Finite Group Databasebeta

← #25112780

Subgroups — #25112780

Order 11008.

1132 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583597C211yesmaximal, characteristic
2M16×C22⋊D43C212yesmaximal, complemented
3#19135586C212yesmaximal, complemented
4#19135058C212yesmaximal, complemented
5#19135057C212yesmaximal, complemented
6#19134677C211yesmaximal, characteristic, complemented
7#19134675C211yesmaximal, characteristic, complemented
8#19134586C211yesmaximal, characteristic, complemented
9#19134386C211yesmaximal, characteristic, complemented
10#19134332C211yesmaximal, characteristic, complemented
11C2×C43×#343C211yesmaximal, characteristic, complemented
12C2×M16×D43C2212yes—
13#14583597—22no—
14#14583597—22no—
15#14583597—22no—
16#14583597—22no—
17C2×#13063320C412yes—
18C2×#13063316C2211yescharacteristic
19C2×#13063310C412yes—
20C2×#13063300C2211yescharacteristic
21C2×#13063299C412yes—
22C2×#13063299C2211yescharacteristic
23C2×#13063287C2211yescharacteristic
24C2×C4×C22⋊D43C412yes—
25C2×C4×C22⋊D43C2211yescharacteristic
26C2×#13063283C2211yescharacteristic
27#14582975—22no—
28#14582970—22no—
29#14582968—22no—
30C8×C22⋊D43—22no—
31#14582922C2212yes—
32C2×#13063241C2212yes—
33C2×#13063241C2212yes—
34#14582863C2212yes—
35#14582862C2212yes—
36M16×Dic43C2212yes—
37#14582668C2212yes—
38#14582668C2211yescharacteristic
39#14582668C2211yescharacteristic
40#14582667C2212yes—
41#14582667C2212yes—
42C22×M16×C43C2212yes—
43C22×C4⋊C4×C43C2211yescharacteristic
44C43×#343C2212yes—
45C43×#343C2211yescharacteristic
46C43×#343C2211yescharacteristic
47C22×D172C2×C412yes—
48C22×D172C2311yescharacteristic
49C22×C22⋊D43C2×C412yes—
50C22×C22⋊D43C2×C411yescharacteristic
51C22×C4×D43C2×C412yes—
52C22×C4×D43C2311yescharacteristic
53C2×#10621877C2312yes—
54C2×#10621877C2312yes—
55C2×#10621872—22no—
56M16×D43—24no—
57M16×D43—42no—
58C2×C8×D43—22no—
59#13063320—24no—
60#13063320—24no—
61#13063316—22no—
62#13063316—22no—
63#13063310—24no—
64#13063310—24no—
65#13063300—22no—
66#13063300—22no—
67#13063299—22no—
68#13063299—22no—
69#13063299—24no—
70#13063299—24no—
71#13063287—22no—
72#13063287—22no—
73C4×C22⋊D43—22no—
74C4×C22⋊D43—22no—
75C4×C22⋊D43—22no—
76C4×C22⋊D43—22no—
77C4×C22⋊D43D412yes—
78C4×C22⋊D43D412yes—
79C4×C22⋊D43D412yes—
80C4×C22⋊D43D412yes—
81#13063283—22no—
82#13063283—22no—
83C2×C4⋊Dic43C2×C412yes—
84C2×C4⋊Dic43C2311yescharacteristic
85C2×Dic43⋊C4C2×C412yes—
86C2×Dic43⋊C4C2×C411yescharacteristic
87C2×C22⋊Dic43C2×C411yescharacteristic
88C2×(C2×D43)⋊C4C2×C412yes—
89C2×(C2×D43)⋊C4C2×C412yes—
90C2×(C2×D43)⋊C4C2×C412yes—
91C2×(C2×D43)⋊C4C2×C412yes—
92C2×(C2×D43)⋊C4C2×C411yescharacteristic
93C2×C4×Dic43C2×C412yes—
94C2×C4×Dic43C2311yescharacteristic
95Dic43⋊C8—22no—
96Dic43⋊C8—22no—
97#13063241—24no—
98#13063241—42no—
99C22⋊(C43⋊C8)—22no—
100C22⋊(C43⋊C8)—22no—
101(C2×D43)⋊C8—22no—
102(C2×D43)⋊C8—22no—
103#13063235—22no—
104C8×Dic43—22no—
105C23×C4×C43C2×C412yes—
106C23×C4×C43C2311yescharacteristic
107C2×M16×C43—22no—
108C2×M16×C43—24no—
109C2×M16×C43—42no—
110C2×M16×C43C2312yes—
111C2×M16×C43C2312yes—
112C22×C8×C43—22no—
113C2×C4⋊C4×C43—22no—
114C2×C4⋊C4×C43—22no—
115C2×C4⋊C4×C43C2×C412yes—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C24×C43C22×C411yescharacteristic
119C23×D43C22×C412yes—
120C23×D43C22×C411yescharacteristic
