Finite Group Databasebeta

← #25149923

Subgroups — #25149923

Order 11008.

1326 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583265C211yesmaximal, characteristic, complemented
2C2×#14583094C211yesmaximal, characteristic, complemented
3#19139541C211yesmaximal, characteristic, complemented
4#19135591C212yesmaximal, complemented
5#19135591C212yesmaximal, complemented
6#19135553C211yesmaximal, characteristic, complemented
7#19135394C211yesmaximal, characteristic, complemented
8#19134917C212yesmaximal, complemented
9#19134912C212yesmaximal, complemented
10#19134420C211yesmaximal, characteristic, complemented
11C2×C43×#553C211yesmaximal, characteristic, complemented
12C22×#10621882C2212yes—
13C2×#13063322C2211yescharacteristic
14C2×#13063321—21no—
15C2×#13063299C2212yes—
16C2×#13063299C2212yes—
17#14583265—24no—
18#14583094—24no—
19C2×C4⋊(C43⋊C8)C2211yescharacteristic
20C2×#13063246C2212yes—
21C2×#13063245C2212yes—
22C2×#13063245C2212yes—
23C2×#13063245C2212yes—
24C2×C22⋊(C43⋊C8)C2212yes—
25C2×C22⋊(C43⋊C8)C2212yes—
26C2×#13063236C2211yescharacteristic
27#14582808—21no—
28#14582808—21no—
29#14582800—21no—
30C4×C4⋊Dic43C2211yescharacteristic
31#14582661C2212yes—
32#14582661C2212yes—
33#14582661C2212yes—
34C43×#553—24no—
35C43×#553—24no—
36C2×#126×C43—21no—
37C2×#125×C43C2211yescharacteristic
38C2×#123×C43—21no—
39C2×#121×C43—21no—
40C2×#121×C43C2211yescharacteristic
41C2×#121×C43C2211yescharacteristic
42C2×C4×D4×C43—21no—
43C2×C4×D4×C43C2211yescharacteristic
44C2×C4×D4×C43C2211yescharacteristic
45C2×#117×C43C2211yescharacteristic
46C22×C4⋊C4×C43C2211yescharacteristic
47C22×D172—21no—
48C22×D172—21no—
49C22×D172C2312yes—
50C22×C22⋊D43—22no—
51C22×C22⋊D43—22no—
52C2×#10621882—24no—
53C2×#10621882—42no—
54C2×#10621882—42no—
55C22×C43⋊C8C2312yes—
56C22×C43⋊C8C2312yes—
57#13063322—22no—
58#13063322—22no—
59#13063321—44no—
60#13063299—24no—
61#13063299—24no—
62#13063299—42no—
63#13063299—42no—
64C2×C4⋊Dic43C2312yes—
65C2×(C2×D43)⋊C4—22no—
66C2×(C2×D43)⋊C4—22no—
67C2×C4×Dic43—21no—
68C4⋊(C43⋊C8)—22no—
69#13063246—24no—
70#13063245—24no—
71#13063245—24no—
72#13063245—24no—
73C22⋊(C43⋊C8)—42no—
74C22⋊(C43⋊C8)—42no—
75#13063236—22no—
76C43⋊#95—21no—
77C22×D4×C43—21no—
78C22×D4×C43—21no—
79C22×D4×C43D411yescharacteristic
80C22×D4×C43C2311yescharacteristic
81C23×C4×C43—21no—
82C23×C4×C43—21no—
83C23×C4×C43C2311yescharacteristic
84C23×C4×C43C2311yescharacteristic
85#126×C43—28no—
86#125×C43—22no—
87#125×C43D414yescomplemented
88#123×C43—28no—
89#121×C43—28no—
90#121×C43—22no—
91#121×C43—22no—
92#121×C43—22no—
93#121×C43—22no—
94C4×D4×C43—28no—
95C4×D4×C43—22no—
96C4×D4×C43—22no—
97C4×D4×C43—22no—
98C4×D4×C43D414yescomplemented
99#117×C43—22no—
100#117×C43—22no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—22no—
105C2×C4⋊C4×C43—22no—
106C2×C4⋊C4×C43D411yescharacteristic
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43D411yescharacteristic
115C2×C22⋊C4×C43D411yescharacteristic
116C2×C42×C43—21no—
117C2×C42×C43C2311yescharacteristic
118C24×C43—21no—
119C24×C43C2×D411yescharacteristic
120C24×C43C2×D411yescharacteristic
121C23×D43—22no—
122C2×D4×C43—24no—
123C2×D4×C43—24no—
124C2×D4×C43—22no—
125C2×D4×C43—21no—
126C2×D4×C43—22no—
127C2×D4×C43—22no—
128C2×D4×C43—22no—
129C2×D4×C43—41no—
