Finite Group Databasebeta

← #14770409

Subgroups — #14770409

Order 2816.

1250 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622637C211yesmaximal, characteristic, complemented
2#13071573C211yesmaximal, characteristic, complemented
3#13069590C212yesmaximal, complemented
4#13069578C211yesmaximal, characteristic, complemented
5#13069569C211yesmaximal, characteristic, complemented
6#13069565C212yesmaximal, complemented
7#13068626C212yesmaximal
8#13068616C211yesmaximal, characteristic
9#13068441C212yesmaximal
10C4×#66896C211yesmaximal, characteristic
11C2×D4×Q8×C11C211yesmaximal, characteristic
12C23×Q8×C11—21no—
13D4×Q8×C11—24no—
14D4×Q8×C11C418yescomplemented
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×C4⋊Q8C2212yes—
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8—22no—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2212yes—
22#10622843—21no—
23C2×#66896C2212yes—
24C2×#66896C2211yescharacteristic
25C2×#66896C2211yescharacteristic
26#10622637—24no—
27#10622594—22no—
28C4⋊C4×Dic11—21no—
29#10622549C2212yes—
30#10622548C2211yescharacteristic
31C4×C4⋊Dic11C2211yescharacteristic
32C4×C4⋊Dic11C2212yes—
33C2×C4⋊(C11⋊C8)C2211yescharacteristic
34C2×C4⋊(C11⋊C8)C2212yes—
35C2×#66867C2212yes—
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622167C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2211yescharacteristic
44C22×Q8×C11—28no—
45C22×Q8×C11—22no—
46C22×Q8×C11—21no—
47C22×Q8×C11—44no—
48C22×Q8×C11—44no—
49C22×Q8×C11D411yescharacteristic
50C22×D4×C11C2311yescharacteristic
51C23×C4×C11—22no—
52C23×C4×C11—21no—
53C11×C4⋊Q8—22no—
54C11×C4⋊Q8—24no—
55C11×C4⋊Q8C2×C414yes—
56C11×C4⋊Q8C2×C418yes—
57C11×C22⋊Q8—216no—
58C11×C22⋊Q8—28no—
59C4×Q8×C11C2×C414yes—
60C4×Q8×C11D414yes—
61C4×D4×C11—22no—
62C4×D4×C11—24no—
63C4×D4×C11C2×C414yes—
64C4×D4×C11C2×C418yes—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C11×C4⋊C4D412yes—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—21no—
73C2×C42×C11C2311yescharacteristic
74C2×C42×C11C2312yes—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11C2312yes—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4×Dic11—21no—
81C2×C4×Dic11—22no—
82C22×C11⋊C8C2311yescharacteristic
83C22×C11⋊C8C2312yes—
84C22×C11⋊C8C2311yescharacteristic
85#66896—24no—
86#66896—22no—
87#66896Q814yescomplemented
88C11⋊#95—22no—
89C11⋊#95—21no—
90C11⋊#95—22no—
91C11⋊#95—22no—
92C4⋊(C11⋊C8)—24no—
93C4⋊(C11⋊C8)—22no—
94#66867—24no—
95C4×C11⋊C8—22no—
96#22523—111nomaximal, Sylow
97C24×C11—21no—
98C2×Q8×C11—28no—
99C2×Q8×C11—24no—
100C2×Q8×C11—22no—
101C2×Q8×C11—22no—
102C2×Q8×C11—44no—
103C2×Q8×C11—44no—
104C2×Q8×C11—432no—
105C2×Q8×C11—42no—
106C2×Q8×C11—42no—
107C2×Q8×C11C22⋊C414yes—
108C2×D4×C11—21no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11C22×C412yes—
112C2×D4×C11C2×Q812yes—
113C2×D4×C11#4112yes—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—28no—
