Finite Group Databasebeta

← #14814833

Subgroups — #14814833

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×#10622387C212yesmaximal, complemented
2#13073563C211yesmaximal, characteristic
3#13071516C211yesmaximal, characteristic, complemented
4#13069797C212yesmaximal, complemented
5#13069796C212yesmaximal, complemented
6#13069544C211yesmaximal, characteristic, complemented
7#13069410C211yesmaximal, characteristic, complemented
8#13069372C211yesmaximal, characteristic, complemented
9#13068930C212yesmaximal, complemented
10C4×#66882C211yesmaximal, characteristic, complemented
11C11×#1957C211yesmaximal, characteristic, complemented
12C2×C11×#127C2211yescharacteristic
13C2×#66993—21no—
14C2×#66991C2212yes—
15C2×#66991C2212yes—
16C2×#66946—21no—
17C2×C4⋊C4×D11C2212yes—
18C2×C4×D44C2211yescharacteristic
19C2×C11×#102C2212yes—
20C2×C11×#102C2212yes—
21C2×C4×C8×C11C2211yescharacteristic
22C11×#384C2211yescharacteristic
23#10622836—22no—
24#10622834—21no—
25C2×#66896C2212yes—
26C2×#66896C2212yes—
27C2×(C2×D11)⋊C8C2212yes—
28C2×(C2×D11)⋊C8C2212yes—
29C2×#66882C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31#10622602—22no—
32#10622600C2212yes—
33#10622586—21no—
34C2×#66871C2212yes—
35C4×C4⋊Dic11C2211yescharacteristic
36C4×C4⋊Dic11C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38#10622387—28no—
39#10622189C2211yescharacteristic
40#10622189C2211yescharacteristic
41#10622167C2212yes—
42C22×D4×C11—21no—
43C22×D4×C11—21no—
44C22×D4×C11C2312yes—
45C22×C22⋊D11—22no—
46C22×C22⋊D11—22no—
47C22×D44D411yescharacteristic
48C22×C4×D11—22no—
49C22×C4×D11C2312yes—
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C11×#127—22no—
53C11×#127—22no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4C2312yes—
57C2×C42×C11C2311yescharacteristic
58C2×C22⋊Dic11—22no—
59C2×C22⋊Dic11—22no—
60#66993—44no—
61#66991—24no—
62#66991—24no—
63#66991—42no—
64#66991—42no—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4D412yes—
67C2×C4⋊Dic11D411yescharacteristic
68C2×C4⋊Dic11C2311yescharacteristic
69C2×C4⋊Dic11C2311yescharacteristic
70C2×C4⋊Dic11C2311yescharacteristic
71C2×C4⋊Dic11C2311yescharacteristic
72C2×Dic11⋊C4—22no—
73C2×C4×Dic11—21no—
74C2×C4×Dic11—21no—
75C22×C11⋊C8C2312yes—
76#66946—44no—
77C4⋊C4×D11—24no—
78C4⋊C4×D11—42no—
79C4×D44—22no—
80C4×D44—22no—
81C11×#102—24no—
82C11×#102—42no—
83C4×C8×C11—22no—
84#66896—24no—
85#66896—42no—
86C11⋊#95—21no—
87C11⋊#95—21no—
88C11⋊#95—22no—
89(C2×D11)⋊C8—24no—
90(C2×D11)⋊C8—42no—
91#66882—22no—
92#66882D414yescomplemented
93#66871—24no—
94C4⋊(C11⋊C8)—22no—
95#26230—111nomaximal, Sylow
96C24×C11—22no—
97C23×D11C2×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—42no—
105C2×D4×C11—42no—
106C2×D4×C11—42no—
107C2×D4×C11—42no—
108C2×D4×C11—81no—
109C2×D4×C11—81no—
110C22×C4×C11—22no—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2411yescharacteristic
114C2×C22⋊D11—44no—
115C2×C22⋊D11—44no—
116C2×C22⋊D11—44no—
