Finite Group Databasebeta

← C103×#19460 #39924735

Subgroups — C103×#19460 #39924735

Order 26368.

642 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3210C211yesmaximal, characteristic, complemented
2C103×#3100C211yesmaximal, characteristic
3C103×#3077C211yesmaximal, characteristic, complemented
4C103×#2974C211yesmaximal, characteristic, complemented
5C103×#1703C211yesmaximal, characteristic, complemented
6C103×#1697C211yesmaximal, characteristic, complemented
7C103×#1689C211yesmaximal, characteristic, complemented
8C103×#1685C211yesmaximal, characteristic, complemented
9C103×#1683C211yesmaximal, characteristic, complemented
10C103×#1677C211yesmaximal, characteristic, complemented
11C103×#1669C211yesmaximal, characteristic, complemented
12C103×#1665C211yesmaximal, characteristic, complemented
13C103×#1574C211yesmaximal, characteristic, complemented
14C103×#1557C211yesmaximal, characteristic, complemented
15C103×#1554C211yesmaximal, characteristic, complemented
16#533×C103C2211yescharacteristic
17#532×C103C2211yescharacteristic
18C2×C4×D4×C103C2211yescharacteristic
19#494×C103C2211yescharacteristic, complemented
20#492×C103C2211yescharacteristic, complemented
21#487×C103C2211yescharacteristic, complemented
22#486×C103C2211yescharacteristic, complemented
23#480×C103—21no—
24#478×C103—21no—
25#478×C103—21no—
26#476×C103C2211yescharacteristic
27#476×C103C2211yescharacteristic
28#474×C103C2211yescharacteristic
29#474×C103C2211yescharacteristic
30#474×C103C2211yescharacteristic
31#474×C103C2211yescharacteristic
32#464×C103—21no—
33#464×C103—21no—
34#459×C103C2211yescharacteristic
35#459×C103C2211yescharacteristic
36#452×C103—21no—
37#452×C103—21no—
38#447×C103—21no—
39C4×D8×C103—21no—
40C4×D8×C103—21no—
41#436×C103C2211yescharacteristic
42#436×C103C2211yescharacteristic
43#435×C103—21no—
44#435×C103—21no—
45C8×D4×C103C2211yescharacteristic
46C8×D4×C103C2211yescharacteristic
47#432×C103C2211yescharacteristic
48#431×C103C2211yescharacteristic
49#431×C103C2211yescharacteristic
50#428×C103—21no—
51#423×C103C2211yescharacteristic
52#418×C103—21no—
53#407×C103—21no—
54C2×C22⋊C8×C103—21no—
55#335×C103C2211yescharacteristic, complemented
56#335×C103C2211yescharacteristic, complemented
57#334×C103C2211yescharacteristic, complemented
58#334×C103C2211yescharacteristic, complemented
59#333×C103C2211yescharacteristic, complemented
60#333×C103C2211yescharacteristic, complemented
61#332×C103C2211yescharacteristic, complemented
62#332×C103C2211yescharacteristic, complemented
63#332×C103C2211yescharacteristic, complemented
64#332×C103C2211yescharacteristic, complemented
65#331×C103C2211yescharacteristic, complemented
66#331×C103C2211yescharacteristic, complemented
67C2×#41×C103—21no—
68C22×D4×C103D411yescharacteristic
69C23×C4×C103—21no—
70C2×Q16×C103—21no—
71C2×Q16×C103—21no—
72C2×SD16×C103—21no—
73C2×SD16×C103—21no—
74C2×D8×C103—21no—
75C2×D8×C103—21no—
76C2×M16×C103—21no—
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#125×C103—21no—
86#124×C103—21no—
87C22⋊Q8×C103—21no—
88C22⋊Q8×C103—21no—
89#121×C103—21no—
90#121×C103—21no—
91C4×Q8×C103—21no—
92C4×Q8×C103—21no—
93C4×D4×C103—21no—
94C4×D4×C103—21no—
95C4×D4×C103—21no—
