Finite Group Databasebeta

← #25153672

Subgroups — #25153672

Order 11008.

966 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583183C211yesmaximal, characteristic, complemented
2C2×#14582892C211yesmaximal, characteristic
3#19138289C211yesmaximal, characteristic, complemented
4#19137434C211yesmaximal, characteristic
5#19135969C211yesmaximal, characteristic, complemented
6#19135967C211yesmaximal, characteristic, complemented
7#19135729C211yesmaximal, characteristic, complemented
8#19134866C211yesmaximal, characteristic, complemented
9#19134846C211yesmaximal, characteristic, complemented
10#19134791C211yesmaximal, characteristic, complemented
11#19134774C211yesmaximal, characteristic, complemented
12#19134617C211yesmaximal, characteristic, complemented
13#19134607C211yesmaximal, characteristic, complemented
14#19134532C211yesmaximal, characteristic
15C43×#2092C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C2×#13063324C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C2×#13063290C2211yescharacteristic
21C2×#13063283C2211yescharacteristic
22#14583183—24no—
23C2×#13063257C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27#14582892—24no—
28C2×#13063250C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×(C2×D43)⋊C8C2211yescharacteristic
35#14582823—21no—
36#14582812—21no—
37#14582803—21no—
38#14582802C2211yescharacteristic
39#14582799—21no—
40#14582799—21no—
41#14582797C2211yescharacteristic
42#14582795C2211yescharacteristic
43#14582781—21no—
44#14582757—21no—
45#14582756C2211yescharacteristic
46#14582756C2211yescharacteristic
47C22⋊C4×Dic43—21no—
48C4×(C2×D43)⋊C4C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C2×#106×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C43×#390C2211yescharacteristic
59C43×#382C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C2×#10621900—22no—
62C2×#10621900—22no—
63C2×#10621900—22no—
64C2×#10621900—41no—
65C2×#10621900—41no—
66C2×#10621900Q814yescomplemented
67C22×Dic86—21no—
68C22×Dic86C2311yescharacteristic
69C22×C22⋊D43—21no—
70C23×Dic43—21no—
71C22×C4×D43C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C2×C8×D43—22no—
75C2×C8×D43—22no—
76C2×C8×D43—41no—
77#13063324—22no—
78#13063324—41no—
79C4×Dic86—22no—
80C4×Dic86—41no—
81#13063290—22no—
82#13063290—41no—
83#13063283—22no—
84#13063283—41no—
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×C22⋊Dic43—21no—
94C2×C22⋊Dic43—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4D411yescharacteristic
99C2×(C2×D43)⋊C4D411yescharacteristic
100C2×C4×Dic43—21no—
101C2×C4×Dic43—21no—
102C2×C4×Dic43—21no—
103C2×C4×Dic43C2311yescharacteristic
104#13063257—41no—
105#13063256—22no—
106C4⋊(C43⋊C8)—41no—
107Dic43⋊C8—22no—
108#13063250—22no—
109#13063250D414yes—
110#13063248—22no—
111#13063248—22no—
112#13063246—22no—
113#13063246—41no—
114(C2×D43)⋊C8—22no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95D411yescharacteristic
120C43⋊#95D411yescharacteristic
121C22×D4×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C42×C43C2311yescharacteristic
130#107×C43—41no—
131#106×C43—22no—
132#102×C43—22no—
133#102×C43—41no—
134#95×C43—21no—
135#95×C43—21no—
136C24×C43—21no—
137C23×D43C2×D411yescharacteristic
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43C2×Q812yes—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2411yescharacteristic
150C2×C22⋊D43—24no—
151C2×C22⋊D43—42no—
152C2×C22⋊D43—42no—
153C22×Dic43—24no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—42no—
