Finite Group Databasebeta

← #24986319

Subgroups — #24986319

Order 11008.

1090 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#407×D43C211yesmaximal, characteristic
2#19136975C211yesmaximal, characteristic
3C4×C22⋊C4×D43C211yesmaximal, characteristic
4#19132449C211yesmaximal, characteristic, complemented
5#19132448C211yesmaximal, characteristic, complemented
6#19132447C211yesmaximal, characteristic, complemented
7C43×#1284C211yesmaximal, characteristic, complemented
8C23×C4×D43C2211yescharacteristic
9C2×M16×D43—21no—
10C2×#13063281—21no—
11C2×C22⋊C4×D43—21no—
12C2×C42×D43C412yescomplemented
13#14582863C2211yescharacteristic
14#14582862—21no—
15#14582861—21no—
16#14582861C412yescomplemented
17C22⋊C8×D43—21no—
18C22⋊C8×D43C412yescomplemented
19#14582762C2211yescharacteristic
20#14582758—21no—
21#14582758C412yescomplemented
22#14582754—21no—
23C22⋊C4×Dic43—21no—
24C4×(C2×D43)⋊C4C412yescomplemented
25C4×C22⋊Dic43C2211yescharacteristic
26#14582746—21no—
27#14582746—21no—
28#14582746C412yescomplemented
29#95×D43—21no—
30C43×#407C2211yescharacteristic
31C43×#381C2211yescharacteristic
32C4×C22⋊C4×C43C2211yescharacteristic
33C24×D43D411yescharacteristic
34C23×Dic43D411yescharacteristic
35C22×C4×D43—22no—
36C22×C4×D43—44no—
37C22×C4×D43C2×C411yescharacteristic
38C22×C4×D43C2×C411yescharacteristic
39C22×C4×D43C2×C411yescharacteristic
40C22×C4×D43C2×C411yescharacteristic
41C22×C4×D43C2×C411yescharacteristic
42C22×C4×D43C2×C411yescharacteristic
43C22×C4×D43D411yescharacteristic
44C22×C4×D43D411yescharacteristic
45C22×C4×D43D411yescharacteristic
46C22×C4×D43D411yescharacteristic
47C22×C4×D43Q811yescharacteristic
48C22×C4×D43Q811yescharacteristic
49C2×#10621877—21no—
50C2×#10621872—22no—
51M16×D43—44no—
52C2×C8×D43—22no—
53#13063281—44no—
54C2×Dic43⋊C4—22no—
55C2×C22⋊Dic43—21no—
56C2×C22⋊Dic43—21no—
57C2×(C2×D43)⋊C4—22no—
58C2×(C2×D43)⋊C4—22no—
59C2×(C2×D43)⋊C4—22no—
60C22⋊C4×D43—28no—
61C2×C4×Dic43—22no—
62C2×C4×Dic43—22no—
63C2×C4×Dic43C2×C412yes—
64C42×D43—44no—
65C22⋊(C43⋊C8)—21no—
66C22⋊(C43⋊C8)C2×C412yescomplemented
67(C2×D43)⋊C8—22no—
68(C2×D43)⋊C8—22no—
69C43⋊#95—21no—
70C43⋊#95—21no—
71C43⋊#95—22no—
72C43⋊#95C2×C412yescomplemented
73C23×C4×C43C2311yescharacteristic
74C2×M16×C43—21no—
75C2×C22⋊C4×C43—21no—
76C2×C22⋊C4×C43—21no—
77C2×C42×C43C2×C412yes—
78C22⋊C8×C43—21no—
79C22⋊C8×C43C2×C412yescomplemented
80#95×C43—21no—
81#95×C43—21no—
82#95×C43C2×C412yescomplemented
83C24×C43C2×D411yescharacteristic
84C23×D43—24no—
85C23×D43—42no—
86C23×D43—42no—
87C23×D43C22⋊C411yescharacteristic
88C23×D43C22⋊C411yescharacteristic
89C23×D43C22⋊C411yescharacteristic
