Finite Group Databasebeta

← C101×#24808 #38806959

Subgroups — C101×#24808 #38806959

Order 25856.

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
1C101×#3069C211yesmaximal, characteristic, complemented
2C101×#3068C211yesmaximal, characteristic
3C2×#471×C101C211yesmaximal, characteristic, complemented
4C2×#471×C101C211yesmaximal, characteristic, complemented
5C101×#2955C211yesmaximal, characteristic, complemented
6C101×#2916C211yesmaximal, characteristic, complemented
7C101×#2070C211yesmaximal, characteristic, complemented
8C101×#2069C211yesmaximal, characteristic, complemented
9C101×#2049C211yesmaximal, characteristic, complemented
10C101×#2048C211yesmaximal, characteristic, complemented
11C101×#1977C211yesmaximal, characteristic, complemented
12C101×#1953C211yesmaximal, characteristic, complemented
13C101×#1903C211yesmaximal, characteristic, complemented
14C101×#1902C211yesmaximal, characteristic, complemented
15C101×#1813C211yesmaximal, characteristic, complemented
16#575×C101C2211yescharacteristic
17C2×#137×C101C2211yescharacteristic
18C2×#137×C101C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C101C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C101C2211yescharacteristic
21C22×SD16×C101C2211yescharacteristic
22#568×C101C2211yescharacteristic
23#568×C101C2211yescharacteristic
24C2×#131×C101C2211yescharacteristic
25C2×#131×C101C2211yescharacteristic
26#473×C101—22no—
27#472×C101—22no—
28#471×C101—22no—
29#471×C101—22no—
30#471×C101—22no—
31#471×C101—22no—
32#471×C101—22no—
33#471×C101—22no—
34#444×C101—22no—
35#443×C101—22no—
36#430×C101—22no—
37#430×C101C2211yescharacteristic
38#430×C101C2211yescharacteristic
39#430×C101C2211yescharacteristic
40#430×C101C2211yescharacteristic
41#430×C101C2211yescharacteristic
42C2×#108×C101—22no—
43C2×#108×C101C2211yescharacteristic
44C2×#108×C101C2211yescharacteristic
45C2×#108×C101C2211yescharacteristic
46#421×C101C2211yescharacteristic
47#421×C101C2211yescharacteristic
48#419×C101C2211yescharacteristic
49#418×C101C2211yescharacteristic
50#413×C101C2211yescharacteristic
51#413×C101C2211yescharacteristic
52C2×#101×C101C2211yescharacteristic
53C2×#101×C101C2211yescharacteristic
54C2×#101×C101C2211yescharacteristic
55C2×#100×C101C2211yescharacteristic
56C2×#100×C101C2211yescharacteristic
57C2×#100×C101C2211yescharacteristic
58#405×C101C2211yescharacteristic
59#344×C101C2211yescharacteristic
60#344×C101C2211yescharacteristic
61#338×C101C2211yescharacteristic
62#338×C101C2211yescharacteristic
63C2×#41×C101C2311yescharacteristic
64C2×#41×C101C2311yescharacteristic
65C22×Q8×C101C2311yescharacteristic
66C22×D4×C101C2311yescharacteristic
67#137×C101—21no—
68#137×C101—22no—
69#137×C101—22no—
70#137×C101—22no—
71#137×C101—41no—
72#137×C101D412yes—
73AGL(1,ℤ/8)×C101—21no—
74AGL(1,ℤ/8)×C101—22no—
75AGL(1,ℤ/8)×C101—22no—
76AGL(1,ℤ/8)×C101—22no—
77AGL(1,ℤ/8)×C101—41no—
78AGL(1,ℤ/8)×C101D412yes—
79#135×C101—22no—
80C2×Q16×C101—21no—
81C2×Q16×C101—21no—
82C2×SD16×C101—21no—
83C2×SD16×C101—21no—
84C2×SD16×C101—21no—
