Finite Group Databasebeta

← #14814824

Subgroups — #14814824

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×#10622580C212yesmaximal, complemented
2#13073562C211yesmaximal, characteristic
3#13069798C212yesmaximal, complemented
4#13069798C212yesmaximal, complemented
5#13069543C211yesmaximal, characteristic, complemented
6#13069421C211yesmaximal, characteristic, complemented
7#13069411C211yesmaximal, characteristic, complemented
8#13069372C211yesmaximal, characteristic, complemented
9#13068933C212yesmaximal, complemented
10C4×#66871C211yesmaximal, characteristic, complemented
11D4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11—21no—
13C2×C4×D4×C11C2211yescharacteristic
14C22×C11×C4⋊C4C2212yes—
15C2×#66993—21no—
16C2×#66983C2212yes—
17C2×#66983C2212yes—
18C2×#66927C2211yescharacteristic
19C11×#389—21no—
20C11×#385—22no—
21C11×#384C2211yescharacteristic
22C11×#380C2212yes—
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×C22⋊(C11⋊C8)C2212yes—
25C2×C22⋊(C11⋊C8)C2212yes—
26#10622601—21no—
27#10622580—28no—
28C2×#66873C2212yes—
29C2×#66873C2212yes—
30C2×#66873C2212yes—
31C2×#66873C2212yes—
32C2×#66871C2212yes—
33C2×#66871C2211yescharacteristic
34C2×#66871C2211yescharacteristic
35#10622573—22no—
36C4×C4⋊Dic11C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C2×C4×C11⋊C8C2211yescharacteristic
39#10622167C2212yes—
40#10622167C2211yescharacteristic
41#10622167C2211yescharacteristic
42C22×D4×C11D411yescharacteristic
43C23×C4×C11—22no—
44C23×C4×C11C2312yes—
45C22×C22⋊D11—22no—
46C22×C22⋊D11—22no—
47C22×D44—21no—
48C22×D44—21no—
49C22×D44C2312yes—
50C4×D4×C11—22no—
51C4×D4×C11—22no—
52C4×D4×C11—44no—
53C2×C11×C4⋊C4—24no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—42no—
58C2×C11×C4⋊C4D411yescharacteristic
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4D412yes—
64C2×C42×C11—21no—
65C2×C42×C11C2311yescharacteristic
66#66993—44no—
67#66983—24no—
68#66983—24no—
69#66983—42no—
70#66983—42no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×C4⋊Dic11C2311yescharacteristic
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4×Dic11—21no—
76C22×C11⋊C8C2311yescharacteristic
77C22×C11⋊C8C2312yes—
78C22×C11⋊C8C2311yescharacteristic
79#66927—22no—
80#66927—22no—
81C11×#95—21no—
82C11×#95—22no—
83C11⋊#95—21no—
84C22⋊(C11⋊C8)—24no—
85C22⋊(C11⋊C8)—42no—
86#66873—24no—
87#66873—24no—
88#66873—42no—
89#66873—42no—
90#66871—24no—
91#66871—22no—
92#66871D414yescomplemented
93C4⋊(C11⋊C8)—22no—
94C4×C11⋊C8—22no—
95#26230—111nomaximal, Sylow
96C24×C11C2×D412yes—
97C23×D11—22no—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11D814yes—
101C22×C4×C11—21no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—44no—
111C22×C4×C11—44no—
112C22×C4×C11—82no—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2411yescharacteristic
117C2×C22⋊D11—44no—
118C2×C22⋊D11—44no—
119C2×C22⋊D11—44no—
120C2×C22⋊D11—44no—
121C2×C22⋊D11—82no—
122C2×C22⋊D11—82no—
123C22×Dic11—21no—
124C22×Dic11—21no—
125C2×D44—22no—
126C2×D44—22no—
127C2×D44—22no—
128C2×D44—22no—
129C2×D44—22no—
130C2×D44—22no—
131C2×D44—42no—
132C2×D44—42no—
133C2×D44—42no—
134C2×D44—42no—
135C2×D44—81no—
136C2×D44—81no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—44no—
144C11×C4⋊C4—42no—
145C11×C4⋊C4—81no—
146C11×C4⋊C4C2×D412yes—
147C11×C22⋊C4—24no—
148C11×C22⋊C4—44no—
149C42×C11—42no—
150C42×C11#4112yes—
151C42×C11#4112yes—
152(C2×D11)⋊C4—44no—
