Finite Group Databasebeta

← C103×#19981 #39925256

Subgroups — C103×#19981 #39925256

Order 26368.

658 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×SD16×C103C211yesmaximal, characteristic, complemented
2C103×#3362C211yesmaximal, characteristic, complemented
3C103×#3298C211yesmaximal, characteristic, complemented
4C103×#3284C211yesmaximal, characteristic
5C103×#1708C211yesmaximal, characteristic, complemented
6C103×#1680C211yesmaximal, characteristic, complemented
7C103×#1677C211yesmaximal, characteristic, complemented
8C103×#1671C211yesmaximal, characteristic, complemented
9C103×#1666C211yesmaximal, characteristic, complemented
10C103×#1645C211yesmaximal, characteristic, complemented
11C103×#1642C211yesmaximal, characteristic, complemented
12C103×#1635C211yesmaximal, characteristic, complemented
13C103×#1627C211yesmaximal, characteristic, complemented
14C8×SD16×C103C211yesmaximal, characteristic, complemented
15C8×SD16×C103C211yesmaximal, characteristic, complemented
16C2×#135×C103—21no—
17Q82×C103C2211yescharacteristic
18#550×C103C2211yescharacteristic
19D4×Q8×C103C2211yescharacteristic
20#547×C103C2211yescharacteristic
21#498×C103—21no—
22#498×C103C2211yescharacteristic
23#492×C103C2211yescharacteristic
24#487×C103C2211yescharacteristic
25#487×C103C2211yescharacteristic
26#486×C103—21no—
27#486×C103C2211yescharacteristic
28#486×C103C2211yescharacteristic
29#483×C103—21no—
30#476×C103—21no—
31#476×C103—21no—
32#476×C103C2211yescharacteristic
33#476×C103C2211yescharacteristic
34#475×C103—21no—
35#475×C103C2211yescharacteristic
36#475×C103C2211yescharacteristic
37#465×C103—21no—
38#465×C103—21no—
39#462×C103C2211yescharacteristic
40#461×C103C2211yescharacteristic
41#460×C103—21no—
42#460×C103C2211yescharacteristic
43#459×C103C2211yescharacteristic
44#452×C103—21no—
45#449×C103—21no—
46#448×C103—21no—
47C8×Q8×C103C2211yescharacteristic
48C8×Q8×C103C2211yescharacteristic
49C4×SD16×C103—21no—
50C4×SD16×C103—21no—
51C4×SD16×C103C2211yescharacteristic
52C4×SD16×C103C2211yescharacteristic
53C8×D4×C103C2211yescharacteristic
54C8×D4×C103C2211yescharacteristic
55C2×#103×C103—21no—
56#334×C103C2211yescharacteristic
57#334×C103C2211yescharacteristic
58#333×C103C2211yescharacteristic
59#332×C103C2211yescharacteristic
60#332×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—
69C22×Q8×C103—21no—
70#135×C103—44no—
71C2×Q16×C103—21no—
72C2×SD16×C103—21no—
73C2×SD16×C103—21no—
74C2×SD16×C103—21no—
75C2×SD16×C103—21no—
76C2×SD16×C103D411yescharacteristic
77C2×SD16×C103D411yescharacteristic
78C2×D8×C103—21no—
79C22×C8×C103—21no—
80C22×C8×C103—21no—
81C4⋊Q8×C103—21no—
82C4⋊Q8×C103—21no—
83C4⋊Q8×C103—21no—
84C4⋊Q8×C103—41no—
85C4⋊Q8×C103C2311yescharacteristic
86C4⋊Q8×C103C2311yescharacteristic
87C4⋊Q8×C103C2311yescharacteristic
88#127×C103—21no—
89#127×C103C2311yescharacteristic
90#123×C103—41no—
91C22⋊Q8×C103—21no—
