Finite Group Databasebeta

← #14765899

Subgroups — #14765899

Order 2816.

836 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4⋊Q8×Dic11C211yesmaximal, characteristic, complemented
2#13071081C211yesmaximal, characteristic
3#13069565C211yesmaximal, characteristic, complemented
4#13069375C211yesmaximal, characteristic, complemented
5#13069360C212yesmaximal, complemented
6#13069315C212yesmaximal
7#13069238C212yesmaximal
8#13069203C212yesmaximal, complemented
9#13068616C211yesmaximal, characteristic
10#13068471C211yesmaximal, characteristic, complemented
11C2×C11×#476C211yesmaximal, characteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C2×Q8×Dic11—21no—
15C2×#66979—21no—
16C11×#476C418yescomplemented
17C2×C11×#106C2212yes—
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#102C2212yes—
20#10622843—21no—
21#10622834C2211yescharacteristic
22#10622834C2211yescharacteristic
23C2×#66896C2212yes—
24C4×C22⋊Dic11—21no—
25C2×#66882C2212yes—
26C2×#66879C2212yes—
27#10622598—21no—
28#10622598C2212yes—
29#10622598C2211yescharacteristic
30#10622598C2211yescharacteristic
31C4⋊C4×Dic11—21no—
32C4⋊C4×Dic11C2212yes—
33#10622564—21no—
34#10622564—21no—
35#10622548C2211yescharacteristic
36C4×C4⋊Dic11C2211yescharacteristic
37C42×Dic11C2211yescharacteristic
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39#10622189C2212yes—
40#10622188C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44C22×Q8×C11—21no—
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C22×C8×C11C2312yes—
48C11×C4⋊Q8—22no—
49C11×C4⋊Q8C2×C414yes—
50C4×D4×C11—22no—
51C4×D4×C11C2×C414yes—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C22⋊C4—21no—
56C2×C42×C11C2311yescharacteristic
57C2×C22⋊Dic11—21no—
58C2×C22⋊Dic11—21no—
59C2×C22⋊Dic11—21no—
60C2×C22⋊Dic11—21no—
61Q8×Dic11—44no—
62#66979—44no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11C2311yescharacteristic
69C2×C4⋊Dic11C2311yescharacteristic
70C2×C4⋊Dic11C2312yes—
71C2×C4×Dic11—21no—
72C2×C4×Dic11—22no—
73C2×C4×Dic11D411yescharacteristic
74C2×C4×Dic11D411yescharacteristic
75C2×C4×Dic11D411yescharacteristic
76C2×C4×Dic11D411yescharacteristic
77C2×C4×Dic11C2311yescharacteristic
78C2×C4×Dic11C2311yescharacteristic
79C22×C11⋊C8C2312yes—
80C11×#106C2×C418yes—
81C11×C4⋊C8C2×C414yes—
82C11×#102C2×C418yes—
83#66896—42no—
84C11⋊#95—21no—
85C11⋊#95—21no—
86C11⋊#95—21no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89#66882—42no—
90#66879—42no—
91C4⋊(C11⋊C8)—22no—
92#22117—111nomaximal, Sylow
93C24×C11—21no—
94C2×Q8×C11—24no—
95C2×Q8×C11—42no—
96C2×Q8×C11—42no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11C22×C412yes—
103C22×C4×C11—22no—
104C22×C4×C11—21no—
105C22×C4×C11—24no—
106C22×C4×C11—42no—
107C22×C4×C11—42no—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2411yescharacteristic
111C22×Dic11—22no—
112C22×Dic11—21no—
113C22×Dic11—21no—
114C22×Dic11C2×D411yescharacteristic
115C22×Dic11C2×D411yescharacteristic
116C22×Dic11C2×D411yescharacteristic
117C22×Dic11C2×D411yescharacteristic
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11C22×C414yes—
121C11×C4⋊C4—24no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4C22×C414yes—
125C11×C4⋊C4C22×C412yes—
126C11×C22⋊C4—24no—
127C42×C11C22×C412yes—
128C42×C11#4112yes—
129C22⋊Dic11—42no—
130C22⋊Dic11—42no—
131C22⋊Dic11—42no—
132C22⋊Dic11—42no—
133C4⋊Dic11—21no—
134C4⋊Dic11—22no—
135C4⋊Dic11—21no—
136C4⋊Dic11—22no—
137C4⋊Dic11—21no—
138C4⋊Dic11—21no—
139C4⋊Dic11—42no—
140C4⋊Dic11—42no—
141C4⋊Dic11—42no—
142C4⋊Dic11—44no—
143C4⋊Dic11—42no—
144C4×Dic11—22no—
145C4×Dic11—22no—
146C4×Dic11—22no—
147C4×Dic11—21no—
148C4×Dic11—21no—
149C4×Dic11—21no—
150C4×Dic11—21no—
151C4×Dic11—41no—
152C4×Dic11—44no—
