Finite Group Databasebeta

← #25066651

Subgroups — #25066651

Order 11008.

648 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144642C211yesmaximal, characteristic
2#19143740C211yesmaximal, characteristic, complemented
3#19143619C211yesmaximal, characteristic, complemented
4#19133456C211yesmaximal, characteristic, complemented
5#19133449C211yesmaximal, characteristic, complemented
6#19133428C211yesmaximal, characteristic, complemented
7#19133421C211yesmaximal, characteristic, complemented
8#19133416C211yesmaximal, characteristic, complemented
9#19133404C211yesmaximal, characteristic, complemented
10#19133398C211yesmaximal, characteristic, complemented
11#19133387C211yesmaximal, characteristic, complemented
12#19133386C211yesmaximal, characteristic, complemented
13#19133004C211yesmaximal, characteristic, complemented
14#19132895C211yesmaximal, characteristic, complemented
15C43×#1486C211yesmaximal, characteristic, complemented
16#14583433C2211yescharacteristic
17#14583234C411yescharacteristic
18#14583217C411yescharacteristic
19#14583199C411yescharacteristic
20#14583199C411yescharacteristic
21#14583114C411yescharacteristic
22#14583114C411yescharacteristic
23#14583050C411yescharacteristic
24#14583033C411yescharacteristic
25#14583026C2211yescharacteristic, complemented
26#14583023C2211yescharacteristic, complemented
27C4×#10621883C2211yescharacteristic
28C4×#10621883C2211yescharacteristic
29C4×#10621882C2211yescharacteristic
30C4×#10621882C2211yescharacteristic
31#14582976C2211yescharacteristic, complemented
32#14582975—21no—
33#14582968—21no—
34D4×C43⋊C8—21no—
35D4×C43⋊C8—21no—
36D4×C43⋊C8C2211yescharacteristic
37D4×C43⋊C8C2211yescharacteristic
38D4×C43⋊C8C2211yescharacteristic
39D4×C43⋊C8C2211yescharacteristic
40#14582964C2211yescharacteristic, complemented
41#14582959—21no—
42#14582952C2211yescharacteristic
43#14582952C2211yescharacteristic
44#14582952C2211yescharacteristic
45#14582924—21no—
46C2×C22⋊(C43⋊C8)—21no—
47C2×C22⋊(C43⋊C8)—21no—
48#14582651C2211yescharacteristic, complemented
49#14582651C2211yescharacteristic, complemented
50#14582649C2211yescharacteristic, complemented
51#14582649C2211yescharacteristic, complemented
52#14582631C2211yescharacteristic, complemented
53#14582631C2211yescharacteristic, complemented
54#14582628C2211yescharacteristic, complemented
55#14582628C2211yescharacteristic, complemented
56#14582621C2211yescharacteristic, complemented
57#14582621C2211yescharacteristic, complemented
58#14582620C2211yescharacteristic, complemented
59C8×C43⋊C8C2211yescharacteristic, complemented
60C2×C4×D4×C43C2211yescharacteristic
61C43×#431C2211yescharacteristic
62C43×#423C2211yescharacteristic
63C43×D4⋊C8C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×D4⋊C8C2211yescharacteristic
67C2×#10621883C2×C411yescharacteristic
68C2×#10621883C2×C411yescharacteristic
69C2×#10621882C2×C411yescharacteristic
70C2×#10621882C2×C411yescharacteristic
71C2×#10621872—21no—
72C22×C43⋊C8—21no—
