Finite Group Databasebeta

← #25125598

Subgroups — #25125598

Order 11008.

902 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×#14582940C211yesmaximal, characteristic
2C2×#14582938C211yesmaximal, characteristic
3#19137076C211yesmaximal, characteristic
4#382×D43C211yesmaximal, characteristic
5#19136082C211yesmaximal, characteristic, complemented
6#19136081C211yesmaximal, characteristic, complemented
7#19136080C211yesmaximal, characteristic, complemented
8#19136079C211yesmaximal, characteristic, complemented
9#19136078C211yesmaximal, characteristic, complemented
10#19136077C211yesmaximal, characteristic, complemented
11#19136076C211yesmaximal, characteristic, complemented
12#19134313C211yesmaximal, characteristic
13#19134313C211yesmaximal, characteristic
14#19134287C211yesmaximal, characteristic
15C43×#2085C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C2×#13063283C2211yescharacteristic
19C2×#13063283C2211yescharacteristic
20C2×C4⋊C4×D43C2211yescharacteristic
21C2×C4⋊C4×D43C2211yescharacteristic
22C2×C42×D43C2211yescharacteristic
23#14582940—24no—
24#14582938—24no—
25C2×#13063259C2211yescharacteristic
26C2×#13063258C2211yescharacteristic
27C2×#13063258C2211yescharacteristic
28C2×#13063257C2211yescharacteristic
29C2×#13063256C2211yescharacteristic
30C2×#13063256C2211yescharacteristic
31#14582798C2211yescharacteristic
32#14582797C2211yescharacteristic
33#14582795C2211yescharacteristic
34#14582773—21no—
35#14582770—21no—
36#14582765C2211yescharacteristic
37#14582764C2211yescharacteristic
38#14582764C2211yescharacteristic
39#14582763—21no—
40#14582763—21no—
41C4⋊C4×Dic43—21no—
42#14582750—21no—
43#95×D43—21no—
44#95×D43—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C2×#106×C43C2211yescharacteristic
56C43×#389C2211yescharacteristic
57C43×#382C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×C4×D43—21no—
62C22×C4×D43—21no—
63C22×C4×D43D411yescharacteristic
64C22×C4×D43D411yescharacteristic
65C22×C4×D43C2311yescharacteristic
66C2×#10621872—22no—
67C2×#10621872—22no—
68C2×#10621872—22no—
69C2×#10621872—22no—
70C2×#10621872Q814yes—
71C2×#10621872Q814yes—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74#13063283—22no—
75#13063283—22no—
76#13063283—22no—
77#13063283D414yes—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C4⋊C4×D43—22no—
88C4⋊C4×D43—22no—
89C4⋊C4×D43—22no—
90C4⋊C4×D43—22no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43D411yescharacteristic
96C2×C4×Dic43D411yescharacteristic
97C2×C4×Dic43C2311yescharacteristic
98C42×D43—22no—
99C42×D43—22no—
100#13063259—22no—
101#13063258—22no—
102#13063258—22no—
103#13063257—22no—
104#13063256—22no—
105#13063256—22no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C22×C8×C43C2311yescharacteristic
116C22×C8×C43C2311yescharacteristic
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C42×C43C2311yescharacteristic
123#107×C43—22no—
124#106×C43—22no—
125#95×C43—21no—
126#95×C43—21no—
127#95×C43—21no—
128C23×D43C2×D411yescharacteristic
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2411yescharacteristic
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43C2×D411yescharacteristic
141C22×Dic43C2×D411yescharacteristic
142C22×Dic43C2×D411yescharacteristic
143C2×C4×D43—22no—
144C2×C4×D43—22no—
145C2×C4×D43—41no—
146C2×C4×D43—41no—
147C2×C4×D43—41no—
148C2×C4×D43—41no—
149C2×C4×D43—42no—
150C2×C4×D43—42no—
151C2×C4×D43—42no—
152C2×C4×D43—42no—
153C2×C4×D43—42no—
154C2×C4×D43—42no—
155C2×C4×D43C2×D412yes—
156C2×C4×D43C2×Q812yes—
157C2×C4×D43C2×Q812yes—
158C2×C4×D43#4112yes—
159C2×C4×D43#4112yes—
160C2×C4×D43#4112yes—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43C2×Q812yes—
166C2×C8×C43C2×Q812yes—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—42no—
175C4⋊C4×C43C2×D412yes—
176C42×C43—21no—
177C42×C43—21no—
178(C2×D43)⋊C4—24no—
179(C2×D43)⋊C4—42no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—42no—
188C4⋊Dic43C2×D412yes—
189Dic43⋊C4—42no—
