Finite Group Databasebeta

← #14680771

Subgroups — #14680771

Order 2816.

1318 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622843C211yesmaximal, characteristic
2C2×C4⋊C4×Dic11C211yesmaximal, characteristic
3#13066887C211yesmaximal, characteristic
4#13066884C212yesmaximal
5#13066873C212yesmaximal
6#13066873C211yesmaximal, characteristic
7#13066869C211yesmaximal, characteristic
8#13066848C212yesmaximal
9#13066841C212yesmaximal
10#13066841C211yesmaximal, characteristic
11C2×C11×#395C211yesmaximal, characteristic
12C23×Q8×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2212yes—
15C22×C4⋊Dic11C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C22×C4×Dic11C2211yescharacteristic
18C22×C4×Dic11C2211yescharacteristic
19C22×C4×Dic11C2211yescharacteristic
20C11×#395C418yescomplemented
21C2×C11×#95C2211yescharacteristic
22C2×C11×#95C2212yes—
23#10622843—24no—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C4⋊C4×Dic11—24no—
38C22×Q8×C11—22no—
39C22×Q8×C11—22no—
40C22×Q8×C11—42no—
41C22×Q8×C11—42no—
42C22×Q8×C11C2×C414yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2312yes—
45C23×C4×C11C2312yes—
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×Dic11C2312yes—
49C23×Dic11C2312yes—
50C23×Dic11C2311yescharacteristic
51C23×Dic11C2311yescharacteristic
52C23×Dic11C2311yescharacteristic
53C23×Dic11C2311yescharacteristic
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—42no—
57C2×C11×C4⋊C4—42no—
58C2×C11×C4⋊C4C2×C414yes—
59C2×C11×C4⋊C4C2×C418yes—
60C2×C4⋊Dic11—22no—
61C2×C4⋊Dic11—22no—
62C2×C4⋊Dic11—22no—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11—42no—
65C2×C4×Dic11—22no—
66C2×C4×Dic11—22no—
67C2×C4×Dic11—22no—
68C2×C4×Dic11—42no—
69C2×C4×Dic11—42no—
70C2×C4×Dic11D414yes—
71C2×C4×Dic11Q814yescomplemented
72C11×#95C2×C414yes—
73C11×#95C2×C418yes—
74C11⋊#95—22no—
75C11⋊#95—22no—
76C11⋊#95—24no—
77C11⋊#95—24no—
78C11⋊#95—24no—
79C11⋊#95—22no—
80C11⋊#95—24no—
81C11⋊#95—24no—
82C11⋊#95—42no—
83C11⋊#95—42no—
84C11⋊#95—42no—
85C11⋊#95—42no—
86C11⋊#95—42no—
87#14320—111nomaximal, Sylow
88C24×C11C2411yescharacteristic
89C2×Q8×C11—28no—
90C2×Q8×C11—48no—
91C2×Q8×C11—44no—
92C2×Q8×C11—44no—
93C2×Q8×C11—48no—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—21no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—21no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11C22×C414yes—
117C22×C4×C11C22×C414yes—
118C22×C4×C11C22×C412yes—
119C22×C4×C11C22×C412yes—
120C22×C4×C11C22×C412yes—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×Q812yes—
123C22×C4×C11#4112yes—
124C22×C4×C11#4112yes—
125C22×Dic11—21no—
126C22×Dic11—21no—
127C22×Dic11—22no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11C2×D412yes—
154C22×Dic11C2×D412yes—
155C22×Dic11C2×Q812yes—
156C22×Dic11C2×Q812yes—
157C22×Dic11#4112yes—
158C22×Dic11#4112yes—
159C11×C4⋊C4—28no—
160C11×C4⋊C4—48no—
161C4⋊Dic11—28no—
162C4⋊Dic11—44no—
163C4×Dic11—28no—
164C4×Dic11—44no—
165C4×Dic11—44no—
166C2×#395D1111yescharacteristic
167C2×#391—111no—
168C2×C4×C4⋊C4—111no—
169#1446—111no—
170#1445—112no—
171#1442—112no—
172#1442—111no—
173#1441—111no—
174#1436—112no—
175#1434—111no—
176#1434—112no—
177C23×C11C23×C411yescharacteristic
178C23×C11C22×D411yescharacteristic
179C23×C11C22×Q811yescharacteristic
180C23×C11C2×#4111yescharacteristic
181C23×C11C2×#4111yescharacteristic
182C23×C11C2×#4111yescharacteristic
183C23×C11C2×#4111yescharacteristic
184C23×C11H(5,𝔽2)12yes—
