Finite Group Databasebeta

← #14914972

Subgroups — #14914972

Order 2816.

2946 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623057C211yesmaximal, characteristic
2C2×#10623047C211yesmaximal, characteristic, complemented
3C2×#10623053C211yesmaximal, characteristic
4#13071687C214yesmaximal, complemented
5#13071674C214yesmaximal, complemented
6#13071610C218yesmaximal, complemented
7#13071299C214yesmaximal, complemented
8#13071209C211yesmaximal, characteristic
9C4×#66950C214yesmaximal, complemented
10#13071100C211yesmaximal, characteristic, complemented
11C2×#10622587C211yesmaximal, characteristic, complemented
12C11×#2274C211yesmaximal, characteristic, complemented
13C22×#4339C2211yescharacteristic
14C23×Dic22C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C22×C4×Dic11C2211yescharacteristic
20#10623057C4116yescomplemented
21#10623053—28no—
22#10623047—28no—
23C2×#66950C2214yes—
24C2×#66946C2212yes—
25C2×#66940C2212yes—
26C2×#66940C2214yes—
27C2×#66939C2214yes—
28C2×(C22⋊D11)⋊C4C2214yes—
29C2×#66930C2214yes—
30C2×#66928C2212yes—
31C2×#66925C2212yes—
32C2×C42×D11C2212yes—
33C2×#66922C2212yes—
34C2×C4×Dic22C2214yes—
35C4×C11×C4⋊C4C2214yes—
36C4×C11×C4⋊C4C2214yes—
37C4×C11×C22⋊C4C2214yes—
38#10622826C2214yes—
39C2×C11⋊#95C2214yes—
40#10622601C2212yes—
41#10622600C2214yes—
42#10622598C2212yes—
43#10622598C2212yes—
44#10622587C2212yes—
45#10622587C2212yes—
46#10622587C2214yes—
47#10622587C2212yes—
48#10622563C2214yes—
49#10622553C2218yes—
50C4×(C2×D11)⋊C4C2218yes—
51C4×C4⋊Dic11C2218yes—
52C4×C4⋊Dic11C2214yes—
53#10622541C2218yes—
54#10622283C2218yes—
55#10622281C2218yes—
56#10622266C2218yes—
57#10622266C2218yes—
58C23×C4×C11C2312yes—
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11C2312yes—
61C23×Dic11C2312yes—
62C23×Dic11C2312yes—
63C2×#4339—24no—
64C2×#4339—24no—
65C2×#4339C2×C418yes—
66C22×D44C2311yescharacteristic
67C22×C4×D11C2314yes—
68C22×C4×D11C2312yes—
69C22×Dic22—24no—
70C22×Dic22—24no—
71C22×Dic22C2×C418yescomplemented
72C22×Dic22C2312yes—
73C22×Dic22C2311yescharacteristic
74C22×Dic22C2312yes—
75C11×#117C2×C418yescomplemented
76C11×#117D418yes—
77C2×C11×C4⋊C4—24no—
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2312yes—
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C22⋊C4C2312yes—
83C2×C11×C22⋊C4C2312yes—
84C2×C42×C11C2318yes—
85C2×C42×C11C2312yes—
86C2×C42×C11C2312yes—
87C2×C22⋊Dic11C2312yes—
88C2×(C2×D11)⋊C4C2314yes—
89C2×(C2×D11)⋊C4C2318yes—
90C2×(C2×D11)⋊C4C2318yes—
91#66979—24no—
92C2×C4⋊Dic11C2312yes—
