Finite Group Databasebeta

← #25140525

Subgroups — #25140525

Order 11008.

940 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583054C211yesmaximal, characteristic
2C2×#14582991C211yesmaximal, characteristic, complemented
3#19138116C211yesmaximal, characteristic
4#19137427C211yesmaximal, characteristic
5#19136130C211yesmaximal, characteristic, complemented
6#19136026C211yesmaximal, characteristic
7#19135916C211yesmaximal, characteristic, complemented
8#19135269C211yesmaximal, characteristic, complemented
9#19135204C211yesmaximal, characteristic
10#19134934C211yesmaximal, characteristic, complemented
11#19134933C211yesmaximal, characteristic, complemented
12#19134846C211yesmaximal, characteristic, complemented
13#19134599C211yesmaximal, characteristic, complemented
14#19134531C211yesmaximal, characteristic
15C43×#2036C211yesmaximal, characteristic
16C23×Dic86C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18C22×#10621885C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic
20C2×#13063290C2211yescharacteristic
21C2×#13063290C2211yescharacteristic
22#14583054—24no—
23#14582991—24no—
24C2×#13063258C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×C22⋊(C43⋊C8)C2211yescharacteristic
33C2×C8×Dic43C2211yescharacteristic
34#14582835—21no—
35#14582829—21no—
36#14582806C2211yescharacteristic
37#14582804C2211yescharacteristic
38#14582804C2211yescharacteristic
39#14582803—21no—
40#14582803—21no—
41#14582795C2211yescharacteristic
42#14582787—21no—
43#14582780—21no—
44#14582768C2211yescharacteristic
45#14582759C2211yescharacteristic
46#14582757—21no—
47C22⋊C4×Dic43—21no—
48C4×C22⋊Dic43C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×C22⋊Q8×C43C2211yescharacteristic
55C2×#107×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C43×#380C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86—21no—
62C22×Dic86—22no—
63C22×Dic86—22no—
64C22×Dic86—22no—
65C22×Dic86—22no—
66C22×Dic86—41no—
67C22×Dic86—41no—
68C22×Dic86C2311yescharacteristic
69C22×Dic86C2311yescharacteristic
70C23×Dic43—21no—
71C2×#10621885—22no—
72C2×#10621885—22no—
73C2×#10621885—22no—
74C2×#10621885—22no—
75C2×#10621885—41no—
76C2×#10621885D414yes—
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79Q8×Dic43—22no—
80Q8×Dic43—41no—
81#13063290—22no—
82#13063290—22no—
83#13063290—41no—
84#13063290—41no—
85C2×C4⋊Dic43—21no—
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⋊Dic43D411yescharacteristic
95C2×C22⋊Dic43D411yescharacteristic
96C2×C4×Dic43—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43C2311yescharacteristic
100C2×C4×Dic43C2311yescharacteristic
101#13063258—22no—
102Dic43⋊C8—41no—
103#13063250—22no—
104#13063250—22no—
105#13063250—22no—
106#13063250—41no—
107#13063248—22no—
108#13063248—22no—
109C22⋊(C43⋊C8)—22no—
110C8×Dic43—22no—
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⋊#95D411yescharacteristic
120C43⋊#95D411yescharacteristic
121C22×Q8×C43C2311yescharacteristic
122C23×C4×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125C22⋊Q8×C43—22no—
126C22⋊Q8×C43—41no—
127C2×C4⋊C4×C43—21no—
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43—21no—
133#107×C43—41no—
134#103×C43—22no—
135#103×C43—41no—
136C22⋊C8×C43—41no—
137#95×C43—21no—
138C24×C43C2×D411yescharacteristic
