Finite Group Databasebeta

← #370568

Subgroups — #370568

Order 512.

1536 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2549C211yesmaximal, characteristic
2C2×#1996C212yesmaximal
3#13908C211yesmaximal, characteristic
4#13802C211yesmaximal, characteristic
5#11381C212yesmaximal
6#11203C212yesmaximal
7#10912C212yesmaximal
8#10854C211yesmaximal, characteristic
9#10854C211yesmaximal, characteristic
10#10846C211yesmaximal, characteristic
11C4×#342C211yesmaximal, characteristic
12C22×C22⋊Q8C2212yes—
13#2549—21no—
14#2549—21no—
15#2549—22no—
16#2549—22no—
17#2549—21no—
18#2549—21no—
19C2×#398C412yescomplemented
20C2×#395C412yescomplemented
21C2×#391C412yescomplemented
22C2×#389C412yescomplemented
23C2×#385C2212yes—
24C2×#380C2211yescharacteristic
25C2×#380C2212yes—
26C2×#380C2211yescharacteristic
27C2×#380C2211yescharacteristic
28C2×C4×C22⋊C4C2211yescharacteristic
29C2×C4×C22⋊C4C2212yes—
30C2×C4×C22⋊C4C2211yescharacteristic
31C2×C4×C22⋊C4C2211yescharacteristic
32C22×#95C2211yescharacteristic
33#1996—28no—
34C2×#342C2212yes—
35C2×#342C2212yes—
36C2×#342C2212yes—
37C2×#342C2212yes—
38C2×#342C2211yescharacteristic
39C2×#342C2211yescharacteristic
40C2×#342C2212yes—
41C2×#342C2212yes—
42C2×#342C2211yescharacteristic
43C2×#342C2211yescharacteristic
44#1444—21no—
45#1442—21no—
46#1436—22no—
47#1436—22no—
48#1434—21no—
49C22⋊#95C2212yes—
50C22⋊#95C2212yes—
51C4×#95—21no—
52C23×Q8C2×C412yes—
53C24×C4C2312yes—
54C24×C4C2311yescharacteristic
55C2×C22⋊Q8—22no—
56C2×C22⋊Q8—22no—
57C2×C22⋊Q8—22no—
58C2×C22⋊Q8—22no—
59C2×C22⋊Q8—24no—
60C2×C22⋊Q8—24no—
61C2×C22⋊Q8—42no—
62C2×C22⋊Q8—42no—
63C22×C4⋊C4—21no—
64C22×C4⋊C4—22no—
65C22×C4⋊C4—21no—
66C22×C4⋊C4C2×C412yes—
67C22×C4⋊C4C2×C412yes—
68C22×C4⋊C4C2×C412yes—
69C22×C4⋊C4C2×C412yes—
70C22×C4⋊C4C2×C412yes—
71C22×C4⋊C4C2×C412yes—
72C22×C22⋊C4C2312yes—
73C22×C22⋊C4C2312yes—
74C22×C22⋊C4C2311yescharacteristic
75C22×C22⋊C4C2311yescharacteristic
76C22×C22⋊C4C2311yescharacteristic
77C22×C22⋊C4C2312yes—
78C22×C22⋊C4C2311yescharacteristic
79C22×C22⋊C4C2311yescharacteristic
80C22×C22⋊C4C2311yescharacteristic
81C22×C42—21no—
82C22×C42—22no—
83C22×C42—21no—
84C22×C42C2×C412yes—
85#398—22no—
86#398—22no—
87#398—22no—
88#398—22no—
89#395—22no—
90#395—22no—
91#395—22no—
92#395—22no—
93#391—22no—
94#391—22no—
95#391—22no—
96#391—22no—
97#389—22no—
98#389—22no—
99#389—22no—
100#389—22no—
101#385—22no—
102#385—22no—
103#385—22no—
104#385—22no—
105#380—21no—
106#380—21no—
107#380—21no—
108#380—21no—
109#380—22no—
110#380—22no—
111#380—22no—
112#380—24no—
113#380—42no—
114#380Q814yescomplemented
115C4×C22⋊C4—21no—
116C4×C22⋊C4—21no—
117C4×C22⋊C4—21no—
118C4×C22⋊C4—21no—
119C4×C22⋊C4—22no—
120C4×C22⋊C4—22no—
121C4×C22⋊C4—22no—
122C4×C22⋊C4—24no—
123C4×C22⋊C4—42no—
124C4×C22⋊C4Q814yescomplemented
125C2×#95—21no—
126C2×#95—21no—
127C2×#95—22no—
128C2×#95—22no—
129C2×#95—22no—
130C2×#95—21no—
131C2×#95—22no—
132C2×#95—21no—
133C2×#95—22no—
134C2×#95—22no—
135C2×#95C2×C412yes—
136C2×#95C2×C412yes—
137C2×#95C2×C412yes—
138C2×#95C2×C411yescharacteristic
139C2×#95C2×C411yescharacteristic
140C2×#95C2×C411yescharacteristic
141C2×#95C2×C411yescharacteristic
142C2×#95C2×C412yes—
143C2×#95D411yescharacteristic
144C2×#95D411yescharacteristic
145C2×#95D412yes—
146C2×#95D412yes—
147C2×#95D411yescharacteristic
148C2×#95D411yescharacteristic
149#342—24no—
150#342—24no—
151#342—24no—
152#342—22no—
