Finite Group Databasebeta

← #14773549

Subgroups — #14773549

Order 2816.

846 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×C4×#4314C211yesmaximal, characteristic
2#13071571C211yesmaximal, characteristic, complemented
3#13071563C211yesmaximal, characteristic
4#13069497C212yesmaximal
5#13069258C212yesmaximal, complemented
6#13069237C212yesmaximal
7#13068776C211yesmaximal, characteristic, complemented
8#13068622C211yesmaximal, characteristic, complemented
9#13068617C211yesmaximal, characteristic
10#13068513C212yesmaximal, complemented
11C11×#1770C211yesmaximal, characteristic, complemented
12C22×#4314C2211yescharacteristic
13C2×#66945—21no—
14C2×C4×D44C2211yescharacteristic
15C2×C4×Dic22C2211yescharacteristic
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×#97C2212yes—
18C2×C4×C8×C11C2211yescharacteristic
19C4×C11×C4⋊C4C2211yescharacteristic
20C2×#66885C2212yes—
21C2×#66885C2211yescharacteristic
22C2×#66882C2212yes—
23C2×#66882C2212yes—
24C2×#66881C2211yescharacteristic
25C2×#66880C2212yes—
26C2×#66880C2211yescharacteristic
27#10622600—21no—
28#10622590—21no—
29C4⋊C4×Dic11—21no—
30#10622552C2212yes—
31#10622548C2211yescharacteristic
32#10622548C2211yescharacteristic
33C4×C4⋊Dic11C2212yes—
34C4×C4⋊Dic11C2212yes—
35#10622542C2212yes—
36C4×#4314C418yescomplemented
37#10622283—22no—
38#10622268—22no—
39C11×#336C2212yes—
40#10622189C2212yes—
41#10622189C2212yes—
42C22×D44C2311yescharacteristic
43C22×C4×D11—21no—
44C22×Dic22C2311yescharacteristic
45C22×C8×C11C2312yes—
46C22×C8×C11C2311yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C42×C11C2312yes—
51C2×C42×C11C2311yescharacteristic
52C2×(C2×D11)⋊C4—21no—
53C2×(C2×D11)⋊C4—22no—
54C2×(C2×D11)⋊C4—22no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11C2312yes—
60C2×C4⋊Dic11C2312yes—
61C2×C4⋊Dic11C2311yescharacteristic
62C2×C4⋊Dic11C2311yescharacteristic
63C2×Dic11⋊C4—21no—
64C2×C4×Dic11—21no—
65C2×C4×Dic11—22no—
66C2×C4×Dic11—22no—
67C2×#4314—22no—
68C2×#4314—22no—
69C2×#4314C2×C414yes—
70#66945—44no—
71C4×D44—22no—
72C4×D44C2×C414yes—
73C4×Dic22—22no—
74C4×Dic22C2×C414yes—
75C11×C4⋊C8—22no—
76C11×#97—24no—
77C4×C8×C11C2×C414yes—
78C11×#95D412yes—
79C11⋊#95—22no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83#66885—42no—
84#66885C2×C414yes—
85#66882—24no—
86#66882—42no—
87#66881C2×C414yes—
88#66880—42no—
89#66880C2×C414yes—
90#22811—111nomaximal, Sylow
91C23×D11—21no—
92C22×C4×C11C2×D412yes—
93C22×C4×C11C2×D412yes—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2411yescharacteristic
97C22×Dic11—21no—
98C22×Dic11—21no—
99C22×Dic11—21no—
100C22×Dic11—22no—
101C22×Dic11—22no—
102C2×D44—21no—
103C2×D44—21no—
104C2×D44—21no—
105C2×D44—21no—
106C2×D44—21no—
107C2×D44C22×C412yes—
108C2×C4×D11—24no—
109C2×C4×D11—42no—
110C2×C4×D11—42no—
111C2×Dic22—21no—
112C2×Dic22—21no—
113C2×Dic22—21no—
114C2×Dic22—21no—
115C2×Dic22—21no—
116C2×Dic22C22×C412yes—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11—21no—
120C2×C8×C11—22no—
121C2×C8×C11—21no—
122C2×C8×C11C22×C412yes—
123C2×C8×C11C22×C412yes—
124C2×C8×C11#4112yes—
125C2×C8×C11#4112yes—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C42×C11—22no—
129C42×C11—22no—
130C42×C11C22×C412yes—
131C42×C11#4112yes—
132(C2×D11)⋊C4—24no—
133(C2×D11)⋊C4—44no—
134(C2×D11)⋊C4—82no—
135C4⋊Dic11—21no—
136C4⋊Dic11—21no—
137C4⋊Dic11—22no—
138C4⋊Dic11—22no—
139C4⋊Dic11—22no—
140C4⋊Dic11—22no—
141C4⋊Dic11—42no—
142C4⋊Dic11—42no—
143C4⋊Dic11—81no—
144C4⋊Dic11—81no—
145C4⋊Dic11C22×C412yes—
146C4⋊Dic11C22×C412yes—
147Dic11⋊C4—24no—
148C4×Dic11—24no—
149C4×Dic11—44no—