93C2×C4⋊Dic11C2314yes—
94C2×C4⋊Dic11C2314yes—
95C2×C4⋊Dic11C2318yes—
96C2×Dic11⋊C4C2318yes—
97C2×Dic11⋊C4C2314yes—
98C2×C4×Dic11—24no—
99C2×C4×Dic11C2318yes—
100C2×C4×Dic11C2311yescharacteristic
101C2×C4×Dic11C2314yes—
102C2×C4×Dic11C2311yescharacteristic
103C2×C4×Dic11C2312yes—
104C2×C4×Dic11C2312yes—
105#66950C2×C4132yescomplemented
106#66946—28no—
107#66940—216no—
108#66940—28no—
109#66939C2×C4132yescomplemented
110(C22⋊D11)⋊C4—216no—
111#66930—216no—
112#66928C2×C4116yescomplemented
113#66925—28no—
114C42×D11—28no—
115#66922C2×C4116yescomplemented
116C4×Dic22—216no—
117C11×#95C2318yes—
118C11⋊#95C2318yes—
119C11⋊#95C2314yes—
120C11⋊#95C2314yes—
121C11⋊#95C2318yes—
122C11⋊#95C2318yes—
123#34268—111nomaximal, Sylow
124C24×C11C2411yescharacteristic
125C23×D11C2412yes—
126C22×C4×C11—24no—
127C22×C4×C11—44no—
128C22×C4×C11C22×C414yes—
129C22×C4×C11C2×D414yes—
130C22×C4×C11#4114yes—
131C22×C4×C11C2414yes—
132C22×C4×C11C2414yes—
133C22×C4×C11C2414yes—
134C22×C4×C11C2411yescharacteristic
135C22×C4×C11C2411yescharacteristic
136C2×C22⋊D11—24no—
137C2×C22⋊D11—24no—
138C2×C22⋊D11C22×C418yes—
139C22×Dic11—24no—
140C22×Dic11—24no—
141C22×Dic11—24no—
142C22×Dic11—24no—
143C22×Dic11—42no—
144C22×Dic11C22×C418yes—
145C22×Dic11C2412yes—
146C22×Dic11C2414yes—
147C22×Dic11C2412yes—
148C22×Dic11C2414yes—
149C22×Dic11C2412yes—
150#4339—232no—
151C2×D44—22no—
152C2×D44—22no—
153C2×D44C22×C414yes—
154C2×C4×D11—28no—
155C2×C4×D11—24no—
156C2×C4×D11—28no—
157C2×C4×D11—24no—
158C2×C4×D11—44no—
159C2×C4×D11C22×C418yes—
160C2×Dic22—232no—
161C2×Dic22—24no—
162C2×Dic22—24no—
163C2×Dic22—22no—
164C2×Dic22—24no—
165C2×Dic22—24no—
166C2×Dic22—22no—
167C2×Dic22C22×C414yes—
168C2×Dic22C22×C418yes—
169C2×Dic22C22×C418yes—
170C11×C4⋊C4—24no—
171C11×C4⋊C4—24no—
172C11×C4⋊C4C22×C418yes—
173C11×C4⋊C4C2×D418yes—
174C11×C22⋊C4C22×C418yes—
175C11×C22⋊C4C2×D418yes—
176C42×C11—48no—
177C42×C11C22×C418yes—
178C42×C11C2×D418yes—
179C22⋊Dic11—24no—
180(C2×D11)⋊C4—28no—
181(C2×D11)⋊C4—48no—
182(C2×D11)⋊C4C22×C4132yes—
183C4⋊Dic11—28no—
184C4⋊Dic11—24no—
185C4⋊Dic11—44no—
186C4⋊Dic11C22×C4132yes—
187Dic11⋊C4—216no—
188Dic11⋊C4—28no—
189C4×Dic11—216no—
190C4×Dic11—22no—
191C4×Dic11—28no—
192C4×Dic11—22no—
193C4×Dic11—24no—
194C4×Dic11—24no—
195C2×#536—111no—
196C2×#519—111no—
197C2×C4×#41—111no—
198#2367—114no—
199#2365—114no—
200#2359—118no—
201#2323—114no—
202#2311—111no—
203C4×C22⋊Q8—114no—
204#2296—111no—
205C2×#391—111no—
206#2274D1111yescharacteristic, complemented
207C23×C11—22no—
208C23×C11—22no—
