Finite Group Databasebeta

← #14769515

Subgroups — #14769515

Order 2816.

1386 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4326C211yesmaximal, characteristic
2C2×#10622402C212yesmaximal, complemented
3Q8×C22⋊Dic11C211yesmaximal, characteristic
4#13071448C211yesmaximal, characteristic
5#13069484C212yesmaximal, complemented
6#13068955C212yesmaximal, complemented
7#13068954C212yesmaximal, complemented
8#13068639C211yesmaximal, characteristic
9#13068552C211yesmaximal, characteristic
10#13068395C211yesmaximal, characteristic
11C11×#1787C211yesmaximal, characteristic
12C23×Q8×C11C2211yescharacteristic
13C23×Dic22C2211yescharacteristic
14C2×Q8×Dic11C2212yes—
15C22×#4326—28no—
16C22×#4326C418yescomplemented
17C22×#4326C2211yescharacteristic
18C22×#4326C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C22×#4326C2211yescharacteristic
21C23×C11⋊C8C2211yescharacteristic
22C2×#66940C2212yes—
23C2×C11×#103C2212yes—
24C2×C11×#103C2212yes—
25C2×C11×C22⋊C8C2211yescharacteristic
26C11×#380C2211yescharacteristic
27#10622843—22no—
28#10622843C2212yes—
29#10622825—21no—
30#10622825C2211yescharacteristic
31C4×C22⋊Dic11—21no—
32C4×C22⋊Dic11C2211yescharacteristic
33C2×#66880C2212yes—
34C2×#66880C2212yes—
35C2×#66879C2212yes—
36#10622587C2212yes—
37C2×#66872C2212yes—
38#10622555—21no—
39C22⋊C4×Dic11—21no—
40#10622402—28no—
41#10622259—22no—
42#10622188C2212yes—
43#10622167C2212yes—
44C22×Q8×C11—21no—
45C22×Q8×C11—22no—
46C22×Q8×C11—24no—
47C22×Q8×C11—42no—
48C22×Q8×C11C2×C414yes—
49C22×Q8×C11C2311yescharacteristic
50C22×Q8×C11C2311yescharacteristic
51C23×C4×C11—21no—
52C23×C4×C11C2311yescharacteristic
53C23×Dic11—21no—
54C22×Dic22—24no—
55C22×Dic22—21no—
56C22×Dic22—22no—
57C22×Dic22—42no—
58C22×Dic22C2×C414yes—
59C22×Dic22C2311yescharacteristic
60C22×Dic22C2311yescharacteristic
61C22×C8×C11C2312yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C22⋊C4—21no—
64C2×C22⋊Dic11—21no—
65C2×C22⋊Dic11D411yescharacteristic
66C2×C22⋊Dic11D411yescharacteristic
67Q8×Dic11—24no—
68Q8×Dic11—42no—
69C2×#4326—24no—
70C2×#4326—24no—
71C2×#4326—232no—
72C2×#4326—24no—
73C2×#4326C2×C414yes—
74C2×#4326C2×C414yes—
75C2×#4326C2×C414yes—
76C2×#4326C2×C414yes—
77C2×#4326D418yes—
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11C2312yes—
80C2×Dic11⋊C4—22no—
81C2×C4×Dic11—22no—
82C2×C4×Dic11—22no—
83C2×C4×Dic11C2312yes—
84C22×C11⋊C8—24no—
85C22×C11⋊C8C2×C414yes—
86C22×C11⋊C8C2311yescharacteristic
87C22×C11⋊C8C2311yescharacteristic
88#66940—24no—
89#66940—42no—
90C11×#103—24no—
91C11×#103—42no—
92C11×C22⋊C8—22no—
93C11×#95—21no—
94C11⋊#95—21no—
95C11⋊#95—22no—
96C11⋊#95—22no—
97C11⋊#95—22no—
98C11⋊#95—22no—
99C11⋊#95D412yes—
100#66880—24no—
101#66880—42no—
102#66879—24no—
103#66872—24no—
104#22440—111nomaximal, Sylow
105C24×C11C2×D411yescharacteristic
106C2×Q8×C11—24no—
