Finite Group Databasebeta

← #25114379

Subgroups — #25114379

Order 11008.

810 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582942C211yesmaximal, characteristic
2#19137462C211yesmaximal, characteristic
3#19135335C211yesmaximal, characteristic, complemented
4#19135320C211yesmaximal, characteristic, complemented
5#19135187C211yesmaximal, characteristic, complemented
6#19135177C211yesmaximal, characteristic, complemented
7#19135170C211yesmaximal, characteristic, complemented
8#19135166C211yesmaximal, characteristic, complemented
9#19134690C211yesmaximal, characteristic
10#19134683C211yesmaximal, characteristic
11#19134626C211yesmaximal, characteristic
12#19134493C211yesmaximal, characteristic, complemented
13C4×#13063258C211yesmaximal, characteristic, complemented
14#19134379C211yesmaximal, characteristic
15C43×#2346C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic
17C2×#13063281—21no—
18C22×C4⋊Dic43C2211yescharacteristic
19#14582942C418yescomplemented
20C2×#13063258C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×C22⋊(C43⋊C8)C2211yescharacteristic
27C2×#13063236C2211yescharacteristic
28C2×C4×C43⋊C8C2211yescharacteristic
29#14582797C2211yescharacteristic
30#14582797C2211yescharacteristic
31#14582784—21no—
32#14582784—21no—
33#14582760—21no—
34#14582759C2211yescharacteristic
35C4×C4⋊Dic43C2211yescharacteristic
36C4×C4⋊Dic43C2211yescharacteristic
37#14582661C2211yescharacteristic
38#14582661C2211yescharacteristic
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582654C2211yescharacteristic
48#14582654C2211yescharacteristic
49C2×#117×C43C2211yescharacteristic
50C43×#389C2211yescharacteristic
51C43×#389C2211yescharacteristic
52C43×#388—21no—
53C43×#388—21no—
54C43×#382—21no—
55C43×#380C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C4×C22⋊C4×C43C2211yescharacteristic
59C43×#376—21no—
60C23×Dic43—21no—
61C2×#10621877—22no—
62C2×#10621877—22no—
63C2×#10621877C2×C414yes—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063281—44no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—22no—
71C2×C4⋊Dic43C2×C414yes—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×C22⋊Dic43—21no—
79C2×C4×Dic43—21no—
80C2×C4×Dic43—21no—
81#13063258—22no—
82#13063258C2×C414yes—
83#13063258C2×C414yes—
84#13063256—22no—
85#13063256C2×C414yes—
86#13063256C2×C414yes—
87C22⋊(C43⋊C8)—22no—
88#13063236—22no—
89C4×C43⋊C8—22no—
90C43⋊#95—21no—
91C43⋊#95—21no—
92C43⋊#95—21no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C23×C4×C43C2311yescharacteristic
96#117×C43—22no—
97#117×C43C2×C414yes—
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×C43—21no—
110C2×C42×C43—21no—
111C2×C42×C43C2311yescharacteristic
112C2×C42×C43C2311yescharacteristic
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×C43C22×C412yes—
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43#4112yes—
136C22×C4×C43C2411yescharacteristic
137C22×Dic43—24no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—42no—
143C22×Dic43—42no—
144C4⋊C4×C43—21no—
145C4⋊C4×C43—21no—
146C4⋊C4×C43—21no—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—81no—
151C4⋊C4×C43—81no—
152C4⋊C4×C43C22×C412yes—
153C4⋊C4×C43C22×C412yes—
154C22⋊C4×C43—22no—
155C22⋊C4×C43—24no—
156C22⋊C4×C43—41no—
157C22⋊C4×C43—81no—
158C42×C43—24no—
159C42×C43—21no—
160C42×C43—21no—
161C42×C43—21no—
162C42×C43—21no—
163C42×C43—42no—
164C42×C43—42no—
165C22⋊Dic43—42no—
166C4⋊Dic43—24no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43C22×C412yes—
174C4⋊Dic43C22×C412yes—
175Dic43⋊C4—42no—
176Dic43⋊C4—42no—
177C4×Dic43—42no—
178C4×Dic43—42no—
179#10621877—28no—
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⋊C8C22×C412yes—
189C2×C43⋊C8C22×C412yes—
190C2×C43⋊C8#4112yes—
191C2×C43⋊C8#4112yes—
192C23×C43—21no—
193C23×C43—21no—
194C23×C43—21no—
195C23×C43—21no—