209C23×C11C23×C412yes—
210C23×C11C22×D412yes—
211C23×C11C2×#4112yes—
212C23×C11C2511yescharacteristic
213C22×D11—22no—
214C22×D11—22no—
215C22×D11—24no—
216C22×D11—24no—
217C22×D11C23×C414yes—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—28no—
224C2×C4×C11—84no—
225C2×C4×C11C4×D4116yes—
226C2×C4×C11C23×C418yes—
227C2×C4×C11C23×C412yes—
228C2×C4×C11C23×C412yes—
229C2×C4×C11C22×D418yes—
230C2×C4×C11C22×D412yes—
231C2×C4×C11C22×D412yes—
232C2×C4×C11C2×#4112yes—
233C2×C4×C11C2×#4112yes—
234C22⋊D11—216no—
235C2×Dic11—216no—
236C2×Dic11—22no—
237C2×Dic11—24no—
238C2×Dic11—22no—
239C2×Dic11—24no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—24no—
243C2×Dic11—22no—
244C2×Dic11—24no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—24no—
248C2×Dic11—48no—
249C2×Dic11C23×C414yes—
250C2×Dic11C23×C418yes—
251C2×Dic112−1+414yes—
252D44—28no—
253C4×D11—216no—
254C4×D11—416no—
255Dic22—216no—
256Dic22—216no—
257Dic22—28no—
258C22×#41—111no—
259C23×Q8—111no—
260#536—1116no—
261C2×C4⋊Q8—112no—
262C2×#124—112no—
263C2×#123—114no—
264C2×C22⋊Q8—114no—
265#519—228no—
266C4×#41—228no—
267C2×C4×Q8—112no—
268C2×C4×Q8—114no—
269C2×C4×Q8—114no—
270C2×C4×D4—112no—
271C2×C4×D4—114no—
272C2×#117—111no—
273C2×#117—114no—
274C2×#117—112no—
275C2×#117C2×D1111yescharacteristic
276C2×#117C2×D1111yescharacteristic
277C22×C4⋊C4C2×D1111yescharacteristic
278C22×C42—111no—
279C22×C42—112no—
280#391—112no—
281#391—112no—
282#391—114no—
283#391—112no—
284#390—112no—
285#389—112no—
286#389—112no—
287#389—118no—
288#388—118no—
289#388—118no—
290#387—118no—
291#387—118no—
292#386—114no—
293#385—114no—
294#385—118no—
295#380—114no—
296C4×C4⋊C4—118no—
297C4×C4⋊C4—114no—
298C4×C4⋊C4C2×D1114yes—
299C4×C4⋊C4C2×D1114yes—
300C4×C22⋊C4—118no—
301C4×C22⋊C4C2×D1114yes—
302C2×#95—114no—
303C22×C11—24no—
304C22×C11—24no—
305C22×C11—22no—
306C22×C11—22no—
307C22×C11C2×C4×D414yes—
308C22×C11C24×C411yescharacteristic
309C22×C11C23×D411yescharacteristic
310C22×C11C22×#4111yescharacteristic
311C22×C11C2×2−1+412yes—
312C22×C11#58512yes—
313C2×D11—24no—
314C2×D11—28no—
315C2×D11—44no—
316C2×D11—42no—
317C2×D11—42no—
318C4×C11—28no—
319C4×C11—28no—
320C4×C11—44no—
321C4×C11C2×C4×D414yes—
322C4×C11C2×C4×D414yes—
323Dic11—28no—
324Dic11—24no—
325Dic11—24no—
326Dic11—44no—
327Dic11—42no—
328C2×#41—118no—
329C2×#41—224no—
330C2×#41—224no—
331C22×Q8—118no—
332C22×Q8—112no—
333C22×Q8—112no—
334C22×Q8—111no—
335C22×Q8—224no—
336C22×Q8—224no—
337C22×D4—112no—
338C22×D4—111no—
339C23×C4—112no—
340C23×C4—112no—
