Finite Group Databasebeta

← #24991972

Subgroups — #24991972

Order 11008.

736 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582949C211yesmaximal, characteristic, complemented
2C2×#14582791C211yesmaximal, characteristic
3#19134661C211yesmaximal, characteristic, complemented
4C2×#14582622C211yesmaximal, characteristic
5C2×#14582622C211yesmaximal, characteristic
6#19132438C211yesmaximal, characteristic, complemented
7C43×#1280C211yesmaximal, characteristic, complemented
8C22×C4⋊Dic43C411yescharacteristic
9C22×(C2×D43)⋊C4C411yescharacteristic
10C22×(C2×D43)⋊C4C411yescharacteristic
11C22×(C2×D43)⋊C4C2211yescharacteristic
12C22×C4×Dic43C2211yescharacteristic
13#14582949—22no—
14#14582949—22no—
15C2×Dic43⋊C8—21no—
16C2×C22⋊(C43⋊C8)C2211yescharacteristic
17C2×C22⋊(C43⋊C8)C2211yescharacteristic
18C2×C8×Dic43—21no—
19#14582791—21no—
20#14582791—21no—
21#14582791—21no—
22#14582791—21no—
23C2×C43⋊#95C411yescharacteristic
24#14582653—21no—
25#14582653—21no—
26#14582622—22no—
27#14582622—22no—
28C2×C22⋊C8×C43C2211yescharacteristic
29C2×C22⋊C8×C43C2211yescharacteristic
30C2×#95×C43C2211yescharacteristic
31C24×D43C2×C411yescharacteristic
32C23×Dic43C2×C411yescharacteristic
33C23×Dic43C2×C411yescharacteristic
34C23×Dic43C2×C411yescharacteristic
35C22×C43⋊C8—21no—
36C22×C43⋊C8—21no—
37C2×C4⋊Dic43—21no—
38C2×C4⋊Dic43—21no—
39C2×C4⋊Dic43—42no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4—22no—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4—21no—
45C2×(C2×D43)⋊C4—21no—
46C2×(C2×D43)⋊C4—21no—
47C2×(C2×D43)⋊C4—21no—
48C2×(C2×D43)⋊C4—21no—
49C2×(C2×D43)⋊C4—21no—
50C2×(C2×D43)⋊C4—21no—
51C2×(C2×D43)⋊C4—42no—
52C2×(C2×D43)⋊C4C814yescomplemented
53C2×C4×Dic43—21no—
54C2×C4×Dic43—21no—
55C2×C4×Dic43—21no—
56C2×C4×Dic43—21no—
57C2×C4×Dic43D411yescharacteristic
58C2×C4×Dic43D411yescharacteristic
59C2×C4×Dic43D411yescharacteristic
60C2×C4×Dic43D411yescharacteristic
61Dic43⋊C8—24no—
62C22⋊(C43⋊C8)—21no—
63C22⋊(C43⋊C8)—21no—
64C22⋊(C43⋊C8)—21no—
65C22⋊(C43⋊C8)D412yes—
66C8×Dic43—24no—
67C43⋊#95—21no—
68C43⋊#95—21no—
69C23×C4×C43C2×C411yescharacteristic
70C23×C4×C43C2×C411yescharacteristic
71C23×C4×C43C2311yescharacteristic
72C22×C8×C43—21no—
73C22×C8×C43—21no—
74C22⋊C8×C43—21no—
75C22⋊C8×C43—21no—
76C22⋊C8×C43—21no—
77C22⋊C8×C43D412yes—
78#95×C43—21no—
79#95×C43—21no—
80C24×C43C22×C411yescharacteristic
81C23×D43—21no—
82C23×D43—21no—
83C23×D43—21no—
84C23×D43—21no—
85C23×D43—21no—
86C23×D43—21no—
87C23×D43—41no—
88C23×D43—41no—
89C23×D43—41no—
90C23×D43—41no—
91C23×D43C2×C812yes—
92C22×C4×C43—21no—
93C22×C4×C43—21no—
94C22×C4×C43—21no—
95C22×C4×C43—21no—
96C22×C4×C43—21no—
97C22×C4×C43—41no—
98C22×C4×C43—41no—
99C22×C4×C43—41no—
100C22×C4×C43—41no—
101C22×C4×C43—41no—
102C22×C4×C43—41no—
103C22×C4×C43C2×C812yes—
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43C2×D411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43C2×D411yescharacteristic
108C22×C4×C43#4111yescharacteristic
109C22×C4×C43#4111yescharacteristic
110C22×Dic43—22no—
111C22×Dic43—21no—
112C22×Dic43—21no—
113C22×Dic43—21no—
114C22×Dic43—21no—
115C22×Dic43—21no—
116C22×Dic43—21no—
117C22×Dic43—21no—
118C22×Dic43—21no—
119C22×Dic43—21no—
120C22×Dic43—41no—
