Finite Group Databasebeta

← #25019266

Subgroups — #25019266

Order 11008.

1646 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582761C211yesmaximal, characteristic
2C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic
3C2×#14582746C211yesmaximal, characteristic
4#19132839C212yesmaximal
5#19132839C212yesmaximal
6#19132830C212yesmaximal, complemented
7#19132826C212yesmaximal, complemented
8Dic43⋊#95C211yesmaximal, characteristic, complemented
9Dic43⋊#95C211yesmaximal, characteristic, complemented
10#19132822C211yesmaximal, characteristic, complemented
11C43×#1434C211yesmaximal, characteristic, complemented
12C23×C4×D43C2211yescharacteristic
13C22×Dic43⋊C4C2212yes—
14C22×Dic43⋊C4C2212yes—
15C22×(C2×D43)⋊C4C2212yes—
16C22×(C2×D43)⋊C4C2211yescharacteristic
17C22×(C2×D43)⋊C4C2211yescharacteristic
18C22×(C2×D43)⋊C4C2212yes—
19C22×C4×Dic43C2212yes—
20C22×C4×Dic43C2211yescharacteristic
21#14582761—24no—
22C4×(C2×D43)⋊C4C418yescomplemented
23#14582746—24no—
24C2×C43⋊#95C2211yescharacteristic
25C2×C43⋊#95C2211yescharacteristic
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2211yescharacteristic
32C2×C43⋊#95C2211yescharacteristic
33C22×C42×C43C2211yescharacteristic
34C2×#95×C43C2211yescharacteristic
35C2×#95×C43C2211yescharacteristic
36C2×#95×C43C2212yes—
37C2×#95×C43C2212yes—
38C24×D43C2311yescharacteristic
39C23×Dic43C2312yes—
40C23×Dic43C2312yes—
41C23×Dic43C2311yescharacteristic
42C23×Dic43C2311yescharacteristic
43C23×Dic43C2311yescharacteristic
44C22×C4×D43—42no—
45C22×C4×D43—42no—
46C22×C4×D43C2×C414yes—
47C22×C4×D43D414yes—
48C22×C4×D43Q814yes—
49C2×Dic43⋊C4—24no—
50C2×Dic43⋊C4—24no—
51C2×Dic43⋊C4—24no—
52C2×Dic43⋊C4—24no—
53C2×Dic43⋊C4—42no—
54C2×Dic43⋊C4—42no—
55C2×(C2×D43)⋊C4—24no—
56C2×(C2×D43)⋊C4—24no—
57C2×(C2×D43)⋊C4—24no—
58C2×(C2×D43)⋊C4—22no—
59C2×(C2×D43)⋊C4—22no—
60C2×(C2×D43)⋊C4—22no—
61C2×(C2×D43)⋊C4—22no—
62C2×(C2×D43)⋊C4—24no—
63C2×(C2×D43)⋊C4—42no—
64C2×(C2×D43)⋊C4—42no—
65C2×(C2×D43)⋊C4C2×C414yes—
66C2×(C2×D43)⋊C4C2×C414yes—
67C2×C4×Dic43—24no—
68C2×C4×Dic43—42no—
69C2×C4×Dic43—42no—
70C2×C4×Dic43—42no—
71C2×C4×Dic43C2×C414yes—
72C43⋊#95—22no—
73C43⋊#95—22no—
74C43⋊#95—24no—
75C43⋊#95—24no—
76C43⋊#95—24no—
77C43⋊#95—24no—
78C43⋊#95—42no—
79C43⋊#95C2×C414yes—
80C43⋊#95C2×C414yes—
81C23×C4×C43C2312yes—
82C23×C4×C43C2311yescharacteristic
83C23×C4×C43C2311yescharacteristic
84C23×C4×C43C2312yes—
85C23×C4×C43C2311yescharacteristic
86C2×C42×C43—42no—
87C2×C42×C43C2×C414yes—
88#95×C43—22no—
89#95×C43—22no—
90#95×C43—24no—
91#95×C43—42no—
92C24×C43C2411yescharacteristic
93C23×D43—21no—
94C23×D43—21no—
95C23×D43—21no—
96C23×D43—21no—
97C23×D43—22no—
98C23×D43—22no—
