Finite Group Databasebeta

← #25067751

Subgroups — #25067751

Order 11008.

650 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144644C211yesmaximal, characteristic
2#19143751C211yesmaximal, characteristic, complemented
3#19143632C211yesmaximal, characteristic, complemented
4#19133484C211yesmaximal, characteristic, complemented
5#19133479C211yesmaximal, characteristic, complemented
6#19133472C211yesmaximal, characteristic, complemented
7#19133458C211yesmaximal, characteristic, complemented
8#19133458C211yesmaximal, characteristic, complemented
9#19133451C211yesmaximal, characteristic, complemented
10#19133394C211yesmaximal, characteristic, complemented
11#19133389C211yesmaximal, characteristic, complemented
12#19133053C211yesmaximal, characteristic, complemented
13C2×#14582626C211yesmaximal, characteristic, complemented
14#19132879C211yesmaximal, characteristic, complemented
15C43×#1573C211yesmaximal, characteristic, complemented
16#14583433C2211yescharacteristic
17C2×C4×D172C2211yescharacteristic
18#14583235C411yescharacteristic
19#14583218C411yescharacteristic
20#14583200C411yescharacteristic
21#14583200C411yescharacteristic
22#14583115C411yescharacteristic
23#14583115C411yescharacteristic
24#14583052C411yescharacteristic
25#14583035C411yescharacteristic
26#14583026C2211yescharacteristic, complemented
27#14583023C2211yescharacteristic, complemented
28C4×#10621873C2211yescharacteristic
29C4×#10621873C2211yescharacteristic
30C4×D344C2211yescharacteristic
31C4×D344C2211yescharacteristic
32#14582976C2211yescharacteristic
33#14582976C2211yescharacteristic
34#14582976C2211yescharacteristic, complemented
35#14582972—21no—
36#14582972—21no—
37#14582970—21no—
38#14582964C2211yescharacteristic
39#14582964C2211yescharacteristic
40#14582964C2211yescharacteristic, complemented
41C8×C22⋊D43—21no—
42#14582959—21no—
43#14582952C2211yescharacteristic
44#14582924—21no—
45#14582861—21no—
46C22⋊C8×D43—21no—
47C2×C4×C43⋊C8C2211yescharacteristic
48#14582629C2211yescharacteristic, complemented
49#14582629C2211yescharacteristic, complemented
50#14582626C2211yescharacteristic
51#14582626C2211yescharacteristic
52#14582626C2211yescharacteristic
53#14582626C2211yescharacteristic
54#14582626C2211yescharacteristic, complemented
55#14582626C2211yescharacteristic, complemented
56#14582621C2211yescharacteristic, complemented
57#14582621C2211yescharacteristic, complemented
58C8×C43⋊C8C2211yescharacteristic, complemented
59C8×C43⋊C8C2211yescharacteristic, complemented
60C43×#432C2211yescharacteristic
61C43×#431C2211yescharacteristic
62C2×C4⋊C8×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic, complemented
64C43×#335C2211yescharacteristic, complemented
65C43×#334C2211yescharacteristic, complemented
66C43×#334C2211yescharacteristic, complemented
67C22×D172C2×C411yescharacteristic
68C22×C4×D43—21no—
69C2×#10621873C2×C411yescharacteristic
70C2×#10621873C2×C411yescharacteristic
71C2×D344C2×C411yescharacteristic
72C2×D344C2×C411yescharacteristic
73C2×#10621872—21no—
74C2×#10621872—21no—
75C2×#10621872—21no—
76C22×C43⋊C8—21no—
77C2×C8×D43—21no—
78C2×C8×D43—21no—
79C2×C8×D43—21no—
80#13063319—21no—
81#13063317C2×C411yescharacteristic
82#13063313C2×C411yescharacteristic
83#13063308—21no—
84#13063304C2×C411yescharacteristic
85#13063299C2×C411yescharacteristic
86C4×Dic86C2311yescharacteristic
87C4×D172—21no—
88C4×D172—21no—
89C4×D172C2×C411yescharacteristic
90C4×D172C2×C411yescharacteristic
