Finite Group Databasebeta

← #14808038

Subgroups — #14808038

Order 2816.

1374 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623008C211yesmaximal, characteristic
2C2×#10622692C211yesmaximal, characteristic, complemented
3C2×#10622701C211yesmaximal, characteristic, complemented
4#13069805C214yesmaximal, complemented
5#13069576C211yesmaximal, characteristic, complemented
6#13069421C211yesmaximal, characteristic, complemented
7#13068876C214yesmaximal, complemented
8C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
9C11×#2857C211yesmaximal, characteristic, complemented
10C22×#4339—21no—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C11×C22⋊Q8—21no—
13C22×C42×C11C2211yescharacteristic
14C2×#66983—21no—
15C2×#66983C2212yes—
16#10623008—24no—
17#10623008—24no—
18C2×#66928—21no—
19C2×#66927C2211yescharacteristic
20C2×C4×D44—21no—
21C2×C4×D44C2212yes—
22C2×#66922C2211yescharacteristic
23C11×#391—21no—
24C11×#389—21no—
25C11×#389C2212yes—
26C11×#384C2211yescharacteristic
27C11×#380—21no—
28C11×#380C2212yes—
29C2×C22⋊(C11⋊C8)C2212yes—
30#10622701—24no—
31#10622692—24no—
32C2×#66873C2214yes—
33C2×#66873C2214yes—
34C2×#66872C2214yes—
35C2×C4×C11⋊C8C2211yescharacteristic
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622167C2214yes—
38#10622162C2212yes—
39C22×Q8×C11—21no—
40C23×C4×C11D411yescharacteristic
41C23×C4×C11D411yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C22×C22⋊D11—22no—
44C2×#4339—28no—
45C2×#4339—44no—
46C2×#4339—44no—
47C22×D44—21no—
48C22×D44—21no—
49C22×D44C2312yes—
50C22×C4×D11—22no—
51C22×Dic22—21no—
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8—22no—
54C11×C22⋊Q8—44no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C22⋊C4—22no—
62C2×C42×C11—22no—
63C2×C42×C11—22no—
64C2×C42×C11D411yescharacteristic
65C2×C42×C11D411yescharacteristic
66C2×C42×C11C2311yescharacteristic
67C2×C42×C11C2311yescharacteristic
68#66983—28no—
69#66983—24no—
70#66983—24no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11C2312yes—
75C22×C11⋊C8C2312yes—
76C22×C11⋊C8C2312yes—
77#66928—28no—
78#66927—22no—
79#66927D414yes—
80C4×D44—28no—
81C4×D44—24no—
82C4×D44—24no—
83#66922—22no—
84#66922D414yes—
85C11×#95—22no—
86C11×#95—22no—
87C22⋊(C11⋊C8)—24no—
88#66873—28no—
89#66873—28no—
90#66872—28no—
91C4×C11⋊C8—22no—
92C4×C11⋊C8—22no—
93#25671—111nomaximal, Sylow
94C24×C11C2×D411yescharacteristic
95C23×D11—22no—
96C2×Q8×C11—42no—
97C2×Q8×C11—42no—
98C2×Q8×C11—42no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11SD1614yes—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2411yescharacteristic
117C2×C22⋊D11—28no—
118C2×C22⋊D11—44no—
119C2×C22⋊D11—44no—
120C22×Dic11—22no—
121#4339—432no—
122C2×D44—24no—
123C2×D44—24no—
124C2×D44—22no—
125C2×D44—24no—
126C2×D44—24no—
127C2×D44—42no—
128C2×D44—42no—
129C2×D44—42no—
130C2×D44—42no—
131C2×D44C2×D414yes—
132C2×C4×D11—28no—
133C2×C4×D11—44no—
134C2×C4×D11—44no—
135C2×Dic22—24no—
136C2×Dic22—42no—
137C2×Dic22—42no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—44no—
142C11×C4⋊C4—42no—
143C11×C4⋊C4—42no—
144C11×C4⋊C4—42no—
145C11×C22⋊C4—44no—
146C42×C11—22no—
147C42×C11—22no—
148C42×C11—21no—
149C42×C11—21no—
150C42×C11C2×D412yes—
151C42×C11C2×D412yes—
152(C2×D11)⋊C4—28no—
153(C2×D11)⋊C4—28no—
154C4⋊Dic11—24no—
155C4⋊Dic11—22no—
156C4⋊Dic11C2×D414yes—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8#4114yescomplemented
163C2×#532—111no—
164C2×#498—111no—
165C2×#486—111no—
166#2857D1111yescharacteristic, complemented
167#2034—114no—
168#1990—111no—
169#1957—111no—
170#1864—114no—
171C4×C22⋊C8—111no—
172C23×C11—21no—
