Finite Group Databasebeta

← #25153571

Subgroups — #25153571

Order 11008.

1054 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583629C211yesmaximal, characteristic, complemented
2C2×#14583260C211yesmaximal, characteristic
3C2×#14583124C211yesmaximal, characteristic
4#19140082C211yesmaximal, characteristic
5#19135734C211yesmaximal, characteristic, complemented
6#19135730C211yesmaximal, characteristic
7#19135728C211yesmaximal, characteristic
8#19135545C211yesmaximal, characteristic, complemented
9#19135533C211yesmaximal, characteristic, complemented
10#19134951C211yesmaximal, characteristic
11#19134949C211yesmaximal, characteristic
12#19134939C211yesmaximal, characteristic, complemented
13#19134933C211yesmaximal, characteristic, complemented
14#19134424C211yesmaximal, characteristic, complemented
15C43×#2024C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18#14583629—24no—
19#14583629—24no—
20C2×#13063324—21no—
21C2×#13063324C2211yescharacteristic
22C2×#13063324C2211yescharacteristic
23C2×#13063323—21no—
24C2×#13063323—21no—
25C2×#13063314C2211yescharacteristic
26C2×C4×Dic86C2211yescharacteristic
27C2×C4×Dic86C2211yescharacteristic
28C2×#13063290—21no—
29C2×#13063290C2211yescharacteristic
30C2×#13063290C2211yescharacteristic
31#14583260—24no—
32#14583124—24no—
33C2×Dic43⋊C8C2211yescharacteristic
34C2×#13063250C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063247C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40C2×#13063235C2211yescharacteristic
41#14582828—21no—
42#14582812—21no—
43#14582806C2211yescharacteristic
44#14582801C2211yescharacteristic
45#14582800C2211yescharacteristic
46#14582791—21no—
47#14582788—21no—
48C4⋊C4×Dic43C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582654C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C2×C4⋊Q8×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C43×#391C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86—21no—
65C22×Dic86D411yescharacteristic
66C22×Dic86C2311yescharacteristic
67C22×D172C2311yescharacteristic
68C2×#10621885—22no—
69C2×#10621885—22no—
70C2×#10621885—22no—
71C2×#10621873—22no—
72C2×#10621873—22no—
73C2×#10621873—22no—
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76#13063324—28no—
77#13063324—22no—
78#13063324—22no—
79#13063324—22no—
80#13063324D414yes—
81#13063323—28no—
82#13063323—28no—
83#13063314—22no—
84#13063314—22no—
85C4×Dic86—22no—
86C4×Dic86—22no—
87C4×Dic86—22no—
88C4×Dic86—22no—
89#13063290—28no—
90#13063290—22no—
91#13063290—22no—
92#13063290—22no—
93#13063290D414yes—
94C2×C4⋊Dic43D411yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4D411yescharacteristic
103C2×Dic43⋊C4D411yescharacteristic
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C2×(C2×D43)⋊C4—21no—
110C2×C4×Dic43—21no—
111C2×C4×Dic43—21no—
112C2×C4×Dic43—21no—
113C2×C4×Dic43—21no—
114C2×C4×Dic43C2311yescharacteristic
115C2×C4×Dic43C2311yescharacteristic
116Dic43⋊C8—22no—
117#13063250—22no—
118#13063249—22no—
119#13063248—22no—
120#13063247—22no—
121#13063245—22no—
122#13063245—22no—
123#13063235—22no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C43⋊#95—21no—
127C22×Q8×C43—21no—
128C22×Q8×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131C4⋊Q8×C43—22no—
132C4⋊Q8×C43—22no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C42×C43C2311yescharacteristic
138#103×C43—22no—
139#103×C43—22no—
140#95×C43—21no—
141#95×C43—21no—
142C23×D43—21no—
