Finite Group Databasebeta

← #14660267

Subgroups — #14660267

Order 2816.

1634 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66982C211yesmaximal, characteristic
2C22×#66870C212yesmaximal
3C2×#10622824C211yesmaximal, characteristic, complemented
4C2×#10622165C212yesmaximal, complemented
5C2×C11×#381C211yesmaximal, characteristic, complemented
6C24×C4×C11C2211yescharacteristic
7C23×C22⋊D11C2211yescharacteristic
8C22×C11×C22⋊C4C2212yes—
9C22×C22⋊Dic11C2212yes—
10C22×C22⋊Dic11C2211yescharacteristic
11C2×#66982—22no—
12C2×#66982—22no—
13C2×#66982—24no—
14C2×#66982—24no—
15C22×(C2×D11)⋊C4C412yescomplemented
16C22×Dic11⋊C4C412yescomplemented
17C11×#381—24no—
18C2×C11×#95—22no—
19#10622824—24no—
20C2×C11⋊#95—22no—
21C2×#66870—24no—
22C2×#66870—24no—
23C2×#66870—24no—
24#10622165—24no—
25C25×C11C2311yescharacteristic
26C24×D11C2×C411yescharacteristic
27C23×C4×C11—22no—
28C23×C4×C11—22no—
29C23×C4×C11—22no—
30C23×C4×C11—22no—
31C23×C4×C11—22no—
32C23×C4×C11—22no—
33C23×C4×C11—22no—
34C23×C4×C11C2×C412yes—
35C23×C4×C11D412yes—
36C23×C4×C11D412yes—
37C22×C22⋊D11—21no—
38C22×C22⋊D11—22no—
39C22×C22⋊D11—21no—
40C22×C22⋊D11—22no—
41C22×C22⋊D11—22no—
42C22×C22⋊D11—22no—
43C22×C22⋊D11—22no—
44C22×C22⋊D11D414yes—
45C23×Dic11—22no—
46C23×Dic11C2×C411yescharacteristic
47C23×Dic11C2×C412yes—
48C2×C11×C22⋊C4—22no—
49C2×C11×C22⋊C4—22no—
50C2×C11×C22⋊C4—22no—
51C2×C11×C22⋊C4—22no—
52C2×C11×C22⋊C4—22no—
53C2×C11×C22⋊C4D414yes—
54C2×C22⋊Dic11—21no—
55C2×C22⋊Dic11—22no—
56C2×C22⋊Dic11—21no—
57C2×C22⋊Dic11—22no—
58C2×C22⋊Dic11—22no—
59C2×C22⋊Dic11—22no—
60C2×C22⋊Dic11—22no—
61C2×C22⋊Dic11—22no—
62C2×C22⋊Dic11D414yes—
63C2×C22⋊Dic11D414yes—
64#66982—216no—
65#66982—216no—
66C2×(C2×D11)⋊C4—24no—
67C2×(C2×D11)⋊C4—24no—
68C2×(C2×D11)⋊C4—24no—
69C2×Dic11⋊C4—24no—
70C2×Dic11⋊C4—24no—
71C2×Dic11⋊C4—24no—
72C11×#95—28no—
73C11⋊#95—28no—
74#66870—216no—
75#10966—111nomaximal, Sylow
76C24×C11—44no—
77C24×C11C22×C411yescharacteristic
78C24×C11C2×D411yescharacteristic
79C24×C11C2×D411yescharacteristic
80C24×C11C2×D412yes—
81C24×C11C2×D412yes—
82C24×C11C2×D412yes—
83C24×C11C2×D412yes—
84C24×C11#4112yes—
85C24×C11#4112yes—
86C23×D11—21no—
87C23×D11—21no—
88C23×D11—22no—
89C23×D11—22no—
90C23×D11—44no—
91C23×D11C22⋊C412yes—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—24no—
95C22×C4×C11—24no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—24no—
99C22×C4×C11—24no—
100C22×C4×C11—24no—
101C22×C4×C11—24no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—24no—
105C22×C4×C11—42no—
106C22×C4×C11—42no—
107C22×C4×C11—42no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11—42no—
112C22×C4×C11—42no—
113C22×C4×C11—48no—
114C22×C4×C11—42no—
115C22×C4×C11—42no—
116C22×C4×C11C22⋊C414yes—
117C2×C22⋊D11—24no—
118C2×C22⋊D11—24no—
119C2×C22⋊D11—24no—
120C2×C22⋊D11—24no—
