Finite Group Databasebeta

← #25126584

Subgroups — #25126584

Order 11008.

880 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#121×Dic43C211yesmaximal, characteristic
2#19136997C211yesmaximal, characteristic, complemented
3#19136156C211yesmaximal, characteristic, complemented
4#19136121C211yesmaximal, characteristic, complemented
5#19136069C211yesmaximal, characteristic, complemented
6#19136021C211yesmaximal, characteristic, complemented
7#19136018C211yesmaximal, characteristic, complemented
8#19136001C211yesmaximal, characteristic, complemented
9#19135774C211yesmaximal, characteristic
10#107×Dic43C211yesmaximal, characteristic, complemented
11#19134487C211yesmaximal, characteristic, complemented
12#102×Dic43C211yesmaximal, characteristic, complemented
13#102×Dic43C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic43C211yesmaximal, characteristic, complemented
15C43×#2033C211yesmaximal, characteristic
16C2×D4×Dic43—21no—
17C2×D4×Dic43C2211yescharacteristic
18C2×#13063281—21no—
19C22×C4×Dic43C2211yescharacteristic
20C2×#13063259C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×C22⋊(C43⋊C8)C2211yescharacteristic
26C2×C8×Dic43C2211yescharacteristic
27C2×C8×Dic43C2211yescharacteristic
28#14582802C2211yescharacteristic
29#14582798C2211yescharacteristic
30#14582792—21no—
31#14582779—21no—
32#14582768C2211yescharacteristic
33#14582768C2211yescharacteristic
34#14582763—21no—
35#14582759C2211yescharacteristic
36#14582759C2211yescharacteristic
37#14582757—21no—
38C4⋊C4×Dic43C2211yescharacteristic
39C4⋊C4×Dic43C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41#14582750—21no—
42C22⋊C4×Dic43—21no—
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#121×C43C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C23×Dic43—21no—
60C23×Dic43D411yescharacteristic
61C23×Dic43D411yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64D4×Dic43—22no—
65D4×Dic43—22no—
66D4×Dic43—44no—
67#13063281—44no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C4×Dic43—22no—
83C2×C4×Dic43—22no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43D411yescharacteristic
88C2×C4×Dic43D411yescharacteristic
89C2×C4×Dic43C2311yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91#13063259—22no—
92#13063258—22no—
93#13063258—22no—
94#13063246—22no—
95#13063246—22no—
96C22⋊(C43⋊C8)—22no—
97C8×Dic43—22no—
98C8×Dic43—22no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C22×D4×C43—21no—
106C22×D4×C43C2311yescharacteristic
107C23×C4×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110#121×C43—22no—
111#121×C43—22no—
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43—21no—
117#107×C43—22no—
118#102×C43—22no—
119#102×C43—22no—
120C22⋊C8×C43—22no—
121#95×C43—21no—
122C24×C43—21no—
123C24×C43C2×D411yescharacteristic
124C2×D4×C43—24no—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—42no—
131C2×D4×C43—42no—
132C2×D4×C43#4112yes—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2411yescharacteristic
144C22×Dic43—22no—
145C22×Dic43—22no—
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—41no—
153C22×Dic43—42no—
154C22×Dic43—42no—
155C22×Dic43—42no—
156C22×Dic43D814yes—
157C22×Dic43C2×D411yescharacteristic
158C22×Dic43C2×D411yescharacteristic
159C22×Dic43C2×D411yescharacteristic
160C22×Dic43C2×D411yescharacteristic
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43#4112yes—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43#4112yes—
173C22⋊C4×C43—24no—
174C22⋊C4×C43—42no—
175C22⋊Dic43—42no—
176C22⋊Dic43—42no—
177C22⋊Dic43—42no—
178C22⋊Dic43—42no—
179C22⋊Dic43—42no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—42no—
189Dic43⋊C4—42no—
190Dic43⋊C4—42no—
191Dic43⋊C4—42no—
192Dic43⋊C4—42no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—22no—
196C4×Dic43—22no—
197C4×Dic43—42no—
198C4×Dic43—42no—
199C4×Dic43—42no—
200C4×Dic43#4112yes—
201C4×Dic43#4112yes—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8#4112yes—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43—22no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43C2×D812yes—
