Finite Group Databasebeta

← #25154673

Subgroups — #25154673

Order 11008.

786 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139622C211yesmaximal, characteristic, complemented
2#19137543C211yesmaximal, characteristic
3#19135983C211yesmaximal, characteristic
4#19135981C211yesmaximal, characteristic
5#19135729C211yesmaximal, characteristic
6#19135548C211yesmaximal, characteristic, complemented
7#19135545C211yesmaximal, characteristic, complemented
8#19135352C211yesmaximal, characteristic, complemented
9#19135312C211yesmaximal, characteristic, complemented
10#19135167C211yesmaximal, characteristic, complemented
11#19135164C211yesmaximal, characteristic, complemented
12#19134721C211yesmaximal, characteristic, complemented
13#19134593C211yesmaximal, characteristic
14#102×Dic43C211yesmaximal, characteristic
15C43×#2023C211yesmaximal, characteristic
16C2×#13063324C2211yescharacteristic
17C2×#13063323—21no—
18C2×D4×Dic43C2211yescharacteristic
19C2×#13063281—21no—
20C2×#13063259C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23C2×Dic43⋊C8C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×C8×Dic43C2211yescharacteristic
28#14582819—21no—
29#14582818—21no—
30#14582802C2211yescharacteristic
31#14582797C2211yescharacteristic
32#14582795C2211yescharacteristic
33#14582794—21no—
34#14582793—21no—
35#14582787—21no—
36#14582768C2211yescharacteristic
37#14582768C2211yescharacteristic
38#14582757—21no—
39C4⋊C4×Dic43C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41C4×Dic43⋊C4C2211yescharacteristic
42C4×C4⋊Dic43C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×C4⋊Q8×C43C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C43×#390C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86—21no—
60C23×Dic43—21no—
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63#13063324—22no—
64#13063324—41no—
65#13063323—44no—
66D4×Dic43—22no—
67D4×Dic43Q814yescomplemented
68#13063281—44no—
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4D411yescharacteristic
81C2×Dic43⋊C4D411yescharacteristic
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43C2311yescharacteristic
89C2×C4×Dic43C2311yescharacteristic
90#13063259—22no—
91#13063258—22no—
92C4⋊(C43⋊C8)—41no—
93Dic43⋊C8—22no—
94Dic43⋊C8—41no—
95#13063246—22no—
96#13063246—41no—
97C8×Dic43—22no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95D411yescharacteristic
104C43⋊#95D411yescharacteristic
105C22×Q8×C43—21no—
106C22×D4×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C4⋊Q8×C43—22no—
110C4⋊Q8×C43—41no—
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×C42×C43C2311yescharacteristic
118#102×C43—22no—
119#102×C43—41no—
120C24×C43—21no—
121C2×Q8×C43—42no—
122C2×Q8×C43—42no—
123C2×Q8×C43—81no—
124C2×D4×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43C2×Q812yes—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2411yescharacteristic
136C22×Dic43—24no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—42no—
142C22×Dic43—42no—
143C22×Dic43C2×D411yescharacteristic
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C2×Dic86—42no—
148C2×Dic86—42no—
149C2×Dic86—81no—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—42no—
162C4⋊C4×C43#4112yes—
163C22⋊C4×C43—42no—
164C22⋊C4×C43—81no—
165C42×C43—21no—
166C42×C43—21no—
167C22⋊Dic43—24no—
168C22⋊Dic43—42no—
169C22⋊Dic43—81no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43C2×Q812yes—
177C4⋊Dic43#4112yes—
178Dic43⋊C4—22no—
179Dic43⋊C4—42no—
180Dic43⋊C4—42no—
181Dic43⋊C4—42no—
182Dic43⋊C4—42no—
183Dic43⋊C4—42no—
184Dic43⋊C4—81no—
185Dic43⋊C4—81no—
186Dic43⋊C4D814yes—
187C4×Dic43—21no—
188C4×Dic43—21no—
189C4×Dic43—42no—
190C4×Dic43—42no—
191C4×Dic43—42no—
192C4×Dic43C2×Q812yes—
193C4×Dic43#4112yes—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C23×C43—22no—
201C23×C43—41no—
202C23×C43—41no—
203C23×C43—41no—
