Finite Group Databasebeta

← #25019300

Subgroups — #25019300

Order 11008.

2078 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063282C211yesmaximal, characteristic
2C2×#14582761C211yesmaximal, characteristic
3C2×#95×D43C211yesmaximal, characteristic
4#19132861C212yesmaximal, complemented
5#19132861C212yesmaximal, complemented
6#19132822C211yesmaximal, characteristic, complemented
7#19132819C211yesmaximal, characteristic, complemented
8#19132819C211yesmaximal, characteristic, complemented
9(C2×D43)⋊#95C212yesmaximal
10(C2×D43)⋊#95C212yesmaximal
11C43×#1434C211yesmaximal, characteristic, complemented
12C23×C4×D43C2212yes—
13C23×C4×D43C2211yescharacteristic
14C2×#13063282—24no—
15C2×#13063282—24no—
16C2×#13063282C418yescomplemented
17C22×Dic43⋊C4C2211yescharacteristic
18C22×Dic43⋊C4C2211yescharacteristic
19C22×(C2×D43)⋊C4C2212yes—
20C22×(C2×D43)⋊C4C2211yescharacteristic
21C22×(C2×D43)⋊C4C2211yescharacteristic
22C22×C4×Dic43C2211yescharacteristic
23#14582761—24no—
24C2×C43⋊#95C2212yes—
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2211yescharacteristic
28C2×C43⋊#95C2211yescharacteristic
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2212yes—
34#95×D43—24no—
35C22×C42×C43C2211yescharacteristic
36C2×#95×C43C2212yes—
37C2×#95×C43C2211yescharacteristic
38C2×#95×C43C2211yescharacteristic
39C2×#95×C43C2212yes—
40C24×D43C2311yescharacteristic
41C23×Dic43C2312yes—
42C23×Dic43C2311yescharacteristic
43C23×Dic43C2311yescharacteristic
44C23×Dic43C2312yes—
45C23×Dic43C2311yescharacteristic
46C22×C4×D43—24no—
47C22×C4×D43—24no—
48C22×C4×D43—24no—
49C22×C4×D43—24no—
50C22×C4×D43—24no—
51C22×C4×D43—24no—
52C22×C4×D43—24no—
53C22×C4×D43—42no—
54C22×C4×D43—42no—
55C22×C4×D43C2×C414yes—
56C22×C4×D43D414yes—
57C22×C4×D43D414yes—
58#13063282—232no—
59C2×Dic43⋊C4—22no—
60C2×Dic43⋊C4—22no—
61C2×Dic43⋊C4—22no—
62C2×Dic43⋊C4—22no—
63C2×Dic43⋊C4C2×C414yescomplemented
64C2×Dic43⋊C4C2×C414yescomplemented
65C2×(C2×D43)⋊C4—22no—
66C2×(C2×D43)⋊C4—22no—
67C2×(C2×D43)⋊C4—22no—
68C2×(C2×D43)⋊C4—22no—
69C2×(C2×D43)⋊C4—24no—
70C2×(C2×D43)⋊C4—24no—
71C2×(C2×D43)⋊C4—24no—
72C2×(C2×D43)⋊C4C2×C414yes—
73C2×(C2×D43)⋊C4C2×C414yes—
74C2×C4×Dic43—22no—
75C2×C4×Dic43—22no—
76C2×C4×Dic43C2×C414yescomplemented
77C43⋊#95—22no—
78C43⋊#95—22no—
79C43⋊#95—24no—
80C43⋊#95—24no—
81C43⋊#95—24no—
82C43⋊#95—24no—
83C43⋊#95—24no—
84C43⋊#95—42no—
85C43⋊#95—42no—
86C43⋊#95—42no—
87C23×C4×C43C2312yes—
88C23×C4×C43C2311yescharacteristic
89C23×C4×C43C2311yescharacteristic
90C23×C4×C43C2312yes—
91C23×C4×C43C2311yescharacteristic
92C2×C42×C43—22no—
93C2×C42×C43—22no—
94C2×C42×C43C2×C414yescomplemented
95#95×C43—22no—
96#95×C43—22no—
97#95×C43—24no—
98#95×C43—42no—
99C24×C43C2411yescharacteristic
100C23×D43—22no—
101C23×D43—22no—
102C23×D43—21no—
103C23×D43—21no—
