Finite Group Databasebeta

← #25100936

Subgroups — #25100936

Order 11008.

874 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583001C211yesmaximal, characteristic
2#19137072C211yesmaximal, characteristic, complemented
3#19137059C211yesmaximal, characteristic
4#19135476C211yesmaximal, characteristic
5#19135449C211yesmaximal, characteristic
6#19135333C211yesmaximal, characteristic, complemented
7#19135328C211yesmaximal, characteristic, complemented
8#19135292C211yesmaximal, characteristic
9#19135285C211yesmaximal, characteristic, complemented
10#19135278C211yesmaximal, characteristic
11#19135271C211yesmaximal, characteristic, complemented
12#19134492C211yesmaximal, characteristic, complemented
13#19134426C211yesmaximal, characteristic, complemented
14#19134421C211yesmaximal, characteristic
15C4×#97×C43C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×#13063282—21no—
20#14583001C418yescomplemented
21C2×#13063259C2211yescharacteristic
22C2×#13063259C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30#14582805C2211yescharacteristic
31#14582805C2211yescharacteristic
32#14582801C2211yescharacteristic
33#14582801C2211yescharacteristic
34#14582797C2211yescharacteristic
35#14582797C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582797C2211yescharacteristic
38#14582790—21no—
39#14582790—21no—
40#14582783—21no—
41#14582783—21no—
42C4×Dic43⋊C4—21no—
43C4×C4⋊Dic43C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45C4×(C2×D43)⋊C4—21no—
46#14582745—21no—
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53C2×#97×C43C2211yescharacteristic
54C2×#97×C43C2211yescharacteristic
55C2×#97×C43C2211yescharacteristic
56C2×#97×C43C2211yescharacteristic
57C2×C4×C8×C43C2211yescharacteristic
58C2×C4×C8×C43C2211yescharacteristic
59C43×C43C2211yescharacteristic
60C22×Dic86C2311yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C4×D43—21no—
63C2×#10621873—22no—
64C2×#10621873—22no—
65C2×#10621873C2×C414yes—
66C4×Dic86—22no—
67C4×Dic86C2×C414yes—
68C4×D172—22no—
69C4×D172C2×C414yes—
70#13063282—44no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊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×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90#13063259—22no—
91#13063259C2×C414yes—
92#13063257—22no—
93#13063250—22no—
94#13063250—22no—
95#13063250C2×C414yes—
96#13063247—22no—
97#13063247—22no—
98#13063247C2×C414yes—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C22×C8×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C2×C42×C43D411yescharacteristic
114C2×C42×C43D411yescharacteristic
115C2×C42×C43D411yescharacteristic
116C2×C42×C43D411yescharacteristic
117C2×C42×C43C2311yescharacteristic
118C2×C42×C43C2311yescharacteristic
119C2×C42×C43C2311yescharacteristic
120#97×C43—22no—
121#97×C43—22no—
122#97×C43—22no—
123#97×C43C2×C414yes—
124C4×C8×C43—22no—
125C4×C8×C43—22no—
126C23×D43—21no—
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2411yescharacteristic
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C2×D172—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172C22×C412yes—
147C2×C4×D43—24no—
148C2×C4×D43—42no—
149C2×C4×D43—42no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86C22×C412yes—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43C22×C412yes—
163C2×C8×C43C22×C412yes—
164C2×C8×C43#4112yes—
165C2×C8×C43#4112yes—
166C2×C8×C43#4112yes—
167C2×C8×C43#4112yes—
168C42×C43—22no—
169C42×C43—22no—
170C42×C43—21no—
171C42×C43—21no—
172C42×C43—21no—
173C42×C43—21no—
174C42×C43—41no—
175C42×C43—41no—
176C42×C43C22×C412yes—
177C42×C43#4112yes—
178(C2×D43)⋊C4—24no—
179(C2×D43)⋊C4—42no—
180(C2×D43)⋊C4—42no—
181(C2×D43)⋊C4—42no—
182(C2×D43)⋊C4—42no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43C22×C412yes—
194C4⋊Dic43C22×C412yes—
195Dic43⋊C4—24no—
196Dic43⋊C4—42no—
197Dic43⋊C4—42no—
198Dic43⋊C4—42no—
199Dic43⋊C4—42no—
200C4×Dic43—24no—
201C4×Dic43—42no—
202C4×Dic43—42no—
203#10621873—28no—
204C23×C43C22×D411yescharacteristic
205C22×D43—22no—
