Finite Group Databasebeta

← C101×#17234 #38799385

Subgroups — C101×#17234 #38799385

Order 25856.

1382 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#1445C211yesmaximal, characteristic, complemented
2C101×#1443C212yesmaximal, complemented
3C101×#1442C211yesmaximal, characteristic, complemented
4C101×#1440C212yesmaximal, complemented
5C101×#1440C212yesmaximal, complemented
6C101×#1439C212yesmaximal, complemented
7C101×#1439C212yesmaximal, complemented
8C101×#1438C211yesmaximal, characteristic
9C101×#1438C212yesmaximal
10C23×D4×C101C2211yescharacteristic
11C22×C4⋊C4×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—
19C2×#95×C101C2212yes—
20C2×#95×C101C2211yescharacteristic
21C2×#95×C101C2211yescharacteristic
22C2×#95×C101C2211yescharacteristic
23C2×#95×C101C2212yes—
24C2×#95×C101C2212yes—
25C2×#95×C101C2212yes—
26C2×#95×C101C2212yes—
27C2×#95×C101C2212yes—
28C2×#95×C101C2212yes—
29C2×#95×C101C2212yes—
30C2×#95×C101C2211yescharacteristic
31C25×C101C2312yes—
32C22×D4×C101—24no—
33C22×D4×C101—22no—
34C22×D4×C101—42no—
35C22×D4×C101—41no—
36C22×D4×C101—41no—
37C23×C4×C101C2312yes—
38C23×C4×C101C2312yes—
39C23×C4×C101C2312yes—
40C23×C4×C101C2312yes—
41C23×C4×C101C2312yes—
42C23×C4×C101C2311yescharacteristic
43C23×C4×C101C2311yescharacteristic
44C23×C4×C101C2311yescharacteristic
45C2×C4⋊C4×C101—22no—
46C2×C4⋊C4×C101—41no—
47C2×C4⋊C4×C101—41no—
48C2×C4⋊C4×C101—41no—
49C2×C4⋊C4×C101—42no—
50C2×C22⋊C4×C101—24no—
51C2×C22⋊C4×C101—24no—
52C2×C22⋊C4×C101—24no—
53C2×C22⋊C4×C101—24no—
54C2×C22⋊C4×C101—42no—
55C2×C22⋊C4×C101—42no—
56C2×C22⋊C4×C101—42no—
57C2×C22⋊C4×C101—42no—
58C2×C22⋊C4×C101—42no—
59C2×C22⋊C4×C101—42no—
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—
68#95×C101—24no—
69#95×C101—22no—
70#95×C101—42no—
71#95×C101—42no—
72#95×C101—41no—
73#95×C101—41no—
74#95×C101—41no—
75#95×C101—42no—
76#95×C101—42no—
77#95×C101—42no—
78#95×C101—42no—
79#95×C101—42no—
80C24×C101—22no—
81C24×C101—22no—
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#4114yes—
95C24×C101C2411yescharacteristic
96C2×D4×C101—48no—
97C2×D4×C101—44no—
98C2×D4×C101—44no—
99C2×D4×C101—48no—
100C2×D4×C101—44no—
101C22×C4×C101—22no—
102C22×C4×C101—22no—
103C22×C4×C101—22no—
104C22×C4×C101—22no—
105C22×C4×C101—21no—
106C22×C4×C101—21no—
107C22×C4×C101—21no—
108C22×C4×C101—21no—
109C22×C4×C101—21no—
110C22×C4×C101—22no—
111C22×C4×C101—22no—
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—22no—
120C22×C4×C101—22no—
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#4112yes—
149C22×C4×C101#4112yes—
150C22×C4×C101#4112yes—
151C4⋊C4×C101—44no—
152C4⋊C4×C101—44no—
153C22⋊C4×C101—48no—
154C22⋊C4×C101—48no—
155C22⋊C4×C101—48no—
156C22⋊C4×C101—48no—
157C22⋊C4×C101—48no—
158C22⋊C4×C101—48no—
159C23×C101—24no—
160C23×C101—24no—
161C23×C101—24no—
162C23×C101—24no—
163C23×C101—24no—
164C23×C101—24no—
165C23×C101—24no—
166C23×C101—42no—
167C23×C101—42no—
168C23×C101—42no—
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×C101C2×#4112yes—
195C23×C101C2×#4111yescharacteristic
196C23×C101C2×#4111yescharacteristic
197C23×C101C2×#4111yescharacteristic
198C23×C101H(5,𝔽2)11yescharacteristic
199C23×C101H(5,𝔽2)11yescharacteristic
200C23×C101H(5,𝔽2)11yescharacteristic
201C23×C101H(5,𝔽2)12yes—
202C23×C101H(5,𝔽2)12yes—
203C23×C101H(5,𝔽2)12yes—
204C23×C1012−1+411yescharacteristic
205D4×C101—416no—
206C2×C4×C101—24no—