190Dic43⋊C4—42no—
191Dic43⋊C4—42no—
192Dic43⋊C4—42no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—24no—
196C4×Dic43—22no—
197C4×Dic43—22no—
198C4×Dic43—42no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8C2×Q812yes—
204C2×C43⋊C8C2×Q812yes—
205#10621872—28no—
206#10621872—28no—
207C23×C43C22×D411yescharacteristic
208C22×D43—21no—
209C22×D43—21no—
210C22×D43—21no—
211C22×D43—21no—
212C22×D43#12112yes—
213C22×D43#12312yes—
214C22×D43C4⋊Q812yes—
215C2×C4×C43—22no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C22×Q811yescharacteristic
235C2×C4×C43C22×Q811yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×Dic43—22no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43#12112yes—
258C2×Dic43#12312yes—
259C2×Dic43C4⋊Q812yes—
260C4×D43—44no—
261C4×D43—44no—
262C4×D43—84no—
263C4×D43—84no—
264C4×D43C22⋊Q814yes—
265C4×D43C22⋊Q814yes—
266C4×D43#12514yes—
267C4×D43#12514yes—
268C8×C43—22no—
269C8×C43—22no—
270C43⋊C8—22no—
271C43⋊C8—22no—
272#23659—431nomaximal, Sylow
273C22×C43C2×#12111yescharacteristic
274C22×C43C2×#12311yescharacteristic
275C22×C43C2×C4⋊Q811yescharacteristic
276C22×C43#57511yescharacteristic
277C22×C43#57511yescharacteristic
278C22×C43#57511yescharacteristic
279C22×C43#57511yescharacteristic
280C2×D43—22no—
281C2×D43—22no—
282C2×D43—22no—
283C2×D43—22no—
284C2×D43—22no—
285C2×D43—22no—
286C2×D43#39814yes—
287C4×C43—41no—
288C4×C43—41no—
289C4×C43—42no—
290C4×C43—81no—
291C4×C43—81no—
292C4×C43—81no—
293C4×C43C2×C22⋊Q811yescharacteristic
294C4×C43C2×C22⋊Q811yescharacteristic
295C4×C43C2×#12511yescharacteristic
296C4×C43C2×#12511yescharacteristic
297Dic43—41no—
298Dic43—41no—
299Dic43—42no—
300Dic43—81no—
301Dic43—81no—
302Dic43—81no—
303Dic43#39814yes—
304C2×#428—431no—
305C2×#428—431no—
306#2296—431no—
307C2×#382—431no—
308#2085—431no—
309#2085—431no—
310#2085—431no—
311#2085—431no—
312#2085—431no—
313#2085—431no—
314#2085—431no—
315#2085D4311yescharacteristic, complemented
316#1736—431no—
317#1736—431no—
318#1728—431no—
319C2×C43C2×#39811yescharacteristic
320C2×C43#304011yescharacteristic
321C2×C43#304011yescharacteristic
322C2×C43#309311yescharacteristic
323C2×C43#309311yescharacteristic
324C2×C43#316611yescharacteristic
325C2×C43#316611yescharacteristic
326D43—24no—
327C22×M16—431no—
328C22×M16—431no—
329C2×#117—431no—
330C2×#117—431no—
331C22×C4⋊C4—431no—
332C22×C4⋊C4—431no—
333C22×C42—431no—
334#428—864no—
335#428—864no—
336C2×#107—431no—
337C2×#107—431no—
338C2×#107—431no—
339C2×#107C2×D4311yescharacteristic
340C2×#106—431no—
341C2×#106—431no—
342C2×#106—431no—
343C2×#106C2×D4311yescharacteristic
344#389—431no—
345#389—431no—
346#389—431no—
347#389C2×D4311yescharacteristic
348#385—861no—
349#385—861no—
350#382—431no—
351#382—431no—
352#382—431no—
353#382—861no—
354#382—861no—
355#382C2×D4311yescharacteristic
356C4×C4⋊C4—861no—
357C4×C4⋊C4—861no—
358C2×#95—861no—
359C2×#95—861no—
360#340—431no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340—431no—
365#340—431no—
366#340C2×D4311yescharacteristic
367#340C2×D4311yescharacteristic
368#336—431no—
369#336—431no—
370#336—431no—
371#336C2×D4311yescharacteristic
372C43#2365911yescharacteristic, complemented, Sylow
373C23×C4—431no—
374C23×C4—431no—
375C23×C4—431no—
376C23×C4—861no—
377C23×C4—861no—
378C2×M16—434no—
379C2×M16—434no—
380C2×M16—862no—
381C2×M16—862no—
382C2×M16—862no—
383C2×M16—862no—
384C22×C8—431no—
385C22×C8—431no—
386C22×C8C22×D4311yescharacteristic
387C22×C8C22×D4311yescharacteristic
388#117—434no—
389#117—862no—
390#117—862no—
391#117—862no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—862no—
398C2×C4⋊C4—862no—
399C2×C4⋊C4—862no—
400C2×C4⋊C4—862no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—861no—
406C2×C4⋊C4C22×D4311yescharacteristic
407C2×C4⋊C4C22×D4311yescharacteristic
408C2×C4⋊C4C22×D4311yescharacteristic
409C2×C4⋊C4C22×D4311yescharacteristic
410C2×C22⋊C4—861no—
411C2×C22⋊C4—861no—
412C2×C42—431no—
413C2×C42—431no—