206C22×D43—41no—
207C22×D43—41no—
208C22×D43—41no—
209C22×D43—41no—
210C22×D43—41no—
211C22×D43—41no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43C4×D412yes—
227C2×C4×C43C4×D412yes—
228C2×C4×C43AGL(1,ℤ/8)12yes—
229C2×C4×C43#13712yes—
230C2×C4×C43C23×C411yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×Dic43—22no—
237C2×Dic43—22no—
238C2×Dic43—22no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257D172—22no—
258D172—22no—
259D172—41no—
260D172—41no—
261C4×D43—48no—
262Dic86—22no—
263Dic86—22no—
264Dic86—41no—
265Dic86—41no—
266C8×C43—22no—
267C8×C43—22no—
268C8×C43—22no—
269C8×C43#11714yescomplemented
270#21288—431nomaximal, Sylow
271C22×C43C2×C4×D411yescharacteristic
272C22×C43#53211yescharacteristic
273C22×C43#53211yescharacteristic
274C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
275C22×C43C2×#13711yescharacteristic
276C22×C43#57511yescharacteristic
277C22×C43#57511yescharacteristic
278C2×D43—42no—
279C2×D43—42no—
280C2×D43—42no—
281C2×D43—81no—
282C2×D43—81no—
283C2×D43—81no—
284C2×D43—81no—
285C4×C43—22no—
286C4×C43—22no—
287C4×C43—22no—
288C4×C43—22no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43C2×#11711yescharacteristic
292C4×C43C4×#4111yescharacteristic
293C4×C43#52911yescharacteristic
294C4×C43#52911yescharacteristic
295Dic43—42no—
296Dic43—42no—
297Dic43—42no—
298Dic43—81no—
299Dic43—81no—
300Dic43—81no—
301Dic43—81no—
302C2×#440—431no—
303#2295—431no—
304#2293—431no—
305#1973—431no—
306#1968—431no—
307#1943—431no—
308#1942—431no—
309#1936—431no—
310#1935—431no—
311#1934—431no—
312#1933—431no—
313#1776—431no—
314#1763—431no—
315#1762—431no—
316C4×#97D4311yescharacteristic, complemented
317C2×C43#229311yescharacteristic
318C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
319C2×C43C4×#13711yescharacteristic
320C2×C43#318011yescharacteristic
321C2×C43#318111yescharacteristic
322C2×C43#318211yescharacteristic
323C2×C43#318311yescharacteristic
324D43—82no—
325C22×SD16—431no—
326C2×C4×Q8—431no—
327C2×C4×D4—431no—
328C2×#117—861no—
329#440—438no—
330C2×#107—431no—
331C2×#107—431no—
332C2×#106—431no—
333C2×#103—431no—
334C2×#103—431no—
335C2×#103—431no—
336C2×#102—431no—
337C2×#102—431no—
338C2×#102—431no—
339C2×#97C2×D4311yescharacteristic
340C2×#97C2×D4311yescharacteristic
341C2×#97C2×D4311yescharacteristic
342C2×#97C2×D4311yescharacteristic
343C2×C4×C8C2×D4311yescharacteristic
344C2×C4×C8C2×D4311yescharacteristic
345#391—431no—
346#391—431no—
347#390—431no—
348#390—431no—
349#389—431no—
350#389—431no—
351#389—431no—
352#389—431no—
353#388—861no—
354#388—861no—
355#387—861no—
356#387—861no—
357C4×C4⋊C4—431no—
358C4×C4⋊C4—431no—
359C4×C4⋊C4—861no—
360C4×C22⋊C4—861no—
361#376—861no—
362C43C2×D4311yescharacteristic
363#340—431no—
364#340—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368#340—431no—
369C43#2128811yescharacteristic, complemented, Sylow
370C22×Q8—431no—
371C22×D4—431no—
372C23×C4—861no—
373C2×SD16—434no—
374C2×SD16—862no—
375C2×SD16—862no—
376C22×C8C22×D4311yescharacteristic
377C22×C8C22×D4311yescharacteristic
378C22×C8C22×D4311yescharacteristic
379C22×C8C22×D4311yescharacteristic
380C4×Q8—434no—
381C4×Q8—862no—
382C4×D4—434no—
383C4×D4—862no—
384#117—1724no—
385C2×C4⋊C4—431no—
386C2×C4⋊C4—431no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—431no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396C2×C22⋊C4—861no—
397C2×C22⋊C4—861no—
398C2×C22⋊C4—861no—
399C2×C22⋊C4—861no—
400C2×C22⋊C4—861no—
401C2×C42—861no—
402C2×C42—861no—
403C2×C42—861no—
404C2×C42D17211yescharacteristic
405C2×C42D17211yescharacteristic
406C2×C42D17211yescharacteristic
407C2×C42D17211yescharacteristic
408C2×C42C22×D4311yescharacteristic
409C2×C42C22×D4311yescharacteristic
410C2×C42C22×D4311yescharacteristic
411#107—434no—
412#107—862no—
413#106—862no—
414#103—434no—
415#103—862no—
416#103—862no—
417#102—434no—
418#102—862no—
419#102—862no—
420#97—22no—
421#97—22no—
422#97—22no—
423#97C4×D4314yes—
424C4×C8—22no—
425C4×C8—22no—