121C2×C22⋊D11—24no—
122C2×C22⋊D11—24no—
123C2×C22⋊D11—41no—
124C2×C22⋊D11—41no—
125C2×C22⋊D11—42no—
126C2×C22⋊D11—42no—
127C2×C22⋊D11—42no—
128C2×C22⋊D11—42no—
129C2×C22⋊D11—41no—
130C2×C22⋊D11—41no—
131C2×C22⋊D11—42no—
132C2×C22⋊D11—42no—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—24no—
140C22×Dic11—44no—
141C22×Dic11—48no—
142C22×Dic11—42no—
143C22×Dic11—42no—
144C22×Dic11C22⋊C412yes—
145C22×Dic11C22⋊C414yes—
146C11×C22⋊C4—24no—
147C11×C22⋊C4—24no—
148C11×C22⋊C4—42no—
149C11×C22⋊C4—42no—
150C22⋊Dic11—24no—
151C22⋊Dic11—24no—
152C22⋊Dic11—24no—
153C22⋊Dic11—24no—
154C22⋊Dic11—42no—
155C22⋊Dic11—42no—
156(C2×D11)⋊C4—216no—
157Dic11⋊C4—216no—
158C22×#123—111no—
159C22×#99—112no—
160C2×#381—111no—
161C2×#381D1111yescharacteristic, complemented
162C2×#342—112no—
163C23×C11—24no—
164C23×C11—24no—
165C23×C11—24no—
166C23×C11—44no—
167C23×C11—44no—
168C23×C11—44no—
169C23×C11—44no—
170C23×C11—44no—
171C23×C11—44no—
172C23×C11C2×C22⋊C411yescharacteristic
173C23×C11C2×C22⋊C411yescharacteristic
174C23×C11C2×C22⋊C411yescharacteristic
175C23×C11C4×D412yes—
176C23×C11C4×D412yes—
177C23×C11#12012yes—
178C23×C11#12011yescharacteristic
179C23×C11#12012yes—
180C23×C11#12012yes—
181C23×C11#12011yescharacteristic
182C23×C11#12112yes—
183C23×C11#12112yes—
184C23×C11#12112yes—
185C23×C11#12112yes—
186C23×C11#12112yes—
187C23×C11#12112yes—
188C23×C11#12312yes—
189C23×C11#12311yescharacteristic
190C23×C11#12311yescharacteristic
191C23×C11#12412yes—
192C23×C11#12712yes—
193C22×D11—22no—
194C22×D11—24no—
195C22×D11—44no—
196C22×D11—41no—
197C22×D11—41no—
198C22×D11—42no—
199C22×D11—44no—
200C22×D11—44no—
201C22×D11—84no—
202C22×D11—84no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—44no—
207C2×C4×C11—44no—
208C2×C4×C11—44no—
209C2×C4×C11—44no—
210C2×C4×C11—44no—
211C2×C4×C11—44no—
212C2×C4×C11—48no—
213C2×C4×C11—44no—
214C2×C4×C11—84no—
215C2×C4×C11—84no—
216C22⋊D11—44no—
217C22⋊D11—44no—
218C22⋊D11—44no—
219C22⋊D11—44no—
220C2×Dic11—22no—
221C2×Dic11—24no—
222C2×Dic11—24no—
223C2×Dic11—44no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—42no—
227C2×Dic11—44no—
228C2×Dic11—44no—
229C2×Dic11—48no—
230C2×Dic11—44no—
231C2×Dic11—84no—
232C2×Dic11—84no—
233C23×D4—111no—
234C24×C4C2×D1111yescharacteristic
235C2×#123—224no—
236C2×#123—224no—
237C2×#123—222no—
238C2×#123—222no—
239C22×C4⋊C4—112no—
240C22×C22⋊C4—111no—
241C22×C22⋊C4—112no—
242C22×C22⋊C4—112no—
243C22×C22⋊C4C2×D1112yes—
244C2×#99—224no—
245C2×#99—224no—
246C2×#99—224no—
247#381—24no—
248#381—224no—
249C2×#95—22no—
250C2×#95—222no—
251#342—224no—
252C22×C11—22no—
253C22×C11—24no—
254C22×C11—24no—
255C22×C11—24no—
256C22×C11—22no—
257C22×C11—24no—
258C22×C11—22no—
259C22×C11—22no—
260C22×C11—24no—
261C22×C11—22no—
262C22×C11—22no—
263C22×C11—24no—
264C22×C11—42no—