85C2×SD16×C101—21no—
86C2×SD16×C101—21no—
87C2×SD16×C101—21no—
88C2×SD16×C101—21no—
89C2×SD16×C101—21no—
90C2×SD16×C101—21no—
91C2×SD16×C101—21no—
92C2×D8×C101—21no—
93C2×D8×C101—21no—
94#131×C101—21no—
95#131×C101—21no—
96#131×C101—22no—
97#131×C101—22no—
98#131×C101—21no—
99#131×C101—21no—
100#131×C101—21no—
101#131×C101—21no—
102#131×C101—41no—
103#131×C101—41no—
104#131×C101D412yes—
105#131×C101D412yes—
106C2×M16×C101—21no—
107C2×M16×C101—21no—
108C2×M16×C101—22no—
109C2×M16×C101—22no—
110C2×M16×C101C2311yescharacteristic
111C2×M16×C101C2311yescharacteristic
112C2×M16×C101C2311yescharacteristic
113C2×M16×C101C2311yescharacteristic
114C2×M16×C101C2311yescharacteristic
115C2×M16×C101C2311yescharacteristic
116C2×M16×C101C2311yescharacteristic
117C2×M16×C101C2311yescharacteristic
118C2×M16×C101C2311yescharacteristic
119C22×C8×C101—21no—
120C22×C8×C101—21no—
121C22×C8×C101C2311yescharacteristic
122#117×C101C2311yescharacteristic
123#108×C101—22no—
124#108×C101—22no—
125#108×C101—22no—
126#108×C101—22no—
127#108×C101—22no—
128#108×C101—21no—
129#108×C101—21no—
130#108×C101—21no—
131#108×C101—21no—
132#108×C101D412yes—
133#108×C101D412yes—
134#104×C101—22no—
135#104×C101—22no—
136#103×C101—41no—
137#102×C101—41no—
138#101×C101—21no—
139#101×C101—21no—
140#101×C101—22no—
141#101×C101—22no—
142#101×C101—22no—
143#100×C101—21no—
144#100×C101—21no—
145#100×C101—22no—
146#100×C101—22no—
147#100×C101—22no—
148#97×C101—21no—
149C4×C8×C101—21no—
150C24×C101—21no—
151#41×C101—21no—
152#41×C101—21no—
153#41×C101—21no—
154#41×C101—21no—
155#41×C101—21no—
156#41×C101—21no—
157#41×C101C2×D412yes—
158#41×C101C2×D412yes—
159C2×Q8×C101—21no—
160C2×Q8×C101—21no—
161C2×Q8×C101—21no—
162C2×Q8×C101—21no—
163C2×Q8×C101—21no—
164C2×Q8×C101—21no—
165C2×Q8×C101C2×D411yescharacteristic
166C2×Q8×C101#4111yescharacteristic
167C2×D4×C101—21no—
168C2×D4×C101—21no—
169C2×D4×C101—21no—
170C2×D4×C101—21no—
171C2×D4×C101—21no—
172C2×D4×C101—21no—
173C2×D4×C101—21no—
174C2×D4×C101—21no—
175C2×D4×C101C2×D411yescharacteristic
176C2×D4×C101#4111yescharacteristic
177C22×C4×C101—21no—
178C22×C4×C101—21no—
179C22×C4×C101—21no—
180C22×C4×C101C2411yescharacteristic
181Q16×C101—22no—
182Q16×C101—42no—
183Q16×C101—42no—
184SD16×C101—22no—
185SD16×C101—22no—
186SD16×C101—42no—
187SD16×C101—42no—
188SD16×C101—42no—
189SD16×C101—42no—
190SD16×C101—41no—
191SD16×C101—41no—
192SD16×C101—41no—
193SD16×C101—41no—
194D8×C101—22no—
195D8×C101—42no—
196D8×C101—42no—
197M16×C101—21no—
198M16×C101—21no—
199M16×C101—21no—
200M16×C101—21no—
201M16×C101—22no—
202M16×C101—22no—
203M16×C101—21no—
204M16×C101—21no—
205M16×C101—21no—
206M16×C101—21no—
207M16×C101—21no—
208M16×C101—21no—
209M16×C101—21no—
210M16×C101—21no—
211M16×C101—21no—
212M16×C101—21no—
213M16×C101—42no—
214M16×C101—42no—
215M16×C101—41no—
216M16×C101—41no—
217M16×C101C2×D412yes—
218M16×C101C2×D412yes—
219M16×C101C2×D412yes—
220M16×C101C2×D412yes—
221C2×C8×C101—21no—
222C2×C8×C101—21no—
223C2×C8×C101—21no—
224C2×C8×C101—21no—
225C2×C8×C101—22no—
