Finite Group Databasebeta

← C103×#19899 #39925174

Subgroups — C103×#19899 #39925174

Order 26368.

666 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3330C211yesmaximal, characteristic, complemented
2C103×#3325C211yesmaximal, characteristic, complemented
3C103×#3303C211yesmaximal, characteristic, complemented
4C103×#3294C211yesmaximal, characteristic, complemented
5C103×#1711C211yesmaximal, characteristic, complemented
6C103×#1699C211yesmaximal, characteristic, complemented
7C103×#1697C211yesmaximal, characteristic, complemented
8C103×#1683C211yesmaximal, characteristic, complemented
9C103×#1681C211yesmaximal, characteristic, complemented
10C103×#1646C211yesmaximal, characteristic, complemented
11C103×#1639C211yesmaximal, characteristic, complemented
12C103×#1635C211yesmaximal, characteristic, complemented
13C103×#1625C211yesmaximal, characteristic, complemented
14C103×#1589C211yesmaximal, characteristic, complemented
15C8×D8×C103C211yesmaximal, characteristic, complemented
16#555×C103C2211yescharacteristic
17#547×C103C2211yescharacteristic
18#547×C103C2211yescharacteristic, complemented
19D42×C103C2211yescharacteristic
20#487×C103C2211yescharacteristic, complemented
21#487×C103C2211yescharacteristic, complemented
22#487×C103C2211yescharacteristic, complemented
23#486×C103C2211yescharacteristic
24#486×C103C2211yescharacteristic
25#486×C103C2211yescharacteristic
26#485×C103—21no—
27#484×C103—21no—
28#482×C103—21no—
29#480×C103—21no—
30#476×C103C2211yescharacteristic
31#476×C103C2211yescharacteristic, complemented
32#474×C103C2211yescharacteristic
33#474×C103C2211yescharacteristic
34#469×C103—21no—
35#468×C103—21no—
36#466×C103—21no—
37#465×C103—21no—
38#461×C103C2211yescharacteristic
39#461×C103C2211yescharacteristic, complemented
40#459×C103C2211yescharacteristic
41#459×C103C2211yescharacteristic
42#449×C103—21no—
43#449×C103—21no—
44#447×C103—21no—
45#447×C103—21no—
46C4×D8×C103C2211yescharacteristic
47C4×D8×C103C2211yescharacteristic
48#436×C103C2211yescharacteristic
49#436×C103C2211yescharacteristic, complemented
50C8×D4×C103C2211yescharacteristic
51C8×D4×C103C2211yescharacteristic, complemented
52#418×C103—21no—
53#417×C103—21no—
54#416×C103—21no—
55C2×#102×C103—21no—
56#335×C103C2211yescharacteristic, complemented
57#335×C103C2211yescharacteristic, complemented
58#333×C103C2211yescharacteristic, complemented
59#332×C103C2211yescharacteristic, complemented
60#332×C103C2211yescharacteristic, complemented
61#331×C103C2211yescharacteristic
62D4⋊C8×C103C2211yescharacteristic
63D4⋊C8×C103C2211yescharacteristic
64D4⋊C8×C103C2211yescharacteristic, complemented
65D4⋊C8×C103C2211yescharacteristic, complemented
66C82×C103C2211yescharacteristic, complemented
67C2×#41×C103—21no—
68C2×#41×C103—21no—
69C22×D4×C103—21no—
70C22×D4×C103—21no—
71C2×SD16×C103—21no—
72C2×SD16×C103—21no—
73C2×D8×C103—21no—
74C2×D8×C103—21no—
75C2×D8×C103D411yescharacteristic
76C2×D8×C103D411yescharacteristic
77C2×M16×C103—21no—
78C2×M16×C103—21no—
79C22×C8×C103—21no—
80C22×C8×C103—21no—
81C4⋊Q8×C103C2311yescharacteristic
82C4⋊Q8×C103C2311yescharacteristic
83C4⋊Q8×C103C2311yescharacteristic
84#127×C103C2311yescharacteristic
85#124×C103—41no—
86#123×C103—41no—
87#123×C103—41no—
88C22⋊Q8×C103—21no—
