Finite Group Databasebeta

← #14760966

Subgroups — #14760966

Order 2816.

964 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22⋊Q8×Dic11C211yesmaximal, characteristic
2C2×C4⋊C4×Dic11C211yesmaximal, characteristic
3#13069259C212yesmaximal, complemented
4#13069196C212yesmaximal, complemented
5#13068924C211yesmaximal, characteristic
6#13068806C211yesmaximal, characteristic
7#13068702C211yesmaximal, characteristic
8#13068516C212yesmaximal, complemented
9#13068448C212yesmaximal, complemented
10#13068380C211yesmaximal, characteristic
11C2×C11×#483C211yesmaximal, characteristic
12C2×C11×C22⋊Q8C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C2×Q8×Dic11C2211yescharacteristic
15C22×C4⋊Dic11C2211yescharacteristic
16C22×C4×Dic11—21no—
17C22×C4×Dic11C2211yescharacteristic
18C11×#483C418yescomplemented
19C2×C11×#106C2212yes—
20C2×C11×#103C2212yes—
21C2×C11×C22⋊C8C2211yescharacteristic
22#10622843C2211yescharacteristic
23C2×#66899C2212yes—
24#10622825C2211yescharacteristic
25C2×C11⋊#95—21no—
26C2×C22⋊(C11⋊C8)C2211yescharacteristic
27C2×#66882C2212yes—
28C2×#66879C2212yes—
29#10622598C2211yescharacteristic
30#10622594—21no—
31C4⋊C4×Dic11—21no—
32C4⋊C4×Dic11—21no—
33C4⋊C4×Dic11—21no—
34C4⋊C4×Dic11C2211yescharacteristic
35C4⋊C4×Dic11C2212yes—
36C4⋊C4×Dic11C2212yes—
37#10622563—21no—
38C22⋊C4×Dic11—21no—
39#10622189C2212yes—
40#10622188C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44C22×Q8×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C23×C4×C11C2311yescharacteristic
47C23×Dic11—21no—
48C23×Dic11D411yescharacteristic
49C23×Dic11D411yescharacteristic
50C22×C8×C11C2312yes—
51C11×C22⋊Q8—22no—
52C11×C22⋊Q8C2×C414yes—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4C2×C414yes—
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C22⋊C4—21no—
60C2×C22⋊Dic11—21no—
61Q8×Dic11—24no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—24no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11C2311yescharacteristic
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2312yes—
69C2×C4×Dic11—24no—
70C2×C4×Dic11—22no—
71C2×C4×Dic11—22no—
72C2×C4×Dic11—21no—
73C2×C4×Dic11—21no—
74C2×C4×Dic11—44no—
75C2×C4×Dic11D411yescharacteristic
76C2×C4×Dic11D411yescharacteristic
77C2×C4×Dic11C2311yescharacteristic
78C2×C4×Dic11C2311yescharacteristic
79C22×C11⋊C8C2312yes—
80C11×#106C2×C418yescomplemented
81C11×#103C2×C418yescomplemented
82C11×C22⋊C8C2×C414yes—
83#66899—24no—
84C11⋊#95—21no—
85C11⋊#95—21no—
86C11⋊#95—21no—
87C11⋊#95—21no—
88C11⋊#95—21no—
89C11⋊#95—22no—
90C11⋊#95—22no—
91C22⋊(C11⋊C8)—22no—
92#66882—24no—
93#66879—24no—
94#21579—111nomaximal, Sylow
95C24×C11C2×D411yescharacteristic
96C2×Q8×C11—21no—
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11C22×C412yes—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—24no—
103C22×C4×C11—22no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—42no—
107C22×C4×C11—42no—
108C22×C4×C11C22×C412yes—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11#4112yes—
111C22×C4×C11C2411yescharacteristic
112C22×Dic11—22no—
113C22×Dic11—22no—
114C22×Dic11—24no—
115C22×Dic11—22no—
116C22×Dic11—22no—
117C22×Dic11—22no—
118C22×Dic11—22no—
119C22×Dic11—21no—
120C22×Dic11—21no—
121C22×Dic11—41no—
122C22×Dic11—42no—
123C22×Dic11—42no—
124C22×Dic11C2×D411yescharacteristic
125C22×Dic11C2×D411yescharacteristic
126C22×Dic11C2×D411yescharacteristic
127C22×Dic11C2×D411yescharacteristic
128C2×C8×C11—22no—
129C2×C8×C11—22no—
130C2×C8×C11C22×C414yes—
131C11×C4⋊C4—24no—
132C11×C4⋊C4—24no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4C22×C414yes—
136C11×C4⋊C4C22×C412yes—
137C11×C22⋊C4—24no—
138C22⋊Dic11—42no—
139C4⋊Dic11—24no—
140C4⋊Dic11—22no—
141C4⋊Dic11—22no—
