Finite Group Databasebeta

← #24991279

Subgroups — #24991279

Order 11008.

934 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143617C211yesmaximal, characteristic, complemented
2C4×#13063294C211yesmaximal, characteristic
3#19134505C211yesmaximal, characteristic, complemented
4#19132911C211yesmaximal, characteristic, complemented
5#19132442C211yesmaximal, characteristic, complemented
6#19132441C211yesmaximal, characteristic, complemented
7C43×#1779C211yesmaximal, characteristic, complemented
8C2×#13063294C411yescharacteristic
9C2×C4×C22⋊D43—21no—
10C2×C4×C22⋊D43C2211yescharacteristic
11C8×C22⋊D43—22no—
12(C22⋊D43)⋊C8—22no—
13#14582949—21no—
14C2×C22⋊(C43⋊C8)—22no—
15C2×C22⋊(C43⋊C8)C2211yescharacteristic
16C2×C22⋊(C43⋊C8)C2211yescharacteristic
17C22⋊C8×D43—21no—
18#14582778—21no—
19#14582778C411yescharacteristic
20#14582772—21no—
21#14582772C411yescharacteristic
22#14582755C411yescharacteristic
23C4×C22⋊Dic43—21no—
24C4×C22⋊Dic43C2211yescharacteristic
25#14582624—21no—
26#14582622—21no—
27C24×C4×C43C2211yescharacteristic
28C2×C22⋊C8×C43—22no—
29C2×C22⋊C8×C43C2211yescharacteristic
30C2×C22⋊C8×C43C2211yescharacteristic
31C22×C22⋊D43—21no—
32C22×C22⋊D43C2×C411yescharacteristic
33C22×C4×D43D411yescharacteristic
34C22×C43⋊C8—21no—
35C22×C43⋊C8D412yescomplemented
36C2×C8×D43—22no—
37#13063294—22no—
38#13063294C814yescomplemented
39C4×C22⋊D43—21no—
40C4×C22⋊D43—21no—
41C4×C22⋊D43—21no—
42C4×C22⋊D43—21no—
43C4×C22⋊D43—44no—
44C2×Dic43⋊C4—21no—
45C2×Dic43⋊C4D411yescharacteristic
46C2×C22⋊Dic43—21no—
47C2×C22⋊Dic43—21no—
48C2×C22⋊Dic43—21no—
49C2×C22⋊Dic43C2×C411yescharacteristic
50C2×C22⋊Dic43C2×C411yescharacteristic
51C2×C22⋊Dic43C2×C411yescharacteristic
52C2×(C2×D43)⋊C4—21no—
53C2×(C2×D43)⋊C4D411yescharacteristic
54C2×C4×Dic43—21no—
55C2×C4×Dic43D411yescharacteristic
56Dic43⋊C8—22no—
57C22⋊(C43⋊C8)—21no—
58C22⋊(C43⋊C8)—21no—
59C22⋊(C43⋊C8)—21no—
60C22⋊(C43⋊C8)—21no—
61C22⋊(C43⋊C8)—44no—
62(C2×D43)⋊C8—22no—
63C8×Dic43—22no—
64C43⋊#95—21no—
65C43⋊#95—21no—
66C43⋊#95—21no—
67C25×C43C2×C411yescharacteristic
68C23×C4×C43—21no—
69C23×C4×C43—21no—
70C23×C4×C43—21no—
71C23×C4×C43—21no—
72C23×C4×C43—21no—
73C23×C4×C43—21no—
74C23×C4×C43—44no—
75C23×C4×C43C2×C411yescharacteristic
76C23×C4×C43C2311yescharacteristic
77C22×C8×C43—21no—
78C22×C8×C43D412yescomplemented
79C22⋊C8×C43—21no—
80C22⋊C8×C43—21no—
81C22⋊C8×C43—21no—
82C22⋊C8×C43—21no—
83C22⋊C8×C43—44no—
84C24×C43—21no—
85C24×C43—21no—
86C24×C43—21no—
87C24×C43—21no—
88C24×C43—21no—
89C24×C43—21no—
90C24×C43—42no—
91C24×C43—42no—
92C24×C43C2×C812yescomplemented
93C24×C43C22×C411yescharacteristic
94C23×D43C22⋊C411yescharacteristic
95C22×C4×C43—24no—
96C22×C4×C43—24no—
97C22×C4×C43—24no—
98C22×C4×C43—21no—
99C22×C4×C43—21no—
100C22×C4×C43—21no—
101C22×C4×C43—42no—
102C22×C4×C43—42no—
103C22×C4×C43—42no—
104C22×C4×C43—42no—
105C22×C4×C43—42no—
106C22×C4×C43—42no—
107C22×C4×C43—42no—
108C22×C4×C43—42no—
109C22×C4×C43—42no—
110C22×C4×C43—42no—
111C22×C4×C43—42no—
112C22×C4×C43—41no—
113C22×C4×C43—41no—
114C22×C4×C43—41no—
115C22×C4×C43—41no—
116C22×C4×C43C2×D411yescharacteristic
117C22×C4×C43C2×D411yescharacteristic
118C22×C4×C43C2×D411yescharacteristic
