Finite Group Databasebeta

← C101×#19859 #38802010

Subgroups — C101×#19859 #38802010

Order 25856.

656 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3354C211yesmaximal, characteristic, complemented
2C101×#3334C211yesmaximal, characteristic, complemented
3C101×#3303C211yesmaximal, characteristic, complemented
4C101×#3283C211yesmaximal, characteristic, complemented
5C101×#1723C211yesmaximal, characteristic, complemented
6C101×#1693C211yesmaximal, characteristic, complemented
7C101×#1683C211yesmaximal, characteristic, complemented
8C101×#1671C211yesmaximal, characteristic, complemented
9C101×#1669C211yesmaximal, characteristic, complemented
10C101×#1647C211yesmaximal, characteristic, complemented
11C101×#1647C211yesmaximal, characteristic, complemented
12C101×#1646C211yesmaximal, characteristic, complemented
13C101×#1635C211yesmaximal, characteristic, complemented
14C101×#1581C211yesmaximal, characteristic, complemented
15C101×#1580C211yesmaximal, characteristic, complemented
16C2×#135×C101—21no—
17#555×C101C2211yescharacteristic
18#547×C101C2211yescharacteristic
19#547×C101C2211yescharacteristic
20#547×C101C2211yescharacteristic
21#500×C101C2211yescharacteristic
22#500×C101C2211yescharacteristic
23#498×C101C2211yescharacteristic
24#494×C101C2211yescharacteristic
25#487×C101C2211yescharacteristic
26#487×C101C2211yescharacteristic
27#485×C101—21no—
28#482×C101—21no—
29#481×C101—21no—
30#480×C101—21no—
31#480×C101—21no—
32#476×C101C2211yescharacteristic
33#476×C101C2211yescharacteristic
34#474×C101C2211yescharacteristic
35#474×C101C2211yescharacteristic
36#474×C101C2211yescharacteristic
37#469×C101—21no—
38#467×C101—21no—
39#466×C101—21no—
40#465×C101—21no—
41#461×C101C2211yescharacteristic
42#461×C101C2211yescharacteristic
43#461×C101C2211yescharacteristic
44#452×C101—21no—
45#452×C101—21no—
46#449×C101—21no—
47C4×D8×C101C2211yescharacteristic
48C4×D8×C101C2211yescharacteristic
49#436×C101C2211yescharacteristic
50C8×D4×C101C2211yescharacteristic
51C8×D4×C101C2211yescharacteristic
52C8×D4×C101C2211yescharacteristic
53#428×C101—21no—
54C2×#107×C101—21no—
55#416×C101—21no—
56#335×C101C2211yescharacteristic
57#334×C101C2211yescharacteristic
58#333×C101C2211yescharacteristic
59#332×C101C2211yescharacteristic
60#332×C101C2211yescharacteristic
61#332×C101C2211yescharacteristic
62D4⋊C8×C101C2211yescharacteristic
63D4⋊C8×C101C2211yescharacteristic
64D4⋊C8×C101C2211yescharacteristic
65D4⋊C8×C101C2211yescharacteristic
66#322×C101C2211yescharacteristic
67C2×#41×C101—21no—
68C2×#41×C101—21no—
69C2×#41×C101—21no—
70#135×C101—44no—
71C2×Q16×C101—21no—
72C2×Q16×C101—21no—
73C2×SD16×C101—21no—
74C2×SD16×C101—21no—
75C2×SD16×C101—21no—
76C2×D8×C101D411yescharacteristic
77C2×D8×C101D411yescharacteristic
78C2×M16×C101—21no—
79C22×C8×C101—21no—
80C22×C8×C101—21no—
81C22×C8×C101—21no—
82C4⋊Q8×C101C2311yescharacteristic
83C4⋊Q8×C101C2311yescharacteristic
84C4⋊Q8×C101C2311yescharacteristic
85C4⋊Q8×C101C2311yescharacteristic
86#124×C101—41no—
87#123×C101—41no—
88#123×C101—41no—
