Finite Group Databasebeta

← #25097371

Subgroups — #25097371

Order 11008.

1462 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582939C211yesmaximal, characteristic, complemented
2C2×#14582935C211yesmaximal, characteristic, complemented
3C2×#14582866C211yesmaximal, characteristic
4#19137187C211yesmaximal, characteristic
5#19134794C212yesmaximal, complemented
6#19134794C212yesmaximal, complemented
7#19134788C212yesmaximal, complemented
8#19134783C212yesmaximal, complemented
9#19134316C211yesmaximal, characteristic, complemented
10C2×#14582661C211yesmaximal, characteristic, complemented
11C2×C43×#520C211yesmaximal, characteristic
12C22×#10621877C2211yescharacteristic
13C23×C43⋊C8C2211yescharacteristic
14C2×#13063284C2211yescharacteristic
15C22×C4⋊Dic43C2211yescharacteristic
16#14582939—24no—
17#14582935—24no—
18C2×#13063258C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063258C2212yes—
21C2×#13063256C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063256C2212yes—
24#14582866C418yescomplemented
25C2×C22⋊(C43⋊C8)C2212yes—
26C2×C22⋊(C43⋊C8)C2212yes—
27#14582806—21no—
28#14582802—21no—
29#14582779—22no—
30#14582759C2212yes—
31#14582759C2212yes—
32#14582661C2212yes—
33#14582661C2212yes—
34#14582661C2212yes—
35#14582661C2212yes—
36C22×#41×C43C2211yescharacteristic
37C43×#520—24no—
38C43×#520—24no—
39C2×C4×Q8×C43—21no—
40C2×C4×D4×C43—21no—
41C2×C4×D4×C43—22no—
42C2×#117×C43C2212yes—
43C2×#117×C43C2211yescharacteristic
44C22×C4⋊C4×C43C2212yes—
45C22×C4⋊C4×C43C2211yescharacteristic
46C23×Dic43—21no—
47C2×#10621877—22no—
48C2×#10621877—22no—
49C2×#10621877C2×C414yescomplemented
50C22×C43⋊C8—22no—
51C22×C43⋊C8—22no—
52C22×C43⋊C8C2×C414yescomplemented
53C22×C43⋊C8C2311yescharacteristic
54C22×C43⋊C8C2311yescharacteristic
55C22×C43⋊C8C2312yes—
56#13063284—22no—
57#13063284—22no—
58C2×C4⋊Dic43—22no—
59C2×C4⋊Dic43—22no—
60C2×C4⋊Dic43—21no—
61C2×C4⋊Dic43C2312yes—
62C2×C4⋊Dic43C2311yescharacteristic
63C2×C4⋊Dic43C2311yescharacteristic
64C2×C22⋊Dic43—21no—
65C2×C22⋊Dic43—22no—
66C2×C22⋊Dic43—22no—
67C2×C4×Dic43—21no—
68#13063258—22no—
69#13063258—22no—
70#13063258—24no—
71#13063256—22no—
72#13063256—22no—
73#13063256—24no—
74C22⋊(C43⋊C8)C2×C418yescomplemented
75C22⋊(C43⋊C8)C2×C418yescomplemented
76C43⋊#95—22no—
77C43⋊#95—22no—
78C2×#41×C43—22no—
79C2×#41×C43—22no—
80C2×#41×C43—22no—
81C2×#41×C43—22no—
82C2×#41×C43C2×C414yes—
83C2×#41×C43Q814yes—
84C22×Q8×C43D411yescharacteristic
85C22×D4×C43D411yescharacteristic
86C22×D4×C43D412yes—
87C23×C4×C43—22no—
88C23×C4×C43—21no—
89C23×C4×C43C2312yes—
90C23×C4×C43C2311yescharacteristic
91C4×Q8×C43—28no—
92C4×D4×C43—216no—
93C4×D4×C43—28no—
94#117×C43—22no—
95#117×C43—24no—
96#117×C43—24no—
97#117×C43D414yes—
98C2×C4⋊C4×C43—22no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—22no—
101C2×C4⋊C4×C43—24no—
102C2×C4⋊C4×C43—24no—
103C2×C4⋊C4×C43D414yes—
104C2×C4⋊C4×C43C2311yescharacteristic
105C2×C4⋊C4×C43C2312yes—
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C22⋊C4×C43—22no—
108C2×C22⋊C4×C43—21no—
109C2×C42×C43—22no—
110C2×C42×C43—21no—
111C24×C43C2×D412yes—
112C24×C43C2×D411yescharacteristic
113#41×C43—28no—
114#41×C43—28no—
115#41×C43—28no—
116#41×C43—28no—
117C2×Q8×C43—22no—
118C2×Q8×C43—22no—
119C2×Q8×C43C4⋊C414yes—
120C2×D4×C43—22no—
121C2×D4×C43—22no—
122C2×D4×C43—24no—
123C2×D4×C43—24no—