121C22×Dic43—41no—
122C22×Dic43—41no—
123C22×Dic43C22⋊C411yescharacteristic
124C22×Dic43C22⋊C411yescharacteristic
125C22×Dic43C22⋊C411yescharacteristic
126C22×Dic43C22⋊C411yescharacteristic
127C22×Dic43C2×C812yes—
128C22×Dic43M1612yes—
129C2×C8×C43—22no—
130C2×C8×C43—41no—
131C2×C8×C43—41no—
132C2×C8×C43—41no—
133C2×C8×C43—41no—
134C2×C8×C43—41no—
135(C2×D43)⋊C4—24no—
136(C2×D43)⋊C4—24no—
137(C2×D43)⋊C4—42no—
138(C2×D43)⋊C4—41no—
139(C2×D43)⋊C4—41no—
140(C2×D43)⋊C4—41no—
141(C2×D43)⋊C4—41no—
142(C2×D43)⋊C4—42no—
143C4⋊Dic43—42no—
144C4⋊Dic43—42no—
145C4×Dic43—21no—
146C4×Dic43—21no—
147C4×Dic43—21no—
148C4×Dic43—21no—
149C4×Dic43—21no—
150C4×Dic43—21no—
151C4×Dic43—21no—
152C4×Dic43—21no—
153C2×C43⋊C8—22no—
154C2×C43⋊C8—41no—
155C2×C43⋊C8—41no—
156C2×C43⋊C8—41no—
157C2×C43⋊C8—41no—
158C2×C43⋊C8—41no—
159C23×C43—21no—
160C23×C43—21no—
161C23×C43—21no—
162C23×C43—21no—
163C23×C43C2×C22⋊C411yescharacteristic
164C23×C43C4×D411yescharacteristic
165C23×C43C4×D411yescharacteristic
166C23×C43C22×C811yescharacteristic
167C23×C43C2×M1611yescharacteristic
168C23×C43#13111yescharacteristic
169C23×C43#13111yescharacteristic
170C22×D43—22no—
171C22×D43—22no—
172C22×D43—22no—
173C22×D43—42no—
174C22×D43—42no—
175C22×D43—41no—
176C22×D43—41no—
177C22×D43—41no—
178C22×D43—41no—
179C22×D43—41no—
180C22×D43—41no—
181C22×D43—41no—
182C22×D43—41no—
183C22×D43—42no—
184C22×D43—42no—
185C22×D43—81no—
186C22×D43—81no—
187C22×D43—81no—
188C22×D43—81no—
189C22×D43—81no—
190C22×D43—81no—
191C22×D43—81no—
192C22×D43—81no—
193C2×C4×C43—21no—
194C2×C4×C43—21no—
195C2×C4×C43—21no—
196C2×C4×C43—21no—
197C2×C4×C43—22no—
198C2×C4×C43—41no—
199C2×C4×C43—41no—
200C2×C4×C43—41no—
201C2×C4×C43—41no—
202C2×C4×C43—42no—
203C2×C4×C43—41no—
204C2×C4×C43—41no—
205C2×C4×C43—42no—
206C2×C4×C43—41no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—81no—
210C2×C4×C43—81no—
211C2×C4×C43#12011yescharacteristic
212C2×C4×C43#12111yescharacteristic
213C2×C4×C43#12111yescharacteristic
214C2×C4×C43#12311yescharacteristic
215C2×Dic43—21no—
216C2×Dic43—21no—
217C2×Dic43—21no—
218C2×Dic43—21no—
219C2×Dic43—21no—
220C2×Dic43—21no—
221C2×Dic43—22no—
222C2×Dic43—22no—
223C2×Dic43—22no—
224C2×Dic43—22no—
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—42no—
229C2×Dic43—42no—
230C2×Dic43—41no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233C2×Dic43—81no—
234C2×Dic43—81no—
235C2×Dic43C22⋊C812yes—
236C2×Dic43C22⋊C812yes—
237C2×Dic43#10012yes—
238C8×C43—42no—
239C8×C43—81no—
240C43⋊C8—42no—
241C43⋊C8—81no—
242#9080—431nomaximal, Sylow
243C22×C43—21no—
244C22×C43—21no—
245C22×C43—21no—
246C22×C43—21no—
247C22×C43—21no—
248C22×C43—21no—
249C22×C43—21no—
250C22×C43—21no—
251C22×C43—21no—
252C22×C43—21no—
253C22×C43—21no—
254C22×C43—21no—
255C22×C43#38611yescharacteristic
256C22×C43C2×C22⋊C811yescharacteristic
257C22×C43#40811yescharacteristic
258C22×C43#41011yescharacteristic
259C22×C43#41011yescharacteristic
260C22×C43C2×#10011yescharacteristic
261C22×C43#41311yescharacteristic
262C22×C43C8×D411yescharacteristic
263C22×C43C8×D411yescharacteristic
264C22×C43#43511yescharacteristic
265C22×C43#43511yescharacteristic
266C2×D43—42no—
267C2×D43—42no—
268C2×D43—42no—
