Finite Group Databasebeta

← C101×#14506 #38796657

Subgroups — C101×#14506 #38796657

Order 25856.

1962 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C101C211yesmaximal, characteristic
2C2×#388×C101C212yesmaximal, complemented
3C101×#1445C212yesmaximal, complemented
4C101×#1439C212yesmaximal, complemented
5C101×#1438C211yesmaximal, characteristic
6C101×#1438C211yesmaximal, characteristic
7C101×#1437C212yesmaximal, complemented
8C101×C4⋊#95C212yesmaximal, complemented
9C101×C22⋊#95C212yesmaximal, complemented
10C23×D4×C101C2211yescharacteristic
11C24×C4×C101C2211yescharacteristic
12C2×#123×C101—28no—
13C2×#123×C101C418yescomplemented
14C22×C4⋊C4×C101C2212yes—
15C22×C4⋊C4×C101C2212yes—
16C22×C22⋊C4×C101C2212yes—
17C22×C22⋊C4×C101C2212yes—
18C22×C22⋊C4×C101C2211yescharacteristic
19C22×C22⋊C4×C101C2212yes—
20C22×C22⋊C4×C101C2212yes—
21C22×C22⋊C4×C101C2211yescharacteristic
22C22×C22⋊C4×C101C2211yescharacteristic
23C22×C42×C101C2212yes—
24#388×C101—28no—
25C2×#95×C101C2212yes—
26C2×#95×C101C2212yes—
27C2×#95×C101C2212yes—
28C2×#95×C101C2212yes—
29C2×#95×C101C2212yes—
30C2×#95×C101C2212yes—
31C2×#95×C101C2211yescharacteristic
32C2×#95×C101C2212yes—
33C2×#95×C101C2211yescharacteristic
34C25×C101C2311yescharacteristic
35C25×C101C2311yescharacteristic
36C22×D4×C101—24no—
37C22×D4×C101—42no—
38C22×D4×C101—41no—
39C22×D4×C101—41no—
40C22×D4×C101C2×C414yes—
41C23×C4×C101—24no—
42C23×C4×C101—42no—
43C23×C4×C101—41no—
44C23×C4×C101—41no—
45C23×C4×C101C2×C414yes—
46C23×C4×C101C2312yes—
47C23×C4×C101C2312yes—
48C23×C4×C101C2312yes—
49C23×C4×C101C2311yescharacteristic
50C23×C4×C101C2312yes—
51C23×C4×C101C2312yes—
52C23×C4×C101C2312yes—
53#123×C101—232no—
54C2×C4⋊C4×C101—24no—
55C2×C4⋊C4×C101—24no—
56C2×C4⋊C4×C101—24no—
57C2×C4⋊C4×C101—24no—
58C2×C4⋊C4×C101—42no—
59C2×C4⋊C4×C101C2×C418yes—
60C2×C22⋊C4×C101—24no—
61C2×C22⋊C4×C101—24no—
62C2×C22⋊C4×C101—24no—
63C2×C22⋊C4×C101—24no—
64C2×C22⋊C4×C101—24no—
65C2×C22⋊C4×C101—24no—
66C2×C22⋊C4×C101—24no—
67C2×C22⋊C4×C101—24no—
68C2×C22⋊C4×C101—41no—
69C2×C22⋊C4×C101—42no—
70C2×C22⋊C4×C101—42no—
71C2×C22⋊C4×C101—42no—
72C2×C22⋊C4×C101—42no—
73C2×C22⋊C4×C101—41no—
74C2×C22⋊C4×C101—42no—
75C2×C22⋊C4×C101C2×C418yes—
76C2×C22⋊C4×C101C2×C414yes—
77C2×C22⋊C4×C101D418yes—
78C2×C42×C101—24no—
79C2×C42×C101—24no—
80C2×C42×C101—42no—
81#95×C101—24no—
82#95×C101—24no—
83#95×C101—41no—
84#95×C101—42no—
85#95×C101—42no—
86#95×C101—42no—
87#95×C101—42no—
88#95×C101—42no—
89#95×C101—41no—
90C24×C101—22no—
91C24×C101—22no—
92C24×C101—22no—
93C24×C101—22no—
94C24×C101—21no—
95C24×C101—21no—
96C24×C101—22no—
97C24×C101—22no—
98C24×C101—22no—
99C24×C101—22no—
100C24×C101—22no—
101C24×C101—22no—
102C24×C101—21no—
103C24×C101—21no—
104C24×C101—22no—
105C24×C101C22×C412yes—
106C24×C101C22×C412yes—
107C24×C101C2×D414yes—
108C24×C101C2411yescharacteristic
109C2×D4×C101—28no—
110C2×D4×C101—44no—
111C2×D4×C101—44no—
112C2×D4×C101—48no—
113C2×D4×C101—48no—
114C22×C4×C101—22no—
115C22×C4×C101—22no—
116C22×C4×C101—22no—
117C22×C4×C101—22no—
118C22×C4×C101—28no—
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—21no—
136C22×C4×C101—21no—
