Finite Group Databasebeta

← #25169357

Subgroups — #25169357

Order 11008.

700 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138995C211yesmaximal, characteristic
2#19137598C211yesmaximal, characteristic
3#19136015C211yesmaximal, characteristic, complemented
4#19135975C211yesmaximal, characteristic, complemented
5#19135799C211yesmaximal, characteristic
6#19135792C211yesmaximal, characteristic
7#19135365C211yesmaximal, characteristic, complemented
8#19135323C211yesmaximal, characteristic, complemented
9#19135188C211yesmaximal, characteristic, complemented
10#19135181C211yesmaximal, characteristic, complemented
11#19134866C211yesmaximal, characteristic, complemented
12#19134790C211yesmaximal, characteristic
13#19134682C211yesmaximal, characteristic
14C4×#13063250C211yesmaximal, characteristic, complemented
15C43×#1923C211yesmaximal, characteristic
16C2×#13063304C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18C22×C4⋊Dic43C2211yescharacteristic
19C2×#13063259C2211yescharacteristic
20C2×#13063257C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C43⋊#401—21no—
28#14582827—21no—
29#14582805C2211yescharacteristic
30#14582797C2211yescharacteristic
31#14582797C2211yescharacteristic
32#14582797C2211yescharacteristic
33#14582796—21no—
34#14582793—21no—
35#14582786—21no—
36#14582781—21no—
37#14582771—21no—
38#14582765C2211yescharacteristic
39#14582759C2211yescharacteristic
40#14582759C2211yescharacteristic
41C4×C4⋊Dic43C2211yescharacteristic
42C4×C4⋊Dic43C2211yescharacteristic
43C22⋊C4×Dic43—21no—
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52C2×C4⋊C8×C43C2211yescharacteristic
53C2×C22⋊C8×C43C2211yescharacteristic
54C2×C22⋊C8×C43C2211yescharacteristic
55C2×C4×C8×C43C2211yescharacteristic
56C4×C22⋊C4×C43C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C23×Dic43—21no—
61#13063304—22no—
62#13063304—22no—
63C4×Dic86—22no—
64C4×Dic86—41no—
65C2×C4⋊Dic43—22no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43—41no—
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86#13063259—22no—
87#13063257—22no—
88#13063257—22no—
89#13063257—41no—
90#13063250—22no—
91#13063250—22no—
92#13063250—22no—
93#13063250—41no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C23×C4×C43C2311yescharacteristic
106C22×C8×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C2×C22⋊C4×C43D411yescharacteristic
111C2×C22⋊C4×C43D411yescharacteristic
112C2×C42×C43C2311yescharacteristic
113C2×C42×C43C2311yescharacteristic
114C4⋊C8×C43—22no—
115C22⋊C8×C43—22no—
116C22⋊C8×C43—41no—
117C4×C8×C43—41no—
118#95×C43D411yescharacteristic
119#95×C43D411yescharacteristic
120C24×C43C2×D411yescharacteristic
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2411yescharacteristic
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—42no—
142C22×Dic43—42no—
143C22×Dic43—81no—
144C2×Dic86—21no—
145C2×Dic86—21no—
146C2×Dic86—21no—
147C2×Dic86—21no—
148C2×Dic86—21no—
149C2×Dic86#4112yes—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43#4112yes—
162C22⋊C4×C43—22no—
163C22⋊C4×C43—22no—
164C42×C43—21no—
165C42×C43—21no—
166C42×C43—21no—
167C42×C43—21no—
168C22⋊Dic43—24no—
169C22⋊Dic43—42no—
170C22⋊Dic43—81no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—42no—
184C4⋊Dic43#4112yes—
185C4⋊Dic43#4112yes—
186Dic43⋊C4—24no—
187Dic43⋊C4—42no—
188Dic43⋊C4—42no—
189Dic43⋊C4—81no—
190Dic43⋊C4—81no—
191C4×Dic43—42no—
192C4×Dic43—81no—
193C4×Dic43—81no—
194C23×C43—21no—
195C23×C43—21no—
196C23×C43—21no—
197C23×C43—21no—
198C23×C43—21no—
199C23×C43—21no—
200C23×C43#13512yes—
201C23×C43C22×D411yescharacteristic
