Finite Group Databasebeta

← #24988046

Subgroups — #24988046

Order 11008.

908 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583435C211yesmaximal, characteristic
2#19134661C211yesmaximal, characteristic, complemented
3C2×#14582636C211yesmaximal, characteristic, complemented
4C2×#14582634C211yesmaximal, characteristic
5C2×#14582632C211yesmaximal, characteristic
6#19132819C211yesmaximal, characteristic, complemented
7C2×C43×#328C211yesmaximal, characteristic, complemented
8#14583435—22no—
9#14583435—22no—
10#14583435—22no—
11#14583435—22no—
12C2×#13063320—21no—
13C2×#13063316C411yescharacteristic, complemented
14C2×#13063314C411yescharacteristic, complemented
15C2×#13063309—21no—
16C2×#13063299C2211yescharacteristic
17C2×Q8×Dic43C411yescharacteristic, complemented
18C2×#13063287C411yescharacteristic, complemented
19C2×(C22⋊D43)⋊C4—21no—
20C2×#13063283—21no—
21C22×C4×Dic43C2211yescharacteristic
22C2×C22⋊(C43⋊C8)C2211yescharacteristic
23C2×C43⋊#95—21no—
24C2×C43⋊#95—21no—
25C2×C43⋊#95C2211yescharacteristic
26#14582653—21no—
27#14582653—21no—
28#14582636—22no—
29#14582634—22no—
30#14582632—22no—
31C2×C22⋊Q8×C43C2211yescharacteristic
32C2×C22⋊C8×C43C2211yescharacteristic
33C2×#95×C43C2211yescharacteristic
34C43×#328—22no—
35C22×D172C2×C411yescharacteristic
36C22×C22⋊D43—21no—
37C23×Dic43—21no—
38C23×Dic43D411yescharacteristic
39C23×Dic43D411yescharacteristic
40C22×C4×D43—21no—
41C22×C43⋊C8—21no—
42#13063320—24no—
43#13063320—24no—
44#13063316—22no—
45#13063316—22no—
46#13063314—22no—
47#13063314—22no—
48#13063309—24no—
49#13063309—24no—
50#13063299—21no—
51#13063299—21no—
52#13063299D412yes—
53#13063299D412yes—
54Q8×Dic43—22no—
55Q8×Dic43—22no—
56#13063287—22no—
57#13063287—22no—
58(C22⋊D43)⋊C4—24no—
59(C22⋊D43)⋊C4—24no—
60#13063283—24no—
61#13063283—24no—
62C2×C4⋊Dic43—21no—
63C2×C4⋊Dic43—21no—
64C2×C4⋊Dic43C2×C411yescharacteristic
65C2×Dic43⋊C4—21no—
66C2×(C2×D43)⋊C4—21no—
67C2×(C2×D43)⋊C4—21no—
68C2×(C2×D43)⋊C4—21no—
69C2×(C2×D43)⋊C4—21no—
70C2×C4×Dic43—21no—
71C2×C4×Dic43—21no—
72C2×C4×Dic43—21no—
73C2×C4×Dic43—21no—
74C2×C4×Dic43—21no—
75C2×C4×Dic43C2×C411yescharacteristic
76C2×C4×Dic43C2×C411yescharacteristic
77C2×C4×Dic43D411yescharacteristic
78C2×C4×Dic43D411yescharacteristic
79C22⋊(C43⋊C8)—21no—
80C22⋊(C43⋊C8)—21no—
81C43⋊#95—24no—
82C43⋊#95—21no—
83C43⋊#95—21no—
84C43⋊#95—42no—
85C22×Q8×C43C2×C411yescharacteristic
86C23×C4×C43—21no—
87C23×C4×C43C2311yescharacteristic
88C22×C8×C43—21no—
89C22⋊Q8×C43—21no—
90C22⋊Q8×C43—21no—
91C22⋊Q8×C43D412yes—
92C22⋊Q8×C43D412yes—
93C2×C4⋊C4×C43—21no—
94C2×C4⋊C4×C43C2×C411yescharacteristic
95C2×C22⋊C4×C43—21no—
96C22⋊C8×C43—21no—
97C22⋊C8×C43—21no—
98#95×C43—21no—
99#95×C43—21no—
100C24×C43C2×D411yescharacteristic
101C23×D43—21no—
102C2×Q8×C43—21no—
103C2×Q8×C43—41no—
104C2×Q8×C43—41no—
105C2×Q8×C43C22⋊C412yes—
106C22×C4×C43—22no—
107C22×C4×C43—21no—
108C22×C4×C43—21no—
109C22×C4×C43—41no—
110C22×C4×C43—41no—
111C22×C4×C43—41no—
112C22×C4×C43—41no—
113C22×C4×C43—41no—
114C22×C4×C43—41no—
115C22×C4×C43—41no—
116C22×C4×C43—41no—
117C22×C4×C43C22×C411yescharacteristic
118C22×C4×C43C2×D411yescharacteristic
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C2×C22⋊D43—22no—
124C2×C22⋊D43—22no—
125C2×C22⋊D43—41no—
126C2×C22⋊D43—41no—
127C2×C22⋊D43—41no—
128C2×C22⋊D43—41no—
129C22×Dic43—22no—
