Finite Group Databasebeta

← #25137867

Subgroups — #25137867

Order 11008.

868 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583202C211yesmaximal, characteristic, complemented
2C2×#14582954C211yesmaximal, characteristic, complemented
3#19142904C211yesmaximal, characteristic, complemented
4#19137103C211yesmaximal, characteristic
5#19136033C211yesmaximal, characteristic, complemented
6#19136019C211yesmaximal, characteristic, complemented
7#19135786C211yesmaximal, characteristic
8#19135780C211yesmaximal, characteristic
9#19135549C211yesmaximal, characteristic, complemented
10#19135364C211yesmaximal, characteristic, complemented
11#19135330C211yesmaximal, characteristic, complemented
12#19135292C211yesmaximal, characteristic, complemented
13#19135291C211yesmaximal, characteristic, complemented
14#19134604C211yesmaximal, characteristic, complemented
15C43×#1944C211yesmaximal, characteristic, complemented
16C2×#13063316C2211yescharacteristic
17C2×#13063300C2211yescharacteristic
18C2×#13063287—21no—
19C2×#13063287C2211yescharacteristic
20C2×C42×D43C2211yescharacteristic
21#14583202—24no—
22#14582954—24no—
23C2×#13063258C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32C2×(C2×D43)⋊C8C2211yescharacteristic
33C2×#13063236C2211yescharacteristic
34#14582801C2211yescharacteristic
35#14582797C2211yescharacteristic
36#14582789—21no—
37#14582785—21no—
38#14582781—21no—
39#14582777—21no—
40#14582773—21no—
41#14582770—21no—
42#14582764C2211yescharacteristic
43#14582756C2211yescharacteristic
44#14582756C2211yescharacteristic
45#14582756C2211yescharacteristic
46C4⋊C4×Dic43C2211yescharacteristic
47#14582746—21no—
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C2×#106×C43C2211yescharacteristic
56C2×#97×C43C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#389C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×D172—21no—
62C22×D172C2311yescharacteristic
63C22×C4×D43—21no—
64C22×C4×D43D411yescharacteristic
65C22×C4×D43D411yescharacteristic
66C22×C4×D43C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063316—22no—
70#13063316—22no—
71#13063300—22no—
72#13063300—22no—
73#13063287—22no—
74#13063287—22no—
75#13063287—44no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43D411yescharacteristic
91C2×C4×Dic43D411yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93C42×D43—22no—
94C42×D43—22no—
95#13063258—22no—
96#13063256—22no—
97Dic43⋊C8—22no—
98Dic43⋊C8D414yescomplemented
99#13063247—22no—
100#13063247—22no—
101#13063245—22no—
102#13063245—22no—
103(C2×D43)⋊C8—22no—
104(C2×D43)⋊C8—22no—
105#13063236—22no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C42×C43C2311yescharacteristic
122#107×C43—22no—
123#106×C43—22no—
124#97×C43—22no—
125#95×C43—21no—
126#95×C43—21no—
127C23×D43—21no—
128C23×D43C2×D411yescharacteristic
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2411yescharacteristic
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43C2×D411yescharacteristic
140C22×Dic43C2×D411yescharacteristic
141C22×Dic43C2×D411yescharacteristic
142C2×D172—24no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172—21no—
147C2×D172—21no—
148C2×D172—42no—
149C2×D172—42no—
150C2×D172#4112yes—
151C2×C4×D43—21no—
152C2×C4×D43—21no—
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—22no—
158C2×C4×D43—22no—
159C2×C4×D43—22no—
160C2×C4×D43—41no—
161C2×C4×D43—41no—
162C2×C4×D43—41no—
163C2×C4×D43—42no—
164C2×C4×D43—42no—
165C2×C4×D43—42no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43C2×D412yes—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—42no—
180C4⋊C4×C43—42no—
181C4⋊C4×C43#4112yes—
182C42×C43—21no—
183C42×C43—21no—
184(C2×D43)⋊C4—24no—
185(C2×D43)⋊C4—42no—
186(C2×D43)⋊C4—42no—
187(C2×D43)⋊C4—42no—
188(C2×D43)⋊C4—42no—
189(C2×D43)⋊C4—42no—
190(C2×D43)⋊C4—42no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—42no—
198Dic43⋊C4—42no—
199Dic43⋊C4—42no—
200C4×Dic43—22no—
201C4×Dic43—22no—
202C4×Dic43—42no—
203C4×Dic43C2×D412yes—
204C4×Dic43#4112yes—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8C2×D412yes—
