Finite Group Databasebeta

← #25166525

Subgroups — #25166525

Order 11008.

800 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583261C211yesmaximal, characteristic
2C2×#14583004C211yesmaximal, characteristic, complemented
3#19138393C211yesmaximal, characteristic
4#19135966C211yesmaximal, characteristic
5#19135925C211yesmaximal, characteristic, complemented
6#19135917C211yesmaximal, characteristic, complemented
7#19135688C211yesmaximal, characteristic
8#19135452C211yesmaximal, characteristic
9#19135291C211yesmaximal, characteristic
10#19135288C211yesmaximal, characteristic, complemented
11#19135270C211yesmaximal, characteristic, complemented
12#19134950C211yesmaximal, characteristic
13#19134862C211yesmaximal, characteristic, complemented
14#19134464C211yesmaximal, characteristic, complemented
15C43×#2451C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C2×#13063313C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20#14583261—24no—
21#14583004—24no—
22C2×#13063256C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×C4⋊(C43⋊C8)C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063236C2211yescharacteristic
34C2×#13063236C2211yescharacteristic
35C2×C4×C43⋊C8C2211yescharacteristic
36#14582834—21no—
37#14582828—21no—
38#14582805C2211yescharacteristic
39#14582801C2211yescharacteristic
40#14582801C2211yescharacteristic
41#14582797C2211yescharacteristic
42#14582789—21no—
43#14582788—21no—
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50C2×C4⋊Q8×C43C2211yescharacteristic
51C2×C4×Q8×C43C2211yescharacteristic
52C43×#398—21no—
53C43×#395—21no—
54C43×#391—21no—
55C43×#391C2211yescharacteristic
56C43×#391C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#389C2211yescharacteristic
59C43×#387—21no—
60C4×C4⋊C4×C43C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C22×D172C2311yescharacteristic
63C2×#10621885—22no—
64C2×#10621885—22no—
65C2×#10621885—22no—
66C2×#10621884—22no—
67C2×#10621884—22no—
68C2×#10621884—41no—
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063313—22no—
74#13063313—41no—
75C4×Dic86—22no—
76C4×Dic86—41no—
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊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×C4×Dic43—21no—
88#13063256—22no—
89#13063256—41no—
90C4⋊(C43⋊C8)—22no—
91#13063249—22no—
92#13063249—22no—
93#13063248—22no—
94#13063248—22no—
95#13063248D414yes—
96#13063245—22no—
97#13063245—22no—
98#13063245—22no—
99#13063236—22no—
100#13063236—22no—
101C4×C43⋊C8—22no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C22×Q8×C43—21no—
106C22×Q8×C43C2311yescharacteristic
107C4⋊Q8×C43—22no—
108C4⋊Q8×C43—41no—
109C4×Q8×C43—22no—
110C4×Q8×C43—41no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43D411yescharacteristic
116C2×C4⋊C4×C43D411yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C42×C43—21no—
121C2×C42×C43C2311yescharacteristic
122C2×C42×C43C2311yescharacteristic
123C2×C42×C43C2311yescharacteristic
124#95×C43—21no—
125#95×C43—21no—
126#95×C43—21no—
127#95×C43—21no—
128#95×C43—21no—
129#95×C43—21no—
130#95×C43D411yescharacteristic
131#95×C43D411yescharacteristic
132C23×D43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43—42no—
139C2×Q8×C43—42no—
140C2×Q8×C43—81no—
141C2×Q8×C43#4112yes—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2411yescharacteristic
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86C2×D412yes—
168C4⋊C4×C43—22no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—41no—
175C4⋊C4×C43—42no—
176C4⋊C4×C43—42no—
177C4⋊C4×C43—81no—
178C4⋊C4×C43—81no—
179C4⋊C4×C43C2×D412yes—
180C42×C43—21no—
181C42×C43—21no—
182C42×C43—21no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43—42no—
187#10621885—28no—
188#10621884—44no—
189(C2×D43)⋊C4—42no—
190(C2×D43)⋊C4—42no—
191(C2×D43)⋊C4—42no—
192(C2×D43)⋊C4—42no—
193(C2×D43)⋊C4—81no—
194(C2×D43)⋊C4—81no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199Dic43⋊C4—42no—
200Dic43⋊C4—81no—
