Finite Group Databasebeta

← #25135323

Subgroups — #25135323

Order 11008.

972 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583053C211yesmaximal, characteristic
2C2×#14582955C211yesmaximal, characteristic
3#19142936C211yesmaximal, characteristic
4#391×D43C211yesmaximal, characteristic
5#19135976C211yesmaximal, characteristic, complemented
6#19135975C211yesmaximal, characteristic, complemented
7#19135917C211yesmaximal, characteristic, complemented
8#19135467C211yesmaximal, characteristic, complemented
9#19135463C211yesmaximal, characteristic, complemented
10#19135287C211yesmaximal, characteristic, complemented
11#19135286C211yesmaximal, characteristic, complemented
12#19134899C211yesmaximal, characteristic
13#19134789C211yesmaximal, characteristic
14#19134528C211yesmaximal, characteristic
15C43×#2056C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18C2×#13063301C2211yescharacteristic
19C2×C4⋊C4×D43C2211yescharacteristic
20C2×C42×D43C2211yescharacteristic
21#14583053—24no—
22#14582955—24no—
23C2×#13063257C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×(C2×D43)⋊C8C2211yescharacteristic
33C2×(C2×D43)⋊C8C2211yescharacteristic
34C2×#13063235C2211yescharacteristic
35C2×#13063235C2211yescharacteristic
36#14582806C2211yescharacteristic
37#14582806C2211yescharacteristic
38#14582805C2211yescharacteristic
39#14582804C2211yescharacteristic
40#14582803—21no—
41#14582803—21no—
42#14582798C2211yescharacteristic
43#14582797C2211yescharacteristic
44#14582782—21no—
45#14582781—21no—
46#14582773—21no—
47#14582761—21no—
48#14582756C2211yescharacteristic
49#95×D43—21no—
50#95×D43—21no—
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54C22×Q16×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C43×#391C2211yescharacteristic
59C43×#391C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86—21no—
62C22×Dic86C2311yescharacteristic
63C2×Q8×D43—22no—
64C2×Q8×D43—22no—
65C2×Q8×D43—22no—
66C2×Q8×D43—22no—
67C2×Q8×D43—41no—
68C2×Q8×D43—41no—
69C22×C4×D43—21no—
70C22×C4×D43—21no—
71C22×C4×D43D411yescharacteristic
72C22×C4×D43D411yescharacteristic
73C22×C4×D43C2311yescharacteristic
74C2×#10621885—22no—
75C2×#10621885—22no—
76C2×#10621885—41no—
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79#13063301—22no—
80#13063301—22no—
81C2×C4⋊Dic43—21no—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C4⋊C4×D43—41no—
89C4⋊C4×D43—41no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×C4×Dic43D411yescharacteristic
93C2×C4×Dic43D411yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95C42×D43—22no—
96C42×D43—22no—
97#13063257—41no—
98#13063256—41no—
99C4⋊(C43⋊C8)—22no—
100#13063250—22no—
101#13063250—41no—
102#13063249—22no—
103#13063249—41no—
104#13063249—41no—
105#13063248—22no—
106(C2×D43)⋊C8—22no—
107(C2×D43)⋊C8D414yes—
108#13063235—22no—
109#13063235—22no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C22×Q8×C43C2311yescharacteristic
122C22×Q8×C43C2311yescharacteristic
123C2×Q16×C43—22no—
124C2×Q16×C43—22no—
125C2×Q16×C43—41no—
126C22×C8×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C42×C43C2311yescharacteristic
131C4⋊C8×C43—22no—
132#103×C43—22no—
133#103×C43—41no—
134#95×C43—21no—
135#95×C43—21no—
136#95×C43—21no—
137#95×C43—21no—
138C23×D43C2×D411yescharacteristic
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
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#4112yes—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2411yescharacteristic
