Finite Group Databasebeta

← #25023580

Subgroups — #25023580

Order 11008.

1622 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582810C211yesmaximal, characteristic
2C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic
3#19132866C211yesmaximal, characteristic, complemented
4#19132858C211yesmaximal, characteristic, complemented
5#19132855C212yesmaximal, complemented
6#19132839C212yesmaximal
7#19132837C211yesmaximal, characteristic
8#19132826C212yesmaximal, complemented
9#19132822C211yesmaximal, characteristic, complemented
10(C2×D43)⋊#95C212yesmaximal
11C2×C43×#391C211yesmaximal, characteristic, complemented
12C23×C4×D43C2211yescharacteristic
13C22×Dic43⋊C4C2212yes—
14C22×(C2×D43)⋊C4C2211yescharacteristic
15C22×(C2×D43)⋊C4C2211yescharacteristic
16C22×(C2×D43)⋊C4C2212yes—
17C22×(C2×D43)⋊C4C2212yes—
18C22×C4×Dic43C2211yescharacteristic
19#14582810C418yescomplemented
20C4×(C2×D43)⋊C4—24no—
21C2×C43⋊#95C2212yes—
22C2×C43⋊#95C2211yescharacteristic
23C2×C43⋊#95C2211yescharacteristic
24C2×C43⋊#95C2211yescharacteristic
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2211yescharacteristic
31C2×C43⋊#95C2212yes—
32C23×Q8×C43C2211yescharacteristic
33C22×C4⋊C4×C43C2211yescharacteristic
34C22×C42×C43C2211yescharacteristic
35C43×#391—24no—
36C2×#95×C43C2212yes—
37C2×#95×C43C2212yes—
38C24×D43C2311yescharacteristic
39C23×Dic43C2312yes—
40C23×Dic43C2311yescharacteristic
41C23×Dic43C2312yes—
42C23×Dic43C2311yescharacteristic
43C23×Dic43C2311yescharacteristic
44C22×C4×D43—22no—
45C22×C4×D43—22no—
46C22×C4×D43—42no—
47C22×C4×D43—42no—
48C22×C4×D43Q814yescomplemented
49C2×Dic43⋊C4—24no—
50C2×Dic43⋊C4—42no—
51C2×Dic43⋊C4—42no—
52C2×(C2×D43)⋊C4—22no—
53C2×(C2×D43)⋊C4—22no—
54C2×(C2×D43)⋊C4—22no—
55C2×(C2×D43)⋊C4—22no—
56C2×(C2×D43)⋊C4—22no—
57C2×(C2×D43)⋊C4—24no—
58C2×(C2×D43)⋊C4—42no—
59C2×(C2×D43)⋊C4—42no—
60C2×(C2×D43)⋊C4—42no—
61C2×(C2×D43)⋊C4—42no—
62C2×(C2×D43)⋊C4C2×C414yes—
63C2×(C2×D43)⋊C4C2×C418yes—
64C2×C4×Dic43—22no—
65C2×C4×Dic43—42no—
66C43⋊#95—22no—
67C43⋊#95—22no—
68C43⋊#95—22no—
69C43⋊#95—24no—
70C43⋊#95—42no—
71C43⋊#95—42no—
72C43⋊#95—42no—
73C43⋊#95—42no—
74C43⋊#95—42no—
75C43⋊#95C2×C418yescomplemented
76C43⋊#95C2×C414yescomplemented
77C22×Q8×C43—22no—
78C22×Q8×C43—22no—
79C22×Q8×C43—42no—
80C22×Q8×C43—42no—
81C22×Q8×C43C2×C414yescomplemented
82C23×C4×C43C2312yes—
83C23×C4×C43C2312yes—
84C23×C4×C43C2311yescharacteristic
85C23×C4×C43C2311yescharacteristic
86C23×C4×C43C2311yescharacteristic
87C2×C4⋊C4×C43—22no—
88C2×C4⋊C4×C43—42no—
89C2×C42×C43—42no—
90C2×C42×C43D414yes—
91#95×C43—24no—
92#95×C43—24no—
93C24×C43C2411yescharacteristic
94C23×D43—21no—
95C23×D43—21no—
96C23×D43—21no—
97C23×D43—21no—
