Finite Group Databasebeta

← #14684802

Subgroups — #14684802

Order 2816.

2222 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66948C211yesmaximal, characteristic
2C2×#10622277C211yesmaximal, characteristic, complemented
3C2×#10622280C211yesmaximal, characteristic, complemented
4#13066884C211yesmaximal, characteristic, complemented
5#13066860C214yesmaximal, complemented
6#13066856C214yesmaximal, complemented
7#13066856C211yesmaximal, characteristic, complemented
8#13066856C211yesmaximal, characteristic, complemented
9C11×#1445C211yesmaximal, characteristic, complemented
10C23×D44C2212yes—
11C23×D44C2211yescharacteristic
12C23×C4×D11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×(C2×D11)⋊C4C2212yes—
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2214yes—
18C22×(C2×D11)⋊C4C2214yes—
19C22×Dic11⋊C4C2212yes—
20C2×#66948—24no—
21C2×#66948—24no—
22C2×#66948C418yescomplemented
23C2×C11×#95C2211yescharacteristic
24C2×C11×#95C2211yescharacteristic
25C2×C11×#95C2214yes—
26C2×C11⋊#95C2211yescharacteristic
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2214yes—
30#10622280—24no—
31#10622277—24no—
32C24×D11C2312yes—
33C24×D11C2311yescharacteristic
34C23×C4×C11C2312yes—
35C23×C4×C11C2312yes—
36C23×C4×C11C2312yes—
37C23×C4×C11C2311yescharacteristic
38C23×Dic11C2312yes—
39C23×Dic11C2312yes—
40C23×Dic11C2311yescharacteristic
41C22×D44—24no—
42C22×D44—24no—
43C22×D44—22no—
44C22×D44—22no—
45C22×D44—44no—
46C22×D44—44no—
47C22×D44—44no—
48C22×D44C2×C418yes—
49C22×D44C2×C414yes—
50C22×C4×D11—44no—
51C22×C4×D11C2×C414yes—
52C22×C4×D11D414yes—
53C22×C4×D11D414yes—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4C2×C414yes—
57C2×(C2×D11)⋊C4—24no—
58C2×(C2×D11)⋊C4—24no—
59C2×(C2×D11)⋊C4—24no—
60C2×(C2×D11)⋊C4—24no—
61C2×(C2×D11)⋊C4—44no—
62C2×(C2×D11)⋊C4—44no—
63C2×(C2×D11)⋊C4—44no—
64C2×(C2×D11)⋊C4—44no—
65C2×(C2×D11)⋊C4—44no—
66C2×(C2×D11)⋊C4—44no—
67C2×(C2×D11)⋊C4—44no—
68C2×(C2×D11)⋊C4—44no—
69C2×(C2×D11)⋊C4C2×C418yes—
70C2×Dic11⋊C4—24no—
71C2×Dic11⋊C4—44no—
72#66948—232no—
73C11×#95—22no—
74C11×#95—22no—
75C11×#95—44no—
76C11⋊#95—22no—
77C11⋊#95—22no—
78C11⋊#95—24no—
79C11⋊#95—44no—
80#14659—111nomaximal, Sylow
81C24×C11C2411yescharacteristic
82C23×D11—22no—
83C23×D11—24no—
84C23×D11—22no—
85C23×D11—22no—
86C23×D11—22no—
87C23×D11—22no—
88C23×D11—22no—
89C23×D11—24no—
90C23×D11—24no—
91C23×D11—24no—
92C23×D11—24no—
93C23×D11—24no—
94C23×D11—24no—
95C23×D11C22×C414yes—
96C23×D11C22×C412yes—
97C23×D11C2×D412yes—
98C23×D11C2×D412yes—
99C22×C4×C11—24no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—24no—
103C22×C4×C11—24no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—24no—
108C22×C4×C11—24no—
109C22×C4×C11—24no—
110C22×C4×C11—24no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11C22×C414yes—
115C22×C4×C11C22×C412yes—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D412yes—
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11—24no—
