Finite Group Databasebeta

← C101×#13080 #38795231

Subgroups — C101×#13080 #38795231

Order 25856.

864 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#100×C101C211yesmaximal, characteristic
2C101×#2405C211yesmaximal, characteristic
3C2×#352×C101C212yesmaximal, complemented
4C101×#1781C211yesmaximal, characteristic
5C101×#1390C212yesmaximal, complemented
6C23×D4×C101C2211yescharacteristic
7C22×M16×C101—21no—
8C2×#123×C101C411yescharacteristic, complemented
9C2×#123×C101C2211yescharacteristic
10C22×C22⋊C4×C101C411yescharacteristic, complemented
11C2×#100×C101—21no—
12C2×#100×C101—24no—
13C2×#100×C101C2212yes—
14C2×#99×C101—21no—
15C2×#99×C101C2212yes—
16#394×C101—21no—
17#394×C101—21no—
18#386×C101C411yescharacteristic, complemented
19#386×C101C2211yescharacteristic
20#385×C101—21no—
21#379×C101—21no—
22#379×C101—21no—
23#379×C101C411yescharacteristic, complemented
24#352×C101—24no—
25C25×C101C2×C411yescharacteristic
26C25×C101D411yescharacteristic
27C22×D4×C101—22no—
28C22×D4×C101—22no—
29C22×D4×C101—42no—
30C22×D4×C101—41no—
31C22×D4×C101—41no—
32C22×D4×C101C2×C411yescharacteristic
33C22×D4×C101D411yescharacteristic
34C22×D4×C101D411yescharacteristic
35C22×D4×C101C2311yescharacteristic
36C23×C4×C101C2×C411yescharacteristic
37C23×C4×C101C2×C411yescharacteristic
38C23×C4×C101D411yescharacteristic
39C2×M16×C101—24no—
40C2×M16×C101—22no—
41C2×M16×C101—41no—
42C2×M16×C101—42no—
43C22×C8×C101—41no—
44#123×C101—22no—
45#123×C101—22no—
46#123×C101—42no—
47C2×C4⋊C4×C101—21no—
48C2×C4⋊C4×C101—21no—
49C2×C22⋊C4×C101—21no—
50C2×C22⋊C4×C101—21no—
51C2×C22⋊C4×C101—21no—
52C2×C22⋊C4×C101—21no—
53C2×C22⋊C4×C101—21no—
54C2×C22⋊C4×C101—22no—
55C2×C22⋊C4×C101—21no—
56C2×C22⋊C4×C101—21no—
57C2×C22⋊C4×C101—21no—
58C2×C22⋊C4×C101—41no—
59C2×C22⋊C4×C101—41no—
60C2×C22⋊C4×C101—41no—
61C2×C22⋊C4×C101—41no—
62C2×C22⋊C4×C101C2×C411yescharacteristic
63C2×C22⋊C4×C101C2×C411yescharacteristic
64#100×C101—24no—
65#100×C101—22no—
66#100×C101D414yes—
67#99×C101—22no—
68#99×C101—22no—
69#99×C101—42no—
70#95×C101—21no—
71#95×C101—21no—
72C24×C101—21no—
73C24×C101—21no—
74C24×C101—21no—
75C24×C101—21no—
76C24×C101—22no—
77C24×C101—22no—
78C24×C101—41no—
79C24×C101—41no—
80C24×C101—42no—
81C24×C101—42no—
82C24×C101—81no—
83C24×C101—81no—
84C24×C101C22⋊C411yescharacteristic
85C24×C101C22⋊C411yescharacteristic
86C24×C101C22⋊C411yescharacteristic
87C24×C101C22×C411yescharacteristic
88C24×C101C2×D411yescharacteristic
89C2×D4×C101—22no—
90C2×D4×C101—22no—
91C2×D4×C101—22no—
92C2×D4×C101—22no—
93C2×D4×C101—21no—
94C2×D4×C101—21no—
95C2×D4×C101—41no—
96C2×D4×C101—41no—
97C2×D4×C101—41no—
98C2×D4×C101—41no—
99C2×D4×C101—41no—
100C2×D4×C101—41no—
101C2×D4×C101—44no—
102C2×D4×C101—44no—
103C2×D4×C101—44no—
104C2×D4×C101—44no—
105C2×D4×C101C2×D412yes—
106C2×D4×C101#4112yes—
107C22×C4×C101—21no—
108C22×C4×C101—21no—
109C22×C4×C101—22no—
110C22×C4×C101—21no—
111C22×C4×C101—21no—
