Finite Group Databasebeta

← C103×#19644 #39924919

Subgroups — C103×#19644 #39924919

Order 26368.

754 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3210C211yesmaximal, characteristic, complemented
2C103×#3207C211yesmaximal, characteristic, complemented
3C103×#3184C211yesmaximal, characteristic, complemented
4C103×#3182C211yesmaximal, characteristic, complemented
5C103×#3169C211yesmaximal, characteristic, complemented
6C103×#3131C211yesmaximal, characteristic, complemented
7C103×#1723C211yesmaximal, characteristic, complemented
8C103×#1721C211yesmaximal, characteristic, complemented
9C103×#1719C211yesmaximal, characteristic, complemented
10C103×#1717C211yesmaximal, characteristic, complemented
11C103×#1711C211yesmaximal, characteristic, complemented
12C103×#1709C211yesmaximal, characteristic, complemented
13C103×#1708C211yesmaximal, characteristic, complemented
14C103×#1706C211yesmaximal, characteristic, complemented
15C8×M16×C103C211yesmaximal, characteristic, complemented
16#533×C103C2211yescharacteristic
17#532×C103C2211yescharacteristic
18#532×C103C2211yescharacteristic
19#532×C103C2211yescharacteristic
20#500×C103C2211yescharacteristic
21#500×C103C2211yescharacteristic
22#498×C103C2211yescharacteristic
23#494×C103C2211yescharacteristic
24#493×C103C2211yescharacteristic
25#493×C103C2211yescharacteristic
26#493×C103C2211yescharacteristic
27#492×C103C2211yescharacteristic
28#492×C103C2211yescharacteristic
29#492×C103C2211yescharacteristic
30#488×C103—22no—
31#487×C103C2211yescharacteristic
32#487×C103C2211yescharacteristic
33#487×C103C2211yescharacteristic
34#487×C103C2211yescharacteristic
35#487×C103C2211yescharacteristic
36#486×C103C2211yescharacteristic
37#486×C103C2211yescharacteristic
38#486×C103C2211yescharacteristic
39#486×C103C2211yescharacteristic
40#486×C103C2211yescharacteristic
41#486×C103C2211yescharacteristic
42#486×C103C2211yescharacteristic
43#486×C103C2211yescharacteristic
44#486×C103C2211yescharacteristic
45#469×C103—22no—
46#468×C103—22no—
47#466×C103—22no—
48#464×C103—22no—
49#463×C103—22no—
50#452×C103—22no—
51#449×C103—22no—
52#442×C103—22no—
53#440×C103—22no—
54C4×D8×C103—22no—
55#431×C103C2211yescharacteristic
56#416×C103—22no—
57C4×M16×C103C2211yescharacteristic
58C2×C4×C8×C103C2211yescharacteristic
59#322×C103C2211yescharacteristic
60#322×C103C2211yescharacteristic
61C82×C103C2211yescharacteristic
62C82×C103C2211yescharacteristic
63C2×#41×C103—21no—
64C2×#41×C103—21no—
65C2×#41×C103—21no—
66C2×Q16×C103—22no—
67C2×SD16×C103—22no—
68C2×SD16×C103—22no—
69C2×SD16×C103—22no—
70C2×D8×C103—22no—
71C2×D8×C103—22no—
72C2×D8×C103—22no—
73C2×M16×C103D412yes—
74C22×C8×C103D412yes—
75C4⋊Q8×C103C2311yescharacteristic
76C4⋊Q8×C103C2311yescharacteristic
77C4⋊Q8×C103C2311yescharacteristic
