Finite Group Databasebeta

← #25129806

Subgroups — #25129806

Order 11008.

1358 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583232C211yesmaximal, characteristic, complemented
2C2×#14582900C211yesmaximal, characteristic, complemented
3#19138903C211yesmaximal, characteristic, complemented
4#19135838C212yesmaximal, complemented
5#19135795C212yesmaximal, complemented
6#19135029C211yesmaximal, characteristic, complemented
7#19134893C211yesmaximal, characteristic, complemented
8#19134842C212yesmaximal, complemented
9#19134535C211yesmaximal, characteristic, complemented
10#19134535C212yesmaximal, complemented
11C2×C43×#547C211yesmaximal, characteristic
12C22×#10621877C2211yescharacteristic
13C2×#13063306—21no—
14C22×C4⋊Dic43C2211yescharacteristic
15#14583232—24no—
16C2×#13063258C2212yes—
17#14582900—24no—
18C2×#13063249C2212yes—
19C2×#13063249C2212yes—
20C2×#13063249C2212yes—
21C2×#13063249C2212yes—
22C2×#13063246C2212yes—
23C2×#13063246C2212yes—
24C2×C22⋊(C43⋊C8)C2211yescharacteristic
25C2×C22⋊(C43⋊C8)C2212yes—
26#14582829—21no—
27#14582824—21no—
28#14582797C2212yes—
29#14582760—21no—
30#14582759C2212yes—
31#14582759C2211yescharacteristic
32#14582661C2212yes—
33#14582654C2212yes—
34C22×#41×C43C2211yescharacteristic
35C22×#41×C43C2211yescharacteristic
36C43×#547—24no—
37C43×#547—24no—
38C2×C4⋊Q8×C43C2211yescharacteristic
39C2×#123×C43—21no—
40C2×#123×C43—21no—
41C2×C22⋊Q8×C43C2211yescharacteristic
42C2×C22⋊Q8×C43C2211yescharacteristic
43C2×#121×C43—21no—
44C2×C4×D4×C43C2211yescharacteristic
45C2×C4×D4×C43C2211yescharacteristic
46C22×C4⋊C4×C43—21no—
47C23×Dic43—21no—
48C2×#10621877—22no—
49C2×#10621877—42no—
50C22×C43⋊C8C2312yes—
51C22×C43⋊C8C2312yes—
52#13063306—44no—
53C2×C4⋊Dic43—22no—
54C2×C4⋊Dic43—22no—
55C2×C4⋊Dic43—21no—
56C2×C4⋊Dic43C2312yes—
57C2×C4⋊Dic43C2312yes—
58C2×Dic43⋊C4—22no—
59C2×C22⋊Dic43—22no—
60C2×C22⋊Dic43—21no—
61#13063258—24no—
62#13063249—24no—
63#13063249—24no—
64#13063249—42no—
65#13063249—42no—
66#13063246—24no—
67#13063246—24no—
68C22⋊(C43⋊C8)—22no—
69C22⋊(C43⋊C8)—42no—
70C43⋊#95—22no—
71C43⋊#95—21no—
72C43⋊#95—22no—
73C2×#41×C43—22no—
74C2×#41×C43—22no—
75C2×#41×C43—22no—
76C2×#41×C43—24no—
77C2×#41×C43—24no—
78C2×#41×C43—42no—
79C2×#41×C43—42no—
80C2×#41×C43D414yes—
81C22×Q8×C43C2311yescharacteristic
82C22×Q8×C43C2311yescharacteristic
83C22×D4×C43—21no—
84C22×D4×C43—21no—
85C22×D4×C43D411yescharacteristic
86C22×D4×C43C2311yescharacteristic
87C23×C4×C43—21no—
88C23×C4×C43—21no—
89C23×C4×C43—21no—
90C23×C4×C43C2311yescharacteristic
91C23×C4×C43C2311yescharacteristic
92C4⋊Q8×C43—22no—
93C4⋊Q8×C43—22no—
94#123×C43—28no—
95#123×C43—28no—
96C22⋊Q8×C43—22no—
97C22⋊Q8×C43—22no—
98C22⋊Q8×C43—22no—
99C22⋊Q8×C43D414yes—
100#121×C43—28no—
101C4×D4×C43—22no—
102C4×D4×C43—22no—
103C4×D4×C43—22no—
104C4×D4×C43—22no—
105C2×C4⋊C4×C43—28no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43D411yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43D411yescharacteristic
116C2×C22⋊C4×C43D411yescharacteristic
117C2×C42×C43C2311yescharacteristic
118C24×C43—21no—
119C24×C43C2×D411yescharacteristic
120C24×C43C2×D411yescharacteristic
121#41×C43—28no—
122#41×C43—44no—
123#41×C43—48no—
124#41×C43—48no—
125#41×C43—44no—
126#41×C43—44no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—22no—
