Finite Group Databasebeta

← #14725800

Subgroups — #14725800

Order 2816.

564 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079199C211yesmaximal, characteristic
2#13077716C211yesmaximal, characteristic
3#13077714C211yesmaximal, characteristic
4#13067523C211yesmaximal, characteristic, complemented
5#13067522C211yesmaximal, characteristic, complemented
6#13067468C211yesmaximal, characteristic, complemented
7#13067467C211yesmaximal, characteristic, complemented
8#13067465C211yesmaximal, characteristic, complemented
9#13067433C211yesmaximal, characteristic, complemented
10#13067432C211yesmaximal, characteristic, complemented
11#13067363C211yesmaximal, characteristic
12#13067035C211yesmaximal, characteristic
13#13067035C211yesmaximal, characteristic
14#13066904C211yesmaximal, characteristic
15C11×#1584C211yesmaximal, 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#10622446C2211yescharacteristic
32#10622446C2211yescharacteristic
33#10622444C2211yescharacteristic
34#10622443—21no—
35#10622443C2211yescharacteristic
36#10622441—21no—
37#10622426C411yescharacteristic
38#10622426C411yescharacteristic
39#10622405C411yescharacteristic
40#10622405C411yescharacteristic
41#10622322—21no—
42#10622314—21no—
43C4×Dic44C2211yescharacteristic
44#10622303—21no—
45C4×#4313C2211yescharacteristic
46#10622298C2211yescharacteristic
47C4×C8×D11C2211yescharacteristic
48#10622292C2211yescharacteristic
49C8×Dic22—21no—
50C8×Dic22C2211yescharacteristic
51C11×#335C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×Q8⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56Q8⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622122C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622118C2211yescharacteristic
61#10622096C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622092C2211yescharacteristic
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×#4313—21no—
78C2×C8×D11C2×C411yescharacteristic
79C2×C8×D11C2×C411yescharacteristic
80#66950C2×C411yescharacteristic
81#66950C2×C411yescharacteristic
82#66949—21no—
83#66949—21no—
84#66942—21no—
85#66942—21no—
86#66941C2×C411yescharacteristic
87#66941C2×C411yescharacteristic
88#66925—21no—
89#66925—21no—
90C42×D11C2311yescharacteristic
91C4×Dic22—21no—
92C4×Dic22—21no—
93C4×Dic22C2311yescharacteristic
94C4×Dic22C2311yescharacteristic
95C11×#107C2×C411yescharacteristic
96C11×C4⋊C8—21no—
97C11×C4⋊C8—21no—
98C11×C4⋊C8C2311yescharacteristic
99C11×C4⋊C8C2311yescharacteristic
100C11×#103C2×C411yescharacteristic
101C11×#103C2×C411yescharacteristic
102C11×#97—21no—
103C4×C8×C11—21no—
104C4×C8×C11C2311yescharacteristic
105C4×C8×C11C2311yescharacteristic
106C4×C8×C11C2311yescharacteristic
107#66899C2×C411yescharacteristic
108#66899C2×C411yescharacteristic
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—
119Dic11⋊C8—21no—
120Dic11⋊C8—21no—
121Dic11⋊C8—21no—
122Dic11⋊C8—21no—
123Dic11⋊C8D411yescharacteristic
124Dic11⋊C8D411yescharacteristic
125C8×Dic11—21no—
126C8×Dic11—21no—
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#18090—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—22no—
170#4326—22no—
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—
202#4313—42no—
203C8×D11—22no—
204C8×D11—41no—
205#3170—111no—
206#2986—111no—
207#2986—111no—
208#1593—111no—
209#1593—111no—
210#1584—111no—
211#1584—111no—
212#1584—111no—
213#1584D1111yescharacteristic, complemented
