Finite Group Databasebeta

← C103×#19825 #39925100

Subgroups — C103×#19825 #39925100

Order 26368.

642 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3394C211yesmaximal, characteristic, complemented
2C103×#3361C211yesmaximal, characteristic, complemented
3C103×#3324C211yesmaximal, characteristic, complemented
4C103×#3295C211yesmaximal, characteristic, complemented
5C103×#1717C211yesmaximal, characteristic, complemented
6C103×#1697C211yesmaximal, characteristic, complemented
7C103×#1682C211yesmaximal, characteristic, complemented
8C103×#1678C211yesmaximal, characteristic, complemented
9C103×#1665C211yesmaximal, characteristic, complemented
10C103×#1644C211yesmaximal, characteristic, complemented
11C103×#1638C211yesmaximal, characteristic, complemented
12C103×#1620C211yesmaximal, characteristic, complemented
13C103×#1619C211yesmaximal, characteristic
14C103×#1583C211yesmaximal, characteristic, complemented
15C103×SD16⋊C8C211yesmaximal, characteristic, complemented
16#559×C103C2211yescharacteristic, complemented
17#556×C103C2211yescharacteristic
18#554×C103C2211yescharacteristic
19D42×C103C2211yescharacteristic
20#495×C103—21no—
21#493×C103C2211yescharacteristic
22#492×C103C2211yescharacteristic, complemented
23#488×C103—21no—
24#487×C103C2211yescharacteristic, complemented
25#486×C103C2211yescharacteristic
26#486×C103C2211yescharacteristic
27#486×C103C2211yescharacteristic, complemented
28#482×C103—21no—
29#481×C103—21no—
30#478×C103—21no—
31#477×C103C2211yescharacteristic, complemented
32#476×C103C2211yescharacteristic
33#474×C103C2211yescharacteristic
34#468×C103—21no—
35#465×C103—21no—
36#464×C103—21no—
37#463×C103—21no—
38#463×C103—21no—
39#462×C103C2211yescharacteristic, complemented
40#460×C103C2211yescharacteristic
41#460×C103C2211yescharacteristic
42#459×C103C2211yescharacteristic
43#459×C103C2211yescharacteristic
44#450×C103—21no—
45#450×C103—21no—
46C8×Q8×C103C2211yescharacteristic, complemented
47C8×Q8×C103C2211yescharacteristic, complemented
48C4×SD16×C103—21no—
49C4×SD16×C103C2211yescharacteristic
50C4×SD16×C103C2211yescharacteristic
51C4×D8×C103—21no—
52#436×C103C2211yescharacteristic
53C8×D4×C103C2211yescharacteristic
54#418×C103—21no—
55C2×#102×C103—21no—
56#335×C103C2211yescharacteristic, complemented
57#334×C103C2211yescharacteristic, complemented
58#333×C103C2211yescharacteristic, complemented
59#332×C103C2211yescharacteristic, complemented
60#331×C103C2211yescharacteristic
61#331×C103C2211yescharacteristic, complemented
62Q8⋊C8×C103C2211yescharacteristic, complemented
63Q8⋊C8×C103C2211yescharacteristic, complemented
64D4⋊C8×C103C2211yescharacteristic
65D4⋊C8×C103C2211yescharacteristic
66#322×C103C2211yescharacteristic, complemented
67C22×D4×C103—21no—
68C22×D4×C103—21no—
69C2×Q16×C103—21no—
70C2×SD16×C103—21no—
71C2×SD16×C103—21no—
72C2×SD16×C103—21no—
73C2×SD16×C103—21no—
74C2×SD16×C103D411yescharacteristic
75C2×SD16×C103D411yescharacteristic
76C2×D8×C103—21no—
77C2×D8×C103—21no—
78C2×D8×C103—41no—
79C2×M16×C103—21no—
80C22×C8×C103—21no—
81C4⋊Q8×C103C2311yescharacteristic
82C4⋊Q8×C103C2311yescharacteristic
