Finite Group Databasebeta

← #24991127

Subgroups — #24991127

Order 11008.

768 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C8×D43C211yesmaximal, characteristic, complemented
2C4×#13063300C211yesmaximal, characteristic
3C4×(C2×D43)⋊C8C211yesmaximal, characteristic, complemented
4C2×#14582628C211yesmaximal, characteristic, complemented
5C2×#14582626C211yesmaximal, characteristic, complemented
6#19132436C211yesmaximal, characteristic, complemented
7C43×#1279C211yesmaximal, characteristic, complemented
8C22×C8×D43—21no—
9C2×#13063300C411yescharacteristic
10C2×C4×D172—21no—
11C2×C4×D172C2211yescharacteristic
12C2×C42×D43C2211yescharacteristic
13C2×C4⋊(C43⋊C8)C2211yescharacteristic
14C2×Dic43⋊C8—21no—
15C4⋊C8×D43—22no—
16C4⋊C8×D43—22no—
17C2×(C2×D43)⋊C8—21no—
18C2×C4×C43⋊C8C2211yescharacteristic
19#14582800C411yescharacteristic
20#14582798C411yescharacteristic
21#14582791—21no—
22#14582777—21no—
23#14582756C411yescharacteristic
24C4×(C2×D43)⋊C4—21no—
25#14582653—21no—
26#14582628—22no—
27#14582626—22no—
28C2×C4⋊C8×C43C2211yescharacteristic
29C2×C4×C8×C43C2211yescharacteristic
30C4×C4⋊C4×C43C2211yescharacteristic
31C22×D172—21no—
32C22×D172C2×C411yescharacteristic
33C22×C4×D43—21no—
34C22×C4×D43C2×C411yescharacteristic
35C22×C4×D43D411yescharacteristic
36C22×C4×D43D411yescharacteristic
37C22×C43⋊C8—21no—
38C22×C43⋊C8—21no—
39C2×C8×D43—24no—
40C2×C8×D43—42no—
41C2×C8×D43—42no—
42#13063300—22no—
43#13063300C814yescomplemented
44C4×D172—21no—
45C4×D172—21no—
46C4×D172—21no—
47C4×D172—21no—
48C4×D172—42no—
49C4×D172—42no—
50C2×C4⋊Dic43—21no—
51C2×C4⋊Dic43C2×C411yescharacteristic
52C2×(C2×D43)⋊C4—21no—
53C2×(C2×D43)⋊C4—21no—
54C2×(C2×D43)⋊C4—21no—
55C2×(C2×D43)⋊C4—21no—
56C2×(C2×D43)⋊C4—21no—
57C2×C4×Dic43C2×C411yescharacteristic
58C2×C4×Dic43D411yescharacteristic
59C2×C4×Dic43D411yescharacteristic
60C42×D43—21no—
61C42×D43—21no—
62C42×D43—21no—
63C42×D43—21no—
64C4⋊(C43⋊C8)—21no—
65C4⋊(C43⋊C8)D412yescomplemented
66Dic43⋊C8—24no—
67(C2×D43)⋊C8—24no—
68C4×C43⋊C8—21no—
69C4×C43⋊C8—21no—
70C43⋊#95—21no—
71C43⋊#95—21no—
72C22×C8×C43—21no—
73C22×C8×C43—21no—
74C2×C4⋊C4×C43C2×C411yescharacteristic
75C2×C4⋊C4×C43C2×C411yescharacteristic
76C2×C42×C43—21no—
77C2×C42×C43C2311yescharacteristic
78C4⋊C8×C43—21no—
79C4⋊C8×C43D412yescomplemented
80C4×C8×C43—21no—
81C4×C8×C43—21no—
82#95×C43—21no—
83C23×D43—21no—
84C23×D43C22⋊C411yescharacteristic
85C22×C4×C43—21no—
86C22×C4×C43—21no—
87C22×C4×C43C22×C411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×Dic43—21no—
91C22×Dic43C22⋊C411yescharacteristic
92C22×Dic43C22⋊C411yescharacteristic
93C22×Dic43C22⋊C411yescharacteristic
