Finite Group Databasebeta

← C103×#19809 #39925084

Subgroups — C103×#19809 #39925084

Order 26368.

632 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×Q16×C103C211yesmaximal, characteristic, complemented
2Q8×SD16×C103C211yesmaximal, characteristic, complemented
3C103×#3362C211yesmaximal, characteristic
4C103×#3278C211yesmaximal, characteristic
5C103×#1714C211yesmaximal, characteristic, complemented
6C103×#1695C211yesmaximal, characteristic, complemented
7C103×#1678C211yesmaximal, characteristic, complemented
8C103×#1672C211yesmaximal, characteristic, complemented
9C103×#1666C211yesmaximal, characteristic, complemented
10C103×#1645C211yesmaximal, characteristic, complemented
11C103×#1637C211yesmaximal, characteristic, complemented
12C103×#1631C211yesmaximal, characteristic
13C103×#1623C211yesmaximal, characteristic, complemented
14C103×#1583C211yesmaximal, characteristic, complemented
15C103×#1579C211yesmaximal, characteristic, complemented
16C2×#137×C103—21no—
17Q82×C103C2211yescharacteristic
18Q82×C103C2211yescharacteristic
19#550×C103C2211yescharacteristic
20D4×Q8×C103C2211yescharacteristic
21#500×C103—21no—
22#500×C103C2211yescharacteristic
23#498×C103—21no—
24#498×C103C2211yescharacteristic
25#492×C103C2211yescharacteristic
26#492×C103C2211yescharacteristic
27#487×C103C2211yescharacteristic
28#486×C103—21no—
29#486×C103C2211yescharacteristic
30#477×C103—21no—
31#477×C103—21no—
32#477×C103C2211yescharacteristic
33#477×C103C2211yescharacteristic
34#476×C103—21no—
35#476×C103—21no—
36#476×C103C2211yescharacteristic
37#476×C103C2211yescharacteristic
38#475×C103—21no—
39#475×C103C2211yescharacteristic
40#468×C103—21no—
41#462×C103C2211yescharacteristic
42#460×C103—21no—
43#460×C103C2211yescharacteristic
44#460×C103C2211yescharacteristic
45#452×C103—21no—
46#448×C103—21no—
47C8×Q8×C103C2211yescharacteristic
48C8×Q8×C103C2211yescharacteristic
49C8×Q8×C103C2211yescharacteristic
50C4×Q16×C103—21no—
51C4×Q16×C103C2211yescharacteristic
52C4×SD16×C103—21no—
53C4×SD16×C103—21no—
54C4×SD16×C103C2211yescharacteristic
55#436×C103C2211yescharacteristic
56#334×C103C2211yescharacteristic
57#334×C103C2211yescharacteristic
58#333×C103C2211yescharacteristic
59#333×C103C2211yescharacteristic
60#332×C103C2211yescharacteristic
61#331×C103C2211yescharacteristic
62Q8⋊C8×C103C2211yescharacteristic
63Q8⋊C8×C103C2211yescharacteristic
64Q8⋊C8×C103C2211yescharacteristic
65D4⋊C8×C103C2211yescharacteristic
66#322×C103C2211yescharacteristic
67C2×#41×C103—21no—
68C22×Q8×C103—21no—
69#137×C103—44no—
70C2×Q16×C103—21no—
71C2×Q16×C103D411yescharacteristic
72C2×SD16×C103—21no—
73C2×SD16×C103—21no—
74C2×SD16×C103—21no—
75C2×SD16×C103—21no—
76C2×SD16×C103—41no—
77C2×SD16×C103D411yescharacteristic
78C2×M16×C103—21no—
79C4⋊Q8×C103—21no—
80C4⋊Q8×C103—21no—
81C4⋊Q8×C103—21no—
82C4⋊Q8×C103—21no—
83C4⋊Q8×C103—21no—
84C4⋊Q8×C103—41no—
85C4⋊Q8×C103—41no—
