Finite Group Databasebeta

← #25126555

Subgroups — #25126555

Order 11008.

782 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137220C211yesmaximal, characteristic
2#19137210C211yesmaximal, characteristic
3#19136167C211yesmaximal, characteristic, complemented
4#19136166C211yesmaximal, characteristic, complemented
5#19136162C211yesmaximal, characteristic, complemented
6#19136160C211yesmaximal, characteristic, complemented
7#19136158C211yesmaximal, characteristic, complemented
8#19136156C211yesmaximal, characteristic, complemented
9#19136154C211yesmaximal, characteristic, complemented
10#19134313C211yesmaximal, characteristic
11#19134313C211yesmaximal, characteristic
12#19134310C211yesmaximal, characteristic
13#340×D43C211yesmaximal, characteristic
14#19134290C211yesmaximal, characteristic
15C43×#2101C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C2×#13063283C2211yescharacteristic
19C2×#13063283C2211yescharacteristic
20C2×#13063282C2211yescharacteristic
21C2×C4⋊C4×D43C2211yescharacteristic
22C2×C4⋊C4×D43C2211yescharacteristic
23#14582798C2211yescharacteristic
24#14582797C2211yescharacteristic
25#14582796—21no—
26#14582796—21no—
27#14582796—21no—
28#14582795C2211yescharacteristic
29#14582794—21no—
30#14582773—21no—
31#14582773—21no—
32#14582769C2211yescharacteristic
33#14582768C2211yescharacteristic
34#14582764C2211yescharacteristic
35#14582758—21no—
36#14582756—21no—
37#14582662C2211yescharacteristic
38#14582662C2211yescharacteristic
39#14582662C2211yescharacteristic
40#14582662C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C43×#389C2211yescharacteristic
53C43×#382C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×C4×D43—21no—
60C22×C4×D43—21no—
61C22×C4×D43C2311yescharacteristic
62C2×#10621872—22no—
63C2×#10621872—22no—
64C2×#10621872—22no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C2×C8×D43—22no—
68C2×C8×D43—22no—
69C2×C8×D43—22no—
70#13063283—22no—
71#13063283—22no—
72#13063283—22no—
73#13063283—22no—
74#13063282—22no—
75#13063282—22no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4D411yescharacteristic
90C2×Dic43⋊C4D411yescharacteristic
91C4⋊C4×D43—22no—
92C4⋊C4×D43—22no—
93C4⋊C4×D43—22no—
94C4⋊C4×D43Q814yes—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4D411yescharacteristic
98C2×(C2×D43)⋊C4D411yescharacteristic
99C2×C4×Dic43—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43C2311yescharacteristic
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C22×C8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C42×C43C2311yescharacteristic
115#95×C43—21no—
116#95×C43—21no—
117#95×C43—21no—
118C23×D43C2×D411yescharacteristic
119C22×C4×C43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2411yescharacteristic
126C22×Dic43—21no—
127C22×Dic43—21no—
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43C2×D411yescharacteristic
131C22×Dic43C2×D411yescharacteristic
132C22×Dic43C2×D411yescharacteristic
133C2×C4×D43—24no—
134C2×C4×D43—42no—
135C2×C4×D43—81no—
136C2×C4×D43—81no—
137C2×C4×D43—81no—
138C2×C4×D43—81no—
139C2×C4×D43C2×Q812yes—
140C2×C4×D43#4112yes—
141C2×C4×D43#4112yes—
142C2×C4×D43#4112yes—
143C2×C4×D43#4112yes—
144C2×C4×D43#4112yes—
145C2×C8×C43—21no—
146C2×C8×C43—21no—
147C2×C8×C43—21no—
148C2×C8×C43—21no—
149C2×C8×C43—21no—
150C2×C8×C43—21no—
151C4⋊C4×C43—21no—
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—81no—
159C4⋊C4×C43C2×Q812yes—
160C42×C43—21no—
161C42×C43—21no—
162(C2×D43)⋊C4—22no—
163(C2×D43)⋊C4—22no—
164(C2×D43)⋊C4—42no—
165(C2×D43)⋊C4—42no—
166C4⋊Dic43—21no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—81no—
174C4⋊Dic43—81no—
175C4⋊Dic43—81no—
176C4⋊Dic43C2×Q812yes—
177Dic43⋊C4—24no—
178Dic43⋊C4—22no—
179Dic43⋊C4—22no—
180Dic43⋊C4—42no—
181Dic43⋊C4—81no—
182Dic43⋊C4—81no—
183Dic43⋊C4—81no—
184Dic43⋊C4—81no—
185C4×Dic43—21no—
186C4×Dic43—21no—
187C4×Dic43—42no—
