Finite Group Databasebeta

← C101×#13877 #38796028

Subgroups — C101×#13877 #38796028

Order 25856.

4046 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C101C211yesmaximal, characteristic
2C23×C22⋊C4×C101C211yesmaximal, characteristic
3C2×#385×C101C212yesmaximal, complemented
4C2×#380×C101C212yesmaximal, complemented
5C2×#379×C101C211yesmaximal, characteristic
6C101×#1439C214yesmaximal, complemented
7C101×C22⋊#95C212yesmaximal, complemented
8C101×C22⋊#95C212yesmaximal, complemented
9C26×C101C2211yescharacteristic
10C24×C4×C101C2212yes—
11C24×C4×C101C2212yes—
12C22×C4⋊C4×C101C2214yescomplemented
13C22×C22⋊C4×C101—24no—
14C22×C22⋊C4×C101—28no—
15C22×C22⋊C4×C101—28no—
16C22×C22⋊C4×C101C418yescomplemented
17C22×C22⋊C4×C101C2212yes—
18C22×C22⋊C4×C101C2211yescharacteristic
19C22×C22⋊C4×C101C2212yes—
20C22×C22⋊C4×C101C2211yescharacteristic
21C22×C22⋊C4×C101C2211yescharacteristic
22C22×C22⋊C4×C101C2212yes—
23C22×C22⋊C4×C101C2212yes—
24C22×C22⋊C4×C101C2212yes—
25C22×C22⋊C4×C101C2211yescharacteristic
26#385×C101—28no—
27#380×C101—28no—
28#379×C101—24no—
29C2×#95×C101C2214yescomplemented
30C2×#95×C101C2214yescomplemented
31C2×#95×C101C2214yescomplemented
32C25×C101—24no—
33C25×C101—24no—
34C25×C101—24no—
35C25×C101—24no—
36C25×C101—44no—
37C25×C101C2×C414yes—
38C25×C101D414yes—
39C25×C101Q814yes—
40C25×C101C2311yescharacteristic
41C25×C101C2311yescharacteristic
42C25×C101C2311yescharacteristic
43C23×C4×C101—24no—
44C23×C4×C101—24no—
45C23×C4×C101—24no—
46C23×C4×C101—28no—
47C23×C4×C101—28no—
48C23×C4×C101—24no—
49C23×C4×C101—24no—
50C23×C4×C101—44no—
51C23×C4×C101—44no—
52C23×C4×C101C2×C418yescomplemented
53C23×C4×C101C2312yes—
54C23×C4×C101C2312yes—
55C23×C4×C101C2312yes—
56C23×C4×C101C2314yes—
57C23×C4×C101C2312yes—
58C2×C4⋊C4×C101—28no—
59C2×C4⋊C4×C101—28no—
60C2×C4⋊C4×C101—44no—
61C2×C22⋊C4×C101—232no—
62C2×C22⋊C4×C101—24no—
63C2×C22⋊C4×C101—24no—
64C2×C22⋊C4×C101—24no—
65C2×C22⋊C4×C101—24no—
66C2×C22⋊C4×C101—28no—
67C2×C22⋊C4×C101—28no—
68C2×C22⋊C4×C101—232no—
69C2×C22⋊C4×C101—24no—
70C2×C22⋊C4×C101—22no—
71C2×C22⋊C4×C101—24no—
72C2×C22⋊C4×C101—22no—
73C2×C22⋊C4×C101—24no—
74C2×C22⋊C4×C101—24no—
75C2×C22⋊C4×C101—24no—
76C2×C22⋊C4×C101—24no—
77C2×C22⋊C4×C101—44no—
78C2×C22⋊C4×C101C2×C414yes—
79C2×C22⋊C4×C101C2×C414yes—
80C2×C22⋊C4×C101C2×C418yescomplemented
81C2×C22⋊C4×C101D418yes—
82C2×C22⋊C4×C101D418yes—
83#95×C101—28no—
84#95×C101—28no—
85#95×C101—44no—
86C24×C101—22no—
87C24×C101—22no—
88C24×C101—22no—
89C24×C101—22no—
90C24×C101—24no—
91C24×C101—24no—
92C24×C101—28no—
93C24×C101—28no—
94C24×C101—216no—
95C24×C101—28no—
96C24×C101—216no—
97C24×C101—216no—
98C24×C101—216no—
99C24×C101—28no—
100C24×C101—22no—
101C24×C101—22no—
102C24×C101—22no—
103C24×C101—22no—
104C24×C101—24no—
105C24×C101—48no—
106C24×C101—48no—
107C24×C101—48no—
108C24×C101—416no—
109C24×C101—416no—
110C24×C101—416no—
111C24×C101—416no—
112C24×C101C4⋊C4116yescomplemented
113C24×C101C22×C412yes—
114C24×C101C22×C412yes—
115C24×C101C22×C412yes—
