Finite Group Databasebeta

← #25169715

Subgroups — #25169715

Order 11008.

672 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137620C211yesmaximal, characteristic
2#19136014C211yesmaximal, characteristic, complemented
3#19135973C211yesmaximal, characteristic, complemented
4#19135798C211yesmaximal, characteristic
5#19135791C211yesmaximal, characteristic
6#19135361C211yesmaximal, characteristic, complemented
7#19135330C211yesmaximal, characteristic, complemented
8#19135210C211yesmaximal, characteristic
9#19135184C211yesmaximal, characteristic, complemented
10#19135180C211yesmaximal, characteristic, complemented
11#19134848C211yesmaximal, characteristic, complemented
12#19134792C211yesmaximal, characteristic
13#19134687C211yesmaximal, characteristic
14#19134428C211yesmaximal, characteristic, complemented
15C43×#2494C211yesmaximal, characteristic
16C2×#13063304C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18C2×#13063284C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×C4⋊(C43⋊C8)C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×C22⋊(C43⋊C8)C2211yescharacteristic
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×#13063236C2211yescharacteristic
31#14582805C2211yescharacteristic
32#14582797C2211yescharacteristic
33#14582793—21no—
34#14582787—21no—
35#14582781—21no—
36C4×C4⋊Dic43C2211yescharacteristic
37#14582750—21no—
38#14582661C2211yescharacteristic
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C43×#401—21no—
49C43×#397—21no—
50C43×#389C2211yescharacteristic
51C43×#389C2211yescharacteristic
52C43×#388—21no—
53C43×#387—21no—
54C43×#382C2211yescharacteristic
55C43×#380C2211yescharacteristic
56C43×#380C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C4×C22⋊C4×C43C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64#13063304—22no—
65#13063304—22no—
66C4×Dic86—22no—
67C4×Dic86—41no—
68#13063284—22no—
69#13063284—41no—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—21no—
78C2×C4×Dic43—21no—
79C2×C4×Dic43—21no—
80C2×C4×Dic43—21no—
81#13063258—22no—
82#13063258—22no—
83#13063256—22no—
84#13063256—41no—
85C4⋊(C43⋊C8)—22no—
86#13063248—22no—
87#13063248—22no—
88#13063248—22no—
89#13063248—41no—
90C22⋊(C43⋊C8)—22no—
91C22⋊(C43⋊C8)—41no—
92#13063236—41no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C23×C4×C43C2311yescharacteristic
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43C2311yescharacteristic
101C2×C4⋊C4×C43C2311yescharacteristic
102C2×C4⋊C4×C43C2311yescharacteristic
103C2×C4⋊C4×C43C2311yescharacteristic
104C2×C22⋊C4×C43—21no—
105C2×C22⋊C4×C43—21no—
106C2×C22⋊C4×C43D411yescharacteristic
107C2×C22⋊C4×C43D411yescharacteristic
108C2×C42×C43—21no—
109C2×C42×C43C2311yescharacteristic
110C2×C42×C43C2311yescharacteristic
111#95×C43—21no—
112#95×C43—21no—
113#95×C43—21no—
114#95×C43—21no—
115#95×C43—21no—
116#95×C43—21no—
117#95×C43—21no—
118#95×C43D411yescharacteristic
119#95×C43D411yescharacteristic
120C24×C43C2×D411yescharacteristic
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2411yescharacteristic
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C2×Dic86—21no—
142C2×Dic86—21no—
143C2×Dic86—21no—
144C2×Dic86—21no—
145C2×Dic86—21no—
146C2×Dic86#4112yes—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—42no—
156C4⋊C4×C43—81no—
157C22⋊C4×C43—41no—
158C22⋊C4×C43—41no—
159C22⋊C4×C43—42no—
160C22⋊C4×C43—81no—
161C42×C43—21no—
162C42×C43—21no—
163C42×C43—21no—
164C42×C43—21no—
165C42×C43—81no—
166C22⋊Dic43—24no—
167C22⋊Dic43—42no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43#4112yes—
173C4⋊Dic43#4112yes—
174Dic43⋊C4—24no—
175Dic43⋊C4—42no—
176Dic43⋊C4—42no—
177C4×Dic43—42no—
178C4×Dic43—42no—
179C4×Dic43—42no—
