Finite Group Databasebeta

← C103×#19556 #39924831

Subgroups — C103×#19556 #39924831

Order 26368.

608 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3245C211yesmaximal, characteristic
2C103×#3235C211yesmaximal, characteristic, complemented
3C103×#3210C211yesmaximal, characteristic, complemented
4C103×#2979C211yesmaximal, characteristic, complemented
5C103×#1703C211yesmaximal, characteristic, complemented
6C103×#1697C211yesmaximal, characteristic, complemented
7C103×#1689C211yesmaximal, characteristic, complemented
8C103×#1685C211yesmaximal, characteristic, complemented
9C103×#1683C211yesmaximal, characteristic, complemented
10C103×#1677C211yesmaximal, characteristic, complemented
11C103×#1669C211yesmaximal, characteristic, complemented
12C103×#1665C211yesmaximal, characteristic, complemented
13C103×#1573C211yesmaximal, characteristic, complemented
14C103×#1553C211yesmaximal, characteristic, complemented
15C103×#1542C211yesmaximal, characteristic, complemented
16#533×C103C2211yescharacteristic
17#532×C103C2211yescharacteristic
18#532×C103C2211yescharacteristic
19#501×C103—21no—
20#494×C103C2211yescharacteristic
21#492×C103C2211yescharacteristic
22#490×C103—21no—
23#487×C103C2211yescharacteristic
24#486×C103C2211yescharacteristic
25#482×C103—21no—
26#482×C103—21no—
27#476×C103C2211yescharacteristic
28#476×C103C2211yescharacteristic
29#474×C103—21no—
30#474×C103C2211yescharacteristic
31#474×C103C2211yescharacteristic
32#474×C103C2211yescharacteristic
33#474×C103C2211yescharacteristic
34#466×C103—21no—
35#466×C103—21no—
36#464×C103—21no—
37#464×C103—21no—
38#459×C103—21no—
39#459×C103C2211yescharacteristic
40#459×C103C2211yescharacteristic
41#452×C103—21no—
42#452×C103—21no—
43#436×C103—21no—
44#436×C103C2211yescharacteristic
45#436×C103C2211yescharacteristic
46C8×D4×C103—21no—
47C8×D4×C103C2211yescharacteristic
48C8×D4×C103C2211yescharacteristic
49#432×C103C2211yescharacteristic
50#431×C103C2211yescharacteristic
51#431×C103C2211yescharacteristic
52C2×C4⋊C8×C103C2211yescharacteristic
53#408×C103—21no—
54#408×C103—21no—
55#335×C103C2211yescharacteristic
56#335×C103C2211yescharacteristic
57#334×C103C2211yescharacteristic
58#334×C103C2211yescharacteristic
59#333×C103C2211yescharacteristic
60#333×C103C2211yescharacteristic
61#332×C103C2211yescharacteristic
62#332×C103C2211yescharacteristic
63#332×C103C2211yescharacteristic
64#332×C103C2211yescharacteristic
65#331×C103C2211yescharacteristic
66#331×C103C2211yescharacteristic
67C2×#41×C103—21no—
68C2×#41×C103—21no—
69C2×Q16×C103—21no—
70C2×Q16×C103—21no—
71C2×SD16×C103—21no—
72C2×SD16×C103—21no—
73C2×D8×C103—21no—
74C2×D8×C103—21no—
75C2×M16×C103—21no—
76C2×M16×C103—21no—
77C22×C8×C103—21no—
78C22×C8×C103—21no—
79C22×C8×C103—21no—
80C4⋊Q8×C103D411yescharacteristic
81C4⋊Q8×C103C2311yescharacteristic
82C4⋊Q8×C103C2311yescharacteristic
83C4⋊Q8×C103C2311yescharacteristic
84#127×C103D411yescharacteristic
85#127×C103C2311yescharacteristic
86#125×C103—21no—
87#124×C103—21no—
88#124×C103—21no—