124C2×D4×C43C4⋊C414yes—
125C2×D4×C43C4⋊C418yes—
126C22×C4×C43—22no—
127C22×C4×C43—22no—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43—28no—
131C22×C4×C43—24no—
132C22×C4×C43—21no—
133C22×C4×C43—22no—
134C22×C4×C43—21no—
135C22×C4×C43—81no—
136C22×C4×C43—81no—
137C22×C4×C43—82no—
138C22×C4×C43—82no—
139C22×C4×C43C22×C414yes—
140C22×C4×C43C22×C412yes—
141C22×C4×C43C2×D412yes—
142C22×C4×C43C2×D412yes—
143C22×C4×C43C2×D412yes—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×Q814yes—
146C22×C4×C43C2×Q812yes—
147C22×C4×C43#4112yes—
148C22×C4×C43#4112yes—
149C22×C4×C43C2411yescharacteristic
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—22no—
153C22×Dic43—42no—
154C22×Dic43—81no—
155C22×Dic43—81no—
156C4⋊C4×C43—28no—
157C4⋊C4×C43—24no—
158C4⋊C4×C43—22no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43C2×D412yes—
162C4⋊C4×C43C2×D414yes—
163C4⋊C4×C43C2×D412yes—
164C22⋊C4×C43—28no—
165C22⋊C4×C43—24no—
166C42×C43—28no—
167C42×C43—24no—
168C22⋊Dic43—42no—
169C22⋊Dic43—82no—
170C22⋊Dic43—82no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—22no—
176C4⋊Dic43—22no—
177C4⋊Dic43—42no—
178C4×Dic43—42no—
179#10621877—28no—
180C2×C43⋊C8—28no—
181C2×C43⋊C8—21no—
182C2×C43⋊C8—22no—
183C2×C43⋊C8—21no—
184C2×C43⋊C8—21no—
185C2×C43⋊C8—21no—
186C2×C43⋊C8—22no—
187C2×C43⋊C8C22×C412yes—
188C2×C43⋊C8C22×C412yes—
189C2×C43⋊C8C22×C414yes—
190C23×C43—21no—
191C23×C43—21no—
192C23×C43—21no—
193C23×C43—21no—
194C23×C43—22no—
195C23×C43—22no—
196C23×C43—22no—
197C23×C43—22no—
198C23×C43—22no—
199C23×C43—22no—
200C23×C43C2×C4⋊C414yes—
201C23×C43C2×C4⋊C412yes—
202C23×C43#12012yes—
203C23×C43#12312yes—
204C23×C43C22×D411yescharacteristic
205Q8×C43—28no—
206D4×C43—216no—
207D4×C43—28no—
208C2×C4×C43—22no—
209C2×C4×C43—22no—
210C2×C4×C43—24no—
211C2×C4×C43—24no—
212C2×C4×C43—24no—
213C2×C4×C43—24no—
214C2×C4×C43—22no—
215C2×C4×C43—24no—
216C2×C4×C43—22no—
217C2×C4×C43—42no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—42no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—84no—
224C2×C4×C43—88no—
225C2×C4×C43C2×C4⋊C414yes—
226C2×C4×C43C2×C4⋊C412yes—
227C2×C4×C43C4×D414yes—
228C2×C4×C43C4×D414yes—
229C2×C4×C43#12012yes—
230C2×C4×C43C22⋊Q814yes—
231C2×C4×C43C22⋊Q814yes—
232C2×C4×C43#12312yes—
233C2×C4×C43C23×C411yescharacteristic
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C22×Q811yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—42no—
242C2×Dic43—41no—
243C2×Dic43—42no—
244C2×Dic43—41no—
245C2×Dic43—42no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—84no—
249C43⋊C8—22no—
250C43⋊C8—22no—
251C43⋊C8—24no—
252#20849—431nomaximal, Sylow
253C22×C43—22no—
254C22×C43—22no—
255C22×C43—22no—
256C22×C43—22no—
257C22×C43—22no—
258C22×C43—22no—
259C22×C43—24no—
260C22×C43—24no—
261C22×C43—24no—
262C22×C43—42no—
263C22×C43—42no—
264C22×C43—42no—
265C22×C43—42no—
266C22×C43#38514yes—
267C22×C43C22×C4⋊C411yescharacteristic
268C22×C43C2×#12011yescharacteristic
269C22×C43C2×#12311yescharacteristic
270C22×C43#57611yescharacteristic
271C22×C43#57711yescharacteristic
272C22×C43#57711yescharacteristic
273C22×C43#57811yescharacteristic
274C4×C43—24no—
275C4×C43—44no—
276C4×C43—42no—
277C4×C43—42no—
278C4×C43#38514yes—
279C4×C43C2×C4×D411yescharacteristic
280C4×C43C2×C4×D411yescharacteristic
281C4×C43C2×C22⋊Q811yescharacteristic