98C23×D43—22no—
99C23×D43—22no—
100C23×D43—22no—
101C23×D43—22no—
102C23×D43C22×C412yes—
103C23×D43C2×Q812yes—
104C23×D43#4112yes—
105C2×Q8×C43—28no—
106C2×Q8×C43—48no—
107C2×Q8×C43—44no—
108C2×Q8×C43—44no—
109C2×Q8×C43—48no—
110C22×C4×C43—22no—
111C22×C4×C43—22no—
112C22×C4×C43—22no—
113C22×C4×C43—21no—
114C22×C4×C43—21no—
115C22×C4×C43—22no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
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×C43C22×C414yes—
132C22×C4×C43C22×C412yes—
133C22×C4×C43C2×D412yes—
134C22×C4×C43C2×D412yes—
135C22×C4×C43C2×D412yes—
136C22×C4×C43C2×Q812yes—
137C22×C4×C43#4112yes—
138C22×C4×C43#4112yes—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—22no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—22no—
146C22×Dic43—21no—
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—22no—
158C22×Dic43—22no—
159C22×Dic43—22no—
160C22×Dic43—22no—
161C22×Dic43—22no—
162C22×Dic43—22no—
163C22×Dic43—22no—
164C22×Dic43C22×C412yes—
165C22×Dic43C22×C414yes—
166C22×Dic43C2×Q812yes—
167C22×Dic43#4112yes—
168C2×C4×D43—28no—
169C2×C4×D43—48no—
170C2×C4×D43—44no—
171C2×C4×D43—44no—
172C2×C4×D43—48no—
173C4⋊C4×C43—44no—
174C42×C43—44no—
175(C2×D43)⋊C4—28no—
176(C2×D43)⋊C4—28no—
177(C2×D43)⋊C4—48no—
178(C2×D43)⋊C4—48no—
179Dic43⋊C4—48no—
180C4×Dic43—44no—
181C23×C43C23×C411yescharacteristic
182C23×C43C22×D411yescharacteristic
183C23×C43C22×Q811yescharacteristic
184C23×C43C2×#4111yescharacteristic
185C23×C43C2×#4111yescharacteristic
186C23×C43C2×#4111yescharacteristic
187C23×C43C2×#4111yescharacteristic
188C23×C43H(5,𝔽2)12yes—
189C23×C43H(5,𝔽2)12yes—
190C23×C43H(5,𝔽2)12yes—
191C23×C432−1+412yes—
192C22×D43—22no—
193C22×D43—22no—
194C22×D43—24no—
195C22×D43—24no—
196C22×D43—22no—
197C22×D43—22no—
198C22×D43—22no—
199C22×D43—22no—
200C22×D43—24no—
201C22×D43—24no—
202C22×D43—24no—
203C22×D43—24no—
204C22×D43—41no—
205C22×D43—41no—
206C22×D43—41no—
207C22×D43—41no—
208C22×D43—42no—
209C22×D43—42no—
210C22×D43—42no—
211C22×D43—42no—
212C22×D43—42no—
213C22×D43—42no—
214C22×D43C4×Q814yes—
215Q8×C43—416no—
216C2×C4×C43—24no—
217C2×C4×C43—22no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—24no—
222C2×C4×C43—24no—
223C2×C4×C43—24no—
224C2×C4×C43—24no—
225C2×C4×C43—24no—
226C2×C4×C43—24no—
227C2×C4×C43—22no—
228C2×C4×C43—22no—
229C2×C4×C43—22no—
230C2×C4×C43—42no—
231C2×C4×C43—42no—
232C2×C4×C43—42no—
233C2×C4×C43—42no—
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×C43C4×D414yes—
244C2×C4×C43C22⋊Q814yes—
245C2×Dic43—22no—
246C2×Dic43—24no—
247C2×Dic43—24no—
248C2×Dic43—24no—
249C2×Dic43—24no—
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—24no—
