Finite Group Databasebeta

← #25099682

Subgroups — #25099682

Order 11008.

938 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583009C211yesmaximal, characteristic
2#19136957C211yesmaximal, characteristic, complemented
3#19135219C211yesmaximal, characteristic, complemented
4#19135212C211yesmaximal, characteristic, complemented
5#19135177C211yesmaximal, characteristic, complemented
6#19135170C211yesmaximal, characteristic, complemented
7#19134946C211yesmaximal, characteristic
8#19134946C211yesmaximal, characteristic
9#19134855C211yesmaximal, characteristic, complemented
10#19134841C211yesmaximal, characteristic, complemented
11#19134493C211yesmaximal, characteristic, complemented
12C4×#13063245C211yesmaximal, characteristic, complemented
13C4×#13063246C211yesmaximal, characteristic, complemented
14#19134347C211yesmaximal, characteristic, complemented
15C43×#2319C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C2×C4×D172C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20#14583009C418yescomplemented
21C2×#13063258C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063236C2211yescharacteristic
31C2×C4×C43⋊C8C2211yescharacteristic
32C4×C4⋊Dic43C2211yescharacteristic
33C4×C4⋊Dic43C2211yescharacteristic
34C4×C4⋊Dic43C2211yescharacteristic
35#14582746—21no—
36#14582746—21no—
37#14582746—21no—
38#95×D43—21no—
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582654C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48#14582654C2211yescharacteristic
49C2×C4×D4×C43C2211yescharacteristic
50C43×#390C2211yescharacteristic
51C43×#390C2211yescharacteristic
52C43×#389C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C43×#388—21no—
55C43×#388—21no—
56C43×#381—21no—
57C43×#380—21no—
58C4×C4⋊C4×C43C2211yescharacteristic
59C43×#376C2211yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C4×D43—21no—
62C22×C4×D43—21no—
63C22×C4×D43—21no—
64C2×#10621882—22no—
65C2×#10621882—22no—
66C2×#10621882C2×C414yes—
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71C4×D172—22no—
72C4×D172—22no—
73C4×D172—22no—
74C4×D172—22no—
75C4×D172—22no—
76C4×D172C2×C414yes—
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86#13063258—22no—
87#13063256—22no—
88#13063256C2×C414yescomplemented
89#13063246—22no—
90#13063246—22no—
91#13063246C2×C414yescomplemented
92#13063245—22no—
93#13063245—22no—
94#13063245C2×C414yes—
95#13063236C2×C414yescomplemented
96C4×C43⋊C8—22no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C22×D4×C43C2311yescharacteristic
101C23×C4×C43—21no—
102C4×D4×C43—22no—
103C4×D4×C43C2×C414yescomplemented
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C22⋊C4×C43—21no—
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C42×C43—21no—
115C2×C42×C43C2311yescharacteristic
116C2×C42×C43C2311yescharacteristic
117C2×C42×C43C2311yescharacteristic
118#95×C43—21no—
119#95×C43—21no—
120#95×C43—21no—
121#95×C43D411yescharacteristic
122#95×C43D411yescharacteristic
123#95×C43D411yescharacteristic
124#95×C43D411yescharacteristic
125C24×C43—21no—
126C23×D43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43C22×C412yes—
133C22×C4×C43—24no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—81no—
138C22×C4×C43—81no—
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172C22×C412yes—
153C2×D172#4112yes—
154C2×D172#4112yes—
155C2×C4×D43—24no—
156C2×C4×D43—24no—
157C2×C4×D43—24no—
158C2×C4×D43—81no—
159C2×C4×D43—81no—
160C2×C4×D43—81no—
161C2×C4×D43—81no—
162C2×C4×D43—81no—
163C2×C4×D43—81no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—81no—
170C4⋊C4×C43—81no—
171C4⋊C4×C43C22×C412yes—
172C22⋊C4×C43—24no—
173C22⋊C4×C43—81no—
174C22⋊C4×C43—81no—
175C22⋊C4×C43—81no—
176C22⋊C4×C43—81no—
177C42×C43—21no—
178C42×C43—21no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43—81no—
182C42×C43C22×C412yes—
183C42×C43#4112yes—
184#10621882—28no—
185(C2×D43)⋊C4—24no—
186(C2×D43)⋊C4—24no—
187(C2×D43)⋊C4—24no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43C22×C412yes—
192C4⋊Dic43#4112yes—
193C4⋊Dic43#4112yes—
194C4×Dic43—81no—
195C4×Dic43—81no—
196C4×Dic43—81no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8C22×C412yes—
208C2×C43⋊C8C22×C412yes—