121C22×Dic11—22no—
122C22×Dic11—24no—
123C22×Dic11—24no—
124C22×Dic11—22no—
125C22×Dic11—24no—
126C22×Dic11—24no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11C22×C412yes—
130C22×Dic11C2×D412yes—
131C22×Dic11C2×D412yes—
132C2×D44—216no—
133C2×D44—28no—
134C2×D44—48no—
135C2×D44—416no—
136C2×D44—48no—
137C2×D44—48no—
138C2×D44—48no—
139C2×D44—416no—
140C2×D44—48no—
141C2×C4×D11—48no—
142C2×C4×D11—48no—
143C2×C4×D11—48no—
144C2×C4×D11C22⋊C4116yescomplemented
145C11×C4⋊C4—28no—
146(C2×D11)⋊C4—216no—
147(C2×D11)⋊C4—48no—
148(C2×D11)⋊C4—48no—
149(C2×D11)⋊C4—416no—
150(C2×D11)⋊C4—416no—
151Dic11⋊C4—48no—
152C22×#121—111no—
153C2×#381—111no—
154C2×#380—111no—
155#1445—111no—
156#1445D1111yescharacteristic, complemented
157#1439—114no—
158#1438—114no—
159#1438—111no—
160#1438—111no—
161C23×C11C23×C411yescharacteristic
162C23×C11C22×D411yescharacteristic
163C23×C11C22×D411yescharacteristic
164C23×C11H(5,𝔽2)12yes—
165C23×C11H(5,𝔽2)14yes—
166C23×C11H(5,𝔽2)12yes—
167C23×C11H(5,𝔽2)12yes—
168C23×C112−1+412yes—
169C22×D11—24no—
170C22×D11—24no—
171C22×D11—24no—
172C22×D11—24no—
173C22×D11—24no—
174C22×D11—22no—
175C22×D11—22no—
176C22×D11—24no—
177C22×D11—22no—
178C22×D11—22no—
179C22×D11—24no—
180C22×D11—24no—
181C22×D11—24no—
182C22×D11—24no—
183C22×D11—28no—
184C22×D11—28no—
185C22×D11—44no—
186C22×D11—44no—
187C22×D11—44no—
188C22×D11—44no—
189C22×D11—44no—
190C22×D11—44no—
191C22×D11—42no—
192C22×D11—44no—
193C22×D11—42no—
194C22×D11—42no—
195C22×D11—42no—
196C22×D11—44no—
197C22×D11—44no—
198C22×D11—44no—
199C22×D11—44no—
200C22×D11—44no—
201C22×D11—44no—
202C22×D11—44no—
203C22×D11—44no—
204C22×D11—44no—
205C22×D11C2×C22⋊C414yes—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—28no—
211C2×C4×C11—42no—
212C2×C4×C11—44no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—44no—
221C2×C4×C11—44no—
222C2×C4×C11—44no—
223C2×C4×C11—44no—
224C2×C4×C11C2×C22⋊C414yes—
225C2×Dic11—24no—
226C2×Dic11—24no—
227C2×Dic11—24no—
228C2×Dic11—42no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234C2×Dic11—44no—
235C2×Dic11—44no—
236C2×Dic11—44no—
237C2×Dic11—44no—
238C2×Dic11C2×C22⋊C414yes—
239D44—416no—
240D44—432no—
241C4×D11—416no—
242C23×D4—112no—
243C23×D4—111no—
244C24×C4—111no—
245C2×#121—118no—
246C2×#121—224no—
247C2×#121—224no—
248C22×C4⋊C4—112no—
249C22×C4⋊C4C2×D1111yescharacteristic
250C22×C22⋊C4—112no—
251C22×C22⋊C4—112no—
252C22×C22⋊C4—112no—
253C22×C22⋊C4—114no—
254C22×C22⋊C4—114no—
255#381—224no—
256#380—224no—
257C2×#95—111no—
258C2×#95—111no—
259C2×#95—112no—
260C2×#95—114no—
261C2×#95C2×D1111yescharacteristic
262C2×#95C2×D1111yescharacteristic
263C2×#95C2×D1114yes—
264C22×C11C22×C22⋊C411yescharacteristic
265C22×C11#51812yes—
266C22×C11#51812yes—
267C22×C11#52012yes—
268C22×C11#53412yes—
269C22×C11#53412yes—
270C22×C11#53511yescharacteristic
271C22×C11#53512yes—
272C22×C11#53511yescharacteristic
