Finite Group Databasebeta

← C103×#20865 #39926140

Subgroups — C103×#20865 #39926140

Order 26368.

1394 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×#3428C211yesmaximal, characteristic
2C2×#428×C103C211yesmaximal, characteristic, complemented
3C2×#421×C103C211yesmaximal, characteristic
4C2×#417×C103C211yesmaximal, characteristic
5C103×#2317C211yesmaximal, characteristic, complemented
6C103×#1860C214yesmaximal, complemented
7C103×#1859C214yesmaximal, complemented
8C103×#1742C211yesmaximal, characteristic, complemented
9C103×#1733C211yesmaximal, characteristic, complemented
10C22×#41×C103C2211yescharacteristic
11C22×M16×C103C2211yescharacteristic
12C22×M16×C103C2211yescharacteristic
13#520×C103—21no—
14#520×C103—21no—
15#520×C103C2212yes—
16#520×C103C2212yes—
17#519×C103—21no—
18#518×C103—21no—
19#518×C103—22no—
20C4×#41×C103—22no—
21C4×#41×C103—22no—
22C2×#117×C103—22no—
23C2×#117×C103C2211yescharacteristic
24C2×#117×C103C2211yescharacteristic
25C2×#117×C103C2211yescharacteristic
26C22×C4⋊C4×C103C2211yescharacteristic
27#428×C103—22no—
28#428×C103C2214yescomplemented
29C2×#107×C103—21no—
30C2×#106×C103—21no—
31#421×C103C418yescomplemented
32C2×#104×C103C2214yes—
33#417×C103—22no—
34#417×C103C2214yes—
35C2×#103×C103—21no—
36C2×#102×C103—21no—
37#389×C103—22no—
38#385×C103—22no—
39#384×C103C2212yescomplemented
40#382×C103C2212yescomplemented
41#343×C103C2212yescomplemented
42#343×C103C2212yescomplemented
43#339×C103C2214yescomplemented
44C2×#41×C103—21no—
45C2×#41×C103—21no—
46C2×#41×C103—22no—
47C2×#41×C103—22no—
48C2×#41×C103C2×C414yes—
49C2×#41×C103D412yes—
50C2×#41×C103Q814yes—
51C2×#41×C103C2312yes—
52C22×Q8×C103D411yescharacteristic
53C22×D4×C103—21no—
54C22×D4×C103D411yescharacteristic
55C23×C4×C103—21no—
56C23×C4×C103—21no—
57C23×C4×C103C2311yescharacteristic
58C2×M16×C103—21no—
59C2×M16×C103—22no—
60C2×M16×C103—21no—
61C2×M16×C103—22no—
62C2×M16×C103—22no—
63C2×M16×C103C2×C414yescomplemented
64C2×M16×C103C2312yes—
65C2×M16×C103C2312yes—
66C22×C8×C103—21no—
67C22×C8×C103—21no—
68C4×Q8×C103—22no—
69C4×Q8×C103—22no—
70C4×Q8×C103—22no—
71C4×Q8×C103—22no—
72C4×D4×C103—24no—
73C4×D4×C103—24no—
74C4×D4×C103—22no—
75C4×D4×C103—22no—
76C4×D4×C103—22no—
77C4×D4×C103—22no—
78C4×D4×C103—24no—
79C4×D4×C103—24no—
80#117×C103—24no—
81#117×C103—24no—
82#117×C103—21no—
83#117×C103—21no—
84#117×C103—21no—
85#117×C103—21no—
86#117×C103—21no—
87#117×C103—21no—
88#117×C103—22no—
89#117×C103—22no—
90#117×C103—22no—
91#117×C103C2×C414yescomplemented
92#117×C103D412yes—
93#117×C103C2312yes—
94C2×C4⋊C4×C103—21no—
95C2×C4⋊C4×C103—22no—
96C2×C4⋊C4×C103—22no—
97C2×C4⋊C4×C103—21no—
98C2×C4⋊C4×C103—21no—
99C2×C4⋊C4×C103—21no—
100C2×C4⋊C4×C103—21no—
101C2×C4⋊C4×C103—21no—
102C2×C4⋊C4×C103—24no—
103C2×C4⋊C4×C103D411yescharacteristic
104C2×C4⋊C4×C103D411yescharacteristic
105C2×C4⋊C4×C103C2312yes—
106C2×C4⋊C4×C103C2311yescharacteristic
107C2×C4⋊C4×C103C2311yescharacteristic
108C2×C22⋊C4×C103—24no—
109C2×C22⋊C4×C103—21no—
110C2×C22⋊C4×C103—21no—
111C2×C22⋊C4×C103D412yes—
112C2×C42×C103—24no—
113C2×C42×C103—21no—