92C22⋊Q8×C103—21no—
93C22⋊Q8×C103—41no—
94#121×C103—21no—
95#121×C103—21no—
96#121×C103—41no—
97C4×Q8×C103—21no—
98C4×Q8×C103—21no—
99C4×Q8×C103C2311yescharacteristic
100C4×Q8×C103C2311yescharacteristic
101C4×D4×C103—21no—
102C4×D4×C103—21no—
103C4×D4×C103C2311yescharacteristic
104C4×D4×C103C2311yescharacteristic
105C2×C4⋊C4×C103—21no—
106#106×C103—21no—
107#106×C103—21no—
108#106×C103—21no—
109#106×C103—21no—
110#106×C103—21no—
111#106×C103—21no—
112#106×C103D411yescharacteristic
113#106×C103D411yescharacteristic
114C4⋊C8×C103—21no—
115C4⋊C8×C103—21no—
116C4⋊C8×C103C2311yescharacteristic
117C4⋊C8×C103C2311yescharacteristic
118C4⋊C8×C103C2311yescharacteristic
119C4⋊C8×C103C2311yescharacteristic
120#103×C103—21no—
121#103×C103—21no—
122#103×C103—21no—
123#103×C103—21no—
124#103×C103—21no—
125#103×C103—21no—
126#103×C103—41no—
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—21no—
135#102×C103—41no—
136#102×C103D411yescharacteristic
137#102×C103D411yescharacteristic
138C22⋊C8×C103—21no—
139C22⋊C8×C103—21no—
140C4×C8×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×C103—21no—
152C2×Q8×C103—41no—
153C2×Q8×C103—41no—
154C2×Q8×C103—42no—
155C2×Q8×C103—81no—
156C2×Q8×C103C2×D411yescharacteristic
157C2×Q8×C103C2×D411yescharacteristic
158C2×D4×C103—21no—
159C2×D4×C103—21no—
160C2×D4×C103—21no—
161C2×D4×C103—41no—
162C2×D4×C103—41no—
163C2×D4×C103—41no—
164C2×D4×C103C2×D411yescharacteristic
165C2×D4×C103C2×D411yescharacteristic
166C22×C4×C103—21no—
167C22×C4×C103—21no—
168C22×C4×C103—41no—
169C22×C4×C103—41no—
170C22×C4×C103—41no—
171Q16×C103—42no—
172SD16×C103—22no—
173SD16×C103—42no—
174SD16×C103—42no—
175SD16×C103—81no—
176SD16×C103—81no—
177SD16×C103SD1614yescomplemented
178D8×C103—42no—
179C2×C8×C103—21no—
180C2×C8×C103—21no—
181C2×C8×C103—21no—
182C2×C8×C103—21no—
183C2×C8×C103—21no—
184C2×C8×C103—42no—
185C2×C8×C103—81no—
186C2×C8×C103C2×D411yescharacteristic
187C2×C8×C103C2×D411yescharacteristic
188C2×C8×C103C2×D411yescharacteristic
189C2×C8×C103C2×D411yescharacteristic
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—21no—
197C4⋊C4×C103—21no—
198C4⋊C4×C103—41no—
199C4⋊C4×C103—41no—
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—
211C42×C103—21no—
212C42×C103—21no—
213C42×C103—41no—
214C42×C103C2411yescharacteristic
215C23×C103—21no—
216C23×C103—21no—
217C23×C103—41no—
218Q8×C103—21no—
219Q8×C103—21no—
220Q8×C103—41no—
221Q8×C103—41no—
222Q8×C103—41no—
223Q8×C103—41no—
224Q8×C103—82no—
225Q8×C103—81no—
226Q8×C103—161no—
227Q8×C103C2×SD1612yes—
228Q8×C103#13512yescomplemented
229D4×C103—21no—
230D4×C103—21no—
231D4×C103—21no—
232D4×C103—41no—
233D4×C103—41no—
234D4×C103—41no—
235D4×C103—41no—
236D4×C103—82no—
237D4×C103—81no—
238D4×C103—82no—
239D4×C103—161no—
240D4×C103C2×SD1612yes—
241C2×C4×C103—21no—
242C2×C4×C103—21no—
243C2×C4×C103—21no—
244C2×C4×C103—21no—
245C2×C4×C103—21no—