414C2×C42—431no—
415C2×C42—862no—
416C2×C42—862no—
417C2×C42—861no—
418C2×C42—861no—
419C2×C42C22×D4311yescharacteristic
420#107—22no—
421#107—862no—
422#107—862no—
423#107—862no—
424#106—22no—
425#106—862no—
426#106—862no—
427#106—862no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—861no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438#95—861no—
439#95—861no—
440C24—431no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—431no—
446C22×C4—432no—
447C22×C4—432no—
448C22×C4—432no—
449C22×C4—432no—
450C22×C4—432no—
451C22×C4—432no—
452C22×C4—431no—
453C22×C4—431no—
454C22×C4—862no—
455C22×C4—862no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—1721no—
461C22×C4—1721no—
462C22×C4—1721no—
463C22×C4—1721no—
464C22×C4—1722no—
465C22×C4—1722no—
466C22×C4—1722no—
467C22×C4—1722no—
468C22×C4—1722no—
469C22×C4—1722no—
470C22×C4D4×D4311yescharacteristic
471C22×C4D4×D4311yescharacteristic
472C22×C4C23×D4311yescharacteristic
473M16—868no—
474M16—868no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—432no—
480C2×C8—432no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8Q8×D4312yes—
486C2×C8Q8×D4312yes—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—42no—
495C4⋊C4—432no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—1722no—
504C4⋊C4—1722no—
505C4⋊C4—1722no—
506C4⋊C4—1722no—
507C4⋊C4—1722no—
508C4⋊C4D4×D4312yes—
509C22⋊C4—864no—
510C22⋊C4—1722no—
511C42—21no—
512C42—21no—
513C42—862no—
514C42—862no—
515C42—864no—
516C42—861no—
517C42—861no—
518C42—1722no—
519C23—432no—
520C23—432no—
521C23—432no—
522C23—861no—
523C23—861no—
524C23—861no—
525C23—861no—
526C23C2×D4×D4311yescharacteristic
527C2×C4—22no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—432no—
546C2×C4—432no—
547C2×C4—432no—
548C2×C4—434no—
549C2×C4—434no—
550C2×C4—434no—
551C2×C4—434no—
552C2×C4—862no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—3444no—
560C2×C4—3444no—
561C2×C4—1724no—
562C2×C4—1724no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4C2×D4×D4311yescharacteristic
575C2×C4C2×Q8×D4311yescharacteristic
576C2×C4C2×Q8×D4311yescharacteristic
577C2×C4#41×D4311yescharacteristic
578C2×C4#41×D4311yescharacteristic
579C2×C4#41×D4311yescharacteristic
580C8—22no—
581C8—22no—
582C8—862no—
583C8—862no—
584C22—434no—
585C22—862no—
586C22—862no—
587C22—862no—
588C22—862no—
589C22—862no—
590C22—862no—
591C22#121×D4311yescharacteristic
592C22#123×D4311yescharacteristic
593C22C4⋊Q8×D4311yescharacteristic
594C22#1458369511yescharacteristic
595C22#1458369611yescharacteristic
596C22#1458369611yescharacteristic
597C22#1458369811yescharacteristic
598C4—41no—
599C4—41no—
600C4—42no—
601C4—81no—
602C4—81no—
603C4—81no—
604C4—434no—
605C4—3441no—
606C4—3441no—
607C4—3441no—
608C4—1721no—
609C4—1721no—
610C4—1722no—
611C4C22⋊Q8×D4311yescharacteristic
612C4C22⋊Q8×D4311yescharacteristic
613C4#125×D4311yescharacteristic
614C4#125×D4311yescharacteristic
615C2—864no—
616C2#398×D4311yescharacteristic
617C2#1914408411yescharacteristic
618C2#1914408611yescharacteristic
619C2#1914452311yescharacteristic
620C2#1914452711yescharacteristic
621C2#1914514311yescharacteristic
622C2#1914514611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2085C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#2085D43
hypocenterC43#23659
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2085

Complements

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

NH ≅ G/Ntype
5. #19136082C2semidirect
6. #19136081C2semidirect
7. #19136080C2semidirect
8. #19136079C2semidirect
9. #19136078C2semidirect
10. #19136077C2semidirect
11. #19136076C2semidirect
15. C43×#2085C2semidirect
315. #2085D43semidirect
372. C43#23659semidirect

Maximal subgroups

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

subgroupindex
C2×#145829402
C2×#145829382
#191370762
#382×D432
#191360822
#191360812
#191360802
#191360792
#191360782
#191360772
#191360762
#191343132
#191342872
C43×#20852
#2365943