99C23×D43—22no—
100C23×D43—22no—
101C23×D43C22×C412yes—
102C23×D43C2×D412yes—
103C23×D43C2×Q812yes—
104C22×C4×C43—22no—
105C22×C4×C43—22no—
106C22×C4×C43—22no—
107C22×C4×C43—22no—
108C22×C4×C43—22no—
109C22×C4×C43—21no—
110C22×C4×C43—21no—
111C22×C4×C43—21no—
112C22×C4×C43—21no—
113C22×C4×C43—22no—
114C22×C4×C43—22no—
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×C43C22×C412yes—
128C22×C4×C43C22×C412yes—
129C22×C4×C43C22×C412yes—
130C22×C4×C43C2×D412yes—
131C22×C4×C43C2×Q812yes—
132C22×C4×C43#4114yes—
133C22×Dic43—22no—
134C22×Dic43—22no—
135C22×Dic43—22no—
136C22×Dic43—22no—
137C22×Dic43—22no—
138C22×Dic43—22no—
139C22×Dic43—22no—
140C22×Dic43—22no—
141C22×Dic43—22no—
142C22×Dic43—22no—
143C22×Dic43—22no—
144C22×Dic43—22no—
145C22×Dic43—22no—
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—22no—
149C22×Dic43—22no—
150C22×Dic43—22no—
151C22×Dic43—22no—
152C22×Dic43C22×C412yes—
153C22×Dic43C22×C412yes—
154C22×Dic43C22×C412yes—
155C22×Dic43C2×D412yes—
156C22×Dic43C2×Q812yes—
157C22×Dic43#4114yes—
158C22×Dic43#4112yes—
159C22×Dic43#4112yes—
160C22×Dic43#4112yes—
161C22×Dic43#4112yes—
162C2×C4×D43—44no—
163C2×C4×D43—44no—
164C2×C4×D43—48no—
165C2×C4×D43—48no—
166C2×C4×D43C4⋊C4116yescomplemented
167C42×C43—44no—
168(C2×D43)⋊C4—216no—
169(C2×D43)⋊C4—28no—
170(C2×D43)⋊C4—28no—
171(C2×D43)⋊C4—48no—
172Dic43⋊C4—48no—
173Dic43⋊C4—48no—
174C4×Dic43—44no—
175C4×Dic43—48no—
176C23×C43C23×C411yescharacteristic
177C23×C43C22×D411yescharacteristic
178C23×C43C22×Q811yescharacteristic
179C23×C43C2×#4111yescharacteristic
180C23×C43C2×#4111yescharacteristic
181C23×C43C2×#4111yescharacteristic
182C23×C43C2×#4111yescharacteristic
183C23×C43C2×#4112yes—
184C23×C43C2×#4112yes—
185C23×C43H(5,𝔽2)12yes—
186C23×C43H(5,𝔽2)12yes—
187C22×D43—22no—
188C22×D43—22no—
189C22×D43—22no—
190C22×D43—22no—
191C22×D43—22no—
192C22×D43—22no—
193C22×D43—24no—
194C22×D43—22no—
195C22×D43—22no—
196C22×D43—24no—
197C22×D43—22no—
198C22×D43—22no—
199C22×D43—24no—
200C22×D43—24no—
201C22×D43—42no—
202C22×D43—42no—
203C22×D43—42no—
204C22×D43—42no—
205C22×D43—42no—
206C22×D43—42no—
207C22×D43—42no—
208C22×D43—42no—
209C22×D43C2×C4⋊C414yes—
210C2×C4×C43—22no—
211C2×C4×C43—22no—
212C2×C4×C43—24no—
213C2×C4×C43—24no—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—22no—
217C2×C4×C43—22no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—24no—
221C2×C4×C43—24no—
222C2×C4×C43—24no—
223C2×C4×C43—42no—
224C2×C4×C43—42no—
225C2×C4×C43—42no—
226C2×C4×C43—42no—
227C2×C4×C43—42no—
228C2×C4×C43—42no—
229C2×C4×C43—42no—
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×C43C2×C4⋊C414yes—
239C2×Dic43—22no—
240C2×Dic43—22no—