94C2×D172—21no—
95C2×D172—24no—
96C2×D172—21no—
97C2×D172—21no—
98C2×D172—21no—
99C2×D172—21no—
100C2×D172—42no—
101C2×D172—42no—
102C2×D172C2×C812yescomplemented
103C2×C4×D43—21no—
104C2×C4×D43—21no—
105C2×C4×D43—21no—
106C2×C4×D43—21no—
107C2×C4×D43—21no—
108C2×C4×D43—21no—
109C2×C4×D43—21no—
110C2×C4×D43—21no—
111C2×C4×D43—21no—
112C2×C4×D43—21no—
113C2×C4×D43—22no—
114C2×C4×D43—41no—
115C2×C4×D43—41no—
116C2×C4×D43—41no—
117C2×C4×D43—41no—
118C2×C4×D43—41no—
119C2×C4×D43—41no—
120C2×C4×D43—41no—
121C2×C4×D43C2×C812yes—
122C2×C4×D43M1612yes—
123C2×C4×D43D812yes—
124C2×C4×D43SD1612yes—
125C2×C8×C43—22no—
126C2×C8×C43—22no—
127C2×C8×C43—41no—
128C2×C8×C43—41no—
129C2×C8×C43—41no—
130C2×C8×C43—41no—
131C4⋊C4×C43—21no—
132C4⋊C4×C43—21no—
133C4⋊C4×C43—21no—
134C4⋊C4×C43C2×C812yescomplemented
135C42×C43—41no—
136C42×C43—41no—
137C42×C43C2×D411yescharacteristic
138C42×C43C2×D411yescharacteristic
139C42×C43#4111yescharacteristic
140C42×C43#4111yescharacteristic
141(C2×D43)⋊C4—24no—
142(C2×D43)⋊C4—42no—
143(C2×D43)⋊C4—41no—
144(C2×D43)⋊C4—41no—
145(C2×D43)⋊C4—42no—
146(C2×D43)⋊C4—42no—
147C4⋊Dic43—21no—
148C4⋊Dic43—21no—
149C4⋊Dic43—42no—
150C4×Dic43—21no—
151C4×Dic43—21no—
152C4×Dic43—21no—
153C4×Dic43—21no—
154C4×Dic43—21no—
155C4×Dic43—21no—
156C2×C43⋊C8—22no—
157C2×C43⋊C8—22no—
158C2×C43⋊C8—41no—
159C2×C43⋊C8—41no—
160C2×C43⋊C8—41no—
161C2×C43⋊C8—41no—
162C8×D43—48no—
163C23×C43C2×C22⋊C411yescharacteristic
164C22×D43—21no—
165C22×D43—21no—
166C22×D43—21no—
167C22×D43—21no—
168C22×D43—22no—
169C22×D43—41no—
170C22×D43—41no—
171C22×D43—41no—
172C22×D43—41no—
173C22×D43—41no—
174C22×D43—41no—
175C22×D43C22⋊C812yes—
176C22×D43#10212yes—
177C22×D43#10412yes—
178C2×C4×C43—21no—
179C2×C4×C43—21no—
180C2×C4×C43—22no—
181C2×C4×C43—41no—
182C2×C4×C43—41no—
183C2×C4×C43—41no—
184C2×C4×C43—41no—
185C2×C4×C43—41no—
186C2×C4×C43C4×D411yescharacteristic
187C2×C4×C43C4×D411yescharacteristic
188C2×C4×C43#12011yescharacteristic
189C2×C4×C43#12111yescharacteristic
190C2×C4×C43#12111yescharacteristic
191C2×C4×C43#12311yescharacteristic
192C2×C4×C43C22×C811yescharacteristic
193C2×C4×C43C2×M1611yescharacteristic
194C2×C4×C43#13111yescharacteristic
195C2×C4×C43#13111yescharacteristic
196C2×C4×C43C2×D811yescharacteristic
197C2×C4×C43C2×SD1611yescharacteristic
198C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
199C2×C4×C43#13711yescharacteristic
200C2×Dic43—21no—
201C2×Dic43—21no—
202C2×Dic43—21no—
203C2×Dic43—21no—
204C2×Dic43—21no—
205C2×Dic43—21no—
206C2×Dic43—21no—
207C2×Dic43—41no—
208C2×Dic43—41no—
209C2×Dic43—41no—
210C2×Dic43C22⋊C812yes—
211C2×Dic43#10212yes—
212D172—22no—
213D172—22no—
