Finite Group Databasebeta

← C103×#19766 #39925041

Subgroups — C103×#19766 #39925041

Order 26368.

650 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3384C211yesmaximal, characteristic, complemented
2C103×#3335C211yesmaximal, characteristic, complemented
3C103×#3298C211yesmaximal, characteristic, complemented
4C103×#3283C211yesmaximal, characteristic
5C103×#1716C211yesmaximal, characteristic, complemented
6C103×#1690C211yesmaximal, characteristic, complemented
7C103×#1679C211yesmaximal, characteristic, complemented
8C103×#1671C211yesmaximal, characteristic, complemented
9C103×#1671C211yesmaximal, characteristic, complemented
10C103×#1654C211yesmaximal, characteristic, complemented
11C103×#1651C211yesmaximal, characteristic, complemented
12C103×#1643C211yesmaximal, characteristic, complemented
13C103×#1635C211yesmaximal, characteristic, complemented
14C103×#1582C211yesmaximal, characteristic, complemented
15C103×#1580C211yesmaximal, characteristic, complemented
16C2×#135×C103—21no—
17#554×C103C2211yescharacteristic
18D4×Q8×C103C2211yescharacteristic
19#547×C103C2211yescharacteristic
20#547×C103C2211yescharacteristic
21#501×C103—21no—
22#498×C103C2211yescharacteristic
23#498×C103C2211yescharacteristic
24#498×C103C2211yescharacteristic
25#494×C103C2211yescharacteristic
26#487×C103C2211yescharacteristic
27#487×C103C2211yescharacteristic
28#483×C103—21no—
29#483×C103—21no—
30#481×C103—21no—
31#478×C103—21no—
32#476×C103—21no—
33#476×C103C2211yescharacteristic
34#476×C103C2211yescharacteristic
35#475×C103C2211yescharacteristic
36#475×C103C2211yescharacteristic
37#474×C103C2211yescharacteristic
38#467×C103—21no—
39#465×C103—21no—
40#465×C103—21no—
41#461×C103C2211yescharacteristic
42#461×C103C2211yescharacteristic
43#461×C103C2211yescharacteristic
44#452×C103—21no—
45#452×C103—21no—
46#448×C103—21no—
47#446×C103C2211yescharacteristic
48#442×C103—21no—
49C4×SD16×C103C2211yescharacteristic
50C4×D8×C103C2211yescharacteristic
51C8×D4×C103C2211yescharacteristic
52C8×D4×C103C2211yescharacteristic
53C8×D4×C103C2211yescharacteristic
54C2×#106×C103—21no—
55C2×#103×C103—21no—
56#334×C103C2211yescharacteristic
57#334×C103C2211yescharacteristic
58#333×C103C2211yescharacteristic
59#332×C103C2211yescharacteristic
60#332×C103C2211yescharacteristic
61#332×C103C2211yescharacteristic
62Q8⋊C8×C103C2211yescharacteristic
63D4⋊C8×C103C2211yescharacteristic
64D4⋊C8×C103C2211yescharacteristic
65D4⋊C8×C103C2211yescharacteristic
66#322×C103C2211yescharacteristic
67C2×#41×C103—21no—
68C2×#41×C103—21no—
69C22×Q8×C103—21no—
70#135×C103—44no—
71C2×Q16×C103—21no—
72C2×Q16×C103—21no—
73C2×SD16×C103—21no—
74C2×SD16×C103—21no—
75C2×SD16×C103—21no—
76C2×SD16×C103D411yescharacteristic
77C2×D8×C103D411yescharacteristic
78C22×C8×C103—21no—
79C22×C8×C103—21no—
80C22×C8×C103—21no—
81C4⋊Q8×C103—21no—
82C4⋊Q8×C103C2311yescharacteristic
83C4⋊Q8×C103C2311yescharacteristic
84C4⋊Q8×C103C2311yescharacteristic
85C4⋊Q8×C103C2311yescharacteristic
86#125×C103—21no—
87#123×C103—41no—
88#123×C103—41no—
89C22⋊Q8×C103—21no—
90C22⋊Q8×C103—21no—
91C22⋊Q8×C103—21no—
92C22⋊Q8×C103—21no—
93C22⋊Q8×C103—41no—
94C22⋊Q8×C103—41no—
95#121×C103—21no—
96#121×C103—21no—
97C4×Q8×C103C2311yescharacteristic
98C4×D4×C103—21no—
99C4×D4×C103—21no—
100C4×D4×C103C2311yescharacteristic
101C4×D4×C103C2311yescharacteristic
102C4×D4×C103C2311yescharacteristic
103C2×C4⋊C4×C103—21no—
104C2×C4⋊C4×C103—21no—
105C2×C4⋊C4×C103—21no—
106#107×C103—21no—
107#107×C103D411yescharacteristic
108#106×C103—21no—
109#106×C103—21no—
110#106×C103—21no—
111#106×C103—21no—
