Finite Group Databasebeta

← #25169353

Subgroups — #25169353

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#19136013C211yesmaximal, characteristic, complemented
3#19135976C211yesmaximal, characteristic, complemented
4#19135795C211yesmaximal, characteristic
5#19135788C211yesmaximal, characteristic
6#19135363C211yesmaximal, characteristic, complemented
7#19135320C211yesmaximal, characteristic, complemented
8#19135203C211yesmaximal, characteristic
9#19135184C211yesmaximal, characteristic, complemented
10#19135180C211yesmaximal, characteristic, complemented
11#19134863C211yesmaximal, characteristic, complemented
12#19134788C211yesmaximal, characteristic
13#19134681C211yesmaximal, characteristic
14C4×#13063249C211yesmaximal, characteristic, complemented
15C43×#2360C211yesmaximal, characteristic
16C2×#13063258C2211yescharacteristic
17C2×#13063256C2211yescharacteristic
18C2×#13063256C2211yescharacteristic
19C2×#13063256C2211yescharacteristic
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21C2×#13063249C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×C22⋊(C43⋊C8)C2211yescharacteristic
26C2×C22⋊(C43⋊C8)C2211yescharacteristic
27C2×C4×C43⋊C8C2211yescharacteristic
28C43⋊#401—21no—
29#14582827—21no—
30#14582797C2211yescharacteristic
31#14582797C2211yescharacteristic
32#14582793—21no—
33#14582781—21no—
34#14582765C2211yescharacteristic
35#14582759C2211yescharacteristic
36#14582759C2211yescharacteristic
37C4×C4⋊Dic43C2211yescharacteristic
38#14582661C2211yescharacteristic
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×C22⋊Q8×C43C2211yescharacteristic
49C2×C4×Q8×C43C2211yescharacteristic
50C22×C4⋊C4×C43C2211yescharacteristic
51C43×#391C2211yescharacteristic
52C43×#389—21no—
53C43×#389C2211yescharacteristic
54C43×#387—21no—
55C43×#385—21no—
56C4×C4⋊C4×C43C2211yescharacteristic
57C4×C22⋊C4×C43—21no—
58C4×C22⋊C4×C43C2211yescharacteristic
59C22×C43⋊C8C2311yescharacteristic
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C2×C4⋊Dic43C2311yescharacteristic
64C2×C4⋊Dic43C2311yescharacteristic
65C2×C4⋊Dic43C2311yescharacteristic
66C2×C4⋊Dic43C2311yescharacteristic
67C2×Dic43⋊C4—21no—
68C2×Dic43⋊C4—21no—
69C2×C22⋊Dic43—21no—
70C2×C22⋊Dic43—21no—
71C2×C4×Dic43—21no—
72#13063258—22no—
73#13063256—22no—
74#13063256—22no—
75#13063256—41no—
76C4⋊(C43⋊C8)—22no—
77#13063249—22no—
78#13063249—22no—
79#13063249—22no—
80#13063249—41no—
81C22⋊(C43⋊C8)—22no—
82C22⋊(C43⋊C8)—41no—
83C4×C43⋊C8—41no—
84C43⋊#95—21no—
85C43⋊#95—21no—
86C43⋊#95—21no—
87C43⋊#95—21no—
88C43⋊#95—21no—
89C43⋊#95—21no—
90C43⋊#95—21no—
91C22×Q8×C43C2311yescharacteristic
92C23×C4×C43—21no—
93C23×C4×C43C2311yescharacteristic
94C22⋊Q8×C43—22no—
95C22⋊Q8×C43—22no—
96C4×Q8×C43—22no—
97C4×Q8×C43—41no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43—22no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43—41no—
104C2×C4⋊C4×C43C2311yescharacteristic
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43D411yescharacteristic
109C2×C22⋊C4×C43D411yescharacteristic
110C2×C42×C43—21no—
111C2×C42×C43—21no—
112C2×C42×C43C2311yescharacteristic
113C2×C42×C43C2311yescharacteristic
114#95×C43—21no—
115#95×C43—21no—
116#95×C43—21no—
117#95×C43—21no—
118#95×C43D411yescharacteristic
119#95×C43D411yescharacteristic
120C24×C43C2×D411yescharacteristic
121C2×Q8×C43—21no—
122C2×Q8×C43—21no—
123C2×Q8×C43—21no—
124C2×Q8×C43—21no—
125C2×Q8×C43—21no—
126C2×Q8×C43#4112yes—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—42no—
138C22×C4×C43—42no—
139C22×C4×C43—81no—
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C4⋊C4×C43—24no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—42no—