196C23×C43—21no—
197C23×C43—21no—
198C23×C43C4×D412yes—
199C23×C43C22×D411yescharacteristic
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—22no—
205C2×C4×C43—22no—
206C2×C4×C43—22no—
207C2×C4×C43—22no—
208C2×C4×C43—22no—
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—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×C43C4×D412yes—
230C2×C4×C43AGL(1,ℤ/8)12yes—
231C2×C4×C43C23×C411yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C432−1+411yescharacteristic
236C2×C4×C432−1+411yescharacteristic
237C2×Dic43—22no—
238C2×Dic43—22no—
239C2×Dic43—48no—
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—
249C2×Dic43—41no—
250C43⋊C8—22no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253C43⋊C8#11714yescomplemented
254#22624—431nomaximal, Sylow
255C22×C43—22no—
256C22×C43—22no—
257C22×C43—22no—
258C22×C43—41no—
259C22×C43—41no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43C2×C4×D411yescharacteristic
263C22×C43#54711yescharacteristic
264C22×C43#54711yescharacteristic
265C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
266C22×C43#57511yescharacteristic
267C22×C43#57711yescharacteristic
268C22×C43#57811yescharacteristic
269C4×C43—22no—
270C4×C43—22no—
271C4×C43—41no—
272C4×C43—41no—
273C4×C43—41no—
274C4×C43—42no—
275C4×C43—42no—
276C4×C43—81no—
277C4×C43—81no—
278C4×C43C2×#11711yescharacteristic
279C4×C43#51911yescharacteristic
280C4×C43#55211yescharacteristic
281C4×C43#55211yescharacteristic
282Dic43—42no—
283Dic43—42no—
284Dic43—81no—
285Dic43—81no—
286C2×#428—431no—
287#2346D4311yescharacteristic
288#2344—431no—
289#1944—431no—
290#1941—431no—
291#1921—431no—
292#1920—431no—
293#1919—431no—
294#1918—431no—
295#1825—431no—
296#1824—431no—
297#1809—431no—
298#1776—431no—
299C4×#107—431no—
300#1753—431no—
301C2×C43—42no—
302C2×C43#234411yescharacteristic
303C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
304C2×C43#294711yescharacteristic
305C2×C43#334311yescharacteristic
306C2×C43#334811yescharacteristic
307C2×C43#335211yescharacteristic
308C2×C43#335411yescharacteristic
309C22×M16—431no—
310C2×#117—861no—
311C2×#117C2×D4311yescharacteristic
312C22×C4⋊C4—431no—
313#428—438no—
314C2×#107—431no—
315C2×#107—431no—
316C2×#107—431no—
317C2×#106—431no—
318C2×#106—431no—
319C2×#106—431no—
320C2×C22⋊C8—431no—
321C2×#97—431no—
322C2×C4×C8—431no—
323#389—431no—
324#389—431no—
325#389C2×D4311yescharacteristic
326#389C2×D4311yescharacteristic
327#388—21no—
328#388—21no—
329#387—861no—
330#387—861no—
331#382—21no—
332#381—861no—
333#380—431no—
334#380C2×D4311yescharacteristic
335C4×C4⋊C4—431no—
336C4×C4⋊C4—431no—
337C4×C4⋊C4C2×D4311yescharacteristic
338C4×C4⋊C4C2×D4311yescharacteristic
339C4×C22⋊C4C2×D4311yescharacteristic
340#376—21no—
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#340—431no—
351#336—431no—
352#336—431no—
353C43#2262411yescharacteristic, complemented, Sylow
354C23×C4—861no—
355C23×C4C22×D4311yescharacteristic
356C2×M16—434no—
357C2×M16—862no—
358C2×M16—862no—
359C22×C8—431no—
360C22×C8—431no—
361C22×C8—431no—
362C22×C8—431no—
363#117—22no—
364#117—1724no—
365#117C4×D4314yes—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—434no—
369C2×C4⋊C4—431no—
370C2×C4⋊C4—431no—
371C2×C4⋊C4—431no—
372C2×C4⋊C4—431no—
373C2×C4⋊C4—862no—
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×C4⋊C4C22×D4311yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—861no—
384C2×C22⋊C4C22⋊D4311yescharacteristic
385C2×C22⋊C4C22⋊D4311yescharacteristic
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—861no—
390C2×C42—861no—
391C2×C42C22×D4311yescharacteristic
392C2×C42C22×D4311yescharacteristic
393#107—434no—
394#107—434no—
395#107—862no—
396#106—434no—
397#106—434no—
398#106—862no—
399C22⋊C8—862no—
400#97—862no—
401C4×C8—862no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—861no—
