Finite Group Databasebeta

← #14724631

Subgroups — #14724631

Order 2816.

544 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079199C211yesmaximal, characteristic
2#13077712C211yesmaximal, characteristic
3#13077707C211yesmaximal, characteristic
4#13067489C211yesmaximal, characteristic, complemented
5#13067488C211yesmaximal, characteristic, complemented
6#13067486C211yesmaximal, characteristic, complemented
7#13067469C211yesmaximal, characteristic, complemented
8#13067466C211yesmaximal, characteristic, complemented
9#13067464C211yesmaximal, characteristic, complemented
10#13067463C211yesmaximal, characteristic, complemented
11#13067376C211yesmaximal, characteristic
12#13067087C211yesmaximal, characteristic
13#13067087C211yesmaximal, characteristic
14#13066907C211yesmaximal, characteristic
15C11×#1587C211yesmaximal, characteristic, complemented
16#10623109C2211yescharacteristic
17#10623109C2211yescharacteristic
18C11×#446C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C4×C11×Q16C2211yescharacteristic
21#10622801C411yescharacteristic
22#10622794C411yescharacteristic
23C4×#4326C2211yescharacteristic
24C4×#4326C2211yescharacteristic
25#10622637C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27#10622500C411yescharacteristic
28#10622487C411yescharacteristic
29#10622453—21no—
30#10622453—21no—
31#10622448C2211yescharacteristic
32#10622448C2211yescharacteristic
33#10622444—21no—
34#10622444C2211yescharacteristic
35#10622443C2211yescharacteristic
36#10622441—21no—
37#10622426C411yescharacteristic
38#10622426C411yescharacteristic
39#10622405C411yescharacteristic
40#10622405C411yescharacteristic
41#10622322—21no—
42#10622314—21no—
43C4×Dic44C2211yescharacteristic
44#10622303—21no—
45#10622298C2211yescharacteristic
46#10622298C2211yescharacteristic
47C4×C8×D11C2211yescharacteristic
48#10622292—21no—
49#10622292C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51C11×#334C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×Q8⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56Q8⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622122C2211yescharacteristic
59#10622117C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622095C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622093C2211yescharacteristic
65#10622092C2211yescharacteristic
66#10622092C2211yescharacteristic
67C2×C11×Q16C2×C411yescharacteristic
68C4×Q8×C11C2311yescharacteristic
69C4×Q8×C11C2311yescharacteristic
70#66999C2×C411yescharacteristic
71#66999C2×C411yescharacteristic
72#66997C2×C411yescharacteristic
73#66997C2×C411yescharacteristic
74C2×#4326C2×C411yescharacteristic
75C2×#4326C2×C411yescharacteristic
76C2×Dic44C2×C411yescharacteristic
77C2×C8×D11C2×C411yescharacteristic
78C2×C8×D11C2×C411yescharacteristic
79#66950C2×C411yescharacteristic
80#66950C2×C411yescharacteristic
81#66949—21no—
82#66949—21no—
83#66942—21no—
84#66942—21no—
85#66941C2×C411yescharacteristic
86#66941C2×C411yescharacteristic
87#66925—21no—
88#66925—21no—
89C42×D11C2311yescharacteristic
90C4×Dic22—21no—
91C4×Dic22—21no—
92C4×Dic22C2311yescharacteristic
93C4×Dic22C2311yescharacteristic
94C11×#107C2×C411yescharacteristic
95C11×C4⋊C8—21no—
96C11×C4⋊C8—21no—
97C11×C4⋊C8C2311yescharacteristic
