Finite Group Databasebeta

← #25116364

Subgroups — #25116364

Order 11008.

862 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582979C211yesmaximal, characteristic
2#19137567C211yesmaximal, characteristic, complemented
3#19137564C211yesmaximal, characteristic, complemented
4#19135460C211yesmaximal, characteristic
5#19135458C211yesmaximal, characteristic
6#19135224C211yesmaximal, characteristic, complemented
7#19135223C211yesmaximal, characteristic, complemented
8#19135221C211yesmaximal, characteristic, complemented
9#19134756C211yesmaximal, characteristic, complemented
10#19134604C211yesmaximal, characteristic, complemented
11#19134603C211yesmaximal, characteristic, complemented
12C4×#13063258C211yesmaximal, characteristic, complemented
13#19134487C211yesmaximal, characteristic, complemented
14#19134456C211yesmaximal, characteristic, complemented
15C43×#1926C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C2×#13063287C2211yescharacteristic
19#14582979C418yescomplemented
20C2×#13063258C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×C4×C43⋊C8C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31C2×C8×Dic43C2211yescharacteristic
32#14582802C2211yescharacteristic
33#14582801C2211yescharacteristic
34#14582800C2211yescharacteristic
35#14582793—21no—
36#14582790—21no—
37#14582788—21no—
38#14582787—21no—
39#14582764C2211yescharacteristic
40#14582764C2211yescharacteristic
41#14582761—21no—
42#14582760—21no—
43C4⋊C4×Dic43C2211yescharacteristic
44C4⋊C4×Dic43C2211yescharacteristic
45C4×Dic43⋊C4C2211yescharacteristic
46C4×C4⋊Dic43C2211yescharacteristic
47C22⋊C4×Dic43—21no—
48C4×(C2×D43)⋊C4—21no—
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×#106×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C22×D172C2311yescharacteristic
61C23×Dic43—21no—
62C22×C4×D43—21no—
63C2×#10621882—22no—
64C2×#10621882—22no—
65C2×#10621882C2×C414yes—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68D4×Dic43—22no—
69D4×Dic43C2×C414yes—
70#13063287—22no—
71#13063287C2×C414yes—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4D411yescharacteristic
76C2×Dic43⋊C4D411yescharacteristic
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43C2311yescharacteristic
89C2×C4×Dic43C2311yescharacteristic
90#13063258—22no—
91#13063258—22no—
92#13063258C2×C414yes—
93#13063257—41no—
94Dic43⋊C8—22no—
95#13063247—41no—
96#13063247C2×C414yes—
97#13063246—41no—
98#13063245—41no—
99C4×C43⋊C8—22no—
100C8×Dic43—22no—
101C8×Dic43C2×C414yes—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95D411yescharacteristic
110C43⋊#95D411yescharacteristic
111C22×D4×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C22⋊C4×C43—21no—
118C2×C22⋊C4×C43—21no—
119C2×C42×C43—21no—
120C2×C42×C43C2311yescharacteristic
121#106×C43—41no—
122#102×C43—41no—
123#102×C43C2×C414yes—
124#95×C43—21no—
125C24×C43—21no—
126C23×D43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43C22×C412yes—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2411yescharacteristic
139C22×Dic43—24no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—81no—
144C22×Dic43—81no—
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172C22×C412yes—
155C2×C4×D43—24no—
156C2×C4×D43—81no—
157C2×C4×D43—81no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43C22×C412yes—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43C22×C412yes—
170C22⋊C4×C43—42no—
171C22⋊C4×C43—81no—
172C42×C43—21no—
173C42×C43—21no—
174C42×C43—81no—
175C22⋊Dic43—24no—
176C22⋊Dic43—42no—
177C22⋊Dic43—81no—
178#10621882—28no—
179(C2×D43)⋊C4—24no—
180(C2×D43)⋊C4—42no—
181(C2×D43)⋊C4—42no—
182(C2×D43)⋊C4—81no—
183(C2×D43)⋊C4—81no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43C22×C412yes—
190Dic43⋊C4—22no—
191Dic43⋊C4—22no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—81no—
195C4×Dic43—81no—
196C4×Dic43—81no—
197C4×Dic43C22×C412yes—
198C4×Dic43#4112yes—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8C22×C412yes—
203C2×C43⋊C8#4112yes—
204C2×C43⋊C8#4112yes—
205C23×C43—22no—
206C23×C43—41no—
207C23×C43—41no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43C22×D411yescharacteristic
213C22×D43—22no—
214C22×D43—41no—
215C22×D43—41no—
216C22×D43—41no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220D4×C43—22no—