226C2×C8×C101—22no—
227C2×C8×C101—21no—
228C2×C8×C101—21no—
229C2×C8×C101—21no—
230C2×C8×C101—21no—
231C2×C8×C101—21no—
232C2×C8×C101—42no—
233C2×C8×C101—42no—
234C2×C8×C101—41no—
235C2×C8×C101—41no—
236C2×C8×C101C2×D411yescharacteristic
237C2×C8×C101C2×D411yescharacteristic
238C2×C8×C101C2×D411yescharacteristic
239C2×C8×C101C2×D411yescharacteristic
240C2×C8×C101#4111yescharacteristic
241C2×C8×C101#4111yescharacteristic
242C4⋊C4×C101—21no—
243C22⋊C4×C101—21no—
244C42×C101—21no—
245C23×C101—21no—
246C23×C101—21no—
247C23×C101—41no—
248C23×C101—41no—
249C23×C101—41no—
250C23×C101—161no—
251C23×C1012−1+411yescharacteristic
252Q8×C101—21no—
253Q8×C101—21no—
254Q8×C101—21no—
255Q8×C101—41no—
256Q8×C101—41no—
257Q8×C101—41no—
258Q8×C101—41no—
259Q8×C101#12112yes—
260D4×C101—22no—
261D4×C101—22no—
262D4×C101—21no—
263D4×C101—21no—
264D4×C101—21no—
265D4×C101—41no—
266D4×C101—41no—
267D4×C101—41no—
268D4×C101—41no—
269D4×C101—41no—
270D4×C101—41no—
271D4×C101#12112yes—
272C2×C4×C101—21no—
273C2×C4×C101—22no—
274C2×C4×C101—22no—
275C2×C4×C101—21no—
276C2×C4×C101—41no—
277C2×C4×C101—41no—
278C2×C4×C101—41no—
279C2×C4×C101—41no—
280C2×C4×C101—41no—
281C2×C4×C101—41no—
282C2×C4×C101C22×D411yescharacteristic
283C2×C4×C101C22×D411yescharacteristic
284C2×C4×C101C22×D411yescharacteristic
285C2×C4×C101C2×#4111yescharacteristic
286C2×C4×C101C2×#4111yescharacteristic
287C2×C4×C101H(5,𝔽2)11yescharacteristic
288C8×C101—22no—
289C8×C101—22no—
290C8×C101—22no—
291C8×C101—22no—
292C8×C101—41no—
293C8×C101—41no—
294C8×C101—41no—
295C8×C101—41no—
296C8×C101—41no—
297C8×C101#12111yescharacteristic
298C8×C101#12111yescharacteristic
299C8×C101#12111yescharacteristic
300C8×C101#12111yescharacteristic
301C22×C101—22no—
302C22×C101—41no—
303C22×C101—41no—
304C22×C101—81no—
305C22×C101—81no—
306C22×C101—81no—
307C22×C101—161no—
308C22×C101—161no—
309C22×C101—161no—
310C22×C101#53711yescharacteristic
311C22×C101#54711yescharacteristic
312C22×C101#54811yescharacteristic
313C4×C101—22no—
314C4×C101—41no—
315C4×C101—81no—
316C4×C101—81no—
317C4×C101C2×#12111yescharacteristic
318C4×C101C2×#12111yescharacteristic
319C4×C101D4211yescharacteristic
320C4×C101#55311yescharacteristic
321#24808C10111yesmaximal, characteristic, direct product factor, Sylow
322C2×C101—21no—
323C2×C101—21no—
324C2×C101—21no—
325C2×C101—42no—
326C2×C101—81no—
327C2×C101—161no—
328C2×C101#241611yescharacteristic
329#3069C2×C10111yescharacteristic, complemented
330#3068C2×C10111yescharacteristic
331C2×#471C2×C10111yescharacteristic, complemented
332C2×#471C2×C10111yescharacteristic, complemented
333#2955C2×C10111yescharacteristic, complemented
334#2916C2×C10111yescharacteristic, complemented
335#2070C2×C10111yescharacteristic, complemented
336#2069C2×C10111yescharacteristic, complemented
337#2049C2×C10111yescharacteristic, complemented
338#2048C2×C10111yescharacteristic, complemented
339#1977C2×C10111yescharacteristic, complemented
340#1953C2×C10111yescharacteristic, complemented
341#1903C2×C10111yescharacteristic, complemented
