Finite Group Databasebeta

← #14804277

Subgroups — #14804277

Order 2816.

1014 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622689C211yesmaximal, characteristic
2C2×#10622667C212yesmaximal, complemented
3C2×#10622644C211yesmaximal, characteristic, complemented
4#13071672C211yesmaximal, characteristic, complemented
5#13069933C212yesmaximal, complemented
6#13069710C212yesmaximal, complemented
7#13069544C211yesmaximal, characteristic
8#13069335C211yesmaximal, characteristic, complemented
9#13068974C212yesmaximal, complemented
10C4×#66899C211yesmaximal, characteristic, complemented
11C11×#2548C211yesmaximal, characteristic
12C2×C11×#127C2211yescharacteristic
13C2×C11×#124C2212yes—
14C2×C4×Q8×C11C2211yescharacteristic
15C22×#4326C2212yes—
16C22×#4324C2212yes—
17C22×#4324C2212yes—
18C2×#66922C2211yescharacteristic
19C2×C4×Dic22C2212yes—
20C11×#394—22no—
21C11×#390—21no—
22C11×#390—21no—
23C11×#390C2212yes—
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×#66899C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27C2×#66896C2212yes—
28C2×#66896C2212yes—
29#10622689—24no—
30#10622667—28no—
31#10622644—24no—
32C4⋊C4×Dic11—21no—
33#10622586—21no—
34C2×#66874C2212yes—
35C4×C4⋊Dic11C2211yescharacteristic
36#10622542C2212yes—
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C2×C4⋊(C11⋊C8)C2212yes—
39C2×C4×C11⋊C8C2211yescharacteristic
40#10622267—22no—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43#10622162C2212yes—
44C22×Q8×C11C2311yescharacteristic
45C22×D4×C11—21no—
46C22×D4×C11—21no—
47C22×D4×C11C2312yes—
48C22×Dic22C2312yes—
49C11×#127—22no—
50C11×#127—22no—
51C11×#124—24no—
52C11×#124—42no—
53C4×Q8×C11—22no—
54C4×Q8×C11—22no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—22no—
63C2×C42×C11—21no—
64C2×C42×C11C2312yes—
65C2×C42×C11C2311yescharacteristic
66C2×#4326—24no—
67C2×#4326—24no—
68C2×#4326—42no—
69C2×#4324—24no—
70C2×#4324—24no—
71C2×#4324—24no—
72C2×#4324—24no—
73C2×#4324—42no—
74C2×#4324—42no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×Dic11⋊C4—22no—
80C2×C4×Dic11—22no—
81C2×C4×Dic11—21no—
82C22×C11⋊C8C2312yes—
83C22×C11⋊C8C2311yescharacteristic
84C22×C11⋊C8C2311yescharacteristic
85#66922—22no—
86#66922D414yes—
87C4×Dic22—24no—
88C4×Dic22—42no—
89C11×#95D412yes—
90#66899—22no—
91#66899D414yescomplemented
92#66896—24no—
93#66896—42no—
94C11⋊#95—21no—
95C11⋊#95—22no—
96C11⋊#95—22no—
97#66874—24no—
98C4⋊(C11⋊C8)—22no—
99C4⋊(C11⋊C8)—24no—
100C4×C11⋊C8—22no—
101#25369—111nomaximal, Sylow
102C24×C11—22no—
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11—21no—
107C2×Q8×C11—21no—
108C2×Q8×C11C2×D412yes—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—42no—
116C2×D4×C11—42no—
117C2×D4×C11—42no—
118C2×D4×C11—42no—
119C2×D4×C11—81no—
120C2×D4×C11—81no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2411yescharacteristic
128C22×Dic11—22no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C2×Dic22—22no—
132C2×Dic22—22no—
133C2×Dic22—22no—
134C2×Dic22—22no—
135C2×Dic22—22no—
136C2×Dic22C2×D414yes—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—42no—
142C11×C22⋊C4—44no—
143C11×C22⋊C4—44no—
144C11×C22⋊C4—82no—
145C11×C22⋊C4—82no—
146C42×C11—22no—
147C42×C11—22no—
148C42×C11—42no—
149C42×C11C2×D412yes—
150C42×C11#4112yes—
151#4326—48no—
152#4324—48no—
153#4324—48no—
154C4⋊Dic11—24no—
155C4⋊Dic11—24no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159C4⋊Dic11C2×D412yes—
160Dic11⋊C4—44no—
161C4×Dic11—44no—
162C4×Dic11—42no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8—21no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—21no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8C2×D412yes—
171C2×C11⋊C8#4112yes—
172C2×#492—111no—