98C11×C4⋊C8C2311yescharacteristic
99C11×#103C2×C411yescharacteristic
100C11×#103C2×C411yescharacteristic
101C11×#97—21no—
102C4×C8×C11—21no—
103C4×C8×C11C2311yescharacteristic
104C4×C8×C11C2311yescharacteristic
105C4×C8×C11C2311yescharacteristic
106#66899C2×C411yescharacteristic
107#66899C2×C411yescharacteristic
108(C2×D11)⋊C8—21no—
109(C2×D11)⋊C8—21no—
110(C2×D11)⋊C8—21no—
111(C2×D11)⋊C8D411yescharacteristic
112(C2×D11)⋊C8D411yescharacteristic
113#66882C2×C411yescharacteristic
114#66880C2×C411yescharacteristic
115#66880C2×C411yescharacteristic
116#66879—21no—
117#66879—21no—
118#66879—21no—
119#66879—21no—
120Dic11⋊C8—21no—
121Dic11⋊C8—21no—
122Dic11⋊C8—21no—
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125Dic11⋊C8D411yescharacteristic
126Dic11⋊C8D411yescharacteristic
127C8×Dic11—21no—
128C8×Dic11—21no—
129C8×Dic11C2×C411yescharacteristic
130C8×Dic11C2×C411yescharacteristic
131#66874C2×C411yescharacteristic
132#66874C2×C411yescharacteristic
133#66871C2×C411yescharacteristic
134#66871C2×C411yescharacteristic
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139#66867—21no—
140C4×C11⋊C8—21no—
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17991—111nomaximal, Sylow
145C2×Q8×C11C22×C411yescharacteristic
146C2×Q8×C11C22×C411yescharacteristic
147C2×C4×D11C22×C411yescharacteristic
148C2×C4×D11C2×D411yescharacteristic
149C2×C4×D11#4111yescharacteristic
150C2×Dic22—21no—
151C2×Dic22—21no—
152C2×Dic22C22×C411yescharacteristic
153C2×Dic22C22×C411yescharacteristic
154C11×Q16—41no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11C22×C411yescharacteristic
159C2×C8×C11C22×C411yescharacteristic
160C2×C8×C11C2×D411yescharacteristic
161C2×C8×C11C2×D411yescharacteristic
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4C22×C411yescharacteristic
165C11×C4⋊C4C22×C411yescharacteristic
166C42×C11—21no—
167C42×C11—21no—
168C42×C11C2411yescharacteristic
169#4326—41no—
170#4326—41no—
171(C2×D11)⋊C4—21no—
172(C2×D11)⋊C4—21no—
173(C2×D11)⋊C4—21no—
174(C2×D11)⋊C4—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11C22×C411yescharacteristic
178C4⋊Dic11C22×C411yescharacteristic
179Dic11⋊C4—21no—
180Dic11⋊C4—21no—
181Dic11⋊C4—21no—
182Dic11⋊C4—21no—
183Dic11⋊C4—21no—
184Dic11⋊C4—21no—
185Dic11⋊C4—21no—
186Dic11⋊C4—21no—
187Dic11⋊C4—21no—
188Dic11⋊C4—21no—
189C4×Dic11—21no—
190C4×Dic11—21no—
191C4×Dic11C22×C411yescharacteristic
192C4×Dic11C2×D411yescharacteristic
193C4×Dic11#4111yescharacteristic
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8C22×C411yescharacteristic
198C2×C11⋊C8C22×C411yescharacteristic
199C2×C11⋊C8C2×D411yescharacteristic
200C2×C11⋊C8C2×D411yescharacteristic
201Dic44—41no—
202C8×D11—41no—
203C8×D11—41no—
204#3170—111no—
205#2985—111no—
206#2985—111no—
207#1587—111no—
208#1587—111no—
209#1587—111no—
210#1587D1111yescharacteristic, complemented
211#1584—111no—
212#1584—111no—
213#1584—111no—
214#1584—111no—
215#1568—111no—
216#1497—111no—
217#1497—111no—
218#1452—111no—
219C22×D11C4×D411yescharacteristic
220Q8×C11—21no—
221Q8×C11—21no—
222Q8×C11—21no—
223Q8×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11C23×C411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×Dic11—21no—
232C2×Dic11—21no—
233C2×Dic11—21no—
234C2×Dic11—21no—