341C23×C4—112no—
342C23×C4—114no—
343C23×C4C22×D1112yes—
344C23×C4C22×D1111yescharacteristic
345C4⋊Q8—1116no—
346#124—1116no—
347#123—1132no—
348C22⋊Q8—1132no—
349C4×Q8—228no—
350C4×Q8—2216no—
351C4×Q8—2216no—
352C4×D4—228no—
353C4×D4—2216no—
354#117—224no—
355#117—2216no—
356#117—228no—
357#117C4×D1118yescomplemented
358#117D4418yes—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—118no—
361C2×C4⋊C4—114no—
362C2×C4⋊C4—112no—
363C2×C4⋊C4—118no—
364C2×C4⋊C4—114no—
365C2×C4⋊C4—114no—
366C2×C4⋊C4C22×D1112yes—
367C2×C4⋊C4C22×D1112yes—
368C2×C4⋊C4C22×D1112yes—
369C2×C4⋊C4C22×D1112yes—
370C2×C22⋊C4—118no—
371C2×C22⋊C4—112no—
372C2×C22⋊C4—114no—
373C2×C22⋊C4—118no—
374C2×C22⋊C4C22×D1112yes—
375C2×C22⋊C4C22×D1112yes—
376C2×C42—111no—
377C2×C42—118no—
378C2×C42—112no—
379C2×C42—114no—
380C2×C42—112no—
381C2×C42—111no—
382C2×C42—224no—
383C2×C42—228no—
384C2×C42C22×D1118yes—
385C2×C42C22×D1112yes—
386C2×C42C22×D1112yes—
387#95—118no—
388#95—118no—
389#95—114no—
390#95—118no—
391#95—114no—
392#95C22×D1118yes—
393C2×C11—24no—
394C2×C11C22×C4×D411yescharacteristic
395C2×C11C4×2−1+412yes—
396C2×C11#348912yes—
397C2×C11#350911yescharacteristic
398C2×C11#351011yescharacteristic
399D11—44no—
400C24—112no—
401C24C23×D1111yescharacteristic
402#41—2232no—
403C2×Q8—118no—
404C2×Q8—118no—
405C2×Q8—114no—
406C2×Q8—2232no—
407C2×Q8—224no—
408C2×Q8—224no—
409C2×Q8—222no—
410C2×Q8—224no—
411C2×Q8—224no—
412C2×Q8—222no—
413C2×D4—118no—
414C2×D4—114no—
415C2×D4—224no—
416C2×D4—224no—
417C2×D4—222no—
418C2×D4—222no—
419C22×C4—24no—
420C22×C4—44no—
421C22×C4—118no—
422C22×C4—112no—
423C22×C4—114no—
424C22×C4—112no—
425C22×C4—118no—
426C22×C4—112no—
427C22×C4—114no—
428C22×C4—228no—
429C22×C4—224no—
430C22×C4—224no—
431C22×C4—224no—
432C22×C4—224no—
433C22×C4—224no—
434C22×C4—224no—
435C22×C4—228no—
436C22×C4—444no—
437C22×C4—442no—
438C22×C4C2×C4×D1114yes—
439C22×C4C2×D4414yes—
440C22×C4#433914yes—
441C22×C4C23×D1114yes—
442C22×C4C23×D1114yes—
443C22×C4C23×D1114yes—
444C22×C4C23×D1111yescharacteristic
445C22×C4C23×D1111yescharacteristic
446C4⋊C4—24no—
447C4⋊C4—24no—
448C4⋊C4—1132no—
449C4⋊C4—228no—
450C4⋊C4—228no—
451C4⋊C4—2216no—
452C4⋊C4—224no—
453C4⋊C4—444no—
454C4⋊C4C2×C4×D1118yes—
455C4⋊C4C2×D4418yes—
456C22⋊C4—1132no—
457C22⋊C4—224no—
458C22⋊C4—228no—
459C22⋊C4—448no—
460C22⋊C4C2×C4×D1118yes—
461C22⋊C4C2×D4418yes—
462C42—48no—
463C42—222no—
464C42—222no—
465C42—228no—
466C42—224no—
467C42—2216no—
468C42—224no—
469C42C2×C4×D1118yes—
470C42C2×D4418yes—