159C22×Dic43—42no—
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163#10621900—28no—
164#10621900—44no—
165#10621900—44no—
166#10621900—44no—
167C2×C4×D43—21no—
168C2×C4×D43—21no—
169C2×C4×D43—21no—
170C2×C4×D43—21no—
171C2×C4×D43C2×Q812yes—
172C2×C4×D43#4112yes—
173C2×Dic86—21no—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—42no—
177C2×Dic86—42no—
178C2×Dic86—81no—
179C2×Dic86C2×D412yes—
180C2×Dic86C2×Q812yes—
181C2×Dic86#4112yes—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43C2×D412yes—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C22⋊C4×C43—42no—
195C22⋊C4×C43—81no—
196C42×C43—21no—
197C42×C43—21no—
198C22⋊Dic43—42no—
199C22⋊Dic43—81no—
200(C2×D43)⋊C4—22no—
201(C2×D43)⋊C4—41no—
202(C2×D43)⋊C4—42no—
203(C2×D43)⋊C4—81no—
204(C2×D43)⋊C4—81no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43C2×D412yes—
211Dic43⋊C4—42no—
212Dic43⋊C4—42no—
213Dic43⋊C4—42no—
214Dic43⋊C4—42no—
215Dic43⋊C4—81no—
216C4×Dic43—21no—
217C4×Dic43—21no—
218C4×Dic43—42no—
219C4×Dic43—42no—
220C4×Dic43—42no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C8×D43—44no—
228C23×C43—22no—
229C23×C43—41no—
230C23×C43—41no—
231C23×C43—41no—
232C23×C43—41no—
233C23×C43—41no—
234C23×C43—41no—
235C23×C43C22×D411yescharacteristic
236C22×D43—21no—
237C22×D43—21no—
238C22×D43—21no—
239C22×D43—21no—
240C22×D43—21no—
241C22×D43—21no—
242C22×D43C22⋊Q812yes—
243D4×C43—22no—
244D4×C43—22no—
245D4×C43—41no—
246D4×C43—41no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
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×C43C22×D411yescharacteristic
263C2×C4×C43C22×Q811yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43H(5,𝔽2)11yescharacteristic
267C2×C4×C43H(5,𝔽2)11yescharacteristic
268C22⋊D43—48no—
269C2×Dic43—22no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—22no—
273C2×Dic43—22no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—21no—
277C2×Dic43—22no—
278C2×Dic43—21no—
279C2×Dic43—21no—
280C2×Dic43—48no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43C22⋊Q812yes—
290C2×Dic43#13512yes—
291C4×D43—22no—
292C4×D43—22no—
293C4×D43—22no—
294C4×D43—22no—
295Dic86—22no—
296Dic86—22no—
297Dic86—22no—
298Dic86—84no—
299Dic86C22⋊Q814yes—
300C8×C43—22no—
301C8×C43—41no—
302C43⋊C8—41no—
303C43⋊C8—41no—
304#25951—431nomaximal, Sylow
305C22×C43—42no—
306C22×C43—42no—
307C22×C43—42no—
308C22×C43—81no—
309C22×C43—81no—
310C22×C43—81no—
311C22×C43—81no—
312C22×C43C2×C22⋊Q811yescharacteristic
313C22×C43D4211yescharacteristic
314C22×C43#54611yescharacteristic
315C22×C43C2×#13511yescharacteristic
316C22×C43#57511yescharacteristic
317C22×C43#57711yescharacteristic
318C22×C43#57711yescharacteristic
319C2×D43—22no—
320C2×D43—22no—
321C2×D43—22no—
322C2×D43—41no—
323C2×D43—41no—
324C2×D43—41no—
325C2×D43—41no—
326C4×C43—41no—
327C4×C43—41no—
328C4×C43—81no—
329C4×C43—81no—
330C4×C43—81no—
331C4×C43C2×C22⋊Q811yescharacteristic
332C4×C43#54311yescharacteristic
333C4×C43#54611yescharacteristic
334C4×C43#55111yescharacteristic
335Dic43—24no—
336Dic43—22no—
337Dic43—22no—
338Dic43—41no—
339Dic43—42no—
340Dic43—81no—
341Dic43—81no—
342C2×#475—431no—
343C2×#416—431no—
344#2439—431no—
345#2341—431no—
346#2092D4311yescharacteristic, complemented
347#2065—431no—
348#2065—431no—
349#2023—431no—
350#1865—431no—
351#1863—431no—
352#1854—431no—
353#1850—431no—
354#1807—431no—
355#1805—431no—
356#1788—431no—
357C2×C43—82no—
358C2×C43#243711yescharacteristic
359C2×C43#307611yescharacteristic
