Finite Group Databasebeta

← #14675544

Subgroups — #14675544

Order 2816.

1942 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66945C211yesmaximal, characteristic
2C2×#10622279C211yesmaximal, characteristic
3C2×#10622279C211yesmaximal, characteristic
4#13066885C211yesmaximal, characteristic, complemented
5#13066884C211yesmaximal, characteristic, complemented
6#13066883C211yesmaximal, characteristic, complemented
7#13066864C214yesmaximal
8#95×Dic11C214yesmaximal, complemented
9C11×#1445C211yesmaximal, characteristic, complemented
10C23×C4×D11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×(C2×D11)⋊C4C2212yes—
13C22×(C2×D11)⋊C4C2212yes—
14C22×(C2×D11)⋊C4C2212yes—
15C22×C4⋊Dic11C2211yescharacteristic
16C22×C4×Dic11C2212yes—
17C22×C4×Dic11C2212yes—
18C22×C4×Dic11C2212yes—
19C2×#66945—24no—
20C2×#66945—24no—
21C2×#66945C418yescomplemented
22C2×C11×#95C2214yes—
23C2×C11×#95C2211yescharacteristic
24C2×C11×#95C2211yescharacteristic
25C2×C11⋊#95C2214yes—
26C2×C11⋊#95C2214yes—
27C2×C11⋊#95C2214yes—
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2211yescharacteristic
30#10622279—24no—
31#10622279—24no—
32C24×D11C2311yescharacteristic
33C23×C4×C11C2312yes—
34C23×C4×C11C2312yes—
35C23×C4×C11C2312yes—
36C23×C4×C11C2311yescharacteristic
37C23×Dic11C2312yes—
38C23×Dic11C2312yes—
39C23×Dic11C2312yes—
40C23×Dic11C2311yescharacteristic
41C22×C4×D11—28no—
42C22×C4×D11C2×C414yes—
43C22×C4×D11D414yes—
44C22×C4×D11D414yes—
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4C2×C414yes—
48C2×(C2×D11)⋊C4—24no—
49C2×(C2×D11)⋊C4—24no—
50C2×(C2×D11)⋊C4—24no—
51C2×(C2×D11)⋊C4—24no—
52C2×(C2×D11)⋊C4—24no—
53C2×(C2×D11)⋊C4—24no—
54C2×(C2×D11)⋊C4—24no—
55C2×(C2×D11)⋊C4—24no—
56C2×(C2×D11)⋊C4C2×C418yes—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11—22no—
59C2×C4⋊Dic11C2×C414yes—
60C2×C4×Dic11—24no—
61C2×C4×Dic11—24no—
62C2×C4×Dic11—24no—
63C2×C4×Dic11—24no—
64C2×C4×Dic11—28no—
65C2×C4×Dic11—28no—
66C2×C4×Dic11C2×C418yes—
67#66945—232no—
68C11×#95—22no—
69C11×#95—22no—
70C11×#95—28no—
71C11⋊#95—22no—
72C11⋊#95—22no—
73C11⋊#95—28no—
74C11⋊#95—28no—
75C11⋊#95—28no—
76#13853—111nomaximal, Sylow
77C24×C11C2411yescharacteristic
78C23×D11—22no—
79C23×D11—22no—
80C23×D11—22no—
81C23×D11—22no—
82C23×D11—24no—
83C23×D11C22×C412yes—
84C23×D11C2×D412yes—
85C23×D11C2×D412yes—
86C22×C4×C11—24no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—24no—
92C22×C4×C11—24no—
93C22×C4×C11—24no—
94C22×C4×C11—24no—
95C22×C4×C11—24no—
96C22×C4×C11—24no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11C22×C414yes—
100C22×C4×C11C22×C412yes—
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D412yes—
103C22×C4×C11#4114yes—
104C22×C4×C11#4114yes—
105C22×Dic11—22no—
106C22×Dic11—22no—
107C22×Dic11—22no—
108C22×Dic11—22no—
109C22×Dic11—24no—
110C22×Dic11—24no—
111C22×Dic11—24no—
112C22×Dic11—24no—
113C22×Dic11—24no—
114C22×Dic11—24no—
115C22×Dic11—22no—
116C22×Dic11—22no—
117C22×Dic11C22×C414yes—
118C22×Dic11C22×C412yes—
119C22×Dic11C2×D412yes—
120C22×Dic11C2×D412yes—
121C22×Dic11#4114yes—
122C22×Dic11#4114yes—
123C22×Dic11#4118yes—
124C2×C4×D11—216no—
125C2×C4×D11—216no—
126C2×C4×D11—216no—
127C2×C4×D11C22⋊C4116yes—
128C11×C4⋊C4—28no—
129(C2×D11)⋊C4—216no—
130(C2×D11)⋊C4—216no—
131(C2×D11)⋊C4—216no—
132C4⋊Dic11—28no—
133C4×Dic11—216no—
134C4×Dic11—48no—
135C4×Dic11—48no—
136C22×#117—111no—
137C2×C4×C22⋊C4—111no—
138C2×C4×C22⋊C4—111no—
139#1445—111no—
140#1445—111no—
141#1445—111no—
142#1445D1111yescharacteristic, complemented