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43C2×D412yes—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2411yescharacteristic
157C22×Dic43—24no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—42no—
163C22×Dic43—42no—
164C22×Dic43C2×D411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166C22×Dic43C2×D411yescharacteristic
167C22×Dic43C2×D411yescharacteristic
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86—21no—
174C2×Dic86—21no—
175C2×Dic86—24no—
176C2×Dic86—21no—
177C2×Dic86—44no—
178C2×Dic86—44no—
179C2×Dic86—44no—
180C2×Dic86—42no—
181C2×Dic86—42no—
182C2×Dic86—44no—
183C2×Dic86C2×D412yes—
184C2×Dic86#4112yes—
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—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—42no—
200C22⋊C4×C43—42no—
201C22⋊C4×C43—42no—
202C22⋊Dic43—41no—
203C22⋊Dic43—81no—
204C22⋊Dic43Q1614yescomplemented
205#10621885—28no—
206#10621885—44no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—42no—
212Dic43⋊C4—42no—
213Dic43⋊C4—42no—
214Dic43⋊C4—42no—
215Dic43⋊C4—81no—
216Dic43⋊C4—81no—
217C4×Dic43—21no—
218C4×Dic43—21no—
219C4×Dic43—21no—
220C4×Dic43—21no—
221C4×Dic43—42no—
222C4×Dic43—42no—
223C4×Dic43—42no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8C2×D412yes—
230C23×C43—21no—
231C23×C43—21no—
232C23×C43—21no—
233C23×C43—21no—
234C23×C43—21no—
235C23×C43—21no—
236C23×C43C2×Q1612yes—
237C23×C43C22×D411yescharacteristic
238Q8×C43—22no—
239Q8×C43—22no—
240Q8×C43—41no—
241Q8×C43—41no—
242C2×C4×C43—21no—
243C2×C4×C43—22no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
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×C43C22×D411yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43H(5,𝔽2)11yescharacteristic
266C2×C4×C43H(5,𝔽2)11yescharacteristic
267C2×Dic43—22no—
268C2×Dic43—21no—
269C2×Dic43—22no—
270C2×Dic43—21no—
271C2×Dic43—22no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—22no—
275C2×Dic43—21no—
276C2×Dic43—21no—
277C2×Dic43—21no—
278C2×Dic43—21no—
279C2×Dic43—21no—
280C2×Dic43—21no—
281C2×Dic43—48no—
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×Dic43C2×Q1612yes—
291C2×Dic43C2×Q1612yes—
292Dic86—22no—
293Dic86—22no—
294Dic86—22no—
295Dic86—22no—
296Dic86—22no—
297Dic86—48no—
298Dic86—41no—
299Dic86—41no—
300Dic86#12314yes—
301C8×C43—41no—
302C8×C43—41no—
303C43⋊C8—22no—
304C43⋊C8—41no—
305#24906—431nomaximal, Sylow
306C22×C43—22no—
307C22×C43—22no—
308C22×C43—22no—
309C22×C43—41no—
310C22×C43—41no—
311C22×C43—41no—
312C22×C43—41no—
313C22×C43#52511yescharacteristic
314C22×C43D4211yescharacteristic
315C22×C43#54611yescharacteristic
316C22×C43C22×Q1611yescharacteristic
317C22×C43#57511yescharacteristic
318C22×C43#57711yescharacteristic
319C22×C43#57811yescharacteristic
320C4×C43—41no—
321C4×C43—42no—
322C4×C43—81no—
323C4×C43—81no—
324C4×C43—81no—
325C4×C43C2×#12311yescharacteristic
326C4×C43#53811yescharacteristic
327C4×C43#54611yescharacteristic
328C4×C43#55111yescharacteristic
329Dic43—24no—
330Dic43—22no—
331Dic43—22no—
332Dic43—42no—
333Dic43—41no—
334Dic43—41no—
335Dic43—81no—
336Dic43—81no—
337C2×#451—431no—
338C2×C4×Q16—431no—
339#2423—431no—
340Q8×C22⋊C4—431no—
341#2095—431no—
342#2076—431no—
343#2056—431no—
344#2036D4311yescharacteristic
345#1933—431no—
346#1923—431no—
347#1878—431no—
348#1878—431no—
349#1863—431no—
350#1803—431no—
351#1787—431no—
352C2×C43—42no—