107C2×Q8×C11—21no—
108C2×Q8×C11—21no—
109C2×Q8×C11—22no—
110C2×Q8×C11—28no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—44no—
114C2×Q8×C11—44no—
115C2×Q8×C11—48no—
116C2×Q8×C11C22×C412yes—
117C2×Q8×C11C22×C412yes—
118C2×Q8×C11C2×D414yes—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—24no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—44no—
126C22×C4×C11C22×C412yes—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11#4112yes—
129C22×C4×C11C2411yescharacteristic
130C22×Dic11—24no—
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11—22no—
134C22×Dic11—44no—
135C22×Dic11C2×D412yes—
136C22×Dic11C2×D412yes—
137C2×Dic22—28no—
138C2×Dic22—24no—
139C2×Dic22—22no—
140C2×Dic22—21no—
141C2×Dic22—21no—
142C2×Dic22—22no—
143C2×Dic22—22no—
144C2×Dic22—44no—
145C2×Dic22—48no—
146C2×Dic22—44no—
147C2×Dic22C22×C412yes—
148C2×Dic22C22×C412yes—
149C2×Dic22C2×D414yes—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C22⋊C4—42no—
156C22⋊Dic11—22no—
157C22⋊Dic11—22no—
158C22⋊Dic11—42no—
159#4326—28no—
160#4326—28no—
161#4326—28no—
162#4326C22⋊C4116yescomplemented
163C4⋊Dic11—22no—
164C4⋊Dic11—22no—
165C4⋊Dic11—44no—
166Dic11⋊C4—44no—
167C4×Dic11—22no—
168C4×Dic11—22no—
169C4×Dic11—44no—
170C4×Dic11—44no—
171C2×C11⋊C8—28no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8C22×C412yes—
174C2×C11⋊C8C22×C412yes—
175C2×C11⋊C8C2×D414yes—
176C23×Q16—111no—
177C2×#441—112no—
178Q8×C22⋊C4—111no—
179Q8×C22⋊C4—111no—
180#1971—112no—
181#1878—112no—
182#1878—112no—
183#1807—111no—
184#1787—111no—
185#1787D1111yescharacteristic
186#1752—111no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11C4×D412yes—
190C23×C11#13712yes—
191C23×C11#13712yes—
192C23×C11C22×D411yescharacteristic
193Q8×C11—22no—
194Q8×C11—24no—
195Q8×C11—22no—
196Q8×C11—22no—
197Q8×C11—48no—
198Q8×C11—42no—
199Q8×C11C2×C22⋊C414yes—
200C2×C4×C11—22no—
201C2×C4×C11—24no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—24no—
206C2×C4×C11—22no—
207C2×C4×C11—48no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11C4×D412yes—
213C2×C4×C11C23×C411yescharacteristic
214C2×C4×C11C22×D412yes—
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11H(5,𝔽2)12yes—
217C2×Dic11—22no—
218C2×Dic11—24no—
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—48no—
227C2×Dic11—42no—
228C2×Dic11—42no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231Dic22—22no—
232Dic22—24no—
233Dic22—22no—
234Dic22—22no—
235Dic22—48no—
236Dic22—42no—
237Dic22C2×C22⋊C414yes—
238C8×C11—42no—
239C11⋊C8—22no—
240C11⋊C8C2×C22⋊C414yes—
241C23×Q8—111no—
242C23×Q8C2×D1111yescharacteristic
243C22×Q16—111no—
244C22×Q16—111no—
245C22×Q16—111no—
246C22×Q16—111no—
247C22×Q16—118no—
248C22×Q16—228no—
249C23×C8—111no—
250C2×C4×Q8—112no—
251C2×C4×Q8—112no—
252#441—228no—
253C2×#106—112no—
254C2×#103—112no—
