Finite Group Databasebeta

← #25169298

Subgroups — #25169298

Order 11008.

784 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138991C211yesmaximal, characteristic, complemented
2#19137611C211yesmaximal, characteristic
3#19136012C211yesmaximal, characteristic, complemented
4#19135984C211yesmaximal, characteristic, complemented
5#19135785C211yesmaximal, characteristic
6#19135777C211yesmaximal, characteristic
7#19135362C211yesmaximal, characteristic, complemented
8#19135327C211yesmaximal, characteristic, complemented
9#19135198C211yesmaximal, characteristic, complemented
10#19135185C211yesmaximal, characteristic, complemented
11#19135172C211yesmaximal, characteristic, complemented
12#19134843C211yesmaximal, characteristic, complemented
13#19134783C211yesmaximal, characteristic, complemented
14#19134409C211yesmaximal, characteristic, complemented
15C43×#1824C211yesmaximal, characteristic, complemented
16C2×#13063299C2211yescharacteristic
17C2×#13063287C2211yescharacteristic
18C2×C4×C22⋊D43—21no—
19C2×#13063258C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×Dic43⋊C8C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×C22⋊(C43⋊C8)C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30C43⋊#401—21no—
31#14582827—21no—
32#14582800C2211yescharacteristic
33#14582798C2211yescharacteristic
34#14582795C2211yescharacteristic
35#14582795C2211yescharacteristic
36#14582792—21no—
37#14582789—21no—
38#14582784—21no—
39#14582778—21no—
40#14582770—21no—
41#14582764C2211yescharacteristic
42#14582759C2211yescharacteristic
43C4⋊C4×Dic43C2211yescharacteristic
44C4⋊C4×Dic43C2211yescharacteristic
45C4×C22⋊Dic43C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C22×C4⋊C4×C43C2211yescharacteristic
53C2×C22⋊C8×C43C2211yescharacteristic
54C43×#380C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×D172C2311yescharacteristic
60C22×C22⋊D43—21no—
61C22×C4×D43—21no—
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64#13063299—22no—
65#13063299—22no—
66#13063287—22no—
67#13063287—41no—
68C4×C22⋊D43—44no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×C22⋊Dic43—21no—
76C2×C22⋊Dic43D411yescharacteristic
77C2×C22⋊Dic43D411yescharacteristic
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43C2311yescharacteristic
85C2×C4×Dic43C2311yescharacteristic
86#13063258—22no—
87#13063258—22no—
88#13063258—41no—
89#13063257—22no—
90Dic43⋊C8—22no—
91#13063247—22no—
92#13063247—41no—
93#13063245—22no—
94#13063245—22no—
95C22⋊(C43⋊C8)—22no—
96C8×Dic43—41no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95D411yescharacteristic
106C43⋊#95D411yescharacteristic
107C23×C4×C43—21no—
108C23×C4×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C2×C4⋊C4×C43—22no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43—41no—
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C22⋊C4×C43—21no—
119C22⋊C8×C43—41no—
120#95×C43—21no—
121C24×C43C2×D411yescharacteristic
122C23×D43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
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—42no—
134C22×C4×C43—42no—
135C22×C4×C43—81no—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2411yescharacteristic
138C2×C22⋊D43—24no—
139C2×C22⋊D43—42no—
140C2×C22⋊D43—42no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C2×D172—21no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172#4112yes—
154C2×C4×D43—42no—
155C2×C4×D43—42no—
156C2×C4×D43—81no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C4⋊C4×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×C43—42no—
171C4⋊C4×C43#4112yes—
172C22⋊C4×C43—42no—
173C22⋊Dic43—22no—
174C22⋊Dic43—22no—
175C22⋊Dic43—81no—
176(C2×D43)⋊C4—24no—
177(C2×D43)⋊C4—42no—
178(C2×D43)⋊C4—42no—
179(C2×D43)⋊C4—81no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—42no—
186C4⋊Dic43#4112yes—
187Dic43⋊C4—42no—
188Dic43⋊C4—81no—
189C4×Dic43—21no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—42no—
194C4×Dic43—81no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8#4112yes—
201C23×C43—21no—
202C23×C43—21no—
