Finite Group Databasebeta

← #25137970

Subgroups — #25137970

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×#14582959C211yesmaximal, characteristic
3#19140417C211yesmaximal, characteristic
4#19137278C211yesmaximal, characteristic
5#19136027C211yesmaximal, characteristic
6#19136022C211yesmaximal, characteristic
7#19135801C211yesmaximal, characteristic
8#19135794C211yesmaximal, characteristic
9#19135363C211yesmaximal, characteristic, complemented
10#19135337C211yesmaximal, characteristic, complemented
11#19135327C211yesmaximal, characteristic, complemented
12#19135283C211yesmaximal, characteristic, complemented
13#19135269C211yesmaximal, characteristic, complemented
14#19134611C211yesmaximal, characteristic, complemented
15C43×#1988C211yesmaximal, characteristic, complemented
16C2×#13063305C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18C2×#13063282C2211yescharacteristic
19#14583191—24no—
20#14582959—24no—
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32C2×#13063235C2211yescharacteristic
33C2×C8×Dic43C2211yescharacteristic
34#14582837—21no—
35#14582834—21no—
36#14582818—21no—
37#14582810—21no—
38#14582804C2211yescharacteristic
39#14582798C2211yescharacteristic
40#14582797—21no—
41#14582795C2211yescharacteristic
42#14582795C2211yescharacteristic
43#14582791—21no—
44#14582790—21no—
45#14582784—21no—
46#14582765C2211yescharacteristic
47#14582756C2211yescharacteristic
48#14582756C2211yescharacteristic
49#14582756C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54C2×C4⋊Q8×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C22×C4×D43C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063305—22no—
66#13063305—22no—
67C4×Dic86—22no—
68C4×Dic86—22no—
69#13063282—22no—
70#13063282—22no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4D411yescharacteristic
80C2×Dic43⋊C4D411yescharacteristic
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4D411yescharacteristic
86C2×(C2×D43)⋊C4D411yescharacteristic
87C2×C4×Dic43—21no—
88C2×C4×Dic43C2311yescharacteristic
89#13063258—22no—
90#13063258—22no—
91#13063258—22no—
92#13063256—22no—
93C4⋊(C43⋊C8)D414yes—
94#13063250—22no—
95#13063250—22no—
96#13063248—22no—
97#13063248—22no—
98(C2×D43)⋊C8—22no—
99(C2×D43)⋊C8—22no—
100#13063235—22no—
101C8×Dic43—22no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C22×Q8×C43—21no—
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C4⋊Q8×C43—22no—
116C4⋊Q8×C43—22no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C42×C43—21no—
123C2×C42×C43C2311yescharacteristic
124C4⋊C8×C43—22no—
125#95×C43—21no—
126C23×D43C2×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×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2411yescharacteristic
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43C2×D411yescharacteristic
142C22×Dic43C2×D411yescharacteristic
143C22×Dic43C2×D411yescharacteristic
144C2×C4×D43—21no—
145C2×C4×D43—21no—
146C2×C4×D43—21no—
147C2×C4×D43—21no—
148C2×C4×D43—21no—
149C2×C4×D43—21no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86#4112yes—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—42no—
170C4⋊C4×C43#4112yes—
171C42×C43—81no—
172C42×C43C2×D412yes—
173C42×C43#4112yes—
174(C2×D43)⋊C4—24no—
175(C2×D43)⋊C4—22no—
176(C2×D43)⋊C4—22no—
177(C2×D43)⋊C4—81no—
178(C2×D43)⋊C4—81no—
179(C2×D43)⋊C4—81no—
180C4⋊Dic43—24no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—81no—
188Dic43⋊C4—22no—
189Dic43⋊C4—22no—
190Dic43⋊C4—42no—
191Dic43⋊C4—81no—
192Dic43⋊C4—81no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—42no—
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×C43C22×D411yescharacteristic
203C22×D43—21no—
