Finite Group Databasebeta

← #14676312

Subgroups — #14676312

Order 2816.

2230 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D11C211yesmaximal, characteristic
2C2×#10622824C211yesmaximal, characteristic, complemented
3#13066863C212yesmaximal, complemented
4#13066855C212yesmaximal
5#13066854C212yesmaximal, complemented
6#13066849C212yesmaximal, complemented
7#13066840C212yesmaximal, complemented
8(C2×D11)⋊#95C212yesmaximal, complemented
9C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
10C24×C4×C11C2211yescharacteristic
11C23×C22⋊D11C2211yescharacteristic
12C23×C4×D11C2211yescharacteristic
13C22×C11×C22⋊C4C2212yes—
14C22×C42×C11C2212yes—
15C22×C22⋊Dic11C2211yescharacteristic
16C22×C22⋊Dic11C2212yes—
17C2×C4×C22⋊D11—24no—
18C2×C4×C22⋊D11—24no—
19C2×C4×C22⋊D11C418yescomplemented
20C22×(C2×D11)⋊C4C2214yes—
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×Dic11⋊C4C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
24C4×C11×C22⋊C4—24no—
25C2×C11×#95C2212yes—
26#10622824—24no—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2214yes—
29C2×C11⋊#95C2214yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2214yes—
32C25×C11C2311yescharacteristic
33C24×D11C2311yescharacteristic
34C23×C4×C11—44no—
35C23×C4×C11C2×C414yes—
36C23×C4×C11D414yes—
37C23×C4×C11D414yes—
38C23×C4×C11C2314yes—
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C22×C22⋊D11—22no—
42C22×C22⋊D11—22no—
43C22×C22⋊D11—24no—
44C22×C22⋊D11—24no—
45C22×C22⋊D11C2×C414yes—
46C23×Dic11C2314yes—
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2311yescharacteristic
50C22×C4×D11—22no—
51C22×C4×D11—22no—
52C22×C4×D11—44no—
53C22×C4×D11C2×C414yes—
54C2×C11×C22⋊C4—24no—
55C2×C11×C22⋊C4—28no—
56C2×C42×C11—24no—
57C2×C42×C11—44no—
58C2×C22⋊Dic11—22no—
59C2×C22⋊Dic11—22no—
60C2×C22⋊Dic11—24no—
61C2×C22⋊Dic11—44no—
62C2×C22⋊Dic11C2×C414yes—
63C4×C22⋊D11—232no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4—28no—
67C2×(C2×D11)⋊C4—28no—
68C2×(C2×D11)⋊C4—44no—
69C2×(C2×D11)⋊C4C2×C414yes—
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4—22no—
72C2×Dic11⋊C4C2×C414yes—
73C2×C4×Dic11—22no—
74C2×C4×Dic11—22no—
75C2×C4×Dic11C2×C414yes—
76C11×#95—24no—
77C11⋊#95—24no—
78C11⋊#95—24no—
79C11⋊#95—28no—
80C11⋊#95—28no—
81C11⋊#95—44no—
82#13940—111nomaximal, Sylow
83C24×C11—24no—
84C24×C11—22no—
85C24×C11—22no—
86C24×C11—24no—
87C24×C11C22×C412yes—
88C24×C11C2×D412yes—
89C24×C11C2×D412yes—
90C24×C11C2411yescharacteristic
91C23×D11—21no—
92C23×D11—21no—
93C23×D11—24no—
94C23×D11—22no—
95C23×D11—24no—
96C23×D11C22×C412yes—
97C23×D11#4114yes—
98C22×C4×C11—24no—
99C22×C4×C11—24no—
100C22×C4×C11—24no—
101C22×C4×C11—24no—
102C22×C4×C11—24no—
103C22×C4×C11—24no—
104C22×C4×C11—24no—
105C22×C4×C11—24no—
106C22×C4×C11—48no—
107C22×C4×C11—48no—
108C22×C4×C11—48no—
109C22×C4×C11C22⋊C4116yescomplemented
110C22×C4×C11C22×C412yes—
111C22×C4×C11C22×C412yes—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D412yes—
