Finite Group Databasebeta

← #25118684

Subgroups — #25118684

Order 11008.

692 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144383C211yesmaximal, characteristic
2#19143542C211yesmaximal, characteristic, complemented
3#19143163C211yesmaximal, characteristic
4#19135576C211yesmaximal, characteristic, complemented
5#19135370C211yesmaximal, characteristic, complemented
6#19135347C211yesmaximal, characteristic, complemented
7#19135342C211yesmaximal, characteristic, complemented
8#19135197C211yesmaximal, characteristic, complemented
9#19135197C211yesmaximal, characteristic, complemented
10#19134868C211yesmaximal, characteristic
11#19134868C211yesmaximal, characteristic
12#19134452C211yesmaximal, characteristic, complemented
13#19134440C211yesmaximal, characteristic
14#19134433C211yesmaximal, characteristic
15C43×#1759C211yesmaximal, characteristic
16C2×#13063332C2211yescharacteristic
17C2×#13063332C2211yescharacteristic
18#14583456C2211yescharacteristic
19#14583206C411yescharacteristic, complemented
20#14583206C411yescharacteristic, complemented
21#14583199C411yescharacteristic, complemented
22#14583199C411yescharacteristic, complemented
23#14583194C411yescharacteristic, complemented
24#14583189C411yescharacteristic, complemented
25#14583184C411yescharacteristic, complemented
26#14583179C411yescharacteristic, complemented
27#14583029—21no—
28#14583027—21no—
29#14583027—21no—
30C8×Dic86—21no—
31C2×#13063260C2211yescharacteristic
32C2×#13063260C2211yescharacteristic
33#14582935C2211yescharacteristic
34#14582935C2211yescharacteristic
35#14582927C2211yescharacteristic
36#14582927C2211yescharacteristic
37#14582926—21no—
38#14582926—21no—
39#14582926C2211yescharacteristic
40#14582926C2211yescharacteristic
41#14582923—21no—
42#14582923C2211yescharacteristic
43C2×C4⋊(C43⋊C8)—21no—
44C2×C4⋊(C43⋊C8)C2211yescharacteristic
45C2×C4⋊(C43⋊C8)C2211yescharacteristic
46#14582895C2211yescharacteristic
47#14582895C2211yescharacteristic
48#14582857C2211yescharacteristic
49#14582857C2211yescharacteristic
50C2×#13063236C2211yescharacteristic
51C2×C4×C43⋊C8C2211yescharacteristic
52#14582663C2211yescharacteristic
53#14582663C2211yescharacteristic
54#14582659C2211yescharacteristic
55#14582659C2211yescharacteristic
56#14582659C2211yescharacteristic
57#14582659C2211yescharacteristic
58#14582654C2211yescharacteristic
59#14582654C2211yescharacteristic
60C4×#41×C43C2211yescharacteristic
61C2×#104×C43C2211yescharacteristic
62C2×#104×C43C2211yescharacteristic
63C4×M16×C43C2211yescharacteristic
64C43×#376C2211yescharacteristic
65C43×#339C2211yescharacteristic
66C43×#339C2211yescharacteristic
67#13063332—22no—
68#13063332—22no—
69#13063332—41no—
70#13063332—41no—
71C2×#10621877—21no—
72C2×#10621877—21no—
73C2×#10621877C2311yescharacteristic
74C2×#10621877C2311yescharacteristic
75C22×C43⋊C8—21no—
76C22×C43⋊C8—21no—
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81#13063325C2×C411yescharacteristic
82#13063325C2×C411yescharacteristic
83#13063317C2×C411yescharacteristic
