Finite Group Databasebeta

← #14909292

Subgroups — #14909292

Order 2816.

514 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079127C211yesmaximal, characteristic
2D11×#500C211yesmaximal, characteristic
3#13070900C214yesmaximal, complemented
4#13070898C211yesmaximal, characteristic, complemented
5#13070896C211yesmaximal, characteristic, complemented
6#13070889C211yesmaximal, characteristic, complemented
7#13070401C214yesmaximal
8C4×#66862C211yesmaximal, characteristic
9C11×#2252C211yesmaximal, characteristic, complemented
10#10623259—21no—
11D11×C4⋊Q8—21no—
12C11×#500C2211yescharacteristic
13C11×#500C2211yescharacteristic
14#10622692—21no—
15#10622691—21no—
16C2×#66862C2212yes—
17#10622493—21no—
18#10622493C2212yes—
19D11×#107—21no—
20D11×#107C2212yes—
21#10622491—21no—
22#10622491C2212yes—
23#10622487—21no—
24#10622487C2212yes—
25C4×C8×D11C2211yescharacteristic
26#10622295C2211yescharacteristic
27#10622295C2211yescharacteristic
28C11×#366C2214yes—
29C4×C11×C16C2211yescharacteristic
30#10622143C2214yes—
31#10622140C2212yes—
32#10622128C2214yes—
33#10622127C2214yes—
34C4×C11⋊C16C2211yescharacteristic
35C2×Q8×D11—41no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38#66999—41no—
39Q8×Dic11—41no—
40#66997—41no—
41C2×C8×D11D411yescharacteristic
42C2×C8×D11C2311yescharacteristic
43#66950—41no—
44#66945—22no—
45C4⋊C4×D11—22no—
46C4⋊C4×D11—41no—
47#66943—22no—
48#66941—22no—
49#66941—41no—
50#66940—41no—
51C42×D11D411yescharacteristic
52#66922—21no—
53#66922—21no—
54C2×C11×C16C2312yes—
55C11×#107—21no—
56C11×#107—21no—
57C11×#107C2312yes—
58C11×#107C2312yes—
59C4×C8×C11C2311yescharacteristic
60#66882—21no—
61#66882—21no—
62#66882C2312yes—
63#66882C2312yes—
64C8×Dic11D411yescharacteristic
65C8×Dic11C2311yescharacteristic
66C2×C11⋊C16C2312yes—
67#66872—22no—
68#66872—22no—
69#66871—22no—
70#66871—22no—
71C4×C11⋊C8D411yescharacteristic
72#66862Q818yescomplemented
73#33731—111nomaximal, Sylow
74C2×Q8×C11—41no—
75C2×Q8×C11—41no—
76Q8×D11—84no—
77C2×C4×D11—42no—
78C2×C4×D11D811yescharacteristic
79C2×C4×D11D811yescharacteristic
80C2×C4×D11C2×D411yescharacteristic
81C2×Dic22—42no—
82C2×Dic22—41no—
83C2×Dic22—41no—
84C2×C8×C11C2×D411yescharacteristic
85C2×C8×C11C2411yescharacteristic
86C11×C4⋊C4—22no—
87C11×C4⋊C4—22no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C42×C11C2×D411yescharacteristic
91(C2×D11)⋊C4—42no—
92C4⋊Dic11—22no—
93C4⋊Dic11—22no—
94C4⋊Dic11—42no—
95C4⋊Dic11—41no—
96C4⋊Dic11—41no—
97Dic11⋊C4—42no—
98Dic11⋊C4—42no—
99Dic11⋊C4—42no—
100C4×Dic11—42no—
101C4×Dic11D811yescharacteristic
102C4×Dic11D811yescharacteristic
103C4×Dic11C2×D411yescharacteristic
104C2×C11⋊C8C2×D411yescharacteristic
105C2×C11⋊C8C2×D411yescharacteristic
106C8×D11Q1614yes—
107C8×D11C2×Q814yes—
108C11×C16C2×Q814yescomplemented
109C11⋊C16C2×Q814yescomplemented
110#3160—111no—
111C2×#500—111no—
112#2255—114no—
113#2254—111no—
114#2254—111no—
115#2252—111no—
116#2252D1111yescharacteristic, complemented
117#2159—114no—
118C4×M32—111no—
119C22×D11C2×D811yescharacteristic
120Q8×C11—82no—
121Q8×C11—82no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11C2×D811yescharacteristic
125C2×C4×C11C2×D811yescharacteristic
126C2×C4×C11C22×D411yescharacteristic
127C2×Dic11—42no—
128C2×Dic11—42no—
129C2×Dic11C2×D811yescharacteristic
130C2×Dic11C2×D811yescharacteristic
131C2×Dic11C2×D811yescharacteristic
132C4×D11—22no—
133C4×D11—22no—
134C4×D11—84no—
135C4×D11C4⋊Q812yes—
136C4×D11C2×Q1612yes—
137Dic22—84no—
138Dic22—82no—
139Dic22—82no—
140C8×C11C2×Q1612yes—
141C8×C11C22×Q812yes—
142C11⋊C8C4⋊Q812yes—
143C11⋊C8C2×Q1612yes—
144#533—221no—
145C2×C4⋊Q8—221no—
146C2×M32—112no—
147#500—112no—
148#500—111no—
149#500—111no—
150#500—221no—
151#500—221no—