185C23×C11H(5,𝔽2)12yes—
186C23×C112−1+412yes—
187C23×C112−1+412yes—
188Q8×C11—416no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—24no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—24no—
199C2×C4×C11—22no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—41no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11C4×D414yes—
219C2×C4×C11C4×Q814yes—
220C2×Dic11—22no—
221C2×Dic11—22no—
222C2×Dic11—24no—
223C2×Dic11—24no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—22no—
227C2×Dic11—22no—
228C2×Dic11—22no—
229C2×Dic11—24no—
230C2×Dic11—24no—
231C2×Dic11—41no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11C22⋊Q814yes—
254C23×Q8C2×D1111yescharacteristic
255C22×C4⋊C4—111no—
256C22×C4⋊C4—111no—
257C22×C4⋊C4C2×D1111yescharacteristic
258C22×C4⋊C4C2×D1112yes—
259C22×C42—111no—
260C22×C42—111no—
261C22×C42—111no—
262#395Dic1118yescomplemented
263#391—224no—
264C4×C4⋊C4—224no—
265C2×#95—112no—
266C2×#95—112no—
267C2×#95—112no—
268C2×#95—111no—
269C2×#95—112no—
270C2×#95—112no—
271C2×#95—111no—
272C2×#95—111no—
273C2×#95—112no—
274C2×#95—112no—
275C2×#95—112no—
276C2×#95—112no—
277C2×#95—112no—
278C2×#95C2×D1112yes—
279C2×#95C2×D1111yescharacteristic
280C22×C11C2×C4×D411yescharacteristic
281C22×C11C2×C4×Q811yescharacteristic
282C22×C11C4×#4111yescharacteristic
283C22×C11#51812yes—
284C22×C11#51912yes—
285C22×C11C2×C22⋊Q811yescharacteristic
286C22×C11#52511yescharacteristic
287C22×C11#52911yescharacteristic
288C22×C11#53311yescharacteristic
289C22×C11#53411yescharacteristic
290C22×C11#53511yescharacteristic
291C22×C11#53611yescharacteristic
292C22×C11#53611yescharacteristic
293C22×C11#53812yes—
294C22×C11#53912yes—
295C22×C11#53912yes—
296C22×C11#54112yes—
297C22×C11#54212yes—
298C22×C11#54212yes—
299C22×C11#54212yes—
300C22×C11#54212yes—
301C22×C11#54412yes—
302C22×C11#54412yes—
303C4×C11—24no—
304C4×C11—24no—
305C4×C11—42no—
306C4×C11—44no—
307C4×C11—44no—
308Dic11—24no—
309Dic11—42no—
310Dic11—42no—
311Dic11—42no—
312Dic11—82no—
313Dic11—82no—
314C22×Q8—22no—
315C22×Q8—22no—
316C22×Q8—42no—
317C22×Q8—42no—
318C22×Q8C2×Dic1114yes—
319C23×C4—111no—
320C23×C4—111no—
321C23×C4—111no—
322C23×C4—111no—
323C23×C4—112no—
324C23×C4—112no—
325C23×C4C22×D1111yescharacteristic
326C23×C4C22×D1112yes—
327C23×C4C22×D1112yes—
328C23×C4C22×D1111yescharacteristic
329C23×C4C22×D1111yescharacteristic
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—222no—
335C2×C4⋊C4—222no—
336C2×C4⋊C4—222no—
337C2×C4⋊C4—222no—
338C2×C4⋊C4—442no—
339C2×C4⋊C4C2×Dic1114yes—
340C2×C4⋊C4C2×Dic1118yes—
341C2×C42—114no—
342C2×C42—114no—
343C2×C42—222no—
344C2×C42—222no—
345C2×C42—222no—
346C2×C42—442no—
347C2×C42—442no—
348#95—224no—
349#95—224no—
350#95—222no—
351#95—224no—
352#95—224no—
353#95—222no—
354#95—222no—
355#95—224no—
356#95—442no—
357#95—442no—
358#95—442no—
359#95—442no—
360#95—442no—
361#95C2×Dic1114yes—
362#95C2×Dic1118yes—
363C2×C11C4×C22⋊Q811yescharacteristic
364C2×C11#232111yescharacteristic
365C2×C11#232711yescharacteristic
366C2×C11#233112yes—
367C2×C11#233212yes—
368C2×C11#262711yescharacteristic
369C2×C11#262811yescharacteristic
370C2×C11#263211yescharacteristic
371C2×C11#263811yescharacteristic
372C2×C11#265012yes—
373C2×C11#266612yes—
374C24C23×D1111yescharacteristic
375C2×Q8—28no—
376C2×Q8—48no—
377C2×Q8—44no—
378C2×Q8—44no—
379C2×Q8—48no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—112no—
403C22×C4—112no—