203C23×C43—21no—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43#13512yes—
208C23×C43C22×D411yescharacteristic
209C22×D43—22no—
210C22×D43—41no—
211C22×D43—41no—
212C22×D43—41no—
213C22×D43—41no—
214C22×D43—41no—
215C22×D43—41no—
216C2×C4×C43—21no—
217C2×C4×C43—22no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—41no—
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×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—84no—
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43H(5,𝔽2)11yescharacteristic
241C2×C4×C432−1+411yescharacteristic
242C22⋊D43—48no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—22no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
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×Dic43AGL(1,ℤ/8)12yes—
264D172—22no—
265D172—22no—
266D172—41no—
267D172—41no—
268C4×D43—84no—
269C8×C43—41no—
270C8×C43—41no—
271C43⋊C8—22no—
272C43⋊C8—41no—
273#27033—431nomaximal, Sylow
274C22×C43—22no—
275C22×C43—22no—
276C22×C43—22no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43#52511yescharacteristic
282C22×C43#54611yescharacteristic
283C22×C43#54711yescharacteristic
284C22×C43C2×#13511yescharacteristic
285C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
286C22×C43#57611yescharacteristic
287C22×C43#57811yescharacteristic
288C2×D43—42no—
289C2×D43—42no—
290C2×D43—42no—
291C2×D43—81no—
292C2×D43—81no—
293C2×D43—81no—
294C2×D43—81no—
295C4×C43—41no—
296C4×C43—42no—
297C4×C43—81no—
298C4×C43—81no—
299C4×C43—81no—
300C4×C43#52911yescharacteristic
301C4×C43#53911yescharacteristic
302C4×C43#55311yescharacteristic
303C4×C43#55611yescharacteristic
304Dic43—22no—
305Dic43—41no—
306Dic43—41no—
307Dic43—42no—
308Dic43—41no—
309Dic43—81no—
310Dic43—81no—
311#2494—431no—
312#2361—431no—
313#2073—431no—
314#2067—431no—
315#2034—431no—
316#2033—431no—
317#1949—431no—
318#1942—431no—
319#1923—431no—
320#1921—431no—
321#1919—431no—
322#1862—431no—
323#1852—431no—
324#1824D4311yescharacteristic, complemented
325C4×#102—431no—
326C2×C43—42no—
327C2×C43#246611yescharacteristic
328C2×C43#310511yescharacteristic
329C2×C43#312411yescharacteristic
330C2×C43#330011yescharacteristic
331C2×C43#331811yescharacteristic
332C2×C43#333911yescharacteristic
333C2×C43#335311yescharacteristic
334D43—82no—
335C2×#121—431no—
336C2×C4×D4—431no—
337C2×C4×D4—861no—
338C22×C4⋊C4C2×D4311yescharacteristic
339C2×#107—431no—
340C2×#107—431no—
341C2×#107—431no—
342C2×#106—431no—
343C2×C4⋊C8—431no—
344C2×#102—431no—
345C2×#102—431no—
346C2×#102—431no—
347C2×#102—431no—
348C2×C22⋊C8—431no—
349C2×C22⋊C8C2×D4311yescharacteristic
350C2×C4×C8—431no—
351#401—861no—
352#397—861no—
353#390—431no—
354#389—431no—
355#389—431no—
356#389—431no—
357#388—861no—
358#388—861no—
359#387—861no—
360#386—861no—
361#385—861no—
362#382—431no—
363#380—431no—
364#380C2×D4311yescharacteristic
365C4×C4⋊C4—431no—
366C4×C4⋊C4—431no—
367C4×C22⋊C4—431no—
368#340—431no—
369#340—431no—
370#340—431no—
371#340—431no—
372#340C2×D4311yescharacteristic
373#340C2×D4311yescharacteristic
374#340C2×D4311yescharacteristic
375#340C2×D4311yescharacteristic
376#336—431no—
377#336—431no—
378C43#2703311yescharacteristic, complemented, Sylow
379C22×D4—431no—
380C22×D4—861no—
381C23×C4—21no—
382C23×C4—861no—
383C23×C4C22×D4311yescharacteristic
384C22×C8—431no—
385C22×C8—431no—
386C22×C8C22×D4311yescharacteristic
387C22×C8C22×D4311yescharacteristic
388#121—862no—
389#121—862no—
390C4×D4—862no—
391C4×D4—1721no—
392C4×D4—1724no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—41no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C4⋊C4C22×D4311yescharacteristic
404C2×C4⋊C4C22×D4311yescharacteristic
405C2×C4⋊C4C22×D4311yescharacteristic
406C2×C22⋊C4—21no—
407C2×C22⋊C4—431no—
408C2×C22⋊C4—431no—
409C2×C22⋊C4—861no—
410C2×C22⋊C4—861no—
411C2×C22⋊C4—861no—
412C2×C22⋊C4—861no—
413C2×C22⋊C4—861no—
414C2×C42—431no—
415C2×C42—431no—
416C2×C42—861no—
417C2×C42—861no—
418#107—862no—
419#107—862no—
420#107—1721no—
421#106—862no—
422C4⋊C8—862no—
423#102—862no—
424#102—862no—
425#102—862no—
