Finite Group Databasebeta

← #14645366

Subgroups — #14645366

Order 2816.

1126 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068560C212yesmaximal, complemented
2C4×#66898C211yesmaximal, characteristic, complemented
3#13067132C212yesmaximal, complemented
4#13066954C211yesmaximal, characteristic, complemented
5C2×C11×#550C211yesmaximal, characteristic
6C22×C11×#41C411yescharacteristic, complemented
7C22×C11×#41C2211yescharacteristic
8C11×#550—24no—
9C11×#550—24no—
10C2×C11×#127—21no—
11C2×C11×#127C411yescharacteristic, complemented
12C2×C11×#121—21no—
13C2×C11×#121—21no—
14C2×C11×#121C411yescharacteristic, complemented
15C2×C11×#121C2211yescharacteristic
16C2×C4×Q8×C11C411yescharacteristic, complemented
17C2×C4×D4×C11—21no—
18C2×C4×D4×C11C2211yescharacteristic
19C2×#66901—24no—
20C2×#66898—21no—
21C4×C22⋊Dic11C2212yes—
22#10622820C2212yes—
23#10622175—24no—
24#10622166—21no—
25#10622164—21no—
26#10622163—21no—
27C2×C11×#41—22no—
28C2×C11×#41—22no—
29C2×C11×#41—22no—
30C2×C11×#41—44no—
31C2×C11×#41—44no—
32C2×C11×#41D414yes—
33C22×Q8×C11C2×C411yescharacteristic
34C22×D4×C11—21no—
35C22×D4×C11—21no—
36C22×D4×C11—21no—
37C22×D4×C11—21no—
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C22×D4×C11C2×C411yescharacteristic
41C22×D4×C11C2×C411yescharacteristic
42C22×D4×C11D411yescharacteristic
43C23×C4×C11—21no—
44C23×C4×C11—21no—
45C23×C4×C11C2×C411yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C11×#127—28no—
48C11×#127—22no—
49C11×#127—22no—
50C11×#121—28no—
51C11×#121—28no—
52C11×#121—22no—
53C11×#121—22no—
54C11×#121—22no—
55C11×#121D414yes—
56C4×Q8×C11—22no—
57C4×Q8×C11—22no—
58C4×D4×C11—28no—
59C4×D4×C11—22no—
60C4×D4×C11—22no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4C2×C411yescharacteristic
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C22⋊C4—21no—
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4D411yescharacteristic
67C2×C11×C22⋊C4D411yescharacteristic
68C2×C42×C11—21no—
69C2×C42×C11C2×C411yescharacteristic
70C2×C22⋊Dic11—22no—
71C2×C4×Dic11—22no—
72C2×#4318—22no—
73#66901—48no—
74#66898—24no—
75C11⋊#95—22no—
76C22⋊(C11⋊C8)—22no—
77C22⋊(C11⋊C8)—22no—
78#8361—111nomaximal, Sylow
79C24×C11—21no—
80C24×C11—21no—
81C24×C11C22⋊C411yescharacteristic
82C24×C11C2×D411yescharacteristic
83C11×#41—28no—
84C11×#41—44no—
85C11×#41—48no—
86C11×#41—48no—
87C11×#41—44no—
88C11×#41—44no—
89C2×Q8×C11—24no—
90C2×Q8×C11—21no—
91C2×Q8×C11C22⋊C412yes—
92C2×D4×C11—24no—
93C2×D4×C11—24no—
94C2×D4×C11—22no—
95C2×D4×C11—24no—
96C2×D4×C11—24no—
97C2×D4×C11—24no—
98C2×D4×C11—24no—
99C2×D4×C11—22no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11—42no—
103C2×D4×C11—41no—
104C2×D4×C11—42no—
105C2×D4×C11—44no—
106C2×D4×C11—44no—
107C2×D4×C11—42no—
108C2×D4×C11—42no—
109C2×D4×C11—82no—
110C2×D4×C11—82no—
