Finite Group Databasebeta

← #25112727

Subgroups — #25112727

Order 11008.

1696 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583545C211yesmaximal, characteristic
2#19137415C212yesmaximal, complemented
3#19135579C212yesmaximal, complemented
4#19135045C214yesmaximal, complemented
5#19134668C212yesmaximal, complemented
6C4×#13063240C211yesmaximal, characteristic, complemented
7#342×D43C212yesmaximal, complemented
8C43×#1799C211yesmaximal, characteristic, complemented
9C22×#10621898C411yescharacteristic, complemented
10C23×D172C2211yescharacteristic
11#14583545—22no—
12#14583545—22no—
13#14583545—24no—
14C2×#13063313C411yescharacteristic, complemented
15C2×#13063310C412yescomplemented
16C2×#13063304C2211yescharacteristic
17C2×#13063299C411yescharacteristic, complemented
18C2×#13063298C412yescomplemented
19C2×#13063293C2212yes—
20C2×C4×D172C411yescharacteristic, complemented
21C2×#13063287—22no—
22C2×C22⋊C4×D43C2212yes—
23C2×C22⋊C4×D43C2214yes—
24C2×#13063240C2212yes—
25#14582800—22no—
26#14582777—24no—
27#14582754C2214yes—
28C4×C22⋊Dic43C2212yes—
29#14582666C2211yescharacteristic
30#14582666C2211yescharacteristic
31#14582665C2214yes—
32#14582665C2214yes—
33C2×C4×D4×C43C2211yescharacteristic
34C2×#99×C43C2212yes—
35C43×#380C2212yes—
36C43×#342C2212yes—
37C24×D43C2312yes—
38C2×#10621898—22no—
39C2×#10621898—21no—
40C2×#10621898—21no—
41C2×#10621898—44no—
42C22×Dic86C2×C411yescharacteristic, complemented
43C22×D172—44no—
44C22×D172C2×C411yescharacteristic
45C22×D172C2×C412yes—
46C22×D172C2×C411yescharacteristic
47C22×D172D412yes—
48C22×D172D412yes—
49C22×D172D414yes—
50C22×C22⋊D43C2×C412yescomplemented
51C22×C22⋊D43C2×C412yescomplemented
52C22×C4×D43—24no—
53C22×C4×D43C2×C412yescomplemented
54C22×C4×D43C2×C412yescomplemented
55#13063313—22no—
56#13063313—22no—
57#13063310—24no—
58#13063310—24no—
59#13063304—22no—
60#13063304—22no—
61#13063299—22no—
62#13063299—22no—
63#13063298—24no—
64#13063298—24no—
65#13063293—24no—
66#13063293—24no—
67C4×D172—22no—
68C4×D172—21no—
69C4×D172—21no—
70#13063287—48no—
71C2×C4⋊Dic43C2×C411yescharacteristic, complemented
72C2×Dic43⋊C4C2×C412yescomplemented
73C2×C22⋊Dic43C2312yes—
74C2×C22⋊Dic43C2312yes—
75C2×C22⋊Dic43C2312yes—
76C2×(C2×D43)⋊C4—24no—
77C2×(C2×D43)⋊C4—24no—
78C2×(C2×D43)⋊C4—24no—
79C2×(C2×D43)⋊C4C2×C412yescomplemented
80C2×(C2×D43)⋊C4C2×C412yescomplemented
81C2×(C2×D43)⋊C4C2×C412yescomplemented
82C2×(C2×D43)⋊C4C2×C412yescomplemented
83C22⋊C4×D43—24no—
84C22⋊C4×D43—24no—
85C22⋊C4×D43—28no—
86C22⋊C4×D43—44no—
87C2×C4×Dic43—22no—
88#13063240—24no—
89C43⋊#95—22no—
90C22×D4×C43C2311yescharacteristic
91C23×C4×C43C2×C411yescharacteristic, complemented
92C23×C4×C43C2311yescharacteristic
93C4×D4×C43—22no—
94C4×D4×C43—22no—
95C2×C4⋊C4×C43—22no—
96C2×C4⋊C4×C43C2×C411yescharacteristic, complemented
97C2×C22⋊C4×C43C2×C411yescharacteristic, complemented
98C2×C22⋊C4×C43C2314yes—
99C2×C22⋊C4×C43C2311yescharacteristic