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165Q8×D43—44no—
166Q8×D43—44no—
167Q8×D43—44no—
168Q8×D43—44no—
169C2×C4×D43—21no—
170C2×C4×D43—21no—
171C2×C4×D43—21no—
172C2×C4×D43—21no—
173C2×C4×D43—24no—
174C2×C4×D43—22no—
175C2×C4×D43—22no—
176C2×C4×D43—22no—
177C2×C4×D43—22no—
178C2×C4×D43—22no—
179C2×C4×D43—41no—
180C2×C4×D43—42no—
181C2×C4×D43—42no—
182C2×C4×D43—42no—
183C2×C4×D43—42no—
184C2×C4×D43—42no—
185C2×C4×D43C2×D412yes—
186C2×C4×D43#4112yes—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86—21no—
190C2×Dic86—21no—
191C2×Dic86—24no—
192C2×Dic86—21no—
193C2×Dic86—42no—
194C2×Dic86—42no—
195C2×Dic86#4112yes—
196Q16×C43—44no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43C2×D412yes—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C42×C43—21no—
208C42×C43—21no—
209#10621885—44no—
210(C2×D43)⋊C4—42no—
211(C2×D43)⋊C4—42no—
212C4⋊Dic43—21no—
213C4⋊Dic43—21no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—42no—
219Dic43⋊C4—42no—
220Dic43⋊C4—42no—
221Dic43⋊C4—42no—
222C4×Dic43—21no—
223C4×Dic43—21no—
224C4×Dic43—22no—
225C4×Dic43—22no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8C2×D412yes—
232C23×C43C22×D411yescharacteristic
233C22×D43—21no—
234C22×D43—21no—
235C22×D43—21no—
236C22×D43—21no—
237C22×D43#12112yes—
238C22×D43#13712yes—
239C22×D43#13712yes—
240Q8×C43—22no—
241Q8×C43—22no—
242Q8×C43—41no—
243Q8×C43—41no—
244Q8×C43—41no—
245Q8×C43—41no—
246Q8×C43—41no—
247Q8×C43—41no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—22no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
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×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43#13712yes—
266C2×C4×C43C22×D411yescharacteristic
267C2×C4×C43C2×#4111yescharacteristic
268C2×C4×C43C2×#4111yescharacteristic
269C2×C4×C43C2×#4111yescharacteristic
270C2×C4×C43H(5,𝔽2)11yescharacteristic
271C2×C4×C43H(5,𝔽2)11yescharacteristic
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—22no—
277C2×Dic43—21no—
278C2×Dic43—21no—
279C2×Dic43—21no—
280C2×Dic43—21no—
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×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43#12112yes—
293C4×D43—22no—
294C4×D43—22no—
295C4×D43—22no—
296C4×D43—22no—
297C4×D43—44no—
298C4×D43—48no—
299C4×D43—44no—
300C4×D43—84no—
301Dic86—22no—
302Dic86—22no—
303Dic86—48no—
304Dic86—41no—
305Dic86—41no—
306C8×C43—22no—
307C8×C43—41no—
308C43⋊C8—22no—
309C43⋊C8—41no—
310#24508—431nomaximal, Sylow
311C22×C43C2×#12111yescharacteristic
312C22×C43#52511yescharacteristic
313C22×C43#53511yescharacteristic
314C22×C43C2×#13711yescharacteristic
315C22×C43C2×#13711yescharacteristic
316C22×C43C2×#13711yescharacteristic
317C22×C43#57511yescharacteristic
318C2×D43—22no—
319C2×D43—22no—
320C2×D43—22no—
321C2×D43—22no—
322C2×D43—22no—
323C2×D43—22no—
324C2×D43#47014yes—
325C4×C43—22no—
326C4×C43—42no—
327C4×C43—41no—
328C4×C43—81no—
329C4×C43—81no—
330C4×C43—81no—
331C4×C43#54611yescharacteristic
332C4×C43#54611yescharacteristic
333C4×C43#55111yescharacteristic
334C4×C43#55111yescharacteristic
335Dic43—22no—
336Dic43—42no—
337Dic43—41no—
338Dic43—41no—
339Dic43—81no—
340Dic43—81no—
341Dic43—81no—
342C2×#451—431no—
343C2×#432—431no—
344#2855—431no—
345C2×#391—431no—
346#2066—431no—
347#2066—431no—
348#2056—431no—
349#2056D4311yescharacteristic, complemented
350#1971—431no—
351#1971—431no—
352#1935—431no—
353#1935—431no—
354#1872—431no—
355#1853—431no—