90C23×D43C22⋊C411yescharacteristic
91C23×D43C4⋊C411yescharacteristic
92C23×D43C4⋊C411yescharacteristic
93C22×C4×C43—22no—
94C22×C4×C43—22no—
95C22×C4×C43—42no—
96C22×C4×C43C22×C411yescharacteristic
97C22×C4×C43C22×C411yescharacteristic
98C22×C4×C43C22×C411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2×Q811yescharacteristic
102C22×Dic43—24no—
103C22×Dic43—22no—
104C22×Dic43—22no—
105C22×Dic43C22⋊C411yescharacteristic
106C22×Dic43C22⋊C411yescharacteristic
107C22×Dic43C22⋊C411yescharacteristic
108C22×Dic43C22⋊C411yescharacteristic
109C22×Dic43C4⋊C411yescharacteristic
110C22×Dic43C4⋊C411yescharacteristic
111C2×C4×D43—24no—
112C2×C4×D43—24no—
113C2×C4×D43—28no—
114C2×C4×D43—42no—
115C2×C4×D43—42no—
116C2×C4×D43—44no—
117C2×C4×D43—44no—
118C2×C4×D43—42no—
119C2×C4×D43—42no—
120C2×C4×D43—42no—
121C2×C4×D43—42no—
122C2×C4×D43—42no—
123C2×C4×D43—42no—
124C2×C4×D43—42no—
125C2×C4×D43—42no—
126C2×C4×D43C4211yescharacteristic
127C2×C4×D43C4211yescharacteristic
128C2×C4×D43C4211yescharacteristic
129C2×C4×D43C4211yescharacteristic
130C2×C4×D43C22⋊C411yescharacteristic
131C2×C4×D43C22⋊C411yescharacteristic
132C2×C4×D43C22⋊C411yescharacteristic
133C2×C4×D43C22⋊C411yescharacteristic
134C2×C4×D43C4⋊C411yescharacteristic
135C2×C4×D43C4⋊C411yescharacteristic
136C2×C4×D43C4⋊C411yescharacteristic
137C2×C4×D43C4⋊C411yescharacteristic
138C2×C4×D43C4⋊C411yescharacteristic
139C2×C4×D43C4⋊C411yescharacteristic
140C2×C4×D43C4⋊C411yescharacteristic
141C2×C4×D43C4⋊C411yescharacteristic
142M16×C43—42no—
143C2×C8×C43—22no—
144C22⋊C4×C43—24no—
145C22⋊C4×C43—42no—
146C42×C43—42no—
147C22⋊Dic43—24no—
148C22⋊Dic43—42no—
149(C2×D43)⋊C4—28no—
150(C2×D43)⋊C4—44no—
151(C2×D43)⋊C4—44no—
152Dic43⋊C4—44no—
153C4×Dic43—44no—
154C4×Dic43—44no—
155C4×Dic43—42no—
156#10621877—42no—
157C2×C43⋊C8—22no—
158#10621872—44no—
159C8×D43—44no—
160C23×C43—22no—
161C23×C43—22no—
162C23×C43—41no—
163C23×C43C2×C22⋊C411yescharacteristic
164C23×C43C2×C22⋊C411yescharacteristic
165C23×C43C2×C4⋊C411yescharacteristic
166C22×D43—22no—
167C22×D43—22no—
168C22×D43—22no—
169C22×D43—22no—
170C22×D43—22no—
171C22×D43—22no—
172C22×D43—22no—
173C22×D43—22no—
174C22×D43—22no—
175C22×D43—22no—
176C22×D43—41no—
177C22×D43—41no—
178C22×D43—41no—
179C22×D43—41no—
180C22×D43—41no—
181C22×D43—41no—
182C22×D43—41no—
183C22×D43—416no—
184C22×D43#9511yescharacteristic
185C22×D43#9511yescharacteristic
186C22×D43#9511yescharacteristic
187C22×D43#9511yescharacteristic
188C22×D43#10414yes—
189C2×C4×C43—22no—
190C2×C4×C43—22no—
191C2×C4×C43—24no—
192C2×C4×C43—41no—
193C2×C4×C43—41no—
194C2×C4×C43—41no—
195C2×C4×C43—41no—
196C2×C4×C43—42no—
197C2×C4×C43—42no—