253C2×Dic43—24no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—42no—
261C2×Dic43—42no—
262C2×Dic43—42no—
263C2×Dic43—42no—
264C2×Dic43—42no—
265C2×Dic43—42no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268C2×Dic43—42no—
269C2×Dic43—42no—
270C2×Dic43—42no—
271C2×Dic43—42no—
272C2×Dic43—42no—
273C2×Dic43—42no—
274C4×D43—416no—
275#14319—431nomaximal, Sylow
276C22×C43C2×C4×D411yescharacteristic
277C22×C43C2×C4×Q811yescharacteristic
278C22×C43C4×#4111yescharacteristic
279C22×C43#51812yes—
280C22×C43#52012yes—
281C22×C43C2×C22⋊Q811yescharacteristic
282C22×C43#52511yescharacteristic
283C22×C43#52911yescharacteristic
284C22×C43#53311yescharacteristic
285C22×C43#53411yescharacteristic
286C22×C43#53511yescharacteristic
287C22×C43#53511yescharacteristic
288C22×C43#53611yescharacteristic
289C22×C43#53812yes—
290C22×C43#53812yes—
291C22×C43#53812yes—
292C22×C43#53812yes—
293C22×C43#53912yes—
294C22×C43#54212yes—
295C22×C43#54212yes—
296C22×C43#54212yes—
297C22×C43#54312yes—
298C22×C43#54412yes—
299C2×D43—28no—
300C2×D43—24no—
301C2×D43—42no—
302C2×D43—42no—
303C2×D43—44no—
304C2×D43—42no—
305C2×D43—42no—
306C2×D43—42no—
307C2×D43—42no—
308C2×D43—44no—
309C2×D43—44no—
310C4×C43—24no—
311C4×C43—24no—
312C4×C43—44no—
313C4×C43—42no—
314C4×C43—82no—
315Dic43—42no—
316Dic43—44no—
317Dic43—42no—
318Dic43—42no—
319Dic43—82no—
320C2×#393—431no—
321C2×#391D4311yescharacteristic, complemented
322C2×C4×C22⋊C4—431no—
323#1446—431no—
324#1444—431no—
325#1443—432no—
326#1439—432no—
327#1439—431no—
328#1436—432no—
329#1434—431no—
330C22⋊#95—432no—
331C2×C43C4×C22⋊Q811yescharacteristic
332C2×C43#232111yescharacteristic
333C2×C43#232611yescharacteristic
334C2×C43#232912yes—
335C2×C43#233712yes—
336C2×C43#262611yescharacteristic
337C2×C43#262811yescharacteristic
338C2×C43#263111yescharacteristic
339C2×C43#263811yescharacteristic
340C2×C43#265312yes—
341C2×C43#266512yes—
342D43—44no—
343C23×Q8C2×D4311yescharacteristic
344C24×C4—431no—
345C22×C4⋊C4—432no—
346C22×C4⋊C4C2×D4311yescharacteristic
347C22×C22⋊C4—431no—
348C22×C22⋊C4—432no—
349C22×C22⋊C4—431no—
350C22×C22⋊C4—432no—
351C22×C42—431no—
352C22×C42C2×D4311yescharacteristic
353#393—438no—
354#391—24no—
355C4×C22⋊C4—864no—
356C2×#95—431no—
357C2×#95—432no—
358C2×#95—432no—
359C2×#95—431no—
360C2×#95—431no—
361C2×#95—431no—
362C2×#95—432no—
363C2×#95—432no—
364C2×#95—432no—
365C2×#95—432no—
366C2×#95—432no—
367C2×#95C2×D4312yes—
368C2×#95C2×D4312yes—
369C43#1431911yescharacteristic, complemented, Sylow
370C25—431no—
371C22×Q8—22no—
372C22×Q8—22no—
373C22×Q8—42no—
374C22×Q8—42no—
375C22×Q8C4×D4314yescomplemented
376C23×C4—431no—
377C23×C4—432no—
378C23×C4—431no—
379C23×C4—431no—
