Finite Group Databasebeta

← #25003518

Subgroups — #25003518

Order 11008.

1454 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063239C212yesmaximal
2C2×#14582778C211yesmaximal, characteristic
3C2×#14582665C212yesmaximal, complemented
4#19132818C211yesmaximal, characteristic, complemented
5C2×C43×#380C211yesmaximal, characteristic, complemented
6C23×C22⋊D43C2211yescharacteristic
7C22×C22⋊Dic43C2211yescharacteristic
8C22×C22⋊Dic43C2212yes—
9C22×(C2×D43)⋊C4C412yescomplemented
10C2×#13063239—24no—
11C2×#13063239—24no—
12C2×#13063239—24no—
13#14582778—22no—
14#14582778—21no—
15#14582778—21no—
16C2×C43⋊#95—22no—
17C2×C43⋊#95C412yescomplemented
18#14582665—24no—
19C24×C4×C43C2211yescharacteristic
20C22×C4⋊C4×C43—21no—
21C22×C22⋊C4×C43C2212yes—
22C43×#380—24no—
23C2×#95×C43—21no—
24C24×D43C2×C411yescharacteristic
25C22×C22⋊D43—22no—
26C22×C22⋊D43—22no—
27C22×C22⋊D43—21no—
28C22×C22⋊D43—21no—
29C22×C22⋊D43—22no—
30C22×C22⋊D43—21no—
31C22×C22⋊D43—21no—
32C22×C22⋊D43—22no—
33C22×C22⋊D43D412yes—
34C22×C22⋊D43Q812yes—
35C23×Dic43—22no—
36C23×Dic43C2×C411yescharacteristic
37C23×Dic43C2×C412yes—
38C2×C22⋊Dic43—22no—
39C2×C22⋊Dic43—22no—
40C2×C22⋊Dic43—22no—
41C2×C22⋊Dic43—22no—
42C2×C22⋊Dic43—22no—
43C2×C22⋊Dic43—21no—
44C2×C22⋊Dic43—21no—
45C2×C22⋊Dic43—22no—
46C2×C22⋊Dic43—22no—
47C2×C22⋊Dic43D414yes—
48C2×(C2×D43)⋊C4—22no—
49C2×(C2×D43)⋊C4—22no—
50C2×(C2×D43)⋊C4—44no—
51#13063239—216no—
52C43⋊#95—22no—
53C43⋊#95—22no—
54C43⋊#95—44no—
55C25×C43C2311yescharacteristic
56C23×C4×C43—22no—
57C23×C4×C43—22no—
58C23×C4×C43—22no—
59C23×C4×C43—44no—
60C23×C4×C43C2×C412yes—
61C23×C4×C43D412yes—
62C23×C4×C43D411yescharacteristic
63C23×C4×C43D411yescharacteristic
64C2×C4⋊C4×C43—24no—
65C2×C4⋊C4×C43—44no—
66C2×C22⋊C4×C43—22no—
67C2×C22⋊C4×C43—22no—
68C2×C22⋊C4×C43—22no—
69C2×C22⋊C4×C43—22no—
70C2×C22⋊C4×C43—22no—
71C2×C22⋊C4×C43D414yes—
72#95×C43—24no—
73C24×C43—42no—
74C24×C43—42no—
75C24×C43C22×C411yescharacteristic
76C24×C43C2×D411yescharacteristic
77C24×C43C2×D411yescharacteristic
78C24×C43C2×D411yescharacteristic
79C24×C43C2×D412yes—
80C24×C43C2×D412yes—
81C24×C43C2×Q811yescharacteristic
82C24×C43#4111yescharacteristic
83C24×C43#4111yescharacteristic
84C24×C43#4112yes—
85C24×C43#4112yes—
86C23×D43—21no—
87C23×D43—21no—
88C23×D43—22no—
89C23×D43—22no—
90C23×D43—42no—
91C23×D43—42no—
92C23×D43C4⋊C412yescomplemented
93C22×C4×C43—24no—
94C22×C4×C43—24no—
95C22×C4×C43—24no—
96C22×C4×C43—24no—
97C22×C4×C43—21no—
98C22×C4×C43—21no—
99C22×C4×C43—24no—
100C22×C4×C43—24no—
101C22×C4×C43—21no—
102C22×C4×C43—21no—
103C22×C4×C43—42no—
104C22×C4×C43—42no—
105C22×C4×C43—42no—
106C22×C4×C43—44no—
107C22×C4×C43—44no—