114C2×C42×C103D412yes—
115C2×C42×C103C2312yes—
116#107×C103—24no—
117#106×C103—24no—
118#104×C103C2×C4116yescomplemented
119#103×C103—24no—
120#102×C103—24no—
121#95×C103—24no—
122C24×C103—21no—
123C24×C103C2×D411yescharacteristic
124#41×C103—24no—
125#41×C103—24no—
126#41×C103—24no—
127#41×C103—24no—
128#41×C103—24no—
129#41×C103—22no—
130#41×C103—22no—
131#41×C103C4⋊C418yescomplemented
132#41×C103C22×C414yes—
133#41×C103C2×Q814yes—
134C2×Q8×C103—21no—
135C2×Q8×C103—22no—
136C2×Q8×C103C4⋊C414yescomplemented
137C2×Q8×C103C2×D412yes—
138C2×D4×C103—24no—
139C2×D4×C103—22no—
140C2×D4×C103—24no—
141C2×D4×C103—22no—
142C2×D4×C103—21no—
143C2×D4×C103—22no—
144C2×D4×C103C4⋊C414yescomplemented
145C2×D4×C103C2×D412yes—
146C22×C4×C103—21no—
147C22×C4×C103—24no—
148C22×C4×C103—22no—
149C22×C4×C103—24no—
150C22×C4×C103—22no—
151C22×C4×C103—22no—
152C22×C4×C103—24no—
153C22×C4×C103—24no—
154C22×C4×C103—21no—
155C22×C4×C103—21no—
156C22×C4×C103—22no—
157C22×C4×C103—41no—
158C22×C4×C103—41no—
159C22×C4×C103—82no—
160C22×C4×C103C22×C412yes—
161C22×C4×C103C2×D412yes—
162C22×C4×C103C2×D412yes—
163C22×C4×C103C2×D411yescharacteristic
164C22×C4×C103C2×D411yescharacteristic
165C22×C4×C103C2×D411yescharacteristic
166C22×C4×C103C2×D411yescharacteristic
167C22×C4×C103C2×D411yescharacteristic
168C22×C4×C103C2×Q812yes—
169C22×C4×C103#4112yes—
170C22×C4×C103#4112yes—
171C22×C4×C103C2411yescharacteristic
172M16×C103—24no—
173M16×C103—22no—
174M16×C103—22no—
175M16×C103—22no—
176M16×C103—42no—
177M16×C103C22×C414yes—
178C2×C8×C103—24no—
179C2×C8×C103—22no—
180C2×C8×C103—22no—
181C2×C8×C103—42no—
182C4⋊C4×C103—24no—
183C4⋊C4×C103—24no—
184C4⋊C4×C103—24no—
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—22no—
192C4⋊C4×C103—22no—
193C4⋊C4×C103—41no—
194C4⋊C4×C103—41no—
195C4⋊C4×C103—84no—
196C4⋊C4×C103C2×D412yes—
197C4⋊C4×C103C2×D412yes—
198C22⋊C4×C103—24no—
199C22⋊C4×C103—24no—
200C22⋊C4×C103—24no—
201C22⋊C4×C103—22no—
202C22⋊C4×C103—22no—
203C22⋊C4×C103—22no—
204C22⋊C4×C103—22no—
205C42×C103—24no—
206C42×C103—24no—
207C42×C103—22no—
208C42×C103—22no—
209C42×C103—22no—
210C42×C103—22no—
211C42×C103—22no—
212C42×C103C22×C414yes—
213C23×C103—22no—
214C23×C103—24no—
215C23×C103—41no—
216C23×C103—41no—
217C23×C103—81no—
218C23×C103—81no—
219C23×C103C4×D412yes—
220C23×C103#12011yescharacteristic
221C23×C103#12011yescharacteristic
222C23×C103C22⋊Q812yes—
223C23×C103C22×D411yescharacteristic
224Q8×C103—22no—
225Q8×C103—24no—
226Q8×C103C2×C4⋊C414yes—
227D4×C103—24no—
228D4×C103—24no—
229D4×C103—28no—
230D4×C103—22no—
231D4×C103—24no—
232D4×C103C2×C4⋊C414yes—
233C2×C4×C103—22no—
234C2×C4×C103—24no—
235C2×C4×C103—24no—
236C2×C4×C103—24no—
237C2×C4×C103—28no—
238C2×C4×C103—24no—
239C2×C4×C103—22no—
240C2×C4×C103—22no—
241C2×C4×C103—22no—
242C2×C4×C103—22no—
243C2×C4×C103—42no—
244C2×C4×C103—42no—
245C2×C4×C103—42no—
246C2×C4×C103—42no—
247C2×C4×C103—44no—
248C2×C4×C103—42no—
249C2×C4×C103—81no—
250C2×C4×C103—81no—
251C2×C4×C103—84no—
252C2×C4×C103—84no—
253C2×C4×C103—82no—
254C2×C4×C103—82no—
255C2×C4×C103C2×C4⋊C412yes—
256C2×C4×C103C2×C4⋊C412yes—
