Finite Group Databasebeta

← #14757472

Subgroups — #14757472

Order 2816.

1526 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623057C211yesmaximal, characteristic
2C2×#10622579C211yesmaximal, characteristic
3C2×#10622617C211yesmaximal, characteristic, complemented
4C2×#10622615C211yesmaximal, characteristic
5C22×#66874C211yesmaximal, characteristic, complemented
6C2×#10622610C211yesmaximal, characteristic, complemented
7#13069435C212yesmaximal, complemented
8#13069430C212yesmaximal, complemented
9#13069425C212yesmaximal, complemented
10#13069417C212yesmaximal, complemented
11C11×#2317C211yesmaximal, characteristic, complemented
12C22×#4339C2211yescharacteristic
13C23×Dic22C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×#4318C2211yescharacteristic
18C23×C11⋊C8C2211yescharacteristic
19#10623057—24no—
20#10623057C418yescomplemented
21C2×#66950—22no—
22C2×#66939—22no—
23C2×#66928C2212yes—
24C2×#66922C2212yes—
25C11×#389—22no—
26C11×#385—22no—
27C11×#384C2212yes—
28C11×#382C2212yes—
29#10622617—24no—
30#10622615—24no—
31#10622610—24no—
32C2×#66874—24no—
33C2×#66874C2211yescharacteristic
34C2×#66874C2212yes—
35C2×#66874C2212yes—
36C2×#66874C2212yes—
37C2×#66874C2212yes—
38C2×#66874C2212yes—
39C2×#66874C2211yescharacteristic
40#10622579—24no—
41C2×#66873C2211yescharacteristic
42C2×#66873C2212yes—
43C2×#66873C2211yescharacteristic
44C2×#66867C2212yes—
45C2×C4×C11⋊C8C2212yes—
46C23×C4×C11—21no—
47C23×C4×C11C2311yescharacteristic
48C22×C22⋊D11—21no—
49C23×Dic11—21no—
50C2×#4339—22no—
51C2×#4339—22no—
52C2×#4339—22no—
53C2×#4339—22no—
54C2×#4339—22no—
55C2×#4339C2×C414yes—
56C22×D44C2311yescharacteristic
57C22×C4×D11—21no—
58C22×Dic22—22no—
59C22×Dic22—22no—
60C22×Dic22—22no—
61C22×Dic22—22no—
62C22×Dic22—21no—
63C22×Dic22—22no—
64C22×Dic22C2×C414yes—
65C22×Dic22C2311yescharacteristic
66C22×Dic22C2312yes—
67C11×#117—22no—
68C11×#117—22no—
69C11×#117C2×C414yes—
70C11×#117D414yes—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—24no—
75C2×C11×C4⋊C4D412yes—
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4D412yes—
81C2×C42×C11—21no—
82C2×C42×C11C2312yes—
83C2×(C2×D11)⋊C4—24no—
84C2×C4⋊Dic11—24no—
85C2×#4318—22no—
86C2×#4318—22no—
87C2×#4318D414yes—
88C22×C11⋊C8—22no—
89C22×C11⋊C8—22no—
90C22×C11⋊C8D414yes—
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2312yes—
93C22×C11⋊C8C2311yescharacteristic
94#66950—216no—
95#66939—216no—
96#66928—24no—
97#66928C2×C418yescomplemented
98#66922—24no—
99#66922C2×C418yescomplemented
100C11×#95—24no—
101#66874—24no—
102#66874—24no—
103#66874—24no—
104#66874—22no—
105#66874—22no—
106#66874—24no—
107#66874—24no—
108#66873—24no—
109#66873—22no—
110#66873—22no—
111#66867—24no—
112C4×C11⋊C8—24no—
113#21205—111nomaximal, Sylow
114C24×C11C2×D411yescharacteristic
115C23×D11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11—42no—
120C22×C4×C11—82no—
121C22×C4×C11C22×C412yes—
122C22×C4×C11C2×D414yes—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11#4112yes—
128C22×C4×C11#4112yes—