111C2×D4×C11—82no—
112C2×D4×C11C22⋊C412yes—
113C2×D4×C11C22⋊C412yes—
114C22×C4×C11—21no—
115C22×C4×C11—24no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—24no—
120C22×C4×C11—42no—
121C22×C4×C11—44no—
122C22×C4×C11—44no—
123C22×C4×C11—42no—
124C22×C4×C11C22⋊C411yescharacteristic
125C22×C4×C11C22⋊C411yescharacteristic
126C22×C4×C11C22⋊C411yescharacteristic
127C22×C4×C11C22×C411yescharacteristic
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D411yescharacteristic
131C22×Dic11—42no—
132C11×C4⋊C4—24no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4C22⋊C412yes—
136C11×C22⋊C4—24no—
137C11×C22⋊C4—22no—
138C11×C22⋊C4—24no—
139C11×C22⋊C4—22no—
140C42×C11—24no—
141C42×C11—21no—
142C42×C11—21no—
143C22⋊Dic11—24no—
144C22⋊Dic11—42no—
145C4×Dic11—44no—
146#4318—44no—
147C2×C11⋊C8—42no—
148C2×#550D1111yescharacteristic
149#1789—112no—
150C4×#99—111no—
151#1507—112no—
152#1465—111no—
153C23×C11—21no—
154C23×C11—21no—
155C23×C11—21no—
156C23×C11—22no—
157C23×C11—22no—
158C23×C11—21no—
159C23×C11—21no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11—42no—
163C23×C11—42no—
164C23×C11—42no—
165C23×C11—42no—
166C23×C11—41no—
167C23×C11—41no—
168C23×C11—41no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11—41no—
172C23×C11C2×C22⋊C411yescharacteristic
173C23×C11#12012yes—
174Q8×C11—24no—
175Q8×C11—22no—
176Q8×C11#9914yescomplemented
177D4×C11—24no—
178D4×C11—44no—
179D4×C11—48no—
180D4×C11—42no—
181D4×C11—48no—
182D4×C11—48no—
183D4×C11—42no—
184D4×C11—42no—
185D4×C11—84no—
186D4×C11—84no—
187D4×C11—84no—
188C2×C4×C11—24no—
189C2×C4×C11—21no—
190C2×C4×C11—22no—
191C2×C4×C11—21no—
192C2×C4×C11—24no—
193C2×C4×C11—22no—
194C2×C4×C11—21no—
195C2×C4×C11—22no—
196C2×C4×C11—21no—
197C2×C4×C11—41no—
198C2×C4×C11—42no—
199C2×C4×C11—48no—
200C2×C4×C11—48no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11#10412yescomplemented
207C2×C4×C11C2×C22⋊C411yescharacteristic
208C2×C4×C11C2×C22⋊C411yescharacteristic
209C2×C4×C11#12012yes—
210C2×Dic11—44no—
211C2×Dic11—82no—
212C2×Dic11—82no—
213C11⋊C8—82no—
214C22×#41Dic1111yescharacteristic, complemented
215C22×#41C2×D1111yescharacteristic
216#550—24no—
217#550—24no—
218C2×#127—21no—
219C2×#127Dic1111yescharacteristic, complemented
220C2×#121—21no—
221C2×#121—21no—
222C2×#121Dic1111yescharacteristic, complemented
223C2×#121C2×D1111yescharacteristic
224C2×C4×Q8Dic1111yescharacteristic, complemented
225C2×C4×D4—21no—
226C2×C4×D4C2×D1111yescharacteristic
227C2×#104—224no—
228C2×#99—221no—
229#407—112no—
230C4×C22⋊C4—112no—
231#342—221no—
232#327—224no—
233#324—221no—
234#323—221no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—22no—
238C22×C11—22no—
239C22×C11—22no—
240C22×C11—41no—
241C22×C11—42no—
242C22×C11—42no—
243C22×C11—42no—
244C22×C11—41no—
245C22×C11—42no—