214#1579—111no—
215#1579—111no—
216#1564—111no—
217#1485—111no—
218#1485—111no—
219#1451—111no—
220C22×D11C4×D411yescharacteristic
221Q8×C11—21no—
222Q8×C11—21no—
223Q8×C11—21no—
224Q8×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11C23×C411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×Dic11—21no—
233C2×Dic11—21no—
234C2×Dic11—21no—
235C2×Dic11—21no—
236C2×Dic11C4×D411yescharacteristic
237C2×Dic11C4×D411yescharacteristic
238C2×Dic11C4×D411yescharacteristic
239C4×D11—21no—
240C4×D11—21no—
241C4×D11—21no—
242C4×D11—21no—
243C4×D11—22no—
244Dic22—21no—
245Dic22—21no—
246Dic22—21no—
247Dic22—21no—
248Dic22—42no—
249Dic22—42no—
250C8×C11—21no—
251C8×C11—21no—
252C8×C11—21no—
253C8×C11—21no—
254C8×C11—41no—
255C8×C11—41no—
256C8×C11—41no—
257C11⋊C8—21no—
258C11⋊C8—21no—
259C11⋊C8—21no—
260C11⋊C8—41no—
261C11⋊C8—41no—
262C11⋊C8—41no—
263C11⋊C8#13112yes—
264#533—111no—
265#533—111no—
266#500—111no—
267#494—111no—
268#487—111no—
269#487—111no—
270#467—111no—
271#467—111no—
272#467—111no—
273#467—111no—
274#446—111no—
275#446—111no—
276#446—111no—
277#446—221no—
278#446—221no—
279#446C2×D1111yescharacteristic
280C8×Q8—111no—
281C8×Q8—111no—
282C8×Q8—111no—
283C8×Q8—221no—
284C8×Q8—221no—
285C8×Q8C2×D1111yescharacteristic
286C4×Q16—111no—
287C4×Q16—111no—
288C4×Q16—111no—
289C4×Q16C2×D1111yescharacteristic
290#433—221no—
291#433—221no—
292#433—221no—
293#433—221no—
294#431—111no—
295#431—111no—
296#431—111no—
297C4×M16—111no—
298C2×C4×C8—111no—
299#335—111no—
300#335C2×D1111yescharacteristic
301#334—111no—
302#334—111no—
303Q8⋊C8—111no—
304Q8⋊C8—111no—
305Q8⋊C8—111no—
306Q8⋊C8—111no—
307Q8⋊C8—111no—
308Q8⋊C8—111no—
309Q8⋊C8C2×D1111yescharacteristic
310Q8⋊C8C2×D1111yescharacteristic
311#322—111no—
312#322—111no—
313#322—111no—
314#322C2×D1111yescharacteristic
315C22×C11C2×C4×D411yescharacteristic
316C2×D11—21no—
317C2×D11—21no—
318C2×D11—21no—
319C4×C11—21no—
320C4×C11—41no—
321C4×C11—41no—
322C4×C11—41no—
323C4×C11—41no—
324C4×C11C2×#13111yescharacteristic
325C4×C11#56811yescharacteristic
326C4×C11#57811yescharacteristic
327C4×C11#57811yescharacteristic
328Dic11—21no—
329Dic11—21no—
330Dic11—41no—
331Dic11—41no—
332Dic11—41no—
333Dic11—41no—
334Dic11#44412yes—
335C2×Q16—111no—
336C2×Q16—111no—
337C2×Q16—111no—
338C2×Q16C4×D1111yescharacteristic
339C2×M16—221no—
340C22×C8—111no—
341C22×C8—111no—
342C4⋊Q8—111no—
343C4⋊Q8—111no—
344C4⋊Q8—111no—
345C4⋊Q8—111no—
346#125—221no—
347#125—221no—
348C22⋊Q8—111no—
349C22⋊Q8—111no—
350C22⋊Q8—111no—
351C22⋊Q8—111no—
352C22⋊Q8—221no—
353C22⋊Q8—221no—
354C4×Q8—111no—
355C4×Q8—111no—
356C4×Q8—221no—
357C4×Q8—221no—
358C4×Q8C22×D1111yescharacteristic
359C4×Q8C22×D1111yescharacteristic
360#117—221no—
361#117—221no—
362C2×C42—111no—
363#107—111no—
364#107—111no—
365#107—111no—
366#107C4×D1111yescharacteristic
367C4⋊C8—21no—
368C4⋊C8—21no—
369C4⋊C8—111no—
370C4⋊C8—111no—
371C4⋊C8—111no—
372C4⋊C8—111no—
373C4⋊C8—221no—
374C4⋊C8—221no—
375C4⋊C8—221no—
376C4⋊C8—221no—
377C4⋊C8—221no—
378C4⋊C8—221no—
379C4⋊C8C22×D1111yescharacteristic
380C4⋊C8C22×D1111yescharacteristic
381#103—111no—
382#103—111no—
383#103—111no—
384#103—111no—
385#103—111no—
386#103—111no—
387#103C4×D1111yescharacteristic
388#103C4×D1111yescharacteristic
389C22⋊C8—111no—
390C22⋊C8—111no—
391C22⋊C8—221no—
392C22⋊C8—221no—
393#97—21no—
394#97—221no—
395#97—221no—
396#97—221no—
397#97—221no—
398C4×C8—21no—
399C4×C8—111no—
400C4×C8—111no—