121C22×C4×C43—22no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—82no—
127C22×C4×C43C22×C411yescharacteristic
128C22×C4×C43C22×C412yes—
129C22×C4×C43C22×C412yes—
130C22×C4×C43C2×D412yes—
131C22×C4×C43C2×D412yes—
132C22×C4×C43C2411yescharacteristic
133C2×C22⋊D43—22no—
134C2×C22⋊D43—22no—
135C2×C22⋊D43—42no—
136C2×C22⋊D43—44no—
137C2×C22⋊D43C22⋊C412yes—
138C2×C22⋊D43C22⋊C412yes—
139C22×Dic43C22×C411yescharacteristic
140C22×Dic43C22×C412yes—
141C22×Dic43C22×C411yescharacteristic
142C22×Dic43C22×C411yescharacteristic
143C2×D172—22no—
144C2×D172—22no—
145C2×D172—21no—
146C2×D172—21no—
147C2×D172—24no—
148C2×D172—82no—
149C2×C4×D43—22no—
150C2×C4×D43—21no—
151C2×C4×D43—21no—
152C2×C4×D43—22no—
153C2×C4×D43—22no—
154C2×C4×D43—82no—
155C2×C4×D43C2×D412yes—
156C2×C4×D43C2×D412yes—
157M16×C43—22no—
158M16×C43—22no—
159M16×C43—22no—
160M16×C43—44no—
161M16×C43#4114yes—
162C2×C8×C43—22no—
163C2×C8×C43—22no—
164C2×C8×C43—44no—
165C4⋊C4×C43—24no—
166C4⋊C4×C43—22no—
167C4⋊C4×C43—22no—
168C22⋊Dic43C22⋊C411yescharacteristic
169C22⋊Dic43C22⋊C411yescharacteristic
170C22⋊Dic43C22⋊C411yescharacteristic
171C22⋊Dic43C22⋊C411yescharacteristic
172(C2×D43)⋊C4—24no—
173(C2×D43)⋊C4—22no—
174(C2×D43)⋊C4—22no—
175(C2×D43)⋊C4—24no—
176(C2×D43)⋊C4—24no—
177(C2×D43)⋊C4C22⋊C412yes—
178(C2×D43)⋊C4C22⋊C412yes—
179C4⋊Dic43—22no—
180C4⋊Dic43—24no—
181Dic43⋊C4—22no—
182Dic43⋊C4—22no—
183Dic43⋊C4C22⋊C412yes—
184Dic43⋊C4C22⋊C412yes—
185C4×Dic43—22no—
186C4×Dic43—22no—
187C4×Dic43C2×D412yes—
188C4×Dic43C2×D412yes—
189#10621877—22no—
190#10621877—22no—
191#10621877—22no—
192#10621877—22no—
193C2×C43⋊C8—22no—
194C2×C43⋊C8—22no—
195#10621872—44no—
196C8×D43—44no—
197C23×C43—21no—
198C23×C43—21no—
199C23×C43—22no—
200C23×C43—41no—
201C23×C43C2×C22⋊C411yescharacteristic
202C23×C43C2×C22⋊C411yescharacteristic
203C23×C43C23×C411yescharacteristic
204C22×D43—21no—
205C22×D43—21no—
206C22×D43—22no—
207C22×D43—22no—
208C22×D43—22no—
209C22×D43—41no—
210C22×D43—41no—
211C22×D43—42no—
212C22×D43—42no—
213C22×D43C2×C22⋊C412yes—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—22no—
217C2×C4×C43—22no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—42no—
223C2×C4×C43—42no—
224C2×C4×C43—82no—
225C2×C4×C43—82no—
226C2×C4×C43C2×C22⋊C412yes—
227C2×C4×C43C22×D412yes—
228C2×C4×C43C2×#4112yes—
229C2×C4×C43H(5,𝔽2)11yescharacteristic
230C2×C4×C432−1+411yescharacteristic
231C22⋊D43—24no—
232C22⋊D43—42no—
233C22⋊D43—44no—
234C22⋊D43—44no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—22no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—42no—
241C2×Dic43C2×C22⋊C411yescharacteristic
242C2×Dic43C2×C22⋊C411yescharacteristic
243C2×Dic43C2×C22⋊C411yescharacteristic
244C2×Dic43C2×C22⋊C411yescharacteristic
245C2×Dic43C2×C22⋊C412yes—
246D172—42no—
247D172—42no—
248D172—84no—
249C4×D43—22no—
250C4×D43—22no—
251C4×D43—22no—
252C4×D43—22no—
253C4×D43—82no—
254C4×D43—82no—
255C8×C43—24no—
256C8×C43—42no—
257C43⋊C8—42no—
258C43⋊C8—42no—
259#22482—431nomaximal, Sylow
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—21no—
263C22×C43—21no—
264C22×C43—21no—
265C22×C43—21no—
266C22×C43—21no—
267C22×C43—42no—
268C22×C43—42no—
269C22×C43#41312yes—
270C22×C43C22×C22⋊C411yescharacteristic
271C22×C43C4×#4111yescharacteristic
272C22×C43#52011yescharacteristic
