Finite Group Databasebeta

← #25137928

Subgroups — #25137928

Order 11008.

802 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583180C211yesmaximal, characteristic, complemented
2#19140416C211yesmaximal, characteristic, complemented
3#19137288C211yesmaximal, characteristic
4#19136023C211yesmaximal, characteristic, complemented
5#19136018C211yesmaximal, characteristic, complemented
6#19135785C211yesmaximal, characteristic
7#19135778C211yesmaximal, characteristic
8#19135542C211yesmaximal, characteristic, complemented
9#19135365C211yesmaximal, characteristic, complemented
10#19135338C211yesmaximal, characteristic, complemented
11#19135328C211yesmaximal, characteristic, complemented
12#19135292C211yesmaximal, characteristic, complemented
13#19135278C211yesmaximal, characteristic, complemented
14#19134606C211yesmaximal, characteristic, complemented
15C2×C43×#433C211yesmaximal, characteristic, complemented
16C2×#13063325C2211yescharacteristic
17C2×#13063299C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19#14583180—24no—
20C2×#13063259C2211yescharacteristic
21C2×#13063259C2211yescharacteristic
22C2×#13063259C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28#14582838—21no—
29#14582835—21no—
30#14582819—21no—
31#14582811—21no—
32#14582801C2211yescharacteristic
33#14582799—21no—
34#14582797C2211yescharacteristic
35#14582797C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582789—21no—
38#14582775—21no—
39#14582770—21no—
40#14582765C2211yescharacteristic
41#14582759C2211yescharacteristic
42#14582759C2211yescharacteristic
43#14582759C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53C2×#117×C43C2211yescharacteristic
54C43×#433—24no—
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×C4⋊C8×C43C2211yescharacteristic
57C2×C22⋊C8×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C2×#97×C43C2211yescharacteristic
60C2×C4×C8×C43C2211yescharacteristic
61C22×Dic86—21no—
62C22×D172C2311yescharacteristic
63C22×C22⋊D43—21no—
64C22×C4×D43—21no—
65#13063325—22no—
66#13063325—22no—
67#13063299—22no—
68#13063299—22no—
69C4×D172—22no—
70C4×D172—22no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—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—
90#13063259—22no—
91#13063259—22no—
92#13063259—22no—
93#13063257—22no—
94#13063247—22no—
95#13063247—22no—
96#13063247—22no—
97#13063247—22no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C23×C4×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112#117×C43—22no—
113#117×C43—22no—
114C2×C4⋊C4×C43D411yescharacteristic
115C2×C4⋊C4×C43D411yescharacteristic
116C2×C22⋊C4×C43D411yescharacteristic
117C2×C22⋊C4×C43D411yescharacteristic
118C2×C42×C43C2311yescharacteristic
119C2×C42×C43C2311yescharacteristic
120C4⋊C8×C43—22no—
121C4⋊C8×C43D414yescomplemented
122C22⋊C8×C43—22no—
123C22⋊C8×C43—22no—
124#97×C43—22no—
125C4×C8×C43—22no—
126C24×C43C2×D411yescharacteristic
127C23×D43—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×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2411yescharacteristic
140C2×C22⋊D43—24no—
141C2×C22⋊D43—81no—
142C2×C22⋊D43—81no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172#4112yes—
156C2×C4×D43—42no—
157C2×C4×D43—81no—
158C2×C4×D43—81no—
159C2×Dic86—42no—
160C2×Dic86—81no—
161C2×Dic86—81no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43C2×D412yes—
173C2×C8×C43C2×D412yes—
174C4⋊C4×C43—22no—
175C4⋊C4×C43—22no—
176C22⋊C4×C43—22no—
177C22⋊C4×C43—22no—
178C42×C43—21no—
179C42×C43—21no—
180C42×C43C2×D412yes—
181C42×C43#4112yes—
182C22⋊Dic43—81no—
183C22⋊Dic43—81no—
184C22⋊Dic43—81no—
185(C2×D43)⋊C4—24no—
186(C2×D43)⋊C4—42no—
187(C2×D43)⋊C4—81no—
188(C2×D43)⋊C4—81no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—42no—
203C4⋊Dic43#4112yes—
204Dic43⋊C4—81no—
205Dic43⋊C4—81no—
206Dic43⋊C4—81no—
207C4×Dic43—81no—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43—21no—
215C23×C43C22×D411yescharacteristic
