Finite Group Databasebeta

← #14724813

Subgroups — #14724813

Order 2816.

670 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078665C211yesmaximal, characteristic
2#13077620C211yesmaximal, characteristic, complemented
3M16×D44C211yesmaximal, characteristic, complemented
4#13067531C211yesmaximal, characteristic, complemented
5#13067508C211yesmaximal, characteristic, complemented
6#13067496C211yesmaximal, characteristic, complemented
7#13067482C211yesmaximal, characteristic, complemented
8#13067454C211yesmaximal, characteristic, complemented
9#13067447C211yesmaximal, characteristic, complemented
10#13067430C211yesmaximal, characteristic, complemented
11C8×D88C211yesmaximal, characteristic, complemented
12#13067405C211yesmaximal, characteristic, complemented
13#13067082C211yesmaximal, characteristic, complemented
14#13067008C211yesmaximal, characteristic, complemented
15C11×#1453C211yesmaximal, characteristic, complemented
16C2×M16×D11—21no—
17#10623010C2211yescharacteristic
18C2×C4×D44C2211yescharacteristic
19C11×#431C2211yescharacteristic
20C11×#431C2211yescharacteristic
21C4×C11×M16C2211yescharacteristic
22#10622741—21no—
23#10622740—21no—
24#10622739—21no—
25#10622538C2211yescharacteristic
26#10622537C2211yescharacteristic
27#10622460C411yescharacteristic
28#10622460C411yescharacteristic
29#10622457C411yescharacteristic
30#10622457C411yescharacteristic
31#10622348C411yescharacteristic
32#10622345C411yescharacteristic
33#10622344C411yescharacteristic
34#10622335C411yescharacteristic
35#10622322—21no—
36#10622321—21no—
37#10622319—21no—
38#10622319—21no—
39C4×D88C2211yescharacteristic
40C4×D88C2211yescharacteristic
41C4×#4314C2211yescharacteristic
42C4×#4314C2211yescharacteristic
43#10622301C2211yescharacteristic
44#10622301C2211yescharacteristic
45#10622301C2211yescharacteristic, complemented
46C8×D44C2211yescharacteristic
47C8×D44C2211yescharacteristic
48C8×D44C2211yescharacteristic, complemented
49#10622292C2211yescharacteristic, complemented
50C8×Dic22C2211yescharacteristic, complemented
51C11×#322C2211yescharacteristic, complemented
52C11×#322C2211yescharacteristic, complemented
53C11×#322C2211yescharacteristic, complemented
54C82×C11C2211yescharacteristic, complemented
55#10622097C2211yescharacteristic
56#10622097C2211yescharacteristic
57#10622097C2211yescharacteristic
58#10622097C2211yescharacteristic
59#10622097C2211yescharacteristic, complemented
60#10622097C2211yescharacteristic, complemented
61#10622096C2211yescharacteristic, complemented
62#10622096C2211yescharacteristic, complemented
63#10622095C2211yescharacteristic, complemented
64#10622095C2211yescharacteristic, complemented
65#10622094C2211yescharacteristic, complemented
66#10622094C2211yescharacteristic, complemented
67C22×D44C2×C411yescharacteristic
68C22×C4×D11—21no—
69C2×C11×M16D411yescharacteristic
70C2×C11×M16D411yescharacteristic
71C2×C42×C11C2311yescharacteristic
72#66983C2×C411yescharacteristic
73#66982—21no—
74C4×C22⋊D11—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×C4⋊Dic11C2×C411yescharacteristic
77#66977C2×C411yescharacteristic
78C2×#4318—21no—
79M16×D11—44no—
80C2×D88C2×C411yescharacteristic
81C2×D88C2×C411yescharacteristic
82C2×#4314C2×C411yescharacteristic
83C2×#4314C2×C411yescharacteristic
84C2×#4313—21no—
85C2×#4313—21no—
86C2×#4313—21no—
87C2×C8×D11—21no—
88C2×C8×D11—21no—
89C2×C8×D11—21no—
90#66929—21no—
91#66928C2×C411yescharacteristic
92C4×D44—21no—
93C4×D44—21no—
94C4×D44C2×C411yescharacteristic
