Finite Group Databasebeta

← #14814832

Subgroups — #14814832

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×#10622495C212yesmaximal, complemented
2#13073558C211yesmaximal, characteristic
3#13071516C211yesmaximal, characteristic, complemented
4#13069801C212yesmaximal, complemented
5#13069800C212yesmaximal, complemented
6#13069542C211yesmaximal, characteristic, complemented
7#13069421C211yesmaximal, characteristic, complemented
8#13069409C211yesmaximal, characteristic, complemented
9#13068932C212yesmaximal, complemented
10C4×#66871C211yesmaximal, characteristic, complemented
11C11×#1947C211yesmaximal, characteristic, complemented
12C2×#66948C2212yes—
13C2×#66948C2212yes—
14C2×#66946—21no—
15C2×C4⋊C4×D11C2212yes—
16C2×#66927—21no—
17C2×#66927C2211yescharacteristic
18C2×C4×D44C2211yescharacteristic
19C2×C11×#107C2212yes—
20C2×C11×C4⋊C8C2211yescharacteristic
21C11×#384C2211yescharacteristic
22C4×C11×C4⋊C4C2211yescharacteristic
23C2×#66885C2212yes—
24C2×#66885C2212yes—
25C2×(C2×D11)⋊C8C2212yes—
26C2×(C2×D11)⋊C8C2212yes—
27#10622602—22no—
28#10622600C2212yes—
29#10622586—21no—
30C2×#66873C2212yes—
31C2×#66873C2212yes—
32C2×#66871C2211yescharacteristic
33C2×#66871C2211yescharacteristic
34#10622552—21no—
35C4×C4⋊Dic11C2211yescharacteristic
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622495—28no—
38#10622284—22no—
39C11×#340C2212yes—
40#10622167C2211yescharacteristic
41#10622167C2211yescharacteristic
42C22×D44—21no—
43C22×D44—22no—
44C22×D44—22no—
45C22×D44—21no—
46C22×D44D411yescharacteristic
47C22×D44C2312yes—
48C22×C4×D11—22no—
49C22×C4×D11C2312yes—
50C22×C8×C11C2312yes—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C42×C11—21no—
57C2×C42×C11C2311yescharacteristic
58C2×(C2×D11)⋊C4—22no—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4D412yes—
62C2×C4⋊Dic11D411yescharacteristic
63C2×C4⋊Dic11C2311yescharacteristic
64C2×C4⋊Dic11C2311yescharacteristic
65C2×Dic11⋊C4—22no—
66C2×C4×Dic11—21no—
67C22×C11⋊C8C2311yescharacteristic
68C22×C11⋊C8C2311yescharacteristic
69#66948—24no—
70#66948—24no—
71#66948—42no—
72#66948—42no—
73#66946—44no—
74C4⋊C4×D11—24no—
75C4⋊C4×D11—42no—
76#66927—22no—
77#66927—22no—
78#66927—44no—
79C4×D44—22no—
80C4×D44—22no—
81C11×#107—24no—
82C11×C4⋊C8—22no—
83C11×#95—21no—
84C11⋊#95—21no—
85C11⋊#95—22no—
86#66885—24no—
87#66885—42no—
88(C2×D11)⋊C8—24no—
89(C2×D11)⋊C8—42no—
90#66873—24no—
91#66873—42no—
92#66871—22no—
93#66871D414yescomplemented
94C4×C11⋊C8—22no—
95#26230—111nomaximal, Sylow
96C23×D11—22no—
97C23×D11C2×D412yes—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—22no—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2411yescharacteristic
104C22×Dic11—21no—
105C22×Dic11—21no—
106C22×Dic11C2×D412yes—
107C2×D44—22no—
108C2×D44—22no—
109C2×D44—22no—
110C2×D44—22no—
111C2×D44—22no—
112C2×D44—22no—
113C2×D44—22no—
114C2×D44—22no—
115C2×D44—44no—
116C2×D44—44no—
117C2×D44—44no—
118C2×D44—44no—
119C2×D44—42no—
120C2×D44—42no—
121C2×D44—42no—
122C2×D44—42no—
123C2×D44—81no—
124C2×D44—81no—
125C2×D44—82no—
126C2×D44—82no—
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—22no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—42no—
145C11×C4⋊C4—81no—
146C11×C4⋊C4C2×D412yes—
147C11×C4⋊C4#4112yes—
148C42×C11—42no—
149C42×C11#4112yes—
150C42×C11#4112yes—
151(C2×D11)⋊C4—24no—
152(C2×D11)⋊C4—44no—
153(C2×D11)⋊C4—44no—
154(C2×D11)⋊C4—44no—
