Finite Group Databasebeta

← #719970

Subgroups — #719970

Order 512.

3312 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2551C211yesmaximal, characteristic, complemented
2C2×#2439C212yesmaximal, complemented
3C2×#2440C212yesmaximal, complemented
4C2×#2352C211yesmaximal, characteristic
5#16984C212yesmaximal, complemented
6#16511C212yesmaximal, complemented
7#15856C214yesmaximal, complemented
8#15325C214yesmaximal
9#15223C212yesmaximal, complemented
10#15178C212yesmaximal, complemented
11#15135C212yesmaximal, complemented
12#14969C212yesmaximal, complemented
13#14354C211yesmaximal, characteristic, complemented
14#13954C211yesmaximal, characteristic, complemented
15#13906C211yesmaximal, characteristic
16#13847C211yesmaximal, characteristic
17#13783C211yesmaximal, characteristic, complemented
18C22×C4⋊Q8C2212yes—
19C22×C4⋊Q8C2212yes—
20C22×C22⋊Q8C2214yes—
21C22×C4×D4C2211yescharacteristic
22C22×#117C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24#2551—28no—
25#2440—216no—
26#2439—216no—
27C2×#399C2214yes—
28C2×#398C2214yes—
29C2×#396C2214yes—
30C2×#395C2214yes—
31C2×#395C2214yes—
32C2×#393C2214yes—
33#2352—28no—
34C2×#391C2214yes—
35C2×#390C2212yes—
36C2×#389C2212yes—
37C2×#389C2212yes—
38C2×#389C2212yes—
39C2×#389C2212yes—
40C2×#389C2212yes—
41C2×#388C2212yes—
42C2×#387C2212yes—
43C2×#387C2214yes—
44C2×#386C2212yes—
45C2×#385C2214yes—
46C2×#384C2212yes—
47C2×#384C2211yescharacteristic
48C2×#382C2211yescharacteristic
49C2×#382C2212yes—
50C2×#380C2211yescharacteristic
51C2×#380C2212yes—
52C2×#380C2211yescharacteristic
53C2×#380C2212yes—
54C2×C4×C4⋊C4C2211yescharacteristic
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C4⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4C2212yes—
58C2×C4×C22⋊C4C2212yes—
59C2×C4×C22⋊C4C2212yes—
60C2×#376C2211yescharacteristic
61#1445C2212yes—
62#1445C2214yes—
63#1445C2214yes—
64#1445C2214yes—
65#1444C2212yes—
66#1444C2212yes—
67#1444C2214yes—
68#1444C2214yes—
69#1444C2212yes—
70#1444C2212yes—
71#1439C2211yescharacteristic
72#1439C2211yescharacteristic
73#1439C2211yescharacteristic
74#1439C2211yescharacteristic
75#1439C2214yes—
76#1439C2212yes—
77#1439C2214yes—
78#1439C2212yes—
79#1439C2214yes—
80#1438C2212yes—
81#1436C2214yes—
82C4⋊#95C2212yes—
83C4⋊#95C2212yes—
84C4⋊#95C2212yes—
85C4⋊#95C2214yes—
86#1434C2212yes—
87C23×Q8C2314yes—
88C23×D4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2312yes—
92C2×C4⋊Q8—28no—
93C2×C4⋊Q8—28no—
94C2×C4⋊Q8—28no—
95C2×C4⋊Q8—28no—
96C2×C4⋊Q8—48no—
97C2×C22⋊Q8—216no—
98C2×C22⋊Q8—48no—
99C2×C22⋊Q8—48no—
100C2×C4×D4—24no—
101C2×C4×D4—24no—
102C2×C4×D4Q818yescomplemented
103C2×#117—24no—
104C2×#117—28no—
105C22×C4⋊C4—24no—
106C22×C4⋊C4—28no—
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2314yes—
109C22×C4⋊C4C2311yescharacteristic
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2314yes—
115C22×C4⋊C4C2314yes—
116C22×C4⋊C4C2314yes—
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2311yescharacteristic
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2311yescharacteristic
134C22×C22⋊C4C2311yescharacteristic
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2312yes—
137C22×C42C2312yes—
138C22×C42C2312yes—
139C22×C42C2312yes—
140C22×C42C2312yes—
141C22×C42C2312yes—
142C22×C42C2311yescharacteristic
143#399—48no—
144#398—216no—
145#396—216no—
146#395—216no—