100C2×C42×C43C2×C411yescharacteristic, complemented
101#99×C43—42no—
102#95×C43—22no—
103C24×C43C22×C411yescharacteristic
104C24×C43C2411yescharacteristic
105C23×D43—24no—
106C23×D43—22no—
107C23×D43—22no—
108C23×D43—44no—
109C23×D43—82no—
110C23×D43C22×C412yes—
111C23×D43C22×C412yes—
112C23×D43C2×D414yes—
113C23×D43C2×D414yes—
114C2×D4×C43—22no—
115C2×D4×C43—22no—
116C2×D4×C43—21no—
117C2×D4×C43—21no—
118C22×C4×C43—21no—
119C22×C4×C43—21no—
120C22×C4×C43—24no—
121C22×C4×C43—42no—
122C22×C4×C43—42no—
123C22×C4×C43C22×C411yescharacteristic
124C22×C4×C43C22×C411yescharacteristic
125C22×C4×C43C22×C411yescharacteristic
126C22×C4×C43C22×C411yescharacteristic
127C22×C4×C43C22×C411yescharacteristic
128C22×C4×C43C2×D412yes—
129C22×C4×C43C2×D412yes—
130C2×C22⋊D43—22no—
131C2×C22⋊D43—22no—
132C2×C22⋊D43—24no—
133C2×C22⋊D43—44no—
134C2×C22⋊D43—82no—
135C22×Dic43—22no—
136C22×Dic43—22no—
137C22×Dic43C22×C412yes—
138C22×Dic43C22×C412yes—
139#10621898—48no—
140#10621898—44no—
141#10621898—44no—
142C2×D172—28no—
143C2×D172—24no—
144C2×D172—44no—
145C2×D172—48no—
146C2×D172—42no—
147C2×D172—44no—
148C2×D172C22⋊C411yescharacteristic
149C2×D172C22⋊C412yes—
150C2×D172C22⋊C414yes—
151C2×D172C22⋊C412yes—
152C2×D172C22⋊C414yes—
153C2×D172C22⋊C412yes—
154C2×D172C22⋊C411yescharacteristic
155C2×C4×D43—22no—
156C2×C4×D43—22no—
157C2×C4×D43—22no—
158C2×C4×D43—22no—
159C2×C4×D43—44no—
160C2×C4×D43—48no—
161C2×C4×D43—48no—
162C2×C4×D43—84no—
163C2×C4×D43—82no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—42no—
167C4⋊C4×C43—22no—
168C4⋊C4×C43—44no—
169C22⋊C4×C43—22no—
170C22⋊C4×C43—22no—
171C22⋊C4×C43—24no—
172C22⋊C4×C43—24no—
173C42×C43—21no—
174C42×C43—21no—
175C22⋊Dic43—24no—
176C22⋊Dic43—22no—
177C22⋊Dic43—22no—
178C22⋊Dic43—22no—
179C22⋊Dic43#4114yescomplemented
180(C2×D43)⋊C4—24no—
181(C2×D43)⋊C4—24no—
182(C2×D43)⋊C4—22no—
183(C2×D43)⋊C4—22no—
184(C2×D43)⋊C4—24no—
185(C2×D43)⋊C4—48no—
186(C2×D43)⋊C4—48no—
187(C2×D43)⋊C4—84no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190Dic43⋊C4—24no—
191C4×Dic43—44no—
192C23×C43—21no—
193C23×C43—21no—
194C23×C43—21no—
195C23×C43—41no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43C23×C411yescharacteristic
200C23×C43C22×D412yes—
201C23×C43C2×#4112yes—
202C23×C43H(5,𝔽2)11yescharacteristic
203C23×C432−1+411yescharacteristic
204C22×D43—22no—
205C22×D43—22no—
206C22×D43—24no—
207C22×D43—24no—
208C22×D43—22no—
209C22×D43—22no—
210C22×D43—24no—
211C22×D43—24no—
212C22×D43—28no—
213C22×D43—24no—
214C22×D43—42no—
215C22×D43—44no—
216C22×D43—44no—
217C22×D43—42no—
218C22×D43—44no—
219C22×D43—42no—
220C22×D43—84no—
221C22×D43—88no—
222C22×D43—84no—
223C22×D43C2×C22⋊C414yes—
224C22×D43C2×C22⋊C412yes—
225C22×D43C2×C22⋊C412yes—
226D4×C43—42no—
227D4×C43—42no—
228C2×C4×C43—24no—
229C2×C4×C43—22no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—41no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—44no—
