Finite Group Databasebeta

← #14757470

Subgroups — #14757470

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×#10623347C211yesmaximal, characteristic
2C2×#10622579C211yesmaximal, characteristic
3C2×#10622838C211yesmaximal, characteristic, complemented
4C2×#10622726C211yesmaximal, characteristic
5C2×#10622714C211yesmaximal, characteristic, complemented
6#13071240C211yesmaximal, characteristic, complemented
7#13069434C212yesmaximal, complemented
8#13069429C212yesmaximal, complemented
9#13069424C212yesmaximal, complemented
10#13069416C212yesmaximal, complemented
11C22×C11×#103C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C22×#4339C2211yescharacteristic
14C23×C8×C11C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16#10623347—24no—
17#10623347C418yescomplemented
18C2×#67000C2212yes—
19C2×#66999—22no—
20C2×#66997C2212yes—
21C2×#66982—22no—
22C2×#66979C2211yescharacteristic
23C2×#66979C2211yescharacteristic
24C22×#4318C2211yescharacteristic
25C2×C11×#103—24no—
26C2×C11×#103C2212yes—
27C2×C11×#103C2212yes—
28#10622838—24no—
29C2×#66899C2212yes—
30C2×#66899C2212yes—
31#10622823—22no—
32#10622726—24no—
33C2×#66885C2211yescharacteristic
34C2×#66885C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37#10622714—24no—
38C2×#66879C2212yes—
39C2×C8×Dic11C2212yes—
40#10622590C2212yes—
41#10622589C2212yes—
42#10622586—22no—
43C2×#66874C2212yes—
44#10622579—24no—
45C2×#66873C2212yes—
46C22×Q8×C11—21no—
47C22×Q8×C11—22no—
48C22×Q8×C11—22no—
49C22×Q8×C11—22no—
50C22×Q8×C11—22no—
51C22×Q8×C11—22no—
52C22×Q8×C11C2×C414yes—
53C22×Q8×C11C2312yes—
54C23×C4×C11—21no—
55C23×C4×C11—21no—
56C23×C4×C11C2311yescharacteristic
57C22×C22⋊D11—21no—
58C2×#4339—22no—
59C2×#4339—22no—
60C2×#4339—22no—
61C2×#4339—22no—
62C2×#4339—22no—
63C2×#4339C2×C414yes—
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C22×Dic22C2311yescharacteristic
67C22×C8×C11—22no—
68C22×C8×C11—22no—
69C22×C8×C11D414yes—
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4C2312yes—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11D412yes—
78#67000—24no—
79#67000C2×C418yescomplemented
80#66999—216no—
81#66997—24no—
82#66997C2×C418yescomplemented
83#66982—216no—
84C2×(C2×D11)⋊C4—24no—
85#66979—22no—
86#66979—22no—
87#66979C2×C414yes—
88#66979D414yes—
89C2×C4⋊Dic11D412yes—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×Dic11⋊C4—24no—
93C2×Dic11⋊C4—24no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11C2312yes—
96C2×#4318—22no—
97C2×#4318—22no—
98C2×#4318D414yes—
99C22×C11⋊C8C2312yes—
100C11×#103—24no—
101C11×#103—24no—
102#66899—24no—
103#66899—24no—
104C11⋊#95—24no—
105#66885—22no—
106#66885—22no—
107#66880—22no—
108#66880—22no—
109#66879—24no—
110C8×Dic11—24no—
111#66874—24no—
112#66873—24no—
113#21205—111nomaximal, Sylow
114C24×C11C2×D411yescharacteristic
115C23×D11—21no—
116C2×Q8×C11—24no—
117C2×Q8×C11—22no—
118C2×Q8×C11—28no—
119C2×Q8×C11—28no—
120C2×Q8×C11—22no—
121C2×Q8×C11—22no—
122C2×Q8×C11—22no—
123C2×Q8×C11—22no—
124C2×Q8×C11—44no—
125C2×Q8×C11—44no—
126C2×Q8×C11—42no—
127C2×Q8×C11—42no—
128C2×Q8×C11C22×C414yes—
129C22×C4×C11—24no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—42no—
133C22×C4×C11—42no—
134C22×C4×C11—42no—
135C22×C4×C11—82no—
136C22×C4×C11C22×C412yes—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D412yes—
141C22×C4×C11#4112yes—
142C22×C4×C11#4112yes—
143C22×C4×C11C2411yescharacteristic
144C2×C22⋊D11—24no—
145C2×C22⋊D11—42no—
146C2×C22⋊D11—42no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11C2×D414yes—
151#4339—28no—
152#4339—28no—
153#4339—44no—
154#4339—44no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44C22×C412yes—
161C2×C4×D11—24no—
162C2×C4×D11—42no—
163C2×C4×D11—42no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22C22×C412yes—
170C2×C8×C11—28no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11C2×D412yes—