117C22×C4×C11—24no—
118C22×C4×C11—44no—
119C22×C4×C11—44no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—22no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—28no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4C22⋊C418yes—
135C11×C4⋊C4C22⋊C414yes—
136C11×C4⋊C4C22×C412yes—
137C11×C4⋊C4C22×C414yes—
138C11×C22⋊C4—24no—
139C11×C22⋊C4—28no—
140C42×C11C22×C414yes—
141C42×C11C22×C412yes—
142C42×C11C2×D412yes—
143C42×C11C2×D414yes—
144C4⋊Dic11—22no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—22no—
148C4⋊Dic11—21no—
149C4⋊Dic11—42no—
150C4⋊Dic11—81no—
151C4⋊Dic11C2×Q812yescomplemented
152C4×Dic11—42no—
153C4×Dic11—82no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8C2×Q812yescomplemented
163C2×D4×Q8D1111yescharacteristic
164C2×#446—111no—
165#2355—111no—
166#1993—112no—
167#1990—111no—
168#1988—111no—
169#1987—112no—
170#1804—112no—
171#1802—111no—
172#1762—112no—
173C4×#102—111no—
174C23×C11—22no—
175C23×C11—22no—
176C23×C11—22no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—41no—
181C23×C11C22×D411yescharacteristic
182Q8×C11—28no—
183Q8×C11—416no—
184Q8×C11—48no—
185D4×C11—22no—
186D4×C11—22no—
187D4×C11—22no—
188D4×C11C4×Q814yes—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—21no—
193C2×C4×C11—22no—
194C2×C4×C11—21no—
195C2×C4×C11—24no—
196C2×C4×C11—22no—
197C2×C4×C11—416no—
198C2×C4×C11—42no—
199C2×C4×C11—41no—
200C2×C4×C11—42no—
201C2×C4×C11—41no—
202C2×C4×C11—48no—
203C2×C4×C11C2×C22⋊C412yes—
204C2×C4×C11C2×C22⋊C414yes—
205C2×C4×C11C2×C22⋊C414yes—
206C2×C4×C11C2×C22⋊C412yes—
207C2×C4×C11AGL(1,ℤ/8)12yes—
208C2×C4×C11AGL(1,ℤ/8)12yes—
209C2×C4×C11C23×C411yescharacteristic
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C22×Q811yescharacteristic
212C2×C4×C11C2×#4111yescharacteristic
213C2×C4×C112−1+411yescharacteristic
214C2×C4×C112−1+411yescharacteristic
215C2×Dic11—22no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—42no—
220C2×Dic11—41no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—41no—
224C11⋊C8—22no—
225C11⋊C8—41no—
226C11⋊C8—42no—
227C23×Q8—21no—
228D4×Q8—24no—
229D4×Q8Dic1118yescomplemented
230C2×C4⋊Q8C2×D1112yes—
231C2×C4⋊Q8C2×D1111yescharacteristic
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8—22no—
234C2×C4×Q8C2×D1111yescharacteristic
235C2×C4×D4C2×D1111yescharacteristic
236C2×C4×D4C2×D1112yes—
237#446—224no—
238C2×C4⋊C8—111no—
239C2×C4⋊C8—112no—
240C2×#102—111no—
241C2×#102—112no—
242C2×#102—111no—
243C2×#97—112no—
244C2×C4×C8—111no—
245#391—221no—
246#387—222no—
247#384—111no—
248#382—112no—
249C4×C4⋊C4—112no—
250C4×C4⋊C4—111no—
251C4×C4⋊C4—221no—
252#340—112no—
253#340—112no—
254#340—112no—
255#340—111no—
256#340—112no—
257#340—112no—
258#340—111no—
259C22×C11—24no—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11—42no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11—42no—
