Finite Group Databasebeta

← #24991969

Subgroups — #24991969

Order 11008.

1136 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
2#19134505C211yesmaximal, characteristic, complemented
3C2×#14582623C212yesmaximal, complemented
4#19132438C212yesmaximal, complemented
5C2×C43×#386C211yesmaximal, characteristic
6C23×C43⋊C8—21no—
7C2×C22⋊(C43⋊C8)—24no—
8C2×C22⋊(C43⋊C8)—21no—
9C2×C22⋊(C43⋊C8)—21no—
10C2×C22⋊(C43⋊C8)—21no—
11C2×C22⋊(C43⋊C8)C2212yes—
12C2×C22⋊(C43⋊C8)C2212yes—
13#14582623—24no—
14C23×D4×C43C411yescharacteristic
15C24×C4×C43C2211yescharacteristic
16C22×C22⋊C4×C43C411yescharacteristic
17C22×C22⋊C4×C43C411yescharacteristic
18C22×C22⋊C4×C43C2211yescharacteristic
19C43×#386—21no—
20C43×#386—21no—
21C43×#386—21no—
22C43×#386—21no—
23C2×#95×C43C411yescharacteristic
24C2×#95×C43C2211yescharacteristic
25C22×C43⋊C8—24no—
26C22×C43⋊C8—22no—
27C22×C43⋊C8—22no—
28C22×C43⋊C8—42no—
29C22×C43⋊C8—42no—
30C22⋊(C43⋊C8)—24no—
31C22⋊(C43⋊C8)—22no—
32C22⋊(C43⋊C8)—22no—
33C22⋊(C43⋊C8)—22no—
34C22⋊(C43⋊C8)—42no—
35C22⋊(C43⋊C8)—42no—
36C22⋊(C43⋊C8)D414yescomplemented
37C25×C43C2×C411yescharacteristic
38C25×C43C2×C411yescharacteristic
39C22×D4×C43—21no—
40C22×D4×C43—21no—
41C22×D4×C43—22no—
42C22×D4×C43—42no—
43C22×D4×C43—42no—
44C22×D4×C43C814yescomplemented
45C23×C4×C43—22no—
46C23×C4×C43—22no—
47C23×C4×C43—42no—
48C23×C4×C43—42no—
49C23×C4×C43C2×C411yescharacteristic
50C23×C4×C43C2×C411yescharacteristic
51C23×C4×C43C2×C411yescharacteristic
52C23×C4×C43C2×C411yescharacteristic
53C23×C4×C43D411yescharacteristic
54C23×C4×C43D411yescharacteristic
55C23×C4×C43D411yescharacteristic
56C23×C4×C43D411yescharacteristic
57C23×C4×C43C2311yescharacteristic
58C2×C22⋊C4×C43—21no—
59C2×C22⋊C4×C43—21no—
60C2×C22⋊C4×C43—21no—
61C2×C22⋊C4×C43—21no—
62C2×C22⋊C4×C43—22no—
63C2×C22⋊C4×C43—21no—
64C2×C22⋊C4×C43—21no—
65C2×C22⋊C4×C43—22no—
66C2×C22⋊C4×C43—42no—
67C2×C22⋊C4×C43—42no—
68#95×C43—21no—
69#95×C43—21no—
70#95×C43—21no—
71#95×C43—21no—
72C24×C43—22no—
73C24×C43—22no—
74C24×C43—22no—
75C24×C43—22no—
76C24×C43—21no—
77C24×C43—21no—
78C24×C43—22no—
79C24×C43—22no—
80C24×C43—41no—
81C24×C43—41no—
82C24×C43—41no—
83C24×C43—41no—
84C24×C43—41no—
85C24×C43—41no—
86C24×C43C22⋊C411yescharacteristic
87C24×C43C22⋊C411yescharacteristic
88C24×C43C2×C812yes—
89C24×C43C2×C812yescomplemented
90C24×C43M1612yes—
91C24×C43C22×C411yescharacteristic
92C2×D4×C43—24no—
93C2×D4×C43—24no—
94C2×D4×C43—48no—
95C2×D4×C43—48no—
96C2×D4×C43—42no—
97C2×D4×C43—42no—
98C2×D4×C43—42no—
99C2×D4×C43—42no—
100C22×C4×C43—22no—
101C22×C4×C43—21no—
102C22×C4×C43—21no—
103C22×C4×C43—22no—
104C22×C4×C43—22no—
105C22×C4×C43—21no—
106C22×C4×C43—22no—
107C22×C4×C43—22no—
108C22×C4×C43—21no—
109C22×C4×C43—22no—
110C22×C4×C43—22no—
111C22×C4×C43—21no—
112C22×C4×C43—21no—
113C22×C4×C43—21no—
114C22×C4×C43—22no—
115C22×C4×C43—22no—
116C22×C4×C43—21no—
117C22×C4×C43—22no—
118C22×C4×C43—41no—
119C22×C4×C43—41no—
120C22×C4×C43—41no—
121C22×C4×C43—41no—
122C22×C4×C43—41no—
