Finite Group Databasebeta

← #14660275

Subgroups — #14660275

Order 2816.

1434 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66977C211yesmaximal, characteristic
2C22×#66888C212yesmaximal, complemented
3C2×#10622820C211yesmaximal, characteristic
4C2×#10622192C212yesmaximal, complemented
5C2×C11×#407C211yesmaximal, characteristic
6C24×C4×C11C2211yescharacteristic
7C23×Dic22C2211yescharacteristic
8C22×C11×M16C2212yes—
9C22×C22⋊Dic11C412yes—
10C22×C4⋊Dic11C2211yescharacteristic
11C2×#66977—22no—
12C2×#66977—22no—
13C2×#66977—24no—
14C2×#66977—24no—
15C22×Dic11⋊C4C412yes—
16C22×#4318C2212yes—
17C11×#407—24no—
18C2×C11×C22⋊C8—22no—
19#10622820—24no—
20C2×C22⋊(C11⋊C8)—22no—
21C2×#66888—24no—
22C2×#66888—24no—
23C2×#66888—24no—
24#10622192—24no—
25C25×C11C2×C411yescharacteristic
26C23×C4×C11—22no—
27C23×C4×C11—22no—
28C23×C4×C11—22no—
29C23×C4×C11—22no—
30C23×C4×C11—22no—
31C23×C4×C11—22no—
32C23×C4×C11C2×C411yescharacteristic
33C23×C4×C11D412yes—
34C23×C4×C11D412yes—
35C23×C4×C11C2311yescharacteristic
36C23×Dic11C2×C412yes—
37C23×Dic11C2×C412yes—
38C22×Dic22—22no—
39C22×Dic22—22no—
40C22×Dic22—21no—
41C22×Dic22—22no—
42C22×Dic22—21no—
43C22×Dic22—22no—
44C22×Dic22—22no—
45C22×Dic22D414yes—
46C2×C11×M16—22no—
47C2×C11×M16—22no—
48C2×C11×M16—22no—
49C2×C11×M16—22no—
50C2×C11×M16—22no—
51C2×C11×M16D414yes—
52C22×C8×C11—22no—
53C2×C22⋊Dic11—24no—
54C2×C22⋊Dic11—24no—
55C2×C22⋊Dic11—24no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11D414yes—
60#66977—216no—
61#66977—216no—
62C2×Dic11⋊C4—24no—
63C2×Dic11⋊C4—24no—
64C2×Dic11⋊C4—24no—
65C2×#4318—22no—
66C2×#4318—22no—
67C2×#4318—22no—
68C2×#4318—22no—
69C2×#4318—22no—
70C2×#4318D414yes—
71C22×C11⋊C8—22no—
72C11×C22⋊C8—28no—
73C22⋊(C11⋊C8)—28no—
74#66888—216no—
75#10968—111nomaximal, Sylow
76C24×C11—24no—
77C24×C11—21no—
78C24×C11—21no—
79C24×C11—22no—
80C24×C11—22no—
81C24×C11—42no—
82C24×C11C22⋊C412yes—
83C24×C11C22×C411yescharacteristic
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—24no—
91C22×C4×C11—24no—
92C22×C4×C11—24no—
93C22×C4×C11—24no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—42no—
97C22×C4×C11—42no—
98C22×C4×C11—42no—
99C22×C4×C11—42no—
100C22×C4×C11—42no—
101C22×C4×C11—42no—
102C22×C4×C11—42no—
103C22×C4×C11—42no—
104C22×C4×C11C22⋊C412yes—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D412yes—
111C22×C4×C11#4112yes—
112C22×C4×C11#4112yes—
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—22no—
116C22×Dic11—22no—
117C22×Dic11—24no—
118C22×Dic11—24no—
119C22×Dic11—44no—
120C22×Dic11C22⋊C414yes—
121C22×Dic11C22⋊C414yes—
122C2×Dic22—24no—
123C2×Dic22—24no—
124C2×Dic22—24no—
125C2×Dic22—24no—
126C2×Dic22—24no—
127C2×Dic22—24no—
128C2×Dic22—41no—
129C2×Dic22—41no—
130C2×Dic22—42no—
131C2×Dic22—42no—
132C2×Dic22—42no—
133C2×Dic22—42no—
134C2×Dic22—41no—
135C2×Dic22—41no—
136C2×Dic22—42no—
137C2×Dic22—42no—
138C11×M16—24no—
139C11×M16—24no—
140C11×M16—42no—
141C11×M16—42no—
142C2×C8×C11—24no—
143C2×C8×C11—42no—
144C2×C8×C11—42no—
145C22⋊Dic11—216no—
146C4⋊Dic11—24no—
147C4⋊Dic11—24no—
148Dic11⋊C4—216no—
149#4318—24no—
150#4318—24no—
151#4318—42no—
152#4318—42no—
153C2×C11⋊C8—24no—
154C2×C11⋊C8—42no—
155C2×C11⋊C8—42no—
156C22×C22⋊Q8—111no—
157C22×#101—112no—
158C2×#407—111no—
159C2×#407D1111yescharacteristic
160C2×#343—112no—
161C23×C11—22no—
162C23×C11—22no—
163C23×C11—24no—
164C23×C11—24no—
165C23×C11—22no—
166C23×C11—22no—
167C23×C11—22no—
168C23×C11—22no—
169C23×C11—22no—
