Finite Group Databasebeta

← #14680983

Subgroups — #14680983

Order 2816.

2150 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66946C211yesmaximal, characteristic
2C2×#10622264C211yesmaximal, characteristic, complemented
3C2×#10622263C211yesmaximal, characteristic, complemented
4#13066884C211yesmaximal, characteristic, complemented
5#13066860C214yesmaximal, complemented
6#13066856C211yesmaximal, characteristic
7#13066856C211yesmaximal, characteristic
8(C2×D11)⋊#95C214yesmaximal, complemented
9C11×#1445C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C23×C4×D11C2212yes—
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×(C2×D11)⋊C4C2212yes—
14C22×(C2×D11)⋊C4C2214yes—
15C22×(C2×D11)⋊C4C2214yes—
16C22×Dic11⋊C4C2212yes—
17C22×C4×Dic11C2211yescharacteristic
18C2×#66946—24no—
19C2×#66946—24no—
20C2×#66946C418yescomplemented
21C2×C11×#95C2211yescharacteristic
22C2×C11×#95C2211yescharacteristic
23C2×C11×#95C2214yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2211yescharacteristic
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2214yes—
30#10622264—24no—
31#10622263—24no—
32C24×D11C2312yes—
33C23×C4×C11C2312yes—
34C23×C4×C11C2312yes—
35C23×C4×C11C2312yes—
36C23×C4×C11C2311yescharacteristic
37C23×Dic11C2312yes—
38C23×Dic11C2312yes—
39C23×Dic11C2311yescharacteristic
40C23×Dic11C2311yescharacteristic
41C22×D44—28no—
42C22×D44—22no—
43C22×D44—22no—
44C22×D44C2×C414yes—
45C22×C4×D11—24no—
46C22×C4×D11—24no—
47C22×C4×D11—44no—
48C22×C4×D11—44no—
49C22×C4×D11C2×C418yes—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4C2×C414yes—
53C2×(C2×D11)⋊C4—24no—
54C2×(C2×D11)⋊C4—24no—
55C2×(C2×D11)⋊C4—28no—
56C2×(C2×D11)⋊C4—28no—
57C2×(C2×D11)⋊C4—44no—
58C2×(C2×D11)⋊C4—44no—
59C2×(C2×D11)⋊C4—44no—
60C2×(C2×D11)⋊C4—44no—
61C2×(C2×D11)⋊C4C2×C418yes—
62C2×Dic11⋊C4—24no—
63C2×Dic11⋊C4—44no—
64C2×C4×Dic11C2×C414yes—
65C2×C4×Dic11D414yes—
66C2×C4×Dic11D414yes—
67#66946—232no—
68C11×#95—22no—
69C11×#95—22no—
70C11×#95—44no—
71C11⋊#95—22no—
72C11⋊#95—22no—
73C11⋊#95—24no—
74C11⋊#95—24no—
75C11⋊#95—24no—
76C11⋊#95—44no—
77#14345—111nomaximal, Sylow
78C24×C11C2411yescharacteristic
79C23×D11—22no—
80C23×D11—22no—
81C23×D11—24no—
82C23×D11—24no—
83C23×D11—24no—
84C23×D11—24no—
85C23×D11—24no—
86C23×D11C22×C414yes—
87C23×D11#4118yes—
88C22×C4×C11—24no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—24no—
92C22×C4×C11—24no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—24no—
96C22×C4×C11—24no—
97C22×C4×C11—22no—
98C22×C4×C11—24no—
99C22×C4×C11—24no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11C22×C414yes—
104C22×C4×C11C22×C412yes—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×D412yes—
107C22×Dic11—22no—
108C22×Dic11—22no—
109C22×Dic11—24no—
110C22×Dic11—24no—
111C22×Dic11—22no—
112C22×Dic11—22no—
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—24no—
116C22×Dic11—24no—
117C22×Dic11—22no—
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11C22×C412yes—
122C22×Dic11C22×C412yes—
123C22×Dic11C2×D412yes—
124C22×Dic11C2×D412yes—
125C22×Dic11C2×D412yes—
126C22×Dic11C2×D412yes—
127C2×D44—216no—
128C2×D44—216no—
129C2×D44—216no—
130C2×D44—28no—
131C2×C4×D11—216no—
132C2×C4×D11—416no—
133C2×C4×D11—48no—
134C2×C4×D11—416no—
135C2×C4×D11—48no—
136C11×C4⋊C4—28no—
137(C2×D11)⋊C4—216no—
138(C2×D11)⋊C4—416no—
139(C2×D11)⋊C4—416no—
140Dic11⋊C4—48no—
141C4×Dic11C22⋊C4116yescomplemented
142C22×C4×D4—111no—
143C2×#383—111no—
144C2×#382—111no—
145#1445—111no—
146#1445D1111yescharacteristic, complemented
147#1439—114no—
148#1438—111no—
149#1438—111no—
150C22⋊#95—114no—
151C23×C11C23×C411yescharacteristic
