Finite Group Databasebeta

← #14723124

Subgroups — #14723124

Order 2816.

592 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077745C211yesmaximal, characteristic
2#13077743C211yesmaximal, characteristic
3#13077580C211yesmaximal, characteristic
4#13067406C211yesmaximal, characteristic, complemented
5#13067406C211yesmaximal, characteristic, complemented
6#13067393C211yesmaximal, characteristic, complemented
7#13067387C211yesmaximal, characteristic, complemented
8#13067385C211yesmaximal, characteristic, complemented
9#13067384C211yesmaximal, characteristic, complemented
10#13067382C211yesmaximal, characteristic, complemented
11#13067370C211yesmaximal, characteristic, complemented
12#13067369C211yesmaximal, characteristic, complemented
13#13067367C211yesmaximal, characteristic, complemented
14#13067361C211yesmaximal, characteristic, complemented
15C11×#1572C211yesmaximal, characteristic, complemented
16C4×#4339C2211yescharacteristic
17C11×#432C2211yescharacteristic
18C11×#431C2211yescharacteristic
19C11×#431C2211yescharacteristic
20#10622537C2211yescharacteristic
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22C4×#4318C2211yescharacteristic
23#10622450C2211yescharacteristic
24#10622450C2211yescharacteristic
25#10622450C2211yescharacteristic
26#10622449C411yescharacteristic
27#10622449C411yescharacteristic
28#10622448C2211yescharacteristic
29#10622446C2211yescharacteristic
30#10622446C2211yescharacteristic
31#10622446C2211yescharacteristic
32D11×C4⋊C8C2211yescharacteristic
33#10622441C411yescharacteristic
34#10622441C411yescharacteristic
35#10622343—21no—
36#10622342—21no—
37#10622342—21no—
38#10622342C411yescharacteristic
39#10622342C411yescharacteristic
40#10622341C411yescharacteristic
41#10622341C411yescharacteristic
42(C22⋊D11)⋊C8—21no—
43#10622319—21no—
44#10622314—21no—
45#10622301—21no—
46C4×#4313C2211yescharacteristic
47#10622298C2211yescharacteristic
48#10622298C2211yescharacteristic
49C4×C8×D11C2211yescharacteristic
50C8×Dic22—21no—
51C11×#335C2211yescharacteristic
52C11×#335C2211yescharacteristic
53C11×#334C2211yescharacteristic
54C11×#334C2211yescharacteristic
55#10622118C2211yescharacteristic
56#10622118C2211yescharacteristic
57#10622118C2211yescharacteristic
58#10622118C2211yescharacteristic
59#10622117C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622117C2211yescharacteristic
62#10622117C2211yescharacteristic
63#10622095C2211yescharacteristic
64#10622095C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C2×#4339Q811yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C4×C22⋊D11C2×C411yescharacteristic
70C4×C22⋊D11C2×C411yescharacteristic
71C4×C22⋊D11D411yescharacteristic
72C4×C22⋊D11D411yescharacteristic
73#66979Q811yescharacteristic
74C2×#4318—21no—
75C2×#4318C2×C411yescharacteristic
76C2×#4318C2×C411yescharacteristic
77C22×C11⋊C8—21no—
78C2×#4313—21no—
79C2×#4313—21no—