112C22×C4×C101—21no—
113C22×C4×C101—21no—
114C22×C4×C101—21no—
115C22×C4×C101—21no—
116C22×C4×C101—22no—
117C22×C4×C101—41no—
118C22×C4×C101—41no—
119C22×C4×C101—41no—
120C22×C4×C101—42no—
121C22×C4×C101—81no—
122C22×C4×C101C22⋊C411yescharacteristic
123C22×C4×C101C2×D411yescharacteristic
124M16×C101—24no—
125M16×C101—44no—
126M16×C101—42no—
127C2×C8×C101—44no—
128C2×C8×C101—42no—
129C4⋊C4×C101—42no—
130C4⋊C4×C101—41no—
131C4⋊C4×C101—41no—
132C22⋊C4×C101—22no—
133C22⋊C4×C101—42no—
134C22⋊C4×C101—42no—
135C22⋊C4×C101—42no—
136C22⋊C4×C101—41no—
137C22⋊C4×C101—41no—
138C22⋊C4×C101—42no—
139C22⋊C4×C101—41no—
140C22⋊C4×C101—42no—
141C22⋊C4×C101—42no—
142C22⋊C4×C101—81no—
143C22⋊C4×C101—81no—
144C22⋊C4×C101—81no—
145C22⋊C4×C101—82no—
146C22⋊C4×C101—82no—
147C23×C101—22no—
148C23×C101—21no—
149C23×C101—21no—
150C23×C101—21no—
151C23×C101—21no—
152C23×C101—21no—
153C23×C101—21no—
154C23×C101—21no—
155C23×C101—21no—
156C23×C101—21no—
157C23×C101—21no—
158C23×C101—21no—
159C23×C101—21no—
160C23×C101—41no—
161C23×C101—42no—
162C23×C101—42no—
163C23×C101—42no—
164C23×C101—42no—
165C23×C101—41no—
166C23×C101—41no—
167C23×C101—41no—
168C23×C101—41no—
169C23×C101—41no—
170C23×C101—41no—
171C23×C101—42no—
172C23×C101—42no—
173C23×C101—41no—
174C23×C101—41no—
175C23×C101—42no—
176C23×C101—42no—
177C23×C101—81no—
178C23×C101—81no—
179C23×C101—81no—
180C23×C101—81no—
181C23×C101—84no—
182C23×C101—84no—
183C23×C101—84no—
184C23×C101—84no—
185C23×C101#9911yescharacteristic
186C23×C101#9911yescharacteristic
187C23×C101C2×C22⋊C411yescharacteristic
188C23×C101C4×D412yes—
189C23×C101#12112yes—
190D4×C101—42no—
191D4×C101—42no—
192D4×C101—44no—
193D4×C101—44no—
194D4×C101—42no—
195D4×C101—42no—
196C2×C4×C101—22no—
197C2×C4×C101—22no—
198C2×C4×C101—22no—
199C2×C4×C101—22no—
200C2×C4×C101—21no—
201C2×C4×C101—21no—
202C2×C4×C101—21no—
203C2×C4×C101—21no—
204C2×C4×C101—41no—
205C2×C4×C101—41no—
206C2×C4×C101—41no—
207C2×C4×C101—41no—
208C2×C4×C101—41no—
209C2×C4×C101—41no—
210C2×C4×C101—41no—
211C2×C4×C101—41no—
212C2×C4×C101—41no—
213C2×C4×C101—41no—
214C2×C4×C101—41no—
215C2×C4×C101—41no—
216C2×C4×C101—82no—
217C2×C4×C101—82no—
218C2×C4×C101—82no—
219C2×C4×C101—82no—
220C2×C4×C101—82no—
221C2×C4×C101#9912yes—
222C2×C4×C101#12011yescharacteristic
223C2×C4×C101#12311yescharacteristic
224C8×C101—44no—
225C22×C101—21no—
226C22×C101—21no—
227C22×C101—21no—
228C22×C101—21no—
229C22×C101—21no—
230C22×C101—21no—
231C22×C101—21no—
232C22×C101—22no—
233C22×C101—22no—
234C22×C101—42no—
235C22×C101—42no—
236C22×C101—42no—
237C22×C101—42no—
238C22×C101—42no—
239C22×C101—42no—
240C22×C101—41no—
241C22×C101—41no—
242C22×C101—41no—
243C22×C101—41no—
244C22×C101—41no—
245C22×C101—41no—
246C22×C101—41no—
247C22×C101—41no—
248C22×C101—41no—
249C22×C101—41no—
250C22×C101—81no—
251C22×C101—84no—
252C22×C101—84no—
253C22×C101—81no—
254C22×C101—81no—
255C22×C101—81no—
256C22×C101—84no—
