Finite Group Databasebeta

← #25105913

Subgroups — #25105913

Order 11008.

1418 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583445C211yesmaximal, characteristic
2C2×#14582949C211yesmaximal, characteristic, complemented
3#19136997C211yesmaximal, characteristic, complemented
4#19135526C212yesmaximal, complemented
5#19135524C212yesmaximal, complemented
6#19135399C212yesmaximal, complemented
7#19135395C212yesmaximal, complemented
8#19134536C211yesmaximal, characteristic, complemented
9#19134535C211yesmaximal, characteristic, complemented
10#19134533C211yesmaximal, characteristic, complemented
11C43×#1788C211yesmaximal, characteristic, complemented
12C22×#10621898C2211yescharacteristic
13#14583445—24no—
14#14583445C418yescomplemented
15C2×#13063323C2211yescharacteristic
16C2×#13063321C2211yescharacteristic
17C2×#13063314C2211yescharacteristic
18C2×#13063312C2211yescharacteristic
19C2×#13063297—21no—
20C2×#13063297—21no—
21C2×C4×C22⋊D43—21no—
22C2×C4×C22⋊D43—21no—
23C2×#13063281—21no—
24C22×C4×Dic43C2211yescharacteristic
25#14582949—24no—
26C2×Dic43⋊C8C2212yes—
27C2×#13063250C2212yes—
28C2×#13063249C2212yes—
29C2×#13063248C2212yes—
30C2×#13063247C2212yes—
31C2×#13063246C2212yes—
32C2×#13063245C2212yes—
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34C2×C8×Dic43C2212yes—
35#14582768C2212yes—
36#14582763—21no—
37#14582759C2211yescharacteristic
38#14582757—21no—
39C4⋊C4×Dic43C2212yes—
40#14582750—21no—
41C22×#41×C43C2211yescharacteristic
42C2×#103×C43C2212yes—
43C2×#102×C43C2212yes—
44C2×C22⋊C8×C43C2211yescharacteristic
45C43×#380C2211yescharacteristic
46C2×#10621898—22no—
47C2×#10621898—42no—
48C2×#10621898—42no—
49C2×#10621898C2×C414yes—
50C22×Dic86C2311yescharacteristic
51C22×D172C2311yescharacteristic
52C22×C22⋊D43—21no—
53C22×C22⋊D43—21no—
54C22×C22⋊D43—21no—
55C23×Dic43D411yescharacteristic
56C23×Dic43D411yescharacteristic
57C22×C4×D43—21no—
58C22×C43⋊C8C2312yes—
59#13063323—22no—
60#13063323C2×C414yes—
61#13063321—22no—
62#13063321C2×C414yes—
63#13063314—22no—
64#13063314C2×C414yes—
65#13063312—22no—
66#13063312C2×C414yes—
67#13063297—28no—
68#13063297—28no—
69C4×C22⋊D43—28no—
70C4×C22⋊D43—28no—
71#13063281—44no—
72C2×C4⋊Dic43C2312yes—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—22no—
76C2×Dic43⋊C4—22no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×C4×Dic43—22no—
83C2×C4×Dic43C2×C414yes—
84C2×C4×Dic43D411yescharacteristic
85C2×C4×Dic43D411yescharacteristic
86C2×C4×Dic43D414yes—
87C2×C4×Dic43C2311yescharacteristic
88C2×C4×Dic43C2311yescharacteristic
89Dic43⋊C8—24no—
90#13063250—42no—
91#13063249—42no—
92#13063248—42no—
93#13063247—42no—
94#13063246—42no—
