Finite Group Databasebeta

← #25165274

Subgroups — #25165274

Order 11008.

712 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139118C211yesmaximal, characteristic, complemented
2#19137665C211yesmaximal, characteristic
3#19135983C211yesmaximal, characteristic
4#19135834C211yesmaximal, characteristic
5#19135834C211yesmaximal, characteristic
6#19135272C211yesmaximal, characteristic, complemented
7#19135234C211yesmaximal, characteristic, complemented
8#19135172C211yesmaximal, characteristic, complemented
9#19135164C211yesmaximal, characteristic, complemented
10#19135155C211yesmaximal, characteristic, complemented
11#19134866C211yesmaximal, characteristic, complemented
12#19134858C211yesmaximal, characteristic
13#19134597C211yesmaximal, characteristic, complemented
14#102×Dic43C211yesmaximal, characteristic
15C43×#2071C211yesmaximal, characteristic
16C2×#13063312C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063257C2211yescharacteristic
21C2×C4⋊(C43⋊C8)C2211yescharacteristic
22C2×#13063250C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×C8×Dic43C2211yescharacteristic
29#14582832—21no—
30#14582829—21no—
31#14582804C2211yescharacteristic
32#14582798C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582795C2211yescharacteristic
35#14582795C2211yescharacteristic
36#14582794—21no—
37#14582793—21no—
38#14582787—21no—
39#14582780—21no—
40#14582771—21no—
41C4⋊C4×Dic43C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43C4×Dic43⋊C4C2211yescharacteristic
44C22⋊C4×Dic43—21no—
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#102×C43C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C43×#390C2211yescharacteristic
55C43×#384C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C23×Dic43—21no—
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63#13063312—22no—
64#13063312—22no—
65C4×Dic86—22no—
66C4×Dic86—41no—
67D4×Dic43—22no—
68D4×Dic43—41no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
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—
88#13063257—22no—
89C4⋊(C43⋊C8)—41no—
90#13063250—22no—
91#13063250—41no—
92#13063248—22no—
93#13063248—22no—
94#13063246—22no—
95#13063246—41no—
96C8×Dic43—41no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95D411yescharacteristic
106C43⋊#95D411yescharacteristic
107C22×D4×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43—21no—
117C2×C42×C43C2311yescharacteristic
118#102×C43—22no—
119#102×C43—22no—
120C24×C43—21no—
121C2×D4×C43—21no—
122C2×D4×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43#4112yes—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2411yescharacteristic
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—42no—
138C22×Dic43—42no—
139C22×Dic43—81no—
140C22×Dic43C2×D411yescharacteristic
141C22×Dic43C2×D411yescharacteristic
142C22×Dic43C2×D411yescharacteristic
143C22×Dic43C2×D411yescharacteristic
144C2×Dic86—21no—
145C2×Dic86—21no—
146C2×Dic86—21no—
147C2×Dic86—21no—
148C2×Dic86—21no—
149C2×Dic86#4112yes—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—81no—
163C4⋊C4×C43—81no—
164C22⋊C4×C43—42no—
165C22⋊C4×C43—81no—
166C42×C43—21no—
167C42×C43—21no—
168C22⋊Dic43—24no—
169C22⋊Dic43—24no—
170C22⋊Dic43—42no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—81no—
176C4⋊Dic43#4112yes—
177C4⋊Dic43#4112yes—
178Dic43⋊C4—22no—
179Dic43⋊C4—22no—
180Dic43⋊C4—42no—
181Dic43⋊C4—42no—
182Dic43⋊C4—81no—
183Dic43⋊C4—81no—
184C4×Dic43—21no—
185C4×Dic43—21no—
186C4×Dic43—21no—
187C4×Dic43—21no—
188C4×Dic43—42no—
189C4×Dic43—81no—
190C4×Dic43—81no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C23×C43—22no—
198C23×C43—41no—
199C23×C43—41no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43—41no—
