Finite Group Databasebeta

← C101×#17224 #38799375

Subgroups — C101×#17224 #38799375

Order 25856.

1530 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#393×C101C212yesmaximal, complemented
2C101×#1446C211yesmaximal, characteristic, complemented
3C101×#1445C211yesmaximal, characteristic, complemented
4C101×#1443C212yesmaximal, complemented
5C101×#1440C212yesmaximal, complemented
6C101×#1440C212yesmaximal, complemented
7C101×#1439C212yesmaximal, complemented
8C101×#1438C211yesmaximal, characteristic
9C101×#1438C212yesmaximal
10C23×Q8×C101C2211yescharacteristic
11C23×D4×C101C2211yescharacteristic
12C22×C4⋊C4×C101C2211yescharacteristic
13C22×C22⋊C4×C101C2212yes—
14C22×C22⋊C4×C101C2212yes—
15C22×C22⋊C4×C101C2212yes—
16C22×C22⋊C4×C101C2212yes—
17C22×C22⋊C4×C101C2212yes—
18C22×C22⋊C4×C101C2212yes—
19#393×C101—28no—
20C2×#95×C101C2212yes—
21C2×#95×C101C2212yes—
22C2×#95×C101C2212yes—
23C2×#95×C101C2212yes—
24C2×#95×C101C2211yescharacteristic
25C2×#95×C101C2212yes—
26C2×#95×C101C2211yescharacteristic
27C2×#95×C101C2212yes—
28C2×#95×C101C2212yes—
29C2×#95×C101C2212yes—
30C2×#95×C101C2211yescharacteristic
31C2×#95×C101C2211yescharacteristic
32C25×C101C2312yes—
33C22×Q8×C101—42no—
34C22×Q8×C101—41no—
35C22×Q8×C101—41no—
36C22×Q8×C101—42no—
37C22×Q8×C101D414yescomplemented
38C22×D4×C101—24no—
39C22×D4×C101—22no—
40C22×D4×C101—42no—
41C22×D4×C101—41no—
42C22×D4×C101—41no—
43C23×C4×C101C2312yes—
44C23×C4×C101C2312yes—
45C23×C4×C101C2312yes—
46C23×C4×C101C2312yes—
47C23×C4×C101C2312yes—
48C23×C4×C101C2311yescharacteristic
49C23×C4×C101C2311yescharacteristic
50C23×C4×C101C2311yescharacteristic
51C2×C4⋊C4×C101—22no—
52C2×C4⋊C4×C101—41no—
53C2×C4⋊C4×C101—41no—
54C2×C22⋊C4×C101—24no—
55C2×C22⋊C4×C101—24no—
56C2×C22⋊C4×C101—24no—
57C2×C22⋊C4×C101—24no—
58C2×C22⋊C4×C101—24no—
59C2×C22⋊C4×C101—24no—
60C2×C22⋊C4×C101—42no—
61C2×C22⋊C4×C101—42no—
62C2×C22⋊C4×C101—42no—
63C2×C22⋊C4×C101—42no—
64C2×C22⋊C4×C101—42no—
65C2×C22⋊C4×C101—42no—
66C2×C22⋊C4×C101—42no—
67C2×C22⋊C4×C101—42no—
68C2×C22⋊C4×C101—42no—
69C2×C22⋊C4×C101—42no—
70C2×C22⋊C4×C101—42no—
71C2×C22⋊C4×C101—42no—
72#95×C101—24no—
73#95×C101—24no—
74#95×C101—24no—
75#95×C101—24no—
76#95×C101—42no—
77#95×C101—41no—
78#95×C101—41no—
79#95×C101—42no—
80#95×C101—41no—
81#95×C101—41no—
82#95×C101—42no—
83#95×C101—42no—
84C24×C101—22no—
85C24×C101—22no—
86C24×C101—22no—
87C24×C101—22no—
88C24×C101—22no—
89C24×C101—22no—
90C24×C101—22no—
91C24×C101—22no—
92C24×C101—22no—
93C24×C101—22no—
94C24×C101—22no—
95C24×C101—22no—
96C24×C101—22no—
97C24×C101—22no—
98C24×C101#4114yes—
99C24×C101C2411yescharacteristic
100C2×Q8×C101—44no—
101C2×Q8×C101—48no—
102C2×Q8×C101—48no—
103C2×Q8×C101—44no—
104C2×Q8×C101—44no—
105C2×D4×C101—48no—
106C2×D4×C101—44no—
107C2×D4×C101—44no—
108C2×D4×C101—48no—
109C2×D4×C101—44no—
110C22×C4×C101—22no—
111C22×C4×C101—22no—
112C22×C4×C101—22no—
113C22×C4×C101—21no—
114C22×C4×C101—21no—
115C22×C4×C101—21no—
116C22×C4×C101—21no—
117C22×C4×C101—22no—
118C22×C4×C101—22no—
