Finite Group Databasebeta

← C101×#19836 #38801987

Subgroups — C101×#19836 #38801987

Order 25856.

670 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3366C211yesmaximal, characteristic, complemented
2C101×#3358C211yesmaximal, characteristic, complemented
3C101×#3299C211yesmaximal, characteristic, complemented
4C101×#3287C211yesmaximal, characteristic, complemented
5C101×#1717C211yesmaximal, characteristic, complemented
6C101×#1702C211yesmaximal, characteristic, complemented
7C101×#1683C211yesmaximal, characteristic, complemented
8C101×#1678C211yesmaximal, characteristic, complemented
9C101×#1667C211yesmaximal, characteristic, complemented
10C101×#1641C211yesmaximal, characteristic, complemented
11C101×#1631C211yesmaximal, characteristic, complemented
12C101×#1627C211yesmaximal, characteristic, complemented
13C101×#1622C211yesmaximal, characteristic, complemented
14C101×#1584C211yesmaximal, characteristic, complemented
15C101×#1580C211yesmaximal, characteristic, complemented
16C2×#135×C101—21no—
17#554×C101C2211yescharacteristic
18#550×C101C2211yescharacteristic
19#550×C101C2211yescharacteristic
20D4×Q8×C101C2211yescharacteristic
21#493×C101C2211yescharacteristic
22#492×C101C2211yescharacteristic
23#490×C101—21no—
24#487×C101C2211yescharacteristic
25#486×C101—21no—
26#486×C101C2211yescharacteristic
27#486×C101C2211yescharacteristic
28#486×C101C2211yescharacteristic
29#484×C101—21no—
30#478×C101—21no—
31#477×C101C2211yescharacteristic
32#476×C101C2211yescharacteristic
33#474×C101—21no—
34#474×C101C2211yescharacteristic
35#467×C101—21no—
36#466×C101—21no—
37#462×C101C2211yescharacteristic
38#460×C101C2211yescharacteristic
39#460×C101C2211yescharacteristic
40#459×C101—21no—
41#459×C101—21no—
42#459×C101C2211yescharacteristic
43#459×C101C2211yescharacteristic
44#451×C101—21no—
45#449×C101—21no—
46#449×C101—21no—
47#446×C101C2211yescharacteristic
48C8×Q8×C101C2211yescharacteristic
49#442×C101—21no—
50C4×Q16×C101C2211yescharacteristic
51C4×D8×C101—21no—
52C4×D8×C101C2211yescharacteristic
53C8×D4×C101C2211yescharacteristic
54C8×D4×C101C2211yescharacteristic
55C2×#103×C101—21no—
56#335×C101C2211yescharacteristic
57#334×C101C2211yescharacteristic
58#333×C101C2211yescharacteristic
59#332×C101C2211yescharacteristic
60#331×C101C2211yescharacteristic
61#331×C101C2211yescharacteristic
62Q8⋊C8×C101C2211yescharacteristic
63Q8⋊C8×C101C2211yescharacteristic
64D4⋊C8×C101C2211yescharacteristic
65D4⋊C8×C101C2211yescharacteristic
66#322×C101C2211yescharacteristic
67C2×#41×C101—21no—
68C2×#41×C101—21no—
69C22×Q8×C101—21no—
70#135×C101—44no—
71C2×Q16×C101—21no—
72C2×Q16×C101D411yescharacteristic
73C2×SD16×C101—21no—
74C2×SD16×C101—21no—
75C2×SD16×C101—41no—
76C2×D8×C101—21no—
77C2×D8×C101—21no—
78C2×D8×C101—21no—
79C2×D8×C101—21no—
80C2×D8×C101D411yescharacteristic
81C22×C8×C101—21no—
82C22×C8×C101—21no—
83C4⋊Q8×C101—21no—
84C4⋊Q8×C101C2311yescharacteristic
85C4⋊Q8×C101C2311yescharacteristic
86#127×C101—21no—
87#127×C101—21no—
88#127×C101C2311yescharacteristic
89#127×C101C2311yescharacteristic
90#125×C101—21no—
91C22⋊Q8×C101—21no—