89C22⋊Q8×C103—21no—
90#121×C103—21no—
91#121×C103—21no—
92#121×C103—21no—
93#121×C103—21no—
94#121×C103—21no—
95#121×C103—21no—
96#120×C103—41no—
97C4×D4×C103C2311yescharacteristic
98C4×D4×C103C2311yescharacteristic
99C4×D4×C103C2311yescharacteristic
100C4×D4×C103C2311yescharacteristic
101#117×C103—21no—
102#117×C103—21no—
103C2×C4⋊C4×C103—21no—
104C2×C4⋊C4×C103—21no—
105#107×C103—21no—
106#107×C103—21no—
107#107×C103D411yescharacteristic
108#107×C103D411yescharacteristic
109#106×C103—21no—
110#106×C103—21no—
111C4⋊C8×C103C2311yescharacteristic
112C4⋊C8×C103C2311yescharacteristic
113C4⋊C8×C103C2311yescharacteristic
114C4⋊C8×C103C2311yescharacteristic
115#103×C103—21no—
116#103×C103—21no—
117#103×C103—21no—
118#103×C103—21no—
119#103×C103—21no—
120#103×C103—21no—
121#103×C103—41no—
122#102×C103—21no—
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—41no—
133#102×C103D411yescharacteristic
134#102×C103D411yescharacteristic
135#102×C103D411yescharacteristic
136#102×C103D411yescharacteristic
137C22⋊C8×C103—21no—
138C22⋊C8×C103—21no—
139C22⋊C8×C103—21no—
140C22⋊C8×C103—21no—
141C4×C8×C103C2311yescharacteristic
142C4×C8×C103C2311yescharacteristic
143C4×C8×C103C2311yescharacteristic
144C24×C103—41no—
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×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—41no—
160C2×D4×C103—41no—
161C2×D4×C103—41no—
162C2×D4×C103—81no—
163C2×D4×C103—81no—
164C2×D4×C103C2×D411yescharacteristic
165C2×D4×C103C2×D411yescharacteristic
166C2×D4×C103C2×D411yescharacteristic
167C2×D4×C103C2×D411yescharacteristic
168C22×C4×C103—21no—
169C22×C4×C103—21no—
170C22×C4×C103—21no—
171C22×C4×C103—21no—
172C22×C4×C103—41no—
173C22×C4×C103—41no—
174SD16×C103—81no—
175SD16×C103—81no—
176D8×C103—22no—
177D8×C103—41no—
178D8×C103—81no—
179D8×C103—81no—
180M16×C103—81no—
181M16×C103—81no—
182C2×C8×C103—21no—
183C2×C8×C103—21no—
184C2×C8×C103—21no—
185C2×C8×C103—21no—
186C2×C8×C103—21no—
187C2×C8×C103—81no—
188C2×C8×C103—81no—
189C2×C8×C103C2×D411yescharacteristic
190C2×C8×C103C2×D411yescharacteristic
191C2×C8×C103C2×D411yescharacteristic
192C2×C8×C103C2×D411yescharacteristic
193C4⋊C4×C103—21no—
194C4⋊C4×C103—21no—
195C4⋊C4×C103—21no—
196C4⋊C4×C103—21no—
197C4⋊C4×C103—21no—
198C4⋊C4×C103—21no—
199C4⋊C4×C103—41no—
200C4⋊C4×C103—41no—
201C4⋊C4×C103C2×D411yescharacteristic
202C4⋊C4×C103C2×D411yescharacteristic
203C4⋊C4×C103C2×D411yescharacteristic
204C4⋊C4×C103C2×D411yescharacteristic
205C22⋊C4×C103—21no—
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—
213C22⋊C4×C103—41no—
214C42×C103—41no—
215C42×C103C2411yescharacteristic
216C23×C103—21no—
217C23×C103—21no—
218C23×C103—21no—
219C23×C103—21no—
220C23×C103—41no—
221C23×C103—82no—
222C23×C103—82no—
223C23×C103—161no—
224Q8×C103—41no—
225Q8×C103—41no—
226Q8×C103—41no—
227Q8×C103—41no—
228Q8×C103—81no—
229D4×C103—21no—
230D4×C103—21no—
231D4×C103—21no—
232D4×C103—21no—
233D4×C103—21no—
234D4×C103—21no—
235D4×C103—21no—
236D4×C103—41no—
237D4×C103—41no—
238D4×C103—41no—
239D4×C103—41no—
240D4×C103—81no—
241D4×C103—82no—
242D4×C103—82no—
243D4×C103—82no—
244D4×C103—82no—
245D4×C103—161no—
246D4×C103#13512yes—
247C2×C4×C103—21no—
248C2×C4×C103—21no—
249C2×C4×C103—21no—
250C2×C4×C103—21no—
251C2×C4×C103—41no—
252C2×C4×C103—41no—