214D172—48no—
215D172—41no—
216D172—41no—
217C4×D43—22no—
218C4×D43—22no—
219C4×D43—22no—
220C4×D43—22no—
221C4×D43—22no—
222C4×D43—22no—
223C4×D43—22no—
224C4×D43—22no—
225C4×D43—42no—
226C4×D43—42no—
227C4×D43—81no—
228C4×D43—81no—
229C4×D43—81no—
230C4×D43—81no—
231C8×C43—42no—
232C8×C43—42no—
233C43⋊C8—42no—
234C43⋊C8—42no—
235#8939—431nomaximal, Sylow
236C22×C43#38611yescharacteristic
237C22×C43C2×C22⋊C811yescharacteristic
238C22×C43#40811yescharacteristic
239C22×C43C2×#10211yescharacteristic
240C22×C43#41711yescharacteristic
241C22×C43C2×#10411yescharacteristic
242C22×C43#42111yescharacteristic
243C2×D43—22no—
244C2×D43—22no—
245C2×D43—22no—
246C2×D43—22no—
247C2×D43—22no—
248C2×D43—22no—
249C2×D43—42no—
250C2×D43—42no—
251C2×D43—42no—
252C2×D43—81no—
253C2×D43—81no—
254C2×D43—81no—
255C2×D43—81no—
256C2×D43D4⋊C814yescomplemented
257C4×C43—21no—
258C4×C43—21no—
259C4×C43—42no—
260C4×C43—81no—
261C4×C43C8×D411yescharacteristic
262C4×C43C8×D411yescharacteristic
263C4×C43#43511yescharacteristic
264C4×C43#43511yescharacteristic
265C4×C43#44711yescharacteristic
266C4×C43#44811yescharacteristic
267C4×C43#48011yescharacteristic
268C4×C43#48111yescharacteristic
269Dic43—22no—
270Dic43—22no—
271Dic43—41no—
272Dic43—81no—
273C22×C4⋊C8—431no—
274C4×#121—431no—
275C4×C22⋊C8—431no—
276C2×D4⋊C8—431no—
277C2×D4⋊C8—431no—
278#1279—431no—
279#1279D4311yescharacteristic, complemented
280C2×C43C2×D4⋊C811yescharacteristic
281C2×C43#147711yescharacteristic
282C2×C43#148011yescharacteristic
283C2×C43#148311yescharacteristic
284C2×C43#186911yescharacteristic
285C2×C43#187111yescharacteristic
286C2×C43#187411yescharacteristic
287D43—24no—
288D43—82no—
289C23×C8—861no—
290C2×#121—431no—
291C2×C4×D4—431no—
292C2×C4×D4—861no—
293C22×C42—431no—
294C2×C4⋊C8—431no—
295C2×C4⋊C8—862no—
296C2×C4⋊C8—861no—
297C2×C4⋊C8—862no—
298C2×C4⋊C8C2×D4311yescharacteristic
299C2×C22⋊C8—861no—
300C2×C4×C8—431no—
301C2×C4×C8C2×D4311yescharacteristic
302#390—431no—
303#389—431no—
304#388—861no—
305#386—861no—
306#380—431no—
307C4×C4⋊C4C2×D4311yescharacteristic
308C4×C22⋊C4—861no—
309#336—861no—
310D4⋊C8—862no—
311D4⋊C8—862no—
312C43#893911yescharacteristic, complemented, Sylow
313C22×D4—431no—
314C22×D4—861no—
315C23×C4—431no—
316C23×C4—431no—
317C23×C4—431no—
318C23×C4—861no—
319C22×C8—21no—
320C22×C8—21no—
321C22×C8—864no—
322C22×C8—861no—
323C22×C8—861no—
324C22×C8—1722no—
325C22×C8—1722no—
326#121—434no—
327#121—862no—
328C4×D4—861no—
329C4×D4—861no—
330C4×D4—861no—
331C4×D4—861no—
332C4×D4—1722no—
333C4×D4—1722no—
334C2×C4⋊C4—431no—
335C2×C4⋊C4—861no—
336C2×C4⋊C4C4×D4311yescharacteristic