89#123×C101—41no—
90C22⋊Q8×C101—21no—
91C22⋊Q8×C101—21no—
92C22⋊Q8×C101—21no—
93#121×C101—21no—
94#121×C101—21no—
95#121×C101—21no—
96#121×C101—21no—
97#121×C101—21no—
98C4×D4×C101C2311yescharacteristic
99C4×D4×C101C2311yescharacteristic
100C4×D4×C101C2311yescharacteristic
101C4×D4×C101C2311yescharacteristic
102#117×C101—21no—
103#117×C101—21no—
104C2×C4⋊C4×C101—21no—
105C2×C4⋊C4×C101—21no—
106C2×C4⋊C4×C101—21no—
107#107×C101—21no—
108#107×C101—21no—
109#107×C101—21no—
110#107×C101—21no—
111#107×C101—21no—
112#107×C101—41no—
113#107×C101D411yescharacteristic
114#107×C101D411yescharacteristic
115#106×C101—21no—
116#106×C101—21no—
117#106×C101—21no—
118#106×C101—21no—
119C4⋊C8×C101C2311yescharacteristic
120C4⋊C8×C101C2311yescharacteristic
121C4⋊C8×C101C2311yescharacteristic
122C4⋊C8×C101C2311yescharacteristic
123#103×C101—21no—
124#103×C101—21no—
125#103×C101—21no—
126#103×C101—21no—
127#103×C101—21no—
128#103×C101—41no—
129#102×C101—21no—
130#102×C101—21no—
131#102×C101—21no—
132#102×C101—21no—
133#102×C101—21no—
134#102×C101D411yescharacteristic
135#102×C101D411yescharacteristic
136#102×C101D411yescharacteristic
137#102×C101D411yescharacteristic
138C22⋊C8×C101—21no—
139C22⋊C8×C101—21no—
140C22⋊C8×C101—21no—
141C22⋊C8×C101—21no—
142C4×C8×C101C2311yescharacteristic
143C4×C8×C101C2311yescharacteristic
144C4×C8×C101C2311yescharacteristic
145#41×C101—42no—
146#41×C101—42no—
147#41×C101—42no—
148#41×C101—81no—
149#41×C101—81no—
150#41×C101—81no—
151C2×Q8×C101—21no—
152C2×Q8×C101—21no—
153C2×Q8×C101—21no—
154C2×Q8×C101—21no—
155C2×D4×C101—41no—
156C2×D4×C101—41no—
157C2×D4×C101—41no—
158C2×D4×C101—41no—
159C2×D4×C101C2×D411yescharacteristic
160C2×D4×C101C2×D411yescharacteristic
161C2×D4×C101C2×D411yescharacteristic
162C2×D4×C101C2×D411yescharacteristic
163C22×C4×C101—21no—
164C22×C4×C101—21no—
165C22×C4×C101—21no—
166C22×C4×C101—21no—
167C22×C4×C101—41no—
168C22×C4×C101—41no—
169C22×C4×C101—41no—
170Q16×C101—42no—
171Q16×C101—81no—
172SD16×C101—42no—
173SD16×C101—42no—
174SD16×C101—81no—
175D8×C101—22no—
176D8×C101—22no—
177M16×C101—42no—
178C2×C8×C101—21no—
179C2×C8×C101—21no—
180C2×C8×C101—21no—
181C2×C8×C101—21no—
182C2×C8×C101—21no—
183C2×C8×C101—42no—
184C2×C8×C101—42no—
185C2×C8×C101—81no—
186C2×C8×C101C2×D411yescharacteristic
187C2×C8×C101C2×D411yescharacteristic
188C2×C8×C101C2×D411yescharacteristic
189C2×C8×C101C2×D411yescharacteristic
190C4⋊C4×C101—21no—
191C4⋊C4×C101—21no—
192C4⋊C4×C101—21no—
193C4⋊C4×C101—21no—
194C4⋊C4×C101—21no—
195C4⋊C4×C101—21no—
196C4⋊C4×C101—21no—
197C4⋊C4×C101—21no—
198C4⋊C4×C101—41no—
199C4⋊C4×C101—41no—
200C4⋊C4×C101—41no—
201C4⋊C4×C101C2×D411yescharacteristic
202C4⋊C4×C101C2×D411yescharacteristic
203C4⋊C4×C101C2×D411yescharacteristic
204C4⋊C4×C101C2×D411yescharacteristic
205C22⋊C4×C101—21no—
206C22⋊C4×C101—21no—
207C22⋊C4×C101—21no—
208C22⋊C4×C101—21no—
209C22⋊C4×C101—41no—
210C22⋊C4×C101—41no—
211C22⋊C4×C101—41no—
212C22⋊C4×C101—41no—
213C22⋊C4×C101—41no—
214C42×C101—41no—
215C42×C101C2411yescharacteristic
216C23×C101—21no—
