Finite Group Databasebeta

← #14759724

Subgroups — #14759724

Order 2816.

1322 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622859C211yesmaximal, characteristic
2C4×#67004C212yesmaximal, complemented
3#13071332C211yesmaximal, characteristic, complemented
4#13069009C211yesmaximal, characteristic, complemented
5#13068985C212yesmaximal, complemented
6#13068849C212yesmaximal, complemented
7#13068831C211yesmaximal, characteristic, complemented
8#13068575C211yesmaximal, characteristic
9#13068426C212yesmaximal, complemented
10C4×#66900C211yesmaximal, characteristic, complemented
11C4×C11×2−1+4C211yesmaximal, characteristic
12C2×C11×2−1+4C2211yescharacteristic
13C11×#520—22no—
14C11×#520—22no—
15C11×#520C2212yes—
16C11×#519—22no—
17C11×#519C2211yescharacteristic
18C4×C11×#41—22no—
19C4×C11×#41—22no—
20C4×C11×#41C2212yes—
21C2×C4×Q8×C11—22no—
22C2×C4×Q8×C11C2211yescharacteristic
23C2×#67004C2212yes—
24C2×#66997C2211yescharacteristic
25C2×C4×Dic22C2211yescharacteristic
26#10622859C418yescomplemented
27C2×#66901C2212yes—
28C2×#66901C2212yes—
29#10622845C2212yes—
30#10622843C2211yescharacteristic
31C2×#66900C2211yescharacteristic
32C2×#66900C2211yescharacteristic
33#10622643—22no—
34C4×#4326—22no—
35#10622631—22no—
36C4×#4324—22no—
37#10622617C2212yes—
38#10622608C2212yes—
39#10622591—22no—
40#10622590C2211yescharacteristic
41#10622587C2211yescharacteristic
42#10622546—22no—
43#10622545C2211yescharacteristic
44C4×#4318C2212yes—
45#10622170C2212yes—
46#10622170C2212yes—
47#10622168C2212yes—
48C11×2−1+4—24no—
49C11×2−1+4—22no—
50C11×2−1+4C2×C414yes—
51C2×C11×#41—22no—
52C2×C11×#41—22no—
53C2×C11×#41C2312yes—
54C22×Q8×C11—22no—
55C22×Q8×C11C2311yescharacteristic
56C22×Dic22C2311yescharacteristic
57C4×Q8×C11—22no—
58C4×Q8×C11—24no—
59C4×Q8×C11—22no—
60C4×Q8×C11—22no—
61C4×Q8×C11—22no—
62C4×Q8×C11—22no—
63C4×Q8×C11—22no—
64C4×Q8×C11—22no—
65C4×Q8×C11D412yes—
66C4×Q8×C11D412yes—
67C4×D4×C11—22no—
68C4×D4×C11—24no—
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C4×D4×C11—24no—
73C4×D4×C11—22no—
74C4×D4×C11D412yes—
75C4×D4×C11D412yes—
76C11×#117—24no—
77C11×#117—24no—
78C11×#117—22no—
79C11×#117—22no—
80C11×#117—22no—
81C11×#117C2312yes—
82C2×C11×C4⋊C4—24no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4D412yes—
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C42×C11—24no—
87C2×C42×C11—22no—
88C2×C42×C11D412yes—
89C2×C42×C11C2311yescharacteristic
90#67004—24no—
91#67004C2×C418yescomplemented
92#66997—22no—
93#66997C2×C414yescomplemented
94C2×#4326—22no—
95C2×#4324—22no—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×Dic11⋊C4—22no—
98C2×Dic11⋊C4—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11C2311yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C2×#4318C2312yes—
103C2×#4318C2312yes—
104C4×Dic22—22no—
105C4×Dic22—22no—
106#66901—24no—
107#66901C2×C418yescomplemented
108#66900—22no—
