Finite Group Databasebeta

← #25107151

Subgroups — #25107151

Order 11008.

858 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582955C211yesmaximal, characteristic
2#19136999C211yesmaximal, characteristic
3#382×D43C211yesmaximal, characteristic
4#19135365C211yesmaximal, characteristic, complemented
5#19135363C211yesmaximal, characteristic, complemented
6#19135361C211yesmaximal, characteristic, complemented
7#19134789C211yesmaximal, characteristic
8#19134786C211yesmaximal, characteristic
9#19134784C211yesmaximal, characteristic
10#19134781C211yesmaximal, characteristic
11#19134762C211yesmaximal, characteristic, complemented
12#19134760C211yesmaximal, characteristic, complemented
13#19134727C211yesmaximal, characteristic, complemented
14#19134727C211yesmaximal, characteristic, complemented
15C43×#1949C211yesmaximal, characteristic, complemented
16C2×#13063282—21no—
17C2×C4⋊C4×D43C2211yescharacteristic
18C2×C4⋊C4×D43C2211yescharacteristic
19C2×C42×D43C2211yescharacteristic
20#14582955C418yescomplemented
21C2×#13063259C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063257C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×#13063256C2211yescharacteristic
27C2×C4⋊(C43⋊C8)C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30C2×#13063235C2211yescharacteristic
31C2×#13063235C2211yescharacteristic
32#14582768C2211yescharacteristic
33#14582768C2211yescharacteristic
34#14582765C2211yescharacteristic
35#14582764C2211yescharacteristic
36#14582764C2211yescharacteristic
37#14582763—21no—
38#14582763—21no—
39#14582763—21no—
40#14582758—21no—
41#14582756C2211yescharacteristic
42#14582756C2211yescharacteristic
43C4×Dic43⋊C4—21no—
44C4×C4⋊Dic43C2211yescharacteristic
45#95×D43—21no—
46#95×D43—21no—
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C2×#106×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C43×#382C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×C4×D43—21no—
61C22×C4×D43—21no—
62C22×C4×D43D411yescharacteristic
63C22×C4×D43D411yescharacteristic
64C22×C4×D43C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063282—44no—
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C4⋊C4×D43—41no—
79C4⋊C4×D43—41no—
80C4⋊C4×D43—41no—
81C4⋊C4×D43—41no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43D411yescharacteristic
86C2×C4×Dic43D411yescharacteristic
87C2×C4×Dic43C2311yescharacteristic
88C42×D43C2×C414yes—
89C42×D43Q814yes—
90#13063259—41no—
91#13063258—41no—
92#13063258—41no—
93#13063257—41no—
94#13063256—41no—
95#13063256—41no—
96C4⋊(C43⋊C8)C2×C414yescomplemented
97(C2×D43)⋊C8C2×C414yes—
98(C2×D43)⋊C8C2×C414yes—
99#13063235C2×C414yescomplemented
100#13063235C2×C414yescomplemented
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C22×C8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C42×C43—21no—
117C2×C42×C43C2311yescharacteristic
118#107×C43—41no—
119#106×C43—41no—
120C4⋊C8×C43C2×C414yescomplemented
121#95×C43—21no—
122#95×C43—21no—
123#95×C43—21no—
124C23×D43C2×D411yescharacteristic
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2411yescharacteristic
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43C2×D411yescharacteristic
137C22×Dic43C2×D411yescharacteristic
138C22×Dic43C2×D411yescharacteristic
139C2×C4×D43—21no—
140C2×C4×D43—21no—
141C2×C4×D43—21no—
142C2×C4×D43—21no—
143C2×C4×D43—22no—
144C2×C4×D43—22no—
145C2×C4×D43—41no—
146C2×C4×D43—41no—
147C2×C4×D43—42no—
148C2×C4×D43—42no—
149C2×C4×D43—42no—
150C2×C4×D43—42no—
151C2×C4×D43—42no—
152C2×C4×D43—42no—
153C2×C4×D43C4⋊C414yes—
154C2×C4×D43C4⋊C414yes—
155C2×C4×D43C22×C412yes—
156C2×C4×D43C2×Q812yes—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43C22×C412yes—
162C2×C8×C43C22×C412yes—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C42×C43—42no—
172C42×C43C22×C412yes—
173C42×C43C2×Q812yes—
174(C2×D43)⋊C4—42no—
175(C2×D43)⋊C4—42no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184Dic43⋊C4—42no—
185Dic43⋊C4—42no—
186Dic43⋊C4—42no—
187Dic43⋊C4—42no—
188Dic43⋊C4—42no—
189Dic43⋊C4—42no—
190C4×Dic43—42no—
191C4×Dic43C4⋊C414yes—
192C4×Dic43C4⋊C414yes—
193C4×Dic43C22×C412yes—
