Finite Group Databasebeta

← #25103758

Subgroups — #25103758

Order 11008.

888 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583240C211yesmaximal, characteristic
2#19137123C211yesmaximal, characteristic
3#117×Dic43C211yesmaximal, characteristic
4#19135234C211yesmaximal, characteristic, complemented
5#19135227C211yesmaximal, characteristic, complemented
6#19135171C211yesmaximal, characteristic, complemented
7#19135164C211yesmaximal, characteristic, complemented
8#19134905C211yesmaximal, characteristic
9#19134792C211yesmaximal, characteristic
10#19134487C211yesmaximal, characteristic, complemented
11#19134483C211yesmaximal, characteristic, complemented
12#19134414C211yesmaximal, characteristic, complemented
13#19134414C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic43C211yesmaximal, characteristic
15C43×#1825C211yesmaximal, characteristic
16C2×#13063304C2211yescharacteristic
17C2×#13063290C2211yescharacteristic
18C2×#13063284C2211yescharacteristic
19C22×C4×Dic43C2211yescharacteristic
20#14583240C418yescomplemented
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31C2×C8×Dic43C2211yescharacteristic
32#14582804C2211yescharacteristic
33#14582795C2211yescharacteristic
34#14582781—21no—
35#14582771—21no—
36C4⋊C4×Dic43C2211yescharacteristic
37C4⋊C4×Dic43C2211yescharacteristic
38C4⋊C4×Dic43C2211yescharacteristic
39C4⋊C4×Dic43C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41#14582750—21no—
42C22⋊C4×Dic43—21no—
43C22⋊C4×Dic43—21no—
44C22⋊C4×Dic43—21no—
45#14582745—21no—
46C42×Dic43—21no—
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×#117×C43C2211yescharacteristic
54C2×C22⋊C8×C43C2211yescharacteristic
55C43×#380C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×Dic86C2311yescharacteristic
61C23×Dic43D411yescharacteristic
62C23×Dic43D411yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063304—22no—
66#13063304C2×C414yes—
67#13063290—22no—
68#13063290—22no—
69#13063284—22no—
70#13063284—22no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C4×Dic43—21no—
80C2×C4×Dic43—22no—
81C2×C4×Dic43—22no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43D411yescharacteristic
89C2×C4×Dic43D411yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91C2×C4×Dic43C2311yescharacteristic
92#13063258—22no—
93#13063258C2×C414yescomplemented
94#13063256—22no—
95#13063256C2×C414yescomplemented
96#13063250—22no—
97#13063250—22no—
98#13063248C2×C414yescomplemented
99#13063248C2×C414yescomplemented
100C22⋊(C43⋊C8)C2×C414yes—
101C8×Dic43—22no—
102C8×Dic43—22no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C23×C4×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114#117×C43—22no—
115#117×C43C2×C414yes—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C42×C43—21no—
123C22⋊C8×C43—22no—
124#95×C43—21no—
125C24×C43C2×D411yescharacteristic
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43C22×C412yes—
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43#4112yes—
137C22×C4×C43C2411yescharacteristic
138C22×Dic43—22no—
139C22×Dic43—22no—
140C22×Dic43—22no—
141C22×Dic43—22no—
142C22×Dic43—22no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—41no—
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86C22×C412yes—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×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—
170C4⋊C4×C43C22×C412yes—
171C4⋊C4×C43C22×C412yes—
172C22⋊C4×C43—24no—
173C22⋊C4×C43—42no—
174C42×C43—24no—
175C22⋊Dic43—24no—
176C22⋊Dic43—24no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43C22×C412yes—
181C4⋊Dic43#4112yes—
182C4⋊Dic43#4112yes—
183Dic43⋊C4—24no—
184Dic43⋊C4—42no—
185Dic43⋊C4—42no—
186C4×Dic43—24no—
187C4×Dic43—21no—
188C4×Dic43—21no—
189C4×Dic43—22no—
190C4×Dic43—22no—
191C4×Dic43—42no—
192C4×Dic43—42no—
193C4×Dic43—42no—
194C4×Dic43—42no—
195C4×Dic43—42no—
196C4×Dic43—42no—
197C4×Dic43#4112yes—
198C4×Dic43#4112yes—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8C22×C412yes—
