Finite Group Databasebeta

← #14789830

Subgroups — #14789830

Order 2816.

1378 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622700C212yesmaximal, complemented
2C4×#66983C211yesmaximal, characteristic
3#13069941C212yesmaximal, complemented
4#13069749C212yesmaximal, complemented
5#13069569C212yesmaximal, complemented
6#13068933C212yesmaximal
7#13068804C212yesmaximal, complemented
8#13068596C211yesmaximal, characteristic, complemented
9C22×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
10C23×Q8×C11—21no—
11C2×C11×C4⋊Q8—28no—
12C2×C11×C4⋊Q8—21no—
13C2×C11×C4⋊Q8—21no—
14C2×C11×C4⋊Q8C2212yes—
15C2×C11×C4⋊Q8C2212yes—
16C22×C11×C4⋊C4—21no—
17C22×C11×C4⋊C4C2212yes—
18C22×C42×C11C2211yescharacteristic
19C2×#66983C2211yescharacteristic
20C2×C4×C22⋊D11—21no—
21C2×C4×D44C2211yescharacteristic
22#10622826—21no—
23#10622825C2211yescharacteristic
24C2×C22⋊(C11⋊C8)C2212yes—
25#10622700—28no—
26C2×#66873C2214yes—
27C2×#66871C2214yes—
28#10622553—21no—
29#10622552C2211yescharacteristic
30C4×(C2×D11)⋊C4—21no—
31C4×C4⋊Dic11C2211yescharacteristic
32#10622541C2211yescharacteristic
33C2×C4⋊(C11⋊C8)C2212yes—
34#10622167C2214yes—
35#10622167C2214yes—
36#10622162C2212yes—
37C22×Q8×C11—28no—
38C22×Q8×C11—22no—
39C22×Q8×C11—22no—
40C22×Q8×C11—44no—
41C22×Q8×C11—44no—
42C23×C4×C11—22no—
43C23×C4×C11D411yescharacteristic
44C23×C4×C11D411yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C22×C22⋊D11—21no—
47C22×D44C2311yescharacteristic
48C22×C4×D11—21no—
49C11×C4⋊Q8—28no—
50C11×C4⋊Q8—28no—
51C11×C4⋊Q8—28no—
52C11×C4⋊Q8—24no—
53C11×C4⋊Q8D418yescomplemented
54C2×C11×C4⋊C4—28no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—28no—
59C2×C11×C4⋊C4C2314yes—
60C2×C42×C11—24no—
61C2×C42×C11D411yescharacteristic
62C2×C42×C11D411yescharacteristic
63C2×C42×C11C2311yescharacteristic
64C2×C42×C11C2311yescharacteristic
65C2×C22⋊Dic11—21no—
66#66983—22no—
67#66983Q814yescomplemented
68C4×C22⋊D11—44no—
69C2×(C2×D11)⋊C4—21no—
70C2×(C2×D11)⋊C4—21no—
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×C4⋊Dic11C2311yescharacteristic
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4⋊Dic11C2311yescharacteristic
76C2×Dic11⋊C4—21no—
77C2×C4×Dic11—21no—
78C22×C11⋊C8C2314yes—
79C4×D44—24no—
80C11⋊#95—21no—
81C11⋊#95—21no—
82C11⋊#95—21no—
83C22⋊(C11⋊C8)—24no—
84#66873—28no—
85#66871—28no—
86C4⋊(C11⋊C8)—24no—
87#24298—111nomaximal, Sylow
88C24×C11C2×D411yescharacteristic
89C23×D11—21no—
90C2×Q8×C11—28no—
91C2×Q8×C11—28no—
92C2×Q8×C11—44no—
93C2×Q8×C11—432no—
94C2×Q8×C11—44no—
95C2×Q8×C11—44no—
96C2×Q8×C11—44no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—28no—
105C22×C4×C11—24no—
106C22×C4×C11—44no—
107C22×C4×C11—44no—
108C22×C4×C11D814yes—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×Q812yes—