173C23×C11—21no—
174C23×C11—21no—
175C23×C11—21no—
176C23×C11—21no—
177C23×C11—21no—
178C23×C11C2×SD1612yes—
179C23×C11C22×D411yescharacteristic
180C22×D11—24no—
181C22×D11—42no—
182C22×D11—42no—
183C22×D11—42no—
184C22×D11—42no—
185C22×D11—42no—
186C22×D11—42no—
187Q8×C11—84no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—28no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—44no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11#12012yes—
207C2×C4×C11#12012yes—
208C2×C4×C11C2×SD1612yes—
209C2×C4×C11C2×SD1612yes—
210C2×C4×C11#13512yes—
211C2×C4×C11AGL(1,ℤ/8)12yes—
212C2×C4×C11AGL(1,ℤ/8)12yes—
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C2×#4112yes—
216C2×C4×C112−1+412yes—
217C22⋊D11—416no—
218C2×Dic11—24no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221D44—28no—
222D44—44no—
223D44—48no—
224D44—48no—
225C4×D11—416no—
226Dic22—48no—
227C11⋊C8—24no—
228C11⋊C8—42no—
229C22×#41—221no—
230#532—224no—
231#532—224no—
232C2×C4⋊Q8—111no—
233C2×C4⋊Q8C2×D1111yescharacteristic
234C2×#127—111no—
235C2×#124—221no—
236C2×C22⋊Q8—21no—
237C2×#121—112no—
238C2×#121—221no—
239C2×C4×D4—112no—
240C2×C4×D4—221no—
241C22×C42C2×D1111yescharacteristic
242#498—224no—
243#486—224no—
244C2×#106—114no—
245C2×#102—114no—
246C2×#102—114no—
247C2×C22⋊C8—112no—
248C2×C4×C8—111no—
249C2×C4×C8—111no—
250#391—21no—
251#389—21no—
252#389C2×D1112yes—
253#384C2×D1111yescharacteristic
254#380—21no—
255#380C2×D1112yes—
256#340—114no—
257#336—112no—
258C22×C11—22no—
259C22×C11—22no—
260C22×C11—22no—
261C22×C11—41no—
262C22×C11—41no—
263C22×C11—41no—
264C22×C11—41no—
265C22×C11C2×#12011yescharacteristic
266C22×C11#53211yescharacteristic
267C22×C11#53611yescharacteristic
268C22×C11C22×SD1611yescharacteristic
269C22×C11C2×#13511yescharacteristic
270C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
271C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
272C2×D11—44no—
273C2×D11—44no—
274C2×D11—44no—
275C2×D11—82no—
276C2×D11—82no—
277C2×D11—82no—
278C2×D11—82no—
279C4×C11—22no—
280C4×C11—41no—
281C4×C11—41no—
282C4×C11—82no—
283C4×C11—82no—
284C4×C11#44914yes—
285C4×C11#45014yes—
286C4×C11#54712yes—
287C4×C11#54812yes—
288Dic11—44no—
289C2×#41—228no—
290C2×#41—444no—
291C2×#41—444no—
292C22×Q8—21no—
293C22×Q8—221no—
294C22×D4—112no—
295C22×D4—222no—
296C22×D4—221no—
297C22×D4—221no—
298C23×C4—222no—
299C23×C4C22⋊D1111yescharacteristic
300C23×C4C22⋊D1111yescharacteristic
301C23×C4C22×D1111yescharacteristic
302C22×C8—112no—
303C22×C8—112no—
304C4⋊Q8—22no—
305C4⋊Q8—22no—
306C4⋊Q8—114no—
307C4⋊Q8—222no—
308#127—114no—
309#127—222no—
310#124—228no—
311C22⋊Q8—44no—
312#121—224no—
313#121—224no—
314#121—228no—
315C4×D4—224no—
316C4×D4—224no—
317C4×D4—228no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—112no—
323C2×C4⋊C4—221no—
324C2×C4⋊C4C22×D1112yes—
325C2×C4⋊C4C22×D1112yes—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—222no—
328C2×C22⋊C4—222no—
329C2×C42—22no—
330C2×C42—22no—
331C2×C42C22⋊D1111yescharacteristic
332C2×C42C22⋊D1111yescharacteristic
333C2×C42C22×D1111yescharacteristic
334C2×C42C22×D1111yescharacteristic
335#106—228no—
336#102—228no—
337#102—228no—
338C22⋊C8—224no—
339C4×C8—222no—
340C4×C8—222no—
341#95—22no—
342#95—22no—
343C2×C11—42no—
344C2×C11#243211yescharacteristic
345C2×C11C2×#45011yescharacteristic
346C2×C11C2×#44911yescharacteristic
347C2×C11#316711yescharacteristic
348C2×C11#318411yescharacteristic
349C2×C11#322711yescharacteristic
350C2×C11#322811yescharacteristic
351D11—84no—
352C24—222no—
353C24C2×C22⋊D1111yescharacteristic
354#41—4432no—
355C2×Q8—42no—
356C2×Q8—42no—
