Finite Group Databasebeta

← #25066657

Subgroups — #25066657

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#19143746C211yesmaximal, characteristic, complemented
3#19133459C211yesmaximal, characteristic, complemented
4#19133452C211yesmaximal, characteristic, complemented
5#19133431C211yesmaximal, characteristic, complemented
6#19133424C211yesmaximal, characteristic, complemented
7#19133417C211yesmaximal, characteristic, complemented
8#19133407C211yesmaximal, characteristic, complemented
9C8×#10621883C211yesmaximal, characteristic, complemented
10C8×#10621882C211yesmaximal, characteristic, complemented
11#19133383C211yesmaximal, characteristic, complemented
12#19133020C211yesmaximal, characteristic, complemented
13#19133001C211yesmaximal, characteristic, complemented
14#19132895C211yesmaximal, characteristic, complemented
15C43×#2972C211yesmaximal, characteristic, complemented
16#14583433C2211yescharacteristic
17#14583234C411yescharacteristic
18#14583217C411yescharacteristic
19#14583199C411yescharacteristic
20#14583199C411yescharacteristic
21#14583114C411yescharacteristic
22#14583114C411yescharacteristic
23#14583050C411yescharacteristic
24#14583033C411yescharacteristic
25#14583029C2211yescharacteristic, complemented
26C8×Dic86C2211yescharacteristic, complemented
27C4×#10621883C2211yescharacteristic
28C4×#10621883C2211yescharacteristic
29C4×#10621882C2211yescharacteristic
30C4×#10621882C2211yescharacteristic
31#14582978C2211yescharacteristic, complemented
32#14582974—21no—
33#14582973—21no—
34C8×D172C2211yescharacteristic, complemented
35#14582959—21no—
36#14582952C2211yescharacteristic
37#14582952C2211yescharacteristic
38#14582924—21no—
39#14582923C2211yescharacteristic
40#14582651C2211yescharacteristic, complemented
41#14582651C2211yescharacteristic, complemented
42#14582649C2211yescharacteristic, complemented
43#14582649C2211yescharacteristic, complemented
44#14582629C2211yescharacteristic, complemented
45#14582629C2211yescharacteristic, complemented
46D4⋊(C43⋊C8)C2211yescharacteristic
47D4⋊(C43⋊C8)C2211yescharacteristic
48D4⋊(C43⋊C8)C2211yescharacteristic
49D4⋊(C43⋊C8)C2211yescharacteristic
50#14582626C2211yescharacteristic, complemented
51#14582626C2211yescharacteristic, complemented
52#14582621C2211yescharacteristic, complemented
53#14582621C2211yescharacteristic, complemented
54#14582620C2211yescharacteristic, complemented
55C8×C43⋊C8C2211yescharacteristic, complemented
56C2×C4×D4×C43C2211yescharacteristic
57C8×D4×C43—21no—
58C8×D4×C43—21no—
59C8×D4×C43C2211yescharacteristic
60C8×D4×C43C2211yescharacteristic
61C8×D4×C43C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#431C2211yescharacteristic
64C43×#431C2211yescharacteristic
65C2×C22⋊C8×C43—21no—
66C2×C22⋊C8×C43—21no—
67C2×#10621883C2×C411yescharacteristic
68C2×#10621883C2×C411yescharacteristic
69C2×#10621882C2×C411yescharacteristic
70C2×#10621882C2×C411yescharacteristic
71C2×#10621877—21no—
72C2×#10621872—21no—
73C2×C8×D43—21no—
74#13063319—21no—
75#13063317C2×C411yescharacteristic
76#13063313C2×C411yescharacteristic
77#13063308—21no—
78#13063304C2×C411yescharacteristic
79#13063299C2×C411yescharacteristic
80C4×Dic86C2311yescharacteristic
81C4×D172C2311yescharacteristic
82C4×C22⋊D43—21no—
83#13063282—21no—
84#13063258C2×C411yescharacteristic
85#13063258C2×C411yescharacteristic
86#13063256C2×C411yescharacteristic
87#13063256C2×C411yescharacteristic
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)—21no—
90C4⋊(C43⋊C8)C2×C411yescharacteristic
91C4⋊(C43⋊C8)C2×C411yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94Dic43⋊C8—21no—
95Dic43⋊C8—21no—
96#13063248C2×C411yescharacteristic
97#13063248C2×C411yescharacteristic
98#13063246C2×C411yescharacteristic
99#13063246C2×C411yescharacteristic
100#13063246C2×C411yescharacteristic
101#13063246C2×C411yescharacteristic
102#13063245C2×C411yescharacteristic
103#13063245C2×C411yescharacteristic
104C22⋊(C43⋊C8)—21no—
105C22⋊(C43⋊C8)C2×C411yescharacteristic
106C22⋊(C43⋊C8)C2×C411yescharacteristic
107(C2×D43)⋊C8—21no—
108(C2×D43)⋊C8—21no—
109#13063235—21no—
110C4×C43⋊C8C2311yescharacteristic
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C22×D4×C43C2×C411yescharacteristic
116C23×C4×C43—21no—
117C22×C8×C43—21no—
118C22×C8×C43—21no—
119C22×C8×C43—21no—
120C22×C8×C43—21no—
121C4×D4×C43—21no—
122C4×D4×C43—21no—
123C4×D4×C43C2×C411yescharacteristic
124C4×D4×C43C2×C411yescharacteristic
125C4×D4×C43C2311yescharacteristic
126C4×D4×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2×C411yescharacteristic
128C2×C22⋊C4×C43—21no—
129C2×C42×C43C2311yescharacteristic
130C4⋊C8×C43D411yescharacteristic
131C4⋊C8×C43D411yescharacteristic
132C4⋊C8×C43C2311yescharacteristic
133C4⋊C8×C43C2311yescharacteristic
134C22⋊C8×C43—21no—
135C22⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138C22⋊C8×C43—21no—
139C22⋊C8×C43D411yescharacteristic
140C22⋊C8×C43D411yescharacteristic
141C4×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
