Finite Group Databasebeta

← #25107126

Subgroups — #25107126

Order 11008.

834 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582951C211yesmaximal, characteristic
2#19136991C211yesmaximal, 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#19134758C211yesmaximal, characteristic, complemented
12#19134756C211yesmaximal, characteristic, complemented
13#19134724C211yesmaximal, characteristic, complemented
14#19134724C211yesmaximal, characteristic, complemented
15C43×#1949C211yesmaximal, characteristic, complemented
16C2×C4⋊C4×D43C2211yescharacteristic
17C2×C4⋊C4×D43C2211yescharacteristic
18C2×C42×D43C2211yescharacteristic
19#14582951C418yescomplemented
20C2×#13063259C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27C2×(C2×D43)⋊C8C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31#14582766—21no—
32#14582765C2211yescharacteristic
33#14582764C2211yescharacteristic
34#14582764C2211yescharacteristic
35#14582764C2211yescharacteristic
36#14582764C2211yescharacteristic
37#14582763—21no—
38#14582763—21no—
39#14582761—21no—
40#14582756C2211yescharacteristic
41#14582756C2211yescharacteristic
42C4×C4⋊Dic43C2211yescharacteristic
43C4×(C2×D43)⋊C4—21no—
44#14582745—21no—
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
67C2×C4⋊Dic43C2311yescharacteristic
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C4⋊C4×D43—41no—
74C4⋊C4×D43—41no—
75C4⋊C4×D43—41no—
76C4⋊C4×D43—41no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×C4×Dic43—21no—
80C2×C4×Dic43D411yescharacteristic
81C2×C4×Dic43D411yescharacteristic
82C2×C4×Dic43C2311yescharacteristic
83C42×D43C2×C414yes—
84C42×D43Q814yes—
85#13063259—41no—
86#13063258—41no—
87#13063258—41no—
88#13063257—41no—
89#13063256—41no—
90#13063256—41no—
91C4⋊(C43⋊C8)C2×C414yescomplemented
92(C2×D43)⋊C8C2×C414yes—
93(C2×D43)⋊C8C2×C414yes—
94C8×Dic43C2×C414yescomplemented
95C8×Dic43C2×C414yescomplemented
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⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C22×C8×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C42×C43—21no—
116C2×C42×C43C2311yescharacteristic
117#107×C43—41no—
118#106×C43—41no—
119C4⋊C8×C43C2×C414yescomplemented
120#95×C43—21no—
121#95×C43—21no—
122#95×C43—21no—
123C23×D43C2×D411yescharacteristic
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2411yescharacteristic
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43C2×D411yescharacteristic
136C22×Dic43C2×D411yescharacteristic
137C22×Dic43C2×D411yescharacteristic
138C2×C4×D43—21no—
139C2×C4×D43—21no—
140C2×C4×D43—21no—
141C2×C4×D43—21no—
142C2×C4×D43—22no—
143C2×C4×D43—22no—
144C2×C4×D43—41no—
145C2×C4×D43—41no—
146C2×C4×D43—42no—
147C2×C4×D43—42no—
148C2×C4×D43—42no—
149C2×C4×D43—42no—
150C2×C4×D43—42no—
151C2×C4×D43—42no—
152C2×C4×D43C4⋊C414yes—
153C2×C4×D43C4⋊C414yes—
154C2×C4×D43C22×C412yes—
155C2×C4×D43C2×Q812yes—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43C22×C412yes—
161C2×C8×C43C22×C412yes—
162C4⋊C4×C43—21no—
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—
170C42×C43—42no—
171C42×C43C22×C412yes—
172C42×C43C2×Q812yes—
173(C2×D43)⋊C4—42no—
174(C2×D43)⋊C4—42no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183Dic43⋊C4—42no—
184Dic43⋊C4—42no—
185C4×Dic43—42no—
186C4×Dic43C4⋊C414yes—
187C4×Dic43C4⋊C414yes—
188C4×Dic43C22×C412yes—
189C4×Dic43C2×Q812yes—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8C22×C412yes—
195C2×C43⋊C8C22×C412yes—
196C23×C43C22×D411yescharacteristic
197C22×D43—21no—
198C22×D43—21no—
199C22×D43—21no—
200C22×D43—21no—
201C22×D43C2×C4⋊C412yes—
202C22×D43#13512yes—
203C22×D43#13512yes—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
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×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43C2×C4⋊C412yes—
