Finite Group Databasebeta

← #14755142

Subgroups — #14755142

Order 2816.

1802 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66995C211yesmaximal, characteristic
2C2×#10622579C211yesmaximal, characteristic
3C2×#10622838C211yesmaximal, characteristic, complemented
4#13071106C211yesmaximal, characteristic
5#13068971C214yesmaximal, complemented
6#13068957C214yesmaximal, complemented
7#13068335C211yesmaximal, characteristic, complemented
8#13068310C211yesmaximal, characteristic, complemented
9C22×C4×Q8×C11C211yesmaximal, characteristic, complemented
10C23×Q8×C11C2211yescharacteristic
11C22×#4339C2211yescharacteristic
12C2×C4×Q8×C11—24no—
13C2×C4×Q8×C11—24no—
14C2×C4×Q8×C11—22no—
15C2×C4×Q8×C11C2214yes—
16C22×C11×C4⋊C4—21no—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C42×C11—21no—
19C22×C42×C11C2211yescharacteristic
20C22×#4326C2212yes—
21C2×#66995—24no—
22C2×#66995—24no—
23C2×#66995C418yescomplemented
24C22×#4325C2212yes—
25C2×#66979C2211yescharacteristic
26C22×#4318C2211yescharacteristic
27C22×#4318C2211yescharacteristic
28#10622838—24no—
29C2×#66899C2214yes—
30#10622826—21no—
31#10622826—21no—
32C2×#66874C2212yes—
33#10622579—24no—
34C2×#66873C2212yes—
35#10622552C2212yes—
36C4×(C2×D11)⋊C4—22no—
37#10622542C2212yes—
38#10622167C2214yes—
39#10622162C2214yes—
40C22×Q8×C11—22no—
41C22×Q8×C11—21no—
42C22×Q8×C11—22no—
43C22×Q8×C11—22no—
44C22×Q8×C11C2×C414yes—
45C22×Q8×C11D414yes—
46C22×Q8×C11D414yes—
47C22×Q8×C11C2312yes—
48C23×C4×C11—21no—
49C23×C4×C11—21no—
50C23×C4×C11D411yescharacteristic
51C23×C4×C11D411yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C22×C22⋊D11—21no—
54C2×#4339—22no—
55C2×#4339—22no—
56C2×#4339—22no—
57C2×#4339—22no—
58C2×#4339—22no—
59C2×#4339C2×C414yes—
60C22×D44C2311yescharacteristic
61C22×C4×D11—21no—
62C22×Dic22C2311yescharacteristic
63C4×Q8×C11—216no—
64C4×Q8×C11—28no—
65C4×Q8×C11—28no—
66C2×C11×C4⋊C4—28no—
67C2×C11×C4⋊C4—24no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4D414yes—
71C2×C11×C4⋊C4C2312yes—
72C2×C42×C11—28no—
73C2×C42×C11—24no—
74C2×C42×C11—22no—
75C2×C42×C11—22no—
76C2×C42×C11D412yes—
77C2×C42×C11C2312yes—
78C2×C22⋊Dic11—21no—
79C2×#4326—24no—
80C2×#4326—24no—
81C2×#4326C2×C418yescomplemented
82#66995—232no—
83C2×#4325—24no—
84C2×#4325—24no—
85C2×#4325C2×C418yescomplemented
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4—22no—
88#66979—22no—
89#66979—22no—
90C2×C4⋊Dic11C2312yes—
91C2×C4×Dic11—21no—
92C2×#4318—22no—
93C2×#4318—22no—
94C2×#4318—22no—
95C2×#4318—22no—
96C2×#4318—22no—
97C2×#4318C2×C414yes—
98C22×C11⋊C8C2312yes—
99C22×C11⋊C8C2312yes—
100#66899—28no—
101C11⋊#95—22no—
102C11⋊#95—22no—
103#66874—24no—
104#66873—24no—
105#20926—111nomaximal, Sylow
106C24×C11C2×D411yescharacteristic
107C23×D11—21no—
108C2×Q8×C11—24no—
109C2×Q8×C11—28no—
110C2×Q8×C11—24no—
111C2×Q8×C11—24no—
112C2×Q8×C11—28no—
113C2×Q8×C11—28no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11C22⋊C4116yescomplemented
118C2×Q8×C11C22×C414yes—
119C2×Q8×C11C2×D414yes—
120C2×Q8×C11C2×D414yes—
121C22×C4×C11—24no—
122C22×C4×C11—22no—