273C2×D43—22no—
274C2×D43—22no—
275C2×D43—22no—
276C2×D43—42no—
277C2×D43—42no—
278C2×D43—42no—
279C2×D43—81no—
280C2×D43—81no—
281C2×D43—82no—
282C2×D43—82no—
283C4×C43—22no—
284C4×C43—42no—
285C4×C43—42no—
286C4×C43#54612yes—
287C4×C43#54712yes—
288Dic43—21no—
289Dic43—21no—
290Dic43—22no—
291Dic43—21no—
292Dic43—21no—
293Dic43—42no—
294C2×#553—431no—
295D4×M16—432no—
296#1998—432no—
297#1900—432no—
298#1900—432no—
299#1822—431no—
300#1821—431no—
301#1800—431no—
302C4×#100—431no—
303#1742—431no—
304C2×#343D4311yescharacteristic, complemented
305C2×C43—21no—
306C2×C43—21no—
307C2×C43—22no—
308C2×C43—41no—
309C2×C43#233911yescharacteristic
310C2×C43C2×#41311yescharacteristic
311C2×C43#288811yescharacteristic
312D43—42no—
313D43—82no—
314C22×M16—432no—
315C22×M16C2×D4312yes—
316#553—862no—
317#553—862no—
318#553—862no—
319#553—862no—
320C2×#126—432no—
321C2×#125—431no—
322C2×#123—432no—
323C2×#121—431no—
324C2×#121—432no—
325C2×#121—431no—
326C2×C4×D4—431no—
327C2×C4×D4—432no—
328C2×C4×D4—431no—
329C2×#117—431no—
330C22×C4⋊C4C2×D4311yescharacteristic
331#436—862no—
332#435—862no—
333#435—862no—
334C8×D4—862no—
335#423—432no—
336C2×#100—432no—
337C2×#100—432no—
338#407—432no—
339#407—432no—
340C4×M16—432no—
341#343—432no—
342#343—432no—
343#343—431no—
344#343—431no—
345#343—432no—
346#343C2×D4311yescharacteristic
347#343C2×D4312yes—
348#343C2×D4311yescharacteristic
349C43#2248211yescharacteristic, complemented, Sylow
350C22×D4—431no—
351C22×D4—432no—
352C22×D4—432no—
353C22×D4—431no—
354C23×C4—431no—
355C23×C4—432no—
356C23×C4C4×D4312yes—
357C23×C4C22×D4311yescharacteristic
358C2×M16—22no—
359C2×M16—24no—
360C2×M16—42no—
361C2×M16—432no—
362C2×M16—432no—
363C2×M16—862no—
364C2×M16—864no—
365C2×M16—1722no—
366C2×M16C22×D4312yes—
367C2×M16C22×D4312yes—
368C22×C8—22no—
369C22×C8—862no—
370#126—864no—
371#126—864no—
372#125—862no—
373#125—862no—
374#123—864no—
375#123—864no—
376#121—862no—
377#121—862no—
378#121—864no—
379#121—864no—
380#121—862no—
381#121—862no—
382C4×D4—432no—
383C4×D4—432no—
384C4×D4—432no—
385C4×D4—432no—
386C4×D4—862no—
387C4×D4—862no—
388C4×D4—862no—
389C4×D4—862no—
390C4×D4—862no—
391C4×D4—862no—
392#117—862no—
393#117—862no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—432no—
398C2×C4⋊C4—432no—
399C2×C4⋊C4—431no—
400C2×C4⋊C4C4×D4312yes—
401C2×C4⋊C4C22×D4311yescharacteristic
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C22⋊C4—431no—
404C2×C22⋊C4—431no—
405C2×C22⋊C4—432no—
406C2×C22⋊C4—432no—
407C2×C22⋊C4—432no—
408C2×C22⋊C4—432no—
409C2×C42—431no—
410C2×C42—432no—
411C4⋊C8—862no—
412C4⋊C8—862no—
413#100—864no—
414#100—1722no—
415C22⋊C8—862no—
416C22⋊C8—862no—
417C22⋊C8—862no—
418C22⋊C8—862no—
419#97—862no—
420C4×C8—862no—
421C24—431no—
422C24—432no—
423C24C2×C4×D4311yescharacteristic
424C2×D4—432no—
425C2×D4—432no—
426C2×D4—864no—
427C2×D4—862no—
428C2×D4—862no—
429C2×D4—862no—
430C2×D4—862no—
431C2×D4—861no—
432C2×D4—861no—
433C2×D4—3442no—
434C2×D4—1722no—
435C2×D4—1724no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—82no—
442C22×C4—431no—
443C22×C4—431no—
444C22×C4—431no—
445C22×C4—432no—
446C22×C4—432no—
447C22×C4—432no—
448C22×C4—862no—
449C22×C4—862no—
450C22×C4—862no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—3442no—
