Finite Group Databasebeta

← #25101244

Subgroups — #25101244

Order 11008.

1338 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583524C211yesmaximal, characteristic
2#19137208C211yesmaximal, characteristic
3#19136947C211yesmaximal, characteristic
4#19135581C211yesmaximal, characteristic, complemented
5#19135580C211yesmaximal, characteristic, complemented
6#19135579C211yesmaximal, characteristic, complemented
7#19135578C214yesmaximal, complemented
8#342×D43C214yesmaximal
9C43×#1996C211yesmaximal, characteristic, complemented
10#14583524—22no—
11#14583524—22no—
12#14583524—22no—
13#14583524—22no—
14C2×#13063305C412yescomplemented
15C2×#13063304C2211yescharacteristic
16C2×#13063303C412yescomplemented
17C2×#13063303C412yescomplemented
18C2×#13063302C2212yes—
19C2×#13063301C412yescomplemented
20C22×(C2×D43)⋊C4C2211yescharacteristic
21C2×C22⋊C4×D43C2212yes—
22C2×C22⋊C4×D43C2212yes—
23C2×C22⋊C4×D43C2212yes—
24#14582773—22no—
25#14582770—22no—
26#14582759C2211yescharacteristic
27#14582757C2212yes—
28C22⋊C4×Dic43C2212yes—
29C4×(C2×D43)⋊C4—22no—
30C4×C22⋊Dic43C2211yescharacteristic
31#14582746—22no—
32#14582666C2214yes—
33#14582665C2214yes—
34#14582665C2214yes—
35C2×C22⋊Q8×C43C2211yescharacteristic
36C43×#380C2211yescharacteristic
37C4×C22⋊C4×C43C2211yescharacteristic
38C43×#342C2214yes—
39C24×D43C2311yescharacteristic
40C22×Dic86C2×C412yescomplemented
41C22×Dic86C2×C411yescharacteristic, complemented
42C23×Dic43C2311yescharacteristic
43C22×C4×D43—22no—
44C22×C4×D43—22no—
45C22×C4×D43C2×C412yes—
46C22×C4×D43C2×C412yes—
47#13063305—24no—
48#13063305—24no—
49#13063304—21no—
50#13063304—21no—
51#13063304—21no—
52#13063304—21no—
53#13063303—24no—
54#13063303—24no—
55#13063303—24no—
56#13063303—24no—
57#13063302—24no—
58#13063302—24no—
59#13063301—24no—
60#13063301—24no—
61C2×C4⋊Dic43—21no—
62C2×C4⋊Dic43C2×C412yescomplemented
63C2×C4⋊Dic43C2×C411yescharacteristic, complemented
64C2×Dic43⋊C4—22no—
65C2×Dic43⋊C4C2×C412yescomplemented
66C2×Dic43⋊C4C2×C412yescomplemented
67C2×Dic43⋊C4C2×C412yescomplemented
68C2×C22⋊Dic43C2312yes—
69C2×C22⋊Dic43C2312yes—
70C2×C22⋊Dic43C2312yes—
71C2×(C2×D43)⋊C4—22no—
72C2×(C2×D43)⋊C4—22no—
73C2×(C2×D43)⋊C4C2×C412yes—
74C2×(C2×D43)⋊C4C2×C412yes—
75C2×(C2×D43)⋊C4C2×C412yes—
76C2×(C2×D43)⋊C4C2×C412yes—
77C2×(C2×D43)⋊C4D412yes—
78C2×(C2×D43)⋊C4D412yes—
79C2×(C2×D43)⋊C4D412yes—
80C2×(C2×D43)⋊C4D412yes—
81C22⋊C4×D43—24no—
82C22⋊C4×D43—24no—
83C22⋊C4×D43—24no—
84C22⋊C4×D43—28no—
85C22⋊C4×D43Q818yescomplemented
86C2×C4×Dic43—21no—
87C2×C4×Dic43—22no—
88C43⋊#95—21no—
89C43⋊#95—21no—
90C43⋊#95—22no—
91C43⋊#95—22no—
92C22×Q8×C43C2×C411yescharacteristic, complemented
