Finite Group Databasebeta

← C101×#20222 #38802373

Subgroups — C101×#20222 #38802373

Order 25856.

642 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3366C211yesmaximal, characteristic, complemented
2C101×#3357C211yesmaximal, characteristic, complemented
3C101×#3354C211yesmaximal, characteristic, complemented
4C101×#3284C211yesmaximal, characteristic, complemented
5C101×#1714C211yesmaximal, characteristic, complemented
6C101×#1697C211yesmaximal, characteristic, complemented
7C101×#1692C211yesmaximal, characteristic, complemented
8C101×#1685C211yesmaximal, characteristic, complemented
9C101×#1675C211yesmaximal, characteristic, complemented
10C101×#1644C211yesmaximal, characteristic, complemented
11C101×#1635C211yesmaximal, characteristic, complemented
12C101×#1631C211yesmaximal, characteristic, complemented
13C101×#1624C211yesmaximal, characteristic, complemented
14C101×#1592C211yesmaximal, characteristic, complemented
15C101×#1581C211yesmaximal, characteristic, complemented
16C2×#135×C101—21no—
17#555×C101C2211yescharacteristic
18#554×C101C2211yescharacteristic
19#550×C101C2211yescharacteristic
20#547×C101C2211yescharacteristic
21#500×C101C2211yescharacteristic
22#498×C101C2211yescharacteristic
23#492×C101C2211yescharacteristic
24#492×C101C2211yescharacteristic
25#490×C101—21no—
26#487×C101C2211yescharacteristic
27#486×C101C2211yescharacteristic
28#485×C101—21no—
29#482×C101—21no—
30#481×C101—21no—
31#480×C101—21no—
32#478×C101—21no—
33#477×C101C2211yescharacteristic
34#476×C101C2211yescharacteristic
35#476×C101C2211yescharacteristic
36#476×C101C2211yescharacteristic
37#474×C101C2211yescharacteristic
38#469×C101—21no—
39#468×C101—21no—
40#465×C101—21no—
41#462×C101C2211yescharacteristic
42#459×C101—21no—
43#459×C101C2211yescharacteristic
44#459×C101C2211yescharacteristic
45#452×C101—21no—
46#449×C101—21no—
47#446×C101C2211yescharacteristic
48#442×C101—21no—
49C4×SD16×C101C2211yescharacteristic
50C4×D8×C101C2211yescharacteristic
51#436×C101C2211yescharacteristic
52#436×C101C2211yescharacteristic
53C8×D4×C101C2211yescharacteristic
54#428×C101—21no—
55#428×C101—21no—
56#335×C101C2211yescharacteristic
57#335×C101C2211yescharacteristic
58#333×C101C2211yescharacteristic
59#333×C101C2211yescharacteristic
60#332×C101C2211yescharacteristic
61#331×C101C2211yescharacteristic
62Q8⋊C8×C101C2211yescharacteristic
63D4⋊C8×C101C2211yescharacteristic
64D4⋊C8×C101C2211yescharacteristic
65D4⋊C8×C101C2211yescharacteristic
66#322×C101C2211yescharacteristic
67C2×#41×C101—21no—
68C2×#41×C101—21no—
69#135×C101—44no—
70C2×Q16×C101—21no—
71C2×SD16×C101—21no—
72C2×SD16×C101—21no—
73C2×SD16×C101—41no—
74C2×SD16×C101D411yescharacteristic
75C2×D8×C101—21no—
76C2×D8×C101—21no—
77C2×D8×C101D411yescharacteristic
78C2×M16×C101—21no—
79C2×M16×C101—21no—
80C22×C8×C101—21no—
81C4⋊Q8×C101C2311yescharacteristic
82C4⋊Q8×C101C2311yescharacteristic
83C4⋊Q8×C101C2311yescharacteristic
84#127×C101—21no—
85#127×C101C2311yescharacteristic
86#125×C101—21no—
87#124×C101—41no—
88#123×C101—41no—
89C22⋊Q8×C101—21no—
90C22⋊Q8×C101—21no—
91C22⋊Q8×C101—41no—
92#121×C101—21no—
93#121×C101—21no—
94#121×C101—21no—
95#121×C101—21no—
96#121×C101—41no—
97C4×Q8×C101C2311yescharacteristic
98C4×D4×C101—21no—
99C4×D4×C101—21no—
100C4×D4×C101C2311yescharacteristic
101C4×D4×C101C2311yescharacteristic
102C4×D4×C101C2311yescharacteristic
103#117×C101—21no—
104#117×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×C101D411yescharacteristic
112#106×C101—21no—
113#106×C101—21no—
114#106×C101—21no—