147#395—216no—
148#393—216no—
149#391—216no—
150#390—44no—
151#389—28no—
152#389—28no—
153#389—28no—
154#389—28no—
155#389D4116yescomplemented
156#388—28no—
157#387—28no—
158#387—216no—
159#386—28no—
160#385—216no—
161#384—28no—
162#384—24no—
163#382—24no—
164#382—28no—
165#380—24no—
166#380—24no—
167#380—28no—
168#380—28no—
169C4×C4⋊C4—24no—
170C4×C4⋊C4—24no—
171C4×C4⋊C4D418yes—
172C4×C22⋊C4—28no—
173C4×C22⋊C4—28no—
174C4×C22⋊C4—28no—
175#376—24no—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2312yes—
184C2×#95C2314yes—
185C2×#95C2311yescharacteristic
186C2×#95C2312yes—
187C2×#95C2311yescharacteristic
188C2×#95C2312yes—
189C2×#95C2314yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2312yes—
200C25C2411yescharacteristic
201C25C2411yescharacteristic
202C22×Q8—28no—
203C22×Q8—28no—
204C22×Q8—28no—
205C22×Q8—28no—
206C22×Q8—44no—
207C22×Q8—44no—
208C22×Q8—44no—
209C22×D4—22no—
210C22×D4—22no—
211C22×D4—22no—
212C22×D4—22no—
213C22×D4—41no—
214C22×D4—41no—
215C22×D4C2×Q814yes—
216C23×C4—22no—
217C23×C4—24no—
218C23×C4—22no—
219C23×C4—24no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—24no—
223C23×C4—24no—
224C23×C4—24no—
225C23×C4—28no—
226C23×C4—24no—
227C23×C4—44no—
228C23×C4—42no—
229C23×C4C2×Q814yes—
230C23×C4C2×Q814yes—
231C23×C4C2414yes—
232C23×C4C2412yes—
233C23×C4C2412yes—
234C23×C4C2412yes—
235C23×C4C2414yes—
236C23×C4C2412yes—
237C23×C4C2412yes—
238C23×C4C2411yescharacteristic
239C23×C4C2411yescharacteristic
240C23×C4C2412yes—
241C23×C4C2412yes—
242C23×C4C2412yes—
243C23×C4C2411yescharacteristic
244C23×C4C2411yescharacteristic
245C23×C4C2411yescharacteristic
246C4⋊Q8—432no—
247C4⋊Q8—432no—
248C22⋊Q8—464no—
249C4×D4—232no—
250#117—416no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—24no—
256C2×C4⋊C4—24no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—24no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—28no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—28no—
267C2×C4⋊C4—28no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—28no—
273C2×C4⋊C4—28no—
274C2×C4⋊C4—28no—
275C2×C4⋊C4—28no—
276C2×C4⋊C4—28no—
277C2×C4⋊C4—28no—
278C2×C4⋊C4—28no—
279C2×C4⋊C4—28no—
280C2×C4⋊C4—28no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—44no—
283C2×C4⋊C4—44no—
284C2×C4⋊C4—44no—
285C2×C4⋊C4—44no—
286C2×C4⋊C4—44no—
287C2×C4⋊C4—44no—
288C2×C4⋊C4—44no—
289C2×C4⋊C4—44no—
290C2×C4⋊C4—416no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—44no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—44no—
295C2×C4⋊C4C2×D414yes—
296C2×C4⋊C4C2×D418yes—
297C2×C4⋊C4C2×D4116yes—
298C2×C4⋊C4C2×D414yes—
299C2×C4⋊C4C2×D418yes—
300C2×C4⋊C4C2×Q814yes—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—22no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—28no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—28no—
315C2×C22⋊C4—28no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—28no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—44no—
327C2×C22⋊C4—44no—
328C2×C22⋊C4—44no—
329C2×C22⋊C4—44no—
330C2×C22⋊C4C2×Q814yes—
331C2×C22⋊C4C2×Q814yes—
332C2×C42—24no—
333C2×C42—24no—
334C2×C42—24no—
335C2×C42—28no—
336C2×C42—24no—
337C2×C42—24no—
338C2×C42—24no—
339C2×C42—24no—
340C2×C42—44no—
341C2×C42—42no—
342C2×C42—42no—
343C2×C42C2×D418yes—
344C2×C42C2×D418yes—
345C2×C42C2×D414yes—
346C2×C42C2×Q814yes—
347C2×C42#4114yes—
