Finite Group Databasebeta

← #14641920

Subgroups — #14641920

Order 2816.

612 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622541C211yesmaximal, characteristic
2#13068684C211yesmaximal, characteristic
3#13066440C214yesmaximal, complemented
4C11×#1728C211yesmaximal, characteristic
5C22×C11×M16—21no—
6C22×C42×C11C2211yescharacteristic
7C22×C4⋊Dic11C411yescharacteristic
8C22×C4⋊Dic11C411yescharacteristic
9C22×Dic11⋊C4—21no—
10C2×C11⋊#95—21no—
11C2×C22⋊(C11⋊C8)—21no—
12#10622541—21no—
13#10622541—21no—
14#10622541C412yes—
15#10622541C2212yes—
16C11×#336—21no—
17C11×#336C2212yes—
18#10622162—21no—
19#10622162C2212yes—
20C23×C4×C11C2×C411yescharacteristic
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×Dic11—21no—
24C23×Dic11—21no—
25C2×C11×M16—24no—
26C2×C11×M16—42no—
27C2×C11×M16—42no—
28C22×C8×C11—22no—
29C2×C42×C11—42no—
30C2×C42×C11C2×C411yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C42×C11C2311yescharacteristic
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—24no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—42no—
38C2×C4⋊Dic11C2×C412yes—
39C2×C4⋊Dic11C2×C412yes—
40C2×Dic11⋊C4—22no—
41C2×Dic11⋊C4—22no—
42C2×Dic11⋊C4—42no—
43C2×Dic11⋊C4—42no—
44C22×C11⋊C8—22no—
45C11⋊#95—22no—
46C11⋊#95—22no—
47C22⋊(C11⋊C8)—42no—
48#7610—111nomaximal, Sylow
49C24×C11C22⋊C411yescharacteristic
50C22×C4×C11—22no—
51C22×C4×C11—22no—
52C22×C4×C11—22no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11—22no—
56C22×C4×C11—22no—
57C22×C4×C11—41no—
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11D812yes—
62C22×C4×C11SD1612yes—
63C22×C4×C11C22×C411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×Dic11—24no—
67C22×Dic11—22no—
68C22×Dic11—22no—
69C22×Dic11—42no—
70C22×Dic11—42no—
71C22×Dic11—42no—
72C22×Dic11—42no—
73C22×Dic11—42no—
74C11×M16—48no—
75C2×C8×C11—24no—
76C2×C8×C11—42no—
77C2×C8×C11—42no—
78C42×C11—41no—
79C42×C11—41no—
80C42×C11—41no—
81C42×C11—41no—
82C4⋊Dic11—24no—
83C4⋊Dic11—22no—
84C4⋊Dic11—42no—
85C4⋊Dic11—42no—
86C4⋊Dic11M1614yescomplemented
87Dic11⋊C4—44no—
88Dic11⋊C4—42no—
89Dic11⋊C4—42no—
90C2×C11⋊C8—42no—
91C2×C11⋊C8—42no—
92C2×C11⋊C8—42no—
93C2×#389—111no—
94#1817—111no—
95#1728D1111yescharacteristic
96#1271—114no—
97C23×C11—21no—
98C23×C11—21no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11#9912yes—
102C23×C11#10212yes—
103C23×C11#10412yes—
104C23×C11C2×C22⋊C411yescharacteristic
105C2×C4×C11—28no—
106C2×C4×C11—24no—
107C2×C4×C11—24no—
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—21no—
121C2×C4×C11—44no—
122C2×C4×C11#10112yes—
123C2×C4×C11#10212yes—
124C2×C4×C11C2×M1612yes—
125C2×C4×C11C2×D811yescharacteristic
126C2×C4×C11C2×SD1611yescharacteristic
127C2×C4×C11#13712yes—
128C2×Dic11—24no—
129C2×Dic11—48no—
130C2×Dic11—42no—
131C2×Dic11—42no—
132C2×Dic11—42no—
133C2×Dic11—42no—
134C2×Dic11—42no—
135C2×Dic11—84no—
136C8×C11—44no—
137C11⋊C8—82no—
138C22×M16—21no—
139C22×C4⋊C4—111no—
140C22×C4⋊C4—111no—
141C22×C4⋊C4—221no—
142C22×C42C2×D1111yescharacteristic
143C2×C22⋊C8—221no—
144#389—112no—
145#389—112no—
146#389—221no—
147#389—221no—
148C2×#95—221no—
149#336—21no—
150#336—112no—
151#336—221no—
152#336C2×D1112yes—
153C22×C11—22no—
154C22×C11—22no—
155C22×C11—22no—
156C22×C11—22no—
157C22×C11—22no—
158C22×C11—22no—
159C22×C11#32714yes—
160C22×C11#40711yescharacteristic
161C22×C11C2×#9911yescharacteristic
162C22×C11C2×#10111yescharacteristic
163C22×C11C2×#10211yescharacteristic
164C22×C11#41911yescharacteristic
165C22×C11C2×#10411yescharacteristic
166C22×C11#42111yescharacteristic
167C4×C11—22no—
168C4×C11—22no—
169C4×C11—22no—
