Finite Group Databasebeta

← C103×#19871 #39925146

Subgroups — C103×#19871 #39925146

Order 26368.

632 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3399C211yesmaximal, characteristic, complemented
2C103×#3396C211yesmaximal, characteristic, complemented
3C103×#3394C211yesmaximal, characteristic, complemented
4C103×#3304C211yesmaximal, characteristic, complemented
5C103×#1721C211yesmaximal, characteristic, complemented
6C103×#1686C211yesmaximal, characteristic, complemented
7C103×#1682C211yesmaximal, characteristic, complemented
8C103×#1668C211yesmaximal, characteristic, complemented
9C103×#1667C211yesmaximal, characteristic, complemented
10C103×#1640C211yesmaximal, characteristic, complemented
11C103×#1628C211yesmaximal, characteristic, complemented
12C103×#1621C211yesmaximal, characteristic, complemented
13C103×#1620C211yesmaximal, characteristic, complemented
14C103×#1584C211yesmaximal, characteristic, complemented
15C103×SD16⋊C8C211yesmaximal, characteristic, complemented
16#559×C103C2211yescharacteristic
17#559×C103C2211yescharacteristic
18#556×C103C2211yescharacteristic
19#550×C103C2211yescharacteristic
20#496×C103—21no—
21#495×C103—21no—
22#495×C103—21no—
23#493×C103C2211yescharacteristic
24#493×C103C2211yescharacteristic
25#493×C103C2211yescharacteristic
26#492×C103C2211yescharacteristic
27#486×C103C2211yescharacteristic
28#486×C103C2211yescharacteristic
29#482×C103—21no—
30#475×C103C2211yescharacteristic
31#465×C103—21no—
32#464×C103—21no—
33#463×C103—21no—
34#463×C103—21no—
35#463×C103—21no—
36#463×C103—21no—
37#462×C103C2211yescharacteristic
38#460×C103C2211yescharacteristic
39#460×C103C2211yescharacteristic
40#460×C103C2211yescharacteristic
41#460×C103C2211yescharacteristic
42#459×C103—21no—
43#459×C103C2211yescharacteristic
44#459×C103C2211yescharacteristic
45#452×C103—21no—
46#446×C103C2211yescharacteristic
47C8×Q8×C103C2211yescharacteristic
48C8×Q8×C103C2211yescharacteristic
49#442×C103—21no—
50C4×Q16×C103C2211yescharacteristic
51C4×SD16×C103—21no—
52C4×SD16×C103C2211yescharacteristic
53C4×D8×C103—21no—
54C8×D4×C103C2211yescharacteristic
55#416×C103—21no—
56#335×C103C2211yescharacteristic
57#335×C103C2211yescharacteristic
58#332×C103C2211yescharacteristic
59#331×C103C2211yescharacteristic
60#331×C103C2211yescharacteristic
61#331×C103C2211yescharacteristic
62Q8⋊C8×C103C2211yescharacteristic
63Q8⋊C8×C103C2211yescharacteristic
64Q8⋊C8×C103C2211yescharacteristic
65D4⋊C8×C103C2211yescharacteristic
66#322×C103C2211yescharacteristic
67C2×#41×C103—21no—
68C2×Q16×C103—21no—
69C2×Q16×C103D411yescharacteristic
70C2×SD16×C103—21no—
71C2×SD16×C103—21no—
72C2×SD16×C103—21no—
73C2×SD16×C103—21no—
74C2×SD16×C103—21no—
75C2×SD16×C103—21no—
76C2×SD16×C103D411yescharacteristic
77C2×D8×C103—21no—
78C2×D8×C103—21no—
79C2×D8×C103—21no—
80C2×D8×C103—21no—
81C2×D8×C103—21no—
82C2×D8×C103—21no—
83C2×D8×C103—41no—
84C22×C8×C103—21no—
