Finite Group Databasebeta

← C103×#19947 #39925222

Subgroups — C103×#19947 #39925222

Order 26368.

658 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3399C211yesmaximal, characteristic, complemented
2C103×#3394C211yesmaximal, characteristic, complemented
3C103×#3353C211yesmaximal, characteristic, complemented
4C103×#3284C211yesmaximal, characteristic, complemented
5C103×#1706C211yesmaximal, characteristic, complemented
6C103×#1694C211yesmaximal, characteristic, complemented
7C103×#1687C211yesmaximal, characteristic, complemented
8C103×#1666C211yesmaximal, characteristic, complemented
9C103×#1665C211yesmaximal, characteristic, complemented
10C103×#1641C211yesmaximal, characteristic, complemented
11C103×#1640C211yesmaximal, characteristic, complemented
12C103×#1628C211yesmaximal, characteristic, complemented
13C103×#1625C211yesmaximal, characteristic, complemented
14C103×#1590C211yesmaximal, characteristic, complemented
15C8×SD16×C103C211yesmaximal, characteristic, complemented
16C2×#135×C103—21no—
17#559×C103C2211yescharacteristic
18#556×C103C2211yescharacteristic
19#550×C103C2211yescharacteristic
20#547×C103C2211yescharacteristic
21#500×C103C2211yescharacteristic
22#496×C103—21no—
23#495×C103—21no—
24#493×C103C2211yescharacteristic
25#492×C103C2211yescharacteristic
26#492×C103C2211yescharacteristic
27#486×C103C2211yescharacteristic
28#486×C103C2211yescharacteristic
29#484×C103—21no—
30#482×C103—21no—
31#475×C103C2211yescharacteristic
32#474×C103C2211yescharacteristic
33#468×C103—21no—
34#465×C103—21no—
35#464×C103—21no—
36#463×C103—21no—
37#463×C103—21no—
38#462×C103C2211yescharacteristic
39#462×C103C2211yescharacteristic
40#460×C103C2211yescharacteristic
41#459×C103—21no—
42#459×C103C2211yescharacteristic
43#459×C103C2211yescharacteristic
44#459×C103C2211yescharacteristic
45#452×C103—21no—
46#449×C103—21no—
47#446×C103C2211yescharacteristic
48C8×Q8×C103C2211yescharacteristic
49#442×C103—21no—
50C4×SD16×C103—21no—
51C4×SD16×C103C2211yescharacteristic
52C4×SD16×C103C2211yescharacteristic
53#436×C103C2211yescharacteristic
54C8×D4×C103C2211yescharacteristic
55#428×C103—21no—
56#334×C103C2211yescharacteristic
57#334×C103C2211yescharacteristic
58#332×C103C2211yescharacteristic
59#332×C103C2211yescharacteristic
60#331×C103C2211yescharacteristic
61#331×C103C2211yescharacteristic
62Q8⋊C8×C103C2211yescharacteristic
63Q8⋊C8×C103C2211yescharacteristic
64D4⋊C8×C103C2211yescharacteristic
65D4⋊C8×C103C2211yescharacteristic
66C82×C103C2211yescharacteristic
67C2×#41×C103—21no—
68C2×#41×C103—21no—
69#135×C103—44no—
70C2×Q16×C103—21no—
71C2×Q16×C103—21no—
72C2×SD16×C103—21no—
73C2×SD16×C103—21no—
74C2×SD16×C103—21no—
75C2×SD16×C103—21no—
76C2×SD16×C103—21no—
77C2×SD16×C103D411yescharacteristic
78C2×SD16×C103D411yescharacteristic
79C2×D8×C103—21no—
80C2×D8×C103—21no—
81C2×D8×C103—21no—
82C2×D8×C103—21no—
83C2×D8×C103—21no—
84C2×M16×C103—21no—
85C22×C8×C103—21no—
86C4⋊Q8×C103C2311yescharacteristic
87C4⋊Q8×C103C2311yescharacteristic
88#127×C103—21no—
89#127×C103C2311yescharacteristic