337C2×C4⋊C4C4×D4311yescharacteristic
338C2×C22⋊C4—861no—
339C2×C22⋊C4—861no—
340C2×C22⋊C4—861no—
341C2×C22⋊C4—861no—
342C2×C22⋊C4—861no—
343C2×C42—21no—
344C2×C42—431no—
345C2×C42—431no—
346C2×C42—431no—
347C2×C42—861no—
348C2×C42—861no—
349C2×C42—861no—
350C2×C42—861no—
351C2×C42C22×D4311yescharacteristic
352C4⋊C8—21no—
353C4⋊C8—432no—
354C4⋊C8—864no—
355C4⋊C8—861no—
356C4⋊C8D17212yescomplemented
357C22⋊C8—864no—
358C4×C8—21no—
359C4×C8—21no—
360C4×C8—861no—
361C4×C8—861no—
362#95—21no—
363#95—861no—
364#95—861no—
365C24—431no—
366C24—861no—
367C2×D4—432no—
368C2×D4—864no—
369C2×D4—861no—
370C2×D4—861no—
371C2×D4—861no—
372C2×D4—861no—
373C2×D4—861no—
374C2×D4—1722no—
375C2×D4—1722no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—431no—
379C22×C4—431no—
380C22×C4—432no—
381C22×C4—432no—
382C22×C4—432no—
383C22×C4—432no—
384C22×C4—431no—
385C22×C4—862no—
386C22×C4—861no—
387C22×C4—861no—
388C22×C4—861no—
389C22×C4—861no—
390C22×C4—861no—
391C22×C4—861no—
392C22×C4—861no—
393C22×C4—861no—
394C22×C4—861no—
395C22×C4—861no—
396C22×C4—861no—
397C22×C4—1721no—
398C22×C4—1721no—
399C22×C4—1721no—
400C22×C4—1721no—
401C22×C4—1721no—
402C22×C4—1721no—
403C22×C4—1721no—
404C22×C4C2×C4×D4311yescharacteristic
405C22×C4D4×D4311yescharacteristic
406C22×C4D4×D4311yescharacteristic
407C2×C8—22no—
408C2×C8—22no—
409C2×C8—41no—
410C2×C8—41no—
411C2×C8—41no—
412C2×C8—41no—
413C2×C8—862no—
414C2×C8—862no—
415C2×C8—1728no—
416C2×C8—1721no—
417C2×C8—1721no—
418C2×C8—1721no—
419C2×C8—1721no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—861no—
424C4⋊C4—861no—
425C4⋊C4—1722no—
426C4⋊C4C8×D4312yescomplemented
427C22⋊C4—864no—
428C22⋊C4—1722no—
429C22⋊C4—1722no—
430C22⋊C4—1722no—
431C22⋊C4—1721no—
432C22⋊C4—1721no—
433C42—41no—
434C42—41no—
435C42—861no—
436C42—861no—
437C42—861no—
438C42—861no—
439C42—861no—
440C42—861no—
441C42C2×D17211yescharacteristic
442C42#1062189811yescharacteristic
443C42D4×D4311yescharacteristic
444C42#1062190211yescharacteristic
445C23—432no—
446C23—432no—
447C23—432no—
448C23—861no—
449C23—861no—
450C23—861no—
451C23—861no—
452C23—862no—
453C23—1721no—
454C23—1721no—
455C23—1721no—
456C23—1721no—
457C23—1721no—
458C23—1721no—
459C23C22⋊C4×D4311yescharacteristic
460D4—862no—
461D4—862no—
462D4—1728no—
463D4—1721no—
464D4—1721no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—22no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—432no—
474C2×C4—432no—
475C2×C4—861no—
476C2×C4—861no—
477C2×C4—861no—
478C2×C4—861no—
479C2×C4—862no—
480C2×C4—862no—
481C2×C4—862no—
482C2×C4—862no—
483C2×C4—862no—
484C2×C4—862no—
485C2×C4—862no—
486C2×C4—862no—
487C2×C4—861no—