222C23×C43C22×D411yescharacteristic
223D4×C43—22no—
224D4×C43—22no—
225D4×C43—48no—
226D4×C43—41no—
227D4×C43—41no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—22no—
231C2×C4×C43—21no—
232C2×C4×C43—41no—
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×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—28no—
257C2×Dic43—44no—
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—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—84no—
271C2×Dic43#12312yes—
272C2×Dic43#12312yes—
273C2×Dic43C2×D812yes—
274C2×Dic43C2×D812yes—
275C2×Dic43#13512yes—
276C2×Dic43#13712yes—
277C8×C43—22no—
278C8×C43—41no—
279C43⋊C8—22no—
280C43⋊C8—41no—
281#23754—431nomaximal, Sylow
282C22×C43—22no—
283C22×C43—22no—
284C22×C43—22no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43—41no—
288C22×C43—41no—
289C22×C43—42no—
290C22×C43—42no—
291C22×C43—42no—
292C22×C43—81no—
293C22×C43—81no—
294C22×C43—81no—
295C22×C43—81no—
296C22×C43C2×#12311yescharacteristic
297C22×C43#52511yescharacteristic
298C22×C43#53211yescharacteristic
299C22×C43C22×D811yescharacteristic
300C22×C43C2×#13511yescharacteristic
301C22×C43C2×#13711yescharacteristic
302C22×C43#57511yescharacteristic
303C4×C43—42no—
304C4×C43—41no—
305C4×C43—81no—
306C4×C43—81no—
307C4×C43#52911yescharacteristic
308C4×C43#52911yescharacteristic
309C4×C43#52911yescharacteristic
310C4×C43#52911yescharacteristic
311Dic43—22no—
312Dic43—22no—
313Dic43—22no—
314Dic43—81no—
315Dic43—81no—
316Dic43—81no—
317Dic43—81no—
318Dic43#48014yes—
319C4×#121—431no—
320#2285—431no—
321#2099—431no—
322#2093—431no—
323#2083—431no—
324#2075—431no—
325#2075—431no—
326#2071—431no—
327#2033—431no—
328#2033D4311yescharacteristic
329C4×#107—431no—
330C4×#107—431no—
331C4×#102—431no—
332C4×#102—431no—
333C4×C22⋊C8—431no—
334C2×C43—42no—
335C2×C43—82no—
336C2×C43#239511yescharacteristic
337C2×C43C2×#48011yescharacteristic
338C2×C43#309111yescharacteristic
339C2×C43#310011yescharacteristic
340C2×C43#310711yescharacteristic
341C2×C43#316911yescharacteristic
342C2×C43#317211yescharacteristic
343C2×#121C2×D4311yescharacteristic
344C2×C4×D4—431no—
345C2×C4×D4—861no—
346C2×#117—861no—
347C22×C42—431no—
348C2×#107—431no—
349C2×#107—431no—
350C2×#107—431no—
351C2×#107C2×D4311yescharacteristic
352C2×#102—431no—
353C2×#102—431no—
354C2×#102C2×D4311yescharacteristic
355C2×#102C2×D4311yescharacteristic
356C2×C22⋊C8—431no—
357C2×C22⋊C8C2×D4311yescharacteristic
358C2×C4×C8—431no—
359C2×C4×C8—431no—
360#390—431no—
361#389—431no—
362#388—861no—
363#386—861no—
364#384—431no—
365#384—431no—
366#382—861no—
367#380—431no—
368#380—431no—
369#380—861no—
370#380C2×D4311yescharacteristic
371C4×C4⋊C4—431no—
372C4×C4⋊C4—431no—
373C4×C4⋊C4—431no—
374C4×C4⋊C4—861no—
375C4×C22⋊C4—861no—
376#340—431no—
377#340—431no—
378#340—431no—
379#340—431no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340C2×D4311yescharacteristic
384#336—431no—
385#336—431no—
386C43#2375411yescharacteristic, complemented, Sylow
387C22×D4—21no—
388C22×D4C22×D4311yescharacteristic
389C23×C4—431no—
390C23×C4—431no—
391C23×C4—861no—
392C23×C4C22×D4311yescharacteristic
393C22×C8—431no—
394C22×C8—431no—
395C22×C8C22×D4311yescharacteristic
396C22×C8C22×D4311yescharacteristic
397#121—22no—
398#121—22no—
399C4×D4—862no—
400C4×D4—862no—
401C4×D4—1724no—
402#117—1724no—
403C2×C4⋊C4—431no—
404C2×C4⋊C4—431no—
405C2×C4⋊C4—431no—
406C2×C4⋊C4—431no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4—861no—
409C2×C4⋊C4—861no—
410C2×C4⋊C4—861no—
411C2×C4⋊C4—861no—
412C2×C4⋊C4C22×D4311yescharacteristic
413C2×C4⋊C4C22×D4311yescharacteristic
414C2×C4⋊C4C22×D4311yescharacteristic
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—861no—
418C2×C22⋊C4—861no—
419C2×C22⋊C4—861no—
420C2×C22⋊C4—861no—
421C2×C22⋊C4—861no—
422C2×C42—431no—
423C2×C42—431no—
424C2×C42—431no—
425C2×C42—431no—
426C2×C42—862no—
427C2×C42—862no—
428C2×C42—861no—
429C2×C42—861no—
