Finite Group Databasebeta

← #25137966

Subgroups — #25137966

Order 11008.

746 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583191C211yesmaximal, characteristic, complemented
2C2×#14582960C211yesmaximal, characteristic
3#19137277C211yesmaximal, characteristic
4#19136026C211yesmaximal, characteristic
5#19136021C211yesmaximal, characteristic
6#19135798C211yesmaximal, characteristic
7#19135791C211yesmaximal, characteristic
8#19135548C211yesmaximal, characteristic, complemented
9#19135361C211yesmaximal, characteristic, complemented
10#19135335C211yesmaximal, characteristic, complemented
11#19135325C211yesmaximal, characteristic, complemented
12#19135284C211yesmaximal, characteristic, complemented
13#19135270C211yesmaximal, characteristic, complemented
14#19134607C211yesmaximal, characteristic, complemented
15C43×#2628C211yesmaximal, characteristic
16C2×#13063304C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18#14583191—24no—
19#14582960—24no—
20C2×#13063258C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×C4⋊(C43⋊C8)C2211yescharacteristic
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31C2×C22⋊(C43⋊C8)C2211yescharacteristic
32C2×#13063236C2211yescharacteristic
33C2×C4×C43⋊C8C2211yescharacteristic
34#14582805C2211yescharacteristic
35#14582797C2211yescharacteristic
36#14582794—21no—
37#14582793—21no—
38#14582787—21no—
39#14582780—21no—
40#14582759C2211yescharacteristic
41C4×C4⋊Dic43C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50C2×C4⋊Q8×C43C2211yescharacteristic
51C2×#117×C43C2211yescharacteristic
52C43×#400—21no—
53C43×#399—21no—
54C43×#395—21no—
55C43×#393—21no—
56C43×#389C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#382C2211yescharacteristic
59C43×#380C2211yescharacteristic
60C43×#380C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66#13063304—22no—
67#13063304—22no—
68C4×Dic86—22no—
69C4×Dic86—22no—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—21no—
78C2×C4×Dic43—21no—
79C2×C4×Dic43—21no—
80#13063258—22no—
81#13063258—22no—
82#13063258—22no—
83#13063256—22no—
84C4⋊(C43⋊C8)—22no—
85C4⋊(C43⋊C8)D414yes—
86#13063248—22no—
87#13063248—22no—
88#13063248—22no—
89#13063248—22no—
90C22⋊(C43⋊C8)—22no—
91C22⋊(C43⋊C8)—22no—
92#13063236—22no—
93C4×C43⋊C8—22no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C22×Q8×C43—21no—
100C23×C4×C43C2311yescharacteristic
101C4⋊Q8×C43—22no—
102C4⋊Q8×C43—22no—
103#117×C43—22no—
104#117×C43—22no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43D411yescharacteristic
109C2×C4⋊C4×C43D411yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43D411yescharacteristic
117C2×C22⋊C4×C43D411yescharacteristic
118C2×C42×C43C2311yescharacteristic
119C2×C42×C43C2311yescharacteristic
120#95×C43—21no—
121#95×C43—21no—
122#95×C43—21no—
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126C24×C43C2×D411yescharacteristic
127C2×Q8×C43—42no—
128C2×Q8×C43—81no—
129C2×Q8×C43—81no—
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—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
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—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86#4112yes—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—22no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—42no—
167C4⋊C4×C43—81no—
168C4⋊C4×C43—81no—
169C22⋊C4×C43—22no—
170C22⋊C4×C43—22no—
171C22⋊C4×C43—81no—
172C22⋊C4×C43—81no—
173C42×C43—21no—
174C42×C43—21no—
175C42×C43C2×D412yes—
176C42×C43#4112yes—
177C22⋊Dic43—24no—
178C22⋊Dic43—81no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43#4112yes—
185Dic43⋊C4—24no—
186Dic43⋊C4—42no—
