Finite Group Databasebeta

← #14810713

Subgroups — #14810713

Order 2816.

1282 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622702C211yesmaximal, characteristic, complemented
2C2×#10622629C211yesmaximal, characteristic
3#13074104C211yesmaximal, characteristic, complemented
4#13069754C212yesmaximal, complemented
5#13069749C212yesmaximal, complemented
6#13069565C211yesmaximal, characteristic, complemented
7#13069557C211yesmaximal, characteristic, complemented
8#13068964C212yesmaximal
9#13068950C212yesmaximal, complemented
10#13068441C211yesmaximal, characteristic, complemented
11C2×D4×Q8×C11C211yesmaximal, characteristic, complemented
12C23×Q8×C11—21no—
13D4×Q8×C11—24no—
14D4×Q8×C11—24no—
15C2×C11×C4⋊Q8C2212yes—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×C22⋊Q8—22no—
18C2×C11×C22⋊Q8—21no—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2212yes—
21C2×C4×D4×C11C2211yescharacteristic
22C22×#4324C2211yescharacteristic
23C22×#4323C2211yescharacteristic
24C2×#66928C2211yescharacteristic
25#10622844—21no—
26C2×#66896C2212yes—
27#10622702—24no—
28#10622629—24no—
29#10622606—21no—
30#10622603—22no—
31C2×#66874C2211yescharacteristic
32C2×#66874C2212yes—
33C2×#66873C2211yescharacteristic
34C2×#66873C2212yes—
35#10622552C2212yes—
36C4×C4⋊Dic11C2211yescharacteristic
37#10622542C2212yes—
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39C2×#66867C2211yescharacteristic
40#10622167C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622162C2212yes—
44#10622162C2212yes—
45C22×Q8×C11—28no—
46C22×Q8×C11—21no—
47C22×Q8×C11—22no—
48C22×Q8×C11—48no—
49C22×Q8×C11D411yescharacteristic
50C22×D4×C11C2311yescharacteristic
51C23×C4×C11—22no—
52C23×C4×C11—21no—
53C22×D44C2311yescharacteristic
54C22×Dic22C2311yescharacteristic
55C11×C4⋊Q8—24no—
56C11×C4⋊Q8—24no—
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8D414yes—
59C11×C22⋊Q8—28no—
60C11×C22⋊Q8—216no—
61C4×Q8×C11—22no—
62C4×Q8×C11—22no—
63C4×D4×C11—24no—
64C4×D4×C11—24no—
65C4×D4×C11—22no—
66C4×D4×C11D414yes—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4D412yes—
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—21no—
75C2×C42×C11C2312yes—
76C2×C42×C11C2311yescharacteristic
77C2×#4324—22no—
78C2×#4324—24no—
79C2×#4323—22no—
80C2×#4323—24no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—22no—
84C2×(C2×D11)⋊C4—22no—
85C2×C4⋊Dic11C2312yes—
86C2×C4×Dic11—21no—
87C22×C11⋊C8C2312yes—
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90#66928—22no—
91#66928—22no—
92#66896—24no—
93C11⋊#95—22no—
94C11⋊#95—22no—
95C11⋊#95—21no—
96#66874—22no—
97#66874—24no—
98#66873—22no—
99#66873—24no—
100C4⋊(C11⋊C8)—22no—
101#66867—22no—
102#25939—111nomaximal, Sylow
103C24×C11—21no—
104C23×D11—21no—
105C2×Q8×C11—28no—
106C2×Q8×C11—22no—
107C2×Q8×C11—24no—
108C2×Q8×C11—24no—
109C2×Q8×C11—44no—
110C2×Q8×C11—44no—
111C2×Q8×C11—432no—
112C2×Q8×C11—44no—
113C2×D4×C11—21no—
114C2×D4×C11—22no—
115C2×D4×C11C2×D412yes—
116C2×D4×C11#4114yes—
117C22×C4×C11—28no—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11—24no—
121C22×C4×C11—44no—
122C22×C4×C11—44no—
123C22×C4×C11—44no—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2411yescharacteristic
129C22×Dic11—21no—
130C22×Dic11—22no—
131C2×D44—21no—
132C2×D44—21no—
133C2×D44—22no—
134C2×D44—22no—
135C2×Dic22—21no—
136C2×Dic22—21no—
137C2×Dic22—22no—
138C2×Dic22—22no—
139C11×C4⋊C4—28no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4C2×D414yes—
146C11×C4⋊C4C2×D412yes—
147C11×C22⋊C4—28no—
148C11×C22⋊C4—24no—
149C42×C11—22no—
150C42×C11—22no—
151C42×C11C2×D412yes—
152C42×C11C2×D412yes—
