Finite Group Databasebeta

← #14668972

Subgroups — #14668972

Order 2816.

452 conjugacy classes of subgroups.

The subgroup lattice has 294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13070301C211yesmaximal, characteristic
2#13070281C211yesmaximal, characteristic
3#13068416C212yesmaximal, complemented
4#13066745C212yesmaximal, complemented
5C11×#2932C211yesmaximal, characteristic
6C2×C11×#131C411yescharacteristic, complemented
7C2×C11×#131C2211yescharacteristic
8C11×#532C2211yescharacteristic
9C11×#435—22no—
10C11×#435—22no—
11C11×#423C411yescharacteristic, complemented
12C11×#408C411yescharacteristic, complemented
13C11×#408C2211yescharacteristic
14C2×C11×#97C411yescharacteristic, complemented
15#10622853C2212yes—
16#10622850C2212yes—
17#10622714—22no—
18#10622194—22no—
19#10622186C412yescomplemented
20#10622183C412yes—
21#10622180C412yescomplemented
22#10622179C412yes—
23C2×C11×#41C2×C411yescharacteristic
24C2×C11×#41C2311yescharacteristic
25C11×#131—42no—
26C11×#131—42no—
27C2×C11×M16—21no—
28C2×C11×M16C2×C411yescharacteristic
29C2×C11×M16C2×C411yescharacteristic
30C2×C11×M16D412yes—
31C22×C8×C11—21no—
32C22×C8×C11C2×C411yescharacteristic
33C22×C8×C11C2×C411yescharacteristic
34C22×C8×C11D412yes—
35C11×C4⋊Q8C2×C411yescharacteristic
36C11×#127C2×C411yescharacteristic
37C11×#124C2×C411yescharacteristic
38C11×#124C2×C411yescharacteristic
39C11×#121—22no—
40C4×D4×C11—22no—
41C2×C42×C11C2×C411yescharacteristic
42#66979—22no—
43C2×#4318—22no—
44C11×C4⋊C8—22no—
45C11×C22⋊C8—22no—
46C11×C22⋊C8—22no—
47C11×#97—21no—
48C11×#97—21no—
49#66900C2×C414yes—
50#66898—22no—
51#66898C2×C414yes—
52#66897—22no—
53#66879—42no—
54C8×Dic11—42no—
55#12634—111nomaximal, Sylow
56C11×#41—41no—
57C11×#41—41no—
58C11×#41—41no—
59C11×#41—41no—
60C2×Q8×C11C4211yescharacteristic
61C2×Q8×C11C22×C411yescharacteristic
62C2×D4×C11—21no—
63C2×D4×C11—22no—
64C2×D4×C11C4211yescharacteristic
65C2×D4×C11C22×C411yescharacteristic
66C2×D4×C11#4112yes—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D412yes—
71C11×M16—41no—
72C11×M16—42no—
73C11×M16—41no—
74C11×M16—42no—
75C2×C8×C11—22no—
76C2×C8×C11—22no—
77C2×C8×C11—22no—
78C2×C8×C11—21no—
79C2×C8×C11—21no—
80C2×C8×C11—41no—
81C2×C8×C11—42no—
82C2×C8×C11C22⋊C411yescharacteristic
83C2×C8×C11C22⋊C412yes—
84C2×C8×C11C22⋊C411yescharacteristic
85C11×C4⋊C4—22no—
86C11×C22⋊C4—22no—
87C11×C22⋊C4—22no—
88C42×C11—21no—
89C42×C11C4211yescharacteristic
90C42×C11C4211yescharacteristic
91C22⋊Dic11—24no—
92C4⋊Dic11—42no—
93C4×Dic11—42no—
94#4318—24no—
95#4318—42no—
96C2×C11⋊C8—42no—
97#2932D1111yescharacteristic
98#2132—111no—
99#2126—111no—
100#1757—112no—
101#1395—112no—
102C23×C11—21no—
103C23×C11#11711yescharacteristic
104C23×C11C4×D412yes—
105Q8×C11—41no—
106Q8×C11—41no—
107D4×C11—41no—
108D4×C11—42no—
109D4×C11—41no—
110D4×C11—42no—
111D4×C11—82no—
112C2×C4×C11—22no—
113C2×C4×C11—21no—
114C2×C4×C11—22no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—81no—
122C2×C4×C11C2×C4211yescharacteristic
123C2×C4×C11C2×C22⋊C411yescharacteristic
124C2×C4×C11C4×D412yes—
125C2×Dic11—44no—
126C8×C11—21no—
127C8×C11—22no—
128C8×C11—41no—
129C8×C11—41no—
130C8×C11#9912yes—
131C11⋊C8—44no—
132C2×#131Dic1111yescharacteristic, complemented
133C2×#131C2×D1111yescharacteristic
134#532C2×D1111yescharacteristic
135#435—22no—
136#435—22no—
137#423Dic1111yescharacteristic, complemented
138#413—112no—
139#410—112no—
140#408Dic1111yescharacteristic, complemented
141#408C2×D1111yescharacteristic
142#405—222no—
143C2×#97Dic1111yescharacteristic, complemented
144#356—112no—
145#355—112no—
146#354—112no—
147#353—112no—
148#344—222no—
