Finite Group Databasebeta

← #25125293

Subgroups — #25125293

Order 11008.

1178 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582942C211yesmaximal, characteristic, complemented
2C2×#14582922C211yesmaximal, characteristic, complemented
3C2×#14582901C211yesmaximal, characteristic
4C2×#14582898C211yesmaximal, characteristic
5#19137083C211yesmaximal, characteristic
6C2×#14582795C211yesmaximal, characteristic, complemented
7#19135991C212yesmaximal, complemented
8#19135984C212yesmaximal, complemented
9#19135977C212yesmaximal, complemented
10#19135970C212yesmaximal, complemented
11C43×#1736C211yesmaximal, characteristic, complemented
12C22×#10621898C2211yescharacteristic
13C22×#10621877C2211yescharacteristic
14C22×C4⋊Dic43C2211yescharacteristic
15C22×Dic43⋊C4—21no—
16C22×C4×Dic43C2211yescharacteristic
17#14582942—24no—
18C2×#13063258C2212yes—
19C2×#13063256C2212yes—
20#14582922—24no—
21C2×Dic43⋊C8C2212yes—
22C2×Dic43⋊C8C2212yes—
23#14582901—24no—
24#14582898—24no—
25C2×#13063250C2212yes—
26C2×#13063248C2212yes—
27C2×#13063247C2212yes—
28C2×#13063245C2212yes—
29#14582804C2211yescharacteristic
30#14582804C2211yescharacteristic
31#14582800C2211yescharacteristic
32#14582800C2211yescharacteristic
33#14582795—21no—
34#14582795—21no—
35#14582795C2212yes—
36#14582795C2212yes—
37#14582776—21no—
38#14582776—21no—
39C4×(C2×D43)⋊C4—21no—
40C4×(C2×D43)⋊C4—21no—
41C2×C43⋊#95—21no—
42C22×M16×C43C2211yescharacteristic
43C2×#117×C43C2211yescharacteristic
44C22×C4⋊C4×C43C2211yescharacteristic
45C43×#340C2212yes—
46C43×#340C2212yes—
47C2×#10621898—22no—
48C2×#10621898—22no—
49C2×#10621898—22no—
50C2×#10621898—22no—
51C2×#10621898—22no—
52C2×#10621898Q814yes—
53C22×Dic86C2311yescharacteristic
54C22×D172C2311yescharacteristic
55C22×C22⋊D43—21no—
56C23×Dic43—21no—
57C23×Dic43D411yescharacteristic
58C23×Dic43D411yescharacteristic
59C22×C4×D43—21no—
60C2×#10621877—22no—
61C2×#10621877—22no—
62C2×#10621877D414yes—
63C22×C43⋊C8C2312yes—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43—22no—
66C2×C4⋊Dic43D414yes—
67C2×C4⋊Dic43C2312yes—
68C2×Dic43⋊C4—22no—
69C2×Dic43⋊C4—22no—
70C2×Dic43⋊C4—44no—
71C2×(C2×D43)⋊C4—21no—
72C2×(C2×D43)⋊C4—21no—
73C2×(C2×D43)⋊C4—21no—
74C2×(C2×D43)⋊C4—21no—
75C2×C4×Dic43—22no—
76C2×C4×Dic43—22no—
77C2×C4×Dic43D411yescharacteristic
78C2×C4×Dic43D411yescharacteristic
79C2×C4×Dic43C2311yescharacteristic
80C2×C4×Dic43C2311yescharacteristic
81#13063258—24no—
82#13063256—24no—
83Dic43⋊C8—24no—
84Dic43⋊C8—24no—
85#13063250—24no—
86#13063248—24no—
87#13063247—24no—
88#13063245—24no—
89C43⋊#95—22no—
90C43⋊#95—22no—
91C43⋊#95—21no—
92C43⋊#95—21no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C23×C4×C43—21no—
96C23×C4×C43C2311yescharacteristic
97C2×M16×C43—22no—
98C2×M16×C43—22no—
99C2×M16×C43—22no—
100C22×C8×C43C2312yes—
101#117×C43—22no—
102#117×C43—22no—
103C2×C4⋊C4×C43—22no—
104C2×C4⋊C4×C43—22no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43C2312yes—
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C22⋊C4×C43—21no—
110C2×C42×C43—21no—
111C24×C43C2×D411yescharacteristic
112C23×D43—21no—
113C22×C4×C43—21no—
114C22×C4×C43—21no—
115C22×C4×C43—22no—
116C22×C4×C43—42no—
117C22×C4×C43—42no—
118C22×C4×C43—42no—
119C22×C4×C43C2×D412yes—
120C22×C4×C43C2×D412yes—
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×Q812yes—
123C22×C4×C43#4112yes—
124C22×C4×C43#4112yes—