255C2×#103—112no—
256C2×#103C2×D1112yes—
257C2×#103C2×D1112yes—
258C2×C22⋊C8C2×D1111yescharacteristic
259C2×#97—112no—
260#391—112no—
261#391—112no—
262#391—222no—
263#391—222no—
264#380—111no—
265#380—221no—
266#380—221no—
267#380C2×D1111yescharacteristic
268C4×C22⋊C4—111no—
269C4×C22⋊C4—221no—
270C4×C22⋊C4—221no—
271#340—112no—
272#336—112no—
273C22×C11—22no—
274C22×C11—22no—
275C22×C11—24no—
276C22×C11—24no—
277C22×C11#44114yescomplemented
278C22×C11C2×C4×D411yescharacteristic
279C22×C11D4212yes—
280C22×C11C2×#13711yescharacteristic
281C22×C11C2×#13711yescharacteristic
282C22×C11#57812yes—
283C4×C11—22no—
284C4×C11—24no—
285C4×C11—42no—
286C4×C11—82no—
287C4×C11C22×C22⋊C411yescharacteristic
288C4×C11#51811yescharacteristic
289C4×C11#54612yes—
290Dic11—24no—
291Dic11—42no—
292Dic11—42no—
293Dic11—42no—
294Dic11—82no—
295C22×Q8—21no—
296C22×Q8—22no—
297C22×Q8—24no—
298C22×Q8—42no—
299C22×Q8—114no—
300C22×Q8—111no—
301C22×Q8—111no—
302C22×Q8—224no—
303C22×Q8—221no—
304C22×Q8—222no—
305C22×Q8—442no—
306C22×Q8C4×D1114yes—
307C22×Q8C22×D1111yescharacteristic
308C22×Q8C22×D1111yescharacteristic
309C23×C4—21no—
310C23×C4—221no—
311C23×C4C22×D1111yescharacteristic
312C2×Q16—114no—
313C2×Q16—118no—
314C2×Q16—114no—
315C2×Q16—114no—
316C2×Q16—114no—
317C2×Q16—224no—
318C2×Q16—2232no—
319C2×Q16—224no—
320C2×Q16—224no—
321C22×C8—111no—
322C22×C8—114no—
323C22×C8—111no—
324C22×C8—224no—
325C22×C8C22×D1112yes—
326C4×Q8—224no—
327C4×Q8—224no—
328C4×Q8—442no—
329C4×Q8—442no—
330C2×C4⋊C4—112no—
331C2×C4⋊C4—222no—
332C2×C4⋊C4—222no—
333C2×C4⋊C4C22×D1112yes—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—111no—
336C2×C22⋊C4—111no—
337C2×C22⋊C4—221no—
338C2×C42—112no—
339C2×C42—222no—
340C2×C42—222no—
341#106—224no—
342#103—24no—
343#103—42no—
344#103—224no—
345#103—442no—
346C22⋊C8—22no—
347#97—224no—
348#95—21no—
349#95—112no—
350#95—222no—
351#95—222no—
352#95—222no—
353#95—222no—
354#95—221no—
355C2×C11—24no—
356C2×C11D4×C22⋊C411yescharacteristic
357C2×C11C2×#44111yescharacteristic
358C2×C11#295011yescharacteristic
359C2×C11#327012yes—
360C2×C11#327012yes—
361C24D4×D1111yescharacteristic
362C2×Q8—24no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×Q8—22no—
366C2×Q8—28no—
367C2×Q8—22no—
368C2×Q8—22no—
369C2×Q8—44no—
370C2×Q8—44no—
371C2×Q8—48no—
372C2×Q8—112no—
373C2×Q8—112no—
374C2×Q8—114no—
375C2×Q8—228no—
376C2×Q8—224no—
377C2×Q8—221no—
378C2×Q8—221no—
379C2×Q8—222no—
380C2×Q8—222no—
381C2×Q8—222no—
382C2×Q8—444no—
383C2×Q8—444no—
384C2×Q8—448no—
385C2×Q8C2×C4×D1112yes—
386C2×Q8C2×C4×D1112yes—
387C2×Q8D4×D1114yes—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—24no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—44no—
395C22×C4—112no—
396C22×C4—112no—
397C22×C4—221no—
398C22×C4—224no—
399C22×C4—221no—
400C22×C4—222no—