130C2×D4×C43—42no—
131C2×D4×C43—42no—
132C2×D4×C43—82no—
133C2×D4×C43C2×D412yes—
134C22×C4×C43—24no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—22no—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—24no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—82no—
148C22×C4×C43—82no—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2411yescharacteristic
154C2×C22⋊D43—44no—
155C2×C22⋊D43—44no—
156C2×C22⋊D43—44no—
157C2×C22⋊D43—44no—
158C2×C22⋊D43—82no—
159C2×C22⋊D43—82no—
160C22×Dic43—22no—
161C2×D172—22no—
162C2×D172—22no—
163C2×D172—22no—
164C2×D172—22no—
165C2×D172—22no—
166C2×D172—22no—
167C2×D172—42no—
168C2×D172—42no—
169C2×D172—42no—
170C2×D172—42no—
171C2×D172—82no—
172C4⋊C4×C43—24no—
173C4⋊C4×C43—24no—
174C4⋊C4×C43—24no—
175C4⋊C4×C43—22no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43C2×D412yes—
180C4⋊C4×C43C2×D412yes—
181C4⋊C4×C43C2×D412yes—
182C22⋊C4×C43—24no—
183C22⋊C4×C43—24no—
184C22⋊C4×C43—24no—
185C22⋊C4×C43—24no—
186C22⋊C4×C43—22no—
187C22⋊C4×C43—22no—
188C42×C43—24no—
189C42×C43C2×D412yes—
190C42×C43C2×D412yes—
191#10621882—48no—
192(C2×D43)⋊C4—44no—
193(C2×D43)⋊C4—44no—
194C4⋊Dic43—22no—
195C4⋊Dic43#4114yes—
196C4×Dic43—42no—
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—21no—
204C23×C43—22no—
205C23×C43—21no—
206C23×C43—22no—
207C23×C43—21no—
208C23×C43—22no—
209C23×C43—22no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—22no—
213C23×C43—42no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—42no—
217C23×C43AGL(1,ℤ/8)12yes—
218C23×C43C22×D411yescharacteristic
219C22×D43—42no—
220C22×D43—42no—
221C22×D43—42no—
222C22×D43—42no—
223C22×D43—42no—
224C22×D43—42no—
225C22×D43—42no—
226D4×C43—22no—
227D4×C43—22no—
228D4×C43—44no—
229D4×C43—48no—
230D4×C43—42no—
231D4×C43—84no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—22no—
235C2×C4×C43—21no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—21no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—42no—
245C2×C4×C43—42no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—42no—
251C2×C4×C43—42no—
252C2×C4×C43—84no—
253C2×C4×C43—84no—
254C2×C4×C43#12012yes—
255C2×C4×C43#12012yes—
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43C22×D411yescharacteristic
258C2×C4×C43C2×#4112yes—
259C2×C4×C43H(5,𝔽2)12yes—
260C22⋊D43—88no—
261C22⋊D43—88no—
262C2×Dic43—24no—
263C2×Dic43—42no—
264C2×Dic43—42no—
265D172—42no—
266D172—42no—
267D172—42no—
268D172—42no—
269D172—84no—
270D172—84no—
271C43⋊C8—42no—
272C43⋊C8—42no—
273#25581—431nomaximal, Sylow
274C22×C43—22no—
275C22×C43—24no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—42no—
279C22×C43—41no—
280C22×C43—42no—
281C22×C43—41no—
282C22×C43—42no—
283C22×C43—41no—
284C22×C43—42no—
285C22×C43—42no—
286C22×C43—42no—
287C22×C43—82no—
288C22×C43—82no—
289C22×C43C2×#12011yescharacteristic
290C22×C43#54612yes—
291C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
292C22×C43#57511yescharacteristic
293C22×C43#57612yes—
294C2×D43—82no—
295C2×D43—82no—
296C2×D43—82no—
297C2×D43—82no—
298C2×D43—82no—
299C2×D43—82no—
300C2×D43—82no—
301C4×C43—22no—
302C4×C43—22no—
303C4×C43—41no—
304C4×C43—41no—
305C4×C43—42no—
306C4×C43—42no—
307C4×C43—42no—
308C4×C43#53211yescharacteristic
309C4×C43#53511yescharacteristic