119C22×C4×C101—21no—
120C22×C4×C101—21no—
121C22×C4×C101—22no—
122C22×C4×C101—22no—
123C22×C4×C101—22no—
124C22×C4×C101—22no—
125C22×C4×C101—22no—
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—22no—
141C22×C4×C101—22no—
142C22×C4×C101—22no—
143C22×C4×C101—22no—
144C22×C4×C101—22no—
145C22×C4×C101—22no—
146C22×C4×C101—22no—
147C22×C4×C101—22no—
148C22×C4×C101—22no—
149C22×C4×C101—22no—
150C22×C4×C101—22no—
151C22×C4×C101—22no—
152C22×C4×C101—22no—
153C22×C4×C101—22no—
154C22×C4×C101—22no—
155C22×C4×C101—22no—
156C22×C4×C101C2×D414yes—
157C22×C4×C101C2×D412yes—
158C22×C4×C101#4112yes—
159C22×C4×C101#4112yes—
160C4⋊C4×C101—44no—
161C22⋊C4×C101—48no—
162C22⋊C4×C101—48no—
163C22⋊C4×C101—48no—
164C22⋊C4×C101—48no—
165C22⋊C4×C101—48no—
166C22⋊C4×C101—48no—
167C23×C101—24no—
168C23×C101—24no—
169C23×C101—24no—
170C23×C101—24no—
171C23×C101—24no—
172C23×C101—24no—
173C23×C101—24no—
174C23×C101—42no—
175C23×C101—42no—
176C23×C101—42no—
177C23×C101—42no—
178C23×C101—42no—
179C23×C101—42no—
180C23×C101—42no—
181C23×C101—42no—
182C23×C101—42no—
183C23×C101—42no—
184C23×C101—42no—
185C23×C101—42no—
186C23×C101—42no—
187C23×C101—42no—
188C23×C101—42no—
189C23×C101—42no—
190C23×C101—42no—
191C23×C101—42no—
192C23×C101—42no—
193C23×C101—42no—
194C23×C101—42no—
195C23×C101—42no—
196C23×C101—42no—
197C23×C101—42no—
198C23×C101—42no—
199C23×C101—42no—
200C23×C101—42no—
201C23×C101—42no—
202C23×C101C22×D411yescharacteristic
203C23×C101C2×#4112yes—
204C23×C101C2×#4111yescharacteristic
205C23×C101C2×#4111yescharacteristic
206C23×C101H(5,𝔽2)11yescharacteristic
207C23×C101H(5,𝔽2)12yes—
208C23×C101H(5,𝔽2)12yes—
209C23×C101H(5,𝔽2)11yescharacteristic
210C23×C101H(5,𝔽2)11yescharacteristic
211C23×C101H(5,𝔽2)11yescharacteristic
212C23×C1012−1+412yes—
213Q8×C101—416no—
214D4×C101—416no—
215C2×C4×C101—24no—
216C2×C4×C101—24no—
217C2×C4×C101—24no—
218C2×C4×C101—22no—
219C2×C4×C101—24no—
220C2×C4×C101—22no—
221C2×C4×C101—22no—
222C2×C4×C101—24no—
223C2×C4×C101—24no—
224C2×C4×C101—42no—
225C2×C4×C101—42no—
226C2×C4×C101—41no—
227C2×C4×C101—41no—
228C2×C4×C101—41no—
229C2×C4×C101—42no—
230C2×C4×C101—42no—
231C2×C4×C101—42no—
232C2×C4×C101—42no—
233C2×C4×C101—41no—
234C2×C4×C101—41no—
235C2×C4×C101—41no—
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—42no—
246C2×C4×C101—42no—
247C2×C4×C101—42no—
248C2×C4×C101—42no—
249C2×C4×C101—42no—
250C2×C4×C101—42no—
251C2×C4×C101—42no—
252C2×C4×C101—42no—
253C2×C4×C101—42no—
254C2×C4×C101—42no—
255C2×C4×C101—42no—
256C2×C4×C101—42no—
257C2×C4×C101—42no—
258C2×C4×C101—42no—
259C2×C4×C101—42no—
260C2×C4×C101—42no—
261C2×C4×C101—42no—
262C2×C4×C101—42no—
263C2×C4×C101—42no—
264C2×C4×C101—42no—
265C22×C101—44no—
266C22×C101—44no—
267C22×C101—44no—
268C22×C101—44no—
269C22×C101—44no—
270C22×C101—44no—
271C22×C101—44no—
272C22×C101—82no—
273C22×C101—82no—
274C22×C101—82no—
275C22×C101—82no—
276C22×C101—82no—
277C22×C101—82no—
278C22×C101—82no—
279C22×C101—82no—
280C22×C101#53411yescharacteristic
281C22×C101#53412yes—
