Finite Group Databasebeta

← C101×#24058 #38806209

Subgroups — C101×#24058 #38806209

Order 25856.

1556 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×#3484C211yesmaximal, characteristic
2C101×#2622C212yesmaximal, complemented
3C101×#2308C211yesmaximal, characteristic, complemented
4C101×#2044C214yesmaximal, complemented
5C101×#1898C212yesmaximal, complemented
6C101×#1867C212yesmaximal, complemented
7C101×#1790C212yesmaximal, complemented
8C101×#1781C211yesmaximal, characteristic, complemented
9C2×H(5,𝔽2)×C101C2211yescharacteristic
10C23×D4×C101C2211yescharacteristic
11#546×C101—24no—
12D42×C101—24no—
13#535×C101—21no—
14#534×C101—21no—
15#534×C101C2212yes—
16#525×C101—21no—
17C2×#120×C101—21no—
18C2×#120×C101C2212yes—
19#518×C101C2211yescharacteristic
20C22×C22⋊C4×C101C2211yescharacteristic, complemented
21C22×C22⋊C4×C101C2211yescharacteristic, complemented
22C2×#99×C101C2212yes—
23C2×#99×C101C2214yescomplemented
24C2×#99×C101C2212yescomplemented
25#397×C101—24no—
26#394×C101—24no—
27#386×C101—21no—
28#386×C101—21no—
29#386×C101C2212yes—
30#386×C101C2212yescomplemented
31#386×C101C2214yescomplemented
32#385×C101C2214yescomplemented
33#381×C101—21no—
34#379×C101—21no—
35#379×C101C2212yescomplemented
36#342×C101C2214yescomplemented
37C25×C101D411yescharacteristic
38C25×C101C2311yescharacteristic
39H(5,𝔽2)×C101—24no—
40H(5,𝔽2)×C101—42no—
41C2×#41×C101—21no—
42C2×#41×C101—22no—
43C22×D4×C101—21no—
44C22×D4×C101—22no—
45C22×D4×C101—24no—
46C22×D4×C101—22no—
47C22×D4×C101—24no—
48C22×D4×C101—42no—
49C22×D4×C101D411yescharacteristic
50C22×D4×C101D411yescharacteristic
51C22×D4×C101D414yes—
52C22×D4×C101C2312yes—
53C22×D4×C101C2311yescharacteristic
54C22×D4×C101C2311yescharacteristic
55C23×C4×C101—21no—
56C23×C4×C101D411yescharacteristic
57C23×C4×C101C2312yes—
58#127×C101—22no—
59#124×C101—22no—
60#123×C101—22no—
61#123×C101—22no—
62#123×C101—22no—
63C22⋊Q8×C101—22no—
64#121×C101—22no—
65#121×C101—24no—
66#121×C101—24no—
67#121×C101—24no—
68#120×C101—24no—
69#120×C101—22no—
70#120×C101—22no—
71#120×C101—22no—
72#120×C101—22no—
73#120×C101—24no—
74#120×C101—22no—
75C4×D4×C101—24no—
76C4×D4×C101—24no—
77#117×C101—21no—
78C2×C4⋊C4×C101—24no—
79C2×C22⋊C4×C101—22no—
80C2×C22⋊C4×C101—21no—
81C2×C22⋊C4×C101—24no—
82C2×C22⋊C4×C101—21no—
83C2×C22⋊C4×C101—21no—
84C2×C22⋊C4×C101—21no—
85C2×C22⋊C4×C101—24no—
86C2×C22⋊C4×C101—22no—
87C2×C22⋊C4×C101—22no—
88C2×C22⋊C4×C101—24no—
89C2×C22⋊C4×C101—42no—
90C2×C22⋊C4×C101D414yes—
91C2×C22⋊C4×C101C2314yes—
92C2×C22⋊C4×C101C2312yes—
93C2×C22⋊C4×C101C2312yes—
94#99×C101—24no—
95#99×C101—42no—
96#99×C101—44no—
97#95×C101—24no—
98#95×C101—24no—
99#95×C101—22no—
100#95×C101—22no—
101C24×C101—22no—
102C24×C101—22no—
