Finite Group Databasebeta

← #14649486

Subgroups — #14649486

Order 2816.

1270 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076903C211yesmaximal, characteristic
2C22×C11⋊#95C211yesmaximal, characteristic
3C2×#10622105C212yesmaximal, complemented
4#13066496C212yesmaximal, complemented
5C11×#1779C211yesmaximal, characteristic
6C24×C4×C11C2211yescharacteristic
7C24×Dic11—21no—
8C2×#66977C412yescomplemented
9C2×#66977C2211yescharacteristic
10C2×C11×C22⋊C8—22no—
11C2×C11×C22⋊C8C2212yes—
12#10622860—21no—
13#10622825C412yescomplemented
14#10622825C2211yescharacteristic
15#10622823—21no—
16#10622823—22no—
17C2×C11⋊#95—21no—
18C2×C11⋊#95—24no—
19C2×C11⋊#95C2212yes—
20#10622105—24no—
21C25×C11D411yescharacteristic
22C23×C4×C11—22no—
23C23×C4×C11—22no—
24C23×C4×C11—44no—
25C23×C4×C11C2×C412yes—
26C23×C4×C11D411yescharacteristic
27C23×C4×C11D412yes—
28C23×C4×C11C2311yescharacteristic
29C23×Dic11—24no—
30C23×Dic11—28no—
31C23×Dic11—22no—
32C23×Dic11—44no—
33C23×Dic11—42no—
34C23×Dic11—42no—
35C22×Dic22C2×C411yescharacteristic, complemented
36C22×C8×C11—22no—
37C2×C22⋊Dic11—22no—
38C2×C22⋊Dic11—22no—
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11—21no—
41C2×C4⋊Dic11C2×C411yescharacteristic, complemented
42C2×C4⋊Dic11C2×C412yescomplemented
43#66977—22no—
44#66977—22no—
45#66977—44no—
46C2×Dic11⋊C4—22no—
47C2×Dic11⋊C4—21no—
48C11×C22⋊C8—22no—
49C11×C22⋊C8—22no—
50C11×C22⋊C8—44no—
51C11⋊#95—24no—
52C11⋊#95—22no—
53C11⋊#95—22no—
54C11⋊#95—21no—
55C11⋊#95D414yes—
56#9143—111nomaximal, Sylow
57C24×C11—24no—
58C24×C11—24no—
59C24×C11—21no—
60C24×C11—21no—
61C24×C11—21no—
62C24×C11—21no—
63C24×C11C22⋊C412yes—
64C24×C11SD1612yes—
65C24×C11Q1612yes—
66C24×C11C2×D411yescharacteristic
67C22×C4×C11—24no—
68C22×C4×C11—24no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—24no—
72C22×C4×C11—24no—
73C22×C4×C11—42no—
74C22×C4×C11—42no—
75C22×C4×C11—42no—
76C22×C4×C11—42no—
77C22×C4×C11—48no—
78C22×C4×C11—48no—
79C22×C4×C11C22⋊C412yes—
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D412yes—
83C22×C4×C11#4112yes—
84C22×Dic11—216no—
85C22×Dic11—28no—
86C22×Dic11—21no—
87C22×Dic11—22no—
88C22×Dic11—21no—
89C22×Dic11—24no—
90C22×Dic11—48no—
91C22×Dic11—416no—
92C22×Dic11—416no—
93C22×Dic11—44no—
94C22×Dic11—48no—
95C22×Dic11—42no—
96C22×Dic11—42no—
97C2×Dic22—22no—
98C2×Dic22—42no—
99C2×C8×C11—44no—
100C2×C8×C11—42no—
101C22⋊Dic11—44no—
102C22⋊Dic11—44no—
103C22⋊Dic11—41no—
104C22⋊Dic11—41no—
105C22⋊Dic11—41no—
106C22⋊Dic11—41no—
107C4⋊Dic11—22no—
108C4⋊Dic11—42no—
109Dic11⋊C4—44no—
110Dic11⋊C4—42no—
111#2848—111no—
112C22×#95—111no—
113#1779D1111yescharacteristic
114C2×#328—112no—
115#1294—112no—
116C23×C11—24no—
117C23×C11—24no—
118C23×C11—28no—
119C23×C11—24no—
120C23×C11—24no—
121C23×C11—28no—
122C23×C11—28no—
123C23×C11—28no—
124C23×C11—22no—
125C23×C11—22no—
126C23×C11—22no—
127C23×C11—22no—
128C23×C11—22no—
129C23×C11—22no—
130C23×C11—22no—
131C23×C11—22no—
132C23×C11—22no—
133C23×C11—22no—
134C23×C11#9914yes—
135C23×C11#10314yes—
136C23×C11#10414yes—