91C4×D172C2311yescharacteristic
92C4×D172C2311yescharacteristic
93C4×D172C2311yescharacteristic
94C4×C22⋊D43—21no—
95#13063282—21no—
96C2×C4⋊Dic43C2×C411yescharacteristic
97C2×(C2×D43)⋊C4—21no—
98#13063259C2×C411yescharacteristic
99#13063259C2×C411yescharacteristic
100#13063257C2×C411yescharacteristic
101#13063257C2×C411yescharacteristic
102C4⋊(C43⋊C8)D411yescharacteristic
103C4⋊(C43⋊C8)D411yescharacteristic
104Dic43⋊C8—21no—
105Dic43⋊C8—21no—
106#13063250C2×C411yescharacteristic
107#13063250C2×C411yescharacteristic
108#13063247C2×C411yescharacteristic
109#13063247C2×C411yescharacteristic
110#13063247C2×C411yescharacteristic
111#13063247C2×C411yescharacteristic
112#13063247C2×C411yescharacteristic
113#13063247C2×C411yescharacteristic
114C22⋊(C43⋊C8)D411yescharacteristic
115C22⋊(C43⋊C8)D411yescharacteristic
116(C2×D43)⋊C8—21no—
117(C2×D43)⋊C8—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8—21no—
122#13063235—21no—
123C4×C43⋊C8—21no—
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
127C4×C43⋊C8C2311yescharacteristic
128C8×Dic43—21no—
129C22×C8×C43—21no—
130C2×C42×C43C2311yescharacteristic
131C4⋊C8×C43—21no—
132C4⋊C8×C43C2×C411yescharacteristic
133C4⋊C8×C43C2×C411yescharacteristic
134C4⋊C8×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C22⋊C8×C43—21no—
139C22⋊C8×C43C2×C411yescharacteristic
140C22⋊C8×C43C2×C411yescharacteristic
141#97×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C23×D43—21no—
145C22×C4×C43C22×C411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43#4111yescharacteristic
148C2×C22⋊D43—21no—
149C22×Dic43—21no—
150C2×D172—21no—
151C2×D172—22no—
152C2×D172—41no—
153C2×D172C22×C411yescharacteristic
154C2×D172C22×C411yescharacteristic
155C2×D172C22×C411yescharacteristic
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—81no—
162C2×C4×D43—81no—
163C2×Dic86C22×C411yescharacteristic
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—81no—
169C2×C8×C43C22×C411yescharacteristic
170C2×C8×C43C22×C411yescharacteristic
171C2×C8×C43C22×C411yescharacteristic
172C2×C8×C43C22×C411yescharacteristic
173C42×C43C22×C411yescharacteristic
174C42×C43C2×D411yescharacteristic
175C42×C43#4111yescharacteristic
176C42×C43C2411yescharacteristic
177C22⋊Dic43—21no—
178(C2×D43)⋊C4—21no—
179(C2×D43)⋊C4—21no—
180(C2×D43)⋊C4—21no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43C22×C411yescharacteristic
188C4⋊Dic43C22×C411yescharacteristic
189C4⋊Dic43C22×C411yescharacteristic
190C4⋊Dic43C22×C411yescharacteristic
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195C4×Dic43—21no—
196C2×C43⋊C8—24no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8C2×D411yescharacteristic
200C2×C43⋊C8C2×D411yescharacteristic
201C2×C43⋊C8C2×D411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203D344—22no—
204D344—41no—
205#10621873—22no—
206#10621873—41no—
207#10621872—81no—
208#10621872—81no—
209#10621872—81no—
210C8×D43—81no—
211C8×D43—81no—
212C8×D43—81no—
213C23×C43C4×D411yescharacteristic
214C22×D43—21no—
215C22×D43—21no—
216C22×D43—21no—
217C22×D43—42no—
218C22×D43—42no—
219C22×D43—81no—
220C2×C4×C43—22no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43C4×D411yescharacteristic
226C2×C4×C43C4×D411yescharacteristic
227C2×C4×C43C4×D411yescharacteristic
228C2×C4×C43C23×C411yescharacteristic
229C2×C4×C43C22×D411yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C22⋊D43—42no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—81no—
