Finite Group Databasebeta

← #14772161

Subgroups — #14772161

Order 2816.

1134 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4323C211yesmaximal, characteristic
2C2×#10622369C212yesmaximal
3D4×C4⋊Dic11C211yesmaximal, characteristic, complemented
4#13071516C211yesmaximal, characteristic, complemented
5#13069348C212yesmaximal, complemented
6#13068864C212yesmaximal, complemented
7#13068861C212yesmaximal, complemented
8#13068775C211yesmaximal, characteristic, complemented
9#13068617C211yesmaximal, characteristic, complemented
10#13068481C211yesmaximal, characteristic, complemented
11C11×#1802C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13C2×D4×Dic11C2212yes—
14C22×#4323C2211yescharacteristic
15C22×C4⋊Dic11—21no—
16C2×#66946C2212yes—
17C2×C4⋊C4×D11—21no—
18C2×C4×D44C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#102C2212yes—
21C11×#384C2211yescharacteristic
22C2×#66896C2211yescharacteristic
23#10622825—21no—
24C2×#66885C2212yes—
25C2×C8×Dic11C2212yes—
26C4×#4323C418yescomplemented
27#10622602—22no—
28#10622600—21no—
29#10622598C2212yes—
30#10622586C2212yes—
31C2×#66873C2211yescharacteristic
32C2×#66871C2212yes—
33C2×#66871C2212yes—
34C2×#66871C2211yescharacteristic
35#10622563—22no—
36#10622548C2211yescharacteristic
37C4×C4⋊Dic11C2211yescharacteristic
38C2×C4×C11⋊C8C2211yescharacteristic
39#10622369—28no—
40C11×#340C2212yes—
41#10622189C2212yes—
42#10622188C2212yes—
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11—21no—
45C23×Dic11—22no—
46C22×D44C2311yescharacteristic
47C22×C4×D11—21no—
48C22×C4×D11—22no—
49C22×C8×C11C2312yes—
50C4×D4×C11—22no—
51C4×D4×C11C2×C414yescomplemented
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C22⋊C4—21no—
57C2×C42×C11C2311yescharacteristic
58C2×C22⋊Dic11—22no—
59D4×Dic11—24no—
60D4×Dic11—42no—
61C2×#4323C2×C414yes—
62C2×#4323D414yes—
63C2×#4323Q814yes—
64C2×(C2×D11)⋊C4—21no—
65C2×(C2×D11)⋊C4—22no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—44no—
70C2×C4⋊Dic11D411yescharacteristic
71C2×C4⋊Dic11D411yescharacteristic
72C2×C4⋊Dic11C2312yes—
73C2×C4⋊Dic11C2311yescharacteristic
74C2×Dic11⋊C4—22no—
75C2×C4×Dic11C2312yes—
76C22×C11⋊C8C2311yescharacteristic
77C22×C11⋊C8C2311yescharacteristic
78#66946—24no—
79#66946—42no—
80C4⋊C4×D11—44no—
81C4×D44—22no—
82C4×D44C2×C414yescomplemented
83C11×C4⋊C8—22no—
84C11×#102—24no—
85#66896C2×C414yescomplemented
86C11⋊#95—22no—
87C11⋊#95—22no—
88C11⋊#95D412yes—
89#66885—24no—
90C8×Dic11—24no—
91#66873C2×C414yescomplemented
92#66871—24no—
93#66871—42no—
94#66871C2×C414yescomplemented
95C4×C11⋊C8C2×C414yescomplemented
96C4⋊C4×D8—111nomaximal, Sylow
97C24×C11—21no—
98C23×D11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11C22×C412yes—
103C2×D4×C11C2×D412yes—
104C2×D4×C11C2×Q812yes—
105C22×C4×C11—21no—
106C22×C4×C11—24no—
107C22×C4×C11—22no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2411yescharacteristic
113C22×Dic11—21no—
114C22×Dic11—22no—
115C22×Dic11—44no—
116C22×Dic11—44no—
117C22×Dic11—82no—
118C22×Dic11C2×D412yes—
119C22×Dic11C2×D412yes—
120C2×D44—21no—
121C2×D44—21no—
122C2×D44—21no—
123C2×D44C22×C412yes—
