Finite Group Databasebeta

← #360045

Subgroups — #360045

Order 512.

1874 conjugacy classes of subgroups.

The subgroup lattice has 769 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×SD16C211yesmaximal, characteristic
2C2×#2354C211yesmaximal, characteristic
3C2×#1803C211yesmaximal, characteristic, complemented
4C2×#1802C211yesmaximal, characteristic
5#13926C211yesmaximal, characteristic, complemented
6#11189C212yesmaximal
7#11023C212yesmaximal
8#10932C212yesmaximal, complemented
9#10908C212yesmaximal, complemented
10#10841C211yesmaximal, characteristic, complemented
11#10834C211yesmaximal, characteristic, complemented
12C23×SD16C2211yescharacteristic
13C22×C4×Q8C2211yescharacteristic
14C22×C4×D4C2211yescharacteristic
15C22×#117—21no—
16C2×C4×SD16—24no—
17C2×C4×SD16—24no—
18C2×C4×SD16C418yescomplemented
19C22×#106C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×#103C2212yes—
22C22×#103C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×#102C2212yes—
25C22×C4×C8C2211yescharacteristic
26#2354—24no—
27#2354—24no—
28C2×#391C2212yes—
29C2×#390C2212yes—
30C2×#388—22no—
31C2×#384C2211yescharacteristic
32C2×#384C2211yescharacteristic
33C2×#380—21no—
34C2×C4×C4⋊C4C2212yes—
35C2×C4×C4⋊C4C2211yescharacteristic
36#1803—24no—
37#1802—24no—
38C2×#340C2212yes—
39C2×#340C2212yes—
40C2×#340C2212yes—
41C2×#340C2212yes—
42C2×#336C2212yes—
43C2×#336C2212yes—
44#1441—22no—
45C4⋊#95—21no—
46C4⋊#95—21no—
47C4⋊#95C2212yes—
48C23×Q8C2311yescharacteristic
49C23×D4C2311yescharacteristic
50C24×C4—21no—
51C22×SD16—22no—
52C22×SD16—22no—
53C22×SD16—22no—
54C22×SD16—22no—
55C22×SD16—22no—
56C22×SD16—22no—
57C22×SD16C2×C414yes—
58C23×C8C2312yes—
59C23×C8C2311yescharacteristic
60C23×C8C2311yescharacteristic
61C2×C4×Q8—22no—
62C2×C4×Q8—22no—
63C2×C4×Q8—22no—
64C2×C4×Q8—22no—
65C2×C4×Q8—22no—
66C2×C4×Q8C2×C414yes—
67C2×C4×D4—22no—
68C2×C4×D4—22no—
69C2×C4×D4—22no—
70C2×C4×D4C2×C414yes—
71C2×C4×D4D414yes—
72C2×C4×D4D414yes—
73C2×#117—28no—
74C2×#117—44no—
75C2×#117—44no—
76C22×C4⋊C4—21no—
77C22×C4⋊C4—21no—
78C22×C4⋊C4—21no—
79C22×C4⋊C4—21no—
80C22×C4⋊C4—21no—
81C22×C4⋊C4D411yescharacteristic
82C22×C4⋊C4D411yescharacteristic
83C22×C4⋊C4C2312yes—
84C22×C4⋊C4C2311yescharacteristic
85C22×C4⋊C4C2312yes—
86C22×C4⋊C4C2311yescharacteristic
87C22×C22⋊C4—21no—
88C22×C22⋊C4—22no—
89C22×C22⋊C4—22no—
90C22×C42—22no—
91C22×C42—21no—
92C22×C42C2312yes—
93C22×C42C2311yescharacteristic
94C4×SD16—232no—
95C2×#106—22no—
96C2×#106—22no—
97C2×#106C2×C414yes—
98C2×C4⋊C8—22no—
99C2×C4⋊C8—22no—
100C2×C4⋊C8—22no—
101C2×#103—22no—
102C2×#103—22no—
103C2×#103—24no—
104C2×#103—24no—
105C2×#103—42no—
106C2×#103C2×C414yes—
107C2×#102—22no—
108C2×#102—22no—
109C2×#102—24no—
110C2×#102—42no—
111C2×#102—42no—
112C2×#102C2×C414yes—
113C2×C4×C8—22no—
114C2×C4×C8—22no—