211C23×C43C22×D411yescharacteristic
212C22×D43—21no—
213C22×D43—21no—
214C22×D43—21no—
215C22×D43—21no—
216C22×D43—21no—
217C22×D43—21no—
218C22×D43—22no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224C22×D43—41no—
225C22×D43AGL(1,ℤ/8)12yes—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—22no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C432−1+411yescharacteristic
249C2×C4×C432−1+411yescharacteristic
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43#12112yes—
267C2×Dic43#12112yes—
268D172—22no—
269D172—22no—
270D172—48no—
271D172—41no—
272D172—41no—
273C4×D43—44no—
274C4×D43—44no—
275C4×D43—41no—
276C4×D43—41no—
277C4×D43—41no—
278C4×D43—41no—
279C4×D43—84no—
280C8×C43—22no—
281C8×C43—41no—
282C43⋊C8—22no—
283C43⋊C8—41no—
284#24706—431nomaximal, Sylow
285C22×C43C2×#12111yescharacteristic
286C22×C43#52511yescharacteristic
287C22×C43#53611yescharacteristic
288C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
289C22×C43#57511yescharacteristic
290C22×C43#57511yescharacteristic
291C22×C43#57511yescharacteristic
292C2×D43—22no—
293C2×D43—22no—
294C2×D43—22no—
295C2×D43—41no—
296C2×D43—41no—
297C2×D43—41no—
298C2×D43—41no—
299C2×D43—42no—
300C2×D43—42no—
301C2×D43—42no—
302C2×D43—81no—
303C2×D43—81no—
304C2×D43—81no—
305C2×D43—81no—
306C4×C43—42no—
307C4×C43—41no—
308C4×C43—41no—
309C4×C43—81no—
310C4×C43—81no—
311C4×C43—81no—
312C4×C43#54711yescharacteristic
313C4×C43#54811yescharacteristic
314C4×C43#55211yescharacteristic
315C4×C43#55611yescharacteristic
316Dic43—22no—
317Dic43—22no—
318Dic43—41no—
319Dic43—81no—
320Dic43—81no—
321Dic43—81no—
322C2×#478—431no—
323C2×#432—431no—
324#2851—431no—
325C4×#121—431no—
326#2077—431no—
327#2075—431no—
328#2034—431no—
329#2033—431no—
330#1989—431no—
331#1949—431no—
332#1944D4311yescharacteristic, complemented
333#1943—431no—
334#1936—431no—
335#1936—431no—
336#1804—431no—
337C2×C43#241511yescharacteristic
338C2×C43#305411yescharacteristic
339C2×C43#305511yescharacteristic
340C2×C43#311111yescharacteristic
341C2×C43#311411yescharacteristic
342C2×C43#323411yescharacteristic
343C2×C43#324011yescharacteristic
344D43—42no—
345D43—82no—
346C2×#125—431no—
347C2×#121—431no—
348C2×C4×D4—431no—
349C2×C4×D4—861no—
350C22×C42—431no—
351#478—864no—
352#432—864no—
353C2×#107—431no—
354C2×#107C2×D4311yescharacteristic
355C2×#106—431no—
356C2×#106C2×D4311yescharacteristic
357C2×C4⋊C8—431no—
358C2×C4⋊C8—431no—
359C2×#102—431no—
360C2×#102—431no—
361C2×#102—431no—
362C2×#102—431no—
363C2×C22⋊C8—431no—
364C2×C22⋊C8—431no—
365C2×#97—431no—
366C2×#97C2×D4311yescharacteristic
367#390—431no—
368#389—431no—
369#389C2×D4311yescharacteristic
370#389C2×D4311yescharacteristic
371#388—861no—
372#387—861no—
373#387—861no—
374#386—861no—
375#385—861no—
376#385—861no—
377#382—431no—
378#380—431no—
379#380—431no—
380#380—431no—
381C4×C4⋊C4—431no—
382C4×C22⋊C4—861no—
383#340—431no—
384#340—431no—
385#340—431no—
386#340—431no—
387#340—431no—
388#340—431no—
389#340C2×D4311yescharacteristic
390#340C2×D4311yescharacteristic
391C43#2470611yescharacteristic, complemented, Sylow
392C22×D4—431no—
393C22×D4—861no—
394C23×C4—431no—
395C23×C4—431no—
396C23×C4—431no—
397C23×C4—861no—
398C22×C8—431no—
399C22×C8—431no—
400C22×C8C22×D4311yescharacteristic
401C22×C8C22×D4311yescharacteristic
402#125—862no—
403#125—862no—
404#121—862no—
405#121—862no—
406C4×D4—862no—
407C4×D4—862no—
408C4×D4—1724no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4C22×D4311yescharacteristic
418C2×C4⋊C4C22×D4311yescharacteristic
419C2×C4⋊C4C22×D4311yescharacteristic
420C2×C4⋊C4C22×D4311yescharacteristic
421C2×C22⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C22⋊C4—861no—
427C2×C22⋊C4—861no—
428C2×C42—431no—
429C2×C42—431no—
430C2×C42—431no—
431C2×C42—862no—
432C2×C42—862no—
433C2×C42—861no—
434C2×C42C22×D4311yescharacteristic
435#107—22no—
436#107—862no—
437#106—22no—
438#106—862no—
439C4⋊C8—434no—
440C4⋊C8—862no—
441#102—862no—
442#102—862no—
443#102—862no—
444#102—862no—