80C2×#4313—21no—
81C2×#4313C2×C411yescharacteristic
82C2×#4313C2×C411yescharacteristic
83C2×C8×D11—21no—
84C2×C8×D11C2×C411yescharacteristic
85C2×C8×D11C2×C411yescharacteristic
86C4×D44C2×C411yescharacteristic
87C4×D44D411yescharacteristic
88#66925Q811yescharacteristic
89#66925Q811yescharacteristic
90C42×D11C2311yescharacteristic
91C42×D11C2311yescharacteristic
92C4×Dic22C2×C411yescharacteristic
93C4×Dic22D411yescharacteristic
94C11×C4⋊C8C2×C411yescharacteristic
95C11×C4⋊C8C2×C411yescharacteristic
96C11×C4⋊C8C2311yescharacteristic
97C11×C4⋊C8C2311yescharacteristic
98C11×C4⋊C8C2311yescharacteristic
99C11×C4⋊C8C2311yescharacteristic
100C11×C22⋊C8—21no—
101C11×C22⋊C8—21no—
102C11×C22⋊C8C2×C411yescharacteristic
103C11×C22⋊C8C2×C411yescharacteristic
104C11×#97—21no—
105C4×C8×C11—21no—
106C4×C8×C11C2311yescharacteristic
107C4×C8×C11C2311yescharacteristic
108(C2×D11)⋊C8—21no—
109(C2×D11)⋊C8—21no—
110(C2×D11)⋊C8—21no—
111(C2×D11)⋊C8—21no—
112(C2×D11)⋊C8C2×C411yescharacteristic
113(C2×D11)⋊C8C2×C411yescharacteristic
114(C2×D11)⋊C8C2×C411yescharacteristic
115(C2×D11)⋊C8C2×C411yescharacteristic
116#66879—21no—
117#66879C2×C411yescharacteristic
118#66879C2×C411yescharacteristic
119Dic11⋊C8—21no—
120Dic11⋊C8—21no—
121Dic11⋊C8—21no—
122Dic11⋊C8—21no—
123Dic11⋊C8C2×C411yescharacteristic
124Dic11⋊C8C2×C411yescharacteristic
125Dic11⋊C8C2×C411yescharacteristic
126Dic11⋊C8C2×C411yescharacteristic
127C8×Dic11—21no—
128C8×Dic11—21no—
129C8×Dic11—21no—
130C8×Dic11C2×C411yescharacteristic
131C8×Dic11C2×C411yescharacteristic
132C4⋊(C11⋊C8)—21no—
133C4⋊(C11⋊C8)—21no—
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138#66867C2×C411yescharacteristic
139#66867C2×C411yescharacteristic
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142#17841—111nomaximal, Sylow
143C22×C4×C11C22×C411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×Q811yescharacteristic
146C2×C22⋊D11C4⋊C411yescharacteristic
147C2×C22⋊D11C4⋊C411yescharacteristic
148#4339—42no—
149C2×D44C4⋊C411yescharacteristic
150C2×C4×D11C22×C411yescharacteristic
151C2×C4×D11C22×C411yescharacteristic
152C2×C4×D11C2×D411yescharacteristic
153C2×C4×D11C2×D411yescharacteristic
154C2×C4×D11C2×Q811yescharacteristic
155C2×C4×D11C2×Q811yescharacteristic
156C2×Dic22C4⋊C411yescharacteristic
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11C22×C411yescharacteristic
162C2×C8×C11C22×C411yescharacteristic
163C2×C8×C11C22×C411yescharacteristic
164C2×C8×C11C22×C411yescharacteristic
165C42×C11C22×C411yescharacteristic
166C42×C11C2×D411yescharacteristic
167C42×C11C2×Q811yescharacteristic
168C42×C11C2411yescharacteristic
169C22⋊Dic11C4⋊C411yescharacteristic
170C22⋊Dic11C4⋊C411yescharacteristic
171(C2×D11)⋊C4C4⋊C411yescharacteristic
172(C2×D11)⋊C4C4⋊C411yescharacteristic
173(C2×D11)⋊C4C4⋊C411yescharacteristic
174(C2×D11)⋊C4C4⋊C411yescharacteristic
175C4⋊Dic11C4⋊C411yescharacteristic