78C4⋊Q8×C103C2311yescharacteristic
79C4⋊Q8×C103C2311yescharacteristic
80#127×C103C2311yescharacteristic
81#127×C103C2311yescharacteristic
82#127×C103C2311yescharacteristic
83#125×C103—21no—
84#124×C103—21no—
85#124×C103—21no—
86#124×C103—21no—
87C22⋊Q8×C103—21no—
88C22⋊Q8×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—
95C4×Q8×C103—21no—
96C4×Q8×C103—21no—
97C4×D4×C103—21no—
98C4×D4×C103—21no—
99C4×D4×C103—21no—
100C4×D4×C103—21no—
101C4×D4×C103—21no—
102C4×D4×C103—21no—
103#117×C103—21no—
104C2×C42×C103C2311yescharacteristic
105#107×C103—22no—
106#107×C103—22no—
107#106×C103—22no—
108C4⋊C8×C103D412yes—
109#103×C103—22no—
110#103×C103—22no—
111#103×C103—22no—
112#103×C103—22no—
113#103×C103—22no—
114#102×C103—22no—
115#102×C103—22no—
116#102×C103—22no—
117#102×C103—22no—
118#102×C103—22no—
119#102×C103—22no—
120#102×C103—22no—
121#102×C103—22no—
122#102×C103—22no—
123C22⋊C8×C103D412yes—
124#97×C103D412yes—
125C4×C8×C103D412yes—
126C4×C8×C103C2311yescharacteristic
127C4×C8×C103C2311yescharacteristic
128C4×C8×C103C2311yescharacteristic
129C4×C8×C103C2311yescharacteristic
130C4×C8×C103C2311yescharacteristic
131C4×C8×C103C2311yescharacteristic
132#41×C103—44no—
133#41×C103—82no—
134#41×C103—82no—
135C2×Q8×C103—21no—
136C2×Q8×C103—21no—
137C2×Q8×C103—21no—
138C2×Q8×C103—21no—
139C2×Q8×C103—21no—
140C2×D4×C103—21no—
141C2×D4×C103—21no—
142C2×D4×C103—21no—
143C2×D4×C103—21no—
144C2×D4×C103—21no—
145C2×D4×C103—21no—
146C2×D4×C103—21no—
147C2×D4×C103—21no—
148C2×D4×C103—21no—
149C2×D4×C103—41no—
150C2×D4×C103—41no—
151C2×D4×C103—41no—
152C22×C4×C103—41no—
153C22×C4×C103—41no—
154C22×C4×C103—41no—
155C22×C4×C103C2×D411yescharacteristic
156C22×C4×C103C2×D411yescharacteristic
157C22×C4×C103C2×D411yescharacteristic
158Q16×C103—82no—
159SD16×C103—44no—
160SD16×C103—82no—
161SD16×C103—82no—
162D8×C103—44no—
163D8×C103—44no—
164D8×C103—82no—
165M16×C103—24no—
166C2×C8×C103—42no—
167C2×C8×C103C2×D412yes—
168C2×C8×C103C2×D412yes—
169C2×C8×C103C2×D412yes—
170C2×C8×C103C2×D412yes—
171C2×C8×C103C2×D412yes—
172C2×C8×C103C2×D412yes—
173C4⋊C4×C103—21no—
174C4⋊C4×C103—21no—
175C4⋊C4×C103—21no—
176C4⋊C4×C103—21no—
177C4⋊C4×C103—21no—
178C4⋊C4×C103—21no—
179C4⋊C4×C103—21no—
180C4⋊C4×C103—21no—
181C4⋊C4×C103—21no—
182C4⋊C4×C103—21no—
183C4⋊C4×C103—41no—
184C4⋊C4×C103—41no—
185C22⋊C4×C103—41no—
186C22⋊C4×C103—41no—
187C22⋊C4×C103—41no—
188C22⋊C4×C103—41no—
189C22⋊C4×C103—41no—
190C22⋊C4×C103—41no—
191C22⋊C4×C103—41no—
192C42×C103—41no—
193C42×C103C2×D411yescharacteristic
194C42×C103C2×D411yescharacteristic
195C42×C103C2×D411yescharacteristic
196C42×C103C2411yescharacteristic
197C23×C103—41no—
198C23×C103—41no—
199C23×C103—41no—
200C23×C103#12711yescharacteristic
201Q8×C103—42no—
202Q8×C103—42no—
203Q8×C103—42no—
204Q8×C103—42no—