360C2×C43#308411yescharacteristic
361C2×C43#327111yescharacteristic
362C2×C43#328211yescharacteristic
363C2×C43#330411yescharacteristic
364C2×C43#332111yescharacteristic
365D43—42no—
366C22×#41—431no—
367C23×C8—431no—
368C2×C4⋊Q8—431no—
369C2×C4×Q8—431no—
370C2×C4×Q8—431no—
371C2×#117—431no—
372#475—864no—
373C2×#107C2×D4311yescharacteristic
374C2×#106—431no—
375C2×#106—431no—
376C2×#106C2×D4311yescharacteristic
377C2×C4⋊C8—431no—
378C2×C4⋊C8—431no—
379#416—864no—
380C2×#103—431no—
381C2×#103—431no—
382C2×#103—431no—
383C2×#103—431no—
384C2×#102—431no—
385C2×#102—431no—
386C2×#102C2×D4311yescharacteristic
387C2×#102C2×D4311yescharacteristic
388C2×C22⋊C8—431no—
389#396—861no—
390#393—861no—
391#391—861no—
392#390—431no—
393#390—861no—
394#390—861no—
395#390C2×D4311yescharacteristic
396#389—431no—
397#389—431no—
398#387—861no—
399#382C2×D4311yescharacteristic
400#380—431no—
401#380—431no—
402#380—861no—
403C4×C22⋊C4—431no—
404C4×C22⋊C4—861no—
405#340—431no—
406#340—431no—
407#340—431no—
408#340—431no—
409#336—431no—
410#336C2×D4311yescharacteristic
411C43#2595111yescharacteristic, complemented, Sylow
412C2×#41—434no—
413C2×#41—862no—
414C2×#41—862no—
415C2×#41—862no—
416C2×#41—1721no—
417C2×#41—1721no—
418C22×Q8—431no—
419C22×Q8—861no—
420C22×D4—861no—
421C22×D4C22×D4311yescharacteristic
422C23×C4—431no—
423C23×C4—861no—
424C22×C8—431no—
425C22×C8—431no—
426C22×C8—862no—
427C22×C8—862no—
428C22×C8—1721no—
429C22×C8C22×D4311yescharacteristic
430C22×C8C22×D4311yescharacteristic
431C4⋊Q8—862no—
432C4⋊Q8—1721no—
433C4×Q8—862no—
434C4×Q8—862no—
435C4×Q8—1721no—
436C4×Q8—1721no—
437#117—862no—
438#117—1721no—
439C2×C4⋊C4—431no—
440C2×C4⋊C4—431no—
441C2×C4⋊C4—431no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4—861no—
446C2×C4⋊C4—861no—
447C2×C4⋊C4C22×D4311yescharacteristic
448C2×C4⋊C4C22×D4311yescharacteristic
449C2×C4⋊C4C22×D4311yescharacteristic
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—431no—
453C2×C22⋊C4—431no—
454C2×C22⋊C4—861no—
455C2×C22⋊C4—861no—
456C2×C22⋊C4—861no—
457C2×C22⋊C4—861no—
458C2×C22⋊C4—861no—
459C2×C42—431no—
460C2×C42—861no—
461C2×C42—861no—
462C2×C42—861no—
463C2×C42C22×D4311yescharacteristic
464#107—41no—
465#106—22no—
466#106—862no—
467#106—1721no—
468C4⋊C8—862no—
469C4⋊C8—1721no—
470#103—434no—
471#103—862no—
472#103—862no—
473#103—862no—
474#102—22no—
475#102—41no—
476#102—862no—
477#102—1721no—
478C22⋊C8—862no—
479#95—21no—
480#95—21no—
481#95—431no—
482#95—431no—
483#95—861no—
484#95—861no—
485#95—861no—
486#95—861no—
487C24—21no—
488C24—431no—
489#41—868no—
490#41—1724no—
491#41—1724no—
492#41—1724no—
493C2×Q8—432no—
494C2×Q8—432no—
495C2×Q8—432no—
496C2×Q8—861no—
497C2×Q8—861no—
498C2×Q8—861no—
499C2×Q8—3441no—
500C2×Q8—1722no—
501C2×Q8—1722no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—864no—
508C2×D4—1722no—
509C2×D4—1722no—
510C2×D4Q8×D4312yes—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—431no—
515C22×C4—431no—
516C22×C4—432no—
517C22×C4—432no—
518C22×C4—431no—
519C22×C4—864no—
520C22×C4—861no—
521C22×C4—861no—
522C22×C4—861no—
523C22×C4—861no—
524C22×C4—861no—
525C22×C4—861no—
526C22×C4—861no—
527C22×C4—861no—
528C22×C4—1722no—
529C22×C4—1722no—
530C22×C4D4×D4311yescharacteristic
531C22×C4D4×D4311yescharacteristic
532C22×C4C23×D4311yescharacteristic
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—861no—
539C2×C8—861no—
540C2×C8—861no—
541C2×C8—861no—
542C2×C8—861no—
543C2×C8—861no—
544C2×C8—1724no—