89C22⋊Q8×C103—21no—
90C22⋊Q8×C103—21no—
91#121×C103—21no—
92#121×C103—21no—
93#121×C103—21no—
94#121×C103D411yescharacteristic
95#121×C103D411yescharacteristic
96C4×Q8×C103—21no—
97C4×Q8×C103—21no—
98C4×D4×C103—21no—
99C4×D4×C103—21no—
100C4×D4×C103—21no—
101C4×D4×C103C2311yescharacteristic
102C4×D4×C103C2311yescharacteristic
103#117×C103—21no—
104C2×C42×C103C2311yescharacteristic
105#107×C103—21no—
106#107×C103—21no—
107#107×C103—21no—
108#107×C103—21no—
109#106×C103—21no—
110#106×C103—21no—
111C4⋊C8×C103—21no—
112C4⋊C8×C103D411yescharacteristic
113C4⋊C8×C103D411yescharacteristic
114C4⋊C8×C103C2311yescharacteristic
115C4⋊C8×C103C2311yescharacteristic
116C4⋊C8×C103C2311yescharacteristic
117C4⋊C8×C103C2311yescharacteristic
118C4⋊C8×C103C2311yescharacteristic
119C4⋊C8×C103C2311yescharacteristic
120#103×C103—21no—
121#103×C103—21no—
122#102×C103—21no—
123#102×C103—21no—
124#102×C103—21no—
125#102×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—
132C22⋊C8×C103—21no—
133C22⋊C8×C103—21no—
134C22⋊C8×C103—21no—
135C22⋊C8×C103—21no—
136C22⋊C8×C103—21no—
137C22⋊C8×C103—21no—
138C22⋊C8×C103D411yescharacteristic
139C22⋊C8×C103D411yescharacteristic
140#97×C103—21no—
141C4×C8×C103—21no—
142C4×C8×C103C2311yescharacteristic
143C4×C8×C103C2311yescharacteristic
144#41×C103—81no—
145#41×C103—81no—
146#41×C103—81no—
147#41×C103—81no—
148C2×Q8×C103—21no—
149C2×Q8×C103—21no—
150C2×Q8×C103—21no—
151C2×Q8×C103—21no—
152C2×D4×C103—21no—
153C2×D4×C103—21no—
154C2×D4×C103—21no—
155C2×D4×C103—21no—
156C2×D4×C103—21no—
157C2×D4×C103—21no—
158C2×D4×C103—21no—
159C2×D4×C103—41no—
160C2×D4×C103C2×D411yescharacteristic
161C2×D4×C103C2×D411yescharacteristic
162C22×C4×C103—21no—
163C22×C4×C103—21no—
164C22×C4×C103—41no—
165C22×C4×C103C2×D411yescharacteristic
166C22×C4×C103C2×D411yescharacteristic
167C22×C4×C103#4111yescharacteristic
168Q16×C103—81no—
169Q16×C103—81no—
170SD16×C103—81no—
171SD16×C103—81no—
172D8×C103—81no—
173D8×C103—81no—
174M16×C103—81no—
175M16×C103—81no—
176C2×C8×C103—21no—
177C2×C8×C103—21no—
178C2×C8×C103—21no—
179C2×C8×C103—21no—
180C2×C8×C103—21no—
181C2×C8×C103—21no—
182C2×C8×C103—81no—
183C2×C8×C103—81no—
184C2×C8×C103—81no—
185C2×C8×C103C2×D411yescharacteristic
186C2×C8×C103C2×D411yescharacteristic
187C2×C8×C103C2×D411yescharacteristic
188C2×C8×C103C2×D411yescharacteristic
189C4⋊C4×C103—21no—
190C4⋊C4×C103—21no—
191C4⋊C4×C103—21no—
192C4⋊C4×C103—21no—
193C4⋊C4×C103—21no—
194C4⋊C4×C103—21no—
195C4⋊C4×C103—21no—
196C4⋊C4×C103—41no—
197C4⋊C4×C103—41no—
198C4⋊C4×C103C2×D411yescharacteristic
199C4⋊C4×C103C2×D411yescharacteristic
200C22⋊C4×C103—21no—
201C22⋊C4×C103—21no—
202C22⋊C4×C103—21no—
203C22⋊C4×C103—21no—
204C22⋊C4×C103—41no—
205C22⋊C4×C103—41no—
206C22⋊C4×C103—41no—
207C42×C103—41no—
208C42×C103C2×D411yescharacteristic
209C42×C103C2×D411yescharacteristic
210C42×C103#4111yescharacteristic
211C42×C103C2411yescharacteristic
212C23×C103—21no—
213C23×C103—21no—
214C23×C103—41no—
215C23×C103#12111yescharacteristic
216Q8×C103—41no—
217Q8×C103—41no—