142C4⋊Dic11—22no—
143C4⋊Dic11—42no—
144C4⋊Dic11—42no—
145C4⋊Dic11#4114yes—
146C4×Dic11—22no—
147C4×Dic11—22no—
148C4×Dic11—22no—
149C4×Dic11—42no—
150C4×Dic11—44no—
151C4×Dic11—44no—
152C4×Dic11—42no—
153C4×Dic11#4114yes—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—22no—
157C2×#483D1111yescharacteristic
158C4×C22⋊Q8—111no—
159C2×C4×C4⋊C4—111no—
160#1928—112no—
161#1919—112no—
162#1872—111no—
163#1852—111no—
164#1823—111no—
165#1776—112no—
166#1763—112no—
167#1749—111no—
168C23×C11—21no—
169C23×C11—21no—
170C23×C11—21no—
171C23×C11—21no—
172C23×C11C4×D412yes—
173C23×C11AGL(1,ℤ/8)12yes—
174C23×C11#13712yes—
175C23×C11C22×D411yescharacteristic
176Q8×C11—24no—
177Q8×C11—42no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—24no—
181C2×C4×C11—24no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—24no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—42no—
188C2×C4×C11—41no—
189C2×C4×C11—42no—
190C2×C4×C11—41no—
191C2×C4×C11—48no—
192C2×C4×C11C4×D412yes—
193C2×C4×C11C23×C411yescharacteristic
194C2×C4×C11C2×#4111yescharacteristic
195C2×C4×C11C2×#4112yes—
196C2×C4×C11C2×#4112yes—
197C2×Dic11—28no—
198C2×Dic11—21no—
199C2×Dic11—21no—
200C2×Dic11—21no—
201C2×Dic11—21no—
202C2×Dic11—21no—
203C2×Dic11—21no—
204C2×Dic11—21no—
205C2×Dic11—24no—
206C2×Dic11—21no—
207C2×Dic11—21no—
208C2×Dic11—44no—
209C2×Dic11—48no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11#12312yes—
219C2×Dic11#12312yes—
220C2×Dic11#13712yes—
221C8×C11—24no—
222C11⋊C8—42no—
223C2×C22⋊Q8C2×D1111yescharacteristic
224C2×C4×Q8—111no—
225C22×C4⋊C4—111no—
226C22×C4⋊C4C2×D1111yescharacteristic
227C22×C42—111no—
228C22×C42—221no—
229#483Dic1118yescomplemented
230C2×#107—112no—
231C2×#106C2×D1112yes—
232C2×#103—112no—
233C2×#103C2×D1112yes—
234C2×C22⋊C8—111no—
235C2×C22⋊C8C2×D1111yescharacteristic
236C2×#97—112no—
237#391—111no—
238#389—111no—
239#387—221no—
240#385—221no—
241#380—111no—
242C4×C4⋊C4—112no—
243C4×C4⋊C4—112no—
244C4×C4⋊C4—111no—
245C4×C4⋊C4—221no—
246C4×C4⋊C4—221no—
247C4×C4⋊C4—221no—
248C4×C22⋊C4—221no—
249C2×#95—221no—
250#340—112no—
251#340—112no—
252#340—112no—
253#340—112no—
254#336—112no—
255C22×C11—22no—
256C22×C11—22no—
257C22×C11—22no—
258C22×C11—22no—
259C22×C11—22no—
260C22×C11—22no—
261C22×C11#44014yes—
262C22×C11C2×C4×D411yescharacteristic
263C22×C11C2×#12311yescharacteristic
264C22×C11#52511yescharacteristic
265C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
266C22×C11C2×#13711yescharacteristic
267C22×C11C2×#13711yescharacteristic
268C22×C11#57511yescharacteristic
269C4×C11—22no—
270C4×C11—44no—
271C4×C11—42no—
272C4×C11—42no—
273C4×C11C4×#4112yes—
274C4×C11#52912yes—
275Dic11—22no—
276Dic11—22no—
277Dic11—22no—
278Dic11—41no—
279Dic11—44no—
280Dic11—81no—
281Dic11—81no—
282C22×Q8C22×D1111yescharacteristic
283C23×C4—21no—
284C23×C4—111no—
285C23×C4—111no—
286C23×C4—221no—
287C23×C4C22×D1111yescharacteristic
288C22×C8—112no—
289C22×C8C22×D1112yes—
290C22⋊Q8—22no—
291C22⋊Q8C2×Dic1114yes—
292C4×Q8—224no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—112no—
297C2×C4⋊C4—111no—
298C2×C4⋊C4—111no—
299C2×C4⋊C4—224no—
300C2×C4⋊C4—221no—
301C2×C4⋊C4—221no—
302C2×C4⋊C4—221no—
303C2×C4⋊C4C2×Dic1114yes—
304C2×C4⋊C4C22×D1112yes—
305C2×C4⋊C4C22×D1111yescharacteristic
306C2×C22⋊C4—21no—
307C2×C22⋊C4—221no—
308C2×C42—111no—
309C2×C42—111no—
310C2×C42—111no—
311C2×C42—111no—
312C2×C42—224no—
313C2×C42—221no—
314C2×C42—221no—
315C2×C42—222no—
316C2×C42—222no—
317C2×C42—444no—
318#107—224no—
319#106C2×Dic1118yescomplemented
320#103—224no—
321#103C2×Dic1118yescomplemented
322C22⋊C8—222no—
323C22⋊C8C2×Dic1114yes—
324#97—224no—
325#95—222no—
326#95—222no—
327#95—221no—
328#95—221no—
329#95—221no—