194C4×Dic43C2×Q812yes—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8C22×C412yes—
200C2×C43⋊C8C22×C412yes—
201C23×C43C22×D411yescharacteristic
202C22×D43—21no—
203C22×D43—21no—
204C22×D43—21no—
205C22×D43—21no—
206C22×D43C2×C4⋊C412yes—
207C22×D43AGL(1,ℤ/8)12yes—
208C22×D43#13712yes—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
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×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43C2×C4⋊C412yes—
226C2×C4×C43C2×C4⋊C412yes—
227C2×C4×C43C23×C411yescharacteristic
228C2×C4×C43C22×Q811yescharacteristic
229C2×C4×C43H(5,𝔽2)11yescharacteristic
230C2×C4×C43H(5,𝔽2)11yescharacteristic
231C2×C4×C432−1+411yescharacteristic
232C2×C4×C432−1+411yescharacteristic
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
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—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43C2×C4⋊C412yes—
252C2×Dic43C2×C4⋊C412yes—
253C2×Dic43C2×C4⋊C412yes—
254C4×D43—28no—
255C4×D43—22no—
256C4×D43—22no—
257C4×D43—22no—
258C4×D43—22no—
259C4×D43—44no—
260C4×D43—84no—
261C4×D43—84no—
262C8×C43—22no—
263C8×C43—22no—
264C43⋊C8—22no—
265C43⋊C8—22no—
266#21986—431nomaximal, Sylow
267C22×C43C22×C4⋊C411yescharacteristic
268C22×C43#53511yescharacteristic
269C22×C43#53611yescharacteristic
270C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
271C22×C43C2×#13711yescharacteristic
272C22×C43#57511yescharacteristic
273C22×C43#57511yescharacteristic
274C2×D43—22no—
275C2×D43—22no—
276C2×D43—22no—
277C2×D43—22no—
278C2×D43—22no—
279C2×D43—22no—
280C2×D43#42814yes—
281C4×C43—22no—
282C4×C43—22no—
283C4×C43—81no—
284C4×C43—81no—
285C4×C43—81no—
286C4×C43—81no—
287C4×C43#52011yescharacteristic
288C4×C43#52011yescharacteristic
289C4×C43#54411yescharacteristic
290C4×C43#54411yescharacteristic
291Dic43—22no—
292Dic43—22no—
293Dic43—22no—
294Dic43—81no—
295Dic43—81no—
296Dic43—81no—
297Dic43—81no—
298C2×#432—431no—
299#2285—431no—
300C2×#382—431no—
301#1949—431no—
302#1949—431no—
303#1949—431no—
304#1949D4311yescharacteristic, complemented
305#1853—431no—
306#1853—431no—
307#1852—431no—
308#1852—431no—
309#1847—431no—
310#1847—431no—
311#1836—431no—
312#1836—431no—
313C2×C43#231711yescharacteristic
314C2×C43C2×#42811yescharacteristic
315C2×C43#291111yescharacteristic
316C2×C43#321311yescharacteristic
317C2×C43#321511yescharacteristic
318C2×C43#323411yescharacteristic
319C2×C43#323611yescharacteristic
320D43—24no—
321C2×#117—861no—
322C22×C4⋊C4—431no—
323C22×C4⋊C4—431no—
324C22×C42—431no—
325#432—438no—
326C2×#107—431no—
327C2×#107—431no—
328C2×#107—431no—
329C2×#107C2×D4311yescharacteristic
330C2×#106—431no—
331C2×#106—431no—
332C2×#106—431no—
333C2×#106C2×D4311yescharacteristic
334C2×C4⋊C8—431no—
335C2×C4⋊C8C2×D4311yescharacteristic
336C2×C22⋊C8—431no—
337C2×C22⋊C8—431no—
338C2×#97—431no—
339C2×#97—431no—
340#384—431no—
341#384—431no—
342#382—431no—
343#382—431no—
344#382—431no—
345#382—861no—
346#382—861no—
347#382—861no—
348#382C2×D4311yescharacteristic
349#380—431no—
350#380—431no—
351#380—861no—
352C4×C4⋊C4—431no—
353C4×C4⋊C4—861no—
354C4×C4⋊C4C2×D4311yescharacteristic
355C2×#95—861no—
356C2×#95—861no—
357#340—431no—
358#340—431no—
359#340—431no—
360#340—431no—
361#340—431no—
362#340—431no—
363#340C2×D4311yescharacteristic
364#340C2×D4311yescharacteristic
365C43#2198611yescharacteristic, complemented, Sylow
366C23×C4—431no—
367C23×C4—431no—
368C23×C4—431no—
369C23×C4—861no—
370C23×C4—861no—
371C22×C8—431no—
372C22×C8—431no—
373C22×C8C22×D4311yescharacteristic
374C22×C8C22×D4311yescharacteristic
375#117—1724no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—431no—
379C2×C4⋊C4—431no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4—1721no—
387C2×C4⋊C4—1721no—
388C2×C4⋊C4—1721no—
389C2×C4⋊C4—1721no—
390C2×C4⋊C4C22×D4311yescharacteristic
391C2×C4⋊C4C22×D4311yescharacteristic
392C2×C4⋊C4C22×D4311yescharacteristic
393C2×C4⋊C4C22×D4311yescharacteristic
394C2×C22⋊C4—861no—
395C2×C22⋊C4—861no—
396C2×C42—21no—
397C2×C42—431no—
398C2×C42—431no—
399C2×C42—431no—
400C2×C42—434no—
401C2×C42—434no—