124C2×D44C2×D412yes—
125C2×D44C2×Q812yes—
126C2×C4×D11—24no—
127C2×C4×D11—44no—
128C2×C4×D11—44no—
129C2×C4×D11—42no—
130C2×C4×D11—42no—
131C2×C4×D11—82no—
132C2×C8×C11—22no—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—42no—
139C11×C4⋊C4—81no—
140C11×C4⋊C4C22×C412yes—
141C11×C22⋊C4—24no—
142C42×C11C22×C412yes—
143C42×C11#4112yes—
144C22⋊Dic11—44no—
145#4323C4⋊C4116yescomplemented
146(C2×D11)⋊C4—24no—
147(C2×D11)⋊C4—44no—
148C4⋊Dic11—22no—
149C4⋊Dic11—22no—
150C4⋊Dic11—21no—
151C4⋊Dic11—22no—
152C4⋊Dic11—44no—
153C4⋊Dic11—42no—
154C4⋊Dic11—81no—
155C4⋊Dic11D814yescomplemented
156C4⋊Dic11C22×C412yes—
157Dic11⋊C4—44no—
158C4×Dic11—22no—
159C4×Dic11—22no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8—21no—
162C2×C11⋊C8C22×C412yes—
163C2×C11⋊C8C22×C412yes—
164C2×C11⋊C8C2×D412yes—
165C2×C11⋊C8C2×Q812yes—
166C2×C4×D8—112no—
167C2×C4×D8—111no—
168D4×C4⋊C4—111no—
169D4×C4⋊C4—111no—
170#1942—112no—
171#1862—112no—
172#1862—112no—
173#1845—111no—
174#1802—111no—
175#1802D1111yescharacteristic, complemented
176C8×C4⋊C4—111no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—22no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11C22×D411yescharacteristic
185C22×D11—22no—
186C22×D11—22no—
187C22×D11—22no—
188C22×D11—41no—
189C22×D11—41no—
190C22×D11—41no—
191C22×D11—41no—
192D4×C11—22no—
193D4×C11—22no—
194D4×C11—22no—
195D4×C11C2×C4⋊C414yescomplemented
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—22no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—48no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11C4×D412yes—
206C2×C4×C11C4×D412yes—
207C2×C4×C11C2×D812yes—
208C2×C4×C11#13512yes—
209C2×C4×C11C23×C411yescharacteristic
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C22×Q811yescharacteristic
212C2×C4×C11C2×#4111yescharacteristic
213C2×C4×C11H(5,𝔽2)11yescharacteristic
214C2×C4×C112−1+411yescharacteristic
215C2×Dic11—22no—
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225C2×Dic11—42no—
226C2×Dic11—88no—
227C2×Dic11C2×D814yes—
228D44—22no—
229D44—22no—
230D44—22no—
231D44C2×C4⋊C414yescomplemented
232C4×D11—48no—
233C4×D11—88no—
234C8×C11—42no—
235C11⋊C8—22no—
236C11⋊C8C2×C4⋊C414yescomplemented
237C22×D8—111no—
238C2×C4×D4—112no—
239C2×C4×D4—112no—
240C2×C4×D4—111no—
241C2×C4×D4C2×D1111yescharacteristic
242C22×C4⋊C4—221no—
243C22×C4⋊C4—221no—
244C4×D8—118no—
245C4×D8—228no—
246C2×#107—111no—
247C2×#107—112no—
248C2×#107—112no—
249C2×C4⋊C8C2×D1111yescharacteristic
250C2×#102—111no—
251C2×#102—111no—
252C2×#102—112no—
253C2×#102C2×D1112yes—
254C2×C4×C8—111no—
255C2×C4×C8—112no—
256#389—112no—
257#389—112no—
258#385—222no—
259#385—222no—
260#384—111no—
261#384C2×D1111yescharacteristic
262#380—221no—
263#380—221no—
264C4×C4⋊C4—111no—
265#340—112no—
266#340C2×D1112yes—
267#336—112no—
268C22×C11—24no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—42no—
274C22×C11—42no—
275C22×C11C2×C4×D411yescharacteristic
276C22×C11D4211yescharacteristic
277C22×C11D4×Q811yescharacteristic
278C22×C11C22×D811yescharacteristic
279C22×C11C2×#13511yescharacteristic
280C22×C11#57611yescharacteristic