253C2×C4×C103—41no—
254C2×C4×C103—41no—
255C2×C4×C103—41no—
256C2×C4×C103—41no—
257C2×C4×C103—41no—
258C2×C4×C103—41no—
259C2×C4×C103—41no—
260C2×C4×C103—41no—
261C2×C4×C103—41no—
262C2×C4×C103—82no—
263C2×C4×C103—82no—
264C2×C4×C103C22×D411yescharacteristic
265C2×C4×C103C22×D411yescharacteristic
266C2×C4×C103H(5,𝔽2)11yescharacteristic
267C8×C103—21no—
268C8×C103—21no—
269C8×C103—21no—
270C8×C103—21no—
271C8×C103—41no—
272C8×C103—41no—
273C8×C103—41no—
274C8×C103—41no—
275C8×C103—41no—
276C22×C103—22no—
277C22×C103—41no—
278C22×C103—41no—
279C22×C103—41no—
280C22×C103—41no—
281C22×C103—41no—
282C22×C103—41no—
283C22×C103—41no—
284C22×C103—41no—
285C22×C103—41no—
286C22×C103—41no—
287C22×C103—41no—
288C22×C103—81no—
289C22×C103—81no—
290C22×C103—81no—
291C22×C103—164no—
292C22×C103D4211yescharacteristic
293C4×C103—21no—
294C4×C103—41no—
295C4×C103—41no—
296C4×C103—41no—
297C4×C103—41no—
298C4×C103—81no—
299C4×C103—81no—
300C4×C103—81no—
301C4×C103C2×#13511yescharacteristic
302C4×C103#57511yescharacteristic
303C4×C103#57611yescharacteristic
304C4×C103#57611yescharacteristic
305#19899C10311yesmaximal, characteristic, direct product factor, Sylow
306C2×C103—42no—
307C2×C103—81no—
308C2×C103—81no—
309C2×C103—81no—
310C2×C103—161no—
311C2×C103#327311yescharacteristic
312C2×C103#328011yescharacteristic
313C2×C103#329011yescharacteristic
314#3330C2×C10311yescharacteristic, complemented
315#3325C2×C10311yescharacteristic, complemented
316#3303C2×C10311yescharacteristic, complemented
317#3294C2×C10311yescharacteristic, complemented
318#1711C2×C10311yescharacteristic, complemented
319#1699C2×C10311yescharacteristic, complemented
320#1697C2×C10311yescharacteristic, complemented
321#1683C2×C10311yescharacteristic, complemented
322#1681C2×C10311yescharacteristic, complemented
323#1646C2×C10311yescharacteristic, complemented
324#1639C2×C10311yescharacteristic, complemented
325#1635C2×C10311yescharacteristic, complemented
326#1625C2×C10311yescharacteristic, complemented
327#1589C2×C10311yescharacteristic, complemented
328C8×D8C2×C10311yescharacteristic, complemented
329C103#1989911yescharacteristic, direct product factor, Sylow
330#555C22×C10311yescharacteristic
331#547C22×C10311yescharacteristic
332#547C22×C10311yescharacteristic, complemented
333D42C22×C10311yescharacteristic
334#487C22×C10311yescharacteristic, complemented
335#487C22×C10311yescharacteristic, complemented
336#487C22×C10311yescharacteristic, complemented
337#486C22×C10311yescharacteristic
338#486C22×C10311yescharacteristic
339#486C22×C10311yescharacteristic
340#485—21no—
341#484—21no—
342#482—21no—
343#480—21no—
344#476C22×C10311yescharacteristic
345#476C22×C10311yescharacteristic, complemented
346#474C22×C10311yescharacteristic
347#474C22×C10311yescharacteristic
348#469—21no—
349#468—21no—
350#466—21no—
351#465—21no—
352#461C22×C10311yescharacteristic
353#461C22×C10311yescharacteristic, complemented
354#459C22×C10311yescharacteristic
355#459C22×C10311yescharacteristic
356#449—21no—
357#449—21no—
358#447—21no—
359#447—21no—
360C4×D8C22×C10311yescharacteristic
361C4×D8C22×C10311yescharacteristic
362#436C22×C10311yescharacteristic
363#436C22×C10311yescharacteristic, complemented
364C8×D4C22×C10311yescharacteristic