95C4×D44C2×C411yescharacteristic
96C4×D44C2311yescharacteristic
97C4×D44C2311yescharacteristic
98C4×D44C2311yescharacteristic
99#66925—21no—
100#66923C2×C411yescharacteristic
101C4×Dic22C2311yescharacteristic
102C11×C4⋊C8—21no—
103C11×C4⋊C8C2×C411yescharacteristic
104C11×C4⋊C8C2×C411yescharacteristic
105C11×C22⋊C8—21no—
106C11×C22⋊C8C2×C411yescharacteristic
107C11×C22⋊C8C2×C411yescharacteristic
108C11×#97D411yescharacteristic
109C11×#97D411yescharacteristic
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2311yescharacteristic
112C4×C8×C11C2311yescharacteristic
113C4×C8×C11C2311yescharacteristic
114C4×C8×C11C2311yescharacteristic
115C4×C8×C11C2311yescharacteristic
116C22⋊(C11⋊C8)—21no—
117#66885C2×C411yescharacteristic
118#66885C2×C411yescharacteristic
119#66885C2×C411yescharacteristic
120#66885C2×C411yescharacteristic
121#66885C2×C411yescharacteristic
122#66885C2×C411yescharacteristic
123(C2×D11)⋊C8—21no—
124(C2×D11)⋊C8—21no—
125(C2×D11)⋊C8—21no—
126(C2×D11)⋊C8—21no—
127(C2×D11)⋊C8—21no—
128(C2×D11)⋊C8—21no—
129#66882C2×C411yescharacteristic
130#66882C2×C411yescharacteristic
131#66881C2×C411yescharacteristic
132#66881C2×C411yescharacteristic
133#66880C2×C411yescharacteristic
134#66880C2×C411yescharacteristic
135#66879—21no—
136Dic11⋊C8—21no—
137Dic11⋊C8—21no—
138C8×Dic11—21no—
139C4⋊(C11⋊C8)—21no—
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4⋊(C11⋊C8)C2311yescharacteristic
144C4×C11⋊C8—21no—
145#18006—111nomaximal, Sylow
146C23×D11—21no—
147C22×C4×C11C22×C411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11#4111yescharacteristic
150C2×C22⋊D11—21no—
151C22×Dic11—21no—
152C2×D44—22no—
153C2×D44—21no—
154C2×D44—41no—
155C2×D44C22×C411yescharacteristic
156C2×D44C22×C411yescharacteristic
157C2×D44C22×C411yescharacteristic
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—42no—
164C2×C4×D11—42no—
165C2×Dic22C22×C411yescharacteristic
166C11×M16—22no—
167C11×M16—41no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11C22×C411yescharacteristic
171C2×C8×C11C22×C411yescharacteristic
172C2×C8×C11C22×C411yescharacteristic
173C2×C8×C11C22×C411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2×D411yescharacteristic
176C2×C8×C11C2×D411yescharacteristic
177C2×C8×C11C2×D411yescharacteristic
178C42×C11C22×C411yescharacteristic
179C42×C11C2×D411yescharacteristic
180C42×C11#4111yescharacteristic
181C42×C11C2411yescharacteristic
182C22⋊Dic11—21no—
183(C2×D11)⋊C4—21no—
184(C2×D11)⋊C4—21no—
185(C2×D11)⋊C4—21no—
186(C2×D11)⋊C4—21no—
187(C2×D11)⋊C4—21no—
188(C2×D11)⋊C4—21no—
189(C2×D11)⋊C4—21no—
190(C2×D11)⋊C4—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11C22×C411yescharacteristic
193C4⋊Dic11C22×C411yescharacteristic
194C4⋊Dic11C22×C411yescharacteristic
195C4⋊Dic11C22×C411yescharacteristic
196Dic11⋊C4—21no—
197Dic11⋊C4—21no—
198Dic11⋊C4—21no—
199Dic11⋊C4—21no—
200C4×Dic11—21no—
201#4318—42no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206D88—22no—
207D88—41no—
208#4314—22no—
209#4314—41no—
210#4313—42no—
211#4313—42no—
212#4313—42no—
213C8×D11—42no—
214C8×D11—42no—
215C8×D11—42no—
216#3105—111no—
217#2969—111no—
218D4×M16—111no—
219#1594—111no—
220#1590—111no—
221#1588—111no—
222#1586—111no—
223#1582—111no—
224#1581—111no—
225SD16⋊C8—111no—
226C8×D8—111no—
227#1574—111no—
228#1495—111no—
229#1478—111no—
230#1453D1111yescharacteristic, complemented
231C23×C11C4×D411yescharacteristic
232C22×D11—21no—
233C22×D11—21no—
234C22×D11—21no—
235C22×D11—42no—
236C22×D11—42no—