90#127×C103C2311yescharacteristic
91#126×C103—41no—
92#124×C103—21no—
93#124×C103—21no—
94#124×C103—21no—
95#123×C103—41no—
96#123×C103—41no—
97C22⋊Q8×C103—21no—
98C22⋊Q8×C103—21no—
99#121×C103—21no—
100#121×C103—21no—
101#121×C103—41no—
102C4×Q8×C103—21no—
103C4×Q8×C103C2311yescharacteristic
104C4×Q8×C103C2311yescharacteristic
105C4×D4×C103—21no—
106C4×D4×C103—21no—
107C4×D4×C103—21no—
108C4×D4×C103C2311yescharacteristic
109C4×D4×C103C2311yescharacteristic
110#117×C103—21no—
111C2×C4⋊C4×C103—21no—
112#107×C103—21no—
113#107×C103—21no—
114#107×C103—21no—
115#106×C103—21no—
116#106×C103D411yescharacteristic
117#106×C103D411yescharacteristic
118C4⋊C8×C103—21no—
119C4⋊C8×C103—21no—
120C4⋊C8×C103C2311yescharacteristic
121C4⋊C8×C103C2311yescharacteristic
122C4⋊C8×C103C2311yescharacteristic
123C4⋊C8×C103C2311yescharacteristic
124#103×C103—21no—
125#103×C103—21no—
126#103×C103—21no—
127#103×C103D411yescharacteristic
128#103×C103D411yescharacteristic
129#102×C103—21no—
130#102×C103—21no—
131#102×C103—21no—
132#102×C103—21no—
133#102×C103—21no—
134#102×C103—41no—
135#102×C103—41no—
136#102×C103D411yescharacteristic
137#102×C103D411yescharacteristic
138C22⋊C8×C103—21no—
139C22⋊C8×C103—21no—
140#97×C103—21no—
141C4×C8×C103—21no—
142C4×C8×C103C2311yescharacteristic
143C4×C8×C103C2311yescharacteristic
144C4×C8×C103C2311yescharacteristic
145#41×C103—42no—
146#41×C103—42no—
147#41×C103—81no—
148#41×C103—81no—
149C2×Q8×C103—21no—
150C2×Q8×C103—21no—
151C2×Q8×C103C2×D411yescharacteristic
152C2×Q8×C103C2×D411yescharacteristic
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×C103—41no—
161C2×D4×C103—41no—
162C2×D4×C103C2×D411yescharacteristic
163C2×D4×C103C2×D411yescharacteristic
164C22×C4×C103—21no—
165C22×C4×C103—21no—
166C22×C4×C103—41no—
167C22×C4×C103—41no—
168C22×C4×C103—41no—
169Q16×C103—42no—
170Q16×C103—81no—
171SD16×C103—22no—
172SD16×C103—22no—
173SD16×C103—42no—
174SD16×C103—42no—
175SD16×C103—81no—
176SD16×C103—81no—
177SD16×C103—81no—
178D8×C103—42no—
179D8×C103—42no—
180D8×C103—81no—
181D8×C103—81no—
182D8×C103—81no—
183M16×C103—42no—
184C2×C8×C103—21no—
185C2×C8×C103—21no—
186C2×C8×C103—21no—
187C2×C8×C103—21no—
188C2×C8×C103—21no—
189C2×C8×C103—42no—
190C2×C8×C103C2×D411yescharacteristic
191C2×C8×C103C2×D411yescharacteristic
192C2×C8×C103C2×D411yescharacteristic
193C2×C8×C103C2×D411yescharacteristic
194C4⋊C4×C103—21no—
195C4⋊C4×C103—21no—
196C4⋊C4×C103—21no—
197C4⋊C4×C103—21no—
198C4⋊C4×C103—21no—
199C4⋊C4×C103—21no—
200C4⋊C4×C103—41no—
201C4⋊C4×C103—41no—
202C4⋊C4×C103C2×D411yescharacteristic
203C4⋊C4×C103C2×D411yescharacteristic
204C4⋊C4×C103C2×D411yescharacteristic
205C4⋊C4×C103C2×D411yescharacteristic
206C22⋊C4×C103—21no—
207C22⋊C4×C103—21no—
208C22⋊C4×C103—41no—
209C22⋊C4×C103—41no—
210C22⋊C4×C103—41no—
211C22⋊C4×C103—41no—
212C22⋊C4×C103—41no—
213C22⋊C4×C103—41no—
214C22⋊C4×C103—41no—
215C42×C103—21no—
216C42×C103—21no—
217C42×C103—41no—
218C42×C103C2411yescharacteristic
219C23×C103—21no—
220C23×C103—21no—
221C23×C103—41no—
222C23×C103—41no—
223Q8×C103—21no—
224Q8×C103—21no—
225Q8×C103—21no—