545C2×C8D4×D4312yes—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—432no—
553C4⋊C4—861no—
554C4⋊C4—861no—
555C4⋊C4—861no—
556C4⋊C4—861no—
557C4⋊C4—861no—
558C4⋊C4—3441no—
559C4⋊C4—1722no—
560C4⋊C4—1722no—
561C4⋊C4—1722no—
562C4⋊C4—1722no—
563C22⋊C4—42no—
564C22⋊C4—81no—
565C22⋊C4—862no—
566C22⋊C4—3441no—
567C22⋊C4—3441no—
568C22⋊C4—3441no—
569C22⋊C4—1721no—
570C22⋊C4—1722no—
571C22⋊C4—1722no—
572C42—21no—
573C42—21no—
574C42—861no—
575C42—861no—
576C42—1722no—
577C42—1722no—
578C42—1722no—
579C23—22no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—432no—
587C23—861no—
588C23—861no—
589C23—861no—
590C23—861no—
591C23—861no—
592C23—861no—
593C23C2×D4×D4311yescharacteristic
594Q8—434no—
595Q8—862no—
596Q8—862no—
597Q8—862no—
598Q8—3444no—
599D4—22no—
600D4—22no—
601D4—41no—
602D4—41no—
603D4—1728no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—432no—
620C2×C4—432no—
621C2×C4—862no—
622C2×C4—861no—
623C2×C4—861no—
624C2×C4—861no—
625C2×C4—862no—
626C2×C4—862no—
627C2×C4—861no—
628C2×C4—862no—
629C2×C4—862no—
630C2×C4—862no—
631C2×C4—862no—
632C2×C4—861no—
633C2×C4—861no—
634C2×C4—861no—
635C2×C4—862no—
636C2×C4—1728no—
637C2×C4—1721no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4—1721no—
641C2×C4—1721no—
642C2×C4—1721no—
643C2×C4—1721no—
644C2×C4—1721no—
645C2×C4C2×D4×D4311yescharacteristic
646C2×C4C2×Q8×D4311yescharacteristic
647C2×C4#41×D4311yescharacteristic
648C2×C4#41×D4311yescharacteristic
649C2×C4#1306337011yescharacteristic
650C2×C4#1306337111yescharacteristic
651C8—22no—
652C8—41no—
653C8—1721no—
654C8—1721no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22—81no—
662C22—862no—
663C22—862no—
664C22—862no—
665C22—1721no—
666C22—1721no—
667C22—1721no—
668C22—1721no—
669C22C22⋊Q8×D4311yescharacteristic
670C22#1458353411yescharacteristic
671C22#1458354111yescharacteristic
672C22#135×D4311yescharacteristic
673C22#1458369511yescharacteristic
674C22#1458370611yescharacteristic
675C22#1458370911yescharacteristic
676C4—41no—
677C4—41no—
678C4—81no—
679C4—81no—
680C4—81no—
681C4—862no—
682C4—862no—
683C4—864no—
684C4—3441no—
685C4—3441no—
686C4—1722no—
687C4—1721no—
688C4C22⋊Q8×D4311yescharacteristic
689C4#1458352411yescharacteristic
690C4#1458354111yescharacteristic
691C4#1458357711yescharacteristic
692C2—82no—
693C2—1722no—
694C2#1913826211yescharacteristic
695C2#1914438011yescharacteristic
696C2#1914445811yescharacteristic
697C2#1914617911yescharacteristic
698C2#1914630111yescharacteristic
699C2#1914653211yescharacteristic
700C2#1914678411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2092C2
socleC23×C43C22×D4
prime radicalC22×#10621900C22
hypercenter#2092D43
hypocenterC43#25951
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2092

Complements

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

NH ≅ G/Ntype
1. C2×#14583183C2semidirect
3. #19138289C2semidirect
5. #19135969C2semidirect
6. #19135967C2semidirect
7. #19135729C2semidirect
8. #19134866C2semidirect
9. #19134846C2semidirect
10. #19134791C2semidirect
11. #19134774C2semidirect
12. #19134617C2semidirect
13. #19134607C2semidirect
15. C43×#2092C2semidirect
66. C2×#10621900Q8semidirect
346. #2092D43semidirect
411. C43#25951semidirect

Maximal subgroups

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

subgroupindex
C2×#145831832
C2×#145828922
#191382892
#191374342
#191359692
#191359672
#191357292
#191348662
#191348462
#191347912
#191347742
#191346172
#191346072
#191345322
C43×#20922
#2595143