Finite Group Databasebeta

← #25137943

Subgroups — #25137943

Order 11008.

794 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583200C211yesmaximal, characteristic, complemented
2#19140425C211yesmaximal, characteristic, complemented
3#19137288C211yesmaximal, characteristic
4#19136028C211yesmaximal, characteristic, complemented
5#19136023C211yesmaximal, characteristic, complemented
6#19135778C211yesmaximal, characteristic
7#19135778C211yesmaximal, characteristic
8#19135550C211yesmaximal, characteristic, complemented
9#19135354C211yesmaximal, characteristic, complemented
10#19135333C211yesmaximal, characteristic, complemented
11#19135328C211yesmaximal, characteristic, complemented
12#19135292C211yesmaximal, characteristic, complemented
13#19135278C211yesmaximal, characteristic, complemented
14#19134596C211yesmaximal, characteristic, complemented
15C2×C43×#433C211yesmaximal, characteristic, complemented
16C2×#13063317C2211yescharacteristic
17C2×#13063299C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19#14583200—24no—
20C2×#13063259C2211yescharacteristic
21C2×#13063259C2211yescharacteristic
22C2×#13063259C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28#14582832—21no—
29#14582832—21no—
30#14582822—21no—
31#14582822—21no—
32#14582801C2211yescharacteristic
33#14582799—21no—
34#14582797C2211yescharacteristic
35#14582797C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582789—21no—
38#14582775—21no—
39#14582770—21no—
40#14582769C2211yescharacteristic
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×D172C2311yescharacteristic
62C22×C22⋊D43—21no—
63C22×C4×D43—21no—
64#13063317—22no—
65#13063317—22no—
66#13063299—22no—
67#13063299—22no—
68C4×D172—22no—
69C4×D172—22no—
70C2×C4⋊Dic43—21no—
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×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×C4×Dic43—21no—
92#13063259—22no—
93#13063259—22no—
94#13063259—22no—
95#13063257—22no—
96#13063247—22no—
97#13063247—22no—
98#13063247—22no—
99#13063247—22no—
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×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
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×C43C2×D412yes—
170C2×C8×C43C2×D412yes—
171C4⋊C4×C43—22no—
172C4⋊C4×C43—22no—
173C22⋊C4×C43—22no—
174C22⋊C4×C43—22no—
175C42×C43—21no—
176C42×C43—21no—
177C42×C43C2×D412yes—
178C42×C43#4112yes—
179C22⋊Dic43—81no—
180C22⋊Dic43—81no—
181C22⋊Dic43—81no—
182(C2×D43)⋊C4—24no—
183(C2×D43)⋊C4—42no—
184(C2×D43)⋊C4—81no—
185(C2×D43)⋊C4—81no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
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—81no—
200C4⋊Dic43—81no—
201C4⋊Dic43#4112yes—
202Dic43⋊C4—42no—
203Dic43⋊C4—42no—
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—
275C8×C43—22no—
276C8×C43—22no—
277C8×C43—41no—
278C8×C43—41no—
279#24713—431nomaximal, Sylow
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43C2×#12111yescharacteristic
288C22×C43#52511yescharacteristic
289C22×C43#53611yescharacteristic
290C22×C43#57611yescharacteristic
291C22×C43#57611yescharacteristic
292C22×C43#57711yescharacteristic
293C22×C43#57811yescharacteristic
294C2×D43—42no—
295C2×D43—42no—
296C2×D43—42no—
297C2×D43—81no—
298C2×D43—81no—
299C2×D43—81no—
300C2×D43—81no—
301C4×C43—22no—
302C4×C43—22no—
303C4×C43—41no—