123C22×C4×C11—24no—
124C22×C4×C11—24no—
125C22×C4×C11—22no—
126C22×C4×C11—24no—
127C22×C4×C11—22no—
128C22×C4×C11—24no—
129C22×C4×C11—22no—
130C22×C4×C11—42no—
131C22×C4×C11—44no—
132C22×C4×C11C22×C412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D412yes—
139C22×C4×C11#4112yes—
140C22×C4×C11#4112yes—
141C22×C4×C11C2411yescharacteristic
142C2×C22⋊D11—24no—
143C2×C22⋊D11—42no—
144C2×C22⋊D11—42no—
145C22×Dic11—21no—
146C22×Dic11—22no—
147#4339—28no—
148#4339—28no—
149#4339—44no—
150#4339—44no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44C22×C412yes—
157C2×C4×D11—24no—
158C2×C4×D11—42no—
159C2×C4×D11—42no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22C22×C412yes—
166C11×C4⋊C4—216no—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4C2×D414yes—
170C42×C11—216no—
171C42×C11—24no—
172C42×C11—22no—
173C42×C11—22no—
174C22⋊Dic11—42no—
175#4326—216no—
176#4325—216no—
177(C2×D11)⋊C4—44no—
178(C2×D11)⋊C4—44no—
179C4⋊Dic11—22no—
180C4⋊Dic11—22no—
181C4×Dic11—42no—
182#4318—28no—
183#4318—44no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8C22×C414yes—
190C22×#137—111no—
191C22×C4×Q8D1111yescharacteristic, complemented
192C2×#417—111no—
193C2×#419—111no—
194#2297—111no—
195#1880—114no—
196#1878—114no—
197#1736—111no—
198#1728—111no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11C4×D412yes—
202C23×C11#12012yes—
203C23×C11#12112yes—
204C23×C11C22×D411yescharacteristic
205C22×D11—22no—
206C22×D11—41no—
207C22×D11—41no—
208C22×D11—42no—
209C22×D11—42no—
210Q8×C11—24no—
211Q8×C11—24no—
212Q8×C11—24no—
213Q8×C11—216no—
214Q8×C11C2×C22⋊C418yes—
215C2×C4×C11—28no—
216C2×C4×C11—24no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—22no—
221C2×C4×C11—216no—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—44no—
227C2×C4×C11—48no—
228C2×C4×C11—44no—
229C2×C4×C11C2×C22⋊C414yes—
230C2×C4×C11C4×D414yes—
231C2×C4×C11C4×D412yes—
232C2×C4×C11#12012yes—
233C2×C4×C11#12114yes—
234C2×C4×C11#12112yes—
235C2×C4×C11#12314yes—
236C2×C4×C11#13714yescomplemented
237C2×C4×C11C23×C411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C22⋊D11—48no—
244C2×Dic11—22no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250D44—22no—
251D44—22no—
252D44—41no—
253D44—41no—
254C4×D11—48no—
255Dic22—22no—
256Dic22—22no—
257Dic22—41no—
258Dic22—41no—
259C11⋊C8—24no—
260C11⋊C8—42no—
261C22×#41—111no—
262C23×Q8C2×D1111yescharacteristic
263C2×#137—118no—
264C2×#137—224no—
265C2×#137—224no—
266C22×Q16—112no—
267C22×SD16—112no—
268C22×M16—111no—
269C22×M16—111no—
270C2×C4×Q8—24no—
271C2×C4×Q8—24no—
272C2×C4×Q8—22no—
273C2×C4×Q8C2×D1114yes—
274C2×#117—111no—
275C22×C4⋊C4—21no—
276C22×C4⋊C4C2×D1111yescharacteristic
277C22×C42—21no—
278C22×C42C2×D1111yescharacteristic
279#419—224no—
280#417—224no—
281C2×#103—114no—
282C2×#103—112no—
283C2×#102—112no—
284#391—112no—
285#390—112no—
286#386—221no—
287#386—221no—
288C4×C22⋊C4—222no—
289#340—114no—
290#336—114no—
291C22×C11—24no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11—24no—
295C22×C11#38614yes—