281C22×C11#57811yescharacteristic
282C2×D11—24no—
283C2×D11—42no—
284C2×D11—42no—
285C2×D11—42no—
286C2×D11—42no—
287C2×D11—42no—
288C2×D11—42no—
289C4×C11—22no—
290C4×C11—42no—
291C4×C11—82no—
292C4×C11C4×D814yescomplemented
293C4×C11C22×C4⋊C411yescharacteristic
294C4×C11#52011yescharacteristic
295C4×C11#54711yescharacteristic
296C4×C11#55411yescharacteristic
297Dic11—24no—
298Dic11—42no—
299Dic11—42no—
300Dic11—82no—
301C22×D4—111no—
302C22×D4C22×D1111yescharacteristic
303C23×C4—21no—
304C23×C4—222no—
305C23×C4—222no—
306C23×C4—221no—
307C2×D8—114no—
308C2×D8—114no—
309C2×D8—114no—
310C22×C8—111no—
311C22×C8—111no—
312C22×C8C22×D1112yes—
313C4×D4—22no—
314C4×D4—114no—
315C4×D4—224no—
316C4×D4—224no—
317C4×D4—222no—
318C4×D4—442no—
319C4×D4—442no—
320C4×D4C4×D1114yescomplemented
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—111no—
324C2×C4⋊C4—111no—
325C2×C4⋊C4—111no—
326C2×C4⋊C4—112no—
327C2×C4⋊C4—222no—
328C2×C4⋊C4—222no—
329C2×C4⋊C4—221no—
330C2×C4⋊C4—221no—
331C2×C4⋊C4—444no—
332C2×C4⋊C4—444no—
333C2×C4⋊C4C22×D1112yes—
334C2×C4⋊C4C22×D1111yescharacteristic
335C2×C22⋊C4—21no—
336C2×C22⋊C4—221no—
337C2×C22⋊C4—222no—
338C2×C22⋊C4—222no—
339C2×C42—112no—
340C2×C42C22×D1111yescharacteristic
341#107—114no—
342#107—224no—
343#107—442no—
344C4⋊C8—22no—
345#102—24no—
346#102—114no—
347#102—114no—
348#102—224no—
349C4×C8—114no—
350C4×C8—224no—
351#95—112no—
352#95—222no—
353#95—222no—
354C2×C11—44no—
355C2×C11D4×C4⋊C411yescharacteristic
356C2×C11C2×C4×D811yescharacteristic
357C2×C11#295111yescharacteristic
358C2×C11D4×D811yescharacteristic
359C2×C11#328311yescharacteristic
360C2×C11Q8×D811yescharacteristic
361C2×C11#338011yescharacteristic
362D11—44no—
363C24—21no—
364C24—221no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—112no—
369C2×D4—112no—
370C2×D4—112no—
371C2×D4—221no—
372C2×D4—221no—
373C2×D4—221no—
374C2×D4C2×C4×D1112yes—
375C2×D4D4×D1112yes—
376C2×D4Q8×D1112yes—
377C22×C4—21no—
378C22×C4—24no—
379C22×C4—22no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—112no—
383C22×C4—112no—
384C22×C4—221no—
385C22×C4—224no—
386C22×C4—222no—
387C22×C4—444no—
388C22×C4—444no—
389C22×C4—444no—
390C22×C4—444no—
391C22×C4—442no—
392C22×C4—442no—
393C22×C4—882no—
394C22×C4—882no—
395C22×C4D4×D1111yescharacteristic
396C22×C4D4×D1111yescharacteristic
397C22×C4C23×D1111yescharacteristic
398D8—1116no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—22no—
402C2×C8—112no—
403C2×C8—112no—
404C2×C8—112no—
405C2×C8—112no—
406C2×C8—221no—
407C2×C8—221no—
408C4⋊C4—21no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—42no—
412C4⋊C4—81no—
413C4⋊C4—114no—
414C4⋊C4—112no—
415C4⋊C4—222no—
416C4⋊C4—221no—
417C4⋊C4—222no—
418C4⋊C4—222no—
419C4⋊C4—444no—
420C4⋊C4—444no—
421C4⋊C4—442no—
422C4⋊C4—881no—
423C4⋊C4C2×C4×D1112yes—
424C22⋊C4—24no—
425C22⋊C4—224no—
426C22⋊C4—444no—
427C22⋊C4—444no—
428C42—222no—
429C42—222no—
430C42C2×C4×D1112yes—
431C42#434112yes—
432C11C4⋊C4×D811yescharacteristic, complemented, Sylow
433C23—22no—
434C23—22no—
435C23—22no—
436C23—41no—
437C23—41no—
438C23—41no—
439C23—41no—
