Finite Group Databasebeta

← C103×#19775 #39925050

Subgroups — C103×#19775 #39925050

Order 26368.

656 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3341C211yesmaximal, characteristic, complemented
2C103×#3325C211yesmaximal, characteristic, complemented
3C103×#3303C211yesmaximal, characteristic, complemented
4C103×#3294C211yesmaximal, characteristic, complemented
5C103×#1719C211yesmaximal, characteristic, complemented
6C103×#1703C211yesmaximal, characteristic, complemented
7C103×#1681C211yesmaximal, characteristic, complemented
8C103×#1677C211yesmaximal, characteristic, complemented
9C103×#1675C211yesmaximal, characteristic, complemented
10C103×#1646C211yesmaximal, characteristic, complemented
11C103×#1635C211yesmaximal, characteristic, complemented
12C103×#1629C211yesmaximal, characteristic, complemented
13C103×#1624C211yesmaximal, characteristic, complemented
14C103×#1581C211yesmaximal, characteristic, complemented
15C103×#1580C211yesmaximal, characteristic, complemented
16#555×C103C2211yescharacteristic
17#555×C103C2211yescharacteristic, complemented
18#547×C103C2211yescharacteristic
19D42×C103C2211yescharacteristic
20#500×C103C2211yescharacteristic, complemented
21#492×C103C2211yescharacteristic
22#487×C103C2211yescharacteristic, complemented
23#487×C103C2211yescharacteristic, complemented
24#486×C103C2211yescharacteristic
25#486×C103C2211yescharacteristic
26#485×C103—21no—
27#482×C103—21no—
28#482×C103—21no—
29#482×C103—21no—
30#480×C103—21no—
31#476×C103C2211yescharacteristic
32#476×C103C2211yescharacteristic
33#476×C103C2211yescharacteristic
34#476×C103C2211yescharacteristic, complemented
35#474×C103C2211yescharacteristic
36#469×C103—21no—
37#466×C103—21no—
38#466×C103—21no—
39#465×C103—21no—
40#461×C103C2211yescharacteristic, complemented
41#459×C103C2211yescharacteristic
42#459×C103C2211yescharacteristic
43#449×C103—21no—
44#447×C103—21no—
45#447×C103—21no—
46C4×D8×C103C2211yescharacteristic
47C4×D8×C103C2211yescharacteristic
48#436×C103C2211yescharacteristic
49C8×D4×C103C2211yescharacteristic
50C8×D4×C103C2211yescharacteristic, complemented
51C8×D4×C103C2211yescharacteristic, complemented
52#427×C103—21no—
53#418×C103—21no—
54#416×C103—21no—
55C2×#102×C103—21no—
56#335×C103C2211yescharacteristic, complemented
57#334×C103C2211yescharacteristic, complemented
58#333×C103C2211yescharacteristic, complemented
59#333×C103C2211yescharacteristic, complemented
60#332×C103C2211yescharacteristic, complemented
61#331×C103C2211yescharacteristic
62D4⋊C8×C103C2211yescharacteristic
63D4⋊C8×C103C2211yescharacteristic
64D4⋊C8×C103C2211yescharacteristic, complemented
65D4⋊C8×C103C2211yescharacteristic, complemented
66#322×C103C2211yescharacteristic, complemented
67C2×#41×C103—21no—
68C22×D4×C103—21no—
69C22×D4×C103—21no—
70C2×SD16×C103—21no—
71C2×SD16×C103—41no—
72C2×D8×C103—21no—
73C2×D8×C103—21no—
74C2×D8×C103D411yescharacteristic
75C2×D8×C103D411yescharacteristic
76C2×M16×C103—21no—
77C22×C8×C103—21no—
78C22×C8×C103—21no—
79C22×C8×C103—21no—
80C4⋊Q8×C103C2311yescharacteristic
81C4⋊Q8×C103C2311yescharacteristic
