Finite Group Databasebeta

← #14755396

Subgroups — #14755396

Order 2816.

1974 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623359C211yesmaximal, characteristic
2#13081819C211yesmaximal, characteristic, complemented
3#13070995C212yesmaximal, complemented
4#13069027C214yesmaximal, complemented
5#13069022C214yesmaximal, complemented
6#13068348C212yesmaximal, complemented
7C2×C11×#410C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C23×C4×D11C2211yescharacteristic
10C2×C11×#117C2212yes—
11#10623359—24no—
12#10623359C418yescomplemented
13#10623358—24no—
14#41×Dic11—24no—
15C2×#66999—21no—
16#10623343—21no—
17C2×#66991—21no—
18C2×#66990C2212yes—
19#10623329—21no—
20#10623329C2214yes—
21C2×#66988C2212yes—
22C2×C4×C22⋊D11—22no—
23C2×#66979—22no—
24C2×#66979C2211yescharacteristic
25C2×#66979C2212yes—
26C11×#410—24no—
27C2×C11×#99C2214yes—
28#10622600—24no—
29#10622568C2214yes—
30#10622556C2214yes—
31C4×(C2×D11)⋊C4—24no—
32#10622165C2218yes—
33C24×D11C2311yescharacteristic
34C2×C11×#41—22no—
35C2×C11×#41—22no—
36C2×C11×#41—24no—
37C2×C11×#41C2×C414yes—
38C2×C11×#41D414yes—
39C22×Q8×C11D411yescharacteristic
40C22×D4×C11D411yescharacteristic
41C22×D4×C11C2312yes—
42C23×C4×C11D412yes—
43C23×C4×C11C2311yescharacteristic
44C22×C22⋊D11—22no—
45C23×Dic11C2311yescharacteristic
46C22×C4×D11—22no—
47C22×C4×D11—21no—
48C22×C4×D11—21no—
49C22×C4×D11—22no—
50C22×C4×D11—22no—
51C22×C4×D11—24no—
52C22×C4×D11C2×C414yescomplemented
53C11×#117—24no—
54C11×#117—24no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C22⋊C4C2314yes—
57C2×C42×C11—22no—
58C2×C22⋊Dic11—24no—
59C2×C22⋊Dic11—22no—
60C2×C22⋊Dic11C2314yes—
61C2×C22⋊Dic11C2312yes—
62#66999—28no—
63Q8×Dic11—28no—
64#66991—28no—
65#66990—24no—
66#66990C2×C418yescomplemented
67#66988—24no—
68#66988C2×C418yescomplemented
69D4×Dic11—28no—
70D4×Dic11—216no—
71C4×C22⋊D11—216no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—28no—
74#66979—24no—
75#66979—24no—
76#66979—22no—
77#66979—24no—
78#66979—22no—
79#66979—22no—
80#66979—22no—
81#66979—22no—
82#66979C2×C414yescomplemented
83C2×C4⋊Dic11—24no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11D414yescomplemented
86C2×Dic11⋊C4—22no—
87C2×C4×Dic11—24no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11D414yescomplemented
90C11×#99—28no—
91C11⋊#95—28no—
92#20959—111nomaximal, Sylow
93C24×C11C2×D412yes—
94C24×C11C2411yescharacteristic
95C23×D11—22no—
96C23×D11—21no—
97C23×D11—21no—
98C23×D11—22no—
99C23×D11—44no—
100C23×D11C22×C412yes—
101C11×#41—28no—
102C11×#41—28no—
103C11×#41—28no—
104C11×#41—28no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11C22⋊C414yescomplemented
108C2×D4×C11—24no—
109C2×D4×C11—24no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11C22⋊C414yescomplemented
113C2×D4×C11C22×C414yes—
114C2×D4×C11C2×D414yes—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—24no—
118C22×C4×C11—24no—
119C22×C4×C11C22⋊C418yescomplemented