84#13063317C2×C411yescharacteristic
85#13063304—21no—
86#13063304—21no—
87C4×Dic86—21no—
88C4×Dic86—21no—
89#13063284C2311yescharacteristic
90#13063284C2311yescharacteristic
91#13063260—41no—
92#13063260—41no—
93#13063258C2×C411yescharacteristic
94#13063258C2×C411yescharacteristic
95#13063258C2×C411yescharacteristic
96#13063258C2×C411yescharacteristic
97#13063256C2×C411yescharacteristic
98#13063256C2×C411yescharacteristic
99#13063256C2×C411yescharacteristic
100#13063256C2×C411yescharacteristic
101C4⋊(C43⋊C8)—21no—
102C4⋊(C43⋊C8)—21no—
103C4⋊(C43⋊C8)—21no—
104C4⋊(C43⋊C8)—21no—
105C4⋊(C43⋊C8)—21no—
106C4⋊(C43⋊C8)—21no—
107C4⋊(C43⋊C8)C2×C411yescharacteristic
108C4⋊(C43⋊C8)C2×C411yescharacteristic
109C4⋊(C43⋊C8)C2×C411yescharacteristic
110C4⋊(C43⋊C8)C2×C411yescharacteristic
111C4⋊(C43⋊C8)D411yescharacteristic
112C4⋊(C43⋊C8)D411yescharacteristic
113C4⋊(C43⋊C8)D411yescharacteristic
114C4⋊(C43⋊C8)D411yescharacteristic
115Dic43⋊C8—21no—
116Dic43⋊C8—21no—
117Dic43⋊C8—21no—
118Dic43⋊C8—21no—
119#13063249C2×C411yescharacteristic
120#13063249C2×C411yescharacteristic
121#13063249C2×C411yescharacteristic
122#13063249C2×C411yescharacteristic
123#13063246C2×C411yescharacteristic
124#13063246C2×C411yescharacteristic
125#13063246C2×C411yescharacteristic
126#13063246C2×C411yescharacteristic
127#13063236—41no—
128#13063235—21no—
129#13063235—21no—
130C4×C43⋊C8—41no—
131C8×Dic43—21no—
132C8×Dic43—21no—
133C2×#41×C43C2311yescharacteristic
134C2×M16×C43C2311yescharacteristic
135C2×M16×C43C2311yescharacteristic
136C4×Q8×C43C2×C411yescharacteristic
137C4×Q8×C43C2×C411yescharacteristic
138C4×D4×C43—21no—
139C4×D4×C43—21no—
140C4×D4×C43C2×C411yescharacteristic
141C4×D4×C43C2×C411yescharacteristic
142#117×C43—21no—
143#117×C43C2311yescharacteristic
144C2×C42×C43—21no—
145C2×C42×C43C2311yescharacteristic
146C2×C42×C43C2311yescharacteristic
147C2×C42×C43C2311yescharacteristic
148#104×C43—22no—
149#104×C43Q814yescomplemented
150#97×C43—21no—
151C4×C8×C43—21no—
152#95×C43—21no—
153#95×C43—21no—
154#41×C43—21no—
155#41×C43—21no—
156#41×C43C2×Q812yes—
157#41×C43#4112yes—
158C2×Q8×C43C22×C411yescharacteristic
159C2×D4×C43—21no—
160C2×D4×C43C22×C411yescharacteristic
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43#4111yescharacteristic
167C22×C4×C43#4111yescharacteristic
168C22×C4×C43C2411yescharacteristic
169C2×Dic86—21no—
170C2×Dic86—21no—
171M16×C43—21no—
172M16×C43—21no—
173M16×C43—21no—
174M16×C43C2×Q812yes—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43C22×C411yescharacteristic
180C4⋊C4×C43C22×C411yescharacteristic
181C22⋊C4×C43—21no—
182C22⋊C4×C43—21no—
183C22⋊C4×C43—21no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43—21no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43—21no—
190C42×C43C22×C411yescharacteristic
191C42×C43C22×C411yescharacteristic
192C42×C43C2×D411yescharacteristic
193C42×C43C2×D411yescharacteristic
194C42×C43C2×Q812yes—
195C22⋊Dic43—21no—
196C22⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43C22×C411yescharacteristic
