Finite Group Databasebeta

← #217111

Subgroups — #217111

Order 512.

866 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34974C211yesmaximal, characteristic
2#21974C211yesmaximal, characteristic, complemented
3C4×#433C211yesmaximal, characteristic, complemented
4#9877C211yesmaximal, characteristic, complemented
5#9870C211yesmaximal, characteristic, complemented
6#9646C211yesmaximal, characteristic, complemented
7#9639C211yesmaximal, characteristic, complemented
8#8944C211yesmaximal, characteristic
9#8942C211yesmaximal, characteristic, complemented
10#8940C211yesmaximal, characteristic
11#8938C211yesmaximal, characteristic, complemented
12#8569C211yesmaximal, characteristic, complemented
13#8567C211yesmaximal, characteristic, complemented
14#8566C211yesmaximal, characteristic, complemented
15#8564C211yesmaximal, characteristic, complemented
16C2×#433—21no—
17C2×#431C2211yescharacteristic
18C2×#423C2211yescharacteristic
19#2532—21no—
20#2529—21no—
21#2512C411yescharacteristic
22#2508C411yescharacteristic
23#2495C411yescharacteristic
24#2491C411yescharacteristic
25#2479—21no—
26#2474—21no—
27#2451C411yescharacteristic
28#2448C411yescharacteristic
29#2426C411yescharacteristic
30#2423C411yescharacteristic
31#2396—21no—
32#2395—21no—
33C4×C4⋊Q8C2211yescharacteristic
34C4×#126—21no—
35C4×#124—21no—
36C4×#124C2211yescharacteristic
37C4×C22⋊Q8C2211yescharacteristic
38C4×#121C2211yescharacteristic
39#2293C2211yescharacteristic
40C42×Q8C2211yescharacteristic
41C4×#117C2211yescharacteristic
42#1939—21no—
43#1939—21no—
44#1851—21no—
45#1851—21no—
46#1842C2211yescharacteristic
47#1842C2211yescharacteristic
48#1831C2211yescharacteristic
49#1831C2211yescharacteristic
50#1768—21no—
51C4×C4⋊C8C2211yescharacteristic
52C4×C4⋊C8C2211yescharacteristic
53#1750—21no—
54C4×C22⋊C8C2211yescharacteristic
55C4×C22⋊C8C2211yescharacteristic
56#1746—21no—
57C4×#97C2211yescharacteristic
58C42×C8C2211yescharacteristic
59C2×Q8⋊C8C2211yescharacteristic
60C2×Q8⋊C8C2211yescharacteristic
61C2×Q8⋊C8C2211yescharacteristic
62C2×Q8⋊C8C2211yescharacteristic
63C2×D4⋊C8C2211yescharacteristic
64C2×D4⋊C8C2211yescharacteristic
65C2×D4⋊C8C2211yescharacteristic
66C2×D4⋊C8C2211yescharacteristic
67#1279C2211yescharacteristic
68#1279C2211yescharacteristic
69#1279C2211yescharacteristic
70#1279C2211yescharacteristic
71#1279C2211yescharacteristic
72#1279C2211yescharacteristic
73#1279C2211yescharacteristic
74#1279C2211yescharacteristic
75C22×M16—21no—
76C2×C4⋊Q8C2×C411yescharacteristic
77C2×#126—21no—
78C2×#124—21no—
79C2×#124C2×C411yescharacteristic
80C2×C22⋊Q8C2×C411yescharacteristic
81C2×#121C2×C411yescharacteristic
82C2×C4×Q8—21no—
83C2×C4×Q8C2×C411yescharacteristic
84C2×C4×Q8C2×C411yescharacteristic
85C2×C4×Q8C2311yescharacteristic
86C2×C4×D4—21no—
87C2×C4×D4C2311yescharacteristic
88C2×#117—21no—
89C2×#117D411yescharacteristic
90C2×#117D411yescharacteristic
91C22×C42C2311yescharacteristic
92#433—28no—
93#431—41no—
94#431—41no—
95#423—41no—
96#423—41no—
97C2×C4⋊C8—21no—
98C2×C4⋊C8—21no—
99C2×C4⋊C8—21no—
100C2×C4⋊C8—21no—
101C2×C4⋊C8—21no—
102C2×C4⋊C8—21no—
103C2×C4⋊C8—21no—
104C2×C4⋊C8C2311yescharacteristic
105C2×C4⋊C8C2311yescharacteristic
106C2×C4⋊C8C2311yescharacteristic
107C2×C4⋊C8C2311yescharacteristic
108C2×C22⋊C8—21no—
109C2×C22⋊C8—21no—
110C2×C22⋊C8—21no—
111C2×#97—21no—
112C2×#97—21no—
113C2×C4×C8—21no—
114C2×C4×C8—21no—
115C2×C4×C8—21no—
116C2×C4×C8C2311yescharacteristic