86C4⋊Q8×C103C2311yescharacteristic
87C4⋊Q8×C103C2311yescharacteristic
88C4⋊Q8×C103C2311yescharacteristic
89#127×C103—21no—
90#127×C103C2311yescharacteristic
91C22⋊Q8×C103—21no—
92C22⋊Q8×C103—41no—
93#121×C103—21no—
94#121×C103—41no—
95C4×Q8×C103—21no—
96C4×Q8×C103—21no—
97C4×Q8×C103—21no—
98C4×Q8×C103—21no—
99C4×Q8×C103C2311yescharacteristic
100C4×Q8×C103C2311yescharacteristic
101C4×Q8×C103C2311yescharacteristic
102C4×D4×C103—21no—
103C4×D4×C103—21no—
104C4×D4×C103C2311yescharacteristic
105#107×C103—21no—
106#107×C103—21no—
107#107×C103—21no—
108#107×C103—21no—
109#107×C103D411yescharacteristic
110#106×C103—21no—
111#106×C103—21no—
112#106×C103—21no—
113#106×C103—21no—
114#106×C103—21no—
115#106×C103D411yescharacteristic
116C4⋊C8×C103—21no—
117C4⋊C8×C103—21no—
118C4⋊C8×C103—21no—
119C4⋊C8×C103C2311yescharacteristic
120C4⋊C8×C103C2311yescharacteristic
121C4⋊C8×C103C2311yescharacteristic
122C4⋊C8×C103C2311yescharacteristic
123#103×C103—21no—
124#103×C103—21no—
125#103×C103—21no—
126#103×C103—21no—
127#103×C103—41no—
128#103×C103D411yescharacteristic
129#103×C103D411yescharacteristic
130#103×C103D411yescharacteristic
131#102×C103—21no—
132#102×C103—21no—
133#102×C103—21no—
134#102×C103—21no—
135#102×C103—21no—
136#102×C103—21no—
137#102×C103D411yescharacteristic
138C22⋊C8×C103—21no—
139C4×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—81no—
147C2×Q8×C103—21no—
148C2×Q8×C103—21no—
149C2×Q8×C103—21no—
150C2×Q8×C103—41no—
151C2×Q8×C103—41no—
152C2×Q8×C103—41no—
153C2×Q8×C103—42no—
154C2×Q8×C103—81no—
155C2×Q8×C103C2×D411yescharacteristic
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×C103C2×D411yescharacteristic
164C22×C4×C103—21no—
165C22×C4×C103—41no—
166C22×C4×C103—41no—
167Q16×C103—42no—
168Q16×C103SD1614yescomplemented
169SD16×C103—22no—
170SD16×C103—42no—
171SD16×C103—42no—
172SD16×C103—42no—
173SD16×C103—81no—
174SD16×C103—82no—
175M16×C103—42no—
176C2×C8×C103—21no—
177C2×C8×C103—21no—
178C2×C8×C103—21no—
179C2×C8×C103—21no—
180C2×C8×C103—21no—
181C2×C8×C103C2×D411yescharacteristic
182C2×C8×C103C2×D411yescharacteristic
183C2×C8×C103C2×D411yescharacteristic
184C2×C8×C103C2×D411yescharacteristic
185C4⋊C4×C103—21no—
186C4⋊C4×C103—21no—
187C4⋊C4×C103—21no—
188C4⋊C4×C103—21no—
189C4⋊C4×C103—21no—
190C4⋊C4×C103—21no—
191C4⋊C4×C103—21no—
192C4⋊C4×C103—21no—
193C4⋊C4×C103—21no—
194C4⋊C4×C103—41no—
195C4⋊C4×C103—41no—
196C4⋊C4×C103—41no—
197C4⋊C4×C103—41no—
198C4⋊C4×C103—41no—
199C4⋊C4×C103C2×D411yescharacteristic
200C4⋊C4×C103C2×D411yescharacteristic
201C4⋊C4×C103C2×D411yescharacteristic
202C4⋊C4×C103C2×D411yescharacteristic
203C22⋊C4×C103—21no—
204C22⋊C4×C103—41no—
205C22⋊C4×C103—41no—
206C42×C103—21no—
207C42×C103—21no—
208C42×C103—21no—
209C42×C103—41no—
210C42×C103—41no—
211C42×C103C2411yescharacteristic
212C23×C103—21no—
213C23×C103—41no—
214Q8×C103—21no—
215Q8×C103—21no—
216Q8×C103—21no—
217Q8×C103—41no—
218Q8×C103—41no—
219Q8×C103—82no—