117C2×C22⋊D11—44no—
118C2×C22⋊D11—82no—
119C2×C22⋊D11—82no—
120C22×Dic11—21no—
121C22×Dic11—21no—
122C22×Dic11—21no—
123C22×Dic11—21no—
124C22×Dic11C2×D412yes—
125C2×D44—22no—
126C2×D44—22no—
127C2×D44D814yes—
128C2×C4×D11—22no—
129C2×C4×D11—22no—
130C2×C4×D11—22no—
131C2×C4×D11—22no—
132C2×C4×D11—22no—
133C2×C4×D11—22no—
134C2×C4×D11—44no—
135C2×C4×D11—44no—
136C2×C4×D11—82no—
137C2×C8×C11—21no—
138C2×C8×C11—21no—
139C2×C8×C11—21no—
140C2×C8×C11—21no—
141C2×C8×C11—21no—
142C2×C8×C11C2×D412yes—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—42no—
146C11×C4⋊C4—81no—
147C42×C11#4112yes—
148C42×C11#4112yes—
149C22⋊Dic11—44no—
150C22⋊Dic11—44no—
151(C2×D11)⋊C4—24no—
152(C2×D11)⋊C4—44no—
153C4⋊Dic11—22no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159C4⋊Dic11C2×D412yes—
160C4⋊Dic11C2×D412yes—
161C4⋊Dic11#4112yes—
162Dic11⋊C4—44no—
163C4×Dic11—42no—
164C4×Dic11—42no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×#480—112no—
169#2541—111no—
170D4×C4⋊C4—111no—
171#2033—112no—
172#2033—112no—
173#1982—111no—
174#1957D1111yescharacteristic, complemented
175#1954—111no—
176#1947—111no—
177#1874—112no—
178C4×#107—111no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11C22×D411yescharacteristic
187C22×D11—22no—
188C22×D11—22no—
189C22×D11—22no—
190C22×D11—22no—
191C22×D11—22no—
192C22×D11—22no—
193C22×D11C2×D814yes—
194D4×C11—42no—
195D4×C11—42no—
196D4×C11—42no—
197D4×C11—42no—
198D4×C11—84no—
199D4×C11—84no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11#12312yes—
206C2×C4×C11#12312yes—
207C2×C4×C11C2×D812yes—
208C2×C4×C11#13712yes—
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C2×#4111yescharacteristic
211C2×C4×C11C2×#4111yescharacteristic
212C2×C4×C11C2×#4111yescharacteristic
213C2×C4×C11H(5,𝔽2)11yescharacteristic
214C2×C4×C11H(5,𝔽2)11yescharacteristic
215C22⋊D11—88no—
216C22⋊D11—88no—
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231C2×Dic11—41no—
232D44—28no—
233C4×D11—42no—
234C4×D11—42no—
235C4×D11—42no—
236C4×D11—42no—
237C4×D11—88no—
238C8×C11—22no—
239C8×C11—41no—
240C11⋊C8—42no—
241C2×#127—221no—
242C2×#127C2×D1111yescharacteristic
243C2×#121—112no—
244C2×#121—112no—
245C2×C4×D4—111no—
246C2×C4×D4—221no—
247C22×C4⋊C4—112no—
248#480—228no—
249C2×#107—111no—
250C2×#107—111no—
251C2×#107—112no—
252C2×C4⋊C8—111no—
253C2×#102—112no—
254C2×#102—112no—
255C2×#102C2×D1112yes—
256C2×#102C2×D1112yes—
257C2×C22⋊C8—112no—
258C2×C22⋊C8—112no—
259C2×C4×C8C2×D1111yescharacteristic
260#392—222no—
261#390—221no—
262#389—221no—
263#385—222no—
264#384C2×D1111yescharacteristic
265#380—112no—
266C4×C4⋊C4—111no—
267C4×C4⋊C4—111no—
268#340—111no—
269#340—111no—
270#340—112no—
271C22×C11—82no—
272C22×C11—82no—
273C22×C11—82no—
274C22×C11—82no—
275C22×C11—82no—
276C22×C11—82no—
277C22×C11—82no—
278C22×C11C2×#12311yescharacteristic
279C22×C11D4211yescharacteristic
280C22×C11#54611yescharacteristic
281C22×C11C22×D811yescharacteristic