82C4⋊Q8×C103C2311yescharacteristic
83#127×C103C2311yescharacteristic
84#124×C103—41no—
85#124×C103—41no—
86#123×C103—41no—
87C22⋊Q8×C103—21no—
88#121×C103—21no—
89#121×C103—21no—
90#121×C103—21no—
91#121×C103—21no—
92#121×C103—21no—
93#121×C103—21no—
94#121×C103—21no—
95#120×C103—41no—
96C4×D4×C103C2311yescharacteristic
97C4×D4×C103C2311yescharacteristic
98C4×D4×C103C2311yescharacteristic
99C4×D4×C103C2311yescharacteristic
100#117×C103—21no—
101#117×C103—21no—
102#117×C103—21no—
103#117×C103—21no—
104C2×C4⋊C4×C103—21no—
105#107×C103—21no—
106#107×C103—21no—
107#107×C103—21no—
108#107×C103D411yescharacteristic
109#107×C103D411yescharacteristic
110#106×C103—21no—
111#106×C103—21no—
112#106×C103—21no—
113#106×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—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—21no—
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—81no—
147C2×Q8×C103—21no—
148C2×Q8×C103—21no—
149C2×Q8×C103—21no—
150C2×D4×C103—21no—
151C2×D4×C103—21no—
152C2×D4×C103—21no—
153C2×D4×C103—41no—
154C2×D4×C103—41no—
155C2×D4×C103—42no—
156C2×D4×C103—42no—
157C2×D4×C103—41no—
158C2×D4×C103—41no—
159C2×D4×C103—41no—
160C2×D4×C103—81no—
161C2×D4×C103—81no—
162C2×D4×C103C2×D411yescharacteristic
163C2×D4×C103C2×D411yescharacteristic
164C2×D4×C103C2×D411yescharacteristic
165C2×D4×C103C2×D411yescharacteristic
166C22×C4×C103—21no—
167C22×C4×C103—21no—
168C22×C4×C103—21no—
169C22×C4×C103—21no—
170C22×C4×C103—41no—
171SD16×C103—81no—
172SD16×C103—82no—
173D8×C103—22no—
174D8×C103—41no—
175D8×C103—81no—
176D8×C103—81no—
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—42no—
184C2×C8×C103—81no—
185C2×C8×C103—81no—
186C2×C8×C103C2×D411yescharacteristic
187C2×C8×C103C2×D411yescharacteristic
188C2×C8×C103C2×D411yescharacteristic
189C2×C8×C103C2×D411yescharacteristic
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—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—21no—
204C22⋊C4×C103—21no—
205C22⋊C4×C103—41no—
206C22⋊C4×C103—41no—
207C22⋊C4×C103—41no—
208C22⋊C4×C103—41no—
209C22⋊C4×C103—41no—
210C22⋊C4×C103—41no—
211C42×C103—41no—
212C42×C103—41no—
213C42×C103C2411yescharacteristic
214C23×C103—21no—
215C23×C103—21no—
216C23×C103—21no—
217C23×C103—21no—
218C23×C103—41no—
219C23×C103—82no—
220C23×C103—82no—
221C23×C103—161no—
222Q8×C103—41no—
223Q8×C103—41no—
224Q8×C103—81no—
225Q8×C103—81no—
226D4×C103—21no—
227D4×C103—21no—
228D4×C103—21no—
229D4×C103—21no—
230D4×C103—21no—
231D4×C103—21no—
232D4×C103—21no—
233D4×C103—41no—
234D4×C103—41no—
235D4×C103—41no—
236D4×C103—41no—
237D4×C103—81no—
238D4×C103—82no—
239D4×C103—82no—
240D4×C103—82no—
241D4×C103—161no—
242D4×C103—161no—
243D4×C103#13512yes—
244C2×C4×C103—21no—
245C2×C4×C103—21no—
246C2×C4×C103—21no—
247C2×C4×C103—21no—
248C2×C4×C103—41no—
249C2×C4×C103—41no—
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—41no—
257C2×C4×C103—41no—
258C2×C4×C103—41no—
259C2×C4×C103—82no—
260C2×C4×C103C22×D411yescharacteristic
261C2×C4×C103C22×D411yescharacteristic
262C2×C4×C103H(5,𝔽2)11yescharacteristic
263C8×C103—21no—
264C8×C103—21no—
265C8×C103—21no—
