Finite Group Databasebeta

← #25199721

Subgroups — #25199721

Order 11008.

724 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142962C211yesmaximal, characteristic
2#19136096C211yesmaximal, characteristic, complemented
3#19135990C211yesmaximal, characteristic, complemented
4#19135980C211yesmaximal, characteristic
5#19135910C211yesmaximal, characteristic
6#19135452C211yesmaximal, characteristic
7#19135325C211yesmaximal, characteristic, complemented
8#19135277C211yesmaximal, characteristic
9#19135274C211yesmaximal, characteristic, complemented
10#19135215C211yesmaximal, characteristic
11#19135180C211yesmaximal, characteristic, complemented
12#19134950C211yesmaximal, characteristic
13#19134849C211yesmaximal, characteristic, complemented
14C4×C4⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
15C43×#2295C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C2×#13063319—21no—
18C2×#13063258C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×C4⋊(C43⋊C8)C2211yescharacteristic
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×C4×C43⋊C8C2211yescharacteristic
30C2×C4×C43⋊C8C2211yescharacteristic
31#14582801C2211yescharacteristic
32#14582801C2211yescharacteristic
33#14582801C2211yescharacteristic
34#14582797C2211yescharacteristic
35#14582797C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582790—21no—
38#14582790—21no—
39#14582790—21no—
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×C4×Q8×C43C2211yescharacteristic
49C43×#391C2211yescharacteristic
50C43×#391C2211yescharacteristic
51C43×#389C2211yescharacteristic
52C43×#389C2211yescharacteristic
53C43×#387—21no—
54C43×#387—21no—
55C4×C4⋊C4×C43—21no—
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#376—21no—
58C43×C43C2211yescharacteristic
59C22×D172C2311yescharacteristic
60C2×#10621884—22no—
61C2×#10621884—22no—
62C2×#10621884—41no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063319—44no—
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×(C2×D43)⋊C4—21no—
75C2×(C2×D43)⋊C4—21no—
76C2×(C2×D43)⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80#13063258—22no—
81#13063258—41no—
82#13063256—22no—
83C4⋊(C43⋊C8)—22no—
84C4⋊(C43⋊C8)—22no—
85#13063249—22no—
86#13063249—22no—
87#13063249—41no—
88#13063245—22no—
89#13063245—22no—
90#13063245—41no—
91C4×C43⋊C8—41no—
92C4×C43⋊C8—41no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C22×Q8×C43C2311yescharacteristic
97C4×Q8×C43—22no—
98C4×Q8×C43—22no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43C2311yescharacteristic
103C2×C4⋊C4×C43C2311yescharacteristic
104C2×C4⋊C4×C43C2311yescharacteristic
105C2×C42×C43—21no—
106C2×C42×C43—21no—
107C2×C42×C43D411yescharacteristic
108C2×C42×C43D411yescharacteristic
109C2×C42×C43D411yescharacteristic
110C2×C42×C43D411yescharacteristic
111C2×C42×C43C2311yescharacteristic
112C2×C42×C43C2311yescharacteristic
113C2×C42×C43C2311yescharacteristic
114#95×C43—21no—
115#95×C43—21no—
116#95×C43—21no—
117#95×C43—21no—
118#95×C43—21no—
119#95×C43—21no—
120#95×C43—21no—
121C23×D43—21no—
122C2×Q8×C43—21no—
123C2×Q8×C43—21no—
124C2×Q8×C43—21no—
125C2×Q8×C43—21no—
126C2×Q8×C43—21no—
127C2×Q8×C43#4112yes—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2411yescharacteristic
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172—21no—
147C2×D172—21no—
148C4⋊C4×C43—24no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—42no—
155C4⋊C4×C43—42no—
156C4⋊C4×C43#4112yes—
157C42×C43—24no—
158C42×C43—22no—
159C42×C43—22no—
160C42×C43—22no—
161C42×C43—22no—
162C42×C43—21no—
163C42×C43—21no—
164C42×C43—21no—
165C42×C43—21no—
166C42×C43—21no—
167C42×C43—21no—
168C42×C43—42no—
169#10621884—44no—
170(C2×D43)⋊C4—42no—
171(C2×D43)⋊C4—42no—
172(C2×D43)⋊C4—42no—
173(C2×D43)⋊C4—42no—
174(C2×D43)⋊C4—42no—
175(C2×D43)⋊C4—42no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182Dic43⋊C4—42no—
183Dic43⋊C4—42no—
184Dic43⋊C4—42no—