83#127×C103C2311yescharacteristic
84#127×C103C2311yescharacteristic
85#126×C103—41no—
86#125×C103—21no—
87#124×C103—21no—
88#124×C103—21no—
89#124×C103—21no—
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#120×C103—41no—
97C4×Q8×C103—21no—
98C4×Q8×C103C2311yescharacteristic
99C4×Q8×C103C2311yescharacteristic
100C4×D4×C103—21no—
101C4×D4×C103—21no—
102C4×D4×C103—21no—
103C4×D4×C103C2311yescharacteristic
104C4×D4×C103C2311yescharacteristic
105#117×C103—21no—
106C2×C4⋊C4×C103—21no—
107#107×C103—21no—
108#107×C103—21no—
109#106×C103—21no—
110#106×C103D411yescharacteristic
111#106×C103D411yescharacteristic
112C4⋊C8×C103—21no—
113C4⋊C8×C103—21no—
114C4⋊C8×C103C2311yescharacteristic
115C4⋊C8×C103C2311yescharacteristic
116C4⋊C8×C103C2311yescharacteristic
117C4⋊C8×C103C2311yescharacteristic
118#103×C103—21no—
119#103×C103—21no—
120#103×C103—41no—
121#103×C103D411yescharacteristic
122#103×C103D411yescharacteristic
123#102×C103—21no—
124#102×C103—21no—
125#102×C103—21no—
126#102×C103—21no—
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×C103D411yescharacteristic
136#102×C103D411yescharacteristic
137C22⋊C8×C103—21no—
138C22⋊C8×C103—21no—
139C4×C8×C103—21no—
140C4×C8×C103—21no—
141C4×C8×C103C2311yescharacteristic
142C4×C8×C103C2311yescharacteristic
143C4×C8×C103C2311yescharacteristic
144C24×C103—41no—
145C2×Q8×C103—21no—
146C2×Q8×C103—21no—
147C2×Q8×C103C2×D411yescharacteristic
148C2×Q8×C103C2×D411yescharacteristic
149C2×D4×C103—21no—
150C2×D4×C103—21no—
151C2×D4×C103—21no—
152C2×D4×C103—21no—
153C2×D4×C103—21no—
154C2×D4×C103—21no—
155C2×D4×C103—41no—
156C2×D4×C103—41no—
157C2×D4×C103—42no—
158C2×D4×C103—42no—
159C2×D4×C103—81no—
160C2×D4×C103—81no—
161C2×D4×C103C2×D411yescharacteristic
162C2×D4×C103C2×D411yescharacteristic
163C22×C4×C103—21no—
164C22×C4×C103—21no—
165C22×C4×C103—41no—
166C22×C4×C103—41no—
167Q16×C103—81no—
168SD16×C103—22no—
169SD16×C103—41no—
170SD16×C103—42no—
171SD16×C103—81no—
172SD16×C103—81no—
173SD16×C103—81no—
174D8×C103—42no—
175D8×C103—81no—
176D8×C103—82no—
177M16×C103—81no—
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×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—41no—
195C4⋊C4×C103—41no—
196C4⋊C4×C103—41no—
197C4⋊C4×C103C2×D411yescharacteristic
198C4⋊C4×C103C2×D411yescharacteristic
199C4⋊C4×C103C2×D411yescharacteristic
200C4⋊C4×C103C2×D411yescharacteristic
201C22⋊C4×C103—21no—
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—
210C42×C103—21no—
211C42×C103—21no—
212C42×C103—41no—
213C42×C103C2411yescharacteristic
214C23×C103—21no—
215C23×C103—21no—
216C23×C103—41no—
217C23×C103—41no—
218C23×C103—82no—
219C23×C103—82no—
220C23×C103—161no—
221Q8×C103—21no—
222Q8×C103—21no—
223Q8×C103—21no—
224Q8×C103—21no—
225Q8×C103—41no—
226Q8×C103—41no—
227Q8×C103—81no—
228D4×C103—21no—
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—81no—
240D4×C103—81no—
241D4×C103—82no—
242D4×C103—82no—
243D4×C103#13512yes—
244C2×C4×C103—21no—
245C2×C4×C103—21no—
246C2×C4×C103—21no—
247C2×C4×C103—21no—
248C2×C4×C103—21no—
249C2×C4×C103—21no—
250C2×C4×C103—41no—
251C2×C4×C103—41no—
