Finite Group Databasebeta

← C101×#14422 #38796573

Subgroups — C101×#14422 #38796573

Order 25856.

1506 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#388×C101C212yesmaximal
2C2×#380×C101C211yesmaximal, characteristic
3C101×#1442C212yesmaximal, complemented
4C101×#1441C212yesmaximal, complemented
5C101×#1440C212yesmaximal
6C101×#1436C212yesmaximal, complemented
7C101×#1434C212yesmaximal, complemented
8C101×C22⋊#95C211yesmaximal, characteristic
9C101×C22⋊#95C211yesmaximal, characteristic
10C24×C4×C101C2211yescharacteristic
11C22×C4⋊C4×C101C2212yes—
12C22×C4⋊C4×C101C2211yescharacteristic
13C22×C4⋊C4×C101C2211yescharacteristic
14C22×C22⋊C4×C101C2212yes—
15C22×C22⋊C4×C101C2212yes—
16C22×C22⋊C4×C101C2211yescharacteristic
17C22×C22⋊C4×C101C2211yescharacteristic
18C22×C42×C101C2212yes—
19#388×C101—28no—
20#380×C101C418yescomplemented
21C2×#95×C101C2212yes—
22C2×#95×C101C2212yes—
23C2×#95×C101C2212yes—
24C2×#95×C101C2212yes—
25C2×#95×C101C2212yes—
26C2×#95×C101C2211yescharacteristic
27C2×#95×C101C2212yes—
28C2×#95×C101C2211yescharacteristic
29C2×#95×C101C2212yes—
30C2×#95×C101C2212yes—
31C2×#95×C101C2212yes—
32C2×#95×C101C2212yes—
33C25×C101C2311yescharacteristic
34C23×C4×C101—24no—
35C23×C4×C101—41no—
36C23×C4×C101—41no—
37C23×C4×C101—42no—
38C23×C4×C101C2×C414yes—
39C23×C4×C101C2312yes—
40C23×C4×C101C2312yes—
41C23×C4×C101C2312yes—
42C23×C4×C101C2312yes—
43C23×C4×C101C2311yescharacteristic
44C23×C4×C101C2312yes—
45C23×C4×C101C2312yes—
46C23×C4×C101C2311yescharacteristic
47C2×C4⋊C4×C101—24no—
48C2×C4⋊C4×C101—41no—
49C2×C4⋊C4×C101—42no—
50C2×C4⋊C4×C101—41no—
51C2×C4⋊C4×C101—42no—
52C2×C4⋊C4×C101—42no—
53C2×C4⋊C4×C101C2×C414yes—
54C2×C4⋊C4×C101C2×C414yes—
55C2×C22⋊C4×C101—24no—
56C2×C22⋊C4×C101—24no—
57C2×C22⋊C4×C101—24no—
58C2×C22⋊C4×C101—22no—
59C2×C22⋊C4×C101—24no—
60C2×C22⋊C4×C101—41no—
61C2×C22⋊C4×C101—41no—
62C2×C22⋊C4×C101—42no—
63C2×C22⋊C4×C101—41no—
64C2×C22⋊C4×C101—41no—
65C2×C22⋊C4×C101C2×C418yes—
66C2×C22⋊C4×C101D414yes—
67C2×C42×C101—24no—
68C2×C42×C101—24no—
69C2×C42×C101—42no—
70#95×C101—24no—
71#95×C101—24no—
72#95×C101—24no—
73#95×C101—24no—
74#95×C101—24no—
75#95×C101—41no—
76#95×C101—42no—
77#95×C101—42no—
78#95×C101—42no—
79#95×C101—42no—
80#95×C101—41no—
81#95×C101C2×C418yes—
82C24×C101—22no—
83C24×C101—22no—
84C24×C101—21no—
85C24×C101—21no—
86C24×C101—21no—
87C24×C101—22no—
88C24×C101—22no—
89C24×C101—21no—
90C24×C101C22×C412yes—
91C24×C101C2×D412yes—
92C24×C101#4112yes—
93C24×C101C2411yescharacteristic
94C22×C4×C101—21no—
95C22×C4×C101—21no—
96C22×C4×C101—22no—
97C22×C4×C101—22no—
98C22×C4×C101—22no—
99C22×C4×C101—22no—
100C22×C4×C101—22no—
101C22×C4×C101—22no—
102C22×C4×C101—22no—
103C22×C4×C101—22no—
104C22×C4×C101—22no—
105C22×C4×C101—22no—
106C22×C4×C101—22no—
107C22×C4×C101—22no—
108C22×C4×C101—22no—
109C22×C4×C101—22no—
110C22×C4×C101—22no—
111C22×C4×C101—22no—
112C22×C4×C101—22no—
113C22×C4×C101—21no—
114C22×C4×C101—21no—
115C22×C4×C101—22no—
116C22×C4×C101—22no—
117C22×C4×C101—22no—
118C22×C4×C101—22no—
119C22×C4×C101—22no—
120C22×C4×C101—22no—
121C22×C4×C101—22no—
122C22×C4×C101—22no—
123C22×C4×C101—22no—
124C22×C4×C101—22no—
125C22×C4×C101—28no—