203C23×C43—41no—
204C23×C43C22×D411yescharacteristic
205D4×C43—22no—
206D4×C43—22no—
207D4×C43—41no—
208D4×C43—41no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43#13512yes—
224C2×C4×C43C2×#4111yescharacteristic
225C2×C4×C43C2×#4111yescharacteristic
226C2×C4×C43C2×#4111yescharacteristic
227C2×C4×C43C2×#4111yescharacteristic
228C2×C4×C43H(5,𝔽2)11yescharacteristic
229C2×C4×C432−1+411yescharacteristic
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—22no—
235C2×Dic43—21no—
236C2×Dic43—22no—
237C2×Dic43—22no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—84no—
254C2×Dic43#13712yes—
255Dic86—22no—
256Dic86—22no—
257Dic86—41no—
258Dic86—41no—
259C8×C43—41no—
260C8×C43—41no—
261C43⋊C8—41no—
262C43⋊C8—41no—
263#26763—431nomaximal, Sylow
264C22×C43—42no—
265C22×C43—42no—
266C22×C43—42no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43#52511yescharacteristic
272C22×C43#54611yescharacteristic
273C22×C43#54811yescharacteristic
274C22×C43C2×#13511yescharacteristic
275C22×C43C2×#13711yescharacteristic
276C22×C43#57611yescharacteristic
277C22×C43#57711yescharacteristic
278C4×C43—22no—
279C4×C43—41no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43—81no—
283C4×C43#52911yescharacteristic
284C4×C43#53911yescharacteristic
285C4×C43#55211yescharacteristic
286C4×C43#55311yescharacteristic
287Dic43—22no—
288Dic43—42no—
289Dic43—41no—
290Dic43—41no—
291Dic43—42no—
292Dic43—41no—
293Dic43—42no—
294Dic43—81no—
295#2507—431no—
296#2367—431no—
297#2071D4311yescharacteristic
298#2067—431no—
299#2042—431no—
300#2042—431no—
301#1933—431no—
302#1928—431no—
303#1919—431no—
304#1918—431no—
305#1916—431no—
306#1865—431no—
307#1864—431no—
308#1803—431no—
309C4×#102—431no—
310C2×C43—82no—
311C2×C43#246011yescharacteristic
312C2×C43#310711yescharacteristic
313C2×C43#311911yescharacteristic
314C2×C43#330111yescharacteristic
315C2×C43#331411yescharacteristic
316C2×C43#336111yescharacteristic
317C2×C43#336911yescharacteristic
318C2×#124—431no—
319C2×C4×Q8—431no—
320C2×C4×D4—431no—
321C2×#107—431no—
322C2×#106—431no—
323C2×C4⋊C8—431no—
324C2×#103—431no—
325C2×#103—431no—
326C2×#103—431no—
327C2×#103—431no—
328C2×#102—431no—
329C2×#102—431no—
330C2×#102C2×D4311yescharacteristic
331C2×#102C2×D4311yescharacteristic
332C2×C4×C8—431no—
333#398—861no—
334#398—861no—
335#391—431no—
336#390C2×D4311yescharacteristic
337#389—431no—
338#389—431no—
339#389—431no—
340#389—431no—
341#389—861no—
342#388—861no—
343#388—861no—
344#387—861no—
345#385—861no—
346#384C2×D4311yescharacteristic
347C4×C4⋊C4—431no—
348C4×C4⋊C4—431no—
349C4×C4⋊C4—431no—
350C4×C22⋊C4—861no—
351#340—431no—
352#340—431no—
353#340—431no—
354#340—431no—
355#340C2×D4311yescharacteristic
356#340C2×D4311yescharacteristic
357#336—431no—
358#336—431no—
359#336—431no—
360#336C2×D4311yescharacteristic
361C43#2676311yescharacteristic, complemented, Sylow
362C22×Q8—431no—
363C22×D4C22×D4311yescharacteristic
364C23×C4—861no—
365C22×C8—431no—
366C22×C8—431no—
367C22×C8C22×D4311yescharacteristic
368C22×C8C22×D4311yescharacteristic
369#124—862no—
370#124—862no—
371C4×Q8—862no—
372C4×Q8—1721no—
373C4×D4—862no—
374C4×D4—1721no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—431no—
379C2×C4⋊C4—431no—
380C2×C4⋊C4—431no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4C22×D4311yescharacteristic
388C2×C4⋊C4C22×D4311yescharacteristic
389C2×C4⋊C4C22×D4311yescharacteristic
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—861no—
393C2×C22⋊C4—861no—
394C2×C22⋊C4—861no—
395C2×C42—431no—
396C2×C42—431no—
397C2×C42—861no—
398C2×C42—861no—
399C2×C42—861no—
400C2×C42C22×D4311yescharacteristic
401#107—862no—
402#106—862no—
403C4⋊C8—1721no—
404#103—862no—