153(C2×D11)⋊C4—44no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11C2×D412yes—
157C4⋊Dic11#4112yes—
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#2541—111no—
170D4×C4⋊C4D1111yescharacteristic, complemented
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×C11C2×D814yes—
186C23×C11C22×D411yescharacteristic
187C22×D11—42no—
188C22×D11—42no—
189C22×D11—42no—
190C22×D11—42no—
191C22×D11—42no—
192C22×D11—42no—
193C22×D11—42no—
194D4×C11—28no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—41no—
213C2×C4×C11—88no—
214C2×C4×C11#12312yes—
215C2×C4×C11#12312yes—
216C2×C4×C11C2×D812yes—
217C2×C4×C11#13712yes—
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C2×C4×C11H(5,𝔽2)11yescharacteristic
223C2×C4×C11H(5,𝔽2)11yescharacteristic
224C22⋊D11—88no—
225C22⋊D11—88no—
226C2×Dic11—22no—
227C2×Dic11—22no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231C2×Dic11—41no—
232D44—42no—
233D44—42no—
234D44—42no—
235D44—42no—
236D44—84no—
237D44—84no—
238C11⋊C8—22no—
239C11⋊C8—41no—
240C11⋊C8—42no—
241C2×#127—111no—
242C2×#127—221no—
243C2×#121—112no—
244C2×#121—112no—
245C2×C4×D4—21no—
246C2×C4×D4C2×D1111yescharacteristic
247C22×C4⋊C4C2×D1112yes—
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—222no—
261#390—221no—
262#389—21no—
263#385—22no—
264#384C2×D1111yescharacteristic
265#380C2×D1112yes—
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×C11C2×#12311yescharacteristic
279C22×C11D4211yescharacteristic
280C22×C11#54611yescharacteristic
281C22×C11C22×D811yescharacteristic
282C22×C11C2×#13711yescharacteristic
283C22×C11#57611yescharacteristic
284C22×C11#57711yescharacteristic
285C2×D11—82no—
286C2×D11—82no—
287C2×D11—82no—
288C2×D11—82no—
289C2×D11—82no—
290C2×D11—82no—
291C2×D11—82no—
292C4×C11—22no—
293C4×C11—42no—
294C4×C11—42no—
295C4×C11—82no—
296C4×C11—81no—
297C4×C11#48014yescomplemented
298C4×C11#53211yescharacteristic
299C4×C11#54011yescharacteristic
300C4×C11#55011yescharacteristic
301C4×C11#55911yescharacteristic
302Dic11—42no—
303Dic11—42no—
304C22×D4—112no—
305C22×D4—222no—
306C22×D4—222no—
307C22×D4—221no—
308C22×D4—221no—
309C22×D4C22⋊D1111yescharacteristic
310C23×C4—22no—
311C23×C4C22×D1112yes—
312C22×C8—111no—
313C22×C8—111no—
314C22×C8—112no—
315#127—222no—
316#127—222no—
317#127—444no—
318#121—224no—
319#121—224no—
320#121—442no—
321#121—442no—
322C4×D4—22no—
323C4×D4—22no—
324C4×D4—44no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—111no—
331C2×C4⋊C4—111no—
332C2×C4⋊C4C22⋊D1111yescharacteristic
333C2×C4⋊C4C22×D1112yes—
334C2×C4⋊C4C22×D1111yescharacteristic
335C2×C4⋊C4C22×D1111yescharacteristic
336C2×C22⋊C4—22no—
337C2×C22⋊C4—222no—
338C2×C22⋊C4—222no—
339C2×C22⋊C4C22⋊D1112yes—
340C2×C42—21no—
341C2×C42—221no—
342C2×C42C22×D1111yescharacteristic
343#107—114no—
344#107—222no—
345#107—224no—
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—22no—
356#95—221no—
357C2×C11—44no—
358C2×C11#244511yescharacteristic
359C2×C11C2×#48011yescharacteristic
360C2×C11#309611yescharacteristic
361C2×C11#327811yescharacteristic
362C2×C11D4×D811yescharacteristic
363C2×C11#329411yescharacteristic
364C2×C11#333311yescharacteristic
365D11—162no—
366C24—222no—
367C24C2×C22⋊D1112yes—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—222no—
371C2×D4—222no—
372C2×D4—222no—
373C2×D4—222no—
374C2×D4—222no—
375C2×D4—222no—
376C2×D4—444no—
377C2×D4—444no—
378C2×D4—444no—
379C2×D4—444no—
380C2×D4—442no—
381C2×D4—442no—
382C2×D4—442no—
