Finite Group Databasebeta

← C103×#19934 #39925209

Subgroups — C103×#19934 #39925209

Order 26368.

610 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3367C211yesmaximal, characteristic, complemented
2C103×#3366C211yesmaximal, characteristic
3C103×#3304C211yesmaximal, characteristic, complemented
4C103×#3299C211yesmaximal, characteristic, complemented
5C103×#1711C211yesmaximal, characteristic, complemented
6C103×#1700C211yesmaximal, characteristic, complemented
7C103×#1698C211yesmaximal, characteristic, complemented
8C103×#1683C211yesmaximal, characteristic, complemented
9C103×#1681C211yesmaximal, characteristic, complemented
10C103×#1643C211yesmaximal, characteristic, complemented
11C103×#1641C211yesmaximal, characteristic, complemented
12C103×#1638C211yesmaximal, characteristic, complemented
13C103×#1627C211yesmaximal, characteristic, complemented
14C103×#1591C211yesmaximal, characteristic, complemented
15C8×D8×C103C211yesmaximal, characteristic, complemented
16#556×C103C2211yescharacteristic
17#554×C103C2211yescharacteristic
18#550×C103C2211yescharacteristic
19D4×Q8×C103C2211yescharacteristic
20#490×C103—21no—
21#489×C103—21no—
22#487×C103C2211yescharacteristic
23#487×C103C2211yescharacteristic
24#487×C103C2211yescharacteristic
25#486×C103C2211yescharacteristic
26#486×C103C2211yescharacteristic
27#486×C103C2211yescharacteristic
28#484×C103—21no—
29#482×C103—21no—
30#478×C103—21no—
31#477×C103—21no—
32#477×C103C2211yescharacteristic
33#476×C103C2211yescharacteristic
34#475×C103C2211yescharacteristic
35#474×C103C2211yescharacteristic
36#467×C103—21no—
37#465×C103—21no—
38#463×C103—21no—
39#462×C103C2211yescharacteristic
40#461×C103C2211yescharacteristic
41#460×C103C2211yescharacteristic
42#459×C103—21no—
43#459×C103C2211yescharacteristic
44#452×C103—21no—
45#451×C103—21no—
46#446×C103C2211yescharacteristic
47#446×C103C2211yescharacteristic
48#442×C103—21no—
49#440×C103—21no—
50C4×Q16×C103C2211yescharacteristic
51C4×D8×C103C2211yescharacteristic
52C8×D4×C103C2211yescharacteristic
53C8×D4×C103C2211yescharacteristic
54#416×C103—21no—
55C2×#103×C103—21no—
56#335×C103C2211yescharacteristic
57#335×C103C2211yescharacteristic
58#333×C103C2211yescharacteristic
59#332×C103C2211yescharacteristic
60#332×C103C2211yescharacteristic
61#331×C103C2211yescharacteristic
62Q8⋊C8×C103C2211yescharacteristic
63Q8⋊C8×C103C2211yescharacteristic
64D4⋊C8×C103C2211yescharacteristic
65D4⋊C8×C103C2211yescharacteristic
66C82×C103C2211yescharacteristic
67C2×#41×C103—21no—
68C22×Q8×C103—21no—
69C2×Q16×C103—21no—
70C2×Q16×C103D411yescharacteristic
71C2×SD16×C103—21no—
72C2×SD16×C103—21no—
73C2×D8×C103—21no—
74C2×D8×C103D411yescharacteristic
75C22×C8×C103—21no—
76C22×C8×C103—21no—
77C4⋊Q8×C103—21no—
78C4⋊Q8×C103C2311yescharacteristic
79C4⋊Q8×C103C2311yescharacteristic
80C4⋊Q8×C103C2311yescharacteristic
81#127×C103—21no—
82#127×C103C2311yescharacteristic
83#126×C103—41no—
84#125×C103—21no—
85#124×C103—21no—
86C22⋊Q8×C103—21no—
87C22⋊Q8×C103—21no—
88C22⋊Q8×C103—21no—
89C22⋊Q8×C103—41no—
90C22⋊Q8×C103—41no—
91#121×C103—21no—
92#121×C103—41no—
93C4×Q8×C103—21no—
94C4×Q8×C103C2311yescharacteristic
95C4×Q8×C103C2311yescharacteristic
96C4×D4×C103—21no—
97C4×D4×C103—21no—
98C4×D4×C103—21no—
99C4×D4×C103C2311yescharacteristic
100C4×D4×C103C2311yescharacteristic
101#117×C103—21no—
102C2×C4⋊C4×C103—21no—
103#107×C103—21no—
104#107×C103—21no—
105#107×C103D411yescharacteristic
106#107×C103D411yescharacteristic
107#106×C103—21no—
108#106×C103—21no—
109C4⋊C8×C103—21no—
110C4⋊C8×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—21no—
