Finite Group Databasebeta

← #25112730

Subgroups — #25112730

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
2C22⋊C4×D172C212yesmaximal, complemented
3#19135580C212yesmaximal, complemented
4#19135045C214yesmaximal, complemented
5#19134668C212yesmaximal, complemented
6#19134583C211yesmaximal, characteristic, complemented
7#342×D43C212yesmaximal, complemented
8C4×#99×C43C211yesmaximal, 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×D172—22no—
21C2×C4×D172C411yescharacteristic, complemented
22C2×C22⋊C4×D43C2212yes—
23C2×C22⋊C4×D43C2214yes—
24C2×#13063240C2212yes—
25#14582801—22no—
26#14582777—24no—
27#14582759C2212yes—
28#14582754C2214yes—
29#14582666C2212yes—
30#14582665C2214yes—
31#14582665C2214yes—
32C2×C4×D4×C43C2211yescharacteristic
33C2×#99×C43C2212yes—
34C4×C22⋊C4×C43C2212yes—
35C43×#342C2211yescharacteristic
36C43×#342C2211yescharacteristic
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—
70C4×D172—48no—
71C2×C4⋊Dic43—22no—
72C2×C4⋊Dic43C2×C411yescharacteristic, complemented
73C2×Dic43⋊C4C2×C412yescomplemented
74C2×C22⋊Dic43C2314yes—
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—
87#13063240—42no—
88C43⋊#95—22no—
89C22×D4×C43C2311yescharacteristic
90C23×C4×C43C2×C411yescharacteristic, complemented
91C23×C4×C43C2311yescharacteristic
92C4×D4×C43—22no—
93C4×D4×C43—22no—
94C2×C4⋊C4×C43C2×C411yescharacteristic, complemented
95C2×C22⋊C4×C43C2×C411yescharacteristic, complemented
96C2×C22⋊C4×C43C2312yes—
97C2×C22⋊C4×C43C2311yescharacteristic
98C2×C22⋊C4×C43C2312yes—
99C2×C42×C43—22no—
100C2×C42×C43C2×C411yescharacteristic, complemented
101#99×C43—24no—
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—22no—
121C22×C4×C43—22no—
122C22×C4×C43—42no—
123C22×C4×C43—42no—
124C22×C4×C43C22×C411yescharacteristic
125C22×C4×C43C22×C411yescharacteristic
126C22×C4×C43C22×C411yescharacteristic
127C22×C4×C43C22×C411yescharacteristic
128C22×C4×C43C22×C411yescharacteristic
129C22×C4×C43C2×D412yes—
130C22×C4×C43C2×D412yes—
131C2×C22⋊D43—22no—
132C2×C22⋊D43—22no—
133C2×C22⋊D43—24no—
134C2×C22⋊D43—44no—
135C2×C22⋊D43—82no—
136C22×Dic43—24no—
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—
168C22⋊C4×C43—22no—
169C22⋊C4×C43—22no—
170C22⋊C4×C43—22no—
171C22⋊C4×C43—22no—
172C22⋊C4×C43—22no—
173C22⋊C4×C43#4114yescomplemented
174C42×C43—21no—
175C42×C43—21no—
176C42×C43—44no—
177C22⋊Dic43—24no—
178C22⋊Dic43—24no—
179C22⋊Dic43—24no—
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—
190C4⋊Dic43—44no—
191Dic43⋊C4—24no—
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—24no—
236C2×C4×C43—41no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—42no—
245C2×C4×C43—42no—
246C2×C4×C43—42no—
247C2×C4×C43C2×C22⋊C412yes—
248C2×C4×C43C2×C22⋊C411yescharacteristic
249C2×C4×C43C2×C22⋊C411yescharacteristic
250C22⋊D43—44no—
251C22⋊D43—44no—
252C22⋊D43—84no—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—42no—
256C2×Dic43—42no—
257C2×Dic43—44no—
258C2×Dic43—44no—
259C2×Dic43—44no—
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—44no—
312C4×C43—41no—
313C4×C43—41no—
314C4×C43—41no—
315C4×C43—82no—
316C4×C43C2×#9912yes—
317Dic43—42no—
318Dic43—42no—
319Dic43—84no—
320C2×#546—431no—
321D4×C22⋊C4—432no—
322#1996—432no—
323#1898—434no—
324#1819—432no—
325#1799—431no—
326C4×#99D4311yescharacteristic, complemented
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#380—432no—
360#379—434no—
361C4×C22⋊C4C2×D4312yes—
362#342—432no—
363#342—434no—
364#342—434no—
365#342C2×D4311yescharacteristic
366#342C2×D4311yescharacteristic
