Finite Group Databasebeta

← #25133264

Subgroups — #25133264

Order 11008.

1462 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148398C211yesmaximal, characteristic, complemented
2#19142882C212yesmaximal, complemented
3#19135948C212yesmaximal, complemented
4#19135759C212yesmaximal, complemented
5#19135580C212yesmaximal, complemented
6#19135004C212yesmaximal
7#19134875C212yesmaximal, complemented
8#19134583C211yesmaximal, characteristic, complemented
9C4×#120×C43C211yesmaximal, characteristic
10#14583608—24no—
11#14583606—22no—
12D4×Dic86—22no—
13#14583530—21no—
14#14583525—21no—
15#14583525C2212yes—
16#14583456—21no—
17C2×#13063304—22no—
18C2×#13063304—21no—
19C2×#13063304C2212yes—
20#14583374C2212yes—
21C2×#13063240C2212yes—
22#14582772—24no—
23#14582772C2214yes—
24#14582759—22no—
25#14582759C2212yes—
26#14582755C2214yes—
27#14582666C2212yes—
28#14582665C2214yes—
29#14582665C2214yes—
30C24×C4×C43C2211yescharacteristic
31C2×#120×C43C2211yescharacteristic
32C2×C4×D4×C43—21no—
33C2×C4×D4×C43C2211yescharacteristic
34C43×#386—21no—
35C43×#386C2211yescharacteristic
36C43×#385—21no—
37C43×#385C2211yescharacteristic
38C43×#379C2211yescharacteristic
39C4×C22⋊C4×C43—21no—
40C4×C22⋊C4×C43C2211yescharacteristic
41C22×Dic86—21no—
42C22×Dic86D412yescomplemented
43#13063325—21no—
44#13063325—21no—
45#13063324—24no—
46#13063317—22no—
47#13063316—24no—
48#13063304—22no—
49#13063304—22no—
50#13063304—22no—
51#13063304—22no—
52#13063304—22no—
53#13063304—22no—
54#13063304—22no—
55#13063304—22no—
56#13063304—48no—
57#13063302—24no—
58#13063302—24no—
59#13063302—24no—
60#13063302—24no—
61C4×Dic86—22no—
62C4×Dic86—22no—
63D4×Dic43—24no—
64D4×Dic43—24no—
65#13063284—22no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43—22no—
68C2×C4⋊Dic43D412yescomplemented
69C2×Dic43⋊C4—22no—
70C2×Dic43⋊C4—24no—
71C2×Dic43⋊C4D414yescomplemented
72C2×C22⋊Dic43—22no—
73C2×C22⋊Dic43—24no—
74C2×C22⋊Dic43—24no—
75C2×C22⋊Dic43C2314yes—
76C2×C22⋊Dic43C2314yes—
77#13063240—24no—
78C43⋊#95—22no—
79C43⋊#95—24no—
80C25×C43C2311yescharacteristic
81C22×D4×C43—21no—
82C22×D4×C43C2311yescharacteristic
83C23×C4×C43—21no—
84C23×C4×C43—22no—
85C23×C4×C43—21no—
86C23×C4×C43—22no—
87C23×C4×C43—44no—
88C23×C4×C43D411yescharacteristic
89C23×C4×C43C2311yescharacteristic
90C23×C4×C43C2311yescharacteristic
91#120×C43—22no—
92#120×C43Q814yescomplemented
93C4×D4×C43—22no—
94C4×D4×C43—22no—
95C4×D4×C43—44no—
96C2×C4⋊C4×C43—21no—
97C2×C4⋊C4×C43D411yescharacteristic
98C2×C22⋊C4×C43—21no—
99C2×C22⋊C4×C43—21no—
100C2×C22⋊C4×C43—21no—
101C2×C22⋊C4×C43—21no—
102C2×C22⋊C4×C43D411yescharacteristic
103C2×C22⋊C4×C43C2311yescharacteristic
104C2×C22⋊C4×C43C2311yescharacteristic
105C2×C22⋊C4×C43C2311yescharacteristic
106C2×C42×C43—21no—
