Finite Group Databasebeta

← #25155415

Subgroups — #25155415

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×#14583300C211yesmaximal, characteristic, complemented
2C2×#14582938C211yesmaximal, characteristic
3#19138322C211yesmaximal, characteristic
4#19138311C211yesmaximal, characteristic
5#19136077C211yesmaximal, characteristic, complemented
6#19136072C211yesmaximal, characteristic, complemented
7#19135935C211yesmaximal, characteristic, complemented
8#19135931C211yesmaximal, characteristic, complemented
9#19135333C211yesmaximal, characteristic, complemented
10#19135321C211yesmaximal, characteristic, complemented
11#19134791C211yesmaximal, characteristic
12#19134786C211yesmaximal, characteristic
13#19134629C211yesmaximal, characteristic
14#19134380C211yesmaximal, characteristic
15C43×#1847C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×#13063316C2211yescharacteristic
19C2×#13063283C2211yescharacteristic
20C2×C4⋊C4×D43C2211yescharacteristic
21#14583300—24no—
22#14582938—24no—
23C2×#13063259C2211yescharacteristic
24C2×#13063258C2211yescharacteristic
25C2×#13063257C2211yescharacteristic
26C2×#13063256C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×#13063256C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31#14582840—21no—
32#14582834—21no—
33#14582833—21no—
34#14582821—21no—
35#14582797C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582795C2211yescharacteristic
38#14582795C2211yescharacteristic
39#14582794—21no—
40#14582785—21no—
41#14582773—21no—
42#14582758—21no—
43#14582756C2211yescharacteristic
44#14582756C2211yescharacteristic
45C4×(C2×D43)⋊C4C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582654C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C2×#107×C43C2211yescharacteristic
56C2×#106×C43C2211yescharacteristic
57C2×#106×C43C2211yescharacteristic
58C2×#97×C43C2211yescharacteristic
59C43×#384C2211yescharacteristic
60C43×#382C2211yescharacteristic
61C22×C4×D43—21no—
62C22×C4×D43C2311yescharacteristic
63C2×#10621872—22no—
64C2×#10621872—22no—
65C2×#10621872Q814yes—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063316—22no—
69#13063316—22no—
70#13063316—41no—
71#13063316—41no—
72#13063283—22no—
73#13063283—41no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C4⋊C4×D43—22no—
88C4⋊C4×D43—41no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4D411yescharacteristic
93C2×(C2×D43)⋊C4D411yescharacteristic
94C2×C4×Dic43—21no—
95C2×C4×Dic43C2311yescharacteristic
96#13063259D414yes—
97#13063258—22no—
98#13063257—22no—
99#13063256—22no—
100#13063256—22no—
101#13063256—22no—
102(C2×D43)⋊C8Q814yes—
103C8×Dic43—22no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95D411yescharacteristic
111C43⋊#95D411yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C42×C43C2311yescharacteristic
121#107×C43—22no—
122#107×C43—41no—
123#106×C43—22no—
124#106×C43—41no—
125#97×C43—22no—
126#95×C43—21no—
127#95×C43—21no—
128C23×D43C2×D411yescharacteristic
129C22×C4×C43—21no—
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—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43C2×D411yescharacteristic
141C22×Dic43C2×D411yescharacteristic
142C22×Dic43C2×D411yescharacteristic
143C2×C4×D43—21no—
144C2×C4×D43—21no—
145C2×C4×D43—21no—
146C2×C4×D43—21no—
147C2×C4×D43—42no—
148C2×C4×D43—42no—
149C2×C4×D43—81no—
150C2×C4×D43C2×Q812yes—
151C2×C4×D43C2×Q812yes—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43C2×D412yes—
155C2×C8×C43C2×Q812yes—
156C2×C8×C43C2×Q812yes—
157C2×C8×C43#4112yes—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—42no—
167C4⋊C4×C43—81no—
168C42×C43—21no—
169C42×C43—21no—
170(C2×D43)⋊C4—41no—
171(C2×D43)⋊C4—41no—
172(C2×D43)⋊C4—42no—
173(C2×D43)⋊C4—42no—
174(C2×D43)⋊C4—81no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—42no—
182C4⋊Dic43—42no—
183C4⋊Dic43C2×D412yes—