125C22×C4×C43#4112yes—
126C22×C4×C43C2411yescharacteristic
127C2×C22⋊D43—24no—
128C2×C22⋊D43—42no—
129C2×C22⋊D43—42no—
130C22×Dic43—22no—
131C22×Dic43—22no—
132C22×Dic43—22no—
133C22×Dic43—22no—
134C22×Dic43—24no—
135C22×Dic43—21no—
136C22×Dic43—22no—
137C22×Dic43—41no—
138C22×Dic43—41no—
139C22×Dic43—42no—
140C22×Dic43—42no—
141C22×Dic43C2×D411yescharacteristic
142C22×Dic43C2×D411yescharacteristic
143C22×Dic43C2×D411yescharacteristic
144C22×Dic43C2×D411yescharacteristic
145#10621898—28no—
146#10621898—28no—
147#10621898—44no—
148#10621898—44no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172C2×Q812yes—
155C2×C4×D43—24no—
156C2×C4×D43—42no—
157C2×C4×D43—42no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86C2×Q812yes—
164M16×C43—44no—
165C2×C8×C43—22no—
166C2×C8×C43—22no—
167C2×C8×C43—22no—
168C4⋊C4×C43—22no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—22no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—42no—
175C22⋊C4×C43—42no—
176C42×C43—42no—
177(C2×D43)⋊C4—42no—
178(C2×D43)⋊C4—42no—
179(C2×D43)⋊C4—42no—
180(C2×D43)⋊C4—42no—
181C4⋊Dic43—24no—
182C4⋊Dic43—22no—
183C4⋊Dic43C2×D414yes—
184Dic43⋊C4—44no—
185Dic43⋊C4—44no—
186C4×Dic43—22no—
187C4×Dic43—22no—
188C4×Dic43—21no—
189C4×Dic43—21no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192#10621877—28no—
193C2×C43⋊C8—22no—
194C2×C43⋊C8—22no—
195C2×C43⋊C8C2×D414yes—
196C23×C43—21no—
197C23×C43—21no—
198C23×C43—21no—
199C23×C43—21no—
200C23×C43#12112yes—
201C23×C43#12112yes—
202C23×C43C22⋊Q812yes—
203C23×C43C22×D411yescharacteristic
204C22×D43—22no—
205C22×D43—41no—
206C22×D43—41no—
207C22×D43—41no—
208C22×D43—41no—
209C22×D43—41no—
210C22×D43—41no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—42no—
220C2×C4×C43—84no—
221C2×C4×C43#12114yes—
222C2×C4×C43#12112yes—
223C2×C4×C43#12112yes—
224C2×C4×C43C22⋊Q814yes—
225C2×C4×C43C22⋊Q814yes—
226C2×C4×C43C22⋊Q812yes—
227C2×C4×C43#12614yes—
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C22×D411yescharacteristic
230C2×C4×C43C22×Q811yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C22⋊D43—48no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—24no—
242C2×Dic43—22no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—44no—
248C2×Dic43—44no—
249C2×Dic43—48no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—42no—
253C2×Dic43—42no—
254C2×Dic43AGL(1,ℤ/8)12yes—
255C2×Dic43#13712yes—
256D172—22no—
257D172—22no—
258D172—41no—
259D172—41no—
260C4×D43—48no—
261Dic86—22no—
262Dic86—22no—
263Dic86—41no—
264Dic86—41no—
265C8×C43—42no—
266C43⋊C8—24no—
267#23617—431nomaximal, Sylow
268C22×C43—22no—
269C22×C43—22no—
270C22×C43—22no—
271C22×C43—22no—
272C22×C43—22no—
273C22×C43—22no—
274C22×C43#39614yes—
275C22×C43C2×#12111yescharacteristic
276C22×C43C2×#12111yescharacteristic
277C22×C43C2×C22⋊Q811yescharacteristic
278C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
279C22×C43C2×#13711yescharacteristic
280C22×C43#57511yescharacteristic
281C22×C43#57511yescharacteristic
282C2×D43—42no—
283C2×D43—42no—
284C2×D43—42no—
285C2×D43—81no—
286C2×D43—81no—
287C2×D43—81no—
288C2×D43—81no—
289C4×C43—81no—
290C4×C43—81no—
291C4×C43—82no—
292C4×C43#39614yes—
293C4×C43C2×#12111yescharacteristic
294C4×C43C2×C22⋊Q811yescharacteristic
295C4×C43C2×C22⋊Q811yescharacteristic
296C4×C43C2×#12611yescharacteristic
297Dic43—22no—
298Dic43—22no—
299Dic43—42no—
300Dic43—44no—
