Finite Group Databasebeta

← C103×#20026 #39925301

Subgroups — C103×#20026 #39925301

Order 26368.

694 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3354C211yesmaximal, characteristic, complemented
2C103×#3303C211yesmaximal, characteristic, complemented
3C103×#3294C211yesmaximal, characteristic, complemented
4C103×#3272C211yesmaximal, characteristic, complemented
5C103×#1714C211yesmaximal, characteristic, complemented
6C103×#1703C211yesmaximal, characteristic, complemented
7C103×#1701C211yesmaximal, characteristic, complemented
8C103×#1671C211yesmaximal, characteristic, complemented
9C103×#1665C211yesmaximal, characteristic, complemented
10C103×#1647C211yesmaximal, characteristic, complemented
11C103×#1647C211yesmaximal, characteristic, complemented
12C103×#1629C211yesmaximal, characteristic, complemented
13C103×#1624C211yesmaximal, characteristic, complemented
14C103×#1586C211yesmaximal, characteristic, complemented
15C103×#1586C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C103—21no—
17#555×C103C2211yescharacteristic, complemented
18#547×C103C2211yescharacteristic
19#547×C103C2211yescharacteristic
20D42×C103C2211yescharacteristic
21#500×C103C2211yescharacteristic, complemented
22#498×C103C2211yescharacteristic, complemented
23#492×C103C2211yescharacteristic
24#492×C103C2211yescharacteristic
25#487×C103C2211yescharacteristic, complemented
26#486×C103C2211yescharacteristic
27#485×C103—21no—
28#482×C103—21no—
29#481×C103—21no—
30#480×C103—21no—
31#476×C103C2211yescharacteristic
32#476×C103C2211yescharacteristic
33#474×C103C2211yescharacteristic
34#474×C103C2211yescharacteristic, complemented
35#469×C103—21no—
36#468×C103—21no—
37#466×C103—21no—
38#465×C103—21no—
39#461×C103C2211yescharacteristic
40#461×C103C2211yescharacteristic, complemented
41#459×C103C2211yescharacteristic
42#459×C103C2211yescharacteristic
43#450×C103—21no—
44#449×C103—21no—
45#449×C103—21no—
46#447×C103—21no—
47C4×D8×C103C2211yescharacteristic
48C4×D8×C103C2211yescharacteristic
49#436×C103C2211yescharacteristic
50#436×C103C2211yescharacteristic, complemented
51C8×D4×C103C2211yescharacteristic
52C8×D4×C103C2211yescharacteristic, complemented
53#428×C103—21no—
54#416×C103—21no—
55C2×#102×C103—21no—
56#334×C103C2211yescharacteristic, complemented
57#334×C103C2211yescharacteristic, complemented
58#333×C103C2211yescharacteristic, complemented
59#332×C103C2211yescharacteristic, complemented
60#332×C103C2211yescharacteristic, complemented
61#331×C103C2211yescharacteristic
62D4⋊C8×C103C2211yescharacteristic
63D4⋊C8×C103C2211yescharacteristic
64D4⋊C8×C103C2211yescharacteristic, complemented
65D4⋊C8×C103C2211yescharacteristic, complemented
66#322×C103C2211yescharacteristic, complemented
67C2×#41×C103—21no—
68C2×#41×C103—21no—
69C22×D4×C103—21no—
70C22×D4×C103—21no—
71AGL(1,ℤ/8)×C103—44no—
72C2×SD16×C103—21no—