296C22×C11C2×C4×D411yescharacteristic
297C22×C11C2×#12011yescharacteristic
298C22×C11C2×#12111yescharacteristic
299C22×C11C2×#13712yes—
300C22×C11#57512yes—
301C2×D11—44no—
302C2×D11—42no—
303C2×D11—81no—
304C2×D11—81no—
305C2×D11—82no—
306C4×C11—24no—
307C4×C11—28no—
308C4×C11—42no—
309C4×C11—44no—
310C4×C11#38614yes—
311C4×C11C22×C22⋊C411yescharacteristic
312C4×C11C2×C4×D411yescharacteristic
313C4×C11C2×#12111yescharacteristic
314C4×C11C2×#12311yescharacteristic
315Dic11—42no—
316Dic11—82no—
317C2×#41—114no—
318C2×#41—222no—
319C2×#41—222no—
320C2×#41—222no—
321C2×#41—222no—
322C2×#41—222no—
323C22×Q8—22no—
324C22×Q8—22no—
325C22×Q8—22no—
326C22×Q8—21no—
327C22×Q8—111no—
328C22×Q8C4×D1114yes—
329C22×Q8D4414yes—
330C22×Q8C22⋊D1114yes—
331C22×Q8C22×D1112yes—
332C22×D4—111no—
333C22×D4—221no—
334C23×C4—21no—
335C23×C4—21no—
336C23×C4—221no—
337C23×C4C22⋊D1111yescharacteristic
338C23×C4C22⋊D1111yescharacteristic
339C23×C4C22×D1111yescharacteristic
340#137—2232no—
341C2×Q16—118no—
342C2×Q16—224no—
343C2×Q16—224no—
344C2×SD16—118no—
345C2×SD16—224no—
346C2×SD16—224no—
347C2×M16—114no—
348C2×M16—222no—
349C2×M16—222no—
350C2×M16—222no—
351C2×M16—222no—
352C2×M16—222no—
353C22×C8—112no—
354C22×C8—112no—
355C4×Q8—216no—
356C4×Q8—28no—
357C4×Q8—28no—
358#117—222no—
359#117—222no—
360C2×C4⋊C4—28no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—112no—
365C2×C4⋊C4C22⋊D1114yes—
366C2×C4⋊C4C22×D1112yes—
367C2×C22⋊C4—221no—
368C2×C22⋊C4—222no—
369C2×C22⋊C4—222no—
370C2×C42—28no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—24no—
374C2×C42—221no—
375C2×C42C22⋊D1112yes—
376C2×C42C22×D1112yes—
377#103—228no—
378#103—224no—
379#102—224no—
380#95—222no—
381#95—222no—
382C2×C11—24no—
383C2×C11C2×#38611yescharacteristic
384C2×C11C4×#13712yes—
385C2×C11#300411yescharacteristic
386C2×C11#300511yescharacteristic
387C2×C11#303712yes—
388D11—82no—
389C24—221no—
390C24C2×C22⋊D1111yescharacteristic
391#41—228no—
392#41—228no—
393#41—444no—
394#41—444no—
395C2×Q8—24no—
396C2×Q8—28no—
397C2×Q8—28no—
398C2×Q8—24no—
399C2×Q8—28no—
400C2×Q8—24no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—112no—
405C2×Q8—221no—
406C2×Q8—221no—
407C2×Q8—221no—
408C2×Q8—221no—
409C2×Q8—221no—
410C2×Q8(C2×D11)⋊C4116yescomplemented
411C2×Q8C2×C4×D1114yes—
412C2×Q8C2×D4414yes—
413C2×Q8C2×C22⋊D1114yes—
414C2×D4—112no—
415C2×D4—224no—
416C2×D4—221no—
417C2×D4—221no—
418C2×D4—221no—
419C2×D4—221no—
420C2×D4—221no—
421C2×D4—442no—
422C2×D4—442no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—22no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—24no—
429C22×C4—22no—
430C22×C4—24no—
431C22×C4—22no—
432C22×C4—42no—
433C22×C4—44no—
434C22×C4—221no—
435C22×C4—224no—
436C22×C4—222no—
437C22×C4—442no—
438C22×C4—442no—
439C22×C4C2×C4×D1112yes—
440C22×C4C2×D4412yes—
441C22×C4#433912yes—
442C22×C4#433912yes—
443C22×C4C2×C22⋊D1112yes—
444C22×C4C2×C22⋊D1112yes—
445C22×C4C2×C22⋊D1112yes—
446C22×C4C2×C22⋊D1111yescharacteristic
447C22×C4C2×C22⋊D1112yes—
448C22×C4C23×D1111yescharacteristic
449Q16—2216no—
450SD16—2216no—
451M16—228no—
