Finite Group Databasebeta

← #25154670

Subgroups — #25154670

Order 11008.

696 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138317C211yesmaximal, characteristic
2#19137476C211yesmaximal, characteristic
3#19136164C211yesmaximal, characteristic, complemented
4#19136098C211yesmaximal, characteristic, complemented
5#19136097C211yesmaximal, characteristic, complemented
6#19135935C211yesmaximal, characteristic, complemented
7#19135549C211yesmaximal, characteristic, complemented
8#19135363C211yesmaximal, characteristic, complemented
9#19135176C211yesmaximal, characteristic, complemented
10#19134786C211yesmaximal, characteristic
11#19134779C211yesmaximal, characteristic
12#19134689C211yesmaximal, characteristic
13#19134627C211yesmaximal, characteristic
14#19134313C211yesmaximal, characteristic
15C43×#1919C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×#13063283C2211yescharacteristic
19C2×C4⋊C4×D43C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×C4⋊(C43⋊C8)C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×(C2×D43)⋊C8C2211yescharacteristic
26#14582839—21no—
27#14582829—21no—
28#14582798C2211yescharacteristic
29#14582797C2211yescharacteristic
30#14582795C2211yescharacteristic
31#14582790—21no—
32#14582788—21no—
33#14582773—21no—
34#14582765C2211yescharacteristic
35#14582763—21no—
36#14582756—21no—
37#14582756C2211yescharacteristic
38#14582756C2211yescharacteristic
39C4⋊C4×Dic43C2211yescharacteristic
40C4×(C2×D43)⋊C4C2211yescharacteristic
41#14582745—21no—
42#14582662C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#106×C43C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C4×C4⋊C4×C43C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×C4×D43—21no—
60C22×C4×D43C2311yescharacteristic
61C2×#10621872—22no—
62C2×#10621872—22no—
63C2×#10621872—41no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66#13063316—22no—
67#13063316—41no—
68#13063283—22no—
69#13063283Q814yes—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C4⋊C4×D43—22no—
81C4⋊C4×D43—41no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4D411yescharacteristic
86C2×(C2×D43)⋊C4D411yescharacteristic
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43C2311yescharacteristic
90#13063258—41no—
91#13063256—22no—
92#13063256—41no—
93C4⋊(C43⋊C8)—22no—
94Dic43⋊C8—41no—
95(C2×D43)⋊C8—22no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95D411yescharacteristic
105C43⋊#95D411yescharacteristic
106C22×C8×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C42×C43—21no—
114C2×C42×C43C2311yescharacteristic
115#106×C43—22no—
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—21no—
134C2×C4×D43—21no—
135C2×C4×D43—21no—
136C2×C4×D43—21no—
137C2×C4×D43—42no—
138C2×C4×D43—42no—
139C2×C4×D43—81no—
140C2×C4×D43C2×Q812yes—
141C2×C4×D43#4112yes—
142C2×C8×C43—21no—
143C2×C8×C43—21no—
144C2×C8×C43—21no—
145C2×C8×C43—21no—
146C2×C8×C43—21no—
147C2×C8×C43—21no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—81no—
155C4⋊C4×C43C2×Q812yes—
156C4⋊C4×C43#4112yes—
157C42×C43—21no—
158C42×C43—21no—
159C42×C43—42no—
160(C2×D43)⋊C4—24no—
161(C2×D43)⋊C4—41no—
162(C2×D43)⋊C4—41no—
163(C2×D43)⋊C4—42no—
164(C2×D43)⋊C4—81no—
165C4⋊Dic43—21no—
166C4⋊Dic43—21no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—42no—
173C4⋊Dic43—81no—
174C4⋊Dic43C2×Q812yes—
175Dic43⋊C4—42no—
176Dic43⋊C4—42no—
177Dic43⋊C4—81no—
178Dic43⋊C4—81no—
179C4×Dic43—21no—
180C4×Dic43—21no—
181C4×Dic43—24no—
182C4×Dic43—42no—
183C2×C43⋊C8—21no—
184C2×C43⋊C8—21no—
185C2×C43⋊C8—21no—
186C2×C43⋊C8—21no—
187C2×C43⋊C8—21no—
188C2×C43⋊C8#4112yes—
189#10621872—44no—
190C23×C43C22×D411yescharacteristic
191C22×D43—21no—
192C22×D43—21no—
193C22×D43—21no—
194C22×D43—21no—
195C22×D43—21no—
196C22×D43—21no—
197C22×D43C22⋊Q812yes—