310C4×C43#55012yes—
311Dic43—44no—
312C2×#553D4311yescharacteristic, complemented
313C2×#490—431no—
314C2×#459—431no—
315#2541—431no—
316#1999—432no—
317#1999—432no—
318#1989—431no—
319#1955—431no—
320#1875—432no—
321#1874—432no—
322#1762—431no—
323C2×C43—42no—
324C2×C43—81no—
325C2×C43—82no—
326C2×C43#243111yescharacteristic
327C2×C43#300611yescharacteristic
328C2×C43#300811yescharacteristic
329C2×C43#330912yes—
330C2×C43#331812yes—
331D43—162no—
332C22×D8—432no—
333#553—24no—
334#553—24no—
335C2×#127—431no—
336C2×#127—861no—
337C2×#126—21no—
338C2×#125C2×D4311yescharacteristic
339C2×#123—21no—
340C2×#121—21no—
341C2×#121—432no—
342C2×#121—432no—
343C2×#121C2×D4311yescharacteristic
344C2×#121C2×D4311yescharacteristic
345C2×C4×D4—21no—
346C2×C4×D4C2×D4311yescharacteristic
347C2×C4×D4C2×D4311yescharacteristic
348C2×#117C2×D4311yescharacteristic
349C22×C4⋊C4C2×D4311yescharacteristic
350#490—864no—
351#459—864no—
352C2×C4⋊C8—431no—
353C2×#102—432no—
354C2×#102—432no—
355C2×#102—432no—
356C2×#102—432no—
357C2×C22⋊C8—432no—
358C2×C22⋊C8—432no—
359C2×#97—431no—
360#392—861no—
361#392—861no—
362#390—861no—
363C4×C4⋊C4—431no—
364#340—432no—
365#340—432no—
366#340—432no—
367C43#2558111yescharacteristic, complemented, Sylow
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—432no—
371C22×D4—862no—
372C22×D4—862no—
373C22×D4—861no—
374C22×D4—861no—
375C22×D4C22⋊D4311yescharacteristic
376C22×D4C22×D4311yescharacteristic
377C23×C4—21no—
378C23×C4—21no—
379C23×C4C22×D4311yescharacteristic
380C23×C4C22×D4311yescharacteristic
381C2×D8—864no—
382C2×D8—1722no—
383C2×D8—1722no—
384C22×C8—432no—
385C22×C8—432no—
386#127—862no—
387#127—862no—
388#127—1724no—
389#126—28no—
390#125—22no—
391#125C22⋊D4314yescomplemented
392#123—28no—
393#121—28no—
394#121—22no—
395#121—22no—
396#121—22no—
397#121—22no—
398#121—864no—
399#121—864no—
400#121—1722no—
401#121—1722no—
402C4×D4—28no—
403C4×D4—22no—
404C4×D4—22no—
405C4×D4—22no—
406C4×D4C22⋊D4314yescomplemented
407#117—22no—
408#117—22no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—432no—
415C2×C4⋊C4C22⋊D4311yescharacteristic
416C2×C4⋊C4C22×D4311yescharacteristic
417C2×C4⋊C4C22×D4311yescharacteristic
418C2×C4⋊C4C22×D4311yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—862no—
424C2×C22⋊C4—862no—
425C2×C22⋊C4C22⋊D4311yescharacteristic
426C2×C22⋊C4C22⋊D4311yescharacteristic
427C2×C42—21no—
428C2×C42—861no—
429C2×C42C22×D4311yescharacteristic
430C4⋊C8—862no—
431#102—864no—
432#102—864no—
433#102—864no—
434#102—864no—
435C22⋊C8—1722no—
436C22⋊C8—1722no—
437#97—862no—
438#95—861no—
439C24—21no—
440C24—862no—
441C24C2×C22⋊D4311yescharacteristic
442C24C2×C22⋊D4311yescharacteristic
443C2×D4—24no—
444C2×D4—22no—
445C2×D4—24no—
446C2×D4—22no—
447C2×D4—21no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—41no—
451C2×D4—42no—
452C2×D4—42no—
453C2×D4—82no—
454C2×D4—862no—
455C2×D4—862no—
456C2×D4—862no—
457C2×D4—862no—
458C2×D4—862no—
459C2×D4—862no—
460C2×D4—3442no—
461C2×D4—3442no—
462C2×D4—3442no—
463C2×D4—1722no—
464C2×D4—1722no—
465C2×D4—1724no—
466C2×D4—1724no—
467C2×D4—1724no—
468C2×D4—1724no—
469C2×D4—1722no—
470C2×D4—1722no—
471C2×D4C2×C22⋊D4312yes—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—24no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—82no—