265C22×C11—42no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11#37911yescharacteristic
273C22×C11#38612yes—
274C22×C11#38611yescharacteristic
275C22×C11#38611yescharacteristic
276C22×C11#39012yes—
277C22×C11#39212yes—
278C22×C11#39212yes—
279C22×C11#39412yes—
280C22×C11#39412yes—
281C22×C11#41014yes—
282C2×D11—42no—
283C2×D11—44no—
284C2×D11—84no—
285C2×D11—82no—
286C2×D11—82no—
287C2×D11—84no—
288C4×C11—44no—
289C4×C11—84no—
290Dic11—42no—
291Dic11—44no—
292Dic11—84no—
293C25—111no—
294C25C22×D1111yescharacteristic
295C22×D4—114no—
296C22×D4—221no—
297C22×D4—222no—
298C22×D4—222no—
299C22×D4—222no—
300C22×D4—222no—
301C22×D4—221no—
302C22×D4—222no—
303C23×C4—22no—
304C23×C4—22no—
305C23×C4—22no—
306C23×C4—22no—
307C23×C4—22no—
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—111no—
311C23×C4—112no—
312C23×C4—222no—
313C23×C4C4×D1112yes—
314C23×C4D4412yes—
315C23×C4C22⋊D1112yes—
316#123—2216no—
317#123—2216no—
318C2×C4⋊C4—224no—
319C2×C4⋊C4—224no—
320C2×C4⋊C4—224no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—114no—
327C2×C22⋊C4—114no—
328C2×C22⋊C4—224no—
329C2×C22⋊C4—224no—
330C2×C22⋊C4—221no—
331C2×C22⋊C4—222no—
332C2×C22⋊C4—221no—
333C2×C22⋊C4—224no—
334C2×C22⋊C4—222no—
335C2×C22⋊C4—222no—
336C2×C22⋊C4—222no—
337C2×C22⋊C4—222no—
338C2×C22⋊C4—222no—
339C2×C22⋊C4C22⋊D1114yes—
340#99—2216no—
341#95—28no—
342#95—228no—
343C2×C11—22no—
344C2×C11—22no—
345C2×C11—22no—
346C2×C11—22no—
347C2×C11—22no—
348C2×C11—22no—
349C2×C11#143811yescharacteristic
350C2×C11#178212yes—
351C2×C11#189912yes—
352C2×C11#189912yes—
353D11—82no—
354C24—44no—
355C24—112no—
356C24—221no—
357C24—221no—
358C24—222no—
359C24—222no—
360C24—444no—
361C24C2×C4×D1111yescharacteristic
362C24C2×D4411yescharacteristic
363C24#433912yes—
364C24D4×D1112yes—
365C24D4×D1112yes—
366C24D4×D1112yes—
367C24#434112yes—
368C24C2×C22⋊D1111yescharacteristic
369C24C2×C22⋊D1112yes—
370C2×D4—224no—
371C2×D4—224no—
372C2×D4—224no—
373C2×D4—224no—
374C2×D4—224no—
375C2×D4—224no—
376C2×D4—441no—
377C2×D4—442no—
378C2×D4—442no—
379C2×D4—441no—
380C2×D4—441no—
381C2×D4—442no—
382C2×D4—442no—
383C2×D4—442no—
384C2×D4—442no—
385C2×D4—441no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—24no—
389C22×C4—22no—
390C22×C4—24no—
391C22×C4—22no—
392C22×C4—24no—
393C22×C4—22no—
394C22×C4—24no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—22no—
398C22×C4—24no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4—42no—
407C22×C4—48no—
408C22×C4—42no—
409C22×C4—42no—
410C22×C4—112no—
411C22×C4—114no—
412C22×C4—222no—
413C22×C4—221no—
414C22×C4—222no—
415C22×C4—222no—
416C22×C4—221no—
417C22×C4—222no—
418C22×C4—224no—
419C22×C4—444no—
420C22×C4—448no—
421C22×C4—442no—
422C22×C4—442no—
423C22×C4(C2×D11)⋊C414yes—
424C4⋊C4—2216no—
425C22⋊C4—24no—
426C22⋊C4—24no—
427C22⋊C4—42no—
428C22⋊C4—42no—
429C22⋊C4—2216no—