198C2×C4×C43—22no—
199C2×C4×C43—22no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—41no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43C22×Q811yescharacteristic
217C2×C4×C43C2×#4111yescharacteristic
218C2×C4×C43C2×#4111yescharacteristic
219C2×C4×C43C2×#4111yescharacteristic
220C2×C4×C43H(5,𝔽2)11yescharacteristic
221C2×C4×C432−1+411yescharacteristic
222C2×Dic43—21no—
223C2×Dic43—21no—
224C2×Dic43—22no—
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43C22⋊Q812yes—
243C4×D43—22no—
244C4×D43—22no—
245C4×D43—22no—
246C4×D43—22no—
247C4×D43—84no—
248C8×C43—41no—
249C8×C43—41no—
250C43⋊C8—22no—
251C43⋊C8—41no—
252#26019—431nomaximal, Sylow
253C22×C43C2×C22⋊Q811yescharacteristic
254C22×C43#54611yescharacteristic
255C22×C43#54711yescharacteristic
256C22×C43#57511yescharacteristic
257C22×C43#57511yescharacteristic
258C22×C43#57711yescharacteristic
259C22×C43#57711yescharacteristic
260C2×D43—22no—
261C2×D43—22no—
262C2×D43—22no—
263C2×D43—41no—
264C2×D43—41no—
265C2×D43—41no—
266C2×D43—41no—
267C4×C43—42no—
268C4×C43—41no—
269C4×C43—41no—
270C4×C43—42no—
271C4×C43—81no—
272C4×C43—81no—
273C4×C43#53311yescharacteristic
274C4×C43#54411yescharacteristic
275C4×C43#55111yescharacteristic
276C4×C43#55211yescharacteristic
277Dic43—22no—
278Dic43—42no—
279Dic43—41no—
280Dic43—41no—
281Dic43—81no—
282Dic43—81no—
283Dic43—81no—
284#2442—431no—
285#2346—431no—
286#2101—431no—
287#2088—431no—
288#2088—431no—
289#2059—431no—
290#1989—431no—
291#1949—431no—
292#1919—431no—
293#1919D4311yescharacteristic, complemented
294#1853—431no—
295#1851—431no—
296#1825—431no—
297#1809—431no—
298#1736—431no—
299C2×C43#243811yescharacteristic
300C2×C43#308011yescharacteristic
301C2×C43#308411yescharacteristic
302C2×C43#332111yescharacteristic
303C2×C43#332311yescharacteristic
304C2×C43#334811yescharacteristic
305C2×C43#335111yescharacteristic
306D43—42no—
307C22×M16—431no—
308C2×#125—431no—
309C2×#117—431no—
310C22×C4⋊C4—431no—
311C2×#107—431no—
312C2×#106—431no—
313C2×#106—431no—
314C2×#106C2×D4311yescharacteristic
315C2×C4⋊C8—431no—
316C2×C4⋊C8—431no—
317C2×C22⋊C8—431no—
318#400—861no—
319#398—861no—
320#389—431no—
321#389—431no—
322#389—431no—
323#389C2×D4311yescharacteristic
324#388—861no—
325#388—861no—
326#385—861no—
327#382—431no—
328#382—861no—
329#380—431no—
330#380—431no—
331#380—861no—
332C4×C4⋊C4—431no—
333C4×C4⋊C4C2×D4311yescharacteristic
334C4×C22⋊C4—431no—
335#376—861no—
336#340—431no—
337#340—431no—
338#340—431no—
339#340—431no—
340#340—431no—
341#340—431no—
342#340—431no—
343#340—431no—
344#340—431no—
345#340C2×D4311yescharacteristic
346#340C2×D4311yescharacteristic
347#340C2×D4311yescharacteristic
348#336—431no—
349#336C2×D4311yescharacteristic
350C43#2601911yescharacteristic, complemented, Sylow
351C23×C4—431no—
352C23×C4—861no—
353C2×M16—862no—
354C2×M16—862no—
355C2×M16—1721no—
356C22×C8—431no—
357C22×C8—431no—
358C22×C8C22×D4311yescharacteristic
359C22×C8C22×D4311yescharacteristic
360#125—862no—
361#125—1721no—
362#117—434no—
363#117—862no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—431no—
366C2×C4⋊C4—431no—
367C2×C4⋊C4—431no—
368C2×C4⋊C4—431no—
369C2×C4⋊C4—862no—
370C2×C4⋊C4—861no—
371C2×C4⋊C4—861no—
372C2×C4⋊C4—861no—
373C2×C4⋊C4—861no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4—1721no—
377C2×C4⋊C4C22×D4311yescharacteristic
378C2×C4⋊C4C22×D4311yescharacteristic
379C2×C4⋊C4C22×D4311yescharacteristic
380C2×C4⋊C4C22×D4311yescharacteristic
381C2×C22⋊C4—431no—
382C2×C22⋊C4—431no—
383C2×C22⋊C4—861no—
384C2×C22⋊C4—861no—
385C2×C22⋊C4—861no—
386C2×C42—21no—
387C2×C42—431no—
388C2×C42—861no—
389C2×C42—861no—
390C2×C42C22×D4311yescharacteristic
391#107—1721no—
392#106—22no—
393#106—862no—
394#106—1721no—
395C4⋊C8—862no—
396C4⋊C8—1721no—
397C22⋊C8—862no—
