Finite Group Databasebeta

← #14660274

Subgroups — #14660274

Order 2816.

1434 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66999C211yesmaximal, characteristic
2C22×#66900C211yesmaximal, characteristic, complemented
3C2×#10622739C212yesmaximal
4C2×#10622192C212yesmaximal, complemented
5C22×C11×#101C211yesmaximal, characteristic, complemented
6C23×Q8×C11C2211yescharacteristic
7C23×C4×D11C2211yescharacteristic
8C22×C11×M16C2212yes—
9C2×#66999—22no—
10C2×#66999—22no—
11C2×#66999—24no—
12C2×#66999—24no—
13C22×(C2×D11)⋊C4C412yes—
14C22×C4⋊Dic11C2211yescharacteristic
15C22×Dic11⋊C4C412yes—
16C22×#4318C2212yes—
17C2×C11×#101—22no—
18C2×C11×#101—24no—
19C2×#66900—22no—
20C2×#66900—24no—
21#10622739—24no—
22#10622739—24no—
23C2×(C2×D11)⋊C8—24no—
24#10622192—24no—
25C24×D11C2×C411yescharacteristic
26C22×Q8×C11—22no—
27C22×Q8×C11—22no—
28C22×Q8×C11—22no—
29C22×Q8×C11—22no—
30C22×Q8×C11—22no—
31C22×Q8×C11—22no—
32C22×Q8×C11D412yes—
33C22×Q8×C11D412yes—
34C23×C4×C11C2×C412yes—
35C23×C4×C11C2311yescharacteristic
36C23×Dic11C2×C411yescharacteristic
37C23×Dic11C2×C412yes—
38C22×C4×D11—22no—
39C22×C4×D11—22no—
40C22×C4×D11—21no—
41C22×C4×D11—22no—
42C22×C4×D11—21no—
43C22×C4×D11—22no—
44C22×C4×D11—22no—
45C22×C4×D11D414yes—
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—
53#66999—216no—
54#66999—216no—
55C2×(C2×D11)⋊C4—24no—
56C2×(C2×D11)⋊C4—24no—
57C2×(C2×D11)⋊C4—24no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—22no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11D414yes—
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×#101—28no—
73#66900—28no—
74(C2×D11)⋊C8—216no—
75#10968—111nomaximal, Sylow
76C24×C11C22×C411yescharacteristic
77C23×D11—21no—
78C23×D11—21no—
79C23×D11—24no—
80C23×D11—22no—
81C23×D11—22no—
82C23×D11—42no—
83C23×D11C22⋊C412yes—
84C2×Q8×C11—22no—
85C2×Q8×C11—22no—
86C2×Q8×C11—24no—
87C2×Q8×C11—24no—
88C2×Q8×C11—24no—
89C2×Q8×C11—24no—
90C2×Q8×C11—22no—
91C2×Q8×C11—22no—
92C2×Q8×C11—42no—
93C2×Q8×C11—42no—
94C2×Q8×C11—42no—
95C2×Q8×C11—42no—
96C2×Q8×C11—42no—
97C2×Q8×C11—42no—
98C2×Q8×C11—42no—
99C2×Q8×C11—42no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—24no—
103C22×C4×C11—24no—
104C22×C4×C11C22⋊C414yes—
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—21no—
114C22×Dic11—21no—
115C22×Dic11—22no—
116C22×Dic11—22no—
117C22×Dic11—22no—
118C22×Dic11—22no—
119C22×Dic11—44no—
120C22×Dic11C22⋊C412yes—
121C22×Dic11C22⋊C414yes—
122C2×C4×D11—24no—
123C2×C4×D11—24no—
124C2×C4×D11—24no—
125C2×C4×D11—24no—
126C2×C4×D11—24no—
127C2×C4×D11—24no—
128C2×C4×D11—41no—
129C2×C4×D11—41no—
130C2×C4×D11—42no—
131C2×C4×D11—42no—
132C2×C4×D11—42no—
133C2×C4×D11—42no—
134C2×C4×D11—41no—
135C2×C4×D11—41no—
136C2×C4×D11—42no—
137C2×C4×D11—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—
145(C2×D11)⋊C4—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—111no—
158C22×#101D1111yescharacteristic, complemented
159C2×#407—112no—
160C2×#343—112no—
161C23×C11—22no—
162C23×C11—22no—
163C23×C11C2×C22⋊C411yescharacteristic
164C23×C11C2×C22⋊C411yescharacteristic
165C23×C11C2×C22⋊C411yescharacteristic
166C23×C11C4×D412yes—
167C23×C11C4×D412yes—
168C22×D11—24no—
169C22×D11—24no—
170C22×D11—22no—
171C22×D11—24no—
172C22×D11—22no—
173C22×D11—24no—
174C22×D11—48no—
175C22×D11—48no—
176C22×D11—42no—
177C22×D11—42no—
178C22×D11—41no—
179C22×D11—41no—
180C22×D11—42no—
181C22×D11#10114yescomplemented
182Q8×C11—44no—
