Finite Group Databasebeta

← C103×#19542 #39924817

Subgroups — C103×#19542 #39924817

Order 26368.

612 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3251C211yesmaximal, characteristic, complemented
2C103×#3247C211yesmaximal, characteristic, complemented
3C103×#3207C211yesmaximal, characteristic, complemented
4C103×#2993C211yesmaximal, characteristic, complemented
5C103×#1698C211yesmaximal, characteristic, complemented
6C103×#1697C211yesmaximal, characteristic, complemented
7C103×#1686C211yesmaximal, characteristic, complemented
8C103×#1685C211yesmaximal, characteristic, complemented
9C103×#1684C211yesmaximal, characteristic, complemented
10C103×#1683C211yesmaximal, characteristic, complemented
11C103×#1668C211yesmaximal, characteristic, complemented
12C103×#1667C211yesmaximal, characteristic, complemented
13C103×#1571C211yesmaximal, characteristic, complemented
14C103×#1560C211yesmaximal, characteristic, complemented
15C103×#1547C211yesmaximal, characteristic, complemented
16#532×C103C2211yescharacteristic
17#532×C103C2211yescharacteristic
18#529×C103C2211yescharacteristic
19#493×C103C2211yescharacteristic
20#492×C103C2211yescharacteristic
21#487×C103C2211yescharacteristic
22#486×C103C2211yescharacteristic
23#478×C103—21no—
24#478×C103—21no—
25#477×C103C2211yescharacteristic
26#476×C103C2211yescharacteristic
27#475×C103C2211yescharacteristic
28#474×C103C2211yescharacteristic
29#469×C103—21no—
30#468×C103—21no—
31#466×C103—21no—
32#465×C103—21no—
33#463×C103—21no—
34#463×C103—21no—
35#463×C103—21no—
36#463×C103—21no—
37#460×C103C2211yescharacteristic
38#460×C103C2211yescharacteristic
39#459×C103C2211yescharacteristic
40#459×C103C2211yescharacteristic
41#449×C103—21no—
42#449×C103—21no—
43#446×C103C2211yescharacteristic
44C8×Q8×C103C2211yescharacteristic
45#436×C103—21no—
46#436×C103C2211yescharacteristic
47#435×C103—21no—
48C8×D4×C103C2211yescharacteristic
49#433×C103—21no—
50#431×C103C2211yescharacteristic
51#424×C103—21no—
52#423×C103C2211yescharacteristic
53#423×C103C2211yescharacteristic
54C2×C4⋊C8×C103C2211yescharacteristic
55#335×C103C2211yescharacteristic
56#335×C103C2211yescharacteristic
57#335×C103C2211yescharacteristic
58#335×C103C2211yescharacteristic
59#333×C103C2211yescharacteristic
60#333×C103C2211yescharacteristic
61#332×C103C2211yescharacteristic
62#332×C103C2211yescharacteristic
63#331×C103C2211yescharacteristic
64#331×C103C2211yescharacteristic
65#331×C103C2211yescharacteristic
66#331×C103C2211yescharacteristic
67C2×#41×C103—21no—
68C2×#41×C103—21no—
69C2×SD16×C103—21no—
70C2×SD16×C103—21no—
71C2×SD16×C103—21no—
72C2×SD16×C103—21no—
73C2×D8×C103—21no—
74C2×D8×C103—21no—
75C2×D8×C103—21no—
76C2×D8×C103—21no—
77C2×M16×C103—21no—
78C2×M16×C103—21no—
79C2×M16×C103—21no—
80C22×C8×C103—21no—
81C22×C8×C103—21no—
82C4⋊Q8×C103C2311yescharacteristic
83C4⋊Q8×C103C2311yescharacteristic
84#127×C103C2311yescharacteristic
85#127×C103C2311yescharacteristic
86#126×C103—21no—
87#125×C103D411yescharacteristic
88#124×C103—21no—
89#124×C103—21no—
90#124×C103D411yescharacteristic
91#123×C103—21no—
92C22⋊Q8×C103D411yescharacteristic
93#121×C103—21no—
94#121×C103—21no—
95#121×C103—21no—
96#121×C103—21no—
97#121×C103D411yescharacteristic
98C4×Q8×C103C2311yescharacteristic
99C4×D4×C103—21no—
100C4×D4×C103—21no—
101C4×D4×C103—21no—
102C4×D4×C103—21no—
103C4×D4×C103—21no—
104C4×D4×C103C2311yescharacteristic
105#117×C103—21no—
106C2×C42×C103C2311yescharacteristic
107#107×C103—21no—
108#107×C103—21no—
109#106×C103—21no—
110#106×C103—21no—
111C4⋊C8×C103—21no—
112C4⋊C8×C103—21no—
113C4⋊C8×C103—21no—