143#1440—114no—
144C4×#95—114no—
145C23×C11C23×C411yescharacteristic
146C23×C11C22×D411yescharacteristic
147C23×C11C22×D411yescharacteristic
148C23×C11C2×#4112yes—
149C23×C11C2×#4112yes—
150C23×C11C2×#4114yes—
151C23×C11C2×#4112yes—
152C23×C11C2×#4112yes—
153C22×D11—24no—
154C22×D11—24no—
155C22×D11—24no—
156C22×D11—24no—
157C22×D11—24no—
158C22×D11—24no—
159C22×D11—24no—
160C22×D11—22no—
161C22×D11—22no—
162C22×D11—22no—
163C22×D11—22no—
164C22×D11—44no—
165C22×D11—44no—
166C22×D11—44no—
167C22×D11—44no—
168C22×D11C2×C22⋊C414yes—
169C2×C4×C11—24no—
170C2×C4×C11—24no—
171C2×C4×C11—24no—
172C2×C4×C11—24no—
173C2×C4×C11—28no—
174C2×C4×C11—24no—
175C2×C4×C11—24no—
176C2×C4×C11—28no—
177C2×C4×C11—28no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—44no—
181C2×C4×C11—44no—
182C2×C4×C11—44no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11C2×C22⋊C414yes—
188C2×Dic11—24no—
189C2×Dic11—28no—
190C2×Dic11—24no—
191C2×Dic11—24no—
192C2×Dic11—28no—
193C2×Dic11—28no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196C2×Dic11—44no—
197C2×Dic11—44no—
198C2×Dic11—44no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11C2×C22⋊C414yes—
204C2×Dic11#11718yes—
205C2×Dic11#12318yes—
206C2×Dic11#12318yes—
207C4×D11—232no—
208C24×C4—111no—
209C2×#117—118no—
210C2×#117—224no—
211C2×#117—224no—
212C22×C4⋊C4—111no—
213C22×C4⋊C4C2×D1111yescharacteristic
214C22×C22⋊C4—112no—
215C22×C22⋊C4—112no—
216C22×C22⋊C4—112no—
217C22×C42—112no—
218C22×C42—112no—
219C22×C42—112no—
220C4×C22⋊C4—224no—
221C4×C22⋊C4—224no—
222C2×#95—114no—
223C2×#95—114no—
224C2×#95—114no—
225C2×#95—111no—
226C2×#95—111no—
227C2×#95C2×D1114yes—
228C2×#95C2×D1111yescharacteristic
229C2×#95C2×D1111yescharacteristic
230C22×C11C22×C22⋊C411yescharacteristic
231C22×C11C2×#11712yes—
232C22×C11C4×#4112yes—
233C22×C11C4×#4112yes—
234C22×C11C2×#12312yes—
235C22×C11C2×#12312yes—
236C22×C11#52512yes—
237C22×C11#52512yes—
238C22×C11#52914yes—
239C22×C11#52914yes—
240C22×C11#52914yes—
241C22×C11#52914yes—
242C22×C11#53211yescharacteristic
243C22×C11#53211yescharacteristic
244C22×C11#53211yescharacteristic
245C22×C11#53211yescharacteristic
246C2×D11—24no—
247C2×D11—24no—
248C2×D11—24no—
249C2×D11—44no—
250C2×D11—44no—
251C2×D11—44no—
252C2×D11—44no—
253C2×D11—48no—
254C4×C11—24no—
255C4×C11—44no—
256C4×C11—44no—
257C4×C11—44no—
258Dic11—44no—
259Dic11—44no—
260Dic11—44no—
261Dic11#38118yes—
262C25—111no—
263C23×C4—111no—
264C23×C4—114no—
265C23×C4—114no—
266C23×C4—114no—
267C23×C4—112no—
268C23×C4—112no—
269C23×C4—112no—
270C23×C4—228no—
271C23×C4C22×D1112yes—
272C23×C4C22×D1112yes—
273C23×C4C22×D1112yes—
274C23×C4C22×D1111yescharacteristic
275#117—2232no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—114no—
279C2×C4⋊C4—222no—
280C2×C4⋊C4—222no—
281C2×C4⋊C4C4×D1114yes—
282C2×C22⋊C4—118no—
283C2×C22⋊C4—224no—
284C2×C22⋊C4—224no—
285C2×C22⋊C4—224no—
286C2×C22⋊C4—224no—
287C2×C22⋊C4—224no—
288C2×C22⋊C4—224no—
289C2×C22⋊C4—224no—
290C2×C22⋊C4—224no—
291C2×C42—118no—
292C2×C42—224no—
293C2×C42—224no—
294C2×C42—224no—
295C2×C42—224no—
296C2×C42—228no—
297C2×C42—228no—
298#95—22no—
299#95—22no—
300#95—28no—
301#95—228no—
302#95—228no—
303#95—222no—
304#95—222no—
305#95—228no—
306C2×C11C2×#38111yescharacteristic
307C2×C11#229711yescharacteristic
308C2×C11#229711yescharacteristic
309C2×C11#229814yes—
310C2×C11#239512yes—
311C2×C11#239512yes—
312C2×C11#239512yes—
313C2×C11#239512yes—
314D11—44no—
315C24—112no—
316C24—112no—
317C24—112no—
318C24—222no—
319C24—222no—