96C4×D4×C103—21no—
97C4×D4×C103D411yescharacteristic
98C4×D4×C103D411yescharacteristic
99C4×D4×C103C2311yescharacteristic
100C4×D4×C103C2311yescharacteristic
101#117×C103—21no—
102C2×C4⋊C4×C103D411yescharacteristic
103C2×C22⋊C4×C103—21no—
104C2×C42×C103C2311yescharacteristic
105#107×C103—21no—
106#107×C103—21no—
107#107×C103—21no—
108#107×C103—21no—
109#106×C103—21no—
110#106×C103—21no—
111C4⋊C8×C103—21no—
112C4⋊C8×C103D411yescharacteristic
113C4⋊C8×C103D411yescharacteristic
114C4⋊C8×C103C2311yescharacteristic
115C4⋊C8×C103C2311yescharacteristic
116C4⋊C8×C103C2311yescharacteristic
117C4⋊C8×C103C2311yescharacteristic
118C4⋊C8×C103C2311yescharacteristic
119C4⋊C8×C103C2311yescharacteristic
120#103×C103—21no—
121#103×C103—21no—
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—
132C22⋊C8×C103—21no—
133C22⋊C8×C103—21no—
134C22⋊C8×C103—21no—
135C22⋊C8×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
144C24×C103—21no—
145#41×C103—81no—
146#41×C103—81no—
147C2×Q8×C103—21no—
148C2×Q8×C103—21no—
149C2×Q8×C103—21no—
150C2×D4×C103—22no—
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×C103C2×D411yescharacteristic
158C2×D4×C103C2×D411yescharacteristic
159C22×C4×C103—21no—
160C22×C4×C103—21no—
161C22×C4×C103—21no—
162C22×C4×C103—21no—
163C22×C4×C103—21no—
164C22×C4×C103—41no—
165C22×C4×C103—81no—
166C22×C4×C103—81no—
167C22×C4×C103C2×D411yescharacteristic
168C22×C4×C103C2×D411yescharacteristic
169C22×C4×C103#4111yescharacteristic
170Q16×C103—81no—
171Q16×C103—81no—
172SD16×C103—81no—
173SD16×C103—81no—
174D8×C103—42no—
175D8×C103—42no—
176M16×C103—42no—
177M16×C103—81no—
178M16×C103—81no—
179C2×C8×C103—21no—
180C2×C8×C103—21no—
181C2×C8×C103—21no—
182C2×C8×C103—21no—
183C2×C8×C103—21no—
184C2×C8×C103—21no—
185C2×C8×C103—81no—
186C2×C8×C103—81no—
187C2×C8×C103C2×D411yescharacteristic
188C2×C8×C103C2×D411yescharacteristic
189C2×C8×C103C2×D411yescharacteristic
190C2×C8×C103C2×D411yescharacteristic
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—21no—
198C4⋊C4×C103—41no—
199C4⋊C4×C103—41no—
200C4⋊C4×C103C2×D411yescharacteristic
201C4⋊C4×C103C2×D411yescharacteristic
202C22⋊C4×C103—21no—
203C22⋊C4×C103—21no—
204C22⋊C4×C103—21no—
205C22⋊C4×C103—21no—
206C22⋊C4×C103—41no—
207C22⋊C4×C103—41no—
208C22⋊C4×C103—41no—
209C42×C103—41no—
210C42×C103C2×D411yescharacteristic
211C42×C103C2×D411yescharacteristic
212C42×C103#4111yescharacteristic
213C42×C103C2411yescharacteristic
214C23×C103—21no—
215C23×C103—21no—
216C23×C103—42no—
217C23×C103—42no—
218C23×C103—41no—
219C23×C103—81no—
220C23×C103#12111yescharacteristic
221Q8×C103—41no—
222Q8×C103—41no—
223Q8×C103—41no—
224Q8×C103—41no—
225Q8×C103—81no—
226D4×C103—21no—
227D4×C103—21no—
228D4×C103—21no—
229D4×C103—42no—
230D4×C103—41no—
231D4×C103—41no—
232D4×C103—41no—
233D4×C103—41no—
234D4×C103—81no—
235D4×C103—82no—
236D4×C103#13712yes—
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—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—81no—
252C2×C4×C103—81no—
253C2×C4×C103—82no—
254C2×C4×C103—81no—
255C2×C4×C103#12111yescharacteristic
256C2×C4×C103#12111yescharacteristic
257C2×C4×C103#12111yescharacteristic
258C2×C4×C103C22×D411yescharacteristic
259C2×C4×C103C22×D411yescharacteristic