357C2×Q8—42no—
358C2×Q8—224no—
359C2×Q8—442no—
360C2×Q8—442no—
361C2×D4—114no—
362C2×D4—228no—
363C2×D4—224no—
364C2×D4—224no—
365C2×D4—222no—
366C2×D4—224no—
367C2×D4—224no—
368C2×D4—444no—
369C2×D4—444no—
370C2×D4—442no—
371C2×D4—442no—
372C2×D4—442no—
373C2×D4—442no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—228no—
386C22×C4—222no—
387C22×C4—444no—
388C22×C4—444no—
389C22×C4#432514yes—
390C22×C4C2×C22⋊D1111yescharacteristic
391C22×C4C2×C22⋊D1111yescharacteristic
392C22×C4C2×C22⋊D1111yescharacteristic
393C22×C4C2×C22⋊D1111yescharacteristic
394C22×C4C2×C22⋊D1111yescharacteristic
395C22×C4C23×D1111yescharacteristic
396C2×C8—114no—
397C2×C8—222no—
398C2×C8—222no—
399C2×C8—222no—
400C2×C8—222no—
401C2×C8—222no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—24no—
405C4⋊C4—44no—
406C4⋊C4—42no—
407C4⋊C4—42no—
408C4⋊C4—42no—
409C4⋊C4—114no—
410C4⋊C4—224no—
411C4⋊C4—222no—
412C22⋊C4—44no—
413C22⋊C4—228no—
414C22⋊C4—228no—
415C42—22no—
416C42—22no—
417C42—21no—
418C42—21no—
419C42D4×D1112yes—
420C42D4×D1112yes—
421C11#2567111yescharacteristic, complemented, Sylow
422C23—21no—
423C23—21no—
424C23—21no—
425C23—21no—
426C23—21no—
427C23—21no—
428C23—224no—
429C23—442no—
430C23—442no—
431C23—442no—
432C23—442no—
433C23—442no—
434C23—442no—
435C23C2×#432512yes—
436C23C22×C22⋊D1111yescharacteristic
437Q8—84no—
438Q8—448no—
439D4—228no—
440D4—4416no—
441D4—448no—
442D4—444no—
443D4—448no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—28no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—44no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—224no—
463C2×C4—4416no—
464C2×C4—442no—
465C2×C4—442no—
466C2×C4#6698512yes—
467C2×C4#6699012yes—
468C2×C4#6699012yes—
469C2×C4C2×#432512yes—
470C2×C4C2×#432512yes—
471C2×C4#6700212yes—
472C2×C4#6700312yes—
473C2×C4C2×D4×D1111yescharacteristic
474C2×C4C2×D4×D1111yescharacteristic
475C2×C4#6704012yes—
476C2×C4#41×D1112yes—
477C8—224no—
478C8—442no—
479C22—22no—
480C22—22no—
481C22—22no—
482C22—41no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—444no—
487C22—444no—
488C22—444no—
489C22—882no—
490C22—882no—
491C22—882no—
492C22—882no—
493C22C2×#6698511yescharacteristic
494C22C2×#6699011yescharacteristic
495C22C22×#432511yescharacteristic
496C22#1062334711yescharacteristic
497C22C2×#6700211yescharacteristic
498C22C2×#6700311yescharacteristic
499C22#1062336311yescharacteristic
500C4—22no—
501C4—41no—
502C4—41no—
503C4—82no—
504C4—82no—
505C4—444no—
506C4#1062265014yes—
507C4#1062265914yes—
508C4#1062316212yes—
509C4#1062316412yes—
510C2—42no—
511C2—884no—
512C2#1307224511yescharacteristic
513C2C2×#1062265911yescharacteristic
514C2C2×#1062265011yescharacteristic
515C2#1307917611yescharacteristic
516C2#1307935011yescharacteristic
517C2#1307974411yescharacteristic
518C2#1307975211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2857C2
socleC23×C11C22×D4
prime radicalC2×#10623008C2
hypercenter#2857D11
hypocenterC11#25671
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2857

Complements

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

NH ≅ G/Ntype
2. C2×#10622692C2semidirect
3. C2×#10622701C2semidirect
4. #13069805C2semidirect
5. #13069576C2semidirect
6. #13069421C2semidirect
7. #13068876C2semidirect
8. C4×C22⋊(C11⋊C8)C2semidirect
9. C11×#2857C2semidirect
162. C2×C11⋊C8#41semidirect
166. #2857D11semidirect
421. C11#25671semidirect

Maximal subgroups

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

subgroupindex
C2×#106230082
C2×#106226922
C2×#106227012
#130698052
#130695762
#130694212
#130688762
C4×C22⋊(C11⋊C8)2
C11×#28572
#2567111