246C2×C4×C103—21no—
247C2×C4×C103—41no—
248C2×C4×C103—41no—
249C2×C4×C103—41no—
250C2×C4×C103—41no—
251C2×C4×C103—41no—
252C2×C4×C103—41no—
253C2×C4×C103—41no—
254C2×C4×C103—82no—
255C2×C4×C103—82no—
256C2×C4×C103—82no—
257C2×C4×C103C22×D411yescharacteristic
258C2×C4×C103C22×D411yescharacteristic
259C2×C4×C103H(5,𝔽2)11yescharacteristic
260C8×C103—21no—
261C8×C103—21no—
262C8×C103—21no—
263C8×C103—41no—
264C8×C103—41no—
265C8×C103—41no—
266C8×C103—41no—
267C8×C103—41no—
268C8×C103C2×SD1612yes—
269C22×C103—22no—
270C22×C103—41no—
271C22×C103—41no—
272C22×C103—41no—
273C22×C103—41no—
274C22×C103—41no—
275C22×C103—81no—
276C22×C103—81no—
277C22×C103—81no—
278C22×C103D4211yescharacteristic
279C4×C103—22no—
280C4×C103—22no—
281C4×C103—21no—
282C4×C103—41no—
283C4×C103—41no—
284C4×C103—41no—
285C4×C103—41no—
286C4×C103—81no—
287C4×C103—81no—
288C4×C103—81no—
289C4×C103C22×SD1611yescharacteristic
290C4×C103C2×#13511yescharacteristic
291C4×C103#57711yescharacteristic
292C4×C103#57711yescharacteristic
293#19981C10311yesmaximal, characteristic, direct product factor, Sylow
294C2×C103—42no—
295C2×C103—81no—
296C2×C103—161no—
297C2×C103D4×SD1611yescharacteristic
298C2×C103#328211yescharacteristic
299C2×C103#329011yescharacteristic
300Q8×SD16C2×C10311yescharacteristic, complemented
301#3362C2×C10311yescharacteristic, complemented
302#3298C2×C10311yescharacteristic, complemented
303#3284C2×C10311yescharacteristic
304#1708C2×C10311yescharacteristic, complemented
305#1680C2×C10311yescharacteristic, complemented
306#1677C2×C10311yescharacteristic, complemented
307#1671C2×C10311yescharacteristic, complemented
308#1666C2×C10311yescharacteristic, complemented
309#1645C2×C10311yescharacteristic, complemented
310#1642C2×C10311yescharacteristic, complemented
311#1635C2×C10311yescharacteristic, complemented
312#1627C2×C10311yescharacteristic, complemented
313C8×SD16C2×C10311yescharacteristic, complemented
314C8×SD16C2×C10311yescharacteristic, complemented
315C103#1998111yescharacteristic, direct product factor, Sylow
316C2×#135—21no—
317Q82C22×C10311yescharacteristic
318#550C22×C10311yescharacteristic
319D4×Q8C22×C10311yescharacteristic
320#547C22×C10311yescharacteristic
321#498—21no—
322#498C22×C10311yescharacteristic
323#492C22×C10311yescharacteristic
324#487C22×C10311yescharacteristic
325#487C22×C10311yescharacteristic
326#486—21no—
327#486C22×C10311yescharacteristic
328#486C22×C10311yescharacteristic
329#483—21no—
330#476—21no—
331#476—21no—
332#476C22×C10311yescharacteristic
333#476C22×C10311yescharacteristic
334#475—21no—
335#475C22×C10311yescharacteristic
336#475C22×C10311yescharacteristic
337#465—21no—
338#465—21no—
339#462C22×C10311yescharacteristic
340#461C22×C10311yescharacteristic
341#460—21no—
342#460C22×C10311yescharacteristic
343#459C22×C10311yescharacteristic
344#452—21no—
345#449—21no—
346#448—21no—
347C8×Q8C22×C10311yescharacteristic