282C22×C101#53812yes—
283C22×C101#53812yes—
284C22×C101#53811yescharacteristic
285C22×C101#53811yescharacteristic
286C22×C101#53912yes—
287C22×C101#54212yes—
288C22×C101#54212yes—
289C22×C101#54812yes—
290C22×C101#55011yescharacteristic
291C22×C101#55011yescharacteristic
292C22×C101#55111yescharacteristic
293C22×C101#55112yes—
294C22×C101#55112yes—
295C22×C101#55511yescharacteristic
296C22×C101#56012yes—
297C22×C101#56011yescharacteristic
298C22×C101H(3,𝔽4)11yescharacteristic
299C22×C101H(3,𝔽4)11yescharacteristic
300C22×C101#56212yes—
301C22×C101#56212yes—
302C22×C101#56311yescharacteristic
303C4×C101—42no—
304C4×C101—42no—
305C4×C101—44no—
306C4×C101—42no—
307C4×C101—82no—
308C4×C101—82no—
309C4×C101—82no—
310C4×C101—82no—
311#17224C10111yesmaximal, characteristic, direct product factor, Sylow
312C2×C101—84no—
313C2×C101#272811yescharacteristic
314C2×C101#273012yes—
315C2×C101#273012yes—
316C2×C101#273311yescharacteristic
317C2×C101#273611yescharacteristic
318C2×C101#273712yes—
319C2×C101#276011yescharacteristic
320C2×C101#281211yescharacteristic
321C2×C101#282412yes—
322C2×C101#283011yescharacteristic
323C2×C101#283211yescharacteristic
324C2×#393C2×C10112yescomplemented
325#1446C2×C10111yescharacteristic, complemented
326#1445C2×C10111yescharacteristic, complemented
327#1443C2×C10112yescomplemented
328#1440C2×C10112yescomplemented
329#1440C2×C10112yescomplemented
330#1439C2×C10112yescomplemented
331#1438C2×C10111yescharacteristic
332#1438C2×C10112yes—
333C101#1722411yescharacteristic, direct product factor, Sylow
334C23×Q8C22×C10111yescharacteristic
335C23×D4C22×C10111yescharacteristic
336C22×C4⋊C4C22×C10111yescharacteristic
337C22×C22⋊C4C22×C10112yes—
338C22×C22⋊C4C22×C10112yes—
339C22×C22⋊C4C22×C10112yes—
340C22×C22⋊C4C22×C10112yes—
341C22×C22⋊C4C22×C10112yes—
342C22×C22⋊C4C22×C10112yes—
343#393—28no—
344C2×#95C22×C10112yes—
345C2×#95C22×C10112yes—
346C2×#95C22×C10112yes—
347C2×#95C22×C10112yes—
348C2×#95C22×C10111yescharacteristic
349C2×#95C22×C10112yes—
350C2×#95C22×C10111yescharacteristic
351C2×#95C22×C10112yes—
352C2×#95C22×C10112yes—
353C2×#95C22×C10112yes—
354C2×#95C22×C10111yescharacteristic
355C2×#95C22×C10111yescharacteristic
356C25C23×C10112yes—
357C22×Q8—42no—
358C22×Q8—41no—
359C22×Q8—41no—
360C22×Q8—42no—
361C22×Q8D4×C10114yescomplemented
362C22×D4—24no—
363C22×D4—22no—
364C22×D4—42no—
365C22×D4—41no—
366C22×D4—41no—
367C23×C4C23×C10112yes—
368C23×C4C23×C10112yes—
369C23×C4C23×C10112yes—
370C23×C4C23×C10112yes—
371C23×C4C23×C10112yes—
372C23×C4C23×C10111yescharacteristic
373C23×C4C23×C10111yescharacteristic
374C23×C4C23×C10111yescharacteristic
375C2×C4⋊C4—22no—
376C2×C4⋊C4—41no—
377C2×C4⋊C4—41no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—42no—
401#95—41no—
402#95—41no—
403#95—42no—
404#95—41no—
405#95—41no—
406#95—42no—
407#95—42no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24#41×C10114yes—
423C24C24×C10111yescharacteristic
424C2×Q8—44no—
425C2×Q8—48no—
426C2×Q8—48no—
427C2×Q8—44no—