218Q8×C103—41no—
219Q8×C103—41no—
220Q8×C103—81no—
221Q8×C103—81no—
222D4×C103—21no—
223D4×C103—21no—
224D4×C103—21no—
225D4×C103—21no—
226D4×C103—42no—
227D4×C103—41no—
228D4×C103—41no—
229D4×C103—41no—
230D4×C103—41no—
231D4×C103—81no—
232D4×C103—81no—
233D4×C103—81no—
234D4×C103—81no—
235D4×C103—82no—
236C2×C4×C103—21no—
237C2×C4×C103—21no—
238C2×C4×C103—21no—
239C2×C4×C103—21no—
240C2×C4×C103—21no—
241C2×C4×C103—21no—
242C2×C4×C103—41no—
243C2×C4×C103—41no—
244C2×C4×C103—41no—
245C2×C4×C103—41no—
246C2×C4×C103—41no—
247C2×C4×C103—41no—
248C2×C4×C103—41no—
249C2×C4×C103—41no—
250C2×C4×C103—82no—
251C2×C4×C103#12111yescharacteristic
252C2×C4×C103#12111yescharacteristic
253C2×C4×C103#12111yescharacteristic
254C2×C4×C103C22×D411yescharacteristic
255C2×C4×C103C22×D411yescharacteristic
256C2×C4×C103C2×#4111yescharacteristic
257C8×C103—21no—
258C8×C103—21no—
259C8×C103—21no—
260C8×C103—21no—
261C8×C103—41no—
262C8×C103—41no—
263C8×C103—41no—
264C8×C103—41no—
265C8×C103—41no—
266C8×C103—41no—
267C22×C103—21no—
268C22×C103—21no—
269C22×C103—21no—
270C22×C103—41no—
271C22×C103—41no—
272C22×C103—41no—
273C22×C103—41no—
274C22×C103—41no—
275C22×C103—41no—
276C22×C103—81no—
277C22×C103—81no—
278C22×C103—81no—
279C22×C103C2×#12111yescharacteristic
280C4×C103—21no—
281C4×C103—21no—
282C4×C103—21no—
283C4×C103—21no—
284C4×C103—41no—
285C4×C103—41no—
286C4×C103—81no—
287C4×C103—81no—
288C4×C103—81no—
289C4×C103#57611yescharacteristic
290C4×C103#57611yescharacteristic
291C4×C103#57711yescharacteristic
292C4×C103#57811yescharacteristic
293#19556C10311yesmaximal, characteristic, direct product factor, Sylow
294C2×C103—41no—
295C2×C103—81no—
296C2×C103—81no—
297C2×C103—161no—
298C2×C103#304111yescharacteristic
299C2×C103#306311yescharacteristic
300C2×C103#306711yescharacteristic
301#3245C2×C10311yescharacteristic
302#3235C2×C10311yescharacteristic, complemented
303#3210C2×C10311yescharacteristic, complemented
304#2979C2×C10311yescharacteristic, complemented
305#1703C2×C10311yescharacteristic, complemented
306#1697C2×C10311yescharacteristic, complemented
307#1689C2×C10311yescharacteristic, complemented
308#1685C2×C10311yescharacteristic, complemented
309#1683C2×C10311yescharacteristic, complemented
310#1677C2×C10311yescharacteristic, complemented
311#1669C2×C10311yescharacteristic, complemented
312#1665C2×C10311yescharacteristic, complemented
313#1573C2×C10311yescharacteristic, complemented
314#1553C2×C10311yescharacteristic, complemented
315#1542C2×C10311yescharacteristic, complemented
316C103#1955611yescharacteristic, direct product factor, Sylow
317#533C22×C10311yescharacteristic
318#532C22×C10311yescharacteristic
319#532C22×C10311yescharacteristic
320#501—21no—
321#494C22×C10311yescharacteristic
322#492C22×C10311yescharacteristic
323#490—21no—
324#487C22×C10311yescharacteristic
325#486C22×C10311yescharacteristic
326#482—21no—
327#482—21no—
328#476C22×C10311yescharacteristic
329#476C22×C10311yescharacteristic
330#474—21no—
331#474C22×C10311yescharacteristic