273C22×C11#53511yescharacteristic
274C22×C11#53611yescharacteristic
275C22×C11#53712yes—
276C22×C11#56014yes—
277C22×C11#56014yes—
278C22×C11#56214yes—
279C22×C11#56214yes—
280C2×D11—24no—
281C2×D11—24no—
282C2×D11—24no—
283C2×D11—44no—
284C2×D11—48no—
285C2×D11—44no—
286C2×D11—44no—
287C2×D11—44no—
288C2×D11—44no—
289C2×D11—44no—
290C2×D11—44no—
291C2×D11—48no—
292C2×D11—48no—
293C2×D11—84no—
294C2×D11—84no—
295C2×D11—84no—
296C2×D11—84no—
297C4×C11—24no—
298C4×C11—44no—
299C4×C11—82no—
300C4×C11—82no—
301Dic11—24no—
302Dic11—82no—
303Dic11—82no—
304C25—111no—
305C25—112no—
306C22×D4—118no—
307C22×D4—114no—
308C22×D4—224no—
309C22×D4—224no—
310C22×D4—222no—
311C22×D4—222no—
312C22×D4—444no—
313C22×D4—444no—
314C22×D4—444no—
315C23×C4—111no—
316C23×C4—114no—
317C23×C4—114no—
318C23×C4—114no—
319C23×C4—112no—
320C23×C4—112no—
321C23×C4—444no—
322C23×C4C22×D1112yes—
323C23×C4C22×D1112yes—
324C23×C4C22×D1112yes—
325C23×C4C22×D1111yescharacteristic
326#121—2232no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—224no—
330C2×C4⋊C4—444no—
331C2×C4⋊C4C4×D1114yes—
332C2×C22⋊C4—118no—
333C2×C22⋊C4—224no—
334C2×C22⋊C4—224no—
335C2×C22⋊C4—224no—
336C2×C22⋊C4—224no—
337C2×C22⋊C4—444no—
338C2×C22⋊C4—444no—
339C2×C22⋊C4—444no—
340C2×C22⋊C4—444no—
341C2×C22⋊C4—444no—
342C2×C22⋊C4—444no—
343C2×C22⋊C4—444no—
344C2×C22⋊C4—444no—
345#95—22no—
346#95—22no—
347#95—44no—
348#95—224no—
349#95—222no—
350#95—222no—
351#95—444no—
352C2×C11#230811yescharacteristic
353C2×C11#230911yescharacteristic
354C2×C11#231111yescharacteristic
355C2×C11#237714yes—
356C2×C11#281312yes—
357C2×C11#281312yes—
358C2×C11#281512yes—
359C2×C11#281612yes—
360D11—44no—
361D11—84no—
362C24—112no—
363C24—112no—
364C24—112no—
365C24—114no—
366C24—222no—
367C24—222no—
368C24—222no—
369C24—224no—
370C24—222no—
371C24—222no—
372C24—222no—
373C24—224no—
374C24—224no—
375C24—224no—
376C24—224no—
377C24—224no—
378C24—224no—
379C24C23×D1111yescharacteristic
380C2×D4—2216no—
381C2×D4—228no—
382C2×D4—448no—
383C2×D4—4416no—
384C2×D4—448no—
385C2×D4—448no—
386C2×D4—448no—
387C2×D4—4416no—
388C2×D4—448no—
389C22×C4—24no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—24no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—24no—
401C22×C4—22no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—112no—
405C22×C4—112no—
406C22×C4—112no—
407C22×C4—1116no—
408C22×C4—224no—
409C22×C4—222no—
410C22×C4—222no—
411C22×C4—222no—
412C22×C4—222no—
413C22×C4—222no—
414C22×C4—224no—
415C22×C4—222no—
416C22×C4—224no—
417C22×C4—224no—
418C22×C4—224no—
419C22×C4—448no—
420C22×C4—448no—
421C22×C4—448no—
422C22×C4C2×C4×D1114yes—
423C22×C4C2×C4×D1112yes—
424C22×C4D4×D1112yes—
425C22×C4D4×D1112yes—
426C4⋊C4—28no—
427C4⋊C4—448no—
428C22⋊C4—2216no—
429C22⋊C4—448no—
430C22⋊C4—448no—
431C22⋊C4—4416no—
432C22⋊C4—4416no—
433C11#1465911yescharacteristic, complemented, Sylow
434C23—114no—
435C23—222no—
436C23—222no—
437C23—224no—