204C23×C43—41no—
205C23×C43—41no—
206C23×C43—41no—
207C23×C43C22×D411yescharacteristic
208Q8×C43—84no—
209D4×C43—22no—
210D4×C43—22no—
211D4×C43—41no—
212D4×C43—41no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—22no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
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×C43C2×D812yes—
228C2×C4×C43C22×Q811yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C43H(5,𝔽2)11yescharacteristic
233C2×C4×C432−1+411yescharacteristic
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—22no—
239C2×Dic43—21no—
240C2×Dic43—22no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—48no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43C22⋊Q812yes—
255C2×Dic43C22⋊Q812yes—
256C2×Dic43C2×D812yes—
257C2×Dic43C2×D812yes—
258C2×Dic43#13712yes—
259Dic86—84no—
260C8×C43—41no—
261C8×C43—41no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264#26020—431nomaximal, Sylow
265C22×C43—42no—
266C22×C43—42no—
267C22×C43—42no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43—81no—
272C22×C43C2×C22⋊Q811yescharacteristic
273C22×C43#54611yescharacteristic
274C22×C43#54811yescharacteristic
275C22×C43C22×D811yescharacteristic
276C22×C43C2×#13711yescharacteristic
277C22×C43#57711yescharacteristic
278C22×C43#57711yescharacteristic
279C4×C43—22no—
280C4×C43—41no—
281C4×C43—42no—
282C4×C43—81no—
283C4×C43—81no—
284C4×C43#53311yescharacteristic
285C4×C43#54411yescharacteristic
286C4×C43#55511yescharacteristic
287C4×C43#55611yescharacteristic
288Dic43—22no—
289Dic43—22no—
290Dic43—41no—
291Dic43—42no—
292Dic43—42no—
293Dic43—81no—
294Dic43—81no—
295Dic43#47414yes—
296#2551—431no—
297#2354—431no—
298#2067—431no—
299#2067—431no—
300#2023—431no—
301#2023D4311yescharacteristic
302#1988—431no—
303#1988—431no—
304#1947—431no—
305#1939—431no—
306#1918—431no—
307#1918—431no—
308#1834—431no—
309#1802—431no—
310C4×#102—431no—
311C2×C43—82no—
312C2×C43#243911yescharacteristic
313C2×C43C2×#47411yescharacteristic
314C2×C43#308411yescharacteristic
315C2×C43#329411yescharacteristic
316C2×C43#332911yescharacteristic
317C2×C43#335811yescharacteristic
318C2×C43#336911yescharacteristic
319C2×C4⋊Q8—431no—
320C2×C4⋊Q8—861no—
321C2×C4⋊Q8C2×D4311yescharacteristic
322C2×C4×D4—431no—
323C2×#117—861no—
324C2×#107—431no—
325C2×#107—431no—
326C2×C4⋊C8—431no—
327C2×C4⋊C8—431no—
328C2×C4⋊C8—431no—
329C2×#102—431no—
330C2×#102—431no—
331C2×#102C2×D4311yescharacteristic
332C2×#102C2×D4311yescharacteristic
333C2×C4×C8—431no—
334#395—861no—
335#395—861no—
336#390—431no—
337#390C2×D4311yescharacteristic
338#389—431no—
339#389—431no—
340#389—861no—
341#388—861no—
342#388—861no—
343#384—431no—
344#384—431no—
345#380—861no—
346C4×C4⋊C4—431no—
347C4×C4⋊C4—431no—
348C4×C4⋊C4—431no—
349C4×C4⋊C4—431no—
350#340—431no—
351#340—431no—
352#340—431no—
353#340—431no—
354#340—431no—
355#340—431no—
356#340—431no—
357#340—431no—
358#340C2×D4311yescharacteristic
359#340C2×D4311yescharacteristic
360#336—431no—
361#336C2×D4311yescharacteristic
362C43#2602011yescharacteristic, complemented, Sylow
363C22×Q8—21no—
364C22×Q8—861no—
365C22×D4C22×D4311yescharacteristic
366C23×C4—861no—
367C22×C8—431no—
368C22×C8—431no—
369C22×C8C22×D4311yescharacteristic
370C22×C8C22×D4311yescharacteristic
371C4⋊Q8—22no—
372C4⋊Q8—41no—
373C4⋊Q8—862no—
374C4⋊Q8—1721no—
375C4⋊Q8—1724no—
376C4×D4—434no—
377C4×D4—862no—
378#117—1724no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—431no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—431no—
384C2×C4⋊C4—431no—
385C2×C4⋊C4—431no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4—861no—
389C2×C4⋊C4—861no—
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×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—861no—
399C2×C22⋊C4—861no—
400C2×C22⋊C4—861no—
401C2×C42—431no—
402C2×C42—431no—
403C2×C42—861no—
404C2×C42—861no—