73C22×C43⋊C8—21no—
74C22×C43⋊C8—21no—
75C22×C43⋊C8—21no—
76C2×C8×D43—21no—
77#13063319—21no—
78#13063317C2×C411yescharacteristic
79#13063313C2×C411yescharacteristic
80#13063308—21no—
81#13063304C2×C411yescharacteristic
82#13063299C2×C411yescharacteristic
83C4×Dic86C2311yescharacteristic
84C4×D172C2311yescharacteristic
85C4×C22⋊D43—21no—
86#13063282—21no—
87#13063258C2×C411yescharacteristic
88#13063258C2×C411yescharacteristic
89#13063256C2×C411yescharacteristic
90#13063256C2×C411yescharacteristic
91C4⋊(C43⋊C8)C2×C411yescharacteristic
92C4⋊(C43⋊C8)C2×C411yescharacteristic
93C4⋊(C43⋊C8)D411yescharacteristic
94C4⋊(C43⋊C8)D411yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97Dic43⋊C8—21no—
98Dic43⋊C8—21no—
99#13063248C2×C411yescharacteristic
100#13063248C2×C411yescharacteristic
101#13063246C2×C411yescharacteristic
102#13063246C2×C411yescharacteristic
103#13063246C2×C411yescharacteristic
104#13063246C2×C411yescharacteristic
105#13063245C2×C411yescharacteristic
106#13063245C2×C411yescharacteristic
107C22⋊(C43⋊C8)—21no—
108C22⋊(C43⋊C8)—21no—
109C22⋊(C43⋊C8)—21no—
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—21no—
112C22⋊(C43⋊C8)C2×C411yescharacteristic
113C22⋊(C43⋊C8)C2×C411yescharacteristic
114C22⋊(C43⋊C8)D411yescharacteristic
115C22⋊(C43⋊C8)D411yescharacteristic
116(C2×D43)⋊C8—21no—
117(C2×D43)⋊C8—21no—
118#13063235—21no—
119C4×C43⋊C8—21no—
120C4×C43⋊C8C2311yescharacteristic
121C4×C43⋊C8C2311yescharacteristic
122C4×C43⋊C8C2311yescharacteristic
123C4×C43⋊C8C2311yescharacteristic
124C8×Dic43—21no—
125C22×D4×C43C2×C411yescharacteristic
126C23×C4×C43—21no—
127C2×M16×C43—21no—
128C4×D4×C43—21no—
129C4×D4×C43—21no—
130C4×D4×C43C2×C411yescharacteristic
131C4×D4×C43C2×C411yescharacteristic
132C4×D4×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2×C411yescharacteristic
135C2×C22⋊C4×C43—21no—
136C2×C42×C43C2311yescharacteristic
137C4⋊C8×C43—21no—
138C4⋊C8×C43—21no—
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141C22⋊C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C24×C43—21no—
145C2×D4×C43—22no—
146C2×D4×C43—22no—
147C2×D4×C43—21no—
148C2×D4×C43C22×C411yescharacteristic
149C2×D4×C43C22×C411yescharacteristic
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—81no—
156C22×C4×C43—81no—
157C22×C4×C43C22×C411yescharacteristic
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43#4111yescharacteristic
160C2×C22⋊D43—21no—
161C2×D172C22×C411yescharacteristic
162C2×C4×D43—21no—
163C2×Dic86C22×C411yescharacteristic
164M16×C43—81no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43C22×C411yescharacteristic
171C4⋊C4×C43C22×C411yescharacteristic
172C22⋊C4×C43—21no—
173C22⋊C4×C43—21no—
174C22⋊C4×C43—21no—
175C22⋊C4×C43—21no—
176C42×C43C22×C411yescharacteristic
177C42×C43C2×D411yescharacteristic
178C42×C43#4111yescharacteristic
179C42×C43C2411yescharacteristic
180C22⋊Dic43—21no—
181#10621883—22no—
182#10621883—22no—
183#10621882—22no—
184#10621882—22no—
185(C2×D43)⋊C4—21no—
186(C2×D43)⋊C4—21no—