95#13063245—42no—
96C22⋊(C43⋊C8)—22no—
97C8×Dic43—24no—
98C43⋊#95—21no—
99C43⋊#95—22no—
100C2×#41×C43—22no—
101C2×#41×C43—42no—
102C2×#41×C43—42no—
103C2×#41×C43C2×C414yes—
104C22×Q8×C43C2311yescharacteristic
105C22×D4×C43—21no—
106C22×D4×C43C2311yescharacteristic
107C23×C4×C43—21no—
108C23×C4×C43C2311yescharacteristic
109C22×C8×C43C2312yes—
110C2×C4⋊C4×C43C2312yes—
111C2×C22⋊C4×C43—21no—
112#103×C43—42no—
113#102×C43—42no—
114C22⋊C8×C43—22no—
115#95×C43—21no—
116C24×C43—21no—
117C24×C43C2×D411yescharacteristic
118C23×D43—21no—
119#41×C43—44no—
120#41×C43—44no—
121#41×C43—48no—
122C2×Q8×C43—21no—
123C2×Q8×C43—22no—
124C2×Q8×C43—22no—
125C2×Q8×C43C22×C412yes—
126C2×D4×C43—21no—
127C2×D4×C43—24no—
128C2×D4×C43—22no—
129C2×D4×C43—22no—
130C2×D4×C43—44no—
131C2×D4×C43C22×C412yes—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—24no—
135C22×C4×C43—21no—
136C22×C4×C43—22no—
137C22×C4×C43—44no—
138C22×C4×C43C22×C412yes—
139C22×C4×C43C2×D412yes—
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2411yescharacteristic
142C2×C22⋊D43—24no—
143C2×C22⋊D43—24no—
144C2×C22⋊D43—24no—
145C2×C22⋊D43—44no—
146C2×C22⋊D43—44no—
147C2×C22⋊D43—42no—
148C2×C22⋊D43—42no—
149C22×Dic43—24no—
150C22×Dic43—22no—
151C22×Dic43—22no—
152C22×Dic43—21no—
153C22×Dic43—22no—
154C22×Dic43C22⋊C414yes—
155C22×Dic43C22⋊C414yes—
156C22×Dic43C2×D411yescharacteristic
157C22×Dic43C2×D411yescharacteristic
158C22×Dic43C2×D411yescharacteristic
159C22×Dic43C2×D411yescharacteristic
160#10621898—44no—
161#10621898—44no—
162#10621898—48no—
163C2×D172—21no—
164C2×D172—22no—
165C2×D172—22no—
166C2×D172C22×C412yes—
167C2×C4×D43—24no—
168C2×C4×D43—44no—
169C2×Dic86—22no—
170C2×Dic86—22no—
171C2×Dic86—21no—
172C2×Dic86C22×C412yes—
173C2×C8×C43—22no—
174C2×C8×C43—22no—
175C2×C8×C43—22no—
176C4⋊C4×C43—22no—
177C4⋊C4×C43—22no—
178C22⋊C4×C43—42no—
179C22⋊Dic43—24no—
180C22⋊Dic43—24no—
181C22⋊Dic43—42no—
182(C2×D43)⋊C4—24no—
183(C2×D43)⋊C4—24no—
184C4⋊Dic43—22no—
185C4⋊Dic43—22no—
186Dic43⋊C4—24no—
187Dic43⋊C4—24no—
188Dic43⋊C4—44no—
189Dic43⋊C4—44no—
190C4×Dic43—44no—
191C4×Dic43C22⋊C414yes—
192C4×Dic43C22⋊C414yes—
193C4×Dic43C22×C412yes—
194C4×Dic43C22×C412yes—
195C4×Dic43C2×D412yes—
196C4×Dic43C2×D412yes—
197C2×C43⋊C8—22no—
198C2×C43⋊C8—22no—
199C2×C43⋊C8—22no—
200C23×C43—22no—
201C23×C43—22no—
202C23×C43—21no—
203C23×C43—21no—
204C23×C43—22no—
205C23×C43—42no—
206C23×C43—42no—
207C23×C43—41no—
208C23×C43—41no—
209C23×C43C2×C22⋊C412yes—
210C23×C43C22×D411yescharacteristic
211C22×D43—22no—
212C22×D43—42no—
213C22×D43—42no—
214C22×D43—41no—
215C22×D43—41no—
216Q8×C43—22no—
217Q8×C43—22no—
218Q8×C43—42no—
219D4×C43—22no—
220D4×C43—22no—
221D4×C43—48no—
