Finite Group Databasebeta

← #25155414

Subgroups — #25155414

Order 11008.

774 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
1C2×#14583298C211yesmaximal, characteristic, complemented
2C2×#14582942C211yesmaximal, characteristic
3#19138319C211yesmaximal, characteristic
4#19136076C211yesmaximal, characteristic, complemented
5#19136072C211yesmaximal, characteristic, complemented
6#19135933C211yesmaximal, characteristic, complemented
7#19135930C211yesmaximal, characteristic, complemented
8#19135330C211yesmaximal, characteristic, complemented
9#19135320C211yesmaximal, characteristic, complemented
10#19134794C211yesmaximal, characteristic
11#19134787C211yesmaximal, characteristic
12#19134761C211yesmaximal, characteristic, complemented
13#19134626C211yesmaximal, characteristic
14#19134379C211yesmaximal, characteristic
15C43×#2441C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic
17C2×#13063317C2211yescharacteristic
18C22×C4⋊Dic43C2211yescharacteristic
19#14583298—24no—
20#14582942—24no—
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063258C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×#13063256C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×#13063256C2211yescharacteristic
29C2×#13063256C2211yescharacteristic
30C2×#13063256C2211yescharacteristic
31C2×C22⋊(C43⋊C8)C2211yescharacteristic
32C2×#13063236C2211yescharacteristic
33C2×C4×C43⋊C8C2211yescharacteristic
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×#125×C43C2211yescharacteristic
51C2×#117×C43C2211yescharacteristic
52C43×#399—21no—
53C43×#396—21no—
54C43×#389—21no—
55C43×#389C2211yescharacteristic
56C43×#389C2211yescharacteristic
57C43×#387—21no—
58C43×#384C2211yescharacteristic
59C43×#380C2211yescharacteristic
60C4×C22⋊C4×C43C2211yescharacteristic
61C23×Dic43—21no—
62C2×#10621877—22no—
63C2×#10621877—22no—
64C2×#10621877Q814yes—
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—41no—
86#13063258D414yes—
87#13063256—22no—
88#13063256—22no—
89#13063256—22no—
90#13063256—22no—
91#13063256—22no—
92#13063256—41no—
93C22⋊(C43⋊C8)Q814yes—
94#13063236—22no—
95C4×C43⋊C8—22no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C23×C4×C43C2311yescharacteristic
102#125×C43—22no—
103#125×C43—41no—
104#117×C43—22no—
105#117×C43—41no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43—21no—
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×C4⋊C4×C43C2311yescharacteristic
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—21no—
118C2×C22⋊C4×C43D411yescharacteristic
119C2×C22⋊C4×C43D411yescharacteristic
120C2×C42×C43—21no—
121C2×C42×C43C2311yescharacteristic
122C2×C42×C43C2311yescharacteristic
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126#95×C43D411yescharacteristic
127#95×C43D411yescharacteristic
128C24×C43C2×D411yescharacteristic
129C22×C4×C43—21no—
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×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×Q812yes—
143C22×C4×C43C2×Q812yes—
144C22×C4×C43C2411yescharacteristic
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—42no—
150C22×Dic43—42no—
151C22×Dic43—81no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—42no—
160C4⋊C4×C43—42no—
161C4⋊C4×C43—42no—
162C4⋊C4×C43—42no—
163C4⋊C4×C43—81no—
164C4⋊C4×C43—81no—
165C4⋊C4×C43C2×D412yes—
166C22⋊C4×C43—41no—
167C22⋊C4×C43—41no—
168C22⋊C4×C43—42no—
169C22⋊C4×C43—81no—
170C42×C43—21no—
171C42×C43—21no—
172C42×C43—21no—
173C42×C43—21no—
174C42×C43—42no—
175C22⋊Dic43—42no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—42no—
184C4⋊Dic43C2×D412yes—
185Dic43⋊C4—42no—
186Dic43⋊C4—42no—
187Dic43⋊C4—81no—
188Dic43⋊C4—81no—
189#10621877—28no—
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⋊C8C2×D412yes—
197C2×C43⋊C8C2×Q812yes—
198C2×C43⋊C8C2×Q812yes—
199C2×C43⋊C8C2×Q812yes—