184C4⋊Dic43C2×D412yes—
185Dic43⋊C4—42no—
186Dic43⋊C4—42no—
187Dic43⋊C4—42no—
188Dic43⋊C4—42no—
189Dic43⋊C4—81no—
190Dic43⋊C4—81no—
191Dic43⋊C4—81no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—42no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8C2×Q812yes—
200C2×C43⋊C8C2×Q812yes—
201#10621872—28no—
202C23×C43C22×D411yescharacteristic
203C22×D43—21no—
204C22×D43—21no—
205C22×D43—21no—
206C22×D43—21no—
207C22×D43—21no—
208C22×D43—21no—
209C22×D43C4⋊Q812yes—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
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—41no—
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C22×Q811yescharacteristic
230C2×C4×C43C22×Q811yescharacteristic
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—22no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—41no—
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×Dic43C4⋊Q812yes—
255C4×D43—22no—
256C4×D43—22no—
257C4×D43—22no—
258C4×D43—22no—
259C4×D43—84no—
260C8×C43—22no—
261C8×C43C22⋊Q814yes—
262C43⋊C8—22no—
263C43⋊C8—22no—
264#26075—431nomaximal, Sylow
265C22×C43C2×C4⋊Q811yescharacteristic
266C22×C43D4211yescharacteristic
267C22×C43#54711yescharacteristic
268C22×C43#57511yescharacteristic
269C22×C43#57511yescharacteristic
270C22×C43#57711yescharacteristic
271C22×C43#57711yescharacteristic
272C2×D43—22no—
273C2×D43—22no—
274C2×D43—22no—
275C2×D43—41no—
276C2×D43—41no—
277C2×D43—41no—
278C2×D43—41no—
279C4×C43—41no—
280C4×C43—41no—
281C4×C43—81no—
282C4×C43—81no—
283C4×C43—81no—
284C4×C43—81no—
285C4×C43C2×C22⋊Q811yescharacteristic
286C4×C43#54411yescharacteristic
287C4×C43D4×Q811yescharacteristic
288C4×C43#55411yescharacteristic
289Dic43—22no—
290Dic43—42no—
291Dic43—41no—
292Dic43—42no—
293Dic43—41no—
294Dic43—81no—
295Dic43—81no—
296C2×#499—431no—
297C2×#428—431no—
298#2442—431no—
299#2441—431no—
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#1847D4311yescharacteristic, complemented
309#1809—431no—
310#1753—431no—
311C2×C43#244011yescharacteristic
312C2×C43#316311yescharacteristic
313C2×C43#316611yescharacteristic
314C2×C43#326711yescharacteristic
315C2×C43#327111yescharacteristic
316C2×C43#335111yescharacteristic
317C2×C43#335111yescharacteristic
318D43—42no—
319C22×M16—431no—
320C2×#125—431no—
321C2×#125—431no—
322C2×#117—431no—
323C22×C4⋊C4—431no—
324#499—864no—
325#428—864no—
326C2×#107—431no—
327C2×#107—431no—
328C2×#107C2×D4311yescharacteristic
329C2×#107C2×D4311yescharacteristic
330C2×#106—431no—
331C2×#106—431no—
332C2×#106—431no—
333C2×#106—431no—
334C2×#106C2×D4311yescharacteristic
335C2×#106C2×D4311yescharacteristic
336C2×C22⋊C8—431no—
337C2×#97C2×D4311yescharacteristic
338C2×C4×C8—431no—
339#400—861no—
340#399—861no—
341#398—861no—
342#396—861no—
343#389—431no—
344#389—431no—
345#389—431no—
346#389—431no—
347#389—861no—
348#387—861no—
349#385—861no—
350#384C2×D4311yescharacteristic
351#382C2×D4311yescharacteristic
352#380—431no—
353#380—431no—
354#380—861no—
355C4×C22⋊C4—431no—
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—431no—
366C23×C4—861no—
367C2×M16—434no—
368C2×M16—862no—
369C2×M16—862no—
370C22×C8—431no—
371C22×C8—431no—
372C22×C8C22×D4311yescharacteristic
373C22×C8C22×D4311yescharacteristic
374#125—862no—
375#125—862no—
376#125—1721no—
377#125—1721no—
378#117—862no—
379#117—1721no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—431no—
384C2×C4⋊C4—431no—
385C2×C4⋊C4—431no—
386C2×C4⋊C4—862no—
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⋊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—431no—
402C2×C22⋊C4—431no—
403C2×C22⋊C4—861no—
404C2×C22⋊C4—861no—
405C2×C22⋊C4—861no—
406C2×C42—431no—
407C2×C42—861no—
408C2×C42C22×D4311yescharacteristic
409#107—22no—
410#107—41no—
411#107—434no—
412#107—862no—
413#106—22no—
414#106—41no—
415#106—862no—
416#106—862no—
417#106—862no—