112#106×C103—21no—
113#106×C103—21no—
114#106×C103—21no—
115#106×C103—21no—
116#106×C103—41no—
117#106×C103D411yescharacteristic
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—21no—
128#103×C103—21no—
129#103×C103—21no—
130#103×C103—41no—
131#103×C103D411yescharacteristic
132#102×C103—21no—
133#102×C103—21no—
134#102×C103—21no—
135#102×C103D411yescharacteristic
136#102×C103D411yescharacteristic
137#102×C103D411yescharacteristic
138C22⋊C8×C103—21no—
139C22⋊C8×C103—21no—
140C22⋊C8×C103—21no—
141#97×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—21no—
153C2×Q8×C103—41no—
154C2×Q8×C103—42no—
155C2×Q8×C103—81no—
156C2×Q8×C103C2×D411yescharacteristic
157C2×D4×C103—41no—
158C2×D4×C103—41no—
159C2×D4×C103C2×D411yescharacteristic
160C2×D4×C103C2×D411yescharacteristic
161C2×D4×C103C2×D411yescharacteristic
162C22×C4×C103—21no—
163C22×C4×C103—21no—
164C22×C4×C103—21no—
165C22×C4×C103—41no—
166C22×C4×C103—41no—
167C22×C4×C103—41no—
168C22×C4×C103—41no—
169Q16×C103—42no—
170Q16×C103—81no—
171SD16×C103—41no—
172SD16×C103—42no—
173SD16×C103—42no—
174SD16×C103—81no—
175D8×C103SD1614yescomplemented
176C2×C8×C103—21no—
177C2×C8×C103—21no—
178C2×C8×C103—21no—
179C2×C8×C103—21no—
180C2×C8×C103—21no—
181C2×C8×C103—42no—
182C2×C8×C103—42no—
183C2×C8×C103—81no—
184C2×C8×C103C2×D411yescharacteristic
185C2×C8×C103C2×D411yescharacteristic
186C2×C8×C103C2×D411yescharacteristic
187C2×C8×C103C2×D411yescharacteristic
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—21no—
195C4⋊C4×C103—21no—
196C4⋊C4×C103—21no—
197C4⋊C4×C103—41no—
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—21no—
209C22⋊C4×C103—41no—
210C22⋊C4×C103—41no—
211C22⋊C4×C103—41no—
212C22⋊C4×C103—41no—
213C42×C103—21no—
214C42×C103C2411yescharacteristic
215C23×C103—21no—
216C23×C103—21no—
217C23×C103—21no—
218Q8×C103—21no—
219Q8×C103—21no—
220Q8×C103—41no—
221Q8×C103—41no—
222Q8×C103—41no—
223Q8×C103—41no—
224Q8×C103—41no—
225Q8×C103—41no—
226Q8×C103—81no—
227Q8×C103—82no—
228D4×C103—21no—
229D4×C103—21no—
230D4×C103—21no—
231D4×C103—21no—
232D4×C103—82no—
233D4×C103—82no—
234D4×C103C2×SD1612yes—
235D4×C103C2×SD1612yes—
236C2×C4×C103—21no—
237C2×C4×C103—21no—
238C2×C4×C103—21no—
239C2×C4×C103—21no—
240C2×C4×C103—21no—
241C2×C4×C103—41no—
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—41no—
251C2×C4×C103—82no—
252C2×C4×C103—82no—
253C2×C4×C103—82no—
254C2×C4×C103—161no—
255C2×C4×C103C22×D411yescharacteristic
256C2×C4×C103C22×D411yescharacteristic
257C2×C4×C103H(5,𝔽2)11yescharacteristic
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×C103C2×SD1612yes—
267C22×C103—22no—
268C22×C103—22no—
269C22×C103—41no—
270C22×C103—41no—
271C22×C103—41no—
272C22×C103—41no—
273C22×C103—41no—
274C22×C103—41no—
275C22×C103—41no—
276C22×C103D4211yescharacteristic
277C4×C103—21no—
278C4×C103—41no—
279C4×C103—41no—
280C4×C103—41no—
281C4×C103—41no—
282C4×C103—41no—
283C4×C103—81no—
284C4×C103—81no—
285C4×C103—81no—
286C4×C103—81no—
287C4×C103C22×SD1611yescharacteristic
288C4×C103#57511yescharacteristic
289C4×C103#57711yescharacteristic
290C4×C103#57711yescharacteristic
291#19766C10311yesmaximal, characteristic, direct product factor, Sylow
292C2×C103—42no—
293C2×C103—42no—
294C2×C103—81no—
295C2×C103#326711yescharacteristic
296C2×C103D4×SD1611yescharacteristic
297C2×C103#328911yescharacteristic
298#3384C2×C10311yescharacteristic, complemented
299#3335C2×C10311yescharacteristic, complemented
300#3298C2×C10311yescharacteristic, complemented
301#3283C2×C10311yescharacteristic
302#1716C2×C10311yescharacteristic, complemented