348#95—24no—
349#95—24no—
350#95—24no—
351#95—24no—
352#95—24no—
353#95—24no—
354#95—24no—
355#95—24no—
356#95—28no—
357#95—28no—
358#95—24no—
359#95—28no—
360#95—28no—
361#95—28no—
362#95—28no—
363#95—28no—
364#95—22no—
365#95—22no—
366#95—24no—
367#95—24no—
368#95—44no—
369#95—44no—
370#95C2×D418yes—
371#95C2×D4116yes—
372C24—22no—
373C24—21no—
374C24—21no—
375C24—22no—
376C24—22no—
377C24—22no—
378C24—21no—
379C24—21no—
380C24—22no—
381C24—21no—
382C24—21no—
383C24—22no—
384C24—21no—
385C24—22no—
386C24—22no—
387C24—21no—
388C24—21no—
389C24—21no—
390C24C22×Q812yes—
391C24C22×Q812yes—
392C24H(5,𝔽2)12yes—
393C242−1+412yes—
394C24C2511yescharacteristic
395C2×Q8—416no—
396C2×Q8—416no—
397C2×Q8—416no—
398C2×Q8—416no—
399C2×Q8—88no—
400C2×Q8—88no—
401C2×Q8—88no—
402C2×D4—28no—
403C2×D4—28no—
404C2×D4—44no—
405C2×D4—44no—
406C2×D4—44no—
407C2×D4—44no—
408C2×D4—44no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—24no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—24no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—24no—
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—22no—
451C22×C4—24no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—28no—
461C22×C4—28no—
462C22×C4—216no—
463C22×C4—216no—
464C22×C4—22no—
465C22×C4—24no—
466C22×C4—22no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—416no—
482C22×C4—48no—
483C22×C4—44no—
484C22×C4—44no—
485C22×C4—44no—
486C22×C4—44no—
487C22×C4—48no—
488C22×C4—48no—
489C22×C4—48no—
490C22×C4—84no—
491C22×C4—88no—
492C22×C4C22×D414yes—
493C22×C4C22×D414yes—
494C22×C4C22×D418yes—
495C22×C4C22×D414yes—
496C22×C4C22×D412yes—
497C22×C4C22×D412yes—
498C22×C4C22×D414yes—
499C22×C4C22×D418yes—
500C22×C4C22×D412yes—
501C22×C4C22×D414yes—
502C22×C4C22×Q812yes—
503C22×C4C22×Q812yes—
504C22×C4C22×Q812yes—
505C22×C4C22×Q812yes—
506C22×C4C22×Q812yes—
507C22×C4C2×#4112yes—
508C22×C4C2×#4112yes—
509C22×C4C2×#4112yes—
510C22×C4H(5,𝔽2)14yes—
511C22×C42−1+414yes—
512C22×C42−1+414yes—
513C4⋊C4—28no—
514C4⋊C4—28no—
515C4⋊C4—28no—
516C4⋊C4—28no—
517C4⋊C4—216no—
518C4⋊C4—416no—
519C4⋊C4—416no—
520C4⋊C4—416no—
521C4⋊C4—416no—
522C4⋊C4—416no—
523C4⋊C4—48no—
524C4⋊C4—48no—
525C4⋊C4—44no—
526C4⋊C4—44no—
527C4⋊C4—416no—
528C4⋊C4—48no—
529C4⋊C4—84no—
530C4⋊C4—88no—
531C4⋊C4#127116yes—
532C22⋊C4—216no—
533C22⋊C4—216no—
534C22⋊C4—28no—
535C22⋊C4—28no—
536C22⋊C4—48no—
537C22⋊C4—48no—
538C22⋊C4—48no—
539C22⋊C4—416no—
540C22⋊C4—48no—
541C22⋊C4—84no—
542C22⋊C4—88no—
543C42—216no—
544C42—48no—
545C42—48no—
546C42—48no—
547C42—84no—
548C42C22⋊Q8116yescomplemented
549C23—22no—
550C23—22no—
551C23—24no—
552C23—24no—
553C23—24no—
554C23—22no—
555C23—22no—
556C23—22no—
557C23—22no—
558C23—24no—
559C23—24no—
560C23—24no—
561C23—22no—
562C23—22no—
563C23—22no—
564C23—24no—
565C23—24no—
566C23—41no—
567C23—41no—
568C23—42no—
569C23—41no—
570C23—41no—
571C23—42no—
572C23—42no—
573C23—42no—
574C23—42no—
575C23—42no—
576C23—41no—
577C23—41no—
578C23—42no—
579C23—42no—
580C23—41no—
581C23—42no—
582C23—41no—
583C23—42no—
584C23—41no—
585C23—42no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23#54414yes—
595C23C23×D411yescharacteristic
596C23C23×D412yes—
597C23C23×Q811yescharacteristic
598C23C22×#4111yescharacteristic
599C23C2×H(5,𝔽2)11yescharacteristic
600C23C2×H(5,𝔽2)12yes—
601C23C2×2−1+412yes—
602C23C2×2−1+411yescharacteristic
