Finite Group Databasebeta

← C101×#10991 #38793142

Subgroups — C101×#10991 #38793142

Order 25856.

3122 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C101C211yesmaximal, characteristic
2C22×#99×C101C211yesmaximal, characteristic, complemented
3C101×#2308C211yesmaximal, characteristic, complemented
4C2×#379×C101C212yesmaximal, complemented
5C2×#342×C101C212yesmaximal, complemented
6C26×C101C2211yescharacteristic
7C23×D4×C101—21no—
8C23×D4×C101C2211yescharacteristic
9C2×#120×C101—24no—
10C2×#120×C101—22no—
11C2×#120×C101—24no—
12C2×#120×C101C414yescomplemented
13C22×C22⋊C4×C101—21no—
14C22×C22⋊C4×C101—24no—
15C22×C22⋊C4×C101C2212yes—
16C22×C22⋊C4×C101C2212yes—
17C22×C22⋊C4×C101C2211yescharacteristic
18C2×#99×C101—22no—
19C2×#99×C101—24no—
20#386×C101—24no—
21#381×C101—21no—
22#379×C101—24no—
23#379×C101—21no—
24#379×C101—24no—
25#342×C101—24no—
26C25×C101—22no—
27C25×C101—21no—
28C25×C101—21no—
29C25×C101—22no—
30C25×C101—22no—
31C25×C101—22no—
32C25×C101—22no—
33C25×C101—48no—
34C25×C101C2×C412yes—
35C25×C101D414yes—
36C25×C101D411yescharacteristic
37C25×C101C2311yescharacteristic
38C22×D4×C101—28no—
39C22×D4×C101—24no—
40C22×D4×C101—22no—
41C22×D4×C101—22no—
42C22×D4×C101—22no—
43C22×D4×C101—22no—
44C22×D4×C101—22no—
45C22×D4×C101—22no—
46C22×D4×C101—48no—
47C22×D4×C101C2×C412yes—
48C22×D4×C101D412yes—
49C23×C4×C101—21no—
50C23×C4×C101—22no—
51C23×C4×C101D411yescharacteristic
52C23×C4×C101D414yescomplemented
53#120×C101—216no—
54#120×C101—28no—
55#120×C101—28no—
56C2×C22⋊C4×C101—28no—
57C2×C22⋊C4×C101—22no—
58C2×C22⋊C4×C101—21no—
59C2×C22⋊C4×C101—24no—
60C2×C22⋊C4×C101—22no—
61C2×C22⋊C4×C101—22no—
62C2×C22⋊C4×C101—22no—
63C2×C22⋊C4×C101—22no—
64C2×C22⋊C4×C101—216no—
65C2×C22⋊C4×C101—22no—
66C2×C22⋊C4×C101—22no—
67C2×C22⋊C4×C101—22no—
68C2×C22⋊C4×C101—22no—
69C2×C22⋊C4×C101—22no—
70C2×C22⋊C4×C101—22no—
71C2×C22⋊C4×C101—22no—
72C2×C22⋊C4×C101—24no—
73C2×C22⋊C4×C101—416no—
74C2×C22⋊C4×C101C2×C412yes—
75C2×C22⋊C4×C101D414yes—
76C2×C22⋊C4×C101D414yescomplemented
77#99×C101—28no—
78#95×C101—24no—
79C24×C101—216no—
80C24×C101—28no—
81C24×C101—22no—
82C24×C101—24no—
83C24×C101—24no—
84C24×C101—24no—
85C24×C101—24no—
86C24×C101—22no—
87C24×C101—24no—
88C24×C101—24no—
89C24×C101—22no—
90C24×C101—21no—
91C24×C101—24no—
92C24×C101—24no—
93C24×C101—22no—
94C24×C101—21no—
95C24×C101—48no—
96C24×C101—416no—
97C24×C101—44no—
98C24×C101—48no—
99C24×C101—44no—
100C24×C101—416no—
101C24×C101—48no—
102C24×C101—416no—
103C24×C101—416no—
104C24×C101—416no—
105C24×C101—44no—
106C24×C101—41no—
107C24×C101—41no—
108C24×C101—42no—
109C24×C101—42no—
110C24×C101—42no—
111C24×C101—42no—
112C24×C101—41no—
113C24×C101—41no—
114C24×C101—42no—
115C24×C101—42no—
116C24×C101C22⋊C414yescomplemented
117C24×C101C22⋊C412yescomplemented
118C24×C101C22×C411yescharacteristic
