Finite Group Databasebeta

← #14772010

Subgroups — #14772010

Order 2816.

1022 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622451C211yesmaximal, characteristic
2C2×#10622494C212yesmaximal, complemented
3#13071567C211yesmaximal, characteristic
4C4⋊C4×D44C211yesmaximal, characteristic
5#13069380C211yesmaximal, characteristic, complemented
6#13068816C212yesmaximal, complemented
7#13068802C212yesmaximal, complemented
8#13068775C211yesmaximal, characteristic, complemented
9#13068648C212yesmaximal, complemented
10C4×#66872C211yesmaximal, characteristic, complemented
11C11×#1947C211yesmaximal, characteristic, complemented
12C22×#4313C2212yes—
13C2×#66945C2212yes—
14C2×C4⋊C4×D11C2212yes—
15C2×C4×D44—21no—
16C2×C4×D44C2211yescharacteristic
17C2×C11×#107C2212yes—
18C2×C11×C4⋊C8C2211yescharacteristic
19C11×#384C2211yescharacteristic
20C4×C11×C4⋊C4C2211yescharacteristic
21C2×(C2×D11)⋊C8C2212yes—
22C2×#66881C2212yes—
23#10622603—22no—
24#10622601—21no—
25#10622600C2212yes—
26#10622600C2212yes—
27C4⋊C4×Dic11—21no—
28C2×#66872C2211yescharacteristic
29C2×#66872C2211yescharacteristic
30C2×#66871C2212yes—
31C2×#66871C2212yes—
32#10622548C2211yescharacteristic
33C4×C4⋊Dic11C2211yescharacteristic
34#10622541—21no—
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622494—28no—
37#10622451C418yescomplemented
38#10622281—22no—
39C11×#340C2212yes—
40#10622189C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43C22×D44D411yescharacteristic
44C22×C4×D11—22no—
45C22×C4×D11C2312yes—
46C22×C8×C11C2312yes—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4C2311yescharacteristic
50C2×C11×C4⋊C4C2312yes—
51C2×C11×C4⋊C4C2311yescharacteristic
52C2×C42×C11—21no—
53C2×C42×C11C2311yescharacteristic
54C2×(C2×D11)⋊C4—22no—
55C2×(C2×D11)⋊C4—22no—
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4D412yes—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11D411yescharacteristic
61C2×C4⋊Dic11C2312yes—
62C2×C4⋊Dic11C2311yescharacteristic
63C2×C4⋊Dic11C2311yescharacteristic
64C2×Dic11⋊C4—22no—
65C2×C4×Dic11—21no—
66C2×C4×Dic11—22no—
67C22×C11⋊C8C2311yescharacteristic
68C22×C11⋊C8C2311yescharacteristic
69C2×#4313—24no—
70C2×#4313—24no—
71C2×#4313C2×C418yescomplemented
72#66945—24no—
73#66945—42no—
74C4⋊C4×D11—24no—
75C4⋊C4×D11—42no—
76C4×D44—44no—
77C4×D44C2×C414yes—
78C4×D44Q814yes—
79C11×#107—24no—
80C11×C4⋊C8C2×C414yescomplemented
81C11×#95—21no—
82C11⋊#95—21no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85(C2×D11)⋊C8C2×C418yescomplemented
86#66881—24no—
87#66872—22no—
88#66872D414yescomplemented
89#66871—24no—
90#66871—42no—
91C4×C11⋊C8C2×C414yescomplemented
92#22665—111nomaximal, Sylow
93C23×D11C2×D412yes—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—22no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2411yescharacteristic
100C22×Dic11—21no—
101C22×Dic11—21no—