173C2×#464—112no—
174C2×#462—111no—
175#2548D1111yescharacteristic
176#2365—111no—
177#2055—112no—
178#2015—112no—
179#1982—111no—
180#1939—111no—
181#1880—112no—
182C4×#103—111no—
183C23×C11—42no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11C22×D411yescharacteristic
191Q8×C11—22no—
192Q8×C11—22no—
193Q8×C11—41no—
194Q8×C11—41no—
195D4×C11—42no—
196D4×C11—42no—
197D4×C11—42no—
198D4×C11—42no—
199D4×C11—84no—
200D4×C11—84no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
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—41no—
215C2×C4×C11#12112yes—
216C2×C4×C11#12112yes—
217C2×C4×C11#13512yes—
218C2×C4×C11#13712yes—
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C2×C4×C11C2×#4111yescharacteristic
223C2×C4×C11H(5,𝔽2)11yescharacteristic
224C2×C4×C11H(5,𝔽2)11yescharacteristic
225C2×Dic11—24no—
226C2×Dic11—22no—
227C2×Dic11—42no—
228C2×Dic11—42no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231C2×Dic11—41no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234Dic22—24no—
235Dic22—24no—
236Dic22—42no—
237Dic22—42no—
238C11⋊C8—22no—
239C11⋊C8—22no—
240C11⋊C8—42no—
241C22×Q16—112no—
242C22×SD16—112no—
243C22×SD16—112no—
244C2×C4⋊Q8—111no—
245C2×#127C2×D1111yescharacteristic
246C2×#124C2×D1112yes—
247C2×C4×Q8—112no—
248C2×C4×Q8C2×D1111yescharacteristic
249#492—224no—
250#464—228no—
251#462—224no—
252C2×C4⋊C8—112no—
253C2×C4⋊C8—111no—
254C2×#103—111no—
255C2×#103—111no—
256C2×#103—112no—
257C2×#102—112no—
258C2×#102—112no—
259C2×C4×C8—111no—
260#394—22no—
261#391—112no—
262#390—21no—
263#390—21no—
264#390C2×D1112yes—
265#389—221no—
266#387—222no—
267C4×C4⋊C4—111no—
268C4×C4⋊C4—221no—
269C4×C4⋊C4C2×D1111yescharacteristic
270#340—111no—
271#340—111no—
272#336—112no—
273C22×C11—82no—
274C22×C11—82no—
275C22×C11—82no—
276C22×C11—82no—
277C22×C11—82no—
278C22×C11—82no—
279C22×C11—82no—
280C22×C11C2×#12111yescharacteristic
281C22×C11D4211yescharacteristic
282C22×C11#55011yescharacteristic
283C22×C11C2×#13511yescharacteristic
284C22×C11C2×#13711yescharacteristic
285C22×C11#57711yescharacteristic
286C22×C11#57711yescharacteristic
287C4×C11—22no—
288C4×C11—42no—
289C4×C11—42no—
290C4×C11—42no—
291C4×C11—81no—
292C4×C11#46414yescomplemented
293C4×C11#53211yescharacteristic
294C4×C11#54011yescharacteristic
295C4×C11D4211yescharacteristic
296C4×C11#54611yescharacteristic
297Dic11—44no—
298Dic11—42no—
299Dic11—81no—
300C22×Q8—112no—
301C22×Q8C22×D1111yescharacteristic
302C22×D4—21no—
303C22×D4—21no—
304C22×D4C22×D1112yes—
305C2×Q16—224no—
306C2×Q16—224no—
307C2×Q16—442no—
308C2×SD16—224no—
309C2×SD16—224no—
310C2×SD16—224no—
311C2×SD16—224no—
312C2×SD16—442no—
313C2×SD16—442no—
314C22×C8—111no—
315C22×C8—111no—
316C22×C8—112no—
317C4⋊Q8—114no—
318C4⋊Q8—222no—
319#127—22no—
320#127—22no—
321#124—24no—
322#124—42no—
323C4×Q8—22no—
324C4×Q8—22no—
325C4×Q8—224no—
326C4×Q8—442no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—111no—
329C2×C4⋊C4—111no—
330C2×C4⋊C4—221no—
331C2×C4⋊C4—221no—
332C2×C4⋊C4—222no—
333C2×C4⋊C4C22⋊D1111yescharacteristic
334C2×C4⋊C4C22⋊D1111yescharacteristic
335C2×C4⋊C4C22×D1111yescharacteristic
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C42—21no—
341C2×C42—222no—
342C2×C42—221no—
343C2×C42C22×D1112yes—
344C2×C42C22×D1111yescharacteristic
345C4⋊C8—224no—
346C4⋊C8—222no—
347#103—114no—
348#103—224no—
349#103—222no—
350#102—224no—
351#102—442no—
352C4×C8—222no—
353#95—221no—
354#95—222no—
355#95—222no—
356#95C22⋊D1112yes—
357C2×C11—162no—
358C2×C11#242811yescharacteristic
359C2×C11C2×#46411yescharacteristic
360C2×C11#304311yescharacteristic
361C2×C11#327811yescharacteristic
362C2×C11#328411yescharacteristic
363C2×C11#339411yescharacteristic