237C22×D11—81no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—41no—
243C2×C4×C11C4×D411yescharacteristic
244C2×C4×C11C4×D411yescharacteristic
245C2×C4×C11C4×D411yescharacteristic
246C2×C4×C11C23×C411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C22⋊D11—81no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—42no—
256D44—21no—
257D44—21no—
258D44—21no—
259D44—21no—
260D44—21no—
261D44—42no—
262D44#13112yes—
263C4×D11—42no—
264C4×D11—42no—
265C4×D11—41no—
266C4×D11—41no—
267C4×D11—41no—
268C4×D11—41no—
269C4×D11—41no—
270C4×D11—41no—
271Dic22—21no—
272Dic22—21no—
273C8×C11—21no—
274C8×C11—21no—
275C8×C11—21no—
276C8×C11—21no—
277C8×C11—21no—
278C8×C11—21no—
279C8×C11—21no—
280C8×C11—41no—
281C8×C11—41no—
282C8×C11AGL(1,ℤ/8)12yes—
283C11⋊C8—41no—
284C11⋊C8—41no—
285C11⋊C8—41no—
286C11⋊C8—41no—
287C22×M16—221no—
288#529—111no—
289C2×C4×D4—111no—
290#484—111no—
291#481—111no—
292#478—111no—
293#478—111no—
294#463—111no—
295#463—111no—
296#450—111no—
297#447—111no—
298#446—111no—
299C8×Q8—111no—
300C4×SD16—111no—
301C4×SD16—111no—
302C4×D8—111no—
303C4×D8—111no—
304#436—111no—
305#436—111no—
306#436—111no—
307#436—221no—
308#435—221no—
309#435—221no—
310#435—221no—
311C8×D4—111no—
312C8×D4—111no—
313C8×D4—111no—
314#433—221no—
315#431—111no—
316#431C2×D1111yescharacteristic
317#431C2×D1111yescharacteristic
318#423—111no—
319#407—221no—
320#405—221no—
321C4×M16C2×D1111yescharacteristic
322#335—111no—
323#335—111no—
324#334—111no—
325#334—111no—
326Q8⋊C8—111no—
327Q8⋊C8—111no—
328D4⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8—111no—
331D4⋊C8—111no—
332D4⋊C8—111no—
333D4⋊C8—111no—
334#322C2×D1111yescharacteristic, complemented
335#322C2×D1111yescharacteristic, complemented
336#322C2×D1111yescharacteristic, complemented
337C82C2×D1111yescharacteristic, complemented
338C22×C11—21no—
339C22×C11—21no—
340C22×C11—21no—
341C22×C11C2×C4×D411yescharacteristic
342C2×D11—22no—
343C2×D11—41no—
344C2×D11—41no—
345C2×D11—41no—
346C2×D11—41no—
347C2×D11—41no—
348C2×D11—41no—
349C2×D11—41no—
350C2×D11—41no—
351C2×D11—84no—
352C4×C11—21no—
353C4×C11—21no—
354C4×C11—21no—
355C4×C11—21no—
356C4×C11C2×#13111yescharacteristic
357C4×C11#56811yescharacteristic
358C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
359C4×C11#57511yescharacteristic
360Dic11—41no—
361Dic11—41no—
362Dic11—41no—
363Dic11—41no—
364Dic11—41no—
365C22×D4—111no—
366C23×C4—221no—
367C2×SD16—111no—
368C2×SD16—111no—
369C2×D8—111no—
370C2×D8—111no—
371C2×M16—221no—
372C2×M16—221no—
373C2×M16—221no—
374C2×M16—221no—
375C2×M16—444no—
376C2×M16D4411yescharacteristic
377C2×M16D4411yescharacteristic
378C22×C8—221no—
379C22×C8—221no—
380C22×C8—221no—
381#126—221no—
382#125—111no—
383#124—111no—
384#123—221no—
385C22⋊Q8—111no—
386#121—111no—
387C4×Q8—111no—
388C4×D4—111no—
389C4×D4—111no—
390C4×D4—111no—
391C4×D4—111no—
392C4×D4—111no—
393C4×D4—221no—
394C4×D4—221no—
395C4×D4—221no—
396#117—221no—
397C2×C4⋊C4—111no—
398C2×C22⋊C4—221no—
399C2×C42C22×D1111yescharacteristic
400#107—111no—
401#107—111no—
402#106—111no—
403#106—111no—
404C4⋊C8—21no—
405C4⋊C8—111no—
406C4⋊C8—111no—
407C4⋊C8—111no—
408C4⋊C8—111no—
409C4⋊C8—221no—
410C4⋊C8—221no—
411C4⋊C8—221no—
412C4⋊C8C4×D1111yescharacteristic
413C4⋊C8C4×D1111yescharacteristic
414#103—111no—
415#103—111no—
416#102—111no—
417#102—111no—
418#102—111no—
419#102—111no—
420#102—111no—
421#102—111no—
422C22⋊C8—21no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426C22⋊C8—221no—
427C22⋊C8—221no—
428C22⋊C8—221no—
429C22⋊C8—221no—
