Finite Group Databasebeta

← #25003521

Subgroups — #25003521

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×#13063240C212yesmaximal
2C2×#14582759C211yesmaximal, characteristic, complemented
3C2×#14582666C212yesmaximal, complemented
4#19132818C211yesmaximal, characteristic, complemented
5C2×C43×#386C211yesmaximal, characteristic
6C22×C4⋊Dic43—21no—
7C22×C22⋊Dic43C2212yes—
8C22×C22⋊Dic43C2212yes—
9C2×#13063240—24no—
10C2×#13063240—24no—
11C2×#13063240—24no—
12#14582759—24no—
13C2×C43⋊#95—21no—
14C2×C43⋊#95—22no—
15#14582666—24no—
16C23×D4×C43C2211yescharacteristic
17C24×C4×C43C2211yescharacteristic
18C22×C22⋊C4×C43C412yescomplemented
19C22×C22⋊C4×C43C2211yescharacteristic
20C43×#386—21no—
21C43×#386—22no—
22C43×#386—21no—
23C2×#95×C43C412yescomplemented
24C23×Dic43—22no—
25C23×Dic43—22no—
26C2×C4⋊Dic43—24no—
27C2×C4⋊Dic43—44no—
28C2×C22⋊Dic43—22no—
29C2×C22⋊Dic43—22no—
30C2×C22⋊Dic43—22no—
31C2×C22⋊Dic43—22no—
32C2×C22⋊Dic43—22no—
33C2×C22⋊Dic43—22no—
34C2×C22⋊Dic43—22no—
35C2×C22⋊Dic43—22no—
36C2×C22⋊Dic43—22no—
37C2×C22⋊Dic43—22no—
38C2×C22⋊Dic43D414yes—
39C2×C22⋊Dic43D414yes—
40#13063240—216no—
41C43⋊#95—24no—
42C43⋊#95—44no—
43C25×C43C2×C411yescharacteristic
44C25×C43C2311yescharacteristic
45C22×D4×C43—22no—
46C22×D4×C43—22no—
47C22×D4×C43—21no—
48C22×D4×C43—21no—
49C22×D4×C43—21no—
50C22×D4×C43—21no—
51C22×D4×C43—22no—
52C22×D4×C43—22no—
53C22×D4×C43D412yes—
54C22×D4×C43Q812yes—
55C23×C4×C43—22no—
56C23×C4×C43—22no—
57C23×C4×C43—44no—
58C23×C4×C43C2×C411yescharacteristic
59C23×C4×C43C2×C412yes—
60C23×C4×C43C2×C412yes—
61C23×C4×C43D411yescharacteristic
62C23×C4×C43D412yes—
63C23×C4×C43D411yescharacteristic
64C2×C22⋊C4×C43—22no—
65C2×C22⋊C4×C43—21no—
66C2×C22⋊C4×C43—21no—
67C2×C22⋊C4×C43—22no—
68C2×C22⋊C4×C43—22no—
69C2×C22⋊C4×C43—22no—
70C2×C22⋊C4×C43—44no—
71#95×C43—22no—
72#95×C43—22no—
73C24×C43—21no—
74C24×C43—21no—
75C24×C43—22no—
76C24×C43—22no—
77C24×C43—42no—
78C24×C43—42no—
79C24×C43—42no—
80C24×C43—42no—
81C24×C43C4⋊C412yescomplemented
82C24×C43C22×C411yescharacteristic
83C24×C43C2×D411yescharacteristic
84C24×C43C2×D411yescharacteristic
85C24×C43C2×D411yescharacteristic
86C24×C43C2×D412yes—
87C24×C43C2×D412yes—
88C24×C43C2×Q811yescharacteristic
89C24×C43#4111yescharacteristic
90C24×C43#4111yescharacteristic
91C24×C43#4112yes—
92C24×C43#4112yes—
93C2×D4×C43—24no—
94C2×D4×C43—22no—
95C2×D4×C43—22no—
96C2×D4×C43—22no—
97C2×D4×C43—22no—
98C2×D4×C43—24no—
99C2×D4×C43—24no—
100C2×D4×C43—24no—
101C2×D4×C43—41no—
102C2×D4×C43—42no—
103C2×D4×C43—42no—
104C2×D4×C43—42no—
105C2×D4×C43—41no—
106C2×D4×C43—42no—
107C2×D4×C43—42no—
108C2×D4×C43—41no—
109C2×D4×C43—42no—
110C2×D4×C43—41no—
111C22×C4×C43—24no—
112C22×C4×C43—24no—
113C22×C4×C43—24no—
114C22×C4×C43—21no—
115C22×C4×C43—22no—
116C22×C4×C43—21no—
117C22×C4×C43—24no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—24no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—24no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—42no—
127C22×C4×C43—42no—
128C22×C4×C43—42no—
129C22×C4×C43—42no—
130C22×C4×C43—42no—
131C22×C4×C43—48no—
132C22×C4×C43—48no—
133C22×C4×C43C22⋊C412yes—
134C22×C4×C43C22⋊C412yes—
