Finite Group Databasebeta

← #25146672

Subgroups — #25146672

Order 11008.

840 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583258C211yesmaximal, characteristic
2C2×#14583118C211yesmaximal, characteristic
3#19139803C211yesmaximal, characteristic, complemented
4#19136003C211yesmaximal, characteristic, complemented
5#19135998C211yesmaximal, characteristic
6#19135917C211yesmaximal, characteristic, complemented
7#19135912C211yesmaximal, characteristic
8#19135547C211yesmaximal, characteristic, complemented
9#19135319C211yesmaximal, characteristic, complemented
10#19134936C211yesmaximal, characteristic, complemented
11#19134929C211yesmaximal, characteristic
12#19134600C211yesmaximal, characteristic, complemented
13#19134595C211yesmaximal, characteristic
14#19134428C211yesmaximal, characteristic, complemented
15C43×#2367C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C2×#13063325C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20#14583258—24no—
21#14583118—24no—
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23C2×C4⋊(C43⋊C8)C2211yescharacteristic
24C2×C4⋊(C43⋊C8)C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063236C2211yescharacteristic
34#14582820—21no—
35#14582820—21no—
36#14582805C2211yescharacteristic
37#14582805C2211yescharacteristic
38#14582798—21no—
39#14582798—21no—
40#14582769C2211yescharacteristic
41#14582769C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50C2×#124×C43C2211yescharacteristic
51C2×C4×Q8×C43C2211yescharacteristic
52C2×C4×D4×C43C2211yescharacteristic
53C43×#391C2211yescharacteristic
54C43×#390C2211yescharacteristic
55C43×#388—21no—
56C43×#388—21no—
57C43×#385—21no—
58C4×C4⋊C4×C43C2211yescharacteristic
59C4×C4⋊C4×C43C2211yescharacteristic
60C4×C22⋊C4×C43—21no—
61C22×Dic86—21no—
62C22×Dic86C2311yescharacteristic
63C2×#10621885—22no—
64C2×#10621885—22no—
65C2×#10621885—41no—
66C2×#10621883—22no—
67C2×#10621883—22no—
68C2×#10621883—41no—
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063325—22no—
74#13063325—22no—
75C4×Dic86—22no—
76C4×Dic86—22no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43—21no—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×Dic43⋊C4—21no—
86C2×C4×Dic43—21no—
87C4⋊(C43⋊C8)—22no—
88C4⋊(C43⋊C8)—41no—
89C4⋊(C43⋊C8)—41no—
90#13063249—22no—
91#13063249—22no—
92#13063249—22no—
93#13063248—22no—
94#13063248—22no—
95#13063246—22no—
96#13063246—22no—
97#13063246—22no—
98#13063236—22no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C22×Q8×C43C2311yescharacteristic
104C22×D4×C43C2311yescharacteristic
105C23×C4×C43—21no—
106#124×C43—22no—
107#124×C43D414yes—
108C4×Q8×C43—22no—
109C4×Q8×C43—41no—
110C4×D4×C43—22no—
111C4×D4×C43—41no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43D411yescharacteristic
114C2×C4⋊C4×C43D411yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C22⋊C4×C43—21no—
118C2×C22⋊C4×C43—21no—
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C42×C43—21no—
123C2×C42×C43—21no—
124C2×C42×C43C2311yescharacteristic
125C2×C42×C43C2311yescharacteristic
126C2×C42×C43C2311yescharacteristic
127#95×C43—21no—
128#95×C43—21no—
129#95×C43—21no—
130#95×C43D411yescharacteristic
131#95×C43D411yescharacteristic
132C24×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43C2×D412yes—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43C2×D412yes—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—42no—
149C22×C4×C43—42no—
150C22×C4×C43—81no—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2411yescharacteristic
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—42no—
168C2×Dic86—81no—
169C2×Dic86—81no—
170C2×Dic86#4112yes—
171C4⋊C4×C43—22no—
172C4⋊C4×C43—22no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—42no—
177C4⋊C4×C43#4112yes—
178C22⋊C4×C43—24no—
179C22⋊C4×C43—24no—
180C22⋊C4×C43—42no—
181C22⋊C4×C43—42no—
182C22⋊C4×C43—81no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43—21no—
187C42×C43—42no—
188C42×C43—81no—
189C42×C43C2×D412yes—
190C42×C43#4112yes—
191#10621885—44no—
192#10621883—44no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—42no—
