Finite Group Databasebeta

← #14680430

Subgroups — #14680430

Order 2816.

1414 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66942C211yesmaximal, characteristic
2C2×#10622264C211yesmaximal, characteristic
3C2×C4⋊C4×Dic11C211yesmaximal, characteristic
4#13066882C212yesmaximal
5#13066882C212yesmaximal
6#13066870C211yesmaximal, characteristic
7#13066869C211yesmaximal, characteristic
8#13066866C211yesmaximal, characteristic
9#13066850C212yesmaximal
10#13066847C212yesmaximal
11C11×#1441C211yesmaximal, characteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C22×C4⋊Dic11C2211yescharacteristic
16C22×Dic11⋊C4C2211yescharacteristic
17C22×Dic11⋊C4C2211yescharacteristic
18C22×Dic11⋊C4C2211yescharacteristic
19C22×Dic11⋊C4C2211yescharacteristic
20C22×C4×Dic11C2212yes—
21C22×C4×Dic11C2211yescharacteristic
22C2×#66942—24no—
23C2×#66942—24no—
24C2×#66942C418yescomplemented
25C2×C11×#95C2212yes—
26C2×C11×#95C2211yescharacteristic
27C2×C11×#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C4⋊C4×Dic11—24no—
39#10622264—24no—
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×Dic11C2312yes—
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2312yes—
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2311yescharacteristic
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—24no—
55C2×C11×C4⋊C4C2×C414yes—
56C2×C4⋊Dic11—22no—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11—22no—
59C2×C4⋊Dic11—24no—
60C2×C4⋊Dic11C2×C414yes—
61C2×Dic11⋊C4—22no—
62C2×Dic11⋊C4—22no—
63C2×Dic11⋊C4—22no—
64C2×Dic11⋊C4—22no—
65C2×Dic11⋊C4—22no—
66C2×Dic11⋊C4—22no—
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4—22no—
69C2×Dic11⋊C4C2×C414yes—
70C2×Dic11⋊C4C2×C414yes—
71C2×Dic11⋊C4C2×C414yes—
72C2×Dic11⋊C4C2×C414yes—
73C2×C4×Dic11—24no—
74C2×C4×Dic11—42no—
75C2×C4×Dic11—42no—
76C2×C4×Dic11C2×C414yes—
77C2×C4×Dic11D414yes—
78C2×C4×Dic11D414yes—
79#66942—232no—
80C11×#95—22no—
81C11×#95—24no—
82C11×#95—42no—
83C11⋊#95—22no—
84C11⋊#95—24no—
85C11⋊#95—24no—
86C11⋊#95—24no—
87C11⋊#95—24no—
88C11⋊#95—24no—
89C11⋊#95—24no—
90C11⋊#95—42no—
91C11⋊#95—42no—
92C11⋊#95—42no—
93#14289—111nomaximal, Sylow
94C24×C11C2411yescharacteristic
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11C22×C412yes—
121C22×C4×C11C22×C412yes—
122C22×C4×C11C22×C412yes—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11#4114yes—
126C22×Dic11—22no—
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—21no—
146C22×Dic11—22no—
147C22×Dic11—21no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11C22×C412yes—
156C22×Dic11C22×C412yes—
157C22×Dic11C22×C412yes—
158C22×Dic11C22×C412yes—
159C22×Dic11C2×D412yes—
160C22×Dic11C2×D412yes—
161C22×Dic11C2×D412yes—
162C22×Dic11C2×D412yes—
163C22×Dic11#4114yes—
164C11×C4⋊C4—28no—
165C11×C4⋊C4—28no—
166C4⋊Dic11—28no—
167C4⋊Dic11—28no—
168Dic11⋊C4—28no—
169Dic11⋊C4—28no—
170Dic11⋊C4—28no—
171Dic11⋊C4—28no—
172C4×Dic11—48no—
173C4×Dic11C22⋊C4116yes—
174C22×#125—111no—
175C2×#383—111no—
176C2×C4×C4⋊C4—111no—
177#1445—112no—
178#1445—112no—
179#1441—111no—
180#1441—111no—
181#1441—111no—
182#1441D1111yescharacteristic
183#1436—112no—
184#1436—112no—
185C23×C11C23×C411yescharacteristic
186C23×C11C22×D411yescharacteristic
187C23×C11C22×D411yescharacteristic
188C23×C11C2×#4112yes—
189C23×C11C2×#4112yes—
190C23×C11H(5,𝔽2)11yescharacteristic
191C23×C11H(5,𝔽2)11yescharacteristic
192C23×C112−1+412yes—
193C23×C112−1+411yescharacteristic
194C23×C112−1+412yes—
195C23×C112−1+411yescharacteristic