204C2×C43⋊C8C22×C412yes—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43C4×D412yes—
212C23×C43C22×D411yescharacteristic
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—22no—
216C2×C4×C43—22no—
217C2×C4×C43—22no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43C4×D412yes—
232C2×C4×C43C23×C411yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—22no—
243C2×Dic43—22no—
244C2×Dic43—21no—
245C2×Dic43—22no—
246C2×Dic43—22no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—44no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—44no—
259C2×Dic43#12312yes—
260C2×Dic43#12312yes—
261C2×Dic43#13512yes—
262C2×Dic43#13512yes—
263C2×Dic43#13712yes—
264Dic86—22no—
265Dic86—22no—
266Dic86—41no—
267Dic86—41no—
268C8×C43—41no—
269C8×C43—41no—
270C43⋊C8—22no—
271C43⋊C8—22no—
272C4×#485—431nomaximal, Sylow
273C22×C43—22no—
274C22×C43—22no—
275C22×C43—22no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43C2×C4×D411yescharacteristic
281C22×C43C2×#12311yescharacteristic
282C22×C43#52511yescharacteristic
283C22×C43C2×#13511yescharacteristic
284C22×C43C2×#13511yescharacteristic
285C22×C43C2×#13711yescharacteristic
286C22×C43#57511yescharacteristic
287C4×C43—22no—
288C4×C43—42no—
289C4×C43—42no—
290C4×C43—81no—
291C4×C43—81no—
292C4×C43C4×#4111yescharacteristic
293C4×C43C4×#4111yescharacteristic
294C4×C43#52911yescharacteristic
295C4×C43#52911yescharacteristic
296Dic43—22no—
297Dic43—22no—
298Dic43—41no—
299Dic43—42no—
300Dic43—42no—
301Dic43—42no—
302Dic43—42no—
303Dic43#48514yescomplemented
304C2×#485—431no—
305C4×C22⋊Q8—431no—
306C4×#117—431no—
307#1928—431no—
308#1927—431no—
309#1919—431no—
310#1918—431no—
311#1873—431no—
312#1854—431no—
313#1825D4311yescharacteristic
314C4×#107—431no—
315C4×#106—431no—
316C4×#103—431no—
317C4×#103—431no—
318C4×C22⋊C8—431no—
319C2×C43—42no—
320C2×C43C4×#12311yescharacteristic
321C2×C43C4×#13511yescharacteristic
322C2×C43C4×#13711yescharacteristic
323C2×C43C2×#48511yescharacteristic
324C2×C43#309111yescharacteristic
325C2×C43#310211yescharacteristic
326C2×C43#310711yescharacteristic
327C2×C22⋊Q8—431no—
328C2×C4×Q8—431no—
329C2×#117—431no—
330C2×#117C2×D4311yescharacteristic
331C22×C42—431no—
332#485—438no—
333C2×#107—431no—
334C2×#107—431no—
335C2×#106—431no—
336C2×#106—431no—
337C2×#103—431no—
338C2×#103—431no—
339C2×#103—431no—
340C2×#103—431no—
341C2×C22⋊C8—431no—
342C2×C22⋊C8C2×D4311yescharacteristic
343C2×C4×C8—431no—
344C2×C4×C8—431no—
345#391—431no—
346#389—431no—
347#387—861no—
348#385—861no—
349#380C2×D4311yescharacteristic
350C4×C4⋊C4—431no—
351C4×C4⋊C4—431no—
352C4×C4⋊C4—431no—
353C4×C4⋊C4—431no—
354C4×C4⋊C4—431no—
355C4×C4⋊C4—861no—
356C4×C22⋊C4—861no—
357C4×C22⋊C4—861no—
358C4×C22⋊C4—861no—
359#376—861no—
360C43—861no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340—431no—
365#340C2×D4311yescharacteristic
366#340C2×D4311yescharacteristic
367#340C2×D4311yescharacteristic
368#340C2×D4311yescharacteristic
369#336—431no—
370#336—431no—
371C43C4×#48511yescharacteristic, complemented, Sylow
372C22×Q8—431no—
373C23×C4—431no—
374C23×C4—431no—
375C23×C4C22×D4311yescharacteristic
376C22×C8—431no—
377C22×C8—431no—
378C22×C8C22×D4311yescharacteristic
379C22×C8C22×D4311yescharacteristic
380C22⋊Q8—434no—
381C22⋊Q8—862no—
382C4×Q8—862no—
383C4×Q8—862no—
384#117—22no—
385#117—862no—
386#117—862no—
387#117C4×D4314yes—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—431no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4C22×D4311yescharacteristic
395C2×C4⋊C4C22×D4311yescharacteristic
396C2×C4⋊C4C22×D4311yescharacteristic
397C2×C4⋊C4C22×D4311yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—861no—
401C2×C22⋊C4—861no—
402C2×C42—21no—
403C2×C42—431no—
404C2×C42—431no—
405C2×C42—431no—
406C2×C42—431no—
407C2×C42—862no—
408C2×C42—862no—
409C2×C42—861no—
410C2×C42—861no—
411C2×C42—861no—
412C2×C42—861no—
413C2×C42—861no—
414C2×C42—861no—
415C2×C42—861no—
416#107—434no—
417#107—862no—
418#106—434no—
419#106—862no—
420#103—434no—
421#103—434no—
