Finite Group Databasebeta

← C101×#19719 #38801870

Subgroups — C101×#19719 #38801870

Order 25856.

840 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3228C211yesmaximal, characteristic, complemented
2C101×#3208C211yesmaximal, characteristic, complemented
3C101×#3207C211yesmaximal, characteristic, complemented
4C101×#3205C211yesmaximal, characteristic, complemented
5C101×#3182C211yesmaximal, characteristic, complemented
6C101×#3151C211yesmaximal, characteristic, complemented
7C101×#1721C211yesmaximal, characteristic, complemented
8C101×#1721C211yesmaximal, characteristic, complemented
9C101×#1719C211yesmaximal, characteristic, complemented
10C101×#1717C211yesmaximal, characteristic, complemented
11C101×#1715C211yesmaximal, characteristic, complemented
12C101×#1714C211yesmaximal, characteristic, complemented
13C101×#1706C211yesmaximal, characteristic, complemented
14C101×#1706C211yesmaximal, characteristic, complemented
15C101×#1453C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C101—22no—
17#533×C101C2211yescharacteristic
18#532×C101C2211yescharacteristic
19#532×C101C2211yescharacteristic
20C2×#127×C101C2211yescharacteristic
21#500×C101C2211yescharacteristic, complemented
22#500×C101C2211yescharacteristic, complemented
23#498×C101C2211yescharacteristic, complemented
24#496×C101—22no—
25#493×C101C2211yescharacteristic
26#493×C101C2211yescharacteristic
27#493×C101C2211yescharacteristic
28#493×C101C2211yescharacteristic
29#493×C101C2211yescharacteristic, complemented
30#492×C101C2211yescharacteristic
31#492×C101C2211yescharacteristic
32#492×C101C2211yescharacteristic
33#492×C101C2211yescharacteristic
34#492×C101C2211yescharacteristic, complemented
35#492×C101C2211yescharacteristic, complemented
36#487×C101C2211yescharacteristic, complemented
37#487×C101C2211yescharacteristic, complemented
38#486×C101C2211yescharacteristic
39#486×C101C2211yescharacteristic
40#486×C101C2211yescharacteristic
41#486×C101C2211yescharacteristic
42#486×C101C2211yescharacteristic, complemented
43#486×C101C2211yescharacteristic, complemented
44#486×C101C2211yescharacteristic, complemented
45#486×C101C2211yescharacteristic, complemented
46#482×C101—22no—
47#478×C101—22no—
48#468×C101—22no—
49#463×C101—22no—
50#460×C101—22no—
51#459×C101—22no—
52#450×C101—22no—
53#449×C101—22no—
54#447×C101—22no—
55#440×C101—22no—
56#431×C101C2211yescharacteristic
57#431×C101C2211yescharacteristic
58C4×M16×C101C2211yescharacteristic
59#322×C101C2211yescharacteristic, complemented
60#322×C101C2211yescharacteristic, complemented
61#322×C101C2211yescharacteristic, complemented
62C82×C101C2211yescharacteristic, complemented
63C2×#41×C101—21no—
64C2×#41×C101—21no—
65C22×D4×C101—21no—
66C22×D4×C101—21no—
67C22×D4×C101—21no—
68AGL(1,ℤ/8)×C101—48no—
69C2×SD16×C101—22no—
70C2×SD16×C101—22no—
71C2×SD16×C101—22no—
72C2×SD16×C101—22no—
73C2×SD16×C101—22no—
74C2×SD16×C101—22no—
75C2×D8×C101—22no—
76C2×D8×C101—22no—
77C2×D8×C101—22no—
78C2×D8×C101—22no—
79C2×D8×C101—22no—
80C2×M16×C101D412yes—
81C4⋊Q8×C101C2311yescharacteristic
82C4⋊Q8×C101C2311yescharacteristic
83C4⋊Q8×C101C2311yescharacteristic
84C4⋊Q8×C101C2311yescharacteristic
