Finite Group Databasebeta

← #25159527

Subgroups — #25159527

Order 11008.

804 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583206C211yesmaximal, characteristic, complemented
2C2×#14582942C211yesmaximal, characteristic
3#19138319C211yesmaximal, characteristic
4#19136143C211yesmaximal, characteristic, complemented
5#19136091C211yesmaximal, characteristic, complemented
6#19135990C211yesmaximal, characteristic, complemented
7#19135933C211yesmaximal, characteristic, complemented
8#19135363C211yesmaximal, characteristic, complemented
9#19135173C211yesmaximal, characteristic, complemented
10#19135029C211yesmaximal, characteristic
11#19134903C211yesmaximal, characteristic
12#19134863C211yesmaximal, characteristic, complemented
13#19134794C211yesmaximal, characteristic
14#19134780C211yesmaximal, characteristic
15C43×#2362C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic
17C2×#13063317C2211yescharacteristic
18C22×C4⋊Dic43C2211yescharacteristic
19#14583206—24no—
20#14582942—24no—
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×#13063256C2211yescharacteristic
27C2×C4⋊(C43⋊C8)C2211yescharacteristic
28C2×C4⋊(C43⋊C8)C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34#14582841—21no—
35#14582833—21no—
36#14582797C2211yescharacteristic
37#14582797C2211yescharacteristic
38#14582771—21no—
39#14582765C2211yescharacteristic
40#14582759C2211yescharacteristic
41#14582757—21no—
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50C2×C22⋊Q8×C43C2211yescharacteristic
51C2×C4×Q8×C43C2211yescharacteristic
52C2×#117×C43C2211yescharacteristic
53C43×#391C2211yescharacteristic
54C43×#389C2211yescharacteristic
55C43×#388—21no—
56C43×#388—21no—
57C43×#387—21no—
58C4×C4⋊C4×C43—21no—
59C4×C4⋊C4×C43C2211yescharacteristic
60C4×C22⋊C4×C43C2211yescharacteristic
61C23×Dic43—21no—
62C2×#10621877—22no—
63C2×#10621877—22no—
64C2×#10621877—22no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063317—22no—
70#13063317—41no—
71C2×C4⋊Dic43—22no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—41no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×C22⋊Dic43—21no—
83#13063258—22no—
84#13063258—22no—
85#13063258—22no—
86#13063256—22no—
87#13063256—41no—
88#13063256D414yes—
89C4⋊(C43⋊C8)—22no—
90C4⋊(C43⋊C8)—22no—
91#13063249—22no—
92#13063249—22no—
93#13063249—22no—
94#13063249—41no—
95C22⋊(C43⋊C8)—22no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C22×Q8×C43C2311yescharacteristic
102C23×C4×C43C2311yescharacteristic
103C22⋊Q8×C43—22no—
104C22⋊Q8×C43Q814yes—
105C4×Q8×C43—22no—
106C4×Q8×C43—41no—
107#117×C43—22no—
108#117×C43—41no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43D411yescharacteristic
118C2×C22⋊C4×C43D411yescharacteristic
119C2×C42×C43—21no—
120C2×C42×C43—21no—
121C2×C42×C43—21no—
122C2×C42×C43C2311yescharacteristic
123C2×C42×C43C2311yescharacteristic
124#95×C43—21no—
125#95×C43—21no—
126#95×C43—21no—
127#95×C43—21no—
128#95×C43D411yescharacteristic
129#95×C43D411yescharacteristic
130C24×C43C2×D411yescharacteristic
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43C2×Q812yes—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×Q812yes—
151C22×C4×C43#4112yes—
152C22×C4×C43C2411yescharacteristic
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—42no—
158C22×Dic43—42no—
159C22×Dic43—81no—
160C4⋊C4×C43—24no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—42no—
166C4⋊C4×C43—42no—
167C4⋊C4×C43C2×D412yes—
168C4⋊C4×C43C2×Q812yes—
169C22⋊C4×C43—24no—
170C22⋊C4×C43—41no—
171C22⋊C4×C43—41no—
172C22⋊C4×C43—42no—
173C42×C43—21no—
174C42×C43—21no—
175C42×C43—21no—
176C42×C43—21no—
177C42×C43—42no—
178C42×C43—42no—
179C42×C43—42no—
180C22⋊Dic43—42no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—42no—
189C4⋊Dic43C2×D412yes—
190Dic43⋊C4—42no—
191Dic43⋊C4—42no—
192Dic43⋊C4—81no—