153C4×Dic11—42no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—22no—
157C2×#476D1111yescharacteristic
158C4×C4⋊Q8—111no—
159#2293—111no—
160#1987—111no—
161#1947—111no—
162#1944—112no—
163#1936—112no—
164#1925—112no—
165#1920—112no—
166#1802—111no—
167#1767—111no—
168C23×C11—22no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11—41no—
172C23×C11—41no—
173C23×C11—41no—
174C23×C11—41no—
175C23×C11C22×D411yescharacteristic
176Q8×C11—48no—
177D4×C11—22no—
178D4×C11—22no—
179D4×C11—41no—
180D4×C11—41no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—22no—
184C2×C4×C11—24no—
185C2×C4×C11—42no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11—48no—
190C2×C4×C11C4×D412yes—
191C2×C4×C11C4×D412yes—
192C2×C4×C11AGL(1,ℤ/8)12yes—
193C2×C4×C11#13712yes—
194C2×C4×C11C23×C411yescharacteristic
195C2×C4×C11C2×#4111yescharacteristic
196C2×C4×C11H(5,𝔽2)11yescharacteristic
197C2×C4×C112−1+411yescharacteristic
198C2×C4×C112−1+411yescharacteristic
199C2×C4×C112−1+411yescharacteristic
200C2×Dic11—21no—
201C2×Dic11—21no—
202C2×Dic11—21no—
203C2×Dic11—21no—
204C2×Dic11—21no—
205C2×Dic11—21no—
206C2×Dic11—21no—
207C2×Dic11—21no—
208C2×Dic11—21no—
209C2×Dic11—21no—
210C2×Dic11—21no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—42no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11AGL(1,ℤ/8)12yes—
221C8×C11—24no—
222C11⋊C8—42no—
223C2×C4⋊Q8C2×D1111yescharacteristic
224C2×C4×Q8—221no—
225C2×C4×D4C2×D1111yescharacteristic
226C2×#117—221no—
227#476Dic1118yescomplemented
228C2×#107—112no—
229C2×#106C2×D1112yes—
230C2×C4⋊C8—111no—
231C2×C4⋊C8C2×D1111yescharacteristic
232C2×#102—112no—
233C2×#102C2×D1112yes—
234C2×#97—112no—
235#391—221no—
236#390—111no—
237#390—111no—
238#389—112no—
239#389—111no—
240#389—111no—
241#389—221no—
242#388—221no—
243#388—221no—
244#384—111no—
245C4×C4⋊C4—112no—
246C4×C4⋊C4—111no—
247C4×C4⋊C4—221no—
248C4×C22⋊C4—221no—
249C43—111no—
250#340—112no—
251#340—112no—
252#340—112no—
253#340—112no—
254#336—112no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11—42no—
258C22×C11—81no—
259C22×C11—81no—
260C22×C11—81no—
261C22×C11—81no—
262C22×C11C2×C4×D411yescharacteristic
263C22×C11#53611yescharacteristic
264C22×C11#53711yescharacteristic
265C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
266C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
267C22×C11C2×#13711yescharacteristic
268C22×C11#57511yescharacteristic
269C4×C11—22no—
270C4×C11—42no—
271C4×C11—44no—
272C4×C11#44014yes—
273C4×C11#51911yescharacteristic
274C4×C11#52011yescharacteristic
275C4×C11#54111yescharacteristic
276C4×C11#54211yescharacteristic
277Dic11—22no—
278Dic11—41no—
279Dic11—41no—
280Dic11—41no—
281Dic11—81no—
282Dic11—82no—
283Dic11—81no—
284C22×Q8—21no—
285C22×D4C22×D1111yescharacteristic
286C23×C4—21no—
287C22×C8—112no—
288C22×C8C22×D1112yes—
289C4⋊Q8—22no—
290C4⋊Q8C2×Dic1114yes—
291C4×Q8—444no—
292C4×D4—22no—
293C4×D4C2×Dic1114yes—
294#117—444no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—111no—
297C2×C4⋊C4—112no—
298C2×C4⋊C4—111no—
299C2×C4⋊C4—221no—
300C2×C4⋊C4—221no—
301C2×C4⋊C4—222no—
302C2×C4⋊C4—221no—
303C2×C4⋊C4—221no—
304C2×C4⋊C4C22×D1111yescharacteristic
305C2×C4⋊C4C22×D1112yes—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—221no—
308C2×C22⋊C4—221no—
309C2×C22⋊C4—221no—
310C2×C22⋊C4—221no—
311C2×C42—111no—
312C2×C42—111no—
313C2×C42—111no—
314C2×C42—111no—
315C2×C42—111no—
316C2×C42—111no—
317C2×C42—222no—
318C2×C42—221no—
319C2×C42C22×D1111yescharacteristic
320#107—442no—
321#106C2×Dic1118yes—
322C4⋊C8—222no—
323C4⋊C8C2×Dic1114yes—
324#102—442no—
325#102C2×Dic1118yes—
326#97—442no—
327#95—221no—
328#95—221no—
329#95—222no—
330#95—222no—
331#95—221no—
332C2×C11—82no—
333C2×C11#232311yescharacteristic
334C2×C11C2×#44011yescharacteristic
