Finite Group Databasebeta

← #14723031

Subgroups — #14723031

Order 2816.

588 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077578C211yesmaximal, characteristic
2#13077281C211yesmaximal, characteristic
3#13077277C211yesmaximal, characteristic
4#13067406C211yesmaximal, characteristic, complemented
5#13067404C211yesmaximal, characteristic, complemented
6#13067399C211yesmaximal, characteristic, complemented
7#13067398C211yesmaximal, characteristic, complemented
8#13067395C211yesmaximal, characteristic, complemented
9#13067393C211yesmaximal, characteristic, complemented
10#13067383C211yesmaximal, characteristic, complemented
11#13067382C211yesmaximal, characteristic, complemented
12#13067378C211yesmaximal, characteristic, complemented
13#13067365C211yesmaximal, characteristic, complemented
14#13067361C211yesmaximal, characteristic, complemented
15C11×#1565C211yesmaximal, characteristic, complemented
16C4×#4339C2211yescharacteristic
17C11×#431C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C4×C11×M16C2211yescharacteristic
20#10622741C411yescharacteristic
21#10622741C411yescharacteristic
22#10622740C411yescharacteristic
23#10622740C411yescharacteristic
24#10622723—21no—
25#10622714—21no—
26#10622539C2211yescharacteristic
27#10622538C2211yescharacteristic
28#10622537C2211yescharacteristic
29#10622453—21no—
30#10622453—21no—
31#10622450C2211yescharacteristic
32#10622448C2211yescharacteristic
33#10622448C2211yescharacteristic
34#10622448C2211yescharacteristic
35#10622446C2211yescharacteristic
36#10622446C2211yescharacteristic
37#10622446C2211yescharacteristic
38D11×C4⋊C8C2211yescharacteristic
39#10622340—21no—
40#10622333—21no—
41#10622319C411yescharacteristic
42#10622319C411yescharacteristic
43#10622314C411yescharacteristic
44#10622314C411yescharacteristic
45#10622303—21no—
46#10622302—21no—
47C4×#4313C2211yescharacteristic
48#10622298C2211yescharacteristic
49#10622298C2211yescharacteristic
50C4×C8×D11C2211yescharacteristic
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#10622096C2211yescharacteristic
64#10622096C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C2×#4339D411yescharacteristic
68C2×C11×M16C2×C411yescharacteristic
69C2×C11×M16C2×C411yescharacteristic
70C22×C8×C11—21no—
71C2×C42×C11C2311yescharacteristic
72C4×C22⋊D11C2×C411yescharacteristic
73C4×C22⋊D11C2×C411yescharacteristic
74C4×C22⋊D11Q811yescharacteristic
75C4×C22⋊D11Q811yescharacteristic
76#66979D411yescharacteristic
77C2×#4318—21no—
78C2×#4313—21no—
79C2×#4313C2×C411yescharacteristic
80C2×#4313C2×C411yescharacteristic
81C2×C8×D11—21no—
82C2×C8×D11C2×C411yescharacteristic
83C2×C8×D11C2×C411yescharacteristic
84C4×D44C2×C411yescharacteristic
85C4×D44Q811yescharacteristic
86#66925D411yescharacteristic
87#66925D411yescharacteristic
88C42×D11C2311yescharacteristic
89C42×D11C2311yescharacteristic
90C4×Dic22C2×C411yescharacteristic
91C4×Dic22Q811yescharacteristic
92C11×C4⋊C8—21no—
93C11×C4⋊C8C2311yescharacteristic
94C11×C4⋊C8C2311yescharacteristic
95C11×C4⋊C8C2311yescharacteristic
96C11×C4⋊C8C2311yescharacteristic
97C11×C22⋊C8—21no—
98C11×#97C2×C411yescharacteristic
99C11×#97C2×C411yescharacteristic
100C4×C8×C11—21no—
101C4×C8×C11C2311yescharacteristic
102C4×C8×C11C2311yescharacteristic
103C22⋊(C11⋊C8)—21no—