282C22×C11C2×#13711yescharacteristic
283C22×C11#57611yescharacteristic
284C22×C11#57711yescharacteristic
285C2×D11—24no—
286C2×D11—24no—
287C2×D11—24no—
288C2×D11—42no—
289C2×D11—42no—
290C2×D11—42no—
291C2×D11—42no—
292C4×C11—22no—
293C4×C11—82no—
294C4×C11#48014yescomplemented
295C4×C11#53211yescharacteristic
296C4×C11#54011yescharacteristic
297C4×C11#55011yescharacteristic
298C4×C11#55911yescharacteristic
299Dic11—42no—
300Dic11—42no—
301Dic11—42no—
302Dic11—42no—
303Dic11—81no—
304C22×D4—21no—
305C22×D4—21no—
306C22×D4—111no—
307C22×D4—222no—
308C22×D4—222no—
309C22×D4C22×D1112yes—
310C23×C4—112no—
311C23×C4—222no—
312C22×C8—112no—
313C22×C8C22×D1111yescharacteristic
314C22×C8C22×D1111yescharacteristic
315#127—22no—
316#127—22no—
317#127—444no—
318#121—224no—
319#121—224no—
320#121—442no—
321#121—442no—
322C4×D4—222no—
323C4×D4—222no—
324C4×D4—444no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—111no—
328C2×C4⋊C4—111no—
329C2×C4⋊C4—111no—
330C2×C4⋊C4—111no—
331C2×C4⋊C4—111no—
332C2×C4⋊C4—224no—
333C2×C4⋊C4—222no—
334C2×C4⋊C4—442no—
335C2×C4⋊C4C22×D1112yes—
336C2×C22⋊C4—112no—
337C2×C22⋊C4—222no—
338C2×C22⋊C4—222no—
339C2×C22⋊C4—222no—
340C2×C42—221no—
341C2×C42—221no—
342C2×C42C22×D1111yescharacteristic
343#107—114no—
344#107—224no—
345#107—222no—
346C4⋊C8—222no—
347#102—24no—
348#102—42no—
349#102—224no—
350#102—442no—
351C22⋊C8—224no—
352C22⋊C8—442no—
353C4×C8—22no—
354#95—222no—
355#95—221no—
356#95—221no—
357C2×C11—162no—
358C2×C11#244511yescharacteristic
359C2×C11C2×#48011yescharacteristic
360C2×C11#309611yescharacteristic
361C2×C11#327811yescharacteristic
362C2×C11D4×D811yescharacteristic
363C2×C11#329411yescharacteristic
364C2×C11#333311yescharacteristic
365D11—44no—
366C24—22no—
367C24—112no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—42no—
375C2×D4—42no—
376C2×D4—42no—
377C2×D4—42no—
378C2×D4—81no—
379C2×D4—81no—
380C2×D4—114no—
381C2×D4—222no—
382C2×D4—222no—
383C2×D4—444no—
384C2×D4—444no—
385C2×D4—444no—
386C2×D4—444no—
387C2×D4—882no—
388C2×D4—882no—
389C22×C4—22no—
390C22×C4—112no—
391C22×C4—221no—
392C22×C4—221no—
393C22×C4—221no—
394C22×C4—222no—
395C22×C4—222no—
396C22×C4—222no—
397C22×C4—222no—
398C22×C4—222no—
399C22×C4—222no—
400C22×C4—221no—
401C22×C4—444no—
402C22×C4—444no—
403C22×C4—882no—
404C22×C4D4×D1111yescharacteristic
405C22×C4D4×D1111yescharacteristic
406C22×C4C23×D1111yescharacteristic
407C2×C8—21no—
408C2×C8—21no—
409C2×C8—21no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—222no—
413C2×C8—222no—
414C2×C8—222no—
415C2×C8D4×D1112yes—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—42no—
419C4⋊C4—81no—
420C4⋊C4—112no—
421C4⋊C4—112no—
422C4⋊C4—112no—
423C4⋊C4—222no—
424C4⋊C4—221no—
425C4⋊C4—221no—
426C4⋊C4—221no—
427C4⋊C4—221no—
428C4⋊C4—221no—
429C4⋊C4—444no—
430C22⋊C4—224no—
431C22⋊C4—444no—
432C22⋊C4—444no—
433C22⋊C4—444no—
434C42—442no—
435C42—442no—
436C42#433912yes—
437C42#434112yes—
