Finite Group Databasebeta

← C103×#24808 #39930083

Subgroups — C103×#24808 #39930083

Order 26368.

820 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3069C211yesmaximal, characteristic, complemented
2C103×#3068C211yesmaximal, characteristic
3C2×#471×C103C211yesmaximal, characteristic, complemented
4C2×#471×C103C211yesmaximal, characteristic, complemented
5C103×#2955C211yesmaximal, characteristic, complemented
6C103×#2916C211yesmaximal, characteristic, complemented
7C103×#2070C211yesmaximal, characteristic, complemented
8C103×#2069C211yesmaximal, characteristic, complemented
9C103×#2049C211yesmaximal, characteristic, complemented
10C103×#2048C211yesmaximal, characteristic, complemented
11C103×#1977C211yesmaximal, characteristic, complemented
12C103×#1953C211yesmaximal, characteristic, complemented
13C103×#1903C211yesmaximal, characteristic, complemented
14C103×#1902C211yesmaximal, characteristic, complemented
15C103×#1813C211yesmaximal, characteristic, complemented
16#575×C103C2211yescharacteristic
17C2×#137×C103C2211yescharacteristic
18C2×#137×C103C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C103C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C103C2211yescharacteristic
21C22×SD16×C103C2211yescharacteristic
22#568×C103C2211yescharacteristic
23#568×C103C2211yescharacteristic
24C2×#131×C103C2211yescharacteristic
25C2×#131×C103C2211yescharacteristic
26#473×C103—22no—
27#472×C103—22no—
28#471×C103—22no—
29#471×C103—22no—
30#471×C103—22no—
31#471×C103—22no—
32#471×C103—22no—
33#471×C103—22no—
34#444×C103—22no—
35#443×C103—22no—
36#430×C103—22no—
37#430×C103C2211yescharacteristic
38#430×C103C2211yescharacteristic
39#430×C103C2211yescharacteristic
40#430×C103C2211yescharacteristic
41#430×C103C2211yescharacteristic
42C2×#108×C103—22no—
43C2×#108×C103C2211yescharacteristic
44C2×#108×C103C2211yescharacteristic
45C2×#108×C103C2211yescharacteristic
46#421×C103C2211yescharacteristic
47#421×C103C2211yescharacteristic
48#419×C103C2211yescharacteristic
49#418×C103C2211yescharacteristic
50#413×C103C2211yescharacteristic
51#413×C103C2211yescharacteristic
52C2×#101×C103C2211yescharacteristic
53C2×#101×C103C2211yescharacteristic
54C2×#101×C103C2211yescharacteristic
55C2×#100×C103C2211yescharacteristic
56C2×#100×C103C2211yescharacteristic
57C2×#100×C103C2211yescharacteristic
58#405×C103C2211yescharacteristic
59#344×C103C2211yescharacteristic
60#344×C103C2211yescharacteristic
61#338×C103C2211yescharacteristic
62#338×C103C2211yescharacteristic
63C2×#41×C103C2311yescharacteristic
64C2×#41×C103C2311yescharacteristic
65C22×Q8×C103C2311yescharacteristic
66C22×D4×C103C2311yescharacteristic
67#137×C103—21no—
68#137×C103—22no—
69#137×C103—22no—
70#137×C103—22no—
71#137×C103—41no—
72#137×C103D412yes—
73AGL(1,ℤ/8)×C103—21no—
74AGL(1,ℤ/8)×C103—22no—
75AGL(1,ℤ/8)×C103—22no—
76AGL(1,ℤ/8)×C103—22no—
77AGL(1,ℤ/8)×C103—41no—
78AGL(1,ℤ/8)×C103D412yes—
79#135×C103—22no—
80C2×Q16×C103—21no—
81C2×Q16×C103—21no—
82C2×SD16×C103—21no—
83C2×SD16×C103—21no—
84C2×SD16×C103—21no—
85C2×SD16×C103—21no—
86C2×SD16×C103—21no—
87C2×SD16×C103—21no—
88C2×SD16×C103—21no—
89C2×SD16×C103—21no—
90C2×SD16×C103—21no—
91C2×SD16×C103—21no—
92C2×D8×C103—21no—
93C2×D8×C103—21no—
94#131×C103—21no—
95#131×C103—21no—
96#131×C103—22no—
97#131×C103—22no—
98#131×C103—21no—
