Finite Group Databasebeta

← #14649493

Subgroups — #14649493

Order 2816.

738 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076955C211yesmaximal, characteristic
2#13068684C211yesmaximal, characteristic
3C2×#10622090C212yesmaximal
4#13066495C212yesmaximal
5C2×C4×C11×C4⋊C4C211yesmaximal, characteristic
6C22×C11×C4⋊C4—21no—
7C22×C42×C11—21no—
8C22×C42×C11C2211yescharacteristic
9C2×#66977C2211yescharacteristic
10C4×C11×C4⋊C4—24no—
11C2×C11×#95C2212yes—
12#10622825C2211yescharacteristic
13#10622824—21no—
14#10622823—21no—
15C2×C22⋊(C11⋊C8)C2212yes—
16#10622546—22no—
17#10622542C412yescomplemented
18#10622541C412yescomplemented
19#10622162—22no—
20#10622090—24no—
21C23×C4×C11—22no—
22C23×C4×C11D411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C23×C4×C11C2311yescharacteristic
25C22×Dic22C2×C411yescharacteristic
26C2×C11×C4⋊C4—28no—
27C2×C11×C4⋊C4—24no—
28C2×C42×C11—22no—
29C2×C42×C11—22no—
30C2×C42×C11—24no—
31C2×C42×C11—42no—
32C2×C42×C11—42no—
33C2×C42×C11C2×C412yes—
34C2×C42×C11D412yes—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×C4⋊Dic11C2×C411yescharacteristic
38C2×C4⋊Dic11C2×C412yes—
39#66977—22no—
40#66977—22no—
41C2×Dic11⋊C4—22no—
42C2×Dic11⋊C4—21no—
43C22×C11⋊C8—22no—
44C11×#95—22no—
45C11×#95D414yes—
46C11⋊#95—22no—
47C11⋊#95—22no—
48C11⋊#95—22no—
49C11⋊#95—21no—
50C22⋊(C11⋊C8)—22no—
51C22⋊(C11⋊C8)—22no—
52#9144—111nomaximal, Sylow
53C24×C11C2×D411yescharacteristic
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—24no—
61C22×C4×C11—28no—
62C22×C4×C11—24no—
63C22×C4×C11—42no—
64C22×C4×C11—44no—
65C22×C4×C11—42no—
66C22×C4×C11—42no—
67C22×C4×C11C22⋊C412yes—
68C22×C4×C11C22⋊C412yes—
69C22×C4×C11SD1612yes—
70C22×C4×C11Q1612yes—
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D412yes—
74C22×C4×C11#4112yes—
75C22×Dic11—22no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C2×Dic22—22no—
79C2×Dic22—42no—
80C11×C4⋊C4—216no—
81C42×C11—24no—
82C42×C11—24no—
83C42×C11—48no—
84C22⋊Dic11—41no—
85C22⋊Dic11—41no—
86C22⋊Dic11—41no—
87C22⋊Dic11—41no—
88C4⋊Dic11—22no—
89C4⋊Dic11—42no—
90Dic11⋊C4—44no—
91Dic11⋊C4—42no—
92C2×C11⋊C8—44no—
93C2×C11⋊C8—42no—
94#2855—111no—
95C2×C4×C4⋊C4D1111yescharacteristic
96#1817—111no—
97C2×#328—112no—
98#1294—112no—
99C23×C11—22no—
100C23×C11—22no—
101C23×C11C2×C22⋊C411yescharacteristic
102C23×C11#12011yescharacteristic
103C23×C11#12311yescharacteristic
104C23×C11C2×SD1611yescharacteristic
105C23×C11C2×Q1611yescharacteristic
106C23×C11AGL(1,ℤ/8)11yescharacteristic
107C23×C11#13711yescharacteristic
108C2×C4×C11—24no—
109C2×C4×C11—24no—
110C2×C4×C11—22no—
111C2×C4×C11—22no—
112C2×C4×C11—22no—
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—22no—
118C2×C4×C11—22no—
119C2×C4×C11—22no—
120C2×C4×C11—28no—
121C2×C4×C11—42no—
122C2×C4×C11—42no—
123C2×C4×C11—44no—
124C2×C4×C11—48no—
125C2×C4×C11—48no—
126C2×C4×C11—44no—
127C2×C4×C11#10314yes—
128C2×C4×C11#10414yes—
129C2×C4×C11C4×D412yes—
130C2×C4×C11#12112yes—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—42no—
134C2×Dic11—42no—
135C2×Dic11—42no—
136C2×Dic11—42no—
137C2×Dic11—42no—
138Dic22—82no—
139C11⋊C8—82no—
140C2×C22⋊Q8—111no—
141C22×C4⋊C4—21no—
142C22×C42—21no—
143C22×C42C2×D1111yescharacteristic
144C2×C22⋊C8—112no—
145#391—112no—
146#389—112no—
147#387—222no—
148#385—221no—
149#381—221no—
150#380—111no—
151C4×C4⋊C4—24no—
152C2×#95C2×D1112yes—
153#336—222no—
154#328—224no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—22no—
160C22×C11—22no—
161C22×C11—22no—
162C22×C11—22no—
163C22×C11#38611yescharacteristic
164C22×C11#41012yes—
165C22×C11C2×#10311yescharacteristic
166C22×C11#41711yescharacteristic
167C22×C11C2×#10412yes—