204C22×D43—21no—
205C22×D43—21no—
206C22×D43—21no—
207C22×D43—21no—
208C22×D43—21no—
209C22×D43—21no—
210Q8×C43—84no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—22no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
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#12112yes—
228C2×C4×C43#12112yes—
229C2×C4×C43C22×D411yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C432−1+411yescharacteristic
234C2×C4×C432−1+411yescharacteristic
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—22no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
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—
256C4×D43—41no—
257C4×D43—41no—
258C4×D43—41no—
259C4×D43—41no—
260Dic86—22no—
261Dic86—22no—
262Dic86—41no—
263Dic86—41no—
264C8×C43—41no—
265C8×C43—41no—
266C43⋊C8—22no—
267C43⋊C8—22no—
268#24714—431nomaximal, Sylow
269C22×C43C2×#12111yescharacteristic
270C22×C43#52511yescharacteristic
271C22×C43#53611yescharacteristic
272C22×C43#57611yescharacteristic
273C22×C43#57711yescharacteristic
274C22×C43#57811yescharacteristic
275C22×C43#57811yescharacteristic
276C2×D43—41no—
277C2×D43—41no—
278C2×D43—41no—
279C2×D43—41no—
280C2×D43—41no—
281C2×D43—41no—
282C2×D43—41no—
283C4×C43—22no—
284C4×C43—22no—
285C4×C43—42no—
286C4×C43—81no—
287C4×C43—81no—
288C4×C43—81no—
289C4×C43#54711yescharacteristic
290C4×C43#54811yescharacteristic
291C4×C43#55211yescharacteristic
292C4×C43#55611yescharacteristic
293Dic43—42no—
294Dic43—41no—
295Dic43—41no—
296Dic43—41no—
297Dic43—81no—
298Dic43—81no—
299Dic43—81no—
300C2×#477—431no—
301C2×#433—431no—
302#2628—431no—
303#2323—431no—
304#2076—431no—
305#2075—431no—
306#2036—431no—
307#2035—431no—
308#1988D4311yescharacteristic, complemented
309#1949—431no—
310#1944—431no—
311#1942—431no—
312#1935—431no—
313#1933—431no—
314#1805—431no—
315C2×C43#241511yescharacteristic
316C2×C43#305911yescharacteristic
317C2×C43#306211yescharacteristic
318C2×C43#312111yescharacteristic
319C2×C43#312411yescharacteristic
320C2×C43#324211yescharacteristic
321C2×C43#324311yescharacteristic
322D43—81no—
323C2×C4⋊Q8C2×D4311yescharacteristic
324C2×C22⋊Q8—431no—
325C2×C4×Q8—431no—
326C2×#117—431no—
327#477—864no—
328#433—864no—
329C2×#107—431no—
330C2×#107—431no—
331C2×#107—431no—
332C2×#106—431no—
333C2×C4⋊C8—431no—
334C2×C4⋊C8C2×D4311yescharacteristic
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—861no—
344#399—861no—
345#395—861no—
346#393—861no—
347#391—431no—
348#389—431no—
349#389—431no—
350#389—431no—
351#389—861no—
352#388—861no—
353#388—861no—
354#387—861no—
355#382—431no—
356#380—431no—
357#380—431no—
358#380—431no—
359C4×C4⋊C4C2×D4311yescharacteristic
360#340—431no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340C2×D4311yescharacteristic
365#340C2×D4311yescharacteristic
366#340C2×D4311yescharacteristic
367#340C2×D4311yescharacteristic
368C43#2471411yescharacteristic, complemented, Sylow
369C22×Q8—21no—
370C22×Q8—431no—
371C23×C4—431no—
372C22×C8—431no—
373C22×C8—431no—
374C22×C8C22×D4311yescharacteristic
375C22×C8C22×D4311yescharacteristic
376C4⋊Q8—22no—
377C4⋊Q8—22no—
378C22⋊Q8—862no—
379C22⋊Q8—862no—
380C4×Q8—862no—
381C4×Q8—862no—
382#117—862no—
383#117—862no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—431no—
386C2×C4⋊C4—431no—
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⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4C22×D4311yescharacteristic
396C2×C4⋊C4C22×D4311yescharacteristic
397C2×C4⋊C4C22×D4311yescharacteristic
398C2×C4⋊C4C22×D4311yescharacteristic
399C2×C22⋊C4—431no—
400C2×C22⋊C4—431no—
401C2×C22⋊C4—861no—
402C2×C22⋊C4—861no—
403C2×C22⋊C4—861no—
404C2×C22⋊C4—861no—