153#342—22no—
154#342—24no—
155#342—42no—
156#342—42no—
157#342D414yes—
158#342Q814yescomplemented
159C25C2411yescharacteristic
160C22×Q8—22no—
161C22×Q8—22no—
162C22×Q8—24no—
163C22×Q8—42no—
164C22×Q8—44no—
165C22×Q8—82no—
166C23×C4—21no—
167C23×C4—22no—
168C23×C4—22no—
169C23×C4—22no—
170C23×C4—22no—
171C23×C4—21no—
172C23×C4—22no—
173C23×C4—21no—
174C23×C4—21no—
175C23×C4—22no—
176C23×C4—44no—
177C23×C4—82no—
178C23×C4—82no—
179C23×C4C22×C412yes—
180C23×C4C22×C412yes—
181C23×C4C22×C412yes—
182C23×C4C22×C412yes—
183C23×C4C22×C412yes—
184C23×C4C22×C412yes—
185C23×C4C22×C411yescharacteristic
186C23×C4C22×C411yescharacteristic
187C23×C4C2×D412yes—
188C23×C4C2×D412yes—
189C23×C4C2×D412yes—
190C23×C4C2×D412yes—
191C23×C4C2×D411yescharacteristic
192C23×C4C2×D411yescharacteristic
193C23×C4C2×D411yescharacteristic
194C23×C4C2×D411yescharacteristic
195C23×C4C2×Q812yes—
196C23×C4C2×Q812yes—
197C23×C4#4112yes—
198C23×C4#4112yes—
199C22⋊Q8—44no—
200C22⋊Q8—44no—
201C22⋊Q8—44no—
202C22⋊Q8—44no—
203C22⋊Q8—44no—
204C22⋊Q8—44no—
205C22⋊Q8—44no—
206C22⋊Q8—44no—
207C2×C4⋊C4—22no—
208C2×C4⋊C4—22no—
209C2×C4⋊C4—22no—
210C2×C4⋊C4—22no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—22no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4—24no—
216C2×C4⋊C4—24no—
217C2×C4⋊C4—24no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—24no—
223C2×C4⋊C4—42no—
224C2×C4⋊C4—42no—
225C2×C4⋊C4—42no—
226C2×C4⋊C4—44no—
227C2×C4⋊C4—44no—
228C2×C4⋊C4—44no—
229C2×C4⋊C4—42no—
230C2×C4⋊C4—82no—
231C2×C4⋊C4—82no—
232C2×C4⋊C4—82no—
233C2×C4⋊C4—82no—
234C2×C4⋊C4—82no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—22no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—22no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—22no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—22no—
262C2×C22⋊C4—22no—
263C2×C22⋊C4—22no—
264C2×C22⋊C4—22no—
265C2×C22⋊C4—22no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—22no—
268C2×C22⋊C4—22no—
269C2×C22⋊C4—22no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—22no—
273C2×C22⋊C4—22no—
274C2×C22⋊C4—22no—
275C2×C22⋊C4—22no—
276C2×C22⋊C4—22no—
277C2×C22⋊C4—22no—
278C2×C22⋊C4C2×D412yes—
279C2×C22⋊C4C2×D412yes—
280C2×C22⋊C4C2×D412yes—
281C2×C22⋊C4C2×Q812yes—
282C2×C22⋊C4C2×Q812yes—
283C2×C22⋊C4C2×Q814yes—
284C2×C22⋊C4C2×Q812yes—
285C2×C22⋊C4C2×Q812yes—
286C2×C22⋊C4C2×Q812yes—
287C2×C22⋊C4#4112yes—
288C2×C22⋊C4#4112yes—
289C2×C42—22no—
290C2×C42—22no—
291C2×C42—24no—
292C2×C42—44no—
293C2×C42—44no—
294C2×C42—42no—
295C2×C42—82no—
296C2×C42—82no—
297C2×C42—82no—
298C2×C42—82no—
299#95—22no—
300#95—22no—
301#95—21no—
302#95—21no—
303#95—21no—
304#95—21no—
305#95—22no—
306#95—22no—
307#95—22no—
308#95—22no—
309#95—24no—
310#95—24no—
311#95—44no—
312#95—44no—
313#95—44no—
314#95—44no—
315#95—42no—
316#95—42no—
317#95—82no—
318#95—82no—
319#95C22⋊C412yes—
320#95C22⋊C412yes—
321#95C22⋊C412yes—
322#95C22⋊C412yes—
323#95C22⋊C411yescharacteristic
324#95C22⋊C412yes—
325#95C22⋊C411yescharacteristic
326#95C22⋊C411yescharacteristic
327#95C22⋊C411yescharacteristic
328#95C22⋊C412yes—
329C24—42no—
330C24—42no—
331C24C23×C411yescharacteristic
332C24C22×D411yescharacteristic
333C24C22×D411yescharacteristic
334C24C22×D411yescharacteristic
335C24C22×Q811yescharacteristic
336C24C22×Q811yescharacteristic
337C24C22×Q811yescharacteristic
338C24C2×#4111yescharacteristic
339C24C2×#4111yescharacteristic