398#95—21no—
399#95—21no—
400#95—431no—
401#95—431no—
402#95—861no—
403#95—861no—
404#95—861no—
405#95—861no—
406#95—861no—
407#95—861no—
408#95—861no—
409#95—861no—
410C24—431no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—431no—
416C22×C4—432no—
417C22×C4—432no—
418C22×C4—431no—
419C22×C4—431no—
420C22×C4—861no—
421C22×C4—861no—
422C22×C4—861no—
423C22×C4—861no—
424C22×C4—861no—
425C22×C4—861no—
426C22×C4—861no—
427C22×C4—861no—
428C22×C4—3441no—
429C22×C4—1722no—
430C22×C4—1722no—
431C22×C4D4×D4311yescharacteristic
432C22×C4D4×D4311yescharacteristic
433C22×C4C23×D4311yescharacteristic
434M16—1724no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—432no—
442C2×C8—861no—
443C2×C8—861no—
444C2×C8—861no—
445C2×C8—861no—
446C2×C8—861no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—81no—
454C4⋊C4—432no—
455C4⋊C4—861no—
456C4⋊C4—861no—
457C4⋊C4—861no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—3441no—
463C4⋊C4—3441no—
464C4⋊C4—3441no—
465C4⋊C4—1722no—
466C4⋊C4—1722no—
467C4⋊C4—1722no—
468C4⋊C4#1062189812yes—
469C4⋊C4Q8×D4312yes—
470C22⋊C4—864no—
471C22⋊C4—3441no—
472C22⋊C4—1721no—
473C22⋊C4—1721no—
474C22⋊C4—1722no—
475C42—21no—
476C42—21no—
477C42—42no—
478C42—864no—
479C42—861no—
480C42—861no—
481C42—1722no—
482C23—432no—
483C23—861no—
484C23—861no—
485C23—861no—
486C23—861no—
487C23—861no—
488C23—861no—
489C23C2×D4×D4311yescharacteristic
490C2×C4—22no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—432no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—862no—
512C2×C4—862no—
513C2×C4—862no—
514C2×C4—862no—
515C2×C4—862no—
516C2×C4—861no—
517C2×C4—861no—
518C2×C4—861no—
519C2×C4—861no—
520C2×C4—861no—
521C2×C4—861no—
522C2×C4—3444no—
523C2×C4—1721no—
524C2×C4—1721no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4C2×Q8×D4311yescharacteristic
535C2×C4#41×D4311yescharacteristic
536C2×C4#41×D4311yescharacteristic
537C2×C4C2×#1062189811yescharacteristic
538C2×C4#1306337111yescharacteristic
539C2×C4#1306337211yescharacteristic
540C8—41no—
541C8—41no—
542C8—862no—
543C8—1721no—
544C22—862no—
545C22—862no—
546C22—862no—
547C22—1721no—
548C22—1721no—
549C22—1721no—
550C22—1721no—
551C22C22⋊Q8×D4311yescharacteristic
552C22#1458354511yescharacteristic
553C22#1458354711yescharacteristic
554C22#1458369511yescharacteristic
555C22#1458369611yescharacteristic
556C22#1458370511yescharacteristic
557C22#1458370811yescharacteristic
558C4—42no—
559C4—41no—
560C4—41no—
561C4—42no—
562C4—81no—
563C4—81no—
564C4—862no—
565C4—3441no—
566C4—3441no—
567C4—3441no—
568C4—1722no—
569C4—1721no—
570C4—1721no—
571C4#1458345311yescharacteristic
572C4#1458352911yescharacteristic
573C4#1458357411yescharacteristic
574C4#1458358811yescharacteristic
575C2—1722no—
576C2#1913827611yescharacteristic
577C2#1914441211yescharacteristic
578C2#1914445411yescharacteristic
579C2#1914678611yescharacteristic
580C2#1914681611yescharacteristic
581C2#1914711411yescharacteristic
582C2#1914715911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1919C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#1919D43
hypocenterC43#26019
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1919

Complements

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

NH ≅ G/Ntype
3. #19136164C2semidirect
4. #19136098C2semidirect
5. #19136097C2semidirect
6. #19135935C2semidirect
7. #19135549C2semidirect
8. #19135363C2semidirect
9. #19135176C2semidirect
15. C43×#1919C2semidirect
293. #1919D43semidirect
350. C43#26019semidirect

Maximal subgroups

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

subgroupindex
#191383172
#191374762
#191361642
#191360982
#191360972
#191359352
#191355492
#191353632
#191351762
#191347862
#191347792
#191346892
#191346272
#191343132
C43×#19192
#2601943