Finite Group Databasebeta

← #25019290

Subgroups — #25019290

Order 11008.

1862 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063283C211yesmaximal, characteristic
2C2×#14582764C211yesmaximal, characteristic, complemented
3C2×#14582744C211yesmaximal, characteristic, complemented
4#19132848C211yesmaximal, characteristic, complemented
5#19132841C211yesmaximal, characteristic
6#19132837C211yesmaximal, characteristic
7#19132831C212yesmaximal
8#19132829C212yesmaximal, complemented
9#19132821C212yesmaximal, complemented
10(C2×D43)⋊#95C212yesmaximal
11C43×#1441C211yesmaximal, characteristic, complemented
12C23×C4×D43C2211yescharacteristic
13C2×#13063283—24no—
14C2×#13063283—24no—
15C2×#13063283C418yescomplemented
16C22×C4⋊Dic43C2211yescharacteristic
17C22×C4⋊Dic43C2211yescharacteristic
18C22×(C2×D43)⋊C4C2212yes—
19C22×(C2×D43)⋊C4C2212yes—
20C22×(C2×D43)⋊C4C2211yescharacteristic
21C22×(C2×D43)⋊C4C2211yescharacteristic
22C22×C4×Dic43C2212yes—
23C22×C4×Dic43C2211yescharacteristic
24C22×C4×Dic43C2211yescharacteristic
25#14582764—24no—
26#14582744—24no—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2211yescharacteristic
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2212yes—
35C22×C4⋊C4×C43C2211yescharacteristic
36C22×C4⋊C4×C43C2211yescharacteristic
37C2×#95×C43C2212yes—
38C2×#95×C43C2211yescharacteristic
39C2×#95×C43C2212yes—
40C24×D43C2311yescharacteristic
41C23×Dic43C2312yes—
42C23×Dic43C2311yescharacteristic
43C23×Dic43C2312yes—
44C23×Dic43C2311yescharacteristic
45C23×Dic43C2311yescharacteristic
46C22×C4×D43—22no—
47C22×C4×D43—22no—
48C22×C4×D43—22no—
49C22×C4×D43—22no—
50C22×C4×D43—22no—
51C22×C4×D43—22no—
52C22×C4×D43C2×C414yes—
53#13063283—232no—
54C2×C4⋊Dic43—22no—
55C2×C4⋊Dic43—22no—
56C2×C4⋊Dic43—22no—
57C2×C4⋊Dic43—42no—
58C2×C4⋊Dic43C2×C414yes—
59C2×(C2×D43)⋊C4—22no—
60C2×(C2×D43)⋊C4—22no—
61C2×(C2×D43)⋊C4—22no—
62C2×(C2×D43)⋊C4—22no—
63C2×(C2×D43)⋊C4—24no—
64C2×(C2×D43)⋊C4—24no—
65C2×(C2×D43)⋊C4—24no—
66C2×(C2×D43)⋊C4—24no—
67C2×(C2×D43)⋊C4—42no—
68C2×(C2×D43)⋊C4—42no—
69C2×(C2×D43)⋊C4C2×C414yes—
70C2×(C2×D43)⋊C4C2×C414yes—
71C2×C4×Dic43—24no—
72C2×C4×Dic43—22no—
73C2×C4×Dic43—22no—
74C2×C4×Dic43—24no—
75C2×C4×Dic43—24no—
76C2×C4×Dic43C2×C414yes—
77C2×C4×Dic43C2×C414yes—
78C2×C4×Dic43D414yes—
79C2×C4×Dic43D414yes—
80C43⋊#95—22no—
81C43⋊#95—24no—
82C43⋊#95—24no—
83C43⋊#95—24no—
84C43⋊#95—24no—
85C43⋊#95—24no—
86C43⋊#95—24no—
87C43⋊#95—42no—
88C23×C4×C43C2312yes—
89C23×C4×C43C2311yescharacteristic
90C23×C4×C43C2312yes—
91C23×C4×C43C2311yescharacteristic
92C23×C4×C43C2311yescharacteristic
93C2×C4⋊C4×C43—22no—
94C2×C4⋊C4×C43—22no—
95C2×C4⋊C4×C43—22no—
96C2×C4⋊C4×C43—42no—
97C2×C4⋊C4×C43C2×C414yes—
98#95×C43—22no—
99#95×C43—24no—
100#95×C43—42no—
101C24×C43C2411yescharacteristic
102C23×D43—21no—
103C23×D43—21no—
104C23×D43—22no—