217C23×C101—21no—
218C23×C101—21no—
219C23×C101—21no—
220Q8×C101—41no—
221Q8×C101—41no—
222Q8×C101—41no—
223Q8×C101—41no—
224Q8×C101—41no—
225Q8×C101—41no—
226Q8×C101—81no—
227D4×C101—21no—
228D4×C101—21no—
229D4×C101—21no—
230D4×C101—21no—
231D4×C101—21no—
232D4×C101—21no—
233D4×C101—21no—
234D4×C101—82no—
235D4×C101—82no—
236D4×C101—82no—
237D4×C101—161no—
238D4×C101AGL(1,ℤ/8)12yes—
239C2×C4×C101—21no—
240C2×C4×C101—21no—
241C2×C4×C101—21no—
242C2×C4×C101—21no—
243C2×C4×C101—41no—
244C2×C4×C101—41no—
245C2×C4×C101—41no—
246C2×C4×C101—41no—
247C2×C4×C101—41no—
248C2×C4×C101—41no—
249C2×C4×C101—41no—
250C2×C4×C101—41no—
251C2×C4×C101—41no—
252C2×C4×C101—41no—
253C2×C4×C101—41no—
254C2×C4×C101—41no—
255C2×C4×C101—82no—
256C2×C4×C101—82no—
257C2×C4×C101—82no—
258C2×C4×C101C22×D411yescharacteristic
259C2×C4×C101C22×D411yescharacteristic
260C2×C4×C101H(5,𝔽2)11yescharacteristic
261C8×C101—21no—
262C8×C101—21no—
263C8×C101—21no—
264C8×C101—41no—
265C8×C101—41no—
266C8×C101—41no—
267C8×C101—41no—
268C8×C101—41no—
269C8×C101#13512yescomplemented
270C22×C101—22no—
271C22×C101—41no—
272C22×C101—41no—
273C22×C101—41no—
274C22×C101—41no—
275C22×C101—41no—
276C22×C101—41no—
277C22×C101—41no—
278C22×C101—41no—
279C22×C101—41no—
280C22×C101—41no—
281C22×C101—41no—
282C22×C101D4211yescharacteristic
283C4×C101—21no—
284C4×C101—41no—
285C4×C101—41no—
286C4×C101—41no—
287C4×C101—41no—
288C4×C101—81no—
289C4×C101—81no—
290C4×C101—81no—
291C4×C101—81no—
292C4×C101C2×#13511yescharacteristic
293C4×C101C2×AGL(1,ℤ/8)11yescharacteristic
294C4×C101#57611yescharacteristic
295C4×C101#57811yescharacteristic
296#19859C10111yesmaximal, characteristic, direct product factor, Sylow
297C2×C101—42no—
298C2×C101—81no—
299C2×C101—81no—
300C2×C101—81no—
301C2×C101#326411yescharacteristic
302C2×C101#328311yescharacteristic
303C2×C101#328911yescharacteristic
304#3354C2×C10111yescharacteristic, complemented
305#3334C2×C10111yescharacteristic, complemented
306#3303C2×C10111yescharacteristic, complemented
307#3283C2×C10111yescharacteristic, complemented
308#1723C2×C10111yescharacteristic, complemented
309#1693C2×C10111yescharacteristic, complemented
310#1683C2×C10111yescharacteristic, complemented
311#1671C2×C10111yescharacteristic, complemented
312#1669C2×C10111yescharacteristic, complemented
313#1647C2×C10111yescharacteristic, complemented
314#1647C2×C10111yescharacteristic, complemented
315#1646C2×C10111yescharacteristic, complemented
316#1635C2×C10111yescharacteristic, complemented
317#1581C2×C10111yescharacteristic, complemented
318#1580C2×C10111yescharacteristic, complemented
319C101#1985911yescharacteristic, direct product factor, Sylow
320C2×#135—21no—
321#555C22×C10111yescharacteristic
322#547C22×C10111yescharacteristic
323#547C22×C10111yescharacteristic
324#547C22×C10111yescharacteristic
325#500C22×C10111yescharacteristic
326#500C22×C10111yescharacteristic
327#498C22×C10111yescharacteristic
328#494C22×C10111yescharacteristic
329#487C22×C10111yescharacteristic
330#487C22×C10111yescharacteristic
331#485—21no—