222D4×C43—42no—
223C2×C4×C43—22no—
224C2×C4×C43—22no—
225C2×C4×C43—22no—
226C2×C4×C43—24no—
227C2×C4×C43—22no—
228C2×C4×C43—48no—
229C2×C4×C43—42no—
230C2×C4×C43—42no—
231C2×C4×C43—42no—
232C2×C4×C43—42no—
233C2×C4×C43C2×C22⋊C412yes—
234C2×C4×C43C23×C411yescharacteristic
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43H(5,𝔽2)12yes—
237C2×C4×C43H(5,𝔽2)12yes—
238C22⋊D43—48no—
239C22⋊D43—48no—
240C22⋊D43—48no—
241C2×Dic43—22no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—28no—
245C2×Dic43—28no—
246C2×Dic43—22no—
247C2×Dic43—42no—
248C2×Dic43—42no—
249C2×Dic43—42no—
250C2×Dic43—42no—
251C2×Dic43C2×C22⋊C412yes—
252C2×Dic43C2×C22⋊C412yes—
253C2×Dic43C2×C22⋊C412yes—
254C2×Dic43C2×C22⋊C412yes—
255C2×Dic43#13514yes—
256C2×Dic43AGL(1,ℤ/8)12yes—
257C2×Dic43#13712yes—
258D172—22no—
259D172—22no—
260D172—42no—
261C4×D43—48no—
262Dic86—22no—
263Dic86—22no—
264Dic86—42no—
265C8×C43—42no—
266C43⋊C8—42no—
267#21805—431nomaximal, Sylow
268C22×C43—22no—
269C22×C43—22no—
270C22×C43—22no—
271C22×C43—42no—
272C22×C43—42no—
273C22×C43—42no—
274C22×C43—42no—
275C22×C43—42no—
276C22×C43—82no—
277C22×C43—82no—
278C22×C43C22×C22⋊C411yescharacteristic
279C22×C43#53512yes—
280C22×C43C2×#13512yes—
281C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
282C22×C43C2×#13711yescharacteristic
283C2×D43—42no—
284C2×D43—42no—
285C2×D43—42no—
286C2×D43—82no—
287C2×D43—82no—
288C4×C43—22no—
289C4×C43—42no—
290C4×C43—82no—
291C4×C43#51811yescharacteristic
292C4×C43#51811yescharacteristic
293C4×C43#53512yes—
294Dic43—22no—
295Dic43—22no—
296Dic43—42no—
297Dic43—82no—
298Dic43#41614yes—
299Dic43#41714yes—
300C2×#532—431no—
301C2×#431—431no—
302#2285—431no—
303#1983—432no—
304#1983—432no—
305#1957—432no—
306#1956—432no—
307#1788—431no—
308#1788—431no—
309#1788—431no—
310#1788D4311yescharacteristic, complemented
311C2×C43—42no—
312C2×C43—82no—
313C2×C43#230911yescharacteristic
314C2×C43C2×#41611yescharacteristic
315C2×C43C2×#41711yescharacteristic
316C2×C43#320712yes—
317C2×C43#321012yes—
318D43—82no—
319C22×#41—431no—
320C22×#41C2×D4311yescharacteristic
321#532—438no—
322#532—864no—
323C2×C4⋊Q8—431no—
324C2×#127—431no—
325C2×#124—431no—
326C2×#124—431no—
327C2×#121—861no—
328C2×#121—861no—
329C2×C4×D4—861no—
330C2×C4×D4—861no—
331C2×#117—861no—
332C22×C42—431no—
333#431—864no—
334C2×C4⋊C8—432no—
335C2×#103—432no—
336C2×#103—432no—
337C2×#103—432no—
338C2×#103C2×D4312yes—
339C2×#102—432no—
340C2×#102—432no—
341C2×#102—432no—
342C2×#102C2×D4312yes—
343C2×C22⋊C8—431no—
344C2×C22⋊C8C2×D4311yescharacteristic
345C2×C4×C8—432no—
346#384—432no—
347#382—861no—
348#380—431no—
349#380—861no—
350#380C2×D4311yescharacteristic