303#1690C2×C10311yescharacteristic, complemented
304#1679C2×C10311yescharacteristic, complemented
305#1671C2×C10311yescharacteristic, complemented
306#1671C2×C10311yescharacteristic, complemented
307#1654C2×C10311yescharacteristic, complemented
308#1651C2×C10311yescharacteristic, complemented
309#1643C2×C10311yescharacteristic, complemented
310#1635C2×C10311yescharacteristic, complemented
311#1582C2×C10311yescharacteristic, complemented
312#1580C2×C10311yescharacteristic, complemented
313C103#1976611yescharacteristic, direct product factor, Sylow
314C2×#135—21no—
315#554C22×C10311yescharacteristic
316D4×Q8C22×C10311yescharacteristic
317#547C22×C10311yescharacteristic
318#547C22×C10311yescharacteristic
319#501—21no—
320#498C22×C10311yescharacteristic
321#498C22×C10311yescharacteristic
322#498C22×C10311yescharacteristic
323#494C22×C10311yescharacteristic
324#487C22×C10311yescharacteristic
325#487C22×C10311yescharacteristic
326#483—21no—
327#483—21no—
328#481—21no—
329#478—21no—
330#476—21no—
331#476C22×C10311yescharacteristic
332#476C22×C10311yescharacteristic
333#475C22×C10311yescharacteristic
334#475C22×C10311yescharacteristic
335#474C22×C10311yescharacteristic
336#467—21no—
337#465—21no—
338#465—21no—
339#461C22×C10311yescharacteristic
340#461C22×C10311yescharacteristic
341#461C22×C10311yescharacteristic
342#452—21no—
343#452—21no—
344#448—21no—
345#446C22×C10311yescharacteristic
346#442—21no—
347C4×SD16C22×C10311yescharacteristic
348C4×D8C22×C10311yescharacteristic
349C8×D4C22×C10311yescharacteristic
350C8×D4C22×C10311yescharacteristic
351C8×D4C22×C10311yescharacteristic
352C2×#106—21no—
353C2×#103—21no—
354#334C22×C10311yescharacteristic
355#334C22×C10311yescharacteristic
356#333C22×C10311yescharacteristic
357#332C22×C10311yescharacteristic
358#332C22×C10311yescharacteristic
359#332C22×C10311yescharacteristic
360Q8⋊C8C22×C10311yescharacteristic
361D4⋊C8C22×C10311yescharacteristic
362D4⋊C8C22×C10311yescharacteristic
363D4⋊C8C22×C10311yescharacteristic
364#322C22×C10311yescharacteristic
365C2×#41—21no—
366C2×#41—21no—
367C22×Q8—21no—
368#135—44no—
369C2×Q16—21no—
370C2×Q16—21no—
371C2×SD16—21no—
372C2×SD16—21no—
373C2×SD16—21no—
374C2×SD16D4×C10311yescharacteristic
375C2×D8D4×C10311yescharacteristic
376C22×C8—21no—
377C22×C8—21no—
378C22×C8—21no—
379C4⋊Q8—21no—
380C4⋊Q8C23×C10311yescharacteristic
381C4⋊Q8C23×C10311yescharacteristic
382C4⋊Q8C23×C10311yescharacteristic
383C4⋊Q8C23×C10311yescharacteristic
384#125—21no—
385#123—41no—
386#123—41no—
387C22⋊Q8—21no—
388C22⋊Q8—21no—
389C22⋊Q8—21no—
390C22⋊Q8—21no—
391C22⋊Q8—41no—
392C22⋊Q8—41no—
393#121—21no—
394#121—21no—
395C4×Q8C23×C10311yescharacteristic
396C4×D4—21no—
397C4×D4—21no—
398C4×D4C23×C10311yescharacteristic
399C4×D4C23×C10311yescharacteristic
400C4×D4C23×C10311yescharacteristic
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404#107—21no—
405#107D4×C10311yescharacteristic
406#106—21no—
407#106—21no—
408#106—21no—
409#106—21no—
410#106—21no—
411#106—21no—
412#106—21no—
413#106—21no—
414#106—41no—
415#106D4×C10311yescharacteristic
416C4⋊C8—21no—
417C4⋊C8C23×C10311yescharacteristic
418C4⋊C8C23×C10311yescharacteristic
419C4⋊C8C23×C10311yescharacteristic
420C4⋊C8C23×C10311yescharacteristic
421#103—21no—
422#103—21no—
423#103—21no—
424#103—21no—
425#103—21no—
426#103—21no—
427#103—21no—
428#103—41no—
429#103D4×C10311yescharacteristic
430#102—21no—
431#102—21no—
432#102—21no—
433#102D4×C10311yescharacteristic
434#102D4×C10311yescharacteristic
435#102D4×C10311yescharacteristic