200C2×C43⋊C8C2×Q812yes—
201C2×C43⋊C8#4112yes—
202C23×C43—21no—
203C23×C43—21no—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43C4⋊Q812yes—
209C23×C43C22×D411yescharacteristic
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—22no—
213C2×C4×C43—22no—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—22no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
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×C43C4⋊Q812yes—
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43C22×Q811yescharacteristic
243C2×C4×C43C22×Q811yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43H(5,𝔽2)11yescharacteristic
246C2×C4×C432−1+411yescharacteristic
247C2×Dic43—22no—
248C2×Dic43—41no—
249C2×Dic43—41no—
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—84no—
260C43⋊C8—22no—
261C43⋊C8—22no—
262C43⋊C8—22no—
263C43⋊C8C22⋊Q814yes—
264#26075—431nomaximal, Sylow
265C22×C43—22no—
266C22×C43—22no—
267C22×C43—22no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43C2×C4⋊Q811yescharacteristic
273C22×C43D4211yescharacteristic
274C22×C43#54711yescharacteristic
275C22×C43#57511yescharacteristic
276C22×C43#57511yescharacteristic
277C22×C43#57711yescharacteristic
278C22×C43#57711yescharacteristic
279C4×C43—22no—
280C4×C43—41no—
281C4×C43—41no—
282C4×C43—41no—
283C4×C43—42no—
284C4×C43—41no—
285C4×C43—81no—
286C4×C43—81no—
287C4×C43—81no—
288C4×C43C2×C22⋊Q811yescharacteristic
289C4×C43#54411yescharacteristic
290C4×C43D4×Q811yescharacteristic
291C4×C43#55411yescharacteristic
292Dic43—42no—
293Dic43—81no—
294Dic43—81no—
295Dic43—81no—
296C2×#499—431no—
297C2×#428—431no—
298#2442—431no—
299#2441D4311yescharacteristic
300#2085—431no—
301#2084—431no—
302#2059—431no—
303#2059—431no—
304#1943—431no—
305#1941—431no—
306#1854—431no—
307#1853—431no—
308#1847—431no—
309#1809—431no—
310#1753—431no—
311C2×C43—42no—
312C2×C43#244011yescharacteristic
313C2×C43#316311yescharacteristic
314C2×C43#316611yescharacteristic
315C2×C43#326711yescharacteristic
316C2×C43#327111yescharacteristic
317C2×C43#335111yescharacteristic
318C2×C43#335111yescharacteristic
319C22×M16—431no—
320C2×#125—431no—
321C2×#125C2×D4311yescharacteristic
322C2×#117C2×D4311yescharacteristic
323C22×C4⋊C4—431no—
324#499—864no—
325#428—864no—
326C2×#107—431no—
327C2×#107—431no—
328C2×#107—431no—
329C2×#107—431no—
330C2×#106—431no—
331C2×#106—431no—
332C2×#106—431no—
333C2×#106—431no—
334C2×#106—431no—
335C2×#106—431no—
336C2×C22⋊C8—431no—
337C2×#97—431no—
338C2×C4×C8—431no—
339#400—861no—
340#399—21no—
341#398—861no—
342#396—21no—
343#389—21no—
344#389—431no—
345#389—431no—
346#389C2×D4311yescharacteristic
347#389C2×D4311yescharacteristic
348#387—21no—
349#385—861no—
350#384C2×D4311yescharacteristic
351#382—431no—
352#380—431no—
353#380—861no—
354#380C2×D4311yescharacteristic
355C4×C22⋊C4C2×D4311yescharacteristic
356#340—431no—
357#340—431no—
358#340—431no—
359#340—431no—
360#340—431no—
361#340—431no—
362#336—431no—
363#336—431no—
364C43#2607511yescharacteristic, complemented, Sylow
365C23×C4—861no—
366C23×C4C22×D4311yescharacteristic
367C2×M16—434no—
368C2×M16—862no—
369C2×M16—862no—
370C22×C8—431no—
371C22×C8—431no—
372C22×C8—431no—
373C22×C8—431no—
374#125—22no—
375#125—41no—
376#125—862no—
377#125—1721no—
378#117—22no—
379#117—41no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—431no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—862no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—1721no—
397C2×C4⋊C4C22×D4311yescharacteristic
398C2×C4⋊C4C22×D4311yescharacteristic
399C2×C4⋊C4C22×D4311yescharacteristic
400C2×C4⋊C4C22×D4311yescharacteristic
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—861no—
404C2×C22⋊C4C22⋊D4311yescharacteristic
405C2×C22⋊C4C22⋊D4311yescharacteristic
406C2×C42—21no—