109#66900C2×C414yescomplemented
110#66899—22no—
111#66896—22no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—22no—
115C11⋊#95—22no—
116C11⋊#95—22no—
117#66874—22no—
118#66874—22no—
119#66872—22no—
120#66871—22no—
121#66867—22no—
122C4×C11⋊C8—22no—
123#21476—111nomaximal, Sylow
124C11×#41—28no—
125C11×#41—28no—
126C11×#41—28no—
127C11×#41—28no—
128C11×#41—22no—
129C11×#41—22no—
130C11×#41C22×C414yes—
131C11×#41#4114yes—
132C2×Q8×C11—22no—
133C2×Q8×C11—28no—
134C2×Q8×C11—28no—
135C2×Q8×C11—22no—
136C2×Q8×C11—22no—
137C2×Q8×C11C22×C412yes—
138C2×Q8×C11C2×D412yes—
139C2×Q8×C11#4112yes—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11C2×D412yes—
143C22×C4×C11—24no—
144C22×C4×C11—22no—
145C22×C4×C11—24no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C2×Dic22—22no—
158C2×Dic22—22no—
159C2×Dic22—21no—
160C2×Dic22C22×C412yes—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—24no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4C2×D412yes—
169C11×C4⋊C4C2×D412yes—
170C11×C22⋊C4—24no—
171C11×C22⋊C4—22no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—22no—
174C42×C11—24no—
175C42×C11—24no—
176C42×C11—22no—
177C42×C11—22no—
178C42×C11—22no—
179C42×C11—22no—
180C42×C11—22no—
181C42×C11C2×D412yes—
182C42×C11C2×D412yes—
183#4326—28no—
184#4324—28no—
185C4⋊Dic11—22no—
186Dic11⋊C4—28no—
187Dic11⋊C4—41no—
188Dic11⋊C4—41no—
189C4×Dic11—21no—
190C4×Dic11—22no—
191C4×Dic11—42no—
192C4×Dic11C22×C412yes—
193#4318—22no—
194#4318—22no—
195#4318—22no—
196#4318C22×C414yes—
197C2×C11⋊C8—22no—
198C2×C11⋊C8—22no—
199C4×2−1+4D1111yescharacteristic
200C2×#456—111no—
201C4×#137—112no—
202#2327—111no—
203#1886—111no—
204#1882—112no—
205#1860—112no—
206#1857—111no—
207#1793—111no—
208#1759—112no—
209C4×#101—111no—
210C23×C11—22no—
211C23×C11C22×D411yescharacteristic
212Q8×C11—28no—
213Q8×C11—24no—
214Q8×C11—22no—
215Q8×C11—24no—
216Q8×C11C4×D414yes—
217D4×C11—28no—
218D4×C11—24no—
219D4×C11—24no—
220D4×C11—22no—
221D4×C11C4×D414yes—
222C2×C4×C11—216no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—44no—
234C2×C4×C11—42no—
235C2×C4×C11—82no—
236C2×C4×C11—84no—
237C2×C4×C11C4×D414yes—
238C2×C4×C11#12012yes—
239C2×C4×C11#12011yescharacteristic
240C2×C4×C11#12011yescharacteristic
241C2×C4×C11C23×C411yescharacteristic
242C2×C4×C11C22×D412yes—
243C2×C4×C11C2×#4112yes—
244C2×C4×C11C2×#4111yescharacteristic
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—42no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256Dic22—24no—
257Dic22—42no—
258C11⋊C8—24no—
259C11⋊C8—42no—
260C2×2−1+4C2×D1111yescharacteristic
261C2×#137—112no—
262C2×C4⋊Q8—111no—
263#520—22no—
264#520—22no—
265#520C2×D1112yes—
266#519—22no—
267#519C2×D1111yescharacteristic
268C4×#41—22no—
269C4×#41—22no—
270C4×#41C2×D1112yes—
271C2×C4×Q8—22no—
272C2×C4×Q8—111no—
273C2×C4×Q8C2×D1111yescharacteristic
274#456—118no—
275#441—222no—
276#440—222no—
277C4×Q16—222no—