126C22×C4×C101—22no—
127C22×C4×C101—22no—
128C22×C4×C101—22no—
129C22×C4×C101—22no—
130C22×C4×C101—22no—
131C22×C4×C101—22no—
132C22×C4×C101—22no—
133C22×C4×C101—22no—
134C22×C4×C101—22no—
135C22×C4×C101—22no—
136C22×C4×C101—22no—
137C22×C4×C101—22no—
138C22×C4×C101—22no—
139C22×C4×C101—22no—
140C22×C4×C101—44no—
141C22×C4×C101—44no—
142C22×C4×C101—48no—
143C22×C4×C101—48no—
144C22×C4×C101C22×C412yes—
145C22×C4×C101C22×C414yes—
146C22×C4×C101C22×C414yes—
147C22×C4×C101C22×C412yes—
148C22×C4×C101C2×D414yes—
149C22×C4×C101#4114yes—
150C22×C4×C101#4114yes—
151C4⋊C4×C101—44no—
152C4⋊C4×C101—44no—
153C4⋊C4×C101—48no—
154C22⋊C4×C101—216no—
155C22⋊C4×C101—44no—
156C22⋊C4×C101—48no—
157C22⋊C4×C101—44no—
158C42×C101—48no—
159C23×C101—22no—
160C23×C101—22no—
161C23×C101—22no—
162C23×C101—22no—
163C23×C101—22no—
164C23×C101—22no—
165C23×C101—22no—
166C23×C101—22no—
167C23×C101—22no—
168C23×C101—22no—
169C23×C101—24no—
170C23×C101—24no—
171C23×C101—24no—
172C23×C101—24no—
173C23×C101—42no—
174C23×C101—42no—
175C23×C101—42no—
176C23×C101—42no—
177C23×C101—42no—
178C23×C101—42no—
179C23×C101—42no—
180C23×C101—42no—
181C23×C101C4×D414yes—
182C23×C101C23×C411yescharacteristic
183C23×C101C22×D411yescharacteristic
184C23×C101C2×#4112yes—
185C23×C101C2×#4111yescharacteristic
186C23×C101C2×#4112yes—
187C23×C101H(5,𝔽2)11yescharacteristic
188C23×C101H(5,𝔽2)11yescharacteristic
189C23×C101H(5,𝔽2)12yes—
190C23×C101H(5,𝔽2)11yescharacteristic
191C23×C1012−1+412yes—
192C23×C1012−1+411yescharacteristic
193C2×C4×C101—22no—
194C2×C4×C101—22no—
195C2×C4×C101—24no—
196C2×C4×C101—24no—
197C2×C4×C101—22no—
198C2×C4×C101—24no—
199C2×C4×C101—24no—
200C2×C4×C101—24no—
201C2×C4×C101—24no—
202C2×C4×C101—24no—
203C2×C4×C101—22no—
204C2×C4×C101—22no—
205C2×C4×C101—24no—
206C2×C4×C101—24no—
207C2×C4×C101—24no—
208C2×C4×C101—24no—
209C2×C4×C101—24no—
210C2×C4×C101—24no—
211C2×C4×C101—24no—
212C2×C4×C101—416no—
213C2×C4×C101—42no—
214C2×C4×C101—42no—
215C2×C4×C101—42no—
216C2×C4×C101—42no—
217C2×C4×C101—42no—
218C2×C4×C101—42no—
219C2×C4×C101—42no—
220C2×C4×C101—42no—
221C2×C4×C101—42no—
222C2×C4×C101—42no—
223C2×C4×C101—42no—
224C2×C4×C101—42no—
225C2×C4×C101—42no—
226C2×C4×C101—42no—
227C2×C4×C101—42no—
228C2×C4×C101—42no—
229C2×C4×C101—42no—
230C2×C4×C101—42no—
231C2×C4×C101—42no—
232C2×C4×C101—42no—
233C2×C4×C101—42no—
234C2×C4×C101—42no—
235C2×C4×C101—42no—
236C2×C4×C101—42no—
237C2×C4×C101—42no—
238C2×C4×C101—42no—
239C2×C4×C101—42no—
240C2×C4×C101—42no—
241C2×C4×C101—42no—
242C2×C4×C101—42no—
243C2×C4×C101—42no—
244C2×C4×C101—42no—
245C2×C4×C101#11714yes—
246C22×C101—24no—
247C22×C101—24no—
248C22×C101—24no—
249C22×C101—42no—
250C22×C101—42no—
251C22×C101—42no—
252C22×C101—42no—
253C22×C101—44no—
254C22×C101—44no—
255C22×C101—44no—
256C22×C101—44no—
257C22×C101C2×#11711yescharacteristic
258C22×C101C2×C4×D411yescharacteristic
259C22×C101C4×#4111yescharacteristic
260C22×C101#51811yescharacteristic
261C22×C101#51811yescharacteristic
262C22×C101#51911yescharacteristic
263C22×C101#52011yescharacteristic
264C22×C101#53411yescharacteristic
265C22×C101#53711yescharacteristic
266C22×C101#53812yes—
267C22×C101#53812yes—
268C22×C101#53811yescharacteristic
