Finite Group Databasebeta

← #25165098

Subgroups — #25165098

Order 11008.

762 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#19138945C211yesmaximal, characteristic
2#19137624C211yesmaximal, characteristic, complemented
3#19135912C211yesmaximal, characteristic, complemented
4#19135793C211yesmaximal, characteristic, complemented
5#19135747C211yesmaximal, characteristic, complemented
6#19135599C211yesmaximal, characteristic
7#19135552C211yesmaximal, characteristic, complemented
8#19135294C211yesmaximal, characteristic, complemented
9#19135209C211yesmaximal, characteristic, complemented
10#19135182C211yesmaximal, characteristic, complemented
11#19134947C211yesmaximal, characteristic, complemented
12#19134914C211yesmaximal, characteristic
13#19134688C211yesmaximal, characteristic, complemented
14#19134424C211yesmaximal, characteristic, complemented
15C43×#1926C211yesmaximal, characteristic, complemented
16C22×#10621883C2211yescharacteristic
17C2×#13063317C2211yescharacteristic
18C2×#13063305C2211yescharacteristic
19C2×#13063296C2211yescharacteristic
20C2×#13063290C2211yescharacteristic
21C2×#13063283C2211yescharacteristic
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×(C2×D43)⋊C8C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×#13063235C2211yescharacteristic
30#14582827—21no—
31#14582814—21no—
32#14582805C2211yescharacteristic
33#14582802C2211yescharacteristic
34#14582799—21no—
35#14582798C2211yescharacteristic
36#14582791—21no—
37#14582790—21no—
38#14582787—21no—
39#14582784—21no—
40#14582756C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4×C4⋊Dic43—21no—
43C4×(C2×D43)⋊C4C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#106×C43C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C43×#390C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×C22⋊D43—21no—
61C22×C4×D43C2311yescharacteristic
62C2×#10621883—22no—
63C2×#10621883—41no—
64C2×#10621883—41no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063317—22no—
68#13063317—41no—
69#13063305—22no—
70#13063305—22no—
71#13063296—22no—
72#13063296—41no—
73#13063290—22no—
74#13063290—41no—
75#13063283—22no—
76#13063283—41no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4D411yescharacteristic
92C2×(C2×D43)⋊C4D411yescharacteristic
93C2×C4×Dic43—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43C2311yescharacteristic
97C4⋊(C43⋊C8)—41no—
98#13063250—22no—
99#13063250—41no—
100#13063248—22no—
101#13063246—41no—
102(C2×D43)⋊C8—41no—
103(C2×D43)⋊C8—41no—
104#13063235—41no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95D411yescharacteristic
111C43⋊#95D411yescharacteristic
112C22×D4×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C22⋊C4×C43—21no—
119C2×C22⋊C4×C43—21no—
120C2×C42×C43—21no—
121C2×C42×C43C2311yescharacteristic
122#106×C43—22no—
123#102×C43—22no—
124#102×C43—22no—
125#95×C43—21no—
126C24×C43—21no—
127C23×D43C2×D411yescharacteristic
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2411yescharacteristic
140C2×C22⋊D43—42no—
141C2×C22⋊D43—42no—
142C2×C22⋊D43—81no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C2×C4×D43—21no—
151C2×C4×D43—21no—
152C2×C4×D43—21no—
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86#4112yes—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43#4112yes—
173C4⋊C4×C43#4112yes—
174C22⋊C4×C43—81no—
175C22⋊C4×C43—81no—
176C42×C43—21no—
177C42×C43—21no—
178C42×C43—42no—
179C22⋊Dic43—42no—
180C22⋊Dic43—42no—
181C22⋊Dic43—81no—
182#10621883—44no—
183(C2×D43)⋊C4—24no—
184(C2×D43)⋊C4—41no—
185(C2×D43)⋊C4—41no—
186(C2×D43)⋊C4—42no—
187(C2×D43)⋊C4—81no—
188C4⋊Dic43—24no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—42no—
195C4⋊Dic43#4112yes—
196Dic43⋊C4—42no—
197Dic43⋊C4—42no—
198Dic43⋊C4—42no—
199C4×Dic43—21no—
200C4×Dic43—21no—
201C4×Dic43—42no—
202C4×Dic43—42no—
203C4×Dic43—81no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43C22×D411yescharacteristic
218C22×D43—21no—
219C22×D43—21no—
220C22×D43—21no—