122#103×C103—21no—
123#103×C103—41no—
124#103×C103D411yescharacteristic
125#103×C103D411yescharacteristic
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—41no—
135#102×C103D411yescharacteristic
136#102×C103D411yescharacteristic
137C22⋊C8×C103—21no—
138C22⋊C8×C103—21no—
139#97×C103—21no—
140#97×C103—21no—
141C4×C8×C103C2311yescharacteristic
142C4×C8×C103C2311yescharacteristic
143C4×C8×C103C2311yescharacteristic
144#41×C103—42no—
145#41×C103—81no—
146C2×Q8×C103—21no—
147C2×Q8×C103—21no—
148C2×Q8×C103—21no—
149C2×Q8×C103—41no—
150C2×Q8×C103—42no—
151C2×Q8×C103—81no—
152C2×Q8×C103C2×D411yescharacteristic
153C2×Q8×C103C2×D411yescharacteristic
154C2×D4×C103—21no—
155C2×D4×C103—21no—
156C2×D4×C103—21no—
157C2×D4×C103—41no—
158C2×D4×C103—41no—
159C2×D4×C103C2×D411yescharacteristic
160C2×D4×C103C2×D411yescharacteristic
161C22×C4×C103—21no—
162C22×C4×C103—21no—
163C22×C4×C103—41no—
164C22×C4×C103—41no—
165C22×C4×C103—41no—
166Q16×C103—41no—
167Q16×C103—81no—
168SD16×C103—42no—
169SD16×C103—81no—
170D8×C103—22no—
171D8×C103—42no—
172C2×C8×C103—21no—
173C2×C8×C103—21no—
174C2×C8×C103—21no—
175C2×C8×C103—21no—
176C2×C8×C103—21no—
177C2×C8×C103—81no—
178C2×C8×C103—81no—
179C2×C8×C103C2×D411yescharacteristic
180C2×C8×C103C2×D411yescharacteristic
181C2×C8×C103C2×D411yescharacteristic
182C2×C8×C103C2×D411yescharacteristic
183C4⋊C4×C103—21no—
184C4⋊C4×C103—21no—
185C4⋊C4×C103—21no—
186C4⋊C4×C103—21no—
187C4⋊C4×C103—21no—
188C4⋊C4×C103—21no—
189C4⋊C4×C103—21no—
190C4⋊C4×C103—21no—
191C4⋊C4×C103—41no—
192C4⋊C4×C103—41no—
193C4⋊C4×C103—41no—
194C4⋊C4×C103—41no—
195C4⋊C4×C103C2×D411yescharacteristic
196C4⋊C4×C103C2×D411yescharacteristic
197C4⋊C4×C103C2×D411yescharacteristic
198C4⋊C4×C103C2×D411yescharacteristic
199C22⋊C4×C103—21no—
200C22⋊C4×C103—21no—
201C22⋊C4×C103—41no—
202C22⋊C4×C103—41no—
203C22⋊C4×C103—41no—
204C22⋊C4×C103—41no—
205C22⋊C4×C103—41no—
206C42×C103—21no—
207C42×C103—21no—
208C42×C103—41no—
209C42×C103C2411yescharacteristic
210C23×C103—21no—
211C23×C103—21no—
212C23×C103—41no—
213Q8×C103—21no—
214Q8×C103—21no—
215Q8×C103—21no—
216Q8×C103—21no—
217Q8×C103—41no—
218Q8×C103—41no—
219Q8×C103—41no—
220Q8×C103—41no—
221Q8×C103—81no—
222Q8×C103—82no—
223D4×C103—21no—
224D4×C103—21no—
225D4×C103—21no—
226D4×C103—41no—
227D4×C103—41no—
228D4×C103—41no—
229D4×C103—41no—
230D4×C103—81no—
231D4×C103—82no—
232D4×C103—161no—
233D4×C103#13512yes—
234C2×C4×C103—21no—
235C2×C4×C103—21no—
236C2×C4×C103—21no—
237C2×C4×C103—21no—
238C2×C4×C103—21no—
239C2×C4×C103—21no—
240C2×C4×C103—41no—
241C2×C4×C103—41no—
242C2×C4×C103—41no—
243C2×C4×C103—41no—
244C2×C4×C103—41no—
245C2×C4×C103—41no—
246C2×C4×C103—41no—
247C2×C4×C103—82no—
248C2×C4×C103—82no—
249C2×C4×C103—161no—
250C2×C4×C103C22×D411yescharacteristic
251C2×C4×C103C22×D411yescharacteristic
252C2×C4×C103H(5,𝔽2)11yescharacteristic
253C8×C103—21no—
254C8×C103—21no—
255C8×C103—21no—
256C8×C103—21no—
257C8×C103—41no—
258C8×C103—41no—
259C8×C103—41no—
260C8×C103—41no—
261C8×C103—41no—
262C22×C103—22no—
263C22×C103—41no—
264C22×C103—41no—
265C22×C103—41no—
266C22×C103—41no—
267C22×C103—41no—
268C22×C103—81no—
269C22×C103—81no—
270C22×C103—81no—
271C22×C103D4211yescharacteristic
272C4×C103—21no—
273C4×C103—41no—
274C4×C103—41no—
275C4×C103—41no—
276C4×C103—41no—
277C4×C103—41no—
278C4×C103—41no—
279C4×C103—81no—
280C4×C103—81no—
281C4×C103—81no—
282C4×C103C2×#13511yescharacteristic
283C4×C103#57511yescharacteristic
284C4×C103#57611yescharacteristic
285C4×C103#57811yescharacteristic
286#19934C10311yesmaximal, characteristic, direct product factor, Sylow