488C2×C4—861no—
489C2×C4—861no—
490C2×C4—3441no—
491C2×C4—3441no—
492C2×C4—3441no—
493C2×C4—3441no—
494C2×C4—1722no—
495C2×C4—1722no—
496C2×C4—1721no—
497C2×C4—1721no—
498C2×C4—1721no—
499C2×C4#1306328711yescharacteristic
500C2×C4C4×D17211yescharacteristic
501C2×C4#1306329511yescharacteristic
502C2×C4#1306329811yescharacteristic
503C2×C4#1306330011yescharacteristic
504C2×C4#1306331011yescharacteristic
505C2×C4C2×C8×D4311yescharacteristic
506C2×C4M16×D4311yescharacteristic
507C2×C4#1306333111yescharacteristic
508C2×C4#1306333311yescharacteristic
509C2×C4D8×D4311yescharacteristic
510C2×C4SD16×D4311yescharacteristic
511C2×C4#1306335211yescharacteristic
512C2×C4#1306335711yescharacteristic
513C8—42no—
514C8—42no—
515C8—1722no—
516C8—1722no—
517C22—434no—
518C22—862no—
519C22—862no—
520C22—862no—
521C22—862no—
522C22—862no—
523C22—862no—
524C22—3441no—
525C22—3441no—
526C22—3441no—
527C22—3441no—
528C22—1722no—
529C22—1722no—
530C22—1722no—
531C22#1458277711yescharacteristic
532C22C22⋊C8×D4311yescharacteristic
533C22#1458286411yescharacteristic
534C22#102×D4311yescharacteristic
535C22#1458289911yescharacteristic
536C22#104×D4311yescharacteristic
537C22#1458291411yescharacteristic
538C4—21no—
539C4—21no—
540C4—42no—
541C4—81no—
542C4—862no—
543C4—862no—
544C4—3441no—
545C4—1721no—
546C4#1458296411yescharacteristic
547C4C8×D17211yescharacteristic
548C4#1458296911yescharacteristic
549C4#1458297211yescharacteristic
550C4#1458303411yescharacteristic
551C4#1458303911yescharacteristic
552C4#1458321411yescharacteristic
553C4#1458321911yescharacteristic
554C2—864no—
555C2—3442no—
556C2D4⋊C8×D4311yescharacteristic
557C2#1913298111yescharacteristic
558C2#1913299211yescharacteristic
559C2#1913300711yescharacteristic
560C2#1913488611yescharacteristic
561C2#1913489611yescharacteristic
562C2#1913491111yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC43×#1279C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#13063300C4
cosocleC2×C42×C43C23
hypercenter#1279D43
hypocenterC43#8939
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C8×D43C2semidirect
3. C4×(C2×D43)⋊C8C2semidirect
4. C2×#14582628C2semidirect
5. C2×#14582626C2semidirect
6. #19132436C2semidirect
7. C43×#1279C2semidirect
43. #13063300C8semidirect
65. C4⋊(C43⋊C8)D4semidirect
79. C4⋊C8×C43D4semidirect
102. C2×D172C2×C8semidirect
134. C4⋊C4×C43C2×C8semidirect
256. C2×D43D4⋊C8semidirect
279. #1279D43semidirect
312. C43#8939semidirect
356. C4⋊C8D172semidirect
426. C4⋊C4C8×D43semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C8×D432
C4×#130633002
C4×(C2×D43)⋊C82
C2×#145826282
C2×#145826262
#191324362
C43×#12792
#893943