Finite Group Databasebeta

← #220077

Subgroups — #220077

Order 512.

1223 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36122C211yesmaximal, characteristic
2#22797C211yesmaximal, characteristic, complemented
3#22648C211yesmaximal, characteristic, complemented
4C2×#1551C211yesmaximal, characteristic, complemented
5C2×#1548C211yesmaximal, characteristic, complemented
6#9707C211yesmaximal, characteristic, complemented
7#9707C211yesmaximal, characteristic, complemented
8#9141C211yesmaximal, characteristic, complemented
9#9136C211yesmaximal, characteristic, complemented
10#9134C211yesmaximal, characteristic, complemented
11#9127C211yesmaximal, characteristic, complemented
12#8587C211yesmaximal, characteristic, complemented
13#8344C211yesmaximal, characteristic, complemented
14#8342C211yesmaximal, characteristic, complemented
15#8232C211yesmaximal, characteristic, complemented
16C2×#548C412yes—
17C2×#532C2211yescharacteristic
18C22×C4⋊Q8C2211yescharacteristic
19C2×#435—21no—
20C2×#432C2211yescharacteristic
21C2×#431C2211yescharacteristic
22C2×#423C2211yescharacteristic
23C22×C4⋊C8C2211yescharacteristic
24#2858C2211yescharacteristic
25#2857C2211yescharacteristic
26#2856C2211yescharacteristic
27#2545C412yes—
28#2491—21no—
29#2491—21no—
30#2452—21no—
31#2452—21no—
32#2436C412yes—
33#2432C412yes—
34#2416—21no—
35#2416—21no—
36#2361—21no—
37#2361—21no—
38C4×C4⋊Q8C2211yescharacteristic
39C42×D4C2211yescharacteristic
40#1955—21no—
41#1940—21no—
42#1924—21no—
43#1923—21no—
44#1851—21no—
45#1850—21no—
46#1842C2211yescharacteristic
47#1842C2211yescharacteristic
48#1797C2211yescharacteristic
49#1797C2211yescharacteristic
50#1797C2211yescharacteristic
51#1797C2211yescharacteristic
52#1771—21no—
53#1767C2211yescharacteristic
54#1767C2211yescharacteristic
55#1551—24no—
56#1548—24no—
57C2×#333C2211yescharacteristic
58C2×#333C2211yescharacteristic
59C2×#333C2211yescharacteristic
60C2×#333C2211yescharacteristic
61C2×#333C2211yescharacteristic
62C2×#333C2211yescharacteristic
63C2×#333C2211yescharacteristic
64C2×#333C2211yescharacteristic
65C2×#331C2211yescharacteristic
66C2×#331C2211yescharacteristic
67C2×#331C2211yescharacteristic
68C2×#331C2211yescharacteristic
69#1296C2211yescharacteristic
70#1296C2211yescharacteristic
71#1296C2211yescharacteristic
72#1296C2211yescharacteristic
73C22×#41C2×C412yes—
74C23×Q8C2×C412yes—
75C22×M16—21no—
76C23×C8—21no—
77#548—48no—
78#532—22no—
79#532—22no—
80#532—41no—
81#532—41no—
82C2×C4⋊Q8—22no—
83C2×C4⋊Q8—22no—
84C2×C4⋊Q8—21no—
85C2×C4⋊Q8—21no—
86C2×C4⋊Q8—41no—
87C2×C4⋊Q8—41no—
88C2×C4⋊Q8C2×C412yes—
89C2×C4⋊Q8C2311yescharacteristic
90C2×C4⋊Q8C2311yescharacteristic
91C2×#127C2311yescharacteristic
92C2×#124—22no—
93C2×#124C2×C412yes—
94C2×#124C2×C412yes—
95C2×#124C2×C412yes—
96C2×C22⋊Q8—22no—
97C2×C22⋊Q8C2×C412yes—
98C2×#121—22no—
99C2×#121—21no—
100C2×#121—21no—
101C2×#121—21no—
102C2×#121—21no—
103C2×#121C2×C412yes—
104C2×C4×Q8C2×C412yes—
105C2×C4×D4—22no—
106C2×C4×D4—21no—
107C2×C4×D4—21no—
108C2×C4×D4C2×C411yescharacteristic
109C2×C4×D4D411yescharacteristic
110C2×C4×D4D411yescharacteristic
111C22×C4⋊C4—21no—
112C22×C4⋊C4—21no—
113C22×C42C2311yescharacteristic
114C22×C42C2311yescharacteristic
115#435—44no—
116#432—22no—
117#432—41no—
118#431—22no—
119#431—41no—
120#423—22no—
121#423—41no—
122C2×C4⋊C8—22no—
123C2×C4⋊C8—21no—
