Finite Group Databasebeta

← #24986479

Subgroups — #24986479

Order 11008.

1026 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582861C211yesmaximal, characteristic
2#19136977C211yesmaximal, characteristic
3#380×D43C211yesmaximal, characteristic
4#19132463C211yesmaximal, characteristic, complemented
5#19132462C211yesmaximal, characteristic, complemented
6#19132462C211yesmaximal, characteristic, complemented
7C43×#1289C211yesmaximal, characteristic, complemented
8C23×C4×D43C2211yescharacteristic
9C22×#10621872C412yescomplemented
10C2×#13063283—21no—
11C2×C4⋊C4×D43—21no—
12C2×C22⋊C4×D43—21no—
13#14582861—21no—
14#14582861—21no—
15#14582861—21no—
16#14582861—21no—
17C2×C22⋊(C43⋊C8)C2211yescharacteristic
18C2×(C2×D43)⋊C8C412yescomplemented
19#14582761C412yescomplemented
20#14582759C2211yescharacteristic
21#14582759C2211yescharacteristic
22#14582758C412yescomplemented
23#14582757—21no—
24#14582756—21no—
25#14582756—21no—
26#14582754—21no—
27C22⋊C4×Dic43—21no—
28#14582746C412yescomplemented
29#95×D43C412yescomplemented
30C2×C22⋊C8×C43C2211yescharacteristic
31C43×#380C2211yescharacteristic
32C43×#380C2211yescharacteristic
33C24×D43D411yescharacteristic
34C23×Dic43D411yescharacteristic
35C22×C4×D43—22no—
36C22×C4×D43—44no—
37C22×C4×D43C2×C411yescharacteristic
38C22×C4×D43C2×C411yescharacteristic
39C22×C4×D43C2×C411yescharacteristic
40C22×C4×D43C2×C411yescharacteristic
41C22×C4×D43C2×C411yescharacteristic
42C22×C4×D43C2×C411yescharacteristic
43C22×C4×D43D411yescharacteristic
44C22×C4×D43D411yescharacteristic
45C22×C4×D43D411yescharacteristic
46C22×C4×D43D411yescharacteristic
47C22×C4×D43Q811yescharacteristic
48C22×C4×D43Q811yescharacteristic
49C2×#10621872—22no—
50C2×#10621872—22no—
51C2×#10621872—44no—
52C22×C43⋊C8C2×C412yescomplemented
53#13063283—44no—
54C2×C4⋊Dic43—21no—
55C2×C4⋊Dic43—21no—
56C2×Dic43⋊C4—22no—
57C4⋊C4×D43—44no—
58C2×C22⋊Dic43—21no—
59C2×C22⋊Dic43—21no—
60C2×(C2×D43)⋊C4—22no—
61C2×(C2×D43)⋊C4—22no—
62C2×(C2×D43)⋊C4—22no—
63C22⋊C4×D43—42no—
64C22⋊C4×D43—42no—
65C2×C4×Dic43—22no—
66C22⋊(C43⋊C8)—21no—
67C22⋊(C43⋊C8)—21no—
68(C2×D43)⋊C8—22no—
69(C2×D43)⋊C8—22no—
70C43⋊#95—22no—
71C43⋊#95—22no—
72C43⋊#95C2×C412yes—
73C43⋊#95C2×C412yescomplemented
74C23×C4×C43C2311yescharacteristic
75C22×C8×C43C2×C412yescomplemented
76C2×C4⋊C4×C43—21no—
77C2×C4⋊C4×C43—21no—
78C2×C22⋊C4×C43—21no—
79C2×C22⋊C4×C43—21no—
80C22⋊C8×C43—21no—
81C22⋊C8×C43—21no—
82#95×C43C2×C412yes—
83#95×C43C2×C412yescomplemented
84C24×C43C2×D411yescharacteristic
85C23×D43—21no—
86C23×D43—21no—
87C23×D43—21no—
88C23×D43—21no—
89C23×D43—42no—
90C23×D43—42no—
91C23×D43C22⋊C411yescharacteristic
92C23×D43C22⋊C411yescharacteristic
93C23×D43C22⋊C411yescharacteristic
94C23×D43C22⋊C411yescharacteristic
95C23×D43C4⋊C411yescharacteristic
96C23×D43C4⋊C411yescharacteristic
97C22×C4×C43—22no—
98C22×C4×C43—22no—
99C22×C4×C43—42no—
100C22×C4×C43C22×C411yescharacteristic
