Finite Group Databasebeta

← C101×#20315 #38802466

Subgroups — C101×#20315 #38802466

Order 25856.

624 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3384C211yesmaximal, characteristic, complemented
2C101×#3357C211yesmaximal, characteristic, complemented
3C101×#3354C211yesmaximal, characteristic
4C101×#3276C211yesmaximal, characteristic, complemented
5C101×#1707C211yesmaximal, characteristic, complemented
6C101×#1695C211yesmaximal, characteristic, complemented
7C101×#1692C211yesmaximal, characteristic, complemented
8C101×#1691C211yesmaximal, characteristic, complemented
9C101×#1689C211yesmaximal, characteristic, complemented
10C101×#1646C211yesmaximal, characteristic, complemented
11C101×#1644C211yesmaximal, characteristic, complemented
12C101×#1637C211yesmaximal, characteristic, complemented
13C101×#1635C211yesmaximal, characteristic, complemented
14C101×#1590C211yesmaximal, characteristic, complemented
15C101×#1589C211yesmaximal, characteristic, complemented
16C2×#137×C101—21no—
17#555×C101C2211yescharacteristic
18#554×C101C2211yescharacteristic
19D4×Q8×C101C2211yescharacteristic
20#547×C101C2211yescharacteristic
21#501×C101—21no—
22#500×C101C2211yescharacteristic
23#498×C101C2211yescharacteristic
24#498×C101C2211yescharacteristic
25#494×C101C2211yescharacteristic
26#487×C101C2211yescharacteristic
27#487×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×C101—21no—
35#476×C101C2211yescharacteristic
36#476×C101C2211yescharacteristic
37#476×C101C2211yescharacteristic
38#474×C101C2211yescharacteristic
39#474×C101C2211yescharacteristic
40#470×C101—21no—
41#469×C101—21no—
42#468×C101—21no—
43#462×C101C2211yescharacteristic
44#461×C101C2211yescharacteristic
45#452×C101—21no—
46#451×C101—21no—
47#446×C101C2211yescharacteristic
48#442×C101—21no—
49C4×SD16×C101C2211yescharacteristic
50C4×D8×C101C2211yescharacteristic
51#436×C101C2211yescharacteristic
52#436×C101C2211yescharacteristic
53#436×C101C2211yescharacteristic
54#428×C101—21no—
55#428×C101—21no—
56#335×C101C2211yescharacteristic
57#334×C101C2211yescharacteristic
58#333×C101C2211yescharacteristic
59#333×C101C2211yescharacteristic
60#332×C101C2211yescharacteristic
61#332×C101C2211yescharacteristic
62Q8⋊C8×C101C2211yescharacteristic
63D4⋊C8×C101C2211yescharacteristic
64D4⋊C8×C101C2211yescharacteristic
65D4⋊C8×C101C2211yescharacteristic
66C82×C101C2211yescharacteristic
67C2×#41×C101—21no—
68C22×Q8×C101—21no—
69#137×C101—44no—
70C2×Q16×C101—21no—
71C2×Q16×C101—21no—
72C2×Q16×C101—21no—
73C2×SD16×C101—21no—
74C2×SD16×C101D411yescharacteristic
75C2×D8×C101D411yescharacteristic
76C2×M16×C101—21no—
77C2×M16×C101—21no—
78C2×M16×C101—21no—
79C4⋊Q8×C101—21no—
80C4⋊Q8×C101C2311yescharacteristic
81C4⋊Q8×C101C2311yescharacteristic
82C4⋊Q8×C101C2311yescharacteristic
83C4⋊Q8×C101C2311yescharacteristic
84#125×C101—21no—
85#124×C101—41no—
86#123×C101—41no—
87C22⋊Q8×C101—21no—
88C22⋊Q8×C101—21no—
89C22⋊Q8×C101—21no—
90C22⋊Q8×C101—41no—
91C22⋊Q8×C101—41no—
92#121×C101—21no—
93#121×C101—21no—
94#121×C101—21no—
95C4×Q8×C101C2311yescharacteristic
96C4×D4×C101—21no—
97C4×D4×C101—21no—
98C4×D4×C101C2311yescharacteristic
99C4×D4×C101C2311yescharacteristic
100C4×D4×C101C2311yescharacteristic
101#117×C101—21no—
102#117×C101—21no—
103C2×C4⋊C4×C101—21no—
104C2×C4⋊C4×C101—21no—
105#107×C101—21no—
106#107×C101—21no—
107#107×C101—21no—
108#107×C101—21no—
109#107×C101—21no—
110#107×C101D411yescharacteristic
111#106×C101—21no—
112#106×C101—21no—
113#106×C101—21no—
114#106×C101—21no—
115#106×C101—21no—
116#106×C101—21no—
117#106×C101—21no—