130C22×Dic43—22no—
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—41no—
141C22×Dic43—41no—
142C22×Dic43—41no—
143C22×Dic43—41no—
144C22×Dic43—41no—
145C22×Dic43—41no—
146C22×Dic43—41no—
147C22×Dic43C22⋊C411yescharacteristic
148C22×Dic43C22⋊C411yescharacteristic
149C22×Dic43C22⋊C411yescharacteristic
150C22×Dic43C22⋊C411yescharacteristic
151C2×D172—21no—
152C2×D172—41no—
153C2×D172—41no—
154C2×D172C22⋊C412yes—
155C2×C4×D43—24no—
156C2×C4×D43—42no—
157C2×C4×D43—42no—
158C2×C8×C43—41no—
159C2×C8×C43—41no—
160C2×C8×C43—41no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—22no—
163C4⋊C4×C43—22no—
164C4⋊C4×C43C22⋊C412yes—
165C22⋊C4×C43—22no—
166C22⋊C4×C43—22no—
167(C2×D43)⋊C4—24no—
168(C2×D43)⋊C4—24no—
169(C2×D43)⋊C4—24no—
170(C2×D43)⋊C4—22no—
171(C2×D43)⋊C4—22no—
172C4⋊Dic43—24no—
173C4⋊Dic43—24no—
174C4⋊Dic43—21no—
175C4⋊Dic43C22⋊C412yes—
176Dic43⋊C4—24no—
177C4×Dic43—24no—
178C4×Dic43—21no—
179C4×Dic43—21no—
180C4×Dic43—21no—
181C4×Dic43—21no—
182C4×Dic43—21no—
183C4×Dic43—21no—
184C4×Dic43—21no—
185C4×Dic43—21no—
186C2×C43⋊C8—41no—
187C2×C43⋊C8—41no—
188C2×C43⋊C8—41no—
189C23×C43—21no—
190C23×C43—21no—
191C23×C43—21no—
192C23×C43—21no—
193C23×C43C2×C22⋊C411yescharacteristic
194C23×C43#12011yescharacteristic
195C23×C43#12011yescharacteristic
196C23×C43#13511yescharacteristic
197C23×C43#13511yescharacteristic
198C23×C43AGL(1,ℤ/8)11yescharacteristic
199C23×C43#13711yescharacteristic
200C22×D43—22no—
201C22×D43—41no—
202C22×D43—41no—
203C22×D43—41no—
204C22×D43—41no—
205C22×D43—41no—
206C22×D43—41no—
207Q8×C43—42no—
208Q8×C43—42no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—22no—
214C2×C4×C43—22no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—42no—
224C2×C4×C43—42no—
225C2×C4×C43—42no—
226C2×C4×C43—81no—
227C2×C4×C43—81no—
228C2×C4×C43—81no—
229C2×C4×C43—81no—
230C2×C4×C43C2×C22⋊C411yescharacteristic
231C2×C4×C43C2×C22⋊C411yescharacteristic
232C2×C4×C43#12011yescharacteristic
233C2×C4×C43#12011yescharacteristic
234C22⋊D43—42no—
235C22⋊D43—42no—
236C22⋊D43—42no—
237C22⋊D43—42no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—22no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—42no—
251C2×Dic43—42no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—42no—
259C2×Dic43—42no—
260C2×Dic43—42no—
261C2×Dic43—81no—
262C2×Dic43—81no—
263C2×Dic43—81no—
264C2×Dic43—81no—
265C2×Dic43#10412yes—
266D172—42no—
267D172—42no—
268C4×D43—48no—
269C8×C43—81no—
270C43⋊C8—81no—
271#8330—431nomaximal, Sylow
272C22×C43—21no—
273C22×C43—21no—
274C22×C43—21no—
275C22×C43—21no—
276C22×C43—21no—
277C22×C43—21no—
278C22×C43—21no—
279C22×C43—21no—
280C22×C43—21no—
281C22×C43—21no—
282C22×C43—21no—
283C22×C43—21no—
284C22×C43#37911yescharacteristic
285C22×C43#41011yescharacteristic
286C22×C43#41011yescharacteristic
287C22×C43#41611yescharacteristic
288C22×C43#41711yescharacteristic
289C22×C43C2×#10411yescharacteristic
290C22×C43#42111yescharacteristic
291C22×C43#44911yescharacteristic
292C22×C43#44911yescharacteristic
293C22×C43#45211yescharacteristic
294C22×C43#45211yescharacteristic
295C2×D43—42no—
296C2×D43—42no—
297C2×D43—42no—
298C2×D43—81no—
299C2×D43—81no—
300C2×D43—81no—
301C2×D43—81no—
302C4×C43—21no—
303C4×C43—21no—
304C4×C43—21no—
305C4×C43—21no—
306C4×C43—42no—
307C4×C43—42no—
308C4×C43—82no—
309Dic43—22no—