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
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—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43#13712yes—
221C2×C4×C43C2×#4111yescharacteristic
222C2×C4×C43C2×#4111yescharacteristic
223C2×C4×C43C2×#4111yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C2×C4×C43H(5,𝔽2)11yescharacteristic
226C2×C4×C432−1+411yescharacteristic
227C2×Dic43—22no—
228C2×Dic43—22no—
229C2×Dic43—22no—
230C2×Dic43—41no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—84no—
252Dic86—22no—
253Dic86—22no—
254Dic86—41no—
255Dic86—41no—
256C8×C43—22no—
257C8×C43—41no—
258C8×C43—41no—
259C8×C43—41no—
260#27037—431nomaximal, Sylow
261C22×C43—22no—
262C22×C43—22no—
263C22×C43—22no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43#52511yescharacteristic
269C22×C43#54611yescharacteristic
270C22×C43#54711yescharacteristic
271C22×C43C2×#13511yescharacteristic
272C22×C43C2×#13711yescharacteristic
273C22×C43#57711yescharacteristic
274C22×C43#57711yescharacteristic
275C4×C43—22no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43—41no—
280C4×C43#52911yescharacteristic
281C4×C43#53911yescharacteristic
282C4×C43#55311yescharacteristic
283C4×C43#55611yescharacteristic
284Dic43—42no—
285Dic43—42no—
286Dic43—42no—
287Dic43—81no—
288Dic43—81no—
289Dic43—81no—
290Dic43—81no—
291Dic43—81no—
292#2494—431no—
293#2360—431no—
294#2074—431no—
295#2066—431no—
296#2036—431no—
297#2035—431no—
298#1949—431no—
299#1941—431no—
300#1923D4311yescharacteristic
301#1921—431no—
302#1920—431no—
303#1865—431no—
304#1853—431no—
305#1823—431no—
306C4×#103—431no—
307C2×C43—42no—
308C2×C43#246611yescharacteristic
309C2×C43#310811yescharacteristic
310C2×C43#312511yescharacteristic
311C2×C43#329611yescharacteristic
312C2×C43#332011yescharacteristic
313C2×C43#333711yescharacteristic
314C2×C43#335611yescharacteristic
315C2×C22⋊Q8—431no—
316C2×C4×Q8—431no—
317C22×C4⋊C4—431no—
318C2×#107—431no—
319C2×#106—431no—
320C2×#106—431no—
321C2×#106—431no—
322C2×C4⋊C8C2×D4311yescharacteristic
323C2×#103—431no—
324C2×#103—431no—
325C2×#103—431no—
326C2×#103—431no—
327C2×C22⋊C8C2×D4311yescharacteristic
328C2×C22⋊C8C2×D4311yescharacteristic
329C2×C4×C8C2×D4311yescharacteristic
330#401—861no—
331#397—861no—
332#391—431no—
333#389—431no—
334#389—431no—
335#389—431no—
336#389—861no—
337#388—861no—
338#387—861no—
339#387—861no—
340#385—861no—
341#382—431no—
342#380—431no—
343#380—431no—
344C4×C4⋊C4—431no—
345C4×C4⋊C4—431no—
346C4×C22⋊C4—861no—
347C4×C22⋊C4C2×D4311yescharacteristic
348#340—431no—
349#340—431no—
350#340—431no—
351#340—431no—
352#340—431no—
353#340—431no—
354#340—431no—
355#340—431no—
356#336C2×D4311yescharacteristic
357#336C2×D4311yescharacteristic
358C43#2703711yescharacteristic, complemented, Sylow
359C22×Q8—431no—
360C23×C4—861no—
361C23×C4C22×D4311yescharacteristic
362C22×C8C22×D4311yescharacteristic
363C22×C8C22×D4311yescharacteristic
364C22×C8C22×D4311yescharacteristic
365C22×C8C22×D4311yescharacteristic
366C22⋊Q8—862no—
367C22⋊Q8—862no—
368C4×Q8—862no—
369C4×Q8—1721no—
370C2×C4⋊C4—431no—
371C2×C4⋊C4—431no—
372C2×C4⋊C4—431no—
373C2×C4⋊C4—431no—
374C2×C4⋊C4—431no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—862no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—1721no—
385C2×C22⋊C4—861no—
386C2×C22⋊C4—861no—
387C2×C22⋊C4—861no—
388C2×C22⋊C4D17211yescharacteristic
389C2×C22⋊C4D17211yescharacteristic
390C2×C42—861no—
391C2×C42—861no—
392C2×C42—861no—
393C2×C42C22×D4311yescharacteristic
394C2×C42C22×D4311yescharacteristic
395#107—862no—
396#106—862no—
397#106—862no—
