Finite Group Databasebeta

← #25019291

Subgroups — #25019291

Order 11008.

1862 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063284C211yesmaximal, characteristic
2C2×#14582763C211yesmaximal, characteristic, complemented
3C2×#14582744C211yesmaximal, characteristic, complemented
4#19132847C212yesmaximal, complemented
5#19132838C212yesmaximal
6#19132832C212yesmaximal
7#19132829C212yesmaximal, complemented
8#19132819C211yesmaximal, characteristic, complemented
9#19132819C211yesmaximal, characteristic, complemented
10#19132818C211yesmaximal, characteristic
11C43×C22⋊#95C211yesmaximal, characteristic
12C2×#13063284—24no—
13C2×#13063284—24no—
14C2×#13063284C418yescomplemented
15C22×C4⋊Dic43C2211yescharacteristic
16C22×C4⋊Dic43C2211yescharacteristic
17C22×Dic43⋊C4C2212yes—
18C22×C22⋊Dic43C2212yes—
19C22×C22⋊Dic43C2211yescharacteristic
20C22×C22⋊Dic43C2211yescharacteristic
21C22×C4×Dic43C2212yes—
22C22×C4×Dic43C2211yescharacteristic
23C22×C4×Dic43C2211yescharacteristic
24#14582763—24no—
25#14582744—24no—
26C2×C43⋊#95C2211yescharacteristic
27C2×C43⋊#95C2211yescharacteristic
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2212yes—
35C24×C4×C43C2211yescharacteristic
36C22×C22⋊C4×C43C2212yes—
37C2×#95×C43C2211yescharacteristic
38C2×#95×C43C2211yescharacteristic
39C2×#95×C43C2212yes—
40C23×Dic43C2312yes—
41C23×Dic43C2311yescharacteristic
42C23×Dic43C2311yescharacteristic
43C23×Dic43C2312yes—
44C23×Dic43C2311yescharacteristic
45C23×Dic43C2311yescharacteristic
46#13063284—232no—
47C2×C4⋊Dic43—22no—
48C2×C4⋊Dic43—22no—
49C2×C4⋊Dic43—22no—
50C2×C4⋊Dic43—22no—
51C2×C4⋊Dic43C2×C414yes—
52C2×C4⋊Dic43C2×C414yes—
53C2×Dic43⋊C4—24no—
54C2×Dic43⋊C4—42no—
55C2×Dic43⋊C4—42no—
56C2×C22⋊Dic43—22no—
57C2×C22⋊Dic43—22no—
58C2×C22⋊Dic43—22no—
59C2×C22⋊Dic43—22no—
60C2×C22⋊Dic43—24no—
61C2×C22⋊Dic43—24no—
62C2×C22⋊Dic43—42no—
63C2×C22⋊Dic43C2×C414yes—
64C2×C22⋊Dic43C2×C414yes—
65C2×C4×Dic43—22no—
66C2×C4×Dic43—22no—
67C2×C4×Dic43—24no—
68C2×C4×Dic43—24no—
69C2×C4×Dic43—24no—
70C2×C4×Dic43C2×C414yes—
71C2×C4×Dic43C2×C414yes—
72C2×C4×Dic43D414yes—
73C2×C4×Dic43D414yes—
74C43⋊#95—22no—
75C43⋊#95—22no—
76C43⋊#95—24no—
77C43⋊#95—24no—
78C43⋊#95—24no—
79C43⋊#95—24no—
80C43⋊#95—24no—
81C43⋊#95—42no—
82C43⋊#95—42no—
83C25×C43C2311yescharacteristic
84C23×C4×C43—24no—
85C23×C4×C43—22no—
86C23×C4×C43—22no—
87C23×C4×C43—24no—
88C23×C4×C43C2×C414yes—
89C23×C4×C43C2312yes—
90C23×C4×C43C2312yes—
91C23×C4×C43C2311yescharacteristic
92C23×C4×C43C2311yescharacteristic
93C2×C22⋊C4×C43—24no—
94C2×C22⋊C4×C43—24no—
95C2×C22⋊C4×C43—42no—
96#95×C43—22no—
97#95×C43—22no—
98#95×C43—24no—
99C24×C43—21no—
100C24×C43—21no—
101C24×C43—22no—
102C24×C43—22no—
103C24×C43—22no—
104C24×C43—21no—
105C24×C43—21no—
106C24×C43—21no—
107C24×C43—21no—
108C24×C43C22×C412yes—
109C24×C43#4114yes—
110C24×C43C2411yescharacteristic
111C22×C4×C43—216no—
112C22×C4×C43—216no—
113C22×C4×C43—28no—
114C22×C4×C43—28no—
115C22×C4×C43—28no—
116C22×C4×C43—21no—
117C22×C4×C43—21no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—22no—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43—22no—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43C22×C412yes—
135C22×C4×C43C22×C412yes—
136C22×C4×C43C2×D412yes—
137C22×C4×C43C2×D412yes—
138C22×C4×C43#4114yes—
139C22×C4×C43#4114yes—
140C22×Dic43—22no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—22no—
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—22no—