426#102—1721no—
427C22⋊C8—41no—
428C22⋊C8—862no—
429C4×C8—1721no—
430#95—21no—
431#95—431no—
432#95—431no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438#95—861no—
439#95—861no—
440#95—861no—
441C24—861no—
442C24D4×D4311yescharacteristic
443C2×D4—432no—
444C2×D4—864no—
445C2×D4—861no—
446C2×D4—861no—
447C2×D4—861no—
448C2×D4—861no—
449C2×D4—861no—
450C2×D4—1722no—
451C2×D4—1722no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—81no—
465C22×C4—431no—
466C22×C4—431no—
467C22×C4—431no—
468C22×C4—431no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—3441no—
473C22×C4—1722no—
474C22×C4—1722no—
475C22×C4D4×D4311yescharacteristic
476C22×C4C23×D4311yescharacteristic
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—432no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—861no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—42no—
497C4⋊C4—432no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—3441no—
504C4⋊C4—1722no—
505C4⋊C4—1722no—
506C4⋊C4#1062189812yes—
507C22⋊C4—42no—
508C22⋊C4—864no—
509C22⋊C4—862no—
510C22⋊C4—862no—
511C22⋊C4—3441no—
512C22⋊C4—3441no—
513C22⋊C4—1722no—
514C22⋊C4—1722no—
515C42—861no—
516C42—861no—
517C42—861no—
518C42—861no—
519C42—3441no—
520C42—1722no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—862no—
528C23—1721no—
529C23—1721no—
530C23—1721no—
531C23—1721no—
532C23—1721no—
533C23—1721no—
534C23#1306334612yes—
535C23C2×D4×D4311yescharacteristic
536D4—862no—
537D4—862no—
538D4—1728no—
539D4—1721no—
540D4—1721no—
541C2×C4—21no—
542C2×C4—22no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—84no—
561C2×C4—432no—
562C2×C4—861no—
563C2×C4—861no—
564C2×C4—862no—
565C2×C4—861no—
566C2×C4—861no—
567C2×C4—861no—
568C2×C4—861no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—861no—
572C2×C4—861no—
573C2×C4—861no—
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#41×D4311yescharacteristic
584C2×C4#41×D4311yescharacteristic
585C2×C4#41×D4311yescharacteristic
586C2×C4C2×#1062189811yescharacteristic
587C2×C4#1306337011yescharacteristic
588C2×C4#1306337211yescharacteristic
589C8—41no—
590C8—41no—
591C8—862no—
592C8—1721no—
593C22—22no—
594C22—22no—
595C22—22no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—3441no—
601C22—3441no—
602C22—3441no—
603C22—3441no—
604C22—1722no—
605C22—1722no—
606C22—1722no—
607C22#1458340711yescharacteristic
608C22#1458353911yescharacteristic
609C22#1458354711yescharacteristic
610C22C2×#1306334611yescharacteristic
611C22AGL(1,ℤ/8)×D4311yescharacteristic
612C22#1458370311yescharacteristic
613C22#1458371211yescharacteristic
614C4—41no—
615C4—42no—
616C4—81no—
617C4—81no—
618C4—81no—
619C4—862no—
620C4—3441no—
621C4—3441no—
622C4—1721no—
623C4—1722no—
624C4—1721no—
625C4—1721no—
626C4#1458342711yescharacteristic
627C4#1458349211yescharacteristic
628C4#1458359411yescharacteristic
629C4#1458361711yescharacteristic
630C2—42no—
631C2—3442no—
632C2#1913863011yescharacteristic
633C2#1914463911yescharacteristic
634C2#1914486011yescharacteristic
635C2#1914647811yescharacteristic
636C2#1914673711yescharacteristic
637C2#1914699511yescharacteristic
638C2#1914717211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1824C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenter#1824D43
hypocenterC43#27033
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1824

Complements

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

NH ≅ G/Ntype
1. #19138991C2semidirect
3. #19136012C2semidirect
4. #19135984C2semidirect
7. #19135362C2semidirect
8. #19135327C2semidirect
9. #19135198C2semidirect
10. #19135185C2semidirect
11. #19135172C2semidirect
12. #19134843C2semidirect
13. #19134783C2semidirect
14. #19134409C2semidirect
15. C43×#1824C2semidirect
324. #1824D43semidirect
378. C43#27033semidirect

Maximal subgroups

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

subgroupindex
#191389912
#191376112
#191360122
#191359842
#191357852
#191357772
#191353622
#191353272
#191351982
#191351852
#191351722
#191348432
#191347832
#191344092
C43×#18242
#2703343