85#127×C101—21no—
86#127×C101—21no—
87#127×C101—21no—
88#127×C101C2311yescharacteristic
89#127×C101C2311yescharacteristic
90#127×C101C2311yescharacteristic
91#127×C101C2311yescharacteristic
92#125×C101—21no—
93#124×C101—21no—
94#124×C101—21no—
95C22⋊Q8×C101—21no—
96C22⋊Q8×C101—21no—
97#121×C101—21no—
98#121×C101—21no—
99#121×C101—21no—
100#121×C101—21no—
101C4×Q8×C101—21no—
102C4×Q8×C101—21no—
103C4×D4×C101—21no—
104C4×D4×C101—21no—
105C4×D4×C101—21no—
106C4×D4×C101—21no—
107#117×C101—21no—
108C2×C42×C101C2311yescharacteristic
109#107×C101—22no—
110#107×C101—22no—
111#106×C101—22no—
112C4⋊C8×C101D412yes—
113C4⋊C8×C101D412yes—
114#103×C101—22no—
115#103×C101—22no—
116#102×C101—22no—
117#102×C101—22no—
118#102×C101—22no—
119#102×C101—22no—
120#102×C101—22no—
121#102×C101—22no—
122#102×C101—22no—
123#102×C101—22no—
124C22⋊C8×C101D412yes—
125C22⋊C8×C101D412yes—
126#97×C101D412yes—
127C4×C8×C101C2311yescharacteristic
128C4×C8×C101C2311yescharacteristic
129C4×C8×C101C2311yescharacteristic
130C4×C8×C101C2311yescharacteristic
131C4×C8×C101C2311yescharacteristic
132C4×C8×C101C2311yescharacteristic
133C24×C101—41no—
134#41×C101—44no—
135#41×C101—82no—
136C2×Q8×C101—21no—
137C2×Q8×C101—21no—
138C2×Q8×C101—21no—
139C2×Q8×C101—21no—
140C2×D4×C101—21no—
141C2×D4×C101—21no—
142C2×D4×C101—21no—
143C2×D4×C101—21no—
144C2×D4×C101—21no—
145C2×D4×C101—21no—
146C2×D4×C101—21no—
147C2×D4×C101—21no—
148C2×D4×C101—21no—
149C2×D4×C101—21no—
150C2×D4×C101—21no—
151C2×D4×C101—21no—
152C2×D4×C101—44no—
153C2×D4×C101—41no—
154C2×D4×C101—41no—
155C2×D4×C101—41no—
156C2×D4×C101—41no—
157C2×D4×C101—41no—
158C2×D4×C101—82no—
159C2×D4×C101—82no—
160C22×C4×C101—41no—
161C22×C4×C101—41no—
162C22×C4×C101C2×D411yescharacteristic
163C22×C4×C101C2×D411yescharacteristic
164C22×C4×C101C2×D411yescharacteristic
165SD16×C101—44no—
166SD16×C101—44no—
167SD16×C101—44no—
168SD16×C101—82no—
169SD16×C101—82no—
170SD16×C101—82no—
171D8×C101—44no—
172D8×C101—44no—
173D8×C101—82no—
174D8×C101—82no—
175D8×C101—82no—
176M16×C101—24no—
177C2×C8×C101C2×D412yes—
178C2×C8×C101C2×D412yes—
179C2×C8×C101C2×D412yes—
180C2×C8×C101C2×D412yes—
181C2×C8×C101C2×D412yes—
182C2×C8×C101C2×D412yes—
183C4⋊C4×C101—21no—
184C4⋊C4×C101—21no—
185C4⋊C4×C101—21no—
186C4⋊C4×C101—21no—
187C4⋊C4×C101—21no—
188C4⋊C4×C101—21no—
189C4⋊C4×C101—21no—
190C4⋊C4×C101—21no—
191C4⋊C4×C101—41no—
192C4⋊C4×C101—41no—
193C22⋊C4×C101—41no—
194C22⋊C4×C101—41no—
195C22⋊C4×C101—41no—
196C22⋊C4×C101—41no—
197C22⋊C4×C101—41no—
198C42×C101—41no—
199C42×C101C2×D411yescharacteristic
200C42×C101C2×D411yescharacteristic
201C42×C101C2×D411yescharacteristic
202C42×C101C2411yescharacteristic
203C23×C101—41no—
204C23×C101—41no—
205C23×C101—41no—
206C23×C101—41no—
207C23×C101—82no—
208C23×C101—82no—
209C23×C101—82no—
210C23×C101#12711yescharacteristic
211Q8×C101—42no—
212Q8×C101—42no—
213Q8×C101—42no—
214Q8×C101—42no—
215D4×C101—42no—
216D4×C101—42no—
217D4×C101—42no—
218D4×C101—42no—
219D4×C101—42no—
220D4×C101—42no—
221D4×C101—42no—
222D4×C101—42no—
223D4×C101—42no—
224D4×C101—42no—
225D4×C101—42no—
226D4×C101—42no—
227D4×C101—82no—
228D4×C101—82no—
229D4×C101—82no—
230D4×C101—82no—