353C2×C43#241811yescharacteristic
354C2×C43#310411yescharacteristic
355C2×C43#312111yescharacteristic
356C2×C43#327111yescharacteristic
357C2×C43D4×Q1611yescharacteristic
358C2×C43#329911yescharacteristic
359C2×C43#332711yescharacteristic
360C23×Q8—431no—
361C22×Q16—431no—
362C22×Q16—431no—
363C2×C22⋊Q8C2×D4311yescharacteristic
364C2×C4×Q8—431no—
365C2×C4×Q8—431no—
366C2×C4×Q8—431no—
367#451—864no—
368C4×Q16—864no—
369C2×#107—431no—
370C2×#107C2×D4311yescharacteristic
371C2×C4⋊C8—431no—
372C2×#103—431no—
373C2×#103—431no—
374C2×#103—431no—
375C2×#103—431no—
376C2×#103—431no—
377C2×#103—431no—
378C2×#103C2×D4311yescharacteristic
379C2×#103C2×D4311yescharacteristic
380C2×C22⋊C8—431no—
381C2×C22⋊C8C2×D4311yescharacteristic
382C2×C4×C8—431no—
383#399—861no—
384#398—861no—
385#391—431no—
386#391—431no—
387#391—431no—
388#391—861no—
389#391—861no—
390#389—431no—
391#388—861no—
392#387—861no—
393#384—431no—
394#380—431no—
395#380—861no—
396#380C2×D4311yescharacteristic
397C4×C22⋊C4—431no—
398C4×C22⋊C4—861no—
399#340—431no—
400#340—431no—
401#340—431no—
402#340C2×D4311yescharacteristic
403#336—431no—
404#336—431no—
405C43#2490611yescharacteristic, complemented, Sylow
406C22×Q8—431no—
407C22×Q8—431no—
408C22×Q8—862no—
409C22×Q8—862no—
410C22×Q8—862no—
411C22×Q8—862no—
412C22×Q8—861no—
413C22×Q8—1721no—
414C22×Q8—1721no—
415C22×Q8C22×D4311yescharacteristic
416C23×C4—861no—
417C23×C4C22×D4311yescharacteristic
418C2×Q16—434no—
419C2×Q16—862no—
420C2×Q16—862no—
421C2×Q16—862no—
422C2×Q16—862no—
423C2×Q16—1721no—
424C22×C8—431no—
425C22×C8—431no—
426C22×C8C22×D4311yescharacteristic
427C22×C8C22×D4311yescharacteristic
428C22⋊Q8—22no—
429C22⋊Q8—41no—
430C4×Q8—862no—
431C4×Q8—862no—
432C4×Q8—862no—
433C4×Q8—1721no—
434C4×Q8—1721no—
435C4×Q8—1721no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—431no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—861no—
440C2×C4⋊C4—861no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4C22×D4311yescharacteristic
446C2×C4⋊C4C22×D4311yescharacteristic
447C2×C4⋊C4C22×D4311yescharacteristic
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—431no—
451C2×C22⋊C4—431no—
452C2×C22⋊C4—861no—
453C2×C42—431no—
454C2×C42—431no—
455C2×C42—861no—
456C2×C42—861no—
457C2×C42—861no—
458#107—41no—
459#107—862no—
460C4⋊C8—1721no—
461#103—22no—
462#103—41no—
463#103—862no—
464#103—862no—
465#103—862no—
466#103—862no—
467#103—862no—
468#103—1721no—
469C22⋊C8—41no—
470C22⋊C8—862no—
471C4×C8—862no—
472#95—21no—
473#95—431no—
474#95—431no—
475#95—861no—
476#95—861no—
477#95—861no—
478#95—861no—
479#95—861no—
480#95—861no—
481#95—861no—
482#95—861no—
483C24D4×D4311yescharacteristic
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—432no—
490C2×Q8—432no—
491C2×Q8—432no—
492C2×Q8—432no—
493C2×Q8—864no—
494C2×Q8—861no—
495C2×Q8—861no—
496C2×Q8—861no—
497C2×Q8—861no—
498C2×Q8—861no—
499C2×Q8—861no—
500C2×Q8—861no—
501C2×Q8—861no—
502C2×Q8—1722no—
503C2×Q8—1722no—
504C2×Q8—1724no—
505C2×Q8—1724no—
506C2×Q8—1724no—
507C2×Q8—1724no—
508C2×Q8D4×D4312yes—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—431no—
520C22×C4—431no—
521C22×C4—431no—
522C22×C4—431no—
523C22×C4—861no—
524C22×C4—864no—
525C22×C4—861no—
526C22×C4—861no—
527C22×C4—861no—
528C22×C4—1722no—
529C22×C4—1722no—
530C22×C4D4×D4311yescharacteristic