205Q8×C103—42no—
206D4×C103—42no—
207D4×C103—42no—
208D4×C103—42no—
209D4×C103—42no—
210D4×C103—42no—
211D4×C103—42no—
212D4×C103—42no—
213D4×C103—42no—
214D4×C103—42no—
215D4×C103—82no—
216D4×C103—82no—
217D4×C103—82no—
218C2×C4×C103—22no—
219C2×C4×C103—22no—
220C2×C4×C103—22no—
221C2×C4×C103—41no—
222C2×C4×C103—41no—
223C2×C4×C103—41no—
224C2×C4×C103—41no—
225C2×C4×C103—41no—
226C2×C4×C103—82no—
227C2×C4×C103—82no—
228C2×C4×C103—82no—
229C2×C4×C103#12711yescharacteristic
230C2×C4×C103#12711yescharacteristic
231C2×C4×C103#12711yescharacteristic
232C2×C4×C103C22×D411yescharacteristic
233C2×C4×C103C22×D411yescharacteristic
234C2×C4×C103C22×D411yescharacteristic
235C8×C103—22no—
236C8×C103—22no—
237C8×C103—22no—
238C8×C103—22no—
239C8×C103—22no—
240C8×C103#13514yes—
241C22×C103—21no—
242C22×C103—21no—
243C22×C103—21no—
244C22×C103—81no—
245C22×C103—81no—
246C22×C103—81no—
247C22×C103—81no—
248C22×C103—81no—
249C22×C103—81no—
250C22×C103—81no—
251C22×C103—81no—
252C22×C103—81no—
253C22×C103C2×#12711yescharacteristic
254C4×C103—21no—
255C4×C103—21no—
256C4×C103—21no—
257C4×C103—81no—
258C4×C103—81no—
259C4×C103—81no—
260C4×C103—81no—
261C4×C103—81no—
262C4×C103C2×#13512yes—
263C4×C103#57512yes—
264C4×C103#57612yes—
265#19644C10311yesmaximal, characteristic, direct product factor, Sylow
266C2×C103—41no—
267C2×C103—161no—
268C2×C103—161no—
269C2×C103—161no—
270C2×C103#314711yescharacteristic
271C2×C103#315311yescharacteristic
272C2×C103#315511yescharacteristic
273#3210C2×C10311yescharacteristic, complemented
274#3207C2×C10311yescharacteristic, complemented
275#3184C2×C10311yescharacteristic, complemented
276#3182C2×C10311yescharacteristic, complemented
277#3169C2×C10311yescharacteristic, complemented
278#3131C2×C10311yescharacteristic, complemented
279#1723C2×C10311yescharacteristic, complemented
280#1721C2×C10311yescharacteristic, complemented
281#1719C2×C10311yescharacteristic, complemented
282#1717C2×C10311yescharacteristic, complemented
283#1711C2×C10311yescharacteristic, complemented
284#1709C2×C10311yescharacteristic, complemented
285#1708C2×C10311yescharacteristic, complemented
286#1706C2×C10311yescharacteristic, complemented
287C8×M16C2×C10311yescharacteristic, complemented
288C103#1964411yescharacteristic, direct product factor, Sylow
289#533C22×C10311yescharacteristic
290#532C22×C10311yescharacteristic
291#532C22×C10311yescharacteristic
292#532C22×C10311yescharacteristic
293#500C22×C10311yescharacteristic
294#500C22×C10311yescharacteristic
295#498C22×C10311yescharacteristic
296#494C22×C10311yescharacteristic
297#493C22×C10311yescharacteristic
298#493C22×C10311yescharacteristic
299#493C22×C10311yescharacteristic
300#492C22×C10311yescharacteristic
301#492C22×C10311yescharacteristic
302#492C22×C10311yescharacteristic