407C2×C42C22×D4311yescharacteristic
408C2×C42C22×D4311yescharacteristic
409#107—434no—
410#107—862no—
411#107—862no—
412#107—1721no—
413#106—862no—
414#106—862no—
415#106—862no—
416#106—862no—
417#106—862no—
418#106—1721no—
419C22⋊C8—434no—
420#97—862no—
421C4×C8—862no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—861no—
426#95—861no—
427#95—861no—
428#95—861no—
429#95—861no—
430#95C22⋊D4311yescharacteristic
431#95C22⋊D4311yescharacteristic
432C24C2×C22⋊D4311yescharacteristic
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4—861no—
444C22×C4—861no—
445C22×C4—3441no—
446C22×C4—1722no—
447C22×C4—1722no—
448C22×C4Q8×D4312yes—
449C22×C4Q8×D4312yes—
450C22×C4C2×C22⋊D4311yescharacteristic
451C22×C4C2×C22⋊D4311yescharacteristic
452C22×C4C2×C22⋊D4311yescharacteristic
453C22×C4C2×C22⋊D4311yescharacteristic
454C22×C4C2×C22⋊D4311yescharacteristic
455C22×C4C23×D4311yescharacteristic
456M16—868no—
457C2×C8—432no—
458C2×C8—432no—
459C2×C8—432no—
460C2×C8—432no—
461C2×C8—432no—
462C2×C8—432no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—861no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—42no—
477C4⋊C4—42no—
478C4⋊C4—42no—
479C4⋊C4—42no—
480C4⋊C4—81no—
481C4⋊C4—81no—
482C4⋊C4—432no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—3441no—
491C4⋊C4—3441no—
492C4⋊C4—1722no—
493C4⋊C4—1722no—
494C4⋊C4—1722no—
495C4⋊C4D4×D4312yes—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—42no—
499C22⋊C4—81no—
500C22⋊C4—1722no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—42no—
506C23—21no—
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23#1306332312yes—
513C23C22×C22⋊D4311yescharacteristic
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
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—862no—
545C2×C4—3444no—
546C2×C4—1721no—
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×C4#1306332312yes—
558C2×C4C2×D4×D4311yescharacteristic
559C2×C4C2×Q8×D4311yescharacteristic
560C2×C4C2×Q8×D4311yescharacteristic
561C2×C4#41×D4311yescharacteristic
562C2×C4#1306337011yescharacteristic
563C2×C4#1306337211yescharacteristic
564C8—434no—
565C8—862no—
566C8—862no—
567C8—862no—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22C2×#1306332311yescharacteristic
576C22D4×C22⋊D4311yescharacteristic
577C22#1458354811yescharacteristic
578C22#1458369711yescharacteristic
579C22#1458369711yescharacteristic
580C22#1458370711yescharacteristic
581C22#1458371011yescharacteristic
582C4—22no—
583C4—41no—
584C4—42no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—81no—
589C4—81no—
590C4—81no—
591C4—3441no—
592C4—3441no—
593C4—3441no—
594C4—1722no—
595C4C22⋊Q8×D4311yescharacteristic
596C4#1458352811yescharacteristic
597C4#1458356211yescharacteristic
598C4#1458360311yescharacteristic
599C2—42no—
600C2#1913829411yescharacteristic
601C2#1914512111yescharacteristic
602C2#1914514811yescharacteristic
603C2#1914612111yescharacteristic
604C2#1914617611yescharacteristic
605C2#1914714911yescharacteristic
606C2#1914715511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2441C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#2441D43
hypocenterC43#26075
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2441

Complements

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

NH ≅ G/Ntype
1. C2×#14583298C2semidirect
4. #19136076C2semidirect
5. #19136072C2semidirect
6. #19135933C2semidirect
7. #19135930C2semidirect
8. #19135330C2semidirect
9. #19135320C2semidirect
12. #19134761C2semidirect
364. C43#26075semidirect

Maximal subgroups

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

subgroupindex
C2×#145832982
C2×#145829422
#191383192
#191360762
#191360722
#191359332
#191359302
#191353302
#191353202
#191347942
#191347872
#191347612
#191346262
#191343792
C43×#24412
#2607543