Finite Group Databasebeta

← #14796400

Subgroups — #14796400

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×#10622621C211yesmaximal, characteristic, complemented
2C2×C4×#4323C211yesmaximal, characteristic
3#13073785C211yesmaximal, characteristic, complemented
4#13070097C212yesmaximal, complemented
5#13069987C212yesmaximal, complemented
6#13069576C211yesmaximal, characteristic, complemented
7#13069335C211yesmaximal, characteristic, complemented
8#13068964C212yesmaximal
9#13068626C212yesmaximal, complemented
10#13068613C211yesmaximal, characteristic, complemented
11D4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2212yes—
13C2×C4×D4×C11C2211yescharacteristic
14C22×C11×C4⋊C4—21no—
15C22×#4323C2211yescharacteristic
16C2×C4×D44C2211yescharacteristic
17C2×#66922C2211yescharacteristic
18C11×#389C2212yes—
19C11×#385—22no—
20C11×#384C2211yescharacteristic
21C11×#380—21no—
22C4×C11×C4⋊C4C2211yescharacteristic
23C2×#66896C2211yescharacteristic
24C2×#66896C2212yes—
25C4×#4323—24no—
26#10622621—24no—
27#10622600—21no—
28#10622600—21no—
29C2×#66873C2211yescharacteristic
30C2×#66873C2212yes—
31C2×#66872C2212yes—
32C2×#66871C2211yescharacteristic
33#10622552C2212yes—
34#10622549C2212yes—
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2212yes—
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622286—22no—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42#10622162C2212yes—
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11—21no—
45C23×C4×C11—22no—
46C22×D44C2311yescharacteristic
47C22×C4×D11—21no—
48C22×Dic22—21no—
49C4×D4×C11—24no—
50C4×D4×C11—22no—
51C4×D4×C11—42no—
52C4×D4×C11D414yes—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—44no—
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C4⋊C4D411yescharacteristic
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C22⋊C4—21no—
62C2×C11×C22⋊C4—22no—
63C2×C42×C11C2312yes—
64C2×C42×C11C2311yescharacteristic
65C2×#4323—22no—
66C2×#4323—22no—
67C2×#4323Q814yescomplemented
68C2×(C2×D11)⋊C4—21no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—22no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11C2312yes—
73C2×C4⋊Dic11C2311yescharacteristic
74C22×C11⋊C8C2311yescharacteristic
75C22×C11⋊C8C2312yes—
76C22×C11⋊C8C2311yescharacteristic
77C4×D44—22no—
78C4×D44—22no—
79#66922—22no—
80#66922—22no—
81C11×#95—22no—
82C11×#95D412yes—
83#66896—24no—
84#66896—22no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87#66873—22no—
88#66873—42no—
89#66872—24no—
90#66871—22no—
91C4⋊(C11⋊C8)—22no—
92C4⋊(C11⋊C8)—42no—
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×C11C2×D412yes—
101C2×D4×C11C2×Q812yes—
102C2×D4×C11#4112yes—
103C22×C4×C11—21no—
104C22×C4×C11—24no—
105C22×C4×C11—22no—
106C22×C4×C11—44no—
107C22×C4×C11—44no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11—82no—
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2411yescharacteristic
116C22×Dic11—21no—
117C22×Dic11—22no—
118C2×D44—21no—
119C2×D44—21no—
120C2×D44—21no—
121C2×D44—21no—
122C2×D44—21no—
123C2×D44C2×Q812yes—
124C2×C4×D11—42no—
125C2×C4×D11—42no—
126C2×C4×D11—42no—
127C2×Dic22—42no—
128C2×Dic22—81no—
129C2×Dic22—81no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—44no—
136C11×C4⋊C4—42no—
137C11×C4⋊C4—81no—
138C11×C4⋊C4C2×D412yes—
139C11×C22⋊C4—24no—
140C11×C22⋊C4—44no—
141C42×C11—22no—
142C42×C11—22no—
143C42×C11C2×D412yes—
144C42×C11#4112yes—
145#4323—28no—
146(C2×D11)⋊C4—42no—
147(C2×D11)⋊C4—82no—
148(C2×D11)⋊C4—82no—
149C4⋊Dic11—21no—
150C4⋊Dic11—22no—
151C4⋊Dic11—22no—
152C4⋊Dic11—21no—
153C4⋊Dic11—42no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8—21no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8C2×Q812yes—