209C23×C43—22no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43C22×D411yescharacteristic
217C22×D43—22no—
218C22×D43—22no—
219C22×D43—22no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224D4×C43—22no—
225D4×C43—22no—
226D4×C43—41no—
227D4×C43—41no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—22no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—84no—
254C2×C4×C43C4×D412yes—
255C2×C4×C43C4×D412yes—
256C2×C4×C43C23×C411yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—22no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271D172—22no—
272D172—22no—
273D172—22no—
274D172#11714yes—
275C4×D43—84no—
276C4×D43—84no—
277C4×D43—84no—
278C43⋊C8—22no—
279C43⋊C8—22no—
280C43⋊C8—41no—
281C43⋊C8—41no—
282#21126—431nomaximal, Sylow
283C22×C43—42no—
284C22×C43—42no—
285C22×C43—42no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43C2×C4×D411yescharacteristic
291C22×C43#52511yescharacteristic
292C22×C43#52511yescharacteristic
293C22×C43#57611yescharacteristic
294C22×C43#57611yescharacteristic
295C22×C43#57711yescharacteristic
296C22×C43#57711yescharacteristic
297C2×D43—24no—
298C2×D43—42no—
299C2×D43—42no—
300C2×D43—42no—
301C2×D43—42no—
302C2×D43—42no—
303C2×D43—42no—
304C4×C43—22no—
305C4×C43—22no—
306C4×C43—41no—
307C4×C43—41no—
308C4×C43—41no—
309C4×C43—41no—
310C4×C43—42no—
311C4×C43—81no—
312C4×C43—81no—
313C4×C43C2×#11711yescharacteristic
314C4×C43C4×#4111yescharacteristic
315C4×C43#52911yescharacteristic
316C4×C43#52911yescharacteristic
317Dic43—42no—
318Dic43—42no—
319Dic43—42no—
320C2×#442—431no—
321#2319D4311yescharacteristic, complemented
322#2275—431no—
323#1926—431no—
324#1925—431no—
325#1920—431no—
326#1919—431no—
327#1879—431no—
328#1879—431no—
329#1864—431no—
330#1862—431no—
331#1776—431no—
332C4×#102—431no—
333C4×#102—431no—
334#1746—431no—
335C2×C43—82no—
336C2×C43#229011yescharacteristic
337C2×C43#294611yescharacteristic
338C2×C43#294611yescharacteristic
339C2×C43#311811yescharacteristic
340C2×C43#311911yescharacteristic
341C2×C43#312211yescharacteristic
342C2×C43#312511yescharacteristic
343D43—44no—
344C22×D8—431no—
345C2×C4×D4—431no—
346C2×C4×D4—431no—
347C2×C4×D4—431no—
348C2×C4×D4C2×D4311yescharacteristic
349#442—438no—
350C2×#107—431no—
351C2×#106—431no—
352C2×#106—431no—
353C2×#102—431no—
354C2×#102—431no—
355C2×#102—431no—
356C2×#102—431no—
357C2×#102—431no—
358C2×#102—431no—
359C2×#97—431no—
360C2×C4×C8—431no—
361#390C2×D4311yescharacteristic
362#390C2×D4311yescharacteristic
363#389C2×D4311yescharacteristic
364#389C2×D4311yescharacteristic
365#388—21no—
366#388—21no—
367#381—21no—
368#380—21no—
369C4×C4⋊C4—431no—
370C4×C4⋊C4—431no—
371C4×C4⋊C4—431no—
372C4×C4⋊C4C2×D4311yescharacteristic
373C4×C22⋊C4—861no—
374C4×C22⋊C4—861no—
375C4×C22⋊C4—861no—
376#376C2×D4311yescharacteristic
377C2×#95—861no—
378#340—431no—
379#340—431no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340—431no—
384#336—431no—
385#336—431no—
386#336—431no—
387#336—431no—
388C43#2112611yescharacteristic, complemented, Sylow
389C22×D4—431no—
390C22×D4C22×D4311yescharacteristic
391C23×C4—21no—
392C23×C4—861no—
393C23×C4—861no—
394C23×C4—861no—
395C2×D8—434no—
396C2×D8—862no—
397C2×D8—862no—
398C22×C8—431no—
399C22×C8—431no—
400C22×C8—431no—
401C22×C8—431no—
402C4×D4—22no—
403C4×D4—434no—
404C4×D4—862no—
405C4×D4—862no—
406C4×D4—862no—
407C4×D4—862no—
408C4×D4—862no—
409C4×D4C4×D4314yescomplemented
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4C22×D4311yescharacteristic
416C2×C4⋊C4C22×D4311yescharacteristic
417C2×C4⋊C4C22×D4311yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C42—21no—
427C2×C42—861no—
428C2×C42—861no—
429C2×C42—861no—
430C2×C42C22×D4311yescharacteristic
431C2×C42C22×D4311yescharacteristic
432C2×C42C22×D4311yescharacteristic
433#107—862no—
434#106—434no—
435#106—862no—
436#102—434no—
437#102—434no—
438#102—862no—
439#102—862no—
440#102—862no—
441#102—862no—
442#97—434no—
443C4×C8—862no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—861no—
448#95—861no—
449#95—861no—
450#95C22⋊D4311yescharacteristic
451#95C22⋊D4311yescharacteristic
452#95C22⋊D4311yescharacteristic
453#95C22⋊D4311yescharacteristic
454C24—21no—