176C4⋊Dic11C4⋊C411yescharacteristic
177Dic11⋊C4C4⋊C411yescharacteristic
178Dic11⋊C4C4⋊C411yescharacteristic
179Dic11⋊C4C4⋊C411yescharacteristic
180Dic11⋊C4C4⋊C411yescharacteristic
181C4×Dic11C22×C411yescharacteristic
182C4×Dic11C22×C411yescharacteristic
183C4×Dic11C2×D411yescharacteristic
184C4×Dic11C2×D411yescharacteristic
185C4×Dic11C2×Q811yescharacteristic
186C4×Dic11C2×Q811yescharacteristic
187#4318—22no—
188#4318—41no—
189#4318—81no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—81no—
195C2×C11⋊C8C22×C411yescharacteristic
196C2×C11⋊C8C22×C411yescharacteristic
197C2×C11⋊C8C22×C411yescharacteristic
198C2×C11⋊C8C22×C411yescharacteristic
199#4313—22no—
200#4313—41no—
201#4313—81no—
202#4313—81no—
203#4313—81no—
204C8×D11—22no—
205C8×D11—41no—
206C8×D11—81no—
207#2991—111no—
208#2990—111no—
209#2965—111no—
210#1574—111no—
211#1574—111no—
212#1572—111no—
213#1572D1111yescharacteristic, complemented
214#1570—111no—
215#1570—111no—
216#1569—111no—
217#1569—111no—
218#1566—111no—
219#1565—111no—
220#1565—111no—
221#1564—111no—
222C23×C11C2×C4⋊C411yescharacteristic
223C22×D11C2×C4⋊C411yescharacteristic
224C22×D11C2×C4⋊C411yescharacteristic
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—41no—
230C2×C4×C11C2×C4⋊C411yescharacteristic
231C2×C4×C11C2×C4⋊C411yescharacteristic
232C2×C4×C11C2×C4⋊C411yescharacteristic
233C2×C4×C11C23×C411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C22×Q811yescharacteristic
236C22⋊D11—22no—
237C22⋊D11—41no—
238C2×Dic11C2×C4⋊C411yescharacteristic
239C2×Dic11C2×C4⋊C411yescharacteristic
240C2×Dic11C2×C4⋊C411yescharacteristic
241C2×Dic11C2×C4⋊C411yescharacteristic
242C2×Dic11C2×C4⋊C411yescharacteristic
243C2×Dic11C2×C4⋊C411yescharacteristic
244D44—41no—
245C4×D11—21no—
246C4×D11—21no—
247C4×D11—21no—
248C4×D11—21no—
249C4×D11—21no—
250C4×D11—21no—
251C4×D11—21no—
252C4×D11—21no—
253C4×D11—22no—
254C4×D11—41no—
255Dic22—22no—
256C8×C11—21no—
257C8×C11—21no—
258C8×C11—21no—
259C8×C11—21no—
260C8×C11—41no—
261C8×C11—41no—
262C8×C11—41no—
263C8×C11—41no—
264C11⋊C8—21no—
265C11⋊C8—21no—
266C11⋊C8—21no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C11⋊C8#13112yes—
272C4×#41—111no—
273#446—111no—
274#446—111no—
275#446—221no—
276C8×Q8—221no—
277#436—111no—
278#436—111no—
279#436—221no—
280#436—221no—
281#436—221no—
282#435—111no—
283#435—111no—
284#435—111no—
285#435—111no—
286#435—221no—
287#435—221no—
288C8×D4—221no—
289#432—111no—
290#432C2×D1111yescharacteristic
291#431—111no—
292#431—111no—
293#431—111no—
294#431—111no—
295#431—111no—
296#431C2×D1111yescharacteristic
297#431C2×D1111yescharacteristic
298#423—111no—
299#423—111no—
300#423—111no—
301#423—111no—
302C2×C4⋊C8—111no—
303C2×C4⋊C8—111no—
304C4×M16—111no—
305C4×M16—111no—
306C2×C4×C8—111no—
307#335—111no—
308#335—111no—
309#335—111no—
310#335—111no—
311#335C2×D1111yescharacteristic
312#335C2×D1111yescharacteristic
313#334—111no—