303#488—22no—
304#487C22×C10311yescharacteristic
305#487C22×C10311yescharacteristic
306#487C22×C10311yescharacteristic
307#487C22×C10311yescharacteristic
308#487C22×C10311yescharacteristic
309#486C22×C10311yescharacteristic
310#486C22×C10311yescharacteristic
311#486C22×C10311yescharacteristic
312#486C22×C10311yescharacteristic
313#486C22×C10311yescharacteristic
314#486C22×C10311yescharacteristic
315#486C22×C10311yescharacteristic
316#486C22×C10311yescharacteristic
317#486C22×C10311yescharacteristic
318#469—22no—
319#468—22no—
320#466—22no—
321#464—22no—
322#463—22no—
323#452—22no—
324#449—22no—
325#442—22no—
326#440—22no—
327C4×D8—22no—
328#431C22×C10311yescharacteristic
329#416—22no—
330C4×M16C22×C10311yescharacteristic
331C2×C4×C8C22×C10311yescharacteristic
332#322C22×C10311yescharacteristic
333#322C22×C10311yescharacteristic
334C82C22×C10311yescharacteristic
335C82C22×C10311yescharacteristic
336C2×#41—21no—
337C2×#41—21no—
338C2×#41—21no—
339C2×Q16—22no—
340C2×SD16—22no—
341C2×SD16—22no—
342C2×SD16—22no—
343C2×D8—22no—
344C2×D8—22no—
345C2×D8—22no—
346C2×M16D4×C10312yes—
347C22×C8D4×C10312yes—
348C4⋊Q8C23×C10311yescharacteristic
349C4⋊Q8C23×C10311yescharacteristic
350C4⋊Q8C23×C10311yescharacteristic
351C4⋊Q8C23×C10311yescharacteristic
352C4⋊Q8C23×C10311yescharacteristic
353#127C23×C10311yescharacteristic
354#127C23×C10311yescharacteristic
355#127C23×C10311yescharacteristic
356#125—21no—
357#124—21no—
358#124—21no—
359#124—21no—
360C22⋊Q8—21no—
361C22⋊Q8—21no—
362#121—21no—
363#121—21no—
364#121—21no—
365#121—21no—
366#121—21no—
367#121—21no—
368C4×Q8—21no—
369C4×Q8—21no—
370C4×D4—21no—
371C4×D4—21no—
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—21no—
375C4×D4—21no—
376#117—21no—
377C2×C42C23×C10311yescharacteristic
378#107—22no—
379#107—22no—
380#106—22no—
381C4⋊C8D4×C10312yes—
382#103—22no—
383#103—22no—
384#103—22no—
385#103—22no—
386#103—22no—
387#102—22no—
388#102—22no—
389#102—22no—
390#102—22no—
391#102—22no—
392#102—22no—
393#102—22no—
394#102—22no—
395#102—22no—
396C22⋊C8D4×C10312yes—
397#97D4×C10312yes—
398C4×C8D4×C10312yes—
399C4×C8C23×C10311yescharacteristic
400C4×C8C23×C10311yescharacteristic
401C4×C8C23×C10311yescharacteristic
402C4×C8C23×C10311yescharacteristic
403C4×C8C23×C10311yescharacteristic
404C4×C8C23×C10311yescharacteristic
405#41—44no—
406#41—82no—
407#41—82no—
408C2×Q8—21no—
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4C2×D4×C10311yescharacteristic
429C22×C4C2×D4×C10311yescharacteristic
430C22×C4C2×D4×C10311yescharacteristic
431Q16—82no—
432SD16—44no—
433SD16—82no—
434SD16—82no—
435D8—44no—
436D8—44no—
437D8—82no—
438M16—24no—
439C2×C8—42no—
440C2×C8C2×D4×C10312yes—
441C2×C8C2×D4×C10312yes—
442C2×C8C2×D4×C10312yes—
443C2×C8C2×D4×C10312yes—
444C2×C8C2×D4×C10312yes—
