Finite Group Databasebeta

← #28610347

Subgroups — #28610347

Order 15104.

730 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21434005C211yesmaximal, characteristic
2#21432823C211yesmaximal, characteristic
3#21432756C211yesmaximal, characteristic, complemented
4#21424848C211yesmaximal, characteristic, complemented
5#21424797C211yesmaximal, characteristic, complemented
6#21424747C211yesmaximal, characteristic, complemented
7#21424698C211yesmaximal, characteristic, complemented
8#21424693C211yesmaximal, characteristic, complemented
9#21424369C211yesmaximal, characteristic, complemented
10#21424300C211yesmaximal, characteristic, complemented
11#21423974C211yesmaximal, characteristic, complemented
12#21423941C211yesmaximal, characteristic, complemented
13#21423862C211yesmaximal, characteristic, complemented
14#21423806C211yesmaximal, characteristic, complemented
15C59×#1897C211yesmaximal, characteristic
16C2×#14273734C2211yescharacteristic
17C22×#11745664C2211yescharacteristic
18C2×#14273686C2211yescharacteristic
19#16837740C411yescharacteristic, complemented
20#16837740C411yescharacteristic, complemented
21#16837735C411yescharacteristic, complemented
22#16837730C411yescharacteristic, complemented
23#16837723C411yescharacteristic, complemented
24#16837723C411yescharacteristic, complemented
25#16837718C411yescharacteristic, complemented
26#16837713C411yescharacteristic, complemented
27#16837480—21no—
28#16837474—21no—
29#16837474—21no—
30D4×C59⋊C8—21no—
31#16837460—21no—
32#16837460—21no—
33#16837456—21no—
34#16837452—21no—
35C2×#14273662C2211yescharacteristic
36C2×#14273662C2211yescharacteristic
37#16837438C2211yescharacteristic
38#16837438C2211yescharacteristic
39#16837430C2211yescharacteristic
40#16837430C2211yescharacteristic
41#16837429C2211yescharacteristic
42#16837398C2211yescharacteristic
43#16837398C2211yescharacteristic
44#16837369C2211yescharacteristic
45C2×C22⋊(C59⋊C8)C2211yescharacteristic
46C2×C22⋊(C59⋊C8)C2211yescharacteristic
47#16837360C2211yescharacteristic
48#16837360C2211yescharacteristic
49#16837358C2211yescharacteristic
50C2×#14273638C2211yescharacteristic
51C2×C4×C59⋊C8C2211yescharacteristic
52#16837166C2211yescharacteristic
53#16837166C2211yescharacteristic
54#16837162C2211yescharacteristic
55#16837162C2211yescharacteristic
56#16837162C2211yescharacteristic
57#16837162C2211yescharacteristic
58#16837157C2211yescharacteristic
59#16837157C2211yescharacteristic
60C59×#525C2211yescharacteristic
61C2×#117×C59C2211yescharacteristic
62C2×#104×C59C2211yescharacteristic
63C2×#104×C59C2211yescharacteristic
64C59×#407C2211yescharacteristic
65C59×#339C2211yescharacteristic
66C59×#339C2211yescharacteristic
67#14273734—22no—
68#14273734—41no—
69C2×#11745664—21no—
70C2×#11745664—21no—
71C2×#11745664—22no—