150C4×Dic11—82no—
151#4314—28no—
152C2×C4×SD16—111no—
153#2355—111no—
154#2354—111no—
155#1973—112no—
156#1928—112no—
157#1925—112no—
158#1845—111no—
159#1803—111no—
160#1802—111no—
161#1776—112no—
162#1770D1111yescharacteristic, complemented
163C23×C11C22×D411yescharacteristic
164C22×D11—22no—
165C22×D11—41no—
166C22×D11—41no—
167C22×D11—41no—
168C22×D11—41no—
169C22×D11—41no—
170C22×D11—41no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11C4×D412yes—
180C2×C4×C11C4×D412yes—
181C2×C4×C11AGL(1,ℤ/8)12yes—
182C2×C4×C11#13712yes—
183C2×C4×C11C23×C411yescharacteristic
184C2×C4×C11C2×#4111yescharacteristic
185C2×C4×C11C2×#4111yescharacteristic
186C2×C4×C11C2×#4111yescharacteristic
187C2×C4×C11H(5,𝔽2)11yescharacteristic
188C2×C4×C112−1+411yescharacteristic
189C2×Dic11—22no—
190C2×Dic11—22no—
191C2×Dic11—22no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204D44—22no—
205D44—22no—
206D44—41no—
207D44—41no—
208C4×D11—48no—
209Dic22—22no—
210Dic22—22no—
211Dic22—41no—
212Dic22—41no—
213C8×C11—22no—
214C8×C11—42no—
215C8×C11#11714yescomplemented
216C22×SD16—111no—
217C2×C4×Q8—111no—
218C2×C4×D4—111no—
219C2×#117—221no—
220C4×SD16—118no—
221C2×#107—112no—
222C2×#107—112no—
223C2×#106—111no—
224C2×C4⋊C8C2×D1111yescharacteristic
225C2×#103—111no—
226C2×#103—112no—
227C2×#102—111no—
228C2×#102—112no—
229C2×#97C2×D1112yes—
230C2×C4×C8C2×D1111yescharacteristic
231#391—112no—
232#390—112no—
233#388—222no—
234#387—222no—
235#384—111no—
236#384—111no—
237#382—221no—
238#380—221no—
239C4×C4⋊C4—112no—
240C4×C4⋊C4—112no—
241C4×C4⋊C4—221no—
242C4×C4⋊C4C2×D1111yescharacteristic
243#340—112no—
244#340—112no—
245#336C2×D1112yes—
246C22×C11C2×C4×D411yescharacteristic
247C22×C11#54711yescharacteristic
248C22×C11#55011yescharacteristic
249C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
250C22×C11C2×#13711yescharacteristic
251C22×C11#57611yescharacteristic
252C22×C11#57811yescharacteristic
253C2×D11—42no—
254C2×D11—42no—
255C2×D11—42no—
256C2×D11—81no—
257C2×D11—81no—
258C2×D11—81no—
259C2×D11—81no—
260C4×C11—22no—
261C4×C11—42no—
262C4×C11—42no—
263C4×C11#44014yes—
264C4×C11C2×#11711yescharacteristic
265C4×C11#52011yescharacteristic
266C4×C11#55511yescharacteristic
267C4×C11#55611yescharacteristic
268Dic11—42no—
269Dic11—42no—
270Dic11—42no—
271Dic11—82no—
272Dic11—82no—
273C22×Q8—111no—
274C22×D4—111no—
275C23×C4—221no—
276C2×SD16—114no—
277C2×SD16—222no—
278C2×SD16—222no—
279C22×C8C22×D1112yes—
280C22×C8C22×D1111yescharacteristic
281C22×C8C22×D1111yescharacteristic
282C4×Q8—114no—
283C4×Q8—222no—
284C4×D4—114no—
285C4×D4—222no—
286#117—444no—
287C2×C4⋊C4—111no—
288C2×C4⋊C4—111no—
289C2×C4⋊C4—112no—
290C2×C4⋊C4—112no—
291C2×C4⋊C4—221no—
292C2×C4⋊C4—221no—
293C2×C4⋊C4—221no—
294C2×C4⋊C4—221no—
295C2×C4⋊C4—221no—
296C2×C4⋊C4D4411yescharacteristic
297C2×C4⋊C4D4411yescharacteristic
298C2×C22⋊C4—221no—
299C2×C22⋊C4—222no—
300C2×C22⋊C4—222no—
301C2×C42—221no—
302C2×C42—222no—
303C2×C42—222no—
304C2×C42C22×D1112yes—
305C2×C42C22×D1111yescharacteristic
306#107—224no—
307#107—442no—
308#106—114no—
309C4⋊C8—22no—
310#103—114no—
311#103—442no—
312#102—114no—
313#102—442no—
314#97—24no—
315C4×C8C4×D1114yes—
316#95—222no—
317#95—222no—
318#95—222no—
319#95—222no—
320#95D4412yes—
321C2×C11#235411yescharacteristic
322C2×C11C2×#44011yescharacteristic
323C2×C11#295111yescharacteristic
324C2×C11#335311yescharacteristic
325C2×C11#335711yescharacteristic
326C2×C11#339811yescharacteristic
327C2×C11#339911yescharacteristic
328D11—82no—
329C24—221no—
330C2×Q8—112no—
331C2×Q8—221no—