332#474C22×C10311yescharacteristic
333#474C22×C10311yescharacteristic
334#474C22×C10311yescharacteristic
335#466—21no—
336#466—21no—
337#464—21no—
338#464—21no—
339#459—21no—
340#459C22×C10311yescharacteristic
341#459C22×C10311yescharacteristic
342#452—21no—
343#452—21no—
344#436—21no—
345#436C22×C10311yescharacteristic
346#436C22×C10311yescharacteristic
347C8×D4—21no—
348C8×D4C22×C10311yescharacteristic
349C8×D4C22×C10311yescharacteristic
350#432C22×C10311yescharacteristic
351#431C22×C10311yescharacteristic
352#431C22×C10311yescharacteristic
353C2×C4⋊C8C22×C10311yescharacteristic
354#408—21no—
355#408—21no—
356#335C22×C10311yescharacteristic
357#335C22×C10311yescharacteristic
358#334C22×C10311yescharacteristic
359#334C22×C10311yescharacteristic
360#333C22×C10311yescharacteristic
361#333C22×C10311yescharacteristic
362#332C22×C10311yescharacteristic
363#332C22×C10311yescharacteristic
364#332C22×C10311yescharacteristic
365#332C22×C10311yescharacteristic
366#331C22×C10311yescharacteristic
367#331C22×C10311yescharacteristic
368C2×#41—21no—
369C2×#41—21no—
370C2×Q16—21no—
371C2×Q16—21no—
372C2×SD16—21no—
373C2×SD16—21no—
374C2×D8—21no—
375C2×D8—21no—
376C2×M16—21no—
377C2×M16—21no—
378C22×C8—21no—
379C22×C8—21no—
380C22×C8—21no—
381C4⋊Q8D4×C10311yescharacteristic
382C4⋊Q8C23×C10311yescharacteristic
383C4⋊Q8C23×C10311yescharacteristic
384C4⋊Q8C23×C10311yescharacteristic
385#127D4×C10311yescharacteristic
386#127C23×C10311yescharacteristic
387#125—21no—
388#124—21no—
389#124—21no—
390C22⋊Q8—21no—
391C22⋊Q8—21no—
392#121—21no—
393#121—21no—
394#121—21no—
395#121D4×C10311yescharacteristic
396#121D4×C10311yescharacteristic
397C4×Q8—21no—
398C4×Q8—21no—
399C4×D4—21no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4C23×C10311yescharacteristic
403C4×D4C23×C10311yescharacteristic
404#117—21no—
405C2×C42C23×C10311yescharacteristic
406#107—21no—
407#107—21no—
408#107—21no—
409#107—21no—
410#106—21no—
411#106—21no—
412C4⋊C8—21no—
413C4⋊C8D4×C10311yescharacteristic
414C4⋊C8D4×C10311yescharacteristic
415C4⋊C8C23×C10311yescharacteristic
416C4⋊C8C23×C10311yescharacteristic
417C4⋊C8C23×C10311yescharacteristic
418C4⋊C8C23×C10311yescharacteristic
419C4⋊C8C23×C10311yescharacteristic
420C4⋊C8C23×C10311yescharacteristic
421#103—21no—
422#103—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433C22⋊C8—21no—
434C22⋊C8—21no—
435C22⋊C8—21no—
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8—21no—
439C22⋊C8D4×C10311yescharacteristic
440C22⋊C8D4×C10311yescharacteristic
441#97—21no—
442C4×C8—21no—
443C4×C8C23×C10311yescharacteristic
444C4×C8C23×C10311yescharacteristic
445#41—81no—
446#41—81no—
447#41—81no—
448#41—81no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—41no—
461C2×D4C2×D4×C10311yescharacteristic
462C2×D4C2×D4×C10311yescharacteristic
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—41no—
466C22×C4C2×D4×C10311yescharacteristic
467C22×C4C2×D4×C10311yescharacteristic
468C22×C4#41×C10311yescharacteristic
469Q16—81no—
470Q16—81no—
471SD16—81no—