115C22×C4×C11#4112yes—
116C22×C4×C11C2411yescharacteristic
117C2×C22⋊D11—24no—
118C2×C22⋊D11—42no—
119C2×C22⋊D11—42no—
120C22×Dic11—21no—
121C22×Dic11—21no—
122C22×Dic11—21no—
123C2×D44—22no—
124C2×D44—21no—
125C2×D44—22no—
126C2×D44C2×Q812yescomplemented
127C2×C4×D11—42no—
128C2×C4×D11—42no—
129C2×C4×D11—42no—
130C11×C4⋊C4—28no—
131C11×C4⋊C4—28no—
132C11×C4⋊C4—28no—
133C11×C4⋊C4—24no—
134C11×C4⋊C4C2×D418yes—
135C42×C11—22no—
136C42×C11—22no—
137C42×C11—22no—
138C42×C11C2×D414yes—
139C22⋊Dic11—42no—
140(C2×D11)⋊C4—24no—
141(C2×D11)⋊C4—42no—
142(C2×D11)⋊C4—42no—
143(C2×D11)⋊C4—42no—
144C4⋊Dic11—22no—
145C4⋊Dic11—21no—
146C4⋊Dic11—22no—
147C4⋊Dic11C2×Q812yescomplemented
148Dic11⋊C4—42no—
149C4×Dic11—42no—
150C2×C11⋊C8—24no—
151C2×C11⋊C8—24no—
152C2×C11⋊C8—24no—
153C22×C4⋊Q8D1111yescharacteristic, complemented
154C2×#474—112no—
155C4×#121—111no—
156#2057—112no—
157#2023—112no—
158#1988—112no—
159#1874—112no—
160#1852—112no—
161#1797—111no—
162C23×C11—21no—
163C23×C11—21no—
164C23×C11—21no—
165C23×C11—21no—
166C23×C11C22⋊Q812yes—
167C23×C11C2×D812yes—
168C23×C11#13712yes—
169C23×C11C22×D411yescharacteristic
170C22×D11—22no—
171C22×D11—41no—
172C22×D11—41no—
173C22×D11—41no—
174C22×D11—41no—
175C22×D11—41no—
176C22×D11—41no—
177Q8×C11—416no—
178Q8×C11—416no—
179C2×C4×C11—28no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—24no—
189C2×C4×C11—24no—
190C2×C4×C11—28no—
191C2×C4×C11—28no—
192C2×C4×C11—416no—
193C2×C4×C11—44no—
194C2×C4×C11—44no—
195C2×C4×C11#12012yes—
196C2×C4×C11#12012yes—
197C2×C4×C11C22⋊Q812yes—
198C2×C4×C11C2×D812yes—
199C2×C4×C11C2×D812yes—
200C2×C4×C11AGL(1,ℤ/8)12yes—
201C2×C4×C11#13712yes—
202C2×C4×C11C22×D412yes—
203C2×C4×C11C22×Q811yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C112−1+412yes—
206C22⋊D11—48no—
207C2×Dic11—22no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216D44—24no—
217D44—42no—
218C4×D11—84no—
219C11⋊C8—44no—
220C23×Q8—21no—
221C2×C4⋊Q8—28no—
222C2×C4⋊Q8—21no—
223C2×C4⋊Q8—21no—
224C2×C4⋊Q8C2×D1112yes—
225C2×C4⋊Q8C2×D1112yes—
226C2×#121—111no—
227C2×C4×D4—111no—
228C2×C4×D4—221no—
229C22×C4⋊C4—21no—
230C22×C4⋊C4C2×D1112yes—
231C22×C42C2×D1111yescharacteristic
232#474—228no—
233C2×#107—114no—
234C2×C4⋊C8—112no—
235C2×#102—114no—
236C2×C22⋊C8—112no—
237#390—111no—
238#389—111no—
239#388—221no—
240#386—221no—
241#380—111no—
242C4×C4⋊C4—111no—
243C4×C22⋊C4—221no—
244#340—114no—
245#340—114no—
246#336—112no—
247C22×C11—22no—
248C22×C11—22no—
249C22×C11—22no—
250C22×C11—22no—
251C22×C11—22no—
252C22×C11—22no—
253C22×C11#47414yescomplemented
254C22×C11C2×#12011yescharacteristic
255C22×C11C2×C22⋊Q811yescharacteristic
256C22×C11#53611yescharacteristic
257C22×C11C22×D811yescharacteristic