176C2×C8×C11C2×D412yes—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—42no—
180C22⋊Dic11—42no—
181C22⋊Dic11C22⋊C418yes—
182(C2×D11)⋊C4—216no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11C22⋊C418yes—
188Dic11⋊C4—216no—
189Dic11⋊C4—84no—
190C4×Dic11—42no—
191C4×Dic11C22×C414yes—
192C4×Dic11C2×D414yes—
193#4318—28no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8C2×D414yes—
197C2×#536—111no—
198C2×#417—111no—
199C2×#419—111no—
200C2×#416—111no—
201C22×#103D1111yescharacteristic, complemented
202C2×#405—111no—
203#2317—111no—
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—
219Q8×C11—24no—
220Q8×C11—24no—
221Q8×C11—42no—
222Q8×C11—42no—
223Q8×C11—48no—
224C2×C4×C11—24no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—48no—
228C2×C4×C11—42no—
229C2×C4×C11—44no—
230C2×C4×C11—84no—
231C2×C4×C11C2×C22⋊C412yes—
232C2×C4×C11C4×D414yes—
233C2×C4×C11C4×D414yes—
234C2×C4×C11#12114yes—
235C2×C4×C11#12114yes—
236C2×C4×C11#12412yes—
237C2×C4×C11#12712yes—
238C2×C4×C11C23×C411yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C22⋊D11—48no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—22no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11C2×C22⋊C418yes—
255D44—22no—
256D44—22no—
257D44—41no—
258D44—41no—
259C4×D11—48no—
260Dic22—22no—
261Dic22—22no—
262Dic22—41no—
263Dic22—41no—
264C8×C11—22no—
265C8×C11—22no—
266C11⋊C8—24no—
267C22×#41—111no—
268C23×Q8C2×D1111yescharacteristic
269C22×M16—111no—
270C23×C8C2×D1111yescharacteristic
271#536—118no—
272#536—224no—
273C2×C4⋊Q8—112no—
274C2×#124—112no—
275C2×#123—222no—
276C2×C22⋊Q8—222no—
277C2×#117—111no—
278C2×#117—111no—
279C22×C4⋊C4C2×D1111yescharacteristic
280#419—224no—
281#417—224no—
282#416—224no—
283C2×#103—24no—
284C2×#103—112no—
285C2×#103—112no—
286C2×#103—111no—
287C2×#103—111no—
288C2×#103—112no—
289C2×#103C2×D1112yes—
290C2×#103C2×D1112yes—
291C2×#102—111no—
292C2×#102—111no—
293C2×#102—112no—
294#405—224no—
295C2×#97—112no—
296C2×C4×C8—112no—
297#389—222no—
298#385—222no—
299#384—112no—
300#382—112no—
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—44no—
317C4×C11—82no—
318C4×C11#39014yes—
319C4×C11C2×C4×D411yescharacteristic
320C4×C11C2×C4×D411yescharacteristic
321C4×C11C2×#12111yescharacteristic
322C4×C11C2×#12111yescharacteristic
323Dic11—28no—
324Dic11—42no—
325Dic11—81no—
326Dic11—81no—
327C2×#41—114no—
328C2×#41—222no—
329C2×#41—222no—
330C2×#41—222no—
331C2×#41—222no—
332C2×#41—222no—
333C22×Q8—21no—
334C22×Q8—22no—
335C22×Q8—22no—
336C22×Q8—22no—
337C22×Q8—22no—
338C22×Q8—22no—
339C22×Q8—111no—
340C22×Q8C4×D1114yes—
341C22×Q8C22×D1112yes—
342C22×D4—111no—
343C22×D4—221no—
344C23×C4—21no—
345C23×C4—21no—
346C23×C4—221no—
347C23×C4C22×D1111yescharacteristic
348C2×M16—114no—
349C2×M16—222no—
350C2×M16—222no—
351C22×C8—22no—
352C22×C8—22no—
353C22×C8—112no—
354C22×C8C22⋊D1114yes—
355C22×C8C22×D1111yescharacteristic
356C22×C8C22×D1111yescharacteristic
357C4⋊Q8—118no—
358C4⋊Q8—224no—
359#124—118no—
360#124—224no—
361#123—2216no—
362C22⋊Q8—2216no—
363#117—114no—
364#117—114no—
365#117—222no—
366#117—222no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—112no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—224no—
374C2×C4⋊C4—224no—
375C2×C4⋊C4C22×D1112yes—
376C2×C22⋊C4—112no—
377C2×C22⋊C4—224no—
378C2×C22⋊C4—221no—
379C2×C42—112no—
380C2×C42—221no—
381#103—24no—
382#103—24no—
383#103—224no—
384#103—224no—
385#103—224no—
386#103—222no—
387#103—222no—
388#102—224no—
389#102—222no—
390#102—222no—
391#97—224no—
392C4×C8—224no—
393#95—224no—
394C2×C11—24no—
395C2×C11C2×#39011yescharacteristic
396C2×C11#289812yes—
397C2×C11#313712yes—
398C2×C11#315411yescharacteristic
399C2×C11#315611yescharacteristic
400D11—82no—
401C24—221no—
402C24D4×D1111yescharacteristic
403#41—228no—