180C2×C43⋊C8—21no—
181C2×C43⋊C8—21no—
182C2×C43⋊C8—21no—
183C2×C43⋊C8—21no—
184C2×C43⋊C8—21no—
185C2×C43⋊C8—21no—
186C2×C43⋊C8—21no—
187C2×C43⋊C8—21no—
188C2×C43⋊C8—21no—
189C2×C43⋊C8—21no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8#4112yes—
192C23×C43—21no—
193C23×C43—21no—
194C23×C43—21no—
195C23×C43—21no—
196C23×C43—21no—
197C23×C43—21no—
198C23×C43—21no—
199C23×C43C22×D411yescharacteristic
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
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—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43H(5,𝔽2)11yescharacteristic
236C2×C4×C432−1+411yescharacteristic
237C2×Dic43—22no—
238C2×Dic43—22no—
239C2×Dic43—22no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249Dic86—22no—
250Dic86—22no—
251Dic86—41no—
252Dic86—41no—
253C43⋊C8—22no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257#27061—431nomaximal, Sylow
258C22×C43—41no—
259C22×C43—41no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43#52511yescharacteristic
266C22×C43#54611yescharacteristic
267C22×C43#54711yescharacteristic
268C22×C43#57511yescharacteristic
269C22×C43#57511yescharacteristic
270C22×C43#57711yescharacteristic
271C22×C43#57811yescharacteristic
272C4×C43—41no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—81no—
278C4×C43—81no—
279C4×C43—81no—
280C4×C43—81no—
281C4×C43#52911yescharacteristic
282C4×C43#53911yescharacteristic
283C4×C43#55311yescharacteristic
284C4×C43#55611yescharacteristic
285Dic43—42no—
286Dic43—42no—
287Dic43—42no—
288Dic43—81no—
289#2494D4311yescharacteristic
290#2362—431no—
291#2074—431no—
292#2066—431no—
293#2036—431no—
294#2035—431no—
295#1949—431no—
296#1943—431no—
297#1924—431no—
298#1921—431no—
299#1920—431no—
300#1863—431no—
301#1854—431no—
302#1825—431no—
303#1763—431no—
304C2×C43—81no—
305C2×C43#246611yescharacteristic
306C2×C43#311111yescharacteristic
307C2×C43#312111yescharacteristic
308C2×C43#330711yescharacteristic
309C2×C43#332711yescharacteristic
310C2×C43#334911yescharacteristic
311C2×C43#335011yescharacteristic
312C2×C22⋊Q8—431no—
313C2×C4×Q8—431no—
314C2×#117—431no—
315C2×#107—431no—
316C2×#107—431no—
317C2×#106—431no—
318C2×#106—431no—
319C2×C4⋊C8—431no—
320C2×#103—431no—
321C2×#103—431no—
322C2×#103—431no—
323C2×#103—431no—
324C2×C22⋊C8—431no—
325C2×C22⋊C8—431no—
326C2×#97—431no—
327#401—21no—
328#397—21no—
329#391—431no—
330#389—431no—
331#389C2×D4311yescharacteristic
332#389C2×D4311yescharacteristic
333#388—21no—
334#388—861no—
335#388—861no—
336#387—21no—
337#387—861no—
338#382C2×D4311yescharacteristic
339#380C2×D4311yescharacteristic
340#380C2×D4311yescharacteristic
341C4×C4⋊C4—431no—
342C4×C4⋊C4—861no—
343C4×C4⋊C4C2×D4311yescharacteristic
344C4×C22⋊C4C2×D4311yescharacteristic
345#340—431no—
346#340—431no—
347#340—431no—
348#340—431no—
349#340—431no—
350#340—431no—
351#340—431no—
352#340—431no—
353#336—431no—
354#336—431no—
355C43#2706111yescharacteristic, complemented, Sylow
356C22×Q8—431no—
357C23×C4C22×D4311yescharacteristic
358C22×C8—431no—
359C22×C8—431no—
360C22×C8—431no—
361C22×C8—431no—
362C22⋊Q8—862no—
363C22⋊Q8—862no—
364C4×Q8—862no—
365C4×Q8—1721no—
366#117—862no—
367#117—1721no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—431no—
371C2×C4⋊C4—431no—
372C2×C4⋊C4—431no—
373C2×C4⋊C4—861no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4C22×D4311yescharacteristic
377C2×C4⋊C4C22×D4311yescharacteristic
378C2×C4⋊C4C22×D4311yescharacteristic
379C2×C4⋊C4C22×D4311yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—861no—
383C2×C22⋊C4—861no—
384C2×C22⋊C4C22⋊D4311yescharacteristic
385C2×C22⋊C4C22⋊D4311yescharacteristic
386C2×C42—21no—
387C2×C42—861no—
388C2×C42—861no—
389C2×C42—861no—