260C2×C4×C103C2×#4111yescharacteristic
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—
270C8×C103—41no—
271C22×C103—21no—
272C22×C103—21no—
273C22×C103—22no—
274C22×C103—21no—
275C22×C103—41no—
276C22×C103—41no—
277C22×C103—41no—
278C22×C103—41no—
279C22×C103—41no—
280C22×C103—84no—
281C22×C103—81no—
282C22×C103—81no—
283C22×C103—81no—
284C22×C103C2×#12111yescharacteristic
285C4×C103—21no—
286C4×C103—21no—
287C4×C103—21no—
288C4×C103—21no—
289C4×C103—41no—
290C4×C103—41no—
291C4×C103—81no—
292C4×C103—81no—
293C4×C103—81no—
294C4×C103C2×#13711yescharacteristic
295C4×C103#57511yescharacteristic
296C4×C103#57611yescharacteristic
297C4×C103#57611yescharacteristic
298#19460C10311yesmaximal, characteristic, direct product factor, Sylow
299C2×C103—41no—
300C2×C103—42no—
301C2×C103—81no—
302C2×C103—161no—
303C2×C103#304111yescharacteristic
304C2×C103#305611yescharacteristic
305C2×C103#306711yescharacteristic
306#3210C2×C10311yescharacteristic, complemented
307#3100C2×C10311yescharacteristic
308#3077C2×C10311yescharacteristic, complemented
309#2974C2×C10311yescharacteristic, complemented
310#1703C2×C10311yescharacteristic, complemented
311#1697C2×C10311yescharacteristic, complemented
312#1689C2×C10311yescharacteristic, complemented
313#1685C2×C10311yescharacteristic, complemented
314#1683C2×C10311yescharacteristic, complemented
315#1677C2×C10311yescharacteristic, complemented
316#1669C2×C10311yescharacteristic, complemented
317#1665C2×C10311yescharacteristic, complemented
318#1574C2×C10311yescharacteristic, complemented
319#1557C2×C10311yescharacteristic, complemented
320#1554C2×C10311yescharacteristic, complemented
321C103#1946011yescharacteristic, direct product factor, Sylow
322#533C22×C10311yescharacteristic
323#532C22×C10311yescharacteristic
324C2×C4×D4C22×C10311yescharacteristic
325#494C22×C10311yescharacteristic, complemented
326#492C22×C10311yescharacteristic, complemented
327#487C22×C10311yescharacteristic, complemented
328#486C22×C10311yescharacteristic, complemented
329#480—21no—
330#478—21no—
331#478—21no—
332#476C22×C10311yescharacteristic
333#476C22×C10311yescharacteristic
334#474C22×C10311yescharacteristic
335#474C22×C10311yescharacteristic
336#474C22×C10311yescharacteristic
337#474C22×C10311yescharacteristic
338#464—21no—
339#464—21no—
340#459C22×C10311yescharacteristic
341#459C22×C10311yescharacteristic
342#452—21no—
343#452—21no—
344#447—21no—
345C4×D8—21no—
346C4×D8—21no—
347#436C22×C10311yescharacteristic
348#436C22×C10311yescharacteristic
349#435—21no—
350#435—21no—
351C8×D4C22×C10311yescharacteristic
352C8×D4C22×C10311yescharacteristic
353#432C22×C10311yescharacteristic
354#431C22×C10311yescharacteristic
355#431C22×C10311yescharacteristic
356#428—21no—
357#423C22×C10311yescharacteristic
358#418—21no—
359#407—21no—
360C2×C22⋊C8—21no—
361#335C22×C10311yescharacteristic, complemented
362#335C22×C10311yescharacteristic, complemented
363#334C22×C10311yescharacteristic, complemented
364#334C22×C10311yescharacteristic, complemented
365#333C22×C10311yescharacteristic, complemented
366#333C22×C10311yescharacteristic, complemented
367#332C22×C10311yescharacteristic, complemented