135C22×C4×C43C4⋊C412yescomplemented
136C22×Dic43—24no—
137C22×Dic43—24no—
138C22×Dic43—44no—
139C22×Dic43—44no—
140C22×Dic43—44no—
141C22×Dic43—44no—
142C22×Dic43—42no—
143C22×Dic43—42no—
144C22×Dic43—42no—
145C22×Dic43—42no—
146C22⋊C4×C43—44no—
147C22⋊C4×C43—44no—
148C22⋊C4×C43—42no—
149C22⋊C4×C43—41no—
150C22⋊C4×C43—41no—
151C22⋊Dic43—24no—
152C22⋊Dic43—24no—
153C22⋊Dic43—24no—
154C22⋊Dic43—24no—
155C22⋊Dic43—42no—
156C22⋊Dic43—42no—
157C22⋊Dic43—42no—
158C22⋊Dic43—42no—
159C4⋊Dic43—48no—
160C23×C43—22no—
161C23×C43—22no—
162C23×C43—22no—
163C23×C43—22no—
164C23×C43—22no—
165C23×C43—22no—
166C23×C43—22no—
167C23×C43—24no—
168C23×C43—42no—
169C23×C43—42no—
170C23×C43—42no—
171C23×C43—42no—
172C23×C43—44no—
173C23×C43—42no—
174C23×C43—42no—
175C23×C43—42no—
176C23×C43—42no—
177C23×C43—44no—
178C23×C43—44no—
179C23×C43—44no—
180C23×C43—41no—
181C23×C43—42no—
182C23×C43—41no—
183C23×C43—42no—
184C23×C43—42no—
185C23×C43—82no—
186C23×C43—82no—
187C23×C43—84no—
188C23×C43C2×C22⋊C411yescharacteristic
189C23×C43C2×C4⋊C411yescharacteristic
190C23×C43#11711yescharacteristic
191C23×C43C4×D412yes—
192C23×C43C4×D412yes—
193C23×C43#12011yescharacteristic
194C23×C43#12012yes—
195C23×C43#12112yes—
196C23×C43#12112yes—
197C23×C43#12112yes—
198C23×C43#12111yescharacteristic
199C23×C43#12111yescharacteristic
200C23×C43C22⋊Q812yes—
201C23×C43C22⋊Q812yes—
202C23×C43C22⋊Q811yescharacteristic
203C23×C43C22⋊Q811yescharacteristic
204C23×C43#12311yescharacteristic
205C23×C43#12312yes—
206C23×C43#12312yes—
207C23×C43#12412yes—
208C23×C43#12411yescharacteristic
209C23×C43#12612yes—
210C23×C43#12711yescharacteristic
211D4×C43—42no—
212D4×C43—42no—
213D4×C43—44no—
214D4×C43—44no—
215D4×C43—42no—
216D4×C43—42no—
217C2×C4×C43—24no—
218C2×C4×C43—24no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—24no—
223C2×C4×C43—22no—
224C2×C4×C43—22no—
225C2×C4×C43—22no—
226C2×C4×C43—48no—
227C2×C4×C43—48no—
228C2×C4×C43—42no—
229C2×C4×C43—42no—
230C2×C4×C43—41no—
231C2×C4×C43—42no—
232C2×C4×C43—41no—
233C2×C4×C43—42no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43—84no—
237C2×C4×C43#9914yescomplemented
238C2×Dic43—44no—
239C2×Dic43—44no—
240C2×Dic43—48no—
241C2×Dic43—44no—
242C2×Dic43—44no—
243C2×Dic43—84no—
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—44no—
276C22×C43—42no—
277C22×C43—84no—
278C22×C43—84no—
279C22×C43—81no—
280C22×C43—81no—
281C22×C43—82no—
282C22×C43#38011yescharacteristic
283C22×C43#38512yes—
284C22×C43#38611yescharacteristic
285C22×C43#38812yes—
286C22×C43#39011yescharacteristic
287C22×C43#39211yescharacteristic
288C22×C43#39311yescharacteristic
289C22×C43#39412yes—
290C22×C43#39612yes—
291C22×C43#39711yescharacteristic
292C22×C43#39911yescharacteristic
293C22×C43C2×#9912yes—
294C22×C43#41012yes—
295C4×C43—24no—
296C4×C43—42no—
297C4×C43—42no—
298C4×C43—82no—
299Dic43—84no—
300Dic43—84no—
301C22×#99—432no—
302C2×#386D4311yescharacteristic
303C2×#380—431no—
304C2×#342—432no—
305C22⋊#95—431no—
306C2×C43—21no—
307C2×C43—22no—
308C2×C43—22no—
309C2×C43—22no—
310C2×C43—21no—
311C2×C43—22no—
312C2×C43—21no—
313C2×C43—21no—
314C2×C43—82no—
315C2×C43#143911yescharacteristic