193Dic43⋊C4—81no—
194#10621877—28no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8C2×D412yes—
206C2×C43⋊C8#4112yes—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43C22⋊Q812yes—
214C23×C43C22×D411yescharacteristic
215Q8×C43—22no—
216Q8×C43—22no—
217Q8×C43—41no—
218Q8×C43—41no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—22no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—22no—
225C2×C4×C43—22no—
226C2×C4×C43—22no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—22no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43C22⋊Q812yes—
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C22×Q811yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43H(5,𝔽2)11yescharacteristic
255C2×C4×C432−1+411yescharacteristic
256C2×Dic43—22no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—84no—
269C43⋊C8—22no—
270C43⋊C8—22no—
271C43⋊C8—41no—
272C43⋊C8—41no—
273#26367—431nomaximal, Sylow
274C22×C43—22no—
275C22×C43—22no—
276C22×C43—22no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43C2×C22⋊Q811yescharacteristic
282C22×C43D4211yescharacteristic
283C22×C43#54711yescharacteristic
284C22×C43#57511yescharacteristic
285C22×C43#57511yescharacteristic
286C22×C43#57711yescharacteristic
287C22×C43#57811yescharacteristic
288C4×C43—22no—
289C4×C43—42no—
290C4×C43—41no—
291C4×C43—41no—
292C4×C43—42no—
293C4×C43—41no—
294C4×C43—42no—
295C4×C43—41no—
296C4×C43—81no—
297C4×C43#52511yescharacteristic
298C4×C43#53911yescharacteristic
299C4×C43D4×Q811yescharacteristic
300C4×C43#55411yescharacteristic
301Dic43—42no—
302Dic43—81no—
303Dic43—81no—
304Dic43—81no—
305C2×#479—431no—
306C2×#428—431no—
307#2442—431no—
308#2362D4311yescharacteristic
309#2097—431no—
310#2087—431no—
311#2068—431no—
312#2059—431no—
313#1949—431no—
314#1919—431no—
315#1894—431no—
316#1872—431no—
317#1865—431no—
318#1854—431no—
319#1851—431no—
320C2×C43—42no—
321C2×C43#244911yescharacteristic
322C2×C43#308011yescharacteristic
323C2×C43#308211yescharacteristic
324C2×C43#326911yescharacteristic
325C2×C43#327511yescharacteristic
326C2×C43#334911yescharacteristic
327C2×C43#335111yescharacteristic
328C22×M16—431no—
329C2×#125—431no—
330C2×C22⋊Q8C2×D4311yescharacteristic
331C2×C4×Q8C2×D4311yescharacteristic
332C2×#117C2×D4311yescharacteristic
333C22×C4⋊C4—431no—
334#479—864no—
335#428—864no—
336C2×#107—431no—
337C2×#107—431no—
338C2×#107—431no—
339C2×#106—431no—
340C2×#106—431no—
341C2×#106—431no—
342C2×C4⋊C8—431no—
343C2×C4⋊C8—431no—
344C2×#103—431no—
345C2×#103—431no—
346C2×#103—431no—
347C2×#103—431no—
348C2×C22⋊C8—431no—
349#400—861no—
350#398—861no—
351#391C2×D4311yescharacteristic
352#389—431no—
353#389—431no—
354#389C2×D4311yescharacteristic
355#388—21no—
356#388—21no—
357#387—21no—
358#385—861no—
359#382—431no—
360#380—431no—
361#380—861no—
362C4×C4⋊C4—21no—
363C4×C4⋊C4C2×D4311yescharacteristic
364C4×C22⋊C4C2×D4311yescharacteristic
365#340—431no—
366#340—431no—
367#340—431no—
368#340—431no—
369#340—431no—
370#340—431no—
371#336—431no—
372#336—431no—
373C43#2636711yescharacteristic, complemented, Sylow
374C22×Q8C22×D4311yescharacteristic
375C23×C4—861no—
376C23×C4C22×D4311yescharacteristic
377C2×M16—862no—
378C2×M16—862no—
379C2×M16—862no—
380C22×C8—431no—
381C22×C8—431no—
382C22×C8—431no—
383C22×C8—431no—
384#125—862no—
385#125—1721no—
386C22⋊Q8—22no—
387C22⋊Q8Dic8614yes—
388C4×Q8—22no—
389C4×Q8—41no—
390#117—22no—
391#117—41no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—862no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—1721no—
406C2×C4⋊C4C22×D4311yescharacteristic
407C2×C4⋊C4C22×D4311yescharacteristic
408C2×C4⋊C4C22×D4311yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—861no—
412C2×C22⋊C4C22⋊D4311yescharacteristic
413C2×C22⋊C4C22⋊D4311yescharacteristic
414C2×C42—21no—
415C2×C42—21no—
