Finite Group Databasebeta

← #14814826

Subgroups — #14814826

Order 2816.

1070 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
1C2×#10622646C212yesmaximal, complemented
2D4×C4⋊Dic11C211yesmaximal, characteristic, complemented
3#13069795C212yesmaximal, complemented
4#13069795C212yesmaximal, complemented
5#13069544C211yesmaximal, characteristic, complemented
6#13069423C211yesmaximal, characteristic, complemented
7#13069411C211yesmaximal, characteristic, complemented
8#13069374C211yesmaximal, characteristic, complemented
9#13068934C212yesmaximal, complemented
10C4×#66871C211yesmaximal, characteristic, complemented
11C11×#2541C211yesmaximal, characteristic
12C2×C11×#127—21no—
13C2×C11×#127C2211yescharacteristic
14C2×C11×#121C2212yes—
15C2×C11×#121C2212yes—
16C2×C4×D4×C11C2211yescharacteristic
17C2×D4×Dic11—21no—
18C22×C4⋊Dic11C2212yes—
19C11×#392—22no—
20C11×#390—21no—
21C4×C11×C4⋊C4C2211yescharacteristic
22C2×#66896C2212yes—
23C2×#66896C2212yes—
24C2×#66896C2212yes—
25C2×#66896C2212yes—
26#10622825C2212yes—
27C2×C22⋊(C11⋊C8)C2212yes—
28C2×C22⋊(C11⋊C8)C2212yes—
29#10622646—28no—
30#10622598—21no—
31C2×#66871C2212yes—
32C2×#66871C2211yescharacteristic
33C2×#66871C2211yescharacteristic
34#10622563—22no—
35#10622548C2211yescharacteristic
36C4×C4⋊Dic11C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C2×C4×C11⋊C8C2211yescharacteristic
39#10622167C2212yes—
40#10622167C2211yescharacteristic
41#10622167C2211yescharacteristic
42C22×D4×C11—22no—
43C22×D4×C11—22no—
44C22×D4×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11D411yescharacteristic
47C22×D4×C11C2312yes—
48C23×C4×C11C2312yes—
49C23×Dic11—22no—
50C11×#127—22no—
51C11×#127—22no—
52C11×#127—44no—
53C11×#121—24no—
54C11×#121—24no—
55C11×#121—42no—
56C11×#121—42no—
57C4×D4×C11—22no—
58C4×D4×C11—22no—
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4D412yes—
65C2×C42×C11—21no—
66C2×C42×C11C2311yescharacteristic
67C2×C22⋊Dic11—22no—
68D4×Dic11—44no—
69C2×C4⋊Dic11—24no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—42no—
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4⋊Dic11C2312yes—
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4×Dic11—21no—
78C22×C11⋊C8C2311yescharacteristic
79C22×C11⋊C8C2312yes—
80C22×C11⋊C8C2311yescharacteristic
81C11×#95—21no—
82#66896—24no—
83#66896—24no—
84#66896—42no—
85#66896—42no—
86C11⋊#95—21no—
87C11⋊#95—22no—
88C22⋊(C11⋊C8)—24no—
89C22⋊(C11⋊C8)—42no—
90#66871—24no—
91#66871—22no—
92#66871D414yescomplemented
93C4⋊(C11⋊C8)—22no—
94C4×C11⋊C8—22no—
95#26230—111nomaximal, Sylow
96C24×C11—22no—
97C24×C11C2×D412yes—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11—44no—
107C2×D4×C11—44no—
108C2×D4×C11—44no—
109C2×D4×C11—44no—
110C2×D4×C11—42no—
111C2×D4×C11—42no—
112C2×D4×C11—42no—
113C2×D4×C11—42no—
114C2×D4×C11—81no—
115C2×D4×C11—81no—
116C2×D4×C11—82no—
117C2×D4×C11—82no—
118C2×D4×C11D814yes—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2411yescharacteristic
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11—22no—
134C22×Dic11—44no—
135C22×Dic11—44no—
136C22×Dic11—82no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4C2×D412yes—
141C11×C4⋊C4#4112yes—
142C11×C22⋊C4—24no—
143C11×C22⋊C4—44no—
144C11×C22⋊C4—44no—
145C42×C11—42no—
146C42×C11#4112yes—
147C42×C11#4112yes—
148C22⋊Dic11—44no—
149C4⋊Dic11—22no—
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11—22no—
154C4⋊Dic11—44no—
155C4⋊Dic11—42no—
156C4⋊Dic11—81no—
157C4⋊Dic11C2×D412yes—
158C4×Dic11—42no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8—21no—
162C2×C11⋊C8—21no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—21no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—21no—
167C2×C11⋊C8C2×D412yes—
168C2×#480—112no—