348C8×Q8C22×C10311yescharacteristic
349C4×SD16—21no—
350C4×SD16—21no—
351C4×SD16C22×C10311yescharacteristic
352C4×SD16C22×C10311yescharacteristic
353C8×D4C22×C10311yescharacteristic
354C8×D4C22×C10311yescharacteristic
355C2×#103—21no—
356#334C22×C10311yescharacteristic
357#334C22×C10311yescharacteristic
358#333C22×C10311yescharacteristic
359#332C22×C10311yescharacteristic
360#332C22×C10311yescharacteristic
361#331C22×C10311yescharacteristic
362Q8⋊C8C22×C10311yescharacteristic
363Q8⋊C8C22×C10311yescharacteristic
364D4⋊C8C22×C10311yescharacteristic
365D4⋊C8C22×C10311yescharacteristic
366C82C22×C10311yescharacteristic
367C2×#41—21no—
368C2×#41—21no—
369C22×Q8—21no—
370#135—44no—
371C2×Q16—21no—
372C2×SD16—21no—
373C2×SD16—21no—
374C2×SD16—21no—
375C2×SD16—21no—
376C2×SD16D4×C10311yescharacteristic
377C2×SD16D4×C10311yescharacteristic
378C2×D8—21no—
379C22×C8—21no—
380C22×C8—21no—
381C4⋊Q8—21no—
382C4⋊Q8—21no—
383C4⋊Q8—21no—
384C4⋊Q8—41no—
385C4⋊Q8C23×C10311yescharacteristic
386C4⋊Q8C23×C10311yescharacteristic
387C4⋊Q8C23×C10311yescharacteristic
388#127—21no—
389#127C23×C10311yescharacteristic
390#123—41no—
391C22⋊Q8—21no—
392C22⋊Q8—21no—
393C22⋊Q8—41no—
394#121—21no—
395#121—21no—
396#121—41no—
397C4×Q8—21no—
398C4×Q8—21no—
399C4×Q8C23×C10311yescharacteristic
400C4×Q8C23×C10311yescharacteristic
401C4×D4—21no—
402C4×D4—21no—
403C4×D4C23×C10311yescharacteristic
404C4×D4C23×C10311yescharacteristic
405C2×C4⋊C4—21no—
406#106—21no—
407#106—21no—
408#106—21no—
409#106—21no—
410#106—21no—
411#106—21no—
412#106D4×C10311yescharacteristic
413#106D4×C10311yescharacteristic
414C4⋊C8—21no—
415C4⋊C8—21no—
416C4⋊C8C23×C10311yescharacteristic
417C4⋊C8C23×C10311yescharacteristic
418C4⋊C8C23×C10311yescharacteristic
419C4⋊C8C23×C10311yescharacteristic
420#103—21no—
421#103—21no—
422#103—21no—
423#103—21no—
424#103—21no—
425#103—21no—
426#103—41no—
427#103D4×C10311yescharacteristic
428#103D4×C10311yescharacteristic
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—41no—
436#102D4×C10311yescharacteristic
437#102D4×C10311yescharacteristic
438C22⋊C8—21no—
439C22⋊C8—21no—
440C4×C8—21no—
441C4×C8—21no—
442C4×C8C23×C10311yescharacteristic
443C4×C8C23×C10311yescharacteristic
444C4×C8C23×C10311yescharacteristic
445#41—42no—
446#41—42no—
447#41—81no—
448#41—81no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—41no—
453C2×Q8—41no—
454C2×Q8—42no—
455C2×Q8—81no—
456C2×Q8C2×D4×C10311yescharacteristic
457C2×Q8C2×D4×C10311yescharacteristic
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4C2×D4×C10311yescharacteristic
465C2×D4C2×D4×C10311yescharacteristic
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471Q16—42no—
472SD16—22no—
473SD16—42no—
474SD16—42no—
475SD16—81no—
476SD16—81no—
477SD16SD16×C10314yescomplemented
478D8—42no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—42no—