108C22×C4×C43—48no—
109C22×C4×C43—48no—
110C22×C4×C43—42no—
111C22×C4×C43—42no—
112C22×C4×C43C22⋊C412yes—
113C22×C4×C43C22⋊C412yes—
114C2×C22⋊D43—24no—
115C2×C22⋊D43—22no—
116C2×C22⋊D43—22no—
117C2×C22⋊D43—22no—
118C2×C22⋊D43—22no—
119C2×C22⋊D43—24no—
120C2×C22⋊D43—24no—
121C2×C22⋊D43—24no—
122C2×C22⋊D43—41no—
123C2×C22⋊D43—42no—
124C2×C22⋊D43—42no—
125C2×C22⋊D43—42no—
126C2×C22⋊D43—41no—
127C2×C22⋊D43—42no—
128C2×C22⋊D43—42no—
129C2×C22⋊D43—41no—
130C2×C22⋊D43—42no—
131C2×C22⋊D43—41no—
132C22×Dic43—21no—
133C22×Dic43—22no—
134C22×Dic43—21no—
135C22×Dic43—22no—
136C22×Dic43—22no—
137C22×Dic43—24no—
138C22×Dic43—24no—
139C22×Dic43—44no—
140C22×Dic43—44no—
141C22×Dic43—42no—
142C22×Dic43—42no—
143C22×Dic43—42no—
144C22×Dic43—42no—
145C22×Dic43C4⋊C412yescomplemented
146C4⋊C4×C43—48no—
147C22⋊C4×C43—24no—
148C22⋊C4×C43—24no—
149C22⋊C4×C43—42no—
150C22⋊C4×C43—42no—
151C22⋊Dic43—24no—
152C22⋊Dic43—24no—
153C22⋊Dic43—42no—
154C22⋊Dic43—42no—
155C22⋊Dic43—41no—
156C22⋊Dic43—42no—
157C22⋊Dic43—41no—
158(C2×D43)⋊C4—44no—
159(C2×D43)⋊C4—44no—
160C23×C43—22no—
161C23×C43—22no—
162C23×C43—22no—
163C23×C43—22no—
164C23×C43—22no—
165C23×C43—22no—
166C23×C43—42no—
167C23×C43—42no—
168C23×C43—42no—
169C23×C43—44no—
170C23×C43—42no—
171C23×C43—42no—
172C23×C43—42no—
173C23×C43—42no—
174C23×C43—42no—
175C23×C43—44no—
176C23×C43C2×C22⋊C411yescharacteristic
177C23×C43C2×C4⋊C411yescharacteristic
178C23×C43#11711yescharacteristic
179C23×C43C4×D412yes—
180C23×C43C4×D412yes—
181C23×C43#12012yes—
182C23×C43#12011yescharacteristic
183C23×C43#12111yescharacteristic
184C23×C43#12112yes—
185C23×C43#12112yes—
186C23×C43#12111yescharacteristic
187C23×C43#12112yes—
188C23×C43C22⋊Q811yescharacteristic
189C23×C43C22⋊Q812yes—
190C23×C43C22⋊Q812yes—
191C23×C43C22⋊Q811yescharacteristic
192C23×C43#12311yescharacteristic
193C23×C43#12312yes—
194C23×C43#12312yes—
195C23×C43#12411yescharacteristic
196C23×C43#12412yes—
197C23×C43#12612yes—
198C23×C43#12711yescharacteristic
199C22×D43—22no—
200C22×D43—24no—
201C22×D43—44no—
202C22×D43—41no—
203C22×D43—42no—
204C22×D43—41no—
205C22×D43—42no—
206C22×D43—42no—
207C22×D43—44no—
208C22×D43—82no—
209C22×D43—82no—
210C22×D43—84no—
211C2×C4×C43—24no—
212C2×C4×C43—24no—
213C2×C4×C43—22no—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—22no—
217C2×C4×C43—22no—
218C2×C4×C43—48no—
219C2×C4×C43—48no—
220C2×C4×C43—42no—
221C2×C4×C43—42no—
222C2×C4×C43—44no—
223C2×C4×C43—44no—
224C2×C4×C43—44no—
225C2×C4×C43—84no—
226C2×C4×C43—84no—
227C2×C4×C43#9914yescomplemented
228C22⋊D43—42no—
229C22⋊D43—42no—
230C22⋊D43—44no—
231C22⋊D43—44no—
232C22⋊D43—42no—
233C22⋊D43—42no—
234C2×Dic43—22no—