169#2541D1111yescharacteristic
170D4×C4⋊C4—111no—
171#2033—112no—
172#2033—112no—
173#1982—111no—
174#1957—111no—
175#1954—111no—
176#1947—111no—
177#1874—112no—
178C4×#107—111no—
179C23×C11—22no—
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11C2×D814yes—
193C23×C11C22×D411yescharacteristic
194D4×C11—28no—
195D4×C11—42no—
196D4×C11—42no—
197D4×C11—42no—
198D4×C11—42no—
199D4×C11—84no—
200D4×C11—88no—
201D4×C11—88no—
202D4×C11—84no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11#12312yes—
219C2×C4×C11#12312yes—
220C2×C4×C11C2×D812yes—
221C2×C4×C11#13712yes—
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C2×C4×C11C2×#4111yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C11H(5,𝔽2)11yescharacteristic
227C2×C4×C11H(5,𝔽2)11yescharacteristic
228C2×Dic11—22no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231C2×Dic11—42no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—41no—
237C2×Dic11—88no—
238C11⋊C8—22no—
239C11⋊C8—41no—
240C11⋊C8—42no—
241C2×#127—21no—
242C2×#127C2×D1111yescharacteristic
243C2×#121C2×D1112yes—
244C2×#121C2×D1112yes—
245C2×C4×D4—221no—
246C2×C4×D4C2×D1111yescharacteristic
247C22×C4⋊C4—112no—
248#480—228no—
249C2×#107—111no—
250C2×#107—112no—
251C2×#107—111no—
252C2×C4⋊C8—111no—
253C2×#102—112no—
254C2×#102—112no—
255C2×#102—112no—
256C2×#102—112no—
257C2×C22⋊C8—112no—
258C2×C22⋊C8—112no—
259C2×C4×C8—111no—
260#392—22no—
261#390—21no—
262#389—221no—
263#385—222no—
264#384—111no—
265#380—112no—
266C4×C4⋊C4—111no—
267C4×C4⋊C4C2×D1111yescharacteristic
268#340—111no—
269#340—112no—
270#340—111no—
271C22×C11—24no—
272C22×C11—24no—
273C22×C11—24no—
274C22×C11—42no—
275C22×C11—42no—
276C22×C11—42no—
277C22×C11—42no—
278C22×C11—82no—
279C22×C11—82no—
280C22×C11—82no—
281C22×C11—82no—
282C22×C11—82no—
283C22×C11—82no—
284C22×C11—82no—
285C22×C11C2×#12311yescharacteristic
286C22×C11D4211yescharacteristic
287C22×C11#54611yescharacteristic
288C22×C11C22×D811yescharacteristic
289C22×C11C2×#13711yescharacteristic
290C22×C11#57611yescharacteristic
291C22×C11#57711yescharacteristic
292C4×C11—22no—
293C4×C11—42no—
294C4×C11—42no—
295C4×C11—42no—
296C4×C11#48014yescomplemented
297C4×C11#53211yescharacteristic
298C4×C11#54011yescharacteristic
299C4×C11#55011yescharacteristic
300C4×C11#55911yescharacteristic
301Dic11—42no—
302Dic11—82no—
303Dic11—81no—
304C22×D4—22no—
305C22×D4—22no—
306C22×D4—21no—
307C22×D4—21no—
308C22×D4C22⋊D1111yescharacteristic
309C22×D4C22×D1112yes—
310C23×C4—222no—
311C23×C4C22×D1112yes—
312C22×C8—111no—
313C22×C8—111no—
314C22×C8—112no—
315#127—22no—
316#127—22no—
317#127—44no—
318#121—24no—
319#121—24no—
320#121—42no—
321#121—42no—
322C4×D4—22no—
323C4×D4—22no—
324C4×D4—444no—
325C2×C4⋊C4—111no—
326C2×C4⋊C4—112no—
327C2×C4⋊C4—111no—
328C2×C4⋊C4—224no—
329C2×C4⋊C4—222no—
330C2×C4⋊C4—221no—
331C2×C4⋊C4—221no—
332C2×C4⋊C4—442no—
333C2×C4⋊C4C22⋊D1111yescharacteristic
334C2×C4⋊C4C22×D1111yescharacteristic
335C2×C4⋊C4C22×D1111yescharacteristic
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—222no—
339C2×C22⋊C4C22⋊D1112yes—
340C2×C42—21no—
341C2×C42—221no—
342C2×C42C22×D1111yescharacteristic
343#107—114no—
344#107—224no—
345#107—222no—
346C4⋊C8—222no—
347#102—224no—
348#102—224no—
349#102—442no—
350#102—442no—
351C22⋊C8—224no—
352C22⋊C8—442no—
353C4×C8—222no—
354#95—21no—
355#95—221no—
356#95—222no—
357C2×C11—44no—
358C2×C11—162no—
359C2×C11#244511yescharacteristic
360C2×C11C2×#48011yescharacteristic
361C2×C11#309611yescharacteristic
362C2×C11#327811yescharacteristic
363C2×C11D4×D811yescharacteristic
364C2×C11#329411yescharacteristic
365C2×C11#333311yescharacteristic
366C24—22no—
367C24C2×C22⋊D1112yes—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—44no—