332#482—21no—
333#481—21no—
334#480—21no—
335#480—21no—
336#476C22×C10111yescharacteristic
337#476C22×C10111yescharacteristic
338#474C22×C10111yescharacteristic
339#474C22×C10111yescharacteristic
340#474C22×C10111yescharacteristic
341#469—21no—
342#467—21no—
343#466—21no—
344#465—21no—
345#461C22×C10111yescharacteristic
346#461C22×C10111yescharacteristic
347#461C22×C10111yescharacteristic
348#452—21no—
349#452—21no—
350#449—21no—
351C4×D8C22×C10111yescharacteristic
352C4×D8C22×C10111yescharacteristic
353#436C22×C10111yescharacteristic
354C8×D4C22×C10111yescharacteristic
355C8×D4C22×C10111yescharacteristic
356C8×D4C22×C10111yescharacteristic
357#428—21no—
358C2×#107—21no—
359#416—21no—
360#335C22×C10111yescharacteristic
361#334C22×C10111yescharacteristic
362#333C22×C10111yescharacteristic
363#332C22×C10111yescharacteristic
364#332C22×C10111yescharacteristic
365#332C22×C10111yescharacteristic
366D4⋊C8C22×C10111yescharacteristic
367D4⋊C8C22×C10111yescharacteristic
368D4⋊C8C22×C10111yescharacteristic
369D4⋊C8C22×C10111yescharacteristic
370#322C22×C10111yescharacteristic
371C2×#41—21no—
372C2×#41—21no—
373C2×#41—21no—
374#135—44no—
375C2×Q16—21no—
376C2×Q16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×D8D4×C10111yescharacteristic
381C2×D8D4×C10111yescharacteristic
382C2×M16—21no—
383C22×C8—21no—
384C22×C8—21no—
385C22×C8—21no—
386C4⋊Q8C23×C10111yescharacteristic
387C4⋊Q8C23×C10111yescharacteristic
388C4⋊Q8C23×C10111yescharacteristic
389C4⋊Q8C23×C10111yescharacteristic
390#124—41no—
391#123—41no—
392#123—41no—
393#123—41no—
394C22⋊Q8—21no—
395C22⋊Q8—21no—
396C22⋊Q8—21no—
397#121—21no—
398#121—21no—
399#121—21no—
400#121—21no—
401#121—21no—
402C4×D4C23×C10111yescharacteristic
403C4×D4C23×C10111yescharacteristic
404C4×D4C23×C10111yescharacteristic
405C4×D4C23×C10111yescharacteristic
406#117—21no—
407#117—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411#107—21no—
412#107—21no—
413#107—21no—
414#107—21no—
415#107—21no—
416#107—41no—
417#107D4×C10111yescharacteristic
418#107D4×C10111yescharacteristic
419#106—21no—
420#106—21no—
421#106—21no—
422#106—21no—
423C4⋊C8C23×C10111yescharacteristic
424C4⋊C8C23×C10111yescharacteristic
425C4⋊C8C23×C10111yescharacteristic
426C4⋊C8C23×C10111yescharacteristic
427#103—21no—
428#103—21no—
429#103—21no—
430#103—21no—
431#103—21no—
432#103—41no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102D4×C10111yescharacteristic
439#102D4×C10111yescharacteristic
440#102D4×C10111yescharacteristic
441#102D4×C10111yescharacteristic
442C22⋊C8—21no—
443C22⋊C8—21no—
444C22⋊C8—21no—
445C22⋊C8—21no—
446C4×C8C23×C10111yescharacteristic
447C4×C8C23×C10111yescharacteristic
448C4×C8C23×C10111yescharacteristic
449#41—42no—
450#41—42no—
451#41—42no—
452#41—81no—
453#41—81no—
454#41—81no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4C2×D4×C10111yescharacteristic
464C2×D4C2×D4×C10111yescharacteristic
465C2×D4C2×D4×C10111yescharacteristic
466C2×D4C2×D4×C10111yescharacteristic
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474Q16—42no—