221C2×C4×C43C2×C4⋊C412yes—
222C2×C4×C43C23×C411yescharacteristic
223C2×C4×C43C22×Q811yescharacteristic
224C2×C4×C43H(5,𝔽2)11yescharacteristic
225C2×C4×C43H(5,𝔽2)11yescharacteristic
226C2×C4×C432−1+411yescharacteristic
227C2×C4×C432−1+411yescharacteristic
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×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43C2×C4⋊C412yes—
247C2×Dic43C2×C4⋊C412yes—
248C2×Dic43C2×C4⋊C412yes—
249C4×D43—28no—
250C4×D43—22no—
251C4×D43—22no—
252C4×D43—22no—
253C4×D43—22no—
254C4×D43—44no—
255C4×D43—84no—
256C4×D43—84no—
257C8×C43—22no—
258C8×C43—22no—
259C43⋊C8—22no—
260C43⋊C8—22no—
261#21983—431nomaximal, Sylow
262C22×C43C22×C4⋊C411yescharacteristic
263C22×C43#53511yescharacteristic
264C22×C43#53611yescharacteristic
265C22×C43C2×#13511yescharacteristic
266C22×C43C2×#13511yescharacteristic
267C22×C43#57511yescharacteristic
268C22×C43#57511yescharacteristic
269C2×D43—22no—
270C2×D43—22no—
271C2×D43—22no—
272C2×D43—22no—
273C2×D43—22no—
274C2×D43—22no—
275C2×D43#42714yes—
276C4×C43—22no—
277C4×C43—22no—
278C4×C43—81no—
279C4×C43—81no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43#52011yescharacteristic
283C4×C43#52011yescharacteristic
284C4×C43#54411yescharacteristic
285C4×C43#54411yescharacteristic
286Dic43—22no—
287Dic43—22no—
288Dic43—22no—
289Dic43—81no—
290Dic43—81no—
291Dic43—81no—
292Dic43—81no—
293C2×#431—431no—
294#2283—431no—
295C2×#382—431no—
296#1949—431no—
297#1949—431no—
298#1949—431no—
299#1949D4311yescharacteristic, complemented
300#1853—431no—
301#1853—431no—
302#1852—431no—
303#1852—431no—
304#1846—431no—
305#1846—431no—
306#1835—431no—
307#1835—431no—
308C2×C43#231711yescharacteristic
309C2×C43C2×#42711yescharacteristic
310C2×C43#291111yescharacteristic
311C2×C43#321111yescharacteristic
312C2×C43#321111yescharacteristic
313C2×C43#323211yescharacteristic
314C2×C43#323211yescharacteristic
315D43—24no—
316C22×C4⋊C4—431no—
317C22×C4⋊C4—431no—
318C22×C42—431no—
319#431—438no—
320C2×#107—431no—
321C2×#107—431no—
322C2×#107—431no—
323C2×#107C2×D4311yescharacteristic
324C2×#106—431no—
325C2×#106—431no—
326C2×#106—431no—
327C2×#106C2×D4311yescharacteristic
328C2×C4⋊C8—431no—
329C2×C4⋊C8C2×D4311yescharacteristic
330C2×C22⋊C8—431no—
331C2×C22⋊C8—431no—
332C2×C4×C8—431no—
333C2×C4×C8—431no—
334#383—861no—
335#382—431no—
336#382—431no—
337#382—431no—
338#382—431no—
339#382—431no—
340#382—861no—
341#382—861no—
342#382C2×D4311yescharacteristic
343#381—861no—
344#380—431no—
345#380—431no—
346C4×C4⋊C4—431no—
347C4×C4⋊C4C2×D4311yescharacteristic
348C4×C22⋊C4—861no—
349#376—861no—
350C2×#95—861no—
351C2×#95—861no—
352#340—431no—
353#340—431no—
354#340—431no—
355#340—431no—
356#340—431no—
357#340—431no—
358#340C2×D4311yescharacteristic
359#340C2×D4311yescharacteristic
360C43#2198311yescharacteristic, complemented, Sylow
361C23×C4—431no—
362C23×C4—431no—
363C23×C4—431no—
364C23×C4—861no—
365C23×C4—861no—
366C22×C8—431no—
367C22×C8—431no—
368C22×C8C22×D4311yescharacteristic
369C22×C8C22×D4311yescharacteristic
370C2×C4⋊C4—431no—
371C2×C4⋊C4—431no—
372C2×C4⋊C4—431no—
373C2×C4⋊C4—431no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4—1721no—
377C2×C4⋊C4—1721no—
378C2×C4⋊C4—1721no—
379C2×C4⋊C4—1721no—
380C2×C4⋊C4C22×D4311yescharacteristic
381C2×C4⋊C4C22×D4311yescharacteristic
382C2×C4⋊C4C22×D4311yescharacteristic
383C2×C4⋊C4C22×D4311yescharacteristic
384C2×C22⋊C4—861no—
385C2×C22⋊C4—861no—
386C2×C42—21no—
387C2×C42—431no—
388C2×C42—431no—
389C2×C42—431no—
390C2×C42—434no—
391C2×C42—434no—
392C2×C42—861no—
393C2×C42C22×D4311yescharacteristic
394#107—41no—
395#107—1721no—
396#107—1721no—
397#107—1721no—
398#106—41no—
399#106—1721no—
400#106—1721no—
401#106—1721no—
402C4⋊C8—434no—
403C4⋊C8C4×D4314yescomplemented
404C22⋊C8—434no—