129C22×C4×C11C2411yescharacteristic
130C2×C22⋊D11—24no—
131C2×C22⋊D11—42no—
132C2×C22⋊D11—42no—
133C22×Dic11—24no—
134C22×Dic11—21no—
135C22×Dic11—22no—
136C22×Dic11—42no—
137C22×Dic11—42no—
138#4339—28no—
139#4339—28no—
140#4339—44no—
141#4339—44no—
142C2×D44—21no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44C22×C412yes—
148C2×C4×D11—24no—
149C2×C4×D11—42no—
150C2×C4×D11—42no—
151C2×Dic22—24no—
152C2×Dic22—28no—
153C2×Dic22—28no—
154C2×Dic22—22no—
155C2×Dic22—22no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—22no—
160C2×Dic22—22no—
161C2×Dic22—22no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—44no—
165C2×Dic22—44no—
166C2×Dic22—42no—
167C2×Dic22—42no—
168C2×Dic22C22×C412yes—
169C2×Dic22C22×C414yes—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—42no—
177C11×C4⋊C4—84no—
178C11×C4⋊C4C22⋊C418yes—
179C11×C22⋊C4—42no—
180C11×C22⋊C4C22⋊C418yes—
181C42×C11—42no—
182C42×C11C22×C414yes—
183C42×C11C2×D414yes—
184(C2×D11)⋊C4—216no—
185C4⋊Dic11—216no—
186#4318—28no—
187C2×C11⋊C8—28no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8C2×D412yes—
195C2×C11⋊C8C2×D412yes—
196C2×C11⋊C8C2×D414yes—
197C2×#536—111no—
198C2×#417—111no—
199C2×#419—111no—
200C2×#416—111no—
201C22×#103—111no—
202C2×#405—111no—
203#2317D1111yescharacteristic, complemented
204#1960—112no—
205#1959—112no—
206#1958—112no—
207#1956—112no—
208C23×C11—22no—
209C23×C11—22no—
210C23×C11C2×C22⋊C412yes—
211C23×C11#12412yes—
212C23×C11#12712yes—
213C23×C11C22×D411yescharacteristic
214C22×D11—22no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—42no—
218C22×D11—42no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—44no—
226C2×C4×C11—42no—
227C2×C4×C11—84no—
228C2×C4×C11C2×C22⋊C418yes—
229C2×C4×C11C2×C22⋊C412yes—
230C2×C4×C11C4×D414yes—
231C2×C4×C11C4×D414yes—
232C2×C4×C11#12114yes—
233C2×C4×C11#12114yes—
234C2×C4×C11#12412yes—
235C2×C4×C11#12712yes—
236C2×C4×C11C23×C411yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C22⋊D11—48no—
243C2×Dic11—22no—
244C2×Dic11—24no—
245C2×Dic11—42no—
246C2×Dic11—41no—
247C2×Dic11—42no—
248C2×Dic11—41no—
249C2×Dic11—48no—
250D44—22no—
251D44—22no—
252D44—41no—
253D44—41no—
254C4×D11—48no—
255Dic22—24no—
256Dic22—24no—
257Dic22—22no—
258Dic22—22no—
259Dic22—42no—
260Dic22—42no—
261Dic22—41no—
262Dic22—41no—
263Dic22—48no—
264C11⋊C8—22no—
265C11⋊C8—22no—
266C11⋊C8—24no—
267C22×#41—111no—
268C23×Q8—111no—
269C22×M16—111no—
270C23×C8—111no—
271#536—118no—
272#536—224no—
273C2×C4⋊Q8—112no—
274C2×#124—112no—
275C2×#123—222no—
276C2×C22⋊Q8—222no—
277C2×#117C2×D1111yescharacteristic
278C2×#117C2×D1111yescharacteristic
279C22×C4⋊C4C2×D1111yescharacteristic
280#419—224no—
281#417—224no—
282#416—224no—
283C2×#103—112no—
284C2×#103—112no—
285C2×#103—111no—
286C2×#103—111no—
287C2×#103—112no—
288C2×#103—112no—
289C2×#103—112no—
290C2×#103—224no—
291C2×#102—111no—
292C2×#102—111no—
293C2×#102—112no—
294#405—224no—
295C2×#97—112no—
296C2×C4×C8—112no—
297#389—22no—
298#385—22no—
299#384C2×D1112yes—
300#382C2×D1112yes—
301C22×C11—24no—