438C23—224no—
439C23—224no—
440C23—224no—
441C23—224no—
442C23—224no—
443C23—224no—
444C23—222no—
445C23—222no—
446C23—224no—
447C23—224no—
448C23—224no—
449C23—228no—
450C23—228no—
451C23—444no—
452C23—444no—
453C23—444no—
454C23—444no—
455C23—444no—
456C23—444no—
457C23—442no—
458C23—442no—
459C23—444no—
460C23—444no—
461C23—444no—
462C23—444no—
463C23—444no—
464C23—444no—
465C23—444no—
466C23—444no—
467C23—442no—
468C23—442no—
469C23—444no—
470C23—444no—
471C23C22×C4×D1111yescharacteristic
472C23C2×D4×D1111yescharacteristic
473C23C2×D4×D1111yescharacteristic
474C23#6703712yes—
475C23#6704012yes—
476C23#6704212yes—
477C23#6704212yes—
478C23#6704214yes—
479D4—4416no—
480D4—4432no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—28no—
486C2×C4—42no—
487C2×C4—44no—
488C2×C4—42no—
489C2×C4—44no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—44no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—44no—
497C2×C4—44no—
498C2×C4—42no—
499C2×C4—114no—
500C2×C4—224no—
501C2×C4—224no—
502C2×C4—224no—
503C2×C4—4416no—
504C2×C4—444no—
505C2×C4—444no—
506C2×C4—442no—
507C2×C4—442no—
508C2×C4—442no—
509C2×C4—442no—
510C2×C4—444no—
511C2×C4—442no—
512C2×C4—442no—
513C2×C4—444no—
514C2×C4C22⋊C4×D1114yes—
515C22—224no—
516C22—224no—
517C22—224no—
518C22—444no—
519C22—444no—
520C22—448no—
521C22—444no—
522C22—444no—
523C22—444no—
524C22—444no—
525C22—444no—
526C22—448no—
527C22—448no—
528C22—884no—
529C22—884no—
530C22—884no—
531C22—884no—
532C22C2×C22⋊C4×D1111yescharacteristic
533C22#1062305212yes—
534C22#1062307612yes—
535C22#1062310512yes—
536C22#1062313812yes—
537C22#1062316012yes—
538C22#1062317814yes—
539C22#1062318412yes—
540C22#1062318412yes—
541C22#1062319714yes—
542C22#1062320511yescharacteristic
543C22#1062320511yescharacteristic
544C22#1062323114yes—
545C22#1062324214yes—
546C22#1062324611yescharacteristic
547C22#1062325511yescharacteristic
548C4—24no—
549C4—44no—
550C4—82no—
551C4—82no—
552C4—224no—
553C4—882no—
554C4—882no—
555C2—444no—
556C2—884no—
557C2#1307119311yescharacteristic
558C2#1307119511yescharacteristic
559C2#1307120711yescharacteristic
560C2#1307177114yes—
561C2#1307661912yes—
562C2#1307662112yes—
563C2#1307663912yes—
564C2#1307664912yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1445C2
socle, cosocleC24×C11C24
prime radicalC22×#66948C2
hypercenter#1445D11
hypocenterC11#14659
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
2. C2×#10622277C2semidirect
3. C2×#10622280C2semidirect
4. #13066884C2semidirect
5. #13066860C2semidirect
6. #13066856C2semidirect
7. #13066856C2semidirect
8. #13066856C2semidirect
9. C11×#1445C2semidirect
22. C2×#66948C4semidirect
144. C2×C4×D11C22⋊C4semidirect
156. #1445D11semidirect
433. C11#14659semidirect

Maximal subgroups

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

subgroupindex
C22×#669482
C2×#106222772
C2×#106222802
#130668842
#130668602
#130668562
C11×#14452
#1465911