130C2×Q8×C43—22no—
131C2×Q8×C43—22no—
132C2×Q8×C43—22no—
133C2×Q8×C43C2×D412yes—
134C2×Q8×C43C2×D412yes—
135C2×D4×C43—24no—
136C2×D4×C43—22no—
137C2×D4×C43—21no—
138C2×D4×C43—22no—
139C2×D4×C43—22no—
140C2×D4×C43—24no—
141C2×D4×C43—41no—
142C2×D4×C43—44no—
143C2×D4×C43—44no—
144C2×D4×C43C2×D412yes—
145C2×D4×C43#4114yes—
146C22×C4×C43—22no—
147C22×C4×C43—22no—
148C22×C4×C43—24no—
149C22×C4×C43—24no—
150C22×C4×C43—24no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—22no—
154C22×C4×C43—22no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—44no—
159C22×C4×C43—44no—
160C22×C4×C43—42no—
161C22×C4×C43—42no—
162C22×C4×C43C2×D412yes—
163C22×C4×C43C2×D412yes—
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43C2411yescharacteristic
169C22×Dic43—22no—
170C22×Dic43—22no—
171C22×Dic43—42no—
172C22×Dic43—42no—
173C22×Dic43—42no—
174C4⋊C4×C43—24no—
175C4⋊C4×C43—24no—
176C4⋊C4×C43—24no—
177C4⋊C4×C43—22no—
178C4⋊C4×C43—24no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43C2×D412yes—
181C22⋊C4×C43—24no—
182C22⋊C4×C43—24no—
183C22⋊C4×C43—22no—
184C22⋊C4×C43—24no—
185C22⋊C4×C43—22no—
186C42×C43—21no—
187C42×C43—21no—
188C22⋊Dic43—42no—
189C22⋊Dic43—44no—
190C4⋊Dic43—22no—
191C4⋊Dic43—22no—
192C4⋊Dic43—22no—
193C4⋊Dic43—22no—
194C4⋊Dic43—42no—
195Dic43⋊C4—44no—
196#10621877—44no—
197C2×C43⋊C8—22no—
198C2×C43⋊C8—22no—
199C2×C43⋊C8—22no—
200C2×C43⋊C8—22no—
201C2×C43⋊C8—22no—
202C2×C43⋊C8—22no—
203C23×C43—22no—
204C23×C43—22no—
205C23×C43—24no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43—22no—
209C23×C43—21no—
210C23×C43—22no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43—22no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—42no—
217C23×C43#12012yes—
218C23×C43C22×D411yescharacteristic
219Q8×C43—22no—
220Q8×C43—22no—
221Q8×C43—24no—
222Q8×C43—41no—
223Q8×C43—41no—
224Q8×C43—42no—
225D4×C43—22no—
226D4×C43—24no—
227D4×C43—44no—
228D4×C43—48no—
229D4×C43—48no—
230D4×C43#12314yescomplemented
231C2×C4×C43—21no—
232C2×C4×C43—22no—
233C2×C4×C43—21no—
234C2×C4×C43—22no—
235C2×C4×C43—22no—
236C2×C4×C43—24no—
237C2×C4×C43—21no—
238C2×C4×C43—22no—
239C2×C4×C43—21no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—22no—
244C2×C4×C43—48no—
245C2×C4×C43—48no—
246C2×C4×C43—48no—
247C2×C4×C43—42no—
248C2×C4×C43—42no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—42no—
254C2×C4×C43#12012yes—
255C2×C4×C43AGL(1,ℤ/8)12yes—
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43C22×D411yescharacteristic
258C2×C4×C43C2×#4112yes—
259C2×C4×C43H(5,𝔽2)12yes—
260C2×Dic43—42no—
261C2×Dic43—42no—
262C2×Dic43—42no—
263C2×Dic43—42no—
264C2×Dic43—42no—
265C2×Dic43—42no—
266C2×Dic43—84no—
267C43⋊C8—42no—
268C43⋊C8—42no—
269#24054—431nomaximal, Sylow
270C22×C43—24no—
271C22×C43—22no—
272C22×C43—22no—
273C22×C43—22no—
274C22×C43—42no—
275C22×C43—44no—
276C22×C43—42no—
277C22×C43—42no—
278C22×C43—42no—
279C22×C43—44no—
280C22×C43—42no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—42no—
285C22×C43C2×#12011yescharacteristic
286C22×C43#54612yes—
287C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
288C22×C43#57511yescharacteristic
289C22×C43#57812yes—
290C4×C43—22no—
291C4×C43—22no—
292C4×C43—41no—
293C4×C43—42no—
294C4×C43—42no—
295C4×C43—42no—
296C4×C43—41no—
297C4×C43C2×#12311yescharacteristic