231D4×C101—82no—
232C2×C4×C101—22no—
233C2×C4×C101—22no—
234C2×C4×C101—22no—
235C2×C4×C101—41no—
236C2×C4×C101—41no—
237C2×C4×C101—41no—
238C2×C4×C101—41no—
239C2×C4×C101—82no—
240C2×C4×C101—82no—
241C2×C4×C101#12711yescharacteristic
242C2×C4×C101#12711yescharacteristic
243C2×C4×C101#12711yescharacteristic
244C2×C4×C101C22×D411yescharacteristic
245C2×C4×C101C22×D411yescharacteristic
246C2×C4×C101C22×D411yescharacteristic
247C8×C101—22no—
248C8×C101—22no—
249C8×C101—22no—
250C8×C101—22no—
251C8×C101—22no—
252C8×C101AGL(1,ℤ/8)14yes—
253C22×C101—21no—
254C22×C101—21no—
255C22×C101—21no—
256C22×C101—81no—
257C22×C101—81no—
258C22×C101—81no—
259C22×C101—81no—
260C22×C101—81no—
261C22×C101—81no—
262C22×C101—81no—
263C22×C101—81no—
264C22×C101—81no—
265C22×C101—81no—
266C22×C101—81no—
267C22×C101—81no—
268C22×C101—164no—
269C22×C101C2×#12711yescharacteristic
270C4×C101—21no—
271C4×C101—21no—
272C4×C101—21no—
273C4×C101—81no—
274C4×C101—81no—
275C4×C101—81no—
276C4×C101—81no—
277C4×C101C2×AGL(1,ℤ/8)12yes—
278C4×C101#57612yes—
279C4×C101#57712yes—
280#19719C10111yesmaximal, characteristic, direct product factor, Sylow
281C2×C101—41no—
282C2×C101—161no—
283C2×C101—161no—
284C2×C101—161no—
285C2×C101—161no—
286C2×C101#315111yescharacteristic
287C2×C101#315411yescharacteristic
288C2×C101#315511yescharacteristic
289#3228C2×C10111yescharacteristic, complemented
290#3208C2×C10111yescharacteristic, complemented
291#3207C2×C10111yescharacteristic, complemented
292#3205C2×C10111yescharacteristic, complemented
293#3182C2×C10111yescharacteristic, complemented
294#3151C2×C10111yescharacteristic, complemented
295#1721C2×C10111yescharacteristic, complemented
296#1721C2×C10111yescharacteristic, complemented
297#1719C2×C10111yescharacteristic, complemented
298#1717C2×C10111yescharacteristic, complemented
299#1715C2×C10111yescharacteristic, complemented
300#1714C2×C10111yescharacteristic, complemented
301#1706C2×C10111yescharacteristic, complemented
302#1706C2×C10111yescharacteristic, complemented
303#1453C2×C10111yescharacteristic, complemented
304C101#1971911yescharacteristic, direct product factor, Sylow
305C2×AGL(1,ℤ/8)—22no—
306#533C22×C10111yescharacteristic
307#532C22×C10111yescharacteristic
308#532C22×C10111yescharacteristic
309C2×#127C22×C10111yescharacteristic
310#500C22×C10111yescharacteristic, complemented
311#500C22×C10111yescharacteristic, complemented
312#498C22×C10111yescharacteristic, complemented
313#496—22no—
314#493C22×C10111yescharacteristic
315#493C22×C10111yescharacteristic
316#493C22×C10111yescharacteristic
317#493C22×C10111yescharacteristic
318#493C22×C10111yescharacteristic, complemented
319#492C22×C10111yescharacteristic
320#492C22×C10111yescharacteristic
321#492C22×C10111yescharacteristic
322#492C22×C10111yescharacteristic
323#492C22×C10111yescharacteristic, complemented
324#492C22×C10111yescharacteristic, complemented
325#487C22×C10111yescharacteristic, complemented
326#487C22×C10111yescharacteristic, complemented
327#486C22×C10111yescharacteristic
328#486C22×C10111yescharacteristic
329#486C22×C10111yescharacteristic
330#486C22×C10111yescharacteristic
331#486C22×C10111yescharacteristic, complemented