187Dic43⋊C4—81no—
188C4×Dic43—42no—
189C4×Dic43—81no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8C2×D412yes—
201C2×C43⋊C8C2×D412yes—
202C23×C43—21no—
203C23×C43—21no—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43C22×D411yescharacteristic
210Q8×C43—84no—
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—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
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—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43#12112yes—
241C2×C4×C43#12112yes—
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C432−1+411yescharacteristic
247C2×C4×C432−1+411yescharacteristic
248C2×Dic43—22no—
249C2×Dic43—22no—
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—41no—
259C2×Dic43—41no—
260Dic86—22no—
261Dic86—22no—
262Dic86—41no—
263Dic86—41no—
264C43⋊C8—22no—
265C43⋊C8—22no—
266C43⋊C8—41no—
267C43⋊C8—41no—
268#24714—431nomaximal, Sylow
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43C2×#12111yescharacteristic
277C22×C43#52511yescharacteristic
278C22×C43#53611yescharacteristic
279C22×C43#57611yescharacteristic
280C22×C43#57711yescharacteristic
281C22×C43#57811yescharacteristic
282C22×C43#57811yescharacteristic
283C4×C43—22no—
284C4×C43—22no—
285C4×C43—41no—
286C4×C43—41no—
287C4×C43—41no—
288C4×C43—81no—
289C4×C43—81no—
290C4×C43—81no—
291C4×C43—81no—
292C4×C43#54711yescharacteristic
293C4×C43#54811yescharacteristic
294C4×C43#55211yescharacteristic
295C4×C43#55611yescharacteristic
296Dic43—42no—
297Dic43—42no—
298Dic43—81no—
299Dic43—81no—
300C2×#477—431no—
301C2×#433—431no—
302#2628D4311yescharacteristic
303#2323—431no—
304#2076—431no—
305#2075—431no—
306#2036—431no—
307#2035—431no—
308#1988—431no—
309#1949—431no—
310#1944—431no—
311#1942—431no—
312#1935—431no—
313#1933—431no—
314#1805—431no—
315C2×C43—81no—
316C2×C43#241511yescharacteristic
317C2×C43#305911yescharacteristic
318C2×C43#306211yescharacteristic
319C2×C43#312111yescharacteristic
320C2×C43#312411yescharacteristic
321C2×C43#324211yescharacteristic
322C2×C43#324311yescharacteristic
323C2×C4⋊Q8C2×D4311yescharacteristic
324C2×C22⋊Q8—431no—
325C2×C4×Q8—431no—
326C2×#117C2×D4311yescharacteristic
327#477—864no—
328#433—864no—
329C2×#107—431no—
330C2×#107—431no—
331C2×#107—431no—
332C2×#106—431no—
333C2×C4⋊C8—431no—
334C2×C4⋊C8—431no—
335C2×#103—431no—
336C2×#103—431no—
337C2×#103—431no—
338C2×#103—431no—
339C2×C22⋊C8—431no—
340C2×C22⋊C8—431no—
341C2×#97—431no—
342C2×C4×C8—431no—
343#400—21no—
344#399—21no—
345#395—21no—
346#393—21no—
347#391—431no—
348#389—431no—
349#389—861no—
350#389C2×D4311yescharacteristic
351#389C2×D4311yescharacteristic
352#388—861no—
353#388—861no—
354#387—861no—
355#382C2×D4311yescharacteristic
356#380—431no—
357#380C2×D4311yescharacteristic
358#380C2×D4311yescharacteristic
359C4×C4⋊C4—431no—
360#340—431no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368C43#2471411yescharacteristic, complemented, Sylow
369C22×Q8—21no—
370C22×Q8—431no—
371C23×C4C22×D4311yescharacteristic
372C22×C8—431no—
373C22×C8—431no—
374C22×C8—431no—
375C22×C8—431no—
376C4⋊Q8—22no—
377C4⋊Q8—22no—
378C22⋊Q8—862no—
379C22⋊Q8—862no—
380C4×Q8—862no—
381C4×Q8—862no—
382#117—22no—
383#117—22no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4C22⋊D4311yescharacteristic
394C2×C4⋊C4C22⋊D4311yescharacteristic
395C2×C4⋊C4C22×D4311yescharacteristic
396C2×C4⋊C4C22×D4311yescharacteristic
397C2×C4⋊C4C22×D4311yescharacteristic
398C2×C4⋊C4C22×D4311yescharacteristic
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—861no—
402C2×C22⋊C4—861no—
403C2×C22⋊C4C22⋊D4311yescharacteristic