104C23×D43—21no—
105C23×D43—21no—
106C23×D43C22×C412yes—
107C23×D43C2×D412yes—
108C23×D43C2×D412yes—
109C23×D43#4114yes—
110C23×D43#4114yes—
111C22×C4×C43—22no—
112C22×C4×C43—21no—
113C22×C4×C43—21no—
114C22×C4×C43—21no—
115C22×C4×C43—21no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—22no—
128C22×C4×C43—21no—
129C22×C4×C43—22no—
130C22×C4×C43—21no—
131C22×C4×C43—22no—
132C22×C4×C43—22no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—22no—
136C22×C4×C43C22×C412yes—
137C22×C4×C43C22×C412yes—
138C22×C4×C43C22×C412yes—
139C22×C4×C43C2×D412yes—
140C22×C4×C43C2×D412yes—
141C22×C4×C43#4114yes—
142C22×Dic43—22no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—22no—
148C22×Dic43—22no—
149C22×Dic43—22no—
150C22×Dic43—22no—
151C22×Dic43—22no—
152C22×Dic43—22no—
153C22×Dic43—22no—
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43—22no—
157C22×Dic43—22no—
158C22×Dic43—22no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—22no—
162C22×Dic43—22no—
163C22×Dic43—22no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—22no—
167C22×Dic43C22×C412yes—
168C22×Dic43C22×C412yes—
169C22×Dic43C22×C412yes—
170C22×Dic43C2×D412yes—
171C22×Dic43C2×D412yes—
172C22×Dic43#4114yes—
173C2×C4×D43—216no—
174C2×C4×D43—28no—
175C2×C4×D43—28no—
176C2×C4×D43—216no—
177C2×C4×D43—216no—
178C2×C4×D43—48no—
179C2×C4×D43—48no—
180C2×C4×D43—48no—
181C2×C4×D43—48no—
182C2×C4×D43—48no—
183C2×C4×D43—48no—
184C2×C4×D43C22⋊C4116yes—
185C42×C43—28no—
186(C2×D43)⋊C4—28no—
187(C2×D43)⋊C4—28no—
188(C2×D43)⋊C4—48no—
189Dic43⋊C4—28no—
190Dic43⋊C4—28no—
191C4×Dic43—28no—
192C23×C43C23×C411yescharacteristic
193C23×C43C22×D411yescharacteristic
194C23×C43C22×D411yescharacteristic
195C23×C43C2×#4112yes—
196C23×C43C2×#4112yes—
197C23×C43C2×#4112yes—
198C23×C43C2×#4112yes—
199C23×C43H(5,𝔽2)11yescharacteristic
200C23×C43H(5,𝔽2)11yescharacteristic
201C23×C432−1+411yescharacteristic
202C23×C432−1+411yescharacteristic
203C22×D43—22no—
204C22×D43—22no—
205C22×D43—22no—
206C22×D43—22no—
207C22×D43—24no—
208C22×D43—24no—
209C22×D43—22no—
210C22×D43—22no—
211C22×D43—22no—
212C22×D43—22no—
213C22×D43—24no—
214C22×D43—24no—
215C22×D43—24no—
216C22×D43—24no—
217C22×D43—24no—
218C22×D43—24no—
219C22×D43—24no—
220C22×D43—24no—
221C22×D43C2×C22⋊C414yes—
222C22×D43#11714yes—
223C22×D43#11714yes—
224C22×D43#12318yes—
225C22×D43#12318yes—
226C2×C4×C43—22no—
227C2×C4×C43—22no—
228C2×C4×C43—24no—
229C2×C4×C43—24no—
230C2×C4×C43—22no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—22no—
235C2×C4×C43—22no—
236C2×C4×C43—24no—
237C2×C4×C43—24no—
238C2×C4×C43—24no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—42no—
248C2×C4×C43—42no—
249C2×C4×C43—42no—
250C2×C4×C43—42no—
251C2×C4×C43—42no—
252C2×C4×C43—42no—
253C2×C4×C43—42no—
254C2×C4×C43—42no—
255C2×C4×C43—42no—