368#332C22×C10311yescharacteristic, complemented
369#332C22×C10311yescharacteristic, complemented
370#332C22×C10311yescharacteristic, complemented
371#331C22×C10311yescharacteristic, complemented
372#331C22×C10311yescharacteristic, complemented
373C2×#41—21no—
374C22×D4D4×C10311yescharacteristic
375C23×C4—21no—
376C2×Q16—21no—
377C2×Q16—21no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×D8—21no—
381C2×D8—21no—
382C2×M16—21no—
383C2×M16—21no—
384C2×M16—21no—
385C22×C8—21no—
386C22×C8—21no—
387C4⋊Q8C23×C10311yescharacteristic
388C4⋊Q8C23×C10311yescharacteristic
389C4⋊Q8C23×C10311yescharacteristic
390#127C23×C10311yescharacteristic
391#125—21no—
392#124—21no—
393C22⋊Q8—21no—
394C22⋊Q8—21no—
395#121—21no—
396#121—21no—
397C4×Q8—21no—
398C4×Q8—21no—
399C4×D4—21no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4—21no—
403C4×D4D4×C10311yescharacteristic
404C4×D4D4×C10311yescharacteristic
405C4×D4C23×C10311yescharacteristic
406C4×D4C23×C10311yescharacteristic
407#117—21no—
408C2×C4⋊C4D4×C10311yescharacteristic
409C2×C22⋊C4—21no—
410C2×C42C23×C10311yescharacteristic
411#107—21no—
412#107—21no—
413#107—21no—
414#107—21no—
415#106—21no—
416#106—21no—
417C4⋊C8—21no—
418C4⋊C8D4×C10311yescharacteristic
419C4⋊C8D4×C10311yescharacteristic
420C4⋊C8C23×C10311yescharacteristic
421C4⋊C8C23×C10311yescharacteristic
422C4⋊C8C23×C10311yescharacteristic
423C4⋊C8C23×C10311yescharacteristic
424C4⋊C8C23×C10311yescharacteristic
425C4⋊C8C23×C10311yescharacteristic
426#103—21no—
427#103—21no—
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—
438C22⋊C8—21no—
439C22⋊C8—21no—
440C22⋊C8—21no—
441C22⋊C8—21no—
442C22⋊C8—21no—
443C22⋊C8—21no—
444C22⋊C8D4×C10311yescharacteristic
445C22⋊C8D4×C10311yescharacteristic
446#97—21no—
447C4×C8—21no—
448C4×C8C23×C10311yescharacteristic
449C4×C8C23×C10311yescharacteristic
450C24—21no—
451#41—81no—
452#41—81no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×D4—22no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4C2×D4×C10311yescharacteristic
464C2×D4C2×D4×C10311yescharacteristic
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—41no—
471C22×C4—81no—
472C22×C4—81no—
473C22×C4C2×D4×C10311yescharacteristic
474C22×C4C2×D4×C10311yescharacteristic
475C22×C4#41×C10311yescharacteristic
476Q16—81no—
477Q16—81no—
478SD16—81no—
479SD16—81no—
480D8—42no—
481D8—42no—
482M16—42no—
483M16—81no—
484M16—81no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—81no—
492C2×C8—81no—
493C2×C8C2×D4×C10311yescharacteristic
494C2×C8C2×D4×C10311yescharacteristic
495C2×C8C2×D4×C10311yescharacteristic
496C2×C8C2×D4×C10311yescharacteristic
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4C2×D4×C10311yescharacteristic
507C4⋊C4C2×D4×C10311yescharacteristic
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C42—41no—
516C42C2×D4×C10311yescharacteristic
517C42C2×D4×C10311yescharacteristic
518C42#41×C10311yescharacteristic
519C42C24×C10311yescharacteristic
520C23—21no—
521C23—21no—
522C23—42no—
523C23—42no—
524C23—41no—
525C23—81no—
526C23#121×C10311yescharacteristic
527Q8—41no—
528Q8—41no—
529Q8—41no—
530Q8—41no—
531Q8—81no—
532D4—21no—
533D4—21no—
534D4—21no—
535D4—42no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—81no—