72C2×#11745664—41no—
73C2×#11745664C2311yescharacteristic
74C2×#11745664C2311yescharacteristic
75C22×C59⋊C8—21no—
76C22×C59⋊C8—21no—
77C22×C59⋊C8C2311yescharacteristic
78C22×C59⋊C8C2311yescharacteristic
79C22×C59⋊C8C2311yescharacteristic
80C22×C59⋊C8C2311yescharacteristic
81#14273686—21no—
82#14273686—21no—
83#14273686C2×C411yescharacteristic
84#14273686C2×C411yescharacteristic
85#14273686C2311yescharacteristic
86#14273686C2311yescharacteristic
87C2×C4⋊Dic59C2×C411yescharacteristic
88C2×C4⋊Dic59C2×C411yescharacteristic
89C2×C22⋊Dic59—21no—
90C2×C4×Dic59—21no—
91#14273662—22no—
92#14273662—41no—
93#14273660C2×C411yescharacteristic
94#14273660C2×C411yescharacteristic
95#14273660C2×C411yescharacteristic
96#14273660C2×C411yescharacteristic
97#14273658C2×C411yescharacteristic
98#14273658C2×C411yescharacteristic
99#14273658C2×C411yescharacteristic
100#14273658C2×C411yescharacteristic
101C4⋊(C59⋊C8)—21no—
102C4⋊(C59⋊C8)—21no—
103Dic59⋊C8—21no—
104Dic59⋊C8—21no—
105Dic59⋊C8—21no—
106Dic59⋊C8—21no—
107#14273651C2×C411yescharacteristic
108#14273651C2×C411yescharacteristic
109#14273651C2×C411yescharacteristic
110#14273651C2×C411yescharacteristic
111#14273648C2×C411yescharacteristic
112#14273648C2×C411yescharacteristic
113#14273648C2×C411yescharacteristic
114#14273648C2×C411yescharacteristic
115C22⋊(C59⋊C8)—21no—
116C22⋊(C59⋊C8)—21no—
117C22⋊(C59⋊C8)C2×C411yescharacteristic
118C22⋊(C59⋊C8)C2×C411yescharacteristic
119C22⋊(C59⋊C8)C2×C411yescharacteristic
120C22⋊(C59⋊C8)C2×C411yescharacteristic
121C22⋊(C59⋊C8)D411yescharacteristic
122C22⋊(C59⋊C8)D411yescharacteristic
123C22⋊(C59⋊C8)D411yescharacteristic
124C22⋊(C59⋊C8)D411yescharacteristic
125#14273638—21no—
126#14273638—41no—
127#14273637—21no—
128#14273637—21no—
129C4×C59⋊C8—22no—
130C4×C59⋊C8—21no—
131C8×Dic59—21no—
132C8×Dic59—21no—
133C2×#41×C59C2311yescharacteristic
134C23×C4×C59C2311yescharacteristic
135C2×M16×C59C2311yescharacteristic
136C2×M16×C59C2311yescharacteristic
137#123×C59—21no—
138C22⋊Q8×C59C2×C411yescharacteristic
139C22⋊Q8×C59C2×C411yescharacteristic
140#121×C59C2×C411yescharacteristic
141#121×C59C2×C411yescharacteristic
142#120×C59—21no—
143C4×D4×C59—21no—
144C4×D4×C59—21no—
145#117×C59—22no—
146#117×C59—41no—
147#117×C59C2311yescharacteristic
148C2×C4⋊C4×C59—21no—
149C2×C22⋊C4×C59—21no—
150C2×C42×C59C2311yescharacteristic
151C2×C42×C59C2311yescharacteristic
152#104×C59—22no—
153#104×C59—41no—
154C22⋊C8×C59—21no—
155C22⋊C8×C59—21no—
156C24×C59#4111yescharacteristic
157#41×C59—21no—
158#41×C59—21no—
159#41×C59—21no—
160#41×C59—21no—
161C2×Q8×C59C22×C411yescharacteristic
162C2×D4×C59—21no—
163C2×D4×C59—21no—
164C2×D4×C59—21no—
165C2×D4×C59C22×C411yescharacteristic
166C22×C4×C59—21no—
167C22×C4×C59—21no—
168C22×C4×C59—21no—
169C22×C4×C59—21no—
170C22×C4×C59—21no—
171C22×C4×C59—21no—