188C4×Dic43—42no—
189C2×C43⋊C8—21no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195#10621872—44no—
196C8×D43—44no—
197C23×C43C22×D411yescharacteristic
198C22×D43—21no—
199C22×D43—21no—
200C22×D43—21no—
201C22×D43—21no—
202C22×D43C22⋊Q812yes—
203C22×D43#12312yes—
204C22×D43#12412yes—
205C2×C4×C43—22no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
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×C43C22×Q811yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C2×C4×C43C2×#4111yescharacteristic
226C2×C4×C43C2×#4111yescharacteristic
227C2×C4×C43C2×#4111yescharacteristic
228C2×C4×C43C2×#4111yescharacteristic
229C2×Dic43—22no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43C22⋊Q812yes—
248C2×Dic43#12312yes—
249C2×Dic43#12412yes—
250C4×D43—84no—
251C4×D43—84no—
252C4×D43#12514yes—
253C4×D43#12514yes—
254C4×D43#12614yes—
255C4×D43#12614yes—
256C8×C43—41no—
257C8×C43—41no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260#23749—431nomaximal, Sylow
261C22×C43C2×C22⋊Q811yescharacteristic
262C22×C43C2×#12311yescharacteristic
263C22×C43C2×#12411yescharacteristic
264C22×C43#57611yescharacteristic
265C22×C43#57711yescharacteristic
266C22×C43#57711yescharacteristic
267C22×C43#57811yescharacteristic
268C2×D43—22no—
269C2×D43—22no—
270C2×D43—22no—
271C2×D43—22no—
272C2×D43—22no—
273C2×D43—22no—
274C2×D43#40014yes—
275C4×C43—42no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—81no—
279C4×C43—81no—
280C4×C43—81no—
281C4×C43C2×#12511yescharacteristic
282C4×C43C2×#12511yescharacteristic
283C4×C43C2×#12611yescharacteristic
284C4×C43C2×#12611yescharacteristic
285Dic43—42no—
286Dic43—41no—
287Dic43—41no—
288Dic43—81no—
289Dic43—81no—
290Dic43—81no—
291Dic43#40014yes—
292#2317—431no—
293#2316—431no—
294#2101—431no—
295#2101—431no—
296#2101—431no—
297#2101D4311yescharacteristic, complemented
298#2100—431no—
299#2100—431no—
300#2099—431no—
301#2099—431no—
302#1736—431no—
303#1736—431no—
304#1735—431no—
305C2×#340—431no—
306#1729—431no—
307C2×C43C2×#40011yescharacteristic
308C2×C43#308111yescharacteristic
309C2×C43#308211yescharacteristic
310C2×C43#309811yescharacteristic
311C2×C43#309911yescharacteristic
312C2×C43#313611yescharacteristic
313C2×C43#313711yescharacteristic
314D43—24no—
315C22×M16—431no—
316C23×C8—431no—
317C2×#117—431no—
318C2×#117—431no—
319C2×#117—431no—
320C22×C4⋊C4—431no—
321C22×C4⋊C4—431no—
322#389—431no—
323#389—431no—
324#389—431no—
325#389—861no—
326#389—861no—
327#389—861no—
328#389—861no—
329#389C2×D4311yescharacteristic
330#385—861no—
331#385—861no—
332#384—431no—
333#384—431no—
334#382—431no—
335#382C2×D4311yescharacteristic
336#380—861no—
337#380—861no—
338#340—431no—
339#340—431no—
340#340—431no—
341#340—431no—
342#340—431no—
343#340—431no—
344#340—431no—
345#340—431no—
346#340—431no—
347#340—431no—
348#340—431no—
349#340—431no—
350#340C2×D4311yescharacteristic
351#340C2×D4311yescharacteristic
352#340C2×D4311yescharacteristic
353#340C2×D4311yescharacteristic
354#336—431no—
355#336—431no—
356#336—431no—
357#336C2×D4311yescharacteristic
358C43#2374911yescharacteristic, complemented, Sylow
359C23×C4—431no—
360C23×C4—861no—
361C23×C4—861no—
362C2×M16—862no—
363C2×M16—862no—
364C2×M16—862no—
365C22×C8—431no—
366C22×C8—431no—
367C22×C8—862no—
368C22×C8—862no—
369C22×C8—862no—
370C22×C8C22×D4311yescharacteristic
371C22×C8C22×D4311yescharacteristic
372#117—862no—
373#117—862no—
374#117—862no—
375#117—862no—
376#117—862no—
377#117—862no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—431no—
380C2×C4⋊C4—434no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—431no—
384C2×C4⋊C4—431no—
385C2×C4⋊C4—431no—
386C2×C4⋊C4—862no—
387C2×C4⋊C4—862no—
388C2×C4⋊C4—862no—
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—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4C22×D4311yescharacteristic
399C2×C4⋊C4C22×D4311yescharacteristic