365C8×D4C22×C10311yescharacteristic, complemented
366#418—21no—
367#417—21no—
368#416—21no—
369C2×#102—21no—
370#335C22×C10311yescharacteristic, complemented
371#335C22×C10311yescharacteristic, complemented
372#333C22×C10311yescharacteristic, complemented
373#332C22×C10311yescharacteristic, complemented
374#332C22×C10311yescharacteristic, complemented
375#331C22×C10311yescharacteristic
376D4⋊C8C22×C10311yescharacteristic
377D4⋊C8C22×C10311yescharacteristic
378D4⋊C8C22×C10311yescharacteristic, complemented
379D4⋊C8C22×C10311yescharacteristic, complemented
380C82C22×C10311yescharacteristic, complemented
381C2×#41—21no—
382C2×#41—21no—
383C22×D4—21no—
384C22×D4—21no—
385C2×SD16—21no—
386C2×SD16—21no—
387C2×D8—21no—
388C2×D8—21no—
389C2×D8D4×C10311yescharacteristic
390C2×D8D4×C10311yescharacteristic
391C2×M16—21no—
392C2×M16—21no—
393C22×C8—21no—
394C22×C8—21no—
395C4⋊Q8C23×C10311yescharacteristic
396C4⋊Q8C23×C10311yescharacteristic
397C4⋊Q8C23×C10311yescharacteristic
398#127C23×C10311yescharacteristic
399#124—41no—
400#123—41no—
401#123—41no—
402C22⋊Q8—21no—
403C22⋊Q8—21no—
404#121—21no—
405#121—21no—
406#121—21no—
407#121—21no—
408#121—21no—
409#121—21no—
410#120—41no—
411C4×D4C23×C10311yescharacteristic
412C4×D4C23×C10311yescharacteristic
413C4×D4C23×C10311yescharacteristic
414C4×D4C23×C10311yescharacteristic
415#117—21no—
416#117—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419#107—21no—
420#107—21no—
421#107D4×C10311yescharacteristic
422#107D4×C10311yescharacteristic
423#106—21no—
424#106—21no—
425C4⋊C8C23×C10311yescharacteristic
426C4⋊C8C23×C10311yescharacteristic
427C4⋊C8C23×C10311yescharacteristic
428C4⋊C8C23×C10311yescharacteristic
429#103—21no—
430#103—21no—
431#103—21no—
432#103—21no—
433#103—21no—
434#103—21no—
435#103—41no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—21no—
444#102—21no—
445#102—21no—
446#102—41no—
447#102D4×C10311yescharacteristic
448#102D4×C10311yescharacteristic
449#102D4×C10311yescharacteristic
450#102D4×C10311yescharacteristic
451C22⋊C8—21no—
452C22⋊C8—21no—
453C22⋊C8—21no—
454C22⋊C8—21no—
455C4×C8C23×C10311yescharacteristic
456C4×C8C23×C10311yescharacteristic
457C4×C8C23×C10311yescharacteristic
458C24—41no—
459#41—42no—
460#41—42no—
461#41—81no—
462#41—81no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4—81no—
477C2×D4—81no—
478C2×D4C2×D4×C10311yescharacteristic
479C2×D4C2×D4×C10311yescharacteristic
480C2×D4C2×D4×C10311yescharacteristic
481C2×D4C2×D4×C10311yescharacteristic
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—41no—
487C22×C4—41no—
488SD16—81no—
489SD16—81no—
490D8—22no—
491D8—41no—
492D8—81no—
493D8—81no—
494M16—81no—
495M16—81no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—81no—
502C2×C8—81no—
503C2×C8C2×D4×C10311yescharacteristic
504C2×C8C2×D4×C10311yescharacteristic
505C2×C8C2×D4×C10311yescharacteristic
506C2×C8C2×D4×C10311yescharacteristic
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4C2×D4×C10311yescharacteristic
516C4⋊C4C2×D4×C10311yescharacteristic
517C4⋊C4C2×D4×C10311yescharacteristic
518C4⋊C4C2×D4×C10311yescharacteristic
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C22⋊C4—41no—
528C42—41no—
529C42C24×C10311yescharacteristic
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—41no—
535C23—82no—