85C4⋊Q8×C103C2311yescharacteristic
86#127×C103—21no—
87#127×C103C2311yescharacteristic
88#127×C103C2311yescharacteristic
89#127×C103C2311yescharacteristic
90#126×C103—41no—
91#124×C103—21no—
92#124×C103—21no—
93#124×C103—21no—
94#124×C103—21no—
95#124×C103—21no—
96#123×C103—41no—
97#123×C103—41no—
98C22⋊Q8×C103—21no—
99#121×C103—21no—
100#121×C103—41no—
101C4×Q8×C103—21no—
102C4×Q8×C103C2311yescharacteristic
103C4×Q8×C103C2311yescharacteristic
104C4×Q8×C103C2311yescharacteristic
105C4×D4×C103—21no—
106C4×D4×C103—21no—
107C4×D4×C103—21no—
108C4×D4×C103—21no—
109C4×D4×C103—21no—
110C4×D4×C103C2311yescharacteristic
111#117×C103—21no—
112#107×C103D411yescharacteristic
113#106×C103—21no—
114#106×C103D411yescharacteristic
115C4⋊C8×C103—21no—
116C4⋊C8×C103—21no—
117C4⋊C8×C103—21no—
118C4⋊C8×C103C2311yescharacteristic
119C4⋊C8×C103C2311yescharacteristic
120C4⋊C8×C103C2311yescharacteristic
121C4⋊C8×C103C2311yescharacteristic
122#103×C103—21no—
123#103×C103—21no—
124#103×C103D411yescharacteristic
125#103×C103D411yescharacteristic
126#103×C103D411yescharacteristic
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×C103—21no—
135#102×C103—41no—
136#102×C103D411yescharacteristic
137C22⋊C8×C103—21no—
138#97×C103—21no—
139C4×C8×C103—21no—
140C4×C8×C103—21no—
141C4×C8×C103C2311yescharacteristic
142C4×C8×C103C2311yescharacteristic
143C4×C8×C103C2311yescharacteristic
144#41×C103—42no—
145#41×C103—81no—
146C2×Q8×C103—21no—
147C2×Q8×C103C2×D411yescharacteristic
148C2×Q8×C103C2×D411yescharacteristic
149C2×Q8×C103C2×D411yescharacteristic
150C2×D4×C103—21no—
151C2×D4×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×C103—41no—
161C2×D4×C103C2×D411yescharacteristic
162C22×C4×C103—21no—
163C22×C4×C103—41no—
164C22×C4×C103—41no—
165C22×C4×C103—41no—
166Q16×C103—41no—
167Q16×C103—81no—
168SD16×C103—22no—
169SD16×C103—42no—
170SD16×C103—81no—
171SD16×C103—81no—
172SD16×C103—81no—
173SD16×C103—81no—
174SD16×C103—81no—
175D8×C103—42no—
176D8×C103—42no—
177D8×C103—81no—
178D8×C103—81no—
179D8×C103—81no—
180D8×C103—81no—
181D8×C103—82no—
182C2×C8×C103—21no—
183C2×C8×C103—21no—
184C2×C8×C103—21no—
185C2×C8×C103—21no—
186C2×C8×C103—21no—
187C2×C8×C103—81no—
188C2×C8×C103C2×D411yescharacteristic
189C2×C8×C103C2×D411yescharacteristic
190C2×C8×C103C2×D411yescharacteristic
191C2×C8×C103C2×D411yescharacteristic
192C4⋊C4×C103—21no—
193C4⋊C4×C103—21no—
194C4⋊C4×C103—21no—
195C4⋊C4×C103—21no—
196C4⋊C4×C103—21no—
197C4⋊C4×C103—41no—
198C4⋊C4×C103C2×D411yescharacteristic
199C4⋊C4×C103C2×D411yescharacteristic
200C4⋊C4×C103C2×D411yescharacteristic
201C4⋊C4×C103C2×D411yescharacteristic
202C22⋊C4×C103—21no—
203C22⋊C4×C103—41no—
204C22⋊C4×C103—41no—
205C22⋊C4×C103—41no—
206C22⋊C4×C103—41no—
207C22⋊C4×C103—41no—
208C22⋊C4×C103—41no—
209C22⋊C4×C103—41no—
210C22⋊C4×C103—41no—
211C22⋊C4×C103—41no—
212C42×C103—21no—
213C42×C103—21no—
214C42×C103—21no—
215C42×C103—41no—
216C42×C103C2411yescharacteristic
