Finite Group Databasebeta

← #25169714

Subgroups — #25169714

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#19138991C211yesmaximal, characteristic
2#19137626C211yesmaximal, characteristic
3#19136016C211yesmaximal, characteristic, complemented
4#19135974C211yesmaximal, characteristic, complemented
5#19135788C211yesmaximal, characteristic
6#19135360C211yesmaximal, characteristic, complemented
7#19135334C211yesmaximal, characteristic, complemented
8#19135211C211yesmaximal, characteristic
9#19135186C211yesmaximal, characteristic, complemented
10#19135183C211yesmaximal, characteristic, complemented
11#19134851C211yesmaximal, characteristic, complemented
12#19134796C211yesmaximal, characteristic
13#19134687C211yesmaximal, characteristic
14#19134427C211yesmaximal, characteristic, complemented
15C43×#2036C211yesmaximal, characteristic
16C2×Q8×Dic43C2211yescharacteristic
17C2×#13063284C2211yescharacteristic
18C2×#13063259C2211yescharacteristic
19C2×#13063257C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×Dic43⋊C8C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×C22⋊(C43⋊C8)C2211yescharacteristic
25C2×#13063235C2211yescharacteristic
26C43⋊#401—21no—
27#14582827—21no—
28#14582806C2211yescharacteristic
29#14582798C2211yescharacteristic
30#14582798C2211yescharacteristic
31#14582795C2211yescharacteristic
32#14582792—21no—
33#14582792—21no—
34#14582792—21no—
35#14582785—21no—
36#14582784—21no—
37#14582764C2211yescharacteristic
38#14582759C2211yescharacteristic
39C4⋊C4×Dic43—21no—
40C4⋊C4×Dic43C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4×C22⋊Dic43C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×C22⋊Q8×C43C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×C43⋊C8C2311yescharacteristic
60C22×C43⋊C8C2311yescharacteristic
61Q8×Dic43—22no—
62Q8×Dic43—41no—
63#13063284—22no—
64#13063284—41no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×Dic43⋊C4—21no—
73C2×C22⋊Dic43—21no—
74C2×C22⋊Dic43—21no—
75C2×C22⋊Dic43D411yescharacteristic
76C2×C22⋊Dic43D411yescharacteristic
77C2×C4×Dic43—21no—
78C2×C4×Dic43—21no—
79C2×C4×Dic43—21no—
80C2×C4×Dic43—21no—
81C2×C4×Dic43C2311yescharacteristic
82C2×C4×Dic43C2311yescharacteristic
83#13063259—22no—
84#13063257—41no—
85#13063256—22no—
86Dic43⋊C8—22no—
87#13063249—22no—
88#13063249—41no—
89C22⋊(C43⋊C8)—41no—
90#13063235—41no—
91C43⋊#95—21no—
92C43⋊#95—21no—
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×Q8×C43C2311yescharacteristic
104C23×C4×C43C2311yescharacteristic
105C22×C8×C43C2311yescharacteristic
106C22×C8×C43C2311yescharacteristic
107C22⋊Q8×C43—22no—
108C22⋊Q8×C43—22no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115#107×C43—22no—
116#103×C43—22no—
117#103×C43—22no—
118C22⋊C8×C43—22no—
119#95×C43—21no—
120C24×C43C2×D411yescharacteristic
121C2×Q8×C43—21no—
122C2×Q8×C43—21no—
123C2×Q8×C43—21no—
124C2×Q8×C43—21no—
125C2×Q8×C43—21no—
126C2×Q8×C43#4112yes—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2411yescharacteristic
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43C2×D411yescharacteristic
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C2×C8×C43—21no—
148C2×C8×C43—21no—
149C2×C8×C43—21no—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43#4112yes—
153C4⋊C4×C43—24no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43#4112yes—
160C22⋊C4×C43—24no—
161C22⋊C4×C43—42no—
162C22⋊Dic43—41no—
163C22⋊Dic43—41no—
164C22⋊Dic43—42no—
165C22⋊Dic43—81no—
166C4⋊Dic43—21no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—42no—