114C4⋊C8×C103—21no—
115C4⋊C8×C103—21no—
116C4⋊C8×C103D411yescharacteristic
117C4⋊C8×C103D411yescharacteristic
118C4⋊C8×C103C2311yescharacteristic
119C4⋊C8×C103C2311yescharacteristic
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×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—21no—
136C22⋊C8×C103—21no—
137C22⋊C8×C103—21no—
138C22⋊C8×C103D411yescharacteristic
139C22⋊C8×C103D411yescharacteristic
140#97×C103—21no—
141C4×C8×C103—21no—
142C4×C8×C103C2311yescharacteristic
143C4×C8×C103C2311yescharacteristic
144#41×C103—81no—
145#41×C103—81no—
146#41×C103—82no—
147C2×Q8×C103—21no—
148C2×Q8×C103—21no—
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—41no—
158C2×D4×C103—41no—
159C2×D4×C103C2×D411yescharacteristic
160C22×C4×C103—21no—
161C22×C4×C103—41no—
162C22×C4×C103—41no—
163C22×C4×C103C2×D411yescharacteristic
164C22×C4×C103C2×D411yescharacteristic
165C22×C4×C103#4111yescharacteristic
166SD16×C103—81no—
167SD16×C103—81no—
168SD16×C103—81no—
169SD16×C103—81no—
170D8×C103—81no—
171D8×C103—81no—
172D8×C103—81no—
173D8×C103—81no—
174M16×C103—81no—
175M16×C103—81no—
176M16×C103—81no—
177C2×C8×C103—21no—
178C2×C8×C103—21no—
179C2×C8×C103—21no—
180C2×C8×C103—21no—
181C2×C8×C103—21no—
182C2×C8×C103—21no—
183C2×C8×C103—81no—
184C2×C8×C103—81no—
185C2×C8×C103C2×D411yescharacteristic
186C2×C8×C103C2×D411yescharacteristic
187C2×C8×C103C2×D411yescharacteristic
188C2×C8×C103C2×D411yescharacteristic
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×C103C2×D411yescharacteristic
198C4⋊C4×C103C2×D411yescharacteristic
199C22⋊C4×C103—21no—
200C22⋊C4×C103—21no—
201C22⋊C4×C103—21no—
202C22⋊C4×C103—21no—
203C22⋊C4×C103—21no—
204C22⋊C4×C103—41no—
205C22⋊C4×C103—41no—
206C22⋊C4×C103—41no—
207C22⋊C4×C103—41no—
208C42×C103—21no—
209C42×C103C2×D411yescharacteristic
210C42×C103C2×D411yescharacteristic
211C42×C103#4111yescharacteristic
212C42×C103C2411yescharacteristic
213C23×C103—21no—
214C23×C103—41no—
215C23×C103—41no—
216C23×C103#12111yescharacteristic
217Q8×C103—21no—
218Q8×C103—21no—
219Q8×C103—41no—
220Q8×C103—41no—
221Q8×C103—81no—
222D4×C103—21no—
223D4×C103—21no—
224D4×C103—41no—
225D4×C103—41no—
226D4×C103—41no—
227D4×C103—41no—
228D4×C103—41no—
229D4×C103—41no—
230D4×C103—41no—
231D4×C103—41no—
232D4×C103—81no—
233D4×C103—81no—
234D4×C103—81no—
235D4×C103—82no—
236D4×C103—82no—
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—21no—
244C2×C4×C103—41no—
245C2×C4×C103—41no—
246C2×C4×C103—41no—
247C2×C4×C103—41no—
248C2×C4×C103—41no—
249C2×C4×C103—82no—
250C2×C4×C103—82no—
251C2×C4×C103#12111yescharacteristic
252C2×C4×C103#12111yescharacteristic
253C2×C4×C103#12111yescharacteristic
254C2×C4×C103C22×D411yescharacteristic
255C2×C4×C103C22×D411yescharacteristic
256C2×C4×C103C2×#4111yescharacteristic
257C8×C103—21no—
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×C103—41no—
267C22×C103—21no—
268C22×C103—21no—
269C22×C103—21no—
270C22×C103—41no—
271C22×C103—41no—
272C22×C103—41no—
273C22×C103—81no—
274C22×C103—81no—
275C22×C103—81no—
276C22×C103—81no—
277C22×C103—81no—
278C22×C103—81no—
279C22×C103C2×#12111yescharacteristic
280C4×C103—21no—
281C4×C103—21no—
282C4×C103—21no—
283C4×C103—21no—
284C4×C103—41no—
285C4×C103—41no—
286C4×C103—41no—
287C4×C103—81no—
288C4×C103—81no—
289C4×C103#57611yescharacteristic
290C4×C103#57611yescharacteristic
291C4×C103#57711yescharacteristic
292C4×C103#57811yescharacteristic
293#19542C10311yesmaximal, characteristic, direct product factor, Sylow
294C2×C103—41no—
295C2×C103—81no—
296C2×C103—161no—
297C2×C103—161no—
298C2×C103#304511yescharacteristic