235C2×Dic43—24no—
236C2×Dic43—41no—
237C2×Dic43—42no—
238C2×Dic43—41no—
239C2×Dic43—48no—
240C2×Dic43—42no—
241C2×Dic43—44no—
242C2×Dic43—42no—
243C2×Dic43—42no—
244C2×Dic43—84no—
245C2×Dic43—82no—
246C2×Dic43—82no—
247C2×Dic43—84no—
248#11043—431nomaximal, Sylow
249C22×C43—22no—
250C22×C43—22no—
251C22×C43—22no—
252C22×C43—22no—
253C22×C43—22no—
254C22×C43—22no—
255C22×C43—22no—
256C22×C43—21no—
257C22×C43—22no—
258C22×C43—21no—
259C22×C43—22no—
260C22×C43—21no—
261C22×C43—22no—
262C22×C43—21no—
263C22×C43—24no—
264C22×C43—24no—
265C22×C43—22no—
266C22×C43—22no—
267C22×C43—42no—
268C22×C43—42no—
269C22×C43—42no—
270C22×C43—42no—
271C22×C43—42no—
272C22×C43—42no—
273C22×C43—42no—
274C22×C43—42no—
275C22×C43#38011yescharacteristic
276C22×C43#38512yes—
277C22×C43#38611yescharacteristic
278C22×C43#38812yes—
279C22×C43#39011yescharacteristic
280C22×C43#39211yescharacteristic
281C22×C43#39311yescharacteristic
282C22×C43#39412yes—
283C22×C43#39612yes—
284C22×C43#39711yescharacteristic
285C22×C43#39911yescharacteristic
286C22×C43C2×#9912yes—
287C22×C43#41012yes—
288C2×D43—44no—
289C2×D43—42no—
290C2×D43—84no—
291C2×D43—81no—
292C2×D43—81no—
293C2×D43—82no—
294C2×D43—84no—
295C4×C43—24no—
296C4×C43—42no—
297C4×C43—84no—
298Dic43—42no—
299Dic43—84no—
300Dic43—82no—
301C22×#99—432no—
302C2×#386—431no—
303C2×#380D4311yescharacteristic, complemented
304C2×#342—432no—
305C22⋊#95—431no—
306C2×C43—22no—
307C2×C43—21no—
308C2×C43—22no—
309C2×C43—22no—
310C2×C43—21no—
311C2×C43—22no—
312C2×C43—21no—
313C2×C43—21no—
314C2×C43#143911yescharacteristic
315C2×C43#179912yes—
316C2×C43#189811yescharacteristic
317C2×C43#189911yescharacteristic
318C2×C43#196412yes—
319D43—82no—
320C23×D4—431no—
321C24×C4C2×D4311yescharacteristic
322C22×C4⋊C4—21no—
323C22×C22⋊C4—432no—
324C22×C22⋊C4—431no—
325C22×C22⋊C4—432no—
326C22×C22⋊C4C2×D4312yes—
327C2×#99—864no—
328C2×#99—864no—
329C2×#99—864no—
330#386—862no—
331#386—861no—
332#386—861no—
333#380—24no—
334C2×#95—21no—
335C2×#95—432no—
336C2×#95—862no—
337#342—864no—
338C43#1104311yescharacteristic, complemented, Sylow
339C25—431no—
340C25C22×D4311yescharacteristic
341C22×D4—432no—
342C22×D4—432no—
343C22×D4—861no—
344C22×D4—862no—
345C22×D4—862no—
346C22×D4—861no—
347C22×D4—861no—
348C22×D4—862no—
349C22×D4—861no—
350C22×D4—862no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—44no—
355C23×C4—431no—
356C23×C4—432no—
357C23×C4—862no—
358C23×C4C4×D4312yes—
359C23×C4D17212yes—
360C23×C4C22⋊D4311yescharacteristic
361C23×C4C22⋊D4311yescharacteristic
362C2×C4⋊C4—24no—
363C2×C4⋊C4—44no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—434no—
370C2×C22⋊C4—862no—