342#1902C2×C10111yescharacteristic, complemented
343#1813C2×C10111yescharacteristic, complemented
344C101#2480811yescharacteristic, direct product factor, Sylow
345#575C22×C10111yescharacteristic
346C2×#137C22×C10111yescharacteristic
347C2×#137C22×C10111yescharacteristic
348C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
349C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
350C22×SD16C22×C10111yescharacteristic
351#568C22×C10111yescharacteristic
352#568C22×C10111yescharacteristic
353C2×#131C22×C10111yescharacteristic
354C2×#131C22×C10111yescharacteristic
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×C10111yescharacteristic
367#430C22×C10111yescharacteristic
368#430C22×C10111yescharacteristic
369#430C22×C10111yescharacteristic
370#430C22×C10111yescharacteristic
371C2×#108—22no—
372C2×#108C22×C10111yescharacteristic
373C2×#108C22×C10111yescharacteristic
374C2×#108C22×C10111yescharacteristic
375#421C22×C10111yescharacteristic
376#421C22×C10111yescharacteristic
377#419C22×C10111yescharacteristic
378#418C22×C10111yescharacteristic
379#413C22×C10111yescharacteristic
380#413C22×C10111yescharacteristic
381C2×#101C22×C10111yescharacteristic
382C2×#101C22×C10111yescharacteristic
383C2×#101C22×C10111yescharacteristic
384C2×#100C22×C10111yescharacteristic
385C2×#100C22×C10111yescharacteristic
386C2×#100C22×C10111yescharacteristic
387#405C22×C10111yescharacteristic
388#344C22×C10111yescharacteristic
389#344C22×C10111yescharacteristic
390#338C22×C10111yescharacteristic
391#338C22×C10111yescharacteristic
392C2×#41C23×C10111yescharacteristic
393C2×#41C23×C10111yescharacteristic
394C22×Q8C23×C10111yescharacteristic
395C22×D4C23×C10111yescharacteristic
396#137—21no—
397#137—22no—
398#137—22no—
399#137—22no—
400#137—41no—
401#137D4×C10112yes—
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×C10112yes—
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×C10112yes—
434#131D4×C10112yes—
435C2×M16—21no—
436C2×M16—21no—
437C2×M16—22no—
438C2×M16—22no—
439C2×M16C23×C10111yescharacteristic
440C2×M16C23×C10111yescharacteristic
441C2×M16C23×C10111yescharacteristic
442C2×M16C23×C10111yescharacteristic
443C2×M16C23×C10111yescharacteristic
444C2×M16C23×C10111yescharacteristic
445C2×M16C23×C10111yescharacteristic
446C2×M16C23×C10111yescharacteristic
447C2×M16C23×C10111yescharacteristic
448C22×C8—21no—
449C22×C8—21no—
450C22×C8C23×C10111yescharacteristic
451#117C23×C10111yescharacteristic
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×C10112yes—
462#108D4×C10112yes—
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×C10112yes—
487#41C2×D4×C10112yes—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8C2×D4×C10111yescharacteristic
495C2×Q8#41×C10111yescharacteristic
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×C10111yescharacteristic
505C2×D4#41×C10111yescharacteristic
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4C24×C10111yescharacteristic
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×C10112yes—
547M16C2×D4×C10112yes—
548M16C2×D4×C10112yes—