252C2×C4×C103—41no—
253C2×C4×C103—41no—
254C2×C4×C103—41no—
255C2×C4×C103—41no—
256C2×C4×C103—161no—
257C2×C4×C103—161no—
258C2×C4×C103C22×D411yescharacteristic
259C2×C4×C103C22×D411yescharacteristic
260C2×C4×C103H(5,𝔽2)11yescharacteristic
261C8×C103—21no—
262C8×C103—21no—
263C8×C103—21no—
264C8×C103—21no—
265C8×C103—41no—
266C8×C103—41no—
267C8×C103—41no—
268C8×C103—41no—
269C8×C103—41no—
270C22×C103—22no—
271C22×C103—41no—
272C22×C103—41no—
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—164no—
283C22×C103D4211yescharacteristic
284C4×C103—21no—
285C4×C103—41no—
286C4×C103—41no—
287C4×C103—41no—
288C4×C103—41no—
289C4×C103—41no—
290C4×C103—41no—
291C4×C103—81no—
292C4×C103—81no—
293C4×C103C2×#13511yescharacteristic
294C4×C103#57511yescharacteristic
295C4×C103#57611yescharacteristic
296C4×C103#57711yescharacteristic
297#19825C10311yesmaximal, characteristic, direct product factor, Sylow
298C2×C103—42no—
299C2×C103—81no—
300C2×C103—161no—
301C2×C103—161no—
302C2×C103#326811yescharacteristic
303C2×C103#328211yescharacteristic
304C2×C103#328811yescharacteristic
305#3394C2×C10311yescharacteristic, complemented
306#3361C2×C10311yescharacteristic, complemented
307#3324C2×C10311yescharacteristic, complemented
308#3295C2×C10311yescharacteristic, complemented
309#1717C2×C10311yescharacteristic, complemented
310#1697C2×C10311yescharacteristic, complemented
311#1682C2×C10311yescharacteristic, complemented
312#1678C2×C10311yescharacteristic, complemented
313#1665C2×C10311yescharacteristic, complemented
314#1644C2×C10311yescharacteristic, complemented
315#1638C2×C10311yescharacteristic, complemented
316#1620C2×C10311yescharacteristic, complemented
317#1619C2×C10311yescharacteristic
318#1583C2×C10311yescharacteristic, complemented
319SD16⋊C8C2×C10311yescharacteristic, complemented
320C103#1982511yescharacteristic, direct product factor, Sylow
321#559C22×C10311yescharacteristic, complemented
322#556C22×C10311yescharacteristic
323#554C22×C10311yescharacteristic
324D42C22×C10311yescharacteristic
325#495—21no—
326#493C22×C10311yescharacteristic
327#492C22×C10311yescharacteristic, complemented
328#488—21no—
329#487C22×C10311yescharacteristic, complemented
330#486C22×C10311yescharacteristic
331#486C22×C10311yescharacteristic
332#486C22×C10311yescharacteristic, complemented
333#482—21no—
334#481—21no—
335#478—21no—
336#477C22×C10311yescharacteristic, complemented
337#476C22×C10311yescharacteristic
338#474C22×C10311yescharacteristic
339#468—21no—
340#465—21no—
341#464—21no—
342#463—21no—
343#463—21no—
344#462C22×C10311yescharacteristic, complemented
345#460C22×C10311yescharacteristic
346#460C22×C10311yescharacteristic
347#459C22×C10311yescharacteristic
348#459C22×C10311yescharacteristic
349#450—21no—
350#450—21no—
351C8×Q8C22×C10311yescharacteristic, complemented
352C8×Q8C22×C10311yescharacteristic, complemented
353C4×SD16—21no—
354C4×SD16C22×C10311yescharacteristic
355C4×SD16C22×C10311yescharacteristic
356C4×D8—21no—
357#436C22×C10311yescharacteristic
358C8×D4C22×C10311yescharacteristic
359#418—21no—
360C2×#102—21no—
361#335C22×C10311yescharacteristic, complemented