119C24×C101C2×D411yescharacteristic
120C24×C101C2×D412yes—
121C24×C101C2×D412yes—
122C24×C101C2×D411yescharacteristic
123C24×C101C2×D412yes—
124C24×C101C2×D412yes—
125C24×C101#4112yes—
126C24×C101#4112yes—
127C2×D4×C101—216no—
128C2×D4×C101—22no—
129C2×D4×C101—22no—
130C2×D4×C101—24no—
131C2×D4×C101—24no—
132C2×D4×C101—22no—
133C2×D4×C101—24no—
134C2×D4×C101—24no—
135C2×D4×C101—22no—
136C2×D4×C101—416no—
137C2×D4×C101—432no—
138C2×D4×C101—42no—
139C2×D4×C101—42no—
140C2×D4×C101—42no—
141C2×D4×C101—42no—
142C2×D4×C101—42no—
143C2×D4×C101—42no—
144C2×D4×C101—42no—
145C2×D4×C101—42no—
146C22×C4×C101—22no—
147C22×C4×C101—22no—
148C22×C4×C101—24no—
149C22×C4×C101—21no—
150C22×C4×C101—22no—
151C22×C4×C101—21no—
152C22×C4×C101—24no—
153C22×C4×C101—24no—
154C22×C4×C101—24no—
155C22×C4×C101—24no—
156C22×C4×C101—44no—
157C22×C4×C101—48no—
158C22×C4×C101—48no—
159C22×C4×C101—42no—
160C22×C4×C101—42no—
161C22×C4×C101C22⋊C412yescomplemented
162C22⋊C4×C101—216no—
163C22⋊C4×C101—22no—
164C22⋊C4×C101—24no—
165C22⋊C4×C101—24no—
166C22⋊C4×C101—24no—
167C22⋊C4×C101—432no—
168C22⋊C4×C101—42no—
169C22⋊C4×C101—42no—
170C22⋊C4×C101—42no—
171C22⋊C4×C101—42no—
172C22⋊C4×C101—42no—
173C22⋊C4×C101—42no—
174C22⋊C4×C101—84no—
175C22⋊C4×C101C22⋊C414yescomplemented
176C23×C101—28no—
177C23×C101—24no—
178C23×C101—216no—
179C23×C101—28no—
180C23×C101—216no—
181C23×C101—216no—
182C23×C101—216no—
183C23×C101—24no—
184C23×C101—28no—
185C23×C101—22no—
186C23×C101—22no—
187C23×C101—22no—
188C23×C101—48no—
189C23×C101—42no—
190C23×C101—42no—
191C23×C101—44no—
192C23×C101—44no—
193C23×C101—44no—
194C23×C101—44no—
195C23×C101—44no—
196C23×C101—44no—
197C23×C101—416no—
198C23×C101—48no—
199C23×C101—48no—
200C23×C101—48no—
201C23×C101—48no—
202C23×C101—416no—
203C23×C101—416no—
204C23×C101—48no—
205C23×C101—416no—
206C23×C101—48no—
207C23×C101—416no—
208C23×C101—416no—
209C23×C101—416no—
210C23×C101—416no—
211C23×C101—44no—
212C23×C101—48no—
213C23×C101—48no—
214C23×C101—416no—
215C23×C101—48no—
216C23×C101—416no—
217C23×C101—42no—
218C23×C101—42no—
219C23×C101—44no—
220C23×C101—44no—
221C23×C101—44no—
222C23×C101—44no—
223C23×C101—44no—
224C23×C101—48no—
225C23×C101—42no—
226C23×C101—42no—
227C23×C101—44no—
228C23×C101—82no—
229C23×C101—84no—
230C23×C101C2×C22⋊C411yescharacteristic
231C23×C101C2×C22⋊C411yescharacteristic
232C23×C101C2×C22⋊C411yescharacteristic
233C23×C101C4×D412yes—
234C23×C101C4×D412yes—
235C23×C101#12012yes—
236C23×C101#12012yes—
237C23×C101#12012yes—
238C23×C101#12011yescharacteristic
239C23×C101#12011yescharacteristic
240C23×C101#12112yes—
241C23×C101#12112yes—
242C23×C101#12112yes—
243C23×C101#12112yes—
244C23×C101#12112yes—
245C23×C101#12112yes—
246C23×C101#12311yescharacteristic
247C23×C101#12311yescharacteristic
248C23×C101#12312yes—
249C23×C101#12412yes—
250C23×C101#12712yes—
