Finite Group Databasebeta

← #14814870

Subgroups — #14814870

Order 2816.

934 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622656C212yesmaximal, complemented
2D4×C4⋊Dic11C211yesmaximal, characteristic
3#13069809C212yesmaximal, complemented
4#13069809C212yesmaximal, complemented
5#13069540C211yesmaximal, characteristic, complemented
6#13069419C211yesmaximal, characteristic, complemented
7#13069411C211yesmaximal, characteristic
8#13069379C211yesmaximal, characteristic, complemented
9#13068924C212yesmaximal, complemented
10C4×#66872C211yesmaximal, characteristic, complemented
11C11×#2542C211yesmaximal, characteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×C22⋊Q8C2212yes—
14C2×C11×C22⋊Q8C2212yes—
15C2×C4×D4×C11C2211yescharacteristic
16C2×D4×Dic11—21no—
17C22×C4⋊Dic11C2212yes—
18C11×#399—22no—
19C11×#390—21no—
20C11×#384—21no—
21C4×C11×C4⋊C4C2211yescharacteristic
22C2×#66899C2212yes—
23C2×#66899C2212yes—
24C2×#66899C2212yes—
25C2×#66899C2212yes—
26#10622825C2212yes—
27C2×C22⋊(C11⋊C8)C2212yes—
28C2×C22⋊(C11⋊C8)C2212yes—
29#10622656—28no—
30#10622598—21no—
31C2×#66872C2212yes—
32C2×#66872C2211yescharacteristic
33C2×#66872C2211yescharacteristic
34#10622563—22no—
35#10622548C2211yescharacteristic
36C4×C4⋊Dic11C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C2×C4×C11⋊C8C2211yescharacteristic
39#10622167C2212yes—
40#10622167C2211yescharacteristic
41#10622167C2211yescharacteristic
42C22×Q8×C11C2312yes—
43C22×D4×C11D411yescharacteristic
44C23×C4×C11C2312yes—
45C23×Dic11—22no—
46C11×C4⋊Q8—22no—
47C11×C4⋊Q8—22no—
48C11×C22⋊Q8—24no—
49C11×C22⋊Q8—24no—
50C11×C22⋊Q8—42no—
51C11×C22⋊Q8—42no—
52C4×D4×C11—22no—
53C4×D4×C11—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4D411yescharacteristic
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4D412yes—
64C2×C42×C11—21no—
65C2×C42×C11C2311yescharacteristic
66C2×C22⋊Dic11—22no—
67D4×Dic11—44no—
68C2×C4⋊Dic11—24no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—22no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—42no—
73C2×C4⋊Dic11C2311yescharacteristic
74C2×C4⋊Dic11C2312yes—
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4×Dic11—21no—
77C22×C11⋊C8C2311yescharacteristic
78C22×C11⋊C8C2312yes—
79C22×C11⋊C8C2311yescharacteristic
80C11×#95—21no—
81#66899—24no—
82#66899—24no—
83#66899—42no—
84#66899—42no—
85C11⋊#95—21no—
86C11⋊#95—22no—
87C22⋊(C11⋊C8)—24no—
88C22⋊(C11⋊C8)—42no—
89#66872—24no—
90#66872—22no—
91#66872D414yescomplemented
92C4⋊(C11⋊C8)—22no—
93C4×C11⋊C8—22no—
94#26234—111nomaximal, Sylow
95C24×C11C2×D412yes—
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11—22no—
100C2×Q8×C11—22no—
101C2×Q8×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11SD1614yes—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2411yescharacteristic
118C22×Dic11—21no—
119C22×Dic11—21no—
120C22×Dic11—22no—
121C22×Dic11—44no—
122C22×Dic11—44no—
123C22×Dic11—82no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—44no—
128C11×C4⋊C4—44no—
129C11×C4⋊C4—42no—
130C11×C4⋊C4—42no—
131C11×C4⋊C4C2×D412yes—
132C11×C4⋊C4#4112yes—
133C11×C22⋊C4—24no—
134C11×C22⋊C4—44no—
135C11×C22⋊C4—44no—
136C42×C11—42no—
137C42×C11#4112yes—
138C42×C11#4112yes—
139C22⋊Dic11—44no—
140C4⋊Dic11—22no—
141C4⋊Dic11—21no—
142C4⋊Dic11—21no—
143C4⋊Dic11—21no—
144C4⋊Dic11—22no—
145C4⋊Dic11—44no—
146C4⋊Dic11—42no—
147C4⋊Dic11—81no—
148C4⋊Dic11C2×D412yes—
149C4×Dic11—42no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—21no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8C2×D412yes—