430C22⋊C4—224no—
431C22⋊C4—224no—
432C22⋊C4—224no—
433C22⋊C4—224no—
434C22⋊C4—442no—
435C22⋊C4—442no—
436C11#1096611yescharacteristic, complemented, Sylow
437C23—24no—
438C23—24no—
439C23—24no—
440C23—44no—
441C23—44no—
442C23—44no—
443C23—44no—
444C23—44no—
445C23—44no—
446C23—222no—
447C23—224no—
448C23—444no—
449C23—444no—
450C23—442no—
451C23—441no—
452C23—441no—
453C23—444no—
454C23—884no—
455C23—884no—
456C23C22⋊C4×D1111yescharacteristic
457C23C22⋊C4×D1111yescharacteristic
458C23(C22⋊D11)⋊C412yes—
459C23#6693512yes—
460C23#6693511yescharacteristic
461C23#6693612yes—
462C23#6693712yes—
463C23#6693712yes—
464C23#6693812yes—
465C23#6693911yescharacteristic
466C23C2×(C2×D11)⋊C411yescharacteristic
467C23C4×C22⋊D1112yes—
468C23#6698211yescharacteristic
469C23#6698312yes—
470C23#6699012yes—
471C23#6699012yes—
472C23#6699112yes—
473C23#6699212yes—
474C23#6699212yes—
475C23#6699312yes—
476C23#6700611yescharacteristic
477D4—444no—
478D4—444no—
479D4—444no—
480D4—444no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—44no—
485C2×C4—44no—
486C2×C4—44no—
487C2×C4—44no—
488C2×C4—44no—
489C2×C4—44no—
490C2×C4—48no—
491C2×C4—44no—
492C2×C4—84no—
493C2×C4—84no—
494C2×C4—224no—
495C2×C4—222no—
496C2×C4—224no—
497C2×C4—444no—
498C2×C4—442no—
499C2×C4—441no—
500C2×C4—441no—
501C2×C4—444no—
502C2×C4—444no—
503C2×C4—448no—
504C2×C4—444no—
505C2×C4—884no—
506C2×C4—884no—
507C22—24no—
508C22—22no—
509C22—24no—
510C22—22no—
511C22—22no—
512C22—24no—
513C22—24no—
514C22—22no—
515C22—24no—
516C22—22no—
517C22—22no—
518C22—24no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—442no—
528C22—444no—
529C22—884no—
530C22—884no—
531C22—882no—
532C22—882no—
533C22#1062256811yescharacteristic
534C22#1062256912yes—
535C22#1062257012yes—
536C22#1062257111yescharacteristic
537C22#1062257212yes—
538C22#1062257312yes—
539C22#1062257412yes—
540C22#1062261914yes—
541C22#1062282611yescharacteristic
542C22#1062283612yes—
543C4—44no—
544C4—84no—
545C4—442no—
546C4—444no—
547C4—884no—
548C2—22no—
549C2—22no—
550C2—22no—
551C2—22no—
552C2—22no—
553C2—22no—
554C2—882no—
555C2#1306685511yescharacteristic
556C2#1306853312yes—
557C2#1306907212yes—
558C2#1306907412yes—
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC24×C11C22×C4
FrattiniC25C22×D11
FittingC2×C11×#381C2
socleC23×C11C2×C22⋊C4
prime radicalC23×C22⋊D11C22
cosocleC25×C11C23
hypercenterC2×#381D11
hypocenterC11#10966
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
3. C2×#10622824C2semidirect
4. C2×#10622165C2semidirect
5. C2×C11×#381C2semidirect
15. C22×(C2×D11)⋊C4C4semidirect
16. C22×Dic11⋊C4C4semidirect
161. C2×#381D11semidirect
436. C11#10966semidirect

Maximal subgroups

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

subgroupindex
C22×#669822
C22×#668702
C2×#106228242
C2×#106221652
C2×C11×#3812
#1096611