Finite Group Databasebeta

← #14754537

Subgroups — #14754537

Order 2816.

1462 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×#10623054C211yesmaximal, characteristic
2C22×#66872C211yesmaximal, characteristic, complemented
3C2×#10622742C211yesmaximal, characteristic
4#13071209C211yesmaximal, characteristic
5#13068812C214yesmaximal, complemented
6#13068807C214yesmaximal, complemented
7#13068336C211yesmaximal, characteristic, complemented
8#13068332C211yesmaximal, characteristic, complemented
9C2×C11×#428C211yesmaximal, characteristic, complemented
10C22×#4339C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C22×C4⋊Dic11C2211yescharacteristic
16C23×C11⋊C8C2211yescharacteristic
17#10623054—24no—
18#10623054—24no—
19C2×#66945C2212yes—
20C2×C4⋊C4×D11C2212yes—
21C2×(C22⋊D11)⋊C4—22no—
22C2×C4×D44—21no—
23C2×C4×Dic22—21no—
24C11×#428—24no—
25C2×C11×#107C2212yes—
26C2×C11×#106C2212yes—
27#10622826—22no—
28#10622742C418yescomplemented
29C2×(C2×D11)⋊C8C2214yes—
30#10622601—21no—
31#10622600C2214yes—
32#10622587—21no—
33C2×#66872—24no—
34C2×#66872C2214yes—
35#10622189C2214yes—
36#10622167C2212yes—
37#10622167C2212yes—
38C23×C4×C11—21no—
39C23×C4×C11C2311yescharacteristic
40C22×C22⋊D11D412yes—
41C23×Dic11—21no—
42C2×#4339—22no—
43C2×#4339—22no—
44C2×#4339—22no—
45C2×#4339—22no—
46C2×#4339C2×C414yes—
47C2×#4339Q814yes—
48C22×D44D411yescharacteristic
49C22×C4×D11—22no—
50C22×C4×D11C2312yes—
51C22×Dic22D411yescharacteristic
52C2×C11×M16—22no—
53C2×C11×M16—22no—
54C2×C11×M16C2×C414yescomplemented
55C22×C8×C11C2312yes—
56C11×#117—22no—
57C11×#117D414yes—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C22⋊C4—21no—
65C2×C42×C11—21no—
66C2×C22⋊Dic11—21no—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—24no—
69#66979—22no—
70#66979—22no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11D414yes—
74C2×C4⋊Dic11C2312yes—
75C2×C4⋊Dic11C2312yes—
76C2×Dic11⋊C4—22no—
77C2×C4×Dic11—22no—
78C2×C4×Dic11—21no—
79C22×C11⋊C8—22no—
80C22×C11⋊C8—22no—
81C22×C11⋊C8C2×C414yescomplemented
82C22×C11⋊C8C2312yes—
83#66945—24no—
84#66945—24no—
85C4⋊C4×D11—24no—
86C4⋊C4×D11—24no—
87(C22⋊D11)⋊C4—216no—
88C4×D44—28no—
89C4×Dic22—28no—
90C11×#107—24no—
91C11×#106—24no—
92C11⋊#95—24no—
93(C2×D11)⋊C8C2×C4116yescomplemented
94#66872—28no—
95#20848—111nomaximal, Sylow
96C24×C11C2×D411yescharacteristic
97C23×D11C2×D412yes—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—22no—
101C22×C4×C11—42no—
102C22×C4×C11—82no—
103C22×C4×C11C22×C412yes—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×Q812yes—
108C22×C4×C11#4112yes—
109C22×C4×C11#4112yes—
110C22×C4×C11C2411yescharacteristic
111C2×C22⋊D11—24no—
112C2×C22⋊D11—24no—
113C2×C22⋊D11C4⋊C418yes—
114C22×Dic11—24no—