102C22×Dic11—22no—
103C22×Dic11C2×D412yes—
104C2×D44—22no—
105C2×D44—22no—
106C2×D44C4⋊C414yes—
107C2×C4×D11—22no—
108C2×C4×D11—22no—
109C2×C4×D11—22no—
110C2×C4×D11—22no—
111C2×C4×D11—44no—
112C2×C4×D11—44no—
113C2×C4×D11—82no—
114C2×C4×D11C22×C414yes—
115C2×C4×D11C2×Q814yes—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11C22×C414yes—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—42no—
125C11×C4⋊C4—81no—
126C11×C4⋊C4C2×D412yes—
127C42×C11—42no—
128C42×C11C22×C412yes—
129C42×C11C2×Q812yes—
130(C2×D11)⋊C4—44no—
131(C2×D11)⋊C4—44no—
132(C2×D11)⋊C4—82no—
133(C2×D11)⋊C4C4⋊C418yes—
134C4⋊Dic11—22no—
135C4⋊Dic11—21no—
136C4⋊Dic11—21no—
137C4⋊Dic11—22no—
138C4⋊Dic11—21no—
139C4⋊Dic11—42no—
140C4⋊Dic11—81no—
141C4⋊Dic11C4⋊C414yes—
142C4⋊Dic11C2×D412yes—
143Dic11⋊C4—44no—
144C4×Dic11—44no—
145C4×Dic11—42no—
146C2×C11⋊C8—21no—
147C2×C11⋊C8—21no—
148C2×C11⋊C8C22×C412yes—
149C2×C11⋊C8C22×C412yes—
150C2×C11⋊C8C2×D412yes—
151C2×C11⋊C8#4112yes—
152#4313—216no—
153C2×#436—111no—
154C2×#428—112no—
155#2354—111no—
156D4×C4⋊C4—111no—
157#1948—111no—
158#1947D1111yescharacteristic, complemented
159#1854—112no—
160#1852—112no—
161#1845—111no—
162#1809—112no—
163C4×#106—111no—
164C23×C11C22×D411yescharacteristic
165C22×D11—22no—
166C22×D11—22no—
167C22×D11—22no—
168C22×D11—22no—
169C22×D11—22no—
170C22×D11—22no—
171C22×D11C2×C4⋊C414yes—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—22no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—42no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—41no—
183C2×C4×C11C2×C4⋊C412yes—
184C2×C4×C11C2×C4⋊C412yes—
185C2×C4×C11AGL(1,ℤ/8)12yes—
186C2×C4×C11#13712yes—
187C2×C4×C11C23×C411yescharacteristic
188C2×C4×C11C22×D411yescharacteristic
189C2×C4×C11C22×Q811yescharacteristic
190C2×C4×C11C2×#4111yescharacteristic
191C2×C4×C11H(5,𝔽2)11yescharacteristic
192C2×C4×C112−1+411yescharacteristic
193C2×Dic11—22no—
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—42no—
199C2×Dic11—41no—
200C2×Dic11—42no—
201C2×Dic11—41no—
202C2×Dic11—42no—
203C2×Dic11—41no—
204C2×Dic11C2×C4⋊C414yes—
205D44—28no—
206C4×D11—24no—
207C4×D11—24no—
208C4×D11—24no—
209C4×D11—24no—
210C4×D11—88no—
211C8×C11—24no—
212C11⋊C8—22no—
213C11⋊C8C4×D414yescomplemented
214C22×M16—112no—
215C2×C4×D4—111no—
216C2×C4×D4—221no—
217C2×#117—112no—
218C22×C4⋊C4—112no—
219#436—118no—
220#428—228no—
221C2×#107—112no—
222C2×#107—112no—
223C2×#107C2×D1112yes—
224C2×#106—111no—
225C2×#106—112no—
226C2×#106—111no—
227C2×C4⋊C8C2×D1111yescharacteristic
228C2×C22⋊C8—112no—
229C2×C4×C8—111no—
230#390—221no—
231#389—221no—
232#388—222no—
233#385—222no—
234#384—111no—
235#384C2×D1111yescharacteristic
236#380—112no—
237#380—112no—
238C4×C4⋊C4—111no—
239C4×C4⋊C4—221no—
240C4×C4⋊C4C2×D1111yescharacteristic
241#340—112no—
242#340—111no—
243#340—111no—
244#340C2×D1112yes—