221C22×D43—21no—
222C22×D43—21no—
223C22×D43—21no—
224C22×D43—21no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—41no—
229C2×C4×C43—22no—
230C2×C4×C43—22no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
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×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43H(5,𝔽2)11yescharacteristic
249C2×C4×C43H(5,𝔽2)11yescharacteristic
250C22⋊D43—84no—
251C2×Dic43—21no—
252C2×Dic43—22no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—22no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
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—41no—
272C4×D43—41no—
273C4×D43—41no—
274C4×D43—41no—
275C4×D43—41no—
276Dic86—22no—
277Dic86—22no—
278Dic86—41no—
279Dic86—41no—
280C8×C43—41no—
281C8×C43—41no—
282C43⋊C8—41no—
283C43⋊C8—41no—
284#26751—431nomaximal, Sylow
285C22×C43—81no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43—81no—
291C22×C43—81no—
292C22×C43#52511yescharacteristic
293C22×C43#54611yescharacteristic
294C22×C43#54611yescharacteristic
295C22×C43#57511yescharacteristic
296C22×C43#57511yescharacteristic
297C22×C43#57711yescharacteristic
298C22×C43#57711yescharacteristic
299C2×D43—41no—
300C2×D43—41no—
301C2×D43—41no—
302C2×D43—41no—
303C2×D43—41no—
304C2×D43—41no—
305C2×D43—41no—
306C4×C43—42no—
307C4×C43—42no—
308C4×C43—41no—
309C4×C43—41no—
310C4×C43—81no—
311C4×C43#52911yescharacteristic
312C4×C43#53811yescharacteristic
313C4×C43#55511yescharacteristic
314C4×C43#55911yescharacteristic
315Dic43—42no—
316Dic43—41no—
317Dic43—41no—
318Dic43—42no—
319Dic43—41no—
320Dic43—81no—
321Dic43—81no—
322#2490—431no—
323#2362—431no—
324#2055—431no—
325#2035—431no—
326#2026—431no—
327#2000—431no—
328#1989—431no—
329#1936—431no—
330#1926D4311yescharacteristic, complemented
331#1924—431no—
332#1920—431no—
333#1880—431no—
334#1875—431no—
335#1825—431no—
336#1763—431no—
337C2×C43—161no—
338C2×C43#245911yescharacteristic
339C2×C43#311111yescharacteristic
340C2×C43#312611yescharacteristic
341C2×C43#330711yescharacteristic
342C2×C43#331111yescharacteristic
343C2×C43#331711yescharacteristic
344C2×C43#332611yescharacteristic
345D43—81no—
346C22×SD16—431no—
347C2×#125—431no—
348C2×C22⋊Q8—431no—
349C2×#121—431no—
350C2×C4×Q8—431no—
351C2×#117—431no—
352C2×#106C2×D4311yescharacteristic
353C2×C4⋊C8—431no—
354C2×#103—431no—
355C2×#103—431no—
356C2×#103—431no—
357C2×#102—431no—
358C2×#102C2×D4311yescharacteristic
359C2×#102C2×D4311yescharacteristic
360C2×C22⋊C8—431no—
361C2×C22⋊C8—431no—
362C2×#97—431no—
363#397—861no—
364#394—861no—
365#391—431no—
366#390—431no—
367#390—861no—
368#390C2×D4311yescharacteristic
369#389—431no—
370#388—861no—
371#388—861no—
372#388—861no—
373#387—861no—
374#380—431no—
375C4×C4⋊C4—431no—
376C4×C4⋊C4—861no—
377C4×C4⋊C4C2×D4311yescharacteristic
378C4×C22⋊C4—431no—
379#340—431no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340—431no—
384#340—431no—
385#340—431no—
386#340C2×D4311yescharacteristic
387#336—431no—
388#336C2×D4311yescharacteristic
389C43#2675111yescharacteristic, complemented, Sylow
390C22×Q8—431no—
391C22×D4—861no—
392C22×D4C22×D4311yescharacteristic
393C23×C4—431no—
394C2×SD16—862no—
395C2×SD16—1721no—
396C2×SD16—1721no—
397C22×C8—431no—
398C22×C8—431no—
399C22×C8C22×D4311yescharacteristic
400C22×C8C22×D4311yescharacteristic
401#125—862no—
402#125—1721no—
403C22⋊Q8—862no—
404C22⋊Q8—862no—
405#121—862no—
406#121—1721no—
407C4×Q8—862no—
408C4×Q8—1721no—
409#117—862no—
410#117—1721no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4C22×D4311yescharacteristic
420C2×C4⋊C4C22×D4311yescharacteristic
421C2×C4⋊C4C22×D4311yescharacteristic
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—431no—
425C2×C22⋊C4—431no—
426C2×C22⋊C4—861no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C42—21no—
433C2×C42—431no—
434C2×C42—861no—
435C2×C42—861no—
436C2×C42—861no—
437C2×C42C22×D4311yescharacteristic
438#106—22no—
439C4⋊C8—1721no—
440#103—862no—
441#103—862no—
442#103—1721no—
