Finite Group Databasebeta

← #14764825

Subgroups — #14764825

Order 2816.

1176 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622624C211yesmaximal, characteristic, complemented
2C22×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
3#13069415C212yesmaximal, complemented
4#13069231C212yesmaximal, complemented
5#13069231C212yesmaximal, complemented
6#13068914C212yesmaximal, complemented
7#13068909C211yesmaximal, characteristic, complemented
8#13068796C211yesmaximal, characteristic, complemented
9#13068526C211yesmaximal, characteristic, complemented
10#13068394C211yesmaximal, characteristic, complemented
11C4×C11×#120C211yesmaximal, characteristic
12C24×C4×C11C2211yescharacteristic
13C2×C11×#120C411yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×C4×D4×C11C2212yes—
16C22×#4318C2211yescharacteristic, complemented
17C23×C11⋊C8C2211yescharacteristic
18C23×C11⋊C8C2211yescharacteristic
19C11×#386C411yescharacteristic
20C11×#386C412yes—
21C11×#385C411yescharacteristic
22C11×#385C412yes—
23C11×#379C411yescharacteristic
24C4×C11×C22⋊C4C2211yescharacteristic
25C4×C11×C22⋊C4C2212yes—
26C2×C22⋊(C11⋊C8)—24no—
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2212yes—
29C2×C22⋊(C11⋊C8)C2212yes—
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2212yes—
32C2×C22⋊(C11⋊C8)C2212yes—
33C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
34C2×C22⋊(C11⋊C8)C2212yescomplemented
35#10622624—24no—
36C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
37C2×C4⋊(C11⋊C8)C2212yescomplemented
38C2×#66867C2211yescharacteristic, complemented
39C2×#66867C2212yescomplemented
40#10622162C2212yescomplemented
41#10622162C2212yescomplemented
42#10622162C2212yescomplemented
43C25×C11C2×C411yescharacteristic
44C22×D4×C11C2×C411yescharacteristic
45C22×D4×C11C2×C412yes—
46C23×C4×C11—22no—
47C23×C4×C11—22no—
48C23×C4×C11—42no—
49C23×C4×C11—42no—
50C23×C4×C11C2×C411yescharacteristic
51C23×C4×C11C2×C412yes—
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2312yes—
54C23×C4×C11C2311yescharacteristic
55C11×#120—24no—
56C4×D4×C11—22no—
57C4×D4×C11—22no—
58C4×D4×C11—42no—
59C4×D4×C11—42no—
60C2×C11×C4⋊C4C2×C411yescharacteristic
61C2×C11×C4⋊C4C2×C412yes—
62C2×C11×C22⋊C4C2×C411yescharacteristic
63C2×C11×C22⋊C4C2×C412yes—
64C2×C11×C22⋊C4C2×C411yescharacteristic
65C2×C11×C22⋊C4C2×C411yescharacteristic
66C2×C11×C22⋊C4C2×C411yescharacteristic
67C2×C11×C22⋊C4C2×C412yes—
68C2×C11×C22⋊C4C2×C412yes—
69C2×C11×C22⋊C4C2×C412yes—
70C2×C42×C11C2311yescharacteristic
71C2×C42×C11C2312yes—
72C2×#4318—22no—
73C2×#4318—42no—
74C22×C11⋊C8—22no—
75C22×C11⋊C8—42no—
76C22×C11⋊C8—42no—
77C22×C11⋊C8D414yescomplemented
78C22×C11⋊C8C2311yescharacteristic
79C22×C11⋊C8C2312yes—
80C22×C11⋊C8C2312yes—
81C22×C11⋊C8C2311yescharacteristic
82C22×C11⋊C8C2311yescharacteristic
83C22×C11⋊C8C2311yescharacteristic
84C11×#95C2×C412yes—
85C11×#95C2×C412yes—
86C11×#95C2×C412yes—
87C22⋊(C11⋊C8)—22no—
88C22⋊(C11⋊C8)—22no—
89C22⋊(C11⋊C8)—24no—
90C22⋊(C11⋊C8)—24no—
91C22⋊(C11⋊C8)—22no—
92C22⋊(C11⋊C8)—42no—
93C22⋊(C11⋊C8)—42no—
94C22⋊(C11⋊C8)—42no—
95C4⋊(C11⋊C8)—22no—
96C4⋊(C11⋊C8)—42no—
