Finite Group Databasebeta

← #25146089

Subgroups — #25146089

Order 11008.

828 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583203C211yesmaximal, characteristic, complemented
2#19139598C211yesmaximal, characteristic
3#19137695C211yesmaximal, characteristic, complemented
4#19135979C211yesmaximal, characteristic, complemented
5#19135965C211yesmaximal, characteristic, complemented
6#19135835C211yesmaximal, characteristic, complemented
7#19135835C211yesmaximal, characteristic, complemented
8#19135526C211yesmaximal, characteristic, complemented
9#19135526C211yesmaximal, characteristic, complemented
10#19135523C211yesmaximal, characteristic
11#19135318C211yesmaximal, characteristic, complemented
12#19135225C211yesmaximal, characteristic, complemented
13#19135218C211yesmaximal, characteristic, complemented
14#19134426C211yesmaximal, characteristic, complemented
15C2×C43×#490C211yesmaximal, characteristic
16C2×#13063312C2211yescharacteristic
17C2×#13063312C2211yescharacteristic
18C2×C4×Dic86C2211yescharacteristic
19#14583203—24no—
20C2×#13063258C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23C2×Dic43⋊C8C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33#14582813—21no—
34#14582813—21no—
35#14582802—21no—
36#14582802—21no—
37#14582802C2211yescharacteristic
38#14582802C2211yescharacteristic
39#14582798—21no—
40#14582798C2211yescharacteristic
41#14582798C2211yescharacteristic
42#14582785—21no—
43#14582785—21no—
44C4⋊C4×Dic43—21no—
45C4⋊C4×Dic43C2211yescharacteristic
46C4⋊C4×Dic43C2211yescharacteristic
47C4×C4⋊Dic43C2211yescharacteristic
48C4×C4⋊Dic43C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×#127×C43C2211yescharacteristic
54C2×#125×C43C2211yescharacteristic
55C43×#490—24no—
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#97×C43C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64#13063312—22no—
65#13063312—22no—
66#13063312—41no—
67#13063312—41no—
68C4×Dic86—22no—
69C4×Dic86—22no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43D411yescharacteristic
73C2×C4⋊Dic43D411yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43C2311yescharacteristic
91C2×C4×Dic43C2311yescharacteristic
92#13063258—22no—
93#13063256—22no—
94C4⋊(C43⋊C8)—22no—
95Dic43⋊C8—41no—
96Dic43⋊C8—41no—
97#13063250—22no—
98#13063250—22no—
99#13063248—22no—
100#13063248—22no—
101#13063246—22no—
102#13063246—22no—
103#13063246—41no—
104#13063246—41no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95D411yescharacteristic
111C43⋊#95D411yescharacteristic
112C22×D4×C43—21no—
113C22×D4×C43—21no—
114C22×D4×C43C2311yescharacteristic
115C22×D4×C43C2311yescharacteristic
116C22×C8×C43C2311yescharacteristic
117C22×C8×C43C2311yescharacteristic
118#127×C43—22no—
119#127×C43—22no—
120#125×C43—22no—
121#125×C43D414yes—
122C2×C4⋊C4×C43—21no—
123C2×C4⋊C4×C43—21no—
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C42×C43C2311yescharacteristic
127#102×C43—22no—
128#102×C43—22no—
129#102×C43—22no—
130#102×C43—22no—
131#97×C43—22no—
132C24×C43—21no—
133C24×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—42no—
147C2×D4×C43—42no—
148C2×D4×C43—42no—
149C2×D4×C43—42no—
150C2×D4×C43—81no—
151C2×D4×C43—81no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2411yescharacteristic
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86#4112yes—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C4⋊C4×C43—24no—
178C4⋊C4×C43—24no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43C2×D412yes—
182C4⋊C4×C43C2×D412yes—
183C42×C43C2×D412yes—
184C42×C43#4112yes—
185C22⋊Dic43—42no—
186C22⋊Dic43—42no—
187C22⋊Dic43—42no—
188C22⋊Dic43—42no—
189C22⋊Dic43—81no—
190C22⋊Dic43—81no—
191C22⋊Dic43—81no—
192C22⋊Dic43—81no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—41no—
199C4⋊Dic43—41no—
200C4⋊Dic43—42no—
201C4⋊Dic43—81no—
202C4⋊Dic43#4112yes—
203Dic43⋊C4—42no—
204C4×Dic43—21no—
205C4×Dic43—21no—
206C4×Dic43—21no—
207C4×Dic43—21no—
208C4×Dic43—42no—
209C4×Dic43—42no—
210C4×Dic43—81no—