103C24×C101—21no—
104C24×C101—22no—
105C24×C101—22no—
106C24×C101—41no—
107C24×C101—82no—
108C24×C101—82no—
109C24×C101C2×D411yescharacteristic
110C24×C101C2×D412yes—
111C24×C101C2×D414yes—
112C24×C101C2×D411yescharacteristic
113C24×C101C2×D411yescharacteristic
114C24×C101C2×D411yescharacteristic
115C24×C101C2411yescharacteristic
116#41×C101—48no—
117#41×C101—42no—
118#41×C101—42no—
119C2×Q8×C101—21no—
120C2×D4×C101—22no—
121C2×D4×C101—22no—
122C2×D4×C101—22no—
123C2×D4×C101—21no—
124C2×D4×C101—24no—
125C2×D4×C101—22no—
126C2×D4×C101—22no—
127C2×D4×C101—22no—
128C2×D4×C101—22no—
129C2×D4×C101—22no—
130C2×D4×C101—22no—
131C2×D4×C101—22no—
132C2×D4×C101—24no—
133C2×D4×C101—22no—
134C2×D4×C101—24no—
135C2×D4×C101—24no—
136C2×D4×C101—24no—
137C2×D4×C101—22no—
138C2×D4×C101—41no—
139C2×D4×C101—41no—
140C2×D4×C101—416no—
141C2×D4×C101—48no—
142C2×D4×C101—42no—
143C2×D4×C101—42no—
144C2×D4×C101—84no—
145C2×D4×C101—84no—
146C2×D4×C101#4114yes—
147C22×C4×C101—21no—
148C22×C4×C101—22no—
149C22×C4×C101—22no—
150C22×C4×C101—22no—
151C22×C4×C101—22no—
152C22×C4×C101—22no—
153C22×C4×C101—24no—
154C22×C4×C101—22no—
155C22×C4×C101—24no—
156C22×C4×C101—41no—
157C22×C4×C101—42no—
158C22×C4×C101—82no—
159C22×C4×C101—82no—
160C22×C4×C101C2×D412yes—
161C22×C4×C101C2×D411yescharacteristic
162C22×C4×C101C2×D411yescharacteristic
163C22×C4×C101C2×D414yes—
164C4⋊C4×C101—22no—
165C4⋊C4×C101—24no—
166C4⋊C4×C101—84no—
167C22⋊C4×C101—22no—
168C22⋊C4×C101—24no—
169C22⋊C4×C101—24no—
170C22⋊C4×C101—24no—
171C22⋊C4×C101—24no—
172C22⋊C4×C101—22no—
173C22⋊C4×C101—22no—
174C22⋊C4×C101—24no—
175C22⋊C4×C101—24no—
176C22⋊C4×C101—24no—
177C22⋊C4×C101—42no—
178C22⋊C4×C101—42no—
179C22⋊C4×C101—42no—
180C22⋊C4×C101—84no—
181C22⋊C4×C101—84no—
182C22⋊C4×C101—82no—
183C22⋊C4×C101—82no—
184C42×C101—22no—
185C23×C101—21no—
186C23×C101—21no—
187C23×C101—21no—
188C23×C101—21no—
189C23×C101—21no—
190C23×C101—21no—
191C23×C101—28no—
192C23×C101—21no—
193C23×C101—22no—
194C23×C101—21no—
195C23×C101—21no—
196C23×C101—24no—
197C23×C101—42no—
198C23×C101—42no—
199C23×C101—42no—
200C23×C101—44no—
201C23×C101—44no—
202C23×C101—44no—
203C23×C101—42no—
204C23×C101—42no—
205C23×C101—44no—
206C23×C101—42no—
207C23×C101—44no—
208C23×C101—82no—
209C23×C101—84no—
210C23×C101—84no—
211C23×C101—84no—
212C23×C101—82no—
213C23×C101—84no—
214C23×C101#12012yes—
215C23×C101#12012yes—
216C23×C101#12312yes—
217C23×C101C22×D411yescharacteristic
218C23×C101C22×D412yes—
219C23×C101C2×#4112yes—
220C23×C101H(5,𝔽2)12yes—
221Q8×C101—42no—
222D4×C101—28no—
223D4×C101—44no—
224D4×C101—42no—
225D4×C101—44no—
226D4×C101—44no—
227D4×C101—48no—
228D4×C101—42no—
229D4×C101—42no—
230D4×C101—44no—
231D4×C101—44no—
232D4×C101—84no—