238D172—21no—
239D172—21no—
240D172—21no—
241D172—21no—
242D172—21no—
243D172—42no—
244D172#13112yes—
245C4×D43—41no—
246C4×D43—41no—
247C4×D43—41no—
248C4×D43—41no—
249C4×D43—41no—
250C4×D43—41no—
251C4×D43—81no—
252C4×D43—81no—
253Dic86—21no—
254Dic86—21no—
255C8×C43—21no—
256C8×C43—21no—
257C8×C43—21no—
258C8×C43—21no—
259C8×C43—41no—
260C8×C43—41no—
261C8×C43—41no—
262C8×C43—41no—
263C43⋊C8—22no—
264C43⋊C8—22no—
265C43⋊C8—21no—
266C43⋊C8—21no—
267C43⋊C8—21no—
268C43⋊C8—21no—
269#18014—431nomaximal, Sylow
270C22×C43—21no—
271C22×C43—21no—
272C22×C43#44312yes—
273C22×C43C2×C4×D411yescharacteristic
274C2×D43—22no—
275C2×D43—41no—
276C2×D43—41no—
277C2×D43—41no—
278C2×D43—41no—
279C2×D43—41no—
280C2×D43—41no—
281C2×D43—41no—
282C2×D43—41no—
283C2×D43—84no—
284C4×C43—21no—
285C4×C43—21no—
286C4×C43—21no—
287C4×C43—21no—
288C4×C43C2×#13111yescharacteristic
289C4×C43#56811yescharacteristic
290C4×C43#57611yescharacteristic
291C4×C43#57711yescharacteristic
292Dic43—41no—
293Dic43—41no—
294Dic43—41no—
295Dic43—41no—
296Dic43—41no—
297#3105—431no—
298#2994—431no—
299#2974—431no—
300#1590—431no—
301#1589—431no—
302#1588—431no—
303#1586—431no—
304#1586—431no—
305#1585—431no—
306C8×SD16—431no—
307C8×D8—431no—
308#1573D4311yescharacteristic, complemented
309#1494—431no—
310C2×D4⋊C8—431no—
311#1450—431no—
312C2×C43—22no—
313C2×C43#293311yescharacteristic
314C2×C43#294611yescharacteristic
315C2×C43C2×#44311yescharacteristic
316D43—42no—
317D43—81no—
318D43—81no—
319#529—431no—
320C2×C4×D4—431no—
321#484—431no—
322#481—431no—
323#478—431no—
324#478—431no—
325#463—431no—
326#463—431no—
327#450—431no—
328#447—431no—
329#446—431no—
330C8×Q8—431no—
331C4×SD16—431no—
332C4×SD16—431no—
333C4×D8—431no—
334C4×D8—431no—
335#436—431no—
336#436—431no—
337#436—431no—
338#435—861no—
339#435—861no—
340#435—861no—
341C8×D4—431no—
342C8×D4—431no—
343C8×D4—431no—
344C8×D4—861no—
345#433—861no—
346#432C2×D4311yescharacteristic
347#431—431no—
348#431C2×D4311yescharacteristic
349#424—861no—
350C2×C4⋊C8C2×D4311yescharacteristic
351#407—861no—
352C2×C22⋊C8—861no—
353C2×C4×C8—431no—
354#335C2×D4311yescharacteristic, complemented
355#335C2×D4311yescharacteristic, complemented
356#334C2×D4311yescharacteristic, complemented
357#334C2×D4311yescharacteristic, complemented
358Q8⋊C8—431no—
359Q8⋊C8—431no—
360D4⋊C8—431no—
361D4⋊C8—431no—
362D4⋊C8—431no—
363D4⋊C8—431no—
364D4⋊C8—431no—
365D4⋊C8—431no—
366#322—431no—
367#322—431no—
368C82—431no—
369C82—431no—
370C43#1801411yescharacteristic, complemented, Sylow
371C22×D4—431no—
372C23×C4—861no—
373C2×SD16—431no—
374C2×SD16—431no—
375C2×D8—431no—
376C2×D8—431no—
377C2×M16—861no—
378C2×M16—861no—
379C2×M16—861no—
380C22×C8—21no—
381C22×C8—861no—
382C22×C8—861no—
383C22×C8—861no—
384C22×C8—861no—
385#126—861no—
386#125—431no—
387#124—431no—
388#123—861no—
389C22⋊Q8—431no—
390#121—431no—
391C4×Q8—431no—
392C4×D4—431no—
393C4×D4—431no—
394C4×D4—431no—
395C4×D4—431no—
396C4×D4—431no—
397C4×D4—861no—
398C4×D4—861no—
399C4×D4—861no—
400#117—861no—
401C2×C4⋊C4—431no—
402C2×C22⋊C4—861no—
403C2×C42C22×D4311yescharacteristic
404#107—431no—
405#107—431no—
406#106—431no—
407#106—431no—
408C4⋊C8—21no—
409C4⋊C8—431no—
410C4⋊C8—431no—
411C4⋊C8—861no—
412C4⋊C8—861no—
413C4⋊C8C4×D4311yescharacteristic
414C4⋊C8C4×D4311yescharacteristic
415C4⋊C8C22×D4311yescharacteristic
416C4⋊C8C22×D4311yescharacteristic
417C4⋊C8C22×D4311yescharacteristic
418C4⋊C8C22×D4311yescharacteristic