316C2×C43#179912yes—
317C2×C43#189811yescharacteristic
318C2×C43#189911yescharacteristic
319C2×C43#196412yes—
320C23×D4C2×D4311yescharacteristic
321C24×C4C2×D4311yescharacteristic
322C22×C4⋊C4—861no—
323C22×C22⋊C4—432no—
324C22×C22⋊C4—432no—
325C22×C22⋊C4Dic4312yescomplemented
326C22×C22⋊C4C2×D4311yescharacteristic
327C2×#99—864no—
328C2×#99—864no—
329C2×#99—864no—
330#386—21no—
331#386—22no—
332#386—21no—
333#380—864no—
334C2×#95—861no—
335C2×#95—862no—
336C2×#95Dic4312yescomplemented
337#342—864no—
338C43#1104311yescharacteristic, complemented, Sylow
339C25C2×Dic4311yescharacteristic
340C25C22×D4311yescharacteristic
341C22×D4—21no—
342C22×D4—21no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—21no—
348C22×D4—21no—
349C22×D4Dic8612yes—
350C22×D4D17212yes—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—44no—
354C23×C4—862no—
355C23×C4—862no—
356C23×C4C2×Dic4311yescharacteristic
357C23×C4C2×Dic4312yes—
358C23×C4C2×Dic4312yes—
359C23×C4C22⋊D4311yescharacteristic
360C23×C4C22⋊D4312yes—
361C23×C4C22⋊D4311yescharacteristic
362C2×C4⋊C4—864no—
363C2×C4⋊C4—1724no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—434no—
372C2×C22⋊C4—434no—
373C2×C22⋊C4—862no—
374C2×C22⋊C4—862no—
375C2×C22⋊C4—862no—
376C2×C22⋊C4—862no—
377C2×C22⋊C4—862no—
378C2×C22⋊C4—862no—
379C2×C22⋊C4—862no—
380C2×C22⋊C4—862no—
381C2×C22⋊C4—862no—
382C2×C22⋊C4—862no—
383#99—8616no—
384#95—22no—
385#95—22no—
386#95—864no—
387#95—1724no—
388C24—21no—
389C24—21no—
390C24—22no—
391C24—22no—
392C24—42no—
393C24—42no—
394C24—42no—
395C24—42no—
396C24C4⋊Dic4312yescomplemented
397C24C2×Dic8611yescharacteristic
398C24C2×D17211yescharacteristic
399C24#1062189811yescharacteristic
400C24#1062189811yescharacteristic
401C24D4×D4312yes—
402C24D4×D4312yes—
403C24#1062190012yes—
404C24#1062190012yes—
405C24C22×Dic4311yescharacteristic
406C24C2×C22⋊D4311yescharacteristic
407C24C2×C22⋊D4311yescharacteristic
408C2×D4—24no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—24no—
412C2×D4—24no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—24no—
416C2×D4—41no—
417C2×D4—42no—
418C2×D4—42no—
419C2×D4—42no—
420C2×D4—41no—
421C2×D4—42no—
422C2×D4—42no—
423C2×D4—41no—
424C2×D4—42no—
425C2×D4—41no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—24no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—24no—
436C22×C4—21no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—22no—
440C22×C4—24no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—48no—
445C22×C4—48no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—864no—
449C22×C4—864no—
450C22×C4—1724no—
451C22×C4—1724no—
452C22×C4—1724no—
453C22×C4—1724no—
454C22×C4—1722no—
455C22×C4—1722no—
456C22×C4—1722no—
457C22×C4—1722no—
458C22×C4C4⋊Dic4312yescomplemented
459C22×C4C22⋊Dic4312yes—
460C22×C4C22⋊Dic4312yes—
461C4⋊C4—1728no—
462C22⋊C4—44no—
463C22⋊C4—42no—
464C22⋊C4—41no—
465C22⋊C4—41no—
466C22⋊C4—44no—
467C22⋊C4—864no—
468C22⋊C4—864no—
469C22⋊C4—864no—
470C22⋊C4—864no—
471C22⋊C4—1722no—
472C22⋊C4—1722no—
473C22⋊C4—1722no—
474C22⋊C4—1722no—
475C23—22no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—24no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—44no—