124C2×C4⋊C8—21no—
125C2×C4⋊C8—21no—
126C2×C4⋊C8—21no—
127C2×C4⋊C8—21no—
128C2×C4⋊C8—21no—
129C2×C4⋊C8—41no—
130C2×C4⋊C8C2311yescharacteristic
131C2×C4⋊C8C2311yescharacteristic
132C2×C4⋊C8C2311yescharacteristic
133C2×C4⋊C8C2311yescharacteristic
134C2×C4⋊C8C2311yescharacteristic
135C2×C4⋊C8C2311yescharacteristic
136C2×C4⋊C8C2311yescharacteristic
137C2×C4⋊C8C2311yescharacteristic
138C2×C22⋊C8—21no—
139C2×C22⋊C8—21no—
140C2×C22⋊C8—21no—
141C2×C22⋊C8—21no—
142C2×C22⋊C8—21no—
143C2×C22⋊C8—21no—
144C2×#97—21no—
145C2×#97—21no—
146C2×#97—21no—
147C2×C4×C8—21no—
148#396—22no—
149#396—22no—
150#394—22no—
151#394—22no—
152#393—22no—
153#393—22no—
154#391C2×C412yes—
155#391C2×C412yes—
156#390—21no—
157#390—21no—
158#390—21no—
159#390—21no—
160#390—21no—
161#390—21no—
162#390C2×C412yes—
163#389—21no—
164#389—21no—
165#389—21no—
166#389—21no—
167#388—22no—
168#388—22no—
169#386—22no—
170#386—22no—
171#385—22no—
172#385—22no—
173#384C2311yescharacteristic
174#380—21no—
175#380—21no—
176C4×C4⋊C4—21no—
177C4×C4⋊C4—21no—
178C4×C4⋊C4C2×C411yescharacteristic
179C4×C4⋊C4D411yescharacteristic
180C4×C4⋊C4D411yescharacteristic
181C4×C22⋊C4C2×C411yescharacteristic
182C4×C22⋊C4C2×C411yescharacteristic
183C4×C22⋊C4D411yescharacteristic
184C4×C22⋊C4D411yescharacteristic
185C4×C22⋊C4D411yescharacteristic
186C4×C22⋊C4D411yescharacteristic
187C43C2311yescharacteristic
188#336—21no—
189#336—21no—
190#336—21no—
191#336—21no—
192#336—21no—
193#336—21no—
194#333—22no—
195#333—22no—
196#333—22no—
197#333—22no—
198#333—22no—
199#333—41no—
200#333—41no—
201#333D414yescomplemented
202#331—22no—
203#331—22no—
204#331—41no—
205#331—41no—
206C2×#41—24no—
207C2×#41—42no—
208C2×#41—44no—
209C2×#41—82no—
210C22×Q8—22no—
211C22×Q8—24no—
212C22×Q8—42no—
213C22×Q8—44no—
214C22×Q8—82no—
215C22×Q8C22×C412yes—
216C22×Q8C22×C412yes—
217C22×D4—22no—
218C22×D4—22no—
219C22×D4—21no—
220C22×D4—21no—
221C22×D4C22⋊C411yescharacteristic
222C22×D4C22×C412yes—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4C22×C411yescharacteristic
226C23×C4C22×C411yescharacteristic
227C23×C4C2×D411yescharacteristic
228C23×C4C2×D411yescharacteristic
229C23×C4C2×D411yescharacteristic
230C23×C4C2×D411yescharacteristic
231C2×M16—42no—
232C2×M16—42no—
233C2×M16—81no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—42no—
243C22×C8—42no—
244C22×C8—81no—
245C4⋊Q8—24no—
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8—21no—
252C4⋊Q8—42no—
253C4⋊Q8—42no—
254C4⋊Q8—42no—
255C4⋊Q8—42no—
256C4⋊Q8—42no—
257C4⋊Q8C2×D412yes—
258C4⋊Q8#4112yes—
259#127—21no—
260#127—21no—
261#127—21no—
262#127—21no—
263#124—24no—
264#124—42no—
265#124—44no—
266#124—48no—
267#124—82no—
268C22⋊Q8—48no—
269C22⋊Q8—44no—
270#121—42no—
271#121—42no—
272#121—42no—
273#121—42no—
274#121—42no—
275#121—42no—
276#121—48no—
277#121—42no—
278#121—42no—
279#121—44no—
280C4×Q8—44no—
281C4×D4—22no—
282C4×D4—22no—
283C4×D4—24no—
284C4×D4—42no—
285C4×D4—42no—
286C4×D4—42no—
287C4×D4—42no—
288C4×D4—41no—
289C4×D4—41no—
290C4×D4—48no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4C22⋊C411yescharacteristic
306C2×C4⋊C4C22⋊C411yescharacteristic
307C2×C4⋊C4C22⋊C411yescharacteristic
308C2×C4⋊C4C22×C412yes—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4C22⋊C411yescharacteristic
320C2×C22⋊C4C22⋊C411yescharacteristic
321C2×C22⋊C4C22⋊C411yescharacteristic