183Q8×C11—44no—
184Q8×C11—44no—
185Q8×C11—44no—
186C2×C4×C11—24no—
187C2×C4×C11—24no—
188C2×C4×C11—24no—
189C2×C4×C11—44no—
190C2×C4×C11—44no—
191C2×C4×C11#12011yescharacteristic
192C2×C4×C11#12012yes—
193C2×C4×C11#12012yes—
194C2×C4×C11#12012yes—
195C2×C4×C11#12011yescharacteristic
196C2×C4×C11#12112yes—
197C2×C4×C11#12112yes—
198C2×C4×C11#12112yes—
199C2×C4×C11#12112yes—
200C2×C4×C11#12112yes—
201C2×C4×C11#12112yes—
202C2×C4×C11#12312yes—
203C2×C4×C11#12311yescharacteristic
204C2×C4×C11#12311yescharacteristic
205C2×C4×C11#12412yes—
206C2×C4×C11#12712yes—
207C2×Dic11—22no—
208C2×Dic11—24no—
209C2×Dic11—24no—
210C2×Dic11—44no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—42no—
214C2×Dic11—44no—
215C2×Dic11—44no—
216C4×D11—44no—
217C4×D11—44no—
218C4×D11—44no—
219C4×D11—44no—
220C8×C11—44no—
221C11⋊C8—44no—
222C23×Q8C2×D1111yescharacteristic
223C24×C4—111no—
224C22×M16—112no—
225C22×M16C2×D1112yes—
226C2×C22⋊Q8—224no—
227C2×C22⋊Q8—224no—
228C2×C22⋊Q8—222no—
229C2×C22⋊Q8—222no—
230C22×C4⋊C4—111no—
231C22×C4⋊C4—112no—
232C22×C22⋊C4—112no—
233C2×#101—22no—
234C2×#101—24no—
235C2×#101—224no—
236C2×#101—222no—
237#407—224no—
238#407—224no—
239C2×C22⋊C8—224no—
240#343—224no—
241C22×C11—24no—
242C22×C11—24no—
243C22×C11—21no—
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—21no—
247C22×C11#37911yescharacteristic
248C22×C11#38612yes—
249C22×C11#38611yescharacteristic
250C22×C11#38611yescharacteristic
251C22×C11#39012yes—
252C22×C11C2×#10112yes—
253C22×C11#41312yes—
254C2×D11—28no—
255C2×D11—24no—
256C2×D11—44no—
257C2×D11—44no—
258C2×D11—48no—
259C2×D11—44no—
260C2×D11—42no—
261C2×D11—42no—
262C4×C11—44no—
263C4×C11#39212yes—
264C4×C11#39212yes—
265C4×C11#39412yes—
266C4×C11#39412yes—
267Dic11—42no—
268Dic11—44no—
269C25—111no—
270C22×Q8—22no—
271C22×Q8—22no—
272C22×Q8—22no—
273C22×Q8—22no—
274C22×Q8—22no—
275C22×Q8—22no—
276C22×Q8D4412yes—
277C22×Q8C22⋊D1112yes—
278C23×C4—111no—
279C23×C4—112no—
280C23×C4—114no—
281C23×C4—221no—
282C23×C4—222no—
283C23×C4—222no—
284C23×C4—222no—
285C23×C4—222no—
286C23×C4—221no—
287C23×C4—222no—
288C23×C4C4×D1112yes—
289C23×C4C22×D1111yescharacteristic
290C2×M16—22no—
291C2×M16—22no—
292C2×M16—22no—
293C2×M16—22no—
294C2×M16—22no—
295C2×M16—114no—
296C2×M16—222no—
297C2×M16—222no—
298C2×M16—222no—
299C2×M16—222no—
300C2×M16—222no—
301C2×M16C22⋊D1114yes—
302C22×C8—22no—
303C22×C8—222no—
304C22⋊Q8—2216no—
305C22⋊Q8—2216no—
306C2×C4⋊C4—114no—
307C2×C4⋊C4—224no—
308C2×C4⋊C4—224no—
309C2×C4⋊C4—224no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4—222no—
312C2×C4⋊C4—221no—
313C2×C22⋊C4—224no—
314C2×C22⋊C4—224no—
315C2×C22⋊C4—224no—
316#101—28no—
317#101—228no—
318C22⋊C8—2216no—
319C2×C11—21no—
320C2×C11—21no—
321C2×C11—22no—
322C2×C11#143811yescharacteristic
323C2×C11#178411yescharacteristic
324C2×C11#178511yescharacteristic
325C2×C11#190114yes—
326D11—44no—
327C24—112no—
328C24—224no—
329C24—221no—
330C24—221no—
331C24—222no—
332C24—222no—
333C24—442no—
334C24C2×C4×D1111yescharacteristic
335C2×Q8—22no—
336C2×Q8—24no—
337C2×Q8—22no—
338C2×Q8—22no—
339C2×Q8—24no—
340C2×Q8—24no—
341C2×Q8—24no—
342C2×Q8—22no—
343C2×Q8—42no—
344C2×Q8—42no—
345C2×Q8—42no—
346C2×Q8—42no—
347C2×Q8—42no—
348C2×Q8—42no—
349C2×Q8—42no—
350C2×Q8—42no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—24no—
354C22×C4—24no—
355C22×C4—112no—
356C22×C4—114no—
357C22×C4—221no—
358C22×C4—222no—
359C22×C4—222no—