419#103—431no—
420#103—431no—
421#102—431no—
422#102—431no—
423#102—431no—
424#102—431no—
425#102—431no—
426#102—431no—
427C22⋊C8—21no—
428C22⋊C8—431no—
429C22⋊C8—431no—
430C22⋊C8—861no—
431C22⋊C8—861no—
432C22⋊C8—861no—
433C22⋊C8—861no—
434C22⋊C8—861no—
435C22⋊C8—861no—
436C22⋊C8C4×D4311yescharacteristic
437C22⋊C8C4×D4311yescharacteristic
438#97—21no—
439#97—861no—
440C4×C8—431no—
441C4×C8—431no—
442C4×C8—431no—
443C4×C8—431no—
444C4×C8—861no—
445C4×C8—861no—
446C4×C8C22×D4311yescharacteristic
447C4×C8C22×D4311yescharacteristic
448C24—861no—
449C2×Q8—431no—
450C2×D4—431no—
451C2×D4—431no—
452C2×D4—431no—
453C2×D4—862no—
454C2×D4—861no—
455C2×D4—861no—
456C2×D4—1721no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—3441no—
464C22×C4—3441no—
465C22×C4C2×C4×D4311yescharacteristic
466C22×C4D4×D4311yescharacteristic
467C22×C4#1062190211yescharacteristic
468SD16—862no—
469SD16—1721no—
470D8—862no—
471D8—1721no—
472M16—3441no—
473M16—3441no—
474M16—3441no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—81no—
480C2×C8—431no—
481C2×C8—431no—
482C2×C8—431no—
483C2×C8—431no—
484C2×C8—864no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—3441no—
488C2×C8—3441no—
489C2×C8—3441no—
490C2×C8C2×C4×D4311yescharacteristic
491C2×C8C2×C4×D4311yescharacteristic
492C2×C8C2×C4×D4311yescharacteristic
493C2×C8C2×C4×D4311yescharacteristic
494C4⋊C4—431no—
495C4⋊C4—431no—
496C4⋊C4—431no—
497C4⋊C4—431no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C22⋊C4—861no—
504C22⋊C4—861no—
505C22⋊C4—861no—
506C22⋊C4—861no—
507C22⋊C4—861no—
508C22⋊C4—861no—
509C22⋊C4—861no—
510C22⋊C4—861no—
511C22⋊C4—861no—
512C42—861no—
513C42C2×C4×D4311yescharacteristic
514C42D4×D4311yescharacteristic
515C42#1062190211yescharacteristic
516C42C23×D4311yescharacteristic
517C23—861no—
518C23—861no—
519C23—861no—
520C23—3441no—
521C23—1722no—
522C23—1722no—
523C23#1306328711yescharacteristic
524Q8—861no—
525Q8—861no—
526D4—432no—
527D4—861no—
528D4—861no—
529D4—861no—
530D4—861no—
531D4—861no—
532D4—1722no—
533D4—1722no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—3441no—
545C2×C4—3441no—
546C2×C4—3441no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4#1306328711yescharacteristic
554C2×C4#1306328711yescharacteristic
555C2×C4#1306328711yescharacteristic
556C2×C4C22×C4×D4311yescharacteristic
557C2×C4C2×D4×D4311yescharacteristic
558C2×C4C2×#1062190211yescharacteristic
559C8—21no—
560C8—21no—
561C8—21no—
562C8—21no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—41no—
567C8—862no—
568C8—862no—
569C8—861no—
570C8—861no—
571C8—861no—
572C8—861no—
573C22—21no—
574C22—21no—
575C22—862no—
576C22—3444no—
577C22—1721no—
578C22—1721no—
579C22—1721no—
580C22—1721no—
581C22—1721no—
582C22—1721no—
583C22—1721no—
584C22—1721no—
585C22#1458301512yes—
586C22C2×#1306328711yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—1721no—
592C4—1721no—
593C4—1721no—
594C4—1721no—
595C4—1721no—
596C4#131×D4311yescharacteristic
597C4#1458366411yescharacteristic
598C4#1458370311yescharacteristic
599C4#1458370811yescharacteristic
600C2—22no—
601C2—3441no—
602C2—3441no—
603C2—1722no—
604C2#1914331911yescharacteristic
605C2#1914342511yescharacteristic
606C2C2×#1458301511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1573C2
socleC22×C43C2×C4×D4
prime radical#14583035C4
cosocleC42×C43C24
hypercenter#1573D43
hypocenterC43#18014
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1573