185C2×C43⋊C8—21no—
186C2×C43⋊C8—21no—
187C2×C43⋊C8—21no—
188C2×C43⋊C8—21no—
189C2×C43⋊C8—21no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8#4112yes—
196C2×C43⋊C8#4112yes—
197C23×C43C22×D411yescharacteristic
198C22×D43—41no—
199C22×D43—41no—
200C22×D43—41no—
201C22×D43—41no—
202C22×D43—41no—
203C22×D43—41no—
204C22×D43—41no—
205Q8×C43—22no—
206Q8×C43—22no—
207Q8×C43—41no—
208Q8×C43—41no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43#13512yes—
236C2×C4×C43#13512yes—
237C2×C4×C43AGL(1,ℤ/8)12yes—
238C2×C4×C43#13712yes—
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43H(5,𝔽2)11yescharacteristic
244C2×C4×C432−1+411yescharacteristic
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254D172—41no—
255D172—41no—
256D172—41no—
257D172—41no—
258C43⋊C8—22no—
259C43⋊C8—22no—
260C43⋊C8—41no—
261C43⋊C8—41no—
262#29435—431nomaximal, Sylow
263C22×C43#52511yescharacteristic
264C22×C43#53211yescharacteristic
265C22×C43#53711yescharacteristic
266C22×C43C2×#13511yescharacteristic
267C22×C43C2×#13511yescharacteristic
268C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
269C22×C43C2×#13711yescharacteristic
270C2×D43—81no—
271C2×D43—81no—
272C2×D43—81no—
273C2×D43—81no—
274C2×D43—81no—
275C2×D43—81no—
276C2×D43—81no—
277C4×C43—22no—
278C4×C43—22no—
279C4×C43—22no—
280C4×C43—22no—
281C4×C43—41no—
282C4×C43—42no—
283C4×C43—42no—
284C4×C43—41no—
285C4×C43—81no—
286C4×C43—81no—
287C4×C43#55111yescharacteristic
288C4×C43#55211yescharacteristic
289C4×C43#55311yescharacteristic
290C4×C43#55611yescharacteristic
291Dic43—81no—
292Dic43—81no—
293Dic43—81no—
294#2860—431no—
295#2295D4311yescharacteristic, complemented
296#2088—431no—
297#2068—431no—
298#2067—431no—
299#2055—431no—
300#1968—431no—
301#1942—431no—
302#1934—431no—
303#1933—431no—
304#1925—431no—
305#1920—431no—
306#1880—431no—
307#1863—431no—
308C4×C4⋊C8—431no—
309C2×C43#260111yescharacteristic
310C2×C43#310611yescharacteristic
311C2×C43#310811yescharacteristic
312C2×C43#316811yescharacteristic
313C2×C43#318211yescharacteristic
314C2×C43#324711yescharacteristic
315C2×C43#324811yescharacteristic
316D43—161no—
317C22×SD16—431no—
318C2×#126—861no—
319C2×C4×Q8C2×D4311yescharacteristic
320C2×#107—431no—
321C2×#107—431no—
322C2×#106—431no—
323C2×C4⋊C8—431no—
324C2×C4⋊C8—431no—
325C2×#103—431no—
326C2×#103—431no—
327C2×#103—431no—
328C2×#102—431no—
329C2×#102—431no—
330C2×#102—431no—
331C2×C4×C8—431no—
332C2×C4×C8—431no—
333#391C2×D4311yescharacteristic
334#391C2×D4311yescharacteristic
335#390—431no—
336#390—431no—
337#390—431no—
338#389—431no—
339#389—431no—
340#389—431no—
341#389C2×D4311yescharacteristic
342#389C2×D4311yescharacteristic
343#388—861no—
344#388—861no—
345#388—861no—
346#387—21no—
347#387—21no—
348C4×C4⋊C4—21no—
349C4×C4⋊C4C2×D4311yescharacteristic
350#376—21no—
351C43C2×D4311yescharacteristic
352#340—431no—
353#340—431no—
354#340—431no—
355#340—431no—
356#340—431no—
357#340—431no—
358#336—431no—
359#336—431no—
360C43#2943511yescharacteristic, complemented, Sylow
361C22×Q8C22×D4311yescharacteristic
362C22×D4—431no—
363C2×SD16—862no—
364C2×SD16—862no—
365C2×SD16—1721no—
366C22×C8—431no—
367C22×C8—431no—
368C22×C8—431no—
369C22×C8—431no—
370#126—1724no—
371C4×Q8—22no—
372C4×Q8—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—431no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4C22×D4311yescharacteristic
383C2×C4⋊C4C22×D4311yescharacteristic
384C2×C4⋊C4C22×D4311yescharacteristic
385C2×C22⋊C4—861no—
386C2×C22⋊C4—861no—
387C2×C22⋊C4—861no—
388C2×C22⋊C4—861no—
389C2×C22⋊C4—861no—
390C2×C22⋊C4—861no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42C22⋊D4311yescharacteristic
394C2×C42C22⋊D4311yescharacteristic
395C2×C42C22⋊D4311yescharacteristic
396C2×C42C22⋊D4311yescharacteristic
397C2×C42C22×D4311yescharacteristic
398C2×C42C22×D4311yescharacteristic
399C2×C42C22×D4311yescharacteristic
