Finite Group Databasebeta

← #14796408

Subgroups — #14796408

Order 2816.

942 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622455C211yesmaximal, characteristic, complemented
2C2×C4×#4323C211yesmaximal, characteristic
3#13073789C211yesmaximal, characteristic, complemented
4#13071516C211yesmaximal, characteristic, complemented
5#13070102C212yesmaximal, complemented
6#13069988C212yesmaximal, complemented
7#13069576C211yesmaximal, characteristic, complemented
8#13069332C211yesmaximal, characteristic, complemented
9#13068961C212yesmaximal
10#13068625C212yesmaximal, complemented
11C11×#1802C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13C22×#4323C2211yescharacteristic
14C2×#66946C2212yes—
15C2×C4⋊C4×D11—21no—
16C2×C4×D44C2211yescharacteristic
17C2×#66922C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#102C2212yes—
20C11×#384C2211yescharacteristic
21#10622834C2212yes—
22C2×#66896C2211yescharacteristic
23#10622825—21no—
24#10622825—21no—
25C2×#66885C2212yes—
26C2×#66881C2212yes—
27C2×Dic11⋊C8C2212yes—
28C4×#4323—24no—
29#10622602—22no—
30#10622600—21no—
31#10622590C2212yes—
32#10622586C2212yes—
33C2×#66873C2211yescharacteristic
34C2×#66871C2211yescharacteristic
35#10622560—22no—
36C4×C4⋊Dic11C2211yescharacteristic
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622455—24no—
39C11×#340C2212yes—
40#10622188C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11—21no—
45C22×D44C2311yescharacteristic
46C22×C4×D11—21no—
47C22×C4×D11—22no—
48C22×Dic22—21no—
49C22×C8×C11C2312yes—
50C4×D4×C11—22no—
51C4×D4×C11—22no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C22⋊C4—21no—
57C2×C42×C11C2311yescharacteristic
58C2×C22⋊Dic11—22no—
59C2×C22⋊Dic11—22no—
60C2×#4323—22no—
61C2×#4323—22no—
62C2×#4323Q814yescomplemented
63C2×(C2×D11)⋊C4—21no—
64C2×(C2×D11)⋊C4—22no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11D411yescharacteristic
67C2×C4⋊Dic11D411yescharacteristic
68C2×C4⋊Dic11C2312yes—
69C2×C4⋊Dic11C2311yescharacteristic
70C2×Dic11⋊C4—22no—
71C2×C4×Dic11C2312yes—
72C22×C11⋊C8C2311yescharacteristic
73C22×C11⋊C8C2311yescharacteristic
74#66946—24no—
75#66946—42no—
76C4⋊C4×D11—44no—
77C4×D44—22no—
78C4×D44D414yes—
79#66922—22no—
80#66922—22no—
81C11×C4⋊C8—22no—
82C11×#102—42no—
83#66896—22no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87C11⋊#95D412yes—
88#66885—24no—
89#66881—24no—
90Dic11⋊C8—42no—
91#66873—22no—
92#66871—22no—
93C4×C11⋊C8—22no—
94#24812—111nomaximal, Sylow
95C24×C11—21no—
96C23×D11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11C2×Q812yes—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11—42no—
106C22×C4×C11—42no—
107C22×C4×C11—42no—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2411yescharacteristic
111C22×Dic11—21no—
112C22×Dic11—22no—
113C22×Dic11C2×D412yes—
114C22×Dic11C2×D412yes—
115C2×D44—21no—
116C2×D44—21no—
117C2×D44—21no—
118C2×D44C2×D412yes—
119C2×D44C2×Q812yes—
120C2×D44#4112yes—
121C2×C4×D11—24no—
122C2×C4×D11—44no—
123C2×C4×D11—44no—
124C2×C4×D11—42no—
125C2×C4×D11—42no—
126C2×C4×D11—82no—
127C2×Dic22—42no—
128C2×Dic22—81no—
129C2×Dic22—81no—
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C2×C8×C11—22no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—42no—
138C11×C4⋊C4—81no—
139C11×C22⋊C4—42no—
140C42×C11C2×D412yes—
141C42×C11#4112yes—
142C22⋊Dic11—82no—
143C22⋊Dic11—82no—
144#4323—28no—
145(C2×D11)⋊C4—24no—
146(C2×D11)⋊C4—44no—
147C4⋊Dic11—22no—
148C4⋊Dic11—22no—
149C4⋊Dic11—22no—
150C4⋊Dic11—21no—
151C4⋊Dic11—22no—
152C4⋊Dic11—42no—
153C4⋊Dic11C2×D412yes—
154Dic11⋊C4—44no—
155C4×Dic11—22no—
156C4×Dic11—22no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8—21no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8—21no—
162C2×C11⋊C8C2×Q812yes—