97#66867—22no—
98#66867—42no—
99#22034—111nomaximal, Sylow
100C24×C11—22no—
101C24×C11—22no—
102C24×C11—42no—
103C24×C11—42no—
104C24×C11M1614yescomplemented
105C24×C11C22×C411yescharacteristic
106C24×C11C22×C412yes—
107C24×C11C22×C411yescharacteristic
108C2×D4×C11—22no—
109C2×D4×C11—24no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—42no—
113C2×D4×C11—42no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—24no—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—42no—
129C22×C4×C11—42no—
130C22×C4×C11—42no—
131C22×C4×C11—44no—
132C22×C4×C11—44no—
133C22×C4×C11—48no—
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C22×C412yes—
136C22×C4×C11C22×C411yescharacteristic
137C22×C4×C11C22×C412yes—
138C22×C4×C11C22×C412yes—
139C22×C4×C11C22×C411yescharacteristic
140C22×C4×C11C22×C411yescharacteristic
141C22×C4×C11C2×D412yes—
142C22×C4×C11#4112yes—
143C22×C4×C11C2411yescharacteristic
144C11×C4⋊C4—22no—
145C11×C4⋊C4—42no—
146C11×C22⋊C4—22no—
147C11×C22⋊C4—24no—
148C11×C22⋊C4—22no—
149C11×C22⋊C4—22no—
150C11×C22⋊C4—22no—
151C11×C22⋊C4—42no—
152C11×C22⋊C4—42no—
153C11×C22⋊C4—42no—
154C42×C11—21no—
155C42×C11—21no—
156C42×C11—22no—
157C42×C11—22no—
158#4318—44no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—44no—
172C2×C11⋊C8—44no—
173C2×C11⋊C8C2×D412yes—
174C2×C11⋊C8C2×D412yes—
175C2×#435—111no—
176C22×C22⋊C8—111no—
177C4×#120D1111yescharacteristic
178#1955—112no—
179#1924—112no—
180#1924—112no—
181#1870—112no—
182#1869—111no—
183#1850—111no—
184#1779—111no—
185#1752—111no—
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—28no—
195C23×C11—21no—
196C23×C11—22no—
197C23×C11—21no—
198C23×C11—21no—
199C23×C11—22no—
200C23×C11—48no—
201C23×C11—44no—
202C23×C11—44no—
203C23×C11—48no—
204C23×C11C4×D412yes—
205C23×C11C2×M1614yes—
206C23×C11C2×M1612yes—
207C23×C11#13112yes—
208C23×C11C23×C411yescharacteristic
209D4×C11—48no—
210D4×C11—44no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—24no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—21no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—21no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—48no—
232C2×C4×C11—44no—
233C2×C4×C11—41no—
234C2×C4×C11—42no—
235C2×C4×C11—41no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11C4×D412yes—
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11H(5,𝔽2)12yes—
244C2×C4×C11H(5,𝔽2)12yes—
245C11⋊C8—22no—
246C11⋊C8—22no—
247C11⋊C8—41no—
248C11⋊C8—41no—
249C11⋊C8—42no—
250C11⋊C8—42no—
251C24×C4C2×D1111yescharacteristic
252C22×M16—111no—
253C23×C8—111no—
254C23×C8—111no—
255C2×#120Dic1111yescharacteristic
256C2×C4×D4C2×D1111yescharacteristic
257C2×C4×D4C2×D1112yes—
258#435—224no—
259C2×C4⋊C8—111no—
260C2×C4⋊C8—112no—
261C2×C22⋊C8—111no—
262C2×C22⋊C8—112no—
263C2×C22⋊C8—112no—
264C2×C22⋊C8—111no—
265C2×C22⋊C8—111no—
266C2×C22⋊C8—112no—
267C2×C22⋊C8—112no—
268C2×C22⋊C8—112no—
269C2×C22⋊C8—224no—
270C2×#97—111no—
271C2×#97—112no—
272#386Dic1112yes—
273#386Dic1111yescharacteristic
274#385Dic1111yescharacteristic
275#385Dic1112yes—
276#379Dic1111yescharacteristic
277C4×C22⋊C4C2×D1111yescharacteristic
278C4×C22⋊C4C2×D1112yes—