287C2×C103—42no—
288C2×C103—81no—
289C2×C103—161no—
290C2×C103#327311yescharacteristic
291C2×C103#328511yescharacteristic
292C2×C103#329011yescharacteristic
293#3367C2×C10311yescharacteristic, complemented
294#3366C2×C10311yescharacteristic
295#3304C2×C10311yescharacteristic, complemented
296#3299C2×C10311yescharacteristic, complemented
297#1711C2×C10311yescharacteristic, complemented
298#1700C2×C10311yescharacteristic, complemented
299#1698C2×C10311yescharacteristic, complemented
300#1683C2×C10311yescharacteristic, complemented
301#1681C2×C10311yescharacteristic, complemented
302#1643C2×C10311yescharacteristic, complemented
303#1641C2×C10311yescharacteristic, complemented
304#1638C2×C10311yescharacteristic, complemented
305#1627C2×C10311yescharacteristic, complemented
306#1591C2×C10311yescharacteristic, complemented
307C8×D8C2×C10311yescharacteristic, complemented
308C103#1993411yescharacteristic, direct product factor, Sylow
309#556C22×C10311yescharacteristic
310#554C22×C10311yescharacteristic
311#550C22×C10311yescharacteristic
312D4×Q8C22×C10311yescharacteristic
313#490—21no—
314#489—21no—
315#487C22×C10311yescharacteristic
316#487C22×C10311yescharacteristic
317#487C22×C10311yescharacteristic
318#486C22×C10311yescharacteristic
319#486C22×C10311yescharacteristic
320#486C22×C10311yescharacteristic
321#484—21no—
322#482—21no—
323#478—21no—
324#477—21no—
325#477C22×C10311yescharacteristic
326#476C22×C10311yescharacteristic
327#475C22×C10311yescharacteristic
328#474C22×C10311yescharacteristic
329#467—21no—
330#465—21no—
331#463—21no—
332#462C22×C10311yescharacteristic
333#461C22×C10311yescharacteristic
334#460C22×C10311yescharacteristic
335#459—21no—
336#459C22×C10311yescharacteristic
337#452—21no—
338#451—21no—
339#446C22×C10311yescharacteristic
340#446C22×C10311yescharacteristic
341#442—21no—
342#440—21no—
343C4×Q16C22×C10311yescharacteristic
344C4×D8C22×C10311yescharacteristic
345C8×D4C22×C10311yescharacteristic
346C8×D4C22×C10311yescharacteristic
347#416—21no—
348C2×#103—21no—
349#335C22×C10311yescharacteristic
350#335C22×C10311yescharacteristic
351#333C22×C10311yescharacteristic
352#332C22×C10311yescharacteristic
353#332C22×C10311yescharacteristic
354#331C22×C10311yescharacteristic
355Q8⋊C8C22×C10311yescharacteristic
356Q8⋊C8C22×C10311yescharacteristic
357D4⋊C8C22×C10311yescharacteristic
358D4⋊C8C22×C10311yescharacteristic
359C82C22×C10311yescharacteristic
360C2×#41—21no—
361C22×Q8—21no—
362C2×Q16—21no—
363C2×Q16D4×C10311yescharacteristic
364C2×SD16—21no—
365C2×SD16—21no—
366C2×D8—21no—
367C2×D8D4×C10311yescharacteristic
368C22×C8—21no—
369C22×C8—21no—
370C4⋊Q8—21no—
371C4⋊Q8C23×C10311yescharacteristic
372C4⋊Q8C23×C10311yescharacteristic
373C4⋊Q8C23×C10311yescharacteristic
374#127—21no—
375#127C23×C10311yescharacteristic
376#126—41no—
377#125—21no—
378#124—21no—
379C22⋊Q8—21no—
380C22⋊Q8—21no—
381C22⋊Q8—21no—
382C22⋊Q8—41no—
383C22⋊Q8—41no—
384#121—21no—
385#121—41no—
386C4×Q8—21no—
387C4×Q8C23×C10311yescharacteristic
388C4×Q8C23×C10311yescharacteristic
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4C23×C10311yescharacteristic
393C4×D4C23×C10311yescharacteristic
394#117—21no—
395C2×C4⋊C4—21no—
396#107—21no—
397#107—21no—
398#107D4×C10311yescharacteristic
399#107D4×C10311yescharacteristic
400#106—21no—
401#106—21no—
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8C23×C10311yescharacteristic
405C4⋊C8C23×C10311yescharacteristic
406C4⋊C8C23×C10311yescharacteristic
407C4⋊C8C23×C10311yescharacteristic
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—41no—
417#103D4×C10311yescharacteristic