426#95—861no—
427#95—861no—
428#95—861no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436C24—861no—
437C2×Q8—432no—
438C2×Q8—861no—
439C2×Q8—861no—
440C2×Q8—861no—
441C2×Q8—861no—
442C2×Q8—861no—
443C2×D4—432no—
444C2×D4—861no—
445C2×D4—861no—
446C2×D4—861no—
447C2×D4—861no—
448C2×D4—861no—
449C22×C4—861no—
450C22×C4—861no—
451C22×C4—861no—
452C22×C4—864no—
453C22×C4—861no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—1722no—
458C22×C4—1722no—
459C22×C4C2×D17211yescharacteristic
460C22×C4C2×D17211yescharacteristic
461C22×C4C2×D17211yescharacteristic
462C22×C4C2×D17211yescharacteristic
463C22×C4C2×D17211yescharacteristic
464C22×C4C2×D17211yescharacteristic
465C22×C4C23×D4311yescharacteristic
466SD16—868no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8C2×C4×D4312yes—
474C2×C8C2×C4×D4312yes—
475C2×C8#1062189812yes—
476C2×C8#1062189812yes—
477C2×C8#1062189812yes—
478C2×C8#1062189812yes—
479C4⋊C4—432no—
480C4⋊C4—432no—
481C4⋊C4—864no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—1722no—
493C4⋊C4—1722no—
494C4⋊C4—1722no—
495C4⋊C4—1722no—
496C22⋊C4—864no—
497C22⋊C4—1722no—
498C22⋊C4—1722no—
499C22⋊C4—1722no—
500C22⋊C4—1722no—
501C42—22no—
502C42—22no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—41no—
508C42—41no—
509C42—864no—
510C42—1722no—
511C42—1722no—
512C42C2×C4×D4312yes—
513C42#1062189812yes—
514C23—862no—
515C23—1721no—
516C23—1721no—
517C23—1721no—
518C23—1721no—
519C23—1721no—
520C23—1721no—
521C23C22×D17211yescharacteristic
522Q8—862no—
523Q8—862no—
524Q8—1721no—
525Q8—1721no—
526D4—862no—
527D4—862no—
528D4—1721no—
529D4—1721no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—862no—
545C2×C4—862no—
546C2×C4—862no—
547C2×C4—1728no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4C4×D17212yes—
567C2×C4C4×D17212yes—
568C2×C4#1306335312yes—
569C2×C4#1306335812yes—
570C2×C4C22×C4×D4311yescharacteristic
571C2×C4C2×#1062189811yescharacteristic
572C2×C4C2×#1062189811yescharacteristic
573C2×C4C2×#1062189811yescharacteristic
574C2×C4C2×#1062189811yescharacteristic
575C2×C4C2×#1062189811yescharacteristic
576C8—22no—
577C8—22no—
578C8—22no—
579C8#1306328214yescomplemented
580C22—3441no—
581C22—3441no—
582C22—3441no—
583C22—3441no—
584C22—1722no—
585C22—1722no—
586C22—1722no—
587C22C2×C4×D17211yescharacteristic
588C22#1458344911yescharacteristic
589C22#1458344911yescharacteristic
590C22C2×#1306335311yescharacteristic
591C22C2×#1306335811yescharacteristic
592C22#1458369911yescharacteristic
593C22#1458369911yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—22no—
598C4—41no—
599C4—41no—
600C4—3441no—
601C4—3441no—
602C4—3441no—
603C4—3441no—
604C4—1722no—
605C4—1722no—
606C4—1722no—
607C4C2×#1306328211yescharacteristic
608C4C4×#1062189811yescharacteristic
609C4#1458343311yescharacteristic
610C4#1458343311yescharacteristic
611C2—3442no—
612C2#1913705911yescharacteristic
613C2C4×#1306335311yescharacteristic
614C2C4×#1306335811yescharacteristic
615C2#1914529311yescharacteristic
616C2#1914530411yescharacteristic
617C2#1914531311yescharacteristic
618C2#1914532411yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#97×C43C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenterC4×#97D43
hypocenterC43#21288
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C43 ◁ C4×#97

Complements

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

NH ≅ G/Ntype
2. #19137072C2semidirect
6. #19135333C2semidirect
7. #19135328C2semidirect
9. #19135285C2semidirect
11. #19135271C2semidirect
12. #19134492C2semidirect
13. #19134426C2semidirect
15. C4×#97×C43C2semidirect
20. #14583001C4semidirect
269. C8×C43#117semidirect
316. C4×#97D43semidirect
369. C43#21288semidirect
579. C8#13063282semidirect

Maximal subgroups

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

subgroupindex
C2×#145830012
#191370722
#191370592
#191354762
#191354492
#191353332
#191353282
#191352922
#191352852
#191352782
#191352712
#191344922
#191344262
#191344212
C4×#97×C432
#2128843