101C22×C4×C43C22×C411yescharacteristic
102C22×C4×C43C22×C411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43C2×Q811yescharacteristic
106C22×Dic43—22no—
107C22×Dic43—22no—
108C22×Dic43—42no—
109C22×Dic43C22⋊C411yescharacteristic
110C22×Dic43C22⋊C411yescharacteristic
111C22×Dic43C22⋊C411yescharacteristic
112C22×Dic43C22⋊C411yescharacteristic
113C22×Dic43C4⋊C411yescharacteristic
114C22×Dic43C4⋊C411yescharacteristic
115C2×C4×D43—24no—
116C2×C4×D43—24no—
117C2×C4×D43—24no—
118C2×C4×D43—42no—
119C2×C4×D43—42no—
120C2×C4×D43—42no—
121C2×C4×D43—44no—
122C2×C4×D43—44no—
123C2×C4×D43—44no—
124C2×C4×D43—42no—
125C2×C4×D43—42no—
126C2×C4×D43—42no—
127C2×C4×D43—42no—
128C2×C4×D43—42no—
129C2×C4×D43—42no—
130C2×C4×D43C4211yescharacteristic
131C2×C4×D43C4211yescharacteristic
132C2×C4×D43C4211yescharacteristic
133C2×C4×D43C4211yescharacteristic
134C2×C4×D43C22⋊C411yescharacteristic
135C2×C4×D43C22⋊C411yescharacteristic
136C2×C4×D43C22⋊C411yescharacteristic
137C2×C4×D43C22⋊C411yescharacteristic
138C2×C4×D43C4⋊C411yescharacteristic
139C2×C4×D43C4⋊C411yescharacteristic
140C2×C4×D43C4⋊C411yescharacteristic
141C2×C4×D43C4⋊C411yescharacteristic
142C2×C4×D43C4⋊C411yescharacteristic
143C2×C4×D43C4⋊C411yescharacteristic
144C2×C4×D43C4⋊C411yescharacteristic
145C2×C4×D43C4⋊C411yescharacteristic
146C2×C8×C43—22no—
147C2×C8×C43—42no—
148C4⋊C4×C43—42no—
149C4⋊C4×C43—42no—
150C22⋊C4×C43—41no—
151C22⋊C4×C43—41no—
152C22⋊C4×C43—41no—
153C22⋊C4×C43—41no—
154C22⋊Dic43—41no—
155C22⋊Dic43—41no—
156C22⋊Dic43—41no—
157C22⋊Dic43—41no—
158(C2×D43)⋊C4—44no—
159(C2×D43)⋊C4—44no—
160(C2×D43)⋊C4—44no—
161C4⋊Dic43—42no—
162C4⋊Dic43—42no—
163Dic43⋊C4—44no—
164C4×Dic43—44no—
165C2×C43⋊C8—22no—
166C2×C43⋊C8—42no—
167#10621872—44no—
168#10621872—44no—
169C23×C43—41no—
170C23×C43—41no—
171C23×C43C2×C22⋊C411yescharacteristic
172C23×C43C2×C22⋊C411yescharacteristic
173C23×C43C2×C4⋊C411yescharacteristic
174C23×C43AGL(1,ℤ/8)11yescharacteristic
175C23×C43AGL(1,ℤ/8)11yescharacteristic
176C23×C43#13711yescharacteristic
177C23×C43#13711yescharacteristic
178C22×D43—21no—
179C22×D43—21no—
180C22×D43—22no—
181C22×D43—22no—
182C22×D43—21no—
183C22×D43—21no—
184C22×D43—21no—
185C22×D43—21no—
186C22×D43—21no—
187C22×D43—21no—
188C22×D43—21no—
189C22×D43—21no—
190C22×D43—21no—
191C22×D43—21no—
192C22×D43—22no—
193C22×D43—22no—
194C22×D43—22no—
195C22×D43—22no—
196C22×D43—41no—
197C22×D43—41no—
198C22×D43—41no—
199C22×D43—41no—
200C22×D43—41no—
201C22×D43—41no—
202C22×D43—44no—
203C22×D43—44no—
204C22×D43—44no—
205C22×D43—44no—
206C22×D43#9511yescharacteristic
207C22×D43#9511yescharacteristic
208C22×D43#9511yescharacteristic
209C22×D43#9511yescharacteristic
210C2×C4×C43—22no—
211C2×C4×C43—22no—
212C2×C4×C43—22no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—42no—
217C2×C4×C43—42no—
218C2×C4×C43—42no—
219C2×C4×C43—42no—
220C2×C4×C43—42no—
221C2×C4×C43—42no—