198C2×C4×C43—42no—
199C2×C4×C43—42no—
200C2×C4×C43—42no—
201C2×C4×C43C2×C4211yescharacteristic
202C2×C4×C43C2×C22⋊C411yescharacteristic
203C2×C4×C43C2×C4⋊C411yescharacteristic
204C2×C4×C43C2×C4⋊C411yescharacteristic
205C2×Dic43—22no—
206C2×Dic43—22no—
207C2×Dic43—22no—
208C2×Dic43—22no—
209C2×Dic43—22no—
210C2×Dic43—24no—
211C2×Dic43—42no—
212C2×Dic43—42no—
213C2×Dic43—42no—
214C2×Dic43—42no—
215C2×Dic43—42no—
216C2×Dic43#9511yescharacteristic
217C2×Dic43#9511yescharacteristic
218C2×Dic43#9511yescharacteristic
219C2×Dic43#9511yescharacteristic
220C2×Dic43#9914yes—
221C4×D43—22no—
222C4×D43—22no—
223C4×D43—22no—
224C4×D43—22no—
225C4×D43—22no—
226C4×D43—22no—
227C4×D43—22no—
228C4×D43—22no—
229C4×D43—41no—
230C4×D43—41no—
231C4×D43—41no—
232C4×D43—41no—
233C4×D43—41no—
234C4×D43—41no—
235C4×D43—41no—
236C4×D43—41no—
237C4×D43—416no—
238C8×C43—42no—
239C43⋊C8—42no—
240#7942—431nomaximal, Sylow
241C22×C43—21no—
242C22×C43—21no—
243C22×C43—21no—
244C22×C43—21no—
245C22×C43—21no—
246C22×C43—21no—
247C22×C43—21no—
248C22×C43—44no—
249C22×C43C2×#9511yescharacteristic
250C22×C43C2×#9912yes—
251C22×C43C2×#10412yes—
252C2×D43—28no—
253C2×D43—21no—
254C2×D43—21no—
255C2×D43—21no—
256C2×D43—21no—
257C2×D43—21no—
258C2×D43—21no—
259C2×D43—21no—
260C2×D43—21no—
261C2×D43—21no—
262C2×D43—44no—
263C2×D43—44no—
264C2×D43—44no—
265C2×D43—44no—
266C2×D43—44no—
267C2×D43H(3,ℤ/4)12yes—
268C2×D43#33912yes—
269C2×D43#33912yes—
270C4×C43—21no—
271C4×C43—21no—
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—44no—
275C4×C43—82no—
276Dic43—21no—
277Dic43—21no—
278Dic43—44no—
279Dic43—82no—
280Dic43#34212yes—
281Dic43#34212yes—
282C2×#407—431no—
283#2280—431no—
284C2×C4×C22⋊C4—431no—
285#1284—431no—
286#1284—431no—
287#1284—431no—
288#1284D4311yescharacteristic, complemented
289C2×C43—22no—
290C2×C43—22no—
291C2×C43—41no—
292C2×C43C2×H(3,ℤ/4)11yescharacteristic
293C2×C43C2×#33911yescharacteristic
294C2×C43C2×#34211yescharacteristic
295D43—22no—
296D43—22no—
297D43—22no—
298D43—41no—
299C24×C4—431no—
300C22×M16—861no—
301C2×#117—861no—
302C22×C22⋊C4—861no—
303C22×C42—432no—
304#407—431no—
305#407—432no—
306#407—861no—
307#407—861no—
308#407C2×D4311yescharacteristic
309C2×C22⋊C8—432no—
310C2×C22⋊C8—861no—
311#381—431no—
312#381C2×D4311yescharacteristic
313#380—432no—
314#380—861no—
315#379—861no—
316C4×C22⋊C4—432no—
317C4×C22⋊C4—431no—
318C4×C22⋊C4—432no—
319C4×C22⋊C4—861no—
320C4×C22⋊C4—861no—
321C4×C22⋊C4—861no—
322C4×C22⋊C4C2×D4311yescharacteristic
323C2×#95—861no—
324C43#794211yescharacteristic, complemented, Sylow
325C25—431no—
326C23×C4—431no—
327C23×C4—431no—
328C23×C4—431no—
