Finite Group Databasebeta

← #25150270

Subgroups — #25150270

Order 11008.

1216 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583289C211yesmaximal, characteristic, complemented
2C2×#14583247C211yesmaximal, characteristic, complemented
3#19140345C211yesmaximal, characteristic, complemented
4#19135596C212yesmaximal, complemented
5#19135591C212yesmaximal, complemented
6#19135569C211yesmaximal, characteristic, complemented
7#19135407C211yesmaximal, characteristic, complemented
8#19134950C212yesmaximal, complemented
9#19134943C212yesmaximal, complemented
10#19134361C211yesmaximal, characteristic, complemented
11C2×C43×#542C211yesmaximal, characteristic, complemented
12C22×#10621884C2212yes—
13C22×#10621882C2212yes—
14C2×#13063322C2211yescharacteristic
15C2×#13063299C2212yes—
16#14583289—24no—
17#14583247—24no—
18C2×#13063249C2212yes—
19C2×#13063246C2212yes—
20C2×#13063245C2212yes—
21C2×#13063245C2212yes—
22C2×C22⋊(C43⋊C8)C2212yes—
23C2×#13063236C2211yescharacteristic
24C2×C4×C43⋊C8C2211yescharacteristic
25#14582816—21no—
26#14582816—21no—
27#14582808—21no—
28#14582808—21no—
29#14582801C2212yes—
30#14582765C2211yescharacteristic
31#14582661C2212yes—
32#14582661C2212yes—
33#14582654C2212yes—
34C43×#542—24no—
35C43×#542—24no—
36C2×C4⋊Q8×C43C2211yescharacteristic
37C2×#126×C43—21no—
38C2×#124×C43—21no—
39C2×#124×C43C2211yescharacteristic
40C2×#123×C43—21no—
41C2×C22⋊Q8×C43—21no—
42C2×C22⋊Q8×C43C2211yescharacteristic
43C2×#121×C43C2211yescharacteristic
44C2×C4×Q8×C43C2211yescharacteristic
45C2×C4×D4×C43C2211yescharacteristic
46C2×#117×C43C2211yescharacteristic
47C22×D172—21no—
48C22×D172—21no—
49C22×D172C2312yes—
50C22×C22⋊D43—22no—
51C2×#10621884—24no—
52C2×#10621884—24no—
53C2×#10621884—42no—
54C2×#10621882—24no—
55C2×#10621882—24no—
56C2×#10621882—42no—
57C22×C43⋊C8C2312yes—
58C22×C43⋊C8C2312yes—
59#13063322—22no—
60#13063322—22no—
61#13063299—42no—
62#13063299—42no—
63C2×C4⋊Dic43C2312yes—
64C2×(C2×D43)⋊C4—22no—
65C2×(C2×D43)⋊C4—22no—
66C2×(C2×D43)⋊C4—22no—
67#13063249—42no—
68#13063246—42no—
69#13063245—24no—
70#13063245—24no—
71C22⋊(C43⋊C8)—24no—
72#13063236—22no—
73C4×C43⋊C8—22no—
74C43⋊#95—21no—
75C43⋊#95—21no—
76C22×Q8×C43—21no—
77C22×Q8×C43C2311yescharacteristic
78C22×D4×C43—21no—
79C22×D4×C43C2311yescharacteristic
80C23×C4×C43—21no—
81C23×C4×C43C2311yescharacteristic
82C4⋊Q8×C43—22no—
83C4⋊Q8×C43D414yescomplemented
84#126×C43—28no—
85#124×C43—28no—
86#124×C43—22no—
87#124×C43D414yescomplemented
88#123×C43—28no—
89C22⋊Q8×C43—28no—
90C22⋊Q8×C43—22no—
91C22⋊Q8×C43—22no—
92#121×C43—22no—
93#121×C43—22no—
94C4×Q8×C43—22no—
95C4×Q8×C43—22no—
96C4×D4×C43—22no—
97C4×D4×C43—22no—
98#117×C43—22no—
99#117×C43—22no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43D411yescharacteristic
104C2×C4⋊C4×C43D411yescharacteristic
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43—21no—
109C2×C22⋊C4×C43—21no—
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43D411yescharacteristic
113C2×C22⋊C4×C43D411yescharacteristic
114C2×C42×C43—21no—
115C2×C42×C43C2311yescharacteristic
116C2×C42×C43C2311yescharacteristic
117C24×C43—21no—
118C24×C43C2×D411yescharacteristic
