Finite Group Databasebeta

← #14727751

Subgroups — #14727751

Order 2816.

1192 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079538C212yesmaximal, complemented
2#13074437C211yesmaximal, characteristic, complemented
3#13067585C214yesmaximal, complemented
4#13067568C214yesmaximal, complemented
5#13067176C212yesmaximal, complemented
6#13066930C211yesmaximal, characteristic, complemented
7C11×#3449C211yesmaximal, characteristic
8C22×C11×#41—21no—
9C11×#537—21no—
10C11×#537C2212yes—
11C11×#536—22no—
12C11×#535—22no—
13C11×#534—21no—
14C11×#534C2212yes—
15C11×#532—21no—
16C11×#532C2212yes—
17C11×#525—24no—
18C2×C11×#117C2211yescharacteristic
19C2×#66922C2211yescharacteristic, complemented
20#10622825—21no—
21#10622706—22no—
22#10622689—22no—
23#10622653C2218yescomplemented
24#10622632—24no—
25#10622599—21no—
26#10622592C2212yescomplemented
27#10622562—21no—
28#10622560C2212yes—
29#10622549C2211yescharacteristic, complemented
30#10622541—21no—
31#10622538C2212yescomplemented
32#10622175C2218yescomplemented
33#10622166C2212yescomplemented
34#10622163C2212yes—
35C2×C11×#41—22no—
36C2×C11×#41—22no—
37C2×C11×#41—22no—
38C2×C11×#41—22no—
39C2×C11×#41—44no—
40C2×C11×#41—44no—
41C22×Q8×C11—21no—
42C22×D4×C11—21no—
43C22×D4×C11—22no—
44C23×C4×C11—22no—
45C23×C4×C11D411yescharacteristic
46C22×Dic22C2312yes—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8D412yes—
49C11×#127—21no—
50C11×#127D412yes—
51C11×#124—22no—
52C11×#124—22no—
53C11×#123—24no—
54C11×#123—24no—
55C11×C22⋊Q8—24no—
56C11×C22⋊Q8—24no—
57C11×#121—24no—
58C11×#121—24no—
59C11×#121—22no—
60C11×#121—22no—
61C11×#121—22no—
62C11×#121C2314yes—
63C11×#120—24no—
64C11×#120—24no—
65C4×D4×C11—22no—
66C4×D4×C11—22no—
67C4×D4×C11—22no—
68C4×D4×C11D414yes—
69C11×#117—22no—
70C11×#117—22no—
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4D411yescharacteristic
74C2×C11×C22⋊C4C2311yescharacteristic
75C2×C42×C11D411yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11—22no—
78C2×#4324—28no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×Dic11⋊C4—22no—
83#66922—22no—
84#66922—22no—
85C11⋊#95—22no—
86C11⋊#95—21no—
87C11⋊#95—22no—
88C11⋊#95C2312yes—
89C22⋊(C11⋊C8)C2314yes—
90#66874—28no—
91C4⋊(C11⋊C8)—22no—
92C4×C11⋊C8—22no—
93#18301—111nomaximal, Sylow
94C24×C11—22no—
95C24×C11C2×D411yescharacteristic
96C11×#41—44no—
97C11×#41—48no—
98C11×#41—48no—
99C11×#41—44no—
100C11×#41—44no—
101C11×#41—44no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11—44no—
105C2×D4×C11—24no—
106C2×D4×C11—22no—
107C2×D4×C11—24no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—44no—
113C2×D4×C11—44no—
114C2×D4×C11—44no—
115C2×D4×C11C2×D414yes—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—24no—
120C22×C4×C11—22no—
121C22×C4×C11—24no—
122C22×C4×C11—48no—
123C22×C4×C11SD1614yescomplemented
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2411yescharacteristic
130C22×Dic11—22no—
131C22×Dic11—22no—
132C2×Dic22—24no—
133C2×Dic22—82no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4C2×D414yes—
140C11×C22⋊C4—24no—
141C11×C22⋊C4—24no—
142C11×C22⋊C4—22no—
143C11×C22⋊C4—24no—
144C11×C22⋊C4—22no—
145C11×C22⋊C4—24no—
146C42×C11—21no—
147C42×C11—21no—
148C42×C11C2×D412yes—
149C42×C11C2×D412yes—
150C22⋊Dic11—82no—
151#4324—88no—
152C4⋊Dic11—42no—
153C4⋊Dic11—41no—
154C4⋊Dic11—41no—
155C4⋊Dic11—42no—
156Dic11⋊C4—82no—