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—44no—
156C22×C4×C101—44no—
157C22×C4×C101—48no—
158C22×C4×C101—48no—
159C22×C4×C101C22×C414yes—
160C22×C4×C101C22×C412yes—
161C22×C4×C101C22×C414yes—
162C22×C4×C101C2×D414yes—
163C22×C4×C101C2×D414yes—
164C22×C4×C101#4114yes—
165C22×C4×C101#4114yes—
166C4⋊C4×C101—216no—
167C4⋊C4×C101—48no—
168C22⋊C4×C101—216no—
169C22⋊C4×C101—44no—
170C22⋊C4×C101—48no—
171C22⋊C4×C101—48no—
172C22⋊C4×C101—48no—
173C22⋊C4×C101—44no—
174C22⋊C4×C101C22⋊C4116yescomplemented
175C42×C101—48no—
176C23×C101—24no—
177C23×C101—22no—
178C23×C101—22no—
179C23×C101—24no—
180C23×C101—24no—
181C23×C101—24no—
182C23×C101—24no—
183C23×C101—24no—
184C23×C101—24no—
185C23×C101—24no—
186C23×C101—22no—
187C23×C101—24no—
188C23×C101—22no—
189C23×C101—22no—
190C23×C101—24no—
191C23×C101—42no—
192C23×C101—42no—
193C23×C101—42no—
194C23×C101—42no—
195C23×C101—41no—
196C23×C101—42no—
197C23×C101—41no—
198C23×C101—41no—
199C23×C101—42no—
200C23×C101—41no—
201C23×C101—42no—
202C23×C101—42no—
203C23×C101—42no—
204C23×C101—42no—
205C23×C101—42no—
206C23×C101—42no—
207C23×C101—42no—
208C23×C101—42no—
209C23×C101—42no—
210C23×C101—42no—
211C23×C101—41no—
212C23×C101—42no—
213C23×C101—41no—
214C23×C101—41no—
215C23×C101—42no—
216C23×C101—41no—
217C23×C101C2×C22⋊C414yes—
218C23×C101C23×C411yescharacteristic
219C23×C101C22×D412yes—
220C23×C101C2×#4112yes—
221C23×C101C2×#4112yes—
222C23×C101H(5,𝔽2)12yes—
223C23×C101H(5,𝔽2)11yescharacteristic
224C23×C101H(5,𝔽2)11yescharacteristic
225C23×C101H(5,𝔽2)12yes—
226C23×C1012−1+412yes—
227D4×C101—416no—
228C2×C4×C101—24no—
229C2×C4×C101—24no—
230C2×C4×C101—24no—
231C2×C4×C101—24no—
232C2×C4×C101—24no—
233C2×C4×C101—24no—
234C2×C4×C101—24no—
235C2×C4×C101—22no—
236C2×C4×C101—24no—
237C2×C4×C101—24no—
238C2×C4×C101—22no—
239C2×C4×C101—22no—
240C2×C4×C101—24no—
241C2×C4×C101—24no—
242C2×C4×C101—24no—
243C2×C4×C101—24no—
244C2×C4×C101—24no—
245C2×C4×C101—24no—
246C2×C4×C101—416no—
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—
265C2×C4×C101—42no—
266C2×C4×C101—42no—
267C2×C4×C101—42no—
268C2×C4×C101—42no—
269C2×C4×C101—42no—
270C2×C4×C101—42no—
271C2×C4×C101—42no—
272C2×C4×C101—42no—
273C2×C4×C101—42no—
274C2×C4×C101—42no—
275C2×C4×C101C2×C22⋊C418yes—
276C22×C101—24no—
277C22×C101—28no—
278C22×C101—44no—
279C22×C101—42no—
280C22×C101—42no—
281C22×C101—44no—
282C22×C101—44no—
283C22×C101—44no—
284C22×C101—44no—
285C22×C101—42no—
286C22×C101—44no—
287C22×C101—44no—
288C22×C101—42no—
289C22×C101—42no—
290C22×C101—82no—
291C22×C101—82no—
292C22×C101—82no—
293C22×C101—82no—
294C22×C101C22×C22⋊C411yescharacteristic
295C22×C101C4×#4112yes—
296C22×C101#51811yescharacteristic
297C22×C101#51811yescharacteristic
298C22×C101#52012yes—
299C22×C101#53512yes—
300C22×C101#53512yes—
301C22×C101#53812yes—
302C22×C101#53912yes—
303C22×C101#54012yes—
304C22×C101#54212yes—
305C22×C101#54612yes—
306C22×C101#54612yes—
307C22×C101#54712yes—
308C22×C101#54712yes—
309C22×C101#55111yescharacteristic
310C22×C101#55312yes—
311C22×C101#55911yescharacteristic
312C22×C101#56011yescharacteristic
313C22×C101#56212yes—
314C22×C101#56311yescharacteristic