246C22×C11—41no—
247C22×C11—42no—
248C22×C11—42no—
249C22×C11—81no—
250C22×C11—81no—
251C22×C11—81no—
252C22×C11—81no—
253C22×C11—82no—
254C22×C11—82no—
255C22×C11—82no—
256C22×C11—82no—
257C22×C11#37911yescharacteristic
258C22×C11C2×#10411yescharacteristic
259C22×C11#42111yescharacteristic
260C4×C11—24no—
261C4×C11—22no—
262C4×C11—21no—
263C4×C11—22no—
264C4×C11—42no—
265C4×C11—41no—
266C4×C11—41no—
267C4×C11C2×#9912yes—
268Dic11—84no—
269C2×#41—22no—
270C2×#41—22no—
271C2×#41—22no—
272C2×#41—44no—
273C2×#41—44no—
274C2×#41C22⋊D1114yes—
275C22×Q8C2×Dic1111yescharacteristic
276C22×D4—21no—
277C22×D4—21no—
278C22×D4—21no—
279C22×D4—21no—
280C22×D4—21no—
281C22×D4—21no—
282C22×D4C2×Dic1111yescharacteristic
283C22×D4C2×Dic1111yescharacteristic
284C22×D4C22⋊D1111yescharacteristic
285C23×C4—21no—
286C23×C4—21no—
287C23×C4C2×Dic1111yescharacteristic
288C23×C4C22×D1111yescharacteristic
289C2×M16—222no—
290#127—28no—
291#127—22no—
292#127—22no—
293#121—28no—
294#121—28no—
295#121—22no—
296#121—22no—
297#121—22no—
298#121C22⋊D1114yes—
299C4×Q8—22no—
300C4×Q8—22no—
301C4×D4—28no—
302C4×D4—22no—
303C4×D4—22no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4C2×Dic1111yescharacteristic
306C2×C4⋊C4C22⋊D1111yescharacteristic
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—222no—
310C2×C22⋊C4C22⋊D1111yescharacteristic
311C2×C22⋊C4C22⋊D1111yescharacteristic
312C2×C42—21no—
313C2×C42—222no—
314C2×C42C2×Dic1111yescharacteristic
315#104—448no—
316#99—224no—
317C22⋊C8—222no—
318C22⋊C8—222no—
319#95—222no—
320C2×C11—21no—
321C2×C11—21no—
322C2×C11—42no—
323C2×C11—81no—
324C2×C11—82no—
325C2×C11—82no—
326C2×C11#178111yescharacteristic
327C2×C11#178911yescharacteristic
328C2×C11#179511yescharacteristic
329C24—21no—
330C24—21no—
331C24C22⋊Dic1111yescharacteristic
332C24C2×C22⋊D1111yescharacteristic
333#41—28no—
334#41—44no—
335#41—48no—
336#41—48no—
337#41—44no—
338#41—44no—
339C2×Q8—24no—
340C2×Q8—21no—
341C2×Q8C22⋊Dic1112yes—
342C2×D4—24no—
343C2×D4—24no—
344C2×D4—22no—
345C2×D4—24no—
346C2×D4—24no—
347C2×D4—24no—
348C2×D4—24no—
349C2×D4—22no—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4—42no—
353C2×D4—41no—
354C2×D4—44no—
355C2×D4—44no—
356C2×D4—42no—
357C2×D4—42no—
358C2×D4—42no—
359C2×D4—82no—
360C2×D4—82no—
361C2×D4—82no—
362C2×D4C22⋊Dic1112yes—
363C2×D4C22⋊Dic1112yes—
364C22×C4—21no—
365C22×C4—24no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—24no—
370C22×C4—42no—
371C22×C4—44no—
372C22×C4—44no—
373C22×C4—42no—
374C22×C4—442no—
375C22×C4C22⋊Dic1111yescharacteristic
376C22×C4C22⋊Dic1111yescharacteristic
377C22×C4C22⋊Dic1111yescharacteristic
378C22×C4C22×Dic1111yescharacteristic
379C22×C4C2×C22⋊D1112yes—
380C22×C4C2×C22⋊D1112yes—
381C22×C4C2×C22⋊D1111yescharacteristic
382M16—444no—
383C2×C8—442no—