360C22×C4—222no—
361C22×C4—221no—
362C22×C4—222no—
363C22×C4—224no—
364C22×C4—224no—
365C22×C4—224no—
366C22×C4—224no—
367C22×C4—224no—
368C22×C4—224no—
369C22×C4—441no—
370C22×C4—442no—
371C22×C4—442no—
372C22×C4—441no—
373C22×C4—441no—
374C22×C4—442no—
375C22×C4—442no—
376C22×C4—442no—
377C22×C4—442no—
378C22×C4—441no—
379C22×C4—444no—
380C22×C4(C2×D11)⋊C414yes—
381C22×C4C2×D4411yescharacteristic
382C22×C4#433912yes—
383C22×C4D4×D1112yes—
384C22×C4D4×D1112yes—
385C22×C4D4×D1112yes—
386C22×C4#434112yes—
387C22×C4C2×C22⋊D1111yescharacteristic
388C22×C4C2×C22⋊D1112yes—
389M16—24no—
390M16—24no—
391M16—42no—
392M16—42no—
393M16—224no—
394M16—224no—
395M16—442no—
396M16—442no—
397C2×C8—24no—
398C2×C8—42no—
399C2×C8—42no—
400C2×C8—224no—
401C2×C8—442no—
402C2×C8—442no—
403C4⋊C4—2216no—
404C4⋊C4—224no—
405C4⋊C4—224no—
406C22⋊C4—2216no—
407C11#1096811yescharacteristic, complemented, Sylow
408C23—22no—
409C23—22no—
410C23—114no—
411C23—224no—
412C23—224no—
413C23—222no—
414C23—224no—
415C23—222no—
416C23—224no—
417C23—448no—
418C23—448no—
419C23—442no—
420C23—442no—
421C23—442no—
422C23—441no—
423C23—441no—
424C23C22⋊C4×D1111yescharacteristic
425C23C22⋊C4×D1111yescharacteristic
426C23(C22⋊D11)⋊C412yes—
427C23C2×(C2×D11)⋊C411yescharacteristic
428C23C4×C22⋊D1112yes—
429Q8—44no—
430Q8—44no—
431Q8—44no—
432Q8—44no—
433C2×C4—24no—
434C2×C4—24no—
435C2×C4—24no—
436C2×C4—44no—
437C2×C4—44no—
438C2×C4—224no—
439C2×C4—222no—
440C2×C4—224no—
441C2×C4—444no—
442C2×C4—442no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—444no—
446C2×C4—444no—
447C2×C4—444no—
448C2×C4—444no—
449C2×C4—444no—
450C2×C4—444no—
451C2×C4#6693511yescharacteristic
452C2×C4#6693512yes—
453C2×C4#6693612yes—
454C2×C4#6693712yes—
455C2×C4#6693712yes—
456C2×C4#6693812yes—
457C2×C4#6693911yescharacteristic
458C2×C4#6698211yescharacteristic
459C2×C4#6698312yes—
460C2×C4#6699012yes—
461C2×C4#6699012yes—
462C2×C4#6699112yes—
463C2×C4#6699212yes—
464C2×C4#6699212yes—
465C2×C4#6699312yes—
466C2×C4#6700611yescharacteristic
467C8—44no—
468C8—444no—
469C22—24no—
470C22—24no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—228no—
476C22—224no—
477C22—448no—
478C22—444no—
479C22—444no—
480C22—444no—
481C22—442no—
482C22—442no—
483C22D11×#10112yes—
484C22#1062236412yes—
485C22#1062256811yescharacteristic
486C22#1062256912yes—
487C22#1062257012yes—
488C22#1062257111yescharacteristic
489C22#1062282611yescharacteristic
490C4—44no—
491C4—442no—
492C4—444no—
493C4#1062257212yes—
494C4#1062257312yes—
495C4#1062257412yes—
496C4#1062283612yes—
497C2—22no—
498C2—21no—
499C2—21no—
500C2—444no—
501C2#1306685511yescharacteristic
502C2#1306853811yescharacteristic
503C2#1306854311yescharacteristic
504C2#1306908114yes—
subgroupG/H
centerC23C22⋊C4×D11
commutatorC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC22×C11×#101C2
socleC23×C11C2×C22⋊C4
prime radicalC24×D11C2×C4
cosocleC23×C4×C11C23
hypercenterC22×#101D11
hypocenterC11#10968
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#101

Complements

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

NH ≅ G/Ntype
2. C22×#66900C2semidirect
4. C2×#10622192C2semidirect
5. C22×C11×#101C2semidirect
158. C22×#101D11semidirect
181. C22×D11#101semidirect
407. C11#10968semidirect

Maximal subgroups

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

subgroupindex
C22×#669992
C22×#669002
C2×#106227392
C2×#106221922
C22×C11×#1012
#1096811