Finite Group Databasebeta

← #24988139

Subgroups — #24988139

Order 11008.

860 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135024C211yesmaximal, characteristic, complemented
2#19135019C211yesmaximal, characteristic, complemented
3#19134888C211yesmaximal, characteristic, complemented
4#19134583C211yesmaximal, characteristic, complemented
5#19133167C211yesmaximal, characteristic, complemented
6#19133163C211yesmaximal, characteristic, complemented
7C43×#3505C211yesmaximal, characteristic
8C23×C43⋊C8C2211yescharacteristic
9C2×#13063249—21no—
10C2×#13063246—21no—
11C2×#13063240—21no—
12C2×C22⋊(C43⋊C8)—21no—
13C2×C22⋊(C43⋊C8)C2211yescharacteristic
14#14582759C2211yescharacteristic
15#14582759C2211yescharacteristic
16#14582666—21no—
17#14582661—21no—
18#14582661—21no—
19#14582654—21no—
20#14582636—22no—
21#14582633—22no—
22C43×#553—22no—
23C43×#553—21no—
24C43×#552—21no—
25C43×#551—22no—
26C43×#548—21no—
27C43×#546—21no—
28C43×#539C412yescomplemented
29C43×#538C412yescomplemented
30C43×#534—21no—
31C43×#529—21no—
32C43×#525—21no—
33C2×C22⋊Q8×C43C2211yescharacteristic
34C2×#121×C43C2211yescharacteristic
35C43×#518—21no—
36C2×C4×D4×C43C2211yescharacteristic
37C22×C43⋊C8—21no—
38C22×C43⋊C8—21no—
39C22×C43⋊C8—21no—
40C22×C43⋊C8—21no—
41C22×C43⋊C8—42no—
42C2×C4⋊Dic43—21no—
43C2×C4⋊Dic43—21no—
44C2×C22⋊Dic43—21no—
45C2×C22⋊Dic43—21no—
46#13063249—42no—
47#13063246—42no—
48#13063240—42no—
49C22⋊(C43⋊C8)—21no—
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)—42no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C2×#41×C43—21no—
55C22×Q8×C43D411yescharacteristic
56C22×D4×C43—21no—
57C22×D4×C43D411yescharacteristic
58C22×D4×C43D411yescharacteristic
59C23×C4×C43D411yescharacteristic
60C23×C4×C43C2311yescharacteristic
61#126×C43—22no—
62#126×C43—22no—
63#126×C43—22no—
64#125×C43—21no—
65#125×C43—22no—
66#124×C43—21no—
67#124×C43—22no—
68#123×C43—22no—
69#123×C43—22no—
70#123×C43—22no—
71#123×C43—22no—
72#123×C43—22no—
73C22⋊Q8×C43—21no—
74C22⋊Q8×C43—22no—
75C22⋊Q8×C43—21no—
76C22⋊Q8×C43—21no—
77C22⋊Q8×C43C2×C412yes—
78C22⋊Q8×C43D412yes—
79#121×C43—21no—
80#121×C43—22no—
81#121×C43—22no—
82#121×C43—22no—
83#121×C43—21no—
84#121×C43—21no—
85#121×C43C2×C412yes—
86#121×C43D412yes—
87#120×C43—22no—
88#120×C43—22no—
89C4×Q8×C43—21no—
90C4×D4×C43—22no—
91C4×D4×C43—22no—
92C4×D4×C43—22no—
93C4×D4×C43—21no—
94C4×D4×C43—22no—
95C4×D4×C43—22no—
96C4×D4×C43—21no—
97C4×D4×C43—21no—
98C4×D4×C43—21no—
99C4×D4×C43—21no—
100#117×C43—22no—
101#117×C43—21no—
102#117×C43—22no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43C2×C411yescharacteristic
105C2×C4⋊C4×C43D411yescharacteristic
106C2×C4⋊C4×C43D411yescharacteristic
107C2×C22⋊C4×C43—22no—
108C2×C22⋊C4×C43—21no—
109C2×C22⋊C4×C43—21no—
110C2×C22⋊C4×C43C2×C411yescharacteristic
111C2×C22⋊C4×C43D411yescharacteristic
112C2×C42×C43D411yescharacteristic
113C24×C43—21no—
114C24×C43C22⋊C411yescharacteristic
115C24×C43C2×D411yescharacteristic
116#41×C43—81no—
117#41×C43—81no—
118C2×Q8×C43—21no—
119C2×Q8×C43—41no—
120C2×Q8×C43—41no—
121C2×Q8×C43C22⋊C412yes—
122C2×D4×C43—22no—
123C2×D4×C43—22no—
124C2×D4×C43—21no—
125C2×D4×C43—22no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—22no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—41no—
134C2×D4×C43—41no—
135C2×D4×C43—41no—
136C2×D4×C43—41no—
137C2×D4×C43—41no—
