Finite Group Databasebeta

← #25199854

Subgroups — #25199854

Order 11008.

788 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142963C211yesmaximal, characteristic, complemented
2#19137056C211yesmaximal, characteristic, complemented
3#19136094C211yesmaximal, characteristic, complemented
4#19135984C211yesmaximal, characteristic, complemented
5#19135970C211yesmaximal, characteristic, complemented
6#19135907C211yesmaximal, characteristic
7#19135469C211yesmaximal, characteristic
8#19135332C211yesmaximal, characteristic, complemented
9#19135293C211yesmaximal, characteristic, complemented
10#19135290C211yesmaximal, characteristic, complemented
11#19135222C211yesmaximal, characteristic, complemented
12#19134942C211yesmaximal, characteristic
13#19134841C211yesmaximal, characteristic, complemented
14#19134447C211yesmaximal, characteristic, complemented
15C43×#1919C211yesmaximal, characteristic, complemented
16C22×D344C2211yescharacteristic
17C2×#13063320—21no—
18C2×C4×D172C2211yescharacteristic
19C2×#13063282—21no—
20C2×#13063258C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×Dic43⋊C8C2211yescharacteristic
23C2×Dic43⋊C8C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063235C2211yescharacteristic
31C2×#13063235C2211yescharacteristic
32#14582801C2211yescharacteristic
33#14582800C2211yescharacteristic
34#14582800C2211yescharacteristic
35#14582800C2211yescharacteristic
36#14582800C2211yescharacteristic
37#14582798C2211yescharacteristic
38#14582795C2211yescharacteristic
39#14582795C2211yescharacteristic
40#14582795C2211yescharacteristic
41#14582791—21no—
42#14582789—21no—
43#14582788—21no—
44#14582788—21no—
45#14582788—21no—
46C4×(C2×D43)⋊C4—21no—
47C42×Dic43C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52C2×#106×C43C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C4×C4⋊C4×C43C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×D172C2311yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C4×D43—21no—
62C2×D344—22no—
63C2×D344—22no—
64C2×D344—41no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063320—44no—
68C4×D172—22no—
69C4×D172—22no—
70#13063282—44no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—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×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×C4×Dic43D411yescharacteristic
89C2×C4×Dic43D411yescharacteristic
90C2×C4×Dic43D411yescharacteristic
91C2×C4×Dic43D411yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93C2×C4×Dic43C2311yescharacteristic
94#13063258—22no—
95#13063256—41no—
96Dic43⋊C8—22no—
97Dic43⋊C8—22no—
98#13063247—22no—
99#13063247—41no—
100#13063245—22no—
101#13063245—22no—
102#13063245—22no—
103#13063245—41no—
104#13063235—41no—
105#13063235—41no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C22×C8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C42×C43—21no—
118C2×C42×C43C2311yescharacteristic
119#106×C43—22no—
120#95×C43—21no—
121#95×C43—21no—
122C23×D43—21no—
123C23×D43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2411yescharacteristic
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43C2×D411yescharacteristic
134C22×Dic43C2×D411yescharacteristic
135C22×Dic43C2×D411yescharacteristic
136C22×Dic43C2×D411yescharacteristic
137C2×D172—21no—
138C2×D172—21no—
139C2×D172—21no—
140C2×D172—21no—
141C2×D172—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172—21no—
147C2×D172—21no—
148C2×D172#4112yes—
149C2×C4×D43—24no—
150C2×C4×D43—42no—
151C2×C4×D43—42no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43#4112yes—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—42no—
167C42×C43—21no—
168C42×C43—21no—
169C42×C43—42no—
170(C2×D43)⋊C4—24no—
171(C2×D43)⋊C4—42no—
172(C2×D43)⋊C4—42no—
173(C2×D43)⋊C4—42no—
174(C2×D43)⋊C4—42no—
175(C2×D43)⋊C4—42no—
176(C2×D43)⋊C4—42no—
177(C2×D43)⋊C4—42no—
178(C2×D43)⋊C4—42no—
179(C2×D43)⋊C4—42no—
180(C2×D43)⋊C4—42no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—42no—
185C4⋊Dic43#4112yes—
186Dic43⋊C4—42no—
187Dic43⋊C4—42no—
188Dic43⋊C4—42no—
189C4×Dic43—22no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—22no—
195C4×Dic43—41no—