266C8×C103—21no—
267C8×C103—41no—
268C8×C103—41no—
269C8×C103—41no—
270C8×C103—41no—
271C8×C103—41no—
272C22×C103—22no—
273C22×C103—41no—
274C22×C103—41no—
275C22×C103—41no—
276C22×C103—41no—
277C22×C103—41no—
278C22×C103—41no—
279C22×C103—41no—
280C22×C103—41no—
281C22×C103—41no—
282C22×C103—41no—
283C22×C103—41no—
284C22×C103—81no—
285C22×C103—81no—
286C22×C103—81no—
287C22×C103—164no—
288C22×C103D4211yescharacteristic
289C4×C103—21no—
290C4×C103—41no—
291C4×C103—41no—
292C4×C103—41no—
293C4×C103—41no—
294C4×C103—81no—
295C4×C103—81no—
296C4×C103—81no—
297C4×C103C2×#13511yescharacteristic
298C4×C103#57511yescharacteristic
299C4×C103#57611yescharacteristic
300C4×C103#57711yescharacteristic
301#19775C10311yesmaximal, characteristic, direct product factor, Sylow
302C2×C103—42no—
303C2×C103—81no—
304C2×C103—81no—
305C2×C103—81no—
306C2×C103—161no—
307C2×C103#326711yescharacteristic
308C2×C103#328011yescharacteristic
309C2×C103#328811yescharacteristic
310#3341C2×C10311yescharacteristic, complemented
311#3325C2×C10311yescharacteristic, complemented
312#3303C2×C10311yescharacteristic, complemented
313#3294C2×C10311yescharacteristic, complemented
314#1719C2×C10311yescharacteristic, complemented
315#1703C2×C10311yescharacteristic, complemented
316#1681C2×C10311yescharacteristic, complemented
317#1677C2×C10311yescharacteristic, complemented
318#1675C2×C10311yescharacteristic, complemented
319#1646C2×C10311yescharacteristic, complemented
320#1635C2×C10311yescharacteristic, complemented
321#1629C2×C10311yescharacteristic, complemented
322#1624C2×C10311yescharacteristic, complemented
323#1581C2×C10311yescharacteristic, complemented
324#1580C2×C10311yescharacteristic, complemented
325C103#1977511yescharacteristic, direct product factor, Sylow
326#555C22×C10311yescharacteristic
327#555C22×C10311yescharacteristic, complemented
328#547C22×C10311yescharacteristic
329D42C22×C10311yescharacteristic
330#500C22×C10311yescharacteristic, complemented
331#492C22×C10311yescharacteristic
332#487C22×C10311yescharacteristic, complemented
333#487C22×C10311yescharacteristic, complemented
334#486C22×C10311yescharacteristic
335#486C22×C10311yescharacteristic
336#485—21no—
337#482—21no—
338#482—21no—
339#482—21no—
340#480—21no—
341#476C22×C10311yescharacteristic
342#476C22×C10311yescharacteristic
343#476C22×C10311yescharacteristic
344#476C22×C10311yescharacteristic, complemented
345#474C22×C10311yescharacteristic
346#469—21no—
347#466—21no—
348#466—21no—
349#465—21no—
350#461C22×C10311yescharacteristic, complemented
351#459C22×C10311yescharacteristic
352#459C22×C10311yescharacteristic
353#449—21no—
354#447—21no—
355#447—21no—
356C4×D8C22×C10311yescharacteristic
357C4×D8C22×C10311yescharacteristic
358#436C22×C10311yescharacteristic
359C8×D4C22×C10311yescharacteristic
360C8×D4C22×C10311yescharacteristic, complemented
361C8×D4C22×C10311yescharacteristic, complemented
362#427—21no—
363#418—21no—
364#416—21no—
365C2×#102—21no—
366#335C22×C10311yescharacteristic, complemented
367#334C22×C10311yescharacteristic, complemented
368#333C22×C10311yescharacteristic, complemented