99#131×C103—21no—
100#131×C103—21no—
101#131×C103—21no—
102#131×C103—41no—
103#131×C103—41no—
104#131×C103D412yes—
105#131×C103D412yes—
106C2×M16×C103—21no—
107C2×M16×C103—21no—
108C2×M16×C103—22no—
109C2×M16×C103—22no—
110C2×M16×C103C2311yescharacteristic
111C2×M16×C103C2311yescharacteristic
112C2×M16×C103C2311yescharacteristic
113C2×M16×C103C2311yescharacteristic
114C2×M16×C103C2311yescharacteristic
115C2×M16×C103C2311yescharacteristic
116C2×M16×C103C2311yescharacteristic
117C2×M16×C103C2311yescharacteristic
118C2×M16×C103C2311yescharacteristic
119C22×C8×C103—21no—
120C22×C8×C103—21no—
121C22×C8×C103C2311yescharacteristic
122#117×C103C2311yescharacteristic
123#108×C103—22no—
124#108×C103—22no—
125#108×C103—22no—
126#108×C103—22no—
127#108×C103—22no—
128#108×C103—21no—
129#108×C103—21no—
130#108×C103—21no—
131#108×C103—21no—
132#108×C103D412yes—
133#108×C103D412yes—
134#104×C103—22no—
135#104×C103—22no—
136#103×C103—41no—
137#102×C103—41no—
138#101×C103—21no—
139#101×C103—21no—
140#101×C103—22no—
141#101×C103—22no—
142#101×C103—22no—
143#100×C103—21no—
144#100×C103—21no—
145#100×C103—22no—
146#100×C103—22no—
147#100×C103—22no—
148#97×C103—21no—
149C4×C8×C103—21no—
150C24×C103—21no—
151#41×C103—21no—
152#41×C103—21no—
153#41×C103—21no—
154#41×C103—21no—
155#41×C103—21no—
156#41×C103—21no—
157#41×C103C2×D412yes—
158#41×C103C2×D412yes—
159C2×Q8×C103—21no—
160C2×Q8×C103—21no—
161C2×Q8×C103—21no—
162C2×Q8×C103—21no—
163C2×Q8×C103—21no—
164C2×Q8×C103—21no—
165C2×Q8×C103C2×D411yescharacteristic
166C2×Q8×C103#4111yescharacteristic
167C2×D4×C103—21no—
168C2×D4×C103—21no—
169C2×D4×C103—21no—
170C2×D4×C103—21no—
171C2×D4×C103—21no—
172C2×D4×C103—21no—
173C2×D4×C103—21no—
174C2×D4×C103—21no—
175C2×D4×C103C2×D411yescharacteristic
176C2×D4×C103#4111yescharacteristic
177C22×C4×C103—21no—
178C22×C4×C103—21no—
179C22×C4×C103—21no—
180C22×C4×C103C2411yescharacteristic
181Q16×C103—22no—
182Q16×C103—42no—
183Q16×C103—42no—
184SD16×C103—22no—
185SD16×C103—22no—
186SD16×C103—42no—
187SD16×C103—42no—
188SD16×C103—42no—
189SD16×C103—42no—
190SD16×C103—41no—
191SD16×C103—41no—
192SD16×C103—41no—
193SD16×C103—41no—
194D8×C103—22no—
195D8×C103—42no—
196D8×C103—42no—
197M16×C103—21no—
198M16×C103—21no—
199M16×C103—21no—
200M16×C103—21no—
201M16×C103—22no—
202M16×C103—22no—
203M16×C103—21no—
204M16×C103—21no—
205M16×C103—21no—
206M16×C103—21no—
207M16×C103—21no—
208M16×C103—21no—
209M16×C103—21no—
210M16×C103—21no—
211M16×C103—21no—
212M16×C103—21no—
213M16×C103—42no—
214M16×C103—42no—
215M16×C103—41no—
216M16×C103—41no—
217M16×C103C2×D412yes—
218M16×C103C2×D412yes—
219M16×C103C2×D412yes—
220M16×C103C2×D412yes—
221C2×C8×C103—21no—
222C2×C8×C103—21no—
223C2×C8×C103—21no—
224C2×C8×C103—21no—
225C2×C8×C103—22no—
226C2×C8×C103—22no—
227C2×C8×C103—21no—
228C2×C8×C103—21no—
229C2×C8×C103—21no—
230C2×C8×C103—21no—
231C2×C8×C103—21no—
232C2×C8×C103—42no—
233C2×C8×C103—42no—
234C2×C8×C103—41no—
235C2×C8×C103—41no—
236C2×C8×C103C2×D411yescharacteristic
237C2×C8×C103C2×D411yescharacteristic
238C2×C8×C103C2×D411yescharacteristic
239C2×C8×C103C2×D411yescharacteristic
240C2×C8×C103#4111yescharacteristic
241C2×C8×C103#4111yescharacteristic
242C4⋊C4×C103—21no—
243C22⋊C4×C103—21no—
244C42×C103—21no—
245C23×C103—21no—
246C23×C103—21no—
247C23×C103—41no—
248C23×C103—41no—
