Finite Group Databasebeta

← #25148665

Subgroups — #25148665

Order 11008.

782 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583197C211yesmaximal, characteristic
2C2×#14583026C211yesmaximal, characteristic, complemented
3#19139982C211yesmaximal, characteristic, complemented
4#19139515C211yesmaximal, characteristic
5#19136098C211yesmaximal, characteristic, complemented
6#19136083C211yesmaximal, characteristic, complemented
7#19135965C211yesmaximal, characteristic
8#19135562C211yesmaximal, characteristic, complemented
9#19135355C211yesmaximal, characteristic, complemented
10#19135339C211yesmaximal, characteristic, complemented
11#19135320C211yesmaximal, characteristic, complemented
12#19135289C211yesmaximal, characteristic
13#19135281C211yesmaximal, characteristic
14#19134422C211yesmaximal, characteristic
15C43×#2065C211yesmaximal, characteristic
16C2×#13063316C2211yescharacteristic
17C2×#13063302—21no—
18C2×C4×Dic86C2211yescharacteristic
19C2×D4×Dic43C2211yescharacteristic
20#14583197—24no—
21#14583026—24no—
22C2×#13063259C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063235C2211yescharacteristic
30C2×#13063235C2211yescharacteristic
31C2×C4×C43⋊C8C2211yescharacteristic
32#14582832—21no—
33#14582822—21no—
34#14582822—21no—
35#14582820—21no—
36#14582802C2211yescharacteristic
37#14582798C2211yescharacteristic
38#14582798C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582797C2211yescharacteristic
41#14582796—21no—
42#14582795—21no—
43#14582795C2211yescharacteristic
44#14582768C2211yescharacteristic
45#14582757—21no—
46C4⋊C4×Dic43C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54C2×#106×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C43×#390C2211yescharacteristic
59C43×#389C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86D411yescharacteristic
62C23×Dic43—21no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063316—22no—
66#13063316—22no—
67#13063302—44no—
68C4×Dic86—22no—
69C4×Dic86—22no—
70D4×Dic43—22no—
71D4×Dic43—22no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43D411yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4D411yescharacteristic
87C2×Dic43⋊C4D411yescharacteristic
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43C2311yescharacteristic
93C2×C4×Dic43C2311yescharacteristic
94#13063259—22no—
95#13063256—22no—
96#13063256—22no—
97Dic43⋊C8—22no—
98Dic43⋊C8D414yes—
99#13063246—22no—
100#13063246Q814yescomplemented
101#13063235—22no—
102#13063235—22no—
103C4×C43⋊C8—22no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C22×D4×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C22⋊C4×C43—21no—
118C2×C22⋊C4×C43—21no—
119C2×C42×C43C2311yescharacteristic
120#106×C43—22no—
121C4⋊C8×C43—22no—
122#102×C43—22no—
123#102×C43—22no—
124#95×C43—21no—
125C24×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43C2×Q812yes—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2411yescharacteristic
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—42no—
143C22×Dic43—42no—
144C22×Dic43—42no—
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C2×Dic86—22no—
150C2×Dic86—22no—
151C2×Dic86—41no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43C2×D412yes—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—81no—
164C4⋊C4×C43#4112yes—
165C22⋊C4×C43—42no—
166C22⋊C4×C43—81no—
167C42×C43—21no—
168C42×C43—21no—
169C22⋊Dic43—42no—
170C22⋊Dic43—42no—
171C22⋊Dic43—81no—
172C4⋊Dic43—21no—
173C4⋊Dic43—22no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—42no—
181C4⋊Dic43—42no—
182C4⋊Dic43—42no—
183C4⋊Dic43C2×Q812yes—
184Dic43⋊C4—22no—
185Dic43⋊C4—22no—
186Dic43⋊C4—42no—
187Dic43⋊C4—42no—
188Dic43⋊C4—42no—
189Dic43⋊C4—42no—
190Dic43⋊C4—81no—
191Dic43⋊C4—81no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—81no—
195C4×Dic43C2×D412yes—
196C4×Dic43#4112yes—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8C2×D412yes—
202C2×C43⋊C8C2×Q812yes—
203C23×C43—22no—