220Q8×C103—81no—
221Q8×C103—81no—
222Q8×C103—161no—
223Q8×C103—161no—
224Q8×C103C2×SD1612yes—
225Q8×C103C2×SD1612yes—
226Q8×C103#13712yescomplemented
227D4×C103—21no—
228D4×C103—21no—
229D4×C103—41no—
230D4×C103—41no—
231D4×C103—41no—
232D4×C103—41no—
233D4×C103—82no—
234D4×C103—81no—
235D4×C103—161no—
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—21no—
243C2×C4×C103—41no—
244C2×C4×C103—41no—
245C2×C4×C103—41no—
246C2×C4×C103—41no—
247C2×C4×C103—41no—
248C2×C4×C103—82no—
249C2×C4×C103—82no—
250C2×C4×C103C22×D411yescharacteristic
251C2×C4×C103C22×D411yescharacteristic
252C2×C4×C103H(5,𝔽2)11yescharacteristic
253C8×C103—21no—
254C8×C103—21no—
255C8×C103—21no—
256C8×C103—41no—
257C8×C103—41no—
258C8×C103—41no—
259C8×C103—41no—
260C8×C103—41no—
261C8×C103C2×SD1612yes—
262C22×C103—41no—
263C22×C103—41no—
264C22×C103—41no—
265C22×C103—81no—
266C22×C103—81no—
267C22×C103—81no—
268C22×C103D4211yescharacteristic
269C4×C103—22no—
270C4×C103—22no—
271C4×C103—22no—
272C4×C103—21no—
273C4×C103—41no—
274C4×C103—41no—
275C4×C103—41no—
276C4×C103—41no—
277C4×C103—81no—
278C4×C103—81no—
279C4×C103—81no—
280C4×C103C22×SD1611yescharacteristic
281C4×C103C2×#13711yescharacteristic
282C4×C103#57711yescharacteristic
283C4×C103#57811yescharacteristic
284#19809C10311yesmaximal, characteristic, direct product factor, Sylow
285C2×C103—81no—
286C2×C103—161no—
287C2×C103#327011yescharacteristic
288C2×C103D4×SD1611yescharacteristic
289C2×C103#328811yescharacteristic
290Q8×Q16C2×C10311yescharacteristic, complemented
291Q8×SD16C2×C10311yescharacteristic, complemented
292#3362C2×C10311yescharacteristic
293#3278C2×C10311yescharacteristic
294#1714C2×C10311yescharacteristic, complemented
295#1695C2×C10311yescharacteristic, complemented
296#1678C2×C10311yescharacteristic, complemented
297#1672C2×C10311yescharacteristic, complemented
298#1666C2×C10311yescharacteristic, complemented
299#1645C2×C10311yescharacteristic, complemented
300#1637C2×C10311yescharacteristic, complemented
301#1631C2×C10311yescharacteristic
302#1623C2×C10311yescharacteristic, complemented
303#1583C2×C10311yescharacteristic, complemented
304#1579C2×C10311yescharacteristic, complemented
305C103#1980911yescharacteristic, direct product factor, Sylow
306C2×#137—21no—
307Q82C22×C10311yescharacteristic
308Q82C22×C10311yescharacteristic
309#550C22×C10311yescharacteristic
310D4×Q8C22×C10311yescharacteristic
311#500—21no—
312#500C22×C10311yescharacteristic
313#498—21no—
314#498C22×C10311yescharacteristic
315#492C22×C10311yescharacteristic
316#492C22×C10311yescharacteristic
317#487C22×C10311yescharacteristic
318#486—21no—
319#486C22×C10311yescharacteristic
320#477—21no—
321#477—21no—
322#477C22×C10311yescharacteristic
323#477C22×C10311yescharacteristic
324#476—21no—
325#476—21no—
326#476C22×C10311yescharacteristic
327#476C22×C10311yescharacteristic
328#475—21no—
329#475C22×C10311yescharacteristic
