Finite Group Databasebeta

← #14653225

Subgroups — #14653225

Order 2816.

398 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622294C211yesmaximal, characteristic
2#13068754C211yesmaximal, characteristic
3#13067300C211yesmaximal, characteristic
4#13067296C211yesmaximal, characteristic
5#13067287C211yesmaximal, characteristic
6#13067287C211yesmaximal, characteristic
7C11×#1450C211yesmaximal, characteristic
8C2×#66922C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C2×C4×C8×C11C2211yescharacteristic
13C2×#66880—22no—
14#10622537C2211yescharacteristic
15#10622537C2211yescharacteristic
16#10622294—21no—
17#10622294—21no—
18#10622294C414yes—
19C11×#322—21no—
20C82×C11—21no—
21#10622190—22no—
22#10622124—22no—
23#10622124—22no—
24#10622120—22no—
25#10622119—22no—
26C22×Dic22—21no—
27C22×Dic22—21no—
28C22×C8×C11D412yes—
29C2×C42×C11C2311yescharacteristic
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×#4318—21no—
35C2×#4318—21no—
36#66922—21no—
37#66922—21no—
38#66922—21no—
39#66922—21no—
40#66922—21no—
41#66922—21no—
42#66922C2×C412yes—
43#66922C2×C412yes—
44C11×C4⋊C8D412yes—
45C11×C4⋊C8D412yes—
46C11×C22⋊C8—21no—
47C11×C22⋊C8—21no—
48C4×C8×C11—21no—
49C4×C8×C11—21no—
50C4×C8×C11C2×C412yes—
51C4×C8×C11D411yescharacteristic
52C4×C8×C11D411yescharacteristic
53#66880—24no—
54#66880—24no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)—21no—
59#9770—111nomaximal, Sylow
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11#4111yescharacteristic
62C22×C4×C11#4111yescharacteristic
63C22×Dic11—41no—
64C22×Dic11—41no—
65C2×Dic22—22no—
66C2×Dic22—22no—
67C2×Dic22—41no—
68C2×Dic22—41no—
69C2×Dic22—42no—
70C2×Dic22—42no—
71C2×Dic22—82no—
72C2×C8×C11—22no—
73C2×C8×C11—22no—
74C2×C8×C11—22no—
75C2×C8×C11—22no—
76C2×C8×C11C22⋊C412yes—
77C2×C8×C11C22⋊C412yes—
78C42×C11C22×C411yescharacteristic
79C42×C11C2×D411yescharacteristic
80C42×C11C2×D411yescharacteristic
81C42×C11C2×D411yescharacteristic
82C4⋊Dic11—22no—
83C4⋊Dic11—22no—
84C4⋊Dic11—22no—
85C4⋊Dic11—22no—
86C4⋊Dic11—41no—
87C4⋊Dic11—41no—
88C4⋊Dic11—41no—
89C4⋊Dic11—41no—
90#4318—42no—
91#4318—42no—
92C2×C11⋊C8—41no—
93C2×C11⋊C8—41no—
94C2×#487—111no—
95#1837—111no—
96#1549—111no—
97#1548—111no—
98#1546—111no—
99#1546—111no—
100#1450D1111yescharacteristic
101C23×C11#12411yescharacteristic
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11C2×C22⋊C411yescharacteristic
105C2×C4×C11C4×D411yescharacteristic
106C2×C4×C11C4×D411yescharacteristic
107C2×C4×C11#12111yescharacteristic
108C2×C4×C11#12111yescharacteristic
109C2×C4×C11#12711yescharacteristic
110C2×C4×C11#13512yes—
111C2×C4×C11#13512yes—
112C2×Dic11—42no—
113C2×Dic11—42no—
114C2×Dic11—82no—
115C2×Dic11—82no—
116Dic22—44no—
117Dic22—82no—
118Dic22—81no—
119Dic22—81no—
120Dic22—82no—
121C8×C11—22no—
122C8×C11—22no—
123C8×C11—42no—
124C8×C11—42no—
125C11⋊C8—81no—
126C11⋊C8—81no—
127C2×C4⋊Q8—111no—
128C2×C4⋊Q8—111no—
129#487—114no—
130#487—221no—
131#487—221no—
132#431C2×D1111yescharacteristic
133#431C2×D1111yescharacteristic
134#423—111no—
135#423—111no—
136C2×#103—222no—
137C2×C4×C8C2×D1111yescharacteristic
138#341—222no—
139#333—222no—
140#332—222no—
141#332—222no—
142#332—222no—
143#322—21no—
144C82—21no—