362#334C22×C10311yescharacteristic, complemented
363#333C22×C10311yescharacteristic, complemented
364#332C22×C10311yescharacteristic, complemented
365#331C22×C10311yescharacteristic
366#331C22×C10311yescharacteristic, complemented
367Q8⋊C8C22×C10311yescharacteristic, complemented
368Q8⋊C8C22×C10311yescharacteristic, complemented
369D4⋊C8C22×C10311yescharacteristic
370D4⋊C8C22×C10311yescharacteristic
371#322C22×C10311yescharacteristic, complemented
372C22×D4—21no—
373C22×D4—21no—
374C2×Q16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16D4×C10311yescharacteristic
380C2×SD16D4×C10311yescharacteristic
381C2×D8—21no—
382C2×D8—21no—
383C2×D8—41no—
384C2×M16—21no—
385C22×C8—21no—
386C4⋊Q8C23×C10311yescharacteristic
387C4⋊Q8C23×C10311yescharacteristic
388#127C23×C10311yescharacteristic
389#127C23×C10311yescharacteristic
390#126—41no—
391#125—21no—
392#124—21no—
393#124—21no—
394#124—21no—
395#123—41no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398C22⋊Q8—41no—
399#121—21no—
400#121—21no—
401#120—41no—
402C4×Q8—21no—
403C4×Q8C23×C10311yescharacteristic
404C4×Q8C23×C10311yescharacteristic
405C4×D4—21no—
406C4×D4—21no—
407C4×D4—21no—
408C4×D4C23×C10311yescharacteristic
409C4×D4C23×C10311yescharacteristic
410#117—21no—
411C2×C4⋊C4—21no—
412#107—21no—
413#107—21no—
414#106—21no—
415#106D4×C10311yescharacteristic
416#106D4×C10311yescharacteristic
417C4⋊C8—21no—
418C4⋊C8—21no—
419C4⋊C8C23×C10311yescharacteristic
420C4⋊C8C23×C10311yescharacteristic
421C4⋊C8C23×C10311yescharacteristic
422C4⋊C8C23×C10311yescharacteristic
423#103—21no—
424#103—21no—
425#103—41no—
426#103D4×C10311yescharacteristic
427#103D4×C10311yescharacteristic
428#102—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—
437#102—21no—
438#102—21no—
439#102—21no—
440#102D4×C10311yescharacteristic
441#102D4×C10311yescharacteristic
442C22⋊C8—21no—
443C22⋊C8—21no—
444C4×C8—21no—
445C4×C8—21no—
446C4×C8C23×C10311yescharacteristic
447C4×C8C23×C10311yescharacteristic
448C4×C8C23×C10311yescharacteristic
449C24—41no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8C2×D4×C10311yescharacteristic
453C2×Q8C2×D4×C10311yescharacteristic
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—42no—
463C2×D4—42no—
464C2×D4—81no—
465C2×D4—81no—
466C2×D4C2×D4×C10311yescharacteristic
467C2×D4C2×D4×C10311yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—41no—
471C22×C4—41no—
472Q16—81no—
473SD16—22no—
474SD16—41no—
475SD16—42no—
476SD16—81no—
477SD16—81no—
478SD16—81no—
479D8—42no—
480D8—81no—
481D8—82no—
482M16—81no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—81no—
489C2×C8C2×D4×C10311yescharacteristic
490C2×C8C2×D4×C10311yescharacteristic
491C2×C8C2×D4×C10311yescharacteristic
492C2×C8C2×D4×C10311yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
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—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C42—21no—
516C42—21no—
517C42—41no—
518C42C24×C10311yescharacteristic
519C23—21no—
520C23—21no—
521C23—41no—
522C23—41no—
523C23—82no—
524C23—82no—
525C23—161no—
526Q8—21no—
527Q8—21no—