405C2×C42—861no—
406C2×C42C22×D4311yescharacteristic
407#107—862no—
408#107—862no—
409C4⋊C8—862no—
410C4⋊C8—1721no—
411C4⋊C8—1721no—
412#102—22no—
413#102—41no—
414#102—862no—
415#102—1721no—
416C4×C8—862no—
417#95—431no—
418#95—431no—
419#95—861no—
420#95—861no—
421#95—861no—
422#95—861no—
423#95—861no—
424C24—21no—
425C2×Q8—42no—
426C2×Q8—42no—
427C2×Q8—81no—
428C2×Q8—3441no—
429C2×Q8—1722no—
430C2×Q8—1722no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4Q8×D4312yes—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—431no—
441C22×C4—431no—
442C22×C4—431no—
443C22×C4—431no—
444C22×C4—864no—
445C22×C4—861no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—861no—
449C22×C4—1722no—
450C22×C4—1722no—
451C22×C4D4×D4311yescharacteristic
452C22×C4D4×D4311yescharacteristic
453C22×C4C23×D4311yescharacteristic
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—42no—
472C4⋊C4—434no—
473C4⋊C4—432no—
474C4⋊C4—432no—
475C4⋊C4—862no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—3441no—
483C4⋊C4—3441no—
484C4⋊C4—1722no—
485C4⋊C4—1722no—
486C4⋊C4—1722no—
487C4⋊C4—1722no—
488C4⋊C4—1722no—
489C4⋊C4#1062190012yes—
490C22⋊C4—42no—
491C22⋊C4—81no—
492C22⋊C4—864no—
493C22⋊C4—3441no—
494C22⋊C4—1722no—
495C42—21no—
496C42—21no—
497C42—432no—
498C42—432no—
499C42—861no—
500C42—861no—
501C42—1722no—
502C42—1722no—
503C42—1722no—
504C23—22no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23C2×D4×D4311yescharacteristic
512Q8—84no—
513Q8—3444no—
514D4—22no—
515D4—22no—
516D4—41no—
517D4—41no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—432no—
533C2×C4—432no—
534C2×C4—432no—
535C2×C4—432no—
536C2×C4—432no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—862no—
542C2×C4—862no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—1728no—
547C2×C4—1721no—
548C2×C4—1721no—
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×C4D8×D4312yes—
558C2×C4C2×Q8×D4311yescharacteristic
559C2×C4#41×D4311yescharacteristic
560C2×C4#41×D4311yescharacteristic
561C2×C4C2×#1062190011yescharacteristic
562C2×C4#1306337011yescharacteristic
563C2×C4#1306337211yescharacteristic
564C8—41no—
565C8—41no—
566C8—1721no—
567C8—1721no—
568C22—42no—
569C22—42no—
570C22—42no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22C22⋊Q8×D4311yescharacteristic
576C22#1458353611yescharacteristic
577C22#1458355711yescharacteristic
578C22C2×D8×D4311yescharacteristic
579C22#137×D4311yescharacteristic
580C22#1458370511yescharacteristic
581C22#1458370911yescharacteristic
582C4—22no—
583C4—41no—
584C4—42no—
585C4—81no—
586C4—81no—
587C4—434no—
588C4—862no—
589C4—862no—
590C4—3441no—
591C4—3441no—
592C4—1721no—
593C4—1722no—
594C4—1722no—
595C4#1458345111yescharacteristic
596C4#1458352811yescharacteristic
597C4#1458361111yescharacteristic
598C4#1458361811yescharacteristic
599C2—82no—
600C2#1913827911yescharacteristic
601C2#474×D4311yescharacteristic
602C2#1914445211yescharacteristic
603C2#1914640111yescharacteristic
604C2#1914688211yescharacteristic
605C2#1914722711yescharacteristic
606C2#1914733211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2023C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2023D43
hypocenterC43#26020
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2023

Complements

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

NH ≅ G/Ntype
1. #19139622C2semidirect
6. #19135548C2semidirect
7. #19135545C2semidirect
8. #19135352C2semidirect
9. #19135312C2semidirect
10. #19135167C2semidirect
11. #19135164C2semidirect
12. #19134721C2semidirect
67. D4×Dic43Q8semidirect
362. C43#26020semidirect

Maximal subgroups

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

subgroupindex
#191396222
#191375432
#191359832
#191359812
#191357292
#191355482
#191355452
#191353522
#191353122
#191351672
#191351642
#191347212
#191345932
#102×Dic432
C43×#20232
#2602043