279#336—112no—
280#336—112no—
281#336—112no—
282C22×C11—22no—
283C22×C11—22no—
284C22×C11—24no—
285C22×C11—24no—
286C22×C11—24no—
287C22×C11—24no—
288C22×C11—24no—
289C22×C11—416no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—41no—
295C22×C11—41no—
296C22×C11—41no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11#43514yes—
300C22×C11C2×C4×D411yescharacteristic
301C22×C11#51812yes—
302C22×C11C22×M1611yescharacteristic
303C22×C11C2×#13111yescharacteristic
304C22×C11#56812yes—
305C4×C11—22no—
306C4×C11—41no—
307C4×C11—42no—
308C4×C11—41no—
309C4×C11—41no—
310C4×C11—42no—
311C4×C11—42no—
312C4×C11#53411yescharacteristic
313C4×C11#53511yescharacteristic
314C4×C11#53812yes—
315C25C2×Dic1111yescharacteristic
316C22×D4C2×Dic1111yescharacteristic
317C22×D4C2×Dic1112yes—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4—42no—
321C23×C4—42no—
322C23×C4C2×Dic1111yescharacteristic
323C23×C4C2×Dic1112yes—
324C23×C4C22×D1111yescharacteristic
325C23×C4C22×D1112yes—
326C23×C4C22×D1111yescharacteristic
327C2×M16—222no—
328C2×M16—442no—
329C22×C8—111no—
330C22×C8—111no—
331C22×C8—114no—
332C22×C8—112no—
333C22×C8—111no—
334C22×C8—112no—
335C22×C8—111no—
336C22×C8—222no—
337C22×C8—442no—
338C22×C8—442no—
339#120—24no—
340C4×D4—22no—
341C4×D4—22no—
342C4×D4—42no—
343C4×D4—42no—
344C2×C4⋊C4C2×Dic1111yescharacteristic
345C2×C4⋊C4C2×Dic1112yes—
346C2×C22⋊C4C2×Dic1111yescharacteristic
347C2×C22⋊C4C2×Dic1111yescharacteristic
348C2×C22⋊C4C2×Dic1112yes—
349C2×C22⋊C4C2×Dic1111yescharacteristic
350C2×C22⋊C4C2×Dic1111yescharacteristic
351C2×C22⋊C4C2×Dic1112yes—
352C2×C22⋊C4C2×Dic1112yes—
353C2×C22⋊C4C2×Dic1112yes—
354C2×C42C22×D1111yescharacteristic
355C2×C42C22×D1112yes—
356C4⋊C8—222no—
357C4⋊C8—442no—
358C22⋊C8—224no—
359C22⋊C8—224no—
360C22⋊C8—222no—
361C22⋊C8—222no—
362C22⋊C8—222no—
363C22⋊C8—442no—
364C22⋊C8—442no—
365C22⋊C8—442no—
366#97—222no—
367#97—442no—
368#95C2×Dic1112yes—
369#95C2×Dic1112yes—
370#95C2×Dic1112yes—
371C2×C11—24no—
372C2×C11—44no—
373C2×C11—81no—
374C2×C11#232111yescharacteristic
375C2×C11C2×#43511yescharacteristic
376C2×C11#293011yescharacteristic
377C2×C11#297312yes—
378C2×C11#297612yes—
379C24—22no—
380C24—22no—
381C24—42no—
382C24—42no—
383C24#431814yescomplemented
384C24C22×Dic1111yescharacteristic
385C24C22×Dic1112yes—
386C24C22×Dic1111yescharacteristic
387C2×D4—24no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—42no—
392C2×D4—42no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—24no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—42no—
408C22×C4—42no—
409C22×C4—42no—
410C22×C4—44no—
411C22×C4—44no—
412C22×C4—48no—
413C22×C4D4×D1112yes—
414C22×C4#434112yes—
415C22×C4C22×Dic1111yescharacteristic
416C22×C4C22×Dic1112yes—
417C22×C4C22×Dic1111yescharacteristic
418C22×C4C22×Dic1112yes—
419C22×C4C22×Dic1112yes—
420C22×C4C22×Dic1111yescharacteristic
421C22×C4C22×Dic1111yescharacteristic
422C22×C4C23×D1111yescharacteristic
423M16—444no—
424C2×C8—112no—
425C2×C8—112no—
426C2×C8—222no—
427C2×C8—222no—
428C2×C8—221no—
429C2×C8—222no—
430C2×C8—221no—
431C2×C8—222no—
432C2×C8—222no—
433C2×C8—222no—