115C2×C4×C8C2×C414yes—
116#391—24no—
117#391—42no—
118#390—24no—
119#390—24no—
120#388—216no—
121#384—22no—
122#384—22no—
123#384—22no—
124#384D414yes—
125#380—28no—
126C4×C4⋊C4—24no—
127C4×C4⋊C4—24no—
128C4×C4⋊C4—22no—
129C4×C4⋊C4—22no—
130C2×#95—22no—
131C2×#95—22no—
132C2×#95—22no—
133C2×#95—22no—
134C2×#95—22no—
135C2×#95D412yes—
136#340—24no—
137#340—24no—
138#340—24no—
139#340—42no—
140#336—24no—
141#336—42no—
142C25—21no—
143C22×Q8—21no—
144C22×Q8—21no—
145C22×Q8—21no—
146C22×Q8—21no—
147C22×Q8—21no—
148C22×Q8—21no—
149C22×Q8—21no—
150C22×Q8—21no—
151C22×Q8—21no—
152C22×Q8—21no—
153C22×Q8—21no—
154C22×Q8C22×C412yes—
155C22×Q8#4112yes—
156C22×Q8#4112yes—
157C22×D4—21no—
158C22×D4—21no—
159C22×D4—21no—
160C22×D4—21no—
161C22×D4—21no—
162C22×D4—21no—
163C22×D4—21no—
164C22×D4—21no—
165C22×D4—21no—
166C22×D4—21no—
167C22×D4—21no—
168C22×D4C22×C412yes—
169C22×D4C2×D412yes—
170C22×D4C2×D412yes—
171C23×C4—21no—
172C23×C4—21no—
173C23×C4—24no—
174C23×C4—24no—
175C23×C4—24no—
176C23×C4—22no—
177C23×C4—21no—
178C23×C4—22no—
179C23×C4—42no—
180C23×C4—42no—
181C23×C4—42no—
182C23×C4—42no—
183C23×C4C2×D412yes—
184C23×C4C2×D412yes—
185C23×C4C2×D411yescharacteristic
186C23×C4C2×D411yescharacteristic
187C23×C4C2411yescharacteristic
188C2×SD16—28no—
189C2×SD16—28no—
190C2×SD16—28no—
191C2×SD16—28no—
192C2×SD16—28no—
193C2×SD16—28no—
194C2×SD16—28no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—21no—
198C22×C8—21no—
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—21no—
202C22×C8—21no—
203C22×C8—21no—
204C22×C8—21no—
205C22×C8—22no—
206C22×C8—22no—
207C22×C8—22no—
208C22×C8—22no—
209C22×C8—22no—
210C22×C8—22no—
211C22×C8—22no—
212C22×C8C22×C412yes—
213C22×C8C22×C412yes—
214C22×C8#4112yes—
215C22×C8#4112yes—
216C4×Q8—28no—
217C4×Q8—28no—
218C4×Q8—44no—
219C4×Q8—44no—
220C4×D4—28no—
221C4×D4—28no—
222C4×D4—28no—
223C4×D4C22⋊C4116yes—
224#117—432no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—24no—
239C2×C4⋊C4—24no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—24no—
252C2×C4⋊C4—42no—
253C2×C4⋊C4—42no—
254C2×C4⋊C4—42no—
255C2×C4⋊C4—42no—
256C2×C4⋊C4—42no—
257C2×C4⋊C4—42no—
258C2×C4⋊C4—42no—
259C2×C4⋊C4—42no—
260C2×C4⋊C4—81no—
261C2×C4⋊C4—81no—
262C2×C4⋊C4—81no—
263C2×C4⋊C4—81no—
264C2×C4⋊C4SD1614yescomplemented
265C2×C4⋊C4C22×C412yes—
266C2×C4⋊C4C22×C412yes—
267C2×C4⋊C4C2×D414yes—
268C2×C4⋊C4C2×D412yes—
269C2×C4⋊C4C2×D412yes—
270C2×C22⋊C4—24no—
271C2×C22⋊C4—24no—
272C2×C22⋊C4—24no—
273C2×C22⋊C4—28no—
274C2×C22⋊C4—28no—
275C2×C22⋊C4—44no—
276C2×C22⋊C4—44no—
277C2×C22⋊C4—82no—
278C2×C22⋊C4—82no—
279C2×C42—28no—
280C2×C42—24no—
281C2×C42—22no—
282C2×C42—22no—
283C2×C42—22no—
284C2×C42—22no—
285C2×C42—22no—
286C2×C42—22no—
287C2×C42—44no—
288C2×C42—42no—
289C2×C42—42no—
290C2×C42—44no—
291C2×C42C22×C412yes—
292C2×C42C2×D412yes—