196C4×Dic43—41no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8#4112yes—
203D344—44no—
204C23×C43C22×D411yescharacteristic
205C22×D43—22no—
206C22×D43—41no—
207C22×D43—41no—
208C22×D43—41no—
209C22×D43—41no—
210C22×D43—41no—
211C22×D43—41no—
212C22×D43—41no—
213C22×D43—41no—
214C22×D43—41no—
215C22×D43—41no—
216C22×D43—41no—
217C22×D43—41no—
218C22×D43—41no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
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—41no—
236C2×C4×C43AGL(1,ℤ/8)12yes—
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43H(5,𝔽2)11yescharacteristic
242C2×C4×C432−1+411yescharacteristic
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×Dic43AGL(1,ℤ/8)12yes—
261D172—22no—
262D172—22no—
263D172—41no—
264D172—41no—
265D172—41no—
266D172—41no—
267D172—41no—
268D172—41no—
269C4×D43—48no—
270C8×C43—22no—
271C8×C43—41no—
272C43⋊C8—22no—
273C43⋊C8—41no—
274#29444—431nomaximal, Sylow
275C22×C43#52511yescharacteristic
276C22×C43#53211yescharacteristic
277C22×C43#53711yescharacteristic
278C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
279C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
280C22×C43#57511yescharacteristic
281C22×C43#57511yescharacteristic
282C2×D43—42no—
283C2×D43—42no—
284C2×D43—42no—
285C2×D43—81no—
286C2×D43—81no—
287C2×D43—81no—
288C2×D43—81no—
289C2×D43—81no—
290C2×D43—81no—
291C2×D43—81no—
292C2×D43—81no—
293C2×D43—81no—
294C2×D43—81no—
295C2×D43—81no—
296C4×C43—22no—
297C4×C43—41no—
298C4×C43—81no—
299C4×C43—81no—
300C4×C43—81no—
301C4×C43—81no—
302C4×C43#55111yescharacteristic
303C4×C43#55211yescharacteristic
304C4×C43#55311yescharacteristic
305C4×C43#55611yescharacteristic
306Dic43—22no—
307Dic43—42no—
308Dic43—41no—
309Dic43—41no—
310Dic43—41no—
311Dic43—81no—
312#2860—431no—
313#2293—431no—
314#2088—431no—
315#2067—431no—
316#2065—431no—
317#2054—431no—
318#1972—431no—
319#1943—431no—
320#1936—431no—
321#1936—431no—
322#1926—431no—
323#1919D4311yescharacteristic, complemented
324#1879—431no—
325#1862—431no—
326#1767—431no—
327C2×C43#260111yescharacteristic
328C2×C43#310911yescharacteristic
329C2×C43#311111yescharacteristic
330C2×C43#317111yescharacteristic
331C2×C43#318011yescharacteristic
332C2×C43#325111yescharacteristic
333C2×C43#325111yescharacteristic
334D43—82no—
335D43—161no—
336C22×D8—431no—
337C2×#126—861no—
338C2×C4×D4—431no—
339C2×#117—861no—
340C2×#107—431no—
341C2×#106—431no—
342C2×#106C2×D4311yescharacteristic
343C2×C4⋊C8—431no—
344C2×C4⋊C8—431no—
345C2×#102—431no—
346C2×#102—431no—
347C2×#102—431no—
348C2×#102—431no—
349C2×#102—431no—
350C2×#102—431no—
351C2×#97—431no—
352C2×#97—431no—
353#390—431no—
354#390—431no—
355#390—431no—
356#390—431no—
357#390—431no—
358#389—431no—
359#389—431no—
360#389—431no—
361#389—431no—
362#389C2×D4311yescharacteristic
363#388—861no—
364#388—861no—
365#388—861no—
366#388—861no—
367#388—861no—
368C4×C4⋊C4C2×D4311yescharacteristic
369C4×C22⋊C4—861no—
370C43—431no—
371#340—431no—
372#340—431no—
373#340—431no—
374#340C2×D4311yescharacteristic
375#340C2×D4311yescharacteristic
376#340C2×D4311yescharacteristic
377#336—431no—
378#336C2×D4311yescharacteristic
379C43#2944411yescharacteristic, complemented, Sylow
380C22×D4—431no—
381C22×D4—431no—
382C23×C4—861no—
383C2×D8—862no—
384C2×D8—862no—
385C2×D8—1721no—
386C22×C8—431no—
387C22×C8—431no—
388C22×C8C22×D4311yescharacteristic
389C22×C8C22×D4311yescharacteristic
390#126—1724no—
391C4×D4—862no—
392C4×D4—862no—
393#117—1724no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4C22×D4311yescharacteristic
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C4⋊C4C22×D4311yescharacteristic
404C2×C4⋊C4C22×D4311yescharacteristic
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
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—431no—
420C2×C42—431no—
421C2×C42—431no—
422C2×C42—431no—
423C2×C42C22×D4311yescharacteristic
424#107—862no—
425#106—22no—
426#106—1721no—
427C4⋊C8—862no—
428C4⋊C8—862no—
429#102—862no—
430#102—862no—
431#102—862no—
432#102—862no—
433#102—1721no—
434#102—1721no—
435#97—1721no—
436#97—1721no—
437#95—21no—
438#95—21no—
439#95—861no—
440#95—861no—