282C4×C43C2×C22⋊Q811yescharacteristic
283Dic43—82no—
284Dic43—81no—
285Dic43—81no—
286C2×#520D4311yescharacteristic
287C2×#428—431no—
288C2×#427—431no—
289C2×#408—431no—
290#2311—431no—
291#1854—432no—
292#1854—432no—
293#1853—432no—
294#1852—432no—
295#1736—431no—
296C2×#340—431no—
297C2×C43—24no—
298C2×C43—44no—
299C2×C43C2×#38511yescharacteristic
300C2×C43#291211yescharacteristic
301C2×C43#291311yescharacteristic
302C2×C43#301211yescharacteristic
303C2×C43#301311yescharacteristic
304C2×C43#309611yescharacteristic
305C2×C43#309711yescharacteristic
306C22×#41C2×D4311yescharacteristic
307C22×M16—431no—
308C23×C8—431no—
309#520—24no—
310#520—24no—
311C2×C4×Q8—21no—
312C2×C4×D4—22no—
313C2×C4×D4—21no—
314C2×#117—431no—
315C2×#117C2×D4312yes—
316C2×#117C2×D4311yescharacteristic
317C22×C4⋊C4—431no—
318C22×C4⋊C4C2×D4312yes—
319C22×C4⋊C4C2×D4311yescharacteristic
320#428—864no—
321#427—864no—
322C2×#107—431no—
323C2×#107—432no—
324C2×#107—431no—
325C2×#106—431no—
326C2×#106—432no—
327C2×#106—431no—
328#408—438no—
329C2×C22⋊C8—432no—
330C2×C22⋊C8—432no—
331#391—861no—
332#390—861no—
333#386—862no—
334#380—432no—
335#380—432no—
336#340—432no—
337#340—432no—
338#340—432no—
339#340—432no—
340C43#2084911yescharacteristic, complemented, Sylow
341C2×#41—22no—
342C2×#41—22no—
343C2×#41—22no—
344C2×#41—22no—
345C2×#41Dic8614yes—
346C2×#41C4×D4314yes—
347C22×Q8C22⋊D4311yescharacteristic
348C22×D4C22⋊D4312yes—
349C22×D4C22⋊D4311yescharacteristic
350C23×C4—22no—
351C23×C4—21no—
352C23×C4—861no—
353C23×C4C22×D4312yes—
354C23×C4C22×D4311yescharacteristic
355C2×M16—434no—
356C2×M16—862no—
357C2×M16—862no—
358C22×C8—434no—
359C22×C8—431no—
360C22×C8—431no—
361C22×C8—432no—
362C22×C8—862no—
363C22×C8—862no—
364C4×Q8—28no—
365C4×D4—216no—
366C4×D4—28no—
367#117—22no—
368#117—24no—
369#117—24no—
370#117—862no—
371#117—862no—
372#117C22⋊D4314yes—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—432no—
379C2×C4⋊C4—431no—
380C2×C4⋊C4—431no—
381C2×C4⋊C4—862no—
382C2×C4⋊C4—862no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4C22⋊D4314yes—
385C2×C4⋊C4C22×D4311yescharacteristic
386C2×C4⋊C4C22×D4312yes—
387C2×C4⋊C4C22×D4311yescharacteristic
388C2×C22⋊C4—22no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—862no—
391C2×C22⋊C4—862no—
392C2×C22⋊C4—861no—
393C2×C42—22no—
394C2×C42—21no—
395C2×C42—861no—
396#107—862no—
397#107—862no—
398#107—864no—
399#106—862no—
400#106—862no—
401#106—864no—
402C22⋊C8—438no—
403C22⋊C8—438no—
404#95—862no—
405#95—862no—
406C24C2×C22⋊D4312yes—
407C24C2×C22⋊D4311yescharacteristic
408#41—28no—
409#41—28no—
410#41—28no—
411#41—28no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8Dic43⋊C414yes—
415C2×D4—24no—
416C2×D4—24no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4Dic43⋊C418yes—
420C2×D4Dic43⋊C414yes—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—28no—
429C22×C4—24no—
430C22×C4—81no—
431C22×C4—82no—
432C22×C4—81no—
433C22×C4—82no—
434C22×C4—861no—
435C22×C4—861no—
436C22×C4—862no—
437C22×C4—3441no—
438C22×C4—3441no—
439C22×C4—1722no—
440C22×C4C2×Dic8614yes—
441C22×C4C2×Dic8612yes—
442C22×C4C2×C4×D4314yes—
443C22×C4C2×C4×D4312yes—
444C22×C4#1062189812yes—
445C22×C4#1062189812yes—
446C22×C4C2×C22⋊D4312yes—
447C22×C4C2×C22⋊D4311yescharacteristic
448C22×C4C2×C22⋊D4312yes—
449C22×C4C2×C22⋊D4312yes—
450C22×C4C23×D4311yescharacteristic