196C2×C4×C11—24no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—24no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—24no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—42no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11C2×C22⋊C414yes—
227C2×Dic11—24no—
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—22no—
231C2×Dic11—22no—
232C2×Dic11—24no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—24no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—24no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—41no—
250C2×Dic11—42no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258C2×Dic11—42no—
259C2×Dic11—42no—
260C2×Dic11—42no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263C2×Dic11C2×C22⋊C414yes—
264C2×Dic11C2×C22⋊C414yes—
265C2×#125—118no—
266C2×#125—224no—
267C2×#125—224no—
268C22×C4⋊C4—111no—
269C22×C4⋊C4—111no—
270C22×C4⋊C4—111no—
271C22×C4⋊C4—111no—
272C22×C4⋊C4—111no—
273C22×C4⋊C4—111no—
274C22×C4⋊C4C2×D1111yescharacteristic
275C22×C4⋊C4C2×D1111yescharacteristic
276C22×C42—111no—
277C22×C42—112no—
278#383—224no—
279C4×C4⋊C4—224no—
280C2×#95—112no—
281C2×#95—112no—
282C2×#95—112no—
283C2×#95—112no—
284C2×#95—111no—
285C2×#95—112no—
286C2×#95—112no—
287C2×#95—112no—
288C2×#95—112no—
289C2×#95—112no—
290C2×#95C2×D1112yes—
291C2×#95C2×D1111yescharacteristic
292C2×#95C2×D1112yes—
293C22×C11C22×C22⋊C411yescharacteristic
294C22×C11C4×#4112yes—
295C22×C11#51912yes—
296C22×C11#52011yescharacteristic
297C22×C11#52011yescharacteristic
298C22×C11#52511yescharacteristic
299C22×C11#52511yescharacteristic
300C22×C11#53212yes—
301C22×C11#53511yescharacteristic
302C22×C11#53611yescharacteristic
303C22×C11#53612yes—
304C22×C11#53611yescharacteristic
305C22×C11#53611yescharacteristic
306C22×C11#53711yescharacteristic
307C22×C11#53711yescharacteristic
308C22×C11#53912yes—
309C22×C11#53912yes—
310C22×C11#53912yes—
311C22×C11#53912yes—
312C22×C11#54112yes—
313C22×C11#54112yes—
314C22×C11#54112yes—
315C22×C11#54112yes—
316C4×C11—24no—
317C4×C11—42no—
318C4×C11—44no—
319C4×C11—42no—
320C4×C11—82no—
321Dic11—24no—
322Dic11—24no—
323Dic11—42no—
324Dic11—44no—
325Dic11—42no—
326Dic11—82no—
327C23×C4—111no—
328C23×C4—111no—
329C23×C4—111no—
330C23×C4—111no—
331C23×C4—112no—
332C23×C4—112no—
333C23×C4C22×D1112yes—
334C23×C4C22×D1111yescharacteristic
335C23×C4C22×D1111yescharacteristic
336C23×C4C22×D1112yes—
337C23×C4C22×D1111yescharacteristic
338#125—2232no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—114no—
344C2×C4⋊C4—114no—
345C2×C4⋊C4—114no—
346C2×C4⋊C4—114no—
347C2×C4⋊C4—114no—
348C2×C4⋊C4—222no—
349C2×C4⋊C4—222no—
350C2×C4⋊C4—222no—
351C2×C4⋊C4—222no—
352C2×C4⋊C4—222no—
353C2×C4⋊C4—222no—
354C2×C4⋊C4—222no—
355C2×C4⋊C4—222no—
356C2×C4⋊C4—224no—
357C2×C4⋊C4—222no—
358C2×C4⋊C4—222no—
359C2×C4⋊C4—222no—
360C2×C4⋊C4C4×D1114yes—
361C2×C42—114no—
362C2×C42—114no—
363C2×C42—114no—
364C2×C42—224no—
365C2×C42—442no—
366C2×C42—442no—
367#95—22no—
368#95—24no—
369#95—42no—
370#95—224no—
371#95—224no—
372#95—224no—
373#95—224no—
374#95—224no—
375#95—222no—
376#95—224no—
377#95—442no—
378#95—442no—
379#95—442no—
380C2×C11#229711yescharacteristic
381C2×C11#231011yescharacteristic
382C2×C11#231111yescharacteristic
383C2×C11#233612yes—
384C2×C11#233612yes—
385C2×C11#263311yescharacteristic
386C2×C11#263311yescharacteristic
387C2×C11#263411yescharacteristic
388C2×C11#263411yescharacteristic
389C2×C11#266412yes—
390C2×C11#266412yes—
391C24C23×D1111yescharacteristic
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—112no—
418C22×C4—112no—