217C23×C103—21no—
218C23×C103—41no—
219C23×C103—41no—
220C23×C103—41no—
221Q8×C103—21no—
222Q8×C103—21no—
223Q8×C103—21no—
224Q8×C103—21no—
225Q8×C103—21no—
226Q8×C103—21no—
227Q8×C103—41no—
228Q8×C103—41no—
229D4×C103—21no—
230D4×C103—21no—
231D4×C103—41no—
232D4×C103—41no—
233D4×C103—41no—
234D4×C103—41no—
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—81no—
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—21no—
255C2×C4×C103—41no—
256C2×C4×C103—41no—
257C2×C4×C103—41no—
258C2×C4×C103—82no—
259C2×C4×C103—161no—
260C2×C4×C103—161no—
261C2×C4×C103C22×D411yescharacteristic
262C2×C4×C103C22×D411yescharacteristic
263C2×C4×C103H(5,𝔽2)11yescharacteristic
264C8×C103—21no—
265C8×C103—21no—
266C8×C103—21no—
267C8×C103—41no—
268C8×C103—41no—
269C8×C103—41no—
270C8×C103—41no—
271C8×C103—41no—
272C8×C103#13512yes—
273C22×C103—41no—
274C22×C103—41no—
275C22×C103—41no—
276C22×C103—81no—
277C22×C103—81no—
278C22×C103—81no—
279C22×C103—81no—
280C22×C103—81no—
281C22×C103—81no—
282C22×C103—81no—
283C22×C103—81no—
284C22×C103—81no—
285C22×C103D4211yescharacteristic
286C4×C103—21no—
287C4×C103—41no—
288C4×C103—41no—
289C4×C103—41no—
290C4×C103—41no—
291C4×C103—41no—
292C4×C103—41no—
293C4×C103—41no—
294C4×C103—81no—
295C4×C103C2×#13511yescharacteristic
296C4×C103#57511yescharacteristic
297C4×C103#57611yescharacteristic
298C4×C103#57611yescharacteristic
299#19871C10311yesmaximal, characteristic, direct product factor, Sylow
300C2×C103—81no—
301C2×C103—161no—
302C2×C103—161no—
303C2×C103—161no—
304C2×C103#326811yescharacteristic
305C2×C103#328711yescharacteristic
306C2×C103#328811yescharacteristic
307#3399C2×C10311yescharacteristic, complemented
308#3396C2×C10311yescharacteristic, complemented
309#3394C2×C10311yescharacteristic, complemented
310#3304C2×C10311yescharacteristic, complemented
311#1721C2×C10311yescharacteristic, complemented
312#1686C2×C10311yescharacteristic, complemented
313#1682C2×C10311yescharacteristic, complemented
314#1668C2×C10311yescharacteristic, complemented
315#1667C2×C10311yescharacteristic, complemented
316#1640C2×C10311yescharacteristic, complemented
317#1628C2×C10311yescharacteristic, complemented
318#1621C2×C10311yescharacteristic, complemented
319#1620C2×C10311yescharacteristic, complemented
320#1584C2×C10311yescharacteristic, complemented
321SD16⋊C8C2×C10311yescharacteristic, complemented
322C103#1987111yescharacteristic, direct product factor, Sylow
323#559C22×C10311yescharacteristic
324#559C22×C10311yescharacteristic
325#556C22×C10311yescharacteristic
326#550C22×C10311yescharacteristic
327#496—21no—
328#495—21no—
329#495—21no—
330#493C22×C10311yescharacteristic
331#493C22×C10311yescharacteristic
332#493C22×C10311yescharacteristic
333#492C22×C10311yescharacteristic
334#486C22×C10311yescharacteristic
335#486C22×C10311yescharacteristic
336#482—21no—
337#475C22×C10311yescharacteristic
338#465—21no—
339#464—21no—