536C23—82no—
537C23—161no—
538Q8—41no—
539Q8—41no—
540Q8—41no—
541Q8—41no—
542Q8—81no—
543D4—21no—
544D4—21no—
545D4—21no—
546D4—21no—
547D4—21no—
548D4—21no—
549D4—21no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—81no—
555D4—82no—
556D4—82no—
557D4—82no—
558D4—82no—
559D4—161no—
560D4#135×C10312yes—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—82no—
577C2×C4—82no—
578C2×C4C22×D4×C10311yescharacteristic
579C2×C4C22×D4×C10311yescharacteristic
580C2×C4H(5,𝔽2)×C10311yescharacteristic
581C8—21no—
582C8—21no—
583C8—21no—
584C8—21no—
585C8—41no—
586C8—41no—
587C8—41no—
588C8—41no—
589C8—41no—
590C22—22no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—164no—
606C22D42×C10311yescharacteristic
607C4—21no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—41no—
612C4—81no—
613C4—81no—
614C4—81no—
615C4C2×#135×C10311yescharacteristic
616C4#575×C10311yescharacteristic
617C4#576×C10311yescharacteristic
618C4#576×C10311yescharacteristic
619C2—42no—
620C2—81no—
621C2—81no—
622C2—81no—
623C2—161no—
624C2C103×#327311yescharacteristic
625C2C103×#328011yescharacteristic
626C2C103×#329011yescharacteristic
subgroupG/H
center, socleC22×C103D42
commutator, Frattini, cosocleC42C24×C103
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×#3330C2semidirect
2. C103×#3325C2semidirect
3. C103×#3303C2semidirect
4. C103×#3294C2semidirect
5. C103×#1711C2semidirect
6. C103×#1699C2semidirect
7. C103×#1697C2semidirect
8. C103×#1683C2semidirect
9. C103×#1681C2semidirect
10. C103×#1646C2semidirect
11. C103×#1639C2semidirect
12. C103×#1635C2semidirect
13. C103×#1625C2semidirect
14. C103×#1589C2semidirect
15. C8×D8×C103C2semidirect
18. #547×C103C22semidirect
20. #487×C103C22semidirect
21. #487×C103C22semidirect
22. #487×C103C22semidirect
31. #476×C103C22semidirect
39. #461×C103C22semidirect
49. #436×C103C22semidirect
51. C8×D4×C103C22semidirect
56. #335×C103C22semidirect
57. #335×C103C22semidirect
58. #333×C103C22semidirect
59. #332×C103C22semidirect
60. #332×C103C22semidirect
64. D4⋊C8×C103C22semidirect
65. D4⋊C8×C103C22semidirect
66. C82×C103C22semidirect
305. #19899C103direct (N × H)
314. #3330C2×C103semidirect
315. #3325C2×C103semidirect
316. #3303C2×C103semidirect
317. #3294C2×C103semidirect
318. #1711C2×C103semidirect
319. #1699C2×C103semidirect
320. #1697C2×C103semidirect
321. #1683C2×C103semidirect
322. #1681C2×C103semidirect
323. #1646C2×C103semidirect
324. #1639C2×C103semidirect
325. #1635C2×C103semidirect
326. #1625C2×C103semidirect
327. #1589C2×C103semidirect
328. C8×D8C2×C103semidirect
329. C103#19899direct (N × H)
332. #547C22×C103semidirect
334. #487C22×C103semidirect
335. #487C22×C103semidirect
336. #487C22×C103semidirect
345. #476C22×C103semidirect
353. #461C22×C103semidirect
363. #436C22×C103semidirect
365. C8×D4C22×C103semidirect
370. #335C22×C103semidirect
371. #335C22×C103semidirect
372. #333C22×C103semidirect
373. #332C22×C103semidirect
374. #332C22×C103semidirect
378. D4⋊C8C22×C103semidirect
379. D4⋊C8C22×C103semidirect
380. C82C22×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#33302
C103×#33252
C103×#33032
C103×#32942
C103×#17112
C103×#16992
C103×#16972
C103×#16832
C103×#16812
C103×#16462
C103×#16392
C103×#16352
C103×#16252
C103×#15892
C8×D8×C1032
#19899103