329C23×C4—431no—
330C23×C4—431no—
331C23×C4—431no—
332C23×C4—431no—
333C23×C4—431no—
334C23×C4—431no—
335C23×C4—431no—
336C23×C4—431no—
337C23×C4—431no—
338C23×C4—431no—
339C23×C4—862no—
340C23×C4—1724no—
341C23×C4C22×D4311yescharacteristic
342C2×M16—21no—
343C2×M16—862no—
344C2×M16—861no—
345C2×M16—1724no—
346C22×C8—862no—
347#117—1724no—
348C2×C4⋊C4—862no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—868no—
352C2×C22⋊C4—862no—
353C2×C22⋊C4—861no—
354C2×C22⋊C4—862no—
355C2×C22⋊C4—862no—
356C2×C22⋊C4—861no—
357C2×C42—432no—
358C2×C42—862no—
359C2×C42—862no—
360C2×C42—1724no—
361C2×C42C4×D4312yes—
362C22⋊C8—21no—
363C22⋊C8—432no—
364C22⋊C8—862no—
365C22⋊C8—862no—
366C22⋊C8—861no—
367C22⋊C8C4×D4312yescomplemented
368#95—21no—
369#95—21no—
370#95—432no—
371#95—862no—
372#95—861no—
373#95—861no—
374#95C4×D4312yescomplemented
375C24—431no—
376C24—431no—
377C24—431no—
378C24—431no—
379C24—431no—
380C24—431no—
381C24—864no—
382C24—1722no—
383C24—1722no—
384C24D4×D4311yescharacteristic
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—42no—
388C22×C4—431no—
389C22×C4—431no—
390C22×C4—431no—
391C22×C4—431no—
392C22×C4—431no—
393C22×C4—431no—
394C22×C4—431no—
395C22×C4—431no—
396C22×C4—431no—
397C22×C4—431no—
398C22×C4—431no—
399C22×C4—431no—
400C22×C4—431no—
401C22×C4—431no—
402C22×C4—431no—
403C22×C4—431no—
404C22×C4—431no—
405C22×C4—431no—
406C22×C4—431no—
407C22×C4—431no—
408C22×C4—431no—
409C22×C4—431no—
410C22×C4—864no—
411C22×C4—864no—
412C22×C4—868no—
413C22×C4—864no—
414C22×C4—862no—
415C22×C4—862no—
416C22×C4—1722no—
417C22×C4—1722no—
418C22×C4—1722no—
419C22×C4—1722no—
420C22×C4—1722no—
421C22×C4—1722no—
422C22×C4—1722no—
423C22×C4—1722no—
424C22×C4—1722no—
425C22×C4—1722no—
426C22×C4—1724no—
427C22×C4—1724no—
428C22×C4C2×C4×D4311yescharacteristic
429C22×C4C2×C4×D4311yescharacteristic
430C22×C4C2×C4×D4311yescharacteristic
431C22×C4D4×D4311yescharacteristic
432C22×C4D4×D4311yescharacteristic
433C22×C4Q8×D4311yescharacteristic
434M16—42no—
435M16—1724no—
436M16—1722no—
437C2×C8—22no—
438C2×C8—862no—
439C2×C8—1724no—
440C4⋊C4—1724no—
441C22⋊C4—24no—
442C22⋊C4—42no—
443C22⋊C4—868no—
444C22⋊C4—864no—
445C22⋊C4—1724no—
446C22⋊C4—1724no—
447C22⋊C4—1722no—
448C42—42no—
449C42—1722no—
450C42—1724no—
451C42—1724no—
452C23—22no—
453C23—22no—
454C23—41no—
455C23—431no—
456C23—431no—
457C23—431no—
458C23—434no—
459C23—431no—
460C23—862no—
461C23—862no—
462C23—862no—
463C23—862no—
464C23—862no—
465C23—862no—
466C23—862no—
467C23—862no—
468C23—862no—
469C23—862no—
470C23—1721no—
471C23—1721no—
472C23—1721no—
473C23—1721no—
474C23—1721no—
475C23—1721no—
476C23—1721no—