116C24×C101C2×D412yes—
117C24×C101C2×D414yes—
118C24×C101C2×D412yes—
119C24×C101C2×D412yes—
120C24×C101C2×D414yes—
121C24×C101C2×Q812yes—
122C24×C101C2×Q812yes—
123C24×C101C2×Q812yes—
124C24×C101#4114yes—
125C24×C101#4114yes—
126C24×C101C2411yescharacteristic
127C22×C4×C101—22no—
128C22×C4×C101—22no—
129C22×C4×C101—24no—
130C22×C4×C101—216no—
131C22×C4×C101—216no—
132C22×C4×C101—22no—
133C22×C4×C101—24no—
134C22×C4×C101—24no—
135C22×C4×C101—24no—
136C22×C4×C101—24no—
137C22×C4×C101—22no—
138C22×C4×C101—24no—
139C22×C4×C101—24no—
140C22×C4×C101—24no—
141C22×C4×C101—24no—
142C22×C4×C101—216no—
143C22×C4×C101—22no—
144C22×C4×C101—24no—
145C22×C4×C101—22no—
146C22×C4×C101—22no—
147C22×C4×C101—22no—
148C22×C4×C101—22no—
149C22×C4×C101—22no—
150C22×C4×C101—24no—
151C22×C4×C101—24no—
152C22×C4×C101—24no—
153C22×C4×C101—48no—
154C22×C4×C101—416no—
155C22×C4×C101—416no—
156C22×C4×C101—416no—
157C22×C4×C101—416no—
158C22×C4×C101—48no—
159C22×C4×C101—48no—
160C22×C4×C101C22×C414yes—
161C22×C4×C101C22×C414yes—
162C22×C4×C101C2×D418yes—
163C22×C4×C101C2×D418yes—
164C4⋊C4×C101—416no—
165C22⋊C4×C101—216no—
166C22⋊C4×C101—28no—
167C22⋊C4×C101—216no—
168C22⋊C4×C101—216no—
169C22⋊C4×C101—48no—
170C22⋊C4×C101—44no—
171C22⋊C4×C101—48no—
172C22⋊C4×C101—44no—
173C22⋊C4×C101C22⋊C4116yescomplemented
174C23×C101—22no—
175C23×C101—22no—
176C23×C101—24no—
177C23×C101—24no—
178C23×C101—24no—
179C23×C101—22no—
180C23×C101—24no—
181C23×C101—24no—
182C23×C101—24no—
183C23×C101—22no—
184C23×C101—24no—
185C23×C101—24no—
186C23×C101—24no—
187C23×C101—24no—
188C23×C101—28no—
189C23×C101—28no—
190C23×C101—28no—
191C23×C101—28no—
192C23×C101—28no—
193C23×C101—28no—
194C23×C101—28no—
195C23×C101—28no—
196C23×C101—22no—
197C23×C101—22no—
198C23×C101—24no—
199C23×C101—24no—
200C23×C101—22no—
201C23×C101—24no—
202C23×C101—24no—
203C23×C101—24no—
204C23×C101—22no—
205C23×C101—24no—
206C23×C101—24no—
207C23×C101—232no—
208C23×C101—232no—
209C23×C101—416no—
210C23×C101—432no—
211C23×C101—432no—
212C23×C101—432no—
213C23×C101—432no—
214C23×C101—464no—
215C23×C101—44no—
216C23×C101—44no—
217C23×C101—44no—
218C23×C101—44no—
219C23×C101C2×C22⋊C414yes—
220C23×C101C2×C4⋊C414yes—
221C23×C101C2×C4⋊C414yes—
222C23×C101C2×C4⋊C414yes—
223C23×C101#11714yes—
224C23×C101C4×D418yes—
225C23×C101#12014yes—
226C23×C101#12118yes—
227C23×C101C22⋊Q818yes—
228C23×C101C22⋊Q818yes—
229C23×C101#12314yes—
230C23×C101C23×C411yescharacteristic
231C23×C101C22×D412yes—
232C23×C101C22×D411yescharacteristic
233C23×C101C22×D412yes—
234C23×C101C22×Q811yescharacteristic
235C23×C101C2×#4112yes—
236C23×C101C2×#4112yes—
237C23×C101H(5,𝔽2)14yes—
238C2×C4×C101—24no—
239C2×C4×C101—24no—
240C2×C4×C101—28no—
241C2×C4×C101—28no—
242C2×C4×C101—24no—
243C2×C4×C101—24no—
244C2×C4×C101—24no—
245C2×C4×C101—28no—
246C2×C4×C101—28no—
247C2×C4×C101—28no—
248C2×C4×C101—432no—
249C2×C4×C101—432no—
250C2×C4×C101—44no—
251C2×C4×C101—44no—
252C2×C4×C101—44no—
253C2×C4×C101—44no—
254C2×C4×C101—44no—
255C2×C4×C101—44no—