105C23×D43—22no—
106C23×D43—21no—
107C23×D43—21no—
108C23×D43—22no—
109C23×D43—22no—
110C23×D43C22×C412yes—
111C23×D43#4112yes—
112C23×D43#4112yes—
113C22×C4×C43—21no—
114C22×C4×C43—21no—
115C22×C4×C43—22no—
116C22×C4×C43—21no—
117C22×C4×C43—21no—
118C22×C4×C43—22no—
119C22×C4×C43—21no—
120C22×C4×C43—21no—
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×C43—22no—
135C22×C4×C43—22no—
136C22×C4×C43C22×C412yes—
137C22×C4×C43C22×C412yes—
138C22×C4×C43C22×C412yes—
139C22×C4×C43C2×D412yes—
140C22×C4×C43C2×D412yes—
141C22×C4×C43#4112yes—
142C22×C4×C43#4114yes—
143C22×C4×C43#4112yes—
144C22×Dic43—22no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—22no—
148C22×Dic43—22no—
149C22×Dic43—22no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43—22no—
157C22×Dic43—22no—
158C22×Dic43—22no—
159C22×Dic43—22no—
160C22×Dic43—22no—
161C22×Dic43—22no—
162C22×Dic43—22no—
163C22×Dic43—22no—
164C22×Dic43—22no—
165C22×Dic43—22no—
166C22×Dic43—22no—
167C22×Dic43C22×C412yes—
168C22×Dic43C22×C412yes—
169C22×Dic43C22×C412yes—
170C22×Dic43C2×D412yes—
171C22×Dic43C2×D412yes—
172C22×Dic43C2×D412yes—
173C22×Dic43C2×D412yes—
174C22×Dic43#4114yes—
175C2×C4×D43—28no—
176C2×C4×D43—28no—
177C2×C4×D43—28no—
178C2×C4×D43—28no—
179C2×C4×D43—28no—
180C2×C4×D43—28no—
181C2×C4×D43—28no—
182C4⋊C4×C43—28no—
183C4⋊C4×C43—44no—
184(C2×D43)⋊C4—28no—
185(C2×D43)⋊C4—28no—
186(C2×D43)⋊C4—48no—
187(C2×D43)⋊C4—48no—
188C4⋊Dic43—28no—
189C4⋊Dic43—44no—
190C4×Dic43—216no—
191C4×Dic43—28no—
192C4×Dic43C22⋊C4116yescomplemented
193C23×C43C23×C411yescharacteristic
194C23×C43C22×D411yescharacteristic
195C23×C43C22×D411yescharacteristic
196C23×C43C2×#4111yescharacteristic
197C23×C43C2×#4111yescharacteristic
198C23×C43C2×#4112yes—
199C23×C43C2×#4111yescharacteristic
200C23×C43C2×#4111yescharacteristic
201C23×C43C2×#4112yes—
202C23×C43H(5,𝔽2)12yes—
203C23×C432−1+412yes—
204C22×D43—22no—
205C22×D43—22no—
206C22×D43—24no—
207C22×D43—24no—
208C22×D43—22no—
209C22×D43—22no—
210C22×D43—22no—
211C22×D43—22no—
212C22×D43—24no—
213C22×D43—24no—
214C22×D43—24no—
215C22×D43—24no—
216C22×D43—42no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—42no—
222C22×D43—42no—
223C22×D43—42no—
224C22×D43—42no—
225C22×D43—42no—
226C22×D43#11714yes—
227C2×C4×C43—22no—
228C2×C4×C43—22no—
229C2×C4×C43—24no—
230C2×C4×C43—22no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—22no—
235C2×C4×C43—22no—
236C2×C4×C43—24no—
237C2×C4×C43—22no—
238C2×C4×C43—24no—
239C2×C4×C43—24no—
240C2×C4×C43—24no—
241C2×C4×C43—24no—
242C2×C4×C43—42no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—42no—
246C2×C4×C43—42no—
247C2×C4×C43—42no—
248C2×C4×C43—42no—
249C2×C4×C43—42no—
250C2×C4×C43—42no—
251C2×C4×C43—42no—
252C2×C4×C43—42no—
253C2×C4×C43—42no—
254C2×C4×C43—42no—
255C2×C4×C43—42no—
256C2×C4×C43C2×C22⋊C414yes—