241C2×Dic43—22no—
242C2×Dic43—22no—
243C2×Dic43—22no—
244C2×Dic43—22no—
245C2×Dic43—24no—
246C2×Dic43—24no—
247C2×Dic43—24no—
248C2×Dic43—24no—
249C2×Dic43—24no—
250C2×Dic43—24no—
251C2×Dic43—24no—
252C2×Dic43—24no—
253C2×Dic43—24no—
254C2×Dic43—42no—
255C2×Dic43—42no—
256C2×Dic43—42no—
257C2×Dic43—42no—
258C2×Dic43—42no—
259C2×Dic43—42no—
260C2×Dic43—42no—
261C2×Dic43—42no—
262C2×Dic43—42no—
263C2×Dic43—42no—
264C2×Dic43—42no—
265C2×Dic43C2×C4⋊C414yes—
266C2×Dic43#11714yes—
267C2×Dic43#11714yes—
268C4×D43—416no—
269#13953—431nomaximal, Sylow
270C22×C43C22×C4⋊C411yescharacteristic
271C22×C43C2×#11711yescharacteristic
272C22×C43C2×#11711yescharacteristic
273C22×C43C4×#4111yescharacteristic
274C22×C43C4×#4111yescharacteristic
275C22×C43#51811yescharacteristic
276C22×C43#51811yescharacteristic
277C22×C43#52512yes—
278C22×C43#53211yescharacteristic
279C22×C43#53211yescharacteristic
280C22×C43#53312yes—
281C22×C43#53311yescharacteristic
282C22×C43#53311yescharacteristic
283C22×C43#53412yes—
284C22×C43#54312yes—
285C22×C43#55112yes—
286C22×C43#55112yes—
287C22×C43#55312yes—
288C22×C43#55312yes—
289C22×C43#55312yes—
290C22×C43#55312yes—
291C22×C43#55912yes—
292C22×C43#55912yes—
293C2×D43—24no—
294C2×D43—24no—
295C2×D43—24no—
296C2×D43—44no—
297C2×D43—44no—
298C2×D43—44no—
299C2×D43—44no—
300C2×D43—42no—
301C2×D43—42no—
302C2×D43—42no—
303C2×D43—42no—
304C4×C43—24no—
305C4×C43—44no—
306C4×C43—42no—
307C4×C43—42no—
308C4×C43—82no—
309Dic43—24no—
310Dic43—24no—
311Dic43—24no—
312Dic43—44no—
313Dic43—82no—
314C2×#381—431no—
315C2×C4×C22⋊C4—431no—
316C2×C4×C22⋊C4—431no—
317#1439—432no—
318#1439—432no—
319#1436—432no—
320#1436—432no—
321C4⋊#95—431no—
322C4⋊#95—431no—
323#1434—431no—
324#1434D4311yescharacteristic, complemented
325C2×C43#228511yescharacteristic
326C2×C43#229611yescharacteristic
327C2×C43#231511yescharacteristic
328C2×C43#235311yescharacteristic
329C2×C43#235311yescharacteristic
330C2×C43#235711yescharacteristic
331C2×C43#235711yescharacteristic
332C2×C43#260212yes—
333C2×C43#260212yes—
334C2×C43#260712yes—
335C2×C43#260812yes—
336D43—44no—
337C24×C4—431no—
338C22×C4⋊C4—432no—
339C22×C4⋊C4—432no—
340C22×C22⋊C4—431no—
341C22×C22⋊C4—431no—
342C22×C22⋊C4—432no—
343C22×C22⋊C4—432no—
344C22×C42—431no—
345C22×C42—432no—
346C22×C42C2×D4311yescharacteristic
347#381—864no—
348C4×C22⋊C4—438no—
349C4×C22⋊C4—864no—
350C2×#95—431no—
351C2×#95—431no—
352C2×#95—431no—
353C2×#95—431no—
354C2×#95—432no—
355C2×#95—432no—
356C2×#95—432no—
357C2×#95—432no—
358C2×#95—432no—
359C2×#95C2×D4311yescharacteristic
360C2×#95C2×D4311yescharacteristic
361C2×#95C2×D4312yes—
362C2×#95C2×D4312yes—