222C2×C4×C43C2×C4211yescharacteristic
223C2×C4×C43C2×C22⋊C411yescharacteristic
224C2×C4×C43C2×C4⋊C411yescharacteristic
225C2×C4×C43C2×C4⋊C411yescharacteristic
226C2×Dic43—22no—
227C2×Dic43—22no—
228C2×Dic43—22no—
229C2×Dic43—41no—
230C2×Dic43—41no—
231C2×Dic43—41no—
232C2×Dic43—42no—
233C2×Dic43—42no—
234C2×Dic43—42no—
235C2×Dic43—42no—
236C2×Dic43—42no—
237C2×Dic43—42no—
238C2×Dic43#9511yescharacteristic
239C2×Dic43#9511yescharacteristic
240C2×Dic43#9511yescharacteristic
241C2×Dic43#9511yescharacteristic
242C4×D43—22no—
243C4×D43—22no—
244C4×D43—22no—
245C4×D43—22no—
246C4×D43—22no—
247C4×D43—22no—
248C4×D43—22no—
249C4×D43—22no—
250C4×D43—22no—
251C4×D43—41no—
252C4×D43—41no—
253C4×D43—41no—
254C4×D43—41no—
255C4×D43—41no—
256C4×D43—41no—
257C4×D43—88no—
258C4×D43#9914yes—
259C8×C43—42no—
260C43⋊C8—42no—
261#7983—431nomaximal, Sylow
262C22×C43—21no—
263C22×C43—21no—
264C22×C43—21no—
265C22×C43—21no—
266C22×C43—21no—
267C22×C43—21no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43C2×#9511yescharacteristic
273C22×C43#41711yescharacteristic
274C22×C43#41711yescharacteristic
275C22×C43#41811yescharacteristic
276C22×C43#41911yescharacteristic
277C22×C43#42811yescharacteristic
278C22×C43#42811yescharacteristic
279C2×D43—24no—
280C2×D43—24no—
281C2×D43—21no—
282C2×D43—21no—
283C2×D43—21no—
284C2×D43—21no—
285C2×D43—21no—
286C2×D43—21no—
287C2×D43—21no—
288C2×D43—21no—
289C2×D43—21no—
290C2×D43—21no—
291C2×D43—42no—
292C2×D43—42no—
293C2×D43—42no—
294C2×D43—42no—
295C2×D43—42no—
296C2×D43—42no—
297C2×D43—42no—
298C2×D43—42no—
299C2×D43—42no—
300C2×D43—42no—
301C2×D43H(3,ℤ/4)12yes—
302C2×D43#34212yes—
303C4×C43—21no—
304C4×C43—21no—
305C4×C43—21no—
306C4×C43—82no—
307C4×C43—82no—
308C4×C43C2×#9912yes—
309Dic43—21no—
310Dic43—21no—
311Dic43—21no—
312Dic43—82no—
313Dic43—82no—
314Dic43#34212yes—
315C2×#407—431no—
316#2280—431no—
317C2×#380—431no—
318#1289—431no—
319#1289—431no—
320#1289—431no—
321#1289D4311yescharacteristic, complemented
322C2×C43—21no—
323C2×C43—21no—
324C2×C43—21no—
325C2×C43—21no—
326C2×C43—21no—
327C2×C43—21no—
328C2×C43C2×H(3,ℤ/4)11yescharacteristic
329C2×C43#173611yescharacteristic
330C2×C43C2×#34211yescharacteristic
331D43—22no—
332D43—22no—
333D43—41no—
334D43—41no—
335C24×C4—431no—
336C22×M16—432no—
337C2×#117—861no—
338C22×C4⋊C4—861no—
339C22×C22⋊C4—861no—
340#407—861no—
341#407—861no—
342#407—861no—
343#407—861no—
344C2×C22⋊C8—431no—
345C2×C22⋊C8—432no—
346C2×C22⋊C8C2×D4311yescharacteristic
347#381—432no—
348#380—431no—
349#380—431no—
350#380—432no—
351#380—861no—
352#380—861no—
353#380—861no—
354#380C2×D4311yescharacteristic
355#380C2×D4311yescharacteristic
356#379—861no—
357C4×C22⋊C4—432no—
358C4×C22⋊C4—861no—
359C2×#95—432no—
360C43#798311yescharacteristic, complemented, Sylow
361C25—431no—
362C23×C4—431no—
363C23×C4—431no—
364C23×C4—431no—
365C23×C4—431no—
366C23×C4—431no—
367C23×C4—431no—