143C2×Q8×C43—24no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—81no—
151C2×Q8×C43—81no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2411yescharacteristic
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172—21no—
171C2×D172—21no—
172C2×Dic86—22no—
173C2×Dic86—21no—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—22no—
177C2×Dic86—22no—
178C2×Dic86—24no—
179C2×Dic86—24no—
180C2×Dic86—81no—
181C2×Dic86—81no—
182C2×Dic86—81no—
183C2×Dic86—81no—
184C2×Dic86C2×D412yes—
185C2×Dic86#4112yes—
186C2×Dic86#4112yes—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C4⋊C4×C43—24no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43C2×D412yes—
199C4⋊C4×C43C2×D412yes—
200C42×C43—21no—
201C42×C43—21no—
202#10621885—44no—
203(C2×D43)⋊C4—42no—
204(C2×D43)⋊C4—42no—
205(C2×D43)⋊C4—42no—
206(C2×D43)⋊C4—42no—
207(C2×D43)⋊C4—81no—
208(C2×D43)⋊C4—81no—
209C4⋊Dic43—21no—
210C4⋊Dic43—22no—
211C4⋊Dic43—21no—
212C4⋊Dic43—21no—
213C4⋊Dic43C2×D412yes—
214Dic43⋊C4—24no—
215Dic43⋊C4—24no—
216Dic43⋊C4—24no—
217Dic43⋊C4—24no—
218Dic43⋊C4—24no—
219Dic43⋊C4—22no—
220Dic43⋊C4—22no—
221C4×Dic43—24no—
222C4×Dic43—24no—
223C4×Dic43—21no—
224C4×Dic43—21no—
225C4×Dic43—24no—
226C4×Dic43—81no—
227C4×Dic43C2×D412yes—
228C4×Dic43C2×D412yes—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235#10621873—44no—
236C23×C43C22×D411yescharacteristic
237C22×D43—41no—
238C22×D43—41no—
239C22×D43—41no—
240C22×D43—41no—
241C22×D43—41no—
242C22×D43—41no—
243C22×D43—41no—
244Q8×C43—41no—
245Q8×C43—41no—
246Q8×C43—41no—
247Q8×C43—41no—
248Q8×C43—84no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—22no—
252C2×C4×C43—22no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43#13712yes—
267C2×C4×C43C22×D411yescharacteristic
268C2×C4×C43C22×D411yescharacteristic
269C2×C4×C43C2×#4111yescharacteristic
270C2×C4×C43C2×#4111yescharacteristic
271C2×C4×C432−1+411yescharacteristic
272C2×C4×C432−1+411yescharacteristic
273C2×Dic43—21no—
274C2×Dic43—22no—
275C2×Dic43—22no—
276C2×Dic43—22no—
277C2×Dic43—21no—
278C2×Dic43—21no—
279C2×Dic43—21no—
280C2×Dic43—21no—
281C2×Dic43—21no—
282C2×Dic43—21no—
283C2×Dic43—22no—
284C2×Dic43—21no—
285C2×Dic43—21no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43#12012yes—
292C2×Dic43#12012yes—
293C2×Dic43#13712yes—
294D172—41no—
295D172—41no—
296D172—41no—
297D172—41no—
298Dic86—28no—
299Dic86—22no—
300Dic86—22no—
301Dic86—22no—
302Dic86—84no—
303Dic86—84no—
304Dic86#12414yes—
305C8×C43—41no—
306C8×C43—41no—
307C43⋊C8—41no—
308C43⋊C8—41no—
309#25942—431nomaximal, Sylow
310C22×C43C2×#12011yescharacteristic
311C22×C43#54811yescharacteristic
312C22×C43#54811yescharacteristic
313C22×C43C2×#13711yescharacteristic
314C22×C43C2×#13711yescharacteristic
315C22×C43#57611yescharacteristic
316C22×C43#57711yescharacteristic
317C2×D43—81no—
318C2×D43—81no—
319C2×D43—81no—
320C2×D43—81no—
321C2×D43—81no—
322C2×D43—81no—
323C2×D43—81no—
324C4×C43—22no—
325C4×C43—42no—
326C4×C43—42no—
327C4×C43—41no—
328C4×C43—81no—
329C4×C43—81no—
330C4×C43C2×#12411yescharacteristic
331C4×C43#53611yescharacteristic
332C4×C43#54811yescharacteristic
333C4×C43#54811yescharacteristic
334Dic43—24no—
335Dic43—22no—
336Dic43—22no—
337Dic43—22no—
338Dic43—41no—
339Dic43—42no—
340Dic43—81no—
341C2×Q82—431no—
342C2×#489—431no—
343C2×#464—431no—
344#2592—431no—
345#2024—431no—
346#2024D4311yescharacteristic, complemented
347#2023—431no—
348#2023—431no—
349#1988—431no—
350#1985—431no—
351#1880—431no—
352#1880—431no—
353#1878—431no—
354#1878—431no—