137C23×C11C2×C22⋊C411yescharacteristic
138C23×C11#12011yescharacteristic
139C23×C11#12311yescharacteristic
140C23×C11C2×SD1611yescharacteristic
141C23×C11C2×Q1611yescharacteristic
142C23×C11AGL(1,ℤ/8)11yescharacteristic
143C23×C11#13711yescharacteristic
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—22no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—48no—
152C2×C4×C11—48no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11C4×D412yes—
156C2×C4×C11#12112yes—
157C2×Dic11—28no—
158C2×Dic11—432no—
159C2×Dic11—44no—
160C2×Dic11—48no—
161C2×Dic11—48no—
162C2×Dic11—44no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—42no—
166C2×Dic11—42no—
167C2×Dic11—42no—
168C2×Dic11—42no—
169C2×Dic11—42no—
170Dic22—82no—
171C8×C11—82no—
172C24×C4—221no—
173C24×C4C2×D1111yescharacteristic
174C2×C22⋊Q8—111no—
175C2×C22⋊Q8—112no—
176C2×C22⋊C8—22no—
177C2×C22⋊C8C2×D1112yes—
178#385—221no—
179#385—222no—
180#380—111no—
181#380—112no—
182#379—221no—
183C2×#95—112no—
184C2×#95—224no—
185C2×#95—221no—
186#328—224no—
187C22×C11—28no—
188C22×C11—28no—
189C22×C11—28no—
190C22×C11—28no—
191C22×C11—24no—
192C22×C11—24no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—24no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—24no—
199C22×C11—22no—
200C22×C11—22no—
201C22×C11—24no—
202C22×C11—24no—
203C22×C11—22no—
204C22×C11—22no—
205C22×C11#32818yescomplemented
206C22×C11#38611yescharacteristic
207C22×C11C2×#9912yes—
208C22×C11C2×#10311yescharacteristic
209C22×C11#41711yescharacteristic
210C22×C11C2×#10412yes—
211C22×C11#45011yescharacteristic
212C22×C11#45111yescharacteristic
213C22×C11#48311yescharacteristic
214C22×C11#48411yescharacteristic
215C4×C11—22no—
216C4×C11—22no—
217C4×C11—42no—
218Dic11—48no—
219Dic11—81no—
220Dic11—81no—
221Dic11—82no—
222C25D4411yescharacteristic
223C22×Q8—111no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—44no—
227C23×C4—224no—
228C23×C4—228no—
229C23×C4—222no—
230C23×C4—444no—
231C23×C4—442no—
232C23×C4—442no—
233C23×C4C4×D1112yes—
234C23×C4D4411yescharacteristic
235C23×C4C22⋊D1112yes—
236C23×C4C22×D1111yescharacteristic
237C22×C8—22no—
238C22⋊Q8—222no—
239C22⋊Q8—222no—
240C22⋊Q8—444no—
241C2×C4⋊C4—111no—
242C2×C4⋊C4—112no—
243C2×C4⋊C4—222no—
244C2×C4⋊C4—221no—
245C2×C22⋊C4—222no—
246C2×C22⋊C4—222no—
247C2×C22⋊C4—221no—
248C2×C22⋊C4—221no—
249C22⋊C8—22no—
250C22⋊C8—22no—
251C22⋊C8—44no—
252#95—114no—
253#95—224no—
254#95—222no—
255#95—222no—
256#95—221no—
257C2×C11—21no—
258C2×C11—28no—
259C2×C11—21no—
260C2×C11—21no—
261C2×C11—21no—
262C2×C11C2×#32812yes—
263C2×C11#150412yes—
264C2×C11#187211yescharacteristic
265C2×C11#189611yescharacteristic
266C2×C11#189811yescharacteristic
267C24—24no—
268C24—24no—
269C24—21no—
270C24—21no—
271C24—21no—
272C24—21no—
273C24#431412yes—
274C24Dic4412yes—
275C24(C2×D11)⋊C412yes—
276C24C2×D4411yescharacteristic
277C2×Q8—222no—
278C2×Q8—442no—
279C22×C4—24no—
280C22×C4—24no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—24no—
284C22×C4—24no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—48no—
290C22×C4—48no—