115#106×C101—21no—
116#106×C101—21no—
117#106×C101D411yescharacteristic
118C4⋊C8×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—41no—
126#103×C101D411yescharacteristic
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×C101D411yescharacteristic
136#102×C101D411yescharacteristic
137#102×C101D411yescharacteristic
138C22⋊C8×C101—21no—
139C22⋊C8×C101—21no—
140C22⋊C8×C101—21no—
141#97×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—21no—
152C2×Q8×C101C2×D411yescharacteristic
153C2×D4×C101—21no—
154C2×D4×C101—21no—
155C2×D4×C101—21no—
156C2×D4×C101—41no—
157C2×D4×C101—41no—
158C2×D4×C101—41no—
159C2×D4×C101—41no—
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—41no—
167C22×C4×C101—41no—
168C22×C4×C101—41no—
169Q16×C101—42no—
170SD16×C101—22no—
171SD16×C101—42no—
172SD16×C101—81no—
173SD16×C101—82no—
174D8×C101—41no—
175D8×C101—42no—
176D8×C101—42no—
177M16×C101—42no—
178M16×C101—42no—
179C2×C8×C101—21no—
180C2×C8×C101—21no—
181C2×C8×C101—21no—
182C2×C8×C101—21no—
183C2×C8×C101—21no—
184C2×C8×C101—42no—
185C2×C8×C101C2×D411yescharacteristic
186C2×C8×C101C2×D411yescharacteristic
187C2×C8×C101C2×D411yescharacteristic
188C2×C8×C101C2×D411yescharacteristic
189C4⋊C4×C101—21no—
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—41no—
197C4⋊C4×C101—41no—
198C4⋊C4×C101—41no—
199C4⋊C4×C101C2×D411yescharacteristic
200C4⋊C4×C101C2×D411yescharacteristic
201C4⋊C4×C101C2×D411yescharacteristic
202C4⋊C4×C101C2×D411yescharacteristic
203C22⋊C4×C101—21no—
204C22⋊C4×C101—21no—
205C22⋊C4×C101—21no—
206C22⋊C4×C101—41no—
207C22⋊C4×C101—41no—
208C22⋊C4×C101—41no—
209C22⋊C4×C101—41no—
210C22⋊C4×C101—41no—
211C42×C101—21no—
212C42×C101—41no—
213C42×C101C2411yescharacteristic
214C23×C101—21no—
215C23×C101—21no—
216C23×C101—21no—
217C23×C101—41no—
218Q8×C101—21no—
219Q8×C101—21no—
220Q8×C101—41no—
221Q8×C101—41no—
222Q8×C101—81no—
223Q8×C101—81no—
224D4×C101—21no—
225D4×C101—21no—
226D4×C101—21no—
227D4×C101—21no—
228D4×C101—21no—
229D4×C101—21no—
230D4×C101—41no—
231D4×C101—41no—
232D4×C101—41no—
233D4×C101—41no—
234D4×C101—81no—
235D4×C101—82no—
236D4×C101—82no—
237D4×C101—161no—
238D4×C101—161no—
239C2×C4×C101—21no—
240C2×C4×C101—21no—
241C2×C4×C101—21no—
242C2×C4×C101—21no—
243C2×C4×C101—21no—
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—82no—
254C2×C4×C101—82no—
255C2×C4×C101—161no—
256C2×C4×C101C22×D411yescharacteristic
257C2×C4×C101C22×D411yescharacteristic
258C2×C4×C101H(5,𝔽2)11yescharacteristic
259C8×C101—21no—
260C8×C101—21no—
261C8×C101—21no—
262C8×C101—41no—
263C8×C101—41no—
264C8×C101—41no—
265C8×C101—41no—
266C8×C101—41no—
267C8×C101AGL(1,ℤ/8)12yes—
268C22×C101—41no—
269C22×C101—41no—
270C22×C101—41no—
271C22×C101—41no—
272C22×C101—41no—
273C22×C101—41no—
274C22×C101—41no—
275C22×C101—41no—
276C22×C101—41no—
277C22×C101—81no—
278C22×C101—81no—
279C22×C101—81no—
280C22×C101D4211yescharacteristic
281C4×C101—21no—
282C4×C101—41no—
283C4×C101—41no—
284C4×C101—41no—
285C4×C101—41no—
286C4×C101—41no—
287C4×C101—81no—
288C4×C101—81no—
289C4×C101—81no—
290C4×C101C2×AGL(1,ℤ/8)11yescharacteristic
291C4×C101#57511yescharacteristic
292C4×C101#57711yescharacteristic
293C4×C101#57811yescharacteristic
294#20222C10111yesmaximal, characteristic, direct product factor, Sylow
295C2×C101—81no—
296C2×C101—81no—
297C2×C101—81no—
298C2×C101—161no—
299C2×C101#326911yescharacteristic
300C2×C101#327211yescharacteristic
301C2×C101#328811yescharacteristic
302#3366C2×C10111yescharacteristic, complemented
303#3357C2×C10111yescharacteristic, complemented
