Finite Group Databasebeta

← C101×#10960 #38793111

Subgroups — C101×#10960 #38793111

Order 25856.

1526 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#99×C101C212yesmaximal
2C2×#386×C101C211yesmaximal, characteristic
3C2×C4×C22⋊C4×C101C211yesmaximal, characteristic, complemented
4C2×#342×C101C212yesmaximal, complemented
5C101×C22⋊#95C211yesmaximal, characteristic, complemented
6C23×D4×C101C2211yescharacteristic
7C24×C4×C101C2211yescharacteristic
8C22×C22⋊C4×C101C412yescomplemented
9C22×C22⋊C4×C101C2211yescharacteristic
10C22×C22⋊C4×C101C2212yes—
11C22×C22⋊C4×C101C2212yes—
12C22×C42×C101—21no—
13C2×#99×C101—24no—
14C2×#99×C101—24no—
15C2×#99×C101C418yescomplemented
16#386×C101—21no—
17#386×C101—22no—
18#386×C101—21no—
19C4×C22⋊C4×C101—24no—
20C2×#95×C101—21no—
21C2×#95×C101—22no—
22C2×#95×C101C412yescomplemented
23#342×C101—24no—
24C25×C101C2×C411yescharacteristic
25C25×C101C2311yescharacteristic
26C22×D4×C101—22no—
27C22×D4×C101—22no—
28C22×D4×C101—21no—
29C22×D4×C101—21no—
30C22×D4×C101—22no—
31C22×D4×C101—22no—
32C22×D4×C101—22no—
33C22×D4×C101C2×C414yes—
34C23×C4×C101—22no—
35C23×C4×C101—22no—
36C23×C4×C101—22no—
37C23×C4×C101—22no—
38C23×C4×C101—44no—
39C23×C4×C101C2×C411yescharacteristic
40C23×C4×C101C2×C412yes—
41C23×C4×C101C2×C412yes—
42C23×C4×C101D411yescharacteristic
43C23×C4×C101D412yes—
44C23×C4×C101D411yescharacteristic
45C2×C22⋊C4×C101—22no—
46C2×C22⋊C4×C101—22no—
47C2×C22⋊C4×C101—22no—
48C2×C22⋊C4×C101—22no—
49C2×C22⋊C4×C101—22no—
50C2×C22⋊C4×C101—22no—
51C2×C22⋊C4×C101—22no—
52C2×C22⋊C4×C101—22no—
53C2×C22⋊C4×C101—21no—
54C2×C22⋊C4×C101—21no—
55C2×C22⋊C4×C101—22no—
56C2×C22⋊C4×C101—22no—
57C2×C22⋊C4×C101—22no—
58C2×C22⋊C4×C101—22no—
59C2×C22⋊C4×C101—44no—
60C2×C22⋊C4×C101C2×C414yes—
61C2×C22⋊C4×C101C2×C414yes—
62C2×C22⋊C4×C101D414yes—
63C2×C22⋊C4×C101D414yes—
64C2×C42×C101—24no—
65C2×C42×C101—44no—
66#99×C101—216no—
67#95×C101—24no—
68#95×C101—22no—
69#95×C101—22no—
70#95×C101—44no—
71C24×C101—21no—
72C24×C101—21no—
73C24×C101—22no—
74C24×C101—22no—
75C24×C101—42no—
76C24×C101—42no—
77C24×C101—42no—
78C24×C101—42no—
79C24×C101C4212yescomplemented
80C24×C101C22×C411yescharacteristic
81C24×C101C22×C412yes—
82C24×C101C2×D411yescharacteristic
83C24×C101C2×D411yescharacteristic
84C24×C101C2×D412yes—
85C24×C101C2×D412yes—
86C24×C101#4112yes—
87C24×C101#4112yes—
88C24×C101#4112yes—
89C2×D4×C101—24no—
90C2×D4×C101—24no—
91C2×D4×C101—24no—
92C2×D4×C101—24no—
93C2×D4×C101—24no—
94C2×D4×C101—24no—
95C2×D4×C101—41no—
96C2×D4×C101—42no—
97C2×D4×C101—42no—
98C2×D4×C101—42no—
99C2×D4×C101—41no—
100C2×D4×C101—42no—
101C2×D4×C101—42no—
102C2×D4×C101—41no—
103C2×D4×C101—42no—
104C2×D4×C101—41no—
105C22×C4×C101—21no—
106C22×C4×C101—21no—
107C22×C4×C101—24no—
108C22×C4×C101—21no—
109C22×C4×C101—21no—
110C22×C4×C101—24no—
111C22×C4×C101—24no—
112C22×C4×C101—22no—
113C22×C4×C101—22no—
114C22×C4×C101—21no—
115C22×C4×C101—24no—
116C22×C4×C101—24no—
117C22×C4×C101—24no—
118C22×C4×C101—21no—
119C22×C4×C101—24no—
120C22×C4×C101—24no—
121C22×C4×C101—22no—
122C22×C4×C101—24no—
123C22×C4×C101—24no—
124C22×C4×C101—42no—
125C22×C4×C101—42no—
126C22×C4×C101—42no—
127C22×C4×C101—48no—
128C22×C4×C101—48no—
129C22×C4×C101—44no—
130C22×C4×C101—44no—