531C22×C4C23×D4311yescharacteristic
532Q16—868no—
533Q16—1724no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—432no—
541C2×C8—861no—
542C2×C8—861no—
543C2×C8—861no—
544C2×C8—861no—
545C2×C8—861no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—42no—
553C4⋊C4—861no—
554C4⋊C4—861no—
555C4⋊C4—861no—
556C4⋊C4—861no—
557C4⋊C4—3441no—
558C4⋊C4—3441no—
559C4⋊C4—1722no—
560C4⋊C4—1722no—
561C4⋊C4—1722no—
562C4⋊C4—1722no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—434no—
566C22⋊C4—3441no—
567C22⋊C4—1721no—
568C42—861no—
569C42—861no—
570C42—861no—
571C42—861no—
572C42—1722no—
573C42—1722no—
574C42—1722no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23Q16×D4312yes—
582C23C2×D4×D4311yescharacteristic
583Q8—22no—
584Q8—22no—
585Q8—41no—
586Q8—41no—
587Q8—434no—
588Q8—862no—
589Q8—862no—
590Q8—862no—
591Q8—862no—
592Q8—862no—
593Q8—1728no—
594Q8—1721no—
595Q8—1721no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—432no—
616C2×C4—432no—
617C2×C4—862no—
618C2×C4—861no—
619C2×C4—861no—
620C2×C4—861no—
621C2×C4—862no—
622C2×C4—861no—
623C2×C4—862no—
624C2×C4—862no—
625C2×C4—861no—
626C2×C4—861no—
627C2×C4—861no—
628C2×C4—861no—
629C2×C4—861no—
630C2×C4—861no—
631C2×C4—1728no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4—1721no—
637C2×C4—1721no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4C2×D4×D4311yescharacteristic
641C2×C4#41×D4311yescharacteristic
642C2×C4#41×D4311yescharacteristic
643C2×C4#41×D4311yescharacteristic
644C2×C4#1306337011yescharacteristic
645C2×C4#1306337011yescharacteristic
646C8—41no—
647C8—41no—
648C8—862no—
649C8—1721no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—41no—
654C22—41no—
655C22—41no—
656C22—41no—
657C22#1458340711yescharacteristic
658C22#1458353111yescharacteristic
659C22#1458353811yescharacteristic
660C22C2×Q16×D4311yescharacteristic
661C22#1458369511yescharacteristic
662C22#1458370611yescharacteristic
663C22#1458371511yescharacteristic
664C4—41no—
665C4—42no—
666C4—81no—
667C4—81no—
668C4—81no—
669C4—864no—
670C4—862no—
671C4—862no—
672C4—3441no—
673C4—3441no—
674C4—1722no—
675C4—1721no—
676C4—1721no—
677C4#123×D4311yescharacteristic
678C4#1458348111yescharacteristic
679C4#1458353811yescharacteristic
680C4#1458357911yescharacteristic
681C2—42no—
682C2#1913805011yescharacteristic
683C2#1914463111yescharacteristic
684C2#1914482711yescharacteristic
685C2#1914617811yescharacteristic
686C2#1914634011yescharacteristic
687C2#1914646611yescharacteristic
688C2#1914686911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2036C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#2036D43
hypocenterC43#24906
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2036

Complements

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

NH ≅ G/Ntype
2. C2×#14582991C2semidirect
5. #19136130C2semidirect
7. #19135916C2semidirect
8. #19135269C2semidirect
10. #19134934C2semidirect
11. #19134933C2semidirect
12. #19134846C2semidirect
13. #19134599C2semidirect
204. C22⋊Dic43Q16semidirect
405. C43#24906semidirect

Maximal subgroups

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

subgroupindex
C2×#145830542
C2×#145829912
#191381162
#191374272
#191361302
#191360262
#191359162
#191352692
#191352042
#191349342
#191349332
#191348462
#191345992
#191345312
C43×#20362
#2490643