153#4324—44no—
154#4323—44no—
155(C2×D11)⋊C4—42no—
156(C2×D11)⋊C4—42no—
157(C2×D11)⋊C4—44no—
158(C2×D11)⋊C4—82no—
159C4⋊Dic11—22no—
160C4⋊Dic11—22no—
161C4×Dic11—81no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8—21no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×D4×Q8D1111yescharacteristic, complemented
170C2×#489—111no—
171C2×#463—111no—
172#2592—111no—
173#2024—112no—
174#2023—112no—
175#1987—111no—
176#1985—111no—
177#1879—112no—
178#1877—112no—
179#1762—111no—
180C23×C11—22no—
181C23×C11—24no—
182C23×C11—42no—
183C23×C11—41no—
184C23×C11—41no—
185C23×C11C22×D411yescharacteristic
186C22×D11—41no—
187C22×D11—42no—
188C22×D11—42no—
189C22×D11—41no—
190C22×D11—41no—
191Q8×C11—28no—
192Q8×C11—48no—
193Q8×C11—416no—
194D4×C11—22no—
195D4×C11—24no—
196D4×C11#12414yes—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—22no—
203C2×C4×C11—24no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—48no—
208C2×C4×C11—416no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11#12012yes—
213C2×C4×C11#12012yes—
214C2×C4×C11AGL(1,ℤ/8)14yes—
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C2×#4112yes—
218C2×C4×C112−1+412yes—
219C2×Dic11—41no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224D44—41no—
225D44—41no—
226D44—42no—
227Dic22—41no—
228Dic22—41no—
229Dic22—42no—
230C11⋊C8—41no—
231C11⋊C8—41no—
232C11⋊C8—42no—
233C23×Q8—21no—
234C22×SD16—111no—
235C22×D8—111no—
236D4×Q8—24no—
237D4×Q8—24no—
238C2×C4⋊Q8C2×D1112yes—
239C2×C4⋊Q8C2×D1111yescharacteristic
240C2×#124—111no—
241C2×C22⋊Q8—22no—
242C2×C22⋊Q8—21no—
243C2×C4×Q8C2×D1111yescharacteristic
244C2×C4×D4C2×D1112yes—
245C2×C4×D4C2×D1111yescharacteristic
246#489—224no—
247#463—224no—
248C2×C4⋊C8—111no—
249C2×#103—112no—
250C2×#103—111no—
251C2×#102—112no—
252C2×#102—112no—
253C2×#102—111no—
254C2×#97—111no—
255#397—221no—
256#393—221no—
257#391—112no—
258#390—112no—
259#388—222no—
260C4×C4⋊C4—111no—
261#340—112no—
262#340—112no—
263#340—112no—
264#336—112no—
265#336—112no—
266C22×C11—24no—
267C22×C11—44no—
268C22×C11—44no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11C2×#12011yescharacteristic
272C22×C11#54812yes—
273C22×C11C2×AGL(1,ℤ/8)12yes—
274C22×C11#57711yescharacteristic
275C22×C11#57811yescharacteristic
276C2×D11—82no—
277C2×D11—82no—
278C2×D11—81no—
279C2×D11—81no—
280C2×D11—81no—
281C4×C11—22no—
282C4×C11—24no—
283C4×C11—22no—
284C4×C11—44no—
285C4×C11—42no—
286C4×C11—42no—
287C4×C11C2×#12411yescharacteristic
288C4×C11#53611yescharacteristic
289C4×C11#54812yes—
290Dic11—82no—
291Dic11—81no—
292C22×Q8—28no—
293C22×Q8—22no—
294C22×Q8—21no—
295C22×Q8—48no—
296C22×Q8—111no—
297C22×Q8C22⋊D1111yescharacteristic
298C22×D4—111no—
299C22×D4C22×D1111yescharacteristic
300C23×C4—22no—
301C23×C4—21no—
302C2×SD16—224no—
303C2×SD16—222no—
304C2×D8—224no—
305C2×D8—222no—
306C22×C8—111no—
307C22×C8—111no—
308C22×C8—112no—
309C4⋊Q8—24no—
310C4⋊Q8—24no—
311C4⋊Q8—22no—
312C4⋊Q8C22⋊D1114yes—
313#124—222no—
314#124—222no—
315C22⋊Q8—28no—
316C22⋊Q8—216no—
317C4×Q8—22no—
318C4×Q8—22no—
319C4×D4—24no—
320C4×D4—24no—
321C4×D4—22no—
322C4×D4C22⋊D1114yes—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—112no—
326C2×C4⋊C4C22⋊D1112yes—
327C2×C4⋊C4C22⋊D1111yescharacteristic
328C2×C4⋊C4C22×D1112yes—
329C2×C4⋊C4C22×D1111yescharacteristic
330C2×C22⋊C4—22no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—221no—
333C2×C22⋊C4—221no—
334C2×C22⋊C4—222no—
335C2×C22⋊C4—222no—
336C2×C42—221no—
337C2×C42C22×D1112yes—
338C2×C42C22×D1111yescharacteristic
339C4⋊C8—222no—
340#103—222no—
341#103—224no—
342#102—224no—
343#102—222no—
344#102—224no—