156C4⋊C4×C43—42no—
157C4⋊C4×C43—81no—
158C4⋊C4×C43#4112yes—
159C4⋊C4×C43#4112yes—
160C22⋊C4×C43—24no—
161C22⋊C4×C43—22no—
162C22⋊C4×C43—22no—
163C42×C43—21no—
164C42×C43—21no—
165C42×C43—21no—
166C42×C43—21no—
167C42×C43—42no—
168C42×C43—81no—
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—
179Dic43⋊C4—42no—
180Dic43⋊C4—81no—
181C4×Dic43—81no—
182C2×C43⋊C8—21no—
183C2×C43⋊C8—21no—
184C2×C43⋊C8—21no—
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#4112yes—
194C23×C43—21no—
195C23×C43—21no—
196C23×C43—21no—
197C23×C43—21no—
198C23×C43—21no—
199C23×C43—21no—
200C23×C43#13512yes—
201C23×C43C22×D411yescharacteristic
202Q8×C43—22no—
203Q8×C43—22no—
204Q8×C43—41no—
205Q8×C43—41no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—22no—
209C2×C4×C43—22no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—22no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
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—41no—
236C2×C4×C43—84no—
237C2×C4×C43#13712yes—
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43H(5,𝔽2)11yescharacteristic
243C2×C4×C432−1+411yescharacteristic
244C2×Dic43—41no—
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—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C43⋊C8—22no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259C43⋊C8—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—42no—
279C4×C43—41no—
280C4×C43—42no—
281C4×C43—41no—
282C4×C43—42no—
283C4×C43—81no—
284C4×C43#52911yescharacteristic
285C4×C43#53911yescharacteristic
286C4×C43#55311yescharacteristic
287C4×C43#55611yescharacteristic
288Dic43—81no—
289Dic43—81no—
290Dic43—81no—
291Dic43—81no—
292#2494—431no—
293#2360D4311yescharacteristic
294#2074—431no—
295#2066—431no—
296#2036—431no—
297#2035—431no—
298#1949—431no—
299#1941—431no—
300#1923—431no—
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⋊Q8C2×D4311yescharacteristic
316C2×C4×Q8C2×D4311yescharacteristic
317C22×C4⋊C4C2×D4311yescharacteristic
318C2×#107—431no—
319C2×#106—431no—
320C2×#106—431no—
321C2×#106—431no—
322C2×C4⋊C8—431no—
323C2×#103—431no—
324C2×#103—431no—
325C2×#103—431no—
326C2×#103—431no—
327C2×C22⋊C8—431no—
328C2×C22⋊C8—431no—
329C2×C4×C8—431no—
330#401—861no—
331#397—861no—
332#391C2×D4311yescharacteristic
333#389—21no—
334#389—431no—
335#389—431no—
336#389C2×D4311yescharacteristic
337#388—861no—
338#387—21no—
339#387—861no—
340#385—21no—
341#382—431no—
342#380—431no—
343#380—431no—
344C4×C4⋊C4—431no—
345C4×C4⋊C4C2×D4311yescharacteristic
346C4×C22⋊C4—21no—
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#336—431no—
357#336—431no—
358C43#2703711yescharacteristic, complemented, Sylow
359C22×Q8C22×D4311yescharacteristic
360C23×C4—21no—
361C23×C4C22×D4311yescharacteristic
362C22×C8—431no—
363C22×C8—431no—
364C22×C8—431no—
365C22×C8—431no—
366C22⋊Q8—22no—
367C22⋊Q8—22no—
368C4×Q8—22no—
369C4×Q8—41no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—41no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—431no—
379C2×C4⋊C4—431no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4C22×D4311yescharacteristic
383C2×C4⋊C4C22×D4311yescharacteristic
384C2×C4⋊C4C22×D4311yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—861no—
387C2×C22⋊C4—861no—
388C2×C22⋊C4C22⋊D4311yescharacteristic
389C2×C22⋊C4C22⋊D4311yescharacteristic
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—861no—
393C2×C42C22×D4311yescharacteristic
394C2×C42C22×D4311yescharacteristic
395#107—862no—
396#106—862no—
397#106—862no—
398#106—1721no—
399C4⋊C8—862no—
400#103—862no—
401#103—862no—
