Finite Group Databasebeta

← #25125751

Subgroups — #25125751

Order 11008.

924 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582990C211yesmaximal, characteristic
2C2×SD16×Dic43C211yesmaximal, characteristic
3#19137164C211yesmaximal, characteristic, complemented
4#19137057C211yesmaximal, characteristic
5#19136075C211yesmaximal, characteristic, complemented
6#19136001C211yesmaximal, characteristic
7#19135976C211yesmaximal, characteristic, complemented
8#19135975C211yesmaximal, characteristic, complemented
9#19135912C211yesmaximal, characteristic
10#19135839C211yesmaximal, characteristic, complemented
11#19135676C211yesmaximal, characteristic
12C4⋊C8×Dic43C211yesmaximal, characteristic, complemented
13#103×Dic43C211yesmaximal, characteristic, complemented
14#19134414C211yesmaximal, characteristic, complemented
15C43×#2055C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C2×#13063323C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19C2×#13063290C2211yescharacteristic
20C2×D4×Dic43C2211yescharacteristic
21C2×#13063281—21no—
22#14582990—24no—
23SD16×Dic43—24no—
24C2×#13063257C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×C8×Dic43C2211yescharacteristic
34C2×C8×Dic43C2211yescharacteristic
35#14582805C2211yescharacteristic
36#14582802C2211yescharacteristic
37#14582797C2211yescharacteristic
38#14582796—21no—
39#14582796—21no—
40#14582795C2211yescharacteristic
41#14582793—21no—
42#14582787—21no—
43#14582768C2211yescharacteristic
44C4⋊C4×Dic43C2211yescharacteristic
45#14582750—21no—
46#14582750—21no—
47C22⋊C4×Dic43—21no—
48C42×Dic43C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C22×SD16×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C43×#391C2211yescharacteristic
59C43×#390C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C23×Dic43—21no—
63C2×#10621883—22no—
64C2×#10621883—22no—
65C2×#10621883—22no—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063323—22no—
69#13063323—22no—
70Q8×Dic43—22no—
71Q8×Dic43—22no—
72#13063290—22no—
73#13063290—22no—
74D4×Dic43—22no—
75D4×Dic43D414yes—
76#13063281—44no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43D411yescharacteristic
95C2×C4×Dic43D411yescharacteristic
96C2×C4×Dic43D411yescharacteristic
97C2×C4×Dic43D411yescharacteristic
98C2×C4×Dic43C2311yescharacteristic
99C2×C4×Dic43C2311yescharacteristic
100#13063257—22no—
101#13063256—22no—
102C4⋊(C43⋊C8)—22no—
103#13063250—22no—
104#13063250—22no—
105#13063249—22no—
106#13063249—22no—
107#13063248—22no—
108#13063246—22no—
109C8×Dic43—22no—
110C8×Dic43—22no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C22×Q8×C43C2311yescharacteristic
117C22×D4×C43C2311yescharacteristic
118C2×SD16×C43—22no—
119C2×SD16×C43—22no—
120C2×SD16×C43—22no—
121C22×C8×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C42×C43C2311yescharacteristic
128C4⋊C8×C43—22no—
129#103×C43—22no—
130#102×C43—22no—
131#95×C43—21no—
132#95×C43—21no—
133C24×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43#4112yes—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43C2×D412yes—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2411yescharacteristic
152C22×Dic43—24no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—42no—
158C22×Dic43—42no—
159C22×Dic43C2×D411yescharacteristic
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86#4112yes—
169SD16×C43—28no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43#4112yes—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C22⋊C4×C43—42no—
181C22⋊C4×C43—42no—
182C42×C43—21no—
183C42×C43—21no—
184C22⋊Dic43—24no—
185C22⋊Dic43—42no—
186C22⋊Dic43—42no—
187#10621883—28no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—42no—
194C4⋊Dic43C2×D412yes—
195Dic43⋊C4—24no—
196Dic43⋊C4—24no—
197Dic43⋊C4—42no—
198Dic43⋊C4—42no—
199Dic43⋊C4—42no—
200Dic43⋊C4—42no—
201Dic43⋊C4—42no—
202C4×Dic43—21no—
203C4×Dic43—21no—
204C4×Dic43—22no—
205C4×Dic43—22no—
206C4×Dic43—41no—
207C4×Dic43—42no—
208C4×Dic43—42no—
209C4×Dic43—42no—