315C4×C101—28no—
316C4×C101—44no—
317C4×C101—42no—
318C4×C101—44no—
319C4×C101—44no—
320C4×C101—82no—
321C4×C101—82no—
322#14506C10111yesmaximal, characteristic, direct product factor, Sylow
323C2×C101—44no—
324C2×C101—82no—
325C2×C101#230911yescharacteristic
326C2×C101#233512yes—
327C2×C101#233912yes—
328C2×C101#237411yescharacteristic
329C2×C101#237611yescharacteristic
330C2×C101#270312yes—
331C2×C101#270612yes—
332C2×C101#271012yes—
333C2×C101#271812yes—
334C22×#123C2×C10111yescharacteristic
335C2×#388C2×C10112yescomplemented
336#1445C2×C10112yescomplemented
337#1439C2×C10112yescomplemented
338#1438C2×C10111yescharacteristic
339#1438C2×C10111yescharacteristic
340#1437C2×C10112yescomplemented
341C4⋊#95C2×C10112yescomplemented
342C22⋊#95C2×C10112yescomplemented
343C101#1450611yescharacteristic, direct product factor, Sylow
344C23×D4C22×C10111yescharacteristic
345C24×C4C22×C10111yescharacteristic
346C2×#123—28no—
347C2×#123C4×C10118yescomplemented
348C22×C4⋊C4C22×C10112yes—
349C22×C4⋊C4C22×C10112yes—
350C22×C22⋊C4C22×C10112yes—
351C22×C22⋊C4C22×C10112yes—
352C22×C22⋊C4C22×C10111yescharacteristic
353C22×C22⋊C4C22×C10112yes—
354C22×C22⋊C4C22×C10112yes—
355C22×C22⋊C4C22×C10111yescharacteristic
356C22×C22⋊C4C22×C10111yescharacteristic
357C22×C42C22×C10112yes—
358#388—28no—
359C2×#95C22×C10112yes—
360C2×#95C22×C10112yes—
361C2×#95C22×C10112yes—
362C2×#95C22×C10112yes—
363C2×#95C22×C10112yes—
364C2×#95C22×C10112yes—
365C2×#95C22×C10111yescharacteristic
366C2×#95C22×C10112yes—
367C2×#95C22×C10111yescharacteristic
368C25C23×C10111yescharacteristic
369C25C23×C10111yescharacteristic
370C22×D4—24no—
371C22×D4—42no—
372C22×D4—41no—
373C22×D4—41no—
374C22×D4C2×C4×C10114yes—
375C23×C4—24no—
376C23×C4—42no—
377C23×C4—41no—
378C23×C4—41no—
379C23×C4C2×C4×C10114yes—
380C23×C4C23×C10112yes—
381C23×C4C23×C10112yes—
382C23×C4C23×C10112yes—
383C23×C4C23×C10111yescharacteristic
384C23×C4C23×C10112yes—
385C23×C4C23×C10112yes—
386C23×C4C23×C10112yes—
387#123—232no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—42no—
393C2×C4⋊C4C2×C4×C10118yes—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—41no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—41no—
408C2×C22⋊C4—42no—
409C2×C22⋊C4C2×C4×C10118yes—
410C2×C22⋊C4C2×C4×C10114yes—
411C2×C22⋊C4D4×C10118yes—
412C2×C42—24no—
413C2×C42—24no—
414C2×C42—42no—
415#95—24no—
416#95—24no—
417#95—41no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—42no—
423#95—41no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—21no—
429C24—21no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—21no—
437C24—21no—
438C24—22no—
439C24C22×C4×C10112yes—
440C24C22×C4×C10112yes—
441C24C2×D4×C10114yes—
442C24C24×C10111yescharacteristic
443C2×D4—28no—
444C2×D4—44no—
445C2×D4—44no—
446C2×D4—48no—
447C2×D4—48no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—28no—
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—21no—
470C22×C4—21no—
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×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—44no—
490C22×C4—44no—
491C22×C4—48no—
492C22×C4—48no—
493C22×C4C22×C4×C10114yes—
494C22×C4C22×C4×C10112yes—