400#107—862no—
401#107—1721no—
402#106—862no—
403C4⋊C8—862no—
404C4⋊C8—862no—
405#103—862no—
406#103—862no—
407#103—1721no—
408#102—862no—
409#102—862no—
410#102—1721no—
411C4×C8—1721no—
412C4×C8—1721no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—861no—
421#95—861no—
422#95—861no—
423C24—861no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8#1062189812yes—
430C2×D4—861no—
431C2×D4—861no—
432C2×D4—861no—
433C2×D4—861no—
434C2×D4—861no—
435C2×D4—861no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—861no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4C2×C22⋊D4311yescharacteristic
444C22×C4C2×C22⋊D4311yescharacteristic
445C22×C4C2×C22⋊D4311yescharacteristic
446C22×C4C2×C22⋊D4311yescharacteristic
447C22×C4C2×C22⋊D4311yescharacteristic
448C22×C4C2×C22⋊D4311yescharacteristic
449C22×C4C23×D4311yescharacteristic
450SD16—1724no—
451C2×C8—432no—
452C2×C8—432no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8—861no—
456C2×C8—861no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—861no—
463C4⋊C4—24no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—42no—
470C4⋊C4—42no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—1722no—
478C4⋊C4—1722no—
479C4⋊C4—1722no—
480C4⋊C4#1062189812yes—
481C22⋊C4—1722no—
482C22⋊C4—1722no—
483C22⋊C4—1722no—
484C22⋊C4—1722no—
485C22⋊C4—1722no—
486C22⋊C4—1722no—
487C42—24no—
488C42—22no—
489C42—22no—
490C42—22no—
491C42—22no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—42no—
499C23—1721no—
500C23—1721no—
501C23—1721no—
502C23—1721no—
503C23—1721no—
504C23—1721no—
505C23—1721no—
506C23C22×C22⋊D4311yescharacteristic
507Q8—22no—
508Q8—22no—
509Q8—41no—
510Q8—41no—
511D4—1721no—
512D4—1721no—
513D4—1721no—
514D4—1721no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4#1306334512yes—
551C2×C4#1306334512yes—
552C2×C4#1306335012yes—
553C2×C4#1306335612yes—
554C2×C4#41×D4311yescharacteristic
555C2×C4#41×D4311yescharacteristic
556C2×C4C2×#1062189811yescharacteristic
557C2×C4C2×#1062189811yescharacteristic
558C2×C4#1306337111yescharacteristic
559C2×C4#1306337211yescharacteristic
560C8—862no—
561C8—862no—
562C8—1721no—
563C8—1721no—
564C22—3441no—
565C22—3441no—
566C22—3441no—
567C22—3441no—
568C22—3441no—
569C22—3441no—
570C22—3441no—
571C22#1458341011yescharacteristic
572C22#1458344511yescharacteristic
573C22#1458347711yescharacteristic
574C22C2×#1306334511yescharacteristic
575C22C2×#1306334511yescharacteristic
576C22C2×#1306335011yescharacteristic
577C22C2×#1306335611yescharacteristic
578C4—22no—
579C4—22no—
580C4—22no—
581C4—22no—
582C4—42no—
583C4—41no—
584C4—41no—
585C4—42no—
586C4—81no—
587C4—81no—
588C4—3441no—
589C4—3441no—
590C4—3441no—
591C4#1458357311yescharacteristic
592C4#1458358211yescharacteristic
593C4#1458359311yescharacteristic
594C4#1458361711yescharacteristic
595C2—6881no—
596C2#1914019211yescharacteristic
597C2#1914465511yescharacteristic
598C2#1914467511yescharacteristic
599C2#1914515911yescharacteristic
600C2#1914531411yescharacteristic
601C2#1914592111yescharacteristic
602C2#1914592611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2295C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#2295D43
hypocenterC43#29435
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C43 ◁ #2295

Complements

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

NH ≅ G/Ntype
2. #19136096C2semidirect
3. #19135990C2semidirect
7. #19135325C2semidirect
9. #19135274C2semidirect
11. #19135180C2semidirect
13. #19134849C2semidirect
14. C4×C4⋊(C43⋊C8)C2semidirect
15. C43×#2295C2semidirect
295. #2295D43semidirect
360. C43#29435semidirect

Maximal subgroups

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

subgroupindex
#191429622
#191360962
#191359902
#191359802
#191359102
#191354522
#191353252
#191352772
#191352742
#191352152
#191351802
#191349502
#191348492
C4×C4⋊(C43⋊C8)2
C43×#22952
#2943543