118#106×C101D411yescharacteristic
119C4⋊C8×C101—21no—
120C4⋊C8×C101C2311yescharacteristic
121C4⋊C8×C101C2311yescharacteristic
122C4⋊C8×C101C2311yescharacteristic
123C4⋊C8×C101C2311yescharacteristic
124#103×C101—21no—
125#103×C101—21no—
126#103×C101—21no—
127#103×C101—41no—
128#103×C101—41no—
129#103×C101D411yescharacteristic
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—81no—
147C2×Q8×C101—21no—
148C2×Q8×C101—21no—
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×D4×C101—41no—
156C2×D4×C101—41no—
157C2×D4×C101C2×D411yescharacteristic
158C2×D4×C101C2×D411yescharacteristic
159C2×D4×C101C2×D411yescharacteristic
160C22×C4×C101—21no—
161C22×C4×C101—21no—
162C22×C4×C101—21no—
163C22×C4×C101—41no—
164C22×C4×C101—41no—
165C22×C4×C101—41no—
166Q16×C101—42no—
167Q16×C101—42no—
168Q16×C101—81no—
169SD16×C101—22no—
170SD16×C101—42no—
171D8×C101—22no—
172M16×C101—42no—
173M16×C101—42no—
174M16×C101—42no—
175C2×C8×C101—21no—
176C2×C8×C101—21no—
177C2×C8×C101—21no—
178C2×C8×C101—21no—
179C2×C8×C101—21no—
180C2×C8×C101C2×D411yescharacteristic
181C2×C8×C101C2×D411yescharacteristic
182C2×C8×C101C2×D411yescharacteristic
183C2×C8×C101C2×D411yescharacteristic
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—21no—
192C4⋊C4×C101—21no—
193C4⋊C4×C101—41no—
194C4⋊C4×C101—41no—
195C4⋊C4×C101—41no—
196C4⋊C4×C101—41no—
197C4⋊C4×C101C2×D411yescharacteristic
198C4⋊C4×C101C2×D411yescharacteristic
199C4⋊C4×C101C2×D411yescharacteristic
200C4⋊C4×C101C2×D411yescharacteristic
201C22⋊C4×C101—21no—
202C22⋊C4×C101—21no—
203C22⋊C4×C101—21no—
204C22⋊C4×C101—41no—
205C22⋊C4×C101—41no—
206C22⋊C4×C101—41no—
207C22⋊C4×C101—41no—
208C22⋊C4×C101—41no—
209C42×C101—21no—
210C42×C101—41no—
211C42×C101C2411yescharacteristic
212C23×C101—21no—
213C23×C101—21no—
214C23×C101—21no—
215Q8×C101—21no—
216Q8×C101—21no—
217Q8×C101—41no—
218Q8×C101—41no—
219Q8×C101—41no—
220Q8×C101—41no—
221Q8×C101—81no—
222Q8×C101—81no—
223Q8×C101—82no—
224D4×C101—21no—
225D4×C101—21no—
226D4×C101—21no—
227D4×C101—21no—
228D4×C101—21no—
229D4×C101—21no—
230D4×C101—82no—
231D4×C101—161no—
232C2×C4×C101—21no—
233C2×C4×C101—21no—
234C2×C4×C101—21no—
235C2×C4×C101—21no—
236C2×C4×C101—21no—
237C2×C4×C101—41no—
238C2×C4×C101—41no—
239C2×C4×C101—41no—
240C2×C4×C101—41no—
241C2×C4×C101—41no—
242C2×C4×C101—41no—
243C2×C4×C101—41no—
244C2×C4×C101—41no—
245C2×C4×C101—41no—
246C2×C4×C101—41no—
247C2×C4×C101—82no—
248C2×C4×C101—82no—
249C2×C4×C101—161no—
250C2×C4×C101C22×D411yescharacteristic
251C2×C4×C101C22×D411yescharacteristic
252C2×C4×C101H(5,𝔽2)11yescharacteristic
253C8×C101—21no—
254C8×C101—21no—
255C8×C101—41no—
256C8×C101—41no—
257C8×C101—41no—
258C8×C101—41no—
259C8×C101—41no—
260C8×C101AGL(1,ℤ/8)12yes—
261C8×C101#13712yescomplemented
262C22×C101—41no—
263C22×C101—41no—
264C22×C101—41no—
265C22×C101—41no—
266C22×C101—41no—
267C22×C101—41no—
268C22×C101—41no—
269C22×C101—41no—
270C22×C101—41no—
271C22×C101D4211yescharacteristic
272C4×C101—21no—
273C4×C101—41no—
274C4×C101—41no—
275C4×C101—41no—
276C4×C101—41no—
277C4×C101—41no—
278C4×C101—81no—
279C4×C101—81no—
280C4×C101—81no—
281C4×C101—81no—
282C4×C101C2×AGL(1,ℤ/8)11yescharacteristic
283C4×C101C2×#13711yescharacteristic
284C4×C101#57711yescharacteristic
285C4×C101#57811yescharacteristic
286#20315C10111yesmaximal, characteristic, direct product factor, Sylow
287C2×C101—81no—
288C2×C101—81no—
289C2×C101—81no—
290C2×C101#327211yescharacteristic
291C2×C101#327611yescharacteristic
292C2×C101#329011yescharacteristic
293#3384C2×C10111yescharacteristic, complemented