428C2×Q8—44no—
429C2×D4—48no—
430C2×D4—44no—
431C2×D4—44no—
432C2×D4—48no—
433C2×D4—44no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4C2×D4×C10114yes—
481C22×C4C2×D4×C10112yes—
482C22×C4#41×C10112yes—
483C22×C4#41×C10112yes—
484C4⋊C4—44no—
485C22⋊C4—48no—
486C22⋊C4—48no—
487C22⋊C4—48no—
488C22⋊C4—48no—
489C22⋊C4—48no—
490C22⋊C4—48no—
491C23—24no—
492C23—24no—
493C23—24no—
494C23—24no—
495C23—24no—
496C23—24no—
497C23—24no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23C22×D4×C10111yescharacteristic
527C23C2×#41×C10112yes—
528C23C2×#41×C10111yescharacteristic
529C23C2×#41×C10111yescharacteristic
530C23H(5,𝔽2)×C10111yescharacteristic
531C23H(5,𝔽2)×C10112yes—
532C23H(5,𝔽2)×C10112yes—
533C23H(5,𝔽2)×C10111yescharacteristic
534C23H(5,𝔽2)×C10111yescharacteristic
535C23H(5,𝔽2)×C10111yescharacteristic
536C232−1+4×C10112yes—
537Q8—416no—
538D4—416no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C22—44no—
590C22—44no—
591C22—44no—
592C22—44no—
593C22—44no—
594C22—44no—
595C22—44no—
596C22—82no—
597C22—82no—
598C22—82no—
599C22—82no—
600C22—82no—
601C22—82no—
602C22—82no—
603C22—82no—
604C22#534×C10111yescharacteristic
605C22#534×C10112yes—
606C22#538×C10112yes—
607C22#538×C10112yes—
608C22#538×C10111yescharacteristic
609C22#538×C10111yescharacteristic
610C22#539×C10112yes—
611C22#542×C10112yes—
612C22#542×C10112yes—
613C22#548×C10112yes—
614C22#550×C10111yescharacteristic
615C22#550×C10111yescharacteristic
616C22#551×C10111yescharacteristic
617C22#551×C10112yes—
618C22#551×C10112yes—
619C22#555×C10111yescharacteristic
620C22#560×C10112yes—
621C22#560×C10111yescharacteristic
622C22H(3,𝔽4)×C10111yescharacteristic
623C22H(3,𝔽4)×C10111yescharacteristic
624C22#562×C10112yes—
625C22#562×C10112yes—
626C22#563×C10111yescharacteristic
627C4—42no—
628C4—42no—
629C4—44no—
630C4—42no—
631C4—82no—
632C4—82no—
633C4—82no—
634C4—82no—
635C2—84no—
636C2C101×#272811yescharacteristic
637C2C101×#273012yes—
638C2C101×#273012yes—
639C2C101×#273311yescharacteristic
640C2C101×#273611yescharacteristic
641C2C101×#273712yes—
642C2C101×#276011yescharacteristic
643C2C101×#281211yescharacteristic
644C2C101×#282412yes—
645C2C101×#283011yescharacteristic
646C2C101×#283211yescharacteristic
subgroupG/H
center, socleC24×C101C24
commutator, Frattini, cosocleC24C24×C101
prime radicalC23×D4×C101C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#393×C101C2semidirect
2. C101×#1446C2semidirect
3. C101×#1445C2semidirect
4. C101×#1443C2semidirect
5. C101×#1440C2semidirect
6. C101×#1440C2semidirect
7. C101×#1439C2semidirect
37. C22×Q8×C101D4semidirect
311. #17224C101direct (N × H)
324. C2×#393C2×C101semidirect
325. #1446C2×C101semidirect
326. #1445C2×C101semidirect
327. #1443C2×C101semidirect
328. #1440C2×C101semidirect
329. #1440C2×C101semidirect
330. #1439C2×C101semidirect
333. C101#17224direct (N × H)
361. C22×Q8D4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#393×C1012
C101×#14462
C101×#14452
C101×#14432
C101×#14402
C101×#14392
C101×#14382
#17224101