257C22×C101—84no—
258C22×C101#35212yescomplemented
259C22×C101#38611yescharacteristic
260C22×C101C2×#9911yescharacteristic
261C22×C101C2×#9911yescharacteristic
262C4×C101—21no—
263C4×C101—22no—
264C4×C101—21no—
265C4×C101—81no—
266C4×C101—81no—
267C4×C101—81no—
268C4×C101—81no—
269C4×C101—162no—
270#13080C10111yesmaximal, characteristic, direct product factor, Sylow
271C2×C101—21no—
272C2×C101—21no—
273C2×C101—22no—
274C2×C101—42no—
275C2×C101—41no—
276C2×C101—42no—
277C2×C101—81no—
278C2×C101—81no—
279C2×C101#189811yescharacteristic
280C2×C101C2×#35211yescharacteristic
281C2×C101#212111yescharacteristic
282C22×#100C2×C10111yescharacteristic
283#2405C2×C10111yescharacteristic
284C2×#352C2×C10112yescomplemented
285#1781C2×C10111yescharacteristic
286#1390C2×C10112yescomplemented
287C101#1308011yescharacteristic, direct product factor, Sylow
288C23×D4C22×C10111yescharacteristic
289C22×M16—21no—
290C2×#123C4×C10111yescharacteristic, complemented
291C2×#123C22×C10111yescharacteristic
292C22×C22⋊C4C4×C10111yescharacteristic, complemented
293C2×#100—21no—
294C2×#100—24no—
295C2×#100C22×C10112yes—
296C2×#99—21no—
297C2×#99C22×C10112yes—
298#394—21no—
299#394—21no—
300#386C4×C10111yescharacteristic, complemented
301#386C22×C10111yescharacteristic
302#385—21no—
303#379—21no—
304#379—21no—
305#379C4×C10111yescharacteristic, complemented
306#352—24no—
307C25C2×C4×C10111yescharacteristic
308C25D4×C10111yescharacteristic
309C22×D4—22no—
310C22×D4—22no—
311C22×D4—42no—
312C22×D4—41no—
313C22×D4—41no—
314C22×D4C2×C4×C10111yescharacteristic
315C22×D4D4×C10111yescharacteristic
316C22×D4D4×C10111yescharacteristic
317C22×D4C23×C10111yescharacteristic
318C23×C4C2×C4×C10111yescharacteristic
319C23×C4C2×C4×C10111yescharacteristic
320C23×C4D4×C10111yescharacteristic
321C2×M16—24no—
322C2×M16—22no—
323C2×M16—41no—
324C2×M16—42no—
325C22×C8—41no—
326#123—22no—
327#123—22no—
328#123—42no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—41no—
341C2×C22⋊C4—41no—
342C2×C22⋊C4—41no—
343C2×C22⋊C4—41no—
344C2×C22⋊C4C2×C4×C10111yescharacteristic
345C2×C22⋊C4C2×C4×C10111yescharacteristic
346#100—24no—
347#100—22no—
348#100D4×C10114yes—
349#99—22no—
350#99—22no—
351#99—42no—
352#95—21no—
353#95—21no—
354C24—21no—
355C24—21no—
356C24—21no—
357C24—21no—
358C24—22no—
359C24—22no—
360C24—41no—
361C24—41no—
362C24—42no—
363C24—42no—
364C24—81no—
365C24—81no—
366C24C22⋊C4×C10111yescharacteristic
367C24C22⋊C4×C10111yescharacteristic
368C24C22⋊C4×C10111yescharacteristic
369C24C22×C4×C10111yescharacteristic
370C24C2×D4×C10111yescharacteristic
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4—41no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4—44no—
384C2×D4—44no—
385C2×D4—44no—
386C2×D4—44no—
387C2×D4C2×D4×C10112yes—
388C2×D4#41×C10112yes—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—42no—
403C22×C4—81no—
404C22×C4C22⋊C4×C10111yescharacteristic
