Finite Group Databasebeta

← #25155700

Subgroups — #25155700

Order 11008.

708 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139829C211yesmaximal, characteristic, complemented
2#19136123C211yesmaximal, characteristic
3#19136116C211yesmaximal, characteristic
4#19135983C211yesmaximal, characteristic
5#19135969C211yesmaximal, characteristic
6#19135363C211yesmaximal, characteristic, complemented
7#19135353C211yesmaximal, characteristic, complemented
8#19135351C211yesmaximal, characteristic, complemented
9#19135319C211yesmaximal, characteristic, complemented
10#19135187C211yesmaximal, characteristic, complemented
11#19135180C211yesmaximal, characteristic, complemented
12#19134761C211yesmaximal, characteristic, complemented
13#19134605C211yesmaximal, characteristic
14#19134420C211yesmaximal, characteristic
15C43×#2354C211yesmaximal, characteristic
16C2×#13063258C2211yescharacteristic
17C2×#13063258C2211yescharacteristic
18C2×#13063258C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23C2×C4⋊(C43⋊C8)C2211yescharacteristic
24C2×C4⋊(C43⋊C8)C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063236C2211yescharacteristic
30#14582838—21no—
31#14582832—21no—
32#14582797C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582786—21no—
35#14582782—21no—
36#14582769C2211yescharacteristic
37#14582765C2211yescharacteristic
38#14582765C2211yescharacteristic
39C4×C4⋊Dic43C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×C4×D4×C43C2211yescharacteristic
49C2×#117×C43—21no—
50C43×#390C2211yescharacteristic
51C43×#390C2211yescharacteristic
52C43×#388—21no—
53C43×#388—21no—
54C43×#384C2211yescharacteristic
55C43×#380—21no—
56C4×C4⋊C4×C43C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C22×C43⋊C8C2311yescharacteristic
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C2×C4⋊Dic43—21no—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43C2311yescharacteristic
66C2×C4⋊Dic43C2311yescharacteristic
67C2×C4⋊Dic43C2311yescharacteristic
68C2×C4⋊Dic43C2311yescharacteristic
69C2×Dic43⋊C4—21no—
70C2×Dic43⋊C4—21no—
71C2×C4×Dic43—21no—
72#13063258—22no—
73#13063258—41no—
74#13063258—41no—
75#13063258—41no—
76#13063256—22no—
77#13063256—41no—
78C4⋊(C43⋊C8)—22no—
79C4⋊(C43⋊C8)—22no—
80C4⋊(C43⋊C8)—22no—
81#13063246—22no—
82#13063246—22no—
83#13063246—41no—
84#13063246—41no—
85#13063236—22no—
86C43⋊#95—21no—
87C43⋊#95—21no—
88C43⋊#95—21no—
89C43⋊#95—21no—
90C43⋊#95—21no—
91C43⋊#95—21no—
92C43⋊#95—21no—
93C22×D4×C43C2311yescharacteristic
94C23×C4×C43—21no—
95C4×D4×C43—22no—
96C4×D4×C43Q814yes—
97#117×C43—44no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43D411yescharacteristic
101C2×C4⋊C4×C43D411yescharacteristic
102C2×C4⋊C4×C43C2311yescharacteristic
103C2×C4⋊C4×C43C2311yescharacteristic
104C2×C4⋊C4×C43C2311yescharacteristic
105C2×C22⋊C4×C43—21no—
106C2×C22⋊C4×C43—21no—
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43—21no—
109C2×C22⋊C4×C43—21no—
110C2×C42×C43—21no—
111C2×C42×C43—21no—
112C2×C42×C43C2311yescharacteristic
113C2×C42×C43C2311yescharacteristic
114C2×C42×C43C2311yescharacteristic
115#95×C43—21no—
116#95×C43—21no—
117#95×C43D411yescharacteristic
118#95×C43D411yescharacteristic
119C24×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43—21no—
122C2×D4×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43—21no—
125C2×D4×C43C2×Q812yes—
126C22×C4×C43—24no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—42no—
131C22×C4×C43—42no—
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2411yescharacteristic
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C4⋊C4×C43—22no—
144C4⋊C4×C43—21no—
145C4⋊C4×C43—21no—
146C4⋊C4×C43—21no—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—41no—
150C4⋊C4×C43—42no—
151C4⋊C4×C43—81no—
152C4⋊C4×C43C2×Q812yes—
153C22⋊C4×C43—24no—
154C22⋊C4×C43—42no—
155C22⋊C4×C43—42no—
156C22⋊C4×C43—81no—
157C22⋊C4×C43—81no—
158C42×C43—21no—
159C42×C43—21no—
160C42×C43—21no—
161C42×C43—21no—