402#103—862no—
403#103—1721no—
404C22⋊C8—862no—
405C22⋊C8—1721no—
406C4×C8—1721no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—861no—
412#95—861no—
413#95—861no—
414#95—861no—
415#95—861no—
416#95—861no—
417#95—861no—
418#95C22⋊D4311yescharacteristic
419#95C22⋊D4311yescharacteristic
420C24C2×C22⋊D4311yescharacteristic
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8#1062189812yes—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—81no—
440C22×C4—861no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4—861no—
444C22×C4C2×C22⋊D4311yescharacteristic
445C22×C4C2×C22⋊D4311yescharacteristic
446C22×C4C2×C22⋊D4311yescharacteristic
447C22×C4C2×C22⋊D4311yescharacteristic
448C22×C4C2×C22⋊D4311yescharacteristic
449C22×C4C23×D4311yescharacteristic
450C2×C8—432no—
451C2×C8—861no—
452C2×C8—861no—
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—
462C4⋊C4—24no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—42no—
468C4⋊C4—42no—
469C4⋊C4—81no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—3441no—
479C4⋊C4—1722no—
480C4⋊C4#1062189812yes—
481C4⋊C4#1062190012yes—
482C22⋊C4—24no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—3441no—
486C22⋊C4—1722no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—42no—
492C42—81no—
493C42—3441no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23#1306334512yes—
501C23C22×C22⋊D4311yescharacteristic
502Q8—22no—
503Q8—22no—
504Q8—41no—
505Q8—41no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—22no—
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—22no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—84no—
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#1306335612yes—
550C2×C4#41×D4311yescharacteristic
551C2×C4C2×#1062190011yescharacteristic
552C2×C4C2×#1062189811yescharacteristic
553C2×C4C2×#1062189811yescharacteristic
554C2×C4#1306337011yescharacteristic
555C2×C4#1306337211yescharacteristic
556C8—862no—
557C8—1721no—
558C8—1721no—
559C8—1721no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22#1458341011yescharacteristic
568C22#1458354311yescharacteristic
569C22#1458354811yescharacteristic
570C22C2×#1306334511yescharacteristic
571C22C2×#1306335611yescharacteristic
572C22#1458370711yescharacteristic
573C22#1458371011yescharacteristic
574C4—22no—
575C4—41no—
576C4—42no—
577C4—42no—
578C4—41no—
579C4—42no—
580C4—41no—
581C4—41no—
582C4—81no—
583C4—3441no—
584C4—3441no—
585C4—3441no—
586C4—3441no—
587C4#1458342911yescharacteristic
588C4#1458349111yescharacteristic
589C4#1458359911yescharacteristic
590C4#1458361911yescharacteristic
591C2—42no—
592C2#1913862511yescharacteristic
593C2#1914467511yescharacteristic
594C2#1914487211yescharacteristic
595C2#1914643011yescharacteristic
596C2#1914676611yescharacteristic
597C2#1914697411yescharacteristic
598C2#1914721011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2360C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#2360D43
hypocenterC43#27037
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2360

Complements

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

NH ≅ G/Ntype
2. #19136013C2semidirect
3. #19135976C2semidirect
6. #19135363C2semidirect
7. #19135320C2semidirect
9. #19135184C2semidirect
10. #19135180C2semidirect
11. #19134863C2semidirect
14. C4×#13063249C2semidirect
358. C43#27037semidirect

Maximal subgroups

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

subgroupindex
#191389952
#191360132
#191359762
#191357952
#191357882
#191353632
#191353202
#191352032
#191351842
#191351802
#191348632
#191347882
#191346812
C4×#130632492
C43×#23602
#2703743