92C22⋊Q8×C101—21no—
93C22⋊Q8×C101—41no—
94C22⋊Q8×C101—41no—
95#121×C101—21no—
96#121×C101—21no—
97#121×C101—41no—
98#121×C101—41no—
99C4×Q8×C101C2311yescharacteristic
100C4×Q8×C101C2311yescharacteristic
101C4×D4×C101—21no—
102C4×D4×C101—21no—
103C4×D4×C101—21no—
104C4×D4×C101—21no—
105C4×D4×C101C2311yescharacteristic
106C4×D4×C101C2311yescharacteristic
107C2×C4⋊C4×C101—21no—
108#107×C101—21no—
109#107×C101—21no—
110#107×C101D411yescharacteristic
111#107×C101D411yescharacteristic
112#106×C101—21no—
113C4⋊C8×C101—21no—
114C4⋊C8×C101—21no—
115C4⋊C8×C101C2311yescharacteristic
116C4⋊C8×C101C2311yescharacteristic
117C4⋊C8×C101C2311yescharacteristic
118C4⋊C8×C101C2311yescharacteristic
119#103×C101—21no—
120#103×C101—21no—
121#103×C101—21no—
122#103×C101—21no—
123#103×C101D411yescharacteristic
124#103×C101D411yescharacteristic
125#102×C101—21no—
126#102×C101—21no—
127#102×C101—21no—
128#102×C101—21no—
129#102×C101—21no—
130#102×C101—21no—
131#102×C101—21no—
132#102×C101—21no—
133#102×C101—21no—
134#102×C101—21no—
135#102×C101—41no—
136#102×C101D411yescharacteristic
137#102×C101D411yescharacteristic
138C22⋊C8×C101—21no—
139C22⋊C8×C101—21no—
140#97×C101—21no—
141C4×C8×C101—21no—
142C4×C8×C101C2311yescharacteristic
143C4×C8×C101C2311yescharacteristic
144C4×C8×C101C2311yescharacteristic
145#41×C101—42no—
146#41×C101—42no—
147#41×C101—81no—
148#41×C101—81no—
149C2×Q8×C101—21no—
150C2×Q8×C101—21no—
151C2×Q8×C101—41no—
152C2×Q8×C101—42no—
153C2×Q8×C101—81no—
154C2×Q8×C101C2×D411yescharacteristic
155C2×Q8×C101C2×D411yescharacteristic
156C2×D4×C101—21no—
157C2×D4×C101—21no—
158C2×D4×C101—21no—
159C2×D4×C101—21no—
160C2×D4×C101—21no—
161C2×D4×C101—21no—
162C2×D4×C101—41no—
163C2×D4×C101—41no—
164C2×D4×C101—41no—
165C2×D4×C101—41no—
166C2×D4×C101C2×D411yescharacteristic
167C2×D4×C101C2×D411yescharacteristic
168C22×C4×C101—21no—
169C22×C4×C101—21no—
170C22×C4×C101—41no—
171C22×C4×C101—41no—
172C22×C4×C101—41no—
173C22×C4×C101—41no—
174Q16×C101—22no—
175Q16×C101—81no—
176SD16×C101—42no—
177SD16×C101—42no—
178SD16×C101—82no—
179D8×C101—22no—
180D8×C101—42no—
181D8×C101—42no—
182D8×C101—42no—
183D8×C101—81no—
184C2×C8×C101—21no—
185C2×C8×C101—21no—
186C2×C8×C101—21no—
187C2×C8×C101—21no—
188C2×C8×C101—21no—
189C2×C8×C101—42no—
190C2×C8×C101—81no—
191C2×C8×C101C2×D411yescharacteristic
192C2×C8×C101C2×D411yescharacteristic
193C2×C8×C101C2×D411yescharacteristic
194C2×C8×C101C2×D411yescharacteristic
195C4⋊C4×C101—21no—
196C4⋊C4×C101—21no—
197C4⋊C4×C101—21no—
198C4⋊C4×C101—21no—
199C4⋊C4×C101—21no—
200C4⋊C4×C101—21no—
201C4⋊C4×C101—41no—
202C4⋊C4×C101—41no—
203C4⋊C4×C101—41no—
204C4⋊C4×C101C2×D411yescharacteristic
205C4⋊C4×C101C2×D411yescharacteristic
206C4⋊C4×C101C2×D411yescharacteristic
207C4⋊C4×C101C2×D411yescharacteristic
208C22⋊C4×C101—21no—
209C22⋊C4×C101—21no—
210C22⋊C4×C101—41no—
211C22⋊C4×C101—41no—
212C22⋊C4×C101—41no—
213C22⋊C4×C101—41no—
214C42×C101—21no—
215C42×C101—21no—
216C42×C101C2411yescharacteristic
217C23×C101—21no—
218C23×C101—21no—
219C23×C101—41no—
220C23×C101—41no—
221Q8×C101—21no—
222Q8×C101—21no—