291C22×C4—2216no—
292C22×C4—228no—
293C22×C4—224no—
294C22×C4—222no—
295C22×C4—221no—
296C22×C4—221no—
297C22×C4—448no—
298C22×C4—4416no—
299C22×C4—444no—
300C22×C4—4416no—
301C22×C4—448no—
302C22×C4—442no—
303C22×C4—442no—
304C22×C4(C2×D11)⋊C412yes—
305C22×C4C2×C4×D1111yescharacteristic
306C22×C4D4×D1112yes—
307C22×C4#434112yes—
308C22×C4C2×C22⋊D1111yescharacteristic
309C2×C8—44no—
310C2×C8—42no—
311C4⋊C4—222no—
312C4⋊C4—442no—
313C4⋊C4—444no—
314C4⋊C4—442no—
315C22⋊C4—444no—
316C22⋊C4—444no—
317C22⋊C4—441no—
318C22⋊C4—441no—
319C22⋊C4—441no—
320C22⋊C4—441no—
321C11#914311yescharacteristic, complemented, Sylow
322C23—24no—
323C23—24no—
324C23—24no—
325C23—28no—
326C23—24no—
327C23—28no—
328C23—22no—
329C23—22no—
330C23—22no—
331C23—22no—
332C23—22no—
333C23—22no—
334C23—22no—
335C23—22no—
336C23—22no—
337C23—22no—
338C23—28no—
339C23—28no—
340C23#6687014yes—
341C23#6688014yes—
342C23#6688914yes—
343C23#6693511yescharacteristic
344C23#6693911yescharacteristic
345C23C2×#431411yescharacteristic
346C23C2×Dic4411yescharacteristic
347C23#6696111yescharacteristic
348C23#6696211yescharacteristic
349C23C2×(C2×D11)⋊C411yescharacteristic
350Q8—882no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—48no—
359C2×C4—48no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—228no—
363C2×C4—4432no—
364C2×C4—444no—
365C2×C4—448no—
366C2×C4—448no—
367C2×C4—444no—
368C2×C4—442no—
369C2×C4—442no—
370C2×C4—442no—
371C2×C4—442no—
372C2×C4—442no—
373C2×C4—441no—
374C2×C4—441no—
375C2×C4(C22⋊D11)⋊C412yes—
376C2×C4#6699212yes—
377C8—82no—
378C22—28no—
379C22—28no—
380C22—28no—
381C22—28no—
382C22—21no—
383C22—24no—
384C22—21no—
385C22—21no—
386C22—24no—
387C22—21no—
388C22—22no—
389C22—24no—
390C22—22no—
391C22—22no—
392C22—24no—
393C22—24no—
394C22—22no—
395C22—24no—
396C22#1062210518yescomplemented
397C22#1062233411yescharacteristic
398C22#1062233511yescharacteristic
399C22#1062234411yescharacteristic
400C22#1062235211yescharacteristic
401C22C2×#6687012yes—
402C22#1062257111yescharacteristic
403C22C2×#6688011yescharacteristic
404C22#1062274611yescharacteristic
405C22C2×#6688912yes—
406C4—22no—
407C4—22no—
408C4—42no—
409C4—448no—
410C4—881no—
411C4—881no—
412C4—882no—
413C2—21no—
414C2—21no—
415C2—21no—
416C2—21no—
417C2—28no—
418C2C2×#1062210512yes—
419C2#1306712112yes—
420C2#1306892111yescharacteristic
421C2#1306905711yescharacteristic
422C2#1306906711yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1779C2
socleC23×C11C2×C22⋊C4
prime radicalC25×C11D4
cosocleC23×C4×C11C23
hypercenter#1779D11
hypocenterC11#9143
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
3. C2×#10622105C2semidirect
4. #13066496C2semidirect
8. C2×#66977C4semidirect
13. #10622825C4semidirect
35. C22×Dic22C2×C4semidirect
41. C2×C4⋊Dic11C2×C4semidirect
42. C2×C4⋊Dic11C2×C4semidirect
205. C22×C11#328semidirect
321. C11#9143semidirect
396. C22#10622105semidirect

Maximal subgroups

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

subgroupindex
#130769032
C22×C11⋊#952
C2×#106221052
#130664962
C11×#17792
#914311