93C23×C4×C43C2311yescharacteristic
94C22⋊Q8×C43—21no—
95C22⋊Q8×C43—21no—
96C22⋊Q8×C43—21no—
97C22⋊Q8×C43—21no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43C2×C411yescharacteristic, complemented
100C2×C4⋊C4×C43C2×C412yescomplemented
101C2×C22⋊C4×C43C2312yes—
102C2×C22⋊C4×C43C2312yes—
103C2×C22⋊C4×C43C2312yes—
104C2×C42×C43—21no—
105#95×C43—21no—
106#95×C43—21no—
107C24×C43C2411yescharacteristic
108C23×D43—81no—
109C23×D43—81no—
110C23×D43C22×C412yes—
111C23×D43C2×D412yes—
112C23×D43C2×D412yes—
113C23×D43C2×Q814yes—
114C23×D43#4114yes—
115C2×Q8×C43—21no—
116C2×Q8×C43—21no—
117C2×Q8×C43—81no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—81no—
121C22×C4×C43C22×C412yes—
122C22×C4×C43C22×C412yes—
123C22×C4×C43C22×C411yescharacteristic
124C22×C4×C43C22×C411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×Dic43—22no—
130C22×Dic43—22no—
131C22×Dic43—81no—
132C22×Dic43C22×C412yes—
133C22×Dic43C22×C412yes—
134C22×Dic43C22×C412yes—
135C22×Dic43C2×D412yes—
136C22×Dic43C2×D412yes—
137C2×C4×D43—24no—
138C2×C4×D43—24no—
139C2×C4×D43—28no—
140C2×C4×D43—44no—
141C2×C4×D43—82no—
142C2×C4×D43—82no—
143C2×C4×D43—82no—
144C2×C4×D43—82no—
145C2×C4×D43—82no—
146C2×C4×D43—82no—
147C2×Dic86—21no—
148C2×Dic86—21no—
149C2×Dic86—24no—
150C2×Dic86—82no—
151C2×Dic86—81no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—22no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—81no—
157C22⋊C4×C43—22no—
158C22⋊C4×C43—22no—
159C22⋊C4×C43—22no—
160C22⋊C4×C43—24no—
161C22⋊C4×C43C2×Q814yes—
162C42×C43—81no—
163C22⋊Dic43—22no—
164C22⋊Dic43—22no—
165C22⋊Dic43—22no—
166C22⋊Dic43—24no—
167C22⋊Dic43C2×Q814yes—
168(C2×D43)⋊C4—24no—
169(C2×D43)⋊C4—24no—
170(C2×D43)⋊C4—28no—
171(C2×D43)⋊C4—44no—
172(C2×D43)⋊C4C22⋊C414yes—
173(C2×D43)⋊C4C22⋊C414yes—
174(C2×D43)⋊C4C22⋊C414yes—
175(C2×D43)⋊C4C22⋊C414yes—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—24no—
179C4⋊Dic43—81no—
180Dic43⋊C4—22no—
181Dic43⋊C4—22no—
182Dic43⋊C4—24no—
183Dic43⋊C4—24no—
184Dic43⋊C4—82no—
185C4×Dic43—82no—
186C4×Dic43—81no—
187C23×C43—41no—
188C23×C43—41no—
189C23×C43C23×C411yescharacteristic
190C23×C43C22×D411yescharacteristic
191C23×C43C22×D411yescharacteristic
192C23×C43C22×Q812yes—
193C23×C43C2×#4112yes—
194C22×D43—42no—
195C22×D43—42no—
196C22×D43—42no—
197C22×D43—42no—
198C22×D43—42no—
199C22×D43—42no—
200C22×D43—84no—
201C22×D43—84no—
202C22×D43C2×C22⋊C414yes—
203C22×D43C4×Q818yes—
204C22×D43C22⋊Q814yes—
205C22×D43C22⋊Q814yes—
206C22×D43#12414yes—
207C22×D43C4⋊Q814yes—
208Q8×C43—81no—
209Q8×C43—81no—
210C2×C4×C43—22no—
211C2×C4×C43—22no—
212C2×C4×C43—24no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—42no—
