Finite Group Databasebeta

← #14642012

Subgroups — #14642012

Order 2816.

434 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068469C211yesmaximal, characteristic
2#13068365C211yesmaximal, characteristic
3#13066442C212yesmaximal
4#13066439C212yesmaximal
5C11×#2295C211yesmaximal, characteristic
6C2×C4×Q8×C11C411yescharacteristic
7C11×#391C411yescharacteristic
8C11×#391C2211yescharacteristic
9C11×#389C411yescharacteristic
10C11×#389C2211yescharacteristic
11C11×#387—21no—
12C11×#387—21no—
13C4×C11×C4⋊C4—21no—
14C4×C11×C4⋊C4C411yescharacteristic
15C11×#376—21no—
16C43×C11C2211yescharacteristic
17C2×C4⋊(C11⋊C8)—21no—
18C2×#66867—21no—
19C2×#66867—21no—
20#10622162—21no—
21#10622162C2212yes—
22#10622162C2212yes—
23C22×Q8×C11C2×C411yescharacteristic
24C4×Q8×C11—22no—
25C4×Q8×C11—22no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4C2×C411yescharacteristic
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C42×C11—21no—
33C2×C42×C11—21no—
34C2×C42×C11C2×C411yescharacteristic
35C2×C42×C11C2×C411yescharacteristic
36C2×C42×C11D411yescharacteristic
37C2×C42×C11D411yescharacteristic
38C2×C42×C11D411yescharacteristic
39C2×C42×C11D411yescharacteristic
40C2×C42×C11C2311yescharacteristic
41C22×C11⋊C8—22no—
42C22×C11⋊C8—22no—
43C11×#95—21no—
44C11×#95—21no—
45C11×#95—21no—
46C11×#95—21no—
47C11×#95—21no—
48C11×#95—21no—
49C11×#95—21no—
50C4⋊(C11⋊C8)—24no—
51#66867—24no—
52#66867—42no—
53#7630—111nomaximal, Sylow
54C2×Q8×C11—21no—
55C2×Q8×C11—41no—
56C2×Q8×C11—41no—
57C2×Q8×C11M1612yes—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22×C411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C11×C4⋊C4—24no—
70C11×C4⋊C4—21no—
71C11×C4⋊C4—41no—
72C11×C4⋊C4—41no—
73C11×C4⋊C4—42no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4M1612yes—
77C42×C11—24no—
78C42×C11—22no—
79C42×C11—22no—
80C42×C11—21no—
81C42×C11—21no—
82C42×C11—21no—
83C42×C11—22no—
84C42×C11—21no—
85C42×C11—41no—
86C42×C11—41no—
87C42×C11—42no—
88C2×C11⋊C8—24no—
89C2×C11⋊C8—24no—
90C2×C11⋊C8—42no—
91C2×C11⋊C8—42no—
92C2×C11⋊C8—42no—
93C2×C11⋊C8—42no—
94#2295D1111yescharacteristic
95#1767—111no—
96#1745—111no—
97#1272—112no—
98#1271—112no—
99C23×C11C2×C22⋊C411yescharacteristic
100Q8×C11—42no—
101Q8×C11—42no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
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—22no—
114C2×C4×C11—22no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11#10412yes—
131C2×C4×C11#10412yes—
132C2×C4×C11C2×M1611yescharacteristic
133C2×C4×C11C2×M1611yescharacteristic
134C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C11#13712yes—
136C2×C4×C11#13711yescharacteristic
137C11⋊C8—44no—
138C11⋊C8—44no—
139C2×C4×Q8Dic1111yescharacteristic
140C2×C4⋊C8—221no—
141C2×#97—221no—
142C2×#97—221no—
143#391Dic1111yescharacteristic
144#391C2×D1111yescharacteristic
145#389Dic1111yescharacteristic
146#389C2×D1111yescharacteristic
147#387—21no—
148#387—21no—
149C4×C4⋊C4—21no—
150C4×C4⋊C4Dic1111yescharacteristic
151#376—21no—
152C43C2×D1111yescharacteristic
153#336—112no—
154#336—112no—
155#336—221no—
156C22×C11#40711yescharacteristic
157C22×C11#41011yescharacteristic
158C22×C11#41311yescharacteristic
159C22×C11#41711yescharacteristic
160C22×C11#41911yescharacteristic
161C22×C11C2×#10411yescharacteristic
162C22×C11C2×#10411yescharacteristic
163C4×C11—21no—
164C4×C11—21no—
165C4×C11—22no—