452M16—444no—
453C2×C8—114no—
454C2×C8—222no—
455C2×C8—222no—
456C2×C8—222no—
457C2×C8—222no—
458C2×C8—222no—
459C4⋊C4—216no—
460C4⋊C4—24no—
461C4⋊C4—22no—
462C4⋊C4—222no—
463C4⋊C4—222no—
464C4⋊C4C2×C22⋊D1114yes—
465C22⋊C4—444no—
466C22⋊C4—442no—
467C22⋊C4—444no—
468C42—216no—
469C42—24no—
470C42—22no—
471C42—22no—
472C42—442no—
473C11#2092611yescharacteristic, complemented, Sylow
474C23—22no—
475C23—22no—
476C23—222no—
477C23—441no—
478C23—442no—
479C23—442no—
480C23—441no—
481C23C4×C22⋊D1112yes—
482C23#6698312yes—
483C23#6700612yes—
484C23C22×C22⋊D1111yescharacteristic
485Q8—24no—
486Q8—24no—
487Q8—24no—
488Q8—216no—
489Q8—222no—
490Q8—222no—
491Q8—441no—
492Q8—441no—
493Q8C2×(C2×D11)⋊C418yes—
494D4—222no—
495D4—222no—
496D4—448no—
497D4—441no—
498D4—441no—
499C2×C4—28no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—216no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—44no—
511C2×C4—48no—
512C2×C4—44no—
513C2×C4—222no—
514C2×C4—441no—
515C2×C4—441no—
516C2×C4—448no—
517C2×C4—442no—
518C2×C4—442no—
519C2×C4—442no—
520C2×C4C2×(C2×D11)⋊C414yes—
521C2×C4C4×C22⋊D1114yes—
522C2×C4C4×C22⋊D1112yes—
523C2×C4#6698214yes—
524C2×C4#6698314yes—
525C2×C4#6698312yes—
526C2×C4#6699514yescomplemented
527C2×C4#6700612yes—
528C2×C4C22×C4×D1111yescharacteristic
529C2×C4C22×D4411yescharacteristic
530C2×C4C2×#433911yescharacteristic
531C2×C4C2×#433911yescharacteristic
532C2×C4C22×C22⋊D1111yescharacteristic
533C2×C4C22×C22⋊D1111yescharacteristic
534C8—224no—
535C8—442no—
536C22—24no—
537C22—22no—
538C22—22no—
539C22—24no—
540C22—442no—
541C22—444no—
542C22—882no—
543C22—881no—
544C22—881no—
545C22#1062282614yes—
546C22C2×C4×C22⋊D1111yescharacteristic
547C22C2×#6698311yescharacteristic
548C22C2×#6699512yes—
549C22#1062335312yes—
550C22C2×#6700611yescharacteristic
551C4—24no—
552C4—28no—
553C4—42no—
554C4—44no—
555C4—442no—
556C4—882no—
557C4#1062282614yes—
558C4C22×(C2×D11)⋊C411yescharacteristic
559C4C2×C4×C22⋊D1111yescharacteristic
560C4C2×#6698211yescharacteristic
561C4C2×#6698311yescharacteristic
562C2—24no—
563C2—882no—
564C2C2×#1062282611yescharacteristic
565C2C4×#6699512yes—
566C2#1307785011yescharacteristic
567C2#1307785811yescharacteristic
568C2#1307808812yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C4×Q8×C11C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenterC22×C4×Q8D11
hypocenterC11#20926
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
3. C2×#10622838C2semidirect
5. #13068971C2semidirect
6. #13068957C2semidirect
7. #13068335C2semidirect
8. #13068310C2semidirect
9. C22×C4×Q8×C11C2semidirect
23. C2×#66995C4semidirect
81. C2×#4326C2×C4semidirect
85. C2×#4325C2×C4semidirect
117. C2×Q8×C11C22⋊C4semidirect
191. C22×C4×Q8D11semidirect
236. C2×C4×C11#137semidirect
410. C2×Q8(C2×D11)⋊C4semidirect
473. C11#20926semidirect
526. C2×C4#66995semidirect

Maximal subgroups

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

subgroupindex
C22×#669952
C2×#106225792
C2×#106228382
#130711062
#130689712
#130689572
#130683352
#130683102
C22×C4×Q8×C112
#2092611