152C23×C11C22×D411yescharacteristic
153C23×C11C22×D411yescharacteristic
154C23×C11C2×#4114yes—
155C23×C11H(5,𝔽2)12yes—
156C23×C11H(5,𝔽2)12yes—
157C23×C11H(5,𝔽2)12yes—
158C23×C112−1+412yes—
159C22×D11—24no—
160C22×D11—24no—
161C22×D11—28no—
162C22×D11—28no—
163C22×D11—28no—
164C22×D11—28no—
165C22×D11—28no—
166C22×D11—28no—
167C22×D11—28no—
168C22×D11—28no—
169C22×D11—42no—
170C22×D11—44no—
171C22×D11—42no—
172C22×D11—42no—
173C22×D11—42no—
174C22×D11—44no—
175C22×D11—44no—
176C22×D11—44no—
177C22×D11—44no—
178C22×D11—44no—
179C22×D11#11718yes—
180C2×C4×C11—24no—
181C2×C4×C11—24no—
182C2×C4×C11—24no—
183C2×C4×C11—24no—
184C2×C4×C11—28no—
185C2×C4×C11—42no—
186C2×C4×C11—44no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—44no—
195C2×C4×C11—44no—
196C2×C4×C11—44no—
197C2×C4×C11—44no—
198C2×C4×C11C2×C22⋊C414yes—
199C2×Dic11—24no—
200C2×Dic11—24no—
201C2×Dic11—22no—
202C2×Dic11—22no—
203C2×Dic11—24no—
204C2×Dic11—22no—
205C2×Dic11—22no—
206C2×Dic11—24no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—44no—
214C2×Dic11—44no—
215C2×Dic11—44no—
216C2×Dic11—44no—
217C2×Dic11C2×C22⋊C414yes—
218C2×Dic11C2×C22⋊C414yes—
219D44—232no—
220C4×D11—432no—
221C23×D4—111no—
222C24×C4—112no—
223C2×C4×D4—118no—
224C2×C4×D4—224no—
225C2×C4×D4—224no—
226C22×C4⋊C4—112no—
227C22×C4⋊C4C2×D1111yescharacteristic
228C22×C22⋊C4—112no—
229C22×C22⋊C4—114no—
230C22×C22⋊C4—114no—
231C22×C42—111no—
232#383—224no—
233#382—224no—
234C2×#95—112no—
235C2×#95—112no—
236C2×#95—111no—
237C2×#95—111no—
238C2×#95—112no—
239C2×#95—114no—
240C2×#95C2×D1111yescharacteristic
241C2×#95C2×D1111yescharacteristic
242C2×#95C2×D1114yes—
243C22×C11C22×C22⋊C411yescharacteristic
244C22×C11C2×#11712yes—
245C22×C11#51812yes—
246C22×C11#52012yes—
247C22×C11#52512yes—
248C22×C11#52512yes—
249C22×C11#53511yescharacteristic
250C22×C11#53512yes—
251C22×C11#53511yescharacteristic
252C22×C11#53511yescharacteristic
253C22×C11#53611yescharacteristic
254C22×C11#53712yes—
255C22×C11#53814yes—
256C22×C11#53814yes—
257C22×C11#53914yes—
258C22×C11#53914yes—
259C2×D11—216no—
260C2×D11—28no—
261C2×D11—44no—
262C2×D11—44no—
263C2×D11—48no—
264C2×D11—48no—
265C2×D11—48no—
266C2×D11—48no—
267C2×D11—48no—
268C4×C11—24no—
269C4×C11—44no—
270C4×C11—82no—
271C4×C11—82no—
272Dic11—24no—
273Dic11—24no—
274Dic11—82no—
275Dic11—82no—
276C25—112no—
277C22×D4—114no—
278C22×D4—228no—
279C22×D4—222no—
280C22×D4—222no—
281C23×C4—111no—
282C23×C4—111no—
283C23×C4—118no—
284C23×C4—112no—
285C23×C4—112no—
286C23×C4—224no—
287C23×C4—224no—
288C23×C4—444no—
289C23×C4—444no—
290C23×C4C22×D1112yes—
291C23×C4C22×D1112yes—
292C23×C4C22×D1112yes—
293C23×C4C22×D1111yescharacteristic
294C4×D4—2232no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—224no—
298C2×C4⋊C4—444no—
299C2×C4⋊C4C4×D1114yes—
300C2×C22⋊C4—118no—
301C2×C22⋊C4—224no—
302C2×C22⋊C4—224no—
303C2×C22⋊C4—228no—
304C2×C22⋊C4—228no—
305C2×C22⋊C4—444no—
306C2×C22⋊C4—444no—
307C2×C22⋊C4—444no—
308C2×C22⋊C4—444no—
309C2×C42—114no—
310C2×C42—114no—
311C2×C42—114no—
312#95—22no—
313#95—22no—
314#95—44no—
315#95—224no—
316#95—224no—
317#95—224no—
318#95—222no—
319#95—222no—
320#95—444no—
321C2×C11#228011yescharacteristic
322C2×C11#230911yescharacteristic
323C2×C11#231111yescharacteristic
324C2×C11#231814yes—
325C2×C11#263112yes—
326C2×C11#263312yes—
327C2×C11#263612yes—
328C2×C11#263612yes—
329D11—48no—
330C24—114no—
331C24—118no—
332C24—222no—
333C24—222no—
334C24—224no—
335C24—224no—
336C24—224no—
337C24—224no—
338C24—224no—
339C24C23×D1111yescharacteristic
340C2×D4—2216no—
341C2×D4—2216no—
342C2×D4—2216no—
343C2×D4—228no—