258C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
259C22×C11C2×#13711yescharacteristic
260C22×C11C2×#13711yescharacteristic
261C2×D11—42no—
262C2×D11—42no—
263C2×D11—42no—
264C2×D11—81no—
265C2×D11—81no—
266C2×D11—81no—
267C2×D11—81no—
268C4×C11—22no—
269C4×C11—22no—
270C4×C11—22no—
271C4×C11—22no—
272C4×C11—48no—
273C4×C11#44714yes—
274C4×C11#54812yes—
275C4×C11D4×Q812yes—
276Dic11—42no—
277Dic11—81no—
278Dic11—81no—
279C22×Q8—28no—
280C22×Q8—22no—
281C22×Q8—22no—
282C22×Q8—44no—
283C22×Q8—44no—
284C22×D4—111no—
285C22×D4—221no—
286C23×C4—22no—
287C23×C4—221no—
288C23×C4C22⋊D1111yescharacteristic
289C23×C4C22⋊D1111yescharacteristic
290C23×C4C22×D1111yescharacteristic
291C22×C8—114no—
292C4⋊Q8—28no—
293C4⋊Q8—28no—
294C4⋊Q8—28no—
295C4⋊Q8—24no—
296C4⋊Q8C22⋊D1118yescomplemented
297#121—114no—
298#121—222no—
299C4×D4—224no—
300C4×D4—444no—
301C2×C4⋊C4—28no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—111no—
307C2×C4⋊C4—111no—
308C2×C4⋊C4—111no—
309C2×C4⋊C4—221no—
310C2×C4⋊C4C22×D1114yes—
311C2×C22⋊C4—221no—
312C2×C22⋊C4—221no—
313C2×C22⋊C4—221no—
314C2×C22⋊C4—221no—
315C2×C22⋊C4—221no—
316C2×C42—24no—
317C2×C42—221no—
318C2×C42C22⋊D1111yescharacteristic
319C2×C42C22⋊D1111yescharacteristic
320C2×C42C22×D1111yescharacteristic
321C2×C42C22×D1111yescharacteristic
322#107—228no—
323C4⋊C8—224no—
324#102—228no—
325C22⋊C8—224no—
326#95—221no—
327#95—221no—
328#95—221no—
329C2×C11—24no—
330C2×C11#240911yescharacteristic
331C2×C11C2×#44711yescharacteristic
332C2×C11#300411yescharacteristic
333C2×C11C2×#47411yescharacteristic
334C2×C11#307911yescharacteristic
335C2×C11#322611yescharacteristic
336C2×C11#323911yescharacteristic
337D11—82no—
338C24—221no—
339C24C2×C22⋊D1111yescharacteristic
340C2×Q8—28no—
341C2×Q8—28no—
342C2×Q8—44no—
343C2×Q8—432no—
344C2×Q8—44no—
345C2×Q8—44no—
346C2×Q8—44no—
347C2×D4—112no—
348C2×D4—224no—
349C2×D4—221no—
350C2×D4—222no—
351C2×D4—222no—
352C2×D4—442no—
353C2×D4—442no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—28no—
362C22×C4—24no—
363C22×C4—44no—
364C22×C4—44no—
365C22×C4—221no—
366C22×C4—221no—
367C22×C4—221no—
368C22×C4—442no—
369C22×C4—442no—
370C22×C4—442no—
371C22×C4#432314yes—
372C22×C4Q8×D1112yes—
373C22×C4#434312yes—
374C22×C4C2×C22⋊D1111yescharacteristic
375C22×C4C2×C22⋊D1111yescharacteristic
376C22×C4C2×C22⋊D1111yescharacteristic
377C22×C4C2×C22⋊D1111yescharacteristic
378C22×C4C2×C22⋊D1111yescharacteristic
379C22×C4C23×D1111yescharacteristic
380C2×C8—224no—
381C2×C8—224no—
382C2×C8—224no—
383C4⋊C4—28no—
384C4⋊C4—28no—
385C4⋊C4—28no—
386C4⋊C4—24no—
387C4⋊C4—112no—
388C4⋊C4—221no—
389C4⋊C4—222no—
390C4⋊C4—222no—
391C4⋊C4—442no—
392C4⋊C4C2×C22⋊D1118yes—
393C22⋊C4—224no—
394C22⋊C4—442no—
395C22⋊C4—442no—
396C22⋊C4—442no—
397C22⋊C4—442no—