418#103D4×C10311yescharacteristic
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—41no—
428#102D4×C10311yescharacteristic
429#102D4×C10311yescharacteristic
430C22⋊C8—21no—
431C22⋊C8—21no—
432#97—21no—
433#97—21no—
434C4×C8C23×C10311yescharacteristic
435C4×C8C23×C10311yescharacteristic
436C4×C8C23×C10311yescharacteristic
437#41—42no—
438#41—81no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—41no—
443C2×Q8—42no—
444C2×Q8—81no—
445C2×Q8C2×D4×C10311yescharacteristic
446C2×Q8C2×D4×C10311yescharacteristic
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4C2×D4×C10311yescharacteristic
453C2×D4C2×D4×C10311yescharacteristic
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459Q16—41no—
460Q16—81no—
461SD16—42no—
462SD16—81no—
463D8—22no—
464D8—42no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—81no—
471C2×C8—81no—
472C2×C8C2×D4×C10311yescharacteristic
473C2×C8C2×D4×C10311yescharacteristic
474C2×C8C2×D4×C10311yescharacteristic
475C2×C8C2×D4×C10311yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4C2×D4×C10311yescharacteristic
489C4⋊C4C2×D4×C10311yescharacteristic
490C4⋊C4C2×D4×C10311yescharacteristic
491C4⋊C4C2×D4×C10311yescharacteristic
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C42—21no—
500C42—21no—
501C42—41no—
502C42C24×C10311yescharacteristic
503C23—21no—
504C23—21no—
505C23—41no—
506Q8—21no—
507Q8—21no—
508Q8—21no—
509Q8—21no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—81no—
515Q8—82no—
516D4—21no—
517D4—21no—
518D4—21no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—81no—
524D4—82no—
525D4—161no—
526D4#135×C10312yes—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—82no—
541C2×C4—82no—
542C2×C4—161no—
543C2×C4C22×D4×C10311yescharacteristic
544C2×C4C22×D4×C10311yescharacteristic
545C2×C4H(5,𝔽2)×C10311yescharacteristic
546C8—21no—
547C8—21no—
548C8—21no—
549C8—21no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8—41no—
555C22—22no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22D42×C10311yescharacteristic
565C4—21no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4C2×#135×C10311yescharacteristic
576C4#575×C10311yescharacteristic
577C4#576×C10311yescharacteristic
578C4#578×C10311yescharacteristic
579C2—42no—
580C2—81no—
581C2—161no—
582C2C103×#327311yescharacteristic
583C2C103×#328511yescharacteristic
584C2C103×#329011yescharacteristic
subgroupG/H
center, socleC22×C103D42
commutator, Frattini, cosocleC42C24×C103
prime radicalC103×#3366C2
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×#3367C2semidirect
3. C103×#3304C2semidirect
4. C103×#3299C2semidirect
5. C103×#1711C2semidirect
6. C103×#1700C2semidirect
7. C103×#1698C2semidirect
8. C103×#1683C2semidirect
9. C103×#1681C2semidirect
10. C103×#1643C2semidirect
11. C103×#1641C2semidirect
12. C103×#1638C2semidirect
13. C103×#1627C2semidirect
14. C103×#1591C2semidirect
15. C8×D8×C103C2semidirect
286. #19934C103direct (N × H)
293. #3367C2×C103semidirect
295. #3304C2×C103semidirect
296. #3299C2×C103semidirect
297. #1711C2×C103semidirect
298. #1700C2×C103semidirect
299. #1698C2×C103semidirect
300. #1683C2×C103semidirect
301. #1681C2×C103semidirect
302. #1643C2×C103semidirect
303. #1641C2×C103semidirect
304. #1638C2×C103semidirect
305. #1627C2×C103semidirect
306. #1591C2×C103semidirect
307. C8×D8C2×C103semidirect
308. C103#19934direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#33672
C103×#33662
C103×#33042
C103×#32992
C103×#17112
C103×#17002
C103×#16982
C103×#16832
C103×#16812
C103×#16432
C103×#16412
C103×#16382
C103×#16272
C103×#15912
C8×D8×C1032
#19934103