344C22×C4—24no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—24no—
348C22×C4—24no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—24no—
353C22×C4—22no—
354C22×C4—24no—
355C22×C4—24no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—24no—
359C22×C4—112no—
360C22×C4—112no—
361C22×C4—112no—
362C22×C4—112no—
363C22×C4—112no—
364C22×C4—112no—
365C22×C4—2216no—
366C22×C4—222no—
367C22×C4—222no—
368C22×C4—222no—
369C22×C4—222no—
370C22×C4—222no—
371C22×C4—222no—
372C22×C4—222no—
373C22×C4—222no—
374C22×C4—224no—
375C22×C4—224no—
376C22×C4—222no—
377C22×C4—224no—
378C22×C4—222no—
379C22×C4—224no—
380C22×C4—4416no—
381C22×C4—448no—
382C22×C4—4416no—
383C22×C4—448no—
384C22×C4C2×C4×D1114yes—
385C22×C4C2×C4×D1112yes—
386C22×C4D4×D1112yes—
387C22×C4D4×D1112yes—
388C4⋊C4—28no—
389C4⋊C4—448no—
390C22⋊C4—2216no—
391C22⋊C4—4416no—
392C22⋊C4—4416no—
393C42—1116no—
394C11#1434511yescharacteristic, complemented, Sylow
395C23—118no—
396C23—228no—
397C23—224no—
398C23—224no—
399C23—228no—
400C23—228no—
401C23—228no—
402C23—228no—
403C23—228no—
404C23—228no—
405C23—228no—
406C23—444no—
407C23—442no—
408C23—442no—
409C23—444no—
410C23—444no—
411C23—444no—
412C23—444no—
413C23—442no—
414C23—442no—
415C23—444no—
416C23C22×C4×D1111yescharacteristic
417C23C2×D4×D1111yescharacteristic
418C23C2×D4×D1111yescharacteristic
419C23#6703712yes—
420C23#6704012yes—
421C23#41×D1114yes—
422C23#6704212yes—
423C23#6704212yes—
424D4—2232no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—24no—
428C2×C4—24no—
429C2×C4—28no—
430C2×C4—42no—
431C2×C4—44no—
432C2×C4—42no—
433C2×C4—44no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—44no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—44no—
441C2×C4—44no—
442C2×C4—42no—
443C2×C4—114no—
444C2×C4—114no—
445C2×C4—222no—
446C2×C4—222no—
447C2×C4—224no—
448C2×C4—224no—
449C2×C4—224no—
450C2×C4—224no—
451C2×C4—222no—
452C2×C4—222no—
453C2×C4—4432no—
454C2×C4—444no—
455C2×C4—444no—
456C2×C4—442no—
457C2×C4—442no—
458C2×C4—442no—
459C2×C4—442no—
460C2×C4—444no—
461C2×C4—442no—
462C2×C4—442no—
463C2×C4—444no—
464C2×C4C22⋊C4×D1114yes—
465C22—2216no—
466C22—228no—
467C22—448no—
468C22—448no—
469C22—448no—
470C22—448no—
471C22—444no—
472C22—444no—
473C22—448no—
474C22C2×C22⋊C4×D1111yescharacteristic
475C22D11×#11712yes—
476C22#1062307612yes—
477C22#1062310512yes—
478C22#1062313812yes—
479C22#1062316012yes—
480C22#1062316914yes—
481C22#1062318712yes—
482C22#1062318712yes—
483C22#1062318814yes—
484C22#1062320511yescharacteristic
485C22#1062320511yescharacteristic
486C22#1062322314yes—
487C22#1062323514yes—
488C22#1062324611yescharacteristic
489C22#1062325511yescharacteristic
490C4—24no—
491C4—44no—
492C4—82no—
493C4—82no—
494C4—224no—
495C4—224no—
496C4—882no—
497C4—882no—
498C2—448no—
499C2#1307099611yescharacteristic
500C2#1307119511yescharacteristic
501C2#1307120711yescharacteristic
502C2#1307124814yes—
503C2#1307447012yes—
504C2#1307448612yes—
505C2#1307451412yes—
506C2#1307451612yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1445C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1445D11
hypocenterC11#14345
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
2. C2×#10622264C2semidirect
3. C2×#10622263C2semidirect
4. #13066884C2semidirect
5. #13066860C2semidirect
8. (C2×D11)⋊#95C2semidirect
9. C11×#1445C2semidirect
20. C2×#66946C4semidirect
141. C4×Dic11C22⋊C4semidirect
146. #1445D11semidirect
394. C11#14345semidirect

Maximal subgroups

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

subgroupindex
C22×#669462
C2×#106222642
C2×#106222632
#130668842
#130668602
#130668562
(C2×D11)⋊#952
C11×#14452
#1434511