301Dic43—41no—
302Dic43—41no—
303C2×#428—431no—
304C2×#423—431no—
305C2×#417—431no—
306C2×#417—431no—
307#2297—431no—
308C2×#389—431no—
309#2068—432no—
310#2067—432no—
311#2066—432no—
312#2065—432no—
313#1736D4311yescharacteristic, complemented
314C2×C43—24no—
315C2×C43C2×#39611yescharacteristic
316C2×C43#303611yescharacteristic
317C2×C43#303711yescharacteristic
318C2×C43#305511yescharacteristic
319C2×C43#305611yescharacteristic
320C2×C43#307911yescharacteristic
321C2×C43#308011yescharacteristic
322D43—82no—
323C22×#41—431no—
324C22×M16—431no—
325C22×M16C2×D4311yescharacteristic
326C2×#117C2×D4311yescharacteristic
327C22×C4⋊C4—431no—
328C22×C4⋊C4—861no—
329C22×C4⋊C4C2×D4311yescharacteristic
330C22×C42—431no—
331#428—864no—
332C2×#107—432no—
333C2×#106—432no—
334#423—864no—
335C2×C4⋊C8—432no—
336C2×C4⋊C8—432no—
337#417—864no—
338#417—864no—
339C2×#103—432no—
340C2×#103—432no—
341C2×#102—432no—
342C2×#102—432no—
343#391—431no—
344#391—431no—
345#390—431no—
346#390—431no—
347#389—432no—
348#389—432no—
349#389—861no—
350#389—861no—
351#386—861no—
352#386—861no—
353C4×C22⋊C4—861no—
354C4×C22⋊C4—861no—
355C2×#95—861no—
356#340C2×D4312yes—
357#340C2×D4312yes—
358C43#2361711yescharacteristic, complemented, Sylow
359C2×#41—434no—
360C2×#41—862no—
361C2×#41—862no—
362C2×#41—862no—
363C2×#41—862no—
364C2×#41—862no—
365C22×Q8—431no—
366C22×D4—431no—
367C22×D4—861no—
368C23×C4—21no—
369C23×C4—431no—
370C23×C4—431no—
371C23×C4—861no—
372C23×C4—861no—
373C23×C4C22×D4311yescharacteristic
374C2×M16—22no—
375C2×M16—22no—
376C2×M16—22no—
377C2×M16—434no—
378C2×M16—862no—
379C2×M16—862no—
380C22×C8—432no—
381C22×C8C22×D4312yes—
382#117—22no—
383#117—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—434no—
388C2×C4⋊C4—432no—
389C2×C4⋊C4—862no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4—862no—
392C2×C4⋊C4—862no—
393C2×C4⋊C4—1724no—
394C2×C4⋊C4C22×D4312yes—
395C2×C4⋊C4C22×D4311yescharacteristic
396C2×C4⋊C4C22×D4311yescharacteristic
397C2×C22⋊C4—21no—
398C2×C22⋊C4—861no—
399C2×C22⋊C4—861no—
400C2×C22⋊C4—861no—
401C2×C22⋊C4—861no—
402C2×C42—21no—
403C2×C42—431no—
404C2×C42—431no—
405C2×C42—431no—
406C2×C42—431no—
407C2×C42—862no—
408C2×C42—862no—
409#107—864no—
410#106—864no—
411C4⋊C8—864no—
412C4⋊C8—864no—
413#103—864no—
414#103—864no—
415#102—864no—
416#102—864no—
417#95—862no—
418#95—862no—
419#95—861no—
420#95—861no—
421#95—861no—
422#95—861no—
423C24—861no—
424C24D4×D4311yescharacteristic
425#41—868no—
426#41—868no—
427#41—1724no—
428#41—1724no—
429C2×Q8—432no—
430C2×Q8—861no—
431C2×Q8—861no—
432C2×Q8—861no—
433C2×Q8—861no—
434C2×Q8—861no—
435C2×D4—432no—
436C2×D4—864no—
437C2×D4—861no—
438C2×D4—861no—
439C2×D4—861no—
440C2×D4—861no—
441C2×D4—861no—
442C2×D4—1722no—
443C2×D4—1722no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—431no—
451C22×C4—431no—
452C22×C4—431no—
453C22×C4—431no—
454C22×C4—862no—
455C22×C4—862no—
456C22×C4—862no—
457C22×C4—862no—
458C22×C4—864no—
459C22×C4—861no—
460C22×C4—862no—
461C22×C4—864no—
462C22×C4—1721no—
463C22×C4—1721no—
464C22×C4—1722no—
465C22×C4—1722no—
466C22×C4—1722no—
467C22×C4—1722no—
468C22×C4#1062189812yes—
469C22×C4#1062189812yes—
470C22×C4#1062189812yes—
471C22×C4D4×D4311yescharacteristic
472C22×C4D4×D4312yes—
473C22×C4D4×D4312yes—
474C22×C4Q8×D4312yes—
475C22×C4C23×D4311yescharacteristic
476M16—44no—