223Q8×C101—21no—
224Q8×C101—41no—
225Q8×C101—41no—
226Q8×C101—82no—
227Q8×C101—81no—
228Q8×C101AGL(1,ℤ/8)12yes—
229D4×C101—21no—
230D4×C101—21no—
231D4×C101—21no—
232D4×C101—41no—
233D4×C101—41no—
234D4×C101—41no—
235D4×C101—41no—
236D4×C101—41no—
237D4×C101—41no—
238D4×C101—41no—
239D4×C101—41no—
240D4×C101—82no—
241D4×C101—81no—
242D4×C101—81no—
243D4×C101—82no—
244D4×C101—161no—
245D4×C101—161no—
246D4×C101#13512yescomplemented
247C2×C4×C101—21no—
248C2×C4×C101—21no—
249C2×C4×C101—21no—
250C2×C4×C101—21no—
251C2×C4×C101—21no—
252C2×C4×C101—21no—
253C2×C4×C101—41no—
254C2×C4×C101—41no—
255C2×C4×C101—41no—
256C2×C4×C101—41no—
257C2×C4×C101—41no—
258C2×C4×C101—41no—
259C2×C4×C101—82no—
260C2×C4×C101—82no—
261C2×C4×C101—82no—
262C2×C4×C101—161no—
263C2×C4×C101C22×D411yescharacteristic
264C2×C4×C101C22×D411yescharacteristic
265C2×C4×C101H(5,𝔽2)11yescharacteristic
266C8×C101—21no—
267C8×C101—21no—
268C8×C101—21no—
269C8×C101—21no—
270C8×C101—41no—
271C8×C101—41no—
272C8×C101—41no—
273C8×C101—41no—
274C8×C101—41no—
275C22×C101—22no—
276C22×C101—41no—
277C22×C101—41no—
278C22×C101—41no—
279C22×C101—41no—
280C22×C101—41no—
281C22×C101—81no—
282C22×C101—81no—
283C22×C101—81no—
284C22×C101—81no—
285C22×C101—81no—
286C22×C101—81no—
287C22×C101D4211yescharacteristic
288C4×C101—22no—
289C4×C101—21no—
290C4×C101—41no—
291C4×C101—41no—
292C4×C101—41no—
293C4×C101—41no—
294C4×C101—41no—
295C4×C101—81no—
296C4×C101—81no—
297C4×C101C2×#13511yescharacteristic
298C4×C101C2×AGL(1,ℤ/8)11yescharacteristic
299C4×C101#57611yescharacteristic
300C4×C101#57811yescharacteristic
301#19836C10111yesmaximal, characteristic, direct product factor, Sylow
302C2×C101—42no—
303C2×C101—81no—
304C2×C101—161no—
305C2×C101—161no—
306C2×C101#326411yescharacteristic
307C2×C101#328511yescharacteristic
308C2×C101#328811yescharacteristic
309#3366C2×C10111yescharacteristic, complemented
310#3358C2×C10111yescharacteristic, complemented
311#3299C2×C10111yescharacteristic, complemented
312#3287C2×C10111yescharacteristic, complemented
313#1717C2×C10111yescharacteristic, complemented
314#1702C2×C10111yescharacteristic, complemented
315#1683C2×C10111yescharacteristic, complemented
316#1678C2×C10111yescharacteristic, complemented
317#1667C2×C10111yescharacteristic, complemented
318#1641C2×C10111yescharacteristic, complemented
319#1631C2×C10111yescharacteristic, complemented
320#1627C2×C10111yescharacteristic, complemented
321#1622C2×C10111yescharacteristic, complemented
322#1584C2×C10111yescharacteristic, complemented
323#1580C2×C10111yescharacteristic, complemented
324C101#1983611yescharacteristic, direct product factor, Sylow
325C2×#135—21no—
326#554C22×C10111yescharacteristic
327#550C22×C10111yescharacteristic
328#550C22×C10111yescharacteristic
329D4×Q8C22×C10111yescharacteristic
330#493C22×C10111yescharacteristic
331#492C22×C10111yescharacteristic
332#490—21no—
333#487C22×C10111yescharacteristic
334#486—21no—
335#486C22×C10111yescharacteristic
336#486C22×C10111yescharacteristic
337#486C22×C10111yescharacteristic
338#484—21no—
339#478—21no—
340#477C22×C10111yescharacteristic