172C22×C4×C59—21no—
173C22×C4×C59C22×C411yescharacteristic
174C22×C4×C59C22×C411yescharacteristic
175C22×C4×C59C2×D411yescharacteristic
176C22×C4×C59C2×D411yescharacteristic
177C22×C4×C59#4111yescharacteristic
178C22×C4×C59C2411yescharacteristic
179C22×Dic59—21no—
180C22×Dic59—21no—
181M16×C59—21no—
182M16×C59—21no—
183M16×C59—21no—
184M16×C59—21no—
185C2×C8×C59—21no—
186C2×C8×C59—21no—
187C4⋊C4×C59—21no—
188C4⋊C4×C59—21no—
189C4⋊C4×C59—42no—
190C4⋊C4×C59C22×C411yescharacteristic
191C4⋊C4×C59C22×C411yescharacteristic
192C22⋊C4×C59—21no—
193C22⋊C4×C59—21no—
194C22⋊C4×C59—21no—
195C22⋊C4×C59—21no—
196C22⋊C4×C59—21no—
197C22⋊C4×C59—42no—
198C42×C59—21no—
199C42×C59—21no—
200C42×C59—21no—
201C42×C59—21no—
202C42×C59#4112yes—
203C22⋊Dic59—21no—
204C22⋊Dic59—21no—
205C22⋊Dic59—21no—
206C22⋊Dic59—21no—
207C4⋊Dic59—21no—
208C4⋊Dic59—21no—
209C4⋊Dic59C22×C411yescharacteristic
210C4⋊Dic59C22×C411yescharacteristic
211C4⋊Dic59C22×C411yescharacteristic
212C4⋊Dic59C22×C411yescharacteristic
213C4×Dic59—21no—
214C4×Dic59—21no—
215C4×Dic59—21no—
216C4×Dic59—21no—
217#11745664—21no—
218#11745664—21no—
219#11745664—21no—
220#11745664—42no—
221#11745664—42no—
222#11745664#4112yes—
223C2×C59⋊C8—21no—
224C2×C59⋊C8—21no—
225C2×C59⋊C8—21no—
226C2×C59⋊C8—21no—
227C2×C59⋊C8—21no—
228C2×C59⋊C8—21no—
229C2×C59⋊C8—21no—
230C2×C59⋊C8—21no—
231C2×C59⋊C8—21no—
232C2×C59⋊C8—21no—
233C2×C59⋊C8—42no—
234C2×C59⋊C8—42no—
235C2×C59⋊C8C22×C411yescharacteristic
236C2×C59⋊C8C22×C411yescharacteristic
237C2×C59⋊C8C22×C411yescharacteristic
238C2×C59⋊C8C22×C411yescharacteristic
239C2×C59⋊C8C2×D411yescharacteristic
240C2×C59⋊C8C2×D411yescharacteristic
241C2×C59⋊C8C2×D411yescharacteristic
242C2×C59⋊C8C2×D411yescharacteristic
243C23×C59—21no—
244C23×C59—21no—
245C23×C59—21no—
246C23×C59—41no—
247C23×C59—41no—
248C23×C59C4×D411yescharacteristic
249C23×C59C4×D411yescharacteristic
250C23×C59C2×#4111yescharacteristic
251Q8×C59—21no—
252Q8×C59—21no—
253D4×C59—21no—
254D4×C59—21no—
255D4×C59—42no—
256D4×C59—41no—
257D4×C59—41no—
258D4×C59—81no—
259C2×C4×C59—21no—
260C2×C4×C59—21no—
261C2×C4×C59—21no—
262C2×C4×C59—21no—
263C2×C4×C59—21no—
264C2×C4×C59—21no—
265C2×C4×C59—21no—
266C2×C4×C59—21no—
267C2×C4×C59—21no—
268C2×C4×C59—21no—
269C2×C4×C59—21no—
270C2×C4×C59—21no—
271C2×C4×C59—21no—
272C2×C4×C59—22no—
273C2×C4×C59—41no—
274C2×C4×C59—41no—
275C2×C4×C59—41no—
276C2×C4×C59—41no—
277C2×C4×C59—41no—
278C2×C4×C59—41no—
279C2×C4×C59—41no—
280C2×C4×C59C4×D411yescharacteristic
281C2×C4×C59C4×D411yescharacteristic
282C2×C4×C59C23×C411yescharacteristic
283C2×C4×C59C22×D411yescharacteristic
284C2×C4×C59C2×#4111yescharacteristic
285C2×C4×C59C2×#4111yescharacteristic
286C2×C4×C59H(5,𝔽2)11yescharacteristic
287C2×C4×C592−1+411yescharacteristic
288C2×Dic59—21no—
289C2×Dic59—21no—