162C42×C43—42no—
163C42×C43—42no—
164C42×C43C2×Q812yes—
165C42×C43#4112yes—
166C4⋊Dic43—21no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—42no—
175C4⋊Dic43—81no—
176Dic43⋊C4—42no—
177Dic43⋊C4—81no—
178C4×Dic43—81no—
179C2×C43⋊C8—21no—
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#4112yes—
190C2×C43⋊C8#4112yes—
191C23×C43—22no—
192C23×C43—41no—
193C23×C43—41no—
194C23×C43—41no—
195C23×C43—41no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43C22×D411yescharacteristic
199D4×C43—22no—
200D4×C43—22no—
201D4×C43—41no—
202D4×C43—41no—
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—22no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—48no—
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×C43C22⋊Q812yes—
229C2×C4×C43C22⋊Q812yes—
230C2×C4×C43AGL(1,ℤ/8)12yes—
231C2×C4×C43C22×Q811yescharacteristic
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—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—41no—
248C2×Dic43—41no—
249C43⋊C8—22no—
250C43⋊C8—22no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253#26098—431nomaximal, Sylow
254C22×C43—42no—
255C22×C43—42no—
256C22×C43—42no—
257C22×C43—81no—
258C22×C43—81no—
259C22×C43—81no—
260C22×C43—81no—
261C22×C43C2×C22⋊Q811yescharacteristic
262C22×C43#54711yescharacteristic
263C22×C43#55011yescharacteristic
264C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
265C22×C43#57511yescharacteristic
266C22×C43#57611yescharacteristic
267C22×C43#57811yescharacteristic
268C4×C43—22no—
269C4×C43—22no—
270C4×C43—22no—
271C4×C43—42no—
272C4×C43—41no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—81no—
276C4×C43—81no—
277C4×C43#53311yescharacteristic
278C4×C43#54411yescharacteristic
279C4×C43#55211yescharacteristic
280C4×C43#55311yescharacteristic
281Dic43—81no—
282Dic43—81no—
283Dic43—81no—
284Dic43—81no—
285#2570—431no—
286#2354D4311yescharacteristic
287#2093—431no—
288#2092—431no—
289#2067—431no—
290#2065—431no—
291#1949—431no—
292#1947—431no—
293#1947—431no—
294#1940—431no—
295#1921—431no—
296#1920—431no—
297#1847—431no—
298#1804—431no—
299#1762—431no—
300C2×C43—82no—
301C2×C43#244111yescharacteristic
302C2×C43#307711yescharacteristic
303C2×C43#308311yescharacteristic
304C2×C43#334311yescharacteristic
305C2×C43#334711yescharacteristic
306C2×C43#339911yescharacteristic
307C2×C43#340211yescharacteristic
308C2×C4×D4C2×D4311yescharacteristic
309C2×#117—21no—
310C2×#107—431no—
311C2×#107—431no—
312C2×#107—431no—
313C2×#107—431no—
314C2×#106—431no—
315C2×#106—431no—
316C2×C4⋊C8—431no—
317C2×C4⋊C8—431no—
318C2×C4⋊C8—431no—
319C2×#102—431no—
320C2×#102—431no—
321C2×#102—431no—
322C2×#102—431no—
323C2×#97—431no—
324#400—861no—
325#398—861no—
326#390C2×D4311yescharacteristic
327#390C2×D4311yescharacteristic
328#389—431no—
329#389—431no—
330#388—21no—
331#388—21no—
332#387—861no—
333#387—861no—
334#384—431no—
335#384C2×D4311yescharacteristic
336#382—431no—
337#382—431no—
338#380—21no—
339C4×C4⋊C4—431no—
340C4×C4⋊C4C2×D4311yescharacteristic
341C4×C4⋊C4C2×D4311yescharacteristic
342C4×C4⋊C4C2×D4311yescharacteristic
343#340—431no—
344#340—431no—
345#340—431no—
346#340—431no—
347#340—431no—
348#340—431no—
349#336—431no—
350#336—431no—
351C43#2609811yescharacteristic, complemented, Sylow
352C22×D4C22×D4311yescharacteristic
353C23×C4—21no—
354C22×C8—431no—
355C22×C8—431no—
356C22×C8—431no—
357C22×C8—431no—
358C4×D4—22no—
359C4×D4Dic8614yes—
360#117—44no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—431no—
364C2×C4⋊C4—431no—
365C2×C4⋊C4—431no—
366C2×C4⋊C4—431no—
367C2×C4⋊C4—861no—
368C2×C4⋊C4—861no—
369C2×C4⋊C4—861no—
370C2×C4⋊C4—861no—
371C2×C4⋊C4C22⋊D4311yescharacteristic
372C2×C4⋊C4C22⋊D4311yescharacteristic
373C2×C4⋊C4C22×D4311yescharacteristic
374C2×C4⋊C4C22×D4311yescharacteristic
375C2×C4⋊C4C22×D4311yescharacteristic
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—861no—
384C2×C42C22×D4311yescharacteristic
385C2×C42C22×D4311yescharacteristic