341#476C22×C10111yescharacteristic
342#474—21no—
343#474C22×C10111yescharacteristic
344#467—21no—
345#466—21no—
346#462C22×C10111yescharacteristic
347#460C22×C10111yescharacteristic
348#460C22×C10111yescharacteristic
349#459—21no—
350#459—21no—
351#459C22×C10111yescharacteristic
352#459C22×C10111yescharacteristic
353#451—21no—
354#449—21no—
355#449—21no—
356#446C22×C10111yescharacteristic
357C8×Q8C22×C10111yescharacteristic
358#442—21no—
359C4×Q16C22×C10111yescharacteristic
360C4×D8—21no—
361C4×D8C22×C10111yescharacteristic
362C8×D4C22×C10111yescharacteristic
363C8×D4C22×C10111yescharacteristic
364C2×#103—21no—
365#335C22×C10111yescharacteristic
366#334C22×C10111yescharacteristic
367#333C22×C10111yescharacteristic
368#332C22×C10111yescharacteristic
369#331C22×C10111yescharacteristic
370#331C22×C10111yescharacteristic
371Q8⋊C8C22×C10111yescharacteristic
372Q8⋊C8C22×C10111yescharacteristic
373D4⋊C8C22×C10111yescharacteristic
374D4⋊C8C22×C10111yescharacteristic
375#322C22×C10111yescharacteristic
376C2×#41—21no—
377C2×#41—21no—
378C22×Q8—21no—
379#135—44no—
380C2×Q16—21no—
381C2×Q16D4×C10111yescharacteristic
382C2×SD16—21no—
383C2×SD16—21no—
384C2×SD16—41no—
385C2×D8—21no—
386C2×D8—21no—
387C2×D8—21no—
388C2×D8—21no—
389C2×D8D4×C10111yescharacteristic
390C22×C8—21no—
391C22×C8—21no—
392C4⋊Q8—21no—
393C4⋊Q8C23×C10111yescharacteristic
394C4⋊Q8C23×C10111yescharacteristic
395#127—21no—
396#127—21no—
397#127C23×C10111yescharacteristic
398#127C23×C10111yescharacteristic
399#125—21no—
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402C22⋊Q8—41no—
403C22⋊Q8—41no—
404#121—21no—
405#121—21no—
406#121—41no—
407#121—41no—
408C4×Q8C23×C10111yescharacteristic
409C4×Q8C23×C10111yescharacteristic
410C4×D4—21no—
411C4×D4—21no—
412C4×D4—21no—
413C4×D4—21no—
414C4×D4C23×C10111yescharacteristic
415C4×D4C23×C10111yescharacteristic
416C2×C4⋊C4—21no—
417#107—21no—
418#107—21no—
419#107D4×C10111yescharacteristic
420#107D4×C10111yescharacteristic
421#106—21no—
422C4⋊C8—21no—
423C4⋊C8—21no—
424C4⋊C8C23×C10111yescharacteristic
425C4⋊C8C23×C10111yescharacteristic
426C4⋊C8C23×C10111yescharacteristic
427C4⋊C8C23×C10111yescharacteristic
428#103—21no—
429#103—21no—
430#103—21no—
431#103—21no—
432#103D4×C10111yescharacteristic
433#103D4×C10111yescharacteristic
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—21no—
444#102—41no—
445#102D4×C10111yescharacteristic
446#102D4×C10111yescharacteristic
447C22⋊C8—21no—
448C22⋊C8—21no—
449#97—21no—
450C4×C8—21no—
451C4×C8C23×C10111yescharacteristic
452C4×C8C23×C10111yescharacteristic
453C4×C8C23×C10111yescharacteristic
454#41—42no—
455#41—42no—
456#41—81no—
457#41—81no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—41no—
461C2×Q8—42no—
462C2×Q8—81no—
463C2×Q8C2×D4×C10111yescharacteristic
464C2×Q8C2×D4×C10111yescharacteristic
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4C2×D4×C10111yescharacteristic
476C2×D4C2×D4×C10111yescharacteristic
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483Q16—22no—
484Q16—81no—
485SD16—42no—
486SD16—42no—
487SD16—82no—
488D8—22no—