418#106—862no—
419C22⋊C8—434no—
420#97—22no—
421C4×C8—862no—
422#95—21no—
423#95—21no—
424#95—431no—
425#95—431no—
426#95—861no—
427#95—861no—
428#95—861no—
429#95—861no—
430#95—861no—
431#95—861no—
432C24—431no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—431no—
438C22×C4—432no—
439C22×C4—432no—
440C22×C4—431no—
441C22×C4—431no—
442C22×C4—861no—
443C22×C4—861no—
444C22×C4—861no—
445C22×C4—861no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—861no—
449C22×C4—861no—
450C22×C4—3441no—
451C22×C4—1722no—
452C22×C4—1722no—
453C22×C4D4×D4311yescharacteristic
454C22×C4D4×D4311yescharacteristic
455C22×C4C23×D4311yescharacteristic
456M16—868no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—432no—
460C2×C8—432no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8#1062189812yes—
466C2×C8D4×D4312yes—
467C2×C8Q8×D4312yes—
468C2×C8Q8×D4312yes—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—42no—
478C4⋊C4—81no—
479C4⋊C4—432no—
480C4⋊C4—432no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—3441no—
488C4⋊C4—3441no—
489C4⋊C4—3441no—
490C4⋊C4—1722no—
491C4⋊C4—1722no—
492C4⋊C4—1722no—
493C4⋊C4—1722no—
494C4⋊C4—1722no—
495C4⋊C4—1722no—
496C22⋊C4—3441no—
497C22⋊C4—1721no—
498C22⋊C4—1721no—
499C22⋊C4—1722no—
500C22⋊C4—1722no—
501C42—21no—
502C42—21no—
503C42—861no—
504C42—861no—
505C42—1722no—
506C23—432no—
507C23—861no—
508C23—861no—
509C23—861no—
510C23—861no—
511C23—861no—
512C23—861no—
513C23C2×D4×D4311yescharacteristic
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
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—861no—
534C2×C4—861no—
535C2×C4—862no—
536C2×C4—862no—
537C2×C4—862no—
538C2×C4—862no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—862no—
546C2×C4—862no—
547C2×C4—3444no—
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—1721no—
558C2×C4C2×D4×D4311yescharacteristic
559C2×C4C2×Q8×D4311yescharacteristic
560C2×C4C2×Q8×D4311yescharacteristic
561C2×C4C2×#1062189811yescharacteristic
562C2×C4#1306337011yescharacteristic
563C2×C4#1306337311yescharacteristic
564C8—22no—
565C8—862no—
566C8—862no—
567C8#1306330314yes—
568C22—862no—
569C22—862no—
570C22—862no—
571C22—1721no—
572C22—1721no—
573C22—1721no—
574C22—1721no—
575C22C4⋊Q8×D4311yescharacteristic
576C22#1458353411yescharacteristic
577C22#1458355011yescharacteristic
578C22#1458369511yescharacteristic
579C22#1458369811yescharacteristic
580C22#1458370811yescharacteristic
581C22#1458370911yescharacteristic
582C4—41no—
583C4—41no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4—81no—
588C4—862no—
589C4—3441no—
590C4—3441no—
591C4—1721no—
592C4—1722no—
593C4—1722no—
594C4—1721no—
595C4C2×#1306330311yescharacteristic
596C4#1458352611yescharacteristic
597C4#1458356411yescharacteristic
598C4#1458360411yescharacteristic
599C2—1722no—
600C2#1913830011yescharacteristic
601C2#1914512211yescharacteristic
602C2#1914514611yescharacteristic
603C2#1914611911yescharacteristic
604C2#1914617911yescharacteristic
605C2#1914715111yescharacteristic
606C2#1914715611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1847C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#1847D43
hypocenterC43#26075
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1847

Complements

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

NH ≅ G/Ntype
1. C2×#14583300C2semidirect
5. #19136077C2semidirect
6. #19136072C2semidirect
7. #19135935C2semidirect
8. #19135931C2semidirect
9. #19135333C2semidirect
10. #19135321C2semidirect
15. C43×#1847C2semidirect
308. #1847D43semidirect
364. C43#26075semidirect

Maximal subgroups

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

subgroupindex
C2×#145833002
C2×#145829382
#191383222
#191383112
#191360772
#191360722
#191359352
#191359312
#191353332
#191353212
#191347912
#191347862
#191346292
#191343802
C43×#18472
#2607543