Finite Group Databasebeta

← #14808159

Subgroups — #14808159

Order 2816.

1088 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623250C211yesmaximal, characteristic
2C2×#10622677C211yesmaximal, characteristic, complemented
3#13074447C211yesmaximal, characteristic, complemented
4#13069803C212yesmaximal, complemented
5#13069796C212yesmaximal, complemented
6#13069585C211yesmaximal, characteristic, complemented
7#13069423C211yesmaximal, characteristic, complemented
8#13068875C212yesmaximal, complemented
9#13068861C212yesmaximal, complemented
10#13068385C211yesmaximal, characteristic, complemented
11C2×C11×#490C211yesmaximal, characteristic, complemented
12C2×C11×#127C2211yescharacteristic
13C2×C11×#125C2211yescharacteristic
14C2×#66992—22no—
15C2×#66991C2212yes—
16C2×#66988—22no—
17C2×D4×Dic11C2212yes—
18#10623250—24no—
19#10623250—24no—
20C2×#66925C2211yescharacteristic
21C2×#66923C2211yescharacteristic
22C11×#490—24no—
23C2×C11×#102C2212yes—
24C2×C11×#102C2212yes—
25C2×C11×#97C2211yescharacteristic
26C2×#66896C2212yes—
27C2×#66896C2212yes—
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30#10622677—24no—
31#10622607—22no—
32#10622600C2212yes—
33#10622597—22no—
34#10622586C2212yes—
35C2×#66872C2212yes—
36C2×#66871C2212yes—
37#10622548C2211yescharacteristic
38C2×C4×C11⋊C8C2211yescharacteristic
39#10622189C2212yes—
40#10622189C2212yes—
41#10622188C2211yescharacteristic
42#10622188C2211yescharacteristic
43C22×D4×C11—22no—
44C22×D4×C11C2312yes—
45C22×C22⋊D11—22no—
46C23×Dic11—22no—
47C22×C4×D11C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C11×#127—22no—
51C11×#127D414yes—
52C11×#125—22no—
53C11×#125—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4C2312yes—
56C2×C42×C11C2311yescharacteristic
57C2×C22⋊Dic11—22no—
58C2×C22⋊Dic11—22no—
59#66992—216no—
60#66991—24no—
61#66991—24no—
62#66988—216no—
63D4×Dic11—24no—
64D4×Dic11—24no—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4D412yes—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11C2312yes—
69C2×C4⋊Dic11C2312yes—
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4—22no—
72C2×Dic11⋊C4D412yes—
73C2×C4×Dic11C2311yescharacteristic
74C22×C11⋊C8C2311yescharacteristic
75C22×C11⋊C8C2311yescharacteristic
76#66925—22no—
77#66925—22no—
78#66923—22no—
79#66923D414yes—
80C11×#102—24no—
81C11×#102—24no—
82C11×#97—22no—
83#66896—24no—
84#66896—24no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87(C2×D11)⋊C8—22no—
88(C2×D11)⋊C8—22no—
89#66872—24no—
90#66871—24no—
91C4×C11⋊C8—22no—
92#25682—111nomaximal, Sylow
93C24×C11—22no—
94C23×D11C2×D411yescharacteristic
95C2×D4×C11—28no—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11—82no—
102C2×D4×C11—82no—
103C2×D4×C11C2×D414yes—
104C22×C4×C11—22no—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2411yescharacteristic
107C2×C22⋊D11—28no—
108C2×C22⋊D11—82no—
109C2×C22⋊D11—82no—
110C22×Dic11—28no—
111C22×Dic11—22no—
112C22×Dic11—22no—
113C22×Dic11—82no—
114C22×Dic11—82no—
115C22×Dic11C2×D411yescharacteristic
116C22×Dic11C2×D412yes—
117C2×C4×D11—21no—
118C2×C4×D11—21no—
119C2×C4×D11—21no—
120C2×C4×D11—21no—
121C2×C4×D11—21no—
122C2×C4×D11—21no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—44no—
132C42×C11C2×D412yes—
133C42×C11C2×D412yes—
134C22⋊Dic11—28no—
135C22⋊Dic11—28no—
136(C2×D11)⋊C4—24no—
137(C2×D11)⋊C4—82no—
138C4⋊Dic11—22no—
139C4⋊Dic11—22no—
140C4⋊Dic11—22no—
141C4⋊Dic11—82no—
142C4⋊Dic11C2×D414yes—
143Dic11⋊C4—28no—
144Dic11⋊C4—24no—
145Dic11⋊C4—82no—
146C4×Dic11—21no—