168C22×C11#45011yescharacteristic
169C22×C11#45111yescharacteristic
170C22×C11#48311yescharacteristic
171C22×C11#48411yescharacteristic
172C4×C11—24no—
173C4×C11—24no—
174C4×C11—22no—
175C4×C11—22no—
176C4×C11—48no—
177Dic11—81no—
178Dic11—81no—
179Dic11—82no—
180C22×Q8—111no—
181C23×C4—22no—
182C23×C4C22⋊D1111yescharacteristic
183C23×C4C22⋊D1111yescharacteristic
184C23×C4C22×D1111yescharacteristic
185C22×C8—222no—
186C22⋊Q8—222no—
187C22⋊Q8—222no—
188C2×C4⋊C4—24no—
189C2×C4⋊C4—28no—
190C2×C4⋊C4—111no—
191C2×C4⋊C4—112no—
192C2×C4⋊C4—222no—
193C2×C4⋊C4—221no—
194C2×C22⋊C4—221no—
195C2×C22⋊C4—221no—
196C2×C42—22no—
197C2×C42—22no—
198C2×C42—24no—
199C2×C42—42no—
200C2×C42—42no—
201C2×C42C4×D1112yes—
202C2×C42D4412yes—
203C22⋊C8—222no—
204C22⋊C8—222no—
205#95—22no—
206#95—222no—
207#95—222no—
208#95—222no—
209#95—221no—
210#95C22⋊D1114yes—
211C2×C11—21no—
212C2×C11—21no—
213C2×C11—21no—
214C2×C11—21no—
215C2×C11#150312yes—
216C2×C11#150912yes—
217C2×C11#187211yescharacteristic
218C2×C11#189611yescharacteristic
219C2×C11#189911yescharacteristic
220C24C2×C22⋊D1111yescharacteristic
221C2×Q8—222no—
222C2×Q8—442no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—24no—
230C22×C4—28no—
231C22×C4—24no—
232C22×C4—42no—
233C22×C4—44no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—222no—
237C22×C4—221no—
238C22×C4—221no—
239C22×C4(C2×D11)⋊C412yes—
240C22×C4(C2×D11)⋊C412yes—
241C22×C4#432412yes—
242C22×C4#432612yes—
243C22×C4C2×C4×D1111yescharacteristic
244C22×C4C2×D4411yescharacteristic
245C22×C4#433912yes—
246C22×C4C2×C22⋊D1112yes—
247C2×C8—444no—
248C2×C8—442no—
249C4⋊C4—216no—
250C4⋊C4—222no—
251C4⋊C4—442no—
252C4⋊C4—444no—
253C4⋊C4—442no—
254C22⋊C4—441no—
255C22⋊C4—441no—
256C22⋊C4—441no—
257C22⋊C4—441no—
258C42—24no—
259C42—24no—
260C42—48no—
261C11#914411yescharacteristic, complemented, Sylow
262C23—22no—
263C23—22no—
264C23C2×(C2×D11)⋊C411yescharacteristic
265C23#6698211yescharacteristic
266C23#6698511yescharacteristic
267C23C2×#432411yescharacteristic
268C23#6699511yescharacteristic
269C23C2×#432611yescharacteristic
270C23#6700611yescharacteristic
271Q8—882no—
272C2×C4—24no—
273C2×C4—24no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—28no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—44no—
288C2×C4—48no—
289C2×C4—48no—
290C2×C4—44no—
291C2×C4—442no—
292C2×C4—442no—
293C2×C4—441no—
294C2×C4—441no—
295C2×C4—442no—
296C2×C4—442no—
297C2×C4—442no—
298C2×C4#6686914yes—
299C2×C4#6687414yes—
300C2×C4C4×C22⋊D1112yes—
301C2×C4#6698312yes—
302C8—882no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—21no—
307C22—22no—
308C22—22no—
309C22—22no—
310C22—22no—
311C22C2×#6686912yes—
312C22#1062257911yescharacteristic
313C22C2×#6687411yescharacteristic
314C22#1062258311yescharacteristic
315C22#1062258411yescharacteristic
316C22#1062261912yes—
317C22#1062282611yescharacteristic
318C22#1062283111yescharacteristic
319C22#1062284111yescharacteristic
320C4—24no—
321C4—22no—
322C4—22no—
323C4—24no—
324C4—48no—
325C4—881no—
326C4—881no—
327C4—882no—
328C2—21no—
329C2—21no—
330C2—21no—
331C2—21no—
332C2#1306711412yes—
333C2#1306713912yes—
334C2#1306892311yescharacteristic
335C2#1306905911yescharacteristic
336C2#1306907411yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C4×C11×C4⋊C4C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenterC2×C4×C4⋊C4D11
hypocenterC11#9144
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
17. #10622542C4semidirect
18. #10622541C4semidirect
261. C11#9144semidirect

Maximal subgroups

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

subgroupindex
#130769552
#130686842
C2×#106220902
#130664952
C2×C4×C11×C4⋊C42
#914411