489D8—42no—
490D8—42no—
491D8—42no—
492D8—81no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—42no—
499C2×C8—81no—
500C2×C8C2×D4×C10111yescharacteristic
501C2×C8C2×D4×C10111yescharacteristic
502C2×C8C2×D4×C10111yescharacteristic
503C2×C8C2×D4×C10111yescharacteristic
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4C2×D4×C10111yescharacteristic
514C4⋊C4C2×D4×C10111yescharacteristic
515C4⋊C4C2×D4×C10111yescharacteristic
516C4⋊C4C2×D4×C10111yescharacteristic
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C42—21no—
524C42—21no—
525C42C24×C10111yescharacteristic
526C23—21no—
527C23—21no—
528C23—41no—
529C23—41no—
530Q8—21no—
531Q8—21no—
532Q8—21no—
533Q8—41no—
534Q8—41no—
535Q8—82no—
536Q8—81no—
537Q8AGL(1,ℤ/8)×C10112yes—
538D4—21no—
539D4—21no—
540D4—21no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—82no—
550D4—81no—
551D4—81no—
552D4—82no—
553D4—161no—
554D4—161no—
555D4#135×C10112yescomplemented
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—82no—
569C2×C4—82no—
570C2×C4—82no—
571C2×C4—161no—
572C2×C4C22×D4×C10111yescharacteristic
573C2×C4C22×D4×C10111yescharacteristic
574C2×C4H(5,𝔽2)×C10111yescharacteristic
575C8—21no—
576C8—21no—
577C8—21no—
578C8—21no—
579C8—41no—
580C8—41no—
581C8—41no—
582C8—41no—
583C8—41no—
584C22—22no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—81no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22D42×C10111yescharacteristic
597C4—22no—
598C4—21no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—81no—
605C4—81no—
606C4C2×#135×C10111yescharacteristic
607C4C2×AGL(1,ℤ/8)×C10111yescharacteristic
608C4#576×C10111yescharacteristic
609C4#578×C10111yescharacteristic
610C2—42no—
611C2—81no—
612C2—161no—
613C2—161no—
614C2C101×#326411yescharacteristic
615C2C101×#328511yescharacteristic
616C2C101×#328811yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC42C24×C101
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#3366C2semidirect
2. C101×#3358C2semidirect
3. C101×#3299C2semidirect
4. C101×#3287C2semidirect
5. C101×#1717C2semidirect
6. C101×#1702C2semidirect
7. C101×#1683C2semidirect
8. C101×#1678C2semidirect
9. C101×#1667C2semidirect
10. C101×#1641C2semidirect
11. C101×#1631C2semidirect
12. C101×#1627C2semidirect
13. C101×#1622C2semidirect
14. C101×#1584C2semidirect
15. C101×#1580C2semidirect
246. D4×C101#135semidirect
301. #19836C101direct (N × H)
309. #3366C2×C101semidirect
310. #3358C2×C101semidirect
311. #3299C2×C101semidirect
312. #3287C2×C101semidirect
313. #1717C2×C101semidirect
314. #1702C2×C101semidirect
315. #1683C2×C101semidirect
316. #1678C2×C101semidirect
317. #1667C2×C101semidirect
318. #1641C2×C101semidirect
319. #1631C2×C101semidirect
320. #1627C2×C101semidirect
321. #1622C2×C101semidirect
322. #1584C2×C101semidirect
323. #1580C2×C101semidirect
324. C101#19836direct (N × H)
555. D4#135×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#33662
C101×#33582
C101×#32992
C101×#32872
C101×#17172
C101×#17022
C101×#16832
C101×#16782
C101×#16672
C101×#16412
C101×#16312
C101×#16272
C101×#16222
C101×#15842
C101×#15802
#19836101