441#95—861no—
442#95—861no—
443C24—861no—
444C24—861no—
445C2×D4—432no—
446C2×D4—861no—
447C2×D4—861no—
448C2×D4—861no—
449C2×D4—861no—
450C2×D4—861no—
451C2×D4—861no—
452C2×D4—861no—
453C2×D4—861no—
454C2×D4—861no—
455C2×D4—861no—
456C2×D4—861no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—431no—
462C22×C4—431no—
463C22×C4—431no—
464C22×C4—431no—
465C22×C4—864no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—1722no—
469C22×C4—1722no—
470C22×C4D4×D4311yescharacteristic
471C22×C4D4×D4311yescharacteristic
472C22×C4C23×D4311yescharacteristic
473D8—1724no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—432no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8#1062189812yes—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—42no—
495C4⋊C4—432no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—1722no—
500C4⋊C4—1722no—
501C4⋊C4—1722no—
502C4⋊C4—1722no—
503C22⋊C4—864no—
504C22⋊C4—1722no—
505C22⋊C4—1722no—
506C22⋊C4—1722no—
507C22⋊C4—1722no—
508C22⋊C4—1722no—
509C22⋊C4—1722no—
510C22⋊C4—1722no—
511C22⋊C4—1722no—
512C22⋊C4—1722no—
513C22⋊C4—1722no—
514C42—21no—
515C42—21no—
516C42—42no—
517C42—862no—
518C42—862no—
519C42—861no—
520C42—861no—
521C42—861no—
522C42—861no—
523C42—1721no—
524C42—1721no—
525C23—862no—
526C23—1721no—
527C23—1721no—
528C23—1721no—
529C23—1721no—
530C23—1721no—
531C23—1721no—
532C23—1721no—
533C23—1721no—
534C23—1721no—
535C23—1721no—
536C23—1721no—
537C23—1721no—
538C23—1721no—
539C23C2×D4×D4311yescharacteristic
540D4—862no—
541D4—862no—
542D4—1721no—
543D4—1721no—
544D4—1721no—
545D4—1721no—
546D4—1721no—
547D4—1721no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
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—861no—
567C2×C4—861no—
568C2×C4—862no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—861no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—1728no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4#1306335212yes—
585C2×C4#41×D4311yescharacteristic
586C2×C4#41×D4311yescharacteristic
587C2×C4#41×D4311yescharacteristic
588C2×C4C2×#1062189811yescharacteristic
589C2×C4#1306337111yescharacteristic
590C2×C4#1306337311yescharacteristic
591C8—22no—
592C8—41no—
593C8—862no—
594C8—1721no—
595C22—3441no—
596C22—3441no—
597C22—3441no—
598C22—3441no—
599C22—3441no—
600C22—3441no—
601C22—3441no—
602C22—3441no—
603C22—3441no—
604C22—3441no—
605C22—3441no—
606C22—1722no—
607C22—1722no—
608C22—1722no—
609C22#1458340711yescharacteristic
610C22#1458344611yescharacteristic
611C22#1458347911yescharacteristic
612C22AGL(1,ℤ/8)×D4311yescharacteristic
613C22C2×#1306335211yescharacteristic
614C22#1458369611yescharacteristic
615C22#1458369811yescharacteristic
616C4—22no—
617C4—41no—
618C4—81no—
619C4—81no—
620C4—81no—
621C4—81no—
622C4—862no—
623C4—3441no—
624C4—1721no—
625C4—1721no—
626C4—1721no—
627C4—1722no—
628C4#1458357311yescharacteristic
629C4#1458358111yescharacteristic
630C4#1458360011yescharacteristic
631C4#1458362111yescharacteristic
632C2—3442no—
633C2—6881no—
634C2#1914019011yescharacteristic
635C2#1914468311yescharacteristic
636C2#1914470711yescharacteristic
637C2#1914518611yescharacteristic
638C2#1914528911yescharacteristic
639C2#1914595611yescharacteristic
640C2#1914596011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1919C2
socleC23×C43C22×D4
prime radicalC22×D344C22
hypercenter#1919D43
hypocenterC43#29444
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1919

Complements

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

NH ≅ G/Ntype
1. #19142963C2semidirect
2. #19137056C2semidirect
3. #19136094C2semidirect
4. #19135984C2semidirect
5. #19135970C2semidirect
8. #19135332C2semidirect
9. #19135293C2semidirect
10. #19135290C2semidirect
11. #19135222C2semidirect
13. #19134841C2semidirect
14. #19134447C2semidirect
15. C43×#1919C2semidirect
323. #1919D43semidirect
379. C43#29444semidirect

Maximal subgroups

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

subgroupindex
#191429632
#191370562
#191360942
#191359842
#191359702
#191359072
#191354692
#191353322
#191352932
#191352902
#191352222
#191349422
#191348412
#191344472
C43×#19192
#2944443