120C22×C4×C11C22×C412yes—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11#4114yes—
128C2×C22⋊D11—28no—
129C2×C22⋊D11—48no—
130C22×Dic11—28no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—22no—
136C22×Dic11C22×C412yes—
137C22×Dic11C2×D418yes—
138C2×C4×D11—24no—
139C2×C4×D11—24no—
140C2×C4×D11—28no—
141C2×C4×D11—28no—
142C2×C4×D11—42no—
143C2×C4×D11—41no—
144C2×C4×D11—41no—
145C2×C4×D11—44no—
146C2×C4×D11—44no—
147C2×C4×D11—42no—
148C2×C4×D11—42no—
149C11×C4⋊C4—44no—
150C11×C22⋊C4—24no—
151C11×C22⋊C4—24no—
152C42×C11—44no—
153C22⋊Dic11—28no—
154C22⋊Dic11—28no—
155C22⋊Dic11—24no—
156C22⋊Dic11—24no—
157C22⋊Dic11—22no—
158C22⋊Dic11C22×C414yes—
159(C2×D11)⋊C4—28no—
160(C2×D11)⋊C4—416no—
161C4⋊Dic11—28no—
162C4⋊Dic11—24no—
163C4⋊Dic11—24no—
164C4⋊Dic11—24no—
165Dic11⋊C4—28no—
166C4×Dic11—28no—
167C4×Dic11—24no—
168C4×Dic11—24no—
169C4×Dic11—24no—
170C2×#525—111no—
171#3428—111no—
172C2×#410D1111yescharacteristic, complemented
173#2280—112no—
174#1890—114no—
175#1889—114no—
176#1740—112no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—42no—
180C23×C11—44no—
181C23×C11C2×C22⋊C414yes—
182C23×C11C23×C411yescharacteristic
183C23×C11C22×D411yescharacteristic
184C23×C11C22×D412yes—
185C23×C11C22×D411yescharacteristic
186C23×C11C2×#4112yes—
187C22×D11—28no—
188C22×D11—24no—
189C22×D11—22no—
190C22×D11—24no—
191C22×D11—44no—
192C22×D11—48no—
193C22×D11—44no—
194C22×D11—44no—
195C22×D11—42no—
196C22×D11—41no—
197C22×D11—42no—
198C22×D11—41no—
199Q8×C11—28no—
200D4×C11—28no—
201D4×C11—28no—
202D4×C11—28no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—28no—
206C2×C4×C11—28no—
207C2×C4×C11—48no—
208C2×C4×C11—44no—
209C2×C4×C11C2×C22⋊C414yes—
210C2×C4×C11C2×C22⋊C412yes—
211C2×C4×C11C2×C22⋊C412yes—
212C2×C4×C11C4×D414yes—
213C2×C4×C11C4×D414yes—
214C2×C4×C11#12012yes—
215C2×C4×C11#12011yescharacteristic
216C2×C4×C11#12011yescharacteristic
217C2×C4×C11#12114yes—
218C2×C4×C11#12114yes—
219C2×C4×C11#12312yes—
220C2×C4×C11#12312yes—
221C22⋊D11—416no—
222C2×Dic11—24no—
223C2×Dic11—22no—
224C2×Dic11—24no—
225C2×Dic11—28no—
226C2×Dic11—44no—
227C2×Dic11—41no—
228C2×Dic11—42no—
229C2×Dic11—41no—
230C2×Dic11—48no—
231C2×Dic11—88no—
232C4×D11—44no—
233C4×D11—44no—
234C4×D11—48no—
235C22×#41C2×D1111yescharacteristic
236C24×C4—111no—
237#525—118no—
238#525—224no—
239C2×#123—112no—
240C2×C22⋊Q8—221no—
241C2×#121—221no—
242C2×#120—112no—
243#520—224no—
244#519—221no—
245#518—114no—
246#518—221no—
247C4×#41—224no—
248C2×C4×D4—222no—
249C2×#117—112no—
250C2×#117—111no—
251C2×#117—222no—
252C2×#117C2×D1112yes—
253#410—24no—
254C2×#99C2×D1114yes—
255#381—114no—
256#380—224no—
257#379—114no—
258C4×C22⋊C4—224no—
259#342—118no—
260C22×C11—24no—
261C22×C11—22no—
262C22×C11—24no—
263C22×C11—41no—
264C22×C11—41no—
265C22×C11—42no—
266C22×C11—44no—
267C22×C11—44no—
268C22×C11—82no—
269C22×C11C22×C22⋊C411yescharacteristic
270C22×C11C2×C4×D412yes—
271C22×C11C2×#12011yescharacteristic