163C2×#476—111no—
164C2×C4×D8—111no—
165#2563—111no—
166D4×C4⋊C4D1111yescharacteristic, complemented
167#2085—112no—
168#2065—112no—
169#1990—111no—
170#1939—111no—
171#1879—112no—
172#1804—112no—
173#1802—111no—
174C23×C11—22no—
175C23×C11—22no—
176C23×C11—22no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—41no—
181C23×C11C22×D411yescharacteristic
182C22×D11—22no—
183C22×D11—41no—
184C22×D11—41no—
185C22×D11—41no—
186C22×D11—41no—
187C22×D11—41no—
188C22×D11—41no—
189D4×C11—22no—
190D4×C11—22no—
191D4×C11—22no—
192D4×C11C22⋊Q814yes—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—48no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—88no—
209C2×C4×C11#12112yes—
210C2×C4×C11#12112yes—
211C2×C4×C11#13512yes—
212C2×C4×C11AGL(1,ℤ/8)12yes—
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C22×Q811yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C11H(5,𝔽2)11yescharacteristic
218C2×C4×C112−1+411yescharacteristic
219C2×Dic11—42no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225D44—22no—
226D44—22no—
227D44—41no—
228D44—41no—
229C4×D11—84no—
230Dic22—84no—
231C11⋊C8—22no—
232C11⋊C8—41no—
233C11⋊C8—42no—
234C22×D8—111no—
235C2×C4⋊Q8—111no—
236C2×C4×D4—111no—
237C2×C4×D4C2×D1112yes—
238C2×C4×D4C2×D1111yescharacteristic
239C22×C4⋊C4—21no—
240#476—224no—
241C4×D8—224no—
242C2×#107—111no—
243C2×#106—112no—
244C2×C4⋊C8—111no—
245C2×C4⋊C8—112no—
246C2×#102—111no—
247C2×#102—112no—
248C2×#102—111no—
249C2×#102—112no—
250C2×C4×C8—111no—
251#393—222no—
252#390—112no—
253#389C2×D1112yes—
254#385—22no—
255#384C2×D1111yescharacteristic
256#382—112no—
257#380—21no—
258#380—221no—
259#380—221no—
260C4×C4⋊C4C2×D1111yescharacteristic
261#340—112no—
262#340—112no—
263#340—112no—
264#336—112no—
265C22×C11—24no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—42no—
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—42no—
280C2×D11—42no—
281C2×D11—42no—
282C2×D11—81no—
283C2×D11—81no—
284C2×D11—81no—
285C2×D11—81no—
286C4×C11—22no—
287C4×C11—42no—
288C4×C11—42no—
289C4×C11—42no—
290C4×C11—82no—
291C4×C11#46314yes—
292C4×C11C2×C22⋊Q811yescharacteristic
293C4×C11#53711yescharacteristic
294C4×C11#55211yescharacteristic
295C4×C11#55411yescharacteristic
296Dic11—81no—
297Dic11—82no—
298C22×Q8—221no—
299C22×D4—111no—
300C22×D4C22×D1111yescharacteristic
301C23×C4—21no—
302C23×C4—22no—
303C23×C4—221no—
304C2×D8—114no—
305C2×D8—222no—
306C2×D8—222no—
307C22×C8—111no—
308C22×C8—112no—
309C22×C8—111no—
310C4⋊Q8—222no—
311C4⋊Q8—222no—
312C4×D4—24no—
313C4×D4—22no—
314C4×D4—42no—
315C4×D4—222no—
316C4×D4—222no—
317C4×D4D4414yes—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4—111no—
323C2×C4⋊C4—112no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4C22⋊D1111yescharacteristic
326C2×C4⋊C4C22⋊D1111yescharacteristic
327C2×C4⋊C4C22×D1112yes—
328C2×C4⋊C4C22×D1111yescharacteristic
329C2×C22⋊C4—21no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—221no—
332C2×C22⋊C4—222no—
333C2×C22⋊C4—222no—
334C2×C42C22×D1112yes—
335C2×C42C22×D1111yescharacteristic
336#107—222no—
337#106—224no—
338C4⋊C8—222no—
339C4⋊C8—442no—
340#102—222no—
341#102—224no—
342#102—222no—
343#102—442no—
344C4×C8—222no—
345#95—22no—
346#95—222no—
347#95—222no—
348#95C22⋊D1112yes—
349C2×C11—44no—
350C2×C11#241711yescharacteristic
351C2×C11C2×#46311yescharacteristic
352C2×C11#304511yescharacteristic
353C2×C11#330311yescharacteristic
354C2×C11#332511yescharacteristic
355C2×C11#338011yescharacteristic
356C2×C11#338411yescharacteristic
357D11—82no—
358C24—21no—
359C24—221no—
360C2×Q8—442no—
361C2×Q8—881no—
362C2×Q8—881no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—112no—
367C2×D4—221no—
368C2×D4—221no—
369C2×D4—221no—