475Q16—81no—
476SD16—42no—
477SD16—42no—
478SD16—81no—
479D8—22no—
480D8—22no—
481M16—42no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—42no—
488C2×C8—42no—
489C2×C8—81no—
490C2×C8C2×D4×C10111yescharacteristic
491C2×C8C2×D4×C10111yescharacteristic
492C2×C8C2×D4×C10111yescharacteristic
493C2×C8C2×D4×C10111yescharacteristic
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—41no—
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4C2×D4×C10111yescharacteristic
506C4⋊C4C2×D4×C10111yescharacteristic
507C4⋊C4C2×D4×C10111yescharacteristic
508C4⋊C4C2×D4×C10111yescharacteristic
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C42—41no—
519C42C24×C10111yescharacteristic
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524Q8—41no—
525Q8—41no—
526Q8—41no—
527Q8—41no—
528Q8—41no—
529Q8—41no—
530Q8—81no—
531D4—21no—
532D4—21no—
533D4—21no—
534D4—21no—
535D4—21no—
536D4—21no—
537D4—21no—
538D4—82no—
539D4—82no—
540D4—82no—
541D4—161no—
542D4AGL(1,ℤ/8)×C10112yes—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—82no—
560C2×C4—82no—
561C2×C4—82no—
562C2×C4C22×D4×C10111yescharacteristic
563C2×C4C22×D4×C10111yescharacteristic
564C2×C4H(5,𝔽2)×C10111yescharacteristic
565C8—21no—
566C8—21no—
567C8—21no—
568C8—41no—
569C8—41no—
570C8—41no—
571C8—41no—
572C8—41no—
573C8#135×C10112yescomplemented
574C22—22no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22D42×C10111yescharacteristic
587C4—21no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—81no—
593C4—81no—
594C4—81no—
595C4—81no—
596C4C2×#135×C10111yescharacteristic
597C4C2×AGL(1,ℤ/8)×C10111yescharacteristic
598C4#576×C10111yescharacteristic
599C4#578×C10111yescharacteristic
600C2—42no—
601C2—81no—
602C2—81no—
603C2—81no—
604C2C101×#326411yescharacteristic
605C2C101×#328311yescharacteristic
606C2C101×#328911yescharacteristic
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×#3354C2semidirect
2. C101×#3334C2semidirect
3. C101×#3303C2semidirect
4. C101×#3283C2semidirect
5. C101×#1723C2semidirect
6. C101×#1693C2semidirect
7. C101×#1683C2semidirect
8. C101×#1671C2semidirect
9. C101×#1669C2semidirect
10. C101×#1647C2semidirect
11. C101×#1647C2semidirect
12. C101×#1646C2semidirect
13. C101×#1635C2semidirect
14. C101×#1581C2semidirect
15. C101×#1580C2semidirect
269. C8×C101#135semidirect
296. #19859C101direct (N × H)
304. #3354C2×C101semidirect
305. #3334C2×C101semidirect
306. #3303C2×C101semidirect
307. #3283C2×C101semidirect
308. #1723C2×C101semidirect
309. #1693C2×C101semidirect
310. #1683C2×C101semidirect
311. #1671C2×C101semidirect
312. #1669C2×C101semidirect
313. #1647C2×C101semidirect
314. #1647C2×C101semidirect
315. #1646C2×C101semidirect
316. #1635C2×C101semidirect
317. #1581C2×C101semidirect
318. #1580C2×C101semidirect
319. C101#19859direct (N × H)
573. C8#135×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#33542
C101×#33342
C101×#33032
C101×#32832
C101×#17232
C101×#16932
C101×#16832
C101×#16712
C101×#16692
C101×#16472
C101×#16462
C101×#16352
C101×#15812
C101×#15802
#19859101