477M16—868no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—434no—
482C2×C8—862no—
483C2×C8—862no—
484C4⋊C4—22no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—22no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—42no—
491C4⋊C4—434no—
492C4⋊C4—864no—
493C4⋊C4—862no—
494C4⋊C4—1724no—
495C4⋊C4—1724no—
496C22⋊C4—42no—
497C22⋊C4—1722no—
498C22⋊C4—1722no—
499C22⋊C4—1722no—
500C22⋊C4—1722no—
501C42—42no—
502C42—862no—
503C42—862no—
504C42—861no—
505C42—861no—
506C42—861no—
507C42—861no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—862no—
513C23—1721no—
514C23—1721no—
515C23—1721no—
516C23—1721no—
517C23—1721no—
518C23—1721no—
519C23#1306329812yes—
520C23#1306329812yes—
521C23#1306330312yes—
522C23C2×D4×D4311yescharacteristic
523Q8—862no—
524Q8—862no—
525Q8—1721no—
526Q8—1721no—
527D4—862no—
528D4—862no—
529D4—1728no—
530D4—1721no—
531D4—1721no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—41no—
541C2×C4—84no—
542C2×C4—432no—
543C2×C4—432no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—861no—
549C2×C4—861no—
550C2×C4—864no—
551C2×C4—862no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—1724no—
557C2×C4—1724no—
558C2×C4—1728no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1722no—
562C2×C4—1722no—
563C2×C4—1728no—
564C2×C4#1306329812yes—
565C2×C4#1306329812yes—
566C2×C4#1306329814yes—
567C2×C4#1306330312yes—
568C2×C4#1306330314yes—
569C2×C4#1306330314yes—
570C2×C4#1306331914yes—
571C2×C4C2×D4×D4311yescharacteristic
572C2×C4C2×D4×D4311yescharacteristic
573C2×C4C2×Q8×D4311yescharacteristic
574C2×C4C2×#1062189811yescharacteristic
575C2×C4C2×#1062189811yescharacteristic
576C2×C4C2×#1062189811yescharacteristic
577C8—42no—
578C8—864no—
579C22—22no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—3441no—
586C22—3441no—
587C22—3441no—
588C22—3441no—
589C22—1722no—
590C22—1722no—
591C22—1722no—
592C22#1458282314yes—
593C22C2×#1306329811yescharacteristic
594C22C2×#1306329811yescharacteristic
595C22C2×#1306330311yescharacteristic
596C22AGL(1,ℤ/8)×D4311yescharacteristic
597C22#137×D4311yescharacteristic
598C22#1458369511yescharacteristic
599C22#1458369811yescharacteristic
600C4—82no—
601C4—81no—
602C4—81no—
603C4—862no—
604C4—862no—
605C4—1721no—
606C4—1722no—
607C4—1721no—
608C4—1724no—
609C4#1458282314yes—
610C4C2×#1306329811yescharacteristic
611C4C2×#1306330311yescharacteristic
612C4C2×#1306330311yescharacteristic
613C4C2×#1306331911yescharacteristic
614C2—24no—
615C2—3442no—
616C2C2×#1458282311yescharacteristic
617C2#1914405811yescharacteristic
618C2#1914406611yescharacteristic
619C2#1914421211yescharacteristic
620C2#1914422311yescharacteristic
621C2#1914440811yescharacteristic
622C2#1914441611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1736C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
hypercenter#1736D43
hypocenterC43#23617
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
1. C2×#14582942C2semidirect
2. C2×#14582922C2semidirect
6. C2×#14582795C2semidirect
7. #19135991C2semidirect
8. #19135984C2semidirect
9. #19135977C2semidirect
10. #19135970C2semidirect
11. C43×#1736C2semidirect
313. #1736D43semidirect
358. C43#23617semidirect

Maximal subgroups

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

subgroupindex
C2×#145829422
C2×#145829222
C2×#145829012
C2×#145828982
#191370832
C2×#145827952
#191359912
#191359842
#191359772
#191359702
C43×#17362
#2361743