Finite Group Databasebeta

← #25154763

Subgroups — #25154763

Order 11008.

706 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
1#19139618C211yesmaximal, characteristic, complemented
2#19137567C211yesmaximal, characteristic
3#19135979C211yesmaximal, characteristic
4#19135739C211yesmaximal, characteristic
5#19135731C211yesmaximal, characteristic
6#19135549C211yesmaximal, characteristic, complemented
7#19135546C211yesmaximal, characteristic, complemented
8#19135364C211yesmaximal, characteristic, complemented
9#19135310C211yesmaximal, characteristic, complemented
10#19135184C211yesmaximal, characteristic, complemented
11#19135182C211yesmaximal, characteristic, complemented
12#19134724C211yesmaximal, characteristic, complemented
13#19134603C211yesmaximal, characteristic
14#102×Dic43C211yesmaximal, characteristic
15C43×#2065C211yesmaximal, characteristic
16C2×#13063325C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×Dic43⋊C8C2211yescharacteristic
21C2×Dic43⋊C8C2211yescharacteristic
22C2×#13063246C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×C8×Dic43C2211yescharacteristic
25#14582832—21no—
26#14582820—21no—
27#14582803—21no—
28#14582802C2211yescharacteristic
29#14582798—21no—
30#14582798C2211yescharacteristic
31#14582793—21no—
32#14582787—21no—
33#14582764C2211yescharacteristic
34#14582764C2211yescharacteristic
35#14582760—21no—
36C4⋊C4×Dic43C2211yescharacteristic
37C4⋊C4×Dic43C2211yescharacteristic
38C4×Dic43⋊C4C2211yescharacteristic
39C4×C4⋊Dic43C2211yescharacteristic
40C22⋊C4×Dic43—21no—
41#14582662C2211yescharacteristic
42#14582662C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#106×C43C2211yescharacteristic
53C2×C4⋊C8×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×Dic86—21no—
60C23×Dic43—21no—
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63#13063325—22no—
64#13063325—41no—
65#13063316—22no—
66#13063316—41no—
67D4×Dic43—22no—
68D4×Dic43Q814yescomplemented
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4D411yescharacteristic
78C2×Dic43⋊C4D411yescharacteristic
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43C2311yescharacteristic
86C2×C4×Dic43C2311yescharacteristic
87#13063258—22no—
88Dic43⋊C8—22no—
89Dic43⋊C8—41no—
90#13063246—22no—
91#13063246—41no—
92C8×Dic43—22no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95D411yescharacteristic
102C43⋊#95D411yescharacteristic
103C22×D4×C43C2311yescharacteristic
104C22×C8×C43C2311yescharacteristic
105C22×C8×C43C2311yescharacteristic
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C42×C43C2311yescharacteristic
113#106×C43—22no—
114C4⋊C8×C43—41no—
115#102×C43—22no—
116#102×C43—41no—
117#95×C43—21no—
118C24×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43—21no—
122C2×D4×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43C2×Q812yes—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2411yescharacteristic
131C22×Dic43—24no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—81no—
137C22×Dic43—81no—
138C22×Dic43C2×D411yescharacteristic
139C22×Dic43C2×D411yescharacteristic
140C22×Dic43C2×D411yescharacteristic
141C22×Dic43C2×D411yescharacteristic
142C2×Dic86—42no—
143C2×Dic86—42no—
144C2×Dic86—81no—
145C2×C8×C43—21no—
146C2×C8×C43—21no—
147C2×C8×C43—21no—
148C2×C8×C43—21no—
149C2×C8×C43—21no—
150C2×C8×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—42no—
157C4⋊C4×C43#4112yes—
158C22⋊C4×C43—42no—
159C22⋊C4×C43—81no—
160C42×C43—21no—
161C42×C43—21no—
162C22⋊Dic43—24no—
163C22⋊Dic43—42no—
164C22⋊Dic43—81no—
165C4⋊Dic43—21no—
166C4⋊Dic43—21no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—42no—
172C4⋊Dic43—42no—
173C4⋊Dic43—81no—
174C4⋊Dic43C2×Q812yes—
175C4⋊Dic43#4112yes—
176Dic43⋊C4—22no—
177Dic43⋊C4—41no—
178Dic43⋊C4—42no—
179C4×Dic43—21no—
180C4×Dic43—21no—
181C4×Dic43—81no—
182C4×Dic43—81no—
183C4×Dic43—81no—
184C4×Dic43C2×Q812yes—
185C4×Dic43#4112yes—
186C2×C43⋊C8—21no—
187C2×C43⋊C8—21no—