131C22×C4×C101—44no—
132C22×C4×C101—44no—
133C22×C4×C101—42no—
134C22×C4×C101—42no—
135C22×C4×C101—42no—
136C22×C4×C101—42no—
137C22×C4×C101C4212yescomplemented
138C22×C4×C101C22⋊C412yes—
139C22×C4×C101C22⋊C412yes—
140C22⋊C4×C101—24no—
141C22⋊C4×C101—24no—
142C22⋊C4×C101—24no—
143C22⋊C4×C101—24no—
144C22⋊C4×C101—24no—
145C22⋊C4×C101—44no—
146C22⋊C4×C101—42no—
147C22⋊C4×C101—42no—
148C22⋊C4×C101—42no—
149C22⋊C4×C101—41no—
150C22⋊C4×C101—41no—
151C22⋊C4×C101—44no—
152C22⋊C4×C101C22⋊C418yescomplemented
153C42×C101—48no—
154C23×C101—22no—
155C23×C101—22no—
156C23×C101—22no—
157C23×C101—22no—
158C23×C101—22no—
159C23×C101—22no—
160C23×C101—22no—
161C23×C101—24no—
162C23×C101—42no—
163C23×C101—42no—
164C23×C101—44no—
165C23×C101—42no—
166C23×C101—44no—
167C23×C101—42no—
168C23×C101—44no—
169C23×C101—44no—
170C23×C101—44no—
171C23×C101—44no—
172C23×C101—41no—
173C23×C101—42no—
174C23×C101—41no—
175C23×C101—42no—
176C23×C101—42no—
177C23×C101—82no—
178C23×C101—82no—
179C23×C101—84no—
180C23×C101C2×C4211yescharacteristic
181C23×C101C2×C22⋊C412yes—
182C23×C101C2×C22⋊C411yescharacteristic
183C23×C101#11711yescharacteristic
184C23×C101#11712yes—
185C23×C101C4×D412yes—
186C23×C101C4×D412yes—
187C23×C101C4×D412yes—
188C23×C101C4×D412yes—
189C23×C101C4×D412yes—
190C23×C101C4×D412yes—
191C23×C101#12011yescharacteristic
192C23×C101#12112yes—
193C23×C101#12112yes—
194C23×C101#12112yes—
195C23×C101#12311yescharacteristic
196C23×C101#12312yes—
197C23×C101#12411yescharacteristic
198C23×C101#12412yes—
199C23×C101#12612yes—
200C23×C101#12711yescharacteristic
201D4×C101—44no—
202D4×C101—44no—
203D4×C101—44no—
204D4×C101—44no—
205C2×C4×C101—24no—
206C2×C4×C101—24no—
207C2×C4×C101—22no—
208C2×C4×C101—22no—
209C2×C4×C101—24no—
210C2×C4×C101—22no—
211C2×C4×C101—28no—
212C2×C4×C101—22no—
213C2×C4×C101—22no—
214C2×C4×C101—22no—
215C2×C4×C101—48no—
216C2×C4×C101—48no—
217C2×C4×C101—44no—
218C2×C4×C101—44no—
219C2×C4×C101—48no—
220C2×C4×C101—48no—
221C2×C4×C101—42no—
222C2×C4×C101—42no—
223C2×C4×C101—41no—
224C2×C4×C101—42no—
225C2×C4×C101—41no—
226C2×C4×C101—48no—
227C2×C4×C101—44no—
228C2×C4×C101—42no—
229C2×C4×C101—42no—
230C2×C4×C101—42no—
231C2×C4×C101—82no—
232C2×C4×C101—82no—
233C2×C4×C101—84no—
234C2×C4×C101—84no—
235C2×C4×C101#9914yescomplemented
236C22×C101—21no—
237C22×C101—21no—
238C22×C101—22no—
239C22×C101—22no—
240C22×C101—21no—
241C22×C101—22no—
242C22×C101—22no—
243C22×C101—21no—
244C22×C101—24no—
245C22×C101—22no—
246C22×C101—24no—
247C22×C101—22no—
248C22×C101—24no—
249C22×C101—24no—
250C22×C101—22no—
251C22×C101—22no—
252C22×C101—42no—
253C22×C101—42no—
254C22×C101—42no—
255C22×C101—42no—
256C22×C101—42no—
257C22×C101—42no—
258C22×C101—42no—
259C22×C101—42no—
260C22×C101—42no—
261C22×C101—44no—
262C22×C101—84no—
263C22×C101—84no—
264C22×C101—81no—
265C22×C101—81no—
266C22×C101—82no—
267C22×C101C4×C22⋊C412yes—
268C22×C101C4×C22⋊C411yescharacteristic
269C22×C101#38612yes—
270C22×C101#38611yescharacteristic
271C22×C101#38812yes—
272C22×C101#38812yes—
273C22×C101#38812yes—
274C22×C101#39012yes—
275C22×C101#39011yescharacteristic
276C22×C101C2×#9912yes—
277C22×C101#41012yes—
278C4×C101—24no—
279C4×C101—48no—
280C4×C101—42no—
281C4×C101—42no—
282C4×C101—84no—