330#468—21no—
331#462C22×C10311yescharacteristic
332#460—21no—
333#460C22×C10311yescharacteristic
334#460C22×C10311yescharacteristic
335#452—21no—
336#448—21no—
337C8×Q8C22×C10311yescharacteristic
338C8×Q8C22×C10311yescharacteristic
339C8×Q8C22×C10311yescharacteristic
340C4×Q16—21no—
341C4×Q16C22×C10311yescharacteristic
342C4×SD16—21no—
343C4×SD16—21no—
344C4×SD16C22×C10311yescharacteristic
345#436C22×C10311yescharacteristic
346#334C22×C10311yescharacteristic
347#334C22×C10311yescharacteristic
348#333C22×C10311yescharacteristic
349#333C22×C10311yescharacteristic
350#332C22×C10311yescharacteristic
351#331C22×C10311yescharacteristic
352Q8⋊C8C22×C10311yescharacteristic
353Q8⋊C8C22×C10311yescharacteristic
354Q8⋊C8C22×C10311yescharacteristic
355D4⋊C8C22×C10311yescharacteristic
356#322C22×C10311yescharacteristic
357C2×#41—21no—
358C22×Q8—21no—
359#137—44no—
360C2×Q16—21no—
361C2×Q16D4×C10311yescharacteristic
362C2×SD16—21no—
363C2×SD16—21no—
364C2×SD16—21no—
365C2×SD16—21no—
366C2×SD16—41no—
367C2×SD16D4×C10311yescharacteristic
368C2×M16—21no—
369C4⋊Q8—21no—
370C4⋊Q8—21no—
371C4⋊Q8—21no—
372C4⋊Q8—21no—
373C4⋊Q8—21no—
374C4⋊Q8—41no—
375C4⋊Q8—41no—
376C4⋊Q8C23×C10311yescharacteristic
377C4⋊Q8C23×C10311yescharacteristic
378C4⋊Q8C23×C10311yescharacteristic
379#127—21no—
380#127C23×C10311yescharacteristic
381C22⋊Q8—21no—
382C22⋊Q8—41no—
383#121—21no—
384#121—41no—
385C4×Q8—21no—
386C4×Q8—21no—
387C4×Q8—21no—
388C4×Q8—21no—
389C4×Q8C23×C10311yescharacteristic
390C4×Q8C23×C10311yescharacteristic
391C4×Q8C23×C10311yescharacteristic
392C4×D4—21no—
393C4×D4—21no—
394C4×D4C23×C10311yescharacteristic
395#107—21no—
396#107—21no—
397#107—21no—
398#107—21no—
399#107D4×C10311yescharacteristic
400#106—21no—
401#106—21no—
402#106—21no—
403#106—21no—
404#106—21no—
405#106D4×C10311yescharacteristic
406C4⋊C8—21no—
407C4⋊C8—21no—
408C4⋊C8—21no—
409C4⋊C8C23×C10311yescharacteristic
410C4⋊C8C23×C10311yescharacteristic
411C4⋊C8C23×C10311yescharacteristic
412C4⋊C8C23×C10311yescharacteristic
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103—41no—
418#103D4×C10311yescharacteristic
419#103D4×C10311yescharacteristic
420#103D4×C10311yescharacteristic
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102D4×C10311yescharacteristic
428C22⋊C8—21no—
429C4×C8—21no—
430C4×C8—21no—
431C4×C8—21no—
432C4×C8C23×C10311yescharacteristic
433C4×C8C23×C10311yescharacteristic
434C4×C8C23×C10311yescharacteristic
435#41—42no—
436#41—81no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—41no—
441C2×Q8—41no—
442C2×Q8—41no—
443C2×Q8—42no—
444C2×Q8—81no—
445C2×Q8C2×D4×C10311yescharacteristic
446C2×Q8C2×D4×C10311yescharacteristic
447C2×Q8C2×D4×C10311yescharacteristic
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4C2×D4×C10311yescharacteristic
454C22×C4—21no—
455C22×C4—41no—
456C22×C4—41no—
457Q16—42no—
458Q16SD16×C10314yescomplemented
459SD16—22no—
460SD16—42no—
461SD16—42no—