249C23×C103—41no—
250C23×C103—161no—
251C23×C1032−1+411yescharacteristic
252Q8×C103—21no—
253Q8×C103—21no—
254Q8×C103—21no—
255Q8×C103—41no—
256Q8×C103—41no—
257Q8×C103—41no—
258Q8×C103—41no—
259Q8×C103#12112yes—
260D4×C103—22no—
261D4×C103—22no—
262D4×C103—21no—
263D4×C103—21no—
264D4×C103—21no—
265D4×C103—41no—
266D4×C103—41no—
267D4×C103—41no—
268D4×C103—41no—
269D4×C103—41no—
270D4×C103—41no—
271D4×C103#12112yes—
272C2×C4×C103—21no—
273C2×C4×C103—22no—
274C2×C4×C103—22no—
275C2×C4×C103—21no—
276C2×C4×C103—41no—
277C2×C4×C103—41no—
278C2×C4×C103—41no—
279C2×C4×C103—41no—
280C2×C4×C103—41no—
281C2×C4×C103—41no—
282C2×C4×C103C22×D411yescharacteristic
283C2×C4×C103C22×D411yescharacteristic
284C2×C4×C103C22×D411yescharacteristic
285C2×C4×C103C2×#4111yescharacteristic
286C2×C4×C103C2×#4111yescharacteristic
287C2×C4×C103H(5,𝔽2)11yescharacteristic
288C8×C103—22no—
289C8×C103—22no—
290C8×C103—22no—
291C8×C103—22no—
292C8×C103—41no—
293C8×C103—41no—
294C8×C103—41no—
295C8×C103—41no—
296C8×C103—41no—
297C8×C103#12111yescharacteristic
298C8×C103#12111yescharacteristic
299C8×C103#12111yescharacteristic
300C8×C103#12111yescharacteristic
301C22×C103—22no—
302C22×C103—41no—
303C22×C103—41no—
304C22×C103—81no—
305C22×C103—81no—
306C22×C103—81no—
307C22×C103—161no—
308C22×C103—161no—
309C22×C103—161no—
310C22×C103#53711yescharacteristic
311C22×C103#54711yescharacteristic
312C22×C103#54811yescharacteristic
313C4×C103—22no—
314C4×C103—41no—
315C4×C103—81no—
316C4×C103—81no—
317C4×C103C2×#12111yescharacteristic
318C4×C103C2×#12111yescharacteristic
319C4×C103D4211yescharacteristic
320C4×C103#55311yescharacteristic
321#24808C10311yesmaximal, characteristic, direct product factor, Sylow
322C2×C103—21no—
323C2×C103—21no—
324C2×C103—21no—
325C2×C103—42no—
326C2×C103—81no—
327C2×C103—161no—
328C2×C103#241611yescharacteristic
329#3069C2×C10311yescharacteristic, complemented
330#3068C2×C10311yescharacteristic
331C2×#471C2×C10311yescharacteristic, complemented
332C2×#471C2×C10311yescharacteristic, complemented
333#2955C2×C10311yescharacteristic, complemented
334#2916C2×C10311yescharacteristic, complemented
335#2070C2×C10311yescharacteristic, complemented
336#2069C2×C10311yescharacteristic, complemented
337#2049C2×C10311yescharacteristic, complemented
338#2048C2×C10311yescharacteristic, complemented
339#1977C2×C10311yescharacteristic, complemented
340#1953C2×C10311yescharacteristic, complemented
341#1903C2×C10311yescharacteristic, complemented
342#1902C2×C10311yescharacteristic, complemented
343#1813C2×C10311yescharacteristic, complemented
344C103#2480811yescharacteristic, direct product factor, Sylow
345#575C22×C10311yescharacteristic
346C2×#137C22×C10311yescharacteristic
347C2×#137C22×C10311yescharacteristic
348C2×AGL(1,ℤ/8)C22×C10311yescharacteristic
349C2×AGL(1,ℤ/8)C22×C10311yescharacteristic
350C22×SD16C22×C10311yescharacteristic
351#568C22×C10311yescharacteristic
352#568C22×C10311yescharacteristic
353C2×#131C22×C10311yescharacteristic
354C2×#131C22×C10311yescharacteristic
355#473—22no—
356#472—22no—
357#471—22no—
358#471—22no—
359#471—22no—
360#471—22no—
361#471—22no—
362#471—22no—
363#444—22no—
364#443—22no—
365#430—22no—
366#430C22×C10311yescharacteristic
367#430C22×C10311yescharacteristic
368#430C22×C10311yescharacteristic