235C2×Dic11C4×D411yescharacteristic
236C2×Dic11C4×D411yescharacteristic
237C2×Dic11C4×D411yescharacteristic
238C4×D11—21no—
239C4×D11—21no—
240C4×D11—21no—
241C4×D11—21no—
242C4×D11—41no—
243Dic22—21no—
244Dic22—21no—
245Dic22—21no—
246Dic22—21no—
247Dic22—81no—
248Dic22—81no—
249C8×C11—21no—
250C8×C11—21no—
251C8×C11—21no—
252C8×C11—21no—
253C8×C11—41no—
254C8×C11—41no—
255C8×C11—41no—
256C11⋊C8—21no—
257C11⋊C8—21no—
258C11⋊C8—21no—
259C11⋊C8—21no—
260C11⋊C8—41no—
261C11⋊C8—41no—
262C11⋊C8—41no—
263#533—111no—
264#533—111no—
265#500—111no—
266#494—111no—
267#487—111no—
268#487—111no—
269#467—111no—
270#467—111no—
271#467—111no—
272#467—111no—
273#446—111no—
274#446—111no—
275#446—111no—
276#446—221no—
277#446—221no—
278#446—221no—
279#446—221no—
280#446C2×D1111yescharacteristic
281C8×Q8—111no—
282C8×Q8—111no—
283C8×Q8—111no—
284C8×Q8C2×D1111yescharacteristic
285C4×Q16—111no—
286C4×Q16—111no—
287C4×Q16—111no—
288C4×Q16C2×D1111yescharacteristic
289#433—221no—
290#433—221no—
291#433—221no—
292#433—221no—
293#432—111no—
294#432—111no—
295#431—111no—
296#431—111no—
297C2×C4×C8—111no—
298#335—111no—
299#335—111no—
300#334—111no—
301#334C2×D1111yescharacteristic
302Q8⋊C8—111no—
303Q8⋊C8—111no—
304Q8⋊C8—111no—
305Q8⋊C8—111no—
306Q8⋊C8—111no—
307Q8⋊C8—111no—
308Q8⋊C8C2×D1111yescharacteristic
309Q8⋊C8C2×D1111yescharacteristic
310#322—111no—
311#322—111no—
312#322—111no—
313#322C2×D1111yescharacteristic
314C22×C11C2×C4×D411yescharacteristic
315C2×D11—21no—
316C2×D11—21no—
317C2×D11—21no—
318C4×C11—21no—
319C4×C11—41no—
320C4×C11—41no—
321C4×C11—41no—
322C4×C11—41no—
323C4×C11#56811yescharacteristic
324C4×C11#56811yescharacteristic
325C4×C11#57811yescharacteristic
326C4×C11#57811yescharacteristic
327Dic11—21no—
328Dic11—21no—
329Dic11—21no—
330Dic11—41no—
331Dic11—41no—
332Dic11—41no—
333Dic11—41no—
334C2×Q16—111no—
335C2×Q16—111no—
336C2×Q16—111no—
337C2×Q16C4×D1111yescharacteristic
338C22×C8—111no—
339C22×C8—111no—
340C4⋊Q8—111no—
341C4⋊Q8—111no—
342C4⋊Q8—111no—
343C4⋊Q8—111no—
344#125—221no—
345#125—221no—
346C22⋊Q8—111no—
347C22⋊Q8—111no—
348C22⋊Q8—111no—
349C22⋊Q8—111no—
350C22⋊Q8—221no—
351C22⋊Q8—221no—
352C4×Q8—111no—
353C4×Q8—111no—
354C4×Q8—221no—
355C4×Q8—221no—
356C4×Q8C22×D1111yescharacteristic
357C4×Q8C22×D1111yescharacteristic
358#117—221no—
359#117—221no—
360C2×C42—111no—
361#107—111no—
362#107—111no—
363#107—111no—
364#107C4×D1111yescharacteristic
365C4⋊C8—21no—
366C4⋊C8—21no—
367C4⋊C8—111no—
368C4⋊C8—111no—
369C4⋊C8—111no—
370C4⋊C8—111no—
371C4⋊C8—221no—
372C4⋊C8—221no—
373C4⋊C8—221no—
374C4⋊C8—221no—
375C4⋊C8—221no—
376C4⋊C8—221no—
377C4⋊C8—221no—
378C4⋊C8C22×D1111yescharacteristic
379C4⋊C8C22×D1111yescharacteristic
380#103—111no—
381#103—111no—
382#103—111no—
383#103—111no—
384#103—111no—
385#103—111no—
386#103C4×D1111yescharacteristic
387#103C4×D1111yescharacteristic
388C22⋊C8—111no—
389C22⋊C8—111no—
390C22⋊C8—221no—
391C22⋊C8—221no—
392C22⋊C8—221no—
393#97—21no—
394#97—221no—
395#97—221no—
396#97—221no—
397#97—221no—
398#97—221no—
399C4×C8—21no—
400C4×C8—111no—
401C4×C8—111no—
402C4×C8—111no—
403C4×C8—111no—
404C4×C8—111no—
405C4×C8—221no—
406C4×C8—221no—
407C4×C8—221no—
408C4×C8C22×D1111yescharacteristic
409C4×C8C22×D1111yescharacteristic
410C4×C8C22×D1111yescharacteristic