204C23×C43—41no—
205C23×C43—41no—
206C23×C43—41no—
207C23×C43—41no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43C22×D411yescharacteristic
211D4×C43—22no—
212D4×C43—22no—
213D4×C43—41no—
214D4×C43—41no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—22no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
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×C43AGL(1,ℤ/8)12yes—
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C22×Q811yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C432−1+411yescharacteristic
235C2×C4×C432−1+411yescharacteristic
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—22no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
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—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—84no—
259C2×Dic43#12112yes—
260C2×Dic43#12112yes—
261Dic86—44no—
262C8×C43—22no—
263C8×C43—41no—
264C43⋊C8—22no—
265C43⋊C8—22no—
266#25486—431nomaximal, Sylow
267C22×C43—42no—
268C22×C43—42no—
269C22×C43—42no—
270C22×C43—81no—
271C22×C43—81no—
272C22×C43—81no—
273C22×C43—81no—
274C22×C43C2×#12111yescharacteristic
275C22×C43#54811yescharacteristic
276C22×C43D4×Q811yescharacteristic
277C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
278C22×C43#57511yescharacteristic
279C22×C43#57711yescharacteristic
280C22×C43#57711yescharacteristic
281C4×C43—22no—
282C4×C43—42no—
283C4×C43—41no—
284C4×C43—81no—
285C4×C43—81no—
286C4×C43#53311yescharacteristic
287C4×C43#54111yescharacteristic
288C4×C43#54711yescharacteristic
289C4×C43D4×Q811yescharacteristic
290Dic43—22no—
291Dic43—22no—
292Dic43—42no—
293Dic43—41no—
294Dic43—41no—
295Dic43—81no—
296Dic43—81no—
297Dic43—81no—
298C2×#478—431no—
299C2×#446—431no—
300#2584—431no—
301#2538—431no—
302#2088—431no—
303#2086—431no—
304#2065—431no—
305#2065D4311yescharacteristic
306#1992—431no—
307#1948—431no—
308#1944—431no—
309#1941—431no—
310#1936—431no—
311#1934—431no—
312#1762—431no—
313C2×C43—82no—
314C2×C43#242911yescharacteristic
315C2×C43#305511yescharacteristic
316C2×C43#306011yescharacteristic
317C2×C43#336811yescharacteristic
318C2×C43#337611yescharacteristic
319C2×C43#338411yescharacteristic
320C2×C43#338811yescharacteristic
321C2×#125—431no—
322C2×C22⋊Q8—861no—
323C2×C4×Q8—431no—
324C2×C4×D4—431no—
325#478—864no—
326#446—864no—
327C2×#107—431no—
328C2×#106—431no—
329C2×#106—431no—
330C2×#106C2×D4311yescharacteristic
331C2×C4⋊C8—431no—
332C2×C4⋊C8—431no—
333C2×C4⋊C8C2×D4311yescharacteristic
334C2×#102—431no—
335C2×#102—431no—
336C2×#102C2×D4311yescharacteristic
337C2×#102C2×D4311yescharacteristic
338C2×#97—431no—
339C2×#97—431no—
340C2×C4×C8—431no—
341#398—861no—
342#396—861no—
343#396—861no—
344#395—861no—
345#390—431no—
346#390C2×D4311yescharacteristic
347#389—431no—
348#389—431no—
349#389—431no—
350#389—431no—
351#389—431no—
352#389—861no—
353#389—861no—
354#389C2×D4311yescharacteristic
355#384—431no—
356#380—861no—
357C4×C4⋊C4—431no—
358#340—431no—
359#340—431no—
360#340—431no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340—431no—
365#340C2×D4311yescharacteristic
366C43#2548611yescharacteristic, complemented, Sylow
367C22×Q8—431no—
368C22×D4C22×D4311yescharacteristic
369C23×C4—861no—
370C22×C8—431no—
371C22×C8—431no—
372C22×C8C22×D4311yescharacteristic
373C22×C8C22×D4311yescharacteristic
374#125—862no—
375#125—862no—
376C22⋊Q8—1724no—
377C4×Q8—862no—
378C4×Q8—862no—
379C4×D4—862no—
380C4×D4—862no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—431no—
384C2×C4⋊C4—431no—
385C2×C4⋊C4—431no—
386C2×C4⋊C4—431no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—861no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4C22×D4311yescharacteristic
399C2×C4⋊C4C22×D4311yescharacteristic
400C2×C4⋊C4C22×D4311yescharacteristic
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—861no—
404C2×C22⋊C4—861no—
405C2×C22⋊C4—861no—
406C2×C42—431no—
407C2×C42—431no—
408C2×C42—861no—