245C22×C11C22×C4⋊C411yescharacteristic
246C22×C11D4211yescharacteristic
247C22×C11#54711yescharacteristic
248C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
249C22×C11C2×#13711yescharacteristic
250C22×C11#57611yescharacteristic
251C22×C11#57811yescharacteristic
252C2×D11—24no—
253C2×D11—24no—
254C2×D11—24no—
255C2×D11—42no—
256C2×D11—42no—
257C2×D11—42no—
258C2×D11—42no—
259C4×C11—22no—
260C4×C11—42no—
261C4×C11—81no—
262C4×C11—82no—
263C4×C11#42814yescomplemented
264C4×C11C2×C4×D411yescharacteristic
265C4×C11#52011yescharacteristic
266C4×C11D4×Q811yescharacteristic
267C4×C11#55411yescharacteristic
268Dic11—24no—
269Dic11—42no—
270Dic11—81no—
271Dic11—82no—
272C22×D4—111no—
273C23×C4—112no—
274C23×C4—222no—
275C2×M16—118no—
276C2×M16—224no—
277C2×M16—224no—
278C22×C8—111no—
279C22×C8—111no—
280C22×C8C22×D1112yes—
281C4×D4—114no—
282C4×D4—114no—
283C4×D4—444no—
284#117—224no—
285#117—442no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—111no—
289C2×C4⋊C4—111no—
290C2×C4⋊C4—112no—
291C2×C4⋊C4—111no—
292C2×C4⋊C4—224no—
293C2×C4⋊C4—222no—
294C2×C4⋊C4—221no—
295C2×C4⋊C4—221no—
296C2×C4⋊C4—442no—
297C2×C4⋊C4C22×D1112yes—
298C2×C4⋊C4C22×D1111yescharacteristic
299C2×C4⋊C4C22×D1111yescharacteristic
300C2×C22⋊C4—112no—
301C2×C22⋊C4—222no—
302C2×C22⋊C4—222no—
303C2×C22⋊C4—222no—
304C2×C42—21no—
305C2×C42—222no—
306C2×C42—221no—
307C2×C42C22×D1111yescharacteristic
308#107—24no—
309#107—224no—
310#107—442no—
311#106—114no—
312#106—222no—
313#106—224no—
314C4⋊C8C4×D1114yescomplemented
315C22⋊C8—118no—
316C4×C8—114no—
317#95—21no—
318#95—222no—
319#95—222no—
320#95—221no—
321C2×C11D4×C4⋊C411yescharacteristic
322C2×C11C2×#42811yescharacteristic
323C2×C11#291311yescharacteristic
324C2×C11#327411yescharacteristic
325C2×C11#327611yescharacteristic
326C2×C11#335311yescharacteristic
327C2×C11#335711yescharacteristic
328D11—44no—
329C24—112no—
330C2×D4—114no—
331C2×D4—222no—
332C2×D4—222no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—112no—
337C22×C4—114no—
338C22×C4—114no—
339C22×C4—222no—
340C22×C4—222no—
341C22×C4—222no—
342C22×C4—222no—
343C22×C4—221no—
344C22×C4—221no—
345C22×C4—222no—
346C22×C4—444no—
347C22×C4—444no—
348C22×C4—882no—
349C22×C4D4×D1111yescharacteristic
350C22×C4D4×D1111yescharacteristic
351C22×C4C23×D1111yescharacteristic
352M16—2216no—
353C2×C8—22no—
354C2×C8—22no—
355C2×C8—112no—
356C2×C8—112no—
357C2×C8—112no—
358C2×C8—112no—
359C2×C8—221no—
360C2×C8—221no—
361C2×C8C2×C4×D1114yes—
362C4⋊C4—21no—
363C4⋊C4—22no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—22no—
367C4⋊C4—42no—
368C4⋊C4—81no—
369C4⋊C4—114no—
370C4⋊C4—112no—
371C4⋊C4—221no—
372C4⋊C4—222no—
373C4⋊C4—221no—
374C4⋊C4—221no—
375C4⋊C4—222no—
376C4⋊C4—444no—
377C4⋊C4—442no—
378C4⋊C4—881no—
379C4⋊C4D4×D1112yes—
380C22⋊C4—118no—
381C22⋊C4—444no—
382C22⋊C4—444no—
383C22⋊C4—882no—