314#334—111no—
315#334—111no—
316#334—111no—
317#334—111no—
318#334—111no—
319#334—111no—
320#334—111no—
321#334C2×D1111yescharacteristic
322#334C2×D1111yescharacteristic
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11C22×C4⋊C411yescharacteristic
327C2×D11—21no—
328C2×D11—21no—
329C2×D11—21no—
330C2×D11—21no—
331C2×D11—21no—
332C2×D11—21no—
333C4×C11—21no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—21no—
337C4×C11C2×#13111yescharacteristic
338C4×C11#56811yescharacteristic
339C4×C11#57711yescharacteristic
340C4×C11#57711yescharacteristic
341Dic11—21no—
342Dic11—21no—
343Dic11—21no—
344Dic11—21no—
345Dic11—21no—
346Dic11#43012yes—
347C2×#41—111no—
348C2×M16—111no—
349C2×M16—111no—
350C2×M16—111no—
351C2×M16—111no—
352C2×M16—221no—
353C2×M16—221no—
354C2×M16—221no—
355C2×M16—221no—
356C22×C8—111no—
357C22×C8—111no—
358C22×C8—221no—
359C22×C8—221no—
360C4×Q8—111no—
361C4×Q8—111no—
362C4×D4—111no—
363C4×D4—111no—
364C4×D4—111no—
365C4×D4—111no—
366C4×D4—111no—
367C4×D4—111no—
368#117—111no—
369#117—111no—
370#117—111no—
371C2×C42—111no—
372C2×C42—111no—
373C2×C42C22×D1111yescharacteristic
374C4⋊C8—111no—
375C4⋊C8—111no—
376C4⋊C8—111no—
377C4⋊C8—111no—
378C4⋊C8—111no—
379C4⋊C8—111no—
380C4⋊C8—111no—
381C4⋊C8—111no—
382C4⋊C8—221no—
383C4⋊C8—221no—
384C4⋊C8—221no—
385C4⋊C8—221no—
386C4⋊C8—221no—
387C4⋊C8—221no—
388C4⋊C8C4×D1111yescharacteristic
389C4⋊C8C4×D1111yescharacteristic
390C4⋊C8C22×D1111yescharacteristic
391C4⋊C8C22×D1111yescharacteristic
392C4⋊C8C22×D1111yescharacteristic
393C4⋊C8C22×D1111yescharacteristic
394C22⋊C8—21no—
395C22⋊C8—21no—
396C22⋊C8—111no—
397C22⋊C8—111no—
398C22⋊C8—111no—
399C22⋊C8—111no—
400C22⋊C8—221no—
401C22⋊C8—221no—
402C22⋊C8—221no—
403C22⋊C8—221no—
404C22⋊C8C4×D1111yescharacteristic
405C22⋊C8C4×D1111yescharacteristic
406#97—21no—
407#97—111no—
408#97—111no—
409#97—111no—
410#97—111no—
411#97—221no—
412C4×C8—21no—
413C4×C8—111no—
414C4×C8—111no—
415C4×C8—111no—
416C4×C8—111no—
417C4×C8—221no—
418C4×C8—221no—
419C4×C8—221no—
420C4×C8C22×D1111yescharacteristic
421C4×C8C22×D1111yescharacteristic
422C2×C11—41no—
423C2×C11#290611yescharacteristic
424C2×C11#291211yescharacteristic
425C2×C11C2×#43011yescharacteristic
426D11—41no—
427D11—41no—
428#41—442no—
429C2×Q8—111no—
430C2×D4—111no—
431C2×D4—111no—
432C2×D4—111no—
433C22×C4—111no—
434C22×C4—111no—
435C22×C4—111no—
436C22×C4—111no—
437C22×C4—111no—
438C22×C4—111no—
439C22×C4C2×C4×D1111yescharacteristic
440C22×C4D4×D1111yescharacteristic
441C22×C4Q8×D1111yescharacteristic
442M16—222no—
443M16—222no—
444M16—441no—
445M16—441no—
446M16—881no—
447M16—881no—
448M16—881no—
449M16—881no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—111no—
455C2×C8—111no—
456C2×C8—111no—
457C2×C8—111no—
458C2×C8—222no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—441no—
464C2×C8—881no—
465C2×C8—881no—
466C2×C8C2×C4×D1111yescharacteristic