242C2×C4×C43—44no—
243C2×C4×C43—44no—
244C2×C4×C43C2×C22⋊C412yes—
245C2×C4×C43C2×C22⋊C411yescharacteristic
246C2×C4×C43C2×C22⋊C411yescharacteristic
247C22⋊D43—44no—
248C22⋊D43—44no—
249C22⋊D43—84no—
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—24no—
253C2×Dic43—42no—
254C2×Dic43—42no—
255C2×Dic43—42no—
256C2×Dic43—42no—
257C2×Dic43—42no—
258C2×Dic43—42no—
259C2×Dic43—42no—
260D172—28no—
261D172—24no—
262D172—24no—
263D172—22no—
264D172—42no—
265D172—44no—
266D172#9914yescomplemented
267C4×D43—44no—
268C4×D43—44no—
269C4×D43—82no—
270C4×D43—82no—
271C4×D43—816no—
272Dic86—42no—
273Dic86—42no—
274#22476—431nomaximal, Sylow
275C22×C43—21no—
276C22×C43—22no—
277C22×C43—21no—
278C22×C43—22no—
279C22×C43—42no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43C22×C22⋊C411yescharacteristic
288C22×C43C4×#4111yescharacteristic
289C22×C43#52011yescharacteristic
290C22×C43#54612yes—
291C22×C43#54712yes—
292C2×D43—22no—
293C2×D43—22no—
294C2×D43—22no—
295C2×D43—24no—
296C2×D43—22no—
297C2×D43—24no—
298C2×D43—22no—
299C2×D43—24no—
300C2×D43—48no—
301C2×D43—44no—
302C2×D43—44no—
303C2×D43—48no—
304C2×D43—84no—
305C2×D43—84no—
306C2×D43—82no—
307C2×D43—82no—
308C2×D43C2×#9914yes—
309C4×C43—21no—
310C4×C43—22no—
311C4×C43—41no—
312C4×C43—41no—
313C4×C43—41no—
314C4×C43—84no—
315C4×C43C2×#9912yes—
316Dic43—44no—
317Dic43—42no—
318Dic43—42no—
319Dic43—82no—
320C2×#546—431no—
321D4×C22⋊C4—432no—
322#1996—432no—
323#1898—434no—
324#1819—432no—
325#1799D4311yescharacteristic, complemented
326C4×#99—431no—
327C2×#342—432no—
328C2×C43—22no—
329C2×C43—22no—
330C2×C43—21no—
331C2×C43—21no—
332C2×C43—81no—
333C2×C43#233911yescharacteristic
334C2×C43C22×#9911yescharacteristic
335C2×C43#288311yescharacteristic
336D43—24no—
337D43—42no—
338D43—44no—
339C22×#41—431no—
340C23×D4—431no—
341#546—862no—
342#546—864no—
343#546—862no—
344C2×#124—431no—
345C2×#123—432no—
346C2×C22⋊Q8—431no—
347C2×#121—431no—
348C2×#121—432no—
349C2×#120—432no—
350C2×C4×D4—431no—
351C2×C4×D4—862no—
352C2×C4×D4C2×D4311yescharacteristic
353C22×C22⋊C4—432no—
354C22×C22⋊C4—434no—
355C2×#99—432no—
356C2×#99C2×D4312yes—
357#390—862no—
358#386—864no—
359#380C2×D4312yes—
360#379—434no—
361C4×C22⋊C4—432no—
362#342—431no—
363#342—434no—
364#342—434no—
365#342—431no—
366#342C2×D4312yes—
367C43#2247611yescharacteristic, complemented, Sylow
368C25—432no—
369C2×#41—861no—
370C2×#41—862no—
371C2×#41—861no—
372C2×#41—1724no—
373C22×Q8—431no—
374C22×D4—432no—
375C22×D4—432no—
376C22×D4—431no—
377C22×D4—432no—
378C22×D4—431no—
379C22×D4—432no—
380C22×D4—434no—
381C22×D4—432no—
382C22×D4—1724no—
383C22×D4C22×D4311yescharacteristic
384C23×C4—432no—
385C23×C4—432no—
386C23×C4—864no—
387C23×C4C4×D4311yescharacteristic, complemented
388C23×C4C22×D4311yescharacteristic
389#124—862no—
390#124—862no—
391#123—864no—
392#123—864no—
393C22⋊Q8—862no—
394C22⋊Q8—862no—
395#121—864no—
396#121—864no—
397#121—862no—