380C23×C4—434no—
381C23×C4—432no—
382C23×C4—862no—
383C23×C4—862no—
384C23×C4—1722no—
385C23×C4—1722no—
386C23×C4C22×D4312yes—
387C23×C4C22×D4312yes—
388C23×C4C22×D4311yescharacteristic
389C23×C4C22×D4311yescharacteristic
390C23×C4C22×D4311yescharacteristic
391C2×C4⋊C4—22no—
392C2×C4⋊C4—42no—
393C2×C4⋊C4—864no—
394C2×C4⋊C4—1722no—
395C2×C4⋊C4—1722no—
396C2×C22⋊C4—434no—
397C2×C22⋊C4—438no—
398C2×C22⋊C4—862no—
399C2×C22⋊C4—862no—
400C2×C22⋊C4—862no—
401C2×C22⋊C4—862no—
402C2×C22⋊C4—862no—
403C2×C22⋊C4—864no—
404C2×C22⋊C4—1722no—
405C2×C22⋊C4—1722no—
406C2×C22⋊C4—1722no—
407C2×C22⋊C4—1722no—
408C2×C42—42no—
409C2×C42—862no—
410C2×C42—1722no—
411C2×C42C22⋊D4314yes—
412#95—24no—
413#95—24no—
414#95—438no—
415#95—434no—
416#95—862no—
417#95—864no—
418#95—862no—
419#95—862no—
420#95—1722no—
421#95—1722no—
422#95—1722no—
423#95—1722no—
424#95—1722no—
425C24—432no—
426C24—432no—
427C24—432no—
428C24—861no—
429C24—861no—
430C24—861no—
431C24—861no—
432C24—862no—
433C24—862no—
434C24—862no—
435C24—862no—
436C24C23×D4311yescharacteristic
437C2×Q8—28no—
438C2×Q8—48no—
439C2×Q8—44no—
440C2×Q8—44no—
441C2×Q8—48no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—432no—
464C22×C4—434no—
465C22×C4—432no—
466C22×C4—432no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—862no—
472C22×C4—861no—
473C22×C4—862no—
474C22×C4—861no—
475C22×C4—862no—
476C22×C4—862no—
477C22×C4—862no—
478C22×C4—862no—
479C22×C4—862no—
480C22×C4—862no—
481C22×C4—862no—
482C22×C4—862no—
483C22×C4—862no—
484C22×C4—862no—
485C22×C4—868no—
486C22×C4—862no—
487C22×C4—862no—
488C22×C4—862no—
489C22×C4—862no—
490C22×C4—862no—
491C22×C4—862no—
492C22×C4—862no—
493C22×C4—1728no—
494C22×C4—1724no—
495C22×C4—1724no—
496C22×C4—1728no—
497C22×C4C2×C4×D4314yes—
498C22×C4C2×C4×D4312yes—
499C22×C4#1062189812yes—
500C22×C4Q8×D4312yes—
501C22×C4#1062190212yes—
502C22×C4C2×C22⋊D4312yes—
503C22×C4C2×C22⋊D4312yes—
504C22×C4C2×C22⋊D4312yes—
505C4⋊C4—44no—
506C4⋊C4—1728no—
507C22⋊C4—868no—
508C22⋊C4—868no—
509C22⋊C4—1728no—
510C22⋊C4—1728no—
511C42—44no—
512C42—1724no—
513C23—434no—
514C23—862no—
515C23—862no—
516C23—864no—
517C23—864no—
518C23—862no—
519C23—862no—
520C23—862no—
521C23—862no—
522C23—864no—
523C23—864no—
524C23—864no—
525C23—864no—
526C23—1721no—
527C23—1721no—
528C23—1721no—
529C23—1721no—
530C23—1722no—
531C23—1722no—
532C23—1722no—
533C23—1722no—
534C23—1722no—
535C23—1722no—
536C23C22×C4×D4311yescharacteristic
537C23C22×C22⋊D4311yescharacteristic
538C23C2×Q8×D4311yescharacteristic
539C23#41×D4311yescharacteristic
540C23#41×D4311yescharacteristic
541C23C2×#1062189811yescharacteristic
542C23C2×#1062190211yescharacteristic
543C23#1306337012yes—