299C2×C103#306111yescharacteristic
300C2×C103#306811yescharacteristic
301#3251C2×C10311yescharacteristic, complemented
302#3247C2×C10311yescharacteristic, complemented
303#3207C2×C10311yescharacteristic, complemented
304#2993C2×C10311yescharacteristic, complemented
305#1698C2×C10311yescharacteristic, complemented
306#1697C2×C10311yescharacteristic, complemented
307#1686C2×C10311yescharacteristic, complemented
308#1685C2×C10311yescharacteristic, complemented
309#1684C2×C10311yescharacteristic, complemented
310#1683C2×C10311yescharacteristic, complemented
311#1668C2×C10311yescharacteristic, complemented
312#1667C2×C10311yescharacteristic, complemented
313#1571C2×C10311yescharacteristic, complemented
314#1560C2×C10311yescharacteristic, complemented
315#1547C2×C10311yescharacteristic, complemented
316C103#1954211yescharacteristic, direct product factor, Sylow
317#532C22×C10311yescharacteristic
318#532C22×C10311yescharacteristic
319#529C22×C10311yescharacteristic
320#493C22×C10311yescharacteristic
321#492C22×C10311yescharacteristic
322#487C22×C10311yescharacteristic
323#486C22×C10311yescharacteristic
324#478—21no—
325#478—21no—
326#477C22×C10311yescharacteristic
327#476C22×C10311yescharacteristic
328#475C22×C10311yescharacteristic
329#474C22×C10311yescharacteristic
330#469—21no—
331#468—21no—
332#466—21no—
333#465—21no—
334#463—21no—
335#463—21no—
336#463—21no—
337#463—21no—
338#460C22×C10311yescharacteristic
339#460C22×C10311yescharacteristic
340#459C22×C10311yescharacteristic
341#459C22×C10311yescharacteristic
342#449—21no—
343#449—21no—
344#446C22×C10311yescharacteristic
345C8×Q8C22×C10311yescharacteristic
346#436—21no—
347#436C22×C10311yescharacteristic
348#435—21no—
349C8×D4C22×C10311yescharacteristic
350#433—21no—
351#431C22×C10311yescharacteristic
352#424—21no—
353#423C22×C10311yescharacteristic
354#423C22×C10311yescharacteristic
355C2×C4⋊C8C22×C10311yescharacteristic
356#335C22×C10311yescharacteristic
357#335C22×C10311yescharacteristic
358#335C22×C10311yescharacteristic
359#335C22×C10311yescharacteristic
360#333C22×C10311yescharacteristic
361#333C22×C10311yescharacteristic
362#332C22×C10311yescharacteristic
363#332C22×C10311yescharacteristic
364#331C22×C10311yescharacteristic
365#331C22×C10311yescharacteristic
366#331C22×C10311yescharacteristic
367#331C22×C10311yescharacteristic
368C2×#41—21no—
369C2×#41—21no—
370C2×SD16—21no—
371C2×SD16—21no—
372C2×SD16—21no—
373C2×SD16—21no—
374C2×D8—21no—
375C2×D8—21no—
376C2×D8—21no—
377C2×D8—21no—
378C2×M16—21no—
379C2×M16—21no—
380C2×M16—21no—
381C22×C8—21no—
382C22×C8—21no—
383C4⋊Q8C23×C10311yescharacteristic
384C4⋊Q8C23×C10311yescharacteristic
385#127C23×C10311yescharacteristic
386#127C23×C10311yescharacteristic
387#126—21no—
388#125D4×C10311yescharacteristic
389#124—21no—
390#124—21no—
391#124D4×C10311yescharacteristic
392#123—21no—
393C22⋊Q8D4×C10311yescharacteristic
394#121—21no—
395#121—21no—
396#121—21no—
397#121—21no—
398#121D4×C10311yescharacteristic
399C4×Q8C23×C10311yescharacteristic
400C4×D4—21no—
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—21no—
405C4×D4C23×C10311yescharacteristic
406#117—21no—
407C2×C42C23×C10311yescharacteristic
408#107—21no—
409#107—21no—
410#106—21no—
411#106—21no—
412C4⋊C8—21no—
413C4⋊C8—21no—
414C4⋊C8—21no—
415C4⋊C8—21no—
416C4⋊C8—21no—
417C4⋊C8D4×C10311yescharacteristic
418C4⋊C8D4×C10311yescharacteristic
419C4⋊C8C23×C10311yescharacteristic
420C4⋊C8C23×C10311yescharacteristic
421C4⋊C8C23×C10311yescharacteristic
422C4⋊C8C23×C10311yescharacteristic
423C4⋊C8C23×C10311yescharacteristic
424C4⋊C8C23×C10311yescharacteristic