322C2×C22⋊C4C22⋊C411yescharacteristic
323C2×C22⋊C4C22⋊C411yescharacteristic
324C2×C22⋊C4C22⋊C411yescharacteristic
325C2×C42—21no—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—22no—
334C2×C42C22×C411yescharacteristic
335C2×C42C22×C411yescharacteristic
336C2×C42C22×C411yescharacteristic
337C2×C42C22×C411yescharacteristic
338C2×C42C2×D411yescharacteristic
339C2×C42C2×D411yescharacteristic
340C2×C42C2×D411yescharacteristic
341C2×C42C2×D411yescharacteristic
342C2×C42C2×D411yescharacteristic
343C2×C42C2×D411yescharacteristic
344C2×C42C2×D411yescharacteristic
345C2×C42C2×D411yescharacteristic
346C2×C42C2411yescharacteristic
347C4⋊C8—21no—
348C4⋊C8—21no—
349C4⋊C8—21no—
350C4⋊C8—21no—
351C4⋊C8—21no—
352C4⋊C8—21no—
353C4⋊C8—21no—
354C4⋊C8—21no—
355C4⋊C8—21no—
356C4⋊C8—21no—
357C4⋊C8—21no—
358C4⋊C8—21no—
359C4⋊C8—21no—
360C4⋊C8—21no—
361C4⋊C8—42no—
362C4⋊C8—42no—
363C4⋊C8—42no—
364C4⋊C8—42no—
365C4⋊C8—81no—
366C4⋊C8—81no—
367C4⋊C8C2×D412yes—
368C4⋊C8C2×D412yes—
369C22⋊C8—42no—
370C22⋊C8—42no—
371C22⋊C8—42no—
372C22⋊C8—42no—
373C22⋊C8—81no—
374C22⋊C8—81no—
375#97—42no—
376#97—42no—
377#97—42no—
378C4×C8—42no—
379#95—22no—
380#95—22no—
381#95—22no—
382#95—22no—
383#95C22⋊C411yescharacteristic
384#95C22⋊C411yescharacteristic
385#95C22⋊C411yescharacteristic
386#95C22⋊C411yescharacteristic
387#95C22⋊C411yescharacteristic
388#95C22⋊C411yescharacteristic
389C24—22no—
390C24C2×C22⋊C411yescharacteristic
391C24C2×C22⋊C411yescharacteristic
392#41—88no—
393#41—88no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—44no—
398C2×Q8—42no—
399C2×Q8—42no—
400C2×Q8—42no—
401C2×Q8—42no—
402C2×Q8—44no—
403C2×Q8—82no—
404C2×Q8—88no—
405C2×Q8—88no—
406C2×Q8C4×D414yes—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—41no—
412C2×D4—44no—
413C2×D4—42no—
414C2×D4—42no—
415C2×D4—44no—
416C2×D4—44no—
417C2×D4—44no—
418C2×D4—44no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—82no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—44no—
466C22×C4—44no—
467C22×C4—44no—
468C22×C4—44no—
469C22×C4—82no—
470C22×C4—82no—
471C22×C4C2×C22⋊C411yescharacteristic
472C22×C4C2×C22⋊C411yescharacteristic
473C22×C4C2×C22⋊C411yescharacteristic
474C22×C4C2×C22⋊C411yescharacteristic
475C22×C4C2×C22⋊C411yescharacteristic
476C22×C4C2×C22⋊C411yescharacteristic
477C22×C4C2×C22⋊C411yescharacteristic
478C22×C4C2×C22⋊C411yescharacteristic
479C22×C4C2×C22⋊C411yescharacteristic
480C22×C4C2×C22⋊C411yescharacteristic
481C22×C4AGL(1,ℤ/8)12yes—
482C22×C4#13712yes—
483C22×C4C23×C411yescharacteristic
484C22×C4C22×D411yescharacteristic
485C22×C4C22×D411yescharacteristic
486M16—84no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—41no—
490C2×C8—41no—
491C2×C8—41no—
492C2×C8—41no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—41no—
499C2×C8—41no—
500C2×C8—41no—
501C2×C8—41no—
502C2×C8—41no—
503C2×C8—41no—
504C2×C8—41no—
505C2×C8—41no—
506C2×C8—41no—
507C2×C8—41no—
508C2×C8—41no—
509C2×C8—41no—
510C2×C8—41no—
511C2×C8—84no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—41no—
519C4⋊C4—44no—
520C4⋊C4—44no—
521C4⋊C4—42no—
522C4⋊C4—44no—
523C4⋊C4—44no—
524C4⋊C4—41no—
525C4⋊C4—41no—
526C4⋊C4—41no—
527C4⋊C4—41no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—41no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—41no—
536C22⋊C4—41no—
537C22⋊C4—44no—
538C22⋊C4—44no—
539C22⋊C4—44no—