401C4×C8—111no—
402C4×C8—111no—
403C4×C8—111no—
404C4×C8—221no—
405C4×C8—221no—
406C4×C8—221no—
407C4×C8—221no—
408C4×C8—221no—
409C4×C8C22×D1111yescharacteristic
410C4×C8C22×D1111yescharacteristic
411C4×C8C22×D1111yescharacteristic
412C2×C11#293511yescharacteristic
413C2×C11#295011yescharacteristic
414C2×C11C2×#44411yescharacteristic
415D11—41no—
416C2×Q8—111no—
417C2×Q8—111no—
418C2×Q8—221no—
419C2×Q8—221no—
420C2×Q8C2×C4×D1111yescharacteristic
421C2×Q8C2×C4×D1111yescharacteristic
422C22×C4—111no—
423C22×C4—111no—
424C22×C4—111no—
425Q16—41no—
426Q16—222no—
427Q16—222no—
428Q16—441no—
429M16—442no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—111no—
434C2×C8—111no—
435C2×C8—111no—
436C2×C8—111no—
437C2×C8—222no—
438C2×C8—221no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—441no—
442C2×C8C2×C4×D1111yescharacteristic
443C2×C8C2×C4×D1111yescharacteristic
444C2×C8D4×D1111yescharacteristic
445C2×C8D4×D1111yescharacteristic
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—111no—
449C4⋊C4—111no—
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⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4C2×C4×D1111yescharacteristic
463C4⋊C4C2×C4×D1111yescharacteristic
464C22⋊C4—221no—
465C22⋊C4—221no—
466C22⋊C4—221no—
467C22⋊C4—221no—
468C42—21no—
469C42—21no—
470C42—111no—
471C42—111no—
472C42—111no—
473C42—221no—
474C42—221no—
475C42C23×D1111yescharacteristic
476C11#1809011yescharacteristic, complemented, Sylow
477C23—111no—
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—221no—
483Q8—221no—
484Q8—221no—
485Q8—221no—
486Q8—442no—
487Q8—442no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—111no—
493C2×C4—111no—
494C2×C4—111no—
495C2×C4—222no—
496C2×C4—221no—
497C2×C4—221no—
498C2×C4—221no—
499C2×C4—221no—
500C2×C4—221no—
501C2×C4—221no—
502C2×C4—221no—
503C2×C4—221no—
504C2×C4C22×C4×D1111yescharacteristic
505C2×C4C2×D4×D1111yescharacteristic
506C2×C4#41×D1111yescharacteristic
507C8—21no—
508C8—21no—
509C8—21no—
510C8—21no—
511C8—41no—
512C8—41no—
513C8—41no—
514C8—112no—
515C8—221no—
516C8—221no—
517C8—221no—
518C8—441no—
519C8—441no—
520C8—441no—
521C22—221no—
522C22—221no—
523C22—221no—
524C22C4×D4×D1111yescharacteristic
525C4—21no—
526C4—41no—
527C4—41no—
528C4—41no—
529C4—41no—
530C4—112no—
531C4—221no—
532C4—221no—
533C4—441no—
534C4—441no—
535C4—441no—
536C4—441no—
537C4#1062327611yescharacteristic
538C4D11×#13111yescharacteristic
539C4#1062329711yescharacteristic
540C4#1062330211yescharacteristic
541C2—441no—
542C2#1307735711yescharacteristic
543C2#1307747911yescharacteristic
544C2D11×#44411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1584C2
socleC22×C11C2×C4×D4
prime radicalC22×D11C4×D4
cosocleC42×C11C24
hypercenter#1584D11
hypocenterC11#18090
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1584

Complements

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

NH ≅ G/Ntype
4. #13067523C2semidirect
5. #13067522C2semidirect
6. #13067468C2semidirect
7. #13067467C2semidirect
8. #13067465C2semidirect
9. #13067433C2semidirect
10. #13067432C2semidirect
15. C11×#1584C2semidirect
213. #1584D11semidirect
476. C11#18090semidirect

Maximal subgroups

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

subgroupindex
#130791992
#130777162
#130777142
#130675232
#130675222
#130674682
#130674672
#130674652
#130674332
#130674322
#130673632
#130670352
#130669042
C11×#15842
#1809011