226Q8×C103—21no—
227Q8×C103—41no—
228Q8×C103—41no—
229Q8×C103—41no—
230Q8×C103—41no—
231D4×C103—21no—
232D4×C103—21no—
233D4×C103—21no—
234D4×C103—21no—
235D4×C103—41no—
236D4×C103—41no—
237D4×C103—41no—
238D4×C103—41no—
239D4×C103—41no—
240D4×C103—41no—
241D4×C103—41no—
242D4×C103—41no—
243D4×C103—81no—
244D4×C103—81no—
245D4×C103—82no—
246D4×C103—82no—
247D4×C103—161no—
248C2×C4×C103—21no—
249C2×C4×C103—21no—
250C2×C4×C103—21no—
251C2×C4×C103—21no—
252C2×C4×C103—21no—
253C2×C4×C103—21no—
254C2×C4×C103—41no—
255C2×C4×C103—41no—
256C2×C4×C103—41no—
257C2×C4×C103—41no—
258C2×C4×C103—41no—
259C2×C4×C103—41no—
260C2×C4×C103—82no—
261C2×C4×C103—82no—
262C2×C4×C103—161no—
263C2×C4×C103C22×D411yescharacteristic
264C2×C4×C103C22×D411yescharacteristic
265C2×C4×C103H(5,𝔽2)11yescharacteristic
266C8×C103—21no—
267C8×C103—21no—
268C8×C103—41no—
269C8×C103—41no—
270C8×C103—41no—
271C8×C103—41no—
272C8×C103—41no—
273C8×C103#13512yescomplemented
274C8×C103AGL(1,ℤ/8)12yes—
275C22×C103—41no—
276C22×C103—41no—
277C22×C103—41no—
278C22×C103—41no—
279C22×C103—41no—
280C22×C103—41no—
281C22×C103—81no—
282C22×C103—81no—
283C22×C103—81no—
284C22×C103—81no—
285C22×C103—81no—
286C22×C103—81no—
287C22×C103D4211yescharacteristic
288C4×C103—21no—
289C4×C103—41no—
290C4×C103—41no—
291C4×C103—41no—
292C4×C103—41no—
293C4×C103—41no—
294C4×C103—41no—
295C4×C103—81no—
296C4×C103—81no—
297C4×C103C2×#13511yescharacteristic
298C4×C103C2×AGL(1,ℤ/8)11yescharacteristic
299C4×C103#57611yescharacteristic
300C4×C103#57711yescharacteristic
301#19947C10311yesmaximal, characteristic, direct product factor, Sylow
302C2×C103—81no—
303C2×C103—81no—
304C2×C103—161no—
305C2×C103—161no—
306C2×C103#327411yescharacteristic
307C2×C103#328411yescharacteristic
308C2×C103#329011yescharacteristic
309#3399C2×C10311yescharacteristic, complemented
310#3394C2×C10311yescharacteristic, complemented
311#3353C2×C10311yescharacteristic, complemented
312#3284C2×C10311yescharacteristic, complemented
313#1706C2×C10311yescharacteristic, complemented
314#1694C2×C10311yescharacteristic, complemented
315#1687C2×C10311yescharacteristic, complemented
316#1666C2×C10311yescharacteristic, complemented
317#1665C2×C10311yescharacteristic, complemented
318#1641C2×C10311yescharacteristic, complemented
319#1640C2×C10311yescharacteristic, complemented
320#1628C2×C10311yescharacteristic, complemented
321#1625C2×C10311yescharacteristic, complemented
322#1590C2×C10311yescharacteristic, complemented
323C8×SD16C2×C10311yescharacteristic, complemented
324C103#1994711yescharacteristic, direct product factor, Sylow
325C2×#135—21no—
326#559C22×C10311yescharacteristic
327#556C22×C10311yescharacteristic
328#550C22×C10311yescharacteristic
329#547C22×C10311yescharacteristic
330#500C22×C10311yescharacteristic
331#496—21no—
332#495—21no—
333#493C22×C10311yescharacteristic
334#492C22×C10311yescharacteristic
335#492C22×C10311yescharacteristic
336#486C22×C10311yescharacteristic
337#486C22×C10311yescharacteristic
338#484—21no—
339#482—21no—
340#475C22×C10311yescharacteristic