364C2×C11#340011yescharacteristic
365C24—22no—
366C2×Q8—21no—
367C2×Q8—21no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—21no—
371C2×Q8—114no—
372C2×Q8—222no—
373C2×Q8—222no—
374C2×Q8—222no—
375C2×Q8—222no—
376C2×Q8—222no—
377C2×Q8D4×D1112yes—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4—42no—
388C2×D4—81no—
389C2×D4—81no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—222no—
393C22×C4—221no—
394C22×C4—221no—
395C22×C4C2×C22⋊D1112yes—
396C22×C4C2×C22⋊D1112yes—
397C22×C4C2×C22⋊D1111yescharacteristic
398C22×C4C2×C22⋊D1111yescharacteristic
399C22×C4C23×D1111yescharacteristic
400Q16—448no—
401SD16—448no—
402SD16—448no—
403C2×C8—112no—
404C2×C8—112no—
405C2×C8—221no—
406C2×C8—221no—
407C2×C8—221no—
408C2×C8—221no—
409C2×C8—222no—
410C2×C8—222no—
411C2×C8—222no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—42no—
417C4⋊C4—112no—
418C4⋊C4—224no—
419C4⋊C4—224no—
420C4⋊C4—221no—
421C4⋊C4—221no—
422C4⋊C4—221no—
423C4⋊C4—444no—
424C22⋊C4—44no—
425C22⋊C4—44no—
426C22⋊C4—82no—
427C22⋊C4—82no—
428C42—22no—
429C42—22no—
430C42—42no—
431C42—444no—
432C42—442no—
433C42D4×D1112yes—
434C42#434112yes—
435C11#2536911yescharacteristic, complemented, Sylow
436C23—42no—
437C23—42no—
438C23—42no—
439C23—42no—
440C23—42no—
441C23—42no—
442C23—42no—
443C23C22×C22⋊D1111yescharacteristic
444Q8—22no—
445Q8—22no—
446Q8—41no—
447Q8—41no—
448Q8—224no—
449Q8—224no—
450Q8—442no—
451Q8—442no—
452D4—42no—
453D4—42no—
454D4—42no—
455D4—42no—
456D4—84no—
457D4—84no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—224no—
473C2×C4—222no—
474C2×C4—442no—
475C2×C4—441no—
476C2×C4—442no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4—441no—
481C2×C4#6699112yes—
482C2×C4#6699112yes—
483C2×C4#6700312yes—
484C2×C4#6700412yes—
485C2×C4C2×D4×D1111yescharacteristic
486C2×C4C2×D4×D1111yescharacteristic
487C2×C4C2×#434111yescharacteristic
488C2×C4#6703711yescharacteristic
489C2×C4#41×D1111yescharacteristic
490C2×C4#6704211yescharacteristic
491C8—222no—
492C8—222no—
493C8—442no—
494C22—82no—
495C22—82no—
496C22—82no—
497C22—82no—
498C22—82no—
499C22—82no—
500C22—82no—
501C22C2×#6699111yescharacteristic
502C22D4×C22⋊D1111yescharacteristic
503C22C2×#6700311yescharacteristic
504C22C2×#6700411yescharacteristic
505C22#1062336511yescharacteristic
506C22#1062336711yescharacteristic
507C22#1062336711yescharacteristic
508C4—22no—
509C4—42no—
510C4—42no—
511C4—42no—
512C4—81no—
513C4—442no—
514C4—444no—
515C4—881no—
516C4#1062266714yescomplemented
517C4#1062312711yescharacteristic
518C4#1062314011yescharacteristic
519C4#1062314311yescharacteristic
520C4#1062315011yescharacteristic
521C2—162no—
522C2#1307220011yescharacteristic
523C2C2×#1062266711yescharacteristic
524C2#1307813311yescharacteristic
525C2#1308028211yescharacteristic
526C2#1308034611yescharacteristic
527C2#1308160811yescharacteristic
528C2#1308166911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2548C2
socleC23×C11C22×D4
prime radicalC2×C11×#127C22
hypercenter#2548D11
hypocenterC11#25369
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2548

Complements

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

NH ≅ G/Ntype
2. C2×#10622667C2semidirect
3. C2×#10622644C2semidirect
4. #13071672C2semidirect
5. #13069933C2semidirect
6. #13069710C2semidirect
8. #13069335C2semidirect
9. #13068974C2semidirect
10. C4×#66899C2semidirect
91. #66899D4semidirect
292. C4×C11#464semidirect
435. C11#25369semidirect
516. C4#10622667semidirect

Maximal subgroups

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

subgroupindex
C2×#106226892
C2×#106226672
C2×#106226442
#130716722
#130699332
#130697102
#130695442
#130693352
#130689742
C4×#668992
C11×#25482
#2536911