73C2×SD16×C103—21no—
74C2×SD16×C103—21no—
75C2×SD16×C103—21no—
76C2×SD16×C103—41no—
77C2×D8×C103—21no—
78C2×D8×C103—21no—
79C2×D8×C103D411yescharacteristic
80C2×D8×C103D411yescharacteristic
81C2×M16×C103—21no—
82C2×M16×C103—21no—
83C22×C8×C103—21no—
84C22×C8×C103—21no—
85C4⋊Q8×C103C2311yescharacteristic
86C4⋊Q8×C103C2311yescharacteristic
87C4⋊Q8×C103C2311yescharacteristic
88#127×C103C2311yescharacteristic
89#124×C103—41no—
90#123×C103—41no—
91#123×C103—41no—
92C22⋊Q8×C103—21no—
93C22⋊Q8×C103—21no—
94#121×C103—21no—
95#121×C103—21no—
96#121×C103—21no—
97#121×C103—21no—
98#121×C103—21no—
99#121×C103—21no—
100#120×C103—41no—
101C4×D4×C103C2311yescharacteristic
102C4×D4×C103C2311yescharacteristic
103C4×D4×C103C2311yescharacteristic
104C4×D4×C103C2311yescharacteristic
105#117×C103—21no—
106#117×C103—21no—
107C2×C4⋊C4×C103—21no—
108C2×C4⋊C4×C103—21no—
109#107×C103—21no—
110#107×C103—21no—
111#107×C103—41no—
112#107×C103D411yescharacteristic
113#107×C103D411yescharacteristic
114#106×C103—21no—
115#106×C103—21no—
116#106×C103—21no—
117#106×C103—21no—
118C4⋊C8×C103C2311yescharacteristic
119C4⋊C8×C103C2311yescharacteristic
120C4⋊C8×C103C2311yescharacteristic
121C4⋊C8×C103C2311yescharacteristic
122#103×C103—21no—
123#103×C103—21no—
124#103×C103—21no—
125#103×C103—21no—
126#102×C103—21no—
127#102×C103—21no—
128#102×C103—21no—
129#102×C103—21no—
130#102×C103—21no—
131#102×C103—21no—
132#102×C103—21no—
133#102×C103—21no—
134#102×C103D411yescharacteristic
135#102×C103D411yescharacteristic
136#102×C103D411yescharacteristic
137#102×C103D411yescharacteristic
138C22⋊C8×C103—21no—
139C22⋊C8×C103—21no—
140C22⋊C8×C103—21no—
141C22⋊C8×C103—21no—
142C4×C8×C103C2311yescharacteristic
143C4×C8×C103C2311yescharacteristic
144C4×C8×C103C2311yescharacteristic
145C24×C103—41no—
146#41×C103—42no—
147#41×C103—42no—
148#41×C103—81no—
149#41×C103—81no—
150C2×Q8×C103—21no—
151C2×Q8×C103—21no—
152C2×Q8×C103—21no—
153C2×D4×C103—21no—
154C2×D4×C103—21no—
155C2×D4×C103—21no—
156C2×D4×C103—41no—
157C2×D4×C103—41no—
158C2×D4×C103—42no—
159C2×D4×C103—42no—
160C2×D4×C103—41no—
161C2×D4×C103—41no—
162C2×D4×C103—41no—
163C2×D4×C103—81no—
164C2×D4×C103—81no—
165C2×D4×C103C2×D411yescharacteristic
166C2×D4×C103C2×D411yescharacteristic
167C2×D4×C103C2×D411yescharacteristic
168C2×D4×C103C2×D411yescharacteristic
169C22×C4×C103—21no—
170C22×C4×C103—21no—
171C22×C4×C103—21no—
172C22×C4×C103—21no—
173C22×C4×C103—41no—
174C22×C4×C103—41no—
175SD16×C103—42no—
176SD16×C103—42no—
177SD16×C103—81no—
178SD16×C103—82no—
179SD16×C103—81no—
180D8×C103—22no—
181D8×C103—41no—
182D8×C103—42no—
183D8×C103—81no—
184M16×C103—42no—
185M16×C103—42no—
186C2×C8×C103—21no—
187C2×C8×C103—21no—
188C2×C8×C103—21no—
189C2×C8×C103—21no—
190C2×C8×C103—21no—
191C2×C8×C103—81no—
192C2×C8×C103—81no—
193C2×C8×C103C2×D411yescharacteristic