377C2×D4—44no—
378C2×D4—44no—
379C2×D4—44no—
380C2×D4—42no—
381C2×D4—42no—
382C2×D4—42no—
383C2×D4—42no—
384C2×D4—81no—
385C2×D4—81no—
386C2×D4—82no—
387C2×D4—82no—
388C2×D4#432314yes—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—221no—
398C22×C4—221no—
399C22×C4—222no—
400C22×C4—444no—
401C22×C4—444no—
402C22×C4—882no—
403C22×C4C2×C22⋊D1112yes—
404C22×C4C2×C22⋊D1111yescharacteristic
405C22×C4C2×C22⋊D1111yescharacteristic
406C22×C4C23×D1111yescharacteristic
407C2×C8—112no—
408C2×C8—221no—
409C2×C8—221no—
410C2×C8—222no—
411C2×C8—221no—
412C2×C8—222no—
413C2×C8—221no—
414C2×C8—222no—
415C2×C8—221no—
416C4⋊C4—22no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—112no—
420C4⋊C4—221no—
421C4⋊C4—222no—
422C4⋊C4—221no—
423C4⋊C4—221no—
424C4⋊C4—222no—
425C4⋊C4—444no—
426C4⋊C4—442no—
427C4⋊C4—881no—
428C4⋊C4D4×D1112yes—
429C4⋊C4#434112yes—
430C22⋊C4—24no—
431C22⋊C4—44no—
432C22⋊C4—44no—
433C22⋊C4—444no—
434C42—42no—
435C42—442no—
436C42#434112yes—
437C42#434112yes—
438C11#2623011yescharacteristic, complemented, Sylow
439C23—22no—
440C23—22no—
441C23—22no—
442C23—22no—
443C23—22no—
444C23—22no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23—42no—
449C23—42no—
450C23—42no—
451C23—42no—
452C23C2×#432314yes—
453C23C22×C22⋊D1111yescharacteristic
454D4—28no—
455D4—42no—
456D4—42no—
457D4—42no—
458D4—42no—
459D4—84no—
460D4—88no—
461D4—88no—
462D4—84no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—222no—
479C2×C4—441no—
480C2×C4—441no—
481C2×C4—441no—
482C2×C4—442no—
483C2×C4—442no—
484C2×C4—441no—
485C2×C4—442no—
486C2×C4—441no—
487C2×C4—888no—
488C2×C4C2×#432312yes—
489C2×C4#6698812yes—
490C2×C4#6698812yes—
491C2×C4#6700412yes—
492C2×C4C2×D4×D1111yescharacteristic
493C2×C4C2×#434111yescharacteristic
494C2×C4C2×#434111yescharacteristic
495C2×C4C2×#434111yescharacteristic
496C2×C4#6703711yescharacteristic
497C2×C4#6703711yescharacteristic
498C8—222no—
499C8—442no—
500C8—441no—
501C22—24no—
502C22—24no—
503C22—24no—
504C22—42no—
505C22—42no—
506C22—42no—
507C22—42no—
508C22—82no—
509C22—82no—
510C22—82no—
511C22—82no—
512C22—82no—
513C22—82no—
514C22—82no—
515C22C22×#432311yescharacteristic
516C22C2×#6698811yescharacteristic
517C22D4×C22⋊D1111yescharacteristic
518C22#1062333711yescharacteristic
519C22C2×#6700411yescharacteristic
520C22#1062336611yescharacteristic
521C22#1062336711yescharacteristic
522C4—22no—
523C4—42no—
524C4—42no—
525C4—42no—
526C4—442no—
527C4—881no—
528C4—882no—
529C4#1062264614yescomplemented
530C4#1062324411yescharacteristic
531C4#1062324711yescharacteristic
532C4#1062324911yescharacteristic
533C4#1062325011yescharacteristic
534C2—44no—
535C2—162no—
536C2#1307237711yescharacteristic
537C2C2×#1062264611yescharacteristic
538C2#1307856811yescharacteristic
539C2#1308028211yescharacteristic
540C2D4×#432311yescharacteristic
541C2#1308042911yescharacteristic
542C2#1308095411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#2541C2
socleC23×C11C22×D4
hypercenter#2541D11
hypocenterC11#26230
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2541

Complements

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

NH ≅ G/Ntype
1. C2×#10622646C2semidirect
2. D4×C4⋊Dic11C2semidirect
3. #13069795C2semidirect
4. #13069795C2semidirect
5. #13069544C2semidirect
6. #13069423C2semidirect
7. #13069411C2semidirect
8. #13069374C2semidirect
9. #13068934C2semidirect
10. C4×#66871C2semidirect
92. #66871D4semidirect
296. C4×C11#480semidirect
438. C11#26230semidirect
529. C4#10622646semidirect

Maximal subgroups

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

subgroupindex
C2×#106226462
D4×C4⋊Dic112
#130697952
#130695442
#130694232
#130694112
#130693742
#130689342
C4×#668712
C11×#25412
#2623011