402C2×C42—861no—
403C2×C42C22×D4311yescharacteristic
404#107—41no—
405#107—1721no—
406#107—1721no—
407#107—1721no—
408#106—41no—
409#106—1721no—
410#106—1721no—
411#106—1721no—
412C4⋊C8—434no—
413C4⋊C8C4×D4314yescomplemented
414C22⋊C8—434no—
415C22⋊C8—434no—
416#97—434no—
417#97—434no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—861no—
422#95—861no—
423#95—861no—
424#95—861no—
425#95—861no—
426#95—861no—
427#95—861no—
428#95—861no—
429#95—861no—
430C24—431no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—431no—
436C22×C4—431no—
437C22×C4—431no—
438C22×C4—434no—
439C22×C4—432no—
440C22×C4—432no—
441C22×C4—434no—
442C22×C4—862no—
443C22×C4—862no—
444C22×C4—861no—
445C22×C4—861no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—861no—
449C22×C4—861no—
450C22×C4—861no—
451C22×C4—861no—
452C22×C4—1721no—
453C22×C4—1721no—
454C22×C4—1722no—
455C22×C4—1722no—
456C22×C4—1722no—
457C22×C4—1722no—
458C22×C4—1722no—
459C22×C4—1722no—
460C22×C4D4×D4311yescharacteristic
461C22×C4D4×D4311yescharacteristic
462C22×C4C23×D4311yescharacteristic
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—432no—
468C2×C8—432no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8C2×C4×D4312yes—
474C2×C8C2×C4×D4312yes—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—1722no—
492C4⋊C4—1722no—
493C4⋊C4—1722no—
494C4⋊C4—1722no—
495C4⋊C4—1722no—
496C4⋊C4—1722no—
497C22⋊C4—1722no—
498C22⋊C4—1722no—
499C42—42no—
500C42—434no—
501C42—434no—
502C42—432no—
503C42—432no—
504C42—1722no—
505C42C2×C4×D4312yes—
506C42Q8×D4312yes—
507C23—432no—
508C23—432no—
509C23—432no—
510C23—861no—
511C23—861no—
512C23—861no—
513C23—861no—
514C23C2×D4×D4311yescharacteristic
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
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—432no—
532C2×C4—432no—
533C2×C4—432no—
534C2×C4—868no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—862no—
542C2×C4—862no—
543C2×C4—862no—
544C2×C4—862no—
545C2×C4—3444no—
546C2×C4—3444no—
547C2×C4—1724no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4C4⋊C4×D4312yes—
561C2×C4C4⋊C4×D4312yes—
562C2×C4C22×C4×D4311yescharacteristic
563C2×C4C2×Q8×D4311yescharacteristic
564C2×C4#1306337011yescharacteristic
565C2×C4#1306337111yescharacteristic
566C2×C4#1306337211yescharacteristic
567C2×C4#1306337311yescharacteristic
568C8—22no—
569C8—22no—
570C8—862no—
571C8—862no—
572C22—434no—
573C22—862no—
574C22—862no—
575C22—862no—
576C22—862no—
577C22—862no—
578C22—862no—
579C22C2×C4⋊C4×D4311yescharacteristic
580C22#1458346511yescharacteristic
581C22#1458347211yescharacteristic
582C22AGL(1,ℤ/8)×D4311yescharacteristic
583C22#137×D4311yescharacteristic
584C22#1458369611yescharacteristic
585C22#1458369611yescharacteristic
586C4—22no—
587C4—22no—
588C4—81no—
589C4—81no—
590C4—81no—
591C4—81no—
592C4—862no—
593C4—862no—
594C4—862no—
595C4—3441no—
596C4—3441no—
597C4—3441no—
598C4—3441no—
599C4#1458337811yescharacteristic
600C4#1458338111yescharacteristic
601C4#1458352611yescharacteristic
602C4#1458352911yescharacteristic
603C2—864no—
604C2#1913721711yescharacteristic
605C2#428×D4311yescharacteristic
606C2#1914318311yescharacteristic
607C2#1914558011yescharacteristic
608C2#1914559611yescharacteristic
609C2#1914578311yescharacteristic
610C2#1914579911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1949C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1949D43
hypocenterC43#21986
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
4. #19135365C2semidirect
5. #19135363C2semidirect
6. #19135361C2semidirect
11. #19134762C2semidirect
12. #19134760C2semidirect
13. #19134727C2semidirect
14. #19134727C2semidirect
15. C43×#1949C2semidirect
20. #14582955C4semidirect
96. C4⋊(C43⋊C8)C2×C4semidirect
99. #13063235C2×C4semidirect
100. #13063235C2×C4semidirect
120. C4⋊C8×C43C2×C4semidirect
304. #1949D43semidirect
365. C43#21986semidirect
413. C4⋊C8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145829552
#191369992
#382×D432
#191353652
#191353632
#191353612
#191347892
#191347862
#191347842
#191347812
#191347622
#191347602
#191347272
C43×#19492
#2198643