293C2×C42C2×D412yes—
294C2×C42C2×D412yes—
295C2×C42#4112yes—
296C2×C42#4112yes—
297#106—28no—
298C4⋊C8—44no—
299#103—28no—
300#103—48no—
301#102—28no—
302#102—48no—
303C4×C8—28no—
304#95—28no—
305#95—24no—
306#95—44no—
307#95—44no—
308#95—82no—
309#95—82no—
310C24—22no—
311C24—22no—
312C24—22no—
313C24—41no—
314C24—41no—
315C24—41no—
316C24—41no—
317C24—41no—
318C24—41no—
319C24—41no—
320C24—41no—
321C24—41no—
322C24—41no—
323C24—41no—
324C24—41no—
325C24C22×D411yescharacteristic
326C2×Q8—22no—
327C2×Q8—22no—
328C2×Q8—22no—
329C2×Q8—22no—
330C2×Q8—22no—
331C2×Q8—22no—
332C2×Q8—22no—
333C2×Q8—22no—
334C2×Q8—22no—
335C2×Q8—22no—
336C2×Q8—22no—
337C2×Q8—22no—
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8—41no—
342C2×Q8—41no—
343C2×Q8—41no—
344C2×Q8—41no—
345C2×Q8—41no—
346C2×Q8—41no—
347C2×Q8—41no—
348C2×Q8—41no—
349C2×Q8—41no—
350C2×Q8—41no—
351C2×Q8—41no—
352C2×Q8—41no—
353C2×Q8#11714yescomplemented
354C2×D4—22no—
355C2×D4—22no—
356C2×D4—22no—
357C2×D4—22no—
358C2×D4—22no—
359C2×D4—22no—
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4—41no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4—41no—
381C2×D4C2×C22⋊C414yes—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—216no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—24no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—48no—
417C22×C4—48no—
418C22×C4—48no—
419C22×C4—48no—
420C22×C4—48no—
421C22×C4—48no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—41no—
429C22×C4—42no—
430C22×C4—41no—
431C22×C4—42no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4C4×D412yes—
442C22×C4C4×D412yes—
443C22×C4#12012yes—
444C22×C4#12012yes—
445C22×C4#12112yes—
446C22×C4#12112yes—
447C22×C4C2×SD1614yes—
448C22×C4C2×SD1612yes—
449C22×C4#13512yes—
450C22×C4AGL(1,ℤ/8)12yes—
451C22×C4#13712yes—
452C22×C4C23×C411yescharacteristic
453C22×C4C22×D411yescharacteristic
454C22×C4C22×D411yescharacteristic
455C22×C4C22×D411yescharacteristic
456C22×C4C2×#4111yescharacteristic
457C22×C4C2×#4111yescharacteristic
458C22×C4C2×#4111yescharacteristic
459C22×C4C2×#4111yescharacteristic
460C22×C4C2×#4111yescharacteristic
461C22×C4C2×#4111yescharacteristic
462C22×C4H(5,𝔽2)11yescharacteristic
463C22×C4H(5,𝔽2)11yescharacteristic
464C22×C42−1+411yescharacteristic
465C22×C42−1+411yescharacteristic
466SD16—232no—
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—42no—
481C2×C8—42no—
482C2×C8—42no—
483C2×C8—42no—
484C2×C8—42no—
485C2×C8—42no—
486C2×C8—42no—
487C2×C8#11714yescomplemented
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—28no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—24no—
495C4⋊C4—24no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—42no—
499C4⋊C4—42no—
500C4⋊C4—48no—
501C4⋊C4—48no—
502C4⋊C4—44no—
503C4⋊C4—42no—
504C4⋊C4—42no—