283C4×C101—82no—
284#10960C10111yesmaximal, characteristic, direct product factor, Sylow
285C2×C101—22no—
286C2×C101—22no—
287C2×C101—22no—
288C2×C101—22no—
289C2×C101—22no—
290C2×C101—22no—
291C2×C101—82no—
292C2×C101#143711yescharacteristic
293C2×C101C4×#9912yes—
294C2×C101#189811yescharacteristic
295C2×C101#189911yescharacteristic
296C2×C101#196412yes—
297C22×#99C2×C10112yes—
298C2×#386C2×C10111yescharacteristic
299C2×C4×C22⋊C4C2×C10111yescharacteristic, complemented
300C2×#342C2×C10112yescomplemented
301C22⋊#95C2×C10111yescharacteristic, complemented
302C101#1096011yescharacteristic, direct product factor, Sylow
303C23×D4C22×C10111yescharacteristic
304C24×C4C22×C10111yescharacteristic
305C22×C22⋊C4C4×C10112yescomplemented
306C22×C22⋊C4C22×C10111yescharacteristic
307C22×C22⋊C4C22×C10112yes—
308C22×C22⋊C4C22×C10112yes—
309C22×C42—21no—
310C2×#99—24no—
311C2×#99—24no—
312C2×#99C4×C10118yescomplemented
313#386—21no—
314#386—22no—
315#386—21no—
316C4×C22⋊C4—24no—
317C2×#95—21no—
318C2×#95—22no—
319C2×#95C4×C10112yescomplemented
320#342—24no—
321C25C2×C4×C10111yescharacteristic
322C25C23×C10111yescharacteristic
323C22×D4—21no—
324C22×D4—21no—
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4C2×C4×C10114yes—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—44no—
336C23×C4C2×C4×C10111yescharacteristic
337C23×C4C2×C4×C10112yes—
338C23×C4C2×C4×C10112yes—
339C23×C4D4×C10111yescharacteristic
340C23×C4D4×C10112yes—
341C23×C4D4×C10111yescharacteristic
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4C2×C4×C10114yes—
358C2×C22⋊C4C2×C4×C10114yes—
359C2×C22⋊C4D4×C10114yes—
360C2×C22⋊C4D4×C10114yes—
361C2×C42—24no—
362C2×C42—44no—
363#99—216no—
364#95—24no—
365#95—22no—
366#95—22no—
367#95—44no—
368C24—21no—
369C24—21no—
370C24—22no—
371C24—22no—
372C24—42no—
373C24—42no—
374C24—42no—
375C24—42no—
376C24C42×C10112yescomplemented
377C24C22×C4×C10111yescharacteristic
378C24C22×C4×C10112yes—
379C24C2×D4×C10111yescharacteristic
380C24C2×D4×C10111yescharacteristic
381C24C2×D4×C10112yes—
382C24C2×D4×C10112yes—
383C24#41×C10112yes—
384C24#41×C10112yes—
385C24#41×C10112yes—
386C2×D4—24no—
387C2×D4—24no—
388C2×D4—24no—
389C2×D4—24no—
390C2×D4—24no—
391C2×D4—24no—
392C2×D4—41no—
393C2×D4—42no—
394C2×D4—42no—
395C2×D4—42no—
396C2×D4—41no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4—41no—
400C2×D4—42no—
401C2×D4—41no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—24no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—21no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—48no—
425C22×C4—48no—
426C22×C4—44no—
427C22×C4—44no—
428C22×C4—44no—
429C22×C4—44no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4C42×C10112yescomplemented
435C22×C4C22⋊C4×C10112yes—
436C22×C4C22⋊C4×C10112yes—
437C22⋊C4—24no—
438C22⋊C4—24no—
439C22⋊C4—24no—
440C22⋊C4—24no—
441C22⋊C4—24no—
442C22⋊C4—44no—
443C22⋊C4—42no—
444C22⋊C4—42no—
445C22⋊C4—42no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C22⋊C4—44no—
449C22⋊C4C22⋊C4×C10118yescomplemented
450C42—48no—
451C23—22no—
452C23—22no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—22no—
457C23—22no—
458C23—24no—
459C23—42no—
460C23—42no—
461C23—44no—
462C23—42no—
463C23—44no—
464C23—42no—
465C23—44no—