405C22⋊C8—434no—
406C4×C8—434no—
407C4×C8—434no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—861no—
412#95—861no—
413#95—861no—
414#95—861no—
415#95—861no—
416#95—861no—
417#95—861no—
418#95—861no—
419#95—861no—
420#95—861no—
421#95—861no—
422#95—861no—
423#95—861no—
424C24—431no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—431no—
430C22×C4—431no—
431C22×C4—431no—
432C22×C4—434no—
433C22×C4—432no—
434C22×C4—432no—
435C22×C4—434no—
436C22×C4—862no—
437C22×C4—862no—
438C22×C4—861no—
439C22×C4—861no—
440C22×C4—861no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4—861no—
444C22×C4—861no—
445C22×C4—861no—
446C22×C4—1721no—
447C22×C4—1721no—
448C22×C4—1722no—
449C22×C4—1722no—
450C22×C4—1722no—
451C22×C4—1722no—
452C22×C4—1722no—
453C22×C4—1722no—
454C22×C4D4×D4311yescharacteristic
455C22×C4D4×D4311yescharacteristic
456C22×C4C23×D4311yescharacteristic
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—432no—
462C2×C8—432no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8C2×C4×D4312yes—
468C2×C8C2×C4×D4312yes—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—1722no—
486C4⋊C4—1722no—
487C22⋊C4—1722no—
488C22⋊C4—1722no—
489C42—42no—
490C42—434no—
491C42—434no—
492C42—432no—
493C42—432no—
494C42—1722no—
495C42C2×C4×D4312yes—
496C42Q8×D4312yes—
497C23—432no—
498C23—432no—
499C23—432no—
500C23—861no—
501C23—861no—
502C23—861no—
503C23—861no—
504C23C2×D4×D4311yescharacteristic
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
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—41no—
521C2×C4—432no—
522C2×C4—432no—
523C2×C4—432no—
524C2×C4—868no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—861no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—862no—
532C2×C4—862no—
533C2×C4—862no—
534C2×C4—862no—
535C2×C4—3444no—
536C2×C4—3444no—
537C2×C4—1724no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4C4⋊C4×D4312yes—
551C2×C4C4⋊C4×D4312yes—
552C2×C4C22×C4×D4311yescharacteristic
553C2×C4C2×Q8×D4311yescharacteristic
554C2×C4#1306337011yescharacteristic
555C2×C4#1306337111yescharacteristic
556C2×C4#1306337211yescharacteristic
557C2×C4#1306337311yescharacteristic
558C8—22no—
559C8—22no—
560C8—862no—
561C8—862no—
562C22—434no—
563C22—862no—
564C22—862no—
565C22—862no—
566C22—862no—
567C22—862no—
568C22—862no—
569C22C2×C4⋊C4×D4311yescharacteristic
570C22#1458346511yescharacteristic
571C22#1458347211yescharacteristic
572C22#135×D4311yescharacteristic
573C22#135×D4311yescharacteristic
574C22#1458369511yescharacteristic
575C22#1458369811yescharacteristic
576C4—22no—
577C4—22no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4—81no—
582C4—862no—
583C4—862no—
584C4—862no—
585C4—3441no—
586C4—3441no—
587C4—3441no—
588C4—3441no—
589C4#1458337811yescharacteristic
590C4#1458338111yescharacteristic
591C4#1458352611yescharacteristic
592C4#1458352911yescharacteristic
593C2—864no—
594C2#1913721711yescharacteristic
595C2#427×D4311yescharacteristic
596C2#1914318211yescharacteristic
597C2#1914555811yescharacteristic
598C2#1914556411yescharacteristic
599C2#1914576111yescharacteristic
600C2#1914576711yescharacteristic
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#21983
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. #19134758C2semidirect
12. #19134756C2semidirect
13. #19134724C2semidirect
14. #19134724C2semidirect
15. C43×#1949C2semidirect
19. #14582951C4semidirect
91. C4⋊(C43⋊C8)C2×C4semidirect
94. C8×Dic43C2×C4semidirect
95. C8×Dic43C2×C4semidirect
119. C4⋊C8×C43C2×C4semidirect
299. #1949D43semidirect
360. C43#21983semidirect
403. C4⋊C8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145829512
#191369912
#382×D432
#191353652
#191353632
#191353612
#191347892
#191347862
#191347842
#191347812
#191347582
#191347562
#191347242
C43×#19492
#2198343