310Dic43—41no—
311Dic43—41no—
312Dic43—42no—
313Dic43—41no—
314Dic43—82no—
315C2×#529—431no—
316#1817—431no—
317C2×#328—431no—
318C2×#328D4311yescharacteristic, complemented
319C2×#327—431no—
320C2×#327—431no—
321#1434—431no—
322C2×C43—21no—
323C2×C43—21no—
324C2×C43—21no—
325C2×C43—21no—
326C2×C43#150011yescharacteristic
327C2×C43#150911yescharacteristic
328C2×C43#151211yescharacteristic
329C2×C43#152111yescharacteristic
330C2×C43#178211yescharacteristic
331C2×C43#178811yescharacteristic
332C2×C43#178911yescharacteristic
333D43—82no—
334#529—862no—
335#529—862no—
336#529—862no—
337#529—862no—
338C2×#126—861no—
339C2×#125—431no—
340C2×#124—431no—
341C2×#123—861no—
342C2×C22⋊Q8C2×D4311yescharacteristic
343C2×#121—431no—
344C2×C4×Q8—431no—
345C2×C4×D4—431no—
346C2×C4×D4—861no—
347C2×#117—861no—
348C22×C42—431no—
349C2×C22⋊C8—431no—
350C2×C22⋊C8C2×D4311yescharacteristic
351C2×#95—431no—
352C2×#95—861no—
353C2×#95—861no—
354C2×#95C2×D4311yescharacteristic
355#336—861no—
356#336—861no—
357#328—22no—
358#328—862no—
359#327—862no—
360#327—862no—
361C43#833011yescharacteristic, complemented, Sylow
362C22×Q8C4×D4311yescharacteristic
363C22×D4—431no—
364C22×D4—861no—
365C23×C4—21no—
366C23×C4—431no—
367C23×C4—431no—
368C23×C4—861no—
369C23×C4—861no—
370C23×C4C22×D4311yescharacteristic
371C22×C8—21no—
372C22×C8—861no—
373#126—864no—
374#126—864no—
375#125—862no—
376#125—862no—
377#124—862no—
378#124—862no—
379#123—864no—
380#123—864no—
381C22⋊Q8—21no—
382C22⋊Q8—21no—
383C22⋊Q8D17212yes—
384C22⋊Q8C22⋊D4312yes—
385#121—432no—
386#121—432no—
387#121—861no—
388#121—861no—
389C4×Q8—862no—
390C4×Q8—862no—
391C4×D4—864no—
392C4×D4—864no—
393C4×D4—862no—
394C4×D4—862no—
395#117—864no—
396#117—864no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4C4×D4311yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—861no—
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C42—431no—
409C2×C42—431no—
410C2×C42—431no—
411C2×C42—431no—
412C2×C42—861no—
413C2×C42—861no—
414C2×C42—861no—
415C2×C42—861no—
416C2×C42—861no—
417C22⋊C8—21no—
418C22⋊C8—21no—
419C22⋊C8—861no—
420C22⋊C8—861no—
421#95—21no—
422#95—21no—
423#95—864no—
424#95—861no—
425#95—861no—
426#95—1722no—
427C24—861no—
428C24D4×D4311yescharacteristic
429C2×Q8—21no—
430C2×Q8—41no—
431C2×Q8—41no—
432C2×Q8(C2×D43)⋊C412yes—
433C2×D4—432no—
434C2×D4—862no—
435C2×D4—862no—
436C2×D4—861no—
437C2×D4—1721no—
438C2×D4—1721no—
439C2×D4—1721no—
440C2×D4—1721no—
441C2×D4—1721no—
442C2×D4—1721no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—431no—
455C22×C4—431no—
456C22×C4—431no—
457C22×C4—431no—
458C22×C4—864no—
459C22×C4—862no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—862no—
470C22×C4—1722no—
471C22×C4—1722no—
472C22×C4—1721no—
473C22×C4—1721no—
474C22×C4—1721no—
475C22×C4—1721no—
476C22×C4—1721no—
477C22×C4—1721no—
478C22×C4—1721no—
479C22×C4C2×C4×D4311yescharacteristic
480C22×C4C2×D17211yescharacteristic
481C22×C4D4×D4311yescharacteristic
482C22×C4D4×D4311yescharacteristic
483C22×C4D4×D4311yescharacteristic
484C22×C4C2×C22⋊D4311yescharacteristic
485C2×C8—41no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—1721no—
489C2×C8—1721no—
490C2×C8—1721no—
491C4⋊C4—21no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—432no—
495C4⋊C4—864no—
496C4⋊C4—864no—
497C4⋊C4—864no—