187(C2×D43)⋊C4—21no—
188(C2×D43)⋊C4—21no—
189C4⋊Dic43C22×C411yescharacteristic
190C4⋊Dic43C22×C411yescharacteristic
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195C4×Dic43—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—81no—
199C2×C43⋊C8—81no—
200C2×C43⋊C8—81no—
201C2×C43⋊C8—81no—
202C2×C43⋊C8C22×C411yescharacteristic
203C2×C43⋊C8C22×C411yescharacteristic
204C2×C43⋊C8C22×C411yescharacteristic
205C2×C43⋊C8C22×C411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209C2×C43⋊C8C2×D411yescharacteristic
210#10621872—81no—
211C8×D43—81no—
212C23×C43—24no—
213C23×C43—21no—
214C23×C43—21no—
215C23×C43—81no—
216C23×C43—81no—
217C23×C43C4×D411yescharacteristic
218C22×D43—21no—
219D4×C43—24no—
220D4×C43—21no—
221D4×C43—21no—
222D4×C43#13112yes—
223D4×C43#13112yes—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—81no—
236C2×C4×C43—81no—
237C2×C4×C43—81no—
238C2×C4×C43C4×D411yescharacteristic
239C2×C4×C43C4×D411yescharacteristic
240C2×C4×C43C4×D411yescharacteristic
241C2×C4×C43C23×C411yescharacteristic
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C22⋊D43—81no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248D172—21no—
249D172—21no—
250C4×D43—41no—
251C4×D43—41no—
252Dic86—21no—
253Dic86—21no—
254C8×C43—41no—
255C8×C43—41no—
256C8×C43—41no—
257C8×C43—41no—
258C43⋊C8—21no—
259C43⋊C8—21no—
260C43⋊C8—21no—
261C43⋊C8—21no—
262C43⋊C8—21no—
263C43⋊C8—21no—
264C43⋊C8—21no—
265C43⋊C8—21no—
266C43⋊C8—41no—
267C43⋊C8—41no—
268#17918—431nomaximal, Sylow
269C22×C43—21no—
270C22×C43—22no—
271C22×C43—22no—
272C22×C43—21no—
273C22×C43—21no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—84no—
279C22×C43C2×C4×D411yescharacteristic
280C2×D43—41no—
281C2×D43—41no—
282C2×D43—41no—
283C4×C43—21no—
284C4×C43—21no—
285C4×C43—21no—
286C4×C43—21no—
287C4×C43—41no—
288C4×C43—41no—
289C4×C43C2×#13111yescharacteristic
290C4×C43C2×#13111yescharacteristic
291C4×C43#57611yescharacteristic
292C4×C43#57711yescharacteristic
293Dic43—41no—
294Dic43—41no—
295Dic43—41no—
296#3105—431no—
297#2993—431no—
298#2972—431no—
299#1586—431no—
300#1585—431no—
301#1582—431no—
302#1581—431no—
303#1580—431no—
304SD16⋊C8—431no—
305C8×SD16—431no—
306C8×D8—431no—
307#1574—431no—
308#1486D4311yescharacteristic, complemented
309#1482—431no—
310#1454—431no—
311C2×C43—41no—
312C2×C43—42no—
313C2×C43—42no—
314C2×C43#292911yescharacteristic
315C2×C43#294611yescharacteristic
316C2×C43#295711yescharacteristic
317D43—81no—
318#529—431no—
319C2×C4×D4C2×D4311yescharacteristic
320#484—431no—
321#481—431no—
322#478—431no—
323#478—431no—
324#463—431no—
325#463—431no—
326#450—431no—
327#447—431no—
328#446—431no—
329C8×Q8—431no—
330C4×SD16—431no—
331C4×SD16—431no—
332C4×D8—431no—
333C4×D8—431no—
334#436—431no—
335#436—861no—
336#435—861no—
337C8×D4—431no—
338C8×D4—431no—
339C8×D4—431no—
340C8×D4—431no—
341C8×D4—431no—
342C8×D4—861no—
343C8×D4—861no—
344#433—861no—
345#431—431no—
346#431—431no—
347#431—431no—
348#431C2×D4311yescharacteristic