138C2×D4×C43—41no—
139C2×D4×C43C22⋊C412yes—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—41no—
148C22×C4×C43—41no—
149C22×C4×C43—41no—
150C22×C4×C43—41no—
151C22×C4×C43C22⋊C411yescharacteristic
152C22×C4×C43C22⋊C411yescharacteristic
153C22×C4×C43C22⋊C411yescharacteristic
154C22×C4×C43C22×C411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×Dic43—41no—
161C22×Dic43—41no—
162C4⋊C4×C43—22no—
163C4⋊C4×C43—22no—
164C4⋊C4×C43—22no—
165C4⋊C4×C43—22no—
166C4⋊C4×C43—22no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—22no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43C22⋊C412yes—
173C4⋊C4×C43C22⋊C412yes—
174C22⋊C4×C43—22no—
175C22⋊C4×C43—22no—
176C22⋊C4×C43—22no—
177C22⋊C4×C43—22no—
178C22⋊C4×C43—22no—
179C22⋊C4×C43—22no—
180C22⋊C4×C43—22no—
181C22⋊C4×C43—21no—
182C22⋊C4×C43—21no—
183C22⋊C4×C43—22no—
184C22⋊C4×C43—22no—
185C22⋊C4×C43—21no—
186C22⋊C4×C43—22no—
187C22⋊C4×C43—21no—
188C42×C43—22no—
189C42×C43—22no—
190C42×C43—21no—
191C42×C43—21no—
192C22⋊Dic43—41no—
193C22⋊Dic43—41no—
194C22⋊Dic43—41no—
195C22⋊Dic43—41no—
196C4⋊Dic43—41no—
197C4⋊Dic43—41no—
198C4⋊Dic43—41no—
199C4⋊Dic43—41no—
200C2×C43⋊C8—22no—
201C2×C43⋊C8—22no—
202C2×C43⋊C8—22no—
203C2×C43⋊C8—41no—
204C2×C43⋊C8—41no—
205C2×C43⋊C8—41no—
206C2×C43⋊C8—41no—
207C2×C43⋊C8—41no—
208C2×C43⋊C8—41no—
209C2×C43⋊C8—41no—
210C23×C43—21no—
211C23×C43—22no—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—81no—
221C23×C43—81no—
222C23×C43C2×C22⋊C411yescharacteristic
223C23×C43#12011yescharacteristic
224C23×C43#12011yescharacteristic
225C23×C43#13511yescharacteristic
226C23×C43#13511yescharacteristic
227C23×C43AGL(1,ℤ/8)11yescharacteristic
228C23×C43#13711yescharacteristic
229Q8×C43—42no—
230Q8×C43—41no—
231Q8×C43—41no—
232D4×C43—42no—
233D4×C43—42no—
234D4×C43—42no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43—42no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—42no—
241D4×C43—41no—
242D4×C43—41no—
243D4×C43—82no—
244D4×C43—82no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—22no—
254C2×C4×C43—21no—
255C2×C4×C43—22no—
256C2×C4×C43—22no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—81no—
269C2×C4×C43—81no—
270C2×C4×C43—81no—
271C2×C4×C43—82no—
272C2×C4×C43—82no—
273C2×C4×C43C2×C22⋊C411yescharacteristic
274C2×C4×C43C2×C22⋊C411yescharacteristic
275C2×C4×C43#12011yescharacteristic
276C2×C4×C43#12011yescharacteristic
277C2×Dic43—81no—
278C2×Dic43—81no—
279C2×Dic43—81no—
280C2×Dic43—81no—
281C2×Dic43—81no—
282C2×Dic43—81no—
283C43⋊C8—42no—
284C43⋊C8—81no—
285#8352—431nomaximal, Sylow
286C22×C43—21no—
287C22×C43—21no—
288C22×C43—21no—
289C22×C43—21no—
290C22×C43—21no—
291C22×C43—21no—
292C22×C43—41no—
293C22×C43—41no—
294C22×C43—41no—
295C22×C43—41no—
296C22×C43—42no—
297C22×C43—41no—
298C22×C43—42no—
299C22×C43—41no—
300C22×C43—42no—
301C22×C43—41no—
302C22×C43—42no—
303C22×C43—81no—
304C22×C43—161no—
305C22×C43—161no—
306C22×C43#37911yescharacteristic
307C22×C43#41611yescharacteristic
308C22×C43#41711yescharacteristic
309C22×C43#44911yescharacteristic
310C22×C43#44911yescharacteristic
311C22×C43#45211yescharacteristic
312C22×C43#45211yescharacteristic
313C4×C43—21no—
314C4×C43—21no—
315C4×C43—21no—
316C4×C43—41no—
317C4×C43—42no—
318C4×C43—41no—
319C4×C43—42no—
320C4×C43—41no—
321C4×C43—42no—
322C4×C43B(4,𝔽2)11yescharacteristic
323C4×C43#45811yescharacteristic