416C2×C42—21no—
417C2×C42C22×D4311yescharacteristic
418C2×C42C22×D4311yescharacteristic
419#107—862no—
420#107—862no—
421#107—862no—
422#106—434no—
423#106—862no—
424#106—1721no—
425C4⋊C8—862no—
426C4⋊C8—862no—
427#103—862no—
428#103—862no—
429#103—862no—
430#103—1721no—
431C22⋊C8—862no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—861no—
437#95—861no—
438#95—861no—
439#95—861no—
440#95—861no—
441#95C22⋊D4311yescharacteristic
442#95C22⋊D4311yescharacteristic
443C24C2×C22⋊D4311yescharacteristic
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8C2×Dic8612yes—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—3441no—
463C22×C4—1722no—
464C22×C4—1722no—
465C22×C4C2×Dic8612yes—
466C22×C4#1062189812yes—
467C22×C4C2×C22⋊D4311yescharacteristic
468C22×C4C2×C22⋊D4311yescharacteristic
469C22×C4C2×C22⋊D4311yescharacteristic
470C22×C4C2×C22⋊D4311yescharacteristic
471C22×C4C2×C22⋊D4311yescharacteristic
472C22×C4C23×D4311yescharacteristic
473M16—868no—
474C2×C8—432no—
475C2×C8—432no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8—861no—
486C4⋊C4—24no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—42no—
492C4⋊C4—42no—
493C4⋊C4—432no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—3441no—
502C4⋊C4—3441no—
503C4⋊C4—1722no—
504C4⋊C4—1722no—
505C4⋊C4—1722no—
506C4⋊C4C2×Dic8612yes—
507C4⋊C4D4×D4312yes—
508C22⋊C4—24no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—42no—
512C22⋊C4—1722no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—21no—
517C42—42no—
518C42—42no—
519C42—42no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23#1306330412yes—
527C23C22×C22⋊D4311yescharacteristic
528Q8—22no—
529Q8—22no—
530Q8—41no—
531Q8—41no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—862no—
563C2×C4—3444no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4#1306330412yes—
576C2×C4C2×D4×D4311yescharacteristic
577C2×C4C22×Dic8611yescharacteristic
578C2×C4#41×D4311yescharacteristic
579C2×C4C2×#1062189811yescharacteristic
580C2×C4#1306337011yescharacteristic
581C2×C4#1306337211yescharacteristic
582C8—862no—
583C8—862no—
584C8—1721no—
585C8—1721no—
586C22—22no—
587C22—22no—
588C22—22no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22C2×#1306330411yescharacteristic
594C22D4×C22⋊D4311yescharacteristic
595C22#1458354811yescharacteristic
596C22#1458369711yescharacteristic
597C22#1458369711yescharacteristic
598C22#1458370711yescharacteristic
599C22#1458371411yescharacteristic
600C4—22no—
601C4—42no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—42no—
606C4—42no—
607C4—41no—
608C4—81no—
609C4—3441no—
610C4—3441no—
611C4—3441no—
612C4—1722no—
613C4#1458340811yescharacteristic
614C4#1458349111yescharacteristic
615C4D4×Dic8611yescharacteristic
616C4#1458360811yescharacteristic
617C2—42no—
618C2#1913839811yescharacteristic
619C2#1914441711yescharacteristic
620C2#1914443711yescharacteristic
621C2#1914614611yescharacteristic
622C2#1914622711yescharacteristic
623C2#1914711911yescharacteristic
624C2#1914715511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2362C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#2362D43
hypocenterC43#26367
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2362

Complements

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

NH ≅ G/Ntype
1. C2×#14583206C2semidirect
4. #19136143C2semidirect
5. #19136091C2semidirect
6. #19135990C2semidirect
7. #19135933C2semidirect
8. #19135363C2semidirect
9. #19135173C2semidirect
12. #19134863C2semidirect
373. C43#26367semidirect

Maximal subgroups

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

subgroupindex
C2×#145832062
C2×#145829422
#191383192
#191361432
#191360912
#191359902
#191359332
#191353632
#191351732
#191350292
#191349032
#191348632
#191347942
#191347802
C43×#23622
#2636743