200C4⋊Dic43—81no—
201C4⋊Dic43—81no—
202C4⋊Dic43—81no—
203C4⋊Dic43—81no—
204Dic43⋊C4—42no—
205C4×Dic43—42no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
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—22no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43C22×D411yescharacteristic
226Q8×C43—22no—
227Q8×C43—22no—
228Q8×C43—41no—
229Q8×C43—41no—
230D4×C43—22no—
231D4×C43—22no—
232D4×C43—41no—
233D4×C43—41no—
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—21no—
241C2×C4×C43—21no—
242C2×C4×C43—22no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—22no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—84no—
258C2×C4×C43#12112yes—
259C2×C4×C43#12112yes—
260C2×C4×C43#13712yes—
261C2×C4×C43#13712yes—
262C2×C4×C43C22×D411yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43H(5,𝔽2)11yescharacteristic
267C2×C4×C432−1+411yescharacteristic
268C2×Dic43—22no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280Dic86—22no—
281Dic86—22no—
282Dic86—41no—
283Dic86—41no—
284Dic86—84no—
285C43⋊C8—41no—
286C43⋊C8—41no—
287C43⋊C8—41no—
288C43⋊C8—41no—
289#25336—431nomaximal, Sylow
290C22×C43—42no—
291C22×C43—42no—
292C22×C43—42no—
293C22×C43—81no—
294C22×C43—81no—
295C22×C43—81no—
296C22×C43—81no—
297C22×C43C2×#12111yescharacteristic
298C22×C43#54611yescharacteristic
299C22×C43#54811yescharacteristic
300C22×C43C2×#13711yescharacteristic
301C22×C43C2×#13711yescharacteristic
302C22×C43#57611yescharacteristic
303C22×C43#57711yescharacteristic
304C4×C43—22no—
305C4×C43—22no—
306C4×C43—22no—
307C4×C43—22no—
308C4×C43—42no—
309C4×C43—41no—
310C4×C43—42no—
311C4×C43—41no—
312C4×C43—81no—
313C4×C43#52911yescharacteristic
314C4×C43#54211yescharacteristic
315C4×C43#54611yescharacteristic
316C4×C43#54711yescharacteristic
317Dic43—42no—
318Dic43—81no—
319Dic43—81no—
320Dic43—81no—
321C2×#489—431no—
322C2×#464—431no—
323#2567—431no—
324#2367D4311yescharacteristic
325#2072—431no—
326#2071—431no—
327#2056—431no—
328#2055—431no—
329#1988—431no—
330#1940—431no—
331#1878—431no—
332#1877—431no—
333#1803—431no—
334#1802—431no—
335#1763—431no—
336C2×C43—82no—
337C2×C43#242711yescharacteristic
338C2×C43#303911yescharacteristic
339C2×C43#304511yescharacteristic
340C2×C43#331411yescharacteristic
341C2×C43#331611yescharacteristic
342C2×C43#336911yescharacteristic
343C2×C43#337511yescharacteristic
344C22×Q16—431no—
345C22×SD16—431no—
346C2×C4⋊Q8—431no—
347C2×#124C2×D4311yescharacteristic
348C2×C4×Q8—431no—
349C2×C4×Q8C2×D4311yescharacteristic
350C2×C4×D4C2×D4311yescharacteristic
351#489—864no—
352#464—864no—
353C2×C4⋊C8—431no—
354C2×C4⋊C8—431no—
355C2×C4⋊C8—431no—
356C2×#103—431no—
357C2×#103—431no—
358C2×#103—431no—
359C2×#103—431no—
360C2×#103—431no—
361C2×#102—431no—
362C2×#102—431no—
363C2×#102—431no—
364C2×#97—431no—
365#395—861no—
366#395—861no—
367#391—431no—
368#391—431no—
369#391C2×D4311yescharacteristic
370#390C2×D4311yescharacteristic
371#389—861no—
372#389—861no—
373#388—21no—
374#388—21no—
375#385—21no—
376#384—431no—
377#384—431no—
378C4×C4⋊C4C2×D4311yescharacteristic
379C4×C4⋊C4C2×D4311yescharacteristic
380C4×C22⋊C4—21no—
381#340—431no—
382#340—431no—
383#340—431no—
384#340—431no—
385#340—431no—
386#340—431no—
387#336—431no—
388#336—431no—
389C43#2533611yescharacteristic, complemented, Sylow
390C22×Q8—431no—
391C22×Q8—861no—
392C22×Q8C22×D4311yescharacteristic
393C22×D4C22×D4311yescharacteristic
394C23×C4—21no—
395C2×Q16—862no—
396C2×Q16—862no—
397C2×Q16—1721no—
398C2×SD16—862no—
399C2×SD16—862no—
400C2×SD16—1721no—
401C22×C8—431no—
402C22×C8—431no—
403C22×C8—431no—
404C22×C8—431no—
405C4⋊Q8—862no—
406C4⋊Q8—862no—
407#124—22no—
408#124D17214yes—
409C4×Q8—22no—
410C4×Q8—41no—
411C4×Q8—862no—
412C4×Q8—862no—
413C4×D4—22no—
414C4×D4—41no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4C22⋊D4311yescharacteristic
426C2×C4⋊C4C22⋊D4311yescharacteristic
427C2×C4⋊C4C22×D4311yescharacteristic
428C2×C4⋊C4C22×D4311yescharacteristic
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C42—21no—
435C2×C42—21no—
436C2×C42—861no—