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43#4111yescharacteristic
121C22×C4×C43#4111yescharacteristic
122C2×C22⋊D43—21no—
123C2×C22⋊D43—21no—
124C2×C22⋊D43—21no—
125C2×C22⋊D43—21no—
126C2×C22⋊D43—24no—
127C2×C22⋊D43—42no—
128C2×C22⋊D43—42no—
129C2×C22⋊D43C2×C812yes—
130C2×C22⋊D43M1612yes—
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43C22⋊C411yescharacteristic
134C22×Dic43C22⋊C411yescharacteristic
135C22×Dic43C22⋊C411yescharacteristic
136C2×C4×D43—21no—
137C2×C4×D43—21no—
138C2×C4×D43—42no—
139C2×C8×C43—22no—
140C2×C8×C43—42no—
141C2×C8×C43—42no—
142C2×C8×C43—41no—
143C22⋊Dic43—24no—
144C22⋊Dic43—21no—
145C22⋊Dic43—21no—
146C22⋊Dic43—21no—
147C22⋊Dic43—21no—
148C22⋊Dic43—21no—
149C22⋊Dic43—42no—
150C22⋊Dic43—42no—
151C22⋊Dic43C2×C812yescomplemented
152(C2×D43)⋊C4—21no—
153(C2×D43)⋊C4—21no—
154(C2×D43)⋊C4—42no—
155Dic43⋊C4—21no—
156Dic43⋊C4—21no—
157Dic43⋊C4—42no—
158C4×Dic43—21no—
159C4×Dic43—21no—
160C4×Dic43—42no—
161C2×C43⋊C8—22no—
162C2×C43⋊C8—42no—
163C2×C43⋊C8—42no—
164C2×C43⋊C8—41no—
165C8×D43—82no—
166C23×C43—22no—
167C23×C43—22no—
168C23×C43—22no—
169C23×C43—22no—
170C23×C43—22no—
171C23×C43—22no—
172C23×C43—22no—
173C23×C43—22no—
174C23×C43—22no—
175C23×C43—41no—
176C23×C43—44no—
177C23×C43—41no—
178C23×C43—41no—
179C23×C43—41no—
180C23×C43—41no—
181C23×C43—41no—
182C23×C43—41no—
183C23×C43—41no—
184C23×C43—44no—
185C23×C43—44no—
186C23×C43—44no—
187C23×C43—41no—
188C23×C43—41no—
189C23×C43—41no—
190C23×C43—41no—
191C23×C43C2×C22⋊C411yescharacteristic
192C23×C43C4×D411yescharacteristic
193C23×C43C4×D411yescharacteristic
194C23×C43C22×C811yescharacteristic
195C23×C43C2×M1611yescharacteristic
196C23×C43#13111yescharacteristic
197C23×C43#13111yescharacteristic
198C22×D43—21no—
199C22×D43—21no—
200C22×D43—41no—
201C22×D43—41no—
202C22×D43C22⋊C812yescomplemented
203C2×C4×C43—22no—
204C2×C4×C43—22no—
205C2×C4×C43—22no—
206C2×C4×C43—22no—
207C2×C4×C43—22no—
208C2×C4×C43—22no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—41no—
212C2×C4×C43—44no—
213C2×C4×C43—44no—
214C2×C4×C43—44no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—44no—
220C2×C4×C43#12011yescharacteristic
221C2×C4×C43#12111yescharacteristic
222C2×C4×C43#12111yescharacteristic
223C2×C4×C43#12311yescharacteristic
224C22⋊D43—22no—
225C22⋊D43—22no—
226C22⋊D43—22no—
227C22⋊D43—22no—
228C22⋊D43—48no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—22no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43C22⋊C812yescomplemented
242C4×D43—42no—
243C4×D43—81no—
244C8×C43—42no—
245C8×C43—81no—
246C43⋊C8—42no—
247C43⋊C8—81no—
248#8965—431nomaximal, Sylow
249C22×C43—21no—
250C22×C43—21no—
251C22×C43—21no—
252C22×C43—21no—
253C22×C43—21no—
254C22×C43—21no—
255C22×C43—24no—
256C22×C43—24no—
257C22×C43—24no—
258C22×C43—41no—
259C22×C43—41no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43—42no—
263C22×C43—42no—
264C22×C43—42no—
265C22×C43—42no—
266C22×C43—42no—
267C22×C43—42no—
268C22×C43—42no—
269C22×C43—42no—
270C22×C43—42no—
271C22×C43—42no—
272C22×C43—42no—
273C22×C43—42no—
274C22×C43#38611yescharacteristic
275C22×C43C2×C22⋊C811yescharacteristic
276C22×C43#40811yescharacteristic
277C22×C43C8×D411yescharacteristic