251D4×C101—432no—
252D4×C101—44no—
253D4×C101—44no—
254D4×C101—44no—
255D4×C101—44no—
256C2×C4×C101—22no—
257C2×C4×C101—24no—
258C2×C4×C101—22no—
259C2×C4×C101—22no—
260C2×C4×C101—44no—
261C2×C4×C101—48no—
262C2×C4×C101—42no—
263C2×C4×C101—42no—
264C2×C4×C101—48no—
265C2×C4×C101—48no—
266C2×C4×C101—44no—
267C2×C4×C101—44no—
268C2×C4×C101—48no—
269C2×C4×C101—84no—
270C2×C4×C101—84no—
271C2×C4×C101—84no—
272C22×C101—22no—
273C22×C101—24no—
274C22×C101—24no—
275C22×C101—22no—
276C22×C101—24no—
277C22×C101—24no—
278C22×C101—24no—
279C22×C101—24no—
280C22×C101—24no—
281C22×C101—24no—
282C22×C101—28no—
283C22×C101—216no—
284C22×C101—41no—
285C22×C101—41no—
286C22×C101—42no—
287C22×C101—42no—
288C22×C101—41no—
289C22×C101—42no—
290C22×C101—42no—
291C22×C101—42no—
292C22×C101—41no—
293C22×C101—42no—
294C22×C101—44no—
295C22×C101—416no—
296C22×C101—48no—
297C22×C101—48no—
298C22×C101—416no—
299C22×C101—416no—
300C22×C101—416no—
301C22×C101—44no—
302C22×C101—48no—
303C22×C101—44no—
304C22×C101—416no—
305C22×C101—44no—
306C22×C101—42no—
307C22×C101—82no—
308C22×C101—84no—
309C22×C101—84no—
310C22×C101#37911yescharacteristic
311C22×C101#38611yescharacteristic
312C22×C101#38612yes—
313C22×C101#38611yescharacteristic
314C22×C101#39012yes—
315C22×C101#39212yes—
316C22×C101#39212yes—
317C22×C101#39412yes—
318C22×C101#39412yes—
319C22×C101B(4,𝔽2)14yes—
320C4×C101—44no—
321C4×C101—42no—
322C4×C101—84no—
323C4×C101—84no—
324#10991C10111yesmaximal, characteristic, direct product factor, Sylow
325C2×C101—21no—
326C2×C101—22no—
327C2×C101—22no—
328C2×C101—21no—
329C2×C101—22no—
330C2×C101—22no—
331C2×C101—22no—
332C2×C101—48no—
333C2×C101—82no—
334C2×C101#143811yescharacteristic
335C2×C101#188912yes—
336C2×C101#202114yes—
337C22×#120C2×C10111yescharacteristic
338C22×#99C2×C10111yescharacteristic, complemented
339#2308C2×C10111yescharacteristic, complemented
340C2×#379C2×C10112yescomplemented
341C2×#342C2×C10112yescomplemented
342C101#1099111yescharacteristic, direct product factor, Sylow
343C26C22×C10111yescharacteristic
344C23×D4—21no—
345C23×D4C22×C10111yescharacteristic
346C2×#120—24no—
347C2×#120—22no—
348C2×#120—24no—
349C2×#120C4×C10114yescomplemented
350C22×C22⋊C4—21no—
351C22×C22⋊C4—24no—
352C22×C22⋊C4C22×C10112yes—
353C22×C22⋊C4C22×C10112yes—
354C22×C22⋊C4C22×C10111yescharacteristic
355C2×#99—22no—
356C2×#99—24no—
357#386—24no—
358#381—21no—
359#379—21no—
360#379—24no—
361#379—24no—
362#342—24no—
363C25—22no—
364C25—21no—
365C25—21no—
366C25—22no—
367C25—22no—
368C25—22no—
369C25—22no—
370C25—48no—
371C25C2×C4×C10112yes—
372C25D4×C10114yes—
373C25D4×C10111yescharacteristic
374C25C23×C10111yescharacteristic
375C22×D4—28no—
376C22×D4—24no—
377C22×D4—22no—
378C22×D4—22no—
379C22×D4—22no—
380C22×D4—22no—
381C22×D4—22no—
382C22×D4—22no—
383C22×D4—48no—