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—44no—
263C2×C4×C101—44no—
264C2×C4×C101—44no—
265C2×C4×C101—44no—
266C2×C4×C101C2×C22⋊C418yescomplemented
267C22×C101—24no—
268C22×C101—24no—
269C22×C101—28no—
270C22×C101—28no—
271C22×C101—28no—
272C22×C101—28no—
273C22×C101—28no—
274C22×C101—28no—
275C22×C101—28no—
276C22×C101—28no—
277C22×C101—216no—
278C22×C101—216no—
279C22×C101—24no—
280C22×C101—24no—
281C22×C101—24no—
282C22×C101—24no—
283C22×C101—24no—
284C22×C101—464no—
285C22×C101—44no—
286C22×C101—44no—
287C22×C101—44no—
288C22×C101—44no—
289C22×C101—48no—
290C22×C101#38018yescomplemented
291C22×C101#38518yescomplemented
292C22×C101C22×C22⋊C411yescharacteristic
293C22×C101C22×C4⋊C411yescharacteristic
294C22×C101C2×#11711yescharacteristic
295C22×C101C2×C4×D412yes—
296C22×C101#51812yes—
297C22×C101C2×#12011yescharacteristic
298C22×C101C2×#12112yes—
299C22×C101C2×C22⋊Q812yes—
300C22×C101C2×C22⋊Q812yes—
301C22×C101C2×#12311yescharacteristic
302C22×C101#53412yes—
303C22×C101#54312yes—
304C22×C101D4214yes—
305C22×C101#54614yes—
306C22×C101#54614yes—
307C22×C101#55114yes—
308C4×C101—28no—
309C4×C101—44no—
310C4×C101—48no—
311C4×C101—82no—
312C4×C101—82no—
313#13877C10111yesmaximal, characteristic, direct product factor, Sylow
314C2×C101—28no—
315C2×C101—28no—
316C2×C101—44no—
317C2×C101C2×#38011yescharacteristic
318C2×C101C2×#38511yescharacteristic
319C2×C101#231511yescharacteristic
320C2×C101D4×C22⋊C412yes—
321C2×C101#234212yes—
322C2×C101#241012yes—
323C2×C101#241212yes—
324C2×C101#243714yes—
325C23×C22⋊C4C2×C10111yescharacteristic
326C23×C22⋊C4C2×C10111yescharacteristic
327C2×#385C2×C10112yescomplemented
328C2×#380C2×C10112yescomplemented
329C2×#379C2×C10111yescharacteristic
330#1439C2×C10114yescomplemented
331C22⋊#95C2×C10112yescomplemented
332C22⋊#95C2×C10112yescomplemented
333C101#1387711yescharacteristic, direct product factor, Sylow
334C26C22×C10111yescharacteristic
335C24×C4C22×C10112yes—
336C24×C4C22×C10112yes—
337C22×C4⋊C4C22×C10114yescomplemented
338C22×C22⋊C4—24no—
339C22×C22⋊C4—28no—
340C22×C22⋊C4—28no—
341C22×C22⋊C4C4×C10118yescomplemented
342C22×C22⋊C4C22×C10112yes—
343C22×C22⋊C4C22×C10111yescharacteristic
344C22×C22⋊C4C22×C10112yes—
345C22×C22⋊C4C22×C10111yescharacteristic
346C22×C22⋊C4C22×C10111yescharacteristic
347C22×C22⋊C4C22×C10112yes—
348C22×C22⋊C4C22×C10112yes—
349C22×C22⋊C4C22×C10112yes—
350C22×C22⋊C4C22×C10111yescharacteristic
351#385—28no—
352#380—28no—
353#379—24no—
354C2×#95C22×C10114yescomplemented
355C2×#95C22×C10114yescomplemented
356C2×#95C22×C10114yescomplemented
357C25—24no—
358C25—24no—
359C25—24no—
360C25—24no—
361C25—44no—
362C25C2×C4×C10114yes—
363C25D4×C10114yes—
364C25Q8×C10114yes—
365C25C23×C10111yescharacteristic
366C25C23×C10111yescharacteristic
367C25C23×C10111yescharacteristic
368C23×C4—24no—
369C23×C4—24no—
370C23×C4—24no—
371C23×C4—28no—
372C23×C4—28no—
373C23×C4—24no—
374C23×C4—24no—
375C23×C4—44no—
376C23×C4—44no—
377C23×C4C2×C4×C10118yescomplemented
378C23×C4C23×C10112yes—