386C2×C42C22×D4311yescharacteristic
387#107—862no—
388#107—1721no—
389#107—1721no—
390#107—1721no—
391#106—862no—
392#106—1721no—
393C4⋊C8—862no—
394C4⋊C8—862no—
395C4⋊C8—862no—
396#102—862no—
397#102—862no—
398#102—1721no—
399#102—1721no—
400#97—862no—
401#95—21no—
402#95—21no—
403#95—861no—
404#95—861no—
405#95—861no—
406#95—861no—
407#95—861no—
408#95—861no—
409#95—861no—
410#95C22⋊D4311yescharacteristic
411#95C22⋊D4311yescharacteristic
412C24—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4C2×Dic8612yes—
419C22×C4—21no—
420C22×C4—24no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—861no—
426C22×C4—861no—
427C22×C4—861no—
428C22×C4—861no—
429C22×C4C2×C22⋊D4311yescharacteristic
430C22×C4C2×C22⋊D4311yescharacteristic
431C22×C4C2×C22⋊D4311yescharacteristic
432C22×C4C2×C22⋊D4311yescharacteristic
433C22×C4C2×C22⋊D4311yescharacteristic
434C22×C4C2×C22⋊D4311yescharacteristic
435C22×C4C23×D4311yescharacteristic
436C2×C8—432no—
437C2×C8—432no—
438C2×C8—861no—
439C2×C8—861no—
440C2×C8—861no—
441C2×C8—861no—
442C2×C8—861no—
443C2×C8—861no—
444C2×C8—861no—
445C2×C8—861no—
446C2×C8—861no—
447C2×C8—861no—
448C4⋊C4—22no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—41no—
455C4⋊C4—42no—
456C4⋊C4—81no—
457C4⋊C4—861no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—3441no—
466C4⋊C4—3441no—
467C4⋊C4—1722no—
468C4⋊C4—1722no—
469C4⋊C4C2×Dic8612yes—
470C22⋊C4—24no—
471C22⋊C4—42no—
472C22⋊C4—42no—
473C22⋊C4—81no—
474C22⋊C4—81no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—42no—
480C42—42no—
481C42—3441no—
482C42C2×Dic8612yes—
483C42#1062189812yes—
484C23—22no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23C22×C22⋊D4311yescharacteristic
492D4—22no—
493D4—22no—
494D4—41no—
495D4—41no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
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—48no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4—1721no—
524C2×C4—1721no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4#1306330412yes—
534C2×C4#1306330412yes—
535C2×C4#1306335112yes—
536C2×C4C22×Dic8611yescharacteristic
537C2×C4#41×D4311yescharacteristic
538C2×C4#41×D4311yescharacteristic
539C2×C4C2×#1062189811yescharacteristic
540C2×C4#1306337111yescharacteristic
541C2×C4#1306337211yescharacteristic
542C8—862no—
543C8—862no—
544C8—1721no—
545C8—1721no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22C2×#1306330411yescharacteristic
554C22#1458354811yescharacteristic
555C22#1458356811yescharacteristic
556C22C2×#1306335111yescharacteristic
557C22#1458369711yescharacteristic
558C22#1458370211yescharacteristic
559C22#1458371411yescharacteristic
560C4—22no—
561C4—22no—
562C4—22no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—42no—
567C4—81no—
568C4—81no—
569C4—3441no—
570C4—3441no—
571C4—3441no—
572C4—3441no—
573C4#1458345211yescharacteristic
574C4#1458352711yescharacteristic
575C4#1458358811yescharacteristic
576C4#1458359311yescharacteristic
577C2—82no—
578C2#1913830211yescharacteristic
579C2#1914439211yescharacteristic
580C2#1914444611yescharacteristic
581C2#1914702911yescharacteristic
582C2#1914709511yescharacteristic
583C2#1914763711yescharacteristic
584C2#1914767011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2354C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2354D43
hypocenterC43#26098
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2354

Complements

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

NH ≅ G/Ntype
1. #19139829C2semidirect
6. #19135363C2semidirect
7. #19135353C2semidirect
8. #19135351C2semidirect
9. #19135319C2semidirect
10. #19135187C2semidirect
11. #19135180C2semidirect
12. #19134761C2semidirect
351. C43#26098semidirect

Maximal subgroups

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

subgroupindex
#191398292
#191361232
#191361162
#191359832
#191359692
#191353632
#191353532
#191353512
#191353192
#191351872
#191351802
#191347612
#191346052
#191344202
C43×#23542
#2609843