356#1787—431no—
357C2×C43#241111yescharacteristic
358C2×C43C2×#47011yescharacteristic
359C2×C43#305611yescharacteristic
360C2×C43#311311yescharacteristic
361C2×C43#311711yescharacteristic
362C2×C43#321511yescharacteristic
363C2×C43#321811yescharacteristic
364D43—24no—
365C23×Q8—431no—
366C22×Q16—431no—
367C22×Q16C2×D4311yescharacteristic
368C2×C22⋊Q8—431no—
369C22×C4⋊C4—431no—
370C22×C42—431no—
371#451—864no—
372#432—864no—
373C2×#106—431no—
374C2×#106—431no—
375C2×C4⋊C8—431no—
376C2×C4⋊C8C2×D4311yescharacteristic
377C2×#103—431no—
378C2×#103—431no—
379C2×#103—431no—
380C2×#103—431no—
381C2×#103—431no—
382C2×#103—431no—
383C2×#103C2×D4311yescharacteristic
384C2×#103C2×D4311yescharacteristic
385C2×C22⋊C8—431no—
386C2×C22⋊C8—431no—
387C2×#97—431no—
388C2×#97—431no—
389#391—431no—
390#391—431no—
391#391—431no—
392#391—431no—
393#391—861no—
394#391—861no—
395#391C2×D4311yescharacteristic
396#391C2×D4311yescharacteristic
397#389—431no—
398#389—431no—
399#387—861no—
400#387—861no—
401#385—861no—
402#381—861no—
403#380—431no—
404C2×#95—861no—
405C2×#95—861no—
406#340—431no—
407#340—431no—
408#340—431no—
409#340C2×D4311yescharacteristic
410C43#2450811yescharacteristic, complemented, Sylow
411C22×Q8—431no—
412C22×Q8—861no—
413C22×Q8—862no—
414C22×Q8—862no—
415C22×Q8—862no—
416C22×Q8—862no—
417C22×Q8—1721no—
418C22×Q8—1721no—
419C22×Q8C22×D4311yescharacteristic
420C22×Q8C22×D4311yescharacteristic
421C23×C4—431no—
422C23×C4—431no—
423C23×C4—431no—
424C23×C4—861no—
425C23×C4—861no—
426C2×Q16—22no—
427C2×Q16—22no—
428C2×Q16—41no—
429C2×Q16—862no—
430C2×Q16—862no—
431C2×Q16—1721no—
432C22×C8—431no—
433C22×C8—431no—
434C22×C8C22×D4311yescharacteristic
435C22×C8C22×D4311yescharacteristic
436C22⋊Q8—862no—
437C22⋊Q8—862no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—431no—
440C2×C4⋊C4—431no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4—1721no—
446C2×C4⋊C4—1721no—
447C2×C4⋊C4C22×D4311yescharacteristic
448C2×C4⋊C4C22×D4311yescharacteristic
449C2×C22⋊C4—861no—
450C2×C22⋊C4—861no—
451C2×C42—431no—
452C2×C42—431no—
453C2×C42—431no—
454C2×C42—862no—
455C2×C42—862no—
456C2×C42C22×D4311yescharacteristic
457#106—1721no—
458#106—1721no—
459C4⋊C8—22no—
460C4⋊C8—862no—
461#103—22no—
462#103—41no—
463#103—862no—
464#103—862no—
465#103—862no—
466#103—1721no—
467#103—1721no—
468#103—1721no—
469C22⋊C8—434no—
470C22⋊C8—862no—
471#97—862no—
472#97—862no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—861no—
478#95—861no—
479#95—861no—
480#95—861no—
481#95—861no—
482#95—861no—
483#95—861no—
484#95—861no—
485#95—861no—
486#95—861no—
487#95—861no—
488C24—431no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—432no—
501C2×Q8—864no—
502C2×Q8—861no—
503C2×Q8—861no—
504C2×Q8—861no—
505C2×Q8—861no—
506C2×Q8—861no—
507C2×Q8—1722no—
508C2×Q8—1722no—
509C2×Q8—1724no—
510C2×Q8—1724no—
511C2×Q8—1724no—
512C2×Q8—1724no—
513C2×Q8#1062190012yes—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—431no—
519C22×C4—432no—
520C22×C4—432no—
521C22×C4—431no—
522C22×C4—431no—
523C22×C4—862no—
524C22×C4—862no—
525C22×C4—862no—
526C22×C4—862no—
527C22×C4—864no—
528C22×C4—861no—
529C22×C4—861no—
530C22×C4—861no—
531C22×C4—861no—
532C22×C4—861no—
533C22×C4—862no—
534C22×C4—861no—
535C22×C4—861no—
536C22×C4—861no—
537C22×C4—1721no—
538C22×C4—1722no—
539C22×C4—1722no—
540C22×C4—1722no—
541C22×C4—1722no—
542C22×C4—1722no—
543C22×C4D4×D4311yescharacteristic
544C22×C4D4×D4311yescharacteristic