379C23×C4C23×C10112yes—
380C23×C4C23×C10112yes—
381C23×C4C23×C10114yes—
382C23×C4C23×C10112yes—
383C2×C4⋊C4—28no—
384C2×C4⋊C4—28no—
385C2×C4⋊C4—44no—
386C2×C22⋊C4—232no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—232no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4C2×C4×C10114yes—
404C2×C22⋊C4C2×C4×C10114yes—
405C2×C22⋊C4C2×C4×C10118yescomplemented
406C2×C22⋊C4D4×C10118yes—
407C2×C22⋊C4D4×C10118yes—
408#95—28no—
409#95—28no—
410#95—44no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—24no—
416C24—24no—
417C24—28no—
418C24—28no—
419C24—216no—
420C24—28no—
421C24—216no—
422C24—216no—
423C24—216no—
424C24—28no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—24no—
430C24—48no—
431C24—48no—
432C24—48no—
433C24—416no—
434C24—416no—
435C24—416no—
436C24—416no—
437C24C4⋊C4×C101116yescomplemented
438C24C22×C4×C10112yes—
439C24C22×C4×C10112yes—
440C24C22×C4×C10112yes—
441C24C2×D4×C10112yes—
442C24C2×D4×C10114yes—
443C24C2×D4×C10112yes—
444C24C2×D4×C10112yes—
445C24C2×D4×C10114yes—
446C24C2×Q8×C10112yes—
447C24C2×Q8×C10112yes—
448C24C2×Q8×C10112yes—
449C24#41×C10114yes—
450C24#41×C10114yes—
451C24C24×C10111yescharacteristic
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—24no—
455C22×C4—216no—
456C22×C4—216no—
457C22×C4—22no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—22no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—216no—
468C22×C4—22no—
469C22×C4—24no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—48no—
479C22×C4—416no—
480C22×C4—416no—
481C22×C4—416no—
482C22×C4—416no—
483C22×C4—48no—
484C22×C4—48no—
485C22×C4C22×C4×C10114yes—
486C22×C4C22×C4×C10114yes—
487C22×C4C2×D4×C10118yes—
488C22×C4C2×D4×C10118yes—
489C4⋊C4—416no—
490C22⋊C4—216no—
491C22⋊C4—28no—
492C22⋊C4—216no—
493C22⋊C4—216no—
494C22⋊C4—48no—
495C22⋊C4—44no—
496C22⋊C4—48no—
497C22⋊C4—44no—
498C22⋊C4C22⋊C4×C101116yescomplemented
499C23—22no—
500C23—22no—
501C23—24no—
502C23—24no—
503C23—24no—
504C23—22no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—22no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—28no—
514C23—28no—
515C23—28no—
516C23—28no—
517C23—28no—
518C23—28no—
519C23—28no—
520C23—28no—
521C23—22no—
522C23—22no—
523C23—24no—
524C23—24no—
525C23—22no—
526C23—24no—
527C23—24no—
528C23—24no—
529C23—22no—
530C23—24no—
531C23—24no—
532C23—232no—
533C23—232no—
534C23—416no—
535C23—432no—
536C23—432no—
537C23—464no—
538C23—432no—
539C23—432no—
540C23—44no—
541C23—44no—
542C23—44no—
543C23—44no—
544C23C2×C22⋊C4×C10114yes—
545C23C2×C4⋊C4×C10114yes—
546C23C2×C4⋊C4×C10114yes—
547C23C2×C4⋊C4×C10114yes—
548C23#117×C10114yes—
549C23C4×D4×C10118yes—
550C23#120×C10114yes—
551C23#121×C10118yes—
552C23C22⋊Q8×C10118yes—
553C23C22⋊Q8×C10118yes—
554C23#123×C10114yes—
555C23C23×C4×C10111yescharacteristic
556C23C22×D4×C10112yes—
557C23C22×D4×C10111yescharacteristic
558C23C22×D4×C10112yes—
559C23C22×Q8×C10111yescharacteristic
560C23C2×#41×C10112yes—
561C23C2×#41×C10112yes—
562C23H(5,𝔽2)×C10114yes—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—28no—