404#41—228no—
405#41—444no—
406#41—444no—
407C2×Q8—24no—
408C2×Q8—22no—
409C2×Q8—28no—
410C2×Q8—28no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—44no—
416C2×Q8—42no—
417C2×Q8—44no—
418C2×Q8—42no—
419C2×Q8—112no—
420C2×Q8—221no—
421C2×Q8—221no—
422C2×Q8—221no—
423C2×Q8—221no—
424C2×Q8—221no—
425C2×Q8C2×C4×D1114yes—
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—24no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—82no—
442C22×C4—114no—
443C22×C4—221no—
444C22×C4—224no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4—442no—
448C22×C4—442no—
449C22×C4C2×C4×D1112yes—
450C22×C4#433912yes—
451C22×C4D4×D1111yescharacteristic
452C22×C4D4×D1112yes—
453C22×C4D4×D1112yes—
454C22×C4#434112yes—
455C22×C4C2×C22⋊D1112yes—
456C22×C4C23×D1111yescharacteristic
457M16—228no—
458C2×C8—28no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—114no—
464C2×C8—222no—
465C2×C8—222no—
466C2×C8C2×C22⋊D1112yes—
467C2×C8C2×C22⋊D1112yes—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—42no—
471C4⋊C4—118no—
472C4⋊C4—2216no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—884no—
478C22⋊C4—118no—
479C22⋊C4—2216no—
480C22⋊C4—442no—
481C42—114no—
482C42—114no—
483C42—442no—
484C11#2120511yescharacteristic, complemented, Sylow
485C23—22no—
486C23—22no—
487C23—222no—
488C23—441no—
489C23—442no—
490C23—442no—
491C23—441no—
492C23C22⋊C4×D1112yes—
493C23#6693812yes—
494C23#6699312yes—
495C23C2×D4×D1111yescharacteristic
496Q8—24no—
497Q8—24no—
498Q8—42no—
499Q8—42no—
500Q8—48no—
501Q8—222no—
502Q8—222no—
503Q8—441no—
504Q8—441no—
505D4—222no—
506D4—222no—
507D4—448no—
508D4—441no—
509D4—441no—
510C2×C4—24no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—48no—
514C2×C4—44no—
515C2×C4—42no—
516C2×C4—84no—
517C2×C4—118no—
518C2×C4—224no—
519C2×C4—224no—
520C2×C4—222no—
521C2×C4—441no—
522C2×C4—441no—
523C2×C4—448no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4C22⋊C4×D1112yes—
529C2×C4(C22⋊D11)⋊C414yes—
530C2×C4#6693714yes—
531C2×C4#6693812yes—
532C2×C4C4×C22⋊D1114yes—
533C2×C4#6699214yes—
534C2×C4#6699312yes—
535C2×C4C22×C4×D1111yescharacteristic
536C2×C4C2×#433911yescharacteristic
537C2×C4C2×D4×D1111yescharacteristic
538C2×C4C2×D4×D1111yescharacteristic
539C2×C4C2×#434111yescharacteristic
540C2×C4C22×C22⋊D1111yescharacteristic
541C8—22no—
542C8—22no—
543C8—224no—
544C22—22no—
545C22—22no—
546C22—24no—
547C22—24no—
548C22—444no—
549C22—442no—
550C22—881no—
551C22—881no—
552C22—882no—
553C22#1062257014yes—
554C22C2×C22⋊C4×D1111yescharacteristic
555C22C2×#6693811yescharacteristic
556C22#1062329312yes—
557C22#1062329712yes—
558C22C2×#6699311yescharacteristic
559C4—44no—
560C4—82no—
561C4—228no—
562C4—442no—
563C4—881no—
564C4—881no—
565C4#1062257014yes—
566C4C2×(C22⋊D11)⋊C411yescharacteristic
567C4C2×#6693711yescharacteristic
568C4C2×C4×C22⋊D1111yescharacteristic
569C4C2×#6699211yescharacteristic
570C2—24no—
571C2—882no—
572C2C2×#1062257011yescharacteristic
573C2#1307714412yes—
574C2#1307897912yes—
575C2#1307908611yescharacteristic
576C2#1307910511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#103C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenterC22×#103D11
hypocenterC11#21205
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
3. C2×#10622838C2semidirect
5. C2×#10622714C2semidirect
6. #13071240C2semidirect
7. #13069434C2semidirect
8. #13069429C2semidirect
9. #13069424C2semidirect
10. #13069416C2semidirect
11. C22×C11×#103C2semidirect
17. #10623347C4semidirect
79. #67000C2×C4semidirect
82. #66997C2×C4semidirect
201. C22×#103D11semidirect
484. C11#21205semidirect

Maximal subgroups

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

subgroupindex
C2×#106233472
C2×#106225792
C2×#106228382
C2×#106227262
C2×#106227142
#130712402
#130694342
#130694292
#130694242
#130694162
C22×C11×#1032
#2120511