115C22×Dic11—22no—
116C22×Dic11—22no—
117C22×Dic11—82no—
118C22×Dic11C2×D412yes—
119#4339—28no—
120#4339—28no—
121#4339—28no—
122#4339—28no—
123C2×D44—22no—
124C2×D44—22no—
125C2×D44C4⋊C414yes—
126C2×C4×D11—28no—
127C2×C4×D11—22no—
128C2×C4×D11—22no—
129C2×C4×D11—22no—
130C2×C4×D11—22no—
131C2×C4×D11—84no—
132C2×C4×D11C22×C414yes—
133C2×C4×D11C2×Q814yes—
134C2×Dic22—22no—
135C2×Dic22—22no—
136C2×Dic22C4⋊C414yes—
137C11×M16—28no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11C22×C414yes—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—42no—
146C11×C4⋊C4C2×D412yes—
147C11×C4⋊C4C2×D412yes—
148C11×C22⋊C4—24no—
149C42×C11—24no—
150C22⋊Dic11—42no—
151(C2×D11)⋊C4—28no—
152(C2×D11)⋊C4—84no—
153C4⋊Dic11—24no—
154C4⋊Dic11—22no—
155C4⋊Dic11—22no—
156C4⋊Dic11—22no—
157C4⋊Dic11C2×D414yes—
158Dic11⋊C4—28no—
159C4×Dic11—28no—
160C4×Dic11—42no—
161C2×C11⋊C8—28no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8C22×C414yes—
165C2×#520—111no—
166C2×#428D1111yescharacteristic, complemented
167C22×#106—111no—
168C2×#408—111no—
169#2311—111no—
170#1854—114no—
171#1853—114no—
172#1736—111no—
173#1735—111no—
174C23×C11—22no—
175C23×C11—22no—
176C23×C11C2×C4⋊C412yes—
177C23×C11#12012yes—
178C23×C11#12312yes—
179C23×C11C22×D411yescharacteristic
180C22×D11—22no—
181C22×D11—22no—
182C22×D11—24no—
183C22×D11—24no—
184C22×D11C2×C4⋊C414yes—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—44no—
191C2×C4×C11—84no—
192C2×C4×C11C2×C4⋊C412yes—
193C2×C4×C11C4×D414yes—
194C2×C4×C11C4×D414yes—
195C2×C4×C11#12012yes—
196C2×C4×C11C22⋊Q814yes—
197C2×C4×C11C22⋊Q814yes—
198C2×C4×C11#12312yes—
199C2×C4×C11C23×C411yescharacteristic
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C22×Q811yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C22⋊D11—216no—
206C2×Dic11—22no—
207C2×Dic11—22no—
208C2×Dic11—24no—
209C2×Dic11—44no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—84no—
214C2×Dic11C2×C4⋊C414yes—
215D44—28no—
216C4×D11—24no—
217C4×D11—24no—
218C4×D11—24no—
219C4×D11—24no—
220C4×D11—88no—
221Dic22—28no—
222C8×C11—24no—
223C11⋊C8—24no—
224C22×#41—111no—
225C22×M16C2×D1111yescharacteristic
226C23×C8—111no—
227#520—224no—
228#520—224no—
229C2×C4×Q8—221no—
230C2×C4×D4—221no—
231C2×C4×D4—222no—
232C2×#117—111no—
233C2×#117—112no—
234C2×#117C2×D1111yescharacteristic
235C22×C4⋊C4—111no—
236C22×C4⋊C4—112no—
237C22×C4⋊C4C2×D1111yescharacteristic
238#428—24no—
239C2×#107C2×D1112yes—
240C2×#106—114no—
241C2×#106—224no—
242C2×#106C2×D1112yes—
243#408—118no—
244C2×C22⋊C8—114no—
245#391—221no—
246#390—221no—
247#386—222no—
248#380—114no—
249#340—114no—
250#340—112no—
251#340—112no—
252C22×C11—24no—
253C22×C11—24no—
254C22×C11—22no—
255C22×C11—22no—
256C22×C11#38514yes—