541D4—82no—
542D4#137×C10312yes—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—81no—
558C2×C4—81no—
559C2×C4—82no—
560C2×C4—81no—
561C2×C4#121×C10311yescharacteristic
562C2×C4#121×C10311yescharacteristic
563C2×C4#121×C10311yescharacteristic
564C2×C4C22×D4×C10311yescharacteristic
565C2×C4C22×D4×C10311yescharacteristic
566C2×C4C2×#41×C10311yescharacteristic
567C8—21no—
568C8—21no—
569C8—21no—
570C8—21no—
571C8—41no—
572C8—41no—
573C8—41no—
574C8—41no—
575C8—41no—
576C8—41no—
577C22—21no—
578C22—21no—
579C22—22no—
580C22—21no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—84no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22C2×#121×C10311yescharacteristic
591C4—21no—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—41no—
596C4—41no—
597C4—81no—
598C4—81no—
599C4—81no—
600C4C2×#137×C10311yescharacteristic
601C4#575×C10311yescharacteristic
602C4#576×C10311yescharacteristic
603C4#576×C10311yescharacteristic
604C2—41no—
605C2—42no—
606C2—81no—
607C2—161no—
608C2C103×#304111yescharacteristic
609C2C103×#305611yescharacteristic
610C2C103×#306711yescharacteristic
subgroupG/H
center, socleC22×C103C2×#121
commutator, Frattini, cosocleC42C24×C103
prime radicalC103×#3100C2
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×#3210C2semidirect
3. C103×#3077C2semidirect
4. C103×#2974C2semidirect
5. C103×#1703C2semidirect
6. C103×#1697C2semidirect
7. C103×#1689C2semidirect
8. C103×#1685C2semidirect
9. C103×#1683C2semidirect
10. C103×#1677C2semidirect
11. C103×#1669C2semidirect
12. C103×#1665C2semidirect
13. C103×#1574C2semidirect
14. C103×#1557C2semidirect
15. C103×#1554C2semidirect
19. #494×C103C22semidirect
20. #492×C103C22semidirect
21. #487×C103C22semidirect
22. #486×C103C22semidirect
55. #335×C103C22semidirect
56. #335×C103C22semidirect
57. #334×C103C22semidirect
58. #334×C103C22semidirect
59. #333×C103C22semidirect
60. #333×C103C22semidirect
61. #332×C103C22semidirect
62. #332×C103C22semidirect
63. #332×C103C22semidirect
64. #332×C103C22semidirect
65. #331×C103C22semidirect
66. #331×C103C22semidirect
298. #19460C103direct (N × H)
306. #3210C2×C103semidirect
308. #3077C2×C103semidirect
309. #2974C2×C103semidirect
310. #1703C2×C103semidirect
311. #1697C2×C103semidirect
312. #1689C2×C103semidirect
313. #1685C2×C103semidirect
314. #1683C2×C103semidirect
315. #1677C2×C103semidirect
316. #1669C2×C103semidirect
317. #1665C2×C103semidirect
318. #1574C2×C103semidirect
319. #1557C2×C103semidirect
320. #1554C2×C103semidirect
321. C103#19460direct (N × H)
325. #494C22×C103semidirect
326. #492C22×C103semidirect
327. #487C22×C103semidirect
328. #486C22×C103semidirect
361. #335C22×C103semidirect
362. #335C22×C103semidirect
363. #334C22×C103semidirect
364. #334C22×C103semidirect
365. #333C22×C103semidirect
366. #333C22×C103semidirect
367. #332C22×C103semidirect
368. #332C22×C103semidirect
369. #332C22×C103semidirect
370. #332C22×C103semidirect
371. #331C22×C103semidirect
372. #331C22×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#32102
C103×#31002
C103×#30772
C103×#29742
C103×#17032
C103×#16972
C103×#16892
C103×#16852
C103×#16832
C103×#16772
C103×#16692
C103×#16652
C103×#15742
C103×#15572
C103×#15542
#19460103