603C23C2×2−1+412yes—
604C23#58511yescharacteristic
605C23#58511yescharacteristic
606Q8—832no—
607D4—416no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—24no—
612C2×C4—28no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—24no—
616C2×C4—28no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—24no—
621C2×C4—24no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—28no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—28no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—28no—
644C2×C4—41no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
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—44no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—44no—
664C2×C4—44no—
665C2×C4—42no—
666C2×C4—44no—
667C2×C4—42no—
668C2×C4—44no—
669C2×C4—42no—
670C2×C4—44no—
671C2×C4—42no—
672C2×C4—416no—
673C2×C4—416no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—44no—
677C2×C4—44no—
678C2×C4—42no—
679C2×C4—44no—
680C2×C4—44no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—42no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—42no—
688C2×C4—44no—
689C2×C4—42no—
690C2×C4—44no—
691C2×C4—816no—
692C2×C4C2×C22⋊Q814yes—
693C2×C4C2×C22⋊Q814yes—
694C2×C4C2×C22⋊Q814yes—
695C2×C4C2×#12718yes—
696C2×C4C2×#12714yes—
697C2×C4#53614yes—
698C2×C4#54718yes—
699C2×C4D4×Q818yes—
700C22—28no—
701C22—24no—
702C22—44no—
703C22—44no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—44no—
709C22—42no—
710C22—42no—
711C22—44no—
712C22—44no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—82no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—82no—
721C22—81no—
722C22C22×C22⋊Q811yescharacteristic
723C22C22×#12711yescharacteristic
724C22C2×#53611yescharacteristic
725C22C2×#54411yescharacteristic
726C22#345811yescharacteristic
727C22C2×#54712yes—
728C22C2×D4×Q812yes—
729C22#348412yes—
730C22#348411yescharacteristic
731C22#348612yes—
732C22#348611yescharacteristic
733C22#348812yes—
734C22#348811yescharacteristic
735C22#348912yes—
736C22#348911yescharacteristic
737C22#349411yescharacteristic
738C22#349511yescharacteristic
739C22#350312yes—
740C22#351112yes—
741C22#354412yes—
742C22#354712yes—
743C22#355212yes—
744C22#355512yes—
745C4—28no—
746C4—24no—
747C4—24no—
748C4—44no—
749C4—44no—
750C4—44no—
751C4—42no—
752C4—42no—
753C4—44no—
754C4—48no—
755C4—44no—
756C4—82no—
757C4—84no—
758C4—82no—
759C4#254218yes—
760C2—44no—
761C2—82no—
762C2C2×#254211yescharacteristic
763C2#3525311yescharacteristic
764C2#3557411yescharacteristic
765C2#3592111yescharacteristic
766C2#3592711yescharacteristic
767C2#3768612yes—
768C2#3769012yes—
769C2#4248511yescharacteristic
770C2#4281311yescharacteristic
771C2#4492812yes—
772C2#4533312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×D4C23
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×#2551C2semidirect
2. C2×#2439C2semidirect
3. C2×#2440C2semidirect
5. #16984C2semidirect
6. #16511C2semidirect
7. #15856C2semidirect
9. #15223C2semidirect
10. #15178C2semidirect
11. #15135C2semidirect
12. #14969C2semidirect
13. #14354C2semidirect
14. #13954C2semidirect
17. #13783C2semidirect
102. C2×C4×D4Q8semidirect
155. #389D4semidirect
548. C42C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#25512
C2×#24392
C2×#24402
C2×#23522
#169842
#165112
#158562
#153252
#152232
#151782
#151352
#149692
#143542
#139542
#139062
#138472
#137832