188C2×C43⋊C8—21no—
189C2×C43⋊C8—21no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192C23×C43—22no—
193C23×C43—41no—
194C23×C43—41no—
195C23×C43—41no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43C22×D411yescharacteristic
200D4×C43—22no—
201D4×C43—22no—
202D4×C43—41no—
203D4×C43—41no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—22no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—41no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43#13512yes—
219C2×C4×C43C22×Q811yescharacteristic
220C2×C4×C43C2×#4111yescharacteristic
221C2×C4×C43C2×#4111yescharacteristic
222C2×C4×C43C2×#4111yescharacteristic
223C2×C4×C43H(5,𝔽2)11yescharacteristic
224C2×C4×C432−1+411yescharacteristic
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—22no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—22no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—84no—
248C2×Dic43C22⋊Q812yes—
249C2×Dic43C22⋊Q812yes—
250Dic86—84no—
251C8×C43—41no—
252C8×C43—41no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255#26028—431nomaximal, Sylow
256C22×C43—42no—
257C22×C43—42no—
258C22×C43—42no—
259C22×C43—81no—
260C22×C43—81no—
261C22×C43—81no—
262C22×C43—81no—
263C22×C43C2×C22⋊Q811yescharacteristic
264C22×C43#54611yescharacteristic
265C22×C43#54811yescharacteristic
266C22×C43C2×#13511yescharacteristic
267C22×C43#57511yescharacteristic
268C22×C43#57611yescharacteristic
269C22×C43#57711yescharacteristic
270C4×C43—22no—
271C4×C43—42no—
272C4×C43—41no—
273C4×C43—81no—
274C4×C43—81no—
275C4×C43#53311yescharacteristic
276C4×C43#54411yescharacteristic
277C4×C43#55511yescharacteristic
278C4×C43#55611yescharacteristic
279Dic43—22no—
280Dic43—22no—
281Dic43—42no—
282Dic43—42no—
283Dic43—41no—
284Dic43—41no—
285Dic43—81no—
286Dic43—81no—
287#2550—431no—
288#2357—431no—
289#2067—431no—
290#2065D4311yescharacteristic
291#2025—431no—
292#2023—431no—
293#1989—431no—
294#1988—431no—
295#1949—431no—
296#1939—431no—
297#1921—431no—
298#1920—431no—
299#1835—431no—
300#1804—431no—
301C4×#102—431no—
302C2×C43—82no—
303C2×C43#243911yescharacteristic
304C2×C43#307611yescharacteristic
305C2×C43#308111yescharacteristic
306C2×C43#329711yescharacteristic
307C2×C43#332611yescharacteristic
308C2×C43#336511yescharacteristic
309C2×C43#337011yescharacteristic
310C2×C4⋊Q8—431no—
311C2×#125—431no—
312C2×C4×D4—431no—
313C2×#107—431no—
314C2×#106C2×D4311yescharacteristic
315C2×C4⋊C8—431no—
316C2×C4⋊C8—431no—
317C2×C4⋊C8C2×D4311yescharacteristic
318C2×#102—431no—
319C2×#102—431no—
320C2×#102C2×D4311yescharacteristic
321C2×#102C2×D4311yescharacteristic
322C2×C4×C8—431no—
323#398—861no—
324#395—861no—
325#391—861no—
326#390—431no—
327#390C2×D4311yescharacteristic
328#389—431no—
329#389—861no—
330#389C2×D4311yescharacteristic
331#388—861no—
332#388—861no—
333#382—431no—
334#382—431no—
335#381—861no—
336C4×C4⋊C4—431no—
337C4×C4⋊C4—431no—
338C4×C4⋊C4—431no—
339C4×C4⋊C4—431no—
340C4×C22⋊C4—861no—
341#340—431no—
342#340—431no—
343#340—431no—
344#340—431no—
345#340—431no—
346#340—431no—
347#340—431no—
348#340—431no—
349#340—431no—
350#340C2×D4311yescharacteristic
351#336—431no—
352#336—431no—
353C43#2602811yescharacteristic, complemented, Sylow
354C22×Q8—861no—
355C22×D4C22×D4311yescharacteristic
356C23×C4—861no—
357C22×C8—431no—
358C22×C8—431no—
359C22×C8C22×D4311yescharacteristic
360C22×C8C22×D4311yescharacteristic
361C4⋊Q8—862no—
362C4⋊Q8—1721no—
363#125—862no—
364#125—1721no—
365C4×D4—434no—
366C4×D4—862no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—431no—
369C2×C4⋊C4—431no—
370C2×C4⋊C4—431no—
371C2×C4⋊C4—431no—
372C2×C4⋊C4—431no—
373C2×C4⋊C4—431no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4—861no—
377C2×C4⋊C4—861no—
378C2×C4⋊C4C22×D4311yescharacteristic
379C2×C4⋊C4C22×D4311yescharacteristic
380C2×C4⋊C4C22×D4311yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—861no—
384C2×C22⋊C4—861no—
385C2×C22⋊C4—861no—
386C2×C42—431no—