221D4×C43—22no—
222D4×C43—41no—
223D4×C43—41no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—22no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
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#13512yes—
239C2×C4×C43C23×C411yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43H(5,𝔽2)11yescharacteristic
244C2×C4×C432−1+411yescharacteristic
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—22no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
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—84no—
264C2×Dic43C4×D412yes—
265C2×Dic43C4×D412yes—
266C2×Dic43#13512yes—
267D172—22no—
268D172—22no—
269D172—41no—
270D172—41no—
271C4×D43—84no—
272C8×C43—22no—
273C8×C43—41no—
274C43⋊C8—41no—
275C43⋊C8#11714yes—
276#22810—431nomaximal, Sylow
277C22×C43—42no—
278C22×C43—42no—
279C22×C43—42no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43—81no—
283C22×C43—81no—
284C22×C43C2×C4×D411yescharacteristic
285C22×C43#54711yescharacteristic
286C22×C43#55011yescharacteristic
287C22×C43C2×#13511yescharacteristic
288C22×C43C2×#13511yescharacteristic
289C22×C43#57611yescharacteristic
290C22×C43#57611yescharacteristic
291C2×D43—42no—
292C2×D43—42no—
293C2×D43—42no—
294C2×D43—81no—
295C2×D43—81no—
296C2×D43—81no—
297C2×D43—81no—
298C4×C43—22no—
299C4×C43—41no—
300C4×C43—42no—
301C4×C43—81no—
302C4×C43—81no—
303C4×C43C2×#11711yescharacteristic
304C4×C43#52011yescharacteristic
305C4×C43#55511yescharacteristic
306C4×C43#55611yescharacteristic
307Dic43—22no—
308Dic43—22no—
309Dic43—22no—
310Dic43—41no—
311Dic43—42no—
312Dic43—81no—
313Dic43—81no—
314C2×C4×D8—431no—
315#2357—431no—
316#2357—431no—
317#1970—431no—
318#1970—431no—
319#1926—431no—
320#1926—431no—
321#1926—431no—
322#1926D4311yescharacteristic, complemented
323#1846—431no—
324#1804—431no—
325#1804—431no—
326C4×#107—431no—
327C4×#107—431no—
328C8×C4⋊C4—431no—
329C2×C43—82no—
330C2×C43#235411yescharacteristic
331C2×C43C4×#13511yescharacteristic
332C2×C43#294811yescharacteristic
333C2×C43#333911yescharacteristic
334C2×C43#333911yescharacteristic
335C2×C43#339611yescharacteristic
336C2×C43#339611yescharacteristic
337D43—82no—
338C22×D8—431no—
339C2×C4×D4—431no—
340C2×C4×D4—431no—
341C4×D8—438no—
342C2×#107—431no—
343C2×#107—431no—
344C2×#107—431no—
345C2×#106—431no—
346C2×#106C2×D4311yescharacteristic
347C2×C4⋊C8—431no—
348C2×#102—431no—
349C2×#102—431no—
350C2×#102—431no—
351C2×#102—431no—
352C2×#102C2×D4311yescharacteristic
353C2×#102C2×D4311yescharacteristic
354C2×C4×C8—431no—
355C2×C4×C8—431no—
356C2×C4×C8—431no—
357#390—431no—
358#390—431no—
359#390—431no—
360#390C2×D4311yescharacteristic
361#388—861no—
362#388—861no—
363#388—861no—
364#388—861no—
365#382—431no—
366#382—431no—
367#381—861no—
368#381—861no—
369C4×C4⋊C4—431no—
370C4×C4⋊C4—431no—
371C4×C4⋊C4—431no—
372C4×C4⋊C4—431no—
373C4×C4⋊C4C2×D4311yescharacteristic
374C4×C22⋊C4—861no—
375C4×C22⋊C4—861no—
376#340—431no—
377#340—431no—
378#340—431no—
379#340C2×D4311yescharacteristic
380#336—431no—
381#336C2×D4311yescharacteristic
382C43#2281011yescharacteristic, complemented, Sylow
383C22×D4—431no—
384C22×D4C22×D4311yescharacteristic
385C23×C4—861no—
386C23×C4—861no—
387C2×D8—434no—
388C2×D8—862no—
389C2×D8—862no—
390C22×C8—431no—
391C22×C8—431no—
392C22×C8C22×D4311yescharacteristic
393C22×C8C22×D4311yescharacteristic
394C4×D4—434no—
395C4×D4—434no—
396C4×D4—862no—
397C4×D4—862no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—431no—
400C2×C4⋊C4—431no—
401C2×C4⋊C4—431no—
402C2×C4⋊C4—431no—
403C2×C4⋊C4C22×D4311yescharacteristic
404C2×C4⋊C4C22×D4311yescharacteristic
405C2×C4⋊C4C22×D4311yescharacteristic
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—861no—
409C2×C22⋊C4—861no—
410C2×C22⋊C4—861no—
411C2×C22⋊C4—861no—
412C2×C22⋊C4—861no—
413C2×C22⋊C4—861no—
414C2×C22⋊C4—861no—
415C2×C22⋊C4—861no—
416C2×C42—21no—
417C2×C42—431no—
418C2×C42—431no—
419C2×C42—861no—
420C2×C42—861no—
421C2×C42—861no—
422C2×C42C22×D4311yescharacteristic
423#107—434no—
424#107—862no—
425#107—862no—
426#106—41no—
427#106—1721no—
428C4⋊C8—862no—
429#102—41no—
430#102—434no—
431#102—1721no—
432#102—1721no—
433#102—1721no—
434#102C4×D4314yes—
435C4×C8—434no—
436C4×C8—862no—