220C2×C4×C43—42no—
221C2×C4×C43—42no—
222C2×C4×C43—42no—
223C2×C4×C43—42no—
224C2×C4×C43—42no—
225C2×C4×C43—42no—
226C2×C4×C43C2×C22⋊C411yescharacteristic
227C2×C4×C43C2×C22⋊C411yescharacteristic
228C2×C4×C43C2×C22⋊C411yescharacteristic
229C2×C4×C43C2×C22⋊C411yescharacteristic
230C2×Dic43—22no—
231C2×Dic43—22no—
232C2×Dic43—24no—
233C2×Dic43—42no—
234C2×Dic43—42no—
235C2×Dic43—42no—
236C2×Dic43—42no—
237C2×Dic43—42no—
238C2×Dic43—42no—
239C2×Dic43—42no—
240C2×Dic43—42no—
241C2×Dic43—42no—
242C2×Dic43—42no—
243C2×Dic43C2×C22⋊C414yes—
244C4×D43—84no—
245C4×D43—84no—
246C4×D43—88no—
247C4×D43—88no—
248Dic86—84no—
249Dic86—81no—
250Dic86—81no—
251#21333—431nomaximal, Sylow
252C22×C43—21no—
253C22×C43—21no—
254C22×C43—21no—
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—21no—
258C22×C43—42no—
259C22×C43—42no—
260C22×C43C22×C22⋊C411yescharacteristic
261C22×C43C2×C4×Q812yes—
262C22×C43C2×C22⋊Q812yes—
263C22×C43C2×#12411yescharacteristic
264C22×C43C2×C4⋊Q811yescharacteristic
265C2×D43—24no—
266C2×D43—24no—
267C2×D43—48no—
268C2×D43—44no—
269C2×D43—44no—
270C2×D43—44no—
271C2×D43—44no—
272C2×D43#39118yes—
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—21no—
276C4×C43—21no—
277C4×C43—44no—
278C4×C43—42no—
279C4×C43—42no—
280C4×C43—82no—
281Dic43—24no—
282Dic43—44no—
283Dic43—42no—
284Dic43—42no—
285Dic43—82no—
286C2×#543—431no—
287#2315—431no—
288#2273—431no—
289#1996—431no—
290#1996—431no—
291#1996—434no—
292#1996—431no—
293#1996D4311yescharacteristic, complemented
294C2×#342—434no—
295C2×C43—22no—
296C2×C43—21no—
297C2×C43—22no—
298C2×C43—21no—
299C2×C43C2×#39111yescharacteristic
300C2×C43#288311yescharacteristic
301C2×C43#288311yescharacteristic
302D43—28no—
303#543—862no—
304#543—862no—
305#543—862no—
306#543—862no—
307C2×C22⋊Q8—432no—
308C2×C22⋊Q8—431no—
309C2×C22⋊Q8—432no—
310C2×C22⋊Q8—432no—
311C2×C22⋊Q8—432no—
312C2×C22⋊Q8—432no—
313C2×C22⋊Q8C2×D4311yescharacteristic
314C22×C22⋊C4—431no—
315C22×C22⋊C4—432no—
316C22×C22⋊C4—432no—
317C22×C22⋊C4—432no—
318#385—862no—
319#385—862no—
320#380—431no—
321#380—432no—
322#380C2×D4311yescharacteristic
323C4×C22⋊C4—431no—
324C4×C22⋊C4—432no—
325C4×C22⋊C4—862no—
326C4×C22⋊C4—862no—
327C4×C22⋊C4C2×D4311yescharacteristic
328#342—434no—
329#342—434no—
330#342—434no—
331#342C2×D4314yes—
332C43#2133311yescharacteristic, complemented, Sylow
333C25—431no—
334C22×Q8—432no—
335C22×Q8—431no—
336C22×Q8C4×D4311yescharacteristic, complemented
337C23×C4—431no—
338C23×C4—432no—
339C23×C4—432no—
340C23×C4—862no—
341C23×C4—862no—
342C23×C4C22×D4311yescharacteristic
343C22⋊Q8—21no—
344C22⋊Q8—21no—
345C22⋊Q8—21no—