408#95—861no—
409#95—861no—
410#95—861no—
411#95—861no—
412#95C22⋊D4311yescharacteristic
413#95C22⋊D4311yescharacteristic
414C24C2×C22⋊D4311yescharacteristic
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—864no—
424C22×C4—861no—
425C22×C4—861no—
426C22×C4—861no—
427C22×C4—861no—
428C22×C4—1722no—
429C22×C4—1722no—
430C22×C4C2×C4×D4312yes—
431C22×C4#1062189812yes—
432C22×C4C2×C22⋊D4311yescharacteristic
433C22×C4C2×C22⋊D4311yescharacteristic
434C22×C4C2×C22⋊D4311yescharacteristic
435C22×C4C2×C22⋊D4311yescharacteristic
436C22×C4C2×C22⋊D4311yescharacteristic
437C22×C4C23×D4311yescharacteristic
438M16—868no—
439C2×C8—432no—
440C2×C8—432no—
441C2×C8—432no—
442C2×C8—432no—
443C2×C8—861no—
444C2×C8—861no—
445C2×C8—861no—
446C2×C8—861no—
447C2×C8—861no—
448C2×C8—861no—
449C2×C8—861no—
450C2×C8—861no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—81no—
458C4⋊C4—81no—
459C4⋊C4—432no—
460C4⋊C4—432no—
461C4⋊C4—864no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—1722no—
469C4⋊C4—1722no—
470C4⋊C4C2×C4×D4312yes—
471C4⋊C4C2×C4×D4312yes—
472C22⋊C4—24no—
473C22⋊C4—22no—
474C22⋊C4—41no—
475C22⋊C4—81no—
476C22⋊C4—1722no—
477C42—24no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—42no—
483C42—42no—
484C42—1722no—
485C42—1722no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23C4×C22⋊D4312yes—
493C23C22×C22⋊D4311yescharacteristic
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
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—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—862no—
524C2×C4—862no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4—1721no—
531C2×C4—1728no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4C4×C22⋊D4312yes—
537C2×C4#1306335012yes—
538C2×C4C22×C4×D4311yescharacteristic
539C2×C4#41×D4311yescharacteristic
540C2×C4#41×D4311yescharacteristic
541C2×C4C2×#1062189811yescharacteristic
542C2×C4#1306337211yescharacteristic
543C2×C4#1306337211yescharacteristic
544C8—434no—
545C8—862no—
546C8—1721no—
547C8—1721no—
548C22—22no—
549C22—22no—
550C22—22no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22C2×C4×C22⋊D4311yescharacteristic
556C22#1458354811yescharacteristic
557C22#1458354811yescharacteristic
558C22C2×#1306335011yescharacteristic
559C22#1458369711yescharacteristic
560C22#1458371011yescharacteristic
561C22#1458371411yescharacteristic
562C4—22no—
563C4—22no—
564C4—42no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—42no—
569C4—81no—
570C4—81no—
571C4—3441no—
572C4—3441no—
573C4—1722no—
574C4—1722no—
575C4#117×D4311yescharacteristic
576C4#1458337611yescharacteristic
577C4#1458358211yescharacteristic
578C4#1458358211yescharacteristic
579C2—42no—
580C2#1913746511yescharacteristic
581C2C4×#1306335011yescharacteristic
582C2#1914343411yescharacteristic
583C2#1914703511yescharacteristic
584C2#1914711011yescharacteristic
585C2#1914716411yescharacteristic
586C2#1914718411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2346C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
cosocleC22×C4×C43C24
hypercenter#2346D43
hypocenterC43#22624
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2346

Complements

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

NH ≅ G/Ntype
3. #19135335C2semidirect
4. #19135320C2semidirect
5. #19135187C2semidirect
6. #19135177C2semidirect
7. #19135170C2semidirect
8. #19135166C2semidirect
12. #19134493C2semidirect
13. C4×#13063258C2semidirect
19. #14582942C4semidirect
253. C43⋊C8#117semidirect
353. C43#22624semidirect

Maximal subgroups

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

subgroupindex
C2×#145829422
#191374622
#191353352
#191353202
#191351872
#191351772
#191351702
#191351662
#191346902
#191346832
#191346262
#191344932
C4×#130632582
#191343792
C43×#23462
#2262443