278C22×C43C8×D411yescharacteristic
279C22×C43#43511yescharacteristic
280C22×C43#43511yescharacteristic
281C2×D43—22no—
282C2×D43—41no—
283C2×D43—41no—
284C2×D43—42no—
285C2×D43—81no—
286C4×C43—21no—
287C4×C43—21no—
288C4×C43—21no—
289C4×C43—42no—
290C4×C43B(4,𝔽2)12yes—
291Dic43—22no—
292Dic43—42no—
293Dic43—41no—
294Dic43—41no—
295Dic43—81no—
296#2972—431no—
297C4×#120—431no—
298#1779—431no—
299#1779D4311yescharacteristic, complemented
300#1459—431no—
301#1282—431no—
302#1282—431no—
303C2×C43—21no—
304C2×C43—21no—
305C2×C43—21no—
306C2×C43—21no—
307C2×C43—21no—
308C2×C43—21no—
309C2×C43—44no—
310C2×C43#186911yescharacteristic
311C2×C43#188911yescharacteristic
312C2×C43#189111yescharacteristic
313D43—42no—
314C24×C4C2×D4311yescharacteristic
315C2×#120—431no—
316C2×C4×D4—431no—
317C2×C4×D4—861no—
318C8×D4—862no—
319C8×D4—862no—
320#431—861no—
321C2×C22⋊C8—22no—
322C2×C22⋊C8—431no—
323C2×C22⋊C8—431no—
324C2×C22⋊C8—861no—
325C2×C22⋊C8—862no—
326C2×C22⋊C8C2×D4311yescharacteristic
327C2×C22⋊C8C2×D4311yescharacteristic
328#386—431no—
329#386—861no—
330#385—431no—
331#385—861no—
332#379—431no—
333C4×C22⋊C4—431no—
334C4×C22⋊C4—861no—
335#324—861no—
336#323—861no—
337C43#896511yescharacteristic, complemented, Sylow
338C25C4×D4311yescharacteristic
339C22×D4—431no—
340C22×D4—861no—
341C23×C4—21no—
342C23×C4—21no—
343C23×C4—21no—
344C23×C4—21no—
345C23×C4—21no—
346C23×C4—21no—
347C23×C4—44no—
348C23×C4—431no—
349C23×C4C4×D4311yescharacteristic
350C23×C4C22×D4311yescharacteristic
351C22×C8—21no—
352C22×C8—432no—
353C22×C8—862no—
354C22×C8—861no—
355C22×C8C22⋊D4312yescomplemented
356#120—434no—
357#120—862no—
358C4×D4—861no—
359C4×D4—861no—
360C4×D4—861no—
361C4×D4—861no—
362C4×D4—1724no—
363C2×C4⋊C4—431no—
364C2×C4⋊C4—861no—
365C2×C22⋊C4—431no—
366C2×C22⋊C4—431no—
367C2×C22⋊C4—431no—
368C2×C22⋊C4—431no—
369C2×C22⋊C4—861no—
370C2×C22⋊C4—861no—
371C2×C22⋊C4—861no—
372C2×C22⋊C4—861no—
373C2×C42—431no—
374C2×C42—861no—
375C4⋊C8—862no—
376C22⋊C8—21no—
377C22⋊C8—21no—
378C22⋊C8—21no—
379C22⋊C8—21no—
380C22⋊C8—44no—
381C22⋊C8—862no—
382C22⋊C8—861no—
383C22⋊C8—861no—
384C22⋊C8—861no—
385C22⋊C8—861no—
386C22⋊C8—1724no—
387C4×C8—862no—
388#95—861no—
389#95—861no—
390#95—861no—
391C24—21no—
392C24—21no—
393C24—21no—
394C24—21no—
395C24—21no—
396C24—21no—
397C24—42no—
398C24—42no—
399C24—431no—
400C24C8×D4312yescomplemented
401C24C2×C4×D4311yescharacteristic
402C2×D4—432no—
403C2×D4—432no—
404C2×D4—861no—
405C2×D4—861no—
406C2×D4—861no—
407C2×D4—861no—
408C2×D4—864no—
409C2×D4—1722no—
410C2×D4—1722no—
411C22×C4—24no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—431no—
433C22×C4—431no—
434C22×C4—431no—
435C22×C4—861no—
436C22×C4—861no—
437C22×C4—861no—
438C22×C4—861no—
439C22×C4—1722no—
440C22×C4#1062189811yescharacteristic
441C22×C4D4×D4311yescharacteristic
442C22×C4D4×D4311yescharacteristic
443C22×C4D4×D4311yescharacteristic
444C22×C4#1062190011yescharacteristic
445C22×C4C2×C22⋊D4311yescharacteristic
446C2×C8—22no—
447C2×C8—42no—
448C2×C8—42no—
449C2×C8—41no—
450C2×C8—862no—
451C2×C8—3442no—
452C2×C8—1722no—
453C2×C8—1721no—
454C2×C8—1722no—
455C4⋊C4—861no—
456C4⋊C4—861no—
457C4⋊C4—1722no—
458C22⋊C4—432no—