540C22⋊C4—44no—
541C22⋊C4—44no—
542C22⋊C4—44no—
543C22⋊C4—44no—
544C22⋊C4—44no—
545C22⋊C4—82no—
546C22⋊C4—82no—
547C22⋊C4#10014yes—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—21no—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—21no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—22no—
569C42—41no—
570C42—44no—
571C42C22×D411yescharacteristic
572C42C2×#4111yescharacteristic
573C42H(5,𝔽2)11yescharacteristic
574C42H(5,𝔽2)11yescharacteristic
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23C2×#10012yes—
595C23#41712yes—
596C23C22×C22⋊C411yescharacteristic
597Q8—44no—
598Q8—44no—
599Q8—88no—
600Q8—82no—
601Q8—82no—
602D4—44no—
603D4—82no—
604D4—82no—
605D4—88no—
606D4—88no—
607D4—81no—
608D4—81no—
609D4—81no—
610D4—81no—
611D4—81no—
612D4—81no—
613D4—81no—
614D4—81no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—24no—
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—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—88no—
674C2×C4—88no—
675C2×C4C2×#10012yes—
676C2×C4C2×#10012yes—
677C2×C4#41712yes—
678C2×C4C2×C4×D411yescharacteristic
679C2×C4#51811yescharacteristic
680C2×C4D4211yescharacteristic
681C2×C4D4211yescharacteristic
682C2×C4#54611yescharacteristic
683C2×C4#54611yescharacteristic
684C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
685C2×C4C2×#13711yescharacteristic
686C2×C4#57511yescharacteristic
687C2×C4#57511yescharacteristic
688C2×C4#57711yescharacteristic
689C2×C4#57711yescharacteristic
690C2×C4#57811yescharacteristic
691C2×C4#57811yescharacteristic
692C8—42no—
693C8—42no—
694C8—81no—
695C8—81no—
696C8—81no—
697C8—81no—
698C8—81no—
699C8—81no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—82no—
715C22—82no—
716C22—82no—
717C22—82no—
718C22—82no—
719C22—82no—
720C22—82no—
721C22D4×C22⋊C411yescharacteristic
722C22C22×#10011yescharacteristic
723C22#288811yescharacteristic
724C22C2×#41711yescharacteristic
725C22#289611yescharacteristic
726C22#289811yescharacteristic
727C22#289811yescharacteristic
728C4—22no—
729C4—21no—
730C4—21no—
731C4—22no—
732C4—22no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—41no—
737C4—44no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—82no—
742C4—82no—
743C4#326511yescharacteristic
744C4#326911yescharacteristic
745C4#327011yescharacteristic
746C4#327111yescharacteristic
747C4#330811yescharacteristic
748C4#331311yescharacteristic
749C4#331611yescharacteristic
750C4#332111yescharacteristic
751C2—42no—
752C2—42no—
753C2—162no—
754C2#1775011yescharacteristic
755C2#1776411yescharacteristic
756C2#1776811yescharacteristic
757C2#1777911yescharacteristic
758C2D4×#10011yescharacteristic
759C2#2242111yescharacteristic
760C2#2242611yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
prime radical#36122C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #22797C2semidirect
3. #22648C2semidirect
4. C2×#1551C2semidirect
5. C2×#1548C2semidirect
6. #9707C2semidirect
7. #9707C2semidirect
8. #9141C2semidirect
9. #9136C2semidirect
10. #9134C2semidirect
11. #9127C2semidirect
12. #8587C2semidirect
13. #8344C2semidirect
14. #8342C2semidirect
15. #8232C2semidirect
201. #333D4semidirect

Maximal subgroups

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

subgroupindex
#361222
#227972
#226482
C2×#15512
C2×#15482
#97072
#91412
#91362
#91342
#91272
#85872
#83442
#83422
#82322