Finite Group Databasebeta

← #14814899

Subgroups — #14814899

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×#10622422C212yesmaximal, complemented
2#13073570C211yesmaximal, characteristic
3#13071516C211yesmaximal, characteristic
4#13069818C212yesmaximal, complemented
5#13069817C212yesmaximal, complemented
6#13069540C211yesmaximal, characteristic, complemented
7#13069410C211yesmaximal, characteristic
8#13069372C211yesmaximal, characteristic, complemented
9#13068920C212yesmaximal, complemented
10C4×#66882C211yesmaximal, characteristic, complemented
11C11×#1956C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×#66999C2212yes—
14C2×#66999C2212yes—
15C2×#66946—21no—
16C2×C4⋊C4×D11C2212yes—
17C2×C4×D44C2211yescharacteristic
18C2×C11×#103C2212yes—
19C2×C11×#103C2212yes—
20C2×C4×C8×C11C2211yescharacteristic
21C11×#384C2211yescharacteristic
22C2×#66899C2212yes—
23C2×#66899C2212yes—
24C2×(C2×D11)⋊C8C2212yes—
25C2×(C2×D11)⋊C8C2212yes—
26C2×#66882C2211yescharacteristic
27C2×#66882C2211yescharacteristic
28#10622605—22no—
29#10622602—22no—
30#10622601—21no—
31#10622600C2212yes—
32#10622589—21no—
33#10622586—21no—
34C2×#66871C2212yes—
35C4×C4⋊Dic11C2211yescharacteristic
36C4×C4⋊Dic11C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38#10622422—28no—
39#10622189C2211yescharacteristic
40#10622189C2211yescharacteristic
41#10622167C2212yes—
42C22×Q8×C11C2312yes—
43C22×D44D411yescharacteristic
44C22×C4×D11—22no—
45C22×C4×D11C2312yes—
46C22×C8×C11C2311yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C11×C4⋊Q8—22no—
49C11×C4⋊Q8—22no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4C2312yes—
55C2×C42×C11C2311yescharacteristic
56#66999—24no—
57#66999—24no—
58#66999—42no—
59#66999—42no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4D412yes—
64C2×C4⋊Dic11D411yescharacteristic
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2311yescharacteristic
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2311yescharacteristic
69C2×Dic11⋊C4—22no—
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4—22no—
72C2×C4×Dic11—21no—
73C2×C4×Dic11—21no—
74C22×C11⋊C8C2312yes—
75#66946—44no—
76C4⋊C4×D11—24no—
77C4⋊C4×D11—42no—
78C4×D44—22no—
79C4×D44—22no—
80C11×#103—24no—
81C11×#103—42no—
82C4×C8×C11—22no—
83#66899—24no—
84#66899—42no—
85C11⋊#95—21no—
86C11⋊#95—21no—
87C11⋊#95—22no—
88(C2×D11)⋊C8—24no—
89(C2×D11)⋊C8—42no—
90#66882—22no—
91#66882D414yescomplemented
92#66871—24no—
93C4⋊(C11⋊C8)—22no—
94#26236—111nomaximal, Sylow
95C23×D11C2×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—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2411yescharacteristic
107C22×Dic11—21no—
108C22×Dic11—21no—
109C22×Dic11—21no—
110C22×Dic11—21no—
111C22×Dic11C2×D412yes—
112C2×D44—22no—
113C2×D44—22no—
114C2×D44Q1614yes—
115C2×C4×D11—22no—
116C2×C4×D11—22no—
117C2×C4×D11—22no—
118C2×C4×D11—22no—
119C2×C4×D11—22no—
120C2×C4×D11—22no—
121C2×C4×D11—44no—
122C2×C4×D11—44no—
123C2×C4×D11—82no—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11C2×D412yes—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—42no—
133C11×C4⋊C4—42no—
134C11×C4⋊C4—42no—
135C11×C4⋊C4—81no—
136C42×C11#4112yes—
137C42×C11#4112yes—
138(C2×D11)⋊C4—24no—
139(C2×D11)⋊C4—44no—
140(C2×D11)⋊C4—44no—
141(C2×D11)⋊C4—44no—
142C4⋊Dic11—22no—
143C4⋊Dic11—21no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11C2×D412yes—
149C4⋊Dic11C2×D412yes—
150C4⋊Dic11#4112yes—
151Dic11⋊C4—44no—
152Dic11⋊C4—44no—
153Dic11⋊C4—44no—
154C4×Dic11—42no—
155C4×Dic11—42no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—22no—
159C2×#484—112no—
160#2542—111no—