341#474C22×C10311yescharacteristic
342#468—21no—
343#465—21no—
344#464—21no—
345#463—21no—
346#463—21no—
347#462C22×C10311yescharacteristic
348#462C22×C10311yescharacteristic
349#460C22×C10311yescharacteristic
350#459—21no—
351#459C22×C10311yescharacteristic
352#459C22×C10311yescharacteristic
353#459C22×C10311yescharacteristic
354#452—21no—
355#449—21no—
356#446C22×C10311yescharacteristic
357C8×Q8C22×C10311yescharacteristic
358#442—21no—
359C4×SD16—21no—
360C4×SD16C22×C10311yescharacteristic
361C4×SD16C22×C10311yescharacteristic
362#436C22×C10311yescharacteristic
363C8×D4C22×C10311yescharacteristic
364#428—21no—
365#334C22×C10311yescharacteristic
366#334C22×C10311yescharacteristic
367#332C22×C10311yescharacteristic
368#332C22×C10311yescharacteristic
369#331C22×C10311yescharacteristic
370#331C22×C10311yescharacteristic
371Q8⋊C8C22×C10311yescharacteristic
372Q8⋊C8C22×C10311yescharacteristic
373D4⋊C8C22×C10311yescharacteristic
374D4⋊C8C22×C10311yescharacteristic
375C82C22×C10311yescharacteristic
376C2×#41—21no—
377C2×#41—21no—
378#135—44no—
379C2×Q16—21no—
380C2×Q16—21no—
381C2×SD16—21no—
382C2×SD16—21no—
383C2×SD16—21no—
384C2×SD16—21no—
385C2×SD16—21no—
386C2×SD16D4×C10311yescharacteristic
387C2×SD16D4×C10311yescharacteristic
388C2×D8—21no—
389C2×D8—21no—
390C2×D8—21no—
391C2×D8—21no—
392C2×D8—21no—
393C2×M16—21no—
394C22×C8—21no—
395C4⋊Q8C23×C10311yescharacteristic
396C4⋊Q8C23×C10311yescharacteristic
397#127—21no—
398#127C23×C10311yescharacteristic
399#127C23×C10311yescharacteristic
400#126—41no—
401#124—21no—
402#124—21no—
403#124—21no—
404#123—41no—
405#123—41no—
406C22⋊Q8—21no—
407C22⋊Q8—21no—
408#121—21no—
409#121—21no—
410#121—41no—
411C4×Q8—21no—
412C4×Q8C23×C10311yescharacteristic
413C4×Q8C23×C10311yescharacteristic
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—21no—
417C4×D4C23×C10311yescharacteristic
418C4×D4C23×C10311yescharacteristic
419#117—21no—
420C2×C4⋊C4—21no—
421#107—21no—
422#107—21no—
423#107—21no—
424#106—21no—
425#106D4×C10311yescharacteristic
426#106D4×C10311yescharacteristic
427C4⋊C8—21no—
428C4⋊C8—21no—
429C4⋊C8C23×C10311yescharacteristic
430C4⋊C8C23×C10311yescharacteristic
431C4⋊C8C23×C10311yescharacteristic
432C4⋊C8C23×C10311yescharacteristic
433#103—21no—
434#103—21no—
435#103—21no—
436#103D4×C10311yescharacteristic
437#103D4×C10311yescharacteristic
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—41no—
444#102—41no—
445#102D4×C10311yescharacteristic
446#102D4×C10311yescharacteristic
447C22⋊C8—21no—
448C22⋊C8—21no—
449#97—21no—
450C4×C8—21no—
451C4×C8C23×C10311yescharacteristic
452C4×C8C23×C10311yescharacteristic
453C4×C8C23×C10311yescharacteristic
454#41—42no—
455#41—42no—
456#41—81no—
457#41—81no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8C2×D4×C10311yescharacteristic
461C2×Q8C2×D4×C10311yescharacteristic
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—41no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4C2×D4×C10311yescharacteristic
472C2×D4C2×D4×C10311yescharacteristic
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478Q16—42no—
479Q16—81no—
