Finite Group Databasebeta

← #14770596

Subgroups — #14770596

Order 2816.

1098 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623073C211yesmaximal, characteristic
2C2×#10622292C211yesmaximal, characteristic, complemented
3C4⋊C4×Dic22C211yesmaximal, characteristic, complemented
4#13069547C212yesmaximal
5#13069539C211yesmaximal, characteristic, complemented
6#13069431C212yesmaximal
7#13069418C211yesmaximal, characteristic, complemented
8#13068620C212yesmaximal, complemented
9#13068616C211yesmaximal, characteristic
10#13068445C212yesmaximal, complemented
11C4×C11×#102C211yesmaximal, characteristic
12C2×C4×D4×C11C2211yescharacteristic
13C2×#66989C2212yes—
14C2×#66979—21no—
15C2×#66977—21no—
16#10623073—24no—
17#10623073C418yescomplemented
18C2×#66940C2212yes—
19C2×#66932—22no—
20C2×#66922C2211yescharacteristic
21C2×C4×Dic22—21no—
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C4×C11×C4⋊C4C2211yescharacteristic
27C2×#66896C2212yes—
28C2×#66880C2212yes—
29C2×#66880C2212yes—
30C2×#66879C2212yes—
31C2×Dic11⋊C8C2212yes—
32#10622589C2212yes—
33C4⋊C4×Dic11C2212yes—
34C2×#66874C2212yes—
35C2×#66874C2212yes—
36#10622548C2211yescharacteristic
37#10622541—21no—
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39#10622292—24no—
40#10622260—22no—
41C11×#340C2211yescharacteristic
42C11×#340C2211yescharacteristic
43#10622167C2212yes—
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C22×Dic22D411yescharacteristic
47C22×Dic22C2312yes—
48C22×C8×C11C2311yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C4×D4×C11—22no—
51C4×D4×C11C2×C414yes—
52C2×C11×C4⋊C4C2311yescharacteristic
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C22⋊C4—21no—
56C2×C42×C11—21no—
57C2×C42×C11C2311yescharacteristic
58C2×C22⋊Dic11—22no—
59C2×C22⋊Dic11—22no—
60#66989—24no—
61#66989C2×C418yes—
62#66979—28no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11D411yescharacteristic
68C2×C4⋊Dic11C2312yes—
69#66977—28no—
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4—22no—
72C2×Dic11⋊C4—22no—
73C2×Dic11⋊C4D412yes—
74C2×C4×Dic11—22no—
75C2×C4×Dic11—22no—
76C2×C4×Dic11C2312yes—
77C22×C11⋊C8C2312yes—
78#66940—24no—
79#66940C2×C418yes—
80#66932—216no—
81#66922—22no—
82#66922C2×C414yes—
83C4×Dic22—44no—
84C4×Dic22C2×C414yes—
85C4×Dic22D414yes—
86C11×#102—22no—
87C11×#102—22no—
88C4×C8×C11—22no—
89C11×#95—21no—
90#66896—42no—
91C11⋊#95—22no—
92#66880—24no—
93#66880—42no—
94#66879—24no—
95Dic11⋊C8—24no—
96#66874—24no—
97#66874—42no—
98C4⋊(C11⋊C8)—22no—
99#22544—111nomaximal, Sylow
100C24×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11—21no—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11C22×C412yes—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—24no—
110C22×C4×C11—21no—
111C22×C4×C11—42no—
112C22×C4×C11—42no—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2411yescharacteristic
116C22×Dic11—22no—
117C22×Dic11—22no—
118C22×Dic11C2×D412yes—
119C22×Dic11C2×D412yes—
120C2×Dic22—22no—
121C2×Dic22—22no—
122C2×Dic22—22no—
123C2×Dic22—22no—
124C2×Dic22—22no—
125C2×Dic22—22no—
126C2×Dic22—22no—
127C2×Dic22C22⋊C414yes—
128C2×Dic22C22×C414yes—
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11#4112yes—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4C22×C412yes—
140C11×C4⋊C4#4112yes—
141C11×C22⋊C4—24no—
142C42×C11—42no—
143C42×C11C22×C412yes—
144C42×C11C2×D412yes—
145C22⋊Dic11—28no—
146C22⋊Dic11—28no—
147C4⋊Dic11—24no—
148C4⋊Dic11—24no—
149C4⋊Dic11—22no—
150C4⋊Dic11—22no—
151C4⋊Dic11—42no—
152C4⋊Dic11—81no—
153C4⋊Dic11C22⋊C414yes—
154Dic11⋊C4—28no—
155Dic11⋊C4—44no—
156Dic11⋊C4—82no—
157Dic11⋊C4C22⋊C418yes—
158C4×Dic11—28no—
159C4×Dic11—44no—