269C22×C101#53911yescharacteristic
270C22×C101#53912yes—
271C22×C101#54212yes—
272C22×C101#54612yes—
273C22×C101#54712yes—
274C22×C101#55212yes—
275C22×C101#55212yes—
276C22×C101#55312yes—
277C22×C101#55512yes—
278C22×C101#56212yes—
279C22×C101#56312yes—
280C4×C101—24no—
281C4×C101—42no—
282C4×C101—44no—
283C4×C101—44no—
284C4×C101—44no—
285C4×C101—44no—
286C4×C101—82no—
287C4×C101—82no—
288#14422C10111yesmaximal, characteristic, direct product factor, Sylow
289C2×C101—44no—
290C2×C101#231211yescharacteristic
291C2×C101#232511yescharacteristic
292C2×C101#233211yescharacteristic
293C2×C101#234411yescharacteristic
294C2×C101#234611yescharacteristic
295C2×C101#236411yescharacteristic
296C2×C101#237811yescharacteristic
297C2×C101#268612yes—
298C2×C101#269512yes—
299C2×C101#277012yes—
300C2×C101#278112yes—
301C2×#388C2×C10112yes—
302C2×#380C2×C10111yescharacteristic
303#1442C2×C10112yescomplemented
304#1441C2×C10112yescomplemented
305#1440C2×C10112yes—
306#1436C2×C10112yescomplemented
307#1434C2×C10112yescomplemented
308C22⋊#95C2×C10111yescharacteristic
309C22⋊#95C2×C10111yescharacteristic
310C101#1442211yescharacteristic, direct product factor, Sylow
311C24×C4C22×C10111yescharacteristic
312C22×C4⋊C4C22×C10112yes—
313C22×C4⋊C4C22×C10111yescharacteristic
314C22×C4⋊C4C22×C10111yescharacteristic
315C22×C22⋊C4C22×C10112yes—
316C22×C22⋊C4C22×C10112yes—
317C22×C22⋊C4C22×C10111yescharacteristic
318C22×C22⋊C4C22×C10111yescharacteristic
319C22×C42C22×C10112yes—
320#388—28no—
321#380C4×C10118yescomplemented
322C2×#95C22×C10112yes—
323C2×#95C22×C10112yes—
324C2×#95C22×C10112yes—
325C2×#95C22×C10112yes—
326C2×#95C22×C10112yes—
327C2×#95C22×C10111yescharacteristic
328C2×#95C22×C10112yes—
329C2×#95C22×C10111yescharacteristic
330C2×#95C22×C10112yes—
331C2×#95C22×C10112yes—
332C2×#95C22×C10112yes—
333C2×#95C22×C10112yes—
334C25C23×C10111yescharacteristic
335C23×C4—24no—
336C23×C4—41no—
337C23×C4—41no—
338C23×C4—42no—
339C23×C4C2×C4×C10114yes—
340C23×C4C23×C10112yes—
341C23×C4C23×C10112yes—
342C23×C4C23×C10112yes—
343C23×C4C23×C10112yes—
344C23×C4C23×C10111yescharacteristic
345C23×C4C23×C10112yes—
346C23×C4C23×C10112yes—
347C23×C4C23×C10111yescharacteristic
348C2×C4⋊C4—24no—
349C2×C4⋊C4—41no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—41no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4C2×C4×C10114yes—
355C2×C4⋊C4C2×C4×C10114yes—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—41no—
362C2×C22⋊C4—41no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—41no—
365C2×C22⋊C4—41no—
366C2×C22⋊C4C2×C4×C10118yes—
367C2×C22⋊C4D4×C10114yes—
368C2×C42—24no—
369C2×C42—24no—
370C2×C42—42no—
371#95—24no—
372#95—24no—
373#95—24no—
374#95—24no—
375#95—24no—
376#95—41no—
377#95—42no—
378#95—42no—
379#95—42no—
380#95—42no—
381#95—41no—
382#95C2×C4×C10118yes—
383C24—22no—
384C24—22no—
385C24—21no—
386C24—21no—
387C24—21no—
388C24—22no—
389C24—22no—
390C24—21no—
391C24C22×C4×C10112yes—
392C24C2×D4×C10112yes—
393C24#41×C10112yes—
394C24C24×C10111yescharacteristic
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—28no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—44no—
442C22×C4—44no—
443C22×C4—48no—