155C4⋊Dic11—22no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159C4⋊Dic11C2×D412yes—
160Dic11⋊C4—44no—
161C4×Dic11—42no—
162C2×C11⋊C8—21no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8—21no—
165C2×C11⋊C8—21no—
166C2×C11⋊C8—21no—
167C2×C11⋊C8C2×D412yes—
168C2×#480—112no—
169#2541—111no—
170D4×C4⋊C4—111no—
171#2033—112no—
172#2033—112no—
173#1982—111no—
174#1957—111no—
175#1954—111no—
176#1947D1111yescharacteristic, complemented
177#1874—112no—
178C4×#107—111no—
179C23×C11C22×D411yescharacteristic
180C22×D11—22no—
181C22×D11—22no—
182C22×D11—22no—
183C22×D11—22no—
184C22×D11—22no—
185C22×D11—22no—
186C22×D11—42no—
187C22×D11—42no—
188C22×D11—42no—
189C22×D11—42no—
190C22×D11—42no—
191C22×D11—42no—
192C22×D11—42no—
193C22×D11C2×D814yes—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
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
215C2×Dic11—22no—
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224D44—28no—
225D44—42no—
226D44—42no—
227D44—42no—
228D44—42no—
229D44—84no—
230D44—88no—
231D44—88no—
232D44—84no—
233C4×D11—42no—
234C4×D11—42no—
235C4×D11—42no—
236C4×D11—42no—
237C4×D11—88no—
238C8×C11—42no—
239C11⋊C8—22no—
240C11⋊C8—41no—
241C2×#127—111no—
242C2×#127—221no—
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×#107C2×D1112yes—
252C2×C4⋊C8C2×D1111yescharacteristic
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—221no—
263#385—222no—
264#384C2×D1111yescharacteristic
265#380—112no—
266C4×C4⋊C4—111no—
267C4×C4⋊C4C2×D1111yescharacteristic
268#340—111no—
269#340—111no—
270#340C2×D1112yes—
271C22×C11C2×#12311yescharacteristic
272C22×C11D4211yescharacteristic
273C22×C11#54611yescharacteristic
274C22×C11C22×D811yescharacteristic
275C22×C11C2×#13711yescharacteristic
276C22×C11#57611yescharacteristic
277C22×C11#57711yescharacteristic
278C2×D11—24no—
279C2×D11—24no—
280C2×D11—24no—
281C2×D11—42no—
282C2×D11—42no—
283C2×D11—42no—
284C2×D11—42no—
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#48014yescomplemented
297C4×C11#53211yescharacteristic
298C4×C11#54011yescharacteristic
299C4×C11#55011yescharacteristic
300C4×C11#55911yescharacteristic
301Dic11—42no—
302Dic11—42no—
303Dic11—81no—
304C22×D4—111no—
305C22×D4—112no—
306C22×D4—222no—
307C22×D4—222no—
308C22×D4—221no—
309C22×D4—221no—
310C23×C4—112no—
311C23×C4—222no—
312C22×C8—111no—
313C22×C8—111no—
314C22×C8C22×D1112yes—
315#127—222no—
316#127—222no—
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—224no—
331C2×C4⋊C4—222no—
332C2×C4⋊C4—442no—
333C2×C4⋊C4C22×D1112yes—
334C2×C4⋊C4C22×D1111yescharacteristic
335C2×C4⋊C4C22×D1111yescharacteristic
336C2×C22⋊C4—112no—
337C2×C22⋊C4—222no—
338C2×C22⋊C4—222no—
339C2×C22⋊C4—222no—
340C2×C42—21no—
341C2×C42—221no—
342C2×C42C22×D1111yescharacteristic
343#107—24no—
344#107—114no—
345#107—222no—
346C4⋊C8—22no—
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—222no—
356#95—221no—
357C2×C11#244511yescharacteristic
358C2×C11C2×#48011yescharacteristic
359C2×C11#309611yescharacteristic
360C2×C11#327811yescharacteristic
361C2×C11D4×D811yescharacteristic
362C2×C11#329411yescharacteristic
363C2×C11#333311yescharacteristic
364D11—44no—
365D11—162no—
366C24—112no—
367C24—222no—
368C2×D4—114no—
369C2×D4—222no—
370C2×D4—222no—
371C2×D4—222no—
372C2×D4—222no—
373C2×D4—222no—
374C2×D4—222no—
375C2×D4—222no—
376C2×D4—222no—
377C2×D4—444no—