330#95—221no—
331#95—221no—
332C2×C11—24no—
333C2×C11C4×#12311yescharacteristic
334C2×C11C2×#44011yescharacteristic
335C2×C11C4×#13711yescharacteristic
336C2×C11#309211yescharacteristic
337C2×C11#309511yescharacteristic
338C2×C11#311311yescharacteristic
339C2×C11#311411yescharacteristic
340C24D4×D1111yescharacteristic
341C2×Q8—21no—
342C2×Q8—22no—
343C2×Q8—22no—
344C2×Q8C22×Dic1112yes—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—24no—
348C22×C4—22no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—111no—
354C22×C4—111no—
355C22×C4—111no—
356C22×C4—111no—
357C22×C4—222no—
358C22×C4—222no—
359C22×C4—222no—
360C22×C4—222no—
361C22×C4—224no—
362C22×C4—222no—
363C22×C4—222no—
364C22×C4—221no—
365C22×C4—221no—
366C22×C4—441no—
367C22×C4—442no—
368C22×C4—442no—
369C22×C4D4×D1111yescharacteristic
370C22×C4#434112yes—
371C22×C4C22×Dic1112yes—
372C22×C4C23×D1111yescharacteristic
373C2×C8—22no—
374C2×C8—22no—
375C2×C8—222no—
376C2×C8—222no—
377C2×C8—222no—
378C2×C8C22×Dic1114yes—
379C4⋊C4—24no—
380C4⋊C4—24no—
381C4⋊C4—22no—
382C4⋊C4—21no—
383C4⋊C4—114no—
384C4⋊C4—224no—
385C4⋊C4—222no—
386C4⋊C4—222no—
387C4⋊C4—222no—
388C4⋊C4—442no—
389C4⋊C4—442no—
390C4⋊C4C22×Dic1114yes—
391C4⋊C4C22×Dic1112yes—
392C22⋊C4—24no—
393C22⋊C4—442no—
394C42—114no—
395C42—222no—
396C42—222no—
397C42—222no—
398C42—442no—
399C42—444no—
400C42—444no—
401C42—442no—
402C11#2157911yescharacteristic, complemented, Sylow
403C23—21no—
404C23—21no—
405C23—21no—
406C23—21no—
407C23#6696712yes—
408C23#6696812yes—
409C23D4×Dic1112yes—
410C23C2×D4×D1111yescharacteristic
411Q8—24no—
412Q8—42no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—24no—
420C2×C4—48no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—112no—
428C2×C4—112no—
429C2×C4—112no—
430C2×C4—228no—
431C2×C4—221no—
432C2×C4—221no—
433C2×C4—221no—
434C2×C4—221no—
435C2×C4—221no—
436C2×C4—221no—
437C2×C4—221no—
438C2×C4—221no—
439C2×C4—221no—
440C2×C4—224no—
441C2×C4—444no—
442C2×C4—448no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4—441no—
446C2×C4—441no—
447C2×C4—441no—
448C2×C4—441no—
449C2×C4—441no—
450C2×C4—441no—
451C2×C4D4×Dic1112yes—
452C2×C4C2×#434111yescharacteristic
453C2×C4#41×D1112yes—
454C2×C4#41×D1112yes—
455C2×C4C23×Dic1111yescharacteristic
456C8—24no—
457C8—442no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—22no—
464C22#1062277714yes—
465C22D11×#12311yescharacteristic
466C22#1062318711yescharacteristic
467C22C2×#6696711yescharacteristic
468C22C2×#6696811yescharacteristic
469C22D11×#13711yescharacteristic
470C22#1062330811yescharacteristic
471C22C2×D4×Dic1111yescharacteristic
472C4—22no—
473C4—42no—
474C4—44no—
475C4—42no—
476C4—222no—
477C4—222no—
478C4—222no—
479C4—441no—
480C4—444no—
481C4—881no—
482C4—881no—
483C4#1062318012yes—
484C4#41×Dic1112yes—
485C2—24no—
486C2#123×Dic1111yescharacteristic
487C2C2×#1062277711yescharacteristic
488C2#137×Dic1111yescharacteristic
489C2#1307854011yescharacteristic
490C2#1307855911yescharacteristic
491C2#1307874311yescharacteristic
492C2#1307875711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#483C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×#483D11
hypocenterC11#21579
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
3. #13069259C2semidirect
4. #13069196C2semidirect
8. #13068516C2semidirect
9. #13068448C2semidirect
18. C11×#483C4semidirect
80. C11×#106C2×C4semidirect
81. C11×#103C2×C4semidirect
229. #483Dic11semidirect
319. #106C2×Dic11semidirect
321. #103C2×Dic11semidirect
402. C11#21579semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×Dic112
C2×C4⋊C4×Dic112
#130692592
#130691962
#130689242
#130688062
#130687022
#130685162
#130684482
#130683802
C2×C11×#4832
#2157911