Finite Group Databasebeta

← #14808037

Subgroups — #14808037

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×#10622293C211yesmaximal, characteristic, complemented
3C2×#10622307C211yesmaximal, characteristic, complemented
4#13076968C211yesmaximal, characteristic, complemented
5#13069806C214yesmaximal, complemented
6#13069577C211yesmaximal, characteristic, complemented
7#13069422C211yesmaximal, characteristic, complemented
8#13068880C214yesmaximal, complemented
9C4×C11×C22⋊C8C211yesmaximal, characteristic, complemented
10C22×#4339—21no—
11C22×C42×C11C2211yescharacteristic
12C2×#66983—21no—
13C2×#66983C2212yes—
14C2×#66977—21no—
15#10623008—24no—
16#10623008—24no—
17C2×#66928—21no—
18C2×#66927C2211yescharacteristic
19C2×C4×D44—21no—
20C2×C4×D44C2212yes—
21C2×#66922C2211yescharacteristic
22C2×#66922C2211yescharacteristic
23C2×C11×C22⋊C8C2212yes—
24C2×C4×C8×C11C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26#10622825—21no—
27#10622825C2212yes—
28C2×#66885C2214yes—
29C2×#66885C2214yes—
30C2×#66881C2214yes—
31#10622548C2211yescharacteristic
32#10622542—21no—
33#10622541—21no—
34#10622541C2212yes—
35#10622307—24no—
36#10622293—24no—
37C11×#336C2212yes—
38#10622189C2214yes—
39C23×C4×C11D411yescharacteristic
40C23×C4×C11D411yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C22×C22⋊D11—22no—
43C2×#4339—28no—
44C2×#4339—44no—
45C2×#4339—44no—
46C22×D44—21no—
47C22×D44—21no—
48C22×D44C2312yes—
49C22×C4×D11—22no—
50C22×Dic22—21no—
51C22×Dic22—21no—
52C22×C8×C11C2312yes—
53C22×C8×C11C2312yes—
54C2×C42×C11—22no—
55C2×C42×C11—22no—
56C2×C42×C11D411yescharacteristic
57C2×C42×C11D411yescharacteristic
58C2×C42×C11C2311yescharacteristic
59C2×C42×C11C2311yescharacteristic
60C2×C22⋊Dic11—22no—
61#66983—28no—
62#66983—24no—
63#66983—24no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—22no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11C2312yes—
71C2×C4⋊Dic11C2312yes—
72C2×C4⋊Dic11C2312yes—
73#66977—44no—
74C2×Dic11⋊C4—22no—
75#66928—28no—
76#66927—22no—
77#66927D414yes—
78C4×D44—28no—
79C4×D44—24no—
80C4×D44—24no—
81#66922—22no—
82#66922—22no—
83#66922—22no—
84#66922D414yes—
85C11×C22⋊C8—24no—
86C4×C8×C11—22no—
87C4×C8×C11—22no—
88C11⋊#95—22no—
89C11⋊#95—22no—
90#66885—28no—
91#66885—28no—
92#66881—28no—
93#25671—111nomaximal, Sylow
94C24×C11C2×D411yescharacteristic
95C23×D11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11SD1614yes—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2411yescharacteristic
112C2×C22⋊D11—28no—
113C2×C22⋊D11—44no—
114C2×C22⋊D11—44no—
115C22×Dic11—22no—
116C22×Dic11—22no—
117C22×Dic11—22no—
118#4339—432no—
119C2×D44—24no—
120C2×D44—24no—
121C2×D44—22no—
122C2×D44—24no—
123C2×D44—24no—
124C2×D44—42no—
125C2×D44—42no—
126C2×D44—42no—
127C2×D44—42no—
128C2×D44C2×D414yes—
129C2×C4×D11—28no—
130C2×C4×D11—44no—
131C2×C4×D11—44no—
132C2×Dic22—24no—
133C2×Dic22—42no—
134C2×Dic22—42no—
135C2×Dic22—42no—
136C2×Dic22—42no—
137C2×Dic22—42no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11#4114yescomplemented