505C4⋊C4—42no—
506C4⋊C4—42no—
507C4⋊C4—84no—
508C4⋊C4—84no—
509C4⋊C4—84no—
510C4⋊C4C2×C22⋊C414yes—
511C22⋊C4—216no—
512C22⋊C4—416no—
513C22⋊C4—88no—
514C42—416no—
515C42—42no—
516C42—42no—
517C42—42no—
518C42—42no—
519C42—48no—
520C42C2×C22⋊C414yes—
521C42C4×D414yes—
522C42#12114yes—
523C42#12314yes—
524C23—24no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—81no—
544C23—81no—
545C23—81no—
546C23—81no—
547C23—81no—
548C23—81no—
549C23—81no—
550C23—81no—
551C23—81no—
552C23—81no—
553C23—81no—
554C23—81no—
555C23—81no—
556C23—81no—
557C23—81no—
558C23—81no—
559C23C2×C4×D411yescharacteristic
560C23C2×#12011yescharacteristic
561C23C2×#12111yescharacteristic
562C23#54611yescharacteristic
563C23#54711yescharacteristic
564C23#54811yescharacteristic
565C23#55011yescharacteristic
566C23C22×SD1611yescharacteristic
567C23C2×#13511yescharacteristic
568C23C2×AGL(1,ℤ/8)11yescharacteristic
569C23C2×#13711yescharacteristic
570C23#57611yescharacteristic
571C23#57711yescharacteristic
572C23#57711yescharacteristic
573C23#57811yescharacteristic
574Q8—24no—
575Q8—24no—
576Q8—42no—
577Q8—42no—
578Q8—42no—
579Q8—42no—
580Q8—42no—
581Q8—42no—
582D4—24no—
583D4—24no—
584D4—42no—
585D4—42no—
586D4—42no—
587D4—42no—
588D4—42no—
589D4—42no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—24no—
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—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—432no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—44no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—44no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—44no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—82no—
632C2×C4—82no—
633C2×C4—82no—
634C2×C4—82no—
635C2×C4—81no—
636C2×C4—81no—
637C2×C4—81no—
638C2×C4—81no—
639C2×C4—82no—
640C2×C4—82no—
641C2×C4—82no—
642C2×C4—82no—
643C2×C4—82no—
644C2×C4—82no—
645C2×C4—82no—
646C2×C4#38614yes—
647C2×C4#38614yes—
648C2×C4C4×SD1614yes—
649C2×C4#44014yes—
650C2×C4#45014yes—
651C2×C4#45214yes—
652C2×C4#46114yes—
653C2×C4#46314yes—
654C2×C4C22×C22⋊C411yescharacteristic
655C2×C4C2×#11711yescharacteristic
656C2×C4C2×#11711yescharacteristic
657C2×C4C2×C4×D411yescharacteristic
658C2×C4#52011yescharacteristic
659C2×C4#52011yescharacteristic
660C2×C4C2×#12111yescharacteristic
661C2×C4C2×#12311yescharacteristic
662C2×C4#52511yescharacteristic
663C2×C4#52511yescharacteristic
664C2×C4#52511yescharacteristic
665C2×C4#52511yescharacteristic
666C2×C4#53511yescharacteristic
667C2×C4#53611yescharacteristic
668C2×C4#53711yescharacteristic
669C2×C4#53711yescharacteristic
670C2×C4#54611yescharacteristic
671C2×C4#54711yescharacteristic
672C2×C4#54811yescharacteristic
673C2×C4#55011yescharacteristic
674C2×C4#55211yescharacteristic
675C2×C4#55211yescharacteristic
676C2×C4#55311yescharacteristic