256C2×C4×C43C2×C22⋊C414yes—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—24no—
260C2×Dic43—24no—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—22no—
265C2×Dic43—22no—
266C2×Dic43—22no—
267C2×Dic43—24no—
268C2×Dic43—24no—
269C2×Dic43—24no—
270C2×Dic43—42no—
271C2×Dic43—42no—
272C2×Dic43—42no—
273C2×Dic43—42no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—42no—
279C2×Dic43—42no—
280C2×Dic43—42no—
281C2×Dic43—42no—
282C2×Dic43—42no—
283C2×Dic43—42no—
284C2×Dic43—42no—
285C2×Dic43—42no—
286C2×Dic43—42no—
287C2×Dic43C2×C22⋊C414yes—
288C4×D43—232no—
289C4×D43—432no—
290#13958—431nomaximal, Sylow
291C22×C43C22×C22⋊C411yescharacteristic
292C22×C43C2×#11711yescharacteristic
293C22×C43C2×#11711yescharacteristic
294C22×C43C4×#4111yescharacteristic
295C22×C43C4×#4111yescharacteristic
296C22×C43#52011yescharacteristic
297C22×C43#52011yescharacteristic
298C22×C43C2×#12312yes—
299C22×C43C2×#12312yes—
300C22×C43#52512yes—
301C22×C43#53212yes—
302C22×C43#53511yescharacteristic
303C22×C43#53611yescharacteristic
304C22×C43#53711yescharacteristic
305C22×C43#53711yescharacteristic
306C22×C43#55112yes—
307C22×C43#55112yes—
308C22×C43#55112yes—
309C22×C43#55112yes—
310C22×C43#55212yes—
311C22×C43#55212yes—
312C22×C43#55212yes—
313C22×C43#55212yes—
314C2×D43—24no—
315C2×D43—24no—
316C2×D43—24no—
317C2×D43—24no—
318C2×D43—24no—
319C2×D43—28no—
320C2×D43—28no—
321C2×D43—28no—
322C2×D43—28no—
323C2×D43—24no—
324C2×D43#38118yes—
325C4×C43—24no—
326C4×C43—42no—
327C4×C43—44no—
328C4×C43—42no—
329C4×C43—82no—
330Dic43—24no—
331Dic43—42no—
332Dic43—44no—
333Dic43—42no—
334Dic43—82no—
335C22×#117—431no—
336C2×#381—431no—
337C22×#95—431no—
338#1445—432no—
339#1445—432no—
340#1434—431no—
341#1434—431no—
342#1434—431no—
343#1434D4311yescharacteristic, complemented
344C22⋊#95—432no—
345C22⋊#95—432no—
346C2×C43C2×#38111yescharacteristic
347C2×C43#229711yescharacteristic
348C2×C43#231111yescharacteristic
349C2×C43#234311yescharacteristic
350C2×C43#234311yescharacteristic
351C2×C43#234311yescharacteristic
352C2×C43#234311yescharacteristic
353C2×C43#248212yes—
354C2×C43#248412yes—
355C2×C43#249812yes—
356C2×C43#249812yes—
357D43—28no—
358C24×C4—431no—
359C24×C4—432no—
360C2×#117—438no—
361C2×#117—864no—
362C2×#117—864no—
363C22×C4⋊C4—431no—
364C22×C4⋊C4—431no—
365C22×C22⋊C4—431no—
366C22×C22⋊C4—431no—
367C22×C22⋊C4—432no—
368C22×C42—431no—
369C22×C42C2×D4311yescharacteristic
370#381—864no—
371C2×#95—432no—
372C2×#95—432no—
373C2×#95—432no—
374C2×#95—431no—
375C2×#95—431no—
376C2×#95—432no—
377C2×#95—432no—
378C2×#95—432no—
379C2×#95—432no—
380C2×#95—432no—
381C2×#95—864no—
382C2×#95C2×D4312yes—
383C2×#95C2×D4311yescharacteristic
384C2×#95C2×D4311yescharacteristic
385C2×#95C2×D4312yes—
386C43#1395811yescharacteristic, complemented, Sylow