216C22×D43—22no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C2×C4×C43—21no—
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—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43#12112yes—
241C2×C4×C43#12112yes—
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C432−1+411yescharacteristic
247C2×C4×C432−1+411yescharacteristic
248C22⋊D43—84no—
249C2×Dic43—22no—
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—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—
270D172—22no—
271D172—22no—
272D172—41no—
273D172—41no—
274C4×D43—84no—
275Dic86—84no—
276C8×C43—22no—
277C8×C43—22no—
278C8×C43—41no—
279C8×C43—41no—
280#24712—431nomaximal, Sylow
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43—41no—
288C22×C43C2×#12111yescharacteristic
289C22×C43#52511yescharacteristic
290C22×C43#53611yescharacteristic
291C22×C43#57611yescharacteristic
292C22×C43#57611yescharacteristic
293C22×C43#57711yescharacteristic
294C22×C43#57811yescharacteristic
295C2×D43—42no—
296C2×D43—42no—
297C2×D43—42no—
298C2×D43—81no—
299C2×D43—81no—
300C2×D43—81no—
301C2×D43—81no—
302C4×C43—22no—
303C4×C43—22no—
304C4×C43—41no—
305C4×C43—41no—
306C4×C43—41no—
307C4×C43#54711yescharacteristic
308C4×C43#54811yescharacteristic
309C4×C43#55211yescharacteristic
310C4×C43#55611yescharacteristic
311Dic43—42no—
312Dic43—81no—
313Dic43—81no—
314Dic43—81no—
315Dic43—81no—
316Dic43—81no—
317Dic43—81no—
318C2×#474—431no—
319C2×#433D4311yescharacteristic, complemented
320#2628—431no—
321#2324—431no—
322#2076—431no—
323#2075—431no—
324#2034—431no—
325#2033—431no—
326#1987—431no—
327#1949—431no—
328#1944—431no—
329#1942—431no—
330#1936—431no—
331#1934—431no—
332#1804—431no—
333C2×C43—81no—
334C2×C43#241511yescharacteristic
335C2×C43#305811yescharacteristic
336C2×C43#306311yescharacteristic
337C2×C43#311811yescharacteristic
338C2×C43#312411yescharacteristic
339C2×C43#324111yescharacteristic
340C2×C43#324311yescharacteristic
341D43—82no—
342C2×C4⋊Q8—431no—
343C2×#121—431no—
344C2×C4×D4—431no—
345C2×#117C2×D4311yescharacteristic
346#474—864no—
347#433—24no—
348C2×#107—431no—
349C2×#107—431no—
350C2×#107—431no—
351C2×#106—431no—
352C2×C4⋊C8C2×D4311yescharacteristic
353C2×C4⋊C8C2×D4311yescharacteristic
354C2×#102—431no—
355C2×#102—431no—
356C2×#102—431no—
357C2×#102—431no—
358C2×C22⋊C8C2×D4311yescharacteristic
359C2×C22⋊C8C2×D4311yescharacteristic
360C2×#97C2×D4311yescharacteristic
361C2×C4×C8C2×D4311yescharacteristic
362#400—861no—
363#399—861no—
364#395—861no—
365#393—861no—
366#390—431no—
367#390—861no—
368#389—431no—
369#389—431no—
370#389—431no—
371#388—861no—
372#386—861no—
373#385—861no—
374#382—431no—
375#380—431no—
376#380—431no—
377#380—431no—
378C4×C4⋊C4—431no—
379#340—431no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340—431no—
384#340—431no—
385#340—431no—
386#340—431no—
387C43#2471211yescharacteristic, complemented, Sylow
388C22×Q8—861no—
389C22×D4—431no—
390C22×D4—861no—
391C23×C4—861no—
392C23×C4C22×D4311yescharacteristic
393C22×C8C22×D4311yescharacteristic
394C22×C8C22×D4311yescharacteristic
395C22×C8C22×D4311yescharacteristic
396C22×C8C22×D4311yescharacteristic
397C4⋊Q8—862no—
398C4⋊Q8—862no—
399#121—862no—
400#121—862no—
401C4×D4—862no—
402C4×D4—862no—
403#117—22no—
404#117—22no—
405C2×C4⋊C4—431no—
406C2×C4⋊C4—431no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4D17211yescharacteristic
417C2×C4⋊C4D17211yescharacteristic
418C2×C22⋊C4—861no—
419C2×C22⋊C4—861no—
420C2×C22⋊C4—861no—
421C2×C22⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4D17211yescharacteristic
426C2×C22⋊C4D17211yescharacteristic
427C2×C42—861no—
428C2×C42C22×D4311yescharacteristic
429C2×C42C22×D4311yescharacteristic
430#107—862no—
431#107—862no—
432#107—862no—
433#106—862no—
434C4⋊C8—22no—
435C4⋊C8C22⋊D4314yescomplemented
436#102—862no—
437#102—862no—
438#102—862no—
439#102—862no—
440C22⋊C8—22no—
441C22⋊C8—22no—
442#97—22no—
443C4×C8—22no—