419C22×C4—112no—
420C22×C4—112no—
421C22×C4—112no—
422C22×C4—112no—
423C22×C4—112no—
424C22×C4—112no—
425C22×C4—114no—
426C22×C4—221no—
427C22×C4—222no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—221no—
431C22×C4—222no—
432C22×C4—222no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4—221no—
437C22×C4—222no—
438C22×C4—221no—
439C22×C4—222no—
440C22×C4—221no—
441C22×C4—222no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—222no—
445C22×C4—221no—
446C22×C4—222no—
447C22×C4—221no—
448C22×C4—222no—
449C22×C4—222no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4C2×C4×D1112yes—
456C22×C4C2×C4×D1112yes—
457C22×C4C2×C4×D1112yes—
458C22×C4D4×D1112yes—
459C22×C4D4×D1112yes—
460C22×C4#434114yes—
461C4⋊C4—28no—
462C4⋊C4—28no—
463C4⋊C4—228no—
464C4⋊C4—228no—
465C4⋊C4—228no—
466C4⋊C4—228no—
467C4⋊C4—228no—
468C4⋊C4—228no—
469C42—1116no—
470C42—448no—
471C11#1428911yescharacteristic, complemented, Sylow
472C23C22×C4×D1111yescharacteristic
473C23C2×D4×D1111yescharacteristic
474C23C2×D4×D1111yescharacteristic
475C23C2×#434112yes—
476C23#6703711yescharacteristic
477C23#6704012yes—
478C23#6704011yescharacteristic
479C23#41×D1112yes—
480C23#6704211yescharacteristic
481C23#6704311yescharacteristic
482C23#6704312yes—
483C2×C4—24no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—114no—
514C2×C4—114no—
515C2×C4—222no—
516C2×C4—222no—
517C2×C4—222no—
518C2×C4—224no—
519C2×C4—222no—
520C2×C4—222no—
521C2×C4—224no—
522C2×C4—222no—
523C2×C4—222no—
524C2×C4—222no—
525C2×C4—222no—
526C2×C4—222no—
527C2×C4—222no—
528C2×C4—222no—
529C2×C4—224no—
530C2×C4—224no—
531C2×C4—224no—
532C2×C4—224no—
533C2×C4—442no—
534C2×C4—441no—
535C2×C4—442no—
536C2×C4—442no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—442no—
542C2×C4—441no—
543C2×C4—442no—
544C2×C4—442no—
545C2×C4—442no—
546C2×C4—442no—
547C2×C4—442no—
548C2×C4—442no—
549C2×C4—442no—
550C2×C4—442no—
551C2×C4C22⋊C4×D1114yes—
552C22C2×C22⋊C4×D1111yescharacteristic
553C22#1062303511yescharacteristic
554C22#1062305411yescharacteristic
555C22C4×#434112yes—
556C22#1062310312yes—
557C22#1062311711yescharacteristic
558C22#1062312712yes—
559C22#1062313312yes—
560C22#1062313811yescharacteristic
561C22#1062313911yescharacteristic
562C22#1062315612yes—
563C22#1062315911yescharacteristic
564C22#1062315912yes—
565C22#1062316011yescharacteristic
566C22#1062316912yes—
567C22#1062318711yescharacteristic
568C22#1062319612yes—
569C22#1062320611yescharacteristic
570C22#1062322312yes—
571C22#1062322712yes—
572C22#1062323212yes—
573C22#1062325511yescharacteristic
574C22#1062326212yes—
575C4—24no—
576C4—44no—
577C4—42no—
578C4—42no—
579C4—82no—
580C4—224no—
581C4—224no—
582C4—444no—
583C4—442no—
584C4—442no—
585C4—882no—
586C2#1307110111yescharacteristic
587C2#1307119911yescharacteristic
588C2#1307120511yescharacteristic
589C2#1307141412yes—
590C2#1307142112yes—
591C2#1307448311yescharacteristic
592C2#1307448611yescharacteristic
593C2#1307449111yescharacteristic
594C2#1307449411yescharacteristic
595C2#1307477412yes—
596C2#1307477612yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1441C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1441D11
hypocenterC11#14289
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
24. C2×#66942C4semidirect
471. C11#14289semidirect

Maximal subgroups

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

subgroupindex
C22×#669422
C2×#106222642
C2×C4⋊C4×Dic112
#130668822
#130668702
#130668692
#130668662
#130668502
#130668472
C11×#14412
#1428911