378C2×D4—444no—
379C2×D4—444no—
380C2×D4—444no—
381C2×D4—442no—
382C2×D4—442no—
383C2×D4—442no—
384C2×D4—442no—
385C2×D4—881no—
386C2×D4—881no—
387C2×D4—882no—
388C2×D4—882no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—112no—
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—22no—
408C2×C8—22no—
409C2×C8—22no—
410C2×C8—112no—
411C2×C8—221no—
412C2×C8—221no—
413C2×C8—221no—
414C2×C8—221no—
415C2×C8—221no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—42no—
421C4⋊C4—81no—
422C4⋊C4—112no—
423C4⋊C4—222no—
424C4⋊C4—221no—
425C4⋊C4—221no—
426C4⋊C4—221no—
427C4⋊C4—444no—
428C4⋊C4D4×D1112yes—
429C4⋊C4#434312yes—
430C22⋊C4—224no—
431C22⋊C4—444no—
432C22⋊C4—444no—
433C22⋊C4—444no—
434C42—42no—
435C42—442no—
436C42#433912yes—
437C42#434312yes—
438C11#2623011yescharacteristic, complemented, Sylow
439C23—114no—
440C23—222no—
441C23—222no—
442C23—222no—
443C23—222no—
444C23—222no—
445C23—222no—
446C23—442no—
447C23—442no—
448C23—442no—
449C23—442no—
450C23—442no—
451C23—442no—
452C23—442no—
453C23C2×D4×D1111yescharacteristic
454D4—228no—
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—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—222no—
475C2×C4—222no—
476C2×C4—222no—
477C2×C4—222no—
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#6694712yes—
489C2×C4#6694712yes—
490C2×C4D8×D1112yes—
491C2×C4#6697112yes—
492C2×C4C2×#433911yescharacteristic
493C2×C4C2×D4×D1111yescharacteristic
494C2×C4C2×#434311yescharacteristic
495C2×C4C2×#434311yescharacteristic
496C2×C4#6704211yescharacteristic
497C2×C4#6704211yescharacteristic
498C8—42no—
499C8—222no—
500C8—441no—
501C22—224no—
502C22—224no—
503C22—224no—
504C22—442no—
505C22—442no—
506C22—442no—
507C22—442no—
508C22—882no—
509C22—882no—
510C22—882no—
511C22—882no—
512C22—882no—
513C22—882no—
514C22—882no—
515C22C2×#6694711yescharacteristic
516C22#1062314011yescharacteristic
517C22#1062316111yescharacteristic
518C22C2×D8×D1111yescharacteristic
519C22C2×#6697111yescharacteristic
520C22#1062330511yescharacteristic
521C22#1062330911yescharacteristic
522C4—22no—
523C4—42no—
524C4—42no—
525C4—82no—
526C4—442no—
527C4—442no—
528C4—881no—
529C4#1062249514yescomplemented
530C4#1062308411yescharacteristic
531C4#1062311611yescharacteristic
532C4#1062322911yescharacteristic
533C4#1062325611yescharacteristic
534C2—444no—
535C2—1762no—
536C2#1307238311yescharacteristic
537C2C2×#1062249511yescharacteristic
538C2#1307857611yescharacteristic
539C2#1308027711yescharacteristic
540C2#1308028811yescharacteristic
541C2#1308042611yescharacteristic
542C2#1308095111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1947C2
socleC23×C11C22×D4
prime radical#13073558C2
hypercenter#1947D11
hypocenterC11#26230
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
1. C2×#10622495C2semidirect
3. #13071516C2semidirect
4. #13069801C2semidirect
5. #13069800C2semidirect
6. #13069542C2semidirect
7. #13069421C2semidirect
8. #13069409C2semidirect
9. #13068932C2semidirect
10. C4×#66871C2semidirect
11. C11×#1947C2semidirect
93. #66871D4semidirect
176. #1947D11semidirect
296. C4×C11#480semidirect
438. C11#26230semidirect
529. C4#10622495semidirect

Maximal subgroups

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

subgroupindex
C2×#106224952
#130735582
#130715162
#130698012
#130698002
#130695422
#130694212
#130694092
#130689322
C4×#668712
C11×#19472
#2623011