384C22×D4C2×C4×C10112yes—
385C22×D4D4×C10112yes—
386C23×C4—21no—
387C23×C4—22no—
388C23×C4D4×C10111yescharacteristic
389C23×C4D4×C10114yescomplemented
390#120—216no—
391#120—28no—
392#120—28no—
393C2×C22⋊C4—28no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—216no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—416no—
411C2×C22⋊C4C2×C4×C10112yes—
412C2×C22⋊C4D4×C10114yes—
413C2×C22⋊C4D4×C10114yescomplemented
414#99—28no—
415#95—24no—
416C24—216no—
417C24—28no—
418C24—22no—
419C24—24no—
420C24—24no—
421C24—24no—
422C24—24no—
423C24—22no—
424C24—24no—
425C24—21no—
426C24—24no—
427C24—22no—
428C24—24no—
429C24—24no—
430C24—22no—
431C24—21no—
432C24—48no—
433C24—416no—
434C24—44no—
435C24—48no—
436C24—44no—
437C24—416no—
438C24—48no—
439C24—416no—
440C24—416no—
441C24—416no—
442C24—44no—
443C24—41no—
444C24—41no—
445C24—42no—
446C24—42no—
447C24—42no—
448C24—42no—
449C24—41no—
450C24—41no—
451C24—42no—
452C24—42no—
453C24C22⋊C4×C10114yescomplemented
454C24C22⋊C4×C10112yescomplemented
455C24C22×C4×C10111yescharacteristic
456C24C2×D4×C10111yescharacteristic
457C24C2×D4×C10112yes—
458C24C2×D4×C10112yes—
459C24C2×D4×C10111yescharacteristic
460C24C2×D4×C10112yes—
461C24C2×D4×C10112yes—
462C24#41×C10112yes—
463C24#41×C10112yes—
464C2×D4—216no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—24no—
468C2×D4—24no—
469C2×D4—22no—
470C2×D4—24no—
471C2×D4—24no—
472C2×D4—22no—
473C2×D4—416no—
474C2×D4—432no—
475C2×D4—42no—
476C2×D4—42no—
477C2×D4—42no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—42no—
482C2×D4—42no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—44no—
494C22×C4—48no—
495C22×C4—48no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4C22⋊C4×C10112yescomplemented
499C22⋊C4—216no—
500C22⋊C4—22no—
501C22⋊C4—24no—
502C22⋊C4—24no—
503C22⋊C4—24no—
504C22⋊C4—432no—
505C22⋊C4—42no—
506C22⋊C4—42no—
507C22⋊C4—42no—
508C22⋊C4—42no—
509C22⋊C4—42no—
510C22⋊C4—42no—
511C22⋊C4—84no—
512C22⋊C4C22⋊C4×C10114yescomplemented
513C23—28no—
514C23—24no—
515C23—216no—
516C23—28no—
517C23—216no—
518C23—216no—
519C23—216no—
520C23—24no—
521C23—28no—
522C23—22no—
523C23—22no—
524C23—22no—
525C23—48no—
526C23—42no—
527C23—42no—
528C23—44no—
529C23—44no—
530C23—44no—
531C23—44no—
532C23—44no—
533C23—44no—
534C23—416no—
535C23—48no—
536C23—48no—
537C23—48no—
538C23—48no—
539C23—416no—
540C23—416no—
541C23—48no—
542C23—416no—
543C23—48no—
544C23—416no—
545C23—416no—
546C23—416no—
547C23—416no—
548C23—44no—
549C23—48no—
550C23—48no—
551C23—416no—
552C23—48no—
553C23—416no—
554C23—48no—
555C23—42no—
556C23—42no—
557C23—44no—
558C23—44no—
559C23—44no—
560C23—44no—
561C23—44no—
562C23—44no—
563C23—42no—
564C23—42no—
565C23—82no—
566C23—84no—
567C23C2×C22⋊C4×C10111yescharacteristic
568C23C2×C22⋊C4×C10111yescharacteristic
569C23C2×C22⋊C4×C10111yescharacteristic