145C22×C11—21no—
146C22×C11—21no—
147C22×C11#39011yescharacteristic
148C22×C11#48812yes—
149C4×C11—21no—
150C4×C11—21no—
151C4×C11#41612yes—
152C4×C11#47112yes—
153C4×C11#47312yes—
154C4×C11#49511yescharacteristic
155C4×C11#49511yescharacteristic
156Dic11—82no—
157Dic11—82no—
158C22×Q8—221no—
159C22×Q8—221no—
160C2×M16—221no—
161C2×M16—221no—
162C22×C8D4412yes—
163C4⋊Q8—112no—
164C4⋊Q8—112no—
165C4⋊Q8—221no—
166C4⋊Q8—221no—
167C4⋊Q8—221no—
168C4⋊Q8—221no—
169C4⋊Q8—221no—
170C4⋊Q8—221no—
171C2×C4⋊C4—221no—
172C2×C4⋊C4—221no—
173C2×C4⋊C4—221no—
174C2×C4⋊C4—221no—
175C2×C42C22×D1111yescharacteristic
176C4⋊C8—221no—
177C4⋊C8—221no—
178C4⋊C8—221no—
179C4⋊C8—221no—
180C4⋊C8D4412yes—
181C4⋊C8D4412yes—
182#103—224no—
183#103—224no—
184C22⋊C8—21no—
185C22⋊C8—21no—
186C4×C8—21no—
187C4×C8—21no—
188C4×C8C4×D1112yes—
189C4×C8C22⋊D1111yescharacteristic
190C4×C8C22⋊D1111yescharacteristic
191C2×C11—22no—
192C2×C11#195811yescharacteristic
193C2×C11#197711yescharacteristic
194C2×C11#197911yescharacteristic
195C2×Q8—222no—
196C2×Q8—222no—
197C2×Q8—441no—
198C2×Q8—441no—
199C2×Q8—442no—
200C2×Q8—442no—
201C2×Q8—882no—
202C22×C4—441no—
203C22×C4—441no—
204C22×C4C2×D4411yescharacteristic
205C22×C4#433911yescharacteristic
206C22×C4#433911yescharacteristic
207M16—442no—
208M16—442no—
209C2×C8—22no—
210C2×C8—22no—
211C2×C8—22no—
212C2×C8—22no—
213C2×C8—441no—
214C2×C8—441no—
215C2×C8(C2×D11)⋊C412yes—
216C2×C8(C2×D11)⋊C412yes—
217C4⋊C4—222no—
218C4⋊C4—222no—
219C4⋊C4—222no—
220C4⋊C4—222no—
221C4⋊C4—441no—
222C4⋊C4—441no—
223C4⋊C4—441no—
224C4⋊C4—441no—
225C42C2×C4×D1111yescharacteristic
226C42C2×D4411yescharacteristic
227C42C2×D4411yescharacteristic
228C42C2×C22⋊D1111yescharacteristic
229C11#977011yescharacteristic, complemented, Sylow
230C23#6692811yescharacteristic
231Q8—444no—
232Q8—882no—
233Q8—882no—
234Q8—881no—
235Q8—881no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—442no—
239C2×C4—442no—
240C2×C4—882no—
241C2×C4—882no—
242C2×C4C4×D4411yescharacteristic
243C2×C4C4×D4411yescharacteristic
244C2×C4#6692711yescharacteristic
245C2×C4#6695712yes—
246C2×C4#6695712yes—
247C2×C4C2×(C2×D11)⋊C411yescharacteristic
248C2×C4#6698311yescharacteristic
249C2×C4#6698311yescharacteristic
250C8—22no—
251C8—22no—
252C8—42no—
253C8—42no—
254C8—881no—
255C8—881no—
256C22—21no—
257C22—21no—
258C22#1062231012yes—
259C22#1062255211yescharacteristic
260C4—21no—
261C4—21no—
262C4—882no—
263C4—882no—
264C4#1062230911yescharacteristic
265C4#1062230911yescharacteristic
266C4#1062272612yes—
267C4#1062275412yes—
268C4#1062275612yes—
269C2—22no—
270C2#1306942711yescharacteristic
271C2#1306951911yescharacteristic
272C2#1306953111yescharacteristic
subgroupG/H
centerC22#10622552
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1450C2
socleC22×C11#390
prime radicalC23×C11#124
cosocleC2×C42×C11C23
hypercenter#1450D11
hypocenterC11#9770
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1450

Complements

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

NH ≅ G/Ntype
229. C11#9770semidirect

Maximal subgroups

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

subgroupindex
C2×#106222942
#130687542
#130673002
#130672962
#130672872
C11×#14502
#977011