411C2×C11#293211yescharacteristic
412C2×C11#295011yescharacteristic
413C2×C11#295711yescharacteristic
414D11—41no—
415C2×Q8—111no—
416C2×Q8—111no—
417C2×Q8—221no—
418C2×Q8—221no—
419C2×Q8C2×C4×D1111yescharacteristic
420C2×Q8C2×C4×D1111yescharacteristic
421C22×C4—111no—
422C22×C4—111no—
423C22×C4—111no—
424Q16—41no—
425Q16—441no—
426Q16—441no—
427Q16—441no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—111no—
432C2×C8—111no—
433C2×C8—111no—
434C2×C8—111no—
435C2×C8—221no—
436C2×C8—221no—
437C2×C8—221no—
438C2×C8—441no—
439C2×C8—441no—
440C2×C8C2×C4×D1111yescharacteristic
441C2×C8C2×C4×D1111yescharacteristic
442C2×C8D4×D1111yescharacteristic
443C2×C8D4×D1111yescharacteristic
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—111no—
447C4⋊C4—111no—
448C4⋊C4—221no—
449C4⋊C4—221no—
450C4⋊C4—221no—
451C4⋊C4—221no—
452C4⋊C4—221no—
453C4⋊C4—221no—
454C4⋊C4—221no—
455C4⋊C4—221no—
456C4⋊C4—221no—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4C2×C4×D1111yescharacteristic
461C4⋊C4C2×C4×D1111yescharacteristic
462C22⋊C4—221no—
463C22⋊C4—221no—
464C22⋊C4—221no—
465C22⋊C4—221no—
466C42—21no—
467C42—21no—
468C42—111no—
469C42—111no—
470C42—111no—
471C42—221no—
472C42—221no—
473C42C23×D1111yescharacteristic
474C11#1799111yescharacteristic, complemented, Sylow
475C23—111no—
476Q8—21no—
477Q8—21no—
478Q8—21no—
479Q8—21no—
480Q8—221no—
481Q8—221no—
482Q8—221no—
483Q8—221no—
484Q8—881no—
485Q8—881no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—111no—
491C2×C4—111no—
492C2×C4—111no—
493C2×C4—221no—
494C2×C4—221no—
495C2×C4—221no—
496C2×C4—221no—
497C2×C4—221no—
498C2×C4—221no—
499C2×C4—221no—
500C2×C4—221no—
501C2×C4—441no—
502C2×C4C22×C4×D1111yescharacteristic
503C2×C4C2×D4×D1111yescharacteristic
504C2×C4#41×D1111yescharacteristic
505C8—21no—
506C8—21no—
507C8—21no—
508C8—21no—
509C8—41no—
510C8—41no—
511C8—41no—
512C8—221no—
513C8—221no—
514C8—221no—
515C8—221no—
516C8—441no—
517C8—441no—
518C8—441no—
519C22—221no—
520C22—221no—
521C22—221no—
522C22C4×D4×D1111yescharacteristic
523C4—21no—
524C4—41no—
525C4—41no—
526C4—41no—
527C4—41no—
528C4—221no—
529C4—221no—
530C4—221no—
531C4—441no—
532C4—441no—
533C4—441no—
534C4—441no—
535C4#1062327611yescharacteristic
536C4#1062328111yescharacteristic
537C4#1062331011yescharacteristic
538C4#1062331011yescharacteristic
539C2—441no—
540C2#1307733011yescharacteristic
541C2#1307748111yescharacteristic
542C2#1307752811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1587C2
socleC22×C11C2×C4×D4
prime radicalC22×D11C4×D4
cosocleC42×C11C24
hypercenter#1587D11
hypocenterC11#17991
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1587

Complements

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

NH ≅ G/Ntype
4. #13067489C2semidirect
5. #13067488C2semidirect
6. #13067486C2semidirect
7. #13067469C2semidirect
8. #13067466C2semidirect
9. #13067464C2semidirect
10. #13067463C2semidirect
15. C11×#1587C2semidirect
210. #1587D11semidirect
474. C11#17991semidirect

Maximal subgroups

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

subgroupindex
#130791992
#130777122
#130777072
#130674892
#130674882
#130674862
#130674692
#130674662
#130674642
#130674632
#130673762
#130670872
#130669072
C11×#15872
#1799111