104C22⋊(C11⋊C8)C2×C411yescharacteristic
105C22⋊(C11⋊C8)C2×C411yescharacteristic
106(C2×D11)⋊C8—21no—
107(C2×D11)⋊C8—21no—
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#66879—21no—
118#66879—21no—
119#66879C2×C411yescharacteristic
120#66879C2×C411yescharacteristic
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)C2×C411yescharacteristic
134C4⋊(C11⋊C8)C2×C411yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139#66867—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142#17831—111nomaximal, Sylow
143C22×C4×C11C22×C411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×Q811yescharacteristic
146C2×C22⋊D11C4⋊C411yescharacteristic
147C2×C22⋊D11C4⋊C411yescharacteristic
148#4339—41no—
149#4339—41no—
150C2×D44C4⋊C411yescharacteristic
151C2×C4×D11C22×C411yescharacteristic
152C2×C4×D11C22×C411yescharacteristic
153C2×C4×D11C2×D411yescharacteristic
154C2×C4×D11C2×D411yescharacteristic
155C2×C4×D11C2×Q811yescharacteristic
156C2×C4×D11C2×Q811yescharacteristic
157C2×Dic22C4⋊C411yescharacteristic
158C11×M16—22no—
159C11×M16—41no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—42no—
165C2×C8×C11C22×C411yescharacteristic
166C2×C8×C11C22×C411yescharacteristic
167C2×C8×C11C22×C411yescharacteristic
168C2×C8×C11C22×C411yescharacteristic
169C42×C11C22×C411yescharacteristic
170C42×C11C2×D411yescharacteristic
171C42×C11C2×Q811yescharacteristic
172C42×C11C2411yescharacteristic
173C22⋊Dic11C4⋊C411yescharacteristic
174C22⋊Dic11C4⋊C411yescharacteristic
175(C2×D11)⋊C4C4⋊C411yescharacteristic
176(C2×D11)⋊C4C4⋊C411yescharacteristic
177(C2×D11)⋊C4C4⋊C411yescharacteristic
178(C2×D11)⋊C4C4⋊C411yescharacteristic
179C4⋊Dic11C4⋊C411yescharacteristic
180C4⋊Dic11C4⋊C411yescharacteristic
181Dic11⋊C4C4⋊C411yescharacteristic
182Dic11⋊C4C4⋊C411yescharacteristic
183Dic11⋊C4C4⋊C411yescharacteristic
184Dic11⋊C4C4⋊C411yescharacteristic
185C4×Dic11C22×C411yescharacteristic
186C4×Dic11C22×C411yescharacteristic
187C4×Dic11C2×D411yescharacteristic
188C4×Dic11C2×D411yescharacteristic
189C4×Dic11C2×Q811yescharacteristic
190C4×Dic11C2×Q811yescharacteristic
191#4318—42no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8C22×C411yescharacteristic
197C2×C11⋊C8C22×C411yescharacteristic
198C2×C11⋊C8C22×C411yescharacteristic
199C2×C11⋊C8C22×C411yescharacteristic
200#4313—22no—
201#4313—41no—
202#4313—42no—
203C8×D11—22no—
204C8×D11—41no—
205C8×D11—42no—
206#2965—111no—
207#2925—111no—
208#2925—111no—
209#1574—111no—
210#1574—111no—
211#1573—111no—
212#1573—111no—
213#1572—111no—
214#1572—111no—
215#1569—111no—
216#1569—111no—
217#1568—111no—
218#1565—111no—
219#1565D1111yescharacteristic, complemented
220#1564—111no—
221C23×C11C2×C4⋊C411yescharacteristic
222C22×D11C2×C4⋊C411yescharacteristic
223C22×D11C2×C4⋊C411yescharacteristic
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—41no—
229C2×C4×C11C2×C4⋊C411yescharacteristic
230C2×C4×C11C2×C4⋊C411yescharacteristic
231C2×C4×C11C2×C4⋊C411yescharacteristic
232C2×C4×C11C23×C411yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×Q811yescharacteristic
235C22⋊D11—41no—
236C22⋊D11—41no—
237C2×Dic11C2×C4⋊C411yescharacteristic
238C2×Dic11C2×C4⋊C411yescharacteristic
239C2×Dic11C2×C4⋊C411yescharacteristic
240C2×Dic11C2×C4⋊C411yescharacteristic
241C2×Dic11C2×C4⋊C411yescharacteristic