369#430C22×C10311yescharacteristic
370#430C22×C10311yescharacteristic
371C2×#108—22no—
372C2×#108C22×C10311yescharacteristic
373C2×#108C22×C10311yescharacteristic
374C2×#108C22×C10311yescharacteristic
375#421C22×C10311yescharacteristic
376#421C22×C10311yescharacteristic
377#419C22×C10311yescharacteristic
378#418C22×C10311yescharacteristic
379#413C22×C10311yescharacteristic
380#413C22×C10311yescharacteristic
381C2×#101C22×C10311yescharacteristic
382C2×#101C22×C10311yescharacteristic
383C2×#101C22×C10311yescharacteristic
384C2×#100C22×C10311yescharacteristic
385C2×#100C22×C10311yescharacteristic
386C2×#100C22×C10311yescharacteristic
387#405C22×C10311yescharacteristic
388#344C22×C10311yescharacteristic
389#344C22×C10311yescharacteristic
390#338C22×C10311yescharacteristic
391#338C22×C10311yescharacteristic
392C2×#41C23×C10311yescharacteristic
393C2×#41C23×C10311yescharacteristic
394C22×Q8C23×C10311yescharacteristic
395C22×D4C23×C10311yescharacteristic
396#137—21no—
397#137—22no—
398#137—22no—
399#137—22no—
400#137—41no—
401#137D4×C10312yes—
402AGL(1,ℤ/8)—21no—
403AGL(1,ℤ/8)—22no—
404AGL(1,ℤ/8)—22no—
405AGL(1,ℤ/8)—22no—
406AGL(1,ℤ/8)—41no—
407AGL(1,ℤ/8)D4×C10312yes—
408#135—22no—
409C2×Q16—21no—
410C2×Q16—21no—
411C2×SD16—21no—
412C2×SD16—21no—
413C2×SD16—21no—
414C2×SD16—21no—
415C2×SD16—21no—
416C2×SD16—21no—
417C2×SD16—21no—
418C2×SD16—21no—
419C2×SD16—21no—
420C2×SD16—21no—
421C2×D8—21no—
422C2×D8—21no—
423#131—21no—
424#131—21no—
425#131—22no—
426#131—22no—
427#131—21no—
428#131—21no—
429#131—21no—
430#131—21no—
431#131—41no—
432#131—41no—
433#131D4×C10312yes—
434#131D4×C10312yes—
435C2×M16—21no—
436C2×M16—21no—
437C2×M16—22no—
438C2×M16—22no—
439C2×M16C23×C10311yescharacteristic
440C2×M16C23×C10311yescharacteristic
441C2×M16C23×C10311yescharacteristic
442C2×M16C23×C10311yescharacteristic
443C2×M16C23×C10311yescharacteristic
444C2×M16C23×C10311yescharacteristic
445C2×M16C23×C10311yescharacteristic
446C2×M16C23×C10311yescharacteristic
447C2×M16C23×C10311yescharacteristic
448C22×C8—21no—
449C22×C8—21no—
450C22×C8C23×C10311yescharacteristic
451#117C23×C10311yescharacteristic
452#108—22no—
453#108—22no—
454#108—22no—
455#108—22no—
456#108—22no—
457#108—21no—
458#108—21no—
459#108—21no—
460#108—21no—
461#108D4×C10312yes—
462#108D4×C10312yes—
463#104—22no—
464#104—22no—
465#103—41no—
466#102—41no—
467#101—21no—
468#101—21no—
469#101—22no—
470#101—22no—
471#101—22no—
472#100—21no—
473#100—21no—
474#100—22no—
475#100—22no—
476#100—22no—
477#97—21no—
478C4×C8—21no—
479C24—21no—
480#41—21no—
481#41—21no—
482#41—21no—
483#41—21no—
484#41—21no—
485#41—21no—
486#41C2×D4×C10312yes—
487#41C2×D4×C10312yes—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8C2×D4×C10311yescharacteristic
495C2×Q8#41×C10311yescharacteristic
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4C2×D4×C10311yescharacteristic
505C2×D4#41×C10311yescharacteristic
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4C24×C10311yescharacteristic
510Q16—22no—
511Q16—42no—
512Q16—42no—
513SD16—22no—
514SD16—22no—
515SD16—42no—
516SD16—42no—
517SD16—42no—
518SD16—42no—
519SD16—41no—
520SD16—41no—
521SD16—41no—
522SD16—41no—
523D8—22no—
524D8—42no—
525D8—42no—
526M16—21no—
527M16—21no—
528M16—21no—
529M16—21no—
530M16—22no—
531M16—22no—
532M16—21no—
533M16—21no—
534M16—21no—