233D4×C101—84no—
234C2×C4×C101—21no—
235C2×C4×C101—21no—
236C2×C4×C101—24no—
237C2×C4×C101—22no—
238C2×C4×C101—21no—
239C2×C4×C101—21no—
240C2×C4×C101—21no—
241C2×C4×C101—24no—
242C2×C4×C101—44no—
243C2×C4×C101—44no—
244C2×C4×C101—42no—
245C2×C4×C101—44no—
246C2×C4×C101—44no—
247C2×C4×C101—44no—
248C2×C4×C101—42no—
249C2×C4×C101—42no—
250C2×C4×C101—44no—
251C2×C4×C101—42no—
252C2×C4×C101—42no—
253C2×C4×C101—44no—
254C2×C4×C101—42no—
255C2×C4×C101—42no—
256C2×C4×C101—44no—
257C2×C4×C101—82no—
258C2×C4×C101—84no—
259C2×C4×C101#12312yes—
260C22×C101—24no—
261C22×C101—22no—
262C22×C101—22no—
263C22×C101—22no—
264C22×C101—22no—
265C22×C101—22no—
266C22×C101—24no—
267C22×C101—22no—
268C22×C101—42no—
269C22×C101—42no—
270C22×C101—42no—
271C22×C101—42no—
272C22×C101—42no—
273C22×C101—42no—
274C22×C101—42no—
275C22×C101—42no—
276C22×C101—42no—
277C22×C101—42no—
278C22×C101—41no—
279C22×C101—44no—
280C22×C101—42no—
281C22×C101—81no—
282C22×C101—88no—
283C22×C101—84no—
284C22×C101—81no—
285C22×C101—88no—
286C22×C101—162no—
287C22×C101C2×#12011yescharacteristic
288C22×C101C2×#12311yescharacteristic
289C22×C101#53411yescharacteristic
290C22×C101#54614yes—
291C4×C101—22no—
292C4×C101—41no—
293C4×C101—42no—
294C4×C101—44no—
295C4×C101—84no—
296C4×C101—82no—
297C4×C101—82no—
298#24058C10111yesmaximal, characteristic, direct product factor, Sylow
299C2×C101—21no—
300C2×C101—24no—
301C2×C101—21no—
302C2×C101—42no—
303C2×C101—42no—
304C2×C101—42no—
305C2×C101—81no—
306C2×C101—82no—
307C2×C101#240511yescharacteristic
308C2×C101#302612yes—
309#3484C2×C10111yescharacteristic
310#2622C2×C10112yescomplemented
311#2308C2×C10111yescharacteristic, complemented
312#2044C2×C10114yescomplemented
313#1898C2×C10112yescomplemented
314#1867C2×C10112yescomplemented
315#1790C2×C10112yescomplemented
316#1781C2×C10111yescharacteristic, complemented
317C101#2405811yescharacteristic, direct product factor, Sylow
318C2×H(5,𝔽2)C22×C10111yescharacteristic
319C23×D4C22×C10111yescharacteristic
320#546—24no—
321D42—24no—
322#535—21no—
323#534—21no—
324#534C22×C10112yes—
325#525—21no—
326C2×#120—21no—
327C2×#120C22×C10112yes—
328#518C22×C10111yescharacteristic
329C22×C22⋊C4C22×C10111yescharacteristic, complemented
330C22×C22⋊C4C22×C10111yescharacteristic, complemented
331C2×#99C22×C10112yes—
332C2×#99C22×C10114yescomplemented
333C2×#99C22×C10112yescomplemented
334#397—24no—
335#394—24no—
336#386—21no—
337#386—21no—
338#386C22×C10112yes—
339#386C22×C10112yescomplemented
340#386C22×C10114yescomplemented
341#385C22×C10114yescomplemented
342#381—21no—
343#379—21no—
344#379C22×C10112yescomplemented
345#342C22×C10114yescomplemented
346C25D4×C10111yescharacteristic
347C25C23×C10111yescharacteristic