242C2×Dic11C2×C4⋊C411yescharacteristic
243D44—41no—
244C4×D11—21no—
245C4×D11—21no—
246C4×D11—21no—
247C4×D11—21no—
248C4×D11—21no—
249C4×D11—21no—
250C4×D11—21no—
251C4×D11—21no—
252C4×D11—41no—
253C4×D11—41no—
254Dic22—41no—
255C8×C11—21no—
256C8×C11—21no—
257C8×C11—21no—
258C8×C11—41no—
259C8×C11—41no—
260C8×C11—41no—
261C8×C11—41no—
262C8×C11#13112yes—
263C11⋊C8—21no—
264C11⋊C8—21no—
265C11⋊C8—21no—
266C11⋊C8—21no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C4×#41—111no—
272#446—111no—
273#446—111no—
274#436—111no—
275#436—111no—
276#435—111no—
277#435—111no—
278#435—111no—
279#435—111no—
280#433—221no—
281#433—221no—
282#433—221no—
283#433—221no—
284#432—111no—
285#432—111no—
286#432—111no—
287#432—111no—
288#431—111no—
289#431—111no—
290#431—111no—
291#431—111no—
292#431—111no—
293#431—111no—
294#431C2×D1111yescharacteristic
295#423—111no—
296#423—111no—
297C2×C4⋊C8—111no—
298C2×C4⋊C8C2×D1111yescharacteristic
299#408—221no—
300#408—221no—
301#405—221no—
302#405—221no—
303C4×M16—111no—
304C4×M16C2×D1111yescharacteristic
305C2×C4×C8—111no—
306#335—111no—
307#335—111no—
308#335—111no—
309#335—111no—
310#335—111no—
311#335—111no—
312#335C2×D1111yescharacteristic
313#335C2×D1111yescharacteristic
314#334—111no—
315#334—111no—
316#334—111no—
317#334—111no—
318#334—111no—
319#334—111no—
320#334C2×D1111yescharacteristic
321#334C2×D1111yescharacteristic
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11C22×C4⋊C411yescharacteristic
326C2×D11—21no—
327C2×D11—21no—
328C2×D11—21no—
329C2×D11—21no—
330C2×D11—21no—
331C2×D11—21no—
332C4×C11—21no—
333C4×C11—21no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11C2×#13111yescharacteristic
337C4×C11#56811yescharacteristic
338C4×C11#57511yescharacteristic
339C4×C11#57511yescharacteristic
340Dic11—21no—
341Dic11—21no—
342Dic11—21no—
343Dic11—21no—
344Dic11—21no—
345Dic11—21no—
346C2×#41—111no—
347C2×M16—111no—
348C2×M16—111no—
349C2×M16—221no—
350C2×M16—221no—
351C2×M16C4×D1111yescharacteristic
352C2×M16C4×D1111yescharacteristic
353C22×C8—21no—
354C22×C8—111no—
355C22×C8—111no—
356C22×C8—221no—
357C4×Q8—111no—
358C4×Q8—111no—
359C4×D4—111no—
360C4×D4—111no—
361C4×D4—111no—
362C4×D4—111no—
363C4×D4—111no—
364C4×D4—111no—
365#117—111no—
366#117—111no—
367#117—111no—
368C2×C42—111no—
369C2×C42—111no—
370C2×C42C22×D1111yescharacteristic
371C4⋊C8—21no—
372C4⋊C8—111no—
373C4⋊C8—111no—
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⋊C8C22×D1111yescharacteristic
386C4⋊C8C22×D1111yescharacteristic
387C4⋊C8C22×D1111yescharacteristic
388C4⋊C8C22×D1111yescharacteristic
389C22⋊C8—21no—
390C22⋊C8—111no—
391C22⋊C8—111no—
392C22⋊C8—111no—
393C22⋊C8—111no—
394C22⋊C8—111no—
395C22⋊C8—111no—
396C22⋊C8—221no—
397C22⋊C8—221no—
398C22⋊C8—221no—
399C22⋊C8—221no—
400C22⋊C8—221no—
401C22⋊C8—221no—
402C22⋊C8—221no—
403#97—111no—
404#97—111no—
405#97—221no—
406#97—221no—
407#97—221no—
408#97—221no—
409#97C4×D1111yescharacteristic
410#97C4×D1111yescharacteristic
411C4×C8—21no—
412C4×C8—111no—
413C4×C8—111no—
414C4×C8—111no—
415C4×C8—111no—
416C4×C8—221no—
417C4×C8—221no—
418C4×C8—221no—
419C4×C8C22×D1111yescharacteristic
420C4×C8C22×D1111yescharacteristic
421C2×C11—41no—
422C2×C11#290611yescharacteristic
423C2×C11#291111yescharacteristic
424C2×C11#291611yescharacteristic
