C23—44no—
629C23—44no—
630C23—48no—
631C23—44no—
632C23—44no—
633C23—816no—
634C23C2×#12012yes—
635C23C2×#12012yes—
636C23C2×#12012yes—
637C23#54714yes—
638C23C2×AGL(1,ℤ/8)14yes—
639C23C2×AGL(1,ℤ/8)14yes—
640C23C23×D411yescharacteristic
641Q8—432no—
642D4—216no—
643D4—216no—
644D4—28no—
645D4—416no—
646D4—432no—
647D4—416no—
648D4—48no—
649D4—42no—
650D4—42no—
651C2×C4—28no—
652C2×C4—28no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—28no—
658C2×C4—28no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—432no—
673C2×C4—44no—
674C2×C4—48no—
675C2×C4—48no—
676C2×C4—48no—
677C2×C4—416no—
678C2×C4—432no—
679C2×C4—44no—
680C2×C4—416no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—48no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—84no—
696C2×C4—84no—
697C2×C4C2×#12012yes—
698C2×C4C2×#12012yes—
699C2×C4C2×#12012yes—
700C2×C4#52514yes—
701C2×C4#53614yes—
702C2×C4#54714yes—
703C2×C4#54718yes—
704C2×C4C2×AGL(1,ℤ/8)14yes—
705C2×C4C23×D411yescharacteristic
706C2×C4C23×D411yescharacteristic
707C2×C4C22×#4112yes—
708C2×C4C2×2−1+412yes—
709C8—28no—
710C8—44no—
711C22—28no—
712C22—28no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—28no—
718C22—22no—
719C22—22no—
720C22—24no—
721C22—22no—
722C22—416no—
723C22—416no—
724C22—44no—
725C22—44no—
726C22—42no—
727C22—42no—
728C22—44no—
729C22—44no—
730C22—44no—
731C22—816no—
732C22—88no—
733C22#240614yes—
734C22#300314yes—
735C22C22×#12011yescharacteristic
736C22C2×#54712yes—
737C22C22×AGL(1,ℤ/8)12yes—
738C22#358612yes—
739C4—22no—
740C4—22no—
741C4—24no—
742C4—42no—
743C4—44no—
744C4—44no—
745C4—44no—
746C4—42no—
747C4—84no—
748C4—82no—
749C4—82no—
750C4#240614yes—
751C4C2×#52511yescharacteristic
752C4C2×#53611yescharacteristic
753C4C2×#54712yes—
754C2—24no—
755C2—24no—
756C2—44no—
757C2—42no—
758C2—84no—
759C2C2×#240611yescharacteristic
760C2C2×#300311yescharacteristic
761C2#6036811yescharacteristic
762C2#6125214yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#547C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3094C2semidirect
3. C22×#428C2semidirect
4. #34809C2semidirect
5. #24100C2semidirect
6. #24089C2semidirect
7. #24088C2semidirect
8. #23552C2semidirect
9. #23480C2semidirect
10. #20973C2semidirect
11. #20898C2semidirect
12. #20873C2semidirect
13. #20844C2semidirect
14. #20700C2semidirect
35. C2×#481C22semidirect
36. C2×#482C22semidirect
37. C2×#480C22semidirect
42. C2×#428C22semidirect
43. C22×#107C22semidirect
44. C22×#106C22semidirect
49. #2487C22semidirect
50. #2486C22semidirect
51. #2485C22semidirect
61. #2058C22semidirect
62. #2057C22semidirect
63. #2034C22semidirect
64. #2033C22semidirect
65. #1895C22semidirect
66. #1893C22semidirect
67. #1870C22semidirect
68. #1869C22semidirect
69. #1864C22semidirect
70. #1862C22semidirect
71. #1853C22semidirect
72. #1852C22semidirect
73. #1824C22semidirect
74. #1823C22semidirect
301. C2×M16#41semidirect
560. C2×C8C2×#41semidirect

Maximal subgroups

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

subgroupindex
C22×#5472
C2×#30942
C22×#4282
#348092
#241002
#240892
#240882
#235522
#234802
#209732
#208982
#208732
#208442
#207002