119C23×D43—22no—
120C2×Q8×C43—24no—
121C2×Q8×C43—21no—
122C2×Q8×C43—22no—
123C2×Q8×C43—22no—
124C2×Q8×C43—82no—
125C2×Q8×C43C2×D412yes—
126C2×D4×C43—24no—
127C2×D4×C43—21no—
128C2×D4×C43—22no—
129C2×D4×C43—22no—
130C2×D4×C43—82no—
131C2×D4×C43C2×D412yes—
132C22×C4×C43—24no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—22no—
136C22×C4×C43—22no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—82no—
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2411yescharacteristic
147C2×C22⋊D43—44no—
148C2×C22⋊D43—82no—
149C2×C22⋊D43—82no—
150C22×Dic43—22no—
151C2×D172—22no—
152C2×D172—22no—
153C2×D172—22no—
154C2×D172—22no—
155C2×D172—22no—
156C2×D172—22no—
157C2×D172—42no—
158C2×D172—42no—
159C2×D172—82no—
160C2×D172—82no—
161C4⋊C4×C43—24no—
162C4⋊C4×C43—24no—
163C4⋊C4×C43—24no—
164C4⋊C4×C43—22no—
165C4⋊C4×C43—22no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43C2×D412yes—
169C4⋊C4×C43C2×D412yes—
170C22⋊C4×C43—24no—
171C22⋊C4×C43—24no—
172C22⋊C4×C43—24no—
173C22⋊C4×C43—24no—
174C22⋊C4×C43—24no—
175C22⋊C4×C43—22no—
176C22⋊C4×C43—22no—
177C42×C43—24no—
178C42×C43—21no—
179C42×C43—21no—
180C42×C43C2×D412yes—
181C42×C43C2×D412yes—
182#10621884—48no—
183#10621882—48no—
184(C2×D43)⋊C4—44no—
185(C2×D43)⋊C4—82no—
186(C2×D43)⋊C4—82no—
187C4⋊Dic43—22no—
188C4⋊Dic43—22no—
189C2×C43⋊C8—22no—
190C2×C43⋊C8—22no—
191C2×C43⋊C8—22no—
192C2×C43⋊C8—22no—
193C2×C43⋊C8—22no—
194C2×C43⋊C8#4114yes—
195C23×C43—21no—
196C23×C43—22no—
197C23×C43—21no—
198C23×C43—21no—
199C23×C43—22no—
200C23×C43—22no—
201C23×C43—41no—
202C23×C43—41no—
203C23×C43—42no—
204C23×C43—42no—
205C23×C43C22×D411yescharacteristic
206C22×D43—42no—
207C22×D43—42no—
208C22×D43—42no—
209C22×D43—42no—
210C22×D43—42no—
211C22×D43—42no—
212C22×D43—42no—
213Q8×C43—24no—
214Q8×C43—42no—
215Q8×C43—84no—
216D4×C43—24no—
217D4×C43—42no—
218D4×C43—84no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—21no—
222C2×C4×C43—22no—
223C2×C4×C43—21no—
224C2×C4×C43—22no—
225C2×C4×C43—21no—
226C2×C4×C43—22no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—22no—
230C2×C4×C43—22no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—42no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43—84no—
238C2×C4×C43#12012yes—
239C2×C4×C43#12012yes—
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43C2×#4112yes—
243C2×C4×C43H(5,𝔽2)12yes—
244C22⋊D43—88no—
245C2×Dic43—42no—
246C2×Dic43—42no—
247C2×Dic43—42no—
248D172—42no—
249D172—42no—
250D172—42no—
251D172—42no—
252D172—84no—
253D172—84no—
254C43⋊C8—24no—
255C43⋊C8—42no—
256#25614—431nomaximal, Sylow
257C22×C43—42no—
258C22×C43—41no—
259C22×C43—42no—
260C22×C43—42no—
261C22×C43—41no—
262C22×C43—42no—
263C22×C43—41no—
264C22×C43—42no—
265C22×C43—82no—
266C22×C43—82no—
267C22×C43C2×#12011yescharacteristic
268C22×C43#53211yescharacteristic
269C22×C43#53511yescharacteristic
270C22×C43#57612yes—
271C22×C43#57712yes—
272C2×D43—82no—
273C2×D43—82no—
274C2×D43—82no—
275C2×D43—82no—
276C2×D43—82no—
277C2×D43—82no—
278C2×D43—82no—
279C4×C43—22no—
280C4×C43—22no—
281C4×C43—41no—
282C4×C43—42no—
283C4×C43—41no—
284C4×C43—42no—
285C4×C43—42no—
286C4×C43—41no—
287C4×C43#54612yes—