363C43#1395311yescharacteristic, complemented, Sylow
364C25—431no—
365C23×C4—431no—
366C23×C4—431no—
367C23×C4—431no—
368C23×C4—434no—
369C23×C4—434no—
370C23×C4—434no—
371C23×C4—432no—
372C23×C4—432no—
373C23×C4—1722no—
374C23×C4—1722no—
375C23×C4C22×D4312yes—
376C23×C4C22×D4311yescharacteristic
377C23×C4C22×D4311yescharacteristic
378C23×C4C22×D4312yes—
379C23×C4C22×D4311yescharacteristic
380C2×C4⋊C4—864no—
381C2×C4⋊C4—864no—
382C2×C4⋊C4—864no—
383C2×C4⋊C4—864no—
384C2×C4⋊C4—1722no—
385C2×C4⋊C4—1722no—
386C2×C22⋊C4—434no—
387C2×C22⋊C4—434no—
388C2×C22⋊C4—862no—
389C2×C22⋊C4—862no—
390C2×C22⋊C4—862no—
391C2×C22⋊C4—862no—
392C2×C22⋊C4—864no—
393C2×C22⋊C4—864no—
394C2×C22⋊C4—864no—
395C2×C22⋊C4—864no—
396C2×C22⋊C4—1722no—
397C2×C22⋊C4—1722no—
398C2×C42—42no—
399C2×C42—434no—
400C2×C42—864no—
401C2×C42—1722no—
402C2×C42—1722no—
403C2×C42—1722no—
404C2×C42C4×D4314yes—
405#95—24no—
406#95—22no—
407#95—22no—
408#95—42no—
409#95—434no—
410#95—434no—
411#95—864no—
412#95—864no—
413#95—864no—
414#95—864no—
415#95—862no—
416#95—862no—
417#95—1722no—
418C24—432no—
419C24—432no—
420C24—432no—
421C24—861no—
422C24—861no—
423C24—861no—
424C24—861no—
425C24—862no—
426C24—862no—
427C24—862no—
428C24—862no—
429C24C23×D4311yescharacteristic
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—432no—
454C22×C4—432no—
455C22×C4—432no—
456C22×C4—432no—
457C22×C4—432no—
458C22×C4—432no—
459C22×C4—432no—
460C22×C4—432no—
461C22×C4—432no—
462C22×C4—4316no—
463C22×C4—434no—
464C22×C4—862no—
465C22×C4—862no—
466C22×C4—862no—
467C22×C4—862no—
468C22×C4—862no—
469C22×C4—862no—
470C22×C4—862no—
471C22×C4—862no—
472C22×C4—862no—
473C22×C4—862no—
474C22×C4—862no—
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—1724no—
484C22×C4—1724no—
485C22×C4—1728no—
486C22×C4—1728no—
487C22×C4C2×C4×D4312yes—
488C22×C4C2×C4×D4312yes—
489C22×C4C2×C4×D4312yes—
490C22×C4#1062189814yes—
491C22×C4D4×D4312yes—
492C22×C4Q8×D4312yes—
493C4⋊C4—1728no—
494C4⋊C4—1728no—
495C22⋊C4—868no—
496C22⋊C4—868no—
497C22⋊C4—8616no—
498C22⋊C4—1728no—
499C42—44no—
500C42—1724no—
501C42—1728no—
502C23—434no—
503C23—862no—
504C23—862no—
505C23—862no—
506C23—862no—
507C23—862no—
508C23—862no—
509C23—864no—
510C23—862no—
511C23—862no—
512C23—864no—
513C23—862no—
514C23—862no—
515C23—864no—
516C23—864no—
517C23—1722no—
518C23—1722no—
519C23—1722no—
520C23—1722no—
521C23—1722no—
522C23—1722no—
523C23—1722no—
524C23—1722no—
525C23C22×C4×D4311yescharacteristic
526C23C2×D4×D4311yescharacteristic
527C23C2×Q8×D4311yescharacteristic
528C23#41×D4311yescharacteristic
529C23#41×D4311yescharacteristic
530C23#41×D4312yes—
531C23#41×D4311yescharacteristic
532C23#41×D4311yescharacteristic