211C4×Dic43—81no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43—41no—
231C23×C43—41no—
232C23×C43C22×D411yescharacteristic
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—41no—
241D4×C43—84no—
242D4×C43—84no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—22no—
248C2×C4×C43—22no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43#12112yes—
254C2×C4×C43#12112yes—
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43H(5,𝔽2)11yescharacteristic
260C2×C4×C432−1+411yescharacteristic
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—22no—
266C2×Dic43—22no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285Dic86—22no—
286Dic86—22no—
287Dic86—41no—
288Dic86—41no—
289C8×C43—41no—
290C8×C43—41no—
291C43⋊C8—41no—
292C43⋊C8—41no—
293#25291—431nomaximal, Sylow
294C22×C43—81no—
295C22×C43—81no—
296C22×C43—81no—
297C22×C43—81no—
298C22×C43—81no—
299C22×C43—81no—
300C22×C43—81no—
301C22×C43—81no—
302C22×C43—81no—
303C22×C43—81no—
304C22×C43—81no—
305C22×C43—81no—
306C22×C43—81no—
307C22×C43—81no—
308C22×C43C2×#12111yescharacteristic
309C22×C43#54611yescharacteristic
310C22×C43#54811yescharacteristic
311C22×C43#57511yescharacteristic
312C22×C43#57511yescharacteristic
313C22×C43#57611yescharacteristic
314C22×C43#57711yescharacteristic
315C4×C43—22no—
316C4×C43—22no—
317C4×C43—42no—
318C4×C43—42no—
319C4×C43#52911yescharacteristic
320C4×C43#54211yescharacteristic
321C4×C43#54811yescharacteristic
322C4×C43#55011yescharacteristic
323Dic43—42no—
324Dic43—42no—
325Dic43—41no—
326Dic43—41no—
327Dic43—41no—
328Dic43—41no—
329Dic43—81no—
330Dic43—81no—
331C2×#490D4311yescharacteristic
332C2×#479—431no—
333#2548—431no—
334#2370—431no—
335#2067—431no—
336#2065—431no—
337#2042—431no—
338#2042—431no—
339#1983—431no—
340#1983—431no—
341#1982—431no—
342#1940—431no—
343#1926—431no—
344#1925—431no—
345#1763—431no—
346C2×C43—161no—
347C2×C43—161no—
348C2×C43#242611yescharacteristic
349C2×C43#304011yescharacteristic
350C2×C43#304511yescharacteristic
351C2×C43#330911yescharacteristic
352C2×C43#331711yescharacteristic
353C2×C43#337011yescharacteristic
354C2×C43#337111yescharacteristic
355C2×#127C2×D4311yescharacteristic
356C2×#125C2×D4311yescharacteristic
357C2×#124—431no—
358C2×#124—431no—
359C2×C4×Q8—431no—
360#490—24no—
361#479—864no—
362C2×#107—431no—
363C2×#106—431no—
364C2×C4⋊C8—431no—
365C2×C4⋊C8—431no—
366C2×C4⋊C8—431no—
367C2×#103—431no—
368C2×#103—431no—
369C2×#103—431no—
370C2×#103—431no—
371C2×#102—431no—
372C2×#102—431no—
373C2×#102—431no—
374C2×#102—431no—
375C2×#102C2×D4311yescharacteristic
376C2×#102C2×D4311yescharacteristic
377C2×#102C2×D4311yescharacteristic
378C2×#102C2×D4311yescharacteristic
379C2×#97C2×D4311yescharacteristic
380#394—861no—
381#394—861no—
382#390—431no—
383#390—431no—
384#390—861no—
385#390—861no—
386#389—431no—
387#389—431no—
388#389—861no—
389#387—861no—
390#387—861no—
391C4×C4⋊C4—431no—
392C4×C4⋊C4—431no—
393C4×C4⋊C4—431no—
394C4×C4⋊C4—431no—
395C4×C4⋊C4—861no—
396#340—431no—
397#340—431no—
398#336—431no—
399#336—431no—
400C43#2529111yescharacteristic, complemented, Sylow
401C22×Q8—431no—
402C22×D4—21no—
403C22×D4—21no—
404C22×D4C22×D4311yescharacteristic
405C22×D4C22×D4311yescharacteristic
406C22×C8—431no—
407C22×C8—431no—
408C22×C8C22×D4311yescharacteristic
409C22×C8C22×D4311yescharacteristic
410#127—22no—
411#127—22no—
412#125—22no—
413#125C22⋊D4314yes—
414#124—862no—
415#124—862no—
416#124—1721no—
417#124—1721no—
418C4×Q8—862no—
419C4×Q8—862no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4C22×D4311yescharacteristic
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C22⋊C4—861no—
435C2×C22⋊C4—861no—
436C2×C22⋊C4—861no—
437C2×C22⋊C4—861no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4—861no—
440C2×C42—431no—
441C2×C42—431no—
442C2×C42—861no—
443C2×C42—861no—
444C2×C42—861no—
445C2×C42—861no—
446C2×C42C22×D4311yescharacteristic
447#107—862no—
448#106—862no—
449C4⋊C8—862no—
450C4⋊C8—1721no—
451C4⋊C8—1721no—
452#103—862no—