467C2×C8C2×C4×D1111yescharacteristic
468C2×C8C2×C4×D1111yescharacteristic
469C2×C8C2×C4×D1111yescharacteristic
470C4⋊C4—111no—
471C4⋊C4—111no—
472C4⋊C4—111no—
473C4⋊C4—111no—
474C4⋊C4—111no—
475C4⋊C4—111no—
476C22⋊C4—111no—
477C22⋊C4—111no—
478C22⋊C4—111no—
479C22⋊C4—111no—
480C22⋊C4—111no—
481C22⋊C4—111no—
482C42—111no—
483C42—111no—
484C42—111no—
485C42—111no—
486C42—111no—
487C42—111no—
488C42C2×C4×D1111yescharacteristic
489C42D4×D1111yescharacteristic
490C42Q8×D1111yescharacteristic
491C42C23×D1111yescharacteristic
492C11#1784111yescharacteristic, complemented, Sylow
493C23—111no—
494C23—111no—
495C23C4⋊C4×D1111yescharacteristic
496Q8—222no—
497D4—222no—
498D4—441no—
499D4—441no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—111no—
506C2×C4—111no—
507C2×C4—111no—
508C2×C4—111no—
509C2×C4—111no—
510C2×C4—111no—
511C2×C4—222no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—221no—
517C2×C4—221no—
518C2×C4—221no—
519C2×C4—221no—
520C2×C4—441no—
521C2×C4C4⋊C4×D1111yescharacteristic
522C2×C4C4⋊C4×D1111yescharacteristic
523C2×C4C4⋊C4×D1111yescharacteristic
524C2×C4C22×C4×D1111yescharacteristic
525C2×C4C2×D4×D1111yescharacteristic
526C2×C4C2×Q8×D1111yescharacteristic
527C8—21no—
528C8—21no—
529C8—21no—
530C8—21no—
531C8—41no—
532C8—41no—
533C8—41no—
534C8—41no—
535C8—112no—
536C8—221no—
537C8—221no—
538C8—221no—
539C8—441no—
540C8—441no—
541C8—441no—
542C8—441no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—221no—
547C22—221no—
548C22—221no—
549C22—221no—
550C22—221no—
551C22—221no—
552C22C2×C4⋊C4×D1111yescharacteristic
553C4—21no—
554C4—21no—
555C4—21no—
556C4—21no—
557C4—112no—
558C4—221no—
559C4—221no—
560C4—221no—
561C4—221no—
562C4—221no—
563C4D11×#13111yescharacteristic
564C4#1062328111yescharacteristic
565C4#1062330111yescharacteristic
566C4#1062330111yescharacteristic
567C2—41no—
568C2—441no—
569C2—441no—
570C2#1307718311yescharacteristic
571C2#1307720811yescharacteristic
572C2D11×#43011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1572C2
socleC22×C11C22×C4⋊C4
prime radicalC2×#4339Q8
cosocleC42×C11C24
hypercenter#1572D11
hypocenterC11#17841
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1572

Complements

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

NH ≅ G/Ntype
4. #13067406C2semidirect
5. #13067406C2semidirect
6. #13067393C2semidirect
7. #13067387C2semidirect
8. #13067385C2semidirect
9. #13067384C2semidirect
10. #13067382C2semidirect
11. #13067370C2semidirect
12. #13067369C2semidirect
13. #13067367C2semidirect
14. #13067361C2semidirect
15. C11×#1572C2semidirect
213. #1572D11semidirect
492. C11#17841semidirect

Maximal subgroups

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

subgroupindex
#130777452
#130777432
#130775802
#130674062
#130673932
#130673872
#130673852
#130673842
#130673822
#130673702
#130673692
#130673672
#130673612
C11×#15722
#1784111