444C22×C4—48no—
445C22×C4C22×C4×C10112yes—
446C22×C4C22×C4×C10114yes—
447C22×C4C22×C4×C10114yes—
448C22×C4C22×C4×C10112yes—
449C22×C4C2×D4×C10114yes—
450C22×C4#41×C10114yes—
451C22×C4#41×C10114yes—
452C4⋊C4—44no—
453C4⋊C4—44no—
454C4⋊C4—48no—
455C22⋊C4—216no—
456C22⋊C4—44no—
457C22⋊C4—48no—
458C22⋊C4—44no—
459C42—48no—
460C23—22no—
461C23—22no—
462C23—22no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—22no—
469C23—22no—
470C23—24no—
471C23—24no—
472C23—24no—
473C23—24no—
474C23—42no—
475C23—42no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—42no—
480C23—42no—
481C23—42no—
482C23C4×D4×C10114yes—
483C23C23×C4×C10111yescharacteristic
484C23C22×D4×C10111yescharacteristic
485C23C2×#41×C10112yes—
486C23C2×#41×C10111yescharacteristic
487C23C2×#41×C10112yes—
488C23H(5,𝔽2)×C10111yescharacteristic
489C23H(5,𝔽2)×C10111yescharacteristic
490C23H(5,𝔽2)×C10112yes—
491C23H(5,𝔽2)×C10111yescharacteristic
492C232−1+4×C10112yes—
493C232−1+4×C10111yescharacteristic
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—22no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—416no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4#117×C10114yes—
547C22—24no—
548C22—24no—
549C22—24no—
550C22—44no—
551C22—44no—
552C22—44no—
553C22—44no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—42no—
558C22C2×#117×C10111yescharacteristic
559C22C2×C4×D4×C10111yescharacteristic
560C22C4×#41×C10111yescharacteristic
561C22#518×C10111yescharacteristic
562C22#518×C10111yescharacteristic
563C22#519×C10111yescharacteristic
564C22#520×C10111yescharacteristic
565C22#534×C10111yescharacteristic
566C22#537×C10111yescharacteristic
567C22#538×C10112yes—
568C22#538×C10112yes—
569C22#538×C10111yescharacteristic
570C22#539×C10112yes—
571C22#539×C10111yescharacteristic
572C22#542×C10112yes—
573C22#546×C10112yes—
574C22#547×C10112yes—
575C22#552×C10112yes—
576C22#552×C10112yes—
577C22#553×C10112yes—
578C22#555×C10112yes—
579C22#562×C10112yes—
580C22#563×C10112yes—
581C4—24no—
582C4—44no—
583C4—44no—
584C4—42no—
585C4—44no—
586C4—44no—
587C4—82no—
588C4—82no—
589C2—44no—
590C2C101×#231211yescharacteristic
591C2C101×#232511yescharacteristic
592C2C101×#233211yescharacteristic
593C2C101×#234411yescharacteristic
594C2C101×#234611yescharacteristic
595C2C101×#236411yescharacteristic
596C2C101×#237811yescharacteristic
597C2C101×#268612yes—
598C2C101×#269512yes—
599C2C101×#277012yes—
600C2C101×#278112yes—
subgroupG/H
center, socleC24×C101C24
commutatorC23C23×C4×C101
Frattini, cosocleC24C24×C101
prime radicalC25×C101C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C101 ◁ G

Complements

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

NH ≅ G/Ntype
3. C101×#1442C2semidirect
4. C101×#1441C2semidirect
6. C101×#1436C2semidirect
7. C101×#1434C2semidirect
20. #380×C101C4semidirect
288. #14422C101direct (N × H)
303. #1442C2×C101semidirect
304. #1441C2×C101semidirect
306. #1436C2×C101semidirect
307. #1434C2×C101semidirect
310. C101#14422direct (N × H)
321. #380C4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#388×C1012
C2×#380×C1012
C101×#14422
C101×#14412
C101×#14402
C101×#14362
C101×#14342
C101×C22⋊#952
#14422101