384C4⋊C4—24no—
385C4⋊C4—21no—
386C4⋊C4—22no—
387C4⋊C4C22⋊Dic1112yes—
388C22⋊C4—24no—
389C22⋊C4—22no—
390C22⋊C4—24no—
391C22⋊C4—22no—
392C22⋊C4—224no—
393C22⋊C4—442no—
394C42—24no—
395C42—21no—
396C42—21no—
397C42—444no—
398C11#836111yescharacteristic, complemented, Sylow
399C23—21no—
400C23—21no—
401C23—21no—
402C23—22no—
403C23—22no—
404C23—21no—
405C23—21no—
406C23—41no—
407C23—41no—
408C23—42no—
409C23—42no—
410C23—42no—
411C23—42no—
412C23—41no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23—41no—
418C23C2×C22⋊Dic1111yescharacteristic
419C23#6700612yes—
420Q8—24no—
421Q8—22no—
422Q8#6689814yescomplemented
423D4—24no—
424D4—44no—
425D4—48no—
426D4—42no—
427D4—48no—
428D4—48no—
429D4—42no—
430D4—42no—
431D4—84no—
432D4—84no—
433D4—84no—
434C2×C4—24no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—22no—
438C2×C4—24no—
439C2×C4—22no—
440C2×C4—21no—
441C2×C4—22no—
442C2×C4—21no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—48no—
446C2×C4—48no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—444no—
453C2×C4—882no—
454C2×C4—882no—
455C2×C4#6690112yescomplemented
456C2×C4C2×C22⋊Dic1111yescharacteristic
457C2×C4C2×C22⋊Dic1111yescharacteristic
458C2×C4#6700612yes—
459C8—882no—
460C22—21no—
461C22—21no—
462C22—22no—
463C22—22no—
464C22—22no—
465C22—41no—
466C22—42no—
467C22—42no—
468C22—42no—
469C22—42no—
470C22—41no—
471C22—42no—
472C22—41no—
473C22—42no—
474C22—81no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22—82no—
479C22—82no—
480C22—82no—
481C22—82no—
482C22C2×#6690111yescharacteristic
483C22#1062284911yescharacteristic
484C22#1062286011yescharacteristic
485C4—22no—
486C4—22no—
487C4—24no—
488C4—21no—
489C4—42no—
490C4—41no—
491C4—41no—
492C4—884no—
493C4C2×#6689812yes—
494C2—21no—
495C2—21no—
496C2—42no—
497C2—82no—
498C2—82no—
499C2—81no—
500C2#1306853111yescharacteristic
501C2#1306856011yescharacteristic
502C2#1306858611yescharacteristic
subgroupG/H
centerC22#10622860
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
Fitting, prime radicalC2×C11×#550C2
socleC22×C11#379
cosocleC23×C4×C11C23
hypercenterC2×#550D11
hypocenterC11#8361
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. #13068560C2semidirect
2. C4×#66898C2semidirect
3. #13067132C2semidirect
4. #13066954C2semidirect
6. C22×C11×#41C4semidirect
11. C2×C11×#127C4semidirect
14. C2×C11×#121C4semidirect
16. C2×C4×Q8×C11C4semidirect
176. Q8×C11#99semidirect
206. C2×C4×C11#104semidirect
214. C22×#41Dic11semidirect
219. C2×#127Dic11semidirect
222. C2×#121Dic11semidirect
224. C2×C4×Q8Dic11semidirect
398. C11#8361semidirect
422. Q8#66898semidirect
455. C2×C4#66901semidirect

Maximal subgroups

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

subgroupindex
#130685602
C4×#668982
#130671322
#130669542
C2×C11×#5502
#836111