Finite Group Databasebeta

← #14723923

Subgroups — #14723923

Order 2816.

586 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078653C211yesmaximal, characteristic
2#13077707C211yesmaximal, characteristic
3#13077695C211yesmaximal, characteristic
4#13067488C211yesmaximal, characteristic, complemented
5#13067486C211yesmaximal, characteristic, complemented
6#13067469C211yesmaximal, characteristic, complemented
7#13067463C211yesmaximal, characteristic, complemented
8#13067436C211yesmaximal, characteristic, complemented
9C8×#4326C211yesmaximal, characteristic, complemented
10C8×#4326C211yesmaximal, characteristic, complemented
11#13067393C211yesmaximal, characteristic
12#13067061C211yesmaximal, characteristic
13#13067035C211yesmaximal, characteristic
14#13066912C211yesmaximal, characteristic
15C11×#1579C211yesmaximal, characteristic, complemented
16#10623109C2211yescharacteristic
17C4×Q8×D11C2211yescharacteristic
18C8×Q8×C11C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C4×C11×Q16C2211yescharacteristic
21#10622799C411yescharacteristic
22#10622795C411yescharacteristic
23C4×#4326C2211yescharacteristic
24C4×#4326C2211yescharacteristic
25#10622637C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27#10622497C411yescharacteristic
28#10622488C411yescharacteristic
29#10622453—21no—
30#10622448C2211yescharacteristic
31#10622446—21no—
32#10622446C2211yescharacteristic
33#10622444C2211yescharacteristic
34#10622443—21no—
35#10622443C2211yescharacteristic
36#10622441—21no—
37#10622422C411yescharacteristic
38#10622421C411yescharacteristic
39#10622407C411yescharacteristic
40#10622406C411yescharacteristic
41C4×Dic44C2211yescharacteristic
42#10622303—21no—
43C4×#4313C2211yescharacteristic
44#10622298—21no—
45#10622298C2211yescharacteristic
46#10622298C2211yescharacteristic
47#10622292—21no—
48C8×Dic22—21no—
49C8×Dic22C2211yescharacteristic
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#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×Q8×D11C2×C411yescharacteristic
68C2×C11×Q16C2×C411yescharacteristic
69C4×Q8×C11C2311yescharacteristic
70C4×Q8×C11C2311yescharacteristic
71#66999C2×C411yescharacteristic
72Q8×Dic11C2×C411yescharacteristic
73#66997C2×C411yescharacteristic
74C2×#4326C2×C411yescharacteristic
75C2×#4326C2×C411yescharacteristic
76C2×Dic44C2×C411yescharacteristic
77C2×#4313—21no—
78#66950C2×C411yescharacteristic
79#66949—21no—
80C4⋊C4×D11—21no—
81C4⋊C4×D11C2×C411yescharacteristic
82#66942—21no—
83#66941C2×C411yescharacteristic
84#66940—21no—
85#66940C2×C411yescharacteristic
86#66925—21no—
87C42×D11—21no—
88C42×D11C2311yescharacteristic
89C4×Dic22—21no—
90C4×Dic22—21no—
91C4×Dic22C2311yescharacteristic
92C4×Dic22C2311yescharacteristic
93C11×#107C2×C411yescharacteristic
94C11×C4⋊C8—21no—
95C11×C4⋊C8—21no—
96C11×C4⋊C8C2311yescharacteristic
97C11×C4⋊C8C2311yescharacteristic
98C11×#103C2×C411yescharacteristic
99C11×#103C2×C411yescharacteristic
100C4×C8×C11—21no—
101C4×C8×C11—21no—
102C4×C8×C11C2311yescharacteristic
103C4×C8×C11C2311yescharacteristic
104C4×C8×C11C2311yescharacteristic
105#66899C2×C411yescharacteristic
106#66899C2×C411yescharacteristic
107(C2×D11)⋊C8—21no—
108(C2×D11)⋊C8—21no—
109(C2×D11)⋊C8C2×C411yescharacteristic
110(C2×D11)⋊C8C2×C411yescharacteristic
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⋊C8C2×C411yescharacteristic
124Dic11⋊C8C2×C411yescharacteristic
125Dic11⋊C8D411yescharacteristic
126Dic11⋊C8D411yescharacteristic
127C8×Dic11—21no—
128C8×Dic11—21no—
129C8×Dic11—21no—
130C8×Dic11—21no—
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#17925—111nomaximal, Sylow
145C2×Q8×C11C22×C411yescharacteristic
146C2×Q8×C11C22×C411yescharacteristic
147Q8×D11—22no—
148Q8×D11—22no—
149C2×C4×D11—21no—
150C2×C4×D11—21no—
151C2×C4×D11C22×C411yescharacteristic
152C2×C4×D11C2×D411yescharacteristic
153C2×C4×D11#4111yescharacteristic
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22C22×C411yescharacteristic