304C4×C43—41no—
305C4×C43—41no—
306C4×C43#54711yescharacteristic
307C4×C43#54811yescharacteristic
308C4×C43#55211yescharacteristic
309C4×C43#55611yescharacteristic
310Dic43—42no—
311Dic43—81no—
312Dic43—81no—
313Dic43—81no—
314Dic43—81no—
315Dic43—81no—
316Dic43—81no—
317C2×#478—431no—
318C2×#433D4311yescharacteristic, complemented
319#2629—431no—
320#2324—431no—
321#2077—431no—
322#2076—431no—
323#2033—431no—
324#2033—431no—
325#1989—431no—
326#1947—431no—
327#1943—431no—
328#1942—431no—
329#1936—431no—
330#1934—431no—
331#1802—431no—
332C2×C43—81no—
333C2×C43#241511yescharacteristic
334C2×C43#306111yescharacteristic
335C2×C43#306211yescharacteristic
336C2×C43#312011yescharacteristic
337C2×C43#312211yescharacteristic
338C2×C43#324111yescharacteristic
339C2×C43#324311yescharacteristic
340D43—82no—
341C2×#125—431no—
342C2×#121—431no—
343C2×C4×D4—431no—
344C2×#117C2×D4311yescharacteristic
345#478—864no—
346#433—24no—
347C2×#107—431no—
348C2×#107—431no—
349C2×#107—431no—
350C2×#106—431no—
351C2×C4⋊C8C2×D4311yescharacteristic
352C2×C4⋊C8C2×D4311yescharacteristic
353C2×#102—431no—
354C2×#102—431no—
355C2×#102—431no—
356C2×#102—431no—
357C2×C22⋊C8C2×D4311yescharacteristic
358C2×C22⋊C8C2×D4311yescharacteristic
359C2×#97C2×D4311yescharacteristic
360C2×C4×C8C2×D4311yescharacteristic
361#398—861no—
362#398—861no—
363#396—861no—
364#396—861no—
365#390—431no—
366#390—861no—
367#389—431no—
368#389—431no—
369#389—431no—
370#388—861no—
371#386—861no—
372#385—861no—
373#384—431no—
374#380—431no—
375#380—431no—
376#380—431no—
377C4×C4⋊C4—431no—
378#340—431no—
379#340—431no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340—431no—
384#340—431no—
385#340—431no—
386C43#2471311yescharacteristic, complemented, Sylow
387C22×D4—431no—
388C22×D4—861no—
389C23×C4—861no—
390C23×C4C22×D4311yescharacteristic
391C22×C8C22×D4311yescharacteristic
392C22×C8C22×D4311yescharacteristic
393C22×C8C22×D4311yescharacteristic
394C22×C8C22×D4311yescharacteristic
395#125—862no—
396#125—862no—
397#121—862no—
398#121—862no—
399C4×D4—862no—
400C4×D4—862no—
401#117—22no—
402#117—22no—
403C2×C4⋊C4—431no—
404C2×C4⋊C4—431no—
405C2×C4⋊C4—431no—
406C2×C4⋊C4—431no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—861no—
411C2×C4⋊C4—861no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4D17211yescharacteristic
418C2×C4⋊C4D17211yescharacteristic
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⋊C4—861no—
426C2×C22⋊C4D17211yescharacteristic
427C2×C22⋊C4D17211yescharacteristic
428C2×C42—861no—
429C2×C42C22×D4311yescharacteristic
430C2×C42C22×D4311yescharacteristic
431#107—862no—
432#107—862no—
433#107—862no—
434#106—862no—
435C4⋊C8—22no—
436C4⋊C8C22⋊D4314yescomplemented
437#102—862no—
438#102—862no—
439#102—862no—
440#102—862no—
441C22⋊C8—22no—
442C22⋊C8—22no—
443#97—22no—
444C4×C8—22no—
445#95—861no—
446#95—861no—
447#95—861no—
448#95—861no—
449#95—861no—
450#95—861no—
451#95—861no—
452C24—861no—
453C24C2×D17211yescharacteristic
454C2×D4—432no—
455C2×D4—864no—
456C2×D4—861no—
457C2×D4—861no—
458C2×D4—861no—
459C2×D4—861no—
460C2×D4—861no—
461C2×D4—3441no—
462C2×D4—3441no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—3441no—
477C22×C4—3441no—
478C22×C4—1722no—
479C22×C4C2×D17211yescharacteristic
480C22×C4C2×D17211yescharacteristic
481C22×C4C2×D17211yescharacteristic