332#486C22×C10111yescharacteristic, complemented
333#486C22×C10111yescharacteristic, complemented
334#486C22×C10111yescharacteristic, complemented
335#482—22no—
336#478—22no—
337#468—22no—
338#463—22no—
339#460—22no—
340#459—22no—
341#450—22no—
342#449—22no—
343#447—22no—
344#440—22no—
345#431C22×C10111yescharacteristic
346#431C22×C10111yescharacteristic
347C4×M16C22×C10111yescharacteristic
348#322C22×C10111yescharacteristic, complemented
349#322C22×C10111yescharacteristic, complemented
350#322C22×C10111yescharacteristic, complemented
351C82C22×C10111yescharacteristic, complemented
352C2×#41—21no—
353C2×#41—21no—
354C22×D4—21no—
355C22×D4—21no—
356C22×D4—21no—
357AGL(1,ℤ/8)—48no—
358C2×SD16—22no—
359C2×SD16—22no—
360C2×SD16—22no—
361C2×SD16—22no—
362C2×SD16—22no—
363C2×SD16—22no—
364C2×D8—22no—
365C2×D8—22no—
366C2×D8—22no—
367C2×D8—22no—
368C2×D8—22no—
369C2×M16D4×C10112yes—
370C4⋊Q8C23×C10111yescharacteristic
371C4⋊Q8C23×C10111yescharacteristic
372C4⋊Q8C23×C10111yescharacteristic
373C4⋊Q8C23×C10111yescharacteristic
374#127—21no—
375#127—21no—
376#127—21no—
377#127C23×C10111yescharacteristic
378#127C23×C10111yescharacteristic
379#127C23×C10111yescharacteristic
380#127C23×C10111yescharacteristic
381#125—21no—
382#124—21no—
383#124—21no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386#121—21no—
387#121—21no—
388#121—21no—
389#121—21no—
390C4×Q8—21no—
391C4×Q8—21no—
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—21no—
395C4×D4—21no—
396#117—21no—
397C2×C42C23×C10111yescharacteristic
398#107—22no—
399#107—22no—
400#106—22no—
401C4⋊C8D4×C10112yes—
402C4⋊C8D4×C10112yes—
403#103—22no—
404#103—22no—
405#102—22no—
406#102—22no—
407#102—22no—
408#102—22no—
409#102—22no—
410#102—22no—
411#102—22no—
412#102—22no—
413C22⋊C8D4×C10112yes—
414C22⋊C8D4×C10112yes—
415#97D4×C10112yes—
416C4×C8C23×C10111yescharacteristic
417C4×C8C23×C10111yescharacteristic
418C4×C8C23×C10111yescharacteristic
419C4×C8C23×C10111yescharacteristic
420C4×C8C23×C10111yescharacteristic
421C4×C8C23×C10111yescharacteristic
422C24—41no—
423#41—44no—
424#41—82no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—44no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—82no—
448C2×D4—82no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4C2×D4×C10111yescharacteristic
452C22×C4C2×D4×C10111yescharacteristic
453C22×C4C2×D4×C10111yescharacteristic
454SD16—44no—
455SD16—44no—
456SD16—44no—
457SD16—82no—
458SD16—82no—
459SD16—82no—
460D8—44no—
461D8—44no—
462D8—82no—
463D8—82no—
464D8—82no—
465M16—24no—
466C2×C8C2×D4×C10112yes—
467C2×C8C2×D4×C10112yes—
468C2×C8C2×D4×C10112yes—
469C2×C8C2×D4×C10112yes—
470C2×C8C2×D4×C10112yes—
471C2×C8C2×D4×C10112yes—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C42—41no—
488C42C2×D4×C10111yescharacteristic
489C42C2×D4×C10111yescharacteristic
490C42C2×D4×C10111yescharacteristic
491C42C24×C10111yescharacteristic
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—82no—
497C23—82no—
498C23—82no—
499C23#127×C10111yescharacteristic
500Q8—42no—
501Q8—42no—
502Q8—42no—
503Q8—42no—
504D4—42no—
505D4—42no—
506D4—42no—
507D4—42no—
508D4—42no—
509D4—42no—