302C22×C11—24no—
303C22×C11—22no—
304C22×C11—22no—
305C22×C11#39014yes—
306C22×C11C22×C22⋊C411yescharacteristic
307C22×C11C2×#12411yescharacteristic
308C22×C11C2×#12711yescharacteristic
309C22×C11#57712yes—
310C22×C11#57812yes—
311C2×D11—44no—
312C2×D11—42no—
313C2×D11—82no—
314C2×D11—81no—
315C2×D11—81no—
316C4×C11—28no—
317C4×C11—81no—
318C4×C11—82no—
319C4×C11—81no—
320C4×C11#39014yes—
321C4×C11C2×C4×D411yescharacteristic
322C4×C11C2×C4×D411yescharacteristic
323C4×C11C2×#12111yescharacteristic
324C4×C11C2×#12111yescharacteristic
325Dic11—44no—
326Dic11—42no—
327C2×#41—114no—
328C2×#41—222no—
329C2×#41—222no—
330C2×#41—222no—
331C2×#41—222no—
332C2×#41—222no—
333C22×Q8—114no—
334C22×Q8—112no—
335C22×Q8—111no—
336C22×Q8—222no—
337C22×Q8—221no—
338C22×Q8—222no—
339C22×Q8—222no—
340C22×Q8—222no—
341C22×Q8—222no—
342C22×D4—111no—
343C22×D4—221no—
344C23×C4—21no—
345C23×C4—221no—
346C23×C4—221no—
347C23×C4C22×D1111yescharacteristic
348C2×M16—114no—
349C2×M16—222no—
350C2×M16—222no—
351C22×C8—114no—
352C22×C8—111no—
353C22×C8—111no—
354C22×C8—112no—
355C22×C8—222no—
356C22×C8—222no—
357C4⋊Q8—118no—
358C4⋊Q8—224no—
359#124—118no—
360#124—224no—
361#123—2216no—
362C22⋊Q8—2216no—
363#117—22no—
364#117—22no—
365#117C4×D1114yes—
366#117D4414yes—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—224no—
372C2×C4⋊C4C22⋊D1112yes—
373C2×C4⋊C4C22×D1112yes—
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C22⋊C4—21no—
377C2×C22⋊C4—224no—
378C2×C22⋊C4C22⋊D1112yes—
379C2×C42—21no—
380C2×C42C22×D1112yes—
381#103—224no—
382#103—224no—
383#103—222no—
384#103—222no—
385#103—224no—
386#103—224no—
387#103—224no—
388#102—222no—
389#102—222no—
390#102—224no—
391#97—224no—
392C4×C8—224no—
393#95—24no—
394C2×C11—24no—
395C2×C11C2×#39011yescharacteristic
396C2×C11#289812yes—
397C2×C11#313712yes—
398C2×C11#315411yescharacteristic
399C2×C11#315611yescharacteristic
400D11—82no—
401C24—221no—
402C24C2×C22⋊D1111yescharacteristic
403#41—228no—
404#41—228no—
405#41—444no—
406#41—444no—
407C2×Q8—114no—
408C2×Q8—112no—
409C2×Q8—224no—
410C2×Q8—222no—
411C2×Q8—221no—
412C2×Q8—228no—
413C2×Q8—228no—
414C2×Q8—222no—
415C2×Q8—222no—
416C2×Q8—221no—
417C2×Q8—221no—
418C2×Q8—222no—
419C2×Q8—222no—
420C2×Q8—221no—
421C2×Q8—221no—
422C2×Q8—444no—
423C2×Q8—444no—
424C2×Q8—442no—
425C2×Q8—442no—
426C2×D4—112no—
427C2×D4—224no—
428C2×D4—221no—
429C2×D4—221no—
430C2×D4—221no—
431C2×D4—221no—
432C2×D4—221no—
433C2×D4—442no—
434C2×D4—442no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—42no—
439C22×C4—82no—
440C22×C4—224no—
441C22×C4—222no—
442C22×C4—221no—
443C22×C4—224no—
444C22×C4—442no—
445C22×C4—442no—
446C22×C4—442no—
447C22×C4—442no—
448C22×C4C2×C4×D1112yes—
449C22×C4C2×D4412yes—
450C22×C4D4×D1112yes—
451C22×C4D4×D1112yes—
452C22×C4#434312yes—
453C22×C4#434312yes—
454C22×C4C2×C22⋊D1114yes—
455C22×C4C2×C22⋊D1111yescharacteristic
456C22×C4C23×D1111yescharacteristic
457M16—228no—
458C2×C8—112no—
459C2×C8—112no—
460C2×C8—114no—
461C2×C8—228no—
462C2×C8—221no—