298C4×C43#53411yescharacteristic
299C4×C43#54612yes—
300Dic43—82no—
301Dic43—82no—
302C2×#547D4311yescharacteristic
303C2×#484—431no—
304C2×#417—431no—
305#2486—431no—
306#2043—432no—
307#2036—432no—
308#1894—431no—
309#1870—431no—
310#1862—432no—
311#1788—432no—
312#1788—431no—
313C2×C43—42no—
314C2×C43—44no—
315C2×C43—81no—
316C2×C43#240511yescharacteristic
317C2×C43#300611yescharacteristic
318C2×C43#301111yescharacteristic
319C2×C43#331512yes—
320C2×C43#333012yes—
321C22×#41C2×D4311yescharacteristic
322C22×#41C2×D4311yescharacteristic
323C22×M16—431no—
324#547—24no—
325#547—24no—
326C2×C4⋊Q8C2×D4311yescharacteristic
327C2×#123—21no—
328C2×#123—21no—
329C2×#123—861no—
330C2×C22⋊Q8C2×D4311yescharacteristic
331C2×C22⋊Q8C2×D4311yescharacteristic
332C2×#121—21no—
333C2×C4×D4C2×D4311yescharacteristic
334C2×C4×D4C2×D4311yescharacteristic
335C22×C4⋊C4—21no—
336C22×C4⋊C4—431no—
337#484—864no—
338C2×#107—432no—
339#417—864no—
340C2×#103—432no—
341C2×#103—432no—
342C2×#103—432no—
343C2×#103—432no—
344C2×#102—432no—
345C2×#102—432no—
346C2×C22⋊C8—431no—
347C2×C22⋊C8—432no—
348#398—861no—
349#397—861no—
350#389—432no—
351#381—861no—
352#380—431no—
353#380—432no—
354#340—432no—
355#336—432no—
356C43#2405411yescharacteristic, complemented, Sylow
357C2×#41—22no—
358C2×#41—22no—
359C2×#41—22no—
360C2×#41—24no—
361C2×#41—24no—
362C2×#41—42no—
363C2×#41—42no—
364C2×#41C22⋊D4314yes—
365C22×Q8C22×D4311yescharacteristic
366C22×Q8C22×D4311yescharacteristic
367C22×D4—21no—
368C22×D4—21no—
369C22×D4C22⋊D4311yescharacteristic
370C22×D4C22×D4311yescharacteristic
371C23×C4—21no—
372C23×C4—21no—
373C23×C4—21no—
374C23×C4—861no—
375C23×C4C22×D4311yescharacteristic
376C23×C4C22×D4311yescharacteristic
377C2×M16—862no—
378C2×M16—1722no—
379C22×C8—432no—
380C22×C8—432no—
381C4⋊Q8—22no—
382C4⋊Q8—22no—
383#123—28no—
384#123—28no—
385#123—1724no—
386C22⋊Q8—22no—
387C22⋊Q8—22no—
388C22⋊Q8—22no—
389C22⋊Q8C22⋊D4314yes—
390#121—28no—
391C4×D4—22no—
392C4×D4—22no—
393C4×D4—22no—
394C4×D4—22no—
395C2×C4⋊C4—28no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—432no—
401C2×C4⋊C4—432no—
402C2×C4⋊C4—862no—
403C2×C4⋊C4—862no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—862no—
406C2×C4⋊C4C22⋊D4311yescharacteristic
407C2×C4⋊C4C22×D4311yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—861no—
412C2×C22⋊C4—862no—
413C2×C22⋊C4C22⋊D4311yescharacteristic
414C2×C22⋊C4C22⋊D4311yescharacteristic
415C2×C42C22×D4311yescharacteristic
416#107—864no—
417#103—864no—
418#103—864no—
419#103—1722no—
420#103—1722no—
421#102—864no—
422#102—864no—
423C22⋊C8—862no—
424C22⋊C8—1722no—
425#95—862no—
426#95—861no—
427#95—862no—
428C24—21no—
429C24C2×C22⋊D4311yescharacteristic
430C24C2×C22⋊D4311yescharacteristic
431#41—28no—
432#41—44no—
433#41—48no—
434#41—48no—
435#41—44no—
436#41—44no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—22no—
440C2×Q8—22no—
441C2×Q8—22no—
442C2×Q8—22no—
443C2×Q8C2×C22⋊D4312yes—
444C2×Q8C2×C22⋊D4312yes—
445C2×D4—24no—
446C2×D4—22no—
447C2×D4—24no—
448C2×D4—22no—
449C2×D4—21no—
450C2×D4—22no—
451C2×D4—41no—
452C2×D4—44no—
453C2×D4—44no—
454C2×D4#1062190014yes—
455C2×D4C2×C22⋊D4312yes—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—24no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—44no—