257C2×C4×C103C4×D412yes—
258C2×C4×C103C4×D412yes—
259C2×C4×C103C4×D412yes—
260C2×C4×C103#12011yescharacteristic
261C2×C4×C103#12011yescharacteristic
262C2×C4×C103C22⋊Q812yes—
263C2×C4×C103C22⋊Q812yes—
264C2×C4×C103C22⋊Q812yes—
265C2×C4×C103#12312yes—
266C2×C4×C103#12312yes—
267C2×C4×C103C23×C411yescharacteristic
268C2×C4×C103C22×D411yescharacteristic
269C2×C4×C103C22×D411yescharacteristic
270C2×C4×C103C22×Q811yescharacteristic
271C2×C4×C103C2×#4111yescharacteristic
272C2×C4×C103C2×#4111yescharacteristic
273C8×C103—24no—
274C8×C103—42no—
275C22×C103—21no—
276C22×C103—21no—
277C22×C103—21no—
278C22×C103—21no—
279C22×C103—21no—
280C22×C103—21no—
281C22×C103—24no—
282C22×C103—42no—
283C22×C103—42no—
284C22×C103—42no—
285C22×C103—42no—
286C22×C103—84no—
287C22×C103#38512yes—
288C22×C103#38512yes—
289C22×C103C2×C4×D411yescharacteristic
290C22×C103C2×#12011yescharacteristic
291C22×C103C2×C22⋊Q811yescharacteristic
292C4×C103—24no—
293C4×C103—44no—
294C4×C103—42no—
295C4×C103—42no—
296C4×C103—42no—
297C4×C103—42no—
298C4×C103—82no—
299C4×C103#38512yes—
300C4×C103#38512yes—
301C4×C103C22×C4⋊C411yescharacteristic
302C4×C103C2×C4×D411yescharacteristic
303C4×C103C2×C22⋊Q811yescharacteristic
304C4×C103C2×#12311yescharacteristic
305#20865C10311yesmaximal, characteristic, direct product factor, Sylow
306C2×C103—21no—
307C2×C103—22no—
308C2×C103—21no—
309C2×C103—22no—
310C2×C103—44no—
311C2×C103C2×#38511yescharacteristic
312C2×C103#302111yescharacteristic
313C2×C103#302211yescharacteristic
314#3428C2×C10311yescharacteristic
315C2×#428C2×C10311yescharacteristic, complemented
316C2×#421C2×C10311yescharacteristic
317C2×#417C2×C10311yescharacteristic
318#2317C2×C10311yescharacteristic, complemented
319#1860C2×C10314yescomplemented
320#1859C2×C10314yescomplemented
321#1742C2×C10311yescharacteristic, complemented
322#1733C2×C10311yescharacteristic, complemented
323C103#2086511yescharacteristic, direct product factor, Sylow
324C22×#41C22×C10311yescharacteristic
325C22×M16C22×C10311yescharacteristic
326C22×M16C22×C10311yescharacteristic
327#520—21no—
328#520—21no—
329#520C22×C10312yes—
330#520C22×C10312yes—
331#519—21no—
332#518—21no—
333#518—22no—
334C4×#41—22no—
335C4×#41—22no—
336C2×#117—22no—
337C2×#117C22×C10311yescharacteristic
338C2×#117C22×C10311yescharacteristic
339C2×#117C22×C10311yescharacteristic
340C22×C4⋊C4C22×C10311yescharacteristic
341#428—22no—
342#428C22×C10314yescomplemented
343C2×#107—21no—
344C2×#106—21no—
345#421C4×C10318yescomplemented
346C2×#104C22×C10314yes—
347#417—22no—
348#417C22×C10314yes—
349C2×#103—21no—
350C2×#102—21no—
351#389—22no—
352#385—22no—
353#384C22×C10312yescomplemented
354#382C22×C10312yescomplemented
355#343C22×C10312yescomplemented
356#343C22×C10312yescomplemented
357#339C22×C10314yescomplemented
358C2×#41—21no—
359C2×#41—21no—
360C2×#41—22no—
361C2×#41—22no—
362C2×#41C2×C4×C10314yes—
363C2×#41D4×C10312yes—
364C2×#41Q8×C10314yes—
365C2×#41C23×C10312yes—
366C22×Q8D4×C10311yescharacteristic
367C22×D4—21no—
368C22×D4D4×C10311yescharacteristic
369C23×C4—21no—
370C23×C4—21no—
371C23×C4C23×C10311yescharacteristic