324Dic43—161no—
325Dic43—161no—
326#3505D4311yescharacteristic
327#1893—431no—
328#1892—431no—
329#1869—431no—
330#1799—431no—
331#1520—431no—
332#1519—431no—
333C2×C43—21no—
334C2×C43—21no—
335C2×C43—21no—
336C2×C43—21no—
337C2×C43—21no—
338C2×C43—21no—
339C2×C43—81no—
340C2×C43—82no—
341C2×C43#178811yescharacteristic
342C2×C43#179011yescharacteristic
343C2×C43#179411yescharacteristic
344C23×C8—431no—
345#553—22no—
346#553—21no—
347#552—21no—
348#551—22no—
349#548—21no—
350#546—21no—
351#539Dic4312yescomplemented
352#538Dic4312yescomplemented
353#534—21no—
354#529—21no—
355#525—21no—
356C2×C22⋊Q8C2×D4311yescharacteristic
357C2×#121C2×D4311yescharacteristic
358#518—21no—
359C2×C4×D4C2×D4311yescharacteristic
360C2×#103—861no—
361C2×#102—861no—
362C2×#99—861no—
363C2×C22⋊C8—431no—
364C2×C22⋊C8—861no—
365#380—431no—
366#380—431no—
367#342—861no—
368#340—861no—
369#340—861no—
370#336—861no—
371#328—862no—
372#327—862no—
373C43#835211yescharacteristic, complemented, Sylow
374C2×#41—21no—
375C22×Q8C22⋊D4311yescharacteristic
376C22×D4—21no—
377C22×D4C22⋊D4311yescharacteristic
378C22×D4C22⋊D4311yescharacteristic
379C23×C4C22⋊D4311yescharacteristic
380C23×C4C22×D4311yescharacteristic
381C22×C8—861no—
382C22×C8—861no—
383C22×C8—861no—
384C22×C8—861no—
385C22×C8—1722no—
386#126—22no—
387#126—22no—
388#126—22no—
389#125—21no—
390#125—22no—
391#124—21no—
392#124—22no—
393#123—22no—
394#123—22no—
395#123—22no—
396#123—22no—
397#123—22no—
398C22⋊Q8—21no—
399C22⋊Q8—22no—
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402C22⋊Q8C2×Dic4312yes—
403C22⋊Q8C22⋊D4312yes—
404#121—21no—
405#121—22no—
406#121—22no—
407#121—22no—
408#121—21no—
409#121—21no—
410#121C2×Dic4312yes—
411#121C22⋊D4312yes—
412#120—22no—
413#120—22no—
414C4×Q8—21no—
415C4×D4—22no—
416C4×D4—22no—
417C4×D4—22no—
418C4×D4—21no—
419C4×D4—22no—
420C4×D4—22no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4—21no—
424C4×D4—21no—
425#117—22no—
426#117—21no—
427#117—22no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4C2×Dic4311yescharacteristic
432C2×C4⋊C4C22⋊D4311yescharacteristic
433C2×C4⋊C4C22⋊D4311yescharacteristic
434C2×C22⋊C4—22no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—861no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4C2×Dic4311yescharacteristic
440C2×C22⋊C4C22⋊D4311yescharacteristic
441C2×C42C22⋊D4311yescharacteristic
442#103—1722no—
443#102—1722no—
444#99—1722no—
445C22⋊C8—861no—
446C22⋊C8—861no—
447C22⋊C8—1722no—
448#95—861no—
449#95—861no—
450C24—21no—
451C24C22⋊Dic4311yescharacteristic
452C24C2×C22⋊D4311yescharacteristic
453#41—81no—
454#41—81no—
455C2×Q8—21no—
456C2×Q8—41no—
457C2×Q8—41no—
458C2×Q8C22⋊Dic4312yes—
459C2×D4—22no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—22no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—21no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4C22⋊Dic4312yes—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—1721no—
489C22×C4—1721no—
490C22×C4C22⋊Dic4311yescharacteristic
491C22×C4C22⋊Dic4311yescharacteristic
492C22×C4C22⋊Dic4311yescharacteristic
493C22×C4C22×Dic4311yescharacteristic
494C22×C4C2×C22⋊D4311yescharacteristic
495C22×C4C2×C22⋊D4311yescharacteristic
496C22×C4C2×C22⋊D4311yescharacteristic
497C22×C4C2×C22⋊D4311yescharacteristic
498C22×C4C2×C22⋊D4311yescharacteristic
499C2×C8—862no—