200C4⋊Dic43C22×C411yescharacteristic
201C4⋊Dic43C22×C411yescharacteristic
202C4⋊Dic43C22×C411yescharacteristic
203Dic43⋊C4—21no—
204Dic43⋊C4—21no—
205Dic43⋊C4—21no—
206Dic43⋊C4—21no—
207C4×Dic43—21no—
208C4×Dic43—21no—
209#10621877—21no—
210#10621877—21no—
211#10621877—21no—
212#10621877—21no—
213#10621877—42no—
214#10621877—42no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—42no—
226C2×C43⋊C8—42no—
227C2×C43⋊C8C22×C411yescharacteristic
228C2×C43⋊C8C22×C411yescharacteristic
229C2×C43⋊C8C22×C411yescharacteristic
230C2×C43⋊C8C22×C411yescharacteristic
231C2×C43⋊C8C2×D411yescharacteristic
232C2×C43⋊C8C2×D411yescharacteristic
233C2×C43⋊C8C2×D411yescharacteristic
234C2×C43⋊C8C2×D411yescharacteristic
235C23×C43—21no—
236C23×C43C2×#4111yescharacteristic
237Q8×C43—21no—
238Q8×C43C4×Q812yes—
239D4×C43—22no—
240D4×C43—22no—
241D4×C43—21no—
242D4×C43C4×Q812yes—
243C2×C4×C43—21no—
244C2×C4×C43—22no—
245C2×C4×C43—22no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—22no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—42no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—81no—
258C2×C4×C43C4×D411yescharacteristic
259C2×C4×C43C4×D411yescharacteristic
260C2×C4×C43C4×D411yescharacteristic
261C2×C4×C43C4×D411yescharacteristic
262C2×C4×C43C23×C411yescharacteristic
263C2×C4×C43C22×D411yescharacteristic
264C2×C4×C43C22×Q811yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43H(5,𝔽2)11yescharacteristic
267C2×C4×C432−1+411yescharacteristic
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272Dic86—42no—
273Dic86—81no—
274C8×C43—22no—
275C8×C43—41no—
276C43⋊C8—21no—
277C43⋊C8—21no—
278C43⋊C8—21no—
279C43⋊C8—21no—
280C43⋊C8—21no—
281C43⋊C8—21no—
282C43⋊C8—21no—
283C43⋊C8—21no—
284C43⋊C8—41no—
285C43⋊C8—41no—
286#22984—431nomaximal, Sylow
287C22×C43—21no—
288C22×C43—21no—
289C22×C43—22no—
290C22×C43—41no—
291C22×C43—41no—
292C22×C43C2×C4×D411yescharacteristic
293C22×C43#55211yescharacteristic
294C22×C43#55411yescharacteristic
295C4×C43—22no—
296C4×C43—21no—
297C4×C43—21no—
298C4×C43—21no—
299C4×C43—21no—
300C4×C43—42no—
301C4×C43—41no—
302C4×C43—41no—
303C4×C43—81no—
304C4×C43C2×C4×Q811yescharacteristic
305C4×C43#52011yescharacteristic
306C4×C43#54611yescharacteristic
307C4×C43D4×Q811yescharacteristic
308Dic43—41no—
309Dic43—41no—
310Dic43—41no—
311Dic43—41no—
312#3076—431no—
313#2962—431no—
314#2906—431no—
315#1995—431no—
316#1950—431no—
317#1946—431no—
318#1945—431no—
319#1922—431no—
320#1922—431no—
321#1866—431no—
322#1866—431no—
323#1768—431no—
324#1765—431no—
325#1764—431no—
326#1759D4311yescharacteristic
327C2×C43—21no—
328C2×C43—21no—
329C2×C43—42no—
330C2×C43#236011yescharacteristic
331C2×C43#295511yescharacteristic
332C2×C43#295711yescharacteristic
333C2×#131—431no—
334C2×#131—431no—
335#533—431no—
336C4×#41C2×D4311yescharacteristic
337#479—431no—
338#479—431no—
339#478—431no—
340#478—431no—
341#477—431no—
342#476—431no—
343#475—431no—
344#474—431no—
345#446—861no—
346#446—861no—
347#446—861no—
348C8×Q8—861no—
349C2×#108—431no—
350C2×#108—431no—