163C2×#476—111no—
164C2×C4×D8—111no—
165#2563—111no—
166D4×C4⋊C4—111no—
167#2085—112no—
168#2065—112no—
169#1990—111no—
170#1939—111no—
171#1879—112no—
172#1804—112no—
173#1802D1111yescharacteristic, complemented
174C23×C11—22no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—41no—
181C23×C11C22×D411yescharacteristic
182C22×D11—22no—
183C22×D11—22no—
184C22×D11—22no—
185C22×D11—41no—
186C22×D11—41no—
187C22×D11—41no—
188C22×D11—41no—
189D4×C11—22no—
190D4×C11—22no—
191D4×C11—41no—
192D4×C11—41no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—41no—
196C2×C4×C11—42no—
197C2×C4×C11—41no—
198C2×C4×C11—42no—
199C2×C4×C11—41no—
200C2×C4×C11—42no—
201C2×C4×C11—84no—
202C2×C4×C11#12112yes—
203C2×C4×C11#12112yes—
204C2×C4×C11#13512yes—
205C2×C4×C11AGL(1,ℤ/8)12yes—
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C22×Q811yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C2×C4×C11H(5,𝔽2)11yescharacteristic
211C2×C4×C112−1+411yescharacteristic
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224D44—22no—
225D44—22no—
226D44—22no—
227D44C22⋊Q814yes—
228C4×D11—48no—
229C4×D11—88no—
230Dic22—84no—
231C8×C11—42no—
232C11⋊C8—22no—
233C11⋊C8—41no—
234C22×D8—111no—
235C2×C4⋊Q8—111no—
236C2×C4×D4—112no—
237C2×C4×D4—111no—
238C2×C4×D4C2×D1111yescharacteristic
239C22×C4⋊C4—221no—
240#476—224no—
241C4×D8—224no—
242C2×#107—111no—
243C2×#106—112no—
244C2×C4⋊C8—112no—
245C2×C4⋊C8C2×D1111yescharacteristic
246C2×#102—111no—
247C2×#102—112no—
248C2×#102—111no—
249C2×#102C2×D1112yes—
250C2×C4×C8—111no—
251#393—222no—
252#390—112no—
253#389—112no—
254#385—222no—
255#384C2×D1111yescharacteristic
256#382—112no—
257#380—221no—
258#380—221no—
259#380—221no—
260C4×C4⋊C4—111no—
261#340—112no—
262#340—112no—
263#340C2×D1112yes—
264#336—112no—
265C22×C11—42no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11—81no—
269C22×C11—81no—
270C22×C11—81no—
271C22×C11—81no—
272C22×C11C2×#12111yescharacteristic
273C22×C11#54611yescharacteristic
274C22×C11D4×Q811yescharacteristic
275C22×C11C2×#13511yescharacteristic
276C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
277C22×C11#57611yescharacteristic
278C22×C11#57711yescharacteristic
279C2×D11—24no—
280C2×D11—42no—
281C2×D11—42no—
282C2×D11—42no—
283C2×D11—42no—
284C2×D11—42no—
285C2×D11—42no—
286C4×C11—22no—
287C4×C11—81no—
288C4×C11—82no—
289C4×C11#46314yes—
290C4×C11C2×C22⋊Q811yescharacteristic
291C4×C11#53711yescharacteristic
292C4×C11#55211yescharacteristic
293C4×C11#55411yescharacteristic
294Dic11—42no—
295Dic11—42no—
296Dic11—42no—
297Dic11—82no—
298C22×Q8—221no—
299C22×D4—111no—
300C22×D4C22×D1111yescharacteristic
301C23×C4—21no—
302C23×C4—222no—
303C23×C4—221no—
304C2×D8—114no—
305C2×D8—222no—
306C2×D8—222no—
307C22×C8—111no—
308C22×C8—111no—
309C22×C8C22×D1112yes—
310C4⋊Q8—222no—
311C4⋊Q8—222no—
312C4×D4—22no—
313C4×D4—22no—
314C4×D4—114no—
315C4×D4—224no—
316C4×D4—222no—
317C4×D4—442no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—111no—
321C2×C4⋊C4—111no—
322C2×C4⋊C4—111no—
323C2×C4⋊C4—112no—
324C2×C4⋊C4—222no—
325C2×C4⋊C4—221no—
326C2×C4⋊C4—444no—
327C2×C4⋊C4C22×D1112yes—
328C2×C4⋊C4C22×D1111yescharacteristic
329C2×C22⋊C4—21no—
330C2×C22⋊C4—221no—
331C2×C22⋊C4—222no—
332C2×C22⋊C4—222no—
333C2×C22⋊C4—222no—
334C2×C42—112no—
335C2×C42C22×D1111yescharacteristic
336#107—222no—
337#106—224no—
338C4⋊C8—22no—
339C4⋊C8—442no—
340#102—42no—
341#102—222no—
342#102—222no—
343#102—224no—
344C4×C8—222no—
345#95—112no—
346#95—222no—
347#95—222no—
348#95—222no—
349C2×C11—82no—
350C2×C11#241711yescharacteristic
351C2×C11C2×#46311yescharacteristic
352C2×C11#304511yescharacteristic
353C2×C11#330311yescharacteristic
354C2×C11#332511yescharacteristic
355C2×C11#338011yescharacteristic
356C2×C11#338411yescharacteristic