160C4×Dic11C22×C414yes—
161C4×Dic11C2×D414yes—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×#556—111no—
166C2×#446—111no—
167Q8×C4⋊C4—111no—
168#1983—112no—
169#1981—111no—
170#1959—112no—
171#1956—111no—
172#1803—112no—
173#1802—111no—
174#1763—112no—
175C4×#102D1111yescharacteristic
176C23×C11—22no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11C22×D411yescharacteristic
184D4×C11—22no—
185D4×C11—22no—
186D4×C11—41no—
187D4×C11—41no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—48no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11C2×C22⋊C412yes—
201C2×C4×C11C2×C22⋊C412yes—
202C2×C4×C11AGL(1,ℤ/8)12yes—
203C2×C4×C11#13712yes—
204C2×C4×C11C23×C411yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×C4×C11H(5,𝔽2)11yescharacteristic
209C2×C4×C112−1+411yescharacteristic
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—24no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11C2×C22⋊C414yes—
221C2×Dic11C2×C22⋊C414yes—
222Dic22—28no—
223Dic22—24no—
224Dic22—24no—
225Dic22—42no—
226Dic22—42no—
227C8×C11—22no—
228C8×C11—41no—
229C11⋊C8—42no—
230#556—118no—
231#556—224no—
232C2×C4⋊Q8—111no—
233C2×#126—222no—
234C2×#124—112no—
235C2×C22⋊Q8—221no—
236C2×C4×Q8—111no—
237C2×C4×Q8—112no—
238C2×C4×Q8—221no—
239C2×C4×D4C2×D1111yescharacteristic
240C2×#117—221no—
241#446—224no—
242C2×C4⋊C8—112no—
243C2×C4⋊C8—111no—
244C2×#103—112no—
245C2×#103—112no—
246C2×#103—112no—
247C2×#103—112no—
248C2×#102—112no—
249C2×#102C2×D1111yescharacteristic
250C2×#102C2×D1111yescharacteristic
251C2×#97—112no—
252C2×C4×C8C2×D1111yescharacteristic
253#389—222no—
254#389—221no—
255#384—112no—
256#384—111no—
257C4×C4⋊C4—112no—
258C4×C4⋊C4C2×D1111yescharacteristic
259#340—112no—
260#340C2×D1111yescharacteristic
261#340C2×D1111yescharacteristic
262C22×C11—42no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11—81no—
266C22×C11—81no—
267C22×C11—81no—
268C22×C11—81no—
269C22×C11C22×C22⋊C411yescharacteristic
270C22×C11#54811yescharacteristic
271C22×C11#55011yescharacteristic
272C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
273C22×C11C2×#13711yescharacteristic
274C22×C11#57711yescharacteristic
275C22×C11#57811yescharacteristic
276C4×C11—22no—
277C4×C11—42no—
278C4×C11—42no—
279C4×C11—81no—
280C4×C11#41714yes—
281C4×C11C4×#4111yescharacteristic
282C4×C11#52011yescharacteristic
283C4×C11#54811yescharacteristic
284C4×C11#55011yescharacteristic
285Dic11—24no—
286Dic11—24no—
287Dic11—44no—
288Dic11—82no—
289C22×Q8—111no—
290C22×Q8—112no—
291C22×D4C22×D1111yescharacteristic
292C23×C4—21no—
293C22×C8—112no—
294C22×C8C22×D1111yescharacteristic
295C22×C8C22×D1111yescharacteristic
296C4⋊Q8—114no—
297C4⋊Q8—222no—
298#126—2216no—
299#124—118no—
300#124—224no—
301C22⋊Q8—228no—
302C4×Q8—114no—
303C4×Q8—114no—
304C4×Q8—118no—
305C4×Q8—224no—
306C4×Q8—444no—
307C4×D4—22no—
308C4×D4C4×D1114yes—
309#117—228no—
310C2×C4⋊C4—111no—
311C2×C4⋊C4—112no—
312C2×C4⋊C4—112no—
313C2×C4⋊C4—222no—
314C2×C4⋊C4—221no—
315C2×C4⋊C4—221no—
316C2×C4⋊C4—222no—
317C2×C4⋊C4—221no—
318C2×C4⋊C4—222no—
319C2×C4⋊C4—221no—
320C2×C4⋊C4C22×D1111yescharacteristic
321C2×C4⋊C4C22×D1111yescharacteristic
322C2×C4⋊C4C22×D1111yescharacteristic
323C2×C22⋊C4—21no—
324C2×C22⋊C4—222no—
325C2×C22⋊C4—222no—
326C2×C42—21no—
327C2×C42—112no—
328C2×C42—222no—
329C2×C42—222no—
330C2×C42C22×D1111yescharacteristic
331C4⋊C8—224no—
332C4⋊C8—222no—
333#103—224no—
334#103—224no—
335#103—442no—
336#103—442no—
337#102—22no—
338#102—22no—
339#102—442no—
340#97—224no—
341C4×C8—22no—
342#95—21no—
343#95—222no—
344C2×C11—82no—
345C2×C11#234111yescharacteristic
346C2×C11C2×#41711yescharacteristic
347C2×C11#289811yescharacteristic