491C23—42no—
492C23—44no—
493C23—44no—
494C23—44no—
495C23—42no—
496C23—41no—
497C23—42no—
498C23—42no—
499C23—41no—
500C23—82no—
501C23—82no—
502C23—84no—
503C23C2×C22⋊Dic4311yescharacteristic
504C23C2×C4⋊Dic4311yescharacteristic
505C23#1306328411yescharacteristic
506C23D4×Dic4312yes—
507C23D4×Dic4312yes—
508C23#1306329311yescharacteristic
509C23#1306329512yes—
510C23#1306329612yes—
511C23#1306329712yes—
512C23#1306329812yes—
513C23#1306329911yescharacteristic
514C23#1306329911yescharacteristic
515C23#1306330212yes—
516C23#1306330212yes—
517C23#1306330411yescharacteristic
518C23#1306330411yescharacteristic
519C23#1306330611yescharacteristic
520C23#1306330712yes—
521C23#1306330912yes—
522C23#1306331112yes—
523C23#1306331211yescharacteristic
524C23#1306331812yes—
525C23#1306332111yescharacteristic
526D4—42no—
527D4—42no—
528D4—44no—
529D4—44no—
530D4—42no—
531D4—42no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—48no—
542C2×C4—48no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—84no—
552C2×C4—3442no—
553C2×C4—3442no—
554C2×C4—3444no—
555C2×C4—3444no—
556C2×C4—3444no—
557C2×C4—1724no—
558C2×C4—1724no—
559C2×C4—1728no—
560C2×C4—1724no—
561C2×C4—1724no—
562C2×C4#1306324014yescomplemented
563C22—21no—
564C22—21no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—21no—
569C22—22no—
570C22—21no—
571C22—22no—
572C22—22no—
573C22—22no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—24no—
578C22—22no—
579C22—24no—
580C22—22no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—44no—
590C22—42no—
591C22—84no—
592C22—84no—
593C22—81no—
594C22—81no—
595C22—82no—
596C22#1458275911yescharacteristic
597C22#1458277412yes—
598C22#1458277911yescharacteristic
599C22#1458279212yes—
600C22#1458280211yescharacteristic
601C22#1458280811yescharacteristic
602C22#1458281111yescharacteristic
603C22#1458281512yes—
604C22#1458282212yes—
605C22#1458282411yescharacteristic
606C22#1458283511yescharacteristic
607C22C2×#1306324012yes—
608C22#1458287312yes—
609C4—24no—
610C4—42no—
611C4—42no—
612C4—82no—
613C4—3444no—
614C4—3444no—
615C2—21no—
616C2—22no—
617C2—22no—
618C2—22no—
619C2—21no—
620C2—22no—
621C2—21no—
622C2—21no—
623C2—82no—
624C2#1913284011yescharacteristic
625C2#1913458312yes—
626C2#1913504911yescharacteristic
627C2#1913505411yescharacteristic
628C2#1913543212yes—
subgroupG/H
centerC23C2×C22⋊Dic43
commutatorC24×C43C22×C4
FrattiniC25C22×D43
FittingC2×C43×#386C2
socleC23×C43C2×C22⋊C4
prime radicalC23×D4×C43C22
cosocleC25×C43C23
hypercenterC2×#386D43
hypocenterC43#11043
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C2×#14582759C2semidirect
3. C2×#14582666C2semidirect
4. #19132818C2semidirect
18. C22×C22⋊C4×C43C4semidirect
23. C2×#95×C43C4semidirect
81. C24×C43C4⋊C4semidirect
135. C22×C4×C43C4⋊C4semidirect
237. C2×C4×C43#99semidirect
325. C22×C22⋊C4Dic43semidirect
336. C2×#95Dic43semidirect
338. C43#11043semidirect
396. C24C4⋊Dic43semidirect
458. C22×C4C4⋊Dic43semidirect
562. C2×C4#13063240semidirect

Maximal subgroups

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

subgroupindex
C22×#130632402
C2×#145827592
C2×#145826662
#191328182
C2×C43×#3862
#1104343