210C4×Dic43SD1614yescomplemented
211C4×Dic43C2×D412yes—
212C4×Dic43#4112yes—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8#4112yes—
219C23×C43—22no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43C22×D411yescharacteristic
227Q8×C43—22no—
228Q8×C43—22no—
229Q8×C43—41no—
230Q8×C43—41no—
231D4×C43—22no—
232D4×C43—22no—
233D4×C43—41no—
234D4×C43—41no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—22no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43C2×SD1612yes—
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—48no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43#12112yes—
276C2×Dic43#12112yes—
277C2×Dic43C2×SD1612yes—
278C2×Dic43C2×SD1612yes—
279C2×Dic43#13512yes—
280C2×Dic43#13712yes—
281Dic86—22no—
282Dic86—22no—
283Dic86—41no—
284Dic86—41no—
285C8×C43—22no—
286C8×C43—41no—
287C43⋊C8—22no—
288C43⋊C8—41no—
289#23677—431nomaximal, Sylow
290C22×C43—42no—
291C22×C43—42no—
292C22×C43—42no—
293C22×C43—81no—
294C22×C43—81no—
295C22×C43—81no—
296C22×C43—81no—
297C22×C43C2×#12111yescharacteristic
298C22×C43#52511yescharacteristic
299C22×C43#53211yescharacteristic
300C22×C43C22×SD1611yescharacteristic
301C22×C43C2×#13511yescharacteristic
302C22×C43C2×#13711yescharacteristic
303C22×C43#57511yescharacteristic
304C4×C43—22no—
305C4×C43—42no—
306C4×C43—41no—
307C4×C43—81no—
308C4×C43—81no—
309C4×C43#52511yescharacteristic
310C4×C43#52511yescharacteristic
311C4×C43#52911yescharacteristic
312C4×C43#52911yescharacteristic
313Dic43—22no—
314Dic43—22no—
315Dic43—22no—
316Dic43—42no—
317Dic43—42no—
318Dic43—81no—
319Dic43—81no—
320Dic43#46114yes—
321C2×C4×SD16—431no—
322C2×C4×SD16—431no—
323C4×C4⋊Q8—431no—
324#2293—431no—
325#2084—431no—
326#2071—431no—
327#2066—431no—
328#2066—431no—
329#2055—431no—
330#2055D4311yescharacteristic
331#2043—431no—
332#2013—431no—
333C4×C4⋊C8—431no—
334C4×#103—431no—
335C4×#103—431no—
336C2×C43—82no—
337C2×C43#239211yescharacteristic
338C2×C43C2×#46111yescharacteristic
339C2×C43#303511yescharacteristic
340C2×C43#310311yescharacteristic
341C2×C43#310811yescharacteristic
342C2×C43#316711yescharacteristic
343C2×C43#317211yescharacteristic
344C22×SD16—431no—
345C22×SD16C2×D4311yescharacteristic
346C2×C4⋊Q8—431no—
347C2×C4×Q8—431no—
348C2×C4×Q8—431no—
349C2×C4×D4—431no—
350C2×#117—861no—
351C4×SD16—864no—
352C4×SD16—864no—
353C2×#106—431no—
354C2×#106—431no—
355C2×C4⋊C8—431no—
356C2×C4⋊C8C2×D4311yescharacteristic
357C2×#103—431no—
358C2×#103—431no—
359C2×#103—431no—
360C2×#103—431no—
361C2×#103—431no—
362C2×#103C2×D4311yescharacteristic
363C2×#102—431no—
364C2×#102C2×D4311yescharacteristic
365C2×C4×C8—431no—
366C2×C4×C8—431no—
367#391—431no—
368#391C2×D4311yescharacteristic
369#390—431no—
370#390C2×D4311yescharacteristic
371#389—431no—
372#389—431no—
373#389—861no—
374#389—861no—
375#388—861no—
376#388—861no—
377#384—431no—
378C4×C4⋊C4—431no—
379C4×C4⋊C4—861no—
380C4×C4⋊C4—861no—
381C4×C22⋊C4—861no—
382C43—431no—
383#340—431no—
384#340—431no—
385#340—431no—
386#340C2×D4311yescharacteristic
387#336—431no—
388#336—431no—
389C43#2367711yescharacteristic, complemented, Sylow
390C22×Q8—431no—
391C22×Q8C22×D4311yescharacteristic
392C22×D4C22×D4311yescharacteristic
393C23×C4—861no—
394C2×SD16—22no—
395C2×SD16—22no—
396C2×SD16—22no—
397C2×SD16—862no—
398C2×SD16—862no—
399C2×SD16—862no—
400C22×C8—431no—
401C22×C8—431no—
402C22×C8C22×D4311yescharacteristic
403C22×C8C22×D4311yescharacteristic
404C4⋊Q8—862no—
405C4⋊Q8—862no—
406C4×Q8—862no—
407C4×Q8—862no—
408C4×Q8—862no—
409C4×Q8—862no—
410C4×D4—434no—
411C4×D4—862no—
412#117—1724no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4C22×D4311yescharacteristic
425C2×C4⋊C4C22×D4311yescharacteristic
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—861no—
431C2×C42—431no—
432C2×C42—431no—
433C2×C42—431no—
434C2×C42—431no—
435C2×C42—431no—
436C2×C42—431no—
437C2×C42—861no—
438C2×C42—861no—
439C2×C42—861no—
440C2×C42C22×D4311yescharacteristic
441#106—862no—
442#106—862no—
443C4⋊C8—22no—
444C4⋊C8—862no—