348C2×C11#336711yescharacteristic
349C2×C11#336911yescharacteristic
350C2×C11#339711yescharacteristic
351C2×C11#339811yescharacteristic
352C24—21no—
353C2×Q8—114no—
354C2×Q8—114no—
355C2×Q8—222no—
356C2×Q8—222no—
357C2×Q8—222no—
358C2×Q8—222no—
359C2×Q8—222no—
360C2×Q8—222no—
361C2×Q8—222no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4C2×C4×D1112yes—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—24no—
371C22×C4—21no—
372C22×C4—42no—
373C22×C4—42no—
374C22×C4—112no—
375C22×C4—112no—
376C22×C4—222no—
377C22×C4—222no—
378C22×C4D4×D1111yescharacteristic
379C22×C4D4×D1111yescharacteristic
380C22×C4C23×D1111yescharacteristic
381C2×C8—21no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—21no—
385C2×C8—21no—
386C2×C8—222no—
387C2×C8—222no—
388C2×C8—222no—
389C2×C8#433912yes—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—114no—
395C4⋊C4—118no—
396C4⋊C4—228no—
397C4⋊C4—224no—
398C4⋊C4—224no—
399C4⋊C4—222no—
400C4⋊C4—222no—
401C4⋊C4—444no—
402C4⋊C4—442no—
403C4⋊C4—881no—
404C4⋊C4—882no—
405C4⋊C4C2×C4×D1112yes—
406C4⋊C4#433912yes—
407C22⋊C4—24no—
408C22⋊C4—228no—
409C22⋊C4—228no—
410C42—42no—
411C42—114no—
412C42—114no—
413C42—228no—
414C42—444no—
415C42C2×C4×D1112yes—
416C42D4×D1112yes—
417C11#2254411yescharacteristic, complemented, Sylow
418C23—22no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—41no—
425C23C2×D4×D1111yescharacteristic
426Q8—228no—
427Q8—224no—
428Q8—224no—
429Q8—442no—
430Q8—442no—
431D4—22no—
432D4—22no—
433D4—41no—
434D4—41no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—48no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—114no—
448C2×C4—114no—
449C2×C4—222no—
450C2×C4—222no—
451C2×C4—222no—
452C2×C4—222no—
453C2×C4—224no—
454C2×C4—442no—
455C2×C4—442no—
456C2×C4—442no—
457C2×C4—442no—
458C2×C4—442no—
459C2×C4C22⋊C4×D1112yes—
460C2×C4C22⋊C4×D1112yes—
461C2×C4#6696412yes—
462C2×C4#6696812yes—
463C2×C4C22×C4×D1111yescharacteristic
464C2×C4C2×#433911yescharacteristic
465C2×C4C2×#433911yescharacteristic
466C2×C4C2×D4×D1111yescharacteristic
467C2×C4#6704211yescharacteristic
468C2×C4#6704311yescharacteristic
469C8—22no—
470C8—41no—
471C8—442no—
472C22—42no—
473C22—42no—
474C22—42no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22—81no—
479C22C2×C22⋊C4×D1111yescharacteristic
480C22#1062308311yescharacteristic
481C22#1062308411yescharacteristic
482C22C2×#6696411yescharacteristic
483C22C2×#6696811yescharacteristic
484C22#1062330111yescharacteristic
485C22#1062330211yescharacteristic
486C4—22no—
487C4—42no—
488C4—42no—
489C4—81no—
490C4—224no—
491C4—224no—
492C4—444no—
493C4—882no—
494C4#1062238414yes—
495C4C4×#433911yescharacteristic
496C4#1062305411yescharacteristic
497C4#1062308311yescharacteristic
498C4#1062308411yescharacteristic
499C2—82no—
500C2#1307145611yescharacteristic
501C2C2×#1062238411yescharacteristic
502C2#1307714511yescharacteristic
503C2#1308133211yescharacteristic
504C2#1308135411yescharacteristic
505C2#1308163411yescharacteristic
506C2#1308164511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#102C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenterC4×#102D11
hypocenterC11#22544
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. C2×#10622292C2semidirect
3. C4⋊C4×Dic22C2semidirect
5. #13069539C2semidirect
7. #13069418C2semidirect
8. #13068620C2semidirect
10. #13068445C2semidirect
17. #10623073C4semidirect
417. C11#22544semidirect

Maximal subgroups

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

subgroupindex
C2×#106230732
C2×#106222922
C4⋊C4×Dic222
#130695472
#130695392
#130694312
#130694182
#130686202
#130686162
#130684452
C4×C11×#1022
#2254411