387C25—431no—
388C23×C4—431no—
389C23×C4—434no—
390C23×C4—434no—
391C23×C4—434no—
392C23×C4—431no—
393C23×C4—431no—
394C23×C4—432no—
395C23×C4—432no—
396C23×C4—864no—
397C23×C4—864no—
398C23×C4—864no—
399C23×C4—864no—
400C23×C4—864no—
401C23×C4—864no—
402C23×C4—864no—
403C23×C4—1722no—
404C23×C4—1722no—
405C23×C4C22×D4312yes—
406C23×C4C22×D4311yescharacteristic
407C23×C4C22×D4311yescharacteristic
408C23×C4C22×D4312yes—
409C23×C4C22×D4311yescharacteristic
410#117—8632no—
411C2×C4⋊C4—434no—
412C2×C4⋊C4—434no—
413C2×C4⋊C4—862no—
414C2×C4⋊C4—862no—
415C2×C4⋊C4—862no—
416C2×C4⋊C4—862no—
417C2×C22⋊C4—434no—
418C2×C22⋊C4—434no—
419C2×C22⋊C4—862no—
420C2×C22⋊C4—862no—
421C2×C22⋊C4—862no—
422C2×C22⋊C4—862no—
423C2×C22⋊C4—864no—
424C2×C22⋊C4—864no—
425C2×C22⋊C4—864no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—434no—
429C2×C42—862no—
430C2×C42—862no—
431C2×C42C4×D4314yescomplemented
432#95—24no—
433#95—22no—
434#95—22no—
435#95—42no—
436#95—864no—
437#95—864no—
438#95—864no—
439#95—864no—
440#95—864no—
441#95—862no—
442#95—862no—
443#95—1722no—
444#95—1722no—
445#95—1722no—
446C24—432no—
447C24—432no—
448C24—432no—
449C24—434no—
450C24—434no—
451C24—862no—
452C24—862no—
453C24—861no—
454C24—861no—
455C24—861no—
456C24—861no—
457C24C23×D4311yescharacteristic
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—432no—
484C22×C4—432no—
485C22×C4—432no—
486C22×C4—4316no—
487C22×C4—432no—
488C22×C4—432no—
489C22×C4—434no—
490C22×C4—868no—
491C22×C4—868no—
492C22×C4—8616no—
493C22×C4—8616no—
494C22×C4—8616no—
495C22×C4—862no—
496C22×C4—862no—
497C22×C4—862no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—862no—
503C22×C4—862no—
504C22×C4—862no—
505C22×C4—862no—
506C22×C4—862no—
507C22×C4—861no—
508C22×C4—862no—
509C22×C4—861no—
510C22×C4—862no—
511C22×C4—861no—
512C22×C4—861no—
513C22×C4—862no—
514C22×C4—862no—
515C22×C4—862no—
516C22×C4—862no—
517C22×C4—862no—
518C22×C4—862no—
519C22×C4—862no—
520C22×C4—1728no—
521C22×C4—1728no—
522C22×C4—1728no—
523C22×C4—1728no—
524C22×C4—1728no—
525C22×C4—1728no—
526C22×C4C2×C4×D4312yes—
527C22×C4C2×C4×D4312yes—
528C22×C4C2×C4×D4312yes—
529C22×C4#1062189814yes—
530C22×C4D4×D4312yes—
531C22×C4D4×D4312yes—
532C4⋊C4—868no—
533C4⋊C4—868no—
534C22⋊C4—868no—
535C22⋊C4—868no—
536C22⋊C4—1728no—
537C42—28no—
538C42—868no—
539C23—434no—
540C23—434no—
541C23—434no—
542C23—438no—
543C23—438no—
544C23—864no—
545C23—864no—
546C23—864no—
547C23—864no—
548C23—864no—
549C23—864no—
550C23—864no—
551C23—864no—
552C23—862no—
553C23—862no—
554C23—862no—
555C23—862no—
556C23—864no—
557C23—864no—
558C23—862no—
559C23—862no—
560C23—862no—
561C23—862no—
562C23C22×C4×D4311yescharacteristic
563C23C2×D4×D4311yescharacteristic
564C23C2×D4×D4311yescharacteristic
565C23#41×D4312yes—
566C23#41×D4312yes—