123C22×C4×C43—41no—
124C22×C4×C43—41no—
125C22×C4×C43—41no—
126C22×C4×C43—41no—
127C22×C4×C43—41no—
128C22×C4×C43—41no—
129C22×C4×C43—41no—
130C22×C4×C43—41no—
131C22×C4×C43—48no—
132C22×C4×C43—48no—
133C22×C4×C43C22⋊C411yescharacteristic
134C22×C4×C43C22⋊C411yescharacteristic
135C22×C4×C43C2×C812yescomplemented
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D412yes—
139C22×C4×C43#4112yes—
140C22⋊C4×C43—42no—
141C22⋊C4×C43—42no—
142C22⋊C4×C43—42no—
143C22⋊C4×C43—41no—
144C22⋊C4×C43—42no—
145C22⋊C4×C43—41no—
146C22⋊C4×C43—42no—
147C2×C43⋊C8—24no—
148C2×C43⋊C8—48no—
149C2×C43⋊C8—42no—
150C2×C43⋊C8—42no—
151C2×C43⋊C8—42no—
152C2×C43⋊C8—42no—
153C2×C43⋊C8—42no—
154C23×C43—21no—
155C23×C43—21no—
156C23×C43—21no—
157C23×C43—21no—
158C23×C43—21no—
159C23×C43—21no—
160C23×C43—21no—
161C23×C43—21no—
162C23×C43—24no—
163C23×C43—24no—
164C23×C43—21no—
165C23×C43—21no—
166C23×C43—21no—
167C23×C43—21no—
168C23×C43—21no—
169C23×C43—21no—
170C23×C43—24no—
171C23×C43—24no—
172C23×C43—22no—
173C23×C43—24no—
174C23×C43—42no—
175C23×C43—42no—
176C23×C43—44no—
177C23×C43—44no—
178C23×C43—44no—
179C23×C43—44no—
180C23×C43—42no—
181C23×C43—42no—
182C23×C43—42no—
183C23×C43—42no—
184C23×C43—41no—
185C23×C43—41no—
186C23×C43—41no—
187C23×C43—41no—
188C23×C43—41no—
189C23×C43—41no—
190C23×C43—42no—
191C23×C43—82no—
192C23×C43—82no—
193C23×C43—82no—
194C23×C43—82no—
195C23×C43C22⋊C812yes—
196C23×C43C22⋊C812yes—
197C23×C43#9912yes—
198C23×C43#10012yes—
199C23×C43C2×C22⋊C411yescharacteristic
200C23×C43C4×D412yes—
201C23×C43C22×C811yescharacteristic
202C23×C43C2×M1611yescharacteristic
203C23×C43#13112yes—
204D4×C43—48no—
205D4×C43—48no—
206C2×C4×C43—24no—
207C2×C4×C43—24no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—22no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—42no—
219C2×C4×C43—42no—
220C2×C4×C43—44no—
221C2×C4×C43—44no—
222C2×C4×C43—44no—
223C2×C4×C43—42no—
224C2×C4×C43—42no—
225C2×C4×C43—42no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—42no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—82no—
236C2×C4×C43—82no—
237C2×C4×C43#9912yes—
238C2×C4×C43#12011yescharacteristic
239C2×C4×C43#12112yes—
240C2×C4×C43#12311yescharacteristic
241C43⋊C8—44no—
242C43⋊C8—82no—
243#9079—431nomaximal, Sylow
244C22×C43—22no—
245C22×C43—22no—
246C22×C43—22no—
247C22×C43—22no—
248C22×C43—22no—
249C22×C43—21no—
250C22×C43—21no—
251C22×C43—21no—
252C22×C43—21no—
253C22×C43—22no—
254C22×C43—22no—
255C22×C43—22no—
256C22×C43—22no—
257C22×C43—22no—
258C22×C43—22no—
259C22×C43—22no—
260C22×C43—22no—
261C22×C43—48no—
262C22×C43—48no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—42no—
268C22×C43—42no—
269C22×C43—42no—
270C22×C43—84no—
271C22×C43—84no—
272C22×C43—81no—
273C22×C43—81no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43#32314yescomplemented
277C22×C43#38611yescharacteristic
278C22×C43C2×C22⋊C811yescharacteristic
279C22×C43#40811yescharacteristic
280C22×C43C2×#9911yescharacteristic