545C22×C4C23×D4311yescharacteristic
546Q16—44no—
547Q16—1724no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—432no—
554C2×C8—861no—
555C2×C8—861no—
556C2×C8—861no—
557C2×C8—861no—
558C2×C8—861no—
559C2×C8D4×D4312yes—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—861no—
565C4⋊C4—861no—
566C4⋊C4—861no—
567C4⋊C4—861no—
568C4⋊C4—861no—
569C4⋊C4—861no—
570C4⋊C4—1722no—
571C4⋊C4—1722no—
572C4⋊C4—1722no—
573C4⋊C4—1722no—
574C22⋊C4—1722no—
575C22⋊C4—1722no—
576C42—21no—
577C42—21no—
578C42—862no—
579C42—862no—
580C42—861no—
581C42—861no—
582C23—432no—
583C23—432no—
584C23—432no—
585C23—861no—
586C23—861no—
587C23—861no—
588C23—861no—
589C23C2×D4×D4311yescharacteristic
590Q8—22no—
591Q8—22no—
592Q8—41no—
593Q8—41no—
594Q8—41no—
595Q8—41no—
596Q8—41no—
597Q8—41no—
598Q8—862no—
599Q8—862no—
600Q8—1728no—
601Q8—1721no—
602Q8—1721no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—41no—
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—41no—
620C2×C4—432no—
621C2×C4—861no—
622C2×C4—861no—
623C2×C4—862no—
624C2×C4—862no—
625C2×C4—862no—
626C2×C4—862no—
627C2×C4—861no—
628C2×C4—861no—
629C2×C4—862no—
630C2×C4—861no—
631C2×C4—861no—
632C2×C4—861no—
633C2×C4—861no—
634C2×C4—3444no—
635C2×C4—1724no—
636C2×C4—1724no—
637C2×C4—1728no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4—1721no—
641C2×C4—1721no—
642C2×C4—1721no—
643C2×C4—1721no—
644C2×C4—1721no—
645C2×C4—1721no—
646C2×C4—1721no—
647C2×C4—1721no—
648C2×C4—1721no—
649C2×C4#1306335712yes—
650C2×C4C2×D4×D4311yescharacteristic
651C2×C4#41×D4311yescharacteristic
652C2×C4#41×D4311yescharacteristic
653C2×C4C2×#1062190011yescharacteristic
654C2×C4#1306337011yescharacteristic
655C2×C4#1306337111yescharacteristic
656C8—22no—
657C8—41no—
658C8—862no—
659C8—1721no—
660C22—434no—
661C22—862no—
662C22—862no—
663C22—862no—
664C22—862no—
665C22—862no—
666C22—862no—
667C22#121×D4311yescharacteristic
668C22#1458340911yescharacteristic
669C22#1458346511yescharacteristic
670C22#137×D4311yescharacteristic
671C22#137×D4311yescharacteristic
672C22C2×#1306335711yescharacteristic
673C22#1458369611yescharacteristic
674C4—22no—
675C4—41no—
676C4—42no—
677C4—81no—
678C4—81no—
679C4—81no—
680C4—862no—
681C4—3441no—
682C4—3441no—
683C4—3441no—
684C4—1721no—
685C4—1721no—
686C4—1722no—
687C4#1458353611yescharacteristic
688C4#1458354211yescharacteristic
689C4#1458357211yescharacteristic
690C4#1458357711yescharacteristic
691C2—864no—
692C2#1913797311yescharacteristic
693C2#470×D4311yescharacteristic
694C2#1914422211yescharacteristic
695C2#1914472411yescharacteristic
696C2#1914476511yescharacteristic
697C2#1914559611yescharacteristic
698C2#1914562611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2056C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#2056D43
hypocenterC43#24508
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2056

Complements

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

NH ≅ G/Ntype
5. #19135976C2semidirect
6. #19135975C2semidirect
7. #19135917C2semidirect
8. #19135467C2semidirect
9. #19135463C2semidirect
10. #19135287C2semidirect
11. #19135286C2semidirect
15. C43×#2056C2semidirect
349. #2056D43semidirect
410. C43#24508semidirect

Maximal subgroups

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

subgroupindex
C2×#145830532
C2×#145829552
#191429362
#391×D432
#191359762
#191359752
#191359172
#191354672
#191354632
#191352872
#191352862
#191348992
#191347892
#191345282
C43×#20562
#2450843