Finite Group Databasebeta

← #14772004

Subgroups — #14772004

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×#10622301C211yesmaximal, characteristic
2C2×#10622494C212yesmaximal, complemented
3#13071567C211yesmaximal, characteristic
4#13071516C211yesmaximal, characteristic
5#13069377C211yesmaximal, characteristic, complemented
6#13069372C211yesmaximal, characteristic, complemented
7#13068812C212yesmaximal, complemented
8#13068802C212yesmaximal, complemented
9#13068650C212yesmaximal, complemented
10C4×#66881C211yesmaximal, characteristic, complemented
11C11×#1845C211yesmaximal, characteristic, complemented
12C22×#4313C2212yes—
13C2×#66946—21no—
14C2×#66945C2212yes—
15C2×C4⋊C4×D11C2212yes—
16C2×C4×D44C2211yescharacteristic
17C2×C11×#107C2212yes—
18C2×C11×#107C2212yes—
19C2×C4×C8×C11C2211yescharacteristic
20C11×#384C2211yescharacteristic
21C11×#384C2211yescharacteristic
22C2×(C2×D11)⋊C8C2212yes—
23C2×#66881C2211yescharacteristic
24C2×#66881C2211yescharacteristic
25#10622603—22no—
26#10622602—22no—
27#10622601—21no—
28#10622600C2212yes—
29#10622600C2212yes—
30C4⋊C4×Dic11—21no—
31#10622586—21no—
32C2×#66872C2212yes—
33C2×#66871C2212yes—
34C4×C4⋊Dic11C2211yescharacteristic
35C4×C4⋊Dic11C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37#10622494—28no—
38#10622301C418yescomplemented
39#10622189C2211yescharacteristic
40#10622189C2211yescharacteristic
41#10622167C2212yes—
42#10622167C2212yes—
43C22×D44D411yescharacteristic
44C22×C4×D11—22no—
45C22×C4×D11C2312yes—
46C22×C8×C11C2311yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4C2312yes—
53C2×C11×C4⋊C4C2312yes—
54C2×C42×C11C2311yescharacteristic
55C2×(C2×D11)⋊C4—22no—
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4—22no—
58C2×(C2×D11)⋊C4D412yes—
59C2×C4⋊Dic11D411yescharacteristic
60C2×C4⋊Dic11C2311yescharacteristic
61C2×C4⋊Dic11C2311yescharacteristic
62C2×C4⋊Dic11C2311yescharacteristic
63C2×C4⋊Dic11C2311yescharacteristic
64C2×Dic11⋊C4—22no—
65C2×C4×Dic11—21no—
66C2×C4×Dic11—21no—
67C2×C4×Dic11—22no—
68C22×C11⋊C8C2312yes—
69C2×#4313—24no—
70C2×#4313—24no—
71C2×#4313C2×C418yescomplemented
72#66946—44no—
73#66945—24no—
74#66945—42no—
75C4⋊C4×D11—24no—
76C4⋊C4×D11—42no—
77C4×D44C2×C414yes—
78C4×D44Q814yes—
79C11×#107—24no—
80C11×#107—42no—
81C4×C8×C11C2×C414yescomplemented
82C11⋊#95—21no—
83C11⋊#95—21no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86(C2×D11)⋊C8C2×C418yescomplemented
87#66881—22no—
88#66881D414yescomplemented
89#66872—24no—
90#66871—24no—
91C4⋊(C11⋊C8)C2×C414yescomplemented
92#22665—111nomaximal, Sylow
93C23×D11C2×D412yes—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2411yescharacteristic
99C22×Dic11—21no—
100C22×Dic11—21no—
101C22×Dic11—21no—
102C22×Dic11—21no—
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—21no—
117C2×C8×C11—21no—
118C2×C8×C11C22×C412yes—
119C2×C8×C11C22×C412yes—
120C2×C8×C11C2×D412yes—
121C2×C8×C11#4112yes—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—42no—
127C11×C4⋊C4—42no—
128C11×C4⋊C4—81no—
129C11×C4⋊C4—81no—
130C42×C11C22×C412yes—
131C42×C11C2×Q812yes—
132(C2×D11)⋊C4—44no—
133(C2×D11)⋊C4—44no—
134(C2×D11)⋊C4—82no—
135(C2×D11)⋊C4C4⋊C418yes—
136C4⋊Dic11—21no—
137C4⋊Dic11—21no—