346C22⋊Q8—21no—
347C22⋊Q8—864no—
348C22⋊Q8—864no—
349C22⋊Q8—864no—
350C22⋊Q8—864no—
351C22⋊Q8—864no—
352C22⋊Q8—864no—
353C22⋊Q8—864no—
354C22⋊Q8—864no—
355C22⋊Q8—864no—
356C22⋊Q8—864no—
357C22⋊Q8—861no—
358C22⋊Q8—861no—
359C22⋊Q8—861no—
360C22⋊Q8—861no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—432no—
363C2×C4⋊C4—432no—
364C2×C4⋊C4—432no—
365C2×C4⋊C4—432no—
366C2×C4⋊C4—431no—
367C2×C4⋊C4—862no—
368C2×C4⋊C4—861no—
369C2×C4⋊C4C4×D4312yescomplemented
370C2×C4⋊C4C4×D4311yescharacteristic, complemented
371C2×C22⋊C4—432no—
372C2×C22⋊C4—432no—
373C2×C22⋊C4—432no—
374C2×C22⋊C4—432no—
375C2×C22⋊C4—432no—
376C2×C22⋊C4—432no—
377C2×C22⋊C4—432no—
378C2×C22⋊C4—438no—
379C2×C22⋊C4—432no—
380C2×C22⋊C4—432no—
381C2×C22⋊C4—432no—
382C2×C22⋊C4—432no—
383C2×C22⋊C4—864no—
384C2×C22⋊C4—864no—
385C2×C22⋊C4—864no—
386C2×C22⋊C4—868no—
387C2×C22⋊C4—862no—
388C2×C22⋊C4—862no—
389C2×C22⋊C4C22×D4312yes—
390C2×C22⋊C4C22×D4312yes—
391C2×C22⋊C4C22×D4312yes—
392C2×C42—21no—
393C2×C42—862no—
394C2×C42—861no—
395#95—21no—
396#95—21no—
397#95—862no—
398#95—862no—
399#95—861no—
400#95—861no—
401C24—434no—
402C24—434no—
403C24—432no—
404C24—432no—
405C24—432no—
406C24—3441no—
407C24—3441no—
408C24C23×D4311yescharacteristic
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8—81no—
412C2×Q8—864no—
413C2×Q8—861no—
414C2×Q8—861no—
415C2×Q8—3441no—
416C2×Q8—3442no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—81no—
420C22×C4—432no—
421C22×C4—432no—
422C22×C4—432no—
423C22×C4—432no—
424C22×C4—432no—
425C22×C4—868no—
426C22×C4—864no—
427C22×C4—864no—
428C22×C4—862no—
429C22×C4—862no—
430C22×C4—3442no—
431C22×C4—3442no—
432C22×C4—3442no—
433C22×C4—3442no—
434C22×C4—3442no—
435C22×C4—3442no—
436C22×C4—3441no—
437C22×C4—1724no—
438C22×C4C2×C4×D4312yes—
439C22×C4C2×C4×D4312yes—
440C22×C4C2×C4×D4311yescharacteristic
441C22×C4C2×C4×D4311yescharacteristic
442C22×C4D4×D4311yescharacteristic
443C22×C4D4×D4311yescharacteristic
444C22×C4D4×D4311yescharacteristic
445C22×C4D4×D4311yescharacteristic
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—81no—
451C4⋊C4—864no—
452C4⋊C4—864no—
453C4⋊C4—864no—
454C4⋊C4—862no—
455C4⋊C4—862no—
456C4⋊C4—861no—
457C4⋊C4—861no—
458C4⋊C4—3442no—
459C4⋊C4—3441no—
460C22⋊C4—22no—
461C22⋊C4—22no—
462C22⋊C4—22no—
463C22⋊C4—24no—
464C22⋊C4—434no—
465C22⋊C4—434no—
466C22⋊C4—434no—
467C22⋊C4—434no—
468C22⋊C4—434no—
469C22⋊C4—864no—
470C22⋊C4—864no—
471C22⋊C4—868no—
472C22⋊C4—862no—
473C22⋊C4—862no—
474C22⋊C4—862no—
475C22⋊C4—864no—
476C22⋊C4—1724no—
477C22⋊C4Q8×D4314yes—
478C42—81no—
479C42—3441no—
480C42—3442no—
481C23—41no—
482C23—41no—
483C23—434no—
484C23—438no—
485C23—434no—