437C4×C8—862no—
438#95—21no—
439#95—431no—
440#95—431no—
441#95—861no—
442#95—861no—
443#95—861no—
444#95—861no—
445#95—861no—
446#95—861no—
447#95—861no—
448C24—21no—
449C24—861no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—432no—
456C2×D4—861no—
457C2×D4—861no—
458C2×D4—861no—
459C2×D4—861no—
460C2×D4—861no—
461C2×D4C2×C4×D4312yes—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—431no—
466C22×C4—431no—
467C22×C4—431no—
468C22×C4—431no—
469C22×C4—864no—
470C22×C4—864no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—3441no—
475C22×C4—3441no—
476C22×C4—3441no—
477C22×C4—3441no—
478C22×C4D4×D4311yescharacteristic
479C22×C4D4×D4311yescharacteristic
480C22×C4C23×D4311yescharacteristic
481D8—868no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—432no—
488C2×C8—432no—
489C2×C8—432no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8C2×C4×D4312yes—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—432no—
500C4⋊C4—862no—
501C4⋊C4—862no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4C2×C4×D4312yes—
508C22⋊C4—42no—
509C22⋊C4—81no—
510C22⋊C4—864no—
511C22⋊C4—864no—
512C22⋊C4—3441no—
513C22⋊C4—3441no—
514C22⋊C4—3441no—
515C22⋊C4—1722no—
516C22⋊C4—1722no—
517C22⋊C4—1722no—
518C42—21no—
519C42—21no—
520C42—81no—
521C42—432no—
522C42—432no—
523C42—861no—
524C42—861no—
525C42—3441no—
526C42—3441no—
527C42—3441no—
528C23—22no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—862no—
536C23—1721no—
537C23—1721no—
538C23—1721no—
539C23—1721no—
540C23—1721no—
541C23—1721no—
542C23C2×D4×D4311yescharacteristic
543D4—22no—
544D4—22no—
545D4—41no—
546D4—41no—
547D4—862no—
548D4—862no—
549D4—1721no—
550D4—1721no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—432no—
566C2×C4—432no—
567C2×C4—432no—
568C2×C4—861no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—861no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—862no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—3444no—
579C2×C4—3444no—
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#1306334612yes—
589C2×C4C22×C4×D4311yescharacteristic
590C2×C4#41×D4311yescharacteristic
591C2×C4#41×D4311yescharacteristic
592C2×C4#41×D4311yescharacteristic
593C2×C4#1306337011yescharacteristic
594C2×C4#1306337211yescharacteristic
595C8—22no—
596C8—41no—
597C8—434no—
598C8—1721no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—3441no—
607C22—3441no—
608C22—3441no—
609C22—3441no—
610C22—1722no—
611C22—1722no—
612C22—1722no—
613C22C4×D4×D4311yescharacteristic
614C22#1458354711yescharacteristic
615C22#1458356711yescharacteristic
616C22#135×D4311yescharacteristic
617C22C2×#1306334611yescharacteristic
618C22#1458370311yescharacteristic
619C22#1458370311yescharacteristic
620C4—22no—
621C4—42no—
622C4—41no—
623C4—81no—
624C4—81no—
625C4—862no—
626C4—862no—
627C4—862no—
628C4—3441no—
629C4—3441no—
630C4—1722no—
631C4—1721no—
632C4#117×D4311yescharacteristic
633C4#1458337811yescharacteristic
634C4#1458361111yescharacteristic
635C4#1458361611yescharacteristic
636C2—82no—
637C2—3442no—
638C2#1913754111yescharacteristic
639C2C4×#1306334611yescharacteristic
640C2#1914344411yescharacteristic
641C2#1914699011yescharacteristic
642C2#1914699511yescharacteristic
643C2#1914760211yescharacteristic
644C2#1914760611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1926C2
socleC23×C43C22×D4
prime radicalC22×#10621882C22
cosocleC22×C4×C43C24
hypercenter#1926D43
hypocenterC43#22810
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1926

Complements

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

NH ≅ G/Ntype
2. #19137567C2semidirect
3. #19137564C2semidirect
6. #19135224C2semidirect
7. #19135223C2semidirect
8. #19135221C2semidirect
9. #19134756C2semidirect
10. #19134604C2semidirect
11. #19134603C2semidirect
12. C4×#13063258C2semidirect
13. #19134487C2semidirect
14. #19134456C2semidirect
15. C43×#1926C2semidirect
19. #14582979C4semidirect
322. #1926D43semidirect
382. C43#22810semidirect

Maximal subgroups

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

subgroupindex
C2×#145829792
#191375672
#191375642
#191354602
#191354582
#191352242
#191352232
#191352212
#191347562
#191346042
#191346032
C4×#130632582
#191344872
#191344562
C43×#19262
#2281043