288C4×C43#55012yes—
289Dic43—82no—
290C2×#542D4311yescharacteristic, complemented
291C2×#496—431no—
292C2×#486—431no—
293#2619—431no—
294#2000—432no—
295#1999—432no—
296#1993—431no—
297#1958—431no—
298#1880—432no—
299#1879—432no—
300#1750—431no—
301C2×C43—81no—
302C2×C43—82no—
303C2×C43#243111yescharacteristic
304C2×C43#300811yescharacteristic
305C2×C43#301011yescharacteristic
306C2×C43#317912yes—
307C2×C43#322412yes—
308D43—162no—
309C22×SD16—432no—
310C22×D8—432no—
311#542—24no—
312#542—24no—
313C2×C4⋊Q8C2×D4311yescharacteristic
314C2×#127—431no—
315C2×#126—21no—
316C2×#124—21no—
317C2×#124C2×D4311yescharacteristic
318C2×#123—21no—
319C2×C22⋊Q8—21no—
320C2×C22⋊Q8C2×D4311yescharacteristic
321C2×#121—432no—
322C2×#121C2×D4311yescharacteristic
323C2×C4×Q8C2×D4311yescharacteristic
324C2×C4×D4C2×D4311yescharacteristic
325C2×#117C2×D4311yescharacteristic
326#496—864no—
327#486—864no—
328C2×#103—432no—
329C2×#102—432no—
330C2×#102—432no—
331C2×#102—432no—
332C2×C22⋊C8—432no—
333C2×#97—431no—
334C2×C4×C8—431no—
335#394—861no—
336#394—861no—
337#392—861no—
338#392—861no—
339#390—432no—
340#382—431no—
341#340—432no—
342#340—432no—
343#336—432no—
344C43#2561411yescharacteristic, complemented, Sylow
345C22×Q8—21no—
346C22×Q8C22×D4311yescharacteristic
347C22×D4—21no—
348C22×D4—432no—
349C22×D4—862no—
350C22×D4—861no—
351C22×D4—861no—
352C22×D4C22×D4311yescharacteristic
353C23×C4—21no—
354C23×C4C22×D4311yescharacteristic
355C2×SD16—864no—
356C2×SD16—864no—
357C2×SD16—1722no—
358C2×D8—864no—
359C2×D8—864no—
360C2×D8—1722no—
361C22×C8—432no—
362C22×C8—432no—
363C4⋊Q8—22no—
364C4⋊Q8C22⋊D4314yescomplemented
365#127—862no—
366#127—862no—
367#126—28no—
368#124—28no—
369#124—22no—
370#124C22⋊D4314yescomplemented
371#123—28no—
372C22⋊Q8—28no—
373C22⋊Q8—22no—
374C22⋊Q8—22no—
375#121—22no—
376#121—22no—
377#121—1722no—
378#121—1722no—
379C4×Q8—22no—
380C4×Q8—22no—
381C4×D4—22no—
382C4×D4—22no—
383#117—22no—
384#117—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—432no—
389C2×C4⋊C4C22⋊D4311yescharacteristic
390C2×C4⋊C4C22⋊D4311yescharacteristic
391C2×C4⋊C4C22×D4311yescharacteristic
392C2×C4⋊C4C22×D4311yescharacteristic
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—862no—
399C2×C22⋊C4—862no—
400C2×C22⋊C4—862no—
401C2×C22⋊C4C22⋊D4311yescharacteristic
402C2×C22⋊C4C22⋊D4311yescharacteristic
403C2×C42—21no—
404C2×C42C22×D4311yescharacteristic
405C2×C42C22×D4311yescharacteristic
406#103—1722no—
407#102—864no—
408#102—864no—
409#102—1722no—
410C22⋊C8—864no—
411#97—862no—
412C4×C8—862no—
413#95—861no—
414#95—861no—
415C24—21no—
416C24—862no—
417C24C2×C22⋊D4311yescharacteristic
418C2×Q8—24no—
419C2×Q8—21no—
420C2×Q8—22no—
421C2×Q8—22no—
422C2×Q8—82no—
423C2×Q8C2×C22⋊D4312yes—
424C2×D4—24no—
425C2×D4—21no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—82no—
429C2×D4—862no—
430C2×D4—862no—
431C2×D4—862no—
432C2×D4—862no—
433C2×D4—862no—
434C2×D4—862no—
435C2×D4—3442no—
436C2×D4—3442no—
437C2×D4—3442no—
438C2×D4—3442no—
439C2×D4—1724no—
440C2×D4—1722no—
441C2×D4—1722no—
442C2×D4C2×C22⋊D4312yes—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—24no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—82no—