384C42—42no—
385C42—444no—
386C42—442no—
387C42C2×C4×D1112yes—
388C42Q8×D1112yes—
389C11#2266511yescharacteristic, complemented, Sylow
390C23—114no—
391C23—222no—
392C23—222no—
393C23—222no—
394C23—222no—
395C23—222no—
396C23—222no—
397C23C2×D4×D1111yescharacteristic
398D4—228no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—22no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—114no—
411C2×C4—222no—
412C2×C4—222no—
413C2×C4—224no—
414C2×C4—224no—
415C2×C4—224no—
416C2×C4—224no—
417C2×C4—222no—
418C2×C4—441no—
419C2×C4—441no—
420C2×C4—442no—
421C2×C4—441no—
422C2×C4—441no—
423C2×C4—442no—
424C2×C4—442no—
425C2×C4—441no—
426C2×C4—888no—
427C2×C4C4⋊C4×D1112yes—
428C2×C4C4⋊C4×D1112yes—
429C2×C4#6696412yes—
430C2×C4#6697112yes—
431C2×C4C22×C4×D1111yescharacteristic
432C2×C4C2×D4×D1111yescharacteristic
433C2×C4C2×Q8×D1111yescharacteristic
434C2×C4#6704011yescharacteristic
435C2×C4#41×D1111yescharacteristic
436C2×C4#6704211yescharacteristic
437C8—24no—
438C8—114no—
439C8—222no—
440C22—224no—
441C22—224no—
442C22—224no—
443C22—442no—
444C22—442no—
445C22—442no—
446C22—442no—
447C22C2×C4⋊C4×D1111yescharacteristic
448C22#1062314011yescharacteristic
449C22#1062316211yescharacteristic
450C22C2×#6696411yescharacteristic
451C22C2×#6697111yescharacteristic
452C22#1062330511yescharacteristic
453C22#1062331011yescharacteristic
454C4—22no—
455C4—42no—
456C4—81no—
457C4—82no—
458C4—224no—
459C4—442no—
460C4—881no—
461C4—882no—
462C4#1062249414yescomplemented
463C4C4×D4×D1111yescharacteristic
464C4#1062310511yescharacteristic
465C4#1062322111yescharacteristic
466C4#1062325811yescharacteristic
467C2—444no—
468C2#1307151711yescharacteristic
469C2C2×#1062249411yescharacteristic
470C2#1307721511yescharacteristic
471C2#1308023911yescharacteristic
472C2#1308025711yescharacteristic
473C2#1308119711yescharacteristic
474C2#1308123911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1947C2
socleC23×C11C22×D4
prime radicalC22×D44D4
cosocleC22×C4×C11C24
hypercenter#1947D11
hypocenterC11#22665
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
2. C2×#10622494C2semidirect
5. #13069380C2semidirect
6. #13068816C2semidirect
7. #13068802C2semidirect
8. #13068775C2semidirect
9. #13068648C2semidirect
10. C4×#66872C2semidirect
11. C11×#1947C2semidirect
37. #10622451C4semidirect
71. C2×#4313C2×C4semidirect
80. C11×C4⋊C8C2×C4semidirect
85. (C2×D11)⋊C8C2×C4semidirect
88. #66872D4semidirect
91. C4×C11⋊C8C2×C4semidirect
158. #1947D11semidirect
213. C11⋊C8C4×D4semidirect
263. C4×C11#428semidirect
314. C4⋊C8C4×D11semidirect
389. C11#22665semidirect
462. C4#10622494semidirect

Maximal subgroups

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

subgroupindex
C2×#106224512
C2×#106224942
#130715672
C4⋊C4×D442
#130693802
#130688162
#130688022
#130687752
#130686482
C4×#668722
C11×#19472
#2266511