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—81no—
167C2×C8×C43—81no—
168C2×C8×C43—81no—
169C2×C8×C43—81no—
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C4⋊C4×C43—21no—
175C4⋊C4×C43C22×C411yescharacteristic
176C4⋊C4×C43C22×C411yescharacteristic
177C22⋊C4×C43—21no—
178C22⋊C4×C43—21no—
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C42×C43C22×C411yescharacteristic
182C42×C43C2×D411yescharacteristic
183C42×C43#4111yescharacteristic
184C42×C43C2411yescharacteristic
185C22⋊Dic43—21no—
186#10621883—22no—
187#10621883—22no—
188#10621882—22no—
189#10621882—22no—
190(C2×D43)⋊C4—21no—
191(C2×D43)⋊C4—21no—
192(C2×D43)⋊C4—21no—
193(C2×D43)⋊C4—21no—
194C4⋊Dic43C22×C411yescharacteristic
195C4⋊Dic43C22×C411yescharacteristic
196Dic43⋊C4—21no—
197Dic43⋊C4—21no—
198Dic43⋊C4—21no—
199Dic43⋊C4—21no—
200C4×Dic43—21no—
201#10621877—81no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8C22×C411yescharacteristic
207C2×C43⋊C8C22×C411yescharacteristic
208C2×C43⋊C8C22×C411yescharacteristic
209C2×C43⋊C8C22×C411yescharacteristic
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—21no—
255C8×C43—21no—
256C8×C43—21no—
257C8×C43—21no—
258C8×C43—41no—
259C8×C43—41no—
260C43⋊C8—21no—
261C43⋊C8—21no—
262C43⋊C8—21no—
263C43⋊C8—21no—
264C43⋊C8—41no—
265C43⋊C8—41no—
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#2972D4311yescharacteristic, complemented
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#1486—431no—
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—21no—
338C8×D4—21no—
339C8×D4—431no—
340C8×D4C2×D4311yescharacteristic
341C8×D4C2×D4311yescharacteristic
342C8×D4C2×D4311yescharacteristic
343C8×D4C2×D4311yescharacteristic
344#433—861no—
345#431—431no—
346#431—431no—
347#431C2×D4311yescharacteristic
348#431C2×D4311yescharacteristic
349#424—861no—
350#423—431no—
351C2×C22⋊C8—21no—
352C2×C22⋊C8—21no—
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⋊C8—431no—
362D4⋊C8—431no—
363D4⋊C8—431no—
364D4⋊C8—431no—
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—861no—
377C2×M16—861no—
378C22×C8—21no—
379C22×C8—21no—
380C22×C8—21no—
381C22×C8—21no—
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—431no—
407C4⋊C8—431no—
408C4⋊C8—431no—
409C4⋊C8—431no—
410C4⋊C8—861no—
411C4⋊C8—861no—
412C4⋊C8—861no—
413C4⋊C8—861no—
414C4⋊C8C22⋊D4311yescharacteristic
415C4⋊C8C22⋊D4311yescharacteristic
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—21no—
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8—21no—
431C22⋊C8—431no—
432C22⋊C8—431no—
433C22⋊C8—861no—
434C22⋊C8—861no—
435C22⋊C8—861no—
436C22⋊C8C22⋊D4311yescharacteristic
437C22⋊C8C22⋊D4311yescharacteristic
438#97—861no—
439C4×C8—21no—
440C4×C8—431no—
441C4×C8—431no—
442C4×C8—431no—
443C4×C8—431no—
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×C4#1062189811yescharacteristic
466C22×C4C2×C22⋊D4311yescharacteristic
467SD16—862no—
468SD16—862no—
469D8—862no—
470D8—862no—
471M16—3441no—
472M16—3441no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—81no—
476C2×C8—81no—
477C2×C8—81no—
478C2×C8—81no—
479C2×C8—431no—
480C2×C8—431no—
481C2×C8—431no—
482C2×C8—431no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—3441no—
488C2×C8C2×C22⋊D4311yescharacteristic
489C2×C8C2×C22⋊D4311yescharacteristic
490C2×C8C2×C22⋊D4311yescharacteristic
491C2×C8C2×C22⋊D4311yescharacteristic
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
512C42#1062189811yescharacteristic
513C42C2×C22⋊D4311yescharacteristic
514C42C23×D4311yescharacteristic
515C23—24no—
516C23—21no—
517C23—21no—
518C23—81no—
519C23—81no—
520C23—861no—
521C23C4×C22⋊D4311yescharacteristic
522Q8—861no—
523Q8—861no—
524D4—24no—
525D4—21no—
526D4—21no—
527D4—861no—
528D4—861no—
529D4—3441no—
530D4#1306333112yes—
531D4#1306333112yes—
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×C4C4×C22⋊D4311yescharacteristic
552C2×C4C4×C22⋊D4311yescharacteristic
553C2×C4C4×C22⋊D4311yescharacteristic
554C2×C4C22×C4×D4311yescharacteristic
555C2×C4C22×C22⋊D4311yescharacteristic
556C2×C4C2×#1062189811yescharacteristic
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—861no—
564C8—861no—
565C8—861no—
566C8—861no—
567C8—1721no—
568C8—1721no—
569C8—1721no—
570C8—1721no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—22no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—84no—
581C22—1721no—
582C22—1721no—
583C22—1721no—
584C22C2×C4×C22⋊D4311yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—41no—
590C4—41no—
591C4—1721no—
592C4—1721no—
593C4—1721no—
594C4C2×#1306333111yescharacteristic
595C4C2×#1306333111yescharacteristic
596C4#1458370211yescharacteristic
597C4#1458371011yescharacteristic
598C2—41no—
599C2—42no—
600C2—42no—
601C2—3441no—
602C2#1914328911yescharacteristic
603C2#1914342711yescharacteristic
604C2#1914351011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#2972C2
socleC22×C43C2×C4×D4
prime radical#14583033C4
cosocleC42×C43C24
hypercenter#2972D43
hypocenterC43#17918
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2972