498C4⋊C4—861no—
499C4⋊C4(C2×D43)⋊C412yes—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—864no—
503C22⋊C4—864no—
504C22⋊C4—864no—
505C22⋊C4—862no—
506C22⋊C4—862no—
507C42—864no—
508C42—861no—
509C42—861no—
510C42—861no—
511C42—861no—
512C42—861no—
513C42—861no—
514C42—861no—
515C42—861no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—862no—
521C23—1721no—
522C23—1721no—
523C23—1721no—
524C23—1721no—
525C23—1721no—
526C23—1721no—
527C23C22⋊C4×D4311yescharacteristic
528C23#1306329311yescharacteristic
529C23#1306329511yescharacteristic
530C23#1306334611yescharacteristic
531C23#1306334811yescharacteristic
532C23#1306335211yescharacteristic
533C23#1306335711yescharacteristic
534Q8—42no—
535Q8—42no—
536D4—1722no—
537D4—1722no—
538D4—1722no—
539D4—1722no—
540D4—1722no—
541D4—1722no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—81no—
560C2×C4—81no—
561C2×C4—81no—
562C2×C4—81no—
563C2×C4—432no—
564C2×C4—861no—
565C2×C4—861no—
566C2×C4—861no—
567C2×C4—861no—
568C2×C4—861no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—861no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—862no—
576C2×C4—3441no—
577C2×C4—3441no—
578C2×C4—3441no—
579C2×C4—3441no—
580C2×C4—1728no—
581C2×C4—1722no—
582C2×C4—1722no—
583C2×C4—1722no—
584C2×C4—1722no—
585C2×C4—1722no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4C22⋊C4×D4311yescharacteristic
593C2×C4C2×(C2×D43)⋊C411yescharacteristic
594C2×C4#1306329311yescharacteristic
595C2×C4#1306329511yescharacteristic
596C8—81no—
597C8—3441no—
598C22—21no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—21no—
604C22—21no—
605C22—21no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—3441no—
611C22—3441no—
612C22—3441no—
613C22—3441no—
614C22—1722no—
615C22—1722no—
616C22—1722no—
617C22#1458275411yescharacteristic
618C22#1458287111yescharacteristic
619C22#1458287111yescharacteristic
620C22#1458289411yescharacteristic
621C22#1458289911yescharacteristic
622C22#104×D4311yescharacteristic
623C22#1458291411yescharacteristic
624C22#1458304311yescharacteristic
625C22#1458304711yescharacteristic
626C22#1458306011yescharacteristic
627C22#1458306411yescharacteristic
628C4—21no—
629C4—21no—
630C4—21no—
631C4—21no—
632C4—42no—
633C4—42no—
634C4—82no—
635C4—862no—
636C4—3442no—
637C4—1721no—
638C4—1721no—
639C4—1722no—
640C4—1721no—
641C2—21no—
642C2—21no—
643C2—21no—
644C2—21no—
645C2—3442no—
646C2#1913308011yescharacteristic
647C2#1913311911yescharacteristic
648C2#1913313211yescharacteristic
649C2#1913317111yescharacteristic
650C2#1913451111yescharacteristic
651C2#1913453411yescharacteristic
652C2#1913453711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#328C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#13063299C22
cosocleC23×C4×C43C23
hypercenterC2×#328D43
hypocenterC43#8330
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
2. #19134661C2semidirect
3. C2×#14582636C2semidirect
6. #19132819C2semidirect
7. C2×C43×#328C2semidirect
13. C2×#13063316C4semidirect
14. C2×#13063314C4semidirect
17. C2×Q8×Dic43C4semidirect
18. C2×#13063287C4semidirect
318. C2×#328D43semidirect
361. C43#8330semidirect

Maximal subgroups

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

subgroupindex
C2×#145834352
#191346612
C2×#145826362
C2×#145826342
C2×#145826322
#191328192
C2×C43×#3282
#833043