Finite Group Databasebeta

← #14649513

Subgroups — #14649513

Order 2816.

800 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076947C211yesmaximal, characteristic
2#13068684C211yesmaximal, characteristic, complemented
3C2×#10622089C212yesmaximal
4#13066495C212yesmaximal, complemented
5C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
6C22×C11×C4⋊C4—21no—
7C22×C42×C11—21no—
8C22×C42×C11C2211yescharacteristic
9C2×#66983C2211yescharacteristic
10C2×#66982—21no—
11C4×C11×C4⋊C4—24no—
12C2×C11×#95C2212yes—
13#10622826—21no—
14#10622825C2211yescharacteristic
15C2×C22⋊(C11⋊C8)C2212yes—
16#10622553—22no—
17#10622552C412yescomplemented
18#10622541C412yescomplemented
19#10622162—22no—
20#10622089—24no—
21C23×C4×C11—22no—
22C23×C4×C11D411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C23×C4×C11C2311yescharacteristic
25C22×C22⋊D11—21no—
26C22×D44C2×C411yescharacteristic
27C2×C11×C4⋊C4—28no—
28C2×C11×C4⋊C4—24no—
29C2×C42×C11—22no—
30C2×C42×C11—22no—
31C2×C42×C11—24no—
32C2×C42×C11—42no—
33C2×C42×C11—42no—
34C2×C42×C11C2×C412yes—
35C2×C42×C11D412yes—
36C2×C22⋊Dic11—21no—
37#66983—22no—
38#66983—22no—
39#66982—42no—
40#66982—42no—
41C2×(C2×D11)⋊C4—22no—
42C2×(C2×D11)⋊C4—22no—
43C2×(C2×D11)⋊C4—21no—
44C2×C4⋊Dic11C2×C411yescharacteristic
45C2×C4⋊Dic11C2×C412yes—
46C2×Dic11⋊C4—22no—
47C22×C11⋊C8—22no—
48C11×#95—22no—
49C11×#95D414yes—
50C11⋊#95—22no—
51C11⋊#95—21no—
52C22⋊(C11⋊C8)—22no—
53C22⋊(C11⋊C8)—22no—
54#9148—111nomaximal, Sylow
55C24×C11C2×D411yescharacteristic
56C23×D11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—24no—
64C22×C4×C11—28no—
65C22×C4×C11—24no—
66C22×C4×C11—42no—
67C22×C4×C11—44no—
68C22×C4×C11—42no—
69C22×C4×C11—42no—
70C22×C4×C11C22⋊C412yes—
71C22×C4×C11C22⋊C412yes—
72C22×C4×C11D812yes—
73C22×C4×C11SD1612yes—
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D412yes—
77C22×C4×C11#4112yes—
78C2×C22⋊D11—41no—
79C2×C22⋊D11—41no—
80C2×C22⋊D11—41no—
81C2×C22⋊D11—41no—
82C2×C22⋊D11—41no—
83C2×C22⋊D11—41no—
84C22×Dic11—21no—
85C22×Dic11—22no—
86C2×D44—22no—
87C2×D44—42no—
88C11×C4⋊C4—216no—
89C42×C11—24no—
90C42×C11—24no—
91C42×C11—48no—
92C22⋊Dic11—41no—
93C22⋊Dic11—41no—
94(C2×D11)⋊C4—44no—
95(C2×D11)⋊C4—44no—
96(C2×D11)⋊C4—42no—
97C4⋊Dic11—22no—
98C4⋊Dic11—42no—
99Dic11⋊C4—44no—
100C2×C11⋊C8—44no—
101C2×C11⋊C8—42no—
102#2854—111no—
103C2×C4×C4⋊C4D1111yescharacteristic, complemented
104#1817—111no—
105C2×#327—112no—
106#1294—112no—
107C23×C11—22no—
108C23×C11—22no—
109C23×C11C2×C22⋊C411yescharacteristic
110C23×C11#12011yescharacteristic
111C23×C11#12311yescharacteristic
112C23×C11C2×D811yescharacteristic
113C23×C11C2×SD1611yescharacteristic
114C23×C11AGL(1,ℤ/8)11yescharacteristic
115C23×C11#13711yescharacteristic
116C22×D11—41no—
117C22×D11—42no—
118C22×D11—41no—
119C22×D11—41no—
120C22×D11—42no—
121C2×C4×C11—24no—
122C2×C4×C11—24no—
123C2×C4×C11—22no—
124C2×C4×C11—22no—
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—22no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—28no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11—44no—
137C2×C4×C11—48no—
138C2×C4×C11—48no—
139C2×C4×C11—44no—
140C2×C4×C11#10214yes—
141C2×C4×C11#10414yes—
142C2×C4×C11C4×D412yes—
143C2×C4×C11#12112yes—
144C22⋊D11—81no—
145C22⋊D11—81no—
146C22⋊D11—81no—
147C22⋊D11—81no—
148C2×Dic11—41no—
149C2×Dic11—42no—
150C2×Dic11—41no—
151C2×Dic11—42no—
152C2×Dic11—41no—
153C2×Dic11—42no—
154D44—82no—
155C11⋊C8—82no—
156C2×#123—221no—
157C2×#121—111no—
158C22×C4⋊C4—21no—
159C22×C42—21no—
160C22×C42C2×D1111yescharacteristic
161C2×C22⋊C8—112no—
162#390—112no—
163#389—112no—
164#388—222no—
165#386—221no—
166#380—111no—
167C4×C4⋊C4—24no—
168C2×#95C2×D1112yes—
169#336—222no—
170#327—224no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—22no—
176C22×C11—22no—
177C22×C11—22no—
178C22×C11—22no—
179C22×C11#38611yescharacteristic
180C22×C11#41012yes—
181C22×C11C2×#10211yescharacteristic
182C22×C11#41711yescharacteristic
183C22×C11C2×#10412yes—
184C22×C11#44711yescharacteristic
185C22×C11#44811yescharacteristic
186C22×C11#48011yescharacteristic