117C2×C4×C8C2311yescharacteristic
118C2×C4×C8C2311yescharacteristic
119C2×C4×C8C2311yescharacteristic
120#400—21no—
121#400—21no—
122#399—21no—
123#399—21no—
124#398—21no—
125#398—21no—
126#398—21no—
127#397—21no—
128#397—21no—
129#397—21no—
130#396—21no—
131#396—21no—
132#395—21no—
133#394—21no—
134#394—21no—
135#393—21no—
136#391—21no—
137#391—21no—
138#391C2×C411yescharacteristic
139#391C2×C411yescharacteristic
140#390—21no—
141#390C2×C411yescharacteristic
142#390C2×C411yescharacteristic
143#390C2×C411yescharacteristic
144#390C2×C411yescharacteristic
145#389—21no—
146#389C2×C411yescharacteristic
147#389C2×C411yescharacteristic
148#389C2×C411yescharacteristic
149#389C2×C411yescharacteristic
150#389C2×C411yescharacteristic
151#389C2×C411yescharacteristic
152#388—21no—
153#388—21no—
154#388—21no—
155#388—21no—
156#388—21no—
157#388—21no—
158#388—21no—
159#388—21no—
160#388—21no—
161#388—21no—
162#388—21no—
163#388—21no—
164#387—21no—
165#387—21no—
166#387—21no—
167#387—21no—
168#386—21no—
169#385—21no—
170#384C2×C411yescharacteristic
171#383—21no—
172#382—21no—
173#382C2×C411yescharacteristic
174#380C2×C411yescharacteristic
175#380C2×C411yescharacteristic
176C4×C4⋊C4—21no—
177C4×C4⋊C4—21no—
178C4×C4⋊C4—21no—
179C4×C4⋊C4—21no—
180C4×C4⋊C4—21no—
181C4×C4⋊C4C2×C411yescharacteristic
182C4×C4⋊C4C2×C411yescharacteristic
183C4×C4⋊C4C2×C411yescharacteristic
184C4×C4⋊C4C2×C411yescharacteristic
185C4×C4⋊C4D411yescharacteristic
186C4×C4⋊C4D411yescharacteristic
187C4×C4⋊C4C2311yescharacteristic
188C4×C4⋊C4C2311yescharacteristic
189C4×C22⋊C4—21no—
190C4×C22⋊C4—21no—
191C4×C22⋊C4—21no—
192C4×C22⋊C4—21no—
193C4×C22⋊C4—21no—
194C4×C22⋊C4C2×C411yescharacteristic
195C4×C22⋊C4C2×C411yescharacteristic
196C4×C22⋊C4D411yescharacteristic
197C4×C22⋊C4D411yescharacteristic
198#376D411yescharacteristic
199#376D411yescharacteristic
200C43—21no—
201C43C2311yescharacteristic
202C43C2311yescharacteristic
203#336—21no—
204#336—21no—
205#336—21no—
206#336—21no—
207#336—21no—
208#336—21no—
209#336—21no—
210#336—21no—
211Q8⋊C8—41no—
212Q8⋊C8—41no—
213Q8⋊C8—41no—
214Q8⋊C8—41no—
215D4⋊C8—41no—
216D4⋊C8—41no—
217D4⋊C8—41no—
218D4⋊C8—41no—
219C22×Q8—21no—
220C22×Q8C22×C411yescharacteristic
221C22×D4—21no—
222C22×D4C22×C411yescharacteristic
223C23×C4—21no—
224C23×C4C22×C411yescharacteristic
225C23×C4C2×D411yescharacteristic
226C23×C4C2×D411yescharacteristic
227C2×M16—42no—
228C2×M16—81no—
229C2×M16—81no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C4⋊Q8—22no—
239C4⋊Q8—41no—
240#126—44no—
241#124—22no—
242#124—41no—
243#124—44no—
244C22⋊Q8—22no—
245C22⋊Q8—41no—
246#121—22no—
247#121—41no—
248C4×Q8—22no—
249C4×Q8—22no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×Q8—21no—
253C4×Q8—21no—
254C4×Q8—41no—
255C4×Q8—41no—
256C4×Q8—81no—
257C4×Q8—81no—
258C4×D4—21no—
259C4×D4—21no—
260C4×D4—21no—
261C4×D4—21no—
262C4×D4—81no—
263C4×D4—81no—
264#117—24no—
265#117—42no—
266#117—81no—
267#117—81no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4C22⋊C411yescharacteristic
282C2×C4⋊C4C22⋊C411yescharacteristic
283C2×C4⋊C4C22⋊C411yescharacteristic
284C2×C4⋊C4C22⋊C411yescharacteristic
285C2×C4⋊C4C22×C411yescharacteristic
286C2×C4⋊C4C22×C411yescharacteristic
287C2×C4⋊C4C22×C411yescharacteristic
288C2×C4⋊C4C22×C411yescharacteristic
289C2×C4⋊C4C22×C411yescharacteristic
290C2×C4⋊C4C22×C411yescharacteristic