549M16C2×D4×C10112yes—
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×C10111yescharacteristic
566C2×C8C2×D4×C10111yescharacteristic
567C2×C8C2×D4×C10111yescharacteristic
568C2×C8C2×D4×C10111yescharacteristic
569C2×C8#41×C10111yescharacteristic
570C2×C8#41×C10111yescharacteristic
571C4⋊C4—21no—
572C22⋊C4—21no—
573C42—21no—
574C23—21no—
575C23—21no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—161no—
580C232−1+4×C10111yescharacteristic
581Q8—21no—
582Q8—21no—
583Q8—21no—
584Q8—41no—
585Q8—41no—
586Q8—41no—
587Q8—41no—
588Q8#121×C10112yes—
589D4—22no—
590D4—22no—
591D4—21no—
592D4—21no—
593D4—21no—
594D4—41no—
595D4—41no—
596D4—41no—
597D4—41no—
598D4—41no—
599D4—41no—
600D4#121×C10112yes—
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×C10111yescharacteristic
612C2×C4C22×D4×C10111yescharacteristic
613C2×C4C22×D4×C10111yescharacteristic
614C2×C4C2×#41×C10111yescharacteristic
615C2×C4C2×#41×C10111yescharacteristic
616C2×C4H(5,𝔽2)×C10111yescharacteristic
617C8—22no—
618C8—22no—
619C8—22no—
620C8—22no—
621C8—41no—
622C8—41no—
623C8—41no—
624C8—41no—
625C8—41no—
626C8#121×C10111yescharacteristic
627C8#121×C10111yescharacteristic
628C8#121×C10111yescharacteristic
629C8#121×C10111yescharacteristic
630C22—22no—
631C22—41no—
632C22—41no—
633C22—81no—
634C22—81no—
635C22—81no—
636C22—161no—
637C22—161no—
638C22—161no—
639C22#537×C10111yescharacteristic
640C22#547×C10111yescharacteristic
641C22#548×C10111yescharacteristic
642C4—22no—
643C4—41no—
644C4—81no—
645C4—81no—
646C4C2×#121×C10111yescharacteristic
647C4C2×#121×C10111yescharacteristic
648C4D42×C10111yescharacteristic
649C4#553×C10111yescharacteristic
650C2—21no—
651C2—21no—
652C2—21no—
653C2—42no—
654C2—81no—
655C2—161no—
656C2C101×#241611yescharacteristic
subgroupG/H
center, socleC2×C101#2416
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC101×#3068C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C101 ◁ C22×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#3069C2semidirect
3. C2×#471×C101C2semidirect
4. C2×#471×C101C2semidirect
5. C101×#2955C2semidirect
6. C101×#2916C2semidirect
7. C101×#2070C2semidirect
8. C101×#2069C2semidirect
9. C101×#2049C2semidirect
10. C101×#2048C2semidirect
11. C101×#1977C2semidirect
12. C101×#1953C2semidirect
13. C101×#1903C2semidirect
14. C101×#1902C2semidirect
15. C101×#1813C2semidirect
321. #24808C101direct (N × H)
329. #3069C2×C101semidirect
331. C2×#471C2×C101semidirect
332. C2×#471C2×C101semidirect
333. #2955C2×C101semidirect
334. #2916C2×C101semidirect
335. #2070C2×C101semidirect
336. #2069C2×C101semidirect
337. #2049C2×C101semidirect
338. #2048C2×C101semidirect
339. #1977C2×C101semidirect
340. #1953C2×C101semidirect
341. #1903C2×C101semidirect
342. #1902C2×C101semidirect
343. #1813C2×C101semidirect
344. C101#24808direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#30692
C101×#30682
C2×#471×C1012
C101×#29552
C101×#29162
C101×#20702
C101×#20692
C101×#20492
C101×#20482
C101×#19772
C101×#19532
C101×#19032
C101×#19022
C101×#18132
#24808101