157C2×C11⋊C8—24no—
158#3449D1111yescharacteristic
159#3206—112no—
160#2628—111no—
161#1604—114no—
162#1601—114no—
163#1517—112no—
164#1458—111no—
165C23×C11—21no—
166C23×C11—21no—
167C23×C11—24no—
168C23×C11—41no—
169C23×C11—41no—
170C23×C11—44no—
171C23×C11—82no—
172C23×C11—82no—
173C23×C11C2×SD1612yes—
174C23×C11C22×D411yescharacteristic
175Q8×C11—44no—
176Q8×C11—44no—
177D4×C11—44no—
178D4×C11—44no—
179D4×C11—48no—
180D4×C11—44no—
181D4×C11—44no—
182D4×C11—44no—
183D4×C11—82no—
184D4×C11—82no—
185D4×C11—82no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—24no—
189C2×C4×C11—24no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—24no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—48no—
196C2×C4×C11—44no—
197C2×C4×C11—48no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11#12012yes—
201C2×C4×C11#12011yescharacteristic
202C2×C4×C11#12011yescharacteristic
203C2×C4×C11C2×SD1612yes—
204C2×C4×C11C2×SD1612yes—
205C2×C4×C11AGL(1,ℤ/8)12yes—
206C2×C4×C11C22×D412yes—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213Dic22—48no—
214C11⋊C8—44no—
215C22×#41—21no—
216#537—21no—
217#537C2×D1112yes—
218#536—22no—
219#535—22no—
220#534—21no—
221#534C2×D1112yes—
222#532—21no—
223#532C2×D1112yes—
224C2×C4⋊Q8—111no—
225#525—24no—
226C2×#117C2×D1111yescharacteristic
227#492—222no—
228#487—222no—
229#461—224no—
230#448—118no—
231#431—112no—
232#400—221no—
233#399—221no—
234#395—112no—
235#393—112no—
236#389—221no—
237#382—111no—
238#380—221no—
239#327—118no—
240#324—112no—
241#323—112no—
242C22×C11—21no—
243C22×C11—21no—
244C22×C11—22no—
245C22×C11—42no—
246C22×C11—41no—
247C22×C11—41no—
248C22×C11—44no—
249C22×C11—44no—
250C22×C11—44no—
251C22×C11—81no—
252C22×C11—88no—
253C22×C11C2×#12011yescharacteristic
254C22×C11C22×SD1611yescharacteristic
255C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
256C4×C11—22no—
257C4×C11—22no—
258C4×C11—22no—
259C4×C11—44no—
260C4×C11—41no—
261C4×C11—41no—
262C4×C11#45012yes—
263C4×C11#45012yes—
264Dic11—82no—
265Dic11—82no—
266C2×#41—22no—
267C2×#41—22no—
268C2×#41—22no—
269C2×#41—22no—
270C2×#41—44no—
271C2×#41—44no—
272C22×Q8—21no—
273C22×Q8—112no—
274C22×D4—21no—
275C22×D4—22no—
276C23×C4—22no—
277C23×C4C22⋊D1111yescharacteristic
278C2×SD16—228no—
279C4⋊Q8—21no—
280C4⋊Q8—222no—
281C4⋊Q8—222no—
282C4⋊Q8C22⋊D1112yes—
283#127—21no—
284#127C22⋊D1112yes—
285#124—22no—
286#124—22no—
287#123—24no—
288#123—24no—
289C22⋊Q8—24no—
290C22⋊Q8—24no—
291#121—24no—
292#121—24no—
293#121—22no—
294#121—22no—
295#121—22no—
296#121C22×D1114yes—
297#120—24no—
298#120—24no—
299C4×D4—22no—
300C4×D4—22no—
301C4×D4—22no—
302C4×D4C22⋊D1114yes—
303#117—22no—
304#117—22no—
305C2×C4⋊C4—221no—
306C2×C4⋊C4—221no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4—222no—
309C2×C4⋊C4C22⋊D1111yescharacteristic
310C2×C4⋊C4C22×D1111yescharacteristic
311C2×C22⋊C4—222no—
312C2×C22⋊C4C22⋊D1111yescharacteristic
313C2×C22⋊C4C22×D1111yescharacteristic
314C2×C42C22⋊D1111yescharacteristic
315C2×C42C22×D1111yescharacteristic
316C4⋊C8—222no—
317#103—228no—
318C22⋊C8—114no—
319C4×C8—222no—
320#95—112no—
321#95—222no—
322#95—221no—
323#95—222no—
324C2×C11—21no—
325C2×C11—21no—
326C2×C11—42no—
327C2×C11—84no—
328C2×C11C2×#45011yescharacteristic
329C2×C11#302211yescharacteristic
330C2×C11#302711yescharacteristic
331C24—22no—
332C24C2×C22⋊D1111yescharacteristic
333#41—44no—