349#424—861no—
350#423C2×D4311yescharacteristic
351C2×C22⋊C8—861no—
352C2×C22⋊C8—861no—
353#335—431no—
354#335—431no—
355#334—431no—
356#334—431no—
357Q8⋊C8—431no—
358Q8⋊C8—431no—
359D4⋊C8—431no—
360D4⋊C8—431no—
361D4⋊C8C2×D4311yescharacteristic
362D4⋊C8C2×D4311yescharacteristic
363D4⋊C8C2×D4311yescharacteristic
364D4⋊C8C2×D4311yescharacteristic
365#322—431no—
366#322—431no—
367#322—431no—
368C82—431no—
369C43#1791811yescharacteristic, complemented, Sylow
370C22×D4C4×D4311yescharacteristic
371C23×C4—21no—
372C2×SD16—431no—
373C2×SD16—431no—
374C2×D8—431no—
375C2×D8—431no—
376C2×M16—21no—
377C2×M16—861no—
378C22×C8—861no—
379C22×C8—861no—
380C22×C8—861no—
381C22×C8—861no—
382C22×C8—861no—
383#126—861no—
384#125—431no—
385#124—431no—
386#123—861no—
387C22⋊Q8—431no—
388#121—431no—
389C4×Q8—431no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—431no—
393C4×D4—861no—
394C4×D4C4×D4311yescharacteristic
395C4×D4C4×D4311yescharacteristic
396C4×D4C22×D4311yescharacteristic
397C4×D4C22×D4311yescharacteristic
398#117—861no—
399C2×C4⋊C4C4×D4311yescharacteristic
400C2×C22⋊C4—21no—
401C2×C42C22×D4311yescharacteristic
402#107—431no—
403#107—431no—
404#106—431no—
405#106—431no—
406C4⋊C8—21no—
407C4⋊C8—21no—
408C4⋊C8—431no—
409C4⋊C8—431no—
410C4⋊C8—431no—
411C4⋊C8—431no—
412C4⋊C8—431no—
413C4⋊C8—431no—
414C4⋊C8—861no—
415C4⋊C8—861no—
416C4⋊C8C22×D4311yescharacteristic
417C4⋊C8C22×D4311yescharacteristic
418#103—431no—
419#103—431no—
420#102—431no—
421#102—431no—
422#102—431no—
423#102—431no—
424#102—431no—
425#102—431no—
426C22⋊C8—21no—
427C22⋊C8—431no—
428C22⋊C8—431no—
429C22⋊C8—431no—
430C22⋊C8—431no—
431C22⋊C8—861no—
432C22⋊C8—861no—
433C22⋊C8—861no—
434C22⋊C8—861no—
435C22⋊C8—861no—
436C22⋊C8—861no—
437C22⋊C8—861no—
438#97—861no—
439C4×C8—431no—
440C4×C8—431no—
441C4×C8—431no—
442C4×C8—431no—
443C4×C8—861no—
444C4×C8—861no—
445C4×C8C22×D4311yescharacteristic
446C4×C8C22×D4311yescharacteristic
447C24—21no—
448C2×Q8—431no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—21no—
452C2×D4—431no—
453C2×D4—861no—
454C2×D4C2×C4×D4311yescharacteristic
455C2×D4C2×C4×D4311yescharacteristic
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—81no—
462C22×C4—81no—
463C22×C4—861no—
464C22×C4C2×C4×D4311yescharacteristic
465C22×C4D4×D4311yescharacteristic
466C22×C4#1062190011yescharacteristic
467SD16—862no—
468SD16—862no—
469D8—862no—
470D8—862no—
471M16—81no—
472M16—3441no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—431no—
478C2×C8—431no—
479C2×C8—431no—
480C2×C8—431no—
481C2×C8—431no—
482C2×C8—431no—
483C2×C8—431no—
484C2×C8—431no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—3441no—
488C2×C8—3441no—
489C2×C8—3441no—
490C2×C8—3441no—
491C2×C8—3441no—
492C4⋊C4—21no—
493C4⋊C4—431no—
494C4⋊C4—431no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4C2×C4×D4311yescharacteristic
500C4⋊C4C2×C4×D4311yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—861no—
506C22⋊C4—861no—
507C22⋊C4—861no—