266C22×C11C22×C22⋊C411yescharacteristic
267C22×C11#54811yescharacteristic
268C22×C11D4×Q811yescharacteristic
269C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
270C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
271C22×C11#57711yescharacteristic
272C22×C11#57811yescharacteristic
273C4×C11—24no—
274C4×C11—24no—
275C4×C11—22no—
276C4×C11—44no—
277C4×C11—42no—
278C4×C11#41814yes—
279C4×C11C2×C4×Q811yescharacteristic
280C4×C11#51911yescharacteristic
281C4×C11#54811yescharacteristic
282C4×C11D4×Q811yescharacteristic
283Dic11—42no—
284Dic11—81no—
285Dic11—82no—
286C22×Q8—28no—
287C22×Q8—22no—
288C22×Q8—21no—
289C22×Q8—44no—
290C22×Q8—44no—
291C22×Q8C22⋊D1111yescharacteristic
292C22×D4C22×D1111yescharacteristic
293C23×C4—22no—
294C23×C4—21no—
295C22×C8—111no—
296C22×C8—111no—
297C22×C8—112no—
298C4⋊Q8—22no—
299C4⋊Q8—24no—
300C4⋊Q8C2×Dic1118yes—
301C4⋊Q8C2×Dic1114yes—
302C22⋊Q8—216no—
303C22⋊Q8—28no—
304C4×Q8C2×Dic1114yes—
305C4×Q8C22⋊D1114yes—
306C4×D4—22no—
307C4×D4—24no—
308C4×D4C2×Dic1114yes—
309C4×D4C2×Dic1118yes—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—111no—
313C2×C4⋊C4—111no—
314C2×C4⋊C4—112no—
315C2×C4⋊C4—221no—
316C2×C4⋊C4—221no—
317C2×C4⋊C4C22⋊D1111yescharacteristic
318C2×C4⋊C4C22⋊D1112yes—
319C2×C4⋊C4C22×D1111yescharacteristic
320C2×C4⋊C4C22×D1112yes—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—21no—
323C2×C42—221no—
324C2×C42—222no—
325C2×C42C22×D1112yes—
326C2×C42C22×D1111yescharacteristic
327C4⋊C8—222no—
328C4⋊C8—224no—
329#102—114no—
330#102—224no—
331#102—222no—
332#97—224no—
333C4×C8—222no—
334#95—221no—
335#95—222no—
336#95—222no—
337#95—222no—
338C2×C11—44no—
339C2×C11Q8×C22⋊C411yescharacteristic
340C2×C11C2×#41811yescharacteristic
341C2×C11#289811yescharacteristic
342C2×C11#336711yescharacteristic
343C2×C11#337311yescharacteristic
344C2×C11#338411yescharacteristic
345C2×C11#338611yescharacteristic
346C24—21no—
347C2×Q8—22no—
348C2×Q8—22no—
349C2×Q8—28no—
350C2×Q8—24no—
351C2×Q8—44no—
352C2×Q8—44no—
353C2×Q8—432no—
354C2×Q8—42no—
355C2×Q8—42no—
356C2×Q8C22⋊Dic1114yes—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4Q8×D1112yes—
361C2×D4#434312yes—
362C2×D4C22×Dic1112yes—
363C22×C4—22no—
364C22×C4—21no—
365C22×C4—28no—
366C22×C4—24no—
367C22×C4—44no—
368C22×C4—44no—
369C22×C4—42no—
370C22×C4—42no—
371C22×C4—221no—
372C22×C4—221no—
373C22×C4—222no—
374C22×C4C2×C22⋊D1112yes—
375C22×C4C2×C22⋊D1112yes—
376C22×C4C2×C22⋊D1111yescharacteristic
377C22×C4C2×C22⋊D1111yescharacteristic
378C22×C4C23×D1111yescharacteristic
379C2×C8—112no—
380C2×C8—221no—
381C2×C8—221no—
382C2×C8—221no—
383C2×C8—222no—
384C2×C8—221no—
385C2×C8—222no—
386C2×C8—221no—
387C2×C8—222no—
388C4⋊C4—24no—
389C4⋊C4—28no—
390C4⋊C4—21no—
391C4⋊C4—22no—
392C4⋊C4—112no—
393C4⋊C4—221no—
394C4⋊C4—221no—
395C4⋊C4—222no—
396C4⋊C4—221no—
397C4⋊C4—222no—
398C4⋊C4—442no—
399C4⋊C4—881no—
400C4⋊C4C22⋊Dic1118yes—