257C22×C11C22×C4⋊C411yescharacteristic
258C22×C11C2×#12011yescharacteristic
259C22×C11C2×#12311yescharacteristic
260C22×C11#57712yes—
261C22×C11#57712yes—
262C2×D11—28no—
263C2×D11—24no—
264C2×D11—44no—
265C2×D11—42no—
266C2×D11—42no—
267C4×C11—42no—
268C4×C11—42no—
269C4×C11—82no—
270C4×C11#38514yes—
271C4×C11C2×C4×D411yescharacteristic
272C4×C11C2×C4×D411yescharacteristic
273C4×C11C2×C22⋊Q811yescharacteristic
274C4×C11C2×C22⋊Q811yescharacteristic
275Dic11—24no—
276Dic11—44no—
277Dic11—82no—
278C2×#41—114no—
279C2×#41—114no—
280C2×#41—222no—
281C2×#41—222no—
282C2×#41—222no—
283C2×#41—222no—
284C22×Q8—111no—
285C22×D4—112no—
286C22×D4—111no—
287C23×C4—21no—
288C23×C4—112no—
289C23×C4—222no—
290C23×C4—221no—
291C23×C4C22×D1111yescharacteristic
292C2×M16—22no—
293C2×M16—22no—
294C2×M16C4×D1114yescomplemented
295C22×C8—114no—
296C22×C8—112no—
297C22×C8—222no—
298C22×C8—222no—
299C22×C8C22×D1112yes—
300C4×Q8—228no—
301C4×D4—228no—
302C4×D4—2216no—
303#117—22no—
304#117—224no—
305#117—224no—
306#117—222no—
307#117—222no—
308#117C22⋊D1114yes—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—114no—
313C2×C4⋊C4—112no—
314C2×C4⋊C4—112no—
315C2×C4⋊C4—224no—
316C2×C4⋊C4—222no—
317C2×C4⋊C4—221no—
318C2×C4⋊C4—222no—
319C2×C4⋊C4—224no—
320C2×C4⋊C4C22×D1112yes—
321C2×C4⋊C4C22×D1111yescharacteristic
322C2×C4⋊C4C22×D1111yescharacteristic
323C2×C22⋊C4—21no—
324C2×C22⋊C4—222no—
325C2×C22⋊C4—221no—
326C2×C22⋊C4—224no—
327C2×C42—21no—
328C2×C42—222no—
329C2×C42—221no—
330#107—24no—
331#106—24no—
332#106—228no—
333C22⋊C8—1116no—
334#95—224no—
335C2×C11—24no—
336C2×C11C2×#38511yescharacteristic
337C2×C11#291212yes—
338C2×C11#300911yescharacteristic
339C2×C11#301011yescharacteristic
340C2×C11#309912yes—
341D11—44no—
342C24—112no—
343C24D4×D1111yescharacteristic
344#41—228no—
345#41—228no—
346#41—228no—
347#41—228no—
348C2×Q8—114no—
349C2×Q8—222no—
350C2×Q8—222no—
351C2×D4—118no—
352C2×D4—114no—
353C2×D4—224no—
354C2×D4—224no—
355C2×D4—222no—
356C2×D4—222no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—22no—
360C22×C4—42no—
361C22×C4—82no—
362C22×C4—112no—
363C22×C4—114no—
364C22×C4—114no—
365C22×C4—228no—
366C22×C4—222no—
367C22×C4—222no—
368C22×C4—222no—
369C22×C4—222no—
370C22×C4—222no—
371C22×C4—224no—
372C22×C4—222no—
373C22×C4—884no—
374C22×C4—882no—
375C22×C4C2×C4×D1112yes—
376C22×C4#433912yes—
377C22×C4D4×D1111yescharacteristic
378C22×C4D4×D1112yes—
379C22×C4Q8×D1112yes—
380C22×C4#434312yes—
381C22×C4C2×C22⋊D1112yes—
382C22×C4C23×D1111yescharacteristic
383M16—28no—
384C2×C8—22no—
385C2×C8—22no—
386C2×C8—114no—
387C2×C8—228no—
388C2×C8—222no—
389C2×C8—222no—
390C2×C8C2×C4×D1114yes—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—42no—
396C4⋊C4—114no—