334#41—48no—
335#41—48no—
336#41—44no—
337#41—44no—
338#41—44no—
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8—44no—
342C2×Q8—224no—
343C2×Q8—882no—
344C2×D4—24no—
345C2×D4—22no—
346C2×D4—24no—
347C2×D4—22no—
348C2×D4—22no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—44no—
352C2×D4—44no—
353C2×D4—44no—
354C2×D4C2×C22⋊D1114yes—
355C22×C4—22no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—24no—
359C22×C4—22no—
360C22×C4—24no—
361C22×C4—48no—
362C22×C4—222no—
363C22×C4—222no—
364C22×C4#432414yescomplemented
365C22×C4C2×C22⋊D1111yescharacteristic
366C22×C4C2×C22⋊D1111yescharacteristic
367C22×C4C2×C22⋊D1111yescharacteristic
368C22×C4C2×C22⋊D1111yescharacteristic
369C22×C4C2×C22⋊D1111yescharacteristic
370C22×C4C23×D1111yescharacteristic
371SD16—888no—
372C2×C8—224no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—442no—
379C4⋊C4—442no—
380C4⋊C4—441no—
381C4⋊C4—441no—
382C4⋊C4—882no—
383C4⋊C4C2×C22⋊D1114yes—
384C22⋊C4—24no—
385C22⋊C4—24no—
386C22⋊C4—22no—
387C22⋊C4—24no—
388C22⋊C4—22no—
389C22⋊C4—24no—
390C22⋊C4—882no—
391C42—21no—
392C42—21no—
393C42C2×C22⋊D1112yes—
394C42C2×C22⋊D1112yes—
395C11#1830111yescharacteristic, complemented, Sylow
396C23—21no—
397C23—21no—
398C23—24no—
399C23—41no—
400C23—41no—
401C23—44no—
402C23—82no—
403C23—82no—
404C23C2×#432412yes—
405C23C22×C22⋊D1111yescharacteristic
406Q8—44no—
407Q8—44no—
408Q8—448no—
409D4—44no—
410D4—44no—
411D4—48no—
412D4—44no—
413D4—44no—
414D4—44no—
415D4—82no—
416D4—82no—
417D4—82no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—24no—
421C2×C4—24no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—24no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—48no—
428C2×C4—44no—
429C2×C4—48no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—442no—
433C2×C4—442no—
434C2×C4—442no—
435C2×C4—442no—
436C2×C4—442no—
437C2×C4—442no—
438C2×C4#6698512yes—
439C2×C4C2×#432412yes—
440C2×C4C2×#432412yes—
441C2×C4#6700612yes—
442C2×C4#6700611yescharacteristic
443C2×C4#6700611yescharacteristic
444C2×C4C22×C22⋊D1112yes—
445C8—444no—
446C22—21no—
447C22—21no—
448C22—22no—
449C22—42no—
450C22—41no—
451C22—41no—
452C22—44no—
453C22—44no—
454C22—44no—
455C22—81no—
456C22—88no—
457C22C2×#6698511yescharacteristic
458C22C22×#432411yescharacteristic
459C22C2×#6700611yescharacteristic
460C4—22no—
461C4—22no—
462C4—22no—
463C4—41no—
464C4—44no—
465C4—41no—
466C4—882no—
467C4—882no—
468C4#1062283112yes—
469C4#1062283112yes—
470C2—21no—
471C2—21no—
472C2—42no—
473C2—84no—
474C2C2×#1062283111yescharacteristic
475C2#1307799511yescharacteristic
476C2#1307801811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3449C2
socleC22×C11C2×#120
hypercenter#3449D11
hypocenterC11#18301
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. #13079538C2semidirect
2. #13074437C2semidirect
3. #13067585C2semidirect
4. #13067568C2semidirect
5. #13067176C2semidirect
6. #13066930C2semidirect
19. C2×#66922C22semidirect
23. #10622653C22semidirect
26. #10622592C22semidirect
29. #10622549C22semidirect
31. #10622538C22semidirect
32. #10622175C22semidirect
33. #10622166C22semidirect
123. C22×C4×C11SD16semidirect
364. C22×C4#4324semidirect
395. C11#18301semidirect

Maximal subgroups

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

subgroupindex
#130795382
#130744372
#130675852
#130675682
#130671762
#130669302
C11×#34492
#1830111