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—22no—
173C4×C11—41no—
174Dic11—44no—
175Dic11—82no—
176C23×C4—221no—
177C23×C4—221no—
178C23×C4C4×D1111yescharacteristic
179C23×C4D4411yescharacteristic
180C23×C4C22⋊D1111yescharacteristic
181C2×M16—24no—
182C2×M16—42no—
183C2×M16—42no—
184C22×C8—22no—
185C22×C8—222no—
186C2×C4⋊C4—112no—
187C2×C4⋊C4—112no—
188C2×C4⋊C4—224no—
189C2×C4⋊C4—221no—
190C2×C4⋊C4—221no—
191C2×C4⋊C4—222no—
192C2×C4⋊C4—222no—
193C2×C4⋊C4—442no—
194C2×C4⋊C4—442no—
195C2×C4⋊C4—442no—
196C2×C42—42no—
197C2×C42C4×D1111yescharacteristic
198C2×C42D4411yescharacteristic
199C2×C42C22⋊D1111yescharacteristic
200C2×C42C22×D1111yescharacteristic
201C22⋊C8—442no—
202#95—222no—
203#95—222no—
204C2×C11—24no—
205C2×C11#146311yescharacteristic
206C2×C11#148611yescharacteristic
207C2×C11#149111yescharacteristic
208C2×C11C2×#32711yescharacteristic
209C2×C11#151111yescharacteristic
210C2×C11#152811yescharacteristic
211C2×C11#154611yescharacteristic
212C24(C2×D11)⋊C411yescharacteristic
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—41no—
221C22×C4—224no—
222C22×C4—222no—
223C22×C4—222no—
224C22×C4—442no—
225C22×C4—442no—
226C22×C4—442no—
227C22×C4—442no—
228C22×C4—442no—
229C22×C4(C2×D11)⋊C411yescharacteristic
230C22×C4(C2×D11)⋊C411yescharacteristic
231C22×C4(C2×D11)⋊C411yescharacteristic
232C22×C4#432312yes—
233C22×C4#432512yes—
234C22×C4C2×C4×D1111yescharacteristic
235C22×C4C2×D4411yescharacteristic
236C22×C4C2×C22⋊D1111yescharacteristic
237M16—48no—
238C2×C8—24no—
239C2×C8—42no—
240C2×C8—42no—
241C2×C8—442no—
242C2×C8—442no—
243C2×C8—442no—
244C4⋊C4—114no—
245C4⋊C4—224no—
246C4⋊C4—222no—
247C4⋊C4—442no—
248C4⋊C4—442no—
249C4⋊C4—444no—
250C4⋊C4—442no—
251C4⋊C4—442no—
252C42—41no—
253C42—41no—
254C42—41no—
255C42—41no—
256C11#761011yescharacteristic, complemented, Sylow
257C23—21no—
258C23—21no—
259C23—21no—
260C23—21no—
261C23#6686912yes—
262C23#6687012yes—
263C23#6687312yes—
264C23C2×(C2×D11)⋊C411yescharacteristic
265C2×C4—28no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—24no—
277C2×C4—24no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—44no—
282C2×C4—224no—
283C2×C4—448no—
284C2×C4—442no—
285C2×C4—442no—
286C2×C4—442no—
287C2×C4—442no—
288C2×C4—442no—
289C2×C4—884no—
290C2×C4#6687312yes—
291C2×C4#6688812yes—
292C2×C4M16×D1112yes—
293C2×C4#6696212yes—
294C2×C4C2×#432311yescharacteristic
295C2×C4C2×#432511yescharacteristic
296C8—44no—
297C8—882no—
298C22—22no—
299C22—22no—
300C22—22no—
301C22—22no—
302C22—22no—
303C22—22no—
304C22#1062208914yes—
305C22C2×#6686911yescharacteristic
306C22C2×#6687011yescharacteristic
307C22C2×#6687311yescharacteristic
308C22#1062273311yescharacteristic
309C22#1062273911yescharacteristic
310C22C2×#6688811yescharacteristic
311C22#1062275211yescharacteristic
312C4—21no—
313C4—22no—
314C4—21no—
315C4—22no—
316C4—22no—
317C4—22no—
318C4—41no—
319C4—444no—
320C4—882no—
321C2—24no—
322C2#1306694511yescharacteristic
323C2#1306704011yescharacteristic
324C2#1306706411yescharacteristic
325C2C2×#1062208911yescharacteristic
326C2#1306715011yescharacteristic
327C2#1306721711yescharacteristic
328C2#1306728911yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1728C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1728D11
hypocenterC11#7610
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1728

Complements

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

NH ≅ G/Ntype
3. #13066440C2semidirect
86. C4⋊Dic11M16semidirect
256. C11#7610semidirect

Maximal subgroups

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

subgroupindex
C2×#106225412
#130686842
#130664402
C11×#17282
#761011