445#103—22no—
446#103—862no—
447#103—862no—
448#103—862no—
449#103—862no—
450#103—862no—
451#102—22no—
452#102—862no—
453C4×C8—862no—
454C4×C8—862no—
455#95—21no—
456#95—21no—
457#95—861no—
458#95—861no—
459#95—861no—
460#95—861no—
461#95—861no—
462C24—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—432no—
469C2×Q8—861no—
470C2×Q8—861no—
471C2×Q8—861no—
472C2×Q8—861no—
473C2×Q8—861no—
474C2×Q8#1062190012yes—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4D4×D4312yes—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—431no—
488C22×C4—864no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—1722no—
494C22×C4—1722no—
495C22×C4D4×D4311yescharacteristic
496C22×C4D4×D4311yescharacteristic
497C22×C4C23×D4311yescharacteristic
498SD16—28no—
499SD16—868no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—432no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8#1062190012yes—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—432no—
517C4⋊C4—864no—
518C4⋊C4—864no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—1722no—
525C4⋊C4—1722no—
526C4⋊C4—1722no—
527C4⋊C4—1722no—
528C4⋊C4—1722no—
529C4⋊C4—1722no—
530C22⋊C4—42no—
531C22⋊C4—42no—
532C22⋊C4—864no—
533C22⋊C4—1722no—
534C22⋊C4—1722no—
535C42—21no—
536C42—21no—
537C42—434no—
538C42—432no—
539C42—432no—
540C42—862no—
541C42—862no—
542C42—861no—
543C42—861no—
544C42—1721no—
545C42—1722no—
546C42—1722no—
547C42—1722no—
548C23—22no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23C2×D4×D4311yescharacteristic
556Q8—22no—
557Q8—22no—
558Q8—41no—
559Q8—41no—
560Q8—862no—
561Q8—862no—
562Q8—1721no—
563Q8—1721no—
564D4—22no—
565D4—22no—
566D4—41no—
567D4—41no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—432no—
583C2×C4—432no—
584C2×C4—432no—
585C2×C4—432no—
586C2×C4—432no—
587C2×C4—432no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—862no—
595C2×C4—862no—
596C2×C4—1728no—
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—1721no—
606C2×C4—1721no—
607C2×C4SD16×D4312yes—
608C2×C4C2×D4×D4311yescharacteristic
609C2×C4#41×D4311yescharacteristic
610C2×C4#41×D4311yescharacteristic
611C2×C4#41×D4311yescharacteristic
612C2×C4C2×#1062190011yescharacteristic
613C2×C4C2×#1062190011yescharacteristic
614C8—22no—
615C8—41no—
616C8—862no—
617C8—1721no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—81no—
622C22—81no—
623C22—81no—
624C22—81no—
625C22#121×D4311yescharacteristic
626C22#1458340911yescharacteristic
627C22#1458344411yescharacteristic
628C22C2×SD16×D4311yescharacteristic
629C22#135×D4311yescharacteristic
630C22#137×D4311yescharacteristic
631C22#1458369511yescharacteristic
632C4—22no—
633C4—42no—
634C4—41no—
635C4—81no—
636C4—81no—
637C4—434no—
638C4—862no—
639C4—862no—
640C4—862no—
641C4—3441no—
642C4—3441no—
643C4—1722no—
644C4—1722no—
645C4#1458340511yescharacteristic
646C4#1458340711yescharacteristic
647C4#1458342611yescharacteristic
648C4#1458342811yescharacteristic
649C2—82no—
650C2#1913783811yescharacteristic
651C2#461×D4311yescharacteristic
652C2#1914404711yescharacteristic
653C2#1914462511yescharacteristic
654C2#1914467411yescharacteristic
655C2#1914514911yescharacteristic
656C2#1914519411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2055C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2055D43
hypocenterC43#23677
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2055

Complements

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

NH ≅ G/Ntype
3. #19137164C2semidirect
5. #19136075C2semidirect
7. #19135976C2semidirect
8. #19135975C2semidirect
10. #19135839C2semidirect
12. C4⋊C8×Dic43C2semidirect
13. #103×Dic43C2semidirect
14. #19134414C2semidirect
210. C4×Dic43SD16semidirect
389. C43#23677semidirect

Maximal subgroups

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

subgroupindex
C2×#145829902
C2×SD16×Dic432
#191371642
#191370572
#191360752
#191360012
#191359762
#191359752
#191359122
#191358392
#191356762
C4⋊C8×Dic432
#103×Dic432
#191344142
C43×#20552
#2367743