116C22×C4×C11#4118yes—
117C2×C22⋊D11—216no—
118C2×C22⋊D11—216no—
119C2×C22⋊D11—28no—
120C2×C22⋊D11—28no—
121C2×C22⋊D11—28no—
122C22×Dic11—21no—
123C22×Dic11—21no—
124C22×Dic11—21no—
125C22×Dic11—21no—
126C22×Dic11—21no—
127C22×Dic11—21no—
128C22×Dic11—24no—
129C22×Dic11—22no—
130C22×Dic11—24no—
131C22×Dic11—24no—
132C22×Dic11—24no—
133C22×Dic11—24no—
134C22×Dic11—24no—
135C22×Dic11—24no—
136C22×Dic11—24no—
137C22×Dic11—24no—
138C22×Dic11C22×C412yes—
139C22×Dic11C22×C412yes—
140C22×Dic11C22×C412yes—
141C22×Dic11#4114yes—
142C2×C4×D11—28no—
143C2×C4×D11—48no—
144C2×C4×D11—48no—
145C2×C4×D11—48no—
146C11×C22⋊C4—216no—
147C42×C11—48no—
148C22⋊Dic11—28no—
149C22⋊Dic11—48no—
150(C2×D11)⋊C4—28no—
151(C2×D11)⋊C4—416no—
152Dic11⋊C4—28no—
153C4×Dic11—28no—
154C22×C4×D4—111no—
155C2×#381—111no—
156C2×C4×C22⋊C4D1111yescharacteristic, complemented
157#1440—112no—
158#1438—112no—
159#1437—112no—
160#1436—112no—
161#1434—112no—
162C22⋊#95—112no—
163C23×C11—22no—
164C23×C11—22no—
165C23×C11—24no—
166C23×C11—24no—
167C23×C11—24no—
168C23×C11—24no—
169C23×C11—24no—
170C23×C11—24no—
171C23×C11—24no—
172C23×C11—24no—
173C23×C11—44no—
174C23×C11—44no—
175C23×C11—44no—
176C23×C11—44no—
177C23×C11C2×C22⋊C414yes—
178C23×C11C23×C411yescharacteristic
179C23×C11C22×D411yescharacteristic
180C23×C11C22×D411yescharacteristic
181C23×C11C2×#4114yes—
182C23×C11C2×#4112yes—
183C23×C11C2×#4112yes—
184C23×C11H(5,𝔽2)14yes—
185C22×D11—22no—
186C22×D11—22no—
187C22×D11—24no—
188C22×D11—24no—
189C22×D11—24no—
190C22×D11—24no—
191C22×D11—28no—
192C22×D11—28no—
193C22×D11—42no—
194C22×D11—42no—
195C22×D11—42no—
196C22×D11—42no—
197C22×D11—44no—
198C22×D11—44no—
199C22×D11#11714yes—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—28no—
207C2×C4×C11—28no—
208C2×C4×C11—28no—
209C2×C4×C11—416no—
210C2×C4×C11—44no—
211C2×C4×C11—44no—
212C2×C4×C11—44no—
213C2×C4×C11—44no—
214C2×C4×C11C2×C22⋊C414yes—
215C2×C4×C11C2×C22⋊C414yes—
216C22⋊D11—232no—
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—24no—
220C2×Dic11—24no—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—24no—
224C2×Dic11—24no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228C2×Dic11—42no—
229C2×Dic11—44no—
230C2×Dic11—44no—
231C2×Dic11—44no—
232C2×Dic11—44no—
233C2×Dic11—44no—
234C2×Dic11—44no—
235C2×Dic11—44no—
236C2×Dic11#11714yes—
237C4×D11—416no—
238C23×D4—111no—
239C24×C4—111no—
240C24×C4C2×D1111yescharacteristic
241C2×C4×D4—118no—
242C2×C4×D4—224no—
243C2×C4×D4—224no—
244C22×C4⋊C4—111no—
245C22×C22⋊C4—111no—
246C22×C22⋊C4—111no—
247C22×C22⋊C4—114no—
248C22×C22⋊C4—112no—
249C22×C22⋊C4C2×D1112yes—
250C22×C42—111no—
251C22×C42C2×D1112yes—
252#381—224no—
253C4×C22⋊C4—24no—
254C2×#95—112no—
255C2×#95—114no—
256C2×#95—114no—
257C2×#95—112no—
258C2×#95—114no—
259C2×#95C2×D1112yes—
260C22×C11—24no—
261C22×C11—24no—
262C22×C11—24no—
263C22×C11—48no—
264C22×C11—48no—
265C22×C11—44no—