398#121—862no—
399#120—864no—
400#120—864no—
401C4×D4—22no—
402C4×D4—22no—
403C4×D4—861no—
404C4×D4—862no—
405C4×D4—861no—
406C4×D4—1728no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—432no—
410C2×C4⋊C4C4×D4311yescharacteristic, complemented
411C2×C22⋊C4—432no—
412C2×C22⋊C4—432no—
413C2×C22⋊C4—432no—
414C2×C22⋊C4—432no—
415C2×C22⋊C4—432no—
416C2×C22⋊C4—432no—
417C2×C22⋊C4—432no—
418C2×C22⋊C4—868no—
419C2×C22⋊C4—864no—
420C2×C22⋊C4—864no—
421C2×C22⋊C4—864no—
422C2×C22⋊C4—864no—
423C2×C22⋊C4—864no—
424C2×C22⋊C4—1724no—
425C2×C22⋊C4C4×D4311yescharacteristic, complemented
426C2×C22⋊C4C22×D4314yes—
427C2×C22⋊C4C22×D4311yescharacteristic
428C2×C42—862no—
429C2×C42C4×D4311yescharacteristic, complemented
430#99—42no—
431#99—864no—
432#95—22no—
433#95—862no—
434C24—432no—
435C24—434no—
436C24—432no—
437C24—434no—
438C24—864no—
439C24—862no—
440C24—862no—
441C24—3442no—
442C24—1724no—
443C24C2×C4×D4311yescharacteristic
444C24C23×D4311yescharacteristic
445#41—1724no—
446#41—1728no—
447#41—1724no—
448C2×Q8—861no—
449C2×Q8—861no—
450C2×Q8—1722no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—431no—
456C2×D4—432no—
457C2×D4—431no—
458C2×D4—434no—
459C2×D4—432no—
460C2×D4—434no—
461C2×D4—432no—
462C2×D4—868no—
463C2×D4—864no—
464C2×D4—864no—
465C2×D4—862no—
466C2×D4—862no—
467C2×D4—3442no—
468C2×D4—1724no—
469C2×D4—1722no—
470C2×D4—1724no—
471C2×D4—1728no—
472C2×D4—1724no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—24no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—432no—
479C22×C4—432no—
480C22×C4—862no—
481C22×C4—862no—
482C22×C4—862no—
483C22×C4—862no—
484C22×C4—862no—
485C22×C4—862no—
486C22×C4—3444no—
487C22×C4—3442no—
488C22×C4—1728no—
489C22×C4—1728no—
490C22×C4—1724no—
491C22×C4C2×C4×D4311yescharacteristic
492C22×C4C2×C4×D4311yescharacteristic
493C22×C4C2×C4×D4311yescharacteristic
494C22×C4C2×C4×D4311yescharacteristic
495C22×C4C2×C4×D4311yescharacteristic
496C22×C4D4×D4312yes—
497C22×C4D4×D4312yes—
498C4⋊C4—22no—
499C4⋊C4—44no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—864no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—24no—
506C22⋊C4—24no—
507C22⋊C4—434no—
508C22⋊C4—864no—
509C22⋊C4—864no—
510C22⋊C4—862no—
511C22⋊C4—862no—
512C22⋊C4—864no—
513C22⋊C4—864no—
514C22⋊C4—862no—
515C22⋊C4—862no—
516C22⋊C4—862no—
517C22⋊C4—3444no—
518C22⋊C4—1728no—
519C22⋊C4—1728no—
520C42—21no—
521C42—21no—
522C42—1724no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—432no—
531C23—434no—
532C23—432no—
533C23—868no—
534C23—864no—
535C23—862no—
536C23—862no—
537C23—864no—
538C23—864no—
539C23—862no—
540C23—862no—
541C23—864no—
542C23—864no—
543C23—3448no—
544C23—3444no—
545C23—3444no—
546C23—1724no—
547C23—1722no—
548C23—1724no—
549C23—1722no—
550C23—1724no—
551C23—1722no—
552C23C22×C4×D4311yescharacteristic
553C23C2×D4×D4312yes—
554C23#41×D4312yes—
555C23#1306337011yescharacteristic
556C23#1306337311yescharacteristic