345#97—222no—
346#95—221no—
347#95—222no—
348#95—222no—
349C2×C11—44no—
350C2×C11#243611yescharacteristic
351C2×C11#300311yescharacteristic
352C2×C11#301311yescharacteristic
353C2×C11#336712yes—
354C2×C11#337312yes—
355D11—161no—
356C24—21no—
357C24—221no—
358C2×Q8—28no—
359C2×Q8—24no—
360C2×Q8—22no—
361C2×Q8—24no—
362C2×Q8—44no—
363C2×Q8—44no—
364C2×Q8—432no—
365C2×Q8—44no—
366C2×Q8—222no—
367C2×Q8—222no—
368C2×Q8—221no—
369C2×Q8—221no—
370C2×D4—22no—
371C2×D4—21no—
372C2×D4—222no—
373C2×D4—222no—
374C2×D4—221no—
375C2×D4—221no—
376C2×D4#434314yes—
377C2×D4C2×C22⋊D1112yes—
378C22×C4—28no—
379C22×C4—22no—
380C22×C4—21no—
381C22×C4—24no—
382C22×C4—44no—
383C22×C4—44no—
384C22×C4—44no—
385C22×C4—221no—
386C22×C4—222no—
387C22×C4C2×C22⋊D1112yes—
388C22×C4C2×C22⋊D1112yes—
389C22×C4C2×C22⋊D1111yescharacteristic
390C22×C4C2×C22⋊D1111yescharacteristic
391C22×C4C23×D1111yescharacteristic
392SD16—444no—
393D8—444no—
394C2×C8—222no—
395C2×C8—222no—
396C2×C8—222no—
397C2×C8—222no—
398C2×C8—222no—
399C2×C8—221no—
400C2×C8—221no—
401C4⋊C4—28no—
402C4⋊C4—24no—
403C4⋊C4—24no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—21no—
407C4⋊C4—222no—
408C4⋊C4—222no—
409C4⋊C4C2×C22⋊D1114yes—
410C4⋊C4C2×C22⋊D1112yes—
411C22⋊C4—28no—
412C22⋊C4—24no—
413C22⋊C4—444no—
414C22⋊C4—442no—
415C22⋊C4—442no—
416C22⋊C4—882no—
417C42—22no—
418C42—22no—
419C42—881no—
420C42C2×C22⋊D1112yes—
421C42C2×C22⋊D1112yes—
422C11#2593911yescharacteristic, complemented, Sylow
423C23—24no—
424C23—22no—
425C23—42no—
426C23—41no—
427C23—41no—
428C23—442no—
429C23—442no—
430C23—441no—
431C23—441no—
432C23—441no—
433C23C22×C22⋊D1111yescharacteristic
434Q8—28no—
435Q8—416no—
436Q8—48no—
437Q8—441no—
438Q8—441no—
439Q8—442no—
440D4—22no—
441D4—24no—
442D4—441no—
443D4—441no—
444D4—442no—
445D4#6700014yes—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—416no—
457C2×C4—48no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—442no—
462C2×C4—442no—
463C2×C4—442no—
464C2×C4—442no—
465C2×C4—441no—
466C2×C4#6698514yes—
467C2×C4#6700612yes—
468C2×C4#6700612yes—
469C2×C4C2×#434312yes—
470C2×C4#6704012yes—
471C2×C4C22×C22⋊D1111yescharacteristic
472C2×C4C22×C22⋊D1111yescharacteristic
473C8—441no—
474C8—441no—
475C8—442no—
476C22—24no—
477C22—44no—
478C22—42no—
479C22—42no—
480C22—44no—
481C22—882no—
482C22—881no—
483C22—881no—
484C22—881no—
485C22—882no—
486C22C2×#6698512yes—
487C22#1062334812yes—
488C22#1062336811yescharacteristic
489C22#1062336911yescharacteristic
490C22C2×#6700611yescharacteristic
491C4—24no—
492C4—22no—
493C4—22no—
494C4—44no—
495C4—42no—
496C4—42no—
497C4—882no—
498C4—881no—
499C4C2×#6700011yescharacteristic
500C4#1062334711yescharacteristic
501C4#1062334812yes—
502C2—44no—
503C2—1761no—
504C2#1307227011yescharacteristic
505C2#1307784311yescharacteristic
506C2#1307793111yescharacteristic
507C2#1308133412yes—
508C2#1308140812yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×D4×Q8×C11C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenterC2×D4×Q8D11
hypocenterC11#25939
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#10622702C2semidirect
3. #13074104C2semidirect
4. #13069754C2semidirect
5. #13069749C2semidirect
6. #13069565C2semidirect
7. #13069557C2semidirect
9. #13068950C2semidirect
10. #13068441C2semidirect
11. C2×D4×Q8×C11C2semidirect
169. C2×D4×Q8D11semidirect
422. C11#25939semidirect

Maximal subgroups

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

subgroupindex
C2×#106227022
C2×#106226292
#130741042
#130697542
#130697492
#130695652
#130695572
#130689642
#130689502
#130684412
C2×D4×Q8×C112
#2593911