174C4⋊Dic43—42no—
175C4⋊Dic43—42no—
176C4⋊Dic43#4112yes—
177Dic43⋊C4—81no—
178C4×Dic43—21no—
179C4×Dic43—21no—
180C4×Dic43—21no—
181C4×Dic43—21no—
182C4×Dic43—42no—
183C4×Dic43—42no—
184C4×Dic43—42no—
185C4×Dic43—81no—
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—21no—
193C23×C43—21no—
194C23×C43—21no—
195C23×C43—21no—
196C23×C43—21no—
197C23×C43—21no—
198C23×C43—21no—
199C23×C43C22×D411yescharacteristic
200Q8×C43—22no—
201Q8×C43—22no—
202Q8×C43—41no—
203Q8×C43—41no—
204C2×C4×C43—22no—
205C2×C4×C43—22no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—41no—
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—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43C2×#4111yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C2×C4×C43C2×#4111yescharacteristic
226C2×C4×C43C2×#4111yescharacteristic
227C2×C4×C43H(5,𝔽2)11yescharacteristic
228C2×C4×C432−1+411yescharacteristic
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—22no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—41no—
243C2×Dic43—41no—
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—
253C8×C43—22no—
254C8×C43—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—42no—
273C4×C43—41no—
274C4×C43—42no—
275C4×C43—81no—
276C4×C43—81no—
277C4×C43#52911yescharacteristic
278C4×C43#53911yescharacteristic
279C4×C43#55311yescharacteristic
280C4×C43#55611yescharacteristic
281Dic43—41no—
282Dic43—41no—
283Dic43—41no—
284Dic43—42no—
285Dic43—41no—
286Dic43—81no—
287Dic43—81no—
288Dic43—81no—
289#2494—431no—
290#2362—431no—
291#2074—431no—
292#2066—431no—
293#2036D4311yescharacteristic
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⋊Q8C2×D4311yescharacteristic
313C2×C4×Q8—431no—
314C2×#117—431no—
315C2×#107—431no—
316C2×#107C2×D4311yescharacteristic
317C2×#106—431no—
318C2×#106—431no—
319C2×C4⋊C8—431no—
320C2×#103—431no—
321C2×#103—431no—
322C2×#103C2×D4311yescharacteristic
323C2×#103C2×D4311yescharacteristic
324C2×C22⋊C8—431no—
325C2×C22⋊C8C2×D4311yescharacteristic
326C2×#97—431no—
327#401—861no—
328#397—861no—
329#391—431no—
330#389—431no—
331#389—431no—
332#389—431no—
333#388—861no—
334#388—861no—
335#388—861no—
336#387—861no—
337#387—861no—
338#382—431no—
339#380—431no—
340#380C2×D4311yescharacteristic
341C4×C4⋊C4—431no—
342C4×C4⋊C4—431no—
343C4×C4⋊C4—861no—
344C4×C22⋊C4—431no—
345#340—431no—
346#340—431no—
347#340—431no—
348#340—431no—
349#340—431no—
350#340—431no—
351#340—431no—
352#340C2×D4311yescharacteristic
353#336—431no—
354#336—431no—
355C43#2706111yescharacteristic, complemented, Sylow
356C22×Q8C22×D4311yescharacteristic
357C23×C4C22×D4311yescharacteristic
358C22×C8—431no—
359C22×C8—431no—
360C22×C8C22×D4311yescharacteristic
361C22×C8C22×D4311yescharacteristic
362C22⋊Q8—22no—
363C22⋊Q8—22no—
364C4×Q8—862no—
365C4×Q8—1721no—
366#117—862no—
367#117—1721no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—431no—
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⋊C4—861no—
377C2×C4⋊C4C22×D4311yescharacteristic
378C2×C4⋊C4C22×D4311yescharacteristic
379C2×C4⋊C4C22×D4311yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—431no—
383C2×C22⋊C4—431no—
384C2×C22⋊C4—861no—
385C2×C22⋊C4—861no—
386C2×C42—431no—
387C2×C42—431no—
388C2×C42—861no—
389C2×C42—861no—
390C2×C42—861no—
391C2×C42—861no—
392#107—22no—
393#107—862no—
394#106—862no—
395#106—1721no—
396C4⋊C8—862no—
397#103—22no—
398#103—22no—
399#103—862no—
400#103—1721no—
401C22⋊C8—22no—
402C22⋊C8—1721no—
403#97—1721no—
404#95—21no—