357D11—44no—
358C24—21no—
359C24—221no—
360C2×Q8—442no—
361C2×Q8—881no—
362C2×Q8—881no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—112no—
369C2×D4—112no—
370C2×D4—112no—
371C2×D4—221no—
372C2×D4—221no—
373C2×D4—221no—
374C2×D4Q8×D1112yes—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4—112no—
381C22×C4—112no—
382C22×C4—221no—
383C22×C4—224no—
384C22×C4—222no—
385C22×C4—444no—
386C22×C4—444no—
387C22×C4—442no—
388C22×C4—442no—
389C22×C4—882no—
390C22×C4D4×D1111yescharacteristic
391C22×C4D4×D1111yescharacteristic
392C22×C4C23×D1111yescharacteristic
393D8—228no—
394C2×C8—22no—
395C2×C8—22no—
396C2×C8—22no—
397C2×C8—112no—
398C2×C8—221no—
399C2×C8—221no—
400C2×C8—221no—
401C2×C8—221no—
402C2×C8—221no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—42no—
408C4⋊C4—81no—
409C4⋊C4—112no—
410C4⋊C4—222no—
411C4⋊C4—222no—
412C4⋊C4—221no—
413C4⋊C4—222no—
414C4⋊C4—222no—
415C4⋊C4—444no—
416C4⋊C4—442no—
417C22⋊C4—42no—
418C22⋊C4—224no—
419C22⋊C4—444no—
420C22⋊C4—882no—
421C22⋊C4—882no—
422C42—222no—
423C42—222no—
424C42#433912yes—
425C42D4×D1112yes—
426C11#2481211yescharacteristic, complemented, Sylow
427C23—22no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—222no—
435C23—222no—
436C23—222no—
437C23—441no—
438C23—441no—
439C23—441no—
440C23—441no—
441C23C2×D4×D1111yescharacteristic
442Q8—884no—
443D4—22no—
444D4—22no—
445D4—41no—
446D4—41no—
447D4—114no—
448D4—222no—
449D4—222no—
450D4—222no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—84no—
460C2×C4—222no—
461C2×C4—222no—
462C2×C4—222no—
463C2×C4—222no—
464C2×C4—222no—
465C2×C4—222no—
466C2×C4—222no—
467C2×C4—441no—
468C2×C4—441no—
469C2×C4—448no—
470C2×C4—442no—
471C2×C4—442no—
472C2×C4—442no—
473C2×C4—888no—
474C2×C4#6693712yes—
475C2×C4#6693712yes—
476C2×C4#6696412yes—
477C2×C4#6696912yes—
478C2×C4C2×#433911yescharacteristic
479C2×C4C2×D4×D1111yescharacteristic
480C2×C4#6703711yescharacteristic
481C2×C4C2×Q8×D1111yescharacteristic
482C2×C4#41×D1111yescharacteristic
483C2×C4#6704311yescharacteristic
484C8—42no—
485C8—222no—
486C8—441no—
487C22—42no—
488C22—42no—
489C22—42no—
490C22—81no—
491C22—81no—
492C22—81no—
493C22—81no—
494C22—224no—
495C22—442no—
496C22—442no—
497C22—442no—
498C22—442no—
499C22—442no—
500C22—442no—
501C22C2×#6693711yescharacteristic
502C22#1062314311yescharacteristic
503C22#1062316311yescharacteristic
504C22C2×#6696411yescharacteristic
505C22C2×#6696911yescharacteristic
506C22#1062330511yescharacteristic
507C22#1062330911yescharacteristic
508C4—22no—
509C4—81no—
510C4—82no—
511C4—442no—
512C4—442no—
513C4—442no—
514C4—882no—
515C4#1062240014yes—
516C4#1062304211yescharacteristic
517C4#1062306011yescharacteristic
518C4#1062313911yescharacteristic
519C4D11×C22⋊Q811yescharacteristic
520C2—82no—
521C2—444no—
522C2#1307206911yescharacteristic
523C2C2×#1062240011yescharacteristic
524C2#1307815411yescharacteristic
525C2#1308054711yescharacteristic
526C2#1308086111yescharacteristic
527C2#1308148211yescharacteristic
528C2#1308151911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1802C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenter#1802D11
hypocenterC11#24812
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
1. C2×#10622455C2semidirect
3. #13073789C2semidirect
4. #13071516C2semidirect
5. #13070102C2semidirect
6. #13069988C2semidirect
7. #13069576C2semidirect
8. #13069332C2semidirect
10. #13068625C2semidirect
11. C11×#1802C2semidirect
62. C2×#4323Q8semidirect
173. #1802D11semidirect
426. C11#24812semidirect

Maximal subgroups

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

subgroupindex
C2×#106224552
C2×C4×#43232
#130737892
#130715162
#130701022
#130699882
#130695762
#130693322
#130689612
#130686252
C11×#18022
#2481211