187C22×C11#48111yescharacteristic
188C2×D11—81no—
189C2×D11—81no—
190C2×D11—81no—
191C2×D11—82no—
192C2×D11—82no—
193C4×C11—24no—
194C4×C11—24no—
195C4×C11—22no—
196C4×C11—22no—
197C4×C11—48no—
198Dic11—81no—
199Dic11—82no—
200C22×D4—111no—
201C22×D4—221no—
202C23×C4—22no—
203C23×C4C22⋊D1111yescharacteristic
204C23×C4C22⋊D1111yescharacteristic
205C23×C4C22×D1111yescharacteristic
206C22×C8—222no—
207#123—442no—
208#123—442no—
209#121—222no—
210#121—222no—
211C2×C4⋊C4—24no—
212C2×C4⋊C4—28no—
213C2×C4⋊C4—111no—
214C2×C4⋊C4—112no—
215C2×C4⋊C4—222no—
216C2×C22⋊C4—221no—
217C2×C22⋊C4—222no—
218C2×C22⋊C4—222no—
219C2×C22⋊C4—221no—
220C2×C42—22no—
221C2×C42—22no—
222C2×C42—24no—
223C2×C42—42no—
224C2×C42—42no—
225C2×C42C4×D1112yes—
226C2×C42D4412yes—
227C22⋊C8—222no—
228C22⋊C8—222no—
229#95—22no—
230#95—222no—
231#95—221no—
232#95C22⋊D1114yes—
233C2×C11—21no—
234C2×C11—21no—
235C2×C11—21no—
236C2×C11—21no—
237C2×C11#150212yes—
238C2×C11#150912yes—
239C2×C11#187411yescharacteristic
240C2×C11#189611yescharacteristic
241C2×C11#189911yescharacteristic
242D11—161no—
243C24—221no—
244C24C2×C22⋊D1111yescharacteristic
245C2×D4—222no—
246C2×D4—442no—
247C2×D4—441no—
248C2×D4—441no—
249C2×D4—441no—
250C2×D4—441no—
251C2×D4—441no—
252C2×D4—441no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—24no—
260C22×C4—28no—
261C22×C4—24no—
262C22×C4—42no—
263C22×C4—44no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4—222no—
267C22×C4—221no—
268C22×C4(C2×D11)⋊C412yes—
269C22×C4(C2×D11)⋊C412yes—
270C22×C4#432312yes—
271C22×C4#432512yes—
272C22×C4C2×C4×D1111yescharacteristic
273C22×C4C2×D4411yescharacteristic
274C22×C4#433912yes—
275C22×C4C2×C22⋊D1112yes—
276C2×C8—444no—
277C2×C8—442no—
278C4⋊C4—216no—
279C4⋊C4—222no—
280C4⋊C4—442no—
281C4⋊C4—444no—
282C22⋊C4—441no—
283C22⋊C4—441no—
284C22⋊C4—444no—
285C22⋊C4—444no—
286C22⋊C4—442no—
287C42—24no—
288C42—24no—
289C42—48no—
290C11#914811yescharacteristic, complemented, Sylow
291C23—22no—
292C23—22no—
293C23—442no—
294C23—441no—
295C23—441no—
296C23—441no—
297C23—442no—
298C23C2×(C2×D11)⋊C411yescharacteristic
299C23#6698211yescharacteristic
300C23C2×#432311yescharacteristic
301C23#6698511yescharacteristic
302C23C2×#432511yescharacteristic
303C23#6699511yescharacteristic
304C23#6700611yescharacteristic
305D4—882no—
306D4—881no—
307D4—881no—
308D4—881no—
309D4—881no—
310C2×C4—24no—
311C2×C4—24no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—28no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—44no—
326C2×C4—48no—
327C2×C4—48no—
328C2×C4—44no—
329C2×C4—442no—
330C2×C4—441no—
331C2×C4—442no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4—442no—
335C2×C4#6686914yes—
336C2×C4#6687314yes—
337C2×C4C4×C22⋊D1112yes—
338C2×C4#6698312yes—
339C8—882no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—22no—
345C22—22no—
346C22—22no—
347C22—22no—
348C22—881no—
349C22—881no—
350C22—882no—
351C22—882no—
352C22—881no—
353C22C2×#6686912yes—
354C22C2×#6687311yescharacteristic
355C22#1062257911yescharacteristic
356C22#1062258011yescharacteristic
357C22#1062258111yescharacteristic
358C22#1062261912yes—
359C22#1062282611yescharacteristic
360C22#1062283011yescharacteristic
361C22#1062284011yescharacteristic
362C4—24no—
363C4—22no—
364C4—22no—
365C4—24no—
366C4—48no—
367C4—882no—
368C4—881no—
369C2—21no—
370C2—21no—
371C2—21no—
372C2—21no—
373C2—1761no—
374C2#1306711012yes—
375C2#1306713912yes—
376C2#1306893311yescharacteristic
377C2#1306905911yescharacteristic
378C2#1306907411yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C4×C11×C4⋊C4C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenterC2×C4×C4⋊C4D11
hypocenterC11#9148
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13068684C2semidirect
4. #13066495C2semidirect
5. C2×C4×C11×C4⋊C4C2semidirect
17. #10622552C4semidirect
18. #10622541C4semidirect
103. C2×C4×C4⋊C4D11semidirect
290. C11#9148semidirect

Maximal subgroups

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

subgroupindex
#130769472
#130686842
C2×#106220892
#130664952
C2×C4×C11×C4⋊C42
#914811