149C22×Dic43—22no—
150C22×Dic43—22no—
151C22×Dic43—22no—
152C22×Dic43—22no—
153C22×Dic43—22no—
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43—22no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—22no—
162C22×Dic43—22no—
163C22×Dic43—22no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—22no—
169C22×Dic43C22×C412yes—
170C22×Dic43C22×C412yes—
171C22×Dic43C22×C412yes—
172C22×Dic43C22×C412yes—
173C22×Dic43C2×D412yes—
174C22×Dic43C2×D412yes—
175C22×Dic43C2×D412yes—
176C22×Dic43C2×D412yes—
177C22×Dic43#4114yes—
178C22⋊C4×C43—48no—
179C22⋊Dic43—28no—
180C22⋊Dic43—28no—
181C22⋊Dic43—48no—
182C4⋊Dic43—28no—
183C4⋊Dic43—28no—
184Dic43⋊C4—48no—
185C4×Dic43—216no—
186C4×Dic43—28no—
187C4×Dic43C22⋊C4116yescomplemented
188C23×C43—22no—
189C23×C43—22no—
190C23×C43—22no—
191C23×C43—22no—
192C23×C43—22no—
193C23×C43—22no—
194C23×C43—24no—
195C23×C43—24no—
196C23×C43—24no—
197C23×C43—24no—
198C23×C43—24no—
199C23×C43—24no—
200C23×C43—42no—
201C23×C43—42no—
202C23×C43—41no—
203C23×C43—41no—
204C23×C43—41no—
205C23×C43—41no—
206C23×C43—42no—
207C23×C43—42no—
208C23×C43—42no—
209C23×C43—42no—
210C23×C43#11714yes—
211C23×C43C23×C411yescharacteristic
212C23×C43C22×D411yescharacteristic
213C23×C43C22×D411yescharacteristic
214C23×C43C2×#4112yes—
215C23×C43C2×#4112yes—
216C23×C43C2×#4112yes—
217C23×C43C2×#4112yes—
218C23×C43H(5,𝔽2)11yescharacteristic
219C23×C43H(5,𝔽2)11yescharacteristic
220C23×C432−1+411yescharacteristic
221C23×C432−1+411yescharacteristic
222C2×C4×C43—232no—
223C2×C4×C43—22no—
224C2×C4×C43—22no—
225C2×C4×C43—22no—
226C2×C4×C43—22no—
227C2×C4×C43—24no—
228C2×C4×C43—24no—
229C2×C4×C43—24no—
230C2×C4×C43—24no—
231C2×C4×C43—24no—
232C2×C4×C43—24no—
233C2×C4×C43—24no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43—42no—
245C2×C4×C43C2×C22⋊C414yes—
246C2×C4×C43#11714yes—
247C2×Dic43—22no—
248C2×Dic43—22no—
249C2×Dic43—22no—
250C2×Dic43—22no—
251C2×Dic43—24no—
252C2×Dic43—24no—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—22no—
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—22no—
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—24no—
264C2×Dic43—24no—
265C2×Dic43—24no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268C2×Dic43—42no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—42no—
274C2×Dic43—42no—
275C2×Dic43—42no—
276C2×Dic43—42no—
277C2×Dic43—42no—
278C2×Dic43—42no—
279C2×Dic43—42no—
280C2×Dic43—42no—
281C2×Dic43—42no—
282C2×Dic43—42no—
283C2×Dic43C2×C22⋊C414yes—
284C2×Dic43C2×C22⋊C414yes—
285#13957—431nomaximal, Sylow
286C22×C43—24no—
287C22×C43—24no—
288C22×C43—24no—
289C22×C43—42no—
290C22×C43—42no—
291C22×C43—42no—
292C22×C43—44no—
293C22×C43—44no—
294C22×C43—44no—
295C22×C43—44no—
296C22×C43—42no—
297C22×C43C22×C22⋊C411yescharacteristic
298C22×C43C2×#11711yescharacteristic
299C22×C43C2×#11711yescharacteristic
300C22×C43C4×#4111yescharacteristic
301C22×C43C4×#4111yescharacteristic
302C22×C43#52011yescharacteristic
303C22×C43#52011yescharacteristic
304C22×C43#52512yes—
305C22×C43#52512yes—
306C22×C43#52512yes—
307C22×C43#53212yes—
308C22×C43#53511yescharacteristic
309C22×C43#53611yescharacteristic
310C22×C43#53711yescharacteristic
311C22×C43#53711yescharacteristic
312C22×C43#55112yes—
313C22×C43#55112yes—
314C22×C43#55212yes—
315C22×C43#55212yes—
316C22×C43#55212yes—
317C22×C43#55212yes—
318C22×C43#55512yes—
319C22×C43#55512yes—
320C4×C43—24no—
321C4×C43—24no—
322C4×C43—44no—
323C4×C43—82no—
324Dic43—24no—