281C22×C43C2×#9911yescharacteristic
282C22×C43C2×#10011yescharacteristic
283C22×C43#41311yescharacteristic
284C22×C43C8×D412yes—
285C22×C43#43512yes—
286C4×C43—21no—
287C4×C43—22no—
288C4×C43—22no—
289C4×C43—21no—
290C4×C43—41no—
291C4×C43—42no—
292C4×C43—81no—
293C4×C43—81no—
294C22×C22⋊C8—431no—
295C2×#386D4311yescharacteristic
296#1779—431no—
297C2×#323—432no—
298#1280—432no—
299C2×C43—22no—
300C2×C43—22no—
301C2×C43—24no—
302C2×C43—42no—
303C2×C43—82no—
304C2×C43C2×#32311yescharacteristic
305C2×C43#145911yescharacteristic
306C2×C43#146811yescharacteristic
307C2×C43#147111yescharacteristic
308C2×C43#186911yescharacteristic
309C2×C43#189811yescharacteristic
310C2×C43#190011yescharacteristic
311C23×D4Dic4311yescharacteristic
312C24×C4C2×D4311yescharacteristic
313C23×C8—861no—
314C22×C22⋊C4Dic4311yescharacteristic
315C22×C22⋊C4Dic4311yescharacteristic
316C22×C22⋊C4C2×D4311yescharacteristic
317C2×C22⋊C8—432no—
318C2×C22⋊C8—432no—
319C2×C22⋊C8—864no—
320C2×C22⋊C8—861no—
321C2×C22⋊C8—861no—
322C2×C22⋊C8—861no—
323#386—21no—
324#386—21no—
325#386—21no—
326#386—21no—
327C2×#95Dic4311yescharacteristic
328C2×#95C2×D4311yescharacteristic
329#323—864no—
330C43#907911yescharacteristic, complemented, Sylow
331C25C2×Dic4311yescharacteristic
332C25C2×Dic4311yescharacteristic
333C22×D4—22no—
334C22×D4—21no—
335C22×D4—21no—
336C22×D4—42no—
337C22×D4—42no—
338C22×D4C43⋊C814yescomplemented
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—42no—
342C23×C4—42no—
343C23×C4C2×Dic4311yescharacteristic
344C23×C4C2×Dic4311yescharacteristic
345C23×C4C2×Dic4311yescharacteristic
346C23×C4C2×Dic4311yescharacteristic
347C23×C4C22⋊D4311yescharacteristic
348C23×C4C22⋊D4311yescharacteristic
349C23×C4C22⋊D4311yescharacteristic
350C23×C4C22⋊D4311yescharacteristic
351C23×C4C22×D4311yescharacteristic
352C22×C8—864no—
353C22×C8—862no—
354C22×C8—862no—
355C22×C8—1722no—
356C22×C8—1722no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C22⋊C8—434no—
368C22⋊C8—864no—
369C22⋊C8—862no—
370C22⋊C8—862no—
371C22⋊C8—862no—
372C22⋊C8—1722no—
373C22⋊C8—1722no—
374#95—21no—
375#95—21no—
376#95—21no—
377#95—21no—
378C24—22no—
379C24—22no—
380C24—22no—
381C24—22no—
382C24—21no—
383C24—21no—
384C24—22no—
385C24—22no—
386C24—41no—
387C24—41no—
388C24—41no—
389C24—41no—
390C24—41no—
391C24—41no—
392C24C2×C43⋊C812yes—
393C24C2×C43⋊C812yescomplemented
394C24#1062187712yes—
395C24C22⋊Dic4311yescharacteristic
396C24C22⋊Dic4311yescharacteristic
397C24C22×Dic4311yescharacteristic
398C2×D4—24no—
399C2×D4—24no—
400C2×D4—48no—
401C2×D4—42no—
402C2×D4—42no—
403C2×D4—42no—
404C2×D4—42no—
405C2×D4—48no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—48no—
432C22×C4—48no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4C2×C43⋊C812yescomplemented
440C22×C4C22⋊Dic4311yescharacteristic
441C22×C4C22⋊Dic4311yescharacteristic
442C22×C4D4×D4312yes—
443C22×C4#1062190012yes—
444C22×C4C2×C22⋊D4311yescharacteristic
445C22×C4C2×C22⋊D4311yescharacteristic
446C2×C8—864no—