147C4×Dic11—21no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8—21no—
152C2×C11⋊C8#4112yes—
153C2×C11⋊C8#4112yes—
154C2×#540—111no—
155C2×#499—111no—
156C2×#490D1111yescharacteristic, complemented
157#2629—111no—
158#2034—112no—
159#2033—112no—
160#1992—111no—
161#1957—111no—
162#1864—112no—
163#1862—112no—
164#1750—111no—
165C23×C11—24no—
166C23×C11—42no—
167C23×C11—42no—
168C23×C11—42no—
169C23×C11—42no—
170C23×C11—42no—
171C23×C11—42no—
172C23×C11C22×D411yescharacteristic
173C22×D11—21no—
174C22×D11—21no—
175C22×D11—21no—
176C22×D11—22no—
177C22×D11—22no—
178D4×C11—24no—
179D4×C11—24no—
180D4×C11—42no—
181D4×C11—42no—
182D4×C11—88no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11#12014yes—
189C2×C4×C11C22×D411yescharacteristic
190C2×C4×C11C22×D411yescharacteristic
191C2×C4×C11C2×#4111yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C2×C4×C112−1+411yescharacteristic
194C2×C4×C112−1+411yescharacteristic
195C22⋊D11—88no—
196C2×Dic11—22no—
197C2×Dic11—24no—
198C2×Dic11—21no—
199C2×Dic11—21no—
200C2×Dic11—21no—
201C2×Dic11—22no—
202C2×Dic11—22no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—88no—
209C4×D11—41no—
210C4×D11—41no—
211C4×D11—41no—
212C4×D11—41no—
213C8×C11—41no—
214C8×C11—41no—
215C11⋊C8—22no—
216C11⋊C8—22no—
217#540—224no—
218#540—224no—
219C2×#127C2×D1111yescharacteristic
220C2×#125—111no—
221C2×#125C2×D1111yescharacteristic
222C2×#123—222no—
223C2×#121—112no—
224C2×#121—222no—
225C2×C4×D4—112no—
226C2×#117—111no—
227#499—224no—
228#490—24no—
229C2×#107—112no—
230C2×#106—112no—
231C2×#102—112no—
232C2×#102—112no—
233C2×#102C2×D1112yes—
234C2×#102C2×D1112yes—
235C2×C22⋊C8—111no—
236C2×C22⋊C8—111no—
237C2×#97C2×D1111yescharacteristic
238C2×C4×C8—111no—
239#398—222no—
240#396—222no—
241#389—112no—
242#384—111no—
243#380—112no—
244#340—112no—
245#340—112no—
246#336—111no—
247#336—111no—
248C22×C11—44no—
249C22×C11—44no—
250C22×C11—44no—
251C22×C11—82no—
252C22×C11—82no—
253C22×C11—82no—
254C22×C11—82no—
255C22×C11C2×#12011yescharacteristic
256C22×C11#53211yescharacteristic
257C22×C11#53611yescharacteristic
258C22×C11#57612yes—
259C22×C11#57712yes—
260C2×D11—41no—
261C2×D11—41no—
262C2×D11—41no—
263C2×D11—42no—
264C2×D11—42no—
265C4×C11—24no—
266C4×C11—82no—
267C4×C11#54711yescharacteristic
268C4×C11#54711yescharacteristic
269C4×C11#54811yescharacteristic
270C4×C11#54811yescharacteristic
271Dic11—41no—
272Dic11—42no—
273Dic11—44no—
274Dic11—82no—
275C22×D4—22no—
276C22×D4—222no—
277C22×D4C22×D1112yes—
278C23×C4—111no—
279C23×C4—222no—
280C22×C8—111no—
281C22×C8—111no—
282C22×C8C22×D1111yescharacteristic
283C22×C8C22×D1111yescharacteristic
284#127—22no—
285#127C22⋊D1114yes—
286#125—22no—
287#125—22no—
288#125—114no—
289#125—222no—
290#123—2216no—
291#121—224no—
292#121—2216no—
293#121—224no—
294C4×D4—224no—
295C4×D4—224no—
296#117—222no—
297#117—222no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—112no—
300C2×C4⋊C4—112no—
301C2×C4⋊C4—112no—
302C2×C4⋊C4—222no—
303C2×C4⋊C4—222no—
304C2×C4⋊C4—222no—
305C2×C4⋊C4C22×D1112yes—
306C2×C22⋊C4—112no—
307C2×C22⋊C4—222no—
308C2×C22⋊C4—222no—
309C2×C22⋊C4—222no—
310C2×C42—111no—
311C2×C42C22×D1111yescharacteristic
312#107—224no—
313#106—224no—
314#102—24no—
315#102—24no—
316#102—224no—
317#102—224no—
318C22⋊C8—222no—
319C22⋊C8—222no—
320#97—22no—
321C4×C8—222no—
322#95—222no—
323#95—222no—
324C2×C11—84no—
325C2×C11#243211yescharacteristic
326C2×C11#301212yes—
327C2×C11#317411yescharacteristic
328C2×C11#317611yescharacteristic
329C2×C11#324112yes—