294#3357C2×C10111yescharacteristic, complemented
295#3354C2×C10111yescharacteristic
296#3276C2×C10111yescharacteristic, complemented
297#1707C2×C10111yescharacteristic, complemented
298#1695C2×C10111yescharacteristic, complemented
299#1692C2×C10111yescharacteristic, complemented
300#1691C2×C10111yescharacteristic, complemented
301#1689C2×C10111yescharacteristic, complemented
302#1646C2×C10111yescharacteristic, complemented
303#1644C2×C10111yescharacteristic, complemented
304#1637C2×C10111yescharacteristic, complemented
305#1635C2×C10111yescharacteristic, complemented
306#1590C2×C10111yescharacteristic, complemented
307#1589C2×C10111yescharacteristic, complemented
308C101#2031511yescharacteristic, direct product factor, Sylow
309C2×#137—21no—
310#555C22×C10111yescharacteristic
311#554C22×C10111yescharacteristic
312D4×Q8C22×C10111yescharacteristic
313#547C22×C10111yescharacteristic
314#501—21no—
315#500C22×C10111yescharacteristic
316#498C22×C10111yescharacteristic
317#498C22×C10111yescharacteristic
318#494C22×C10111yescharacteristic
319#487C22×C10111yescharacteristic
320#487C22×C10111yescharacteristic
321#485—21no—
322#482—21no—
323#481—21no—
324#480—21no—
325#478—21no—
326#477C22×C10111yescharacteristic
327#476—21no—
328#476C22×C10111yescharacteristic
329#476C22×C10111yescharacteristic
330#476C22×C10111yescharacteristic
331#474C22×C10111yescharacteristic
332#474C22×C10111yescharacteristic
333#470—21no—
334#469—21no—
335#468—21no—
336#462C22×C10111yescharacteristic
337#461C22×C10111yescharacteristic
338#452—21no—
339#451—21no—
340#446C22×C10111yescharacteristic
341#442—21no—
342C4×SD16C22×C10111yescharacteristic
343C4×D8C22×C10111yescharacteristic
344#436C22×C10111yescharacteristic
345#436C22×C10111yescharacteristic
346#436C22×C10111yescharacteristic
347#428—21no—
348#428—21no—
349#335C22×C10111yescharacteristic
350#334C22×C10111yescharacteristic
351#333C22×C10111yescharacteristic
352#333C22×C10111yescharacteristic
353#332C22×C10111yescharacteristic
354#332C22×C10111yescharacteristic
355Q8⋊C8C22×C10111yescharacteristic
356D4⋊C8C22×C10111yescharacteristic
357D4⋊C8C22×C10111yescharacteristic
358D4⋊C8C22×C10111yescharacteristic
359C82C22×C10111yescharacteristic
360C2×#41—21no—
361C22×Q8—21no—
362#137—44no—
363C2×Q16—21no—
364C2×Q16—21no—
365C2×Q16—21no—
366C2×SD16—21no—
367C2×SD16D4×C10111yescharacteristic
368C2×D8D4×C10111yescharacteristic
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C4⋊Q8—21no—
373C4⋊Q8C23×C10111yescharacteristic
374C4⋊Q8C23×C10111yescharacteristic
375C4⋊Q8C23×C10111yescharacteristic
376C4⋊Q8C23×C10111yescharacteristic
377#125—21no—
378#124—41no—
379#123—41no—
380C22⋊Q8—21no—
381C22⋊Q8—21no—
382C22⋊Q8—21no—
383C22⋊Q8—41no—
384C22⋊Q8—41no—
385#121—21no—
386#121—21no—
387#121—21no—
388C4×Q8C23×C10111yescharacteristic
389C4×D4—21no—
390C4×D4—21no—
391C4×D4C23×C10111yescharacteristic
392C4×D4C23×C10111yescharacteristic
393C4×D4C23×C10111yescharacteristic
394#117—21no—
395#117—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398#107—21no—
399#107—21no—
400#107—21no—
401#107—21no—
402#107—21no—
403#107D4×C10111yescharacteristic
404#106—21no—
405#106—21no—
406#106—21no—
407#106—21no—
408#106—21no—
409#106—21no—
410#106—21no—
411#106D4×C10111yescharacteristic
412C4⋊C8—21no—
413C4⋊C8C23×C10111yescharacteristic
414C4⋊C8C23×C10111yescharacteristic
415C4⋊C8C23×C10111yescharacteristic
416C4⋊C8C23×C10111yescharacteristic
417#103—21no—
418#103—21no—
419#103—21no—
420#103—41no—
421#103—41no—
422#103D4×C10111yescharacteristic