452C22×C4—862no—
453C22×C4C2×C22⋊D4311yescharacteristic
454C22×C4C2×C22⋊D4311yescharacteristic
455C22×C4C2×C22⋊D4311yescharacteristic
456C22×C4C2×C22⋊D4311yescharacteristic
457C22×C4C2×C22⋊D4311yescharacteristic
458C22×C4C23×D4311yescharacteristic
459SD16—1728no—
460D8—1728no—
461C2×C8—434no—
462C2×C8—862no—
463C2×C8—862no—
464C2×C8—862no—
465C2×C8—862no—
466C2×C8—862no—
467C4⋊C4—24no—
468C4⋊C4—24no—
469C4⋊C4—24no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—862no—
475C4⋊C4—862no—
476C4⋊C4C2×C22⋊D4312yes—
477C4⋊C4C2×C22⋊D4312yes—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4—24no—
481C22⋊C4—24no—
482C22⋊C4—24no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—3442no—
486C22⋊C4—3442no—
487C22⋊C4—1724no—
488C42—24no—
489C42—21no—
490C42—21no—
491C42C2×C22⋊D4312yes—
492C42C2×C22⋊D4312yes—
493C23—21no—
494C23—22no—
495C23—21no—
496C23—22no—
497C23—22no—
498C23—21no—
499C23—41no—
500C23—42no—
501C23—42no—
502C23—41no—
503C23—1722no—
504C23—1722no—
505C23—1722no—
506C23—1722no—
507C23—1722no—
508C23—1722no—
509C23—1722no—
510C23C22×C22⋊D4311yescharacteristic
511Q8—24no—
512Q8—42no—
513Q8—84no—
514D4—24no—
515D4—42no—
516D4—84no—
517D4—3444no—
518D4—3444no—
519D4—3448no—
520D4—1722no—
521D4—1722no—
522D4—1722no—
523D4—1722no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—84no—
543C2×C4—1722no—
544C2×C4—1722no—
545C2×C4—1722no—
546C2×C4#1306329412yes—
547C2×C4#1306329412yes—
548C2×C4C22×C22⋊D4311yescharacteristic
549C2×C4C22×C22⋊D4311yescharacteristic
550C2×C4#41×D4312yes—
551C2×C4#1306337112yes—
552C8—864no—
553C8—1722no—
554C22—42no—
555C22—41no—
556C22—42no—
557C22—42no—
558C22—41no—
559C22—41no—
560C22—42no—
561C22—42no—
562C22—82no—
563C22—82no—
564C22—3442no—
565C22—3442no—
566C22—3442no—
567C22—3442no—
568C22—3442no—
569C22—3442no—
570C22—3442no—
571C22C2×#1306329411yescharacteristic
572C22#1458344511yescharacteristic
573C22#1458346311yescharacteristic
574C22#1458370212yes—
575C22#1458370712yes—
576C4—22no—
577C4—22no—
578C4—41no—
579C4—42no—
580C4—41no—
581C4—42no—
582C4—42no—
583C4—41no—
584C4—3442no—
585C4#1458353712yes—
586C4#1458356812yes—
587C2—81no—
588C2—82no—
589C2—6882no—
590C2#1913821011yescharacteristic
591C2#1914386311yescharacteristic
592C2#1914388111yescharacteristic
593C2#1914527212yes—
594C2#1914568312yes—
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#542C2
socleC23×C43C22×D4
hypercenterC2×#542D43
hypocenterC43#25614
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#14583289C2semidirect
2. C2×#14583247C2semidirect
3. #19140345C2semidirect
4. #19135596C2semidirect
5. #19135591C2semidirect
6. #19135569C2semidirect
7. #19135407C2semidirect
8. #19134950C2semidirect
9. #19134943C2semidirect
10. #19134361C2semidirect
11. C2×C43×#542C2semidirect
83. C4⋊Q8×C43D4semidirect
87. #124×C43D4semidirect
290. C2×#542D43semidirect
344. C43#25614semidirect
364. C4⋊Q8C22⋊D43semidirect
370. #124C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145832892
C2×#145832472
#191403452
#191355962
#191355912
#191355692
#191354072
#191349502
#191349432
#191343612
C2×C43×#5422
#2561443