207C2×C4×C101—22no—
208C2×C4×C101—22no—
209C2×C4×C101—22no—
210C2×C4×C101—24no—
211C2×C4×C101—24no—
212C2×C4×C101—42no—
213C2×C4×C101—42no—
214C2×C4×C101—41no—
215C2×C4×C101—41no—
216C2×C4×C101—41no—
217C2×C4×C101—41no—
218C2×C4×C101—41no—
219C2×C4×C101—41no—
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—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—
256C22×C101—44no—
257C22×C101—44no—
258C22×C101—44no—
259C22×C101—44no—
260C22×C101—44no—
261C22×C101—44no—
262C22×C101—44no—
263C22×C101—82no—
264C22×C101—82no—
265C22×C101—82no—
266C22×C101—82no—
267C22×C101—82no—
268C22×C101—82no—
269C22×C101—82no—
270C22×C101—82no—
271C22×C101#53812yes—
272C22×C101#53812yes—
273C22×C101#53812yes—
274C22×C101#53811yescharacteristic
275C22×C101#53811yescharacteristic
276C22×C101#53912yes—
277C22×C101#53911yescharacteristic
278C22×C101#54012yes—
279C22×C101#54012yes—
280C22×C101#55112yes—
281C22×C101#55111yescharacteristic
282C22×C101#55112yes—
283C22×C101#55312yes—
284C22×C101#55511yescharacteristic
285C22×C101#55611yescharacteristic
286C22×C101#55911yescharacteristic
287C22×C101#56011yescharacteristic
288C22×C101#56012yes—
289C22×C101#56011yescharacteristic
290C22×C101#56012yes—
291C22×C101H(3,𝔽4)11yescharacteristic
292C22×C101#56212yes—
293C22×C101#56211yescharacteristic
294C4×C101—42no—
295C4×C101—42no—
296C4×C101—42no—
297C4×C101—82no—
298C4×C101—82no—
299C4×C101—82no—
300C4×C101—82no—
301C4×C101—82no—
302#17234C10111yesmaximal, characteristic, direct product factor, Sylow
303C2×C101—84no—
304C2×C101#273511yescharacteristic
305C2×C101#274012yes—
306C2×C101#275612yes—
307C2×C101#276011yescharacteristic
308C2×C101#278211yescharacteristic
309C2×C101#279712yes—
310C2×C101#280811yescharacteristic
311C2×C101#282611yescharacteristic
312C2×C101#282612yes—
313C2×C101#282811yescharacteristic
314C2×C101#282811yescharacteristic
315#1445C2×C10111yescharacteristic, complemented
316#1443C2×C10112yescomplemented
317#1442C2×C10111yescharacteristic, complemented
318#1440C2×C10112yescomplemented
319#1440C2×C10112yescomplemented
320#1439C2×C10112yescomplemented
321#1439C2×C10112yescomplemented
322#1438C2×C10111yescharacteristic
323#1438C2×C10112yes—
324C101#1723411yescharacteristic, direct product factor, Sylow
325C23×D4C22×C10111yescharacteristic
326C22×C4⋊C4C22×C10111yescharacteristic
327C22×C4⋊C4C22×C10111yescharacteristic
328C22×C22⋊C4C22×C10112yes—
329C22×C22⋊C4C22×C10112yes—
330C22×C22⋊C4C22×C10112yes—
331C22×C22⋊C4C22×C10112yes—
332C22×C22⋊C4C22×C10112yes—
333C22×C22⋊C4C22×C10112yes—
334C2×#95C22×C10112yes—
335C2×#95C22×C10111yescharacteristic
336C2×#95C22×C10111yescharacteristic
337C2×#95C22×C10111yescharacteristic
338C2×#95C22×C10112yes—
339C2×#95C22×C10112yes—
340C2×#95C22×C10112yes—
341C2×#95C22×C10112yes—
342C2×#95C22×C10112yes—
343C2×#95C22×C10112yes—
344C2×#95C22×C10112yes—
345C2×#95C22×C10111yescharacteristic
346C25C23×C10112yes—
347C22×D4—24no—
348C22×D4—22no—
349C22×D4—42no—
350C22×D4—41no—
351C22×D4—41no—
352C23×C4C23×C10112yes—
353C23×C4C23×C10112yes—
354C23×C4C23×C10112yes—
355C23×C4C23×C10112yes—
356C23×C4C23×C10112yes—
357C23×C4C23×C10111yescharacteristic
358C23×C4C23×C10111yescharacteristic
359C23×C4C23×C10111yescharacteristic
360C2×C4⋊C4—22no—
361C2×C4⋊C4—41no—
362C2×C4⋊C4—41no—
363C2×C4⋊C4—41no—
364C2×C4⋊C4—42no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383#95—24no—