166C4×C11—22no—
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—22no—
170C4×C11—41no—
171C4×C11—42no—
172C4×C11—41no—
173C4×C11—42no—
174C4×C11—81no—
175C4×C11—81no—
176C22×Q8C2×Dic1111yescharacteristic
177C22×C8—222no—
178C22×C8—222no—
179C4×Q8—22no—
180C4×Q8—22no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4C2×Dic1111yescharacteristic
185C2×C4⋊C4C2×Dic1111yescharacteristic
186C2×C4⋊C4C2×Dic1111yescharacteristic
187C2×C42—21no—
188C2×C42—21no—
189C2×C42C2×Dic1111yescharacteristic
190C2×C42C2×Dic1111yescharacteristic
191C2×C42C22⋊D1111yescharacteristic
192C2×C42C22⋊D1111yescharacteristic
193C2×C42C22⋊D1111yescharacteristic
194C2×C42C22⋊D1111yescharacteristic
195C2×C42C22×D1111yescharacteristic
196C4⋊C8—224no—
197#97—224no—
198#97—442no—
199#95—21no—
200#95—21no—
201#95—21no—
202#95—21no—
203#95—21no—
204#95—21no—
205#95—21no—
206C2×C11#146411yescharacteristic
207C2×C11#148911yescharacteristic
208C2×C11#149111yescharacteristic
209C2×C11#150611yescharacteristic
210C2×C11#150911yescharacteristic
211C2×C11#152411yescharacteristic
212C2×C11#155911yescharacteristic
213C2×Q8—21no—
214C2×Q8—41no—
215C2×Q8—41no—
216C2×Q8#431812yes—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4C22⋊Dic1111yescharacteristic
222C22×C4C22⋊Dic1111yescharacteristic
223C22×C4C22⋊Dic1111yescharacteristic
224C22×C4C22⋊Dic1111yescharacteristic
225C22×C4C22×Dic1111yescharacteristic
226C22×C4C2×C22⋊D1111yescharacteristic
227C22×C4C2×C22⋊D1111yescharacteristic
228C2×C8—224no—
229C2×C8—224no—
230C2×C8—442no—
231C2×C8—442no—
232C2×C8—442no—
233C2×C8—442no—
234C4⋊C4—24no—
235C4⋊C4—21no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—42no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4#431812yes—
242C42—24no—
243C42—22no—
244C42—22no—
245C42—21no—
246C42—21no—
247C42—22no—
248C42—21no—
249C42—21no—
250C42—41no—
251C42—41no—
252C42—42no—
253C11#763011yescharacteristic, complemented, Sylow
254C23C2×C22⋊Dic1111yescharacteristic
255Q8—42no—
256Q8—42no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4#6690112yes—
286C2×C4#6690112yes—
287C2×C4C2×#431811yescharacteristic
288C2×C4C2×#431811yescharacteristic
289C2×C4#6699512yes—
290C2×C4#6700211yescharacteristic
291C2×C4#6700411yescharacteristic
292C8—444no—
293C8—444no—
294C22#1062282011yescharacteristic
295C22#1062283811yescharacteristic
296C22#1062284511yescharacteristic
297C22C2×#6690111yescharacteristic
298C22C2×#6690111yescharacteristic
299C22#1062285011yescharacteristic
300C22#1062285311yescharacteristic
301C4—22no—
302C4—22no—
303C4—21no—
304C4—21no—
305C4—22no—
306C4—21no—
307C4—21no—
308C4—41no—
309C4—42no—
310C4—41no—
311C4—42no—
312C4—81no—
313C4—81no—
314C2#1306695011yescharacteristic
315C2#1306705511yescharacteristic
316C2#1306706311yescharacteristic
317C2#1306712811yescharacteristic
318C2#1306714111yescharacteristic
319C2#1306720411yescharacteristic
320C2#1306734611yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2295C2
socle, prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2295D11
hypocenterC11#7630
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #2295

Complements

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

NH ≅ G/Ntype
253. C11#7630semidirect

Maximal subgroups

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

subgroupindex
#130684692
#130683652
#130664422
#130664392
C11×#22952
#763011