159C2×#483—112no—
160#2542D1111yescharacteristic
161D4×C4⋊C4—111no—
162#2035—112no—
163#2035—112no—
164#1981—111no—
165#1956—111no—
166#1954—111no—
167#1948—111no—
168#1872—112no—
169C4×#106—111no—
170C23×C11—22no—
171C23×C11—22no—
172C23×C11—22no—
173C23×C11—22no—
174C23×C11—22no—
175C23×C11—22no—
176C23×C11C2×SD1614yes—
177C23×C11C22×D411yescharacteristic
178Q8×C11—42no—
179Q8×C11—42no—
180Q8×C11—42no—
181Q8×C11—42no—
182D4×C11—28no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11#12312yes—
202C2×C4×C11#12312yes—
203C2×C4×C11C2×SD1612yes—
204C2×C4×C11#13712yes—
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11H(5,𝔽2)11yescharacteristic
210C2×C4×C11H(5,𝔽2)11yescharacteristic
211C2×Dic11—22no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—42no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—41no—
220C2×Dic11—88no—
221C11⋊C8—22no—
222C11⋊C8—41no—
223C11⋊C8—42no—
224C2×C4⋊Q8C2×D1111yescharacteristic
225C2×C22⋊Q8C2×D1112yes—
226C2×C22⋊Q8C2×D1112yes—
227C2×C4×D4—221no—
228C2×C4×D4C2×D1111yescharacteristic
229C22×C4⋊C4—112no—
230#483—228no—
231C2×#106—111no—
232C2×#106—112no—
233C2×#106—111no—
234C2×C4⋊C8—111no—
235C2×#103—112no—
236C2×#103—112no—
237C2×#103—112no—
238C2×#103—112no—
239C2×C22⋊C8—112no—
240C2×C22⋊C8—112no—
241C2×C4×C8—111no—
242#399—22no—
243#390—21no—
244#389—221no—
245#385—222no—
246#384—21no—
247#384—111no—
248#380—112no—
249C4×C4⋊C4—111no—
250C4×C4⋊C4C2×D1111yescharacteristic
251#340—111no—
252#340—112no—
253#340—111no—
254C22×C11—24no—
255C22×C11—24no—
256C22×C11—24no—
257C22×C11—42no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11C2×#12311yescharacteristic
262C22×C11D4211yescharacteristic
263C22×C11#54611yescharacteristic
264C22×C11C22×SD1611yescharacteristic
265C22×C11C2×#13711yescharacteristic
266C22×C11#57711yescharacteristic
267C22×C11#57811yescharacteristic
268C4×C11—22no—
269C4×C11—42no—
270C4×C11—42no—
271C4×C11—42no—
272C4×C11—82no—
273C4×C11#48314yescomplemented
274C4×C11#53211yescharacteristic
275C4×C11#54011yescharacteristic
276C4×C11#55011yescharacteristic
277C4×C11#55911yescharacteristic
278Dic11—42no—
279Dic11—82no—
280Dic11—81no—
281C22×Q8C22×D1112yes—
282C22×D4C22⋊D1111yescharacteristic
283C23×C4—222no—
284C23×C4C22×D1112yes—
285C22×C8—111no—
286C22×C8—111no—
287C22×C8—112no—
288C4⋊Q8—22no—
289C4⋊Q8—22no—
290C22⋊Q8—24no—
291C22⋊Q8—24no—
292C22⋊Q8—42no—
293C22⋊Q8—42no—
294C4×D4—22no—
295C4×D4—22no—
296C4×D4—444no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—111no—
302C2×C4⋊C4—112no—
303C2×C4⋊C4—111no—
304C2×C4⋊C4—224no—
305C2×C4⋊C4—222no—
306C2×C4⋊C4—221no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4—442no—
309C2×C4⋊C4C22⋊D1111yescharacteristic
310C2×C4⋊C4C22×D1111yescharacteristic
311C2×C4⋊C4C22×D1111yescharacteristic
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—222no—
315C2×C22⋊C4C22⋊D1112yes—
316C2×C42—21no—
317C2×C42—221no—
318C2×C42C22×D1111yescharacteristic
319#106—114no—
320#106—224no—
321#106—222no—
322C4⋊C8—222no—
323#103—224no—
324#103—224no—
325#103—442no—
326#103—442no—
327C22⋊C8—224no—
328C22⋊C8—442no—
329C4×C8—222no—
330#95—21no—
331#95—221no—
332#95—222no—
333C2×C11—44no—
334C2×C11#244511yescharacteristic
335C2×C11C2×#48311yescharacteristic
336C2×C11#309711yescharacteristic
337C2×C11#327611yescharacteristic
338C2×C11D4×SD1611yescharacteristic
339C2×C11#329811yescharacteristic
340C2×C11#333111yescharacteristic