405C22×C4C2×D4×C10111yescharacteristic
406M16—24no—
407M16—44no—
408M16—42no—
409C2×C8—44no—
410C2×C8—42no—
411C4⋊C4—42no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C22⋊C4—22no—
415C22⋊C4—42no—
416C22⋊C4—42no—
417C22⋊C4—42no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—42no—
421C22⋊C4—41no—
422C22⋊C4—42no—
423C22⋊C4—42no—
424C22⋊C4—81no—
425C22⋊C4—81no—
426C22⋊C4—81no—
427C22⋊C4—82no—
428C22⋊C4—82no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—22no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—41no—
443C23—42no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—41no—
451C23—41no—
452C23—41no—
453C23—42no—
454C23—42no—
455C23—41no—
456C23—41no—
457C23—42no—
458C23—42no—
459C23—81no—
460C23—81no—
461C23—81no—
462C23—81no—
463C23—84no—
464C23—84no—
465C23—84no—
466C23—84no—
467C23#99×C10111yescharacteristic
468C23#99×C10111yescharacteristic
469C23C2×C22⋊C4×C10111yescharacteristic
470C23C4×D4×C10112yes—
471C23#121×C10112yes—
472D4—42no—
473D4—42no—
474D4—44no—
475D4—44no—
476D4—42no—
477D4—42no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—82no—
499C2×C4—82no—
500C2×C4—82no—
501C2×C4—82no—
502C2×C4—82no—
503C2×C4#99×C10112yes—
504C2×C4#120×C10111yescharacteristic
505C2×C4#123×C10111yescharacteristic
506C8—44no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—22no—
513C22—22no—
514C22—21no—
515C22—21no—
516C22—42no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—41no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—81no—
533C22—84no—
534C22—84no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—84no—
539C22—84no—
540C22#352×C10112yescomplemented
541C22#386×C10111yescharacteristic
542C22C2×#99×C10111yescharacteristic
543C22C2×#99×C10111yescharacteristic
544C4—21no—
545C4—22no—
546C4—21no—
547C4—81no—
548C4—81no—
549C4—81no—
550C4—81no—
551C4—162no—
552C2—21no—
553C2—21no—
554C2—22no—
555C2—42no—
556C2—41no—
557C2—42no—
558C2—81no—
559C2—81no—
560C2C101×#189811yescharacteristic
561C2C2×#352×C10111yescharacteristic
562C2C101×#212111yescharacteristic
subgroupG/H
center, socleC22×C101C2×#99
commutatorC24C22×C4×C101
Frattini, cosocleC22×D4C23×C101
prime radicalC23×D4×C101C22
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C101 ◁ C24×C101 ◁ C23×D4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#352×C101C2semidirect
5. C101×#1390C2semidirect
8. C2×#123×C101C4semidirect
10. C22×C22⋊C4×C101C4semidirect
18. #386×C101C4semidirect
23. #379×C101C4semidirect
258. C22×C101#352semidirect
270. #13080C101direct (N × H)
284. C2×#352C2×C101semidirect
286. #1390C2×C101semidirect
287. C101#13080direct (N × H)
290. C2×#123C4×C101semidirect
292. C22×C22⋊C4C4×C101semidirect
300. #386C4×C101semidirect
305. #379C4×C101semidirect
540. C22#352×C101semidirect

Maximal subgroups

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

subgroupindex
C22×#100×C1012
C101×#24052
C2×#352×C1012
C101×#17812
C101×#13902
#13080101