445C2×C8C2×D4×C10312yes—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C22⋊C4—41no—
459C22⋊C4—41no—
460C22⋊C4—41no—
461C22⋊C4—41no—
462C22⋊C4—41no—
463C22⋊C4—41no—
464C22⋊C4—41no—
465C42—41no—
466C42C2×D4×C10311yescharacteristic
467C42C2×D4×C10311yescharacteristic
468C42C2×D4×C10311yescharacteristic
469C42C24×C10311yescharacteristic
470C23—41no—
471C23—41no—
472C23—41no—
473C23#127×C10311yescharacteristic
474Q8—42no—
475Q8—42no—
476Q8—42no—
477Q8—42no—
478Q8—42no—
479D4—42no—
480D4—42no—
481D4—42no—
482D4—42no—
483D4—42no—
484D4—42no—
485D4—42no—
486D4—42no—
487D4—42no—
488D4—82no—
489D4—82no—
490D4—82no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—82no—
500C2×C4—82no—
501C2×C4—82no—
502C2×C4#127×C10311yescharacteristic
503C2×C4#127×C10311yescharacteristic
504C2×C4#127×C10311yescharacteristic
505C2×C4C22×D4×C10311yescharacteristic
506C2×C4C22×D4×C10311yescharacteristic
507C2×C4C22×D4×C10311yescharacteristic
508C8—22no—
509C8—22no—
510C8—22no—
511C8—22no—
512C8—22no—
513C8#135×C10314yes—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—81no—
518C22—81no—
519C22—81no—
520C22—81no—
521C22—81no—
522C22—81no—
523C22—81no—
524C22—81no—
525C22—81no—
526C22C2×#127×C10311yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—81no—
531C4—81no—
532C4—81no—
533C4—81no—
534C4—81no—
535C4C2×#135×C10312yes—
536C4#575×C10312yes—
537C4#576×C10312yes—
538C2—41no—
539C2—161no—
540C2—161no—
541C2—161no—
542C2C103×#314711yescharacteristic
543C2C103×#315311yescharacteristic
544C2C103×#315511yescharacteristic
subgroupG/H
center, socleC22×C103C2×#127
commutator, Frattini, cosocleC42C24×C103
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
2. C103×#3207C2semidirect
3. C103×#3184C2semidirect
4. C103×#3182C2semidirect
5. C103×#3169C2semidirect
6. C103×#3131C2semidirect
7. C103×#1723C2semidirect
8. C103×#1721C2semidirect
9. C103×#1719C2semidirect
10. C103×#1717C2semidirect
11. C103×#1711C2semidirect
12. C103×#1709C2semidirect
13. C103×#1708C2semidirect
14. C103×#1706C2semidirect
15. C8×M16×C103C2semidirect
265. #19644C103direct (N × H)
273. #3210C2×C103semidirect
274. #3207C2×C103semidirect
275. #3184C2×C103semidirect
276. #3182C2×C103semidirect
277. #3169C2×C103semidirect
278. #3131C2×C103semidirect
279. #1723C2×C103semidirect
280. #1721C2×C103semidirect
281. #1719C2×C103semidirect
282. #1717C2×C103semidirect
283. #1711C2×C103semidirect
284. #1709C2×C103semidirect
285. #1708C2×C103semidirect
286. #1706C2×C103semidirect
287. C8×M16C2×C103semidirect
288. C103#19644direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#32102
C103×#32072
C103×#31842
C103×#31822
C103×#31692
C103×#31312
C103×#17232
C103×#17212
C103×#17192
C103×#17172
C103×#17112
C103×#17092
C103×#17082
C103×#17062
C8×M16×C1032
#19644103