Finite Group Databasebeta

← #14653861

Subgroups — #14653861

Order 2816.

598 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068378C211yesmaximal, characteristic
2#13066843C211yesmaximal, characteristic
3#13066494C214yesmaximal
4C11×#2857C211yesmaximal, characteristic
5C2×C11×C4⋊Q8C411yescharacteristic, complemented
6C2×C11×C22⋊Q8—21no—
7C22×C42×C11C2211yescharacteristic
8C11×#391—21no—
9C11×#389—21no—
10C11×#389C412yescomplemented
11C11×#384C411yescharacteristic, complemented
12C11×#380—21no—
13C11×#380C2212yes—
14C2×C11⋊#95—21no—
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2212yes—
17C2×C22⋊(C11⋊C8)C2212yes—
18C2×#66867—21no—
19#10622162—21no—
20C22×Q8×C11—21no—
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11C2311yescharacteristic
24C23×Dic11—22no—
25C11×C4⋊Q8—42no—
26C11×C22⋊Q8—44no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—22no—
31C2×C11×C4⋊C4C2×C412yes—
32C2×C11×C4⋊C4C2×C412yes—
33C2×C11×C22⋊C4—22no—
34C2×C42×C11—42no—
35C2×C42×C11C2×C411yescharacteristic
36C2×C42×C11C2×C411yescharacteristic
37C2×C42×C11D411yescharacteristic
38C2×C42×C11D411yescharacteristic
39C22×C11⋊C8—22no—
40C11×#95—22no—
41C11×#95—22no—
42C11⋊#95—24no—
43C11⋊#95—24no—
44C11⋊#95—42no—
45C22⋊(C11⋊C8)—22no—
46C22⋊(C11⋊C8)Q814yescomplemented
47#66867—42no—
48#9889—111nomaximal, Sylow
49C24×C11C2×D411yescharacteristic
50C2×Q8×C11—42no—
51C2×Q8×C11—42no—
52C2×Q8×C11—42no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11—22no—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11—41no—
60C22×C4×C11—41no—
61C22×C4×C11—41no—
62C22×C4×C11—41no—
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22×C411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×Q812yes—
70C22×C4×C11#4112yes—
71C22×Dic11—24no—
72C22×Dic11—42no—
73C22×Dic11—42no—
74C22×Dic11—42no—
75C22×Dic11—42no—
76C22×Dic11—42no—
77C22×Dic11—42no—
78C11×C4⋊C4—42no—
79C11×C4⋊C4—44no—
80C11×C4⋊C4—42no—
81C11×C4⋊C4—42no—
82C11×C4⋊C4—42no—
83C11×C4⋊C4—42no—
84C11×C22⋊C4—44no—
85C42×C11—22no—
86C42×C11—22no—
87C42×C11—41no—
88C42×C11—41no—
89C2×C11⋊C8—24no—
90C2×C11⋊C8—42no—
91C2×C11⋊C8—42no—
92#2857D1111yescharacteristic
93#1749—111no—
94#1434—111no—
95#1294—114no—
96C23×C11—21no—
97C23×C11—21no—
98C23×C11—21no—
99C23×C11—21no—
100C23×C11C2×C22⋊C411yescharacteristic
101C23×C11#12411yescharacteristic
102C23×C11C4⋊Q811yescharacteristic
103C23×C11AGL(1,ℤ/8)12yes—
104C23×C11#13712yes—
105Q8×C11—84no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11—44no—
123C2×C4×C11—44no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
128C2×C4×C11—42no—
129C2×C4×C11—42no—
130C2×C4×C11#9912yes—
131C2×C4×C11#10412yes—
132C2×C4×C11C4×Q812yes—
133C2×C4×C11C22⋊Q812yes—
134C2×Dic11—44no—
135C2×Dic11—44no—
136C2×Dic11—44no—
137C2×Dic11—82no—
138C2×Dic11—82no—
139C2×Dic11—82no—
140C2×Dic11—82no—
141C11⋊C8—44no—
142C2×C4⋊Q8Dic1111yescharacteristic, complemented
143C2×C22⋊Q8—21no—
144C22×C42C2×D1111yescharacteristic
145C2×C22⋊C8—112no—
146C2×#97—221no—
147#391—21no—
148#389—21no—
149#389Dic1112yescomplemented
150#384Dic1111yescharacteristic, complemented
151#380—21no—
152#380C2×D1112yes—
153C2×#95—112no—
154C2×#95—221no—
155C2×#95—221no—
156#336—221no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—22no—
162C22×C11—22no—
163C22×C11—22no—
164C22×C11—22no—
165C22×C11#39111yescharacteristic
166C22×C11C2×#9911yescharacteristic
167C22×C11#41011yescharacteristic
168C22×C11#41811yescharacteristic
169C22×C11#41911yescharacteristic
170C22×C11C2×#10411yescharacteristic
171C22×C11#42111yescharacteristic
172C22×C11#48912yes—
173C22×C11#50112yes—
174C4×C11—22no—
175C4×C11—22no—
176C4×C11—22no—
177C4×C11—22no—
178C4×C11—41no—