330D11—81no—
331C24—22no—
332C24—111no—
333C2×D4—28no—
334C2×D4—22no—
335C2×D4—22no—
336C2×D4—22no—
337C2×D4—22no—
338C2×D4—22no—
339C2×D4—82no—
340C2×D4—82no—
341C2×D4—228no—
342C2×D4—882no—
343C2×D4—882no—
344C2×D4C2×C22⋊D1114yes—
345C22×C4—22no—
346C22×C4—111no—
347C22×C4—112no—
348C22×C4—222no—
349C22×C4—228no—
350C22×C4—221no—
351C22×C4—221no—
352C22×C4—221no—
353C22×C4—221no—
354C22×C4—221no—
355C22×C4—221no—
356C22×C4—222no—
357C22×C4—882no—
358C22×C4—882no—
359C22×C4D4×D1112yes—
360C22×C4C23×D1111yescharacteristic
361C2×C8—21no—
362C2×C8—21no—
363C2×C8—21no—
364C2×C8—21no—
365C2×C8—21no—
366C2×C8—21no—
367C2×C8—112no—
368C2×C8—112no—
369C2×C8—221no—
370C2×C8—221no—
371C2×C8—221no—
372C2×C8—221no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—44no—
376C4⋊C4—114no—
377C4⋊C4—224no—
378C4⋊C4—228no—
379C4⋊C4—222no—
380C4⋊C4—222no—
381C4⋊C4—222no—
382C4⋊C4—882no—
383C4⋊C4—882no—
384C22⋊C4—228no—
385C22⋊C4—228no—
386C22⋊C4—224no—
387C22⋊C4—882no—
388C42—221no—
389C42—221no—
390C42D4×D1112yes—
391C42C2×C22⋊D1112yes—
392C11#2568211yescharacteristic, complemented, Sylow
393C23—24no—
394C23—42no—
395C23—42no—
396C23—42no—
397C23—42no—
398C23—42no—
399C23—42no—
400C23—222no—
401C23—222no—
402C23—221no—
403C23—221no—
404C23—221no—
405C23C2×D4×D1111yescharacteristic
406D4—24no—
407D4—24no—
408D4—42no—
409D4—42no—
410D4—88no—
411D4—888no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—222no—
418C2×C4—222no—
419C2×C4—222no—
420C2×C4—221no—
421C2×C4—224no—
422C2×C4—221no—
423C2×C4—221no—
424C2×C4—442no—
425C2×C4—442no—
426C2×C4—441no—
427C2×C4—441no—
428C2×C4—441no—
429C2×C4—441no—
430C2×C4—442no—
431C2×C4—442no—
432C2×C4—442no—
433C2×C4—888no—
434C2×C4#6699014yes—
435C2×C4C2×D4×D1111yescharacteristic
436C2×C4#41×D1111yescharacteristic
437C2×C4#41×D1111yescharacteristic
438C2×C4#6704311yescharacteristic
439C2×C4#6704311yescharacteristic
440C2×C4C22×C22⋊D1111yescharacteristic
441C8—41no—
442C8—41no—
443C8—222no—
444C8—222no—
445C22—44no—
446C22—44no—
447C22—44no—
448C22—82no—
449C22—82no—
450C22—82no—
451C22—82no—
452C22—442no—
453C22—441no—
454C22—442no—
455C22—441no—
456C22—441no—
457C22#1062319911yescharacteristic
458C22#1062320611yescharacteristic
459C22#1062330512yes—
460C22#1062330612yes—
461C22C2×#6699011yescharacteristic
462C4—24no—
463C4—82no—
464C4—441no—
465C4—442no—
466C4—444no—
467C4—882no—
468C4#1062320811yescharacteristic
469C4#1062320811yescharacteristic
470C4#1062335511yescharacteristic
471C4#1062335511yescharacteristic
472C2—84no—
473C2—881no—
474C2#1307224711yescharacteristic
475C2#1307791912yes—
476C2#1307924311yescharacteristic
477C2#1307926511yescharacteristic
478C2#1307986412yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#490C2
socleC23×C11C22×D4
prime radicalC2×#10623250C2
hypercenterC2×#490D11
hypocenterC11#25682
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#490

Complements

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

NH ≅ G/Ntype
2. C2×#10622677C2semidirect
3. #13074447C2semidirect
4. #13069803C2semidirect
5. #13069796C2semidirect
6. #13069585C2semidirect
7. #13069423C2semidirect
8. #13068875C2semidirect
9. #13068861C2semidirect
10. #13068385C2semidirect
11. C2×C11×#490C2semidirect
156. C2×#490D11semidirect
392. C11#25682semidirect

Maximal subgroups

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

subgroupindex
C2×#106232502
C2×#106226772
#130744472
#130698032
#130697962
#130695852
#130694232
#130688752
#130688612
#130683852
C2×C11×#4902
#2568211