Finite Group Databasebeta

← C101×#17193 #38799344

Subgroups — C101×#17193 #38799344

Order 25856.

1466 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#394×C101C212yesmaximal
2C101×#1444C211yesmaximal, characteristic, complemented
3C101×#1442C212yesmaximal, complemented
4C101×#1442C211yesmaximal, characteristic, complemented
5C101×#1440C212yesmaximal, complemented
6C101×#1440C212yesmaximal, complemented
7C101×#1439C212yesmaximal, complemented
8C101×#1439C212yesmaximal, complemented
9C101×#1438C211yesmaximal, characteristic
10C23×D4×C101C2211yescharacteristic
11C22×C4⋊C4×C101C2212yes—
12C22×C4⋊C4×C101C2211yescharacteristic
13C22×C4⋊C4×C101C2211yescharacteristic
14C22×C22⋊C4×C101C2212yes—
15C22×C22⋊C4×C101C2212yes—
16C22×C22⋊C4×C101C2212yes—
17C22×C22⋊C4×C101C2212yes—
18C22×C22⋊C4×C101C2212yes—
19C22×C22⋊C4×C101C2212yes—
20#394×C101—28no—
21C2×#95×C101C2212yes—
22C2×#95×C101C2211yescharacteristic
23C2×#95×C101C2211yescharacteristic
24C2×#95×C101C2212yes—
25C2×#95×C101C2211yescharacteristic
26C2×#95×C101C2211yescharacteristic
27C2×#95×C101C2212yes—
28C2×#95×C101C2212yes—
29C2×#95×C101C2212yes—
30C2×#95×C101C2212yes—
31C2×#95×C101C2212yes—
32C25×C101C2312yes—
33C22×D4×C101—41no—
34C22×D4×C101—41no—
35C22×D4×C101—42no—
36C22×D4×C101—42no—
37C22×D4×C101D414yes—
38C23×C4×C101C2312yes—
39C23×C4×C101C2312yes—
40C23×C4×C101C2312yes—
41C23×C4×C101C2312yes—
42C23×C4×C101C2311yescharacteristic
43C23×C4×C101C2312yes—
44C23×C4×C101C2311yescharacteristic
45C23×C4×C101C2311yescharacteristic
46C2×C4⋊C4×C101—24no—
47C2×C4⋊C4×C101—42no—
48C2×C4⋊C4×C101—42no—
49C2×C4⋊C4×C101—41no—
50C2×C4⋊C4×C101—41no—
51C2×C4⋊C4×C101—42no—
52C2×C4⋊C4×C101—42no—
53C2×C22⋊C4×C101—24no—
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—24no—
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—
71#95×C101—24no—
72#95×C101—22no—
73#95×C101—24no—
74#95×C101—22no—
75#95×C101—42no—
76#95×C101—42no—
77#95×C101—41no—
78#95×C101—42no—
79#95×C101—41no—
80#95×C101—42no—
81#95×C101—42no—
82C24×C101—22no—
83C24×C101—22no—
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×C101C2×D414yes—
97C24×C101C2411yescharacteristic
98C2×D4×C101—48no—
99C2×D4×C101—44no—
100C2×D4×C101—44no—
101C2×D4×C101—48no—
102C2×D4×C101—44no—
103C22×C4×C101—22no—
104C22×C4×C101—22no—
105C22×C4×C101—22no—
106C22×C4×C101—22no—
107C22×C4×C101—22no—
108C22×C4×C101—21no—
109C22×C4×C101—21no—
110C22×C4×C101—22no—
111C22×C4×C101—21no—
112C22×C4×C101—21no—
113C22×C4×C101—22no—
114C22×C4×C101—22no—
115C22×C4×C101—22no—
116C22×C4×C101—22no—
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×C101C2×D412yes—
150C22×C4×C101#4112yes—
151C22×C4×C101#4112yes—
152C22×C4×C101#4114yes—
153C4⋊C4×C101—48no—
154C4⋊C4×C101—44no—
155C4⋊C4×C101—44no—
156C22⋊C4×C101—48no—
157C22⋊C4×C101—48no—
158C22⋊C4×C101—48no—
159C22⋊C4×C101—48no—
160C22⋊C4×C101—48no—
161C22⋊C4×C101—48no—
162C23×C101—24no—
163C23×C101—24no—
164C23×C101—24no—
165C23×C101—24no—
166C23×C101—24no—
167C23×C101—24no—
168C23×C101—24no—
169C23×C101—42no—
170C23×C101—42no—
171C23×C101—42no—
172C23×C101—42no—
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×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×C101C22×D411yescharacteristic
198C23×C101C2×#4111yescharacteristic
199C23×C101C2×#4111yescharacteristic
200C23×C101C2×#4112yes—
201C23×C101H(5,𝔽2)12yes—
202C23×C101H(5,𝔽2)12yes—
203C23×C101H(5,𝔽2)11yescharacteristic
204C23×C101H(5,𝔽2)11yescharacteristic
205C23×C101H(5,𝔽2)12yes—