325Dic43—24no—
326Dic43—42no—
327Dic43—44no—
328Dic43—42no—
329Dic43—82no—
330C22×#117—431no—
331C2×#382—431no—
332C2×#376—431no—
333#1441—432no—
334#1439—432no—
335#1437—432no—
336#1436—432no—
337#1434—431no—
338#1434—431no—
339C22⋊#95—431no—
340C22⋊#95D4311yescharacteristic
341C2×C43—44no—
342C2×C43#228011yescharacteristic
343C2×C43#229711yescharacteristic
344C2×C43#231111yescharacteristic
345C2×C43#234311yescharacteristic
346C2×C43#234311yescharacteristic
347C2×C43#234611yescharacteristic
348C2×C43#234611yescharacteristic
349C2×C43#260912yes—
350C2×C43#260912yes—
351C2×C43#261012yes—
352C2×C43#261112yes—
353C24×C4C2×D4311yescharacteristic
354C2×#117—438no—
355C2×#117—864no—
356C2×#117—864no—
357C22×C4⋊C4—431no—
358C22×C4⋊C4—431no—
359C22×C4⋊C4—432no—
360C22×C22⋊C4—431no—
361C22×C22⋊C4—431no—
362C22×C22⋊C4—432no—
363C22×C22⋊C4C2×D4312yes—
364C22×C42—431no—
365C22×C42—431no—
366C22×C42—432no—
367#382—864no—
368#376—864no—
369C2×#95—431no—
370C2×#95—431no—
371C2×#95—432no—
372C2×#95—432no—
373C2×#95—432no—
374C2×#95—432no—
375C2×#95—432no—
376C2×#95—432no—
377C2×#95—432no—
378C2×#95C2×D4311yescharacteristic
379C2×#95C2×D4311yescharacteristic
380C2×#95C2×D4312yes—
381C43#1395711yescharacteristic, complemented, Sylow
382C25C22×D4311yescharacteristic
383C23×C4—24no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—24no—
387C23×C4—431no—
388C23×C4—431no—
389C23×C4—431no—
390C23×C4—431no—
391C23×C4—432no—
392C23×C4—432no—
393C23×C4C4×D4314yes—
394C23×C4C22×D4312yes—
395C23×C4C22×D4312yes—
396C23×C4C22×D4311yescharacteristic
397C23×C4C22×D4311yescharacteristic
398#117—8632no—
399C2×C4⋊C4—434no—
400C2×C4⋊C4—434no—
401C2×C4⋊C4—862no—
402C2×C4⋊C4—862no—
403C2×C4⋊C4—862no—
404C2×C4⋊C4—862no—
405C2×C4⋊C4—864no—
406C2×C4⋊C4—1722no—
407C2×C4⋊C4—1722no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—42no—
411C2×C22⋊C4—434no—
412C2×C22⋊C4—434no—
413C2×C22⋊C4—862no—
414C2×C22⋊C4—862no—
415C2×C22⋊C4—862no—
416C2×C22⋊C4—862no—
417C2×C22⋊C4—864no—
418C2×C22⋊C4—864no—
419C2×C22⋊C4—1722no—
420C2×C42—434no—
421C2×C42—434no—
422C2×C42—434no—
423C2×C42—434no—
424C2×C42—864no—
425C2×C42—864no—
426C2×C42—864no—
427C2×C42—862no—
428C2×C42—862no—
429#95—22no—
430#95—22no—
431#95—24no—
432#95—864no—
433#95—864no—
434#95—864no—
435#95—864no—
436#95—862no—
437#95—862no—
438#95—864no—
439#95—1722no—
440#95—1722no—
441C24—21no—
442C24—21no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—21no—
447C24—21no—
448C24—21no—
449C24—21no—
450C24C2×C4×D4312yes—
451C24#1062190014yes—
452C24C23×D4311yescharacteristic
453C22×C4—216no—
454C22×C4—216no—
455C22×C4—28no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—28no—
462C22×C4—28no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—432no—
477C22×C4—432no—
478C22×C4—432no—
479C22×C4—432no—
480C22×C4—432no—
481C22×C4—432no—
482C22×C4—432no—
483C22×C4—432no—
484C22×C4—434no—
485C22×C4—862no—
486C22×C4—862no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—862no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—862no—
497C22×C4—862no—
498C22×C4—862no—
499C22×C4—862no—
500C22×C4—862no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—862no—
504C22×C4—861no—
505C22×C4—862no—
506C22×C4—861no—
507C22×C4—862no—
508C22×C4—862no—
509C22×C4—862no—
510C22×C4—862no—
511C22×C4—862no—
512C22×C4—862no—
513C22×C4—862no—
514C22×C4C2×C4×D4312yes—
515C22×C4C2×C4×D4312yes—
516C22×C4#1062189814yes—
517C22×C4D4×D4312yes—