566C2×C4—28no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—28no—
571C2×C4—28no—
572C2×C4—28no—
573C2×C4—432no—
574C2×C4—432no—
575C2×C4—44no—
576C2×C4—44no—
577C2×C4—44no—
578C2×C4—44no—
579C2×C4—44no—
580C2×C4—44no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—44no—
588C2×C4—44no—
589C2×C4—44no—
590C2×C4—44no—
591C2×C4C2×C22⋊C4×C10118yescomplemented
592C22—28no—
593C22—28no—
594C22—28no—
595C22—28no—
596C22—216no—
597C22—216no—
598C22—24no—
599C22—24no—
600C22—24no—
601C22—24no—
602C22—28no—
603C22—28no—
604C22—28no—
605C22—28no—
606C22—24no—
607C22—24no—
608C22—24no—
609C22—464no—
610C22—44no—
611C22—44no—
612C22—48no—
613C22—44no—
614C22—44no—
615C22#380×C10118yescomplemented
616C22#385×C10118yescomplemented
617C22C22×C22⋊C4×C10111yescharacteristic
618C22C22×C4⋊C4×C10111yescharacteristic
619C22C2×#117×C10111yescharacteristic
620C22C2×C4×D4×C10112yes—
621C22#518×C10112yes—
622C22C2×#120×C10111yescharacteristic
623C22C2×#121×C10112yes—
624C22C2×C22⋊Q8×C10112yes—
625C22C2×C22⋊Q8×C10112yes—
626C22C2×#123×C10111yescharacteristic
627C22#534×C10112yes—
628C22#543×C10112yes—
629C22D42×C10114yes—
630C22#546×C10114yes—
631C22#546×C10114yes—
632C22#551×C10114yes—
633C4—28no—
634C4—48no—
635C4—44no—
636C4—82no—
637C4—82no—
638C2—28no—
639C2—28no—
640C2—44no—
641C2C2×#380×C10111yescharacteristic
642C2C2×#385×C10111yescharacteristic
643C2C101×#231511yescharacteristic
644C2D4×C22⋊C4×C10112yes—
645C2C101×#234212yes—
646C2C101×#241012yes—
647C2C101×#241212yes—
648C2C101×#243714yes—
subgroupG/H
center, socleC24×C101C24
commutatorC23C23×C4×C101
Frattini, cosocleC24C24×C101
prime radicalC26×C101C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C101 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#385×C101C2semidirect
4. C2×#380×C101C2semidirect
6. C101×#1439C2semidirect
7. C101×C22⋊#95C2semidirect
8. C101×C22⋊#95C2semidirect
12. C22×C4⋊C4×C101C22semidirect
16. C22×C22⋊C4×C101C4semidirect
29. C2×#95×C101C22semidirect
30. C2×#95×C101C22semidirect
31. C2×#95×C101C22semidirect
52. C23×C4×C101C2×C4semidirect
80. C2×C22⋊C4×C101C2×C4semidirect
112. C24×C101C4⋊C4semidirect
173. C22⋊C4×C101C22⋊C4semidirect
266. C2×C4×C101C2×C22⋊C4semidirect
290. C22×C101#380semidirect
291. C22×C101#385semidirect
313. #13877C101direct (N × H)
327. C2×#385C2×C101semidirect
328. C2×#380C2×C101semidirect
330. #1439C2×C101semidirect
331. C22⋊#95C2×C101semidirect
332. C22⋊#95C2×C101semidirect
333. C101#13877direct (N × H)
337. C22×C4⋊C4C22×C101semidirect
341. C22×C22⋊C4C4×C101semidirect
354. C2×#95C22×C101semidirect
355. C2×#95C22×C101semidirect
356. C2×#95C22×C101semidirect
377. C23×C4C2×C4×C101semidirect
405. C2×C22⋊C4C2×C4×C101semidirect
437. C24C4⋊C4×C101semidirect
498. C22⋊C4C22⋊C4×C101semidirect
591. C2×C4C2×C22⋊C4×C101semidirect
615. C22#380×C101semidirect
616. C22#385×C101semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C1012
C2×#385×C1012
C2×#380×C1012
C2×#379×C1012
C101×#14392
C101×C22⋊#952
#13877101