444#95—861no—
445#95—861no—
446#95—861no—
447#95—861no—
448#95—861no—
449#95—861no—
450#95—861no—
451#95—861no—
452#95—861no—
453C24—861no—
454C24C2×D17211yescharacteristic
455C2×Q8—3441no—
456C2×Q8—3441no—
457C2×Q8—1722no—
458C2×D4—432no—
459C2×D4—864no—
460C2×D4—861no—
461C2×D4—861no—
462C2×D4—861no—
463C2×D4—861no—
464C2×D4—861no—
465C2×D4—3441no—
466C2×D4—3441no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4—861no—
480C22×C4—3441no—
481C22×C4—3441no—
482C22×C4—1722no—
483C22×C4C2×D17211yescharacteristic
484C22×C4C2×D17211yescharacteristic
485C22×C4C2×D17211yescharacteristic
486C22×C4C2×D17211yescharacteristic
487C22×C4C2×D17211yescharacteristic
488C22×C4C23×D4311yescharacteristic
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8C2×C22⋊D4312yes—
500C2×C8C2×C22⋊D4312yes—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—432no—
504C4⋊C4—861no—
505C4⋊C4—861no—
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—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—3441no—
518C4⋊C4—3441no—
519C4⋊C4—3441no—
520C4⋊C4—1722no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—864no—
524C22⋊C4—3441no—
525C22⋊C4—3441no—
526C22⋊C4—3441no—
527C22⋊C4—3441no—
528C22⋊C4—3441no—
529C22⋊C4—1722no—
530C42—21no—
531C42—21no—
532C42—3441no—
533C42#1062189812yes—
534C42C2×C22⋊D4312yes—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—862no—
543C23—1721no—
544C23—1721no—
545C23—1721no—
546C23—1721no—
547C23—1721no—
548C23—1721no—
549C23C22×D17211yescharacteristic
550Q8—3444no—
551D4—862no—
552D4—862no—
553D4—3444no—
554D4—1721no—
555D4—1721no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
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—862no—
574C2×C4—3444no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
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#1306329912yes—
596C2×C4#1306329912yes—
597C2×C4C22×C22⋊D4311yescharacteristic
598C2×C4#41×D4311yescharacteristic
599C2×C4#41×D4311yescharacteristic
600C2×C4C2×#1062189811yescharacteristic
601C2×C4#1306337211yescharacteristic
602C2×C4#1306337211yescharacteristic
603C8—22no—
604C8—22no—
605C8—41no—
606C8—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—3441no—
615C22—3441no—
616C22—3441no—
617C22—3441no—
618C22—1722no—
619C22—1722no—
620C22—1722no—
621C22C2×#1306329911yescharacteristic
622C22#1458341111yescharacteristic
623C22#1458347511yescharacteristic
624C22#1458370411yescharacteristic
625C22#1458370411yescharacteristic
626C22#1458371111yescharacteristic
627C22#1458371611yescharacteristic
628C4—22no—
629C4—22no—
630C4—41no—
631C4—41no—
632C4—41no—
633C4—3441no—
634C4—3441no—
635C4—3441no—
636C4—3441no—
637C4—3441no—
638C4—3441no—
639C4—1722no—
640C4#1458354811yescharacteristic
641C4#1458355611yescharacteristic
642C4#1458358811yescharacteristic
643C4#1458361711yescharacteristic
644C2—81no—
645C2—3442no—
646C2#1913801811yescharacteristic
647C2#1914424311yescharacteristic
648C2#1914428611yescharacteristic
649C2#1914478111yescharacteristic
650C2#1914485911yescharacteristic
651C2#1914585011yescharacteristic
652C2#1914588011yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#433C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenterC2×#433D43
hypocenterC43#24712
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#14583180C2semidirect
2. #19140416C2semidirect
4. #19136023C2semidirect
5. #19136018C2semidirect
8. #19135542C2semidirect
9. #19135365C2semidirect
10. #19135338C2semidirect
11. #19135328C2semidirect
12. #19135292C2semidirect
13. #19135278C2semidirect
14. #19134606C2semidirect
15. C2×C43×#433C2semidirect
121. C4⋊C8×C43D4semidirect
319. C2×#433D43semidirect
387. C43#24712semidirect
435. C4⋊C8C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831802
#191404162
#191372882
#191360232
#191360182
#191357852
#191357782
#191355422
#191353652
#191353382
#191353282
#191352922
#191352782
#191346062
C2×C43×#4332
#2471243