138C4⋊Dic11—21no—
139C4⋊Dic11—21no—
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142C4⋊Dic11C4⋊C414yes—
143C4⋊Dic11C2×D412yes—
144C4⋊Dic11C2×D412yes—
145Dic11⋊C4—44no—
146C4×Dic11—44no—
147C4×Dic11—42no—
148C4×Dic11—42no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8C22×C414yes—
152#4313—216no—
153C2×#436—111no—
154C2×#428—112no—
155#2354—111no—
156D4×C4⋊C4—111no—
157#1948—111no—
158#1947—111no—
159#1854—112no—
160#1852—112no—
161#1845D1111yescharacteristic, complemented
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—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11C2×C4⋊C412yes—
181C2×C4×C11C2×C4⋊C412yes—
182C2×C4×C11AGL(1,ℤ/8)12yes—
183C2×C4×C11#13712yes—
184C2×C4×C11C23×C411yescharacteristic
185C2×C4×C11C22×D411yescharacteristic
186C2×C4×C11C22×Q811yescharacteristic
187C2×C4×C11C2×#4111yescharacteristic
188C2×C4×C11H(5,𝔽2)11yescharacteristic
189C2×C4×C112−1+411yescharacteristic
190C2×Dic11—22no—
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—22no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
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—22no—
212C8×C11C4×D414yescomplemented
213C11⋊C8—24no—
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×#107C2×D1112yes—
223C2×#107C2×D1112yes—
224C2×#106—111no—
225C2×#106—111no—
226C2×#106—112no—
227C2×C4⋊C8—111no—
228C2×C22⋊C8—112no—
229C2×C4×C8C2×D1111yescharacteristic
230#390—221no—
231#389—221no—
232#388—222no—
233#385—222no—
234#384C2×D1111yescharacteristic
235#384C2×D1111yescharacteristic
236#380—112no—
237#380—112no—
238C4×C4⋊C4—111no—
239C4×C4⋊C4—111no—
240C4×C4⋊C4—221no—
241#340—111no—
242#340—111no—
243#340—112no—
244#340—112no—
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—82no—
261C4×C11—82no—
262C4×C11#42814yescomplemented
263C4×C11C2×C4×D411yescharacteristic
264C4×C11#52011yescharacteristic
265C4×C11D4×Q811yescharacteristic
266C4×C11#55411yescharacteristic
267Dic11—24no—
268Dic11—42no—
269Dic11—42no—
270Dic11—81no—
271Dic11—81no—
272C22×D4—111no—
273C23×C4—112no—
274C23×C4—222no—
275C2×M16—118no—
276C2×M16—224no—
277C2×M16—224no—
278C22×C8—112no—
279C22×C8C22×D1111yescharacteristic
280C22×C8C22×D1111yescharacteristic
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—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—111no—
291C2×C4⋊C4—111no—
292C2×C4⋊C4—111no—
293C2×C4⋊C4—111no—
294C2×C4⋊C4—111no—
295C2×C4⋊C4—224no—
296C2×C4⋊C4—222no—
297C2×C4⋊C4—442no—
298C2×C4⋊C4C22×D1112yes—
299C2×C4⋊C4C22×D1112yes—
300C2×C22⋊C4—112no—
301C2×C22⋊C4—222no—
302C2×C22⋊C4—222no—
303C2×C22⋊C4—222no—
304C2×C42—222no—
305C2×C42—221no—
306C2×C42—221no—
307C2×C42C22×D1111yescharacteristic
308#107—24no—
309#107—42no—
310#107—224no—
311#106—114no—
312#106—224no—
313#106—222no—
314C4⋊C8—114no—
315C22⋊C8—118no—
316C4×C8C4×D1114yescomplemented
317#95—222no—
318#95—222no—
319#95—221no—
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—22no—
334C22×C4—22no—
335C22×C4—112no—
336C22×C4—114no—
337C22×C4—114no—
338C22×C4—222no—
339C22×C4—222no—
340C22×C4—222no—
341C22×C4—222no—
342C22×C4—221no—
343C22×C4—221no—
344C22×C4—221no—
345C22×C4—221no—
346C22×C4—444no—
347C22×C4—444no—
348C22×C4—882no—