355#1763—431no—
356C2×C43#243611yescharacteristic
357C2×C43#300411yescharacteristic
358C2×C43#301211yescharacteristic
359C2×C43#336911yescharacteristic
360C2×C43#336911yescharacteristic
361C2×C43#337511yescharacteristic
362C2×C43#337511yescharacteristic
363D43—161no—
364C22×Q16—431no—
365C22×SD16—431no—
366Q82—864no—
367Q82—864no—
368C2×C4⋊Q8—431no—
369C2×C4⋊Q8—431no—
370C2×C4⋊Q8—861no—
371C2×C4⋊Q8—861no—
372C2×C4⋊Q8—861no—
373C2×C4⋊Q8C2×D4311yescharacteristic
374C2×#124—431no—
375C2×C4×Q8—431no—
376C2×C4×Q8—431no—
377C2×C4×Q8—431no—
378C2×C4×Q8—431no—
379C2×C4×Q8—861no—
380#489—864no—
381#464—864no—
382C2×C4⋊C8—431no—
383C2×#103—431no—
384C2×#103—431no—
385C2×#103—431no—
386C2×#103C2×D4311yescharacteristic
387C2×#103C2×D4311yescharacteristic
388C2×#102—431no—
389C2×#102—431no—
390C2×#102—431no—
391C2×#97—431no—
392#397—861no—
393#393—861no—
394#391—431no—
395#391C2×D4311yescharacteristic
396#390—431no—
397#390—431no—
398#388—861no—
399#388—861no—
400C4×C4⋊C4—431no—
401#340—431no—
402#340—431no—
403#340—431no—
404#340—431no—
405#340C2×D4311yescharacteristic
406#340C2×D4311yescharacteristic
407#336—431no—
408#336—431no—
409#336—431no—
410#336C2×D4311yescharacteristic
411C43#2594211yescharacteristic, complemented, Sylow
412C22×Q8—21no—
413C22×Q8—431no—
414C22×Q8—431no—
415C22×Q8—861no—
416C22×Q8—861no—
417C22×Q8C22×D4311yescharacteristic
418C22×D4—431no—
419C2×Q16—862no—
420C2×Q16—862no—
421C2×Q16—862no—
422C2×SD16—862no—
423C2×SD16—862no—
424C2×SD16—862no—
425C22×C8—431no—
426C22×C8—431no—
427C22×C8C22×D4311yescharacteristic
428C22×C8C22×D4311yescharacteristic
429C4⋊Q8—22no—
430C4⋊Q8—22no—
431C4⋊Q8—434no—
432C4⋊Q8—862no—
433C4⋊Q8—862no—
434C4⋊Q8—868no—
435C4⋊Q8—868no—
436C4⋊Q8—868no—
437C4⋊Q8—862no—
438#124—862no—
439#124—862no—
440C4×Q8—434no—
441C4×Q8—862no—
442C4×Q8—862no—
443C4×Q8—862no—
444C4×Q8—862no—
445C4×Q8—862no—
446C4×Q8—862no—
447C4×Q8—868no—
448C4×Q8—862no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—431no—
451C2×C4⋊C4—431no—
452C2×C4⋊C4—431no—
453C2×C4⋊C4—431no—
454C2×C4⋊C4—431no—
455C2×C4⋊C4—861no—
456C2×C4⋊C4—861no—
457C2×C4⋊C4—861no—
458C2×C4⋊C4—861no—
459C2×C4⋊C4—861no—
460C2×C4⋊C4C22×D4311yescharacteristic
461C2×C4⋊C4C22×D4311yescharacteristic
462C2×C4⋊C4C22×D4311yescharacteristic
463C2×C22⋊C4—861no—
464C2×C22⋊C4—861no—
465C2×C22⋊C4—861no—
466C2×C22⋊C4—861no—
467C2×C22⋊C4—861no—
468C2×C22⋊C4—861no—
469C2×C42—431no—
470C2×C42—431no—
471C2×C42—861no—
472C2×C42—861no—
473C2×C42—861no—
474C2×C42—861no—
475C2×C42C22×D4311yescharacteristic
476C4⋊C8—862no—
477#103—22no—
478#103—22no—
479#103—862no—
480#103—862no—
481#103—862no—
482#102—862no—
483#102—862no—
484#102—862no—
485#97—862no—
486#95—21no—
487#95—21no—
488#95—861no—
489#95—861no—
490#95—861no—
491C24—861no—
492C2×Q8—24no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—81no—
500C2×Q8—81no—
501C2×Q8—432no—
502C2×Q8—432no—
503C2×Q8—432no—
504C2×Q8—862no—
505C2×Q8—862no—
506C2×Q8—864no—
507C2×Q8—864no—
508C2×Q8—862no—
509C2×Q8—861no—
510C2×Q8—861no—
511C2×Q8—861no—
512C2×Q8—3441no—
513C2×Q8—3441no—
514C2×Q8—3441no—
515C2×Q8—3441no—
516C2×D4—861no—
517C2×D4—861no—
518C2×D4—861no—
519C2×D4—861no—
520C2×D4—861no—
521C2×D4—861no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—431no—
527C22×C4—431no—
528C22×C4—431no—
529C22×C4—431no—
530C22×C4—861no—
531C22×C4—861no—
532C22×C4—861no—
533C22×C4D4×D4311yescharacteristic
534C22×C4D4×D4311yescharacteristic
535C22×C4C23×D4311yescharacteristic