257C2×C4×C43#11714yes—
258C2×Dic43—22no—
259C2×Dic43—22no—
260C2×Dic43—24no—
261C2×Dic43—24no—
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—22no—
265C2×Dic43—22no—
266C2×Dic43—22no—
267C2×Dic43—22no—
268C2×Dic43—22no—
269C2×Dic43—24no—
270C2×Dic43—24no—
271C2×Dic43—24no—
272C2×Dic43—24no—
273C2×Dic43—42no—
274C2×Dic43—42no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—42no—
278C2×Dic43—42no—
279C2×Dic43—42no—
280C2×Dic43—42no—
281C2×Dic43—42no—
282C2×Dic43—42no—
283C2×Dic43—42no—
284C2×Dic43—42no—
285C2×Dic43—42no—
286C2×Dic43—42no—
287C2×Dic43C2×C22⋊C414yes—
288C2×Dic43C2×C22⋊C414yes—
289C4×D43—232no—
290#13957—431nomaximal, Sylow
291C22×C43C22×C22⋊C411yescharacteristic
292C22×C43C2×#11711yescharacteristic
293C22×C43C2×#11711yescharacteristic
294C22×C43C4×#4112yes—
295C22×C43#52012yes—
296C22×C43#52511yescharacteristic
297C22×C43#52511yescharacteristic
298C22×C43#52511yescharacteristic
299C22×C43#52512yes—
300C22×C43#52511yescharacteristic
301C22×C43#53211yescharacteristic
302C22×C43#53211yescharacteristic
303C22×C43#53511yescharacteristic
304C22×C43#53611yescharacteristic
305C22×C43#53712yes—
306C22×C43#55112yes—
307C22×C43#55112yes—
308C22×C43#55212yes—
309C22×C43#55212yes—
310C22×C43#55212yes—
311C22×C43#55212yes—
312C22×C43#55512yes—
313C22×C43#55512yes—
314C2×D43—28no—
315C2×D43—24no—
316C2×D43—42no—
317C2×D43—44no—
318C2×D43—44no—
319C2×D43—44no—
320C2×D43—42no—
321C2×D43—42no—
322C2×D43—42no—
323C2×D43—42no—
324C2×D43—42no—
325C4×C43—24no—
326C4×C43—24no—
327C4×C43—42no—
328C4×C43—44no—
329C4×C43—82no—
330Dic43—24no—
331Dic43—24no—
332Dic43—44no—
333Dic43—42no—
334Dic43—82no—
335C22×#117—431no—
336C2×#382—431no—
337C2×#376—431no—
338#1441—431no—
339#1441D4311yescharacteristic, complemented
340#1439—431no—
341#1439—431no—
342#1437—432no—
343#1436—432no—
344#1434—432no—
345C22⋊#95—432no—
346C2×C43#228011yescharacteristic
347C2×C43#229711yescharacteristic
348C2×C43#231111yescharacteristic
349C2×C43#234312yes—
350C2×C43#234612yes—
351C2×C43#260912yes—
352C2×C43#260912yes—
353C2×C43#261011yescharacteristic
354C2×C43#261011yescharacteristic
355C2×C43#261111yescharacteristic
356C2×C43#261111yescharacteristic
357D43—44no—
358C24×C4—431no—
359C2×#117—438no—
360C2×#117—864no—
361C2×#117—864no—
362C22×C4⋊C4—431no—
363C22×C4⋊C4—431no—
364C22×C4⋊C4C2×D4311yescharacteristic
365C22×C4⋊C4C2×D4311yescharacteristic
366C22×C22⋊C4—431no—
367C22×C22⋊C4—431no—
368C22×C22⋊C4—432no—
369C22×C22⋊C4—432no—
370C22×C42—431no—
371C22×C42—431no—
372C22×C42—432no—
373#382—864no—
374#376—864no—
375C2×#95—432no—
376C2×#95—432no—
377C2×#95—432no—
378C2×#95—432no—
379C2×#95—432no—
380C2×#95—432no—
381C2×#95—431no—
382C2×#95—432no—
383C2×#95C2×D4312yes—
384C2×#95C2×D4311yescharacteristic
385C2×#95C2×D4312yes—
386C43#1395711yescharacteristic, complemented, Sylow