369#333C22×C10311yescharacteristic, complemented
370#332C22×C10311yescharacteristic, complemented
371#331C22×C10311yescharacteristic
372D4⋊C8C22×C10311yescharacteristic
373D4⋊C8C22×C10311yescharacteristic
374D4⋊C8C22×C10311yescharacteristic, complemented
375D4⋊C8C22×C10311yescharacteristic, complemented
376#322C22×C10311yescharacteristic, complemented
377C2×#41—21no—
378C22×D4—21no—
379C22×D4—21no—
380C2×SD16—21no—
381C2×SD16—41no—
382C2×D8—21no—
383C2×D8—21no—
384C2×D8D4×C10311yescharacteristic
385C2×D8D4×C10311yescharacteristic
386C2×M16—21no—
387C22×C8—21no—
388C22×C8—21no—
389C22×C8—21no—
390C4⋊Q8C23×C10311yescharacteristic
391C4⋊Q8C23×C10311yescharacteristic
392C4⋊Q8C23×C10311yescharacteristic
393#127C23×C10311yescharacteristic
394#124—41no—
395#124—41no—
396#123—41no—
397C22⋊Q8—21no—
398#121—21no—
399#121—21no—
400#121—21no—
401#121—21no—
402#121—21no—
403#121—21no—
404#121—21no—
405#120—41no—
406C4×D4C23×C10311yescharacteristic
407C4×D4C23×C10311yescharacteristic
408C4×D4C23×C10311yescharacteristic
409C4×D4C23×C10311yescharacteristic
410#117—21no—
411#117—21no—
412#117—21no—
413#117—21no—
414C2×C4⋊C4—21no—
415#107—21no—
416#107—21no—
417#107—21no—
418#107D4×C10311yescharacteristic
419#107D4×C10311yescharacteristic
420#106—21no—
421#106—21no—
422#106—21no—
423#106—21no—
424C4⋊C8C23×C10311yescharacteristic
425C4⋊C8C23×C10311yescharacteristic
426C4⋊C8C23×C10311yescharacteristic
427C4⋊C8C23×C10311yescharacteristic
428#103—21no—
429#103—21no—
430#103—21no—
431#103—41no—
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#102—21no—
441#102—21no—
442#102—21no—
443#102D4×C10311yescharacteristic
444#102D4×C10311yescharacteristic
445#102D4×C10311yescharacteristic
446#102D4×C10311yescharacteristic
447C22⋊C8—21no—
448C22⋊C8—21no—
449C22⋊C8—21no—
450C22⋊C8—21no—
451C4×C8C23×C10311yescharacteristic
452C4×C8C23×C10311yescharacteristic
453C4×C8C23×C10311yescharacteristic
454C24—41no—
455#41—42no—
456#41—81no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—42no—
466C2×D4—42no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—41no—
470C2×D4—81no—
471C2×D4—81no—
472C2×D4C2×D4×C10311yescharacteristic
473C2×D4C2×D4×C10311yescharacteristic
474C2×D4C2×D4×C10311yescharacteristic
475C2×D4C2×D4×C10311yescharacteristic
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—41no—
481SD16—81no—
482SD16—82no—
483D8—22no—
484D8—41no—
485D8—81no—
486D8—81no—
487M16—81no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—42no—
494C2×C8—81no—
495C2×C8—81no—
496C2×C8C2×D4×C10311yescharacteristic
497C2×C8C2×D4×C10311yescharacteristic
498C2×C8C2×D4×C10311yescharacteristic
499C2×C8C2×D4×C10311yescharacteristic
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—41no—
507C4⋊C4C2×D4×C10311yescharacteristic
508C4⋊C4C2×D4×C10311yescharacteristic
509C4⋊C4C2×D4×C10311yescharacteristic
510C4⋊C4C2×D4×C10311yescharacteristic
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C42—41no—
522C42—41no—
523C42C24×C10311yescharacteristic
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—41no—
529C23—82no—
530C23—82no—