443#102—22no—
444#102—22no—
445#102—1721no—
446C22⋊C8—1721no—
447C22⋊C8—1721no—
448#97—1721no—
449#95—21no—
450#95—431no—
451#95—431no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456#95—861no—
457C24—21no—
458C24—431no—
459C2×Q8—432no—
460C2×Q8—861no—
461C2×Q8—861no—
462C2×Q8—861no—
463C2×Q8—861no—
464C2×Q8—861no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—3441no—
472C2×D4—1722no—
473C2×D4—1722no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—431no—
478C22×C4—431no—
479C22×C4—431no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4D4×D4311yescharacteristic
491C22×C4D4×D4311yescharacteristic
492C22×C4C23×D4311yescharacteristic
493SD16—1724no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8—861no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—432no—
511C4⋊C4—864no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—1722no—
518C4⋊C4—1722no—
519C4⋊C4—1722no—
520C4⋊C4—1722no—
521C4⋊C4#1062189812yes—
522C4⋊C4#1062190012yes—
523C22⋊C4—81no—
524C22⋊C4—81no—
525C22⋊C4—864no—
526C22⋊C4—3441no—
527C22⋊C4—3441no—
528C22⋊C4—1721no—
529C22⋊C4—1721no—
530C22⋊C4—1722no—
531C22⋊C4—1722no—
532C22⋊C4—1722no—
533C42—21no—
534C42—21no—
535C42—42no—
536C42—861no—
537C42—861no—
538C42—3441no—
539C42—1722no—
540C42—1722no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—861no—
549C23—861no—
550C23—861no—
551C23—861no—
552C23—861no—
553C23—861no—
554C23—861no—
555C23C2×D4×D4311yescharacteristic
556Q8—862no—
557Q8—862no—
558Q8—1721no—
559Q8—1721no—
560D4—41no—
561D4—41no—
562D4—41no—
563D4—41no—
564D4—3444no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—862no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—862no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
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×C4#41×D4311yescharacteristic
606C2×C4#41×D4311yescharacteristic
607C2×C4C2×#1062190011yescharacteristic
608C2×C4C2×#1062189811yescharacteristic
609C2×C4#1306337111yescharacteristic
610C2×C4#1306337111yescharacteristic
611C8—41no—
612C8—41no—
613C8—1721no—
614C8—1721no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22—81no—
620C22—81no—
621C22—81no—
622C22—1721no—
623C22—1721no—
624C22—1721no—
625C22—1721no—
626C22—1721no—
627C22—1721no—
628C22—1721no—
629C22#1458340911yescharacteristic
630C22#1458354111yescharacteristic
631C22#1458354511yescharacteristic
632C22#1458369511yescharacteristic
633C22#1458369611yescharacteristic
634C22#1458370511yescharacteristic
635C22#1458370911yescharacteristic
636C4—42no—
637C4—41no—
638C4—41no—
639C4—42no—
640C4—81no—
641C4—3441no—
642C4—3441no—
643C4—1721no—
644C4—1721no—
645C4—1722no—
646C4—1721no—
647C4—1722no—
648C4#1458342711yescharacteristic
649C4#1458348811yescharacteristic
650C4#1458361411yescharacteristic
651C4#1458363111yescharacteristic
652C2—161no—
653C2—3441no—
654C2#1913853711yescharacteristic
655C2#1914470111yescharacteristic
656C2#1914488411yescharacteristic
657C2#1914657611yescharacteristic
658C2#1914662911yescharacteristic
659C2#1914672411yescharacteristic
660C2#1914685311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1926C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
hypercenter#1926D43
hypocenterC43#26751
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1926

Complements

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

NH ≅ G/Ntype
2. #19137624C2semidirect
3. #19135912C2semidirect
4. #19135793C2semidirect
5. #19135747C2semidirect
7. #19135552C2semidirect
8. #19135294C2semidirect
9. #19135209C2semidirect
10. #19135182C2semidirect
11. #19134947C2semidirect
13. #19134688C2semidirect
14. #19134424C2semidirect
15. C43×#1926C2semidirect
330. #1926D43semidirect
389. C43#26751semidirect

Maximal subgroups

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

subgroupindex
#191389452
#191376242
#191359122
#191357932
#191357472
#191355992
#191355522
#191352942
#191352092
#191351822
#191349472
#191349142
#191346882
#191344242
C43×#19262
#2675143