425#103—21no—
426#103—21no—
427#103—21no—
428#103—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437C22⋊C8—21no—
438C22⋊C8—21no—
439C22⋊C8D4×C10311yescharacteristic
440C22⋊C8D4×C10311yescharacteristic
441#97—21no—
442C4×C8—21no—
443C4×C8C23×C10311yescharacteristic
444C4×C8C23×C10311yescharacteristic
445#41—81no—
446#41—81no—
447#41—82no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8C2×D4×C10311yescharacteristic
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4C2×D4×C10311yescharacteristic
461C22×C4—21no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4C2×D4×C10311yescharacteristic
465C22×C4C2×D4×C10311yescharacteristic
466C22×C4#41×C10311yescharacteristic
467SD16—81no—
468SD16—81no—
469SD16—81no—
470SD16—81no—
471D8—81no—
472D8—81no—
473D8—81no—
474D8—81no—
475M16—81no—
476M16—81no—
477M16—81no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—81no—
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⋊C4C2×D4×C10311yescharacteristic
499C4⋊C4C2×D4×C10311yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C42—21no—
510C42C2×D4×C10311yescharacteristic
511C42C2×D4×C10311yescharacteristic
512C42#41×C10311yescharacteristic
513C42C24×C10311yescharacteristic
514C23—21no—
515C23—41no—
516C23—41no—
517C23#121×C10311yescharacteristic
518Q8—21no—
519Q8—21no—
520Q8—41no—
521Q8—41no—
522Q8—81no—
523D4—21no—
524D4—21no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—81no—
534D4—81no—
535D4—81no—
536D4—82no—
537D4—82no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—82no—
551C2×C4—82no—
552C2×C4#121×C10311yescharacteristic
553C2×C4#121×C10311yescharacteristic
554C2×C4#121×C10311yescharacteristic
555C2×C4C22×D4×C10311yescharacteristic
556C2×C4C22×D4×C10311yescharacteristic
557C2×C4C2×#41×C10311yescharacteristic
558C8—21no—
559C8—21no—
560C8—21no—
561C8—21no—
562C8—41no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—41no—
567C8—41no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22C2×#121×C10311yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—81no—
589C4—81no—
590C4#576×C10311yescharacteristic
591C4#576×C10311yescharacteristic
592C4#577×C10311yescharacteristic
593C4#578×C10311yescharacteristic
594C2—41no—
595C2—81no—
596C2—161no—
597C2—161no—
598C2C103×#304511yescharacteristic
599C2C103×#306111yescharacteristic
600C2C103×#306811yescharacteristic
subgroupG/H
center, socleC22×C103C2×#121
commutator, Frattini, cosocleC42C24×C103
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C103×#3251C2semidirect
2. C103×#3247C2semidirect
3. C103×#3207C2semidirect
4. C103×#2993C2semidirect
5. C103×#1698C2semidirect
6. C103×#1697C2semidirect
7. C103×#1686C2semidirect
8. C103×#1685C2semidirect
9. C103×#1684C2semidirect
10. C103×#1683C2semidirect
11. C103×#1668C2semidirect
12. C103×#1667C2semidirect
13. C103×#1571C2semidirect
14. C103×#1560C2semidirect
15. C103×#1547C2semidirect
293. #19542C103direct (N × H)
301. #3251C2×C103semidirect
302. #3247C2×C103semidirect
303. #3207C2×C103semidirect
304. #2993C2×C103semidirect
305. #1698C2×C103semidirect
306. #1697C2×C103semidirect
307. #1686C2×C103semidirect
308. #1685C2×C103semidirect
309. #1684C2×C103semidirect
310. #1683C2×C103semidirect
311. #1668C2×C103semidirect
312. #1667C2×C103semidirect
313. #1571C2×C103semidirect
314. #1560C2×C103semidirect
315. #1547C2×C103semidirect
316. C103#19542direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#32512
C103×#32472
C103×#32072
C103×#29932
C103×#16982
C103×#16972
C103×#16862
C103×#16852
C103×#16842
C103×#16832
C103×#16682
C103×#16672
C103×#15712
C103×#15602
C103×#15472
#19542103