290C2×Dic59—21no—
291C2×Dic59—21no—
292C2×Dic59—42no—
293C2×Dic59—81no—
294C8×C59—41no—
295C8×C59—41no—
296C59⋊C8—21no—
297C59⋊C8—21no—
298C59⋊C8—21no—
299C59⋊C8—21no—
300C59⋊C8—21no—
301C59⋊C8—21no—
302C59⋊C8—22no—
303C59⋊C8—21no—
304C59⋊C8—21no—
305C59⋊C8—41no—
306#22951—591nomaximal, Sylow
307C22×C59—21no—
308C22×C59—21no—
309C22×C59—21no—
310C22×C59—21no—
311C22×C59—21no—
312C22×C59—21no—
313C22×C59—21no—
314C22×C59—21no—
315C22×C59—41no—
316C22×C59—41no—
317C22×C59—41no—
318C22×C59—81no—
319C22×C59—81no—
320C22×C59C2×C4×D411yescharacteristic
321C22×C59#55111yescharacteristic
322C22×C59#55211yescharacteristic
323C4×C59—21no—
324C4×C59—21no—
325C4×C59—42no—
326C4×C59—41no—
327C4×C59—41no—
328C4×C59—41no—
329C4×C59—81no—
330C4×C59C4×#4111yescharacteristic
331C4×C59#52011yescharacteristic
332C4×C59#54611yescharacteristic
333C4×C59#54711yescharacteristic
334Dic59—41no—
335Dic59—41no—
336Dic59—41no—
337Dic59—41no—
338#3091—591no—
339#2933—591no—
340#2924—591no—
341#1946—591no—
342#1937—591no—
343#1929—591no—
344#1922—591no—
345#1922—591no—
346#1897D5911yescharacteristic
347#1866—591no—
348#1855—591no—
349#1772—591no—
350#1765—591no—
351#1750—591no—
352#1733—591no—
353C2×C59—21no—
354C2×C59—21no—
355C2×C59—41no—
356C2×C59—41no—
357C2×C59—81no—
358C2×C59#235911yescharacteristic
359C2×C59#295511yescharacteristic
360C2×C59#295711yescharacteristic
361C2×#131—591no—
362C22×M16—591no—
363#525C2×D5911yescharacteristic
364C2×#117—591no—
365C2×#117C2×D5911yescharacteristic
366#485—591no—
367#485—591no—
368#484—591no—
369#483—591no—
370#482—591no—
371#482—591no—
372#481—591no—
373#480—591no—
374#436—1181no—
375#435—1181no—
376#435—1181no—
377C8×D4—1181no—
378#433—1181no—
379#433—1181no—
380#432—1181no—
381#431—1181no—
382C2×#108—591no—
383C2×#108—591no—
384#427—591no—
385#427—591no—
386#424—591no—
387#424—591no—
388#424—591no—
389C2×#104C2×D5911yescharacteristic
390C2×#104C2×D5911yescharacteristic
391#416—591no—
392#416—591no—
393#408—591no—
394#407C2×D5911yescharacteristic
395C2×C22⋊C8—591no—
396C2×C22⋊C8—591no—
397#405—591no—
398#405—591no—
399#405—591no—
400C2×#97—591no—
401C2×C4×C8—591no—
402#341—591no—
403#341—591no—
404#339—591no—
405#339—591no—
406#339—591no—
407#339—591no—
408#339C2×D5911yescharacteristic
409#339C2×D5911yescharacteristic
410#336—591no—
411#336—591no—
412C59#2295111yescharacteristic, complemented, Sylow
413C2×#41C22×D5911yescharacteristic
414C23×C4C22×D5911yescharacteristic
415#131—1182no—
416#131—2361no—
417C2×M16—591no—
418C2×M16—591no—
419C2×M16—1181no—
420C2×M16—1181no—
421C2×M16—1182no—
422C2×M16—2361no—
423C2×M16C22×D5911yescharacteristic
424C2×M16C22×D5911yescharacteristic
425C22×C8—591no—
426C22×C8—591no—
427C22×C8—591no—
428C22×C8—591no—
429C22×C8—1181no—
430C22×C8—1181no—
431#123—21no—