405#95—431no—
406#95—431no—
407#95—861no—
408#95—861no—
409#95—861no—
410#95—861no—
411#95—861no—
412#95—861no—
413#95—861no—
414#95—861no—
415#95—861no—
416#95—861no—
417C24D4×D4311yescharacteristic
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8#1062190012yes—
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—431no—
435C22×C4—431no—
436C22×C4—431no—
437C22×C4—431no—
438C22×C4—861no—
439C22×C4—861no—
440C22×C4—861no—
441C22×C4—861no—
442C22×C4D4×D4311yescharacteristic
443C22×C4C23×D4311yescharacteristic
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—861no—
450C2×C8—861no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8#1062190012yes—
456C4⋊C4—24no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—432no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—3441no—
471C4⋊C4—1722no—
472C4⋊C4—1722no—
473C4⋊C4—1722no—
474C4⋊C4#1062190012yes—
475C22⋊C4—24no—
476C22⋊C4—42no—
477C22⋊C4—3441no—
478C22⋊C4—1721no—
479C22⋊C4—1721no—
480C22⋊C4—1722no—
481C42—861no—
482C42—861no—
483C42—861no—
484C42—861no—
485C42—3441no—
486C42—1722no—
487C42—1722no—
488C42—1722no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23C2×D4×D4311yescharacteristic
497Q8—22no—
498Q8—22no—
499Q8—41no—
500Q8—41no—
501C2×C4—22no—
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—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—861no—
521C2×C4—861no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—861no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—862no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—1721no—
534C2×C4—1721no—
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×C4C2×#1062190011yescharacteristic
546C2×C4C2×#1062190011yescharacteristic
547C2×C4C2×#1062190011yescharacteristic
548C2×C4#1306337111yescharacteristic
549C2×C4#1306337211yescharacteristic
550C8—22no—
551C8—41no—
552C8—1721no—
553C8—1721no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22#1458340511yescharacteristic
562C22#1458354111yescharacteristic
563C22#1458354911yescharacteristic
564C22#1458369511yescharacteristic
565C22#1458369611yescharacteristic
566C22#1458370811yescharacteristic
567C22#1458371211yescharacteristic
568C4—41no—
569C4—42no—
570C4—42no—
571C4—81no—
572C4—81no—
573C4—3441no—
574C4—3441no—
575C4—3441no—
576C4—1721no—
577C4—1722no—
578C4—1721no—
579C4—1721no—
580C4—1721no—
581C4#1458343011yescharacteristic
582C4#1458349311yescharacteristic
583C4#1458360111yescharacteristic
584C4#1458361811yescharacteristic
585C2—81no—
586C2#1913862611yescharacteristic
587C2#1914469711yescharacteristic
588C2#1914482511yescharacteristic
589C2#1914656911yescharacteristic
590C2#1914686611yescharacteristic
591C2#1914713111yescharacteristic
592C2#1914713511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2036C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#2036D43
hypocenterC43#27061
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2036

Complements

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

NH ≅ G/Ntype
3. #19136016C2semidirect
4. #19135974C2semidirect
6. #19135360C2semidirect
7. #19135334C2semidirect
9. #19135186C2semidirect
10. #19135183C2semidirect
11. #19134851C2semidirect
14. #19134427C2semidirect
355. C43#27061semidirect

Maximal subgroups

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

subgroupindex
#191389912
#191376262
#191360162
#191359742
#191357882
#191353602
#191353342
#191352112
#191351862
#191351832
#191348512
#191347962
#191346872
#191344272
C43×#20362
#2706143