536Q16—1724no—
537SD16—1724no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—861no—
545C2×C8—861no—
546C2×C8—861no—
547C2×C8—861no—
548C2×C8—861no—
549C2×C8—861no—
550C4⋊C4—24no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—432no—
556C4⋊C4—862no—
557C4⋊C4—862no—
558C4⋊C4—862no—
559C4⋊C4—864no—
560C4⋊C4—864no—
561C4⋊C4—864no—
562C4⋊C4—864no—
563C4⋊C4—864no—
564C4⋊C4—861no—
565C4⋊C4—861no—
566C4⋊C4—861no—
567C4⋊C4D4×D4312yes—
568C4⋊C4D4×D4312yes—
569C22⋊C4—3441no—
570C22⋊C4—3441no—
571C22⋊C4—1722no—
572C22⋊C4—1722no—
573C22⋊C4—1722no—
574C22⋊C4—1722no—
575C42—21no—
576C42—21no—
577C42—432no—
578C42—432no—
579C42—864no—
580C42—864no—
581C42—864no—
582C42—861no—
583C42—861no—
584C42—3441no—
585C23—1721no—
586C23—1721no—
587C23—1721no—
588C23—1721no—
589C23—1721no—
590C23—1721no—
591C23—1721no—
592C23C2×D4×D4311yescharacteristic
593Q8—41no—
594Q8—41no—
595Q8—41no—
596Q8—41no—
597Q8—84no—
598Q8—434no—
599Q8—868no—
600Q8—862no—
601Q8—862no—
602Q8—862no—
603Q8—3444no—
604Q8—3444no—
605D4—1721no—
606D4—1721no—
607D4—1721no—
608D4—1721no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—432no—
627C2×C4—432no—
628C2×C4—432no—
629C2×C4—862no—
630C2×C4—862no—
631C2×C4—861no—
632C2×C4—862no—
633C2×C4—861no—
634C2×C4—861no—
635C2×C4—861no—
636C2×C4—861no—
637C2×C4—861no—
638C2×C4—862no—
639C2×C4—861no—
640C2×C4—861no—
641C2×C4—861no—
642C2×C4—1721no—
643C2×C4—1721no—
644C2×C4—1721no—
645C2×C4—1721no—
646C2×C4—1721no—
647C2×C4#1306335712yes—
648C2×C4C2×D4×D4311yescharacteristic
649C2×C4C2×D4×D4311yescharacteristic
650C2×C4#41×D4311yescharacteristic
651C2×C4#41×D4311yescharacteristic
652C2×C4#1306337211yescharacteristic
653C2×C4#1306337311yescharacteristic
654C8—41no—
655C8—41no—
656C8—1721no—
657C8—1721no—
658C22—3441no—
659C22—3441no—
660C22—3441no—
661C22—3441no—
662C22—3441no—
663C22—3441no—
664C22—3441no—
665C22#120×D4311yescharacteristic
666C22#1458355711yescharacteristic
667C22#1458355911yescharacteristic
668C22#137×D4311yescharacteristic
669C22C2×#1306335711yescharacteristic
670C22#1458370311yescharacteristic
671C22#1458370511yescharacteristic
672C4—22no—
673C4—41no—
674C4—42no—
675C4—42no—
676C4—81no—
677C4—81no—
678C4—862no—
679C4—862no—
680C4—864no—
681C4—862no—
682C4—3441no—
683C4—1721no—
684C4—1722no—
685C4#124×D4311yescharacteristic
686C4#1458347211yescharacteristic
687C4#1458355711yescharacteristic
688C4#1458355911yescharacteristic
689C2—6881no—
690C2#1913824811yescharacteristic
691C2#1914383011yescharacteristic
692C2#1914390011yescharacteristic
693C2#1914733811yescharacteristic
694C2#1914734011yescharacteristic
695C2#1914740611yescharacteristic
696C2#1914740811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2024C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#2024D43
hypocenterC43#25942
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2024

Complements

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

NH ≅ G/Ntype
1. C2×#14583629C2semidirect
5. #19135734C2semidirect
8. #19135545C2semidirect
9. #19135533C2semidirect
12. #19134939C2semidirect
13. #19134933C2semidirect
14. #19134424C2semidirect
15. C43×#2024C2semidirect
346. #2024D43semidirect
411. C43#25942semidirect

Maximal subgroups

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

subgroupindex
C2×#145836292
C2×#145832602
C2×#145831242
#191400822
#191357342
#191357302
#191357282
#191355452
#191355332
#191349512
#191349492
#191349392
#191349332
#191344242
C43×#20242
#2594243