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—21no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4C2×D4×C10311yescharacteristic
503C4⋊C4C2×D4×C10311yescharacteristic
504C4⋊C4C2×D4×C10311yescharacteristic
505C4⋊C4C2×D4×C10311yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C42—21no—
512C42—21no—
513C42—41no—
514C42C24×C10311yescharacteristic
515C23—21no—
516C23—21no—
517C23—41no—
518Q8—21no—
519Q8—21no—
520Q8—41no—
521Q8—41no—
522Q8—41no—
523Q8—41no—
524Q8—82no—
525Q8—81no—
526Q8—161no—
527Q8C2×SD16×C10312yes—
528Q8#135×C10312yescomplemented
529D4—21no—
530D4—21no—
531D4—21no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—82no—
537D4—81no—
538D4—82no—
539D4—161no—
540D4C2×SD16×C10312yes—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—82no—
555C2×C4—82no—
556C2×C4—82no—
557C2×C4C22×D4×C10311yescharacteristic
558C2×C4C22×D4×C10311yescharacteristic
559C2×C4H(5,𝔽2)×C10311yescharacteristic
560C8—21no—
561C8—21no—
562C8—21no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—41no—
567C8—41no—
568C8C2×SD16×C10312yes—
569C22—22no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22D42×C10311yescharacteristic
579C4—22no—
580C4—22no—
581C4—21no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4C22×SD16×C10311yescharacteristic
590C4C2×#135×C10311yescharacteristic
591C4#577×C10311yescharacteristic
592C4#577×C10311yescharacteristic
593C2—42no—
594C2—81no—
595C2—161no—
596C2D4×SD16×C10311yescharacteristic
597C2C103×#328211yescharacteristic
598C2C103×#329011yescharacteristic
subgroupG/H
center, socleC22×C103D42
commutator, Frattini, cosocleC42C24×C103
prime radicalC103×#3284C2
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. Q8×SD16×C103C2semidirect
2. C103×#3362C2semidirect
3. C103×#3298C2semidirect
5. C103×#1708C2semidirect
6. C103×#1680C2semidirect
7. C103×#1677C2semidirect
8. C103×#1671C2semidirect
9. C103×#1666C2semidirect
10. C103×#1645C2semidirect
11. C103×#1642C2semidirect
12. C103×#1635C2semidirect
13. C103×#1627C2semidirect
14. C8×SD16×C103C2semidirect
15. C8×SD16×C103C2semidirect
177. SD16×C103SD16semidirect
228. Q8×C103#135semidirect
293. #19981C103direct (N × H)
300. Q8×SD16C2×C103semidirect
301. #3362C2×C103semidirect
302. #3298C2×C103semidirect
304. #1708C2×C103semidirect
305. #1680C2×C103semidirect
306. #1677C2×C103semidirect
307. #1671C2×C103semidirect
308. #1666C2×C103semidirect
309. #1645C2×C103semidirect
310. #1642C2×C103semidirect
311. #1635C2×C103semidirect
312. #1627C2×C103semidirect
313. C8×SD16C2×C103semidirect
314. C8×SD16C2×C103semidirect
315. C103#19981direct (N × H)
477. SD16SD16×C103semidirect
528. Q8#135×C103semidirect

Maximal subgroups

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

subgroupindex
Q8×SD16×C1032
C103×#33622
C103×#32982
C103×#32842
C103×#17082
C103×#16802
C103×#16772
C103×#16712
C103×#16662
C103×#16452
C103×#16422
C103×#16352
C103×#16272
C8×SD16×C1032
#19981103