401C22×C4—444no—
402C22×C4C2×C4×D1112yes—
403C22×C4D4×D1111yescharacteristic
404C22×C4#434112yes—
405C22×C4C23×D1111yescharacteristic
406Q16—1116no—
407Q16—228no—
408Q16—228no—
409Q16—228no—
410C2×C8—22no—
411C2×C8—22no—
412C2×C8—22no—
413C2×C8—112no—
414C2×C8—114no—
415C2×C8—112no—
416C2×C8—228no—
417C2×C8—222no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—222no—
421C4⋊C4—222no—
422C4⋊C4—444no—
423C4⋊C4—444no—
424C22⋊C4—42no—
425C22⋊C4—222no—
426C22⋊C4—222no—
427C22⋊C4—442no—
428C42—222no—
429C42—222no—
430C42—444no—
431C42—444no—
432C11#2244011yescharacteristic, complemented, Sylow
433C23—22no—
434C23—22no—
435C23(C22⋊D11)⋊C412yes—
436C23#6696812yes—
437C23#6697112yes—
438C23C2×D4×D1111yescharacteristic
439Q8—22no—
440Q8—24no—
441Q8—22no—
442Q8—22no—
443Q8—48no—
444Q8—42no—
445Q8—114no—
446Q8—222no—
447Q8—224no—
448Q8—222no—
449Q8—222no—
450Q8—448no—
451Q8—442no—
452Q8C22⋊C4×D1114yes—
453C2×C4—22no—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—22no—
460C2×C4—48no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—222no—
466C2×C4—224no—
467C2×C4—222no—
468C2×C4—222no—
469C2×C4—222no—
470C2×C4—222no—
471C2×C4—222no—
472C2×C4—222no—
473C2×C4—222no—
474C2×C4—448no—
475C2×C4—442no—
476C2×C4—442no—
477C2×C4—442no—
478C2×C4—442no—
479C2×C4(C22⋊D11)⋊C412yes—
480C2×C4C22×C4×D1111yescharacteristic
481C2×C4C2×D4×D1112yes—
482C2×C4C2×#434111yescharacteristic
483C2×C4#6703712yes—
484C8—42no—
485C8—114no—
486C8—222no—
487C22—22no—
488C22—24no—
489C22—24no—
490C22—22no—
491C22#1062240214yescomplemented
492C22C2×(C22⋊D11)⋊C411yescharacteristic
493C22#1062312112yes—
494C22C2×#6696811yescharacteristic
495C22C2×#6697111yescharacteristic
496C22#1062331012yes—
497C4—22no—
498C4—24no—
499C4—42no—
500C4—82no—
501C4—224no—
502C4—442no—
503C4—442no—
504C4—442no—
505C4—882no—
506C4C2×C22⋊C4×D1111yescharacteristic
507C4#1062301711yescharacteristic
508C4#1062312212yes—
509C2—24no—
510C2#1307143211yescharacteristic
511C2C2×#1062240211yescharacteristic
512C2#1307748011yescharacteristic
513C2#1308017912yes—
514C2#1308019012yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1787C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1787D11
hypocenterC11#22440
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1787

Complements

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

NH ≅ G/Ntype
2. C2×#10622402C2semidirect
5. #13069484C2semidirect
6. #13068955C2semidirect
7. #13068954C2semidirect
16. C22×#4326C4semidirect
162. #4326C22⋊C4semidirect
277. C22×C11#441semidirect
432. C11#22440semidirect
491. C22#10622402semidirect

Maximal subgroups

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

subgroupindex
C23×#43262
C2×#106224022
Q8×C22⋊Dic112
#130714482
#130694842
#130689552
#130689542
#130686392
#130685522
#130683952
C11×#17872
#2244011