528Q8—21no—
529Q8—21no—
530Q8—41no—
531Q8—41no—
532Q8—81no—
533D4—21no—
534D4—21no—
535D4—21no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—81no—
545D4—81no—
546D4—82no—
547D4—82no—
548D4#135×C10312yes—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—161no—
562C2×C4—161no—
563C2×C4C22×D4×C10311yescharacteristic
564C2×C4C22×D4×C10311yescharacteristic
565C2×C4H(5,𝔽2)×C10311yescharacteristic
566C8—21no—
567C8—21no—
568C8—21no—
569C8—21no—
570C8—41no—
571C8—41no—
572C8—41no—
573C8—41no—
574C8—41no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—164no—
588C22D42×C10311yescharacteristic
589C4—21no—
590C4—41no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4—81no—
597C4—81no—
598C4C2×#135×C10311yescharacteristic
599C4#575×C10311yescharacteristic
600C4#576×C10311yescharacteristic
601C4#577×C10311yescharacteristic
602C2—42no—
603C2—81no—
604C2—161no—
605C2—161no—
606C2C103×#326811yescharacteristic
607C2C103×#328211yescharacteristic
608C2C103×#328811yescharacteristic
subgroupG/H
center, socleC22×C103D42
commutator, Frattini, cosocleC42C24×C103
prime radicalC103×#1619C2
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×#3394C2semidirect
2. C103×#3361C2semidirect
3. C103×#3324C2semidirect
4. C103×#3295C2semidirect
5. C103×#1717C2semidirect
6. C103×#1697C2semidirect
7. C103×#1682C2semidirect
8. C103×#1678C2semidirect
9. C103×#1665C2semidirect
10. C103×#1644C2semidirect
11. C103×#1638C2semidirect
12. C103×#1620C2semidirect
14. C103×#1583C2semidirect
15. C103×SD16⋊C8C2semidirect
16. #559×C103C22semidirect
22. #492×C103C22semidirect
24. #487×C103C22semidirect
27. #486×C103C22semidirect
31. #477×C103C22semidirect
39. #462×C103C22semidirect
46. C8×Q8×C103C22semidirect
47. C8×Q8×C103C22semidirect
56. #335×C103C22semidirect
57. #334×C103C22semidirect
58. #333×C103C22semidirect
59. #332×C103C22semidirect
61. #331×C103C22semidirect
62. Q8⋊C8×C103C22semidirect
63. Q8⋊C8×C103C22semidirect
66. #322×C103C22semidirect
297. #19825C103direct (N × H)
305. #3394C2×C103semidirect
306. #3361C2×C103semidirect
307. #3324C2×C103semidirect
308. #3295C2×C103semidirect
309. #1717C2×C103semidirect
310. #1697C2×C103semidirect
311. #1682C2×C103semidirect
312. #1678C2×C103semidirect
313. #1665C2×C103semidirect
314. #1644C2×C103semidirect
315. #1638C2×C103semidirect
316. #1620C2×C103semidirect
318. #1583C2×C103semidirect
319. SD16⋊C8C2×C103semidirect
320. C103#19825direct (N × H)
321. #559C22×C103semidirect
327. #492C22×C103semidirect
329. #487C22×C103semidirect
332. #486C22×C103semidirect
336. #477C22×C103semidirect
344. #462C22×C103semidirect
351. C8×Q8C22×C103semidirect
352. C8×Q8C22×C103semidirect
361. #335C22×C103semidirect
362. #334C22×C103semidirect
363. #333C22×C103semidirect
364. #332C22×C103semidirect
366. #331C22×C103semidirect
367. Q8⋊C8C22×C103semidirect
368. Q8⋊C8C22×C103semidirect
371. #322C22×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#33942
C103×#33612
C103×#33242
C103×#32952
C103×#17172
C103×#16972
C103×#16822
C103×#16782
C103×#16652
C103×#16442
C103×#16382
C103×#16202
C103×#16192
C103×#15832
C103×SD16⋊C82
#19825103