332C2×Q8—221no—
333C2×Q8—221no—
334C2×Q8—221no—
335C2×Q8—221no—
336C2×D4—112no—
337C2×D4—221no—
338C2×D4—221no—
339C2×D4—221no—
340C2×D4—221no—
341C2×D4—221no—
342C22×C4—221no—
343C22×C4—221no—
344C22×C4—221no—
345C22×C4—224no—
346C22×C4—222no—
347C22×C4—222no—
348C22×C4—442no—
349C22×C4—442no—
350C22×C4C2×D4412yes—
351C22×C4C2×D4412yes—
352C22×C4C2×D4411yescharacteristic
353C22×C4C2×D4411yescharacteristic
354C22×C4C23×D1111yescharacteristic
355SD16—228no—
356C2×C8—21no—
357C2×C8—21no—
358C2×C8—22no—
359C2×C8—22no—
360C2×C8—22no—
361C2×C8C2×C4×D1112yes—
362C2×C8C2×C4×D1112yes—
363C2×C8#434112yes—
364C2×C8#434312yes—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—112no—
368C4⋊C4—112no—
369C4⋊C4—224no—
370C4⋊C4—221no—
371C4⋊C4—221no—
372C4⋊C4—222no—
373C4⋊C4—222no—
374C4⋊C4—222no—
375C4⋊C4—222no—
376C4⋊C4—442no—
377C4⋊C4—442no—
378C4⋊C4—881no—
379C4⋊C4—881no—
380C22⋊C4—224no—
381C22⋊C4—444no—
382C22⋊C4—882no—
383C42—22no—
384C42—22no—
385C42—224no—
386C42—444no—
387C42—882no—
388C42C2×C4×D1112yes—
389C42#433912yes—
390C11#2281111yescharacteristic, complemented, Sylow
391C23—222no—
392C23—441no—
393C23—441no—
394C23—441no—
395C23—441no—
396C23—441no—
397C23—441no—
398C23C22×D4411yescharacteristic
399Q8—222no—
400Q8—222no—
401Q8—441no—
402Q8—441no—
403D4—222no—
404D4—222no—
405D4—441no—
406D4—441no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—222no—
416C2×C4—222no—
417C2×C4—222no—
418C2×C4—441no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4—441no—
423C2×C4—441no—
424C2×C4—448no—
425C2×C4—442no—
426C2×C4—442no—
427C2×C4—442no—
428C2×C4—442no—
429C2×C4—442no—
430C2×C4—442no—
431C2×C4C4×D4412yes—
432C2×C4C4×D4412yes—
433C2×C4#6696112yes—
434C2×C4#6696212yes—
435C2×C4C22×C4×D1111yescharacteristic
436C2×C4C2×#433911yescharacteristic
437C2×C4C2×#434111yescharacteristic
438C2×C4C2×#434311yescharacteristic
439C2×C4#6704211yescharacteristic
440C2×C4#6704311yescharacteristic
441C8—22no—
442C8—42no—
443C8#6694514yescomplemented
444C22—442no—
445C22—442no—
446C22—442no—
447C22—881no—
448C22—881no—
449C22—881no—
450C22—881no—
451C22C2×C4×D4411yescharacteristic
452C22#1062308611yescharacteristic
453C22#1062310811yescharacteristic
454C22C2×#6696111yescharacteristic
455C22C2×#6696211yescharacteristic
456C22#1062328311yescharacteristic
457C22#1062328411yescharacteristic
458C4—22no—
459C4—42no—
460C4—42no—
461C4—442no—
462C4—442no—
463C4—442no—
464C4—882no—
465C4—882no—
466C4#1062232314yes—
467C4C2×#6694511yescharacteristic
468C4#1062305411yescharacteristic
469C4#1062309411yescharacteristic
470C4#1062311511yescharacteristic
471C2—882no—
472C2#1307156311yescharacteristic
473C2C2×#1062232311yescharacteristic
474C2#1307749311yescharacteristic
475C2#1308120111yescharacteristic
476C2#1308124311yescharacteristic
477C2#1308164911yescharacteristic
478C2#1308166011yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1770C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1770D11
hypocenterC11#22811
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1770

Complements

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

NH ≅ G/Ntype
2. #13071571C2semidirect
5. #13069258C2semidirect
7. #13068776C2semidirect
8. #13068622C2semidirect
10. #13068513C2semidirect
11. C11×#1770C2semidirect
36. C4×#4314C4semidirect
162. #1770D11semidirect
215. C8×C11#117semidirect
390. C11#22811semidirect
443. C8#66945semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43142
#130715712
#130715632
#130694972
#130692582
#130692372
#130687762
#130686222
#130686172
#130685132
C11×#17702
#2281111