531C23—161no—
532Q8—41no—
533Q8—41no—
534Q8—81no—
535Q8—81no—
536D4—21no—
537D4—21no—
538D4—21no—
539D4—21no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—81no—
548D4—82no—
549D4—82no—
550D4—82no—
551D4—161no—
552D4—161no—
553D4#135×C10312yes—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—82no—
570C2×C4C22×D4×C10311yescharacteristic
571C2×C4C22×D4×C10311yescharacteristic
572C2×C4H(5,𝔽2)×C10311yescharacteristic
573C8—21no—
574C8—21no—
575C8—21no—
576C8—21no—
577C8—41no—
578C8—41no—
579C8—41no—
580C8—41no—
581C8—41no—
582C22—22no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22—164no—
598C22D42×C10311yescharacteristic
599C4—21no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—81no—
605C4—81no—
606C4—81no—
607C4C2×#135×C10311yescharacteristic
608C4#575×C10311yescharacteristic
609C4#576×C10311yescharacteristic
610C4#577×C10311yescharacteristic
611C2—42no—
612C2—81no—
613C2—81no—
614C2—81no—
615C2—161no—
616C2C103×#326711yescharacteristic
617C2C103×#328011yescharacteristic
618C2C103×#328811yescharacteristic
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×#3341C2semidirect
2. C103×#3325C2semidirect
3. C103×#3303C2semidirect
4. C103×#3294C2semidirect
5. C103×#1719C2semidirect
6. C103×#1703C2semidirect
7. C103×#1681C2semidirect
8. C103×#1677C2semidirect
9. C103×#1675C2semidirect
10. C103×#1646C2semidirect
11. C103×#1635C2semidirect
12. C103×#1629C2semidirect
13. C103×#1624C2semidirect
14. C103×#1581C2semidirect
15. C103×#1580C2semidirect
17. #555×C103C22semidirect
20. #500×C103C22semidirect
22. #487×C103C22semidirect
23. #487×C103C22semidirect
34. #476×C103C22semidirect
40. #461×C103C22semidirect
50. C8×D4×C103C22semidirect
51. C8×D4×C103C22semidirect
56. #335×C103C22semidirect
57. #334×C103C22semidirect
58. #333×C103C22semidirect
59. #333×C103C22semidirect
60. #332×C103C22semidirect
64. D4⋊C8×C103C22semidirect
65. D4⋊C8×C103C22semidirect
66. #322×C103C22semidirect
301. #19775C103direct (N × H)
310. #3341C2×C103semidirect
311. #3325C2×C103semidirect
312. #3303C2×C103semidirect
313. #3294C2×C103semidirect
314. #1719C2×C103semidirect
315. #1703C2×C103semidirect
316. #1681C2×C103semidirect
317. #1677C2×C103semidirect
318. #1675C2×C103semidirect
319. #1646C2×C103semidirect
320. #1635C2×C103semidirect
321. #1629C2×C103semidirect
322. #1624C2×C103semidirect
323. #1581C2×C103semidirect
324. #1580C2×C103semidirect
325. C103#19775direct (N × H)
327. #555C22×C103semidirect
330. #500C22×C103semidirect
332. #487C22×C103semidirect
333. #487C22×C103semidirect
344. #476C22×C103semidirect
350. #461C22×C103semidirect
360. C8×D4C22×C103semidirect
361. C8×D4C22×C103semidirect
366. #335C22×C103semidirect
367. #334C22×C103semidirect
368. #333C22×C103semidirect
369. #333C22×C103semidirect
370. #332C22×C103semidirect
374. D4⋊C8C22×C103semidirect
375. D4⋊C8C22×C103semidirect
376. #322C22×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#33412
C103×#33252
C103×#33032
C103×#32942
C103×#17192
C103×#17032
C103×#16812
C103×#16772
C103×#16752
C103×#16462
C103×#16352
C103×#16292
C103×#16242
C103×#15812
C103×#15802
#19775103