144C42×C11—22no—
145C42×C11—22no—
146C42×C11—21no—
147C42×C11—21no—
148C42×C11C2×D412yes—
149C42×C11C2×D412yes—
150C22⋊Dic11—44no—
151(C2×D11)⋊C4—28no—
152(C2×D11)⋊C4—28no—
153C4⋊Dic11—24no—
154C4⋊Dic11—22no—
155C4⋊Dic11—22no—
156C4⋊Dic11—22no—
157C4⋊Dic11—24no—
158C4⋊Dic11—42no—
159C4⋊Dic11—42no—
160C4⋊Dic11—42no—
161C4⋊Dic11C2×D414yes—
162Dic11⋊C4—44no—
163C2×#532—111no—
164C2×#498—111no—
165C2×#486—111no—
166#2857—111no—
167#2034—114no—
168#1990—111no—
169#1957—111no—
170#1864—114no—
171C4×C22⋊C8D1111yescharacteristic, complemented
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—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—28no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—44no—
199C2×C4×C11#12012yes—
200C2×C4×C11#12012yes—
201C2×C4×C11C2×SD1612yes—
202C2×C4×C11C2×SD1612yes—
203C2×C4×C11#13512yes—
204C2×C4×C11AGL(1,ℤ/8)12yes—
205C2×C4×C11AGL(1,ℤ/8)12yes—
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C22×D411yescharacteristic
208C2×C4×C11C2×#4112yes—
209C2×C4×C112−1+412yes—
210C22⋊D11—416no—
211C2×Dic11—24no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220D44—28no—
221D44—44no—
222D44—48no—
223D44—48no—
224C4×D11—416no—
225Dic22—48no—
226Dic22—84no—
227C8×C11—24no—
228C8×C11—42no—
229C22×#41—221no—
230#532—224no—
231#532—224no—
232C2×C4⋊Q8—111no—
233C2×C4⋊Q8—111no—
234C2×#127—111no—
235C2×#124—221no—
236C2×C22⋊Q8—221no—
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⋊C8C2×D1112yes—
248C2×C4×C8C2×D1111yescharacteristic
249C2×C4×C8C2×D1111yescharacteristic
250#391—221no—
251#389—112no—
252#389—221no—
253#384—111no—
254#380—112no—
255#380—221no—
256#340—114no—
257#336C2×D1112yes—
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#44914yes—
283C4×C11#45014yes—
284C4×C11#54712yes—
285C4×C11#54812yes—
286Dic11—44no—
287Dic11—82no—
288Dic11—82no—
289C2×#41—228no—
290C2×#41—444no—
291C2×#41—444no—
292C22×Q8—221no—
293C22×Q8—221no—
294C22×D4—112no—
295C22×D4—222no—
296C22×D4—221no—
297C22×D4—221no—
298C23×C4—222no—
299C23×C4D4411yescharacteristic
300C23×C4D4411yescharacteristic
301C23×C4C22×D1111yescharacteristic
302C22×C8C22×D1112yes—
303C22×C8C22×D1112yes—
304C4⋊Q8—114no—
305C4⋊Q8—222no—
306C4⋊Q8—222no—
307C4⋊Q8—222no—
308#127—114no—
309#127—222no—
310#124—228no—
311C22⋊Q8—444no—
312#121—224no—
313#121—224no—
314#121—228no—
315C4×D4—224no—
316C4×D4—224no—
317C4×D4—228no—
318C2×C4⋊C4—112no—
319C2×C4⋊C4—112no—
320C2×C4⋊C4—112no—
321C2×C4⋊C4—221no—
322C2×C4⋊C4—221no—
323C2×C4⋊C4—222no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4—221no—
326C2×C22⋊C4—222no—
327C2×C22⋊C4—222no—
328C2×C22⋊C4—222no—
329C2×C42—22no—
330C2×C42—22no—
331C2×C42D4411yescharacteristic
332C2×C42D4411yescharacteristic
333C2×C42C22×D1111yescharacteristic
334C2×C42C22×D1111yescharacteristic
335#106—228no—
336#102—228no—
337#102—228no—
338C22⋊C8—24no—
339C4×C8—22no—
340C4×C8—22no—
341#95—222no—
342#95—222no—
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×D4411yescharacteristic
354#41—4432no—
355C2×Q8—224no—
356C2×Q8—442no—