434C2×C8—222no—
435C2×C8—222no—
436C2×C8—222no—
437C2×C8—222no—
438C2×C8—444no—
439C2×C8—444no—
440C4⋊C4—22no—
441C4⋊C4—42no—
442C22⋊C4—24no—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—22no—
446C22⋊C4—22no—
447C22⋊C4—42no—
448C22⋊C4—42no—
449C22⋊C4—42no—
450C42—21no—
451C42—21no—
452C42—22no—
453C42—22no—
454C11#2203411yescharacteristic, complemented, Sylow
455C23—22no—
456C23—22no—
457C23—22no—
458C23—22no—
459C23—22no—
460C23—22no—
461C23—22no—
462C23—22no—
463C23—28no—
464C23—21no—
465C23—21no—
466C23—22no—
467C23—21no—
468C23—22no—
469C23—48no—
470C23—44no—
471C23—44no—
472C23—48no—
473C23C2×#431814yes—
474C23C2×#431812yes—
475C23D4×Dic1112yes—
476C23#6700112yes—
477C23C23×Dic1111yescharacteristic
478D4—48no—
479D4—44no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—21no—
485C2×C4—22no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—48no—
501C2×C4—44no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4D4×Dic1112yes—
510C2×C4C2×D4×D1111yescharacteristic
511C2×C4C2×#434111yescharacteristic
512C2×C4#6703712yes—
513C2×C4#6703712yes—
514C8—222no—
515C8—222no—
516C8—441no—
517C8—442no—
518C8—441no—
519C8—442no—
520C22—22no—
521C22—24no—
522C22—24no—
523C22—22no—
524C22—24no—
525C22—24no—
526C22—24no—
527C22—416no—
528C22—42no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—41no—
533C22—41no—
534C22—42no—
535C22—42no—
536C22—41no—
537C22#1062262414yes—
538C22C22×#431811yescharacteristic
539C22C2×D4×Dic1111yescharacteristic
540C22#1062332912yes—
541C22C2×#6700111yescharacteristic
542C22#1062335012yes—
543C4—22no—
544C4—41no—
545C4—41no—
546C4—42no—
547C4—42no—
548C4—42no—
549C4—41no—
550C4#1062312011yescharacteristic
551C4#1062312311yescharacteristic
552C4#1062312412yes—
553C2—24no—
554C2—44no—
555C2—81no—
556C2#1307127711yescharacteristic
557C2C2×#1062262411yescharacteristic
558C2#1307732011yescharacteristic
559C2#1307764512yes—
560C2#1307766412yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC4×C11×#120C2
prime radicalC2×C11×#120C4
cosocleC22×C4×C11C24
hypercenterC4×#120D11
hypocenterC11#22034
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#120

Complements

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

NH ≅ G/Ntype
1. C2×#10622624C2semidirect
2. C22×C22⋊(C11⋊C8)C2semidirect
3. #13069415C2semidirect
4. #13069231C2semidirect
5. #13069231C2semidirect
6. #13068914C2semidirect
7. #13068909C2semidirect
8. #13068796C2semidirect
9. #13068526C2semidirect
10. #13068394C2semidirect
16. C22×#4318C22semidirect
33. C2×C22⋊(C11⋊C8)C22semidirect
34. C2×C22⋊(C11⋊C8)C22semidirect
36. C2×C4⋊(C11⋊C8)C22semidirect
37. C2×C4⋊(C11⋊C8)C22semidirect
38. C2×#66867C22semidirect
39. C2×#66867C22semidirect
40. #10622162C22semidirect
41. #10622162C22semidirect
42. #10622162C22semidirect
77. C22×C11⋊C8D4semidirect
104. C24×C11M16semidirect
383. C24#4318semidirect
454. C11#22034semidirect

Maximal subgroups

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

subgroupindex
C2×#106226242
C22×C22⋊(C11⋊C8)2
#130694152
#130692312
#130689142
#130689092
#130687962
#130685262
#130683942
C4×C11×#1202
#2203411