170C23×C11—22no—
171C23×C11—48no—
172C23×C11—48no—
173C23×C11—42no—
174C23×C11—42no—
175C23×C11—42no—
176C23×C11—42no—
177C23×C11#10114yescomplemented
178C23×C11C2×C22⋊C411yescharacteristic
179C23×C11C2×C22⋊C411yescharacteristic
180C23×C11C2×C22⋊C411yescharacteristic
181C23×C11C4×D412yes—
182C23×C11C4×D412yes—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—44no—
189C2×C4×C11—44no—
190C2×C4×C11—44no—
191C2×C4×C11—44no—
192C2×C4×C11#12011yescharacteristic
193C2×C4×C11#12012yes—
194C2×C4×C11#12012yes—
195C2×C4×C11#12012yes—
196C2×C4×C11#12011yescharacteristic
197C2×C4×C11#12112yes—
198C2×C4×C11#12112yes—
199C2×C4×C11#12112yes—
200C2×C4×C11#12112yes—
201C2×C4×C11#12112yes—
202C2×C4×C11#12112yes—
203C2×C4×C11#12312yes—
204C2×C4×C11#12311yescharacteristic
205C2×C4×C11#12311yescharacteristic
206C2×C4×C11#12412yes—
207C2×C4×C11#12712yes—
208C2×Dic11—24no—
209C2×Dic11—24no—
210C2×Dic11—28no—
211C2×Dic11—44no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—44no—
215C2×Dic11—44no—
216C2×Dic11—44no—
217Dic22—44no—
218Dic22—44no—
219Dic22—44no—
220Dic22—44no—
221C8×C11—44no—
222C11⋊C8—44no—
223C23×Q8—111no—
224C24×C4C2×D1111yescharacteristic
225C22×M16—112no—
226C22×M16C2×D1112yes—
227C2×C22⋊Q8—224no—
228C2×C22⋊Q8—224no—
229C2×C22⋊Q8—222no—
230C2×C22⋊Q8—222no—
231C22×C4⋊C4—111no—
232C22×C4⋊C4—112no—
233C22×C22⋊C4—112no—
234C2×#101—224no—
235C2×#101—224no—
236C2×#101—224no—
237#407—24no—
238#407—224no—
239C2×C22⋊C8—22no—
240C2×C22⋊C8—222no—
241#343—224no—
242C22×C11—24no—
243C22×C11—24no—
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—21no—
247C22×C11—21no—
248C22×C11—24no—
249C22×C11—24no—
250C22×C11—24no—
251C22×C11—48no—
252C22×C11—48no—
253C22×C11—42no—
254C22×C11—42no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11#37911yescharacteristic
258C22×C11#38612yes—
259C22×C11#38611yescharacteristic
260C22×C11#38611yescharacteristic
261C22×C11#39012yes—
262C22×C11C2×#10112yes—
263C22×C11#41312yes—
264C4×C11—42no—
265C4×C11#39212yes—
266C4×C11#39212yes—
267C4×C11#39412yes—
268C4×C11#39412yes—
269Dic11—44no—
270Dic11—44no—
271C25C4×D1111yescharacteristic
272C22×Q8—114no—
273C22×Q8—221no—
274C22×Q8—222no—
275C22×Q8—222no—
276C22×Q8—222no—
277C22×Q8—222no—
278C22×Q8—221no—
279C22×Q8—222no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—112no—
287C23×C4—112no—
288C23×C4C4×D1111yescharacteristic
289C23×C4D4412yes—
290C23×C4C22⋊D1112yes—
291C23×C4C22×D1111yescharacteristic
292C2×M16—22no—
293C2×M16—22no—
294C2×M16—22no—
295C2×M16—22no—
296C2×M16—22no—
297C2×M16—114no—
298C2×M16—222no—
299C2×M16—222no—
300C2×M16—222no—
301C2×M16—222no—
302C2×M16—222no—
303C2×M16C22⋊D1114yes—
304C22×C8—22no—
305C22×C8—222no—
306C22⋊Q8—2216no—
307C22⋊Q8—2216no—
308C2×C4⋊C4—114no—
309C2×C4⋊C4—224no—
310C2×C4⋊C4—224no—
311C2×C4⋊C4—224no—
312C2×C4⋊C4—221no—
313C2×C4⋊C4—222no—
314C2×C4⋊C4—221no—
315C2×C22⋊C4—224no—
316C2×C22⋊C4—224no—
317C2×C22⋊C4—224no—
318#101—2216no—
319C22⋊C8—28no—
320C22⋊C8—228no—
321C2×C11—22no—
322C2×C11—22no—
323C2×C11—44no—
324C2×C11#143811yescharacteristic
325C2×C11#178411yescharacteristic
326C2×C11#178511yescharacteristic
327C2×C11#190112yes—
328C2×C11#190112yes—
329C24—24no—
330C24—21no—
331C24—21no—
332C24—22no—
333C24—22no—
334C24—42no—
335C24(C2×D11)⋊C412yes—
336C24C2×C4×D1111yescharacteristic
337C2×Q8—224no—
338C2×Q8—224no—
339C2×Q8—224no—
340C2×Q8—224no—
341C2×Q8—224no—
342C2×Q8—224no—
343C2×Q8—441no—
344C2×Q8—442no—
345C2×Q8—442no—