370C2×D4—221no—
371C2×D4—221no—
372C2×D4C2×D4412yes—
373C2×D4#434112yes—
374C2×D4Q8×D1112yes—
375C22×C4—21no—
376C22×C4—24no—
377C22×C4—22no—
378C22×C4—44no—
379C22×C4—44no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—82no—
383C22×C4—221no—
384C22×C4—222no—
385C22×C4—442no—
386C22×C4—442no—
387C22×C4—442no—
388C22×C4C2×C22⋊D1112yes—
389C22×C4C2×C22⋊D1112yes—
390C22×C4C2×C22⋊D1111yescharacteristic
391C22×C4C2×C22⋊D1111yescharacteristic
392C22×C4C23×D1111yescharacteristic
393D8—228no—
394C2×C8—112no—
395C2×C8—221no—
396C2×C8—221no—
397C2×C8—221no—
398C2×C8—222no—
399C2×C8—222no—
400C2×C8—221no—
401C2×C8—222no—
402C2×C8—221no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—21no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—44no—
409C4⋊C4—42no—
410C4⋊C4—81no—
411C4⋊C4—222no—
412C4⋊C4—221no—
413C4⋊C4—221no—
414C4⋊C4—222no—
415C4⋊C4—442no—
416C4⋊C4C2×D4412yes—
417C22⋊C4—24no—
418C22⋊C4—44no—
419C22⋊C4—442no—
420C22⋊C4—882no—
421C22⋊C4—882no—
422C42—22no—
423C42—22no—
424C42C2×D4412yes—
425C42#433912yes—
426C11#2481211yescharacteristic, complemented, Sylow
427C23—22no—
428C23—22no—
429C23—22no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—222no—
435C23—441no—
436C23—441no—
437C23—441no—
438C23—441no—
439C23—441no—
440C23—441no—
441C23C22×C22⋊D1111yescharacteristic
442Q8—884no—
443D4—22no—
444D4—22no—
445D4—22no—
446D4—222no—
447D4—222no—
448D4—441no—
449D4—441no—
450D4#6695014yes—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—48no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—88no—
467C2×C4—441no—
468C2×C4—442no—
469C2×C4—441no—
470C2×C4—441no—
471C2×C4—442no—
472C2×C4—442no—
473C2×C4—884no—
474C2×C4#6698312yes—
475C2×C4#6698312yes—
476C2×C4#6698512yes—
477C2×C4#6700312yes—
478C2×C4C22×D4411yescharacteristic
479C2×C4C2×#433911yescharacteristic
480C2×C4C2×#434111yescharacteristic
481C2×C4#6703711yescharacteristic
482C2×C4C2×Q8×D1111yescharacteristic
483C2×C4#6704011yescharacteristic
484C8—222no—
485C8—441no—
486C8—442no—
487C22—24no—
488C22—42no—
489C22—42no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—442no—
495C22—442no—
496C22—442no—
497C22—881no—
498C22—881no—
499C22—881no—
500C22—881no—
501C22C2×#6698311yescharacteristic
502C22C2×#6698511yescharacteristic
503C22#1062333711yescharacteristic
504C22Q8×C22⋊D1111yescharacteristic
505C22C2×#6700311yescharacteristic
506C22#1062336611yescharacteristic
507C22#1062336811yescharacteristic
508C4—22no—
509C4—42no—
510C4—42no—
511C4—42no—
512C4—82no—
513C4—881no—
514C4—882no—
515C4#1062262914yes—
516C4C2×#6695011yescharacteristic
517C4#1062304111yescharacteristic
518C4#1062304211yescharacteristic
519C4#1062304411yescharacteristic
520C2—44no—
521C2—882no—
522C2#1307206111yescharacteristic
523C2C2×#1062262911yescharacteristic
524C2#1307815511yescharacteristic
525C2#1308054411yescharacteristic
526C2#1308085811yescharacteristic
527C2#1308147911yescharacteristic
528C2#1308151111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingD4×C11×C4⋊C4C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenterD4×C4⋊C4D11
hypocenterC11#24812
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10622621C2semidirect
3. #13073785C2semidirect
4. #13070097C2semidirect
5. #13069987C2semidirect
6. #13069576C2semidirect
7. #13069335C2semidirect
9. #13068626C2semidirect
10. #13068613C2semidirect
11. D4×C11×C4⋊C4C2semidirect
67. C2×#4323Q8semidirect
166. D4×C4⋊C4D11semidirect
426. C11#24812semidirect

Maximal subgroups

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

subgroupindex
C2×#106226212
C2×C4×#43232
#130737852
#130700972
#130699872
#130695762
#130693352
#130689642
#130686262
#130686132
D4×C11×C4⋊C42
#2481211