194C2×C8×C103C2×D411yescharacteristic
195C2×C8×C103C2×D411yescharacteristic
196C2×C8×C103C2×D411yescharacteristic
197C4⋊C4×C103—21no—
198C4⋊C4×C103—21no—
199C4⋊C4×C103—21no—
200C4⋊C4×C103—21no—
201C4⋊C4×C103—21no—
202C4⋊C4×C103—21no—
203C4⋊C4×C103—41no—
204C4⋊C4×C103—41no—
205C4⋊C4×C103C2×D411yescharacteristic
206C4⋊C4×C103C2×D411yescharacteristic
207C4⋊C4×C103C2×D411yescharacteristic
208C4⋊C4×C103C2×D411yescharacteristic
209C22⋊C4×C103—21no—
210C22⋊C4×C103—21no—
211C22⋊C4×C103—21no—
212C22⋊C4×C103—21no—
213C22⋊C4×C103—41no—
214C22⋊C4×C103—41no—
215C22⋊C4×C103—41no—
216C22⋊C4×C103—41no—
217C22⋊C4×C103—41no—
218C42×C103—41no—
219C42×C103C2411yescharacteristic
220C23×C103—21no—
221C23×C103—21no—
222C23×C103—21no—
223C23×C103—21no—
224C23×C103—41no—
225C23×C103—82no—
226C23×C103—82no—
227C23×C103—161no—
228Q8×C103—41no—
229Q8×C103—41no—
230Q8×C103—41no—
231Q8×C103—41no—
232Q8×C103—81no—
233D4×C103—21no—
234D4×C103—21no—
235D4×C103—21no—
236D4×C103—21no—
237D4×C103—21no—
238D4×C103—21no—
239D4×C103—21no—
240D4×C103—41no—
241D4×C103—41no—
242D4×C103—41no—
243D4×C103—41no—
244D4×C103—81no—
245D4×C103—82no—
246D4×C103—82no—
247D4×C103—82no—
248D4×C103—82no—
249D4×C103—161no—
250D4×C103AGL(1,ℤ/8)12yes—
251C2×C4×C103—21no—
252C2×C4×C103—21no—
253C2×C4×C103—21no—
254C2×C4×C103—21no—
255C2×C4×C103—41no—
256C2×C4×C103—41no—
257C2×C4×C103—41no—
258C2×C4×C103—41no—
259C2×C4×C103—41no—
260C2×C4×C103—41no—
261C2×C4×C103—41no—
262C2×C4×C103—41no—
263C2×C4×C103—41no—
264C2×C4×C103—41no—
265C2×C4×C103—41no—
266C2×C4×C103—82no—
267C2×C4×C103—82no—
268C2×C4×C103C22×D411yescharacteristic
269C2×C4×C103C22×D411yescharacteristic
270C2×C4×C103H(5,𝔽2)11yescharacteristic
271C8×C103—22no—
272C8×C103—21no—
273C8×C103—21no—
274C8×C103—21no—
275C8×C103—21no—
276C8×C103—41no—
277C8×C103—41no—
278C8×C103—41no—
279C8×C103—41no—
280C22×C103—22no—
281C22×C103—41no—
282C22×C103—41no—
283C22×C103—41no—
284C22×C103—41no—
285C22×C103—41no—
286C22×C103—41no—
287C22×C103—41no—
288C22×C103—41no—
289C22×C103—41no—
290C22×C103—41no—
291C22×C103—41no—
292C22×C103—81no—
293C22×C103—81no—
294C22×C103—81no—
295C22×C103—164no—
296C22×C103D4211yescharacteristic
297C4×C103—21no—
298C4×C103—41no—
299C4×C103—41no—
300C4×C103—41no—
301C4×C103—41no—
302C4×C103—81no—
303C4×C103—81no—
304C4×C103—81no—
305C4×C103C2×AGL(1,ℤ/8)11yescharacteristic
306C4×C103#57511yescharacteristic
307C4×C103#57611yescharacteristic
308C4×C103#57711yescharacteristic
309#20026C10311yesmaximal, characteristic, direct product factor, Sylow
310C2×C103—42no—
311C2×C103—81no—
312C2×C103—81no—
313C2×C103—81no—
314C2×C103—161no—
315C2×C103#326411yescharacteristic
316C2×C103#326711yescharacteristic
317C2×C103#329111yescharacteristic
318#3354C2×C10311yescharacteristic, complemented
319#3303C2×C10311yescharacteristic, complemented
320#3294C2×C10311yescharacteristic, complemented
