Finite Group Databasebeta

← #25114368

Subgroups — #25114368

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×#14582940C211yesmaximal, characteristic
2#19137476C211yesmaximal, characteristic
3#19137460C211yesmaximal, characteristic
4#19135336C211yesmaximal, characteristic, complemented
5#19135323C211yesmaximal, characteristic, complemented
6#19135185C211yesmaximal, characteristic, complemented
7#19135180C211yesmaximal, characteristic, complemented
8#19135171C211yesmaximal, characteristic, complemented
9#19135166C211yesmaximal, characteristic, complemented
10#19134689C211yesmaximal, characteristic
11#19134684C211yesmaximal, characteristic
12#19134629C211yesmaximal, characteristic
13#19134494C211yesmaximal, characteristic, complemented
14#19134378C211yesmaximal, characteristic
15C4×#107×C43C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C2×#13063283C2211yescharacteristic
18C2×#13063282—21no—
19C2×C4⋊C4×D43C2211yescharacteristic
20#14582940C418yescomplemented
21C2×#13063258C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×(C2×D43)⋊C8C2211yescharacteristic
26C2×#13063235C2211yescharacteristic
27#14582797C2211yescharacteristic
28#14582797C2211yescharacteristic
29#14582795C2211yescharacteristic
30#14582795C2211yescharacteristic
31#14582790—21no—
32#14582788—21no—
33#14582783—21no—
34#14582781—21no—
35#14582763—21no—
36#14582761—21no—
37#14582756C2211yescharacteristic
38#14582756C2211yescharacteristic
39C4⋊C4×Dic43C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41C4×(C2×D43)⋊C4C2211yescharacteristic
42#14582745—21no—
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C2×C4×C8×C43C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×C4×D43—21no—
61C22×C4×D43C2311yescharacteristic
62C2×#10621872—22no—
63C2×#10621872—22no—
64C2×#10621872C2×C414yes—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063283—22no—
68#13063283C2×C414yes—
69#13063282—44no—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C4⋊C4×D43—22no—
80C4⋊C4×D43C2×C414yes—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4D411yescharacteristic
85C2×(C2×D43)⋊C4D411yescharacteristic
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43C2311yescharacteristic
90#13063258C2×C414yes—
91#13063257—22no—
92#13063257C2×C414yes—
93#13063256C2×C414yes—
94(C2×D43)⋊C8—22no—
95#13063235—22no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95D411yescharacteristic
105C43⋊#95D411yescharacteristic
106C22×C8×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C42×C43—21no—
113C2×C42×C43—21no—
114C2×C42×C43C2311yescharacteristic
115#107×C43—22no—
116#107×C43C2×C414yes—
117C4×C8×C43—22no—
118#95×C43—21no—
119#95×C43—21no—
120C23×D43C2×D411yescharacteristic
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2411yescharacteristic
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43—21no—
132C22×Dic43C2×D411yescharacteristic
133C22×Dic43C2×D411yescharacteristic
134C22×Dic43C2×D411yescharacteristic
135C2×C4×D43—21no—
136C2×C4×D43—21no—
137C2×C4×D43—21no—
138C2×C4×D43—21no—
139C2×C4×D43—24no—
140C2×C4×D43—42no—
141C2×C4×D43—42no—
142C2×C4×D43C22×C412yes—
143C2×C4×D43#4112yes—
144C2×C8×C43—21no—
145C2×C8×C43—21no—
146C2×C8×C43—21no—
147C2×C8×C43C22×C412yes—
148C2×C8×C43#4112yes—
149C2×C8×C43#4112yes—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43C22×C412yes—
157C4⋊C4×C43C22×C412yes—
158C42×C43—21no—
159C42×C43—21no—
160C42×C43—42no—
161C42×C43—42no—
162(C2×D43)⋊C4—22no—
163(C2×D43)⋊C4—24no—
164(C2×D43)⋊C4—41no—
165(C2×D43)⋊C4—42no—
166(C2×D43)⋊C4—81no—
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—24no—
176Dic43⋊C4—42no—
177Dic43⋊C4—42no—
178Dic43⋊C4—81no—
179Dic43⋊C4—81no—
180C4×Dic43—21no—
181C4×Dic43—21no—
182C4×Dic43—24no—
183C4×Dic43—42no—
184C4×Dic43—42no—
185C2×C43⋊C8—21no—
186C2×C43⋊C8—21no—
187C2×C43⋊C8—21no—
188C2×C43⋊C8—21no—
189C2×C43⋊C8—21no—