157C2×Dic22C22×C411yescharacteristic
158C11×Q16—22no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11C22×C411yescharacteristic
163C2×C8×C11C22×C411yescharacteristic
164C2×C8×C11C2×D411yescharacteristic
165C2×C8×C11C2×D411yescharacteristic
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4C22×C411yescharacteristic
169C11×C4⋊C4C22×C411yescharacteristic
170C42×C11—21no—
171C42×C11—21no—
172C42×C11C2411yescharacteristic
173#4326—22no—
174#4326—22no—
175(C2×D11)⋊C4—21no—
176(C2×D11)⋊C4—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11C22×C411yescharacteristic
180C4⋊Dic11C22×C411yescharacteristic
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×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11C22×C411yescharacteristic
194C4×Dic11C2×D411yescharacteristic
195C4×Dic11#4111yescharacteristic
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8C22×C411yescharacteristic
200C2×C11⋊C8C22×C411yescharacteristic
201C2×C11⋊C8C2×D411yescharacteristic
202C2×C11⋊C8C2×D411yescharacteristic
203Dic44—22no—
204#4313—42no—
205#3104—111no—
206#2985—111no—
207#2982—111no—
208#1587—111no—
209#1587—111no—
210#1584—111no—
211#1584—111no—
212#1579—111no—
213#1579D1111yescharacteristic, complemented
214C8×Q16—111no—
215C8×Q16—111no—
216#1572—111no—
217#1491—111no—
218#1485—111no—
219#1453—111no—
220C22×D11C4×D411yescharacteristic
221Q8×C11—21no—
222Q8×C11—21no—
223Q8×C11—21no—
224Q8×C11#13112yes—
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—24no—
240C4×D11—21no—
241C4×D11—21no—
242C4×D11—21no—
243C4×D11—21no—
244C4×D11—41no—
245C4×D11—81no—
246Dic22—24no—
247Dic22—21no—
248Dic22—21no—
249Dic22—21no—
250Dic22—81no—
251Dic22#13112yes—
252C8×C11—21no—
253C8×C11—21no—
254C8×C11—21no—
255C8×C11—21no—
256C8×C11—41no—
257C8×C11—41no—
258C8×C11—41no—
259C11⋊C8—22no—
260C11⋊C8—21no—
261C11⋊C8—21no—
262C11⋊C8—21no—
263C11⋊C8—21no—
264C11⋊C8—41no—
265C11⋊C8—41no—
266#533—111no—
267C2×C4×Q8—111no—
268#484—111no—
269#484—111no—
270#477—111no—
271#477—111no—
272#462—111no—
273#462—111no—
274#451—111no—
275#451—111no—
276#446—111no—
277#446—111no—
278#446—221no—
279#446—221no—
280C8×Q8—111no—
281C8×Q8—111no—
282C8×Q8—111no—
283C8×Q8—111no—
284C8×Q8—221no—
285C8×Q8—221no—
286C8×Q8C2×D1111yescharacteristic
287C8×Q8C2×D1111yescharacteristic
288C4×Q16—111no—
289C4×Q16—111no—
290C4×Q16—111no—
291C4×Q16C2×D1111yescharacteristic
292#433—221no—
293#433—221no—
294#432—111no—
295#431—111no—
296#431—111no—
297#431—111no—
298#431—221no—
299#431—221no—
300C4×M16—111no—
301#335—111no—
302#335—111no—
303#334—111no—
304#334C2×D1111yescharacteristic
305Q8⋊C8—111no—
306Q8⋊C8—111no—
307Q8⋊C8—111no—
308Q8⋊C8—111no—
309Q8⋊C8—111no—
310Q8⋊C8—111no—
311Q8⋊C8C2×D1111yescharacteristic
312Q8⋊C8C2×D1111yescharacteristic
313#322—111no—
314#322—111no—
315#322C2×D1111yescharacteristic
316C82—111no—
317C22×C11C2×C4×D411yescharacteristic
318C2×D11—21no—
319C2×D11—21no—
320C2×D11—21no—
321C4×C11—22no—
322C4×C11—21no—
323C4×C11—41no—
324C4×C11—41no—
325C4×C11—41no—
326C4×C11C2×#13111yescharacteristic
327C4×C11C2×#13111yescharacteristic
328C4×C11#57811yescharacteristic
329C4×C11#57811yescharacteristic
330Dic11—21no—
331Dic11—22no—
332Dic11—21no—
333Dic11—21no—
334Dic11—41no—
335Dic11—41no—
336Dic11—41no—
337C22×Q8—111no—
338C2×Q16—111no—
339C2×Q16—111no—
340C2×Q16—111no—
341C2×Q16C4×D1111yescharacteristic
342C2×M16—221no—
343C4⋊Q8—111no—
344C4⋊Q8—111no—
345#125—221no—
346C22⋊Q8—111no—
347C22⋊Q8—111no—
348C22⋊Q8—221no—
349C4×Q8—111no—
350C4×Q8—111no—
351C4×Q8—111no—
352C4×Q8—111no—
353C4×Q8—221no—
354C4×Q8—221no—
355C4×Q8—221no—
356C4×Q8C22×D1111yescharacteristic
357C4×Q8C22×D1111yescharacteristic
358#117—221no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—221no—
361C2×C42—111no—
362C2×C42—221no—
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—111no—
374C4⋊C8—111no—
375C4⋊C8—221no—
376C4⋊C8—221no—
377C4⋊C8—221no—
378C4⋊C8—221no—
379C4⋊C8—221no—