340#463—21no—
341#463—21no—
342#463—21no—
343#463—21no—
344#462C22×C10311yescharacteristic
345#460C22×C10311yescharacteristic
346#460C22×C10311yescharacteristic
347#460C22×C10311yescharacteristic
348#460C22×C10311yescharacteristic
349#459—21no—
350#459C22×C10311yescharacteristic
351#459C22×C10311yescharacteristic
352#452—21no—
353#446C22×C10311yescharacteristic
354C8×Q8C22×C10311yescharacteristic
355C8×Q8C22×C10311yescharacteristic
356#442—21no—
357C4×Q16C22×C10311yescharacteristic
358C4×SD16—21no—
359C4×SD16C22×C10311yescharacteristic
360C4×D8—21no—
361C8×D4C22×C10311yescharacteristic
362#416—21no—
363#335C22×C10311yescharacteristic
364#335C22×C10311yescharacteristic
365#332C22×C10311yescharacteristic
366#331C22×C10311yescharacteristic
367#331C22×C10311yescharacteristic
368#331C22×C10311yescharacteristic
369Q8⋊C8C22×C10311yescharacteristic
370Q8⋊C8C22×C10311yescharacteristic
371Q8⋊C8C22×C10311yescharacteristic
372D4⋊C8C22×C10311yescharacteristic
373#322C22×C10311yescharacteristic
374C2×#41—21no—
375C2×Q16—21no—
376C2×Q16D4×C10311yescharacteristic
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×SD16—21no—
381C2×SD16—21no—
382C2×SD16—21no—
383C2×SD16D4×C10311yescharacteristic
384C2×D8—21no—
385C2×D8—21no—
386C2×D8—21no—
387C2×D8—21no—
388C2×D8—21no—
389C2×D8—21no—
390C2×D8—41no—
391C22×C8—21no—
392C4⋊Q8C23×C10311yescharacteristic
393#127—21no—
394#127C23×C10311yescharacteristic
395#127C23×C10311yescharacteristic
396#127C23×C10311yescharacteristic
397#126—41no—
398#124—21no—
399#124—21no—
400#124—21no—
401#124—21no—
402#124—21no—
403#123—41no—
404#123—41no—
405C22⋊Q8—21no—
406#121—21no—
407#121—41no—
408C4×Q8—21no—
409C4×Q8C23×C10311yescharacteristic
410C4×Q8C23×C10311yescharacteristic
411C4×Q8C23×C10311yescharacteristic
412C4×D4—21no—
413C4×D4—21no—
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—21no—
417C4×D4C23×C10311yescharacteristic
418#117—21no—
419#107D4×C10311yescharacteristic
420#106—21no—
421#106D4×C10311yescharacteristic
422C4⋊C8—21no—
423C4⋊C8—21no—
424C4⋊C8—21no—
425C4⋊C8C23×C10311yescharacteristic
426C4⋊C8C23×C10311yescharacteristic
427C4⋊C8C23×C10311yescharacteristic
428C4⋊C8C23×C10311yescharacteristic
429#103—21no—
430#103—21no—
431#103D4×C10311yescharacteristic
432#103D4×C10311yescharacteristic
433#103D4×C10311yescharacteristic
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—41no—
443#102D4×C10311yescharacteristic
444C22⋊C8—21no—
445#97—21no—
446C4×C8—21no—
447C4×C8—21no—
448C4×C8C23×C10311yescharacteristic
449C4×C8C23×C10311yescharacteristic
450C4×C8C23×C10311yescharacteristic
451#41—42no—
452#41—81no—
453C2×Q8—21no—
454C2×Q8C2×D4×C10311yescharacteristic
455C2×Q8C2×D4×C10311yescharacteristic
456C2×Q8C2×D4×C10311yescharacteristic
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4C2×D4×C10311yescharacteristic
469C22×C4—21no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473Q16—41no—
474Q16—81no—
475SD16—22no—