432C22⋊Q8C4×D5911yescharacteristic
433C22⋊Q8C4×D5911yescharacteristic
434#121C4×D5911yescharacteristic
435#121C4×D5911yescharacteristic
436#120—21no—
437C4×D4—21no—
438C4×D4—21no—
439#117—22no—
440#117—41no—
441#117—591no—
442#117—591no—
443#117—591no—
444#117—591no—
445#117—1181no—
446#117—1181no—
447#117C22×D5911yescharacteristic
448C2×C4⋊C4—21no—
449C2×C4⋊C4—591no—
450C2×C4⋊C4—591no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—1181no—
453C2×C42—1181no—
454C2×C42C22×D5911yescharacteristic
455C2×C42C22×D5911yescharacteristic
456#108—1182no—
457#108—2361no—
458#107—591no—
459#107—591no—
460#107—591no—
461#107—591no—
462#106—591no—
463#106—591no—
464#106—591no—
465#106—591no—
466C4⋊C8—1181no—
467C4⋊C8—1181no—
468C4⋊C8—1181no—
469C4⋊C8—1181no—
470C4⋊C8—1181no—
471C4⋊C8—1181no—
472#104—22no—
473#104—41no—
474#103—591no—
475#103—591no—
476#103—591no—
477#103—591no—
478#102—591no—
479#102—591no—
480#102—591no—
481#102—591no—
482C22⋊C8—21no—
483C22⋊C8—21no—
484C22⋊C8—591no—
485C22⋊C8—591no—
486C22⋊C8—591no—
487C22⋊C8—591no—
488C22⋊C8—591no—
489C22⋊C8—591no—
490C22⋊C8—591no—
491C22⋊C8—591no—
492C22⋊C8—1181no—
493C22⋊C8—1181no—
494#97—1181no—
495#97—1181no—
496#97—1181no—
497#97—2361no—
498C4×C8—1181no—
499C4×C8—1181no—
500C4×C8—1181no—
501C4×C8—1182no—
502C24#1174568711yescharacteristic
503#41—21no—
504#41—21no—
505#41—21no—
506#41—21no—
507C2×Q8C2×C4×D5911yescharacteristic
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4C2×C4×D5911yescharacteristic
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—1181no—
520C22×C4—1181no—
521C22×C4C2×C4×D5911yescharacteristic
522C22×C4C2×C4×D5911yescharacteristic
523C22×C4D4×D5911yescharacteristic
524C22×C4D4×D5911yescharacteristic
525C22×C4#1174568711yescharacteristic
526C22×C4C23×D5911yescharacteristic
527M16—21no—
528M16—21no—
529M16—21no—
530M16—21no—
531M16—592no—
532M16—1181no—
533M16—1181no—
534M16—1181no—
535M16—2362no—
536M16—2362no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—591no—
540C2×C8—591no—
541C2×C8—591no—
542C2×C8—591no—
543C2×C8—591no—
544C2×C8—591no—
545C2×C8—591no—
546C2×C8—591no—
547C2×C8—1181no—
548C2×C8—1181no—
549C2×C8—1181no—
550C2×C8—1181no—
551C2×C8—1181no—
552C2×C8—1181no—
553C2×C8—1181no—
554C2×C8—1181no—
555C2×C8—1181no—
556C2×C8—1181no—
557C2×C8—2362no—
558C2×C8—2362no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—42no—
562C4⋊C4—591no—
563C4⋊C4—591no—
564C4⋊C4—591no—
565C4⋊C4—591no—
566C4⋊C4—1181no—
567C4⋊C4—1181no—
568C4⋊C4C2×C4×D5911yescharacteristic
569C4⋊C4C2×C4×D5911yescharacteristic
570C22⋊C4—21no—
571C22⋊C4—21no—
572C22⋊C4—21no—
573C22⋊C4—21no—
574C22⋊C4—21no—
575C22⋊C4—42no—
576C22⋊C4—1181no—
577C22⋊C4—1181no—
578C22⋊C4—1181no—
579C22⋊C4—1181no—
580C42—21no—
581C42—21no—
582C42—21no—
583C42—21no—
584C42—1181no—
585C42—1181no—
