Finite Group Databasebeta

← #25196698

Subgroups — #25196698

Order 11008.

844 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142900C211yesmaximal, characteristic, complemented
2#19137111C211yesmaximal, characteristic
3#19136164C211yesmaximal, characteristic, complemented
4#19136116C211yesmaximal, characteristic, complemented
5#19135930C211yesmaximal, characteristic, complemented
6#19135178C211yesmaximal, characteristic, complemented
7#19135164C211yesmaximal, characteristic, complemented
8#19135030C211yesmaximal, characteristic
9#19135030C211yesmaximal, characteristic
10#19134854C211yesmaximal, characteristic, complemented
11#19134840C211yesmaximal, characteristic, complemented
12#19134627C211yesmaximal, characteristic, complemented
13#19134627C211yesmaximal, characteristic, complemented
14#19134287C211yesmaximal, characteristic, complemented
15C43×#2025C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C2×#13063296C2211yescharacteristic
19C2×D4×Dic43C2211yescharacteristic
20C2×(C22⋊D43)⋊C4—21no—
21C2×C42×D43C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28#14582797C2211yescharacteristic
29#14582795C2211yescharacteristic
30#14582795C2211yescharacteristic
31#14582793—21no—
32#14582780—21no—
33#14582780—21no—
34#14582775—21no—
35#14582770—21no—
36#14582770—21no—
37#14582765C2211yescharacteristic
38#14582756C2211yescharacteristic
39#14582756C2211yescharacteristic
40#14582756C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C22⋊C4×Dic43—21no—
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#125×C43C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C43×#390C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×C22⋊D43—21no—
60C23×Dic43—21no—
61C22×C4×D43D411yescharacteristic
62C22×C4×D43D411yescharacteristic
63C22×C4×D43C2311yescharacteristic
64C2×#10621872—22no—
65C2×#10621872—22no—
66C2×#10621872—22no—
67C2×#10621872—22no—
68C2×#10621872—41no—
69C2×#10621872—41no—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72#13063296—22no—
73#13063296Q814yes—
74D4×Dic43—41no—
75D4×Dic43—41no—
76(C22⋊D43)⋊C4—44no—
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43D411yescharacteristic
91C2×C4×Dic43D411yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93C42×D43—41no—
94C42×D43—41no—
95#13063258—22no—
96#13063258—41no—
97#13063256—22no—
98#13063256—41no—
99#13063246—22no—
100#13063246—22no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C22×D4×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113#125×C43—41no—
114#125×C43—41no—
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C42×C43C2311yescharacteristic
123#102×C43—41no—
124#102×C43—41no—
125C24×C43—21no—
126C23×D43C2×D411yescharacteristic
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43C2×Q812yes—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2411yescharacteristic
139C2×C22⋊D43—24no—
140C2×C22⋊D43—42no—
141C2×C22⋊D43—42no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—42no—
147C22×Dic43—42no—
148C22×Dic43—42no—
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C2×C4×D43—21no—
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—22no—
157C2×C4×D43—41no—
158C2×C4×D43—41no—
159C2×C4×D43—41no—
160C2×C4×D43—41no—
161C2×C4×D43—41no—
162C2×C4×D43C2×Q812yes—
163C2×C4×D43#4112yes—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—42no—
177C4⋊C4×C43—42no—
178C22⋊C4×C43—42no—
179C22⋊C4×C43—42no—
180C42×C43—21no—
181C42×C43—21no—
182C22⋊Dic43—24no—
183C22⋊Dic43—42no—
184(C2×D43)⋊C4—42no—
185(C2×D43)⋊C4—42no—
186(C2×D43)⋊C4—42no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43C2×Q812yes—
195Dic43⋊C4—42no—
196Dic43⋊C4—42no—
197Dic43⋊C4—42no—
198C4×Dic43—21no—
199C4×Dic43—21no—
200C4×Dic43—41no—
201C4×Dic43—41no—
202C4×Dic43—42no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8#4112yes—
208C2×C43⋊C8#4112yes—
209#10621872—44no—
210#10621872—44no—
211C23×C43—22no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43C22×D411yescharacteristic
219C22×D43—21no—