387C2×C42—431no—
388C2×C42—861no—
389C2×C42—861no—
390C2×C42—861no—
391C2×C42C22×D4311yescharacteristic
392#107—862no—
393#106—22no—
394C4⋊C8—41no—
395C4⋊C8—862no—
396C4⋊C8—1721no—
397#102—22no—
398#102—41no—
399#102—862no—
400#102—1721no—
401C4×C8—862no—
402#95—21no—
403#95—431no—
404#95—431no—
405#95—861no—
406#95—861no—
407#95—861no—
408#95—861no—
409#95—861no—
410#95—861no—
411#95—861no—
412#95—861no—
413C24—21no—
414C2×Q8—3441no—
415C2×Q8—1722no—
416C2×Q8—1722no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4Q8×D4312yes—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—431no—
427C22×C4—431no—
428C22×C4—431no—
429C22×C4—431no—
430C22×C4—864no—
431C22×C4—861no—
432C22×C4—861no—
433C22×C4—861no—
434C22×C4—861no—
435C22×C4—3441no—
436C22×C4—3441no—
437C22×C4D4×D4311yescharacteristic
438C22×C4D4×D4311yescharacteristic
439C22×C4C23×D4311yescharacteristic
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—861no—
447C2×C8—861no—
448C2×C8—861no—
449C2×C8—861no—
450C2×C8—861no—
451C2×C8—861no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—42no—
458C4⋊C4—432no—
459C4⋊C4—432no—
460C4⋊C4—862no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—3441no—
468C4⋊C4—1721no—
469C4⋊C4—1722no—
470C4⋊C4—1722no—
471C4⋊C4—1722no—
472C4⋊C4#1062190012yes—
473C22⋊C4—42no—
474C22⋊C4—81no—
475C22⋊C4—864no—
476C22⋊C4—3441no—
477C22⋊C4—1722no—
478C42—21no—
479C42—21no—
480C42—432no—
481C42—432no—
482C42—861no—
483C42—861no—
484C42—3441no—
485C42—3441no—
486C42—3441no—
487C23—22no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23C2×D4×D4311yescharacteristic
495Q8—3444no—
496D4—22no—
497D4—22no—
498D4—41no—
499D4—41no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—432no—
515C2×C4—432no—
516C2×C4—861no—
517C2×C4—861no—
518C2×C4—861no—
519C2×C4—861no—
520C2×C4—862no—
521C2×C4—861no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—862no—
528C2×C4—3444no—
529C2×C4—1721no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4#1306334612yes—
540C2×C4C2×Q8×D4311yescharacteristic
541C2×C4#41×D4311yescharacteristic
542C2×C4#41×D4311yescharacteristic
543C2×C4C2×#1062190011yescharacteristic
544C2×C4#1306337011yescharacteristic
545C2×C4#1306337211yescharacteristic
546C8—41no—
547C8—41no—
548C8—1721no—
549C8—1721no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22C22⋊Q8×D4311yescharacteristic
558C22#1458353811yescharacteristic
559C22#1458355511yescharacteristic
560C22C2×#1306334611yescharacteristic
561C22#1458369511yescharacteristic
562C22#1458370111yescharacteristic
563C22#1458370911yescharacteristic
564C4—22no—
565C4—42no—
566C4—41no—
567C4—81no—
568C4—81no—
569C4—862no—
570C4—862no—
571C4—3441no—
572C4—3441no—
573C4—1721no—
574C4—1721no—
575C4—1722no—
576C4—1722no—
577C4#1458345111yescharacteristic
578C4#1458352811yescharacteristic
579C4#1458361311yescharacteristic
580C4#1458361611yescharacteristic
581C2—82no—
582C2#1913828111yescharacteristic
583C2#1914438411yescharacteristic
584C2#1914442311yescharacteristic
585C2#1914645111yescharacteristic
586C2#1914685411yescharacteristic
587C2#1914729511yescharacteristic
588C2#1914734511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2065C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2065D43
hypocenterC43#26028
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2065

Complements

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

NH ≅ G/Ntype
1. #19139618C2semidirect
6. #19135549C2semidirect
7. #19135546C2semidirect
8. #19135364C2semidirect
9. #19135310C2semidirect
10. #19135184C2semidirect
11. #19135182C2semidirect
12. #19134724C2semidirect
68. D4×Dic43Q8semidirect
353. C43#26028semidirect

Maximal subgroups

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

subgroupindex
#191396182
#191375672
#191359792
#191357392
#191357312
#191355492
#191355462
#191353642
#191353102
#191351842
#191351822
#191347242
#191346032
#102×Dic432
C43×#20652
#2602843