348H(5,𝔽2)—24no—
349H(5,𝔽2)—42no—
350C2×#41—21no—
351C2×#41—22no—
352C22×D4—21no—
353C22×D4—22no—
354C22×D4—24no—
355C22×D4—22no—
356C22×D4—24no—
357C22×D4—42no—
358C22×D4D4×C10111yescharacteristic
359C22×D4D4×C10111yescharacteristic
360C22×D4D4×C10114yes—
361C22×D4C23×C10112yes—
362C22×D4C23×C10111yescharacteristic
363C22×D4C23×C10111yescharacteristic
364C23×C4—21no—
365C23×C4D4×C10111yescharacteristic
366C23×C4C23×C10112yes—
367#127—22no—
368#124—22no—
369#123—22no—
370#123—22no—
371#123—22no—
372C22⋊Q8—22no—
373#121—22no—
374#121—24no—
375#121—24no—
376#121—24no—
377#120—24no—
378#120—22no—
379#120—22no—
380#120—22no—
381#120—22no—
382#120—24no—
383#120—22no—
384C4×D4—24no—
385C4×D4—24no—
386#117—21no—
387C2×C4⋊C4—24no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4D4×C10114yes—
400C2×C22⋊C4C23×C10112yes—
401C2×C22⋊C4C23×C10114yes—
402C2×C22⋊C4C23×C10112yes—
403#99—24no—
404#99—42no—
405#99—44no—
406#95—22no—
407#95—22no—
408#95—24no—
409#95—24no—
410C24—22no—
411C24—22no—
412C24—21no—
413C24—22no—
414C24—22no—
415C24—41no—
416C24—82no—
417C24—82no—
418C24C2×D4×C10111yescharacteristic
419C24C2×D4×C10112yes—
420C24C2×D4×C10114yes—
421C24C2×D4×C10111yescharacteristic
422C24C2×D4×C10111yescharacteristic
423C24C2×D4×C10111yescharacteristic
424C24C24×C10111yescharacteristic
425#41—48no—
426#41—42no—
427#41—42no—
428C2×Q8—21no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—21no—
433C2×D4—24no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—24no—
442C2×D4—22no—
443C2×D4—24no—
444C2×D4—24no—
445C2×D4—24no—
446C2×D4—22no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—416no—
450C2×D4—48no—
451C2×D4—42no—
452C2×D4—42no—
453C2×D4—84no—
454C2×D4—84no—
455C2×D4#41×C10114yes—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—41no—
466C22×C4—42no—
467C22×C4—82no—
468C22×C4—82no—
469C22×C4C2×D4×C10112yes—
470C22×C4C2×D4×C10111yescharacteristic
471C22×C4C2×D4×C10111yescharacteristic
472C22×C4C2×D4×C10114yes—
473C4⋊C4—22no—
474C4⋊C4—24no—
475C4⋊C4—84no—
476C22⋊C4—22no—
477C22⋊C4—24no—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4—24no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—24no—
484C22⋊C4—24no—
485C22⋊C4—24no—
486C22⋊C4—42no—
487C22⋊C4—42no—
488C22⋊C4—42no—
489C22⋊C4—84no—
490C22⋊C4—84no—
491C22⋊C4—82no—
492C22⋊C4—82no—
493C42—22no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—28no—
501C23—21no—
502C23—22no—
503C23—21no—
504C23—21no—
505C23—24no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—44no—
510C23—44no—
511C23—44no—
512C23—42no—
513C23—42no—
514C23—44no—
515C23—42no—
516C23—44no—
517C23—82no—
518C23—84no—
519C23—84no—
520C23—84no—
521C23—82no—
522C23—84no—
523C23#120×C10112yes—
524C23#120×C10112yes—