438C11#2623011yescharacteristic, complemented, Sylow
439C23—42no—
440C23—42no—
441C23—42no—
442C23—42no—
443C23—42no—
444C23—42no—
445C23—42no—
446C23—114no—
447C23—222no—
448C23—222no—
449C23—222no—
450C23—222no—
451C23—222no—
452C23—222no—
453C23C2×D4×D1111yescharacteristic
454D4—42no—
455D4—42no—
456D4—42no—
457D4—42no—
458D4—84no—
459D4—84no—
460D4—228no—
461D4—888no—
462D4—888no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—222no—
469C2×C4—222no—
470C2×C4—222no—
471C2×C4—222no—
472C2×C4—222no—
473C2×C4—222no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—441no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4—442no—
481C2×C4—442no—
482C2×C4—442no—
483C2×C4—442no—
484C2×C4—441no—
485C2×C4—441no—
486C2×C4—441no—
487C2×C4—888no—
488C2×C4#6693612yes—
489C2×C4#6693612yes—
490C2×C4D8×D1112yes—
491C2×C4#6696812yes—
492C2×C4C2×#433911yescharacteristic
493C2×C4C2×D4×D1111yescharacteristic
494C2×C4C2×#434111yescharacteristic
495C2×C4#6703711yescharacteristic
496C2×C4#41×D1111yescharacteristic
497C2×C4#6704211yescharacteristic
498C8—22no—
499C8—41no—
500C8—442no—
501C22—82no—
502C22—82no—
503C22—82no—
504C22—82no—
505C22—82no—
506C22—82no—
507C22—82no—
508C22—224no—
509C22—224no—
510C22—224no—
511C22—442no—
512C22—442no—
513C22—442no—
514C22—442no—
515C22C2×#6693611yescharacteristic
516C22#1062320711yescharacteristic
517C22#1062324811yescharacteristic
518C22C2×D8×D1111yescharacteristic
519C22#1062328811yescharacteristic
520C22C2×#6696811yescharacteristic
521C22#1062329311yescharacteristic
522C4—22no—
523C4—82no—
524C4—442no—
525C4—442no—
526C4—442no—
527C4—442no—
528C4—881no—
529C4#1062238714yescomplemented
530C4#1062308411yescharacteristic
531C4#1062309011yescharacteristic
532C4#1062312711yescharacteristic
533C4#1062315011yescharacteristic
534C2—162no—
535C2—444no—
536C2#1307238411yescharacteristic
537C2C2×#1062238711yescharacteristic
538C2#1307857011yescharacteristic
539C2#1308028111yescharacteristic
540C2#1308029111yescharacteristic
541C2#1308042811yescharacteristic
542C2#1308095311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1957C2
socleC23×C11C22×D4
prime radical#13073563C2
hypercenter#1957D11
hypocenterC11#26230
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1957

Complements

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

NH ≅ G/Ntype
1. C2×#10622387C2semidirect
3. #13071516C2semidirect
4. #13069797C2semidirect
5. #13069796C2semidirect
6. #13069544C2semidirect
7. #13069410C2semidirect
8. #13069372C2semidirect
9. #13068930C2semidirect
10. C4×#66882C2semidirect
11. C11×#1957C2semidirect
92. #66882D4semidirect
174. #1957D11semidirect
294. C4×C11#480semidirect
438. C11#26230semidirect
529. C4#10622387semidirect

Maximal subgroups

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

subgroupindex
C2×#106223872
#130735632
#130715162
#130697972
#130697962
#130695442
#130694102
#130693722
#130689302
C4×#668822
C11×#19572
#2623011