266C22×C11—44no—
267C22×C11C22×C22⋊C411yescharacteristic
268C22×C11C2×#11711yescharacteristic
269C22×C11C2×#11711yescharacteristic
270C22×C11C4×#4112yes—
271C22×C11#51812yes—
272C22×C11#52512yes—
273C22×C11#52512yes—
274C22×C11#52512yes—
275C22×C11#53212yes—
276C22×C11#53412yes—
277C22×C11#53412yes—
278C22×C11#55114yes—
279C22×C11#55314yes—
280C22×C11#55314yes—
281C22×C11#55914yes—
282C2×D11—28no—
283C2×D11—24no—
284C2×D11—42no—
285C2×D11—48no—
286C2×D11—48no—
287C2×D11—44no—
288C2×D11—42no—
289C4×C11—24no—
290C4×C11—24no—
291C4×C11—48no—
292Dic11—24no—
293Dic11—42no—
294Dic11—42no—
295Dic11—84no—
296C25—111no—
297C25C22×D1111yescharacteristic
298C22×D4—114no—
299C22×D4—224no—
300C22×D4—224no—
301C22×D4—222no—
302C22×D4—222no—
303C23×C4—44no—
304C23×C4—111no—
305C23×C4—111no—
306C23×C4—111no—
307C23×C4—114no—
308C23×C4—114no—
309C23×C4—222no—
310C23×C4—222no—
311C23×C4—444no—
312C23×C4C4×D1114yes—
313C23×C4D4414yes—
314C23×C4C22⋊D1114yes—
315C23×C4C22×D1114yes—
316C23×C4C22×D1111yescharacteristic
317C23×C4C22×D1111yescharacteristic
318C4×D4—2232no—
319C2×C4⋊C4—114no—
320C2×C4⋊C4—222no—
321C2×C4⋊C4—222no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—28no—
324C2×C22⋊C4—114no—
325C2×C22⋊C4—114no—
326C2×C22⋊C4—222no—
327C2×C22⋊C4—222no—
328C2×C22⋊C4—222no—
329C2×C22⋊C4—222no—
330C2×C22⋊C4—228no—
331C2×C22⋊C4—224no—
332C2×C22⋊C4—228no—
333C2×C22⋊C4—444no—
334C2×C22⋊C4—444no—
335C2×C42—24no—
336C2×C42—44no—
337C2×C42—114no—
338C2×C42—222no—
339C2×C42—222no—
340#95—24no—
341#95—228no—
342#95—224no—
343#95—224no—
344#95—228no—
345#95—444no—
346C2×C11—44no—
347C2×C11#228011yescharacteristic
348C2×C11#229711yescharacteristic
349C2×C11#230811yescharacteristic
350C2×C11#235312yes—
351C2×C11#235712yes—
352C2×C11#260014yes—
353C2×C11#260214yes—
354D11—44no—
355C24—24no—
356C24—24no—
357C24—22no—
358C24—22no—
359C24—112no—
360C24—114no—
361C24—221no—
362C24—224no—
363C24—224no—
364C24—222no—
365C24—221no—
366C24C2×C4×D1112yes—
367C24C2×D4412yes—
368C24C2×C22⋊D1112yes—
369C24C23×D1111yescharacteristic
370C2×D4—228no—
371C2×D4—228no—
372C2×D4—2216no—
373C2×D4—2216no—
374C2×D4—228no—
375C22×C4—24no—
376C22×C4—24no—
377C22×C4—24no—
378C22×C4—24no—
379C22×C4—24no—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—24no—
383C22×C4—48no—
384C22×C4—48no—
385C22×C4—48no—
386C22×C4—112no—
387C22×C4—114no—
388C22×C4—112no—
389C22×C4—112no—
390C22×C4—221no—
391C22×C4—222no—
392C22×C4—221no—
393C22×C4—221no—
394C22×C4—221no—
395C22×C4—224no—
396C22×C4—224no—
397C22×C4—221no—
398C22×C4—221no—
399C22×C4—228no—
400C22×C4—224no—
401C22×C4—224no—
402C22×C4—224no—
403C22×C4—224no—
404C22×C4—224no—
405C22×C4—224no—
406C22×C4—224no—
407C22×C4—448no—
408C22×C4—448no—
409C22×C4—448no—
410C22×C4(C2×D11)⋊C4116yescomplemented
411C22×C4C2×C4×D1112yes—
412C22×C4C2×C4×D1112yes—
413C22×C4C2×D4412yes—
414C22×C4C2×D4412yes—
415C22×C4#433918yes—
416C22×C4C2×C22⋊D1112yes—