351C4×C4⋊C4—432no—
352C4×C4⋊C4—861no—
353C43#2180511yescharacteristic, complemented, Sylow
354C2×#41—22no—
355C2×#41—42no—
356C2×#41—42no—
357C2×#41—434no—
358C2×#41—862no—
359C2×#41—1722no—
360C2×#41—1722no—
361C2×#41C4×D4314yes—
362C22×Q8—431no—
363C22×Q8C22×D4311yescharacteristic
364C22×D4—21no—
365C22×D4—431no—
366C22×D4—861no—
367C22×D4—861no—
368C22×D4—861no—
369C22×D4C22×D4311yescharacteristic
370C23×C4—21no—
371C23×C4—431no—
372C23×C4—431no—
373C23×C4—861no—
374C23×C4C22×D4311yescharacteristic
375C22×C8—432no—
376C22×C8C22×D4312yes—
377C4⋊Q8—434no—
378C4⋊Q8—862no—
379#127—434no—
380#127—862no—
381#124—434no—
382#124—434no—
383#124—862no—
384#124—862no—
385#121—868no—
386#121—868no—
387C4×D4—868no—
388C4×D4—868no—
389#117—1724no—
390C2×C4⋊C4—432no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—862no—
394C2×C4⋊C4—862no—
395C2×C4⋊C4C22×D4312yes—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—861no—
398C2×C22⋊C4—861no—
399C2×C22⋊C4—861no—
400C2×C22⋊C4—861no—
401C2×C22⋊C4—861no—
402C2×C42—434no—
403C2×C42—431no—
404C2×C42—431no—
405C2×C42—434no—
406C2×C42—431no—
407C2×C42—431no—
408C2×C42—862no—
409C4⋊C8—864no—
410#103—42no—
411#103—1722no—
412#103—1722no—
413#103—1722no—
414#102—42no—
415#102—1722no—
416#102—1722no—
417#102—1722no—
418C22⋊C8—22no—
419C22⋊C8—862no—
420C4×C8—864no—
421#95—21no—
422#95—862no—
423#95—861no—
424C24—21no—
425C24—861no—
426C24D4×D4311yescharacteristic
427#41—44no—
428#41—44no—
429#41—48no—
430#41—1724no—
431#41—1724no—
432#41—1728no—
433C2×Q8—21no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—432no—
437C2×Q8—861no—
438C2×Q8—862no—
439C2×Q8—862no—
440C2×Q8C2×C4×D4312yes—
441C2×D4—24no—
442C2×D4—21no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—44no—
446C2×D4—432no—
447C2×D4—864no—
448C2×D4—864no—
449C2×D4—864no—
450C2×D4—861no—
451C2×D4—862no—
452C2×D4—862no—
453C2×D4—1724no—
454C2×D4—1722no—
455C2×D4—1722no—
456C2×D4—1724no—
457C2×D4C2×C4×D4312yes—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—24no—
462C22×C4—22no—
463C22×C4—44no—
464C22×C4—431no—
465C22×C4—431no—
466C22×C4—434no—
467C22×C4—434no—
468C22×C4—431no—
469C22×C4—431no—
470C22×C4—862no—
471C22×C4—864no—
472C22×C4—862no—
473C22×C4—861no—
474C22×C4—864no—
475C22×C4—862no—
476C22×C4—1724no—
477C22×C4C2×C4×D4312yes—
478C22×C4D4×D4311yescharacteristic
479C22×C4D4×D4312yes—
480C22×C4C23×D4311yescharacteristic
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—862no—
485C2×C8—862no—
486C2×C8—862no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—864no—
490C4⋊C4—864no—
491C4⋊C4—862no—
492C4⋊C4—862no—
493C4⋊C4—1724no—
494C4⋊C4—1724no—
495C22⋊C4—42no—
496C22⋊C4—864no—