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—21no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4C22⋊C411yescharacteristic
307C2×C22⋊C4C22⋊C411yescharacteristic
308C2×C22⋊C4C22⋊C411yescharacteristic
309C2×C22⋊C4C22⋊C411yescharacteristic
310C2×C42—21no—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—21no—
314C2×C42—21no—
315C2×C42—21no—
316C2×C42—21no—
317C2×C42—21no—
318C2×C42—21no—
319C2×C42—21no—
320C2×C42—21no—
321C2×C42C22×C411yescharacteristic
322C2×C42C22×C411yescharacteristic
323C2×C42C22×C411yescharacteristic
324C2×C42C22×C411yescharacteristic
325C2×C42C22×C411yescharacteristic
326C2×C42C2×D411yescharacteristic
327C2×C42C2×D411yescharacteristic
328C2×C42C2×D411yescharacteristic
329C2×C42C2×D411yescharacteristic
330C2×C42C2×D411yescharacteristic
331C2×C42C2×D411yescharacteristic
332C2×C42C2×D411yescharacteristic
333C2×C42C2×D411yescharacteristic
334C2×C42C2×D411yescharacteristic
335C2×C42C2×D411yescharacteristic
336C2×C42C2411yescharacteristic
337C4⋊C8—24no—
338C4⋊C8—24no—
339C4⋊C8—21no—
340C4⋊C8—21no—
341C4⋊C8—21no—
342C4⋊C8—21no—
343C4⋊C8—21no—
344C4⋊C8—21no—
345C4⋊C8—21no—
346C4⋊C8—21no—
347C4⋊C8—42no—
348C4⋊C8—81no—
349C4⋊C8—81no—
350C4⋊C8—81no—
351C4⋊C8—81no—
352C22⋊C8—24no—
353C22⋊C8—24no—
354C22⋊C8—42no—
355#97—24no—
356#97—42no—
357C4×C8—24no—
358C4×C8—21no—
359C4×C8—21no—
360C4×C8—21no—
361C4×C8—21no—
362C4×C8—21no—
363C4×C8—21no—
364C4×C8—21no—
365C4×C8—21no—
366C4×C8—42no—
367C4×C8—42no—
368#95—21no—
369#95—21no—
370#95—21no—
371#95—21no—
372#95—21no—
373#95—21no—
374#95—21no—
375#95—21no—
376#95—21no—
377#95—21no—
378#95—21no—
379#95—21no—
380#95—21no—
381#95—21no—
382#95—21no—
383#95—21no—
384#95—21no—
385#95—21no—
386#95C22⋊C411yescharacteristic
387#95C22⋊C411yescharacteristic
388#95C22⋊C411yescharacteristic
389#95C22⋊C411yescharacteristic
390#95C22⋊C411yescharacteristic
391#95C22⋊C411yescharacteristic
392#95C22⋊C411yescharacteristic
393#95C22⋊C411yescharacteristic
394C24—21no—
395C24C2×C22⋊C411yescharacteristic
396C2×Q8—21no—
397C2×Q8—21no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—42no—
402C2×Q8—42no—
403C2×Q8—81no—
404C2×Q8#13112yes—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—42no—
412C2×D4—42no—
413C2×D4—81no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4C2×C22⋊C411yescharacteristic
444C22×C4C2×C22⋊C411yescharacteristic
445C22×C4C2×C22⋊C411yescharacteristic
446C22×C4C2×C22⋊C411yescharacteristic
447C22×C4C2×C22⋊C411yescharacteristic
448C22×C4C2×C22⋊C411yescharacteristic
449C22×C4C2×C22⋊C411yescharacteristic
450C22×C4C2×C22⋊C411yescharacteristic
451C22×C4C2×C22⋊C411yescharacteristic
452C22×C4C2×C22⋊C411yescharacteristic
453C22×C4C2×C22⋊C411yescharacteristic
454C22×C4C23×C411yescharacteristic
455C22×C4C22×D411yescharacteristic
456C22×C4C22×D411yescharacteristic
457M16—84no—
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—41no—
463C2×C8—41no—
464C2×C8—41no—
465C2×C8—41no—
466C2×C8—41no—
467C2×C8—41no—
468C2×C8—41no—
469C2×C8—41no—
470C2×C8—41no—
471C2×C8—41no—
472C2×C8—41no—
473C2×C8—41no—
474C2×C8—41no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C4⋊C4—21no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—41no—
496C4⋊C4—42no—
497C4⋊C4—42no—
498C4⋊C4—42no—
499C4⋊C4—42no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4—42no—
503C4⋊C4—42no—
504C4⋊C4—81no—
505C4⋊C4—81no—
506C4⋊C4—81no—
507C4⋊C4—81no—
508C4⋊C4—81no—
509C4⋊C4—81no—
510C4⋊C4#10414yes—