533C23C2×#1062189812yes—
534C23#1306337012yes—
535C23#1306337112yes—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—24no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—434no—
565C2×C4—434no—
566C2×C4—434no—
567C2×C4—864no—
568C2×C4—864no—
569C2×C4—864no—
570C2×C4—864no—
571C2×C4—862no—
572C2×C4—862no—
573C2×C4—862no—
574C2×C4—862no—
575C2×C4—862no—
576C2×C4—862no—
577C2×C4—864no—
578C2×C4—864no—
579C2×C4—864no—
580C2×C4—864no—
581C2×C4—864no—
582C2×C4—17216no—
583C2×C4—1722no—
584C2×C4—1722no—
585C2×C4—1722no—
586C2×C4—1722no—
587C2×C4—1722no—
588C2×C4—1722no—
589C2×C4—1722no—
590C2×C4—1722no—
591C2×C4—1722no—
592C2×C4—1722no—
593C2×C4—1722no—
594C2×C4C4⋊C4×D4314yes—
595C22—864no—
596C22—864no—
597C22—864no—
598C22—1722no—
599C22—1722no—
600C22—1722no—
601C22—1724no—
602C22—1724no—
603C22—1724no—
604C22—1724no—
605C22—1722no—
606C22C2×C4⋊C4×D4311yescharacteristic
607C22#117×D4311yescharacteristic
608C22#117×D4311yescharacteristic
609C22#1458336711yescharacteristic
610C22C4×#1062189811yescharacteristic
611C22#1458337211yescharacteristic
612C22#1458337311yescharacteristic
613C22#1458340812yes—
614C22#1458344811yescharacteristic
615C22#1458344811yescharacteristic
616C22#1458345312yes—
617C22#1458345511yescharacteristic
618C22#1458345511yescharacteristic
619C22#1458345712yes—
620C22#1458352412yes—
621C22#1458357312yes—
622C22#1458357412yes—
623C22#1458359312yes—
624C22#1458359412yes—
625C22#1458359812yes—
626C22#1458360012yes—
627C22#1458363212yes—
628C22#1458363312yes—
629C4—24no—
630C4—42no—
631C4—42no—
632C4—44no—
633C4—82no—
634C4—864no—
635C4—864no—
636C4—864no—
637C4—3442no—
638C4—1724no—
639C2—1724no—
640C2#1913700111yescharacteristic
641C2#1913707511yescharacteristic
642C2#1913720811yescharacteristic
643C2#1913752811yescharacteristic
644C2#1913753611yescharacteristic
645C2#1913756311yescharacteristic
646C2#1913756911yescharacteristic
647C2#1914021212yes—
648C2#1914021412yes—
649C2#1914025912yes—
650C2#1914026412yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1434C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenter#1434D43
hypocenterC43#13953
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
6. #19132830C2semidirect
7. #19132826C2semidirect
8. Dic43⋊#95C2semidirect
9. Dic43⋊#95C2semidirect
10. #19132822C2semidirect
11. C43×#1434C2semidirect
22. C4×(C2×D43)⋊C4C4semidirect
166. C2×C4×D43C4⋊C4semidirect
324. #1434D43semidirect
363. C43#13953semidirect

Maximal subgroups

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

subgroupindex
C2×#145827612
C2×C4×(C2×D43)⋊C42
C2×#145827462
#191328392
#191328302
#191328262
Dic43⋊#952
#191328222
C43×#14342
#1395343