437C2×C42C22×D4311yescharacteristic
438C2×C42C22×D4311yescharacteristic
439C2×C42C22×D4311yescharacteristic
440C4⋊C8—862no—
441C4⋊C8—1721no—
442C4⋊C8—1721no—
443#103—862no—
444#103—862no—
445#103—862no—
446#103—862no—
447#103—862no—
448#102—862no—
449#102—862no—
450#102—862no—
451#97—862no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—861no—
456#95—861no—
457#95—861no—
458#95—861no—
459#95C22⋊D4311yescharacteristic
460#95C22⋊D4311yescharacteristic
461C24—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—432no—
468C2×Q8—861no—
469C2×Q8—861no—
470C2×Q8—861no—
471C2×Q8—861no—
472C2×Q8—861no—
473C2×Q8—3441no—
474C2×Q8—3441no—
475C2×Q8—1722no—
476C2×Q8C2×D17212yes—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4C2×D17212yes—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—81no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4C2×C22⋊D4311yescharacteristic
494C22×C4C2×C22⋊D4311yescharacteristic
495C22×C4C2×C22⋊D4311yescharacteristic
496C22×C4C2×C22⋊D4311yescharacteristic
497C22×C4C2×C22⋊D4311yescharacteristic
498C22×C4C2×C22⋊D4311yescharacteristic
499C22×C4C23×D4311yescharacteristic
500Q16—1724no—
501SD16—1724no—
502C2×C8—861no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—42no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—3441no—
527C4⋊C4—3441no—
528C4⋊C4—3441no—
529C4⋊C4—3441no—
530C4⋊C4—1722no—
531C4⋊C4—1722no—
532C4⋊C4#1062190012yes—
533C22⋊C4—24no—
534C22⋊C4—24no—
535C22⋊C4—42no—
536C22⋊C4—42no—
537C22⋊C4—81no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—42no—
543C42—81no—
544C42—1722no—
545C42C2×D17212yes—
546C42#1062189812yes—
547C23—22no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23C22×C22⋊D4311yescharacteristic
555Q8—22no—
556Q8—22no—
557Q8—41no—
558Q8—41no—
559Q8—862no—
560Q8—862no—
561Q8—3444no—
562Q8—1721no—
563Q8—1721no—
564D4—22no—
565D4—22no—
566D4—41no—
567D4—41no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—84no—
592C2×C4—862no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4#1306329912yes—
605C2×C4#1306329912yes—
606C2×C4#1306335512yes—
607C2×C4#1306335512yes—
608C2×C4C22×D17211yescharacteristic
609C2×C4#41×D4311yescharacteristic
610C2×C4C2×#1062190011yescharacteristic
611C2×C4C2×#1062189811yescharacteristic
612C2×C4#1306337011yescharacteristic
613C2×C4#1306337211yescharacteristic
614C8—1721no—
615C8—1721no—
616C8—1721no—
617C8—1721no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—81no—
622C22—81no—
623C22—81no—
624C22—81no—
625C22C2×#1306329911yescharacteristic
626C22#1458354311yescharacteristic
627C22#1458355611yescharacteristic
628C22C2×#1306335511yescharacteristic
629C22C2×#1306335511yescharacteristic
630C22#1458370211yescharacteristic
631C22#1458370711yescharacteristic
632C4—22no—
633C4—22no—
634C4—22no—
635C4—22no—
636C4—42no—
637C4—41no—
638C4—42no—
639C4—41no—
640C4—81no—
641C4—3441no—
642C4—3441no—
643C4—3441no—
644C4—1722no—
645C4#1458343111yescharacteristic
646C4#1458351411yescharacteristic
647C4#1458354411yescharacteristic
648C4#1458355311yescharacteristic
649C2—82no—
650C2#1913816611yescharacteristic
651C2#1914408211yescharacteristic
652C2#1914413411yescharacteristic
653C2#1914667611yescharacteristic
654C2#1914670611yescharacteristic
655C2#1914733111yescharacteristic
656C2#1914740511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2367C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2367D43
hypocenterC43#25336
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2367

Complements

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

NH ≅ G/Ntype
3. #19139803C2semidirect
4. #19136003C2semidirect
6. #19135917C2semidirect
8. #19135547C2semidirect
9. #19135319C2semidirect
10. #19134936C2semidirect
12. #19134600C2semidirect
14. #19134428C2semidirect
389. C43#25336semidirect

Maximal subgroups

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

subgroupindex
C2×#145832582
C2×#145831182
#191398032
#191360032
#191359982
#191359172
#191359122
#191355472
#191353192
#191349362
#191349292
#191346002
#191345952
#191344282
C43×#23672
#2533643