477C23—17216no—
478C23C22⋊C4×D4311yescharacteristic
479C23C22⋊C4×D4311yescharacteristic
480C23C4⋊C4×D4311yescharacteristic
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—434no—
494C2×C4—431no—
495C2×C4—431no—
496C2×C4—431no—
497C2×C4—431no—
498C2×C4—862no—
499C2×C4—862no—
500C2×C4—862no—
501C2×C4—862no—
502C2×C4—862no—
503C2×C4—862no—
504C2×C4—862no—
505C2×C4—862no—
506C2×C4—862no—
507C2×C4—862no—
508C2×C4—862no—
509C2×C4—862no—
510C2×C4—862no—
511C2×C4—864no—
512C2×C4—1721no—
513C2×C4—1721no—
514C2×C4—1721no—
515C2×C4—1721no—
516C2×C4—1721no—
517C2×C4—1721no—
518C2×C4—1721no—
519C2×C4—1721no—
520C2×C4—17216no—
521C2×C4—1722no—
522C2×C4—1722no—
523C2×C4—1722no—
524C2×C4—1722no—
525C2×C4—1722no—
526C2×C4C42×D4311yescharacteristic
527C2×C4C22⋊C4×D4311yescharacteristic
528C2×C4C4⋊C4×D4311yescharacteristic
529C2×C4C4⋊C4×D4311yescharacteristic
530C8—42no—
531C8—1722no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—44no—
540C22—432no—
541C22—432no—
542C22—432no—
543C22—868no—
544C22—861no—
545C22—861no—
546C22—861no—
547C22—861no—
548C22—861no—
549C22—861no—
550C22—861no—
551C22—861no—
552C22—861no—
553C22—1724no—
554C22—1724no—
555C22—1724no—
556C22—1724no—
557C22—1724no—
558C22#95×D4311yescharacteristic
559C22#99×D4312yes—
560C22#104×D4312yes—
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—44no—
566C4—82no—
567C4—432no—
568C4—432no—
569C4—861no—
570C4—861no—
571C4—3442no—
572C4—1724no—
573C2—22no—
574C2—22no—
575C2—41no—
576C2—862no—
577C2—862no—
578C2—862no—
579C2—1721no—
580C2H(3,ℤ/4)×D4311yescharacteristic
581C2#339×D4311yescharacteristic
582C2#342×D4311yescharacteristic
subgroupG/H
centerC22#95×D43
commutatorC2×C4×C43C2×C42
FrattiniC23×C4C22×D43
FittingC43×#1284C2
socleC22×C43C2×#95
prime radicalC24×D43D4
cosocleC23×C4×C43C23
hypercenter#1284D43
hypocenterC43#7942
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1284

Complements

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

NH ≅ G/Ntype
4. #19132449C2semidirect
5. #19132448C2semidirect
6. #19132447C2semidirect
7. C43×#1284C2semidirect
12. C2×C42×D43C4semidirect
16. #14582861C4semidirect
18. C22⋊C8×D43C4semidirect
21. #14582758C4semidirect
24. C4×(C2×D43)⋊C4C4semidirect
28. #14582746C4semidirect
66. C22⋊(C43⋊C8)C2×C4semidirect
72. C43⋊#95C2×C4semidirect
79. C22⋊C8×C43C2×C4semidirect
82. #95×C43C2×C4semidirect
288. #1284D43semidirect
324. C43#7942semidirect
367. C22⋊C8C4×D43semidirect
374. #95C4×D43semidirect

Maximal subgroups

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

subgroupindex
#407×D432
#191369752
C4×C22⋊C4×D432
#191324492
#191324482
#191324472
C43×#12842
#794243