161D4×C4⋊C4—111no—
162#2036—112no—
163#2036—112no—
164#1981—111no—
165#1956D1111yescharacteristic, complemented
166#1954—111no—
167#1947—111no—
168#1872—112no—
169C4×#107—111no—
170C23×C11C22×D411yescharacteristic
171C22×D11—22no—
172C22×D11—22no—
173C22×D11—22no—
174C22×D11—22no—
175C22×D11—22no—
176C22×D11—22no—
177C22×D11C2×Q1614yes—
178Q8×C11—42no—
179Q8×C11—42no—
180Q8×C11—42no—
181Q8×C11—42no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11#12312yes—
191C2×C4×C11#12312yes—
192C2×C4×C11C2×Q1612yes—
193C2×C4×C11AGL(1,ℤ/8)12yes—
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C2×#4111yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C2×C4×C11H(5,𝔽2)11yescharacteristic
199C2×C4×C11H(5,𝔽2)11yescharacteristic
200C2×Dic11—22no—
201C2×Dic11—22no—
202C2×Dic11—22no—
203C2×Dic11—22no—
204C2×Dic11—22no—
205C2×Dic11—22no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215D44—28no—
216C4×D11—42no—
217C4×D11—42no—
218C4×D11—42no—
219C4×D11—42no—
220C4×D11—88no—
221C8×C11—22no—
222C8×C11—41no—
223C11⋊C8—42no—
224C2×C4⋊Q8C2×D1111yescharacteristic
225C2×C22⋊Q8—112no—
226C2×C22⋊Q8—112no—
227C2×C4×D4—111no—
228C2×C4×D4—221no—
229C22×C4⋊C4—112no—
230#484—228no—
231C2×#107—111no—
232C2×#107—111no—
233C2×#107—112no—
234C2×C4⋊C8—111no—
235C2×#103—112no—
236C2×#103—112no—
237C2×#103C2×D1112yes—
238C2×#103C2×D1112yes—
239C2×C22⋊C8—112no—
240C2×C22⋊C8—112no—
241C2×C4×C8C2×D1111yescharacteristic
242#399—222no—
243#390—221no—
244#389—221no—
245#385—222no—
246#384—221no—
247#384C2×D1111yescharacteristic
248#380—112no—
249C4×C4⋊C4—111no—
250C4×C4⋊C4—111no—
251#340—111no—
252#340—111no—
253#340—112no—
254C22×C11C2×#12311yescharacteristic
255C22×C11D4211yescharacteristic
256C22×C11#54611yescharacteristic
257C22×C11C22×Q1611yescharacteristic
258C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
259C22×C11#57711yescharacteristic
260C22×C11#57811yescharacteristic
261C2×D11—24no—
262C2×D11—24no—
263C2×D11—24no—
264C2×D11—42no—
265C2×D11—42no—
266C2×D11—42no—
267C2×D11—42no—
268C4×C11—22no—
269C4×C11—82no—
270C4×C11—82no—
271C4×C11#48414yescomplemented
272C4×C11#53211yescharacteristic
273C4×C11#54011yescharacteristic
274C4×C11#55011yescharacteristic
275C4×C11#55911yescharacteristic
276Dic11—42no—
277Dic11—42no—
278Dic11—42no—
279Dic11—42no—
280Dic11—81no—
281C22×Q8C22×D1112yes—
282C22×D4—111no—
283C23×C4—112no—
284C23×C4—222no—
285C22×C8—112no—
286C22×C8C22×D1111yescharacteristic
287C22×C8C22×D1111yescharacteristic
288C4⋊Q8—22no—
289C4⋊Q8—22no—
290C22⋊Q8—224no—
291C22⋊Q8—224no—
292C22⋊Q8—442no—
293C22⋊Q8—442no—
294C4×D4—222no—
295C4×D4—222no—
296C4×D4—444no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—111no—
302C2×C4⋊C4—111no—
303C2×C4⋊C4—111no—
304C2×C4⋊C4—111no—
305C2×C4⋊C4—111no—
306C2×C4⋊C4—224no—
307C2×C4⋊C4—222no—
308C2×C4⋊C4—222no—
309C2×C4⋊C4—222no—
310C2×C4⋊C4—442no—
311C2×C4⋊C4C22×D1112yes—
312C2×C22⋊C4—112no—
313C2×C22⋊C4—222no—
314C2×C22⋊C4—222no—
315C2×C22⋊C4—222no—
316C2×C42—221no—
317C2×C42—221no—
318C2×C42C22×D1111yescharacteristic
319#107—114no—
320#107—224no—
321#107—222no—
322C4⋊C8—222no—
323#103—24no—
324#103—42no—
325#103—224no—
326#103—442no—
327C22⋊C8—224no—
328C22⋊C8—442no—
329C4×C8—22no—
330#95—222no—
331#95—221no—
332#95—221no—
333C2×C11#244511yescharacteristic
334C2×C11C2×#48411yescharacteristic
335C2×C11#309711yescharacteristic
336C2×C11#327211yescharacteristic
337C2×C11D4×Q1611yescharacteristic
338C2×C11#329911yescharacteristic
339C2×C11#333011yescharacteristic
340D11—44no—
341C24—112no—
342C2×Q8—22no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8—22no—