190C2×C43⋊C8C22×C412yes—
191#10621872—28no—
192C23×C43C22×D411yescharacteristic
193C22×D43—21no—
194C22×D43—21no—
195C22×D43—21no—
196C22×D43—21no—
197C22×D43—21no—
198C22×D43—21no—
199C22×D43C4×D412yes—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—22no—
203C2×C4×C43—22no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
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×C43AGL(1,ℤ/8)12yes—
218C2×C4×C43C23×C411yescharacteristic
219C2×C4×C43C2×#4111yescharacteristic
220C2×C4×C43C2×#4111yescharacteristic
221C2×C4×C43C2×#4111yescharacteristic
222C2×C4×C432−1+411yescharacteristic
223C2×C4×C432−1+411yescharacteristic
224C2×Dic43—21no—
225C2×Dic43—21no—
226C2×Dic43—22no—
227C2×Dic43—22no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43C4×D412yes—
245C4×D43—22no—
246C4×D43—22no—
247C4×D43—22no—
248C4×D43—22no—
249C4×D43—48no—
250C8×C43—41no—
251C8×C43#11714yescomplemented
252C43⋊C8—22no—
253C43⋊C8—41no—
254#22624—431nomaximal, Sylow
255C22×C43C2×C4×D411yescharacteristic
256C22×C43#54711yescharacteristic
257C22×C43#54711yescharacteristic
258C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
259C22×C43#57511yescharacteristic
260C22×C43#57711yescharacteristic
261C22×C43#57811yescharacteristic
262C2×D43—22no—
263C2×D43—22no—
264C2×D43—22no—
265C2×D43—41no—
266C2×D43—41no—
267C2×D43—41no—
268C2×D43—41no—
269C4×C43—22no—
270C4×C43—41no—
271C4×C43—42no—
272C4×C43—42no—
273C4×C43—81no—
274C4×C43—81no—
275C4×C43C2×#11711yescharacteristic
276C4×C43#51911yescharacteristic
277C4×C43#55211yescharacteristic
278C4×C43#55211yescharacteristic
279Dic43—22no—
280Dic43—41no—
281Dic43—41no—
282Dic43—42no—
283Dic43—42no—
284Dic43—81no—
285Dic43—81no—
286C2×#428—431no—
287#2346—431no—
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×#107D4311yescharacteristic, complemented
300#1753—431no—
301C2×C43#234411yescharacteristic
302C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
303C2×C43#294711yescharacteristic
304C2×C43#334311yescharacteristic
305C2×C43#334811yescharacteristic
306C2×C43#335211yescharacteristic
307C2×C43#335411yescharacteristic
308D43—42no—
309C22×M16—431no—
310C2×#117—431no—
311C2×#117—861no—
312C22×C4⋊C4—431no—
313#428—438no—
314C2×#107—431no—
315C2×#107C2×D4311yescharacteristic
316C2×#107C2×D4311yescharacteristic
317C2×#106—431no—
318C2×#106—431no—
319C2×#106—431no—
320C2×C22⋊C8—431no—
321C2×#97—431no—
322C2×C4×C8C2×D4311yescharacteristic
323#389—431no—
324#389—431no—
325#389—431no—
326#389—431no—
327#388—861no—
328#388—861no—
329#387—861no—
330#387—861no—
331#382—861no—
332#381—861no—
333#380—431no—
334#380—431no—
335C4×C4⋊C4—431no—
336C4×C4⋊C4—431no—
337C4×C4⋊C4C2×D4311yescharacteristic
338C4×C4⋊C4C2×D4311yescharacteristic
339C4×C22⋊C4—431no—
340#376—861no—
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#340C2×D4311yescharacteristic
350#340C2×D4311yescharacteristic
351#336—431no—
352#336—431no—
353C43#2262411yescharacteristic, complemented, Sylow
354C23×C4—431no—
355C23×C4—861no—
356C2×M16—434no—
357C2×M16—862no—
358C2×M16—862no—
359C22×C8—431no—
360C22×C8—431no—
361C22×C8C22×D4311yescharacteristic
362C22×C8C22×D4311yescharacteristic
363#117—434no—
364#117—862no—
365#117—1724no—
366C2×C4⋊C4—431no—
367C2×C4⋊C4—431no—
368C2×C4⋊C4—434no—
369C2×C4⋊C4—431no—
370C2×C4⋊C4—431no—
371C2×C4⋊C4—862no—
372C2×C4⋊C4—861no—
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×C4⋊C4C22×D4311yescharacteristic
381C2×C22⋊C4—431no—
382C2×C22⋊C4—431no—
383C2×C22⋊C4—861no—
384C2×C22⋊C4—861no—
385C2×C22⋊C4—861no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—431no—
389C2×C42—861no—
390C2×C42—861no—
391C2×C42—861no—
392C2×C42C22×D4311yescharacteristic
393#107—22no—
394#107—434no—
395#107C4×D4314yes—
396#106—434no—
397#106—434no—
398#106—862no—
399C22⋊C8—862no—
400#97—862no—
401C4×C8—22no—
402#95—21no—
403#95—21no—
404#95—431no—