417C22×C4C2×C22⋊D1112yes—
418C4⋊C4—228no—
419C22⋊C4—216no—
420C22⋊C4—228no—
421C22⋊C4—228no—
422C22⋊C4—4416no—
423C22⋊C4—448no—
424C42—48no—
425C42—228no—
426C11#1394011yescharacteristic, complemented, Sylow
427C23—24no—
428C23—24no—
429C23—24no—
430C23—24no—
431C23—22no—
432C23—22no—
433C23—24no—
434C23—24no—
435C23—24no—
436C23—24no—
437C23—44no—
438C23—44no—
439C23—44no—
440C23—44no—
441C23—114no—
442C23—224no—
443C23—224no—
444C23—222no—
445C23—224no—
446C23—222no—
447C23—228no—
448C23—228no—
449C23—224no—
450C23—442no—
451C23—442no—
452C23—442no—
453C23—444no—
454C23—442no—
455C23—444no—
456C23C2×(C2×D11)⋊C414yes—
457C23C22×C4×D1111yescharacteristic
458C23C22×D4411yescharacteristic
459C23C2×#433914yes—
460C23#6703714yes—
461C23#41×D1112yes—
462C23#41×D1112yes—
463C23C22×C22⋊D1111yescharacteristic
464D4—2232no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—28no—
472C2×C4—28no—
473C2×C4—28no—
474C2×C4—416no—
475C2×C4—44no—
476C2×C4—44no—
477C2×C4—44no—
478C2×C4—44no—
479C2×C4—114no—
480C2×C4—222no—
481C2×C4—224no—
482C2×C4—222no—
483C2×C4—224no—
484C2×C4—224no—
485C2×C4—224no—
486C2×C4—222no—
487C2×C4—222no—
488C2×C4—4416no—
489C2×C4—442no—
490C2×C4—442no—
491C2×C4—442no—
492C2×C4—442no—
493C2×C4—444no—
494C2×C4—444no—
495C2×C4—444no—
496C2×C4—444no—
497C2×C4—444no—
498C2×C4—444no—
499C2×C4—444no—
500C2×C4C2×(C2×D11)⋊C414yes—
501C2×C4C2×(C2×D11)⋊C414yes—
502C22—24no—
503C22—24no—
504C22—24no—
505C22—48no—
506C22—48no—
507C22—44no—
508C22—44no—
509C22—224no—
510C22—228no—
511C22—442no—
512C22—448no—
513C22—448no—
514C22—442no—
515C22—444no—
516C22C4×#433912yes—
517C22#1062300812yes—
518C22#1062301712yes—
519C22#1062302412yes—
520C22D11×#11711yescharacteristic
521C22D11×#11711yescharacteristic
522C22#1062305512yes—
523C22#1062307114yes—
524C22#1062308714yes—
525C22#1062308914yes—
526C22#1062309014yes—
527C22C22×(C2×D11)⋊C411yescharacteristic
528C22#1062332212yes—
529C22#1062333512yes—
530C22#1062335912yes—
531C4—24no—
532C4—24no—
533C4—48no—
534C4—224no—
535C4—442no—
536C4—442no—
537C4—884no—
538C2—44no—
539C2—444no—
540C2#1307099511yescharacteristic
541C2#1307110611yescharacteristic
542C2#1307119111yescharacteristic
543C2#1307155912yes—
544C2#1307159012yes—
545C2#1307419814yes—
546C2#1307422214yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C4×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#13940
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#10622824C2semidirect
3. #13066863C2semidirect
5. #13066854C2semidirect
6. #13066849C2semidirect
7. #13066840C2semidirect
8. (C2×D11)⋊#95C2semidirect
9. C2×C4×C11×C22⋊C4C2semidirect
19. C2×C4×C22⋊D11C4semidirect
109. C22×C4×C11C22⋊C4semidirect
156. C2×C4×C22⋊C4D11semidirect
410. C22×C4(C2×D11)⋊C4semidirect
426. C11#13940semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D112
C2×#106228242
#130668632
#130668552
#130668542
#130668492
#130668402
(C2×D11)⋊#952
C2×C4×C11×C22⋊C42
#1394011