511C4⋊C4#13112yes—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—41no—
516C22⋊C4—42no—
517C22⋊C4—42no—
518C22⋊C4—42no—
519C22⋊C4—42no—
520C22⋊C4—42no—
521C22⋊C4—42no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—42no—
525C22⋊C4—42no—
526C22⋊C4—42no—
527C22⋊C4—42no—
528C22⋊C4—81no—
529C22⋊C4—81no—
530C22⋊C4—81no—
531C22⋊C4—81no—
532C42—21no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—21no—
553C42—21no—
554C42—22no—
555C42—22no—
556C42—22no—
557C42—41no—
558C42—42no—
559C42—42no—
560C42—42no—
561C42—41no—
562C42—41no—
563C42—41no—
564C42—41no—
565C42—41no—
566C42—41no—
567C42—42no—
568C42H(5,𝔽2)11yescharacteristic
569C42H(5,𝔽2)11yescharacteristic
570C422−1+411yescharacteristic
571C422−1+411yescharacteristic
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23C22×C22⋊C411yescharacteristic
587Q8—22no—
588Q8—22no—
589Q8—41no—
590Q8—41no—
591Q8—84no—
592D4—41no—
593D4—41no—
594D4—41no—
595D4—41no—
596D4—84no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—81no—
660C2×C4—81no—
661C2×C4—81no—
662C2×C4—81no—
663C2×C4C2×#10412yes—
664C2×C4C2×#10412yes—
665C2×C4C2×#10412yes—
666C2×C4#42112yes—
667C2×C4#52011yescharacteristic
668C2×C4#52011yescharacteristic
669C2×C4#53511yescharacteristic
670C2×C4#53611yescharacteristic
671C2×C4#53711yescharacteristic
672C2×C4#53711yescharacteristic
673C2×C4C2×#13111yescharacteristic
674C2×C4C2×#13111yescharacteristic
675C2×C4#56811yescharacteristic
676C2×C4#56811yescharacteristic
677C2×C4#57611yescharacteristic
678C2×C4#57711yescharacteristic
679C2×C4#57711yescharacteristic
680C2×C4#57811yescharacteristic
681C8—42no—
682C8—42no—
683C8—42no—
684C8—42no—
685C8—81no—
686C8—81no—
687C8—81no—
688C8—81no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—81no—
697C22—81no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22—81no—
703C22#231111yescharacteristic
704C22#288011yescharacteristic
705C22#288011yescharacteristic
706C22#289711yescharacteristic
707C22#289811yescharacteristic
708C22C22×#10411yescharacteristic
709C22C2×#42111yescharacteristic
710C4—21no—
711C4—21no—
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—41no—
717C4—42no—
718C4—41no—
719C4—41no—
720C4—41no—
721C4—41no—
722C4—42no—
723C4—41no—
724C4—41no—
725C4—81no—
726C4—81no—
727C4—81no—
728C4—81no—
729C4—81no—
730C4#299211yescharacteristic
731C4#299311yescharacteristic
732C4#299411yescharacteristic
733C4#299511yescharacteristic
734C4#322411yescharacteristic
735C4#322511yescharacteristic
736C4#324311yescharacteristic
737C4#324411yescharacteristic
738C2—81no—
739C2—161no—
740C2#1751911yescharacteristic
741C2#1752011yescharacteristic
742C2#1752111yescharacteristic
743C2#1752511yescharacteristic
744C2#2185511yescharacteristic
745C2#2185611yescharacteristic
746C2#2187111yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
socleC23C22×C22⋊C4
prime radicalC2×#121C2×C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C4×#117 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #21974C2semidirect
3. C4×#433C2semidirect
4. #9877C2semidirect
5. #9870C2semidirect
6. #9646C2semidirect
7. #9639C2semidirect
9. #8942C2semidirect
11. #8938C2semidirect
12. #8569C2semidirect
13. #8567C2semidirect
14. #8566C2semidirect
15. #8564C2semidirect

Maximal subgroups

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

subgroupindex
#349742
#219742
C4×#4332
#98772
#98702
#96462
#96392
#89442
#89422
#89402
#89382
#85692
#85672
#85662
#85642