445C22⋊C8—862no—
446C22⋊C8—862no—
447#97—22no—
448#97—862no—
449#95—21no—
450#95—21no—
451#95—861no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456#95—861no—
457#95—861no—
458C24—431no—
459C24—861no—
460C2×D4—432no—
461C2×D4—864no—
462C2×D4—861no—
463C2×D4—861no—
464C2×D4—861no—
465C2×D4—861no—
466C2×D4—861no—
467C2×D4—1722no—
468C2×D4—1722no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—862no—
477C22×C4—862no—
478C22×C4—862no—
479C22×C4—861no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—1721no—
489C22×C4—1721no—
490C22×C4—1721no—
491C22×C4—1722no—
492C22×C4—1722no—
493C22×C4—1722no—
494C22×C4D4×D4311yescharacteristic
495C22×C4D4×D4311yescharacteristic
496C22×C4C23×D4311yescharacteristic
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—432no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8D4×D4312yes—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—42no—
517C4⋊C4—42no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—1722no—
525C4⋊C4—1722no—
526C4⋊C4—1722no—
527C4⋊C4#1062189812yes—
528C22⋊C4—864no—
529C22⋊C4—1722no—
530C22⋊C4—1722no—
531C22⋊C4—1722no—
532C22⋊C4—1722no—
533C22⋊C4—1722no—
534C22⋊C4—1722no—
535C42—21no—
536C42—21no—
537C42—432no—
538C42—432no—
539C42—862no—
540C42—862no—
541C42—1722no—
542C23—432no—
543C23—861no—
544C23—861no—
545C23—861no—
546C23—861no—
547C23—861no—
548C23—861no—
549C23—862no—
550C23—1721no—
551C23—1721no—
552C23—1721no—
553C23—1721no—
554C23—1721no—
555C23—1721no—
556C23C2×D4×D4311yescharacteristic
557D4—862no—
558D4—862no—
559D4—1728no—
560D4—1721no—
561D4—1721no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—432no—
581C2×C4—432no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—3444no—
590C2×C4—1724no—
591C2×C4—1724no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4C2×D4×D4311yescharacteristic
606C2×C4#41×D4311yescharacteristic
607C2×C4#41×D4311yescharacteristic
608C2×C4C2×#1062189811yescharacteristic
609C2×C4#1306337311yescharacteristic
610C2×C4#1306337311yescharacteristic
611C8—22no—
612C8—41no—
613C8—862no—
614C8—1721no—
615C22—862no—
616C22—862no—
617C22—862no—
618C22—3441no—
619C22—3441no—
620C22—3441no—
621C22—3441no—
622C22—1722no—
623C22—1722no—
624C22—1722no—
625C22—1721no—
626C22—1721no—
627C22—1721no—
628C22—1721no—
629C22#121×D4311yescharacteristic
630C22#1458340811yescharacteristic
631C22#1458347411yescharacteristic
632C22AGL(1,ℤ/8)×D4311yescharacteristic
633C22#1458369511yescharacteristic
634C22#1458369811yescharacteristic
635C22#1458369811yescharacteristic
636C4—41no—
637C4—41no—
638C4—42no—
639C4—81no—
640C4—81no—
641C4—81no—
642C4—862no—
643C4—862no—
644C4—3441no—
645C4—3441no—
646C4—3441no—
647C4—1721no—
648C4#1458355011yescharacteristic
649C4#1458355911yescharacteristic
650C4#1458358111yescharacteristic
651C4#1458362111yescharacteristic
652C2—3442no—
653C2—1722no—
654C2#1913802311yescharacteristic
655C2#1914420611yescharacteristic
656C2#1914421311yescharacteristic
657C2#1914470211yescharacteristic
658C2#1914473711yescharacteristic
659C2#1914578611yescharacteristic
660C2#1914583611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1944C2
socleC23×C43C22×D4
prime radicalC2×#13063300C22
hypercenter#1944D43
hypocenterC43#24706
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1944

Complements

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

NH ≅ G/Ntype
1. C2×#14583202C2semidirect
2. C2×#14582954C2semidirect
3. #19142904C2semidirect
5. #19136033C2semidirect
6. #19136019C2semidirect
9. #19135549C2semidirect
10. #19135364C2semidirect
11. #19135330C2semidirect
12. #19135292C2semidirect
13. #19135291C2semidirect
14. #19134604C2semidirect
15. C43×#1944C2semidirect
98. Dic43⋊C8D4semidirect
332. #1944D43semidirect
391. C43#24706semidirect

Maximal subgroups

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

subgroupindex
C2×#145832022
C2×#145829542
#191429042
#191371032
#191360332
#191360192
#191357862
#191357802
#191355492
#191353642
#191353302
#191352922
#191352912
#191346042
C43×#19442
#2470643