455C24—861no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—432no—
462C2×D4—432no—
463C2×D4—432no—
464C2×D4—861no—
465C2×D4—861no—
466C2×D4—861no—
467C2×D4C2×C4×D4312yes—
468C22×C4—21no—
469C22×C4—24no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—81no—
473C22×C4—81no—
474C22×C4—864no—
475C22×C4—864no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4—864no—
480C22×C4—3441no—
481C22×C4—3441no—
482C22×C4—3441no—
483C22×C4—3441no—
484C22×C4—3441no—
485C22×C4—3441no—
486C22×C4C2×C22⋊D4311yescharacteristic
487C22×C4C2×C22⋊D4311yescharacteristic
488C22×C4C2×C22⋊D4311yescharacteristic
489C22×C4C2×C22⋊D4311yescharacteristic
490C22×C4C2×C22⋊D4311yescharacteristic
491C22×C4C2×C22⋊D4311yescharacteristic
492C22×C4C23×D4311yescharacteristic
493D8—868no—
494C2×C8—432no—
495C2×C8—432no—
496C2×C8—861no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8—861no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—81no—
512C4⋊C4—81no—
513C4⋊C4—432no—
514C4⋊C4—432no—
515C4⋊C4—432no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4C2×C4×D4312yes—
520C22⋊C4—24no—
521C22⋊C4—81no—
522C22⋊C4—81no—
523C22⋊C4—81no—
524C22⋊C4—81no—
525C22⋊C4—864no—
526C22⋊C4—864no—
527C22⋊C4—864no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—81no—
533C42—3441no—
534C42—3441no—
535C42—3441no—
536C42C2×C4×D4312yes—
537C42#1062189812yes—
538C23—22no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—862no—
546C23—862no—
547C23—862no—
548C23—1721no—
549C23—1721no—
550C23—1721no—
551C23—1721no—
552C23C22×C22⋊D4311yescharacteristic
553D4—22no—
554D4—22no—
555D4—41no—
556D4—41no—
557D4—434no—
558D4—862no—
559D4—862no—
560D4—862no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—84no—
587C2×C4—862no—
588C2×C4—862no—
589C2×C4—862no—
590C2×C4—3444no—
591C2×C4—3444no—
592C2×C4—3444no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4C4×C22⋊D4312yes—
600C2×C4C4×C22⋊D4312yes—
601C2×C4C22×C4×D4311yescharacteristic
602C2×C4#41×D4311yescharacteristic
603C2×C4#41×D4311yescharacteristic
604C2×C4#41×D4311yescharacteristic
605C2×C4#41×D4311yescharacteristic
606C2×C4C2×#1062189811yescharacteristic
607C8—862no—
608C8—862no—
609C8—1721no—
610C8—1721no—
611C22—42no—
612C22—42no—
613C22—42no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—864no—
619C22—1722no—
620C22—1722no—
621C22—1722no—
622C22—1722no—
623C22—1722no—
624C22—1722no—
625C22C2×C4×C22⋊D4311yescharacteristic
626C22#1458340611yescharacteristic
627C22#1458340611yescharacteristic
628C22#1458370211yescharacteristic
629C22#1458370211yescharacteristic
630C22#1458370711yescharacteristic
631C22#1458371011yescharacteristic
632C4—22no—
633C4—22no—
634C4—42no—
635C4—41no—
636C4—41no—
637C4—41no—
638C4—41no—
639C4—81no—
640C4—81no—
641C4—1722no—
642C4—1722no—
643C4—1722no—
644C4#117×D4311yescharacteristic
645C4#1458336711yescharacteristic
646C4#1458342711yescharacteristic
647C4#1458342711yescharacteristic
648C2—82no—
649C2—1724no—
650C2#1913703211yescharacteristic
651C2#1914342311yescharacteristic
652C2#1914342711yescharacteristic
653C2#1914477311yescharacteristic
654C2#1914478811yescharacteristic
655C2#1914483311yescharacteristic
656C2#1914486611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2319C2
socleC23×C43C22×D4
prime radicalC22×#10621882C22
cosocleC22×C4×C43C24
hypercenter#2319D43
hypocenterC43#21126
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ #376 ◁ #2319

Complements

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

NH ≅ G/Ntype
2. #19136957C2semidirect
3. #19135219C2semidirect
4. #19135212C2semidirect
5. #19135177C2semidirect
6. #19135170C2semidirect
9. #19134855C2semidirect
10. #19134841C2semidirect
11. #19134493C2semidirect
12. C4×#13063245C2semidirect
13. C4×#13063246C2semidirect
14. #19134347C2semidirect
15. C43×#2319C2semidirect
20. #14583009C4semidirect
88. #13063256C2×C4semidirect
91. #13063246C2×C4semidirect
95. #13063236C2×C4semidirect
103. C4×D4×C43C2×C4semidirect
321. #2319D43semidirect
388. C43#21126semidirect
409. C4×D4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830092
#191369572
#191352192
#191352122
#191351772
#191351702
#191349462
#191348552
#191348412
#191344932
C4×#130632452
C4×#130632462
#191343472
C43×#23192
#2112643