320C24—222no—
321C24—222no—
322C24—224no—
323C24C23×D1111yescharacteristic
324C22×C4—24no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—24no—
330C22×C4—24no—
331C22×C4—24no—
332C22×C4—24no—
333C22×C4—24no—
334C22×C4—24no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—112no—
338C22×C4—112no—
339C22×C4—112no—
340C22×C4—118no—
341C22×C4—1116no—
342C22×C4—114no—
343C22×C4—114no—
344C22×C4—114no—
345C22×C4—2216no—
346C22×C4—2216no—
347C22×C4—2216no—
348C22×C4—222no—
349C22×C4—222no—
350C22×C4—222no—
351C22×C4—222no—
352C22×C4—222no—
353C22×C4—224no—
354C22×C4—224no—
355C22×C4—222no—
356C22×C4—224no—
357C22×C4—224no—
358C22×C4—224no—
359C22×C4—224no—
360C22×C4C2×C4×D1114yes—
361C22×C4C2×C4×D1112yes—
362C22×C4D4×D1112yes—
363C22×C4D4×D1112yes—
364C22×C4#434114yes—
365C22×C4#434314yes—
366C4⋊C4—28no—
367C4⋊C4—228no—
368C22⋊C4—2216no—
369C22⋊C4—2216no—
370C22⋊C4—2216no—
371C42—2216no—
372C42—448no—
373C42—448no—
374C11#1385311yescharacteristic, complemented, Sylow
375C23—114no—
376C23—222no—
377C23—222no—
378C23—224no—
379C23—224no—
380C23—224no—
381C23—224no—
382C23—224no—
383C23—224no—
384C23—224no—
385C23—222no—
386C23—222no—
387C23—444no—
388C23—444no—
389C23—444no—
390C23—444no—
391C23C22×C4×D1111yescharacteristic
392C23C2×D4×D1111yescharacteristic
393C23C2×D4×D1111yescharacteristic
394C23C2×#434112yes—
395C23C2×#434312yes—
396C23#41×D1112yes—
397C23#41×D1112yes—
398C23#41×D1114yes—
399C2×C4—24no—
400C2×C4—24no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—28no—
404C2×C4—24no—
405C2×C4—28no—
406C2×C4—24no—
407C2×C4—28no—
408C2×C4—44no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—44no—
412C2×C4—44no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—114no—
418C2×C4—118no—
419C2×C4—118no—
420C2×C4—118no—
421C2×C4—2232no—
422C2×C4—228no—
423C2×C4—224no—
424C2×C4—228no—
425C2×C4—224no—
426C2×C4—224no—
427C2×C4—228no—
428C2×C4—442no—
429C2×C4—442no—
430C2×C4—444no—
431C2×C4—444no—
432C2×C4—442no—
433C2×C4—442no—
434C2×C4—442no—
435C2×C4—442no—
436C2×C4—444no—
437C2×C4C22⋊C4×D1114yes—
438C22—224no—
439C22—224no—
440C22—224no—
441C22—448no—
442C22—444no—
443C22—444no—
444C22—444no—
445C22—444no—
446C22C2×C22⋊C4×D1111yescharacteristic
447C22D11×#11712yes—
448C22C4×#434112yes—
449C22C4×#434312yes—
450C22#1062313712yes—
451C22#1062315514yes—
452C22#1062315812yes—
453C22#1062318014yes—
454C22D11×#12312yes—
455C22D11×#12312yes—
456C22#1062319911yescharacteristic
457C22#1062319911yescharacteristic
458C22#1062322214yes—
459C22#1062323714yes—
460C22#1062324711yescharacteristic
461C22#1062325611yescharacteristic
462C4—24no—
463C4—44no—
464C4—44no—
465C4—44no—
466C4—118no—
467C4—444no—
468C4—444no—
469C4—444no—
470C2—444no—
471C2D11×#38111yescharacteristic
472C2#1307110311yescharacteristic
473C2#1307110511yescharacteristic
474C2#1307110814yes—
475C2#1307187812yes—
476C2#1307188012yes—
477C2#1307188112yes—
478C2#1307188212yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1445C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1445D11
hypocenterC11#13853
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
4. #13066885C2semidirect
5. #13066884C2semidirect
6. #13066883C2semidirect
8. #95×Dic11C2semidirect
9. C11×#1445C2semidirect
21. C2×#66945C4semidirect
142. #1445D11semidirect
374. C11#13853semidirect

Maximal subgroups

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

subgroupindex
C22×#669452
C2×#106222792
#130668852
#130668842
#130668832
#130668642
#95×Dic112
C11×#14452
#1385311