430C22⋊C8C4×D1111yescharacteristic
431C22⋊C8C4×D1111yescharacteristic
432#97—221no—
433#97D4411yescharacteristic
434#97D4411yescharacteristic
435C4×C8—221no—
436C4×C8—221no—
437C4×C8C22×D1111yescharacteristic
438C4×C8C22×D1111yescharacteristic
439C4×C8C22×D1111yescharacteristic
440C4×C8C22×D1111yescharacteristic
441C4×C8C22×D1111yescharacteristic
442C4×C8C22×D1111yescharacteristic
443C2×C11—41no—
444C2×C11#293311yescharacteristic
445C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
446C2×C11#295711yescharacteristic
447D11—42no—
448D11—81no—
449D11—81no—
450C24—221no—
451C2×Q8—111no—
452C2×D4—111no—
453C2×D4—111no—
454C2×D4—111no—
455C2×D4—222no—
456C2×D4—221no—
457C2×D4—221no—
458C2×D4—441no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—442no—
466C22×C4—442no—
467C22×C4C2×C4×D1111yescharacteristic
468C22×C4C2×D4411yescharacteristic
469C22×C4#433911yescharacteristic
470SD16—222no—
471SD16—441no—
472D8—222no—
473D8—441no—
474M16—22no—
475M16—41no—
476M16—442no—
477M16—442no—
478M16—442no—
479M16—442no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—442no—
487C2×C8—442no—
488C2×C8—442no—
489C2×C8C2×C4×D1111yescharacteristic
490C2×C8C2×C4×D1111yescharacteristic
491C2×C8C2×C4×D1111yescharacteristic
492C2×C8C2×C4×D1111yescharacteristic
493C2×C8C2×D4411yescharacteristic
494C2×C8C2×D4411yescharacteristic
495C2×C8C2×D4411yescharacteristic
496C2×C8C2×D4411yescharacteristic
497C4⋊C4—111no—
498C4⋊C4—111no—
499C4⋊C4—111no—
500C4⋊C4—111no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C22⋊C4—221no—
507C22⋊C4—221no—
508C22⋊C4—221no—
509C22⋊C4—221no—
510C22⋊C4—221no—
511C22⋊C4—221no—
512C22⋊C4—221no—
513C22⋊C4—221no—
514C22⋊C4—221no—
515C42—221no—
516C42C2×C4×D1111yescharacteristic
517C42C2×D4411yescharacteristic
518C42#433911yescharacteristic
519C42C23×D1111yescharacteristic
520C11#1800611yescharacteristic, complemented, Sylow
521C23—221no—
522C23—221no—
523C23—221no—
524C23—442no—
525C23—442no—
526C23—881no—
527C23C4×D4411yescharacteristic
528Q8—221no—
529Q8—221no—
530D4—112no—
531D4—221no—
532D4—221no—
533D4—221no—
534D4—221no—
535D4—221no—
536D4—442no—
537D4—881no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—442no—
549C2×C4—442no—
550C2×C4—442no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4C4×D4411yescharacteristic
558C2×C4C4×D4411yescharacteristic
559C2×C4C4×D4411yescharacteristic
560C2×C4C22×C4×D1111yescharacteristic
561C2×C4C22×D4411yescharacteristic
562C2×C4C2×#433911yescharacteristic
563C8—21no—
564C8—21no—
565C8—21no—
566C8—21no—
567C8—21no—
568C8—21no—
569C8—21no—
570C8—41no—
571C8—41no—
572C8—441no—
573C8—441no—
574C8—441no—
575C8—441no—
576C8#6696112yes—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—222no—
581C22—441no—
582C22—441no—
583C22—441no—
584C22—441no—
585C22—441no—
586C22—441no—
587C22—441no—
588C22—441no—
589C22—884no—
590C22C2×C4×D4411yescharacteristic
591C4—21no—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—441no—
596C4—441no—
597C4—441no—
598C4—441no—
599C4—441no—
600C4C2×#6696111yescharacteristic
601C4#1062327911yescharacteristic
602C4D11×#13111yescharacteristic
603C4#1062328111yescharacteristic
604C2—41no—
605C2—442no—
606C2—881no—
607C2—881no—
608C2#1307734411yescharacteristic
609C2C4×#6696111yescharacteristic
610C2#1307753411yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1453C2
socleC22×C11C2×C4×D4
prime radical#10622345C4
cosocleC42×C11C24
hypercenter#1453D11
hypocenterC11#18006
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #1453