544C23#1306337012yes—
545C23#1306337112yes—
546C23#1306337312yes—
547Q8—416no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—862no—
576C2×C4—864no—
577C2×C4—864no—
578C2×C4—864no—
579C2×C4—864no—
580C2×C4—862no—
581C2×C4—862no—
582C2×C4—864no—
583C2×C4—864no—
584C2×C4—17216no—
585C2×C4—1722no—
586C2×C4—1722no—
587C2×C4—1722no—
588C2×C4—1722no—
589C2×C4—1722no—
590C2×C4—1722no—
591C2×C4—1722no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1722no—
599C2×C4—1722no—
600C2×C4—1722no—
601C2×C4—1722no—
602C2×C4—1722no—
603C2×C4—1722no—
604C2×C4—1722no—
605C2×C4C4×C22⋊D4314yes—
606C2×C4#1306330114yes—
607C22—868no—
608C22—864no—
609C22—1722no—
610C22—1722no—
611C22—1724no—
612C22—1722no—
613C22—1722no—
614C22—1724no—
615C22—1722no—
616C22—1724no—
617C22—1722no—
618C22C2×C4×C22⋊D4311yescharacteristic
619C22C4×Q8×D4311yescharacteristic
620C22C4×#1062190211yescharacteristic
621C22#1458337212yes—
622C22#1458338112yes—
623C22C2×#1306330111yescharacteristic
624C22#1458340611yescharacteristic
625C22#1458343611yescharacteristic
626C22#1458345311yescharacteristic
627C22#1458345811yescharacteristic
628C22#1458346311yescharacteristic
629C22#1458346611yescharacteristic
630C22#1458347311yescharacteristic
631C22#1458348312yes—
632C22#1458348312yes—
633C22#1458348712yes—
634C22#1458348912yes—
635C22#1458349512yes—
636C22#1458351912yes—
637C22#1458352112yes—
638C22#1458352312yes—
639C22#1458352412yes—
640C22#1458352612yes—
641C4—24no—
642C4—24no—
643C4—42no—
644C4—44no—
645C4—82no—
646C4—3442no—
647C4—1722no—
648C4—1722no—
649C4—1722no—
650C4—1724no—
651C2—1724no—
652C2C4×#1306330111yescharacteristic
653C2#1913725311yescharacteristic
654C2#1913730211yescharacteristic
655C2#1913732712yes—
656C2#1913740712yes—
657C2#1914040211yescharacteristic
658C2#1914041711yescharacteristic
659C2#1914044811yescharacteristic
660C2#1914051311yescharacteristic
661C2#1914066412yes—
662C2#1914076912yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#391C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenterC2×#391D43
hypocenterC43#14319
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
3. #19132866C2semidirect
4. #19132858C2semidirect
5. #19132855C2semidirect
8. #19132826C2semidirect
9. #19132822C2semidirect
11. C2×C43×#391C2semidirect
19. #14582810C4semidirect
48. C22×C4×D43Q8semidirect
75. C43⋊#95C2×C4semidirect
76. C43⋊#95C2×C4semidirect
81. C22×Q8×C43C2×C4semidirect
321. C2×#391D43semidirect
369. C43#14319semidirect
375. C22×Q8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145828102
C2×C4×(C2×D43)⋊C42
#191328662
#191328582
#191328552
#191328392
#191328372
#191328262
#191328222
(C2×D43)⋊#952
C2×C43×#3912
#1431943