304#3354C2×C10111yescharacteristic, complemented
305#3284C2×C10111yescharacteristic, complemented
306#1714C2×C10111yescharacteristic, complemented
307#1697C2×C10111yescharacteristic, complemented
308#1692C2×C10111yescharacteristic, complemented
309#1685C2×C10111yescharacteristic, complemented
310#1675C2×C10111yescharacteristic, complemented
311#1644C2×C10111yescharacteristic, complemented
312#1635C2×C10111yescharacteristic, complemented
313#1631C2×C10111yescharacteristic, complemented
314#1624C2×C10111yescharacteristic, complemented
315#1592C2×C10111yescharacteristic, complemented
316#1581C2×C10111yescharacteristic, complemented
317C101#2022211yescharacteristic, direct product factor, Sylow
318C2×#135—21no—
319#555C22×C10111yescharacteristic
320#554C22×C10111yescharacteristic
321#550C22×C10111yescharacteristic
322#547C22×C10111yescharacteristic
323#500C22×C10111yescharacteristic
324#498C22×C10111yescharacteristic
325#492C22×C10111yescharacteristic
326#492C22×C10111yescharacteristic
327#490—21no—
328#487C22×C10111yescharacteristic
329#486C22×C10111yescharacteristic
330#485—21no—
331#482—21no—
332#481—21no—
333#480—21no—
334#478—21no—
335#477C22×C10111yescharacteristic
336#476C22×C10111yescharacteristic
337#476C22×C10111yescharacteristic
338#476C22×C10111yescharacteristic
339#474C22×C10111yescharacteristic
340#469—21no—
341#468—21no—
342#465—21no—
343#462C22×C10111yescharacteristic
344#459—21no—
345#459C22×C10111yescharacteristic
346#459C22×C10111yescharacteristic
347#452—21no—
348#449—21no—
349#446C22×C10111yescharacteristic
350#442—21no—
351C4×SD16C22×C10111yescharacteristic
352C4×D8C22×C10111yescharacteristic
353#436C22×C10111yescharacteristic
354#436C22×C10111yescharacteristic
355C8×D4C22×C10111yescharacteristic
356#428—21no—
357#428—21no—
358#335C22×C10111yescharacteristic
359#335C22×C10111yescharacteristic
360#333C22×C10111yescharacteristic
361#333C22×C10111yescharacteristic
362#332C22×C10111yescharacteristic
363#331C22×C10111yescharacteristic
364Q8⋊C8C22×C10111yescharacteristic
365D4⋊C8C22×C10111yescharacteristic
366D4⋊C8C22×C10111yescharacteristic
367D4⋊C8C22×C10111yescharacteristic
368#322C22×C10111yescharacteristic
369C2×#41—21no—
370C2×#41—21no—
371#135—44no—
372C2×Q16—21no—
373C2×SD16—21no—
374C2×SD16—21no—
375C2×SD16—41no—
376C2×SD16D4×C10111yescharacteristic
377C2×D8—21no—
378C2×D8—21no—
379C2×D8D4×C10111yescharacteristic
380C2×M16—21no—
381C2×M16—21no—
382C22×C8—21no—
383C4⋊Q8C23×C10111yescharacteristic
384C4⋊Q8C23×C10111yescharacteristic
385C4⋊Q8C23×C10111yescharacteristic
386#127—21no—
387#127C23×C10111yescharacteristic
388#125—21no—
389#124—41no—
390#123—41no—
391C22⋊Q8—21no—
392C22⋊Q8—21no—
393C22⋊Q8—41no—
394#121—21no—
395#121—21no—
396#121—21no—
397#121—21no—
398#121—41no—
399C4×Q8C23×C10111yescharacteristic
400C4×D4—21no—
401C4×D4—21no—
402C4×D4C23×C10111yescharacteristic
403C4×D4C23×C10111yescharacteristic
404C4×D4C23×C10111yescharacteristic
405#117—21no—
406#117—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409#107—21no—
410#107—21no—
411#107—21no—
412#107—21no—
413#107D4×C10111yescharacteristic
414#106—21no—
415#106—21no—
416#106—21no—
417#106—21no—
418#106—21no—
419#106D4×C10111yescharacteristic
420C4⋊C8—21no—
421C4⋊C8C23×C10111yescharacteristic
422C4⋊C8C23×C10111yescharacteristic
423C4⋊C8C23×C10111yescharacteristic
424C4⋊C8C23×C10111yescharacteristic
425#103—21no—
426#103—21no—
427#103—41no—
428#103D4×C10111yescharacteristic
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102D4×C10111yescharacteristic