518C22×C4D4×D4312yes—
519C22×C4#1062190014yes—
520C4⋊C4—868no—
521C4⋊C4—868no—
522C4⋊C4—1728no—
523C22⋊C4—48no—
524C22⋊C4—868no—
525C22⋊C4—868no—
526C22⋊C4—1728no—
527C42—4316no—
528C42—8616no—
529C42—868no—
530C23—24no—
531C23—24no—
532C23—24no—
533C23—24no—
534C23—22no—
535C23—22no—
536C23—22no—
537C23—22no—
538C23—22no—
539C23—22no—
540C23—24no—
541C23—24no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23#1306328114yes—
553C23C22×C4×D4311yescharacteristic
554C23C2×D4×D4311yescharacteristic
555C23C2×D4×D4311yescharacteristic
556C23#41×D4312yes—
557C23C2×#1062190012yes—
558C23C2×#1062190012yes—
559C23C2×#1062189812yes—
560C23#1306337011yescharacteristic
561C23#1306337111yescharacteristic
562C23#1306337211yescharacteristic
563C23#1306337311yescharacteristic
564C2×C4—232no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—434no—
588C2×C4—434no—
589C2×C4—862no—
590C2×C4—862no—
591C2×C4—862no—
592C2×C4—862no—
593C2×C4—864no—
594C2×C4—864no—
595C2×C4—862no—
596C2×C4—862no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—864no—
600C2×C4—864no—
601C2×C4—862no—
602C2×C4—862no—
603C2×C4—862no—
604C2×C4—862no—
605C2×C4—862no—
606C2×C4—862no—
607C2×C4—864no—
608C2×C4—1722no—
609C2×C4—1722no—
610C2×C4—1722no—
611C2×C4—1722no—
612C2×C4—1722no—
613C2×C4—1722no—
614C2×C4—1722no—
615C2×C4—1722no—
616C2×C4—1722no—
617C2×C4—1722no—
618C2×C4—1722no—
619C2×C4—1722no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1722no—
625C2×C4C22⋊C4×D4314yes—
626C2×C4#1306328114yes—
627C22—24no—
628C22—24no—
629C22—24no—
630C22—42no—
631C22—42no—
632C22—44no—
633C22—44no—
634C22—44no—
635C22—44no—
636C22—42no—
637C22—42no—
638C22C2×C22⋊C4×D4311yescharacteristic
639C22C2×#1306328111yescharacteristic
640C22C2×#1306328111yescharacteristic
641C22#1458336711yescharacteristic
642C22C4×#1062189811yescharacteristic
643C22#1458337911yescharacteristic
644C22#1458338011yescharacteristic
645C22#1458340512yes—
646C22#1458340512yes—
647C22#1458340812yes—
648C22#1458344612yes—
649C22#1458346511yescharacteristic
650C22#1458347211yescharacteristic
651C22#1458347811yescharacteristic
652C22#1458347911yescharacteristic
653C22#1458357212yes—
654C22#1458357512yes—
655C22#1458358312yes—
656C22#1458358412yes—
657C22#1458358612yes—
658C22#1458358912yes—
659C22#1458361312yes—
660C22#1458361412yes—
661C4—24no—
662C4—24no—
663C4—44no—
664C4—82no—
665C4—864no—
666C4—864no—
667C4—3442no—
668C4—1722no—
669C4—1722no—
670C4—1724no—
671C2—44no—
672C2#1913697311yescharacteristic
673C2#1913708111yescharacteristic
674C2#1913718411yescharacteristic
675C2#1913745111yescharacteristic
676C2#1913745711yescharacteristic
677C2#1913747811yescharacteristic
678C2#1913748211yescharacteristic
679C2#1914026912yes—
680C2#1914027112yes—
681C2#1914027812yes—
682C2#1914028912yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×C22⋊#95C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenterC22⋊#95D43
hypocenterC43#13957
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#14582763C2semidirect
3. C2×#14582744C2semidirect
4. #19132847C2semidirect
7. #19132829C2semidirect
8. #19132819C2semidirect
9. #19132819C2semidirect
14. C2×#13063284C4semidirect
187. C4×Dic43C22⋊C4semidirect
381. C43#13957semidirect

Maximal subgroups

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

subgroupindex
C22×#130632842
C2×#145827632
C2×#145827442
#191328472
#191328382
#191328322
#191328292
#191328192
#191328182
C43×C22⋊#952
#1395743