380C4⋊C8—221no—
381C4⋊C8C22×D1111yescharacteristic
382C4⋊C8C22×D1111yescharacteristic
383#103—111no—
384#103—111no—
385#103—111no—
386#103—111no—
387#103—111no—
388#103—111no—
389#103C4×D1111yescharacteristic
390#103C4×D1111yescharacteristic
391C22⋊C8—111no—
392C22⋊C8—111no—
393C22⋊C8—111no—
394C22⋊C8—111no—
395C22⋊C8—221no—
396C22⋊C8—221no—
397#97—221no—
398#97—221no—
399#97—221no—
400#97—221no—
401C4×C8—21no—
402C4×C8—21no—
403C4×C8—111no—
404C4×C8—111no—
405C4×C8—111no—
406C4×C8—221no—
407C4×C8—221no—
408C4×C8—221no—
409C4×C8—221no—
410C4×C8—221no—
411C4×C8C22×D1111yescharacteristic
412C4×C8C22×D1111yescharacteristic
413C4×C8C22×D1111yescharacteristic
414C2×C11#292911yescharacteristic
415C2×C11#295011yescharacteristic
416C2×C11#295611yescharacteristic
417D11—41no—
418C2×Q8—111no—
419C2×Q8—111no—
420C2×Q8—221no—
421C2×Q8—221no—
422C2×Q8—222no—
423C2×Q8—222no—
424C2×Q8C2×C4×D1111yescharacteristic
425C2×Q8C2×C4×D1111yescharacteristic
426C22×C4—111no—
427C22×C4—111no—
428C22×C4—111no—
429C22×C4—221no—
430C22×C4—221no—
431Q16—22no—
432Q16—222no—
433Q16—222no—
434Q16—222no—
435M16—442no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—111no—
440C2×C8—111no—
441C2×C8—111no—
442C2×C8—111no—
443C2×C8—221no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8C2×C4×D1111yescharacteristic
447C2×C8C2×C4×D1111yescharacteristic
448C2×C8D4×D1111yescharacteristic
449C2×C8D4×D1111yescharacteristic
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—111no—
453C4⋊C4—111no—
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⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4C2×C4×D1111yescharacteristic
465C4⋊C4C2×C4×D1111yescharacteristic
466C22⋊C4—221no—
467C22⋊C4—221no—
468C42—21no—
469C42—21no—
470C42—111no—
471C42—111no—
472C42—111no—
473C42—221no—
474C42—221no—
475C42—221no—
476C42—221no—
477C42C23×D1111yescharacteristic
478C11#1792511yescharacteristic, complemented, Sylow
479C23—111no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—112no—
484Q8—224no—
485Q8—221no—
486Q8—221no—
487Q8—221no—
488Q8—881no—
489Q8#6695412yes—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—111no—
495C2×C4—111no—
496C2×C4—111no—
497C2×C4—224no—
498C2×C4—221no—
499C2×C4—221no—
500C2×C4—221no—
501C2×C4—221no—
502C2×C4—221no—
503C2×C4—221no—
504C2×C4—221no—
505C2×C4—221no—
506C2×C4—441no—
507C2×C4—881no—
508C2×C4C22×C4×D1111yescharacteristic
509C2×C4C2×D4×D1111yescharacteristic
510C2×C4#41×D1111yescharacteristic
511C8—21no—
512C8—21no—
513C8—21no—
514C8—21no—
515C8—41no—
516C8—41no—
517C8—41no—
518C8—222no—
519C8—221no—
520C8—221no—
521C8—221no—
522C8—221no—
523C8—441no—
524C8—441no—
525C22—221no—
526C22—221no—
527C22—221no—
528C22C4×D4×D1111yescharacteristic
529C4—21no—
530C4—22no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—221no—
535C4—221no—
536C4—222no—
537C4—221no—
538C4—441no—
539C4—441no—
540C4—441no—
541C4C2×#6695411yescharacteristic
542C4D11×#13111yescharacteristic
543C4#1062331011yescharacteristic
544C4#1062331011yescharacteristic
545C2—441no—
546C2#1307730511yescharacteristic
547C2#1307748111yescharacteristic
548C2#1307752411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1579C2
socleC22×C11C2×C4×D4
prime radicalC22×D11C4×D4
cosocleC42×C11C24
hypercenter#1579D11
hypocenterC11#17925
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1579

Complements

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

NH ≅ G/Ntype
4. #13067488C2semidirect
5. #13067486C2semidirect
6. #13067469C2semidirect
7. #13067463C2semidirect
8. #13067436C2semidirect
9. C8×#4326C2semidirect
10. C8×#4326C2semidirect
15. C11×#1579C2semidirect
213. #1579D11semidirect
478. C11#17925semidirect

Maximal subgroups

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

subgroupindex
#130786532
#130777072
#130776952
#130674882
#130674862
#130674692
#130674632
#130674362
C8×#43262
#130673932
#130670612
#130670352
#130669122
C11×#15792
#1792511