405#95—431no—
406#95—861no—
407#95—861no—
408#95—861no—
409#95—861no—
410#95—861no—
411#95—861no—
412#95—861no—
413#95—861no—
414C24—431no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—431no—
420C22×C4—432no—
421C22×C4—432no—
422C22×C4—431no—
423C22×C4—431no—
424C22×C4—864no—
425C22×C4—861no—
426C22×C4—861no—
427C22×C4—861no—
428C22×C4—861no—
429C22×C4—861no—
430C22×C4—861no—
431C22×C4—861no—
432C22×C4—861no—
433C22×C4—1722no—
434C22×C4—1722no—
435C22×C4D4×D4311yescharacteristic
436C22×C4D4×D4311yescharacteristic
437C22×C4C23×D4311yescharacteristic
438M16—868no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—432no—
443C2×C8—861no—
444C2×C8—861no—
445C2×C8—861no—
446C2×C8—861no—
447C2×C8—861no—
448C2×C8C2×C4×D4312yes—
449C2×C8#1062189812yes—
450C2×C8#1062189812yes—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—432no—
458C4⋊C4—432no—
459C4⋊C4—864no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—3441no—
467C4⋊C4—3441no—
468C4⋊C4—1722no—
469C4⋊C4—1722no—
470C4⋊C4C2×C4×D4312yes—
471C4⋊C4C2×C4×D4312yes—
472C22⋊C4—864no—
473C22⋊C4—862no—
474C22⋊C4—3441no—
475C22⋊C4—1721no—
476C22⋊C4—1722no—
477C42—21no—
478C42—21no—
479C42—42no—
480C42—42no—
481C42—864no—
482C42—861no—
483C42—861no—
484C42—1722no—
485C42—1722no—
486C23—432no—
487C23—861no—
488C23—861no—
489C23—861no—
490C23—861no—
491C23—861no—
492C23—861no—
493C23C2×D4×D4311yescharacteristic
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—432no—
512C2×C4—861no—
513C2×C4—861no—
514C2×C4—862no—
515C2×C4—862no—
516C2×C4—862no—
517C2×C4—862no—
518C2×C4—861no—
519C2×C4—861no—
520C2×C4—862no—
521C2×C4—862no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—1728no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4#1306334912yes—
538C2×C4C22×C4×D4311yescharacteristic
539C2×C4#41×D4311yescharacteristic
540C2×C4C2×#1062189811yescharacteristic
541C2×C4C2×#1062189811yescharacteristic
542C2×C4#1306337211yescharacteristic
543C2×C4#1306337311yescharacteristic
544C8—41no—
545C8—862no—
546C8—1721no—
547C8#1306328214yescomplemented
548C22—862no—
549C22—862no—
550C22—862no—
551C22—1721no—
552C22—1721no—
553C22—1721no—
554C22—1721no—
555C22C4×D4×D4311yescharacteristic
556C22#1458355011yescharacteristic
557C22#1458355411yescharacteristic
558C22C2×#1306334911yescharacteristic
559C22#1458369611yescharacteristic
560C22#1458370611yescharacteristic
561C22#1458371211yescharacteristic
562C4—22no—
563C4—41no—
564C4—42no—
565C4—42no—
566C4—81no—
567C4—81no—
568C4—862no—
569C4—3441no—
570C4—3441no—
571C4—1722no—
572C4—1721no—
573C4—1721no—
574C4—1722no—
575C4C2×#1306328211yescharacteristic
576C4#1458337511yescharacteristic
577C4#1458358811yescharacteristic
578C4#1458359011yescharacteristic
579C2—1722no—
580C2#1913746011yescharacteristic
581C2C4×#1306334911yescharacteristic
582C2#1914343311yescharacteristic
583C2#1914703111yescharacteristic
584C2#1914710611yescharacteristic
585C2#1914717111yescharacteristic
586C2#1914719211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#107×C43C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenterC4×#107D43
hypocenterC43#22624
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#107

Complements

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

NH ≅ G/Ntype
4. #19135336C2semidirect
5. #19135323C2semidirect
6. #19135185C2semidirect
7. #19135180C2semidirect
8. #19135171C2semidirect
9. #19135166C2semidirect
13. #19134494C2semidirect
15. C4×#107×C43C2semidirect
20. #14582940C4semidirect
251. C8×C43#117semidirect
299. C4×#107D43semidirect
353. C43#22624semidirect
547. C8#13063282semidirect

Maximal subgroups

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

subgroupindex
C2×#145829402
#191374762
#191374602
#191353362
#191353232
#191351852
#191351802
#191351712
#191351662
#191346892
#191346842
#191346292
#191344942
#191343782
C4×#107×C432
#2262443