368C23×C4—431no—
369C23×C4—431no—
370C23×C4—431no—
371C23×C4—431no—
372C23×C4—431no—
373C23×C4—431no—
374C23×C4—431no—
375C23×C4—862no—
376C23×C4—1724no—
377C23×C4C22×D4311yescharacteristic
378C2×M16—862no—
379C2×M16—862no—
380C2×M16—1724no—
381C22×C8—432no—
382C22×C8C4×D4312yescomplemented
383#117—1724no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—862no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4—861no—
389C2×C4⋊C4—1724no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—862no—
393C2×C22⋊C4—862no—
394C2×C22⋊C4—862no—
395C2×C22⋊C4—861no—
396C2×C22⋊C4—861no—
397C2×C22⋊C4—1722no—
398C2×C22⋊C4—1722no—
399C2×C42—862no—
400C22⋊C8—21no—
401C22⋊C8—21no—
402C22⋊C8—862no—
403C22⋊C8—862no—
404C22⋊C8—861no—
405C22⋊C8—861no—
406#95—432no—
407#95—432no—
408#95—862no—
409#95—862no—
410#95C4×D4312yes—
411#95C4×D4312yescomplemented
412C24—431no—
413C24—431no—
414C24—431no—
415C24—431no—
416C24—431no—
417C24—431no—
418C24—861no—
419C24—861no—
420C24—861no—
421C24—861no—
422C24—1722no—
423C24—1722no—
424C24D4×D4311yescharacteristic
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—42no—
428C22×C4—431no—
429C22×C4—431no—
430C22×C4—431no—
431C22×C4—431no—
432C22×C4—431no—
433C22×C4—431no—
434C22×C4—431no—
435C22×C4—431no—
436C22×C4—431no—
437C22×C4—431no—
438C22×C4—431no—
439C22×C4—431no—
440C22×C4—431no—
441C22×C4—431no—
442C22×C4—431no—
443C22×C4—431no—
444C22×C4—431no—
445C22×C4—431no—
446C22×C4—431no—
447C22×C4—431no—
448C22×C4—431no—
449C22×C4—431no—
450C22×C4—864no—
451C22×C4—864no—
452C22×C4—864no—
453C22×C4—862no—
454C22×C4—862no—
455C22×C4—1722no—
456C22×C4—1722no—
457C22×C4—1722no—
458C22×C4—1722no—
459C22×C4—1722no—
460C22×C4—1722no—
461C22×C4—1722no—
462C22×C4—1722no—
463C22×C4—1722no—
464C22×C4—1724no—
465C22×C4—1724no—
466C22×C4—1724no—
467C22×C4—1722no—
468C22×C4C2×C4×D4311yescharacteristic
469C22×C4C2×C4×D4311yescharacteristic
470C22×C4C2×C4×D4311yescharacteristic
471C22×C4D4×D4311yescharacteristic
472C22×C4D4×D4311yescharacteristic
473C22×C4Q8×D4311yescharacteristic
474M16—1724no—
475M16—1724no—
476C2×C8—22no—
477C2×C8—42no—
478C2×C8—862no—
479C2×C8—1722no—
480C4⋊C4—42no—
481C4⋊C4—42no—
482C4⋊C4—1722no—
483C4⋊C4—1722no—
484C4⋊C4—1724no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—1724no—
490C22⋊C4—1724no—
491C22⋊C4—1724no—
492C22⋊C4—1721no—
493C22⋊C4—1721no—
494C22⋊C4—1721no—
495C22⋊C4—1721no—
496C42—1724no—
497C23—41no—
498C23—41no—
499C23—431no—
500C23—431no—
501C23—431no—
502C23—431no—
503C23—862no—
504C23—862no—
505C23—862no—
506C23—862no—
507C23—862no—
508C23—862no—
509C23—861no—
510C23—861no—
511C23—861no—
512C23—861no—
513C23—861no—
514C23—861no—
515C23—861no—
516C23—861no—
517C23—861no—
518C23—861no—
519C23—861no—
520C23—861no—
521C23—1721no—
522C23—1721no—
523C23—1721no—
524C23—1721no—
525C23—1721no—
526C23—1721no—
527C23—1724no—
528C23—1724no—
529C23—1724no—