425D11—41no—
426D11—41no—
427#41—441no—
428#41—441no—
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—22no—
443M16—41no—
444M16—222no—
445M16—441no—
446M16—442no—
447M16—442no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—42no—
453C2×C8—111no—
454C2×C8—111no—
455C2×C8—111no—
456C2×C8—111no—
457C2×C8—222no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—441no—
463C2×C8—442no—
464C2×C8C2×C4×D1111yescharacteristic
465C2×C8C2×C4×D1111yescharacteristic
466C2×C8C2×C4×D1111yescharacteristic
467C2×C8C2×C4×D1111yescharacteristic
468C4⋊C4—111no—
469C4⋊C4—111no—
470C4⋊C4—111no—
471C4⋊C4—111no—
472C4⋊C4—111no—
473C4⋊C4—111no—
474C22⋊C4—111no—
475C22⋊C4—111no—
476C22⋊C4—111no—
477C22⋊C4—111no—
478C22⋊C4—111no—
479C22⋊C4—111no—
480C42—111no—
481C42—111no—
482C42—111no—
483C42—111no—
484C42—111no—
485C42—111no—
486C42C2×C4×D1111yescharacteristic
487C42D4×D1111yescharacteristic
488C42Q8×D1111yescharacteristic
489C42C23×D1111yescharacteristic
490C11#1783111yescharacteristic, complemented, Sylow
491C23—111no—
492C23—111no—
493C23C4⋊C4×D1111yescharacteristic
494Q8—441no—
495D4—441no—
496D4—441no—
497D4—441no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—111no—
504C2×C4—111no—
505C2×C4—111no—
506C2×C4—111no—
507C2×C4—111no—
508C2×C4—111no—
509C2×C4—221no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—221no—
517C2×C4—441no—
518C2×C4—441no—
519C2×C4C4⋊C4×D1111yescharacteristic
520C2×C4C4⋊C4×D1111yescharacteristic
521C2×C4C4⋊C4×D1111yescharacteristic
522C2×C4C22×C4×D1111yescharacteristic
523C2×C4C2×D4×D1111yescharacteristic
524C2×C4C2×Q8×D1111yescharacteristic
525C8—21no—
526C8—21no—
527C8—21no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—221no—
533C8—221no—
534C8—221no—
535C8—221no—
536C8—441no—
537C8—441no—
538C8—441no—
539C8—441no—
540C8#6695412yes—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—221no—
545C22—221no—
546C22—221no—
547C22—221no—
548C22—221no—
549C22—221no—
550C22C2×C4⋊C4×D1111yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—221no—
556C4—221no—
557C4—221no—
558C4—221no—
559C4—221no—
560C4—221no—
561C4C2×#6695411yescharacteristic
562C4#1062327611yescharacteristic
563C4#1062330411yescharacteristic
564C4#1062330811yescharacteristic
565C2—41no—
566C2—441no—
567C2—441no—
568C2#1307718111yescharacteristic
569C2#1307720311yescharacteristic
570C2#1307722611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1565C2
socleC22×C11C22×C4⋊C4
prime radicalC2×#4339D4
cosocleC42×C11C24
hypercenter#1565D11
hypocenterC11#17831
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1565

Complements

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

NH ≅ G/Ntype
4. #13067406C2semidirect
5. #13067404C2semidirect
6. #13067399C2semidirect
7. #13067398C2semidirect
8. #13067395C2semidirect
9. #13067393C2semidirect
10. #13067383C2semidirect
11. #13067382C2semidirect
12. #13067378C2semidirect
13. #13067365C2semidirect
14. #13067361C2semidirect
15. C11×#1565C2semidirect
219. #1565D11semidirect
490. C11#17831semidirect

Maximal subgroups

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

subgroupindex
#130775782
#130772812
#130772772
#130674062
#130674042
#130673992
#130673982
#130673952
#130673932
#130673832
#130673822
#130673782
#130673652
#130673612
C11×#15652
#1783111