557Q8—1722no—
558Q8—1722no—
559D4—42no—
560D4—42no—
561D4—434no—
562D4—864no—
563D4—868no—
564D4—862no—
565D4—864no—
566D4—3444no—
567D4—1722no—
568D4—1724no—
569D4—1724no—
570D4—1724no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—44no—
585C2×C4—44no—
586C2×C4—44no—
587C2×C4—862no—
588C2×C4—862no—
589C2×C4—864no—
590C2×C4—3442no—
591C2×C4—3442no—
592C2×C4—34416no—
593C2×C4—1724no—
594C2×C4—1724no—
595C2×C4—1722no—
596C2×C4—1722no—
597C2×C4—1722no—
598C2×C4—1722no—
599C2×C4—1722no—
600C2×C4—1722no—
601C2×C4—1722no—
602C2×C4C22⋊C4×D4311yescharacteristic
603C2×C4C22⋊C4×D4312yes—
604C2×C4C22⋊C4×D4311yescharacteristic
605C22—22no—
606C22—21no—
607C22—22no—
608C22—21no—
609C22—42no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—81no—
616C22—81no—
617C22—434no—
618C22—862no—
619C22—862no—
620C22—862no—
621C22—864no—
622C22—862no—
623C22—864no—
624C22—864no—
625C22—862no—
626C22—3444no—
627C22—3444no—
628C22—3442no—
629C22—3442no—
630C22—1728no—
631C22—1728no—
632C22—1724no—
633C22—1724no—
634C22C2×C22⋊C4×D4311yescharacteristic
635C22#1458336711yescharacteristic
636C22#1458338011yescharacteristic
637C22#1458354612yes—
638C22#1458355112yes—
639C4—21no—
640C4—22no—
641C4—41no—
642C4—41no—
643C4—41no—
644C4—84no—
645C4—3442no—
646C4—1724no—
647C4—1722no—
648C4—1722no—
649C4#99×D4312yes—
650C2—22no—
651C2—22no—
652C2—21no—
653C2—21no—
654C2—81no—
655C2—864no—
656C2—1722no—
657C2—1724no—
658C2#1913742311yescharacteristic
659C2C2×#99×D4311yescharacteristic
660C2#1914305411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#1799C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583545C2
cosocleC24×C43C24
hypercenter#1799D43
hypocenterC43#22476
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. #19137415C2semidirect
3. #19135579C2semidirect
4. #19135045C2semidirect
5. #19134668C2semidirect
6. C4×#13063240C2semidirect
7. #342×D43C2semidirect
8. C43×#1799C2semidirect
9. C22×#10621898C4semidirect
14. C2×#13063313C4semidirect
15. C2×#13063310C4semidirect
17. C2×#13063299C4semidirect
18. C2×#13063298C4semidirect
20. C2×C4×D172C4semidirect
42. C22×Dic86C2×C4semidirect
50. C22×C22⋊D43C2×C4semidirect
51. C22×C22⋊D43C2×C4semidirect
53. C22×C4×D43C2×C4semidirect
54. C22×C4×D43C2×C4semidirect
71. C2×C4⋊Dic43C2×C4semidirect
72. C2×Dic43⋊C4C2×C4semidirect
79. C2×(C2×D43)⋊C4C2×C4semidirect
80. C2×(C2×D43)⋊C4C2×C4semidirect
81. C2×(C2×D43)⋊C4C2×C4semidirect
82. C2×(C2×D43)⋊C4C2×C4semidirect
91. C23×C4×C43C2×C4semidirect
96. C2×C4⋊C4×C43C2×C4semidirect
97. C2×C22⋊C4×C43C2×C4semidirect
100. C2×C42×C43C2×C4semidirect
179. C22⋊Dic43#41semidirect
266. D172#99semidirect
325. #1799D43semidirect
367. C43#22476semidirect
387. C23×C4C4×D43semidirect
410. C2×C4⋊C4C4×D43semidirect
425. C2×C22⋊C4C4×D43semidirect
429. C2×C42C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835452
#191374152
#191355792
#191350452
#191346682
C4×#130632402
#342×D432
C43×#17992
#2247643