525C23#123×C10112yes—
526C23C22×D4×C10111yescharacteristic
527C23C22×D4×C10112yes—
528C23C2×#41×C10112yes—
529C23H(5,𝔽2)×C10112yes—
530Q8—42no—
531D4—28no—
532D4—44no—
533D4—42no—
534D4—44no—
535D4—44no—
536D4—48no—
537D4—42no—
538D4—42no—
539D4—44no—
540D4—44no—
541D4—84no—
542D4—84no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—24no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—24no—
551C2×C4—44no—
552C2×C4—44no—
553C2×C4—42no—
554C2×C4—44no—
555C2×C4—44no—
556C2×C4—44no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—44no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—44no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—44no—
566C2×C4—82no—
567C2×C4—84no—
568C2×C4#123×C10112yes—
569C22—24no—
570C22—22no—
571C22—22no—
572C22—22no—
573C22—22no—
574C22—22no—
575C22—24no—
576C22—22no—
577C22—42no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—41no—
588C22—44no—
589C22—42no—
590C22—81no—
591C22—88no—
592C22—81no—
593C22—84no—
594C22—88no—
595C22—162no—
596C22C2×#120×C10111yescharacteristic
597C22C2×#123×C10111yescharacteristic
598C22#534×C10111yescharacteristic
599C22#546×C10114yes—
600C4—22no—
601C4—41no—
602C4—42no—
603C4—44no—
604C4—82no—
605C4—84no—
606C4—82no—
607C2—21no—
608C2—24no—
609C2—21no—
610C2—42no—
611C2—42no—
612C2—42no—
613C2—81no—
614C2—82no—
615C2C101×#240511yescharacteristic
616C2C101×#302612yes—
subgroupG/H
center, socleC22×C101C2×#120
commutator, Frattini, cosocleC24C24×C101
prime radicalC101×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C101 ◁ C25×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#2622C2semidirect
3. C101×#2308C2semidirect
4. C101×#2044C2semidirect
5. C101×#1898C2semidirect
6. C101×#1867C2semidirect
7. C101×#1790C2semidirect
8. C101×#1781C2semidirect
20. C22×C22⋊C4×C101C22semidirect
21. C22×C22⋊C4×C101C22semidirect
23. C2×#99×C101C22semidirect
24. C2×#99×C101C22semidirect
30. #386×C101C22semidirect
31. #386×C101C22semidirect
32. #385×C101C22semidirect
35. #379×C101C22semidirect
36. #342×C101C22semidirect
298. #24058C101direct (N × H)
310. #2622C2×C101semidirect
311. #2308C2×C101semidirect
312. #2044C2×C101semidirect
313. #1898C2×C101semidirect
314. #1867C2×C101semidirect
315. #1790C2×C101semidirect
316. #1781C2×C101semidirect
317. C101#24058direct (N × H)
329. C22×C22⋊C4C22×C101semidirect
330. C22×C22⋊C4C22×C101semidirect
332. C2×#99C22×C101semidirect
333. C2×#99C22×C101semidirect
339. #386C22×C101semidirect
340. #386C22×C101semidirect
341. #385C22×C101semidirect
344. #379C22×C101semidirect
345. #342C22×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#34842
C101×#26222
C101×#23082
C101×#20442
C101×#18982
C101×#18672
C101×#17902
C101×#17812
#24058101