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102D4×C10111yescharacteristic
429#102D4×C10111yescharacteristic
430#102D4×C10111yescharacteristic
431C22⋊C8—21no—
432C22⋊C8—21no—
433C22⋊C8—21no—
434#97—21no—
435C4×C8C23×C10111yescharacteristic
436C4×C8C23×C10111yescharacteristic
437C4×C8C23×C10111yescharacteristic
438#41—42no—
439#41—81no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—41no—
445C2×Q8—42no—
446C2×Q8—81no—
447C2×Q8C2×D4×C10111yescharacteristic
448C2×D4—41no—
449C2×D4—41no—
450C2×D4C2×D4×C10111yescharacteristic
451C2×D4C2×D4×C10111yescharacteristic
452C2×D4C2×D4×C10111yescharacteristic
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459Q16—42no—
460Q16—42no—
461Q16—81no—
462SD16—22no—
463SD16—42no—
464D8—22no—
465M16—42no—
466M16—42no—
467M16—42no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8C2×D4×C10111yescharacteristic
474C2×C8C2×D4×C10111yescharacteristic
475C2×C8C2×D4×C10111yescharacteristic
476C2×C8C2×D4×C10111yescharacteristic
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4C2×D4×C10111yescharacteristic
491C4⋊C4C2×D4×C10111yescharacteristic
492C4⋊C4C2×D4×C10111yescharacteristic
493C4⋊C4C2×D4×C10111yescharacteristic
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C42—21no—
503C42—41no—
504C42C24×C10111yescharacteristic
505C23—21no—
506C23—21no—
507C23—21no—
508Q8—21no—
509Q8—21no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—81no—
515Q8—81no—
516Q8—82no—
517D4—21no—
518D4—21no—
519D4—21no—
520D4—21no—
521D4—21no—
522D4—21no—
523D4—82no—
524D4—161no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—82no—
541C2×C4—82no—
542C2×C4—161no—
543C2×C4C22×D4×C10111yescharacteristic
544C2×C4C22×D4×C10111yescharacteristic
545C2×C4H(5,𝔽2)×C10111yescharacteristic
546C8—21no—
547C8—21no—
548C8—41no—
549C8—41no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8AGL(1,ℤ/8)×C10112yes—
554C8#137×C10112yescomplemented
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22D42×C10111yescharacteristic
565C4—21no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4C2×AGL(1,ℤ/8)×C10111yescharacteristic
576C4C2×#137×C10111yescharacteristic
577C4#577×C10111yescharacteristic
578C4#578×C10111yescharacteristic
579C2—81no—
580C2—81no—
581C2—81no—
582C2C101×#327211yescharacteristic
583C2C101×#327611yescharacteristic
584C2C101×#329011yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC42C24×C101
prime radicalC101×#3354C2
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×#3384C2semidirect
2. C101×#3357C2semidirect
4. C101×#3276C2semidirect
5. C101×#1707C2semidirect
6. C101×#1695C2semidirect
7. C101×#1692C2semidirect
8. C101×#1691C2semidirect
9. C101×#1689C2semidirect
10. C101×#1646C2semidirect
11. C101×#1644C2semidirect
12. C101×#1637C2semidirect
13. C101×#1635C2semidirect
14. C101×#1590C2semidirect
15. C101×#1589C2semidirect
261. C8×C101#137semidirect
286. #20315C101direct (N × H)
293. #3384C2×C101semidirect
294. #3357C2×C101semidirect
296. #3276C2×C101semidirect
297. #1707C2×C101semidirect
298. #1695C2×C101semidirect
299. #1692C2×C101semidirect
300. #1691C2×C101semidirect
301. #1689C2×C101semidirect
302. #1646C2×C101semidirect
303. #1644C2×C101semidirect
304. #1637C2×C101semidirect
305. #1635C2×C101semidirect
306. #1590C2×C101semidirect
307. #1589C2×C101semidirect
308. C101#20315direct (N × H)
554. C8#137×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#33842
C101×#33572
C101×#33542
C101×#32762
C101×#17072
C101×#16952
C101×#16922
C101×#16912
C101×#16892
C101×#16462
C101×#16442
C101×#16372
C101×#16352
C101×#15902
C101×#15892
#20315101