398#106—1721no—
399C4⋊C8—22no—
400#103—862no—
401#103—862no—
402#103—862no—
403#103—1721no—
404C22⋊C8—22no—
405C22⋊C8—41no—
406C4×C8—41no—
407#95—861no—
408#95—861no—
409#95—861no—
410#95—861no—
411#95—861no—
412#95—861no—
413#95—861no—
414#95—861no—
415#95—861no—
416#95—861no—
417#95—861no—
418#95D17211yescharacteristic
419#95D17211yescharacteristic
420C24C2×D17211yescharacteristic
421C2×Q8—432no—
422C2×Q8—861no—
423C2×Q8—861no—
424C2×Q8—861no—
425C2×Q8—861no—
426C2×Q8—861no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—861no—
434C22×C4—861no—
435C22×C4—861no—
436C22×C4—861no—
437C22×C4—861no—
438C22×C4—861no—
439C22×C4—861no—
440C22×C4—861no—
441C22×C4—3441no—
442C22×C4—1722no—
443C22×C4—1722no—
444C22×C4C2×D17211yescharacteristic
445C22×C4C2×D17211yescharacteristic
446C22×C4C2×D17211yescharacteristic
447C22×C4C2×D17211yescharacteristic
448C22×C4C2×D17211yescharacteristic
449C22×C4C23×D4311yescharacteristic
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8#1062190012yes—
462C4⋊C4—432no—
463C4⋊C4—432no—
464C4⋊C4—864no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—3441no—
478C4⋊C4—3441no—
479C4⋊C4—1722no—
480C4⋊C4—1722no—
481C4⋊C4—1722no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—864no—
485C22⋊C4—3441no—
486C22⋊C4—1722no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—3441no—
492C42—3441no—
493C42—1722no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23#1306334712yes—
501C23C22×D17211yescharacteristic
502Q8—862no—
503Q8—862no—
504Q8—1721no—
505Q8—1721no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—862no—
525C2×C4—862no—
526C2×C4—862no—
527C2×C4—3444no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4—1721no—
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#1306335812yes—
550C2×C4#41×D4311yescharacteristic
551C2×C4#41×D4311yescharacteristic
552C2×C4#41×D4311yescharacteristic
553C2×C4C2×#1062190011yescharacteristic
554C2×C4#1306337011yescharacteristic
555C2×C4#1306337211yescharacteristic
556C8—22no—
557C8—41no—
558C8—41no—
559C8—41no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22#1458341111yescharacteristic
568C22#1458354411yescharacteristic
569C22#1458355311yescharacteristic
570C22C2×#1306334711yescharacteristic
571C22C2×#1306335811yescharacteristic
572C22#1458371111yescharacteristic
573C22#1458371111yescharacteristic
574C4—22no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—3441no—
580C4—3441no—
581C4—3441no—
582C4—3441no—
583C4—3441no—
584C4—1722no—
585C4—1722no—
586C4—1722no—
587C4#1458342811yescharacteristic
588C4#1458349211yescharacteristic
589C4#1458359211yescharacteristic
590C4#1458361611yescharacteristic
591C2—42no—
592C2#1913862911yescharacteristic
593C2#1914467711yescharacteristic
594C2#1914487411yescharacteristic
595C2#1914643211yescharacteristic
596C2#1914676811yescharacteristic
597C2#1914697611yescharacteristic
598C2#1914721111yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1923C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#1923D43
hypocenterC43#27037
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
3. #19136015C2semidirect
4. #19135975C2semidirect
7. #19135365C2semidirect
8. #19135323C2semidirect
9. #19135188C2semidirect
10. #19135181C2semidirect
11. #19134866C2semidirect
14. C4×#13063250C2semidirect
358. C43#27037semidirect

Maximal subgroups

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

subgroupindex
#191389952
#191375982
#191360152
#191359752
#191357992
#191357922
#191353652
#191353232
#191351882
#191351812
#191348662
#191347902
#191346822
C4×#130632502
C43×#19232
#2703743