220C22×D43—21no—
221C22×D43—21no—
222C22×D43—21no—
223C22×D43—21no—
224C22×D43—21no—
225C22×D43C22⋊Q812yes—
226D4×C43—22no—
227D4×C43—22no—
228D4×C43—41no—
229D4×C43—41no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43C22×Q811yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43H(5,𝔽2)11yescharacteristic
250C2×C4×C43H(5,𝔽2)11yescharacteristic
251C22⋊D43—48no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—22no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—84no—
272C2×Dic43C22⋊Q812yes—
273C2×Dic43AGL(1,ℤ/8)12yes—
274C4×D43—22no—
275C4×D43—22no—
276C4×D43—22no—
277C4×D43—22no—
278C4×D43—44no—
279C4×D43—44no—
280C8×C43—41no—
281C8×C43—41no—
282C43⋊C8—22no—
283C43⋊C8—22no—
284#29167—431nomaximal, Sylow
285C22×C43—42no—
286C22×C43—42no—
287C22×C43—42no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43—81no—
291C22×C43—81no—
292C22×C43C2×C22⋊Q811yescharacteristic
293C22×C43#53211yescharacteristic
294C22×C43#53411yescharacteristic
295C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
296C22×C43#57511yescharacteristic
297C22×C43#57511yescharacteristic
298C22×C43#57511yescharacteristic
299C2×D43—22no—
300C2×D43—22no—
301C2×D43—22no—
302C2×D43—41no—
303C2×D43—41no—
304C2×D43—41no—
305C2×D43—41no—
306C4×C43—41no—
307C4×C43—41no—
308C4×C43—81no—
309C4×C43—81no—
310C4×C43—81no—
311C4×C43#55111yescharacteristic
312C4×C43#55111yescharacteristic
313C4×C43#55411yescharacteristic
314C4×C43#55411yescharacteristic
315Dic43—22no—
316Dic43—22no—
317Dic43—42no—
318Dic43—41no—
319Dic43—81no—
320Dic43—81no—
321Dic43—81no—
322#2851—431no—
323C4×#121—431no—
324#2101—431no—
325#2092—431no—
326#2059—431no—
327#2025D4311yescharacteristic, complemented
328#1920—431no—
329#1918—431no—
330#1895—431no—
331#1895—431no—
332#1864—431no—
333#1862—431no—
334#1809—431no—
335#1809—431no—
336#1728—431no—
337C2×C43—82no—
338C2×C43#256411yescharacteristic
339C2×C43#307711yescharacteristic
340C2×C43#308011yescharacteristic
341C2×C43#317111yescharacteristic
342C2×C43#318311yescharacteristic
343C2×C43#319411yescharacteristic
344C2×C43#319711yescharacteristic
345D43—42no—
346C22×M16—431no—
347C22×M16—431no—
348C2×#125C2×D4311yescharacteristic
349C2×#121—431no—
350C2×C4×D4—431no—
351C2×C4×D4—861no—
352C22×C42—431no—
353C2×#107—431no—
354C2×#107—431no—
355C2×#106—431no—
356C2×#106—431no—
357C2×#102—431no—
358C2×#102—431no—
359C2×#102C2×D4311yescharacteristic
360C2×#102C2×D4311yescharacteristic
361#390C2×D4311yescharacteristic
362#389—431no—
363#389—431no—
364#389—431no—
365#388—861no—
366#387—861no—
367#387—861no—
368#386—861no—
369#385—861no—
370#385—861no—
371#382—431no—
372#380—431no—
373#380—431no—
374#380—431no—
375C4×C4⋊C4—431no—
376C4×C22⋊C4—861no—
377#340—431no—
378#340—431no—
379#340—431no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340C2×D4311yescharacteristic
384#340C2×D4311yescharacteristic
385#336—431no—
386#336—431no—
387#336—431no—
388#336C2×D4311yescharacteristic
389C43#2916711yescharacteristic, complemented, Sylow
390C22×D4—861no—
391C22×D4C22×D4311yescharacteristic
392C23×C4—431no—
393C23×C4—431no—
394C23×C4—431no—
395C23×C4—861no—
396C2×M16—862no—
397C2×M16—862no—
398C2×M16—862no—
399C2×M16—862no—
400C2×M16—1721no—
401C2×M16—1721no—
402C22×C8—431no—
403C22×C8—431no—
404C22×C8C22×D4311yescharacteristic
405C22×C8C22×D4311yescharacteristic
406#125—41no—
407#125—41no—
408#121—434no—
409#121—862no—
410C4×D4—1721no—
411C4×D4—1721no—
412C4×D4—1724no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4C22×D4311yescharacteristic
423C2×C4⋊C4C22×D4311yescharacteristic
424C2×C4⋊C4C22×D4311yescharacteristic
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C42—431no—
433C2×C42—431no—
434C2×C42—431no—
435C2×C42—861no—
436C2×C42—1721no—
437C2×C42—1721no—
438C2×C42C22×D4311yescharacteristic
439#107—862no—
440#107—1721no—
441#106—862no—
442#106—1721no—
443#102—41no—
444#102—41no—
445#102—862no—
446#102—862no—
447#95—861no—
448#95—861no—
449#95—861no—
450#95—861no—