404C2×C22⋊C4C22⋊D4311yescharacteristic
405C2×C42—861no—
406C2×C42—861no—
407C2×C42C22×D4311yescharacteristic
408C2×C42C22×D4311yescharacteristic
409#107—862no—
410#107—862no—
411#107—862no—
412#106—862no—
413C4⋊C8—434no—
414C4⋊C8—862no—
415#103—862no—
416#103—862no—
417#103—862no—
418#103—862no—
419C22⋊C8—862no—
420C22⋊C8—862no—
421#97—862no—
422C4×C8—862no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434C24C2×C22⋊D4311yescharacteristic
435C2×Q8—42no—
436C2×Q8—81no—
437C2×Q8—81no—
438C2×Q8—432no—
439C2×Q8—861no—
440C2×Q8—861no—
441C2×Q8—861no—
442C2×Q8—861no—
443C2×Q8—861no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4C2×C22⋊D4311yescharacteristic
459C22×C4C2×C22⋊D4311yescharacteristic
460C22×C4C2×C22⋊D4311yescharacteristic
461C22×C4C2×C22⋊D4311yescharacteristic
462C22×C4C2×C22⋊D4311yescharacteristic
463C22×C4C23×D4311yescharacteristic
464C2×C8—432no—
465C2×C8—432no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—861no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—42no—
487C4⋊C4—81no—
488C4⋊C4—81no—
489C4⋊C4—432no—
490C4⋊C4—864no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—3441no—
497C4⋊C4—1722no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—81no—
501C22⋊C4—81no—
502C22⋊C4—864no—
503C22⋊C4—3441no—
504C42—21no—
505C42—21no—
506C42—3441no—
507C42—1722no—
508C42D4×D4312yes—
509C42#1062190012yes—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23C22×C22⋊D4311yescharacteristic
518Q8—84no—
519Q8—862no—
520Q8—862no—
521Q8—1721no—
522Q8—1721no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—862no—
553C2×C4—862no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4#1306329712yes—
565C2×C4#1306329712yes—
566C2×C4C2×D4×D4311yescharacteristic
567C2×C4#41×D4311yescharacteristic
568C2×C4#41×D4311yescharacteristic
569C2×C4C2×#1062190011yescharacteristic
570C2×C4#1306337311yescharacteristic
571C2×C4#1306337311yescharacteristic
572C8—862no—
573C8—862no—
574C8—1721no—
575C8—1721no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22C2×#1306329711yescharacteristic
584C22#1458340611yescharacteristic
585C22#1458347311yescharacteristic
586C22#1458370211yescharacteristic
587C22#1458371011yescharacteristic
588C22#1458371411yescharacteristic
589C22#1458371411yescharacteristic
590C4—22no—
591C4—22no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—81no—
596C4—81no—
597C4—81no—
598C4—81no—
599C4—3441no—
600C4—3441no—
601C4—1722no—
602C4—1722no—
603C4#1458355111yescharacteristic
604C4#1458355911yescharacteristic
605C4#1458358311yescharacteristic
606C4#1458362011yescharacteristic
607C2—81no—
608C2#1913802511yescharacteristic
609C2#1914424711yescharacteristic
610C2#1914427111yescharacteristic
611C2#1914481811yescharacteristic
612C2#1914485111yescharacteristic
613C2#1914586311yescharacteristic
614C2#1914587811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2628C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#2628D43
hypocenterC43#24714
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2628

Complements

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

NH ≅ G/Ntype
1. C2×#14583191C2semidirect
8. #19135548C2semidirect
9. #19135361C2semidirect
10. #19135335C2semidirect
11. #19135325C2semidirect
12. #19135284C2semidirect
13. #19135270C2semidirect
14. #19134607C2semidirect
368. C43#24714semidirect

Maximal subgroups

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

subgroupindex
C2×#145831912
C2×#145829602
#191372772
#191360262
#191360212
#191357982
#191357912
#191355482
#191353612
#191353352
#191353252
#191352842
#191352702
#191346072
C43×#26282
#2471443