107C2×C42×C43D411yescharacteristic
108#95×C43—21no—
109#95×C43—21no—
110#95×C43—21no—
111C24×C43—21no—
112C24×C43—22no—
113C24×C43—21no—
114C24×C43—22no—
115C24×C43—42no—
116C24×C43—42no—
117C24×C43C2×D411yescharacteristic
118C24×C43C2×Q812yescomplemented
119C24×C43C2411yescharacteristic
120C2×D4×C43—24no—
121C2×D4×C43—22no—
122C2×D4×C43—22no—
123C2×D4×C43—42no—
124C2×D4×C43—42no—
125C2×D4×C43C2×Q812yes—
126C2×D4×C43#4112yes—
127C22×C4×C43—24no—
128C22×C4×C43—28no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—22no—
134C22×C4×C43—21no—
135C22×C4×C43—44no—
136C22×C4×C43—42no—
137C22×C4×C43—42no—
138C22×C4×C43—42no—
139C22×C4×C43—44no—
140C22×C4×C43—42no—
141C22×C4×C43—44no—
142C22×C4×C43—42no—
143C22×C4×C43—42no—
144C22×C4×C43—41no—
145C22×C4×C43—42no—
146C22×C4×C43—41no—
147C22×C4×C43C2×D412yes—
148C22×C4×C43C2×D412yes—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43—24no—
157C22×Dic43C2×D414yes—
158C22×Dic43C2×D414yes—
159C2×Dic86—22no—
160C2×Dic86—22no—
161C2×Dic86—22no—
162C2×Dic86—22no—
163C2×Dic86—44no—
164C2×Dic86—82no—
165C4⋊C4×C43—22no—
166C4⋊C4×C43—42no—
167C22⋊C4×C43—22no—
168C22⋊C4×C43—24no—
169C22⋊C4×C43—22no—
170C22⋊C4×C43—21no—
171C22⋊C4×C43—22no—
172C22⋊C4×C43—42no—
173C22⋊C4×C43—42no—
174C22⋊C4×C43—42no—
175C22⋊C4×C43C2×Q812yescomplemented
176C42×C43—21no—
177C42×C43—21no—
178C42×C43—42no—
179C22⋊Dic43—24no—
180C22⋊Dic43—24no—
181C22⋊Dic43—24no—
182C22⋊Dic43—24no—
183C22⋊Dic43—24no—
184C22⋊Dic43—48no—
185C22⋊Dic43—48no—
186C4⋊Dic43—22no—
187C4⋊Dic43—22no—
188C4⋊Dic43—22no—
189C4⋊Dic43—22no—
190C4⋊Dic43—22no—
191C4⋊Dic43—22no—
192C4⋊Dic43—44no—
193Dic43⋊C4—24no—
194Dic43⋊C4—24no—
195Dic43⋊C4—24no—
196Dic43⋊C4—24no—
197Dic43⋊C4—48no—
198C4×Dic43—24no—
199C23×C43—24no—
200C23×C43—24no—
201C23×C43—22no—
202C23×C43—22no—
203C23×C43—21no—
204C23×C43—22no—
205C23×C43—24no—
206C23×C43—21no—
207C23×C43—41no—
208C23×C43—44no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—42no—
212C23×C43—41no—
213C23×C43—42no—
214C23×C43—48no—
215C23×C43—44no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—42no—
221C23×C43C22⋊Q812yescomplemented
222C23×C43C22×D412yes—
223C23×C43C22×D411yescharacteristic
224C23×C43C22×Q811yescharacteristic
225C23×C43C2×#4111yescharacteristic
226C23×C432−1+412yes—
227D4×C43—24no—
228D4×C43—24no—
229D4×C43—48no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—24no—
233C2×C4×C43—22no—
234C2×C4×C43—24no—
235C2×C4×C43—22no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—22no—
239C2×C4×C43—42no—
240C2×C4×C43—41no—
241C2×C4×C43—48no—
242C2×C4×C43—44no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—42no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—42no—
249C2×C4×C43—44no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—81no—