463C2×C8—222no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—222no—
468C4⋊C4—22no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—22no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—42no—
475C4⋊C4—84no—
476C4⋊C4—2216no—
477C4⋊C4(C2×D11)⋊C418yes—
478C22⋊C4—42no—
479C22⋊C4—2216no—
480C22⋊C4(C2×D11)⋊C418yes—
481C42—42no—
482C42C2×C4×D1114yes—
483C42C2×D4414yes—
484C11#2120511yescharacteristic, complemented, Sylow
485C23—22no—
486C23—22no—
487C23—222no—
488C23—441no—
489C23—441no—
490C23—442no—
491C23—442no—
492C23C2×(C2×D11)⋊C412yes—
493C23#6699312yes—
494C23#6700012yes—
495C23C22×C22⋊D1111yescharacteristic
496Q8—224no—
497Q8—224no—
498Q8—222no—
499Q8—222no—
500Q8—442no—
501Q8—442no—
502Q8—441no—
503Q8—441no—
504Q8—448no—
505D4—222no—
506D4—222no—
507D4—448no—
508D4—441no—
509D4—441no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—44no—
517C2×C4—42no—
518C2×C4—84no—
519C2×C4—224no—
520C2×C4—222no—
521C2×C4—441no—
522C2×C4—442no—
523C2×C4—441no—
524C2×C4—442no—
525C2×C4—448no—
526C2×C4—448no—
527C2×C4#6694614yes—
528C2×C4#6694614yes—
529C2×C4#6694814yes—
530C2×C4#6694814yes—
531C2×C4C2×(C2×D11)⋊C418yes—
532C2×C4C2×(C2×D11)⋊C412yes—
533C2×C4#6699312yes—
534C2×C4#6700012yes—
535C2×C4C22×C4×D1111yescharacteristic
536C2×C4C22×D4411yescharacteristic
537C2×C4C2×D4×D1111yescharacteristic
538C2×C4C2×D4×D1111yescharacteristic
539C2×C4C2×#434311yescharacteristic
540C2×C4C2×#434311yescharacteristic
541C8—222no—
542C8—222no—
543C8—224no—
544C22—22no—
545C22—22no—
546C22—24no—
547C22—24no—
548C22—444no—
549C22—442no—
550C22—881no—
551C22—881no—
552C22—882no—
553C22#1062260114yes—
554C22C22×(C2×D11)⋊C411yescharacteristic
555C22C2×#6699311yescharacteristic
556C22C2×#6700011yescharacteristic
557C22#1062336712yes—
558C22#1062336912yes—
559C4—28no—
560C4—82no—
561C4—81no—
562C4—81no—
563C4—442no—
564C4—444no—
565C4#1062260114yes—
566C4C2×#6694611yescharacteristic
567C4C2×#6694611yescharacteristic
568C4C2×#6694811yescharacteristic
569C4C2×#6694811yescharacteristic
570C2—24no—
571C2—882no—
572C2C2×#1062260111yescharacteristic
573C2#1307714612yes—
574C2#1307898612yes—
575C2#1307908811yescharacteristic
576C2#1307910711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2317C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenter#2317D11
hypocenterC11#21205
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2317

Complements

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

NH ≅ G/Ntype
3. C2×#10622617C2semidirect
5. C22×#66874C2semidirect
6. C2×#10622610C2semidirect
7. #13069435C2semidirect
8. #13069430C2semidirect
9. #13069425C2semidirect
10. #13069417C2semidirect
11. C11×#2317C2semidirect
20. #10623057C4semidirect
97. #66928C2×C4semidirect
99. #66922C2×C4semidirect
203. #2317D11semidirect
484. C11#21205semidirect

Maximal subgroups

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

subgroupindex
C2×#106230572
C2×#106225792
C2×#106226172
C2×#106226152
C22×#668742
C2×#106226102
#130694352
#130694302
#130694252
#130694172
C11×#23172
#2120511