Finite Group Databasebeta

← #25196784

Subgroups — #25196784

Order 11008.

720 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140429C211yesmaximal, characteristic
2#19137279C211yesmaximal, characteristic
3#19136161C211yesmaximal, characteristic, complemented
4#19136136C211yesmaximal, characteristic, complemented
5#19135936C211yesmaximal, characteristic, complemented
6#19135744C211yesmaximal, characteristic, complemented
7#19135179C211yesmaximal, characteristic, complemented
8#19135176C211yesmaximal, characteristic, complemented
9#19135019C211yesmaximal, characteristic
10#19134861C211yesmaximal, characteristic, complemented
11#19134851C211yesmaximal, characteristic, complemented
12#19134628C211yesmaximal, characteristic
13#19134618C211yesmaximal, characteristic
14#19134293C211yesmaximal, characteristic
15C43×#1894C211yesmaximal, characteristic
16C23×C43⋊C8C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19C2×#13063284C2211yescharacteristic
20C2×#13063259C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26#14582833—21no—
27#14582831—21no—
28#14582822—21no—
29#14582822—21no—
30#14582806C2211yescharacteristic
31#14582798—21no—
32#14582798C2211yescharacteristic
33#14582798C2211yescharacteristic
34#14582795C2211yescharacteristic
35#14582792—21no—
36#14582792—21no—
37#14582785—21no—
38#14582768C2211yescharacteristic
39#14582759C2211yescharacteristic
40#14582759C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42#14582662C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582653C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C22×M16×C43C2211yescharacteristic
53C2×C22⋊Q8×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C43×#380C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×C43⋊C8—22no—
60C22×C43⋊C8—22no—
61C22×C43⋊C8—41no—
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64#13063316—41no—
65#13063316—41no—
66Q8×Dic43—41no—
67Q8×Dic43—41no—
68#13063284—41no—
69#13063284—41no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43D411yescharacteristic
75C2×C4⋊Dic43D411yescharacteristic
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×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43D411yescharacteristic
87C2×C22⋊Dic43D411yescharacteristic
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43C2311yescharacteristic
91C2×C4×Dic43C2311yescharacteristic
92#13063259—41no—
93#13063257—22no—
94#13063256—22no—
95#13063256—41no—
96#13063249—22no—
97#13063249—41no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C22×Q8×C43C2311yescharacteristic
107C23×C4×C43C2311yescharacteristic
108C2×M16×C43—22no—
109C2×M16×C43—22no—
110C2×M16×C43—41no—
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C22⋊Q8×C43—22no—
114C22⋊Q8×C43Q814yes—
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121#103×C43—22no—
122#103×C43—41no—
123#95×C43—21no—
124C24×C43C2×D411yescharacteristic
125C2×Q8×C43—21no—
126C2×Q8×C43—21no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43C2×Q812yes—
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×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×Q812yes—
141C22×C4×C43#4112yes—
142C22×C4×C43C2411yescharacteristic
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151M16×C43—44no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43#4112yes—
158C4⋊C4×C43—24no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43C2×Q812yes—
165C22⋊C4×C43—24no—
166C22⋊C4×C43—81no—
167C22⋊Dic43—41no—
168C22⋊Dic43—41no—
169C22⋊Dic43—81no—
170C22⋊Dic43—81no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—41no—
180C4⋊Dic43—41no—
181C4⋊Dic43—42no—
182C4⋊Dic43—42no—
183C4⋊Dic43—81no—
184C4⋊Dic43—81no—
185Dic43⋊C4—42no—
186Dic43⋊C4—81no—
187Dic43⋊C4—81no—