459C22⋊C4—864no—
460C22⋊C4—861no—
461C22⋊C4—861no—
462C22⋊C4—861no—
463C22⋊C4—861no—
464C22⋊C4—861no—
465C22⋊C4—861no—
466C22⋊C4—861no—
467C22⋊C4—1722no—
468C22⋊C4—1722no—
469C22⋊C4—1722no—
470C42—861no—
471C42—861no—
472C42—1722no—
473C23—22no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—41no—
483C23—44no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—44no—
492C23—44no—
493C23—44no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—432no—
499C23—861no—
500C23—861no—
501C23—1721no—
502C23—1721no—
503C23C22⋊C4×D4311yescharacteristic
504C23(C22⋊D43)⋊C411yescharacteristic
505C23C4×C22⋊D4311yescharacteristic
506C23C2×C8×D4311yescharacteristic
507C23M16×D4311yescharacteristic
508C23#1306333111yescharacteristic
509C23#1306333311yescharacteristic
510D4—862no—
511D4—862no—
512D4—862no—
513D4—862no—
514D4—1728no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—44no—
525C2×C4—44no—
526C2×C4—44no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—44no—
532C2×C4—432no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—862no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—3441no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1722no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4#1306329311yescharacteristic
548C2×C4#1306329611yescharacteristic
549C2×C4#1306329811yescharacteristic
550C2×C4#1306330711yescharacteristic
551C8—42no—
552C8—81no—
553C8—3441no—
554C8—1722no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—24no—
562C22—24no—
563C22—24no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—42no—
569C22—42no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—42no—
580C22—862no—
581C22—3441no—
582C22—1722no—
583C22—1721no—
584C22—1721no—
585C22#1458277511yescharacteristic
586C22C22⋊C8×D4311yescharacteristic
587C22#1458286411yescharacteristic
588C22(C22⋊D43)⋊C811yescharacteristic
589C22C8×C22⋊D4311yescharacteristic
590C22#1458296811yescharacteristic
591C22#1458297311yescharacteristic
592C4—21no—
593C4—21no—
594C4—21no—
595C4—42no—
596C4—862no—
597C4—3441no—
598C4—1722no—
599C4—1721no—
600C4—1721no—
601C4#1458308512yes—
602C2—21no—
603C2—21no—
604C2—21no—
605C2—21no—
606C2—21no—
607C2—21no—
608C2—44no—
609C2—1722no—
610C2#1913488411yescharacteristic
611C2#1913500011yescharacteristic
612C2#1913501011yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC23×C43C22×C8
FrattiniC23×C4C22×D43
FittingC43×#1779C2
socleC22×C43#386
prime radicalC2×#13063294C4
cosocleC23×C4×C43C23
hypercenter#1779D43
hypocenterC43#8965
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
1. #19143617C2semidirect
3. #19134505C2semidirect
4. #19132911C2semidirect
5. #19132442C2semidirect
6. #19132441C2semidirect
7. C43×#1779C2semidirect
35. C22×C43⋊C8D4semidirect
38. #13063294C8semidirect
78. C22×C8×C43D4semidirect
92. C24×C43C2×C8semidirect
151. C22⋊Dic43C2×C8semidirect
202. C22×D43C22⋊C8semidirect
241. C2×Dic43C22⋊C8semidirect
299. #1779D43semidirect
337. C43#8965semidirect
355. C22×C8C22⋊D43semidirect
400. C24C8×D43semidirect

Maximal subgroups

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

subgroupindex
#191436172
C4×#130632942
#191345052
#191329112
#191324422
#191324412
C43×#17792
#896543