372C2×M16—21no—
373C2×M16—22no—
374C2×M16—21no—
375C2×M16—22no—
376C2×M16—22no—
377C2×M16C2×C4×C10314yescomplemented
378C2×M16C23×C10312yes—
379C2×M16C23×C10312yes—
380C22×C8—21no—
381C22×C8—21no—
382C4×Q8—22no—
383C4×Q8—22no—
384C4×Q8—22no—
385C4×Q8—22no—
386C4×D4—24no—
387C4×D4—24no—
388C4×D4—22no—
389C4×D4—22no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—24no—
393C4×D4—24no—
394#117—24no—
395#117—24no—
396#117—21no—
397#117—21no—
398#117—21no—
399#117—21no—
400#117—21no—
401#117—21no—
402#117—22no—
403#117—22no—
404#117—22no—
405#117C2×C4×C10314yescomplemented
406#117D4×C10312yes—
407#117C23×C10312yes—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—24no—
417C2×C4⋊C4D4×C10311yescharacteristic
418C2×C4⋊C4D4×C10311yescharacteristic
419C2×C4⋊C4C23×C10312yes—
420C2×C4⋊C4C23×C10311yescharacteristic
421C2×C4⋊C4C23×C10311yescharacteristic
422C2×C22⋊C4—24no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4D4×C10312yes—
426C2×C42—24no—
427C2×C42—21no—
428C2×C42D4×C10312yes—
429C2×C42C23×C10312yes—
430#107—24no—
431#106—24no—
432#104C2×C4×C103116yescomplemented
433#103—24no—
434#102—24no—
435#95—24no—
436C24—21no—
437C24C2×D4×C10311yescharacteristic
438#41—24no—
439#41—24no—
440#41—24no—
441#41—24no—
442#41—24no—
443#41—22no—
444#41—22no—
445#41C4⋊C4×C10318yescomplemented
446#41C22×C4×C10314yes—
447#41C2×Q8×C10314yes—
448C2×Q8—21no—
449C2×Q8—22no—
450C2×Q8C4⋊C4×C10314yescomplemented
451C2×Q8C2×D4×C10312yes—
452C2×D4—24no—
453C2×D4—22no—
454C2×D4—24no—
455C2×D4—22no—
456C2×D4—21no—
457C2×D4—22no—
458C2×D4C4⋊C4×C10314yescomplemented
459C2×D4C2×D4×C10312yes—
460C22×C4—21no—
461C22×C4—24no—
462C22×C4—22no—
463C22×C4—24no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—82no—
474C22×C4C22×C4×C10312yes—
475C22×C4C2×D4×C10312yes—
476C22×C4C2×D4×C10312yes—
477C22×C4C2×D4×C10311yescharacteristic
478C22×C4C2×D4×C10311yescharacteristic
479C22×C4C2×D4×C10311yescharacteristic
480C22×C4C2×D4×C10311yescharacteristic
481C22×C4C2×D4×C10311yescharacteristic
482C22×C4C2×Q8×C10312yes—
483C22×C4#41×C10312yes—
484C22×C4#41×C10312yes—
485C22×C4C24×C10311yescharacteristic
486M16—24no—
487M16—22no—
488M16—22no—
489M16—22no—
490M16—42no—
491M16C22×C4×C10314yes—
492C2×C8—24no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—42no—
496C4⋊C4—24no—
497C4⋊C4—24no—
498C4⋊C4—24no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—41no—
508C4⋊C4—41no—
509C4⋊C4—84no—
510C4⋊C4C2×D4×C10312yes—
511C4⋊C4C2×D4×C10312yes—
512C22⋊C4—24no—
513C22⋊C4—24no—
514C22⋊C4—24no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C42—24no—
520C42—24no—
521C42—22no—
522C42—22no—
523C42—22no—
524C42—22no—
525C42—22no—
526C42C22×C4×C10314yes—
527C23—22no—
528C23—24no—
529C23—41no—
530C23—41no—
531C23—81no—
532C23—81no—
533C23C4×D4×C10312yes—
534C23#120×C10311yescharacteristic
535C23#120×C10311yescharacteristic
536C23C22⋊Q8×C10312yes—
537C23C22×D4×C10311yescharacteristic
538Q8—24no—
539Q8—22no—
540Q8C2×C4⋊C4×C10314yes—
541D4—28no—
542D4—24no—
543D4—24no—
544D4—24no—
545D4—22no—