179C4×C11—41no—
180C4×C11—82no—
181C4×C11—82no—
182Dic11—84no—
183C22×Q8—21no—
184C23×C4—222no—
185C23×C4C22⋊D1111yescharacteristic
186C23×C4C22⋊D1111yescharacteristic
187C23×C4C22×D1111yescharacteristic
188C22×C8—222no—
189C4⋊Q8—42no—
190C22⋊Q8—44no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4C2×Dic1112yes—
196C2×C4⋊C4C2×Dic1112yes—
197C2×C22⋊C4—22no—
198C2×C42—42no—
199C2×C42C2×Dic1111yescharacteristic
200C2×C42C2×Dic1111yescharacteristic
201C2×C42C22⋊D1111yescharacteristic
202C2×C42C22⋊D1111yescharacteristic
203C22⋊C8—114no—
204C22⋊C8—222no—
205#97—442no—
206#95—22no—
207#95—22no—
208#95—224no—
209#95—224no—
210#95—442no—
211C2×C11—22no—
212C2×C11—22no—
213C2×C11#150511yescharacteristic
214C2×C11#150811yescharacteristic
215C2×C11#151011yescharacteristic
216C2×C11#151511yescharacteristic
217C2×C11#198611yescharacteristic
218C2×C11#199311yescharacteristic
219C2×C11#199611yescharacteristic
220C24C2×C22⋊D1111yescharacteristic
221C2×Q8—42no—
222C2×Q8—42no—
223C2×Q8—42no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—41no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—224no—
235C22×C4—442no—
236C22×C4—442no—
237C22×C4—442no—
238C22×C4—442no—
239C22×C4—442no—
240C22×C4—442no—
241C22×C4C22⋊Dic1111yescharacteristic
242C22×C4C22⋊Dic1111yescharacteristic
243C22×C4C22⋊Dic1111yescharacteristic
244C22×C4C22⋊Dic1111yescharacteristic
245C22×C4Q8×D1112yes—
246C22×C4#434312yes—
247C22×C4C22×Dic1111yescharacteristic
248C22×C4C2×C22⋊D1111yescharacteristic
249C2×C8—224no—
250C2×C8—442no—
251C2×C8—442no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—44no—
256C4⋊C4—42no—
257C4⋊C4—42no—
258C22⋊C4—44no—
259C42—22no—
260C42—22no—
261C42—41no—
262C42—41no—
263C11#988911yescharacteristic, complemented, Sylow
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23#6698512yes—
269C23#6699512yes—
270C23#6699711yescharacteristic
271C23#6700011yescharacteristic
272C23C2×C22⋊Dic1111yescharacteristic
273Q8—84no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—44no—
291C2×C4—44no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—444no—
299C2×C4—444no—
300C2×C4—444no—
301C2×C4—882no—
302C2×C4—882no—
303C2×C4—882no—
304C2×C4—882no—
305C2×C4#6689812yes—
306C2×C4#6690112yes—
307C2×C4Q8×Dic1112yes—
308C2×C4#6699912yes—
309C8—444no—
310C22—21no—
311C22—21no—
312C22—22no—
313C22—22no—
314C22—22no—
315C22—22no—
316C22—21no—
317C22—21no—
318C22#1062269312yes—
319C22#1062270212yes—
320C22#1062282811yescharacteristic
321C22C2×#6689811yescharacteristic
322C22#1062283811yescharacteristic
323C22#1062284311yescharacteristic
324C22C2×#6690111yescharacteristic
325C22#1062284911yescharacteristic
326C22#1062285311yescharacteristic
327C4—22no—
328C4—22no—
329C4—22no—
330C4—22no—
331C4—41no—
332C4—41no—
333C4—82no—
334C4—82no—
335C4—884no—
336C2—22no—
337C2—22no—
338C2#1306712411yescharacteristic
339C2#1306713611yescharacteristic
340C2#1306714511yescharacteristic
341C2#1306716711yescharacteristic
342C2#1306956111yescharacteristic
343C2#1306959011yescharacteristic
344C2#1306960211yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2857C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#2857D11
hypocenterC11#9889
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2857

Complements

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

NH ≅ G/Ntype
5. C2×C11×C4⋊Q8C4semidirect
10. C11×#389C4semidirect
11. C11×#384C4semidirect
46. C22⋊(C11⋊C8)Q8semidirect
142. C2×C4⋊Q8Dic11semidirect
149. #389Dic11semidirect
150. #384Dic11semidirect
263. C11#9889semidirect

Maximal subgroups

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

subgroupindex
#130683782
#130668432
#130664942
C11×#28572
#988911