404C22×C4—112no—
405C22×C4—112no—
406C22×C4—112no—
407C22×C4—112no—
408C22×C4—222no—
409C22×C4—222no—
410C22×C4—221no—
411C22×C4—221no—
412C22×C4—222no—
413C22×C4—222no—
414C22×C4—222no—
415C22×C4—221no—
416C22×C4—221no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4—221no—
421C22×C4—221no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—222no—
432C22×C4—222no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4D4×D1112yes—
437C22×C4#434112yes—
438C22×C4Q8×D1112yes—
439C22×C4#434312yes—
440C22×C4C22×Dic1114yes—
441C22×C4C22×Dic1114yes—
442C22×C4C22×Dic1112yes—
443C22×C4C22×Dic1112yes—
444C22×C4C22×Dic1112yes—
445C4⋊C4—28no—
446C4⋊C4—48no—
447C4⋊C4—228no—
448C4⋊C4—444no—
449C42—228no—
450C42—444no—
451C42—444no—
452C11#1432011yescharacteristic, complemented, Sylow
453C23C2×D4×D1111yescharacteristic
454C23C2×#434111yescharacteristic
455C23#6703712yes—
456C23#6703712yes—
457C23C2×Q8×D1111yescharacteristic
458C23C2×#434311yescharacteristic
459C23#6704012yes—
460C23#6704012yes—
461C23#41×D1111yescharacteristic
462C23#41×D1111yescharacteristic
463C23C23×Dic1111yescharacteristic
464Q8—416no—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—24no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—114no—
495C2×C4—222no—
496C2×C4—224no—
497C2×C4—222no—
498C2×C4—224no—
499C2×C4—222no—
500C2×C4—224no—
501C2×C4—222no—
502C2×C4—222no—
503C2×C4—222no—
504C2×C4—222no—
505C2×C4—224no—
506C2×C4—441no—
507C2×C4—441no—
508C2×C4—442no—
509C2×C4—442no—
510C2×C4—441no—
511C2×C4—441no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4—442no—
518C2×C4—442no—
519C2×C4—442no—
520C2×C4—442no—
521C2×C4—442no—
522C2×C4—442no—
523C2×C4—442no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4—442no—
527C2×C4—442no—
528C2×C4D4×Dic1114yes—
529C2×C4Q8×Dic1114yes—
530C22#1062312011yescharacteristic
531C22#1062312311yescharacteristic
532C22#1062312412yes—
533C22#1062315311yescharacteristic
534C22#1062315511yescharacteristic
535C22D11×C22⋊Q811yescharacteristic
536C22#1062315811yescharacteristic
537C22#1062316912yes—
538C22#1062316912yes—
539C22#1062317112yes—
540C22#1062317112yes—
541C22#1062325511yescharacteristic
542C22#1062325511yescharacteristic
543C22#1062326012yes—
544C22#1062326012yes—
545C22#1062326212yes—
546C22#1062326412yes—
547C22#1062326412yes—
548C22C2×D4×Dic1111yescharacteristic
549C22#1062332912yes—
550C22C2×Q8×Dic1111yescharacteristic
551C22#1062334312yes—
552C22#41×Dic1111yescharacteristic
553C4—24no—
554C4—24no—
555C4—44no—
556C4—44no—
557C4—42no—
558C4—224no—
559C4—442no—
560C4—442no—
561C4—442no—
562C4—882no—
563C4—882no—
564C2C22⋊Q8×Dic1111yescharacteristic
565C2#1307127711yescharacteristic
566C2#1307133611yescharacteristic
567C2#1307136512yes—
568C2#1307137412yes—
569C2#1307442811yescharacteristic
570C2#1307443911yescharacteristic
571C2#1307448211yescharacteristic
572C2#1307454211yescharacteristic
573C2#1307463712yes—
574C2#1307479412yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#395C2
socle, prime radical, cosocleC24×C11C24
hypercenterC2×#395D11
hypocenterC11#14320
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
20. C11×#395C4semidirect
71. C2×C4×Dic11Q8semidirect
262. #395Dic11semidirect
452. C11#14320semidirect

Maximal subgroups

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

subgroupindex
C2×#106228432
C2×C4⋊C4×Dic112
#130668872
#130668842
#130668732
#130668692
#130668482
#130668412
C2×C11×#3952
#1432011