206C23×C1012−1+411yescharacteristic
207C23×C1012−1+411yescharacteristic
208D4×C101—416no—
209C2×C4×C101—24no—
210C2×C4×C101—22no—
211C2×C4×C101—24no—
212C2×C4×C101—24no—
213C2×C4×C101—22no—
214C2×C4×C101—22no—
215C2×C4×C101—24no—
216C2×C4×C101—24no—
217C2×C4×C101—24no—
218C2×C4×C101—42no—
219C2×C4×C101—42no—
220C2×C4×C101—42no—
221C2×C4×C101—41no—
222C2×C4×C101—41no—
223C2×C4×C101—41no—
224C2×C4×C101—41no—
225C2×C4×C101—42no—
226C2×C4×C101—41no—
227C2×C4×C101—41no—
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—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—
259C22×C101—44no—
260C22×C101—44no—
261C22×C101—44no—
262C22×C101—44no—
263C22×C101—44no—
264C22×C101—44no—
265C22×C101—44no—
266C22×C101—82no—
267C22×C101—82no—
268C22×C101—82no—
269C22×C101—82no—
270C22×C101—82no—
271C22×C101—82no—
272C22×C101—82no—
273C22×C101—82no—
274C22×C101#53412yes—
275C22×C101#53411yescharacteristic
276C22×C101#53812yes—
277C22×C101#53812yes—
278C22×C101#53911yescharacteristic
279C22×C101#53911yescharacteristic
280C22×C101#53912yes—
281C22×C101#54012yes—
282C22×C101#54212yes—
283C22×C101#54612yes—
284C22×C101#54711yescharacteristic
285C22×C101#54711yescharacteristic
286C22×C101#55312yes—
287C22×C101#55512yes—
288C22×C101#55511yescharacteristic
289C22×C101#55911yescharacteristic
290C22×C101#56011yescharacteristic
291C22×C101#56011yescharacteristic
292C22×C101#56012yes—
293C22×C101H(3,𝔽4)11yescharacteristic
294C22×C101#56212yes—
295C22×C101#56212yes—
296C22×C101#56311yescharacteristic
297C4×C101—42no—
298C4×C101—42no—
299C4×C101—44no—
300C4×C101—42no—
301C4×C101—82no—
302C4×C101—82no—
303C4×C101—82no—
304C4×C101—82no—
305#17193C10111yesmaximal, characteristic, direct product factor, Sylow
306C2×C101—84no—
307C2×C101#268612yes—
308C2×C101#269911yescharacteristic
309C2×C101#270812yes—
310C2×C101#272411yescharacteristic
311C2×C101#278511yescharacteristic
312C2×C101#279511yescharacteristic
313C2×C101#280312yes—
314C2×C101#281211yescharacteristic
315C2×C101#282411yescharacteristic
316C2×C101#282611yescharacteristic
317C2×C101#283712yes—
318C2×#394C2×C10112yes—
319#1444C2×C10111yescharacteristic, complemented
320#1442C2×C10112yescomplemented
321#1442C2×C10111yescharacteristic, complemented
322#1440C2×C10112yescomplemented
323#1440C2×C10112yescomplemented
324#1439C2×C10112yescomplemented
325#1439C2×C10112yescomplemented
326#1438C2×C10111yescharacteristic
327C101#1719311yescharacteristic, direct product factor, Sylow
328C23×D4C22×C10111yescharacteristic
329C22×C4⋊C4C22×C10112yes—
330C22×C4⋊C4C22×C10111yescharacteristic
331C22×C4⋊C4C22×C10111yescharacteristic
332C22×C22⋊C4C22×C10112yes—
333C22×C22⋊C4C22×C10112yes—
334C22×C22⋊C4C22×C10112yes—
335C22×C22⋊C4C22×C10112yes—
336C22×C22⋊C4C22×C10112yes—
337C22×C22⋊C4C22×C10112yes—
338#394—28no—
339C2×#95C22×C10112yes—
340C2×#95C22×C10112yes—
341C2×#95C22×C10111yescharacteristic
342C2×#95C22×C10111yescharacteristic
343C2×#95C22×C10111yescharacteristic
344C2×#95C22×C10111yescharacteristic
345C2×#95C22×C10112yes—
346C2×#95C22×C10112yes—
347C2×#95C22×C10112yes—
348C2×#95C22×C10112yes—
349C2×#95C22×C10112yes—
350C25C23×C10112yes—
351C22×D4—41no—
352C22×D4—41no—
353C22×D4—42no—
354C22×D4—42no—
355C22×D4D4×C10114yes—
356C23×C4C23×C10112yes—
357C23×C4C23×C10112yes—
358C23×C4C23×C10112yes—
359C23×C4C23×C10112yes—
360C23×C4C23×C10111yescharacteristic
361C23×C4C23×C10112yes—
362C23×C4C23×C10111yescharacteristic
363C23×C4C23×C10111yescharacteristic