462SD16—42no—
463SD16—81no—
464SD16—82no—
465M16—42no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8C2×D4×C10311yescharacteristic
472C2×C8C2×D4×C10311yescharacteristic
473C2×C8C2×D4×C10311yescharacteristic
474C2×C8C2×D4×C10311yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4C2×D4×C10311yescharacteristic
490C4⋊C4C2×D4×C10311yescharacteristic
491C4⋊C4C2×D4×C10311yescharacteristic
492C4⋊C4C2×D4×C10311yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—41no—
500C42—41no—
501C42C24×C10311yescharacteristic
502C23—21no—
503C23—41no—
504Q8—21no—
505Q8—21no—
506Q8—21no—
507Q8—41no—
508Q8—41no—
509Q8—82no—
510Q8—81no—
511Q8—81no—
512Q8—161no—
513Q8—161no—
514Q8C2×SD16×C10312yes—
515Q8C2×SD16×C10312yes—
516Q8#137×C10312yescomplemented
517D4—21no—
518D4—21no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—82no—
524D4—81no—
525D4—161no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—82no—
539C2×C4—82no—
540C2×C4C22×D4×C10311yescharacteristic
541C2×C4C22×D4×C10311yescharacteristic
542C2×C4H(5,𝔽2)×C10311yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—41no—
547C8—41no—
548C8—41no—
549C8—41no—
550C8—41no—
551C8C2×SD16×C10312yes—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22D42×C10311yescharacteristic
559C4—22no—
560C4—22no—
561C4—22no—
562C4—21no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4C22×SD16×C10311yescharacteristic
571C4C2×#137×C10311yescharacteristic
572C4#577×C10311yescharacteristic
573C4#578×C10311yescharacteristic
574C2—81no—
575C2—161no—
576C2C103×#327011yescharacteristic
577C2D4×SD16×C10311yescharacteristic
578C2C103×#328811yescharacteristic
subgroupG/H
center, socleC22×C103D42
commutator, Frattini, cosocleC42C24×C103
prime radical#550×C103C22
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×Q16×C103C2semidirect
2. Q8×SD16×C103C2semidirect
5. C103×#1714C2semidirect
6. C103×#1695C2semidirect
7. C103×#1678C2semidirect
8. C103×#1672C2semidirect
9. C103×#1666C2semidirect
10. C103×#1645C2semidirect
11. C103×#1637C2semidirect
13. C103×#1623C2semidirect
14. C103×#1583C2semidirect
15. C103×#1579C2semidirect
168. Q16×C103SD16semidirect
226. Q8×C103#137semidirect
284. #19809C103direct (N × H)
290. Q8×Q16C2×C103semidirect
291. Q8×SD16C2×C103semidirect
294. #1714C2×C103semidirect
295. #1695C2×C103semidirect
296. #1678C2×C103semidirect
297. #1672C2×C103semidirect
298. #1666C2×C103semidirect
299. #1645C2×C103semidirect
300. #1637C2×C103semidirect
302. #1623C2×C103semidirect
303. #1583C2×C103semidirect
304. #1579C2×C103semidirect
305. C103#19809direct (N × H)
458. Q16SD16×C103semidirect
516. Q8#137×C103semidirect

Maximal subgroups

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

subgroupindex
Q8×Q16×C1032
Q8×SD16×C1032
C103×#33622
C103×#32782
C103×#17142
C103×#16952
C103×#16782
C103×#16722
C103×#16662
C103×#16452
C103×#16372
C103×#16312
C103×#16232
C103×#15832
C103×#15792
#19809103