510D4—42no—
511D4—42no—
512D4—42no—
513D4—42no—
514D4—42no—
515D4—42no—
516D4—82no—
517D4—82no—
518D4—82no—
519D4—82no—
520D4—82no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4#127×C10111yescharacteristic
531C2×C4#127×C10111yescharacteristic
532C2×C4#127×C10111yescharacteristic
533C2×C4C22×D4×C10111yescharacteristic
534C2×C4C22×D4×C10111yescharacteristic
535C2×C4C22×D4×C10111yescharacteristic
536C8—22no—
537C8—22no—
538C8—22no—
539C8—22no—
540C8—22no—
541C8AGL(1,ℤ/8)×C10114yes—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—81no—
546C22—81no—
547C22—81no—
548C22—81no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22—164no—
558C22C2×#127×C10111yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—81no—
563C4—81no—
564C4—81no—
565C4—81no—
566C4C2×AGL(1,ℤ/8)×C10112yes—
567C4#576×C10112yes—
568C4#577×C10112yes—
569C2—41no—
570C2—161no—
571C2—161no—
572C2—161no—
573C2—161no—
574C2C101×#315111yescharacteristic
575C2C101×#315411yescharacteristic
576C2C101×#315511yescharacteristic
subgroupG/H
center, socleC22×C101C2×#127
commutator, Frattini, cosocleC42C24×C101
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C2×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#3228C2semidirect
2. C101×#3208C2semidirect
3. C101×#3207C2semidirect
4. C101×#3205C2semidirect
5. C101×#3182C2semidirect
6. C101×#3151C2semidirect
7. C101×#1721C2semidirect
8. C101×#1721C2semidirect
9. C101×#1719C2semidirect
10. C101×#1717C2semidirect
11. C101×#1715C2semidirect
12. C101×#1714C2semidirect
13. C101×#1706C2semidirect
14. C101×#1706C2semidirect
15. C101×#1453C2semidirect
21. #500×C101C22semidirect
22. #500×C101C22semidirect
23. #498×C101C22semidirect
29. #493×C101C22semidirect
34. #492×C101C22semidirect
35. #492×C101C22semidirect
36. #487×C101C22semidirect
37. #487×C101C22semidirect
42. #486×C101C22semidirect
43. #486×C101C22semidirect
44. #486×C101C22semidirect
45. #486×C101C22semidirect
59. #322×C101C22semidirect
60. #322×C101C22semidirect
61. #322×C101C22semidirect
62. C82×C101C22semidirect
280. #19719C101direct (N × H)
289. #3228C2×C101semidirect
290. #3208C2×C101semidirect
291. #3207C2×C101semidirect
292. #3205C2×C101semidirect
293. #3182C2×C101semidirect
294. #3151C2×C101semidirect
295. #1721C2×C101semidirect
296. #1721C2×C101semidirect
297. #1719C2×C101semidirect
298. #1717C2×C101semidirect
299. #1715C2×C101semidirect
300. #1714C2×C101semidirect
301. #1706C2×C101semidirect
302. #1706C2×C101semidirect
303. #1453C2×C101semidirect
304. C101#19719direct (N × H)
310. #500C22×C101semidirect
311. #500C22×C101semidirect
312. #498C22×C101semidirect
318. #493C22×C101semidirect
323. #492C22×C101semidirect
324. #492C22×C101semidirect
325. #487C22×C101semidirect
326. #487C22×C101semidirect
331. #486C22×C101semidirect
332. #486C22×C101semidirect
333. #486C22×C101semidirect
334. #486C22×C101semidirect
348. #322C22×C101semidirect
349. #322C22×C101semidirect
350. #322C22×C101semidirect
351. C82C22×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#32282
C101×#32082
C101×#32072
C101×#32052
C101×#31822
C101×#31512
C101×#17212
C101×#17192
C101×#17172
C101×#17152
C101×#17142
C101×#17062
C101×#14532
#19719101