188Dic43⋊C4—81no—
189C4×Dic43—21no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—42no—
194C4×Dic43—81no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—44no—
201C2×C43⋊C8#4112yes—
202C23×C43—21no—
203C23×C43—21no—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43C22⋊Q812yes—
209C23×C43C22×D411yescharacteristic
210Q8×C43—22no—
211Q8×C43—22no—
212Q8×C43—41no—
213Q8×C43—41no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—22no—
217C2×C4×C43—22no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
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×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43C22⋊Q812yes—
233C2×C4×C43C22×Q811yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43H(5,𝔽2)11yescharacteristic
238C2×C4×C43H(5,𝔽2)11yescharacteristic
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
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—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C8×C43—22no—
264C8×C43—41no—
265C43⋊C8—22no—
266C43⋊C8—41no—
267#29172—431nomaximal, Sylow
268C22×C43—22no—
269C22×C43—22no—
270C22×C43—22no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43C2×C22⋊Q811yescharacteristic
276C22×C43#53211yescharacteristic
277C22×C43#53411yescharacteristic
278C22×C43#57711yescharacteristic
279C22×C43#57711yescharacteristic
280C22×C43#57711yescharacteristic
281C22×C43#57811yescharacteristic
282C4×C43—22no—
283C4×C43—42no—
284C4×C43—42no—
285C4×C43—81no—
286C4×C43—81no—
287C4×C43#55111yescharacteristic
288C4×C43#55111yescharacteristic
289C4×C43#55411yescharacteristic
290C4×C43#55411yescharacteristic
291Dic43—41no—
292Dic43—41no—
293Dic43—41no—
294Dic43—41no—
295Dic43—81no—
296Dic43—81no—
297Dic43—81no—
298Dic43—81no—
299#2629—431no—
300#2323—431no—
301#2100—431no—
302#2096—431no—
303#2059—431no—
304#2026—431no—
305#1920—431no—
306#1919—431no—
307#1894D4311yescharacteristic
308#1892—431no—
309#1865—431no—
310#1863—431no—
311#1809—431no—
312#1807—431no—
313#1729—431no—
314C2×C43—42no—
315C2×C43#256411yescharacteristic
316C2×C43#308211yescharacteristic
317C2×C43#308411yescharacteristic
318C2×C43#317411yescharacteristic
319C2×C43#317811yescharacteristic
320C2×C43#320111yescharacteristic
321C2×C43#320411yescharacteristic
322C22×M16C2×D4311yescharacteristic
323C23×C8—431no—
324C2×#125—431no—
325C2×C22⋊Q8C2×D4311yescharacteristic
326C2×C4×Q8—431no—
327C2×#117—431no—
328C2×#107—431no—
329C2×#106—431no—
330C2×#106—431no—
331C2×#106—431no—
332C2×#103—431no—
333C2×#103—431no—
334C2×#103C2×D4311yescharacteristic
335C2×#103C2×D4311yescharacteristic
336#398—861no—
337#398—861no—
338#396—861no—
339#396—861no—
340#391—431no—
341#389—431no—
342#389—431no—
343#389—431no—
344#389—861no—
345#388—861no—
346#388—861no—
347#387—861no—
348#384—431no—
349#380—431no—
350#380—431no—
351#380C2×D4311yescharacteristic
352C4×C4⋊C4—431no—
353#340—431no—
354#340—431no—
355#340—431no—
356#340—431no—
357#340—431no—
358#340—431no—
359#340C2×D4311yescharacteristic
360#340C2×D4311yescharacteristic
361#336—431no—
362#336—431no—
363#336—431no—
364#336—431no—
365C43#2917211yescharacteristic, complemented, Sylow
366C22×Q8C22×D4311yescharacteristic
367C23×C4C22×D4311yescharacteristic
368C2×M16—22no—
369C2×M16—22no—
370C2×M16—41no—
371C22×C8—431no—
372C22×C8—431no—
373C22×C8—862no—
374C22×C8—862no—
375C22×C8—1721no—
376C22×C8C22×D4311yescharacteristic
377C22×C8C22×D4311yescharacteristic
378#125—1721no—
379#125—1721no—
380C22⋊Q8—22no—
381C22⋊Q8Dic8614yes—
382C4×Q8—1721no—
383C4×Q8—1721no—
384#117—1721no—
385#117—1721no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—431no—
391C2×C4⋊C4—431no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4C22×D4311yescharacteristic