321#3272C2×C10311yescharacteristic, complemented
322#1714C2×C10311yescharacteristic, complemented
323#1703C2×C10311yescharacteristic, complemented
324#1701C2×C10311yescharacteristic, complemented
325#1671C2×C10311yescharacteristic, complemented
326#1665C2×C10311yescharacteristic, complemented
327#1647C2×C10311yescharacteristic, complemented
328#1647C2×C10311yescharacteristic, complemented
329#1629C2×C10311yescharacteristic, complemented
330#1624C2×C10311yescharacteristic, complemented
331#1586C2×C10311yescharacteristic, complemented
332#1586C2×C10311yescharacteristic, complemented
333C103#2002611yescharacteristic, direct product factor, Sylow
334C2×AGL(1,ℤ/8)—21no—
335#555C22×C10311yescharacteristic, complemented
336#547C22×C10311yescharacteristic
337#547C22×C10311yescharacteristic
338D42C22×C10311yescharacteristic
339#500C22×C10311yescharacteristic, complemented
340#498C22×C10311yescharacteristic, complemented
341#492C22×C10311yescharacteristic
342#492C22×C10311yescharacteristic
343#487C22×C10311yescharacteristic, complemented
344#486C22×C10311yescharacteristic
345#485—21no—
346#482—21no—
347#481—21no—
348#480—21no—
349#476C22×C10311yescharacteristic
350#476C22×C10311yescharacteristic
351#474C22×C10311yescharacteristic
352#474C22×C10311yescharacteristic, complemented
353#469—21no—
354#468—21no—
355#466—21no—
356#465—21no—
357#461C22×C10311yescharacteristic
358#461C22×C10311yescharacteristic, complemented
359#459C22×C10311yescharacteristic
360#459C22×C10311yescharacteristic
361#450—21no—
362#449—21no—
363#449—21no—
364#447—21no—
365C4×D8C22×C10311yescharacteristic
366C4×D8C22×C10311yescharacteristic
367#436C22×C10311yescharacteristic
368#436C22×C10311yescharacteristic, complemented
369C8×D4C22×C10311yescharacteristic
370C8×D4C22×C10311yescharacteristic, complemented
371#428—21no—
372#416—21no—
373C2×#102—21no—
374#334C22×C10311yescharacteristic, complemented
375#334C22×C10311yescharacteristic, complemented
376#333C22×C10311yescharacteristic, complemented
377#332C22×C10311yescharacteristic, complemented
378#332C22×C10311yescharacteristic, complemented
379#331C22×C10311yescharacteristic
380D4⋊C8C22×C10311yescharacteristic
381D4⋊C8C22×C10311yescharacteristic
382D4⋊C8C22×C10311yescharacteristic, complemented
383D4⋊C8C22×C10311yescharacteristic, complemented
384#322C22×C10311yescharacteristic, complemented
385C2×#41—21no—
386C2×#41—21no—
387C22×D4—21no—
388C22×D4—21no—
389AGL(1,ℤ/8)—44no—
390C2×SD16—21no—
391C2×SD16—21no—
392C2×SD16—21no—
393C2×SD16—21no—
394C2×SD16—41no—
395C2×D8—21no—
396C2×D8—21no—
397C2×D8D4×C10311yescharacteristic
398C2×D8D4×C10311yescharacteristic
399C2×M16—21no—
400C2×M16—21no—
401C22×C8—21no—
402C22×C8—21no—
403C4⋊Q8C23×C10311yescharacteristic
404C4⋊Q8C23×C10311yescharacteristic
405C4⋊Q8C23×C10311yescharacteristic
406#127C23×C10311yescharacteristic
407#124—41no—