486C23—434no—
487C23—434no—
488C23—434no—
489C23—3444no—
490C23—3444no—
491C23—1722no—
492C23—1722no—
493C23—1722no—
494C23—1722no—
495C23—1722no—
496C23—1722no—
497C23C22×C4×D4311yescharacteristic
498C23C2×D4×D4311yescharacteristic
499C23C2×D4×D4311yescharacteristic
500C23C2×Q8×D4312yes—
501C23#41×D4312yes—
502Q8—81no—
503Q8—81no—
504Q8—3441no—
505Q8—3441no—
506Q8—3444no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—434no—
524C2×C4—862no—
525C2×C4—862no—
526C2×C4—864no—
527C2×C4—3444no—
528C2×C4—3444no—
529C2×C4—3448no—
530C2×C4—3448no—
531C2×C4—1722no—
532C2×C4—1722no—
533C2×C4—1722no—
534C2×C4—1722no—
535C2×C4—1722no—
536C2×C4—1722no—
537C2×C4—1722no—
538C2×C4—1722no—
539C2×C4—1722no—
540C2×C4—1722no—
541C2×C4C22⋊C4×D4311yescharacteristic
542C2×C4C22⋊C4×D4311yescharacteristic
543C2×C4C22⋊C4×D4311yescharacteristic
544C2×C4C22⋊C4×D4311yescharacteristic
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—21no—
551C22—42no—
552C22—42no—
553C22—438no—
554C22—864no—
555C22—864no—
556C22—1724no—
557C22—1724no—
558C22—1724no—
559C22—1728no—
560C22—1724no—
561C22C2×C22⋊C4×D4311yescharacteristic
562C22C4×Q8×D4312yes—
563C22C22⋊Q8×D4312yes—
564C22#124×D4311yescharacteristic
565C22C4⋊Q8×D4311yescharacteristic
566C4—21no—
567C4—21no—
568C4—21no—
569C4—21no—
570C4—44no—
571C4—42no—
572C4—42no—
573C4—82no—
574C4—864no—
575C4—3442no—
576C4—1724no—
577C4—1722no—
578C4—1722no—
579C2—22no—
580C2—21no—
581C2—22no—
582C2—21no—
583C2—868no—
584C2#391×D4311yescharacteristic
585C2#1914305311yescharacteristic
586C2#1914305411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#1996C2
socleC22×C43C22×C22⋊C4
prime radicalC24×D43C23
cosocleC24×C43C24
hypercenter#1996D43
hypocenterC43#21333
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
4. #19135581C2semidirect
5. #19135580C2semidirect
6. #19135579C2semidirect
7. #19135578C2semidirect
9. C43×#1996C2semidirect
14. C2×#13063305C4semidirect
16. C2×#13063303C4semidirect
17. C2×#13063303C4semidirect
19. C2×#13063301C4semidirect
40. C22×Dic86C2×C4semidirect
41. C22×Dic86C2×C4semidirect
62. C2×C4⋊Dic43C2×C4semidirect
63. C2×C4⋊Dic43C2×C4semidirect
65. C2×Dic43⋊C4C2×C4semidirect
66. C2×Dic43⋊C4C2×C4semidirect
67. C2×Dic43⋊C4C2×C4semidirect
85. C22⋊C4×D43Q8semidirect
92. C22×Q8×C43C2×C4semidirect
99. C2×C4⋊C4×C43C2×C4semidirect
100. C2×C4⋊C4×C43C2×C4semidirect
293. #1996D43semidirect
332. C43#21333semidirect
336. C22×Q8C4×D43semidirect
369. C2×C4⋊C4C4×D43semidirect
370. C2×C4⋊C4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835242
#191372082
#191369472
#191355812
#191355802
#191355792
#191355782
#342×D432
C43×#19962
#2133343