454C22×C4C2×C4×D4311yescharacteristic
455C22×C4C2×C4×D4312yes—
456C22×C4C2×C4×D4312yes—
457C22×C4D4×D4312yes—
458C22×C4D4×D4312yes—
459C22×C4C23×D4311yescharacteristic
460M16—22no—
461M16—22no—
462M16—22no—
463M16—44no—
464M16—862no—
465M16—862no—
466M16—862no—
467M16—862no—
468M16—1724no—
469M16#1062189814yes—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—44no—
473C2×C8—862no—
474C2×C8—862no—
475C2×C8—1724no—
476C4⋊C4—24no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—432no—
480C4⋊C4—432no—
481C4⋊C4—862no—
482C4⋊C4—862no—
483C4⋊C4—864no—
484C4⋊C4—862no—
485C22⋊C4—431no—
486C22⋊C4—431no—
487C22⋊C4—431no—
488C22⋊C4—431no—
489C22⋊C4—432no—
490C22⋊C4—432no—
491C22⋊C4—864no—
492C22⋊C4—862no—
493C22⋊C4—862no—
494C22⋊C4—864no—
495C22⋊C4—864no—
496C42—432no—
497C42—432no—
498C42—862no—
499C42—862no—
500C23—21no—
501C23—21no—
502C23—22no—
503C23—41no—
504C23—432no—
505C23—861no—
506C23—861no—
507C23—862no—
508C23—862no—
509C23—862no—
510C23—1721no—
511C23—1721no—
512C23—1722no—
513C23—1722no—
514C23C22⋊C4×D4311yescharacteristic
515C23C22⋊C4×D4311yescharacteristic
516C23C22×C4×D4311yescharacteristic
517D4—864no—
518D4—3444no—
519D4—1722no—
520D4—1724no—
521D4—1724no—
522D4—1722no—
523D4—1722no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—82no—
535C2×C4—82no—
536C2×C4—431no—
537C2×C4—431no—
538C2×C4—432no—
539C2×C4—431no—
540C2×C4—431no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—862no—
544C2×C4—862no—
545C2×C4—862no—
546C2×C4—862no—
547C2×C4—862no—
548C2×C4—3442no—
549C2×C4—3442no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1722no—
553C2×C4C22⋊C4×D4312yes—
554C2×C4C2×D4×D4312yes—
555C2×C4C2×#1062189812yes—
556C2×C4#1306337011yescharacteristic
557C2×C4#1306337311yescharacteristic
558C8—24no—
559C8—42no—
560C8—1722no—
561C8—1722no—
562C22—21no—
563C22—21no—
564C22—21no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—42no—
570C22—42no—
571C22—862no—
572C22—862no—
573C22—862no—
574C22—3442no—
575C22—3442no—
576C22—3441no—
577C22—3441no—
578C22—1722no—
579C22—1722no—
580C22—1722no—
581C22#1458288212yes—
582C22C2×C22⋊C4×D4311yescharacteristic
583C22C4×#1062189811yescharacteristic
584C22#1458338011yescharacteristic
585C4—22no—
586C4—42no—
587C4—42no—
588C4—861no—
589C4—861no—
590C4—862no—
591C4—861no—
592C4—861no—
593C4—1722no—
594C4#1458353912yes—
595C4#1458355012yes—
596C2—21no—
597C2—21no—
598C2—22no—
599C2—41no—
600C2—3442no—
601C2—1722no—
602C2#1913742211yescharacteristic
603C2C2×#1458288211yescharacteristic
604C2#1914307111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#343C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583597C2
cosocleC22×C4×C43C24
hypercenterC2×#343D43
hypocenterC43#22482
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
2. M16×C22⋊D43C2semidirect
3. #19135586C2semidirect
4. #19135058C2semidirect
5. #19135057C2semidirect
6. #19134677C2semidirect
7. #19134675C2semidirect
8. #19134586C2semidirect
9. #19134386C2semidirect
10. #19134332C2semidirect
11. C2×C43×#343C2semidirect
304. C2×#343D43semidirect
349. C43#22482semidirect

Maximal subgroups

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

subgroupindex
C2×#145835972
M16×C22⋊D432
#191355862
#191350582
#191350572
#191346772
#191346752
#191345862
#191343862
#191343322
C2×C43×#3432
#2248243