495C22×C4C22×C4×C10114yes—
496C22×C4C2×D4×C10114yes—
497C22×C4C2×D4×C10114yes—
498C22×C4#41×C10114yes—
499C22×C4#41×C10114yes—
500C4⋊C4—216no—
501C4⋊C4—48no—
502C22⋊C4—216no—
503C22⋊C4—44no—
504C22⋊C4—48no—
505C22⋊C4—48no—
506C22⋊C4—48no—
507C22⋊C4—44no—
508C22⋊C4C22⋊C4×C101116yescomplemented
509C42—48no—
510C23—24no—
511C23—22no—
512C23—22no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—22no—
521C23—24no—
522C23—22no—
523C23—22no—
524C23—24no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—41no—
530C23—42no—
531C23—41no—
532C23—41no—
533C23—42no—
534C23—41no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—41no—
546C23—42no—
547C23—41no—
548C23—41no—
549C23—42no—
550C23—41no—
551C23C2×C22⋊C4×C10114yes—
552C23C23×C4×C10111yescharacteristic
553C23C22×D4×C10112yes—
554C23C2×#41×C10112yes—
555C23C2×#41×C10112yes—
556C23H(5,𝔽2)×C10112yes—
557C23H(5,𝔽2)×C10111yescharacteristic
558C23H(5,𝔽2)×C10111yescharacteristic
559C23H(5,𝔽2)×C10112yes—
560C232−1+4×C10112yes—
561D4—416no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—416no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4C2×C22⋊C4×C10118yes—
610C22—24no—
611C22—28no—
612C22—44no—
613C22—44no—
614C22—44no—
615C22—44no—
616C22—44no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—44no—
621C22—44no—
622C22—42no—
623C22—42no—
624C22—82no—
625C22—82no—
626C22—82no—
627C22—82no—
628C22C22×C22⋊C4×C10111yescharacteristic
629C22C4×#41×C10112yes—
630C22#518×C10111yescharacteristic
631C22#518×C10111yescharacteristic
632C22#520×C10112yes—
633C22#535×C10112yes—
634C22#535×C10112yes—
635C22#538×C10112yes—
636C22#539×C10112yes—
637C22#540×C10112yes—
638C22#542×C10112yes—
639C22#546×C10112yes—
640C22#546×C10112yes—
641C22#547×C10112yes—
642C22#547×C10112yes—
643C22#551×C10111yescharacteristic
644C22#553×C10112yes—
645C22#559×C10111yescharacteristic
646C22#560×C10111yescharacteristic
647C22#562×C10112yes—
648C22#563×C10111yescharacteristic
649C4—28no—
650C4—44no—
651C4—44no—
652C4—44no—
653C4—42no—
654C4—82no—
655C4—82no—
656C2—44no—
657C2—82no—
658C2C101×#230911yescharacteristic
659C2C101×#233512yes—
660C2C101×#233912yes—
661C2C101×#237411yescharacteristic
662C2C101×#237611yescharacteristic
663C2C101×#270312yes—
664C2C101×#270612yes—
665C2C101×#271012yes—
666C2C101×#271812yes—
subgroupG/H
center, socleC24×C101C24
commutatorC23C23×C4×C101
Frattini, cosocleC24C24×C101
prime radicalC23×D4×C101C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#388×C101C2semidirect
3. C101×#1445C2semidirect
4. C101×#1439C2semidirect
7. C101×#1437C2semidirect
8. C101×C4⋊#95C2semidirect
9. C101×C22⋊#95C2semidirect
13. C2×#123×C101C4semidirect
174. C22⋊C4×C101C22⋊C4semidirect
322. #14506C101direct (N × H)
335. C2×#388C2×C101semidirect
336. #1445C2×C101semidirect
337. #1439C2×C101semidirect
340. #1437C2×C101semidirect
341. C4⋊#95C2×C101semidirect
342. C22⋊#95C2×C101semidirect
343. C101#14506direct (N × H)
347. C2×#123C4×C101semidirect
508. C22⋊C4C22⋊C4×C101semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C1012
C2×#388×C1012
C101×#14452
C101×#14392
C101×#14382
C101×#14372
C101×C4⋊#952
C101×C22⋊#952
#14506101