269C2×D43—82no—
270C2×D43—82no—
271C2×D43—81no—
272C2×D43—81no—
273C2×D43—81no—
274C2×D43—81no—
275C2×D43—82no—
276C2×D43—82no—
277C4×C43—21no—
278C4×C43—21no—
279C4×C43—21no—
280C4×C43—21no—
281C4×C43—42no—
282C4×C43—81no—
283Dic43—22no—
284Dic43—22no—
285Dic43—22no—
286Dic43—41no—
287Dic43—81no—
288C2×#431—431no—
289C2×#388—431no—
290#1817—431no—
291C2×#323—431no—
292C2×#323—431no—
293#1280—431no—
294#1280D4311yescharacteristic, complemented
295C2×C43—21no—
296C2×C43—21no—
297C2×C43—21no—
298C2×C43—21no—
299C2×C43#145811yescharacteristic
300C2×C43#146011yescharacteristic
301C2×C43#146911yescharacteristic
302C2×C43#147311yescharacteristic
303C2×C43#186911yescharacteristic
304C2×C43#189911yescharacteristic
305C2×C43#190011yescharacteristic
306D43—82no—
307C22×C4⋊C4—431no—
308C22×C22⋊C4—431no—
309C22×C22⋊C4—431no—
310C22×C22⋊C4—431no—
311C22×C42—431no—
312#431—862no—
313#431—862no—
314C2×C4⋊C8—861no—
315C2×C22⋊C8—431no—
316C2×C22⋊C8—431no—
317C2×C22⋊C8C2×D4311yescharacteristic
318C2×C22⋊C8C2×D4311yescharacteristic
319C2×C4×C8—861no—
320#388—861no—
321#388—861no—
322#388—861no—
323#388—861no—
324C2×#95—431no—
325C2×#95C2×D4311yescharacteristic
326#336—861no—
327#336—861no—
328#323—862no—
329#323—862no—
330C43#908011yescharacteristic, complemented, Sylow
331C25—431no—
332C23×C4—431no—
333C23×C4—431no—
334C23×C4—431no—
335C23×C4C4×D4311yescharacteristic
336C23×C4C4×D4311yescharacteristic
337C23×C4C22×D4311yescharacteristic
338C22×C8—21no—
339C22×C8—21no—
340C22×C8—861no—
341C22×C8—861no—
342C2×C4⋊C4—861no—
343C2×C4⋊C4—861no—
344C2×C4⋊C4—1722no—
345C2×C22⋊C4—434no—
346C2×C22⋊C4—862no—
347C2×C22⋊C4—861no—
348C2×C22⋊C4—861no—
349C2×C22⋊C4—861no—
350C2×C22⋊C4—861no—
351C2×C22⋊C4—861no—
352C2×C22⋊C4—861no—
353C2×C22⋊C4—861no—
354C2×C22⋊C4—861no—
355C2×C22⋊C4—861no—
356C2×C22⋊C4—861no—
357C2×C22⋊C4—1722no—
358C2×C42—431no—
359C2×C42—431no—
360C2×C42—431no—
361C2×C42—431no—
362C2×C42—861no—
363C2×C42—861no—
364C2×C42—861no—
365C2×C42—861no—
366C4⋊C8—864no—
367C22⋊C8—21no—
368C22⋊C8—21no—
369C22⋊C8—21no—
370C22⋊C8—432no—
371C22⋊C8—861no—
372C22⋊C8—861no—
373C22⋊C8—861no—
374C22⋊C8D17212yes—
375C4×C8—864no—
376#95—21no—
377#95—21no—
378#95—861no—
379#95—861no—
380C24—432no—
381C24—861no—
382C24—861no—
383C24—861no—
384C24—861no—
385C24—861no—
386C24—861no—
387C24—1721no—
388C24—1721no—
389C24—1721no—
390C24—1721no—
391C24C2×C4×D4311yescharacteristic
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—41no—
403C22×C4—431no—
404C22×C4—431no—
405C22×C4—431no—
406C22×C4—432no—
407C22×C4—432no—
408C22×C4—431no—
409C22×C4—862no—
410C22×C4—861no—
411C22×C4—861no—
412C22×C4—861no—
413C22×C4—861no—
414C22×C4—861no—
415C22×C4—861no—
416C22×C4—861no—
417C22×C4—861no—
418C22×C4—861no—
419C22×C4—1721no—
420C22×C4—1721no—
421C22×C4—1721no—
422C22×C4C8×D4312yes—
423C22×C4C2×D17211yescharacteristic
424C22×C4#1062189811yescharacteristic
425C22×C4D4×D4311yescharacteristic
426C22×C4D4×D4311yescharacteristic
427C22×C4D4×D4311yescharacteristic
428C22×C4#1062190211yescharacteristic
429C2×C8—22no—
430C2×C8—41no—
431C2×C8—41no—
432C2×C8—41no—
433C2×C8—41no—
434C2×C8—41no—
435C2×C8—862no—
436C2×C8—1721no—
437C2×C8—1721no—
438C2×C8—1721no—
439C2×C8—1721no—