408#123—41no—
409#123—41no—
410C22⋊Q8—21no—
411C22⋊Q8—21no—
412#121—21no—
413#121—21no—
414#121—21no—
415#121—21no—
416#121—21no—
417#121—21no—
418#120—41no—
419C4×D4C23×C10311yescharacteristic
420C4×D4C23×C10311yescharacteristic
421C4×D4C23×C10311yescharacteristic
422C4×D4C23×C10311yescharacteristic
423#117—21no—
424#117—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427#107—21no—
428#107—21no—
429#107—41no—
430#107D4×C10311yescharacteristic
431#107D4×C10311yescharacteristic
432#106—21no—
433#106—21no—
434#106—21no—
435#106—21no—
436C4⋊C8C23×C10311yescharacteristic
437C4⋊C8C23×C10311yescharacteristic
438C4⋊C8C23×C10311yescharacteristic
439C4⋊C8C23×C10311yescharacteristic
440#103—21no—
441#103—21no—
442#103—21no—
443#103—21no—
444#102—21no—
445#102—21no—
446#102—21no—
447#102—21no—
448#102—21no—
449#102—21no—
450#102—21no—
451#102—21no—
452#102D4×C10311yescharacteristic
453#102D4×C10311yescharacteristic
454#102D4×C10311yescharacteristic
455#102D4×C10311yescharacteristic
456C22⋊C8—21no—
457C22⋊C8—21no—
458C22⋊C8—21no—
459C22⋊C8—21no—
460C4×C8C23×C10311yescharacteristic
461C4×C8C23×C10311yescharacteristic
462C4×C8C23×C10311yescharacteristic
463C24—41no—
464#41—42no—
465#41—42no—
466#41—81no—
467#41—81no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4—42no—
477C2×D4—42no—
478C2×D4—41no—
479C2×D4—41no—
480C2×D4—41no—
481C2×D4—81no—
482C2×D4—81no—
483C2×D4C2×D4×C10311yescharacteristic
484C2×D4C2×D4×C10311yescharacteristic
485C2×D4C2×D4×C10311yescharacteristic
486C2×D4C2×D4×C10311yescharacteristic
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—41no—
492C22×C4—41no—
493SD16—42no—
494SD16—42no—
495SD16—81no—
496SD16—82no—
497SD16—81no—
498D8—22no—
499D8—41no—
500D8—42no—
501D8—81no—
502M16—42no—
503M16—42no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—81no—
510C2×C8—81no—
511C2×C8C2×D4×C10311yescharacteristic
512C2×C8C2×D4×C10311yescharacteristic
513C2×C8C2×D4×C10311yescharacteristic
514C2×C8C2×D4×C10311yescharacteristic
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4C2×D4×C10311yescharacteristic
524C4⋊C4C2×D4×C10311yescharacteristic
525C4⋊C4C2×D4×C10311yescharacteristic
526C4⋊C4C2×D4×C10311yescharacteristic
527C22⋊C4—21no—
528C22⋊C4—21no—
529C22⋊C4—21no—
530C22⋊C4—21no—
531C22⋊C4—41no—
532C22⋊C4—41no—
533C22⋊C4—41no—
534C22⋊C4—41no—
535C22⋊C4—41no—
536C42—41no—
537C42C24×C10311yescharacteristic
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—41no—
543C23—82no—
544C23—82no—
545C23—161no—
546Q8—41no—
547Q8—41no—
548Q8—41no—
549Q8—41no—
550Q8—81no—
551D4—21no—
552D4—21no—
553D4—21no—
554D4—21no—
555D4—21no—
556D4—21no—
557D4—21no—
558D4—41no—
559D4—41no—
560D4—41no—
561D4—41no—
562D4—81no—
563D4—82no—
564D4—82no—
565D4—82no—
566D4—82no—
567D4—161no—
568D4AGL(1,ℤ/8)×C10312yes—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—82no—
585C2×C4—82no—