497C22⋊C4—864no—
498C22⋊C4—864no—
499C22⋊C4—864no—
500C22⋊C4—1722no—
501C42—434no—
502C42—434no—
503C42—432no—
504C42—432no—
505C42—432no—
506C42—432no—
507C42—1724no—
508C23—22no—
509C23—21no—
510C23—21no—
511C23—22no—
512C23—22no—
513C23—42no—
514C23—41no—
515C23—41no—
516C23—42no—
517C23—862no—
518C23—1722no—
519C23—1721no—
520C23—1721no—
521C23—1722no—
522C23C22⋊C4×D4312yes—
523C23C2×D4×D4311yescharacteristic
524Q8—22no—
525Q8—22no—
526Q8—42no—
527Q8—862no—
528Q8—862no—
529Q8—1722no—
530D4—22no—
531D4—22no—
532D4—48no—
533D4—42no—
534D4—862no—
535D4—862no—
536D4—1728no—
537D4—1728no—
538D4—1728no—
539D4—1722no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—48no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—432no—
551C2×C4—432no—
552C2×C4—434no—
553C2×C4—432no—
554C2×C4—432no—
555C2×C4—432no—
556C2×C4—432no—
557C2×C4—868no—
558C2×C4—868no—
559C2×C4—862no—
560C2×C4—861no—
561C2×C4—861no—
562C2×C4—862no—
563C2×C4—1728no—
564C2×C4—1722no—
565C2×C4—1722no—
566C2×C4—1722no—
567C2×C4—1722no—
568C2×C4C22⋊C4×D4312yes—
569C2×C4C22×C4×D4311yescharacteristic
570C2×C4C2×D4×D4311yescharacteristic
571C2×C4#1306337012yes—
572C2×C4#1306337012yes—
573C8—42no—
574C8—1722no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—82no—
584C22—82no—
585C22—3442no—
586C22—3442no—
587C22—1722no—
588C22—1722no—
589C22—1722no—
590C22C2×C22⋊C4×D4311yescharacteristic
591C22#1458346412yes—
592C22#135×D4312yes—
593C22AGL(1,ℤ/8)×D4311yescharacteristic
594C22#137×D4311yescharacteristic
595C4—22no—
596C4—42no—
597C4—82no—
598C4—434no—
599C4—434no—
600C4—862no—
601C4—862no—
602C4—3442no—
603C4—1722no—
604C4#1458337211yescharacteristic
605C4#1458337211yescharacteristic
606C4#1458346412yes—
607C2—42no—
608C2—82no—
609C2—3442no—
610C2#1913717611yescharacteristic
611C2#416×D4311yescharacteristic
612C2#417×D4311yescharacteristic
613C2#1914552612yes—
614C2#1914554912yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1788C2
socleC23×C43C22×D4
prime radicalC2×#14583445C2
cosocleC22×C4×C43C24
hypercenter#1788D43
hypocenterC43#21805
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#14582949C2semidirect
3. #19136997C2semidirect
4. #19135526C2semidirect
5. #19135524C2semidirect
6. #19135399C2semidirect
7. #19135395C2semidirect
8. #19134536C2semidirect
9. #19134535C2semidirect
10. #19134533C2semidirect
11. C43×#1788C2semidirect
14. #14583445C4semidirect
310. #1788D43semidirect
353. C43#21805semidirect

Maximal subgroups

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

subgroupindex
C2×#145834452
C2×#145829492
#191369972
#191355262
#191355242
#191353992
#191353952
#191345362
#191345352
#191345332
C43×#17882
#2180543