422#103—862no—
423#103—862no—
424C22⋊C8—22no—
425C22⋊C8—434no—
426C4×C8—862no—
427C4×C8—862no—
428#95—21no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437C24D4×D4311yescharacteristic
438C2×Q8—432no—
439C2×Q8—861no—
440C2×Q8—861no—
441C2×Q8—861no—
442C2×Q8—861no—
443C2×Q8—861no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—431no—
453C22×C4—431no—
454C22×C4—431no—
455C22×C4—431no—
456C22×C4—862no—
457C22×C4—862no—
458C22×C4—862no—
459C22×C4—862no—
460C22×C4—862no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—1721no—
466C22×C4C2×C4×D4312yes—
467C22×C4D4×D4311yescharacteristic
468C22×C4#1062190012yes—
469C22×C4C23×D4311yescharacteristic
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—432no—
477C2×C8—432no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—861no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—432no—
489C4⋊C4—432no—
490C4⋊C4—432no—
491C4⋊C4—864no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—1722no—
496C4⋊C4—1722no—
497C4⋊C4C2×C4×D4312yes—
498C4⋊C4C2×C4×D4312yes—
499C22⋊C4—24no—
500C22⋊C4—42no—
501C22⋊C4—864no—
502C22⋊C4—864no—
503C42—24no—
504C42—432no—
505C42—432no—
506C42—862no—
507C42—862no—
508C42—864no—
509C42—861no—
510C42—861no—
511C42—1722no—
512C42—1722no—
513C42—1722no—
514C42—1722no—
515C42—1722no—
516C42—1722no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23(C22⋊D43)⋊C412yes—
524C23C2×D4×D4311yescharacteristic
525Q8—862no—
526Q8—862no—
527Q8—1721no—
528Q8—1721no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—432no—
548C2×C4—432no—
549C2×C4—432no—
550C2×C4—432no—
551C2×C4—432no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—862no—
557C2×C4—862no—
558C2×C4—861no—
559C2×C4—862no—
560C2×C4—862no—
561C2×C4—861no—
562C2×C4—861no—
563C2×C4—1724no—
564C2×C4—1724no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4(C22⋊D43)⋊C412yes—
574C2×C4C22×C4×D4311yescharacteristic
575C2×C4#41×D4311yescharacteristic
576C2×C4#41×D4311yescharacteristic
577C2×C4#41×D4311yescharacteristic
578C2×C4#41×D4311yescharacteristic
579C2×C4C2×#1062190011yescharacteristic
580C8—41no—
581C8—41no—
582C8—862no—
583C8—862no—
584C22—22no—
585C22—22no—
586C22—22no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22C2×(C22⋊D43)⋊C411yescharacteristic
592C22#123×D4311yescharacteristic
593C22#1458340711yescharacteristic
594C22#135×D4311yescharacteristic
595C22#135×D4311yescharacteristic
596C22#137×D4311yescharacteristic
597C22#1458369511yescharacteristic
598C4—22no—
599C4—42no—
600C4—42no—
601C4—81no—
602C4—81no—
603C4—434no—
604C4—862no—
605C4—862no—
606C4—1721no—
607C4—1722no—
608C4—1722no—
609C4—1722no—
610C4—1722no—
611C4#1458336711yescharacteristic
612C4#1458336711yescharacteristic
613C4#1458342611yescharacteristic
614C4#1458342611yescharacteristic
615C2—42no—
616C2#1913711211yescharacteristic
617C2#1914336311yescharacteristic
618C2#1914341911yescharacteristic
619C2#485×D4311yescharacteristic
620C2#1914450711yescharacteristic
621C2#1914460811yescharacteristic
622C2#1914466111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1825C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
cosocleC22×C4×C43C24
hypercenter#1825D43
hypocenterC43C4×#485
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1825

Complements

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

NH ≅ G/Ntype
4. #19135234C2semidirect
5. #19135227C2semidirect
6. #19135171C2semidirect
7. #19135164C2semidirect
10. #19134487C2semidirect
11. #19134483C2semidirect
12. #19134414C2semidirect
13. #19134414C2semidirect
20. #14583240C4semidirect
93. #13063258C2×C4semidirect
95. #13063256C2×C4semidirect
98. #13063248C2×C4semidirect
99. #13063248C2×C4semidirect
303. Dic43#485semidirect
371. C43C4×#485semidirect

Maximal subgroups

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

subgroupindex
C2×#145832402
#191371232
#117×Dic432
#191352342
#191352272
#191351712
#191351642
#191349052
#191347922
#191344872
#191344832
#191344142
C22⋊C8×Dic432
C43×#18252
C4×#48543