201C4×Dic43—42no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8C2×D412yes—
212C2×C43⋊C8#4112yes—
213C2×C43⋊C8#4112yes—
214C23×C43C22×D411yescharacteristic
215C22×D43—41no—
216C22×D43—41no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222Q8×C43—22no—
223Q8×C43—22no—
224Q8×C43—41no—
225Q8×C43—41no—
226Q8×C43—84no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—22no—
235C2×C4×C43—22no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43#13712yes—
257C2×C4×C43C22×D411yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43H(5,𝔽2)11yescharacteristic
262C2×C4×C432−1+411yescharacteristic
263C2×Dic43—22no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272D172—41no—
273D172—41no—
274D172—41no—
275D172—41no—
276Dic86—22no—
277Dic86—22no—
278Dic86—41no—
279Dic86—41no—
280C43⋊C8—22no—
281C43⋊C8—22no—
282C43⋊C8—22no—
283C43⋊C8—41no—
284#26846—431nomaximal, Sylow
285C22×C43#53211yescharacteristic
286C22×C43D4211yescharacteristic
287C22×C43#54811yescharacteristic
288C22×C43C2×#13711yescharacteristic
289C22×C43#57511yescharacteristic
290C22×C43#57711yescharacteristic
291C22×C43#57711yescharacteristic
292C2×D43—81no—
293C2×D43—81no—
294C2×D43—81no—
295C2×D43—81no—
296C2×D43—81no—
297C2×D43—81no—
298C2×D43—81no—
299C4×C43—22no—
300C4×C43—41no—
301C4×C43—42no—
302C4×C43—41no—
303C4×C43—41no—
304C4×C43—42no—
305C4×C43—41no—
306C4×C43—41no—
307C4×C43—81no—
308C4×C43—81no—
309C4×C43#52511yescharacteristic
310C4×C43#54211yescharacteristic
311C4×C43#54711yescharacteristic
312C4×C43#55111yescharacteristic
313Dic43—42no—
314Dic43—81no—
315Dic43—81no—
316C2×#489—431no—
317C2×#441—431no—
318#2451D4311yescharacteristic, complemented
319#2448—431no—
320#2065—431no—
321#2058—431no—
322#2056—431no—
323#2015—431no—
324#1968—431no—
325#1936—431no—
326#1935—431no—
327#1933—431no—
328#1880—431no—
329#1865—431no—
330#1770—431no—
331C2×C43#246111yescharacteristic
332C2×C43#317311yescharacteristic
333C2×C43#318111yescharacteristic
334C2×C43#327511yescharacteristic
335C2×C43#327811yescharacteristic
336C2×C43#336911yescharacteristic
337C2×C43#337111yescharacteristic
338D43—161no—
339C22×Q16—431no—
340C22×SD16—431no—
341C2×C4⋊Q8C2×D4311yescharacteristic
342C2×#124—431no—
343C2×C4×Q8—431no—
344C2×C4×Q8C2×D4311yescharacteristic
345#489—864no—
346#441—864no—
347C2×#106—431no—
348C2×#106—431no—
349C2×C4⋊C8—431no—
350C2×#103—431no—
351C2×#103—431no—
352C2×#103—431no—
353C2×#103—431no—
354C2×#103—431no—
355C2×#102—431no—
356C2×#102—431no—
357C2×#102—431no—
358C2×#97—431no—
359C2×#97—431no—
360C2×C4×C8—431no—
361#399—861no—
362#398—21no—
363#397—861no—
364#395—21no—
365#391—21no—
366#391—431no—
367#391C2×D4311yescharacteristic
368#391C2×D4311yescharacteristic
369#390—431no—
370#390—431no—
371#389—431no—
372#389C2×D4311yescharacteristic
373#389C2×D4311yescharacteristic
374#388—861no—
375#388—861no—
376#387—21no—
377C4×C4⋊C4C2×D4311yescharacteristic
378#340—431no—
379#340—431no—
380#340—431no—
381#340—431no—
382#336—431no—
383#336—431no—
384C43#2684611yescharacteristic, complemented, Sylow
385C22×Q8—21no—
386C22×Q8—431no—
387C22×Q8C22×D4311yescharacteristic
388C22×D4—431no—
389C2×Q16—862no—
390C2×Q16—862no—
391C2×Q16—862no—
392C2×SD16—862no—
393C2×SD16—862no—
394C2×SD16—1721no—
395C22×C8—431no—
396C22×C8—431no—
397C22×C8—431no—
398C22×C8—431no—
399C4⋊Q8—22no—
400C4⋊Q8—41no—
401#124—862no—
402#124—1721no—
403C4×Q8—22no—
404C4×Q8—41no—
405C4×Q8—862no—
406C4×Q8—1721no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4C22⋊D4311yescharacteristic
416C2×C4⋊C4C22⋊D4311yescharacteristic
417C2×C4⋊C4C22×D4311yescharacteristic
418C2×C4⋊C4C22×D4311yescharacteristic
419C2×C4⋊C4C22×D4311yescharacteristic
420C2×C22⋊C4—861no—
421C2×C22⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C42—21no—
427C2×C42—861no—
428C2×C42C22×D4311yescharacteristic
429C2×C42C22×D4311yescharacteristic
430C2×C42C22×D4311yescharacteristic
431#106—862no—
432#106—1721no—
433C4⋊C8—862no—
434#103—434no—