567C23#41×D4312yes—
568C23C2×#1062189812yes—
569C23#1306337011yescharacteristic
570C23#1306337111yescharacteristic
571C23#1306337211yescharacteristic
572C23#1306337311yescharacteristic
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—434no—
604C2×C4—8632no—
605C2×C4—862no—
606C2×C4—862no—
607C2×C4—864no—
608C2×C4—864no—
609C2×C4—864no—
610C2×C4—864no—
611C2×C4—862no—
612C2×C4—862no—
613C2×C4—862no—
614C2×C4—862no—
615C2×C4—862no—
616C2×C4—862no—
617C2×C4—864no—
618C2×C4—17232no—
619C2×C4—1722no—
620C2×C4—1722no—
621C2×C4—1722no—
622C2×C4—1722no—
623C2×C4—1722no—
624C2×C4—1722no—
625C2×C4—1722no—
626C2×C4—1722no—
627C2×C4—1722no—
628C2×C4—1722no—
629C2×C4—1722no—
630C2×C4—1722no—
631C2×C4—1722no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4C22⋊C4×D4314yes—
637C22—438no—
638C22—868no—
639C22—864no—
640C22—868no—
641C22—864no—
642C22—864no—
643C22—864no—
644C22—864no—
645C22—864no—
646C22—868no—
647C22—868no—
648C22C2×C22⋊C4×D4311yescharacteristic
649C22#117×D4311yescharacteristic
650C22#117×D4311yescharacteristic
651C22#1458336711yescharacteristic
652C22C4×#1062189811yescharacteristic
653C22#1458337911yescharacteristic
654C22#1458338011yescharacteristic
655C22#123×D4312yes—
656C22#123×D4312yes—
657C22#1458340812yes—
658C22#1458344612yes—
659C22#1458346511yescharacteristic
660C22#1458347211yescharacteristic
661C22#1458347811yescharacteristic
662C22#1458347911yescharacteristic
663C22#1458357312yes—
664C22#1458357412yes—
665C22#1458357812yes—
666C22#1458357912yes—
667C22#1458358112yes—
668C22#1458358512yes—
669C22#1458358812yes—
670C22#1458359012yes—
671C4—24no—
672C4—44no—
673C4—42no—
674C4—42no—
675C4—82no—
676C4—864no—
677C4—3442no—
678C4—1724no—
679C4—1722no—
680C4—1722no—
681C2—868no—
682C2#381×D4311yescharacteristic
683C2#1913708111yescharacteristic
684C2#1913718411yescharacteristic
685C2#1913744811yescharacteristic
686C2#1913745211yescharacteristic
687C2#1913745611yescharacteristic
688C2#1913745811yescharacteristic
689C2#1913886712yes—
690C2#1913888012yes—
691C2#1913903612yes—
692C2#1913903812yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1434C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenter#1434D43
hypocenterC43#13958
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
4. #19132861C2semidirect
5. #19132861C2semidirect
6. #19132822C2semidirect
7. #19132819C2semidirect
8. #19132819C2semidirect
11. C43×#1434C2semidirect
16. C2×#13063282C4semidirect
63. C2×Dic43⋊C4C2×C4semidirect
64. C2×Dic43⋊C4C2×C4semidirect
76. C2×C4×Dic43C2×C4semidirect
94. C2×C42×C43C2×C4semidirect
343. #1434D43semidirect
386. C43#13958semidirect
431. C2×C42C4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×#130632822
C2×#145827612
C2×#95×D432
#191328612
#191328222
#191328192
(C2×D43)⋊#952
C43×#14342
#1395843