469C22×C4—44no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—862no—
473C22×C4—862no—
474C22×C4—1722no—
475C22×C4—1722no—
476C22×C4—1722no—
477C22×C4C2×C22⋊D4311yescharacteristic
478C22×C4C2×C22⋊D4311yescharacteristic
479C22×C4C2×C22⋊D4311yescharacteristic
480C22×C4C2×C22⋊D4312yes—
481C22×C4C2×C22⋊D4312yes—
482C22×C4C2×C22⋊D4311yescharacteristic
483C22×C4C23×D4311yescharacteristic
484M16—1724no—
485C2×C8—862no—
486C2×C8—862no—
487C2×C8—862no—
488C2×C8—862no—
489C2×C8—862no—
490C2×C8—862no—
491C4⋊C4—24no—
492C4⋊C4—24no—
493C4⋊C4—24no—
494C4⋊C4—22no—
495C4⋊C4—24no—
496C4⋊C4—21no—
497C4⋊C4—862no—
498C4⋊C4—862no—
499C4⋊C4—862no—
500C4⋊C4—862no—
501C4⋊C4—1722no—
502C4⋊C4—1724no—
503C4⋊C4C2×C22⋊D4312yes—
504C22⋊C4—24no—
505C22⋊C4—24no—
506C22⋊C4—24no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—1722no—
510C22⋊C4—1724no—
511C42—21no—
512C42—21no—
513C23—22no—
514C23—21no—
515C23—21no—
516C23—22no—
517C23—22no—
518C23—24no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—22no—
523C23—22no—
524C23—41no—
525C23—41no—
526C23—42no—
527C23#1306329412yes—
528C23C22×C22⋊D4311yescharacteristic
529Q8—22no—
530Q8—22no—
531Q8—24no—
532Q8—41no—
533Q8—41no—
534Q8—42no—
535D4—22no—
536D4—24no—
537D4—44no—
538D4—48no—
539D4—48no—
540D4#1306330614yescomplemented
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—21no—
548C2×C4—22no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—48no—
555C2×C4—48no—
556C2×C4—48no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—42no—
564C2×C4—3444no—
565C2×C4—1722no—
566C2×C4—1722no—
567C2×C4—1722no—
568C2×C4—1722no—
569C2×C4—1722no—
570C2×C4—1722no—
571C2×C4#1306329412yes—
572C2×C4#1306335012yes—
573C2×C4C22×C22⋊D4311yescharacteristic
574C2×C4C22×C22⋊D4311yescharacteristic
575C2×C4C2×#1062190012yes—
576C2×C4#1306337012yes—
577C8—1722no—
578C8—1722no—
579C22—22no—
580C22—24no—
581C22—22no—
582C22—22no—
583C22—42no—
584C22—44no—
585C22—42no—
586C22—42no—
587C22—44no—
588C22—42no—
589C22—41no—
590C22—42no—
591C22—41no—
592C22—42no—
593C22—41no—
594C22C2×#1306329411yescharacteristic
595C22#1458354312yes—
596C22C2×#1306335011yescharacteristic
597C22#1458369711yescharacteristic
598C22#1458371412yes—
599C4—22no—
600C4—22no—
601C4—41no—
602C4—42no—
603C4—42no—
604C4—42no—
605C4—41no—
606C4—3442no—
607C4—3442no—
608C4C2×#1306330611yescharacteristic
609C4#1458345811yescharacteristic
610C4#1458354312yes—
611C2—42no—
612C2—44no—
613C2—81no—
614C2#1913791811yescharacteristic
615C2#1914384711yescharacteristic
616C2#1914389011yescharacteristic
617C2#1914669112yes—
618C2#1914690012yes—
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#547C2
socleC23×C43C22×D4
hypercenterC2×#547D43
hypocenterC43#24054
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#14583232C2semidirect
2. C2×#14582900C2semidirect
3. #19138903C2semidirect
4. #19135838C2semidirect
5. #19135795C2semidirect
6. #19135029C2semidirect
7. #19134893C2semidirect
8. #19134842C2semidirect
9. #19134535C2semidirect
10. #19134535C2semidirect
230. D4×C43#123semidirect
356. C43#24054semidirect
540. D4#13063306semidirect

Maximal subgroups

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

subgroupindex
C2×#145832322
C2×#145829002
#191389032
#191358382
#191357952
#191350292
#191348932
#191348422
#191345352
C2×C43×#5472
#2405443