405C2×C42—21no—
406C2×C42—431no—
407C2×C42—861no—
408C2×C42C22×D4311yescharacteristic
409#107—862no—
410#107—862no—
411#107—862no—
412#106—862no—
413C4⋊C8—22no—
414C4⋊C8—434no—
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—861no—
425#95—861no—
426#95—861no—
427#95—861no—
428#95—861no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434C24—431no—
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—431no—
449C22×C4—431no—
450C22×C4—431no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—861no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4D4×D4311yescharacteristic
462C22×C4D4×D4311yescharacteristic
463C22×C4C23×D4311yescharacteristic
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—432no—
471C2×C8—432no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—861no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—42no—
484C4⋊C4—864no—
485C4⋊C4—862no—
486C4⋊C4—862no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—3441no—
494C4⋊C4—3441no—
495C4⋊C4—3441no—
496C4⋊C4—1722no—
497C4⋊C4#1062190212yes—
498C22⋊C4—864no—
499C22⋊C4—862no—
500C22⋊C4—862no—
501C22⋊C4—3441no—
502C22⋊C4—3441no—
503C22⋊C4—3441no—
504C42—81no—
505C42—861no—
506C42—861no—
507C42—1722no—
508C42#1062189812yes—
509C42D4×D4312yes—
510C23—861no—
511C23—861no—
512C23—861no—
513C23—861no—
514C23—861no—
515C23—861no—
516C23—861no—
517C23C2×D4×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—22no—
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—41no—
537C2×C4—41no—
538C2×C4—41no—
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—1721no—
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—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4#1306329812yes—
565C2×C4#1306329812yes—
566C2×C4C2×D4×D4311yescharacteristic
567C2×C4#41×D4311yescharacteristic
568C2×C4C2×#1062189811yescharacteristic
569C2×C4C2×#1062190211yescharacteristic
570C2×C4#1306337211yescharacteristic
571C2×C4#1306337311yescharacteristic
572C8—41no—
573C8—41no—
574C8—862no—
575C8—862no—
576C22—1721no—
577C22—1721no—
578C22—1721no—
579C22—1721no—
580C22—1721no—
581C22—1721no—
582C22—1721no—
583C22C2×#1306329811yescharacteristic
584C22#1458341211yescharacteristic
585C22#1458347211yescharacteristic
586C22#1458370011yescharacteristic
587C22#1458370511yescharacteristic
588C22#1458371511yescharacteristic
589C22#1458371511yescharacteristic
590C4—22no—
591C4—22no—
592C4—42no—
593C4—81no—
594C4—81no—
595C4—81no—
596C4—3441no—
597C4—3441no—
598C4—3441no—
599C4—1721no—
600C4—1721no—
601C4—1721no—
602C4—1722no—
603C4#1458355211yescharacteristic
604C4#1458355711yescharacteristic
605C4#1458359011yescharacteristic
606C4#1458362211yescharacteristic
607C2—3441no—
608C2#1913802711yescharacteristic
609C2#1914424911yescharacteristic
610C2#1914427311yescharacteristic
611C2#1914483111yescharacteristic
612C2#1914486211yescharacteristic
613C2#1914587011yescharacteristic
614C2#1914587511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1988C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#1988D43
hypocenterC43#24714
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1988

Complements

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

NH ≅ G/Ntype
1. C2×#14583191C2semidirect
9. #19135363C2semidirect
10. #19135337C2semidirect
11. #19135327C2semidirect
12. #19135283C2semidirect
13. #19135269C2semidirect
14. #19134611C2semidirect
15. C43×#1988C2semidirect
308. #1988D43semidirect
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×#145829592
#191404172
#191372782
#191360272
#191360222
#191358012
#191357942
#191353632
#191353372
#191353272
#191352832
#191352692
#191346112
C43×#19882
#2471443