387C25—431no—
388C23×C4—431no—
389C23×C4—431no—
390C23×C4—431no—
391C23×C4—432no—
392C23×C4—434no—
393C23×C4—432no—
394C23×C4—862no—
395C23×C4—862no—
396C23×C4—862no—
397C23×C4—862no—
398C23×C4—862no—
399C23×C4—862no—
400C23×C4C22×D4312yes—
401C23×C4C22×D4311yescharacteristic
402C23×C4C22×D4312yes—
403C23×C4C22×D4311yescharacteristic
404C23×C4C22×D4311yescharacteristic
405#117—8632no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—42no—
410C2×C4⋊C4—434no—
411C2×C4⋊C4—862no—
412C2×C4⋊C4—862no—
413C2×C4⋊C4—862no—
414C2×C4⋊C4—1722no—
415C2×C4⋊C4C4×D4314yes—
416C2×C22⋊C4—434no—
417C2×C22⋊C4—434no—
418C2×C22⋊C4—862no—
419C2×C22⋊C4—862no—
420C2×C22⋊C4—862no—
421C2×C22⋊C4—862no—
422C2×C22⋊C4—864no—
423C2×C22⋊C4—864no—
424C2×C22⋊C4—864no—
425C2×C22⋊C4—864no—
426C2×C22⋊C4—1722no—
427C2×C22⋊C4—1722no—
428C2×C42—434no—
429C2×C42—434no—
430C2×C42—434no—
431C2×C42—434no—
432C2×C42—862no—
433C2×C42—862no—
434C2×C42—864no—
435C2×C42—864no—
436C2×C42—864no—
437#95—22no—
438#95—24no—
439#95—42no—
440#95—864no—
441#95—864no—
442#95—864no—
443#95—864no—
444#95—862no—
445#95—864no—
446#95—864no—
447#95—1722no—
448C24—432no—
449C24—432no—
450C24—432no—
451C24—861no—
452C24—861no—
453C24—862no—
454C24—861no—
455C24—862no—
456C24—861no—
457C24—862no—
458C24—862no—
459C24C23×D4311yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—432no—
484C22×C4—432no—
485C22×C4—432no—
486C22×C4—432no—
487C22×C4—432no—
488C22×C4—432no—
489C22×C4—432no—
490C22×C4—434no—
491C22×C4—868no—
492C22×C4—868no—
493C22×C4—868no—
494C22×C4—868no—
495C22×C4—868no—
496C22×C4—868no—
497C22×C4—862no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—862no—
502C22×C4—861no—
503C22×C4—868no—
504C22×C4—862no—
505C22×C4—861no—
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×C4—862no—
515C22×C4—862no—
516C22×C4—862no—
517C22×C4—862no—
518C22×C4—862no—
519C22×C4—862no—
520C22×C4—862no—
521C22×C4C2×C4×D4312yes—
522C22×C4C2×C4×D4312yes—
523C22×C4C2×C4×D4312yes—
524C22×C4D4×D4312yes—
525C22×C4D4×D4312yes—
526C22×C4#1062190012yes—
527C22×C4#1062190214yes—
528C22×C4#1062190212yes—
529C4⋊C4—28no—
530C4⋊C4—44no—
531C4⋊C4—868no—
532C4⋊C4—1724no—
533C22⋊C4—868no—
534C22⋊C4—868no—
535C22⋊C4—1728no—
536C22⋊C4—1728no—
537C42—4316no—
538C42—868no—
539C42—8616no—
540C23—434no—
541C23—864no—
542C23—864no—
543C23—864no—
544C23—864no—
545C23—862no—
546C23—862no—
547C23—864no—
548C23—864no—
549C23—862no—
550C23—862no—
551C23—862no—
552C23—862no—
553C23—1722no—
554C23—1722no—
555C23—1722no—
556C23—1722no—
557C23—1722no—
558C23—1721no—
559C23—1721no—
560C23—1721no—
561C23—1721no—
562C23—1722no—
563C23C22×C4×D4311yescharacteristic
564C23C2×D4×D4311yescharacteristic
565C23C2×D4×D4311yescharacteristic
566C23#41×D4311yescharacteristic
567C23#41×D4311yescharacteristic
568C23#41×D4312yes—