471C11#3426811yescharacteristic, complemented, Sylow
472C23—22no—
473C23—22no—
474C23—114no—
475C23—222no—
476C23—222no—
477C23—224no—
478C23—224no—
479C23C22×C4×D1112yes—
480C23C22×D4412yes—
481C23C2×#433912yes—
482C23C24×D1111yescharacteristic
483Q8—2216no—
484Q8—2216no—
485Q8—228no—
486D4—2216no—
487D4—228no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—28no—
494C2×C4—84no—
495C2×C4—118no—
496C2×C4—114no—
497C2×C4—114no—
498C2×C4—2216no—
499C2×C4—222no—
500C2×C4—222no—
501C2×C4—224no—
502C2×C4—222no—
503C2×C4—224no—
504C2×C4—222no—
505C2×C4—2216no—
506C2×C4—224no—
507C2×C4—222no—
508C2×C4—224no—
509C2×C4—222no—
510C2×C4—224no—
511C2×C4—222no—
512C2×C4—4416no—
513C2×C4—448no—
514C2×C4C4×D44116yes—
515C2×C4C22×C4×D1118yes—
516C2×C4C22×C4×D1112yes—
517C2×C4C22×C4×D1112yes—
518C2×C4C22×D4418yes—
519C2×C4C22×D4412yes—
520C2×C4C22×D4412yes—
521C2×C4C2×#433912yes—
522C2×C4C2×#433912yes—
523C22—22no—
524C22—22no—
525C22—24no—
526C22—24no—
527C22—224no—
528C22—228no—
529C22—442no—
530C22—442no—
531C22—444no—
532C22C2×C4×D4414yes—
533C22C23×C4×D1111yescharacteristic
534C22C23×D4411yescharacteristic
535C22C22×#433911yescharacteristic
536C22#1062345512yes—
537C22D11×2−1+412yes—
538C4—28no—
539C4—28no—
540C4—44no—
541C4—224no—
542C4—224no—
543C4—228no—
544C4—442no—
545C4—444no—
546C4C2×C4×D4414yes—
547C4C2×C4×D4414yes—
548C2—24no—
549C2—444no—
550C2C22×C4×D4411yescharacteristic
551C2#1308182712yes—
552C2#1308229712yes—
553C2#1308249711yescharacteristic
554C2#1308250711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2274C2
socle, cosocleC23×C11C25
prime radicalC22×#4339C22
hypercenter#2274D11
hypocenterC11#34268
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2274

Complements

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

NH ≅ G/Ntype
2. C2×#10623047C2semidirect
4. #13071687C2semidirect
5. #13071674C2semidirect
6. #13071610C2semidirect
7. #13071299C2semidirect
9. C4×#66950C2semidirect
10. #13071100C2semidirect
11. C2×#10622587C2semidirect
12. C11×#2274C2semidirect
20. #10623057C4semidirect
71. C22×Dic22C2×C4semidirect
75. C11×#117C2×C4semidirect
105. #66950C2×C4semidirect
109. #66939C2×C4semidirect
112. #66928C2×C4semidirect
115. #66922C2×C4semidirect
206. #2274D11semidirect
357. #117C4×D11semidirect
471. C11#34268semidirect

Maximal subgroups

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

subgroupindex
C2×#106230572
C2×#106230472
C2×#106230532
#130716872
#130716742
#130716102
#130712992
#130712092
C4×#669502
#130711002
C2×#106225872
C11×#22742
#3426811