451#95—861no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456C24—21no—
457C24—431no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—864no—
464C2×D4—1722no—
465C2×D4—1722no—
466C2×D4Q8×D4312yes—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—431no—
471C22×C4—431no—
472C22×C4—432no—
473C22×C4—432no—
474C22×C4—431no—
475C22×C4—862no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4—861no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—1721no—
485C22×C4—1721no—
486C22×C4—1721no—
487C22×C4—1721no—
488C22×C4—1721no—
489C22×C4—1722no—
490C22×C4—1722no—
491C22×C4—1722no—
492C22×C4D4×D4311yescharacteristic
493C22×C4D4×D4311yescharacteristic
494C22×C4C23×D4311yescharacteristic
495M16—1724no—
496M16—1724no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—432no—
504C2×C8—432no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—42no—
516C4⋊C4—42no—
517C4⋊C4—432no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—1722no—
526C4⋊C4—1722no—
527C4⋊C4—1722no—
528C22⋊C4—42no—
529C22⋊C4—42no—
530C22⋊C4—864no—
531C22⋊C4—1722no—
532C22⋊C4—1722no—
533C22⋊C4—1722no—
534C22⋊C4—1722no—
535C42—21no—
536C42—21no—
537C42—861no—
538C42—861no—
539C42—1721no—
540C42—1721no—
541C42—1722no—
542C23—22no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—432no—
550C23—861no—
551C23—861no—
552C23—861no—
553C23—861no—
554C23—861no—
555C23—861no—
556C23C2×D4×D4311yescharacteristic
557D4—22no—
558D4—22no—
559D4—41no—
560D4—41no—
561D4—1728no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—432no—
578C2×C4—432no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—862no—
584C2×C4—862no—
585C2×C4—862no—
586C2×C4—862no—
587C2×C4—862no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—3444no—
592C2×C4—1724no—
593C2×C4—1724no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4C2×Q8×D4311yescharacteristic
606C2×C4#41×D4311yescharacteristic
607C2×C4#41×D4311yescharacteristic
608C2×C4#41×D4311yescharacteristic
609C2×C4#1306337011yescharacteristic
610C2×C4#1306337011yescharacteristic
611C8—41no—
612C8—41no—
613C8—862no—
614C8—862no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—81no—
619C22—81no—
620C22—81no—
621C22—81no—
622C22—862no—
623C22—862no—
624C22—862no—
625C22—1721no—
626C22—1721no—
627C22—1721no—
628C22—1721no—
629C22C22⋊Q8×D4311yescharacteristic
630C22#1458344811yescharacteristic
631C22#1458345911yescharacteristic
632C22AGL(1,ℤ/8)×D4311yescharacteristic
633C22#1458369511yescharacteristic
634C22#1458369611yescharacteristic
635C22#1458369611yescharacteristic
636C4—41no—
637C4—41no—
638C4—81no—
639C4—81no—
640C4—81no—
641C4—862no—
642C4—862no—
643C4—3441no—
644C4—3441no—
645C4—3441no—
646C4—1722no—
647C4—1721no—
648C4#1458357911yescharacteristic
649C4#1458357911yescharacteristic
650C4#1458360311yescharacteristic
651C4#1458360311yescharacteristic
652C2—82no—
653C2—1722no—
654C2#1913977211yescharacteristic
655C2#1914439011yescharacteristic
656C2#1914441211yescharacteristic
657C2#1914518911yescharacteristic
658C2#1914532311yescharacteristic
659C2#1914540711yescharacteristic
660C2#1914543411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2025C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
hypercenter#2025D43
hypocenterC43#29167
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2025

Complements

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

NH ≅ G/Ntype
1. #19142900C2semidirect
3. #19136164C2semidirect
4. #19136116C2semidirect
5. #19135930C2semidirect
6. #19135178C2semidirect
7. #19135164C2semidirect
10. #19134854C2semidirect
11. #19134840C2semidirect
12. #19134627C2semidirect
13. #19134627C2semidirect
14. #19134287C2semidirect
15. C43×#2025C2semidirect
327. #2025D43semidirect
389. C43#29167semidirect

Maximal subgroups

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

subgroupindex
#191429002
#191371112
#191361642
#191361162
#191359302
#191351782
#191351642
#191350302
#191348542
#191348402
#191346272
#191342872
C43×#20252
#2916743