500C2×C8—862no—
501C2×C8—862no—
502C2×C8—1721no—
503C2×C8—1721no—
504C2×C8—1721no—
505C2×C8—1721no—
506C2×C8—1721no—
507C2×C8—1721no—
508C2×C8—1721no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—22no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—1721no—
520C4⋊C4—1721no—
521C4⋊C4—1721no—
522C4⋊C4—1721no—
523C4⋊C4C22⋊Dic4312yes—
524C4⋊C4C22⋊Dic4312yes—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—21no—
533C22⋊C4—22no—
534C22⋊C4—21no—
535C22⋊C4—22no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—22no—
539C22⋊C4—1721no—
540C22⋊C4—1721no—
541C22⋊C4—1721no—
542C22⋊C4—1721no—
543C42—22no—
544C42—22no—
545C42—21no—
546C42—21no—
547C23—21no—
548C23—21no—
549C23—22no—
550C23—21no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—81no—
558C23—81no—
559C23C2×C22⋊Dic4311yescharacteristic
560C23#1306329411yescharacteristic
561C23#1306329411yescharacteristic
562C23#1306334511yescharacteristic
563C23#1306334511yescharacteristic
564C23#1306335011yescharacteristic
565C23#1306335511yescharacteristic
566Q8—42no—
567Q8—41no—
568Q8—41no—
569D4—42no—
570D4—41no—
571D4—41no—
572D4—42no—
573D4—41no—
574D4—41no—
575D4—42no—
576D4—42no—
577D4—42no—
578D4—41no—
579D4—41no—
580D4—82no—
581D4—82no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—81no—
606C2×C4—81no—
607C2×C4—81no—
608C2×C4—82no—
609C2×C4—82no—
610C2×C4—3441no—
611C2×C4—3441no—
612C2×C4—3441no—
613C2×C4—3441no—
614C2×C4—3441no—
615C2×C4—3441no—
616C2×C4C2×C22⋊Dic4311yescharacteristic
617C2×C4C2×C22⋊Dic4311yescharacteristic
618C2×C4#1306329411yescharacteristic
619C2×C4#1306329411yescharacteristic
620C8—3441no—
621C8—1722no—
622C22—21no—
623C22—21no—
624C22—21no—
625C22—21no—
626C22—21no—
627C22—21no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—42no—
633C22—41no—
634C22—42no—
635C22—41no—
636C22—42no—
637C22—42no—
638C22—41no—
639C22—81no—
640C22—161no—
641C22—161no—
642C22#1458275511yescharacteristic
643C22#1458289511yescharacteristic
644C22#1458290011yescharacteristic
645C22#1458304411yescharacteristic
646C22#1458304411yescharacteristic
647C22#1458306111yescharacteristic
648C22#1458306111yescharacteristic
649C4—21no—
650C4—21no—
651C4—21no—
652C4—41no—
653C4—42no—
654C4—41no—
655C4—42no—
656C4—41no—
657C4—42no—
658C4—6881no—
659C4—6881no—
660C4#1458308611yescharacteristic
661C4#1458308911yescharacteristic
662C2—21no—
663C2—21no—
664C2—21no—
665C2—21no—
666C2—21no—
667C2—21no—
668C2—81no—
669C2—82no—
670C2#1913453511yescharacteristic
671C2#1913454311yescharacteristic
672C2#1913455911yescharacteristic
subgroupG/H
centerC22#14582755
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
Fitting, prime radicalC43×#3505C2
socleC22×C43#379
cosocleC23×C4×C43C23
hypercenter#3505D43
hypocenterC43#8352
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3505

Complements

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

NH ≅ G/Ntype
1. #19135024C2semidirect
2. #19135019C2semidirect
3. #19134888C2semidirect
4. #19134583C2semidirect
5. #19133167C2semidirect
6. #19133163C2semidirect
28. C43×#539C4semidirect
29. C43×#538C4semidirect
351. #539Dic43semidirect
352. #538Dic43semidirect
373. C43#8352semidirect

Maximal subgroups

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

subgroupindex
#191350242
#191350192
#191348882
#191345832
#191331672
#191331632
C43×#35052
#835243