409C2×C42C22×D4311yescharacteristic
410#107—862no—
411#106—22no—
412#106—862no—
413#106—862no—
414C4⋊C8—22no—
415C4⋊C8—434no—
416C4⋊C8—862no—
417#102—22no—
418#102—22no—
419#102—434no—
420#102—862no—
421#97—862no—
422#97—862no—
423C4×C8—862no—
424#95—21no—
425#95—861no—
426#95—861no—
427#95—861no—
428#95—861no—
429#95—861no—
430#95—861no—
431C24—21no—
432C2×Q8—862no—
433C2×Q8—862no—
434C2×Q8—1721no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4Q8×D4312yes—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—431no—
445C22×C4—431no—
446C22×C4—431no—
447C22×C4—431no—
448C22×C4—861no—
449C22×C4—861no—
450C22×C4—861no—
451C22×C4—861no—
452C22×C4—1722no—
453C22×C4—1722no—
454C22×C4—1722no—
455C22×C4D4×D4311yescharacteristic
456C22×C4D4×D4311yescharacteristic
457C22×C4C23×D4311yescharacteristic
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—432no—
464C2×C8—432no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8D4×D4312yes—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—81no—
476C4⋊C4—432no—
477C4⋊C4—862no—
478C4⋊C4—862no—
479C4⋊C4—862no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—3441no—
488C4⋊C4—3441no—
489C4⋊C4—1722no—
490C4⋊C4—1722no—
491C4⋊C4—1722no—
492C4⋊C4—1722no—
493C4⋊C4—1722no—
494C4⋊C4—1722no—
495C4⋊C4—1722no—
496C4⋊C4#1062190012yes—
497C22⋊C4—42no—
498C22⋊C4—81no—
499C22⋊C4—3441no—
500C22⋊C4—1722no—
501C22⋊C4—1722no—
502C42—21no—
503C42—21no—
504C42—432no—
505C42—432no—
506C42—861no—
507C42—861no—
508C42—3441no—
509C23—22no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23C2×D4×D4311yescharacteristic
517Q8—1724no—
518D4—22no—
519D4—22no—
520D4—41no—
521D4—41no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
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—432no—
537C2×C4—432no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—862no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—861no—
549C2×C4—3444no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4#1306335212yes—
562C2×C4C2×D4×D4311yescharacteristic
563C2×C4C2×Q8×D4311yescharacteristic
564C2×C4#41×D4311yescharacteristic
565C2×C4C2×#1062190011yescharacteristic
566C2×C4#1306337211yescharacteristic
567C2×C4#1306337211yescharacteristic
568C8—22no—
569C8—41no—
570C8—862no—
571C8—862no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22#121×D4311yescharacteristic
580C22#1458355511yescharacteristic
581C22#1458356211yescharacteristic
582C22C2×#1306335211yescharacteristic
583C22#1458369611yescharacteristic
584C22#1458370911yescharacteristic
585C22#1458370911yescharacteristic
586C4—22no—
587C4—41no—
588C4—42no—
589C4—81no—
590C4—81no—
591C4—862no—
592C4—862no—
593C4—3441no—
594C4—3441no—
595C4—3441no—
596C4—1721no—
597C4—1721no—
598C4—1722no—
599C4#1458345111yescharacteristic
600C4#1458350611yescharacteristic
601C4#1458354911yescharacteristic
602C4#1458356211yescharacteristic
603C2—82no—
604C2#1913818711yescharacteristic
605C2#1914420711yescharacteristic
606C2#1914425511yescharacteristic
607C2#1914732811yescharacteristic
608C2#1914742611yescharacteristic
609C2#1914749311yescharacteristic
610C2#1914754411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2065C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2065D43
hypocenterC43#25486
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2065

Complements

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

NH ≅ G/Ntype
2. C2×#14583026C2semidirect
3. #19139982C2semidirect
5. #19136098C2semidirect
6. #19136083C2semidirect
8. #19135562C2semidirect
9. #19135355C2semidirect
10. #19135339C2semidirect
11. #19135320C2semidirect
100. #13063246Q8semidirect
366. C43#25486semidirect

Maximal subgroups

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

subgroupindex
C2×#145831972
C2×#145830262
#191399822
#191395152
#191360982
#191360832
#191359652
#191355622
#191353552
#191353392
#191353202
#191352892
#191352812
#191344222
C43×#20652
#2548643