447C2×C8—1722no—
448C2×C8—1722no—
449C2×C8—1722no—
450C2×C8—1728no—
451C2×C8—1722no—
452C2×C8—1722no—
453C22⋊C4—42no—
454C22⋊C4—42no—
455C22⋊C4—42no—
456C22⋊C4—42no—
457C22⋊C4—41no—
458C22⋊C4—42no—
459C22⋊C4—41no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—21no—
466C23—21no—
467C23—21no—
468C23—21no—
469C23—21no—
470C23—21no—
471C23—21no—
472C23—24no—
473C23—24no—
474C23—21no—
475C23—24no—
476C23—24no—
477C23—21no—
478C23—22no—
479C23—24no—
480C23—42no—
481C23—42no—
482C23—44no—
483C23—44no—
484C23—44no—
485C23—44no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—42no—
496C23—41no—
497C23—82no—
498C23—82no—
499C23—82no—
500C23—82no—
501C23C22⋊(C43⋊C8)12yes—
502C23C22⋊(C43⋊C8)12yes—
503C23#1306324012yes—
504C23#1306324212yes—
505C23C2×C22⋊Dic4311yescharacteristic
506C23D4×Dic4312yes—
507C23C22×C43⋊C811yescharacteristic
508C23C2×#1062187711yescharacteristic
509C23#1306333212yes—
510D4—48no—
511D4—48no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—44no—
527C2×C4—44no—
528C2×C4—44no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—82no—
542C2×C4—82no—
543C2×C4#1306324012yes—
544C2×C4#1306329311yescharacteristic
545C2×C4#1306329712yes—
546C2×C4#1306330611yescharacteristic
547C8—3442no—
548C8—1724no—
549C22—22no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—22no—
566C22—48no—
567C22—48no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—84no—
576C22—84no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22#1458262314yescomplemented
582C22#1458277911yescharacteristic
583C22C2×C22⋊(C43⋊C8)11yescharacteristic
584C22#1458286611yescharacteristic
585C22C2×#1306324011yescharacteristic
586C22C2×#1306324011yescharacteristic
587C22C2×#1306324211yescharacteristic
588C22#1458288311yescharacteristic
589C22D4×C43⋊C812yes—
590C22#1458297112yes—
591C4—22no—
592C4—21no—
593C4—22no—
594C4—21no—
595C4—41no—
596C4—42no—
597C4—81no—
598C4—81no—
599C2—22no—
600C2—22no—
601C2—24no—
602C2—42no—
603C2—82no—
604C2C2×#1458262311yescharacteristic
605C2#1913291311yescharacteristic
606C2#1913294311yescharacteristic
607C2#1913295511yescharacteristic
608C2#1913488811yescharacteristic
609C2#1913504911yescharacteristic
610C2#1913505911yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic43
commutatorC23×C43C22×C8
FrattiniC23×C4C22×D43
FittingC2×C43×#386C2
socleC23×C43C2×C22⋊C4
prime radicalC23×D4×C43C4
cosocleC23×C4×C43C23
hypercenterC2×#386D43
hypocenterC43#9079
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊(C43⋊C8)C2semidirect
2. #19134505C2semidirect
3. C2×#14582623C2semidirect
4. #19132438C2semidirect
36. C22⋊(C43⋊C8)D4semidirect
44. C22×D4×C43C8semidirect
89. C24×C43C2×C8semidirect
135. C22×C4×C43C2×C8semidirect
276. C22×C43#323semidirect
330. C43#9079semidirect
338. C22×D4C43⋊C8semidirect
393. C24C2×C43⋊C8semidirect
439. C22×C4C2×C43⋊C8semidirect
581. C22#14582623semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊(C43⋊C8)2
#191345052
C2×#145826232
#191324382
C2×C43×#3862
#907943