586C42—1181no—
587C42—1181no—
588C42#1174568712yes—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—41no—
593C23—41no—
594C23(C22⋊D59)⋊C411yescharacteristic
595C23(C22⋊D59)⋊C411yescharacteristic
596C23C2×#1174568711yescharacteristic
597Q8—21no—
598Q8—21no—
599D4—21no—
600D4—21no—
601D4—42no—
602D4—41no—
603D4—41no—
604D4—81no—
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—21no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—1181no—
627C2×C4—1181no—
628C2×C4—1181no—
629C2×C4—1181no—
630C2×C4—4721no—
631C2×C4—2362no—
632C2×C4(C22⋊D59)⋊C411yescharacteristic
633C2×C4(C22⋊D59)⋊C411yescharacteristic
634C2×C4C22×C4×D5911yescharacteristic
635C2×C4C2×D4×D5911yescharacteristic
636C2×C4#41×D5911yescharacteristic
637C2×C4C2×#1174568711yescharacteristic
638C2×C4#1427377211yescharacteristic
639C2×C4#1427377411yescharacteristic
640C8—41no—
641C8—41no—
642C8—1181no—
643C8—1181no—
644C8—1182no—
645C8—1181no—
646C8—1181no—
647C8—1181no—
648C8—1181no—
649C8—1181no—
650C8—1181no—
651C8—2361no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—21no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—81no—
664C22—81no—
665C22C2×(C22⋊D59)⋊C411yescharacteristic
666C22#1683808311yescharacteristic
667C22#1683808911yescharacteristic
668C4—21no—
669C4—21no—
670C4—42no—
671C4—41no—
672C4—41no—
673C4—41no—
674C4—81no—
675C4—2361no—
676C4—2361no—
677C4—2361no—
678C4—2361no—
679C4C4×#1174568711yescharacteristic
680C4#1683788111yescharacteristic
681C4#1683804111yescharacteristic
682C4#1683805211yescharacteristic
683C2—21no—
684C2—21no—
685C2—41no—
686C2—41no—
687C2—81no—
688C2#2142709411yescharacteristic
689C2#2143299511yescharacteristic
690C2#2143300911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#1897C2
socleC22×C59C2×C4×D4
prime radicalC59×#525C22
cosocleC22×C4×C59C24
hypercenter#1897D59
hypocenterC59#22951
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1897

Complements

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

NH ≅ G/Ntype
3. #21432756C2semidirect
4. #21424848C2semidirect
5. #21424797C2semidirect
6. #21424747C2semidirect
7. #21424698C2semidirect
8. #21424693C2semidirect
9. #21424369C2semidirect
10. #21424300C2semidirect
11. #21423974C2semidirect
12. #21423941C2semidirect
13. #21423862C2semidirect
14. #21423806C2semidirect
19. #16837740C4semidirect
20. #16837740C4semidirect
21. #16837735C4semidirect
22. #16837730C4semidirect
23. #16837723C4semidirect
24. #16837723C4semidirect
25. #16837718C4semidirect
26. #16837713C4semidirect
412. C59#22951semidirect

Maximal subgroups

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

subgroupindex
#214340052
#214328232
#214327562
#214248482
#214247972
#214247472
#214246982
#214246932
#214243692
#214243002
#214239742
#214239412
#214238622
#214238062
C59×#18972
#2295159