401C4⋊C4C22⋊Dic1114yes—
402C4⋊C4C22×Dic1112yes—
403C4⋊C4C22×Dic1114yes—
404C22⋊C4—24no—
405C22⋊C4—28no—
406C42—442no—
407C42—882no—
408C42C22×Dic1114yes—
409C42C22×Dic1112yes—
410C42C2×C22⋊D1112yes—
411C42C2×C22⋊D1114yes—
412C11#2252311yescharacteristic, complemented, Sylow
413C23—22no—
414C23—22no—
415C23—22no—
416C23—41no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23C22×C22⋊D1111yescharacteristic
421Q8—28no—
422Q8—416no—
423Q8—48no—
424D4—22no—
425D4—22no—
426D4—22no—
427D4Q8×Dic1114yes—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—21no—
432C2×C4—22no—
433C2×C4—21no—
434C2×C4—24no—
435C2×C4—22no—
436C2×C4—416no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—48no—
442C2×C4—222no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—441no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—441no—
449C2×C4—442no—
450C2×C4—441no—
451C2×C4#6698512yes—
452C2×C4#6698512yes—
453C2×C4C2×C22⋊Dic1112yes—
454C2×C4C2×C22⋊Dic1114yes—
455C2×C4C2×C22⋊Dic1114yes—
456C2×C4C2×C22⋊Dic1112yes—
457C2×C4C2×Q8×D1111yescharacteristic
458C2×C4C2×#434311yescharacteristic
459C2×C4#6704011yescharacteristic
460C2×C4#6704011yescharacteristic
461C2×C4C23×Dic1111yescharacteristic
462C2×C4C22×C22⋊D1111yescharacteristic
463C8—222no—
464C8—441no—
465C8—442no—
466C22—24no—
467C22—42no—
468C22—42no—
469C22—42no—
470C22—42no—
471C22—42no—
472C22—42no—
473C22C2×#6698511yescharacteristic
474C22C2×#6698511yescharacteristic
475C22Q8×C22⋊D1111yescharacteristic
476C22#1062334811yescharacteristic
477C22#1062336811yescharacteristic
478C22#1062336911yescharacteristic
479C22C22×C22⋊Dic1111yescharacteristic
480C4—24no—
481C4—24no—
482C4—22no—
483C4—44no—
484C4—42no—
485C4—442no—
486C4—882no—
487C4—881no—
488C4#1062282814yes—
489C4C2×Q8×Dic1111yescharacteristic
490C4#1062334311yescharacteristic
491C4Q8×C22⋊D1111yescharacteristic
492C4#1062334811yescharacteristic
493C2—44no—
494C2Q8×C22⋊Dic1111yescharacteristic
495C2C2×#1062282811yescharacteristic
496C2#1307714911yescharacteristic
497C2#1308133411yescharacteristic
498C2#1308140811yescharacteristic
499C2#1308151111yescharacteristic
500C2#1308153711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×D4×Q8×C11C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenterC2×D4×Q8D11
hypocenterC11#22523
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#10622637C2semidirect
2. #13071573C2semidirect
3. #13069590C2semidirect
4. #13069578C2semidirect
5. #13069569C2semidirect
6. #13069565C2semidirect
14. D4×Q8×C11C4semidirect
87. #66896Q8semidirect
151. C4⋊Dic11C2×Q8semidirect
162. C2×C11⋊C8C2×Q8semidirect
229. D4×Q8Dic11semidirect
412. C11#22523semidirect

Maximal subgroups

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

subgroupindex
C2×#106226372
#130715732
#130695902
#130695782
#130695692
#130695652
#130686262
#130686162
#130684412
C4×#668962
C2×D4×Q8×C112
#2252311