476SD16—42no—
477SD16—81no—
478SD16—81no—
479SD16—81no—
480SD16—81no—
481SD16—81no—
482D8—42no—
483D8—42no—
484D8—81no—
485D8—81no—
486D8—81no—
487D8—81no—
488D8—82no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—81no—
495C2×C8C2×D4×C10311yescharacteristic
496C2×C8C2×D4×C10311yescharacteristic
497C2×C8C2×D4×C10311yescharacteristic
498C2×C8C2×D4×C10311yescharacteristic
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—41no—
505C4⋊C4C2×D4×C10311yescharacteristic
506C4⋊C4C2×D4×C10311yescharacteristic
507C4⋊C4C2×D4×C10311yescharacteristic
508C4⋊C4C2×D4×C10311yescharacteristic
509C22⋊C4—21no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—41no—
523C42C24×C10311yescharacteristic
524C23—21no—
525C23—41no—
526C23—41no—
527C23—41no—
528Q8—21no—
529Q8—21no—
530Q8—21no—
531Q8—21no—
532Q8—21no—
533Q8—21no—
534Q8—41no—
535Q8—41no—
536D4—21no—
537D4—21no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—81no—
551D4—81no—
552D4—81no—
553D4—82no—
554D4—161no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—82no—
566C2×C4—161no—
567C2×C4—161no—
568C2×C4C22×D4×C10311yescharacteristic
569C2×C4C22×D4×C10311yescharacteristic
570C2×C4H(5,𝔽2)×C10311yescharacteristic
571C8—21no—
572C8—21no—
573C8—21no—
574C8—41no—
575C8—41no—
576C8—41no—
577C8—41no—
578C8—41no—
579C8#135×C10312yes—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—81no—
592C22D42×C10311yescharacteristic
593C4—21no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—81no—
602C4C2×#135×C10311yescharacteristic
603C4#575×C10311yescharacteristic
604C4#576×C10311yescharacteristic
605C4#576×C10311yescharacteristic
606C2—81no—
607C2—161no—
608C2—161no—
609C2—161no—
610C2C103×#326811yescharacteristic
611C2C103×#328711yescharacteristic
612C2C103×#328811yescharacteristic
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×#3396C2semidirect
3. C103×#3394C2semidirect
4. C103×#3304C2semidirect
5. C103×#1721C2semidirect
6. C103×#1686C2semidirect
7. C103×#1682C2semidirect
8. C103×#1668C2semidirect
9. C103×#1667C2semidirect
10. C103×#1640C2semidirect
11. C103×#1628C2semidirect
12. C103×#1621C2semidirect
13. C103×#1620C2semidirect
14. C103×#1584C2semidirect
15. C103×SD16⋊C8C2semidirect
299. #19871C103direct (N × H)
307. #3399C2×C103semidirect
308. #3396C2×C103semidirect
309. #3394C2×C103semidirect
310. #3304C2×C103semidirect
311. #1721C2×C103semidirect
312. #1686C2×C103semidirect
313. #1682C2×C103semidirect
314. #1668C2×C103semidirect
315. #1667C2×C103semidirect
316. #1640C2×C103semidirect
317. #1628C2×C103semidirect
318. #1621C2×C103semidirect
319. #1620C2×C103semidirect
320. #1584C2×C103semidirect
321. SD16⋊C8C2×C103semidirect
322. C103#19871direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#33992
C103×#33962
C103×#33942
C103×#33042
C103×#17212
C103×#16862
C103×#16822
C103×#16682
C103×#16672
C103×#16402
C103×#16282
C103×#16212
C103×#16202
C103×#15842
C103×SD16⋊C82
#19871103