364C2×C4⋊C4—24no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—41no—
368C2×C4⋊C4—41no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—42no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389#95—24no—
390#95—22no—
391#95—24no—
392#95—22no—
393#95—42no—
394#95—42no—
395#95—41no—
396#95—42no—
397#95—41no—
398#95—42no—
399#95—42no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24C2×D4×C10114yes—
415C24C24×C10111yescharacteristic
416C2×D4—48no—
417C2×D4—44no—
418C2×D4—44no—
419C2×D4—48no—
420C2×D4—44no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
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×C4C2×D4×C10112yes—
468C22×C4#41×C10112yes—
469C22×C4#41×C10112yes—
470C22×C4#41×C10114yes—
471C4⋊C4—48no—
472C4⋊C4—44no—
473C4⋊C4—44no—
474C22⋊C4—48no—
475C22⋊C4—48no—
476C22⋊C4—48no—
477C22⋊C4—48no—
478C22⋊C4—48no—
479C22⋊C4—48no—
480C23—24no—
481C23—24no—
482C23—24no—
483C23—24no—
484C23—24no—
485C23—24no—
486C23—24no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—42no—
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—
515C23C22×D4×C10111yescharacteristic
516C23C2×#41×C10111yescharacteristic
517C23C2×#41×C10111yescharacteristic
518C23C2×#41×C10112yes—
519C23H(5,𝔽2)×C10112yes—
520C23H(5,𝔽2)×C10112yes—
521C23H(5,𝔽2)×C10111yescharacteristic
522C23H(5,𝔽2)×C10111yescharacteristic
523C23H(5,𝔽2)×C10112yes—
524C232−1+4×C10111yescharacteristic
525C232−1+4×C10111yescharacteristic
526D4—416no—
527C2×C4—24no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
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—
577C22—44no—
578C22—44no—
579C22—44no—
580C22—44no—
581C22—44no—
582C22—44no—
583C22—44no—
584C22—82no—
585C22—82no—
586C22—82no—
587C22—82no—
588C22—82no—
589C22—82no—
590C22—82no—
591C22—82no—
592C22#534×C10112yes—
593C22#534×C10111yescharacteristic
594C22#538×C10112yes—
595C22#538×C10112yes—
596C22#539×C10112yes—
597C22#539×C10111yescharacteristic
598C22#539×C10111yescharacteristic
599C22#540×C10112yes—
600C22#542×C10112yes—
601C22#546×C10112yes—
602C22#547×C10111yescharacteristic
603C22#547×C10111yescharacteristic
604C22#553×C10112yes—
605C22#555×C10112yes—
606C22#555×C10111yescharacteristic
607C22#559×C10111yescharacteristic
608C22#560×C10111yescharacteristic
609C22#560×C10111yescharacteristic
610C22#560×C10112yes—
611C22H(3,𝔽4)×C10111yescharacteristic
612C22#562×C10112yes—
613C22#562×C10112yes—
614C22#563×C10111yescharacteristic
615C4—44no—
616C4—42no—
617C4—42no—
618C4—42no—
619C4—82no—
620C4—82no—
621C4—82no—
622C4—82no—
623C2—84no—
624C2C101×#268612yes—
625C2C101×#269911yescharacteristic
626C2C101×#270812yes—
627C2C101×#272411yescharacteristic
628C2C101×#278511yescharacteristic
629C2C101×#279511yescharacteristic
630C2C101×#280312yes—
631C2C101×#281211yescharacteristic
632C2C101×#282411yescharacteristic
633C2C101×#282611yescharacteristic
634C2C101×#283712yes—
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
2. C101×#1444C2semidirect
3. C101×#1442C2semidirect
4. C101×#1442C2semidirect
5. C101×#1440C2semidirect
6. C101×#1440C2semidirect
7. C101×#1439C2semidirect
8. C101×#1439C2semidirect
305. #17193C101direct (N × H)
319. #1444C2×C101semidirect
320. #1442C2×C101semidirect
321. #1442C2×C101semidirect
322. #1440C2×C101semidirect
323. #1440C2×C101semidirect
324. #1439C2×C101semidirect
325. #1439C2×C101semidirect
327. C101#17193direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#394×C1012
C101×#14442
C101×#14422
C101×#14402
C101×#14392
C101×#14382
#17193101