430C2×C42—861no—
431#107—22no—
432#107—862no—
433#107—862no—
434#107—862no—
435#102—22no—
436#102—22no—
437#102—862no—
438#102—862no—
439C22⋊C8—22no—
440C22⋊C8—862no—
441C4×C8—862no—
442C4×C8—862no—
443#95—21no—
444#95—861no—
445#95—861no—
446#95—861no—
447#95—861no—
448#95—861no—
449#95—861no—
450C24—21no—
451C24D4×D4311yescharacteristic
452C2×D4—24no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—42no—
459C2×D4—42no—
460C2×D4#1062190012yes—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—431no—
471C22×C4—434no—
472C22×C4—431no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—862no—
476C22×C4—862no—
477C22×C4—862no—
478C22×C4—862no—
479C22×C4—861no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—1722no—
484C22×C4—1722no—
485C22×C4—1722no—
486C22×C4—1721no—
487C22×C4D4×D4311yescharacteristic
488C22×C4C23×D4311yescharacteristic
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—432no—
495C2×C8—861no—
496C2×C8—861no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8#1062190012yes—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—1722no—
515C4⋊C4—1722no—
516C4⋊C4—1722no—
517C4⋊C4—1722no—
518C4⋊C4—1722no—
519C4⋊C4#1062190012yes—
520C22⋊C4—24no—
521C22⋊C4—42no—
522C22⋊C4—1722no—
523C22⋊C4—1722no—
524C22⋊C4—1722no—
525C22⋊C4—1722no—
526C22⋊C4—1722no—
527C42—432no—
528C42—432no—
529C42—862no—
530C42—862no—
531C42—861no—
532C42—861no—
533C42—1722no—
534C42—1722no—
535C42—1722no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—22no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23D8×D4312yes—
550C23C2×D4×D4311yescharacteristic
551D4—22no—
552D4—22no—
553D4—48no—
554D4—41no—
555D4—41no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—432no—
573C2×C4—432no—
574C2×C4—432no—
575C2×C4—432no—
576C2×C4—432no—
577C2×C4—432no—
578C2×C4—868no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—3444no—
586C2×C4—1724no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4#41×D4311yescharacteristic
600C2×C4#41×D4311yescharacteristic
601C2×C4#41×D4311yescharacteristic
602C2×C4C2×#1062190011yescharacteristic
603C2×C4C2×#1062190011yescharacteristic
604C2×C4C2×#1062190011yescharacteristic
605C8—22no—
606C8—41no—
607C8—862no—
608C8—1721no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—81no—
620C22—81no—
621C22—81no—
622C22—81no—
623C22#123×D4311yescharacteristic
624C22#1458340511yescharacteristic
625C22#1458344411yescharacteristic
626C22C2×D8×D4311yescharacteristic
627C22#135×D4311yescharacteristic
628C22#137×D4311yescharacteristic
629C22#1458369511yescharacteristic
630C4—41no—
631C4—42no—
632C4—81no—
633C4—81no—
634C4—434no—
635C4—862no—
636C4—862no—
637C4—862no—
638C4—3441no—
639C4—3441no—
640C4—3441no—
641C4—3441no—
642C4#1458342611yescharacteristic
643C4#1458342811yescharacteristic
644C4#1458343011yescharacteristic
645C4#1458343011yescharacteristic
646C2—42no—
647C2—82no—
648C2#1913785111yescharacteristic
649C2#480×D4311yescharacteristic
650C2#1914450711yescharacteristic
651C2#1914459011yescharacteristic
652C2#1914465911yescharacteristic
653C2#1914516911yescharacteristic
654C2#1914519411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2033C2
socleC23×C43C22×D4
prime radicalC2×#121×C43C22
hypercenter#2033D43
hypocenterC43#23754
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2033

Complements

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

NH ≅ G/Ntype
2. #19136997C2semidirect
3. #19136156C2semidirect
4. #19136121C2semidirect
5. #19136069C2semidirect
6. #19136021C2semidirect
7. #19136018C2semidirect
8. #19136001C2semidirect
10. #107×Dic43C2semidirect
11. #19134487C2semidirect
12. #102×Dic43C2semidirect
13. #102×Dic43C2semidirect
14. C22⋊C8×Dic43C2semidirect
386. C43#23754semidirect

Maximal subgroups

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

subgroupindex
#121×Dic432
#191369972
#191361562
#191361212
#191360692
#191360212
#191360182
#191360012
#191357742
#107×Dic432
#191344872
#102×Dic432
C22⋊C8×Dic432
C43×#20332
#2375443