530C23—1724no—
531C23C22⋊C4×D4311yescharacteristic
532C23C22⋊C4×D4311yescharacteristic
533C23C4⋊C4×D4311yescharacteristic
534C23#1306334911yescharacteristic
535C23#1306335211yescharacteristic
536C23#1306335411yescharacteristic
537C23#1306335711yescharacteristic
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—431no—
551C2×C4—434no—
552C2×C4—431no—
553C2×C4—431no—
554C2×C4—431no—
555C2×C4—862no—
556C2×C4—862no—
557C2×C4—862no—
558C2×C4—862no—
559C2×C4—862no—
560C2×C4—862no—
561C2×C4—862no—
562C2×C4—862no—
563C2×C4—862no—
564C2×C4—862no—
565C2×C4—862no—
566C2×C4—862no—
567C2×C4—3448no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1722no—
578C2×C4—1722no—
579C2×C4—1722no—
580C2×C4—1722no—
581C2×C4—1722no—
582C2×C4—1722no—
583C2×C4C42×D4311yescharacteristic
584C2×C4C22⋊C4×D4311yescharacteristic
585C2×C4C4⋊C4×D4311yescharacteristic
586C2×C4C4⋊C4×D4311yescharacteristic
587C8—42no—
588C8—1722no—
589C22—21no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—432no—
600C22—432no—
601C22—864no—
602C22—864no—
603C22—861no—
604C22—861no—
605C22—861no—
606C22—861no—
607C22—861no—
608C22—861no—
609C22—861no—
610C22—861no—
611C22—861no—
612C22—861no—
613C22—1722no—
614C22—1722no—
615C22—1722no—
616C22—1722no—
617C22—1722no—
618C22—1722no—
619C22—1722no—
620C22—1722no—
621C22—1722no—
622C22—1722no—
623C22#95×D4311yescharacteristic
624C22#1458289711yescharacteristic
625C22#1458289911yescharacteristic
626C22#1458290211yescharacteristic
627C22#1458290611yescharacteristic
628C22#1458293811yescharacteristic
629C22#1458294011yescharacteristic
630C4—21no—
631C4—21no—
632C4—21no—
633C4—82no—
634C4—82no—
635C4—432no—
636C4—861no—
637C4—861no—
638C4—861no—
639C4—3442no—
640C4—3442no—
641C4#99×D4312yes—
642C2—21no—
643C2—21no—
644C2—21no—
645C2—21no—
646C2—21no—
647C2—21no—
648C2—862no—
649C2—862no—
650C2—1721no—
651C2—1721no—
652C2H(3,ℤ/4)×D4311yescharacteristic
653C2#1913431311yescharacteristic
654C2#342×D4311yescharacteristic
subgroupG/H
centerC22#95×D43
commutatorC2×C4×C43C2×C42
FrattiniC23×C4C22×D43
FittingC43×#1289C2
socleC22×C43C2×#95
prime radicalC24×D43D4
cosocleC23×C4×C43C23
hypercenter#1289D43
hypocenterC43#7983
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1289

Complements

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

NH ≅ G/Ntype
4. #19132463C2semidirect
5. #19132462C2semidirect
6. #19132462C2semidirect
7. C43×#1289C2semidirect
9. C22×#10621872C4semidirect
18. C2×(C2×D43)⋊C8C4semidirect
19. #14582761C4semidirect
22. #14582758C4semidirect
28. #14582746C4semidirect
29. #95×D43C4semidirect
52. C22×C43⋊C8C2×C4semidirect
73. C43⋊#95C2×C4semidirect
75. C22×C8×C43C2×C4semidirect
83. #95×C43C2×C4semidirect
321. #1289D43semidirect
360. C43#7983semidirect
382. C22×C8C4×D43semidirect
411. #95C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145828612
#191369772
#380×D432
#191324632
#191324622
C43×#12892
#798343