440C2×C8—1721no—
441C4⋊C4—1722no—
442C4⋊C4—1722no—
443C22⋊C4—864no—
444C22⋊C4—864no—
445C22⋊C4—1722no—
446C22⋊C4—1722no—
447C22⋊C4—1721no—
448C22⋊C4—1721no—
449C22⋊C4—1721no—
450C22⋊C4—1721no—
451C42—861no—
452C42—861no—
453C42—861no—
454C42—861no—
455C42—861no—
456C42—861no—
457C42—861no—
458C42—861no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—862no—
464C23—862no—
465C23—862no—
466C23—3441no—
467C23—3441no—
468C23—3441no—
469C23—3441no—
470C23—3441no—
471C23—3441no—
472C23—3441no—
473C23—3441no—
474C23—1722no—
475C23—1722no—
476C23—1722no—
477C23—1722no—
478C23—1721no—
479C23—1721no—
480C23—1721no—
481C23—1721no—
482C23—1721no—
483C23—1721no—
484C23—1721no—
485C23—1721no—
486C23C22⋊C4×D4311yescharacteristic
487C23#1306328711yescharacteristic
488C23C4×D17211yescharacteristic
489C23C2×C8×D4311yescharacteristic
490C23M16×D4311yescharacteristic
491C23#1306333111yescharacteristic
492C23#1306333311yescharacteristic
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—81no—
510C2×C4—81no—
511C2×C4—432no—
512C2×C4—432no—
513C2×C4—432no—
514C2×C4—861no—
515C2×C4—861no—
516C2×C4—861no—
517C2×C4—862no—
518C2×C4—862no—
519C2×C4—862no—
520C2×C4—862no—
521C2×C4—861no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—3441no—
528C2×C4—3441no—
529C2×C4—1722no—
530C2×C4—1722no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4#1306329511yescharacteristic
535C2×C4#1306329811yescharacteristic
536C2×C4#1306330011yescharacteristic
537C2×C4#1306331011yescharacteristic
538C8—42no—
539C8—81no—
540C8—3441no—
541C8—1722no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—3442no—
555C22—3442no—
556C22—3442no—
557C22—3442no—
558C22—3441no—
559C22—3441no—
560C22—3441no—
561C22—3441no—
562C22—1722no—
563C22—1722no—
564C22—1722no—
565C22#1458277711yescharacteristic
566C22C22⋊C8×D4311yescharacteristic
567C22#1458286411yescharacteristic
568C22#1458287111yescharacteristic
569C22#1458287111yescharacteristic
570C22#100×D4311yescharacteristic
571C22#1458288211yescharacteristic
572C22#1458296411yescharacteristic
573C22C8×D17211yescharacteristic
574C22#1458296911yescharacteristic
575C22#1458297211yescharacteristic
576C4—21no—
577C4—21no—
578C4—21no—
579C4—21no—
580C4—42no—
581C4—81no—
582C4—862no—
583C4—862no—
584C4—862no—
585C4—3441no—
586C4—1721no—
587C2—21no—
588C2—21no—
589C2—21no—
590C2—21no—
591C2—3442no—
592C2#1913290811yescharacteristic
593C2#1913291411yescharacteristic
594C2#1913294511yescharacteristic
595C2#1913296311yescharacteristic
596C2#1913488611yescharacteristic
597C2#1913505211yescharacteristic
598C2#1913505711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC23×C43C22×C8
FrattiniC23×C4C22×D43
FittingC43×#1280C2
socleC23×C43C2×C22⋊C4
prime radicalC24×D43C2×C4
cosocleC23×C4×C43C23
hypercenter#1280D43
hypocenterC43#9080
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
1. C2×#14582949C2semidirect
3. #19134661C2semidirect
6. #19132438C2semidirect
7. C43×#1280C2semidirect
52. C2×(C2×D43)⋊C4C8semidirect
294. #1280D43semidirect
330. C43#9080semidirect

Maximal subgroups

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

subgroupindex
C2×#145829492
C2×#145827912
#191346612
C2×#145826222
#191324382
C43×#12802
#908043