398C42—22no—
399C42—22no—
400C42—22no—
401C42—442no—
402C42C2×C22⋊D1114yes—
403C11#2429811yescharacteristic, complemented, Sylow
404C23—21no—
405C23—21no—
406C23—21no—
407C23—21no—
408C23—222no—
409C23—441no—
410C23—441no—
411C23—441no—
412C23—441no—
413C23—441no—
414C23—441no—
415C23C2×#432312yes—
416C23#6699512yes—
417C23#6699912yes—
418C23C22×C22⋊D1111yescharacteristic
419Q8—416no—
420Q8—416no—
421D4—224no—
422D4—448no—
423D4—442no—
424C2×C4—28no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—28no—
434C2×C4—24no—
435C2×C4—24no—
436C2×C4—28no—
437C2×C4—416no—
438C2×C4—44no—
439C2×C4—44no—
440C2×C4—222no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—441no—
446C2×C4—441no—
447C2×C4—441no—
448C2×C4—441no—
449C2×C4—884no—
450C2×C4C2×#432312yes—
451C2×C4C2×#432312yes—
452C2×C4#6698512yes—
453C2×C4#6699512yes—
454C2×C4#6699912yes—
455C2×C4#6700612yes—
456C2×C4#6700612yes—
457C2×C4C2×Q8×D1111yescharacteristic
458C2×C4C2×#434311yescharacteristic
459C2×C4#6704012yes—
460C2×C4C22×C22⋊D1112yes—
461C8—444no—
462C22—22no—
463C22—22no—
464C22—22no—
465C22—22no—
466C22—22no—
467C22—22no—
468C22—442no—
469C22—442no—
470C22—442no—
471C22—881no—
472C22—881no—
473C22—881no—
474C22—881no—
475C22#1062270014yescomplemented
476C22C22×#432311yescharacteristic
477C22C2×#6698511yescharacteristic
478C22C2×#6699511yescharacteristic
479C22C2×#6699511yescharacteristic
480C22C2×#6699911yescharacteristic
481C22#1062334711yescharacteristic
482C22C2×#6700611yescharacteristic
483C4—22no—
484C4—22no—
485C4—22no—
486C4—22no—
487C4—48no—
488C4—442no—
489C4—881no—
490C4—881no—
491C4#1062283014yes—
492C4Q8×C22⋊D1112yes—
493C4#1062334812yes—
494C2—24no—
495C2—882no—
496C2#1307197511yescharacteristic
497C2C2×#1062283011yescharacteristic
498C2#1307785011yescharacteristic
499C2C2×#1062270011yescharacteristic
500C2#1307842511yescharacteristic
501C2#1307973711yescharacteristic
502C2#1307984611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×C4⋊Q8C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenterC22×C4⋊Q8D11
hypocenterC11#24298
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#10622700C2semidirect
3. #13069941C2semidirect
4. #13069749C2semidirect
5. #13069569C2semidirect
7. #13068804C2semidirect
8. #13068596C2semidirect
9. C22×C11×C4⋊Q8C2semidirect
53. C11×C4⋊Q8D4semidirect
67. #66983Q8semidirect
126. C2×D44C2×Q8semidirect
147. C4⋊Dic11C2×Q8semidirect
153. C22×C4⋊Q8D11semidirect
253. C22×C11#474semidirect
296. C4⋊Q8C22⋊D11semidirect
403. C11#24298semidirect
475. C22#10622700semidirect

Maximal subgroups

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

subgroupindex
C2×#106227002
C4×#669832
#130699412
#130697492
#130695692
#130689332
#130688042
#130685962
C22×C11×C4⋊Q82
#2429811