405#103—862no—
406#103—862no—
407#103—1721no—
408#102—22no—
409#102—22no—
410#102—862no—
411#102—1721no—
412C4×C8—1721no—
413#95—431no—
414#95—431no—
415#95—861no—
416#95—861no—
417#95—861no—
418#95—861no—
419#95—861no—
420#95—861no—
421#95—861no—
422#95—861no—
423C24—21no—
424C2×Q8—432no—
425C2×Q8—861no—
426C2×Q8—861no—
427C2×Q8—861no—
428C2×Q8—861no—
429C2×Q8—861no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4#1062190012yes—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—431no—
440C22×C4—431no—
441C22×C4—431no—
442C22×C4—431no—
443C22×C4—861no—
444C22×C4—861no—
445C22×C4—861no—
446C22×C4—861no—
447C22×C4—3441no—
448C22×C4—1722no—
449C22×C4—1722no—
450C22×C4D4×D4311yescharacteristic
451C22×C4D4×D4311yescharacteristic
452C22×C4C23×D4311yescharacteristic
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—81no—
472C4⋊C4—81no—
473C4⋊C4—432no—
474C4⋊C4—432no—
475C4⋊C4—862no—
476C4⋊C4—862no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—3441no—
482C4⋊C4—3441no—
483C4⋊C4—3441no—
484C4⋊C4—1722no—
485C4⋊C4—1722no—
486C22⋊C4—42no—
487C22⋊C4—81no—
488C22⋊C4—864no—
489C22⋊C4—864no—
490C22⋊C4—1722no—
491C42—21no—
492C42—21no—
493C42—861no—
494C42—861no—
495C42—861no—
496C42—861no—
497C42—3441no—
498C42—3441no—
499C42—1722no—
500C23—22no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23C2×D4×D4311yescharacteristic
508Q8—862no—
509Q8—862no—
510Q8—1721no—
511Q8—1721no—
512D4—22no—
513D4—22no—
514D4—41no—
515D4—41no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—432no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—862no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—862no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—862no—
545C2×C4—3444no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4#1306334612yes—
556C2×C4#41×D4311yescharacteristic
557C2×C4#41×D4311yescharacteristic
558C2×C4#41×D4311yescharacteristic
559C2×C4C2×#1062190011yescharacteristic
560C2×C4#1306337111yescharacteristic
561C2×C4#1306337211yescharacteristic
562C8—41no—
563C8—41no—
564C8—1721no—
565C8—1721no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22#1458340911yescharacteristic
574C22#1458354111yescharacteristic
575C22#1458355711yescharacteristic
576C22C2×#1306334611yescharacteristic
577C22#137×D4311yescharacteristic
578C22#1458370011yescharacteristic
579C22#1458370911yescharacteristic
580C4—22no—
581C4—41no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4—862no—
586C4—3441no—
587C4—1721no—
588C4—1722no—
589C4—1721no—
590C4—1722no—
591C4—1722no—
592C4—1721no—
593C4#1458342611yescharacteristic
594C4#1458349311yescharacteristic
595C4#1458358511yescharacteristic
596C4#1458360011yescharacteristic
597C2—82no—
598C2#1913854811yescharacteristic
599C2#1914466311yescharacteristic
600C2#1914479111yescharacteristic
601C2#1914649511yescharacteristic
602C2#1914667911yescharacteristic
603C2#1914726011yescharacteristic
604C2#1914733211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2071C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2071D43
hypocenterC43#26763
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2071

Complements

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

NH ≅ G/Ntype
1. #19139118C2semidirect
6. #19135272C2semidirect
7. #19135234C2semidirect
8. #19135172C2semidirect
9. #19135164C2semidirect
10. #19135155C2semidirect
11. #19134866C2semidirect
13. #19134597C2semidirect
361. C43#26763semidirect

Maximal subgroups

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

subgroupindex
#191391182
#191376652
#191359832
#191358342
#191352722
#191352342
#191351722
#191351642
#191351552
#191348662
#191348582
#191345972
#102×Dic432
C43×#20712
#2676343