586C2×C4C22×D4×C10311yescharacteristic
587C2×C4C22×D4×C10311yescharacteristic
588C2×C4H(5,𝔽2)×C10311yescharacteristic
589C8—22no—
590C8—21no—
591C8—21no—
592C8—21no—
593C8—21no—
594C8—41no—
595C8—41no—
596C8—41no—
597C8—41no—
598C22—22no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22—164no—
614C22D42×C10311yescharacteristic
615C4—21no—
616C4—41no—
617C4—41no—
618C4—41no—
619C4—41no—
620C4—81no—
621C4—81no—
622C4—81no—
623C4C2×AGL(1,ℤ/8)×C10311yescharacteristic
624C4#575×C10311yescharacteristic
625C4#576×C10311yescharacteristic
626C4#577×C10311yescharacteristic
627C2—42no—
628C2—81no—
629C2—81no—
630C2—81no—
631C2—161no—
632C2C103×#326411yescharacteristic
633C2C103×#326711yescharacteristic
634C2C103×#329111yescharacteristic
subgroupG/H
center, socleC22×C103D42
commutator, Frattini, cosocleC42C24×C103
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#3354C2semidirect
2. C103×#3303C2semidirect
3. C103×#3294C2semidirect
4. C103×#3272C2semidirect
5. C103×#1714C2semidirect
6. C103×#1703C2semidirect
7. C103×#1701C2semidirect
8. C103×#1671C2semidirect
9. C103×#1665C2semidirect
10. C103×#1647C2semidirect
11. C103×#1647C2semidirect
12. C103×#1629C2semidirect
13. C103×#1624C2semidirect
14. C103×#1586C2semidirect
15. C103×#1586C2semidirect
17. #555×C103C22semidirect
21. #500×C103C22semidirect
22. #498×C103C22semidirect
25. #487×C103C22semidirect
34. #474×C103C22semidirect
40. #461×C103C22semidirect
50. #436×C103C22semidirect
52. C8×D4×C103C22semidirect
56. #334×C103C22semidirect
57. #334×C103C22semidirect
58. #333×C103C22semidirect
59. #332×C103C22semidirect
60. #332×C103C22semidirect
64. D4⋊C8×C103C22semidirect
65. D4⋊C8×C103C22semidirect
66. #322×C103C22semidirect
309. #20026C103direct (N × H)
318. #3354C2×C103semidirect
319. #3303C2×C103semidirect
320. #3294C2×C103semidirect
321. #3272C2×C103semidirect
322. #1714C2×C103semidirect
323. #1703C2×C103semidirect
324. #1701C2×C103semidirect
325. #1671C2×C103semidirect
326. #1665C2×C103semidirect
327. #1647C2×C103semidirect
328. #1647C2×C103semidirect
329. #1629C2×C103semidirect
330. #1624C2×C103semidirect
331. #1586C2×C103semidirect
332. #1586C2×C103semidirect
333. C103#20026direct (N × H)
335. #555C22×C103semidirect
339. #500C22×C103semidirect
340. #498C22×C103semidirect
343. #487C22×C103semidirect
352. #474C22×C103semidirect
358. #461C22×C103semidirect
368. #436C22×C103semidirect
370. C8×D4C22×C103semidirect
374. #334C22×C103semidirect
375. #334C22×C103semidirect
376. #333C22×C103semidirect
377. #332C22×C103semidirect
378. #332C22×C103semidirect
382. D4⋊C8C22×C103semidirect
383. D4⋊C8C22×C103semidirect
384. #322C22×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#33542
C103×#33032
C103×#32942
C103×#32722
C103×#17142
C103×#17032
C103×#17012
C103×#16712
C103×#16652
C103×#16472
C103×#16292
C103×#16242
C103×#15862
#20026103