472SD16—81no—
473D8—81no—
474D8—81no—
475M16—81no—
476M16—81no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—81no—
484C2×C8—81no—
485C2×C8—81no—
486C2×C8C2×D4×C10311yescharacteristic
487C2×C8C2×D4×C10311yescharacteristic
488C2×C8C2×D4×C10311yescharacteristic
489C2×C8C2×D4×C10311yescharacteristic
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4C2×D4×C10311yescharacteristic
500C4⋊C4C2×D4×C10311yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C42—41no—
509C42C2×D4×C10311yescharacteristic
510C42C2×D4×C10311yescharacteristic
511C42#41×C10311yescharacteristic
512C42C24×C10311yescharacteristic
513C23—21no—
514C23—21no—
515C23—41no—
516C23#121×C10311yescharacteristic
517Q8—41no—
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8—81no—
522Q8—81no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—42no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—81no—
533D4—81no—
534D4—81no—
535D4—81no—
536D4—82no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—82no—
552C2×C4#121×C10311yescharacteristic
553C2×C4#121×C10311yescharacteristic
554C2×C4#121×C10311yescharacteristic
555C2×C4C22×D4×C10311yescharacteristic
556C2×C4C22×D4×C10311yescharacteristic
557C2×C4C2×#41×C10311yescharacteristic
558C8—21no—
559C8—21no—
560C8—21no—
561C8—21no—
562C8—41no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—41no—
567C8—41no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22C2×#121×C10311yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—81no—
588C4—81no—
589C4—81no—
590C4#576×C10311yescharacteristic
591C4#576×C10311yescharacteristic
592C4#577×C10311yescharacteristic
593C4#578×C10311yescharacteristic
594C2—41no—
595C2—81no—
596C2—81no—
597C2—161no—
598C2C103×#304111yescharacteristic
599C2C103×#306311yescharacteristic
600C2C103×#306711yescharacteristic
subgroupG/H
center, socleC22×C103C2×#121
commutator, Frattini, cosocleC42C24×C103
prime radicalC103×#3245C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#3235C2semidirect
3. C103×#3210C2semidirect
4. C103×#2979C2semidirect
5. C103×#1703C2semidirect
6. C103×#1697C2semidirect
7. C103×#1689C2semidirect
8. C103×#1685C2semidirect
9. C103×#1683C2semidirect
10. C103×#1677C2semidirect
11. C103×#1669C2semidirect
12. C103×#1665C2semidirect
13. C103×#1573C2semidirect
14. C103×#1553C2semidirect
15. C103×#1542C2semidirect
293. #19556C103direct (N × H)
302. #3235C2×C103semidirect
303. #3210C2×C103semidirect
304. #2979C2×C103semidirect
305. #1703C2×C103semidirect
306. #1697C2×C103semidirect
307. #1689C2×C103semidirect
308. #1685C2×C103semidirect
309. #1683C2×C103semidirect
310. #1677C2×C103semidirect
311. #1669C2×C103semidirect
312. #1665C2×C103semidirect
313. #1573C2×C103semidirect
314. #1553C2×C103semidirect
315. #1542C2×C103semidirect
316. C103#19556direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#32452
C103×#32352
C103×#32102
C103×#29792
C103×#17032
C103×#16972
C103×#16892
C103×#16852
C103×#16832
C103×#16772
C103×#16692
C103×#16652
C103×#15732
C103×#15532
C103×#15422
#19556103