152#500C2×D1111yescharacteristic
153#500C2×D1111yescharacteristic
154#499—112no—
155#499—221no—
156#498—221no—
157#427—112no—
158#427—221no—
159C2×#107—112no—
160C2×#107—221no—
161C2×C4×C8—111no—
162#367—114no—
163#367—114no—
164#366—114no—
165#366C2×D1114yes—
166#346—112no—
167C4×C16—111no—
168C4×C16C2×D1111yescharacteristic
169C22×C11C22×D811yescharacteristic
170C2×D11—21no—
171C2×D11—21no—
172C2×D11#50012yes—
173C4×C11—82no—
174C4×C11—82no—
175C4×C11#50912yes—
176C4×C11#51012yes—
177C4×C11C2×C4⋊Q811yescharacteristic
178C4×C11C22×Q1611yescharacteristic
179Dic11—21no—
180Dic11—21no—
181Dic11—82no—
182Dic11—82no—
183Dic11#50012yes—
184C22×Q8—441no—
185C22×C8—111no—
186C22×C8—111no—
187C4⋊Q8—21no—
188C4⋊Q8—21no—
189C4⋊Q8—222no—
190C4⋊Q8—221no—
191C4⋊Q8—221no—
192C4⋊Q8—441no—
193C4⋊Q8—441no—
194#125—222no—
195C22⋊Q8—441no—
196C22⋊Q8—441no—
197C4×Q8—441no—
198C4×Q8—441no—
199#117—222no—
200C2×C4⋊C4—222no—
201C2×C4⋊C4—441no—
202C2×C42—111no—
203M32—118no—
204C2×C16—112no—
205C2×C16C22×D1112yes—
206#107—21no—
207#107—21no—
208#107—112no—
209#107—112no—
210#107—222no—
211#107—222no—
212#107—221no—
213#107—221no—
214#107C22×D1112yes—
215#107C22×D1112yes—
216#106—222no—
217#106—222no—
218C4×C8—111no—
219C4×C8—111no—
220C4×C8—111no—
221C4×C8C22×D1111yescharacteristic
222C2×C11C2×#50011yescharacteristic
223C2×C11C2×#50911yescharacteristic
224C2×C11C2×#51011yescharacteristic
225D11—22no—
226C2×Q8—41no—
227C2×Q8—41no—
228C2×Q8—442no—
229C2×Q8—441no—
230C2×Q8—441no—
231C2×Q8—884no—
232C22×C4—111no—
233C22×C4—111no—
234C22×C4—111no—
235C22×C4—442no—
236C2×C8—111no—
237C2×C8—111no—
238C2×C8—114no—
239C2×C8—114no—
240C2×C8D4×D1111yescharacteristic
241C2×C8C23×D1111yescharacteristic
242C4⋊C4—22no—
243C4⋊C4—22no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—222no—
247C4⋊C4—222no—
248C4⋊C4—442no—
249C4⋊C4—442no—
250C4⋊C4—442no—
251C4⋊C4—442no—
252C4⋊C4—441no—
253C4⋊C4—441no—
254C22⋊C4—442no—
255C42—111no—
256C42—111no—
257C42—111no—
258C42—442no—
259C42D4×D1111yescharacteristic
260C16—114no—
261C16Q8×D1114yescomplemented
262C11#3373111yescharacteristic, complemented, Sylow
263C23—111no—
264Q8—82no—
265Q8—82no—
266Q8—884no—
267Q8—882no—
268Q8—882no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—111no—
272C2×C4—112no—
273C2×C4—112no—
274C2×C4—111no—
275C2×C4—111no—
276C2×C4—222no—
277C2×C4—222no—
278C2×C4—442no—
279C2×C4—442no—
280C2×C4—884no—
281C2×C4D8×D1111yescharacteristic
282C2×C4D8×D1111yescharacteristic
283C2×C4C2×D4×D1111yescharacteristic
284C8—112no—
285C8—112no—
286C8Q16×D1112yes—
287C8C2×Q8×D1112yes—
288C22—112no—
289C22—221no—
290C22—221no—
291C22C2×D8×D1111yescharacteristic
292C4—82no—
293C4—82no—
294C4—112no—
295C4—221no—
296C4—221no—
297C4—882no—
298C4—882no—
299C4#1062252412yes—
300C4#1062253112yes—
301C4D11×C4⋊Q811yescharacteristic
302C4C2×Q16×D1111yescharacteristic
303C2—222no—
304C2D11×#50011yescharacteristic
305C2C2×#1062252411yescharacteristic
306C2C2×#1062253111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2252C2
socleC22×C11C22×D8
prime radicalC22×D11C2×D8
hypercenter#2252D11
hypocenterC11#33731
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2252

Complements

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

NH ≅ G/Ntype
3. #13070900C2semidirect
4. #13070898C2semidirect
5. #13070896C2semidirect
6. #13070889C2semidirect
9. C11×#2252C2semidirect
72. #66862Q8semidirect
108. C11×C16C2×Q8semidirect
109. C11⋊C16C2×Q8semidirect
116. #2252D11semidirect
261. C16Q8×D11semidirect
262. C11#33731semidirect

Maximal subgroups

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

subgroupindex
#130791272
D11×#5002
#130709002
#130708982
#130708962
#130708892
#130704012
C4×#668622
C11×#22522
#3373111