Complements

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

NH ≅ G/Ntype
2. #19143751C2semidirect
3. #19143632C2semidirect
4. #19133484C2semidirect
5. #19133479C2semidirect
6. #19133472C2semidirect
7. #19133458C2semidirect
8. #19133458C2semidirect
9. #19133451C2semidirect
10. #19133394C2semidirect
11. #19133389C2semidirect
12. #19133053C2semidirect
13. C2×#14582626C2semidirect
14. #19132879C2semidirect
15. C43×#1573C2semidirect
26. #14583026C22semidirect
27. #14583023C22semidirect
34. #14582976C22semidirect
40. #14582964C22semidirect
48. #14582629C22semidirect
49. #14582629C22semidirect
54. #14582626C22semidirect
55. #14582626C22semidirect
56. #14582621C22semidirect
57. #14582621C22semidirect
58. C8×C43⋊C8C22semidirect
59. C8×C43⋊C8C22semidirect
63. C43×#335C22semidirect
64. C43×#335C22semidirect
65. C43×#334C22semidirect
66. C43×#334C22semidirect
308. #1573D43semidirect
354. #335C2×D43semidirect
355. #335C2×D43semidirect
356. #334C2×D43semidirect
357. #334C2×D43semidirect
370. C43#18014semidirect

Maximal subgroups

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

subgroupindex
#191446442
#191437512
#191436322
#191334842
#191334792
#191334722
#191334582
#191334512
#191333942
#191333892
#191330532
C2×#145826262
#191328792
C43×#15732
#1801443