466C23—44no—
467C23—44no—
468C23—44no—
469C23—42no—
470C23—42no—
471C23—41no—
472C23—42no—
473C23—41no—
474C23—82no—
475C23—82no—
476C23—84no—
477C23C2×C42×C10111yescharacteristic
478C23C2×C22⋊C4×C10112yes—
479C23C2×C22⋊C4×C10111yescharacteristic
480C23#117×C10111yescharacteristic
481C23#117×C10112yes—
482C23C4×D4×C10112yes—
483C23C4×D4×C10112yes—
484C23C4×D4×C10112yes—
485C23C4×D4×C10112yes—
486C23C4×D4×C10112yes—
487C23C4×D4×C10112yes—
488C23#120×C10111yescharacteristic
489C23#121×C10112yes—
490C23#121×C10112yes—
491C23#121×C10112yes—
492C23#123×C10111yescharacteristic
493C23#123×C10112yes—
494C23#124×C10111yescharacteristic
495C23#124×C10112yes—
496C23#126×C10112yes—
497C23#127×C10111yescharacteristic
498D4—44no—
499D4—44no—
500D4—44no—
501D4—44no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—28no—
511C2×C4—22no—
512C2×C4—48no—
513C2×C4—48no—
514C2×C4—44no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—44no—
518C2×C4—48no—
519C2×C4—48no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—48no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—44no—
527C2×C4—42no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4—84no—
531C2×C4—84no—
532C2×C4#99×C10114yescomplemented
533C22—21no—
534C22—21no—
535C22—22no—
536C22—22no—
537C22—21no—
538C22—22no—
539C22—22no—
540C22—21no—
541C22—24no—
542C22—22no—
543C22—24no—
544C22—22no—
545C22—24no—
546C22—24no—
547C22—22no—
548C22—22no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—42no—
558C22—44no—
559C22—84no—
560C22—84no—
561C22—81no—
562C22—81no—
563C22—82no—
564C22C4×C22⋊C4×C10112yes—
565C22C4×C22⋊C4×C10111yescharacteristic
566C22#386×C10112yes—
567C22#386×C10111yescharacteristic
568C22#388×C10112yes—
569C22#388×C10112yes—
570C22#388×C10112yes—
571C22#390×C10112yes—
572C22#390×C10111yescharacteristic
573C22C2×#99×C10112yes—
574C22#410×C10112yes—
575C4—24no—
576C4—48no—
577C4—42no—
578C4—42no—
579C4—84no—
580C4—82no—
581C2—22no—
582C2—22no—
583C2—22no—
584C2—22no—
585C2—22no—
586C2—22no—
587C2—82no—
588C2C101×#143711yescharacteristic
589C2C4×#99×C10112yes—
590C2C101×#189811yescharacteristic
591C2C101×#189911yescharacteristic
592C2C101×#196412yes—
subgroupG/H
center, socleC23×C101C2×C22⋊C4
commutatorC23C2×C42×C101
Frattini, cosocleC25C23×C101
prime radicalC23×D4×C101C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C24×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C4×C22⋊C4×C101C2semidirect
4. C2×#342×C101C2semidirect
5. C101×C22⋊#95C2semidirect
8. C22×C22⋊C4×C101C4semidirect
15. C2×#99×C101C4semidirect
22. C2×#95×C101C4semidirect
79. C24×C101C42semidirect
137. C22×C4×C101C42semidirect
152. C22⋊C4×C101C22⋊C4semidirect
235. C2×C4×C101#99semidirect
284. #10960C101direct (N × H)
299. C2×C4×C22⋊C4C2×C101semidirect
300. C2×#342C2×C101semidirect
301. C22⋊#95C2×C101semidirect
302. C101#10960direct (N × H)
305. C22×C22⋊C4C4×C101semidirect
312. C2×#99C4×C101semidirect
319. C2×#95C4×C101semidirect
376. C24C42×C101semidirect
434. C22×C4C42×C101semidirect
449. C22⋊C4C22⋊C4×C101semidirect
532. C2×C4#99×C101semidirect

Maximal subgroups

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

subgroupindex
C22×#99×C1012
C2×#386×C1012
C2×C4×C22⋊C4×C1012
C2×#342×C1012
C101×C22⋊#952
#10960101