256C2×C4×C43#12011yescharacteristic
257C2×C4×C43#12012yes—
258C2×C4×C43#12011yescharacteristic
259C2×C4×C43C22⋊Q812yescomplemented
260C2×Dic43—24no—
261C2×Dic43—24no—
262C2×Dic43—44no—
263C2×Dic43—44no—
264C2×Dic43—44no—
265C2×Dic43—44no—
266C2×Dic43—44no—
267C2×Dic43—82no—
268C2×Dic43—82no—
269Dic86—44no—
270Dic86—82no—
271Dic86—82no—
272Dic86—82no—
273#24350—431nomaximal, Sylow
274C22×C43—21no—
275C22×C43—22no—
276C22×C43—21no—
277C22×C43—22no—
278C22×C43—28no—
279C22×C43—24no—
280C22×C43—22no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—42no—
284C22×C43—42no—
285C22×C43—44no—
286C22×C43—44no—
287C22×C43—42no—
288C22×C43—42no—
289C22×C43—42no—
290C22×C43—44no—
291C22×C43—42no—
292C22×C43—42no—
293C22×C43—41no—
294C22×C43—42no—
295C22×C43—41no—
296C22×C43—81no—
297C22×C43C2×#12011yescharacteristic
298C22×C43C2×C22⋊Q811yescharacteristic
299C22×C43#53611yescharacteristic
300C22×C43#54812yes—
301C22×C43D4×Q812yes—
302C4×C43—22no—
303C4×C43—22no—
304C4×C43—21no—
305C4×C43—42no—
306C4×C43—41no—
307C4×C43—42no—
308C4×C43—41no—
309C4×C43—81no—
310C4×C43B(4,𝔽2)12yes—
311Dic43—44no—
312Dic43—44no—
313Dic43—84no—
314#3501—431no—
315#2848—432no—
316C4×#120D4311yescharacteristic
317#2062—432no—
318#2029—432no—
319#1996—432no—
320#1889—432no—
321#1867—432no—
322#1799—431no—
323C2×C43—22no—
324C2×C43—21no—
325C2×C43—21no—
326C2×C43—22no—
327C2×C43—44no—
328C2×C43—42no—
329C2×C43#240911yescharacteristic
330C2×C43C2×B(4,𝔽2)11yescharacteristic
331C2×C43#302511yescharacteristic
332C24×C4C2×D4311yescharacteristic
333#554—862no—
334#554—864no—
335D4×Q8—862no—
336#544—861no—
337#543—432no—
338#543—861no—
339#533—861no—
340C2×C22⋊Q8—432no—
341C2×C22⋊Q8—861no—
342C2×C22⋊Q8—862no—
343C2×#120C2×D4311yescharacteristic
344#518—432no—
345C2×C4×D4—21no—
346C2×C4×D4C2×D4311yescharacteristic
347C2×#99—432no—
348#386—21no—
349#386C2×D4311yescharacteristic
350#385—21no—
351#385—434no—
352#385—864no—
353#385C2×D4311yescharacteristic
354#380—432no—
355#380—862no—
356#379—434no—
357#379C2×D4311yescharacteristic
358C4×C22⋊C4—21no—
359C4×C22⋊C4C2×D4311yescharacteristic
360#342—432no—
361#342—434no—
362#342—434no—
363C43#2435011yescharacteristic, complemented, Sylow
364C25C22×D4311yescharacteristic
365C22×Q8—432no—
366C22×Q8—861no—
367C22×D4—21no—
368C22×D4C22×D4311yescharacteristic
369C23×C4—22no—
370C23×C4—21no—
371C23×C4—22no—
372C23×C4—21no—
373C23×C4—44no—
374C23×C4C22⋊D4311yescharacteristic
375C23×C4C22×D4311yescharacteristic
376C23×C4C22×D4311yescharacteristic
377C4⋊Q8—861no—
378C4⋊Q8—861no—
379C4⋊Q8—864no—
380#125—862no—
381#125—864no—
382C22⋊Q8—864no—
383C22⋊Q8—864no—
384C22⋊Q8—864no—
385C22⋊Q8—864no—
386C22⋊Q8—862no—
387C22⋊Q8—862no—
388C22⋊Q8—862no—