546D4C2×C4⋊C4×C10314yes—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—28no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—44no—
562C2×C4—42no—
563C2×C4—81no—
564C2×C4—81no—
565C2×C4—84no—
566C2×C4—84no—
567C2×C4—82no—
568C2×C4—82no—
569C2×C4C2×C4⋊C4×C10312yes—
570C2×C4C2×C4⋊C4×C10312yes—
571C2×C4C4×D4×C10312yes—
572C2×C4C4×D4×C10312yes—
573C2×C4C4×D4×C10312yes—
574C2×C4#120×C10311yescharacteristic
575C2×C4#120×C10311yescharacteristic
576C2×C4C22⋊Q8×C10312yes—
577C2×C4C22⋊Q8×C10312yes—
578C2×C4C22⋊Q8×C10312yes—
579C2×C4#123×C10312yes—
580C2×C4#123×C10312yes—
581C2×C4C23×C4×C10311yescharacteristic
582C2×C4C22×D4×C10311yescharacteristic
583C2×C4C22×D4×C10311yescharacteristic
584C2×C4C22×Q8×C10311yescharacteristic
585C2×C4C2×#41×C10311yescharacteristic
586C2×C4C2×#41×C10311yescharacteristic
587C8—24no—
588C8—42no—
589C22—21no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—24no—
596C22—42no—
597C22—42no—
598C22—42no—
599C22—42no—
600C22—84no—
601C22#385×C10312yes—
602C22#385×C10312yes—
603C22C2×C4×D4×C10311yescharacteristic
604C22C2×#120×C10311yescharacteristic
605C22C2×C22⋊Q8×C10311yescharacteristic
606C4—24no—
607C4—44no—
608C4—42no—
609C4—42no—
610C4—42no—
611C4—42no—
612C4—82no—
613C4#385×C10312yes—
614C4#385×C10312yes—
615C4C22×C4⋊C4×C10311yescharacteristic
616C4C2×C4×D4×C10311yescharacteristic
617C4C2×C22⋊Q8×C10311yescharacteristic
618C4C2×#123×C10311yescharacteristic
619C2—21no—
620C2—22no—
621C2—22no—
622C2—21no—
623C2—44no—
624C2C2×#385×C10311yescharacteristic
625C2C103×#302111yescharacteristic
626C2C103×#302211yescharacteristic
subgroupG/H
center, socleC22×C103C2×#120
commutatorC2×C4C23×C4×C103
Frattini, cosocleC22×C4C24×C103
prime radicalC22×#41×C103C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C23×C4×C103 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#428×C103C2semidirect
5. C103×#2317C2semidirect
6. C103×#1860C2semidirect
7. C103×#1859C2semidirect
8. C103×#1742C2semidirect
9. C103×#1733C2semidirect
28. #428×C103C22semidirect
31. #421×C103C4semidirect
39. #384×C103C22semidirect
40. #382×C103C22semidirect
41. #343×C103C22semidirect
42. #343×C103C22semidirect
43. #339×C103C22semidirect
63. C2×M16×C103C2×C4semidirect
91. #117×C103C2×C4semidirect
118. #104×C103C2×C4semidirect
131. #41×C103C4⋊C4semidirect
136. C2×Q8×C103C4⋊C4semidirect
144. C2×D4×C103C4⋊C4semidirect
305. #20865C103direct (N × H)
315. C2×#428C2×C103semidirect
318. #2317C2×C103semidirect
319. #1860C2×C103semidirect
320. #1859C2×C103semidirect
321. #1742C2×C103semidirect
322. #1733C2×C103semidirect
323. C103#20865direct (N × H)
342. #428C22×C103semidirect
345. #421C4×C103semidirect
353. #384C22×C103semidirect
354. #382C22×C103semidirect
355. #343C22×C103semidirect
356. #343C22×C103semidirect
357. #339C22×C103semidirect
377. C2×M16C2×C4×C103semidirect
405. #117C2×C4×C103semidirect
432. #104C2×C4×C103semidirect
445. #41C4⋊C4×C103semidirect
450. C2×Q8C4⋊C4×C103semidirect
458. C2×D4C4⋊C4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#34282
C2×#428×C1032
C2×#421×C1032
C2×#417×C1032
C103×#23172
C103×#18602
C103×#18592
C103×#17422
C103×#17332
#20865103