390C2×C42C22×D4311yescharacteristic
391C2×C42C22×D4311yescharacteristic
392#107—862no—
393#107—862no—
394#106—862no—
395#106—1721no—
396C4⋊C8—862no—
397#103—862no—
398#103—862no—
399#103—862no—
400#103—1721no—
401C22⋊C8—862no—
402C22⋊C8—1721no—
403#97—1721no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—861no—
412#95—861no—
413#95—861no—
414#95—861no—
415#95C22⋊D4311yescharacteristic
416#95C22⋊D4311yescharacteristic
417C24C2×C22⋊D4311yescharacteristic
418C2×Q8—432no—
419C2×Q8—861no—
420C2×Q8—861no—
421C2×Q8—861no—
422C2×Q8—861no—
423C2×Q8—861no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—861no—
435C22×C4—861no—
436C22×C4—861no—
437C22×C4—861no—
438C22×C4C2×C22⋊D4311yescharacteristic
439C22×C4C2×C22⋊D4311yescharacteristic
440C22×C4C2×C22⋊D4311yescharacteristic
441C22×C4C2×C22⋊D4311yescharacteristic
442C22×C4C2×C22⋊D4311yescharacteristic
443C22×C4C23×D4311yescharacteristic
444C2×C8—432no—
445C2×C8—861no—
446C2×C8—861no—
447C2×C8—861no—
448C2×C8—861no—
449C2×C8—861no—
450C2×C8—861no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8—861no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—42no—
465C4⋊C4—81no—
466C4⋊C4—432no—
467C4⋊C4—432no—
468C4⋊C4—864no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—1722no—
474C4⋊C4—1722no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C22⋊C4—42no—
478C22⋊C4—81no—
479C22⋊C4—864no—
480C22⋊C4—1722no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—81no—
486C42—1722no—
487C42—1722no—
488C42—1722no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23C22×C22⋊D4311yescharacteristic
497Q8—862no—
498Q8—862no—
499Q8—1721no—
500Q8—1721no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
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—41no—
531C2×C4—41no—
532C2×C4—862no—
533C2×C4—862no—
534C2×C4—862no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4#41×D4311yescharacteristic
545C2×C4#41×D4311yescharacteristic
546C2×C4#41×D4311yescharacteristic
547C2×C4#41×D4311yescharacteristic
548C2×C4#1306337111yescharacteristic
549C2×C4#1306337211yescharacteristic
550C8—862no—
551C8—1721no—
552C8—1721no—
553C8—1721no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22#1458340611yescharacteristic
562C22#1458353711yescharacteristic
563C22#1458354811yescharacteristic
564C22#1458369711yescharacteristic
565C22#1458369711yescharacteristic
566C22#1458371011yescharacteristic
567C22#1458371411yescharacteristic
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4—3441no—
578C4—1722no—
579C4—1722no—
580C4—1722no—
581C4#1458343211yescharacteristic
582C4#1458349011yescharacteristic
583C4#1458360011yescharacteristic
584C4#1458361611yescharacteristic
585C2—81no—
586C2#1913862711yescharacteristic
587C2#1914469811yescharacteristic
588C2#1914481811yescharacteristic
589C2#1914656511yescharacteristic
590C2#1914685711yescharacteristic
591C2#1914711911yescharacteristic
592C2#1914713411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2494C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#2494D43
hypocenterC43#27061
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2494

Complements

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

NH ≅ G/Ntype
2. #19136014C2semidirect
3. #19135973C2semidirect
6. #19135361C2semidirect
7. #19135330C2semidirect
9. #19135184C2semidirect
10. #19135180C2semidirect
11. #19134848C2semidirect
14. #19134428C2semidirect
355. C43#27061semidirect

Maximal subgroups

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

subgroupindex
#191376202
#191360142
#191359732
#191357982
#191357912
#191353612
#191353302
#191352102
#191351842
#191351802
#191348482
#191347922
#191346872
#191344282
C43×#24942
#2706143