677C2×C4#55311yescharacteristic
678C2×C4#55511yescharacteristic
679C2×C4#55511yescharacteristic
680C2×C4#55611yescharacteristic
681C2×C4#55611yescharacteristic
682C8—24no—
683C8—42no—
684C8—82no—
685C22—44no—
686C22—44no—
687C22—44no—
688C22—82no—
689C22—82no—
690C22—82no—
691C22—82no—
692C22—82no—
693C22—82no—
694C22—82no—
695C22—82no—
696C22—82no—
697C22—82no—
698C22—82no—
699C22—82no—
700C22C2×#38611yescharacteristic
701C22#235211yescharacteristic
702C22#235411yescharacteristic
703C22#240711yescharacteristic
704C22#240711yescharacteristic
705C22#241411yescharacteristic
706C22#241511yescharacteristic
707C22C2×C4×SD1611yescharacteristic
708C22C2×#44011yescharacteristic
709C22#295111yescharacteristic
710C22#295211yescharacteristic
711C22C2×#45011yescharacteristic
712C22C2×#45211yescharacteristic
713C22#301211yescharacteristic
714C22#301311yescharacteristic
715C22C2×#46111yescharacteristic
716C22C2×#46311yescharacteristic
717C22#304511yescharacteristic
718C22#304611yescharacteristic
719C22#329811yescharacteristic
720C22#330511yescharacteristic
721C22#332911yescharacteristic
722C22#333211yescharacteristic
723C22#333511yescharacteristic
724C22#334011yescharacteristic
725C22#335311yescharacteristic
726C22#335711yescharacteristic
727C22#336211yescharacteristic
728C22#336411yescharacteristic
729C22#336811yescharacteristic
730C22#336911yescharacteristic
731C22#339211yescharacteristic
732C22#339411yescharacteristic
733C22#339811yescharacteristic
734C22#339911yescharacteristic
735C4—24no—
736C4—44no—
737C4—44no—
738C4—44no—
739C4—82no—
740C4—84no—
741C4—82no—
742C4—162no—
743C4#187718yes—
744C4#228011yescharacteristic
745C4#231111yescharacteristic
746C4#235211yescharacteristic
747C4#235411yescharacteristic
748C4#241411yescharacteristic
749C4#241511yescharacteristic
750C4#248511yescharacteristic
751C4#248511yescharacteristic
752C2—84no—
753C2#1387111yescharacteristic
754C2C2×#187711yescharacteristic
755C2#2093711yescharacteristic
756C2#2275911yescharacteristic
757C2#2276711yescharacteristic
758C2#2280511yescharacteristic
759C2#2281111yescharacteristic
760C2#2412011yescharacteristic
761C2#2412111yescharacteristic
762C2#2418811yescharacteristic
763C2#2418911yescharacteristic
764C2#2463011yescharacteristic
765C2#2463111yescharacteristic
766C2#2468011yescharacteristic
767C2#2468111yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#1803C2semidirect
5. #13926C2semidirect
8. #10932C2semidirect
9. #10908C2semidirect
10. #10841C2semidirect
11. #10834C2semidirect
18. C2×C4×SD16C4semidirect
264. C2×C4⋊C4SD16semidirect
353. C2×Q8#117semidirect
487. C2×C8#117semidirect

Maximal subgroups

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

subgroupindex
C22×C4×SD162
C2×#23542
C2×#18032
C2×#18022
#139262
#111892
#110232
#109322
#109082
#108412
#108342