384#95—22no—
385#95—42no—
386#95—42no—
387#95—41no—
388#95—41no—
389#95—41no—
390#95—42no—
391#95—42no—
392#95—42no—
393#95—42no—
394#95—42no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24#41×C10114yes—
410C24C24×C10111yescharacteristic
411C2×D4—48no—
412C2×D4—44no—
413C2×D4—44no—
414C2×D4—48no—
415C2×D4—44no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—21no—
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—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#41×C10112yes—
464C22×C4#41×C10112yes—
465C22×C4#41×C10112yes—
466C4⋊C4—44no—
467C4⋊C4—44no—
468C22⋊C4—48no—
469C22⋊C4—48no—
470C22⋊C4—48no—
471C22⋊C4—48no—
472C22⋊C4—48no—
473C22⋊C4—48no—
474C23—24no—
475C23—24no—
476C23—24no—
477C23—24no—
478C23—24no—
479C23—24no—
480C23—24no—
481C23—42no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—42no—
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—
509C23C2×#41×C10112yes—
510C23C2×#41×C10111yescharacteristic
511C23C2×#41×C10111yescharacteristic
512C23C2×#41×C10111yescharacteristic
513C23H(5,𝔽2)×C10111yescharacteristic
514C23H(5,𝔽2)×C10111yescharacteristic
515C23H(5,𝔽2)×C10111yescharacteristic
516C23H(5,𝔽2)×C10112yes—
517C23H(5,𝔽2)×C10112yes—
518C23H(5,𝔽2)×C10112yes—
519C232−1+4×C10111yescharacteristic
520D4—416no—
521C2×C4—24no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
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—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—
571C22—44no—
572C22—44no—
573C22—44no—
574C22—44no—
575C22—44no—
576C22—44no—
577C22—44no—
578C22—82no—
579C22—82no—
580C22—82no—
581C22—82no—
582C22—82no—
583C22—82no—
584C22—82no—
585C22—82no—
586C22#538×C10112yes—
587C22#538×C10111yescharacteristic
588C22#538×C10112yes—
589C22#538×C10112yes—
590C22#538×C10111yescharacteristic
591C22#539×C10112yes—
592C22#539×C10111yescharacteristic
593C22#540×C10112yes—
594C22#540×C10112yes—
595C22#551×C10112yes—
596C22#551×C10111yescharacteristic
597C22#551×C10112yes—
598C22#553×C10112yes—
599C22#555×C10111yescharacteristic
600C22#556×C10111yescharacteristic
601C22#559×C10111yescharacteristic
602C22#560×C10111yescharacteristic
603C22#560×C10112yes—
604C22#560×C10111yescharacteristic
605C22#560×C10112yes—
606C22H(3,𝔽4)×C10111yescharacteristic
607C22#562×C10112yes—
608C22#562×C10111yescharacteristic
609C4—42no—
610C4—42no—
611C4—42no—
612C4—82no—
613C4—82no—
614C4—82no—
615C4—82no—
616C4—82no—
617C2—84no—
618C2C101×#273511yescharacteristic
619C2C101×#274012yes—
620C2C101×#275612yes—
621C2C101×#276011yescharacteristic
622C2C101×#278211yescharacteristic
623C2C101×#279712yes—
624C2C101×#280811yescharacteristic
625C2C101×#282611yescharacteristic
626C2C101×#282612yes—
627C2C101×#282811yescharacteristic
628C2C101×#282811yescharacteristic
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. C101×#1445C2semidirect
2. C101×#1443C2semidirect
3. C101×#1442C2semidirect
4. C101×#1440C2semidirect
5. C101×#1440C2semidirect
6. C101×#1439C2semidirect
7. C101×#1439C2semidirect
302. #17234C101direct (N × H)
315. #1445C2×C101semidirect
316. #1443C2×C101semidirect
317. #1442C2×C101semidirect
318. #1440C2×C101semidirect
319. #1440C2×C101semidirect
320. #1439C2×C101semidirect
321. #1439C2×C101semidirect
324. C101#17234direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#14452
C101×#14432
C101×#14422
C101×#14402
C101×#14392
C101×#14382
#17234101