400C2×C4⋊C4C22×D4311yescharacteristic
401C2×C4⋊C4C22×D4311yescharacteristic
402C2×C22⋊C4—431no—
403C2×C22⋊C4—431no—
404C2×C22⋊C4—861no—
405C2×C22⋊C4—861no—
406C2×C42—431no—
407C2×C42—861no—
408C2×C42—861no—
409C2×C42C22×D4311yescharacteristic
410#95—21no—
411#95—21no—
412#95—21no—
413#95—861no—
414#95—861no—
415#95—861no—
416#95—861no—
417#95—861no—
418C24—431no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—431no—
424C22×C4—432no—
425C22×C4—432no—
426C22×C4—432no—
427C22×C4—432no—
428C22×C4—432no—
429C22×C4—432no—
430C22×C4—431no—
431C22×C4—431no—
432C22×C4—864no—
433C22×C4—861no—
434C22×C4—861no—
435C22×C4—861no—
436C22×C4—861no—
437C22×C4—3441no—
438C22×C4—3441no—
439C22×C4—3441no—
440C22×C4—3441no—
441C22×C4—1722no—
442C22×C4D4×D4311yescharacteristic
443C22×C4D4×D4311yescharacteristic
444C22×C4C23×D4311yescharacteristic
445M16—1724no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8—861no—
456C2×C8—861no—
457C2×C8—861no—
458C2×C8—1724no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—81no—
467C4⋊C4—432no—
468C4⋊C4—864no—
469C4⋊C4—862no—
470C4⋊C4—862no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—3441no—
479C4⋊C4—3441no—
480C4⋊C4—3441no—
481C4⋊C4—3441no—
482C4⋊C4—3441no—
483C4⋊C4—3441no—
484C4⋊C4—3441no—
485C4⋊C4—1722no—
486C4⋊C4Q8×D4312yes—
487C22⋊C4—862no—
488C22⋊C4—862no—
489C22⋊C4—1722no—
490C22⋊C4—1722no—
491C42—21no—
492C42—21no—
493C42—861no—
494C42—861no—
495C42—1722no—
496C42—1722no—
497C23—432no—
498C23—432no—
499C23—432no—
500C23—861no—
501C23—861no—
502C23—861no—
503C23—861no—
504C23C2×D4×D4311yescharacteristic
505C2×C4—22no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—432no—
524C2×C4—432no—
525C2×C4—432no—
526C2×C4—434no—
527C2×C4—434no—
528C2×C4—434no—
529C2×C4—434no—
530C2×C4—862no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—3444no—
538C2×C4—3444no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4C2×Q8×D4311yescharacteristic
551C2×C4#41×D4311yescharacteristic
552C2×C4#41×D4311yescharacteristic
553C2×C4#41×D4311yescharacteristic
554C2×C4#41×D4311yescharacteristic
555C2×C4#41×D4311yescharacteristic
556C8—41no—
557C8—41no—
558C8—1721no—
559C8—1721no—
560C22—434no—
561C22—862no—
562C22—862no—
563C22—862no—
564C22—862no—
565C22—862no—
566C22—862no—
567C22C22⋊Q8×D4311yescharacteristic
568C22#123×D4311yescharacteristic
569C22#124×D4311yescharacteristic
570C22#1458370111yescharacteristic
571C22#1458370611yescharacteristic
572C22#1458370911yescharacteristic
573C22#1458371511yescharacteristic
574C4—41no—
575C4—41no—
576C4—42no—
577C4—81no—
578C4—81no—
579C4—81no—
580C4—434no—
581C4—3441no—
582C4—3441no—
583C4—3441no—
584C4—1721no—
585C4—1721no—
586C4—1722no—
587C4#125×D4311yescharacteristic
588C4#125×D4311yescharacteristic
589C4#126×D4311yescharacteristic
590C4#126×D4311yescharacteristic
591C2—864no—
592C2#400×D4311yescharacteristic
593C2#1914442311yescharacteristic
594C2#1914443411yescharacteristic
595C2#1914457611yescharacteristic
596C2#1914458711yescharacteristic
597C2#1914494811yescharacteristic
598C2#1914495711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2101C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#2101D43
hypocenterC43#23749
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2101

Complements

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

NH ≅ G/Ntype
3. #19136167C2semidirect
4. #19136166C2semidirect
5. #19136162C2semidirect
6. #19136160C2semidirect
7. #19136158C2semidirect
8. #19136156C2semidirect
9. #19136154C2semidirect
15. C43×#2101C2semidirect
297. #2101D43semidirect
358. C43#23749semidirect

Maximal subgroups

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

subgroupindex
#191372202
#191372102
#191361672
#191361662
#191361622
#191361602
#191361582
#191361562
#191361542
#191343132
#191343102
#340×D432
#191342902
C43×#21012
#2374943