480SD16—22no—
481SD16—22no—
482SD16—42no—
483SD16—42no—
484SD16—81no—
485SD16—81no—
486SD16—81no—
487D8—42no—
488D8—42no—
489D8—81no—
490D8—81no—
491D8—81no—
492M16—42no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—42no—
499C2×C8C2×D4×C10311yescharacteristic
500C2×C8C2×D4×C10311yescharacteristic
501C2×C8C2×D4×C10311yescharacteristic
502C2×C8C2×D4×C10311yescharacteristic
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4C2×D4×C10311yescharacteristic
512C4⋊C4C2×D4×C10311yescharacteristic
513C4⋊C4C2×D4×C10311yescharacteristic
514C4⋊C4C2×D4×C10311yescharacteristic
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C42—21no—
525C42—21no—
526C42—41no—
527C42C24×C10311yescharacteristic
528C23—21no—
529C23—21no—
530C23—41no—
531C23—41no—
532Q8—21no—
533Q8—21no—
534Q8—21no—
535Q8—21no—
536Q8—41no—
537Q8—41no—
538Q8—41no—
539Q8—41no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—81no—
553D4—81no—
554D4—82no—
555D4—82no—
556D4—161no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—82no—
570C2×C4—82no—
571C2×C4—161no—
572C2×C4C22×D4×C10311yescharacteristic
573C2×C4C22×D4×C10311yescharacteristic
574C2×C4H(5,𝔽2)×C10311yescharacteristic
575C8—21no—
576C8—21no—
577C8—41no—
578C8—41no—
579C8—41no—
580C8—41no—
581C8—41no—
582C8#135×C10312yescomplemented
583C8AGL(1,ℤ/8)×C10312yes—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—81no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22D42×C10311yescharacteristic
597C4—21no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—81no—
605C4—81no—
606C4C2×#135×C10311yescharacteristic
607C4C2×AGL(1,ℤ/8)×C10311yescharacteristic
608C4#576×C10311yescharacteristic
609C4#577×C10311yescharacteristic
610C2—81no—
611C2—81no—
612C2—161no—
613C2—161no—
614C2C103×#327411yescharacteristic
615C2C103×#328411yescharacteristic
616C2C103×#329011yescharacteristic
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×#3399C2semidirect
2. C103×#3394C2semidirect
3. C103×#3353C2semidirect
4. C103×#3284C2semidirect
5. C103×#1706C2semidirect
6. C103×#1694C2semidirect
7. C103×#1687C2semidirect
8. C103×#1666C2semidirect
9. C103×#1665C2semidirect
10. C103×#1641C2semidirect
11. C103×#1640C2semidirect
12. C103×#1628C2semidirect
13. C103×#1625C2semidirect
14. C103×#1590C2semidirect
15. C8×SD16×C103C2semidirect
273. C8×C103#135semidirect
301. #19947C103direct (N × H)
309. #3399C2×C103semidirect
310. #3394C2×C103semidirect
311. #3353C2×C103semidirect
312. #3284C2×C103semidirect
313. #1706C2×C103semidirect
314. #1694C2×C103semidirect
315. #1687C2×C103semidirect
316. #1666C2×C103semidirect
317. #1665C2×C103semidirect
318. #1641C2×C103semidirect
319. #1640C2×C103semidirect
320. #1628C2×C103semidirect
321. #1625C2×C103semidirect
322. #1590C2×C103semidirect
323. C8×SD16C2×C103semidirect
324. C103#19947direct (N × H)
582. C8#135×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#33992
C103×#33942
C103×#33532
C103×#32842
C103×#17062
C103×#16942
C103×#16872
C103×#16662
C103×#16652
C103×#16412
C103×#16402
C103×#16282
C103×#16252
C103×#15902
C8×SD16×C1032
#19947103