348C2×D4—114no—
349C2×D4—222no—
350C2×D4—222no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—112no—
354C22×C4—221no—
355C22×C4—221no—
356C22×C4—221no—
357C22×C4—222no—
358C22×C4—222no—
359C22×C4—222no—
360C22×C4—222no—
361C22×C4—222no—
362C22×C4—222no—
363C22×C4—221no—
364C22×C4—444no—
365C22×C4—444no—
366C22×C4—882no—
367C22×C4D4×D1111yescharacteristic
368C22×C4D4×D1111yescharacteristic
369C22×C4C23×D1111yescharacteristic
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—21no—
374C2×C8—21no—
375C2×C8—222no—
376C2×C8—222no—
377C2×C8—222no—
378C2×C8D4×D1112yes—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—42no—
382C4⋊C4—42no—
383C4⋊C4—42no—
384C4⋊C4—81no—
385C4⋊C4—112no—
386C4⋊C4—112no—
387C4⋊C4—112no—
388C4⋊C4—222no—
389C4⋊C4—221no—
390C4⋊C4—221no—
391C4⋊C4—221no—
392C4⋊C4—221no—
393C4⋊C4—221no—
394C4⋊C4—444no—
395C4⋊C4—444no—
396C4⋊C4—444no—
397C22⋊C4—224no—
398C22⋊C4—444no—
399C22⋊C4—444no—
400C22⋊C4—444no—
401C42—442no—
402C42—442no—
403C42#433912yes—
404C42#434112yes—
405C11#2623611yescharacteristic, complemented, Sylow
406C23—114no—
407C23—222no—
408C23—222no—
409C23—222no—
410C23—222no—
411C23—222no—
412C23—222no—
413C23C2×D4×D1111yescharacteristic
414Q8—42no—
415Q8—42no—
416Q8—42no—
417Q8—42no—
418D4—228no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—222no—
428C2×C4—222no—
429C2×C4—222no—
430C2×C4—222no—
431C2×C4—222no—
432C2×C4—222no—
433C2×C4—441no—
434C2×C4—441no—
435C2×C4—441no—
436C2×C4—441no—
437C2×C4—441no—
438C2×C4—441no—
439C2×C4—442no—
440C2×C4—442no—
441C2×C4—442no—
442C2×C4—442no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—441no—
446C2×C4—888no—
447C2×C4#6693612yes—
448C2×C4#6693612yes—
449C2×C4#6696712yes—
450C2×C4Q16×D1112yes—
451C2×C4C2×#433911yescharacteristic
452C2×C4C2×D4×D1111yescharacteristic
453C2×C4C2×#434111yescharacteristic
454C2×C4#6703711yescharacteristic
455C2×C4#41×D1111yescharacteristic
456C2×C4#6704211yescharacteristic
457C8—22no—
458C8—41no—
459C8—442no—
460C22—224no—
461C22—224no—
462C22—224no—
463C22—442no—
464C22—442no—
465C22—442no—
466C22—442no—
467C22C2×#6693611yescharacteristic
468C22#1062320711yescharacteristic
469C22#1062324811yescharacteristic
470C22C2×#6696711yescharacteristic
471C22#1062329311yescharacteristic
472C22C2×Q16×D1111yescharacteristic
473C22#1062329711yescharacteristic
474C4—22no—
475C4—82no—
476C4—82no—
477C4—442no—
478C4—442no—
479C4—442no—
480C4—442no—
481C4—881no—
482C4#1062242214yescomplemented
483C4#1062308411yescharacteristic
484C4#1062309011yescharacteristic
485C4#1062312711yescharacteristic
486C4#1062315011yescharacteristic
487C2—444no—
488C2#1307238411yescharacteristic
489C2C2×#1062242211yescharacteristic
490C2#1307858111yescharacteristic
491C2#1308021511yescharacteristic
492C2#1308036611yescharacteristic
493C2#1308049111yescharacteristic
494C2#1308092011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1956C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenter#1956D11
hypocenterC11#26236
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
1. C2×#10622422C2semidirect
4. #13069818C2semidirect
5. #13069817C2semidirect
6. #13069540C2semidirect
8. #13069372C2semidirect
9. #13068920C2semidirect
10. C4×#66882C2semidirect
11. C11×#1956C2semidirect
91. #66882D4semidirect
165. #1956D11semidirect
271. C4×C11#484semidirect
405. C11#26236semidirect
482. C4#10622422semidirect

Maximal subgroups

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

subgroupindex
C2×#106224222
#130735702
#130715162
#130698182
#130698172
#130695402
#130694102
#130693722
#130689202
C4×#668822
C11×#19562
#2623611