349C22×C4D4×D1111yescharacteristic
350C22×C4D4×D1111yescharacteristic
351C22×C4C23×D1111yescharacteristic
352M16—2216no—
353C2×C8—21no—
354C2×C8—21no—
355C2×C8—114no—
356C2×C8—222no—
357C2×C8—222no—
358C2×C8C2×C4×D1112yes—
359C2×C8C2×C4×D1112yes—
360C2×C8D4×D1112yes—
361C2×C8#434312yes—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—42no—
367C4⋊C4—42no—
368C4⋊C4—81no—
369C4⋊C4—81no—
370C4⋊C4—114no—
371C4⋊C4—112no—
372C4⋊C4—112no—
373C4⋊C4—221no—
374C4⋊C4—221no—
375C4⋊C4—221no—
376C4⋊C4—221no—
377C4⋊C4—221no—
378C4⋊C4—221no—
379C4⋊C4—444no—
380C22⋊C4—118no—
381C22⋊C4—444no—
382C22⋊C4—444no—
383C22⋊C4—882no—
384C42—444no—
385C42—442no—
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—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—114no—
408C2×C4—222no—
409C2×C4—222no—
410C2×C4—224no—
411C2×C4—224no—
412C2×C4—224no—
413C2×C4—224no—
414C2×C4—222no—
415C2×C4—222no—
416C2×C4—441no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4—441no—
423C2×C4—441no—
424C2×C4—441no—
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×C4#6703711yescharacteristic
434C2×C4C2×Q8×D1111yescharacteristic
435C2×C4C2×#434311yescharacteristic
436C2×C4#6704011yescharacteristic
437C8—22no—
438C8—224no—
439C8#6694614yescomplemented
440C22—224no—
441C22—224no—
442C22—224no—
443C22—442no—
444C22—442no—
445C22—442no—
446C22—442no—
447C22C2×C4⋊C4×D1111yescharacteristic
448C22#1062324811yescharacteristic
449C22#1062325711yescharacteristic
450C22C2×#6696411yescharacteristic
451C22#1062328811yescharacteristic
452C22C2×#6697111yescharacteristic
453C22#1062329711yescharacteristic
454C4—22no—
455C4—82no—
456C4—82no—
457C4—224no—
458C4—442no—
459C4—442no—
460C4—881no—
461C4—881no—
462C4#1062249414yescomplemented
463C4C2×#6694611yescharacteristic
464C4#1062303511yescharacteristic
465C4#1062325811yescharacteristic
466C4#1062326111yescharacteristic
467C2—444no—
468C2#1307151611yescharacteristic
469C2C2×#1062249411yescharacteristic
470C2#1307721211yescharacteristic
471C2#1308023511yescharacteristic
472C2#1308026111yescharacteristic
473C2#1308119911yescharacteristic
474C2#1308124111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1845C2
socleC23×C11C22×D4
prime radicalC22×D44D4
cosocleC22×C4×C11C24
hypercenter#1845D11
hypocenterC11#22665
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1845

Complements

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

NH ≅ G/Ntype
2. C2×#10622494C2semidirect
5. #13069377C2semidirect
6. #13069372C2semidirect
7. #13068812C2semidirect
8. #13068802C2semidirect
9. #13068650C2semidirect
10. C4×#66881C2semidirect
11. C11×#1845C2semidirect
38. #10622301C4semidirect
71. C2×#4313C2×C4semidirect
81. C4×C8×C11C2×C4semidirect
86. (C2×D11)⋊C8C2×C4semidirect
88. #66881D4semidirect
91. C4⋊(C11⋊C8)C2×C4semidirect
161. #1845D11semidirect
212. C8×C11C4×D4semidirect
262. C4×C11#428semidirect
316. C4×C8C4×D11semidirect
389. C11#22665semidirect
439. C8#66946semidirect
462. C4#10622494semidirect

Maximal subgroups

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

subgroupindex
C2×#106223012
C2×#106224942
#130715672
#130715162
#130693772
#130693722
#130688122
#130688022
#130686502
C4×#668812
C11×#18452
#2266511