272C22×C11C2×#12112yes—
273C22×C11C2×#12311yescharacteristic
274C2×D11—28no—
275C2×D11—24no—
276C2×D11—42no—
277C2×D11—48no—
278C2×D11—44no—
279C2×D11—44no—
280C2×D11—44no—
281C2×D11—42no—
282C4×C11—24no—
283C4×C11—84no—
284C4×C11#38612yes—
285C4×C11#38612yes—
286C4×C11#38614yes—
287Dic11—44no—
288Dic11—48no—
289Dic11—42no—
290C25—111no—
291C2×#41—22no—
292C2×#41—22no—
293C2×#41—24no—
294C2×#41C4×D1114yes—
295C2×#41C22⋊D1114yes—
296C22×Q8D4411yescharacteristic
297C22×D4—222no—
298C22×D4D4411yescharacteristic
299C22×D4C22×D1112yes—
300C23×C4—111no—
301C23×C4—114no—
302C23×C4—221no—
303C23×C4—221no—
304C23×C4—222no—
305C23×C4—222no—
306C23×C4—224no—
307C23×C4—222no—
308C23×C4D4412yes—
309C23×C4C22×D1111yescharacteristic
310#123—118no—
311#123—224no—
312C22⋊Q8—228no—
313#121—228no—
314#120—118no—
315#120—224no—
316C4×Q8—228no—
317C4×D4—2216no—
318C4×D4—228no—
319C4×D4—2216no—
320#117—24no—
321#117—24no—
322#117—114no—
323#117—224no—
324#117—224no—
325#117—222no—
326#117—222no—
327#117—224no—
328#117—222no—
329#117—222no—
330#117—222no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—114no—
333C2×C4⋊C4—224no—
334C2×C4⋊C4—221no—
335C2×C4⋊C4—222no—
336C2×C22⋊C4—112no—
337C2×C22⋊C4—114no—
338C2×C22⋊C4—224no—
339C2×C22⋊C4—222no—
340C2×C22⋊C4—222no—
341C2×C22⋊C4—228no—
342C2×C22⋊C4C22×D1114yes—
343C2×C42—22no—
344C2×C42—114no—
345C2×C42—224no—
346C2×C42—221no—
347#99—28no—
348#95—228no—
349C2×C11—21no—
350C2×C11—22no—
351C2×C11—22no—
352C2×C11—21no—
353C2×C11—44no—
354C2×C11C2×#38611yescharacteristic
355C2×C11#302512yes—
356D11—44no—
357C24—112no—
358C24—221no—
359C24—222no—
360C24—222no—
361C24—221no—
362C24—444no—
363C24C2×D4412yes—
364C24C23×D1111yescharacteristic
365#41—28no—
366#41—28no—
367#41—28no—
368#41—28no—
369C2×Q8—22no—
370C2×Q8—22no—
371C2×Q8(C2×D11)⋊C414yescomplemented
372C2×D4—24no—
373C2×D4—24no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—228no—
377C2×D4—448no—
378C2×D4(C2×D11)⋊C414yescomplemented
379C2×D4C2×C4×D1114yes—
380C2×D4C2×C22⋊D1114yes—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—24no—
384C22×C4—24no—
385C22×C4—112no—
386C22×C4—118no—
387C22×C4—222no—
388C22×C4—221no—
389C22×C4—222no—
390C22×C4—222no—
391C22×C4—221no—
392C22×C4—228no—
393C22×C4—228no—
394C22×C4—228no—
395C22×C4—224no—
396C22×C4—224no—
397C22×C4—442no—
398C22×C4—441no—
399C22×C4—441no—
400C22×C4—442no—
401C22×C4—442no—
402C22×C4—444no—
403C22×C4—444no—
404C22×C4(C2×D11)⋊C418yescomplemented
405C22×C4C2×C4×D1112yes—
406C22×C4C2×D4412yes—
407C22×C4C2×D4411yescharacteristic
408C22×C4C2×D4411yescharacteristic
409C22×C4D4×D1112yes—
410C22×C4D4×D1112yes—
411C22×C4#434114yes—
412C22×C4C2×C22⋊D1112yes—
413C4⋊C4—44no—
414C4⋊C4—228no—
415C4⋊C4—224no—
416C4⋊C4—224no—
417C4⋊C4—224no—
418C4⋊C4—228no—
419C22⋊C4—24no—
420C22⋊C4—24no—
421C22⋊C4—114no—
422C22⋊C4—228no—
423C22⋊C4—228no—
424C22⋊C4—224no—
425C22⋊C4—224no—
426C22⋊C4—222no—
427C22⋊C4—228no—