438#102D4×C10111yescharacteristic
439#102D4×C10111yescharacteristic
440C22⋊C8—21no—
441C22⋊C8—21no—
442C22⋊C8—21no—
443#97—21no—
444C4×C8C23×C10111yescharacteristic
445C4×C8C23×C10111yescharacteristic
446C4×C8C23×C10111yescharacteristic
447#41—42no—
448#41—42no—
449#41—81no—
450#41—81no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8C2×D4×C10111yescharacteristic
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4C2×D4×C10111yescharacteristic
463C2×D4C2×D4×C10111yescharacteristic
464C2×D4C2×D4×C10111yescharacteristic
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471Q16—42no—
472SD16—22no—
473SD16—42no—
474SD16—81no—
475SD16—82no—
476D8—41no—
477D8—42no—
478D8—42no—
479M16—42no—
480M16—42no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—42no—
487C2×C8C2×D4×C10111yescharacteristic
488C2×C8C2×D4×C10111yescharacteristic
489C2×C8C2×D4×C10111yescharacteristic
490C2×C8C2×D4×C10111yescharacteristic
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4C2×D4×C10111yescharacteristic
502C4⋊C4C2×D4×C10111yescharacteristic
503C4⋊C4C2×D4×C10111yescharacteristic
504C4⋊C4C2×D4×C10111yescharacteristic
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C42—21no—
514C42—41no—
515C42C24×C10111yescharacteristic
516C23—21no—
517C23—21no—
518C23—21no—
519C23—41no—
520Q8—21no—
521Q8—21no—
522Q8—41no—
523Q8—41no—
524Q8—81no—
525Q8—81no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—21no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—81no—
537D4—82no—
538D4—82no—
539D4—161no—
540D4—161no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—41no—
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—82no—
556C2×C4—82no—
557C2×C4—161no—
558C2×C4C22×D4×C10111yescharacteristic
559C2×C4C22×D4×C10111yescharacteristic
560C2×C4H(5,𝔽2)×C10111yescharacteristic
561C8—21no—
562C8—21no—
563C8—21no—
564C8—41no—
565C8—41no—
566C8—41no—
567C8—41no—
568C8—41no—
569C8AGL(1,ℤ/8)×C10112yes—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22D42×C10111yescharacteristic
583C4—21no—
584C4—41no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—81no—
590C4—81no—
591C4—81no—
592C4C2×AGL(1,ℤ/8)×C10111yescharacteristic
593C4#575×C10111yescharacteristic
594C4#577×C10111yescharacteristic
595C4#578×C10111yescharacteristic
596C2—81no—
597C2—81no—
598C2—81no—
599C2—161no—
600C2C101×#326911yescharacteristic
601C2C101×#327211yescharacteristic
602C2C101×#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×#3357C2semidirect
3. C101×#3354C2semidirect
4. C101×#3284C2semidirect
5. C101×#1714C2semidirect
6. C101×#1697C2semidirect
7. C101×#1692C2semidirect
8. C101×#1685C2semidirect
9. C101×#1675C2semidirect
10. C101×#1644C2semidirect
11. C101×#1635C2semidirect
12. C101×#1631C2semidirect
13. C101×#1624C2semidirect
14. C101×#1592C2semidirect
15. C101×#1581C2semidirect
294. #20222C101direct (N × H)
302. #3366C2×C101semidirect
303. #3357C2×C101semidirect
304. #3354C2×C101semidirect
305. #3284C2×C101semidirect
306. #1714C2×C101semidirect
307. #1697C2×C101semidirect
308. #1692C2×C101semidirect
309. #1685C2×C101semidirect
310. #1675C2×C101semidirect
311. #1644C2×C101semidirect
312. #1635C2×C101semidirect
313. #1631C2×C101semidirect
314. #1624C2×C101semidirect
315. #1592C2×C101semidirect
316. #1581C2×C101semidirect
317. C101#20222direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#33662
C101×#33572
C101×#33542
C101×#32842
C101×#17142
C101×#16972
C101×#16922
C101×#16852
C101×#16752
C101×#16442
C101×#16352
C101×#16312
C101×#16242
C101×#15922
C101×#15812
#20222101