341C24C2×C22⋊D1112yes—
342C2×Q8—22no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8—22no—
348C2×D4—22no—
349C2×D4—22no—
350C2×D4#432514yes—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—221no—
361C22×C4—221no—
362C22×C4—222no—
363C22×C4—444no—
364C22×C4—444no—
365C22×C4—882no—
366C22×C4C2×C22⋊D1112yes—
367C22×C4C2×C22⋊D1111yescharacteristic
368C22×C4C2×C22⋊D1111yescharacteristic
369C22×C4C23×D1111yescharacteristic
370C2×C8—112no—
371C2×C8—221no—
372C2×C8—221no—
373C2×C8—222no—
374C2×C8—221no—
375C2×C8—222no—
376C2×C8—221no—
377C2×C8—222no—
378C2×C8—221no—
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—44no—
383C4⋊C4—44no—
384C4⋊C4—42no—
385C4⋊C4—42no—
386C4⋊C4—112no—
387C4⋊C4—221no—
388C4⋊C4—222no—
389C4⋊C4—221no—
390C4⋊C4—221no—
391C4⋊C4—222no—
392C4⋊C4—444no—
393C4⋊C4—442no—
394C4⋊C4—881no—
395C4⋊C4D4×D1112yes—
396C4⋊C4#434112yes—
397C22⋊C4—24no—
398C22⋊C4—44no—
399C22⋊C4—44no—
400C22⋊C4—444no—
401C42—42no—
402C42—442no—
403C42#434112yes—
404C42#434112yes—
405C11#2623411yescharacteristic, complemented, Sylow
406C23—22no—
407C23—22no—
408C23—22no—
409C23—22no—
410C23—22no—
411C23—22no—
412C23C2×#432514yes—
413C23C22×C22⋊D1111yescharacteristic
414Q8—42no—
415Q8—42no—
416Q8—42no—
417Q8—42no—
418D4—28no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—222no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—442no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4—441no—
446C2×C4—888no—
447C2×C4#6698812yes—
448C2×C4#6698812yes—
449C2×C4C2×#432512yes—
450C2×C4#6700412yes—
451C2×C4C2×D4×D1111yescharacteristic
452C2×C4C2×#434111yescharacteristic
453C2×C4C2×#434111yescharacteristic
454C2×C4C2×#434111yescharacteristic
455C2×C4#6703711yescharacteristic
456C2×C4#6703711yescharacteristic
457C8—222no—
458C8—442no—
459C8—441no—
460C22—24no—
461C22—24no—
462C22—24no—
463C22—42no—
464C22—42no—
465C22—42no—
466C22—42no—
467C22C2×#6698811yescharacteristic
468C22D4×C22⋊D1111yescharacteristic
469C22#1062333711yescharacteristic
470C22C22×#432511yescharacteristic
471C22C2×#6700411yescharacteristic
472C22#1062336811yescharacteristic
473C22#1062336911yescharacteristic
474C4—22no—
475C4—42no—
476C4—42no—
477C4—42no—
478C4—82no—
479C4—442no—
480C4—881no—
481C4—882no—
482C4#1062265614yescomplemented
483C4#1062324411yescharacteristic
484C4#1062324711yescharacteristic
485C4#1062324911yescharacteristic
486C4#1062325011yescharacteristic
487C2—44no—
488C2#1307237711yescharacteristic
489C2C2×#1062265611yescharacteristic
490C2#1307857911yescharacteristic
491C2#1308025811yescharacteristic
492C2D4×#432511yescharacteristic
493C2#1308048111yescharacteristic
494C2#1308093211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2542C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenter#2542D11
hypocenterC11#26234
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2542

Complements

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

NH ≅ G/Ntype
1. C2×#10622656C2semidirect
3. #13069809C2semidirect
4. #13069809C2semidirect
5. #13069540C2semidirect
6. #13069419C2semidirect
8. #13069379C2semidirect
9. #13068924C2semidirect
10. C4×#66872C2semidirect
91. #66872D4semidirect
273. C4×C11#483semidirect
405. C11#26234semidirect
482. C4#10622656semidirect

Maximal subgroups

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

subgroupindex
C2×#106226562
D4×C4⋊Dic112
#130698092
#130695402
#130694192
#130694112
#130693792
#130689242
C4×#668722
C11×#25422
#2623411