351#427—431no—
352#427—431no—
353#424—431no—
354#424—431no—
355#424—431no—
356#424—431no—
357#424—861no—
358#424—861no—
359#423—431no—
360#423—861no—
361C2×C4⋊C8—431no—
362C2×C4⋊C8—431no—
363C2×C4⋊C8—861no—
364C2×#104C2×D4311yescharacteristic
365C2×#104C2×D4311yescharacteristic
366#416—431no—
367#416—431no—
368#405—431no—
369#405—431no—
370C4×M16C2×D4311yescharacteristic
371C2×#97—431no—
372C2×C4×C8—431no—
373#376C2×D4311yescharacteristic
374#341—431no—
375#341—431no—
376#339—431no—
377#339—431no—
378#339—431no—
379#339—431no—
380#339C2×D4311yescharacteristic
381#339C2×D4311yescharacteristic
382#336—431no—
383#336—431no—
384C43#2298411yescharacteristic, complemented, Sylow
385C2×#41C22×D4311yescharacteristic
386#131—862no—
387#131—862no—
388#131—1721no—
389#131—1721no—
390C2×M16—431no—
391C2×M16—431no—
392C2×M16—861no—
393C2×M16—861no—
394C2×M16C22×D4311yescharacteristic
395C2×M16C22×D4311yescharacteristic
396C22×C8—431no—
397C22×C8—431no—
398C22×C8—431no—
399C22×C8—431no—
400C22×C8—861no—
401C22×C8—861no—
402C4⋊Q8—431no—
403C4⋊Q8—431no—
404#125—431no—
405#125—431no—
406C22⋊Q8—861no—
407C22⋊Q8—861no—
408C4×Q8—861no—
409C4×Q8—861no—
410C4×Q8C4×D4311yescharacteristic
411C4×Q8C4×D4311yescharacteristic
412C4×D4—21no—
413C4×D4—21no—
414C4×D4C4×D4311yescharacteristic
415C4×D4C4×D4311yescharacteristic
416#117—21no—
417#117—431no—
418#117—431no—
419#117C22×D4311yescharacteristic
420C2×C42—21no—
421C2×C42C22×D4311yescharacteristic
422C2×C42C22×D4311yescharacteristic
423C2×C42C22×D4311yescharacteristic
424#108—1721no—
425#108—1721no—
426#107—431no—
427#107—431no—
428#107—431no—
429#107—431no—
430#106—431no—
431#106—431no—
432#106—431no—
433#106—431no—
434C4⋊C8—431no—
435C4⋊C8—431no—
436C4⋊C8—431no—
437C4⋊C8—431no—
438C4⋊C8—431no—
439C4⋊C8—431no—
440C4⋊C8—431no—
441C4⋊C8—431no—
442C4⋊C8—861no—
443C4⋊C8—861no—
444C4⋊C8—861no—
445C4⋊C8—861no—
446C4⋊C8—861no—
447C4⋊C8—861no—
448C4⋊C8—861no—
449C4⋊C8—861no—
450C4⋊C8—861no—
451C4⋊C8—861no—
452#104—22no—
453#104Dic8614yescomplemented
454#103—431no—
455#103—431no—
456#103—431no—
457#103—431no—
458#102—431no—
459#102—431no—
460#102—431no—
461#102—431no—
462#97—21no—
463#97—861no—
464#97—861no—
465#97—1721no—
466C4×C8—21no—
467C4×C8—861no—
468C4×C8—861no—
469C4×C8—1721no—
470#95—21no—
471#95—21no—
472#41—21no—
473#41—21no—
474#41C2×Dic8612yes—
475#41#1062189812yes—
476C2×Q8—861no—
477C2×Q8—861no—
478C2×Q8C2×C4×D4311yescharacteristic
479C2×D4—21no—
480C2×D4C2×C4×D4311yescharacteristic
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4#1062190011yescharacteristic
487C22×C4#1062190011yescharacteristic
488C22×C4C23×D4311yescharacteristic
489M16—21no—
490M16—21no—
491M16—21no—
492M16—861no—
493M16—861no—
494M16—861no—
495M16—861no—
496M16—1722no—
497M16—1722no—
498M16C2×Dic8612yes—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—431no—
502C2×C8—431no—
503C2×C8—431no—
504C2×C8—431no—
505C2×C8—431no—
506C2×C8—431no—
507C2×C8—431no—
508C2×C8—431no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—1722no—