149C22×C11—21no—
150C22×C11—22no—
151C22×C11—41no—
152C22×C11—42no—
153C22×C11—42no—
154C22×C11—41no—
155C22×C11C4×C22⋊C411yescharacteristic
156C4×C11—21no—
157C4×C11—22no—
158C4×C11—41no—
159C4×C11—41no—
160C4×C11—41no—
161C4×C11C2×#9911yescharacteristic
162C4×C11#41011yescharacteristic
163Dic11—84no—
164C2×#41C2×Dic1111yescharacteristic
165C2×#41C22×D1111yescharacteristic
166#131—42no—
167#131—42no—
168C2×M16—21no—
169C2×M16—222no—
170C2×M16C2×Dic1111yescharacteristic
171C2×M16C2×Dic1111yescharacteristic
172C2×M16C22⋊D1112yes—
173C22×C8—21no—
174C22×C8C2×Dic1111yescharacteristic
175C22×C8C2×Dic1111yescharacteristic
176C22×C8C22⋊D1112yes—
177C4⋊Q8C4×D1111yescharacteristic
178#127C4×D1111yescharacteristic
179#124C4×D1111yescharacteristic
180#124C4×D1111yescharacteristic
181#121—22no—
182C4×D4—22no—
183#117—222no—
184C2×C42C2×Dic1111yescharacteristic
185C4⋊C8—22no—
186#101—114no—
187#100—222no—
188#99—114no—
189#99—222no—
190C22⋊C8—22no—
191C22⋊C8—22no—
192#97—21no—
193#97—21no—
194#97—442no—
195C4×C8—442no—
196C2×C11—21no—
197C2×C11—42no—
198C2×C11—41no—
199C2×C11—81no—
200C2×C11C4×#9911yescharacteristic
201#41—41no—
202#41—41no—
203#41—41no—
204#41—41no—
205C2×Q8C4×Dic1111yescharacteristic
206C2×Q8C2×C4×D1111yescharacteristic
207C2×D4—21no—
208C2×D4—22no—
209C2×D4C4×Dic1111yescharacteristic
210C2×D4C2×C4×D1111yescharacteristic
211C2×D4#433912yes—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4C22×Dic1111yescharacteristic
215C22×C4C2×C22⋊D1112yes—
216M16—41no—
217M16—42no—
218M16—42no—
219M16—41no—
220M16—224no—
221M16—442no—
222C2×C8—22no—
223C2×C8—22no—
224C2×C8—22no—
225C2×C8—21no—
226C2×C8—21no—
227C2×C8—42no—
228C2×C8—41no—
229C2×C8—442no—
230C2×C8C22⋊Dic1111yescharacteristic
231C2×C8C22⋊Dic1112yes—
232C2×C8C22⋊Dic1111yescharacteristic
233C4⋊C4—22no—
234C4⋊C4—442no—
235C22⋊C4—22no—
236C22⋊C4—22no—
237C22⋊C4—224no—
238C42—21no—
239C42—442no—
240C42C4×Dic1111yescharacteristic
241C42C4×Dic1111yescharacteristic
242C11#1263411yescharacteristic, complemented, Sylow
243C23—21no—
244C23#6697911yescharacteristic
245C23C4×C22⋊D1112yes—
246Q8—41no—
247Q8—41no—
248D4—41no—
249D4—42no—
250D4—41no—
251D4—42no—
252D4—82no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—81no—
263C2×C4—444no—
264C2×C4C2×C4×Dic1111yescharacteristic
265C2×C4C4×C22⋊D1112yes—
266C2×C4C2×C22⋊Dic1111yescharacteristic
267C8—21no—
268C8—22no—
269C8—41no—
270C8—41no—
271C8—444no—
272C8#6689812yes—
273C22—22no—
274C22—21no—
275C22—41no—
276C22—42no—
277C22—42no—
278C22—41no—
279C22C4×C22⋊Dic1111yescharacteristic
280C4—22no—
281C4—21no—
282C4—41no—
283C4—41no—
284C4—41no—
285C4—884no—
286C4C2×#6689811yescharacteristic
287C4#1062285311yescharacteristic
288C2—21no—
289C2—42no—
290C2—41no—
291C2—81no—
292C2C4×#6689811yescharacteristic
subgroupG/H
centerC4C2×#66898
commutatorC2×C4×C11C2×C42
FrattiniC2×#41C22×D11
FittingC11×#2932C2
socleC2×C11C4×#99
prime radicalC11×#532C22
cosocleC2×C11×#41C23
hypercenter#2932D11
hypocenterC11#12634
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C2×C8 ◁ C2×#131 ◁ #2932

Complements

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

NH ≅ G/Ntype
3. #13068416C2semidirect
4. #13066745C2semidirect
6. C2×C11×#131C4semidirect
11. C11×#423C4semidirect
12. C11×#408C4semidirect
14. C2×C11×#97C4semidirect
19. #10622186C4semidirect
21. #10622180C4semidirect
132. C2×#131Dic11semidirect
137. #423Dic11semidirect
140. #408Dic11semidirect
143. C2×#97Dic11semidirect
242. C11#12634semidirect

Maximal subgroups

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

subgroupindex
#130703012
#130702812
#130684162
#130667452
C11×#29322
#1263411