Complements

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

NH ≅ G/Ntype
2. #13077620C2semidirect
3. M16×D44C2semidirect
4. #13067531C2semidirect
5. #13067508C2semidirect
6. #13067496C2semidirect
7. #13067482C2semidirect
8. #13067454C2semidirect
9. #13067447C2semidirect
10. #13067430C2semidirect
11. C8×D88C2semidirect
12. #13067405C2semidirect
13. #13067082C2semidirect
14. #13067008C2semidirect
15. C11×#1453C2semidirect
45. #10622301C22semidirect
48. C8×D44C22semidirect
49. #10622292C22semidirect
50. C8×Dic22C22semidirect
51. C11×#322C22semidirect
52. C11×#322C22semidirect
53. C11×#322C22semidirect
54. C82×C11C22semidirect
59. #10622097C22semidirect
60. #10622097C22semidirect
61. #10622096C22semidirect
62. #10622096C22semidirect
63. #10622095C22semidirect
64. #10622095C22semidirect
65. #10622094C22semidirect
66. #10622094C22semidirect
230. #1453D11semidirect
334. #322C2×D11semidirect
335. #322C2×D11semidirect
336. #322C2×D11semidirect
337. C82C2×D11semidirect
520. C11#18006semidirect

Maximal subgroups

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

subgroupindex
#130786652
#130776202
M16×D442
#130675312
#130675082
#130674962
#130674822
#130674542
#130674472
#130674302
C8×D882
#130674052
#130670822
#130670082
C11×#14532
#1800611