383C2×D4—442no—
384C2×D4—881no—
385C2×D4—881no—
386C2×D4—882no—
387C2×D4—882no—
388C2×D4#432314yes—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—44no—
399C22×C4—44no—
400C22×C4—82no—
401C22×C4—221no—
402C22×C4—221no—
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—221no—
411C2×C8—222no—
412C2×C8—222no—
413C2×C8—221no—
414C2×C8—221no—
415C2×C8—222no—
416C4⋊C4—22no—
417C4⋊C4—21no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—44no—
423C4⋊C4—42no—
424C4⋊C4—81no—
425C4⋊C4—112no—
426C4⋊C4—112no—
427C4⋊C4—221no—
428C4⋊C4—221no—
429C4⋊C4D4×D1112yes—
430C22⋊C4—24no—
431C22⋊C4—44no—
432C22⋊C4—444no—
433C22⋊C4—444no—
434C42—42no—
435C42—442no—
436C42#433912yes—
437C42#433912yes—
438C11#2623011yescharacteristic, complemented, Sylow
439C23—22no—
440C23—22no—
441C23—22no—
442C23—22no—
443C23—22no—
444C23—22no—
445C23—442no—
446C23—442no—
447C23—442no—
448C23—442no—
449C23—442no—
450C23—442no—
451C23—442no—
452C23C2×#432314yes—
453C23C22×C22⋊D1111yescharacteristic
454D4—28no—
455D4—442no—
456D4—442no—
457D4—442no—
458D4—442no—
459D4—884no—
460D4—888no—
461D4—888no—
462D4—884no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—41no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—88no—
482C2×C4—222no—
483C2×C4—222no—
484C2×C4—441no—
485C2×C4—441no—
486C2×C4—441no—
487C2×C4—441no—
488C2×C4#6698212yes—
489C2×C4#6698212yes—
490C2×C4C2×#432312yes—
491C2×C4#6699512yes—
492C2×C4C2×#433911yescharacteristic
493C2×C4C2×#433911yescharacteristic
494C2×C4C2×D4×D1111yescharacteristic
495C2×C4#6703711yescharacteristic
496C2×C4#41×D1111yescharacteristic
497C2×C4#6704211yescharacteristic
498C8—222no—
499C8—442no—
500C8—441no—
501C22—24no—
502C22—24no—
503C22—24no—
504C22—42no—
505C22—42no—
506C22—42no—
507C22—42no—
508C22—882no—
509C22—882no—
510C22—882no—
511C22—882no—
512C22—882no—
513C22—882no—
514C22—882no—
515C22C2×#6698211yescharacteristic
516C22C22×#432311yescharacteristic
517C22D4×C22⋊D1111yescharacteristic
518C22C2×#6699511yescharacteristic
519C22#1062336011yescharacteristic
520C22#1062336611yescharacteristic
521C22#1062336811yescharacteristic
522C4—22no—
523C4—42no—
524C4—42no—
525C4—81no—
526C4—82no—
527C4—442no—
528C4—442no—
529C4#1062258014yescomplemented
530C4#1062307911yescharacteristic
531C4#1062308411yescharacteristic
532C4#1062309011yescharacteristic
533C4#1062309311yescharacteristic
534C2—44no—
535C2—1762no—
536C2#1307237511yescharacteristic
537C2C2×#1062258011yescharacteristic
538C2#1307857411yescharacteristic
539C2#1308027811yescharacteristic
540C2D4×#432311yescharacteristic
541C2#1308042311yescharacteristic
542C2#1308094811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingD4×C11×C4⋊C4C2
socleC23×C11C22×D4
prime radical#13073562C2
hypercenterD4×C4⋊C4D11
hypocenterC11#26230
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10622580C2semidirect
3. #13069798C2semidirect
4. #13069798C2semidirect
5. #13069543C2semidirect
6. #13069421C2semidirect
7. #13069411C2semidirect
8. #13069372C2semidirect
9. #13068933C2semidirect
10. C4×#66871C2semidirect
11. D4×C11×C4⋊C4C2semidirect
92. #66871D4semidirect
170. D4×C4⋊C4D11semidirect
297. C4×C11#480semidirect
438. C11#26230semidirect
529. C4#10622580semidirect

Maximal subgroups

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

subgroupindex
C2×#106225802
#130735622
#130697982
#130695432
#130694212
#130694112
#130693722
#130689332
C4×#668712
D4×C11×C4⋊C42
#2623011