440C23—222no—
441C23—222no—
442C23—222no—
443C23—441no—
444C23—441no—
445C23—441no—
446C23—441no—
447C23C2×D4×D1111yescharacteristic
448D4—22no—
449D4—22no—
450D4—22no—
451D4—114no—
452D4—222no—
453D4—222no—
454D4—222no—
455D4C4⋊C4×D1114yescomplemented
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—22no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—48no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—114no—
466C2×C4—222no—
467C2×C4—222no—
468C2×C4—222no—
469C2×C4—222no—
470C2×C4—222no—
471C2×C4—222no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4—448no—
475C2×C4—442no—
476C2×C4—442no—
477C2×C4—442no—
478C2×C4—888no—
479C2×C4—888no—
480C2×C4(C22⋊D11)⋊C412yes—
481C2×C4(C22⋊D11)⋊C412yes—
482C2×C4D8×D1112yes—
483C2×C4#6696912yes—
484C2×C4C22×C4×D1111yescharacteristic
485C2×C4C2×D4×D1111yescharacteristic
486C2×C4C2×#434111yescharacteristic
487C2×C4C2×Q8×D1111yescharacteristic
488C2×C4#6704211yescharacteristic
489C2×C4#6704311yescharacteristic
490C8—42no—
491C8—114no—
492C8—222no—
493C22—24no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22—42no—
499C22—42no—
500C22—224no—
501C22—442no—
502C22—442no—
503C22—442no—
504C22—442no—
505C22—442no—
506C22—442no—
507C22C2×(C22⋊D11)⋊C411yescharacteristic
508C22#1062314011yescharacteristic
509C22#1062316311yescharacteristic
510C22C2×D8×D1111yescharacteristic
511C22C2×#6696911yescharacteristic
512C22#1062330511yescharacteristic
513C22#1062331011yescharacteristic
514C4—22no—
515C4—42no—
516C4—82no—
517C4—224no—
518C4—442no—
519C4—442no—
520C4—882no—
521C4#1062236914yescomplemented
522C4C2×C4⋊C4×D1111yescharacteristic
523C4#1062305411yescharacteristic
524C4#1062314211yescharacteristic
525C4#1062316611yescharacteristic
526C2—44no—
527C2—444no—
528C2#1307151211yescharacteristic
529C2C2×#1062236911yescharacteristic
530C2#1307748711yescharacteristic
531C2#1308028811yescharacteristic
532C2#1308033311yescharacteristic
533C2#1308146611yescharacteristic
534C2#1308148211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1802C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
cosocleC22×C4×C11C24
hypercenter#1802D11
hypocenterC11C4⋊C4×D8
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
3. D4×C4⋊Dic11C2semidirect
4. #13071516C2semidirect
5. #13069348C2semidirect
6. #13068864C2semidirect
7. #13068861C2semidirect
8. #13068775C2semidirect
9. #13068617C2semidirect
10. #13068481C2semidirect
11. C11×#1802C2semidirect
26. C4×#4323C4semidirect
51. C4×D4×C11C2×C4semidirect
82. C4×D44C2×C4semidirect
85. #66896C2×C4semidirect
91. #66873C2×C4semidirect
94. #66871C2×C4semidirect
95. C4×C11⋊C8C2×C4semidirect
145. #4323C4⋊C4semidirect
155. C4⋊Dic11D8semidirect
175. #1802D11semidirect
195. D4×C11C2×C4⋊C4semidirect
231. D44C2×C4⋊C4semidirect
236. C11⋊C8C2×C4⋊C4semidirect
292. C4×C11C4×D8semidirect
320. C4×D4C4×D11semidirect
432. C11C4⋊C4×D8semidirect
455. D4C4⋊C4×D11semidirect
521. C4#10622369semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43232
C2×#106223692
D4×C4⋊Dic112
#130715162
#130693482
#130688642
#130688612
#130687752
#130686172
#130684812
C11×#18022
C4⋊C4×D811