520C2×C8—1722no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—431no—
524C4⋊C4—431no—
525C4⋊C4—431no—
526C4⋊C4—431no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4C2×C4×D4311yescharacteristic
534C4⋊C4C2×C4×D4311yescharacteristic
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—861no—
539C22⋊C4—861no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—861no—
547C42—861no—
548C42C2×Dic8612yes—
549C42C2×C4×D4311yescharacteristic
550C42C2×C4×D4311yescharacteristic
551C42D4×D4311yescharacteristic
552C42D4×D4311yescharacteristic
553C23—21no—
554C23C2×#1062190011yescharacteristic
555Q8—21no—
556Q8—3441no—
557Q8—1722no—
558Q8C4×Dic8612yes—
559D4—22no—
560D4—22no—
561D4—21no—
562D4C4×Dic8612yes—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—81no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—861no—
582C2×C4(C22⋊D43)⋊C411yescharacteristic
583C2×C4(C22⋊D43)⋊C411yescharacteristic
584C2×C4(C22⋊D43)⋊C411yescharacteristic
585C2×C4(C22⋊D43)⋊C411yescharacteristic
586C2×C4C22×C4×D4311yescharacteristic
587C2×C4C2×D4×D4311yescharacteristic
588C2×C4C22×Dic8611yescharacteristic
589C2×C4C2×#1062189811yescharacteristic
590C2×C4#1306337111yescharacteristic
591C2×C4#1306337211yescharacteristic
592C8—22no—
593C8—41no—
594C8—861no—
595C8—861no—
596C8—861no—
597C8—861no—
598C8—861no—
599C8—861no—
600C8—861no—
601C8—861no—
602C8—1721no—
603C8—1721no—
604C22—21no—
605C22—21no—
606C22—22no—
607C22—41no—
608C22—41no—
609C22C2×(C22⋊D43)⋊C411yescharacteristic
610C22#1458358911yescharacteristic
611C22#1458360611yescharacteristic
612C4—22no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—21no—
617C4—42no—
618C4—41no—
619C4—41no—
620C4—81no—
621C4—1721no—
622C4—1721no—
623C4—1721no—
624C4—1721no—
625C4C2×C4×Dic8611yescharacteristic
626C4#1458337911yescharacteristic
627C4#1458354511yescharacteristic
628C4D4×Dic8611yescharacteristic
629C2—21no—
630C2—21no—
631C2—42no—
632C2#1913759811yescharacteristic
633C2#1914349411yescharacteristic
634C2#1914350811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1759C2
socleC22×C43C2×C4×D4
prime radicalC2×#41×C43C23
cosocleC22×C4×C43C24
hypercenter#1759D43
hypocenterC43#22984
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1759

Complements

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

NH ≅ G/Ntype
2. #19143542C2semidirect
4. #19135576C2semidirect
5. #19135370C2semidirect
6. #19135347C2semidirect
7. #19135342C2semidirect
8. #19135197C2semidirect
9. #19135197C2semidirect
12. #19134452C2semidirect
19. #14583206C4semidirect
20. #14583206C4semidirect
21. #14583199C4semidirect
22. #14583199C4semidirect
23. #14583194C4semidirect
24. #14583189C4semidirect
25. #14583184C4semidirect
26. #14583179C4semidirect
149. #104×C43Q8semidirect
384. C43#22984semidirect
453. #104Dic86semidirect

Maximal subgroups

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

subgroupindex
#191443832
#191435422
#191431632
#191355762
#191353702
#191353472
#191353422
#191351972
#191348682
#191344522
#191344402
#191344332
C43×#17592
#2298443