508C22⋊C4—861no—
509C22⋊C4—861no—
510C42—861no—
511C42C2×C4×D4311yescharacteristic
512C42D4×D4311yescharacteristic
513C42#1062190011yescharacteristic
514C42C23×D4311yescharacteristic
515C23—24no—
516C23—21no—
517C23—21no—
518C23—81no—
519C23—81no—
520C23—861no—
521C23(C22⋊D43)⋊C411yescharacteristic
522Q8—861no—
523Q8—861no—
524D4—24no—
525D4—21no—
526D4—21no—
527D4—861no—
528D4—861no—
529D4—3441no—
530D4#1306333312yes—
531D4#1306333312yes—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—81no—
544C2×C4—81no—
545C2×C4—81no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—861no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4(C22⋊D43)⋊C411yescharacteristic
552C2×C4(C22⋊D43)⋊C411yescharacteristic
553C2×C4(C22⋊D43)⋊C411yescharacteristic
554C2×C4C22×C4×D4311yescharacteristic
555C2×C4C2×D4×D4311yescharacteristic
556C2×C4C2×#1062190011yescharacteristic
557C8—41no—
558C8—41no—
559C8—41no—
560C8—41no—
561C8—861no—
562C8—861no—
563C8—861no—
564C8—861no—
565C8—861no—
566C8—861no—
567C8—861no—
568C8—861no—
569C8—1721no—
570C8—1721no—
571C22—21no—
572C22—21no—
573C22—22no—
574C22—22no—
575C22—21no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—84no—
581C22—1721no—
582C22—1721no—
583C22—1721no—
584C22C2×(C22⋊D43)⋊C411yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—41no—
590C4—41no—
591C4—1721no—
592C4—1721no—
593C4—1721no—
594C4C2×#1306333311yescharacteristic
595C4C2×#1306333311yescharacteristic
596C4#1458370011yescharacteristic
597C4#1458370511yescharacteristic
598C2—41no—
599C2—42no—
600C2—42no—
601C2—3441no—
602C2#1914328511yescharacteristic
603C2#1914342111yescharacteristic
604C2#1914350811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1486C2
socleC22×C43C2×C4×D4
prime radical#14583033C4
cosocleC42×C43C24
hypercenter#1486D43
hypocenterC43#17918
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
2. #19143740C2semidirect
3. #19143619C2semidirect
4. #19133456C2semidirect
5. #19133449C2semidirect
6. #19133428C2semidirect
7. #19133421C2semidirect
8. #19133416C2semidirect
9. #19133404C2semidirect
10. #19133398C2semidirect
11. #19133387C2semidirect
12. #19133386C2semidirect
13. #19133004C2semidirect
14. #19132895C2semidirect
15. C43×#1486C2semidirect
25. #14583026C22semidirect
26. #14583023C22semidirect
31. #14582976C22semidirect
40. #14582964C22semidirect
48. #14582651C22semidirect
49. #14582651C22semidirect
50. #14582649C22semidirect
51. #14582649C22semidirect
52. #14582631C22semidirect
53. #14582631C22semidirect
54. #14582628C22semidirect
55. #14582628C22semidirect
56. #14582621C22semidirect
57. #14582621C22semidirect
58. #14582620C22semidirect
59. C8×C43⋊C8C22semidirect
308. #1486D43semidirect
369. C43#17918semidirect

Maximal subgroups

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

subgroupindex
#191446422
#191437402
#191436192
#191334562
#191334492
#191334282
#191334212
#191334162
#191334042
#191333982
#191333872
#191333862
#191330042
#191328952
C43×#14862
#1791843