371C2×C22⋊C4—862no—
372C2×C22⋊C4—862no—
373C2×C22⋊C4—862no—
374C2×C22⋊C4—861no—
375C2×C22⋊C4—862no—
376C2×C22⋊C4—862no—
377C2×C22⋊C4—862no—
378C2×C22⋊C4—861no—
379C2×C22⋊C4—862no—
380C2×C22⋊C4—862no—
381C2×C22⋊C4—1724no—
382C2×C22⋊C4C22⋊D4314yes—
383#99—8616no—
384#95—24no—
385#95—862no—
386#95—862no—
387#95—1724no—
388C24—42no—
389C24—42no—
390C24—432no—
391C24—862no—
392C24—862no—
393C24—861no—
394C24—861no—
395C24—1722no—
396C24—1722no—
397C24C2×C4×D4311yescharacteristic
398C24C2×D17211yescharacteristic
399C24#1062189812yes—
400C24D4×D4311yescharacteristic
401C24D4×D4312yes—
402C24#1062190011yescharacteristic
403C24Q8×D4311yescharacteristic
404C24#1062190211yescharacteristic
405C24#1062190212yes—
406C24C2×C22⋊D4311yescharacteristic
407C24C2×C22⋊D4312yes—
408C2×D4—864no—
409C2×D4—862no—
410C2×D4—862no—
411C2×D4—862no—
412C2×D4—864no—
413C2×D4—864no—
414C2×D4—862no—
415C2×D4—864no—
416C2×D4—1721no—
417C2×D4—1722no—
418C2×D4—1722no—
419C2×D4—1722no—
420C2×D4—1721no—
421C2×D4—1722no—
422C2×D4—1722no—
423C2×D4—1721no—
424C2×D4—1722no—
425C2×D4—1721no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—21no—
431C22×C4—24no—
432C22×C4—21no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—48no—
440C22×C4—48no—
441C22×C4—44no—
442C22×C4—44no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—432no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—862no—
449C22×C4—862no—
450C22×C4—864no—
451C22×C4—862no—
452C22×C4—864no—
453C22×C4—1724no—
454C22×C4—1724no—
455C22×C4—1722no—
456C22×C4—1722no—
457C22×C4—1722no—
458C22×C4—1722no—
459C22×C4(C2×D43)⋊C412yes—
460C22×C4(C2×D43)⋊C412yes—
461C4⋊C4—48no—
462C22⋊C4—24no—
463C22⋊C4—24no—
464C22⋊C4—42no—
465C22⋊C4—42no—
466C22⋊C4—864no—
467C22⋊C4—864no—
468C22⋊C4—1724no—
469C22⋊C4—1722no—
470C22⋊C4—1722no—
471C22⋊C4—1721no—
472C22⋊C4—1722no—
473C22⋊C4—1721no—
474C22⋊C4—1724no—
475C23—22no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—42no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—44no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—44no—
490C23—42no—
491C23—864no—
492C23—862no—
493C23—3442no—
494C23—3442no—
495C23—3444no—
496C23—1724no—
497C23—1724no—
498C23—1722no—
499C23—1721no—
500C23—1722no—
501C23—1722no—
502C23—1721no—
503C23C2×(C2×D43)⋊C411yescharacteristic
504C23C4⋊C4×D4311yescharacteristic
505C23#1306328311yescharacteristic
506C23C4×C22⋊D4312yes—
507C23#1306328712yes—
508C23#1306329312yes—
509C23#1306329411yescharacteristic
510C23#1306329611yescharacteristic
511C23#1306329712yes—
512C23#1306329912yes—
513C23#1306330012yes—
514C23#1306330011yescharacteristic
515C23#1306330111yescharacteristic
516C23#1306330112yes—