357C2×Q8—442no—
358C2×Q8—442no—
359C2×Q8—442no—
360C2×Q8—442no—
361C2×D4—114no—
362C2×D4—228no—
363C2×D4—224no—
364C2×D4—224no—
365C2×D4—224no—
366C2×D4—222no—
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—22no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—228no—
384C22×C4—222no—
385C22×C4—222no—
386C22×C4—222no—
387C22×C4—444no—
388C22×C4—444no—
389C22×C4#431414yes—
390C22×C4C2×D4411yescharacteristic
391C22×C4C2×D4411yescharacteristic
392C22×C4C2×D4411yescharacteristic
393C22×C4C2×D4411yescharacteristic
394C22×C4C2×D4411yescharacteristic
395C22×C4C23×D1111yescharacteristic
396C2×C8—22no—
397C2×C8—22no—
398C2×C8—22no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8#433914yescomplemented
402C4⋊C4—114no—
403C4⋊C4—224no—
404C4⋊C4—222no—
405C4⋊C4—224no—
406C4⋊C4—222no—
407C4⋊C4—222no—
408C4⋊C4—444no—
409C4⋊C4—442no—
410C4⋊C4—442no—
411C4⋊C4—442no—
412C22⋊C4—228no—
413C22⋊C4—228no—
414C22⋊C4—444no—
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×#431412yes—
436C23C22×D4411yescharacteristic
437Q8—448no—
438Q8—884no—
439D4—228no—
440D4—4416no—
441D4—444no—
442D4—448no—
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—42no—
454C2×C4—42no—
455C2×C4—44no—
456C2×C4—224no—
457C2×C4—4416no—
458C2×C4—442no—
459C2×C4—442no—
460C2×C4—442no—
461C2×C4—442no—
462C2×C4—442no—
463C2×C4—442no—
464C2×C4—442no—
465C2×C4—442no—
466C2×C4#6693512yes—
467C2×C4#6693512yes—
468C2×C4C2×#431412yes—
469C2×C4C2×#431412yes—
470C2×C4#6695712yes—
471C2×C4#6696112yes—
472C2×C4#6696112yes—
473C2×C4C2×#433912yes—
474C2×C4C2×D4×D1111yescharacteristic
475C2×C4C2×D4×D1111yescharacteristic
476C2×C4#6704312yes—
477C8—24no—
478C8—42no—
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—
493C22#1062300811yescharacteristic
494C22C2×#6693511yescharacteristic
495C22#1062305711yescharacteristic
496C22C22×#431411yescharacteristic
497C22C2×#6695711yescharacteristic
498C22C2×#6696111yescharacteristic
499C22C2×#6696111yescharacteristic
500C4—22no—
501C4—41no—
502C4—41no—
503C4—444no—
504C4—882no—
505C4—882no—
506C4#1062234414yes—
507C4#1062234714yes—
508C4#1062308212yes—
509C4#1062308312yes—
510C2—42no—
511C2—884no—
512C2#1307224411yescharacteristic
513C2C2×#1062234411yescharacteristic
514C2C2×#1062234711yescharacteristic
515C2#1307917511yescharacteristic
516C2#1307935411yescharacteristic
517C2#1307974611yescharacteristic
518C2#1307975411yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×C22⋊C8C2
socleC23×C11C22×D4
prime radicalC2×#10623008C2
hypercenterC4×C22⋊C8D11
hypocenterC11#25671
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#10622293C2semidirect
3. C2×#10622307C2semidirect
4. #13076968C2semidirect
5. #13069806C2semidirect
6. #13069577C2semidirect
7. #13069422C2semidirect
8. #13068880C2semidirect
9. C4×C11×C22⋊C8C2semidirect
143. C2×C8×C11#41semidirect
171. C4×C22⋊C8D11semidirect
401. C2×C8#4339semidirect
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×#106222932
C2×#106223072
#130769682
#130698062
#130695772
#130694222
#130688802
C4×C11×C22⋊C82
#2567111