340C24C2×#4111yescharacteristic
341C24C2×#4111yescharacteristic
342C24H(5,𝔽2)11yescharacteristic
343C24H(5,𝔽2)11yescharacteristic
344C242−1+411yescharacteristic
345C242−1+411yescharacteristic
346C2×Q8—44no—
347C2×Q8—44no—
348C2×Q8—44no—
349C2×Q8—44no—
350C2×Q8—82no—
351C2×Q8—82no—
352C2×Q8—88no—
353C2×Q8—88no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—24no—
374C22×C4—24no—
375C22×C4—24no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—24no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—42no—
387C22×C4—42no—
388C22×C4—42no—
389C22×C4—42no—
390C22×C4—42no—
391C22×C4—42no—
392C22×C4—42no—
393C22×C4—42no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4—42no—
397C22×C4—42no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4—42no—
407C22×C4—42no—
408C22×C4—42no—
409C22×C4—42no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—42no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—42no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—42no—
424C22×C4—41no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—82no—
437C22×C4—82no—
438C22×C4—82no—
439C22×C4—82no—
440C22×C4—84no—
441C22×C4—84no—
442C22×C4—84no—
443C22×C4—84no—
444C22×C4C2×C22⋊C412yes—
445C22×C4C2×C22⋊C412yes—
446C22×C4C2×C22⋊C412yes—
447C22×C4C2×C22⋊C411yescharacteristic
448C22×C4C2×C22⋊C411yescharacteristic
449C22×C4C2×C22⋊C411yescharacteristic
450C22×C4C2×C22⋊C411yescharacteristic
451C22×C4C2×C22⋊C412yes—
452C22×C4C4×D414yes—
453C22×C4C4×Q814yes—
454C22×C4C4×Q812yes—
455C22×C4C4×Q812yes—
456C22×C4C4×Q812yes—
457C22×C4C4×Q812yes—
458C22×C4C22⋊Q812yes—
459C22×C4C22⋊Q812yes—
460C22×C4C22⋊Q812yes—
461C22×C4C22⋊Q812yes—
462C22×C4#12412yes—
463C22×C4#12412yes—
464C22×C4C4⋊Q812yes—
465C22×C4C4⋊Q812yes—
466C4⋊C4—44no—
467C4⋊C4—44no—
468C4⋊C4—44no—
469C4⋊C4—44no—
470C4⋊C4—44no—
471C4⋊C4—44no—
472C4⋊C4—44no—
473C4⋊C4—44no—
474C4⋊C4—82no—
475C4⋊C4—82no—
476C4⋊C4—82no—
477C4⋊C4—82no—
478C4⋊C4—84no—
479C4⋊C4—88no—
480C4⋊C4—84no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—22no—
496C22⋊C4—22no—
497C22⋊C4—24no—
498C22⋊C4—24no—
499C22⋊C4—22no—
500C22⋊C4—42no—
501C22⋊C4—42no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—42no—
505C22⋊C4—42no—
506C22⋊C4—42no—
507C22⋊C4—42no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—42no—
513C22⋊C4—42no—
514C22⋊C4—42no—
515C22⋊C4—42no—
516C22⋊C4C4⋊Q814yes—
517C42—82no—
518C42—82no—
519C42—84no—
520C42—88no—
521C42—84no—
522C23—22no—
523C23—22no—
524C23—22no—
525C23—22no—
526C23—22no—
527C23—22no—
528C23—42no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—41no—
537C23—41no—
538C23—42no—
539C23—41no—
540C23—41no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23C22×C22⋊C411yescharacteristic
545C23C2×C4×D411yescharacteristic
546C23C2×C4×Q811yescharacteristic
547C23C2×C4×Q811yescharacteristic
548C23C2×C4×Q811yescharacteristic
549C23#51811yescharacteristic
550C23#51911yescharacteristic
551C23C2×C22⋊Q811yescharacteristic
552C23C2×C22⋊Q811yescharacteristic
553C23C2×#12411yescharacteristic
554C23C2×C4⋊Q811yescharacteristic
555C23C2×C4⋊Q811yescharacteristic
556C23#53211yescharacteristic
557C23#53311yescharacteristic
558C23#53311yescharacteristic
559C23#54211yescharacteristic
560C23#54211yescharacteristic
561C23#54411yescharacteristic
562C23#54411yescharacteristic
563C23D4211yescharacteristic
564C23D4211yescharacteristic
565C23#54611yescharacteristic