335C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
336C2×C11#323511yescharacteristic
337C2×C11#323811yescharacteristic
338C2×C11#325211yescharacteristic
339C2×C11#325311yescharacteristic
340C24—21no—
341C2×Q8—24no—
342C2×Q8—42no—
343C2×Q8—42no—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4—21no—
349C2×D4C22×Dic1112yes—
350C22×C4—22no—
351C22×C4—21no—
352C22×C4—24no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—111no—
356C22×C4—111no—
357C22×C4—111no—
358C22×C4—111no—
359C22×C4—221no—
360C22×C4—221no—
361C22×C4—222no—
362C22×C4D4×D1111yescharacteristic
363C22×C4D4×D1111yescharacteristic
364C22×C4C23×D1111yescharacteristic
365C2×C8—22no—
366C2×C8—22no—
367C2×C8—222no—
368C2×C8—222no—
369C2×C8—222no—
370C2×C8C22×Dic1114yes—
371C4⋊C4—24no—
372C4⋊C4—21no—
373C4⋊C4—22no—
374C4⋊C4—221no—
375C4⋊C4—222no—
376C4⋊C4—221no—
377C4⋊C4—222no—
378C4⋊C4—221no—
379C4⋊C4—221no—
380C4⋊C4—442no—
381C4⋊C4—442no—
382C4⋊C4—442no—
383C4⋊C4—444no—
384C4⋊C4—442no—
385C4⋊C4C22×Dic1114yes—
386C4⋊C4C22×Dic1112yes—
387C22⋊C4—24no—
388C22⋊C4—442no—
389C22⋊C4—442no—
390C22⋊C4—442no—
391C22⋊C4—442no—
392C42—222no—
393C42—222no—
394C42—222no—
395C42—221no—
396C42—221no—
397C42—221no—
398C42—221no—
399C42—441no—
400C42—444no—
401C42—442no—
402C42#434112yes—
403C42C22×Dic1112yes—
404C11#2211711yescharacteristic, complemented, Sylow
405C23—22no—
406C23—41no—
407C23—41no—
408C23—41no—
409C23—41no—
410C23—41no—
411C23—41no—
412C23C2×D4×D1111yescharacteristic
413Q8—48no—
414D4—22no—
415D4—22no—
416D4—41no—
417D4—41no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—48no—
427C2×C4—112no—
428C2×C4—221no—
429C2×C4—221no—
430C2×C4—221no—
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—441no—
440C2×C4—441no—
441C2×C4—442no—
442C2×C4—442no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—441no—
446C2×C4—442no—
447C2×C4—441no—
448C2×C4#6696712yes—
449C2×C4#6696812yes—
450C2×C4D4×Dic1112yes—
451C2×C4D4×Dic1112yes—
452C2×C4C2×#434111yescharacteristic
453C2×C4#6704011yescharacteristic
454C2×C4#6704011yescharacteristic
455C2×C4#6704211yescharacteristic
456C2×C4#6704311yescharacteristic
457C2×C4C23×Dic1111yescharacteristic
458C8—24no—
459C8—442no—
460C22—42no—
461C22—42no—
462C22—42no—
463C22—81no—
464C22—81no—
465C22—81no—
466C22—81no—
467C22#1062315911yescharacteristic
468C22#1062316011yescharacteristic
469C22C2×#6696711yescharacteristic
470C22C2×#6696811yescharacteristic
471C22D11×AGL(1,ℤ/8)11yescharacteristic
472C22#1062330411yescharacteristic
473C22C2×D4×Dic1111yescharacteristic
474C4—22no—
475C4—42no—
476C4—44no—
477C4—222no—
478C4—441no—
479C4—441no—
480C4—441no—
481C4—881no—
482C4—881no—
483C4—882no—
484C4#1062277714yes—
485C4#1062315611yescharacteristic
486C4#1062317411yescharacteristic
487C4#1062334311yescharacteristic
488C4#1062335811yescharacteristic
489C2—82no—
490C2#1307130011yescharacteristic
491C2C2×#1062277711yescharacteristic
492C2AGL(1,ℤ/8)×Dic1111yescharacteristic
493C2#1307981211yescharacteristic
494C2#1307983611yescharacteristic
495C2#1307999111yescharacteristic
496C2#1307999611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#476C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenterC2×#476D11
hypocenterC11#22117
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C4⋊Q8×Dic11C2semidirect
3. #13069565C2semidirect
4. #13069375C2semidirect
5. #13069360C2semidirect
8. #13069203C2semidirect
10. #13068471C2semidirect
16. C11×#476C4semidirect
227. #476Dic11semidirect
404. C11#22117semidirect

Maximal subgroups

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

subgroupindex
C4⋊Q8×Dic112
#130710812
#130695652
#130693752
#130693602
#130693152
#130692382
#130692032
#130686162
#130684712
C2×C11×#4762
#2211711