278C4×SD16—222no—
279#428—112no—
280C2×#104—112no—
281C2×#104—112no—
282#419—112no—
283#417—112no—
284C2×#101—111no—
285C2×#101—111no—
286C4×M16—112no—
287#391—111no—
288#391—111no—
289#387—222no—
290#387—222no—
291#382—111no—
292#376—111no—
293#343—112no—
294#339—112no—
295#339—112no—
296C22×C11—21no—
297C22×C11—21no—
298C22×C11—24no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11C2×C4×D411yescharacteristic
302C22×C11C2×#12011yescharacteristic
303C22×C11#52511yescharacteristic
304C4×C11—21no—
305C4×C11—21no—
306C4×C11—22no—
307C4×C11—24no—
308C4×C11—24no—
309C4×C11—42no—
310C4×C11—42no—
311C4×C11—42no—
312C4×C11C2×C4×D412yes—
313C4×C11#52512yes—
314Dic11—42no—
315Dic11—42no—
316Dic11—81no—
317Dic11—81no—
3182−1+4—24no—
3192−1+4—22no—
3202−1+4C4×D1114yes—
321C2×#41—22no—
322C2×#41—22no—
323C2×#41C22×D1112yes—
324C22×Q8—22no—
325C22×Q8—111no—
326C22×Q8C22×D1111yescharacteristic
327#137—118no—
328#137—224no—
329C2×Q16—222no—
330C2×SD16—222no—
331C2×M16—112no—
332C2×M16—112no—
333C4⋊Q8—114no—
334C4⋊Q8—222no—
335C4×Q8—22no—
336C4×Q8—24no—
337C4×Q8—22no—
338C4×Q8—22no—
339C4×Q8—22no—
340C4×Q8—22no—
341C4×Q8—22no—
342C4×Q8—22no—
343C4×Q8—222no—
344C4×Q8—222no—
345C4×Q8C22⋊D1112yes—
346C4×Q8C22⋊D1112yes—
347C4×D4—22no—
348C4×D4—24no—
349C4×D4—22no—
350C4×D4—22no—
351C4×D4—22no—
352C4×D4—24no—
353C4×D4—22no—
354C4×D4C22⋊D1112yes—
355C4×D4C22⋊D1112yes—
356#117—24no—
357#117—24no—
358#117—22no—
359#117—22no—
360#117—22no—
361#117C22×D1112yes—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—222no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4C22⋊D1112yes—
368C2×C4⋊C4C22×D1111yescharacteristic
369C2×C42—24no—
370C2×C42—22no—
371C2×C42—111no—
372C2×C42—111no—
373C2×C42—221no—
374C2×C42C22⋊D1112yes—
375C2×C42C22×D1111yescharacteristic
376#107—222no—
377#106—222no—
378#104—118no—
379#104—224no—
380#103—222no—
381#103—222no—
382#103—222no—
383#102—222no—
384#101—114no—
385#101—222no—
386#97—222no—
387C4×C8—222no—
388#95—221no—
389#95—221no—
390#95—222no—
391#95—222no—
392#95—222no—
393C2×C11—21no—
394C2×C11—21no—
395C2×C11—44no—
396C2×C11C4×#12011yescharacteristic
397C2×C11#302011yescharacteristic
398C2×C11#302211yescharacteristic
399#41—28no—
400#41—28no—
401#41—28no—
402#41—28no—
403#41—22no—
404#41—22no—
405#41C2×C4×D1114yes—
406#41#433914yes—
407C2×Q8—22no—
408C2×Q8—28no—
409C2×Q8—28no—
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8—112no—
413C2×Q8—221no—
414C2×Q8—222no—
415C2×Q8—222no—
416C2×Q8C2×C4×D1112yes—
417C2×Q8#433912yes—
418C2×Q8C2×C22⋊D1112yes—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4C2×C22⋊D1112yes—
422C22×C4—24no—
423C22×C4—22no—
424C22×C4—24no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—221no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—221no—
431C22×C4C2×C22⋊D1112yes—
432C22×C4C2×C22⋊D1112yes—
433C22×C4C2×C22⋊D1111yescharacteristic
434C22×C4C2×C22⋊D1111yescharacteristic