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—431no—
408C2×C4⋊C4—432no—
409C2×C4⋊C4—862no—
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—434no—
417C2×C22⋊C4—864no—
418C2×C22⋊C4—864no—
419C2×C22⋊C4—868no—
420C2×C22⋊C4—864no—
421C2×C22⋊C4—864no—
422C2×C22⋊C4—864no—
423C2×C22⋊C4—1724no—
424C2×C22⋊C4C4×D4311yescharacteristic, complemented
425C2×C22⋊C4C22×D4312yes—
426C2×C22⋊C4C22×D4311yescharacteristic
427C2×C22⋊C4C22×D4312yes—
428C2×C42—22no—
429C2×C42C4×D4311yescharacteristic, complemented
430#99—24no—
431#99—1722no—
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—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—432no—
480C22×C4—432no—
481C22×C4—862no—
482C22×C4—862no—
483C22×C4—862no—
484C22×C4—862no—
485C22×C4—864no—
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—861no—
500C4⋊C4—861no—
501C4⋊C4—864no—
502C4⋊C4—1724no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—864no—
509C22⋊C4—864no—
510C22⋊C4—862no—
511C22⋊C4—862no—
512C22⋊C4—864no—
513C22⋊C4—864no—
514C22⋊C4—864no—
515C22⋊C4—864no—
516C22⋊C4—3444no—
517C22⋊C4—1728no—
518C22⋊C4—1728no—
519C22⋊C4#1062189814yescomplemented
520C42—21no—
521C42—21no—
522C42—44no—
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—864no—
536C23—862no—
537C23—862no—
538C23—864no—
539C23—864no—
540C23—862no—
541C23—862no—
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—
554C23C2×#1062189812yes—
555C23#1306337111yescharacteristic
556C23#1306337211yescharacteristic
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—24no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—862no—
591C2×C4—862no—
592C2×C4—34416no—
593C2×C4—3442no—
594C2×C4—3442no—
595C2×C4—1724no—
596C2×C4—1724no—
597C2×C4—1724no—
598C2×C4—1724no—
599C2×C4—1724no—
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
635C22C4×#1062189811yescharacteristic
636C22#1458337911yescharacteristic
637C22#1458354512yes—
638C22#1458355412yes—
639C4—21no—
640C4—22no—
641C4—44no—
642C4—41no—
643C4—41no—
644C4—41no—
645C4—82no—
646C4—3444no—
647C4—1722no—
648C4—1722no—
649C4#99×D4312yes—
650C2—22no—
651C2—22no—
652C2—21no—
653C2—21no—
654C2—81no—
655C2—864no—
656C2—1722no—
657C2—1724no—
658C2#1913742611yescharacteristic
659C2C2×#99×D4311yescharacteristic
660C2#1914305411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC4×#99×C43C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583545C2
cosocleC24×C43C24
hypercenterC4×#99D43
hypocenterC43#22476
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. C22⋊C4×D172C2semidirect
3. #19135580C2semidirect
4. #19135045C2semidirect
5. #19134668C2semidirect
6. #19134583C2semidirect
7. #342×D43C2semidirect
8. C4×#99×C43C2semidirect
9. C22×#10621898C4semidirect
14. C2×#13063313C4semidirect
15. C2×#13063310C4semidirect
17. C2×#13063299C4semidirect
18. C2×#13063298C4semidirect
21. 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
72. C2×C4⋊Dic43C2×C4semidirect
73. 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
90. C23×C4×C43C2×C4semidirect
94. C2×C4⋊C4×C43C2×C4semidirect
95. C2×C22⋊C4×C43C2×C4semidirect
100. C2×C42×C43C2×C4semidirect
173. C22⋊C4×C43#41semidirect
266. D172#99semidirect
326. C4×#99D43semidirect
367. C43#22476semidirect
387. C23×C4C4×D43semidirect
410. C2×C4⋊C4C4×D43semidirect
424. C2×C22⋊C4C4×D43semidirect
429. C2×C42C4×D43semidirect
519. C22⋊C4#10621898semidirect

Maximal subgroups

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

subgroupindex
C2×#145835452
C22⋊C4×D1722
#191355802
#191350452
#191346682
#191345832
#342×D432
C4×#99×C432
#2247643