569C23C2×#1062190011yescharacteristic
570C23C2×#1062190212yes—
571C23C2×#1062190211yescharacteristic
572C23#1306337012yes—
573C23#1306337212yes—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—22no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—434no—
604C2×C4—434no—
605C2×C4—8632no—
606C2×C4—862no—
607C2×C4—862no—
608C2×C4—864no—
609C2×C4—862no—
610C2×C4—862no—
611C2×C4—864no—
612C2×C4—862no—
613C2×C4—862no—
614C2×C4—862no—
615C2×C4—862no—
616C2×C4—864no—
617C2×C4—864no—
618C2×C4—862no—
619C2×C4—864no—
620C2×C4—864no—
621C2×C4—1722no—
622C2×C4—1722no—
623C2×C4—1722no—
624C2×C4—1722no—
625C2×C4—1722no—
626C2×C4—1722no—
627C2×C4—1722no—
628C2×C4—1722no—
629C2×C4—1722no—
630C2×C4—1722no—
631C2×C4—1722no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4—1722no—
635C2×C4C22⋊C4×D4314yes—
636C2×C4#1306328314yes—
637C22—868no—
638C22—864no—
639C22—1722no—
640C22—1722no—
641C22—1724no—
642C22—1724no—
643C22—1722no—
644C22—1722no—
645C22—1722no—
646C22—1724no—
647C22—1722no—
648C22C2×C22⋊C4×D4311yescharacteristic
649C22#117×D4311yescharacteristic
650C22C2×#1306328311yescharacteristic
651C22C4×#1062190212yes—
652C22#1458337812yes—
653C22#1458340911yescharacteristic
654C22#1458340911yescharacteristic
655C22#1458341212yes—
656C22#1458341211yescharacteristic
657C22#1458341211yescharacteristic
658C22#1458344811yescharacteristic
659C22#1458345011yescharacteristic
660C22#1458346411yescharacteristic
661C22#1458347111yescharacteristic
662C22#1458347612yes—
663C22#1458357612yes—
664C22#1458357712yes—
665C22#1458358512yes—
666C22#1458358712yes—
667C22#1458358712yes—
668C22#1458359112yes—
669C22#1458361312yes—
670C22#1458361512yes—
671C4—24no—
672C4—24no—
673C4—42no—
674C4—44no—
675C4—82no—
676C4—864no—
677C4—864no—
678C4—3442no—
679C4—1722no—
680C4—1724no—
681C2—1724no—
682C2#1913697711yescharacteristic
683C2#1913708411yescharacteristic
684C2#1913718211yescharacteristic
685C2#1913745412yes—
686C2#1913747912yes—
687C2#1914026812yes—
688C2#1914027312yes—
689C2#1914027711yescharacteristic
690C2#1914028511yescharacteristic
691C2#1914028811yescharacteristic
692C2#1914029611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1441C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenter#1441D43
hypocenterC43#13957
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
2. C2×#14582764C2semidirect
3. C2×#14582744C2semidirect
4. #19132848C2semidirect
8. #19132829C2semidirect
9. #19132821C2semidirect
11. C43×#1441C2semidirect
15. C2×#13063283C4semidirect
192. C4×Dic43C22⋊C4semidirect
339. #1441D43semidirect
386. C43#13957semidirect

Maximal subgroups

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

subgroupindex
C22×#130632832
C2×#145827642
C2×#145827442
#191328482
#191328412
#191328372
#191328312
#191328292
#191328212
(C2×D43)⋊#952
C43×#14412
#1395743