535M16—21no—
536M16—21no—
537M16—21no—
538M16—21no—
539M16—21no—
540M16—21no—
541M16—21no—
542M16—42no—
543M16—42no—
544M16—41no—
545M16—41no—
546M16C2×D4×C10312yes—
547M16C2×D4×C10312yes—
548M16C2×D4×C10312yes—
549M16C2×D4×C10312yes—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—42no—
562C2×C8—42no—
563C2×C8—41no—
564C2×C8—41no—
565C2×C8C2×D4×C10311yescharacteristic
566C2×C8C2×D4×C10311yescharacteristic
567C2×C8C2×D4×C10311yescharacteristic
568C2×C8C2×D4×C10311yescharacteristic
569C2×C8#41×C10311yescharacteristic
570C2×C8#41×C10311yescharacteristic
571C4⋊C4—21no—
572C22⋊C4—21no—
573C42—21no—
574C23—21no—
575C23—21no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—161no—
580C232−1+4×C10311yescharacteristic
581Q8—21no—
582Q8—21no—
583Q8—21no—
584Q8—41no—
585Q8—41no—
586Q8—41no—
587Q8—41no—
588Q8#121×C10312yes—
589D4—22no—
590D4—22no—
591D4—21no—
592D4—21no—
593D4—21no—
594D4—41no—
595D4—41no—
596D4—41no—
597D4—41no—
598D4—41no—
599D4—41no—
600D4#121×C10312yes—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4C22×D4×C10311yescharacteristic
612C2×C4C22×D4×C10311yescharacteristic
613C2×C4C22×D4×C10311yescharacteristic
614C2×C4C2×#41×C10311yescharacteristic
615C2×C4C2×#41×C10311yescharacteristic
616C2×C4H(5,𝔽2)×C10311yescharacteristic
617C8—22no—
618C8—22no—
619C8—22no—
620C8—22no—
621C8—41no—
622C8—41no—
623C8—41no—
624C8—41no—
625C8—41no—
626C8#121×C10311yescharacteristic
627C8#121×C10311yescharacteristic
628C8#121×C10311yescharacteristic
629C8#121×C10311yescharacteristic
630C22—22no—
631C22—41no—
632C22—41no—
633C22—81no—
634C22—81no—
635C22—81no—
636C22—161no—
637C22—161no—
638C22—161no—
639C22#537×C10311yescharacteristic
640C22#547×C10311yescharacteristic
641C22#548×C10311yescharacteristic
642C4—22no—
643C4—41no—
644C4—81no—
645C4—81no—
646C4C2×#121×C10311yescharacteristic
647C4C2×#121×C10311yescharacteristic
648C4D42×C10311yescharacteristic
649C4#553×C10311yescharacteristic
650C2—21no—
651C2—21no—
652C2—21no—
653C2—42no—
654C2—81no—
655C2—161no—
656C2C103×#241611yescharacteristic
subgroupG/H
center, socleC2×C103#2416
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC103×#3068C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C103 ◁ C22×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#3069C2semidirect
3. C2×#471×C103C2semidirect
4. C2×#471×C103C2semidirect
5. C103×#2955C2semidirect
6. C103×#2916C2semidirect
7. C103×#2070C2semidirect
8. C103×#2069C2semidirect
9. C103×#2049C2semidirect
10. C103×#2048C2semidirect
11. C103×#1977C2semidirect
12. C103×#1953C2semidirect
13. C103×#1903C2semidirect
14. C103×#1902C2semidirect
15. C103×#1813C2semidirect
321. #24808C103direct (N × H)
329. #3069C2×C103semidirect
331. C2×#471C2×C103semidirect
332. C2×#471C2×C103semidirect
333. #2955C2×C103semidirect
334. #2916C2×C103semidirect
335. #2070C2×C103semidirect
336. #2069C2×C103semidirect
337. #2049C2×C103semidirect
338. #2048C2×C103semidirect
339. #1977C2×C103semidirect
340. #1953C2×C103semidirect
341. #1903C2×C103semidirect
342. #1902C2×C103semidirect
343. #1813C2×C103semidirect
344. C103#24808direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#30692
C103×#30682
C2×#471×C1032
C103×#29552
C103×#29162
C103×#20702
C103×#20692
C103×#20492
C103×#20482
C103×#19772
C103×#19532
C103×#19032
C103×#19022
C103×#18132
#24808103