346C2×Q8—441no—
347C2×Q8—441no—
348C2×Q8—442no—
349C2×Q8—442no—
350C2×Q8—442no—
351C2×Q8—442no—
352C2×Q8—441no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—24no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—24no—
362C22×C4—24no—
363C22×C4—24no—
364C22×C4—22no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4—42no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4—42no—
373C22×C4—114no—
374C22×C4—114no—
375C22×C4—222no—
376C22×C4—222no—
377C22×C4—224no—
378C22×C4—222no—
379C22×C4—222no—
380C22×C4—224no—
381C22×C4—444no—
382C22×C4(C2×D11)⋊C412yes—
383C22×C4C2×D4411yescharacteristic
384C22×C4#433912yes—
385C22×C4D4×D1112yes—
386C22×C4D4×D1112yes—
387C22×C4D4×D1112yes—
388C22×C4#434112yes—
389C22×C4C2×C22⋊D1111yescharacteristic
390C22×C4C2×C22⋊D1112yes—
391M16—24no—
392M16—24no—
393M16—42no—
394M16—42no—
395M16—224no—
396M16—224no—
397M16—442no—
398M16—442no—
399C2×C8—24no—
400C2×C8—42no—
401C2×C8—42no—
402C2×C8—224no—
403C2×C8—442no—
404C2×C8—442no—
405C4⋊C4—2216no—
406C4⋊C4—224no—
407C4⋊C4—224no—
408C22⋊C4—2216no—
409C11#1096811yescharacteristic, complemented, Sylow
410C23—22no—
411C23—22no—
412C23—24no—
413C23—24no—
414C23—22no—
415C23—22no—
416C23—22no—
417C23—22no—
418C23—22no—
419C23—22no—
420C23—48no—
421C23—48no—
422C23—42no—
423C23—42no—
424C23—42no—
425C23—42no—
426C23#6688814yescomplemented
427C23C22⋊C4×D1111yescharacteristic
428C23C22⋊C4×D1111yescharacteristic
429C23(C22⋊D11)⋊C412yes—
430C23C2×(C2×D11)⋊C411yescharacteristic
431C23C4×C22⋊D1112yes—
432Q8—444no—
433Q8—444no—
434Q8—444no—
435Q8—444no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—44no—
442C2×C4—44no—
443C2×C4—44no—
444C2×C4—44no—
445C2×C4—224no—
446C2×C4—224no—
447C2×C4—228no—
448C2×C4—444no—
449C2×C4—444no—
450C2×C4—444no—
451C2×C4—442no—
452C2×C4—442no—
453C2×C4—444no—
454C2×C4#6693511yescharacteristic
455C2×C4#6693512yes—
456C2×C4#6693612yes—
457C2×C4#6693712yes—
458C2×C4#6693712yes—
459C2×C4#6693812yes—
460C2×C4#6693911yescharacteristic
461C2×C4#6698211yescharacteristic
462C2×C4#6698312yes—
463C2×C4#6699012yes—
464C2×C4#6699012yes—
465C2×C4#6699112yes—
466C2×C4#6699212yes—
467C2×C4#6699212yes—
468C2×C4#6699312yes—
469C2×C4#6700611yescharacteristic
470C8—44no—
471C8—444no—
472C22—24no—
473C22—24no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—24no—
479C22—24no—
480C22—24no—
481C22—48no—
482C22—48no—
483C22—42no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22#1062256811yescharacteristic
488C22#1062256912yes—
489C22#1062257012yes—
490C22#1062257111yescharacteristic
491C22#1062274512yes—
492C22C2×#6688812yes—
493C22#1062282611yescharacteristic
494C4—42no—
495C4—444no—
496C4—444no—
497C4#1062257212yes—
498C4#1062257312yes—
499C4#1062257412yes—
500C4#1062283612yes—
501C2—22no—
502C2—22no—
503C2—44no—
504C2#1306685511yescharacteristic
505C2#1306853911yescharacteristic
506C2#1306854211yescharacteristic
507C2#1306908212yes—
508C2#1306908412yes—
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#407C2
socleC23×C11C2×C22⋊C4
prime radicalC25×C11C2×C4
cosocleC23×C4×C11C23
hypercenterC2×#407D11
hypocenterC11#10968
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C22×#66888C2semidirect
4. C2×#10622192C2semidirect
177. C23×C11#101semidirect
409. C11#10968semidirect
426. C23#66888semidirect

Maximal subgroups

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

subgroupindex
C22×#669772
C22×#668882
C2×#106228202
C2×#106221922
C2×C11×#4072
#1096811