397C4⋊C4—228no—
398C4⋊C4—224no—
399C4⋊C4—222no—
400C4⋊C4—222no—
401C4⋊C4—222no—
402C4⋊C4C2×C22⋊D1112yes—
403C4⋊C4C2×C22⋊D1112yes—
404C22⋊C4—24no—
405C22⋊C4—228no—
406C22⋊C4—442no—
407C22⋊C4—884no—
408C42—24no—
409C42—228no—
410C42—442no—
411C11#2084811yescharacteristic, complemented, Sylow
412C23—22no—
413C23—22no—
414C23—114no—
415C23—222no—
416C23—224no—
417C23—224no—
418C23—222no—
419C23C4⋊C4×D1112yes—
420C23#6694712yes—
421C23#6699012yes—
422C23C2×D4×D1111yescharacteristic
423Q8—228no—
424D4—2216no—
425D4—228no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—44no—
431C2×C4—42no—
432C2×C4—84no—
433C2×C4—114no—
434C2×C4—222no—
435C2×C4—222no—
436C2×C4—224no—
437C2×C4—224no—
438C2×C4—224no—
439C2×C4—224no—
440C2×C4—224no—
441C2×C4—444no—
442C2×C4—442no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4—888no—
446C2×C4—884no—
447C2×C4C4⋊C4×D1112yes—
448C2×C4#6694614yes—
449C2×C4#6694712yes—
450C2×C4#6694914yes—
451C2×C4C4×C22⋊D1114yes—
452C2×C4#6699012yes—
453C2×C4#6699914yes—
454C2×C4C22×C4×D1111yescharacteristic
455C2×C4C2×#433911yescharacteristic
456C2×C4C2×D4×D1111yescharacteristic
457C2×C4C2×Q8×D1111yescharacteristic
458C2×C4C2×#434311yescharacteristic
459C2×C4C22×C22⋊D1111yescharacteristic
460C8—24no—
461C8—224no—
462C22—24no—
463C22—22no—
464C22—22no—
465C22—24no—
466C22—224no—
467C22—228no—
468C22—444no—
469C22—442no—
470C22—442no—
471C22#1062260214yes—
472C22C2×C4⋊C4×D1111yescharacteristic
473C22C2×#6694711yescharacteristic
474C22#1062330612yes—
475C22#1062330912yes—
476C22C2×#6699011yescharacteristic
477C4—42no—
478C4—42no—
479C4—82no—
480C4—224no—
481C4—444no—
482C4—882no—
483C4#1062260214yes—
484C4C2×#6694611yescharacteristic
485C4C2×#6694911yescharacteristic
486C4C2×C4×C22⋊D1111yescharacteristic
487C4C2×#6699911yescharacteristic
488C2—24no—
489C2—444no—
490C2C2×#1062260211yescharacteristic
491C2#1307721012yes—
492C2#1307789211yescharacteristic
493C2#1307790111yescharacteristic
494C2#1307860912yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#428C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenterC2×#428D11
hypocenterC11#20848
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
2. C22×#66872C2semidirect
5. #13068812C2semidirect
6. #13068807C2semidirect
7. #13068336C2semidirect
8. #13068332C2semidirect
9. C2×C11×#428C2semidirect
28. #10622742C4semidirect
54. C2×C11×M16C2×C4semidirect
81. C22×C11⋊C8C2×C4semidirect
93. (C2×D11)⋊C8C2×C4semidirect
166. C2×#428D11semidirect
294. C2×M16C4×D11semidirect
411. C11#20848semidirect

Maximal subgroups

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

subgroupindex
C2×#106230542
C22×#668722
C2×#106227422
#130712092
#130688122
#130688072
#130683362
#130683322
C2×C11×#4282
#2084811