517C23#1306330312yes—
518C23#1306330511yescharacteristic
519C23#1306330811yescharacteristic
520C23#1306331012yes—
521C23#1306331012yes—
522C23#1306331411yescharacteristic
523C23#1306331412yes—
524C23#1306332012yes—
525C23#1306332111yescharacteristic
526D4—1722no—
527D4—1722no—
528D4—1724no—
529D4—1724no—
530D4—1722no—
531D4—1722no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—48no—
540C2×C4—48no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—44no—
544C2×C4—44no—
545C2×C4—44no—
546C2×C4—84no—
547C2×C4—84no—
548C2×C4—862no—
549C2×C4—864no—
550C2×C4—3442no—
551C2×C4—3442no—
552C2×C4—3444no—
553C2×C4—3444no—
554C2×C4—1728no—
555C2×C4—1722no—
556C2×C4—1724no—
557C2×C4—1722no—
558C2×C4—1722no—
559C2×C4—1722no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4#1306323914yescomplemented
563C22—21no—
564C22—21no—
565C22—22no—
566C22—22no—
567C22—21no—
568C22—22no—
569C22—22no—
570C22—21no—
571C22—22no—
572C22—22no—
573C22—22no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—24no—
579C22—24no—
580C22—22no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—3444no—
590C22—3444no—
591C22—3441no—
592C22—3441no—
593C22—3442no—
594C22—1724no—
595C22—1722no—
596C22#1458275611yescharacteristic
597C22#1458277012yes—
598C22#1458277811yescharacteristic
599C22#1458278912yes—
600C22#1458280011yescharacteristic
601C22#1458280711yescharacteristic
602C22#1458281011yescharacteristic
603C22#1458281612yes—
604C22#1458282112yes—
605C22#1458282511yescharacteristic
606C22#1458283411yescharacteristic
607C22C2×#1306323912yes—
608C22#1458287212yes—
609C4—24no—
610C4—42no—
611C4—84no—
612C4—3444no—
613C4—3442no—
614C4—1722no—
615C2—21no—
616C2—22no—
617C2—22no—
618C2—22no—
619C2—21no—
620C2—22no—
621C2—21no—
622C2—21no—
623C2—3442no—
624C2#1913283711yescharacteristic
625C2#1913458012yes—
626C2#1913504811yescharacteristic
627C2#1913505311yescharacteristic
628C2#1913543012yes—
subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC24×C43C22×C4
FrattiniC25C22×D43
FittingC2×C43×#380C2
socleC23×C43C2×C22⋊C4
prime radicalC23×C22⋊D43C22
cosocleC25×C43C23
hypercenterC2×#380D43
hypocenterC43#11043
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
3. C2×#14582665C2semidirect
4. #19132818C2semidirect
5. C2×C43×#380C2semidirect
9. C22×(C2×D43)⋊C4C4semidirect
17. C2×C43⋊#95C4semidirect
92. C23×D43C4⋊C4semidirect
145. C22×Dic43C4⋊C4semidirect
227. C2×C4×C43#99semidirect
303. C2×#380D43semidirect
338. C43#11043semidirect
562. C2×C4#13063239semidirect

Maximal subgroups

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

subgroupindex
C22×#130632392
C2×#145827782
C2×#145826652
#191328182
C2×C43×#3802
#1104343