389C22⋊Q8—862no—
390C22⋊Q8—862no—
391C22⋊Q8—862no—
392C22⋊Q8—862no—
393C22⋊Q8—862no—
394C22⋊Q8—1728no—
395#120—22no—
396#120Dic8614yescomplemented
397C4×Q8—862no—
398C4×Q8—862no—
399C4×D4—22no—
400C4×D4—22no—
401C4×D4—44no—
402C4×D4—864no—
403C4×D4—864no—
404#117—862no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—434no—
407C2×C4⋊C4—432no—
408C2×C4⋊C4—862no—
409C2×C4⋊C4—861no—
410C2×C4⋊C4—864no—
411C2×C4⋊C4—862no—
412C2×C4⋊C4C22⋊D4311yescharacteristic
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—434no—
418C2×C22⋊C4—434no—
419C2×C22⋊C4—862no—
420C2×C22⋊C4—864no—
421C2×C22⋊C4—864no—
422C2×C22⋊C4C22⋊D4311yescharacteristic
423C2×C22⋊C4C22×D4311yescharacteristic
424C2×C22⋊C4C22×D4311yescharacteristic
425C2×C22⋊C4C22×D4311yescharacteristic
426C2×C42—21no—
427C2×C42C22⋊D4311yescharacteristic
428#99—864no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—864no—
433#95—862no—
434C24—22no—
435C24—21no—
436C24—21no—
437C24—22no—
438C24—42no—
439C24—42no—
440C24C2×Dic8612yescomplemented
441C24C2×C22⋊D4311yescharacteristic
442C24C23×D4311yescharacteristic
443C2×Q8—862no—
444C2×Q8—862no—
445C2×Q8—862no—
446C2×Q8—862no—
447C2×Q8—3442no—
448C2×Q8—1724no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—24no—
452C2×D4—42no—
453C2×D4—42no—
454C2×D4C2×Dic8612yes—
455C2×D4#1062189812yes—
456C22×C4—24no—
457C22×C4—28no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—44no—
468C22×C4—42no—
469C22×C4—44no—
470C22×C4—42no—
471C22×C4—44no—
472C22×C4—42no—
473C22×C4—41no—
474C22×C4—42no—
475C22×C4—41no—
476C22×C4—434no—
477C22×C4—434no—
478C22×C4—862no—
479C22×C4—862no—
480C22×C4—864no—
481C22×C4D4×D4312yes—
482C22×C4D4×D4312yes—
483C22×C4C2×C22⋊D4311yescharacteristic
484C22×C4C2×C22⋊D4311yescharacteristic
485C22×C4C2×C22⋊D4311yescharacteristic
486C22×C4C2×C22⋊D4311yescharacteristic
487C22×C4C2×C22⋊D4311yescharacteristic
488C4⋊C4—22no—
489C4⋊C4—42no—
490C4⋊C4—862no—
491C4⋊C4—864no—
492C4⋊C4—862no—
493C4⋊C4—862no—
494C4⋊C4—864no—
495C4⋊C4—862no—
496C4⋊C4—864no—
497C4⋊C4—862no—
498C4⋊C4—862no—
499C4⋊C4—864no—
500C4⋊C4—1728no—
501C4⋊C4—1724no—
502C22⋊C4—22no—
503C22⋊C4—21no—
504C22⋊C4—22no—
505C22⋊C4—24no—
506C22⋊C4—22no—
507C22⋊C4—42no—
508C22⋊C4—42no—
509C22⋊C4—42no—
510C22⋊C4—864no—
511C22⋊C4—864no—
512C22⋊C4—864no—
513C22⋊C4—864no—
514C22⋊C4—864no—
515C22⋊C4—1728no—
516C22⋊C4—1728no—
517C22⋊C4C2×Dic8612yescomplemented
518C42—21no—
519C42—21no—
520C42—42no—
521C42—864no—
522C23—22no—
523C23—22no—
524C23—24no—
525C23—24no—
526C23—24no—
527C23—21no—
528C23—22no—
529C23—21no—
530C23—41no—
531C23—44no—
532C23—41no—
533C23—41no—
534C23—42no—
535C23—41no—
536C23—42no—
537C23—44no—
538C23—48no—
539C23—41no—
540C23—41no—
541C23—42no—
542C23—41no—
543C23—41no—