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8—21no—
439#97—21no—
440C4×C8C23×C10311yescharacteristic
441C4×C8C23×C10311yescharacteristic
442C4×C8C23×C10311yescharacteristic
443#41—42no—
444#41—42no—
445#41—81no—
446#41—81no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—41no—
452C2×Q8—42no—
453C2×Q8—81no—
454C2×Q8C2×D4×C10311yescharacteristic
455C2×D4—41no—
456C2×D4—41no—
457C2×D4C2×D4×C10311yescharacteristic
458C2×D4C2×D4×C10311yescharacteristic
459C2×D4C2×D4×C10311yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467Q16—42no—
468Q16—81no—
469SD16—41no—
470SD16—42no—
471SD16—42no—
472SD16—81no—
473D8SD16×C10314yescomplemented
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—42no—
480C2×C8—42no—
481C2×C8—81no—
482C2×C8C2×D4×C10311yescharacteristic
483C2×C8C2×D4×C10311yescharacteristic
484C2×C8C2×D4×C10311yescharacteristic
485C2×C8C2×D4×C10311yescharacteristic
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4C2×D4×C10311yescharacteristic
501C4⋊C4C2×D4×C10311yescharacteristic
502C4⋊C4C2×D4×C10311yescharacteristic
503C4⋊C4C2×D4×C10311yescharacteristic
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C42—21no—
512C42C24×C10311yescharacteristic
513C23—21no—
514C23—21no—
515C23—21no—
516Q8—21no—
517Q8—21no—
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8—41no—
522Q8—41no—
523Q8—41no—
524Q8—81no—
525Q8—82no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—82no—
531D4—82no—
532D4C2×SD16×C10312yes—
533D4C2×SD16×C10312yes—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—82no—
550C2×C4—82no—
551C2×C4—82no—
552C2×C4—161no—
553C2×C4C22×D4×C10311yescharacteristic
554C2×C4C22×D4×C10311yescharacteristic
555C2×C4H(5,𝔽2)×C10311yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—41no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8C2×SD16×C10312yes—
565C22—22no—
566C22—22no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22D42×C10311yescharacteristic
575C4—21no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—81no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4C22×SD16×C10311yescharacteristic
586C4#575×C10311yescharacteristic
587C4#577×C10311yescharacteristic
588C4#577×C10311yescharacteristic
589C2—42no—
590C2—42no—
591C2—81no—
592C2C103×#326711yescharacteristic
593C2D4×SD16×C10311yescharacteristic
594C2C103×#328911yescharacteristic
subgroupG/H
center, socleC22×C103D42
commutator, Frattini, cosocleC42C24×C103
prime radicalC103×#3283C2
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×#3384C2semidirect
2. C103×#3335C2semidirect
3. C103×#3298C2semidirect
5. C103×#1716C2semidirect
6. C103×#1690C2semidirect
7. C103×#1679C2semidirect
8. C103×#1671C2semidirect
9. C103×#1671C2semidirect
10. C103×#1654C2semidirect
11. C103×#1651C2semidirect
12. C103×#1643C2semidirect
13. C103×#1635C2semidirect
14. C103×#1582C2semidirect
15. C103×#1580C2semidirect
175. D8×C103SD16semidirect
291. #19766C103direct (N × H)
298. #3384C2×C103semidirect
299. #3335C2×C103semidirect
300. #3298C2×C103semidirect
302. #1716C2×C103semidirect
303. #1690C2×C103semidirect
304. #1679C2×C103semidirect
305. #1671C2×C103semidirect
306. #1671C2×C103semidirect
307. #1654C2×C103semidirect
308. #1651C2×C103semidirect
309. #1643C2×C103semidirect
310. #1635C2×C103semidirect
311. #1582C2×C103semidirect
312. #1580C2×C103semidirect
313. C103#19766direct (N × H)
473. D8SD16×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#33842
C103×#33352
C103×#32982
C103×#32832
C103×#17162
C103×#16902
C103×#16792
C103×#16712
C103×#16542
C103×#16512
C103×#16432
C103×#16352
C103×#15822
C103×#15802
#19766103