453#103—862no—
454#103—862no—
455#103—862no—
456#102—22no—
457#102—22no—
458#102—22no—
459#102—22no—
460#102—862no—
461#102—862no—
462#102—1721no—
463#102—1721no—
464#97—22no—
465#95—431no—
466#95—431no—
467#95—861no—
468#95—861no—
469#95—861no—
470#95—861no—
471#95—861no—
472C24—21no—
473C24—21no—
474C2×Q8—432no—
475C2×Q8—861no—
476C2×Q8—861no—
477C2×Q8—861no—
478C2×Q8—861no—
479C2×Q8—861no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—81no—
497C2×D4—81no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—431no—
501C22×C4—431no—
502C22×C4—431no—
503C22×C4—431no—
504C22×C4—861no—
505C22×C4—861no—
506C22×C4—861no—
507C22×C4—861no—
508C22×C4D4×D4311yescharacteristic
509C22×C4D4×D4311yescharacteristic
510C22×C4C23×D4311yescharacteristic
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C4⋊C4—24no—
524C4⋊C4—24no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—432no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—3441no—
534C4⋊C4—1721no—
535C4⋊C4—1721no—
536C4⋊C4—1722no—
537C4⋊C4—1722no—
538C4⋊C4C2×C22⋊D4312yes—
539C4⋊C4C2×C22⋊D4312yes—
540C22⋊C4—3441no—
541C22⋊C4—3441no—
542C22⋊C4—3441no—
543C22⋊C4—3441no—
544C22⋊C4—1722no—
545C22⋊C4—1722no—
546C22⋊C4—1722no—
547C22⋊C4—1722no—
548C42—861no—
549C42—861no—
550C42—861no—
551C42—861no—
552C42—3441no—
553C42—3441no—
554C42—1722no—
555C42—1722no—
556C42#1062190012yes—
557C42C2×C22⋊D4312yes—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23C2×D4×D4311yescharacteristic
573Q8—862no—
574Q8—862no—
575Q8—1721no—
576Q8—1721no—
577D4—41no—
578D4—41no—
579D4—41no—
580D4—41no—
581D4—41no—
582D4—41no—
583D4—41no—
584D4—41no—
585D4—84no—
586D4—84no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—862no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—861no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—861no—
610C2×C4—862no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4#1306329712yes—
622C2×C4#1306329712yes—
623C2×C4C22×C22⋊D4311yescharacteristic
624C2×C4#41×D4311yescharacteristic
625C2×C4#41×D4311yescharacteristic
626C2×C4C2×#1062190011yescharacteristic
627C2×C4#1306337111yescharacteristic
628C2×C4#1306337211yescharacteristic
629C8—41no—
630C8—41no—
631C8—1721no—
632C8—1721no—
633C22—81no—
634C22—81no—
635C22—81no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22C2×#1306329711yescharacteristic
648C22#1458354211yescharacteristic
649C22#1458355711yescharacteristic
650C22#1458369511yescharacteristic
651C22#1458369511yescharacteristic
652C22#1458370311yescharacteristic
653C22#1458370911yescharacteristic
654C4—22no—
655C4—22no—
656C4—42no—
657C4—42no—
658C4—3441no—
659C4—3441no—
660C4—1722no—
661C4—1721no—
662C4—1721no—
663C4—1722no—
664C4—1721no—
665C4—1721no—
666C4#1458342811yescharacteristic
667C4#1458351811yescharacteristic
668C4#1458355611yescharacteristic
669C4#1458356811yescharacteristic
670C2—161no—
671C2—161no—
672C2#1913816411yescharacteristic
673C2#1914408711yescharacteristic
674C2#1914413811yescharacteristic
675C2#1914660011yescharacteristic
676C2#1914672011yescharacteristic
677C2#1914734311yescharacteristic
678C2#1914735811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#490C2
socleC23×C43C22×D4
prime radicalC2×#127×C43C22
hypercenterC2×#490D43
hypocenterC43#25291
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#490

Complements

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

NH ≅ G/Ntype
1. C2×#14583203C2semidirect
3. #19137695C2semidirect
4. #19135979C2semidirect
5. #19135965C2semidirect
6. #19135835C2semidirect
7. #19135835C2semidirect
8. #19135526C2semidirect
9. #19135526C2semidirect
11. #19135318C2semidirect
12. #19135225C2semidirect
13. #19135218C2semidirect
14. #19134426C2semidirect
400. C43#25291semidirect

Maximal subgroups

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

subgroupindex
C2×#145832032
#191395982
#191376952
#191359792
#191359652
#191358352
#191355262
#191355232
#191353182
#191352252
#191352182
#191344262
C2×C43×#4902
#2529143