435#103—862no—
436#103—862no—
437#103—862no—
438#103—862no—
439#102—862no—
440#102—862no—
441#102—862no—
442#97—862no—
443#97—862no—
444C4×C8—862no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—861no—
452#95—861no—
453#95—861no—
454#95C22⋊D4311yescharacteristic
455#95C22⋊D4311yescharacteristic
456C24—861no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—42no—
463C2×Q8—42no—
464C2×Q8—81no—
465C2×Q8—432no—
466C2×Q8—861no—
467C2×Q8—861no—
468C2×Q8—861no—
469C2×Q8—861no—
470C2×Q8—861no—
471C2×Q8#1062190212yes—
472C2×D4—861no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—861no—
476C2×D4—861no—
477C2×D4—861no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4C2×C22⋊D4311yescharacteristic
486C22×C4C2×C22⋊D4311yescharacteristic
487C22×C4C2×C22⋊D4311yescharacteristic
488C22×C4C2×C22⋊D4311yescharacteristic
489C22×C4C2×C22⋊D4311yescharacteristic
490C22×C4C2×C22⋊D4311yescharacteristic
491C22×C4C23×D4311yescharacteristic
492Q16—868no—
493SD16—1724no—
494C2×C8—432no—
495C2×C8—432no—
496C2×C8—432no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8—861no—
506C4⋊C4—22no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—41no—
513C4⋊C4—42no—
514C4⋊C4—42no—
515C4⋊C4—81no—
516C4⋊C4—81no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—3441no—
522C4⋊C4—1722no—
523C4⋊C4D4×D4312yes—
524C22⋊C4—3441no—
525C22⋊C4—3441no—
526C22⋊C4—1722no—
527C22⋊C4—1722no—
528C22⋊C4—1722no—
529C22⋊C4—1722no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—42no—
537C42—1722no—
538C23—1721no—
539C23—1721no—
540C23—1721no—
541C23—1721no—
542C23—1721no—
543C23—1721no—
544C23—1721no—
545C23C22×C22⋊D4311yescharacteristic
546Q8—22no—
547Q8—22no—
548Q8—41no—
549Q8—41no—
550Q8—84no—
551Q8—862no—
552Q8—862no—
553Q8—1721no—
554Q8—1721no—
555D4—1721no—
556D4—1721no—
557D4—1721no—
558D4—1721no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—862no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4#1306335612yes—
598C2×C4C2×D4×D4311yescharacteristic
599C2×C4#41×D4311yescharacteristic
600C2×C4#41×D4311yescharacteristic
601C2×C4C2×#1062190211yescharacteristic
602C2×C4#1306337011yescharacteristic
603C2×C4#1306337311yescharacteristic
604C8—862no—
605C8—862no—
606C8—862no—
607C8—1721no—
608C22—3441no—
609C22—3441no—
610C22—3441no—
611C22—3441no—
612C22—3441no—
613C22—3441no—
614C22—3441no—
615C22#1458344511yescharacteristic
616C22D4×C22⋊D4311yescharacteristic
617C22#1458356011yescharacteristic
618C22C2×#1306335611yescharacteristic
619C22#1458369711yescharacteristic
620C22#1458370711yescharacteristic
621C22#1458371011yescharacteristic
622C4—22no—
623C4—42no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—41no—
628C4—42no—
629C4—41no—
630C4—81no—
631C4—81no—
632C4—3441no—
633C4—3441no—
634C4—1722no—
635C4#1458341211yescharacteristic
636C4#1458351911yescharacteristic
637C4#1458355111yescharacteristic
638C4#1458357611yescharacteristic
639C2—6881no—
640C2#1913856911yescharacteristic
641C2#1914520611yescharacteristic
642C2#1914529811yescharacteristic
643C2#1914622211yescharacteristic
644C2#1914625711yescharacteristic
645C2#1914733511yescharacteristic
646C2#1914736311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2451C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#2451D43
hypocenterC43#26846
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2451

Complements

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

NH ≅ G/Ntype
2. C2×#14583004C2semidirect
5. #19135925C2semidirect
6. #19135917C2semidirect
10. #19135288C2semidirect
11. #19135270C2semidirect
13. #19134862C2semidirect
14. #19134464C2semidirect
15. C43×#2451C2semidirect
318. #2451D43semidirect
384. C43#26846semidirect

Maximal subgroups

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

subgroupindex
C2×#145832612
C2×#145830042
#191383932
#191359662
#191359252
#191359172
#191356882
#191354522
#191352912
#191352882
#191352702
#191349502
#191348622
#191344642
C43×#24512
#2684643