566C23#54611yescharacteristic
567C23#54711yescharacteristic
568C23#54811yescharacteristic
569C23#54811yescharacteristic
570C23D4×Q811yescharacteristic
571C23D4×Q811yescharacteristic
572C23D4×Q811yescharacteristic
573C23#55411yescharacteristic
574C23#55411yescharacteristic
575C23#55511yescharacteristic
576C23#55611yescharacteristic
577C23#55711yescharacteristic
578C23Q8211yescharacteristic
579Q8—88no—
580Q8—88no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—24no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—24no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—24no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—44no—
612C2×C4—44no—
613C2×C4—44no—
614C2×C4—44no—
615C2×C4—44no—
616C2×C4—44no—
617C2×C4—42no—
618C2×C4—44no—
619C2×C4—42no—
620C2×C4—44no—
621C2×C4—44no—
622C2×C4—44no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—44no—
628C2×C4—44no—
629C2×C4—42no—
630C2×C4—44no—
631C2×C4—44no—
632C2×C4—42no—
633C2×C4—44no—
634C2×C4—44no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—44no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—82no—
646C2×C4—82no—
647C2×C4—82no—
648C2×C4—82no—
649C2×C4—82no—
650C2×C4—82no—
651C2×C4—81no—
652C2×C4—81no—
653C2×C4—82no—
654C2×C4—81no—
655C2×C4—81no—
656C2×C4—82no—
657C2×C4—82no—
658C2×C4—82no—
659C2×C4—82no—
660C2×C4—82no—
661C2×C4—82no—
662C2×C4—82no—
663C2×C4—82no—
664C2×C4—82no—
665C2×C4—82no—
666C2×C4—82no—
667C2×C4—82no—
668C2×C4—82no—
669C2×C4—82no—
670C2×C4—82no—
671C2×C4—82no—
672C2×C4—82no—
673C2×C4—82no—
674C2×C4#39112yes—
675C2×C4#39112yes—
676C2×C4#39112yes—
677C2×C4#39112yes—
678C2×C4#41014yes—
679C22—21no—
680C22—21no—
681C22—21no—
682C22—21no—
683C22—21no—
684C22—21no—
685C22—21no—
686C22—21no—
687C22—21no—
688C22—21no—
689C22—21no—
690C22—21no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22C2×#39111yescharacteristic
720C22C4×C4⋊Q811yescharacteristic
721C22#233111yescharacteristic
722C22D4×C22⋊C411yescharacteristic
723C22Q8×C22⋊C411yescharacteristic
724C22#236511yescharacteristic
725C22#236911yescharacteristic
726C22#243911yescharacteristic
727C22#244011yescharacteristic
728C22#245111yescharacteristic
729C22#245211yescharacteristic
730C22#249111yescharacteristic
731C22#249211yescharacteristic
732C22#255011yescharacteristic
733C22#255111yescharacteristic
734C22C2×#41012yes—
735C22#288312yes—
736C4—22no—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—24no—
741C4—44no—
742C4—42no—
743C4—42no—
744C4—42no—
745C4—44no—
746C4—44no—
747C4—84no—
748C4—82no—
749C4—82no—
750C4—82no—
751C4—82no—
752C4—82no—
753C4—162no—
754C2—21no—
755C2—21no—
756C2—21no—
757C2—21no—
758C2—21no—
759C2—21no—
760C2—21no—
761C2—21no—
762C2—21no—
763C2—21no—
764C2—21no—
765C2—21no—
766C2#1405311yescharacteristic
767C2#2133211yescharacteristic
768C2#2133311yescharacteristic
769C2#2240512yes—
770C2#2251312yes—
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC24C23×C4
Frattini, prime radical, cosocleC25C24
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×#95 ◁ G
LECSG ▷ C25 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
19. C2×#398C4semidirect
20. C2×#395C4semidirect
21. C2×#391C4semidirect
22. C2×#389C4semidirect
114. #380Q8semidirect
124. C4×C22⋊C4Q8semidirect
158. #342Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#25492
C2×#19962
#139082
#138022
#113812
#112032
#109122
#108542
#108462
C4×#3422