435C22×C4C23×D1111yescharacteristic
436Q16—228no—
437SD16—228no—
438M16—114no—
439M16—222no—
440M16—222no—
441M16—222no—
442C2×C8—222no—
443C2×C8—222no—
444C4⋊C4—24no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—24no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—228no—
452C4⋊C4—222no—
453C4⋊C4—441no—
454C4⋊C4—441no—
455C4⋊C4C2×C22⋊D1112yes—
456C4⋊C4C2×C22⋊D1112yes—
457C22⋊C4—24no—
458C22⋊C4—22no—
459C22⋊C4—22no—
460C22⋊C4—22no—
461C42—24no—
462C42—24no—
463C42—22no—
464C42—22no—
465C42—22no—
466C42—22no—
467C42—22no—
468C42—112no—
469C42—221no—
470C42—222no—
471C42—442no—
472C42C2×C22⋊D1112yes—
473C42C2×C22⋊D1112yes—
474C11#2147611yescharacteristic, complemented, Sylow
475C23—22no—
476C23C22×C22⋊D1111yescharacteristic
477Q8—28no—
478Q8—24no—
479Q8—24no—
480Q8—22no—
481Q8—224no—
482Q8—442no—
483Q8C4×C22⋊D1114yes—
484D4—28no—
485D4—24no—
486D4—24no—
487D4—22no—
488D4C4×C22⋊D1114yes—
489C2×C4—216no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—44no—
501C2×C4—42no—
502C2×C4—82no—
503C2×C4—84no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—441no—
507C2×C4—441no—
508C2×C4—441no—
509C2×C4—441no—
510C2×C4—441no—
511C2×C4—441no—
512C2×C4—442no—
513C2×C4—441no—
514C2×C4—441no—
515C2×C4C4×C22⋊D1114yes—
516C2×C4#6700611yescharacteristic
517C2×C4#6700611yescharacteristic
518C2×C4#6700612yes—
519C2×C4C22×C4×D1111yescharacteristic
520C2×C4C2×#433912yes—
521C2×C4C2×#433911yescharacteristic
522C2×C4C22×C22⋊D1112yes—
523C8—224no—
524C8—442no—
525C22—21no—
526C22—21no—
527C22—24no—
528C22—42no—
529C22—42no—
530C22C2×C4×C22⋊D1111yescharacteristic
531C22#1062332211yescharacteristic
532C22C2×#6700611yescharacteristic
533C4—24no—
534C4—24no—
535C4—21no—
536C4—21no—
537C4—22no—
538C4—42no—
539C4—42no—
540C4—42no—
541C4—442no—
542C4—442no—
543C4—881no—
544C4—881no—
545C4C2×C4×C22⋊D1112yes—
546C4#1062332212yes—
547C2—21no—
548C2—21no—
549C2—44no—
550C2C4×#6700611yescharacteristic
551C2#1307798011yescharacteristic
552C2#1307799511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×2−1+4C2
socleC22×C11C2×#120
prime radicalC2×C11×2−1+4C22
cosocleC22×C4×C11C24
hypercenterC4×2−1+4D11
hypocenterC11#21476
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×2−1+4

Complements

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

NH ≅ G/Ntype
2. C4×#67004C2semidirect
3. #13071332C2semidirect
4. #13069009C2semidirect
5. #13068985C2semidirect
6. #13068849C2semidirect
7. #13068831C2semidirect
9. #13068426C2semidirect
10. C4×#66900C2semidirect
26. #10622859C4semidirect
91. #67004C2×C4semidirect
93. #66997C2×C4semidirect
107. #66901C2×C4semidirect
109. #66900C2×C4semidirect
474. C11#21476semidirect

Maximal subgroups

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

subgroupindex
C2×#106228592
C4×#670042
#130713322
#130690092
#130689852
#130688492
#130688312
#130685752
#130684262
C4×#669002
C4×C11×2−1+42
#2147611