570C23C4×D4×C10112yes—
571C23C4×D4×C10112yes—
572C23#120×C10112yes—
573C23#120×C10112yes—
574C23#120×C10112yes—
575C23#120×C10111yescharacteristic
576C23#120×C10111yescharacteristic
577C23#121×C10112yes—
578C23#121×C10112yes—
579C23#121×C10112yes—
580C23#121×C10112yes—
581C23#121×C10112yes—
582C23#121×C10112yes—
583C23#123×C10111yescharacteristic
584C23#123×C10111yescharacteristic
585C23#123×C10112yes—
586C23#124×C10112yes—
587C23#127×C10112yes—
588D4—432no—
589D4—44no—
590D4—44no—
591D4—44no—
592D4—44no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—44no—
598C2×C4—48no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—48no—
602C2×C4—48no—
603C2×C4—48no—
604C2×C4—44no—
605C2×C4—44no—
606C2×C4—84no—
607C2×C4—84no—
608C2×C4—84no—
609C22—22no—
610C22—24no—
611C22—24no—
612C22—22no—
613C22—24no—
614C22—24no—
615C22—24no—
616C22—24no—
617C22—24no—
618C22—24no—
619C22—28no—
620C22—216no—
621C22—41no—
622C22—41no—
623C22—42no—
624C22—42no—
625C22—41no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—41no—
630C22—42no—
631C22—44no—
632C22—416no—
633C22—48no—
634C22—48no—
635C22—416no—
636C22—416no—
637C22—416no—
638C22—44no—
639C22—48no—
640C22—44no—
641C22—416no—
642C22—44no—
643C22—42no—
644C22—82no—
645C22—84no—
646C22—84no—
647C22#379×C10111yescharacteristic
648C22#386×C10111yescharacteristic
649C22#386×C10112yes—
650C22#386×C10111yescharacteristic
651C22#390×C10112yes—
652C22#392×C10112yes—
653C22#392×C10112yes—
654C22#394×C10112yes—
655C22#394×C10112yes—
656C22B(4,𝔽2)×C10114yes—
657C4—44no—
658C4—42no—
659C4—84no—
660C4—84no—
661C2—21no—
662C2—22no—
663C2—22no—
664C2—21no—
665C2—22no—
666C2—22no—
667C2—22no—
668C2—48no—
669C2—82no—
670C2C101×#143811yescharacteristic
671C2C101×#188912yes—
672C2C101×#202114yes—
subgroupG/H
center, socleC23×C101#120
commutatorC24C22×C4×C101
Frattini, cosocleC25C23×C101
prime radicalC22×#120×C101C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C25×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#99×C101C2semidirect
3. C101×#2308C2semidirect
4. C2×#379×C101C2semidirect
5. C2×#342×C101C2semidirect
12. C2×#120×C101C4semidirect
52. C23×C4×C101D4semidirect
76. C2×C22⋊C4×C101D4semidirect
116. C24×C101C22⋊C4semidirect
117. C24×C101C22⋊C4semidirect
161. C22×C4×C101C22⋊C4semidirect
175. C22⋊C4×C101C22⋊C4semidirect
324. #10991C101direct (N × H)
338. C22×#99C2×C101semidirect
339. #2308C2×C101semidirect
340. C2×#379C2×C101semidirect
341. C2×#342C2×C101semidirect
342. C101#10991direct (N × H)
349. C2×#120C4×C101semidirect
389. C23×C4D4×C101semidirect
413. C2×C22⋊C4D4×C101semidirect
453. C24C22⋊C4×C101semidirect
454. C24C22⋊C4×C101semidirect
498. C22×C4C22⋊C4×C101semidirect
512. 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×#120×C1012
C22×#99×C1012
C101×#23082
C2×#379×C1012
C2×#342×C1012
#10991101