Complements

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

NH ≅ G/Ntype
2. #19143746C2semidirect
3. #19133459C2semidirect
4. #19133452C2semidirect
5. #19133431C2semidirect
6. #19133424C2semidirect
7. #19133417C2semidirect
8. #19133407C2semidirect
9. C8×#10621883C2semidirect
10. C8×#10621882C2semidirect
11. #19133383C2semidirect
12. #19133020C2semidirect
13. #19133001C2semidirect
14. #19132895C2semidirect
15. C43×#2972C2semidirect
25. #14583029C22semidirect
26. C8×Dic86C22semidirect
31. #14582978C22semidirect
34. C8×D172C22semidirect
40. #14582651C22semidirect
41. #14582651C22semidirect
42. #14582649C22semidirect
43. #14582649C22semidirect
44. #14582629C22semidirect
45. #14582629C22semidirect
50. #14582626C22semidirect
51. #14582626C22semidirect
52. #14582621C22semidirect
53. #14582621C22semidirect
54. #14582620C22semidirect
55. C8×C43⋊C8C22semidirect
298. #2972D43semidirect
369. C43#17918semidirect

Maximal subgroups

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

subgroupindex
#191446422
#191437462
#191334592
#191334522
#191334312
#191334242
#191334172
#191334072
C8×#106218832
C8×#106218822
#191333832
#191330202
#191330012
#191328952
C43×#29722
#1791843