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C4⋊C4C22×D4311yescharacteristic
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—431no—
407C2×C22⋊C4—431no—
408C2×C22⋊C4—861no—
409C2×C22⋊C4—861no—
410C2×C42—431no—
411C2×C42—431no—
412C2×C42—861no—
413C2×C42—861no—
414#107—1721no—
415#106—862no—
416#106—862no—
417#106—1721no—
418#103—22no—
419#103—41no—
420#103—862no—
421#103—1721no—
422#95—21no—
423#95—861no—
424#95—861no—
425#95—861no—
426#95—861no—
427#95—861no—
428#95—861no—
429#95—861no—
430#95—861no—
431C24D4×D4311yescharacteristic
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8C2×Dic8612yes—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—431no—
447C22×C4—431no—
448C22×C4—431no—
449C22×C4—431no—
450C22×C4—861no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—861no—
454C22×C4C2×Dic8612yes—
455C22×C4D4×D4311yescharacteristic
456C22×C4#1062190012yes—
457C22×C4C23×D4311yescharacteristic
458M16—44no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—432no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8—1724no—
471C2×C8#1062190012yes—
472C4⋊C4—24no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—3441no—
487C4⋊C4—3441no—
488C4⋊C4—3441no—
489C4⋊C4—3441no—
490C4⋊C4—3441no—
491C4⋊C4—1721no—
492C4⋊C4—1721no—
493C4⋊C4—1722no—
494C4⋊C4—1722no—
495C4⋊C4—1722no—
496C4⋊C4C2×Dic8612yes—
497C22⋊C4—24no—
498C22⋊C4—81no—
499C22⋊C4—3441no—
500C22⋊C4—3441no—
501C22⋊C4—1721no—
502C22⋊C4—1721no—
503C42—861no—
504C42—861no—
505C42—861no—
506C42—861no—
507C42—3441no—
508C42—1722no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23#1306330212yes—
516C23C2×D4×D4311yescharacteristic
517Q8—22no—
518Q8—22no—
519Q8—41no—
520Q8—41no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—861no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4#1306330212yes—
564C2×C4C22×Dic8611yescharacteristic
565C2×C4#41×D4311yescharacteristic
566C2×C4C2×#1062190011yescharacteristic
567C2×C4C2×#1062190011yescharacteristic
568C2×C4#1306337011yescharacteristic
569C2×C4#1306337111yescharacteristic
570C8—22no—
571C8—41no—
572C8—862no—
573C8—1721no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22C2×#1306330211yescharacteristic
582C22#1458344411yescharacteristic
583C22#1458345711yescharacteristic
584C22#1458370811yescharacteristic
585C22#1458370811yescharacteristic
586C22#1458370911yescharacteristic
587C22#1458371511yescharacteristic
588C4—22no—
589C4—42no—
590C4—42no—
591C4—81no—
592C4—81no—
593C4—3441no—
594C4—3441no—
595C4—3441no—
596C4—3441no—
597C4—1721no—
598C4—1721no—
599C4—1721no—
600C4—1721no—
601C4#1458357211yescharacteristic
602C4#1458358011yescharacteristic
603C4#1458360611yescharacteristic
604C4#1458360811yescharacteristic
605C2—42no—
606C2#1913977911yescharacteristic
607C2#1914443911yescharacteristic
608C2#1914446111yescharacteristic
609C2#1914521811yescharacteristic
610C2#1914526411yescharacteristic
611C2#1914547211yescharacteristic
612C2#1914550211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1894C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#1894D43
hypocenterC43#29172
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1894

Complements

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

NH ≅ G/Ntype
3. #19136161C2semidirect
4. #19136136C2semidirect
5. #19135936C2semidirect
6. #19135744C2semidirect
7. #19135179C2semidirect
8. #19135176C2semidirect
10. #19134861C2semidirect
11. #19134851C2semidirect
365. C43#29172semidirect

Maximal subgroups

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

subgroupindex
#191404292
#191372792
#191361612
#191361362
#191359362
#191357442
#191351792
#191351762
#191350192
#191348612
#191348512
#191346282
#191346182
#191342932
C43×#18942
#2917243