451M16—868no—
452C2×C8—432no—
453C2×C8—432no—
454C2×C8—434no—
455C2×C8—868no—
456C2×C8—861no—
457C2×C8—862no—
458C2×C8—861no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—862no—
462C4⋊C4—28no—
463C4⋊C4—24no—
464C4⋊C4—22no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—862no—
472C4⋊C4—862no—
473C4⋊C4—1722no—
474C4⋊C4C2×C22⋊D4312yes—
475C4⋊C4C2×C22⋊D4314yes—
476C4⋊C4C2×C22⋊D4312yes—
477C22⋊C4—28no—
478C22⋊C4—24no—
479C22⋊C4—3442no—
480C22⋊C4—3442no—
481C22⋊C4—1722no—
482C42—28no—
483C42—24no—
484C42—1722no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—22no—
495C23C2×Dic43⋊C414yes—
496C23C2×Dic43⋊C412yes—
497C23#1306329412yes—
498C23#1306330812yes—
499C23C22×C22⋊D4311yescharacteristic
500Q8—28no—
501D4—216no—
502D4—28no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—22no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—84no—
519C2×C4—88no—
520C2×C4—3444no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4—1722no—
524C2×C4—1721no—
525C2×C4—1722no—
526C2×C4—1721no—
527C2×C4—1722no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4C2×Dic43⋊C414yes—
531C2×C4C2×Dic43⋊C412yes—
532C2×C4C4×C22⋊D4314yes—
533C2×C4C4×C22⋊D4314yes—
534C2×C4#1306329412yes—
535C2×C4#1306330414yes—
536C2×C4#1306330414yes—
537C2×C4#1306330812yes—
538C2×C4C22×C4×D4311yescharacteristic
539C2×C4C22×C22⋊D4311yescharacteristic
540C2×C4C22×C22⋊D4311yescharacteristic
541C2×C4C22×Dic8611yescharacteristic
542C2×C4C2×#1062189811yescharacteristic
543C2×C4C2×#1062189811yescharacteristic
544C8—862no—
545C8—862no—
546C8—864no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—24no—
554C22—24no—
555C22—24no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—42no—
560C22#1458277214yes—
561C22C22×Dic43⋊C411yescharacteristic
562C22C2×#1306329411yescharacteristic
563C22C2×#1306330811yescharacteristic
564C22#1458370211yescharacteristic
565C22#1458370711yescharacteristic
566C22#1458371011yescharacteristic
567C22#1458371411yescharacteristic
568C4—24no—
569C4—44no—
570C4—42no—
571C4—42no—
572C4—3442no—
573C4—3441no—
574C4—3441no—
575C4#1458277214yes—
576C4C2×C4×C22⋊D4311yescharacteristic
577C4C2×C4×C22⋊D4311yescharacteristic
578C4C2×#1306330411yescharacteristic
579C4C2×#1306330411yescharacteristic
580C2—24no—
581C2—44no—
582C2C2×#1458277211yescharacteristic
583C2#1914318811yescharacteristic
584C2#1914319311yescharacteristic
585C2#1914389911yescharacteristic
586C2#1914391011yescharacteristic
587C2#1914455311yescharacteristic
588C2#1914456411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#520C2
socleC23×C43C22×D4
prime radicalC22×#41×C43C22
cosocleC22×C4×C43C24
hypercenterC2×#520D43
hypocenterC43#20849
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. C2×#14582939C2semidirect
2. C2×#14582935C2semidirect
5. #19134794C2semidirect
6. #19134794C2semidirect
7. #19134788C2semidirect
8. #19134783C2semidirect
9. #19134316C2semidirect
10. C2×#14582661C2semidirect
24. #14582866C4semidirect
49. C2×#10621877C2×C4semidirect
52. C22×C43⋊C8C2×C4semidirect
74. C22⋊(C43⋊C8)C2×C4semidirect
75. C22⋊(C43⋊C8)C2×C4semidirect
340. C43#20849semidirect

Maximal subgroups

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

subgroupindex
C2×#145829392
C2×#145829352
C2×#145828662
#191371872
#191347942
#191347882
#191347832
#191343162
C2×#145826612
C2×C43×#5202
#2084943