482C22×C4C2×D17211yescharacteristic
483C22×C4C2×D17211yescharacteristic
484C22×C4C23×D4311yescharacteristic
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8C2×C22⋊D4312yes—
496C2×C8C2×C22⋊D4312yes—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—432no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
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—3441no—
514C4⋊C4—3441no—
515C4⋊C4—3441no—
516C4⋊C4—3441no—
517C4⋊C4—3441no—
518C4⋊C4—1722no—
519C4⋊C4—1722no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—864no—
523C22⋊C4—3441no—
524C22⋊C4—3441no—
525C22⋊C4—3441no—
526C22⋊C4—3441no—
527C22⋊C4—3441no—
528C22⋊C4—1722no—
529C42—21no—
530C42—21no—
531C42—3441no—
532C42#1062189812yes—
533C42C2×C22⋊D4312yes—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—862no—
542C23—1721no—
543C23—1721no—
544C23—1721no—
545C23—1721no—
546C23—1721no—
547C23—1721no—
548C23C22×D17211yescharacteristic
549D4—862no—
550D4—862no—
551D4—3444no—
552D4—1721no—
553D4—1721no—
554C2×C4—21no—
555C2×C4—21no—
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—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—862no—
572C2×C4—3444no—
573C2×C4—1721no—
574C2×C4—1721no—
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#1306329912yes—
594C2×C4#1306329912yes—
595C2×C4C22×C22⋊D4311yescharacteristic
596C2×C4#41×D4311yescharacteristic
597C2×C4#41×D4311yescharacteristic
598C2×C4C2×#1062189811yescharacteristic
599C2×C4#1306337211yescharacteristic
600C2×C4#1306337211yescharacteristic
601C8—22no—
602C8—22no—
603C8—41no—
604C8—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—3441no—
613C22—3441no—
614C22—3441no—
615C22—3441no—
616C22—1722no—
617C22—1722no—
618C22—1722no—
619C22C2×#1306329911yescharacteristic
620C22#1458341111yescharacteristic
621C22#1458347511yescharacteristic
622C22#1458370411yescharacteristic
623C22#1458370411yescharacteristic
624C22#1458371111yescharacteristic
625C22#1458371611yescharacteristic
626C4—22no—
627C4—22no—
628C4—41no—
629C4—41no—
630C4—41no—
631C4—3441no—
632C4—3441no—
633C4—3441no—
634C4—3441no—
635C4—3441no—
636C4—3441no—
637C4—1722no—
638C4#1458354811yescharacteristic
639C4#1458355611yescharacteristic
640C4#1458358811yescharacteristic
641C4#1458361711yescharacteristic
642C2—81no—
643C2—3442no—
644C2#1913801811yescharacteristic
645C2#1914426511yescharacteristic
646C2#1914427511yescharacteristic
647C2#1914481111yescharacteristic
648C2#1914483911yescharacteristic
649C2#1914585011yescharacteristic
650C2#1914588011yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#433C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenterC2×#433D43
hypocenterC43#24713
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×#14583200C2semidirect
2. #19140425C2semidirect
4. #19136028C2semidirect
5. #19136023C2semidirect
8. #19135550C2semidirect
9. #19135354C2semidirect
10. #19135333C2semidirect
11. #19135328C2semidirect
12. #19135292C2semidirect
13. #19135278C2semidirect
14. #19134596C2semidirect
15. C2×C43×#433C2semidirect
121. C4⋊C8×C43D4semidirect
318. C2×#433D43semidirect
386. C43#24713semidirect
436. C4⋊C8C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145832002
#191404252
#191372882
#191360282
#191360232
#191357782
#191355502
#191353542
#191353332
#191353282
#191352922
#191352782
#191345962
C2×C43×#4332
#2471343