428C22⋊C4—4416no—
429C42—44no—
430C42—228no—
431C42—224no—
432C42—224no—
433C42—224no—
434C11#2095911yescharacteristic, complemented, Sylow
435C23—22no—
436C23—22no—
437C23—42no—
438C23—44no—
439C23—228no—
440C23—224no—
441C23—224no—
442C23—222no—
443C23—444no—
444C23—442no—
445C23—444no—
446C23—448no—
447C23—444no—
448C23—441no—
449C23—441no—
450C23—442no—
451C23C2×(C2×D11)⋊C414yes—
452C23C22×C4×D1111yescharacteristic
453C23C22×D4411yescharacteristic
454C23C2×D4×D1112yes—
455C23C2×#434112yes—
456C23C22×C22⋊D1111yescharacteristic
457Q8—28no—
458D4—28no—
459D4—28no—
460D4—28no—
461D4—4416no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—28no—
465C2×C4—28no—
466C2×C4—48no—
467C2×C4—44no—
468C2×C4—224no—
469C2×C4—228no—
470C2×C4—224no—
471C2×C4—222no—
472C2×C4—444no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—442no—
476C2×C4—444no—
477C2×C4—444no—
478C2×C4—448no—
479C2×C4—448no—
480C2×C4—888no—
481C2×C4(C22⋊D11)⋊C414yes—
482C2×C4(C22⋊D11)⋊C414yes—
483C2×C4#6693512yes—
484C2×C4#6693511yescharacteristic
485C2×C4#6693511yescharacteristic
486C2×C4#6693912yes—
487C2×C4#6693912yes—
488C2×C4C2×(C2×D11)⋊C414yes—
489C2×C4C2×(C2×D11)⋊C412yes—
490C2×C4C2×(C2×D11)⋊C412yes—
491C2×C4#6699214yes—
492C2×C4#6699214yes—
493C22—24no—
494C22—22no—
495C22—24no—
496C22—41no—
497C22—42no—
498C22—41no—
499C22—44no—
500C22—44no—
501C22—82no—
502C22—224no—
503C22—228no—
504C22—448no—
505C22—442no—
506C22—444no—
507C22—444no—
508C22—442no—
509C22—444no—
510C22C2×(C22⋊D11)⋊C412yes—
511C22C2×#6693511yescharacteristic
512C22C2×#6693911yescharacteristic
513C22C22×(C2×D11)⋊C411yescharacteristic
514C22C2×#6699212yes—
515C4—24no—
516C4—84no—
517C4—444no—
518C4—442no—
519C4—448no—
520C4#1062257112yes—
521C4#1062257112yes—
522C4#1062257114yes—
523C2—22no—
524C2—21no—
525C2—21no—
526C2—22no—
527C2—44no—
528C2—444no—
529C2C2×#1062257111yescharacteristic
530C2#1307801012yes—
subgroupG/H
centerC2×C4#66935
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC2×C11×#410C2
socleC22×C11C2×#120
prime radicalC2×#10623359C2
cosocleC24×C11C24
hypercenterC2×#410D11
hypocenterC11#20959
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
2. #13081819C2semidirect
3. #13070995C2semidirect
4. #13069027C2semidirect
5. #13069022C2semidirect
6. #13068348C2semidirect
7. C2×C11×#410C2semidirect
12. #10623359C4semidirect
52. C22×C4×D11C2×C4semidirect
66. #66990C2×C4semidirect
68. #66988C2×C4semidirect
82. #66979C2×C4semidirect
85. C2×C4⋊Dic11D4semidirect
89. C2×C4×Dic11D4semidirect
107. C2×Q8×C11C22⋊C4semidirect
112. C2×D4×C11C22⋊C4semidirect
119. C22×C4×C11C22⋊C4semidirect
172. C2×#410D11semidirect
371. C2×Q8(C2×D11)⋊C4semidirect
378. C2×D4(C2×D11)⋊C4semidirect
404. C22×C4(C2×D11)⋊C4semidirect
434. C11#20959semidirect

Maximal subgroups

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

subgroupindex
C2×#106233592
#130818192
#130709952
#130690272
#130690222
#130683482
C2×C11×#4102
#2095911