486C22×C4—82no—
487C22×C4—862no—
488C22×C4C2×C22⋊D4311yescharacteristic
489C22×C4C2×C22⋊D4311yescharacteristic
490C22×C4C2×C22⋊D4311yescharacteristic
491C22×C4C2×C22⋊D4311yescharacteristic
492C22×C4C23×D4311yescharacteristic
493D8—1728no—
494C2×C8—862no—
495C2×C8—862no—
496C2×C8—862no—
497C2×C8—862no—
498C2×C8—862no—
499C2×C8—862no—
500C4⋊C4—24no—
501C4⋊C4—24no—
502C4⋊C4—24no—
503C4⋊C4—22no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—434no—
508C4⋊C4—862no—
509C4⋊C4C2×C22⋊D4312yes—
510C4⋊C4C2×C22⋊D4312yes—
511C4⋊C4C2×C22⋊D4312yes—
512C22⋊C4—24no—
513C22⋊C4—24no—
514C22⋊C4—24no—
515C22⋊C4—24no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—1724no—
519C22⋊C4—1724no—
520C42—24no—
521C42—1722no—
522C42C2×C22⋊D4312yes—
523C42C2×C22⋊D4312yes—
524C23—21no—
525C23—21no—
526C23—22no—
527C23—22no—
528C23—21no—
529C23—22no—
530C23—21no—
531C23—21no—
532C23—22no—
533C23—22no—
534C23—41no—
535C23—41no—
536C23—42no—
537C23—42no—
538C23—1722no—
539C23—1722no—
540C23—1722no—
541C23—1722no—
542C23—1722no—
543C23—1722no—
544C23—1722no—
545C23#1306335012yes—
546C23C22×C22⋊D4311yescharacteristic
547D4—22no—
548D4—22no—
549D4—44no—
550D4—48no—
551D4—42no—
552D4—84no—
553D4—3444no—
554D4—3444no—
555D4—3448no—
556D4—3448no—
557D4—1722no—
558D4—1722no—
559D4—1722no—
560D4—1722no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—84no—
582C2×C4—84no—
583C2×C4—864no—
584C2×C4—1722no—
585C2×C4—1722no—
586C2×C4#1306329412yes—
587C2×C4#1306329412yes—
588C2×C4C22×C22⋊D4311yescharacteristic
589C2×C4C22×C22⋊D4311yescharacteristic
590C2×C4#41×D4312yes—
591C2×C4#1306337112yes—
592C8—1722no—
593C8—1722no—
594C22—22no—
595C22—24no—
596C22—42no—
597C22—41no—
598C22—41no—
599C22—42no—
600C22—41no—
601C22—42no—
602C22—41no—
603C22—42no—
604C22—42no—
605C22—41no—
606C22—42no—
607C22—82no—
608C22—82no—
609C22—3442no—
610C22—3442no—
611C22—3442no—
612C22—3442no—
613C22—3442no—
614C22—3442no—
615C22—3442no—
616C22C2×#1306329411yescharacteristic
617C22#1458353712yes—
618C22C2×#1306335011yescharacteristic
619C22#1458369711yescharacteristic
620C22#1458370212yes—
621C4—22no—
622C4—22no—
623C4—41no—
624C4—41no—
625C4—42no—
626C4—42no—
627C4—42no—
628C4—1724no—
629C4#1458344511yescharacteristic
630C4#1458346311yescharacteristic
631C4#1458356812yes—
632C2—42no—
633C2—81no—
634C2—82no—
635C2—6882no—
636C2#1913821011yescharacteristic
637C2#1914384711yescharacteristic
638C2#1914386311yescharacteristic
639C2#1914659512yes—
640C2#1914673012yes—
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#553C2
socleC23×C43C22×D4
hypercenterC2×#553D43
hypocenterC43#25581
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#14583265C2semidirect
2. C2×#14583094C2semidirect
3. #19139541C2semidirect
4. #19135591C2semidirect
5. #19135591C2semidirect
6. #19135553C2semidirect
7. #19135394C2semidirect
8. #19134917C2semidirect
9. #19134912C2semidirect
10. #19134420C2semidirect
11. C2×C43×#553C2semidirect
87. #125×C43D4semidirect
98. C4×D4×C43D4semidirect
312. C2×#553D43semidirect
367. C43#25581semidirect
391. #125C22⋊D43semidirect
406. C4×D4C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145832652
C2×#145830942
#191395412
#191355912
#191355532
#191353942
#191349172
#191349122
#191344202
C2×C43×#5532
#2558143