544C23#1306330412yescomplemented
545C23C2×D4×D4312yes—
546C23C22×C22⋊D4311yescharacteristic
547C23C22×Dic8611yescharacteristic
548C23C2×#1062189811yescharacteristic
549C23#1306337212yes—
550Q8—3442no—
551Q8—3442no—
552Q8—3442no—
553Q8—1724no—
554D4—24no—
555D4—24no—
556D4—48no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—22no—
562C2×C4—24no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—42no—
567C2×C4—41no—
568C2×C4—44no—
569C2×C4—48no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—44no—
576C2×C4—42no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—81no—
583C2×C4—864no—
584C2×C4—864no—
585C2×C4—3442no—
586C2×C4—3442no—
587C2×C4—1724no—
588C2×C4—1724no—
589C2×C4—1724no—
590C2×C4—1724no—
591C2×C4—1724no—
592C2×C4#1306329311yescharacteristic
593C2×C4#1306329312yes—
594C2×C4#1306329311yescharacteristic
595C2×C4#1306330412yescomplemented
596C22—21no—
597C22—22no—
598C22—21no—
599C22—22no—
600C22—24no—
601C22—28no—
602C22—22no—
603C22—41no—
604C22—41no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—44no—
611C22—44no—
612C22—44no—
613C22—42no—
614C22—41no—
615C22—41no—
616C22—42no—
617C22—42no—
618C22—81no—
619C22C2×#1306329311yescharacteristic
620C22C2×#1306330411yescharacteristic
621C22#1458347011yescharacteristic
622C22#1458355812yes—
623C22D4×Dic8612yes—
624C4—21no—
625C4—22no—
626C4—22no—
627C4—42no—
628C4—42no—
629C4—41no—
630C4—41no—
631C4—81no—
632C4—3444no—
633C4—1724no—
634C4—1724no—
635C4#1458308512yes—
636C2—21no—
637C2—21no—
638C2—22no—
639C2—22no—
640C2—44no—
641C2—42no—
642C2#1913796011yescharacteristic
643C2C2×#1458308511yescharacteristic
644C2#1914398611yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC24×C43C24
FrattiniC24C23×D43
FittingC4×#120×C43C2
socleC22×C43C2×#120
prime radicalC2×#120×C43C22
hypercenterC4×#120D43
hypocenterC43#24350
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#120

Complements

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

NH ≅ G/Ntype
1. #19148398C2semidirect
2. #19142882C2semidirect
3. #19135948C2semidirect
4. #19135759C2semidirect
5. #19135580C2semidirect
7. #19134875C2semidirect
8. #19134583C2semidirect
42. C22×Dic86D4semidirect
68. C2×C4⋊Dic43D4semidirect
71. C2×Dic43⋊C4D4semidirect
92. #120×C43Q8semidirect
118. C24×C43C2×Q8semidirect
175. C22⋊C4×C43C2×Q8semidirect
221. C23×C43C22⋊Q8semidirect
259. C2×C4×C43C22⋊Q8semidirect
363. C43#24350semidirect
396. #120Dic86semidirect
440. C24C2×Dic86semidirect
517. C22⋊C4C2×Dic86semidirect
544. C23#13063304semidirect
595. C2×C4#13063304semidirect

Maximal subgroups

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

subgroupindex
#191483982
#191428822
#191359482
#191357592
#191355802
#191350042
#191348752
#191345832
C4×#120×C432
#2435043